CUSAT CAT 2019 Question Paper B.Tech
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CUSAT CAT 2019 Question Paper B.Tech – Text
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Page 1
(BTECH-CAT2019)
019
2
S T
E
1. The function T is
N
O
(A)
(B)
not periodic
SI
periodic, with period 2n!
(C) IS
periodic, with period 2(n + 1)!
M
M
(D) constant
D
A
N
O
M
SA2.T
CO
If
M
O
C T E , then the value of at x = 0 is
CU (A)
(B)
(C)
–1
0
1
AT N 19
S IO 0
(D) 2
2
3.
U
C IS
(A) 1 S T E S
If i=√ −1, then the value of i 21isT
N
(B)
O
(C) i
M IS
S I
(D)
D M
A O
N
A
D
M
M
C O
4. The value of
AT
(A) 5! S
(B) 6!
CU
019
2
S T
E
1. The function T is
N
O
(A)
(B)
not periodic
SI
periodic, with period 2n!
(C) IS
periodic, with period 2(n + 1)!
M
M
(D) constant
D
A
N
O
M
SA2.T
CO
If
M
O
C T E , then the value of at x = 0 is
CU (A)
(B)
(C)
–1
0
1
AT N 19
S IO 0
(D) 2
2
3.
U
C IS
(A) 1 S T E S
If i=√ −1, then the value of i 21isT
N
(B)
O
(C) i
M IS
S I
(D)
D M
A O
N
A
D
M
M
C O
4. The value of
AT
(A) 5! S
(B) 6!
CU
Page 2
(C) 1.22.3.43.5.64
19
(D) 1.22.33.44
5. Which of the following statements are correct?
20
(i) If lim
f ( x )− f (a)
S T
exists, then f is differentiable at a
E
x−a
(ii)
x→ a
T
If f is continuous at a, then f is differentiable at a
N
(iii O
If limit of f at x=a exists, then f is differentiable at a
) SI
IS
(iv) If f is differentiable at a, then f is continuous at a
M
D
(A) i andAii
M
(B) iiNand iii
(C) O
iii and iv
M i and iv
O
(D)
M
SA6.T
CO
The function corresponding to the graph shown below is
CU
AT N 19
S IO 2 0
(A)
(B)
U
C IS S
y2 = (1 – x)
y2 = (x – 1) T E ST
(C) y2 + 1 = (x – 1)
N
O
M
(D) y2 = (1 + x)
S I
IS
D M
7.
(A)
A O
N
=
A
D
M
M
(B)
C O
(C) AT
S
CU
19
(D) 1.22.33.44
5. Which of the following statements are correct?
20
(i) If lim
f ( x )− f (a)
S T
exists, then f is differentiable at a
E
x−a
(ii)
x→ a
T
If f is continuous at a, then f is differentiable at a
N
(iii O
If limit of f at x=a exists, then f is differentiable at a
) SI
IS
(iv) If f is differentiable at a, then f is continuous at a
M
D
(A) i andAii
M
(B) iiNand iii
(C) O
iii and iv
M i and iv
O
(D)
M
SA6.T
CO
The function corresponding to the graph shown below is
CU
AT N 19
S IO 2 0
(A)
(B)
U
C IS S
y2 = (1 – x)
y2 = (x – 1) T E ST
(C) y2 + 1 = (x – 1)
N
O
M
(D) y2 = (1 + x)
S I
IS
D M
7.
(A)
A O
N
=
A
D
M
M
(B)
C O
(C) AT
S
CU
Page 3
(D)
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 4
8. Let f ( x )=x 2 −1and g ( x )=4 x+2. The composition of two functions ( f ∘ g ) ( x ) is given by
(A) 8 x 2+ 8 x+3 019
(B) 2
16 x +16 x +3 2
(C) 4 x2 −2 S T
E
2
(D) 4 x +2
T
N
O
SI
4 2
x +10 x + 3 x +36
9. The partial fraction Sdecomposition of f ( x )= is of the form
I ( x −1 ) ( x +1 ) 2 2
M
(A) x −1A+
A D
M
Bx+ C Cx+ D
+
N x +1 ( x +1 )
2 2 2
OA B C
M
O
(B) x −1 + +
M 2
x +1 ( x +1 )2 2
SA T
O
C (C) x A−1 + B + Cx+ D
C T 2
E
x +1 ( x +1 )2 2
T
A Bx+ C D
CU (D) + +
N
x −1 2
x +1 ( x 2 +1 )
2
10.
A
S IO
The equation 2 0 19
represents a hyperbola, if
(A)
(B)
U
C IS S T E ST
N
O
M I
(C)
S
IS
D
(D)
M
11. A O
N
A
D
is equal to
(A) M
M
(B)
C O
(C)
AT
S
CU
(A) 8 x 2+ 8 x+3 019
(B) 2
16 x +16 x +3 2
(C) 4 x2 −2 S T
E
2
(D) 4 x +2
T
N
O
SI
4 2
x +10 x + 3 x +36
9. The partial fraction Sdecomposition of f ( x )= is of the form
I ( x −1 ) ( x +1 ) 2 2
M
(A) x −1A+
A D
M
Bx+ C Cx+ D
+
N x +1 ( x +1 )
2 2 2
OA B C
M
O
(B) x −1 + +
M 2
x +1 ( x +1 )2 2
SA T
O
C (C) x A−1 + B + Cx+ D
C T 2
E
x +1 ( x +1 )2 2
T
A Bx+ C D
CU (D) + +
N
x −1 2
x +1 ( x 2 +1 )
2
10.
A
S IO
The equation 2 0 19
represents a hyperbola, if
(A)
(B)
U
C IS S T E ST
N
O
M I
(C)
S
IS
D
(D)
M
11. A O
N
A
D
is equal to
(A) M
M
(B)
C O
(C)
AT
S
CU
Page 5
(D)
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 6
2 1
12. If sin θ= and 0<θ <90 ° ,then the value of tan θ is equal to
4
019
2 2
(A)
√3 S T
E
(B)
√3 T
2 N
O
(C) 1 SI
1 IS
M
M
(D)
√3 D
A
N
O
13.
M
The sum of all three digit numbers which are odd is
SA
M
CO (B) 155700
(A) 247500
T (C) 175500 O
T
(D) 156500
CU
A N 19
S IO
14. The differentiation of an nth order polynomial is
(A) zero 2 0
(B)
(C)
(D) U
C IS S
a polynomial of order n
a non-zero constant
T E
a polynomial of order 2
ST
N
O
15.
M S I
Last two digits of the natural number
IS
is
(A)
D 29
M
A D
(B) 39
(C)
(D)
90
19 A
N
O
b b
M
16.
M
If ∫ f ( x ) dx=a+2 b, then ∫ ( f ( x )+ 5 ) dx=¿ ¿
a
(A) a+ 2b+ 5
a
C O
(B) 5 b −5 a
AT
(C) 7b−4a
S
(D) 7b−6a
CU
12. If sin θ= and 0<θ <90 ° ,then the value of tan θ is equal to
4
019
2 2
(A)
√3 S T
E
(B)
√3 T
2 N
O
(C) 1 SI
1 IS
M
M
(D)
√3 D
A
N
O
13.
M
The sum of all three digit numbers which are odd is
SA
M
CO (B) 155700
(A) 247500
T (C) 175500 O
T
(D) 156500
CU
A N 19
S IO
14. The differentiation of an nth order polynomial is
(A) zero 2 0
(B)
(C)
(D) U
C IS S
a polynomial of order n
a non-zero constant
T E
a polynomial of order 2
ST
N
O
15.
M S I
Last two digits of the natural number
IS
is
(A)
D 29
M
A D
(B) 39
(C)
(D)
90
19 A
N
O
b b
M
16.
M
If ∫ f ( x ) dx=a+2 b, then ∫ ( f ( x )+ 5 ) dx=¿ ¿
a
(A) a+ 2b+ 5
a
C O
(B) 5 b −5 a
AT
(C) 7b−4a
S
(D) 7b−6a
CU
Page 7
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 8
17. The number of ways that a circle can be made out of 6 black and 4 white men standing on
19
a ring, so that all the white men come together is
0
(A) 8564 2
(B) 8640
S T
E
(C) 8644
(D) 8665 T
N
O
SI
IS
M
18. If
A
D
M then is equal to
(A) 2N
(B) O– 2
M –4
O
(C)
M 4
E
(D)
CO
A T
S 19. C T
T
The equation represents
CU (A)
(B)
A N
a hyperbola
a straight line
19
S IO 0
(C) an ellipse
(D) a circle 2
20. U
C IS S T E ST
Let f be a polynomial. Then the second derivative of is
N
(A)
O
M IS
S I
D
(B)
M
A D
(C)
A
(D)
N
O
M
21.
M
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the
O
length of its conjugate axis is equal to half of the distance between its foci, is
C
(A)
AT
S
(B) 4/3
CU
19
a ring, so that all the white men come together is
0
(A) 8564 2
(B) 8640
S T
E
(C) 8644
(D) 8665 T
N
O
SI
IS
M
18. If
A
D
M then is equal to
(A) 2N
(B) O– 2
M –4
O
(C)
M 4
E
(D)
CO
A T
S 19. C T
T
The equation represents
CU (A)
(B)
A N
a hyperbola
a straight line
19
S IO 0
(C) an ellipse
(D) a circle 2
20. U
C IS S T E ST
Let f be a polynomial. Then the second derivative of is
N
(A)
O
M IS
S I
D
(B)
M
A D
(C)
A
(D)
N
O
M
21.
M
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the
O
length of its conjugate axis is equal to half of the distance between its foci, is
C
(A)
AT
S
(B) 4/3
CU
Page 9
(C) 4/
(D) 2/ 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
(D) 2/ 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 10
19
22. is equal to
(A) 20
S T
E
(B)
T
(C) N
O
SI
(D)
IS
M
A
D
M
23. ThousandN tickets are sold in a lottery in which there is one top prize of Rs.500, four
prizes O
of Rs.100 each and five prizes of Rs. 10 each. A ticket costs Rs.1. The expected
M
M
O
gain when you buy a ticket is
SA T
O
C (A) Rs.2
C T
(B) – 0.25 of a rupee
E
T
(C) – 0.5 of a rupee
CU (D) Rs.1
A N 19
24. If
S IOand 0
are one to one, real valued functions, then the value of the
2
(A) U
integral
C IS S T E ST is
(B) N
O
(C) 1
M IS
S I
D
(D) 0
M
25.
(A)
(B)
A 0
16 O
N
A
D
If E(X2) =276 and Variance of X = 20, then the value of E(X) is
(C) 20 M
(D) 256 M
C O
AT
S
CU
22. is equal to
(A) 20
S T
E
(B)
T
(C) N
O
SI
(D)
IS
M
A
D
M
23. ThousandN tickets are sold in a lottery in which there is one top prize of Rs.500, four
prizes O
of Rs.100 each and five prizes of Rs. 10 each. A ticket costs Rs.1. The expected
M
M
O
gain when you buy a ticket is
SA T
O
C (A) Rs.2
C T
(B) – 0.25 of a rupee
E
T
(C) – 0.5 of a rupee
CU (D) Rs.1
A N 19
24. If
S IOand 0
are one to one, real valued functions, then the value of the
2
(A) U
integral
C IS S T E ST is
(B) N
O
(C) 1
M IS
S I
D
(D) 0
M
25.
(A)
(B)
A 0
16 O
N
A
D
If E(X2) =276 and Variance of X = 20, then the value of E(X) is
(C) 20 M
(D) 256 M
C O
AT
S
CU
Page 11
26.
019
2
(A) S T
E
T
N
O
(B)
SI
IS
M
M
(C)
D
A
(D) 2
N
O
M
S
27.
AT
M
COLet
(A) if
O
C T E Then can be continuous at
CU (B) if
AT N 19
S IO 0
(C) if
2
U S T
(D) for no definite value of
S
28. C IS N
T E
If one of the diameters of the circle, given by the equation
O
, is a
M I
chord of a circle S, whose centre is at (–3, 2), then the radius of S is
S
IS
D
(A) 10
M
A D
(B)
(C) A
N
(D) 5 O
M
Mbe
29. Let . Then
C O
must
(A)
(B)
an even function
an odd function AT
(C) S
a periodic function
(D)
CU
neither even nor odd
019
2
(A) S T
E
T
N
O
(B)
SI
IS
M
M
(C)
D
A
(D) 2
N
O
M
S
27.
AT
M
COLet
(A) if
O
C T E Then can be continuous at
CU (B) if
AT N 19
S IO 0
(C) if
2
U S T
(D) for no definite value of
S
28. C IS N
T E
If one of the diameters of the circle, given by the equation
O
, is a
M I
chord of a circle S, whose centre is at (–3, 2), then the radius of S is
S
IS
D
(A) 10
M
A D
(B)
(C) A
N
(D) 5 O
M
Mbe
29. Let . Then
C O
must
(A)
(B)
an even function
an odd function AT
(C) S
a periodic function
(D)
CU
neither even nor odd
Page 12
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 13
30. Let be a vector coplanar with the vectors If is
0 19
perpendicular to and 2
, then is equal to
(A) 84 ST
TE
(B) 336
(C) 315 N
O
(D) 256
SI
IS
M
31.
D
A of
The expression
M of the function is
N
O
M
(A)
SA T
M
CO (B) O
CU (C)
AT N 19
(D)
S IO 2 0
U
C IS S T E ST
32.
N
The fixed point P on the curve such that the tangent at P is perpendicular
O
M I
to the line is given by
S
IS
D
(A) (1, 2)
(B) (2, 1)
M
A D
(C) (3, 2)
(D) (2, 3)
A
N
O
33. If the tangent at to the curve
M touches the circle
then the value of c is
M
(A) 85
C O
(B)
(C)
195
185
AT
(D) 95
S
CU
0 19
perpendicular to and 2
, then is equal to
(A) 84 ST
TE
(B) 336
(C) 315 N
O
(D) 256
SI
IS
M
31.
D
A of
The expression
M of the function is
N
O
M
(A)
SA T
M
CO (B) O
CU (C)
AT N 19
(D)
S IO 2 0
U
C IS S T E ST
32.
N
The fixed point P on the curve such that the tangent at P is perpendicular
O
M I
to the line is given by
S
IS
D
(A) (1, 2)
(B) (2, 1)
M
A D
(C) (3, 2)
(D) (2, 3)
A
N
O
33. If the tangent at to the curve
M touches the circle
then the value of c is
M
(A) 85
C O
(B)
(C)
195
185
AT
(D) 95
S
CU
Page 14
34.
19
Let y = y(x) be the solution of the differential equation
0
. If
2
is equal to
S T
E
T
(A) N
O
SI
(B) IS
M
A
D
M
(C)
N
O
M
O
(D)
M
A T
S 35.
CO
T
The value of b for which the function is decreasing in the interval
CU
N
is given by
(A)
A
S IO 2 0 19
U
(B)
C IS
(C)
(D)
S N
T E ST
O
M IS
S I
36.
D
The least value of M occurs at
A
(A)
(B)
(C) O
N
A
D
G.M. of a, b
A.M. of a, b
H.M. of a, b
(D) square of a and b
M
M
37. Let
O
C the vector
. Then satisfying and is
AT
(A)
S
CU
19
Let y = y(x) be the solution of the differential equation
0
. If
2
is equal to
S T
E
T
(A) N
O
SI
(B) IS
M
A
D
M
(C)
N
O
M
O
(D)
M
A T
S 35.
CO
T
The value of b for which the function is decreasing in the interval
CU
N
is given by
(A)
A
S IO 2 0 19
U
(B)
C IS
(C)
(D)
S N
T E ST
O
M IS
S I
36.
D
The least value of M occurs at
A
(A)
(B)
(C) O
N
A
D
G.M. of a, b
A.M. of a, b
H.M. of a, b
(D) square of a and b
M
M
37. Let
O
C the vector
. Then satisfying and is
AT
(A)
S
CU
Page 15
(B)
019
(C) 2
(D) S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
019
(C) 2
(D) S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 16
38. If then
19
where
0
is equal to
2
(A)
S T
E
T
(B)
N
O
SI
(C) IS
M
(D) A
D
M
N
O
M
SA
T
C
M
(A)
O
39. OThe area of the region bounded by the curves and is
CU
(B)
AT N 19
S IO 2 0
U
(C)
40. C IS
(D) 3
S N
T E ST
The differential equation of the family of circles with centre on the x axis is
O
M IS
S I
D
(A)
M
(B)
A O
N
A
D
(C) M
M
(D) C O
AT
S
CU
19
where
0
is equal to
2
(A)
S T
E
T
(B)
N
O
SI
(C) IS
M
(D) A
D
M
N
O
M
SA
T
C
M
(A)
O
39. OThe area of the region bounded by the curves and is
CU
(B)
AT N 19
S IO 2 0
U
(C)
40. C IS
(D) 3
S N
T E ST
The differential equation of the family of circles with centre on the x axis is
O
M IS
S I
D
(A)
M
(B)
A O
N
A
D
(C) M
M
(D) C O
AT
S
CU
Page 17
41. The value of the integral
19
lies in the interval
0
(A) (0, 1) 2
(B) (– 1, 0)
S T
E
(C) (1, e)
(D) (– 1, e) T
N
O
I
The equation of aSSplane passing through the line of intersection of the planes
42.
I
M
x+2y+3z = 2 D
M
Aand x – y + z = 3 and at a distance from the point (3, 1, – 1) is
5xN– 11y + z = 17
(A) O
M
M
O
(B)
SA T
CO (C)
x+y+z=
CU
T
(D)
A N 19
S IO 2 0
U S T
43. The integrating factor of the differential equation is
S
C IS E
(A)
T
(B)
N
O
(C)
M IS
S I
D
(D)
M
44. A N
A
D
Consider the system of equations x – 2y + 3z = –1; –x + y – 2z = k; x – 3y + 4z = 1.
O
STATEMENT-1: The system of equations has no solution for k ≠ 3 and
M
M
O
-2: The determinant
C
STATEMENT
A T
S
C U
19
lies in the interval
0
(A) (0, 1) 2
(B) (– 1, 0)
S T
E
(C) (1, e)
(D) (– 1, e) T
N
O
I
The equation of aSSplane passing through the line of intersection of the planes
42.
I
M
x+2y+3z = 2 D
M
Aand x – y + z = 3 and at a distance from the point (3, 1, – 1) is
5xN– 11y + z = 17
(A) O
M
M
O
(B)
SA T
CO (C)
x+y+z=
CU
T
(D)
A N 19
S IO 2 0
U S T
43. The integrating factor of the differential equation is
S
C IS E
(A)
T
(B)
N
O
(C)
M IS
S I
D
(D)
M
44. A N
A
D
Consider the system of equations x – 2y + 3z = –1; –x + y – 2z = k; x – 3y + 4z = 1.
O
STATEMENT-1: The system of equations has no solution for k ≠ 3 and
M
M
O
-2: The determinant
C
STATEMENT
A T
S
C U
Page 18
Then 019
2
S T
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
E
Statement-1
T
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct
N
O
explanation for Statement-1
SI
(C) Statement-1 is True and Statement-2 is False
IS
(D) Statement-1 is False and Statement-2 is True
M
45.
D
M
A seat themselves indiscriminately at round table. The probability that two
Seven people
N
O
distinguished persons will be next to each other is
M
M
O
(A)
SA T
CO (B)
T
(C)
CU (D)
A N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
E
Statement-1
T
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct
N
O
explanation for Statement-1
SI
(C) Statement-1 is True and Statement-2 is False
IS
(D) Statement-1 is False and Statement-2 is True
M
45.
D
M
A seat themselves indiscriminately at round table. The probability that two
Seven people
N
O
distinguished persons will be next to each other is
M
M
O
(A)
SA T
CO (B)
T
(C)
CU (D)
A N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 19
46. For a normal curve, the greatest ordinate is
(A) 019
2
(B)
S T
E
T
(C) N
O
SI
(D) IS
M
A
D
M
N
O
M
M
O
47. If lines and are mutually perpendicular, then
SAT
CO is equal to
(A)
CU (B)
AT N 19
S IO
(C)
2 0
U S
(D)
ST
48.
C IS T E
If A is an 3 × 3 non-singular matrix such that AAt = AtA and B = A–1 At, then BBt equals
O
N
M I
(A) I+B
(B) I S
IS
D
(C) B–1
(D) (B–1 )
t
M
49. A N
A
D
If the median of 21 observations is 40 and if the observations greater than the median are
O
increased by 5, then the median of the new data will be
M
(A) 45
M
(B) 40
C O
AT
(C)
S
CU
(A) 019
2
(B)
S T
E
T
(C) N
O
SI
(D) IS
M
A
D
M
N
O
M
M
O
47. If lines and are mutually perpendicular, then
SAT
CO is equal to
(A)
CU (B)
AT N 19
S IO
(C)
2 0
U S
(D)
ST
48.
C IS T E
If A is an 3 × 3 non-singular matrix such that AAt = AtA and B = A–1 At, then BBt equals
O
N
M I
(A) I+B
(B) I S
IS
D
(C) B–1
(D) (B–1 )
t
M
49. A N
A
D
If the median of 21 observations is 40 and if the observations greater than the median are
O
increased by 5, then the median of the new data will be
M
(A) 45
M
(B) 40
C O
AT
(C)
S
CU
Page 20
(D)
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 21
50. The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the
0 19
latus rectum to the ellipse 2is
S T
E
(A) 18
T
(B) 27 N
O
SI
IS
(C)
M
D
M
(D)
A
N
O
M
S
51.
AT
M
COwhere
(A)
O
Let A and B be two events such that = 1/ 6, = 1/ 4 and
stands for the complement of the event A. Then the events A and B are
mutually exclusive and independent
= 1/ 4,
CU (B)
(C)
(D) T
equally likely but not independent
A N
independent but not equally likely
independent and equally likely
19
S IO 2 0
52.
(A)
U
C IS S
Solution of the equation
T E ST is
N
O
M I
(B)
S
IS
D
(C)
M
A D
(D)
A
N
53. O
Which of the following functions is not one to one?
M
(A) M
(B) C O
(C) AT
S
CU
0 19
latus rectum to the ellipse 2is
S T
E
(A) 18
T
(B) 27 N
O
SI
IS
(C)
M
D
M
(D)
A
N
O
M
S
51.
AT
M
COwhere
(A)
O
Let A and B be two events such that = 1/ 6, = 1/ 4 and
stands for the complement of the event A. Then the events A and B are
mutually exclusive and independent
= 1/ 4,
CU (B)
(C)
(D) T
equally likely but not independent
A N
independent but not equally likely
independent and equally likely
19
S IO 2 0
52.
(A)
U
C IS S
Solution of the equation
T E ST is
N
O
M I
(B)
S
IS
D
(C)
M
A D
(D)
A
N
53. O
Which of the following functions is not one to one?
M
(A) M
(B) C O
(C) AT
S
CU
Page 22
(D)
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 23
019
54. If 2
(A) u S T
E
T
(B) N
O
SI
(C) IS
M
(D) 0 A
D
M
N
O
M
55.
SA
T
O
M
C (A) i O
The value of the sum
where is equal to
CU
T
(B)
(C)
A N 19
(D) 0
S IO 2 0
56.
U S ST
Let A and B be two 2 × 2 matrices. Consider the statements
(i)
C IS or
T E
(ii) N
O
(iii)
M IS
S I Then
(A)
(B)
D
(i) is false, (ii) and (iii) are true
M
(i) and (iii) are false, (ii) is true
A D
(C) (i) and (ii) are false, (iii) is true
(D) A
(ii) and (iii) are false, (i) is true
N
O
57. The remainder when
M is divided by 240, is
M
(A)
(B)
187
33
C O
(C)
(D)
73
153
AT
S
CU
54. If 2
(A) u S T
E
T
(B) N
O
SI
(C) IS
M
(D) 0 A
D
M
N
O
M
55.
SA
T
O
M
C (A) i O
The value of the sum
where is equal to
CU
T
(B)
(C)
A N 19
(D) 0
S IO 2 0
56.
U S ST
Let A and B be two 2 × 2 matrices. Consider the statements
(i)
C IS or
T E
(ii) N
O
(iii)
M IS
S I Then
(A)
(B)
D
(i) is false, (ii) and (iii) are true
M
(i) and (iii) are false, (ii) is true
A D
(C) (i) and (ii) are false, (iii) is true
(D) A
(ii) and (iii) are false, (i) is true
N
O
57. The remainder when
M is divided by 240, is
M
(A)
(B)
187
33
C O
(C)
(D)
73
153
AT
S
CU
Page 24
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 25
58. A black and a red dice are rolled. The conditional probability of obtaining a sum greater
19
than 9, given that the black die resulted in a 5 is
0
(A) 1/6 2
(B) 1/9
S T
E
(C) 3/4
(D) 1/3 T
N
O
SI
59. S the curve
The area bounded Iby is
M
(A) 1
A
D
M
(B) 3 N
(C) O2
M4
(D)
SA
CO
T If
60.
M
O
C T E having n radical signs, then by methods of mathematical
CU
T
induction which of the following is true?
(A)
A N 19
(B)
S IO 2 0
(C)
(D)
U
C IS S T E ST
N
O
M IS
S I
D
61. The period of is
M
A D
(A)
A
(B)
N
(C) O
M
(D) M
C O
AT
62. Consider the function S . The value of so that f is continuous at
is
CU
19
than 9, given that the black die resulted in a 5 is
0
(A) 1/6 2
(B) 1/9
S T
E
(C) 3/4
(D) 1/3 T
N
O
SI
59. S the curve
The area bounded Iby is
M
(A) 1
A
D
M
(B) 3 N
(C) O2
M4
(D)
SA
CO
T If
60.
M
O
C T E having n radical signs, then by methods of mathematical
CU
T
induction which of the following is true?
(A)
A N 19
(B)
S IO 2 0
(C)
(D)
U
C IS S T E ST
N
O
M IS
S I
D
61. The period of is
M
A D
(A)
A
(B)
N
(C) O
M
(D) M
C O
AT
62. Consider the function S . The value of so that f is continuous at
is
CU
Page 26
(A) 1
(B) e
019
2
(C)
S T
E
(D) T
N
O
SI
IS
M
63. If
A
D
M
then the value of is
(A) N
O
(B)M
SAT
M
CO (C) 0
(D) 1
O
CU 64.
AT N
The sine of the angle between the pair of lines represented by the equation
19
S IO 2 0
U
(A)
(B)
(C)
C IS S N
T E ST
O
(D)
M IS
S I
D M
65.
A
(A) 4 O
N
A
D
If the tangent at the point P on the circle meets the straight line
at a point Q on the y-axis, then the length of PQ is
M
(B) 5 M
(C) C O
AT
(D)
S
CU
(B) e
019
2
(C)
S T
E
(D) T
N
O
SI
IS
M
63. If
A
D
M
then the value of is
(A) N
O
(B)M
SAT
M
CO (C) 0
(D) 1
O
CU 64.
AT N
The sine of the angle between the pair of lines represented by the equation
19
S IO 2 0
U
(A)
(B)
(C)
C IS S N
T E ST
O
(D)
M IS
S I
D M
65.
A
(A) 4 O
N
A
D
If the tangent at the point P on the circle meets the straight line
at a point Q on the y-axis, then the length of PQ is
M
(B) 5 M
(C) C O
AT
(D)
S
CU
Page 27
019
66. Let the matrix 2 Then
S T
E
(A)
T
N
(B) O
SI
(C) IS
M
(D)
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
66. Let the matrix 2 Then
S T
E
(A)
T
N
(B) O
SI
(C) IS
M
(D)
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 28
67. If a line is equally inclined with the coordinate axes, then the angle of inclination is
(A) 019
2
(B) S T
E
T
(C) N
O
SI
IS
(D)
M
A
D
M
68. If N (where m is a fixed positive integer > 2), then
O
M
SAT
M
CO (A) O
T
(B)
CU (C) 0
A N 19
S IO
(D) 1
2 0
U S T
69. The monthly sales for the first 11 months of the year of a certain salesman were
S
C IS
Rs.12,000. But due to his illness during the last month the average sales for the whole
T E
year came down to Rs. 11,375. The value of the sale during the last month was
(A) Rs 4,500 N
O
M I
(B) Rs 6,000
(C) Rs 10,000 S
IS
D
(D) Rs 8,000
M
70. If A O
N
A
D
then the value of is
(A) –1
M
(B) 0
M
(C)
(D)
1
3
C O
AT
S
CU
(A) 019
2
(B) S T
E
T
(C) N
O
SI
IS
(D)
M
A
D
M
68. If N (where m is a fixed positive integer > 2), then
O
M
SAT
M
CO (A) O
T
(B)
CU (C) 0
A N 19
S IO
(D) 1
2 0
U S T
69. The monthly sales for the first 11 months of the year of a certain salesman were
S
C IS
Rs.12,000. But due to his illness during the last month the average sales for the whole
T E
year came down to Rs. 11,375. The value of the sale during the last month was
(A) Rs 4,500 N
O
M I
(B) Rs 6,000
(C) Rs 10,000 S
IS
D
(D) Rs 8,000
M
70. If A O
N
A
D
then the value of is
(A) –1
M
(B) 0
M
(C)
(D)
1
3
C O
AT
S
CU
Page 29
71. The sum of the series
019 is
(A) e
2
S T
E
(B) T
N
O
SI
(C) IS
M
(D) A
D
M
N
O
M
SA
T
72.
CO
M
O
C T
Using the fact that
E the value of is
CU (A)
AT N 19
(B)
S IO 2 0
(C)
U
C IS S T E ST
N
(D)
O
M IS
S I
D M
A D
73. If and are both in G.P. with the same common ratio, then the points
A
and
N
(A) O
lie on a straight line
(B) lie on an ellipse
M
(C) lie on a circle
M
(D) are vertices of a triangle
C O
74.
AT
A peacock perched on the top of a 12 m high tree spots a snake moving towards its hole
S
at the base of the tree from a distance equal to thrice the height of the tree. The peacock
CU
019 is
(A) e
2
S T
E
(B) T
N
O
SI
(C) IS
M
(D) A
D
M
N
O
M
SA
T
72.
CO
M
O
C T
Using the fact that
E the value of is
CU (A)
AT N 19
(B)
S IO 2 0
(C)
U
C IS S T E ST
N
(D)
O
M IS
S I
D M
A D
73. If and are both in G.P. with the same common ratio, then the points
A
and
N
(A) O
lie on a straight line
(B) lie on an ellipse
M
(C) lie on a circle
M
(D) are vertices of a triangle
C O
74.
AT
A peacock perched on the top of a 12 m high tree spots a snake moving towards its hole
S
at the base of the tree from a distance equal to thrice the height of the tree. The peacock
CU
Page 30
flies towards the snake in a straight line and they both move at the same speed. At what
19
distance from the base of the tree will the peacock catch the snake?
0
(A) 16 m 2
S T
E
(B) 18 m
T
(C) 14 m N
O
SI
IS
(D) 12 m
M
75. Let
A
D
M Then number of elements in M is
(A) N
O89
M
(B)
M 10
O
(C)
CO
E
(D)12
A T
S 76. C T
CU
T
A solution curve of the differential equation passing through (1, 2) also passes
N
through
(A)
(B) A
S IO
(2, 1)
(0, 0)
2 0 19
U
(C) (4, 24)
77.
(D)
C IS
If the line
S
(24, 4)
N
T E ST
and its perpendicular line are conjugate with respect to
O
M I
then the equation to conjugate line is
S
IS
D
(A)
M
A D
(B)
A
(C)
N
(D) O
M
M
78.
O
C if and only if
An event A is independent of itself is
A T
(A) 0 or 1
S
C U
19
distance from the base of the tree will the peacock catch the snake?
0
(A) 16 m 2
S T
E
(B) 18 m
T
(C) 14 m N
O
SI
IS
(D) 12 m
M
75. Let
A
D
M Then number of elements in M is
(A) N
O89
M
(B)
M 10
O
(C)
CO
E
(D)12
A T
S 76. C T
CU
T
A solution curve of the differential equation passing through (1, 2) also passes
N
through
(A)
(B) A
S IO
(2, 1)
(0, 0)
2 0 19
U
(C) (4, 24)
77.
(D)
C IS
If the line
S
(24, 4)
N
T E ST
and its perpendicular line are conjugate with respect to
O
M I
then the equation to conjugate line is
S
IS
D
(A)
M
A D
(B)
A
(C)
N
(D) O
M
M
78.
O
C if and only if
An event A is independent of itself is
A T
(A) 0 or 1
S
C U
Page 31
(B)
(C) 0 019
2
(D)
S T
E
T
N
O
SI
79. IS of the differential equation
The order and degree are respectively
M
(A) A
D
M
(B) O
N
3, 1
(C)M 3, 3
SA
T
CO
M
(D) 1, 2
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
(C) 0 019
2
(D)
S T
E
T
N
O
SI
79. IS of the differential equation
The order and degree are respectively
M
(A) A
D
M
(B) O
N
3, 1
(C)M 3, 3
SA
T
CO
M
(D) 1, 2
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 32
80. The differential equation whose linearly independent solutions are is
019
(A) 2
S T
E
(B)
T
(C) N
O
SI
(D)
IS
M
A
D
M
81. N of a function which is continuous but not differentiable is
An example
O
M
O
(A)
M
SA T
CO (B)
(C)
CU (D)
AT N 19
S IO 2 0
U
82. If three distinct numbers are chosen randomly from the first 100 natural numbers, then
(A)
C IS S N
T E ST
the probability that all three of them are divisible by both 2 and 3 is
O
(B)
M IS
S I
D M
A D
(C)
A
N
(D)
O
M
M
83.
C O
The family of curves that is orthogonal to is
(A) A T
S
C U
019
(A) 2
S T
E
(B)
T
(C) N
O
SI
(D)
IS
M
A
D
M
81. N of a function which is continuous but not differentiable is
An example
O
M
O
(A)
M
SA T
CO (B)
(C)
CU (D)
AT N 19
S IO 2 0
U
82. If three distinct numbers are chosen randomly from the first 100 natural numbers, then
(A)
C IS S N
T E ST
the probability that all three of them are divisible by both 2 and 3 is
O
(B)
M IS
S I
D M
A D
(C)
A
N
(D)
O
M
M
83.
C O
The family of curves that is orthogonal to is
(A) A T
S
C U
Page 33
(B)
(C) 019
2
(D) S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
(C) 019
2
(D) S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 34
84. If are in a group, then the inverse of is
019
(A) 2
(B) identity element S T
E
T
(C) N
O
SI
IS
(D)
M
A
D
M
85. Let N
be the set of all integers and let * be a binary operation in defined by
O
M for all The identity element of this group is
SA
CO
M
(A) 0
T (B) 10 O
CU (C)
(D) 1
AT N 19
S IO 2 0
U S T
86. The angle between the lines and is
S
(A)
C IS O
N
T E
M I
(B) 0
S
IS
(C)
D M
(D)
A O
N
A
D
M
87. The equation of the tangent at (
M ) to the parabola is
(A) C O
(B) AT
S
CU
019
(A) 2
(B) identity element S T
E
T
(C) N
O
SI
IS
(D)
M
A
D
M
85. Let N
be the set of all integers and let * be a binary operation in defined by
O
M for all The identity element of this group is
SA
CO
M
(A) 0
T (B) 10 O
CU (C)
(D) 1
AT N 19
S IO 2 0
U S T
86. The angle between the lines and is
S
(A)
C IS O
N
T E
M I
(B) 0
S
IS
(C)
D M
(D)
A O
N
A
D
M
87. The equation of the tangent at (
M ) to the parabola is
(A) C O
(B) AT
S
CU
Page 35
(C)
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 36
88. Let
19
be continuous and satisfy
0
for .
Then equals 2
(A) S T
E
T
(B) N
O
SI
(C)
IS
M
D
M
(D) 1
A
N
O
M
89.
SA
T
O
M
The value of
C (A) e 2
O
is
CU
T
(B)
(C) 1
A N 19
S IO
(D) 0
2 0
90.
U S ST
The shortest distance of the point (2, 10, 1) from the plane
(A)
C IS T E
is
N
O
M I
(B)
S
IS
D
(C) 2
M
A D
(D)
A
N
O
91.
M
The equation of the plane passing through the point (2, 1, ) and the line of intersection
of the planes and M
(A) CO
AT
(B)
S
CU
19
be continuous and satisfy
0
for .
Then equals 2
(A) S T
E
T
(B) N
O
SI
(C)
IS
M
D
M
(D) 1
A
N
O
M
89.
SA
T
O
M
The value of
C (A) e 2
O
is
CU
T
(B)
(C) 1
A N 19
S IO
(D) 0
2 0
90.
U S ST
The shortest distance of the point (2, 10, 1) from the plane
(A)
C IS T E
is
N
O
M I
(B)
S
IS
D
(C) 2
M
A D
(D)
A
N
O
91.
M
The equation of the plane passing through the point (2, 1, ) and the line of intersection
of the planes and M
(A) CO
AT
(B)
S
CU
Page 37
(C)
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 38
92. If then the value of is
019
(A) 2
S T
E
(B)
T
(C) N
O
SI
(D)
IS
M
A
D
M
N
O
M
SA T
C
M
(A) 8
O
93. OThe value of x for which the matrix is singular, is
T
(B) 6
CU
N
(C) 4
A
(D) 12
19
S IO 2 0
94. U
C IS S
The determinant of the matrix
T E ST
is equal to
(A) N
O
(B)
M IS
S I
(C)
D M
(D)
A O
N
A
D
95. M
The probability of obtaining ‘no head’ in an infinite sequence of independent tosses of a
M
coin is
C O
(A) 0
AT
(B) 1
S
CU
019
(A) 2
S T
E
(B)
T
(C) N
O
SI
(D)
IS
M
A
D
M
N
O
M
SA T
C
M
(A) 8
O
93. OThe value of x for which the matrix is singular, is
T
(B) 6
CU
N
(C) 4
A
(D) 12
19
S IO 2 0
94. U
C IS S
The determinant of the matrix
T E ST
is equal to
(A) N
O
(B)
M IS
S I
(C)
D M
(D)
A O
N
A
D
95. M
The probability of obtaining ‘no head’ in an infinite sequence of independent tosses of a
M
coin is
C O
(A) 0
AT
(B) 1
S
CU
Page 39
(C)
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 40
96. If X is a Poisson random variable such that then the variance of X is
019
(A)
(B)
6
5
2
(C) 30 S T
E
(D) 25
T
N
O
97. SI is given to three students A, B, C and their respective
A problem in Mathematics
IS
M
A
M
probability ofDsolving the problem is and . Probability that the problem is
solved is
N
O
M
O
(A)
M
SA
CO
T (B)
CU (C)
AT N 19
(D)
S IO 2 0
98.
U
C IS S T E ST
The value of the constant c for which the function defined by
N
O
M IS
S I is a probability density function, is
(A)
D1
M
A D
(B) 0
(C)
(D)
3
6 A
N
O
M
M
99. If then
C O equals
(A)
(B)
208.34
212.12
AT
(C) 212.16 S
(D) 213.16
CU
019
(A)
(B)
6
5
2
(C) 30 S T
E
(D) 25
T
N
O
97. SI is given to three students A, B, C and their respective
A problem in Mathematics
IS
M
A
M
probability ofDsolving the problem is and . Probability that the problem is
solved is
N
O
M
O
(A)
M
SA
CO
T (B)
CU (C)
AT N 19
(D)
S IO 2 0
98.
U
C IS S T E ST
The value of the constant c for which the function defined by
N
O
M IS
S I is a probability density function, is
(A)
D1
M
A D
(B) 0
(C)
(D)
3
6 A
N
O
M
M
99. If then
C O equals
(A)
(B)
208.34
212.12
AT
(C) 212.16 S
(D) 213.16
CU
Page 41
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 42
100. The value of is
019
(A) 2 14
2
(B) S T
E
T
(C) 27 N
O
(D) SI
IS
M
D
A and
M
101. If N then least possible value of 2y – 3x is
O
M0
(A)
SAT
M
(B) – 4
CO (C) –5
(D) – 3 O
CU 102.
AT N
The solution set of is
19
S IO 0
(A) (–, 2)
(B) (0, 2)
2
U S
(C) [2, ]
(D) [0, 2]
ST
103. If C IS N
T E
are the position vectors of the vertices of an equilateral triangle whose
O
M I
orthocenter is at the origin, then
S
IS
D
(A)
M
A D
(B)
A
(C)
N
O
(D)
M
M
104. The number of ways in which 6C
O
men and 5 women can sit at a round table if no two
women are to sit together is T
S A given by
(A) 6! × 5!
(B) 30
C U
019
(A) 2 14
2
(B) S T
E
T
(C) 27 N
O
(D) SI
IS
M
D
A and
M
101. If N then least possible value of 2y – 3x is
O
M0
(A)
SAT
M
(B) – 4
CO (C) –5
(D) – 3 O
CU 102.
AT N
The solution set of is
19
S IO 0
(A) (–, 2)
(B) (0, 2)
2
U S
(C) [2, ]
(D) [0, 2]
ST
103. If C IS N
T E
are the position vectors of the vertices of an equilateral triangle whose
O
M I
orthocenter is at the origin, then
S
IS
D
(A)
M
A D
(B)
A
(C)
N
O
(D)
M
M
104. The number of ways in which 6C
O
men and 5 women can sit at a round table if no two
women are to sit together is T
S A given by
(A) 6! × 5!
(B) 30
C U
Page 43
(C) 4! × 5!
19
(D) 7! × 5!
20
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
19
(D) 7! × 5!
20
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 44
105. If z1 and z2 are any two complex numbers, then Re(z1z2) is
(A) Re(z1)Re(z2) + Im(z1)Im(z2) 019
(B) Re(z )Re(z ) – Im(z )Im(z )
2
1
S T2 1 2
E
(C) Re(z )Im(z ) + Re(z )Im(z
1 ) 2 2 1
T
(D) Re(z )Im(z ) – Re(z )Im(z )
N1 1 2 2
O
SI
2/3 IS dy/dx is
2/3
106. If x + y = a , then 2/3
M
x A
D
M
T
(A) N
√
Oy
M y
M S
M √ O
3
E
(B) −
CO
x
SA
T (C) −
√y
x
C T
CU
T
y2
N
(D)
A
x
19
107.
S I O 2 0
If a, b and c are in arithmetic progression, then the value of the determinant
| U |S T
x+ 2 x+ 3 x +2 a
S
C IS E
x+3 x + 4 x +2 b is
x +4 x+5 x+2 c
T
N
(A) 0
O
M I
(B) 1
S
IS
(C) x
D
(D) 2x
M
108.
A A
D −1
The solution of tan ( 2 x ) + tan (3 x )=
O
N
−1 π
4
is
(A)
(B)
–1
1/6 M
(C) 0 M
(D) –½
C O
AT
S
CU
(A) Re(z1)Re(z2) + Im(z1)Im(z2) 019
(B) Re(z )Re(z ) – Im(z )Im(z )
2
1
S T2 1 2
E
(C) Re(z )Im(z ) + Re(z )Im(z
1 ) 2 2 1
T
(D) Re(z )Im(z ) – Re(z )Im(z )
N1 1 2 2
O
SI
2/3 IS dy/dx is
2/3
106. If x + y = a , then 2/3
M
x A
D
M
T
(A) N
√
Oy
M y
M S
M √ O
3
E
(B) −
CO
x
SA
T (C) −
√y
x
C T
CU
T
y2
N
(D)
A
x
19
107.
S I O 2 0
If a, b and c are in arithmetic progression, then the value of the determinant
| U |S T
x+ 2 x+ 3 x +2 a
S
C IS E
x+3 x + 4 x +2 b is
x +4 x+5 x+2 c
T
N
(A) 0
O
M I
(B) 1
S
IS
(C) x
D
(D) 2x
M
108.
A A
D −1
The solution of tan ( 2 x ) + tan (3 x )=
O
N
−1 π
4
is
(A)
(B)
–1
1/6 M
(C) 0 M
(D) –½
C O
AT
S
CU
Page 45
109. Which of the following statements is false? 019
2
T
(A) An equation of form a * x = b has a unique solution for x in a group
S
E
T
(B) An equation of form a * x = e has a unique solution for x in a group
N
O
I
(C) Given n N, there exist a group with n elements
S
IS abelian groups, then H K need not be abelian
(D) If H and K are
M
110. Define A
D
M and The value of is
(A) O
N
145
(B)M 286
SA T
O
M
(C) 436
C (D) 572 O
U
T
111. In a Poisson distribution, P(X = 2) = P(X = 3). Given that e– 3 = 0.050. Then P(X = 5) is
N
C
A 9
(A) 0.202
1
S IO
(B) 0.352
(C) 0.125
2 0
U
(D) 0.101
112.
C IS S T E ST
There are four prime numbers written in ascending order. The product of the first three is
N
385 and that of the last three is 1001. The last number is
O
M I
(A) 11
S
IS
(B) 13
D
(C) 17
(D) 19
M
113. A N
A
D
If the area of a triangle is 4 sq. units with vertices at (–2, 0), (0, 4) and (0, k), then the
value of k is
O
(A) 2 M
(B) 0 M
(C) 8
C O
(D) 4
AT
S
CU
2
T
(A) An equation of form a * x = b has a unique solution for x in a group
S
E
T
(B) An equation of form a * x = e has a unique solution for x in a group
N
O
I
(C) Given n N, there exist a group with n elements
S
IS abelian groups, then H K need not be abelian
(D) If H and K are
M
110. Define A
D
M and The value of is
(A) O
N
145
(B)M 286
SA T
O
M
(C) 436
C (D) 572 O
U
T
111. In a Poisson distribution, P(X = 2) = P(X = 3). Given that e– 3 = 0.050. Then P(X = 5) is
N
C
A 9
(A) 0.202
1
S IO
(B) 0.352
(C) 0.125
2 0
U
(D) 0.101
112.
C IS S T E ST
There are four prime numbers written in ascending order. The product of the first three is
N
385 and that of the last three is 1001. The last number is
O
M I
(A) 11
S
IS
(B) 13
D
(C) 17
(D) 19
M
113. A N
A
D
If the area of a triangle is 4 sq. units with vertices at (–2, 0), (0, 4) and (0, k), then the
value of k is
O
(A) 2 M
(B) 0 M
(C) 8
C O
(D) 4
AT
S
CU
Page 46
114. The value of sin(15o) is
1 9
(A)
√3+ 1
20
2 √2
√3 − 1 S T
TE
(B)
√2
N
√3 − 1 O
(C)
2 √2 SI
√3 − 1 M
IS
M
(D)
3 √2 D
A
N
O
115. M
If x – 3 and x + 3 are the factors of 4x3 + ax2 + bx, then the values of a and b are
SAT
M
respectively
CO (A) 3, 18
(B) 6,12
O
CU
T
(C) 0, – 36
N
(D) 12, – 5
116. A
S IO 2 0 19
The point at which the tangent to the curve y= √ 4 x − 3− 1has its slope 2/3 is
(A)
(B)
(C)
(D)
U
C IS S
(2,3)
(3,2)
(1,3)
(3,1) T E ST
N
O
M IS
S I
D
117. The area enclosed by the graph of above the x-axis is
M
A
(A) 12
(B) 10 D
(C) 6 A
(D) 24 N
O
M
118. If are the distinct roots of theM 2
equation x – x + 1 = 0, then is equal to
(A) 2 CO
(B) –1 A T
S
(C) 0
C U
1 9
(A)
√3+ 1
20
2 √2
√3 − 1 S T
TE
(B)
√2
N
√3 − 1 O
(C)
2 √2 SI
√3 − 1 M
IS
M
(D)
3 √2 D
A
N
O
115. M
If x – 3 and x + 3 are the factors of 4x3 + ax2 + bx, then the values of a and b are
SAT
M
respectively
CO (A) 3, 18
(B) 6,12
O
CU
T
(C) 0, – 36
N
(D) 12, – 5
116. A
S IO 2 0 19
The point at which the tangent to the curve y= √ 4 x − 3− 1has its slope 2/3 is
(A)
(B)
(C)
(D)
U
C IS S
(2,3)
(3,2)
(1,3)
(3,1) T E ST
N
O
M IS
S I
D
117. The area enclosed by the graph of above the x-axis is
M
A
(A) 12
(B) 10 D
(C) 6 A
(D) 24 N
O
M
118. If are the distinct roots of theM 2
equation x – x + 1 = 0, then is equal to
(A) 2 CO
(B) –1 A T
S
(C) 0
C U
Page 47
(D) 1
019
2
S T
E
119. The solution of the differential equation is
T
(A) N
O
SI
(B)
IS
M
(C)
A
D
M
(D) N
O
M
S
120.
AT
M
(A)
O E
COA polynomial of odd degree with real coefficients must have
C T
at least one real root
CU
T
(B) no real root
N
(C) only real roots
(D)
A
S IO 2 0 19
at least one root which is not real
U S T
121. The length of the latus rectum of the rectangular hyperbola is
S
C IS E
(A)
T
(B) 32
N
(C) 8
O
(D) 16
M IS
S I
D M
A D
122. The foci of the ellipse are
(A) A
N
(B) O
M
(C) M
(D) C O
AT
S
CU
019
2
S T
E
119. The solution of the differential equation is
T
(A) N
O
SI
(B)
IS
M
(C)
A
D
M
(D) N
O
M
S
120.
AT
M
(A)
O E
COA polynomial of odd degree with real coefficients must have
C T
at least one real root
CU
T
(B) no real root
N
(C) only real roots
(D)
A
S IO 2 0 19
at least one root which is not real
U S T
121. The length of the latus rectum of the rectangular hyperbola is
S
C IS E
(A)
T
(B) 32
N
(C) 8
O
(D) 16
M IS
S I
D M
A D
122. The foci of the ellipse are
(A) A
N
(B) O
M
(C) M
(D) C O
AT
S
CU
Page 48
019
2
S T
E
T
N
O
SI
IS
M
123. If
A
D , then
M is
N
(A) O
M
SAT
M
CO (B) O
CU (C)
AT N 19
(D)
S IO 2 0
124. If
U
C IS S T E
and
ST
then is
N
O
M
(A)
S I
IS
D
(B)
M
A D
(C)
A
(D) N
O
M
M A = 0, is
O
2
125. If , then the value x satisfying
(A) 0 C
A T
(B)
S
(C) –1
C U
2
S T
E
T
N
O
SI
IS
M
123. If
A
D , then
M is
N
(A) O
M
SAT
M
CO (B) O
CU (C)
AT N 19
(D)
S IO 2 0
124. If
U
C IS S T E
and
ST
then is
N
O
M
(A)
S I
IS
D
(B)
M
A D
(C)
A
(D) N
O
M
M A = 0, is
O
2
125. If , then the value x satisfying
(A) 0 C
A T
(B)
S
(C) –1
C U
Page 49
(D) 1
019
2
S T
E
126. The average translational kinetic energy of O2 molecules at a particular temperature is
T
0.048 eV. The translational kinetic energy of N2 molecules at the same temperature is
N
O
I
(A) 0.0015 eV SS
(B) 0.048 eV I
M
D
(C) 0.003 eV
AeV
(D) 0.768
M
N
O
M
SA T
CO
127.
M
O
Arrange the following electromagnetic radiation per quantum in the order of increasing
CU
T
energy: (i) Red light (ii) γ-ray (iii) X-ray (iv) Radiowave
(A)
A N
i, ii, iv, iii
19
S IO
(B) iii, i, ii, iv
(C) ii, i, iv, iii
2 0
U
(D) iv, i, iii, ii
128.
is C IS S T E ST
nucleus decays into two α-particles and an unknown nucleus. The unknown nucleus
N
O
(A)
M
nitrogen
IS
S I
D
(B) carbon
(C) boron
M
A D
(D) oxygen
A
129. N
Which of the following cannot be accelerated in a cyclotron?
O
(A) Protons M
(B) Deuterons
M
(C) Alpha particles
(D) Neutrons C O
AT
S
CU
019
2
S T
E
126. The average translational kinetic energy of O2 molecules at a particular temperature is
T
0.048 eV. The translational kinetic energy of N2 molecules at the same temperature is
N
O
I
(A) 0.0015 eV SS
(B) 0.048 eV I
M
D
(C) 0.003 eV
AeV
(D) 0.768
M
N
O
M
SA T
CO
127.
M
O
Arrange the following electromagnetic radiation per quantum in the order of increasing
CU
T
energy: (i) Red light (ii) γ-ray (iii) X-ray (iv) Radiowave
(A)
A N
i, ii, iv, iii
19
S IO
(B) iii, i, ii, iv
(C) ii, i, iv, iii
2 0
U
(D) iv, i, iii, ii
128.
is C IS S T E ST
nucleus decays into two α-particles and an unknown nucleus. The unknown nucleus
N
O
(A)
M
nitrogen
IS
S I
D
(B) carbon
(C) boron
M
A D
(D) oxygen
A
129. N
Which of the following cannot be accelerated in a cyclotron?
O
(A) Protons M
(B) Deuterons
M
(C) Alpha particles
(D) Neutrons C O
AT
S
CU
Page 50
130. For a paramagnetic material, the dependence of the magnetic susceptibility χ on the
absolute temperature T is given by
019
(A) χ =CT 2
(B) χ =C/T
S T
E
(C) χ =C T 2
(D) χ =C/T
−2 T
N
O
S I
S a lens is
131. The unit of power Iof
M
(A) metre D
(B) wattA
M
N /m
(C) watt
O
M
(D) dioptre
SA T
CO
M
O
132. The momentum of an X-ray photon is kgms . The energy of this photon is
T
−15
(A)
CU
9 ×10 J
N
(B) 3 ×10− 15 J
A 9
(C) 3 ×10− 23 J
1
S IO
(D) 12 ×10−15 J
2 0
133.
U
C IS
(A)
(B)
S T E
T
To convert a galvanometer into an ammeter, one should connect
S
a low resistance ∈ series with it
a high resistance ∈ series with it
(C) N
a low resistance ∈ withit
O
M I
(D) a high resistance in parallel with it
S
IS
134.
D M
The wavelength of blue light (λ=420 nm) in water (refractive index 1.33) is about
A
(A)
(B)
(C)
(D)
420 nm
390 nm
O
315 nm
560 nm
N
A
D
M
M
C O
AT
S
CU
absolute temperature T is given by
019
(A) χ =CT 2
(B) χ =C/T
S T
E
(C) χ =C T 2
(D) χ =C/T
−2 T
N
O
S I
S a lens is
131. The unit of power Iof
M
(A) metre D
(B) wattA
M
N /m
(C) watt
O
M
(D) dioptre
SA T
CO
M
O
132. The momentum of an X-ray photon is kgms . The energy of this photon is
T
−15
(A)
CU
9 ×10 J
N
(B) 3 ×10− 15 J
A 9
(C) 3 ×10− 23 J
1
S IO
(D) 12 ×10−15 J
2 0
133.
U
C IS
(A)
(B)
S T E
T
To convert a galvanometer into an ammeter, one should connect
S
a low resistance ∈ series with it
a high resistance ∈ series with it
(C) N
a low resistance ∈ withit
O
M I
(D) a high resistance in parallel with it
S
IS
134.
D M
The wavelength of blue light (λ=420 nm) in water (refractive index 1.33) is about
A
(A)
(B)
(C)
(D)
420 nm
390 nm
O
315 nm
560 nm
N
A
D
M
M
C O
AT
S
CU
Page 51
135. The root mean square speed of the molecules of an enclosed gas is v. What will be the
19
root mean square speed if the pressure is doubled, the temperature remaining the same?
0
(A) v /2 2
(B) v
S T
E
(C) 2v
(D) 4v T
N
O
S I
IS
136. Which one of the following forms a virtual and erect image for all positions of the object?
M
(A) Convex
(B) Concave
D lens
A lens
M
N
(C) Plano-convex lens
O
(D) Concave mirror
M
SA
O
M
O E
137.C If the distance between two masses is doubled, the gravitational attraction between them
T is
C T
CU
AT
(A) reduced to half
N
(B) reduced to a quarter
(C) doubled
19
S IO 0
(D) unaltered
2
138.
U S ST
A piece of copper and another of germanium are cooled from room temperature to 80 K.
C IS
The resistance of
T E
(A)
N
each of them increases
O
M
(B) each of them decreases
(C)
S I
copper increases ∧ germanium decreases
IS
D
(D) copper decreases and germanium increases
M
139.
A
particles will be
(A) O
N
D
When 73 Li nuclei are bombarded by protons, the resultant nuclei is 84 Be . The emitted
A
gamma photons
(B) neutrons M
(C) alpha particle M
(D) beta particle
C O
AT
S
CU
19
root mean square speed if the pressure is doubled, the temperature remaining the same?
0
(A) v /2 2
(B) v
S T
E
(C) 2v
(D) 4v T
N
O
S I
IS
136. Which one of the following forms a virtual and erect image for all positions of the object?
M
(A) Convex
(B) Concave
D lens
A lens
M
N
(C) Plano-convex lens
O
(D) Concave mirror
M
SA
O
M
O E
137.C If the distance between two masses is doubled, the gravitational attraction between them
T is
C T
CU
AT
(A) reduced to half
N
(B) reduced to a quarter
(C) doubled
19
S IO 0
(D) unaltered
2
138.
U S ST
A piece of copper and another of germanium are cooled from room temperature to 80 K.
C IS
The resistance of
T E
(A)
N
each of them increases
O
M
(B) each of them decreases
(C)
S I
copper increases ∧ germanium decreases
IS
D
(D) copper decreases and germanium increases
M
139.
A
particles will be
(A) O
N
D
When 73 Li nuclei are bombarded by protons, the resultant nuclei is 84 Be . The emitted
A
gamma photons
(B) neutrons M
(C) alpha particle M
(D) beta particle
C O
AT
S
CU
Page 52
140. Let i^ ∧ ^j be the unit vectors along x and y directions. Then the magnitude of i+
^ ^j is
(A) 1 019
(B) 2 2
(C) 0
S T
E
(D) √ 2
T
N
O
141. I
A projectile has a maximum range of 100 m. Neglecting air resistance, what is the
S
IS
maximum height attained by it?
M
(A)
(B)
50 m
100 mA
D
M
(C) N
5m
(D) O
25 m
M
S
142.
AT
M
O E
COThe frequency of the charged particle circulating at right angles to a uniform magnetic
C T
field does not depend upon the
CU (A)
(B)
(C) T
speed of the particle
A N
mass of the particle
charge of the particle
19
S IO 0
(D) magnetic field
2
143.
U S ST
The following four gases are at the same temperature. In which gas do the molecules
C IS E
have the maximum root mean square speed?
T
(A) Carbon dioxide
N
O
M I
(B) Oxygen
(C) Nitrogen
S
IS
D
(D) Hydrogen
M
A O
N
A
D
M
M
C O
AT
S
CU
^ ^j is
(A) 1 019
(B) 2 2
(C) 0
S T
E
(D) √ 2
T
N
O
141. I
A projectile has a maximum range of 100 m. Neglecting air resistance, what is the
S
IS
maximum height attained by it?
M
(A)
(B)
50 m
100 mA
D
M
(C) N
5m
(D) O
25 m
M
S
142.
AT
M
O E
COThe frequency of the charged particle circulating at right angles to a uniform magnetic
C T
field does not depend upon the
CU (A)
(B)
(C) T
speed of the particle
A N
mass of the particle
charge of the particle
19
S IO 0
(D) magnetic field
2
143.
U S ST
The following four gases are at the same temperature. In which gas do the molecules
C IS E
have the maximum root mean square speed?
T
(A) Carbon dioxide
N
O
M I
(B) Oxygen
(C) Nitrogen
S
IS
D
(D) Hydrogen
M
A O
N
A
D
M
M
C O
AT
S
CU
Page 53
144. In the following, column I lists some physical quantities and the column II gives
19
approximate energy values associated with those. Choose appropriate values of energies
as per the choices given below
20
Column I
S T Column II
E
(i) Energy of thermal neutronsT a 3 eV
(ii) N
Binding energy per nucleon b 10 keV
O
(iii) Energy of X-rays
SI c 8 MeV
(iv) IS
Photoelectric threshold of a metal d 0.025 eV
M
M
e 1 eV
D f 0.8 eV
A
(A) N
O
M
M
O
(B)
SAT
CO (C)
T
(D)
CU
A N 19
S IO 0
145. The unit of momentum is
2
U S T
(A) Nm
(B) Ns
S
C IS E
(C) Nm–1
(D) Ns–1 T
N
O
146.
M S I
The ratio of electrostatic force and gravitational force between a proton and an electron is
IS
(A)
(B)
D
2.4 × 1039
2.4 × 10– 39 M
(C)
(D)
A2.4 × 10– 37
2.4 × 1037
O
N
A
D
147. The charge carriers in an electrolyte are
M
M
(A)
(B)
Negative ions
Positive ions
C O
(C)
(D)
AT
Negative and positive ions
None of the above
S
CU
19
approximate energy values associated with those. Choose appropriate values of energies
as per the choices given below
20
Column I
S T Column II
E
(i) Energy of thermal neutronsT a 3 eV
(ii) N
Binding energy per nucleon b 10 keV
O
(iii) Energy of X-rays
SI c 8 MeV
(iv) IS
Photoelectric threshold of a metal d 0.025 eV
M
M
e 1 eV
D f 0.8 eV
A
(A) N
O
M
M
O
(B)
SAT
CO (C)
T
(D)
CU
A N 19
S IO 0
145. The unit of momentum is
2
U S T
(A) Nm
(B) Ns
S
C IS E
(C) Nm–1
(D) Ns–1 T
N
O
146.
M S I
The ratio of electrostatic force and gravitational force between a proton and an electron is
IS
(A)
(B)
D
2.4 × 1039
2.4 × 10– 39 M
(C)
(D)
A2.4 × 10– 37
2.4 × 1037
O
N
A
D
147. The charge carriers in an electrolyte are
M
M
(A)
(B)
Negative ions
Positive ions
C O
(C)
(D)
AT
Negative and positive ions
None of the above
S
CU
Page 54
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 55
148. A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the
19
radius were halved and the temperature doubled, the power radiated in watt would be
0
(A) 225 2
(B) 450
S T
E
(C) 1800
(D) 1000 T
N
O
SI
IS
149. The ratio of resolving powers of an optical microscope for two wavelengths λ = 4000 Å
1
Mis
M
and λ = 6000 Å
2
D
(A) 8 : 27A
(B) 3 N :2
(C) O 9:4
M
M
O
(D) 16 : 81
SA
CO
T The centripetal acceleration required for a particle to move on a circle of radius r with
150.
T
speed v is
CU (A)
(B)
A v/r
N
v2/r
19
S IO 0
(C) v/r2
(D) vr2/2 2
151. U
C IS S E ST
The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series
is T
N
O
M I
(A) 2
(B) 4
S
IS
D
(C) 1
(D) 0.5
M
152.
A A
D
Two cars moving in opposite directions approach each other with speed of 22 m/s and
N
16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz.
O
The frequency heard by the driver of the second car is [velocity of sound 340 m/s]
M
(A) 350 Hz M
(B)
(C)
361 Hz
411 Hz C O
(D) 448 Hz
AT
S
CU
19
radius were halved and the temperature doubled, the power radiated in watt would be
0
(A) 225 2
(B) 450
S T
E
(C) 1800
(D) 1000 T
N
O
SI
IS
149. The ratio of resolving powers of an optical microscope for two wavelengths λ = 4000 Å
1
Mis
M
and λ = 6000 Å
2
D
(A) 8 : 27A
(B) 3 N :2
(C) O 9:4
M
M
O
(D) 16 : 81
SA
CO
T The centripetal acceleration required for a particle to move on a circle of radius r with
150.
T
speed v is
CU (A)
(B)
A v/r
N
v2/r
19
S IO 0
(C) v/r2
(D) vr2/2 2
151. U
C IS S E ST
The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series
is T
N
O
M I
(A) 2
(B) 4
S
IS
D
(C) 1
(D) 0.5
M
152.
A A
D
Two cars moving in opposite directions approach each other with speed of 22 m/s and
N
16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz.
O
The frequency heard by the driver of the second car is [velocity of sound 340 m/s]
M
(A) 350 Hz M
(B)
(C)
361 Hz
411 Hz C O
(D) 448 Hz
AT
S
CU
Page 56
153. The magnetic susceptibility is negative for
(A) diamagnetic material only 019
(B) paramagnetic material only 2
(C) ferromagnetic material only
S T
E
(D) paramagnetic and ferromagnetic materials
T
N
O
154. I
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two
S
IS
vectors, the angle between these vectors is
M
(A)
(B)
0o
90o A
D
M
(C) N
45o
(D) O
180o
M
S
155.
AT
M
O E
COGiven the value of Rydberg constant is 1 × 10 m , the wave number of the last line of
C T
the Balmer series in hydrogen spectrum will be
7 −1
CU (A)
(B)
(C)
AT
0.025 × 104 m−1
N
0.5 × 107 m−1
0.25 × 107 m−1
19
S IO 0
(D) 2.5 × 107 m−1
2
156.
(A)
U
C IS S
a = 2, b = 3, c = –4 T E ST
The vectors 2ri+3rj+4rk, ari+brj+crk are normal to each other only if
(B)
N
a = 4, b = 4, c = –5
O
M
(C) a = 4, b = 4, c = 5
(D)
S I
a = –2, b = 3, c = 4
IS
D M
A D
157. The order and degree of the differential equation are
(A) (3, 2) A
(B) (2, 3) N
(C) (2, 2)O
(D) (3, 3) M
M
C O
AT
S
CU
(A) diamagnetic material only 019
(B) paramagnetic material only 2
(C) ferromagnetic material only
S T
E
(D) paramagnetic and ferromagnetic materials
T
N
O
154. I
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two
S
IS
vectors, the angle between these vectors is
M
(A)
(B)
0o
90o A
D
M
(C) N
45o
(D) O
180o
M
S
155.
AT
M
O E
COGiven the value of Rydberg constant is 1 × 10 m , the wave number of the last line of
C T
the Balmer series in hydrogen spectrum will be
7 −1
CU (A)
(B)
(C)
AT
0.025 × 104 m−1
N
0.5 × 107 m−1
0.25 × 107 m−1
19
S IO 0
(D) 2.5 × 107 m−1
2
156.
(A)
U
C IS S
a = 2, b = 3, c = –4 T E ST
The vectors 2ri+3rj+4rk, ari+brj+crk are normal to each other only if
(B)
N
a = 4, b = 4, c = –5
O
M
(C) a = 4, b = 4, c = 5
(D)
S I
a = –2, b = 3, c = 4
IS
D M
A D
157. The order and degree of the differential equation are
(A) (3, 2) A
(B) (2, 3) N
(C) (2, 2)O
(D) (3, 3) M
M
C O
AT
S
CU
Page 57
158. A bag contains 6 green balls, 8 white balls and 10 black balls. If a ball is drawn from the
19
bag, what is the probability of it being either white or black?
0
(A) 1/18 2
(B) 1/8
S T
E
(C) 3/4
(D) 1/12 T
N
O
SI
IS is _________ erg-sec.
159. The value of (h bar)
M
(A) 6.6253D × 10
A × 10
M
–27
–27
(B) 1.0545
N
O
–31
(C) 6.6253 × 10
M
–34
(D) 1.0544 × 10
SA
O
M
O E
160.C According to Bohr’s postulates, which of the following quantity takes discrete values?
T
C T
T
(A) Kinetic energy
CU
N
(B) Angular momentum
A
(C) Potential energy
(D) Momentum
19
S IO 2 0
U S T
161. A chain reaction is possible when the mass of the fuel is greater than the
S
C IS E
(A) critical mass
(B) neutron mass T
(C) proton mass
N
O
M
(D) electron mass
S I
IS
162.
D
In Raman effect, the spectral line with lower frequency than the incident frequency is
M
A D
(A) Anti-Stokes’ line
(B) A
Fraunhofer line
(C)
N
Rayleigh line
(D) O
Stokes’ line
M
M with
O
163. In n-type semiconductor, Silicon is doped
C
(A) Aluminium
(B) Arsenic
A T
(C) Indium
S
(D) Germanium
C U
19
bag, what is the probability of it being either white or black?
0
(A) 1/18 2
(B) 1/8
S T
E
(C) 3/4
(D) 1/12 T
N
O
SI
IS is _________ erg-sec.
159. The value of (h bar)
M
(A) 6.6253D × 10
A × 10
M
–27
–27
(B) 1.0545
N
O
–31
(C) 6.6253 × 10
M
–34
(D) 1.0544 × 10
SA
O
M
O E
160.C According to Bohr’s postulates, which of the following quantity takes discrete values?
T
C T
T
(A) Kinetic energy
CU
N
(B) Angular momentum
A
(C) Potential energy
(D) Momentum
19
S IO 2 0
U S T
161. A chain reaction is possible when the mass of the fuel is greater than the
S
C IS E
(A) critical mass
(B) neutron mass T
(C) proton mass
N
O
M
(D) electron mass
S I
IS
162.
D
In Raman effect, the spectral line with lower frequency than the incident frequency is
M
A D
(A) Anti-Stokes’ line
(B) A
Fraunhofer line
(C)
N
Rayleigh line
(D) O
Stokes’ line
M
M with
O
163. In n-type semiconductor, Silicon is doped
C
(A) Aluminium
(B) Arsenic
A T
(C) Indium
S
(D) Germanium
C U
Page 58
164. 019
The Bragg’s equation 2dsinθ = nλ has no solution for
2
(A) λ<d
S T
E
(B) λ <2d
(C) λ >2d T
(D) λ =2d N
O
SI
IS1000 turns. When a current of 4A flows through it, the magnetic flux
165. A long solenoid has
M
M
D turn of the solenoid is 4 × 10 Wb. The self-inductance of the solenoid
−3
linked with each
is A
N
(A) O4H
(B)M 2H
SA T
O
M(C) 3H
C (D) 1H O
CU 166.
AT
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth
N
‘d’ below the surface of earth. Then
19
S IO 0
(A) d = 05 km
(B) 1 km 2
U S T
(C) 0.75 km
(D) 2 km
S
167. C IS N
T E
The least distance of distinct vision for a normal eye is
O
(A)
(B)
M
100 m
5m
IS
S I
(C)
(D)
D 0.25 m
infinity M
168. A N
A
D
Sound travels fastest in
O
(A) vacuum
M
(B) liquids
M
(C)
(D)
gases
solids
C O
AT
S
CU
The Bragg’s equation 2dsinθ = nλ has no solution for
2
(A) λ<d
S T
E
(B) λ <2d
(C) λ >2d T
(D) λ =2d N
O
SI
IS1000 turns. When a current of 4A flows through it, the magnetic flux
165. A long solenoid has
M
M
D turn of the solenoid is 4 × 10 Wb. The self-inductance of the solenoid
−3
linked with each
is A
N
(A) O4H
(B)M 2H
SA T
O
M(C) 3H
C (D) 1H O
CU 166.
AT
The acceleration due to gravity at a height 1 km above the earth is the same as at a depth
N
‘d’ below the surface of earth. Then
19
S IO 0
(A) d = 05 km
(B) 1 km 2
U S T
(C) 0.75 km
(D) 2 km
S
167. C IS N
T E
The least distance of distinct vision for a normal eye is
O
(A)
(B)
M
100 m
5m
IS
S I
(C)
(D)
D 0.25 m
infinity M
168. A N
A
D
Sound travels fastest in
O
(A) vacuum
M
(B) liquids
M
(C)
(D)
gases
solids
C O
AT
S
CU
Page 59
169. The law that states “The induced e.m.f. is proportional to the rate of change of its number
19
of lines of magnetic force linking the circuit” is
0
(A) Lenz’s law 2
(B) Faraday law
S T
E
(C) Ohms law
(D) Joule-Thomson law T
N
O
S I
IS a certain distance apart in air. When a dielectric sheet is placed
170. Two charges are placed
M electrostatic force between them will
M
between them, the
D
A zero
(A) become
N
(B) increase
O
(C) remain unchanged
M
M
O
(D) decrease
SA
CO
T The resistance of a conductor carrying a current 3 A which has a potential difference of
171.
T
15 V between its two ends is
CU (A)
(B)
A
15 Ohm
5 Ohm
N 19
S IO 0
(C) 0.5 Ohm
(D) 1/5 Ohm 2
172. U
C IS S
The value of A ⋅ B+ Ā + A is
T E ST
(A) B
N
O
M
(B) always 0
IS
S I
D
(C) always 1
M
A D
(D) B̄
A
N
173. O
Which of the following flip-flops does not have race problem?
M
(A) D-flip-flop M
(B)
(C)
T-flip-flop
Master-slave flip-flop C O
(D) JK flip-flop
AT
S
CU
19
of lines of magnetic force linking the circuit” is
0
(A) Lenz’s law 2
(B) Faraday law
S T
E
(C) Ohms law
(D) Joule-Thomson law T
N
O
S I
IS a certain distance apart in air. When a dielectric sheet is placed
170. Two charges are placed
M electrostatic force between them will
M
between them, the
D
A zero
(A) become
N
(B) increase
O
(C) remain unchanged
M
M
O
(D) decrease
SA
CO
T The resistance of a conductor carrying a current 3 A which has a potential difference of
171.
T
15 V between its two ends is
CU (A)
(B)
A
15 Ohm
5 Ohm
N 19
S IO 0
(C) 0.5 Ohm
(D) 1/5 Ohm 2
172. U
C IS S
The value of A ⋅ B+ Ā + A is
T E ST
(A) B
N
O
M
(B) always 0
IS
S I
D
(C) always 1
M
A D
(D) B̄
A
N
173. O
Which of the following flip-flops does not have race problem?
M
(A) D-flip-flop M
(B)
(C)
T-flip-flop
Master-slave flip-flop C O
(D) JK flip-flop
AT
S
CU
Page 60
174. A microprocessor with a 12 bit address bus will be able to access ______ kilobytes of
memory.
019
(A) 8 2
(B) 4
S T
E
(C) 1
(D) 2 T
N
O
I
175. The displacement ofSaSparticle is given by
I
M
D sin kt
M
2 2
x=A
A
N time. The unit of k is
where t denotes
O
M Hertz
O
(A)
M
E
(B) Meter
O
C (C)
C T
Radian
A T (D) Second
S
CU 176.
T N
Planck’s constant has the dimension of
A 19
S IO
(A) Force
(B) Energy
2 0
U
(C) Linear momentum
177.
(D)
C IS S
Angular momentum
T E ST
The statement that the velocity of light in vacuum = velocity of light in the medium is
N
O
M I
(A) Dimensionally correct
(B) S
Dimensionally incorrect
IS
D
(C) Numerically incorrect
(D)
M
Both (A) and (C)
178.
A N
A
D
Two vectors have magnitude 3 and 5. If the angle between them is 60o, then the dot
O
product of two vectors will be
(A) 6.5 M
(B) 7.5 M
(C)
(D)
7.9
8 C O
AT
S
CU
memory.
019
(A) 8 2
(B) 4
S T
E
(C) 1
(D) 2 T
N
O
I
175. The displacement ofSaSparticle is given by
I
M
D sin kt
M
2 2
x=A
A
N time. The unit of k is
where t denotes
O
M Hertz
O
(A)
M
E
(B) Meter
O
C (C)
C T
Radian
A T (D) Second
S
CU 176.
T N
Planck’s constant has the dimension of
A 19
S IO
(A) Force
(B) Energy
2 0
U
(C) Linear momentum
177.
(D)
C IS S
Angular momentum
T E ST
The statement that the velocity of light in vacuum = velocity of light in the medium is
N
O
M I
(A) Dimensionally correct
(B) S
Dimensionally incorrect
IS
D
(C) Numerically incorrect
(D)
M
Both (A) and (C)
178.
A N
A
D
Two vectors have magnitude 3 and 5. If the angle between them is 60o, then the dot
O
product of two vectors will be
(A) 6.5 M
(B) 7.5 M
(C)
(D)
7.9
8 C O
AT
S
CU
Page 61
179. If the distance covered by a particle happens to be zero, then the displacement of the
particle
019
(A) must be zero 2
(B) may or may not be zero
S T
E
(C) cannot be zero
(D) T
depends upon the particle
N
O
SI
IS
180. Two bullets are fired horizontally with different velocities from the same height. Which
Mground first?
M
one will reach the
D
(A) The A slower one
N one
(B) Faster
O
(C) It cannot be predicted
M
M
O
(D) Both will reach simultaneously
SA
CO
T The angular velocity of a particle rotating in a circular orbit 100 times per minute is
181.
CU
AT
(A) 60 deg/s
N
(B) 1.66 rad/s
(C) 1.66 deg/s
19
S IO 0
(D) 1.66 rad/minute
2
182.
U S ST
Frictional forces act in a direction
(A)
C IS T E
perpendicular to the surface in contact
(B)
N
parallel to surface in contact
O
M
(C) parallel to normal reaction
(D)
S I
inclined at 45o to normal reaction
IS
183.
D M
Which one of the following is true for an elastic collision between two bodies?
(A)
(B)
(C)
A O
N
A
D
Kinetic energy of the system is conserved
Total momentum of the system is conserved
Both kinetic energy and momentum of the system are conserved
(D)
M
Neither kinetic energy nor momentum of the system is conserved
M
184. When a mass is rotating in an orbitO
C about a fixed axis, its angular momentum is directed
(A) along the radius of theTorbit
A
(C) along the axis ofS
(B) tangential to the orbit
(D) perpendicularU
rotation
C to the plane of the orbit.
particle
019
(A) must be zero 2
(B) may or may not be zero
S T
E
(C) cannot be zero
(D) T
depends upon the particle
N
O
SI
IS
180. Two bullets are fired horizontally with different velocities from the same height. Which
Mground first?
M
one will reach the
D
(A) The A slower one
N one
(B) Faster
O
(C) It cannot be predicted
M
M
O
(D) Both will reach simultaneously
SA
CO
T The angular velocity of a particle rotating in a circular orbit 100 times per minute is
181.
CU
AT
(A) 60 deg/s
N
(B) 1.66 rad/s
(C) 1.66 deg/s
19
S IO 0
(D) 1.66 rad/minute
2
182.
U S ST
Frictional forces act in a direction
(A)
C IS T E
perpendicular to the surface in contact
(B)
N
parallel to surface in contact
O
M
(C) parallel to normal reaction
(D)
S I
inclined at 45o to normal reaction
IS
183.
D M
Which one of the following is true for an elastic collision between two bodies?
(A)
(B)
(C)
A O
N
A
D
Kinetic energy of the system is conserved
Total momentum of the system is conserved
Both kinetic energy and momentum of the system are conserved
(D)
M
Neither kinetic energy nor momentum of the system is conserved
M
184. When a mass is rotating in an orbitO
C about a fixed axis, its angular momentum is directed
(A) along the radius of theTorbit
A
(C) along the axis ofS
(B) tangential to the orbit
(D) perpendicularU
rotation
C to the plane of the orbit.
Page 62
185. In practice, Poisson’s ratio σ lies between
(A) – ∞ to + ∞
019
(B) 0 and + ∞ 2
(C) 0 and 0.5
S T
E
(D) – 0.5 and 0
T
N
O
186. I
Two wires of the same material and length but cross sectional area in the ratio 1 : 2 are
S
IS
used to suspend the same loads. The extension in them will be in the ratio
M
(A)
(B)
1:2
2:1 A
D
M
(C) N
4:1
(D) O
1:4
M
S
187.
AT
M
(A) 0o
O E
COA liquid will not wet the surface of a solid, if the angle of contact is
C T
CU
T
(B) 45o
A N
(C) 60o
(D) > 90o
19
S IO 2 0
U S
188. When two capillary tubes of different diameters are dipped in liquid vertically, the rise of
ST
the liquid in the capillary tube is
C IS
(A)
(B)
T
same in both the tubes
N
E
more in the tube of larger diameter
O
M
(C) more in the tube of smaller diameter
(D)
S I
less in the tube of smaller diameter
IS
189.
D M
Pyrometer is a device for measuring
A
(A)
(B)
(C)
pressure
O
densityN
A
D
temperature
(D) viscosity
M
M
C O
AT
S
CU
(A) – ∞ to + ∞
019
(B) 0 and + ∞ 2
(C) 0 and 0.5
S T
E
(D) – 0.5 and 0
T
N
O
186. I
Two wires of the same material and length but cross sectional area in the ratio 1 : 2 are
S
IS
used to suspend the same loads. The extension in them will be in the ratio
M
(A)
(B)
1:2
2:1 A
D
M
(C) N
4:1
(D) O
1:4
M
S
187.
AT
M
(A) 0o
O E
COA liquid will not wet the surface of a solid, if the angle of contact is
C T
CU
T
(B) 45o
A N
(C) 60o
(D) > 90o
19
S IO 2 0
U S
188. When two capillary tubes of different diameters are dipped in liquid vertically, the rise of
ST
the liquid in the capillary tube is
C IS
(A)
(B)
T
same in both the tubes
N
E
more in the tube of larger diameter
O
M
(C) more in the tube of smaller diameter
(D)
S I
less in the tube of smaller diameter
IS
189.
D M
Pyrometer is a device for measuring
A
(A)
(B)
(C)
pressure
O
densityN
A
D
temperature
(D) viscosity
M
M
C O
AT
S
CU
Page 63
190. The internal energy of a gas during isothermal expansion
(A) increases 019
(B) remains constant 2
(C) decreases
S T
E
(D) becomes zero
T
N
O
191. I
Which one of the following expressions does not represent simple harmonic motion
S
(SMH)?
IS
M
(A)
(B)
D
A sin ωt
A
A sin 2ωt
M
(C) N
A sin ωt + A cos ωt
(D) O
A sin2 ωt
M
S
192.
AT
M
O E
COIf x is the displacement of the particle from the mean position, the total energy of a
C T
particle executing simple harmonic motion is
CU (A)
(B)
(C) T
proportional to x
A N
proportional to x2
independent of x
19
S IO 0
(D) proportional to √ x
2
193.
U S ST
If the refractive index of water is 1.33, the speed of light in water will be
(A)
C IS
3 x 108 m/s T E
(B) 0.44 x 108 m/s
N
O
M
(C) 1.33 x 108 m/s
(D) 2.25 x 108 m/s
S I
IS
194.
D M
The correct arrangement of colors in the descending order of their wavelength
(A)
(B)
(C)
A O
N
A
D
yellow, violet, green, orange
orange, yellow, green, violet
violet, green, yellow, orange
(D) orange, green, violet, yellow
M
M
C O
AT
S
CU
(A) increases 019
(B) remains constant 2
(C) decreases
S T
E
(D) becomes zero
T
N
O
191. I
Which one of the following expressions does not represent simple harmonic motion
S
(SMH)?
IS
M
(A)
(B)
D
A sin ωt
A
A sin 2ωt
M
(C) N
A sin ωt + A cos ωt
(D) O
A sin2 ωt
M
S
192.
AT
M
O E
COIf x is the displacement of the particle from the mean position, the total energy of a
C T
particle executing simple harmonic motion is
CU (A)
(B)
(C) T
proportional to x
A N
proportional to x2
independent of x
19
S IO 0
(D) proportional to √ x
2
193.
U S ST
If the refractive index of water is 1.33, the speed of light in water will be
(A)
C IS
3 x 108 m/s T E
(B) 0.44 x 108 m/s
N
O
M
(C) 1.33 x 108 m/s
(D) 2.25 x 108 m/s
S I
IS
194.
D M
The correct arrangement of colors in the descending order of their wavelength
(A)
(B)
(C)
A O
N
A
D
yellow, violet, green, orange
orange, yellow, green, violet
violet, green, yellow, orange
(D) orange, green, violet, yellow
M
M
C O
AT
S
CU
Page 64
195. Field inside a solenoid is
(A) directly proportional to its length 019
(B) 2
directly proportional to the current
(C) T
inversely proportional to the number of turns
S
E
(D) inversely proportional to the current
T
N
O
196. I
L, C and R represent the quantities inductance, capacitance and resistance respectively.
S
IS
The combination which has the dimensions of frequency is
M
(A)
(B)
(1/RC)
(C/L) A
D
M
(C) N
(R/LC)
(D) O
(RL/C)
M
S
197.
AT
M
O E
COPoynting vector of a plane electromagnetic wave propagating in the direction k^ is
C T
(A) perpendicular to k^
CU
AT N
(B) parallel to k^
19
S IO
(C) antiparallel to k^
2 0
U
C IS S
(D) at an angle π/4 to k^
T E ST
198. N
Two identical fuses are rated at 10 A
O
(A)
M S I
in parallel, the combination acts as a fuse of rating 10 A
IS
D
(B) in parallel, the combination acts as a fuse of rating 20 A
(C) in series, the combination acts as a fuse of rating 20 A
M
A
(D) in series, the combination acts as a fuse of rating 5 A
D
A
199. N
A half-wave rectifier is being used to rectify an alternating voltage of frequency 50 Hz.
O
The number of pulses of rectified current obtained in one second is
M
(A) 50
M
(B)
(C)
25
100 C O
(D) 1
AT
S
CU
(A) directly proportional to its length 019
(B) 2
directly proportional to the current
(C) T
inversely proportional to the number of turns
S
E
(D) inversely proportional to the current
T
N
O
196. I
L, C and R represent the quantities inductance, capacitance and resistance respectively.
S
IS
The combination which has the dimensions of frequency is
M
(A)
(B)
(1/RC)
(C/L) A
D
M
(C) N
(R/LC)
(D) O
(RL/C)
M
S
197.
AT
M
O E
COPoynting vector of a plane electromagnetic wave propagating in the direction k^ is
C T
(A) perpendicular to k^
CU
AT N
(B) parallel to k^
19
S IO
(C) antiparallel to k^
2 0
U
C IS S
(D) at an angle π/4 to k^
T E ST
198. N
Two identical fuses are rated at 10 A
O
(A)
M S I
in parallel, the combination acts as a fuse of rating 10 A
IS
D
(B) in parallel, the combination acts as a fuse of rating 20 A
(C) in series, the combination acts as a fuse of rating 20 A
M
A
(D) in series, the combination acts as a fuse of rating 5 A
D
A
199. N
A half-wave rectifier is being used to rectify an alternating voltage of frequency 50 Hz.
O
The number of pulses of rectified current obtained in one second is
M
(A) 50
M
(B)
(C)
25
100 C O
(D) 1
AT
S
CU
Page 65
200. Two coils of inductances L1 and L2 are linked such that their mutual inductance is M.
Then
019
(A) M = L1 – L2 2
(B) M = L1 + L2
S T
E
(C) M = (L1 + L2)/2
(D) T
the maximum value of M is √ L1 L2
N
O
S I
IS the quantum numbers n = 3, l = 2, m = +2 are possible?
201. For how many orbitals,
M
(A) 1
(B) 2 A
D
M
(C) 3 N
(D) O
M4
SA T
O
M
(A) Mn
O
C T
2+ E
202.C Which of the following ions has maximum magnetic moment?
CU
T
2+
(B) Fe
A
(C) Ti2+
(D) Cr2+
N 19
S IO 2 0
U S
203. Arrange the following molecular species in increasing order of stability.
ST
C IS E
(A) N2+ > N2 > N2 – > N22–
T
N
(B) N2 2 – > N2 – > N2 > N2+
O
M
(C) N2 > =
IS
S I
>
(D)
D M
204. A N
A
D
The compound formed by elements A and B crystallizes in the cubic structure where A
O
atoms are at the corners of a cube and B atoms are at the face centers. The formula of the
compound is M
M
(A)
(B)
AB3
AB
C O
(C)
(D)
A3B
A2B2 AT
S
CU
Then
019
(A) M = L1 – L2 2
(B) M = L1 + L2
S T
E
(C) M = (L1 + L2)/2
(D) T
the maximum value of M is √ L1 L2
N
O
S I
IS the quantum numbers n = 3, l = 2, m = +2 are possible?
201. For how many orbitals,
M
(A) 1
(B) 2 A
D
M
(C) 3 N
(D) O
M4
SA T
O
M
(A) Mn
O
C T
2+ E
202.C Which of the following ions has maximum magnetic moment?
CU
T
2+
(B) Fe
A
(C) Ti2+
(D) Cr2+
N 19
S IO 2 0
U S
203. Arrange the following molecular species in increasing order of stability.
ST
C IS E
(A) N2+ > N2 > N2 – > N22–
T
N
(B) N2 2 – > N2 – > N2 > N2+
O
M
(C) N2 > =
IS
S I
>
(D)
D M
204. A N
A
D
The compound formed by elements A and B crystallizes in the cubic structure where A
O
atoms are at the corners of a cube and B atoms are at the face centers. The formula of the
compound is M
M
(A)
(B)
AB3
AB
C O
(C)
(D)
A3B
A2B2 AT
S
CU
Page 66
019
2
205. T
Schottky defect in crystals is observed when
S
E
(A) T
unequal number of cations and anions are missing from the lattice
(B) N
equal number of cations and anions are missing from the lattice
O
(C) I
an ion leaves its normal site and occupies an interstitial site
S
IS
(D) density of the crystal is increased
M
206. Which one A D
M
of the following octahedral complexes does not show geometric isomerism?
(A and BNare monodentate ligands)
O
M [MA B ]
O
(A)
M
2 4
E
(B) [MA B ]
O
C (C)
3 3
C T
[MA B ] 4 2
A T (D) [MA B] 5
S
CU 207.
T N
Which of the following is the strongest ligand?
A 19
S IO
(A) Cl–
(B) F–
2 0
U
(C) NO2–
208.
(D)
C IS
CN–
S T E ST
The product obtained after positron emission from 31Ga68 is
N
O
M I
(A) Ge68
S
31
68
(B) 30Zn
IS
D
69
(C) 30Zn
M
69
(D) 31Ga
209.
A N
A
D
Which of the following is not a mineral of aluminum?
(A) O
Bauxite
(B) Cryolite M
(C) China clay M
(D) Malachite
C O
210. AT
When bismuth chloride is dissolved in water a white precipitate appears. The white
S
precipitate is
CU
2
205. T
Schottky defect in crystals is observed when
S
E
(A) T
unequal number of cations and anions are missing from the lattice
(B) N
equal number of cations and anions are missing from the lattice
O
(C) I
an ion leaves its normal site and occupies an interstitial site
S
IS
(D) density of the crystal is increased
M
206. Which one A D
M
of the following octahedral complexes does not show geometric isomerism?
(A and BNare monodentate ligands)
O
M [MA B ]
O
(A)
M
2 4
E
(B) [MA B ]
O
C (C)
3 3
C T
[MA B ] 4 2
A T (D) [MA B] 5
S
CU 207.
T N
Which of the following is the strongest ligand?
A 19
S IO
(A) Cl–
(B) F–
2 0
U
(C) NO2–
208.
(D)
C IS
CN–
S T E ST
The product obtained after positron emission from 31Ga68 is
N
O
M I
(A) Ge68
S
31
68
(B) 30Zn
IS
D
69
(C) 30Zn
M
69
(D) 31Ga
209.
A N
A
D
Which of the following is not a mineral of aluminum?
(A) O
Bauxite
(B) Cryolite M
(C) China clay M
(D) Malachite
C O
210. AT
When bismuth chloride is dissolved in water a white precipitate appears. The white
S
precipitate is
CU
Page 67
(A) Bi(OH)3
19
(B) BiOH
(C) BiO(OH)
(D) BiOCl 20
211.
S T
Which of the following compound is formed when I2 is dissolved in ammonium
E
hydroxide (density = 0.88 g/cm3)?
T
N
(A) NH4I
O
(B) NI3·6NH3
SI
(C) NI3·4NH3 IS
M
M
(D) NI3·NH4OH
D
A
212. N
Which of the following is NOT a metal ion indicator?
O
M Bromocresol blue
O
(A)
M
CO (C) Calmagite
E
(B) Murexide
SAT
C T
(D) Solochrome black T
CU 213.
AT N
In brown ring test for nitrate ions, brown ring is formed having composition
19
S IO 0
(A) [Fe(H2O)6]2+
(B) [Fe (H2O)5NO]2+
2
U S
(C) [Fe(H2O)5 NO]3+
(D) [Fe(H2O)5 NO2]2+
ST
214.
C IS N
T E
Which is mismatched regarding the shape?
O
(A)
(B)
M IS
S I
XeF4 – Square planar
XeOF4 - Square pyramidal
D
(C) XeF6 – Distorted octahedral
(D) M
XeO3 – Bent T shape
215. A N
A
D
Which of the following is not a product of the breakdown of organic matter in water by
O
aerobic bacteria?
M
(A) CO2
M
(B) H2O
C O
(C)
AT
S
(D) H2S
CU
19
(B) BiOH
(C) BiO(OH)
(D) BiOCl 20
211.
S T
Which of the following compound is formed when I2 is dissolved in ammonium
E
hydroxide (density = 0.88 g/cm3)?
T
N
(A) NH4I
O
(B) NI3·6NH3
SI
(C) NI3·4NH3 IS
M
M
(D) NI3·NH4OH
D
A
212. N
Which of the following is NOT a metal ion indicator?
O
M Bromocresol blue
O
(A)
M
CO (C) Calmagite
E
(B) Murexide
SAT
C T
(D) Solochrome black T
CU 213.
AT N
In brown ring test for nitrate ions, brown ring is formed having composition
19
S IO 0
(A) [Fe(H2O)6]2+
(B) [Fe (H2O)5NO]2+
2
U S
(C) [Fe(H2O)5 NO]3+
(D) [Fe(H2O)5 NO2]2+
ST
214.
C IS N
T E
Which is mismatched regarding the shape?
O
(A)
(B)
M IS
S I
XeF4 – Square planar
XeOF4 - Square pyramidal
D
(C) XeF6 – Distorted octahedral
(D) M
XeO3 – Bent T shape
215. A N
A
D
Which of the following is not a product of the breakdown of organic matter in water by
O
aerobic bacteria?
M
(A) CO2
M
(B) H2O
C O
(C)
AT
S
(D) H2S
CU
Page 68
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 69
216. Addition of phosphate containing fertilizers in water bodies causes
(i) enhanced growth of algae 019
(ii) 2
increase in amount of dissolved oxygen
(iii deposition of calcium phosphate
S T
E
)
(iv) T
decrease in fish population
N
O
(A) (i) and (ii)
SI
(B) (i) and (iv)
IS
M
M
(C) (ii) and (iii)
(D) D
(i) and (iii)
A
N
O
217. The compound which is not isomeric with methoxypropane
M
SA T
O
M
(C) butanone O
(A) diethyl ether
C (B) butan-1-ol
(D) 2-methylpropan-2-ol
CU
218.
AT N 9
Which of the following will evolve CO2 on reaction with NaHCO3?
1
S IO 0
I Salicylic acid, II Benzoic acid, III Ascorbic acid, IV Phenol
2
U S T
(A) I, II, III and IV
(B) I, II and III S
C IS
(C)
(D)
I and III
II and IV
O
N
T E
219.
M S I
What is the product formed in the following reaction?
IS
D M
A
(A) CHCl3
O
N
A
D
(B) M
M
(C) CH3CHO
C O
AT
(D)
S
CU
(i) enhanced growth of algae 019
(ii) 2
increase in amount of dissolved oxygen
(iii deposition of calcium phosphate
S T
E
)
(iv) T
decrease in fish population
N
O
(A) (i) and (ii)
SI
(B) (i) and (iv)
IS
M
M
(C) (ii) and (iii)
(D) D
(i) and (iii)
A
N
O
217. The compound which is not isomeric with methoxypropane
M
SA T
O
M
(C) butanone O
(A) diethyl ether
C (B) butan-1-ol
(D) 2-methylpropan-2-ol
CU
218.
AT N 9
Which of the following will evolve CO2 on reaction with NaHCO3?
1
S IO 0
I Salicylic acid, II Benzoic acid, III Ascorbic acid, IV Phenol
2
U S T
(A) I, II, III and IV
(B) I, II and III S
C IS
(C)
(D)
I and III
II and IV
O
N
T E
219.
M S I
What is the product formed in the following reaction?
IS
D M
A
(A) CHCl3
O
N
A
D
(B) M
M
(C) CH3CHO
C O
AT
(D)
S
CU
Page 70
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 71
220. Which of the following reagent does not convert propanone to propane?
(A) Zn-Hg/HCl 019
(B) NH2-NH2/KOH 2
(C) HS-CH2-CH2-SH, Raney Ni
S T
E
(D) NaBH4
T
N
O
221.
SI
Arrange the following +CH3, CH4 and –CH3 in order of increasing H-C-H bond angles
IS
M
M
(A)
D
A
(B) N
O
M
M
O
(C)
SAT
CO (D)
CU
222.
AT N
IUPAC name of the below compound is
19
S IO 2 0
(A)
(B)
(C)
U
C IS S ST
N-Phenylcyclohexanecarboxamide
N-Cyclohexylbenzamide
T E
N-Phenylcyclohexylmethanamide
(D) N
N-Cyclohexyl-N-phenylmethanamide
O
M IS
S I
D
223. Arrange n-pentane (I), isopentane (II) and neopentane (III) in the decreasing order of
M
their boiling point.
(A)
(B)
(C)
A III>II>I
I>II>III
O
II>III>IN
A
D
(D) III>I>II
M
224. Which of the following reagent is O
M
not useful for direct oxidation of toluene to
benzaldehyde? C
A T
(A) CrO Cl /CCl
2
S
2 4
(B) MnO /CCl
(C) Alkaline KMnO
2
C U 4
4
(A) Zn-Hg/HCl 019
(B) NH2-NH2/KOH 2
(C) HS-CH2-CH2-SH, Raney Ni
S T
E
(D) NaBH4
T
N
O
221.
SI
Arrange the following +CH3, CH4 and –CH3 in order of increasing H-C-H bond angles
IS
M
M
(A)
D
A
(B) N
O
M
M
O
(C)
SAT
CO (D)
CU
222.
AT N
IUPAC name of the below compound is
19
S IO 2 0
(A)
(B)
(C)
U
C IS S ST
N-Phenylcyclohexanecarboxamide
N-Cyclohexylbenzamide
T E
N-Phenylcyclohexylmethanamide
(D) N
N-Cyclohexyl-N-phenylmethanamide
O
M IS
S I
D
223. Arrange n-pentane (I), isopentane (II) and neopentane (III) in the decreasing order of
M
their boiling point.
(A)
(B)
(C)
A III>II>I
I>II>III
O
II>III>IN
A
D
(D) III>I>II
M
224. Which of the following reagent is O
M
not useful for direct oxidation of toluene to
benzaldehyde? C
A T
(A) CrO Cl /CCl
2
S
2 4
(B) MnO /CCl
(C) Alkaline KMnO
2
C U 4
4
Page 72
(D) Cl2/hv followed by treatment with Cu(NO3)2
019
2 is
225. The material used by dentists in root canals
S T
TE
(A) gutta-percha
(B) neoprene
(C) ebonite N
O
(D) dynel
S I
IS
M is made up of 30% molecules of mass 20,000, 40% of 30,000 and the
D
M
226. A polymer sample
rest mass ofA60,000. Its number average molecule mass is
N
(A) O 36,000
(B)M 46,000
SA
T
O
M
(C) 50,000
C (D) 3,60,000 O
CU
T
227. False statement about synthetic detergents is:
(A)
A N 9
It has a non-polar organic part and a polar group
1
S IO
(B) It is a surface active reagent
(C)
2 0
It is not easily biodegradable
U S
(D) It is a sodium salt of fatty acid
ST
228.
C IS T E
The transition metal ion present in vitamin B12 is
(A) Mg2+
O
N
M I
(B) Fe2+
S
IS
(C) Zn2+
D
(D) Co2+
M
229.
A A
D
Which of the following reactions would give the best yield of t-butylmethyl ether?
(A) O
N
M
M
(B)
C O
(C)
AT
S
CU
019
2 is
225. The material used by dentists in root canals
S T
TE
(A) gutta-percha
(B) neoprene
(C) ebonite N
O
(D) dynel
S I
IS
M is made up of 30% molecules of mass 20,000, 40% of 30,000 and the
D
M
226. A polymer sample
rest mass ofA60,000. Its number average molecule mass is
N
(A) O 36,000
(B)M 46,000
SA
T
O
M
(C) 50,000
C (D) 3,60,000 O
CU
T
227. False statement about synthetic detergents is:
(A)
A N 9
It has a non-polar organic part and a polar group
1
S IO
(B) It is a surface active reagent
(C)
2 0
It is not easily biodegradable
U S
(D) It is a sodium salt of fatty acid
ST
228.
C IS T E
The transition metal ion present in vitamin B12 is
(A) Mg2+
O
N
M I
(B) Fe2+
S
IS
(C) Zn2+
D
(D) Co2+
M
229.
A A
D
Which of the following reactions would give the best yield of t-butylmethyl ether?
(A) O
N
M
M
(B)
C O
(C)
AT
S
CU
Page 73
(D)
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 74
230. The Cannizzaro’s reaction is not given by
(A) 019
2
(B)
S T
E
T
(C) N
O
(D) SI
IS
M
A
D
M
231. When p-nitrobenzenesulphonic acid and picric acid are treated with NaHCO , the gases
N 3
O respectively are
released
M
M
O
(A) SO , NO
E
2 2
CO (B) NO , NO
C T
2
(C) NO , H
A T (D) CO , CO 2 2
S
2 2
CU 232.
AT N
The following reaction is known as
19
S IO 2 0
(A)
(B)
(C)
U
C IS S
Finkelstein reaction
Swarts reaction
Darzen reaction T E ST
(D) N
Hunsdiecker reaction
O
M IS
S I
D
233. Benzene diazonium chloride on treatment with H3PO2 in the presence of cuprous ions
gives
M
A
(A)
(B)
(C)
Phenol
Aniline
O
BenzeneN
A
D
(D) Chlorobenzene
M
M M and N. The element N forms ccp and M atom
O
234. A compound is formed by two elements
C The formula of the compound is
occupies 1/3 of the tetrahedral voids.
A T
(A) M N 3
S
(B) M N
(C) M N
2
2
C
2
3
U
(A) 019
2
(B)
S T
E
T
(C) N
O
(D) SI
IS
M
A
D
M
231. When p-nitrobenzenesulphonic acid and picric acid are treated with NaHCO , the gases
N 3
O respectively are
released
M
M
O
(A) SO , NO
E
2 2
CO (B) NO , NO
C T
2
(C) NO , H
A T (D) CO , CO 2 2
S
2 2
CU 232.
AT N
The following reaction is known as
19
S IO 2 0
(A)
(B)
(C)
U
C IS S
Finkelstein reaction
Swarts reaction
Darzen reaction T E ST
(D) N
Hunsdiecker reaction
O
M IS
S I
D
233. Benzene diazonium chloride on treatment with H3PO2 in the presence of cuprous ions
gives
M
A
(A)
(B)
(C)
Phenol
Aniline
O
BenzeneN
A
D
(D) Chlorobenzene
M
M M and N. The element N forms ccp and M atom
O
234. A compound is formed by two elements
C The formula of the compound is
occupies 1/3 of the tetrahedral voids.
A T
(A) M N 3
S
(B) M N
(C) M N
2
2
C
2
3
U
Page 75
(D) MN
0 19
235. An element with molar mass 2.7×10 kg 2 mol forms a cubic unit cell with edge length
-2 -1
407pm. If the density is 2.7×10 kgTm , the nature of the cubic unit cell is
S
-3 -3
E
(A) fcc T
(B) ccp N
O
(C) simple cubic I
S
(D) bcc
IS
M
D
M
A the cation has left a lattice site and is located at an interstitial position.
236. In a solid lattice,
N
The lattice defect is
O
M
O
(A) n-type
M
CO (C) Schottky defect
E
(B) p-type
SA
C T
T (D) Frenkel defect
CU 237.
AT N
The resistance of a conductivity cell containing 0.001 M KCl solution at 298 K is
19
1500 Ω. What is the cell constant if the conductivity of 0.001 M KCl solution at 298 K is
S IO
0.146 × 10-3 Scm-1.
2 0
U S T
(A) 0.119 cm-1
(B) 0.169 cm-1 S
(C)
(D)
C IS
0.129 cm-1
0.159 cm-1
O
N
T E
238.
M S I
An iron wire is immersed in a solution containing ZnSO 4 and NiSO4. When the
IS
D
concentration of each salt is 1 M, predict which of the following reaction is likely to
proceed.
M
A A
D
Given E0 (Zn+2/Zn) = -0.76 V
N
E0 (Fe+2/Fe) = -0.44 V and
O
M
E0 (Ni+2/Ni) = -0.25 V
M
O
+2
(A) Iron reduces Zn ions
+2
(B) Zn reduces Iron ions
C
(D) Ni reduces Iron ionsT
+2
(C) Iron reduces Ni ions
SA
+2
CU
0 19
235. An element with molar mass 2.7×10 kg 2 mol forms a cubic unit cell with edge length
-2 -1
407pm. If the density is 2.7×10 kgTm , the nature of the cubic unit cell is
S
-3 -3
E
(A) fcc T
(B) ccp N
O
(C) simple cubic I
S
(D) bcc
IS
M
D
M
A the cation has left a lattice site and is located at an interstitial position.
236. In a solid lattice,
N
The lattice defect is
O
M
O
(A) n-type
M
CO (C) Schottky defect
E
(B) p-type
SA
C T
T (D) Frenkel defect
CU 237.
AT N
The resistance of a conductivity cell containing 0.001 M KCl solution at 298 K is
19
1500 Ω. What is the cell constant if the conductivity of 0.001 M KCl solution at 298 K is
S IO
0.146 × 10-3 Scm-1.
2 0
U S T
(A) 0.119 cm-1
(B) 0.169 cm-1 S
(C)
(D)
C IS
0.129 cm-1
0.159 cm-1
O
N
T E
238.
M S I
An iron wire is immersed in a solution containing ZnSO 4 and NiSO4. When the
IS
D
concentration of each salt is 1 M, predict which of the following reaction is likely to
proceed.
M
A A
D
Given E0 (Zn+2/Zn) = -0.76 V
N
E0 (Fe+2/Fe) = -0.44 V and
O
M
E0 (Ni+2/Ni) = -0.25 V
M
O
+2
(A) Iron reduces Zn ions
+2
(B) Zn reduces Iron ions
C
(D) Ni reduces Iron ionsT
+2
(C) Iron reduces Ni ions
SA
+2
CU
Page 76
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 77
239. The amount of silver (At mass 108) deposited from a solution of silver nitrate when a
current of 965 coulombs was passed is,
019
(A) 10.8 g 2
(B) 1.08 g
S T
E
(C) 0.108 g
(D) 1.08 × 103 g T
N
O
S I
IS statements are not correct regarding rate of catalyst in a chemical
240. Which of the following
M
M
reaction?
D
i. Changes Athe ΔH of the reaction
N
O the activation energy for the forward and backward reaction equally
ii. Decrease
M
M
O
iii. Provides a new path of higher activation energy
SA
O
T (A) (i) and (ii)
C iv. Increases the average kinetic energy of reacting molecules
CU
T
(B) (i) and (iii)
N
(C) (i) and (iv)
A 9
(D) (ii) and (iii)
1
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
current of 965 coulombs was passed is,
019
(A) 10.8 g 2
(B) 1.08 g
S T
E
(C) 0.108 g
(D) 1.08 × 103 g T
N
O
S I
IS statements are not correct regarding rate of catalyst in a chemical
240. Which of the following
M
M
reaction?
D
i. Changes Athe ΔH of the reaction
N
O the activation energy for the forward and backward reaction equally
ii. Decrease
M
M
O
iii. Provides a new path of higher activation energy
SA
O
T (A) (i) and (ii)
C iv. Increases the average kinetic energy of reacting molecules
CU
T
(B) (i) and (iii)
N
(C) (i) and (iv)
A 9
(D) (ii) and (iii)
1
S IO 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 78
241. Which of the following curve is in accordance with Freundlich adsorption isotherm?
019
2
(A)
S T
E
T
log P
N
O
O 20SI
IS
M
M
(B)
D
A
N
O log P
M
SAT
M
CO (C) O
CU
AT N 19
S IO
(D)
2 0
242.
U
C IS S T E ST
Freshly prepared precipitate sometimes gets converted to colloidal solution by
N
O
M
(A) coagulation
(B) diffusion
S I
IS
D
(C) electrolysis
(D) peptisation
M
243.
A A
D
Ammonia and oxygen react at high temperature as;
O
N
4NH3 (g) + 5O2 (g) 4NO(g) + 6H2O(g)
M
In an experiment rate of formation of NO is 3 x 10-3 mol L-1 s-1. Calculate rate of
M
disappearance of ammonia.
C O
(A)
(B)
AT
3.6 x 10-3 mol L-1 s-1
3.6 x 10-6 mol L-1 s-1
(C) S
0.36 mol L-1 s-1
(D)
CU
7.2 x 103 mol L-1 s-1
019
2
(A)
S T
E
T
log P
N
O
O 20SI
IS
M
M
(B)
D
A
N
O log P
M
SAT
M
CO (C) O
CU
AT N 19
S IO
(D)
2 0
242.
U
C IS S T E ST
Freshly prepared precipitate sometimes gets converted to colloidal solution by
N
O
M
(A) coagulation
(B) diffusion
S I
IS
D
(C) electrolysis
(D) peptisation
M
243.
A A
D
Ammonia and oxygen react at high temperature as;
O
N
4NH3 (g) + 5O2 (g) 4NO(g) + 6H2O(g)
M
In an experiment rate of formation of NO is 3 x 10-3 mol L-1 s-1. Calculate rate of
M
disappearance of ammonia.
C O
(A)
(B)
AT
3.6 x 10-3 mol L-1 s-1
3.6 x 10-6 mol L-1 s-1
(C) S
0.36 mol L-1 s-1
(D)
CU
7.2 x 103 mol L-1 s-1
Page 79
244. 019
The average energy per molecule of a gas at a given temperature, T is
2
(A)
3
RT S T
E
2
3 RT T
(B)
√ M O
N
SI
( N )MT IS
R
(C)
√ 3
3 A
πMD
A
M
(D) N kT
O2
M
S
245.
AT
M
COThe
Cl (g) + 3F (g)
2 2 O E
exothermic formation of ClF is represented by the reaction
C T
3
2ClF (g) ΔH = -329 kJ
3
Which of the following will increase the quantity of ClF3 in an equilibrium mixture of
CU
(A)
AT
Cl2, F2 and ClF3?
N
Increasing temperature
19
S IO 0
(B) Removing Cl2
(C) 2
Increasing volume of the container
U S T
(D) Adding F2
S
246.
C IS T E
Which of the following options will be correct for the stage of half completion of the
reaction A B?
O
N
(A)
M
ΔG° = 0
IS
S I
D
(B) ΔG° ˂ 0
(C) ΔG° ˃ 0
M
A
(D) ΔG° = -RTln2
D
A
247. N
A system gives out 30J of heat and does 75J of work. What is the internal energy change?
O
(A) +105J
M
(B) –105J
M
(C)
(D)
+45J
– 45J
C O
AT
S
CU
The average energy per molecule of a gas at a given temperature, T is
2
(A)
3
RT S T
E
2
3 RT T
(B)
√ M O
N
SI
( N )MT IS
R
(C)
√ 3
3 A
πMD
A
M
(D) N kT
O2
M
S
245.
AT
M
COThe
Cl (g) + 3F (g)
2 2 O E
exothermic formation of ClF is represented by the reaction
C T
3
2ClF (g) ΔH = -329 kJ
3
Which of the following will increase the quantity of ClF3 in an equilibrium mixture of
CU
(A)
AT
Cl2, F2 and ClF3?
N
Increasing temperature
19
S IO 0
(B) Removing Cl2
(C) 2
Increasing volume of the container
U S T
(D) Adding F2
S
246.
C IS T E
Which of the following options will be correct for the stage of half completion of the
reaction A B?
O
N
(A)
M
ΔG° = 0
IS
S I
D
(B) ΔG° ˂ 0
(C) ΔG° ˃ 0
M
A
(D) ΔG° = -RTln2
D
A
247. N
A system gives out 30J of heat and does 75J of work. What is the internal energy change?
O
(A) +105J
M
(B) –105J
M
(C)
(D)
+45J
– 45J
C O
AT
S
CU
Page 80
248. For the reaction at 298K 2A + B C
019
ΔH = 40 kJmol-1 and ΔS = 0.02 kJmol-1 . At what temperature will the reaction becomes
2
spontaneous considering ΔH and ΔS to be constant over the temperature range,
S T
E
(A) 20K
(B) 200°C T
(C) 2000K N
O
(D) 2000° C
SI
IS
M
249. D
M
Equilibrium constructs K1 and K2 for the following equilibria
A
N and are related as
O
M K = 1/K
O
(A)
M 2 1
CO (C) K = 1/K
E
2
(B) K = K
2 1
C T
2
2 1
AT (D) K2 = K1/2
S
CU 250.
AT N
The pH of a solution increase from 1 to 2. The concentration of H+ ion
19
S IO 0
(A) decreases
(B) increases
2
U S
(C) remains the same
(D) becomes zero
ST
C IS O
N
T E
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
019
ΔH = 40 kJmol-1 and ΔS = 0.02 kJmol-1 . At what temperature will the reaction becomes
2
spontaneous considering ΔH and ΔS to be constant over the temperature range,
S T
E
(A) 20K
(B) 200°C T
(C) 2000K N
O
(D) 2000° C
SI
IS
M
249. D
M
Equilibrium constructs K1 and K2 for the following equilibria
A
N and are related as
O
M K = 1/K
O
(A)
M 2 1
CO (C) K = 1/K
E
2
(B) K = K
2 1
C T
2
2 1
AT (D) K2 = K1/2
S
CU 250.
AT N
The pH of a solution increase from 1 to 2. The concentration of H+ ion
19
S IO 0
(A) decreases
(B) increases
2
U S
(C) remains the same
(D) becomes zero
ST
C IS O
N
T E
M IS
S I
D M
A O
N
A
D
M
M
C O
AT
S
CU
Page 81
B.TECH 9– ANSWER KEY (Page 1)
1
20 TEST CODE: 101
QN. NO. KEY QN. NO. KEY QN. NO. KEYT QN. NO. KEY QN. NO. KEY QN. NO.
E S
1 C 26 D 51 TC 76 B 101 B 126
2 B 27 D 52 N
O A 77 D 102 D 127
3 C 28 C 53 S I D 78 A 103 A 128
IS
4 A 29 B 54M D 79 C 104 A 129
5 D 30 B A
D55
M B 80 A 105 B 130
6 A 31 C N
7 A 32 C M
O 56 57
B
D
81
82
A
D
106
107
B
A
131
132
8
9
10
B
A
D
33
34
35
T
SA B
DOM
CD O
C TE
58
59
60
D
C
A
83
84
85
D
D
C
108
109
110
B
D
C
133
134
135
11
12
C
D
36 C
37
U A
A
AT 61
62
N
B
C
86
87
1
D
9
D
111
112
D
B
136
137
13 A 38 B
S I O
63 C 88
2 0 D 113 C 138
U S
14 A 39 A 64 A 89 B 114 C 139
15 D 40 A 65 B ST90 C 115 C 140
16
17
C
B
41
42
C
AC IS 66
67
O
B
N
C
T E 91
92
B
A
116
117
B
C
141
142
18 D 43 A
M 68
IS
S I D 93 C 118 D 143
D
19 D 44 A 69 A 94 A 119 D 144
20 B 45 A 70 M B 95 A 120 A 145
21
22
23
D
D
C
46
47
48
D
A
B
A 71
72
O
73
N
A
D C
D
A
96
97
98
B
A
D
121
122
123
D
B
A
146
147
148
M
24 D 49 B 74 A
M 99 C 124 A 149
CO
25 B 50 B 75 C 100 A 125 B 150
AT
S
CU
1
20 TEST CODE: 101
QN. NO. KEY QN. NO. KEY QN. NO. KEYT QN. NO. KEY QN. NO. KEY QN. NO.
E S
1 C 26 D 51 TC 76 B 101 B 126
2 B 27 D 52 N
O A 77 D 102 D 127
3 C 28 C 53 S I D 78 A 103 A 128
IS
4 A 29 B 54M D 79 C 104 A 129
5 D 30 B A
D55
M B 80 A 105 B 130
6 A 31 C N
7 A 32 C M
O 56 57
B
D
81
82
A
D
106
107
B
A
131
132
8
9
10
B
A
D
33
34
35
T
SA B
DOM
CD O
C TE
58
59
60
D
C
A
83
84
85
D
D
C
108
109
110
B
D
C
133
134
135
11
12
C
D
36 C
37
U A
A
AT 61
62
N
B
C
86
87
1
D
9
D
111
112
D
B
136
137
13 A 38 B
S I O
63 C 88
2 0 D 113 C 138
U S
14 A 39 A 64 A 89 B 114 C 139
15 D 40 A 65 B ST90 C 115 C 140
16
17
C
B
41
42
C
AC IS 66
67
O
B
N
C
T E 91
92
B
A
116
117
B
C
141
142
18 D 43 A
M 68
IS
S I D 93 C 118 D 143
D
19 D 44 A 69 A 94 A 119 D 144
20 B 45 A 70 M B 95 A 120 A 145
21
22
23
D
D
C
46
47
48
D
A
B
A 71
72
O
73
N
A
D C
D
A
96
97
98
B
A
D
121
122
123
D
B
A
146
147
148
M
24 D 49 B 74 A
M 99 C 124 A 149
CO
25 B 50 B 75 C 100 A 125 B 150
AT
S
CU
Page 82
B.TECH SHIFT I9- KEY (Page 2)
1
20
TEST CODE: 101
KEY QN. NO. KEY QN. NO. KEY
ST
QN. NO.
E
KEY QN. NO. KEY
B 151 B 176 D T201 A 226 A
D 152 D 177 D N
O 202 A 227 D
B 153 A 178 B S I 203 C 228 D
IS
D 154 B 179 AM 204 A 229 D
B 155 C 180 AD
D
M 205 B 230 D
D 156 B 181 N B 206 D 231 D
A 157 B 182 M
O B 207 D 232 B
C
C
B
158
159
160
C
B
B SA
183
C O
T 184
185
M B
C
C
O
C TE
208
209
210
B
D
D
233
234
235
C
C
B
B
B
161
162
A CU
D
186
187
B
A
DT N
211
212
B
A
236
9
237
1
D
C
D 163 B 188
S I
C
O 213 B
2 0238 C
U S
A 164 C 189 B 214 D 239 B
D 165 D 190 B 215 D ST 240 B
D
A
166
167
D
C
191
192 C IS D
C
216
217
O
N
TB
C
E 241
242
C
D
D 168 D 193
M D 218
IS
S I B 243 A
D
A 169 A 194 B 219 A 244 D
B 170 D 195 B M
220 D 245 D
A
C
C
171
172
173
B
C
C
196
197
198
A A
B
B O
N
A
D
221
222
223
A
A
B
246
247
248
A
B
C
M
B 174 B 199 A 224
M C 249 C
CO
A 175 A 200 D 225 A 250 A
AT
S
CU
1
20
TEST CODE: 101
KEY QN. NO. KEY QN. NO. KEY
ST
QN. NO.
E
KEY QN. NO. KEY
B 151 B 176 D T201 A 226 A
D 152 D 177 D N
O 202 A 227 D
B 153 A 178 B S I 203 C 228 D
IS
D 154 B 179 AM 204 A 229 D
B 155 C 180 AD
D
M 205 B 230 D
D 156 B 181 N B 206 D 231 D
A 157 B 182 M
O B 207 D 232 B
C
C
B
158
159
160
C
B
B SA
183
C O
T 184
185
M B
C
C
O
C TE
208
209
210
B
D
D
233
234
235
C
C
B
B
B
161
162
A CU
D
186
187
B
A
DT N
211
212
B
A
236
9
237
1
D
C
D 163 B 188
S I
C
O 213 B
2 0238 C
U S
A 164 C 189 B 214 D 239 B
D 165 D 190 B 215 D ST 240 B
D
A
166
167
D
C
191
192 C IS D
C
216
217
O
N
TB
C
E 241
242
C
D
D 168 D 193
M D 218
IS
S I B 243 A
D
A 169 A 194 B 219 A 244 D
B 170 D 195 B M
220 D 245 D
A
C
C
171
172
173
B
C
C
196
197
198
A A
B
B O
N
A
D
221
222
223
A
A
B
246
247
248
A
B
C
M
B 174 B 199 A 224
M C 249 C
CO
A 175 A 200 D 225 A 250 A
AT
S
CU
Page 83
019
2
S T
TE
O
N
SI
IS
M
A
D
M
N
O
M
SA
T
CO
M
O
C TE
CU
AT N 19
S I O 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
CO
AT
S
CU
2
S T
TE
O
N
SI
IS
M
A
D
M
N
O
M
SA
T
CO
M
O
C TE
CU
AT N 19
S I O 2 0
U
C IS S T E ST
N
O
M IS
S I
D M
A O
N
A
D
M
M
CO
AT
S
CU
Document Details
| Board / Org | Cochin University |
| Exam | CUSAT CAT |
| Type | Question Paper |
| Pages | 83 |
| Updated | 30 Apr 2026 |