TG EAPCET 2027 Sample Paper Engineering

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

TG EAPCET (Engineering) 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

160 160 180 Min +1 / 0

GENERAL INSTRUCTIONS

1. This paper contains 160 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 1 mark; there is no negative marking.

4. Total time allowed is 180 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

TG EAPCET (Engineering) 2027
SAMPLE QUESTION PAPER

Questions 160 Max Marks 160 Time 180 Min Marking +1 / 0

Attempt all questions. Choose the one correct option for each.

MATHEMATICS

1. 2.

If f: R --------> R is defined as f(x+y)=f(x)+f(y) for all x, y If each element, of a determinant of third order with
in R and f(1)=5, then find the value of the following: value A. is multiplied by 3, then the value of newly
formed determinant is
(A)
(A)
5n(n+1)/2
3A
(B)
(B)
7n(n-1)/2
9A
(C)
(C)
5n(n-1)/2
27A
(D)
(D)
7n(n+1)/2
-27A

3. 4. If the line joining the points A(α) and B(ß) on the
ellipse x225+y29=1 is a focal chord, then one possible
The circle x2 + y2 + 4x —4y +4 =0 touches .................
value of (α)/(2) · (β)/(2) is

(A) (A) -3

(B) 3
x-axis only
(C) -9
(B)
(D) 9

y-axis only

(C)

x-axis and y-axis

(D)

x=y

5. If a. b. c are distinct real numbers and P, Q. R are 6. ∫ x d t√et-1=(π)/(6) ⇒ x=
2
three points whose position vectors are respectively a i +
(A) 4
b j + c k , b i + c j + a k and c i + a j + b k , then ∠ Q P R =
(B) ln4
(A) ^ - 1 ( a + b + c )
(C) 8
(B) ( π )/( 2 )
(D) ln8
(C) ( π )/( 3 )

(D) ^ - 1 ( a ^ 2 + b ^ 2 + c ^ 2 a b c )

7. Let A be the centre of the circle x ^ 2 + y ^ 2 - 2 x - 4 y 8.
- 20 = 0 . If the tangents at the points B (1, 7) and D (4, -
If y = cos(x°), z = cos x then dy/dx =
2) on the given circle meet at the point C. then the area
of the quadrilateral ABCD is
(A)
(A) 60
-π/180 sin(x°) cosec x
(B) 65

(C) 70 (B)
(D) 75
sin(x°) cosec x

(C)

π/180 sin(x°) cosec x

(D)

π/180 cos(x°) cos x

9. The equations of two altitudes of an equilateral 10. If 3(x-1)(x2+x+1)=(1)/(x-1)-x+2x2+x+1=f (x)-f (x)
1 2
triangle are √( 3 ) x - y + 8 - 4 √( 3 ) = 0 and √( 3 ) x + y - and x+1(x-1)2(x2+x+1)=A f (x)+(B+(D)/(x-1)) f (x)+C(x-
1 2
12 - 4 √( 3 ) = 0 . The equation of the third altitude is 1)2 then A + B + C + D =

(A) √( 3 ) x + y = 4 (A) 1

(B) y = 10 (B) (-⅓)

(C) x = 10 (C) 0

(D) x - √( 3 y ) = 4 (D) 1/3

11. 12.

If the point (a, 2a) is an interior point of the region The equation of the circle which touches the x-axis and y-
bounded by the parabola y2 = 16x and the double axis at the points (1,0) and (0,1) respectively is...............
ordinate through focus, then
(A)
(A)
x2+y2-4y+3=0
a<4
(B)
(B)
x2+y2-2y+2=0
0<a<4

(C)
(C)
x2+y2-2x-2y+2=0
0<a<2

(D)
(D)

x2+y2-2x-2y+1=0
a>4

13. If x ^ 2 - 3 a x + 14 = 0 and x ^ 2 + 2 a x - 16 = 0 14. In A B C (1)/(r2)+(1)/(r 2)+(1)/(r 2)+(1)/(r 2)=
1 2 1
have a common root then a ^ 4 + a ^ 2 =
(A) (a+b+c)/(Δ)
(A) 2 (B) (a2+b2+c2)/(Δ2)
(B) 90 (C) (1)/(2 R r)
(C) 6 (D) R
(D) 20

15. 16. If 4cos3θ then y=3 2 θ, then d2 yd x2 at θ= π/4 is

The length of the chord intercepted by the circle x2 + y2 - (A) 1/3

8x — 2y — 8 = 0 on the line x + y + 1=0 is units. (B) 1/6

(C) -1/6
(A)
(D) -1/3
14

(B)

7

(C)

2√7

(D)

√7

17. 18. A(2, 3, 5). B(α,3.3) and C(7, 5,β) are the vertices of a
triangle. If the median through A is equally inclined with
In an examination, a student has to write exams in 8
the co- ordinate axes then -1((α)/(β))=
different subjects. He is declared fail if he fails in at least
one subject. The number of ways in which he can fail is (A) -1((-1)/(9))

(B) (π)/(2)
(A)
(C) (π)/(3)

127 (D) -1((2)/(5))

(B)

256

(C)

255

(D)

7

19. Let φ(x)=x(x2+1)(x+1) . If a , b and c are the roots of 20. ∫ d x ( 2 a x + x ^ 2 ) ^ ( 3 )/( 2 ) =
the equations x3-3 x+λ =0 (λ ≠ 0) then φ( a) φ( b) φ( c)=
(A) - 1 a ^ 2 ( x + a ) √ 2 a x + x ^ 2 + c
(A) λ (B) - ( x + a ) √ 2 a x + x ^ 2 + c
(B) -λ(λ+2)(λ2+16) (C) 1 2 a ^ 2 ( x + a ) √ 2 a x + x ^ 2 + c
(C) (λ)/((λ+2)) (D) ( - 1 )/( a ) ( x + a ) √ 2 a x + x ^ 2 + c
(D) λ(λ+2)(λ2+16)

21. In Δ A B C , if ( A )/( 2 ) : ( B )/( 2 ) : ( C )/( 2 ) = 4 : 3 : 22.
2 , then a : b : c =
The larger of cos(log θ ) and log(cos θ ) if e-π/2< θ <
(A) 2 : 3: 4 π /2is
(B) 6 : 5 : 7
(A)
(C) 4 : 5 : 6

(D) 5 : 6 : 7 cos(log θ )

(B)

log (cosθ)

(C)

None of function is larger

(D)

One of the two function is undefined on domain even to
compare

23. A straight line meets the X and Y axes at the points 24.
A. B respectively. If AB = 6 units. then the locus of the
A person standing at the junction (crossing) of 2 straight
point P which divides the line segment AB such that AP :
paths represented by the equations 2x -3y +4 =0 and 3x
PB = 2:1 is
+ 4y —5 = 0, wants to reach the path whose equation is
(A) 3x2+ y2 = 36 6x —7y + 8 = 0 in the least time, then the equation of the
(B) 4x2 + y2 = 36 path he should follow is...............

(C) 3x2 + y2 = 16
(A)
(D) 4x2 + y2 = 16
119x - 102y — 125=0

(B)

119x + 102y — 125=0

(C)

102x + 119y —125=0

(D)

102x + 119y +125 =0

25. 26. probability that a mechanic making an error while
using a machine on the n ^ th day is given by P ( E _ n ) =
Suppose a circle passes through (2,2) and (9,9) and
1 2 ^ n . If he has operated the machine for 4 days. The
touches the x-axis at P. If 0 is the origin. then OP is equal
probability that he had not made a mistake on 3 out of 4
to .........
days is

(A) (A) 1/2

(B) 1/4
4
(C) 243/512
(B)
(D) 343/1024

5

(C)

6

(D)

9

27. 28. If the equation of the plane passing through the
point (2, - 1. 3) and perpendicular to the planes 3 x - 2 y
The equation of a line though the point (1,2) whose
+ z = 9 and x + y + z = 9 is x + b y + c z + d = 0 then d =
distance from the point (3,1) has the greatest value is
(A) 11/3

(A) (B) 0

y=2x (C) 3

(D) ⅓
(B)

y=x+1

(C)

x+2y=5

(D)

y=3x-1

29. 30.

Given P(A)=0.5, P(B)=0.4, P(A∩ B)=0.3, then P(A'/B') What is the range the function h(x)=x-2/x+3 ?

is equal to
(A)

(A) (-∞, 2) (2, ∞)

1/3
(B)

(B) (-∞, 1) (1, ∞)

1/2
(C)

(C) (-∞,-3) (-3, ∞)

2/3
(D)

(D) (-∞,-1) (-1, ∞)

3/4

31. If z=x + iy , x, y ∈ R and if the point P in the Argand 32. If x is so small, that x5 and higher power of x may be
plane represents 2, then the locus of P satisfying the neglected. then the coefficient of x4 in the expansion of
condition Arg ((z-1)/(z-3 i))=(π)/(2) is √x2+4-√x2+9 is

(A) \z C /|z-(1+3 i)/(2)|=√(10)2\ (A) 19/1728

(B) \z C /(3-i) z+(3+i) z-6=0\ (B) -19/1728

(C) \z C /(3-i) z+(3+i) z-6>0,|z-(1+3 i)/(2)|=√(10)2\ (C) 43/1728

(D) \z C /(3-i) z+(3+i) z-60,|z-(1+3 i)/(2)|=√(10)2\ (D) -43/1728

33. 34.

The distance between the lines 3x +4y =9 and 6x +8y = Which among the following represents the combined
15 is equation of a pair of lines through point (1,0) and parallel
to the lines represented by 2x2 — xy — y2 = 0.
(A)
(A)
3/2
2x2 - xy - 2y2+ 4x - y =6
(B)
(B)
3/10
2x2 — xy —y2—4x —y +2 =0
(C)
(C)
6
2x2 —xy—y2—4x+y+2=0
(D)
(D)
3/5
2x2 —xy—y2—4x - y - 2=0

35. If a function f(x) defined by f ( x ) = \ array l l a x + b 36.
, & x ≤ - 1 \ 2 x ^ 2 + 2 b x - ( a )/( 2 ) , & - 1 x 1 \ 7 , & x ≥
If α, β, γ are the roots of the equation x3+3 x2-7 x+5=0 ,
1 array . is continuous on R then (a , b) =
then the value of (1)/(α)+(1)/(β)+(1)/(γ) is
(A) (-22 , -3)

(B) (22 , 3) (A)

(C) (11 , -6) -7/5
(D) (-22 , -6)
(B)

7/5

(C)

-3/5

(D)

3/5

37. The number of non trivial even divisors of the number 38. A new tetrahedron is formed by joining the centroids
2160 is of the faces of a given tetrahedron OABC. Then the ratio
of the volume of the new tetrahedron to that of the given
(A) 40
tetrahedron is
(B) 39
(A) 3/25
(C) 38
(B) 1/27
(D) 18
(C) 5/62

(D) 1/162

39. 40. If cos A = -(60/61) and tan B = -(7/24) and neither A
nor B is in the second quadrant, then the angle A + (B/2)
Choose the correct option regarding the following
lies in the quadrant
statements:
(A) 1
Statement-1 : The length of common chord of the circles
(B) 2
x2+ y2 + ax + by +c = 0 and x2 + y2+ bx + ay + c =0
(C) 3

(D) 4
equals

Statement-2 : If two circles intersect at two distinct
points. then their radical axis is their common chord.

(A)

Both statements are true and Statement-2 is a correct
explanation for Statement-1

(B)

Both statements are true but Statement-2 is not a correct
explanation for Statement-1.

(C)

Statement-1 is true, Statement-2 is false.

(D)

Statement-1 is false, Statement-2 is true.

41. 42.

If y= 5x2 + 6x +6, x = 2 and Δx = 0.001. then the values If the lines x + 2y —5 = O and 3x — y — 1 = 0 denote two

of Δy and dy respectively are: diameters of a circle of radius 5 units. then the equation
of the circle is
(A)
(A)
0.026 & 0.026005
x2+y2-2x+4y-20=0
(B)
(B)
0.026005 & 0.026
x2+y2-2x-4y-20=0
(C)
(C)
0.026005 & 0.26
x2+y2+2x-4y+20=0
(D)
(D)
0.0026 & 0.026
x2+y2+2x+4y+20=0

43. 44.

If the point ( λ ,1+ λ ) lies inside the circle x2 + y2 = 1, The value of Σ 4 (19-r) C + 15 C is equal to
r=0 3 4
then
(A)
(A)
21C
4
λ>0
(B)
(B)
19C
4
λ<0
(C)
(C)
20C
4
-1 < λ < 0
(D)

(D) 16C
4

0<λ<1

45. 46.

In ΔABC, ifa: b:c=4: 5: 6 then the ratio between the If (6,—k) and (3, 2) are conjugate points with respect to
circumradius and the inradius is.............................. circle x2 + y2 + 6x + 4y + 12 = 0. then ‘k’ equals

(A) (A)

16/7 -7/4

(B) (B)

16/9 7/4

(C) (C)

7/16 4/7

(D) (D)

11/7 -4/7

47. 48.

The angle between any two diagonals of a cube is Let A and B be events with P(A) =1/3, P(B)=1/4 and
P(AUB) =1/2, then which of the following statement is
(A) incorrect?

Cos-1 (1/3)
(A)

(B) A and B are independent

Cos-1 (1/√3) (B)

(C) P(A/B) = 1/3

Cos-1 (1/2) (C)

(D) P(AC∩ B) = 1/3

Cos-1 (2/3)
(D)

P(A∩ BC) = 1/4

49. 50. Let [x] denote the greatest integer less than or equal
to x. Then the number of points where the function y =
The position vectors of A and B are (i+j+k) and ((1)/(3)
[x] +|1-x|, is not differentiable. is
j+(1)/(3) k) . If ' B ' divides the line A C in the ratio 2: 1,
then position vector of ' C ' is (A) 1

(B) 2
(A)
(C) 3

(1/2, 0, 0) (D) 4

(B)

(0, 1/3, 0)

(C)

(-1/2, -1/2, 0)

(D)

(-1/2, 0, 0)

51. 52.

The condition that x3 - px2 + qx - 7 = 0 may have two of The solution of the equation 2x3 — x2 — 22x — 24 = 0
its roots equal to each other but of opposite sign is when two of the roots are in the ration 3 : 4 is

(A) (A)

r=pq 3, 4, 1/2

(B) (B)

r=2p3+pq -3/2, -2, 4

(C) (C)

r=p2q -1/2, 3/2, 2

(D) (D)

r=p2q2 -3/2, 2, 5/2

53. Let f (x) be continuous on [0, 4]. differentiable on (0. 54. If y = 2 x is a tangent to the curve y ^ 2 = a x ^ 3 + b
4). f(0) = 4 and f (4) = -2 , then the value of g’( c ) for at ( 1,2 ) , then ( a , b ) =
some Lagrange's constant c ( 0,4 ) is
(A) (8 , 4)
(A) ½ (B) ( ( 2 )/( 3 ) , 1 )
(B) 5/12 (C) ( ( 8 )/( 3 ) , ( 4 )/( 3 ) )
(C) - 5/12 (D) ( ( 8 )/( 3 ) , ( 2 )/( 3 ) )
(D) -7/12

55. For k > 0 Σ ∞ kxx ! (n !)/((n-x) !)(1-(k)/(n)) 56. If the probability of a bad reaction from a vaccination
x=0 n arrow ∞
n-x((1)/(n))x= is 0.01. then the probability that exactly two out of 300
people will get bad reaction is
(A) 0

(B) k (A) 7 2 e ^ 3

(C) x (B) 9 2 e ^ 3

(D) 1 (C) 7 e ^ 3

(D) 9 e ^ 3

57. Let m be a vector of magnitude √3 and perpendicular 58.
to the vectors i+j and j-k be another vector of magnitude
The value of the determinant |arrayccc a+b & a+2 b &
2√6 and perpendicular to the vectors 2 i-j and j+2 k The
a+3 b \\ a+2 b & a+3 b & a+4 b \\ a+4 b & a+5 b & a+6 b
area (in sq. units) of the triangle formed with m and n as
array| is
sides is

(A) √2 (A)

(B) √6
a
(C) 2√3
(B)
(D) 3√2

b

(C)

0

(D)

a+b

59. 60.

The mean of the numbers a,b, 8,5,10 is 6 and the In a triangle ABC, suppose none on the angles are
variance is 6.80, then the possible values of a and b are multiples of π/2 then what is the value cot A cot B + cot
B cot C + cot A cot C =
(A)

(A)
a=2,b=3

∞
(B)

(B)
a=4,b=5

1
(C)

(C)
a=1,b=3

-1
(D)

(D)
a=3,b=4

0

61. If the angle between a pair of tangents from a point 62.
P to the circle x2 + y2 + 4x -6y + 9sin2α +13 cos2α = 0 is
If two curves x = y2, xy = a3 cut each other orthogonally
2α . Then the equation of the locus of P is
at a point, then a2 =
(A) x2 + y2 +4x -6y +4 = 0

(B) x2 + y2 +4x - 6y - 9 = 0 (A)

(C) x2 + y2 +4x + 6y - 4 = 0 1/3
(D) x2 + y2 +4x - 6y + 9 = 0
(B)

1/2

(C)

2

(D)

3

63. Let A (3, 2, - 4) and B (9. 8, -10) be two points. Let P 64.
_ 1 divide AB in the ratio 1 : 2 and P _ 2 divide AB in the
Let u, v and w are non coplanar vectors, then the value
ratio 2:1. If the point P ( α , β , γ ) divides P _ 1 P _ 2 in
of (u+2 v-w) ·[(u-v) ×(u-v-w)][arraylll u & v & w array] is
the ratio 1 : 1 then α + 2 β + 2 γ =
equal to
(A) 1

(B) 2 (A)

(C) 3 1
(D) 4
(B)

3

(C)

4

(D)

2

65. 66.

What is the value of Sin-1 (12)/(13)+Cos-1 (4)/(5)+Tan-1 The set of all points where the function f(x)=2x|x| is
(63)/(16)= differentiable is...................

(A) (A)

π (-∞, ∞)

(B) (B)

π/2
(-∞, 0) U (0, ∞)

(C)
(C)
π/6
(0, ∞)

(D)
(D)
3π/4
[0, ∞)

67. 68. Tangents are drawn to the ellipse x ^ 2 25 + y ^ 2 16
= 1 at all the four ends of its Iatusrecta. Then the area (in
sinπ/16sin3π/16sin5π/16sin7π/16 = square units) of the quadrilateral formed by these
tangents is
(A)
(A) 125/6
√2/16
(B) 250/3

(B) (C) 80/3

(D) 260/3
1/8

(C)

1/16

(D)

√2/32

69. 70.

If the lines 2x —y + 3 = 0 and 4x + ky +3 = 0 are Which of the following matrices is not a square-matrix?
conjugate with respect to the ellipse 5x2 + 6y2 — 15 = 0,
then ‘k’ equals (A)

[1]
(A)

1 (B)

[arrayll 2 & 2 \\ 2 & 2 array]
(B)

2 (C)

[arraylll3 & 3 & 3array]
(C)

3 (D)

[arraylll 1 & 1 & 1 \ 1 & 1 & 1 \ 1 & 1 & 1 array]
(D)

6

71. Let x ≠ 0 , | x | ( 1 )/( 2 ) and f ( x ) = 1 + 2 x + 4 x ^ 2 72.
+ 8 x ^ 3 + … . Then f ^ - 1 ( x ) =
∫ d x√7-6 x-x2=
(A) ( x - 1 )/( 2 x )

(B) ( x - 1 )/( 2 ) (A)

(C) ( x - 1 )/( x ) Sinh-1((x+3)/(4))+c
(D) 1 - 2x
(B)

|(x+3)/(4)|+c

(C)

Sin-1((x+3)/(4))+c

(D)

(1)/(2) Sin-1((x+3)/(4))+c

73. 74. In a Poisson distribution with unit mean, Σ ∞|x-x|
x=0
P(X=x)= ( x is the mean of the distribution )
The point on the curve x2 + y2 = a2, y ≥ 0, at which the
tangent is parallel to the x-axis, is (A) e

(B) 1/e
(A)
(C) 2/e

(a, 0) (D) 2/3e

(B)

(-a, 0)

(C)

(0, a)

(D)

(0, -a)

75. 76.

A straight rod of length 4 units slides such that its ends If f(x) = x5 — 5x4 +. 5x3 — 10 has its local maxima and
‘A’ and ‘B' always lie on the x and y axes respectively. minima at x = a and x = b respectively, then 2a + b =
Then the locus of the centroid of △OAB 1s
(A)
(A)
5
x2 + y2 =4
(B)
(B)
4
x2 + y2 =3
(C)
(C)
7
x2 + y2 =9/16
(D)
(D)
3
x2 + y2 =16/9

77. 78.

If the origin is the centroid of the triangle for which (—2 If S = x2 + y2 + 2x + 17y + 4=0, S' =x2 + y2 + 7x + 6y +
3, 4) and (3 ,-1, 5) are two vertices, then the third vertex 11 =0 and S" =x2 + y2—x+22y +3 =0 are three circles.
is ..................... then the length of tangent from their radical center to
S=0 is......... units
(A)
(A)
(1,2,9)
√ 53
(B)
(B)
(-1,-2,9)
√ 57
(C)
(C)
(1,-2,-9)
√ 15
(D)
(D)
(-1,-2,-9)
√ 17

79. In a battery manufacturing factory. machines P. Q 80.
and R manufacture 20%, 30%, and 50% respectively of
Let S be the set of all quadratic equations of the form x2
the total output. The chances that a defective battery is
+ bx + c = 0 where b,c € {1, 2,3,4,5, 6}. If an equation is
produced by these machines are 1%, 1.5% and 2%
selected at random from S, then the probability that the
respectively. If a battery is selected as random from
equation has real roots is ...................
production then the probability that it is defective is

(A) ( 69 )/( 2000 ) (A)

(B) ( 33 )/( 2000 )
9/12
(C) ( 1 )/( 40 )
(B)
(D) ( 29 )/( 2000 )

9/36

(C)

19/36

(D)

7/36

PHYSICS

81. 82.

A point source is located at a distance of 20 cm from the A copper rod is moved in a magnetic field. The charge
front surface of a symmetrical glass biconvex lens with developed across its ends will be proportional
equal radii of curvature 5 cm. The distance at which to............................
image formed from the rear surface of this lens is: [Given
refractive index of the glass is 1.5] (A)

Magnetic flux
(A)

20/3 cm (B)

Rate of change of magnetic flux
(B)

10/3 cm (C)

1/ velocity of the rod
(C)

5 cm (D)

1/ magnitude of the magnetic field
(D)

190 cm

83. 84. When an inductor L and a resistor R in series are
connected across a 12 V. 50 Hz supply. a current of 0.5 A
Thermopile Bolometer is used to detect
flows in the circuit. The current differs in the phase from
applied voltage by π/3 radian. Then the value of R is
(A)
(A) 10Ω
ultraviolet radiation
(B) 3Ω

(B) (C) 12Ω

X — rays (D) 15Ω

(C)

gamma radiation

(D)

infrared radiation

85. 86.

A particle of mass ‘m’ is under an influence of a force If ‘R’ is the radius of orbit of a satellite. then the kinetic
energy of the satellite is.....................
. The particle when disturbed will

oscillate ...................... (A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

87. 88. The ratio of heats generated through shunt and
galvanometer is 7:5 when they are connected to make an
The self-inductance of two coils of a transformer is 20 mH
ammeter. If the resistance of the galvanometer is 112 Ω
and 30 mH. What is the resistance between them?
then the resistance of the shunt is

(A) (A) 80 Ω

(B) 8 Ω
0
(C) 15.6 Ω
(B)
(D) 1.56 Ω

1.5Ω

(C)

600Ω

(D)

Infinite

89. 90.

The moment of inertia of a body about a certain axis is A toroid of n turns, mean radius R and cross-sectional
1.2 kg.m2. Initially, the body is at rest. In order to radius a carries current J. It is placed on a horizontal
produce rotational kinetic energy of 1800, an angular table taken as xy-plane. Its magnetic moment m
acceleration of 30 rad.s-2 must be applied about the
given axis for a duration of....................... seconds, (A)

is non—zero and pomts in the z-direction by symmetry
(A)

√10/3 (B)

points along the axis of the toroid (m = mΦ )
(B)

√30/3 (C)

is zero, otherwise there would be a field falling as 1/r3 at
(C)
large distances outside the toroid
√3/10
(D)
(D)
is pointing radially outwards

1/√ 3

91. 92.

The coil of a moving coil galvanometer has an effective Which of the following, in general is a slow process?
area of 4X 10-2m2 It is suspended in a magnetic field of
5x 10-2whm-2. If the deflection in the galvanometer coil (A)

is 0.2 rad when a current of 5SmA is passed through it,
Isothermal
then

(B)
(A)
Adiabatic
Torsional constant is 8 x 10-5Nmrad-1

(C)
(B)
Isobaric
Current sensitivity is 40 rad A-1

(D)
(C)
Isochoric
Torsional constant is 3 x 10-3Nmrad-1

(D)

Current sensitivity is 40 deg A-1

93. 94.

When a piece of a magnetic substance is put in a uniform

For the resultant of two vectors to maximum, magnetic field, the flux density inside it is four times the
flux density away from the piece. The magnetic
the angle between them should be
permeability of the material is

(A)
(A)
180°
1

(B)
(B)
0°
2

(C)
(C)
90°
3

(D)
(D)
60°
4

95. 96.

An object is moving with a constant speed along a A light bulb of power 100 W is placed at the centre of a
straight-line path. A force is not required to ........ hollow sphere of radius 10 cm. If the 66 % of the energy
is converted into light, then the pressure exerted by the
(A) light on the surface of the sphere will be: (Assume the
surface of sphere to be perfectly absorbing)
increase its speed

(A)
(B)

1.0x10-5 N/m2
decrease its momentum

(B)
(C)

1.5x10-7 N/m2
change its direction

(C)
(D)

1.75x10-6 N/m2
keep it moving with uniform velocity

(D)

7.5x10-5 N/m2

97. Match the following List-I with List-IT The correct 98.  If 1% and 2% are the errors in the measurement of
answer is mass and density of a cube respectively. then the error in
the measurement of length is
(A) A-III B-II C-I D-IV

(B) A-IV B-I C-III D-II (A) 1 %

(C) A-III B-I C-III D-II (B) 3 %

(D) A-III B-I C-IV D-II (C) 2 %

(D) 4 %

99. An Aluminium rod of length 1 m and a steel rod of 100.
length 2 m both having same cross sectional area, are
Ina given process, for an ideal gas, ΔW =O and ΔQ < 0.
soldered together end-to-end. The thermal conductivity
Then for the gas, ................
of aluminium rod and steel rod is 200 J s ^ - 1 m ^ - 1 K ^
- 1 and 50 J s ^ - 1 m ^ - 1 K ^ - 1 respectively. The
(A)
temperatures of the free ends are maintained at 300 K
and 500 K. What is the temperature of the junction? The temperature will decrease

(A) 322 K
(B)
(B) 350 K
The volume will increase
(C) 367 K

(D) 400 K (C)

The pressure will remain constant

(D)

The temperature will increase

101. 102.

In an amplitude modulation with modulation index 0.5, Hairs of shaving brush cling together when it is removed
the ratio of the amplitude of the carrier wave to that of from water due to.............................
the side band in the modulated wave is
(A)
(A)
Force of attraction between hairs
4:1
(B)
(B)
Surface tension
1:4
(C)
(C)
Viscosity of water
1:2
(D)
(D)
Characteristic property of hairs
2:1

103. 104. Which of the following statements is correct
regarding P - V graph?
Speed of a sound in air...............
(A) Slope of P-V graph in an isothermal process is -P/V

(A) (B) Slope of P-V graph in an adiabatic process is -P/V

is independent of temperature (C) Slope of P-V graph in an isochoric process is -γP/V

(D) Slope of P-V graph is an isobaric process is zero.
(B)

increases with pressure

(C)

increases with increase in humidity

(D)

decreases with increase in humidity

105. 106.

A wooden block of density 0.5 g/cc 1s tied to a string. The Let A = {1,2,3,4,5,6 } Number of functions ‘f” from A to A
other end of the string is fixed to the bottom of a tank. such that f(m) + f(n) =7 whenever m+n = 7 is
The tank is filled with a liquid of density 1 g/cc. If the
tension of the string is 20 N, then the mass of the blocks: (A)

(Take g = 10 m/s2)
525

(A)
(B)

1 kg
216

(B)
(C)

2 kg
200

(C)
(D)

3 kg
729

(D)

0.5 kg

107. A particle moves in a circle with speed v vawing 108.
with time as v (t) = 2t. The total acceleration of the
The flow rate of water from a tap of diameter 1.25 cm is 3
particle after it completes 2 rounds of cycle is
litres per minute. If coefficient of viscosity of water is 10-
(A) 16 π 3 Pa. s, the nature of flow is

(B) 2 √ 1 + 64 π ^ 2
(A)
(C) 2 √ 1 + 49 π ^ 2

(D) 14 π Unsteady

(B)

Turbulent

(C)

Streamlined

(D)

Laminar

109. 110. The magnetic induction at point 'O ' of the given
infinitely long current carrying wire shown in the figure
A body of mass 2 kg is acted upon by two forces each of
below is
magnitude 1.N, making an angle of 60° with each other,
The net acceleration of the body (in m.s-2) is: (A) μ _ o I 4 π R ( 1 - ( 3 π )/( 2 ) )

(B) μ _ 0 I 2 R ( 1 + π )
(A)
(C) μ _ o I 4 π R [ 1 + ( 3 π )/( 2 ) ]

0.5 (D) μ _ o I 4 π R

(B)

1.0

(C)

√3/2

(D)

√2/3

111. The focal length of a spherical mirror made of steel 112.
is 150 cm. If the temperature of the mirror increases by
Which one of the following is the property of a
200 K, its focal length becomes (coefficient of linear
monochromatic, plane electromagnetic wave in free
expansion of steel = 12 x 10-6 °C1)
space?
(A) 186.3 cm

(B) 153.6 cm (A)

(C) 150.036 cm Electric and magnetic fields have a phase difference of
(D) 150.36 cm π /2

(B)

The energy contributions of both electric and magnetic fields
are equal

(C)

The direction of propagation is in the direction of

(D)

The pressure exerted by the wave is the product of its speed
and energy density

113. A solid sphere of radius r _ 1 = 1 cm carries charge 114.
distributed uniformly over it with density ρ _ 1 = - 3 C /
When a vehicle of mass m is moving with a velocity v
cm ^ 3 . It is surrounded by a concentric spherical shell
over a concave over-bridge. of radius of curvature r, the
of radius r _ 2 = 2 cm carrying uniform charge density ρ _
thrust on the road at the lowest point on the bridge will
2 = ( 1 )/( 2 ) C / cm ^ 2 . If E _ d denotes the magnitude
be....................
of the electric field at distance d from the common centre
of the spheres, then
(A)
(A) E _ d = 1 3 ε _ 0 d ^ 2 , d ≤ 1 cm
mg+mv2/r
(B) E _ d = 1 ε _ o d ^ 2 , d ≤ 1 c m

(C) E _ d = d 3 ε _ 0 , d ≤ 1 cm (B)

(D) E _ d = d ε _ o , d ≤ 1 cm mg-mv2/r

(C)

m2v2g/r

(D)

v2g/r

115. 116.

A particle of mass m and charge q is thrown A coil wrapped around toroid has inner radius of 20 cm
perpendicular to an electric field of intensity E with an and an outer radius of 25 cm . If the wire wrapping makes
initial velocity v. The particle moves a distance x 800 turns and carries a current of 12A. The maximum and
perpendicular to the field and a distance y along the minimum values of the magnetic field with in the toroid
are _______
direction of the field. If y=ax2 then the is given by:

(A)
(A)
9.6mT, 7.68 mT
(q E)/(m)
(B)
(B)
4mT, 2.5 mT
q E v2m
(C)
(C)
7mT, 5.6 mT
2 q Em v2
(D)
(D)
6mT, 3.3 mT
q E2 m v2

117. 118. Choose the incorrect statement from the following

A magnetic field given by B(t) = (0.2 t - 0.05 t2) T is (A) Strong nuclear force is a short range force

directed perpendicular to the plane of a circular coil (B) Weak nuclear force is weakest among gravitational,
containing 25 turns of radius 1.8 cm and whose total electromagnetic. weak and strong nuclear forces
resistance is 5 Ω. The power dissipation at 3 seconds is (C) Electromagnetic force is a long range force
nearly
(D) Gravitational force acts on all objects

(A)

4μW

(B)

7μW

(C)

2.3μW

(D)

1.25μW

119. Under standard conditions the density of a gas is 120.
(1400)/(1089) kg m-3 and the speed of sound propagation
A particle slides down along an inclined plane AC. If the A
in it is 330 ms-1, then the number of degrees of freedom
plane is frictionless, kinetic energy of particle at 'C’ is
of the gas molecules is

(A) 2 (A)

(B) 7
mgy
(C) 5
(B)
(D) 3

mgx

(C)

mg ( y/ Sin θ )

(D)

mg ( y/ Cos θ )

CHEMISTRY

121. 122. Which one of the following is the correct order of
ionic radii?
Which of the following is not an electrophile?
(A) Pr3+ > Gd3+ > Tm3+
(A) (B) Pr3+ Gd3+ Tm3+

CN- (C) Pr3+ > Tm3+ > Gd3+

(D) Pr3+ Tm3+ Gd3+
(B)

BF3

(C)

NO+
2

(D)

AICI
3

123. 124.

The shortest wavelength in hydrogen spectrum is ‘X’ and ‘Y” are optically active isomers having formula C
5
approximately.......................................... H Cl . When treated with one mole of H , ‘X’ gets
9 2
converted to an optically inactive compound 'Z', but "Y”
(A) gives an optically active compound ‘P’. The structure of X
and Y respectively are
121 nm

(A)
(B)

91.2 nm

(C)

182 nm

(D)

89.2nm

(B)

(C)

(D)

125. 6 g of a mixture of naphthalene (C H ) and 126.
10 8
anthracene (C H ) is dissolved in 300 g of benzene. If
14 10
The anhydride of the oxoacid HOCL is
the depression in freezing point is 0.70 K, the
composition of naphthalene and anthracene in the
(A)
mixture respectively in g axe (molal depression constant
of benzene is 5.1 K kg mol-1) ClO
2

(A) 2.60, 3.40
(B)
(B) 3.40, 2.60
Cl O
(C) 2.90, 3.10 2

(D) 3.10, 2.90 (C)

Cl O
2 7

(D)

Cl O
2 6

127. Which of the following metals exist in liquid state 128.
during the summer season?
The figure represents PV vs P relation for CO, CH , H
4 2
(A) Ga and He gases under identical conditions. Which curve,
(B) Al shown in the figure, represents He gas?

(C) Pb

(D) Sn

(A)

1

(B)

2

(C)

3

(D)

4

129. 130.

Which of the following statement is incorrect? Which of the following statement is false?

(A) (A)

A cation is smaller than an anion if they are isoelectronic Only tollens reagent can oxide both aliphatic and aromatic
aldehydes
(B)
(B)
Out of P3-,S2- & CI-, CI- ion is larger in size
Oximes are less acidic than hydroxylamine
(C)
(C)
All transition elements are metals
Sodium borohydride does not reduce carboxyl group
(D)
(D)
The ionic radii of lanthanoids in trivalent state decrease with
increasing atomic numbers. Di alkyl cadmium is considered superior to Grignard reagent
for the preparation of a ketone from an acid chloride

131. Wurtz reaction of bromoethane gives n-butane. 132.
Sodium salt of X on heating with sodalime also results in
At what temperature will the total kinetic energy of 0.30
n-butane. Compound X is
moles of He be same as the total kinetic energy of 0.40
(A) CH CH CH COOH moles of Ar at 400 K?
3 2 2
(B) CH (CH ) COOH
3 2 3
(A)
(C) CH (CH) ) ,COOH
3 2 4
(D) CH CH COOH 400K
3 2

(B)

300K

(C)

273K

(D) 533k

133. 134. The non-biodegradable waste fonned in fertilizer
industries is
The number of voids in 1 mole of a compounds forming a
hep structure are (A) fly ash

(B) carbon monoxide
(A)
(C) gypsum

1.8 x 1024 (D) lead

(B)

3.6 x 1024

(C)

6.0 x 1023

(D)

7.2 x 1024

135. 136. Which one of the following statements is correct?

If for a hypothetical reaction, E = 0 at 273 K, then find (A) In collision theory e-EaRT corresponds to the fraction of
a
the ratio of the rate constants at 383 K. molecules that have energy equal or greater than E
a
(B) The number of collisions of reacting molecules per
(A) second per unit volume of the reaction mixture is activated
complex
10
(C) Molecularity is the number of molecules involved in a
(B) complex reaction

1 (D) A catalyst catalyses the non-spontaneous reaction

(C)

0

(D)

100

137. 138.

Which of the following species acts as both Bronsted acid A catalyst is a substance which ....................
and base?
(A)
(A)
Changes the equilibrium concentration of the products
OH
(B)
(B)
Changes the energy of the reactants
NH
3
(C)
(C)
Shortens the time to reach equilibrium
Nacl
(D)
(D)
Changes the equilibrium constant
HSO
4

139.  The wavelength of a microscopic particle of mass 140.
9.1 x 10-31 kg is 182 nm, its kinetic energy in J is (h =
At what temperature will the total kinetic energy of 0.30
6.625 x 10-34 Js)
moles of He be same as the total
(A) 7.28 x 10-23

(B) 7.28 x 10-24 (A)

(C) 3.64 x 10-23 400K
(D) 3.64 x 10-24
(B)

300K

(C)

273K

(D)

533K

141. 142. If the most probable speed of CO at 27°C is 400 m
2
s-1, the root mean square velocity of CO at the same
2
Which of the following species acts as both Bronsted acid
temperature in m s-1 is approximately
and base?
(A) 600

(A) (B) 490

OH- (C) 267

(D) 245
(B)

NH
3

(C)

Nacl

(D)

HSO-
4

143. 144. 1 mole of gas A and 1 mole of gas B at 27 ^ ° C were
pumped into a 24.6 L volume pre-evacuated isolated
A 90 g of ethyl amine on reaction with methyl chloride
flask. The catalyst coated inside the flask catalyzes the
produced a tertiary amine as an exclusive product. The
following reaction A _ ( g ) + B _ ( g ) 2 D _ ( g ) The
amount of methyl chloride required 1s [Given mass in
kinetic energy of D is 98.03 L atm. Calculate the pressure
amu : H=1, C= 12,N=14, Cl=35.5]
realized at the end of the reaction.

(A) (A) 1.66 atm

(B) 2.66 atm
50.5 g
(C) 5.33 atm
(B)
(D) 4.3 atm

101 g

(C)

202 g

(D)

303 g

145. Identify the reactions in which H _ 2 is liberated a) 146.
Zn + NaOH _ ( aq ) b) HCOOH 373 K conc · H _ 2 SO _ 4 c)
Which of the following practices will not come under
CH _ 4 ( g ) + H _ 2 O _ ( g ) ( 1270 K )/( Ni ) d) Zn + H _ (
green chemistry?
aq ) ^ + e) C _ ( s ) + H _ 2 O _ ( g ) 1270 K

(A) a, c, d, e (i) Using soaps made of vegetable oils instead synthetic
detergents, whenever possible,
(B) a, b, c, d

(C) b, c, d, e (ii) Using H O , for bleaching purposes instead chlorine
2 2
based bleaching agents.
(D) a, b, c, e

(iii) Using liquefied C0 for dry cleaning clothes and
2
laundry.

(iv) Using plastic cans for neatly storing substances

(A)

(i) only

(B)

(ii) only

(C)

(iii) only

(D)

(iv) only

147. 148.

If two molecules of A and B having mass 100 Kg and 64 Which of the following molecules has T-shaped
Kg and rate of diffusion of A is 12x 10-3, then rate of geometry?
diffusion of B will be
(A)
(A)
PF
3
15 x 10-3
(B)
(B)
BCl
3
64 x 10-3
(C)

(C)
IF
3

36 x 10-3
(D)

(D) NH
3

10 x 10-3

149. 150.

A 3 mL of solution was made by dissolving 20 mg of Glucose on prolonged heating with HI, gives product P.
protein at 0 °C. The osmotic pressure of the resulting The product P is
solution is 3.8 torr. The molecular weight of the protein is
approximately (in g / mol) (A)

(A)

300

(B)

3 X 105

(C)

(B)
3 X 104

(D)

3 X 103

(C)

(D)

151. Identify the correct statements from the following. 152.
[1] Tendency to form halide hydrates gradually increases
from Be to Ba down the group. [2] Tendency to form
The reaction is exothermic
stable super oxides increases from Li to Cs dovm the
group. [3] Low solubility of LiF is due to its high lattice and reversible. A mixture of N ,h and NH is at
2(g) 2(g) 3(g)
energy.. [4] Solubility of carbonates of group-2 elements equilibrium in a closed container. When a certain

increases down the group. quantity of extra Hoy is introduced into the container,
while keeping the volume constant, then which
(A) 1, 2
statement among the following is true?
(B) 3, 4

(C) 2, 3 (A)

(D) 1, 3 The pressure inside the container will not change

(B)

Equilibrium condition will not change

(C)

The temperature will increase

(D)

The temperature will decrease

153. AlCl _ 3 in water at pH 7 154. Which are structures of X, Y and Z in the above
given reaction sequence?
(A) tetrahedral Al ( OH ) _ 4 ^ - ions

(B) Octahedral Al ( OH ) _ 6 ^ 3 - ions (A)

(C) Square planar Al ( OH ) _ 4 ^ - ions (B)

(D) Octahedral Al ( OH _ 2 ) _ 6 ^ 3 + ions (C)

(D)

155. 156. The number of moles of solute present in the
solutions of l, II and III is respectively. [1] 500 mL of 0.2
A hydrogen electrode is made by dipping platinum wire in
M NaOH [2] 200mL of 0.1 N H S0 [3] 6 g of urea in 1 kg
2 4
a solution of nitric acid of pH= 9 and passing hydrogen
of water
gas around the platinum wire at 1.2 atm pressure. The
oxidation potential of such an electrode equals (A) 0.1, 0.02, 0.3

................V. (B) 0.1, 0.02, 0.1

(C) 0.2, 0.01, 0.1
(A)
(D) 0.1, 0.01, 0.2
+0.059

(B)

-0.0531

(C)

-0.059

(D)

+0.0531

157. 158. If the crystal field splitting energy of a tetrahedral
complex (Δ) of the type [ML ]n+ is x eV. what is the
4
The major product of the following reaction sequence is:
crystal field splitting energy with respect to an
octahedral complex. [ML ]n+
6

(A) (9 x)/(4) eV

(B) (9 x)/(8) eV

(C) (4 x)/(9) eV

(D) (4 x)/(5) eV

(A)

(B)

(C)

(D)

159. 160. If a suitable photon is employed to locate an
electron (mass = 9.11 x 10-31> kg) in an atom within a
1 L each of gases A and B diffused through a membrane
distance of 10.98 nm. the uncertainty involved in the
in 15 and 30 minutes, respectively, under identical
measurement of its velocity is ms-1 is
conditions. What is the ratio of molecular weight of A and
B? (A) 1.6565 × 106π

(B) 1.6565 × 104π
(A)
(C) 1.6565 × 10-8π

1:2 (D) 1.6565 × 108π

(B)

2:1

(C)

4:1

(D)

1:4

ANSWER KEY

1. (A) 2. (C) 3. (C) 4. (C) 5. (C) 6. (B) 7. (D)

8. (C) 9. (B) 10. (C) 11. (B) 12. (D) 13. (B) 14. (A)

15. (C) 16. (B) 17. (C) 18. (A) 19. (D) 20. (A) 21. (D)

22. (A) 23. (D) 24. (B) 25. (C) 26. (C) 27. (A) 28. (A)

29. (C) 30. (B) 31. (C) 32. (B) 33. (B) 34. (C) 35. (A)

36. (A) 37. (C) 38. (B) 39. (D) 40. (A) 41. (B) 42. (B)

43. (C) 44. (C) 45. (A) 46. (B) 47. (A) 48. (C) 49. (D)

50. (D) 51. (A) 52. (B) 53. (D) 54. (C) 55. (D) 56. (B)

57. (D) 58. (C) 59. (D) 60. (B) 61. (D) 62. (B) 63. (B)

64. (B) 65. (A) 66. (A) 67. (A) 68. (B) 69. (D) 70. (C)

71. (A) 72. (C) 73. (C) 74. (C) 75. (D) 76. (A) 77. (D)

78. (B) 79. (B) 80. (C) 81. (A) 82. (B) 83. (D) 84. (C)

85. (C) 86. (A) 87. (D) 88. (A) 89. (B) 90. (C) 91. (B)

92. (A) 93. (B) 94. (D) 95. (D) 96. (C) 97. (C) 98. (A)

99. (A) 100. (A) 101. (A) 102. (B) 103. (C) 104. (C) 105. (B)

106. (B) 107. (B) 108. (B) 109. (C) 110. (C) 111. (D) 112. (B)

113. (D) 114. (A) 115. (D) 116. (A) 117. (D) 118. (B) 119. (C)

120. (A) 121. (A) 122. (A) 123. (B) 124. (B) 125. (B) 126. (B)

127. (A) 128. (C)
Get Free Sample129. (B)Question Papers,
Papers, 130. (B)Tests & Study Material
Mock 131. (B) 132. (D)
at 133. (A)

134. (C) 135. (B) 136. (A) 137. (D) 138. (C) 139. (B) 140. (D)

141. (D) 142. (B) 143. (C) 144. (B) 145. (A) 146. (D) 147. (A)

148. (C) 149. (C) 150. (C) 151. (C) 152. (C) 153. (D) 154. (A)

155. (D) 156. (C) 157. (A) 158. (A) 159. (D) 160. (B)