AP 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

AP 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

AP 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. The maximum value of the determinant of the matrix
[arrayccc 1+ 2 x & 2 x & 4 2 x \\ 2 x & 1+ 2 x & 4 2 x \\ 2 x
If a square ABCD where A(0 ,0), B(2 , 0), C(2 , 2), D(O, 2)
& 2 x & 1+4 2 x array]
undergoes the following transformations successively,
then the final figure would be a .............. (A) 0

(B) 2

(C) 4

(D) 6
(A)

Square

(B)

Rhombus

(C)

Rectangle

(D)

Parallelogram

3. If ∫ 2 d x √ ^ 2 x - ^ 2 x = - √( f ( x ) ) + c , then f ( x ) = 4. Assertion [A] : (1) + (1+2+4) + (4+6+9) + (9+12+16)
+ …… (81+90+100) =1000 Reason [R] : Σ n(r3-(r-1)3)=n
(A) cot x r=1
3 for any natural number n
(B) sin 2x
(A) Both [A] and [R] are true and [R] is the correct
(C) cos 2x
explanation of [A]
(D) tan x
(B) Both [A] and [R] are true But [R] is not the correct
explanation of [A]

(C) [A] is true but [R] is false

(D) [A] is false but [R] is true

5. If y = 2 x is a tangent to the curve y ^ 2 = a x ^ 3 + b 6. A bag contains 2n coins out of which n -1 are unfair
at ( 1,2 ) , then ( a , b ) = with heads on both sides and the remaining are fair. One
coin is picked from the bag at random and tossed. If the
(A) (8 , 4)
probability that head falls in the toss is 41/56. then the
(B) ( ( 2 )/( 3 ) , 1 )
number of unfair coins in the bag is
(C) ( ( 8 )/( 3 ) , ( 4 )/( 3 ) )
(A) 18
(D) ( ( 8 )/( 3 ) , ( 2 )/( 3 ) )
(B) 15

(C) 13

(D) 14

7. 8. If a , aa .........a are in an arithmetic progression
0 1 11
with common difference d, then their mean deviation
Two of the lines represented by the equation ay4 + bxy3
from their arithmetic mean is
+cx2y2 + dx3y + ex4 = O will be perpendicular, then
(A) 30/11 |d|

(A) (B) 2|d|

(b+ d)(ad + be) +(e—a)2(a+c+e)=0 (C) 3|d|

(D) 12|d|
(B)

(b+ d)(ad + be) +(e+a)2(a+c+e)=0

(C)

(b- d)(ad - be) +(e—a)2(a+c+e)=0

(D)

(b- d)(ad - be) +(e+a)2(a+c+e)=0

9. 10.

Let u and v be two non zero vectors in R3. Then |u X v|2 Which of the following points lie on the plane passing
2
+ |u * v| is equal to through 2i+ 3j -k,3i+ 2j +k and i+j+4k?

(A) (A)

|u|2+|v|2 2i -3j +12k & 2i +j +5/2k

(B) (B)

2|u||v| 2i -3j +13k & 2i +j +6k

(C) (C)

|u|2|v|2 2i -3j +13k & 2i +3/2j +5/2k

(D) (D)

(|u|+|v|)2 2i +6k & 2i +3/2j +3k

11. 12.

In any △ ABC, b2 sin2C +c2 sin B = If y= 5x2 + 6x +6, x = 2 and Δx = 0.001. then the values

of Δy and dy respectively are:
(A)

(A)
△

0.026 & 0.026005
(B)

(B)
2△
0.026005 & 0.026
(C)
(C)
3△
0.026005 & 0.26
(D)
(D)
4△
0.0026 & 0.026

13. If α,β are the roots of x2 + b x + c = 0 and γ, �� β then 14.
1 1
(c-c )2
1
The length of the chord joining points (4.cos θ ,4sin θ )
(A) (b - b) (bcsub>1 - bsub>1c) and [4.cos( θ + 60°), 4 sin(θ + 60°)] on the circle x2 + y2
1
(B) 1 = 16 is

(C) (b - b )
1 2
(A)
(D) (c-c ) (bsub>1c - b csub>1)
1 1
4

(B)

8

(C)

16

(D)

2

15. 16. ∫ x-1(x+1) √x3+x2+x d x=

The center of ellipse x2 + 2y2- 4x +12y+14=0 is (A) 2 -1(√1+x+x2x)+c

(B) -1(√1+x+x2x)+c
(A)
(C) -1(√x1+x+x2)+c

(-2, -3) (D) -1(√1+x2x)+c

(B)

(-2, 3)

(C)

(2, -3)

(D)

(2, 6)

17. 18.

If the area of the region enclosed by the curve x2 + y2 = The solution of the equation 2x3 — x2 — 22x — 24 = 0

16 and the lines x = 2 and x = 3 is (3√ 7 - 4√3 - 8π/3 + when two of the roots are in the ration 3 : 4 is

k) sq.units, then ‘k” equals.......
(A)

(A)
3, 4, 1/2

16 sin-1(3/4)
(B)

(B)
-3/2, -2, 4

8 sin-1(3/4)
(C)

(C) -1/2, 3/2, 2

4 sin-1(3/4) (D)

(D) -3/2, 2, 5/2

2 sin-1(3/4)

19. 20.

Let a, b and c be the three vectors. If |a|=1,|b|=17,|c|=8 If the line px — gy =r intersects the coordinate axes at (a,
and the angle between a and b is θ and a ×(a × b)-c=0 , 0) and (0, b) then the value of (a +b) is equal to
then θ+cosec θ= $
(A)
(A)
r(q+p)/pq
409/136
(B)
(B)
r(q-p)/pq
309/136
(C)
(C)
r(p-q)/pq
419/126
(D)
(D)
r(p-q)/p+q
409/126

21. If f: A→ B is an onto function such that f(x)=√(|x|- 22.
x)+1√(|x|-x) then A and B are respectively
Which of the following condition imply that roots of the
(A) (-∞, ∞), (0,∞) equation (1/4)x2 + bx + c =0 are integers?
(B) (-∞, 0), (2,∞)
(A)
(C) (0,∞), (2,∞)

(D) (-∞, 0], (0,∞) b2-c>0

(B)

b & c are even integers

(C)

b2 — c is the square of an integer and b is an integer

(D)

b & c are integers

23. 24. Let [x] denote the greatest integer less than or equal
to x. Then the number of points where the function y =
7 relatives of a man comprises 4 ladies and 3 gentlemen.
[x] +|1-x|, is not differentiable. is
His wife also has 7 relatives - 3 of them are ladies and 4
are gentlemen. In how many ways can they invite a (A) 1

dinner party of 3 ladies and 3 gentlemen so that there (B) 2
are 3 of man’s relative and 3 of wife’s relative? (C) 3

(D) 4
(A)

485

(B)

500

(C)

486

(D)

102

25. 26.

A random variable X takes values 0, 1, 2,3, ...... with If a point ‘P” on the line 3x + 5y = 15 is equidistant from
probability P(Y = x) = K(x +1) (1/5)x where K is constant, the coordinate axes, then P lies
then P(X = 0) is
(A)
(A)
Only in the first quadrant
7/25
(B)
(B)
Either in first or in second quadrant
18/25
(C)
(C)
Either in first or in third quadrant
16/25
(D)
(D)
Only in the third quadrant
13/25

27. 28.

A man is known to speak truth 7 out of 10 times. After Which of the following matrices is not a square-matrix?
throwing a die with 100 faces marked 1,2,3, ......, 100 on
it’s faces, the man reports that he got a prime number on (A)

the die. What is the probability that it is actually a prime?
[1]

(A)
(B)

5/16
[arrayll 2 & 2 \\ 2 & 2 array]

(B)
(C)

7/16
[arraylll3 & 3 & 3array]

(C)
(D)

11/16
[arraylll 1 & 1 & 1 \ 1 & 1 & 1 \ 1 & 1 & 1 array]

(D)

10/16

29. array l If ω _ 0 , ω _ 1 , … , ω _ n - 1 are the n ^ th 30.
roots of unity, then \ ( 1 + 2 ω _ 0 ) ( 1 + 2 ω _ 1 ) ( 1 + 2
If the straight lines 2x - y + 1=0.4, x + y+2=0 and x + y -
ω _ 2 ) … ( 1 + 2 ω _ n - 1 ) = array
k = 0 are concurrent, then ‘k equals
(A) 1 + ( - 1 ) ^ n 2 ^ n

(B) 1 + 2 ^ n (A)

(C) ( - 1 ) ^ n + 2 ^ n 1/2
(D) 1 + ( - 1 ) ^ n - 1 2 ^ n
(B)

2

(C)

-2

(D)

-1/2

31. 32. Let f (x) be continuous on [0, 4]. differentiable on (0.
4). f(0) = 4 and f (4) = -2 , then the value of g’( c ) for
If the parametric values of two points A, B on the circle x?
some Lagrange's constant c ( 0,4 ) is
+ y? - 6x + 4y — 12 = 0 are 30° and 90° respectively, then
(A) ½
the equation of chord is
(B) 5/12

(C) - 5/12
(A)
(D) -7/12
x + √3y =0

(B)

x - √3y =0

(C)

x + √3y -3( 1+√3) =0

(D)

√3x + √3y + 61 =0

33. 34.

A one-rupee coin, a two-rupee coin, a five coin and a ten- Define f:C + R by f(z) = |z| ∀z ∈ C. Then which of the
rupee coin are tossed simultaneously. Then the expected following is false?
value of the sum of the values of coms that show heads
up is........... (A)

(A) f(-z)=f(z) ∀z ∈ C.

8 (B)

(B) f(z)=f(z) ∀z ∈ C.

7 (C)

(C) f(z2)=(f(z))2 ∀z ∈ C.

10 (D)

(D) f(z 2+z 2)=f(z 2)+f(z2 ) ∀z z ∈ C.
1 2 1 2 1 2

9

35. 36. array l If P _ 1 , P _ 2 , P _ 3 , … … , P _ n are n points
on the line y = x all lying in the first quadrant, such that \
What is the range the function h(x)=x-2/x+3 ?
( O P _ n ) = n ( O P _ n - 1 ) ( O is origin), O P _ 1 = 1 and
P _ n = ( 2520 √( 2 ) , 2520 √( 2 ) ) , then n = . array
(A)
(A) 5
(-∞, 2) (2, ∞)
(B) 6

(B) (C) 7

(-∞, 1) (1, ∞) (D) 8

(C)

(-∞,-3) (-3, ∞)

(D)

(-∞,-1) (-1, ∞)

37. 38. All the letter-s of the word ANIMAL are permuted in
all possible ways and the permutations formed are
If the lines x2 + 2vy —35y2 —4x + 44y— 12 = O and 5x +
arranged in dictionary- order If the rank of the world,
λy —8 = 0 are concurrent then λ equals ANIMAL is.x. then the permutation with rank x, among
the permutations obtained by permuting the letters of
(A)
the word PERSON and arranging the permutations thus

0 formed in dictionary order is

(A) ENOPRS
(B)
(B) NOSPRE
1 (C) NOEPRS

(D) ESORNP
(C)

-1

(D)

2

39. 40.

Determine the value of ‘a’ in tan 70° — tan 20° = a.tan If y=Tan-1 √((1- x)/(1+ x)) , then the values of (d y)/(d x)
50° ? and d2 yd x2 respectively are

(A) (A)

-4 1, 0

(B) (B)

4 x/2, 1/2

(C) (C)

-2 1/2, 0

(D) (D)

2 -1/2, 0

41. 42.

If A is a non-singular matrix such that A.AT = AT. A and B If 14 + 24 +34 +44...............+ n4 = f(n)(12 + 22 + .......+n
= A-1. AT then
2), , then f(4) =

(A)
(A)
A.BT = I
58/5
(B)
(B)
B.BT = I
57/5

(C)
(C)
AT.BT = I
59/5

(D)
(D)
B-1.BT = I
56/5

43. -1[((π)/(2))/((-π)/(2)) x1+ex d x]= 44.

(A) π/4 If the direction cosines of a straight line are (1/c, 1/c, 1/c)
(B) π/3 . then c =

(C) π/6
(A)
(D) π/2

±√ 2

(B)

±√ 3

(C)

±2

(D)

±3

45. 46. If Anish is moving along the boundary of a triangular
field of sides 35, 53m and 66m and you are moving along
sin2 5° + sin210° + sin2 15° +.....................+sin290° = the boundary of a circular field whose area is double the
area of the triangular field, then the radius of the circular
(A)
field is :

8 1/2 (A) 14√5

(B) 15√4
(B)
(C) 16√4
9
(D) 14√3

(C)

9 1/2

(D)

4 1/2

47. 48.

The equation of a curve passing through the point (0 , 1). The number of distinct positive integers can be formed
given that the slope of the tangent to the curve at any using 0, 1, 2, 3 where each integer used at most once is
point (x , y) is equal to the sum of the x-coordinate, and equal to
the product of x and y coordinates at that point, is
(A)
(A)
84

(B)

64
(B)
(C)

48

(D)

(C) 36

(D)

49. If 3x2-7x+2 = 0 and 15x2-11x+a = 0 have a common 50. If z=x+i y, x, y R,(x, y) ≠(0,-4) and Arg((2 z-3)/(z+4
root and a is a positive real number , then the sum of the i))=(π)/(4) and Arg ((2 z-3)/(z+4 i))=(π)/(4) then locus of z
roots of the equation 15x2 -ax +7 =0 is is

(A) 76/15 (A) 2x2 + 2y2 +5x + 5y - 12 =0

(B) 38/15 (B) 2x2 - 3xy + y2 + 5x +y -12 = 0

(C) 2/15 (C) 2x2 +3xy +y2 +5x +y +12 =0

(D) 36/15 (D) 2x2 +2y2 -11x +7y -12 = 0

51. 52.

If mn =3 and 1/m +1/n =4/3, then the value of 0.1+0.1 If 0θ(π)/(2) and θ θ=(12)/(25) then 4 θ+ 4 θ=
1/m+ 0.11/n is

(A)
(A)
327/625
0.2 + 0.11/3
(B)
(B)
337/625
0.1 + 0.11/3 + 0.11/2
(C)
(C)
347/625
0.1 + 0.14/3 + 0.11/2
(D)
(D)
340/625
0.1 + 0.11/4 + 0.11/2

53. If Δ _ 1 = | array c c c 1 & a ^ 2 & a ^ 3 \ 1 & b ^ 2 & b 54.
^ 3 \ 1 & c ^ 2 & c ^ 3 array | and Δ _ 2 = | array c c c b c
If a circle of a constant radius 6 passes through origin O
& b + c & 1 \ c a & c + a & 1 \ a b & a + b & 1 array | then
and meets the coordinate axes at A and B, then find the
Δ_1Δ_2=
locus of the centroid of triangle OAB.
(A) ab + bc + ca

(B) abc (A)

(C) 2(ab + bc + ca) x2 + y2 = 4
(D) ( a + b + c ) ^ 2
(B)

x2 + y2 = 36

(C)

x2 + y2 = 16

(D)

x2 + y2 = 6

55. 56.

A variable plane x/a + x/b + x/c =1, which is at a unit If (1)/((3-5 x)(2+3 x))=(A)/(3-5 x)+(B)/(2+3 x) then A+B=
distance from the origin cuts the coordinate axes at A, B
(A)
and C. If the centroid (x,y,z) of △ABC satisfies 1/x2 +1/y2
+ 1/z2 =k then ‘k’ equals 7/19

(A) (B)

9 8/19

(B) (C)

3 9/19

(C) (D)

1/9 10/19

(D)

1/3

57. ∫ x5 d x(x2+x+1)(x6+1)(x4-x3+x-1)= 58. Consider the following lists.

(A) |x6-1x6+1|+c (A) A-V, B-III, C-II, D-I
e
(B) (1)/(12) x6-1|x6+1|+c (B) A-III, B-II, C-IV, D-I
e
(C) (1)/(12) |x4+1x4-1|+c (C) A-V, B-III, C-IV, D-I
e
(D) |x8+4x6-1|+c (D) A-I, B-II, C-III, D-IV
e

59. 60. A(z ) and B(z ) are two points in the Argand plane.
1 2
Then the locus of the complex number z satisfying Arg(z-
Find the absolute maximum of x40 — x20 on the interval
z z-z )=0 or π is
1 2
[0,1]
(A) The circle with arrayl A B array as a diameter

(A) (B) The ellipse with A, B as extremities of the major axis.

-1/4 (C) The perpendicular bisector of arrayl A B array

(D) The straight line passing through the points A and B
(B)

0

(C)

1/4

(D)

1/2

61. Suppose that a bag A contains n red and 2 black balls 62.
and another bag B contains 2 red and n black balls. One
The sum of two lower triangular matrices is always
of the two bags is selected at random and two balls are
drawn from it at a time. When it is known that the two
(A)
balls drawn are red. if the probability that those two balls
drawn are from bag A is 6/7 then n= an upper triangular matrix

(A) 6
(B)
(B) 4
an lower triangular matrix
(C) 8

(D) 7 (C)

a diagonal matrix

(D)

a scalar matrix

63. 64.

Consider the vectors u=ai + bj + ck, v= a2i + b2j +c2k,
For all n N , (n+ 24)(n + 25)(n + 26)(n + 27) 1s
w=a3i + b3j + c3k, These vectors are coplanar if and only
divisible by
if

(A)
(A)

27
All a,b and c are equal

(B)
(B)

26
One of a,b and c is zero

(C)
(C)

29
Any two of a,b and c are equal

(D)
(D)

24
Either one of a, b and c is zero, or any two of a,b and c are
equal

65. If (1-p x)-1(1-q x)=a +a x+a x2+a x3+… … … then 66.
0 1 2 3
a =
n
Let u and v are unit vectors such that u · v=0 . If r is any
(A) pn+1-qn+1q-p vector coplanar with u and v then the magnitude of the
(B) pn+1-qn+1p-q vector r ×(u × v) is

(C) pn-qnq-p
(A)
(D) pn-qnp-q
1

(B)

0

(C)

|r|

(D)

2|r|

67. The area bounded by the curves y = 2 x ^ 2 , y = Max 68.
\ x - [ x ] , x + | x | \ and the lines x = 0, x = 2 (in square
The figure formed by the four points
units). is

(A) 2
is:
(B) ½

(C) ⅓ (A)
(D) 4/3
Trapezium

(B)

Rectangle

(C)

Parallelogram

(D)

Quadrilateral

69. 70. The general solution of the differential equation ( 1 +
y ^ 2 ) d x = ( ^ - 1 y - x ) d y is
Solve the following Differential equation.
(A) 2 x e ^ ^ - 1 y = e ^ 2 ^ - 1 y + c
(x2 +1) dy/dx + 4xy = 1/x2+1
(B) x y + ^ - 1 y = c

(A) (C) 2 ^ - 1 y = ( y ^ 2 - 1 ) x + c

(D) x e ^ tan ^ - 1 y = e ^ ^ - 1 y ( ^ - 1 y - 1 ) + c
y(x2-1)2 = x + c

(B)

y(x2+ 1)2 = x + c

(C)

y(x2+ 1)2 = x2 + c

(D)

y(x2-1)2 = x2 + c

71. If 8(x+3)2(x-2)=A x+B(x+3)2+(C)/(x-2) then 25( 72.
B+8C-A)
If ' θ ' is the angle between the unit vectors a and b , then
(A) 25 (θ)/(2) is equal to ....
(B) 1
(A)
(C) 8

(D) -8 |a-ba+b|

(B)

|a+b|

(C)

|a-b|

(D)

(1)/(2)|a-b|

73. A straight line meets the X and Y axes at the points 74.
A. B respectively. If AB = 6 units. then the locus of the
The angle between the lines ab(x2 - y2) + (a2 — b2)xy = O
point P which divides the line segment AB such that AP :
is
PB = 2:1 is

(A) 3x2+ y2 = 36 (A)

(B) 4x2 + y2 = 36
π/2
(C) 3x2 + y2 = 16
(B)
(D) 4x2 + y2 = 16

π/3

(C)

π/4

(D)

π/6

75. The probability of occurrence of an event is ⅖ and 76. If c is a parameter then the different equation of the
the probability of non-occurrence of another event is family of curves x2 = c(y+c)2 is
3/10. If these events are independent. then the
(A) x((d y)/(d x))3+y((d y)/(d x))2-1=0
probability that only one of the two events occur is
(B) x((d y)/(d x))3-y((d y)/(d x))2+1=0
(A) 27/55
(C) x((d y)/(d x))3+y((d y)/(d x))2+1=0
(B) 27/50
(D) x((d y)/(d x))3-y((d y)/(d x))2-1=0
(C) 7/25

(D) 14/25

77. 78. A random variable X has the probability distribution

The mean marks of 25 boys ina class is 61 and the mean (A) 0.31

marks of 35 girls in the same class 1s 58. Then the mean (B) 0.62
of all 60 students is (C) 0.82

(D) 0.41
(A)

56.25

(B)

59.25

(C)

57.25

(D)

63.25

79. If x is so small, that x5 and higher power of x may be 80. If x ^ 2 - 3 a x + 14 = 0 and x ^ 2 + 2 a x - 16 = 0
neglected. then the coefficient of x4 in the expansion of have a common root then a ^ 4 + a ^ 2 =
√x2+4-√x2+9 is
(A) 2
(A) 19/1728 (B) 90
(B) -19/1728 (C) 6
(C) 43/1728 (D) 20
(D) -43/1728

PHYSICS

81. A car starts from rest and moves with a constant 82.
acceleration of 5 m / s ^ 2 for 10 seconds before the
The book “Pisces of Physics” has been written by
driver applies the brake. It then decelerates for 5
seconds before coming to rest. The average speed of the
(A)
car over the entire journey of the car is
Newton
(A) 23 m/s

(B) 30 m/s (B)
(C) 33 m/s
Einstein
(D) 25 m/s
(C)

Archimedes

(D)

Galileo

83. 84.

When a vehicle of mass m is moving with a velocity v Zero error belongs to the category of:
over a concave over-bridge, of radius of curvature r, the
thrust on the road at the lowest point on the bridge will (A)

be
Constant errors

(A)
(B)

mg + mv2/ r
Instrumental errors

(B)
(C)

mg - mv2/ r
Personal errors

(C)
(D)

m2v2g/ r
Random errors

(D)

v2g/ r

85. Three moles of an ideal monatomic gas performs a 86. A point source of electromagnetic radiation has an
cycle ABCDA as shown in the figure. The temperatures of average power output of 960 W. The peak value of the
the gas at the states A, B. C and D are 400 K, 800 K, 2400 electric field at a distance 400 cm from the source is
K and 1200 K respectively. The workdone by the gas
(A) 60 Vm-1
during this cycle is (R- universal gas constant)
(B) 120 Vm-1
(A) 1200 R
(C) 30 Vm-1
(B) 3600 R
(D) 180 Vm-1
(C) 2400 R

(D) 2000 R

87. 88.

A person is managing to be at rest between two vertical A particle executing simple harmonic motion has a
walls by pressing one wall by lus hands and feet and maximum speed of 40 m.s-1 and maximum acceleration of
second wall with his back. The coefficient of friction is 0.5 60 m.s-2. The period of oscillation is
between his body and the wall. If the force with which
the person pushes the wall is 500.N, then the mass of the (A)

person is: (Take g= 10 m/s2 )
4π /3 sec

(A)
(B)
80kg
π /2 sec

(B)
(C)
40kg
2π sec
(C)
(D)
75kg
1/π sec
(D)

50kg

89. 90.

A solenoid has 2000 turns wound over a length of 0.30 m. A spherical shell is cut into two pieces along a chord as
The area of its cross-section is 1.2 X 10-3 m. Around its shown in the figure. ‘P’ is a point on the plane of the
central section, a coil of 300 turns is wound. If an initial chord. The gravitational field at ‘P’ due to the upper part
current of 2 A in the solenoid is reversed in 0.25 s, the is I and that due to the lower part is I . What is the
1 2
emf. induced in the coil is equal to: relation between them?

(A)

6x10-4V

(B)

4.8x 10-2 V

(C)

6x10-2 V (A)

I >I
(D) 1 2

48kV (B) I >I
2 1
(C)

I =I
1 2

(D)

No definite relation

91. 92.

The displacement of a simple harmonic motion of The wavelength of the radiation emitted by a black body
amplitude 6 cm when its kinetic energy is equal to its is 6mm and Wein’s constant is 3 X 10-3 mK. The
potential energy is temperature of black body is:

(A) (A)

2√2 cm 5k

(B) (B)

2 cm 3k

(C) (C)

0.5 k
3√2 cm

(D)
(D)
50 k
3/√2 cm

93. 94.

A silver wire of length 3 m and of cross-sectional area The current and emf through an inductance differ by
6.14 x 10-6 m2 carries a current of 6 A. Atomic weight and phase by:
density of silver are 108 and 10500 kg.m-3 respectively.
A silver atom contributes one free electron for (A)

conduction. Avogadro number is 6.023 x 1023 / mole.
π/4
Drift velocity of electrons in silver is, close
to...................... (B)

(A) π/2

10-2ms-1 (C)

(B) π/3

10-4ms-1 (D)

(C) π

0.1ms-1

(D)

1ms-1

95. 96.

A wheel is rotating at 480 rpm. Find the magnitude of A body of mass 0.15 kg moving with a velocity of 15 m.s-1
angular acceleration required to stop the wheel in 8 comes to rest when it hits a spring that is fixed at
seconds? another end. If the force constant of the spring is 1500
N.m-1, the compression in the spring is.............
(A)
(A)
2 π rad.sec-2
0.15m
(B)
(B)
2.5 π rad.sec-2
0.1m
(C)
(C)
2 rad.sec-2
0.2m
(D)
(D)
3.5 rad.sec-2
0.5m

97. 98.

A solid float such that its (1/3)rd part is above water A uniform disc of radius ‘a’ and mass ‘m’ is rotating
surface, Then, the density of solid is freely with an angular speed of ‘w’ in a horizontal plane
about a smooth fixed vertical axis passing through its
(A) center. A particle, also of mass ‘m’ is suddenly attached
to the rim of the disc and starts to rotate with it. The new
744 kg.m-3
angular speed of this system is.............

(B)
(A)
1000/3 kg.m-3
w/3

(C)
(B)

2000/3 kg.m-3 w/6

(D) (C)

910 kg.m-3 w/2

(D)

w/5

99. 100. In a nuclear reactor the activity of a radioactive
substance is 2000/s- If the mean life of the products is 50
Newton’s law of cooling holds good provided the
minutes, then in the steady power generation, the
temperature difference between body and surrounding is
number of radio nuclides is
.................
(A) 12 x 105
(A) (B) 60 x 105

very large (C) 90 x 105

(D) 15 x 105
(B)

large

(C)

small

(D)

very small

101. 102.

The current gain for a transistor working as common- An infinitely long cylinder is kept parallel to an uniform
base amplifier is 0.96. If the emitter current is 7.2 mA, magnetic field B directed along the positive z-axis. The
then the base current is........... direction of induced current as seen from the z-axis will
be:
(A)
(A)
0.29 mA
zero
(B)
(B)
0.35 mA
along the magnetic field
(C)
(C)
0.39 mA
clockwise of the +ve z-axis
(D)
(D)
10mA
anti-clockwise of the +ve z-axis

103. 104. An insulated system contains 4 moles of an ideal
diatomic gas at temperature T. When a heat ‘Q’ is
An 100 eV electron is fired directly towards a large metal
supplied to the gas. 2 moles of the gas is dissociated into
plate having surface charge density -2x 10-6cm-2, The
atoms and the temperature remained constant. Then the
distance from where the electron be projected so that it
relation between Q and T is (R- Universal gas constant)
just fails to strike the plate is.........
(A) Q = RT

(A) (B) Q = 2RT

0.22 mm (C) Q = 3RT

(D) Q = 4RT
(B)

0.44 mm

(C)

0.66 mm

(D)

0.88 mm

105. 106.

Liquid A rises to a height of 10 cm ma capillary tube and Two capacitors each having a capacitance 2 X 10-6F and a
liquid B falls to a depth of 2 cm in the same tube. The breakdown voltage 5000 V, are joined in series. What will
density of A and B are | g/cm3 and 10 g/cm3 respectively. be the resultant capacitance and the breakdown voltage
The contact angle of A and B with the tube is 0° and 139° of the combination?
respectively. If the surface tension of A and B are S and
A
S then the ratio S /S is: (A)
B B A

4 x 10-6F & 1000 V
(A)

√2 (B)

10-6F & 10000 V
(B)

2√2 (C)

2 x 10-6F & 5000 V
(C)

1/√2 (D)

10-6F & 2500 V
(D)

1/2√2

107. 108.

Molar specific heat at constant pressure C is related to A wheel undergoes a constant angular acceleration from
p
internal energy U and absolute temperature T as C = time t = 0 to t = 20s and thereafter angular acceleration
p
is zero. If angular velocity at t =2 s is found to be S rad/s,
(A) then the number of revolutions made by the wheel in
time interval t = 0 s to t=50s is:
U/T

(A)
(B)

1000/π
dU/dT

(B)
(C)

600π
dU/dT + R

(C)
(D)

1500/π
UxT

(D)

2000/π

109. 110.

If rotational inertia parameter of a body rolling down a 50 g of copper is heated to increase its temperature by
rough inclined plane (of inclination θ and height h) 10 °C. If the same quantity of heat is given to 10 g of
without slipping is given by β=I / M R2 . then time water, the rise in temperature is (specific heat of Cu =
CM
taken by the body to reach the bottom of the mclined 420 J.kg-1.°C-1 and specific heat of water is 4200 J.kg-1°C-
plane is given by ................. 1)

(A) (A)

t=(1)/( θ) √(((1+β) 2 h)/(g)) 6°C

(B) (B)

t=(1)/( θ) √(((1+β) 2 h)/(g)) 10°C

(C) (C)

t=(1)/( θ) √(((1-β) 2 h)/(g))
5°C

(D)
(D)
t=(1)/( θ) √(((1+β) h)/(g))
15°C

111. 112.

The ratio of maximum and minimum intensities in an In an intrinsic semiconductor at room temperature
interference pattern is 36:1, The ratio of the amplitude of number of electrons and holes are
the two interfering waves will be
(A)
(A)
equal
5:7
(B)
(B)
zero
7:4
(C)
(C)
unequal
4:7
(D)
(D)
electrons more than holes
7:5

113. 114.

The moment of inertia of a thin rod of mass “M’ and Ina given process, for an ideal gas, ΔW =O and ΔQ < 0.
length ‘L” about an axis passing through a point at a Then for the gas, ................
distance L/4 from its center and perpendicular to its
length is (A)

The temperature will decrease
(A)

ML3/48 (B)

The volume will increase
(B)

ML2/48 (C)

The pressure will remain constant
(C)

ML2/12 (D)

The temperature will increase
(D)

7ML2/48

115. 116.

The water on the surface of a lake is just about to freeze. An ideal monoatomic gas of volume V is adiabatically
The most likely temperature at the bottom of the lake is expanded to a volume 3V at 27oC.. The final temperature
in Kelvins is: (use & C /C =5/3)
p v
(A)
(A)
4°C
144.2
(B)
(B)
0°C
170.3
(C)
(C)
-4°C
50.4

(D)
(D)

-273 °C
100.2

117. 118.

A person is managing to be at rest between two vertical The volume of a liquid is proportional to
walls by pressing one wall by lus hands and feet and ................................ given its density p, viscosity 7 and
second wall with his back. The coefficient of friction is 0.5 ¢ the time of flow through a capillary tube of length L
between his body and the wall. If the force with which and radius R, with a pressure difference P across its ends
the person pushes the wall is 500.N, then the mass of the
person is: (Take g= 10 m/s2) (A)

P2R2t/nL
(A)

80 kg (B)

PR4/nLt
(B)

40 kg (C)

PR4t/nL
(C)

75 kg (D)

P2R2t/nL2
(D)

50 kg

119. 120.

If refractive index of water is 4/3 and that of a given slab If 5 mg of 235U is completely destroyed in an atom bomb,
immersed in it is 5/3. The value of critical angle for a zray then approximate total energy released is: (given that
of light tending to go from glass to water is: the energy released per fission is 200 MeV)

(A) (A)

Sin-1(4/5) 4x108J

(B) (B)

Sin-1(3/4) 6x109J

(C) (C)

Sin-1(5/3) 5x107J

(D) (D)

Sin-1(4/3) 3x1010J

CHEMISTRY

121. 122.

In Kjeldahl’s method. organic ‘N’ is estimated as The geometry and dipole moment of H S respectively are
2

(A) (A)

Nitrogen Angular and Non-zero

(B) (B)

Ammonia Angular and Zero

(C) (C)

Nitric-acid Linear and Zero

(D) (D)

Nitrogen dioxide Linear and Non-zero

123. 124.

A 3 mL of solution was made by dissolving 20 mg of Hex-I—yne on reaction with Br (excess)/ CCl , gives
2 4
protein at 0 °C. The osmotic pressure of the resulting
solution is 3.8 torr. The molecular weight of the protein is (A)

approximately (in g / mol)
1,1,3,3 — Tetrabromohexane

(A)
(B)

300
2,2,3,3—Tetrabromohexane

(B)
(C)

3 X 105
1,1,1,2—Tetrabromohexane

(C)
(D)

3 X 104
1,1,2,2—Tetrabromohexane

(D)

3 X 103

125. 126.

Which of the following is not an electrophile?

(A)

CN-

(B)

BF3

(A) (C)

i-d, ii—a, iii—b, iv—c NO+
2

(B) (D)

i-c, ii—b, iii-a, iv—d AICI
3

(C)

i-a, ii-d, iii—e, iv—b

(D)

i b, ii-c, ii d, iv—a

127. Acetic acid on heating with NH forms A. When A 128. Identify the reactions that occur in photochemical
3
reacts with LiAlH followed by hydrolysis gives B. When B smog a) CH _ 2 = O + H _ 2 CH _ 3 OH b) NO _ 2 ( g ) hv NO
4
is heated with chloroform in KOH medium gives C. What _ ( g ) + O _ ( g ) ; O _ ( g ) + O _ 2 ( g ) O _ 3 ( g ) c) 3 CH _
are B and C respectively? 4 + 2 O _ 3 3 CH _ 2 = O + 3 H _ 2 O d) NO _ ( g ) + O _ 3 (
g ) NO _ 2 ( g ) + O _ 2 ( g )
(A) CH CONH , CH CH NC
3 2 3 2
(B) CH CH NH , CH CH NC (A) b, c, d
3 2 2 3 2
(C) CH CH NH , CH COOH (B) a, b, c
3 2 2 3
(D) CH CH CH NH , CH CH NC (C) a, b, d
3 2 2 2 3 2
(D) a, c, d

129. 130.

The geometries of [Ni(CO) ] , [PtCl ]2- and [Co (NH ) ]3+ The ratio of de-Broglie wavelength of two particles A and
4 4 3 6
respectively are: B is 2: 1. If the velocities of A and B are 0.05 m.s-1 and
0,02 m.s-1. respectively, then the ratio of their masses m
(A) :m must be...........................
A B

Tetrahedral, Tetrahedral and Octahedral
(A)

(B) 5:1

Tetrahedral, Square planar and Square pyramidal
(B)

(C) 10:1

Square planar, Square planar and Octahedral
(C)

(D) 1:5

Tetrahedral, Square planar and Octahedral
(D)

1:8

131. 132.

Strongest conjugate base is .......................... Which reaction(s) among the following produce
Dinitrogen?
(A)
i) NH Clt + NaNO —>
4 (aq) 2(aq)
Cl-
(ii) NH CONH + 2 H 0 —>
2 2 2
(B)
(iii) Ba(N ) —>
3 2
Br-
(iv) NH Cl+ Ca(OH) —>
4 2

(C)
(A)
I-
(i) & (iii) only

(D)
(B)
F-
(ii) & (iii) only

(C)

(iii) & (iv) only

(D)

(ii) & (iv) only

133. 20mL of Fe2+ solution of certain concentration has 134. What are A, B and C in the following reactions?
completely reacted with 20 mL of 0.01 M K ,Cr ,O , in
2 2 7 (A)
acid medium. If 20 mL of same Fe2+ solution has reacted
(B)
completely with 20 mL of KMnO , solution in acid
4
medium, the molarity of KMnO , solution is (C)
4
(D)
(A) 0.01 M

(B) 0.12 M

(C) 0.10 M

(D) 0.012 M

135. Which of the following statements about BF _ 4 ^ - 136.
and AlF _ 6 ^ 3 - are correct? a) B and Al differ in their
Which one of the following oxide dissolves in both
oxidation states. b) B and Al differ in their covalency. c) B
hydrochloric acid and sodium hydroxide?
obeys the octet rule d) B and Al are in diagonal
relationship.
(A)
(A) a,b
MgO
(B) b, c, d

(C) a, b, c (B)

(D) b, c Na O
2

(C)

Al O
2 3

(D)

Bao

137. 138.

Identify the product of the following reaction: The dominant intermolecular force that must be
overcome to convert liquid methanol to its vapour is

(A)

Covalent Bonds

(B)

Dipole-Dipole Interactions
(A)

(C)

Hydrogen Bonds

(D)

Coordinate Bonds

(B)

(C)

(D)

139. 140. Mixed aldol products obtained from aldol
condensation of ethanal and propanone are
Henrys law constant for CO , in water is 1.67 x 10° Pa.
2
Calculate the approximate quantity of C0 , in 500 ml of (A)
2
soda water when packed under 5 atm CO , at 298 K. (B)
2
(C)
(A)
(D)
3.7g

(B)

1.84 g

(C)

2.2g

(D)

4.4 g

141. 142.

in a mixed oxide of ‘A’ and ‘B’, ‘A’ occupies all the If the maximum kinetic energy of photoelectrons ejected
octahedral voids while ‘B” occupies from a metal surface when it is inradiated with a
radiation of frequency 4 x1014 s-1is 6.63 x 10-20 J, then
(A) the threshold frequency of the metal is

A B 0
3 4 3 (A)

(B) 2 * 10 14

AB 0
2 3 (B)

(C) 1x 10 14

A B0
3 3 (C)

(D) 3* 10
14

A B 0
3 2 3 (D)

1 *10 -14

143. 144. In which of the following the electron gain enthalpy
of elements is correctly arranged?
An organic compound contains 60% C; 4.48% H and
35.5% O. Its empirical formula is (A) S > Se > Te > 0

(B) F > Cl > Br > I
(A)
(C) Na > Li > K > Rb

C H O (D) O > S > Se > Te
9 8 4

(B)

C H O
5 4 2

(C)

C H O
5 4 4

(D)

C H O
9 7 6

145. Which of the following is known as silicone? 146. Identify the non-reducing sugar from the following

(A) Polymer of (A) Maltose

(B) (B) Sucrose

(C) Polymer SiO _ 2 (C) Lactose

(D) Polymer of [SiO ]4- (D) Glucose
4

147. 148. Arrange the following organic halides in collect
order of reactivity towards S 2 displacement. P- (CH )
N 3 2
If the rate constant of a first order reaction is 4.606 X 10-
C(Br)CH CH Q- BrCH (CH ) CH R- CH CH(Br)(CH ) CH
3s-1, then find the time required for 400 g of the reactant 2 3 2 2 3 3 3 2 2 3

to reduce to 50 g. (A) P > Q > R

(B) R > P > Q
(A)
(C) P > R > Q

7.52 minutes (D) Q > R > P

(B)

0.45 minutes

(C)

46.06 minutes

(D)

15.05 minutes

149. What are Y and Z in the following reaction 150.
sequence?
Among the following, which transition in the Hydrogen
(A) spectrum would have the same wavelength as Balmer
(B) transition, n = 4 ton = 2 in He+ spectrum?

(C)
(A)
(D)
n=3 —>n=1

(B)

n=3 —>n=2

(C)

n=4 —>n=1

(D)

n=2 —>n=1

151. 152. Sodium acetate was electrolysed by Kolbe's method
to form two gases A and B at anode. C and D are formed
An ideal gas expanded irreversibly against 10 bar
when B is heated with regulated supply of O or air in the
2
pressure from 20 L to 30 l. Calculate Q if the process is
presence of (CH COO) Mn C reacts with NaOH to form a
3 2
Isoenthalpic. 1 L bar = 100]
salt. A and D are respectively.

(A) (A) CO , CH COOH
2 3
(B) CO , H O
0J 2 2
(C) C H , H O
2 6 2
(B)
(D) CO , H O
2 2 2

100 J

(C)

- 100J

(D)

10 KJ

153. Noble metals like gold and platinum are soluble in 154.
which of the following mixtures ?
Molecular bromine on reaction with three moles of
(A) 1:1 mixture of conc. HNO and conc. H SO molecular fluorine produces an inter halogen compound.
3 2 4
(B) 1:3 mixture of conc. HCl and conc. HNO The total number of lone pairs at the central halogen
3
(C) 1:3 mixture of conc HNO and HNO atom is
3 3
(D) 1:3 mixture of conc H SO and conc. HCl
2 4 (A)

3

(B)

2

(C)

1

(D)

0

155. Which of the elements possess only one electron in 156. The non-biodegradable waste fonned in fertilizer
5d orbital? industries is

(A) ^ 69 Tm , ^ 61 Pm (A) fly ash

(B) ^ 59 Pr , ^ 71 Lu (B) carbon monoxide

(C) ^ 57 La , ^ 61 Pm (C) gypsum

(D) ^ 57 La , ^ 71 Lu (D) lead

157. The correct option for the first ionization enthalpy ( 158.
in kJ mol ^ - 1 ) of Li, Na, K and Cs respectively is
The angular shape of the ozone molecule consists of
(A) 496, 520, 419, 374

(B) 374, 419, 496, 520 (A)

(C) 520, 496, 419, 374
1 σ and 1π bonds with bond angle 109°
(D) 374, 419, 520, 496
(B)

2 σ and 1π bonds with bond angle 117°

(C)

2 σ and 2π bonds with bond angle 120°

(D)

1 σ and 2π bonds with bond angle 60°

159. In Dumas method one gram of carbon compound 160. In the below given synthetic sequence, the product
gives 50 mL of N at 300 K and 740 mm Hg pressure, If "C" is
2
the aqueous tension at 300 K is 15 mm Hg, what is the
(A)
percentage of nitrogen in it?
(B)
(A) 5.42
(C)
(B) 10.84
(D)
(C) 21.68

(D) 2.71

ANSWER KEY

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

127. (B) 128. (A) 129. (D) 130. (C) 131. (D) 132. (A) 133. (D)

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

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

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

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