WBJEE 2027 Sample Paper

SAMPLE PAPER

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

WBJEE 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

155 155 120 Min +1 / −0.25

GENERAL INSTRUCTIONS

1. This paper contains 155 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; 0.25 mark is deducted for each wrong answer.

4. Total time allowed is 120 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

WBJEE 2027
SAMPLE QUESTION PAPER

Questions 155 Max Marks 155 Time 120 Min Marking +1 / −0.25

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

MATHEMATICS

1. If 0 ≤ A ≤ ( π )/( 4 ) then ( ^ - 1 ( ( 1 )/( 2 ) 2 A ) ) + ^ - 2. Let I = ∫ _ π 4 ^ π / 3 ( x )/( x ) d x then
1 ( A ) + ^ - 1 ( ^ 3 A ) is equal to
(A) ( 1 )/( 2 ) ≤ I ≤ 1
(A) ( n π )/( 4 ) , n π ± ( π )/( 3 ) (B) 4 ≤ 1 ≤ 2 √( 30 )
(B) ( n π )/( 4 ) , n π ± ( π )/( 6 ) (C) √( 3 ) 8 ≤ 1 ≤ √( 2 ) 6
(C) ( n π )/( 4 ) , 2 n π ± ( π )/( 3 ) (D) 1 ≤ 1 ≤ 2 √( 3 ) √( 2 )
(D) ( n π )/( 4 ) , 2 n π ± ( π )/( 6 )

3. A chord AB is drawn from the lx»int A (O, 3) on the 4. The equation x log x -3-x
circle x ^ 2 + 4 x + ( y - 3 ) ^ 2 = 0 and is extended to M
(A) has no root in (1,3)
such that AM =2AB. The locus of M is
(B) has exactly one root in (1,3)
(A) x ^ 2 + y ^ 2 - 8 x - 6 y + 9 = 0
(C) x log x -(3-x) >0 in [1,3]
(B) x ^ 2 + y ^ 2 + 8 x + 6 y + 9 = 0
(D) x log x -(3-x) >0 in [1,3]
(C) x ^ 2 + y ^ 2 + 8 x - 6 y + 9 = 0

(D) x ^ 2 + y ^ 2 - 8 x + 6 y + 9 = 0

5. The value of the integral 1 = ∫ _ 1 / 2014 ^ 2014 ^ - 1 6. On R, the relation ρ be defined by ‘xρy holds if and
x x d x is only if x - y is zero or irrational’. Then

(A) ( π )/( 4 ) 2014 (A) ρ is reflexive and transitive but not symmetric.

(B) ( π )/( 2 ) 2014 (B) ρ is reflexive and symmetric but not transitive.

(C) π 2014 (C) ρ is symmetric and transitive but not reflexive.

(D) ( 1 )/( 2 ) 2014 (D) ρ is equivalence relation

7. Consider the function y = _ a ( x + √ x ^ 2 + 1 ) , a > 0 8. If the sum of two unit vectors is a unit vector, then the
, a ≠ 1 .The inverse of the function magnitude of their difference is

(A) does not exist (A) √2 units

(B) is x = _ 1 / 2 ( y + √ y ^ 2 + 1 ) (B) 2 units

(C) is x = ( y / n a ) (C) √3 units

(D) is x = ( - y ( 1 )/( a ) ) (D) √5 units

9. Let A=(arraylll 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 array) 10. If M = ∫ _ 0 ^ π / 2 ( x )/( x + 2 ) d x , N = ∫ _ 0 ^ π / 4
Then for positive integer n, An is x x ( x + 1 ) ^ 2 d x then the value of M-N is

(A) (arrayccc 1 & n & n2 \\ 0 & n2 & n \\ 0 & 0 & n array) (A) π

(B) (arrayccc 1 & n & n((n+1)/(2)) \\ 0 & 1 & n \\ 0 & 0 & 1 (B) ( π )/( 4 )
array) (C) ( 2 )/( π - 4 )
(C) (arraylll 1 & n2 & n \\ 0 & n & n2 \\ 0 & 0 & n2 array) (D) ( 2 )/( π + 4 )
(D) (arrayccc 1 & n & 2 n-1 \\ 0 & (n+1)/(2) & n2 \\ 0 & 0 &
(n+1)/(2) array)

11. On the set of real numbers, the relation p is defined 12. Let and α and β be the roots of x2 + x + 1 =0. If n be
by xpy, (x,y) R positive integer, then αn + βn is

(A) if | x - y | 2 then p is reflexive but neither symmetric nor (A) 2 (2 n π)/(3)
transitive. (B) 2 (2 n π)/(3)
(B) if x - y 2 then p is reflexive and symmetric but not (C) 2 ( n π)/(3)
transitive
(D) 2 ( n π)/(3)
(C) if | x | ≥ y then p is reflexive and transitive but not
symmetric

(D) if x > | y | then p is transitive but neither reflexive nor
symmetric.

13. The angle between a pair of tangents drawn from a 14. ∫ ( x) d v=F(x)+c where c is an arbitrary constant,
point p to the circle x ^ 2 + y ^ 2 + 4 x - 6 y + 9 ^ 2 α + Here F(x) =
13 ^ 2 α = 0 is 2 α The equation of the locus of the point
(A) x[cos(log x) + sin(log x)]
P is.
(B) x[(cos(log x) - sin(log x)]
(A) x ^ 2 + y ^ 2 + 4 x + 6 y + 9 = 0
(C) x[(cos(log x) + sin(log x)]
(B) x ^ 2 + y ^ 2 - 4 x + 6 y + 9 = 0
(D) x/2[(cos(log x) - sin(log x)]
(C) x ^ 2 + y ^ 2 - 4 x - 6 y + 9 = 0

(D) x ^ 2 + y ^ 2 + 4 x - 6 y + 9 = 0

15. The chord of the curve y = x2 + 2ax +b, joining the 16. Given that n numbers Of A-Ms are inserted between
points x =α and x = β is parallel to the tangent to the two sas of a, 2b and 2a, b where a , b R . Suppose further
curve at abscissa x = that the mth means between these sets of numbers are
same, then the ratio a : b equals
(A) (a+b)/(2)

(B) (2 a+b)/(3) (A) n - m + 1 : m

(C) 2 (α+β)/(2) (B) n - m + 1 : n

(D) (α+β)/(2) (C) n : n - m + 1

(D) m : n - m + 1

17. The line segment joining the foci of the hyperbola x2 18. Let P be the set of all non-singular matrices of order
- y2 + 1 = 0 is one of the diameters of a circle. The 3 over R and Q be the set of all orthogonal matrices of
equation of the circle is order 3 over R. Then

(A) x2 + y2 = 4 (A) P is proper subset of Q

(B) x2 + y2 =√2 (B) Q is proper subset of P

(C) x2 + y2 =2 (C) Neither P is proper subset of Q nor Q is proper subset of

(D) x2 + y2 = 2√2 P

(D) P∩Q = Φ. the void set

19. The probability that a non leap year selected at 20. Let A=(arraycc x+2 & 3 x \\ 3 & x+2 array) .
random will have 53 Sundays is B=(arraycc x & 0 \\ 5 & x+2 array) Then all solutions of
the equation det (AB) = 0 is
(A) 0

(B) 1/7 (A) 1, -1, 0, 2

(C) 2/7 (B) 1, 4, 0, -2

(D) 3/7 (C) 1, -1, 4, 3

(D) -1, 4, 0, 3

21. Let I = ∫ _ 0 ^ 1 x ^ 3 3 x 2 + x ^ 2 d x then 22.  Transforming to parallel axes through a point (p,q),
the equation 2x2 + 3xy + 4y2 + x + 18y + 25 = 0 becomes
(A) - ( 1 )/( 2 ) I ( 1 )/( 2 )
2x2 + 3xy + 4y2 = Then
(B) - ( 1 )/( 3 ) 1 ( 1 )/( 3 )
(A) p = -2, q= 3
(C) - 1 1 1
(B) p = 2, q= -3
(D) - ( 3 )/( 2 ) 1 ( 3 )/( 2 )
(C) p = 3, q= -4

(D) p= -4, q= 3

23. The integrating factor of the first order differential 24. Let for all x > 0 f(x) = n(x(1)/(n)-1) then
a arrow ∞
equation x2(x2-1) (d y)/(d x)+x(x2+1) y=x2-1 is
(A) f(x) + f(1/x) =1
(A) ex (B) f(xy) = f(x) +f(y)
(B) x - 1/x (C) f(xy) = xf(y) + yf(x)
(C) x + 1/x (D) f(xy) = xf(x) + yf(x)
(D) 1x2

25. ∫ x ^ 2 - 1 x ^ 4 + 3 x ^ 2 + 1 d x ( x > 0 ) is 26. Let f ( x ) = \ array l l - 2 x , & if x ≤ - ( π )/( 2 ) \ A x +
B , & if - ( π )/( 2 ) x ( π )/( 2 ) \ x , & if x ≥ ( π )/( 2 ) array .
(A) ^ - 1 ( x + ( 1 )/( x ) ) + c
Then
(B) ^ - 1 ( x - ( 1 )/( x ) ) + c
(A) f is discontinuous for all A and B
(C) _ e | ( x + ( 1 )/( x ) - 1 )/( x + ( 1 )/( x ) + 1 ) | + c
(B) f is continuous for all A=-1 and B= 1
(D) _ c | ( x - ( 1 )/( x ) - 1 )/( x - ( 1 )/( x ) + 1 ) | + c
(C) f is continuous for all A=-1 and B= -1

(D) f is continuous for all real values of A,B

27. If f : R arrow R be defined by f ( x ) = e ^ x and g : R 28. Let P be a point on the ellipse x ^ 2 9 + y ^ 2 4 = 1
arrow R defined by g ( x ) = x ^ 2 . The mapping g ° f : R and the line through P parallel to the y-axis meets the
arrow B be defined by ( g ° f ) ( x ) = g [ f ( x ) ] x R . Then circle x ^ 2 + y ^ 2 = 9 where P, Q are on the same side
of the x-axis. If R is a point on PQ such that PR/RQ=½
(A) g ° f is bijective but f is not injective
then the locus of R is
(B) g ° f is injective and g is injective
(A) x ^ 2 9 + 9 y ^ 2 49 = 1
(C) g ° f is injective but g is not bijective
(B) x ^ 2 49 + y ^ 2 9 = 1
(D) g ° f is surjective and g is surjective
(C) x ^ 2 9 + y ^ 2 49 = 1

(D) 9 x ^ 2 49 + y ^ 2 9 = 1

29. If one of the diameters of the curve x2 + y2 - 4x- 6y + 30. ( x)2+ta n x
r arrow 0
9 = 0 is a chord of a circle with centre (1, 1). the radius of
(A) is 2
this circle is
(B) is 3
(A) 3
(C) is 0
(B) 2
(D) does not exist
(C) √2

(D) 1

31. The point P (3, 6) is first reflected on the line y =x 32. If y = esin then (1-x2) (1-x2) d2 yd x2-x (d y)/(d x)-k y-
and then the image point Q is again reflected on the line 0 where k is equal to
y = - x to get the image point Q’ , Then the circumcentre
(A) m2
of the △PQQ' is
(B) 2
(A) (6, 3)
(C) -1
(B) (6, -3)
(D) -m2
(C) (3, -6)

(D) (0, 0)

33. For real x, the greatest value of x2+2 x+42 x2+4 x+9 34. If z _ 1 and z _ 2 be two non zero complex numbers
is such that z _ 1 z _ 2 + z _ 2 z _ 1 = 1 then,the origin and
the points represented by z _ 1 and z _ 2
(A) 1

(B) -1 (A) lie on a straight line

(C) 1/2 (B) form an right angled triangle

(D) 1/4 (C) form an equilateral triangle

(D) form an isosceles triangle

35. On set A = {1,2,3} relations R and S are given by R = 36. A point P lies on a line Q(1, —2, 3) and is parallel to
{(1,2) ,(2,2), (3,3) ,(1,2), (2,1)} S = {(1,2), (2,2), (3,3), the line ( x )/( 1 ) - ( y )/( 4 ) = ( z )/( 5 ) If p Iles the 2 x +
(1,3), (3,1)} Then 3 y - 4 z + 22 = 0 then segment PQ equals to

(A) R U S is an equivalence relation (A) √( 42 ) units

(B) R U S is reflexive and transitive but not symmetric (B) √( 32 ) units

(C) R U S is reflexive and symmetric but not transitive (C) 4 units

(D) R U S is symmetric and transitive but not reflexive (D) 5 units

37. Let f: [ : | a , b | arrow R be differentiable on [ a , b ] 38. If a _ r = ( 2 r π + i 2 r π ) ^ 1 / 9 then the value of |
\& k R .Let f ( a ) = 0 = f ( b ) Also let J ( x ) = f ^ ′ ( x ) + k array c c c a _ 1 & a _ 2 & a _ 3 \ a _ 4 & a _ 5 & a \ a _ 7 & a
f ( x ) Then _ 8 & a \ 7 & 8 & 9 array | is

(A) J ( x ) > 0 for all x [ a , b ] (A) 1

(B) J ( x ) 0 for all x [ a , b ] (B) -1

(C) J ( x ) - 0 for all x [ a , b ] (C) 0

(D) J ( x ) = 0 through ( a , b ) (D) 2

39. If ∫ e ^ x · [ x ^ 3 x - x ^ 2 x ] d x = c ^ x · f ( x ) + c 40. Number of common tangents of y = x ^ 2 and -x2+4x-
where c is a constant of integration , then f(x) = 4 is

(A) x - x (A) 1

(B) x - x (B) 2

(C) x - x (C) 3

(D) x - x (D) 4

41. Let f: KR —> R be such that f is injective and f(x) f(y) 42. A ladder 20 ft long leans against vertical wall. The
= f(x+ y) for all x, y ∈ R. If f(x), f(y), f(z) are in G.P. then top end slides downwards at the rate of 2 ft per second.
x, y, z are in The rate at which the lower end moves on a horizontal
floor when it is 12 ft from the wall is
(A) A.P always

(B) GP always (A) ( 8 )/( 3 )

(C) AP depending on the value of x.y, z (B) ( 6 )/( 5 )

(D) G.P depending on the value of x. y, z (C) ( 3 )/( 2 )

(D) ( 17 )/( 4 )

43. The number ( 101 ) ^ 100 - 1 is divisible by 44. If the following three linear equations have a non-
trivial solution, then x + 4ay+ az =0 x+3by + bz = 0 x +
(A) 10 ^ 4
2cy + cz = 0
(B) 10 ^ 6
(A) a, b, c are in A.P.
(C) 10 ^ 8
(B) a,b,c are in G.P.
(D) 10 ^ 12
(C) a, b, are in H.P.

(D) a, b, c are in G.P.

45. A student tests l, II and Ill. The student is successful 46. Three lines are drawn from the origin O with
if he passes in tests l, II,or Ill. The probabilities of the direction cosines proportional to (1,-1.1). (2, -3, 0) and
student passing in tests I, II and Ill are respectively p, q (1, 0, 3). The three lines are
and ½ .If the probability of the student to be successful
(A) not coplanar
is ½ then
(B) coplanar
(A) p ( 1 + q ) = 1
(C) perpendicular to each other
(B) q ( 1 + p ) = 1
(D) coincident
(C) pq = 1

(D) ( 1 )/( p ) + ( 1 )/( q ) = 1

47. The value of det A. where A=(arrayccc 1 & θ & 0 \\ - θ 48. Let α , β , γ be three unit vectors such that α · β = α ·
& 1 & θ \\ -1 & - θ & 1 array) lies γ = 0 and the angle between β and γ is 30 ^ ° .Then α is
________________
(A) in the closed interval [1, 2]

(B) in the closed interval [0, 1] (A) 2 ( β × γ )

(C) in the open interval (0, 1) (B) - 2 ( β × γ )

(D) in the open interval (1, 2) (C) ± 2 ( β × γ )

(D) ( β × γ )

49. Out of 7 consonants and 4 vowels. words are formed 50. Let z _ 1 and z _ 2 be complex numbers such that z _
each having 3 consonants and 2 vowels. The number of 1 ≠ z _ 2 and | z _ 1 | = | z _ 2 | . If Re ( z _ 1 ) > 0 and Im (
such words that can be formed is z _ 2 ) 0 , then z _ 1 + z _ 2 z _ 1 - z _ 2 is

(A) 210 (A) one

(B) 25200 (B) real and positive

(C) 2520 (C) real and negative

(D) 302400 (D) purely imaginary

51. If 6 θ + 4 θ + 2 θ = 0 , then general value of θ is 52. Let A be the centre of the circle x ^ 2 + y ^ 2 - 2 x - 4
y - 20 = 0 .Let B (1, 7) and D(4, —2) be two points on the
(A) ( n π )/( 4 ) , n π ± ( π )/( 3 )
circle such that tangents at B and D at C. The area of the
(B) n π 4 , n π ± ( π )/( 6 )
quadrilateral ABCD is
(C) ( n π )/( 4 ) , 2 n π ± ( π )/( 3 )
(A) 150 sq. units (C) 7S sq. units
(D) ( n π )/( 4 ) , 2 n π ± ( π )/( 6 )
(B) 50 sq. unit

(C) 7S sq. units (B) 50 sq. units

(D) 70 sq.units

53. If f’’(0) =k, k ≠ 0, then the value of 2 f(x)-3 54. Let (1+x+x2)9 = a x1 x then
x arrow 0 18
f(2 x)+f(4)x2 is
(A) a + a + …… + a = a + a + ……. + a
0 2 18 1 3 17
(A) k (B) a + a + …….. + a is even
0 2 18
(B) 2k (C) a + a + …….. + a is divisible by 9
0 2 18
(C) 3k (D) a + a + …….. + a is divisible by 3 but not by 9
0 2 18
(D) 4k

55. The value of [nn2+12+nn2+22+…+(1)/(2 n)] 56. Let I = ∫ _ 10 ^ 19 x 1 + x ^ x d x then
n arrow ∞
is
(A) \| I 10 ^ - 9 .
(A) nπ/4 (B) | I | 10 ^ - 7
(B) π/4 (C) | I | 10 ^ - 5
(C) π/4n (D) | I | > 10 ^ - 7
(D) π/2n

57. Let y(x) be a solution of ( 1 + x ^ 2 ) ( d y )/( d x ) + 2 58. On R , a relation ρ is defined by x p y if and only if x-y
x y - 4 x ^ 2 = 0 and y ( 0 ) = - 1 . Then y(1) is equal to is zero or irrational .Then

(A) ( 1 )/( 2 ) (A) ρ is equivalence relation

(B) ( 1 )/( 3 ) (B) ρ is reflexive but neither symmetric nor transitive

(C) ( 1 )/( 6 ) (C) ρ is reflexive & symmetric but not transitive

(D) - 1 (D) ρ is symmetric & transitive but not reflexive

59. The equation sin x(sin x + cos x) = k has real 60. The value of _ n arrow ∞ ( 1 )/( n ) \ scc ^ 2 ( π )/( 4 n
solutions, where k is a real number. Then ) + ^ 2 ( 2 π )/( 4 n ) + … … + ^ 2 ( n π )/( 4 n ) ] is

(A) 0 ≤ k ≤ 1+√(2)2 (A) _ e 2

(B) 2-√(3) ≤ k ≤ 2+√(3) (B) ( π )/( 2 )

(C) 0 ≤ k ≤ 2-√(3) (C) ( 4 )/( π )

(D) 1-√(2)2 ≤ k ≤ 1+√(2)2 (D) e

61. For any vector x the value of (x × i)2+(x × j)2+(x × k) 62. If S _ r = | array c c c 2 r & x & n ( n + 1 ) \ 6 r ^ 2 - 1
2 is equal to Where i · · k have their usual meanings. &y&n^2(2n+3)\4r^3-2nr&z&n^3(n+1)
array | then the value of Σ _ r = 1 ^ n s _ r is independent
(A) |x|2
of
(B) 2 |x|2
(A) x only
(C) 3 |x|2
(B) y only
(D) 4 |x|2
(C) n only

(D) x,y,z and n

63. In a GP. series consisting of positive terms, cach 64. Mean of n observations x , x ……… x is x . IF an
1 2 n
term is equal to the sum of next two terms. Then the observation x is replaced by x’ then the new mean is
q q
common ratio of this G.P series is
(A) x-x +x ′
q q
(A) √5 (B) (n-1) x+x ′n
q
(B) √(5)2 (C) (n-1) x-x ′n
q
(C) √(5)-12 (D) n x-x +x ′n
q q
(D) √(5)+12

65. Let α = i + j + k , β = i - j - k and y = i + - k be three 66. Let d and d be the lengths of the perpendiculars
1 2
vectors A vector δ in the plane of α and β projections on γ drawn from any point of the line 7x - 9y + 10 = 0 upon
Is 1 √( 3 ) given by the lines 3x + 4y = 5 and 12x + 5y = 7 respectively. Then

(A) - i - 3 j - 3 k (A) d , > d ,
1 2
(B) i - 3 j - 3 k (B) d , = d ,
1 2
(C) - i + 3 j + 3 k (C) d , d ,
1 2
(D) i + 3 j - 3 k (D) d , = 2d ,
1 2

67. Let A (-1. 0) and B (2,0) be two points. A point M 68. The angular points of a triangle are A ( - 1 , - 7 ) , B (
moves in the pline in such a way that ∠MBA = 2∠MAB. 5,1 ) and C ( 1,4 ) The equation of the bisector of the
Then the point M moves along angle ∠ A B C is

(A) a straight fine (A) x = 7 y + 2

(B) a parabola (B) 7 y = x + 2

(C) an ellipse (C) y = 7 x + 2

(D) a hyperbola (D) 7 x = y + 2

69. The law of motion of a body moving along a straight 70.  Without changing the direction of the the origin is to
line is x = ( 1 )/( 2 ) v t , x . x being its distance from a the point (2. 3). Then the equation x ^ 2 + y ^ 2 - 4 x - 6 y
fixed point on the line at time t and is its velocity there. + 9 = 0 changes to
Then
(A) x ^ 2 + y ^ 2 + 4 = 0
(A) acceleration f varies directly with x (B) x ^ 2 + y ^ 2 = 4
(B) acceleration f varies inversely with x (C) x ^ 2 + y ^ 2 - 8 x - 12 y + 48 = 0
(C) acceleration f is constant (D) x ^ 2 + y ^ 2 = 9
(D) acceleration f varies directly with t

71. The domain of definition: of f ( x ) = √( ( 1 - | x | )/( 2 - 72. The differential equation representing the family of
|x|)) curves y ^ 2 = 2 d ( x + √( d ) )

(A) ( - ∞ , - 1 ) ( 2 , ∞ ) (A) order 4

(B) [ - 1,1 ] ( 2 , ∞ ) ( - ∞ , - 2 ) (B) degree 2

(C) ( - ∞ , 1 ) ( 2 , ∞ ) (C) degree 3

(D) [ - 1,1 ] ( 2 , ∞ ) (D) degree 4

73. Let l _ 1 = ∫ _ 0 ^ n [ x ] d x and I _ 2 = ∫ _ 0 ^ n \ x \ d 74. Let f : R arrow R be a twice continuously
x where [ x ] and \ x \ are integral and fractional parts of differentiable function such that f ( 0 ) = f ( 1 ) - f ^ ′ ( 0 )
x and n H - \ 1 \ Then I _ 1 / l _ 2 is equal to = 0 then

(A) ( 1 )/( n - 1 ) (A) f ^ ′ ′ ( 0 ) = 0

(B) ( 1 )/( n ) (B) f ^ ′ ′ ( c ) = 0 for some c R

(C) n (C) c ≠ 0 , then f ^ ′ ′ ( c ) ≠ 0

(D) n - 1 (D) f ^ ′ ( x ) > 0 for all x ≠ 0

75. Let a, b, c be such that b(a +c) ≠ 0.

(A) any integer

(B) zero

(C) any even integer

(D) any odd integer

PHYSICS

76. ‘When the value of R in the balanced Wheatstone 77. A square conducting loop is placed near an infinitely
bridge, shown in the figure: is increased from 5 Ω to 7 Ω, long current carrying wire with one edge parallel to the
the value of S has to be increased by 3 Ω in order to wire as shown in the figure. If the current in the straight
maintain the balance. What is the initial value of S ? wire is suddenly halved, which of the following
statements will be true ? “The loop will
(A) 25 Ω

(B) 3 Ω (A) stay stationary.

(C) 5 Ω (B) move towards the wire.

(D) 7.5 Ω (C) move away from the wire.

(D) move parallel to the wire.

78. What will be the molar specific heat at constant 79. A unit negative charge with mass M resides at the
volume of an ideal gas consisting of rigid diatomic midpoint of the straight line of length 2a adjoining two
molecules ? : fixed charges of magnitude +Q cach. If it is given a very
small displacement x(x a) in a direction perpendicular to
(A) 3/2 R
the straight tine. it will
(B) 5/2 R
(A) come back to its original position and stay there
(C) R
(B) execute oscillations with (1)/(2 π) √Q2 π ε M a2
(D) 3R i
(C) fly to infinity

(D) execute oscillations with frequency on (1)/(2 π) √Q2 π ε
i
M a2

80. Temperature of an ideal gas. initially at 27°C, is 81. Two black bodies A and B have equal surface areas
raised by 6°C. The rms velocity of the gas molecules will, and are maintained at temperatures 27° C and 177° C
respectively. What will be the ratio of the thermal energy
(A) increase by nearly 2%
radiated per second by A to that by B?
(B) decrease by nearly 2%
(A) 4:9
(C) increase by nearly 1%
(B) 2:3
(D) decrease by nearly 1%
(C) 16:81

(D) 27:177

82. A positive charge Q is situated at the centre of a 83. Eleven equal point charges, all of them having a
cube. The electric flux through any face of the cube is (in charge +Q, are placed at all the hour positions of a
SI units) circular clock of radius r, except at the 10 hour position.
What is the electric field strength at the centre of the
(A) Q6 π ε
0
clock ?
(B) 4πQ
(A) Q4 π ε r2 from the centre towards the mark 10
(C) Q4 π ε 0
0
(B) Q4 π ε r2 from the mark 10 towards the centre
(D) Q6 π ε 0
2
(C) Q4 π ε r2 from the centre towards the mark 6
0
(D) Zero

84. The magnetic field due to a current in a straight wire 85. There is a small air bubble at the centre of a solid
segment of length L at a point on its perpendicular glass sphere Of radius 'r' and refractive index What Will
bisector at a distance r (r >> L) be apparent distance of the bubble from the centre of the
sphere, when viewed from outside ?
(A) decreases as 1/r

(B) decreases as 1r2 (A) r

(C) decreases as 1r3 (B) ( r )/( μ )

(D) approaches a finite limit as r -->∞ . (C) r ( 1 - ( 1 )/( μ ) )

(D) zero

86. When a semiconducting device is connected in series 87. A solid rectangular sheet has two different
with a battery and a resistance a current is found to flow coefficients of linear expansion α , and , α along its
1 1
in the circuit. If, however, the polarity of the battery is length and breadth respectively, The coefficient of
reversed practically no current flows in the circuit. The surface expansion is (for α , t 1, α t 1)
1 2
device may be
(A) a +a 2
1 2
(A) a p-type semiconductor (B) 2(α + α )
1 1
(B) a n-type semiconductor (C) 4 a α α +α
1 2 1 2
(C) an intrinsic semiconductor (D) α + α
1 1
(D) a p-n junction

88. A particle with charge q moves with velocity v in a 89. A liquid of bulk modulus k is compressed by applying
direction perpendicular to the directions of uniform an external pressure such that its density increased by
electric and magnetic fields, E and B respectively, which 0.01 %. The pressure applied on the liquid is
are mutually perpendicular to each other. Which one of
(A) k/1000
the following gives the condition for which the particle
(B) k/1000
moves undeflected in its original trajectory ?
(C) 1000 k
(A) v = E/B
(D) 0.01 k
(B) v = B/E

(C) v=√((E)/(B))

(D) v=q (B)/(E)

90. A body starts from rest, under the action of an 91. Radon-222 has a half-life of 3.8 days. If one starts
engine working at a constant power and moves along a with 0.064 kg of Radon-222, the quantity of Radon-222
straight line. The displacement S is given as a function of left after 19 days will be
time (t) as
(A) 0.002 ke
(A) S = at+bt2, a, b are constants (B) 0.062 ke
(B) S = bt2, b is a constant (C) 0.032 kg
(C) S = at3/2 a is a constant (D) 0.024 kg
(D) S = at, a is a constant

92. When the frequency of the light used is changed 93. Four equal charges of value +Q are placed at any
from 4 x 1014s-1 to 5 x 1014s-1 the angular width of the tour vertices of a regular hexagon of side By suitably
principal (central ) maximum in a single slit Fraunhofer choosing the vertices, what can be the maximum possible
diffraction pattern changes by 0.6 radian. What is the magnitude of electric field at the centre of the hexagon ?
width of the slit (assume that the experiment is
(A) Q 4 π ε _ 0 a ^ 2
performed in vacuum) ?
(B) √( 2 ) Q 4 π ε _ 0 a ^ 2
(A) 15x10-7m
(C) √( 3 ) Q 4 π ε _ 0 a ^ 2
(B) 3x10-7m
(D) 2 Q 4 π ε _ 0 a ^ 2
(C) 5x10-7m

(D) 6x10-7m

94. A point object is held above a thin equiconvex lens at 95. A current ‘I’ is flowing along an infinite, straight
its focus. The focal length is 0.1 m and the lens rests on a wire, in the positive Z-direction and the same current is
horizontal thin plane mirror. The final image will be flowing along a similar parallel wire 5 m apati, in the
formed at negative Z- direction. A point P is at a perpendicular
distance 3 m from the first wire and 4 m from the second.
(A) infinite distance above the lens.
What will be magnitude of the magnetic field B at P?
(B) 0.1 m above the center of the lens.
(A) (5)/(12)(μ I)
(C) infinite distance below the lens. 0
(B) (7)/(24)(μ I)
(D) 0.1 m below the center of the lens. 0
(C) (5)/(24)(μ I)
0
(D) (25)/(288)(μ I)
0

96. When a 60 mH inductor and a resistor are connected 97. In the circuit shown in the figure all the resistances
in series with an AC voltage source, the voltage leads the are identical and each has the value r Ω. The equivalent
current by 60°. If the inductor is replaced by a 0.5 μF resistance of the combination between the points A and B
Capacitor, the voltage lags behind the current by 30°. will remain unchanged even when the following pairs of
What is the frequency of the AC supply ? points marked in the figure are connected through a
resistance R.
(A) (1)/(2 π) × 104 Hz

(B) (1)/( π) × 104 Hz (A) 2 and 8

(C) (3)/(2 π) × 104 Hz (B) 3 and 6

(D) (1)/(2 π) × 108 Hz (C) 4 and 7

(D) 4 and 6

98. Three vectors A=a i+j+k: B=i+b j+k and C= i+j+k are 99. A block of mass 1 kg starts from rest at x = 0 and
mutually perpendicular i j and k are unit vectors along X. moves along the y-axis uader the action of a force F = kt,
Y and Z axis respectively). The respective values of a, b where t is time and k = 1 Ns-1 The distance the block will
and c are travel in 6 seconds is

(A) 0,0,0 (A) 36m

(B) yy (B) 72m

(C) 1,-1,1 (C) 108m

(D) ½, ½, ½ (D) 18m

100. The ratio of the diameter of the sun to the distance 101. A metallic loop is placed in a uniform magnetic field
between the carth and the sun is approximately 0.009, B with the plane of the loop perpendicular to B . Under
The approximate diameter of the image of the sun which condition( s) given below an emf will be induced in
formed by a concave spherical mirror of radius of the loop ? “If the loop is ........ ”
curvature 0.4m is
(A) moved along the direction of B
(A) 4.5 x 10-6 m (B) squeezed to a larger area.
(B) 4.0 x 10-6 m (C) rotated about its axis.
(C) 3.6 x 10-3 m (D) rotated about one of its diameters.
(D) 1.8 x 10-3 m

102. A proton and an electron initially at rest are 103. A block of mass m _ 2 is placed on a horizontal table
accelerated by the same potential difference. Assuming and another block of mass m _ 1 is placed on top of it. An
that a proton is 2000 times heavier than an’'electron, increasing horizontal force F = α t is exerted on the upper
what will be the relation between the de Broglie block but the lower block never moves as a result. If the
wavelength of the proton (λ ) and that of electron (λ ) ? coefficient of friction between the blocks is μ _ 1 and that
p e
between the lower block and the table is μ _ 2 , then
(A) λ =2000 λ
p e
what' is the maximum possible value of μ _ 1 / μ _ 2 ? ?
(B) λ =λ 2000
p c
(A) m _ 2 m _ 1
(C) λ =20 √(5) λ
p e
(B) 1 + m _ 2 m _ 1
(D) λ =λ 20 √(5)
p e
(C) m _ 1 m _ 2

(D) 1 + m _ 1 m _ 2

104. Consider the circuit shown in the figure where all 105. The dimension of the universal constült of
the resistances are of magnitude 1 kΩ. If the current in gravitation. G. is
the extreme right resistance X is 1 mA, the potential
(A) [ ML ^ 2 T ^ - l ]
difference between A and B is
(B) [ M ^ - 1 L ^ 3 T ^ - 2 ]
(A) 34 V
(C) [ M ^ - 1 L ^ 2 T ^ - 2 ]
(B) 21 V
(D) [ ML ^ 3 T ^ - 2 ]
(C) 68 V

(D) 55 V

106. A parallel plate capacitor in series with a resistance 107. In the circuit shown, what will be the current
of 100Ω , an inductor of 20 mH and an AC voltage source through the 6V zener ?
of variable frequency shows resonance at a frequency of
(A) 6mA, from A to B
1250/π Hz: If this capacitor is charged by a DC voltage.
(B) 2mA, from A toB
source to a voltage 25 V, what amount of charge will be
stored in each plate of the capacitor ? (C) 2mA, from B to A

(D) Zero
(A) 0.2 pC ;

(B) 2mC

(C) 0.2 mC

(D) 0.2 C

108. The de Broglie wavelength of an electron is 0.4 x 10 109. Let V , and E , be the respective speed and energy
n n
10 m when its kinetic energy is 1.0 keV. Its wavelength of an electron in the orbit of radius r,. in a hydrogen
will be 1.0 x 1010 m. when its kinetic energy is atom, as predicted by Bohr’s model, Then

(A) 0.02 keV (A) plot of E r E r function of n is a straight line of slope
n n 1 1
(B) 0.8 keV 1.

(C) 0.63 keV (B) plot of r r N N a function of n is a straight line of
n n 1 1
slope 0.
(D) 0.16 keV
(C) plot of (r r ) as a function of In (n) is a straight line of
n 1
slope 3.

(D) plot of In (r E E r \ as a function of ln(n) is a straight
n 1 n 1
line of slope 4

110. An electric current ‘I’ enters and leaves a uniform 111. Consider the circuit shown in the figure. The value
circular wire of radius r through diametrically opposite of the resistance X for which the thermal power
points. A particle carrying a charge q moves along the generated in it is practically independent of small
axis of the circular wire with speed v. What is the variation of its resistance its resistance is
magnetic force experienced by the particle when it
(A) X =R
passes through the centre of the circle ?
(B) X= R/3
(A) q v μ ia
0 (C) X =R/2
(B) q v μ i2a
0 (D) X = 2R
(C) qv μ i2 π a
0
(D) Zero

112. A particle with charge e and mass m. moving along 113. In the given circuit, the binary inputs at A and B are
the X-axis with a uniform speed u. enters a region where both 1 in one case and both 0 in the next case. The
a uniform electric field E is acting along the Y-axis. The respective outputs at Y in these two cases will be :
particle starts to move in a parabola, Its focal length
(A) 1,1
(neglecting any effect of gravity) is
(B) 0,0
(A) 2 m u2c E
(C) 0,1
(B) c E2 m u2
(D) 1,0
(C) mu/2cE

(D) m u2c E

114. The magnets of two suspended coil galvanometers 115. Two monochromatic coherent light beams A and B
are of the same strength so that they produce identical have intensities L and L/4 respectively, If these beams
uniform magnetic fields in the region of the coils. The coil are superposed. the maximum and minimum intensities
of the first one is in the shape of a square of side a and will be
that of the second one is circular of radius a /√π . When
(A) 9L/4, L/4
the same current is passed through the coils, the ratio of
(B) 5L/4, 0
the torque experienced by the first coil to that
experienced by the second one is (C) 5L/2, 0

(D) 2L, L/2
(A) 1: 1√(π)

(B) 1 : 1

(C) π : 1

(D) 1 : π

CHEMISTRY

116. Oxidation of allyl alcohol ‘with a péracid gives a 117. If electrolysis of aqueous CuSO solution is carried
4
compound of molecular formula C H O , which contains out using Cu-electrodes, the reaction taking place at the
3 6 2
an asymmetric carbon atom. The structure of the anode is
compound is
(A) H+ + e --> H
(A) (B) Cu2+(aq) + 2e --> Cu (s)
(B) (C) SO 2--(aq)- 2e --> SO
4 4
(C) (D) Cu(s) + 2e --> Cu (aq)
2+
(D)

118. One of the products of the following reaction is P. 119. Which of the following solutions will turn violet
when a drop of lime juice is added to it ?
(A)

(B) (A) A solution of Nal

(C) (B) A solution mixture of KI and NalO
3

(D) (C) A solution mixture of Nal and KI

(D) A solution mixture of KIO , and NalO ,
3 3

120. The conformations of n-butane, commonly known as 121. The ground state magnetic property of B and C ,
2 2
eclipsed, gauche and anti-conformations can be molecules will be
interconverted by
(A) B paramagnetic and C diamagnetic
2 2
(A) rotation around C-H bond of a methyl group (B) B , diamagnetic and C paramagnetic
2 2
(B) rotation around C-H bond of a methylene group (C) Both are diamagnetic
(C) rotation around C1-C2 linkage (D) Both are paramagnetic
(D) rotation around C2-C3 linkage

122. Out of the following outer electronic configurations 123. The reaction sequence given below gives product R.
of atoms, the highest oxidation state is achieved by The structure of the product R is
which one ?
(A)
(A) ( n - 1 ) d ^ 8 n s ^ 2 (B)
(B) ( n - 1 ) d ^ 5 n s ^ 2 (C)
(C) ( n - 1 ) d ^ 3 n s ^ 2 (D)
(D) ( n - 1 ) d ^ 5 n s ^ 1

124. Which one of the following electronic arrangements 125. Which one of the following is a condensation
is absurd ? polymer ?

(A) n = 3, I=1, m=-1 (A) PVC

(B) n = 3, I=0,m=0 (B) Tenon

(C) n = 2, I=0,m=-1 (C) Dacron

(D) n = 2, 1=1,m=0 (D) Polystyrene

126. The compound, which evolves carbon dioxide on 127. The half-life period of 53I 125 is 60 days. The
treatment with aqueous solution of sodium bicarbonate radioactivity after 180 days will be
at 25°C, is Pa
(A) 25%
(A) C H (B) 12.5%
6 5
(B) CH COCl (C) 33.3%
3
(C) CH CONH (D) 3.0%
3 2
(D) CH COOC H
3 2 5

128.  ADP and ATP differ in the number of 129. CH _ 3 - C ≡ C MgBr can be prepared by the reaction
of
(A) phosphate units

(B) ribose units (A) CH _ 3 - C = C - Br with MgBr _ 2

(C) adenine base (B) CH _ 3 - C = CH with MgBr _ 2

(D) nitrogen atom (C) CH _ 3 - C ≡ CH with KBr and Mg

(D) CH _ 3 - C = ClI with CH _ 3 MgBr

130. [ X ] + dil. H _ 2 SO _ 4 arrow [ Y ] 131. For a van der Waal’s gas the term (a bv2)
Colorless,suffocating gas [ Y ] + K _ 2 Cr _ 2 O _ 7 + H _ 2 represents some
SO _ 4 arrow Green colouration of solution Then [ X ] and
(A) Pressure
[ Y ] are
(B) Energy
(A) so _ 3 ^ 2 - , sO _ 2
(C) Critical density
(B) Cl ^ - , HCl
(D) Molar mass
(C) s ^ 2 - , H _ 2 S

(D) co _ 3 ^ 2 - , co _ 2

132. The half life of C ^ 14 is 5760 years. For a 200 mg 133. During a reversible adiabatic process, the pressure
sample of C ^ 14 the time taken to change to 25 mg is of a gas is found to be proportional to the cube of its
absolute temperature. The ratio C _ p C _ v of gas is
(A) 11520 years

(B) 23040 years (A) ( 3 )/( 2 )

(C) 5760 years (B) ( 7 )/( 2 )

(D) 17280 years (C) ( 5 )/( 3 )

(D) ( 9 )/( 7 )

134. Which one of the following corresponds to a photon 135. For the reaction below the product is Q.
of highest energy ?
(A)
(A) λ = 300 nm (B)
(B) v = 3 x 10 s-1 (C)
(C) v = 30 cm-1 (D)
(D) € = 6.626 x 10-27 J

136. The melting points of (i) BeCl , (ii) CaCl , and (iii) 137. A compound formed by elements X and Y
2 2
HgCl follows the order (i) BeCl (ii) CaCl (iii) HgCl crystallizes in the cubic structure, where X atoms at the
2 2 2 2
corners Of a cube and Y atoms are at the centres of the
(A) i ii iii
body. The formula of thc compound is
(B) iii i ii
(A) XY
(C) i iii ii
(B) XY _ 2
(D) ii i iii
(C) X _ 2 Y _ 3

(D) XY _ 3

138. The correct order of reactivity 6r the addition 139. The correct order of acid strengths of benzoic acid
reaction of the following carbonyl compounds with ethyl (X), peroxybenzoic acid (Y) and p-nitrobenzoic acid (Z) is
magnesium iodide is
(A) Y > Z >X
(A) I > III > II > IV (B) Z > Y > X
(B) IV > III > II > I (C) Z > X > Y
(C) I > II > IV > II (D) Y > X > Z
(D) Π I > I I > 1 > IV

140. The total number of isomeric linear dipeptides 141. Consider the following two first order reactions
which can be synthesized from racemic alanine is occurring at 298 K with same initial concentration of A:
[1] A --> B; rate constant, k = 0.693 min-1 [2] A --> C;
(A) 1
half- life, t, = 0.693 min Choose the correct option :
½
(B) 2
(A) Reaction [1] is faster than Reaction [2].
(C) 3
(B) Reaction [1] is slower than Reaction [2].
(D) 4
(C) Both reactions proceed at the same rate.

(D) Since two different products are formed, rates can not
be compared.

142. The kinetic study of a reaction like vA —> P at 300 K 143. ADP and ATP differ in the number of
provides the following curve, where concentration is
(A) phosphate units
taken in mol dm” and time in min. Identify the correct
(B) ribose units
order-(n) and rate constant (k) :
(C) adenine base
(A) n = 0, k = 4.0 mol dm-3 min-1
(D) nitrogen atom
(B) n = 1/2, k = 2.0 mol1/2 dm-3/2min-1.

(C) n = 1, k = 8.0min-1

(D) n = 2, k=16.0 dm3mol-1min-1

144. Of the following compounds. which one is the 145. Assuming the compounds to be completely
strongest Bronsted acid in a aqueous solution dissociated in aqueous solution ,identify the pair of the
solutions that can be isotonic at the same temperature:
(A) HClO
3
(B) HClO (A) 0.01 M Urea and 0.01 M NaCl
2
(C) HOCl (B) 0.02 M NaCl and 0.01 M Na _ 2 SO _ 4

(D) HOBr (C) 0.03 M NaCl and 0.02 M MgCl _ 2

(D) 0.01 M sucrose and 0.02 M glucose

146. Here N is 147. What amount of electricity can deposit 1 mole of Al
metal at cathode when passed through molten A / Cl _ 3
(A)

(B) (A) 0.3 F

(C) (B) 1 F

(D) (C) 3 F

(D) 1 / 3 F

148. The shape of XeF - 149. Which of these species will have non-zero magnetic
5
moment ?
(A) Square pyramid

(B) Trigonal bipyramidal (A) Na+

(C) Planar (B) Mg

(D) Pentagonal bipyramid (C) F-

(D) Ar+

150. The heat of neutralization of a strong base and a 151. If aniline is treated with conc. H _ 2 SO _ 4 and
strong acid is 13.7 kcal. The heat released when 0.6 mole heated at 200 ^ ° C the product is
HCI solution is added to 0.25 mole of NaOH is
(A) Anilinium sulphate
(A) 3.425 kcal (B) m-Aminobenzenesulphonic acid
(B) 8.22 kcal (C) Benzenesulphonic acid
(C) 11.645 kcal (D) Sulphanilic acid
(D) 13.7 kcal

152. Which of the following sets of quantum numbers 153. The species P,Q,R and S respectively are
represents the 19th electron of Cr(Z= 24)?
(A) ethene, ethyne, ethanal, ethane
(A) (4, 1, -1, + 1/2) (B) ethane, ethyne, ethanal. ethene
(B) (4, 0, 0, + 1/2) (C) ethane, ethyne, ethanal. ethanol
(C) (3, 2, 0, -1/2) (D) ethyne, ethane, ethene, ethanal
(D) (3,2,-2, +1/2)

154. Which Of the set of oxides are arranged in the 155. The number of possible organobromine compounds
proper order of basic, amphoteric, acidic ? which can be obtained in the allylic bromination Of 1-
butene with N — bromosuccinimide is
(A) SO _ 2 , P _ 2 O _ 5 , CO

(B) BaO , Al _ 2 O _ 3 , SO _ 2 (A) 1

(C) CaO , SiO _ 2 , Al _ 2 O _ 3 (B) 2

(D) CO _ 2 , A l _ 2 O _ 3 , CO (C) 3

(D) 4

ANSWER KEY

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

155. (D)