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July 3rd, 2014, 01:30 PM
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Re: West Bengal Joint Entrance Examination for admission to Master of Computer Application papers

As you want to get the West Bengal Joint Entrance Examination for admission to Master of Computer Application papers so here is the information of the same for you:

Q.1) If ( ) 32 3
53 5
x fx x x
+ ⎛ ⎞ = ≠ ⎜ ⎟ − ⎝ ⎠, then which one of the following is correct?
(a) ( ) ( ) 1 f x fx = (b) ( ) ( ) 1 f x fx = −
(c) ( )( ) fof x x = − (d) ( ) ( ) 1 1
19 f x fx − = −

Q.2) The population of a country doubles in 50 years. Assuming that the rate of increase of population
is proportional to the number of inhabitants, in how many years would the population become
three times?
(a) 3 50
2
In
In (b) 2 50
3
In
In
(c) 50 In 6 (d) 75

Q.3) Which one of the following represents the differential equation of all parabolas having the axes of
symmetry coincident with the axis of x?
(a)
2 2
2 0 d y dy y
dx dx
⎛ ⎞ + = ⎜ ⎟ ⎝ ⎠ (b)
2 3 2
3 2 0 dy dy y
dx dx
⎛ ⎞
+⎜ ⎟ =
⎝ ⎠

(c)
2 2
2 0 dy d y y
dx dx
⎛ ⎞
+ = ⎜ ⎟ ⎝ ⎠
(d)
2 3
3 0 dy d y y
dx dx
⎛ ⎞
+⎜ ⎟ =
⎝ ⎠


Q.4) Which one of the following definite integrals represents the area included between the parabola 4y
= 3x
2
and the straight line 2y = 3x + 12?
(a)
4 2
2
3
4
x dx

∫ (b)
4
2
0
3 12 3
2 4
x x dx ⎛ ⎞ + − ⎜ ⎟ ⎝ ⎠ ∫
(c)
4
2
2
3 12 3
2 4
x x dx

⎛ ⎞ + − ⎜ ⎟ ⎝ ⎠ ∫ (d)
2
2
2
3 12 3
2 4
x x dx

⎛ ⎞ + − ⎜ ⎟ ⎝ ⎠ ∫

Q.5) What is the value of
( ) 4 4
0
cos x dx x x
π
π − ∫ ?
(a) zero (b) π
(c) 4
π (d) 2
π

Q.6) What is the value of
100
0
sin x dx
π
∫ ?
(a) 100 π (b) 100
(c) 200 (d) 200 π

Q.7) What is the integration of ( )1
3 3
4
x x
x
− ? (a)
4
3
2
3 1 1
8 c x
⎛ ⎞ − + ⎜ ⎟ ⎝ ⎠ (b)
4
3
2
3 1 1
8 c x
⎛ ⎞ − − + ⎜ ⎟ ⎝ ⎠
(c)
4
3
2
1 1 1
8 c x
⎛ ⎞ − + ⎜ ⎟ ⎝ ⎠ (d) ( )1
3 3
4
x x c x
− +

Q.8) What is the integration of x e ?
(a) ( ) 1 x ex c − + (b) 2 1 ( ) x ex c − +
(c) 2 1 ( ) x ex c + + (d) x e c +

Q.9) Which one of the following equations represents the differential equation of circles, with centres
on the x-axis and all passing through the origin?
(a)
2 2
2
dy x y
dx xy
+ = (b)
2 2
2
dy x y
dx xy
− =
(c)
2 2
2
dy y x
dx xy
− = (d) dy x
dx y = −

Q.10) What is the degree of the differential equation
2
3 2 3
3 2 3 5 40 d y d y dy
dx dx dx
⎛ ⎞ ⎜ ⎟ − + +=
⎝ ⎠
?
(a) 3 (b) 2
3

(c) 2 (d) 6

Q.11) If ( ) 1
1
x n
mI = In x dx ∫ satisfies the relation ( ) 1 1 m
m m I x In x I = − − , then which one of the following is
correct?
(a) I = m - 1 (b) I = m
(c) I = m + 1 (d) I = m2
+ 1

Q.12) What is the integration of e
x In
a
e
x
?
(a) (ae)
x
(b) ( )
( )
x
ae
In ae
(c) ( ) 1
x e
+ In a (d) ( )
x e
In a

Q.13) If abc
rrr are three mutually perpendicular vectors each of magnitude unity, then what is the
magnitude of abc + +
r r r ?
(a) 3 (b) 1
(c) 3 (d) 1
3


Q.14) For what value of k, the points with position vectors 60 3 , 40 8 ˆˆˆˆ i ji j + − and ki j ˆ ˆ −52 collinear?
(a) k = 40 (b) k = -40
(c) k = -30 (d) k = 20
Q.15) If a b,
r r and c
r
are three vectors of which every pair is non-collinear and if the vector a b +
r r and
b c +
r r are collinear with the vectors c
r
and a
r
respectively, then which one of the following is
correct?
(a) abc + +
rrr is a null vector.
(b) abc + +
rrr is a unit vector
(c) abc + +
rrr is a vector of magnitude 2 units
(d) abc + +
rrr is a vector of magnitude 3 units

Q.16) If a b ab = +−=1 r r rr , then what is the angle between vectors a
r
and b
r
?
(a) 6
π (b) 3
π
(c) 2
π (d) 4
π

Q.17) What is the area of the parallelogram having diagonal ˆ ˆ ˆ a ij k +3 2 + − r and ˆ ˆ ˆ bi j k = − + 3 4 r ?
(a) 5 2 square units (b) 4 3 square units
(c) 5 3 square units (d) 10 3 square units

Q.18) If ˆˆ ˆ ˆ a i jb j k =+ = − , 2 r r and r a b ar b a b ×=× ×=× , r r r rr r r r then what is the value of r
r
r
r ?
(a) ( ) ˆ ˆ ˆ 3
11
i jk + −
(b) ( ) ˆ ˆ ˆ 3
11
i jk − +
(c) ( ) ˆ ˆ ˆ 3
11
i jk + +
(d) ( ) ˆ ˆ ˆ 3
11
i jk − −

Q.19) Which one of the following vectors represents the unit vector parallel to the YZ plane and
perpendicular to the vector ˆ ˆ ˆ 34 2 i jk + − ?
(a) ( ) ˆ ˆ ˆ 2
6
− +− i jk
(b) ( ) ˆ ˆ 2
5
j k +
(c) ( ) ˆ ˆ
2
j k +
(d) ( ) ˆ ˆ ˆ 239
94
i jk + +

Q.20) In an experiment, two variables X and Y are observed on some units. It was recorded that σx = 2σy.
Which one of the following statements is correct?
(a) The regression coefficient of Y on X is four times the regression coefficient of X on Y.
(b) The regression coefficient of Y on X is equal to the regression coefficient of X on Y.
(c) The regression coefficient of X on Y is four times the regression coefficient of Y on X.
(d) The value of correlation coefficient exceeds unity?

Q.21) An electric device consists of two bulbs A and B. From previous testing procedure, the following
results are known:
P[A is fused] = 0.20;
P[B is fused alone] = 0.15;
P[A and B are fused] = 0.15
What is the probability that bulb A is fused alone?
(a) 0.15 (b) 0.20
(c) 0.05 (d) 0.25

Q.22) Which one of the following statistical measures cannot be determined graphically?
(a) Median (b) Mode
(c) Harmonic Mean (d) Arithmetic Mean

Q.23) The following relative frequency distribution shows the distribution of 50 members of a country
social programme according to their age:
Age (in years) Relative frequency
30-39 0.02
40-49 0.06
50-59 0.16
60-69 0.32
70-79 0.20
80-89 0.16
90-99 0.08

What is the number of members who are older than 50?
(a) 4 (b) 8
(c) 46 (d) 16

Q.24) Match List I with List II and select the correct answer using the codes given below the lists:
List I List II
A. Average shoe size 1. Geometric Mean
B. Average speed for equal distances covered 2. Harmonic Mean
C. Average speed for equal times spent 3. Arithmetic Mean
D. Average rate of population growth 4. Mode

Codes :
A B C D
(a) 1 2 3 4
(b) 1 3 2 4
(c) 4 2 3 1
(d) 4 2 1 3

Q.25) If the variates are independent, then which one of the following is correct?
(a) The covariance is negative (b) The covariance is positive
(c) The covariance is zero (d) The covariance cannot be calculated

Q.26) What is the value of 10 10 10
111 log 1 log 1 log 1 234
+−+ …upto 198 terms?
(a) 100 (b) 10
(c) 2 (d) 0

Q.27) If i = −1, what is the value of i ?
(a) 1
2
−i
(b) 1
2
+i

(c) 2
2
+i
(d) 2
2
−i


Q.28) If the two quadratic equation x
2
– bc + c = 0 and x
2
– b’x + c’ = 0 have a common root, what is the
value of the common root? (a) '
'
b b
c c

− (b) '
'
c c
b b


(c) '
'
b b
c c

− (d) '
'
c c
b b



Q.29) What is the sum of numbers lying between 107 and 253, which are divisible by 5?
(a) 5220 (b) 5210
(c) 5200 (d) 5000

Q.30) A man on top of a rock rising on a sea-shore observes a boat coming towards it. If it takes 10
minutes for the angle of depression to change from 300
to 600
, how soon will the boat reach the
shore?
(a) 20 minutes (b) 15 minutes
(c) 10 minutes (d) 5 minutes

Q.31) If x = cos2
θ + sec2
θ, then which one of the following is correct?
(a) x = 2 (b) x < 2
(c) x > 2 (d) x > 2

Q.32) If 24 sin
25
θ = and 0 0 90 o < < θ , then what is the value of sin
2
⎛ ⎞ θ
⎜ ⎟ ⎝ ⎠ ?
(a) 12
25 (b) 7
25
(c) 3
5
(d) 4
5


Q.33) If tan θ + sec θ = 4, then what is the value of sin θ?
(a) 15
18 (b) 8
15
(c) 15
17 (d) 3
5


Q.34) In a triangle ABC, b2
= c
2
+ a2
, then what is the value of tan A + tan C?
(a) tan B (b) tan A – tan C
(c) b
ac (d)
2 b
ac

Q.35) M and G are two matrices such that
1 2 3 123
1 2 3 123
1 2 3 1 23
mmm q q q
M n n n and M G n r r
pp p pps
⎡ ⎤ ⎡⎤
⎢ ⎥ ⎢⎥ = −=
⎣ ⎦ ⎣⎦

What type of matrix G is?
(a) Null matrix (b) Scalar matrix
(c) Lower triangle matrix (d) Upper triangle matrix

Q.36) There are three matrices , ElF f ij ij = = ⎡⎤ ⎡ ⎤ ⎣⎦ ⎣ ⎦ andG gij = ⎡ ⎤ ⎣ ⎦such that EF = G. The element gup of the
matrix G is zero. Which one of the following conclusions is correct?
(a) All elements of uth column of the matrix E are zero.
(b) All elements of uth column of the matrix F are zero.
(c) All elements of uth row of the matrix F are zero. (d) All elements of uth row of the matrix E are zero.

Q.37) If , ,
222
α β γ are the angles which a line makes with positive x, y, z axes respectively, what is the
value of cos α + cos β + cos γ?
(a) 1 (b) -1
(c) 2 (d) 3

Q.38) An equilateral triangle is inscribed in a parabola y
2
= x whose one vertex is the vertex is the vertex
of the parabola. What is the length of side of the triangle?
(a) 3 units (b) 2 3 units
(c) 3 3 units (d) 1 unit

Q.39) The lines 5x – 12y – 5 = 0 and 10x + 24y + 3 = 0 are tangents to the same circle. What is the
diameter of the circle?
(a) 1 unit (b) 5 units
(c) 8 units (d) ½ unit

Q.40) What is the difference of the focal distance of any point on the hyperbola?
(a) Eccentricity (b) Distance between foci
(c) Length of transverse axis (d) Length of semi-transverse axis

Q.41) What is the radius of the sphere if the sphere 2 22 ax y z bxy x c +222 4 0 + + + += passes through
origin where a, b, c are constants?
(a) 1 unit (b) 2 units
(c) c units (d) cannot be determined as the values of a, b, c are not given

Q.42) Which one of the following points is on the line of intersection of the planes x = 3z – 4, y = 2z – 3?
(a) (4, 3, 0) (b) (-3, -4, 0)
(c) (3, 2, 1) (d) (-4, -3, 0)

Q.43) ABC is a triangle and AD is the median. If the coordinates of A are (4, 7, 8) and the coordinates of
the centroid of triangle ABC are (1, 1, 1), what are the coordinates of D?
(a) 1 ,2,11
2
⎛ ⎞
−⎜ ⎟ ⎝ ⎠ (b) 1 11 , 2,
2 2
⎛ ⎞
− − ⎜ ⎟ ⎝ ⎠
(c) (-1, 2, 11) (d) (-5, -11, 19)

Q.44) If the points (5, -1, 1), (-1, -3, 4) and (1, -6, 10) are the three vertices of a rhombus taken in order,
then which one of the following is the fourth vertex?
(a) (7, -4, 11) (b) 7 11 3, , 2 2
⎛ ⎞ − ⎜ ⎟ ⎝ ⎠
(c) (7, -4, 7) (d) (7, 4, 11)

Q.45) What is the area of the triangle whose vertices are (0, 0, 0), (3, 4, 0) and (3, 4, 6)?
(a) 12 square units (b) 15 square units
(c) 30 square units (d) 36 square units

Q.46) What is the shortest distance from the point (2, -7) to the circle 2 2 xy x y +− − − = 14 10 151 0?
(a) 2 units (b) 3 units
(c) 5 units (d) 7 units
Q.47) P, Q, R, S are the middle points of the respective sides of a quadrilateral EFGH and vectors
proportional to and along the sides SR, SP, QP, QR are acting. Which one of the following is
correct?
(a) Resultant vector is a unit vector.
(b) Resultant vector is a null vector.
(c) Resultant vector is a vector whose magnitude is greater than unity.
(d) Resultant vector is neither a unit vector nor a null vector.

Q.48) A vector v
r
of magnitude 4 units is equally inclined to the vectors ˆ ˆˆ ˆ ˆ ˆ i j j kk i + , , + + . Which one of
the following is correct?
(a) ( ) 4 ˆ ˆ ˆ
3 v i jk = −−
r (b) ( ) 4 ˆ ˆ ˆ
3 v i jk = + − r
(c) ( ) 4 ˆ ˆ ˆ
3 v i jk = ++
r (d) ( ) ˆ ˆ ˆ v i jk = 4 + + r

Q.49) If a = − ( ) 1,2, 3 r andb = − ( ) 3, 1, 2 r then which one of the following vectors is perpendicular to a b +
r r
?
(a) 2a b−
r r (b) 2a b +
r r

(c) a b +2 r r (d) a b−
r r


Q.50) How many unit vectors are perpendicular to both the vectors ˆ ˆ ˆ 23 4 i jk + + and ˆ ˆ ˆ i jk − + 2 3 ?
(a) 1 (b) 2
(c) zero (d) ∞

Q.51) Three dice are rolled. What is the probability of getting different faces?
(a) 1
3
(b) 1
4

(c) 5
9
(d) 4
9


Q.52) If the correlation coefficient between X and Y is 0.7, what is the correlation coefficient between
U X = + 4 3and 3 4
2
Y V − = ?
(a) 0.6 (b) 0.7
(c) 0.8 (d) 1

Q.53) If in 6 trials, X is a binomial variate which follows the relation 9P(X = 4) = P(X = 2), then what is
the probability of success?
(a) 3
4
(b) 1
4

(c) 3
8 (d) 1
8

Q.54) Ten numbered bails are placed in an urn. Balls numbered 1 to 4 are red and rest of the 6 balls are
blue. The probability of drawing the ball numbered 3, of course, is 0.1. A ball is drawn and it is
red. Which one of the following statements is correct?
(a) P(ball drawn is numbered 3 | ball drawn is red) > 0.1
(b) P(ball drawn is numbered 3 | ball drawn is red) = 0.1
(c) P(ball drawn is numbered 3 | ball drawn is red) < 0.1
(d) P(ball drawn is red | ball drawn is numbered 3) = 0.25
Directions : The following 6 (six) items consist of two statements, one labeled as the ‘Assertion (A)’ and the
other as ‘Reason (R)’. You are to examine these two statements carefully and select the answers to these
items using the codes given below:
(a) Both A and R are individually true and R is the correct explanation of A.
(b) Both A and R are individually 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.

Q.55) Assertion (A) : lim lim .lim , 1. n n
n nn nx n x where x →∞ →∞ →∞ ≠ <
Reason (R) : lim lim .lim . () () ( ) ( ) n nn f xgx f x gx →∞ →∞ →∞ =

Q.56) Assertion (A) : Mean deviation can never be negative.
Reason (R) : Mean deviation is the A.M. of absolute deviation of the different values from a
central tendency.

Q.57) Assertion (A) : There is no practical difference between frequency polygon and frequency
curve.
Reason (R) : Under frequency polygon the points are joined by straight lines whereas under
frequency curve the points are joined by a smooth curve.

Q.58) Assertion (A) : If f(x) = x and ( ) 2 x F x x = , then F(x) = f(x) always.
Reason (R) : At x = 0, F(x) is not defined.

Q.59) Assertion (A) : Perimeter of a regular pentagon inscribed in a circle with centre O and radius x
cm equals 12x sin 360
cm.
Reason (R) : Perimeter of a regular polygon inscribed in a circle with centre O and radius x
cm equals 2nx sin (3600
/2n) cm, if it is n-sided, where n > 3.

Q.60) Assertion (A) : Four consecutive numbers which are not prime are uniquely given by 122, 123,
124, 125.
Reason (R) : Every composite number is divisible by a prime less than its square root.


ANSWER KEYS
1. (a) 2. (a) 3. (a) 4. (c) 5. (a) 6. (b) 7. (b) 8. (b) 9. (c) 10. (c) 11. (b) 12. (b) 13. (c) 14. (b) 15. (a) 16. (b) 17. (c) 18. (a) 19. (b) 20. (a) 21. (b) 22. (c) 23. (c) 24. (c) 25. (c) 26. (c) 27. (b) 28. (b) 29. (a) 30. (b) 31. (d) 32. (c) 33. (c) 34. (d) 35. (b) 36. (d) 37. (b) 38. (b) 39. (d) 40. (c) 41. (b) 42. (d) 43. (b) 44. (c) 45. (b) 46. (b) 47. (b) 48. (c) 49. (d) 50. (b) 51. (c) 52. (b) 53. (b) 54. (b) 55. (d) 56. (b) 57. (a) 58. (d) 59. (a) 60. (c)

Q.1) Suppose A represents the symbol 1, B represents the symbol 0, C represents the symbol 1, D
represents the symbol 0 and so on. If we divide INDIA by AGRA, then which one of the
following is the remainder in Binary Representation?
(a) (1101)2 (b) (101)2
(c) (11)2 (d) (110)2

Q.2) How many number of digits are there in 298? (Given that log102 = 0.30103)
(a) 98 (b) 99
(c) 30 (d) 29

Q.3) What is the area of the triangle on the Argand diagram formed by the complex number z, -iz,
z – iz?
(a) | z |
2
(b) 2| z |
2

(c)
2
2
z (d)
2
4
z

Q.4) In a quadratic equation, with leading coefficient 1. Sheela reads the coefficient 16 of x wrongly as
19 and obtains the roots as -15 and -4. Which of the following are the correct roots of the
equation?
(a) 8, 8 (b) 6, 10
(c) -6, -10 (d) 12, 5

Q.5) Out of 40 children 30 can swim, 27 can play chess and only 5 can do neither. How many children
can swim only?
(a) 30 (b) 22
(c) 12 (d) 8

Q.6) Both the roots of a quadratic equation x
2
– mx + 121 = 0 are greater than 10. What is the minimum
value of m?
(a) 21 (b) 22
(c) 23 (d) Cannot be determined

Q.7) What is the simplified representation of(A' ' ∩∩ ∪ ∩ ∩ B C BCAC ) ( )( ) where A, B, C are subsets
of set X?
(a) A (b) B
(c) C (d) X ∩ ∪∪ (ABC)

Q.8) Which one of the following is the domain of the relation R defined on the set N of natural numbers
as
R mn m n mn N = += ∈ { } ( ) , :2 3 30; , ?
(a) {2, 4, 6, 8} (b) {3, 7, 11, 15}
(c) {3, 6, 9, 12} (d) {3, 6, 9, 12, 15}

Q.9) How many terms are there in the expansion of ( )10
x+ +y z ?
(a) 11 (b) 33
(c) 66 (d) 310
Q.10) Which one of the following is correct?
(a) The relation R0 defined on the set of Real number as R0 = {(a, b such that a2 + b2 = 1 for all
a, b ∈ R} is an equivalence relation.
(b) The relation R0 defined on the set of Real numbers as R0 = {(a, b) such that |a-b|}<
1
3
for all
a, b ∈ R} is an equivalence relation.
(c) The relation I0 defined on the set of integers as 2 2
102 1 12 2 III I II I :3 20 − + = for all
1 2 I ,I I ∈ is an equivalence relation.
(d) We defined AEC B by the open sentence: A is cardinally equivalent to B on the family of
sets. Then the relation EC on family of sets is an equivalence relation.

Q.11) How many arrangements can be made out of the letters of the word “MOTHER” taken four at a
time so that each arrangement contains the letter ‘M’?
(a) 240 (b) 120
(c) 60 (d) 360

Q.12) What are the value of k if the term independent of x in the expansion of
10
2
k x x
⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ is 405?
(a) +3 (b) +6
(c) +5 (d) +4

Q.13) If the equation (1) x
2
– px + q = 0 and (2) x
2
– rx + x = 0 have a root in common and the second
equation has equal roots then q + s is equal to which one of the following?
(a) 2
pr (b) 2pr
(c) pr (d) p2
r

Q.14) If the pth, qth and r
th terms of a G.P. are again in G.P., then which one of the following is correct?
(a) p, q, r are in A.P. (b) p, q, r are in G.P.
(c) p, q, r are in H.P. (d) p, q, r are neither in A.P. nor in G.P. nor in H.P.

Q.15) In how many ways can 10 lions and 6 tigers be arranged in a row so that no two tigers are
together?
(a) 11
6 10!× P (b) 10
6 10!× P
(c) 10
7 6!× P (d) 10
6 6!× P

Q.16) The Geometric Mean of two numbers is 6. Their Arithmetic Mean A and Harmonic Mean H
satisfy the equation 90A + 5H = 918.
Which one of the following is correct?
(a) A = 10 (b) A = 1/5, A = 10
(c) A = 5, A = 10 (d) A = 1/5, A = 5

Q.17) Eighteen football teams take part in the national championship and every team meets the same
opponent twice. How many matches are played during the championship?
(a) 306 (b) 300
(c) 72 (d) 153

Q.18) If x, y, z are distinct positive numbers different from 1 such that
( )( ) log .log log log .log log log .log log 0 yz x xz y xy z xx x yy y zz z − + −+ −= ( ) , which is the value
of xyz?
(a) 2 (b) 1 (c) -1 (d) 0

Q.19) Which one of the following is the union of the closed sets 1 1 2 ,10 , 1, 2,...? n n n
⎛ ⎞ ⎜ ⎟ +− = ⎝ ⎠
(a) [2, 10] (b) (2, 10)
(c) [2, 10) (d) (2, 10]

Q.20) Indicate which one of the points given below is not a part of the solution of the inequation 3x + 4y
> 12: x > 0, y > 0?
(a) (4, 2) (b) (1, 3)
(c) (2, 1) (d) 2 11 ,
3 4
⎛ ⎞ ⎜ ⎟ ⎝ ⎠

Q.21) If A is a square matrix of order m × n and k is a scalar, then adj (kA) is equal to which one of the
following?
(a) k adj A (b) k
2
adj A
(c) k
n-1 adj A (d) k
n
adj A

Q.22) For what value of k, the system of linear equations x y z x y z x y kz + += +−= + + = 2, 2 3,3 2 4
has a unique solution?
(a) k is any real number other than zero
(b) k is any real number
(c) k is any integer
(d) k = 0

Q.23) If the determinant of a non-singular matrix
111
222
333
abc
abc
abc
⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦
is denoted by Δ, what is the determinant
of the matrix
1 1 11 1
2 2 22 2
3 3 33 3
24 4
34 4
34 4
a b cb c
a b cb c
a b cb c
⎡ ⎤ + −
⎢ ⎥ + −
⎣ ⎦ + −
?
(a) Δ (b) - Δ
(c) 7 Δ (d) 4 Δ

Q.24) What is the value of the determinant
2
2
2
1
1
1
a a bc
b b ca
c c ab



?
(a) abc (b) ab + bc + ca
(c) 0 (d) (a – b) (b – c) (c – a)

Q.25) If A is non-singular matrix of order n × m, then which one of the following is equal to |adj A|?
(a) | A |
n+1 (b) | A |
n

(c) | A |
n-1 (d) | A |

Q.26) If
x
M y
z
⎡ ⎤
⎢ ⎥ = ⎢ ⎥
⎢ ⎥ ⎣ ⎦
and G = [3, 4, 5] are two matrices, then which one of the following is correct?
(a) In the product matrix MG = [hij], the element h32 is 5y.
(b) In the product matrix MG = [hij], the element h32 is 3x + 4y + 5z.
(c) In the product matrix MG = [hij], the element h32 is 4z. (d) In the product matrix MG = [hij], the element h32 does not exist.

Q.27) If 0 1
0 0
A ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦
, then which one of the following is equal to ( )n
aI bA + ?
(a) n n 1 A I na bA − + (b) n n 1 a na bA − +
(c) n n 1 a I a bA − + (d) n nn aI bA +

Q.28) If A is a non-singular matrix such that 1 T A A − = , then which one of the following represents A?
(Here A’ denotes the transpose of A).
(a)
122
1 21 1
3
22 1
⎡ ⎤
⎢ ⎥ − ⎢ ⎥
⎢ ⎥ ⎣ ⎦ − −
(b)
122
1 21 2
3
22 1
⎡ ⎤ ⎢ ⎥ − ⎢ ⎥ ⎢− − ⎥ ⎣ ⎦

(c)
122
1 21 1
2
22 1
⎡ ⎤
⎢ ⎥ − ⎢ ⎥
⎢ ⎥ ⎣ ⎦ − −
(d)
122
1 21 1
2
22 1
⎡ ⎤ ⎢ ⎥ − ⎢ ⎥ ⎢− − ⎥ ⎣ ⎦


Q.29) The matrix X satisfies the following equation
13 1 1
01 0 1
X ⎡⎤ ⎡ ⎤ = ⎢⎥ ⎢ ⎥ ⎣⎦ ⎣ ⎦ −
Which one of the following represents X?
(a)
1 4
1 0
⎡ ⎤
⎢ ⎥ ⎣ ⎦ − (b)
1 4
1 0
⎡ − ⎤ ⎢ ⎥ ⎣ ⎦

(c)
1 4
0 1
⎡ ⎤
⎢ ⎥ ⎣ ⎦ − (d)
1 2
0 1
⎡ − ⎤ ⎢ ⎥ ⎣ − ⎦


Q.30) The matrix
012
123
311
M
⎡ ⎤
⎢ ⎥ = ⎢ ⎥
⎢ ⎥ ⎣ ⎦
and its inverse N nij = ⎡ ⎤ ⎣ ⎦. What is the element n23 of the matrix N?
(a) 2 (b) -2
(c) 1 (d) -1

Q.31) If 111 3 sin sin sin
2 xyz −−− π ++= , then what is the value of x + y + z?
(a) -3 (b) 3
(c) 1
3
− (d) 1
3


Q.32) If 11Y = 900
, then what is the value of the expression
tan tan 2 tan 3 tan 4 tan 5 tan 6 tan 7 tan 8 tan 9 tan10 ? YYYYYYYYY Y
(a) 0 (b) -1
(c) 1 (d) 2

Q.33) If sin A = p and sin B = q where | p | and | q | are both less than 1, then what are the total number
of possible (and distinct) values of sin (A + B)?
(a) 1 (b) 2
(c) 3 (d) 4

Q.34) If 3 3 x y sin cos sin cos θ + = θ θθ and x y sin cos θ = θ , then which one of the following is correct? (a) 2 2 x y + = 0 (b) 2 2 x y + =1
(c) 2 2 x y − = 0 (d) 2 2 x y − =1

Q.35) If sin C and cos C are two roots of a quadratic equation 2 2 10 x px − + = where 0
2
C π < < , then
how many possible values can p have?
(a) 1 (b) 2
(c) 3 (d) 4

Q.36) Let n be the natural number such that n > 4 and sin cos n n U XX n = + . Which one of the
following is correct?
(a) 2 2
2 4 sin cos UU U X X nn n = − − − (b) 2 3 sin cos UU U X X nn n = − − +
(c) 2 2
4 2 sin cos UU U X X nn n = − − − (d) 2
2 4 2 sin cos U U U XX nn n =− + − −

Q.37) The three angles A, B and C of a triangle ABC are in A.P. and 2 22 c ab = + . If c = 50 metres, then
what is the area of the triangle in square metres?
(a) 625
2 (b) 625 2
2
(c) 625 3
2 (d) 625

Q.38) If ( ) 4 1
4 xy n π −= + (where n is an integer) and x + y is not an odd multiple of 2
π , then what is the
value of the following expression:
sin 2 sin 2
cos 2 cos 2
x y
x y

+
(a) -1 (b) 0
(c) 1
2
(d) 1

Q.39) From the top of a tower 60 metres high, the angle of depression of two objects which are on the
horizontal plane and in a line with the foot of the tower are α and β with β > α. What is the
distance between the two objects in metres?
(a) 60sin cosec cosec ( ) β −α αβ (b) 60cos sec sec (β −α αβ )
(c) 60 cot cot ( ) α − β (d) 60 tan tan ( β − α)

Q.40) The points (3, 4) and (2, -6) lie on opposite sides of which one of the following lines?
(a) 10x – y = 26 (b) 5x + 3y = -9
(c) 3x – 4y = 8 (d) x – y = 10

Q.41) Two equal parabolas have the same vertex and their axes are at right angles. What is the angle
between the tangents drawn to them at their point of intersection (other than vertex)?
(a) 4
π (b) tan-12
(c) 3
π (d) 1 3
tan
4
− ⎛ ⎞ ⎜ ⎟ ⎝ ⎠

Q.42) Which one of the following is the nearest point on the line3 4 25 x y − = from the origin?
(a) (-1, -7) (b) (3, -4) (c) (-5, -8) (d) (3, 4)

Q.43) Which one of the following is the reflection of the point (4, 3) on the line x + y = 0?
(a) (-4, 3) (b) (-3, -4)
(c) (-3, 4) (d) (4, -3)

Q.44) Which one of the following is the orthocenter of the triangle whose sides are x = 0, y = 1 and x + y
– 2 = 0?
(a) (1, 1) (b) (0, 1)
(c) (-1, 0) (d) (0, -1)

Q.45) What is the length of the focal distance from the point “t” of the parabola y
2
= 4ax?
(a) at2
(b) a(1 + t
2
)
(c)
2
1
a t
t
⎛ ⎞ ⎜ ⎟ + ⎝ ⎠ (d) at-2

Q.46) Which of the following are the equations of circles which touch the x-axis at a distance 3 from the
origin and intercept a distance 6 on the y-axis?
(a) 2 2 xy x y + − ± += 6 62 9 0 (b) 2 2 xy x y + + ± += 6 62 9 0
(c) 2 2 xy x y + ± + += 6 62 9 0 (d) 2 2 xy xy + ± − += 62 6 9 0

Q.47) Under what condition the lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ are
perpendicular to each other?
(a) a/a’ + c/c’ = 0 (b) aa’ + cc’ = -1
(c) a/a’ + c/c’ = 1 (d) aa’ + cc’ = 1

Q.48) What is the range of the function () ( ) 1
f x x 3 cos 2 −
= − ?
(a) 1 ,1
4
⎡ ⎤
⎢ ⎥ ⎣ ⎦ (b) 1 1,
4 2
⎛ ⎞ ⎜ ⎟ ⎝ ⎠
(c) 1 1 ,
4 2
⎡ ⎤
− − ⎢ ⎥ ⎣ ⎦ (d) 1 1,
4 2
⎡ ⎤ ⎢ ⎥ ⎣ ⎦


Q.49) Let f : R → R be defined as f(x) = x | x |. Which one of the following is correct?
(a) f is only onto (b) f is only one-one
(c) f is neither onto nor one-one (d) f is one-one and onto

Q.50) What is the value of
3
3 lim
1
x
x
x
x
+
→∞
⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ − ?
(a) e
2
(b) e
3

(c) e
4
(d) e
-4

Q.51) If x
1 lim sin x A →∞ x
⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ and x
1 lim sin x B →∞ x
⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ , then which one of the following is correct?
(a) A = 1 and B = 0 (b) A = 0 and B = 1
(c) A = 0 and B = 0 (d) A = 1 and B = 1

Q.52) What is the value of x
10 2 5 1 lim
sin
xxx
→∞ x x
−−+ ?
(a) (In 2) (In 5) (b) (In 3) (In 5)
(c) (In 10) (In 5) (d) 0
Q.53) Let f(x) = [x], where [x] denotes the greatest integer contained in x. Consider the following
statements:
1. f(x) is not onto
2. f(x) is continuous at x = 0
3. f(x) is discontinuous for all positive integral values of x.

Which of the statements given above are correct?
(a) 1 and 2 (b) 1 and 3
(c) 2 and 3 (d) 1, 2 and 3

Q.54) If( )m n m n x y xy +
+ = then what is the value of dy
dx
?
(a) x
y
(b) xy
(c) y
x
(d) 1

Q.55) For what values of ‘p’ the function ( ) 2 1 1
1
px if x f x x p if x
⎧ + ≤ = ⎨
⎩ + >
is derivable at x = 1?
(a) 1
2
(b) 2
(c) - 1
2
(d) -2

Q.56) What is the derivative of log 2x x?
(a) 1
x
(b) zero
(c) ( )
1
2x (d) 1
2


Q.57) A function f : R → R satisfies f(x + y) = f(x) f(y) for all x, y ∈ R and f(x) ≠ 0 for all x ∈ R. If f(x) is
differentiable at x = 0 and f(0) = 2 then f’(x) is equal to which one of the following?
(a) f(x) (b) - f(x)
(c) 2 f(x) (d) ( )
2
f x

Q.58) Let f(x) be a differentiable even function. Consider the following statements:
1. f’(x) is an even function.
2. f’(x) is an odd function.
3. f’(x) may be even or odd.

Which of the above statement is/are correct?
(a) 1 only (b) 2 only
(c) 1 and 3 (d) 2 and 3

Q.59) What is the derivative of |x – 1| + |x – 4 at x = 3?
(a) -3 (b) 3
(c) 0 (d) 2

Q.60) Let g(x) be the inverse of an invertible function f(x) which is differentiable at x = c. Which one of
the following is equal to g’[f(c)]? (a) f’(c) (b) ( )
1
f ' c
(c) f(c) (d) ( )
1
f c


ANSWER KEYS
1. (d)
2. (c)
3. (c)
4. (c)
5. (d)
6. (c)
7. (c)
8. (a)
9. (c)
10. (d)
11. (a)
12. (a)
13. (a)
14. (a)
15. (a)
16. (b)
17. (a)
18. (b)
19. (a)
20. (c)
21. (c)
22. (a)
23. (d)
24. (c)
25. (c)
26. (c)
27. (a)
28. (b)
29. (c)
30. (d)
31. (b)
32. (c)
33. (d)
34. (b)
35. (a)
36. (a)
37. (c)
38. (d)
39. (c)
40. (c)
41. (d)
42. (b)
43. (b)
44. (b)
45. (b)
46. (a)
47. (b)
48. (d)
49. (d)
50. (c)
51. (a)
52. (a)
53. (b)
54. (c)
55. (a)
56. (b)
57. (c)
58. (b)
59. (c)
60. (b)

Contact Details:
The West Bengal Joint Entrance Examinations Board
AQ Block,
Salt Lake City,
Kolkata,
West Bengal ‎
India

Map Location:


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