# WBJEE Maths Sample paper

Apr 14 • Engineering Sample Papers • 3372 Views • 3 Comments on WBJEE Maths Sample paper

State Govt. organize WBJEE(West Bengal Joint Entrance Examination) as a centralised test for admission of students to various private and govt. medical and engineering institutions in West Bengal.Students after their 12th can appear for this test for graduation courses.Two different tests are conducted for medical colleges and engineering colleges and there is a biology paper for medical test whereas mathematics paper for engineering test.Physics and chemistry are common to both the test.

Exam Pattern has been changed from 2012,the question paper contains only MCQ questions having same weightage as that of 2 marks short answer questions in the previous years question paper.Each paper contains 80 questions and it has been divided in to two test-1st test contains 60 MCQ questions of 1 mark each and 2nd test 20 MCQ of 2 marks each.Negative marking is also there.

WBJEE Maths Sample papers

Sample Paper:

Choose the correct one:

1)    The general solution of,  y2dx + (x2 – xy + y2)dy =0 is

a)    tan^-1 (x/y) + logy + c = 0

b)    2tan^-1 (x/y) + logx + c = 0

c)    log [y + (x2 + y2)^1/2] + logy + c = 0

d)    None of these

2)    The value of, tan9 – tan27 – tan63 + tan81 is equal to: (all values are in degree)

a)    2

b)    3

c)    4

d)    None of these

3)    If C is the reflection of A (2, 4) in x-axis and B is the reflection of C in y-axis, then |AB| is

a)    20

b)    2 x 5^1/2

c)    4 x 5^1/2

d)    4

4)    The number of solutions of, 2cos^2 (x/2) sin^2x = x^2 + 1/x^2 where x ranges between o to 90

a)    Zero

b)    1

c)    Infinite

d)    None of these

5)    The co-ordinates of the focus of the parabola described parametrically by x = 5t^2 + 2, y = 10t + 4 are

a)       (7, 4)              b)    (3, 4)                 c)    (3, –4)                  d)    (–7, 4)

6)    If a= 2 x 2^1/2 , b= 6, A= 45 then

a)    No triangle is possible

b)    One triangle is possible

c)    Two triangle is possible

d)    Either two triangle or no triangle are possible

7)    In a triangle ABC if sinAsinB= ab/c^2, then the triangle is

a)    Equilateral

b)    Isosceles

c)    Right angled⌠⌠⌠

d)    Obtuse angled

8)    If a,b,c be in gp then log a^n, log b^n, log c^n will be

a)    AP

b)    GP

c)    HP

d)    None of these

9)    If, ⌠ 2^x / (1-4^x)^1/2 dx = [k/ sin(2x)] +c then k is

a)    Log 2

b)    0.5 log 2

c)    0.5

d)    1/log 2

10)  The value of, ⌠ (x^1/2) / [(5-x)^1/2 + x^1/2] dx , when the upper and lower limits are 3 and 2 respectively,

a)    1

b)    0.5

c)    2

d)    None of these

11)  If the sum of the series 2,5,8.11,……is 60100, then n is equal to

a)    100

b)    200

c)    150

d)    250

12)  If the pth term of an AP is q and qth term is p, then rth term is-

a)    q-p+r

b)    p-q+r

c)    p+q+r

d)    p+q-r

13)  The area bounded by the curve, y^2.(2a-x) = x^3 and the line x = 2a is

a)    3πa^2 sq unit

b)    3πa^2 / 2 sq unit

c)    3πa^2 / 4 sq unit

d)    6πa^2 / 5 sq unit

14)  A positive acute angle is divided into two parts whose tangents are ½ and 1/3 . Then the angle is

a)    π/4

b)    π/5

c)    π/3

d)    π/6

15)  The smallest value of 5 cos θ + 12 is

a)      5                b) 12                c)  7                 d)  17

16)  The general solution of the differential equation,  dy/dx = e^(y+x) + e^(y-x) is

a)    e^(-y) = e^x – e^(-x) + c

b)    e^(-y) = e^(-x) – e^x + c

c)    e^(-y) = e^x + e^(-x) + c

d)    e^y = e^x + e^(-x) + c

17)  Product of any r consecutive natural numbers is always divisible by

a)     r !           b)  (r + 4) !             c) (r + 1) !               d) (r+2)!

18)  A polygon has 44 diagonals. The number of its different sides are

a)  10           b)    11            c)    12              d)   13

19)  The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90º. The eccentricity of the ellipse is

a)    1/8

b)    1/3^0.5

c)    (2/3)^0.5

d)    (1/2)^0.5

20)  The number of common terms to the two sequences 17, 21, 25, ……, 417 and 16, 21, 26, ….., 466 is:

a)    21

b)    19

c)    20

d)    91

21)  The co-efficient of x^5 in the expression of,  (1+x)^21 + (1+x)^22 + …. + (1+x)^30 is equal to:

a)    51 C 5

b)    9 C 5

c)    31 C 6 – 21 C 6

d)    30 C 5 + 20 C 5

22)  Which of the following is the integrating factor of,  xlogx.dy/dx + y = 2logx

a)    X

b)    e^x

c)    logx

d)    log(logx)

23)  What is the integrating factor of, dy/dx + ysecx = tanx

a)    Secx + tanx

b)    Log(secx + tanx)

c)    e^secx

d)    secx

24)  Angle between the lines (x^2 – y^2 – 2y – 1) = 0 is

a)    π/2

b)    π/3

c)    5π/12

d)    π/5

25)  The area bounded by the curves, x+ 2. │y│= 1 and x=0 is

a)    ¼

b)    ½

c)    1

d)    2

26)  The equation of the circle passing through (4,5) having the centre at the centre at (2,2) is

a)    x^2+ y^2+ 4x+ 4y -5=0

b)    x^2 – y^2 – 4x – 4y -5= 0

c)    x^2 + Y^2 + 4x – 13 = 0

d)    x^2+ y^2+ 4x- 4y + 5 = 0

27)  The number of common tangents to the circles x^2+y^2 = 4, and

x^2+y^2 – 6x – 8y = 24 is

a)    0

b)    1

c)    3

d)    4

28)  The value of, (3)^1/2 cosec 20 – sec 20 is equal to

a)    2

b)    1

c)    4

d)    None of these

29)  If sinx+sin^2x=1, then value of (cos^2x+cos^4x) is equal to

a)    1

b)    2

c)    1.5

d)    None of these

30)  The solution of, tan2ⱷ.tanⱷ= 1 is,

a)    π/3

b)    (6n+1)π/6

c)    (4n+1)π/ 6

d)    (2n+π)π/6

31)  For every point P (x,y,z) on the xy-plane

a)    X=0

b)    Y=0

c)    Z=0

d)    None of these

32)  Find the solution of the differential equation

dy/dx=(x^2+xy+y^2)/x^2 is

a)    1/(tanx/y) = logy + c

b)    1/ (tany/x) = logx + c

c)    1/ (tanx/y) = logx+c

d)    1 / (tany/x) = logy+c

33) If four Dice are thrown together, then the probability that the sum of the numbers appearing on them

a)    35/324

b)    5/216

c)    11/216

d)    11/432

34)  If the determinant of          a   a^2   1+a^3

b   b^2   1+b^3

c   c^2    1+c^3

is 0 then vector A= (1,a,a^2) , B= (1,b,b^2) , C= (1,c,c^3) are non-coplanar, then abc is equal to

a)    0

b)    -1

c)    1

d)    None of these

35)  1+ 2^3/2! + 3^3/3! + 4^3/4! + …………. Equals

a)    5e

b)    4e

c)    3e

d)    2e

36)  Sum of the n terms of the series, ½+3/4+7/8+15/16+……… is

a)    2^-n

b)    2^-n (n-1)

c)    2^n(n-1)+1

d)    2^-n +n – 1

37) The domain of the function f(x)= log (x-1) [ the base of the logarithm is 2x-1]

Is

a)    (1,∞)

b)    (1/2,∞)

c)    (0,∞)

d)    None of these

38) Both the roots of the given equation

(x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a) = 0 are always

a)    Positive

b)    Negative

c)    Real

d)    Imaginary

39) The argument of the complex number (13-5i)/(4-9i) is

a)    π/3

b)    π/4

c)    π/5

d)    π/6

40) In the expansion of (2x^2 – 1/x)^12 the term independent of x is

a)    8th

b)    7th

c)    9th

d)    10th

41)  The locus of the equation x^2 – y^2 = 0 is

a)    A circle

b)    A hyperbola

c)    A pair of lines

d)    A pair of lines at right angles

42)  The mid point of the line joining the common points of the line 2x-3y+8=0 and y^2=8x is

a)    (3,2)

b)    (5,6)

c)    (4,-1)

d)    (2,-3)

43)  The unit place digit in the number, 13^25 + 11^25 – 3^25 is

a)    0

b)    1

c)    2

d)    3

44)  If p=cos55 ,q=cos65 , r=cos175 then the value of 1/p + 1/q + r/pq is

a)    0

b)    -1

c)    1

d)    None of these

45) The image of the point (5,4,6) in the plane, x+y+2z-15=0 is

a)    (3,2,2)

b)    (2,3,2)

c)    (2,2,3)

d)    (-5,-4,-6)

46) The locus of the centre of the circle for which one end of a diameter is (1,1) while the other end is on the line x+y=3, is

a)    x+y=1

b)    2(x-y)=5

c)    2x+2y=5

d)    None of These

47) ⌠ (x.e^x) / (1+x)^2 dx is equal to

a)    e^x /(x+1) +c

b)    e^x (x+1) +c

c)    – e^x / (x+1)^2 +c

d)    e^x/(1+x^2) +c

48) One card is drawn at random from a pack of 52 cards. What is the probability that the card

drawn is a face card?

a)    1/13

b)    4/13

c)    1/4

d)    9/52

49) Two dice are tossed. The probability that the total score is a prime number is:

a)    1/6

b)    5/12

c)    1/2

d)    7/9

50) How many 3-digit numbers can be formed from the digits 2,3,5,6,7 and 9, which are divisible by 5 and non of the digits is repeated?

a)    5

b)    10

c)    15

d)    20