WBJEE Mathematics Sample Paper II


80 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests | WBJEE Mathematics Sample Paper II


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Attempt WBJEE Mathematics Sample Paper II | 80 questions in 120 minutes | Mock test for JEE preparation | Free important questions MCQ to study WBJEE Sample Papers, Section Wise & Full Mock Tests for JEE Exam | Download free PDF with solutions
QUESTION: 1

The value of  

Solution:

QUESTION: 2

The number of points of intersection of

Solution:

     
    

QUESTION: 3

Let R be the set of real numbers and the mapping f : R → R and g : R → R be defined by f(x) = 5 – x2 and g(x) = 3x – 4 , then the value of (fog)(–1) is

Solution:

f(g(–1)) = f(–3–4) = f(–7) = 5 – 49 = – 44

QUESTION: 4

A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5, 6} are two sets, and function f : A → B is defined by f(x) =   then the function f is

Solution:

QUESTION: 5

If the matrices   and    then AB will be

Solution:

QUESTION: 6

ω is an imaginary cube root of unity and   then one of the values of x is

Solution:


   One value of x = 0

*Multiple options can be correct
QUESTION: 7

If    then A–1 is

Solution:

|A| = – 1 + 8 = 7

QUESTION: 8

. The value of 

Solution:


QUESTION: 9

If sum of an infinite geometric series is 4/5 and its 1st term is 3/4 , then its common ratio is​

Solution:


QUESTION: 10

The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places is

Solution:

Vowels : O, I, E

No. of Odd place : 4
No of ways 

QUESTION: 11

If    then n is just greater than integer

Solution:


QUESTION: 12

If in the expansion of (a – 2b)n , the sum of the 5th and 6th term is zero, then the value of a/b is

Solution:


t5 + t6 = 0

QUESTION: 13

  will be divisible by 

Solution:



∴ divisible by 7

QUESTION: 14

Sum of the last 30 coeffivients in the expansion of (1 + x)59 , when expanded in ascending powers of x is

Solution:

Total terms = 60
Sum of first 30 terms

QUESTION: 15

If (1 – x + x2)n = a0 + a1 x +.....+ a2n x2n , then the value of a0 + a2 + a4 + ....... + a2n is

Solution:

x = 1

QUESTION: 16

If α,β be the roots of the quadratic equation x2 + x + 1 = 0 then the equation whose roots are α19 , β7 is

Solution:

Roots are ω,ω2
Let α = ω,β = ω2
α 19  = ω,β= ω2
∴ Equation remains same i.e. x2 + x+ 1 = 0

QUESTION: 17

The roots of the quadratic equation x2  - 2√3x 22 = 0 are :

Solution:

x2  - 2√3x 22 = 0


∴ Roots are irrational, real, unequl.

QUESTION: 18

The qudratic equation x2 + 15 |x| + 14 = 0 has

Solution:


Hence no solution

QUESTION: 19

  is complex conjugate of z )

Solution:


QUESTION: 20

Solution:


QUESTION: 21

. Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is

Solution:

A = getting even no on 1st dice
B = getting sum 8

QUESTION: 22

The probability that at least one of A and B occurs is 0.6 . If A and B occur simultaneously with probability 0.3, then P(A') P(B')  is

Solution:

    
   

QUESTION: 23

The value of 

Solution:

QUESTION: 24

In a right-angled triangle, the sides are a, b and c, with c as hypotenuse, and . Then the value of  will be​

Solution:

c2 = a2 + b2

QUESTION: 25

Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ is

Solution:

∑ (2n - 1)3

QUESTION: 26

G.. M. and H. M. of two numbers are 10 and 8 respectively. The numbers are :

Solution:

√ab = 10  ⇒ ab 100


a + b = 25
So a = 5, b = 20

QUESTION: 27

The value of n for which  is the geometric mean of x and y is

Solution:


QUESTION: 28

If angles A, B and C are in A.P., then   is equal to

Solution:

2B = A + C

QUESTION: 29

If    then value of 2 sinA + 4 sinB is

Solution:


QUESTION: 30

The value of 

Solution:

QUESTION: 31

If sin6θ + sin4θ + sin2θ = 0 then the general value of θ is

Solution:

2 sin 4θ cos 2θ + sin 4θ = 0

QUESTION: 32

In a ΔABC,     is equal to

Solution:




QUESTION: 33

Value of   is

Solution:



 

QUESTION: 34

The straight line 3x+y=9 divides the line segment joining the points (1,3) and (2,7) in the ratio

Solution:

QUESTION: 35

If the sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then the locus of P is

Solution:

| x | + | y |= 1

QUESTION: 36

The straight line x + y – 1 = 0 meets the circle  at A and B. Then the equation of the circle of which AB is a diameter is
 

Solution:


QUESTION: 37

If t1 and t2 be the parameters of the end points of a focal chord for the parabola y2 = 4ax, then which one is true?

Solution:

t1t2 = -1 Fact

QUESTION: 38

S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is

Solution:


QUESTION: 39

For different values of D , the locus of the point of intersection of the two straight lines    and  

Solution:


QUESTION: 40

The area of the region bounded by y2 = x and y =|x| is

Solution:

y= x

QUESTION: 41

If the displacement, velocity and acceleration of a particle at time, t be x, v and f respectively, then which one is true?

Solution:


QUESTION: 42

The displacement x of a particle at time t is given by x = At+ Bt + C where A, B, C are constants and v is velocity of a particle, then the value of 4Ax–v2 is

Solution:

x = At2 + Bt + c

QUESTION: 43

For what values of x, the function is monotone decreasing?

Solution:


= 4x (x – 1) (x – 2)

∴ x is decreasing for x∈ (1, 2)

QUESTION: 44

The displacement of a particle at time t is x, where x = t - Kt3 . If the velocity of the particle at time t = 2 is minimum, then

Solution:


QUESTION: 45

The point in the interval [0,2π], where x f(x) ex sin x has maximum slope, is

Solution:



QUESTION: 46

The minimum value of 

Solution:



⇒ f(x) is decreasing for x < 0, increasing for x > 0
∴ Minimum is at x = 0   ∴f(0) = e0 1

QUESTION: 47

Solution:

QUESTION: 48

  is equal to

Solution:

QUESTION: 49

The value of the integral  

Solution:


QUESTION: 50

The value of 

Solution:

 

QUESTION: 51

The value of 

Solution:

QUESTION: 52

In which of the following functions, Rolle’s theorem is applicable?

Solution:


QUESTION: 53

If f (5) = 7 and f'(5) 7 then   is given by

Solution:

QUESTION: 54

If   then the value of   is 
 

Solution:

T-log & Differentiate

QUESTION: 55

The value of f(0) so that the function   is continuous everywhere is  

Solution:


QUESTION: 56

 is equal to

Solution:

QUESTION: 57

The function 

Solution:


∵ sec is an even function

QUESTION: 58

Solution:

LHL = -1    RHL  = 1
Limit does not exist

QUESTION: 59

The co-ordinates of the point on the curve y = x2 – 3x + 2 where the tangent is perpendicular to the straight line y = x are

Solution:

y = x2 – 3x + 2

∴ Point is (1,0)

QUESTION: 60

The domain of the function 

Solution:


QUESTION: 61

If the line ax + by + c = 0 is a tangent to the curve xy = 4, then

Solution:



a < 0, b < 0

QUESTION: 62

If the normal to the curve y = f(x) at the point (3, 4) make an angle 3π/4 with the positive x-axis, then f'(3) is 

Solution:


f'(3) 1

QUESTION: 63

The general solution of the different equation 

Solution:

100p2 – 20p + 1 =

QUESTION: 64

If y''– 3y'+ 2y = 0 where y(0) = 1, y'(0) = 0, then the value of y at x = log, 2 is

Solution:


QUESTION: 65

The degree of the differential equation 

Solution:

QUESTION: 66

The equation of one of the curves whose slope at any point is equal to y + 2x is

Solution:


QUESTION: 67

Solution of the differential equation xdy – ydx = 0 represents a

Solution:


y = xc

QUESTION: 68

The value of the integral   xdx is

Solution:


QUESTION: 69

 is equal to

Solution:


QUESTION: 70

   then

Solution:

QUESTION: 71

The value of 

Solution:

QUESTION: 72

Solution:


QUESTION: 73

The area enclosed by y = 3x – 5, y = 0, x = 3 and x = 5 is

Solution:


QUESTION: 74

The area bounded by the parabolas  and the line y = 2 is

Solution:

y = 4x2 ......... (i)

QUESTION: 75

The equation of normal of x2 + y2 – 2x + 4y – 5 = 0 at (2, 1) is

Solution:

0(1, – 2) A (2, 1)

QUESTION: 76

If the three points (3q, 0), (0, 3p) and (1, 1) are collinear then which one is true ?

Solution:

A(3q, 0) B (0, 3p) C (11)
Slope = 1 AC = 5 log BC

QUESTION: 77

The equations  are the sides of

Solution:

y = tan60ºx, y = – tan60ºx
y = 1, equilateral

QUESTION: 78

The equations of the lines through (1, 1) and making angles of 45º with the line x + y = 0 are

Solution:


y = 1, x = 1

QUESTION: 79

In a triangle PQR,   are roots of ax2 + bx + c = 0, where a ≠ 0, then which one is true ?

Solution:


QUESTION: 80

The value of