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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 – x^{2 }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:

t_{5} + t_{6 }= 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 + x^{2})^{n }= a_{0} + a_{1} x +.....+ a_{2n} x^{2n} , then the value of a_{0} + a_{2} + a_{4} + ....... + a_{2n} is

Solution:

x = 1

QUESTION: 16

If α,β be the roots of the quadratic equation x^{2} + x + 1 = 0 then the equation whose roots are α^{19} , β^{7} is

Solution:

Roots are ω,ω2

Let α = ω,β = ω^{2}

α ^{19 }= ω,β^{7 }= ω^{2 }

∴ Equation remains same i.e. x^{2} + x+ 1 = 0

QUESTION: 17

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

Solution:

x^{2} - 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:

c^{2} = a^{2 }+ b^{2}

QUESTION: 25

Sum of n terms of the following series 1^{3 }+ 3^{3} + 5^{3} + 7^{3} + ........ 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 t_{1} and t_{2} be the parameters of the end points of a focal chord for the parabola y^{2} = 4ax, then which one is true?

Solution:

t_{1}t_{2} = -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 y^{2} = x and y =|x| is

Solution:

y^{2 }= 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^{2 }+ Bt + C where A, B, C are constants and v is velocity of a particle, then the value of 4Ax–v^{2} is

Solution:

x = At^{2} + 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^{4 } - Kt^{3} . 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) e^{x} 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) = e^{0} 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 = x^{2 }– 3x + 2 where the tangent is perpendicular to the straight line y = x are

Solution:

y = x^{2 }– 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:

100p^{2} – 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 = 4x^{2} ......... (i)

QUESTION: 75

The equation of normal of x^{2} + y^{2} – 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 ax^{2} + bx + c = 0, where a ≠ 0, then which one is true ?

Solution:

QUESTION: 80

The value of