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Detailed Solution for WBJEE Mathematics Sample Paper II - Question 1

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 2

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 3

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

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 4

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 5

WBJEE Mathematics Sample Paper II - Question 6

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 6

One value of x = 0

*Multiple options can be correct

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 7

|A| = – 1 + 8 = 7

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 8

WBJEE Mathematics Sample Paper II - Question 9

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 9

WBJEE Mathematics Sample Paper II - Question 10

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 10

Vowels : O, I, E

No. of Odd place : 4

No of ways

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 11

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 12

t_{5} + t_{6 }= 0

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 13

∴ divisible by 7

WBJEE Mathematics Sample Paper II - Question 14

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 14

Total terms = 60

Sum of first 30 terms

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 15

x = 1

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 16

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

WBJEE Mathematics Sample Paper II - Question 17

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 17

x^{2} - 2√3x 22 = 0

∴ Roots are irrational, real, unequl.

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 18

Hence no solution

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 19

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 20

WBJEE Mathematics Sample Paper II - Question 21

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 21

A = getting even no on 1st dice

B = getting sum 8

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 22

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 23

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 24

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

WBJEE Mathematics Sample Paper II - Question 25

Sum of n terms of the following series 1^{3 }+ 3^{3} + 5^{3} + 7^{3} + ........ is

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 25

∑ (2n - 1)^{3}

WBJEE Mathematics Sample Paper II - Question 26

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 26

√ab = 10 ⇒ ab 100

a + b = 25

So a = 5, b = 20

WBJEE Mathematics Sample Paper II - Question 27

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 27

WBJEE Mathematics Sample Paper II - Question 28

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 28

2B = A + C

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 29

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 30

WBJEE Mathematics Sample Paper II - Question 31

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 31

2 sin 4θ cos 2θ + sin 4θ = 0

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 32

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 33

WBJEE Mathematics Sample Paper II - Question 34

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 34

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 35

| x | + | y |= 1

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 36

WBJEE Mathematics Sample Paper II - 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?

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 37

t_{1}t_{2} = -1 Fact

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 38

WBJEE Mathematics Sample Paper II - Question 39

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 39

WBJEE Mathematics Sample Paper II - Question 40

The area of the region bounded by y^{2} = x and y =|x| is

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 40

y^{2 }= x

WBJEE Mathematics Sample Paper II - 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?

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 41

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 42

x = At^{2} + Bt + c

WBJEE Mathematics Sample Paper II - Question 43

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 43

= 4x (x – 1) (x – 2)

∴ x is decreasing for x∈ (1, 2)

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 44

WBJEE Mathematics Sample Paper II - Question 45

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 45

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 46

⇒ f(x) is decreasing for x < 0, increasing for x > 0

∴ Minimum is at x = 0 ∴f(0) = e^{0} 1

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 47

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 48

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 49

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 50

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 51

WBJEE Mathematics Sample Paper II - Question 52

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 52

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 53

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 54

T-log & Differentiate

WBJEE Mathematics Sample Paper II - Question 55

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 55

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 56

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 57

∵ sec is an even function

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 58

LHL = -1 RHL = 1

Limit does not exist

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 59

y = x^{2 }– 3x + 2

∴ Point is (1,0)

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 60

WBJEE Mathematics Sample Paper II - Question 61

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 61

a < 0, b < 0

WBJEE Mathematics Sample Paper II - 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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 62

f'(3) 1

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 63

100p^{2} – 20p + 1 =

WBJEE Mathematics Sample Paper II - Question 64

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 64

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 65

WBJEE Mathematics Sample Paper II - Question 66

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 66

WBJEE Mathematics Sample Paper II - Question 67

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 67

y = xc

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 68

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 69

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 70

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 71

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 72

WBJEE Mathematics Sample Paper II - Question 73

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 73

WBJEE Mathematics Sample Paper II - Question 74

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 74

y = 4x^{2} ......... (i)

WBJEE Mathematics Sample Paper II - Question 75

The equation of normal of x^{2} + y^{2} – 2x + 4y – 5 = 0 at (2, 1) is

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 75

0(1, – 2) A (2, 1)

WBJEE Mathematics Sample Paper II - Question 76

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 76

A(3q, 0) B (0, 3p) C (11)

Slope = 1 AC = 5 log BC

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 77

y = tan60ºx, y = – tan60ºx

y = 1, equilateral

WBJEE Mathematics Sample Paper II - Question 78

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

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 78

y = 1, x = 1

WBJEE Mathematics Sample Paper II - Question 79

In a triangle PQR, are roots of ax^{2} + bx + c = 0, where a ≠ 0, then which one is true ?

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 79

Detailed Solution for WBJEE Mathematics Sample Paper II - Question 80