# WBJEE Maths Test - 6

## 75 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests | WBJEE Maths Test - 6

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Attempt WBJEE Maths Test - 6 | 75 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

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QUESTION: 2

Solution:
QUESTION: 3

### If in the expansion of (1 + x)20, the coefficients of rth and (r + 4)th terms are equal, then r is

Solution:
QUESTION: 4

The coordinates of the point from which equal tangents are drawn to the circle x2+y2=1, x2+y2+8x+15=0 and x2+y2+10y+24=0 are

Solution:
QUESTION: 5

Circles x2+y2+2gx+2fy=0 and x2+y2+2g'x+2f'y=0 touch externally, if

Solution:
QUESTION: 6

(1 − ω + ω2)7 + (1 + ω − ω2)7 =

Solution:
QUESTION: 7
The area bounded by the curve y=sinx, y=0, x=0 and x=(π/2) is
Solution:
QUESTION: 8

If a ≠ 6, b, c satisfy = 0 then abc =

Solution:
QUESTION: 9
The reciprocal of 3+√7i is
Solution:
QUESTION: 10

Solution:
QUESTION: 11

is equal to

Solution:
QUESTION: 12

Solution:
QUESTION: 13

The differential equation dy/dx+sin 2y=x3cos2y is reduced to linear from dv/dx+Pv=Q where P and Q are function of x alone, by changing the variable as :

Solution:
QUESTION: 14

The roots of the equation = 0 are

Solution:

QUESTION: 15

The eccentricity of the ellipse 9x2 + 5y2 − 30y = 0 is

Solution:
QUESTION: 16

The derivative of is

Solution:
QUESTION: 17

If f (x)   = (x − x0) φ (x) and φ (x) is continuous at x = x0 , then f ′(x) 0 is equal to

Solution:
QUESTION: 18

The solution of differential equation

Solution:
QUESTION: 19

The sum of distances of any point on the ellipse 3x2 + 4y2 = 24 from its foci is

Solution:
QUESTION: 20

The locus of the middle points of chords of the hyperbola 3x2 − 2y2 + 4x − 6y = 0 parallel to y = 2x is

Solution:
QUESTION: 21

The eccentricity of the conic 9x2 - 16y= 144 is

Solution:
QUESTION: 22

If f(x) = x3 + 4x2 + λx + 1 is a monotonically decreasing function of x in the largest possible interval (- 2, -2/3) then

Solution:

QUESTION: 23

If cos⁻1x+cos⁻1y+cos⁻1z = 3π then xy + yz + zx is equal to

Solution:
QUESTION: 24

The maximum area of the rectangle that can be inscribed in a circle of radius r is

Solution:
QUESTION: 25

If |z₁|=|z₂| and amp. z₁+amp.z₂=0, then

Solution:
QUESTION: 26

Solution:

L=lim(n->∞) n(13+23+…….n3)2/12+22+…..n2)3=?

Prerequisite r. rΣn =13+23+…..n3=n2(n+1)2/4

r=1Σn r2=12+22+…..n2=n[(n+1)(2n+1)]/6

L=lim(n->∞) n[(n2(n+1)2)]/[(n+1)(2n+1)/6]3

L=lim(n->∞)[n2(n+1)/2]/[(2n+1)3/27]

=(1+1/∞)/(1+1/2n∞)3 x (27/16)

=27/16

lim(n->∞) n(13+23+…….n3)2/12+22+…..n2)3=27/16

QUESTION: 27

If A and B are any 2 x 2 matrics, then det (A + B) = 0 implies

Solution:
QUESTION: 28

The parabola with directrix x + 2y − 1 = 0 and focus (1, 0) is

Solution:
QUESTION: 29

The line y=mx+c touches the parabola x2=4ay if

Solution:
QUESTION: 30
How many total words can be formed from the letters of the word INSURANCE in which vowels are always together?
Solution:
QUESTION: 31

Twelve students compete for a race. The number of ways in which first three prizes can be taken is

Solution:
QUESTION: 32
P,Q,R and S have to deliver lecture, then in how many ways can the lectures be arranged?
Solution: Total no. of ways delivering lectures = 4P4 = 4! = 24
QUESTION: 33

Card is drawn at random from a pocket of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is

Solution:
QUESTION: 34

Three letters are written to different persons, and addresses on three envelopes are also written without looking at the addresses, the probability that the letters go into right envelope is

Solution:
QUESTION: 35
For any two independent events E₁ and E₂
P{E₁∪E₂)∩(E̅₁∩E̅₂)} is
Solution:
QUESTION: 36

In ΔABC , if = 0 then B =

Solution:
QUESTION: 37

Let α, β be the roots of the quadratic equation x2 + px + p3 = 0. If (α, β) is a pt. on the parabola y2 = x, then the roots of the qudratic equation are

Solution:
QUESTION: 38

If a, b, c are distinct +ve real numbers and a2 + b2 + c2 = 1 then ab + bc + ca is

Solution:
QUESTION: 39

If f(x) and g(x) are differentiable functions for 0≤x≤1 such that f(0) = 2, g(0) = 0, f(1) = 6, g(1) = 2, then in the interval (0,1),

Solution:

Since f(x) and g(x) are differentiable in [0,1], h(x) is also differentiable in [0,1]. Hence, h(x) is also continuous in [0,1].So, all the conditions of Rolle's theorem are satisfied. Hence, there exists a point c, 0 < c < 1 for which h'(c) = 0.
∴ f ′(c) − 2 g ′ c = 0, i . e . , f ′(c) = 2 g ′(c)

QUESTION: 40

In ΔABC , if x = tan , then x + y + z in terms of x , y , z only is

Solution:
QUESTION: 41
The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is
Solution:
QUESTION: 42

The harmonic Mean of a/1 - ab and a/1 + ab is

Solution:
QUESTION: 43
For a series whose nth term is (n/x) + (y), the sum of r terms is
Solution:
QUESTION: 44
The two geometric means between 1 and 64 are
Solution:
QUESTION: 45
In Rule Method the null set is represented by
Solution:
QUESTION: 46
The relation "less than" in the set of natural numbers is
Solution:
QUESTION: 47
The equation of line passing through lines 5x-6y-1=0 and 3x+2y+5=0 and perpendicular to 3x-5y+11=0 is
Solution:
QUESTION: 48
For what value of a line x = 3, y = 4 and 4x - 3y + a = 0 are con-current.
Solution:
QUESTION: 49
If sec4θ-sec2θ=2, the general value of θ is
Solution:
QUESTION: 50
A quadratic equation whose one root is 3 + 2i is_____
Solution: Every quadratic equation has only two roots one root is 3 + 2i, second root will be its conjugate 3 - 2i.
QUESTION: 51

If the pair of lines ax2 + 2a + bxy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one sector is thrice that of another then

Solution:
QUESTION: 52

If A is the set of the divisors of the number 15, B is the set of prime number smaller than 10 and C is the set of even number smaller than 9, then A ∪ C ∩ B is the following set

Solution:
QUESTION: 53

In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement-1: The number of different ways the child can buy the six ice-creams is 10C5 .
Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6A's and 4B's in a row.

Solution:
QUESTION: 54

If then the value of K is

Solution:
QUESTION: 55

∗ is a binary operation defined on Q. Find which of the following operation is Associative.

Solution:
QUESTION: 56

If the line x cosθ + y sinθ = 2 is the equation of a transverse common tangent to the circles x2 + y2 = 16 and x2 + y2 − 6y + 20 = 0, then θ equals

Solution:
QUESTION: 57

A circle with centre at the origin and radius equal to 'a' meets the axis of x at A and B.P( α ) and Q(β) are two points on this circle so that α − β = 2γ , where γ is a constant. The locus of the point of intersection of AP and BQ is

Solution:
QUESTION: 58

The medians PS of a triangle PQR is perpendicular to PQ then the value of tan P + 2tan Q is

Solution:
QUESTION: 59

If then the maximum value of n is

Solution:
QUESTION: 60

Solution:
QUESTION: 61

Let two non-collinear unit vector â and b̂ and form an acute angle. A point P moves so that at any time t the position vector (where O is the origin) is given by â cos t + b̂ sin t. When P is farthest from origin O, let M be the length of and û be the unit vector along . Then,

Solution:
QUESTION: 62

Solution:
QUESTION: 63

The values of θ and λ for which the following equations (sinθ)x − (cosθ) y + (λ + 1)z = 0;(cosθ)x − (sinθ) y−λz=0;λx + (λ+1)y − cosθz=0 have non-trivial solution, is

Solution:
QUESTION: 64

The most general solution of 2sin x + 2cos x = are

Solution:
QUESTION: 65

If , then k is

Solution:
*Multiple options can be correct
QUESTION: 66

The extremities of the latera recta of the ellipses   having a given major axis 2a lies on

Solution:
*Multiple options can be correct
QUESTION: 67

Let A and B be two square matrices of same order that satisfy A + B = 2B and 3A + 2B = l then which of the following statements is true?

Solution:
*Multiple options can be correct
QUESTION: 68

Forthe solution(s) of

is(are)

Solution:
*Multiple options can be correct
QUESTION: 69

If ( α , α 2) lies inside the triangle formed by the lines 2x + 3y − 1 = 0, x + 2y − 3 = 0, 5x − 6y − 1 = 0, then:

Solution:
*Multiple options can be correct
QUESTION: 70

Let f(x) = (ax + b)cosx + (cx + d)sinx and f ′ ( x ) = x sinx, ∀ x ∈ R . Then

Solution:
*Multiple options can be correct
QUESTION: 71

can be equal to

Solution:
*Multiple options can be correct
QUESTION: 72

If and x + y + z = π , then

Solution:
*Multiple options can be correct
QUESTION: 73

If z1 and z2 are fixed complex numbers, the locus of z so that

Solution:
*Multiple options can be correct
QUESTION: 74

For real x, the function will assume all real values provided

Solution:
*Multiple options can be correct
QUESTION: 75

Which of the following function is periodic?

Solution:
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