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WBJEE Maths Test - 7 - JEE MCQ


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75 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests 2024 - WBJEE Maths Test - 7

WBJEE Maths Test - 7 for JEE 2024 is part of WBJEE Sample Papers, Section Wise & Full Mock Tests 2024 preparation. The WBJEE Maths Test - 7 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Maths Test - 7 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Maths Test - 7 below.
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WBJEE Maths Test - 7 - Question 1

To expand (1+2x)⁻1/2 as an infinite series, the range of x should be

WBJEE Maths Test - 7 - Question 2

The sum of the coefficients in the expansion of (1+x-3x2)3148 is

WBJEE Maths Test - 7 - Question 3

The coefficient of x4 in the expansion of (1+x+x2+x3)11 is

WBJEE Maths Test - 7 - Question 4

WBJEE Maths Test - 7 - Question 5

The value of k for which the circles x2 + y2 -3x + ky - 5 = 0 and 4x2 + 4y2 - 12x - y - 9 = 0 becomes concentric is

WBJEE Maths Test - 7 - Question 6
If 2x-4y-9=0 and 6x-12y+7=0 are tangents to a circle, its radius is
WBJEE Maths Test - 7 - Question 7
The amplitude of sin(π/5) + i(1 - cos(π/5))is
WBJEE Maths Test - 7 - Question 8

(1 − i)6 + (1 − i)3 =

WBJEE Maths Test - 7 - Question 9

WBJEE Maths Test - 7 - Question 10

WBJEE Maths Test - 7 - Question 11
If the system of equations x - ky - z = 0, kx - y - x = 0, x + y - z = 0 has a non-zero solution, then the possible values of k are
WBJEE Maths Test - 7 - Question 12

The solution of differential equation (dy/dx)=x2+sin3x is

WBJEE Maths Test - 7 - Question 13

If f x = A sin then what is the value of B ?

WBJEE Maths Test - 7 - Question 14

The order and degree of the differential equation d2y/dx2 + (dy/dx)1/3 + x1=0 are respectively

WBJEE Maths Test - 7 - Question 15

If a + b + c = 0 and  then x =

Detailed Solution for WBJEE Maths Test - 7 - Question 15



⇒ x = a + b + c or 1(bc - bx - cx + x2 - a2) - c (c - x - a) + b (a - b + x) = 0
⇒ x = 0 or x2 + bc - bx - cx - a2 - c2 + cx + ac + ab - b2 + bx = 0
⇒ x = 0 or x2 = a2 + b2 + c2 - ab - bc - ca = a2 + b2 + c2 - (a2 + b2 c2)

WBJEE Maths Test - 7 - Question 16
If f(x)=logx(logx), the value of f'(x) at x=c is
WBJEE Maths Test - 7 - Question 17

Pole of the line 2x + 3y + 4 = 0 w.r.t the ellipse   is

WBJEE Maths Test - 7 - Question 18

If y=sin((1+x2)/(1-x2)), (dy/dx)=

WBJEE Maths Test - 7 - Question 19

The locus of the point of intersection of the perpendicular tangents to the ellipse is

WBJEE Maths Test - 7 - Question 20
The eccentricity of the hyperbola 9x2 - 16y2 + 72x - 32y - 16 = 0 is
WBJEE Maths Test - 7 - Question 21

The equation of the conic with focus at (1, -1), directrix along x - y + 1 = 0 and with eccentricity √2 is

WBJEE Maths Test - 7 - Question 22

Let f be a differentiable function such that,
f ′(x) If f(x) is increasing for all values of x then

WBJEE Maths Test - 7 - Question 23
For a square matrix A, it is given that AA' = I, then A is a
WBJEE Maths Test - 7 - Question 24

WBJEE Maths Test - 7 - Question 25

What is the value of

WBJEE Maths Test - 7 - Question 26
The max value of the function sinx(1+cosx) is
WBJEE Maths Test - 7 - Question 27
Multiplication of a complex number z by i corresponds to (z ≠ o)
WBJEE Maths Test - 7 - Question 28
If the normal to the parabola y2 = 4x at P(1, 2) meets the parabola again in Q, then Q =
WBJEE Maths Test - 7 - Question 29

The focus of the parabola x2-8x+2y+7=0 is

WBJEE Maths Test - 7 - Question 30
A group of 7 is to be formed from 6 boys and 4 girls. In many ways can this be done if the boys are in majority?
WBJEE Maths Test - 7 - Question 31
The number of lines joining 8 points on a circle is
WBJEE Maths Test - 7 - Question 32

All letters of the word EAMCET can be written in all possible ways. In how many ways can the letters of the word EAMCET be arranged so that two vowels are never together.

Detailed Solution for WBJEE Maths Test - 7 - Question 32

* M * C * T *
In places of *, E, A, E can be filled
No. of ways of filling M, C, T = 3! = 6
No. of ways of filling x by vowels

WBJEE Maths Test - 7 - Question 33
The chance of throwing a total of 7 or 12 with 2 dice, is
WBJEE Maths Test - 7 - Question 34

The probability of two events A and B are 0.25 and 0.40 respectively. The probability that both A and B occur is 0.15 . The probability that neither A nor B occurs is

WBJEE Maths Test - 7 - Question 35

The probability of getting a number between 1 and 100 which is divisible by one and itself only is

WBJEE Maths Test - 7 - Question 36

If a = 4, b = 3, angle A = 60º, then c is the root of the equation

WBJEE Maths Test - 7 - Question 37

If to form a ΔABC it is given that a=5, b=7, sinA= , then possible triangles are

Detailed Solution for WBJEE Maths Test - 7 - Question 37

Thus is this case no triangle in possible

WBJEE Maths Test - 7 - Question 38

The maximum value of (x-p)2+(x-q)2+(x-r)2 will be at x is equal to

WBJEE Maths Test - 7 - Question 39
The equation sin x + x cos x = 0 has at least one root in the interval
Detailed Solution for WBJEE Maths Test - 7 - Question 39
sin x + x cos x d x = cos x + x cos x d x = cos x + { x sin x sin x d x }
= cos x + x sin x + cos x = x sin x .
Now , x sin x = 0 has two roots x = 0, π .
its derived equation sin x + x cos x = 0 has a root lying between 0 and π
WBJEE Maths Test - 7 - Question 40

If the product of the roots of the equation ax2+ 6x + α2 + 1 = 0 is -2 then α equals

WBJEE Maths Test - 7 - Question 41

The fourth, seventh and tenth terms of a G.P. are p, q and r respectively, then

WBJEE Maths Test - 7 - Question 42

If log 2,log (2x - 1),log (2x + 3) are in A.P.Then x is equal to

WBJEE Maths Test - 7 - Question 43
99th term of the series 2 + 7 + 14 + 23 + 34 ...is
WBJEE Maths Test - 7 - Question 44

The equation of perpendicular bisector of a line passing through the points (7,4) and (-1,-2) is

Detailed Solution for WBJEE Maths Test - 7 - Question 44


WBJEE Maths Test - 7 - Question 45

If f : R → R is given by f (x) = |x| and A = {x ∈ R : x < 0}, then f⁻1(A) equals

WBJEE Maths Test - 7 - Question 46

Which of the following functions is not periodic?

WBJEE Maths Test - 7 - Question 47
Sum of infinite number of terms in G.P. is 20 and sum of their squares is 100. the common ratio of G.P is
WBJEE Maths Test - 7 - Question 48
Angle between the lines y-2x=9 and x+2y=-7 is
WBJEE Maths Test - 7 - Question 49
A quadratic equation whose one root is 3 + 2i is_____
Detailed Solution for WBJEE Maths Test - 7 - Question 49
Every quadratic equation has only two roots one root is 3 + 2i, second root will be its conjugate 3 - 2i.
WBJEE Maths Test - 7 - Question 50

If x ∈ (−π , π)    such that y = 1 + |cosx| + |cos2x| + |cos3x| + … and 8y = 64, then y =

WBJEE Maths Test - 7 - Question 51

The number of functions f from the set A = {0, 1, 2} in to the set B = {0, 1, 2, 3, 4, 5, 6, 7} such that f(i) ≤ f(j) for i < j and i, j ∈ A is

WBJEE Maths Test - 7 - Question 52

Let the tangent to the curve at any point on it cut the axes OX and OY at P and Q respectively. Then OP + OQ equals

WBJEE Maths Test - 7 - Question 53

The value of tan 20º + 2 tan 50º − tan 70º is:

WBJEE Maths Test - 7 - Question 54

In an acute angled triangle ABC, the least value of sec A + sec B + sec C is

WBJEE Maths Test - 7 - Question 55

Let A = N x N, and let ' ∗ ' be a binary operation on A defined by (a,b) ∗ (c,d) = (ad+bc,bd) for all (a,b), (c,d) ∈ N x N. Then find identity element in A.

WBJEE Maths Test - 7 - Question 56

ABC is a triangle, the point P is on side BC such that , the point Q is on the line . The ratio in which the line joining the common point R of   and the point C divides is:

WBJEE Maths Test - 7 - Question 57

If the solution set for f (x) < 3 is (0 , ∞) and the solution set for f (x) > − 2 is  (−∞ , 5), then the true solution set for (f (x))2  ≥ f (x) + 6 , is

WBJEE Maths Test - 7 - Question 58

Let P(3, 2, 6) be a point in space and Q be a point on the line

Then the value of μ for which the vector is parallel to the plane x - 4y+3z = 1 is

WBJEE Maths Test - 7 - Question 59

If tan (π cos θ) = cot (π sin θ) , then the value(s) of cos is/are

WBJEE Maths Test - 7 - Question 60

Let f (x) = min(x, x2), for every real number x then,

WBJEE Maths Test - 7 - Question 61

Tangents are drawn to a unit circle with centre at (0, 0) from each point on the line 2x + y = 4, then the locus of mid-points of chord of contact is

WBJEE Maths Test - 7 - Question 62

There are N boxes, each containing at most r balls. If the number of boxes containing at least i balls is Ni for i = 1, 2, ....r, then the total number of balls contained in these N boxes is

WBJEE Maths Test - 7 - Question 63

Two of the lines represented by x3 − 6x2y + 3xy2 + dy3 = 0 are perpendicular for

WBJEE Maths Test - 7 - Question 64

If 0º < θ < 180º then  

WBJEE Maths Test - 7 - Question 65

Statement-1 :
Statement-2 :

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 66

Let α ∈ and cos =  (sin 54º − cos 72º) , then the value of α must be

WBJEE Maths Test - 7 - Question 67

Let A(z1), B(z2), C(z3) be the vertices of a triangle in the Argand plane. then which of the following statements is correct?

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 68

is possible, if

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 69

If M ans N are two events, the pobability that exactly one of them occurs is

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 70

The equation of the line which divides the distance between the lines x - y - 7 = 0 and x - y + 3 = 0 in the ratio of 3 : 2 can be

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 71

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 72

The range of values of 'a' such that angle θ between the pair of tangents drawn from (a, 0) to the circle x2 + y2 = 1 satisfies π/2 < θ < π , lies in

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 73

The equation represents an ellipse if a ∈

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 74

The tangents drawn from (0, 0) to x2 + y2 + 2fy + 2gx + c = 0 are perpendicular if (where c = g2)

*Multiple options can be correct
WBJEE Maths Test - 7 - Question 75

If 8 sin θ + 7 cos θ = 8 , then the value of 7 sin θ − 8 cos θ is equal to

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