WBJEE Maths Test - 9 - JEE MCQ

# WBJEE Maths Test - 9 - JEE MCQ

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## 75 Questions MCQ Test - WBJEE Maths Test - 9

WBJEE Maths Test - 9 for JEE 2024 is part of JEE preparation. The WBJEE Maths Test - 9 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Maths Test - 9 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Maths Test - 9 below.
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WBJEE Maths Test - 9 - Question 1

### In the expansion of (1+x)(p+q) the ratio of coefficients of xp and xq is :

Detailed Solution for WBJEE Maths Test - 9 - Question 1
WBJEE Maths Test - 9 - Question 2

### If T₂/T₃ in the expansion of (a+b)n and T₃/T₄ in the expansion of (a+b)(n+3) are equal, then n=

WBJEE Maths Test - 9 - Question 3

### If 1, ω, ω2 are cube roots of unity and a + b + c = 0, then (a + bω + cω2)3 + (a + bω2 + cω)3 =

WBJEE Maths Test - 9 - Question 4

If circles x2+y2+2ax+c=0 and x2+y2+2by+c=0 touch each other, then

WBJEE Maths Test - 9 - Question 5
If the coefficient of x7 and x8 are equal in the expansion of [(2)+(x/3)]n then the value of n is :
WBJEE Maths Test - 9 - Question 6

The locus of the centre of the circle which cuts circles x2+y2+2g₁x+2f₁y+c₁=0 and x2+y2+2g₂x+2f₂y+c₂=0 orthogonally, is

WBJEE Maths Test - 9 - Question 7
If the imaginary part of [(2z+1)/(iz+1)] is -2, then the locus of z in complex plane represent.
WBJEE Maths Test - 9 - Question 8

WBJEE Maths Test - 9 - Question 9

WBJEE Maths Test - 9 - Question 10

WBJEE Maths Test - 9 - Question 11
Given 2x-y+2z=2, x-2y+z=-4, x+y+λz=4, then the value of λ such that the given system of equation has no solution, is :
WBJEE Maths Test - 9 - Question 12

Detailed Solution for WBJEE Maths Test - 9 - Question 12

WBJEE Maths Test - 9 - Question 13

Detailed Solution for WBJEE Maths Test - 9 - Question 13

WBJEE Maths Test - 9 - Question 14

The solution of differential equation (dy/dx)=[(x(2logx+1))/(siny+ycosy)] is

WBJEE Maths Test - 9 - Question 15

The differential equation corresponding to the family of curves y=c(x-c)2, where c is a constant, is :

WBJEE Maths Test - 9 - Question 16

If f(x)=logx2log(x), then at x=e, f'(x)=

WBJEE Maths Test - 9 - Question 17

(d/dx)[cos⁻1((x-x⁻1)/(x+x⁻1))]=

WBJEE Maths Test - 9 - Question 18

The latus rectum of an ellipse is 1/3 of the major axis. It's eccentricity is

WBJEE Maths Test - 9 - Question 19
In an ellipse the distance between its foci is 6 and its minor axis is 8. Then its eccentricity is
WBJEE Maths Test - 9 - Question 20

The foci of the hyperbola 9x2 - 16y2 = 144 are

WBJEE Maths Test - 9 - Question 21

Equation of the tangent to the hyperbola 2x2 - 3y2 = 6 which is parallel to the line y = 3x + 4 is

Detailed Solution for WBJEE Maths Test - 9 - Question 21

Given equation of hyperbola is 2x2 - 3y2 = 6
Dividing by 6 we get

Therefore equations are:
y = 3x + 5
and y = 3x - 5

WBJEE Maths Test - 9 - Question 22

In the interval (- 3,3) the function

WBJEE Maths Test - 9 - Question 23

The value of the is

WBJEE Maths Test - 9 - Question 24

sin⁻1[2x/(1+x)] = 2tan⁻1x for

WBJEE Maths Test - 9 - Question 25
A square matrix can always be expressed as a
WBJEE Maths Test - 9 - Question 26

Largest value of min (2 + x2, 6 - 3x) when x > 0 is :

WBJEE Maths Test - 9 - Question 27
The value of 0.423 is
WBJEE Maths Test - 9 - Question 28

The vertex of the parabola x2 + 8x + 12y + 4 = 0 is

WBJEE Maths Test - 9 - Question 29

The length of the latus rectum of the parabola y2 + 8x − 2y + 17 = 0 is

WBJEE Maths Test - 9 - Question 30
The number of ways in which 5 boys and 3 girls be seated in a row so that each girl is between two boys is
Detailed Solution for WBJEE Maths Test - 9 - Question 30
First boys are seated in 5 position in 5! Ways, now remaining 4 places can be filled by 4 girls in 4! Ways.
So number of ways = 5! 4! = 2880
WBJEE Maths Test - 9 - Question 31
In an examination there are three objective questions and in each question there are 4 options. The number of ways in which any candidate may not give correct answers to all questions is
WBJEE Maths Test - 9 - Question 32
The number of 3 digit odd numbers, that can be formed by using the digits 1, 2, 3, 4, 5, 6 when the repetition is allowed is
WBJEE Maths Test - 9 - Question 33

A problem in EAMCET examination is given to 3 students A, B and C whose chances of solving it are respectively. The probability that the problem will be solved is

WBJEE Maths Test - 9 - Question 34

A person puts three cards addressed to three different people in three envelopes with three different addresses without looking. What is the probability that the cards go into their respective envelopes

Detailed Solution for WBJEE Maths Test - 9 - Question 34

Number of ways the letter can be put into envelops = 3! = 6
Probability = 1/6

WBJEE Maths Test - 9 - Question 35
A person draws a card from a pack of playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail in first two times is
WBJEE Maths Test - 9 - Question 36

In a ΔABC , the correct formulae among the following are:

WBJEE Maths Test - 9 - Question 37

In a ΔABC , is equal to

Detailed Solution for WBJEE Maths Test - 9 - Question 37

WBJEE Maths Test - 9 - Question 38

If the cube roots of unity are 1, ω, ω2 then the roots of the equation(x - 1)3 + 8 = 0, are

WBJEE Maths Test - 9 - Question 39

If a, b and c are real numbers such that a2 + b2 + c2 = 1, then ab + bc + ca lies in the interval

WBJEE Maths Test - 9 - Question 40

The absiccae of the points of the curve y = x3 in the interval [-2, 2], when the slope of the tangent can be obtained by mean value theorem for the interval [-2, 2] are

Detailed Solution for WBJEE Maths Test - 9 - Question 40

Given that equation of curve y = x 3 = f x

WBJEE Maths Test - 9 - Question 41

If the sum of the first n terms of a series be 5n2 + 2n, then its second term is

WBJEE Maths Test - 9 - Question 42

If the sum of first n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term is

WBJEE Maths Test - 9 - Question 43
The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is
WBJEE Maths Test - 9 - Question 44
The sum of integers from 1 to 100 which are divisible by 2 or 5 is
WBJEE Maths Test - 9 - Question 45
If A, B and C are non-empty sets, then (A - B} ∪ (B - A) equals
WBJEE Maths Test - 9 - Question 46

If √3 + i = (a + i b) (c + i d) then tan⁻1 (b/a) + tan⁻1 (d/c) is equal to

WBJEE Maths Test - 9 - Question 47

The equation of bisectors between the lines 3x+4y-7=0 and 12x+5y+17=0 are

WBJEE Maths Test - 9 - Question 48
The line joining point (3,5) to the intersection point of lines 4x+y-1=0 and 7x-3y-35=0 is at equal distances from points (0,0) and (8,34) is the statement
WBJEE Maths Test - 9 - Question 49

The condition that one root of the equation ax2 + bx + c = 0 be reciprocal of other root is___

Detailed Solution for WBJEE Maths Test - 9 - Question 49

From given hypothesis take roots α and 1/α then

WBJEE Maths Test - 9 - Question 50
If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=
WBJEE Maths Test - 9 - Question 51

The locus of the orthocentre of the triangle formed by the lines
(1 + p)x - py + p(1 + p) = 0,
(1 + q)x - qy + q(1 + q) = 0,
and y = 0, where p ≠ q , is

WBJEE Maths Test - 9 - Question 52

Let

WBJEE Maths Test - 9 - Question 53

If l is the length of the intercept made by a common tangent to the circle x2 + y2 = 16 and the ellipse x2/25 + y2/4 = 1, on the coordinate axes, then 81l2 + 3 is equal to

WBJEE Maths Test - 9 - Question 54

equals

WBJEE Maths Test - 9 - Question 55

In a triangle ABC, let ∠C = π ∕ 2 . If r is the inradius and R is the circumradius of the triangle, then 2(r + R) is equal to

WBJEE Maths Test - 9 - Question 56

equals

WBJEE Maths Test - 9 - Question 57

The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction cosines of the vector are:

WBJEE Maths Test - 9 - Question 58

How many real solutions does the equation x7 + 14x5 + 16x3 + 30x − 560 = 0 have?

WBJEE Maths Test - 9 - Question 59

f:[1, ∞) → [2, ∞) is given by equals

WBJEE Maths Test - 9 - Question 60

Let f (x) =  then

WBJEE Maths Test - 9 - Question 61

Tangents are drawn from the point (- 1, 2) to y2 = 4x. The length of these tangents with intercept on line x = 2 is

WBJEE Maths Test - 9 - Question 62

The differential equation (x4 − 2xy2 + y4) dx − (2x2y − 4xy3 + sin y)  dy = 0 has its solution as

WBJEE Maths Test - 9 - Question 63

Let f (x) can be continuous at x = 0

WBJEE Maths Test - 9 - Question 64

A line is drawn from A( − 2, 0) to intersect the curve y2 = 4x in P and Q in the first quadrant such that then slope of the line is always

WBJEE Maths Test - 9 - Question 65

are non-coplanar non-zero vectors and is any vector in space then,
is equal to

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 66

If f(x) = x4(1-x)2, x ∈ [0,1], then which of the following is true?

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 67

If the points where a, b, c are different from 1, lie on the line lx + my + n = 0, then:

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 68

(m + 2) sin θ + 2(m − 1) cos θ = 2m + 1 , if:

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 69

Let a, b, c, d real numbers. Suppose that all the roots of the equation z4 + az3 + bz2 + cz + d = 0 are complex numbers lying on the circle |z| = 1 in the complex plane. The sum of the reciprocals of the roots is necessarily

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 70

There exist a triangle ABC satisfying the conditions,

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 71

If are any two vectors then the vector bisecting the angle between

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 72

is equal to

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 73

If a, b, c are non zero real numbers such that 3 (a2 + b2 + c2 + 1)   = 2 (a + b + c + ab + bc + ca)    , then a, b, c are in

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 74

The value of is equal to

*Multiple options can be correct
WBJEE Maths Test - 9 - Question 75

Let f (x)  = |x − 1 | − [ x ] , then

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