WBJEE Maths Test - 11 - JEE MCQ

# WBJEE Maths Test - 11 - JEE MCQ

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## 75 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 - WBJEE Maths Test - 11

WBJEE Maths Test - 11 for JEE 2024 is part of WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 preparation. The WBJEE Maths Test - 11 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Maths Test - 11 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Maths Test - 11 below.
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WBJEE Maths Test - 11 - Question 1

### In the expansion of [(x)-(1/x)]6, the term independent of x is

WBJEE Maths Test - 11 - Question 2

### If (2r + 3)th and (r - 1)th terms in the expansion of (1 + x)15 have equal coefficients then r =

Detailed Solution for WBJEE Maths Test - 11 - Question 2
T2r + 3 = T2r + 2 + 1 = 15C2r + 2
Tr - 1 = Tr - 2 + 1 = 15Cr - 2
15C2r + 2 = 15Cr - 2
⇒ 2r + 2 + r - 2 = 15
⇒ r = 5
WBJEE Maths Test - 11 - Question 3

### x2 + y2 + 2(2K+3)x - 2Ky +(2K+3)2 + K2 - r2 = 0 represents the family of circles with centres on the line

WBJEE Maths Test - 11 - Question 4

If the equation [(k(x+1)2/3)]+[(y+2)2/4]=1 represents a circle, then k=

WBJEE Maths Test - 11 - Question 5
For any complex number z, the minimum value of |z| + |z - 1| is
WBJEE Maths Test - 11 - Question 6

WBJEE Maths Test - 11 - Question 7
The maximum distance from the origin to the point z satisfying z+(1/z) = 2, is
WBJEE Maths Test - 11 - Question 8

Let (1 + x)n =
C0 + C1x + C2x2 + ... + Cnxn and (C1/C0) + (2 C2/C1) + (3 C3/C2) + .... + ((n Cn)/(Cn - 1)) = (1/k)n(n + 1), then the value of k is

Detailed Solution for WBJEE Maths Test - 11 - Question 8

WBJEE Maths Test - 11 - Question 9

WBJEE Maths Test - 11 - Question 10

WBJEE Maths Test - 11 - Question 11

WBJEE Maths Test - 11 - Question 12
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 - 11 - Question 13

Detailed Solution for WBJEE Maths Test - 11 - Question 13

WBJEE Maths Test - 11 - Question 14

Solution of the differential equation tan y sec2 x dx + tan x sec2 y dy = 0 is

WBJEE Maths Test - 11 - Question 15

The solution of

Detailed Solution for WBJEE Maths Test - 11 - Question 15

Put x + y + 1 = z
⇒ 1 + dy /dx = dz /dx ⇒ dy /dx = dz /dx - 1
(x + y + 1) dy dx = 1
⇒ z( dz /dx - 1) = 1 ⇒ dz /dx = 1 + 1 z ⇒ z z + 1 dz = dx ⇒ ∫(1 - 1 z + 1 )dz = ∫dx
⇒ z - log(z + 1) = x + c ⇒ x + y + 1 = log(x + y + 2) + x + c ⇒ y = log(x + y + 2) + log c
⇒ ey = (x + y + z)c ⇒ x + y + 2 = cey

WBJEE Maths Test - 11 - Question 16
If x=a(t-sint) and y=a(1-cost), (dy/dx)=
WBJEE Maths Test - 11 - Question 17

If y=cot⁻1[(1+x)/(1-x)], (dy/dx)=

WBJEE Maths Test - 11 - Question 18

The latus rectum of the conic 3x2 + 4y2 - 6x + 8y - 5 = 0 is

WBJEE Maths Test - 11 - Question 19

If the length of the major axis of an ellipse is three times the length of its minor axis, then it's eccentricity is

WBJEE Maths Test - 11 - Question 20
The vertices of a hyperbola are (2, 0), (-2, 0) and the foci are (3, 0), (-3, 0). The equation of the hyperbola is
WBJEE Maths Test - 11 - Question 21

The eccentricity of the conic 9x2 - 16y2 = 144 is

WBJEE Maths Test - 11 - Question 22

In the interval (- 3,3) the function

WBJEE Maths Test - 11 - Question 23

WBJEE Maths Test - 11 - Question 24

The value of

WBJEE Maths Test - 11 - Question 25
If A, B are two square matrices such that AB = A and BA = B, then
WBJEE Maths Test - 11 - Question 26

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

WBJEE Maths Test - 11 - Question 27

If z2 = -i, then z =

WBJEE Maths Test - 11 - Question 28

The equation of the normal to the curve x2 = 4y at (1, 2) is

WBJEE Maths Test - 11 - Question 29

The length of the latus rectum of the parabola x2-4x-8y+12=0 is

WBJEE Maths Test - 11 - Question 30
In an election there are five candidates for three places. A man can vote for maximum number of candidates. In how many total ways can a men vote?
WBJEE Maths Test - 11 - Question 31

If nPr=840, nCr=35, then n=

Detailed Solution for WBJEE Maths Test - 11 - Question 31

WBJEE Maths Test - 11 - Question 32

Four numbers are chosen at random from {1, 2, 3, . . . , 40}. The probability that they are not consecutive is

WBJEE Maths Test - 11 - Question 33
Three mangoes and three apples are in box. If two fruits are chosen at random, the probability that one is a mango and other is an apple is
WBJEE Maths Test - 11 - Question 34

A purse contains 4 copper coins and 3 silver coins, the second purse contains 6 copper coins and 2 silver coins. A coin is taken out from any purse. The probability that it is a copper coin is

WBJEE Maths Test - 11 - Question 35
If the ratio in angles of any ∆ABC 2:3:7 then the ratio is in its sides are
WBJEE Maths Test - 11 - Question 36
If a = 2, b = 3, c = 5 in triangle ABC, then C =
WBJEE Maths Test - 11 - Question 37

If two equations x2+a2=1-2ax and x2+b2=1-2bx have only one common root, then

WBJEE Maths Test - 11 - Question 38

If 2a + 3b + 6c = 0, then at least one root of the equation ax2+bx+c = 0 lies in the interval

WBJEE Maths Test - 11 - Question 39
If $f″\left(x\right)<0\forall x\in \left(a,b\right)$, then f'(x) = 0
Detailed Solution for WBJEE Maths Test - 11 - Question 39
Suppose, there are two points x1 and x2 in (a,b) such that f'(x1) = f'(x2) = 0. By Rolle's theorem applied to f' on [x1 , x2], there must then be a c $\in$ (x1, x2 ) such that f''(c) = 0. This contradicts the given condition $f″\left(x\right)<0\forall x\in \left(a,b\right)$ . Hence, our assumption is wrong. Therefore, there can be at most one point in (a,b) at which f'(x) is zero.
WBJEE Maths Test - 11 - Question 40
If a, b, c are in A.P., then (a + 2b - c) (2b + c - a) ( c + a - b) equals
WBJEE Maths Test - 11 - Question 41
If (m + 1)th, (n + 1)th and (r + 1)th terms of an A.P. are in G.P. and m, n, r are in H.P., then ratio of the first term of the A.P. to its common diference in terms of n is
WBJEE Maths Test - 11 - Question 42

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

WBJEE Maths Test - 11 - Question 43
In a H.P.pth term is q and qth term p. Then the (pq)th term is
WBJEE Maths Test - 11 - Question 44
In Rule Method the null set is represented by
WBJEE Maths Test - 11 - Question 45
If A and B are matrices of order 2 such that A * B = (AB - BA)/2 then which of the following is false?
WBJEE Maths Test - 11 - Question 46
The opposite vertices of a square are (3,4) and (1,-1) then coordinates of rest vertices are
WBJEE Maths Test - 11 - Question 47

The equation of lines passing through the intersection of 4x-3y-1=0 and 2x-5y+3=0 which are equally inclined with axes, are

WBJEE Maths Test - 11 - Question 48

The number of roots of the equation |x|2-7|x|+12=0 is

WBJEE Maths Test - 11 - Question 49

If α , β are different values of x satisfying a cos x + b sin x = c then tan (α + β)  /2 =

WBJEE Maths Test - 11 - Question 50
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is
WBJEE Maths Test - 11 - Question 51

In how many different ways can the letters of the word DETAIL be arranged in such a way that the vowels occupy only the odd positions?

WBJEE Maths Test - 11 - Question 52

Let d 1 , d 2 , d 3 , … …, d k be all the divisors of a positive integer n including 1 and n.
Suppose d 1 + d 2 + d 3 + … … + d k = 72 , then the
value of 1 d 1 + 1 d 2 + 1 d 3 + … … + 1 d k is

WBJEE Maths Test - 11 - Question 53

For all x ∈ (0,1):

WBJEE Maths Test - 11 - Question 54

The value of tan− 1 e (i θ)is equal to

WBJEE Maths Test - 11 - Question 55

The value of cot

WBJEE Maths Test - 11 - Question 56

WBJEE Maths Test - 11 - Question 57

For a positive integer n, let

WBJEE Maths Test - 11 - Question 58

Statement-1: For every natural number
Statement-2: For every natural number

WBJEE Maths Test - 11 - Question 59

Let be two unit vectors and α the angle between them. Vector → will be a unit vector is α is equal to

WBJEE Maths Test - 11 - Question 60

The quadratic equations x2-6x+a=0 and x2-cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4:3. Then the common root is

WBJEE Maths Test - 11 - Question 61

Let be three non-zero vectors. Then if and only if

WBJEE Maths Test - 11 - Question 62

The value of p for which the function:
f

WBJEE Maths Test - 11 - Question 63

Given P x = x 4 + a x 3 + b x 2 + c x + d such that x=0 is the only real root of P ′ x = 0. If P − 1 < P 1 , then in the interval [-1, 1]:

WBJEE Maths Test - 11 - Question 64

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only, is

WBJEE Maths Test - 11 - Question 65

For which of the values of m the area of the region bounded by the curve y = x − x2 and y = mx equal 9 2 .

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 66

be a continuous function, then λ is equal to

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 67

If equals

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 68

Let a, b, c, d be real numbers such that
(a 2 + b 2 − 1 )(c 2 + d 2 − 1 )> (a c + b d − 1 )2
then which of the following statements is correct?

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 69

For a positive interger n, let

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 70

Let D be the domain of the function,

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 71

Let [x] = the greatest integer less than or equal to x. Then equation sinx = [1+sin x] +[1-cos x] has

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 72

If 1, logyx, logzy, -15logxz are in A.P., then

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 73

Let a 1, a 2, a 3, … … , a n n > 2 be real numbers such that a i = − a n − i + 1 for 1 ≤ i ≤ n and k = ∑ 1 ≤ i < j < k ≤ n ∑ ∑ x i x j x k , then which of the following is not true?

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 74

The solutions of are given by (where p = dy/dx and k is constant)

*Multiple options can be correct
WBJEE Maths Test - 11 - Question 75

If A = [ α β 0 α ] is the nth root of I2, then choose the correct statement

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