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WBJEE Maths Test - 12 - JEE MCQ


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75 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 - WBJEE Maths Test - 12

WBJEE Maths Test - 12 for JEE 2024 is part of WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 preparation. The WBJEE Maths Test - 12 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Maths Test - 12 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Maths Test - 12 below.
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WBJEE Maths Test - 12 - Question 1

If in the expansion of (1+x)20 the coefficient of rth and (r+4)th terms are equal, r=

WBJEE Maths Test - 12 - Question 2

The maximum coefficients in the expansion of (1+x)(2n+2) is :

WBJEE Maths Test - 12 - Question 3

The positive integer just greater than (1 + .0001)10000 is

WBJEE Maths Test - 12 - Question 4

The angle between the tangents drawn from (0,0) to the circle x2 + y2 + 4x - 6y + 4 = 0 is

WBJEE Maths Test - 12 - Question 5
The locus of the point of intersection of two perpendicular tangents to a circle is called
WBJEE Maths Test - 12 - Question 6
Complex numbers z₁,z₂ and z₃ in A.P.
WBJEE Maths Test - 12 - Question 7
If w = z/[z-(1/3i)] and |w| = 1,then z lies on
WBJEE Maths Test - 12 - Question 8

WBJEE Maths Test - 12 - Question 9

WBJEE Maths Test - 12 - Question 10

WBJEE Maths Test - 12 - Question 11

WBJEE Maths Test - 12 - Question 12
x + ay = 0, y + az = 0, z + ax = 0. The value of a for which the system of equations has infinitely many solutions is
WBJEE Maths Test - 12 - Question 13
The solution of differential equation (dy/dx)=[((1+x)y)/((y-1)x)] is
WBJEE Maths Test - 12 - Question 14

If a, b, c are different and

WBJEE Maths Test - 12 - Question 15

The solution of the equation cosylog(secx+tanx)dx=cosxlog(secy+tany)dy is

WBJEE Maths Test - 12 - Question 16
If y=(1+x1/4)(1+x1/2)(1-x1/4), (dy/dx)=
WBJEE Maths Test - 12 - Question 17

Let y=x2e-x, then period in which y is increasing is

WBJEE Maths Test - 12 - Question 18

The centre of the ellipse

WBJEE Maths Test - 12 - Question 19

The equation of the ellipse whose focus is at (4, 0) and whose eccentricity is 4/5 is

WBJEE Maths Test - 12 - Question 20

The line p = x cos α + y sin α. becomes tangent to x2/a2 - y2/b2 = 1 is

WBJEE Maths Test - 12 - Question 21
The eccentricity of hyperbola is
WBJEE Maths Test - 12 - Question 22

If cot⁻1[(cos α)12] - tan⁻1[(cot α)12] = x, then sin x =

WBJEE Maths Test - 12 - Question 23

WBJEE Maths Test - 12 - Question 24
For a square matrix A, it is given that AA' = I, then A is a
WBJEE Maths Test - 12 - Question 25
The maximum value of x-x is
WBJEE Maths Test - 12 - Question 26

If the equation x - sin x = k has a unique root in , , then the range of values of k are

Detailed Solution for WBJEE Maths Test - 12 - Question 26

Consider the function

WBJEE Maths Test - 12 - Question 27
Let z₁,z₂,z₃ be three vertices of an equilateral triangle circumscribing the circle |z| =1/2. If z₁=1/2+√3/2i and z₁,z₂,z₃ werein anticlockwise sense, then z₂ is
WBJEE Maths Test - 12 - Question 28

The equation of the parabola whose focus is the point (0,0) and the tangent at the vertex is x-y+1=0 is

WBJEE Maths Test - 12 - Question 29

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

WBJEE Maths Test - 12 - Question 30
The number of five digits telephone numbers having atleast one of their digits repeated is
WBJEE Maths Test - 12 - Question 31
In how many ways can a book or more than one book be chosen from 6 books?
WBJEE Maths Test - 12 - Question 32

Out of 15 students studying in a class, 7 are from Maharashtra, 5 are from karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karantaka?

Detailed Solution for WBJEE Maths Test - 12 - Question 32

No. of ways of selecting 4 students out of 15 students
= 15C4 = 15 x 14 x 13 x 12 /1 x 2 x 3 x 4 = 1365
The no of ways of selecting 4 students in which no student belongs to Karnataka = 10C4
∴ No of ways of selecting at least one student from Karnataka = 15C4 - 10C4 = 1155
∴ Required probability = 1155 1365 = 77 91 = 11 13

WBJEE Maths Test - 12 - Question 33

From a box containing 10 cards, numbered 1, 2,3,......,10. Four cards are drawn together, what is the probability of their sum is even ?

WBJEE Maths Test - 12 - Question 34
The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, then the probability that the student will miss at least one test is
WBJEE Maths Test - 12 - Question 35

A and B play 12 games of chess of which 6 are won by A. 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately is,

WBJEE Maths Test - 12 - Question 36

If b,c and sinB are given such that ∠B is acute and b<c sinB, then

Detailed Solution for WBJEE Maths Test - 12 - Question 36

When two sides and angle opposite to one of then be given. In this case, the triangle is not always uniquely determined. It is quite possible to have no triangle, one triangle and two triangles with this type of data.
So, it is called an ambiguous case.
Let b, c and B are given parts.
When B is acute and b < c sin B, then there is no triangle
By Cosine Law
b2 = c2 + a2 - 2ac cos B
⇒ a2 - 2ac cos B = b2 - c2
⇒ a2 - 2ac cos B + c2 cos2 B
= b2 - c2 + c2 cos2 B
⇒ (a - c cos B)2 = b2 - c2 (1 - cos2 B)
= b2 - c2 sin2 B

This equation helps us to determine a, when b, c and B are being given. We observe that:
When b < c sin B, then a is imaginary and so there is no solution.

WBJEE Maths Test - 12 - Question 37

In Δ A B C , r

WBJEE Maths Test - 12 - Question 38

For what value of p, the difference of the roots of the equation x2 - px + 8 = 0 is 2 ?

WBJEE Maths Test - 12 - Question 39

Let α and β be the roots of the equation x2+x+1=0, then the equation whose roots are α197 is

WBJEE Maths Test - 12 - Question 40

If f : R → R is continuous and differentiable function such that

Then, value of f'(4) is

WBJEE Maths Test - 12 - Question 41
7th term of an A.P. is 40.Then the sum of first 13 terms is
WBJEE Maths Test - 12 - Question 42
If a, b, c of a triangle are in A.P., then cot C/2 =
WBJEE Maths Test - 12 - Question 43

if A, G and H are respectively the A.M., the G.M and the H.M. between two positive numbers 'a' and 'b', then the correct relationship is

WBJEE Maths Test - 12 - Question 44
The A.M., H.M. and G.M. between two numbers are 144/15, 15 and 12, but not necessarily in this order. Then H.M., G.M. and A.M. respectively are
WBJEE Maths Test - 12 - Question 45

If x, y, z are positive real numbers, then (x3/z) < (x3 + y3 + z3)/(x + y + z) < (z3/x) if

WBJEE Maths Test - 12 - Question 46

If A = {x : x2 - 5x + 6 = 0}, B = {2, 4}, C = {4, 5} then A x (B ∩ C) is

WBJEE Maths Test - 12 - Question 47

The obtuse angle between lines y=-2 and y=x+2 is

WBJEE Maths Test - 12 - Question 48
Let x₁, x₂, x₃ and y₁, y₂, y₃ are in G.P. whose common ratio is r, then point P(x₁,y₁) , Q(x₂,y₂), R(x₃,y₃) are on
WBJEE Maths Test - 12 - Question 49
The set of values of x for which [(tan3x-tan2x)/(1+tan3xtan2x)]=1, is
WBJEE Maths Test - 12 - Question 50

The condition for the roots of the equation (c2-ab)x2-2(a2-bc)x+(b2-ac)=d are equal, is

WBJEE Maths Test - 12 - Question 51
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
WBJEE Maths Test - 12 - Question 52
When 730 is divided by 5, then remainder is
WBJEE Maths Test - 12 - Question 53

The sum to infinity of the series

WBJEE Maths Test - 12 - Question 54

The equation of the curves for which the tangent is of constant length, is

WBJEE Maths Test - 12 - Question 55

The remainder left out when 82n − (62)2n + 1 is divided by 9 is:

WBJEE Maths Test - 12 - Question 56

Let f x be an odd function in the interval with a period T, then  is

WBJEE Maths Test - 12 - Question 57

If f x = x5 − 20x3 + 240 x , then f x satisfies which of the following?

WBJEE Maths Test - 12 - Question 58

If , then value of x, y, z are respectively (where m , n , r ∈ I )

WBJEE Maths Test - 12 - Question 59

The shortest distance between the lines

WBJEE Maths Test - 12 - Question 60

The area of the region bounded by the parabola (y − 2 )2 = x − 1 , the tangent to the parabola at the point (2, 3) and the x-axis is:

WBJEE Maths Test - 12 - Question 61

Two of the lines represented by are perpendicular for

WBJEE Maths Test - 12 - Question 62

The direction ratios of two lines are a, b, c and . The lines are

WBJEE Maths Test - 12 - Question 63

Let the line lie in the plane . Then α , β equals:

WBJEE Maths Test - 12 - Question 64

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 - 12 - Question 65

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 66

A fair coin is tossed 9 times the probability that at least 5 consecutive heads occurs is

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 67

The value of

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 68

Let f(x) then for all x

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 69

If in a Δ A B C , a = 6, b = 3 and cos (A − B )= 4/ 5 then

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 70

Let f(x) is a quadratic expression with positive integral coefficients such that for every

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 71

Let d has local extrema at x = α and β such that α , β < 0, f α , f β > 0 ; Then the equation f(x)=0

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 72

The equation x2 − 6 x + 8 + λ (x2 − 4 x + 3)   = 0 , λ ∈ R has

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 73

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 74

If has the value equal to

*Multiple options can be correct
WBJEE Maths Test - 12 - Question 75

is possible, if

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