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# WBJEE Maths Test - 12

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

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Attempt WBJEE Maths Test - 12 | 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

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QUESTION: 3

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

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QUESTION: 4

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

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QUESTION: 5
The locus of the point of intersection of two perpendicular tangents to a circle is called
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QUESTION: 6
Complex numbers z₁,z₂ and z₃ in A.P.
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QUESTION: 7

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QUESTION: 8
If w = z/[z-(1/3i)] and |w| = 1,then z lies on
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QUESTION: 9

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QUESTION: 10

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QUESTION: 11

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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
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QUESTION: 13

If a, b, c are different and

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QUESTION: 14
The solution of differential equation (dy/dx)=[((1+x)y)/((y-1)x)] is
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QUESTION: 15

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

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QUESTION: 16
If y=(1+x1/4)(1+x1/2)(1-x1/4), (dy/dx)=
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QUESTION: 17

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

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QUESTION: 18

The centre of the ellipse

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QUESTION: 19

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

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QUESTION: 20

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

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QUESTION: 21
The eccentricity of hyperbola is
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QUESTION: 22

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

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QUESTION: 23

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QUESTION: 24
For a square matrix A, it is given that AA' = I, then A is a
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QUESTION: 25
The maximum value of x-x is
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QUESTION: 26

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

Solution:

Consider the function

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
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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

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QUESTION: 29

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?

Solution:

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

QUESTION: 30
In how many ways can a book or more than one book be chosen from 6 books?
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QUESTION: 31

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

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QUESTION: 32
The number of five digits telephone numbers having atleast one of their digits repeated is
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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 ?

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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
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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,

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QUESTION: 36

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

Solution:

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.

QUESTION: 37

In Δ A B C , r

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QUESTION: 38

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

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QUESTION: 39

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

Solution:
QUESTION: 40

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

Then, value of f'(4) is

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QUESTION: 41
If a, b, c of a triangle are in A.P., then cot C/2 =
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QUESTION: 42
7th term of an A.P. is 40.Then the sum of first 13 terms is
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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

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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
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QUESTION: 45

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

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QUESTION: 46

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

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QUESTION: 47

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

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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
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QUESTION: 49
The set of values of x for which [(tan3x-tan2x)/(1+tan3xtan2x)]=1, is
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QUESTION: 50

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

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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 $\left(A\cup C\right)\cap B$ is the following set
Solution:
QUESTION: 52
When 730 is divided by 5, then remainder is
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QUESTION: 53

The sum to infinity of the series

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QUESTION: 54

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

Solution:
QUESTION: 55

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

Solution:
QUESTION: 56

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

Solution:
QUESTION: 57

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

Solution:
QUESTION: 58

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

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QUESTION: 59

The shortest distance between the lines

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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:

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QUESTION: 61

Two of the lines represented by are perpendicular for

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QUESTION: 62

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

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QUESTION: 63

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

Solution:
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

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QUESTION: 65

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*Multiple options can be correct
QUESTION: 66

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

Solution:
*Multiple options can be correct
QUESTION: 67

The value of

Solution:
*Multiple options can be correct
QUESTION: 68

Let f(x) then for all x

Solution:
*Multiple options can be correct
QUESTION: 69

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

Solution:
*Multiple options can be correct
QUESTION: 70

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

Solution:
*Multiple options can be correct
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

Solution:
*Multiple options can be correct
QUESTION: 72

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

Solution:
*Multiple options can be correct
QUESTION: 73

Solution:
*Multiple options can be correct
QUESTION: 74

If has the value equal to

Solution:
*Multiple options can be correct
QUESTION: 75

is possible, if

Solution:
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