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Attempt WBJEE Mathematics Sample Paper III | 80 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

If C is the reflecton of A (2, 4) in x-axis and B is the reflection of C in y-axis, then |AB| is

Solution:

QUESTION: 2

The value of cos15° cos

Solution:

QUESTION: 3

The value of integral

Solution:

QUESTION: 4

The line y = 2t^{2} intersects the ellipse in real points if

Solution:

QUESTION: 5

General solution of sin x + cosx =

Solution:

QUESTION: 6

If A and B square matrices of the same order and AB = 3I, then A^{–1} is equal to

Solution:

QUESTION: 7

The co-ordinates of the focus of the parabola described parametrically by x = 5t^{2} + 2, y = 10t + 4 are

Solution:

x = 5t^{2 }+ 2 ; y = 10t + 4 ,

QUESTION: 8

For any two sets A and B, A – (A – B) equals

Solution:

QUESTION: 9

If a = 2√2 , b = 6, A = 45º, then

Solution:

a = 2√2 ;b = 6, A = 45º

QUESTION: 10

A Mapping from IN to IN is defined as follows :

f : IN o IN

f(n) = (n + 5)^{2} , n ∈ IN

(IN is the set of natural numbers). Then

Solution:

f : IN o IN ; f(n) = (n + 5)^{2}

(n_{1} + 5)^{2} = (n_{2} + 5)^{2}

⇒ (n_{1} – n_{2} ) (n_{1} + n_{2} + 10) = 0

⇒ n_{1} = n_{2} → one-to-one

There does not exist n ∈ IN such that (n + 5)^{2} = 1

Hence f is not onto

QUESTION: 11

In a triangle ABC if sin A sin then the triangle is

Solution:

QUESTION: 12

Solution:

QUESTION: 13

The value of

Solution:

QUESTION: 14

Solution:

QUESTION: 15

A positive acute angle is divided into two parts whose tangents are and . Then the angle is

Solution:

QUESTION: 16

If

Solution:

QUESTION: 17

The value of

Solution:

QUESTION: 18

Solution:

I_{1}

QUESTION: 19

The second order derivative of a sin^{3}t with respect to a cos^{3}t at

Solution:

y = a sin^{3}t ; x = a cos^{3}t

QUESTION: 20

The smallest value of 5 cos θ + 12 is

Solution:

QUESTION: 21

The general solution of the differential equation

Solution:

QUESTION: 22

Product of any r consecutive natural numbers is always divisible by

Solution:

(n + 1) (n + 2) ......... (n + r)

QUESTION: 23

The integrating factor of the differential equation is given by

Solution:

QUESTION: 24

If x^{2} + y^{2} = 1 then

Solution:

2x + 2yy' = 0

x + yy' = 0

QUESTION: 25

If c_{0} , c_{1} , c_{2} , ..................., c_{n} denote the co-efficients in the expansion of (1 + x)^{n} then the value of c_{1} + 2c_{2} + 3c_{3} + ..... + nc_{n} is

Solution:

QUESTION: 26

A polygon has 44 diagonals. The number of its sides is

Solution:

''C_{2} – n = 44

n(n – 3) = 88

n(n – 3) = 11 × 8

n = 11

QUESTION: 27

If α,β be the roots of x^{2} – a(x – 1) + b = 0, then the value of

Solution:

x^{2} – ax = a + 3 αβ = a + b

QUESTION: 28

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90º. The eccentricity of the ellipse is

Solution:

QUESTION: 29

The order of the differential equation

Solution:

QUESTION: 30

The sum of all real roots of the equation |x – 2|^{2} + |x – 2| – 2 = 0

Solution:

Put 1x – 21 = y

y^{2} + y – 2 = 0

(y – 1) (y + 2) = 0

y = 1 y = – 2 (Not possible)

| x – 2 | = 1

x – 2 = ± 1

x = 2 ± 1

x = 3, 1

Sum = 4

QUESTION: 31

then the value of

Solution:

QUESTION: 32

For each n∈ N, 2^{3n} – 1 is divisible by

where N is a set of natural numbers

Solution:

QUESTION: 33

The Rolle’s theorem is applicable in the interval for the function

Solution:

f(x) = x^{2 }and f(1) = f(–1) for f(x) = |x| but at x = 0, f(x) = |x| is not differentiable hence (B) is the correct option

QUESTION: 34

The distance covered by a particle in t seconds is given by x = 3 + 8t – 4t^{2} . After 1 second velocity will be

Solution:

t = 1, v = 8 – 8 = 0

QUESTION: 35

If the co-efficients of x^{2} and x^{3} in the expansion of (3 + ax)^{9 }be same, then the value of ‘a’ is

Solution:

QUESTION: 36

The value of

Solution:

: log_{12}3 + log_{12}4 = log_{12}12 = 1

QUESTION: 37

If x = loga bc, y = logbca, z = logcab, then the value of

Solution:

1 + x = log_{a}a + log_{a}bc = log_{a}abc

QUESTION: 38

Using binomial theorem, the value of (0.999)^{3} correct to 3 decimal places is

Solution:

= 1 – .003 + 3 (.000001) – (.000000001) = 0.997

QUESTION: 39

If the rate of increase of the radius of a circle is 5 cm/.sec., then the rate of increase of its area, when the radius is 20 cm, will be

Solution:

= 200π

QUESTION: 40

The quadratic equation whose roots are three times the roots of 3ax^{2} + 3bx + c = 0 is

Solution:

QUESTION: 41

Angle between y^{2} = x and x^{2} = y at the origin is

Solution:

Angle between axes (since co-ordinate axes are the tangents for the given curve).

QUESTION: 42

In triangle ABC, a = 2, b = 3 and then B is equal to

Solution:

QUESTION: 43

is equal to

Solution:

Period of function is 1

QUESTION: 44

The coefficient of x^{n} , where n is any positive integer, in the expansion of is

Solution:

QUESTION: 45

The circles x^{2} + y^{2} – 10x + 16 = 0 and x^{2} + y^{2} = a^{2} intersect at two distinct points if

Solution:

QUESTION: 46

Solution:

QUESTION: 47

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is

Solution:

x + y = 4

QUESTION: 48

Simplest form of

Solution:

QUESTION: 49

then the value of

Solution:

QUESTION: 50

If three positive real numbers a, b, c are in A.P. and abc = 4 then minimum possible value of b is

Solution:

(b - d) b (b + d) = 4

(b^{2} – d^{2} ) b = 4

b^{3} = 4 + d^{2 }b

QUESTION: 51

If when (0 < θ < S), then the values of θ are :

Solution:

QUESTION: 52

For any complex number z, the minimum value of | z | + | z – 1 | is

Solution:

QUESTION: 53

For the two circles x^{2} + y^{2} = 16 and x^{2} + y^{2} – 2y = 0 there is / are

Solution:

C_{1} (0, 0) r_{1 }= 4

C_{2} (0, 1)

QUESTION: 54

If C is a point on the line segment joining A (–3, 4) and B (2, 1) such that AC = 2BC, then the coordinate of C is

Solution:

QUESTION: 55

If a, b, c are real, then both the roots of the equation (x – b) (x – c) + (x – c) (x – a) + (x – a) (x – b) = 0 are always

Solution: