EduRev

Get the App Signup / Login

Welcome Back

Forgot Password?

New User? Sign Up

Create your account now

I accept the Terms & Conditions.

Already Have an Account? Login

WBJEE Maths Test - 7

75 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests | WBJEE Maths Test - 7

Description

Attempt WBJEE Maths Test - 7 | 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

To expand (1+2x)⁻¹/² as an infinite series, the range of x should be

A.
[-1/2,1/2]
B.
(-1/2,1/2)
C.
[-2,2]
D.
(-2,2)

Solution:

QUESTION: 2

The sum of the coefficients in the expansion of (1+x-3x²)³¹⁴⁸ is

A.
8
B.
7
C.
1
D.
-1

Solution:

QUESTION: 3

The coefficient of x⁴ in the expansion of (1+x+x²+x³)¹¹ is

A.
900
B.
909
C.
999
D.
990

Solution:

QUESTION: 4

A.
0
B.
π/2
C.
π/4
D.
π/6

Solution:

QUESTION: 5

The amplitude of sin(π/5) + i(1 - cos(π/5))is

A.
2π/5
B.
π/5
C.
π/15
D.
π/10

Solution:

QUESTION: 6

The value of k for which the circles x² + y² -3x + ky - 5 = 0 and 4x² + 4y² - 12x - y - 9 = 0 becomes concentric is

A.
1/8
B.
-1/8
C.
1/4
D.
-1/4

Solution:

QUESTION: 7

If 2x-4y-9=0 and 6x-12y+7=0 are tangents to a circle, its radius is

A.
(17/3√5)
B.
(17/6√5)
C.
(34/3√5)
D.
(34/√5)

Solution:

QUESTION: 8

(1 − i)⁶ + (1 − i)³ =

A.
2 + i
B.
2 − 10i
C.
− 2 + i
D.
− 2 − 10i

Solution:

QUESTION: 9

Solution:

QUESTION: 10

A.
π ∕ 4
B.
π ∕ 2
C.
2006 (sin x)²⁰⁰⁷
D.
none of these

Solution:

QUESTION: 11

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

A.
-1, 2
B.
1, 2
C.
0, 1
D.
-1, 1

Solution:

QUESTION: 12

The solution of differential equation (dy/dx)=x²+sin3x is

A.
y=(x³/3)+(cos3x/3)+c
B.
y=(x³/3)-(cos3x/3)+c
C.
y=(x³/3)+sin3x+c
D.
none of these

Solution:

QUESTION: 13

If f x = A sin then what is the value of B ?

A.
2 ∕ π
B.
4 ∕ π
C.
0
D.
1

Solution:

QUESTION: 14

The order and degree of the differential equation d²y/dx² + (dy/dx)¹/³ + x¹=0 are respectively

A.
2,3
B.
3,3
C.
2,6
D.
2,4

Solution:

QUESTION: 15

If a + b + c = 0 and then x =

A.
0
B.
C.
D.

Solution:

⇒ x = a + b + c or 1(bc - bx - cx + x² - a²) - c (c - x - a) + b (a - b + x) = 0
⇒ x = 0 or x² + bc - bx - cx - a² - c² + cx + ac + ab - b² + bx = 0
⇒ x = 0 or x² = a² + b² + c² - ab - bc - ca = a² + b² + c² - (a² + b² c²)

QUESTION: 16

If f(x)=log_x(logx), the value of f'(x) at x=c is

A.
0
B.
e
C.
1/e
D.
2e

Solution:

QUESTION: 17

Pole of the line 2x + 3y + 4 = 0 w.r.t the ellipse is

A.
(1, 3)
B.
1, − 3
C.
− 1 , 3
D.
− 1, − 3

Solution:

QUESTION: 18

If y=sin((1+x²)/(1-x²)), (dy/dx)=

A.
[(4x)/(1-x²)]. cos[(1+x²)/(1-x²)]
B.
[(x)/(1-x²)²]. cos[(1+x²)/(1-x²)]
C.
[(x)/(1-x²)]. cos[(1+x²)/(1-x²)]
D.
[(4)/(1-x²)²]. cos[(1+x²)/(1-x²)]

Solution:

QUESTION: 19

The locus of the point of intersection of the perpendicular tangents to the ellipse is

A.
x²+ y²= a²
B.
x²+ y²= b²
C.
x² + y²= a²+ b²
D.
x² + y² = a² − b²

Solution:

QUESTION: 20

The eccentricity of the hyperbola 9x² - 16y² + 72x - 32y - 16 = 0 is

A.
5/4
B.
4/5
C.
9/16
D.
16/9

Solution:

QUESTION: 21

The equation of the conic with focus at (1, -1), directrix along x - y + 1 = 0 and with eccentricity √2 is

A.
x² - y² = 1
B.
xy = 1
C.
2xy - 4x + 4y + 1 = 0
D.
2xy + 4x - 4y - 1 = 0

Solution:

QUESTION: 22

Let f be a differentiable function such that,
f ′(x) If f(x) is increasing for all values of x then

A.
a ∈ 5, ∞
B.
C.
D.
none of these

Solution:

QUESTION: 23

What is the value of

A.
1
B.
-1
C.
∞
D.
limit does not exist

Solution:

QUESTION: 24

The max value of the function sinx(1+cosx) is

A.
3
B.
3√3/4
C.
4
D.
3√3

Solution:

QUESTION: 25

For a square matrix A, it is given that AA' = I, then A is a

A.
orthogonal matrix
B.
diagonal matrix
C.
symmetric matrix
D.
none of these

Solution:

QUESTION: 26

A.
1
B.
2
C.
3
D.
4

Solution:

QUESTION: 27

If the normal to the parabola y² = 4x at P(1, 2) meets the parabola again in Q, then Q =

A.
$(- 6, 9)$
B.
$(9, - 6)$
C.
$(- 9, - 6)$
D.
$(- 6, - 9)$

Solution:

QUESTION: 28

Multiplication of a complex number z by i corresponds to (z ≠ o)

A.
clockwise rotation of the line joining z to the origin in Argand diagram through an angle (π/2)
B.
anti-clockwise rotation of the line joining z to the origin in Argand diagram through an angle (π/2)
C.
rotation of the line joining z to orgin in the Argand diagram through an angle (π/2)
D.
no rotation

Solution:

QUESTION: 29

The focus of the parabola x²-8x+2y+7=0 is

A.
(0,-1/2)
B.
(4,9/2)
C.
(4,4)
D.
(-4,-9/2)

Solution:

QUESTION: 30

A group of 7 is to be formed from 6 boys and 4 girls. In many ways can this be done if the boys are in majority?

A.
120
B.
90
C.
100
D.
80

Solution:

QUESTION: 31

The number of lines joining 8 points on a circle is

A.
8
B.
16
C.
24
D.
28

Solution:

QUESTION: 32

All letters of the word EAMCET can be written in all possible ways. In how many ways can the letters of the word EAMCET be arranged so that two vowels are never together.

A.
360
B.
144
C.
72
D.
54

Solution:

* M * C * T *
In places of *, E, A, E can be filled
No. of ways of filling M, C, T = 3! = 6
No. of ways of filling x by vowels

QUESTION: 33

The chance of throwing a total of 7 or 12 with 2 dice, is

A.
(2/9)
B.
(5/9)
C.
(5/36)
D.
(7/36)

Solution:

QUESTION: 34

The probability of two events A and B are 0.25 and 0.40 respectively. The probability that both A and B occur is 0.15 . The probability that neither A nor B occurs is

A.
0.35
B.
0.65
C.
0.5
D.
0.75

Solution:

QUESTION: 35

The probability of getting a number between 1 and 100 which is divisible by one and itself only is

A.
27/185
B.
23/97
C.
25/98
D.
None

Solution:

QUESTION: 36

If to form a ΔABC it is given that a=5, b=7, sinA= , then possible triangles are

A.
only one
B.
two
C.
infinite
D.
not possible

Solution:

Thus is this case no triangle in possible

QUESTION: 37

The maximum value of (x-p)²+(x-q)²+(x-r)² will be at x is equal to

A.
(p+q+r)/3
B.
3√pqr
C.
pqr
D.
p²+q²+r²

Solution:

QUESTION: 38

If a = 4, b = 3, angle A = 60º, then c is the root of the equation

A.
c² - 3c - 7 = 0
B.
c² + 3c + 7 = 0
C.
c² - 3c + 7 = 0
D.
c² + 3c - 7 = 0

Solution:

QUESTION: 39

If the product of the roots of the equation ax²+ 6x + α² + 1 = 0 is -2 then α equals

A.
- 1
B.
1
C.
2
D.
- 2

Solution:

QUESTION: 40

The equation sin x + x cos x = 0 has at least one root in the interval

A.
(-π/2, 0)
B.
(0, π)
C.
(-π/2, π/2)
D.
none of these

Solution:

\int (\sin x + x \cos x) d x = - \cos x + \int x \cos x d x = - \cos x + {x \sin x - \int \sin x d x}

= - \cos x + x \sin x + \cos x = x \sin x .

Now, x \sin x = 0 has two roots x = 0, π .

∴

its derived equation sin x + x cos x = 0 has a root lying between 0 and π

QUESTION: 41

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

A.
p² = q² + r²
B.
p² = qr
C.
q² = pr
D.
r² = p² + q²

Solution:

QUESTION: 42

If log 2,log (2^x - 1),log (2^x + 3) are in A.P.Then x is equal to

A.
5/2
B.
log₂5
C.
log₃2
D.
log₅3

Solution:

QUESTION: 43

99th term of the series 2 + 7 + 14 + 23 + 34 ...is

A.
9998
B.
9999
C.
10000
D.
100000

Solution:

QUESTION: 44

Which of the following functions is not periodic?

A.
|sin 3x| + sin²x
B.
cos √x + cos²x
C.
cos 4x + tan²x
D.
cos 2x + sin x

Solution:

QUESTION: 45

Sum of infinite number of terms in G.P. is 20 and sum of their squares is 100. the common ratio of G.P is

A.
5
B.
3/5
C.
8/5
D.
1/5

Solution:

QUESTION: 46

The equation of perpendicular bisector of a line passing through the points (7,4) and (-1,-2) is

A.
ax-3y=15
B.
3x+4y=15
C.
4x+3y=15
D.
3x-4y=15

Solution:

QUESTION: 47

If f : R → R is given by f (x) = |x| and A = {x ∈ R : x < 0}, then f⁻¹(A) equals

A.
R
B.
φ
C.
A
D.
A ∪ {0}

Solution:

QUESTION: 48

Angle between the lines y-2x=9 and x+2y=-7 is

A.
π/3
B.
π/2
C.
-(π/2)
D.
π/4

Solution:

QUESTION: 49

A quadratic equation whose one root is 3 + 2i is_____

A.
x² + 6x + 13 = 0
B.
x² - 6x - 13 = 0
C.
x² - 6x + 13 = 0
D.
2x² - 6x + 13 = 0

Solution: Every quadratic equation has only two roots one root is 3 + 2i, second root will be its conjugate 3 - 2i.

QUESTION: 50

A.
1
B.
2
C.
3
D.
4

Solution:

QUESTION: 51

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

A.
B.
C.
D.
None of these

Solution:

QUESTION: 52

Let the tangent to the curve at any point on it cut the axes OX and OY at P and Q respectively. Then OP + OQ equals

A.
a
B.
2a
C.
a/2
D.
a²

Solution:

QUESTION: 53

The value of tan 20º + 2 tan 50º − tan 70º is:

A.
1
B.
0
C.
tan 50º
D.
None of these

Solution:

QUESTION: 54

In an acute angled triangle ABC, the least value of sec A + sec B + sec C is

A.
3
B.
6
C.
4
D.
9

Solution:

QUESTION: 55

ABC is a triangle, the point P is on side BC such that , the point Q is on the line . The ratio in which the line joining the common point R of and the point C divides is:

A.
6 : 1
B.
4 : 1
C.
3 : 1
D.
3 : 2

Solution:

QUESTION: 56

Let A = N x N, and let ' ∗ ' be a binary operation on A defined by (a,b) ∗ (c,d) = (ad+bc,bd) for all (a,b), (c,d) ∈ N x N. Then find identity element in A.

A.
There is no identity element
B.
(-1,0)
C.
(0,0)
D.
(3,2)

Solution:

QUESTION: 57

If the solution set for f (x) < 3 is (0 , ∞) and the solution set for f (x) > − 2 is (−∞ , 5), then the true solution set for (f (x))² ≥ f (x) + 6 , is

A.
− ∞ , + ∞
B.
( − ∞ , 0 ]
C.
[0, 5]
D.
( − ∞ , 0 ] ∪ [ 5 , ∞ )

Solution:

QUESTION: 58

Let P(3, 2, 6) be a point in space and Q be a point on the line

Then the value of μ for which the vector is parallel to the plane x - 4y+3z = 1 is

A.
1/4
B.
-1/4
C.
1/8
D.
-1/8

Solution:

QUESTION: 59

If tan (π cos θ) = cot (π sin θ) , then the value(s) of cos is/are

A.
1/2
B.
C.
D.
None of these

Solution:

QUESTION: 60

Let f (x) = min(x, x²), for every real number x then,

A.
f is continuous for all x
B.
f is differentiable for all x
C.
f ′ (x) = 2 for all x > 1
D.
f is differentiable at x = 0 and x = 1

Solution:

QUESTION: 61

Tangents are drawn to a unit circle with centre at (0, 0) from each point on the line 2x + y = 4, then the locus of mid-points of chord of contact is

A.
2(x² + y²) = x + y
B.
2(x² + y²) = x + 2y
C.
4(x² + y²) = 2x + y
D.
None of these

Solution:

QUESTION: 62

Two of the lines represented by x³ − 6x²y + 3xy² + dy³ = 0 are perpendicular for

A.
All Real Values of d
B.
Two real values of d
C.
Three Real Values of d
D.
No real value of d

Solution:

QUESTION: 63

There are N boxes, each containing at most r balls. If the number of boxes containing at least i balls is N_i for i = 1, 2, ....r, then the total number of balls contained in these N boxes is

A.
Exactly equal to N₁ + N₂ + .... + N_r
B.
Is strictly larger than N₁ + N₂ + .... + N_r
C.
Is strictly smaller than N₁ + N₂ + .... + N_r
D.
Can not be determined from the given information

Solution:

QUESTION: 64

If 0º < θ < 180º then

A.
B.
C.
D.
None of these

Solution:

QUESTION: 65

Statement-1 :
Statement-2 :

A.
Statement-1 is false, Statement-2 is true
B.
Statement-1 is true, Statement-2 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1
C.
Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1
D.
Statement-1 is true, Statement-2 is false