# WBJEE Maths Test - 5

## 75 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests | WBJEE Maths Test - 5

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Attempt WBJEE Maths Test - 5 | 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

Solution:
QUESTION: 2

Solution:
QUESTION: 3

### The coefficient of the middle term in the binomial expansion in powers of x of (1+αx)4 and (1-αx)6 is the same, if α equals

Solution:
QUESTION: 4

The length of tangents drawn from the point (5,1) is to the circle x2+y2+6x-4y-3=0

Solution:
QUESTION: 5

Solution:
QUESTION: 6
The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangent to the same circle. The radius of this circle is
Solution:
QUESTION: 7

If ω is cube root of unity, then (1 + ω3) - (1 + ω2)3 =

Solution:
QUESTION: 8

is equal to

Solution:
QUESTION: 9

Solution:
QUESTION: 10

If is a singular matrix, then x =

Solution:
QUESTION: 11

Solution:
QUESTION: 12

Solution:
QUESTION: 13

Let f(x) be a function satisfying f ′(x)= f x with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2, then value of integral
is equal to

Solution:
QUESTION: 14

A singular solution of the differential equation y2[1+(dy/dx)2]=R2 is :

Solution:
QUESTION: 15

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

Solution:
QUESTION: 16

If y=sin((1+x2)/(1-x2)), (dy/dx)=

Solution:
QUESTION: 17

The latus rectum of the ellipse 5x2 + 9y2 = 45 is

Solution:
QUESTION: 18

Solution:

QUESTION: 19

The eccentricity of the ellipse 9x2 + 5y2 − 30y = 0 is

Solution:
QUESTION: 20
The locus of the centre of a circle which touches given circles externally is
Solution:
QUESTION: 21

The product of the perpendicular, drawn from any point on a hyperbola to its asymptotes is

Solution:
QUESTION: 22

The value of

Solution:
QUESTION: 23

A and B are square matrices of order n x n, then (A - B)2 is equal to

Solution:

(A - B) x (A - B)
(A - B) x A - (A - B) x B
= A2 - AB - BA + B2

QUESTION: 24

The coordinates of a point of the parabola y=x2+7x+2 which is the closest to the straight line y=3x-3 is

Solution:
QUESTION: 25

[sin(tan⁻1(3/4))]2=

Solution:
QUESTION: 26

Let a + b = 4, a < 2 and g(x) be a monotonically increasing function of x.
Then,

Solution:

We have a + b = 4 ⇒ b = 4 − a and b − a = 4 − 2 a = t (say)

Thus, f(a) is an increasing function of t. Hence, the given expression increases with increase in (b-a).

QUESTION: 27

The number (1-i)3/1-i3 is equal to

Solution:
QUESTION: 28

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

Solution:
QUESTION: 29

The length of the latus rectum of the parabola 4y2+2x-20y+17=0 is

Solution:
QUESTION: 30
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of there parallel lines is :
Solution:
QUESTION: 31
If nP4=30.nC5, then n=
Solution:
QUESTION: 32

Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers is

Solution:

A number is divisible by 3 if and only if the sum of its digits are divisible by 3
Notice that 1 + 2 + 3 + 4 + 5 = 15, which is divisible by 3
The only other way we can have a sum of 5 digits divisible by 3 is to replace the 3 by the 0 making the sum 3 less:
1 + 2 + 0 + 4 + 5 = 12, which is divisible by 3
No other choice of 5 digits can have a sum divisible by 3, because there is no other way to make the sum 12 or 15, and we certainly can't have a sum of 9 or 18
So the number of 5-digit numbers that can be formed from the digits {1,2,3,4,5} is

Number of ways = 1 x 2 x 3 x 4 x 5 = 120
And the number of 5-digit numbers that can be formed from the digits {1, 2, 0, 4, 5} is figured this way

Number of ways = 1 x 2 x 3 x 4 x 4 = 96
Total Number of ways = 120 + 96 = 216

QUESTION: 33
A person draws a card from a pack of playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail in first two times is
Solution:
QUESTION: 34
A five digit number is formed by writing the digits 1,2,3,4,5 in a random order without repetitions. Then the probability that the number is divisible by 4, is
Solution:
QUESTION: 35
You are given a box with 20 cards in it. 10 of these cards have the letter 1 printed on them. The other ten have the letter T printed on them. If you pick up 3 cards at random and keep them in the same order, the probability of making the word IIT is
Solution:
QUESTION: 36

In ΔABC , cosA + cosB + cosC =

Solution:

cos A + cos B + cos C = 1 + 4 sin

QUESTION: 37

In a ΔABC , ∑(b + c) tan

Solution:

Σ(b + c) tan A 2 tan ( B - C 2 ) = Σ(b + c) tan

QUESTION: 38
If both the roots of the quadratic eqution x2 - 2kx + k2 + k - 5 = 0 are less than 5, then k lies in the interval
Solution:
QUESTION: 39

If f(x) is continuous and differentiable over [−2,5] and −4 ≤ f′ (x) ≤ 3 for all x in (−2,5) then the greatest possible value of f(5) − f(−2), is

Solution:

QUESTION: 40

The sum of the series 1.32 + 2.52 + 3.72 +.....upto 20 terms is

Solution:
QUESTION: 41
Let α, β be the roots of the equation (x - a)(x - b) + c = 0, c ≠ 0. The roots of the equation (x - α)(x - β)+ c = 0 are
Solution: Since α, β are the roots of equation
(x - a) (x - b) = c
or x2 - (a + b) x + ab - c = 0
Then α + β = a + b
and αβ = ab - c
or ab = αβ + c
Then the roots of equation is
x2 - x(α + β) + αβ + c = 0
⇒ x2 - x(a + b) + ab = 0
⇒ a and b are the roots
QUESTION: 42
Every term of a G.P. is positive and also every term is the sum of two preceding terms. Then the common ratio of the G.P. is
Solution:
QUESTION: 43

If a,b,c are in G.P.,then equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root if d/a,e/b,f/c are in

Solution:
QUESTION: 44

The sum of n terms of two A.P.'s are in the ratio of (7n + 1) : (4n + 27). The ratio of their 11 terms is

Solution:

Hence the ratio of the 11th terms is 148 : 111

QUESTION: 45

4 [cot⁻13 + cosec⁻1 (√5)] is equal to

Solution:
QUESTION: 46
With reference to a universal set, the inclusion of a subset in another, is relation, which is
Solution:
QUESTION: 47
The locus of a point such that the sum of whose distances from two rectangular lines is 2 units is
Solution:
QUESTION: 48
If the intercept on y-axis is double the intercept on x-axis by any line and if the line passes through (1,2), then equation of line is
Solution:
QUESTION: 49
The general solution of the equation tan2θ.tanθ=1 for n∈I is, θ is equal to
Solution:
QUESTION: 50

The condition that the cubic equation x3 - px2 + qx - r = 0 should have roots in G.P. is given by____

Solution:

The roots of the cubic equation

QUESTION: 51

The equation 4 sin2x + 4 sin x + a2 − 3 = 0 possesses a solution if a belongs to the interval

Solution:
QUESTION: 52

If p , x1 , x2 , … xi … and q , y1 , y2 , … yi … are in A.P., with common difference a and b respectively, then the centre of mean position of the points Ai(xi, yi) where i = 1, 2, ..., n lies on the line

Solution:
QUESTION: 53

If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x. The expression
3b2x2 + 6bc x + 2c2 is

Solution:
QUESTION: 54

The value of is equal to

Solution:
QUESTION: 55

The locus of the orthocentre of the triangle formed by the lines
(1 + p)x - py + p(1 + p) = 0,
(1 + q)x - qy + q(1 + q) = 0,
and y = 0, where p ≠ q , is

Solution:
QUESTION: 56

The differential equation determines a family of circles with

Solution:
QUESTION: 57

The area of the region between the curves bounded by the lines x = 0 and x = is

Solution:
QUESTION: 58

dx  equals

Solution:
QUESTION: 59

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.

Solution:
QUESTION: 60

If the curves intersect each other at right angles, then

Solution:
QUESTION: 61

Let A be a non-empty set and S be the set of functions from A to itself. The composition of function 'O' is a.

Solution:
QUESTION: 62

Let A1 , A2 , A3 , … … , An be n skew-symmetric matrix of same order then will be

Solution:
QUESTION: 63

Let a,b,c be any real numbers. Suppose that there are real numbers x,y,z not all zero such that x=cy+bz, y=az+cx and z=bx+ay. Then a2+b2+c2+2abc is equal to

Solution:
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

Solution:
QUESTION: 65

Given that converges, what is the value to which it converges?

Solution:
*Multiple options can be correct
QUESTION: 66

Circles are drawn on chords of the rectangular hyperbola xy = c2 parallel to the line y = x as diameters. All such circles pass through two fixed points whose co-ordinates are

Solution:
*Multiple options can be correct
QUESTION: 67

Let f(x)   = 1 + 2 sinx + 2 cos2 x , 0 ≤ x ≤ π/2 . Then

Solution:
*Multiple options can be correct
QUESTION: 68

If sinβ is the G.M. between sinα and cos α , then cos2 β is equal to

Solution:
*Multiple options can be correct
QUESTION: 69

Z1 , Z2 , Zcorrespond to the vertices of an equilateral triangle and |Z1 − 1| = |Z2 − 1| = |Z3 − 1| . Then

Solution:
*Multiple options can be correct
QUESTION: 70

In a certain culture of bacteria, the rate of increase is proportional to the number present. It if be known that the number doubles in 4 hours, then

Solution:
*Multiple options can be correct
QUESTION: 71

The polynomial 1 − x + x2 − x3 + . . . + x16 − x17 may be written in the form where y = x + 1 and are constants . Then a2 equals

Solution:
*Multiple options can be correct
QUESTION: 72

The set of discontinuities of the function f (x)   = ( 1/2 − cos2x ) contains the set

Solution:
*Multiple options can be correct
QUESTION: 73

If pth, 2pth, 4pth terms of an A.P. are in G.P. then common ratio of G.P. is

Solution:
*Multiple options can be correct
QUESTION: 74

An integral solution of the equation tan−1 x + tan−1 = tan−1 3 is

Solution:
*Multiple options can be correct
QUESTION: 75

If represent the equations of three planes, then point of intersection of these planes is

Solution:
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