WBJEE Maths Test - 10 - JEE MCQ

WBJEE Maths Test - 10 - JEE MCQ

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75 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 - WBJEE Maths Test - 10

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WBJEE Maths Test - 10 - Question 1

In the expansion of [7 1 3 + 11 1 9 ]6561, the number of terms free from radicals is

Detailed Solution for WBJEE Maths Test - 10 - Question 1

General term,
tr + 1 = 6564Cr (7 1 3 )6561-r (11 1 9 )r
⇒ tr + 1 = 6561Cr . 7( 6561-r 3 ) . 11( r 9 )
tr + 1
will be free from radical signs, if
( 6561-r 3 ) and ( r 9 )
are integers for
0 ≤ r ≤ 6561
∴ r = 0, 9, 18, 27, ...6561
0, 9, 18, ...6561 is in A.P.
First term, a = 0
Common - difference = 18 - 9 = 9
Last term, t = 6561
l = a + (n - 1)d, where n = number of terms
⇒ 6561 = 0 + (n - 1)9
⇒ 9(n - 1) = 6561
⇒ n - 1 = 729
⇒ n = 729 + 1
⇒ n = 730

WBJEE Maths Test - 10 - Question 2

If the sum of the coefficients in the expansion of (x+y)n is 1024, then the value of the greatest coefficient in the the expansion is

WBJEE Maths Test - 10 - Question 3

The equation of the normal to the circle x2 + y2 + 6x + 4y - 3 = 0 at (1, -2) is

WBJEE Maths Test - 10 - Question 4

The approx value of (7.995)13correct to four decimal places is

WBJEE Maths Test - 10 - Question 5

WBJEE Maths Test - 10 - Question 6

Two circles x2 + y2 - 2x + 6y + 6 = 0 and x2 + y2 - 5x + 6y + 15 = 0

WBJEE Maths Test - 10 - Question 7

If |z₁ + z₂| = |z₁ - z₂|, then the difference of arguments of z₁ and z₂ is

WBJEE Maths Test - 10 - Question 8

(1 − ω + ω 2 ) (1 − ω 2 + ω 4 ) (1 − ω 4 + ω 8 ) (1 − ω 8 + ω 16)    =

WBJEE Maths Test - 10 - Question 9
The area of the curve |x|+|y|=4 is
WBJEE Maths Test - 10 - Question 10

WBJEE Maths Test - 10 - Question 11

WBJEE Maths Test - 10 - Question 12

WBJEE Maths Test - 10 - Question 13

The singular solution of the differential equation y=px+p3, (p=dy/dx) is :

WBJEE Maths Test - 10 - Question 14

WBJEE Maths Test - 10 - Question 15

The solution of the differential equation

Detailed Solution for WBJEE Maths Test - 10 - Question 15

WBJEE Maths Test - 10 - Question 16

( d dx )(x2 + cos x)4 =

Detailed Solution for WBJEE Maths Test - 10 - Question 16

d dx

(x2 + cos x)4
= 4.(x2 + cos x)3 x d dx (x2 + cos x)
= 4(x2 + cos x)3 x (2x - sin x)

WBJEE Maths Test - 10 - Question 17

(d/dx)[tan⁻1(secx+tanx)]=

WBJEE Maths Test - 10 - Question 18

The radius of the circle passing through the foci of the ellipse ((x2/16) + (y2/9) = 1), and having its centre (0,3) is

WBJEE Maths Test - 10 - Question 19

The equation of the ellipse in the form of ((x2/a2) + (y2/b2) = 1), given the eccentricity to be 2/3 and latus rectum 2/3, is

WBJEE Maths Test - 10 - Question 20

The tangents to the hyperbola x2 - y2 = 3 are parallel to the st. line 2x + y + 8 = 0 at the following points

WBJEE Maths Test - 10 - Question 21

The st. line lx + my + n = 0 touches the hyperbola x2/a2- y2/b2 = 1 if

WBJEE Maths Test - 10 - Question 22

The function f(x) = sin 4x + cos 4x increases if

Detailed Solution for WBJEE Maths Test - 10 - Question 22

f ′ x > ⇒ 4 sin 3 x . cos x − 4 cos 3 x . sin x > 0

⇒ sin x . cos x sin 2 x − cos 2 x > 0
o r sin 2 x . cos 2 x < 0 o r sin 4 x < 0
∴ π < 4 x < 2 π o r 3 π < 4 x < 4 π
∴ π 4 < x < π 2 o r 3 π 4 < x < π .

WBJEE Maths Test - 10 - Question 23

WBJEE Maths Test - 10 - Question 24

tan⁻1(x/y) - tan⁻1 (x - y/x + y) is

WBJEE Maths Test - 10 - Question 25

If A and B are two square matrices such that B = -A⁻1 BA, then (A + B)2 =

WBJEE Maths Test - 10 - Question 26

The strength of a beam varies as the product of its breadth b and square of its depth d. A beam cut out of a circular log of radius r would be strong when

Detailed Solution for WBJEE Maths Test - 10 - Question 26

WBJEE Maths Test - 10 - Question 27

|(1)/(2 + i)2 −(1)/(2 − i)2 | =

WBJEE Maths Test - 10 - Question 28

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

WBJEE Maths Test - 10 - Question 29

The axis of the parabola 9y2-16x-12y-57=0 is

WBJEE Maths Test - 10 - Question 30

Number of divisors of n = 38808 (except 1 and n) is

Detailed Solution for WBJEE Maths Test - 10 - Question 30

Factorizing the given number, we have
38808 = 23 . 32 . 72 . 11
Therefore the total number of divisors
= (3 + 1) (2 + 1) (1 + 1) - 1 = 71
But this includes the division by the number itself
Hence, the required number of divisors
= 71 - 1 = 70

WBJEE Maths Test - 10 - Question 31
If nP4:nP3=1:2, then n=
WBJEE Maths Test - 10 - Question 32

The number of straight lines that can be formed by joining 20 points of which 4 points are collinear is

Detailed Solution for WBJEE Maths Test - 10 - Question 32

Number of straight lines = 20C2 - 4C2 + 1

WBJEE Maths Test - 10 - Question 33
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
WBJEE Maths Test - 10 - Question 34
A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement the probability that second drawn ball is white, is
WBJEE Maths Test - 10 - Question 35
Three six faced dice are tossed together, then the probability that exactly two of the three numbers are equal, is
WBJEE Maths Test - 10 - 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 - 10 - 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 - 10 - Question 37

If k be the perimeter of the Δ A B C then b cos2 C/ 2 + c cos2 B /2 is equal to

Detailed Solution for WBJEE Maths Test - 10 - Question 37

WBJEE Maths Test - 10 - Question 38

If x2+ax+10 = 0 and x2+bx-10=0 have a common rooot,then a2-b2 is equal to

WBJEE Maths Test - 10 - Question 39

The range of values of a so that the equation x3 - 3x + a = 0 has three real and distinct roots is

Detailed Solution for WBJEE Maths Test - 10 - Question 39

⇒ a − 2 a + 2 < 0 or ⇒ − 2 < a < 2
Thus the given equation would have real and distinct roots is a ∈ (-2,2)

WBJEE Maths Test - 10 - Question 40

If (1 -p) is a root of quadratic equation x2 + px + (1 -p) = 0 then its roots are

WBJEE Maths Test - 10 - Question 41
The number of terms common to two A.P.'s 3, 7, 11, ..., 407 and 2, 9, 16,...., 709 is
WBJEE Maths Test - 10 - Question 42

If a, b, c are in A.P., , mb, c are in G.P.then a, m2b, c are in

WBJEE Maths Test - 10 - Question 43

21/4 41/8 81/16 161/32 ... upto ∞ is equal to

WBJEE Maths Test - 10 - Question 44
The sum of all 2-digit odd numbers is
WBJEE Maths Test - 10 - Question 45
Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is
WBJEE Maths Test - 10 - Question 46
In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by car or bus is
WBJEE Maths Test - 10 - Question 47
The equation of a line passing through (1,2) and perpendicular to 3x+4y+5=0 is
WBJEE Maths Test - 10 - Question 48
A line L passes through points (1,1) and (2,0) and Line L' passes through [(1/2),0] and perpendicular to L, then the area triangle formed by L, L' and y-axis is
WBJEE Maths Test - 10 - Question 49

If α,β are the roots of x2+ax+b=0, α33=

WBJEE Maths Test - 10 - Question 50

If 2tan2θ=sec2θ, the general value of θ is

WBJEE Maths Test - 10 - Question 51

Consider the equation 3 . The parameter 'a' so that the given equation has a solution which satisfies

WBJEE Maths Test - 10 - Question 52

The sum to infinity of the series

WBJEE Maths Test - 10 - Question 53

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

WBJEE Maths Test - 10 - Question 54

Let α , β be any two positive values of x for which 2 cos x , | cos x | and 1 − 3 cos 2 x are in G.P., then the minimum value of | α − β | is

WBJEE Maths Test - 10 - Question 55

If ω is cube root of unity, then the value of is equal to

WBJEE Maths Test - 10 - Question 56

The range of value of β such that (0, β ) lie on or inside the triangle formed by the lines y + 3x + 2 = 0, 3y − 2x − 5 = 0, 4x + x − 14 = 0 is:

WBJEE Maths Test - 10 - Question 57

If the line x cos θ + y sin θ = 2 is the equation of a transverse common tangent to the circles

WBJEE Maths Test - 10 - Question 58

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C , then :

WBJEE Maths Test - 10 - Question 59

The solution of the differential equation

WBJEE Maths Test - 10 - Question 60

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

WBJEE Maths Test - 10 - Question 61

If a ‸ , b ‸ and c ‸ are three unit vectors, such that a ‸ + b ‸ + c ‸ is also a unit vector and θ 1 , θ 2 and θ 3 are angles between the vectors a ‸ , b ‸ ; b ‸ , c ‸ and c ‸ , a ‸ respectively then among θ 1 , θ 2 and θ 3

WBJEE Maths Test - 10 - Question 62

If is equal to

WBJEE Maths Test - 10 - Question 63

The value of the expression
, where ω is an imaginary cube roots of unity, is:

WBJEE Maths Test - 10 - Question 64

WBJEE Maths Test - 10 - Question 65

The set of all value of a ∈ R for which the equation 2x2 − 2(2a+1)x + a(a-1) = 0 has roots α and β satisfying α < a < β is

*Multiple options can be correct
WBJEE Maths Test - 10 - Question 66

The tangents drawn from (0, 0) to x2 + y2 + 2fy + 2gx + c = 0 are perpendicular if (where c = g2)

*Multiple options can be correct
WBJEE Maths Test - 10 - Question 67

About the equation which of the following statements is correct?

WBJEE Maths Test - 10 - Question 68

If P is any point lying on the ellipse , whose foci are S and S'. Let ∠ P S S ′ = α and ∠ P S ′ S = β , then:

*Multiple options can be correct
WBJEE Maths Test - 10 - Question 69

If in a triangle ABC, CD is the angular bisector of the angle ACB then CD is equal to

*Multiple options can be correct
WBJEE Maths Test - 10 - Question 70

If

WBJEE Maths Test - 10 - Question 71

In a triangle ABC, tan C < 0. Then

*Multiple options can be correct
WBJEE Maths Test - 10 - Question 72

Z 1 , Z 2 , Z 3

correspond to the vertices of an equilateral triangle and | Z 1 − 1 | = | Z 2 − 1 | = | Z 3 − 1 | . Then

*Multiple options can be correct
WBJEE Maths Test - 10 - Question 73

If the equation cx2 + bx - 2a = 0 has no roots and then,

*Multiple options can be correct
WBJEE Maths Test - 10 - Question 74

If y = tan x tan 2 x tan 3 x then dy /dx has the value equal to

*Multiple options can be correct
WBJEE Maths Test - 10 - Question 75

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