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WBJEE Maths Test - 1 - JEE MCQ


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30 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 - WBJEE Maths Test - 1

WBJEE Maths Test - 1 for JEE 2024 is part of WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 preparation. The WBJEE Maths Test - 1 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Maths Test - 1 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Maths Test - 1 below.
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WBJEE Maths Test - 1 - Question 1

The coefficient of x3 in ((√x5) + (3/√x3))6 is

WBJEE Maths Test - 1 - Question 2

If the coefficient of x7 in [ax2+(1/bx)]11 equals the coefficient of x-7 in [ax-(1/bx2)]11, then a and b satisfy the relation

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WBJEE Maths Test - 1 - Question 3

The third term in the expansion of ((x2) - (1/x3))n is independent of x, when n is equal to

WBJEE Maths Test - 1 - Question 4

The equation of the circle passing through intersection of circles x2+y2-1=0 and x2+y2-2x-4y+1=0 and touching x+2y=0 is

WBJEE Maths Test - 1 - Question 5

The square root of the number 5 + 12i is

WBJEE Maths Test - 1 - Question 6

The equation of circle which passes through (4,5) and whose centre is (2,2) is

WBJEE Maths Test - 1 - Question 7

The area bounded by the ellipse x2+9y2=9 and the straight line x+3y=3 is

Detailed Solution for WBJEE Maths Test - 1 - Question 7

WBJEE Maths Test - 1 - Question 8

WBJEE Maths Test - 1 - Question 9

WBJEE Maths Test - 1 - Question 10

If

WBJEE Maths Test - 1 - Question 11

The degree of the differential equation d2y/dx2+(dy/dx)3+6y=0 is

WBJEE Maths Test - 1 - Question 12

The roots of the equation =0 are

Detailed Solution for WBJEE Maths Test - 1 - Question 12

WBJEE Maths Test - 1 - Question 13

Differential of x6 w.r. to x3 is equal to

WBJEE Maths Test - 1 - Question 14
The solution of the differential equation 2x dy/dx-y=3 represent
WBJEE Maths Test - 1 - Question 15
If |z| = 4 and arg z = (5π/6), then the value of z is
WBJEE Maths Test - 1 - Question 16

If x = a cos3 θ, y = a sin3 θ, then
√[1 + (dy/dx)2] =

WBJEE Maths Test - 1 - Question 17

The eccentricity of the conic 9x2 + 25y2 = 225 is

Detailed Solution for WBJEE Maths Test - 1 - Question 17

 9x2 + 25y2 = 225   [ send this 225 on left side in divide ]
9/225 x2 +25/225 y2 = 1
 x2 +  y2 = 1
25      9
after sending 225 in divide in lhs

e=√25-9
       5
e=4/5

WBJEE Maths Test - 1 - Question 18

The graph represented by the equations x = sin2t,y = 2cost is

WBJEE Maths Test - 1 - Question 19

If the major axis of an ellipse is thrice the minor axis, then its eccentricity is equal to

Detailed Solution for WBJEE Maths Test - 1 - Question 19

WBJEE Maths Test - 1 - Question 20

The curve represented by x = a (coshθ + sinhθ) , y = b(coshθ − sinhθ) is

WBJEE Maths Test - 1 - Question 21

The least possible value of k for which the function f(x) = x2 + kx + 1 may be increasing on [1,2] is

Detailed Solution for WBJEE Maths Test - 1 - Question 21

We have , f x = x 2 + k x + 1
⇒ f ′ x = 2 x + k . Also , f ″ x = 2
Now , f ″ x = 2, ∀ x ∈ [ 1,2 ]
⇒ f ″ x > 0, ∀ x ∈ [ 1,2 ]
⇒ f ′ x is an increasing function in the interval [ 1,2 ] .
⇒ f ′ 1 is the least value of f′(x) on [ 1,2 ]
But f ′ x > 0 ∀ x ∈ [ 1,2 ]
[ ∵ f x is increasing on [1,2] ]
∴ f ′ 1 > 0, ∀ x ∈ [ 1,2 ] ⇒ k > − 2
Thus, the least value of k is -2

WBJEE Maths Test - 1 - Question 22

WBJEE Maths Test - 1 - Question 23
The system of equations
αx+y+z = α-1
x+αy+z = α-1
x+y+αz, = α-1 has no solution, if α is
WBJEE Maths Test - 1 - Question 24

Detailed Solution for WBJEE Maths Test - 1 - Question 24

WBJEE Maths Test - 1 - Question 25

If z=1+i,then the multiplicative inverse of z2 is

WBJEE Maths Test - 1 - Question 26
If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1 + a)(1 + b)(1 + c)(1 + d)?
WBJEE Maths Test - 1 - Question 27

The equation of the parabola whose vertex is at (2,-1) and focus at (2,-3) is

WBJEE Maths Test - 1 - Question 28

sin[(1/2)cos⁻1(4/5)] is equal to

WBJEE Maths Test - 1 - Question 29

The pole of the line 2x + 3y − 4 = 0 with respect to the parabola y2 = 4x is

WBJEE Maths Test - 1 - Question 30

How many total words can be formed from the letters of the word INSURANCE in which vowels are always together?

Detailed Solution for WBJEE Maths Test - 1 - Question 30

Given word has 9 letters out which I, U, A and E are wovels.

So if we club them together, we are left with 5 letters and 1 group of letters.

N, S, R, N, C and IUAE.

In this, N comes twice.

So number of arrangements will be,

6! / 2! = 360.

Also, the group of wovels has 4 distinct letters.

So, it can be arranged in,

4! = 24 ways.

Therefore, total number of arrangements,

= 360 * 24

= 8640.

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