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WBJEE Maths Test - 1 - JEE MCQ


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30 Questions MCQ Test - WBJEE Maths Test - 1

WBJEE Maths Test - 1 for JEE 2024 is part of JEE 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
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The coefficient of x3 in ((√x5) + (3/√x3))6 is

WBJEE Maths Test - 1 - Question 2
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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
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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
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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
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The square root of the number 5 + 12i is
WBJEE Maths Test - 1 - Question 6
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The equation of circle which passes through (4,5) and whose centre is (2,2) is
WBJEE Maths Test - 1 - Question 7
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The area bounded by the ellipse x2+9y2=9 and the straight line x+3y=3 is
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WBJEE Maths Test - 1 - Question 8
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WBJEE Maths Test - 1 - Question 9
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WBJEE Maths Test - 1 - Question 10
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If

WBJEE Maths Test - 1 - Question 11
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The degree of the differential equation d2y/dx2+(dy/dx)3+6y=0 is
WBJEE Maths Test - 1 - Question 12
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The roots of the equation =0 are
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WBJEE Maths Test - 1 - Question 13
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Differential of x6 w.r. to x3 is equal to
WBJEE Maths Test - 1 - Question 14
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The solution of the differential equation 2x dy/dx-y=3 represent
WBJEE Maths Test - 1 - Question 15
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If |z| = 4 and arg z = (5π/6), then the value of z is
WBJEE Maths Test - 1 - Question 16
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If x = a cos3 θ, y = a sin3 θ, then
√[1 + (dy/dx)2] =
WBJEE Maths Test - 1 - Question 17
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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
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The graph represented by the equations x = sin2t,y = 2cost is
WBJEE Maths Test - 1 - Question 19
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If the major axis of an ellipse is thrice the minor axis, then its eccentricity is equal to
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WBJEE Maths Test - 1 - Question 20
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The curve represented by x = a (coshθ + sinhθ) , y = b(coshθ − sinhθ) is
WBJEE Maths Test - 1 - Question 21
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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
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WBJEE Maths Test - 1 - Question 23
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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
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WBJEE Maths Test - 1 - Question 25
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If z=1+i,then the multiplicative inverse of z2 is
WBJEE Maths Test - 1 - Question 26
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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
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The equation of the parabola whose vertex is at (2,-1) and focus at (2,-3) is
WBJEE Maths Test - 1 - Question 28
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sin[(1/2)cos⁻1(4/5)] is equal to
WBJEE Maths Test - 1 - Question 29
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The pole of the line 2x + 3y − 4 = 0 with respect to the parabola y2 = 4x is
WBJEE Maths Test - 1 - Question 30
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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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