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WBJEE Maths Test - 4 - JEE MCQ


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30 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 - WBJEE Maths Test - 4

WBJEE Maths Test - 4 for JEE 2024 is part of WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 preparation. The WBJEE Maths Test - 4 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Maths Test - 4 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Maths Test - 4 below.
Solutions of WBJEE Maths Test - 4 questions in English are available as part of our WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 for JEE & WBJEE Maths Test - 4 solutions in Hindi for WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt WBJEE Maths Test - 4 | 75 questions in 120 minutes | Mock test for JEE preparation | Free important questions MCQ to study WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 for JEE Exam | Download free PDF with solutions
WBJEE Maths Test - 4 - Question 1
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If the coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)n, n ∈ N, are in A.P., then n is equal to

WBJEE Maths Test - 4 - Question 2
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The angle between tangents drawn from origin to the circle (x-7)2 + (y+1)2=25 is

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WBJEE Maths Test - 4 - Question 3
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If in the expansion of (1 + x)20, the coefficients of rth and (r + 4)th terms are equal, then r is

WBJEE Maths Test - 4 - Question 4
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If the co-efficients of rth and (r+1)th terms in the expansion of (3+7x)29 are equal, the r is equal to
WBJEE Maths Test - 4 - Question 5
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Circles x2+y2-6x-2y+1=0 and x2+y2+2x-8y+13=0
WBJEE Maths Test - 4 - Question 6
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If = a + ib , then a and b are
WBJEE Maths Test - 4 - Question 7
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For what values of x and y ,the complex numbers 9y2 - 4 - 10xi and 8y2 + 20i7 are conjugate to each other ?
WBJEE Maths Test - 4 - Question 8
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The area bounded by two curves y2=4ax and x2=4ay is
Detailed Solution for WBJEE Maths Test - 4 - Question 8

The curves y2 = 4ax and x2 = 4ay intersects at points where (x2/4a)2=4ax

WBJEE Maths Test - 4 - Question 9
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If a < 0 < b then

WBJEE Maths Test - 4 - Question 10
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If a ≠ 6, b, c satisfy   = 0 then abc =
WBJEE Maths Test - 4 - Question 11
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WBJEE Maths Test - 4 - Question 12
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WBJEE Maths Test - 4 - Question 13
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WBJEE Maths Test - 4 - Question 14
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The solution of the equation ydx-2xdy=0 gives parabolas whose common axis and the tangent at the vertex respectively, are :
WBJEE Maths Test - 4 - Question 15
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The solution of the equation xdy-ydx=0 is
WBJEE Maths Test - 4 - Question 16
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If f(x)=logx2log(x), then at x=e, f'(x)=
WBJEE Maths Test - 4 - Question 17
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For real values of x the minimum value of [(1-x+x2)/(1+x+x2)] is
WBJEE Maths Test - 4 - Question 18
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The eccentricity of the ellipse 9x2 + 5y2 − 30y = 0 is
WBJEE Maths Test - 4 - Question 19
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The eccentricity of the ellipse 4x2 + 9y2 + 8x + 36y + 4 = 0 is
WBJEE Maths Test - 4 - Question 20
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If the two intersecting lines intersect the hyperbola and neither of them is a tangent to it, then number of intersecting points are
Detailed Solution for WBJEE Maths Test - 4 - Question 20
The general equation of a straight line is linear: ax + by + c = and the general equation of a hyperbola (but it's the same for all conics) is a second degree equation:
1. Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
So, finding y ( or x ) from the first equation and substituting in the second, we have a second degree equation that has, at most, two real solutions. The possible cases are:
1) two real distinct solutions: the line is secant at two points
2) two coincident solution: the line is tangent
3) no real solution : the line is e''external''
4) the equation reduce to a first degree equation so we have one real solution and we say that the other solution goes to infinity.
So, for two lines that are not tangent we can have:
no common point with the conic if the two lines are external,
2 points if one is secant at two pints and the other is external or if both have one real common point with the conic an the other at infinity,
3 common points if one is secant at two points and the other at one point,
4 common points if the two lines are both secants at two points.
WBJEE Maths Test - 4 - Question 21
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If sin⁻1x + sin⁻1y = 2π/3, then cos⁻1 x + cos⁻1 y is equal to
WBJEE Maths Test - 4 - Question 22
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If φ (x) = f (x) + f (1 − x) and f ″ (x) < 0 in − 1,1 , then φ (x) strictly increases in the interval
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WBJEE Maths Test - 4 - Question 23
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if f : R→R be such that f(1) = 4 and f'(1) = 12 then
WBJEE Maths Test - 4 - Question 24
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If each element of a 3 x 3 matrix is multiplie by 3, then the determinant of the newly formed matrix is
WBJEE Maths Test - 4 - Question 25
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The minimum value of f(x) = x4-x2-2x+6 is
Detailed Solution for WBJEE Maths Test - 4 - Question 25
f'(x) = 4x3 - 2x - 2
∴ f'(x) = 0 ⇒ 2x3 - x - 1 = 0 ⇒ (x - 1)(2x2 + 2x + 1) = 0
∴ x = 1.
Now, f" (x) = 12x 2 - 2 ∴ f" (1) = 12 - 2 > 0.
Hence, global min f(x) = 1 - 1 - 2 + 6 = 4.
WBJEE Maths Test - 4 - Question 26
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The HCF of 155 and 1385 is
WBJEE Maths Test - 4 - Question 27
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The focus of the parabola x2-8x+2y+7=0 is
WBJEE Maths Test - 4 - Question 28
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The tangents at the points ( ,2at1) , ( , 2at2) on the parabola y2 = 4ax are at right angles if
Detailed Solution for WBJEE Maths Test - 4 - Question 28

Tangent at t1 is yt1 = x +
Tangent at t2 is yt2 = x +
Tangents are at right angles
⇒ t1t2 = - 1

WBJEE Maths Test - 4 - Question 29
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In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?
WBJEE Maths Test - 4 - Question 30
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The equation 16x2 + y2 + 8xy − 74 x − 78y + 212 = 0 represents
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