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JEE Exam  >  JEE Tests  >  WBJEE Maths Test - 8 - JEE MCQ

WBJEE Maths Test - 8 - JEE MCQ


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30 Questions MCQ Test - WBJEE Maths Test - 8

WBJEE Maths Test - 8 for JEE 2024 is part of JEE preparation. The WBJEE Maths Test - 8 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Maths Test - 8 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Maths Test - 8 below.
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WBJEE Maths Test - 8 - Question 1
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In the expansion of   the number of terms free from radicals is

Detailed Solution for WBJEE Maths Test - 8 - Question 1

General term,

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 - 8 - Question 2
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The coefficient of x-9 in the expansion of ((x2/2) - (2/x))9 is

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WBJEE Maths Test - 8 - Question 3
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The coefficient of x3 in ((√x5) + (3/√x3))6 is

WBJEE Maths Test - 8 - Question 4
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Equation x2+2ax-b2=0 has real roots α , β and equation x2+2px-q2=0 has real roots γ , δ . If the circle C is drawn with the points ( α , γ ), ( β , δ ) as extremities of a diameter, then the equation of C is
WBJEE Maths Test - 8 - Question 5
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The equation of circle which passes through (4,5) and whose centre is (2,2) is
WBJEE Maths Test - 8 - Question 6
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If the cube roots of unity are 1,ω,ω2 then the roots of the equation (x - 2)3+27 = 0 are
WBJEE Maths Test - 8 - Question 7
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Let z1 and z2 be two complex numbers whose principle argument are α and β then, arg (z1.z2) =
Detailed Solution for WBJEE Maths Test - 8 - Question 7
Let z1 and z2 have polar representations z1 = r1( cos α + isinα)
and z2 = r2 (cosβ + isinβ ).
Then z1 z2 = r1 (cosα+i sinα) r2 (cosβ + isinβ )
= r1 r2 (cosαcosβ − sinαsinβ) + i(cosαsinβ + sinαcosβ )
= r1 r2 (cos (α+β ) + isin (α+β )),
which is the polar representation of z1 z2 , as r1 r2 = |z1 ||z2 |=|z1 z2 |.
Hence α+β is an argument of z1 z2
WBJEE Maths Test - 8 - Question 8
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If m and n are integers, then what is the value of sin mx sin nxdx . If m ≠ n
Detailed Solution for WBJEE Maths Test - 8 - Question 8

Since sin mx, sin nx is an odd function if m ≠ n, then  sin mx . sin nx dx = 0

WBJEE Maths Test - 8 - Question 9
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WBJEE Maths Test - 8 - Question 10
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WBJEE Maths Test - 8 - Question 11
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WBJEE Maths Test - 8 - Question 12
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WBJEE Maths Test - 8 - Question 13
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The area bounded by the parabola y2=4ax and the straight line y=2ax is
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WBJEE Maths Test - 8 - Question 14
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The solution of the differential equation 2xy(dy/dx)=x2+3y2 is (where c is a constant)
WBJEE Maths Test - 8 - Question 15
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What is the solution of x2y2dy = (1−xy3) dx?
WBJEE Maths Test - 8 - Question 16
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If
then f ′(1) =
WBJEE Maths Test - 8 - Question 17
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The curve represented by x = 2(cos t + sin t), y = 5 (cos t - sin t) is
WBJEE Maths Test - 8 - Question 18
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The eccentric angles of the extremities of the latus-rectum intersecting positive x-axis of the ellipse ((x2/a2) + (y2/b2) = 1) are given by
WBJEE Maths Test - 8 - Question 19
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If

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WBJEE Maths Test - 8 - Question 20
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The slopes of the common tangents to the hyperbola x2/y - y2/16 = 1 and y2/9 - x2/16 = 1 are
WBJEE Maths Test - 8 - Question 21
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The foci of the hyperbola 9x2 - 16y2 + 18x + 32y - 151 = 0 are
WBJEE Maths Test - 8 - Question 22
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The function is increasing in
WBJEE Maths Test - 8 - Question 23
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The value of cos⁻1(cos 5π/3) + sin⁻1 (sin 5π/3) is
WBJEE Maths Test - 8 - Question 24
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is equal to
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WBJEE Maths Test - 8 - Question 25
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The system of linear equation x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = 4 has a unique solution, then
Detailed Solution for WBJEE Maths Test - 8 - Question 25

Augmented matrix is



∴ Given system of equations has a unique solution ⇒ k ≠ 0

WBJEE Maths Test - 8 - Question 26
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For all real x, the minimum value of (1 - x + x2)/(1 + x + x2) is
WBJEE Maths Test - 8 - Question 27
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If the vertices O,A,B of any equilateral triangle are situated at z=0, z=z₁ and z=z₂ respectively, then which of the following are true ?
WBJEE Maths Test - 8 - Question 28
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Which of the following points lie on the parabola x2=4ay ?
WBJEE Maths Test - 8 - Question 29
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The length of the normal chord to the parabola y2 = 4x which subtends a right angle at the vertex is
Detailed Solution for WBJEE Maths Test - 8 - Question 29


Again AB subtends a right angle at the vertex O (0, 0) of the parabola

WBJEE Maths Test - 8 - Question 30
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P,Q,R and S have to deliver lecture, then in how many ways can the lectures be arranged?
Detailed Solution for WBJEE Maths Test - 8 - Question 30
Total no. of ways delivering lectures = 4P4 = 4! = 24
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