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WBJEE Maths Test - 10 - JEE MCQ


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30 Questions MCQ Test - WBJEE Maths Test - 10

WBJEE Maths Test - 10 for JEE 2024 is part of JEE preparation. The WBJEE Maths Test - 10 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Maths Test - 10 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Maths Test - 10 below.
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WBJEE Maths Test - 10 - Question 1
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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
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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

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WBJEE Maths Test - 10 - Question 3
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The equation of the normal to the circle x2 + y2 + 6x + 4y - 3 = 0 at (1, -2) is

WBJEE Maths Test - 10 - Question 4
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The approx value of (7.995)1∕3correct to four decimal places is
WBJEE Maths Test - 10 - Question 5
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WBJEE Maths Test - 10 - Question 6
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Two circles x2 + y2 - 2x + 6y + 6 = 0 and x2 + y2 - 5x + 6y + 15 = 0
WBJEE Maths Test - 10 - Question 7
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If |z₁ + z₂| = |z₁ - z₂|, then the difference of arguments of z₁ and z₂ is
WBJEE Maths Test - 10 - Question 8
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(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
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The area of the curve |x|+|y|=4 is
WBJEE Maths Test - 10 - Question 10
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WBJEE Maths Test - 10 - Question 11
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WBJEE Maths Test - 10 - Question 12
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WBJEE Maths Test - 10 - Question 13
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The singular solution of the differential equation y=px+p3, (p=dy/dx) is :
WBJEE Maths Test - 10 - Question 14
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WBJEE Maths Test - 10 - Question 15
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The solution of the differential equation

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WBJEE Maths Test - 10 - Question 16
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( 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
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(d/dx)[tan⁻1(secx+tanx)]=
WBJEE Maths Test - 10 - Question 18
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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
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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
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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
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The st. line lx + my + n = 0 touches the hyperbola x2/a2- y2/b2 = 1 if
WBJEE Maths Test - 10 - Question 22
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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
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WBJEE Maths Test - 10 - Question 24
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tan⁻1(x/y) - tan⁻1 (x - y/x + y) is
WBJEE Maths Test - 10 - Question 25
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If A and B are two square matrices such that B = -A⁻1 BA, then (A + B)2 =
WBJEE Maths Test - 10 - Question 26
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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
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|(1)/(2 + i)2 −(1)/(2 − i)2 | =
WBJEE Maths Test - 10 - Question 28
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The focus of the parabola x2-8x+2y+7=0 is
WBJEE Maths Test - 10 - Question 29
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The axis of the parabola 9y2-16x-12y-57=0 is
WBJEE Maths Test - 10 - Question 30
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If nP4:nP3=1:2, then n=
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