In the print window choose “Save as PDF”. The file prints without a web address or date line.
Mere Teacher · Previous Year Questions
JEE Main Mathematics · Inverse Trigonometric Functions · Set 3 (Q61-90)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
61.
tan(2tan−151+sec−125+2tan−181) is equal to:
(1)1
(2)2
(3)41
(4)45
62.
If α=cos−1(53),β=tan−1(31), where 0<α,β<2π, then α−β is equal to :
(1)tan−1(5109)
(2)cos−1(5109)
(3)tan1(149)
(4)sin−1(5109)
63.
Considering the principal values of inverse trigonometric functions, the value of the expression tan(2sin−1(132)−2cos−1(103)) is equal to :
(1)6316
(2)−5633
(3)−6316
(4)5633
64.
If cot−1(α)=cot−12+cot−18+cot−118+cot−132+…upto100terms, then α is :
(1)1.01
(2)1
(3)1.02
(4)1.03
65.
Let f(x)=cos(2tan−1sin(cot−1x1−x)),0 < x < 1. Then :
(1)(1−x)2f'(x) − 2(f(x)) 2 = 0
(2)(1 + x) 2f'(x) + 2(f(x)) 2 = 0
(3)(1 − x) 2f'(x) + 2(f(x))2 = 0
(4)(1 + x) 2 f'(x) − 2(f(x)) 2 = 0
66.
Let f(x)=(sin(tan−1x)+sin(cot−1x))2−1,∣x∣>1. If dxdy=21dxd(sin−1(f(x))) and y(3)=6π, then y(−3) is equal to:
(1)65π
(2)6−π
(3)3π
(4)32π
67.
If S is the sum of the first 10 terms of the series tan−1(31)+tan−1(71)+tan−1(131)+tan−1(211)+…thentan(S)is equal to:
(1)−56
(2)115
(3)1110
(4)65
68.
If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296, respectively, then the sum of common ratios of all such GPs is
(1)7
(2)29
(3)3
(4)14
69.
The solution of tan−1x+2cot−1x=32π is
(1)−31
(2)31
(3)−3
(4)3
70.
The domain of the function f(x)=sin−1(log4(4x))+17x−x2−16 is
(1)[−1,1]
(2)[1,4]
(3)[0,16]
(4)[1,16]
71.
Assertion: cosech−1(3)=log31+10. Reason: ecosech−1x is a root of the quadratic equation xp2−2p−x=0. The correct option among the following is
(1)(A) is true, (R) is true and (R) is the correct explanation for (A)
(2)(A) is true, (R) is true but (R) is not the correct explanation for (A)
(3)(A) is true but (R) is false
(4)(A) is false but (R) is true
72.
If a>b>0,sec−1(a−ba+b)=2sin−1x, then x=
(1)a+bb
(2)−a+bb
(3)a+ba
(4)−a+ba
73.
If x1,x2,x3 are the real roots of the equation x3−x2tanθ+xtan2θ+tanθ=0 and 0<θ<4π, then the value of tan−1x1+tan−1x2+tan−1x3 at θ=12π is
(1)6π
(2)4π
(3)3π
(4)2π
74.
The value of tan−1(sin(4π)cos(415π)−1) is equal to
(1)−4π
(2)−8π
(3)−125π
(4)−94π
75.
If (sin−1x)2−(cos−1x)2=a;0<x<1,a=0, then the value of 2x2-1 is :
(1)cos(π4a)
(2)sin(π2a)
(3)cos(π2a)
(4)sin(π4a)
76.
If a+2π<2tan−1x+3cot−1x<b then ' a ' and ' b ' are respectively
(1)0 and π
(2)0 and 2π
(3)2π and 2π
(4)2−π and 2π
77.
If cosh−1x=2loge(2+1), then x=
(1)1
(2)2
(3)4
(4)3
78.
If sinh−1(8)+sinh−1(24)=α, then sinhα=
(1)66−102
(2)66+102
(3)166
(4)166+42
79.
sinh−1(−2)+cosech−1(−2)+coth−1(−2)=
(1)log(237−35)
(2)log(233−5)
(3)log(237+35)
(4)log(233+5)
80.
If the domain of the function f(x)=sin−1(x2−2x−21), is (−∞,α]∪[β,γ]∪[δ,∞), then α+β+γ+δ is equal to
(1)2
(2)3
(3)4
(4)5
81.
Ifsin−1(x−2x2+4x3−…∞)+cos−1(x2−2x4+4x6−…∞)=2πand0<x<2,then x is equal to
(1)21
(2)1
(3)−21
(4)-1
82.
Solve for x,tan−1(1+x1−x)=21tan−1x,x>0
(1)1
(2)31
(3)3
(4)-1
83.
tan−1(31sin25π)+sin−1(cos(sin−123))=
(1)0
(2)6π
(3)3π
(4)π
84.
Given that the inverse trigonometric functions take principal values only. Then, the number of real values of xwhich satisfysin−1(53x)+sin−1(54x)=sin−1x is equal to:
(1)2
(2)1
(3)3
(4)0
85.
The number of solutions of tan−14x+tan−16x=6π, where −261<x<261, is equal to
(1)3
(2)0
(3)2
(4)1
86.
The sum of possible values of x fortan−1(x+1)+cot−1(x−11)=tan−1(318) is
(1)−432
(2)−431
(3)−430
(4)−433
87.
Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2sin−1x+3cos−1x=52π, is______
88.
Considering only the principal values of the inverse trigonometric functions, the value of 23cos−12+π22+41sin−12+π222π+tan−12/πis [2022 Adv.]
89.
If sin−1x+sin−1y+sin−1z=π, then x4+y4+z4+4x2y2z2=k(x2y2+y2z2+z2x2), where k= [JEE (Adv) 2015]
