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## Numerical

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Considering only the principal values of the inverse trigonometric functions, the value of $$\frac{3}{2} \cos ^{-1} \s... JEE Advanced 2022 Paper 1 Online The value of$${\sec ^{ - 1}}\left( \matrix{ {1 \over 4}\sum\limits_{k = 0}^{10} {\sec \left( {{{7\pi } \over {12}} + ...
JEE Advanced 2019 Paper 2 Offline
The number of real solutions of the equation \eqalign{ &amp; {\sin ^{ - 1}}\left( {\sum\limits_{i = 1}^\infty {} {x... JEE Advanced 2018 Paper 1 Offline Let f : [0, 4\pi$$]$$\to$$[0,$$\pi$$] be defined by f(x) = cos$$-$$1 (cos x). The number of points x$$\in$$[0, 4... JEE Advanced 2014 Paper 1 Offline ## MCQ (More than One Correct Answer) More For any positive integer n, let Sn : (0,$$\infty$$)$$\to$$R be defined by$${S_n}(x) = \sum\nolimits_{k = 1}^n {{{\co...
JEE Advanced 2021 Paper 1 Online
For any positive integer n, define $${f_n}:(0,\infty ) \to R$$ as$${f_n} = \sum\limits_{j = 1}^n {{{\tan }^{ - 1}}} \lef... JEE Advanced 2018 Paper 2 Offline If$$\alpha  = 3{\sin ^{ - 1}}\left( {{6 \over {11}}} \right)$$and$$\beta = 3{\cos ^{ - 1}}\left( {{4 \over 9}} ...
JEE Advanced 2015 Paper 2 Offline

## MCQ (Single Correct Answer)

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Match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists: $$\,\,\,\,$$ $$\,\... JEE Advanced 2014 Paper 2 Offline Match List$$I$$with List$$II$$and select the correct answer using the code given below the lists: List$$IP.$$... JEE Advanced 2013 Paper 2 Offline The value of$$\cot \left( {\sum\limits_{n = 1}^{23} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{k = 1}^n {2k} } \right)...
JEE Advanced 2013 Paper 1 Offline
If $$0 &lt; x &lt; 1$$, then $$\sqrt {1 + {x^2}} {\left[ {{{\left\{ {x\cos \left( {{{\cot }^{ - 1}}x} \right) + \sin \l... IIT-JEE 2008 The value of$$x$$for which$$sin\left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = \cos \left( {{{\tan }^{ - 1}...
IIT-JEE 2004 Screening
If $${\sin ^{ - 1}}\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 4} - ....} \right)$$ $$+ {\cos ^{ - 1}}\left( {{x^2... IIT-JEE 2001 Screening The number of real solutions of$${\tan ^{ - 1}}\,\,\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\,\,\sqrt {{x^2} +...
IIT-JEE 1999
If we consider only the principle values of the inverse trigonometric functions then the value of $$\tan \left( {{{\cos... IIT-JEE 1994 The principal value of$${\sin ^{ - 1}}\left( {\sin {{2\pi } \over 3}} \right)$$is IIT-JEE 1986 The value of$$\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\tan }^{ - 1}}\left( {{2 \over 3}} \right)}...
IIT-JEE 1983

## Subjective

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Let $$(x, y)$$ be such that $${\sin ^{ - 1}}\left( {ax} \right) + {\cos ^{ - 1}}\left( y \right) + {\cos ^{ - 1}}\left( ... IIT-JEE 2007 Match the following Column$$I$$(A)$$\sum\limits_{i = 1}^\infty {{{\tan }^{ - 1}}\left( {{1 \over {2{i^2}}}} \right)...
IIT-JEE 2006
Prove that $$\cos \,ta{n^{ - 1}}\sin \,{\cot ^{ - 1}}x = \sqrt {{{{x^2} + 1} \over {{x^2} + 2}}}$$.
IIT-JEE 2002
Find all the solution of $$4$$ $${\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x$$
IIT-JEE 1983
Find the value of : $$\cos \left( {2{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \right)$$ at $$x = {1 \over 5}$$, where $$0 ... IIT-JEE 1981 ## Fill in the Blanks More The greater of the two angles$$A = 2{\tan ^{ - 1}}\left( {2\sqrt 2 - 1} \right)$$and$$B = 3{\sin ^{ - 1}}\left( {1/3...
IIT-JEE 1989
The numerical value of $$\tan \left\{ {2{{\tan }^{ - 1}}\left( {{1 \over 5}} \right) - {\pi \over 4}} \right\}$$ is eq...
IIT-JEE 1984
Let $$a, b, c$$ be positive real numbers Let \theta = {\tan ^{ - 1}}\sqrt {{{a\left( {a + b + c} \right)} \over {bc}...
IIT-JEE 1981

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