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MCQ (More than One Correct Answer)

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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 $$\beta = 3{\cos ^{ - 1}}\left( {{4 \over 9}} ... JEE Advanced 2015 Paper 2 Offline Numerical More The value of$${\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$$[0, 4... JEE Advanced 2014 Paper 1 Offline MCQ (Single Correct Answer) More Match List$$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 $$I$$ $$P.$$...
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 $$\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\tan }^{ - 1}}\left( {{2 \over 3}} \right)}... IIT-JEE 1983 Subjective More Let$$(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

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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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