Algebra
Sets and RelationsLogarithmsSequence and SeriesQuadratic EquationsPermutations and CombinationsMathematical Induction and Binomial TheoremMathematical InductionBinomial TheoremMatrices and DeterminantsVector AlgebraThree Dimensional GeometryProbabilityComplex NumbersStatisticsTrigonometry
Trigonometric Functions & EquationsInverse Trigonometric FunctionsProperties of TriangleCoordinate Geometry
Straight Lines and Pair of Straight LinesCircleParabolaEllipseHyperbolaCalculus
FunctionsLimits, Continuity and DifferentiabilityDifferentiationApplication of DerivativesIndefinite IntegralsDefinite IntegrationApplication of IntegrationDifferential EquationsInverse Trigonometric Functions
Practice QuestionsMCQ (Single Correct Answer)
1
The value of $$\tan \alpha + 2\tan (2\alpha ) + 4\tan (4\alpha ) + ... + {2^{n - 1}}\tan ({2^{n - 1}}\alpha ) + {2^n}\cot ({2^n}\alpha )$$ is
WB JEE 2008
2
$$\tan \left[ {{\pi \over 4} + {1 \over 2}{{\cos }^{ - 1}}\left( {{a \over b}} \right)} \right] + \tan \left[ {{\pi \over 4} - {1 \over 2}{{\cos }^{ - 1}}\left( {{a \over b}} \right)} \right]$$ is equal to
WB JEE 2009
3
Value of $${\tan ^{ - 1}}\left( {{{\sin 2 - 1} \over {\cos 2}}} \right)$$ is
WB JEE 2010
4
The solution set of the inequation $${\cos ^{ - 1}}x < {\sin ^{ - 1}}x$$ is
WB JEE 2011
5
If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$, then $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$ is equal to
WB JEE 2025
6
The number of solutions of $\sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x$ is
WB JEE 2025
7
For $$y = {\sin ^{ - 1}}\left\{ {{{5x + 12\sqrt {1 - {x^2}} } \over {13}}} \right\};\left| x \right| \le 1$$, if $$a(1 - {x^2}){y_2} + bx{y_1} = 0$$ then (a, b) =
WB JEE 2021
8
If $$0 \le A \le {\pi \over 4}$$, then $${\tan ^{ - 1}}\left( {{1 \over 2}\tan 2A} \right) + {\tan ^{ - 1}}(\cot A) + {\tan ^{ - 1}}({\cot ^3}A)$$
WB JEE 2018
9
The possible values of x, which satisfy the trigonometric equation
$${\tan ^{ - 1}}\left( {{{x - 1} \over {x - 2}}} \right) + {\tan ^{ - 1}}\left( {{{x + 1} \over {x + 2}}} \right) = {\pi \over 4}$$ are
$${\tan ^{ - 1}}\left( {{{x - 1} \over {x - 2}}} \right) + {\tan ^{ - 1}}\left( {{{x + 1} \over {x + 2}}} \right) = {\pi \over 4}$$ are
WB JEE 2017
10
If $$f(x) = {\tan ^{ - 1}}\left[ {{{\log \left( {{e \over {{x^2}}}} \right)} \over {\log (e{x^2})}}} \right] + {\tan ^{ - 1}}\left[ {{{3 + 2\log x} \over {1 - 6\log x}}} \right]$$, then the value of f''(x) is equal to
WB JEE 2016