JEE Main 2024 (Online) 27th January Morning Shift

Numerical

-1

Let the set of all $a \in \mathbf{R}$ such that the equation $\cos 2 x+a \sin x=2 a-7$ has a solution be $[p, q]$ and $r=\tan 9^{\circ}-\tan 27^{\circ}-\frac{1}{\cot 63^{\circ}}+\tan 81^{\circ}$, then pqr is equal to ____________.

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JEE Main 2023 (Online) 6th April Evening Shift

Numerical

-1

The value of $$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$$ is __________.

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JEE Main 2022 (Online) 26th June Morning Shift

Numerical

-1

If $${\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin (10^\circ )$$, then $$16 + {\alpha ^{ - 1}}$$ is equal to __________.

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JEE Main 2021 (Online) 26th February Morning Shift

Numerical

-1

The number of integral values of 'k' for which the equation $$3\sin x + 4\cos x = k + 1$$ has a solution, k$$\in$$R is ___________.

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