1
JEE Main 2022 (Online) 26th June Morning Shift
Numerical
+4
-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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2
JEE Main 2022 (Online) 25th June Morning Shift
Numerical
+4
-1

The number of values of x in the interval $$\left( {{\pi \over 4},{{7\pi } \over 4}} \right)$$ for which

$$14\cos e{c^2}x - 2{\sin ^2}x = 21 - 4{\cos ^2}x$$ holds, is ____________.

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3
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
Let S be the sum of all solutions (in radians) of the equation $${\sin ^4}\theta + {\cos ^4}\theta - \sin \theta \cos \theta = 0$$ in [0, 4$$\pi$$]. Then $${{8S} \over \pi }$$ is equal to ____________.
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4
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
The probability distribution of random variable X is given by :

X 1 2 3 4 5
P(X) K 2K 2K 3K K

Let p = P(1 < X < 4 | X < 3). If 5p = $$\lambda$$K, then $$\lambda$$ equal to ___________.
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