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1
JEE Main 2022 (Online) 29th June Morning Shift
Numerical  +4  -1
English
Hindi

The number of elements in the set $$S = \{ \theta \in [ - 4\pi ,4\pi ]:3{\cos ^2}2\theta + 6\cos 2\theta - 10{\cos ^2}\theta + 5 = 0\}$$ is __________.

2
JEE Main 2022 (Online) 29th June Morning Shift
Numerical  +4  -1
English
Hindi

The number of solutions of the equation

$$2\theta - {\cos ^2}\theta + \sqrt 2 = 0$$ in R is equal to ___________.

3
JEE Main 2022 (Online) 26th June Morning Shift
Numerical  +4  -1
English
Hindi
Bengali

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 __________.

4
JEE Main 2022 (Online) 25th June Morning Shift
Numerical  +4  -1
English
Hindi
Bengali

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 ____________.