1
JEE Advanced 2016 Paper 1 Offline
+3
-1
Let $$S = \left\{ {x \in \left( { - \pi ,\pi } \right):x \ne 0, \pm {\pi \over 2}} \right\}.$$ The sum of all distinct solutions of the equation $$\sqrt 3 \,\sec x + \cos ec\,x + 2\left( {\tan x - \cot x} \right) = 0$$ in the set S is equal to
A
$$- {{7\pi } \over 9}$$
B
$$- {{2\pi } \over 9}$$
C
0
D
$${{5\pi } \over 9}$$
2
JEE Advanced 2014 Paper 2 Offline
+3
-1
For $$x \in \left( {0,\pi } \right),$$ the equation $$\sin x + 2\sin 2x - \sin 3x = 3$$ has
A
infinitely many solutions
B
three solutions
C
one solution
D
no solution
3
JEE Advanced 2013 Paper 1 Offline
+4
-1
The number of points in $$\left( { - \infty \,\infty } \right),$$ for which $${x^2} - x\sin x - \cos x = 0,$$ is
A
6
B
4
C
2
D
0
4
IIT-JEE 2011 Paper 1 Offline
+3
-1

Let $$P = \{ \theta :\sin \theta - \cos \theta = \sqrt 2 \cos \theta \}$$ and $$Q = \{ \theta :\sin \theta + \cos \theta = \sqrt 2 \sin \theta \}$$ be two sets. Then

A
$$P \subset Q$$ and $$Q - P \ne \emptyset$$
B
$$Q \not\subset P$$
C
$$P \not\subset Q$$
D
$$P = Q$$
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