1

JEE Advanced 2016 Paper 1 Offline

MCQ (Single Correct Answer)
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

MCQ (Single Correct Answer)
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

MCQ (Single Correct Answer)
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

MCQ (Single Correct Answer)

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
$$P = Q$$

Explanation

$$P = \{ \theta :\sin \theta - \cos \theta = \sqrt 2 \cos \theta \} $$

$$ \Rightarrow \cos \theta \left( {\sqrt 2 + 1} \right) = \sin \theta $$

$$ \Rightarrow \tan \theta = \sqrt 2 + 1$$ ..... (i)

$$Q = \{ \theta :\sin \theta + \cos \theta = \sqrt 2 \sin \theta \} $$

$$ \Rightarrow \sin \theta \left( {\sqrt 2 - 1} \right) = \cos \theta $$

$$ \Rightarrow \tan \theta = {1 \over {\sqrt 2 - 1}} \times {{\sqrt 2 + 1} \over {\sqrt 2 + 1}}$$

$$ = \left( {\sqrt 2 + 1} \right)$$ ...... (ii)

$$\therefore$$ $$P = Q$$

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12