JEE Advanced 2014 Paper 2 Offline | Trigonometric Functions & Equations Question 16 | Mathematics

1

JEE Advanced 2014 Paper 2 Offline

MCQ (Single Correct Answer)

+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

2

JEE Advanced 2013 Paper 1 Offline

MCQ (Single Correct Answer)

+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

3

IIT-JEE 2011 Paper 1 Offline

MCQ (Single Correct Answer)

+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

$$P = Q$$

4

IIT-JEE 2009 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-0

Match the statements/expressions in Column I with the values given in Column II:

	Column I		Column II
(A)	Root(s) of the expression $$2{\sin ^2}\theta + {\sin ^2}2\theta = 2$$	(P)	$${\pi \over 6}$$
(B)	Points of discontinuity of the function $$f(x) = \left[ {{{6x} \over \pi }} \right]\cos \left[ {{{3x} \over \pi }} \right]$$, where $$[y]$$ denotes the largest integer less than or equal to y	(Q)	$${\pi \over 4}$$
(C)	Volume of the parallelopiped with its edges represented by the vectors $$\widehat i + \widehat j + \widehat i + 2\widehat j$$ and $$\widehat i + \widehat j + \pi \widehat k$$	(R)	$${\pi \over 3}$$
(D)	Angle between vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ where $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ are unit vectors satisfying $$\overrightarrow a + \overrightarrow b + \sqrt 3 \overrightarrow c = \overrightarrow 0 $$	(S)	$${\pi \over 2}$$
		(T)	$$\pi $$

A

(A)$$\to$$(Q), (S); (B)$$\to$$(P), (R), (S), (T); (C)$$\to$$(Q); (D)$$\to$$(T)

B

(A)$$\to$$(R), (S); (B)$$\to$$(P), (R), (S), (T); (C)$$\to$$(T); (D)$$\to$$(P)

C

(A)$$\to$$(Q), (S); (B)$$\to$$(P), (R), (S), (T); (C)$$\to$$(T); (D)$$\to$$(R)

D

(A)$$\to$$(P), (S); (B)$$\to$$(Q), (R), (S), (T); (C)$$\to$$(T); (D)$$\to$$(R)