1
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
2
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
3
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
$$P = Q$$
4
IIT-JEE 2009 Paper 2 Offline
+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)
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