IIT-JEE 2011 Paper 1 Offline | Trigonometric Functions & Equations Question 21 | Mathematics

1

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

$$P = Q$$

2

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)

3

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-1

Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

	Column I		Column II
(A)	The minimum value of $${{{x^2} + 2x + 4} \over {x + 2}}$$ is	(P)	0
(B)	Let A and B be 3 $$\times$$ 3 matrices of real numbers, where A is symmetric, B is skew-symmetric and (A + B) (A $$-$$ B) = (A $$-$$ B) (A + B). If (AB)$$^t$$ = ($$-1$$)$$^k$$ AB, where (AB)$$^t$$ is the transpose of the matrix AB, then the possible values of k are	(Q)	1
(C)	Let $$a=\log_3\log_3 2$$. An integer k satisfying $$1 < {2^{( - k + 3 - a)}} < 2$$, must be less than	(R)	2
(D)	If $$\sin \theta = \cos \varphi $$, then the possible values of $${1 \over \pi }\left( {\theta + \varphi - {\pi \over 2}} \right)$$ are	(S)	3

A

A - iii; B - ii, iv; C - iii, iv; D - i, iii

B

A - iii; B - ii; C - iii, iv; D - i, iii

C

A - ii; B - ii, iv; C - iii, iv; D - i

D

A - ii; B - ii, iv; C - iii, iv; D - i, iii

4

IIT-JEE 2007

MCQ (Single Correct Answer)

+3

-0.75

The number of solutions of the pair of equations $$$\,2{\sin ^2}\theta - \cos 2\theta = 0$$$ $$$2co{s^2}\theta - 3\sin \theta = 0$$$

in the interval $$\left[ {0,2\pi } \right]$$

A

zero

B

one

C

two

D

four