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1

WB JEE 2010

MCQ (Single Correct Answer)

The number of points of intersection of 2y = 1 and y = sinx, in $$-$$2$$\pi$$ $$\le$$ x $$\le$$ 2$$\pi$$ is

A
1
B
2
C
3
D
4

Explanation

2y = 1 ..... (i)

y = sinx .... (ii)

On solving, $$\sin x = {1 \over 2}$$, which has 4 solutions in $$ - 2\pi \le x \le 2\pi $$

2

WB JEE 2010

MCQ (Single Correct Answer)

The value of $${{\cot x - \tan x} \over {\cot 2x}}$$ is

A
1
B
2
C
$$-$$1
D
4

Explanation

$${{\cot x - \tan x} \over {\cot 2x}} = {{1 - {{\tan }^2}x} \over {\tan x}}.\,\tan x$$

$$ = 2{1 \over {\left( {{{2\tan x} \over {1 - {{\tan }^2}x}}} \right)}}\tan 2x = {2 \over {\tan 2x}}.\,\tan 2x = 2$$

3

WB JEE 2010

MCQ (Single Correct Answer)

The value of $${{\sin 55^\circ - \cos 55^\circ } \over {\sin 10^\circ }}$$ is

A
$${1 \over {\sqrt 2 }}$$
B
2
C
1
D
$$\sqrt 2 $$

Explanation

$${{\sin 55^\circ - \cos (90^\circ - 35^\circ )} \over {\sin 10^\circ }} = {{\sin 55^\circ - \cos 35^\circ } \over {\sin 10^\circ }}$$

$$ = {{2\cos 45^\circ \sin 10^\circ } \over {\sin 10^\circ }} = 2{1 \over {\sqrt 2 }} = \sqrt 2 $$

4

WB JEE 2009

MCQ (Single Correct Answer)

If $$5\cos 2\theta + 2{\cos ^2}\theta /2 + 1 = 0$$, when $$(0 < \theta < \pi )$$, then the values of $$\theta$$ are

A
$${\pi \over 3} \pm \pi $$
B
$${\pi \over 3},{\cos ^{ - 1}}(3/5)$$
C
$${\cos ^{ - 1}}(3/5) \pm \pi $$
D
$${\pi \over 3},\pi - {\cos ^{ - 1}}(3/5)$$

Explanation

$$5\cos 2\theta + 2{\cos ^2}{\theta \over 2} + 1 = 0$$

$$ \Rightarrow 5(2{\cos ^2}\theta - 1) + (1 + \cos \theta ) + 1 = 0$$

$$ \Rightarrow 10{\cos ^2}\theta + \cos \theta - 3 = 0$$

$$ \Rightarrow \cos \theta = {1 \over 2}$$ or $$ - {3 \over 5}$$

If $$\cos \theta = {1 \over 2} \Rightarrow \theta = {\pi \over 3}$$,

If $$\cos \theta = - {3 \over 5} \Rightarrow \theta = {\cos ^{ - 1}}\left( { - {3 \over 5}} \right) = \pi - {\cos ^{ - 1}}{3 \over 5}$$

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