NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

### WB JEE 2009

Simplest form of $${2 \over {\sqrt {2 + \sqrt {2 + \sqrt {2 + 2\cos 4x} } } }}$$ is

A
sec x/2
B
sec x
C
cosec x
D
1

## Explanation

$${2 \over {\sqrt {2 + \sqrt {2 + \sqrt {2 + 2\cos 4x} } } }}$$

$$= {2 \over {\sqrt {2 + \sqrt {2 + \sqrt {2(1 + 2{{\cos }^2}2x - 1)} } } }}$$

$$= {2 \over {\sqrt {2 + \sqrt {2(1 + 2{{\cos }^2}x - 1)} } }} = {2 \over {\sqrt {2 + 2\cos x} }}$$

$$= {2 \over {\sqrt {2(1 + 2{{\cos }^2}{x \over 2} - 1)} }} = {1 \over {\cos {x \over 2}}} = \sec {x \over 2}$$

2

### WB JEE 2009

In triangle ABC, a = 2, b = 3 and sin A = 2/3, thne B is equal to

A
30$$^\circ$$
B
60$$^\circ$$
C
90$$^\circ$$
D
120$$^\circ$$

## Explanation

Apply $${{\sin A} \over a} = {{\sin B} \over b}$$ (sine Rule)

$${{2/3} \over 2} = {{\sin B} \over 3} \Rightarrow \sin B = 1 = \sin 90^\circ$$

$$\Rightarrow B = 90^\circ$$

3

### WB JEE 2009

The smallest value of $$5\cos \theta + 12$$ is

A
5
B
12
C
7
D
17

## Explanation

$$\because$$ $$- 1 \le \cos \theta \le 1 \Rightarrow - 5 \le 5\cos \theta \le 5$$

$$\Rightarrow 12 - 5 \le 5\cos \theta + 12 \le 5 + 12$$

$$\Rightarrow 7 \le 5\cos \theta + 12 \le 17$$

$$\therefore$$ Smallest value of $$5\cos \theta + 12$$ is 7

4

### WB JEE 2009

A positive acute angle is divided into two parts whose tangents are 1/2 and 1/3. Then the angle is

A
$$\pi$$/4
B
$$\pi$$/5
C
$$\pi$$/3
D
$$\pi$$/6

## Explanation

Let $$\alpha$$ + $$\beta$$ = $$\theta$$ where tan $$\alpha$$ = $${1 \over 2}$$, tan $$\beta$$ = $${1 \over 3}$$

$$\therefore$$ $$\tan \theta = \tan (\alpha + \beta ) = {{\tan \alpha + \tan \beta } \over {1 - \tan \alpha \tan \beta }}$$

$$= {{{1 \over 2} + {1 \over 3}} \over {1 - {1 \over 2}.{1 \over 3}}} = 1$$

$$\Rightarrow \theta = {\pi \over 4}$$

### 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

NEET

Class 12