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

AIEEE 2002

MCQ (Single Correct Answer)
Which one is not periodic
A
$$\left| {\sin 3x} \right| + {\sin ^2}x$$
B
$$\cos \sqrt x + {\cos ^2}x$$
C
$$\cos \,4x + {\tan ^2}x$$
D
$$cos\,2x + \sin x$$

Explanation

$$\sqrt x$$ is non periodic function and $$\cos \left( {something} \right)$$ is a periodic function so here in $$\cos \sqrt x$$ $$\to$$ inside periodic function there is non periodic function which always produce non periodic function.

$${{{\cos }^2}x}$$ is a periodic function with period $$\pi$$

Note :
(1) When $$n$$ is odd then the period of $${\sin ^n}\theta$$, $${\cos ^n}\theta$$, $${\csc ^n}\theta$$, $${\sec ^n}\theta$$ = $$2\pi$$

(2) When $$n$$ is even then the period of $${\sin ^n}\theta$$, $${\cos ^n}\theta$$, $${\csc ^n}\theta$$, $${\sec ^n}\theta$$ = $$\pi$$

(3) When $$n$$ is even/odd then the period of $${\tan ^n}\theta$$, $${\cot ^n}\theta$$ = $$\pi$$

(3) When $$n$$ is even/odd then the period of $$\left| {{{\sin }^n}\theta } \right|$$, $$\left| {{{\cos }^n}\theta } \right|$$, $$\left| {{{\csc }^n}\theta } \right|$$, $$\left| {{{\sec }^n}\theta } \right|$$, $$\left| {{{\tan }^n}\theta } \right|$$, $$\left| {{{\cot }^n}\theta } \right|$$ = $$\pi$$

$$\cos \sqrt x + {\cos ^2}x$$ = non periodic function + periodic function = non periodic function
2

AIEEE 2002

MCQ (Single Correct Answer)
The number of solution of $$\tan \,x + \sec \,x = 2\cos \,x$$ in $$\left[ {0,\,2\,\pi } \right]$$ is
A
2
B
3
C
0
D
1

Explanation

Given equation is $$\tan \,x + \sec \,x = 2\cos \,x$$

$$\Rightarrow$$ $${{\sin x} \over {\cos x}}$$$$+ {1 \over {\cos x}}$$ $$= 2\cos x$$

$$\Rightarrow$$ $${{\sin x + 1} \over {\cos x}} = 2\cos x$$

$$\Rightarrow$$ $${\sin x + 1}$$ $$=$$ $$2{\cos ^2}x$$

$$\Rightarrow$$ $${\sin x + 1}$$ $$= 2\left( {1 - {{\sin }^2}x} \right)$$

$$\Rightarrow$$ $$2{\sin ^2}x + \sin x - 1 = 0$$

$$\Rightarrow$$ $$\left( {2\sin x - 1} \right)\left( {1 + \sin x} \right)$$$$= 0$$

$$\Rightarrow$$ $${\sin x = {1 \over 2}}$$ and $${\sin x = - 1}$$

When $${\sin x = {1 \over 2}}$$ then possible $$x$$ = $$30^\circ$$, $$150^\circ$$

When $${\sin x = - 1}$$ then possible $$x$$ = $$270^\circ$$

So three solutions possible.
3

AIEEE 2002

MCQ (Single Correct Answer)
The period of $${\sin ^2}\theta$$ is
A
$${\pi ^2}$$
B
$$\pi$$
C
$$2\pi$$
D
$$\pi /2$$

Explanation

The period of $${\sin ^2}\theta$$ is = $$\pi$$

Note :
(1) When $$n$$ is odd then the period of $${\sin ^n}\theta$$, $${\cos ^n}\theta$$, $${\csc ^n}\theta$$, $${\sec ^n}\theta$$ = $$2\pi$$

(2) When $$n$$ is even then the period of $${\sin ^n}\theta$$, $${\cos ^n}\theta$$, $${\csc ^n}\theta$$, $${\sec ^n}\theta$$ = $$\pi$$

(3) When $$n$$ is even/odd then the period of $${\tan ^n}\theta$$, $${\cot ^n}\theta$$ = $$\pi$$

(3) When $$n$$ is even/odd then the period of $$\left| {{{\sin }^n}\theta } \right|$$, $$\left| {{{\cos }^n}\theta } \right|$$, $$\left| {{{\csc }^n}\theta } \right|$$, $$\left| {{{\sec }^n}\theta } \right|$$, $$\left| {{{\tan }^n}\theta } \right|$$, $$\left| {{{\cot }^n}\theta } \right|$$ = $$\pi$$

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