`pi` is

A

an integer

B

a rational number

C

an irrational number

D

None of these

Text Solution

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The correct Answer is:
C
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Let f(x)={pi-|x|,|x|

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The smallest positive root of the equation tan x-x=0 lies in (0,(pi)/(2)) (b) ((pi)/(2),pi)(pi,(3 pi)/(2)) (d) ((3 pi)/(2),2 pi)

f(x)=min(sin x,cos x),x in(-pi,pi) the values of x where f(x) is non differentiable,is the set A. Then A is subset of (A) {(-3 pi)/(4),(-pi)/(4),(3 pi)/(4)}(B){(-pi)/(4),(pi)/(4),(3 pi)/(3)}(C){(-3 pi)/(4),(3 pi)/(4)}(D){(-3 pi)/(4),(pi)/(4),(pi)/(4),(3 pi)/(4)}

The range of function f(x)=cot^(-1)x+sec^(-1)x+ cosec^(-1)x is (A) [(pi)/(2), pi)uu(pi, (3 pi)/(2)] (B) ((pi)/(2), (3 pi)/(4)] uu [(5 pi)/(4), (3 pi)/(2)) (C) ((pi)/(2), pi)uu(pi ,(3 pi)/(2)) (D) ((pi)/(2), (3 pi)/(2))

int _ (- 1) ^ ((3) / (2)) | x sin pi x | dx = [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (- 1) ^ (1) - [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (1) ^ ((3) / (2) )

int_(-(3pi)/2)^(-pi/2) {(pi+x)^3+cos^2(x+3pi)}dx is equal to (A) pi/4-1 (B) pi^4/32 (C) pi^4/32+pi/2 (D) pi/2

ARIHANT PUBLICATION JHARKHAND-MODEL SOLVED PAPER-SECTION-I : MATHEMATICS
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