If `lim_(x->0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0`,where `theta in (-pi,pi],` then the value of `theta` is (a)`+-pi/4` (b) `+-pi/3` (c) `+-pi/6` (d) `+-pi/2`

If lim_(xto0) [1+xln(1+b^(2))]^(1//x)=2bsin^(2)theta,bgt0," and "thetain(-pi,pi], then the value of theta is

If (costheta+cos2theta)^3=cos^3theta+cos^3 2theta, then the least positive value of theta is equal to pi/6 (b) pi/4 (c) pi/3 (d) pi/2

If (1-tan theta)(1+tan theta)sec^2 theta+2^(tan^2 theta)=0 then in the interval (-pi/2,pi/2), the value of theta is

Let f(x) be positive, continuous, and differentiable on the interval (a , b)a n d lim_(x->a^+)f(x)=1,lim_(x->b^-)f(x)=3^(1/4)dot If f^(prime)(x)geqf^3(x)+1/(f(x)), then the greatest value of b-a is (a) pi/(48) (b) pi/(36) (c) pi/(24) (d) pi/(12)

If sintheta=1/2a n dcostheta=-(sqrt(3))/2, then the general value of theta is (n in Z)dot (a) 2npi+(5pi)/6 (b) 2npi+pi/6 2npi+(7pi)/6 (d) 2npi+pi/4

If theta in (pi//4, pi//2) and sum_(n=1)^(oo)(1)/(tan^(n)theta)=sin theta + cos theta , then the value of tan theta is

Tangent is drawn to ellipse (x^2)/(27)+y^2=1 at (3sqrt(3)costheta,sintheta) [where theta in (0,pi/2)] Then the value of theta such that sum of intercepts on axes made by this tangent is minimum is pi/3 (b) pi/6 (c) pi/8 (d) pi/4

One of the root equation cosx-x+1/2=0 lies in the interval (a) (0,pi/2) (b) (-pi/(2,0)) (c) (pi/2,pi) (d) (pi,(3pi)/2)

If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z) (a) 2npi (b) 2npi+pi/2 (c) 2npi-pi/2 (d) npi

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to (a) pi/2 (b) -pi (c) pi (d) -pi/2