Let `g(x)=cosx^2,f(x)=sqrt(x)` and `alpha,beta(alpha < beta)` be the roots of equation

Let g (x) =x ^(2),f (x) = sqrtx, and alpha, beta ( alpha lt beta) be the roots of the quadratic equation 18 x ^(2) - 9pix + pi^(2) =0. Then the area (is sq. units) bounded by curve y = (gof) (x) and the lines x =alpha, x = betaand y =0 is :

Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1) =5 alpha'(2) =7 then 2nd the vlaue of beta'(1)-10

Let f(x)=sin^(2)(x +alpha)+sin^(2)(x +beta)-2cos(alpha-beta)sin(x+alpha)sin(x +beta) . Which of the following is TRUE ?

Show that the solution of the equation [(x, y),(z, t)]^(2)=O is [(x,y),(z,t)]=[(pm sqrt(alpha beta),-beta),(alpha,pm sqrt(alpha beta))] where alpha, beta are arbitrary.

Let g(x)=|(f(x+alpha), f(x+2a), f(x+3alpha)), f(alpha), f(2alpha), f(3alpha),(f\'(alpha),(f\'(2alpha), f\'(3alpha))| , where alpha is a constant then Lt_(xrarr0(g(x))/x= (A) 0 (B) 1 (C) -1 (D) none of these

Let alpha_(1),beta_(1) be the roots x^(2)-6x+p=0 and alpha_(2),beta_(2) be the roots x^(2)-54x+q=0 .If alpha_(1),beta_(1),alpha_(2),beta_(2) form an increasing G.P.then sum of the digits of the value of (q-p) is

If alpha,beta, are roots of the equation x^(2)+sqrt(x)alpha+beta=0,beta beta then values of alpha and beta are 1. alpha=1 and beta=12 .alpha=1 and beta=-2 3.alpha=2 and beta=1alpha=2 and beta=-2

Let alpha,beta be real number with 0<=alpha<=beta and f(x)=x^(2)-(alpha+beta)x+alpha beta such that int_(1)^(1)f(x)dx=1. Find the maximum value of int_(alpha)^( alpha)f(x)dx