If `int_0^1 e^(x^2)(x-alpha)dx=0`, then (a)`alphalt2` (b)= `alphalt0` `(c)="" 0ltalphalt1` (d)= `alpha="0`

If int_(0)^(1) (3x^(2) + 2x+ alpha)dx =0, " then " alpha=

If I=int_(0)^(2)e^(x^(4))(x-alpha)dx=0 , then alpha lies in the interval

int_(0)^(1)(x^(alpha)-1)/(log x)dx=

If int_(0)^(alpha) (3x^(2) + 2x + 1) dx = 14, " then " alpha =

int_(0)^(1)(e^(-2x))/(1+e^(-x))dx=

If alpha and beta (alphaltbeta) are the roots of equationx^2+bx+c=0, where clt0ltb,then a) 0ltalphaltbeta (b) alphalt0ltbetalt|alpha|(c) alphaltbetalt0(d) alphalt0|alpha|ltbeta

The value of int_(0)^((pi)/(2))sin|2x-alpha|dx, where alpha in[0,pi], is (a) 1-cos alpha(b)1+cos alpha(c)1 (d) cos alpha

If int_(0)^(1)e^(x^(2))(x-a)dx=0 , then the value of int_(0)^(1)e^(X^(2))dx is euqal to

If alpha and beta (alphaltbeta) are the roots of the equation x^2+bx+a=0, where alt0ltb, then (A) alphagt0 (B) alphalt0 (C) betalt0 (D) betalt|alpha|

Let f (x) = log _e (sinx ), ( 0 lt x lt pi ) and g(x) = sin ^(-1) (e ^(-x)), (x ge 0) . If alpha is a positive real number such that a = ( fog)' ( alpha ) and b = (fog ) ( alpha ) , then (A) aalpha ^(2) - b alpha - a = 0 (B) a alpha ^(2) - b alpha - a = 1 (C) a alpha ^(2) + b alpha - a = - 2 alpha ^(2) (D) a alpha ^(2) + b alpha + a = 0