`Ifint(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c ,t h e n` (a) `a=(sqrt(2))/5,b=1/(sqrt(5))` (b)`a=(sqrt(2))/5,b=5` (c)`a=(sqrt(2))/5,b=-1/(sqrt(5))` (d) `a=(sqrt(2))/5, b=sqrt(5)`

(a) sqrt(175) (b) 2sqrt(112) (c) sqrt(125) (d) 5sqrt(119)

If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a) (n y)/(sqrt(x^2+a^2)) (b) -(n y)/(sqrt(x^2+a^2)) (c) (n x)/(sqrt(x^2+a^2)) (d) -(n x)/(sqrt(x^2+a^2))

The centroid of an equilateral triangle is (0, 0). If two vertices of the triangle lie on x+y=2sqrt(2), then one of them will have its coordinates. (a) (sqrt(2)+sqrt(6),sqrt(2)-sqrt(6)) (b) (sqrt(2)+sqrt(3),sqrt(2)-sqrt(3)) (c) (sqrt(2)+sqrt(5),sqrt(2)-sqrt(5)) (d) none of these

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

The values of parameter a for which the point of minimum of the function f(x)=1+a^2x-x^3 satisfies the inequality (x^2+x+2)/(x^2+5x+6)<0a r e (a) (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (c) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))

The value of lim_(x->1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(sin^(-1)x))) is (a) -1/(sqrt(2)) (b) 1/(sqrt(2)) (c) sqrt(2) (d) -sqrt(2)

The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)))dx is equal to (a)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^3)))+c (b)e^x(1/(sqrt(1+x^2))-x/(sqrt((1+x^2)^3)))+c (c)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^5)))+c (d)none of these

Show that 4sin27^0=(5+sqrt(5))^(1/2)+(3-sqrt(5))^(1/2)

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

cos ^(-1)"" (1)/(sqrt(5))+ cos ^(-1) ""(2)/(sqrt(5))=(pi)/(2)