If `af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2)` is equal to (a)`(2a+b)/(2(a^2-b^2))` (b) `a/(a^2-b^2)` (c)`(a+2b)/(a^2-b^2)` (d) none of these

IfI=int(dx)/((a^2-b^2x^2)^(3/2)),t h e nIe q u a l (a) x/(a^2sqrt(a^2-b^2x^2))+C (b) x/(2sqrt(a^2-b^2x^2))+C (c) (a x)/(sqrt(a^2-b^2x^2))+C (d) none of these

If a x^2+2h x y+b y^2=1,t h e n(d^2y)/(dx^2) is (a) (h^2-a b)/((h x+b y)^2) (b) (a b-h^2)/((h x+b y)^2) (h^2+a b)/((h x+b y)^2) (d) none of these

If asinx+bcos(x+theta)+bcos(x-theta)=d , then the minimum value of |costheta| is equal to (a) 1/(2|b|)sqrt(d^2-a^2) (b) 1/(2|a|)sqrt(d^2-a^2) (c) 1/(2|d|)sqrt(d^2-a^2) (d) none of these

If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then a^2-b^2 is equal to 1/(a^2e^2) (b) a^2e^2 b^2e^2 (d) none of these

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (d) none of these

The locus of the point which divides the double ordinates of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 in the ratio 1:2 internally is (x^2)/(a^2)+(9y^2)/(b^2)=1 (b) (x^2)/(a^2)+(9y^2)/(b^2)=1/9 (9x^2)/(a^2)+(9y^2)/(b^2)=1 (d) none of these

The minimum value of 2^(x^2-3)^(3+27) is a) 2^(27) (b) 2 (c) 1 (d) none of these

If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a. a^2+c^2=-a b b. a^2-c^2=-a b c. a^2-c^2=a b d. none of these

lim_(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

If b >1,sint >0,cost >0a n d(log)_b(sint)=x ,t h e n(log)_b(cost) is equal to (a) 1/2(log)_b(1-b^(2x)) (b) 2log(1-b^(x/2)) (log)_bsqrt(1-b^(2x)) (d) sqrt(1-x^2)