`Ifx^2+y^2=1a n dP=(3x-4x^3)^2+(3y-4y^3)^2,t h e nPi se q u a lto`

If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e nai se q u a l 1/3 (b) 2/3 (c) -1/3 (d0 -2/3

Ifint_0^1cot^(-1)(1-x+x^2)dx=lambdaint_0^1tan^(-1)x dx ,t h e nlambdai se q u a lto 1 (b) 2 (c) 3 (d) 4

L e tI_1=thetaint_0^1(e^xdx)/(1+x)a n dI_2thetaint_0^1(x^2dx)/(e^x^3(2-x^3))dott e h n(I_1)/(I_2)i se q u a lto 3/e (b) e/3 (c) 3e (d) 1/(3e)

intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e r ea , b in R^+)i se q u a lto 1/(6lna^2b^3)a^(2x)b^(3x)ln(a^(2x)b^(3x))/e+k 1/(6lna^2b^3)1/(a^(2x)b^(3x))ln1/(e a^(2x)b^(3x))+k 1/(6lna^2b^3)1/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k -1/(6lna^2b^3)1/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k

If x ,y ,a n dz are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2x y ,t h e nu is always a. non-negative b. zero c. non-positive d. none of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) non of these

(lim)_(nvecoo)1/x[int_y^a e^(sin^2t))dt-int_(x+y)^a e^(sin^2t))dt-]i se q u a lto (0,1] (b) [1,oo) (0,oo) (d) none of these

The HCF of x^(2) - y^(2), x^(3) - y^(3), …... x^(n) - y^(n) , where n in N is ………. .

Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot