If a= ` 2^(x) and b= 2^(x+ 1) , `
Show that , `( 8 a^(3))/( b^(2)) = 2^(x+1)`

If a = b^(2x) , b = c^(2y) and c = a^(2z) , show that 8xyz = 1.

If (x+i y)^(1//3)=a+i b ,x ,y ,a b in Rdot Show that x/a+y/b=4(a^2-b^2) (ii) x/a-y/b=2(a^2+b^2)

If A=[{:( 0,-x),(x,0):}].B=[{:(0,1),(1,0):}] and x^(2)=-1 , then show that (A+B)^(2)=A^(2)+B^(2) .

If the coefficient x^(2) and x^(3) in the expansion of (1 + 8x + bx^(2))(1 - 3x)^(9) in the power of x are equal , then b is :

If two circles x^(2)+y^(2)+2a_(1)x+2b_(1)y=0 and x^(2)+y^(2)+2a_(2)x+2b_(2)y=0 touches then show that a_(1)b_(2)=a_(2)b_(1)

If X=1+a+a^(2)+a^(3)+"..."+infty " and " y=1+b+b^(2)+b^(3)+"..."+infty " show that 1+ab+a^(2)b^(2)+a^(3)b^(3)+"..."+infty=(xy)/(x+y-1), "where " 0ltalt1" and "0ltblt1 .

If the image of the point (x_1, y_1) with respect to the mirror ax+by+c=0 be (x_2 , y_2) then. (a) (x_2-x_1)/a = (a x_1 + b y_1+ c)/(a^(2)+b^(2)) (b) (x_2-x_1)/a = (y_2 - y_1)/b (c) (x_2-x_1)/a = -2 ((a x_1 + b y_1+ c)/(a^(2)+b^(2))) (d) None of these

If (x-2)/3=(2x-1)/3-1, then x= (a) 2 (b) 4 (c) 6 (d) 8

If A=[(0,-x),(x,0)] , B=[(0 ,1 ),(1 ,0)] and x^2=-1 , then show that (A+B)^2=A^2+B^2 .

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