If `intx^5(1+x^3)^(2/3)dx=A(1+x^3)^(8/3)+B(1+x^3)^(5/3)+C ,`then A) `A=1/4,B=1/5`` (b) `A=1/8,B=-1/ `A=-1/8,B=1/5 (d) none of these`

intx^(8)(1+x^(9))^(5)dx :

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

int_0^oo(dx)/([x+sqrt(x^2+1)]^3)i se q u a lto 3/8 (b) 1/8 (c) -3/8 (d) none of these

If S=(1/2)^2+((1/2)^2 1)/3+((1/2)^3 1)/4+((1/2)^4 1)/5+...... ,t h e n (a) S=ln8-2 (b) S=ln(4/e) (c) S=ln4+1 (d) none of these

If A=[(1, 9), (3, 4), (8, -3)], B=[(5, 7), (3, 3), (1, 0)] then verify that A+B=B+A

The range of the function f(x)=|x-1|+|x-2|,-1lt=xlt=3, is [1,3] (b) [1,5] (c) [3,5] (d) none of these

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these

The straight lines 4a x+3b y+c=0 , where a+b+c are concurrent at the point a) (4,3) b) (1/4,1/3) c) (1/2,1/3) d) none of these