All the values of `a` for which `int_1^2 [a^2+(4-4a)x+4x^3]dxle12` are given by (A) `a=3` (B) `ale4` (C) `0lealt3` (D) none of these

int_2^4 log[x]dx is (A) log2 (B) log3 (C) log5 (D) none of these

(2^3)^4 = 2^4^3 (b) 2^3^4 (2^4)^3 (d) none of these

The set of all values of a for which both roots of equation x^2-2ax+a^2-1=0 lies between -2 and 4 is (A) (-1,2) (B) (1,3) (C) (-1,3) (D) none of these

The value of k for which x -1 is a factor of 4X^3 + 3x^2 - 4x + k is (A) A 3 (B) 1 (C) -2 (D) -3

The value of int_0^(log5) (e^xsqrt(e^x-1))/(e^x+3)dx is (A) 3+2pi (B) 4-pi (C) 2+pi (D) none of these

If the two equations ax^(2)+bx+c=0 and 2x^(2)-3x+4=0 have a common root then (A) 6a=4b=-3c(B)3a=-4b=3c(C)6a=-4b=3c (D) none of these

Find the values of a for which all roots of the equation 3x^(4) + 4x^(3) – 12x^(2) + a = 0 are real and distinct.

For x>=0, the smallest possible value of the expression,log_(2)(x^(3)-4x^(2)+x+26)-log_(2)(x+2) is ( A ) 1(B) 2(C)5(D) None of these

The value of int_(a)^(b)(x-a)^(3)(b-x)^(4)dx is (A)((b-a)^(4))/(6^(4))(B)((b-a)^(8))/(280) (C) ((b-a)^(7))/(7^(3)) (D) none of these

The area bounded in the first quadrant by the normal at (1,2)on the curve ,y^2=4x,x-axis &the curve is given by (A) 10/3 (B) 7/3 (C) 4/3 (D) 9/2