The total number of distinct `x in R` for which `|[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10` is (A) 0 (B) 1 (C) 2 (D) 3

If x+1/x=2, then x^3+1/(x^3)=? (a)64 (b) 14 (c) 8 (d) 2

Total number of positive integers x for which f(x)=x^(3)-8x^(2)+20x-13 is prime number,is 1 b.2 c.3 d.4

Total number of positive integers x for which f(x)=x^(3)-8x^(2)+20x-13 is a prime number,is 1( b) 2(c)3 (d) 4

If X^2+4x+3=0 , then the value of (X^3)/(X^6+27x^3+27 is (A) -1 (B) -frac(1)(2) (C) 1 (D) 1/2

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2) ,((x-1)^2, (x-2)^2, (x-3)^2), ((x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

If (x_i , 1/x_i), i = 1, 2, 3, 4 are four distinct points on a circle, then (A) x_1 x_2 = x_3 x_4 (B) x_1 x_2 x_3 x_4 = 1 (C) x_1 + x_2 + x_3 + x_4 = 1 (D) 1/x_1 + 1/x_2 + 1/x_3 + 1/x_4 = 1

If (x_i , 1/x_i), i = 1, 2, 3, 4 are four distinct points on a circle, then (A) x_1 x_2 = x_3 x_4 (B) x_1 x_2 x_3 x_4 = 1 (C) x_1 + x_2 + x_3 + x_4 = 1 (D) 1/x_1 + 1/x_2 + 1/x_3 + 1/x_4 = 1

The coefficient of x^(2) in the expansion of the determinant |(x^(2) , x^(3) +1, x^(5)+2),(x^(3)+3, x^(2)+x, x^(3)+x^(4)),(x+4,x^(3)+x^(4),2^(3))| is a) -10 b) -8 c) -2 d) -6

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

If 8x^(4) - 2x^(3) - 27x^(2) + 6x + 9 = 0 then s_(1), s_(2), s_(3) , s_(4) are