Let a,b,c be even natural numbers, then` /_\=|(a-x, a, a+x),(b-x, b, b+x),(c-x, c, c+x)|` is a multiple of (A) 2 (B) 5 (C) 3 (D) none of these

if a+b+c=0 then Delta=|{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 is

Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2dot Then, f(x) has a minimum at x= (a+b+c)/3 (b) 1/2 (c) 1/8 (d) none of these

In a A B C ,ifA B=x , B C=x+1,/_C=pi/3 , then the least integer value of x is 6 (b) 7 (c) 8 (d) none of these

The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are different) is satisfied by (A) x=(a+b+c0 (B) x= 1/3 (a+b+c) (C) x=0 (D) none of these

If a,b,c in G.P. x,y be the A.M.\'s between a,b and b,c respectively then (a/x+c/y)(b/x+b/y)= (A) 2 (B) -4 (C) 4 (D) none of these

If a ,\ b ,\ c are real numbers, then find the intervals in which f(x)=|(x+a^2,a b, a c),( a b, x+b^2,b c),( a c, b c, x+c^2)| is increasing or decreasing.

If a >0 and discriminant of a x^2+2b x+c is negative, then Delta = |(a,b,ax +b),(b,c,bx +c),(ax +b,bx +c,0)| is a. +v e b. (a c-b)^2(a x^2+2b x+c) c. -v e d. 0

Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a+b+c!=0.

If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x-b)(x-c) is (a) a+b+c (b) (a-b)(b-c)(c-a) (c) 0 (d) None of these

Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R . Then (a) a+c^2 2b (c) a-3b+c^2 < 0 (d) none of these