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 (A) x=0 (B) x=1 (C) x=2 (D) None of these.

If a , b , c , , x , y , z are 26 natural numbers, then the value of (x-a)(x-b)(x-c)ddot(x-y)(x-z) is (a) 0 (b) 1 (c) 13 (d) 26

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 = { x : x is an even natural number}, B = { x : x is a natural number and multiple of 5 } and C= { x : x is a natural number and multiple of 10}, then what is A cap(B cup C) equal to ?

If A= {x : x is a natural number}, B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number }, find (i) A nnB (ii) A nnC (iii) A nnD (iv) B nnC (v) B nnD (vi) C nnD

Let a, b, c, d be distinct real numbers such that a, b are roots of x^2-5cx-6d=0 and c, d are roots of x^2-5ax-6b=0 . Then b+d is

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