The vectors `(x,x+1,x+2),(x+3,x+3,x+5) and (x+6,x+7,x+8)` are coplanar for (A) all values of x (B) `xlt0` (C) `xgt0` (D) none of these

If the points (-0,-1,-2),(-3,-4,-5),(-6,-7,-8) and (x,x,x) are coplanar then x is (A) -2 (B) 0 (C) 3 (D) any real number

If the points (-0,-1,-2),(-3,-4,-5),(-6,-7,-8) and (x,x,x) are non coplanar then x is (A) -2 (B) 0 (C) 3 (D) any real number

If f(x)=x+1/x ,\ \ x >0 , then its greatest value is -2 (b) 0 (c) 3 (d) none of these

If f(1/x)+x^2f(x)=0, xgt0 and a=int_(1/x)^x f(t)dt, 1/2lexle2 , then a= (A) 1 (B) 0 (C) f(2)-f(1/2) (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 3/4 is equivalent to x/(28), then the value of x is (a) 6 (b) 7 (c) 8 (d) None of the above

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

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

If x^3+1/(x^3)=110 , then x+1/x=? (a) 5 (b) 10 (c) 15 (d) none of these

If x satisfies |x-1|+x-2|+|x-3| >= 6, then (a) 0 le x le 4 (b) x le 4 (c) x le 0 or x >= 4 (d) none of these