If the determinant `|a+p l+x u+fb+q x+y v+gc+r n+z w+h|` splits into exactly `K` determinants of order 3, each element of which contains only one term, then the values of `K` is

If the determinant |(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h)| splits into exactly k determinants of order 3, each element of which contains onlyone term, then the value of k is 8.

Find the value of the determinant |b cc a a b p q r1 1 1|,w h e r ea ,b ,a n dc are respectively, the pth, qth, and rth terms of a harmonic progression.

If the equation of plane containing the line x-y+z=0a n dx+y+z-2=0 and which is farthest from origin is a x+b y+c z=d ,w h e r ea , b ,c ,d in N , then find the minimum value of (a+b+c+d)dot

Determine the value of k for which x+2 is a factor of (x+1)^7+(2x+k)^3dot

Determine the value of k for which x+2 is a factor of (x+1)^7+(2x+k)^3dot

If the line (x-2)/-1=(y+2)/1=(z+k)/4 is one of the angle bisector of the lines x/1=y/-2=z/3 and x/-2=y/3=z/1 then the value of k is

If vec u , vec v , vec w are noncoplanar vectors and p, q are real numbers, then the equality [3 vec u ,""p vec v , p vec w]-[p vec v ,"" vec w , q vec u]-[2 vec w ,""q vec v , q vec u]=0 holds for (A) exactly one value of (p, q) (B) exactly two values of (p, q) (C) more than two but not all values of (p, q) (D) all values of (p, q)

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot

If the value of the definite integral int_0^1 "^(207)C_7x^(200)(1-x)^7dx is equal to 1/k ,w h e r ek in N , then the value of k/(26) is____

Let If the set of values of k for which f(x) 0 is (p,q) then find the value of (4p+3q), where f(x)=kx^2+x(3-4k)-12.