Roots of the equation `|x m n1a x n1a b x1a b c1|=0` are
independent of `m ,and n`
independent of `a ,b ,and c`
depend on `m ,n ,and a ,b ,c`
independent of `m , n and a ,b ,c`

Roots of the equations |{:(x,,m,,n,,1),(a,,x,,n,,1),(a,,b,,x,,1),(a,,b,,c,,1):}|=0 are

The term independent of x in (1+x)^m (1+1/x)^n is

The term independent of x in (1+x)^m (1+1/x)^n is

If a and b are respective coefficients of x^m and x^n in the expansion of (1+ x)^(m+n) then

The expression log_p.log_p(((p)^(1/p))^(1/p)........n time)^(1/p) where p>= 2 , when simplified is (A)independent of p, but dependent on n (B) independent of n, but dependent on p (C) dependent on both p & n (D) negative

The value of the determinant |a^2a1cosn xcos(n+1)xcos(n+2)xsinn xsin(n+1)xsin(n+2)x| is independent of n (b) a (c) x (d) none of these

The value of the determinant |a^2a1cosn xcos(n+a)xcos(n+2)xsinn xsin(n+1)xsin(n+2)x| is independent of n (b) a (c) x (d) none of these

In Figure, M ,N and P are the mid-points of A B ,A C and B C respectively. If M N=3c m ,N P=3. 5c m and M P=2. 5c m , calculate B C ,A B and A Cdot

The value of the determinant |(alpha,beta,l),(alpha,x, n),(alpha,beta,x)| is independent of l b. independent of n c. alpha(x-l)(x-beta) d. alphabeta(x-l)(x-n)

If mgt0, ngt0 , the definite integral I=int_0^1 x^(m-1)(1-x)^(n-1)dx depends upon the values of m and n is denoted by beta(m,n) , called the beta function.Obviously, beta(n,m)=beta(m,n) .Now answer the question:If int_0^oo x^(m-1)/(1+x)^(m+n)dx=k int_0^oo x^(n-1)/(1+x)^(m+n)dx , then k is equal to (A) m/n (B) 1 (C) n/m (D) none of these