If `k in R_o` then `det{adj(k I_n)}` is equal to (A) `K^(n-1)` (B) `K^((n-1)n)` (C) `K^n` (D) `k`

If A be any n xx n matrix and k any scalar, then detkA is equal to -

Let f(n ,k) denote the number of ways in which k identical balls can be colored with n colors so that there is at least one ball of each color. Then f(n ,2n) must be equal to a. ""^(2n) C_n b. ""^(2n-1)C_(n+1) c. ""^(2n-1)C_n d. none of these

(n)p_(r)=k^(n)C_(n-r),k=

Let x_1 , x_2 , x_3,....., x_k be the divisors of positive integer n (including 1 and n). If x_1 + x_2 + x_3 + ...... + x_k = 75 Then sum_(i=1)^k (1/x_i) is equal to (A) 75/k (B) 75/n (C) 1/n (D) 1/75

If .^(n)C_(3)=k.n(n-1)(n-2) then k=

Given (1-x^(3))^(n)=sum_(k=0)^(n)a_(k)x^(k)(1-x)^(3n-2k) then the value of 3*a_(k-1)+a_(k) is (a) "^(n)C_(k)*3^(k) (b) "^(n+1)C_(k)*3^(k) (c) "^(n+1)C_(k)*3^(k-1) (d) "^(n)C_(k-1)*3^(k)

sum_(i = 1)^n sum_(j = 1)^i sum_(k = 1)^j 1 is equal to

Let A be an nth-order square matrix and B be its adjoint, then |A B+K I_n| is (where K is a scalar quantity) a. (|A|+K)^(n-2) b. (|A|+K)^n c. (|A|+K)^(n-1) d. none of these

n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is a. sum_(k=1)^(n-1)k b. n(n-1) c. n^2 d. none of these

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is (a) ( b ) (c) y=( d ) e^(( e ) (f) K(( g ) (h) x-1( i ))( j ))( k ) (l) (m) (b) ( n ) (o) y=( p ) e^(( q ) (r) K e (s))( t ) (u) (v) (c) ( d ) (e) y=( f ) e^(( g ) (h) K(( i ) (j) x-2( k ))( l ))( m ) (n) (o) (d) None of these