Statement 1:
`"Delta"=`
`|[m y+n z, m q+n r, m b+n c],[k z-m x, k r-m p, k c-m a],[-n x-k y,-n p-k q,-n a-k b]|` is equal to 0. Statement 2: The value of skew symmetric matrix of order 3 is zero.

For 3xx3 matrices M \ a n d \ N , which of the following statement (s) is (are) NOT correct ? Statement - I : N^T M N is symmetric or skew-symmetric, according as M is symmetric or skew-symmetric. Statement - II : M N-N M is skew-symmetric for all symmetric matrices Ma n dN . Statement - III : M N is symmetric for all symmetric matrices M a n dN . Statement - IV : (a d jM)(a d jN)=a d j(M N) for all invertible matrices Ma n dN .

Statement 1: ""^m C_r+ ""^m C_(r-1)(""^nC_1)+ ""^mC_(r-2)(""^n C_2)+....+ ""^n C_r=0 , if m+n lt r Statement 2: ""^n C_r=0 , if n lt r (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Assume X, Y, Z, W and P are matrices of order 2xx n, 3xxk, 2xxp, n xx 3 and p xx k , respectively. If n = p, then the order of the matrix 7X-5Z is:

Let m in N and C_(r) = ""^(n)C_(r) , for 0 le r len Statement-1: (1)/(m!)C_(0) + (n)/((m +1)!) C_(1) + (n(n-1))/((m +2)!) C_(2) +… + (n(n-1)(n-2)….2.1)/((m+n)!) C_(n) = ((m + n + 1 )(m+n +2)…(m +2n))/((m +n)!) Statement-2: For r le 0 ""^(m)C_(r)""^(n)C_(0)+""^(m)C_(r-1)""^(n)C_(1) + ""^(m)C_(r-2) ""^(n)C_(2) +...+ ""^(m)C_(0)""^(n)C_(r) = ""^(m+n)C_(r) . (a) Statement-1 and Statement-2 both are correct and Statement-2 is the correct explanation for the Statement-1. (b) Statement-1 and Statement-2 both are correct and Statement-2 is not the correct explanation for the Statement-1. (c) Statement-1 is correct but Statement-2 is wrong. (d) Statement-2 is correct but Statement-1 is wrong.

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P= {m, n} and Q = {n, m}, then P xx Q= {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x, y) such that x in A and y in B. (iii) If A={1,2}, B={3,4} then A xx (B cap phi)=phi

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

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

The value of sum_(r=1)^(n+1)(sum_(k=1)^n ^kC_(r-1)) (where r, k, n in N ) is equal to

Each question contains statements given in two columns which have to be matched. Statements (a,b,c,d) in column I have to be matched with statements (p,q,r,s) in column II. If the correct match are a-p, s, b-r c-p, q. and d-s, then the correctly bubbled 4x4 matrix should be as follows: figure Column I, a) If int(2^x)/(sqrt(1-4^x))dx=ksin^(-1)(f(x))+C , then k is greater than, b) If int((sqrt(x))^5)/((sqrt(x))^7+x^6)dx=aln(x^k)/(x^k+1)+c , then a k is less than, c) If int(x^4+1)/(x(x^2+1)^2)dx=kln|x|+m/(1+x^2)+n , where n is the constant of integration, then m k is greater than, d) If int(dx)/(5+4cosx)=ktan^(-1)(mt a n x/2)+C , then k//m is greater than, COLUMN II p) 0 q) 1 r) 3 s)4