`E v a l u a t e\ (2. 3 a^5b^2)xx(1. 2 a^2b^2)w h e n\ a=1\ a n d\ b=0. 5.`

E v a l u a t e\ (3. 2 x^6y^3)xx(2. 1 x^2y^2)w h e n\ x=1\ a n d\ y=0. 5

Find the locus of P\ if\ P A^2+P B^2=2k^2w h e r e\ A\ a n d\ B are points (3,4,5) and (-1,3,7).

Prove that t a n(i(log)_e((a-i b)/(a+i b)))=(2a b)/(a^2-b^2)(w h e r ea ,b in R^+)

If \ ^(n+1)C_3=2.\ \ ^n C_2\ t h e n= 3 b. 4 c. 6 d. 5

If A and B are two events such that P(A)=0. 4 ,\ P(B)=03\ a n d\ P(AuuB)=0. 5 ,\ t h e n\ P( B nnA) equals 23\ b. 1/2 c. 3/(10) d. 1/5

Let D_1=|a b a+b c d c+d a b a-b|a n dD_2=|a c a+c b d b+d a c a+b+c| then the value of |(D_1)/(D_2)|,w h e r eb!=0a n da d!=b c , is _____.

If AD, BE and CF are the medians of a DeltaA B C ,t h e n(A D^2+B E^2+C F^2):(B C^2+C A^2+A B^2) is equal to

Find the volume in cubic metre (cu. m) of each of the cuboids whose dimensions are: l e n g t h\ =\ 12 m ,\ b r e a dt h=10 m ,\ h e igh t=4. 5 m l e n g t h\ =\ 4m ,\ b r e a dt h\ =\ 2. 5 m ,\ h e igh t\ =\ 50 c mdot l e n g t h\ =\ 10 m ,\ b r e a dt h\ =\ 25 d m ,\ h e igh t\ =\ 25 c mdot

Consider the determinant Delta = |[a_1+b_1x^2,a_1x^2+b_1,c_1],[a_2+b_2x^2,a_2x^2+b_2,c_2],[a_3+b_3x^2,a_3x^2+b_3,c_3]| = 0 , \ w h e r e \ a_i ,b_i , c_i in R \ (i = 1,2,3) \ a n d \ x in R . Statement 1: The value of x satisfying Delta=0 are x=1,-1. Statement 2: If |[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|=0,t h e n \ Delta=0.

If S is the sample space and P(A)=1/3P\ (B)a n d\ S=AuuB ,\ w h e r e\ A\ a n d\ B are two mutually exclusive events then P(A)= 1//4 b. 1//2 c. 3//4 d. 3//8