`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).

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

If o+ is an operation such that a+b={2a , w h e n a > b a+b , w h e n a

Let f,\ g\ a n d\ h be real-valued functions defined on the interval [0,\ 1] by f(x)=e^x^2+e^-x^2,\ g(x)=x e^x^2+e^-x^2\ a n d\ h(x)=x^2e^x^2+e^-x^2 . If a , b ,\ a n d\ c denote respectively, the absolute maximum of f,\ g\ a n d\ h on [0,\ 1], then a=b\ a n d\ c!=b (b) a=c\ a n d\ a!=b a!=b\ a n d\ c!=b (d) a=b=c

If (1+i)(1+2i)(1+3i)........(1+n i)=a+i b ,t h e n2xx5xx10 ....(1+n^2) is equal to sqrt(a^2+b^2) (b) sqrt(a^2-b^2) (c) a^2+b^2 (d) a^2-b^2 (e) a+b

Comprehension 1 Let a^((log)_b x)=c w h e r e a , b , c & x are parameters. On the basis of above information, answer the following questions: If b=(log)_(sqrt(3))3, c=2(log)_bsqrt(b) a n d s intheta=a(w h e r e x >1) t h e n theta can be a.pi/4 b. (3pi)/2 c. pi/2 d. 0

If in triangle A B C , vec A B= vec u/(| vec u|)- vec v/(| vec v|)a n d vec A C=(2 vec u)/(| vec u|),w h e r e| vec u|!=| vec v|, then a. 1+cos2A+cos2B+cos2C=0 b. sinA=cos C c. projection of A C on B C is equal to B C d. projection of A B on B C is equal to A B

If in triangle A B C , vec A B= vec u/(| vec u|)- vec v/(| vec v|)a n d vec A C=(2 vec u)/(| vec u|),w h e r e| vec u|!=| vec v|, then a. 1+cos2A+cos2B+cos2C=0 b. sinA=cos C c. projection of A C on B C is equal to B C d. projection of A B on B C is equal to A B

Let A and B be two sets such that n(A)=3 a n d n(B)=2. if (x ,1), (y ,2), (z ,1)a r e in AxxB , find A a n d B , w h e r e x , y , z are distinct elements.