If `u_r` denotes the number of one-one functions from `(x_1,x_2,…………..x_r) to (y_1,y_2,………,y_r)` such that `f(x_i)!=y_i,` for ` i= 1,2,3,………r` then ` t_4=`
(A) 9
(B) 44
(C) 265
(D) none of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is: (a) . 0 (b) . 1 (c) . 100 (d) . none of these

In a binomial expansion (x_y)^n gretest term means numericaly greatest term and therefore greatest term in (x-y)^n and (x+y)^n are ame. I frth therm t_r be the greatest term in the expansion of (x+y)^n whose therms are all ositive, then t_rget_(r+1) and t_rget_=(r-1)i.e. t_r/t_mge1 and t_r/t_(r-)ge1 On the basis of above information answer the following question:If rth term is the greatest term in the expansion f (2-3x0^10 then r= (A) 5 (B) 6 (C) 7 (D) none of these

Let f be a differentiable function from R to R such that |f(x) - f(y) | le 2|x-y|^(3/2), for all x, y in R . If f(0) =1, then int_(0)^(1) f^(2)(x) dx is equal to

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y_2+x y_1 is (where y_r represents the r t h derivative of y w.r.t. xdot (a) m^2y (b) m y^2 (c) m^2y^2 (d) none of these

The range of the function f(x)=(x^2-x)/(x^2+2x) is R (b) R-[1] (c) R={-1/2,1} (d) none of these

Let x_1, x_2, ...... ,x_n be values taken by a variable Xa n dy_1, y_2,.......... ,y_n be the values taken by a variable Y such that y_i=a x_i+b ,i=1,2, ,ndot Then, (a) V a r(Y)=a^2V a r(X) (b) V a r(X)=a^2V a r(Y) (c) V a r(X)=V a r(X)+b (d) none of these

If x_1, x_2, ,\ x_n are n values of a variable X\ a n d\ y_1, y_2, ......,yn are n values of variable Y such that y_i=a x_i+b , i=1,2,\...., n then write Va r\ (Y) in terms of Va r(X)

Let vec a_r=x_r hat i+y_r hat j+z_r hat k ,r=1,2,3 be three mutually perpendicular unit vectors, then the value of |[x_1,x_2,x_3],[y_1,y_2,y_3],[z_1,z_2,z_3]| is equal to a. 0 b. +-1 c. +-2 d. none of these