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`

Let x_(1),x_(2),x_(3), . . .,x_(k) be the divisors of positive integer ' n ' (including 1 and x ). If x_(1)+x_(2)+ . . .+x_(k)=75 , then sum_(i=1)^(k)(1)/(x_(i)) is equal to:

Q. if x_1,x_2......x_n are in H.P ., then sum_(r=1)^n x_r x_(r+1) is equal to : (A) (n-1)x_1 x_n (B) n x_1 x_n (C) (n+1)x_1 x_n (D) (n+2)x_1 x_n

Let f (x ) = | 3 - | 2- | x- 1 |||, AA x in R be not differentiable at x _ 1 , x _ 2 , x _ 3, ….x_ n , then sum _ (i= 1 ) ^( n ) x _ i^2 equal to :

If x^n-1 is divisible by x-k then the least positive integral value of k is(a) 1 (b) 2 (c) 3 (d) 4

If x^(n)-1 is divisible by x-k, then the least positive integral value of k is: (i) 1 (ii) 2 (iii) 3 (iv) 4

If a, x_1, x_2, …, x_k and b, y_1, y_2, …, y_k from two A. Ps with common differences m and n respectively, the the locus of point (x, y) , where x= (sum_(i=1)^k x_i)/k and y= (sum_(i=1)^k yi)/k is: (A) (x-a) m = (y-b)n (B) (x-m) a= (y-n) b (C) (x-n) a= (y-m) b (D) (x-a) n= (y-b)m

If the arithmetic mean of the observations x_1,x_2,x_3,.............x_n is 1 , then the arithmetic mean of x_1/k,x_2/k,x_3/k,.............x_n/k , (k >0) is

The standard deviation of n observations x_(1), x_(2), x_(3),…x_(n) is 2. If sum_(i=1)^(n) x_(i)^(2) = 100 and sum_(i=1)^(n) x_(i) = 20 show the values of n are 5 or 20

Let n_(k) be the number of real solution of the equation |x+1| + |x-3| = K , then

A sequence x_1, x_2, x_3,.... is defined by letting x_1=2 and x_k=x_(k-1)/k for all natural numbers k,k>=2 Show that x_n=2/(n!) for all n in N .