True or False :
In an A.P. `(t_(n+1))/(t_n)` is a constant, independent of n.

True or False: int x^ndx=(x^(n+1))/(n+1)+C , where n is any integer.

If the sum of the first n terms of a sequence is of the form An^2+ Bn , where A, B are constants independent of n, show that the sequence is an A.P. Is the converse true ? Justify your answer.

True or False : If A is any square matrix, then det (A^n) = (detA)^n where n is any natural number.

If the sum of n terms of an A.P is nP+1/2 n(n-1)Q , where P and Q are constant, find the common difference.

Evaluate int_(0)^(1)(tx+1-x)^(n)dx , where n is a positive integer and t is a parameter independent of x . Hence , show that int_0^1 ​ x^k (1−x)^(n−k) dx= P/([.^nC_k(n+1)]) ​ for k=0,1,......n , then P=

If the sum of n terms of an A.P. is (pn + qn^2) , where p and q are constants, find the common difference.

Suppose that a random variabe X follows Binomial distribution with parameters n and p, where 0 < p < 1 . If [P(X=r)]/[P(X=n-r)] is independent of n and r, then p is equal to

If the sum of n terms of an A.P. is (pn+qn^2) , where p and g are constants, find the common difference.

If P and Q are two points whose coordinates are (a t^2,2a t)a n d(a/(t^2),(2a)/t) respectively and S is the point (a,0). Show that 1/(S P)+1/(s Q) is independent of t.

Let T_r be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers, m,n, m ne n, T_m =1/n and T_n=1/m , then a-d equals :