- The greatest integer which divides(p+1) (p + 2) (p + 3).... (p+q) for allpe N and fixed qe N is.(a) p! (b) q! (C) p(d) q

The greatest integer which divides (p+1)(p+2)(p+3)......(p+q) for all p""inNN and fixed q""inNN is

(p ^^ ~ q)vv q is logical equivalent to (a) p vv q (b) ~P (c) p (d) ~q

P ** q = p^2 - q^2 p $ q = p^2 - q^2 p $ q = p^2 + q^2 p @ q = pq + p + q p Delta q = Remainder of p/q p © q = greatest integer less than or equal to p/q . If p = 8 and q = 10 , then the value of [(p $ q) Delta (p @ q)] ** [(q ** p) @ (q © p)] is :

P ** q = p^2 - q^2 p % q = p^2 - q^2 p $ q = p^2 + q^2 p @ q = pq + p + q p Delta q = Remainder of p/q p © q = greatest integer less than or equal to p/q . If p = 11 and q = 7 , then the value of (p ** q) @ (p $ q) is:

Let a_(n) denote the n -th term of an A.P.and p and q be two positive integers with p

If m , n , o, p a n d q are integers, then m (n +o) (p-q) must be even when which of the following is even? m (b) p (c) m + n (d) n + p

Let a_(n) denote the n-th term of an A.P. and p and q be two positive integers with p lt q . If a_(p+1) + a_(p+2) + a_(p+3)+…+a_(q) = 0 find the sum of first (p+q) terms of the A.P.

If p^(3)-q^(3)=(p-q)((p-q)^(2)-xpq), then find the value of x is (a) 1 (b) -3(c)3(d)-1