If `(1+3+5+…..+p)+(1+3+5+….+q)=(1+3+5+…..+r)` where each set of parentheses contains the sum consecutive odd integers as shown , the smallest possible value of P+q+r (where`p gt 6)` is

If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of p+q+r(w h e r ep >6) is 12 b. 21 c. 45 d. 54

Use division algorithm to show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer

Show that any positive odd integer is of the form 4q+1 or 4q+3, where q is some integer.

If the energy E=G^(p)h^(q)c^(r ) where G is the universal gravitational constant, h is the planck's constant and c is the velocity of light, then the values of p, q and r are respectively: a) -1/2,1/2 and 5/2 b) 1/2, -1/2 and -5/2 c) -1/2,1/2 and 3/2 d) 1/2, -1/2 and -3/2

Find the number of distinct rational numbers x such that o

In an A.P. if p^(th) term is 1/q and q^(th) term is 1/p , prove that the sum of first pq terms is 1/2(pq+1) , where p ne q .

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

Express 1.bar(62) in (p)/(q) from where qne0,p, q are integers.