Let a and b be natural numbers and let q and r be the quotient and remainder respectively when `a^2+b^2` is divided by a + b . Determine the number q and r if `q^2+ r = 2000`.

Let p, q and r be three statements, then (~p to q) to r is equivalent to

Suppose ,m divided by n , then quotient q and remainder r or m= nq + r , AA m,n,q, r in 1 and n ne 0 If 13^(99) is divided by 81 , the remainder is

Let P be an interior point of a triangle ABC , Let Q and R be the reflections of P in AB and AC , respectively if Q .A , R are collinear then angle A equals -

Two concentric shells have radii R and 2R charges q_A and q_B and potentials 2V and (3/2)V respectively. Now, shell B is earthed and let charges on them become q_A' and q_B' . Then,

Let Q be the set of rational numbers and R be a relation on Q defined by R {":"x,y inQ,x^2+y^2=5} is

Two concentric conducting shells of radii R and 2R are having charges Q and -2Q respectively.In a region r

Let a,b,c are the A.M. between two numbers such that a+b+c=15 and p,q,r be the H.M. between same numbers such that 1/p+1/q+1/r=5/3 , then the numbers are

Let N be the set of all natural numbers and let R be relation in N. Defined by R={(a,b):"a is a multiple of b"}. show that R is reflexive transitive but not symmetric .

Let AP and BQ be two vertical poles at points A and B, respectively. If A P = 16 m , B Q = 22 m a n d A B = 20 m , then find the distance of a point R on AB from the point A such that R P^2+R Q^2 is minimum.

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number " and r be the statement "x is a rational number iff y is a transcendental number". Statement - 1 : r is equivalent to either q or p. Statement -2 : r is equivalent to ~(p harr ~q)