Identify the correct statement If `x in Q=>x in Q` If `x^3 in Qa n dx^7 in Q=>x in Q` If `x^4 in Qa n dx^(11) in Q=>x in Q`

Which of the following statements are always correct (where Q denotes the set of rationals)? cos2theta in Qa n dsin2theta in Q tantheta in Q (ifd efin e d) tantheta in Q sin2theta,cos2thetaa n dtan2theta in Q(ifd efin e d) ifs intheta in Qa n dcostheta in Qtan3theta in Q(ifd efin e d) fi sin theta in Q cos3theta in Q

Prove that the function f: Q->Q given by f(x)=2x-3 for all x in Q is a bijection.

Let P = { x: x is a factor of 18 } and Q = { x : x is a factor of 24}. Find : (a) P uu Q (b) P nn Q

If p a n d q are positive, then prove that the coefficients of x^pa n dx^q in the expansion of (1+x)^(p+q) will be equal.

If p and q are positive, then prove that the coefficients of x^p and x^q in the expansion of (1+x)^(p+q) will be equal.

If f : R -> R be a function such that f(x) = { x|x| -4; x in Q, x|x| - sqrt3; x !in Q then f(x) is

The coefficients of x^(p) and x^(q)(p,q in N) in the expansion of (1+x)^(p+q) are

The function f(x)={{:( 1, x in Q),(0, x notin Q):} , is

Find the value of a for which f(x)={x^2,x in Q x+a ,x !in Q is not continuous at any xdot

If P {x : x is a letter in the word CHANDIGARH } and Q = {x : x is a letter in the word JAMNAGAR }, then find n(P) , n(Q) n(P cup Q) and n (P cap Q)