If `x^2+px+q` is an integer for every integral value of x then which is necessarily true? (A) `p epsilonI, q cancelepsilon I` (B) `pcancel epsilonI, qepsilon I` (C) `pepsilonI, qepsilonI` (D) `pcancel epsilon, qcancel epsilon I`

The general solution of the equation 2^(cos2x)=1=3.2^(-sin^2x) is (A) n pi,n epsilon i (B) (n+1/2) pi, n epsilon I (C) (n- 1/2) pi, n epsilon I (D) none of these

If px^(3)+qx^(2)+rx+s is exactly divisible by x^(2)-1 , then which of the following is /are necessarily true ? (A) p = r )B) q = s (C ) p =- r (D) q =- s

If x^(2)-2x-1 is a factor of px^(3)+qx^(2)+1 , (where p , q are integers) then find the value of p +q.

If 2+sqrt3 i is a root of the equation x^2+px+q=0 then find p and q

The alongside is a plot of binding energy per nucleon E_(b) ,against the nuclear mass M,A,B,C,D,E,F correspond to different nuclei. Consider four reactions. (i) A + B to C + epsilon (ii) C to A + B + epsilon (iii) D + E to F + epsilon (iv) F to D + E + epsilon where epsilon is the energy released. In which reactions , is epsilon positive?

Find the values of p and q respectively for which the equation 2x^(2) + px = q has root - 3 and factor (x-5).