`intc o s e c^(p /3)xsec^(q /3)x dx=(p,q in I^+ and p+q=12)`

int csc^((p)/(3))x sec^((q)/(3))xdx=(p,q in I^(+) and p+q=12)

For any natural number p and q (i) p # q = p 3 + q 3 + 3 and p ∗ q = p 2 + q 2 + 2 and p $ q = | p − q | (ii) Max (p,q) = Maximum of (p,q) and Min (p and q) = Minimum of (p,q)The value of [(1 $ 2) # (3$ 4)]*[(5 $ 6) # (7 $ 8)] is :

If P(x)=intx^(3)/(x^(3)-x^(2))dx, Q(x)=int1/(x^(3)-x^(2))dx " and " (P+Q)(2)=5/2, " then " P(3)+Q(3)=

If P(x)=intx^(3)/(x^(3)-x^(2))dx, Q(x)=int1/(x^(3)-x^(2))dx " and " (P+Q)(2)=5/2, then P(3)+Q(3)=

If the lines p_1 x + q_1 y = 1, p_2 x + q_2 y=1 and p_3 x + q_3 y = 1 be concurrent, show that the points (p_1 , q_1), (p_2 , q_2 ) and (p_3 , q_3) are colliner.

If S(p, q, r) = (~p) vv [-(q ^^ r)] is a compound statement, then S(~p, ~q, ~r) is a) ~S(p, q, r) b) S(p, q, r) c) p vv (q ^^ r) d) p vv (q vv r)

(p-q)^(3)-(p+q)^(3) is equal to

If A be one A.M. and p ,q be two G.M. ' s between two numbers, then 2A is equal to (a) (p^3+q^3)/(p q) (b) (p^3-q^3)/(p q) (c) (p^2+q^2)/2 (d) (p q)/2

If A be one A.M. and p ,q be two G.M. ' s between two numbers, then 2A is equal to (a)(p^3+q^3)/(p q) (b) (p^3-q^3)/(p q) (c) (p^2+q^2)/2 (d) (p q)/2