Given that `q^2-p r ,0,\ p >0,` then the value of `|p q p x+q y q r q x+r y p x+q y q x+r y0|` is- a. zero b. positive c. negative`\ ` d. `q^2+p r`

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

The incorrect statement is (A) p →q is logically equivalent to ~p ∨ q. (B) If the truth-values of p, q r are T, F, T respectively, then the truth value of (p ∨ q) ∧ (q ∨ r) is T. (C) ~(p ∨ q ∨ r) = ~p ∧ ~q ∧ ~r (D) The truth-value of p ~ (p ∧ q) is always T

If p,q,r be three distinct real numbers, then the value of (p+q)(q+r)(r+p), is

Show that: |b+c c+a a+b q+r r+p p+q y+z z+x x+y|=2|a b c p q r x y z|

If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s (a) 0 (b) p a+q b+r c (c) 1 (d) none of these

If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x, a+p], [q+y ,b+y, b+q],[ r+z, c+z, c+r]| is (a) 4 (b) 8 (c) 16 (d) 32

For p, q in R , the roots of (p^(2) + 2)x^(2) + 2x(p +q) - 2 = 0 are

(a) If r^(2) = pq , show that p : q is the duplicate ratio of (p + r) : (q + r) . (b) If (p - x) : (q - x) be the duplicate ratio of p : q then show that : (1)/(p) + (1)/(q) = (1)/(r) .

Statement-l: If the diagonals of the quadrilateral formed by the lines px+ gy+ r= 0, p'x +gy +r'= 0, p'x +q'y +r'= 0 , are at right angles, then p^2 +q^2= p^2+q^2 . Statement-2: Diagonals of a rhombus are bisected and perpendicular to each other.