Using properties of determinants, show that
`|{:(x, p, q), ( p, x, q), (q,q,x):}|= (x-p) (x ^(2) + px - 2q ^(2))`

Show that: x p q p x q q q xx-p)(x^2+p x-2q^2) .

If x nearly equal to 1 show that (px^q - qx^p)/(x^q - x^p) = (1)/(1 -x) ( nearly)

If x nearly equal to 1 show that (px^p - qx^q)/(p-q) = x^(p+q) (nearly)

If x^(p) y^(q) = (x + y)^((p + q)) " then " (dy)/(dx)= ?

If p, q, r, s in R , then equaton (x^2 + px + 3q) (-x^2 + rx + q) (-x^2 + sx-2q) = 0 has

If P be the sum of odd terms and Q be the sum of even terms in the expansion of (x+a)^(n) , then (x+a)^(2n)+(x-a)^(2n) is (i) P^(2)-Q^(2) (ii) P^(2)+Q^(2) (iii) 2(P^(2)+Q^(2)) (iv) 4PQ

Solve for x and y, px + qy = 1 and qx + py = ((p + q)^(2))/(p^2 + q^2)-1 .

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

If the difference of the roots of the equation, x^2+p x+q=0 be unity, then (p^2+4q^2) equal to: (1-2q)^2 (b) (1-2q)^2 4(p-q)^2 (d) 2(p-q)^2

The base B C of a A B C is bisected at the point (p ,q) & the equation to the side A B&A C are p x+q y=1 & q x+p y=1 . The equation of the median through A is: (p-2q)x+(q-2p)y+1=0 (p+q)(x+y)-2=0 (2p q-1)(p x+q y-1)=(p^2+q^2-1)(q x+p y-1) none of these