The value of the determinant `|(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c, k^2+c^2, 1)|` is (A) `k(a+b)(b+c)(c+a)` (B) `k a b c(a^2+b^(2)+c^2)` (C) `k(a-b)(b-c)(c-a)` (D) `k(a+b-c)(b+c-a)(c+a-b)`

The value of the determinant |k a k^2+a^2 1k b k^2+b^2 1k c k^2+c^2 1| is k(a+b)(b+c)(c+a) k a b c(a^2+b^(f2)+c^2) k(a-b)(b-c)(c-a) k(a+b-c)(b+c-a)(c+a-b)

The determinant Delta=|(a^2(a+b),a b,a c),(a b,b^2(a+k),b c),(a c,b c,c^2(1+k))| is divisible by

If |(a^2,b^2,c^2),((a+1)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

In A B C ,(a+b+c)(b+c-a)=k b c if k 0 = 4

(a)/(b) = (c)/(d) = (e)/(f) = k(a, b, c, d, e, f gt 0) then (A) k = (a + c +e)/(b + d + f) (B) k = (a^(2) + c^(2) +e^(2))/(b^(2) + d^(2) + f^(2)) (C) k = (c^(2)e^(2))/(d^(2)f^(2)) (D) k = ((ace)/(bdf))^((1)/(3))

If s e ctheta+t a ntheta=k ,\ costheta= a. (k^2+1)/(2k) b. (2k)/(k^2+1) c. k/(k^2+1) d. k/(k^2-1)

Four distinct points (k, 2k), (2, 0), (0, 2) and (0,0) lie on a circle for : (A) k = 0 (B) k = 6/5 (C) k = 1 (D) k = -1

The value of int(a x^2-b)/(xsqrt(c^2x^2-(a x^2+b)^2)) (a) 1/csin^(-1)(a x+b/x)+k (b) csin^(-1)(a+b/x)+e (c) sin^(-1)((a x+b/x)/c)+k (d) none of these

The centre of circle which passes through A (h, 0), B (0, k) and C (0, 0) is : (A) (h/2, 0) (B) (0, k/2) (C) (h/2, k/2) (D) (h, k)

If the roots of the equation a x^2+b x+c=0 are of the form (k+1)//ka n d(k+2)//(k+1),t h e n(a+b+c)^2 is equal to 2b^2-a c b. a 62 c. b^2-4a c d. b^2-2a c