" 62"(d)/((x-b))+(b)/((x-a))=2,x!=b,a

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))| = (a - b) (b - c) (c - a) (a + b + c) , where a,b,c are all different, then the determinant |(1,1,1),((x-a)^(2),(x-b)^(2),(x-c)^(2)),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))| vanishes when a)a + b + c = 0 b) x = (1)/(3) (a + b + c) c) x = (1)/(2) (a + b + c) d) x = a + b + c

If (x^(2))/((x-a)(x-b))=1+(a^(2))/((a-b)(x-a))+(B)/((x-b)) , then B is _________.

If ((x-a)(x-b))/((x-c)(x-d)^(2))>=0; where a>b>c>=d>0, then x in

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a)(x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c)-((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

If tanx=b/a then sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b))= ........................... A) (2 sin x)/(sqrt(sin2x)) B) (2 cos x)/(sqrt(cos2x)) C) (2 cos x)/(sqrt(sin2x)) D) (2 sin x)/(sqrt(cos2x))

Differentiate ((x^(a))/(x^(b)))^(a+b)*((x^(b))/(x^(c)))^(b+c)*((x^(c))/(x^(a)))^(c+a) with respect to x.

If x_(1) and x_(2) are two distinct roots of the equation a cos x+b sin x=c, then tan((x_(1)+x_(2))/(2)) is equal to (a)(a)/(b) (b) (b)/(a) (c) (c)/(a) (d) (a)/(c)