" 4."[sqrt(AFI)=M:sqrt(ADD)=L],[qquad [" (b) "1," (b) "K],[" (c) "N]]

Q.Which of the following is/are always true? (a) Every irrational number is a surd.(b) Any surd of the form n sqrt(a)+n sqrt(b) can be rationalised by a surd of the form (n sqrt(a)-n sqrt(b)) a where n sqrt(a) and n sqrt(b) are surds.(c) Both (a) and (b) Neither (a) nor (b)

If sum_(k = 1)^(oo) (1)/((k + 2)sqrt(k) + ksqrt(k + 2)) = (sqrt(a) + sqrt(b))/(sqrt(c)) , where a, b, c in N and a,b,c in [1, 15] , then a + b + c is equal to

If sum_(k = 1)^(oo) (1)/((k + 2)sqrt(k) + ksqrt(k + 2)) = (sqrt(a) + sqrt(b))/(sqrt(c)) , where a, b, c in N and a,b,c in [1, 15] , then a + b + c is equal to

log_(ksqrt(k)) (sqrt(k sqrt(k sqrt(k sqrt(k))))) (a) (5/8) (b) (15/16) (c) (5/4)

If ratio of the roots of the equation ax^(2)+bx+c=0 is m:n then (A) (m)/(n)+(n)/(m)=(b^(2))/(ac) (B) sqrt((m)/(n))+sqrt((n)/(m))=(b)/(sqrt(ac))],[" (C) sqrt((m)/(n))+sqrt((n)/(m))=(b^(2))/(ac)]

If a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family of lines sqrt(a)x+sqrt(b)y+sqrt(c)=0 passes though the fixed point given by (a) (1,1) (b) (1,-2) (c) (-1,2) (d) (-1,1)

If a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family of lines sqrt(a)x+sqrt(b)y+sqrt(c)=0 passes though the fixed point given by (a) (1,1) (b) (1,-2) (c) (-1,2) (d) (-1,1)

If a/sqrt(b c)-2=sqrt(b/c)+sqrt(c/b), where a , b , c >0, then the family of lines sqrt(a)x+sqrt(b)y+sqrt(c)=0 passes though the fixed point given by (a) (1,1) (b) (1,-2) (c) (-1,2) (d) (-1,1)

sum_(n=1)^oo sin^-1( (sqrt(n)-(sqrt(n-1)))/(sqrt((n)(n+1)) )= (A) pi/4 (B) pi/2 (C) - pi/3 (D) pi/3