[" Tf "m=(1)/(3-2sqrt(2))" and "n=(1)/(3+2sqrt(2))],[[" (i) "m^(2)," (ii) "n^(2)," (iii) "mn]]

If m = (1)/(3-2sqrt(2)) and n = (1)/(3+2sqrt(2)) find : (i) m^(2) (ii) n^(2) (iii) mn

If m=(1)/(3-2sqrt(2)) and n=(1)/(3+2sqrt(2)) find :(1)m^(2)(2)n^(2)(3)mn

If m = 9 and n = (1)/(3)m , then sqrt((m)^(2) - (n)^(2) = ?)

Find (m+n)-:(m-n) , if : (i) m=(2)/(3) "and" n=(3)/(2) (ii) m=(3)/(4) "and" n=(4)/(3) (iii) m=(4)/(5) "and" n=-(3)/(10)

If sec theta=(m+n)/(2sqrt(mn)) find sin theta

((-1+i sqrt(3))/(2))^(3 n)+((-1-i sqrt(3))/(2))^(3 n)=

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)]

lim_ (n-> oo) (sqrt (n))/(sqrt (n)+sqrt (n+1)) = (i) 1 (ii) 1/2 (iii) 0 (iv) infty

Factorise the following. (i) (p-q) ^(2) -6( p-q) -16 (ii) m^(2) +2mn -24n^(2) (iii) sqrt5 a^(2) + 2a -3sqrt 5 (iv) a^(4) -3a^(2) +2 (v) 8m^(3) -2m^(2) n -15mn^(2) (vi ) (1)/( x^(2)) +(1) /( y^(2)) +(2)/( xy )

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively. Column I, Column 2, Column 3 I, x^2+y^2=a , (i), m y=m^2x+a , (P), (a/(m^2),(2a)/m) II, x^2+a^2y^2=a , (ii), y=m x+asqrt(m^2+1) , (Q), ((-m a)/(sqrt(m^2+1)), a/(sqrt(m^2+1))) III, y^2=4a x , (iii), y=m x+sqrt(a^2m^2-1) , (R), ((-a^2m)/(sqrt(a^2m^2+1)),1/(sqrt(a^2m^2+1))) IV, x^2-a^2y^2=a^2 , (iv), y=m x+sqrt(a^2m^2+1) , (S), ((-a^2m)/(sqrt(a^2m^2+1)),(-1)/(sqrt(a^2m^2+1))) The tangent to a suitable conic (Column 1) at (sqrt(3),1/2) is found to be sqrt(3)x+2y=4, then which of the following options is the only CORRECT combination? (IV) (iii) (S) (b) (II) (iii) (R) (II) (iv) (R) (d) (IV) (iv) (S)