21) If the nth term of the sequence is defined by \( a_{n}- \) 22) Find the \( 12^{\text {th }} \) term of an A.P from the lasi term of \( -2,-4,-6, \ldots,-100 \) 23) Simplify: \( \frac{4 x^{2} y}{2 z^{2}} \times \frac{6 x z^{3}}{20 y^{4}} \) 24) Which rational expression should be subtracted from \( \frac{x^{2}+6 x+8}{x^{6}+8} \) to get \( \frac{-3}{x^{2}}-\frac{3}{2 x+4} \) 25) If \( x=\frac{a^{2}+3 a-4}{3 a^{2}-3} \) and \( y=\frac{a^{2}+2 a-8}{2 a^{2}-2 a-4} \) then find the value of \( x^{2} y^{-2} \) 26) The product of Kumaran's age (in years) two years ago and his age four years from now is one more than twice his present age. What is his present age? 27) If one root of the equation \( 3 x^{2}+k x+81=0 \) (having real roots) is the square of the other then find \( k \). 28) Det

Question

Find the \( 12^{\text {th }} \) term of an A.P from the lasi term of \( -2,-4,-6, \ldots,-100 \) 

23) Simplify: \( \frac{4 x^{2} y}{2 z^{2}} \times \frac{6 x z^{3}}{20 y^{4}} \) 

24) Which rational expression should be subtracted from \( \frac{x^{2}+6 x+8}{x^{6}+8} \) to get \( \frac{-3}{x^{2}}-\frac{3}{2 x+4} \) 25) If \( x=\frac{a^{2}+3 a-4}{3 a^{2}-3} \) and \( y=\frac{a^{2}+2 a-8}{2 a^{2}-2 a-4} \) then find the value of \( x^{2} y^{-2} \)

 26) The product of Kumaran's age (in years) two years ago and his age four years from now is one more than twice his present age. What is his present age? 

27) If one root of the equation \( 3 x^{2}+k x+81=0 \) (having real roots) is the square of the other then find \( k \). 

28) Determine the quadratic equation, whose sun and product of roots are \( \frac{-3}{2} \) and \( -1 \).