(i) Simplify `(2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3))` (ii) `[(root(6)(7))^(2)+(root(6)(7))^(-2)][(root(6)(7))^(4)-1+(root(6)(7))^(-4)]`

Correct Answer - B `(b)` Since one root is `3`, let `f(x)=(x-3)(ax+b)` `implies f(x)=ax^(2)+(b-3a)x-3b`……….`(1)` Given, `f(-1)+f(2)=0` `implies (a+(3a-b)-3b)+(4a+2b-6a-3b)=0` `implies 2a-5b=0` `implies (b)/(a)=(2)/(5)` ………..`(2)` Now, product of roots `=(-3b)/(a)=-3((2)/(5))` since one root...

Correct Answer - `1394 ms^(-1)`

Correct Answer - (i) `(729)^(1/3), root(3)(729)` (ii) `(1990)^(1/5), root(5)(1990)` (iii) `(2001)^(1/2), sqrt(2001)` (iv) `(777)^(1/7), root(7)(777)`

Correct Answer - (i) 3 (ii) 0.2

Correct Answer - `root(9)(5),root(6)(9),root(3)(7)`

Correct Answer - (i)`(5)/(2)` (ii) 4 (iii)` (9)/(8)` (iv)` (5)/(2)` (v) 4 (vi)`(4)/(3)`

Correct Answer - (i)`sqrt(2)` (ii)`(1)/(sqrt(3))` (iii)`(sqrt(3))/(2)` (iv)`3sqrt(2)` (v)`(1)/(2sqrt(5))` (vi)`2sqrt(2)`

Correct Answer - `{:((i),(12+13i),(ii),(-1+7i),(iii),(-3+5i),(iv),"(11-9i)"),((v),(9+22i),(vi),28,(vii),(18-i),(vii),-7sqrt(3)i):}`

\(\sqrt{-16}+3\sqrt{-25}+\sqrt{-36}-\sqrt{-625}\) = \(\sqrt{16\times-1}+3\sqrt{25\times-1}+\sqrt{36\times-1}-\sqrt{625\times-1}\)  = 4i + 3(5i) + 6i - 25i = 25i - 25i = 0

\(4\sqrt{-4}+5\sqrt{-9}-3\sqrt{-16}\)  = \(4\sqrt{4\times-1}+5\sqrt{9\times-1}-3\sqrt{16\times-1}\)  = 4(2i) + 5(3i) - 3(4i) = 8i + 15i - 12i = 11i