Directions:In the following questions choose the word opposite in meaning to the given word.
DISSOLUTION

Solution
The word Dissolution (Noun) means: the act of officially ending a marriage. a business agreement or a parliament.
Hence. the words dissolution and establishment are antonymous.
Directions:In the following questions choose the word opposite in meaning to the given word.
ENDURIN

Solution
The word Enduring (Adjective) means : lasting for a long time.
Look at the sentence : What is the reason for the game's enduring appeal ?
The word Fleeting (Adjective) means : not lasting; brief. Hence, the words enduring and fleeting are antonymous
Directions:In the following questions choose the word opposite in meaning to the given word.
ASCETICISM

Solution
The word Asceticism (Noun) means: related to a simple and strict way of living. Hence, its antonym should be luxury which means: the enjoyment of special and expensive things
If \(x=\frac{1}{2+\sqrt{3}}\) and \(y=\frac{1}{2\sqrt{3}}\) then the value of \(\left ( \frac{1}{x+1}+\frac{1}{y+1} \right )\) is

Solution
\(x=\frac{1}{2+\sqrt{3}}=\frac{2\sqrt{3}}{(2+\sqrt{3})(2\sqrt{3})}\)
\(=2\sqrt{3}\)
and Y= \(=\frac{1}{2\sqrt{3}}=2+\sqrt{3}\)
\(∴\frac{1}{x + 1}+\frac{1}{Y + 1}=\frac{1}{3\sqrt{3}}+\frac{1}{3+\sqrt{3}}\)
\(=\frac{3+\sqrt{3}+3\sqrt{3}}{(3\sqrt{3})(3+\sqrt{3})}=\frac{6}{6}=1\)
If \(x+\frac{1}{x}=2\), then the value of\(\left ( \sqrt{x}+\frac{1}{\sqrt{x}} \right )\) is

Solution
\(\left ( \sqrt{x}+\frac{1}{\sqrt{x}} \right )^{2}\)
= x+^{1}⁄_{x}+2 =2+2=4
\(∴\sqrt{x}+\frac{1}{\sqrt{x}}=2\)
If \(a\left ( 2\sqrt{3} \right )=b\left ( 2+\sqrt{3} \right )=1\) then the value of \(\left ( a^{2}b^{2} \right )\) is

Solution
\(a\left ( 2\sqrt{3} \right )=b\left ( 2+\sqrt{3} \right )=1\)
\(∴\frac{a}{2+\sqrt{3}}=\frac{b}{2\sqrt{3}}=1\)
\(∴a=2+\sqrt{3}and b = 2 \sqrt{3}\)
∴ a^{2}  b^{2}= (a + b) (a  b)
\(=\left ( 2+\sqrt{3}+2\sqrt{3} \right )\left ( 2+\sqrt{3}2+\sqrt{3} \right )\)
\(=4\times 2\sqrt{3}=8\sqrt{3}\)

Solution
\(\frac{1}{\sqrt{2}+\sqrt{1}}=\frac{1}{\sqrt{2}+1}\times \frac{\sqrt{2}1}{\sqrt{2}1}\)
\(=\sqrt{2}1\)
∴ Expression=\(\sqrt{2}1+\sqrt{3}\sqrt{2}+\sqrt{4}\sqrt{3}+.......+\sqrt{99}\sqrt{98}+\sqrt{100}\sqrt{99}\)
\(=\sqrt{100}1= 10  1 = 9\)
In a code TIGER is written as SHFDQ. how shall HORSE be written in that code?

Solution
If A is coded as 2. B as 3 and so on. what is the code for FACE?

Solution
F A C E
↓ ↓ ↓ ↓
7 2 4 6
Which one of the following rivers forms an estuary ?

Solution
Narmada