Correct Answer: 2

Solution : Given:
$x=\frac{4\sqrt ab}{\sqrt a+\sqrt b}$
Equation $=\frac{x+2\sqrt a}{x-2\sqrt a}+\frac{x+2\sqrt b}{x-2\sqrt b}$
Put the value of $x$ in equation:
$=\frac{\frac{4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}+2\sqrt{a}}{\frac{4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-2\sqrt a}+\frac{\frac{4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}+2\sqrt{b}}{\frac{4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-2\sqrt b}$
$=\frac{\frac{4\sqrt{ab}+2a+2\sqrt {ab}}{\sqrt{a}+\sqrt{b}}}{\frac{4\sqrt{ab}-2a-2\sqrt {ab}}{\sqrt{a}+\sqrt{b}}}+\frac{\frac{4\sqrt{ab}+2\sqrt {ab}+2b}{\sqrt{a}+\sqrt{b}}}{\frac{4\sqrt{ab}-2\sqrt {ab}-2b}{\sqrt{a}+\sqrt{b}}}$
$=\frac{\frac{4\sqrt{ab}+2a+2\sqrt {a}b}{\sqrt{a}+\sqrt{b}}}{\frac{4\sqrt{ab}-2a-2\sqrt {a}b}{\sqrt{a}+\sqrt{b}}}+\frac{\frac{4\sqrt{ab}+2\sqrt {ab}+2b}{\sqrt{a}+\sqrt{b}}}{\frac{4\sqrt{ab}-2\sqrt {a}b-2b}{\sqrt{a}+\sqrt{b}}}$
$=\frac{4\sqrt{ab}+2a+2\sqrt {a}b}{4\sqrt{ab}-2a-2\sqrt {ab}}+\frac{4\sqrt{ab}+2\sqrt {ab}+2b}{4\sqrt{ab}-2\sqrt {ab}-2b}$
$=\frac{2}{2}\left [\frac{2\sqrt{ab}+a+\sqrt {a}b}{2\sqrt{ab}-a-\sqrt {a}b} \right ]+\frac{2}{2}\left[\frac{2\sqrt{ab}+\sqrt {ab}+b}{2\sqrt{ab}-\sqrt {a}b-b}\right]$
$=\frac{3\sqrt{ab}+a}{\sqrt{ab}-a}+\frac{3\sqrt{ab}+b}{\sqrt{ab}-b}$

Correct Answer: $0$

Solution : Given: $x+\frac{1}{x}=\sqrt{3}$
Cubing both sides we get
$(x+\frac{1}{x})^3=(\sqrt{3})^3$
⇒ $x^3+\frac{1}{x^3}+3×x×\frac{1}{x}(x+\frac{1}{x})=(3\sqrt{3})$
⇒ $x^3+\frac{1}{x^3}=3\sqrt{3}–3(x+\frac{1}{x})$
$\because x+\frac{1}{x}=\sqrt{3}$
Thus, $x^3+\frac{1}{x^3}=3\sqrt{3}–3\sqrt{3} = 0$
Hence, the correct answer is $0$.

Correct Answer: Javelin Throw 

Solution : The correct option is - Javelin Throw .

Neeraj Chopra is an Indian javelin thrower, born on 24 December 1997. He now holds the title of Olympic champion in the javelin throw and has won silver at the World Championships and the Diamond League.

Correct Answer: are visiting

Solution : The most appropriate choice is the fourth option.

The original sentence is incorrect as per the subject-verb agreement. Since "My friend Meera and her mother" is a compound subject involving more than one person, the verb should also be in the plural form to

Correct Answer: Husband’s sister

Solution : Given:
A – B ⇒ A is the mother of B
A * B ⇒ A is the sister of B
A % B ⇒ A is the husband of B
A & B ⇒ A is the son of B

As per the

Correct Answer: 11

Solution :
Given, AB = AD = 7 cm, and AC = AE, and BC = 11 cm
$\angle BAC = \angle DAE$ (vertically opposite angles)
In the given figure, $\frac{AB}{BC}=\frac{AD}{ED}$
So, $\triangle ABC \cong \triangle ADE$ [by Side-Angle-Side criteria]
⇒ $ED = BC = 11$ cm

Correct Answer: 91

Solution : Given:
7 : 13 :: 16 : 31 :: 46 : ?

Like, 7 : 13→7 × 2 = 14; 14 – 1 = 13
16 : 31→16 × 2 = 32; 32 – 1 = 31
Similarly, for 46 : ?→(46 × 2) =

Correct Answer: 42 – 29 

Solution : Let's check the options –
First option: 73 – 61→73 – 61 = 12
Second option: 57 – 69→69 – 57 = 12
Third option: 47 – 59→59 – 47 = 12
Fourth option: 42 – 29

Correct Answer: 2

Solution : Given: $a^2 + b^2 + c^2 = 9$ and $ab + bc + ca = 8$
We know, $(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$
⇒ $(a+b+c)^2=9+2\times 8$
⇒ $(a+b+c)^2=9+16$
⇒ $a+b+c=\sqrt{25}=5$
$\therefore$ $(a+b+c)-3 = 5-3 = 2$
Hence, the correct answer is 2.

Correct Answer: Machiavelli

Solution : The correct option is Machiavelli.

Niccol Machiavelli (1469-1527), an Italian philosopher, is credited with coining the term "state" in its contemporary connotation. He describes the state in his book The Prince as "a political unit that is sovereign and has a monopoly on the legitimate