Correct Answer: $\frac{1}{8}$

Solution : Given:
$x+3y=-3x+y$
Solution:
⇒ $x+3y+3x-y=0$
⇒ $4x+2y=0$
⇒ $2(2x+y)=0$
⇒ $2x+y=0$
⇒ $y=–2x$
Put the value of $y$ in $\frac{x^{2}}{2y^{2}}$
= $\frac{x^{2}}{2(–2x)^{2}}$
= $\frac{x^{2}}{8x^{2}}$
= $\frac{1}{8}$
Hence, the correct answer is $\frac{1}{8}$.

Correct Answer: $1$

Solution : $\cot A = 1= \cot 45°$
$\therefore A = 45°$
$\sin B = \frac{1}{\sqrt{2}}=\sin45°$
$\therefore B = 45°$
$\sin (A+B) = \sin 90° = 1$
$\cot (A+B) = \cot 90° = 0$
$\therefore \sin (A+B) -\cot (A+B) =1-0= 1$
Hence, the correct answer is $1$.

Correct Answer: 10.5 cm

Solution : The volume of hemisphere = $2425 \frac{1}{2} \mathrm{~cm}^3$
Volume of Hemisphere = $\frac{2}{3} × \pi r^3$
⇒ $\frac{2}{3} × \frac{22}{7} × r^3 =  \frac{4851}{2} \mathrm{~cm}^3$
⇒ $r^3 = 1157.63$
⇒ $r = 10.5$ cm
$\therefore$ The correct answer is 10.5 cm.
Hence, the correct

Correct Answer: 30

Solution : $\tan (4α − 50°)$ = $\cot (50° − α)$ = $\tan(90°–(50° − α))$
⇒ $\tan (4α − 50°)$ = $\tan(90°–(50° − α))$
⇒ $(4α − 50°) = 90°–(50° − α)$
⇒ $4α − 50° = 40°+α$
⇒ $3α = 90°$
⇒ $α = 30°$
Hence,

Correct Answer: 2302

Solution : Given: $\left(x+\frac{1}{x}\right)=5 \sqrt{2}$
Squaring both sides, we get,
⇒ $(x+\frac{1}{x})^2=(5 \sqrt{2})^2$
⇒ $x^2+\frac{1}{x^2}+2=50$
⇒ $x^2+\frac{1}{x^2}=48$
Again squaring both sides, we get:
⇒ $(x^2+\frac{1}{x^2})^2=48^2$
⇒ $x^4+\frac{1}{x^4}+2=2304$
$\therefore x^4+\frac{1}{x^4}=2302$
Hence, the correct answer is 2302.

Correct Answer: Yajurveda

Solution : The correct answer is Yajurveda.

The Yajurveda is a detailed manual on how to carry out religious rites and ceremonies properly. The Yajurveda is the Veda of prose mantras; its name is derived from yajus, which means prose mantra, and veda, which means knowledge.

Correct Answer:

Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection.
Here, according to the information provided, the mirror is placed on the right side of the figure (on line AB). So, the left side of the reflected image will appear

Correct Answer: $-\frac{5}{4}$

Solution : $\sin A=-\frac{3}{5}$
So, $\cos A = \sqrt{1-\sin^2 A}$
⇒ $\cos A= \sqrt{1-(\frac{3}{5})^2}$
⇒ $\cos A = \sqrt\frac{16}{25}$
$\therefore\cos A= \pm \frac{4}{5}$
Since it is 3rd quadrant, $\cos A = -\frac{4}{5}$
$\therefore\sec A = -\frac{5}{4}$
Hence, the correct answer is $-\frac{5}{4}$.

Correct Answer:

Solution : In the given figures, as we move from one to another, the number of triangles in each box increases by 1. Therefore, the next box will have 5 triangles.
So, the next box in the series will be –

Hence, the second option is correct.

Correct Answer: 3

Solution : The correct choice is the third option.

Explanation: The correct form should be "during the reign of", where "reign" is the appropriate term to refer to the period of Bahadur Shah Zafar's rule.

So, the correct sentence would be: "The revolt of 1857