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 MN). So, the left side of the reflected image will appear as the right side, and the right side will appear as the left side. However, the top and bottom of the reflected image will remain the same.
Thus, the correct mirror image of the given figure will be –

Hence, the third option is correct.

Correct Answer: – 8

Solution : $4\left(\operatorname{cosec}^2 57^\circ-\tan ^2 33^\circ\right)-\cos 90^\circ+y \tan ^2 66^\circ  \tan ^2 24^\circ=\frac{y}{2}$
Using, $\cos 90^\circ = 0$, $ \operatorname {cosec}^2 A - 1 = \cot^2 A$ and $\tan (90^\circ - A) = \cot A$ where $A$ is an angle. 
Substituting these identities into the given equation,
$⇒4\left[1 + \cot^2 57^\circ - (\tan^2 (90^\circ-57^\circ))\right] + y \tan^2 66^\circ \tan^2 (90^\circ - 66^\circ) = \frac{y}{2}$
We know that $\cot A = \tan (90^\circ - A)$ 
$⇒4\left[1 +\cot^2 57^\circ - \cot^2 57^\circ\right] + y \tan^2 66^\circ \cot^2 66^\circ = \frac{y}{2}$
$⇒4\left[1\right] + y = \frac{y}{2}$
$⇒\frac{y}{2}=-4$
$⇒y = -8$
Hence, the correct answer is '– 8'.

Correct Answer: Talking nonsense

Solution : The correct answer is the third option.

The idiom "talking through his hat" is an expression used to indicate that someone is talking or making statements without possessing proper knowledge or understanding of the subject. It suggests that the person is speaking nonsense, often confidently or assertively, but the information they are providing is inaccurate or baseless.

Therefore, the correct answer is talking nonsense.

Correct Answer: Ink pen

Solution : The correct option is an Ink pen.

Ink pens do not contain silicon. Silicon is frequently employed as a coating or substrate in the manufacture of precision optical components and equipment. Silicon is used in the production of photovoltaic solar cells, which use sunlight to generate electricity. Solar panels made of silicon are frequently used to harvest solar energy.

Correct Answer: 13

Solution :
In $\triangle$ ABC, $\angle$ BCA = $90^{\circ}$, AC = 24 cm and BC = 10 cm
AB² = AC² + BC²
$AB = \sqrt{24^2 + 10^2} = \sqrt{576+100} = \sqrt{676} = 26$ cm
Circumradius of $\triangle ABC = \frac{AB}{2} = \frac{26}{2} = 13$ cm
Hence, the correct answer is 13.

Correct Answer: GMRVY

Solution : Let's check each option –

First option: MSWCH; S – M = 6; W – S = 4; C – W = 6; H – C = 5; The difference between the letters is not in decreasing order.
Second option: NSWAH; S – N = 5; W – S = 4; A – W = 4; H – A = 7; The difference between the letters is not in decreasing order.
Third option: GMRVY; M – G = 6; R – M = 5; V – R = 4; Y – V = 3; The difference between the letters is in decreasing order.
Fourth option: UZEIL; Z – U = 5; E – Z = 5; I – E = 4; L – I = 3; The difference between the letters is not in decreasing order.

Therefore, the third option is different from the other three options. Hence, the third option is correct.

Correct Answer: Vagabond

Solution : The correct answer is the third option.

The word "vagrancy" refers to the state of being homeless, wandering, or having no settled place of residence. A vagabond is a person who wanders from place to place, often without a permanent home or employment.

The meanings of the other options are as follows:

• Vagueness refers to the quality of being unclear, indistinct, or not well-defined.
• Exploration pertains to the action of exploring or investigating new places or territories.
• Fragrance refers to a pleasant or sweet smell.

Therefore, the correct answer is vagabond.

Correct Answer: XWCZ

Solution : Given: 
POUR, MLRO, IHNK, DCIF, ?

Subtract consecutive numbers from each letter cluster to obtain the next term in the series.
POUR→P – 3 = M; O – 3 = L; U – 3 = R; R – 3 = O→MLRO
MLRO→M – 4 = I; L – 4 = H; R – 4 = N; O – 4 = K→IHNK
IHNK→I – 5 = D; H – 5 = C; N – 5 = I; K – 5 = F→DCIF
DCIF→D – 6 = X; C – 6 = W; I – 6 = C; F – 6 = Z→XWCZ

So, the required missing term in the series is XWCZ. Hence, the second option is correct.

Correct Answer: HMLQ

Solution : Given
RVLP : SWMQ :: GLKP : ?

Add 1 to the letters of RVLP and GLKP to get their codes.
R + 1 = S; V + 1 = W; L + 1 = M; P + 1 = Q
Similarly, G + 1 = H; L + 1 = M; K + 1 = L; P + 1 = Q

GLKP is related to HMLQ. Hence, the third option is correct.

Correct Answer: so much to

Solution : The error lies in the fourth option.

Explanation: The error occurs because "so much" is used incorrectly in the sentence. "So much" is typically used to refer to an excessive or considerable amount of something. However, in this context, the intended meaning is about earning an adequate amount, which is better conveyed by using "enough". "Enough" signifies a sufficient quantity or degree for a specific purpose, making it the appropriate word choice in this sentence.

Therefore, the correct sentence would be: Do you earn enough to make both ends meet?