Correct Answer: $(1,1)$

Solution : Given: $y = x$ is a linear equation, so, check in which option $y=x$ is given
Only one option (1,1) satisfies the condition. 
Hence, the correct answer is (1,1).

Correct Answer: $x = 37.5^\circ, y = 7.5^\circ$

Solution : $\tan (x + y)=1=\tan 45^\circ$
$⇒x+y=45^\circ$ ____(i)
$\cos (x-y)={\frac{\sqrt3}{2}}=\cos 30^\circ$
$⇒x+y=30^\circ$ ____(ii)
Adding both equations,
$⇒2x=75^\circ$
$⇒x=37.5^\circ$
And,
$⇒2y=15^\circ$
$⇒y=7.5^\circ$
Hence, the correct answer is $x = 37.5^\circ, y = 7.5^\circ$.

Correct Answer: Spade : Labourer

Solution : Given:
Axe : woodcutter (Woodcutter uses the axe to cut the trees.)

Let's check the options –
First option: Author : Pen; Pen is used by the Writer, not the Author.
Second option: Surgeon : Scalpel; The Surgeon uses a scalpel but the

Correct Answer: 1913

Solution : The correct answer is 1913.

In 1913, Niels Bohr introduced his quantum theory-based model for the hydrogen atom. The Bohr model, a groundbreaking contribution to atomic physics, was pivotal in comprehending electron behaviour in atoms through the concept of distinct energy levels.

Correct Answer: Refined

Solution : The second option is correct.

Inchoate: It is often used to describe things that are in the initial or rudimentary stages of existence.

Refined: Showing sophistication, culture, polish, or improvement in manners or taste. They are antonyms, representing opposite ends of the spectrum in terms

Correct Answer:

Solution : As per the mirror image properties, closer things appear closer to the mirror in the reflection.
So, according to the above property and the information provided, the mirror is placed on the right side of the figure (on line MN). So, the left side of the

Correct Answer: 14

Solution : Given:
7 : ? :: 15 : 150 :: 18 : 234

Multiply the first number with a number that is five less than the first number to get the second number.
Like, 15 : 150→15 × (15 – 5) = 15 × 10 =

Correct Answer:

Solution : As per the mirror image properties, closer things appear closer to the mirror in the reflection.
Here, according to the information provided, the mirror is placed at the bottom of the figure (on line MN). So, the top of the reflected image will appear as the

Correct Answer: 45°

Solution : Given: $2\tan^2A+4\cos^4A=3$
Take $A = 45°$ then,
$2\tan^2A+4\cos^4A=2(1)^2+4(\frac{1}{\sqrt2})^4 = 2 + 1 = 3$
So, $A = 45°$ satisfies the given equation.
Hence, the correct answer is 45°.

Correct Answer:

Solution : As per mirror image properties, closer things appear closer to the mirror in reflection.
According to the information provided, if the mirror is placed on the right side of the figure (on line MN), the right of the reflected image will appear as the left, and