Correct Answer: Corporation tax

Solution : The correct option is Corporation tax.

The Union Government, as the central authority, sets the tax rates and regulations governing corporation tax. The revenue collected from corporation tax contributes to the central government's funds, supporting a range of national-level endeavours, including infrastructure projects,

Correct Answer: Vacant

Solution : The correct answer is the second option.

The most appropriate synonym for empty is vacant. Both "empty" and "vacant" refer to a lack or absence of something. Empty implies a total absence or lack of content or substance, while vacant typically refers to an empty

Correct Answer: 55

Solution : Let the numbers be $3x$ and $8x$.
LCM of ($3x$, $8x$) = 3 × 8 × $x$
⇒ 120 = $24x$
⇒ $x$ = 5
Sum of numbers = $3x+8x$ = $11x$ = 55
Hence, the correct answer is 55.

Correct Answer: Oblivious

Solution : The correct one-word substitute is the first option.

Explanation: Oblivious is the correct choice. It means not being aware of something, often due to inattention or a lack of information.

The meanings of the other options are as follows:

• Uneducated: It refers to a

Correct Answer: Mahatma Gandhi

Solution : The answer is Mahatma Gandhi.

The International Day of Non-Violence is celebrated on October 2 each year to commemorate the birthday of Mahatma Gandhi. He had developed the Satyagraha ideology of nonviolent resistance, which he used as a potent instrument for social and political

Correct Answer: met

Solution : The fourth option is the correct answer for the sentence because 'met' is correctly used with the noun 'failure' and contextually fits in the sentence. "Caught with failure", "gone with failure" and "got with failure" do not convey the proper meaning. Hence, it makes the

Correct Answer: (72, 4, 18)

Solution : Given:
(76, 4, 19); (98, 2, 49)

Here, the pattern followed is as follows –
⇒ (76, 4, 19)→76 ÷ 19 = 4
⇒ (98, 2, 49)→98 ÷ 49 = 2

Let's check the options –

First option: (84, 12, 4)→84 ÷ 4

Correct Answer: i-d, ii-c, iii-b, iv-a

Solution : The correct options are i-d, ii-c, iii-b, and iv-a.

The correct matching is

• Alkali metals- Group number in the Modern Periodic Table: 1
• Alkaline earth metals- Group number in the Modern Periodic Table: 2
• Halogens- Group number in the Modern Periodic Table:

Correct Answer: 48

Solution : Given:
+ means minus, – means multiplication, ÷ means plus, and × means division.
15 – 3 + 10 × 5 ÷ 5 = ?

On replacing the symbols according to the instructions given, the equation becomes –
= 15 × 3 – 10 ÷

Correct Answer: $\sqrt{2}\sin\theta$

Solution : Given: $\cos\theta+\sin\theta=\sqrt{2}\cos\theta$
Squaring on both sides, we get,
$\cos^{2}\theta+\sin^{2}\theta+2\cos\theta\sin\theta=2\cos^{2}\theta$
$⇒\cos^{2}\theta-\sin^{2}\theta=2\cos\theta\sin\theta$
$⇒(\cos\theta+\sin\theta)(\cos\theta-\sin\theta)=2\cos\theta\sin\theta$
$⇒\sqrt{2}\cos\theta(\cos\theta-\sin\theta)=2\cos\theta\sin\theta$
$\therefore \cos\theta-\sin\theta=\sqrt{2}\sin\theta$
Hence, the correct answer is $\sqrt{2}\sin\theta$.