Correct Answer: 7 : 3

Solution : Given: $21 \tan \theta=20$
⇒ $\tan \theta = \frac{20}{21}=\frac{\text{Perpendicular}}{\text{Base}}$
Let the perpendicular and the base be 20 units and 21 units respectively.
Use the formulas,
$\tan \theta=\frac{\text{Perpendicular}}{\text{Base}}$,
$\sin \theta=\frac{\text{Perpendicular}}{\text{Hypotenuse}}$,
$\cos \theta=\frac{\text{Base}}{\text{Hypotenuse}}$,
Pythagoras's theorem: $\text{Hypotenuse}^2=\text{Base}^2+\text{Perpendicular}^2$
⇒ $\text{Hypotenuse}^2={21}^2+{20}^2$
⇒ $\text{Hypotenuse}^2=441+400$
⇒ $\text{Hypotenuse}^2=841$
⇒ $\text{Hypotenuse}=\sqrt{841}$
⇒

Correct Answer: Gopal Krishna Gokhale

Solution : The correct option is Gopal Krishna Gokhale

Gopal Krishna Gokhale advocated in 1905 from the Congress platform for "swarajya," or self-government, inside the British Empire, based on the model of self-governing colonies like Australia and Canada. Prominent statesman and social reformer Gokhale was

Correct Answer: unparalleled

Solution : The correct choice is the second option.

Explanation: 

Unparalleled beauty means that the beauty of these destinations is unmatched. It suggests that these destinations are exceptionally beautiful and stand out.

Therefore, the complete sentence is: The State is home to several destinations of unparalleled

Correct Answer: 4

Solution : The correct choice is the fourth option.

The sentence is grammatically accurate and doesn't need any changes. The sentence conveys the idea that Vishal is capable of working out the issues easily.

Therefore, the given sentence requires no improvement.

Correct Answer: 20 metres to the south

Solution : Firstly, we will draw the diagram as per the given instructions –

Now we have to find the distance and direction between Sarita's Initial and final point.

From the above diagram, D is the initial point and F is the final

Correct Answer: 21

Solution : Given:
1, 3, 6, 10, 15, ?

Add consecutive natural numbers from 2 onwards to find the next term of the series –
1 + 2 = 3; 3 + 3 = 6; 6 + 4 = 10; 10 + 5 = 15; 15 +

Correct Answer: $\frac{x^{256}-1}{x-1}$

Solution : Given: $(x^{128}+1)(x^{32}+1)(x^{64}+1)(x^{16}+1)(x^{8}+1)(x^{4}+1)(x^{2}+1)(x+1)$
Multiplying $(x-1)$ in both numerator and denominator,
$\frac{(x^{128}+1)(x^{32}+1)(x^{64}+1)(x^{16}+1)(x^{8}+1)(x^{4}+1)(x^{2}+1)(x+1)(x-1)}{(x-1)}$
Using identity: $(a^2-b^2)=(a-b)(a+b)$,
= $\frac{(x^{128}+1)(x^{32}+1)(x^{64}+1)(x^{16}+1)(x^{8}+1)(x^{4}+1)(x^{2}+1)(x^2-1)}{(x-1)}$
= $\frac{(x^{128}+1)(x^{32}+1)(x^{64}+1)(x^{16}+1)(x^{8}+1)(x^{4}+1)(x^4-1)}{(x-1)}$ 
= $\frac{(x^{128}+1)(x^{32}+1)(x^{64}+1)(x^{16}+1)(x^{8}+1)(x^8-1)}{(x-1)}$
= $\frac{(x^{128}+1)(x^{32}+1)(x^{64}+1)(x^{16}+1)(x^{16}-1)}{(x-1)}$
= $\frac{(x^{128}+1)(x^{32}+1)(x^{64}+1)(x^{32}-1)}{(x-1)}$
= $\frac{(x^{128}+1)(x^{64}+1)(x^{64}-1)}{(x-1)}$
= $\frac{(x^{128}+1)(x^{128}-1)}{(x-1)}$
= $\frac{(x^{256}-1)}{(x-1)}$
Hence, the correct answer is $\frac{(x^{256}-1)}{(x-1)}$.

Correct Answer: 3

Solution : The correct choice is the third option.

Explanation: The error is due to verb consistency, as "were laid" should be replaced with "are laid", as the sentence is in the simple present tense. 

Therefore, the correct sentence would be: "No country can long

Correct Answer: Expert

Solution : The correct choice is the second option.

Explanation:

The underlined word novice refers to someone who is a beginner or has limited experience in a particular activity or field. The opposite of a novice is an expert, someone who has a high

Correct Answer: 5 : 2

Solution : Person in the class interval 20–25 = 250
Person in the class interval 30–35 = 100
Required ratio = 250 : 100 = 5 : 2
Hence, the correct answer is 5 : 2.