Correct Answer: 14

Solution : Given that $x^2+\frac{1}{x^2}=4$,
Squaring both sides, we get,
$⇒(x^2+\frac{1}{x^2})^2 = 4^2$
$⇒x^4 + 2 + \frac{1}{x^4} = 16$
$⇒x^4 + \frac{1}{x^4} = 16 - 2 = 14$
Hence, the correct answer is 14.

Correct Answer: TEAM

Solution : Given:
CALCULATE

Now, let's compare all the option words with the word CALCULATE –
First option: CAT; All the letters of CAT are present in the word CALCULATE.
Second option: TEA; All the letters of TEA are present in the word CALCULATE.
Third option: LATE; All the letters of LATE are present in the word CALCULATE.
Fourth option: TEAM; M is not present in the word CALCULATE. Therefore, all the letters of TEAM are not present in the word CALCULATE.

So, from the above, only TEAM cannot be formed from the word CALCULATE. Hence, the fourth option is correct.

Correct Answer: 29 cm

Solution :
Given that OP = y cm, QP = 21 cm, OQ = 20 cm.
To find the length of OP, apply Pythagoras theorem in $\triangle$OPQ.
⇒ OQ² + QP² = OP²
⇒ 20² + 21² = y²
⇒ y² = 400 + 441 = 841 cm
⇒ OP = $\sqrt{841}$ = 29 cm
Thus, the length of the point from the centre of the circle is 29 cm.
Hence, the correct answer is 29 cm.

Correct Answer: 14

Solution : Let the number be $x$.
Reciprocal = $\frac{1}{x}$
According to the question,
$x + \frac{1}{x} = 4$
Squaring both sides, we get:
⇒ $(x + \frac{1}{x})^2 = 4^2$
⇒ $x^2+ \frac{1}{x^2}+2 = 16$
⇒ $x^2 + \frac{1}{x^2} = 16 - 2 = 14$
Hence, the correct answer is 14.

Correct Answer: QPRS

Solution : The fourth option is the correct choice.

The sentence should start with the subject and its description, followed by the reasons or evidence, and then its widespread recognition.

Therefore, the sentence in the correct order is: The Lotus Temple has always enjoyed an unparalleled popularity, as shown by its predominance in literature and art throughout the length and breadth of India, from the earliest times down to the present day.

Correct Answer: 29

Solution : $117 ÷ 45 \;\text {of} \frac{1}{5} + \frac{12}{5} × \frac{20}{3}$ 
= 117 ÷ 9 + 4 × 4
= 13 + 16
= 29
Hence, the correct answer is 29.

Correct Answer: Both I and II

Solution : The correct option is Both I and II.

In a socialist system, there can be different degrees of government involvement, ranging from limited regulation and social ownership to more extensive control over the means of production.

In a socialist economy, the emphasis is often on meeting the needs of the population rather than allowing the market forces of supply and demand to determine distribution. The government or the community may play a significant role in planning and controlling the production and distribution of goods to ensure that basic needs are met.

Correct Answer: Sidgwick and Powell

Solution : The correct option is Sidgwick and Powell.

In 1940, Herbert Powell and Nevil Sidgwick proposed the notion that molecule shape and the number of valence electrons were correlated. They claimed that the number of valence electron pairs surrounding the core atom determines the shape of a molecule.

Correct Answer: Uniforms create a sense of belongingness

Solution : Let's analyse the given options –
First option: Students look smart in uniforms – In the above statement, there is no relation between smartness and uniforms. Thus, this conclusion doesn't follow.
Second option: Uniforms are compulsory – In the above statement, there is no indication that uniforms are compulsory. Thus, this conclusion doesn't follow.
Third option: Uniforms are easily available – In the above statement, there is no indication whether the uniforms are easily available or not. Thus, this conclusion doesn't follow.
Fourth option: Uniforms create a sense of belongingness – In the above statement, it has been mentioned that students go to school in uniforms. As such, uniforms help them to identify themselves as students. Thus, this conclusion follows.

So, only the fourth conclusion follows. Hence, the fourth option is correct.

Correct Answer: (3)

Solution : The first option is the correct answer.

This is because "with open hands" should be replaced with the idiom "with open arms" which means "in an enthusiastic manner", thereby indicating that when the prodigal son returned, the father gave him a warm and enthusiastic welcome.

Therefore, the correct sentence is: "When the prodigal son returned home, his father welcomed him with open arms."