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Correct Answer: 1

Solution : Given: $(x^{b+c})^{b–c}(x^{c+a})^{c–a}(x^{a+b})^{a–b}$ $(x\neq 0)$
= $(x^{(b+c)×(b–c)})(x^{(c+a)(c–a)})(x^{(a+b)×(a–b)})$
= $(x^{(b^{2}–c^{2})})(x^{(c^{2}–a^{2})})(x^{(a^{2}–b^{2})})$
= $x^{(b^{2}–c^{2}+c^{2}–a^{2}+a^{2}–b^{2})}$
= $x^{0}$
= 1
Hence, the correct answer is 1.

Correct Answer: 3

Solution : Given: $x^4+\frac{1}{x^4} = 119$
⇒ $(x^2+\frac{1}{x^2})^2–2×x^2×\frac{1}{x^2} = 119$
⇒ $(x^2+\frac{1}{x^2})^2–2 = 119$
⇒ $(x^2+\frac{1}{x^2})^2 = 119+2 = 121$
⇒ $x^2+\frac{1}{x^2} = \sqrt{121} = 11$
Now, $(x–\frac{1}{x})^2+2×x×\frac{1}{x} = 11$
⇒ $(x–\frac{1}{x})^2+2 = 11$
⇒ $(x–\frac{1}{x})^2 = 11–2 = 9$
⇒ $x–\frac{1}{x} = \sqrt9 = 3$
Hence,

Correct Answer: Neither conclusion I nor II follows

Solution : The possible Venn diagram according to the statements is as follows –

Let's analyse the conclusions –
Conclusion (I): Some knives are forks – According to the Venn diagram, there is no definite relation between knives and forks. Therefore, this

Correct Answer: seventh

Solution : The correct answer is seventh.

In terms of area, India is the seventh largest country in the world. The total land area of India is 3,287,263 square kilometres. The largest country by land area is Russia, followed by Canada, the United States, China,

Correct Answer: Geneva

Solution : The correct answer is Geneva.

An international body that deals with international trade regulations is called the World Trade Organisation (WTO). The WTO is headquartered in Geneva, Switzerland, which is a special location because it is home to numerous missions for the WTO as

Correct Answer: RUXAE

Solution : Let's check the options –
First option: QTWZC; Q + 3 = T; T + 3 = W; W + 3 = Z; Z + 3 = C
Second option: HKNQT; H + 3 = K; K + 3 = N; N + 3 =

Correct Answer: joule

Solution : The correct option is joule.

The SI (International System of Units) unit of work is the joule and is represented by the symbol "J". One joule is defined as the amount of work done when a force of one newton displaces an

Correct Answer: Malicious

Solution : The correct answer is the first option.

The word "diabolical" is an adjective that means extremely wicked or cruel, often associated with the devil or evil forces. A suitable synonym for "diabolical" is "malicious", which also conveys a strong sense of intending harm or evil.

Correct Answer: There is an increase in rainfall generally from east to west in the Northern plains.

Solution : The correct answer is There is an increase in rainfall generally from east to west in the Northern plains.

1. Most parts of the country receive rainfall from June to

Correct Answer:

Solution : When the paper is unfolded, the following figures will be obtained –

Hence, the fourth option is correct.