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Staff Selection Commission Combined Graduate Level Exam

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Question : If $x^{4}+\frac{1}{x^{4}}=34$, what is the value of $x^{3}-\frac{1}{x^{3}} $?

Option 1: 0

Option 2: 6

Option 3: 8

Option 4: 14

Team Careers360 22nd Jan, 2024

Correct Answer: 14


Solution : Given: $x^{4}+\frac{1}{x^{4}}=34$
Adding 2 to both sides, we get,
$⇒x^{4}+\frac{1}{x^{4}}+2=34+2$
$⇒(x^{2}+\frac{1}{x^{2}})^{2}=(6)^{2}$
$⇒x^{2}+\frac{1}{x^{2}}=6$
Subtracting 2 from both sides, we get,
$⇒x^{2}+\frac{1}{x^{2}}-2=6-2$
$⇒(x-\frac{1}{x})^{2}=(2)^{2}$
$⇒x-\frac{1}{x}=2$
Now, $(x-\frac{1}{x})^3=x^3-\frac{1}{x^3}-3×x×\frac{1}{x}(x-\frac{1}{x})$
$⇒2^3=x^3-\frac{1}{x^3}-3×2$
$\therefore x^{3}-\frac{1}{x^{3}}=14$
Hence, the correct answer is 14.

8 Views

Question : Who decides disputes regarding the disqualification of members of Parliament?

Option 1: The Supreme Court

Option 2: The Election Commission

Option 3: The Prime Minister in Consultation with the Election Commission

Option 4: The President in Consultation with the Election Commission

Team Careers360 22nd Jan, 2024

Correct Answer: The President in Consultation with the Election Commission


Solution : The correct answer is The President in Consultation with the Election Commission.

Depending on whether it is the Lok Sabha or the Rajya Sabha, the Speaker or the House Chairman decides on disqualification in defection-related cases. Even if

35 Views

Question : Select the most appropriate ANTONYM for the word 'often' in the following sentence.

Usually at Christmas, uncle often brings lovely and cherished gifts for us.

Option 1: seldom

Option 2: cherished

Option 3: lovely

Option 4: usually

Team Careers360 22nd Jan, 2024

Correct Answer: seldom


Solution : The correct choice is the first option.

Explanation:

The word often indicates a high frequency or regular occurrence. In contrast, "seldom" means infrequent or rarely. The use of seldom as the antonym provides a clear contrast to the frequency implied by "often" in the

21 Views

Question : Directions: In the following question, the sentence given with a blank is to be filled in with an appropriate word. Select the correct alternative out of the four.
The manager was ___ an explanation of his conduct.

Option 1: called for

Option 2: called off

Option 3: called to

Option 4: called up

Team Careers360 22nd Jan, 2024

Correct Answer: called for


Solution : The first option is the correct answer for the sentence because 'called for' means 'required' and makes the explanation of the sentence as 'the manager was required an explanation for his code of conduct'.

'Called off' means to cancel; 'called to' means to shout

17 Views

Question : Select the most appropriate antonym of the given word.

TEMPORARY

Option 1: Transitory

Option 2: Lasting

Option 3: Interim

Option 4: Momentary

Team Careers360 22nd Jan, 2024

Correct Answer: Lasting


Solution : The correct choice is the second option.

Temporary means something that is temporary and not permanent.

Lasting refers to something that endures, continues, or exists for a long time, which makes it the correct antonym.

The meanings of the other options are as follows:

13 Views

Question : Which of the following is not a Union trtrritory

Option 1: Podicherry

Option 2: Nagaland

Option 3: Daman and Diu

Option 4: Lakshadweep

Team Careers360 24th Jan, 2024

Correct Answer: Nagaland


Solution : Correct Answer is  Nagaland

The largest city in the state is Dimapur, and Kohima serves as its capital. Nagaland became a Union Territory following several discussions between the NNC and the Indian government. It was given the status of a state on December 1st, 1963.

30 Views

Question : The remainder when $19^{19}+20$ is divided by 18, is:

Option 1: 3

Option 2: 2

Option 3: 1

Option 4: 0

Team Careers360 24th Jan, 2024

Correct Answer: 3


Solution : To find: The remainder when $19^{19}+20$ is divided by 18.
Now, 19 $\equiv$ 1 (mod 18)
⇒ 1919 $\equiv$ 119 (mod 18)
⇒ 1919 $\equiv$ 1 (mod 18)
⇒ (1919 + 20) $\equiv$ (1 + 20) (mod 18)
⇒ (1919

18 Views

Question : ROM stands for

Option 1: Real Office Manager

Option 2: Read Only Memory

Option 3: Read Only Memorandum

Option 4: Role On Memory

Team Careers360 23rd Jan, 2024

Correct Answer: Read Only Memory


Solution : The Correct Answer is- Read Only Memory

The read-only memory (ROM) category includes non-volatile memory. This means that it continuously operates even after your computer has been turned off by ingesting data, permanently storing it on a chip. Read-only memory is only employed

19 Views

Question : Directions: Which of the following interchange of numbers and mathematical signs would make the given equation correct?
30 ÷ 6 × 4 + 15 − 35 = 25

Option 1: 25 and 30; × and –

Option 2: 4 and 6; + and –

Option 3: 25 and 35; × and ÷

Option 4: 30 and 35; – and ÷

Team Careers360 24th Jan, 2024

Correct Answer: 25 and 35; × and ÷


Solution : Given:
30 ÷ 6 × 4 + 15 − 35 = 25

Replace the given symbols and numbers in the options one by one with the original symbols and numbers in the given equation.

Let's check each option –
First

94 Views

Question : If electric resistance is to be decreased, then the number of resistances should be connected in_________

Option 1: Series

Option 2: Parallel

Option 3: Mixed arrangement

Option 4: None of these

Team Careers360 24th Jan, 2024

Correct Answer: Parallel


Solution : The correct option is parallel.

In a parallel circuit, each resistor has its own path for current to flow through. This reduces the overall resistance because there are multiple paths for the current to take, making it easier for electrons to flow. So, If the

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