Staff Selection Commission Combined Graduate Level Exam
Question : If $a + b = 11$ and $ab=35$, then what is the value of $\left(a^4+b^4\right)$?
Option 1: 151
Option 2: 261
Option 3: 124
Option 4: 102
Correct Answer: 151
Solution : Given, $a + b = 11$ and $ab=35$ Consider, $a+b=11$ Squaring both sides, we get, ⇒ $(a+b)^2=11^2$ ⇒ $a^2+b^2+2ab=121$ ⇒ $a^2+b^2+2(35)=121$ ⇒ $a^2+b^2+70=121$ ⇒ $a^2+b^2=51$ Squaring both sides, ⇒ $(a^2+b^2)^2=51^2$ ⇒ $a^4+b^4+2a^2b^2=2601$ ⇒ $a^4+b^4+2(35)^2=2601$ ⇒ $a^4+b^4+2\times1225=2601$ ⇒ $a^4+b^4+2450=2601$ ⇒ $a^4+b^4=2601-2450$ $\therefore a^4+b^4=151$ Hence, the correct
Question : Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph. A. Because of the region's scorching heat and aridity, a considerable amount of water evaporates. B. As a result, the salt and other minerals become increasingly concentrated. C. It is then unable to exit the lake and is forced to evaporate. D. The Dead Sea is one of the saltiest bodies of water on the planet, with about ten times the salt content of typical saltwater. E. This is because water flows into the Dead Sea from a single primary tributary, the Jordan River.
Option 1: DECAB
Option 2: DCBAE
Option 3: DEABC
Option 4: DACEB
Correct Answer: DECAB
Solution : The correct answer is the first option.
Here are the sentences arranged in the correct order to form a meaningful and coherent paragraph:
D. The Dead Sea is one of the saltiest bodies of water on the planet, with about ten times the salt content
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
A robot is a mechanical or virtual artificial agent, usually an electromechanical machine that is (1)______ by a computer programme or electronic circuitry. In general, robots can be autonomous or semi-autonomous and are now used in different fields. They have replaced (2)_______ in performing repetitive and dangerous tasks which humans prefer not to do, or are unable to do because of size limitations, or which take place in extreme (3)________ such as outer space or the bottom of the sea. For instance, robots can now be used in industry, as in car manufacturing, or they can be used in homes to do the (4)_______. Some robots may respond to speech or even be medical operating tools. There are concerns about the increasing use of robots and their role in society. Robots are blamed for the rising (5)________ as they replace workers in increasing numbers of functions.
Question:
Select the most appropriate option to fill in the blank number 4.
Option 1: network
Option 2: housework
Option 3: software
Option 4: handwork
Correct Answer: housework
Solution : The correct choice is the second option.
The sentence discusses the usage of robots in different settings. In this context, it contrasts industrial use (like in car manufacturing) with domestic use.
Housework refers to tasks performed in a household, such as cleaning, cooking, or
Question : Directions: Three different positions of the same dice are shown. Find the number on the face opposite the face showing 1.
Option 1: 6
Option 2: 3
Option 3: 2
Option 4: 4
Correct Answer: 6
Solution : Taking dice in Figures 1 and 3 with 6 as the common face,
Moving clockwise from the common face with 6,
Pairs of opposite faces –
So, the opposite face to the face containing 1 is 6. Hence, the first option is correct.
Question : Comprehension: In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each number.
A no-examination policy would kill the competitive (1) __________among the students. It is (2) ____________to encourage healthy competition in today's (3) ___________where all admissions and job (4) _________are based on elimination. Also, (5) _________the total absence of examinations, (6) ________who truly deserve may not get fair (7) __________, while those who need to (8) ___________may not get the right (9)___________. Moreover, examinations help to assess the (10) ___________of teaching.
Question: Select the most appropriate option to fill in the blank number 2.
Option 1: convenient
Option 2: important
Option 3: auspicious
Option 4: applicable
Correct Answer: important
In this context, important fits well to convey that it is crucial or significant to encourage healthy competition.
Using important emphasises the necessity of fostering healthy competition for the overall development and success of students in the given
Question : A metallic solid spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 2 cm and 1.5 cm. What is the surface area (in cm2) of the third ball?
Option 1: $50 \pi$
Option 2: $\frac{25}{4} \pi$
Option 3: $25 \pi$
Option 4: $\frac{25}{2} \pi$
Correct Answer: $25 \pi$
Solution : Let the radius of the smaller balls be r1, r2, and r3. The radius of the larger sphere is r. So, $\frac{4}{3}\pi$r3 = $\frac{4}{3}\pi$(r13 + r23 + r33) ⇒ r3 =
Question : Equilibrium out is determined by:
Option 1: the equality between total variable cost and marginal revenue
Option 2: the equality between Marginal cost and Marginal revenue
Option 3: the equality between Average cost and Average revenue
Option 4: the equality between total cost and total revenue
Correct Answer: the equality between Marginal cost and Marginal revenue
Solution : The correct option is the equality between total cost and total revenue.
A company maximises its profit in a competitive market by generating the amount of production where the difference between total revenue and the total cost
Question : The song "Vande Mataram" occurs in the book
Option 1: Geetanjali
Option 2: Anandmath
Option 3: Indian People
Option 4: Poverty and un-British Rule in India
Correct Answer: Anandmath
Solution : The correct answer is Anandmath.
"Vande Mataram" was written by Bankim Chandra Chattopadhyay in Sanskrit in his Bengali novel Anandmath, and later made the national song of India. "Gitanjali" is a collection of poems written by Rabindranath Tagore. "Poverty and un-British Rule in India" was
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
The poor man saves the money (1) / but then he began to worry (2) / that thieves might take it away (3) / No Error (4)
Option 1: 1
Option 2: 2
Option 3: 3
Correct Answer: 1
Solution : The correct choice is the first option.
The sentence is in the past tense, and the word "saves" is in the simple present tense. So, the verb "saves" should be replaced with "saved", which is a simple past tense.
Therefore, the correct
Question : Which of the following statements is true?
A) The wage bill of the government is a capital expenditure.
B) Disinvestment by the government in a company is a capital receipt.
Option 1: Only (A)
Option 2: Neither (A) nor (B)
Option 3: Both (A) and (B)
Option 4: Only (B)
Correct Answer: Only (B)
Solution : The correct option is Only (B).
Disinvestment by the government refers to the sale of its assets, which can include the sale of its stake in a company. The money received from disinvestment is treated as a capital receipt, as it involves a
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