Staff Selection Commission Combined Graduate Level Exam
Question : If $a+b+c=6$ and $a^2+b^2+c^2=14$, then what is the value of $(a-b)^2+(b-c)^2+(c-$ a) ${ }^2$?
Option 1: –8
Option 2: 8
Option 3: 10
Option 4: 6
Correct Answer: 6
Solution : $a^2+b^2+c^2=14$ $a+b+c=6$ Squaring on both sides, $(a+b+c)^2=6^2$ ⇒ $a^2+b^2+c^2+2ab+2bc+2ca = 36$ ⇒ $14 + 2ab+2bc+2ca = 36$ ⇒ $2ab+2bc+2ca = 36-14 = 22$ --------------------(i) $(a-b)^2+(b-c)^2+(c-$ a) ${ }^2$ $= a^2+b^2-2ab+b^2+c^2-2bc+c^2+a^2-2ca$ $= 2(a^2+b^2+c^2)-(2ab+2bc+2ca)$ $=2×14 – 22$ $= 6$ Hence, the correct answer is 6.
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (49, 63, 441) (7, 14, 14)
Option 1: (7, 28, 35)
Option 2: (14, 28, 56)
Option 3: (7, 14, 45)
Option 4: (12, 18, 324)
Correct Answer: (14, 28, 56)
Solution : Given: (49, 63, 441); (7, 14, 14)
In the given set of numbers, multiply the first two numbers and divide the result by 7 to get the third number. (49, 63, 441)→49 × 63 = 3087; 3087 ÷ 7 = 441 (7, 14,
Question : Select the option that expresses the given sentence in direct speech. Hira inquired how I was doing being all alone in my house.
Option 1: Hira said to me, “Are you doing fine being all alone in your house.”
Option 2: Hira said to me, “How are you doing being all alone in my house.”
Option 3: Hira said to me, “How are you doing being all alone in your house?”
Option 4: Hira said to me, “How you are doing being all alone in your house?”
Correct Answer: Hira said to me, “How are you doing being all alone in your house?”
Solution : The third option is the correct choice.
When changing a sentence from indirect speech to direct speech, the transformation involves quoting the speaker's words directly.
In conversion to direct speech, we follow
Question : Which of the digestive organs contains acid?
Option 1: Stomach
Option 2: Small intestine
Option 3: Appendix
Option 4: Colon
Correct Answer: Stomach
Solution : The correct option is the Stomach.
The stomach is the digestive organ that contains acid. It secretes hydrochloric acid (HCl) and digestive enzymes to help break down food and generate an acidic environment that assists in protein, and nutrient digestion. The stomach's acidic pH
Question : Which organic compound has the structure R-COOH, with R referring to the alkyl, alkenyl, aryl or other groups?
Option 1: Carboxylic acid
Option 2: Ester
Option 3: Ketone
Option 4: Aldehydes
Correct Answer: Carboxylic acid
Solution : The answer is Carboxylic acid.
The organic compound with the structure R-COOH, where R refers to the alkyl, alkenyl, aryl, or other organic groups, is known as a carboxylic acid. The general formula for a carboxylic acid is R-COOH, and the functional group it
Question : Select the option that expresses the given sentence in reported speech. The old man said, "I was walking in my garden at six o'clock."
Option 1: The old man said that I had been walking in my garden at six o'clock.
Option 2: The old man said that he had been walking in his garden at six o'clock.
Option 3: The old man said that I was been walking in my garden at six o'clock.
Option 4: The old man said that he was walking in his garden at six o'clock.
Correct Answer: The old man said that he had been walking in his garden at six o'clock.
Solution : The correct choice is the second option.
The steps of conversion are as follows:
Question : India recently signed land boundary agreement with which country?
Option 1: China
Option 2: Nepal
Option 3: Bhutan
Option 4: Bangladesh
Correct Answer: Bangladesh
Solution : The correct answer is Bangladesh.
India and Bangladesh signed a land boundary agreement in 2015. It was ratified by India through 100th Constitutional Amendment Act. According to this India and Bangladesh exchanged 162 disputed enclaves of which India transfer 111 enclaves to Bangladesh and Bangladesh
Question : ABCD is a cyclic quadrilateral and BC is the diameter of the circle. If $\angle D B C=29^{\circ}$, then $\angle B A D=$?
Option 1: 129°
Option 2: 119°
Option 3: 111°
Option 4: 122°
Correct Answer: 119°
Solution : In a circle, the angle subtended by the diameter at any point on the circle is always 90°. $\angle BAC = 90^{\circ}$ Given that $\angle DBC = 29^{\circ}$ So, $\angle BCD = 90^{\circ} - 29^{\circ} = 61^{\circ}$ Also, the property of a cyclic quadrilateral states
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence. If there is no need to substitute it, select ‘No substitution required’. Edward II is tragic than some other plays by the dramatist.
Option 1: as least tragic as
Option 2: No substitution required
Option 3: the most tragic
Option 4: less tragic than
Correct Answer: less tragic than
Solution : The fourth option is the correct choice.
In the original sentence, the comparative structure is incorrect because it uses tragic directly without the proper comparative form. When making a comparison between two things, the comparative form is used. The correct comparative form is
Question : Select the most appropriate adverb to fill in the blank. They supplied the required human resource ____________.
Option 1: faultlessly
Option 2: heavy
Option 3: clear
Option 4: able
Correct Answer: faultlessly
Solution : The correct choice is the first option.
"Faultlessly" is an adverb that describes the manner in which the action of supplying the required human resource was carried out. It means that the supply process was executed without any errors, mistakes, or flaws.
Here, it emphasises
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