Staff Selection Commission Combined Graduate Level Exam
Question : If $\frac{\sqrt{38-5 \sqrt{3}}}{\sqrt{26+7 \sqrt{3}}}=\frac{a+b \sqrt{3}}{23}, b>0$, then the value of $(b-a)$ is:
Option 1: 7
Option 2: 18
Option 3: 29
Option 4: 11
Correct Answer: 29
Solution : $\frac{\sqrt{38-5 \sqrt{3}}}{\sqrt{26+7 \sqrt{3}}}=\frac{a+b \sqrt{3}}{23}, b>0$ $⇒\frac{\sqrt{38-5 \sqrt{3}}}{\sqrt{26+7 \sqrt{3}}}=\frac{a+b \sqrt{3}}{23}$ $⇒\frac{\sqrt{(38-5 \sqrt{3)}({26-7 \sqrt{3}})}}{\sqrt{(26+7 \sqrt{3})({26-7 \sqrt{3}})}}=\frac{a+b \sqrt{3}}{23}$ $⇒\frac{\sqrt{(988+105-396\sqrt3)}}{\sqrt{(529)}}=\frac{a+b \sqrt{3}}{23}$ $⇒\frac{\sqrt{(11^2+(18\sqrt3)^2-2\times11\times18\sqrt3)}}{\sqrt{(23^2)}}=\frac{a+b \sqrt{3}}{23}$ $⇒\frac{\sqrt{(18\sqrt3-11)^2}}{23}=\frac{a+b \sqrt{3}}{23}$ $⇒\frac{(18\sqrt3-11)}{23}=\frac{a+b \sqrt{3}}{23}$ On comparing, $a=-11$ and $b=18$ So, $(b-a)=18+11 = 29$ Hence, the correct answer is 29.
Question : Identify the option that can be substituted as the correct idiom for the underlined part of the given sentence.
As soon as the principal came to know about the inspection in the school, he put everything in perfect order.
Option 1: Apple pie order
Option 2: Apple of discord
Option 3: Alley apple
Option 4: Apple of one’s eye
Correct Answer: Apple pie order
Solution : The first option is the correct answer.
Apple pie order: It refers to something being extremely neat, tidy, or well-organised.
The meanings of the other options are as follows:
Apple of Discord is a small conflict that evolves into a bigger one.
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.
Everything we know about non-avian dinosaurs is ________ (1) fossils, which include bones, teeth, footprints, tracks, eggs, and skin impressions. For centuries, people throughout the world have ________ (2) amazing fossilised bones and footprints. Early finds inspired_______ (3) and fairy tales, and people ________ (4) that these bones belonged to________ (5) or huge monsters.
Question:
Select the most appropriate option to fill in the blank number 1.
Option 1: taken after
Option 2: held on
Option 3: given in
Option 4: based on
Correct Answer: based on
Solution : The correct choice is the fourth option.
The phrase "based on" is a prepositional phrase that emphasises the dependence of our understanding of the fossil record.
The preposition "on" connects the verb to its object, "fossils" indicating that knowledge about non-avian dinosaurs is
Question : Direction: The following bar graph shows the production of table fans in a factory for one week. Study the bar graph and answer the given question.
The average production of table fans in that week is:
Option 1: 370
Option 2: 280
Option 3: 300
Option 4: 250
Correct Answer: 300
Solution : Total production of table fans in the week = 260 + 540 + 360 + 120 + 200 + 320 = 1800 Required average production of table fans in the week = $\frac{1800}{6}=300$ Hence, the correct answer is 300.
Question : Directions: Select the option that is related to the fifth letter cluster in the same way as the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster. GPK : MSI :: RHT : VKT :: IDW : ?
Option 1: YGK
Option 2: ZHL
Option 3: KGY
Option 4: YIK
Correct Answer: YGK
Solution : Given: GPK : MSI :: RHT : VKT :: IDW : ?
Add the numbers to the positional value of the letters to get the required code. Like, GPK : MSI –
And, RHT : VKT –
Similarly, for IDW –
So, YGK is related
Question : It is difficult to fix a nail on a free-suspended wooden frame. Which law supports this statement?
Option 1: Law of inertia
Option 2: Newton's second law
Option 3: Newton's third law
Option 4: Pascal's law
Correct Answer: Newton's third law
Solution : The correct option is Newton's third law.
When a hammer is used to drive a nail into a wooden block that is not resting against a support, both the block and the nail advance. However, if the block is tightly pressed up
Question : Select the most appropriate meaning of the underlined idiom in the given sentence. After several years of cheating on his PhD work, the candidate finally had to face the music and lose the opportunity.
Option 1: Accept ignorance.
Option 2: To accept unpleasant consequences.
Option 3: Choose another alternative that is uninteresting.
Option 4: Be exposed.
Correct Answer: To accept unpleasant consequences.
Solution : The second option is correct.
In the given sentence, the idiom face the music means to accept the consequences or take responsibility for one's actions, especially after doing something wrong or unacceptable, which is similar to the meaning given in the second
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error."
Raghu came out of the bathroom (1) / with a towel (2) / in the hand. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The error lies in the third part of the sentence.
Articles are not used with parts of the body. So, the article "the" should be omitted. Hence, "in his hand" is the right usage.
Therefore, the correct sentence is: "Raghu came out of the bathroom
Question : What is the minimum quorum required in the Lok Sabha that can transact any business?
Option 1: One-tenth of the total number of Members of the Lok Sabha
Option 2: One-fourth of the total number of Members of the Lok Sabha
Option 3: One-third of the total number of Members of the Lok Sabha
Option 4: One-fifth of the total number of Members of the Lok Sabha
Correct Answer: One-tenth of the total number of Members of the Lok Sabha
Solution : The correct answer is One-tenth of the total number of members of the Lok Sabha.
The quorum needed for a Lok Sabha meeting is defined as 55 members or one-tenth of the total strength
Question : Select the most appropriate ANTONYM of the given word. Compulsory
Option 1: Obligatory
Option 2: Mandatory
Option 3: Voluntary
Option 4: Subsidiary
Correct Answer: Voluntary
Solution : The correct choice is the third option.
Compulsory means something that is required, mandatory, or enforced by rules or laws. It must be done, and there's no choice in the matter. Whereas voluntary refers to something that is done willingly, by choice, or without
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