Staff Selection Commission Combined Graduate Level Exam
Question : In triangle PQR, the sides PQ and PR are produced to A and B respectively. The bisectors of $\angle {AQR}$ and $\angle {BRQ}$ intersect at point O. If $\angle {QOR} = 50^{\circ}$ what is the value of $\angle {QPR}$ ?
Option 1: $50^{\circ}$
Option 2: $60^{\circ}$
Option 3: $80^{\circ}$
Option 4: $100^{\circ}$
Correct Answer: $80^{\circ}$
Solution :
In triangle PQR, the bisectors of $\angle {AQR}$ and $\angle {BRQ}$ intersect at point O. According to the Angle bisector theorem, the angles formed at the incenter by the angle bisectors are half the sum of the other two angles of the triangle. $\angle {QOR}=
Question : If $\text{a}= {\sqrt{2}+1}$ and $\text{b} = {\sqrt{2}–1}$, then the value of $\frac{1}{a+1}+\frac{1}{b+1}$ will be:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –1
Correct Answer: 1
Solution : Given: $\text{a}= {\sqrt{2}+1}$ and $\text{b} = {\sqrt{2}–1}$ $\frac{1}{a+1}+\frac{1}{b+1}$ $= \frac{1}{(\sqrt{2}+1)+1}+\frac{1}{(\sqrt{2}–1)+1}$ $= \frac{1}{(\sqrt{2}+2)}+\frac{1}{\sqrt{2}}$ $=\frac{1}{\sqrt{2}}[\frac{1}{(1+\sqrt{2})}+1]$ $=\frac{1}{\sqrt{2}}[\frac{(1–\sqrt{2})}{(1–2)}+1]$ $=\frac{1}{\sqrt{2}}[\sqrt{2}–1+1]$ $=\frac{1}{\sqrt{2}}×\sqrt{2}$ $= 1$ Hence, the correct answer is 1.
Question : Two toys are sold for Rs. 504 each. One toy brings the dealer a gain of 12% and the other a loss of 4%. The gain, or loss percentage, from selling both toys is:
Option 1: $3\frac{5}{13}$% profit
Option 2: $4\frac{5}{13}$% profit
Option 3: $5\frac{1}{13}$% profit
Option 4: $2\frac{3}{13}$% profit
Correct Answer: $3\frac{5}{13}$% profit
Solution : For the first toy, Selling price = Rs. 504 Gain% = 12% 504 = Cost price + 12% of Cost price 504 = 1.12 × Cost price Cost price = Rs. 450 For the second toy, Selling price = Rs. 504 Loss% = 4%
Question : Aditya buys 300 mangoes for Rs. 1,100. Some of these mangoes are rotten and are thrown away. He sells the remaining mangoes at Rs. 5 each and makes a profit of Rs. 150. Find the percentage of mangoes thrown away.
Option 1: $16 \frac{1}{2} \%$
Option 2: $15 \frac{2}{3} \%$
Option 3: $16 \frac{2}{3} \%$
Option 4: $16 \frac{1}{3} \%$
Correct Answer: $16 \frac{2}{3} \%$
Solution : Number of mangoes purchased = 300 Selling Price = Rs. 5/mango Total Profit = Rs. 150 Number of mangoes sold = $\frac{\text{CP + Profit}}{5}$ = $\frac{1100+150}{5} = 250$ $\therefore$ Number of mangoes thrown away = 300 – 250 = 50 Percentage = $\frac{50}{300}\times
Question : Lens is made up of:
Option 1: Pyrex glass
Option 2: Flint glass
Option 3: Ordinary glass
Option 4: Cobalt glass
Correct Answer: Flint glass
Solution : The correct option is Flint glass.
There are several materials that can be used to make lenses, and flint glass is one of the most widely utilized types of glass in lens manufacturing. Since flint glass has a relatively high refractive index compared to
Question : In which of the following Indian states is the Lokrang festival observed?
Option 1: Jharkhand
Option 2: Gujarat
Option 3: Rajasthan
Option 4: Madhya Pradesh
Correct Answer: Madhya Pradesh
Solution : The correct option is Madhya Pradesh.
The Lokrang Festival is a cultural festival celebrated in the Indian state of Madhya Pradesh, mainly in the city of Bhopal. The festival typically takes place in January and lasts for several days. This festival is organised to
Question : Select the most appropriate option to improve the underlined segment in the given sentence. If there is no need to improve it, select ‘No improvement required’. I had to wait for fifteen minutes to the bus.
Option 1: of
Option 2: for
Option 3: No improvement required
Option 4: at
Correct Answer: for
Solution : The second option is the correct choice.
We generally use the preposition for to state the purpose of an object or action.
Hence, the correct sentence is: "I had to wait for fifteen minutes for the bus."
Question : Thomas Cup is a/an ______.
Option 1: annual event
Option 2: biennial event
Option 3: quarterly event
Option 4: triennial event
Correct Answer: biennial event
Solution : The correct option is a biennial event.
The Thomas Cup is an international men's badminton championship, often referred to as the World Men's Team Championships in badminton. It was inaugurated in 1949 and held every two years.
The Thomas Cup was named after
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."
It is (1) / nothing else (2) / than pride. (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.
Both the words "than" and "but" can be used as a conjunction, but they differ in their usages, as than is used for making comparisons, whereas but is used to highlight contrasts or contradictions between
Question : Select the most appropriate one-word substitution for the given words.
A detailed list of things in a place
Option 1: Inventory
Option 2: Glossary
Option 3: Itinerary
Option 4: Directory
Correct Answer: Inventory
Solution : The first option is the correct choice.
An inventory specifically refers to a detailed and itemised list of goods, assets, or items in a particular location. It is commonly used in the context of business or logistics to keep track of stock or supplies in
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