Staff Selection Commission Combined Graduate Level Exam
Question : In an examination, 73% of the candidates passed the quantitative aptitude test, 70% passed the general awareness test, and 64% passed both. If 6300 failed in both subjects, the total number of examinees was:
Option 1: 60000
Option 2: 50000
Option 3: 30000
Option 4: 25000
Correct Answer: 30000
Solution : Given: Passed the quantitative aptitude test = 73% Passed the general awareness test = 70% Passed in both subjects = 64% Failed in both subjects = 6300 Total candidates = 100% Percentage of candidates who passed in at least one subject = 73% + 70%
Question : In August 2022, the Union government has appointed______________ as a director in the Prime Minister's Office (PMO).
Option 1: Gopal Vittal
Option 2: Rajesh Verma
Option 3: Anuj Poddar
Option 4: Shweta Singh
Correct Answer: Shweta Singh
Solution : The Correct Option is Shweta Singh
Indian Foreign Service (IFS) officer Shweta Singh was on 2 August 2022 appointed as a director in the Prime Minister's Office (PMO).
Question : Select the correct statement about the properties of a triangle.
Option 1: The sum of two sides may be equal to the third side.
Option 2: The sum of two sides is always equal to the third side.
Option 3: The sum of two sides is always greater than the third side.
Option 4: The sum of two sides is always less than the third side.
Correct Answer: The sum of two sides is always greater than the third side.
Solution : In a triangle, the sum of two sides is always greater than the third. Hence, the correct answer is 'The sum of two sides is always greater than the third side'.
Question : Directions: In the following question, some parts of the sentence may have 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".
He built the theatre as a tribute to his rootings (1) / and the thought of it outlasting him, (2) / would surely have given him the greatest joy. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct choice is the first option.
It should be "roots" instead of "rootings" as "roots" is a noun and cannot be used as a gerund. "Roots" is the appropriate word, as it refers to one's origins, ancestry, or cultural background.
So, the correct
Question : A wide inlet of the sea usually concave in shape, is termed as a:
Option 1: Strait
Option 2: Sound
Option 3: Bay
Option 4: Fjord
Correct Answer: Bay
Solution : The correct answer is Bay.
Bay is a coastal erosional landform formed by the marine wave actions. It is a large concave shaped land formation which encloses ocean water, having a medium sized opening which connects it with bigger ocean. It is smaller and less
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed on the right side of the figure.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per mirror image properties, closer things appear closer to the mirror in reflection. Here, according to the information provided, the mirror is placed on the right side of the figure (on line AB). So, the left side of the reflected image will appear as the
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. This book (1) _ writing practice to pre-schoolers to help them learn to write (2) _ of the English alphabet. Directional arrows, (3) _ with the letters and numbers, guide children in writing. (4) _ and copying activities encourage children to read and write letters and numbers (5) _ to count.
Select the most appropriate option to fill in the blank no 2.
Option 1: letter
Option 2: letters
Option 3: phrases
Option 4: words
Correct Answer: letters
Solution : The correct choice is the second option.
The most appropriate option to fill in the blank is letters, as the sentence discusses writing practice for pre-schoolers to help them learn to write. Specifically, the focus is on the English alphabet. Since the English
Question : If $k^4+\frac{1}{k^4}=47$, then what is the value of $k^3+\frac{1}{k^3}$?
Option 1: 4.5
Option 2: 54
Option 3: 18
Option 4: 9
Correct Answer: 18
Solution : Given, $k^4+\frac{1}{k^4}=47$ Adding 2 on both sides, ⇒ $k^4+\frac{1}{k^4}+2=47+2$ ⇒ $(k^2)^2+\frac{1}{(k^2)^2}+2\times k^2\times \frac{1}{k^2}=49$ ⇒ $(k^2+\frac{1}{k^2})^2=49$ ⇒ $k^2+\frac{1}{k^2}=7$ Again adding 2 on both sides, $k^2+\frac{1}{k^2}+2=7+2$ ⇒ $(k+\frac{1}{k})^2=9$ ⇒ $k+\frac{1}{k}=3$ cubing both sides, we get, ⇒ $k^3+\frac{1}{k^3}+3×k\times \frac{1}{k}(k+\frac{1}{k})=27$ ⇒ $k^3+\frac{1}{k^3}+3×3=27$ $\therefore k^3+\frac{1}{k^3}=27-9=18$ Hence, the correct answer is
Question : Directions: Select the odd group of numbers. (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.)
Option 1: 13 – 159
Option 2: 9 – 71
Option 3: 5 – 31
Option 4: 17 – 279
Correct Answer: 5 – 31
Solution : Let's check the options – First option: 13 – 159→(13)2 = 169; 169 – 10 = 159 Second option: 9 – 71→(9)2 = 81; 81 – 10 = 71 Third option: 5 – 31→(5)2 = 25; 25 – 10 =
Question : If areas of similar triangles $\triangle {ABC}$ and $\triangle {DEF}$ are $ {x}^2 \ \text{cm}^2$ and $ {y}^2 \ \text{cm}^2$, respectively, and EF = a cm, then BC (in cm) is:
Option 1: $\frac{y^2}{a^2 x^2}$
Option 2: $\frac{y}{a x}$
Option 3: $\frac{ax}{y}$
Option 4: $\frac{a^2 x^2}{y^2}$
Correct Answer: $\frac{ax}{y}$
Solution : Given: $\triangle{ABC}\sim\triangle{DEF}$ $\frac{\text{Area of}\triangle{ABC}}{\text{Area of}\triangle{DEF}}=\frac{{BC}^2}{{EF}^2}$ ⇒ $\frac{ {x}^2 }{{y}^2 }=\frac{{BC}^2}{{a}^2}$ ⇒ $\frac{ {x}}{ {y}}=\frac{{BC}}{{a}}$ $\therefore {BC} = \frac{{ax}}{{y}}$ Hence, the correct answer is $\frac{{ax}}{{y}}$.
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