Staff Selection Commission Combined Graduate Level Exam
Question : Directions: If A – B means that A is the mother of B, A + B means that A is the father of B, and A ÷ B means that A is the sister of B, then which of the following expressions shows that P is the aunt of Q?
Option 1: P + R ÷ Q
Option 2: Q ÷ R + P
Option 3: P ÷ R – Q
Option 4: R ÷ P – Q
Correct Answer: P ÷ R – Q
Solution : Given: A – B ⇒ A is the mother of B A + B ⇒ A is the father of B A ÷ B ⇒ A is the sister of B
Let's check each option – First option: P + R
Question : Direction: If the first and second letters in the word COMMUNICATIONS were interchanged, also the third and the fourth letters, the 5th and 6th letters, and so on, which letter would be the tenth letter counting from the right end?
Option 1: N
Option 2: U
Option 3: A
Option 4: T
Correct Answer: N
Solution : Assign the numbers consecutively to each letter individually of the given letter cluster as shown below –
Question : If $a+b=1$, then $a^4+b^4-a^3-b^3-2a^2b^2+ab$ is equal to:
Option 1: 1
Option 2: 2
Option 3: 4
Option 4: 0
Correct Answer: 0
Solution : Given: $a+b=1$ (equation 1) We know that the algebraic identities are $(a-b)^2=a^2+b^2-2ab$, $(a^3+b^3)=(a+b)(a^2-ab+b^2)$ and $(a^2-b^2)=(a+b)(a-b)$. So, $a^4+b^4-2a^2b^2-a^3-b^3+ab$ $=(a^2-b^2)^2-(a^3+b^3)+ab$ $=(a+b)^2(a-b)^2-(a+b)(a^2-ab+b^2)+ab$ Substituting the value from equation 1 in the above expression we get, $a^4+b^4-2a^2b^2-a^3-b^3+ab=(a-b)^2-a^2+ab-b^2+ab$ $=(a-b)^2-(a^2-2ab+b^2)$ $=(a-b)^2-(a-b)^2=0$ Hence, the correct answer is 0.
Question : Directions: Select the Venn diagram that best illustrates the relationship between the following classes. Fathers, Brothers, and Males
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Males encompass both brothers and fathers, thus their circles will be contained within the larger circle of males. Additionally, there may be overlap as a brother can also be a father, and a father can also be a brother. Therefore, the Venn diagram will be as
Question : Directions: In a certain code language, travel for fun is coded as dv pa vi, fun will begin is coded as cr dv em, and will travel today is coded as vi cr hz. (All the codes are two-letter codes only.) How will for today be coded in that language?
Option 1: dv hz
Option 2: pa hz
Option 3: pa em
Option 4: cr dv
Correct Answer: pa hz
Solution : Given: 1. travel for fun is coded as dv pa vi 2. fun will begin is coded as cr dv em 3. will travel today is coded as vi cr hz
By comparing all the three coded sentences, we find that – In sentences
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed on the right side of the figure.
Solution : As per mirror image properties, closer things appear closer to the mirror in reflection. According to the information provided, if the mirror is placed on the right side of the figure, the right of the reflected image will appear as the left, and the left will
Question : How liberty can be limited
Option 1: By Rule
Option 2: By Law
Option 3: By Authority
Option 4: by Equality
Correct Answer: By Law
Solution : The Correct Answer is- by law
Liberty is defined as the law-abiding exercise of one's freedom without obstructing the rights of others. The removal of freedom is a form of punishment. It can, however, be limited by law or restricted in specific situations where
Question : The major use of sulphur is in the manufacture of
Option 1: H2SO4
Option 2: H2S
Option 3: SO2
Option 4: Fungicide
Correct Answer: H2SO4
Solution : The correct option is Sulphuric acid.
Sulphur is mostly used in the production of sulphuric acid (H2SO4). Sulpuric acid is one of the most commonly used industrial chemicals in the world, with uses ranging from metallurgy to petroleum refining, battery production, water
Question : Direction: In the following question, select the one which is different from other three alternatives.
Option 1: I
Option 2: N
Option 3: W
Option 4: H
Correct Answer: I
Solution : Given:
First option: I ; Vowel
Second option: N ; Consonant
Third option: W ; Consonant
Fourth option: H ; Consonant
Here, only I is vowel.
Hence, first option is correct.
Question : Directions: Select the number from among the given options that can replace the question mark (?) in the following series. 242, 288, ?, 392, 450
Option 1: 338
Option 2: 375
Option 3: 316
Option 4: 324
Correct Answer: 338
Solution : Given: 242, 288, ?, 392, 450
Multiply the square of the consecutive natural numbers (starting from 11) by 2 to get the terms given in the series. (11)2 × 2 = 121 × 2 = 242 (12)2 × 2 = 144 × 2
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