Staff Selection Commission Combined Graduate Level Exam
Question : If $ \frac{(5x\:-\:y)}{(5x\:+\:y)}=\frac{3}{7},$ what is the value of $\frac{(4x^{2}\:+\:y^{2}\:–\:4xy)}{(9x^{2}\:+\:16y^{2}\:+\:24xy)}$?
Option 1: $0$
Option 2: $\frac{3}{7}$
Option 3: $\frac{18}{49}$
Option 4: $\frac{1}{6}$
Correct Answer: $0$
Solution : Given: $\frac{(5x\:-\:y)}{(5x\:+\:y)}=\frac{3}{7}$ $⇒35x-7y=15x+3y$ $⇒20x-10y=0$ $⇒2x-y=0$---------------(i) $\frac{(4x^{2}\:+\:y^{2}\:-\:4xy)}{(9x^{2}\:+\:16y^{2}\:+\:24xy)}$ = $\frac{(2x\:-\:y)^{2}}{(9x^{2}\:+\:16y^{2}\:+\:24xy)}$ Since from equation (i), we know $2x-y=0$, substituting the value in the above equation, we get, $=\frac{0}{(9x^{2}\:+\:16y^{2}\:+\:24xy)}=$ 0 Hence, the correct answer is $0$.
Question : The ordinary and maximum tolerance limit of sound by human being is:
Option 1: 50 dB to 70 dB (decibel)
Option 2: 60 dB to 80 dB (decibel)
Option 3: 65 dB to 75 dB (decibel)
Option 4: 70 dB to 85 dB (decibel)
Correct Answer: 60 dB to 80 dB (decibel)
Solution : The correct option is 60 dB to 80 dB (decibel).
A human's normal sound tolerance level is between 60 and 80 decibels (dB). Sounds exceeding 80 dB are potentially dangerous and can cause hearing damage or pain, especially if exposed
Question : By which name is the historical road built by Sher Shah Suri known?
Option 1: Grand trunk road
Option 2: Expressway
Option 3: Highway
Option 4: Cart road
Correct Answer: Grand trunk road
Solution : The correct option is Grand Trunk Road.
We refer to the ancient route Sher Shah Suri constructed as the "Grand Trunk Road." It is also known as the "G.T. Road" and is among the Indian subcontinent's oldest and longest road networks.
Question : The Gross domestic product (GDP) estimation method measuring the aggregate value of goods and services produced by the firms is called _______.
Option 1: expenditure method
Option 2: consumption method
Option 3: income method
Option 4: product method
Correct Answer: product method
Solution : The correct answer is the product method.
One method of calculating a nation's national income is the product or value-added method. The output or inventory method is another name for this system. It shows how each producing unit contributes to the production process. Value-added
Question : Directions: Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: l. All phones are laptops. ll. All pen drives are phones. lll. All pen drives are pens. Conclusions: I. All pens are phones. II. All laptops are pens. III. All pen drives are laptops.
Option 1: Only conclusion III follows
Option 2: Only conclusions I and II follow
Option 3: Only conclusions II and III follow
Option 4: Only conclusions I and III follow
Correct Answer: Only conclusion III follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All pens are phones – From the Venn diagram, it is evident that the circles representing pens and phones overlap each other
Question : If x + y = 7 and xy = 19, calculate the value of x2 + y2.
Option 1: 17
Option 2: 12
Option 3: 11
Option 4: 19
Correct Answer: 11
Solution : Given: x + y = 7 and xy = 19. On squaring both sides of the equation x + y = 7, we get, (x + y)2 = 72 ⇒ (x2 + y2 + 2xy) = 49 ⇒ x2 +
Question : The greater of the two numbers whose product is 900 and whose sum exceeds their difference by 30 is:
Option 1: 60
Option 2: 75
Option 3: 90
Option 4: 100
Correct Answer: 60
Solution : Let the numbers be $x$ and $y$ where $x > y$. According to the question, ⇒ $(x + y) – (x – y) = 30$ ⇒ $x + y–x + y = 30$ ⇒ $y = \frac{30}{2} = 15$ Also, $xy = 900$ ⇒ $15x
Question : In an examination, 92% of the students passed and 480 students failed. If so, how many students appeared in the examination?
Option 1: 5,800
Option 2: 6,200
Option 3: 6,000
Option 4: 5,000
Correct Answer: 6,000
Solution : Given: In an examination, 92% of the students passed and 480 students failed. Let the number of the students who appeared in the examination = 100%. The number of the students failed = 100 – 92 = 8%. 8% = 480 The number of students
Question : Directions: From the given option figures, select the one in which the question figure is embedded.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Since there is no restriction on the rotation of the figure, we will check all possible angles where the question figure can fit itself in all the given option figures. The question figure is embedded only in the first option figure.
Hence, the first option is
Question : The cost price of an article is decreased by 10% and then increased by 20%. If the final price is INR 540, then the original cost price is:
Option 1: INR 500
Option 2: INR 650
Option 3: INR 550
Option 4: INR 600
Correct Answer: INR 500
Solution : Let the cost price be INR $x$. The cost price first decreased by 10%, then increased by 20%. So, $\frac{x×90×120}{100×100}=540$ ⇒ $108x=54000$ ⇒ $x=500$ Therefore, the original cost price = INR 500 Hence, the correct answer is INR 500.
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