Staff Selection Commission Combined Graduate Level Exam
Question : Select the option that expresses the given sentence in passive voice. Who teaches her geography?
Option 1: By who geography is taught to her?
Option 2: By whom she is taught geography?
Option 3: By whom is she taught geography?
Option 4: By whom was she taught geography?
Correct Answer: By whom is she taught geography?
Solution : The correct answer is the third option.
In the original sentence, "Who teaches her geography?" is in the active voice, in which the subject who is performing the action as the subject is the doer in the active voice whereas
Question : What is the value of $3 \sin ^2 30^{\circ}+\frac{3}{5} \cos ^2 60^{\circ}–2 \sec ^2 45^{\circ} $?
Option 1: $-\frac{5}{2}$
Option 2: $-\frac{5}{8}$
Option 3: $-\frac{31}{10}$
Option 4: $-\frac{25}{17}$
Correct Answer: $-\frac{31}{10}$
Solution : Given: The trigonometric expression is $3 \sin ^2 30^{\circ}+\frac{3}{5} \cos ^2 60^{\circ}–2 \sec ^2 45^{\circ} $. We know the values of trigonometric ratios, $\sin 30^{\circ} =\frac{1}{2}$, $\cos 60^{\circ}=\frac{1}{2}$ and $\sec 45^{\circ}=\sqrt2$. ⇒ $3 \sin ^2 30^{\circ}+\frac{3}{5} \cos ^2 60^{\circ}–2 \sec ^2 45^{\circ}$ $= 3\times(\frac{1}{2})^2+\frac{3}{5}\times(\frac{1}{2})^2–2 \times
Question : The word "Satyameva Jayate" has been derived from which Upanishad?
Option 1: Akshi Upanishad
Option 2: Mundaka Upanishad
Option 3: Garuda Upanishad
Option 4: Mahavakya Upanishad
Correct Answer: Mundaka Upanishad
Solution : The correct answer is Mundaka Upanishad.
The phrase "Satyameva Jayate" in the Devanagari script is taken from the Mundaka Upanishad. It means truth alone triumphs. "Satyameva Jayate" is written below the Lion Capital of Ashoka, adopted as India's national emblem.
Question : Which of the following is not mentioned in the Indian Constitution as a Fundamental Duty?
Option 1: To respect elders
Option 2: To promote harmony
Option 3: To safeguard public property
Option 4: To defend the country
Correct Answer: To respect elders
Solution : The Correct Option is To respect elders.
The Indian Constitution lays out a set of moral and civic duties known as fundamental duties. The 42nd Amendment Act of 1976 adds these duties to the Indian Constitution. India's residents are supposed to feel more
Question : The total surface area of a solid hemisphere is $942 \mathrm{~cm}^2$. Its volume (in $\mathrm{cm}^3$ ) is closest to: (Take $\pi=3.14$ )
Option 1: 2089
Option 2: 2093
Option 3: 2037
Option 4: 2097
Correct Answer: 2093
Solution : Given: The total surface area of a solid hemisphere = $942\ cm^2$ $3 \pi r^2=942$ ⇒ $3\times 3.14\times r^2=942$ ⇒ $3.14\times r^2=314$ ⇒ $ r^2=100$ ⇒ $ r=10$ Volume of hemisphere = $\frac{2}{3}\pi r^3$ = $\frac{2}{3}\times 3.14\times10\times10\times10$ = $\frac{6280}{3}$ = $2093.33 \approx 2093$ cm3
Question : A person marks an article 36% above the cost price and offers a 30% discount on the marked price. What is the loss or gain percentage?
Option 1: Loss 6.5%
Option 2: Loss 4.8%
Option 3: Gain 8.5%
Option 4: Gain 7.2%
Correct Answer: Loss 4.8%
Solution : Let the cost price be 100. Marked price above 36% = 100 + 36 = 136 Discount = 30% Selling price = $\frac{100-\text{discount %}}{100}\times$ marked price = $\frac{100-30}{100}\times136$ = $\frac{70}{100}\times136$ = $95.2$ Loss = Cost price – selling price = 100 – 95.2 =
Question : Directions: Which of the following interchange of numbers and signs would make the given equation correct? 24 × 9 + 6 ÷ 24 – 18 = 22
Option 1: 18 and 22, + and –
Option 2: 24 and 6, × and +
Option 3: 6 and 9, ÷ and +
Option 4: 6 and 18, ÷ and ×
Correct Answer: 6 and 9, ÷ and +
Solution : Given: 24 × 9 + 6 ÷ 24 – 18 = 22
Let's check the given options – First option: 18 and 22, + and – ⇒ 24 × 9 – 6 ÷ 24 + 22 = 18 Solving the
Question : Given that $\sqrt3=1.732$, the value of $\frac{3+\sqrt6}{5\sqrt3-2\sqrt{12}-\sqrt{32}+\sqrt{50}}$ is:
Option 1: 4.899
Option 2: 2.551
Option 3: 1.414
Option 4: 1.732
Correct Answer: 1.732
Solution : Given: $\sqrt{3}=1.732$ $\frac{3+\sqrt{6}}{5\sqrt{3}-2\sqrt{12}-\sqrt{32}+\sqrt{50}}$ Now evaluate: $= \frac{3+\sqrt{6}}{5\sqrt{3}-2\sqrt{4\times3}-\sqrt{16\times2}+\sqrt{25\times2}}$ $=\frac{3+\sqrt{6}}{5\sqrt{3}-4\sqrt{3}-4\sqrt{2}+5\sqrt{2}}$ $=\frac{3+\sqrt{6}}{5(\sqrt{3}+\sqrt{2})-4(\sqrt{3}+\sqrt{2})}$ $=\frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}$ Now multiply and divide with $\sqrt{3}-\sqrt{2}.$ $=\frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ $=\frac{3\sqrt{3}-3\sqrt{2}+\sqrt{18}-\sqrt{12}}{3-2}$ $=\frac{3\sqrt{3}-3\sqrt{2}+\sqrt{9\times2}-\sqrt{4\times3}}{1}$ $=3\sqrt{3}-3\sqrt{2}+3\sqrt{2}-2\sqrt{3}$ $=3\sqrt{3}-2\sqrt{3}$ $=\sqrt{3}(3-2)$ $=\sqrt{3}$ $=1.732$ Hence, the correct answer is 1.732.
Question : At Barren Island ,the only active volcano in India is situated in
Option 1: Andaman Island
Option 2: Nicobar Island
Option 3: Lakshdweep
Option 4: Minicoy
Correct Answer: Andaman Island
Solution : The correct answer is Andaman Island.
Andaman and Nicobar islands are of volcanic origin. Barren Island is the only active stratovolcano in India. It is located in Andaman Island. Recently it has erupted in May 2023. It also had small eruptions in 2017 and
Question : If $p-\frac{1}{p}=6$, then what is the value of $p^4+\frac{1}{p^4}$?
Option 1: 1562
Option 2: 1432
Option 3: 1442
Option 4: 1444
Correct Answer: 1442
Solution : $\mathrm{p}-\frac{1}{\mathrm{p}}=6$ Squaring both sides, we get, $⇒p^2+\frac{1}{p^2}-2(p)(\frac{1}{p})=36$ $⇒p^2+\frac{1}{p^2}-2=36$ $⇒p^2+\frac{1}{p^2}=38$ Squaring both sides again, we get, $⇒p^4+\frac{1}{p^4}+2(p^2)(\frac{1}{p^2})=1444$ $⇒p^4+\frac{1}{p^4}+2=1444$ $\therefore p^4+\frac{1}{p^4}=1442$ Hence, the correct answer is 1442.
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