Staff Selection Commission Combined Graduate Level Exam
Question : Directions: In this question, 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 follows/follow from the statements. Statements: Some mirrors are glass. All glasses are taps. Some taps are pens. Conclusions: I. Some glass are mirrors. II. All taps are glass. III. Some pens are taps.
Option 1: None of the conclusions follows
Option 2: Only conclusions I and II follow
Option 3: Only conclusion II follows
Option 4: Only conclusions I and III follow
Correct Answer: Only conclusions I and III follow
Solution : The possible Venn diagram according to the given statements –
Let's analyse the conclusions – Conclusion I: Some glass are mirrors – From the above Venn diagram, it is evident that the circles representing glass and mirror overlap each other
Question : What is the value of $\cos ^2 15°?$
Option 1: $(2+\sqrt{3})$
Option 2: $\frac{(2+\sqrt{3})}{4}$
Option 3: $\frac{(2+\sqrt{3})}{2}$
Option 4: $\frac{(1+\sqrt{3})}{2}$
Correct Answer: $\frac{(2+\sqrt{3})}{4}$
Solution : According to the formula, $\cos 2A = 2\cos^2 A - 1$ Let A = 15° ⇒ $\cos 30° = 2\cos^2 15° - 1$ ⇒ $\cos^2 15° = \frac{\cos 30°+1}{2}$ ⇒ $\cos^2 15° = \frac{\frac{\sqrt3}{2}+1}{2}$ $\therefore\cos^2 15°=\frac{\sqrt3 + 2}{4}$ Hence, the correct answer is $\frac{2+\sqrt3}{4}$.
Question : Parts of the following sentence are given as options. Identify the segment that contains a grammatical error. The bus broke down because we had to walk some distance.
Option 1: because we
Option 2: The bus broke down
Option 3: some distance
Option 4: had to walk
Correct Answer: because we
Solution : The first option is the correct choice.
When we read the sentence, we get to know that something happened because of which someone has to suffer. When the reason is given first and then the result or action, we must use "that is why",
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: AEIM
Option 2: BFJN
Option 3: CGKO
Option 4: FDKN
Correct Answer: FDKN
Solution : Let's check the options – First option: AEIM; A + 4 = E; E + 4 = I; I + 4 = M Second option: BFJN; B + 4 = F; F + 4 = J; J + 4 = N Third option: CGKO; C
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 =
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