Staff Selection Commission Combined Graduate Level Exam
Question : The radius of a circle is 5 cm. Calculate the length of a tangent drawn to this circle from a point at a distance of 10 cm from its centre.
Option 1: $5 \sqrt{5}$ cm
Option 2: $5 \sqrt{2}$ cm
Option 3: $5$ cm
Option 4: $5 \sqrt{3}$ cm
Correct Answer: $5 \sqrt{3}$ cm
Solution : In $\triangle OAB$, $AO^2 = AB^2 + OB^2$ ⇒ $10^2 = AB^2 + 5^2$ ⇒ $100 = AB^2 + 25$ ⇒ $75 = AB^2$ ⇒ $AB = 5\sqrt3$ Hence, the correct answer is $5\sqrt3$ cm.
Question : Direction: In the following question, select the one which is different from the other three alternatives.
Option 1: 5061
Option 2: 4025
Option 3: 7202
Option 4: 6023
Correct Answer: 5061
Solution : Let's check the options —
First option: 5061; the sum of digits is 5 + 0 + 6 + 1 = 12. This option is different from the other options.
Second option: 4025; the sum of digits is 4 + 0 + 2 + 5
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold parts at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
A foolish person is someone who is easily taken-in and tricked by others.
(1) Sober
(2) Stupid
(3) gullible
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The correct answer is the third option: Gullible
Gullible is a term that specifically means easily deceived or tricked, making it more appropriate in the context of someone who is easily taken in by others. The meanings of the other options are as follows:
Question : Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph. A. India has an upbeat vision of a liberal, nonviolent, relatively pluralistic democracy with non-threatening global leadership. B. Epics from mythologies like the Mahabharata and Ramayana are likened to classic Greek works like the Odyssey and Iliad and between 1 and 1000 AD, India was lauded as the ‘Golden Bird’ for its GDP, which was higher than China at the time. C. Luminaries like Mahatma Gandhi and Rabindranath Tagore, as well as the arts of literature, music, dance, the software industry, Ayurveda, etc., generate a staggering array of soft power assets that highlight India's appeal to the world's population. D. With Ashoka, Buddha, and Gandhi serving as the primary leaders, Indians are known for their core values of respect, harmony, and fraternity.
Option 1: ACDB
Option 2: CBAD
Option 3: ABDC
Option 4: BCDA
Correct Answer: ACDB
Solution : The correct choice is the first option, i.e., ACDB.
To form a meaningful and coherent paragraph, the sentences should be in the following order:
Explanation: The paragraph begins by discussing India's cultural and historical contributions (sentence A), then goes on to highlight
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: All rice is wheat. Some wheats are pulses. No pulses are a vegetable. Conclusions: I. Some vegetables are rice. II. Some pulses are rice. III. Some vegetables are wheat.
Option 1: None of the conclusions follows
Option 2: Both conclusions I and II follow
Option 3: Both conclusions II and III follow
Option 4: All conclusions follow
Correct Answer: None of the conclusions follows
Solution : According to the given statements, the following Venn diagram can be drawn – Let's check each conclusion – Conclusion I: Some vegetables are rice – As per the above Venn diagram, there is no direct relation between vegetables and rice. Therefore,
Question : Inside a square ABCD, $\triangle$BEC is an equilateral triangle. If CE and BD intersect at O, then $\angle$BOC is equal to:
Option 1: 60°
Option 2: 75°
Option 3: 90°
Option 4: 120°
Correct Answer: 75°
Solution : Given: Inside a square ABCD, $\triangle$BEC is an equilateral triangle. In $\triangle$BOC, $\angle$BCO = 60° (angle of an equilateral triangle) $\angle$OBC = $\frac{90°}{2}$ = 45° (as the diagonal of a square bisects its angle into two equal parts) So, $\angle$BOC = 180° – (60° +
Question : If $\left(x+\frac{1}{x}\right)=\sqrt{6}$ and $x>1$, what is the value of $\left(x^8-\frac{1}{x^8}\right)$?
Option 1: $120\sqrt{3}$
Option 2: $128\sqrt{3}$
Option 3: $112\sqrt{3}$
Option 4: $108\sqrt{3}$
Correct Answer: $112\sqrt{3}$
Solution : $\left(x+\frac{1}{x}\right)=\sqrt{6}$ Squaring both sides, $\left(x^2+\frac{1}{x^2}+2\right)=6$ ⇒ $x^4-4x^2+1=0$ ⇒ $x^2=\frac{4\pm2\sqrt{3}}2$ ⇒ $x^2 = 2+\sqrt{3}$ (Since $x>0$) Squaring both sides, ⇒ $x^4 = 7+4\sqrt{3}$ Squaring both sides ⇒ $x^8 = 97+56\sqrt{3}$ So, $\frac{1}{x^8}=97-56\sqrt{3}$ So, $x^8-\frac{1}{x^8}=112\sqrt{3}$ Hence, the correct answer is $112\sqrt{3}$.
Question : Direction: In the following question, from the given alternative words, select the word which cannot be formed using the letters of the given word.
PROVINCIALISM
Option 1: SAILOR
Option 2: NAIL
Option 3: MAN
Option 4: INITIAL
Correct Answer: INITIAL
Solution : Given:
First option: SAILOR; All the letters of SAILOR are present in the word PROVINCIALISM.
Second option: NAIL; All the letters of NAIL are present in the word PROVINCIALISM.
Third option: MAN; All the letters of MAN are present in the word
Question : In cells, proteins are synthesised in ______.
Option 1: mitochondria
Option 2: Golgi apparatus
Option 3: nucleus
Option 4: ribosome
Correct Answer: ribosome
Solution : The correct option is ribosomes.
The ribosomes are temporarily linked to the rough endoplasmic reticulum, which is where the proteins are synthesised. In a cell, ribosomes are where protein synthesis takes place. All live cells include ribosomes, which are vital organelles in charge of
Question : Directions: In the following question, select the number that can be placed at the sign of the question mark (?) from the given alternatives.
Option 1: 35
Option 2: 42
Option 3: 45
Option 4: 95
Correct Answer: 35
In each row, add 1 to the product of the first two numbers, then multiply the result by the third number to get the fourth number. Row 1:
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