Staff Selection Commission Combined Graduate Level Exam
Question : Directions: In the following question, you have to identify the correct response from the given premises stated according to the following symbols. If + means ÷, ÷ means –, – means ×, × means +, then 24 + 8 ÷ 2 – 6 × 6 = ?
Option 1: –10
Option 2: –3
Option 3: 12
Option 4: 21
Correct Answer: –3
Solution : Given: + means ÷, ÷ means –, – means ×, × means +. 24 + 8 ÷ 2 – 6 × 6 = ?
After interchanging the symbols according to the question, the equation becomes – = 24 ÷ 8 – 2 × 6 +
Question : ABC is an equilateral triangle. If the area of the triangle is $36 \sqrt{3}$, then what is the radius of the circle circumscribing the $\triangle ABC$?
Option 1: $2 \sqrt{3}$
Option 2: $3 \sqrt{3}$
Option 3: $4 \sqrt{3}$
Option 4: $6 \sqrt{3}$
Correct Answer: $4 \sqrt{3}$
Solution : Given: ABC is an equilateral triangle. The area of the triangle is $36 \sqrt{3}$. The area of the equilateral triangle $=\frac{\sqrt3}{4}\times (s)^2$, where $s$ is the sides of the triangle. The radius of the circle circumscribing the equilateral triangle $=\frac{s}{\sqrt3}$. ⇒ $\frac{\sqrt3}{4}\times (s)^2= 36
Question : The marked price on a book is INR 1,000. In a book fair, it is available for sale with a discount scheme offering two successive discounts of 12% and 8%. What is the final selling price (in INR) of the book for a customer (rounded off to the nearest integer)?
Option 1: 810
Option 2: 790
Option 3: 825
Option 4: 800
Correct Answer: 810
Solution : Marked Price on a book = INR 1,000 Successive discounts of 12% and 8% For two successive discounts Selling price = $\frac{100-\text{Discount}_1\%}{100}× \frac{100-\text{Discount}_2\%}{100}×$ marked price Selling Price = $\frac{88}{100}$×$\frac{92}{100}$×1,000 = 809.6 $\approx$ INR 810 Hence, the correct answer is 810.
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.
I _______ very much like to see my old classmates.
Option 1: can
Option 2: should
Option 3: would
Option 4: might
Correct Answer: would
Solution : The third option is the most appropriate answer.
We often use would to make requests. It is a more polite and indirect form of will.
The meanings of the other options are as follows:
Can is used for informal permission or capacity.
Should suggests an
Question : Select the most appropriate ANTONYM of the underlined word.
Those streets are very lonely.
Option 1: Crowded
Option 2: Isolated
Option 3: Empty
Option 4: Remote
Correct Answer: Crowded
Solution : The correct answer is the first option.
Crowded refers to a place or area filled with a large number of people or things, suggesting a lack of solitude or loneliness. In the context of the sentence, if the streets are crowded, they are not lonely.
Question : If the volume of a sphere is $179 \frac{2}{3}$ m3, what is its surface area?
Option 1: 221 m2
Option 2: 154 m2
Option 3: 144 m2
Option 4: 151 m2
Correct Answer: 154 m2
Solution : Given, the volume of a sphere is $179 \frac{2}{3} = \frac{539}{3}$ Volume of a sphere with radius, $r$ = $\frac{4}{3}\pi r^3$ ⇒ $\frac{4}{3}\pi r^3=\frac{539}{3}$ ⇒ $\frac{4}{3}\times \frac{22}{7}\times r^3=\frac{539}{3}$ ⇒ $r^3=\frac{49\times 7}{4\times 2}$ $\therefore r=\frac{7}{2}$ m Surface area = $4\pi r^2$ = $4\times \frac{22}{7}\times
Question : The first session of the Indian National Congress was held at:
Option 1: Bombay
Option 2: Madras
Option 3: Calcutta
Option 4: Surat
Correct Answer: Bombay
Solution : The correct option is Bombay.
The first session of the Indian National Congress was held in Bombay (now Mumbai) in 1885. Session at Gokuldas Tejpal Sanskrit College, now known as Elphinstone College.
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer. I was conscious ____ a break in my voice.
Option 1: to
Option 2: of
Option 3: over
Option 4: for
Correct Answer: of
Solution : The second option is the correct answer: of.
"conscious" means to be aware of something. Hence, you must be "conscious of" something
Therefore, the correct answer is "I was conscious of a break in my voice."
Question : Directions: Which of the answer figures is the exact mirror image of the given problem figure when the mirror is held on the right side?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per the mirror image properties, closer things appear closer to the mirror in the reflection. Here, according to the information provided, the mirror is placed on the right side of the figure (on line AB). So, the left side of the reflected image will appear
Question : If $x+\frac{16}{x}=8$, then the value of $x^2+\frac{32}{x^2}$ is:
Option 1: 20
Option 2: 24
Option 3: 16
Option 4: 18
Correct Answer: 18
Solution : Given: The value of $x+\frac{16}{x}=8$. We know the algebraic identity, $(a–b)^2=a^2+b^2–2ab$. $x+\frac{16}{x}=8$ ⇒ $x^2+16=8x$ ⇒ $x^2–8x+16=0$ ⇒ $(x–4)^2=0$ ⇒ $x=4,4$ The value of $x^2+\frac{32}{x^2}$ is given as, ⇒ $4^2+\frac{32}{4^2}=16+\frac{32}{16}$ = $16+2=18$ Hence, the correct answer is 18.
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