Staff Selection Commission Combined Graduate Level Exam
Question : A pyramid has an equilateral triangle as its base, of which each side is 8 cm. Its slant edge is 24 cm. The whole surface area of the pyramid (in cm2) is:
Option 1: $(16 \sqrt{3}+24 \sqrt{35})$
Option 2: $(12 \sqrt{3}+24 \sqrt{35})$
Option 3: $(24\sqrt{3}+36\sqrt{35})$
Option 4: $(16\sqrt{3}+48\sqrt{35})$
Correct Answer: $(16\sqrt{3}+48\sqrt{35})$
Solution : Total Surface area of a pyramid = Base area + 3 × The area of each triangular face The area of a equilateral triangle with sides 8 cm = $\frac{\sqrt{3}}{4}×(\text{side})^2=\frac{\sqrt{3}}{4}×8^2=16\sqrt{3}\ \text{cm}^2$ Let the height of the pyramid be $h$. $h^2=\text{Slant height}^2-(\frac{1}{2}×\text{base})^2$ $⇒h^2=24^2-(\frac{1}{2}×8)^2$ $h^2=576-16$ $\therefore h=\sqrt{560}=4\sqrt{35}\
Question : R’s weighing machine shows 400 gm when the actual weight is 350 gm. The cost price of almonds is INR 880 per kg and packets of 200 gm are made using the faulty machine. What should be the selling price (in INR) of each packet to get a profit of 25%?
Option 1: 197.50
Option 2: 175.50
Option 3: 182.50
Option 4: 192.50
Correct Answer: 192.50
Solution : The cost price of almonds = INR 880 per kg Weight of packets sold = 200 gm Given that the weighing machine shows 400 gm when the actual weight is 350 gm. So, the weighing machine shows 200 gm when the actual weight is 175
Question : $\triangle$LMN is right angled at M. If $\angle$N = 45$^\circ$, what is the length of MN (in cm), if NL = 9$\sqrt2$cm?
Option 1: $9\sqrt2$
Option 2: $\frac{9}{\sqrt2}$
Option 3: $18$
Option 4: $9$
Correct Answer: $9$
Solution : $\triangle$LMN is right angled at M. $\angle$M = 90$^\circ$ $\angle$N = 45$^\circ$ $\angle$L = 180$^\circ$ – (45$^\circ$ + 90$^\circ$) = 45$^\circ$ So, $\triangle$LMN is an isosceles right-angled triangle. ⇒ LM = MN Also, NL = 9$\sqrt2$ cm Using the Pythagoras theorem, LM$^2$ + MN$^2$ =
Question : The iron mines in Jharkhand contributed to the rise of which ancient Indian kingdom?
Option 1: Kuru
Option 2: Magadha
Option 3: Kashi
Option 4: Kushan
Correct Answer: Magadha
Solution : The correct answer is Magadha.
Magadha became the most powerful state in ancient India, situated in modern Bihar and Jharkhand. The first significant and powerful dynasty in Magadha was the Haryanka dynasty. The iron mines in modern-day Jharkhand were easily accessible and offered supplies for
Question : If $x$ men can do a piece of work in $x$ days, then the number of days in which $y$ men can do the same work is:
Option 1: $xy$ days
Option 2: $\frac{y^{2}}{x}$ days
Option 3: $\frac{x^{2}}{y}$ days
Option 4: $x^{2}y$ days
Correct Answer: $\frac{x^{2}}{y}$ days
Solution : Given: $x$ men can do a piece of work in $x$ days. We know the concept $M_1D_1=M_2D_2$, where $M_1$, $M_2$ are the persons and $D_1$, $D_2$ are the number of days. According to the question, ⇒ $x×x=y×D_2$ $\therefore D_2=\frac{x^{2}}{y}$ days Hence, the correct answer
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
A new world research shows that the French (1) ______ large amounts of cheese and butter. Therefore, they have low levels of heart disease. The research (2) ______ that animal fat is good for the human body and helps in reducing the risks of heart attack. This study was (3) ______ in 2018 in 21 low and middle income countries. However, it (4) ______ that eating moderately is the (5) ______ key in this regard.
Question:
Select the most appropriate option to fill in the blank number 5.
Option 1: crucial
Option 2: diligent
Option 3: principle
Option 4: eminent
Correct Answer: crucial
Solution : The first option is the correct answer.
The word crucial is the most suitable choice in the context of emphasising the importance of eating moderately. It means something of great importance or significance.
The meanings of the other options are as follows:
Question : What is the difference in the number of years between the summer and winter Olympic events?
Option 1: 1
Option 2: 2
Option 3: 4
Option 4: 3
Correct Answer: 2
Solution : The correct answer is 2.
The difference in the number of years between the summer and winter Olympic events is two years. There is a staggered timetable for the Summer and Winter Olympics. The two competitions alternate every two years, although they are overseen
Question : Directions: If 18 × 12 = 206 and 19 × 22 = 408, then 23 × 36 = ?
Option 1: 878
Option 2: 818
Option 3: 794
Option 4: 776
Correct Answer: 818
Solution : Given: 18 × 12 = 206; 19 × 22 = 408; 23 × 36 = ?
Like, 18 × 12 = 206 is 18 × 12 = 216. Then→216 – 10 = 206 And, 19 × 22 = 408 is 19 × 22
Question : According to census 2011, which is the least populous state in India?
Option 1: Nagaland
Option 2: Sikkim
Option 3: Arunachal Pradesh
Option 4: Goa
Correct Answer: Sikkim
Solution : The correct answer is Sikkim.
Sikkim is the least populous state according to census 2011. The population of Sikkim was recorded as 611k in the 2011 population census. Sikkim is a state located in the northeastern part of India. The capital and largest town of
Question : Direction: A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series.
IGT, JHS, KIR, LJQ, MKP, ?
Option 1: LOP
Option 2: NOP
Option 3: NLO
Option 4: LNO
Correct Answer: NLO
Solution : Given: IGT, JHS, KIR, LJQ, MKP, ?
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