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Staff Selection Commission Sub Inspector Exam

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Question : An article is marked at 100% above its cost price. After allowing two successive discounts of 5% and 20% respectively on the marked price, it is sold at $x$% profit. What is the value of $x$?

Option 1: 48

Option 2: 75

Option 3: 72

Option 4: 52

Team Careers360 19th Jan, 2024

Correct Answer: 52


Solution : Given: An article is marked at 100% above its cost price.
After allowing two successive discounts of 5% and 20% respectively on the marked price, it is sold at $x$% profit.
Use the formula, Profit percentage = $\frac{\text{SP – CP}}{\text{CP}}\times 100$, where $SP$, $CP$ are

19 Views

Question : X can do a work in 3 days, Y can do three times the same work in 8 days, and Z can do five times the same work in 12 days. If they have to work together for 6 hours a day, then how much time will they take to complete the work?

Option 1: 4 hours

Option 2: 5 hours 20 minutes

Option 3: 4 hours 10 minutes

Option 4: 5 hours

Team Careers360 17th Jan, 2024

Correct Answer: 5 hours 20 minutes


Solution : X can complete the work in 3 days.
Y can do three times the same work in 8 days.
Z does five times the same work in 12 days.
Working hours per day = 6 hours
Efficiency = $\frac{\text{Total work}}{\text{Total Time}}$
Let

51 Views

Question : AB is the common tangent to both circles as shown in the given figure. What is the distance between the centres of the circles?

Option 1: 20 cm

Option 2: 15 cm

Option 3: 10 cm

Option 4: 30 cm

Team Careers360 23rd Jan, 2024

Correct Answer: 30 cm


Solution :
Given that AB is the common tangent to both circles.
In the circle with centre C, $\angle$CAE = 90°
In the circle with centre D, $\angle$DBA = 90°
and $\angle$AEC = $\angle$BED (vertically opposite angle)
So, $\triangle$CAE $\sim$ $\triangle$DBC
⇒ $\frac{CA}{AE}=\frac{DB}{BE}$
⇒ $\frac{4}{3}=\frac{DB}{15}$
⇒

13 Views

Question : If $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $y=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, then the value of $x^{3} + y^{3}$ is:

Option 1: 950

Option 2: 730

Option 3: 650

Option 4: 970

Team Careers360 19th Jan, 2024

Correct Answer: 970


Solution : $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}=\frac{(\sqrt{3}-\sqrt{2})×(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})×(\sqrt{3}-\sqrt{2})}=(\sqrt{3}-\sqrt{2})^2$ = $5-2\sqrt6$
$y=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}=\frac{(\sqrt{3}+\sqrt{2})×(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})×(\sqrt{3}+\sqrt{2})}=(\sqrt{3}+\sqrt{2})^2$ = $5+2\sqrt6$
$⇒x+y=5-2\sqrt6+5+2\sqrt6 =10$
Also, $xy=(5-2\sqrt6)(5+2\sqrt6)=25-24=1$
$\therefore x^3+y^3=(x+y)^{3} -3xy(x+y)$
$=10^3-3\times 1 \times 10$
$=1000-30$
$= 970$
Hence, the correct answer is 970.

47 Views

Question : In which of the following years did the government opt for a planned holiday after the seventh five-year plan?

Option 1: From 1991 to 1993

Option 2: From 1990 to 1992

Option 3: From 1992 to 1993

Option 4: From 1989 to 1991

Team Careers360 24th Jan, 2024

Correct Answer: From 1990 to 1992


Solution : The correct answer is From 1990 to 1992.

The term "Plan Holiday" refers to the interruption in the continuous series of Five-Year Plans in India. During the Eighth Five-Year Plan (1990-1995), there was a break in 1990, and the subsequent years

17 Views

Question : The value of $2 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}+\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)$ is:

Option 1: $\frac{25}{24}$

Option 2: $\frac{29}{24}$

Option 3: $\frac{35}{24}$

Option 4: $\frac{5}{24}$

Team Careers360 18th Jan, 2024

Correct Answer: $\frac{29}{24}$


Solution : Given: $2 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}+\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)$
= $\frac{7}{3} \div \frac{5}{2}$ of $\frac{8}{5}+\left(\frac{3}{8}+\frac{1}{7} \times \frac{7}{4}\right)$
= $\frac{7}{3} \div (\frac{5}{2}\times\frac{8}{5})+\frac{5}{8}$
= $\frac{7}{3}\times\frac{1}{4}+\frac{5}{8}$
= $\frac{7}{12}+\frac{5}{8}$
= $\frac{14+15}{24}$
= $\frac{29}{24}$
Hence, the correct answer is $\frac{29}{24}$.

21 Views

Question : Comprehension:
Read the given passage and answer the questions that follow.
It is not an exaggeration to say that the question of where and when the Black Death, the deadliest pandemic ever, originated is one of the biggest mysteries in human history. After all, the Black Death was the first wave of the second plague pandemic of the 14th to early 19th centuries. It killed some 50–60% of the population in Europe, the Middle East, and North Africa, and an unaccountable number of people in Central Asia. Different proposals, based on competing theories, have been put forward. But in 2017, I came across some records describing an intriguing medieval cemetery in Kara-Djigach, Chüy Valley, northern Kyrgyzstan, which I suspected may hold the key. As part of a multidisciplinary team co-led by Maria Spyrou at the University of Tubingen, we have now investigated several specimens from individuals buried at that site and come up with an answer. The idea that the Black Death originated in the east—territories overlapping, roughly speaking, Central Asia, Mongolia, and China—dates back to the contemporaries of the pandemic in Europe and the Islamic world. The modern, academic Chinese origin theory dates back at least to 1756–8, and a publication about the history of Central Asia by French scholar Joseph de Guignes.


Which of the following may be the probable origin of the Black Death, according to the passage?

Option 1: Kyrgyzstan

Option 2: India

Option 3: Mongolia

Option 4: China

Team Careers360 14th Jan, 2024

Correct Answer: Kyrgyzstan


Solution : The first option is correct.

The probable origin of the Black Death, according to the passage, is Kyrgyzstan. The passage mentions the discovery of an intriguing medieval cemetery in Kara-Djigach, Chüy Valley, northern Kyrgyzstan, in 2017. The speaker suspected that this site may hold

6 Views

Question : Directions: Select the related letter cluster from the given alternatives.
LSFW : NTHX :: PKWE : ?

Option 1: RYLF

Option 2: RLYE

Option 3: RLYF

Option 4: RLGF

Team Careers360 23rd Jan, 2024

Correct Answer: RLYF


Solution : Given:
LSFW : NTHX :: PKWE : ?

Add 2 and 1 alternately to the letters in LSFW and PKWE to obtain the related clusters.
L + 2 = N; S + 1 = T; F + 2 = H; W + 1 = X

169 Views

Question : What will be the area of a plot of quadrilateral shape, one of whose diagonals is 20 m and lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively?

Option 1: 400 m2

Option 2: 250 m2

Option 3: 200 m2

Option 4: 300 m2

Team Careers360 17th Jan, 2024

Correct Answer: 300 m2


Solution :
Given: The diagonals are 20 m and the lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively.
Use the formula, $\text{Area of the triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}$.
The area of the $\triangle ABC=\frac{1}{2}\times \text{AC}\times \text{BO}=\frac{1}{2} \times

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