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Staff Selection Commission Combined Higher Secondary Level Exam

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Question : The six-digit number $\mathrm{N = 4a6b9c}$ is divisible by $99$, then the maximum sum of the digits of $\mathrm{N}$ is:

Option 1: 18

Option 2: 36

Option 3: 45

Option 4: 27

Team Careers360 25th Jan, 2024

Correct Answer: 27


Solution : We have, the six-digit number $\mathrm{N = 4a6b9c}$ is divisible by $99$.
Divisibility rule for $9$,
A number is divisible by $9$ if the sum of digits is divisible by $9$.
As $\mathrm{N = 4a6b9c}$ is divisible by $9$.
The sum of the digits $=\mathrm{(4+a+6+b+9+c)}$

38 Views

Question : Choose the option that is the correct passive form of the sentence.

Daniel and Mary invited us to their wedding.

Option 1: We have been invited to Daniel and Mary's wedding.

Option 2: We were invited to Daniel and Mary's wedding.

Option 3: We are invited to Daniel and Mary's wedding.

Option 4: We had been invited to Daniel and Mary's wedding.

Team Careers360 25th Jan, 2024

Correct Answer: We were invited to Daniel and Mary's wedding.


Solution : The correct choice is the second option.

Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in

11 Views

Question : A is three times as good a worker as B and therefore, able to finish a piece of work in 60 days less than B. The time (in days) in which they can do it working together is:

Option 1: 22 days

Option 2: $22\frac{1}{2}$ days

Option 3: 23 days

Option 4: $23\frac{1}{4}$ days

Team Careers360 24th Jan, 2024

Correct Answer: $22\frac{1}{2}$ days


Solution : Given: A : B = 3 : 1
A takes = $x$ days and
B takes = $x$ + 60 days
If the difference of time is 2 days, B takes 3 days.
If the difference in time is 60 days,
B takes =

15 Views

Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No Error".

In India, (1) / there are (2) / many poors. (3) / No Error (4)

Option 1: (1)

Option 2: (2)

Option 3: (3)

Option 4: (4)

Team Careers360 20th Jan, 2024

Correct Answer: (3)


Solution : The error lies in the third part of the sentence. 

"Poors" is not grammatically correct, it should be replaced with "poor people". Here, it refers to a group of people who have little or no money. So, the correct sentence is, "In India, there are

14 Views

Question : If $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$, then the positive value of $\cot \theta+\cos \theta$ is:

Option 1: $\frac{3 \sqrt{3}}{2}$

Option 2: $\frac{\sqrt{3}}{2}$

Option 3: $\frac{2}{3 \sqrt{3}}$

Option 4: $\frac{2}{\sqrt{3}}$

Team Careers360 23rd Jan, 2024

Correct Answer: $\frac{3 \sqrt{3}}{2}$


Solution : Given: $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$...................(equation 1)
We know that
$\sec^2\theta-\tan^2\theta=1$
$⇒(\sec\theta-\tan\theta)(\sec\theta+\tan\theta)=1$
Putting the value, we get
$⇒(\sec\theta-\tan\theta)(\frac{1}{\sqrt3})=1$
$⇒(\sec\theta-\tan\theta)=\sqrt3$............(equation 2)
From equations 1 and 2, we get:
$⇒2\sec\theta=\sqrt3+\frac{1}{\sqrt3}$
$⇒2\sec\theta=\frac{4}{\sqrt3}$
$⇒\sec\theta=\frac{2}{\sqrt3}$
We know that, $\sec\theta=\frac{h}{b}=\frac{2}{\sqrt3}$
So, $p=\sqrt{ h^2-b^2}$
$⇒p=\sqrt{2^2-\sqrt3^2}=1$
$\therefore \cot\theta+\cos\theta=\frac{b}{p}+\frac{b}{h}=\frac{\sqrt3}{1}+\frac{\sqrt3}{2}=\frac{3\sqrt3}{2}$
Hence, the correct answer is $\frac{3\sqrt3}{2}$.

8 Views

Question : Simplify the given expression $\frac{4\left[(17)^3-(7)^3\right]}{(17)^2+(7)^2+119}$

Option 1: 40

Option 2: 50

Option 3: 60

Option 4: 30

Team Careers360 17th Jan, 2024

Correct Answer: 40


Solution : Given, $\frac{4\left[(17)^3-(7)^3\right]}{(17)^2+(7)^2+119}$
= $\frac{4(17-7)((17)^2+(7)^2+(17)(7))}{(17)^2+(7)^2+(17)(7)}$
= $4×10$
= $40$
Hence, the correct answer is 40.

20 Views

Question : Directions: In the following question, arrange the following words as per their order in the dictionary.
1. Intervention
2. Intertwine
3. Interview
4. Intervene

Option 1: 4, 3, 2, 1

Option 2: 2, 3, 4, 1

Option 3: 2, 4, 1, 3

Option 4: 3, 4, 1, 2

Team Careers360 19th Jan, 2024

Correct Answer: 2, 4, 1, 3


Solution : Given:
1. Intervention 2. Intertwine 3. Interview 4. Intervene

Step 1: Compare the first letter of the word. Since all the letters start with the same letter I, then move on to the next letter.
Step 2: The second, third, fourth,

17 Views

Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at 1, 2 and 3 that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).

Einstein was one (of the wisest men) that ever lived.

(1) of the wisest man

(2) wise man 

(3) wisest man

(4) No Improvement 

 

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

Team Careers360 25th Jan, 2024

Correct Answer: 4


Solution : The fourth option is the correct answer i.e. "No improvement."

In this case, the original sentence is already correct. The use of the superlative "wisest" correctly compares Einstein to a group of individuals, and "men" is the appropriate plural form in this context.

Therefore, the

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