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Staff Selection Commission Combined Higher Secondary Level Exam

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Question : A triangle $\text{PQR}$ has three sides equal in measurement and if $\text{PM}$ is perpendicular to $\text{QR}$, then which of the following equality holds?

Option 1: $3 \text{PM}^2=2 \text{PQ}^2$

Option 2: $3 \text{PQ}^2=4 \text{PM}^2$

Option 3: $3 \text{PM}^2=4 \text{PQ}^2$

Option 4: $3 \text{PQ}^2=2 \text{PM}^2$

Team Careers360 15th Jan, 2024

Correct Answer: $3 \text{PQ}^2=4 \text{PM}^2$


Solution :
In an equilateral triangle $\text{PQR}$, all three sides are equal, so let's denote the length of each side as $a$.
Given: $\text{PM}\perp \text{QR}$
$\therefore$ $PQ^2 = PM^2 + MQ^2$ [By Pythagoras theorem]
$\text{MQ}$ is half of $\text{QR}$ (as it bisects $\text{QR}$ when $\text{PM}$

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Question : Parts of a sentence are given below in jumbled order. Arrange the parts in the correct order to form a meaningful sentence.
A. groups such as migrants and
B. collecting data on vulnerable population
C. persons with disabilities is crucial
D. understanding who are being left behind
E. in identifying the challenges they face and

Option 1: EADCB

Option 2: CABED

Option 3: BACED

Option 4: DACBE

Team Careers360 24th Jan, 2024

Correct Answer: BACED


Solution : The correct sequence is BACED.

Explanation:

  • Part B establishes the main action or topic of the sentence, introducing the idea of collecting data on vulnerable populations.
  • Part A specifies the groups for which collecting data is crucial, providing more details about the subjects involved.
  • Part
17 Views

Question : Choose the word that means the same as the given word.

Oblate

Option 1: Mendicant

Option 2: Heathen

Option 3: Layperson

Option 4: Secular

Team Careers360 6th Jan, 2024

Correct Answer: Mendicant


Solution : The first option is the correct answer.

An oblate generally denotes someone dedicated to religious life or service. On the other hand, a mendicant specifically describes a beggar or someone, often in a religious order, who relies on charity and takes a vow of poverty.

12 Views

Question : What is the value of $\sqrt{\frac{\operatorname{cosec} A+1}{\operatorname{cosec} A-1}}+\sqrt{\frac{\operatorname{cosec} A-1}{\operatorname{cosec} A+1}}$?

Option 1: $2 \cos A$

Option 2: $\sec A$

Option 3: $2\cos A$

Option 4: $2 \sec A$

Team Careers360 11th Jan, 2024

Correct Answer: $2 \sec A$


Solution : $\sqrt{\frac{\operatorname{cosec} A+1}{\operatorname{cosec} A-1}}+\sqrt{\frac{\operatorname{cosec} A-1}{\operatorname{cosec} A+1}}$
= ${\frac{(\sqrt{\operatorname{cosec} A+1})^2+(\sqrt{\operatorname{cosec} A-1})^2}{\sqrt{(\operatorname{cosec} A-1)(\operatorname{cosec} A+1)}}}$
= ${\frac{\operatorname{cosec} A+1+{\operatorname{cosec} A-1}}{\sqrt{(\operatorname{cosec}^2A-1)}}}$
= ${\frac{2\operatorname{cosec} A}{\sqrt{\cot^2A}}}$
= ${\frac{2\operatorname{cosec} A}{\cot A}}$
= ${\frac{2\sin A}{\sin A\cos A}}$
= ${\frac{2}{\cos A}}$
= $2\sec A$
Hence, the correct answer is $2\sec A$.

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Question : Which of the following shortcut keys is used to make the contents of a cell underlined in MS Excel 365?

Option 1: Ctrl + 6

Option 2: Ctrl + 3

Option 3: Ctrl + 2

Option 4: Ctrl + U

Team Careers360 16th Jan, 2024

Correct Answer: Ctrl + U


Solution : The correct option is Ctrl + U.

Ctrl + U key is commonly used across various applications, including Microsoft Excel, to underline text.

To apply underline to the contents of a cell:

  • Select the cell or range of cells whose contents you want
20 Views

Question : Select the most appropriate ANTONYM of the word 'Facilitated' from the given sentence.

The author's recent bout of writer's block had hindered her typically prolific output of novels.

Option 1: Bout

Option 2: Prolific

Option 3: Hindered

Option 4: Output

Team Careers360 13th Jan, 2024

Correct Answer: Hindered


Solution : The third option is the correct answer.

Here, hindered represents the opposite of facilitated because the writer's block acted as an obstacle or barrier, making it difficult for the author to produce novels efficiently.

The meanings of the other options are as follows:

  • Bout: It
25 Views

Question : Which of the following supports the particle nature of photons?

Option 1: Diffraction

Option 2: Polarisation

Option 3: Photoelectric effect

Option 4: Interference

Team Careers360 19th Jan, 2024

Correct Answer: Photoelectric effect


Solution : The correct answer is the Photoelectric effect.

In the photoelectric effect, when light shines on a material surface, it can eject electrons from that material. The key observation is that the intensity of light doesn't determine whether electrons are emitted but rather the frequency

11 Views

Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at MN as shown.

Option 1:

Option 2:

Option 3:

Option 4:

Team Careers360 13th Jan, 2024

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 MN). So, the left side of the reflected image will appear

20 Views

Question : Kerala is famous for which of the following festivals?

Option 1: Pongal

Option 2: Ugadi

Option 3: Bihu

Option 4: Onam

Team Careers360 3rd Jan, 2024

Correct Answer: Onam


Solution : The correct option is Onam.

Kerala, a state in southern India, is famous for several festivals, but one of its most well-known and widely celebrated festivals is Onam. Onam is a harvest festival and is celebrated with great enthusiasm and grandeur in Kerala. The festival

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