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Staff Selection Commission Combined Higher Secondary Level Exam

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Question : If $4 \sin ^2 \mathrm{A}-3=0$ and $0 \leq \mathrm{A} \leq 90^{\circ}$, then $3 \sin \mathrm{A}-4 \sin ^3 \mathrm{A}$ is:

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

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

Option 3: $0$

Option 4: $1$

Team Careers360 27th Jan, 2024

Correct Answer: $0$


Solution : $4 \sin ^2 \mathrm{A}-3=0$
$⇒\sin ^2 A = \frac{3}{4}$
$⇒\sin  A = \frac{\sqrt{3}}{2}$
$3 \sin \mathrm{A}-4 \sin ^3 \mathrm{A}$
$=3 (\frac{\sqrt{3}}{2}) - 4 (\frac{\sqrt{3}}{2})^3 $
$=3 (\frac{\sqrt{3}}{2}) - 4 (\frac{\sqrt{3}}{2})^3 $
$=3 (\frac{\sqrt{3}}{2}) - 4 (\frac{3\sqrt{3}}{8}) $
$=(\frac{3\sqrt{3}}{2}) - (\frac{3\sqrt{3}}{2}) $
$= 0$
Hence, the

6 Views

Question : Fill in the blank with an appropriate option.

No matter how many times I try, I always end up in the same ____________.

Option 1: account

Option 2: meal

Option 3: pickle

Option 4: sauce

Team Careers360 26th Jan, 2024

Correct Answer: pickle


Solution : The correct choice is the third option.

End up in a pickle is an idiom that means to end up in a troublesome or difficult situation. Pickle is the correct choice here, as it helps convey the intended meaning that no matter how many times

11 Views

Question : Directions: In the following question, select the one that is different from the other three alternatives.

Option 1: DEFY

Option 2: HINT

Option 3: MOST

Option 4: SUVY

Team Careers360 26th Jan, 2024

Correct Answer: SUVY


Solution : Let's check the options –
First option: DEFY; DEFY is a meaningful word that means refuse to obey.
Second option: HINT; HINT is a meaningful word that means clue.
Third option: MOST; Most is a meaningful word that means to the greatest extent.
Fourth option: 

11 Views

Question :  Which of the following is included in the M1 measure of money supply?

A) Currency with Public

B) Time Deposit with Post Office

C) Demand Deposits with Commercial Banks/RBI of Public Financial Institutions

Option 1: Both B and C

Option 2: Both A and C

Option 3: Only B

Option 4: Only A

Team Careers360 26th Jan, 2024

Correct Answer: Both A and C


Solution : The correct option is Both A and C.

In the M1 measure of money supply, the following is included: Currency with the Public and Demand Deposits with Commercial Banks/RBIs of Public Financial Institutions. M1 includes the most liquid components of the

18 Views

Question : Which are the four quantum numbers for an electron present in 4f orbital?

Option 1: n=4, I=3, m=+1, s=+1 / 2

Option 2: n=3, I=2, m=-2, s=+1 / 2

Option 3: n=4, I=4, m=-4, s=-1 / 2

Option 4: n=4, I=3, m=+4, s=+1 / 2

Team Careers360 27th Jan, 2024

Correct Answer: n=4, I=3, m=+1, s=+1 / 2


Solution : The correct option is n=4, I=3, m=+1, s=+1 / 2.

The four quantum numbers for an electron in a 4f orbital are:

  1. Principal quantum number (n) = 4.
  2. Azimuthal quantum number (l) = 3.
  3. Magnetic quantum number (m_l) can
14 Views

Question : Which among the following is the official sport of Maharashtra, as of 2022?

Option 1: Mallakhamb

Option 2: Kalaripayattu

Option 3: Sand sculptures

Option 4: Dahi Handi

Team Careers360 27th Jan, 2024

Correct Answer: Dahi Handi


Solution : The correct option is Dahi Handi.

In October 2022, Maharashtra formally designated Dahi Handi as an adventure sport, although it is not yet classified as a mainstream sport by the Sports Authority of India. This recognition underscores its cultural importance and encourages athleticism

12 Views

Question : Directions: In the following question, select the related word from the given alternatives.
Nest : Bird :: Den : ? 

Option 1: Owl

Option 2: Lion

Option 3: Rat

Option 4: Goat

Team Careers360 27th Jan, 2024

Correct Answer: Lion


Solution : Given:
Nest : Bird :: Den : ? 

Like, birds live in nests.
Similarly, lions live in dens.

Hence, the second option is correct.

19 Views

Question : Find the value of $\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}+2$.

Option 1: $1+2 \sec A$

Option 2: $2-\sec A$

Option 3: $2+\sec A$

Option 4: $2(1+\sec A)$

Team Careers360 27th Jan, 2024

Correct Answer: $2(1+\sec A)$


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

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