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19 Views

Question : If $\cos \theta+\cos ^2 \theta=1$, find the value of $\sqrt{\sin ^4 \theta+\cos ^2 \theta}$.

Option 1: $\sqrt{2} \cos \theta$

Option 2: $2 \operatorname{cos} \theta$

Option 3: $\sqrt{2} \operatorname{sin} \theta$

Option 4: $2 \operatorname{sin} \theta$

Team Careers360 25th Jan, 2024

Correct Answer: $\sqrt{2} \cos \theta$


Solution : Given: $\cos \theta+\cos ^2 \theta=1$
⇒ $\cos\theta + \cos^2\theta = \sin^2\theta + \cos^2\theta$
⇒ $\cos\theta = \sin^2\theta$
Putting the value in the given equation,
$\sqrt{\sin ^4 \theta+\cos ^2 \theta}$
$=\sqrt{\cos^2\theta + \cos^2\theta}$
$=\sqrt{2} \cos\theta$
Hence, the correct answer is $\sqrt{2} \cos\theta.$

42 Views

Question : Select the most appropriate synonym of the underlined word in the given sentence.

The professor refused to comment on the erroneous description of the historical events in the journal.

Option 1: Suitable

Option 2: Lucid

Option 3: Inaccurate

Option 4: Sensitive

Team Careers360 25th Jan, 2024

Correct Answer: Inaccurate


Solution : The most appropriate option is the third option.

ExplanationErroneous means containing errors or mistakes. Inaccurate also means not accurate or containing mistakes, aligning closely in meaning with erroneous.

The meanings of the other options are as follows:

  • Suitable means appropriate or fitting for
16 Views

Question : The value of $117 ÷ 45 \;\text {of} \frac{1}{5} + \frac{12}{5} × \frac{20}{3}$ is:

Option 1: 29

Option 2: 27

Option 3: 28

Option 4: 31

Team Careers360 25th Jan, 2024

Correct Answer: 29


Solution : $117 ÷ 45 \;\text {of} \frac{1}{5} + \frac{12}{5} × \frac{20}{3}$ 
= 117 ÷ 9 + 4 × 4
= 13 + 16
= 29
Hence, the correct answer is 29.

100 Views

Question : Comprehension:

Read the following passage and answer the questions given after it.

The Indian Space Research Organisation (ISRO) announced another successful mission. ISRO chairman S. Somanath said that three small satellites successfully separated and were injected into orbit. ISRO launched three small satellites powered by its SSLV-D2 launch vehicle from Satish Dhawan Space Centre at Sriharikota on February 10, 2023, at 09:18 AM IST. The launch vehicle was carrying EOS-07, Janus-1 & AzaadiSAT-2 satellites and aimed to inject them into a 450 km circular orbit. The launch took place at the first launch pad at SDSC SHAR,
Sriharikota. The SSLV-D2 had to take a 15-minute flight to inject EOS-07, Janus-1, and AzaadiSAT-2 satellites into a 450 km circular lower orbit. “It is configured with three solid propulsion stages and a velocity terminal module. It is a 34 m tall, 2 m diameter vehicle having a lift-off mass of 120 t,” said ISRO. The EOS-07 satellite weighs 156.3 kg and is made by ISRO.

About 13 minutes into its flight, the SSLV rocket ejected EOS-07 and soon after that the other two satellites Janus-1 and AzaadiSAT-2 were ejected — all at an altitude of 450 km, said ISRO.

With the new rocket in its portfolio, ISRO will have three rockets — Polar Satellite Launch Vehicle (PSLV) and its variants (cost about Rs 200 crore), Geosynchronous Satellite Launch Vehicle (GSLV-MkII cost about Rs 272 crore and LVM3 Rs 434 crore) and SSLV (Development cost of three rockets about Rs 56 crore each) and production cost may go down later.

“New experiments include mm-Wave Humidity Sounder and Spectrum Monitoring Payload. Janus-1, a 10.2 kg satellite belongs to ANTARIS, USA. An 8.7 kg satellite AzaadiSAT-2 is a combined effort of about 750 girl students across India guided by Space Kidz India, Chennai,” it added.

SSLV caters to the launch of up to 500 kg satellites to Low Earth Orbits on a ‘launch-on-demand’ basis. “It provides low-cost access to Space, offers low turn-around time and flexibility in accommodating multiple satellites, and demands minimal launch infrastructure,” as per a statement by ISRO.

Question:

After reading the passage it can be inferred that it is

Option 1: a government release

Option 2: a news item

Option 3: a magazine article

Option 4: an editorial

Team Careers360 25th Jan, 2024

Correct Answer: a news item


Solution : The correct choice is the second option.

The language used is factual and objective, providing information about a recent event (the successful launch of three small satellites by ISRO) without expressing opinions or providing analysis. The use of quotes from ISRO officials

19 Views

Question : Which of the following statements is correct regarding the socialist society in the economy?

I. The government decides what goods are to be produced.
II. Distribution of goods under socialism is supposed to be based on what people need.

Option 1: Only I

Option 2: Neither I nor II

Option 3: Both I and II

Option 4: Only II

Team Careers360 25th Jan, 2024

Correct Answer: Both I and II


Solution : The correct option is Both I and II.

In a socialist system, there can be different degrees of government involvement, ranging from limited regulation and social ownership to more extensive control over the means of production.

In a socialist economy, the emphasis

229 Views

Question : If the difference between the selling prices of an article at profits of 10% and 7% is INR 6, then the cost price (in INR) of the article is:

Option 1: 175

Option 2: 150

Option 3: 200

Option 4: 100

Team Careers360 25th Jan, 2024

Correct Answer: 200


Solution : The difference in selling price by selling an article at a profit of 10% and 7% = INR 6
Let the cost price (CP) of the article be $x$.
According to the question,
110% of $x$ – 107% of $x$ = 6
⇒ 3% of

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