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Question : BL and CM are medians of $\triangle$ABC right-angled at A and BC = 5 cm. If BL=$\frac{3\sqrt5}{2}$ cm, then the length of CM is

Option 1: $2\sqrt5$ cm

Option 2: $5\sqrt2$ cm

Option 3: $10\sqrt2$ cm

Option 4: $4\sqrt5$ cm

Team Careers360 22nd Jan, 2024

Correct Answer: $2\sqrt5$ cm


Solution :
Given: BC = 5 cm. and BL=$\frac{3\sqrt5}{2}$ cm
According to the question,
$4(BL^2+CM^2)=5BC^2$
⇒ $4[(\frac{3\sqrt5}{2})^2+CM^2]=5×5^2$
⇒ $4×\frac{45}{4}+4CM^2=125$
⇒ $4CM^2=125-45$
⇒ $4CM^2=80$
⇒ $CM^2=\frac{80}{4}$
⇒ $CM=\sqrt20=2\sqrt5$
Hence, the correct answer is $2\sqrt5$ cm.

87 Views

Question : Comprehension:
Read the given passage carefully and answer the questions that follow.

As a society, we have come a long way in terms of progress and development. We have eradicated diseases, explored space, and created technological wonders that were once thought impossible. Yet, there is still one issue that continues to plague us: stupidity. Yes, stupidity. The thing that seems to be contagious and has been spreading faster than the common cold. It's everywhere you look - on social media, in politics, in the workplace. You can't escape it.

It's as if we've all collectively decided that intelligence and common sense are no longer important. Why bother using your brain when you can just rely on your gut feelings and conspiracy theories?

Take politics, for example. It used to be that politicians were expected to be knowledgeable and well-informed about the issues they were dealing with. Now, it seems that all you need is a catchy slogan and some empty promises to win an election.

And don't even get me started on social media. It's a breeding ground for stupidity. People will believe anything they read as long as it confirms their preconceived biases. And don't even think about trying to present them with actual facts and evidence. That's just a waste of time. But it's not just individuals who are to blame for this epidemic of stupidity. Our education system is failing us as well. We're teaching our kids how to pass tests instead of how to think critically and solve problems. It's no wonder we have a generation of adults who can't even find their way around a basic math problem.

Of course, there are some who would argue that stupidity is just a different way of thinking. That it's a valid perspective that deserves to be respected. To those people, I say this: if you want to be stupid, go ahead. Just don't expect the rest of us to respect your opinions when they're based on nothing but ignorance and misinformation.

It's time for us to take a stand against stupidity. We need to start valuing intelligence and critical thinking again. We need to hold our leaders accountable for their actions and demand that they be knowledgeable and well-informed. We need to teach our children how to think, not just how to memorise.

It won't be easy, but it's a fight worth fighting. Because if we don't, we'll be stuck in a world where stupidity reigns supreme, and there's no telling what kind of damage that could do. So let's all do our part and start using our brains again. It's time to put an end to the epidemic of stupidity once and for all.

Question:
What is the tone of the passage?

Option 1: Sarcastic

Option 2: Serious

Option 3: Melancholic

Option 4: joyful

Team Careers360 22nd Jan, 2024

Correct Answer: Sarcastic


Solution : The correct answer to this question is the first option.

Explanation: The tone of the passage can be described as critical, concerned, and urgent. The author expresses a critical view of the current state of society, particularly regarding what they perceive as a widespread problem

19 Views

Question : Directions: Which of the option figures is the exact mirror image of the given problem figure when the mirror is held on the right side?

Option 1:

Option 2:

Option 3:

Option 4:

Team Careers360 25th 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 (on line MN) of the figure. So, the left side of the reflected image will appear

20 Views

Question : The sides of two similar triangles are in the ratio 5 : 7. The areas of these triangles are in the ratio of:

Option 1: 35 : 49

Option 2: 15 : 49

Option 3: 25 : 49

Option 4: 36 : 49

Team Careers360 21st Jan, 2024

Correct Answer: 25 : 49


Solution : The sides of two similar triangles are in the ratio of 5 : 7.
Let the sides be $5x$ and $7x$.
In two similar triangles, the ratio of their areas is square of the ratio of their sides.
$\frac{\textnormal{Area of triangle 1}}{\textnormal{Area of

7 Views

Question : The most distinctive type of folk songs of Assam are________.

Option 1: Qawwali songs

Option 2: Bihu songs

Option 3: Teej songs

Option 4: Bhuta songs

Team Careers360 21st Jan, 2024

Correct Answer: Bihu songs


Solution : The correct option is Bihu songs.

Bihu songs are vibrant folk songs from Assam, India, traditionally associated with the Bihu festival. Bihu songs are often performed with traditional Bihu dance, which involves rhythmic movements and gestures that reflect the themes of the songs.

7 Views

Question : Tokyo 2020 Paralympic Games bronze medallist Manoj Sarkar is associated with which of the following events?

Option 1: Shooting

Option 2: Badminton

Option 3: Table Tennis

Option 4: Athletics

Team Careers360 22nd Jan, 2024

Correct Answer: Badminton


Solution : The correct option is Badminton.

Manoj Sarkar is a distinguished para-badminton athlete hailing from Uttarakhand. His remarkable medal tally includes 19 gold medals, 13 silver medals, and 18 bronze medals, showcasing his exceptional prowess on the badminton court. His notable accomplishments include winning a

43 Views

Question : The perimeter of a sector of a circle of radius 7.4 cm is 20.6 cm. The area of this sector is:

Option 1: 42.92 cm2

Option 2: 5.8 cm2

Option 3: 10.73 cm2

Option 4: 21.46 cm2

Team Careers360 25th Jan, 2024

Correct Answer: 21.46 cm2


Solution : The radius of the circle = 7.4 cm
Let the length of the arc be $l$ cm.
The perimeter of the sector = Radius + Length of the arc + Radius
$⇒20.6 = 7.4 + l + 7.4$
$⇒l = 20.6 -14.8 =

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