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15 Views

Question : An aeroplane flying horizontally at a height of 3 km above the ground is observed at a certain point on earth to subtend an angle of $60^\circ$. After 15 seconds of flight, its angle of elevation is changed to $30^\circ$. The speed of the aeroplane (Take $\sqrt{3}=1.732$) is:

Option 1: 230.63 m/s

Option 2: 230.93 m/s

Option 3: 235.85 m/s

Option 4: 236.25 m/s

Team Careers360 25th Jan, 2024

Correct Answer: 230.93 m/s


Solution :

AB = CD = 3 km = 3000 m
In $\triangle$AOB,
$\tan60^{\circ}=\frac{AB}{OB}$
⇒ $OB=\frac{3000}{\sqrt3}=1000\sqrt3$ m
In $\triangle$COD,
$\tan30^{\circ}=\frac{CD}{OC}$
⇒ $OC=3000\sqrt3$ m
So, BC = AD = ($3000\sqrt3–1000\sqrt3)=2000\sqrt3$ m
Therefore, the speed of the aeroplane
= $\frac{2000\sqrt3}{15}$ m/s
= 230.93 m/s
Hence, the correct answer

15 Views

Question : Directions: Select the correct combination of mathematical signs to replace the * signs and to balance the given equation.
23 * 12 * 36 * 2 * 9 * 285

Option 1: –, =, ×, ×, ÷

Option 2: ×, +, ÷, –, =

Option 3: +, +, =, ×, ×

Option 4: =, +, +, ×, –

Team Careers360 25th Jan, 2024

Correct Answer: ×, +, ÷, –, =


Solution : Given:
23 * 12 * 36 * 2 * 9 * 285

Replace * with the mathematical signs and solve the equations one by one using the BODMAS.
Let's check the given options –
First option: –, =, ×, ×, ÷

10 Views

Question : Fill in the blank with an appropriate option.
Habitat loss received little attention from all Twitter ______.

Option 1: band

Option 2: users

Option 3: forces

Option 4: pools

Team Careers360 25th Jan, 2024

Correct Answer: users


Solution : The correct choice is the second option.

The word "users" is the appropriate option to fill in the blank.

The sentence suggests that habitat loss didn't receive much attention from the collective group of people using Twitter. In the context of the sentence, the term

12 Views

Question : Among the following Himalayan peaks, which is the easternmost?

Option 1: Kangchenjunga

Option 2: Trishul

Option 3: Nanda Devi

Option 4: Kamet

Team Careers360 25th Jan, 2024

Correct Answer: Kangchenjunga


Solution : The correct option is Kangchenjunga.

Kangchenjunga is the third-highest mountain in the world and is located on the India-Nepal border. It's the tallest mountain in India and the easternmost Himalayan summit, situated on the border between Nepal and the Indian state of Sikkim.

106 Views

Question : The bar chart given below shows the annual production (in 1000 tonnes) of coffee of a country for the years 2018 to 2022.

What is the average production (in 1000 tonnes) of coffee for the years 2018, 2019, and 2020?

Option 1: 530

Option 2: 810

Option 3: 720

Option 4: 640

Team Careers360 25th Jan, 2024

Correct Answer: 640


Solution : Production of coffee in 2018 = 700 (in 1000 tonnes)
Production of coffee in 2019 = 550 (in 1000 tonnes)
Production of coffee in 2020 = 670 (in 1000 tonnes)
Average = $\frac{\text{Sum of yearly production}}{{\text{Total number of years}}}$
= $\frac{700+550+670}{3}$
= $\frac{1920}{3}$
= $640$

33 Views

Question : Akham Lakshmi Devi, a recipient of the Sangeet Natak Akademi award, is renowned for which of the following dances?

Option 1: Kathak

Option 2: Odissi

Option 3: Sattriya

Option 4: Manipuri

Team Careers360 25th Jan, 2024

Correct Answer: Manipuri


Solution : The correct option is Manipuri.

Akham Lakshmi Devi is renowned for the Manipuri dance form. She was a renowned Manipuri dancer and advocate, showcasing this traditional dance style from the northeastern state of Manipur. Akham Lakshmi Devi was conferred with the Sangeet Natak Akademi Award

19 Views

Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?

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

Option 2: $\sqrt{3}$

Option 3: $1$

Option 4: $\frac{1}{\sqrt{3}}$

Team Careers360 25th Jan, 2024

Correct Answer: $1$


Solution : Given: $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$
= $\frac{\sin (90^{\circ}-60^{\circ}) \sin (90^{\circ}-50^{\circ}) \sin (90^{\circ}-40^{\circ}) \sin (90^{\circ}-30^{\circ})}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$
= $\frac{\cos 60^{\circ} \cos 50^{\circ} \cos 40^{\circ} \cos 30^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos

20 Views

Question : Which state of India has made rainwater harvesting compulsory for all houses?

Option 1: Haryana

Option 2: Maharashtra

Option 3: Tamil Nadu

Option 4: Punjab

Team Careers360 25th Jan, 2024

Correct Answer: Tamil Nadu


Solution : The correct option is Tamil Nadu.

The first state in India that mandates rooftop rainwater harvesting systems for every home is Tamil Nadu. The act of collecting and storing rainwater as opposed to letting it run off is called rainwater harvesting. Rainwater is collected

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