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16 Views

Question : What is the value of $\sin 30^{\circ}+\cos 30^{\circ}+\tan 30^{\circ}$?

Option 1: $\frac{5+\sqrt{3}}{2 \sqrt{3}}$

Option 2: $\frac{5-\sqrt{3}}{2 \sqrt{3}}$

Option 3: $\frac{5+\sqrt{3}}{\sqrt{3}}$

Option 4: $\frac{5-\sqrt{3}}{\sqrt{3}}$

Team Careers360 25th Jan, 2024

Correct Answer: $\frac{5+\sqrt{3}}{2 \sqrt{3}}$


Solution : Given: $\sin 30^{\circ}+\cos 30^{\circ}+\tan 30^{\circ}$
Putting the values, we get:
$=\frac{1}{2}+\frac{\sqrt3}{2}+\frac{1}{\sqrt3}$
$=\frac{\sqrt3+3+2}{2\sqrt3}$
$=\frac{5+\sqrt3}{2\sqrt3}$
Hence, the correct answer is $\frac{5+\sqrt3}{2\sqrt3}$.

201 Views

Question : Which of the following is not an allotrope of carbon?

Option 1: Trisulphur

Option 2: Diamond

Option 3: Lonsdaleite

Option 4: Graphite

Team Careers360 25th Jan, 2024

Correct Answer: Trisulphur


Solution : The correct option is Trisulfur

Trisulfur, often represented as S3, is not an allotrope of carbon. Trisulfur refers to a molecule composed of three sulfur atoms, while allotropes of carbon include forms like diamond, graphite, graphene, carbon nanotubes, and fullerenes, among others. Carbon allotropes have

21 Views

Question : The profit earned when a painting is sold for INR 1,200 is 15 times the loss incurred when it is sold for INR 240. At what price should the painting be sold to make a profit of 40%?

Option 1: INR 300

Option 2: INR 480

Option 3: INR 420

Option 4: INR 360

Team Careers360 25th Jan, 2024

Correct Answer: INR 420


Solution : Selling price = INR 1200
Profit = selling price – cost price
Profit = 1200 – cost price -----------(i)
Selling price = INR 240
Loss = cost price – selling price
Loss = cost price – 240 ------------(ii)
Profit = 15 × loss

14 Views

Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.

He worked ________ of his ability.

Option 1: at the best

Option 2: with the best

Option 3: in the best

Option 4: to the best

Team Careers360 25th Jan, 2024

Correct Answer: to the best


Solution : The fourth option is the correct answer.

To the best means to the greatest degree and fits contextually in the sentence. It conveys the meaning that he worked with the highest quality of his ability.

Other options don't fit contextually because different prepositions

12 Views

Question : Which of the following are constituents of the Indian Parliament?

(i) The President

(ii) The Council of States (Rajya Sabha)

(iii) The House of the People (Lok Sabha) 

Option 1: (i) and (ii)

Option 2: (ii) and (iii)

Option 3: (i) and (iii)

Option 4: (i) , (ii) and (iii)

Team Careers360 25th Jan, 2024

Correct Answer: (i) , (ii) and (iii)


Solution : The correct option is (i), (ii) and (iii)

The President, the Rajya Sabha (Council of States), and the Lok Sabha (House of the People) comprise the Indian Parliament. The President has the authority to call a special session of either House

18 Views

Question : The bar chart given below shows the sales (in 000 units) of 4 mobile brands for 3 years.
In 2017, the sales of each brand increased by the same percentage as it did in the year 2016. What will be the approximate average sales (in units) of mobiles per brand in the year 2017?

Option 1: 9175

Option 2: 8360

Option 3: 9436

Option 4: 9678

Team Careers360 25th Jan, 2024

Correct Answer: 9175


Solution : As per the given graph:
In 2017, the sales of each brand increased by the same percentage as it did in the year 2016.
The increase in sales of Brand 1 in 2016 = $\frac{7.5-5.5}{5.5}×100=36.36\%$
The sales of Brand 1 in 2017 = $7.5+(7.5×\frac{36.36}{100})=10.2$ units

15 Views

Question : Directions: If A means ×, B means +, C means –, and D means ÷, then
66 A 3 D 11 B 43 C 48 D 12 = ?

Option 1: 57

Option 2: 47

Option 3: 43

Option 4: 61

Team Careers360 25th Jan, 2024

Correct Answer: 57


Solution : Given:
66 A 3 D 11 B 43 C 48 D 12 = ?

After replacing the letters with the mathematical signs, we get –
= 66 × 3 ÷ 11 + 43 – 48 ÷ 12
= 18 + 43 – 4
= 61

15 Views

Question : If $x^4+x^{-4}=47, x>0$, then what is the value of $x+\frac{1}{x}-2?$

Option 1: 1

Option 2: 0

Option 3: 5

Option 4: 3

Team Careers360 25th Jan, 2024

Correct Answer: 1


Solution : Given expression,
$x^4+x^{-4}=47$
⇒ $x^4+\frac{1}{x^4}=47$
Adding 2 on both sides,
⇒ $x^4+\frac{1}{x^4}+2=47+2$
⇒ $x^4+\frac{1}{x^4}+2\times x^2\times\frac{1}{x^2}=49$
⇒ $(x^2+\frac{1}{x^2})^2=7^2$ [As $a^2+b^2+2ab=(a+b)^2$]
⇒ $x^2+\frac{1}{x^2}=7$
Again adding 2 on both sides,
⇒ $x^2+\frac{1}{x^2}+2=7+2$
⇒ $x^2+\frac{1}{x^2}+2\times x\times\frac1x=9$
⇒ $(x+\frac1x)^2=3^2$
⇒ $x+\frac1x=3$
⇒ $x+\frac1x-2=3-2$
$\therefore x+\frac1x-2=1$
Hence, the correct answer is

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