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11 Views

Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?

Option 1: $a^2+b^2+c^2-3abc$

Option 2: $0$

Option 3: $3abc$

Option 4: $a^2+b^2+c^2-ab-bc-ca$

Team Careers360 23rd Jan, 2024

Correct Answer: $3abc$


Solution : Using the identity: $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$.
If $a + b + c = 0$, 
$a^3 + b^3 + c^3 - 3abc = 0$
⇒ $a^3

8 Views

Question : Which of the following is the green algae?

Option 1: Liverwort

Option 2: Rhodophyceae

Option 3: Phaeophyceae

Option 4: Chlorophyceae

Team Careers360 22nd Jan, 2024

Correct Answer: Chlorophyceae


Solution : The correct option is Chlorophyceae.

Green algae belong to the class Chlorophyceae. They lack some of the intricate structures present in actual plants, although they do share other traits with them, such as the existence of chlorophyll for photosynthesis. There are many different kinds of

69 Views

Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.

Primitive cultures are those that exist in societies that have not yet developed advanced technology or complex social (1)_________ These cultures are often characterised by their close relationship with the natural world. Despite being considered 'primitive', these cultures have a rich history and a unique way of life that is (2)___________ studying and preserving. These cultures often have a deep understanding of the environment and its cycles, and they have developed intricate systems of knowledge and belief that are closely tied to nature. For example, indigenous cultures in the Amazon rainforest have an (3)_____________ knowledge of the medicinal properties of plants and the cycles of the seasons, which they use to sustain themselves and their communities. Another important aspect is that these cultures often have complex systems of kinship and social hierarchy. Despite many challenges that primitive cultures face, including the (4)____________ of modern societies and environmental degradation, these cultures have an important role to play in our understanding of the human experience. They offer a different (5)____________ on the world and its complexities, and their traditions and knowledge have the potential to inform and enrich our modern lives.
Select the most appropriate option to fill in the blank 1.

Option 1: borders

Option 2: outlines

Option 3: structures

Option 4: configurations

Team Careers360 22nd Jan, 2024

Correct Answer: structures


Solution : The correct choice is the third option.

Explanation: In the context of discussing societies that have not yet developed advanced technology or complex social structures, the word "structures" makes logical sense. It refers to the organisation or arrangement of elements in a society.

The other

11 Views

Question : India won the Border-Gavaskar trophy in 2023 by defeating _____ and qualified for the World Test Championship Final.

Option 1: Sri Lanka

Option 2: New Zealand

Option 3: Australia

Option 4: South Africa

Team Careers360 25th Jan, 2024

Correct Answer: Australia


Solution : The correct option is Australia.

India emerged victorious in the Border-Gavaskar Trophy of the year 2023 by defeating Australia. The fourth and final test of the 2023 BGT between India and Australia ended in a draw. India clinched the series 2-1, marking their fourth

13 Views

Question : Which among the following lakes is also known as the "Srinagar's Jewel"?

Option 1: Tsomgo

Option 2: Vembanad

Option 3: Dal

Option 4: Loktak

Team Careers360 21st Jan, 2024

Correct Answer: Dal


Solution : The correct answer is Dal.

Dal is one of Srinagar's lakes. It's an urban lake, the second biggest in Jammu and Kashmir's Union territory. It is also known as the "Lake of Flowers," "Jewel in the Crown of Kashmir," or "Srinagar's Jewel."

142 Views

Question : The following bar graph shows the production of wheat (in 1000 tonnes) in India over the years.

What was the percentage decline in the production of wheat from 2013 to 2014?

Option 1: 25%

Option 2: 5%

Option 3: 15%

Option 4: 35%

Team Careers360 22nd Jan, 2024

Correct Answer: 25%


Solution : As per the graph,
The production of wheat in the year 2013 = 100 thousand tonnes/ years
The production of wheat in the year 2014 = 75 thousand tonnes/ years
The percentage decrease = $\frac{100-75}{100}× 100= 25\%$
Hence, the correct answer is 25%.

12 Views

Question : Harshavardhana (r. 606-647 CE) was a ruler of _____ dynasty.

Option 1: Mughal

Option 2: Maurya

Option 3: Gupta

Option 4: Pushyabhuti

Team Careers360 25th Jan, 2024

Correct Answer: Pushyabhuti


Solution : The correct answer is Pushyabhuti.

He belonged to the Vardhana dynasty, also known as the Pushyabhuti. At some point in the sixth and seventh centuries, the Pushyabhuti dynasty—also referred to as the Vardhana dynasty—ruled over northern India. From north and northwest India to the

18 Views

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

The terrorist made a vain attempt to __________ the bridge.

Option 1: Blow over

Option 2: Blow up

Option 3: Blow out

Option 4: Blow down

Team Careers360 22nd Jan, 2024

Correct Answer: Blow up


Solution : The second option is the correct answer as "blow up" means to destroy something using explosives, and it fits perfectly in the sentence conveying that the terrorist unsuccessfully tried to destroy the bridge using explosives.

The meanings of the other options are as follows:

9 Views

Question : If $2 \sin \theta+2 \sin ^2 \theta=2$, then the value of $2 \cos ^4 \theta+2 \cos ^2 \theta$ is:

Option 1: 4

Option 2: 2

Option 3: 1

Option 4: 0

Team Careers360 21st Jan, 2024

Correct Answer: 2


Solution : Given: $2 \sin \theta+2 \sin ^2 \theta=2$
⇒ $2\sin\theta + 2\sin^2\theta = 2(\sin^2\theta + \cos^2\theta)$
⇒ $2\sin\theta + 2\sin^2\theta = 2\sin^2\theta + 2\cos^2\theta$
⇒ $2\sin\theta = 2\cos^2\theta$
⇒ $\sin\theta = \cos^2\theta$
Putting the value in the given equation,
$2 \cos ^4 \theta+2 \cos ^2 \theta$

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