Exams

Allotropes are the different physical forms of an element. Here in the given options, diamond and graphite are the pair of allotropes of carbon.

Some more examples are Molecular oxygen and ozone are pair of allotropes, Black and red phosphorous are also pairs of allotropes.

Total number of possible ways = 

9C5 = 9 x 8 x 7 x 6 x 55 x 4 x 3 x 2 x 1 = 126

Number of favorable cases = 

$$\begin{gathered} 4C2 x 5C3 + 4C3 x 5C2 + 4C4 x 5C1 \\ 4 x 32 x 1 x 5 x 4 x 33 x 2 x 1 + 4 x 3 x 23 x 2 x 1 x 5 x 4 2 x 1 + 1 x 5 \\ = 6 x 10 + 4 x 10 + 5 \\ = 60 + 40 + 5 \\ = 105 \end{gathered}$$

Therefore, required probability = 105/126 = 5/6

Mumbai Indians

As you were asleep, none of the things could have happened without doing "open your eyes" first.

Ramdev promoted Patanjali Ayurveda and Reliance Jio have featured among the top 10 most influential brand in India, according to a study by the global research firm Ipsos.

Home grown Patanjali and Mukesh Ambani’s controlled Reliance Jio have bagged the fourth and ninth position, respectively. Interestingly, Patanjali and Reliance Jio made an impressive entry as they did not figure in the previous edition of the study.

Besides, Google has been ranked at the top slot while Microsoft and Facebook were ranked at number two and three, respectively. State Bank of India (SBI) being the only financial institution that made to the list, moved up four ranks to take the fifth position. E-commerce player Flipkart dropped three spots to take the tenth place while Amazon climbed couple of steps to take the sixth place. Other companies that made to the list include Samsung (7th) and Airtel (8th).

Let number of boys = B

Number of girls = G

From the given data,

1B/3 + 1G/2 = 300

But given B/3 = 100

=> B = 300

G/2 = 300 - 100

G = 200 x 2

=> G = 400

Therefore, total number of students in the college = B + G = 700.

From the given series of numbers, if half of the second highest number is subtracted from the third highest number, what will be the value ?

Now arranging the given numbers in descending order.
837 746 519 495 328

519 - 746/2 = 519 - 373 = 146.