The Human Resource Development Ministry and the External Affairs Ministry launched an online verification portal to make the document verification process easier for students who planning to study abroad. The Central Board of Secondary Education’s (CBSE) academic repository of degrees and certificates “Parinam Manjusha” was also involved in the project of creating “eSanad”.

Indian Oil Corp (IOC) has overtaken Oil and Natural Gas Corp (ONGC) to become India’s most profitable state-owned company. IOC, which has for decades been India’s biggest company by turnover, posted a 70 per cent jump in net profit to Rs 19,106.40 crore in the financial year ended March 31, 2017.

Iconic attraction of India Taj Mahal has emerged as the 5th most popular landmark in the world and 2nd in Asia, according to the online travel portal TripAdvisor’s ‘Travellers’ Choice Awards for Landmarks. Globally, Angkor Wat in Cambodia, Sheikh Zayed Grand Mosque Center in Abu Dhabi, Mezquita Cathedral de Cordoba in Spain, and St Peter’s Basilica in Italy, bagged the first four ranks respectively. Whereas, the top 10 landmarks in Asia has been topped by Angkor Wat, followed by Taj Mahal on the second place. Apart from this, Taj Mahal has also ranked first in the list of popular landmarks in India, followed by AmberFort, Jaipur; Swaminarayan Akshardham, New Delhi, etc.

Let the smallest number be x.
Then larger number = (x + 1365)
x + 1365 = 6x + 15
= 5x = 1350
x = 270
Smaller number = 270.

x = √8 - √7 = 1/(√8 + √7) and y = √6 - √5 = 1/(√6 + √5) and z = √10 - 3 = 1/(√10 + 3)

As (√8 + √7) > (√6 + √5), (√8 - √7) < (√6 - √5)

As (√10 + 3) > (√8 + √7) > (√6 + √5)

z < x < y.

Milk = 3/5 x 20 = 12 liters, water = 8 liters

If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.

Remaining milk = 12 - 6 = 6 liters

Remaining water = 8 - 4 = 4 liters

10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.

The ratio of milk and water in the new mixture = 16:4 = 4:1

If the process is repeated one more time and 10 liters of the mixture are removed,
then amount of milk removed = 4/5 x 10 = 8 liters.

Amount of water removed = 2 liters.

Remaining milk = (16 - 8) = 8 liters.

Remaining water = (4 -2) = 2 liters.

Now 10 lts milk is added => total milk = 18 lts

The required ratio of milk and water in the final mixture obtained

= (8 + 10):2 = 18:2 = 9:1.