Atul Dixit, Professor of Mathematics at IIT Gandhinagar has been honored with which prestigious award in the United States?

In the following question, select the related word from the given alternatives.
Spring: Summer :: ?

Direction: In the following question, select the related letters from the given alternatives. 

DRIVEN: EIDRVN:: BEGUMF: ?

Find the value tanθ-cosθ in the given figure.

Direction:  In the following passage, there are blanks each of which has been numbered. Five words/ phrases have been suggested, one of which fills the blanks appropriately.

Jerimoth Hill (812 ft, 247 m) is the highest point in the U.S. state of Rhode Island. (1) town of Foster near Providence, the site is used as an observatory. It is also a (2) highpointers, and prior to 2005 was known for being difficult to access due to a local landowner who prohibited entry. The hill is located on Route 101 in Foster, a half mile from the Connecticut line. To (3), for which there is a sign, there is a .3-mile (480 m) long trail that has a mere 10-foot (3.0 m) elevation gain. The mountain is 812 feet (247 m) high and is located 15 miles (24 km) west of Providence, Rhode Island, and 35 miles (56 km) east of Willimantic, Connecticut. The high point was donated to Brown University by Walter Raymond Turner, a Brown alumnus of the class of 1911. In 1938 (4) saltbox house to the west and the surrounding 360 acres (150 ha). Turner provided a right of way, straight north from the high point to Route 101, though eventually (5).

Find out the appropriate word for blank 4.

A man had a certain amount with him. He spent 20% of that to buy an article and 5% of the remaining on transport. Then he gifted ₹ 120. If he is left with ₹ 1,400, the amount he spent on transport is: 

Vedantam Satyanarayana is considered the best master of which dance?