What should come in place of the question mark (?) in the following mathematical statement?
$${{?^6÷16=108}}$$

AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62⁰, then find the measure of the minor arc AC.

Directions: The pie– chart shows the proposed outlay for different sectors during a Five–Year plan of Government of India. Total outlay is Rs. 40,000 crores. By reading the pie–chart answer the following three questions.

What is the proposed outlay for Education? 

If x = a secθ cos∅, y = b secθ sin∅, z=c tanθ, then the value of $$ {x^2\over a^2}+{y^2\over b^2}-{z^2\over c^2} $$

A and B enter into a partnership with capital in the ratio 5: 6. After 4 months, A withdraws $$1\over 5$$of his capital, while B increases his capital by $$33{1\over 3}\%$$. What is the share (in ₹ lakhs) of B in the annual profit of ₹6.3 lakhs?

In a triangle, two sides of 4 cm and 3 cm are at right angle. If the triangle is revolved along the 4 cm side, the curved surface area of the cone so formed will be

Directions: Read the following data carefully and answer the questions given below:

There are 6300 students in Manipur University in the academic year 2020. The ratio of the boys to the girls in the University is 5 : 4. All the students are enrolled in different indoor activities (Chess, Carom, Debating, Painting, and Quiz) and one student is enrolled in only one indoor activity. The number of boys enrolled in the Painting is 621. The ratio of the number of boys who enrolled in Chess to the number of boys who enrolled in Carom is 5 : 3. 36% of the students are enrolled in Quiz. The number of boys enrolled in Debating is 25% of the total number of boys. The number of girls enrolled in Quiz is 640 which is 150 less than the number of girls enrolled in Carom. The number of girls enrolled in Chess is 186 more than the number of boys enrolled in the same activity. The total number of students enrolled in Painting is 816.

Find the ratio of the number of boys enrolled in Carom to the number of girls enrolled in the same

The average of twenty-five numbers is 54. The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2, respectively. If the 13th number is excluded, then what is the average of the remaining numbers (correct to one decimal place)?