In an exam, 3 marks are scored on the correct solution, but 2 marks are deducted on the wrong solution. If a student scores 75 questions and gets 75 marks, the correct answer is the number of questions.

In ΔPQR, PQ=QR and O is an interior point of ΔPQR such that ∠OPR=∠ORP.

Consider the following statements:

(i) ΔPOR is an isosceles triangle.

(ii) O is the centroid of ΔPQR.

(iii) ΔPQO is congruent to ΔRQO.

Which of the above statements are correct?

If the height and the radius of the base of a cone are both doubled, the volume of the cone becomes _______ of its previous volume.

What is the greatest common factor of 2³ × 7² and 2⁵ × 3¹?

The third proportional of two numbers 9 and  24 is

3x² = 36 then what is the value of x?

Find the standard deviation of the following data (rounded off to two decimal places). 5, 3, 4, 7 

A person lent Rs. 8000 partly at the rate of 5% and partly at the rate of 6% per annum simple interest. The total interest after 2 years is Rs. 820 then in which ratio will Rs. 8000 is to be divided?