HOTs for Maths Olympiad - 5 - Class 10 MCQ

Read the following statements carefully and state ‘T’ for true and ‘F’ for false.

(i) The derivative of 
(ii) The integral of 
(iii) The second derivative of 

Fill in the blanks and select the correct option.

(i) The area of a triangle with vertices at (1,2), (4, 6), and (5, 8) is P.
(ii) The length of the median to the side joining (4,6) and (5, 8) is Q.

Fill in the blanks and select the correct option.

(i) The distance between the points (x₁, y₁) and (x₂, y₂) is given by
 and (x₂, y₂) = (4, 6), the distance is P.
(ii) The midpoint of the same points is Q.

Read the following statements and select the correct option.

Statement-I: The perimeter of a rectangle is given by 2 (l + b), where l is the length and b is the breadth.

Statement-II: The area of a rectangle is given by 2lb, where l is the length and b is the breadth.

Read the following statements and select the correct option.

Statement-I: The roots of the equation x² + 4x + 4 = 0, are real and equal.
Statement-II: The discriminant of the quadratic equation ax² + bx  + c = 0 is b² - 4ac

Solve the following and select the correct option.

(i) If the roots of the quadratic equation ax² + bx + c = 0 are in the ratio 3:5, find the value of b²/ac
(ii) If the sum of the first 10 terms of an arithmetic progression is 155, find the first term given that the common difference is 2.

Solve the following and select the correct option.

(i) If a = 3 and b = 4, find the value of 
(ii) The hypotenuse of a right-angled triangle is 13 cm, and one of its legs is 5 cm.

Find the other leg.