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HOTs for Maths Olympiad - 3 - Class 10 MCQ


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10 Questions MCQ Test Olympiad Preparation for Class 10 - HOTs for Maths Olympiad - 3

HOTs for Maths Olympiad - 3 for Class 10 2024 is part of Olympiad Preparation for Class 10 preparation. The HOTs for Maths Olympiad - 3 questions and answers have been prepared according to the Class 10 exam syllabus.The HOTs for Maths Olympiad - 3 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for HOTs for Maths Olympiad - 3 below.
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HOTs for Maths Olympiad - 3 - Question 1

Read the given statements and select the incorrect option.

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 1

The quadratic equation x2 - 2x - 3 = 0 has discriminant A = (-2)2 -4 × 1 × (-3) = 4 + 12 = 16. Since Δ>0, the roots are real and distinct, not equal.

HOTs for Maths Olympiad - 3 - Question 2

Read the given statements and select the incorrect option.

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 2

The product of two irrational numbers can be rational (e.g.,√2 ​ × √2 ​ = 2).

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HOTs for Maths Olympiad - 3 - Question 3

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

(i) The sum of the interior angles of a triangle is 180 degrees.
(ii) The area of a triangle with base b and height h is given by 1/2bh.
(iii) The perimeter of an equilateral triangle with side length s is 3s

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 3

(i) The sum of the interior angles of any triangle is always 180 degrees. True.
(ii) The area of a triangle with base b and height h is given by 1/2 bh. True.
(iii) The perimeter of an equilateral triangle with side length s is 3s. True.

HOTs for Maths Olympiad - 3 - Question 4

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

(i) The circumference of a circle with radius r is 2πr.
(ii) The area of a circle with diameter d is πd2.
(iii) The volume of a sphere with radius r is 4/3 πr3.

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 4

(i) The circumference of a circle with radius r is 2πr. True.
(ii) The area of a circle with diameter d is π(d/2)2 = πd2/4 , not πd2 . False.
(iii) The volume of a sphere with radius r is 4/3 πr3.True.

HOTs for Maths Olympiad - 3 - Question 5

Fill in the blanks and select the correct option.

(i) If the roots of the quadratic equation x2 - 7x + k = 0 are equal, then the value of k is P.
(ii) If one of the roots of the quadratic equation x2 + kx + 12 = 0 is 3, then the value of k is Q.

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 5

HOTs for Maths Olympiad - 3 - Question 6

Fill in the blanks and select the correct option.

(i) The sum of the roots of the quadratic equation ax2 + bx + c = 0 is -b/a. For the equation  2x2 - 4x + 2 = 0, the sum of the roots is P.
(ii) The product of the roots of the same equation is Q.

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 6

(i) The sum of the roots is given by -b/a. Here, a = 2, b = -4, so the sum is -(-4)/2 = 4/2 = 2.
(ii) The product of the roots is given by c/a. Here, c = 2, a = 2, so the product is 2/2 = 1.

HOTs for Maths Olympiad - 3 - Question 7

Read the following statements and select the correct option.

Statement-I: The sum of the roots of the quadratic equation ax2 + bx + c = 0 is -b/a
Statement-II: The product of the roots of the quadratic equation ax2 + bx + c = 0 is c/a

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 7

For a quadratic equation ax2 + bx + c = 0, the sum of the roots is given by-b/a and the product of the roots is given by c/a. Therefore, both statements are true.

HOTs for Maths Olympiad - 3 - Question 8

Read the following statements and select the correct option.

Statement-I: The value of logb,(mn) is logb, m + logb, n.

Statement-Il: The value of logb (m/n) is logb m - logb, n.

HOTs for Maths Olympiad - 3 - Question 9

Solve the following and select the correct option.

(i) If the sum of the squares of two consecutive positive integers is 365, find the integers.
(ii) If the length of the diagonal of a square is 8√2 cm, find the side length of the square.

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 9

HOTs for Maths Olympiad - 3 - Question 10

Solve the following and select the correct option.

(i) Find the sum of the first 20 terms of the arithmetic sequence where the first term is 7 and the common difference is 3.

(ii) If a solid sphere is melted and recast into 8 smaller spheres of equal size, each having a radius 1/2 of the original, find the ratio of the surface area of one of the smaller spheres to that of the original sphere.

Detailed Solution for HOTs for Maths Olympiad - 3 - Question 10


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