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Class 8 Exam  >  Class 8 Tests  >  Mathematical Olympiad Class 8  >  Olympiad Test: Achieves Section-3 - Class 8 MCQ

Olympiad Test: Achieves Section-3 - Class 8 MCQ


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10 Questions MCQ Test Mathematical Olympiad Class 8 - Olympiad Test: Achieves Section-3

Olympiad Test: Achieves Section-3 for Class 8 2024 is part of Mathematical Olympiad Class 8 preparation. The Olympiad Test: Achieves Section-3 questions and answers have been prepared according to the Class 8 exam syllabus.The Olympiad Test: Achieves Section-3 MCQs are made for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Achieves Section-3 below.
Solutions of Olympiad Test: Achieves Section-3 questions in English are available as part of our Mathematical Olympiad Class 8 for Class 8 & Olympiad Test: Achieves Section-3 solutions in Hindi for Mathematical Olympiad Class 8 course. Download more important topics, notes, lectures and mock test series for Class 8 Exam by signing up for free. Attempt Olympiad Test: Achieves Section-3 | 10 questions in 20 minutes | Mock test for Class 8 preparation | Free important questions MCQ to study Mathematical Olympiad Class 8 for Class 8 Exam | Download free PDF with solutions
Olympiad Test: Achieves Section-3 - Question 1
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Read the given statements carefully and select the correct option.
Statement-1: The sum of the interior angles of a polygon is always greater than the sum of its exterior angles.
Statement-2: For any triangle, the sum of its exterior angles is always 360 degrees.

Detailed Solution for Olympiad Test: Achieves Section-3 - Question 1
The sum of the interior angles of a polygon is not always greater than the sum of its exterior angles, as the sum of exterior angles is always 360 degrees for any polygon. However, for any triangle, the sum of its exterior angles is indeed always 360 degrees.
Olympiad Test: Achieves Section-3 - Question 2
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Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The probability of getting a head when tossing a fair coin is 1/2.
(ii) The probability of getting a 5 when rolling a fair six-sided die is 1/6.
(iii) The sum of probabilities of all possible outcomes in a random experiment is always 1.

Detailed Solution for Olympiad Test: Achieves Section-3 - Question 2

(i) The probability of getting a head when tossing a fair coin is 1/2, which is correct.
(ii) The probability of getting a 5 when rolling a fair six-sided die is 1/6, which is also correct.
(iii) The sum of probabilities of all possible outcomes in a random experiment is always 1, which is correct.

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Olympiad Test: Achieves Section-3 - Question 3
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Read the given statements carefully and select the correct option.
Statement-1: If the length and breadth of a rectangle are increased by 20%, the area of the rectangle is increased by 44%.
Statement-2: The diagonal of a square with side length 'a' is given by a√2.

Detailed Solution for Olympiad Test: Achieves Section-3 - Question 3
If the length and breadth of a rectangle are each increased by 20%, the new area becomes 1.2 * 1.2 = 1.44 times the original area, which is a 44% increase. The diagonal of a square with side length 'a' is indeed given by a√2, so Statement-2 is true.
Olympiad Test: Achieves Section-3 - Question 4
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Read the given statements carefully and select the correct option.
Statement-1: In any parallelogram, the diagonals bisect each other.
Statement-2: The diagonals of a rhombus are equal in length.
Detailed Solution for Olympiad Test: Achieves Section-3 - Question 4
In any parallelogram, the diagonals do bisect each other, so Statement-1 is true. However, the diagonals of a rhombus are not equal in length; they are only equal in a square, so Statement-2 is false.
Olympiad Test: Achieves Section-3 - Question 5
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Read the given statements carefully and select the correct option.
Statement-1: If the sides of a triangle are in the ratio 3:4:5, then the triangle is a right-angled triangle.
Statement-2: The area of an equilateral triangle with side length 'a' is (√3/4)a².
Detailed Solution for Olympiad Test: Achieves Section-3 - Question 5
If the sides of a triangle are in the ratio 3:4:5, it is a right-angled triangle by the Pythagorean theorem. The area of an equilateral triangle with side length 'a' is indeed (√3/4)a². Hence, both statements are true.
Olympiad Test: Achieves Section-3 - Question 6
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Read the given statements carefully and select the correct option.
Statement-1: The number of diagonals in a polygon with 'n' sides is given by n(n-3)/2.
Statement-2: A regular hexagon can be divided into 6 equilateral triangles.
Detailed Solution for Olympiad Test: Achieves Section-3 - Question 6
The formula for the number of diagonals in a polygon with 'n' sides is n(n-3)/2. A regular hexagon can be divided into 6 equilateral triangles. Thus, both statements are true.
Olympiad Test: Achieves Section-3 - Question 7
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Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The volume of a sphere is given by the formula (4/3)πr³.
(ii) If the radius of a sphere is doubled, the volume becomes eight times.
(iii) The surface area of a sphere is given by 4πr².
Detailed Solution for Olympiad Test: Achieves Section-3 - Question 7

(i) The volume of a sphere is indeed given by the formula (4/3)πr³, which is correct.
(ii) If the radius of a sphere is doubled, the volume becomes (2r)³ = 8r³, making it eight times the original volume, which is also correct.
(iii) The surface area of a sphere is given by 4πr², which is correct.

Olympiad Test: Achieves Section-3 - Question 8
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Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The determinant of a 2x2 matrix [a b; c d] is ad - bc.
(ii) The inverse of a non-singular matrix always exists.
(iii) If a matrix is singular, its determinant is zero.
Detailed Solution for Olympiad Test: Achieves Section-3 - Question 8

(i) The determinant of a 2x2 matrix [a b; c d] is indeed ad - bc, which is correct.
(ii) The inverse of a non-singular matrix (a matrix with a non-zero determinant) always exists, which is also correct.
(iii) If a matrix is singular, its determinant is zero, which is correct.

Olympiad Test: Achieves Section-3 - Question 9
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Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The roots of the quadratic equation ax² + bx + c = 0 are given by (-b ± √(b²-4ac)) / 2a.
(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac.
(iii) If the discriminant is negative, the quadratic equation has two real and distinct roots.
Detailed Solution for Olympiad Test: Achieves Section-3 - Question 9

(i) The roots of the quadratic equation ax² + bx + c = 0 are indeed given by (-b ± √(b²-4ac)) / 2a, which is correct.
(ii) The discriminant of the quadratic equation ax² + bx + c = 0 is b² - 4ac, which is also correct.
(iii) If the discriminant is negative, the quadratic equation has two complex conjugate roots, not two real and distinct roots, which makes this statement false.

Olympiad Test: Achieves Section-3 - Question 10
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Read the given statements carefully and state 'T' for true and 'F' for false.
(i) The sum of the first n natural numbers is given by n(n+1)/2.
(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6.
(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)².
Detailed Solution for Olympiad Test: Achieves Section-3 - Question 10

(i) The sum of the first n natural numbers is indeed given by n(n+1)/2, which is correct.
(ii) The sum of the squares of the first n natural numbers is given by n(n+1)(2n+1)/6, which is also correct.
(iii) The sum of the cubes of the first n natural numbers is given by (n(n+1)/2)², which is correct.

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