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CBSE Class 8  >  Class 8 Test  >  Mathematical Olympiad   >  Olympiad Test: Achieves Section-4 - Class 8 MCQ

Olympiad Test: Achieves Section-4 - Free MCQ with solutions Class 8 Mathematical


MCQ Practice Test & Solutions: Olympiad Test: Achieves Section-4 (10 Questions)

You can prepare effectively for Class 8 Mathematical Olympiad Class 8 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Olympiad Test: Achieves Section-4". These 10 questions have been designed by the experts with the latest curriculum of Class 8 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 10

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Olympiad Test: Achieves Section-4 - Question 1
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Match the following:

Detailed Solution: Question 1

  • (P) The Curved Surface Area (C.S.A.) of a cylinder is 2πrh.
  • (Q) The Curved Surface Area (C.S.A.) of a cube is 4 × Side2.
  • (R) The volume of a cylinder is πr2h.
  • (S) The volume of a cube is Side3.

Olympiad Test: Achieves Section-4 - Question 2
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Detailed Solution: Question 2

  • (P) The perimeter of a square is 4 × Side.
  • (Q) The area of a rectangle is l × b.
  • (R) The circumference of a circle is 2πr.
  • (S) The perimeter of a rectangle is 2(l + b).

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Olympiad Test: Achieves Section-4 - Question 3
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Detailed Solution: Question 3

  • (P) The area of a triangle is 1/2 × Base × Height.
  • (Q) The area of a parallelogram is Base × Height.
  • (R) The area of a trapezium is 1/2 × (Base1 + Base2) × Height.
  • (S) The area of a rhombus is 1/2 × Diagonal1 × Diagonal2​.

Olympiad Test: Achieves Section-4 - Question 4
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Detailed Solution: Question 4

  • (P) The total surface area of a cube is 6a2.
  • (Q) The total surface area of a cylinder is 2πrh + 2πr2 = 2πr(h + r).
  • (R) The volume of a sphere is 4/3​πr3.
  • (S) The surface area of a sphere is 4πr2.

Olympiad Test: Achieves Section-4 - Question 5
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Detailed Solution: Question 5

  • (P) The sum of the interior angles of a triangle is 180∘.
  • (Q) The sum of the exterior angles of any polygon is 360∘.
  • (R) The sum of the interior angles of a pentagon is 540∘.
  • (S) The sum of the interior angles of a hexagon is 720∘.

Olympiad Test: Achieves Section-4 - Question 6
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A man can row upstream at 5 km/hr and downstream at 9 km/hr. Find the speed of the man in still water and the speed of the stream.

Detailed Solution: Question 6

Let the speed of the man in still water be x km/hr and the speed of the stream be y km/hr.
Upstream speed =  x − y = 5 km/hr
Downstream speed = x + y = 9 km/hr
Adding the two equations:
(x − y) + (x + y) = 5 + 9
2x = 14
x =7km/hr
Subtracting the two equations:
(x + y) − (x − y) = 9 − 5
2y = 4
y = 2km/hr

Olympiad Test: Achieves Section-4 - 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: 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-4 - 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.
(i) (ii) (iii)

Detailed Solution: 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-4 - 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: 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-4 - 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.
(i) (ii) (iii)

Detailed Solution: 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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About this Class 8 Practice Test

This test contains 10 MCQs on Olympiad Test: Achieves Section-4 with detailed solutions for each question. It is part of the Mathematical Olympiad Class 8 course on EduRev, designed to align with the current Class 8 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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