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UP Board Class 10 Rational Numbers & Playing with Numbers — practice questions

Explore 4 free Rational Numbers & Playing with Numbers questions in UP Board Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Rational Numbers & Playing with Numbers questions and exercises with answers

Showing questions 1–4 of 4.

The sum of three consecutive multiples of 11 is 363. What is the largest of these three multiples?Read the answer and worked solution →Two angles of a triangle are equal, and the third angle is greater than each of them by 30°. What are the three angles of the triangle?Read the answer and worked solution →The sum of three consecutive multiples of 11 is 363. What is the largest of these three multiples?Read the answer and worked solution →Two angles of a triangle are equal, and the third angle is greater than each of them by 30°. What are the three angles of the triangle?Read the answer and worked solution →

Worked practice questions

The sum of three consecutive multiples of 11 is 363. What is the largest of these three multiples?

  1. 121
  2. 132
  3. 143
  4. 154
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Correct answer: B. 132

Let the three consecutive multiples of 11 be 11n, 11(n+1), 11(n+2). Their sum is 11(3n + 3) = 33(n + 1). Setting 33(n+1) = 363 gives n + 1 = 11, so n = 10. The three multiples are 110, 121, 132, and the largest is 132. Distractor 143 belongs to the next set (121+132+143 = 396), and 121 is the middle multiple, not the largest.

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Two angles of a triangle are equal, and the third angle is greater than each of them by 30°. What are the three angles of the triangle?

  1. 40°, 40°, 100°
  2. 50°, 50°, 80°
  3. 60°, 60°, 60°
  4. 45°, 45°, 90°
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Correct answer: B. 50°, 50°, 80°

Let each of the two equal angles be x°. The third angle is (x + 30)°. **By the angle sum property:** x + x + (x + 30) = 180, so 3x = 150 and x = 50. The angles are 50°, 50°, 80°. The 80° angle is exactly 30° more than 50°, as required. Distractor 40°,40°,100° sums to 180° but the difference between 100 and 40 is 60, not 30.

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The sum of three consecutive multiples of 11 is 363. What is the largest of these three multiples?

  1. 121
  2. 132
  3. 143
  4. 154
Show answer and solution

Correct answer: B. 132

Let the three consecutive multiples of 11 be 11n, 11(n+1), 11(n+2). Their sum is 11(3n + 3) = 33(n + 1). Setting 33(n+1) = 363 gives n + 1 = 11, so n = 10. The three multiples are 110, 121, 132, and the largest is 132. Distractor 143 belongs to the next set (121+132+143 = 396), and 121 is the middle multiple, not the largest.

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More Mathematics topics

Arithmetic ProgressionReal Numbers and PolynomialsStatistics and ProbabilityMensuration: Surface Areas & VolumesIntroduction to TrigonometryAlgebra: Simultaneous Linear Equations & QuadraticsTriangles and CirclesCoordinate Geometry