Tales By Dots and Lines — Class 8 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Tales By Dots and Lines" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Tales By Dots and Lines" — 8 important questions with detailed answers for CBSE boa…
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NCERT Solutions for Class 8 Mathematics — Tales By Dots and Lines. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Tales By Dots and Lines — All 8 Questions Solved
Q1. The scores of 10 students in a test are: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. Find the mean score.
Step 1: Mean = Sum of all scores / Number of students
Step 2: Sum = 45 + 50 + 55 + 60 + 65 + 70 + 75 + 80 + 85 + 90 = 675
Step 3: Number of students = 10
Step 4: Mean = 675 / 10 = 67.5
Step 5: The mean score is 67.5
Q2. In a class, 60 students play cricket, 40 play football, and 20 play both. How many students play at least one sport?
Step 1: Using the principle: Total = Cricket + Football − Both
Step 2: Total = 60 + 40 − 20 = 80
Step 3: 80 students play at least one sport
Q3. A pie chart shows the distribution of 180 students into four streams: Science (90), Commerce (45), Humanities (36), and Vocational (9). What angle should be allocated to each stream?
Step 1: Angle = (Frequency / Total) × 360°
Step 2: Science: (90/180) × 360° = (1/2) × 360° = 180°
Step 3: Commerce: (45/180) × 360° = (1/4) × 360° = 90°
Step 4: Humanities: (36/180) × 360° = (1/5) × 360° = 72°
Step 5: Vocational: (9/180) × 360° = (1/20) × 360° = 18°
Step 6: Total: 180° + 90° + 72° + 18° = 360° ✓
Q4. From a bag containing 5 red balls and 3 blue balls, what is the probability of drawing a red ball?
Step 1: Probability = Favorable outcomes / Total possible outcomes
Step 2: Total balls = 5 + 3 = 8
Step 3: Favorable outcomes (red balls) = 5
Step 4: Probability of drawing red ball = 5/8
Q5. A coin is tossed. What is the probability of getting heads?
Step 1: A coin has two equally likely outcomes: heads or tails.
Step 2: Favorable outcomes (heads) = 1
Step 3: Total possible outcomes = 2
Step 4: Probability of heads = 1/2 = 0.5
Q6. The marks of 8 students are 35, 42, 55, 60, 68, 72, 85, 90. Find the median.
Step 1: Arrange in ascending order (already arranged):
35, 42, 55, 60, 68, 72, 85, 90
Step 2: Number of values = 8 (even)
Step 3: Median = (Middle two values) / 2 = (60 + 68) / 2
Step 4: Median = 128 / 2 = 64
Q7. If a die is rolled, what is the probability of getting an even number?
Step 1: A die has 6 faces numbered 1, 2, 3, 4, 5, 6.
Step 2: Even numbers on a die = 2, 4, 6
Step 3: Favorable outcomes = 3
Step 4: Total possible outcomes = 6
Step 5: Probability = 3/6 = 1/2
Q8. A bar graph shows rainfall (in mm) for 5 months: Jan = 50, Feb = 60, Mar = 80, Apr = 100, May = 120. What is the average rainfall?
Step 1: Average = Sum of rainfall / Number of months
Step 2: Sum = 50 + 60 + 80 + 100 + 120 = 410 mm
Step 3: Number of months = 5
Step 4: Average = 410 / 5 = 82 mm
Tales By Dots and Lines — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. What is a fundamental concept in geometry that represents an exact location and has no dimension?
- A. Line
- B. Ray
- C. Point
- D. Segment
Answer: C. Point — A point is a basic unit in geometry, indicating a specific position without any length, width, or depth.
MCQ 2. How many distinct straight lines can pass through two given distinct points?
- A. Zero
- B. One
- C. Two
- D. Infinitely many
Answer: B. One — Through any two distinct points in a plane, there is exactly one unique straight line that can be drawn.
MCQ 3. An angle that measures exactly 90 degrees is called a/an ________ angle.
- A. Acute
- B. Obtuse
- C. Right
- D. Straight
Answer: C. Right — A right angle is defined as an angle that measures exactly 90 degrees.
MCQ 4. If two angles are complementary, their sum is always equal to:
- A. 90 degrees
- B. 180 degrees
- C. 360 degrees
- D. 0 degrees
Answer: A. 90 degrees — Complementary angles are two angles whose sum is 90 degrees.
MCQ 5. What is the supplement of an angle measuring 75 degrees?
- A. 15 degrees
- B. 105 degrees
- C. 285 degrees
- D. 75 degrees
Answer: B. 105 degrees — Supplementary angles add up to 180 degrees. So, 180 - 75 = 105 degrees.
MCQ 6. A simple closed figure made up entirely of line segments is called a:
- A. Circle
- B. Oval
- C. Polygon
- D. Curve
Answer: C. Polygon — A polygon is a closed figure formed by three or more line segments.
MCQ 7. What is the sum of the measures of the exterior angles of any convex polygon?
- A. 90 degrees
- B. 180 degrees
- C. 360 degrees
- D. (n-2) * 180 degrees
Answer: C. 360 degrees — The sum of the measures of the exterior angles of any convex polygon, taken one at each vertex, is always 360 degrees.
MCQ 8. When two parallel lines are intersected by a transversal, which pair of angles are always equal?
- A. Consecutive interior angles
- B. Alternate interior angles
- C. Interior angles on the same side
- D. Supplementary angles
Answer: B. Alternate interior angles — When parallel lines are cut by a transversal, alternate interior angles are equal.
MCQ 9. If the sum of the interior angles of a polygon is 1080 degrees, how many sides does the polygon have?
- A. 6
- B. 7
- C. 8
- D. 9
Answer: C. 8 — The sum of interior angles of an n-sided polygon is given by (n-2) * 180 degrees. So, (n-2) * 180 = 1080, which means n-2 = 6, and n = 8.
MCQ 10. If two straight lines intersect, and one of the angles formed is 45 degrees, what is the measure of its vertically opposite angle?
- A. 45 degrees
- B. 135 degrees
- C. 90 degrees
- D. 180 degrees
Answer: A. 45 degrees — Vertically opposite angles formed by the intersection of two lines are always equal.
MCQ 11. A part of a line with one endpoint and extending infinitely in one direction is called a:
- A. Line segment
- B. Line
- C. Ray
- D. Plane
Answer: C. Ray — A ray has a starting point (endpoint) and extends infinitely in one direction.
MCQ 12. How many diagonals does a hexagon have?
- A. 6
- B. 7
- C. 8
- D. 9
Answer: D. 9 — The number of diagonals in an n-sided polygon is given by n(n-3)/2. For a hexagon, n=6, so 6(6-3)/2 = 6*3/2 = 9.
MCQ 13. An angle measuring 180 degrees is known as a ________ angle.
- A. Acute
- B. Obtuse
- C. Right
- D. Straight
Answer: D. Straight — A straight angle measures exactly 180 degrees and forms a straight line.
MCQ 14. What is the order of rotational symmetry for a square?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: D. 4 — A square can be rotated by 90, 180, 270, and 360 degrees and still look the same, meaning it has an order of rotational symmetry of 4.
MCQ 15. What is the measure of each interior angle of a regular octagon?
- A. 108 degrees
- B. 120 degrees
- C. 135 degrees
- D. 144 degrees
Answer: C. 135 degrees — The sum of interior angles of an octagon (n=8) is (8-2)*180 = 1080 degrees. Since it's regular, each interior angle is 1080/8 = 135 degrees.
MCQ 16. In which quadrant does the point (-3, 5) lie?
- A. First Quadrant
- B. Second Quadrant
- C. Third Quadrant
- D. Fourth Quadrant
Answer: B. Second Quadrant — In the Cartesian coordinate system, points with a negative x-coordinate and a positive y-coordinate lie in the Second Quadrant.
MCQ 17. A figure has line symmetry if it can be folded along a line such that both halves match exactly. This line is called the:
- A. Diagonal
- B. Axis of rotation
- C. Line of symmetry
- D. Transversal
Answer: C. Line of symmetry — The line along which a figure can be folded to produce two identical halves is known as the line of symmetry or axis of symmetry.
MCQ 18. If two angles form a linear pair and one angle is 60 degrees, what is the measure of the other angle?
- A. 30 degrees
- B. 120 degrees
- C. 180 degrees
- D. 60 degrees
Answer: B. 120 degrees — Angles in a linear pair are supplementary, meaning their sum is 180 degrees. So, 180 - 60 = 120 degrees.
MCQ 19. In a triangle, one angle is 40 degrees. The other two angles are in the ratio 2:3. What is the measure of the largest angle in the triangle?
- A. 40 degrees
- B. 56 degrees
- C. 84 degrees
- D. 90 degrees
Answer: C. 84 degrees — The sum of angles in a triangle is 180 degrees. The remaining sum is 180 - 40 = 140 degrees. The two angles are 2x and 3x, so 2x + 3x = 140 => 5x = 140 => x = 28. The angles are 2*28 = 56 degrees and 3*28 = 84 degrees. The angles in the triangle are 40, 56, 84 degrees. The largest is 84 degrees.
MCQ 20. A point whose x-coordinate is zero and y-coordinate is non-zero will lie on which axis?
- A. X-axis
- B. Y-axis
- C. Origin
- D. Quadrant I
Answer: B. Y-axis — Any point with an x-coordinate of zero (e.g., (0, y)) lies on the Y-axis.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.