NMMS - National Means-cum-Merit Scholarship Mathematics: Data Handling and Geometry Questions and Answers — Questions and Answers
Question 1: The mean score of a student in 5 subjects is 80. When the score of a sixth subject is included, the new mean score becomes 82. What was the student's score in the sixth subject?
- 82
- 92 (Correct answer)
- 88
- 90
Correct answer: 92
The total score for the first 5 subjects is 5 * 80 = 400. The total score for all 6 subjects is 6 * 82 = 492. The score in the sixth subject is the difference between the new total and the old total: 492 - 400 = 92.
Question 2: A bag contains 5 red balls, 8 blue balls, and 7 green balls. If one ball is drawn at random, what is the probability that it is NOT a blue ball?
- 8/20
- 13/20
- 3/5 (Correct answer)
- 2/5
Correct answer: 3/5
The total number of balls is 5 + 8 + 7 = 20. The number of balls that are not blue (i.e., red or green) is 5 + 7 = 12. The probability of an event is the ratio of favorable outcomes to the total number of outcomes. Therefore, the probability of drawing a ball that is not blue is 12/20, which simplifies to 3/5.
Question 3: The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. What is the measure of the largest angle?
- 144° (Correct answer)
- 72°
- 108°
- 36°
Correct answer: 144°
The sum of the interior angles of any quadrilateral is 360°. Let the angles be x, 2x, 3x, and 4x based on the given ratio. Their sum is x + 2x + 3x + 4x = 10x. Setting this equal to 360°, we get 10x = 360°, which means x = 36°. The largest angle corresponds to the largest part of the ratio (4), so its measure is 4 * 36° = 144°.
Question 4: A circular garden has a circumference of 88 meters. What is the area of the garden? (Use π = 22/7)
- 154 m²
- 308 m²
- 1232 m²
- 616 m² (Correct answer)
Correct answer: 616 m²
First, find the radius (r) using the circumference formula, C = 2πr. Given C = 88 m, we have 88 = 2 * (22/7) * r, which simplifies to 88 = (44/7) * r. Solving for r gives r = (88 * 7) / 44 = 14 m. Now, calculate the area using the formula A = πr². So, A = (22/7) * (14)² = (22/7) * 196 = 616 square meters.
Question 5: A pie chart shows a family's monthly expenditure. If the family's total monthly income is ₹36,000 and the angle of the sector representing 'Rent' is 90°, how much does the family spend on rent?
- ₹6,000
- ₹12,000
- ₹9,000 (Correct answer)
- ₹18,000
Correct answer: ₹9,000
A complete circle in a pie chart represents 360°. The fraction of the total income spent on rent is the ratio of the sector's angle to the total angle, which is 90°/360° = 1/4. Therefore, the amount spent on rent is 1/4 of the total income, which is (1/4) * ₹36,000 = ₹9,000.
Question 6: A water tank is in the shape of a cuboid with length 5 m, width 2 m, and height 1.5 m. How many liters of water can it hold? (Given: 1 m³ = 1000 liters)
- 1,500 liters
- 15,000 liters (Correct answer)
- 8,500 liters
- 150 liters
Correct answer: 15,000 liters
First, calculate the volume of the cuboidal tank using the formula V = length × width × height. V = 5 m × 2 m × 1.5 m = 15 cubic meters (m³). Since 1 cubic meter is equivalent to 1000 liters, the capacity of the tank in liters is 15 × 1000 = 15,000 liters.
NMMS - National Means-cum-Merit Scholarship Mathematics: Data Handling and Geometry Questions and Answers
The mean score of a student in 5 subjects is 80.
When the score of a sixth subject is included, the new mean score becomes 82.
What was the student's score in the sixth subject?