Mathematics: Data Handling and Geometry Flashcards

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?

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.

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?

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.

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. What is the measure of the largest angle?

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°.

A circular garden has a circumference of 88 meters. What is the area of the garden? (Use π = 22/7)

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.

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?

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.

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)

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.