Which of the following cannot be determined graphically for a grouped frequency distribution? (a) Median (b) Mode (c) Quartiles (d) Mean

Naveen deposits ₹800 every month in a recurring deposit account for 6 months. If he receives ₹4884 at the time of maturity, then the interest he earns is: (a) ₹84 (b) ₹42 (c) ₹24 (d) ₹284

The volume of a cylinder of height 3 cm is 48π cm3. The radius of the cylinder is: (a) 48 cm (b) 16 cm (c) 4 cm (d) 24 cm

The solution set for the inequation 2x + 4 ≤ 14, x ∈ W is: (a) {1, 2, 3, 4, 5} (b) {0, 1, 2, 3, 4, 5} (c) {1, 2, 3, 4} (d) {0, 1, 2, 3, 4}

What number must be added to each of the numbers 4, 6, 8 and 11 so that the resulting four numbers are in proportion?

A bag contains 25 cards numbered from 1 to 25. A card is drawn at random. Find the probability that the number on the card drawn is: (a) a multiple of 5 (b) a perfect square (c) a prime number.

The following distribution gives the daily wages of 60 workers of a factory: Daily income (₹) Number of workers 200–300 6 300–400 10 400–500 14 500–600 16 600–700 10 700–800 4 Use graph paper. Take 2 cm = ₹100 along one axis and 2 cm = 2 workers along the other axis. Draw a histogram and hence find the mode of the distribution.

Find the value of ‘a’ if x − a is a factor of the polynomial 3x3 + x2 − ax − 81.

Use graph paper to answer this question. During a medical check-up of 60 students in a school, their weights were recorded as follows: Weight (kg) Number of students 28–30 2 30–32 4 32–34 10 34–36 13 36–38 15 38–40 9 40–42 5 42–44 2 Taking 2 cm = 2 kg along one axis and 2 cm = 10 students along the other axis, draw an ogive. Use the graph to find: (a) the median (b) the upper quartile (c) the number of students whose weight is above 37 kg.

From the top of a tower 100 m high, a man observes the angles of depression of two ships A and B on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line, find the distance between ships A and B to the nearest metre. Use mathematical tables.

Using componendo and dividendo, solve for x: = 3

Using ruler and compass, construct a triangle ABC in which AB = 6 cm, ∠BAC = 120° and AC = 5 cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle.