A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
Without solving the following quadratic equation, find the value of ‘p' for which the given equation has real and equal roots:
x2 + (p – 3)x + p = 0.
In the figure alongside, OAB is a quadrant of a circle. The radius OA = 3.5 cm and OD = 2 cm. Calculate the area of the shaded portion. (Take ).
A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball, find the number of black balls in the box.
Find the mean of the following distribution by step deviation method:
Class Interval | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
Frequency | 10 | 6 | 8 | 12 | 5 | 9 |
Using a ruler and compasses only:
(i) Construct a triangle ABC with the following data:
AB = 3.5 cm, BC = 6 cm and ABC = 120
(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
(iii) Measure BCP.
The marks obtained by 120 students in a test are given below:
Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
No. of students | 5 | 9 | 16 | 22 | 26 | 18 | 11 | 6 | 4 | 3 |
Draw an ogive for the given distribution on a graph sheet.
Use suitable scale for ogive to estimate the following:
(i) The median.
(ii) The number of students who obtained more than 75% marks in the test.
(iii) The number of students who did not pass the test if minimum marks required to pass is 40.
Marks | No. of students | Cumulative Frequency |
0 - 10 | 5 | 5 |
10 - 20 | 9 | 14 |
20 - 30 | 16 | 30 |
30 - 40 | 22 | 52 |
40 - 50 | 26 | 78 |
50 - 60 | 18 | 96 |
60 - 70 | 11 | 107 |
70 - 80 | 6 | 113 |
80 - 90 | 4 | 117 |
90 - 100 | 3 | 120 |
In the figure given below, the line segment AB meets X-axis at A and Y-axis at B. The point P(-3, 4) on AB divides it in the ratio 2:3. Find the coordinates of A and B.