Find the equation of the circle with centre (–2, 3) and radius 4
The equation of a circle with centre (h, k) and radius r is given as
(x – h)2 + (y – k)2 = r2
It is given that centre (h, k) = (–2, 3) and radius (r) = 4.
Therefore, the equation of the circle is
(x + 2)2 + (y – 3)2 = (4)2
x2 + 4x + 4 + y2 – 6y + 9 = 16
x2 + y2 + 4x – 6y – 3 = 0
Solve 24x < 100, when
(i) x is a natural number. (ii) x is an integer.
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
A point is on the x-axis. What are its y-coordinates and z-coordinates?
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed?
Describe the sample space for the indicated experiment: A coin is tossed three times.
Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal length.
(vi) Answer this question.
(vii) The product of (–1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).
The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
A point is in the XZ-plane. What can you say about its y-coordinate?
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.
Find the sum to n terms of the sequence, 8, 88, 888, 8888…
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If is the A.M. between a and b, then find the value of n.
Find the sum to n terms of the series 3 × 12 + 5 × 22 + 7 × 32 + …
Describe the sample space for the indicated experiment: A coin is tossed four times.