Class 11 Mathematics - Chapter Complex Number & Quadratic Equations NCERT Solutions | Solve each of the following equations:

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?

Find the equation of the circle with centre (0, 2) and radius 2

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.

Find the 20th and nthterms of the G.P.

If the p^th, q^th and r^th terms of a G.P. are a, b and c, respectively. Prove that a^q-rb^r-pc^p-q=1

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are .

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m – 1)thnumbers is 5:9. Find the value of m.

Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from

Calculate the mean deviation about median age for the age distribution of 100 persons given below:

Age            16-20   21-25   26-30   31-35   36-40   41-45   46-50   51-55
Number         5          6          12        14         26        12        16        9