Class 11 Mathematics - Chapter Mathematical Reasoning NCERT Solutions | Give three examples of sentences which a

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.

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.

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?

Find the value of n so that  may be the geometric mean between a and b.

Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.

2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)

Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q² = ps.

Solve 24x < 100, when
   (i)   x is a natural number.         (ii)   x is an integer.

If f is a function satisfying f(x +y) = f(x) f(y) for all x,y N  such that f(1) = 3

 and  , find the value of n.

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.