Class 11 Mathematics - Chapter Permutations & Combinations NCERT Solutions | How many 4-letter code can be formed usi

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?

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

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?

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.

A point is in the XZ-plane. What can you say about its y-coordinate?

Find the sum to n terms of the series 1² + (1² + 2²) + (1² + 2² + 3²) + …

The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

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

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)

The sum of first three terms of a G.P. is  and their product is 1. Find the common ratio and the terms.

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

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

Describe the sample space for the indicated experiment: A coin is tossed four times.

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P²Rⁿ = Sⁿ

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.