Class 11 Mathematics - Chapter Permutations & Combinations NCERT Solutions | How many 3-digit even numbers can be for

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

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 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 5² + 6² + 7² + ... + 20²

What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

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.

Show that the products of the corresponding terms of the sequences a,ar,ar², ...ar^n-1 and A, AR, AR², ,,,AR^n-1 form a G.P, and find the common ratio.

Describe the sample space for the indicated experiment: A die is thrown two times.

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

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

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Find the sum to n terms of the series whose nth terms is given by (2n – 1)²