Class 11 Mathematics - Chapter Straight Lines NCERT Solutions | Draw a quadrilateral in the Cartesian pl

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 distance between P (x₁, y₁) and Q (x₂, y₂) when : (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis.

Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, – 4) and B (8, 0).

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

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).

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

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

Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.

If the sum of n terms of an A.P. is 3n² + 5n and its mth term is 164, find the value of m.

Find the sum to n terms of the sequence, 8, 88, 888, 8888…

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

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 derivative of x at x = 1.

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

A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?