Class 11 Mathematics - Chapter Straight Lines NCERT Solutions | Find the distance between P (x1, y1) and

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 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).

Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

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?

The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Find the sum to n terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …

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

Which term of the following sequences:

Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Find the derivative of x at x = 1.

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment?

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