Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

If a + ib  = `(x + i)^2/(2x^2 + 1)` prove that a² + b² = `(x^2 + 1)^2/(2x + 1)^2`

Let z₁ = 2 – i, z₂ = –2 + i. Find Re`((z_1z_2)/barz_1)`

Let z₁ = 2 – i, z₂ = –2 + i. Find `"Im"(1/(z_1barz_1))`

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed?

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

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?

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

The base of an equilateral triangle with side 2a lies along they 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 :

1. PQ is parallel to the y-axis,
2. PQ is parallel to the x-axis

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).

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.

Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.

The slope of a line is double of the slope of another line. If tangent of the angle between them is `1/3`, find the slopes of the lines.