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

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17} B = {2, 4, ..., 18} and N the set of natural numbers is the universal set, then A′ ∪ (A ∪ B) ∩ B′) is ______.

Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be ______.

For all sets A and B, A – (A ∩ B) is equal to ______.

Match the following sets for all sets A, B, and C.

State True or False for the following statement.

If (x – 2, y + 5) = `(-2, 1/3)` are two equal ordered pairs, then x = 4, y = `(-14)/3`

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

If ⁿP_r = 840, ⁿC_r = 35, then r = ______.

The 10th common term between the series 3 + 7 + 11 + ... and 1 + 6 + 11 + ... is ______.

We know the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.

A side of an equilateral triangle is 20 cm long. A second equilateral triangle is inscribed in it by joining the midpoints of the sides of the first triangle. The process is continued as shown in the accompanying diagram. Find the perimeter of the sixth inscribed equilateral triangle.

In a potato race 20 potatoes are placed in a line at intervals of 4 metres with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?

In a cricket tournament 16 school teams participated. A sum of Rs 8000 is to be awarded among themselves as prize money. If the last-placed team is awarded Rs 275 in prize money and the award increases by the same amount for successive finishing places, how much amount will the first-place team receive?

Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.

Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.

In what direction should a line be drawn through the point (1, 2) so that its point of intersection with the line x + y = 4 is at a distance `sqrt(6)/3` from the given point.

A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`

The equation of the line passing through the point (1, 2) and perpendicular to the line x + y + 1 = 0 is ______.

The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line `sqrt(3)  x + y` = 1 is ______.

If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ______.