Science (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Write the complex number z = `(1 - i)/(cos  pi/3 + i sin  pi/3)` in polar form.

If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = `pi/2`, then show that `barz`w = –i.

arg(z) + arg`barz  (barz ≠ 0)` is ______.

If |z| = 4 and arg(z) = `(5pi)/6`, then z = ______.

State True or False for the following:

Let z₁ and z₂ be two complex numbers such that |z₁ + z₂| = |z₁| + |z₂|, then arg(z₁ – z₂) = 0.

Find z if |z| = 4 and arg(z) = `(5pi)/6`.

Find principal argument of `(1 + i sqrt(3))^2`.

|z₁ + z₂| = |z₁| + |z₂| is possible if ______.

The value of arg (x) when x < 0 is ______.

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Show that the following system of linear inequalities has no solution x + 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1

Solve the following system of linear inequalities:

3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4

Show that the solution set of the following system of linear inequalities is an unbounded region 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0.

Solution set of x ≥ 0 and y ≤ 0 is

Solution set of x ≥ 0 and y ≤ 1 is

At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250, find the value at the end of 5 years.

If a, b, c, d are in G.P., prove that a² – b², b² – c², c² – d² are also in G.P.

If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c