Arts (English Medium) Class 11 - CBSE Question Bank Solutions

A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true?\[\left\{ 2 \left\{ 1 \right\} \right\} \not\subset A\] 

Write down all possible subsets of each of the following set:

\[\left\{ \phi \right\}\]

Find the conjugate of the following complex number:

4 − 5 i

Find the conjugate of the following complex number:

\[\frac{1}{3 + 5i}\]

Find the conjugate of the following complex number:

\[\frac{1}{1 + i}\]

Find the conjugate of the following complex number:

\[\frac{(3 - i )^2}{2 + i}\]

Find the conjugate of the following complex number:

\[\frac{(1 + i)(2 + i)}{3 + i}\]

Find the conjugate of the following complex number:

\[\frac{(3 - 2i)(2 + 3i)}{(1 + 2i)(2 - i)}\]

Find the modulus of \[\frac{1 + i}{1 - i} - \frac{1 - i}{1 + i}\].

Find the modulus and argument of the following complex number and hence express in the polar form:

1 + i

Find the modulus and argument of the following complex number and hence express in the polar form:

\[\sqrt{3} + i\]

Find the modulus and argument of the following complex number and hence express in the polar form:

1 − i

Find the modulus and argument of the following complex number and hence express in the polar form:

\[\frac{1 - i}{1 + i}\]

Find the modulus and argument of the following complex number and hence express in the polar form:

\[\frac{1}{1 + i}\]

Find the modulus and argument of the following complex number and hence express in the polar form:

\[\frac{1 + 2i}{1 - 3i}\]

Find the modulus and argument of the following complex number and hence express in the polar form:

 sin 120° - i cos 120° 

Find the modulus and argument of the following complex number and hence express in the polar form:

 \[\frac{- 16}{1 + i\sqrt{3}}\]

If z₁, z₂ and z₃, z₄ are two pairs of conjugate complex numbers, prove that \[\arg\left( \frac{z_1}{z_4} \right) + \arg\left( \frac{z_2}{z_3} \right) = 0\].