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

Find the value of the following expression:

i⁵ + i¹⁰ + i¹⁵

What is the total number of proper subsets of a set consisting of n elements? 

Find the value of the following expression:

\[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\]

If A is any set, prove that: \[A \subseteq \phi \Leftrightarrow A = \phi .\] 

Find the value of the following expression:

1+ i² + i⁴ + i⁶ + i⁸ + ... + i²⁰

Prove that: 

\[A \subseteq B, B \subseteq C \text{ and } C \subseteq A \Rightarrow A = C .\] 

Find the value of the following expression:

(1 + i)⁶ + (1 − i)³

Express the following complex number in the standard form a + i b:

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

Express the following complex number in the standard form a + i b:

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

Express the following complex number in the standard form a + i b:

\[(1 + i)(1 + 2i)\]

Express the following complex number in the standard form a + i b:

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

Express the following complex number in the standard form a + ib:

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

Express the following complex number in the standard form a + i b:

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

Express the following complex number in the standard form a + i b:

\[\frac{2 + 3i}{4 + 5i}\]

Express the following complex number in the standard form a + i b:

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

Express the following complex number in the standard form a + i b:

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

Express the following complex number in the standard form a + i b:

\[\frac{3 - 4i}{(4 - 2i)(1 + i)}\]

Express the following complex number in the standard form a + i b:

\[\left( \frac{1}{1 - 4i} - \frac{2}{1 + i} \right)\left( \frac{3 - 4i}{5 + i} \right)\]

Express the following complex number in the standard form a + i b:

\[\frac{5 + \sqrt{2}i}{1 - 2\sqrt{i}}\]

Find the real value of x and y, if

\[(x + iy)(2 - 3i) = 4 + i\]