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

Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that \[A \cup B\] 

If A = {x ∈ C : x² = 1} and B = {x ∈ C : x⁴ = 1}, then write A − B and B − A. 

Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]

If A and B are two sets such that \[A \subset B\], then write B' − A' in terms of A and B.

Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that \[A \cup B\] can have. 

If \[A = \left\{ \left( x, y \right) : y = \frac{1}{x}, 0 \neq x \in R \right\}\]and\[B = \left\{ \left( x, y \right) : y = - x, x \in R \right\}\] then write\[A \cap B\]

If \[A = \left\{ \left( x, y \right) : y = e^x , x \in R \right\} and B = \left\{ \left( x, y \right) : y = e^{- x} , x \in R \right\}\]write\[A \cap B\] 

If A and B are two sets such that \[n \left( A \right) = 20, n \left( B \right) = 25\]\text{ and } \[n \left( A \cup B \right) = 40\], then write \[n \left( A \cap B \right)\] 

If A and B are two sets such that \[n \left( A \right) = 115, n \left( B \right) = 326, n \left( A - B \right) = 47,\] then write \[n \left( A \cup B \right)\] 

Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0

The number of subsets of a set containing n elements is 

For any two sets A and B,\[A \cap \left( A \cup B \right) =\]

If A = {1, 3, 5, B} and B = {2, 4}, then 

Prove that: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]

Prove that:

Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]

Prove that

If A = |1, 2, 3, 4, 5|, then the number of proper subsets of A is 

In set-builder method the null set is represented by