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

a + ar + ar² + ... + arⁿ⁻¹ =  \[a\left( \frac{r^n - 1}{r - 1} \right), r \neq 1\]

a + (a + d) + (a + 2d) + ... (a + (n − 1) d) = \[\frac{n}{2}\left[ 2a + (n - 1)d \right]\]

If \[\cos x = - \frac{3}{5}\text{ and }\pi < x < \frac{3\pi}{2}\] find the values of other five trigonometric functions and hence evaluate \[\frac{cosec x + \cot x}{\sec x - \tan x}\]

5²ⁿ −1 is divisible by 24 for all n ∈ N.

Find the value of the following trigonometric ratio:

Find the value of the following trigonometric ratio:
sin 17π

Find the value of the following trigonometric ratio:
\[\tan\frac{11\pi}{6}\]

Find the value of the following trigonometric ratio:

Find the value of the following trigonometric ratio:
\[\tan \frac{7\pi}{4}\]

A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.

Given \[a_1 = \frac{1}{2}\left( a_0 + \frac{A}{a_0} \right), a_2 = \frac{1}{2}\left( a_1 + \frac{A}{a_1} \right) \text{ and }  a_{n + 1} = \frac{1}{2}\left( a_n + \frac{A}{a_n} \right)\] for n ≥ 2, where a > 0, A > 0.
Prove that \[\frac{a_n - \sqrt{A}}{a_n + \sqrt{A}} = \left( \frac{a_1 - \sqrt{A}}{a_1 + \sqrt{A}} \right) 2^{n - 1}\]