Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

Which of the following are true:

(2 × 3)! = 2! × 3!

\[\frac{1}{1 . 4} + \frac{1}{4 . 7} + \frac{1}{7 . 10} + . . . + \frac{1}{(3n - 2)(3n + 1)} = \frac{n}{3n + 1}\]

\[\frac{1}{3 . 5} + \frac{1}{5 . 7} + \frac{1}{7 . 9} + . . . + \frac{1}{(2n + 1)(2n + 3)} = \frac{n}{3(2n + 3)}\]

\[\frac{1}{3 . 7} + \frac{1}{7 . 11} + \frac{1}{11 . 5} + . . . + \frac{1}{(4n - 1)(4n + 3)} = \frac{n}{3(4n + 3)}\] 

2 + 5 + 8 + 11 + ... + (3n − 1) = \[\frac{1}{2}n(3n + 1)\]

1.3 + 2.4 + 3.5 + ... + n. (n + 2) = \[\frac{1}{6}n(n + 1)(2n + 7)\]

1.3 + 3.5 + 5.7 + ... + (2n − 1) (2n + 1) =\[\frac{n(4 n^2 + 6n - 1)}{3}\]

1.2 + 2.3 + 3.4 + ... + n (n + 1) = \[\frac{n(n + 1)(n + 2)}{3}\]

Find the value of the other five trigonometric functions 

Find the value of the other five trigonometric functions 

\[\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + . . . + \frac{1}{2^n} = 1 - \frac{1}{2^n}\]

Find the value of the other five trigonometric functions 
\[\tan x = \frac{3}{4},\] x in quadrant III

Find the value of the other five trigonometric functions
\[\sin x = \frac{3}{5},\] x in quadrant I

1² + 3² + 5² + ... + (2n − 1)² = \[\frac{1}{3}n(4 n^2 - 1)\]

If sin \[x = \frac{12}{13}\] and x lies in the second quadrant, find the value of sec x + tan x.

If sin\[x = \frac{3}{5}, \tan y = \frac{1}{2}\text{ and }\frac{\pi}{2} < x < \pi < y < \frac{3\pi}{2},\]  find the value of 8 tan \[x - \sqrt{5} \sec y\]

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