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

Check whether the statement are true or not: 

p : If x and y are odd integers, then x + y is an even integer.

Check whether the statement are true or not: 

 q : If x, y are integers such that xy is even, then at least one of x and y is an even integer.

Insert 6 geometric means between 27 and  \[\frac{1}{81}\] .

Insert 5 geometric means between 16 and \[\frac{1}{4}\] .

Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .

Find the geometric means of the following pairs of number:

2 and 8

Find the geometric means of the following pairs of number:

a³b and ab³

Find the geometric means of the following pairs of number:

−8 and −2

The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio `(3+2sqrt2):(3-2sqrt2)`.

If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is \[\frac{9}{2}\], then write its first term and common difference.

\[\lim_{x \to 1} \frac{x^2 + 1}{x + 1}\] 

\[\lim_{x \to 0} \frac{2 x^2 + 3x + 4}{x^2 + 3x + 2}\] 

\[\lim_{x \to 3} \frac{\sqrt{2x + 3}}{x + 3}\] 

\[\lim_{x \to 1} \frac{\sqrt{x + 8}}{\sqrt{x}}\] 

\[\lim_{x \to a} \frac{\sqrt{x} + \sqrt{a}}{x + a}\] 

\[\lim_{x \to 1} \frac{1 + \left( x - 1 \right)^2}{1 + x^2}\]

\[\lim_{x \to 0} \frac{x^{2/3} - 9}{x - 27}\]