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

If `f(x) = {{:(sin[x]/[x]",", [x] ≠ 0),(0",", [x] = 0):}`, where [.] denotes the greatest integer function, then `lim_(x -> 0) f(x)` is equal to ______.

`lim_(x -> 0) |sinx|/x` is ______.

If `f(x) = {{:(x^2 - 1",", 0 < x < 2),(2x + 3",", 2 ≤ x < 3):}`, the quadratic equation whose roots are `lim_(x -> 2^-) f(x)` and `lim_(x -> 2^+) f(x)` is ______. 

`lim_(x -> 0) (tan 2x - x)/(3x - sin x)` is equal to ______.

If `f(x) = tanx/(x - pi)`, then `lim_(x -> pi) f(x)` = ______.

`lim_(x -> 0) (sin mx cot  x/sqrt(3))` = 2, then m = ______. 

`lim_(x -> 3^+) x/([x])` = ______.

Prove the following statement by contradication method.
p: The sum of an irrational number and a rational number is irrational.

What universal set (s) would you propose for the following:

The set of right triangles.

What universal set (s) would you propose for the following:

The set of isosceles triangles.

Given the sets, A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?

{0, 1, 2, 3, 4, 5, 6}

Given the sets, A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?

Φ

Given the sets, A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?

{1, 2, 3, 4, 5, 6, 7, 8}

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

`x^2/36 + y^2/16 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

`x^2/4 + y^2/25 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

`x^2/16 + y^2/9 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

`x^2/25 + y^2/100 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

`x^2/49 + y^2/36 = 1`

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

`x^2/100 + y^2/400 = 1`