Commerce (English Medium) कक्षा ११ - CBSE Question Bank Solutions

For any two sets A and B, \[A \cap \left( A \cup B \right)'\]is equal to

Find the derivative of f(x) = xⁿ, where n is positive integer, by first principle.

`lim_(x -> 0) x sin  1/x` is equal to ______.

Find the equation of the hyperbola satisfying the given conditions:

Foci (±4, 0), the latus rectum is of length 12.

Find the equation of the hyperbola satisfying the given conditions:

Vertices (±7, 0), e = `4/3`

Find the axes, eccentricity, latus-rectum and the coordinates of the foci of the hyperbola 25x² − 36y² = 225.

Find the equation of the hyperbola satisfying the given condition :

 foci (± \[3\sqrt{5}\] 0), the latus-rectum = 8

find the equation of the hyperbola satisfying the given condition:

 foci (± \[3\sqrt{5}\]  0), the latus-rectum = 8

find the equation of the hyperbola satisfying the given condition:

foci (0, ± 12), latus-rectum = 36

Write the eccentricity of the hyperbola whose latus-rectum is half of its transverse axis.

If the latus-rectum through one focus of a hyperbola subtends a right angle at the farther vertex, then write the eccentricity of the hyperbola.

The latus-rectum of the hyperbola 16x² − 9y² = 144 is

Find the equation of the circle with:

Centre (−2, 3) and radius 4.

Find the equation of the circle with:

Centre (a, b) and radius\[\sqrt{a^2 + b^2}\]

Find the equation of the circle with:

Centre (0, −1) and radius 1.

Find the equation of the circle with:

Centre (a cos α, a sin α) and radius a.

Find the equation of the circle with:

Centre (a, a) and radius \[\sqrt{2}\]a.

Find the centre and radius of each of the following circles:

 (x − 1)² + y² = 4

Find the centre and radius of each of the following circles:

(x + 5)² + (y + 1)² = 9