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

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.

36x² + 4y² = 144

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.

16x² + y² = 16

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.

4x² + 9y² = 36

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

Find the derivative of the following function from first principle.

x³ – 27

Find the derivative of the following function from first principle.

(x – 1) (x – 2)

Find the derivative of the following function from first principle.

`1/x^2`

Find the derivative of the following function from first principle.

`(x+1)/(x -1)`

Find the derivative of the following function from first principle:

−x

Find the derivative of the following function from first principle:

(–x)^–1

Find the derivative of the following function from first principle: 

sin (x + 1)

Find the derivative of the following function from first principle: 

`cos (x - pi/8)`

(i) If \[\left( \frac{a}{3} + 1, b - \frac{2}{3} \right) = \left( \frac{5}{3}, \frac{1}{3} \right)\] find the values of a and b. 

(ii) If (x + 1, 1) = (3, y − 2), find the values of x and y.

Prove the following identites

sec⁴x - sec²x = tan⁴x + tan²x

Prove the following identities
\[\sin^6 x + \cos^6 x = 1 - 3 \sin^2 x \cos^2 x\]

Prove the following identities
\[\left( cosec x - \sin x \right) \left( \sec x - \cos x \right) \left( \tan x + \cot x \right) = 1\]

Prove the following identities 
\[cosec x \left( \sec x - 1 \right) - \cot x \left( 1 - \cos x \right) = \tan x - \sin x\]

Prove the following identities
\[\frac{1 - \sin x \cos x}{\cos x \left( \sec x - cosec x \right)} \cdot \frac{\sin^2 x - \cos^2 x}{\sin^3 x + \cos^3 x} = \sin x\]