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

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

Prove the following identitie

Prove the following identities
\[\frac{\sin^3 x + \cos^3 x}{\sin x + \cos x} + \frac{\sin^3 x - \cos^3 x}{\sin x - \cos x} = 2\]

Prove the following identities
\[\left( \sec x \sec y + \tan x \tan y \right)^2 - \left( \sec x \tan y + \tan x \sec y \right)^2 = 1\]