Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Integrate the function:

`(x^2 + x + 1)/((x + 1)^2 (x + 2))`

Integrate the function:

`tan^(-1) sqrt((1-x)/(1+x))`

Integrate the function:

`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`

Find the area of the circle 4x² + 4y² = 9 which is interior to the parabola x² = 4y

Find the area bounded by curves (x – 1)² + y² = 1 and x² + y ² = 1

Using integration finds the area of the region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).

Using integration find the area of the triangular region whose sides have the equations y = 2x +1, y = 3x + 1 and x = 4.

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is

A. 2 (π – 2)

B. π – 2

C. 2π – 1

D. 2 (π + 2)

Area lying between the curve y² = 4x and y = 2x is

A. 2/3

B. 1/3

C. 1/4

D. 3/4

Using the method of integration find the area bounded by the curve |x| + |y| = 1 .

[Hint: The required region is bounded by lines x + y = 1, x– y = 1, – x + y = 1 and
– x – y = 1].

Find the area bounded by curves {(x, y) : y ≥ x2 and y = |x|}.

Choose the correct answer The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is

A. `4/3 (4pi - sqrt3)`

B. `4/3 (4pi + sqrt3)`

C. `4/3 (8pi - sqrt3)`

D.`4/3 (4pi + sqrt3)`

The area bounded by the y-axis, y = cos x and y = sin x when  0 <= x <= `pi/2`

(A) 2 ( 2 −1)

(B) `sqrt2 -1`

(C) `sqrt2 + 1`

D. `sqrt2`

If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.

The volume of a sphere is increasing at the rate of 8 cm³/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.

The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm

Using integration, find the area of region bounded by the triangle whose vertices are (–2, 1), (0, 4) and (2, 3).

The total cost C(x) associated with the production of x units of an item is given by C(x) = 0.005x³ – 0.02x² + 30x + 5000. Find the marginal cost when 3 units are produced, whereby marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Let A = {x ∈ Z : 0 ≤ x ≤ 12}. Show that R = {(a, b) : a, b ∈ A, |a – b| is divisible by 4}is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]