ISC (Arts) Class 12 - CISCE Question Bank Solutions for Mathematics

Find the area of the region bounded by the curve x² = 4y and the line x = 4y – 2.

The cost function C(x) = 3x² – 6x + 5. Find the average cost when x = 2.

Let L be a set of all straight lines in a plane. The relation R on L defined as 'perpendicular to' is ______.

Given that `1/y + 1/x = 1/12` and y decreases at a rate of 1 cms^–1, find the rate of change of x when x = 5 cm and y = 1 cm.

Using integration, find the area bounded by the curve y² = 4ax and the line x = a.

Using integration, find the area of the region bounded by the curve y² = 4x and x² = 4y.

The Average Cost function associated with producing and marketing x units of an item is given by AC = `x + 5 + 36/x`.

1. Find the Total cost function.
2. Find the range of values of x for which Average Cost is increasing.

Assertion: Degree of the differential equation: `a(dy/dx)^2 + bdx/dy = c`, is 3

Reason: If each term involving derivatives of a differential equation is a polynomial (or can be expressed as polynomial) then highest exponent of the highest order derivative is called the degree of the differential equation.

Which of the following is correct?

Statement 1: The intersection of two equivalence relations is always an equivalence relation.

Statement 2: The Union of two equivalence relations is always an equivalence relation.

Which one of the following is correct?

If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.

A kite is being pulled down by a string that goes through a ring on the ground 8 meters away from the person pulling it. If the string is pulled in at 1 meter per second, how fast is the kite coming down when it is 15 meters high?

Consider the following statements and choose the correct option:

Statement 1: If `veca` and `vecb` represents two adjacent sides of a parallelogram then the diagonals are represented by `veca + vecb` and `veca - vecb`.

Statement 2: If `veca` and `vecb` represents two diagonals of a parallelogram then the adjacent sides are represented by `2(veca + vecb)` and `2(veca - vecb)`.

Which of the following is correct?

Show that the line whose vector equation is `vecr = (2hati - 2hatj + 3hatk) + λ(hati - hatj + 4hatk)` is parallel to the plane whose vector equation is `vecr.(hati + 5hatj + hatk) = 5`. Also find the distance between them.

Sketch the region enclosed bounded by the curve, y = x |x| and the ordinates x = −1 and x = 1.

Evaluate:

`int_0^1x^2dx`

Hence find the area bounded by the curve, y = x |x| and the coordinates x = −1 and x = 1.

Which condition is true if Average Cost (AC) is constant at all levels of output?

The cost function of a commodity is `C(x) = 200 + 20x - 1/2x^2` (in rupees). Find the range where AC falls.

Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

Find the differential equation representing the curve y = cx + c².