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

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

• Let R = {(L₁, L₂ ): L₁ is parallel to L₂ and L₁: y = x – 4} then which of the following can be taken as L₂?

If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘x is smaller than y’. The range of R is ____________.

The relation R = {(1,1),(2,2),(3,3)} on {1,2,3} is ____________.

Let A be a square matrix of order 2 x 2, then `abs("KA")` is equal to ____________.

The radius of a cylinder is increasing at the rate of 3 m/s and its height is decreasing at the rate of 4 m/s. The rate of change of volume when the radius is 4 m and height is 6 m, is ____________.

A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform ____________.

The rate of change of area of a circle with respect to its radius r at r = 6 cm is ____________.

Total revenue in rupees received from the sale of x units of a product is given by R(x)= 3x²+ 36x + 5. The marginal revenue, when x = 15 is ____________.

If the rate of change of the area of the circle is equal to the rate of change of its diameter then its radius is equal to ____________.

The rate of change of volume of a sphere is equal to the rate of change of the radius than its radius equal to ____________.

If the rate of change of volume of a sphere is equal to the rate of change of its radius then the surface area of a sphere is ____________.

Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2^nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3^rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

State the order of the above given differential equation.

Write the sum of the order and the degree of the following differential equation:

`d/(dx) (dy/dx)` = 5

Find: `int (x + 1)/((x^2 + 1)x) dx`

The value of ‘k’ for which the function f(x) = `{{:((1 - cos4x)/(8x^2)",",  if x ≠ 0),(k",",  if x = 0):}` is continuous at x = 0 is ______.

If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.

A man 1.6 m tall walks at the rate of 0.3 m/sec away from a street light that is 4 m above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?

Find the direction ratio and direction cosines of a line parallel to the line whose equations are 6x − 12 = 3y + 9 = 2z − 2

Define the relation R in the set N × N as follows:

For (a, b), (c, d) ∈ N × N, (a, b) R (c, d) if ad = bc. Prove that R is an equivalence relation in N × N.

Given a non-empty set X, define the relation R in P(X) as follows:

For A, B ∈ P(X), (4, B) ∈ R iff A ⊂ B. Prove that R is reflexive, transitive and not symmetric.