List of practice Questions

A person standing at the junction (crossing) of two straight paths represented by the equations 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 wants to reach the path whose equation is 6x - 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y - 5 = 0 and 3x - 2y + 7 = 0 is always 10. Show that P must move on a line.

The given figure shows a relationship between the sets P and Q. Write this relation

1. in set-builder form
2. in roster form.

What is its domain and range?

Average energy density of electromagnetic field of a wave having amplitude of 48 $V m^{-1}$ is

Write the relation R = {(x, x³ ): x is a prime number less than 10} in roster form.

Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by 
{(a, b): a, b ∈ A, b is exactly divisible by a}.

1. Write R in roster form
2. Find the domain of R
3. Find the range of R

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈A, y ∈B}. Write R in roster form.

Define a relation R on the set Non natural numbers by R = {(x, y): y= x+ 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.

Let A = {1, 2, 3, ... ,14}. Define a relation R from A to A by R = {(x, y): 3x - y = 0, where x, y ∈ A}. Write down its domain, codomain and range.

The Cartesian product A x A has 9 elements among which are found (-1, 0) and (0, 1). Find the set A and the remaining elements of A x A.

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A x B, find A and B, where x, y and z are distinct elements.

Let A = {1, 2} and B = {3, 4}. Write A x B. How many subsets will A x B have? List them.

If A x B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.

Evaluate the Given limit: \(\lim_{x\rightarrow 2}\) \(\frac{3x^2-x-10}{x^2-4}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \((x+1)^5-\frac{1}{x}\)

Evaluate the Given limit: \(\lim_{x\rightarrow -1}\) \(\frac{x^{10}+x^5+1}{x-1}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 1}4\) \(\frac{4x-3}{x-2}\)

Evaluate the Given limit: \(\lim_{x\rightarrow 1}\pi r^2\)

Evaluate the Given limit: \(\lim_{x\rightarrow \pi}\)(x - \(\frac{22}7{}\))

Evaluate the Given limit: lim \(\lim_{x\rightarrow 3}\)x+3

Find the sum of the products of the corresponding terms of the sequences 2, 4, 8,16, 32 and 128, 32, 8, 2, \(\frac{1}{2}\).

If A and B be the points (3, 4, 5) and (–1, 3, –7), respectively, find the equation of the set of points P such that PA²+PB²= k², where k is a constant.

If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then find the values of a, b and c.