List of top Mathematics Questions

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.

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.

Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).

Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.

Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (-4, 0, 0) is equal to 10.

Find the sum to n terms of the sequence, 8, 88, 888, 8888… .

If the 4\(^{th}\), 10\(^{th}\) and 16\(^{th}\) terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Evaluate \(\displaystyle\sum_{k=1}^{11}\) (2 + 3k).

Find the sum to indicated number of terms in each of the geometric progressions in\(x^3,x^5,x^7\), ... n terms (if x ≠ ± 1).

Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.