List of top Mathematics Questions

Find the equation of the line which passes through the point (-4, 3) with slope \(\frac 12\).

A die is thrown, find the probability of the following events:(i) A prime number will appear,(ii) A number greater than or equal to \(3\) will appear,(iii) A number less than or equal to one will appear,(iv) A number more than \(6\) will appear,(v) A number less than 6 will appear.

If three point (h, 0), (a, b) and (0, k) lie on a line, show that \(\frac ah+ \frac bk=1\).
Write the equations for the x and y-axes.
Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?
Graph between population and year
A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine
(i) P (2)   (ii) P (1 or 3)    (iii) P (not 3)
Expand the expression \((\frac{x}{3} + \frac{1}{x})^5\).
4 cards are drawn from a well–shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
Expand the expression \((2x - 3) ^6\).
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that 
(i) all will be blue. 
(ii) at least one will be green.
Find the angle between the x-axis and the line joining the points (3, -1) and (4, -2).
Without using distance formula, show that points (-2, -1), (4, 0), (3, 3) and (-3, 2) are vertices of a parallelogram.
Expand the expression\( (\frac{2}{x} - \frac{x}{2})^5\).
Find the value of x for which the points (x, -1), (2, 1) and (4, 5) are collinear.
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
If f(x) = \(f(x)=\left\{\begin{matrix} mx^2+n, &\,\,\,\,x<0 \\   nx+m,&\,\,\,\, 0\leq x\leq1 \\   nx^3+m,&\,\,\,\, x>1  \end{matrix}\right.\). For what integers m and n does both \(\lim_{x\rightarrow 1}\)f(x) and \(\lim_{x\rightarrow 1}\) f(x) exist?
If the function f(x) satisfies \(\lim_{x\rightarrow 1}\) \(\frac{f(x)-2}{x^2-1}\) =\(\pi\), evaluate \(\lim_{x\rightarrow 1}\) f(x).
Expand the expression \((1- 2x)^ 5\).

Two dice are thrown. The events A, B, and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die.C: getting the sum of the numbers on the dice ≤ 5 Describe the events (i) A'(ii)not B(iii)A or B(iv) A and B(v)A but not C(vi)B or C(vii)B and C(viii)\(A∩B'∩C'\)

Three coins are tossed. Describe (i)Two events which are mutually exclusive. (ii)Three events which are mutually exclusive and exhaustive.(iii)Two events, which are not mutually exclusive.(iv)Two events which are mutually exclusive but not exhaustive.(v)Three events which are mutually exclusive but not exhaustive.

Let a1, a2,..., an be fixed real numbers and define a function f(x)=(x-a1)(x-a2)...(x-an).
What is \(\lim_{x\rightarrow a_1}\) f(x)? 
For some a ≠ a1, a2 .....an, Compute \(\lim_{x\rightarrow a}\) f(x).

Three coins are tossed once. Let \(A\) denote the event ‘three heads show”, \(B\) denote the event “two heads and one tail show”, \(C\) denote the event” three tails show and \(D\) denotes the event a head shows on the first coin”. Which events are (I) mutually exclusive? (ii) simple? (iii) Compound?

The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?
In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: \(A:\) the sum is greater than \(8\), \(B:\)\(2\) occurs on either die \(C:\)The sum is at least \(7\), and a multiple of \(3\). Which pairs of these events are mutually exclusive?