List of top Mathematics Questions

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?

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?

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. 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.

IQ of a person is given by the formula \(IQ = \frac{MA}{CA}×100, \)  Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.
If E and F are events such that P(E)=\(\frac{1}{4}\) ,P(F)=\(\frac{ 1}{2}\) and P(E and F)=\(\frac{1}{8}\) ,find: (i) P(E or F),(ii) P(not E and not F).

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)\(A∩B'∩C'\)

If f(x)={|x|+1, x <0 0, x=0 |x|-1, x>0}
For what value (s) of a does lim x\(\rightarrow\)af(x) exist?
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Find the 20th and n th terms of the G.P. \(\frac{5 }{ 2} ,\frac{ 5}{ 4} ,\frac{ 5 }{ 8} \),......
Given a G.P. with a = 729 and 7th term 64, determine S7.
Expand the expression \((1- 2x)^ 5\).
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).
Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, -4) and B (8, 0).
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?

Find the range of each of the following functions.
(i) f(x) = 2 - 3x, x ∈ R, x> 0.
(ii) f(x) = x2+ 2, x, is a real number.
(iii) f(x) = x, x is a real number

Find the derivative of x2 – 2 at x = 10
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
Find the value of x for which the points (x, -1), (2, 1) and (4, 5) are collinear.
A card is selected from a pack of 52 cards.
(a) How many points are there in the sample space?
(b) Calculate the probability that the card is an ace of spades.
(c) Calculate the probability that the card is (i) an ace (ii) black card.
Without using distance formula, show that points (-2, -1), (4, 0), (3, 3) and (-3, 2) are vertices of a parallelogram.
Expand the expression\( (\frac{2}{x} - \frac{x}{2})^5\).
In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i)The student opted for NCC or NSS.
(ii)The student has opted neither NCC nor NSS.
(iii)The student has opted NSS but not NCC
Expand the expression \((2x - 3) ^6\).