List of top Mathematics Questions

Using Binomial Theorem, evaluate \((101)^4\)
Find the expansion of \((3x^2 – 2ax + 3a^2)^3\) using binomial theorem.
A and B are two events such that \(P(A)=0.54,P(B)=0.69 \text{ and } P(A∩B)=0.35\). Find\((i)P(A∪B)(ii)P(A´∩B´)(iii)P(A∩B´)(iv)P(B∩A´)\)
The vertices of ΔPQR are P (2, 1), Q (-2, 3) and R (4, 5). Find equation of the median through the vertex R.
Using Binomial Theorem, evaluate \((99)^5\).

From the employees of a company, \(5\) persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows: A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over \(35\) years?

In a lottery, person choses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [Hint: order of the numbers is not important.]
If 4-digit numbers greater than \(5,000\) are randomly formed from the digits \(0,1,3,5\), and \(7\), what is the probability of forming a number divisible by \(5 \) when (i)the digits are repeated? (ii)the repetition of digits is not allowed?
Using Binomial Theorem, indicate which number is larger \((1.1)^{10000}\) or \( 1000.\)
Check whether the following probabilities P(A) and P(B) are consistently defined
(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).

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. 

State true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii)A and B are mutually exclusive and exhaustive
(iii) A=B′
(iv)A and C are mutually exclusive
(v)A and B′ are mutually exclusive.
(vi) A′,B′,C are mutually exclusive and exhaustive.

A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1:n. Find the equation of the line.
Find \((a + b)^4 - (a - b)^4\). Hence, evaluate \((\sqrt3 + \sqrt2)^4 - (\sqrt3 - \sqrt2)^4\).
The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
Find the derivative of x at x = 1.

If a and b are distinct integers, prove that a - b is a factor of \(a^n - b^n\) , whenever n is a positive integer. 
[Hint: write\( a ^n = (a - b + b)^n\) and expand]

Find the derivative of 99x at x = 100.
Find the derivative of the following functions from first principle. 
(i) x3 − 27 (ii) ( x −1)( x- 2 )
(iii) \(\frac{1}{x^2}\) (iv) \(\frac{x+1}{x-1}\)
Find \((x + 1)^6 - (x - 1)^6\). Hence or otherwise evaluate \((\sqrt2 + 1)^6 + (\sqrt2 - 1)^6.\)
For the function f(x) = \(\frac{x^{100}}{100}\) + \(\frac{x^{99}}{99}\) + ......+ \(\frac{x^2}{2}\)+ x+1. Prove that f ′(1)= 100 f'(0 )
Find the derivative of xn + ax n-1 + a2xn-2+……...+a n-1x + an for some fixed real number a.
Expand using Binomial Theorem \(( 1+ \frac{X}{2} - \frac{2}{X})^4, X≠0\)
Find an approximation of (0.99)5 using the first three terms of its expansion