List of top Mathematics Questions

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 the derivative of 99x at x = 100.
Find the derivative of x at x = 1.

Which of the following can not be a valid assignment of probabilities for outcomes of sample Space \(S =\{ω_1, ω_2 , ω_3,  ω_4,  ω_5,  ω_6,  ω_7\}\)

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 the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).
Using Binomial Theorem, indicate which number is larger \((1.1)^{10000}\) or \( 1000.\)
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?

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?

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 \((99)^5\).
Using Binomial Theorem, evaluate \((101)^4\)
A and B are two events such that \(P(A)=0.54,P(B)=0.69 \text{ and } P(A∩B)=0.35\). Find\((i)P(A∪B)(ii)P(A´∩B´)(iii)P(A∩B´)(iv)P(B∩A´)\)
Find the expansion of \((3x^2 – 2ax + 3a^2)^3\) using binomial theorem.
Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope. 
Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x-axis.
Using Binomial Theorem, evaluate \((102)^5\).
Find the equation of the line which intersects the x-axis at a distance of 3 units to the left of origin with slope -2.
Using Binomial Theorem, evaluate \((96)^3\).
Find the equation of the line that passes though \((2, 2\sqrt 3)\) and is inclined with the x-axis at an angle of 75°.
Out of \(100\) students, two sections of \(40\) and \(60\) are formed. If you and your friend are among the \(100\) students, what is the probability that (a) you both enter the same sections? (b) you both enter the different sections? 
Expand the expression \((x+ \frac{1}{x})^6\).
Find the equation of the line which passes though (0, 0) with slope m.
In a certain lottery, \(10,000\) tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy(a) one ticket (b) two tickets (c) Ten tickets?