List of top Questions asked in CBSE Class XI

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 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).
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
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 the derivative of the following functions (it is to be understood that \(a, \,b,\, c,\, d,\, p,\, q,\, r\) and \(s\) are fixed non-zero constants and \(m\) and \(n\) are integers), \((x+a)\).

Find the derivative of cos x from first principle.
Prove that \(\underset{r=0} {\overset{n}∑} { 3^r }\,{ ^nC_r} = 4^n\) 
Find the derivative of \(\frac{x^n-a^n}{x-a}\) for some constant a.
For some constants a and b, find the derivative of
(i) (x-a)(x-b) (ii) (ax2+b)2 (iii)\(\frac{x-a}{x-b}\)
Show that \(9^{ n+1} -8n -9\) is divisible by \(64\), whenever n is a positive integer.
Find the derivative of xn + ax n-1 + a2xn-2+……...+a n-1x + an for some fixed real number a.
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 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.
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\((i)P(A∪B)(ii)P(A´∩B´)(iii)P(A∩B´)(iv)P(B∩A´)\)