List of top Mathematics Questions asked in CBSE Class XI

Find an approximation of (0.99)5 using the first three terms of its expansion

Find the value of \(( a^2 + \sqrt{a^2-1})^4 + ( a^2 - \sqrt{a^2-1})^4\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): 4\(\sqrt x\) -2

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{a}{x^4}-\frac{b}{x^2}\) + cosx

Find the derivative of
(i) 2x - \(\frac{3}{4}\) 
(ii)(5x³+3x-1)(x-1)
(iii) x-3(5+3x) (iv)x⁵(3-6x-9)
(v) x-4(3-4x-5) (vi)\(\frac{2}{x+1}-\frac{x^2}{3x-1}\)

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 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 + a²x^n-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?