List of top Mathematics Questions

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
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
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 coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse \(16x^2 + y^2 = 16\).
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.

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).