List of top Mathematics Questions

in the given figure , if AD=\(7\sqrt3\), then find the length of BC.

$\displaystyle \lim_{x \to 0}$ $\frac{cosec\,x-cot\,x}{x}$ is
Let $s_n = \cos \left(\frac{n\pi}{10}\right), n=1,2,3,\ldots$ Then the value of $\frac{s_{1}s_{2}\ldots s_{10}}{s_{1}+s_{2}+\ldots+s_{10}}$ is equal to
If the normal at point P (at12,2at1) and Q(at22,2at2) on the parabola y2=4ax meet on the parabola, thet1t2 equals
PQ and RS are two perpendicular chords of the rectangular hyperbola xy=c2. If C is the centre of the rectangular hyperbola, then the product of the slopes of CP,CQ,CR and CS is equal to:
Find the following integral: \(\int (ax^2+bx+c)dx\)
(i) If z = 10, find the value of z3 – 3(z – 10) 
(ii) If p = – 10, find the value of p2 – 2p – 100
Solution of the equation $x^2 dy + y (x + y) dx = 0$ is
For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) – 8 is to the right of – 10 on a number line.
(b) – 100 is to the right of – 50 on a number line.
(c) Smallest negative integer is – 1.
(d) – 26 is greater than – 25.
If $cos x = -\frac{4}{5}$, where $x\in\left[0, \pi\right]$, then the value of $cos \left(\frac{x}{2}\right)$ is equal to
If $x=sin^{-1}\left(3t-4t^{3}\right)$ and $y=cos^{-1}\left(\sqrt{1-t^{2}}\right)$, then $\frac{dy}{dx}$ is equal to
If $log_e\,5$, $log_e(5^x-1)$ and $log_e$ $\left(5^{x}-\frac{11}{5}\right)$ are in $A.P.$, then the values of $x$ are
The domain and range of relation $R = \{ (x , y ) /x , y \in N , x + 2y = 5\}$ is
Let f : R $\rightarrow$ R be function defined by f(x) = sin (2x -3), then f is
Order of $\left(3x + 2y\right) \left(\frac{dy}{dx}\right)^{2} +5x \frac{d^{2}y}{dx^{2}} = 0 $ is
By using the properties of definite integrals, evaluate the integral: \(∫_0^π log(1+cosx)dx\)
The circle x2+y2+4x−7y+12=0 cuts an intercept on y -axis of length
The derivative of sec-1 12x2-1 with respect to 1-x2 at x=12 is:
The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is:
If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?
The number of terms of an AP is even. The sum of the odd terms is 24 and of the even terms is 30. The last term exceeds the first by 1012. Then the number of terms in the series is ______.

 If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

If |x + 1||x + 3| – 4|x + 2| + 5 = 0, then sum of squares of solutions is
Find \(x\) in the following figures.
Polygon a   Polygon b
It is known from past experience that in a certain plant there are on the average 4 industrial accidents per month. Find the probability that there will be less than 4 accidents in a given month. Given: (e−4=0.0183)