List of top Mathematics Questions

Differentiate the functions with respect to x.
\(sin(x^2+5)\)

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

determine whether the given planes are parallel or perpendicular,and in case they are neither, find the angles between them. (a)7x+5y+6z+30=0 and 3x-y-10z+4=0 

(b)2x+y+3z-2=0 and x-2y+5=0 

(c)2x-2y+4z+5=0 and 3x-3y+6z-1=0 

(d)2x-y+3z-1=0 and 2x-y+3z+3=0 

(e)4x+8y+z-8=0 and y+z-4=0

Find \(\frac{dy}{dx} y=sin^{-1}(\frac{1-x^2}{1+x^2}),0<x<1\)
Let $X$, $Y$, $Z$ be subsets of $U$, where $n(U) = 35$, $n(X) = 15$, $n(Y) = 22$, $n(Z) = 14$ and $n(X \cap Y) = 11$, $n(Y \cap Z) = 8$, $n(X \cap Z) = 5$, $n(X \cap Y \cap Z) = 3$ then $n(X \cup Y \cup Z)'$ equals

Find the derivative of \(log(x+\sqrt{x^2+1})\)

A rectangular sheet of tin 45cm by 24cm is to be made into a box without top,by cutting off square from each corner and folding up the flaps.What should be the side of the square to be cut off so that the volume of the box is the maximum possible?
Find the second order derivatives of the function
\(x^2+3x+2\)

Differentiate the functions with respect to x.
\(cos\ x^3.sin^2(x^5)\)

Differentiate the functions with respect to x.
\(sec(tan(\sqrt x))\)

Differentiate the functions with respect to x.
\(cos(sin\ x)\)

Compute the following:
\((i)\begin{bmatrix}a&b\\-b&a\end{bmatrix}+\begin{bmatrix}a&b\\b&a\end{bmatrix}\)
\((ii)\begin{bmatrix}a^2+b^2& b^2+c^2\\ a^2+c^2& a^2+b^2\end{bmatrix}+\begin{bmatrix}2ab& 2bc \\-2ac& -2ab\end{bmatrix}\)
\((iii)\begin{bmatrix}-1&4&-6\\ 8&5&16\\ 2&8&5\end{bmatrix}+\begin{bmatrix}12&7&6 \\8&0&5\\ 3&2&4\end{bmatrix}\)
\((iv)\begin{bmatrix}cos^2x& sin^2x\\ sin^2x& cos^2x\end{bmatrix}+\begin{bmatrix}sin^2x& cos^2x\\ cos^2x& sin2x\end{bmatrix}\)
Express the following matrices as the sum of a symmetric and a skew-symmetric matrix:
\((i)\begin{bmatrix}3&5\\1&-1\end{bmatrix}\)
\((ii)\begin{bmatrix}6&-2&2\\ -2&3&-1\\ 2&-1&3\end{bmatrix}\)
\((iii)\begin{bmatrix}3&3&-1\\ -2&-2&1\\ -4&-5&2\end{bmatrix}\)
\((iv)\begin{bmatrix}1&5\\-1&2\end{bmatrix}\)
Maximise Z=-x+2y
subject to the constraints:
x≥3,x+y≥5,x+2y≥6,y≥0.
Minimise and Maximise Z=5x+10y
Subject to x+2y≤120,x+y≥60,x-2y≥0,x,y≥0.

Prove that \(x^2-y^2=c(x^2+y^2)\)is the general solution of differential equation(\(x^3-3xy^2)dx=(y^3-3x^2y)dy\),where \(c\) is parameter.

Show that the points \(A(1,2,7),B(2,6,3)\),and \(C(3,10,-1)\) are collinear.

Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. What is the value of E(X)?

For each of the exercises given below, verify that the given function (implicit or explicit)
is a solution of the corresponding differential equation.

i) \(y=ae^x+be^{-x}+x^2: x\frac{d^2y}{dx^2}+2\frac{dy}{dx}-xy+x^2-2=0\)

ii) \(y=e^x(a \cos x+ b \sin x):\frac{d^2y}{dx^2}-2\frac{dy}{dx}+2y=0\)

iii) \(y= x \sin 3x:\frac{d^2y}{dx^2}+9y-6\cos3x=0\)

iv) \(x^2=2y^2\log y:(x^2+y^2)\frac{dy}{dx}-xy=0\)

Find the vector equation of the line passing through(1, 2, 3)and parallel to the planes \(\vec r.=(\hat i-\hat j+2\hat k)=5\) and \(\vec r.(3\hat i+\hat j+\hat k)=6\).

Let X denotes the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

Solve the system of the following equations
\(\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4\)
\(\frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1\)
\(\frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2\)

Determine P(E|F): A dice is thrown three times. 
E: 4 appears on the third toss,
F: 6 and 5 appears respectively on first two tosses.

Find the distance of the point (-1,-5,-10) from the point of intersection of the line \(\hat r= 2\hat i\hat -j+2\hat k+λ(3\hat i+4\hat j+2\hat k)\) and the plane \(\vec r.(\hat i-\hat j+\hat k)=5\).