List of top Mathematics Questions

Find X and Y,if \((i)X+Y=\begin{bmatrix}7&0\\2&5\end{bmatrix}\) and \(X-Y=\begin{bmatrix}3&0\\0&3\end{bmatrix}\)\((ii)2X+3Y=\begin{bmatrix}2&3\\4&0\end{bmatrix}\)and \(3X+2Y=\begin{bmatrix}2&-2\\-1&5\end{bmatrix}\)
If \(A=\begin{bmatrix}1&2&-3\\ 5&0&2\\ 1&-1&1\end{bmatrix}\)\(,B=\begin{bmatrix}3&-1&2\\ 4&2&5\\ 2&0&3\end{bmatrix}\)\(,and\space C=\begin{bmatrix}4&1&2\\ 0&3&2\\ 1&-2&3\end{bmatrix}\), then compute(A+B)and(B-C). Also, verify that A+(B-C)=(A+B)-C.

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x,y) is equal to the sum of coordinates of the point.

Which of the following differential equations has y= c1ex+c2e-x as the general solution?

Let \(f: R→ R\) be defined as \(f(x)=x^4\). Choose the correct answer.
Let \(A=R−\{3\}\) and \(B=R−\{1\}\). Consider the function \(f: A→B\) defined by \(f(x)=\bigg(\frac{x-2}{x-3}\bigg)\). Is f one-one and onto? Justify your answer.
Let \(f: N → N\) be defined by \(f(n) =   \begin{cases} \frac{n+1}{2} & \quad \text{if } n \text{ is odd}\\ \frac{n}{2}  & \quad \text{if } n \text{ is even} \end{cases}\) for all \(n∈N\).
State whether the function f is bijective. Justify your answer.

Find general solution: \(y dx+(x-y^2)dy=0\)

Find the general solution: \(x\frac {dy}{dx}+2y=x^2log\ x\)

Find the general solution: \(\frac {dy}{dx}+\frac yx=x^2\)

Find the general solution: \(\frac {dy}{dx}+3y=e^{-2x}\)

\(Find\ \frac {dy}{dx}:\)
\(y=cos^{-1}(\frac {2x}{1+x^2}),\  -1<x<1\)

\(Find\ \frac {dy}{dx}:\)
\(y=sin^{-1}(2x\sqrt {1-x^2},\ \frac {-1}{\sqrt 2}<x<\frac {1}{\sqrt2}\)

\(Find \ \frac {dy}{dx}:\)
\(y=sec^{-1}(\frac {1}{2x^2-1}),\ 0<x< \frac {1}{\sqrt2}\)

Prove that\(\begin{vmatrix}  a^2&bc  &ac+c^2 \\   a^2+ab&b^2  &ac\\   ab&b^2+bc  &c^2  \end{vmatrix}=4a^2b^2c^2\)

Solve the equation \(\begin{vmatrix} x+a &x  &x \\  x &x+a  &x \\   x&x  &x+a  \end{vmatrix}=0\) , a≠0

If a,b, and c are real numbers and determinant \(\Delta = \begin{vmatrix} b+c &c+a  &a+b \\   c+a&a+b  &b+c \\   a+b&b+c  &c+a  \end{vmatrix}\)
Show that either a+b+c=0 or a=b=c. 

Find the general solution: \((x+y)\frac {dy}{dx}=1\)

Let A and B be sets. Show that f: \(A \times B → B \times A\) such that (a,b)=(b,a) is bijective function

Prove that the determinant \(\begin{vmatrix} x &sin\theta  &cos\theta \\   -sin\theta&-x  &1 \\   cos\theta&1  &x  \end{vmatrix}\) is independent of θ. 

Compute the magnitude of the following vectors:\(\overrightarrow{a}\)=\(\hat{i}\)+\(\hat j+\hat k\);\(\overrightarrow{b}\)=2\(\hat{i}\)-7\(\hat{j}\)-3\(\hat{k}\); \(\overrightarrow{c}\)= \(\frac{1}{\sqrt 3}\hat i+\frac{1}{\sqrt 3}\hat j-\frac{1}{\sqrt 3}\hat k\)

The order of the differential equation \(2x^2\,\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0\) is

The degree of the differential equation \(\bigg(\frac{d^2y}{dx^2}\bigg)^3+\bigg(\frac{dy}{dx}\bigg)^2+\sin\bigg(\frac{dy}{dx}\bigg)+1=0\) is

Answer the following as true or false. 
(i)a→and -a→are collinear. 
(ii)Two collinear vectors are always equal in magnitude. 
(iii)Two vectors having same magnitude are collinear. 
(iv)Two collinear vectors having the same magnitude are equal.

In figure, identify the following vectors.

 

(i)Coinitial (ii)Equal (iii)Collinear but not equal