List of top Mathematics Questions

Match List I with List II

List I Differential Equation		List II Particular Integral (P.I)
A.	(D2+6D+9)y=e3x	I.	\(\frac{x}{6}\sin3x\)
B.	(D2-6D+9)y=3	II.	\(-\frac{1}{5}\cos3x\)
C.	(D2+4)y=cos3x	III.	\(\frac{1}{3}\)
D.	(D2+9)y= cos3x	IV.	\(\frac{1}{36}e^{3x}\)

Choose the correct answer from the options given below:

If \(\int \int\limits_{R} \int xyz\ dxdydz=\frac{m}{n}\) where, m,n, are coprime and R:0≤x≤1,1≤ y ≤2, 2 ≤ z ≤3 , then m.n is equal to:

The solution of the differential equation \(\frac{dy}{dx}+y=3e^xy^3\) is :

The rank of matrix A = \(\begin{bmatrix} 1&3&1&-2&-3\\1&4&3&-1&-4\\2&3&-4&-7&-3\\3&8&1&-7&-8 \end{bmatrix}\)

Let A =\(\begin{bmatrix}2&3\\4&-1\end{bmatrix}\) then the matrix B that represents the linear operator A relative to the basis
S = {\(u_1,u_2\)}=\({[1, 3]^T, [2, 5]^T}\), is:

Which one of the following is a cyclic group?

Given below are two statements
Statement I: If A = \(\begin{bmatrix}2 &2\\ 1& 3\end{bmatrix}\) then sum of eigenvalues of A is 3.
Statement II: If \(λ\) is an eigenvalue of \(T\), where \(T\) is invertible linear operator, then \(λ^{-1}\) is an eigenvalue of \(T^{-1}\)
In the light of the above statements, choose the correct answer from the options given below

If particular Integral (P.I) of \((D^2-4D+4)y=x^3e^{2x}\) is \(e^{mx}\frac{x^n}{20}\), then m²+n² is equal to:

The integral \(\int\limits_0^1\int\limits_0^x(x^2+ y^2) dy dx\) is:

A scalar potential \(\Psi\) has the gradient defined as  \(\nabla\Psi=yz\hat{i}+xz\hat{j}+xy\hat{k}\). The value of the integral \(\int_c\nabla\Psi.d\overrightarrow{r}\) on the curve \(\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}\), where curve C: x=t, y = t², z = 3t² (1 ≤ t ≤ 3) is:

Match List I with List II

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The value of double integal \(\int\limits_0^∞\int\limits_0^xe^{-xy} ydydx\) is equal to:

The infinite series \(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{4^{n+2}}\) is:

Double integral \(\int\limits_0^2\int\limits_0^{\sqrt{2x-x^2}}\frac{xdydx}{\sqrt{x^2+y^2}}\) equals:

The value of C in Rolle's theorem where \(-\frac{π}{2}\)<C<\(\frac{π}{2}\) and \(f(x)=cos x\) on \([-\frac{π}{2},\frac{π}{2}]\) is equal to :

The infinite series \(\displaystyle\sum_{n=1}^{∞} (1+\frac{1}{n})^{-n^2}\) is:

Given below are two statements
Statement I: In cylindrical co-ordinates, \(Volume = \int \int\limits_{V} \int rdrdødz \)
Statement II: In spherical polar Co-ordinates, \(Volume = \int \int\limits_{V} \int r^2\ \cos\theta\ drd\theta d\phi\)
In the light of the above statements, choose the correct answer from the options given below :

If there is no feasible region in LPP, then the problem has:

Given below are two statements :
Statement I: Mdx+Ndy = 0 is said to be an exact differential equation if it satisfies the following condition \(\frac{∂M}{∂x}=\frac{∂N}{∂y}\)
Statement II: If Mdx + Ndy = 0 is not an exact differential equation and \(\frac{1}{N}(\frac{∂M}{∂y}-\frac{∂N}{∂x})=f(x)\), then \(I.F.=e^{\int f(x)dx}\)
In the light of the above statements, choose the correct answer from the options given below :

Match List I with List II

Choose the correct answer from the options given below:

Match List I with List II

List I		List II
A.	Φ=y2,∇Φ at (1, 1, 1)	I.	\(\hat{i}\)
B.	Φ=x,∇Φ at (1, -1, 2)	II.	\(-6\hat{k}\)
C.	Φ=2x3,∇Φ at (0, 1, 2)	III.	\(2\hat{j}\)
D.	Φ=3z2,∇Φ at (1, 2, -1)	IV.	\(\vec{0}\)

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If \(u=sin^{-1}[\frac{x+y}{\sqrt{x}+\sqrt{y}}]\) and \(x^2u_{xx}+2xyu_{xy}+y^2u_{yy}=-\frac{sinucos2u}{m^2cos^3u}\) then, m is equal to

From the given system of constraints
A. 3x+5y≤90
B. x + 2y≤30
C. 2x + y≤30
D. x≥0, y≥0
The redundant constraint is :

The set of all points, where the function \(f(x)=\frac{x}{(1+|x|)}\) is differentiable, is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The given vector \(\vec{F}=(y^2-z^2+3yz-2x)\hat{i} +(3xz+2xy)\hat{j}+(3xy-2xz+2z)\hat{k}\) is solenoidal
Reason R: A vector \(\vec{F}\) is said to be solenoidal if div \(\vec{F}\) = 0
In the light of the above statements, choose the correct answer from the options given below :