List of top Mathematics Questions

The set of all points, where the function \(f(x)=\frac{x}{(1+|x|)}\) is differentiable, is
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 :
If \(f(x,y)=x^2+y^2+6x+12\), then minimum value of f is:
Match List I with List II
LIST I LIST II
A.A square matrix A is said to be symmetric if I.A=A'
B.A square matrix A is said to be skew symmetric ifII.A= -A'
C.If A is any square matrix thenIII.A+A' is a symmetric matrix
D.If A is any square matrix thenIV.A-A' is a skew symmetric matrix
Choose the correct answer from the options given below:
Match List I with List II
Homogeneous function Degree
A.\(f(x,y)=\frac{x^\frac{1}{3}+y^\frac{1}{3}}{x^\frac{1}{2}+y^\frac{1}{2}}\)I.3
B.\(f(x,y)=\frac{x+y}{\sqrt{x}+\sqrt{y}}\)II.\(\frac{1}{2}\)
C.\(f(x,y)=\frac{x^4+y^4}{x+y}\)III.1
D.\(f(x,y)=\frac{\sqrt{x^3+y^3}}{\sqrt{x}+\sqrt{y}}\)IV.\(-\frac{1}{6}\)
Choose the correct answer from the options given below:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A given family of curves is said to be 'self- orthogonal' if the family of orthogonal trajectory is the same as the given family of curves.
Reason R: For finding orthogonal trajectory, replace \(\frac{dy}{dx}by-\frac{dx}{dy}\) in \(f(x,y,\frac{dy}{dx})=0\)
In the light of the above statements, choose the correct answer from the options given below:
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?
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:
Which one of the following is harmonic function
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 :
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 :
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 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 infinite series \(\displaystyle\sum_{n=1}^{∞} (1+\frac{1}{n})^{-n^2}\) is:
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
The infinite series \(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{4^{n+2}}\) is:
Match List I with List II
LIST I LIST II
A.Series \(\displaystyle\sum_{n=1}^{∞} \frac{1}{n^\frac{3}{2}}\) isI.Monotone and 
convergent both
B.Series \(\displaystyle\sum_{n=1}^{∞} \frac{3^n}{n^2}\) isII.\(e^{-2}\)
C.\(\lim\limits_{n \to \infty} (\frac{n+1}{n+2})^{2n+1}\)III.Divergent to ∞
D.sequence \(x_n=1+\frac{1}{2!}+\frac{1}{3!}+…\frac{1}{n!}\) for n∈NIV.Convergent
Choose the correct answer from the options given below:
The value of \(\lim\limits_{n \to \infty} \frac{1}{n} [1+2^{\frac{1}{2}}+3^{\frac{1}{3}}+...n^{\frac{1}{n}}]\) is
Given below are two statements
Statement I: Draw back in Lagrange's method of undetermined multipliers is that nature of stationary point cannot be determined
Statement II: \(\displaystyle\sum_{n=1}^{∞} (-1)^{n-1}\frac{1}{n\sqrt n}\)convergent
In the light of the above statements, choose the correct answer from the options given below
The integral \(\int\limits_0^1\int\limits_0^x(x^2+ y^2) dy dx\) is:
If \(\vec{F} = (x+2y+az)\hat{i} + (bx −3y-z)\hat{j}+(4x+cy+2z)\hat{k}\) is irrotational, where a, b and c are constant, then a2 + b2 + c2 is equal to :
A. vector \(\vec{V}\) is said to be solenoidal if div \(\vec{V} = 0\)
B. Vector \(\vec{F}\) is said to be irrotational if curl \(\vec{F} = \vec{0}\)
C. If \(\vec{F}\) represents the force acting on a particle along are AB, then total work done \(\int^{B}_A \vec{F}\times \vec{dr}\)
D. Volume integral \(\int \int\limits_{V} \int \vec{F}\times dV\)
choose the correct answer from the options given below
If \(\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\) and \(r=\sqrt{x^2+y^2+z^2}\), then grad \((\frac{1}{r})\) is equal to :