List of top Mathematics Questions

The particular integral of \((D^2-1)y=4\cosh x\) is

The order of the permutation \(\begin{pmatrix}1& 2& 3& 4& 5& 6\\2& 4& 6& 5& 1& 3\end{pmatrix}\) is

The congruence \(10x \equiv 15 \pmod{35}\) has

If \(N\) be the set of natural numbers and \(*\) is a binary operation defined by \(a*b=a+b\), then \((N,*)\) is

The number of subgroups of \(Z_{48}\) is

Particular integral of \(\left(\dfrac{d^3}{dx^3}+4\dfrac{d}{dx}\right)y=\sin 2x\) is

Complementary function of the differential equation \(\dfrac{d^2x}{dt^2}+4x=a\sin t\cos t\) is

The differential equation whose C.F. is \(y=c_1\cos 2x+c_2\sin 2x+c_3e^{-x}\) is

Which of the following is the singular solution of \(p=\log(px-y)\), \(p=\dfrac{dy}{dx}\)?

The particular integral of \((D^2-4D+4)y=\cos 2x\) is

The particular integral of \(\dfrac{d^2y}{dx^2}-2\dfrac{dy}{dx}+y=e^x\sin x\) is

Which of the following is the differential equation whose auxiliary roots are \(0,-1,-1\)?

Which of the following is NOT a solution of the differential equation \(\dfrac{d^2y}{dx^2}+y=1\)?

The solution of the differential equation \(3y\dfrac{dy}{dx}+2x=0\) represents a family of

Which of the following is a solution of the differential equation \(\dfrac{d^2y}{dx^2}+4\dfrac{dy}{dx}+4y=0\)?

The solution for the differential equation \(\dfrac{d^2y}{dx^2}=3x-2\) with boundary conditions \(y(0)=2\) and \(y'(1)=-3\) is

For what value(s) of the constants \(a\), \(b\) and \(c\) is the quadrature formula \[\int_{-1}^1 f(x)\,dx \approx af(-1)+bf(0)+cf(1)\] exact for polynomials of degree up to 3?

What is the approximate value of the integral \(\int_0^1(x+x^2)\,dx\), when Simpson's 1/3-rd rule is applied with 2 sub-intervals?

Which one of the following statements about the central difference and averaging operators is correct?

Using Newton's divided difference method, the second divided difference for the function values f(1)=2, f(2)=3, f(4)=7 is approximately equal to ____.

Which of the following statements is/are true?
(I) Gauss-Seidel method for solving a linear system converges faster than the Gauss-Jacobi method.
(II) In the Gauss-Jordan method for solving a linear system, the coefficient matrix is transformed into an upper triangular matrix.

The solution of the system of ODEs: \(\frac{dx}{dt}=x+2y\), \(\frac{dy}{dt}=3x+2y\) with initial conditions x(0)=6 and y(0)=4 is ____.

Using Lagrange interpolation with the following function values, find the approximate value of \(f(2)\).

x	0	1	3
f(x)	1	2	4

Regula Falsi method is used to find a root of the equation \(f(x)=x^3-x-1\) by choosing the initial guesses \(x_0=1\) and \(x_1=2\). What would be the value of the next iteration (i.e. \(x_3\)) up to two decimal places?

In solving the heat equation using separation of variables, the eigenvalues correspond to ____.