List of top Mathematics Questions

Mean and variance pair is given below. A pair representing the data of a binomial distribution is

A multistep method used to solve differential equations is

The general solution of one dimensional wave equation \[ \frac{\partial^2v}{\partial t^2} = c^2 \frac{\partial^2v}{\partial x^2} \] is \(u(x,t)=\)

If \(x_0=1.2\) is the initial guess of the solution of \(x^3+2x-1=0\), then the \(1^{\text{st}}\) iteration solution \(x_1=\)

If \[ F(x)= \begin{cases} 0, & x[2mm] \left(\dfrac{x+7}{a}\right), & -7[2mm] 1, & x>7, \end{cases} \] represents the probability distribution function of a continuous random variable, then \(a=\)

The matrix \[ A= \begin{bmatrix} 1 & 1+i & 2i 1-i & 3 & 4 -2i & 4 & 5 \end{bmatrix} \] has

An eigen vector of the matrix \[ A= \begin{bmatrix} 3 & 2 1 & 2 \end{bmatrix} \] is

A convergent series from the given series is

Fourier series of \(x^2,\;0<x<2\) is \[ f(x)=\frac{a_0}{2} +\sum_{n=1}^{\infty}a_n\cos(n\pi x) +\sum_{n=1}^{\infty}b_n\sin(n\pi x), \] then \(b_2=\)

A multistep method for solving a differential equation numerically among the following is

The iterative formula for finding \(2^{\frac{1}{5}}\) using Newton-Raphson method is

The complete solution of \[ y^3\frac{\partial u}{\partial x} + x^2\frac{\partial u}{\partial y} = 0 \] is \(u(x,y)=\)

The solution of \[ \frac{dy}{dx} + \left[2(x-1)\sin x+x(x-2)\cos x\right]y = \frac{e^{2x\sin x}}{e^{x^2\sin x}}, \] at \(x=2\) if \(y(\pi)=0\) is

Let \[ f(x)=x^3-\frac32x^2, \] which of the following is not correct?

The Laplace transform of \[ \int_{0}^{t} p\sin(t-p)\,dp \] is

If \[ I=\int_C x^2y\,dx-xy^2\,dy, \] where \(C\) is the circle \[ x^2+y^2=16, \] then \(2I=\)

Consider the system of equations \[ x+y+z=4\mu,\qquad x+2y+2z=10\mu,\qquad x+3y+4\lambda z=\mu^2+15, \] where \(\lambda\) and \(\mu\) are real numbers. Which of the following is correct?

If \(P\) is an orthogonal matrix of order \(3\times3\), \(A=\begin{bmatrix}1& 2& 2\\2& 1& 2\\2& 2& 1\end{bmatrix}\) and the eigenvalues of \(P^{T}AP\) are \(\alpha,\beta,\gamma\), then \(\alpha^2+\beta^2+\gamma^2=\)

Evaluate \[ \lim_{x\to0}\frac{e^{\tan x}-e^{\sin x}}{(1-\cos x)\tan x} \]

Let the sum of the first n terms of an A.P. be $3n^2 + 5n$. Then the sum of squares of the first 10 terms of the A.P. is:

Let \( \alpha \) and \( \beta \) respectively be the maximum and the minimum values of the function \( f(\theta) = 4\left(\sin^4\left(\frac{7\pi}{2} - \theta\right) + \sin^4(11\pi + \theta)\right) - 2\left(\sin^6\left(\frac{3\pi}{2} - \theta\right) + \sin^6(9\pi - \theta)\right) \). Then \( \alpha + 2\beta \) is equal to :

\[ \int \frac{1}{x^{1/2}+x^{1/3}}\,dx \] is equal to:

If \(\sin 3A = \cos (A - 26^{\circ})\), where 3A is an acute angle, find the value of A.

Given the linear equation \(y = 2x + k\), determine the value of k if the point P(3, 7) lies on the line.

Which of the following cannot be the sides of a triangle ?