List of top Mathematics Questions

If \(\alpha,\beta\) are the roots of the equation \[ 2x^2+6x+k=0, \] then the maximum value of \[ \frac{\alpha}{\beta}+\frac{\beta}{\alpha} \] when \(k<0\) is:
If \[ y^2+z^2=ayz,\quad z^2+x^2=bxz,\quad x^2+y^2=cxy, \] then the value of \[ \frac{xz}{y^2}+\frac{y^2}{zx} \] is:
The number of pairs of consecutive positive even integers such that the sum of their squares is \(290\) is:
If \[ |z-3i|+|z+5i|=4, \] then the locus of \(z\) is:
If \[ A= \begin{bmatrix} 1 & 1 & a+1 1 & a+1 & 1 a+1 & 1 & 1 \end{bmatrix} \] is not an invertible matrix, then the sum of all the values of \(a\) is:
If \[ (x-iy)^{\frac{1}{3}}=2-i\sqrt{3} \] and the point \(z=(x,y)\) lies on the line \[ \frac{x}{2}+\frac{y}{\sqrt{3}}=k, \] then \(k=\)
If \[ \left|z+\frac{2}{z}\right|=2, \] then the maximum value of \(|z|\) is:
A complex number \(z\) among the following which does not satisfy \[ z^3+27i=0 \] is:
If \[ \begin{pmatrix} 5 & a & -7 \\ b & -7 & c \\ -7 & d & -1 \end{pmatrix} \] is the adjoint of the matrix \[ \begin{pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{pmatrix}, \] then \(a+b+c+d=\)
The domain of the real valued function \[ f(x)=\sqrt{\frac{2-|x|}{3-|x|}} \] is:
If \(A\) and \(B\) are \(n\times n\) square matrices such that \[ (2A+B)^2+(A-3B)^2=5A^2-2AB+10B^2, \] then \(ABAB=\)
The rank of the matrix \[ A= \begin{bmatrix} 1 & -1 & 0 & -2 -4 & 4 & 0 & 8 -2 & 1 & 2 & 4 \end{bmatrix} \] is:
If the function \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=x|x|\), then \(f\) is:
At any point \((x,y)\) on a curve if the length of the subnormal is \((x-1)\) and the curve passes through \((1,2)\), then the curve is a conic. A vertex of the curve is
\(y=Ae^x+Be^{-2x}\) satisfies which of the following differential equations?
If the solution of \[ \frac{dy}{dx}-y\log_e0.5=0,\quad y(0)=1, \] and \(y(x)\to k\), as \(x\to\infty\) then \(k=\)
The parametric form of a curve is \(x=\dfrac{t^3}{t^2-1},\; y=\dfrac{t}{t^2-1}\), then \(\displaystyle \int \frac{dx}{x-3y}=\)
The value of
\[ \int_0^1 a^k x^k\,dx \] is
Let \(\alpha\) and \(\beta\), \((\alpha\lt \beta)\), are roots of \(18x^2-9\pi x+\pi^2=0\), \(f(x)=x^2\), \(g(x)=\cos x\). Then \(\displaystyle \int_{\alpha}^{\beta} x(gof(x))dx=\)
\[ \int_{0}^{\pi} x\left(\sin^2(\sin x)+\cos^2(\cos x)\right)dx= \]
\[ \lim_{n\to\infty} \left( \frac{1}{1+n^5} + \frac{2^4}{2^5+n^5} + \frac{3^4}{3^5+n^5} +\cdots+ \frac{n^4}{n^5+n^5} \right) = \]
If
\[ I_n=\int \tan^n x\,dx \] and
\[ I_0+I_1+2I_2+2I_3+2I_4+I_5+I_6=\sum_{k=1}^{n}\frac{\tan^k x}{k}, \] then \(n=\)
Evaluate
\[ \int \frac{e^{\cot x}}{\sin^2 x}\left(2\log\cosec x+\sin2x\right)\,dx \]
The minimum value of \(f(x)=x+\dfrac{4}{x+2}\) is
The condition that \(f(x)=ax^3+bx^2+cx+d\) has no extreme value is