List of top Mathematics Questions asked in MET

If \( \alpha, \beta \) are the roots of \( x^2 - 3x + 1 = 0 \), then the equation whose roots are \( \frac{1}{\alpha - 2} \) and \( \frac{1}{\beta - 2} \) is:

The value of \[ \int \frac{dx}{x \sqrt{1 - (\log x)^2}} \] is:

The value of \[ \int \frac{x^2}{(x^2 + 2)(x^2 + 3)} \, dx \] is equal to:

Which of the following statements is/are correct?
I. Adjoint of a unit matrix is a unit matrix.
II. \( A (\text{adj } A) = (\text{adj } A) A = |A|I \)
III. Adjoint of a symmetric matrix is symmetric.
IV. Adjoint of a diagonal matrix is a diagonal matrix.

The degree and order of the differential equation of the family of all parabolas whose axis is the x-axis, are respectively:

The differential equation satisfied by the family of curve \( y = ax \cos \left( \frac{1}{x} + b \right) \), where \( a, b \) are parameters, is:

Integrating factor of the equation: \[ (x^2 + 1) \frac{dy}{dx} + 2xy = x^2 - 1 \] is:

The value of \[ \left| \begin{array}{ccc} (a+1)^2 & (b+1)^2 & (c+1)^2 (a-1)^2 & (b-1)^2 & (c-1)^2 \end{array} \right| \] is:

Let \( A \) be a square matrix all of whose entries are integers. Then, which one of the following is true?

If \[ q_1x + b_1y + c_1z = 0, \quad a_2x + b_2y + c_2z = 0, \quad a_3x + b_3y + c_3z = 0 \] then the given system has:

The function \( f(x) = \frac{ax + b}{(x-1)(x-4)} \) has a local maxima at \( (2, -1) \), then

The point in the interval [0, 2π], where $f(x)=eˣsin~x$ has maximum slope, is

If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is

If $f(x)=(ax+b)sin~x+(cx+d)cos~x$, then the values of a, b, c and d such that $f^\prime(x)=x~cos~x$ for all x, are

If $y=sin(m~sin^-1x)$, then $(1-x²)y^\prime\prime-xy^\prime}$ is equal to

If \( x^y = e^{x - y} \), then \( \frac{dy}{dx} \) is equal to

Radius of the circle \( \vec{r}^2 + \vec{r} \cdot (2\hat{i} - 2\hat{j} - 4\hat{k}) - 19 = 0, \vec{r} \cdot (\hat{i} - 2\hat{j} + 2\hat{k}) + 8 = 0 \) is

If $f(x)=logₓ(log~x)$, then $f^\prime(x)$ at $x=e$ is

If \( f(x) = \begin{cases} b, & 0 \leq x < 1 \\ x + 3, & 1 < x \leq 2 \\ 4, & x = 1 \end{cases} \) , then the value of \( (a, b) \) for which \( f(x) \) cannot be continuous at \( x = 1 \) is

\( \lim_{x \to 0} \frac{\sqrt{1 - \cos(2x)}}{\sqrt{2} \cdot x} \) is

The reflection of the point (2, 1, 3) in the plane $3x-2y-z=9$ is

The locus of the equation $xy+yz=0$ is

The direction cosines of any normal to the xy-plane are

The tangent and normal to a rectangular hyperbola $xy=c²$ at a point cut off intercepts $a₁, a₂$ on one axis and $b₁, b₂$ on the other, then $a₁a₂ + b₁b₂$ is equal to

If $e$ is the eccentricity of the hyperbola $x²/a² - y²/b² = 1$ and $θ$ is the angle between the asymptotes, then $\cos(θ/2)$ is equal to