List of top Mathematics Questions asked in MET

Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them is ________.

There are P copies of n-different books. The number of different ways in which a non-empty selection can be made from them is ________.

Nishi has 5 coins each of different denomination. The number of different sums of money she can form is ________.

The numbers $aₙ$ are defined by $a₀=1$ and $aₙ+1=3n²+n+aₙ$ for $n ≥ 0$. Then, $aₙ$ is equal to ________.

The domain of the function \( f(x) = \frac{\sqrt{9 - x^2}}{\sin^{-1}(3 - x)} \) is ________.

The range of the function $f(x)=\logₑ(3x²-4x+5)$ is ________.

If \( z = \tan(y + ax) + \sqrt{y} - ax \), then \( z_{xx} - a^2 z_{yy} \) is equal to

If $\int f(x)dx=F(x)$, then $\int x³f(x²)dx$ is equal to

\( \int \frac{x^2 + 4x^4 + 16}{dx} \) is equal to

The value of the integral $\int_π/2³π/2[sin~x]dx$, where $[·]$ denotes the greatest integer function, is

The area of the loop of the curve $ay²=x²(a-x)$ is

Solution of the differential equation \[ x = 1 + xy \frac{dy}{dx} + \frac{(xy)^2}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{(xy)^3}{3!} \left(\frac{dy}{dx}\right)^3 + \cdots \] is

If the solution of the differential equation \( \frac{dy}{dx} = ax + 32y + f \) represents a circle, then the value of \( a \) is

The approximate value of $\int₁⁵x²dx$ using trapezoidal rule with $n=4$ is

Let \( f(x) = x^{2} + ax + b \), where \( a, b \in \mathbb{R} \). If \( f(x)=0 \) has all its roots imaginary, then the roots of \( f(x) + f'(x) + f''(x) = 0 \) are

If \( \alpha, \beta, \gamma \) are the roots of \( x^{3} + 4x + 1 = 0 \), then the equation whose roots are \[ \frac{\alpha^{2}}{\beta+\gamma}, \quad \frac{\beta^{2}}{\gamma+\alpha}, \quad \frac{\gamma^{2}}{\alpha+\beta} \] is

If \( f(x) = 2x^{4} - 13x^{2} + ax + b \) is divisible by \( x^{2} - 3x + 2 \), then \( (a, b) \) is equal to

If one of the roots of \( \begin{vmatrix} 3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3 \end{vmatrix} = 0 \), then the other roots are

If \( x, y, z \) are all positive and are the \( p \)th, \( q \)th and \( r \)th terms of a geometric progression respectively, then the value of the determinant \( \begin{vmatrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{vmatrix} \) equals

If \( \begin{bmatrix} 1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1 \end{bmatrix} \) has no inverse, then the real value of \( x \) is

If \( \alpha \) and \( \beta \) are the roots of \( x^{2} - 2x + 4 = 0 \), then the value of \( \alpha^{6} + \beta^{6} \) is

If \( n \) is an integer which leaves remainder one when divided by three, then \( (1+\sqrt{3}i)^{n} + (1-\sqrt{3}i)^{n} \) equals

The period of \( \sin(4x + \cos^{4} x) \) is

\( \frac{\cos x}{\cos(x - 2y)} = \lambda \Rightarrow \tan(x - y)\tan y \) is equal to