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List of top Mathematics Questions

The slope of the line which makes $\frac {3\pi}{4}$angle with the positive direction of x-axis is

The objective function of L.L.P. defined over the convex set attains its optimum value at

If $\begin{bmatrix} 2 & 1 \\ 3 & 2\end{bmatrix}$ A $\begin{bmatrix} -3 & 2 \\ 5 & -3\end{bmatrix}$ =$\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}$, then A =?

If $y(x)$ is the solution of the differential equation $x d y-\left(y^2-4 y\right) d x=0 \text { for } x>0, y(1)=2,$ and the slope of the curve $y=y(x)$ is never zero, then the value of $10 y(\sqrt{2})$ is ____.

Let $\alpha$ be a positive real number. Let $f: R \rightarrow R$ and $g:(\alpha, \infty) \rightarrow R$ be the functions defined by
$f(x)=\sin \left(\frac{\pi x}{12}\right) \text { and } g(x)=\frac{2 \log _e(\sqrt{ x }-\sqrt{\alpha})}{\log _e\left( e ^{\sqrt{x}}- e ^{\sqrt{\alpha}}\right)} $
Then the value of $\displaystyle\lim _{x \rightarrow \alpha^{+}} f( g ( x ))$ is _______.

$\displaystyle\lim_{x\rightarrow-2}\frac{3x^2+ax-2}{x^2-x-6}$ is a finite number, then the value of a is equal to

The end points of the major axis of an ellipse are (2, 4) and (2,-8). If the distance between foci of this ellipse is 4, then the equation of the ellipse is

If the solution set of the inequality $|a+3x|\leq6\ is\ [\frac{-8}{3},\frac{4}{3}]$, then the value of a is

In a certain code, BANKER is written as LFSCBO. How will CONFER be written in that code?

An accurate clock shows 8 O'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 20:00 (8 O'clock in the evening)?

Shade the feasible region for the inequalities
$ 6x + 4y \leq 120 $, $ 3x + 10y \leq 180 $, $ x, y \geq 0 $ in a rough figure.

If $ \lim_{x \to 0} \frac{(1 + a^3)^x + 8e^{1/x}}{1 + (1 - b^3)^x e^{1/x}} = 2 $, then:

The approximate value of $ (0.007)^{1/3} $ is:

Let $ f(x) = a - (x-3)^{8/9} $, then the maxima of $ f(x) $ is:

If the derivative of the function $ f(x) = \begin{cases} b x^2 + ax + 4; & x \geq -1 \\ a x^2 + b; & x < -1 \end{cases} $ is everywhere continuous, then

If $ \lim_{x \to \infty} \left( 1 + \frac{a}{x} + \frac{b}{x^2} \right)^{2x} = e^2 $, then:

If for any $ 2 \times 2 $ square matrix $ A $, $ A(\text{adj} A) = \begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix} $, then find the value of $ \det(A) $.

If $ A = \begin{bmatrix} 2 - k & 2 \\ 1 & 3 - k \end{bmatrix} $ is a singular matrix, then the value of $ 5k - k^2 $ is:

If $ A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix} $, then $ |A| \cdot \text{adj}(A) $ is equal to:

The argument of $ \dfrac{1 - i\sqrt{3}}{1 + i\sqrt{3}} $ is:

$ (i + \sqrt{3})^{100} + (i - \sqrt{3})^{100} + 2^{100} $ is equal to:

The total number of terms in the expansion of $ (x + y)^{100} + (x - y)^{100} $:

The coefficient of $ x^{20} $ in the expansion of $ (1 + 3x + 3x^2 + x^3)^{20} $:

The base of common logarithm is

The value of $log_{1250} 1250$ is