List of top Mathematics Questions

The values of $ x $ for which $ 4^x + 4^{1-x} - 5 < 0 $ , is given by

For $ 'c' $ is the arbitrary constant, the solution of the differential equation $ (x^2 + 2y^2)dx - xy\,dy= 0 $ is

The eccentricity of the ellipse $ \frac{\left(x-1\right)^{2}}{2} + \left(y + \frac{3}{4}\right)^{2} = \frac{1}{16}$ is

If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$

The function $ f (x) = x^2 + 2x - 5$ is strictly increasing in the interval

If a matrix $A$ is both symmetric and skew symmetric, then

The integrating factor of the differential equation $x . \frac{dy}{x} + 2y = x^2 $ is $(x \neq 0)$

The area of triangle with vertices ${(K, 0),(4,0) , (0, 2)}$ is $4$ square units, then value of $K$ is

Reflection of the point $( a , ? , ? )$ in $XY$ plane is

The perpendicular distance of the point ${P(6,7,8)}$ from $XY$-plane is

If coefficient of variation is $60$ and standard deviation is $24$, then Arithmetic mean is

If $z_1$ and $z_2$ are z co-ordinates of the points of trisection of the segment joining the points $A(2, 1, 4), B _1 + z_2 =$

If the function \[ f(x) = \begin{cases} [ tan (\frac {\pi}{4}+x)]^{1/x} & \quad for\, x \neq 0\\ K \,\,\,\,\,\,\,\,\,\text{if } x =0 \end{cases} \] is continuous at $x = 0$, then $K = ?$

The area of the region bounded by the lines $y = 2x + 1, y = 3x + 1$ and $x = 4$ is

The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is

If $c$ denotes the contradiction then dual of the compound statement $\sim p \wedge ( q \vee c)$ is

The objective function $z = 4x_1 + 5x_2$, subject to $2x_1 + x_2 \geq 7 , 2x_1 + 3x_2 \leq 15 , x_2 \leq 3, x_1 , x_2 \geq 0 $ has minimum value at the point

The common chord of the circles $x^2 + y^2 - 4x - 4y = 0$ and $2x^2 + 2y^2 = 32$ subtends at the origin an angle equal to

Let $A=\begin{pmatrix}x+2&3x\\ 3&x+2\end{pmatrix}, B=\begin{pmatrix}x&0\\ 5&x+2\end{pmatrix}$. Then all solutions of the equation det $(AB) = 0$ is

Out of $7$ consonants and $4$ vowels, words are formed each having $3$ consonants and $2$ vowels. The number of such words that can be formed is

The equation of the plane through \((1, 2, -3)\) and \((2, -2, 1)\) and parallel to \(X-\)axis is

The probability that a non leap year selected at random will have $53$ Sundays is

The axis of the parabola $x^2 + 2xy + y^2 - 5x + 5y - 5 = 0$ is

Let P be the foot of the perpendicular from focus S of hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ on the line $bx - ay = 0$ and let $C$ be the centre of hyperbola. Then the area of the rectangle whose sides are equal to that of $SP$ and $CP$ is

The line segment joining the foci of the hyperbola $x^2 - y^2 + 1 = 0$ is one of the diameters of a circle. The equation of the circle is