List of top Mathematics Questions

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 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 $K = ?$

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

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

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

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

For any vector $x$, where $\hat{ i }, \hat{ j }, \hat{ k }$ have their usual meanings the value of $( x \times \hat{ i })^{2}+( x \times \hat{ j })^{2}+( x \times \hat{ k })^{2}$ where $\hat{ i }, \hat{ j }, \mathbf { k }$ have their usual meanings, is equal to

Mean of $n$ observations $x_{1}, x_{2}, ........ , x_{n}$ is $\bar{x}.$ If an observation $x_q$ is replaced by $x'_q$ then the new mean is

The integrating factor of the first order differential equation $x^{2}\left(x^{2}-1\right) \frac{dy}{dx}+x\left(x^{2}+1\right)y=x^{2}-1$ is

Let $d_1$ and $d_2$ be the lengths of the perpendiculars drawn from any point of the line $7x - 9y + 10 = 0$ upon the lines $3x + 4y = 5$ and $12x + 5y = 7$ respectively. Then

The point $P \,(3, 6)$ is first reflected on the line $y = x$ and then the image point $Q$ is again reflected on the line $y = - x$ to get the image point $Q'$. Then the circumcentre of the $\Delta PQQ'$ is

If $\left( \frac{1 + i}{1 - i} \right)^m =1$, then the least positive integral value of $m$ is