List of top Mathematics Questions

Let $O$ be the origin and let $P Q R$ be an arbitrary triangle. The point $S$ is such that $\overrightarrow{O P} \cdot \overrightarrow{O Q}+\overrightarrow{O R} \cdot \overrightarrow{O S}=\overrightarrow{O R} \cdot \overrightarrow{O P}+\overrightarrow{O Q} \cdot \overrightarrow{O S}=\overrightarrow{O Q} \cdot \overrightarrow{O R}+\overrightarrow{O P} \cdot \overrightarrow{O S}$ Then the triangle $P Q R$ has $S$ as its

If $8\sqrt{x}\left(\sqrt{9+\sqrt{x}}\right)dy = \left(\sqrt{4+\sqrt{9+\sqrt{x}}}\right)^{-1}\,\,dx, \,\,\,\,x > 0$ and $

What will be the distance of $ (1, 0, 2) $ from the point of intersection of plane $ x - y + z = 16 $ and the line $ \left(\frac{x-2}{3}\right) = \left(\frac{y+1}{4}\right) = \left(\frac{z-2}{12}\right) $ ?

$ P $ speaks truth in $ 70\% $ cases and $ Q $ speaks in $ 80\% $ of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

If $R\left(t\right) = \begin{bmatrix}\cos t&\sin t\\ -\sin t&\cos t\end{bmatrix}$, then R(s) R(t) equals

If = $\int x \log\left(1+ \frac{1}{x}\right)dx = f\left(x\right)\log\left(x+1\right)+g\left(x\right)x^{2}+Lx +C$, then

The integral $\displaystyle\int \frac{dx}{(1+ \sqrt{x}) \sqrt{x - x^2}}$ is equal to (where $C$ is a constant of integration)

A cylindrical pipe of radius $1.4\,\text{m$ has water flowing out at $2.5\,\text{m/s}$ into a cuboidal tank of dimensions $28\,\text{m}\times 11\,\text{m}\times 25\,\text{m}$. The flow completely occupies the pipe’s cross-section. What percentage of the tank is filled up in $8$ min $20$ s?}

The area of a trapezium of height $40\,\text{cm$ is $1600\,\text{cm}^2$. One parallel side is $10\,\text{cm}$ longer than the other side. Find the ratio of the lengths of the parallel sides.}

Some spherical balls of diameter $2.8\,\text{cm$ are dropped into a cylindrical container containing some water and are fully submerged. The diameter of the container is $14\,\text{cm}$. Find how many balls have been dropped in it if the water rises by $11.2\,\text{cm}$.}

If $x+\dfrac{1{x-1}=5$, then find the value of $\,(x-1)^2+\dfrac{1}{(x-1)^2}\,$?}

In an equilateral triangle $ABC$, if the area of its in-circle is $4\pi\ \text{cm^2$, then find the length of the angle bisector $AD$?}

Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?

If the tangent at a point $P$, with parameter $t$, on the curve $x = 4t^2 + 3, y = 8t^3 - 1, t \in R$, meets the curve again at a point $Q$, then the coordinates of $Q$ are :

The number of distinct real roots of the equation, $\begin{vmatrix}\cos x&\sin x &\sin x\\ \sin x&\cos x&\sin x\\ \sin x&\sin x&\cos x\end{vmatrix}= 0$ in the interval $ \left[- \frac{\pi}{4}, \frac{\pi}{4}\right]$ is :

If the number of terms in the expansion of $\left( 1 - \frac{2}{x} + \frac{4}{x^2} \right)^n , x \neq 0$ , is $28$ , then the sum of the coefficients of all the terms in this expansion, is :

For $ x \epsilon R , f (x) = | \log 2 - \sin x|$ and $g(x) = f(f(x))$, then :

A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x^2}{3} + \frac{y^2}{4} = 4 $ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does NOT lie on it ?

The point $(2, 1)$ is translated parallel to the line $L : x-y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is :