List of top Mathematics Questions

Let the eccentricity of an ellipse be $\frac{1}{2}$. If $S(3,2)$ is a focus and $x-9=0$ is the corresponding directrix of the ellipse, then the equation of the ellipse is}

The vectors $2\vec{a}+6\vec{b}$ and $3\vec{a}-7\vec{b}$ are position vectors of the points A and B respectively. A point P divides the line segment AB internally in the ratio 3:5. Then $\vec{PB}=$

The nearest point on the line $x+2y=5$ from the point $P(7,9)$ is equal to

The eccentricity of the hyperbola $25x^{2}-36y^{2}-50x-72y-911=0$, is

The domain of the function $f(x)=\sin^{-1}(5-4x^{2})+\cos^{-1}(5-4x^{2})$ is

Let O be the origin and R be any point on $y^{2}=2x$. The locus of the midpoint of the line segment OR, is

A straight line has y -intercept -5. If it makes $120^{\circ}$ with the x-axis, then the equation of the line is

The value of $\cos^{-1}\left(\cos\frac{5\pi}{9}\cos\frac{\pi}{9}+\sin\frac{\pi}{9}\sin\frac{5\pi}{9}\right)$ is equal to

If $A\le2\sin^{-1}x+\cos^{-1}x\le B$, then A and B respectively, are

The value of $\sin 5^{\circ}\sin 10^{\circ}\sin 15^{\circ}\sin 20^{\circ}\dots\sin 240^{\circ}$ is equal to

$\sin(\frac{3\pi}{4}+x)+\cos(\frac{3\pi}{4}+x)-\sin(\frac{3\pi}{4}-x)-\cos(\frac{3\pi}{4}-x)=$

If $\frac{2x-10}{x+2}\ge x-5$ then $x$ lies in

If $10<|x+10|\le 25$, then $x$ lies in

$2^{11}\sin(\frac{x}{2^{10}})\cos(\frac{x}{2})\cos(\frac{x}{2^{2}})\cos(\frac{x}{2^{3}})\dots\cos(\frac{x}{2^{10}})$ is equal to

The value of $3\cot(-405^{\circ})\tan315^{\circ}-5\cot495^{\circ}\tan(-585^{\circ})$ is equal to

Let $A=\begin{pmatrix}1&\tan x\\ -\tan x& 1\end{pmatrix}.$ Then $AA^{T}$ is equal to

The value of the determinant $\begin{vmatrix}(10^{5}+10^{-5})^{2}&(10^{5}-10^{-5})^{2}& 1\\ (100^{5}+100^{-5})^{2}&(100^{5}-100^{-5})^{2}& 1\\ (6^{100}+6^{-100})^{2}&(6^{100}-6^{-100})^{2}& 1\end{vmatrix}$ is equal to

Let $A$ be a square matrix and $A^{T}$ be its transpose. Which one of the following is true?

If $^{n}P_{5}=6720$ and $^{(n-1)}P_{4}=840$, then $^{n}P_{3}$ is equal to

The coefficient of $x^{8}$ in the expansion of $(x^{2}+\sqrt{1-x^{2}})^{5}+(x^{2}-\sqrt{1-x^{2}})^{5}$ is

The two geometric means between 2 and 8 are $g_{1}$ and $g_{2}$. Then $g_{1}^{3}+g_{2}^{3}$ is equal to

Let $a_{1}, a_{2}, 6, a_{4}$ be in G.P. Then the value of $(6a_{1}+6a_{2}+a_{1}a_{4}+a_{2}a_{4})^{2}$ is equal to

If $^{n}C_{4}=1365$ then the value of n is equal to

A polygon has 170 diagonals. The number of sides of the polygon, is