List of top Mathematics Questions

Let the orthocenter an centroid of a triangle be $A(-3, 5)$ and $B(3, 3)$ respectively. If $C$ is the circumcentre of this triangle, then the radius of the circle having line segment $AC$ as diameter, is:

If $A = \frac{1}{3} \begin{bmatrix}1&2&2\\ 2&1&-2\\ a&2&b\end{bmatrix} $ is an orthogonal matrix, then

Consider the equation of a parabola $y^2 + 4ax = 0$, where $a > 0$ which of the following is/are correct?

The equation of the circle which passes through the point $(4, 5)$ and has its centre at $(2, 2)$ is

\(\int \frac{e^{x^2}\left(2x+x^{3}\right)}{\left(3+x^{2}\right)^{2}} dx\)  is equal to :

If the constraints in a linear programming problem are changed then

In a binomial distribution, the mean is $4$ and variance is $3$. Then its mode is :

The value of $\displaystyle\lim_{n \to\infty} \frac{1+2+3+...n}{n^{2}+100}$ is equal to :

Eccentricity of ellipse $\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1 $ if it passes through point $(9, 5)$ and $(12, 4)$ is

$\displaystyle\lim_{x\to0} \sqrt{\frac{x-\sin x}{x+\sin^{2}x}} $ is equal to

Number of solutions of equation $\sin 9 \theta=\sin \theta$ in the interval $[0,2 \pi]$ is

If $ \hat{i} + \hat{j}, \hat{j} + \hat{k}, \hat{i} + \hat{k}$ are the position vectors of the vertices of a triangle $ABC$ taken in order, then $\angle A$ is equal to

The coefficient of $x^3$ in the expansion of $\left(x -\frac{1}{x}\right)^{7}$ is :

The probability of getting $10$ in a single throw of three fair dice is :

If $x > 0,$ the $ 1 + \frac{\log_{e^{2}}x}{1!} + \frac{\left(\log_{e^{2}}x\right)^{2}}{2!} + ....=$

Let $y = e^{2x}$ . Then $\left(\frac{d^{2}y}{dx^{2}}\right) \left(\frac{d^{2}x}{dy^{2}}\right) $ is

If $a, b, c$ are in G.P., then

In how many ways can $12$ gentlemen sit around a round table so that three specified gentlemen are always together?

The number of ways in which first, second and third prizes can be given to $5$ competitors is

The population of a town increases geometrically. If the population is 10000 now and was 8000 two years ago, what will it be two years hence if it grows at the same rate?

In what proportion should one variety of oil at Rs. 9.50 per kg be mixed with another at Rs. 10 per kg to get a mixture worth Rs. 9.60 per kg?

There are two squares one of whose diagonal is double that of the other. The ratio of area of the bigger one to that of the smaller one is

Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns will it take for both the buckets P and Q together to fill the empty drum?

The ratio of the ages of Anjali and Smita is 2 : 3. After 6 years the ratio of their ages becomes 5 : 7. What is the present age of Smita?

I went to a shop to purchase some refills costing Rs. 1.60 each but the clerk did not have change for my 20rupee note. I was constrained to purchase some 30 paise labels as well so that no money needed to be returned. After purchasing the maximum number of refills under the given constraints, how many labels did I have to purchase?