List of top Mathematics Questions

Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4$. Then $x$ and $y$ are the roots of

Find three different irrational numbers between the rational numbers \(\frac{5}{7}\) and \(\frac{9}{11}\).

The area of the circle $x^2 - 2x + y^2 - 10\,y + k = 0$ is $25 \pi $ . The value of k is equal to

The angle between the planes $3x + 4y + 5z = 3$ and $4 x-3 y + 5z = 9$ is equal to

If $tan \left(\frac{\theta}{2}\right)=\frac{2}{3}$, then $sec\,\theta $ is equal to

If $ A= \begin{bmatrix} 1 & 0 & 0 \\ x & 1 & 0 \\ x & x & 1 \\ \end{bmatrix} $ and $ I= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} , $ then $ {{A}^{3}}-4{{A}^{2}}+3A+I $ is equal to

$ \tan\left(\frac{\pi}{4} +\frac{\theta}{2}\right) + \tan\left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is equal to

The power of $x$ in the term with the greatest coefficient in the expansion of $\left(1+\frac{x}{2}\right)^{10}$ is:

$ \frac{1}{\cos 80{}^\circ }-\frac{\sqrt{3}}{\sin 80{}^\circ } $ is equal to:

If $p : 2$ plus $3$ is five and $q $ : Delhi is the capital of India < are two statements, then the statement "Delhi is the capital of India and it is not that $2$ plus $3$ is five" is

If the two pair of lines $ {{x}^{2}}-2mxy-{{y}^{2}}=0 $ and $ {{x}^{2}}-2nxy-{{y}^{2}}=0 $ are such that one of them represents the bisector of the angles between the other, then:

An integrating factor of the differential equation $xdy - ydx + x^2e^xdx = 0$ is

If $\tan^{-1} x$ + $\tan^{-1} y$ = $\frac{2\pi}{3 }$ , then $\cot^{-1} x$ + $\cot^{-1} y$ is equal to

The position of a particle is given by $ r =\hat{i}+2\hat{j}-\hat{k} $ and its linear momentum is given by $ p = 3\hat{i}+4\hat{j}-2\hat{k} $ . Then its angular momentum, about the origin is perpendicular to

A plane makes intercepts $a, b, c$ at $A, B, C$ on the coordinate axes respectively. If the centroid of the $ \Delta ABC $ is at $(3, 2, 1)$, then the equation of the plane is

How many four digit numbers $abcd$ exist such that $a$ is odd, $b$ is divisible by $3$, $c$ is even and $d$ is prime?

If the combined mean of two groups is $\frac{40}{3}$ and if the mean of one group with $10$ observations is $15$, then the mean of the other group with $8$ observations is equal to

In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is

The distance between the line $ \overrightarrow{r}=(2\hat{i}+2\hat{j}-\hat{k})+\lambda (2\hat{i}+\hat{j}-2\hat{k}) $ and the plane $ \overrightarrow{r}.(\hat{i}+2\hat{j}+2\hat{k})=10 $ is equal to

Suppose that two persons $A$ and $B$ solve the equation $ {{x}^{2}}+ax+b=0 $ . While solving $A$ commits a mistake in the coefficient of $ x $ was taken as $15$ in place of $-9$ and finds the roots as $ -7 $ and $ -2 $ . Then, the equation is

If the set $A$ contains $5$ elements, then the number of elements in the power set $ P(A) $ is equal to

If the straight line $y = 4x + c$ touches the ellipse $\frac{x^2}{4} + y^2 = 1 $ then c is equal to

If \(\begin{bmatrix}e^{x}&e^{y}\\ e^{y}&e^{x}\end{bmatrix} = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}\), then the values of \(x\) and \(y\) are respectively: