List of top Mathematics Questions

If $A = \begin{pmatrix}1&0\\ 1&1\end{pmatrix}$ , then $A^n + nI$ is equal to

A complete cycle of a traffic light takes $60\, seconds$. During each cycle the light is green for $25\, seconds$, yellow for $5 \,seconds$ and red for $30\, seconds$. At a randomly chosen time, the probability that the light will not be green, is

If tan $\frac{\theta}{2}=\frac{1}{2}$,then the value of sin $\theta$ is

If $ y={{\sin }^{-1}}\sqrt{1-x}, $ then $ \frac{dy}{dx} $ is equal to

Which one of the following functions is one-to-one?

If $A = \begin{pmatrix}1&5\\ 0&2\end{pmatrix}$ , then

$\int\frac{1}{\sin x\, \cos x}$ dx is equal to

Find the projection of the vector \(\hat{i}+3\hat{j}+7\hat{k}\) on the vector \(7\hat{i}-\hat{j}+8\hat{k}.\)

If $|z + 1| < |z - 1|$ , then $z$ lies

If $a$ is positive and if $A$ and $G$ are the arithmetic mean and the geometric mean of the roots of $ {{x}^{2}}-2ax+{{a}^{2}}=0 $ respectively, then

If a$_1$ = 4 and $a_{n+1}=a_{n}+4n\quad for\quad n\ge1. $ then the value of a$_{100}$ is

If $a_1, a_2 , a_3 , a_4$ are in A.P., then $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\frac{1}{\sqrt{a_{3}}+\sqrt{a_{4}}}=$

A die has four blank faces and two faces marked $3$. The chance of getting a total of $12$ in $5$ throws is

If $ \alpha $ and $ \beta $ are the roots of the equation $ a{{x}^{2}}+ $ $ bx+c=0,\text{ }\alpha \beta =3 $ and $a, b, c$ are in $A.P.$, then $ \alpha +\beta $ is equal to

The value of $ \displaystyle\lim _{x \rightarrow 0} \frac{\cot 4 x}{\text{cosec} 3 x}$ is equal to

The period of the function $f\left(x\right)= cos 4x+$ tan $3x$ is

The solution set of inequality $\frac{2x}{x^2 - 9} \leq \frac{1}{x + 2 }$ is

The perpendicular distance (d) of a line Ax + By + C = 0 from a point $(x_1, y_1)$ is given by :

A random variable X has the following probability distribution:

If the mean of the random variable X is \(\frac{1}{3}\), then the variance is

$\int\left(\frac{x-a}{x}-\frac{x}{x+a}\right) dx$ is equal to

If the 21st and 22nd terms in the expansion of $(1 + x)^{44}$, are equal, then x =

Three numbers $x, y$ and $z $ are in arithmetic progression. If $x + y + z = - 3$ and $xyz= 8$, then $x^2 + y^2 + z^2$ is equal to

Solve the following equations: 
(a) 10p = 100
(b) 10p + 10 = 100
(c)\(\frac{p}{4}\)=5
(d) \(\frac{-p}{3}\)=5
(e)\(\frac{3p}{4}\)=6
(f)3s=-9
(g)3s+12=0
(h)3s=0
(i)2q=6
(j)2q-6=0
(k)2q+6=0
(l)2q+6=12