List of top Mathematics Questions

Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the second roll?

A firm needs both skilled labour and unskilled labour. Skilled wage = ₹ 40,000 per month; unskilled wage = ₹ 15,000 per month. The total wage bill for 100 labourers is ₹ 23,75,000 in a month. How many skilled labour are employed? (in Integer)

The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

A square with sides of length $6\,\text{cm}$ is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is $\underline{\hspace{1cm}}$ $\text{cm}^2$.

The digit in the unit's place of the product $3^{999\times 7^{1000}}$ is $\underline{\hspace{1cm}}$.

Select the correct relation between $E$ and $F$. $E=\dfrac{x}{1+x}$ \; and \; $F=\dfrac{-x}{\,1-x\,}$, \; with $x>1$.

Which one of the following options represents the given graph?

The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

A square with sides of length $6\,\text{cm}$ is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown. The area of the shaded region is $\underline{\hspace{1cm}}$ $\text{cm}^2$.

The digit in the unit's place of the product $3^{999\times 7^{1000}}$ is $\underline{\hspace{1cm}}$.

Which one of the following options represents the given graph?

A firm needs both skilled labour and unskilled labour. Skilled wage = ₹ 40,000 per month; unskilled wage = ₹ 15,000 per month. The total wage bill for 100 labourers is ₹ 23,75,000 in a month. How many skilled labour are employed? (in Integer)

$\sim q$ can be deduced from $\sim(p \supset (q \lor r))$ by using rules of propositional logic in the following sequence(s):

(i) $p \supset (q \cdot r)$ (ii) $\sim(p \supset s)$
Taking (i) and (ii) as premises, which of the following can be deduced?

Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the second roll?

If $\vec{a}+2\vec{b}+3\vec{c}=\vec{0}$ and
$(\vec{a}\times\vec{b})+(\vec{b}\times\vec{c})+(\vec{c}\times\vec{a})=\lambda(\vec{b}\times\vec{c})$
then the value of λ is equal to

Let f be a non-negative function defined on [$0,\frac{\pi}{2}$]. If $\int_{0}^{x}(f'(t)-sin\,2t)dt=\int_{0}^{x}f(t)tan\,t\,dt$. $f(0)=1$, then $\int_{0}^{\frac{\pi}{2}}f(x)dx$ is

If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___

The tangent to the parabola, x² = 2y at the point $(1,\frac{1}{2})$ makes with the x-axis an angle of :

For a given vector $ \mathbf{w} = [1 \; 2 \; 3]^T $, the vector normal to the plane defined by $ \mathbf{w}^T \mathbf{x} = 1 $ is:

Which one of the following options represents the given graph? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}

Let $x, y, z>1$ and $A=\begin{bmatrix}1 & \log _x y & \log _x z \\ \log _y x & 2 & \log _y z \\ \log _z x & \log _z y & 3\end{bmatrix}$ Then ∣adj(adjA2)∣ is equal to

The converse of ((~ p) ∧ q) ⇒ r is

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to