List of top Mathematics Questions

The number of real solution of equation x$|$x+4$|$+3$|$x+2$|$+10=0 is/are :
f(x) = x\(^{2025}\) - x\(^{2000}\), x \(\in\) [0, 1], then minimum value of f(x) is :

Let \(M = \{1, 2, 3, ....., 16\}\), if a relation R defined on set M such that R = \((x, y) : 4y = 5x – 3, x, y (\in) M\). How many elements should be added to R to make it symmetric.

The value of \( \int_{-\pi/2}^{\pi/2} \frac{dx}{[x]+4} \) is, where [.] denotes greatest integer function:
If a line x = -1 divides the area of region bounded by \(\{(x,y):1+x^2 \leq y \leq 3-x\}\) in the ratio \(\frac{m}{n}\) then (m + n) equal (where HCF of (m,n) = 1) :
The no. of solution in \(x \in \left(-\frac{1}{2\sqrt{6}}, \frac{1}{2\sqrt{6}}\right)\) of equation \(\tan^{-1}4x + \tan^{-1}6x = \frac{\pi}{6}\) is :
If \(\int(\sin x)^{-11/2} (\cos x)^{-5/2} dx = \frac{p_1}{q_1}(\cot x)^{9/2} - \frac{p_2}{q_2}(\cot x)^{5/2} - \frac{p_3}{q_3}(\cot x)^{1/2} + \frac{p_4}{q_4}(\cot x)^{-3/2} + C\) where H.C.F. \(\{p_i, q_i\} = 1\) \& \(i \in \{1, 2, 3, 4\}\). Then value of \(\sum_{i=1}^{4}(p_i +q_i)\) is:
If the value of \(\frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ}\) is \(\frac{\alpha + \beta\sqrt{5}}{\gamma}\) then value of \((\alpha + \beta + \gamma)\) (where \(\alpha, \beta, \gamma \in \mathbb{N}\) and are in lowest form) :
If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5}\,\beta}{2}, \] then the value of \((\alpha + \beta)\) is
Let \( A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} \) and \( B = \begin{bmatrix} 29 & 49 \\1 & 2 \end{bmatrix} \). If \( (A^5 + B)\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \), then find \( (x, y) \).
The number of values of \(x\) satisfying \[ \tan^{-1}(4x)+\tan^{-1}(6x)=\frac{\pi}{6}, \quad x\in\left[-\frac{1}{2\sqrt{6}},\,\frac{1}{2\sqrt{6}}\right] \] is
The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{dx}{[x]+4} \] where \([\,\cdot\,]\) denotes the greatest integer function, is
If \[ A=\begin{bmatrix}2 & 3\\3 & 5\end{bmatrix}, \] then find the value of \[ \left|A^{2025}-3A^{2024}+A^{2023}\right|. \]
If the sum of first 4 terms of an A.P. is \(6\) and the sum of first 6 terms is \(4\), then the sum of first 12 terms of the A.P. is
If the domain of the function \[ f(x)=\frac{1}{\ln(10-x)}+\sin^{-1}\!\left(\frac{x+2}{2x+3}\right) \] is \[ (-\infty,-a]\ \cup\ (-1,b)\ \cup\ (b,c), \] then find the value of \( (b+c+3a) \).
Let \( M = \{1,2,3,\ldots,16\} \) and \( R \) be a relation on \( M \) defined by \( xRy \) if and only if \( 4y = 5x - 3 \). Then, the number of ordered pairs required to be added to \( R \) to make it symmetric is
The value of \( \csc 10^\circ - \sqrt{3}\sec 10^\circ \) is:
If five men can build a house in 27 days, how long will it take nine men to build the same house, assuming they all work at the same rate?
The ages of a group of people are: 34, 27, 36, 18, 15, 72, 67, 12, 24, 45. What percentage of people in the group are above the average age for the group?
A train travels $120 \text{ km}$ in $2 \text{ hours}$. What is its speed?
If 3 pens cost 45, what is the cost of 10 pens?
What is the simple interest on 2000 at $5%$ per annum for 2 years?
If the cost price of an article is 500 and it is sold at a profit of $10%$, what is the selling price?
If the average of 5 numbers is 18, what is their total sum?

What is the simple interest on ₹2000 at 5% per annum for 2 years?