List of top Mathematics Questions

In a triangle \( ABC \) with usual notations, if \[ \tan \left( \frac{B-C}{2} \right) = x \cot \left( \frac{A}{2} \right), \] then \( x = \, ? \) 

The perimeter of a square whose two sides have equations \(\frac{x-1}{2} = \frac{y+2}{3} = \frac{z-3}{4}\) and \(\frac{x}{2} = \frac{y-1}{3} = \frac{z+1}{4}\) is
If \(x\) is real, then the difference between the greatest and least values of \(\frac{x^2 - x + 1}{x^2 + x + 1}\) is
If the planes \(\bar{r} \cdot (2\hat{i} - \lambda\hat{j} + \hat{k}) = 3\) and \(\bar{r} \cdot (4\hat{i} - \hat{j} + \mu\hat{k}) = 5\) are parallel, then \(\lambda + \mu =\)
In \(\triangle ABC\), with usual notations, if \(a^4 + b^4 + c^4 - 2a^2 c^2 - 2c^2 b^2 = 0\), then \(\angle C = \dots\)
\(\bar{a} = \hat{i} - \hat{j}, \bar{b} = \hat{j} - \hat{k}, \bar{c} = \hat{k} - \hat{i}\) then a unit vector \(\bar{d}\) such that \(\bar{a} \cdot \bar{d} = 0 = [\bar{b} \bar{c} \bar{d}]\) is
If the truth value of the statement pattern \([p \wedge \sim r] \to \sim r \wedge q\) is False, then which of the following has truth value False?
From the following options, the nearest line to the origin is ....
The probability that a certain kind of component will survive a given test is \(\frac{2}{3}\). The probability that at most \(2\) components out of \(4\) tested, will survive is
If \(\bar{a}, \bar{b}, \bar{c}\) are three unit vectors such that \(|\bar{a} + \bar{b}|^2 + |\bar{a} + \bar{c}|^2 = 8\), then \(|\bar{a} + 3\bar{b}|^2 + |\bar{a} + 3\bar{c}|^2 =\)
If \(A = \left[ \begin{array}{cc} 1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1 \end{array} \right]\) then \(A^{-1} =\)

If \( y = y(x) \) and \[ \left( \frac{2+\sin x}{y+1} \right)\frac{dy}{dx} = -\cos x, \] with the initial condition \( y(0) = 1 \), then find \[ y\left(\frac{\pi}{2}\right) = \, ? \] 

Four digit numbers are formed using \( 0, 3, 4, 5, 9, 8 \) without repetitions. Then the number of such 4 digit numbers is
When a metallic sphere is heated, maximum percentage change will be observed in its
The shaded region \(ABC\) shown in the diagram is given by the inequalities

The solution of the linear differential equation \( \dfrac{dy}{dx}+y=e^{-x} \), when \( x=0,\ y=1 \), is
The general solution of the differential equation \( y\,dx-x\,dy=y^2(x\,dy+y\,dx) \) is
Area of the region bounded by the function $f(x)=\begin{cases} x, & x\leq 3 \\ -x+6, & x>3 \end{cases}$ with the $x$-axis (in square units) in the first quadrant is:
The value of \(\int_{1}^{2} [x-1]\,dx\), where \([x]\) denotes the greatest integer function in \(x\), is equal to
\(\int_{0}^{\frac{\pi}{2}} \sin 2x\,e^{\sin x}\,dx\) is equal to
$\int_{0}^{1}\frac{\sin x}{\sin x+\sin(1-x)}\,dx$ is equal to:
\(\int \left(\frac{\sin 3x}{\sin x}-\frac{\cos 3x}{\cos x}\right)\,dx\) is equal to
$\int x(1-x)^{10}\,dx =$
\( \displaystyle \int \frac{dx}{\cos^{2/3}x\ \sin^{4/3}x} \) is
\( \displaystyle \int \ cot x (1-\ cosec x)e^x\,dx \) is