List of top Questions asked in JEE Main

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \(v\), the electrical power output will be most likely proportional to

Let ABC be a triangle with vertices at points \(A(2,3,5),\ B(-1,3,2)\) and \(C(\lambda,5,\mu)\) in three dimensional space. If the median through A is equally inclined with the axes, then \((\lambda,\mu)\) is equal to:

Let \(f:[-2,3]\to[0,\infty)\) be a continuous function such that \(f(1-x)=f(x)\) for all \(x\in[-2,3]\). If \(R_1\) is the numerical value of the area of the region bounded by \(y=f(x),\ x=-2,\ x=3\) and the axis of \(x\) and \(R_2=\int_{-2}^{3}xf(x)\,dx\), then :

Let \(\vec a=2\hat i+\hat j-2\hat k,\ \vec b=\hat i+\hat j\). If \(\vec c\) is a vector such that \(\vec a\cdot\vec c=|\vec c|,\ |\vec c-\vec a|=2\sqrt2\) and the angle between \(\vec a\times\vec b\) and \(\vec c\) is \(30^\circ\), then \(|(\vec a\times\vec b)\times\vec c|\) equals:

The equation of the curve passing through the origin and satisfying the differential equation \((1+x^2)\frac{dy}{dx}+2xy=4x^2\) is

The equation of a plane through the line of intersection of the planes \(x+2y=3,\ y-2z+1=0\), and perpendicular to the first plane is :

For \(0 \le x \le \frac{\pi}{2}\), the value of \(\displaystyle\int_0^{\sin^2 x}\sin^{-1}(\sqrt{t})\,dt+\int_0^{\cos^2 x}\cos^{-1}(\sqrt{t})\,dt\) equals :

Let \(f(1) = -2\) and \(f'(x) \ge 4.2\) for \(1 \le x \le 6\). The possible value of \(f(6)\) lies in the interval :

A spherical balloon is being inflated at the rate of 35cc/min. The rate of increase in the surface area (in \(\mathrm{cm^2}\)/min.) of the balloon when its diameter is 14 cm, is :

If an equation of a tangent to the curve, \(y - \cos(x + y) = 0,\ -1 \le x \le 1 + \pi\), is \(x + 2y = k\) then \(k\) is equal to :

Let \(p\) and \(q\) be any two logical statements and \(r : p \rightarrow (\sim p \vee q)\). If \(r\) has a truth value \(F\), then the truth values of \(p\) and \(q\) are respectively:

In a set of \(2n\) observations, half of them are equal to 'a' and the remaining half are equal to '\(-a\)'. If the standard deviation of all the observations is 2 ; then the value of \(|a|\) is :

Let \(S=\left\{\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}: a_{ij}\in\{0,1,2\},\ a_{11}=a_{22}\right\}\). Then the number of non-singular matrices in the set \(S\) is :

Consider the function : \(f(x)=[x]+|1-x|,\ -1\le x\le3\) where \([x]\) is the greatest integer function. Statement 1 : \(f\) is not continuous at \(x=0,1,2\) and \(3\) Statement 2 : \(f(x)=\begin{cases}-x, & -1\le x\lt0\\ 1-x, & 0\le x\lt1\\ 1+x, & 1\le x\lt2\\ 2+x, & 2\le x\le3\end{cases}\)

If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle \(60^\circ\) on the circumference of the first circle, then the radius of the arc is:

Let \(A = \{\theta : \sin(\theta) = \tan(\theta)\}\) and \(B = \{\theta : \cos(\theta) = 1\}\) be two sets. Then:

A point on the ellipse, \(4x^2 + 9y^2 = 36\), where the normal is parallel to the line, \(4x - 2y - 5 = 0\), is :

Consider the system of equations : \(x + ay = 0,\ y + az = 0\) and \(z + ax = 0\). Then the set of all real values of 'a' for which the system has a unique solution is:

If for positive integers \(r \gt 1, n \gt 2\), the coefficients of the \((3r)^{\text{th}}\) and \((r+2)^{\text{th}}\) powers of \(x\) in the expansion of \((1 + x)^{2n}\) are equal, then \(n\) is equal to:

5 - digit numbers are to be formed using \(2, 3, 5, 7, 9\) without repeating the digits. If \(p\) be the number of such numbers that exceed \(20000\) and \(q\) be the number of those that lie between \(30000\) and \(90000\), then \(p : q\) is:

Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference six. If first and last terms of this sequence are equal, then the last term is :

The value of \(1^2 + 3^2 + 5^2 + \ldots\ldots + 25^2\) is :

If \(p\) and \(q\) are non-zero real numbers and \(\alpha^3 + \beta^3 = -p,\ \alpha\beta = q\), then a quadratic equation whose roots are \(\frac{\alpha^2}{\beta},\ \frac{\beta^2}{\alpha}\) is :

Let \(z\) satisfy \(|z| = 1\) and \(z = 1 - \bar{z}\). Statement 1 : \(z\) is a real number. Statement 2 : Principal argument of \(z\) is \(\frac{\pi}{3}\).

\(\mathrm{H_1}\)-Receptor antagonists is a term associated with :