List of top Questions asked in JEE Main- 2019

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to -

The increasing order of the pKa values of the following compounds is :

(A) phenol; (B) 4-nitrophenol; (C) 3-nitrophenol; (D) 4-methoxyphenol

A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower is LOS (Line of Sight) mode ? (Given : radius of earth = \(6.4 \times 10^{6}\) m).

A mixture of 100 m mol of Ca(OH)\(_2\) and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. The mass of calcium sulphate formed and the concentration of OH\(^-\) in resulting solution, respectively, are : (Molar mass of Ca (OH)\(_2\), Na\(_2\)SO\(_4\) and CaSO\(_4\) are 74, 143 and 136 g mol\(^{-1}\), respectively; K\(_{sp}\) of Ca(OH)\(_2\) is \(5.5 \times 10^{-6}\) )

Which dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride?

A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is -

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -

If the magnetic field of a plane electromagnetic wave is given by (the speed of light = \(3\times10^{8}\) B = \(100\times10^{-6}\) sin
\(\left[2\pi\times2\times10^{15}\left(t-\frac{x}{c}\right)\right]\)
then the maximum electric field associated with it is -

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of \(7.5\times10^{-12}\) m, the minimum electron energy required is close to -

To get output 1 at R, for the given logic gate circuit the input values must be

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time \(t\) is -

Consider the statement : "P(n) : \(n^2 - n + 41\) is prime". Then which one of the following is true ?

If \(\sum_{i=1}^{20}\left(\frac{{}^{20}C_{i-1}}{{}^{20}C_i + {}^{20}C_{i-1}}\right)^3 = \frac{k}{21}\) then k is equal to

If the parabolas \(y^2 = 4b(x - c)\) and \(y^2 = 8ax\) have a common normal, then which one of the following is a valid choice for the ordered triad (a, b, c)?

The plane passing through the point \((4, -1, 2)\) and parallel to the lines
\(\frac{x+2}{3} = \frac{y-2}{-1} = \frac{z+1}{2}\) and \(\frac{x-2}{1} = \frac{y-3}{2} = \frac{z-4}{3}\)
also passes through the point -

Let A be a point on the line \(\vec{r} = (1-3\mu)\hat{i} + (\mu-1)\hat{j} + (2+5\mu)\hat{k}\) and B(3, 2, 6) be a point in the space. Then the value of \(\mu\) for which the vector \(\overrightarrow{AB}\) is parallel to the plane \(x - 4y + 3z = 1\) is -

Let \(n \ge 2\) be a natural number and \(0 \lt \theta \lt \frac{\pi}{2}\). Then
\(\int \frac{(\sin^n\theta - \sin\theta)^{1/n}\cos\theta}{\sin^{n+1}\theta}\,d\theta\)
is equal to - (where C is a constant of integration)

Let \(d\in\mathbb{R}\), and \(A=\begin{bmatrix}-2&4+d&(\sin\theta)-2\\1&(\sin\theta)+2&d\\5&(2\sin\theta)-d&(-\sin\theta)+2+2d\end{bmatrix}\), \(\theta\in[0,2\pi]\). If the minimum value of \(\det(A)\) is 8, then a value of \(d\) is -

Let \(I=\displaystyle\int_a^b\left(x^4-2x^2\right)dx\). If \(I\) is minimum then the ordered pair \((a,b)\) is -

Let \(f:\mathbb{R}\to\mathbb{R}\) be a function such that \(f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3)\), \(x\in\mathbb{R}\). Then \(f(2)\) equals -

The equation of a tangent to the hyperbola \(4x^2 - 5y^2 = 20\) parallel to the line \(x - y = 2\) is :

The shortest distance between the point \(\left(\frac32,0\right)\) and the curve \(y=\sqrt{x}\), \((x>0)\), is -

A point \(P\) moves on the line \(2x-3y+4=0\). If \(Q(1,4)\) and \(R(3,-2)\) are fixed points, then the locus of the centroid of \(\triangle PQR\) is a line :

If the third term in the binomial expansion of \(\left(1+x^{\log_2x}\right)^5\) equals 2560, then a possible value of \(x\) is -

The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -