List of top Questions asked in JEE Main- 2020

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s^-2. The density of water is 1 gm cm^-3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s²).

On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by \(\frac{Ax}{(x^2+a^2)^{3/2}}\) in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is :

A battery of \(3.0\ \mathrm{V}\) is connected to a resistor dissipating \(0.5\ \mathrm{W}\) of power. If the terminal voltage of the battery is \(2.5\ \mathrm{V}\), the power dissipated within the internal resistance is :

Let \((2x^2+3x+4)^{10}=\sum_{r=0}^{20}a_rx^r\). Then \(\frac{a_7}{a_{13}}\) is equal to ______.

A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If \(\angle BAC=90^\circ\), and \(\mathrm{ar}(\Delta ABC)=5\sqrt{5}\) sq. units, then the abscissa of the vertex C is :

The value of \(\sum_{r=0}^{20}{}^{50-r}C_6\) is equal to :

If the system of equations
\(x-2y+3z=9\)
\(2x+y+z=b\)
\(x-7y+az=24\),
has infinitely many solutions, then \(a-b\) is equal to ______.

Let P(3, 3) be a point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\). If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair \((a^2, e^2)\) is equal to :

Suppose a differentiable function \(f(x)\) satisfies the identity \(f(x+y)=f(x)+f(y)+xy^2+x^2y\), for all real \(x\) and \(y\). If \(\lim_{x\to 0}\frac{f(x)}{x}=1\), then \(f'(3)\) is equal to ______.

If \((a+\sqrt{2}\,b\cos x)(a-\sqrt{2}\,b\cos y)=a^2-b^2\), where \(a \gt b \gt 0\), then \(\frac{dx}{dy}\) at \(\left(\frac{\pi}{4},\frac{\pi}{4}\right)\) is :

If \(1+(1-2^2\cdot 1)+(1-4^2\cdot 3)+(1-6^2\cdot 5)+\ldots+(1-20^2\cdot 19)=\alpha-220\beta\), then an ordered pair \((\alpha,\beta)\) is equal to :

Let \(u=\frac{2z+i}{z-ki},\ z=x+iy\) and \(k>0\). If the curve represented by \(\mathrm{Re}(u)+\mathrm{Im}(u)=1\) intersects the \(y\)-axis at the points P and Q where \(PQ=5\), then the value of \(k\) is :

Let \([t]\) denote the greatest integer \(\le t\). Then the equation in \(x\), \([x]^2+2[x+2]-7=0\) has :

Let \(x_0\) be the point of local maxima of \(f(x)=\vec{a}\cdot(\vec{b}\times\vec{c})\), where \(\vec{a}=x\hat{i}-2\hat{j}+3\hat{k}\), \(\vec{b}=-2\hat{i}+x\hat{j}-\hat{k}\) and \(\vec{c}=7\hat{i}-2\hat{j}+x\hat{k}\). Then the value of \(\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}+\vec{c}\cdot\vec{a}\) at \(x=x_0\) is :

Let \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\ (a>b)\) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, \(\phi(t)=\frac{5}{12}+t-t^2\), then \(a^2+b^2\) is equal to :

Let \(y=y(x)\) be the solution of the differential equation, \(xy^{\prime}-y=x^2(x\cos x+\sin x),\ x>0\). If \(y(\pi)=\pi\), then \(y^{\prime\prime}\left(\frac{\pi}{2}\right)+y\left(\frac{\pi}{2}\right)\) is equal to :

Two vertical poles \(AB=15\) m and \(CD=10\) m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is :

If \(A=\begin{bmatrix}\cos\theta & i\sin\theta\\ i\sin\theta & \cos\theta\end{bmatrix},\ \left(\theta=\frac{\pi}{24}\right)\) and \(A^5=\begin{bmatrix}a & b\\ c & d\end{bmatrix}\), where \(i=\sqrt{-1}\), then which one of the following is not true?

A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If \(x\)% of the people read both the newspapers, then a possible value of \(x\) can be :

Let \(f(x)=\int\frac{\sqrt{x}}{(1+x)^2}dx\ (x\ge 0)\). Then \(f(3)-f(1)\) is equal to :

Let \(f(x)=|x-2|\) and \(g(x)=f(f(x)),\ x\in[0,4]\). Then \(\int_0^3 \left(g(x)-f(x)\right)dx\) is equal to :

The integral \(\int\left(\frac{x}{x\sin x+\cos x}\right)^2dx\) is equal to (where C is a constant of integration) :

Let \(\alpha\) and \(\beta\) be the roots of \(x^2-3x+p=0\) and \(\gamma\) and \(\delta\) be the roots of \(x^2-6x+q=0\). If \(\alpha,\beta,\gamma,\delta\) form a geometric progression. Then ratio \((2q+p):(2q-p)\) is :

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

The volume (in mL) of 0.1 N NaOH required to neutralise 10 mL of 0.1 N phosphinic acid is ___________.