List of top Questions asked in JEE Main- 2018

One mole of an ideal monoatomic gas is taken along the path ABCA as show in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

Let \(\vec{A}=(\hat{i}+\hat{j})\) and,
\(\vec{B}=(2\hat{i}-\hat{j})\).
The magnitude of a coplanar vector \(\vec{C}\) such that
\(\vec{A}\cdot\vec{C}=\vec{B}\cdot\vec{C}=\vec{A}\cdot\vec{B}\),
is given by :

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let \(P_2\) be the pressure inside the inner bubble and \(P_0\), the pressure outside the outer bubble. Radius of another bubble with pressure difference \(P_2-P_0\) between its inside and outside would be :

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :

The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity \(A=\frac{P^3Q^2}{\sqrt{R}\,S}\).
The maximum percentage error in the value of A will be :

A galvanometer with its coil resistance \(25\,\Omega\) requires a current of 1 mA for its full deflection. In order to construct an ammeter to read upto a current of 2 A, the approximate value of the shunt resistance should be :

Let P be a point on the parabola, \(x^2=4y\). If the distance of P from the center of the circle, \(x^2+y^2+6x+8=0\) is minimum, then the equation of the tangent to the parabola at P, is :

The coefficient of \(x^2\) in the expansion of the product
\((2-x^2)\cdot\left((1+2x+3x^2)^6+(1-4x^2)^6\right)\) is :

The de-Broglie wavelength (\(\lambda_B\)) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (\(\lambda_G\)) by :

The sum of the first 20 terms of the series
\(1+\frac{3}{2}+\frac{7}{4}+\frac{15}{8}+\frac{31}{16}+\ldots,\)
is :

If the angle between the lines, \(\frac{x}{2} = \frac{y}{2} = \frac{z}{1}\) and \(\frac{5-x}{-2} = \frac{7y-14}{p} = \frac{z-3}{4}\) is \(\cos^{-1}\left(\frac{2}{3}\right)\), then p is equal to :

Let p, q and r be real numbers (\(p \neq q,\ r \neq 0\)), such that the roots of the equation \(\frac{1}{x+p} + \frac{1}{x+q} = \frac{1}{r}\) are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :

If the area of the region bounded by the curves, \(y = x^2,\ y = \frac{1}{x}\) and the lines y = 0 and x = t (t > 1) is 1 sq. unit, then t is equal to :

Let \(A = \begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}\) and \(B = A^{20}\). Then the sum of the elements of the first column of B is :

The sum of the intercepts on the coordinate axes of the plane passing through the point \((-2,-2,2)\) and containing the line joining the points \((1,-1,2)\) and \((1,1,1)\) is :

The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is \(\frac{1}{12}\), then the number of children in each family is :

If a circle C, whose radius is 3, touches externally the circle, \(x^2 + y^2 + 2x - 4y - 4 = 0\) at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

If an angle A of a \(\Delta\)ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, \(9x^2 + 27x + 20 = 0\) are :

If \(\int \frac{\tan x}{1 + \tan x + \tan^2 x}\,dx = x - \frac{K}{\sqrt{A}}\tan^{-1}\left(\frac{K\tan x + 1}{\sqrt{A}}\right) + C\), (C is a constant of integration) then the ordered pair (K, A) is equal to :

Let A, B and C be three events, which are pair-wise independent and \(\overline{E}\) denotes the completement of an event E. If \(P(A \cap B \cap C) = 0\) and \(P(C) \gt 0\), then \(P\left[(\overline{A} \cap \overline{B}) \mid C\right]\) is equal to :

\(\lim_{x \to 0} \frac{(27+x)^{\frac{1}{3}} - 3}{9 - (27+x)^{\frac{2}{3}}}\) equals.

The number of values of k for which the system of linear equations,
\((k+2)x + 10y = k\)
\(kx + (k+3)y = k-1\)
has no solution, is :

Let \(\vec{a} = \hat{i} + \hat{j} + \hat{k},\ \vec{c} = \hat{j} - \hat{k}\) and a vector \(\vec{b}\) be such that \(\vec{a} \times \vec{b} = \vec{c}\) and \(\vec{a} \cdot \vec{b} = 3\). Then \(|\vec{b}|\) equals :

If the function f defined as
\(f(x) = \frac{1}{x} - \frac{k-1}{e^{2x}-1},\ x \neq 0,\)
is continuous at x = 0, then the ordered pair (k, f(0)) is equal to :