List of top Questions asked in JEE Main

The foot of the perpendicular drawn from the point (4, 2, 3) to the line joining the points (1, \(-\)2, 3) and (1, 1, 0) lies on the plane :
The proposition \(p \to \sim(p \wedge \sim q)\) is equivalent to :
If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :
Let [t] denote the greatest integer \(\le\) t. If for some \(\lambda \in \mathbb{R} - \{1, 0\}\),
\(\lim_{x \to 0}\left|\frac{1 - x + |x|}{\lambda - x + [x]}\right| = L\), then L is equal to :
The diameter of the circle, whose centre lies on the line \(x + y = 2\) in the first quadrant and which touches both the lines \(x = 3\) and \(y = 2\), is _______ .
A dice is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :
The value of (\(2\cdot{}^{1}P_0 - 3\cdot{}^{2}P_1 + 4\cdot{}^{3}P_2 \ldots\) up to 51th term) + (\(1! - 2! + 3! - \ldots\) up to 51th term) is equal to :
The solution curve of the differential equation, \((1 + e^{-x})(1 + y^2)\frac{dy}{dx} = y^2\), which passes through the point \((0, 1)\), is :
A hyperbola having the transverse axis of length \(\sqrt{2}\) has the same foci as that of the ellipse \(3x^2 + 4y^2 = 12\), then this hyperbola does not pass through which of the following points?
\(2\pi - \left(\sin^{-1}\frac{4}{5} + \sin^{-1}\frac{5}{13} + \sin^{-1}\frac{16}{65}\right)\) is equal to :
If \(y^2 + \log_e(\cos^2 x) = y\), \(x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), then :
The lines
\(\vec{r} = (\hat{i} - \hat{j}) + l(2\hat{i} + \hat{k})\)
and
\(\vec{r} = (2\hat{i} - \hat{j}) + m(\hat{i} + \hat{j} + \hat{k})\)
If \(\Delta = \begin{vmatrix} x - 2 & 2x - 3 & 3x - 4 \\ 2x - 3 & 3x - 4 & 4x - 5 \\ 3x - 5 & 5x - 8 & 10x - 17 \end{vmatrix} = Ax^3 + Bx^2 + Cx + D\), then \(B + C\) is equal to :
Consider the two sets :
\(A = \{m \in \mathbb{R} : \text{both the roots of } x^2 - (m + 1)x + m + 4 = 0 \text{ are real}\}\)
and \(B = [-3, 5)\).
Which of the following is not true?
\(\int_{-\pi}^{\pi} \left| \pi - |x| \right| dx\) is equal to :
If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2 + px + 2 = 0\) and \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\) are the roots of the equation \(2x^2 + 2qx + 1 = 0\), then \(\left(\alpha - \frac{1}{\alpha}\right)\left(\beta - \frac{1}{\beta}\right)\left(\alpha + \frac{1}{\beta}\right)\left(\beta + \frac{1}{\alpha}\right)\) is equal to :
Let P be a point on the parabola, \(y^2 = 12x\) and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is \(\frac{4}{3}\), then :
If the number of integral terms in the expansion of \((3^{1/2} + 5^{1/8})^n\) is exactly 33, then the least value of \(n\) is :
For the frequency distribution :
Variate (x) : \(x_1\) \(x_2\) \(x_3\) .... \(x_{15}\)
Frequency (f) : \(f_1\) \(f_2\) \(f_3\) ...... \(f_{15}\)
where \(0 \lt x_1 \lt x_2 \lt x_3 \lt ... \lt x_{15} = 10\) and \(\sum_{i=1}^{15} f_i \gt 0\), the standard deviation cannot be :
The function, \(f(x) = (3x - 7)x^{2/3}\), \(x \in \mathbb{R}\), is increasing for all \(x\) lying in :
The area (in sq. units) of the region \(\{(x, y) : 0 \le y \le x^2 + 1,\ 0 \le y \le x + 1,\ \frac{1}{2} \le x \le 2\}\) is :
For the disproportionation reaction
\(\mathrm{2Cu^+(aq) \rightleftharpoons Cu(s) + Cu^{2+}(aq)}\) at 298 K. \(\ln K\) (where K is the equilibrium constant) is ___________ \(\times 10^{-1}\).
Given : ( \(E^0_{\mathrm{Cu^{2+}/Cu^+}} = 0.16\) V, \(E^0_{\mathrm{Cu^+/Cu}} = 0.52\) V, \(\dfrac{RT}{F} = 0.025\) )
Two elements A and B have similar chemical properties. They don’t form solid hydrogencarbonates, but react with nitrogen to form nitrides. A and B, respectively, are :
Amongst the following statements regarding adsorption, those that are valid are

(a) \(\Delta H\) becomes less negative as adsorption proceeds
(b) On a given adsorbent, ammonia is adsorbed more than nitrogen gas
(c) On adsorption, the residual force acting along the surface of the adsorbent increases
(d) With increase in temperature, the equilibrium concentration of adsorbate increases
The ratio of the mass percentages of ‘C & H’ and ‘C & O’ of a saturated acyclic organic compound ‘X’ are 4 : 1 and 3 : 4 respectively. Then, the moles of oxygen gas required for complete combustion of two moles of organic compound ‘X’ is ________.