List of top Questions asked in JEE Main

Let \(n > 2\) be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is :

A plane passing through the point \((3, 1, 1)\) contains two lines whose direction ratios are \(1, -2, 2\) and \(2, 3, -1\) respectively. If this plane also passes through the point \((\alpha, -3, 5)\), then \(\alpha\) is equal to:

\(\lim\limits_{x\to0}\left(\tan\left(\frac{\pi}{4}+x\right)\right)^{\frac1x}\) is equal to :

The set of all possible values of \(\theta\) in the interval
\((0, \pi)\) for which the points \((1, 2)\) and \((\sin\theta, \cos\theta)\) lie
on the same side of the line \(x + y = 1\) is :

Let a, b, c \(\in \mathbb{R}\) be all non-zero and satisfy \(a^3+b^3+c^3=2\). If the matrix \(A=\begin{pmatrix} a & b & c \\ b & c & a \\ c & a & b \end{pmatrix}\) satisfies \(A^TA = I\), then a value of abc can be :

If the sum of first 11 terms of an A.P., \(a_1, a_2, a_3, \ldots\) is 0 \((a_1 \ne 0)\), then the sum of the A.P., \(a_1, a_3, a_5, \ldots, a_{23}\) is \(ka_1\), where k is equal to :

Let \(f : \mathbb{R} \to \mathbb{R}\) be a function which satisfies \(f(x+y) = f(x) + f(y)\ \forall\ x, y \in \mathbb{R}\). If \(f(1) = 2\) and \(g(n) = \sum\limits_{k=1}^{(n-1)} f(k)\), \(n \in \mathbb{N}\), then the value of n, for which \(g(n) = 20\), is :

Let \(E^C\) denote the complement of an event E. Let \(E_1\), \(E_2\) and \(E_3\) be any pairwise independent events with \(P(E_1) > 0\) and \(P(E_1 \cap E_2 \cap E_3) = 0\).
Then \(P\left(E_2^C \cap E_3^C / E_1\right)\) is equal to :

Consider a region \(R = \{(x, y) \in \mathbb{R}^2 : x^2 \le y \le 2x\}\). If a line \(y = \alpha\) divides the area of region R into two equal parts, then which of the following is true?

If a curve \(y = f(x)\), passing through the point \((1, 2)\), is the solution of the differential equation, \(2x^2\,dy = (2xy + y^2)\,dx\), then \(f\left(\frac{1}{2}\right)\) is equal to :

The imaginary part of \(\left(3+2\sqrt{-54}\right)^{\frac12}-\left(3-2\sqrt{-54}\right)^{\frac12}\) can be :

If the equation \(\cos^4\theta + \sin^4\theta + \lambda = 0\) has real solutions for \(\theta\), then \(\lambda\) lies in the interval :

Let \(A = \{X = (x, y, z)^T : PX = 0 \text{ and } x^2+y^2+z^2 = 1\}\) where \(P = \begin{bmatrix} 1 & 2 & 1 \\ -2 & 3 & -4 \\ 1 & 9 & -1 \end{bmatrix}\), then the set A :

For some \(\theta \in \left(0, \frac{\pi}{2}\right)\), if the eccentricity of the hyperbola, \(x^2 - y^2\sec^2\theta = 10\) is \(\sqrt{5}\) times the eccentricity of the ellipse, \(x^2\sec^2\theta + y^2 = 5\), then the length of the latus rectum of the ellipse, is :

The mass of gas adsorbed, x, per unit mass of adsorbate, m, was measured at various pressures, p. A graph between \(\log \frac{x}{m}\) and \(\log p\) gives a straight line with slope equal to 2 and the intercept equal to 0.4771. The value of \(\frac{x}{m}\) at a pressure of 4 atm is :
(Given \(\log 3 = 0.4771\))

The internal energy change (in J) when 90 g of water undergoes complete evaporation at \(100^\circ\mathrm{C}\) is ____________.
(Given : \(\Delta H_{vap}\) for water at 373 K = 41 kJ/mol, \(R = 8.314\ \mathrm{J\,K^{-1}\,mol^{-1}}\))

The metal mainly used in devising photoelectric cells is :

The Gibbs change (in J) for the given reaction at [Cu²⁺] = [Sn²⁺] = 1 M and 298 K is :
Cu(s) + Sn²⁺(aq.) \(\to\) Cu²⁺(aq.) + Sn(s);
(\(E^0_{\mathrm{Sn^{2+}|Sn}} = -0.16\) V, \(E^0_{\mathrm{Cu^{2+}|Cu}} = 0.34\) V)
Take F = 96500 C mol^-1

On heating compound (A) gives a gas (B) which is a constituent of air. This gas when treated with H₂ in the presence of a catalyst gives another gas (C) which is basic in nature. (A) should not be :

Which of the following is used for the preparation of colloids?

The statement that is not true about ozone is :

If AB₄ molecule is a polar molecule, a possible geometry of AB₄ is

An open beaker of water in equilibrium with water vapour is in a sealed container. When a few grams of glucose are added to the beaker of water, the rate at which water molecules :

While titrating dilute HCl solution with aqueous NaOH, which of the following will not be required?

For octahedral Mn(II) and tetrahedral Ni(II) complexes, consider the following statements:

(I) both the complexes can be high spin.
(II) Ni(II) complex can very rarely be low spin.
(III) with strong field ligands, Mn(II) complexes can be low spin.
(IV) aqueous solution of Mn(II) ions is yellow in colour.

The correct statements are :