List of top Questions asked in JEE Main

Contrapositive of the statement :
'If a function f is differentiable at a, then it is also continuous at a', is:

The circle passing through the intersection of the circles,
\(x^2 + y^2 - 6x = 0\) and \(x^2 + y^2 - 4y = 0\), having its centre on
the line, \(2x - 3y + 12 = 0\), also passes through the point :

Let \(\{x\}\) and \([x]\) denote the fractional part of x and
the greatest integer \(\le x\) respectively of a real number x. If \(\int_0^n \{x\}\,dx\), \(\int_0^n [x]\,dx\) and \(10(n^2 - n)\), \((n \in N, n \gt 1)\) are three consecutive terms of a G.P., then n is equal to ______.

If \(\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}\), then the value of
\(\left|\hat{i} \times (\vec{a} \times \hat{i})\right|^2 + \left|\hat{j} \times (\vec{a} \times \hat{j})\right|^2 + \left|\hat{k} \times (\vec{a} \times \hat{k})\right|^2\) is equal to ____

Let \(\bigcup_{i=1}^{50} X_i = \bigcup_{i=1}^{n} Y_i = T\) where each \(X_i\) contains 10 elements and each \(Y_i\) contains 5 elements. If each element of the set T is an element of exactly 20 of sets \(X_i\)'s and exactly 6 of sets \(Y_i\)'s, then n is equal to :

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is \(\frac{1}{2}\). If P(1, \(\beta\)), \(\beta \gt 0\) is a point on this ellipse, then the equation of the normal to it at P is :

The integral
\(\int_{\pi/6}^{\pi/3} \tan^3 x \cdot \sin^2 3x\left(2\sec^2 x \cdot \sin^2 3x + 3\tan x \cdot \sin 6x\right)dx\)
is equal to:

The function
\(f(x) = \begin{cases} \frac{\pi}{4} + \tan^{-1}x, & |x| \le 1 \\ \frac12(|x| - 1), & |x| \gt 1 \end{cases}\)
is :

Let \(f:(0,\infty) \to (0,\infty)\) be a differentiable function such that \(f(1) = e\) and
\(\lim_{t \to x} \frac{t^2 f^2(x) - x^2 f^2(t)}{t - x} = 0\).
If \(f(x) = 1\), then x is equal to :

If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to -4, then a value of k is :

If a and b are real numbers such that
\((2+\alpha)^4 = a + b\alpha\)
where \(\alpha = \frac{-1+i\sqrt{3}}{2}\)
then a + b is equal to :

Let \(a_1, a_2, \ldots, a_n\) be a given A.P. whose common difference is an integer and \(S_n = a_1 + a_2 + \ldots + a_n\). If \(a_1 = 1\), \(a_n = 300\) and \(15 \le n \le 50\), then the ordered pair \((S_{n-4},\ a_{n-4})\) is equal to:

If the system of equations
\(x + y + z = 2\)
\(2x + 4y - z = 6\)
\(3x + 2y + \lambda z = \mu\)
has infinitely many solutions, then

Suppose the vectors \(x_1, x_2\) and \(x_3\) are the solutions of the system of linear equations, \(Ax = b\) when the vector b on the right side is equal to \(b_1, b_2\) and \(b_3\) respectively. if
\(x_1 = \begin{bmatrix}1\\1\\1\end{bmatrix},\ x_2 = \begin{bmatrix}0\\2\\1\end{bmatrix},\ x_3 = \begin{bmatrix}0\\0\\1\end{bmatrix}\),
\(b_1 = \begin{bmatrix}1\\0\\0\end{bmatrix},\ b_2 = \begin{bmatrix}0\\2\\0\end{bmatrix}\) and \(b_3 = \begin{bmatrix}0\\0\\2\end{bmatrix}\),
then the determinant of A is equal to :

The solution of the differential equation
\(\frac{dy}{dx} - \frac{y+3x}{\log_e (y+3x)} + 3 = 0\)
is:
(where c is a constant of integration)

The minimum value of \(2^{\sin x} + 2^{\cos x}\) is :

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, \(y = x^2 - 1\) below the x-axis, is :

If 75% of a first order reaction was completed in 90 minutes, 60% of the same reaction would be completed in approximately (in minutes) __________.
(Take : \(\log 2 = 0.30\); \(\log 2.5 = 0.40\))

At 300 K, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of n-heptane is 550 mm of Hg. At the same temperature, if one more mole of n-heptane is added to this solution, the vapour pressure of the solution increases by 10 mm of Hg. What is the vapour pressure in mm Hg of n-heptane in its pure state ______ ?

A 20.0 mL solution containing 0.2 g impure H₂O₂ reacts completely with 0.316 g of KMnO₄ in acid solution. The purity of H₂O₂ (in %) is ____________ (mol. wt. of H₂O₂ = 34; mol. wt. of KMnO₄ = 158)

Match the following :

(i)	Foam	(a)	smoke
(ii)	Gel	(b)	cell fluid
(iii)	Aerosol	(c)	jellies
(iv)	Emulsion	(d)	rubber
		(e)	froth
		(f)	milk

The mass of ammonia in grams produced when 2.8 kg of dinitrogen quantitatively reacts with 1 kg of dihydrogen is ________.

For one mole of an ideal gas, which of these statements must be true ?
(a) U and H each depends only on temperature
(b) Compressibility factor z is not equal to 1
(c) \(C_{P,m} - C_{V,m} = R\)
(d) \(dU = C_V dT\) for any process

Among statements (a) - (d), the correct ones are :
(a) Lime stone is decomposed to CaO during the extraction of iron from its oxides.
(b) In the extraction of silver, silver is extracted as an anionic complex.
(c) Nickel is purified by Mond's process.
(d) Zr and Ti are purified by Van Arkel method.

On heating, lead (II) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid (B). (B) on heating with NO changes to a blue solid (C). The oxidation number of nitrogen in solid (C) is :