List of top Questions asked in JEE Main

If the mirror image of the point \((1,3,5)\) with respect to the plane \(4x-5y+2z=8\) is \((\alpha,\beta,\gamma)\), then \(5(\alpha+\beta+\gamma)\) equals :

The sum of the series
\(\displaystyle\sum_{n=1}^{\infty}\frac{n^2+6n+10}{(2n+1)!}\)
is equal to :

Let \(L\) be a line obtained from the intersection of two planes \(x + 2y + z = 6\) and \(y + 2z = 4\). If point \(P(\alpha, \beta, \gamma)\) is the foot of perpendicular from \((3, 2, 1)\) on \(L\), then the value of \(21(\alpha + \beta + \gamma)\) equals :

The triangle of maximum area that can be inscribed in a given circle of radius 'r' is :

Let slope of the tangent line to a curve at any point \(P(x,y)\) be given by \(\frac{xy^2+y}{x}\). If the curve intersects the line \(x+2y=4\) at \(x=-2\), then the value of \(y\), for which the point \((3,y)\) lies on the curve, is :

A seven digit number is formed using digits \(3, 3, 4, 4, 4, 5, 5\). The probability, that number so formed is divisible by 2, is :

Let \(f : R \to R\) be defined as
\(f(x) = \begin{cases} 2\sin\left(-\frac{\pi x}{2}\right), & \text{if } x \lt -1 \\ |ax^2 + x + b|, & \text{if } -1 \le x \le 1 \\ \sin(\pi x), & \text{if } x \gt 1 \end{cases}\)
If \(f(x)\) is continuous on \(R\), then \(a + b\) equals :

If the locus of the mid-point of the line segment from the point \((3, 2)\) to a point on the circle, \(x^2 + y^2 = 1\) is a circle of radius \(r\), then \(r\) is equal to :

If vectors \(\vec{a_1} = x\hat{i} - \hat{j} + \hat{k}\) and \(\vec{a_2} = \hat{i} + y\hat{j} + z\hat{k}\) are collinear, then a possible unit vector parallel to the vector \(x\hat{i} + y\hat{j} + z\hat{k}\) is :

Let \(f(x) = \sin^{-1}x\) and \(g(x) = \frac{x^2 - x - 2}{2x^2 - x - 6}\). If \(g(2) = \displaystyle\lim_{x \to 2} g(x)\), then the domain of the function \(f \circ g\) is :

If \(0 \lt a, b \lt 1\), and \(\tan^{-1}a + \tan^{-1}b = \frac{\pi}{4}\), then the value of
\((a + b) - \left(\frac{a^2 + b^2}{2}\right) + \left(\frac{a^3 + b^3}{3}\right) - \left(\frac{a^4 + b^4}{4}\right) + \dots\)
is :

A natural number has prime factorization given by \(n = 2^x 3^y 5^z\), where \(y\) and \(z\) are such that \(y + z = 5\) and \(y^{-1} + z^{-1} = \frac{5}{6}\), \(y \gt z\). Then the number of odd divisions of \(n\), including 1, is :

Let \(A = \{1, 2, 3, \dots, 10\}\) and \(f : A \to A\) be defined as
\(f(k) = \begin{cases} k + 1 & \text{if } k \text{ is odd} \\ k & \text{if } k \text{ is even} \end{cases}\)
Then the number of possible functions \(g : A \to A\) such that \(g \circ f = f\) is :

Let \(f(x) = \displaystyle\int_0^x e^t f(t)\,dt + e^x\) be a differentiable function for all \(x \in R\). Then \(f(x)\) equals :

For \(x \gt 0\), if \(f(x) = \displaystyle\int_1^x \frac{\log_e t}{(1 + t)}\,dt\), then \(f(e) + f\left(\frac{1}{e}\right)\) is equal to :

Consider the following system of equations :
\(x + 2y - 3z = a\)
\(2x + 6y - 11z = b\)
\(x - 2y + 7z = c\),
where \(a\), \(b\) and \(c\) are real constants. Then the system of equations :

Let \(A(1, 4)\) and \(B(1, -5)\) be two points. Let \(P\) be a point on the circle \((x - 1)^2 + (y - 1)^2 = 1\) such that \((PA)^2 + (PB)^2\) have maximum value, then the points, \(P\), \(A\) and \(B\) lie on :

Let \(f(x)\) be a differentiable function at \(x = a\) with \(f'(a) = 2\) and \(f(a) = 4\).
Then \(\displaystyle\lim_{x \to a} \frac{x f(a) - a f(x)}{x - a}\) equals :

A certain gas obeys \(\mathrm{P(V_m - b) = RT}\). The value of \(\left(\dfrac{\partial Z}{\partial P}\right)_T\) is \(\dfrac{xb}{RT}\). The value of x is _________. (Integer answer) (Z : compressibility factor)

3.12 g of oxygen is adsorbed on 1.2 g of platinum metal. The volume of oxygen adsorbed per gram of the adsorbent at 1 atm and 300 K in L is __________.

[R = 0.0821 L atm \(\mathrm{K^{-1}\ mol^{-1}}\)]

The number of significant figures in \(50000.020 \times 10^{-3}\) is _____________.

224 mL of \(\mathrm{SO_{2(g)}}\) at 298 K and 1 atm is passed through 100 mL of 0.1 M NaOH solution. The non-volatile solute produced is dissolved in 36g of water. The lowering of vapour pressure of solution (assuming the solution in dilute) (\(\mathrm{P^o_{(H_2O)}}\) - 24 mm of Hg) is x \(\times\) \(10^{-2}\) mm of Hg, the value of x is ___________. (Integer answer)

Consider the following reaction

\(\mathrm{MnO_4^- + 8H^+ + 5e^- \to Mn^{2+} + 4H_2O},\ E^\circ = 1.51\ \mathrm{V}\).

The quantity of electricity required in Faraday to reduce five moles of \(\mathrm{MnO_4^-}\) is ___________. (Integer answer)

Dichromate ion is treated with base, the oxidation number of Cr in the product formed is ___________.

A homogeneous ideal gaseous reaction \(\mathrm{AB_{2(g)} \rightleftharpoons A_{(g)} + 2B_{(g)}}\) is carried out in a 25 litre flask at \(27^\circ\mathrm{C}\). The initial amount of \(\mathrm{AB_2}\) was 1 mole and the equilibrium pressure was 1.9 atm. The value of \(\mathrm{K_p}\) is x \(\times\) \(10^{-2}\). The value of x is _________. (Integer answer)

[R = 0.08206 \(\mathrm{dm^3\ atm\ K^{-1}\ mol^{-1}}\)]