List of top Questions asked in JEE Main

A rod of length eight units moves such that its ends A and B always lie on the lines \( x - y + 2 = 0 \) and \( y + 2 = 0 \), respectively. If the locus of the point \( P \), that divides the rod AB internally in the ratio 2:1, is \[ 9(x^2 + \alpha y^2 + \beta xy + \gamma x + 28 y) - 76 = 0, \] then \[ \alpha - \beta - \gamma \text{ is equal to:} \]

Given below are two statements: Statement (I): \textit{An element in the extreme left of the periodic table forms acidic oxides.}
Statement (II): \textit{Acid is formed during the reaction between water and oxide of a reactive element present in the extreme right of the periodic table.} In the light of the above statements, choose the correct answer from the options given below:

Let the point \( A \) divide the line segment joining the points \( P(-1, -1, 2) \) and \( Q(5, 5, 10) \) internally in the ratio \( r : 1 \) (\( r > 0 \)). If \( O \) is the origin and \[ \left( \frac{|\overrightarrow{OQ} \cdot \overrightarrow{OA}|}{5} \right) - \frac{1}{5} |\overrightarrow{OP} \times \overrightarrow{OA}|^2 = 10, \] then the value of \( r \) is:

Consider the given figure and choose the correct option: \includegraphics[width=1\linewidth]{322.png}

\includegraphics[width=1\linewidth]{brc.png}

The molar solubility(s) of zirconium phosphate with molecular formula \( \text{Zr}^{4+} \text{PO}_4^{3-} \) is given by relation: \includegraphics[width=1\linewidth]{333.png}

Match the Compounds (List - I) with the appropriate Catalyst/Reagents (List - II) for their reduction into corresponding amines. \includegraphics[width=1\linewidth]{b.png}

If the area of the region \[ \{(x, y) : -1 \leq x \leq 1, 0 \leq y \leq a + e^{|x|} - e^{-x}, a> 0\} \] is \[ \frac{e^2 + 8e + 1}{e}, \] then the value of \(a\) is:

If the square of the shortest distance between the lines \[ \frac{x-2}{1} = \frac{y-1}{2} = \frac{z+3}{-3} \] and \[ \frac{x+1}{2} = \frac{y+3}{4} = \frac{z+5}{-5} \] is \( \frac{m}{n} \), where \( m \) and \( n \) are co-prime numbers, then \( m+n \) is equal to:

Match List - I with List - II. List - I (Partial Derivatives) \quad List - II (Thermodynamic Quantity)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The binding energy per nucleon is found to be practically independent of the atomic number \( A \), for nuclei with mass numbers between 30 and 170. Reason (R): Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below:

The most stable carbocation from the following is: \includegraphics[width=1\linewidth]{3333.png}

In the photoelectric effect, an electromagnetic wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and the stopping potential is 2V, what is the wavelength of the electromagnetic wave? Given \( hc = 1242 \, \text{eV} \cdot \text{nm} \) where \( h \) is the Planck constant and \( c \) is the speed of light in vacuum.

A board has 16 squares as shown in the figure. Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is: \includegraphics[]{10.PNG}

Arrange the following compounds in increasing order of their dipole moment:
HBr, H\(_2\)S, NF\(_3\), and CCl\(_3\)