List of top Questions asked in JEE Main

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27 °C to 87 °C. The rate of consumption of the gas is_________ g/s. (Take heat of combustion of gas = \(5.0 \times 10^4\) J/g, specific heat capacity of water = 4200 J/kg.°C).
Given below are two statements:
Statement I: When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules dissociate and the energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequencies.
Statement II: The frequency of second line of Balmer series obtained from He⁺ is equal to that of first line of Lyman series obtained from hydrogen atom.
In the light of the above statements, choose the correct answer from the options given below:

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is \(\frac{x}{12} ML^2\) kg m\(^2\). The value of x is ______ .

An organic compound (P) on treatment with aqueous ammonia under hot condition forms compound (Q) which on heating with Br₂ and KOH forms compound (R) having molecular formula C₆H₇N. Names of P, Q and R respectively are.
An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30\(^\circ\)C. The coefficient of linear expansion of aluminium and steel are \(24 \times 10^{-6}\)/\(^\circ\)C and \(1.2 \times 10^{-5}\)/\(^\circ\)C, respectively. The length of this composite rod when its temperature is raised to 100\(^\circ\)C, is________ cm.
14.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure and 273 K. Which of the following statements is incorrect?
\([Given: \text{Molar mass of } Ca = 40, Cl = 35.5, H = 1 \text{ g mol}^{-1}] \)
Find the volume flow rate in the venturi meter given below in which water is flowing.
Find the concentration of \( \mathrm{X^{2-}} \) at equilibrium in \(0.1\,\mathrm{M}\) \( \mathrm{H_2X} \). Given: \[ K_{a1} = 2.5 \times 10^{-7}, \qquad K_{a2} = 1 \times 10^{-13} \]
The value of \[ \frac{{}^{100}C_{50}}{51} + \frac{{}^{100}C_{51}}{52} + \cdots + \frac{{}^{100}C_{100}}{101} \] is:
Find the number of matrices $A$ of order $3\times 2$ whose elements are from the set $\{\pm2,\pm1,0\}$, if $\mathrm{Tr}(A^TA)=5$.
A complex number 'z' satisfy both \(|z-6|=5\) & \(|z+2-6i|=5\) simultaneously. Find the value of \(z^3 + 3z^2 - 15z + 141\).

\(1\,\text{g}\) of \( \mathrm{AB_2} \) is dissolved in \(50\,\text{g}\) of a solvent such that \( \Delta T_f = 0.689\,\text{K} \). When \(1\,\text{g}\) of \( \mathrm{AB} \) is dissolved in \(50\,\text{g}\) of the same solvent, \( \Delta T_f = 1.176\,\text{K} \). Find the molar mass of \( \mathrm{AB_2} \). Given \( K_f = 5\,\text{K kg mol}^{-1} \). \((\textit{Report to nearest integer.})\) Both \( \mathrm{AB_2} \) and \( \mathrm{AB} \) are non-electrolytes.

For the given set of measurements, find the relative error. \[ 20.00,\ 19.75,\ 18.25,\ 17.01 \]
If \( A = \{1,2,3,4,5,6\} \) and \( B = \{1,2,3,\ldots,9\} \), then the number of strictly increasing functions \( f : A \to B \) such that \( f(i) \neq i \) for all \( i = 1,2,3,4,5,6 \) is:
A conducting rod of mass \( m \) and length \( l \) is moving on an infinite pair of conducting rails as shown. Conducting rails are connected to a resistance \( R \) at one end. Motion is in the vertical plane and horizontal magnetic field in the region is \( B \). Find the terminal speed of the rod.
If the end points of chord of parabola \(y^2 = 12x\) are \((x_1, y_1)\) and \((x_2, y_2)\) and it subtend \(90^\circ\) at the vertex of parabola then \((x_1x_2 - y_1y_2)\) equals :
After release, the blocks moves 81 cm in 9 seconds. Find moment of inertia of the pulley :
(Given $m_{1} = 400$ gm, $m_{2} = 350$ gm, R = 2 cm, g = 10 m/s$^2$)
Density of water at 4\(^\circ\)C is 1000 kg/m\(^3\) and at 20\(^\circ\)C it is 998 kg/m\(^3\). If 4kg of water is heated from 4\(^\circ\)C to 20\(^\circ\)C, the change in internal energy of water is : (Given : specific heat capacity of water = 4200 J/kg K, Atmospheric pressure P = \(10^5\) Pa).
From the following : (A) $[\text{Co}(\text{NH}_3)_6]^{3+}$ : Inner orbital complex, $d^2sp^3$ hybridization (B) $[\text{MnCl}_4]^{2-}$ : Outer orbital complex, $sp^3d^2$ hybridization (C) $[\text{CoF}_6]^{3-}$ : Outer orbital complex, $d^2sp^3$ hybridization (D) $[\text{FeF}_6]^{3-}$ : Outer orbital complex, $sp^3d^2$ hybridization (E) $[\text{Ni}(\text{CN})_4]^{2-}$ : Inner orbital complex, $sp^3$ hybridization Choose the correct answer from the given options.

Let \[ f(x)=\int \frac{7x^{10}+9x^8}{(1+x^2+2x^9)^2}\,dx \] and $f(1)=\frac14$. Given that 

 

If $f(a)$ is the area bounded in the first quadrant by $x=0$, $x=1$, $y=x^2$ and $y=|ax-5|-|1-ax|+ax^2$, then find $f(0)+f(1)$.
There is a weak base 'B' having $\text{pK}_b = 5.691$ of molarity 0.02M. When 0.02M HCl solution has been added, then pH of resultant buffer solution has been found to be 9. Take total volume of resultant buffer solution to be 100 ml. Find the value of 'x' & 'y', where 'x' is volume of HCl solution in ml & 'y' is volume of 'B' solution in ml. Given $\log(5) = 0.691$
Which of the following graph is correct between log P$_{CO_2}$ vs log X$_{CO_2}$? [given P$_{CO_2}$ = Partial Pressure of CO$_2$, X$_{CO_2}$ = Mole fraction of CO$_2$ in solution]
The coefficient of \( x^{48} \) in the expansion of \[ 1 + (1+x) + 2(1+x)^2 + 3(1+x)^3 + \dots + 100(1+x)^{100} \] is
The coefficient of x\(^{48}\) in \(1(1+x)+2(1+x)^2+3(1+x)^3 +.....+100(1+x)^{100}\) is: