List of top Questions asked in JEE Main- 2019

An amplitude modulated signal is given by $V(t) = 10[1 + 0.3 \cos(2.2 \times 10^4)] \sin(5.5 \times 10^5t)$. Here t is in seconds. The sideband frequencies (in kHz) are, [Given $\pi = 22/7$]

Amylopectin is composed of :

Among the following species, the diamagnetic molecule is

Among the following molecules / ions, $C^{2-}_{2}, N^{2-}_{2}, O^{2-}_{2}, O_{2}$ which one is diamagnetic and has the shortest bond length?

Among the following compounds most basic amino acid is :

All possible numbers are formed using the digits \(1,1,2,2,2,2,3,4,4\) taken all at a time. The number of such numbers in which the odd digits occupy even places is :

A value of $\theta \ \ \in \ (0, \pi /3)$ for which $\begin {vmatrix} 1 + cos^2 \theta & sin^2\theta & 4 cos 6\theta \\ cos^2 \theta & 1+sin^2 \theta & 4 cos6 \theta \\ cos^2 \theta & sin^2 \theta & 1+4 cos6 \theta \end {vmatrix} $ =0 , is :

A uniform rectangular thin sheet $ABCD$ of mass $M$ has length $a$ and breadth $b$, as shown in the figure. If the shaded portion $HBGO$ is cut-off, the coordinates of the centre of mass of the remaining portion will be :

A uniform metallic wire has a resistance of $18 \; \Omega$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is :

A uniform cylindrical rod of length $L$ and radius $r$, is made from a material whose Young's modulus of Elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to :

A uniform cable of mass $'M'$ and length $'L'$ is placed on a horizontal surface such that its $\bigg(\frac{1}{n}\bigg)^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be :

A tuning fork of frequency $480\, Hz$ is used in an experiment for measuring speed of sound (n) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, $l_1$ = 30 cm and $l_2$ = $70 \,cm$. Then, $v$ is equal to :

A travelling harmonic wave is represented by the equation $y (x, t) = 10^{-3} sin (50 t + 2x)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave? The wave is propagating along the

A thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma (r) = kr^2$ where $r$ is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :

A thin circular plate of mass $M$ and radius $R$ has its density varying as $\rho (r) = \rho_0 r$ with $\rho_0$ as constant and $r$ is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is $I = aMR^2$. The value of the coefficient $a$ is :

A thermometer graduated according to a linear scale reads a value $x_0$ when in contact with boiling water, and $x_0/3$ when in contact with ice. What is the temperature of an object in $0 {^{\circ}C}$, if this thermometer in the contact with the object reads $x_0/2$ ?

A thermally insulated vessel contains $150\,g$ of water at $0^{\circ}C$. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at $0^{\circ}C$ itself. The mass of evaporated water will be closest to : (Latent heat of vaporization of water $= 2.10 \times 10^6 \; J \; kg^{-1}$ and Latent heat of Fusion of water = $3.36 \times 10^5 \; J \; kg^{-1}$)

A student scores the following marks in five tests : $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

A string of length $1\, m$ and mass $5\, g$ is fixed at both ends. The tension in the string is $8.0\, N$. The siring is set into vibration using an external vibrator of frequency $100\, Hz$. The separation between successive nodes on the string is close to :

A string is wound around a hollow cylinder of mass $5\, kg$ and radius $0.5\, m$. If the string is now pulled with a horizontal force of $40\, N$, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) :

A steel wire having a radius of $2.0\, mm$, carrying a load of $4 \,kg$, is hanging from a ceiling. Given that $g = 3.1 \; \pi \; ms^{-2}$, what will be the tensile stress that would be developed in the wire ?

A spring whose unstretched length is $l$ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $l_1$ and $l_2$ where, $l_1$ = $nl_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants, $k_1$ and $k_2$ will be :

A solution of ${Ni(NO3)2}$ is electrolysed between platinum electrodes using $0.1$ Faraday electricity. How many mole of $Ni$ will be deposited at the cathode?

A solution is prepared by dissolving $0.6\, g$ of urea (molar mass = $60\, g\, mol^{-1})$ and $1.8\, g$ of glucose (molar mass = $180\, g$ mol${-1}$) in $100\, mL$ of water at $27^{\circ}C$. The osmotic pressure of the solution is : $(R = 0.08206 \; L \; atm \; K^{-1} \; mol^{-1} ) $

A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius $2R$. The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of the disc about its axis and $I_2$ be the moment of inertia of the new sphere about its axis. The ratio $I_1/I_2$ is given by :