JEE Main 2019 · 09 Apr 2019 · Shift 2

Q1.Two coils P and Q are separated by some distance. When a current of 3 A flows through coil P a magnetic flux of $10^{-3}\mathrm{Wb}$ passes through Q. No current is passed through Q. When no current passes through P and a current of 2 A passes through Q, the flux through P is:

Q2.A metal wire of resistance $3\Omega$ is elongated to make a uniform wire of double its previous length. The new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle $60^{\circ }$ at the centre, the equivalent resistance between these t …

Q3.The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range $0-0.5\mathrm{A}$?

Q4.The position of a particle as a function of time $t$, is given by $x(t)=at+b{t}^2-c{t}^3$ where $a$, $b$ and $c$ are constants. When the particle attains zero acceleration, then its velocity will be:

Q5.A thin convex lens $L$ (refractive index $=1.5$) is placed on a plane mirror $M$. When a pin is placed at A, such that $\mathrm{OA}=18\mathrm{cm}$, its real inverted image is formed at A itself, as shown in figure. When a liquid of refractive index ${\mu }_1$ is put between the …

Q6.A moving coil galvanometer has a coil with 175 turns and area $1{\mathrm{cm}}^2$ It uses a torsion band of torsion constant $10^{-6}\mathrm{N}-\mathrm{m}/\mathrm{rad}$. The coil is placed in a magnetic field B parallel to its plane. The coil deflects by $1^0$ for a curren …

Q7.A very long solenoid of radius $R$ is carrying current $I(t)=kt{e}^{-\alpha t}(k>0)$, as a function of time ( $\mathrm{t}\ge 0$ ). counter clockwise current is taken to be positive. A circular conducting coil of radius 2 R is placed in the equatorial plane of the solenoid and c …

Q8.A massless spring ( $\mathrm{k}=800\mathrm{N}/\mathrm{m}$ ), attached with a mass ( 500 g ) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature …

Q9.A particle P is formed due to a completely inelastic collision of particles x and y having de - Broglie wavelengths ${\lambda }_{\mathrm{x}}$ and ${\lambda }_{\mathrm{y}}$ respectively. If x and y were moving in opposite directions, then the de - Broglie wavelength of $P$ is:

Q10.A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances ${\mathrm{x}}_1$ and ${\mathrm{x}}_2\left({\mathrm{x}}_1>{\mathrm{x}}_2\right)$ from the lens. The ratio of ${\mathrm{x}}_1$ and ${\mathrm{x}}_2$ is:

Q11.Diameter of the objective lens of a telescope is 250 cm . For light of wavelength 600 nm . Coming from a distant object, the limit of resolution of the telescope is close to:-

Q12.Moment of inertia of a body about a given axis is $1.5\mathrm{kg}{\mathrm{m}}^2$ Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J , the angular acceleration of $20\mathrm{rad}/{\mathrm{s}}^2$ must be applied about the axis of rotatio …

Q13.The logic gate equivalent to the given logic circuit is:

Q14.$50\mathrm{W}/{\mathrm{m}}^2$ energy density of sunlight is normally incident on the surface of a solar panel. Some part of incident energy ( $25\%$ ) is reflected from the surface and the rest is absorbed. The force exerted on $1{\mathrm{m}}^2$ surface area will be close …

Q15.The area of a square is $5.29{\mathrm{cm}}^2$ The area of 7 such squares taking into account the significant figures is:

Q16.The physical sizes of the transmitter and receiver antenna in a communication system are:

Q17.Four point charges $-q,+q,+q$ and $-q$ are placed on $y$ axis at $y=-2d,y=-d,y=+d$ and $\mathrm{y}=+2\mathrm{d}$, respectively. The magnitude of the electric field E at a point on the x -axis at x $=D$, with $D\gg d$, will vary as:

Q18.The specific heats, $C_P$ and $C_V$ of a gas of diatomic molecules, A, are given (in units of J ${\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$) by 29 and 22, respectively. Another gas of diatomic molecules B, has the corresponding values 30 and 21. If they are treated as ideal gases, t …

Q19.The position vector of a particle changes with time according to the relation $\vec{r}(t)=15t^2\hat{i}+(4-20t^2)\hat{j}$. What is the magnitude of the acceleration at $t=1$?

Q20.A test particle is moving in a circular orbit in the gravitational field produced by a mass density $\rho (r)=\frac{K}{r^2}$. Identify the correct relation between the radius $R$ of the particle's orbit and its period T:

Q21.A particle of mass $m$ is moving with speed $2v$ collides with a mass $2m$ moving with speed v in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass m, which move at angle $45^0$ with respect to …

Q22.A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relati …

Q23.Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of $20{\mathrm{ms}}^{-1}$ with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency o …

Q24.A wedge of mass $M=4m$ lies on a frictionless plane. A particle of mass $m$ approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by:

Q25.A He${}^{+}$ ion is in its first excited state. Its ionization energy is:

Q26.Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d, respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are ${\theta }_2$ and ${\theta }_1$ respectively $({\theta }_2>{\theta }_1)$. The temperat …

Q27.A thin smooth rod of length $L$ and mass $M$ is rotating freely with angular speed ${\omega }_0$ about an axis perpendicular to the rod and passing through its centre. Two beads of mass m and negligible size are at the centre of the rod initially. The beads are free to slide along …

Q28.The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the t …

Q29.In a conductor, if the number of conduction electrons per unit volume is $8.5\times 10^{28}{\mathrm{m}}^{-3}$ and mean free time is 25fs (femto second), its approximate resistivity is: $({\mathrm{m}}_{\mathrm{e}}=9.1\times 10^{-31}\mathrm{kg})$

Q30.A string 2.0 m long and fixed at its end is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is:

Q1.Increasing order of reactivity of the following compounds for ${\mathrm{S}}_{\mathrm{N}}1$ substitution is:

Q2.The one that is not a carbonate is:

Q3.During compression of a spring the work done is 10 kJ and 2 kJ escaped to the surroundings as heat. The change in internal energy, $\Delta \mathrm{U}$ (in kJ) is:

Q4.The amorphous form of silica is:

Q5.The major products A and B for the following reactions are, respectively

Q6.Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (The Bohr radius is represented by ${\mathrm{a}}_0$)

Q7.The maximum possible denticities of a ligand given below towards a common transition and inner-transition metal ion, respectively, are:

Q8.The correct statements among I to III regarding group 13 element oxides are,
I. Boron trioxide is acidic
II. Oxides of aluminium and gallium are amphoteric
III. Oxides of indium and thallium are basic

Q9.Among the following species, the diamagnetic molecule is

Q10.The peptide that gives positive ceric ammonium nitrate and carbylamine tests is:

Q11.Assertion : For the extraction of iron, haematite ore is used

Reason : Haematite is a carbonate ore of iron

Q12.10 mL of 1 mM surfactant solution forms a monolayer covering $0.24{\mathrm{cm}}^2$ on a polar substrate. If the polar head is approximated as cube, what is its edge length?

Q13.Consider the given plot of enthalpy of the following reaction between A and B .

Identify the incorrect statement

Q14.At a given temperature T , gases $\mathrm{Ne},\mathrm{Ar},\mathrm{Xe}$ and Kr are found to deviate from ideal gas behaviour. Their equation of state is given as $\mathrm{P}=\frac{\mathrm{RT}}{\mathrm{V}-\mathrm{b}}$ at T . Here, b is the van der Waals constant. Which gas will e …

Q15.A solution of $\mathrm{Ni}{\left({\mathrm{NO}}_3\right)}_2$ is electrolysed between platinum electrodes using 0.1 Faraday electricity. How many mole of Ni will be deposited at the cathode?

Q16.In the following reaction

Carbonyl compound $+\mathrm{MeOH}\stackrel{\mathrm{HCl}}{\rightleftharpoons }$ acetal
Rate of the reaction is the highest for:

Q17.The structures of beryllium chloride in the solid state and vapour, phase, respectively, are:

Q18.Which of the following potential energy (PE) diagrams represents the ${\mathrm{S}}_{\mathrm{N}}1$ reaction?

Q19.The maximum number of possible oxidation states of actinoids are shown by

Q20.Molal depression constant for a solvent is $4.0\mathrm{K}\mathrm{Kg}{\mathrm{mol}}^{-1}$. The depression in the freezing point of the solvent for $0.03\mathrm{mol}{\mathrm{kg}}^{-1}$ solution of ${\mathrm{K}}_2{\mathrm{SO}}_4$ is: (Assume complete dissociation of the electro …

Q21.Noradrenaline is a/an

Q22.Hinsberg's reagent is:

Q23.The layer of atmosphere between 10 km to 50 km above the sea level is called as:

Q24.HF has highest boiling point among hydrogen halides, because it has:

Q25.What would be the molality of $20\%$ (mass/mass) aqueous solution of KI ? (molar mass of KI $=166\mathrm{g}{\mathrm{mol}}^{-1}$)

Q26.Which of the following compounds is a constituent of the polymer?

Q27.The correct statements among I to III are:
I. Valence bond theory cannot explain the color exhibited by transition metal complexes
II. Valence bond theory can predict quantitatively the magnetic properties of transition metal complexes
III. Valence bond theory cannot distinguish …

Q28.In an acid - base titration, 0.1 M HCl solution was added to the NaOH solution of unknown strength. Which of the following correctly shows the change of pH of the titration mixture in this experiment?

Q29.p -Hydroxybenzophenone upon reaction with bromine in carbon tetrachloride gives:

Q1.If the tangent to the parabola $y^2=x$ at a point $(\alpha ,\beta ),(\beta >0)$ is also a tangent to the ellipse, $x^2+2y^2=1$, then $\alpha$ is equal to

Q2.Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all thes …

Q3.If $f:R\to R$ is a differentiable function and $f(2)=6$, then ${\lim }_{x\to 2}{\int }_6^{f(x)}\frac{2tdt}{(x-2)}$ is:

Q4.If the system of equations $2x+3y-z=0,x+ky-2z=0$ and $2x-y+z=0$ has a non trivial solution $(x,y,z)$, then $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+k$ is equal to

Q5.The common tangent to the circles $x^2+y^2=4$ and $x^2+y^2+6x+8y-24=0$ also passes through the point

Q6.If the sum and product of the first three term in an A.P. are 33 and 1155, respectively, then a value of its $11^{\text{th}}$ term is

Q7.The value of the integral ${\int }_0^{1}x{\cot }^{-1}\left(1-x^2+x^4\right)dx$ is

Q8.The value of $\sin 10^{\circ }\sin 30^{\circ }\sin 50^{\circ }\sin 70^{\circ }$ is

Q9.Let $z\in \mathbb{C}$ be such that $|z|<1$. If $w=\frac{5+3z}{5(1-z)}$, then

Q10.If some three consecutive coefficients in the binomial expansion of $(x+1{)}^n$ in powers of $x$ are in the ratio $2:15:70$, then the average of these three coefficients is:

Q11.If $\cos x\frac{dy}{dx}-y\sin x=6x,\left(0<x<\frac{\pi }{2}\right)$ and $y\left(\frac{\pi }{3}\right)=0$, then $y\left(\frac{\pi }{6}\right)$ is equal to:

Q12.If the two lines $x+(a-1)y=1$ and $2x+a^{2}y=1(a\in \mathbb{R}-\{0,1\})$ are perpendicular, then the distance of their point of intersection from the origin is:

Q13.A water tank has the shape of an inverted right circular cone, whose semi vertical angle is ${\tan }^{-1}\left(\frac{1}{2}\right)$. Water is poured in at a constant rate of 5 cubic meter per minute. Then the rate (in $\mathrm{m}/\min$) at which the level of water is rising …

Q14.Two poles standing on a horizontal ground are of heights 5 m and 10 m respectively. The line joining their tops makes an angle of $15^{\circ }$ with ground. Then the distance (in m) between the poles, is

Q15.The vertices $B$ and $C$ of a $△ABC$ lie on the line, $\frac{x+2}{3}=\frac{y-1}{0}=\frac{z}{4}$ such that $BC=5$ units. Then the area (in sq. units) of this triangle, given that the point $\mathrm{A}(1,-1,2)$ is:

Q16.The total number of matrices $A=\left[\begin{array}{ccc}0& 2x& 2x\\ 2y& y& -y\\ 1& -1& 1\end{array}\right]$; $(x,y\in R,x\ne y)$ for which $A^{\top }A=3I_3$

Q17.The area in sq. units) of the smaller of the two circles that touch the parabola, $y^2=4x$ at the points $(1,2)$ and the axis is

Q18.If the function $f(x)=\{\begin{array}{l}a|\pi -x|+1,x\le 5\\ b|\pi -x|+3,x>5\end{array}$ is continuous at $x=5$, then the value of $a-b$ is

Q19.If $f(x)=[x]-\left[\frac{x}{4}\right],x\in R$, where $[x]$ denotes the greatest integer function, then:

Q20.If $\int e^{\sec x}\left(\sec x+\tan xf(x)+\left(\sec x\tan x+{\sec }^{2}x\right)\right)dx=e^{\sec x}f(x)+C$, then a possible choice of $f(x)$ is

Q21.If $m$ is chosen in the quadratic equation $\left(m^2+1\right)x^2-3x+{\left(m^2+1\right)}^2=0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is:

Q22.Two newspaper A and B are published in a city. It is known that $25\%$ of the city populations reads A and $20\%$ reads B while $8\%$ reads both A and B. Further, $30\%$ of those who read A but not B look into advertisements and $40\%$ of those who read B but not A also look into …

Q23.Let P be the plane, which contains the line of intersection of the planes, $\mathrm{x}+\mathrm{y}+\mathrm{z}-6=0$ and $2x+3y+z+5=0$ and it is perpendicular to the $xy$-plane. Then the distance of the point $(0,0,256)$ from $P$ is equal to:

Q24.If $P\Rightarrow (q\vee r)$ is false, then the truth values of $p,q,r$ are respectively

Q25.The domain of the definition of the function $f(x)=\frac{1}{4-x^2}+\log \left(x^3-x\right)$ is

Q26.The sum of the series $1+2\times 3+3\times 5+4\times 7+\dots$ upto $11^{\text{th}}$ term is

Q27.The mean and the median of the following ten numbers in increasing order $10,22,26$, $29,34,x,42,67,70,y$ are 42 and 35 respectively, then $\frac{y}{x}$ is equal to

Q28.The area (in sq. units) of the region $\mathrm{A}=\left\{(\mathrm{x},\mathrm{y}):\frac{{\mathrm{y}}^2}{2}\le x\le y+4\right\}$ is:

Q29.If a unit vector $\vec{r}$ makes angles $\frac{\pi }{3}$ with $\hat{i}$, $\frac{\pi }{4}$ with $\hat{j}$ and $\theta \in (0,\pi )$ with $\hat{k}$, then a value of $\theta$ is

Q30.A rectangle is inscribed in a circle with a diameter lying along the line $3y=x+7$. If the two adjacent vertices of the rectangle are $(-8,5)$ and $(6,5)$ then the area of the rectangle (in sq. units) is