JEE Main 2019 · 11 Jan 2019 · Shift 2

Q1.A particle moves from the point $(2.0\hat{\mathrm{i}}+4.0\hat{\mathrm{j}})\mathrm{m}$, at $\mathrm{t}=0$ with an initial velocity $(5.0\hat{\mathrm{i}}+4.0\hat{\mathrm{j}}){\mathrm{ms}}^{-1}$. It is acted upon by a constant force which produces a constant acceleration …

Q2.A thermometer graduated according to a linear scale reads a value ${\mathrm{x}}_0$ when in contact with boiling water, and $x_0/3$ when in contact with ice. What is the temperature of an object in ${}^0\mathrm{C}$, if this thermometer in the contact with the object reads …

Q3.A galvanometer having a resistance of $20\Omega$ and 30 divisions on both sides has figure of merit 0.005 ampere /division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt is:

Q4.In the experimental setup of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A . If a $10\Omega$ resistor is connected in series with ${\mathrm{R}}_1$, the null point shifts by 10 cm . The resistance that should be connected in parallel w …

Q5.A circular disc $D_1$ of mass $M$ and radius $R$ has two identical discs $D_2$ and $D_3$ of the same mass M and radius R attached rigidly as its opposite ends (see figure). The moment of inertia of the system about the axis ${\mathrm{OO}}^{\prime }$, passing through the centre …

Q6.The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is IN, and the distance of the particle from the origin is 5 m , the angle between the force and the position vector is (in radians):

Q7.A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3 , keeping the number of turns of the coil per unit length of the frame the same, then self inductance of the c …

Q8.A particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t=0$, a force $F=kt$ acts in the same direction on the moving particle during time interval $T$ so that its momentum changes from $p$ to $3p$. Here $k$ is a constant. The value of $T$ is:

Q9.A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of $20\times 10^{-6}\mathrm{J}/\mathrm{T}$ when a magnetic intensity of $60\times 10^3\mathrm{A}/\mathrm{m}$ is applied. Its magnetic susceptibility is:

Q10.A simple pendulum of length 1 m is oscillating with an angular frequency $10\mathrm{rad}/\mathrm{s}$. The support of the pendulum starts oscillating up and down with a small angular frequency of $1\mathrm{rad}/\mathrm{s}$ and an amplitude of $10^{-2}\mathrm{m}$. The relat …

Q11.The circuit shown below contains two ideal diodes, each with a forward resistance of $50\Omega$. If the battery voltage is 6 V , the current through the $100\Omega$ resistance (in Amperes) is:

Q12.An electric field of $1000\mathrm{V}/\mathrm{m}$ is applied to an electric dipole at angle of $45^{\circ }$. The value of electric dipole moment is $10^{-29}\mathrm{C}.\mathrm{m}$. What is the potential energy of the electric dipole?

Q13.A metal bal of mass 0.1 kg is heated upto $500^{\circ }\mathrm{C}$ and dropped into a vessel of heat capacity $800{\mathrm{JK}}^{-1}$ and containing 0.5 kg water. The initial temperature of water and vessel is $30^0\mathrm{C}$. What is the approximate percentage increment in th …

Q14.A pendulum is executing simple harmonic motion and its maximum kinetic energy is ${\mathrm{K}}_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is ${\mathrm{K}}_2$ then:

Q15.Two rods A and B of identical dimensions are at temperature $30^{\circ }\mathrm{C}$. If a heated upto $180^{\circ }\mathrm{C}$ and B upto ${\mathrm{T}}^{\circ }\mathrm{C}$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is …

Q16.If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be:

Q17.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 …

Q18.A 27 mW laser beam has a cross-sectional area of $10{\mathrm{mm}}^2$. The magnitude of the maximum electric field in this electromagnetic wave is given by:
[Given permittivity of space ${ϵ}_0=9\times 10^{-12}\mathrm{SI}$ units, speed of light …

Q19.In the circuit shown, the potential difference between $A$ and $B$ is:

Q20.The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2s. The period of oscillation of the same pendulum on the planet would be:

Q21.An amplitude modulated signal is plotted below:

Which one of the following best described the above signal?

Q22.In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $\mathrm{VT}=\mathrm{K}$, where K is a constant. In this process the temperature of the gas is increased by $\Delta T$. The amount of heat absorbed by gas is ($R$ is g …

Q23.When 100 g of a liquid A at $100^{\circ }\mathrm{C}$ is added to 50 g of a liquid B at temperature $75^{\circ }\mathrm{C}$, the temperature of the mixture becomes $90^{\circ }\mathrm{C}$. The temperature of the mixture, if 100 g of liquid A at $100^{\circ }\mathrm{C}$ is added to …

Q24.In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell the wavelength of emitted radiation is $\lambda$. If an electron jumps from N-shell to the L-shell the wavelength of emitted radiation will be:

Q25.A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is $\sqrt{3}$, then the angle of incidence

Q26.In a double-slit experiment, green light (5303 Å) falls on a double slit having a separation of $19.44\mu \mathrm{m}$ and a width of $4.05\mu \mathrm{m}$. The number of bright fringes between the first and the second diffraction minima is:

Q27.Seven capacitors, each of the capacitance $2\mu \mathrm{F}$, are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right)\mu \mathrm{F}$. Which of the combinations, shown in figures below, will achieve the desired value?

Q28.A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by:

The charged particle is shifted from the origin to the point $P(x=1;y=1)$ along a straight path. The magnitude of the total work done i …

Q29.In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to $\left(\frac{\mathrm{hc}}{\mathrm{e}}=1240\mathrm{nm}-\mathrm{V}\right)$

Q1.The reaction:
$\mathrm{MgO}(\mathrm{s})+\mathrm{C}(\mathrm{s})\to \mathrm{Mg}(\mathrm{s})+\mathrm{CO}(\mathrm{g})$, for which ${\Delta }_{\mathrm{r}}{\mathrm{H}}^0=+491.1\mathrm{kJ}{\mathrm{mol}}^{-1}$ and …

Q2.The correct match between Item I and Item II is

Item I
A. Allosteric effect
B. Competitive inhibitor
C. Receptor
D. Poison

Item II
P. Molecule binding to the active site of enzyme
Q. Molecule crucial for communication in the body
R. Molecule binding to a site other than the act …

Q3.The coordination number of Th in ${\mathrm{K}}_4\left[\mathrm{Th}{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_4{\left({\mathrm{OH}}_2\right)}_2\right]$ is: $({\mathrm{C}}_2{\mathrm{O}}_4^{2-}=\mathrm{O}$ xalato $)$

Q4.The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by
${\Delta }_{\mathrm{r}}{\mathrm{G}}^0=\mathrm{A}-\mathrm{BT}$
Where $A$ and $B$ are non - zero constant. Which of the following is TRUE about this reaction?

Q5.The radius of the largest sphere which fits properly at the centre of the edge of a body centered cubic unit cell is: (Edge length is represented by ' $a$ ')

Q6.The hydride that is NOT electron deficient is:

Q7.Given the equilibrium constant:
${\mathrm{K}}_{\mathrm{C}}$ of the reaction:
$\mathrm{Cu}(\mathrm{s})+2\mathrm{Ag}+(\mathrm{aq})\to {\mathrm{Cu}}^2+(\mathrm{aq})+2\mathrm{Ag}(\mathrm{s})$ is …

Q8.The correct option with respect to the Pauling electronegativity values of the elements is:

Q9.Which of the following compounds will produce a precipitate with ${\mathrm{AgNO}}_3$ ?

Q10.The de Broglie wavelength ( $\lambda$ ) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [ ${\mathrm{v}}_0$ is threshold frequency]:

Q11.Which of the following compounds reacts with ethylmagnesium bromide and also decolourizes bromine water solution:

Q12.In the following compound

The favourable site/s for protonation is/are

Q13.Taj Mahal is being slowly disfigured and discoloured. This is primarily due to:

Q14.The relative stability of +1 oxidation state of group 13 elements follows the order:

Q15.For the equilibrium
$2{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{OH}}^{-}$, the value of $\Delta {\mathrm{G}}^0$ at 298 K is approximately:

Q16.The reaction that does NOT define calcination is:

Q17.A compound ' $X$ ' on treatment with ${\mathrm{Br}}_2/\mathrm{NaOH}$, provided ${\mathrm{C}}_3{\mathrm{H}}_9\mathrm{N}$, which gives positive carbylamine test. Compound ' X ' is:

Q18.Among the colloids cheese (C), milk (M) and smoke (S), the correct combination of the dispersed phase and dispersion medium, respectively is:

Q19.The homopolymer formed from 4 - hydroxybutanoic acid is:

Q20.${\mathrm{K}}_2{\mathrm{HgI}}_4$ is $40\%$ ionized in aqueous solution. The value of its van't Hoff factor (i) is:

Q21.25 mL of the given HCl solution requires 30 mL of 0.1 M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution?

Q22.The reaction $2X\to B$ is a zeroth order reaction. If the initial concentration of $X$ is $0.2M$, the half life is 6 h . When the initial concentration of $X$ is 0.5 M , the time required to reach its final concentration of 0.2 M will be:

Q23.Match the following items in column I with the corresponding items in column II.

Column I
I. ${\mathrm{Na}}_2{\mathrm{CO}}_3.10{\mathrm{H}}_2\mathrm{O}$
II. $\mathrm{Mg}{\left({\mathrm{HCO}}_3\right)}_2$
III. NaOH
IV. ${\mathrm{Ca}}_3{\mathrm{Al}}_2{\mathrm{O}}_6$

Column …

Q24.The major product obtained in the following conversion is:

Q25.The higher concentration of which gas in air can cause stiffness of flower buds?

Q26.The correct match between Item I and Item II is

Item I
Item II
A. Ester test
P. Tyr
B. Carbylamine test
Q. Asp
C. Phthalein dye test
R. Ser
S. Lys

Q27.The number of bridging CO ligand(s) and Co - Co bond $(\mathrm{s})$ in ${\mathrm{Co}}_2(\mathrm{CO}{)}_8$ respectively are:

Q28.$\underline{\mathrm{A}}\stackrel{4\mathrm{KOH},{\mathrm{O}}_2}{\to }\underset{\text{ (Green) }}{2\mathrm{B}}+2{\mathrm{H}}_2\mathrm{O}$
$3\mathrm{B}\stackrel{4\mathrm{HCl}}{\to }\underset{\text{ (Purple) }}{2\mathrm{C}}+{\mathrm{MnO}}_2+2{\mathrm{H}}_2\mathrm{O}$ …

Q1.${\lim }_{x\to 0}\frac{x\cot (4x)}{{\sin }^{2}x{\cot }^2(2x)}$ is equal to:

Q2.All $x$ satisfying the inequality $({\cot }^{-1}x{)}^2-7({\cot }^{-1}x)+10>0$, lie in the interval:

Q3.If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is:

Q4.If the area of the triangle whose one vertex is at the vertex of the parabola, $y^2+4(x-a^2)=0$ and the other two vertices are the points of intersection of the parabola and $y$-axis, is 250 sq. units, then a value of '$a$' is:

Q5.Two lines $\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$ and $\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}$ intersect at the point $R$. The reflection of $R$ in the $xy$-plane has coordinates:

Q6.Contrapositive of the statement "If two numbers are not equal, then their squares are not equal" is:

Q7.If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is:

Q8.The integral ${\int }_{\pi /6}^{\pi /4}\frac{dx}{\sin 2x({\tan }^{5}x+{\cot }^{5}x)}$ equals:

Q9.Let $x$, $y$ be positive real numbers and $m$, $n$ positive integers. The maximum value of the expression $\frac{x^m{y}^n}{(1+x^{2m})(1+y^{2n})}$ is:

Q10.Let $S_n=1+q+q^2+\dots +q^n$ and $T_n=1+\left(\frac{q+1}{2}\right)+{\left(\frac{q+1}{2}\right)}^2+\dots +{\left(\frac{q+1}{2}\right)}^n$ where $q$ is a real number and $q\ne 1$. If ${}^{101}{C}_1{+}^{101}{C}_2\cdot S_1+\dots {+}^{101}{C}_{101}\cdot S_{100}=\alpha T_{100}$ …

Q11.Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^2\sin \theta -x(\sin \theta \cos \theta +1)+\cos \theta =0$ $(0<\theta <45^0)$, and $\alpha <\beta$. Then ${\sum }_{n=0}^{\infty }\left({\alpha }^n+\frac{(-1{)}^n}{{\beta }^n}\right)$ is equal to:

Q12.A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If $X$ be the number of white balls drawn, then $\left(\frac{\text{mean of }X}{\text{standard deviation of }X}\right)$ is equal to:

Q13.Let z be a complex number such that $|z|+z=3+i$ (where $i=\sqrt{-1}$). Then $|z|$ is equal to:

Q14.If $\left|\begin{array}{ccc}a-b-c& 2a& 2a\\ 2b& b-c-a& 2b\\ 2c& 2c& c-a-b\end{array}\right|=(a+b+c)(x+a+b+c{)}^2$, $x\ne 0$ and $a+b+c\ne 0$, then x is equal to:

Q15.Let $\sqrt{3}\hat{i}+\hat{j}$, $\hat{i}+\sqrt{3}\hat{j}$ and $\beta \hat{i}+(1-\beta )\hat{j}$ respectively be the position vectors of the points $A$, $B$ and $C$ with respect to the origin $O$. If the distance of $C$ from the bisector of the acute angle between OA …

Q16.If $19^{\text{th}}$ term of a non-zero A.P. is zero, then its $(49^{\text{th}}\text{ term}):(29^{\text{th}}\text{ term})$ is:

Q17.If $\int \frac{x+1}{\sqrt{2x-1}}dx=f(x)\sqrt{2x-1}+C$, where $C$ is a constant of integration, then $f(x)$ is equal to:

Q18.Let a function $f:(0,\infty )\to (0,\infty )$ be defined by $f(x)=\left|1-\frac{1}{x}\right|$. Then $f$ is:

Q19.Let K be the set of all real values of x where the function $f(x)=\sin |x|-|x|+2(x-\pi )\cos |x|$ is not differentiable. Then the set $K$ is equal to:

Q20.The area (in sq. units) in the first quadrant bounded by the parabola $y=x^2+1$, the tangent to it at the point $(2,5)$ and the coordinate axes is:

Q21.Given $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$ for a $△ABC$ with usual notation. If $\frac{\cos A}{\alpha }=\frac{\cos B}{\beta }=\frac{\cos C}{\gamma }$, then the ordered triad $(\alpha ,\beta ,\gamma )$ has a value:

Q22.The solution of the differential equation $\frac{dy}{dx}=(x-y{)}^2$ when $y(1)=1$, is:

Q23.Let the length of the latus rectum of an ellipse with its major axis along x-axis and center at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

Q24.Let $S=\{1,2,\dots ,20\}$. A subset $B$ of $S$ is said to be "nice", if the sum of the elements of $B$ is 203. Then the probability that a randomly chosen subset of $S$ is 'nice' is:

Q25.If the point $(2,\alpha ,\beta )$ lies on the plane which passes through the points $(3,4,2)$ and $(7,0,6)$ and is perpendicular to the plane $2x-5y=15$, then $2\alpha -3\beta$ is equal to:

Q26.Let $(x+10{)}^{50}+(x-10{)}^{50}=a_0+a_{1}x+a_2{x}^2+\dots +a_{50}{x}^{50}$, for $x\in R$; then $\frac{a_2}{a_0}$ is equal to:

Q27.The number of functions from $\{1,2,3,\dots ,20\}$ onto $\{1,2,3,\dots ,20\}$ such that $f(k)$ is a multiple of 3, whenever k is a multiple of 4, is:

Q28.A circle cuts a chord of length 4a on the $x$-axis and passes through a point on the $y$-axis, distant 2b from the origin. Then the locus of the center of this circle, is:

Q29.Let $f(x)=\frac{x}{\sqrt{a^2+x^2}}-\frac{d-x}{\sqrt{b^2+(d-x{)}^2}}$, $x\in R$, where $a,b$ and $d$ are non-zero real constants. Then:

Q30.Let $A$ and $B$ be two invertible matrices of order $3\times 3$. If $\det \left(AB{A}^{\top }\right)=8$ and $\det \left(A{B}^{-1}\right)=8$, then $\det \left(B{A}^{-1}{B}^{\top }\right)$ is equal to: