JEE Main 2021 · 26 Aug 2021 · Shift 2

Q1.A refrigerator consumes an average 35 W power to operate between temperature $-10^{\circ }\mathrm{C}$ to $25^{\circ }\mathrm{C}$. If there is no loss of energy then how much average heat per second does it transfer?

Q2.The angle between vector $(\vec{A})$ and $(\vec{A}-\vec{B})$ is:

Q3.Four NOR gates are connected as shown in figure. The truth table for the given figure is:

Q4.An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W.

Q5.If you are provided a set of resistances $2\Omega ,4\Omega ,6\Omega$ and $8\Omega$. Connect these resistances so as to obtain an equivalent resistance of $\frac{46}{3}\Omega$.

Q6.The de-Broglie wavelength of a particle having kinetic energy E is $\lambda$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to $75\%$ of the initial value?

Q7.Match List-I with List-II:

List - I
(a) Magnetic Induction
(b) Magnetic Flux
(c) Magnetic Permeability
(d) Magnetization

List - II
(i) ${\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{A}}^{-1}$
(ii) ${\mathrm{M}}^0{\mathrm{L}}^{-1}\mathrm{A}$
(iii) $M{T}^{-2}{A}^{-1}$
(iv) …

Q8.A cylindrical container of volume $4.0\times 10^{-3}{\mathrm{m}}^3$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K . The pressure of the mixture of gases is: [Take gas constant as …

Q9.In the given circuit the AC source has $\omega =100\mathrm{rad}{\mathrm{s}}^{-1}$. Considering the inductor and capacitor to be ideal, what will be the current I flowing through the circuit?

Q10.A particle of mass $m$ is suspended form a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r=\frac{L}{\sqrt{2}}$. The speed of particle will be:

Q11.At time $t=0$, a material is composed of two radioactive atoms $A$ and $B$, where $N_A(0)=2N_B(0)$. The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to B and B disintegrates to $C$. Which of the following figures represe …

Q12.The two thin coaxial rings, each of radius ' $a$ ' and having charges $+Q$ and $-Q$ respectively are separated by a distance of ' $s$ '. The potential difference between the centres of the two rings is:

Q13.A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a:

Q14.The solid cylinder of length 80 cm and mass M has a radius of 20 cm . Calculate the density of the material used if the moment of inertia of the cylinder about an axis $CD$ parallel to $AB$ as shown in figure is $2.7\mathrm{kg}{\mathrm{m}}^2$.

Q15.A light beam is described by $E=800\sin \omega \left(t-\frac{x}{c}\right)$. An electron is allowed to move normal to the propagation of light beam with a speed of $3\times 10^7{\mathrm{ms}}^{-1}$. What is the maximum magnetic force exerted on the electron?

Q16.If the length of the pendulum in pendulum clock increases by $0.1\%$, then the error in time per day is

Q17.Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi }\times 10^2{\mathrm{Nm}}^{-2}$. What is the minimum radius of the wire? (take $\mathrm{g}=10{\mathrm{ms}}^{-2}$ )

Q18.A transmitting antenna at top of a tower has a height of 50 m and the height of receiving antenna is 80 m. What is the range of communication for Line of Sight (LoS) mode? [use radius of earth = 6400 km]

Q19.A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ of same area $\mathrm{A}/2$ and thickness $\mathrm{d}/2$ are inserted in the space between the plates. The capac …

Q20.The temperature of equal masses of three different liquids $x,y$ and $z$ are $10^{\circ }\mathrm{C},20^{\circ }\mathrm{C}$ and $30^{\circ }\mathrm{C}$ respectively. The temperature of mixture when x is mixed with y is $16^{\circ }\mathrm{C}$ and that when y is mixed with z is …

Q21.The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _____ N. (take $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

Q22.A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids $P_1$ and $P_2$ are so placed in between the source of light and screen that the intensity of light on screen is $1/2$. $P_2$ should be rotated by an angle of _____ (deg …

Q23.If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolution made by proton in a cyclotron to achieve one sixth of the speed of light is _____.
[ …

Q24.The acceleration due to gravity is found upto an accuracy of $4\%$ on a planet. The energy supplied to a simple pendulum of known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of $3\%$, the accuracy to which E …

Q25.An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object. When the convex mirror is removed, a real and inverted image is formed a …

Q26.Two simple harmonic motions are represented by the equations $x_1=5\sin \left(2\pi t+\frac{\pi }{4}\right)$ and $x_2=5\sqrt{2}(\sin 2\pi t+\cos 2\pi t)$. The amplitude of second motion is _____ times the amplitude in first motion.

Q27.A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of $50\mathrm{rad}{\mathrm{s}}^{-1}$ in a uniform horizontal magnetic field of $3.0\times 10^{-2}\mathrm{T}$. The maximum emf induced in the coil will be _____ …

Q28.A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel …

Q29.Two waves are simultaneously passing through a string and their equations are: $y_1=A_1\sin k(x-vt),y_2=A_2\sin k\left(x-vt+x_0\right)$. Given amplitudes $A_1=12\mathrm{mm}$ and $A_2=5\mathrm{mm},x_0=$ 3.5 cm and wave number …

Q30.For the given circuit, the power across zener diode is ______ mW.

Q1.The Major Product in the above reaction is:

Q2.Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Barium carbonate is insoluble in water and is highly stable.
Reason (R): The thermal stability of the carbonates increases with increasing cationic size. Choos …

Q3.The interaction energy of London forces between two particles is proportional to $r^x$, where $r$ is the distance between the particles. The value of $x$ is:

Q4.Which one for the following phenols does not give colour when condensed with phthalic anhydride in presence of conc. ${\mathrm{H}}_2{\mathrm{SO}}_4$ ?

Q5.Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Sucrose is a disaccharide and a non-reducing sugar.
Reason (R): Sucrose involves glycosidic linkage between ${\mathrm{C}}_1$ of $\beta$-glucose and …

Q6.Arrange the following Cobalt complexes in the order of increasing Crystal Field Stabilization Energy (CFSE) value.
Complexes: …

Q7.Chlorodiazepoxide

The class of drug to which chlordiazepoxide with above structure belongs is:

Q8.Consider the given reaction, Identify ' $X$ ' and ' $Y$ '

Q9.Which one of the following compounds is not aromatic?

Q10.The number of stereoisomers possible for 1,2-dimethyl cyclopropane is

Q11.Consider the given reaction, the Product A is:

Q12.The number of non-ionisable hydrogen atoms present in the final product obtained from the hydrolysis of ${\mathrm{PCl}}_5$ is:

Q13.The sol given below with negatively charged colloidal particles is:

Q14.Indicate the complex / complex ion which did not show any geometrical isomerism:

Q15.Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Heavy water is used for the study of reaction mechanism.
Reason (R): The rate of reaction for the cleavage of $\mathrm{O}-\mathrm{H}$ bond is slower than that …

Q16.The bond order and magnetic behaviour of ${\mathrm{O}}_2^{-}$ ion are, respectively:

Q17.Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Photochemical smog causes cracking of rubber.
Reason (R): Presence of ozone, nitric oxide, acrolein, formaldehyde and peroxyacetyl nitrate in photochemical smo …

Q18.Chalcogen group elements are:

Q19.Given below are two statements:
Statement I: Sphalerite is a sulphide ore of zinc and copper glance is a sulphide ore of copper.
Statement II: It is possible to separate two sulphide ores by adjusting proportion of oil to water or by using 'depressants' in a froth flotation metho …

Q20.For water ${\Delta }_{\text{vap}}\mathrm{H}=41\mathrm{kJ}{\mathrm{mol}}^{-1}$ at 373 K and 1 bar pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water, the internal energy change during evaporation of water is $\_\_\_\_$ …

Q21.83 g of ethylene glycol dissolved in 625 g of water. The freezing point of the solution is $\_\_\_\_$ K. (Nearest integer).
[Use: Molal Freezing point depression constant of water $=1.86\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1}$
Freezing point of water $=273\mathrm{K}$
Atomi …

Q22.In the sulphur estimation, 0.471 g of an organic compound gave 1.44 g of barium sulphate. The percentage of sulphur in the compound is $\_\_\_\_$ %. (Nearest integer)
(Atomic mass of $\mathrm{Ba}=137\mathrm{u}$).

Q23.A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is $4.3\times 10^{14}\mathrm{Hz}$. The velocity of ejected electron is $\_\_\_\_$ $\times 10^5{\mathrm{ms}}^{-1}$.
(Nearest integer)
[Use: …

Q24.The equilibrium constant ${\mathrm{K}}_{\mathrm{c}}$ at 298 K for the reaction
A + B ⇌ C + D
is 100. Starting with an equimolar solution with concentrations of $\mathrm{A},\mathrm{B},\mathrm{C}$ and D all equal to 1 M, the equilibrium concentration of D is $\_\_\_\_$ …

Q25.The reaction rate for the reaction
${\left[{\mathrm{PtCl}}_4\right]}^{2-}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\left[\mathrm{Pt}\left({\mathrm{H}}_2\mathrm{O}\right){\mathrm{Cl}}_3\right]}^{-}+{\mathrm{Cl}}^{-}$
was measured as a function of concentrations of different specie …

Q26.For the galvanic cell,
$\mathrm{Zn}(\mathrm{s})+{\mathrm{Cu}}^{2+}(0.02\mathrm{M})\to {\mathrm{Zn}}^{2+}(0.04\mathrm{M})+\mathrm{Cu}(\mathrm{s})$,
${\mathrm{E}}_{\text{cell }}=$ $\_\_\_\_$ $\times 10^{-2}\mathrm{V}$.
(Nearest integer)
[Use: …

Q27.A chloro compound "A"
(i) forms aldehydes on ozonolysis followed by the hydrolysis.
(ii) when vaporized completely 1.53 g of A, gives 448 mL of vapour at STP.

The number of carbon atoms in a molecule of compound $A$ is $\_\_\_\_$.

Q28.The overall stability constant of the complex ion ${\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4\right]}^{2+}$ is $2.1\times 10^{13}$. The overall dissociation constant is $\mathrm{y}\times 10^{-14}$. Then y is $\_\_\_\_$. (Nearest integer)

Q29.100 mL of ${\mathrm{Na}}_3{\mathrm{PO}}_4$ solution contains 3.45 g of sodium. The molarity of the solution is $\_\_\_\_$ $\times 10^{-2}\mathrm{mol}{\mathrm{L}}^{-1}$. (Nearest integer)
[Atomic Masses - Na : …

Q30.Match List-I (Chemical Reaction) with List-II (Reagent used) :

Q1.Let P be the plane passing through the point $(1,2,3)$ and the line of intersection of the planes $\vec{r}\cdot (\hat{i}+\hat{j}+4\hat{k})=16$ and $\vec{r}\cdot (-\hat{i}+\hat{j}+\hat{k})=6$.
Then which of the following points does NOT lie on P ?

Q2.A fair die is tossed until six is obtained on it. Let $X$ be the number of required tosses, then the conditional probability $P(X\ge 5\mid X>2)$ is:

Q3.A 10 inches long pencil $AB$ with mid point $C$ and a small eraser $P$ are placed on the horizontal top of a table such that $\mathrm{PC}=\sqrt{5}$ inches and $\angle PCB={\tan }^{-1}(2)$.
The acute angle through which the pencil must be rotated about C so that the perpend …

Q4.Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations
$x+y+z=5$
$x+2y+3z=\mu$
$x+3y+\lambda z=1$
is constructed. If $\rho$ is the probability that the system has a unique solution $q$ is the probability that …

Q5.The locus of the mid points of the chords of the hyperbola $x^2-y^2=4$, which touch the parabola $y^2=8x$, is:

Q6.The local maximum value of the function $f(x)={\left(\frac{2}{x}\right)}^{x^2},x>0$, is:

Q7.Let $[t]$ denote the greatest integer less than or equal to $t$.
Let $\mathrm{f}(\mathrm{x})=\mathrm{x}-[\mathrm{x}]$, $\mathrm{g}(\mathrm{x})=1-\mathrm{x}+[\mathrm{x}]$, and $\mathrm{h}(\mathrm{x})=\min \{\mathrm{f}(\mathrm{x}),\mathrm{g}(\mathrm{x})\}$, …

Q8.The domain of the function ${\mathrm{cosec}}^{-1}\left(\frac{1+x}{x}\right)$ is:

Q9.If the value of the integral ${\int }_0^5\frac{x+[x]}{e^{x-[x]}}dx=\alpha e^{-1}+\beta$, where $\alpha ,\beta \in R$, $5\alpha +6\beta =0$, and $[x]$ denotes the greatest integer less than or equal to $x$; then the value of $(\alpha +\beta {)}^2$ is equal to

Q10.The value of $2\sin \left(\frac{\pi }{8}\right)\sin \left(\frac{2\pi }{8}\right)\sin \left(\frac{3\pi }{8}\right)\sin \left(\frac{5\pi }{8}\right)\sin \left(\frac{6\pi }{8}\right)\sin \left(\frac{7\pi }{8}\right)$ is :

Q11.Consider the two statements:
(S1): $(p\to q)\vee (\sim q\to p)$ is a tautology.
(S2): $(p\wedge \sim q)\wedge (\sim p\vee q)$ is a fallacy.
Then:

Q12.A circle $C$ touches the line $x=2y$ at the point $(2,1)$ and intersects the circle $C_1:x^2+y^2+2y-5=0$ at two points $P$ and $Q$ such that $PQ$ is a diameter of $C_1$. Then the diameter of $C$ is

Q13.Let $\mathrm{A}=\left(\begin{array}{lll}1& 0& 0\\ 0& 1& 1\\ 1& 0& 0\end{array}\right)$. Then ${\mathrm{A}}^{2025}-{\mathrm{A}}^{2020}$ is equal to:

Q14.The value of ${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\left(\frac{1+{\sin }^{2}x}{1+{\pi }^{\sin x}}\right)dx$ is:

Q15.If $(\sqrt{3}+i{)}^{100}=2^{99}(p+iq)$, then $p$ and $q$ are roots of the equation:

Q16.${\lim }_{x\to 2}\left({\sum }_{n=1}^9\frac{x}{n(n+1)x^2+2(2n+1)x+4}\right)$ is equal to:

Q17.A hall has a square floor of dimension $10\mathrm{m}\times 10\mathrm{m}$ (see the figure) and vertical walls. If the angle GPH between diagonals AG and BH is ${\cos }^{-1}\frac{1}{5}$, then the height of the hall (in meters) is:

Q18.The point $\mathrm{P}(-2\sqrt{6},\sqrt{3})$ lies on the hyperbola $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ having eccentricity $\frac{\sqrt{5}}{2}$. If the tangent and normal at P to the hyperbola intersect its conjugate axis at the point …

Q19.Let $y(x)$ be the solution of the differential equation $2x^{2}dy+\left(e^y-2x\right)dx=0,x>0$. If $y(e)=1$, then $y(1)$ is equal to:

Q20.If ${\sum }_{r=1}^{50}{\tan }^{-1}\frac{1}{2r^2}=p$, then the value of $\tan p$ is:

Q21.Let $\left(\genfrac{}{}{0ex}{}{n}{k}\right)$ denote ${}^n{C}_k$ and $\left[\begin{array}{c}n\\ k\end{array}\right]=\{\begin{array}{l}\left(\genfrac{}{}{0ex}{}{n}{k}\right)\text{, if }0\le k\le n\\ 0\text{, otherwise }\end{array}$ If …

Q22.Let $a$ and $b$ respectively be the points of local maximum and local minimum of the function $F(x)=2x^3-3x^2-12x$. If $A$ is the total area of the region bounded by $y=f(x)$, the $x$-axis and the lines $x=$ a and $\mathrm{x}=\mathrm{b}$, then 4 A is equal to ______.

Q23.Let $\lambda \ne 0$ be in R . If $\alpha$ and $\beta$ are the roots of the equation ${\mathrm{x}}^2-\mathrm{x}+2\lambda =0$, and $\alpha$ and $\gamma$ are the roots of the equation $3x^2-10x+27\lambda =0$, then $\frac{\beta \gamma }{\lambda }$ is equal to ______.

Q24.Let A be a $3\times 3$ real matrix. If $\det (2\mathrm{adj}(2\mathrm{Adj}(\mathrm{adj}(2\mathrm{A})))=2^{41}$, then the value of $\det \left({\mathrm{A}}^2\right)$ equals ______.

Q25.The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is ____.

Q26.If the projection of the vector $\hat{i}+2\hat{j}+\hat{k}$ on the sum of the two vectors $2\hat{i}+4\hat{j}-5\hat{k}$ and $-\lambda \hat{i}+2\hat{j}+3\hat{k}$ is 1, then $\lambda$ is equal to ____.

Q27.The least positive integer n such that $\frac{(2i{)}^n}{(1-i{)}^{n-2}}$, $i=\sqrt{-1}$, is a positive integer, is ____.

Q28.Let the mean and variance of four numbers 3, 7, $x$ and $y$ $(x>y)$ be 5 and 10 respectively. Then the mean of four numbers $3+2x$, $7+2y$, $x+y$ and $x-y$ is ____.

Q29.Let Q be the foot of the perpendicular from the point $P(7,-2,13)$ on the plane containing the lines $\frac{x+1}{6}=\frac{y-1}{7}=\frac{z-3}{8}$ and $\frac{x-1}{3}=\frac{y-2}{5}=\frac{z-3}{7}$. Then $(PQ{)}^2$ is equal to ____.

Q30.Let $a_1,a_2,\dots ,a_{10}$ be an AP with common difference -3 and $b_1,b_2,\dots ,b_{10}$ be a GP with common ratio 2. Let $c_k=a_k+b_k$, $k=1,2,\dots ,10$. If $c_2=12$ and $c_3=13$, then ${\sum }_{k=1}^{10}{c}_k$ is equal to ____.