JEE Main 2023 · 08 Apr 2023 · Shift 1

Q1.A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

Q2.Two projectiles A and B are thrown with initial velocities of $40\mathrm{m}/\mathrm{s}$ and $60\mathrm{m}/\mathrm{s}$ at angles $30^{\circ }$ and $60^{\circ }$ with the horizontal respectively. The ratio of their ranges respectively is …

Q3.Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

Q4.A TV transmitting antenna is 98 m high and the receiving antenna is at the ground level. If the radius of the earth is 6400 km, the surface area covered by the transmitting antenna is approximately:

Q5.In a reflecting telescope, a secondary mirror is used to:

Q6.Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer fr …

Q7.The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:

Q8.An aluminium rod with Young's modulus $Y=7.0\times 10^{10}\mathrm{N}/{\mathrm{m}}^2$ undergoes elastic strain of $0.04\%$. The energy per unit volume stored in the rod in SI unit is:

Q9.At any instant the velocity of a particle of mass 500 g is $\left(2t\hat{\mathrm{i}}+3{\mathrm{t}}^2\hat{\mathrm{j}}\right){\mathrm{ms}}^{-1}$. If the force acting on the particle at $\mathrm{t}=1\mathrm{s}$ is …

Q10.For the logic circuit shown, the output waveform at Y is:

Q11.For a nucleus ${}_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}$ having mass number A and atomic number Z

A. The surface energy per nucleon $\left(b_s\right)=a_1{A}^{2/3}$

B. The Coulomb contribution to the binding energy …

Q12.Given below are two statements:

Statement I:

If E be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$.

Statement II:

The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total e …

Q13.Dimension of $\frac{1}{{\mu }_0{ϵ}_0}$ should be equal to

Q14.In this figure the resistance of the coil of galvanometer G is $2\Omega$. The emf of the cell is 4 V. The ratio of potential difference across ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is:

Q15.Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$, with distance $r$ from the centre $O$ is represented by:

Q16.Two forces having magnitude A and $\frac{\mathrm{A}}{2}$ are perpendicular to each other. The magnitude of their resultant is

Q17.The engine of a train moving with speed $10{\mathrm{ms}}^{-1}$ towards a platform sounds a whistle at frequency 400 Hz. The frequency heard by a passenger inside the train is (neglect air speed. Speed of sound in air $330{\mathrm{ms}}^{-1}$)

Q18.An air bubble of volume $1{\mathrm{cm}}^3$ rises from the bottom of a lake 40 m deep to the surface at a temperature of $12^{\circ }\mathrm{C}$. The atmospheric pressure is $1\times 10^5\mathrm{Pa}$, the density of water is $1000\mathrm{kg}/{\mathrm{m}}^3$ and …

Q19.A cylindrical wire of mass $(0.4\pm 0.01)\mathrm{g}$ has length $(8\pm 0.04)\mathrm{cm}$ and radius $(6\pm 0.03)\mathrm{mm}$. The maximum error in its density will be

Q20.Proton (P) and electron (e) will have same deBroglie wavelength when the ratio of their momentum is (assume, ${\mathrm{m}}_{\mathrm{p}}=1849{\mathrm{m}}_{\mathrm{e}}$)

Q21.An electric dipole of dipole moment is $6.0\times 10^{-6}\mathrm{Cm}$ placed in a uniform electric field of $1.5\times 10^3{\mathrm{NC}}^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180^{\circ }$ in this field will …

Q22.Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is ____ cm

Q23.The momentum of a body is increased by $50\%$. The percentage increase in the kinetic energy of the body is ____ %

Q24.The moment of inertia of semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $\frac{1}{\mathrm{x}}{\mathrm{MR}}^2$, where R is the radius and M is the mass of semicircular ring. The value of x will be

Q25.An organ pipe 40 cm long is open at both ends. The speed of sound in air is $360{\mathrm{ms}}^{-1}$. The frequency of the second harmonic is $\_\_\_\_$ Hz.

Q26.An air bubble of diameter 6 mm rises steadily through a solution of density $1750\mathrm{kg}/{\mathrm{m}}^3$ at the rate of $0.35\mathrm{cm}/\mathrm{s}$. The co-efficient of viscosity of the solution (neglect density of air) is $\_\_\_\_$ Pas (given, …

Q27.An oscillating LC circuit consists of a 75 mH inductor and a $1.2\mu \mathrm{F}$ capacitor. If the maximum charge to the capacitor is $2.7\mu \mathrm{C}$. The maximum current in the circuit will be $\_\_\_\_$ mA.

Q28.The magnetic intensity at the centre of a long current carrying solenoid is found to be $1.6\times 10^3{\mathrm{Am}}^{-1}$. If the number of turns is 8 per cm, then the current flowing through the solenoid is $\_\_\_\_$ A.

Q29.A current of 2 A flows through a wire of cross-sectional area $25.0{\mathrm{mm}}^2$. The number of free electrons in a cubic meter are $2.0\times 10^{28}$. The drift velocity of the electrons is $\_\_\_\_$ $\times 10^{-6}{\mathrm{ms}}^{-1}$ (given, charge on electron …

Q30.A nucleus with mass number 242 and binding energy per nucleon as 7.6 MeV breaks into fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is $\_\_\_\_$ MeV

Q1.$2{\mathrm{IO}}_3^{-}+{\mathrm{xI}}^{-}+12{\mathrm{H}}^{+}\to 6{\mathrm{I}}_2+6{\mathrm{H}}_2\mathrm{O}$

What is the value of x ?

Q2.Which of the following metals can be extracted through alkali leaching technique?

Q3.Which of the following represent the Freundlich adsorption isotherms?
(A)
(B)
(C)
(D)

Choose the correct answer from the options given below:

Q4.Choose the halogen which is most reactive towards ${\mathrm{S}}_{\mathrm{N}}1$ reaction in the given compounds (A, B, C & D)
A.
B.
C.
D.

Q5.Sulphur (S) containing amino acids from the following are:
(a) isoleucine
(b) cysteine
(c) lysine
(d) methionine
(e) glutamic acid

Q6.The water gas on reacting with cobalt as a catalyst forms

Q7.The major product formed in the following reaction is:

(i) $\underset{\text{ EtOH }}{\overset{{\mathrm{LiBH}}_4}{\to }}$ major product
(ii) ${\mathrm{H}}_3{\mathrm{O}}^{+}$

Q8.Which of the following complex is octahedral, diamagnetic and the most stable?

Q9.The reaction
$\frac{1}{2}{\mathrm{H}}_2(\mathrm{g})+\mathrm{AgCl}(\mathrm{s})\rightleftharpoons {\mathrm{H}}^{+}(\mathrm{aq})+{\mathrm{Cl}}^{-}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s})$
occurs in which of the given galvanic cell.

Q10.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Butan -1- ol has higher boiling point than ethoxyethane.
Reason R: Extensive hydrogen bonding leads to stronger association of molecules.
In the light of the above s …

Q11.In chromyl chloride, the number of d-electrons present on chromium is same as in (Given at no. of Ti: 22, V: 23, Cr: 24, Mn: 25, Fe: 26)

Q12.What is the purpose of adding gypsum to cement?

Q13.The correct order of spin only magnetic moments for the following complex ions is

Q14.Which halogen is known to cause the reaction given below:

Q15.The correct order of electronegativity for given elements is:

Q16.Match List I with List II:
Benzenediazonium chloride is reacted with reagents in List I to form products in List II.

Q17.Given below are two statements:
Statement I: Lithium and Magnesium do not form superoxide
Statement II: The ionic radius of ${\mathrm{Li}}^{+}$ is larger than ionic radius of ${\mathrm{Mg}}^{2+}$
In the light of the above statements, choose the most appropriate answer from the option …

Q18.Molar mass of the hydrocarbon (X) which on ozonolysis consumes one mole of ${\mathrm{O}}_3$ per mole of (X) and gives one mole each of ethanal and propanone is ______ ${\mathrm{g}\mathrm{mol}}^{-1}$ (Molar mass of C: $12{\mathrm{g}\mathrm{mol}}^{-1}$, H: $1{\mathrm{g}\mathrm{mol}}^{-1}$)

Q19.The number of following factors which affect the percent covalent character of the ionic bond is ______
(a) Polarising power of cation
(b) Extent of distortion of anion
(c) Polarisability of the anion
(d) Polarising power of anion

Q20.When a 60 W electric heater is immersed in a gas for 100s in a constant volume container with adiabatic walls, the temperature of the gas rises by $5^{\circ }\mathrm{C}$. The heat capacity of the given gas is ______ J K${}^{-1}$ (Nearest integer)

Q21.The number of given statement/s which is/are correct is ______
(A) The stronger the temperature dependence of the rate constant, the higher is the activation energy.
(B) If a reaction has zero activation energy, its rate is independent of temperature.
(C) The stronger the tempera …

Q22.The vapour pressure vs. temperature curve for a solution solvent system is shown below.

The boiling point of the solvent is ______ °C

Q23.$\mathrm{XeF}{}_4$ reacts with $\mathrm{SbF}{}_5$ to form $[\mathrm{XeF}{}_m{]}^{n+}[\mathrm{SbF}{}_y{]}^{z-}$

$m+n+y+z=$ ______

Q24.0.5 g of an organic compound (X) with 60% carbon will produce ______ $\times 10^{-1}$ g of $\mathrm{CO}{}_2$ on complete combustion.

Q25.The titration curve of weak acid vs. strong base (with phenolphthalein as indicator) is shown below. The $K_{\text{phenolphthalein}}=4\times 10^{-10}$. Given: $\log 2=0.3$

The number of following statements which is/are correct about phenolphthalein is ______
(A) It can be …

Q26.Three bulbs are filled with $\mathrm{CH}{}_4$, $\mathrm{CO}{}_2$ and Ne as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout, the pressure of the system is found to be ______ atm. (Nearest i …

Q27.The number of following statement/s which is/are incorrect is ______
(A) Line emission spectra are used to study the electronic structure
(B) The emission spectra of atoms in the gas phase show a continuous spread of wavelength from red to violet
(C) An absorption spectrum is lik …

Q1.Let $\mathrm{I}(\mathrm{x})=\int \frac{(\mathrm{x}+1)}{\mathrm{x}{\left(1+{\mathrm{xe}}^{\mathrm{x}}\right)}^2}\mathrm{dx},\mathrm{x}>0$,

If ${\lim }_{\mathrm{x}\to \infty }\mathrm{I}(\mathrm{x})=0$, then $\mathrm{I}(1)$ is equal to

Q2.If the equation of the plane containing the line $x+2y+3z-4=0=2x+y-z+5$ and perpendicular to the plane $\vec{r}=(\hat{i}-\hat{j})+\lambda (\hat{i}+\hat{j}+\hat{k})+\mu (\hat{i}-2\hat{j}+3\hat{k})$ is $\mathrm{ax}+\mathrm{by}+\mathrm{cz}=4$, then …

Q3.Let R be the focus of the parabola ${\mathrm{y}}^2=20\mathrm{x}$ and the line $\mathrm{y}=\mathrm{mx}+\mathrm{c}$ intersect the parabola at two points P and Q. Let the point $\mathrm{G}(10,10)$ be the centroid of the triangle PQR. If $\mathrm{c}-\mathrm{m}=6$, then …

Q4.Let $C(\alpha ,\beta )$ be the circumcenter of the triangle formed by the lines
$4x+3y=69$
$4y-3x=17$ and
$x+7y=61$

Then $(\alpha -\beta {)}^2+\alpha +\beta$ is equal to

Q5.Let $\mathrm{P}=\left[\begin{array}{cc}\frac{\sqrt{3}}{2}& \frac{1}{2}\\ -\frac{1}{2}& \frac{\sqrt{3}}{2}\end{array}\right],\mathrm{A}=\left[\begin{array}{ll}1& 1\\ 0& 1\end{array}\right]$ and $\mathrm{Q}={\mathrm{PAP}}^{\mathrm{T}}$. If …

Q6.Let $\alpha ,\beta ,\gamma$ be the three roots of the equation ${\mathrm{x}}^3+\mathrm{bx}+\mathrm{c}=0$. If $\beta \gamma =1=-\alpha$, then $b^3+2c^3-3{\alpha }^3-6{\beta }^3-8{\gamma }^3$ is equal to

Q7.The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is

Q8.In a bolt factory, machines A, B and C manufacture respectively $20\%$, $30\%$ and $50\%$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found the defective, then the probab …

Q9.The number of arrangements of the letter of the word "INDEPENDENCE" in which all the vowels always occur together is

Q10.Let $f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x},x\in [0,\pi ]-\left\{\frac{\pi }{4}\right\}$. Then $\mathrm{f}\left(\frac{7\pi }{12}\right){\mathrm{f}}^{\prime \prime }\left(\frac{7\pi }{12}\right)$ is equal to

Q11.If the points with vectors $\alpha \hat{\mathrm{i}}+10\hat{\mathrm{j}}+13\hat{\mathrm{k}}$, $6\hat{i}+11\hat{j}+11\hat{k}$, $\frac{9}{2}\hat{i}+\beta \hat{j}-8\hat{k}$ are collinear, then $(19\alpha -6\beta {)}^2$ is equal to

Q12.If the coefficients of the three consecutive terms in the expansion of $(1+x{)}^n$ are in the ratio $1:5:20$, then the coefficient of the fourth term is

Q13.Let ${\mathrm{S}}_{\mathrm{k}}=\frac{1+2+\dots ..+\mathrm{K}}{\mathrm{K}}$ and
${\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{S}}_{\mathrm{j}}^2=\frac{\mathrm{n}}{\mathrm{A}}\left({\mathrm{Bn}}^2+\mathrm{Cn}+\mathrm{D}\right)$, where …

Q14.Let $\mathrm{A}=\left[\begin{array}{ccc}2& 1& 0\\ 1& 2& -1\\ 0& -1& 2\end{array}\right]$. If $|\mathrm{adj}(\mathrm{adj}(\mathrm{adj}2\mathrm{A}))|=(16{)}^{\mathrm{n}}$, then n is equal to

Q15.Negation of $(p\Rightarrow q)\Rightarrow (q\Rightarrow p)$ is

Q16.The shortest distance between the lines $\frac{x-4}{4}=\frac{y+2}{5}=\frac{z+3}{3}$ and $\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{2}$ is

Q17.The area of the region $\left\{(\mathrm{x},\mathrm{y}):{\mathrm{x}}^2\le \mathrm{y}\le 8-{\mathrm{x}}^2,\mathrm{y}\le 7\right\}$ is

Q18.Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of $\mathrm{A}\times \mathrm{B}$ each having at least 3 and at most 6 element is :

Q19.${\lim }_{x\to 0}\left(\left(\frac{1-{\cos }^2(3x)}{{\cos }^3(4x)}\right)\left(\frac{{\sin }^3(4x)}{{\left({\log }_e(2x+1)\right)}^5}\right)\right)$ is equal to

Q20.If for $\mathrm{z}=\alpha +\mathrm{i}\beta ,|\mathrm{z}+2|=\mathrm{z}+4(1+\mathrm{i})$, then $\alpha +\beta$ and $\alpha \beta$ are the roots of the equation

Q21.Let $[\mathrm{t}]$ denotes the greatest integer $\le \mathrm{t}$. Then $\frac{2}{\pi }{\int }_{\pi /6}^{5\pi /6}(8[\mathrm{cosec}x]-5[\cot x])dx$ is equal to

Q22.Let $[\mathrm{t}]$ denotes the greatest integer $\le \mathrm{t}$. If the constant term in the expansion of ${\left(3x^2-\frac{1}{2x^5}\right)}^7$ is $\alpha$, then $[\alpha ]$ is equal to

Q23.Let $\vec{a}=6\hat{i}+9\hat{j}+12\hat{k},\vec{b}=\alpha \hat{i}+11\hat{j}-2\hat{k}$ and $\vec{c}$ be vectors such that $\vec{a}\times \vec{c}=\vec{a}\times \vec{b}$. If $\vec{a}\cdot \vec{c}=-12$, …

Q24.The largest natural number $n$ such that $3^n$ divides 66! is ______.

Q25.If $a_n$ is the greatest term in the sequence $a_n=\frac{n^3}{n^4+147},n=1,2,3\dots$, then $n$ is equal to ______.

Q26.Let $A=\{0,3,4,6,7,8,9,10\}$ and $R$ be the relation defined on $A$ such that $R=\{(x,y)\in A\times A:x-y$ is odd positive integer or $x-y=2\}$. The minimum number of elements that must be added to the relation $R$, so that it is a symmetric relation, is equal to …

Q27.Consider a circle $C_1:x^2+y^2-4x-2y=\alpha -5$.

Let its mirror image in the line $y=2x+1$ be another circle $C_2:5x^2+5y^2-10fx-10gy+36=0$. Let $r$ be the radius of $C_2$. Then $\alpha +r$ is equal to ______.

Q28.If the solution curve of the differential equation $(y-2{\log }_{e}x)dx+(x{\log }_e{x}^2)dy=0,x>1$ passes through the points $\left(e,\frac{4}{3}\right)$ and $(e^4,\alpha )$, then $\alpha$ is equal to ______.

Q29.Let ${\lambda }_1,{\lambda }_2$ be the values of $\lambda$ for which the points $\left(\frac{5}{2},1,\lambda \right)$ and $(-2,0,1)$ are at equal distance from the plane $2x+3y-6z+7=0$. If ${\lambda }_1>{\lambda }_2$, then the distance of the point …

Q30.Let the mean and variance of 8 numbers $x,y,10,12,6,12,4,8$ be 9 and 9.25 respectively. If $x>y$, then $3x-2y$ is equal to ______.