JEE Main 8 April 2024 Shift 1 Question Paper

Question 1

The value of $k\in\mathbb{N}$ for which the integral $I_n=\displaystyle\int_0^1(1-x^k)^n\,dx$, $n\in\mathbb{N}$, satisfies $147\,I_{20}=148\,I_{21}$ is:

Accepted Answer

(D) $7$

Answer

(A) $10$

Answer

(B) $8$

Answer

(C) $14$

Question 2

The sum of all the solutions of the equation $(8)^{2x}-16\cdot(8)^x+48=0$ is:

Accepted Answer

(C) $1+\log_8(6)$

Answer

(A) $1+\log_6(8)$

Answer

(B) $\log_8(6)$

Answer

(D) $\log_8(4)$

Question 3

Let the circles $C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2:(x-8)^2+\left(y-\dfrac{15}{2}\right)^2=r_2^2$ touch each other externally at the point $(6,6)$. If the point $(6,6)$ divides the line segment joining the centres of the circles $C_1$ and $C_2$ internally in the ratio $2:1$, then $(\alpha+\beta)+4(r_1^2+r_2^2)$ equals:

Accepted Answer

(B) $130$

Answer

(A) $110$

Answer

(C) $125$

Answer

(D) $145$

Question 4

Let $P(x,y,z)$ be a point in the first octant, whose projection in the xy-plane is the point $Q$. Let $OP=\gamma$; the angle between $OQ$ and the positive x-axis be $	heta$; and the angle between $OP$ and the positive z-axis be $\phi$, where $O$ is the origin. Then the distance of $P$ from the x-axis is:

Accepted Answer

(A) $\gamma\sqrt{1-\sin^2\phi\cos^2	heta}$

Answer

(B) $\gamma\sqrt{1+\cos^2	heta\sin^2\phi}$

Answer

(C) $\gamma\sqrt{1-\sin^2	heta\cos^2\phi}$

Answer

(D) $\gamma\sqrt{1+\cos^2\phi\sin^2	heta}$

Question 5

The number of critical points of the function $f(x)=(x-2)^{2/3}(2x+1)$ is:

Accepted Answer

(A) $2$

Answer

(B) $0$

Answer

(C) $1$

Answer

(D) $3$

Question 6

Let $f(x)$ be a positive function such that the area bounded by $y=f(x)$, $y=0$ from $x=0$ to $x=a>0$ is $e^{-a}+4a^2+a-1$. Then the differential equation, whose general solution is $y=c_1 f(x)+c_2$, where $c_1$ and $c_2$ are arbitrary constants, is:

Accepted Answer

(C) $(8e^x+1)\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}=0$

Answer

(A) $(8e^x-1)\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}=0$

Answer

(B) $(8e^x-1)\dfrac{d^2y}{dx^2}-\dfrac{dy}{dx}=0$

Answer

(D) $(8e^x+1)\dfrac{d^2y}{dx^2}-\dfrac{dy}{dx}=0$

Question 7

Let $f(x)=4\cos^3 x+3\sqrt3\cos^2 x-10$. The number of points of local maxima of $f$ in interval $(0,2\pi)$ is:

Accepted Answer

(B) $2$

Answer

(A) $1$

Answer

(C) $3$

Answer

(D) $4$

Question 8

Let $A=\begin{bmatrix}2 & a & 0\ 1 & 3 & 1\ 0 & 5 & b\end{bmatrix}$. If $A^3=4A^2-A-21I$, where $I$ is the identity matrix of order $3	imes3$, then $2a+3b$ is equal to:

Accepted Answer

(B) $-13$

Answer

(A) $-10$

Answer

(C) $-9$

Answer

(D) $-12$

Question 9

If the shortest distance between the lines $L_1:\vec r=(2+\lambda)\hat i+(1-3\lambda)\hat j+(3+4\lambda)\hat k$, $\lambda\in\mathbb{R}$ and $L_2:\vec r=2(1+\mu)\hat i+3(1+\mu)\hat j+(5+\mu)\hat k$, $\mu\in\mathbb{R}$ is $\dfrac{m}{\sqrt n}$, where $\gcd(m,n)=1$, then the value of $m+n$ equals:

Accepted Answer

(B) $387$

Answer

(A) $384$

Answer

(C) $377$

Answer

(D) $390$

Question 10

Let the sum of two positive integers be $24$. If the probability, that their product is not less than $\dfrac34$ times their greatest possible product, is $\dfrac{m}{n}$, where $\gcd(m,n)=1$, then $n-m$ equals:

Accepted Answer

(D) $10$

Answer

(A) $9$

Answer

(B) $11$

Answer

(C) $8$

Question 11

If $\sin x=-\dfrac35$, where $\pi<x<\dfrac{3\pi}{2}$, then $80(	an^2 x-\cos x)$ is equal to:

Accepted Answer

(A) $109$

Answer

(B) $108$

Answer

(C) $18$

Answer

(D) $19$

Question 12

Let $I(x)=\displaystyle\int\dfrac{6}{\sin^2 x\cdot(1-\cot x)^2}\,dx$. If $I(0)=3$, then $I\left(\dfrac{\pi}{12}\right)$ is equal to:

Accepted Answer

(B) $3\sqrt3$

Answer

(A) $\sqrt3$

Answer

(C) $6\sqrt3$

Answer

(D) $2\sqrt3$

Question 13

The equations of two sides $AB$ and $AC$ of a triangle $ABC$ are $4x+y=14$ and $3x-2y=5$, respectively. The point $\left(2,-\dfrac43\right)$ divides the third side $BC$ internally in the ratio $2:1$. The equation of the side $BC$ is:

Accepted Answer

(C) $x+3y+2=0$

Answer

(A) $x-6y-10=0$

Answer

(B) $x-3y-6=0$

Answer

(D) $x+6y+6=0$

Question 14

Let $[t]$ be the greatest integer less than or equal to $t$. Let $A$ be the set of all prime factors of $2310$ and $f:A	o\mathbb{Z}$ be the function $f(x)=\left[\log_2\left(x^2+\left[\dfrac{x^3}{5}ight]ight)ight]$. The number of one-to-one functions from $A$ to the range of $f$ is:

Accepted Answer

(B) $120$

Answer

(A) $20$

Answer

(C) $25$

Answer

(D) $24$

Question 15

Let $z$ be a complex number such that $|z+2|=1$ and $\mathrm{Im}\left(\dfrac{z+1}{z+2}\right)=\dfrac15$. Then the value of $\left|\mathrm{Re}\left(\overline{z+2}\right)\right|$ is:

Accepted Answer

(D) $\dfrac{2\sqrt{6}}{5}$

Answer

(A) $\dfrac{\sqrt{6}}{5}$

Answer

(B) $\dfrac{1+\sqrt{6}}{5}$

Answer

(C) $\dfrac{24}{5}$

Question 16

If the set $R=\{(a,b):a+5b=42,\ a,b\in\mathbb{N}\}$ has $m$ elements and $\displaystyle\sum_{n=1}^{m}i^{n!}=x+iy$, where $i=\sqrt{-1}$, then the value of $m+x+y$ is:

Accepted Answer

(B) $12$

Answer

(A) $8$

Answer

(C) $4$

Answer

(D) $5$

Question 17

For the function $f(x)=\cos x-x+1$, $x\in\mathbb{R}$, between the following two statements: $(S_1)$ $f(x)=0$ for only one value of $x$ in $[0,\pi]$. $(S_2)$ $f(x)$ is decreasing in $\left[0,\dfrac\pi2\right]$ and increasing in $\left[\dfrac\pi2,\pi\right]$.

Accepted Answer

(B) Only $(S_1)$ is correct

Answer

(A) Both $(S_1)$ and $(S_2)$ are correct

Answer

(C) Both $(S_1)$ and $(S_2)$ are incorrect

Answer

(D) Only $(S_2)$ is correct

Question 18

The set of all $\alpha$, for which the vectors $\vec a=\alpha t\hat i+6\hat j-3\hat k$ and $\vec b=t\hat i-2\hat j-2\alpha t\hat k$ are inclined at an obtuse angle for all $t\in\mathbb{R}$ is:

Accepted Answer

(C) $\left(-\dfrac43,0\right]$

Answer

(A) $[0,1)$

Answer

(B) $(-2,0]$

Answer

(D) $\left(-\dfrac43,1\right]$

Question 19

Let $y=y(x)$ be the solution of the differential equation $(1+y^2)e^{	an x}\,dx+\cos^2 x(1+e^{2	an x})\,dy=0$, $y(0)=1$. Then $y\left(\dfrac\pi4ight)$ is equal to:

Accepted Answer

(C) $\dfrac1e$

Answer

(A) $\dfrac2e$

Answer

(B) $\dfrac{1}{e^2}$

Answer

(D) $\dfrac{2}{e^2}$

Question 20

Let $H:\dfrac{-x^2}{a^2}+\dfrac{y^2}{b^2}=1$ be the hyperbola, whose eccentricity is $\sqrt3$ and the length of the latus rectum is $4\sqrt3$. Suppose the point $(\alpha,6)$, $\alpha>0$ lies on $H$. If $\beta$ is the product of the focal distances of the point $(\alpha,6)$, then $\alpha^2+\beta$ is equal to:

Accepted Answer

(B) $171$

Answer

(A) $170$

Answer

(C) $169$

Answer

(D) $172$

Question 21

Let $A=\begin{bmatrix}2 & -1\ 1 & 1\end{bmatrix}$. If the sum of the diagonal elements of $A^{13}$ is $3^n$, then $n$ is equal to ___

Accepted Answer

7

Question 22

If the orthocentre of the triangle formed by the lines $2x+3y-1=0$, $x+2y-1=0$ and $ax+by-1=0$, is the centroid of another triangle, whose circumcentre and orthocentre respectively are $(3,4)$ and $(-6,-8)$, then the value of $|a-b|$ is ___

Accepted Answer

16

Question 23

Three balls are drawn at random from a bag containing $5$ blue and $4$ yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\bar X$ and $\bar Y$ are the means of $X$ and $Y$ respectively, then $7\bar X+4\bar Y$ is equal to ___

Accepted Answer

17

Question 24

The number of $3$-digit numbers, formed using the digits $2,3,4,5$ and $7$, when the repetition of digits is not allowed, and which are not divisible by $3$, is equal to ___

Accepted Answer

36

Question 25

Let the positive integers be written in the form: $1$ (row 1); $2,3$ (row 2); $4,5,6$ (row 3); $7,8,9,10$ (row 4); and so on. If the $k^{th}$ row contains exactly $k$ numbers for every natural number $k$, then the row in which the number $5310$ will be, is ___

Accepted Answer

103

Question 26

If the range of $f(	heta)=\dfrac{\sin^4	heta+3\cos^2	heta}{\sin^4	heta+\cos^2	heta}$, $	heta\in\mathbb{R}$ is $[\alpha,\beta]$, then the sum of the infinite G.P., whose first term is $64$ and the common ratio is $\dfrac\alpha\beta$, is equal to ___

Accepted Answer

96

Question 27

Let $\alpha=\displaystyle\sum_{r=0}^{n}(4r^2+2r+1)\,{}^nC_r$ and $\beta=\displaystyle\sum_{r=0}^{n}\dfrac{{}^nC_r}{r+1}$. If $140<\dfrac{2\alpha}{\beta}<281$, then the value of $n$ is ___

Accepted Answer

5

Question 28

Let $\vec a=9\hat i-13\hat j+25\hat k$, $\vec b=3\hat i+7\hat j-13\hat k$ and $\vec c=17\hat i-2\hat j+\hat k$ be three given vectors. If $\vec r$ is a vector such that $\vec r	imes\vec a=(\vec b+\vec c)	imes\vec a$ and $\vec r\cdot(\vec b-\vec c)=0$, then $\dfrac{\left|593\vec r+67\vec aight|^2}{(593)^2}$ is equal to ___

Accepted Answer

569

Question 29

Let the area of the region enclosed by the curve $y=\min\{\sin x,\cos x\}$ and the x-axis between $x=-\pi$ to $x=\pi$ be $A$. Then $A^2$ is equal to ___

Accepted Answer

16

Question 30

The value of $\displaystyle\lim_{x	o0}2\left(\dfrac{1-\sqrt{\cos 2x}\,\sqrt[3]{\cos 3x}\cdots\sqrt[10]{\cos 10x}}{x^2}ight)$ is ___

Accepted Answer

55

Question 31

Three bodies $A$, $B$ and $C$ have equal kinetic energies and their masses are $400\,g$, $1.2\,kg$ and $1.6\,kg$ respectively. The ratio of their linear momenta is:

Accepted Answer

(A) $1:\sqrt3:2$

Answer

(B) $1:\sqrt3:\sqrt2$

Answer

(C) $\sqrt2:\sqrt3:1$

Answer

(D) $\sqrt3:\sqrt2:1$

Question 32

Average force exerted on a non-reflecting surface at normal incidence is $2.4	imes10^{-4}$ N. If $360\,W/cm^2$ is the light energy flux during span of $1$ hour $30$ minutes. Then the area of the surface is:

Accepted Answer

(B) $0.02\,m^2$

Answer

(A) $0.2\,m^2$

Answer

(C) $20\,m^2$

Answer

(D) $0.1\,m^2$

Question 33

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume $h=6.63	imes10^{-34}$ J s, $m_e=9.0	imes10^{-31}$ kg and $m_p=1836$ times $m_e$)

Accepted Answer

(A) $1:1836$

Answer

(B) $1:\dfrac{1}{1836}$

Answer

(C) $1:\dfrac{1}{\sqrt{1836}}$

Answer

(D) $1:\sqrt{1836}$

Question 34

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature ($27^\circ C$). The ratio of specific heat of gases at constant volume respectively is:

Accepted Answer

(C) $\dfrac35$

Answer

(A) $\dfrac75$

Answer

(B) $\dfrac32$

Answer

(D) $\dfrac53$

Question 35

In an expression $a	imes10^b$:

Accepted Answer

(B) $b$ is order of magnitude for $a\le5$

Answer

(A) $a$ is order of magnitude for $b\le5$

Answer

(C) $b$ is order of magnitude for $5<a\le10$

Answer

(D) $b$ is order of magnitude for $a\ge5$

Question 36

In the given circuit, the terminal potential difference of the cell is:

Accepted Answer

(A) $2\,V$

Answer

(B) $4\,V$

Answer

(C) $1.5\,V$

Answer

(D) $3\,V$

Question 37

Binding energy of a certain nucleus is $18	imes10^8$ J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Accepted Answer

(B) $20\,\mu g$

Answer

(A) $0.02\,\mu g$

Answer

(C) $2\,\mu g$

Answer

(D) $10\,\mu g$

Question 38

Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

Accepted Answer

(D) A, C Only

Answer

(A) A, B, C, D

Answer

(B) B, D Only

Answer

(C) A, B, C Only

Question 39

A clock has $75\,cm$, $60\,cm$ long second hand and minute hand respectively. In $30$ minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi=3.14$):

Accepted Answer

(A) $139.4$

Answer

(B) $140.5$

Answer

(C) $220.0$

Answer

(D) $118.9$

Question 40

Young's modulus is determined by the equation $Y=49000\dfrac{m}{\ell}\dfrac{	ext{dyne}}{cm^2}$ where $M$ is the mass and $\ell$ is the extension of wire used in the experiment. Now error in Young modulus $(Y)$ is estimated by taking data from M-$\ell$ plot in graph paper. The smallest scale divisions are $5\,g$ and $0.02\,cm$ along load axis and extension axis respectively. If the value of $M$ and $\ell$ are $500\,g$ and $2\,cm$ respectively then percentage error of $Y$ is:

Accepted Answer

(C) $2\%$

Answer

(A) $0.2\%$

Answer

(B) $0.02\%$

Answer

(D) $0.5\%$

Question 41

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\dfrac{V_a}{V_d}$ and the ratio $\dfrac{V_b}{V_c}$ is:

Accepted Answer

(B) $\dfrac{V_a}{V_d}=\dfrac{V_b}{V_c}$

Answer

(A) $\dfrac{V_a}{V_d}=\left(\dfrac{V_b}{V_c}\right)^{\gamma-1}$

Answer

(C) $\dfrac{V_a}{V_d}=\left(\dfrac{V_b}{V_c}\right)^{1/2}$

Answer

(D) $\dfrac{V_a}{V_d}=\left(\dfrac{V_b}{V_c}\right)^2$

Question 42

Two planets $A$ and $B$ having masses $m_1$ and $m_2$ move around the sun in circular orbits of $r_1$ and $r_2$ radii respectively. If angular momentum of $A$ is $L$ and that of $B$ is $3L$, the ratio of time period $\left(\dfrac{T_A}{T_B}\right)$ is:

Accepted Answer

(C) $\dfrac{1}{27}\left(\dfrac{m_2}{m_1}\right)^3$

Answer

(A) $\left(\dfrac{r_1}{r_2}\right)^{3/2}$

Answer

(B) $\left(\dfrac{r_1}{r_2}\right)^2$

Answer

(D) $27\left(\dfrac{m_2}{m_1}\right)^3$

Question 43

A LCR circuit is at resonance for a capacitor $C$, inductance $L$ and resistance $R$. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

Accepted Answer

(B) double

Answer

(A) Zero

Answer

(C) same

Answer

(D) halved

Question 44

The output $Y$ of following circuit for given inputs is:

Accepted Answer

(C) $0$

Answer

(A) $A\cdot\overline{(A+B)}$

Answer

(B) $A\cdot B$

Answer

(D) $\bar A\cdot B$

Question 45

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Accepted Answer

(C) $\dfrac{a}{b}$

Answer

(A) $\sqrt{ab}$

Answer

(B) $ab$

Answer

(D) $\dfrac{b}{a}$

Question 46

Correct Bernoulli's equation is (symbols have their usual meaning):

Accepted Answer

(B) $P+\rho gh+\dfrac12\rho v^2=$ constant

Answer

(A) $P+mgh+\dfrac12 mv^2=$ constant

Answer

(C) $P+\rho gh+\rho v^2=$ constant

Answer

(D) $P+\dfrac12\rho gh+\dfrac12\rho v^2=$ constant

Question 47

A player caught a cricket ball of mass $150\,g$ moving at a speed of $20\,m/s$. If the catching process is completed in $0.1\,s$, the magnitude of force exerted by the ball on the hand of the player is:

Accepted Answer

(C) $30\,N$

Answer

(A) $150\,N$

Answer

(B) $3\,N$

Answer

(D) $300\,N$

Question 48

A stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $(K_B:K_A)$ is:

Accepted Answer

(A) $v_B:v_A$

Answer

(B) $m_B:m_A$

Answer

(C) $m_B v_B:m_A v_A$

Answer

(D) $1:1$

Question 49

Critical angle of incidence for a pair of optical media is $45^\circ$. The refractive indices of first and second media are in the ratio:

Accepted Answer

(A) $\sqrt2:1$

Answer

(B) $1:2$

Answer

(C) $1:\sqrt2$

Answer

(D) $2:1$

Question 50

The diameter of a sphere is measured using a vernier caliper whose $9$ divisions of main scale are equal to $10$ divisions of vernier scale. The shortest division on the main scale is equal to $1\,mm$. The main scale reading is $2\,cm$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is $8.635\,g$, the density of the sphere is:

Accepted Answer

(D) $2.0\,g/cm^3$

Answer

(A) $2.5\,g/cm^3$

Answer

(B) $1.7\,g/cm^3$

Answer

(C) $2.2\,g/cm^3$

Question 51

A uniform thin metal plate of mass $10\,kg$ with dimensions as shown. The ratio of $x$ and $y$ coordinates of center of mass of plate is $\dfrac{n}{9}$. The value of $n$ is ___

Accepted Answer

15

Question 52

An electron with kinetic energy $5\,eV$ enters a region of uniform magnetic field of $3\,\mu T$ perpendicular to its direction. An electric field is applied perpendicular to the direction of velocity and magnetic field. The value of $E$, so that electron moves along the same path, is ___ $NC^{-1}$. (Given, mass of electron $=9	imes10^{-31}$ kg, electric charge $=1.6	imes10^{-19}$ C)

Accepted Answer

4

Question 53

A square loop PQRS having $10$ turns, area $3.6	imes10^{-3}\,m^2$ and resistance $100\,\Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $B=0.5$ T as shown. Work done in pulling the loop out of the field in $1.0$ s is ___ $	imes10^{-6}$ J.

Accepted Answer

3

Question 54

Resistance of a wire at $0\,^\circ C$, $100\,^\circ C$ and $t\,^\circ C$ is found to be $10\,\Omega$, $10.2\,\Omega$ and $10.95\,\Omega$ respectively. The temperature $t$ in Kelvin scale is ___

Accepted Answer

748

Question 55

An electric field, $\vec E=\dfrac{2\hat i+6\hat j+8\hat k}{\sqrt6}$ passes through the surface of $4\,m^2$ area having unit vector $\hat n=\left(\dfrac{2\hat i+\hat j+\hat k}{\sqrt6}\right)$. The electric flux for that surface is ___ V m.

Accepted Answer

12

Question 56

A liquid column of height $0.04\,cm$ balances excess pressure of soap bubble of certain radius. If density of liquid is $8	imes10^3\,kg\,m^{-3}$ and surface tension of soap solution is $0.28\,Nm^{-1}$, then diameter of the soap bubble is ___ cm. (if $g=10\,ms^{-2}$)

Accepted Answer

7

Question 57

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\dfrac{a-1}{a}\right)$ then the value of $a$ is ___

Accepted Answer

16

Question 58

Three vectors $\overrightarrow{OP}$, $\overrightarrow{OQ}$ and $\overrightarrow{OR}$ each of magnitude $A$ are acting as shown in figure. The resultant of the three vectors is $A\sqrt x$. The value of $x$ is ___

Accepted Answer

3

Question 59

A parallel beam of monochromatic light of wavelength $600\,nm$ passes through single slit of $0.4\,mm$ width. Angular divergence corresponding to second order minima would be ___ $	imes10^{-3}$ rad.

Accepted Answer

6

Question 60

In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5	imes10^{-14}$ m. If target nucleus has atomic number $80$, then maximum velocity of $\alpha$-particle is ___ $	imes10^5$ m/s approximately. $\left(\dfrac{1}{4\pi\varepsilon_0}=9	imes10^9	ext{ SI unit, mass of }\alpha	ext{ particle}=6.72	imes10^{-27}	ext{ kg}ight)$

Accepted Answer

156

Question 61

Given below are two statements:
Statement I: IUPAC name of Compound A (shown) is 4-chloro-1,3-dinitrobenzene.
Statement II: IUPAC name of Compound B (shown) is 4-ethyl-2-methylaniline.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(B) Statement I is incorrect but Statement II is correct

Answer

(A) Both Statement I and Statement II are correct

Answer

(C) Statement I is correct but Statement II is incorrect

Answer

(D) Both Statement I and Statement II are incorrect

Question 62

Which among the following compounds will undergo fastest $S_N2$ reaction?

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 63

Combustion of glucose $(C_6H_{12}O_6)$ produces $CO_2$ and water. The amount of oxygen (in g) required for the complete combustion of $900\,g$ of glucose is: [Molar mass of glucose in $g\,mol^{-1}=180$]

Accepted Answer

(B) $960$

Answer

(A) $480$

Answer

(C) $800$

Answer

(D) $32$

Question 64

Identify the major products $A$ and $B$ respectively in the following set of reactions (shown).

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

List-I (Name of the test)	List-II (Reaction sequence)
A.Borax bead test	I. $MCO_3\to MO\xrightarrow{CO/\Delta}$ coloured residue with CoO
B.Charcoal cavity test	II. $MCO_3\to MCl_2\to M^{2+}$ (volatile chloride coloured flame)
C.Cobalt nitrate test	III. $MSO_4\xrightarrow{Na_2CO_3/\Delta}M(BO_2)_2$ (coloured borate bead)
D.Flame test	IV. $MSO_4\xrightarrow{Na_2CO_3/\Delta}MCO_3\to MO\to M$ (reduction to metal in cavity)

List-I (Molecule)	List-II (Shape)
A. $NH_3$	I.Square pyramidal
B. $BrF_5$	II.Tetrahedral
C. $PCl_5$	III.Trigonal pyramidal
D. $CH_4$	IV.Trigonal bipyramidal

List-I (Elements)	List-II (Property in their respective groups)
A.Cl, S	I.Elements with highest electronegativity
B.Ge, As	II.Elements with largest atomic size
C.Fr, Ra	III.Elements which show properties of both metals and non-metals
D.F, O	IV.Elements with highest negative electron gain enthalpy

List-I (Compound)	List-II (Colour)
A. $Fe_4[Fe(CN)_6]_3\cdot xH_2O$	I.Violet
B. $[Fe(CN)_5NOS]^{4-}$	II.Blood Red
C. $[Fe(SCN)]^{2+}$	III.Prussian Blue
D. $(NH_4)_3PO_4\cdot12MoO_3$	IV.Yellow

JEE Main 8 April 2024 Shift 1 Question Paper with Answers

Physics — JEE Main 8 April 2024 Shift 1

Chemistry — JEE Main 8 April 2024 Shift 1

Mathematics — JEE Main 8 April 2024 Shift 1

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