JEE Main 2023 25th January Morning Shift Question Paper Question Paper with Solutions | JEE Main Mock Test | JeeMate

Q 1PhysicsSection A • MCQelectronic devices

+4 / -1

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : Photodiodes are used in forward bias usually for measuring the light intensity.

Reason R : For a p-n junction diode, at applied voltage V the current in the forward bias is more than the current in the reverse bias for $\mathrm{|{V_z}| > \pm v \ge |{v_0}|}$ where $\mathrm{v_0}$ is the threshold voltage and $\mathrm{V_z}$ is the breakdown voltage.

In the light of the above statements, choose the correct answer from the options given below

A

Both A and R are true but R is NOT the correct explanation of A

B

A is true but R is false

C

Both A and R are true and R is the correct explanation of A

D

A is false but R is true

Q 2PhysicsSection A • MCQheat and thermodynamics

+4 / -1

The root mean square velocity of molecules of gas is

A

Proportional to temperature (

T

)

B

Inversely proportional to square root of temperature

\left( {\sqrt {{1 \over T}} } \right)

C

Proportional to square of temperature (

T^2

)

D

Proportional to square root of temperature (

\sqrt T

)

Q 3PhysicsSection A • MCQcapacitor

+4 / -1

A parallel plate capacitor has plate area 40 cm $^2$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is :

A

\mathrm{10\varepsilon_0~F}

B

\mathrm{24\varepsilon_0~F}

C

\mathrm{\frac{3}{10}\varepsilon_0~F}

D

\mathrm{\frac{10}{3}\varepsilon_0~F}

Q 4PhysicsSection A • MCQproperties of matter

+4 / -1

Match List I with List II

	List I		List II
A.	Surface tension	I.	$\mathrm{kg~m^{-1}~s^{-1}}$
B.	Pressure	II.	$\mathrm{kg~ms^{-1}}$
C.	Viscosity	III.	$\mathrm{kg~m^{-1}~s^{-2}}$
D.	Impulse	IV.	$\mathrm{kg~s^{-2}}$

Choose the correct answer from the options given below :

A

A-IV, B-III, C-I, D-II

B

A-IV, B-III, C-II, D-I

C

A-I, B-I, C-III, D-IV

D

A-III, B-IV, C-I, D-II

Q 5PhysicsSection A • MCQmagnetics

+4 / -1

Match List I with List II

		List II (Magnitude of Magnetic Field at point O)
A.	I.	${B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 2]$
B.	II.	${B_0} = {{{\mu _0}} \over {4 }}{I \over r}$
C.	III.	${B_0} = {{{\mu _0}I} \over {2\pi r}}[\pi - 1]$
D.	IV.	${B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 1]$

Choose the correct answer from the options given below :

A

A-III, B-IV, C-I, D-II

B

A-II, B-I, C-IV, D-III

C

A-III, B-I, C-IV, D-II

D

A-I, B-III, C-IV, D-II

Q 6PhysicsSection B • Numericalwork power and energy

+4 / -1

An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta=\mathrm{k}x$ , where k is a constant and $x$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $E = {n \over k}\sin \theta$ . The value of n is ___________.

qImage-energy-work-power-and-energy-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 7PhysicsSection A • MCQcurrent electricity

+4 / -1

A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 $\times$ 10 $^{-3}$ kg, density is 8.92 $\times$ 10 $^{3}$ kg/m $^3$ and resistivity is 1.7 $\times$ 10 $^{-8}~\Omega$ - $\mathrm{m}$ . The length of wire is :

A

l=100

m

B

l=6.8

m

C

l=5

m

D

l=10

m

Q 8PhysicsSection A • MCQheat and thermodynamics

+4 / -1

A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :

A

300 K

B

1000 K

C

900 K

D

360 K

Q 9PhysicsSection B • Numericalatoms and nuclei

+4 / -1

The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will $\frac{20}{x}\lambda_0$ . The value of $x$ is _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 10PhysicsSection A • MCQcommunication systems

+4 / -1

A message signal of frequency 5 kHz is used to modulate a carrier signal of frequency 2 MHz. The bandwidth for amplitude modulation is :

A

10 kHz

B

2.5 kHz

C

20 kHz

D

5 kHz

Q 11PhysicsSection A • MCQatoms and nuclei

+4 / -1

The ratio of the density of oxygen nucleus ( $_8^{16}O$ ) and helium nucleus ( $_2^{4}\mathrm{He}$ ) is

A

4 : 1

B

1 : 1

C

2 : 1

D

8 : 1

Q 12PhysicsSection A • MCQdual nature of radiation

+4 / -1

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $\lambda_0$ . IF the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be :

A

3

\lambda_0

B

9

\lambda_0

C

\frac{\lambda_0}{\sqrt2}

D

\frac{\lambda_0}{2}

Q 13PhysicsSection A • MCQwave optics

+4 / -1

In Young's double slits experiment, the position of 5 $\mathrm{^{th}}$ bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation between the slits is :

A

60

\mu

m

B

48

\mu

m

C

36

\mu

m

D

12

\mu

m

Q 14PhysicsSection A • MCQcircular motion

+4 / -1

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/s $^2$ )

A

\frac{\pi}{2}

B

\frac{\pi}{6}

C

\frac{\pi}{4}

D

\frac{\pi}{3}

Q 15PhysicsSection B • Numericalvector algebra

+4 / -1

If $\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k$ and $\overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k$ then, the unit vector in the direction of $\overrightarrow P \times \overrightarrow Q$ is ${1 \over x}\left( {\sqrt 3 \widehat i + \widehat j - 2\sqrt 3 \widehat k} \right)$ . The value of $x$ is _________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 16PhysicsSection B • Numericalproperties of matter

+4 / -1

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45 $^\circ$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $x\times10^4$ Nm $^{-2}$ . The value of $x$ is ___________.

qImage-stress-strain-curve-thermal-stress-and-elastic-pe-properties-of-matter-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 17PhysicsSection B • Numericalwaves

+4 / -1

The distance between two consecutive points with phase difference of 60 $^\circ$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is __________ km/s

Answer Format:Enter numerical value rounded to the nearest integer

Q 18PhysicsSection B • Numericalelectrostatics

+4 / -1

A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ( $\theta$ ) of deviation of the path of electron as it comes out of the field is ___________ (in degree).

qImage-electric-field-and-electric-field-intensity-electrostatics-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 19PhysicsSection A • MCQmotion

+4 / -1

A car travels a distance of ' $x$ ' with speed $v_1$ and then same distance ' $x$ ' with speed $v_2$ in the same direction. The average speed of the car is :

A

{{{v_1}{v_2}} \over {2({v_1} + {v_2})}}

B

{{2{v_1}{v_2}} \over {{v_1} + {v_2}}}

C

{{2x} \over {{v_1} + {v_2}}}

D

{{{v_1} + {v_2}} \over 2}

Q 20PhysicsSection A • MCQalternating current

+4 / -1

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency $\omega_0$ . The value of $x$ is :

A

1/4

B

1/16

C

4

D

16

Q 21PhysicsSection A • MCQmagnetic properties of matter

+4 / -1

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is :

A

\mathrm{1~A~m^{-1}}

B

\mathrm{2.4\times10^{-3}~A~m^{-1}}

C

\mathrm{1.2\times10^{3}~A~m^{-1}}

D

\mathrm{2.4\times10^{3}~A~m^{-1}}

Q 22PhysicsSection A • MCQproperties of matter

+4 / -1

A bowl filled with very hot soup cools from 98 $^\circ$ C to 86 $^\circ$ C in 2 minutes when the room temperature is 22 $^\circ$ C. How long it will take to cool from 75 $^\circ$ C to 69 $^\circ$ C?

A

2 minutes

B

0.5 minute

C

1.4 minutes

D

1 minute

Q 23PhysicsSection A • MCQrotational motion

+4 / -1

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 m/s $^2$ )

qImage--rotational-motion-mechanics-Jeemate

A

90 N

B

240 N

C

30 N

D

300 N

Q 24PhysicsSection A • MCQelectromagnetic waves

+4 / -1

An electromagnetic wave is transporting energy in the negative $z$ direction. At a certain point and certain time the direction of electric field of the wave is along positive $y$ direction. What will be the direction of the magnetic field of the wave at that point and instant?

A

Negative direction of

y

B

Positive direction of

z

C

Positive direction of

x

D

Negative direction

x

Q 25PhysicsSection B • Numericalalternating current

+4 / -1

An LCR series circuit of capacitance 62.5 nF and resistance of 50 $\Omega$ , is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is __________ mH.

(Take $\pi^2=10$ )

Answer Format:Enter numerical value rounded to the nearest integer

Q 26PhysicsSection A • MCQsimple harmonic motion

+4 / -1

T is the time period of simple pendulum on the earth's surface. Its time period becomes $x$ T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be :

A

4

B

\frac{1}{2}

C

2

D

\frac{1}{4}

Q 27PhysicsSection A • MCQgravitation

+4 / -1

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately)

(Take g = 10 m s $^{-2}$ , radius of earth = 6400 km)

A

12 hours

B

1 hour 24 minutes

C

24 hours

D

1 hour 40 minutes

Q 28PhysicsSection B • Numericalrotational motion

+4 / -1

$\mathrm{I_{CM}}$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $\mathrm{I_{AB}}$ is it's moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $\frac{2}{3}$ R from center. Where R is the radius of the disc. The ratio of $\mathrm{I_{AB}}$ and $\mathrm{I_{CM}}$ is $x:9$ . The value of $x$ is _____________.

qImage-moment-of-inertia-rotational-motion-mechanics-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 29PhysicsSection B • Numericalcurrent electricity

+4 / -1

In the given circuit, the equivalent resistance between the terminal A and B is __________ $\Omega$ .

qImage-combination-of-resistances-current-electricity-electricity-Jeemate

Answer Format:Enter numerical value rounded to the nearest integer

Q 30PhysicsSection B • Numericalray optics

+4 / -1

A ray of light is incident from air on a glass plate having thickness $\sqrt3$ cm and refractive index $\sqrt2$ . The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ____________ $\times$ 10 $^{-2}$ cm. (given $\sin 15^\circ = 0.26$ )

Answer Format:Enter numerical value rounded to the nearest integer

Q 31ChemistrySection A • MCQbiomolecules

+4 / -1

Match items of Row I with those of Row II.

Row I :

qImage-carbohydrates-biomolecules-organic-chemistry-Jeemate

Row II :

(i) $\alpha$ - $\mathrm{D}$ - $(-)$ - $\mathrm{Fructofuranose}$

(ii) $\beta$ -D- $(-)$ -Fructofuranose

(iii) $\alpha$ -D- $(-)$ Glucopyranose

(iv) $\beta$ -D- $(-)$ -Glucopyranose

Correct match is

A

\to

iii, B

\to

iv, C

\to

i, D

\to

ii

B

A

\to

iv, B

\to

iii, C

\to

i, D

\to

ii

C

A

\to

i, B

\to

ii, C

\to

iii, D

\to

iv

D

A

\to

iii, B

\to

iv, C

\to

ii, D

\to

i

Q 32ChemistrySection A • MCQp block elements

+4 / -1

Reaction of thionyl chloride with white phosphorus forms a compound [A], which on hydrolysis gives [B], a dibasic acid. [A] and [B] are respectively :

A

P

_4

O

_6

and H

_3

PO

_3

B

POCl

_3

and H

_3

PO

_4

C

PCl

_5

and H

_3

PO

_4

D

PCl

_3

and H

_3

PO

_3

Q 33ChemistrySection B • Numericalthermodynamics

+4 / -1

An athlete is given 100 g of glucose (C $_6$ H $_{12}$ O $_6$ ) for energy. This is equivalent to 1800kJ of energy. The 50% of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the weight of extra water he would need to perspire is ____________ g (Nearest integer)

Assume that there is no other way of consuming stored energy.

Given : The enthalpy of evaporation of water is 45 kJ mol $^{-1}$

Molar mass of C, H & O are 12, 1 and 16 g mol $^{-1}$ .

Answer Format:Enter numerical value rounded to the nearest integer

Q 34ChemistrySection A • MCQisolation of elements

+4 / -1

Which one of the following reactions does not occur during extraction of copper?

A

\mathrm{2FeS + 3{O_2} \to 2FeO + 2S{O_2}}

B

\mathrm{FeO + Si{O_2} \to FeSi{O_3}}

C

\mathrm{CaO + Si{O_2} \to CaSi{O_3}}

D

\mathrm{2C{u_2}s + 3{O_2} \to 2C{u_2}O + 2S{O_2}}

Q 35ChemistrySection A • MCQpractical organic chemistry

+4 / -1

Match the List-I with List-II :

	List-I Cations		List-II Group reagents
A.	$\mathrm{Pb^{2+},Cu^{2+}}$	i)	$\mathrm{H_2S}$ gas in presence of dilute HCl
B.	$\mathrm{Al^{3+},Fe^{3+}}$	ii)	$\mathrm{(NH_4)_2CO_3}$ in presence of $\mathrm{NH_4OH}$
C.	$\mathrm{Co^{2+},Ni^{2+}}$	iii)	$\mathrm{NH_4OH}$ in presence of $\mathrm{NH_4Cl}$
D.	$\mathrm{Ba^{2+},Ca^{2+}}$	iv)	H₂S in presence of NH₄OH

Correct match is -

A

\to

i, B

\to

iii, C

\to

iv, D

\to

ii

B

A

\to

i, B

\to

iii, C

\to

ii, D

\to

iv

C

A

\to

iii, B

\to

i, C

\to

iv, D

\to

ii

D

A

\to

iv, B

\to

ii, C

\to

iii, D

\to

i

Official Correct Answer:Option (A)

Step-by-Step Solution:

Cations	Group No.	Group reagent
$\mathrm{Pb}^{+2}, \mathrm{Cu}^{+2}$	II	$\mathrm{H}_2 \mathrm{S}(\mathrm{g}) \text { in presence of } \text { dil HCl }$
$\mathrm{Al}^{+3}, \mathrm{Fe}^{+3}$	III	$\begin{aligned}  &  \mathrm{NH}_4 \mathrm{OH} \text { in presence of } \\ &  \mathrm{NH}_4 \mathrm{Cl}\end{aligned}$
$\mathrm{CO}^{+2}, \mathrm{Ni}^{+2}$	$\mathrm{IV}$	$\begin{aligned}  &  \mathrm{H}_2 \mathrm{~S} \text { in presence of } \\ &  \mathrm{NH}_4 \mathrm{OH}\end{aligned}$
$\mathrm{Ba}^{+2}, \mathrm{Ca}^{+2}$	$\mathrm{~V}$	$\begin{aligned}  &  \left(\mathrm{NH}_4\right)_2 \mathrm{CO}_3 \text { in presence } \\ &  \text { of } \mathrm{NH}_4 \mathrm{OH}\end{aligned}$

Q 36ChemistrySection A • MCQperiodic classification of elements

+4 / -1

Inert gases have positive electron gain enthalpy. Its correct order is :

A

He < Ne < Kr < Xe

B

He < Xe < Kr < Ne

C

Xe < Kr < Ne < He

D

He < Kr < Xe < Ne

Official Correct Answer:Option (B)

Step-by-Step Solution:

$\begin{gathered}\text { Electron } \\text { gain }\end{gathered}$	$\mathrm{He}$	$\mathrm{Ne}$	$\mathrm{Ar}$	$\mathrm{Kr}$	$\mathrm{Xe}$
$\begin{gathered}\text { Enthalpyl } / \\mathrm{kJ} ~\mathrm{mol}^{-1}\end{gathered}$	48	116	96	96	77

Q 37ChemistrySection A • MCQsolid state

+4 / -1

A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. Y is at $\frac{1}{3}^{\mathrm{rd}}$ of the total faces. The empirical formula of the compound is :

A

\mathrm{{X_2}{Y_{1.5}}}

B

\mathrm{{X_{3}}{Y_2}}

C

\mathrm{X{Y_{2.5}}}

D

\mathrm{{X_{2.5}}Y}

Q 38ChemistrySection A • MCQpractical organic chemistry

+4 / -1

Match List I with List II

	List I Elements		List II Colour imparted to the flame
A.	K	I.	Brick Red
B.	Ca	II.	Violet
C.	Sr	III.	Apple Green
D.	Ba	IV.	Crimson Red

Choose the correct answer from the options given below :

A

A-II, B-IV, C-I, D-III

B

A-II, B-I, C-IV, D-III

C

A-II, B-I, C-III, D-IV

D

A-IV, B-III, C-II, D-I

Official Correct Answer:Option (B)

Step-by-Step Solution:

	Element	$\begin{aligned}  &  \text { Colour imparted to } \\ &  \text { the flame }\end{aligned}$
(A)	$\mathrm{K}$	Violet
(B)	$\mathrm{Ca}$	Brick red
(C)	$\mathrm{Sr}$	Crimson red
(D)	$\mathrm{Ba}$	Apple green

Q 39ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

In the cumene to phenol preparation in presence of air, the intermediate is

A

B

C

D

Q 40ChemistrySection B • Numericalsome basic concepts of chemistry

+4 / -1

In sulphur estimation, 0.471 g of an organic compound gave 1.4439 g of barium sulphate. The percentage of sulphur in the compound is ____________ (Nearest Integer)

(Given : Atomic mass Ba: 137 u, S: 32 u, O: 16 u)

Answer Format:Enter numerical value rounded to the nearest integer

Q 41ChemistrySection A • MCQp block elements

+4 / -1

Compound A reacts with NH $_4$ Cl and forms a compound B. Compound B reacts with H $_2$ O and excess of CO $_2$ to form compound C which on passing through or reaction with saturated NaCl solution forms sodium hydrogen carbonate. Compound A, B and C, are respectively :

A

\mathrm{Ca{(OH)_2},NH_4^ \oplus ,{(N{H_4})_2}C{O_3}}

B

\mathrm{CaC{l_2},NH_4^ \oplus ,{(N{H_4})_2}C{O_3}}

C

\mathrm{CaC{l_2},N{H_3},N{H_4}HC{O_3}}

D

\mathrm{Ca{(OH)_2},N{H_3},N{H_4}HC{O_3}}

Q 42ChemistrySection B • Numericalelectrochemistry

+4 / -1

Consider the cell

$\mathrm{Pt(s)|{H_2}(g)\,(1\,atm)|{H^ + }\,(aq,[{H^ + }] = 1)||F{e^{3 + }}(aq),F{e^{2 + }}(aq)|Pt(s)}$

Given $\mathrm{E_{F{e^{3 + }}/F{e^{2 + }}}^o = 0.771\,V}$ and $\mathrm{E_{{H^ + }/1/2\,{H_2}}^o = 0\,V,\,T = 298\,K}$

If the potential of the cell is 0.712 V, the ratio of concentration of Fe $^{2+}$ to Fe $^{3+}$ is _____________ (Nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 43ChemistrySection A • MCQaldehydes ketones and carboxylic acids

+4 / -1

Identify the product formed (A and E)

qImage-preparation-properties-and-uses-of-carboxylic-acids-aldehydes-ketones-and-carboxylic-acids-organic-chemistry-Jeemate

A

B

C

D

Q 44ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

A

\mathrm{NH_3 > Me_3N > MeNH_2 > Me_2NH}

B

\mathrm{Me_3N > Me_2NH > MeNH_2 > NH_3}

C

\mathrm{Me_2NH > MeNH_2 > Me_3N > NH_3}

D

\mathrm{Me_2NH > Me_3N > MeNH_2 > NH_3}

Q 45ChemistrySection A • MCQsome basic concepts of chemistry

+4 / -1

'25 volume' hydrogen peroxide means

A

1 L marketed solution contains 75 g of H

_2

O

_2

.

B

1 L marketed solution contains 250 g of H

_2

O

_2

.

C

1 L marketed solution contains 25 g of H

_2

O

_2

.

D

100 mL marketed solution contains 25 g of H

_2

O

_2

.

Q 46ChemistrySection A • MCQsurface chemistry

+4 / -1

The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph :

qImage-catalysis-surface-chemistry-physical-chemistry-Jeemate

A

(a)

B

(b)

C

(d)

D

(c)

Q 47ChemistrySection B • Numericalchemical bonding and molecular structure

+4 / -1

The total number of lone pairs of electrons on oxygen atoms of ozone is __________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 48ChemistrySection A • MCQhydrocarbons

+4 / -1

qImage-reaction-of-alkanes-hydrocarbons-organic-chemistry-Jeemate

The correct sequence of reagents for the preparation of Q and R is :

A

\mathrm{(i)C{r_2}{O_3},770K,20~atm; (ii)Cr{O_2}C{l_2},{H_3}{O^ + }; (iii)NaOH;(iv){H_3}{O^ + }}

B

\mathrm{(i)Cr{O_2}C{l_2},{H_3}{O^ + };(ii)C{r_2}{O_3},770K,20~atm;(iii)NaOH;(iv){H_3}{O^ + }}

C

\mathrm{(i)KMn{O_4},O{H^ - };(ii)M{o_2}{O_3},\Delta ;(iii)NaOH;(iv){H_3}{O^ + }}

D

\mathrm{(i)M{o_2}{O_3},\Delta ;(ii)Cr{O_2}C{l_2},{H_3}{O^ + };(iii)NaOH;(iv){H_3}{O^ + }}

Q 49ChemistrySection A • MCQbasics of organic chemistry

+4 / -1

Which of the following conformations will be the most stable?

A

B

C

D

Q 50ChemistrySection B • Numericald and f block elements

+4 / -1

How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? ______________

(Given : Atomic number V, 23; Cr, 24; Fe, 26; Ni, 28)

V $^{3+}$ , Cr $^{3+}$ , Fe $^{2+}$ , Ni $^{3+}$

Answer Format:Enter numerical value rounded to the nearest integer

Q 51ChemistrySection B • Numericalchemical kinetics and nuclear chemistry

+4 / -1

For the first order reaction A $\to$ B, the half life is 30 min. The time taken for 75% completion of the reaction is _________ min. (Nearest integer)

Given : log 2 = 0.3010

log 3 = 0.4771

log 5 = 0.6989

Answer Format:Enter numerical value rounded to the nearest integer

Q 52ChemistrySection A • MCQatomic structure

+4 / -1

The radius of the $\mathrm{2^{nd}}$ orbit of $\mathrm{Li^{2+}}$ is $x$ . The expected radius of the $\mathrm{3^{rd}}$ orbit of $\mathrm{Be^{3+}}$ is

A

\frac{16}{27}x

B

\frac{4}{9}x

C

\frac{9}{4}x

D

\frac{27}{16}x

Q 53ChemistrySection B • Numericalsolutions

+4 / -1

The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the graph.

The molar mass of PVC is ____________ g mol $^{-1}$ (Nearest integer)

qImage-osmotic-pressure-solutions-physical-chemistry-Jeemate

(Given : R = 0.083 L atm K $^{-1}$ mol $^{-1}$ )

Answer Format:Enter numerical value rounded to the nearest integer

Q 54ChemistrySection A • MCQenvironmental chemistry

+4 / -1

Some reactions of NO $_2$ relevant to photochemical smog formation are

qImage-air-pollution-environmental-chemistry-inorganic-chemistry-Jeemate

Identify A, B, X and Y :

A

\mathrm{X = [O],Y = NO,A = {O_2},B = {O_3}}

B

\mathrm{X = {N_2}O,Y = [O],A = {O_3},B = NO}

C

\mathrm{X = {1 \over 2}{O_2},Y = N{O_2},A = {O_3},B = {O_2}}

D

\mathrm{X = NO,Y = [O],A = {O_2},B = {N_2}{O_3}}

Q 55ChemistrySection B • Numericalionic equilibrium

+4 / -1

A litre of buffer solution contains 0.1 mole of each of NH $_3$ and NH $_4$ Cl. On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the solution is found to be _____________ $\times$ 10 $^{-3}$ (Nearest integer)

[Given : $\mathrm{pK_b(NH_3)=4.745}$

$\mathrm{\log2=0.301}$

$\mathrm{\log3=0.477}$

$\mathrm{T=298~K]}$

Answer Format:Enter numerical value rounded to the nearest integer

Q 56ChemistrySection B • Numericalredox reactions

+4 / -1

The density of a monobasic strong acid (Molar mass 24.2 g/mol) is 1.21 kg/L. The volume of its solution required for the complete neutralization of 25 mL of 0.24 M NaOH is __________ $\times$ 10 $^{-2}$ mL (Nearest integer)

Answer Format:Enter numerical value rounded to the nearest integer

Q 57ChemistrySection A • MCQchemistry in everyday life

+4 / -1

Which of the following statements is incorrect for antibiotics?

A

An antibiotic should promote the growth or survival of microorganisms.

B

An antibiotic must be a product of metabolism.

C

An antibiotic should be effective in low concentrations.

D

An antibiotic is a synthetic substance produced as a structural analogue of naturally occurring antibiotic.

Q 58ChemistrySection A • MCQhaloalkanes and haloarenes

+4 / -1

The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with OH $^-$ is

A

B

C

D

Q 59ChemistrySection A • MCQalcohols phenols and ethers

+4 / -1

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :

Assertion A : Acetal / Ketal is stable in basic medium.

Reason R : The high leaving tendency of alkoxide ion gives the stability to acetal/ketal in basic medium.

In the light of the above statements, choose the correct answer from the options given below :

A

A is false but R is true.

B

Both A and R are true but R is NOT the correct explanation of A

C

Both A and R are true and R is the correct explanation of A

D

A is true but R is false.

Q 60ChemistrySection B • Numericalcoordination compounds

+4 / -1

The number of paramagnetic species from the following is _____________.

$\mathrm{{[Ni{(CN)_4}]^{2 - }},[Ni{(CO)_4}],{[NiC{l_4}]^{2 - }}}$

$\mathrm{{[Fe{(CN)_6}]^{4 - }},{[Cu{(N{H_3})_4}]^{2 + }}}$

$\mathrm{{[Fe{(CN)_6}]^{3 - }}\,and\,{[Fe{({H_2}O)_6}]^{2 + }}}$

Answer Format:Enter numerical value rounded to the nearest integer

Q 61MathematicsSection A • MCQdefinite integration

+4 / -1

The minimum value of the function $f(x) = \int\limits_0^2 {{e^{|x - t|}}dt}$ is :

A

2

B

2(e-1)

C

e(e-1)

D

2e-1

Q 62MathematicsSection B • Numerical3d geometry

+4 / -1

Let the equation of the plane passing through the line $x - 2y - z - 5 = 0 = x + y + 3z - 5$ and parallel to the line $x + y + 2z - 7 = 0 = 2x + 3y + z - 2$ be $ax + by + cz = 65$ . Then the distance of the point (a, b, c) from the plane $2x + 2y - z + 16 = 0$ is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 63MathematicsSection A • MCQparabola

+4 / -1

The distance of the point $(6,-2\sqrt2)$ from the common tangent $\mathrm{y=mx+c,m > 0}$ , of the curves $x=2y^2$ and $x=1+y^2$ is :

A

\frac{1}{3}

B

5

C

\frac{14}{3}

D

5

\sqrt3

Q 64MathematicsSection A • MCQindefinite integration

+4 / -1

Let $f(x) = \int {{{2x} \over {({x^2} + 1)({x^2} + 3)}}dx}$ . If $f(3) = {1 \over 2}({\log _e}5 - {\log _e}6)$ , then $f(4)$ is equal to

A

{\log _e}19 - {\log _e}20

B

{\log _e}17 - {\log _e}18

C

{1 \over 2}({\log _e}19 - {\log _e}17)

D

{1 \over 2}({\log _e}17 - {\log _e}19)

Q 65MathematicsSection B • Numericalsets and relations

+4 / -1

Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 66MathematicsSection A • MCQprobability

+4 / -1

Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S = \left\{ {x \in \mathbb{Z}:x(66 - x) \ge {5 \over 9}M} \right\}$ and the event $\mathrm{A = \{ x \in S:x\,is\,a\,multiple\,of\,3\}}$ . Then P(A) is equal to :

A

\frac{1}{3}

B

\frac{1}{5}

C

\frac{7}{22}

D

\frac{15}{44}

Q 67MathematicsSection A • MCQvector algebra

+4 / -1

The vector $\overrightarrow a = - \widehat i + 2\widehat j + \widehat k$ is rotated through a right angle, passing through the y-axis in its way and the resulting vector is $\overrightarrow b$ . Then the projection of $3\overrightarrow a + \sqrt 2 \overrightarrow b$ on $\overrightarrow c = 5\widehat i + 4\widehat j + 3\widehat k$ is :

A

\sqrt6

B

2

\sqrt3

C

1

D

3

\sqrt2

Official Correct Answer:Option (D)

Step-by-Step Solution:

First, we write $\overrightarrow{b}$ as a linear combination of $\overrightarrow{a}$ and $\overrightarrow{j}$ since $\overrightarrow{b}$ is a rotation of $\overrightarrow{a}$ about the y-axis.

$\vec{b}=\lambda \vec{a}+\mu \hat{j}=\lambda(-\hat{i}+2 \hat{j}+\hat{k})+\mu \hat{j}=-\lambda \hat{i}+(2 \lambda+\mu \hat{j})+\lambda \hat{k}$

$\overrightarrow{b}$ is orthogonal to $\overrightarrow{a}$ due to the right angle rotation, so $\overrightarrow{b} \cdot \overrightarrow{a} = 0$ .

This implies :

$\begin{aligned} & (-\hat{i}+2 \hat{j}+\hat{k}) \cdot(-\lambda \hat{i}+(2 \lambda+\mu) \hat{j}+\lambda \hat{k})=0 \\ & \lambda+2(2 \lambda+\mu)+\lambda=0 \Rightarrow 6 \lambda+2 \mu=0 \Rightarrow \mu+3 \lambda=0\end{aligned}$

$\therefore$ $\vec{b}=\lambda \vec{a}-3 \lambda \hat{j}=\lambda(-\hat{i}+2 \hat{j}+\hat{k})-3 \lambda \hat{j}=\lambda(-\hat{i}-\hat{j}+\hat{k})$

The magnitude of $\overrightarrow{b}$ is the same as the magnitude of $\overrightarrow{a}$ because a rotation doesn't change the magnitude of a vector. This gives us :

$|\vec{b}|=\sqrt{3}|\lambda|=\sqrt{6}[\because|a|=\sqrt{6}] \Rightarrow|\lambda|=\sqrt{2} \Rightarrow \lambda \neq \sqrt{2}$

as for this value of $\lambda$ angle between $b$ and $y$ -axis is not acute.

Therefore $\lambda=-\sqrt{2}$

Thus, we have :

$\overrightarrow{b} = -\sqrt{2}(-\hat{i} - \hat{j} + \hat{k}) = \sqrt{2}\hat{i} + \sqrt{2}\hat{j} - \sqrt{2}\hat{k}$

Then, we find the vector $3\overrightarrow{a} + \sqrt{2}\overrightarrow{b}$ :

$3\overrightarrow{a} + \sqrt{2}\overrightarrow{b} = 3(-\hat{i} + 2\hat{j} + \hat{k}) + \sqrt{2}(\sqrt{2}\hat{i} + \sqrt{2}\hat{j} - \sqrt{2}\hat{k})$

$= -3\hat{i} + 6\hat{j} + 3\hat{k} + 2\hat{i} + 2\hat{j} - 2\hat{k} = -\hat{i} + 8\hat{j} + \hat{k}$

The projection of this vector onto $\overrightarrow{c}$ is given by the dot product divided by the magnitude of $\overrightarrow{c}$ :

$\frac{(-\hat{i} + 8\hat{j} + \hat{k}) \cdot (5\hat{i} + 4\hat{j} + 3\hat{k})}{\sqrt{5^2 + 4^2 + 3^2}} = \frac{-5 + 32 + 3}{\sqrt{50}} = \frac{30}{5\sqrt{2}} = 3\sqrt{2}$

So the projection of $3\overrightarrow{a} + \sqrt{2}\overrightarrow{b}$ onto $\overrightarrow{c}$ is $3\sqrt{2}$ which is option D.

Q 68MathematicsSection A • MCQbinomial theorem

+4 / -1

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1 + x)^{10}$ , then $\sum\limits_{r = 1}^{10} {{r^3}{{\left( {{{{a_r}} \over {{a_{r - 1}}}}} \right)}^2}}$ is equal to

A

3025

B

4895

C

5445

D

1210

Q 69MathematicsSection A • MCQstatistics

+4 / -1

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new variance is equal to :

A

3.92

B

4.08

C

3.96

D

4.04

Q 70MathematicsSection B • Numericalhyperbola

+4 / -1

The vertices of a hyperbola H are ( $\pm$ 6, 0) and its eccentricity is ${{\sqrt 5 } \over 2}$ . Let N be the normal to H at a point in the first quadrant and parallel to the line $\sqrt 2 x + y = 2\sqrt 2$ . If d is the length of the line segment of N between H and the y-axis then d $^2$ is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 71MathematicsSection A • MCQcomplex numbers

+4 / -1

Let $\mathrm{z_1=2+3i}$ and $\mathrm{z_2=3+4i}$ . The set $\mathrm{S = \left\{ {z \in \mathbb{C}:{{\left| {z - {z_1}} \right|}^2} - {{\left| {z - {z_2}} \right|}^2} = {{\left| {{z_1} - {z_2}} \right|}^2}} \right\}}$ represents a

A

hyperbola with the length of the transverse axis 7

B

hyperbola with eccentricity 2

C

straight line with the sum of its intercepts on the coordinate axes equals

-18

D

straight line with the sum of its intercepts on the coordinate axes equals

14

Q 72MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let S $_1$ and S $_2$ be respectively the sets of all $a \in \mathbb{R} - \{ 0\}$ for which the system of linear equations

$ax + 2ay - 3az = 1$

$(2a + 1)x + (2a + 3)y + (a + 1)z = 2$

$(3a + 5)x + (a + 5)y + (a + 2)z = 3$

has unique solution and infinitely many solutions. Then

A

\mathrm{n({S_1}) = 2}

and S

_2

is an infinite set

B

\mathrm{{S_1} = \Phi}

and

\mathrm{{S_2} = \mathbb{R} - \{ 0\}}

C

\mathrm{{S_1} = \mathbb{R} - \{ 0\}}

and

\mathrm{{S_2} = \Phi}

D

S

_1

is an infinite set and n(S

_2

) = 2

Q 73MathematicsSection A • MCQmathematical reasoning

+4 / -1

The statement $\left( {p \wedge \left( { \sim q} \right)} \right) \Rightarrow \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is

A

a tautology

B

equivalent to

\left( { \sim p} \right) \vee \left( { \sim q} \right)

C

a contradiction

D

p \vee q

Official Correct Answer:Option (A)

Step-by-Step Solution:

Making truth table (Let $(p \wedge \sim q) \Rightarrow(p \Rightarrow \sim q)=E$ )

$p$	$q$	$\sim p$	$\sim q$	$p \wedge \sim q$	$p \Rightarrow \sim q$	$E$
$\mathrm{T}$	$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$
$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$
$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$
$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$	$\mathrm{F}$	$\mathrm{T}$	$\mathrm{T}$

$\therefore E$ is a tautology

Q 74MathematicsSection B • Numericalinverse trigonometric functions

+4 / -1

If the sum of all the solutions of ${\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right) + {\cot ^{ - 1}}\left( {{{1 - {x^2}} \over {2x}}} \right) = {\pi \over 3}, - 1 < x < 1,x \ne 0$ , is $\alpha - {4 \over {\sqrt 3 }}$ , then $\alpha$ is equal to _____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 75MathematicsSection B • Numericalfunctions

+4 / -1

For some a, b, c $\in\mathbb{N}$ , let $f(x) = ax - 3$ and $\mathrm{g(x)=x^b+c,x\in\mathbb{R}}$ . If ${(fog)^{ - 1}}(x) = {\left( {{{x - 7} \over 2}} \right)^{1/3}}$ , then $(fog)(ac) + (gof)(b)$ is equal to ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 76MathematicsSection B • Numericalpermutations and combinations

+4 / -1

Let $x$ and $y$ be distinct integers where $1 \le x \le 25$ and $1 \le y \le 25$ . Then, the number of ways of choosing $x$ and $y$ , such that $x+y$ is divisible by 5, is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 77MathematicsSection A • MCQcircle

+4 / -1

The points of intersection of the line $ax + by = 0,(a \ne b)$ and the circle ${x^2} + {y^2} - 2x = 0$ are $A(\alpha ,0)$ and $B(1,\beta )$ . The image of the circle with AB as a diameter in the line $x + y + 2 = 0$ is :

A

{x^2} + {y^2} + 5x + 5y + 12 = 0

B

{x^2} + {y^2} + 3x + 5y + 8 = 0

C

{x^2} + {y^2} - 5x - 5y + 12 = 0

D

{x^2} + {y^2} + 3x + 3y + 4 = 0

Q 78MathematicsSection A • MCQapplication of derivatives

+4 / -1

Let $x=2$ be a local minima of the function $f(x)=2x^4-18x^2+8x+12,x\in(-4,4)$ . If M is local maximum value of the function $f$ in ( $-4,4)$ , then M =

A

18\sqrt6-\frac{33}{2}

B

18\sqrt6-\frac{31}{2}

C

12\sqrt6-\frac{33}{2}

D

12\sqrt6-\frac{31}{2}

Q 79MathematicsSection B • Numericalmatrices and determinants

+4 / -1

Let $\mathrm{A_1,A_2,A_3}$ be the three A.P. with the same common difference d and having their first terms as $\mathrm{A,A+1,A+2}$ , respectively. Let a, b, c be the $\mathrm{7^{th},9^{th},17^{th}}$ terms of $\mathrm{A_1,A_2,A_3}$ , respective such that $\left| {\matrix{ a & 7 & 1 \cr {2b} & {17} & 1 \cr c & {17} & 1 \cr } } \right| + 70 = 0$ .

If $a=29$ , then the sum of first 20 terms of an AP whose first term is $c-a-b$ and common difference is $\frac{d}{12}$ , is equal to ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 80MathematicsSection A • MCQvector algebra

+4 / -1

Let $\overrightarrow a$ , $\overrightarrow b$ and $\overrightarrow c$ be three non zero vectors such that $\overrightarrow b$ . $\overrightarrow c$ = 0 and $\overrightarrow a \times (\overrightarrow b \times \overrightarrow c ) = {{\overrightarrow b - \overrightarrow c } \over 2}$ . If $\overrightarrow d$ be a vector such that $\overrightarrow b \,.\,\overrightarrow d = \overrightarrow a \,.\,\overrightarrow b$ , then $(\overrightarrow a \times \overrightarrow b )\,.\,(\overrightarrow c \times \overrightarrow d )$ is equal to

A

\frac{1}{2}

B

-\frac{1}{4}

C

\frac{1}{4}

D

\frac{3}{4}

Q 81MathematicsSection A • MCQlimits continuity and differentiability

+4 / -1

The value of $\mathop {\lim }\limits_{n \to \infty } {{1 + 2 - 3 + 4 + 5 - 6\, + \,.....\, + \,(3n - 2) + (3n - 1) - 3n} \over {\sqrt {2{n^4} + 4n + 3} - \sqrt {{n^4} + 5n + 4} }}$ is :

A

{3 \over {2\sqrt 2 }}

B

{3 \over 2}(\sqrt 2 + 1)

C

3(\sqrt 2 + 1)

D

{{\sqrt 2 + 1} \over 2}

Q 82MathematicsSection B • Numericalarea under the curves

+4 / -1

If the area enclosed by the parabolas $\mathrm{P_1:2y=5x^2}$ and $\mathrm{P_2:x^2-y+6=0}$ is equal to the area enclosed by $\mathrm{P_1}$ and $\mathrm{y=\alpha x,\alpha > 0}$ , then $\alpha^3$ is equal to ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 83MathematicsSection A • MCQdifferential equations

+4 / -1

Let $y = y(x)$ be the solution curve of the differential equation ${{dy} \over {dx}} = {y \over x}\left( {1 + x{y^2}(1 + {{\log }_e}x)} \right),x > 0,y(1) = 3$ . Then ${{{y^2}(x)} \over 9}$ is equal to :

A

{{{x^2}} \over {5 - 2{x^3}(2 + {{\log }_e}{x^3})}}

B

{{{x^2}} \over {3{x^3}(1 + {{\log }_e}{x^2}) - 2}}

C

{{{x^2}} \over {7 - 3{x^3}(2 + {{\log }_e}{x^2})}}

D

{{{x^2}} \over {2{x^3}(2 + {{\log }_e}{x^3}) - 3}}

Q 84MathematicsSection B • Numericalbinomial theorem

+4 / -1

The constant term in the expansion of ${\left( {2x + {1 \over {{x^7}}} + 3{x^2}} \right)^5}$ is ___________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 85MathematicsSection A • MCQ3d geometry

+4 / -1

Consider the lines $L_1$ and $L_2$ given by

${L_1}:{{x - 1} \over 2} = {{y - 3} \over 1} = {{z - 2} \over 2}$

${L_2}:{{x - 2} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$ .

A line $L_3$ having direction ratios 1, $-$ 1, $-$ 2, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively. Then the length of line segment $PQ$ is

A

4\sqrt3

B

2\sqrt6

C

4

D

3\sqrt2

Q 86MathematicsSection B • Numericallogarithms

+4 / -1

Let $S = \left\{ {\alpha :{{\log }_2}({9^{2\alpha - 4}} + 13) - {{\log }_2}\left( {{5 \over 2}.\,{3^{2\alpha - 4}} + 1} \right) = 2} \right\}$ . Then the maximum value of $\beta$ for which the equation ${x^2} - 2{\left( {\sum\limits_{\alpha \in s} \alpha } \right)^2}x + \sum\limits_{\alpha \in s} {{{(\alpha + 1)}^2}\beta = 0}$ has real roots, is ____________.

Answer Format:Enter numerical value rounded to the nearest integer

Q 87MathematicsSection A • MCQdifferentiation

+4 / -1

Let $y(x) = (1 + x)(1 + {x^2})(1 + {x^4})(1 + {x^8})(1 + {x^{16}})$ . Then $y' - y''$ at $x = - 1$ is equal to

A

496

B

976

C

464

D

944

Q 88MathematicsSection A • MCQmatrices and determinants

+4 / -1

Let $x,y,z > 1$ and $A = \left[ {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 2 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 3 \cr } } \right]$ . Then $\mathrm{|adj~(adj~A^2)|}$ is equal to

A

6^4

B

2^8

C

4^8

D

2^4

Q 89MathematicsSection A • MCQ3d geometry

+4 / -1

The distance of the point P(4, 6, $-$ 2) from the line passing through the point ( $-$ 3, 2, 3) and parallel to a line with direction ratios 3, 3, $-$ 1 is equal to :

A

3

B

\sqrt{14}

C

\sqrt6

D

2\sqrt3

Q 90MathematicsSection A • MCQapplication of derivatives

+4 / -1

Let $f:(0,1)\to\mathbb{R}$ be a function defined $f(x) = {1 \over {1 - {e^{ - x}}}}$ , and $g(x) = \left( {f( - x) - f(x)} \right)$ . Consider two statements

(I) g is an increasing function in (0, 1)

(II) g is one-one in (0, 1)

Then,

A

Both (I) and (II) are true

B

Neither (I) nor (II) is true

C

Only (II) is true

D

Only (I) is true

JEE Main 2023 25th January Morning Shift Question Paper with Solutions