datavorous/entrance-exam-dataset huggingface dataset:
A convex, rearview mirror of focal length 20 cm, is fitted in a car. A second car 2 m broad and 1.6 m high is 6 m away from the first car and overtakes the first car at a relative speed of 15 m s-1, then the speed of the image of the second car with respect to the first car is

Options:
A 0.016 m s-1
B 0.0257 m s-1
C 0.162 m s-1
D 0.0073 m s-1

The correct answer is:
0.016 m s-1

Solution:
Mirror formula 1v+1u=1f
Differentiating w.r.t. t,
0=-1v2dvdt-1u2dudt
dvdt=-v2u2dudt
Butdudt=15 m s-1
Now1v=(120+1600)∴v=60031 cm
andvu=600/31600=131
Speed of image=dvdt=-(131)2×15
=0.016 m s-1

Topic: Physics, Ray Optics, NEET
A conveyor belt is moving at a constant speed of 2 m s-1. A box is gently dropped on it. The coefficient of friction between them is Î¼=0.5. The distance that the box will move relative to the belt before coming to rest on it taking g=10 m s-2, is

Options:
A 1.2 m

B 0.6 m

C Zero
D 0.4 m

The correct answer is:
0.4 m

Solution:
Frictional force on the box f=μmg
∴ Acceleration in the box
a=μg=5 m s-2
v2=u2+2as
⇒ 0=22+2×(5)s
⇒ s=-25 m (with respect to the belt)
⇒ distance=0.4 m

Topic: Physics, Laws of Motion, NEET
A co-ordination complex of cobalt has molecular formula containing five ammonia molecules, one nitro group and two chlorine atoms for one cobalt atom. One mole of this compound produces three mole ions in an aqueous solution. In reacting this solution with excess of silver nitrate solution, two moles of AgCl get precipitated. The ionic formula of this complex would be –

Options:
A CoNH34.NO2Cl.NH3Cl]
B CoNH35Cl.ClNO2]
C [CoNH35NO2Cl2
D CoNH35.NO22Cl2]

The correct answer is:
[CoNH35NO2Cl2

Solution:
[Co(NH3)5NO2]Cl2→[Co(NH3)5NO2]2++2Cl- ,
Two moles of AgCl is formed, thus two Cl atoms are present outside coordination sphere.

Topic: Chemistry, Coordination Compounds, NEET
A copper disc of the radius 0.1 m is rotated about its centre with ω=20 revolutions per second in a uniform magnetic field of 0.1 T with its plane perpendicular to the field. The emf induced across the radius of the disc is

Options:
A π20 V
B π10 V
C 20π mV
D 100π mV

The correct answer is:
20π mV

Solution:
ε = B ω R 2 2
= 0.1 × 2 π × 2 0 0.1 2 2
=20π×10-3 V

Topic: Physics, Electromagnetic Induction, NEET
A copper rod is suspended in a non-homogenous magnetic field region. The rod when in equilibrium will align itself

Options:
A In the region where magnetic field is strongest
B In the region where magnetic field is weakest and parallel to direction of magnetic field there
C In the direction in which it was originally suspended
D In the region where magnetic field is weakest and perpendicular to the direction of magnetic field there

The correct answer is:
In the region where magnetic field is weakest and perpendicular to the direction of magnetic field there

Solution:
Copper is a diamagnetic material, therefore its rod align itself where magnetic field is weaker and perpendicular to the direction of magnetic field there.

Topic: Physics, Magnetic Properties of Matter, NEET
A copper rod of 88 cm and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of aluminum rod is αCu=1.7×10-5 K-1 and αAl=2.2×10-5 K-1

Options:
A 6.8 cm
B 113.9 cm
C 88 cm
D 68 cm

The correct answer is:
68 cm

Solution:
Increase in length is independent of temperature,
Lcu αcu=LAl αAl
LAl=88 cm1.7×10-52.2×10-5
=68 cm

Topic: Physics, Thermal Properties of Matter, NEET, NEET 2019 (All India)
A copper rod of length l0 at 0 oC is placed on a smooth surface. Now the rod is heated up to 100 oC. Find the longitudinal strain developed
( Î±= coefficient of linear expansion)

Options:
A 100- Î±l0+100l0Î±
B 100Î±
C Zero
D None of these

The correct answer is:
Zero

Solution:
Since, the surface is smooth, so no stress is developed inside the rod.
Hence, strain is zero,
Mathematically,
Y×strain=stress=Y×0=0

Topic: Physics, Thermal Properties of Matter, NEET
A copper wire of length 10 m and radius 10-2πm has electrical resistance of 10Ω. The current density in the wire for an electric field strength of 10 V m-1 is:

Options:
A 106 A m-2
B 10-5 A m-2
C 105 A m-2
D 104 A m-2

The correct answer is:
105 A m-2

Solution:
Length =10 m

Radius =10-2π m

Electrical resistance =10 Ω

Electric field strength =10 V m-1

Current density, J=IA=VRA=ELRA

⇒J=10×1010×π10-2π2=105 A m-2

Topic: Physics, Current Electricity, NEET, NEET 2022 (Phase 1)
A copper wire of radius $1 \mathrm{~mm}$ contains $10^{22}$ free electrons per cubic metre. The drift velocity for free electrons when $10 \mathrm{~A}$ current flows through the wire will be (Given, charge on electron $=1.6 \times 10^{-19} \mathrm{C}$ )

Options:
A $\frac{6.25}{\pi} \mathrm{m} \mathrm{s}^{-1}$
B $\frac{6.25 \times 10^5}{\pi} \mathrm{m} \mathrm{s}^{-1}$
C $\frac{6.25 \times 10^4}{\pi} \mathrm{m} \mathrm{s}^{-1}$
D $\frac{6.25}{\pi} \times 10^3 \mathrm{~m} \mathrm{~s}^{-1}$

The correct answer is:
$\frac{6.25}{\pi} \times 10^3 \mathrm{~m} \mathrm{~s}^{-1}$

Solution:
$V_d=\frac{i}{n e A}$
$\begin{aligned} & V_d=\frac{10}{10^{22} \times 1.6 \times 10^{-19} \times \pi\left(10^{-3}\right)^2} \\ & V_d=\frac{10}{1.6 \pi \times 10^{-3}} \\ & =\frac{6.25}{\pi} \times 10^3 \mathrm{~m} / \mathrm{s}\end{aligned}$

Topic: Physics, Current Electricity, NEET, NEET 2023 (Manipur)
A coprophillous fungus belongs to

Options:
A Ascomycetes
B Phycomycetes
C Both (a) and (b)
D None of these

The correct answer is:
Both (a) and (b)

Solution:
Ascomycetes are commonly known as sac-fungi. These are either unicellular e.g., yeast (Saccharomyces) or multicellular e.g., Penicillium. They are saprophytic, decomposing, parasitic or coprophilous (growing on dung) in nature.
Zygomycetes are found in aquatic habitats and on decaying wood in moist and damp places or as obligate parasites on plants. The mycelium is aseptate and coenocytic. Squirting fungus-Pilobolus crystallinus is a coprophilous or dung mould.

Topic: Biology, Biological Classification, NEET
A country with a high rate of population growth took measures to reduce it. The figure below shows age sex pyramids of populations. A and B twenty years apart. Select the correct interpretation about them
Interpretations

Options:
A ' $A$ ' is more recent and shows slight reduction in the growth rate
B ' $\mathrm{B}$ ' is earlier pyramid and shows stabilised growth rate
C ' $\mathrm{B}$ ' is more recent showing that population is very young
D ' $A$ ' is the earlier pyramid and no change has occurred in the growth rate

The correct answer is:
' $A$ ' is more recent and shows slight reduction in the growth rate

Solution:
Interpretion ' $\mathrm{A}$ ' is correct for the given figures.

Topic: Biology, Plant - Growth and Development, NEET, NEET 2009 (Screening)
A couple had two sons, one was colour blind while the other wasn't. They also had a colour blind daughter. Which statement about this couple is true?

Options:
A Husband is colour blind but wife is not
B Husband is normal and wife is colour blind
C Husband and wife both are colour blind
D Husband and wife both are normal

The correct answer is:
Husband is colour blind but wife is not

Solution:
Colour blind man has one X chromosome with the gene for colour blindness which he receives from his mother. His colour blind sister has two X chromosomes each with the gene for colour blindness. She has received one of these from her father and one from her mother. Thus from this information we can conclude that their father is colour blind and their mother has at least one X chromosome for colour blindness. Also they have a normal brother. That means their mother has one X chromosome without colour blindness genes. Hence mother is a carrier.

Topic: Biology, Principles of Inheritance and Variation, NEET
A couple has a child whose blood group is different from his mother as well as his father. The possible blood group of the parents could not be

Options:
A A and AB
B B and AB
C AB and O
D A and O

The correct answer is:
AB and O

Solution:
The possible offsprings of parents with blood groups A (IA IO) and AB (IA IB) are A, B and AB

IA	IO
IA	IAIA (Blood group A)	IAIO (Blood group A)
IB	IAIB (Blood group AB)	IBIO (Blood group B)

Thus in this combination there is B blood group which doesn't match with the parents.
The possible offsprings of parents with blood groups B IAIO and AB IAIB are A, B and AB

IB	IO
I A	I A I B (Blood group AB)	IAIO (Blood group A)
IB	IBIB (Blood group B)	IBIO (Blood group B)

Thus in this combination there is A blood group which doesn't match with the parents.
The possible offsprings of parents with blood groups O IO IO and AB IA IB are A and B

IO
I A	IAIO (Blood group A)
IB	IBIO (Blood group B)

Thus in this combination there is A and B blood groups which doesn't match with the parents.
The possible offsprings of parents with blood groups A IA IO and O IO IO are A and O

IO
IA	IA IO (Blood group A)
IO	IO IO (Blood group O)

In this combination there is A and O blood groups which match with the parents.

Topic: Biology, Principles of Inheritance and Variation, NEET
A couple has a normal vision, although both of their fathers are red-green colour-blind. What is the probability in the following cases?

i. A normal son
ii. A carrier daughter
iii. A colour-blind son
iv. A colour blind daughter

Options:
A i= 14, ii=14,iii=14,iv=14
B i=14,ii=14,iii=14,iv=04
C i=04,ii=12,iii=14,iv=14
D i=14,ii=12,iii=14,iv=0

The correct answer is:
i=14,ii=14,iii=14,iv=04

Solution:
Mother is a carrier (because her father is colour-blind) and father is normal. Thus, their genotype Xc X and XY respectively. So the probability that their first child will be A normal son =1/4, A carrier daughter =1/4. A colour-blind son =1/4, A colour-blind daughter =0. (Both husband and wife have normal vision through their fathers were colour-blind, the probability of their daughter becoming colour-blind is 0%. The chances of a daughter becoming colour blind arise only when the father is also colour-blind.)

Topic: Biology, Principles of Inheritance and Variation, NEET
A couple has three children: a 14-year-old daughter and two sons that are 12 and 10 years old. If the mother and daughter are both known to have a genetic disorder, what would the pedigree of this family look like?

Options:
A
B
C
D

The correct answer is:

Solution:
In a pedigree chart a square symbol resembles male and circle symbol resembles a female. It the square / circled is filled it indicates disease while if it is unfilled it indicates no disease. While denoting the offsprings, the eldest to youngest offsprings are depicted from left to right. Mother and daughter both are affected. So Circles should be shaded. Also in the offspring from left to right there should be a circle (daughter), square (son) and square (youngest son)

Topic: Biology, Principles of Inheritance and Variation, NEET
A couple having five daughters only is expecting sixth progeny. The chance of the progeny being a son is

Options:
A 0
B 25%
C 50%
D 100%

The correct answer is:
50%

Solution:
A family of five daughter only is expecting sixth issue. The chance of its beings a son is 50%.
Human have 22 pairs of autosome and a pair of sex chromosomes which are XX in females and XY in males. So if we cross the parents there is 1 : 1 chance for boy and girl.

Topic: Biology, Principles of Inheritance and Variation, NEET
A couple is unable to bear a child despite having unprotected coitus. They decided to have a test-tube baby. On being diagnosed, the doctor advised them for a technique which requires the transfer of an embryo with more than 8 blastomeres. Identify the technique adopted by the couple.

Options:
A ICSI
B IUT
C ZIFT
D AI

The correct answer is:
IUT

Solution:
Assisted reproductive technologies help a couple to bear a child. There are various such methods. The famous is the test tube baby. In this the sperms and eggs are collected and are fertilised in the test tube. This results in formation of zygote. The zygote forms an embryo and then starts cleavage. This fertilised product is then transferred to the female body for further development. If the fertilised embryo has less than 8 blastomeres it is transferred into the fallopian tube but if the embryo has more than 8 blastomeres it is transferred into the uterus so that it can get implanted there. This is known as IUT (Intrauterine transport).

Topic: Biology, Reproductive Health, NEET
A couple produces

Options:
A No motion
B Linear and rotational motion
C Purely rotational motion
D Purely linear motion

The correct answer is:
Purely rotational motion

Solution:
A couple consists of two equal and opposite forces acting at a separation, so that net force becomes zero. When a couple acts on a body it rotates the body but does not produce any translatory motion. Hence, only rotational motion is produced.

Topic: Physics, Rotational Motion, NEET
A cricket ball is thrown by a player at a speed of $20 \mathrm{~m} / \mathrm{s}$ in a direction $30^{\circ}$ above the horizontal. The maximum height attained by the ball during its motion is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$ :

Options:
A $5 \mathrm{~m}$
B $10 \mathrm{~m}$
C $20 \mathrm{~m}$
D $25 \mathrm{~m}$

The correct answer is:
$5 \mathrm{~m}$

Solution:
Given : \(\mathrm{u}=20 \mathrm{~m} / \mathrm{s} \theta=30^{\circ}, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\)
We get \(\sin \theta=\sin 30^{\circ}=\frac{1}{2}\)
Maximum height reached \(\mathrm{H}=\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}}=\frac{20 \times 20 \times\left(\frac{1}{2}\right)^2}{20}=5 \mathrm{~m}\)

Topic: Physics, Motion In Two Dimensions, NEET, NEET 2022 (Phase 2)
A cricket ball of mass 0.25 kg with speed 10 m s-1 hits a bat and returns with same speed within 0.01 s. The force acted on the bat is

Options:
A 25 N

B 50 N

C 250 N

D 500 N

The correct answer is:
500 N

Solution:
v=v'=10 m s-1
F= Îp Ît
F= mÎv Ît
F= m( v'âv ) Ît
F= 0.25( 10â( â10 ) ) 0.01âs
F= 5 0.01
F=500âN

Topic: Physics, Laws of Motion, NEET
A cricket fielder can throw the cricket ball with a speed vo. If he throws the ball while running with speed u at an angle θ to the horizontal, find the effective angle to the horizontal at which the ball is projected in air as seen by a spectator.

Options:
A $ta{{n}^{-1}}\left( \frac{{{v}_{o}}sin\theta }{{{v}_{o}}sin\theta ~+~u} \right)$
B $ta{{n}^{-1}}\left( \frac{{{v}_{o}}cos\theta }{{{v}_{o}}sin\theta ~+~u} \right)$
C $ta{{n}^{-1}}\left( \frac{{{v}_{o}}cos\theta }{{{v}_{o}}cos\theta ~+~u} \right)$
D $ta{{n}^{-1}}\left( \frac{{{v}_{o}}sin\theta }{{{v}_{o}}cos\theta ~+~u} \right)$

The correct answer is:
$ta{{n}^{-1}}\left( \frac{{{v}_{o}}sin\theta }{{{v}_{o}}cos\theta ~+~u} \right)$

Solution:
Correct Option is : (D)
$ta{{n}^{-1}}\left( \frac{{{v}_{o}}sin\theta }{{{v}_{o}}cos\theta ~+~u} \right)$

Topic: Chemistry, Motion In Two Dimensions, NEET
A cricket fielder can throw the cricket ball with a speed vo. If he throws the ball while running with speed u at an angle θ to the horizontal, what will be time of flight?

Options:
A $\frac{{{v}_{o}}cos\theta }{g}$
B $\frac{2{{v}_{o}}sin\theta }{g}$
C $\frac{{{v}_{o}}sin\theta }{g}$
D $\frac{2{{v}_{o}}cos\theta }{g}$

The correct answer is:
$\frac{2{{v}_{o}}sin\theta }{g}$

Solution:
Correct Option is : (B)
$\frac{2{{v}_{o}}sin\theta }{g}$

Topic: Chemistry, Motion In Two Dimensions, NEET
A cricket player is fast chasing a ball in the field. Which one of the following groups of bones are directly contributing in this movement ?

Options:
A Femur, malleus, tibia, metatarsals
B Pelvis, ulna, patella, tarsals
C Sternum, femur, tibia, fibula
D Tarsals, femur, metatarsals, tibia.

The correct answer is:
Tarsals, femur, metatarsals, tibia.

Solution:
Tarsals, femur, metatarsals and tibia are bones of the legs which are involved in running during chasing the ball by cricket player.

Topic: Biology, Locomotion and Movement, NEET
A crop must be tested for at least ________ growing season(s) before releasing for commercialization.

Options:
A One
B Two
C Three
D Four

The correct answer is:
Three

Solution:
Testing release and commercialization of new cultivars are done by growing hybrids in the research fields and recording their performance under ideal fertilizer application, irrigation, and other crop management practices. This is followed by testing in farmer fields for three growing seasons at several locations representing all the agroclimatic zones.

Topic: Biology, Strategies for Enhancement in Food Production, NEET
A cross between a pure pea plant with yellow pod and round seeds with a pure pea plant with green pods and round seeds yields_____ green round plants in F1.

Options:
A 50%
B 25%
C 0%
D 100%

The correct answer is:
100%

Solution:
In pea plant, Green pod (G) is dominant over yellow pod (g) and Round seed (R) is dominant over wrinkled seed (r). Genotype of a pure pea plant with yellow pod and round seeds: ggRR. It will produce gametes with gR. Genotype of a pure pea plant with green pods and wrinkled seeds: GGrr. It will produce gametes with Gr. Thus their F1 offspring will have GgRr genotype which is a pea plant with green pod and round seeds

Topic: Biology, Principles of Inheritance and Variation, NEET
A cross between an F1 hybrid and its homozygous recessive parent is called:

Options:
A Test cross
B Back cross
C Reciprocal cross
D All of these

The correct answer is:
Test cross

Solution:
Test crosses are used to test an individual's genotype by crossing it with an individual of a known genotype. Individuals that show the recessive phenotype are known to have a homozygous recessive genotype. Individuals that show the dominant phenotype, however, may either be homozygous dominant or heterozygous.

Topic: Biology, Principles of Inheritance and Variation, NEET
A cross of an F individual that has a dominant phenotype with its homozygous recessive parent is called a ___.

Options:
A Test cross
B Back cross
C Homozygous
D Heterozygous

The correct answer is:
Test cross

Solution:
A cross of an F individual that has a dominant phenotype with its homozygous recessive parent is called a test cross.

Topic: Biology, Principles of Inheritance and Variation, NEET
A crown glass prism of refracting angle 6° is to be used for deviation without dispersion with a flint glass of angle of prism α. Given: for crown glass μr=1.513 and μv=1.523 , for flint glass μr=1.645 and μv=1.665. Find α

Options:
A 3°
B 4°
C 4.5°
D 5°

The correct answer is:
3°

Solution:
For deviation without dispersion
μV1-μr1α1=μV2-μr12α2
or α2=(1.523-1.513)(1.665-1.645)6°
α=3°

Topic: Physics, Ray Optics, NEET
A crown glass prism of refracting angle 6o is to be used for deviation without dispersion with a flint glass of angle of prism α . Given: for crown glass μr=1.513 and μv=1.523, for flint glass μr=1.645 and μv=1.665. What should be the value of α?

Options:
A 3o
B 4o
C 4.5o
D 5o

The correct answer is:
3o

Solution:
⇒μV1-μr1α1=μV2-μr2α2
or ⇒α2=(1.523-1.513)(1.665-1.645)6o=3o

Topic: Physics, Ray Optics, NEET
A Crystal is made of particles X, Y and Z. X Forms FCC packing, Y occupies all octahedral voids of X and Z occupies all tetrahedral voids of X. If all the particles along one body diagonal are removed, then the formula of crystal would be

Options:
A XYZ2
B X2YZ2
C X8Y4Z5
D X5Y4Z8

The correct answer is:
X5Y4Z8

Solution:
When all particles along body diagonal are removed, 2X atoms from corner are removed one Y particle removed and 2Z particle removed
Xparticle=18×6+12×6=154
(Y particle =3 , Z particle =6 )
∴X154Y3Z6=X5Y4Z8

Topic: Chemistry, Solid State, NEET
A crystal of intrinsic silicon at room temperature has a carrier concentration of 1.6Ã1016 m-3. If the donor concentration level is 4.8Ã1020 m-3, then the concentration of holes in the semiconductor is

Options:
A 53×1012 m-3
B 4×1011 m-3
C 4×1012 m-3
D 5.3×1011 m-3

The correct answer is:
5.3×1011 m-3

Solution:
Given,
n1=1.6×1016 m-3
ne=4.8×1020 m-3
nh= ?
The concentration of holes in the semiconductor is given by the expression,
n12=ne×nh
1.6×10162=4.8×1020×nh
nh=2.56×10324.8×1020=5.3×1011 m-3

Topic: Physics, Semiconductors, NEET
A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm, if the density of the substance in the crystal is 8 g cm-3 , then the number of atoms present in 256 g of the crystal is N×1024 . The value of N is

Options:
A 4
B 2
C 3
D 5

The correct answer is:
2

Solution:
d=Z×Ma3×NA
M=(400)3×10-30×8×NA4
On solving M=64×2×10-24 NAg
Now, (64×2×10-24NA) g contains NA atoms
As 256 g =NA64×2×10-24NA×256
=2×1024

Topic: Chemistry, Solid State, NEET
A cubic solid is made of two elements P and Q. Atoms of Q are at the corners of the cube and P at the body-centre. What is the formula of the compound? What are the coordination numbers of P and Q?

Options:
A The formula is PQ; Coordination number of P is 8 and of Q is 1.
B The formula is PQ2; Coordination number of P is 1 and of Q is 8.
C The formula is P2Q; Coordination number of P is 1 and of Q is 8.
D The formula is PQ; Coordination number of P is 1 and of Q is 8.

The correct answer is:
The formula is P2Q; Coordination number of P is 1 and of Q is 8.

Solution:
Correct Option is : (C)
The formula is P2Q; Coordination number of P is 1 and of Q is 8.

Topic: Chemistry, Solid State, NEET
A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?
[Take, density of water =103 kg/m3 ]

Options:
A 87.5 kg
B 65.4 kg
C 30.1 kg
D 46.3 kg

The correct answer is:
87.5 kg

Solution:
In first case, when 30% of the cube inside water,
ρwVin g=ρcVg
VinV=ρcρw=0.3
Additional weight we can put w is,
Vρwg=ρcVg+w
w=Vρw-ρcg
=0.53×0.7×103×g
=87.5g N
Addition of mass that we can put =87.5 kg

Topic: Physics, Mechanical Properties of Fluids, NEET
A cubical block of side a is moving with velocity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is

Options:
A 3v4a
B 3v2a
C 3v2a
D zero

The correct answer is:
3v4a

Solution:
I0 is moment of inertia of block about an axis through O and perpendicular to the plane of block.

If Ic is moment of inertia about center of mass then Ic=Ma26

hence from parallel axis theorem I0=Ic+Mr2 and r2=a22+a22=a22

I0=Ma26+Ma22=2Ma23
From conservation of angular momentum about O
Mva2=23Ma2Ï
Ï=3v4a

Topic: Physics, Rotational Motion, NEET
A cuboidal piece of wood has dimensions a, b and c. Its relative density is d. It is floating in a large body of water such that side a is vertical. It is pushed down a bit and released. The time period of SHM of the wooden piece is

Options:
A 2πabcg
B 2πgda
C 2πbcdg
D 2Ïdag

The correct answer is:
2πdag

Solution:
The net force on the block when it is displaced slightly is

F=-bcxg

⇒acceleration=-bcxgabcd

⇒ω=gad

T=2πadg

Topic: Physics, Mechanical Properties of Fluids, NEET
A cup of coffee cools from 90°C to 80°C in t min, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is :

Options:
A 1310t
B 1013t
C 135t
D 513t

The correct answer is:
135t

Solution:
From Newton's Law of cooling,

ΔTΔt=kT-Ts

where,

⇒T2-T1t-kT1+T22-TsTs

Where, T1= Initial temperature of body

T2= Final temperature of body

Ts= surrounding temperature

t= time taken

For case1,

90-80t=k90+802-20

⇒10t=65k

⇒k=1065t …i

For case 2 ,

80-60t'=k80+602-20

⇒20t'=50k

Put the value k from eq.i,

⇒20t'=50×1065t

⇒t'=20×65500t

⇒t'=135t

Topic: Physics, Thermal Properties of Matter, NEET, NEET 2021