datavorous/entrance-exam-dataset huggingface dataset:
The rate of decomposition is faster in the ecosystem due to following factors EXCEPT:

Options:
A Detritus rich in sugars
B Warm and moist environment
C Presence of aerobic soil microbes
D Detritus richer in lignin and chitin

The correct answer is:
Detritus richer in lignin and chitin

Solution:
The rate of decomposition of detritus is controlled by the chemical nature of detritus and a number of climatic factors given below.

Chemical nature of detritus: The decomposition of detritus is slow if it contains lignin, chitin, tannins (phenolics) and cellulose. It is rapid if detritus possesses more nitrogenous compounds (like proteins, nucleic acids) and water-soluble reserve carbohydrates or sugars.

The temperature above 25oC favours the growth of microorganisms.

Soil moisture is the most important climatic factors that regulate decomposition through their effects on the activities of soil microbes.

Aeration: It is required for the activity of decomposers and detritivores. Reduced aeration will slow down the process of decomposition.

Soil pH: The growth of microbes is low in acidic soils as compared to basic soils.

So, the detritus rich in lignin and chitin will undergo slow decomposition.

Topic: Biology, Ecosystem, NEET, NEET 2020 (Phase 2)
The rate of esterification of acetic acid with methyl alcohol (I), ethyl alcohol (II), isopropyl alcohol (III) and tertiary butyl alcohol (IV) follows in the order â

Options:
A I>II>III>IV
B IV>III>II>I
C II>I>IV>III
D III>IV>I>III

The correct answer is:
I>II>III>IV

Solution:
The order rate of esterification of acetic acid is
methyl alcohol (I) > ethyl alcohol (II) > isopropyl alcohol III> tertiary butyl alcohol (IV)
Increase in size of alkyl group in ROH decreases the rate of etherification

Topic: Chemistry, Carboxylic Acid Derivatives, NEET
The rate of increase of thermo-emf with temperature at the neutral temperature of a thermocouple

Options:
A is zero
B depends upon the choice of the two materials of the thermocouple
C is negative
D is positive

The correct answer is:
is zero

Solution:
We have
$$
e=a t+b t^2
$$
Natural temperature $\frac{d e}{d t}=a+2 b t$
$$
T_n=-\frac{a}{2 b}
$$
At netural temperature
$$
\frac{d e}{d t}=0
$$

Topic: Physics, Current Electricity, NEET, NEET 2011 (Screening)
The rate of oxidation of oxalic acid by acidified potassium permanganate is shown in the given graph.

5H2C2O4+2KMnO4+3H2SO4→2MnSO4+K2SO4+10CO2+8H2O
The type of catalyst shown by such reaction is

Options:
A heterogeneous catalysis
B induced catalysis
C auto-catalysis
D negative catalysis

The correct answer is:
auto-catalysis

Solution:
In these reactions, one of the products formed (MnSO4) acts as auto catalyst and thus accelerate the rate of reaction.

Topic: Chemistry, Surface Chemistry, NEET
The rate of radioactive disintegration at an instant for a radioactive sample of half life $2.2 \times 10^9 \mathrm{~s}$ is $10^{10} \mathrm{~s}^{-1}$. The number of radioactive atoms in that sample at that instant is

Options:
A $3.17 \times 10^{20}$
B $3.17 \times 10^{17}$
C $3.17 \times 10^{18}$
D $3.17 \times 10^{19}$

The correct answer is:
$3.17 \times 10^{19}$

Solution:
Given, half life $T_{1 / 2}=2.2 \times 10^9 \mathrm{~s}$
Rate of disintegration, $R=10^{10} \mathrm{~s}^{-1}$
If $\mathrm{N}$ be the number of nuclei present, then the rate of disintegration is
$$
\begin{aligned}
\frac{\mathrm{dN}}{\mathrm{dt}}=\lambda \mathrm{N} \quad(\lambda=\text { decay constant }) \\
\Rightarrow \quad \mathrm{R}=\lambda \mathrm{N} \quad \text { or } \mathrm{N}=\frac{\mathrm{R}}{\lambda} \quad \ldots \text { (i) }
\end{aligned}
$$
Also, the half life is given by,
$$
\mathrm{T}_{1 / 2}=\frac{0.693}{\lambda} \Rightarrow \lambda=\frac{0.693}{\mathrm{~T}_{1 / 2}}
$$
From Eq. (i) and (ii), we get
$$
\mathrm{N}=\frac{\mathrm{R}}{0.693} \times \mathrm{T}_{1 / 2}=\frac{10^{10} \times 2.2 \times 10^9}{0.693}=3.17 \times 10^{19}
$$

Topic: Physics, Nuclear Physics, NEET, NEET 2019 (Odisha)
The rate of reaction between two reactants $\mathrm{A}$ and $\mathrm{B}$ decreases by a factor of 4 if the concentration of reactant $B$ is doubled. The order of this reaction iwth respect is reactant $\mathrm{B}$ is:

Options:
A 2
B -2
C 1
D -1

The correct answer is:
-2

Solution:
Rate of reaction $=\mathrm{K}\left[\mathrm{A}_0\right]^\alpha\left[\mathrm{B}_0\right]^\beta$
$$
\begin{aligned}
{[\mathrm{B}] } & =2\left[\mathrm{~B}_0\right] \\
\frac{r_1}{r_2} & =\frac{\mathrm{K}\left[\mathrm{A}_0\right]^\alpha\left[\mathrm{B}_0\right]^\beta}{\left[\mathrm{A}_0\right]^\alpha\left[2 \mathrm{~B}_0\right]^\beta} ; \\
4 & =\left(\frac{1}{2}\right)^\beta=\beta=-2 .
\end{aligned}
$$

Topic: Chemistry, Chemical Kinetics, NEET, NEET 2005
The rate of reaction is expressed as

12+ddt[C]=13-ddt[D]=14+ddt[A]=-ddt[B] ,

The reaction is

Options:
A 14A+12C→B+13D
B 4A+2C→B+3D
C B+3D→4A+2C
D B+13D→14A+12C

The correct answer is:
B+3D→4A+2C

Solution:
Rate =12d[C]dt=13-d[D]dt=14d[A]dt=-d[B]dt
So Stoichiometric coefficient of B = 1
Stoichiometric coefficient of D = 3
Stoichiometric coefficient of A = 4
Stoichiometric coefficient of C = 2
Therefore, the reaction is B + 3D → 4A + 2C.

Topic: Chemistry, Chemical Kinetics, NEET
The rate of respiration depends upon the

Options:
A quantity of protoplasm in cell
B quality of protoplasm in cell
C both a and b
D none of the above

The correct answer is:
both a and b

Solution:
There are eight major environmental factors that affects the rate of respiration and they are as follows:

Oxygen Content of the Atmosphere

Temperature

Light

Water Contents

Respirable Material

Carbon Dioxide concentration

Protoplasmic conditions

Other factors.

The rate of respiration depends upon the quality and quantity of protoplasm.

Topic: Biology, Respiration in Plants, NEET
The rate of steady volume flow of water through a capillary tube of length l and radius r, under a pressure difference of p is V. This tube is connected with another tube of the same length but half the radius, in series. Then the rate of steady volume flow through them is (the pressure difference across the combination is p)

Options:
A V16
B V17
C 16V17
D 17V16

The correct answer is:
V17

Solution:
The rate of flow of water inside a capillary
V=π p r48 n l,
Path difference p=V8 n lπ r4
In series combination p=p1+p2
where p1 and p2 are the pressure difference in the two tubes.
In series combination, the rate of flow of water V' will be the same in both the tubes.
Vr4=V′r4+V′×16r4
V=V′+16V′
V′=V17

Topic: Physics, Mechanical Properties of Fluids, NEET
The rate of the chemical reaction doubles for an increase of 10 K in absolute temperature from 298 K. What is Ea?

Options:
A Ea= 69.985 kJ mol–1
B Ea= 52.897 kJ mol–1
C Ea= 30.137 kJ mol–1
D Ea= 24.457 kJ mol–1

The correct answer is:
Ea= 52.897 kJ mol–1

Solution:
Correct Option is : (B)
Ea= 52.897 kJ mol–1

Topic: Chemistry, Chemical Kinetics, NEET
The rate of the reaction, A+B+C→P is given by, r= d[A] dt =K [A] 1/2 [B] 1/2 [C] 1/4 . The order of the reaction is

Options:
A 1
B 1/2
C 2
D 5/4

The correct answer is:
5/4

Solution:
For a reaction, A+B→ Products, if rate =K[A]m[B]n , then order of reaction = m + n.
r= d[A] dt =K [A] 1/2 [B] 1/2 [C] 1/4
Here order =12+12+14=54

Topic: Chemistry, Chemical Kinetics, NEET
The rate of the reaction, A+B+C→ Products, is given by

r=-dAdt=k[A]12[B]13[C]14

The order of reaction is

Options:
A 1
B 2
C 12
D 1312

The correct answer is:
1312

Solution:
Rate =k[A]12[B]13[C]14
Order = sum of powers
Order =12+13+14=1312

Topic: Chemistry, Chemical Kinetics, NEET
The rate of transpiration increases with the decrease of

Options:
A temperature
B wind velocity
C light
D atmospheric pressure

The correct answer is:
atmospheric pressure

Solution:
With the decrease in atmospheric pressure, the vapour pressure gradient across the stomata increases, and this causes rapid flow of vapours to the atmosphere. So with the decrease in atmospheric pressure rate of transpiration increases.

Topic: Biology, Transport in Plants, NEET
The rates of heat radiation from two patches of skin each of area A, on a patient's chest differ by 2%. If the patch of the lower temperature is at 300 K and emissivity of both the patches is assumed to be unity, the temperature of other patch would be

Options:
A 306 K
B 312 K
C 308.5 K
D 301.5 K

The correct answer is:
301.5 K

Solution:
According to Stefan's law.
E1=ÏT4 and E2=ÏT+âT4
â´ E2-E1E1= Ï[T+âT4-T4]ÏT4=4âTT
Now, E2-E1E1=2100=4âT300
â´ âT= 300Ã24Ã100=1.5 K
â´ Temperature of other patch = T+âT
= 300 +1.5 = 301.5 K

Topic: Physics, Thermal Properties of Matter, NEET
The ratio a/b (the terms used in van der Waal's equation) has the unit

Options:
A atm litre mol-1
B atm dm3mol-1
C dyne cm mol-1
D All of these

The correct answer is:
All of these

Solution:
P+ a n 2 v 2 vânb =nRT
The units of 'a' = atm litre2mol-2
=atm dm6 mol-2=dyne cm2mol-2
And the untis of 'b' = litre mol-1 = m3mol-1 =cm3mol-1
Hence, unit of a/b = atm litre2mol-1 / litre mol-1=atm litre mol-1
Similarly all other units are possible.

Topic: Chemistry, States of Matter, NEET
The ratio among the most probable velocity, mean velocity and root mean square velocity at T temperature for same gas is given by

Options:
A 1 : 2 : 3
B 1:2:3
C 2:3:8/π
D 2:8/π:3

The correct answer is:
2:8/π:3

Solution:
ump:uav:urms=2RTM:8RTπM:3RTM
=2:8/π:3 .

Topic: Chemistry, States of Matter, NEET
The ratio amongst most probable velocity, mean velocity and root mean square velocity is given by

Options:
A 2 : 3 : 8 π
B 2 : 8 Ï : 3
C 1: 2 : 3
D 1:2:3

The correct answer is:
2 : 8 π : 3

Solution:
Most probable velocity C mpv = 2RT M
Mean velocity C avg = 8RT ÏM
Root mean square velocity C rms = 3RT M
C mpv : C avg : C rms = 2RT M : 8RT ÏM : 3RT M âââââââââââââââââââââââ= 2 : 8 Ï : 3

Topic: Chemistry, States of Matter, NEET
The ratio between 2-carbon and 3-carbon intermediates having –NH2 group formed in photosynthetic oxidation cycle is

Options:
A 1 : 1
B 2 : 1
C 3 : 2
D 3 : 4

The correct answer is:
2 : 1

Solution:
During photorespiration in Peroxisome, two molecules of glycine (2H2NCH2-CO2) are transferred into mitochondrion, where they are converted into one molecule of serine (HOCH2-H2NCH-CO2). Thus, the ratio between 2C and 3C intermediates having –NH2 group is 2:1.

Topic: Biology, Photosynthesis in Higher Plants, NEET
The ratio between total acceleration of the electron in singly ionized helium atom and hydrogen atom (both in ground state) is

Options:
A 1
B 8
C 4
D 16

The correct answer is:
8

Solution:
Required acceleration is given by centripetal acceleration.
⇒ a=v2r
⇒ a ∝z21z
a∝z3
∴ a1a2=213=8

Topic: Physics, Atomic Physics, NEET
The ratio of acceleration due to gravity at a height 3R above earth's surface to the acceleration due to gravity on the surface of the earth is (R = radius of earth)

Options:
A 19
B 14
C 116
D 13

The correct answer is:
116

Solution:
The value of acceleration due to gravity changes with height (ie,Â altitude). If g′ is the acceleration due to gravity at a point, at height h above the surface of earth, then
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â g′=GMR+h2
but,Â Â Â Â Â Â Â Â Â Â Â Â Â Â g=GMR2
â´Â Â Â g′g=GMR+h2ÃR2GM=R2R+h2
Here,Â Â Â g′=GMR+h2=GMR+3R2
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =GM4R2=GM16R2=ge16

Topic: Physics, Gravitation, NEET
The ratio of acid strength of HOCN and HCN is about

Given Ka of HOCN= 1.2 Ã 10â4 and Ka of HCN=4.2 Ã 10â10

Options:
A 535 : 1
B 1 : 535
C 2.86Â ÃÂ 105Â :Â 1
D 2.86Â ÃÂ 104Â :Â 1

The correct answer is:
535 : 1

Solution:
H+HOCNH+HCN =Ka of HOCN1/2Ka of HCN1/2
=1.2Ã10-44.2Ã10-101/2= 535

Topic: Chemistry, Ionic Equilibrium, NEET
The ratio of angular momentum of electron in two successive orbit is a (a > 1) and their difference is b. then ab is equal to

Options:
A nn+1
B n+1n
C n+1n.h2π
D n+1n.2πh

The correct answer is:
n+1n.2πh

Solution:
Angular momentum in two successive orbits are nh2π and (n+1)h2π
So a=n+1nb=h2π
ab=(n+1)n.2πh

Topic: Chemistry, Structure of Atom, NEET
The ratio of angular speeds of minute hand and hour hand of a watch is

Options:
A 1 : 12

B 12 : 1

C 6 : 1

D 1 : 6

The correct answer is:
12 : 1

Solution:
In one hour, hour hand moves by 1 hour distance on clock while minute hand moves by 12 hour distance. marked on clock.
thus w1w2=2π1×122π
⇒w1w2=121

Topic: Physics, Laws of Motion, NEET
The ratio of area of orbit of first excited state of electron to the area of orbit of ground state, for hydrogen atom will be

Options:
A 16:1
B 4:1
C 8:1
D 1:8

The correct answer is:
16:1

Solution:
For first excited state, n = 2
A2A1=πr22πr12
rn∝n2Z

Topic: Chemistry, Structure of Atom, NEET
The ratio of areas of the electron orbits for the first excited state and the ground state for the hydrogen atom is

Options:
A 4 : 1

B 16 : 1
C 8 : 1
D 2 : 1

The correct answer is:
16 : 1

Solution:
The radius of the orbit of the electron in the nth excited state
re = n24ÏÎµ0h24Ï2mZe2
For the first excited state
n=2 , Z=1
âµ râ¡ â² = 4Îµ0h2Ïme2
For the ground state of hydrogen atom
n=1 , Z=1
âµ râ¡ â³ = h2Îµ0Ïme2
The ratio of radius
râ¡ â² râ¡ â³ =41
The ratio of area of the electron orbit for hydrogen atom
Aâ¡ â² Aâ¡ â³ =4Ïr'24Ïr''2
Aâ¡ â² Aâ¡ â³ =161

Topic: Physics, Atomic Physics, NEET
The ratio of close packed atoms to tetrahedral holes in cubic close packing is

Options:
A 1 : 1
B 1 : 3
C 1 : 2
D 2 : 1

The correct answer is:
1 : 2

Solution:
In close packed lattice atoms =Nc8+Nf2
=8×18+6×12=1+3=4
Every constitute has 2 tetrahedral voids
So tetrahedral voids =4×2=8
Ratio will be 4 : 8 = 1 : 2.

Topic: Chemistry, Solid State, NEET
The ratio of coefficients of HNO3,Fe(NO3)2 and NH4NO3 in the following redox equation.
Fe+HNO3→Fe(NO3)2+NH4NO3+H2O in the balance form will be

Options:
A 10:1:4
B 10:4:1
C 4:10:1
D 4:1:10

The correct answer is:
10:4:1

Solution:
The balanced redox equation is
4Fe+10HNO3→4Fe(NO3)2+NH4NO3+3H2O
Thus, the coefficients ratio of HNO3,Fe(NO3)2 and NH4NO3 respectively are 10:4:1.

Topic: Chemistry, Redox Reactions, NEET
The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is:
(c= speed of electromagnetic waves)

Options:
A 1 :1
B 1 :c
C 1 :c2
D c :1

The correct answer is:
1 :1

Solution:
​​​In EMW, electric field and magnetic field have same energy density and same intensities.

Topic: Physics, Electromagnetic Waves, NEET, NEET 2020 (Phase 1)
The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4 \times 10^{39}$. The ratio of the proportionality constant, $\mathrm{K}=$ $\frac{1}{4 \pi \varepsilon_0}$ to the Gravitational constant G is nearly (Given that the charge of the proton and electron each $=1.6 \times 10^{-19} \mathrm{C}$, the mass of the electron $=9.11 \times 10^{-31} \mathrm{~kg}$, the mass of the proton $=$ $\left.1.67 \times 10^{-27} \mathrm{~kg}\right)$

Options:
A $10^{20}$
B $10^{30}$
C $10^{40}$
D 10

The correct answer is:
$10^{20}$

Solution:
A.T.Q, we have,
$\begin{aligned}
\frac{\mathrm{F}_e}{\mathrm{~F}_{\mathrm{G}}} & =\frac{\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r^2}}{\frac{\mathrm{G} m_1 m_2}{r^2}} \\
2.4 \times 10^{39} & =\frac{\mathrm{K}}{\mathrm{G}} \times \frac{\left(1.6 \times 10^{-19}\right)^2}{\left(9.1 \times 10^{-31} \times 1.67 \times 10^{-22}\right)} \\
& {\left[\because \mathrm{K}=\frac{1}{4 \pi \varepsilon_0}\right] }
\end{aligned}$
Hence,
$\begin{aligned}
\frac{\mathrm{K}}{\mathrm{G}} & =\frac{2.4 \times 10^{39} \times 9.1 \times 10^{-31} \times 1.67 \times 10^{-27}}{1.6 \times 10^{-19} \times 1.6 \times 10^{-19}} \\
& =14.247 \times 10^{19} \\
& =1.4247 \times 10^{20} \approx 10^{20}
\end{aligned}$

Topic: Physics, Electrostatics, NEET, NEET 2022 (Phase 2)
The ratio of density of a gas A and gas B is three. If the molecular mass of A is M , then molecular mass of B is

Options:
A 3M
B M/3
C M/3
D 3M

The correct answer is:
M/3

Solution:
dâM⇒d1d2=M1M2 ; 3dd=MM2 ; M2=M3

Topic: Chemistry, States of Matter, NEET
The ratio of displacement to amplitude, when the kinetic energy of a body executing SHM is thrice the potential energy is,

Options:
A 32
B 43
C 12
D 23

The correct answer is:
12

Solution:
Kinetic energy in SHM,
K=12mÏ2a2-x2
Potential energy in SHM,
U=12mÏ2x2
Given that, K=3U
â 12mÏ2a2-x2=3⋅12mÏ2x2
a2-x2=3x2
a2=4x2
a=2x
2x=a
xa=12

Topic: Physics, Oscillations, NEET
The ratio of electric field intensity at P & Q in the shown arrangement is

Options:
A 1Â :2
B 2Â :1
C 1 :1
D 4Â :3

The correct answer is:
1 :1

Solution:
EP=kqr2
EQ=kq2r2+k3q2r2=4kq4r2
Because the charges are positive on both the spheres so electric field at point Q is in the same direction, so they added algebraically
EP :EQ=1 :1

Topic: Physics, Electrostatics, NEET
The ratio of energies of emitted radiation by a black body at 600 k and 900 k, when the surrounding temperature is 300 k, is

Options:
A 516
B 716
C 316
D 916

The correct answer is:
316

Solution:
E1E2=T12-Ts4T24-T24
=6004-30049004-3004=316

Topic: Physics, Thermal Properties of Matter, NEET
The ratio of escape velocity at earth υe to the escape velocity at a planet υp whose radius and mean density are twice as that of earth is:

Options:
A 1:2
B 1:22
C 1:4
D 1:2

The correct answer is:
1:22

Solution:
vevP=2GMeRe2GMPRP=MeRPMPRe=ρe43 πRe3RPρp43 πRP3Re
vevP=ρeRe2ρpRP2=12×22=122

Topic: Physics, Gravitation, NEET, NEET 2016 (Phase 1)
The ratio of F2 generation of a dihybrid cross having pure, monohybrids, dihybrids plants is

Options:
A 1:2:1
B 1:2 :4
C 1: 4 :8
D 1:1:2

The correct answer is:
1:2:1

Solution:
A typical Dihybrid Cross AaBb x AaBb will produce 16 types of offsprings as follows:
Homozygous/ Pure genotypes: AABB 1, AAbb 1, aaBB 1, aabb 1 : Total 4
Monohybrid genotypes: AaBB 2, AABb 2, aaBb 2, Aabb 2 : Total 8
Dihybrid genotypes : AaBb 4 : Total 4
Thus the ratio of pures : monohybrids : dihybrids in the F2 generation of a dihybrid cross is 4: 8: 4 which is 1:2:1

Topic: Biology, Principles of Inheritance and Variation, NEET
The ratio of frequencies of two pendulum are 2:3, then their lengths are in ratio

Options:
A 2/3
B 3/2
C 4/9
D 9/4

The correct answer is:
9/4

Solution:
The time period (T) of a simple pendulum length l, is given by
T=2πlg=1frequency(n)
where g is acceleration due to gravity.
∴ n1n2=l2l1
⇒ l1l2=n2n12
Given, n2n1=32
∴ l1l2=322=94

Topic: Physics, Oscillations, NEET
The ratio of intensity of magnetization and magnetizing field is called

Options:
A Permeability
B Magnetic intensity
C Diamagnetics
D Magnetic susceptibility

The correct answer is:
Magnetic susceptibility

Solution:
The ratio of intensity of magnetization and magnetizing field is called Magnetic Susceptibility ImH=Xm .

Topic: Physics, Magnetic Properties of Matter, NEET
The ratio of kinetic energy and the total energy of the electron in the nth quantum state of Bohr's atomic model of a hydrogen atom is

Options:
A -2
B -1
C 2
D 1

The correct answer is:
-1

Solution:
The Kinetic energy of the electron in the nth state
K=mZ2e48ε02h2n2
The total energy of the electron in the nth state
T = -mZ2e48ε02h2n2
∴ KT= -1

Topic: Physics, Atomic Physics, NEET
The ratio of kinetic energy at mean position to potential energy at A 2 ( A is the amplitude) of a particle performing SHM is (Consider the mean position as reference point)

Options:
A 2:1
B 4:1
C 8:1
D 1:1

The correct answer is:
4:1

Solution:
Kinetic energy K=12mÏ2(A2-y)2
At mean position y=0
K=12mÏ2(A2)
Potential energy U=12mÏ2y2 ...(i)
U at y=A2
U=12 mA24 Ï2 ...(ii)
Dividing Eq. (i) by Eq. (ii), we get
KU=41

Topic: Physics, Oscillations, NEET
The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is

Options:
A 2:â1
B 1:â1
C 1:1
D 1:−2

The correct answer is:
1:−1

Solution:
In Hydrogen atom, for an electron
undefined
KEETotal=1-1

Topic: Physics, Atomic Physics, NEET, NEET 2018
The ratio of magnetic fields due to a bar magnet at the two axial points P1 and P2 which are separated from each other by 10 cm is 25:2. P1 Point is situated at 10 cm from the centre of the magnet. (Points P1 and P2 are on the same side of magnet and distance of P1 and P2 from the centre of magnet is much greater than the distance of two ends of the magnet from the centre). Magnetic length of the bar magnet is

Options:
A 5 cm

B 10 cm

C 15 cm

D 20 cm

The correct answer is:
10 cm

Solution:
B 1 B 2 = 25 2
Î¼ 0 4Ï M d 1 ( d 1 2 â l 2 ) 2 Î¼ 0 4Ï M d 2 ( d 2 2 â l 2 ) 2 = 25 2
d 1 d 2 Ã ( d 2 2 â l 2 ) 2 ( d 1 2 â l 2 ) 2 = 25 2
d 1 =10 cm, d 2 =20 cm
10 20 Ã ( 20 2 â l 2 10 2 â l 2 ) 2 = 25 2
400â l 2 =5( 100â l 2 )
4 l 2 =100â l 2 =25
l=5 cm

Topic: Physics, Magnetic Properties of Matter, NEET
The ratio of magnetic fields due to a smaller bar magnet in the end-on position and broadside-on position is

Options:
A 14
B 12
C 1
D 2

The correct answer is:
2

Solution:
End on position corresponds to axial line and Broadside on position corresponds to equatorial line. Therefore, B1B2=2.

Topic: Physics, Magnetic Properties of Matter, NEET
The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecules is:

Options:
A 1 : 4
B 7 : 32
C 1 : 8
D 3 : 16

The correct answer is:
7 : 32

Solution:
Let the mass of oxygen be x gm
â´ Mass of nitrogen = 4x gm
Number of molecules = 6.023 x 1023 x number of moles
â´ Ratio = 6.023 Ã 1 0 2 3 Ã no. of moles of oxygen 6.023 Ã 1 0 2 3 Ã no. of moles of nitrogen
= m O 2 M O 2 m N 2 M N 2 = x 3 2 4 x 2 8
= 7 3 2 = 7 : 32

Topic: Chemistry, Some Basic Concepts of Chemistry, NEET
The ratio of methane, ammonia and hydrogen in Stanley Miller's experiment was

Options:
A 3 : 1 : 2
B 2 : 1 : 2
C 1 : 2 : 1
D 5 : 4 : 1

The correct answer is:
2 : 1 : 2

Solution:
Stanley Miller and Harold Urey synthesized amino acid by passing an electric discharge in a mixture of ammonia (NH3), hydrogen (H2), water vapours (H2O) and methane (The ratio of CH4, NH3 and H2 in large flask was 2 : 1 : 2.

Topic: Biology, Evolution, NEET
The ratio of minimum to maximum wavelengths in Balmer series of H-atom is

Options:
A 5:9
B 5:36
C 1:4
D 3:4

The correct answer is:
5:9

Solution:
For Balmer series n1=2

We know that
1λmin=R14-1∞=R4
1λmax=R14-19=5R36⇒λminλmax=4R365R=59

Topic: Physics, Atomic Physics, NEET
The ratio of minimum to maximum wavelengths in Balmer series of H-atom is

Options:
A 5:9
B 5:36
C 1:4
D 3:4

The correct answer is:
5:9

Solution:
We know that
1λmin=R14-1∞=R4
1λmax=R14-19=5R36⇒λminλmax=4R365R=59

Topic: Physics, Atomic Physics, NEET
The ratio of orbit of first excited state of electron to the area of orbit of ground level, for hydrogen atom, will be

Options:
A 16 : 1
B 4 : 1
C 8 : 1
D 2 : 1

The correct answer is:
16 : 1

Solution:
For first excited state
n = 2
A2A1=πr22πr12=n24n14=161
r=n2Z×0.529Å .

Topic: Chemistry, Structure of Atom, NEET
The ratio of packing density in fcc, bcc and simple cubic structure is respectively,

Options:
A 1 : 0.92 : 0.70
B 0.70 : 0.92 : 1
C 1 : 0.70 : 0.92
D 0.92 : 0.70 : 1

The correct answer is:
1 : 0.92 : 0.70

Solution:
Packing fraction ion fcc, bcc and sc are 0.74, 0.68 and 0.52 respectively.
So ratio =0.740.74:0.680.74:0.520.74
=1:0.92:0.70.

Topic: Chemistry, Solid State, NEET
The ratio of potential differences between 1 Î¼F and 5 Î¼F capacitors is

Options:
A 1:2
B 3:1
C 1:5
D 10:1

The correct answer is:
1:5

Solution:
3 Î¼F & 1 Î¼F are in parallel hence Cnet=C1+C2 hence is equal to 4 Î¼F.
Now 2 Î¼F & 2 Î¼F are in series with this equivalent capacitor 4 Î¼F .Solving 2 Î¼F and 2 Î¼F are in series, we get 1 Î¼F.
â´V4Î¼F=VÃC1Î¼FC1Î¼F+C4Î¼F
âV4Î¼F=10Ã11+4=2
âV4Î¼F=2 V
(potential difference across 4 Î¼F capacitor is calculated by voltage division rule)
â´ V5Î¼F=10 V
(Potential difference across 5 Î¼F is same as battery)
â´ V1Î¼FV5Î¼F=210=15

Topic: Physics, Electrostatics, NEET