AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The population \( P \) of a town decreases at a rate proportional to the number by which the population exceeds-10 30, proportionality constant being \( \mathrm{k}>0 \) Find Population at any time \( t \) given initial population of the town being \( 2500 ., \) then \( P=1000+1500 e^{-k t} \)
then \( k=? \)
A \( \cdot k=\frac{1}{10} \ln \left(\frac{5}{3}\right) \)
B . \( k=\frac{-1}{10} \ln \left(\frac{5}{3}\right) \)
c. \( k=\ln \left(\frac{5}{3}\right) \)
D \cdot \( k=\frac{1}{10} \ln \left(\frac{3}{5}\right) \)
Subject: Physics
Assertion
Weight of solid in air is \( \mathrm{W} \) and in water is \( T=\frac{2 W}{3} \) Then relative density of
solid is 3.0
Reason
Relative density of any solid is given by \( R D=\frac{\text { Weight in air }}{\text { Change in weight in water }} \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
\( f(x)=\left\{\begin{array}{cc}-1, & x<-1 \\ x^{3}, & -1 \leq x \leq 1 \\ 1-x, & 1<x<2 \\ 3-x^{2} & x>2\end{array}, \) then \right.
A. \( \lim _{x \rightarrow-1} f(x)=1 \)
B \( \cdot \lim _{x \rightarrow 1} f(x)=1 \)
c. \( \lim _{x \rightarrow 2} f(x)=-1 \)
D. \( \lim _{x \rightarrow 2^{-}} f(x)=0 \)
Subject: Maths
The probability that a marksman will hit a target is given as \( \frac{1}{5}, \) then his probability of at least one hit in 10 shots is
\( ^{\mathrm{A}} \cdot_{1}-\left(\frac{4}{5}\right)^{10} \)
в. \( \frac{1}{510} \)
c. \( _{1-\frac{1}{5^{10}}} \)
D. None of these
Subject: Physics
A body undergoing \( S H M \) about the
origin has its equation is given by \( \boldsymbol{x}= \) \( 0.2 \cos 5 \pi t . \) Find its average speed in
\( \boldsymbol{m} / \boldsymbol{s} \) from \( \boldsymbol{t}=\mathbf{0} \) to \( \boldsymbol{t}=\mathbf{0 . 7} \boldsymbol{s e c} \)
Subject: Maths
Let \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{n \times n} \) be a square matirx and
let \( c_{i j} \) be cofactor of \( a_{i j} \) in A. If \( C=\left[c_{i j}\right] \)
then
B . \( |C|=|A|^{n-1} \)
c. \( |C|=|A|^{n-2} \)
D. none of these
Subject: Physics
A person travels along a straight road for the first half length with a velocity
\( V_{1} \) and the second half length with a
velocity \( V_{2} . \) Then the mean velocity v is given by
A \( \cdot v=\frac{v_{1}+v_{2}}{2} \)
B. \( v=\sqrt{v_{1} v_{2}} \)
c. \( v=\sqrt{\frac{v_{1}}{v_{2}}} \)
D. \( \frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}} \)
Subject: Chemistry
If the pH of pure water is \( 7, \) then the
hydrogen ion concentration, \( \left[\boldsymbol{H}^{+}\right] \) in mol
\( \mathbf{L}^{-1} \) will be:
A \( \cdot 10^{-7} \)
7
B. 0
\( c \cdot 7 \)
D. \( 10^{+7} \)
Subject: Chemistry
The boiling points of neon and krypton
\( \operatorname{are}-245.9^{\circ} \mathrm{C} \) and \( -152.9^{\circ} \mathrm{C} \)
respectively. Using these data estimate the boiling point of argon. (report answer as the negative of the closest integer)
A \( \cdot-289^{\circ} C \)
в. \( -299^{\circ} \mathrm{C} \)
c. \( -199^{\circ} \mathrm{C} \)
D. \( -189^{\circ} \mathrm{C} \)
Subject: Physics
Initially the spheres \( A \) and \( B \) are at
potential \( V_{A} \) and \( V_{B} \) respectively. Now
sphere \( \mathrm{B} \) is earthed by closing the
switch. The potential of \( A \) will now
become:
\( A \)
B. \( V_{A} \)
\( \mathbf{c} \cdot V_{A}-V_{B} \)
D. \( V_{B} \)
Subject: Maths
Calculate the area of a trapezoid with bases of 22 and \( 10 \mathrm{m}, \) and a height of 15
\( \mathrm{m} \)
A \( .240 m^{2} \)
В. \( 230 m^{2} \)
c. \( 220 m^{2} \)
D. \( 210 m^{2} \)
Subject: Physics
The radius of a nucleus of an atom
\( (Z=50) \) is \( 9 \times 10^{-10} m \) then potential
on its surface, will be:
A . \( 80 V \)
B. \( 8 k V \)
\( \mathrm{c} .9 \mathrm{V} \)
D. \( 9 k V \)
Subject: Chemistry
The plot of \( \log _{10} K_{p} \) against \( 1 / T \) for the reaction:
\[
\boldsymbol{S O}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g})
\]
is a straight line with slope \( =4.95 \times \)
\( 10^{3} . \) If the \( K_{p} \) at 25 if standard
entropies for \( \boldsymbol{S O}_{2}(\boldsymbol{g}), \boldsymbol{O}_{2}(\boldsymbol{g}) \) and
\[
\boldsymbol{S O}_{3}(\boldsymbol{g}) \text { are } \mathbf{2 4 8 . 2}, \mathbf{2 0 5 . 1} \text { and }
\]
\( 256.8 J K^{-1} m o l^{-1} \) at 25 respectively is
\[
\boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{X} \times \mathbf{1 0}^{11} \text { then } \mathbf{1 0} \boldsymbol{X}
\]
is
Subject: Physics
A particle of charge \( 16 \times 10^{-18} C \)
moving with velocity \( 10 m / s \) along the
X-axis enters a region where a
magnetic field of induction \( B \) is along the \( Y \) -axis, and an electric field of
magnitude \( 10 V m^{-1} \) is along the negative Z-axis. If the charged particle continues moving along the X-axis, the
magnitude of \( B \) is :
A \( \cdot 1 W b / m^{2} \)
B . \( 10^{5} \mathrm{Wb} / \mathrm{m}^{2} \)
\( \mathbf{c} \cdot 10^{6} W b / m^{2} \)
D. \( 10^{-3} W b / m^{2} \)
Subject: Biology
Assertion
Human ancestors never used their tails
and so the tail expressing gene has disappeared in them.
Reason
Lamarck's theory of evolution is popularly called theory of continuity of germplasm.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
Let \( \boldsymbol{f} \) be a positive function. If \( \boldsymbol{I}_{\mathbf{1}}= \) \( \int_{1-k}^{k} x f x(1-x) d x, I_{2}= \)
\( \int_{1-k}^{k} f x(1-x) d x, \) where \( 2 k-1>0 \)
then \( \frac{\boldsymbol{I}_{1}}{\boldsymbol{I}_{2}} \) is
A . 2
B. \( k \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Physics
Three forces \( A, B \) and \( C \) acting at a point are in equilibrium. The ratio of angles between \( A \) and \( B ; B \) and \( C ; \) and
\( A \) and \( C \) is \( 1: 2: 3 . \) Then, \( A: B: C \) is
A. \( 1: \frac{\sqrt{3}}{2}: \frac{1}{2} \)
B. \( \frac{1}{2}: \frac{\sqrt{3}}{2}: 1 \)
c. \( _{1: \frac{1}{2}: \frac{1}{3}} \)
D. \( 1: \frac{1}{\sqrt{2}}: \frac{1}{\sqrt{3}} \)
E. None of these
Subject: Chemistry
The equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) for the reaction \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \) is 4.5
What would be the average molar mass (in g/mol) of an equilibrium
mixture of \( N_{2} O_{4} \) and \( N O_{2} \) formed by
the dissociation of pure \( N_{2} O_{4} \) at a total
pressure of 2 atm?
\( \mathbf{A} \cdot 69 \)
в. 57.5
\( c .80 .5 \)
D. 85.5
Subject: Physics
A planet has a core and on outer shell of
radii \( \boldsymbol{R} \) and \( 2 \boldsymbol{R} \) respectively. The density
of the core is \( x \) and that of outer shell is
\( y . \) The acceleration due to gravity at
the surface of planet is same as that at
depth \( R \) The ratio of \( x \) and \( y \) is \( \frac{-}{3} . \) Find
\( n \)
Subject: Physics
If the Poisson's ratio of a solid is \( \frac{2}{5}, \) then the ratio of its young's modulus to the rigidity modulus is
A \( \cdot \frac{5}{4} \)
в. \( \frac{7}{15} \)
c. \( \frac{14}{9} \)
D. \( \frac{14}{5} \)
Subject: Physics
The magnetic field \( B=2 t^{2}+4 t^{2} \)
(where \( t= \) time ) is applied perpendicular to the plane of a circular wire of radius \( r \) and resistance \( R \). If all
the units are in SI the electric charge that flows through the circular wire during \( t=0 s \) to \( t=2 s \) is
A \( \cdot \frac{6 \pi r^{2}}{R} \)
в. \( \frac{24 \pi r^{2}}{R} \)
c. \( \frac{32 \pi r^{2}}{R} \)
D. \( \frac{48 \pi r^{2}}{R} \)
Subject: Chemistry
Assertion
\( X e F_{4} \) exists while \( X e H_{4} \) does not exist
Reason
\( \ln X e H_{4} \) d-orbital contraction is absent
A. The Assertion is true, the Reason is true and Reason is the correct explanation for Assertion
B. The Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
c. Assertion is true, Reason is false.
D. Assertion is false, Reason is true.
Subject: Maths
If \( x, y \) and \( z \) are positive real numbers
such that \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{a} \) then \( - \)
A \( \cdot \frac{1}{x}+\frac{1}{y}+\frac{1}{z} \geq \frac{9}{a} \)
B. \( \frac{1}{x}+\frac{1}{y}+\frac{1}{z}<\frac{9}{a} \)
C \( \cdot(a-x)(a-y)(a-z)>\frac{8}{27} a^{3} \)
D. \( (a-x)(a-y)(a-z)>a^{3} \)
Subject: Physics
The distance of closest approach of the particle to the nucleus will be
A \( \cdot 6.4 \times 10^{-13} \mathrm{m} \)
B . \( 4.3 \times 10^{-13} \mathrm{m} \)
c. \( 2.1 \times 10^{-13} \mathrm{m} \)
D. \( 3.4 \times 10^{-14} \mathrm{m} \)
Subject: Physics
A body is executing S.H.M. When its displacement from the mean position is \( 4 \mathrm{cm} \) and \( 5 \mathrm{cm}, \) the corresponding
velocity of the body is \( 10 \mathrm{cm} / \mathrm{sec} \) and 8 \( \mathrm{cm} / \mathrm{sec} . \) Then the time period of the body is:
A \( .2 \pi \sec \)
B . \( \pi / 2 \) sec
\( c . \pi \mathrm{sec} \)
D. 3\pi/2 sec
Subject: Maths
There are \( n \) distinct white and \( n \)
distinct black balls. The number of ways of arranging them in a row so that neighbouring balls are of different colours is:
A \( \cdot n+1 C_{2} \)
B \( \cdot(2)(n !)^{2} \)
c. \( \frac{(n !)}{2} \)
D. none of these
Subject: Physics
For a ideal gas.
This question has multiple correct options
A. The change in internal energy in a constant pressure process from temperature \( T_{1} \) to \( T_{2} \) is equal to \( N C_{V}\left(T_{2}-T_{1}\right), \) where \( C_{V} \) is the molar specific heat at
constant volume and \( n \) is the number of moles of the
gas
B. The change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process
C. The internal energy does not change in an isothermal process
D. No heat is added or removed in an adiabatic process
Subject: Chemistry
:he rate constant of reaction \( 2 A+ \)
\( B \longrightarrow C \) is \( 2.57 \times 10^{-5} \) it \( m o l e^{-1} s e c^{-1} \)
after 10 sec. \( 2.65 \times 10^{-5} \) it
mole \( ^{-1} \) sec \( ^{-1} \) after 20 sec. and \( 2.55 \times \)
\( 10^{-5} \) it mole\( ^{-1} \)sec\( ^{-1} \) after 30 sec. The
order of the reaction is:
A.
B. 1
\( c \cdot 2 \)
D. 3
Subject: Chemistry
Select the correct statement(s):
This question has multiple correct options
A. When Al is added to potassium hydroxide solution,hydrogen gas is evolved
B. \( H_{2} S i F_{6} \) is formed when silica reacts with hydrogen fluoride followed by hydrolysis
C. Phosphine gas is formed when red phosphorus is heated with NaOH
D. \( \left(N H_{4}\right)_{2} S O_{4} . F e S O_{4} .6 H_{2} O \) is called alums
Subject: Maths
If \( \boldsymbol{y}=\log _{e}\left(\boldsymbol{x}+\log _{e}(\boldsymbol{x}+\ldots .)\right), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
at \( \left(x=e^{2}-2, y=\sqrt{2}\right) \) is
A \( \cdot \frac{1}{e^{\sqrt{2}}-1} \)
B. \( \frac{\log 2}{2 \sqrt{2}\left(e^{2}-1\right)} \)
\( ^{\mathbf{c}} \cdot \frac{\sqrt{2} \log \frac{e}{2}}{\left(e^{2}-1\right)} \)
D. None of these
Subject: Physics
Two identical concentric coils \( X \) and \( Y \)
carrying currents in the ratio 1: 2 are
arranged in mutually perpendicular planes. If the magnetic field due to coil \( X \) is \( B \) the net field at their common
centre is:
A. \( B \)
в. \( 2 B \)
\( c .3 B \)
D. \( \sqrt{5} B \)
Subject: Physics
Q Type your question-
respectively as shown in figure.
Assuming that these are placed in the same plane, the magnetic fields will be zero at the centre of the loop when the
separation H is
\( A \cdot \frac{1_{e}}{I_{I} \pi} \)
В \( \cdot \frac{I_{c} R}{I_{e}} \)
\( c \cdot \frac{\pi 1}{I F} \)
D. \( \frac{1_{e}}{I_{R}} \)
Subject: Physics
A rubber ball is dropped from a height of \( 5 \mathrm{m} \) on a plane. On bouncing it rises to 1.8m. The ball loses its velocity on
bouncing by a factor of
A \( .16 / 25 \)
в. \( 2 / 5 \)
c. \( 3 / 5 \)
D. \( 9 / 25 \)
Subject: Maths
Verify:
\( \boldsymbol{x}^{3}+\boldsymbol{y}^{3}=(\boldsymbol{x}+\boldsymbol{y})\left(\boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}\right) \)
Subject: Maths
Let \( \boldsymbol{f} \) be differential for all \( \boldsymbol{x} \). If \( \boldsymbol{f}(\mathbf{1})= \)
-2 and \( f^{\prime}(x) \geq 2 \) for \( x \epsilon[1,6], \) then \( ? \)
A. \( f(6)=5 \)
В. \( f(6)<5 \)
C. \( f(6)<8 \)
D. \( f(6) \geq 5 \)
is \( 5(6) \geq 5 \)
Subject: Maths
Consider the equation \( 2+\mid x^{2}+4 x+ \)
\( \mathbf{2} \mid=\boldsymbol{m}, \boldsymbol{m} \in \boldsymbol{R} \) Set of all real values of
\( m \) so that given equation has four distinct solutions, is
в. (1,2)
\( c \cdot(1,3) \)
D. (2,4)
Subject: Chemistry
Four samples of water \( A, B, C \) and \( D \) have the DO values 1 mg/litre, 3 mg / litre, 5 mg/litre and \( 8 \mathrm{mg} / \) litre respectively Which one is more polluted sample of
water?
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
Subject: Chemistry
Which of the following reactions will not get affected on increasing the pressure?
\( \mathbf{A} \cdot 2 H_{2(g)}+C O_{(g)} \rightleftharpoons C H_{3} O H_{(g)} \)
B. \( 4 N H_{3(g)}+5 O_{2(g)} \rightleftharpoons 4 N O_{(g)}+6 H_{2} O_{(g)} \)
C. \( C H_{4(g)}+2 S_{2(g)} \rightleftharpoons C S_{2(g)}+2 H_{2} S_{(g)} \)
D. \( P C l_{5(g)} \rightleftharpoons P C l_{3(g)}+C l_{2 g} \)
Subject: Maths
The following distribution gives the
state-wise teacher-student ratio in
higher secondary schools of India. Find
the mode and mean of this data.
Interpret, the two measures.
\( \begin{array}{llll}\text { Number } & & \text { Number } & \\ \text { of } & \text { Number } & \text { of } & \text { Numb } \\ \text { students } & \text { of } & \text { students } & \text { of } \\ \text { per } & \text { States/U.T } & \text { per } & \text { states } \\ \text { teacher } & & \text { Teacher } & \\ \text { 15-20 } & 3 & \text { 35-40 } & 3 \\ \text { 20-25 } & 8 & 40-45 & 0 \\ \text { 25-30 } & 9 & \text { 45-50 } & 0 \\ \text { 30-35 } & 10 & \text { 50-55 } & 2\end{array} \)
Subject: Physics
Five particles each of mass ' \( m \) ' are kept
at five vertices of a regular pentagon. A sixth particle of mass ' \( M^{\prime} \) is kept at
centre of the pentagon' \( O \) '. Distance
between ' \( M \) ' and ' \( m \) ' is 'a'. Find
(i) net force on \( ^{\prime} \boldsymbol{M}^{\prime} \)
(ii) magnitude of net force on ' \( M^{\prime} \) if any one particle is removed from one of the vertices.
Subject: Chemistry
For the cell reaction \( : C u^{2+}(a q)\left(C_{1}\right)+ \)
\( Z n(s) \rightarrow Z n^{2+}(a q)\left(C_{2}\right)+C u(s) \) the
change in free energy \( \Delta G \) at a given temperature is a function of
\( A \cdot \ln C_{1} \)
в. \( \ln \left(\frac{C_{2}}{C_{1}}\right) \)
\( \mathrm{c} \cdot \ln \left(C_{2}+C_{2}\right) \)
D. \( \ln \left(C_{2}\right) \)
Subject: Chemistry
Which of the following order is correct for the IR vibrational frequency of CO?
\( ^{\mathbf{A}} \cdot\left[F e(C O)_{4}\right]^{2-}<\left[C o(C O)_{4}\right]^{-}<\left[N i(C O)_{4}\right] \)
\( ^{\mathrm{B}}\left[F e(C O)_{4}\right]^{2-}>\left[C o(C O)_{4}\right]^{-}>\left[N i(C O)_{4}\right] \)
\( ^{\mathbf{c}} \cdot\left[F e(C O)_{4}\right]^{2-}>\left[C o(C O)_{4}\right]^{-}<\left[N i(C O)_{4}\right] \)
D \( \cdot\left[F e(C O)_{4}\right]^{2-}<\left[C o(C O)_{4}\right]^{-}>\left[N i(C O)_{4}\right] \)
Subject: Physics
Assertion
The stress-strain relationship in elastic region need not be linear and can be
non-linear.
Reason
Steel has non linear,profile in elastic
zone
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
Two connected charges of \( +q \) and \( -q \)
respectively are at a fixed distance \( \boldsymbol{A B} \)
apart in a non uniform electric field
whose lines of force are shown in the
figure. The resultant effect on the two
charges is
A. a torque in the plane of the paper and no resultant force
B. a resultant force in the plane of the paper and no torque
c. a torque normal to the plane of the paper and no resultant force
D. a torque normal to the plane of the paper and a resultant force in the plane of the paper
Subject: Physics
\( 660 J \) heat energy is supplied to a solid
of mass \( 275 g . \) When its temperature rises by \( 1^{\circ} \mathrm{C} \), calculate specific heat capacity of the solid:
A \( \cdot 1.2 J / g^{o} C \)
в. \( 4.8 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C} \)
c \( \cdot 2.4 J / g^{\circ} C \)
D. \( 9.6 J / g^{o} C \)
Subject: Chemistry
Which of the following is true regarding an Ne atom with a mass number of 20
and an \( O^{2-} \) ion with a mass number of
\( 16 ? \)
A. The contain the same number of protons
B. The contain the same number of neutrons
C. The contain the same number of protons plus neutrons
D. They are isoelectronic.
E. They are isomers
Subject: Chemistry
Which of the following is the correct increasing order of boiling point of the following compounds?
I) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
II) \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \)
\( \boldsymbol{O} \boldsymbol{H} \)
III) \( \boldsymbol{C H}_{3}-\boldsymbol{O}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
\( \mathbf{A} \cdot l l<l<l l l \)
в. \( \| l<l l<l \)
c. \( l<l l<l l l \)
D. \( l l<l l l<l \)
Subject: Physics
A scooterist travels at \( 30 \mathrm{km} / \mathrm{h} \) along
straight path for 20 min. What is distance?
A . \( 1.5 \mathrm{km} \)
B. \( 6 \mathrm{km} \)
\( c \cdot 10 \mathrm{km} \)
D. 90 km
Subject: Chemistry
The conversion factor to change
kilograms to pounds is:
A \( \cdot \frac{1 \mathrm{kg}}{2.20 \mathrm{lb}} \)
B. \( \frac{2.20 l b}{1 k g} \)
C. \( \frac{1 l b}{454 k g} \)
D. \( \frac{454 \mathrm{kg}}{1 \mathrm{lb}} \)
Subject: Chemistry
Assertion
Red phosphorus is preferred to white phosphorus in the manufacture of
matches.
Reason
Red phosphorus is non-poisonous in
nature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
The end \( B \) of uniform rod \( A B \) which
makes angle \( \theta \) with the floor is being
pulled with a velocity \( v_{0} \) as shown
Taking the length of rod as \( l \), calculate
the following at the instant when \( \boldsymbol{\theta}= \)
\( 37^{\circ} \)
(a) The velocity of end \( \boldsymbol{A} \)
(b) The angular velocity of rod
(c) Velocity of \( C M \) of the rod.
Subject: Maths
Three vectors of magnitudes \( a, 2 a, 3 a \) meeting a point and three directions are along the diagonals of three adjacent faces of a cube. The magnitude of their resultant is
\( \mathbf{A} \cdot 3 a \)
B. \( 5 a \)
\( c \cdot 2 a \)
D. \( 4 a \)
Subject: Maths
Let \( A \) and \( B \) be two invertible matrices of
order \( 3 \times 3 . \) If det \( \left(A B A^{T}\right)=8 \) and det
\( \left(A B^{-1}\right)=8, \) then det \( \left(B A^{-1} B^{T}\right) \) is
equal to:
A \( \cdot \frac{1}{4} \)
B. 16
\( c \)
D. \( \frac{1}{16} \)
Subject: Physics
A ray of light is normally incident on one face of an equilateral glass prism. What is the angle of incidence on the first
face of the prism?
\( \mathbf{A} \cdot 0^{\circ} \)
B . \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
A current of \( 10 \mathrm{A} \) is flowing in a wire of
length \( 1.5 \mathrm{m} . \) A force of \( 15 \mathrm{N} \) acts on it when it is placed in a uniform magnetic field of 2 T. The angle between the magnetic field and the direction of the
current is:
A \( .30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 90^{\circ} \)
Subject: Chemistry
The equilibrium constants for the two complex formation are :
\( \boldsymbol{4} \boldsymbol{K}^{+}+\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}^{4-} \longrightarrow \)
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] ; \boldsymbol{K}=\mathbf{3} . \boldsymbol{8} \times \mathbf{1 0}^{-\mathbf{3 8}} \)
\( \mathbf{3} \boldsymbol{K}^{+}+\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}^{\boldsymbol{3}-} \longrightarrow \)
\( \boldsymbol{K}_{3}\left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right] ; \boldsymbol{K}=\mathbf{5} \times \mathbf{1 0}^{-18} \)
A \( \cdot K_{4} F e(C N)_{6} \) is more stable
B . \( K_{3} F e(C N)_{6} \) is more stable
c. both are equally stable
D. stability of complexes cannot be decrease
Subject: Chemistry
Assertion
A mixture of sodium acetate and
sodium propionate forms a buffer
solution.
Reason
A buffer solution reacts with small
quantities of hydrogen or hydroxyl ions and keeps the pH almost same.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
If \( y \) represents pressure and \( x \) represents velocity gradient, then the dimensions of \( \frac{d^{2} y}{d x^{2}} \) are
\( \mathbf{A} \cdot\left[M L^{-1} T^{-2}\right] \)
B. \( \left[M^{2} L^{-2} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{-1} T^{0}\right] \)
D \cdot \( \left[M^{2} L^{-2} T^{-4}\right] \)
Subject: Physics
A transformer consists of a coil of 1200
turns and another coil, with a total of
120 turns, which can be tapped at various places. Primary voltage is \( 240 V . \) At which pair of terminals would
you connect to a \( 12 V, 24 W \) lamp for it
to be lit normally?
A. \( N_{s}=60 \)
is \( N_{s}=60 \)
В. \( N_{s}=40 \)
\( \mathbf{C} \cdot N_{s}=80 \)
D. \( N_{s}=50 \)
Subject: Chemistry
Assertion
Both 138 g of \( K_{2} C O_{3} \) and 12 g of carbon have same number of carbon atoms.
Reason

Both contain 1 g atom of carbon which contains \( 6.022 \times 10^{23} \) carbon atoms.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
In triangle \( A B C . D \) and \( E \) are points on side \( A B \) such that \( A D=D E=E B \)
Through \( D \) and \( E \), lines are drawn
parallel to \( B C \) which meet side \( A C \) at
points \( \boldsymbol{F} \) and \( \boldsymbol{G} \) respectively. Through \( \boldsymbol{F} \)
and \( G \) lines are drawn parallel to \( A B \)
which meet side \( B C \) at points \( M \) and
\( N \) respectively
State whether true or false \( \boldsymbol{B} \boldsymbol{M}= \)
\( M N=N C .(\text { Enter } 1 \text { if true or } 0 \)
otherwise)
Subject: Chemistry
The formation of water from \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) and
\( O_{2}(g) \) is an exothermic process because:
A. the chemical energy of \( H_{2}(g) \) and \( O_{2}(g) \) is more than that of water
B. the chemical energy of \( H_{2}(g) \) and \( O_{2}(g) \) is less than that of water
C. the temperature of \( H_{2}(g) \) and \( O_{2}(g) \) is higher than that of water
D. the temperature of \( H_{2}(g) \) and \( O_{2}(g) \) is lower than that of water
Subject: Chemistry
Which of the following does not produce
\( \mathrm{H}_{2} \) at the anode on electrolysing using
Pt electrode?
This question has multiple correct options
A . molten CaH \( _{2} \)
B. \( N a C l(a q) \)
\( c \cdot \operatorname{cus} 0_{4}(a q) \)
D. \( \operatorname{dil} \mathrm{H}_{2} \mathrm{SO}_{4} \)