AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
For the reaction \( \boldsymbol{A}+\boldsymbol{B} \rightarrow \mathbf{3} \boldsymbol{C} ; \) at \( \mathbf{2 5}^{\boldsymbol{o}} \boldsymbol{C} \)
a \( 3 L \) vessel contains 1,2 and 4 moles of
\( A, B \) and \( C \) respectively. If reaction is in equilibrium then
A \( \cdot K_{c}=10 \)
В. \( K_{c}=12 \)
C . \( K_{c}=10.66 \)
D. \( K_{c}=9.56 \)
Subject: Biology
Which of the following hormone is correctly matched with it's source and
function?
A. Vasopressin - Anterior pituitary - Induces reabsorption of water in nephron
B. Oxytocin - Anterior pituitray - Contraction in uterine muscles during birth (parturation)
C. Thymosin - Thymus - Helps in differentiation of \( T \) Lymphocyte
D. Glucagon - Pancreatic \( \alpha \) cells- Induces the uptake of utilization of glucose inside cells
Subject: Physics
Let air be at rest at the front edge of a wing and air passing over the surface of wing at a fast speed v. If density of air is
\( \rho, \) the highest value for \( v \) in streamline flow when atmospheric pressure is
\( \boldsymbol{P}_{\text {atmosphere}} \) is:
\( ^{\mathrm{A}}\left[\frac{P_{\text {atnosphere}}}{\rho}\right]^{\frac{1}{2}} \)
\( \left[\frac{P_{a t m o s p h e r e}}{\rho}\right]^{2} \)
\( ^{\mathrm{c}}\left[\frac{P_{\text {atmosphere}}}{\rho}\right]^{\frac{1}{2}} \)
D. \( \frac{P_{\text {atmosphere }}}{\rho} \)
Subject: Physics
The magnetic field intensity due to a bar
magnet is \( 100 \mathrm{Am}^{-1} \). The magnetic
induction field strength due to it is:
A \( \cdot \frac{4 \pi}{10^{7}} T \)
B. \( \frac{4 \pi}{10^{5} T} \)
\( ^{\mathbf{C}} \cdot \frac{10^{3}}{4 \pi} T \)
D. \( \frac{10^{5}}{4 \pi} T \)
Subject: Maths
If three positive real numbers \( x, y, z \)
satisfy \( \boldsymbol{y}-\boldsymbol{x}=\boldsymbol{z}-\boldsymbol{y} \) and \( \boldsymbol{x} \boldsymbol{y} \boldsymbol{z}=\boldsymbol{4} \)
then what is the minimum possible
value of \( y ? \)
\( A \cdot 2^{\frac{1}{5}} \)
B. \( 2^{\frac{2}{5}} \)
\( c \cdot 2^{\frac{1}{4}} \)
\( D \cdot 2^{\frac{3}{7}} \)
Subject: Physics
Assertion
A magnetic field exert a force on a
moving charge in the same direction as the direction of field itself
Reason
The direction of force is given by Fleming's left hand rule.
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
An object is placed \( 0.40 \mathrm{m} \) from one of
the two lenses \( L_{1} \) and \( L_{2} \) of focal
lengths \( 0.20 \mathrm{m} \) and \( 0.10 \mathrm{m} \) respectively
as depicted in the figure. The
separation between the lenses is 0.30
\( \mathrm{m} \)
The final image formed by this two lens
system is at
A. \( 0.13 \mathrm{m} \) to the right of the second lens
B. \( 0.05 \mathrm{m} \) to the right of the second lens
c. \( 0.13 \mathrm{m} \) to the left of the second lens
D. Infinity
Subject: Maths
If \( f(x)= \)
\( \left|\begin{array}{ccc}\cos ^{2} x & \cos x \cdot \sin x & -\sin x \\ \cos x \cdot \sin x & \sin ^{2} x & \cos x \\ \sin x & -\cos x & 0\end{array}\right|, \) then
for all \( x \epsilon R, \) the value of \( f(x)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \)
D. None of the above
Subject: Maths
In the diagram \( M N \) is a straight line on a Cartesian plane. The coordinates of \( N \) \( \operatorname{are}(12,13) \) and \( M N^{2}=9 \) units. The
coordinates of \( M \) are:
A \( .(21,13) \)
B. (12,22)
c. (12,4)
D. (3,13)
Subject: Chemistry
Compound \( X\left(C_{5} H_{8} O_{2}\right) \) forms a
dioxime with \( N H_{2} O H . \) On

Clemmensen reduction it forms a
compound which forms only one monochloro derivative. 'X' can be :
\( A \)
в.
\( c \)
D. онс-снд \( -\mathrm{cH}_{2}-\mathrm{cH}_{2}- \) сно
Subject: Maths
\( P Q R S \) is a parallelogram. \( Q M \) is the
height from \( Q \) to \( S R \) and \( Q N \) is the height from \( Q \) to \( P S . \) If \( S R=12 c m \)
and \( Q M=7.6 \mathrm{cm} . \) Find:
the area of the parallelogram PQRS
\( Q N, \) if \( P S=8 c m \)
Subject: Maths
Two towns \( A \) and \( B \) are \( 60 \mathrm{km} \) apart. \( A \)
school is to be built to serve 150
students in town \( A \) and 50 students in
town B. If the total distance to be
travelled by all 200 students is to be as small as possible, then the school be built is
A. town B
B. \( 45 \mathrm{km} \) from town
c. town A
D. \( 45 \mathrm{km} \) from town \( \mathrm{B} \)
Subject: Chemistry
Nitrogen can form only one chloride with
chlorine which is \( N C l_{3} \) whereas \( P \) can
form \( P C l_{3} \) and \( P C l_{5} . \) This is:
A. due to absence of \( d \) -orbitals in nitrogen
B. due to difference in size of \( N \) and \( P \)
c. due to higher reactivity of \( P \) towards \( C l \) than \( N \)
D. due to presence of multiple bonding in nitrogen
Subject: Chemistry
Molar conductances of \( B a C l_{2}, H_{2} S O_{4} \)
and \( H C l \) are \( x_{1}, x_{2} \) and \( x_{3} S c m^{2} m o l^{-1} \)
at infinite dilution. If specific
conductance of saturated \( B a Z O_{4} \)
solution is of \( y S c m^{-1}, \) then \( k_{s p} \) of
\( B a S O_{4} \) is:
A. \( \frac{10^{3} y}{2\left(x_{1}+x_{2}-2 x_{3}\right)} \)
В. \( \frac{10^{6} y^{2}}{\left(x_{1}+x_{2}-2 x_{3}\right)^{2}} \)
c. \( \frac{10^{6} y^{2}}{4\left(x_{1}+x_{2}-2 x_{3}\right)^{2}} \)
D. \( \frac{x_{1}+x_{2}-2 x_{3}}{10^{6} y^{2}} \)
Subject: Maths
\( \int \frac{1}{1+x^{3}} d x= \)
A \( \cdot \frac{1}{3} \log |x+1|-\frac{1}{6} \log \left|x^{2}-x+1\right|+ \)
\( \quad \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c \)
B \( \cdot \frac{1}{3} \log |x+1|+\frac{1}{6} \log \left|x^{2}-x+1\right|+ \)
\( \quad \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c \)
c. \( \frac{1}{3} \log |x+1|-\frac{1}{6} \log \left|x^{2}-x+1\right|- \)
\( \quad \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c \)
D. \( -\frac{1}{3} \log |x+1|+\frac{1}{6} \log \left|x^{2}-x+1\right|+ \)
\( \quad \frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c \)
Subject: Chemistry
\( \boldsymbol{C}_{4} \boldsymbol{H}_{10}(\boldsymbol{g})+\frac{13}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{4} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) ; \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{2} \mathbf{8} \mathbf{7} \mathbf{8} \boldsymbol{k} \boldsymbol{J} \)
\( \Delta H \) is the heat of combustion of
butane gas.If true enter 1 else 0
\( A \)
Subject: Physics
A thermodynamic system is taken from an initial state i with internal energy
\( U_{i}=100 J \) to final state \( f \) along two
different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the path
\( a f, i b \) and \( b f \) are \( W_{a f}=200 J, W_{i b}= \)
\( 50 J \) and \( W_{b f}=100 J \) respectively. The
heat supplied to the system along the
path iaf, ib and bf are \( Q_{i a f}, Q_{i b} \) and \( Q_{b f} \) respectively. If the internal energy of the
system in the state b is \( U_{b}=200 J \) and
\( Q_{i a f}=500 J, \) the ratio \( Q_{b f} / Q_{i b} \) is
Subject: Physics
Find the velocity \( v \) of the rocket at the
moment when its mass is equal to \( m \), if at the initial moment it possessed the
mass \( m_{0} \) and its velocity was equal to
zero.
A \( \cdot \vec{v}=-\vec{u} \ln \frac{m}{m_{0}} \)
B・ \( \vec{v}=\vec{u} \ln \frac{m}{m_{0}} \)
c. \( \vec{v}=\vec{u} \ln \frac{m_{0}}{m} \)
D・ \( \vec{v}=-\vec{u} \ln \frac{m_{0}}{m} \)
Subject: Maths
\( f A=\left[\begin{array}{ccc}1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9\end{array}\right], \) then trace of
matrix \( \boldsymbol{A} \) is
A . 17
B . 25
\( c .3 \)
D. 12
Subject: Physics
A stair case contains ten step each 10
\( \mathrm{cm} \) high and \( 20 \mathrm{cm} \) wide.The maximum horizontal velocity with which the ball has to be rolled off the upper most
step,so as to hit directly the edge of the lowest step is (approximately)
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. \( 4.2 m s^{-1} \)
\( \mathrm{c} \cdot 24 \mathrm{ms}^{-1} \)
D. \( 2.4 m s^{-1} \)
Subject: Physics
A progressive wave of frequency
\( \mathbf{5 0 0} \boldsymbol{H z} \) is travelling with a velocity of
\( 360 m s^{-1} . \) The distance between two
point \( 60^{\circ} \) out of phase is
A \( .2 .1 m \)
B. \( 0.12 m \)
c. \( 0.21 m \)
D. \( 1.2 m \)
Subject: Chemistry
Potassium hexachloroplatinate
\( \boldsymbol{K}_{2}\left[\boldsymbol{P}_{2} \boldsymbol{i} \boldsymbol{C l}_{3}\right] \) adopts anti-fluorite crystal
structure. Which of the following ions adopts \( f c c \) arrangement?
A \( \cdot C l^{-} \) ions
B. \( K^{+} \) ions
\( \mathbf{c} \cdot P t^{4+} \) ions
D. \( \left[P t C l_{6}\right]^{2-} \) ions
Subject: Maths
A point on the line \( y=x \) whose
perpendicular distance from the line \( \frac{x}{4}+\frac{y}{3}=1 \) is 4 has the coordinates
This question has multiple correct options
\( \mathbf{A} \cdot\left(-\frac{8}{7},-\frac{8}{7}\right) \)
B \( \cdot\left(\frac{32}{7}, \frac{32}{7}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{3}{2}, \frac{3}{2}\right) \)
D. none of these
Subject: Chemistry
Calculate the heat energy that will be
released when \( 5.0 \mathrm{kg} \) of steam at \( 100^{\circ} \mathrm{C} \)
condenses to form water at \( 100^{\circ} \mathrm{C} \)
Express your answer in S.I. unit (specific heat of vapourisation of steam is \( 2268 \mathrm{kJ} / \mathrm{kg} \) )
Subject: Maths
\( \boldsymbol{C}_{3} / \boldsymbol{4}+\boldsymbol{C}_{5} / \boldsymbol{6}+\boldsymbol{C}_{7} / \boldsymbol{8}+\ldots \ldots= \)
\( ^{\mathbf{A} \cdot \frac{2^{n+1}-n^{2}-n-2}{2(n+1)}} \)
\( ^{\text {В } \cdot \frac{\left.2^{n+2}+n^{2}+n-2\right)}{n+1}} \)
c. \( \frac{\left(3^{n+2}-n^{2}-n-2\right)}{n+1} \)
D. None of these
Subject: Chemistry
Some statements about heavy water
are given below:
(a) Heavy water is used as a moderator in nuclear reactions
(b) Heavy water is more associated
than ordinary water
(c) Heavy water is more effective solvent than ordinary water Select correct statements:
A. \( (a),(b) \) and \( (c) \)
\( c \)
B. \( (b) \) and \( (c) \)
c. \( (a) \) and \( (c) \)
D. \( (a) \) and \( (b) \)
Subject: Maths
In the following figure, the circle
centered at \( N \) has a radius of \( 4 . \) What is
the area of the shaded region?
\( A \cdot 3 \pi \)
B. \( 6 \pi \)
\( c .9 \pi \)
D. \( 12 \pi \)
E . \( 16 \pi \)
Subject: Maths
The production of saleable steel in some of the steel plants of our country during 1999 is given below:

Plant \( \quad \) Bhilai \( \quad \) Durgapur \( \quad \) Rourkel
Production
In thousand tonnes
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions \( =20 \) thousand
tonnes.
Subject: Physics
A particle moves in a straight line with constant acceleration a. The
displacements of particle from origin in
times \( t_{1}, t_{2} \) and \( t_{3} \) are \( s_{1}, s_{2} \) and \( s_{3} \) respectively. If time are in AP with
common difference d and
displacements are in GP, then prove that \( a=\frac{(\sqrt{s_{1}-\sqrt{s_{3}}})^{2}}{d^{2}} \)
Subject: Maths
Determine the three planes through the intersection of the planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{1} \)
and \( 2 x+3 y-z+4=0 \) which are
parallel to the three co - ordinate axes.
Also find the equation of the plane
perpendicular to the \( y z- \) plane and
passing through the point (2,3,1) and
(4,-5,3)
A \( \cdot y-3 z-6=0 ; x-4 z=7 \) and \( 3 x-4 y-3=0 \)
\( y+4 z+7=0 \)
B. \( y-3 z+6=0 ; x+4 z=7 \) and \( 3 x+4 y+3=0 \)
\( y-4 z+7=0 \)
c. \( y+3 z+6=0 ; x+4 z=7 \) and \( 3 x+4 y+3=0 \)
\( y-4 z-7=0 \)
D. \( y-3 z+6=0 ; x+4 z=7 \) and \( 3 x+4 y+3=0 \)
\( y+4 z-7=0 \)
Subject: Chemistry
Which of the following combinations is correctly matched?
\( ^{\mathbf{A}} \cdot_{C H_{3}-C_{D}^{H}-C l, S_{N^{2}} W a l d e n i n v e r s i o n} \)
\( ^{\text {B. }} C H_{3}-_{J}^{\text {I }} C-C l, S_{N 1} \) Waldeninversion
\( \mathrm{c}_{C_{6} H_{5}-} \stackrel{c_{2}, \text { Нь}}{C}-\mathrm{Cl}, S_{N 1} \) Only retension
\( ^{\mathrm{D}} C_{6} H_{5}-\begin{array}{c}c_{2}, H_{5} \\ C_{H} \\ C H_{3}\end{array}-C l, S_{N^{1}} O n l y \) inversion
Subject: Maths
The equation of the plane passing through \( (a, b, c) \) and parallel to the plane \( r \cdot(\hat{i}+\hat{j}+\hat{k})=2 \) is
A. \( x+y+z=1 \)
B . \( a x+b y+c z=1 \)
c. \( x+y+z=a+b+c \)
D. None of these
Subject: Physics
A small sphere of mass \( m=2 k g \) moving with a velocity \( \bar{u}=\hat{4} i-7 \hat{j} m / s \) collides
with a smooth wall and returns with a velocity \( \bar{v}=\hat{i}-3 \hat{j} m / s . \) The magnitude
of the impulse received by the ball is
\( \mathbf{A} \cdot 5 k g m s^{-1} \)
В. \( 10 k g m s^{-1} \)
c. \( 20 \mathrm{kgms}^{-1} \)
D. \( 15 k g m s^{-1} \)
Subject: Physics
The ratio of the absorption of an
auditorium to that of a person is \( 1000 . \) If 500 persons are accommodated in that
auditorium then the ratio of the
reverberation times with and without
audience is:
A \( \cdot 1 / 3 \)
B. 2/3
\( c \cdot 3 / 2 \)
D. \( 3 / 4 \)
Subject: Maths
Mode of the following frequency
distribution
\( \begin{array}{lccccc}\mathrm{x}: & 4 & 5 & 6 & 7 & 8 \\ \mathrm{f}: & 6 & 7 & 10 & 8 & 3\end{array} \)
A. 5
B. 6
\( c \cdot 8 \)
D. 19
Subject: Physics
The relation between the time of flight of projectile \( T, \) and the time to reach the
maximum height \( t_{m} \) is
A \( \cdot T_{f}=2 t_{m} \)
B . \( T_{f}=t_{m} \)
c. \( T_{f}=t_{m} / 2 \)
\( \mathbf{D} \cdot T_{f}=\sqrt{2} t_{m} \)
Subject: Maths
f mean of given data is 21 then value of
p is
\( \begin{array}{llllll}\mathrm{x} & 10 & 15 & 20 & 25 & 36 \\ \mathrm{f} & 6 & 10 & \mathrm{p} & 10 & 8\end{array} \)
A . 24
B . 10
c. 26
D. none of the above
Subject: Chemistry
Choose the correct answer from the
alternative given. When an oxide of manganese (P) is fused with KOH in the presence of an
oxidizing agent and dissolved in water, it gives a dark green solution of compound (Q). Compound (Q) disproportionates in neutral or acidic solution to give purple compound (R). An alkaline solution of compound (R)
oxidizes potassium iodide solution to a compound (S) and compound (P) is also formed. Compounds \( P \) to \( S \) are:
A \( \cdot(P)-M n O_{4}^{-},(Q)-K I O_{3},(R)-M n O_{2},(S)- \)
\( K_{2} M n O_{4} \)
B . \( (P)-M n O_{2},(Q)-K_{2} M n O_{4},(R)-M n O_{4}^{-},(S)- \)
\( K I O_{3} \)
C \( \cdot(P)-M n O_{2},(Q)-M n O_{4}^{-},(R)-K 2 M n O_{4},(S) \)
\( K I O_{3} \)
D \( \cdot(P)-K_{2} M n O_{4},(Q)-M n O_{2},(R)-M n O_{4}^{-},(S)- \)
\( K I O_{3} \)
Subject: Chemistry
A metallic carbide on treatment with
water gives a colourless gas which burns readily in air and gives a precipitate with ammonical silver nitrate solution. The gas evolved is :
A \( . C H_{4} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{2} H_{2} \)
Subject: Maths
If the function \( \boldsymbol{E}: \boldsymbol{R} \rightarrow \) defines by
\( f(x) \frac{3^{x}+3^{-x}}{2} \) than show that \( f(x+y)+ \)
\( \boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})=2 \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \)
Subject: Chemistry
Balance the following equation and find the values of \( a, b, c, d \) \( \boldsymbol{a} \boldsymbol{P b O}_{2}+\boldsymbol{b C l}^{\ominus} \longrightarrow \boldsymbol{c} \boldsymbol{C l O}^{\ominus}+ \)
\( \boldsymbol{d}\left[\boldsymbol{P b}(\boldsymbol{O H})_{3}\right]^{\ominus}(\text { in basic solution }) \)
В. \( a=1, b=1, c=1, d=1 \)
c. \( a=2, b=1, c=1, d=2 \)
D. \( a=1, b=1, c=2, d=2 \)
Subject: Physics
Two concentric thin metallic spheres of
radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}\left(\boldsymbol{R}_{1}>\boldsymbol{R}_{2}\right) \) bear charges
\( Q_{1} \) and \( Q_{2} \) respectively. Then the
potential at a radius \( r \) between \( R_{1} \) and
\( \boldsymbol{R}_{2} \) will be \( 1 / 4\left(\pi \varepsilon_{0}\right) \) times:
A. \( \frac{Q_{1}+Q_{2}}{4} \)
в. \( \frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{r} \)
c. \( \frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{R_{2}} \)
D. \( \frac{Q_{1}}{R_{2}}+\frac{Q_{2}}{R_{1}} \)
Subject: Chemistry
\( P C l_{5} \) dissociates according to the
reaction \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
At \( 523 \mathrm{K}, K_{p}=1.78 a t m . \) Find the density of the equilibrium mixture at a total pressure of 1 atm :
A. \( 0.271 \mathrm{g} / \mathrm{L} \)
B. 2.71 \( \$ / L \)
c. 27.1 \( g / L \)
D. None of these
Subject: Chemistry
Statement I: Water has a higher boiling point than expected. Statement II: Each molecule forms a
hydrogen bond with an adjacent molecule.
A. Both Statement I and Statement II are correct and Statement I I is the correct explanation of Statement
B. Both Statement I and Statement II are correct, but Statement II is not the correct explanation of Statement I.
c. statement lis correct, but Statement II is incorrect.
D. Statement I is incorrect, but Statement II is correct
Subject: Maths
Given the geometric progression
\( \mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{2 4}, \dots . \) The term 12288 would
occur as the
A \( \cdot 11^{t h} \) term
B. \( 12^{\text {th}} \)term
\( \mathbf{c} \cdot 13^{t h} \)term
D. \( 14^{\text {th}} \)term
Subject: Chemistry
Select correct statement(s).
A. Equivalent of \( X e O_{3} \) in \( I \) and \( I I \) is in the ratio 1: 1
B . Equivalent mass of \( I_{2}=\frac{\text { molar mass }}{9} \)
c. Equivalent mass of \( F e^{2+}=\frac{\text { molar mass }}{6} \)
D. All the above are correct statements
Subject: Physics
The armature of a DC motor has \( 20 \Omega \)
resistance. It draws a current of 1.5
amp when run by \( 200 V \) DC supply. The value of back emf induced in it will be
\( \mathbf{A} \cdot 150 V \)
в. \( 170 V \)
\( \mathbf{c} \cdot 180 V \)
D. \( 190 V \)
Subject: Physics
Find the value of \( \frac{\boldsymbol{a}+\boldsymbol{b}-\boldsymbol{c}}{\mathbf{2} \boldsymbol{a}} \) when \( \boldsymbol{a}= \)
\( \mathbf{5}, \boldsymbol{b}=\mathbf{7} \) and \( \boldsymbol{c}=\mathbf{2} \)
Subject: Chemistry
For the given bond pairs, decide which is the more polar?
\( \boldsymbol{S} \boldsymbol{i}-\boldsymbol{O} \) and \( \boldsymbol{P}-\boldsymbol{P} \)
A \( . S i-O>P-P \)
в. \( S i-O<P-P \)
c. \( s i-O=P-P \)
D. None of these
Subject: Chemistry
The cryoscopic constant for acid is \( 3.6 \mathrm{K} \) kg/mol. A solution of 1 g of a hydrocarbon in 100 g of acetic acid
freezes at \( 16.60^{\circ} \mathrm{C} \). The hydrocarbon contains \( 92.3 \% \) carbon.lf the molecular
formula is \( C_{x} H_{y} \). Find the value of \( x \) and
\( y: \)
A. \( x=2, y=4 \)
В. \( x=3, y=8 \)
c. \( x=4, y=10 \)
D. \( x=6, y=6 \)
Subject: Physics
A glass prism of refractive index 1.5 is immersed in water of refractive index
4/3. A light ray incident normally on
face \( A B \) is totally reflected at face \( A C \) if
\( \mathbf{A} \cdot \sin \theta>8 / 9 \)
B. \( \sin \theta<2 / 3 \)
\( c \cdot \sin \theta=\sqrt{3} / 2 \)
D. \( 2 / 3<\sin \theta \leq 8 / 9 \)
Subject: Physics
The displacement - time graph for a
particle executing SHM is as shown in
figure
Which of the following statement is
correct?
A \( \cdot \) the velocity of the particle is maximum at \( t=\frac{3}{4} T \)
B. The velocity of the particle is maximum at \( t=\frac{T}{2} \)
C the acceleration of the particle is maximum at \( t=\frac{T}{4} \)
D. The acceleration of the particle is maximum at \( t=\frac{3}{4} T \)
Subject: Maths
Suppose a girl throws a die. If she gets 1 or \( 2, \) she tosses a coin three times and notes the number of tails. If she gets
3,4,5 or \( 6, \) she tosses a coin once and
notes whether a 'head' or 'tail' is
obtained. If she obtained exactly one
tail', what is the probability that she
threw 3,4,5 or 6 with the die?
Subject: Chemistry
Two glucose solutions are mixed of \( 1 M \)
and \( 2 M \) respectively in equal volume ratio then the new molarity will be:
\( \mathbf{A} \cdot 1.4 M \)
в. \( 1.25 M \)
c. \( 1.5 M \)
D. \( 1.27 M \)
Subject: Chemistry
For the following reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
If initially \( 25 m L \) of \( H_{2} \) and \( 20 m L \) of \( I_{2} \) are present in a container and at
equilibrium \( 30 m L \) of \( H I \) is formed then calculate equilibrium constant.
Subject: Maths
Let \( f(x) \) be differentiable on the interval
\( (0, \infty) \) such that \( f(1)=1, \) and \( \lim _{t \rightarrow x} \frac{t^{2} f(x)-x^{2} f(t)}{t-x}=1 \) for \( \operatorname{each} x>0 \)
Then \( f(x) \) is
A \( \frac{1}{3 x}+\frac{2 x^{2}}{3} \)
в. \( -\frac{1}{3 x}+\frac{4 x^{2}}{3} \)
c. \( -\frac{1}{x}+\frac{2}{x^{2}} \)
D.
Subject: Physics
The relation between \( [\boldsymbol{E}] \) and \( [\boldsymbol{B}] \) is
\( \mathbf{A} \cdot[E]=[B][L][T] \)
B . \( [E]=[B][L]^{-1}[T] \)
c. \( [E]=[B][L][T]^{-1} \)
D・ \( [E]=[B][L]^{-1}[T]^{-1} \)
Subject: Physics
Let \( I_{A} \) and \( I_{B} \) be the moments of inertia
of two solid cylinders of identical geometrical shape and size about their axes, the first made of aluminum and
the second of iron then:
A \( \cdot I_{A}<I_{B} \)
в. \( I_{A}=I_{B} \)
с. \( I_{A}>I_{B} \)
D. The relation between \( I_{A} \) and \( I_{B} \) depends on the actual shape of the bodies
Subject: Physics
Which of the following is NOT true for
comets?
A. Some comets are believed to have originated in a region near the edge of the orbit of the outer planets in our solar system called the "scattered disk" that overlaps a region called the Kulper belt.
B. Some comets are believed to have originated in the outer-most region associated with our solar system, called the Oort cloud.
C. The tail of a comet gives the comet its propulsion, like rocket fuel out the back end of a rocket.
D. The tails of a comet generally point away from the Sun and are made of two major parts - a dusty part (that curves a bit) and an ionic part
E. Comets of ten contain significant amount of water.
Subject: Physics
If \( 1 \mathrm{kg} \) wt \( =10 \mathrm{N}, \) the value of gravitational intensity will be
A \( \cdot 10 m / s^{2} \)
в. \( \frac{1}{10} m / s^{2} \)
c. \( 1 m / s^{2} \)
D. \( \frac{1}{100} m / s^{2} \)
Subject: Chemistry
The standard e.m.f. of a cell involving one electron change is found to \( 0.591 \mathrm{V} \)
at \( 25^{\circ} \mathrm{C} \). The equilibrium constant of the
reaction is:
A \( \cdot 10^{30} \)
B . \( 10^{5} \)
\( c \cdot 10^{10} \)
D. \( 10^{\text { }} \)
Subject: Maths
\( f\left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & 1\end{array}\right|=\left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \mathbf{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \mathbf{1} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & 1\end{array}\right| \), then the
two triangles with vertices \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \) and \( \left(a_{1}, b_{1}\right) \)
\( \left(a_{2}, b_{2}\right),\left(a_{3}, b_{3}\right) \) must be congruent
A. True
B. False
Subject: Chemistry
Assertion
Statement-I: If an aqueous solution of NaCl is electrolysed, the product
obtained at the cathode is \( H_{2} \) gas and
not Na.
Reason
Statement-II : Gases are liberated faster
than the metals.
A. Statement-l is true, Statement-II is true; Statement-II is correct explanation for Statement-I
B. Statement-lis true, Statement-II is true; Statement-II is NOT a correct explanation for statement-
c. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true
Subject: Chemistry
The acidity of the compounds
\( \boldsymbol{R} \boldsymbol{C O O H}, \boldsymbol{H}_{2} \boldsymbol{C O}_{3}, \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{O H}, \boldsymbol{R O H} \)
decreases in the order:
A \( \cdot R C O O H>H_{2} C O_{3}>C_{6} H_{5} O H>R O H \)
в. \( C_{6} H_{5} \)ОН\( > \)RСООН\( >H_{2} \)СО\( _{3}> \)ВОН
c. \( R O H>C_{6} H_{5} O H>R C O O H>H_{2} C O_{3} \)
D. \( H_{2} C O_{3}>R C O O H>C_{6} H_{5} O H>R O H \)