AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A small body \( A \) starts sliding off the top
of a smooth sphere of radius \( R \). Find the
angle \( \theta \) (shown in figure
above) corresponding to the point at which the body breaks off the sphere as
well as the break-off velocity of the body
A \( \quad \theta=\arccos \left(\frac{1}{3}\right) \approx 52^{\circ}, v=\sqrt{\frac{2 g R}{3}} \)
B. \( \theta=\arccos \left(\frac{2}{3}\right) \approx 48^{\circ}, v=\sqrt{\frac{2 g R}{3}} \)
\( ^{\mathrm{c}} \cdot_{\theta}=\arccos \left(\frac{2}{3}\right) \approx 48^{\circ}, v=\sqrt{\frac{g R}{3}} \)
D. \( _{\theta}=\arccos \left(\frac{1}{3}\right) \approx 52^{\circ}, v=\sqrt{\frac{g R}{3}} \)
Subject: Physics
The average kinetic energy of the
molecules of an ideal gas at \( 10^{\circ} \mathrm{C} \) has the value E. The temperature at which the kinetic energy of the same gas becomes \( 2 \mathrm{E} \) is
\( \mathbf{A} \cdot 5^{\circ} C \)
В \( \cdot 10^{\circ} \mathrm{C} \)
\( c \cdot 40^{\circ} C \)
D. None of these
Subject: Maths
Draw a circle with centre \( O \) and radius
\( 6 \mathrm{cm} . \) Take a point \( P \) outside the circle
at a distance of \( 10 \mathrm{cm} \) from \( 0 . \) Draw
tangents to the circle from point \( P . \) Let the tangents intersect the circle in
points \( A \) and \( B \). Find the area of triangle
OBPin sq.cm.
A .24
B . 26
c. 25
D. None of these
Subject: Maths
Rhombus PQRB is inscribed in \( \triangle \boldsymbol{A B C} \)
such that \( \angle B \) is one of the its angle, \( P, Q \)
and \( \mathrm{R} \) lie on \( \mathrm{AB}, \mathrm{AC} \) and \( \mathrm{BC} \) respectively. If \( A B=12 \mathrm{cm} \) and \( B C=6 \mathrm{cm} \) find the
sides of rhombus PQRB.
Subject: Maths
\( \operatorname{Let} f\left(x+\frac{1}{x}\right)=x^{2}+\frac{1}{x^{2}}(x \neq 0), \) then
\( \boldsymbol{f}(\boldsymbol{x}) \) equals:
A \( \cdot x^{2}-2 \)
B . \( x^{2}-1 \)
\( \mathbf{c} \cdot x^{2} \)
D. None of these
Subject: Physics
Assertion
Potential difference across, resistor,
capacitor and inductor each is \( 10 V \) Then, voltage function and current functions should be in phase.
Reason
At this condition current in the circuit
should be maximum.
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
A small object \( Q \) of length 1 mm lies
along the principal axis of a spherical glass of radius \( \mathrm{R}=10 \mathrm{cm} \) and refractive
index is \( 3 / 2 . \) The object is seen from air
along the pricipal axis from left. The distance of object from the center \( P \) is 5
cm. Find the size of the image. Is it real,
inverted?
\( A \)
B.
c. \( \frac{8}{3} m m ; \) virtual
D. Noneofthese
Subject: Chemistry
Incorrect statement about Ge is:
\( \mathbf{A} \cdot G e O_{2} \) is weakly acidic
B. \( G e(O H)_{2} \) is amphoteric
C \( \cdot G e C l_{2} \) is more stable than \( G e C l_{4} \)
D. \( G e-G e \) bond energy is lesser than that of \( S i-S i \)
Subject: Physics
A tank is filled with water up to height
H. Water is allowed to come out of a hole
Pin one of the walls at a depth D below the surface of water as shown in the
figure. Express the horizontal distance
in terms of H and D:
A. \( x=\sqrt{D(H-D)} \)
B. \( x=\sqrt{\frac{D(H-D)}{2}} \)
c. \( x=2 \sqrt{D(H-D)} \)
D. \( x=4 \sqrt{D(H-D)} \)
Subject: Chemistry
Which is formed when
\( K_{2} C r_{2} O_{7}, C a C l_{2}, \) and conc. \( H_{2} S O_{4} \) are
heated?
\( \mathbf{A} \cdot C r_{2}\left(S O_{4}\right) \)
в. \( C r C l_{3} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)
D. \( K_{2} C r O_{4} \)
Subject: Chemistry
If \( x \) is amount of adsorbate and \( m \) is
amount of adsorbent, which of the
following relations is not related to adsorption process?
A \( \cdot \frac{x}{m}=f(T) \) at constant \( P \)
B \( \cdot P=f(T) \) at constant \( \left(\frac{x}{m}\right) \)
c. \( \frac{x}{m}=P \times T \)
D. \( \frac{x}{m}=f(P) \) at constant \( T \)
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\}, \boldsymbol{B}=\{\mathbf{3}, \boldsymbol{4}\} \) and \( \boldsymbol{C}= \)
\( \{1,3,5\}, \) then \( A \times(B-C)= \)
A \( \cdot(A \times B)-(A \times C) \)
в. \( (A \times B)+(A \times C) \)
c. \( (A \times B)-(B \times C) \)
D. \( (A \times B)-(C \times A) \)
Subject: Chemistry
Which of the following mixture is called
aqua regia?
A. Three parts of \( d i l . H C I \) and 1 part of conc.\( H N O_{3} \)
B. Two parts of cone. \( H C I \) and two parts of conc.H\( N O_{3} \)
C. Three parts of cone. \( H C I \) and 1 part of \( d i l . H N O_{3} \)
D. Three parts of conc.\( H C I \) and 1 part of conc.H\( N O_{3} \)
Subject: Maths
Perimeter of the figure is
\( \mathbf{A} \cdot 68.2 \mathrm{cm} \)
\( \mathbf{B} \cdot 68.1 \mathrm{cm} \)
\( \mathrm{C} \cdot 86.3 \mathrm{cm} \)
D. \( 68.3 \mathrm{cm} \)
Subject: Maths
If \( \frac{1}{2}, \frac{1}{2}, n(n<0) \) are the dos of a line,
then the angle made by that line with \( \boldsymbol{O} \boldsymbol{Z} \) where \( \boldsymbol{O}=(\mathbf{0}, \mathbf{0}, \mathbf{0}) \) is
A \( \cdot \frac{-1}{\sqrt{2}} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 135^{\circ} \)
Subject: Physics
The average kinetic energy of thermal
neutron is of the order of :
(Boltzmann's constant \( k_{B}=8 \times \)
\( \left.10^{-5} e V / K\right) \)
A . \( 0.03 e V \)
в. \( 3 e V \)
c. \( 3 k e V \)
D. 3MeV
Subject: Chemistry
A photon of wavelength \( 4400 \dot{A} \) is passing through vacuum. The effective mass and momentum of the photon are
respectively?
A \( .5 \times 10^{-36} k g, 1.5 \times 10^{-27} k g-m / s \)
B . \( 5 \times 10^{-25} \mathrm{kg}^{\text {' }}, 1.5 \times 10^{-26} \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
C. Zero, \( 1.5 \times 10^{-26} \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
D. \( 5 \times 10^{-36} \) в \( g \), \( 1.36 \times 10^{-43} \) kg \( -m / s \)
Subject: Chemistry
Read the given statements and mark
the correct option.

Statement 1: While fixing a metal rim on a wooden wheel of a cart, the size of
the metal rim is kept slightly smaller than that of the wooden wheel.
Statement 2: Metals expand on heating and contract on cooling.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1
c. statement 1 is true and statement 2 is false.
D. Both statements 1 and 2 are false.
Subject: Maths
If for two events \( A \) and \( B, P(A \cup B)= \) \( \frac{1}{2}, P(A \cap B)=\frac{2}{5} \) and \( \operatorname{then} P\left(A^{c}\right)+ \)
\( \boldsymbol{P}\left(\boldsymbol{B}^{c}\right) \) equals
A \( \cdot \frac{4}{5} \)
в.
c. \( \frac{11}{10} \)
D. None of these
Subject: Physics
The electrostatic force between two
point charges \( q_{1} \) and \( q_{2} \) at separation ' \( r^{\prime} \) is given by \( F=\frac{K q_{1} q_{2}}{r^{2}} . \) The constant \( K \)
A. depends on the system of units only
B. depends on the medium between the charges only.
c. depends on both the system of units and the medium between the charges.
D. is independent of both the system of units and the medium between the charges
Subject: Physics
The P-V diagram of path followed by one
mole of perfect gas in a cylindrical container is shown in figure, the work
done when the gas is taken from state \( A \)
to state B is:
\( ^{\mathrm{A}} \cdot_{2 P_{2} V_{1}\left[1-\frac{\sqrt{V}}{\sqrt{V}_{1}}\right]} \)
в. \( 2 P_{1} V_{1}\left[1-\frac{\sqrt{V}_{1}}{\sqrt{V}_{2}}\right] \)
\( c \cdot_{2 P_{2} V_{2}\left[1-\frac{\sqrt{V}}{\sqrt{V}_{2}}\right]} \)
D. \( 2 P_{1} V_{2}\left[1-\frac{\sqrt{V}_{1}}{\sqrt{V}_{2}}\right] \)
Subject: Physics
The capacitor of an oscillatory circuit of negligible resistance is enclosed in a evacuated container. The frequency of the circuit is \( 150 \mathrm{kHZ} \) and when the
container is filled with a gas, the frequency changes by 100 HZ. The dielectric constant of the gas.
\( A \cdot 2 \)
B. 1.53
c. 1.0012
D. 3
Subject: Physics
A brick with dimensions of \( 20 \mathrm{cm} \times \)
\( 10 c m \times 5 c m \) has a weight 500 gwt.
Calculate the pressure exerted by it when it rests on different faces.
A \( \cdot \) case (i) \( P_{1}=1.25 g w t c m^{-2}, \) Case (ii) \( P_{2}=5 g w t c m^{-2} \) Case (iii) \( P_{3}=5 g w t c m^{-2} \)
B. case (i) \( P_{1}=2.5 g w t c m^{-2} \), Case (ii) \( P_{2}=5 g w t c m^{-2} \)
Case (iii) \( P_{3}=10 \) gwtem \( ^{-2} \)
C. case (i) \( P_{1}=5 g w t c m^{-2} \), Case (ii) \( P_{2}=25 g w t c m^{-2} \) Case (iii) \( P_{3}=15 \) gwtcm \( ^{-2} \)
D. case (i) \( P_{1}=2.5 g w t c m^{-2} \), Case
(ii) \( P_{2}=2.5 g w t c m^{-2} \)
Case (iii) \( P_{3}=10 g w t c m^{-2} \)
Subject: Maths
Compute the median for the following cumulative frequency distribution:
\( \begin{array}{lllll}\text { Less } & \text { Less } & \text { Less } & \text { Less } & \text { Less } \\ \text { than } & \text { than } & \text { than } & \text { than } & \text { than } \\ 20 & 30 & 40 & 50 & 60\end{array} \)
१६ 30
Subject: Physics
The horizontal component of earth's magnetic field at a certain place is \( 3.0 \times 10^{-5} \mathrm{T} \) and having a direction
from the geographic south to geographic north. The force per unit length on a very long straight conductor carrying a steady current of \( 1.2 \mathrm{A} \) in east to west direction is then
A. \( 3.0 \times 10^{-5} \mathrm{N} \mathrm{m}^{-1} \)
В. \( 3.2 \times 10^{-5} \mathrm{N} \mathrm{m}^{-1} \)
c. \( 3.6 \times 10^{-5} \mathrm{N} \mathrm{m}^{-1} \)
D. \( 3.8 \times 10^{-5} \mathrm{N} \mathrm{m}^{-1} \)
Subject: Physics
Three moles of an ideal gas being
initially at a temperature \( \boldsymbol{T}_{\boldsymbol{i}}=\mathbf{2 7 3} \mathbf{K} \)
were isothermally expanded 5 times its initial volume and then isochorically heated so that the pressure in the final
state become equal to that in the initial state. The total heat supplied in the process is \( 80 \mathrm{kJ} \). If \( \gamma=\frac{C_{p}}{C_{v}} \) of the gas is \( \frac{x}{10}, \) find \( x \)
Subject: Maths
If \( f(x)=\sin ^{-1} x+\sec ^{-1} x \) is defined
then which of the following value/values is/are in its range?
A \( \cdot \frac{-\pi}{2} \)
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D. \( \frac{3 \pi}{2} \)
Subject: Maths
The equations of the lines through
(1,1) and making angles of \( 45^{\circ} \) with
the line \( \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \) are
A \( . x-1=0, x-y=0 \)
В. \( x-y=0, y-1=0 \)
c. \( x+y-2=0, y-1=0 \)
D. \( x-1=0, y-1=0 \)
Subject: Biology
regarding biological museums.
(i) Biological museums are generally set up in educational institutes such as
schools and colleges.
(ii) Museums have collections of
preserved plant and animal specimens for study and reference.
(iii) Specimens are preserved in the containers or jars in preservative solutions.
(iv) Insects are preserved in insect boxes after collecting killing and
pinning.
(v) Larger animals like birds and mammals are usually stuffed and
preserved.
(vi Skeletons of mammals are not
allowed to be kept in museums. Which of the given statements is/are
not correct?
A . (ii) and (iii)
B. (i) and (vi)
\( \mathbf{C} \cdot(v) \) only
D. (vi) only
Subject: Maths
\( \int\left(\tan ^{10} x+\tan ^{12} x\right) d x= \)
A. \( \frac{\tan ^{9} x}{9}+c \)
B. \( \frac{\tan ^{13} x}{13}+c \)
c. \( \frac{\tan ^{11} x}{11}+c \)
D. \( \frac{\tan ^{8} x}{8}+c \)
Subject: Chemistry
On passing a current through a molten aluminium chloride for some time
produced 11.28 lit of \( C l_{2} \) at \( \mathrm{NTP} \) at anode.
The quantity of aluminium deposited at
cathode is:
A. 27grams
B. 18gram
c. \( \operatorname{ggram} \)
D. 36 gram
Subject: Chemistry
The work of \( 146 k J \) is performed in
order to compress 1 kilo mole of a gas adiabatically and in the process the temperature of the gas increases by
\( \mathbf{7}^{\circ} \mathbf{C} . \) The gas is:
\( \left(\boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
A. Diatomic
B. A mixture of monoatomic and diatomic
c. Monoatomic
D. Triatomic
Subject: Physics
An \( L-C-R \) series circuit with \( L= \)
\( 0.120 H, R=240 \Omega, \) and \( C=7.30 \mu F \)
carries an rms current of \( 0.450 A \) with a
frequency of \( 400 H z . \) The average rate at
which electrical energy is converted to thermal energy in the resistor is given as \( \frac{x}{10} W . \) Find \( x \)
Subject: Maths
The value of \( \frac{\tan 45^{\circ}}{\sin 30^{\circ}+\cos 30^{\circ}} \) is:
This question has multiple correct options
A. \( \frac{2}{\sqrt{3}+1} \)
B.
\( \frac{1+\sqrt{3}}{2} \)
D. \( \sqrt{3}-1 \)
Subject: Physics
A mass \( m \) is thrown vertically upward
into air with initial speed \( u . \) A constant
force \( F \) due to air resistance acts on the
mass during it's travel. Taking into
account the work done against air drag, the maximum distance covered by the mass to reach the top is (Given acceleration due to gravity \( =g \) )
A \( \cdot \frac{u^{2}}{2 g} \)
в. \( \frac{u^{2}}{2 g+2 F / m} \)
с. \( \frac{u^{2}}{2 g+F / m} \)
D. \( \frac{u^{2}}{g+F / m} \)
Subject: Maths
n given figure \( \angle P Q R=100^{\circ}, \) where
\( P, Q \) and \( R \) are points on a circle with
centre \( O . \) Then, \( \angle O P R \) is
\( A \cdot 20 \)
B. 10
\( c \cdot 30^{\circ} \)
D. 40
Subject: Physics
The instantaneous potential difference between points \( A \) and \( B \) is (Phase angle
is \( \left.37^{0}\right) \)
A \( \cdot 8 \sin \left(50 \pi t+37 \frac{\pi}{180}\right) \)
B. \( 8 \sin \left(50 \pi t-37 \frac{\pi}{180}\right) \)
c. \( 10 \sin (50 \pi t) \)
D. \( 10 \cos (50 \pi t) \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{lll}\boldsymbol{a}^{2} & \boldsymbol{a b} & \boldsymbol{a c} \\ \boldsymbol{a b} & \boldsymbol{b}^{2} & \boldsymbol{b c} \\ \boldsymbol{a c} & \boldsymbol{b c} & \boldsymbol{c}^{2}\end{array}\right] \) and \( \boldsymbol{a}^{2}+\boldsymbol{b}^{2}+ \)
\( c^{2}=1 \) then \( A^{2}= \)
A \( .2 A \)
в.
\( c .3 A \)
D. \( \frac{1}{2} \)
Subject: Maths
\( \triangle \mathrm{ABC} \) and \( \triangle \) DEF are two triangles, then to ensure that two triangles ABC and DEF are congruent, 3 conditions \( \operatorname{given} ; A B=D E, A C=D F, \angle A B C=\angle \)
DEF are
A. sufficient but not necessary
B. necessary but not sufficient
c. neither necessary nor sufficient
D. both necessary and sufficient
Subject: Chemistry
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \) (Ammonium
dichromate) is used in fire works. The
green coloured powder blown in air is :
A. \( C r_{2} O_{3} \)
в. \( C r O_{2} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{4} \)
D. \( \operatorname{Cr} \mathrm{O}_{3} \)
Subject: Physics
The current in a coil of inductance \( 2 \mathrm{H} \) is
changing according to varying current \( \boldsymbol{I}=\sin (2 t) . \) The amount of magnetic
energy in the inductor during \( t=0 \) to \( \boldsymbol{t}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \boldsymbol{s} \) is:
A . 4
B . 3J
c. 1 J
D. 2
Subject: Chemistry
Boron can be obtained by various
methods but not by
A. Thermal decomposition of \( B_{2} H_{6} \)
B. Pyrolysis of \( B I_{3} \) (van Arkel)
C. Reducing \( B C l_{3} \) with \( H_{2} \)
D. Electrolysis of fused \( B C l_{3} \)
Subject: Chemistry
The decreasing order of boiling points of the following is :
(।) \( R C O C l,(\|)(R C O)_{2} O,(\| I) \)
\( R C O N H_{2},(I V) R C O O H \)
A . ।> IV > || > II
B. |||>|| > IV > |
c. IV > III > I> II
D. II >|>||| > IV
Subject: Biology
Assertion
Granulocytes are white blood cells.
Reason
They contain lobed nuclei and
tiny granules.
A. If both the assertion and the reason are true and the
reason is correct explanation of the assertion.
B. If both the assertion and the reason are true but the
reason is not correct explanation of the assertion.
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Physics
Two capacitors of capacity \( C_{1} \) and \( C_{2} \)
are connected in parallel, then the
equivalent capacity is:
A \( \cdot C_{1}+C_{2} \)
в. \( C_{1} C_{2} /\left(C_{1}+C_{2}\right) \)
c. \( C_{1} / C_{2} \)
D. \( C_{2} / C_{1} \)
Subject: Physics
A stream of water flowing horozintally with a speed of \( 15 \mathrm{ms}^{-1} \) gushes out of a
tube of cross-sectional area \( 10^{-2} m^{2} \)
and hits a vertical wall nearly. The force exerted on the wall by the impact of water assuming it does not rebound is
A \( \cdot 2.25 \times 10^{3} N \)
В. \( 2.5 \times 10^{3} N \)
c. \( 3.0 \times 10^{3} N \)
D. \( 35 \times 10^{3} N \)
Subject: Physics
Two balls, each of radius \( R \), equal mass
and density are placed in contact, than the force of gravitation between them is
proportional to
\( ^{\mathrm{A}} \cdot F \propto \frac{1}{R^{2}} \)
в. \( F \propto R \)
\( c \cdot F \propto R^{4} \)
D. \( F \propto \frac{1}{R} \)
Subject: Physics
Fill in the blanks in the following:
(a) A person \( 1 \mathrm{m} \) in front of a plane mirror seems to be
from his image.
(b) If you touch your ear with
right hand in front of a plane mirror it will be seen in the mirror that your right
ear is touched with
(c) The size of the pupil becomes when you see in dim
light.
(d) Night birds have
cones than rods in their eyes.
Subject: Chemistry
A translucent white waxy solid \( (A) \) on
heating in an inert atmosphere is
converted to its allotropic form \( (\boldsymbol{B}) \)
Allotrope \( (A) \) on reaction with very
dilute aqueous \( K O H \) liberates a highly poisonous gas \( (C) \) having rotten fish smell. With excess of chlorine it forms
\( (D) \) which hydrolyses to compound \( (E) \) Identify compounds
\( (A) \) to \( (E) \)
Subject: Maths
The mean deviation of a frequency dist. is equal to
A \( \frac{\sum d_{i}}{\sum f_{i}} \)
в. \( \frac{\sum\left|d_{i}\right|}{\sum f_{i}} \)
\( c \cdot \frac{\sum f_{i} d_{i}}{\sum f_{i}} \)
D \( \cdot \frac{\sum f_{i}\left|d_{i}\right|}{\sum f_{i}} \)
Subject: Physics
A refrigerator converts \( 100 g \) of water at
\( 20^{\circ} \mathrm{C} \) to ice at \( -10^{\circ} \mathrm{C} \) in 35 minutes
Calculate the average rate of heat extraction in terms of watts.
Given:
Specific heat capacity of ice \( = \) \( 2.1 J g^{-1 o} C^{-1} \)
Specific heat capacity of water \( = \) \( 4.2 J g^{-1 o} C^{-1} \)
Specific Latent heat of fusion of ice
\( 336 J g^{-1} \)
Subject: Maths
if \( A=\left[\begin{array}{cc}2 & 3 \\ 5 & -7\end{array}\right] \) then \( \quad\left(A^{1}\right)^{2}= \)
A. \( \left[\begin{array}{ccc}5 & -7 & 12 \\ 1 & 4 & 22\end{array}\right] \)
B \( \cdot\left[\begin{array}{cc}1 & 17 \\ 1 & -4 \\ 0 & 2\end{array}\right] \)
c. \( \left[\begin{array}{cc}-19 & -25 \\ -15 & 64\end{array}\right] \)
D. \( \left[\begin{array}{cc}19 & -25 \\ -15 & 64\end{array}\right] \)
Subject: Maths
The number of integral values of \( \boldsymbol{m}, \) for
which the roots of \( x^{2}-2 m x+m^{2}- \)
\( \mathbf{1}=\mathbf{0} \) will between \( -\mathbf{2} \) and \( \mathbf{4} \) is :
A .2
B. 0
\( c .3 \)
D.
Subject: Chemistry
Which of the following coordination compounds will give precipitate with an
aqueous solution of \( A g N O_{3} ? \)
\( \mathbf{A} \cdot\left[C r\left(N H_{3}\right)_{6}\right] C l_{3} \)
B \( \cdot\left[C r\left(N H_{3}\right)_{3}\right] C l_{3} \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(N H_{3}\right)_{4}\right] S O_{4} \)
D. \( N a_{3}\left[C r(C N)_{6}\right] \)
Subject: Maths
f \( \boldsymbol{P Q \perp P S}, \boldsymbol{P Q} \| \boldsymbol{S R}, \angle \boldsymbol{S O R}=\mathbf{2 8}^{\boldsymbol{o}} \)
and \( \angle Q R T=65^{\circ}, \) then find \( x \& y \)
Subject: Maths
The converse of converse of the
statement \( \boldsymbol{p} \Longrightarrow \sim \boldsymbol{q} \) is
\( \mathbf{A} \cdot \sim q \Longrightarrow p \)
в. \( p \Longrightarrow q \)
\( \mathbf{c} \cdot p \Longrightarrow \sim q \)
D. \( q \Longrightarrow \sim p \)
Subject: Chemistry
Ammonia gas is formed by the combination of nitrogen and hydrogen.
\( N_{2}+3 H_{2} \rightarrow 2 N H \)
In the above equation:
This question has multiple correct options
A. nitrogen and hydrogen are reactants
B. one molecule of nitrogen combine with 3 molecule of hydrogen and forms two molecule of ammonia
C. one volume of nitrogen and three volume of hydrogen combine and give 2 volume of ammonia gas
D. reactants and products are not gases
Subject: Maths
Solve:
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} & -\boldsymbol{b} \\ -\boldsymbol{a} & \boldsymbol{0} & -\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{0}\end{array}\right|=0 \)
Subject: Maths
A function \( f(x) \) defined as \( f(x)= \) \( \left\{\begin{array}{ll}\sin x, & x \text { is rational } \\ \cos x, & x \text { is irrational }\end{array} \) is continuous \right.
at
A \( \cdot x=n \pi+\frac{\pi}{4}, n \in I \)
В \( \cdot x=n \pi+\frac{\pi}{8}, n \in I \)
c. \( x=n \pi+\frac{\pi}{6}, n \in I \)
D・ \( x=n \pi+\frac{\pi}{3}, n \in I \)
Subject: Physics
A ball with momentum \( 0.5 k g m s^{-1} \) coming towards a batsman is hit by him such that it goes on the same path in opposite direction with momentum \( 0.3 k g m s^{-1} . \) If the time of contact of
the ball with the bat is \( 0.02 s \), find the
force on the ball by the bat.
A . \( 10 N \)
в. \( 40 N \)
\( c .75 N \)
D. 30 N
Subject: Physics
One reversible heat engine operates
between \( 1600 \mathrm{K} \) and \( T_{2} \mathrm{K}, \) and another reversible heat engine operates
between \( T_{2} \) K and 400 K. If both the
engines have the same heat input and
output, then the temperature \( T_{2} \) must
be equal to:
A. 600
B. 800
\( c \cdot 650 \)
D. 675
Subject: Chemistry
\( Z n(O H)_{2} \) is an amphoteric hydroxide which is involved in the following two equilibria existing simultaneously in aqueous solution.
\( \boldsymbol{Z n}(\boldsymbol{O} \boldsymbol{H})_{2}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2 O H}^{-}(\boldsymbol{a q}) ; \boldsymbol{K}_{s p}=\mathbf{1 . 2} \times \mathbf{1 0}^{-\mathbf{1 7}} \)
\( \operatorname{Zn}(O H)_{2}(s)+2 O H^{-}(a q) \rightleftharpoons \)
\( \left[Z n(O H)_{4}\right]^{2-}(a q) ; K_{c}=0.12 \)
At what \( p H \) the solubility of \( Z n(O H)_{2} \) will be minimum?
A. \( p H=4.11 \)
в. \( p H=6.32 \)
c. \( p H=7.68 \)
D. \( p H=9.99 \)
Subject: Chemistry
Statement 1: Novolac is soft and has a
low melting point.

Statement 2: It is highly cross-linked
polymer.
A. Statement 1 is true; statement 2 is true; statement 2 is the correct explanation of statement
B. Statement 1 is true; statement 2 is true; statement 2 is not the correct explanation of statement 1
c. Statement 1 is true; statement 2 is false
D. Statement 1 is false; statement 2 is true
Subject: Maths
Solve the following equations by substitution method.
\( \boldsymbol{x}=\mathbf{2} \boldsymbol{y}-\mathbf{1} ; \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{7} \)
A. \( x=8, y=3 \)
в. \( x=2, y=3 \)
c. \( x=5, y=3 \)
D. \( x=1, y=3 \)
Subject: Maths
From the top of a cliff \( 24 \mathrm{mt} \) height, a man observes the angle of depression of
a boat is to be \( 60^{\circ} . \) The distance of the
boat from the foot of the cliff is
A. \( 8 \sqrt{3} \mathrm{mt} \)
t
B. \( 8 \sqrt{2} \mathrm{mt} \)
c. \( 8 \sqrt{5} \mathrm{m} \) t
D. \( 8 \mathrm{m} \)
Subject: Physics
A man of mass \( 62 \mathrm{kg} \) is standing on a stationary boat of mass 238 kg. The man is carrying a sphere of mass \( 0.5 \mathrm{kg} \) in his hands. If the man throws the
sphere horizontally with a velocity of
\( 12 m s-1, \) find the velocity with which the boat will move (in magnitude)
A \( .0 .02 m s^{-1} \)
B. \( 0.5 m s^{-1} \)
C. \( 0.04 m s^{-1} \)
D. \( 0.06 m s^{-1} \)
Subject: Chemistry
The equilibrium expression, \( \boldsymbol{K}=\left[\boldsymbol{C O}_{2}\right] \)
represents the reaction:
A. \( C(s)+O_{2}(g) \rightleftharpoons C O_{2}(g) \)
B. \( C O(g)+\frac{1}{2} O_{2}(g) \rightleftharpoons C O_{2}(g) \)
c. \( \operatorname{CaCO}_{3}(s) \rightleftharpoons C a O(s)+C O_{2}(g) \)
D. \( C O_{2}(g) \rightleftharpoons C(s)+O_{2}(g) \)
E \( \cdot \operatorname{CaO}(s)+C O_{2}(g) \rightleftharpoons \operatorname{CaCO}_{3}(s) \)