AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following is true regarding
sign of heat and work?
A. Heat absorbed by the system has positive sign. Heat released to the surrounding has negative sign. Work done on the system has positive sign. Work done by the system has negative sign.
B. Heat absorbed by the system has negative sign. Heat released to the surrounding has positive sign. Work done on the system has positive sign. Work done by the system has negative sign.
C. Heat absorbed by the system has negative sign. Heat released to the surrounding has positive sign. Work done on the system has negative sign. Work done by the system has positive sign.
D. Heat absorbed by the system has positive sign. Heat released to the surrounding has negative sign. Work done on the system has negative sign. Work done by the system has positive sign.
Subject: Biology
Identify the correct order of the size of the structures from the smallest to the
largest.
I= Bacterium
II = Enzyme
III= Nucleus
\( \mathrm{IV}= \) Chromosome
\( \mathrm{V}= \) Molecule of water
A. V- II-I-IV-III
c. \( v-1-11-111-1 v \)
E . II-V-IV-III
Subject: Physics
Five identical conducting plates, 1.2,3,4 and 5 are fixed parallel plates equidistant from each other (see
figure). A conductor connects plates 2
and 5 while another conductor joins 1
and 3. The junction of 1 and 3 and the plate 4 are connected to a source of
constant emf \( V_{o} \). Find the effective
capacitance of the system between the terminals of source where \( d \) is the
distance between any two successive
plates
Subject: Maths
The range of a random variable \( \boldsymbol{X} \) is
\{0,1,2\} and given that \( P(X=0)= \)
\( \mathbf{3 c}^{3}, \quad \boldsymbol{P}(\boldsymbol{X}=\mathbf{1})=\mathbf{4 c}- \)
\( \mathbf{1 0 c}^{2}, \quad \boldsymbol{P}(\boldsymbol{X}=\mathbf{2})=\mathbf{5} c-\mathbf{1}, \) find (i)
the value of \( c \)
(ii) \( \boldsymbol{P}(\boldsymbol{X}<\mathbf{1}), \quad \boldsymbol{P}(1<\boldsymbol{X} \leq \)
2) \( , \quad P(0<X \leq 3) \)
Subject: Physics
The current voltage relationship of a
diode is \( I=I_{x}\left[\exp \left(\frac{e V}{k T}\right)-1\right] \) where e is
charge on an electron, \( V \) is voltage applied, k is Boltzmann's constant, T is
temperature in Kelvin. Find the
resistance of the diode if \( \mathrm{I},=1.5 \mathrm{m} A \)
and \( \boldsymbol{T}=\mathbf{3 9 8 K} \)
A \( \cdot \frac{100}{3} \Omega \)
B. \( \frac{50}{3} \Omega \)
\( c \cdot \frac{500}{3} \Omega \)
D. \( \frac{200}{3} \Omega \)
Subject: Physics
An electric dipole moment \( \vec{P}=(2.0 \hat{i}+3.0 \hat{j}) \mu C . . m \) is placed in a
uniform electric field \( \vec{E}=(3.0 \hat{\mathrm{i}}+2.0 \widehat{k}) \times 10^{5} \)
A \( \cdot \) The torque that \( \overrightarrow{\mathrm{E}} \) exert on \( \overrightarrow{\mathrm{P}} \) is \( (0.6 \hat{\mathrm{f}}+0.4 \hat{\mathrm{j}}-0.9 \widehat{\mathrm{k}}) \mathrm{Nm} \)
B. The potential energy of the dipole is -0.6
c. The potential energy of the dipole is 0.6 .
D. None of these
Subject: Physics
A parallel beam of light is incident from
air at an angle \( \alpha \) on the side PQ of a
right-angled triangular prism of refractive index \( n=\sqrt{2} . \) Light
undergoes total internal reflection in
the prism at the face PR when \( \alpha \) has
minimum value of \( 45^{\circ} . \) The angle \( \theta \) of
the prism is:
A . \( 15^{\circ} \)
B . \( 22.5^{\circ} \)
\( c .30 \)
D. 45
Subject: Maths
Use the Venn diagram to answer the
following questions
(i) List \( U, G \) and \( H \)
(ii) Find \( G^{\prime}, H^{\prime}, G^{\prime} \cap H^{\prime}, n(G \cup H)^{\prime} \) and
\( \boldsymbol{n}(\boldsymbol{G} \cap \boldsymbol{H})^{\prime} \)
Subject: Chemistry
Which of the following is true
statement?
A. The lower aldehydes have pungent ordour, but as molecular mass increases odour becomes less pungent and more fragrant.
B. The lower aldehydes have fragrant ordour, but as molecular mass increases odour becomes less
fragrant and more pungent.
C. The lower aldehydes have pungent ordour, but as molecular mass increases odour disappears.
D. The lower aldehydes have fragrant ordour, but as molecular mass increases odour disappears.
Subject: Maths
For the differential equation \( x \frac{d y}{d x}- \) \( \boldsymbol{y}=\sqrt{\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right)}, \) show that its solution
is \( y+\sqrt{\left(x^{2}+y^{2}\right)}=k x^{2} \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\}, \boldsymbol{B}= \)
\{1,3,5,7,9,10,17,26,30\} Which of the
following sets of ordered pairs are (i) relations (ii) functions (iii) neither,from
\( A \) to \( B \)
\( (a) R_{1}=\{(1,3),(3,3),(5,17),(1,2)\} \)
(b) \( R_{2}=\{(3,7),(4,5),(5,30)\} \)
(c) \( R_{3}=\{(x, y): x \epsilon A, y \epsilon B, x+y=8\} \)
(d) \( R_{4}= \)
\( \left\{(x, y): x \epsilon A, y \epsilon B, y=x^{2}+1\right\}(e) \)
\( \boldsymbol{R}_{5}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{A}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{B}, \boldsymbol{y}=\boldsymbol{2} \boldsymbol{x}-\mathbf{1}\} \)
Subject: Maths
If \( P(3,2,-4), Q(5,4,-6) \) and \( R \)
(9,8,-10) are collinear, then \( R \) divides PQ in the ratio
A. 3: 2 internally
B. 3: 2 externally
c. 2: 1 internally
D. 2: 1 externally
Subject: Maths
The relation \( R \) defined on the \( \operatorname{set} A= \)
\{1,2,3,4,5\} by \( R= \)
\( \left\{(x, y):\left|x^{2}-y^{2}\right|<16\right\} \) is given by
A \( \cdot\{(1,1),(2,1),(3,1),(4,1),(2,3)\} \)
B - \{(2,2),(3,2),(4,2),(2,4)\}
C \( \cdot\{(3,3),(4,3),(5,4),(3,4)\} \)
D. None of these
Subject: Chemistry
4 mol of a solution containing \( \boldsymbol{A}^{\boldsymbol{n}} \) requires 1.6 mol of \( M n O_{4}^{\ominus} \) for the oxidation of \( A^{n+} \) to \( A O_{3}^{\ominus} \) in acidic
medium. The value of \( n \) is :
A . 1
B . 2
\( c .3 \)
D.
Subject: Physics
toppr
Q Type your question
\( r, \) as seen in the picture.
If each of the diagrams among the
possible answers shows flies with the same acceleration as the one pictured
directly below, which fly has a speed that is twice the speed of the fly pictured directly below?
\( A \)
B.
\( c \)
radius \( =r / 2 \)
D.
radius \( =r / 4 \)
E. None of the objects in this question are accelerating
since thev al speed
Subject: Physics
A long block \( A \) is at rest on a smooth horizontal surface. A small block B
whose mass is half of mass of A is
placed on \( A \) at one end and is given an
initial velocity u as shown in Fig. 8.274 The coefficient of friction between the
blocks is \( \mu \)
This question has multiple correct options
A. Finally both move with a common velocity \( 2 u / 3 \)
B. Acceleration of B relative to A initially is \( 3 \mu g / 2 \) towards left.
c. Magnitude of total work done by friction is equal to the final kinetic energy of the system.
D. The ratio of initial to final momentum of the system is
1
Subject: Chemistry
Which of the following is not a balanced
equation?
A \( \cdot C a(O H)_{2}+C O_{2} \rightarrow C a C O_{3}+H_{2} O \)
в. \( F e+C u S O_{4} \rightarrow F e S O_{4}+C u \)
c. \( K C l O_{4} \stackrel{\Delta}{\longrightarrow} K C l+2 O_{2} \)
D. \( C u+2 H N O_{3} \rightarrow C u\left(N O_{3}\right)_{2}+2 N O_{2}+H_{2} O \)
Subject: Physics
A concave mirror of radius of curvature
\( 40 \mathrm{cm} \) forms an image of an object placed on the principal axis at a distance \( 45 \mathrm{cm} \) in front of it. Now if the system (including object) is completely immersed in water \( (\mu=1.33), \) then:
A. the image will shift towards the mirror
B. the magnification will reduce.
c. the image will shift away from the mirror and magnification will increase.
D. the position of the image and magnification will not change.
Subject: Physics
A \( \alpha \) - particle is accelerated through a potential difference of \( V \) volts from rest. The de-Broglie wavelength associated with it is (in angstrom):
A \( \cdot \sqrt{\frac{150}{V}} \)
в. \( \frac{0.286}{\sqrt{V}} \)
c. \( \frac{0.101}{\sqrt{V}} \)
D. \( \frac{0.983}{\sqrt{V}} \)
Subject: Physics
The angular velocity of a rotating body is \( \vec{\omega}=4 \hat{i}+\hat{j}-2 \hat{k} . \) The linear velocity of the body whose position vector is \( 2 \hat{i}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}-\mathbf{3} \hat{\boldsymbol{k}} \) is:
A \( .5 \hat{i}+8 \hat{j}+14 \hat{k} \)
B . \( 3 \hat{i}+8 \hat{j}+10 \hat{k} \)
c. \( 8 \hat{i}-3 \hat{j}+2 \hat{k} \)
D . \( -8 \hat{i}+3 \hat{j}+2 \hat{k} \)
Subject: Chemistry
Of the two solvent \( H_{2} O \) and \( D_{2} O \)
NaCl dissolves:
A. equally in both solvents
B. only in \( H_{2} O \) but remains insoluble in \( D_{2} O \)
c. more in \( D_{2} \) O
D. more in \( H_{2} \) O
Subject: Chemistry
In the commercial extraction of iron,
roasting is adopted because:
This question has multiple correct options
A. it removes impurities of \( S, A s \), and \( S b \) in the form of their elemental vapor
B. it prevents slag formation by \( F e_{2} O_{3} \)
C. it prevents slag formation by \( \mathrm{FeO} \)
D. limonite is converted into its anhydrous form
Subject: Physics
A \( p \) -type semiconductor has acceptor levels 57 me \( V \) above the valance band.
The maximum wavelength of light required to create a hole is (Planck's
constant \( \left.h=6.6 \times 10^{-34} J-s\right) \)
A \( .57 \AA \)
В. \( 57 \times 10^{-3} \dot{A} \)
c. 217100 月
D . \( 11.61 \times 10^{-33} \dot{A} \)
Subject: Chemistry
Correct order of bond angles for the following is:
A. \( N H_{3}>P C l_{3}>B C l_{3} \)
В. \( B C l_{3}>C H_{4}>P C l_{3} \)
c. \( B C l_{3}>P C l_{3}>N H_{3} \)
D. \( P C l_{3}>B C l_{3}>N H_{3} \)
Subject: Physics
A Cathode ray tube emits \( 1.875 \times 10^{3} \)
electrons per second when heated. When \( 600 \mathrm{V} \) is applied to the anode all the electrons emitted reach the anode.
The maximum electron current will be
A. \( 3 A \)
в. \( 3 \mu A \)
\( c .3 m A \)
D. None of these
Subject: Physics
Assertion
Work-energy theorem can be applied for
non-inertial frames also.
Reason
Earth is a non-inertial frame.
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: Chemistry
Which of the following statement is not
correct?
A. Fe, Ni, Co form interstetial compound
в. \( C u S O_{4}+C a(O H)_{2} \) is called Bordeaux mixture
c. verdigris is basic copper acetate \( \left[C u\left(C O O C H_{3}\right)_{2} C u(O H)_{2}\right] \)
D. 24 carat gold is an alloy of Au and cu
Subject: Maths
Let \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\}, \boldsymbol{B}=\{\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w}\} . \) Then
the function \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{u}, \boldsymbol{f}(\boldsymbol{y})=\boldsymbol{v}, \boldsymbol{f}(\boldsymbol{z})=\boldsymbol{w} \) is
A. Many-one into
B. One-one into
c. One-one onto
D. Many-one onto
Subject: Physics
A parallel plate capacitor of capacitance \( 5 \mu F \) and plate separation \( 6 \mathrm{cm} \) is connected to a \( 1 \mathrm{V} \) battery and charged. A dielectric of dielectric
constant 4 and thickness \( 4 \mathrm{cm} \) is
introduced between the plates of the
capacitor. The additional charge that flows into the capacitor from the battery is
A. \( 2 \mu C \)
в. \( 3 \mu C \)
\( c \cdot 5 \mu C \)
D. 10 \( \mu C \)
Subject: Maths
The focal length of a mirror is given by \( \frac{2}{f}=\frac{1}{v}-\frac{1}{u} . \) In finding the values of
and \( v, \) the errors are equal and equal to
'p'. The the relative error in \( f \) is
A \( \cdot \frac{p}{2}\left(\frac{1}{u}+\frac{1}{v}\right) \)
в. \( p\left(\frac{1}{u}+\frac{1}{v}\right) \)
c. \( \frac{p}{2}\left(\frac{1}{u}-\frac{1}{v}\right) \)
D. \( _{p}\left(\frac{1}{u}-\frac{1}{v}\right) \)
Subject: Physics
Match the following:
\( A \cdot A-r, B-s, C-p \)
D-q, \( E-L \)
1, E-U \( D-q \)
\( B \cdot A-S, B-r, C-p, \)
\( C \cdot A-r, B-S, C-u, D-q, E-p \)
D. A-q, B-s, C-p, D-r \( E-L \)
Subject: Chemistry
Dilute nitric acid is generally
considered a typical acid except for its reaction with metals. In what way is
dilute nitric acid different from other
acids when it reacts with metals.
A. It acts as an reducing agent so hydrogen gas is liberated
B. It acts as an oxidising agent so hydrogen gas is liberated
c. It acts as an oxidising agent so NO gas and water are formed
D. It acts as an reducing agent so NO gas and water are formed
Subject: Maths
The height (in \( \mathrm{cm} \) ) of 50 students in a particular class are given. Find the median.
\( \begin{array}{lll}\mathbf{1 5 6} & \mathbf{1 5 5} & \mathbf{1 5 4}\end{array} \) Height
(in \( \mathrm{cm} \) )
Numbe of studen
Subject: Physics
A proton moves at a speed \( \boldsymbol{v}=\mathbf{2} \times \)
\( 10^{6} m / s \) in a region of constant
magnetic field of magnitude \( \boldsymbol{B}= \)
\( 0.05 T . \) The direction of the proton when
it enters this field is \( \theta=30^{\circ} \) to the field.
When you look along the direction of the magnetic field, the path is a circle projected on a plane perpendicular to the magnetic field. How far will the
protons move along the direction of \( \boldsymbol{B} \)
when 2 projected circles have been completed?
Subject: Chemistry
Identify \( A \) and \( B \) in the following reaction
sequence:
\( C_{2} H_{6} \stackrel{A}{\longrightarrow} C_{2} H_{5} C l \frac{Z n / T H F}{\longrightarrow} B \)
A \( \cdot C l_{2} / u v \) light and \( C_{4} H_{1} \)
B. \( P C l_{3} \) and \( C_{2} H_{4} \)
c. \( H C l \) and \( C_{2} H_{6} \)
D. \( C l_{2} \) and \( C_{2} H_{2} \)
Subject: Physics
If \( \overrightarrow{\boldsymbol{A}}=2 \hat{\boldsymbol{i}}+\boldsymbol{7} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+ \)
\( 5 \hat{k} \) Find the component of \( \vec{A} \) and \( \vec{B} \)
Subject: Physics
For the circuit shown in Figure, the
equivalent resistance between \( \boldsymbol{A} \) and \( \boldsymbol{C} \)
is
\( A \cdot \frac{12}{11} \)
B. \( \frac{13}{11} \)
\( c \cdot \frac{14}{11} r \)
\( D \cdot \frac{15}{11} \)
Subject: Chemistry
Assertion
Clothes washed with soap using hard
water do not absorb dyes evenly.
Reason

Hard water contains calcium and
magnesium ions.
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: Biology
Given below are five groups of five terms in each. Arrange the terms in each group in their proper sequence.
I.Renal Pelvis, Urethra, Ureter Kidney
Urinary Bladder
ii. Sodium ions move into the axon,
Repolarisation. Polarisation, Stimulus, Depolarisation
iii. ATP is produced, guard cells photosynthesise during the day guard cells become more turgid. guard cells become hypertonic, Potassium ions are actively pumped into the guard cells iv Efferent ducts, Network of ducts,
Seminiferous tubules. Urethra, Vas
deferens v. Response, Effector Brain or Spinal Cord, Receptor Stimulus
Subject: Physics
on x-axis at \( (-a, 0) \) and \( (+a, 0) \)
respectively, as shown in Fig. They are
connected by a light string. A force F is applied at the origin along vertical direction. As a result, the masses move
towards each other without loosing
contact with ground. What is the
acceleration of each mass? Assuming
the instantaneous position of the masses as \( (-x, 0) \) and \( (x, 0) \)
respectively.
\( ^{\mathbf{A}} \cdot \frac{2 F}{m} \cdot \frac{\sqrt{a^{2}-x^{2}}}{x} \)
B. \( \frac{2 F}{m} \cdot \frac{x}{\sqrt{a^{2}-x^{2}}} \)
c. \( \frac{F}{2 m} \cdot \frac{x}{\sqrt{a^{2}-x^{2}}} \)
D. \( \frac{F}{m} \cdot \frac{x}{\sqrt{a^{2}-x^{2}}} \)
Subject: Chemistry
Consider the equilibrium \( 2 N O(g)+ \)
\( \boldsymbol{C l}_{2} \rightleftharpoons 2 \boldsymbol{N} \boldsymbol{O} \boldsymbol{C l}(\boldsymbol{g}) \) for which \( \boldsymbol{\Delta} \boldsymbol{H}^{\boldsymbol{o}}= \)
\( -77.07 k J m o l^{-1} . \) How will the amount
of \( C l_{2} \) at equilibrium be affected?
A. Removal of NO (g)
B. Addition of NOCI \( (g) \)
c. Raising the temperature
D. All the above
Subject: Physics
Gravitational potential difference between surface of a planet and a point
situated at a height of \( 20 m \) above its
surface is 2 joule/kg. If gravitational field is uniform, then the work done in
taking a \( 5 k g \) body of height 4 meter above surface will be :-
\( A \cdot 2 J \)
B. \( 20 J \)
c. \( 40 J \)
D. \( 10 J \)
Subject: Physics
The potential difference between points \( A \) and \( B \) in the circuit shown in figure
is \( 16 \mathrm{V} \). Then,
This question has multiple correct options
A. the current through the \( 2 \Omega \) resistance is 3.5 A
B. the current through the \( 4 \Omega \) resistance is 2.5 A
c. the current through the \( 3 \Omega \) resistance is 1.5 A
D. the potential difference between the terminals of the V battery is 7 V
Subject: Physics
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. the
energy required to rotate it by \( 60^{\circ} \) is \( W \) Now the torque required to keep the magnet in this new position is.
A. \( \frac{2 W}{\sqrt{3}} \)
B. \( \frac{W}{\sqrt{3}} \)
c. \( \sqrt{3} W \)
D. \( \frac{\sqrt{3}}{2} W \)
Subject: Chemistry
The main reaction(s) which occur(s) in
blast furnace during extraction of iron from haematite is(are):
This question has multiple correct options
A. \( 2 F e_{2} O_{3}+3 C \rightarrow 4 F e+3 C O_{2} \)
в. \( F e O+S i O_{2} \rightarrow F e S i O_{3} \)
c. \( F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)
D. \( C a O+S i O_{2} \rightarrow C a S i O_{3} \)
Subject: Maths
If \( f(x)=\left[\cos x \cos (x+2)-\cos ^{2}(x+\right. \)
1) \( ] \) where \( [.] \) denotes the greatest integer function \( \leq x \). Then solution of
the equation \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. none of these
Subject: Physics
The initial velocity of a particle is \( u \)
\( (a t t=0) \) and the acceleration is given
by \( \boldsymbol{f}=\boldsymbol{a t} . \) Which of the following
relations is valid?
A \( \cdot v=u+a t^{2} \)
B. \( v=u+\frac{a t^{2}}{2} \)
\( \mathbf{c} \cdot v=u+a t \)
\( \mathbf{D} \cdot v=u \)
Subject: Physics
Taking the earth to be a uniform sphere of radius \( 6400 \mathrm{km} \) and the value of \( g \) at
the surface to be \( 10 \mathrm{m} s^{-2} \), calculate the
energy needed to raise a satellite of
mass \( 2000 \mathrm{kg} \) to a height of \( 800 \mathrm{km} \) above the earth's surface and to set it
into circular orbit at that altitude.
B. \( 8 \times 10^{10} \) J.
\( \mathbf{c} \cdot 9 \times 10^{10} J \)
D. \( 1.8 \times 10^{10} \) J.
Subject: Physics
On a platform a man is watching two trains one leaving the station the other approaching the station, both with the same velocity \( 2 \mathrm{m} / \mathrm{s} \) and blowing their horn with a frequency 480 Hz. The number of beats heard by the man will
be (Velocity of sound in air is \( 320 \mathrm{m} / \mathrm{s} \) )
A . 6
B. 3
c. 2
D. 4
Subject: Chemistry
Which of the following is not true?
A. Ordinary water is electrolysed more rapidly than \( D_{2} O \)
B. \( D_{2} O \) freezes at lower temperature than \( H_{2} O \)
C. Reaction between \( H_{2} \) and \( C l_{2} \) is much faster than \( D_{2} \)
and \( C l_{2} \)
D. Bond dissociation energy for \( D_{2} \) is greater than \( H_{2} \)
Subject: Physics
The area of cross-section of the wider
tube shown in figure is \( 800 \mathrm{cm}^{2} . \) If \( \mathrm{a} \)
mass of \( 12 \mathrm{kg} \) is placed on the massless piston, the difference in heights h in the level of water in the two tubes is :
\( A \cdot 10 \mathrm{cm} \)
B. 6 cm
\( c \cdot 15 \mathrm{cm} \)
D. \( 2 \mathrm{cm} \)
Subject: Physics
A body falls freely from rest. If at an instant, the velocity acquired is numerically equal to the displacement, then the velocity acquired is:
A. \( 9.8 \mathrm{m} / \mathrm{s} \)
B. \( 19.6 \mathrm{m} / \mathrm{s} \)
c. \( 29.4 \mathrm{m} / \mathrm{s} \)
D. \( 39.2 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.294 to \( 1.139 \mathrm{gm} L^{-1} \). Sulphuric acid
of density \( 1.294 \mathrm{gm} L^{-1} \) is \( 39 \% \) by weight
and that of density 1.139 gm \( L^{-1} \) is \( 20 \% \) by
weight. The battery holds 3.5 litres of acid and the column practically remained
constant during the discharge.

Calculate the number of ampere-hours for which the battery must have been used. The charging and discharging reactions are :
\( P b+S O_{4}^{2-} \rightarrow P b S O_{4}+2 e^{-}(\text {charging }) \)
\( P b O_{2}+4 H^{+}+S O_{4}^{2-}+2 e^{-} \rightarrow P b S O_{4}+ \)
\( 2 H_{2} O(\text { discharging }) \)
\( \mathbf{A} \cdot 297 \)
B. 189
c. 274
D. 200
Subject: Maths
If \( ^{n} C_{r} \) denots the number of
combinations of \( n \) things taken \( r \) at a
time, then the expression \( ^{n} C_{r+1}+^{n} \)
\( C_{r-1}+2 \times^{n} C_{r} \) equals
A. \( ^{n+2} C_{r} \)
B. \( ^{n+2} C_{r+1} \)
c. \( ^{n+1} C_{r} \)
D. \( n+1 C_{r+1} \)
Subject: Maths
The angle between the lines \( x+y- \)
\( \mathbf{3}=\mathbf{0} \) and \( \boldsymbol{x}-\boldsymbol{y}+\mathbf{3}=\mathbf{0} \) is \( \boldsymbol{\alpha} \) and the
acute angle between the lines \( x- \) \( \sqrt{3 y}+2 \sqrt{3}=0 \) and \( \sqrt{3 x}-y+1=0 \)
is
\( \beta . \) Which one of the following is
correct?
A. \( \alpha=\beta \)
в. \( \alpha>\beta \)
c. \( \alpha<\beta \)
D. \( \alpha=2 \beta \)
Subject: Physics
\( 10^{22} \) particle each of mass \( 10^{-26} \mathrm{Kg} \) are
striking perpendicularly on a wall of \( \operatorname{area} 1 m^{2} \) with speed \( 10^{4} m / s \) in 1 sec
The pressure on the wall if collisions are
perfectly elastic is:
A \( \cdot 2 N / m^{2} \)
в. \( 4 N / m^{2} \)
\( \mathrm{c} \cdot 6 N / m^{2} \)
D. \( 8 N / m^{2} \)
Subject: Maths
Let \( \bar{a}, \bar{b}, \bar{c} \) be three non-zero vectors, no two of which are collinear. If the vector
\( \bar{a}+2 \bar{b} \) is collinear with \( \bar{c} \) and \( \bar{b}+3 \bar{c} \) is
collinear with \( \bar{a}, \) then \( \bar{a}+\bar{b}+3 \bar{c}= \)
\( \mathbf{A} \cdot \lambda \bar{a} \bar{a} \)
в. \( \lambda \bar{b} \)
\( c \cdot \lambda \bar{c} \)
D.
Subject: Chemistry
A constant electric current flows for 4
hours through two electrolytic cells connected in series. One contains
\( \mathrm{AgNO}_{3} \) solution and second contains
\( \mathrm{CuCl}_{2} \) solution. During this time 4 grams of Ag are deposited in the first cell.
(a) How many grams of Cu are deposited in the second cell?
(b) What is the current flowing in amperes?
Subject: Physics
Figure shows a conducting loop \( A B C D A \) placed in a uniform magnetic field (strength \( B \) ) perpendicular to its plane. The part \( A B C \) is the (three-
fourth) portion of the square of side Iength \( l \). The part \( A D C \) is a circular arc
of radius \( R \). The points \( A \) and \( C \) are
connected to a battery which supplies a current \( I \) to the circuit. The magnetic force on the loop due to the field \( B \) is :
A . zero
В. \( B I l \)
c. \( 2 B I R \)
D.
\[
\frac{B I l R}{I+R}
\]
Subject: Physics
A highly rigid cubical block A of smal mass M and side L is fixed rigidly onto another cubical block B of same
dimensions and of low modulus of
rigidly \( \eta \) such that lower face of \( A \) completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force is
applied perpendicular to one the side face of A. After the force is withdrawn, block A executes small oscillations, the
time period of which is given by
в. \( 2 \pi \sqrt{\frac{M}{\eta L}} \)
c. \( 2 \pi \sqrt{\frac{M L}{\eta}} \)
D. \( \sqrt{\frac{M \eta}{L}} \)
Subject: Maths
Find the area of \( \square A B C D \)
\( \mathbf{A} \cdot 4(24+25 \sqrt{3}) c m^{2} \)
B \( \cdot 4(25+24 \sqrt{3}) c m^{2} \)
\( \mathbf{c} \cdot 2(24+25 \sqrt{3}) c m^{2} \)
D. None of these