AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A uniform disc of mass \( \mathrm{m} \) and radius \( \mathrm{R} \)
is projected horizontally with velocity \( v_{0} \) on a rough horizontal floor so that it starts off with a purely sliding motion at
\( t=0 . \) After \( t_{0} \) seconds it acquires a pure rolling motion. Calculate the velocity of
the centre of mass of the disc at \( t_{0} \)
A \( \cdot v=(2 / 4) v_{0} \)
B. \( v=(2 / 3) v_{0} \)
\( c \cdot v=(3 / 3) v_{0} \)
\( D \cdot v=(4 / 3) v_{0} \)
Subject: Chemistry
Balance the following equation by oxidation number method
¡) \( K_{2} C r_{2} O_{7}+K I+H_{2} S O_{4} \rightarrow \)
\( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{C r}_{2}\left(\boldsymbol{S O}_{4}\right)_{3}+\boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
ii) \( K M n O_{4}+N a_{2} S O_{3} \rightarrow M n O_{2}+ \)
\( N a_{2} S O_{4}+K O H \)
iii) \( \boldsymbol{C u}+\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+ \)
\( N O_{2}+H_{2} O \)
iv) \( K M n O_{4}+H_{2} C_{2} O_{4}+H_{2} S O_{4} \rightarrow \)
\( \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
Subject: Physics
large metal sheet carries an electric current along its surface. Current per unit length is \( \lambda . \) Magnetic field near the metal sheet is
(0)(0)(0)(0)(0)(0)(0)(0)
\( A \cdot \frac{\lambda \mu}{2} \)
B. \( \frac{\lambda \mu}{2 \pi} \)
c. \( \lambda \mu_{0} \)
\( D \cdot \frac{\mu}{2 \pi \pi} \)
Subject: Maths
For construction of a quadrilateral \( A B C D, \) where \( A B=4.2 \mathrm{cm}, B C=3.8 \)
\( \mathrm{cm}, C D=4.9 \mathrm{cm}, A D=5.4 \mathrm{cm} \) and
\( \angle B=72 . \) Its steps for construction is
given injumbled form. Identify the first step from the following:
1) From \( B \), set off \( B C=3.8 \mathrm{cm} \)
2) Draw \( A B=4.2 \mathrm{cm} \) and Make
\( \angle A B X=72^{\circ} \)
3) With \( A \) as center and radius equal to
\( \mathbf{5 . 4} \mathrm{cm} \) draw an arc.
4) With \( C \) as center and radius equal to \( 4.9 \mathrm{cm}, \) draw another arc, cutting the previous arc at \( D . \) Join \( A D \) and \( C D \)
\( A \)
в. 3
\( c \cdot 4 \)
\( D \)
Subject: Biology
toppr
Q Type your question
Nucleus
\( \sqrt{c} \)
es
Yes

Yes res
The three cell types were grown in separate cultures with plenty of oxygen and nutrients available. Figure 1 shows
their rates of growth. At time 1 , oxygen was no longer available to the cells.
Given below are three equations.
(।) \( C_{6} H_{12} O_{6}+6 O_{2} \rightarrow 6 C O_{2}+ \)
\( 6 H_{2} O+A T P \)
(II) \( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{l i g h t} \rightarrow \boldsymbol{O}_{2}+\boldsymbol{A} \boldsymbol{T} \boldsymbol{P}+ \)
\( N A D P H \)
(III) \( 6 \mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O}+\mathrm{ATP}+\mathrm{NADPH} \rightarrow \)
\( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O} \)
Cell type \( C \) would show equation
A. I only
B. II only
c. I and III only
D. II and III only
E. I, II and III
Subject: Physics
An electric dipole is placed at an angle
of \( 30^{\circ} \) with an electric field of intensity
\( 2 \times 10^{5} N C^{-1} . \) It experiences a torque
of \( 4 N m . \) Calculate the charge on the
dipole if the dipole length is \( 2 \mathrm{cm} \) :
\( A \cdot 8 m C \)
в. \( 4 m C \)
\( c \cdot 8 \mu C \)
D. \( 2 m C \)
Subject: Physics
The filament of a bulb takes a current
\( 100 \mathrm{mA} \) when potential difference across it is \( 0.2 \mathrm{V} \). When the potential difference across it becomes \( 1.0 \mathrm{V} \), the
current becomes 400 mA. Calculate the
resistance of filament in each case and
account for the difference.
\( A \cdot 2,2.5 \)
B. 3, 3.5
\( c \cdot 4,0 \)
D. 5,
Subject: Maths
The Point \( (s) \) on the cure \( y^{3}+3 x^{2}= \)
\( 12 y \) where the tangent is vertical
(parallel to y-axis), is/are.
\( \mathbf{A} \cdot\left[\pm \frac{4}{\sqrt{3}},-2\right] \)
B \( \cdot\left(\pm \frac{\sqrt{11}}{3}, 1\right) \)
D \( \cdot\left(\pm \frac{4}{\sqrt{3}}, 2\right) \)
Subject: Physics
Effective capacitance between \( A \) and \( B \)
in the figure shown is (all capacitances
\( \operatorname{are} \operatorname{in} \mu \boldsymbol{F}) \)
\( ^{A} \cdot \frac{3}{14} \mu F \)
в. \( \frac{14}{3} \mu F \)
\( c \cdot 21 \mu F \)
D. \( 23 \mu F \)
Subject: Chemistry
Liver of sulphur is a mixture of :
A. Potassium pentasulphide \( (A) \) and potassium thiosulphate \( (B) \)
B. Potassium carbonate \( (C) \) and potassium thiosulphate
\( (B) \) above
C. Potassium disulphide \( (D) \) and potassium thiosulphate \( (B) \) above
D. \( (B) \) and \( (D) \) above
Subject: Physics
Alida runs her toy car on dry marble floor, wet marble floor, newspaper and towel spread on the floor. The force of friction acting on the car on different surfaces in increasing order will be
A. wet marble floor, dry marble floor, newspaper, towel.
B. newspaper,towel, dry marble floor, wet marble floor.
c. towel,newspaper, dry marble floor, wet marble floor.
D. wet marble floor, dry marble floor, towel, newspaper.
Subject: Physics
The resistive force suffered by a motor
boat is \( \propto V^{2} . \) When the engine was
shutdown, the velocity is \( V_{0} . \) Find the
average velocity at any time \( t \)
A \( \cdot V_{a V}=\frac{V_{0}+V}{2} \)
B. \( \frac{V V_{0}}{2\left(V_{0}+V\right)} \)
\( c \)
\( \frac{2 V V_{0} \log _{e} \frac{V_{0}}{V}}{\left(V_{0}+V\right)} \)
Subject: Physics
When \( M_{1} \) gram of ice at \( -10^{0} C \)
(specific heat \( =\mathbf{0 . 5} \) calg\( ^{10} \boldsymbol{C}^{-1} \) ) is
added to \( M_{2} \) gram of water at \( 50^{\circ} C \) finally no ice is left and the water is at
\( 0^{o} C . \) The value of latent heat of ice, in
cal \( g^{-1} \) is:
\( ^{\mathrm{A}} \cdot \frac{5 M_{1}}{M_{2}}-50 \)
в. \( \frac{5 M_{2}}{M_{1}} \)
c. \( \frac{50 M_{2}}{M_{1}}-5 \)
D. \( \frac{5 M_{2}}{M_{1}}-5 \)
Subject: Chemistry
An aqueous solution of a metal salt \( (X) \)
reacts with carbon dioxide to give a water soluble compound (Y) which on heating gives the starting metal salt back Y when present in water does not produce lather with soap. The compounds \( X \) and \( Y \), respectively are
A. \( C a C O_{3} \) and \( C a\left(H C O_{3}\right)_{2} \)
в. \( M g\left(H C O_{3}\right)_{2} \) and \( M g C O_{3} \)
c. \( C a\left(H C O_{3}\right)_{2} \) and \( C a C O_{3} \)
D. \( M g C O_{3} \) and \( M g\left(H C O_{3}\right)_{2} \)
Subject: Maths
Chose the correct alternative from the
given below questions:
The sequency -25,-23,-21,-19
A. is an \( A \).P. Reason \( d=3 \)
B. is an A.P. Reason \( d=2 \)
c. is an A.P. Reason \( d=4 \)
D. is not an \( A . P \)
Subject: Chemistry
Which will have the lowest freezing
point?
A. A 0.01-molar solution of HNO
B. A 0.01-molar solution of \( \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)
C. A 0.01-molar solution of Cu(NO \( _{3} \) )
D. A 0.01-molar solution of NaNO
Subject: Chemistry
The increasing \( d \) -character in
hybridisation of \( X e \) in
\( X e F_{2}, X e F_{4}, X e F_{6} \) is :
A. \( \mathrm{XeF}_{2}<\mathrm{XeF}_{4}<\mathrm{XeF}_{6} \)
B. \( \mathrm{XeF}_{4}<\mathrm{XeF}_{2}<\mathrm{XeF}_{6} \)
\( \mathbf{c} \cdot \mathbf{X}_{\mathbf{e}} F_{6}<\mathbf{X} \mathbf{e} F_{4}<\mathbf{X}_{\mathbf{e}} F_{2} \)
D. \( \mathrm{XeF}_{2}<\mathrm{XeF}_{6}<\mathrm{XeF}_{4} \)
Subject: Physics
A silicon piece and a silver piece are connected in series and a potential
difference is applied between their free ends. The potential difference applied
on them are \( V_{1} \) and \( V_{2} \) respectively
They are then cooled to \( 200 K . \) Now
A \( \cdot V_{1} \) increases and \( V_{2} \) decreases
B. Both increase
c. Both decrease
D. \( V_{1} \) decreases and \( V_{2} \) increases
Subject: Biology
Which of the following statements is wrong about symmetry, while the other
three are correct?
A. Any plane that passes through the centre does not divide the body into equal halves in most sponges
B. The body of an arthropod can be divided into identical halves in two planes
c. Any plane passing through the central axis of the body divides Hydra into two identical halves
D. The body of an annelid can be divided into identical halves in only one plane.
Subject: Chemistry
By passing \( H_{2} S \) gas in acidified
\( K M n O_{4} \) solution, we
get
\( A \cdot K_{2} S \)
B. s
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{SO}_{3} \)
D. \( M n O_{2} \)
Subject: Chemistry
The vapour pressure of two miscible liquids \( A \) and \( B \) are 300 and 500 mm of
Hg respectively. In a flask, 10 moles of \( A \)
is mixed with 12 moles of \( B \). However,
as soon as \( B \) is added, \( A \) starts
polymerizing into a completely insoluble solid. After 100 minutes,
0.525 moles of a non-volatile solute is
dissolved which arrests the polymerization completely. The final vapour pressure of the solution is 400 mm of Hg. Assume negligible volume
change on mixing, polymerization and ideal behaviour for the final solution.
If a number of moles of \( \boldsymbol{A} \) polymerized
in 100 minutes are expressed as \( x, \) then
a value of \( 10 x \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
Subject: Chemistry
An experiment showed that a lead chloride solution is formed when \( 6.21 \mathrm{g} \)
of lead combines with \( 4.26 \mathrm{g} \) of chlorine. What is the empirical formula of this chloride?
\( [P b=207 ; C l=35.5] \)
A. \( P b C l_{3} \)
в. \( P b C l_{2} \)
\( \mathbf{c} \cdot P b C l_{4} \)
D. \( P b C l \)
Subject: Physics
The frequency of the visible light of wave length \( 6000 A . U . \) (Angstrom
units) is
A \( \cdot 4 \times 10^{14} \mathrm{Hz} \)
B. 6000
c. \( 5 \times 10^{10} H z \)
D. \( 5 \times 10^{14} \mathrm{Hz} \)
Subject: Chemistry
The equilibrium constant for the given
reaction: \( \boldsymbol{S O}_{3}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \frac{1}{2} O_{2}(g) ; K_{c}=4.9 \times \)
\( 10^{-2} m o l^{1 / 2} l i t r e^{-1 / 2} \)
What is the value of \( K_{c} \) for the reaction:
\( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons 2 S O_{3}(g) ? \)
A. 416 litre \( m o l^{-1} \)
B . \( 2.40 \times 10^{-3} \) litre \( \mathrm{mol}^{-1} \)
c. \( 9.8 \times 10^{-2} \) litre mole\( ^{-1} \)
D. \( 4.9 \times 10^{-2} \) litre \( m o l^{-1} \)
Subject: Physics
Two tiny spheres carrying charges 1.8 \( \mu C \) and \( 2.8 \mu C \) are located at \( 40 \mathrm{cm} \)
apart. The potential at the mid-point of the line joining the two charges is
A \( \cdot 3.8 \times 10^{4} v \)
B . \( 2.1 \times 10^{5} \mathrm{v} \)
c. \( 4.3 \times 10^{4} v \)
D. 3.6 \( \times 10^{5} \mathrm{v} \)
Subject: Physics
An electric dipple has dipple moment
\( 4 \times 10^{-11} \) and the two charges have
magnitudes 4 nC each. Calculate the electric field due to the dipole
i) At a point on the axis at a distance \( 0.01 \mathrm{m} \) from one of the charges and
ii) At a point on the perpendicular bisector at a distance \( 0.02 \mathrm{m} \) from the
middle point.
Subject: Maths
Find the coordinates of the point on the \( x \) -axis that is equidistant from
\( \boldsymbol{P}(\mathbf{4}, \mathbf{3}, \mathbf{1}) \) and \( \boldsymbol{Q}(-\mathbf{2},-\mathbf{6},-\mathbf{2}) \)
A \( \cdot\left(\frac{3}{2}, 0,0\right) \)
B \( \cdot\left(-\frac{3}{2}, 0,0\right) \)
c. \( \left(0,-\frac{3}{2}, 0\right) \)
D. \( \left(0, \frac{3}{2}, 0\right) \)
Subject: Biology
Figure shows human urinary system
with structures labelled \( A \) to \( D \). Select
options which correctly identifies and gives their characteristics and
functions.
A. B - Pelvis-Broad funnel shaped space inner to hillum directly connected to loops of Henle
B. c- -Medulla - -Inner zone of kidney and contains complete nephrons
c. D - cortex - Outer part of kidney and do not contain any part of nephrons
D. A-Adrenal gland-Located at the anterior part of kidney, secrete catecholamines, which stimulate glycogen breakdown
Subject: Chemistry
In the following Haber synthesis of \( N H_{3} \)
the equilibrium constant for \( \boldsymbol{N} \boldsymbol{H}_{3} \) formation, on increase in temperature,
is:
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 H N_{3}(g)+ \) heat
energy
A. Decreased
B. Increased
c. First decreased and then increased
D. Not altered
Subject: Chemistry
How much AgBr could dissolve in 1.0L of
\( 0.40 \mathrm{M} N H_{3} ? \) Assume that \( A g\left(N H_{3}\right)_{2}^{-} \)
is the only complex formed.
\( \left[\boldsymbol{K}_{f}\left(\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}^{+}\right)=\mathbf{1} \times \mathbf{1 0}^{8}\right. \)
\( \left.\boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{B r})=\mathbf{5} \times \mathbf{1 0}^{-\mathbf{1 3}}\right] \)
\( [\sqrt{\mathbf{5 0}}=\mathbf{7}] \)
Subject: Chemistry
Which of the following statements is
correct about the reaction given below?
4 Fe \( (s)+3 O_{2}(g) \rightarrow 2 F e_{2} O_{3}(g) \)
A. The total mass of reactants \( = \) Total mass of the products. It follows the law of conservation of mass.
B. The total mass of reactants = Total mass of the products. Therefore, the law of multiple proportions is followed.
C. Amount of \( F e_{2} O_{3} \) can be increased by taking any one of the reactants (iron or oxygen) in excess.
D. Amount of \( F e_{2} O_{3} \) produced will decrease if the amount of any one of the reactants (iron or oxygen) is taken in excess.
Subject: Chemistry
Assertion
2-butyne on controlled hydrogenation
with \( P d / C a C O_{3} \) in presence of \( P b O \)
gives \( c i s-2 \) -butene
Reason
Hydrogenation occur at the surface of
metal containing adsorbed hydrogen.
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: Chemistry
For the reaction \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( C l_{2}(g), \) the forward reaction at constant
temperatureis favoured by:
This question has multiple correct options
A. Introducing an inert gas at constant volume.
B. Introducing chlorine gas at constant volume.
c. Introducing an inert gas at constant pressure.
D. Increasing the volume of the container.
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)(\boldsymbol{C l})-\boldsymbol{C H}_{3} \) is
\( \mathbf{a} \)
alkyl chloride.
A. primary
B. secondary
c. tertiary
D. none of these
Subject: Maths
\( \frac{1}{\boldsymbol{x}^{4}+1}= \)
A. \( \quad\left[\frac{x+\sqrt{2}}{2 \sqrt{2} \sqrt{2}} \frac{x+\sqrt{2}}{2 \sqrt{2}\left(x^{2}-\sqrt{2} x+1\right)}\right] \)
B. \( \quad\left[\frac{x+\sqrt{2}}{x^{2}+\sqrt{2} x+1}-\frac{x+\sqrt{2}}{\left(x^{2}-\sqrt{2} x+1\right)}\right] \)
C \( \quad\left[\frac{x+\sqrt{2}}{2 \sqrt{2}\left(x^{2}+\sqrt{2} x+1\right)} \frac{\sqrt{2}-x}{(-\sqrt{2})}\right] \)
D. \( \frac{1}{2 \sqrt{2}}\left[\frac{x+\sqrt{2}}{\left(x^{2}+\sqrt{2} x+1\right)}+\frac{\sqrt{2}-x}{\left(x^{2}-\sqrt{2} x+1\right)}\right] \)
Subject: Physics
At room temperature, if the relative
permittivity of water be 80 and the relative permeability be 0.0222 , then the velocity of light in water is
\( \boldsymbol{m} / \boldsymbol{s}^{-1} \)
A . \( 3 \times 10^{8} \)
В. \( 2.25 \times 10^{8} \)
c. \( 2.5 \times 10^{8} \)
D. \( 3.5 \times 10^{8} \)
Subject: Physics
Match the following:
Section - A section - B
(P) Converts electric energy into
(1) Fuse \( \quad \) mechanical energy
(2) Electric
(Q) Heating effect of electric current
(3) Electric
(R) Converts mechanical energy Motor \( \quad \) into electrical energy
A \( \cdot(1-\mathrm{Q}),(2-\mathrm{R}),(3-\mathrm{P}) \)
B. (1 - Q), (2 - P), (3 - R)
c. \( (1-P),(2-Q),(3-R) \)
D. \( (1-P),(2-R),(3-Q) \)
Subject: Chemistry
The correct relationship between free energy change in a reaction and the
corresponding equilibrium constant \( \boldsymbol{K}_{c} \)
is:
A \( \cdot \Delta G^{o}=R T I n K_{c} \)
в. \( -\Delta G^{o}=R T I n K_{c} \)
c. \( \Delta G=R T I n K_{c} \)
D. \( -\Delta G=R T I n K_{c} \)
Subject: Physics
A man of mass \( \mathrm{m} \) speeds up while running from rest to a speed v in a straight track along an inclined plane, after rising through a height h.
\( W_{\text {gravity}}= \) work done by gravity on the
man.
\( W_{\text {friction}}= \) work done by gravity on the
man.
\( W_{\text {man}}= \) work done by man
If in the previous problem, we replace the man by a block of mass \( \mathrm{m} \) and release it from top of the inclined plane, and let it gain a speed \( v, \) then This question has multiple correct options
A \( \cdot W_{f r i c t i o n}=-m g h+\frac{1}{2} m v^{2} \)
B. \( W_{\text {gravity}}=-m g h \)
C. \( W_{\text {friction}}=0 \)
D. \( W_{\text {friction}}=-\mu g x, \) where \( x \) is the horizontal distance covered and \( \mu \) is the coefficient of friction between the block and the ground
Subject: Chemistry
Q Type your question
si und changes taking place against external atmospheric pressure:
1. \( \quad \boldsymbol{N}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \)
Il. \( \quad \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{H} \boldsymbol{S}(\boldsymbol{s}) \longrightarrow \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
III. \( C(s)+C O_{2}(g) \longrightarrow 2 C O(g) \)
IV. \( C_{2} H_{6}(g)+3.5 O_{2}(g) \longrightarrow \)
\[
\mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})
\]
\( \|\quad\| I \)
\( a+-\quad+ \)
b. - \( +0+ \)
\( \mathbf{C}_{\cdot}-\quad-\quad+\quad+ \)
\[
\mathbf{d}+++-
\]
\( A \cdot a \)
B.
\( c \cdot c \)
\( D \)
Subject: Chemistry
The isothermal diagram of a gas at
three different temperatures \( T_{1}, T_{2} \)
and \( T_{3} \), is shown in the given figure.
Then
A \( \cdot T_{1}<T_{2}<T_{3} \)
в. \( T_{1}<T_{2}>T_{3} \)
c. \( T_{1}>T_{2}>T_{3} \)
\( \Omega_{1}>T_{2}<T_{3} \)
Subject: Maths
A line \( 4 x+y=1 \) passes through the
point \( \boldsymbol{A}(\mathbf{2},-\mathbf{7}) \) and meets line \( \boldsymbol{B} \boldsymbol{C} \) at \( \boldsymbol{B} \)
whose equation is \( 3 x-4 y+1=0, \) the
equation of line \( A C \) such that \( A B= \) \( \boldsymbol{A C} \) is
A \( .52 x+89 y+519=0 \)
В. \( 52 x+89 y-519=0 \)
c. \( 82 x+52 y+519=0 \)
D. \( 89 x+52 y-519=0 \)
Subject: Physics
You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags \( 15 \mathrm{cm} \) when the entire automobile is places on ¡t. Also the amplitude of oscillation decreases by 50\% during one complete oscillation. Estimate the values of
(a) the spring constant \( k \) and
(b) the damping constant b for the
spring and shock absorber system of one wheel, assuming that each wheel supports \( 750 \mathrm{kg} \)
Subject: Maths
Construct a \( \triangle A B C \) in which \( A B= \)
\( 6 \mathrm{cm}, \angle A=30^{\circ} \) and \( \angle B=60^{\circ} \)
Construct another \( \triangle A B^{\prime} C^{\prime} \) similar to
\( \triangle A B C \) with base \( A B^{\prime}=8 \mathrm{cm} \)
Subject: Maths
\( \int\left(\frac{1}{\log x}-\frac{1}{(\log x)^{2}}\right) d x_{-----}+c \)
A . \( x \log . x \)
B. \( \frac{x}{2}(\log x)^{2} \)
c. \( \frac{x}{\log x} \)
D. \( \frac{x}{(\log x)^{2}} \)
Subject: Chemistry
A solution is prepared by urea and
water. If mole fraction of water is 0.8 in
the solution. Find the ratio of mass of
water and urea.
A \( \cdot \frac{5}{6} \)
B. \( \frac{6}{5} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{4}{1} \)
Subject: Physics
A proton is kept at rest. A positively charged particle is released from rest at
a distance \( d \) in its field. Consider two
experiments; one in which the charged particle is a proton and in another a positron. In the same time \( t, \) the work
done on the two moving charged
particles is
A. Same as the same force law is involved in the two experiments
B. Less for the case of a positron, as the positron moves away more rapidly and the force on it weakens
C. More for the case of a positron, as the positron moves away a larger distance
D. Same as the work done by charged particle on the stationary proton
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
A. The nitration of phenol is faster than phenyl acetate
B. The reaction of \( P h O^{\ominus} \) is faster than \( p-N C- \)
\( C_{6} H_{4} O^{\ominus} \) with \( P h C H_{2} C l \)
C. Base-catalysed hydrolysis of p-nitrophenyl acetate is faster than phenyl acetate
D. Acid-catalysed esterification of PhOH is faster than \( p \) nitrophenol with MeCOOH
Subject: Chemistry
If 1.0 mol of \( N O \) is mixed with 1.0 mol
of \( O_{2} \) as given in the following reaction
then the number of moles of \( N O_{2} \)
produced is
\( \mathbf{2} N O(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
A. 0.5
B.
\( c \cdot 2 \)
D. 1.5
Subject: Biology
Examine the figure given and select the
correct options giving all the four parts \( (a, b, c, d) \) correctly identified.
A. A - Seta, B - Sporophyte, C - Protonema, D - Rhizoids
B. A - Antheridio-phore, B - Male thallus, C - Globule, D Roots
C. A - Archegonio-phore, B - Female thallus, C - Bud, D Foot
D. A - Archegonio-phore, B - Female thallus, C - Gemma cup, D - Rhizoids
Subject: Maths
If \( \boldsymbol{y}(\boldsymbol{n})=\boldsymbol{e}^{\boldsymbol{x}} \boldsymbol{e}^{\boldsymbol{x}^{2}} \ldots \boldsymbol{e}^{\boldsymbol{x}^{n}}, \boldsymbol{0}<\boldsymbol{x}<1 . \) Then
\( \lim _{n \rightarrow \infty} \frac{\boldsymbol{d} \boldsymbol{y}(\boldsymbol{n})}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}=\frac{\mathbf{1}}{\mathbf{2}} \) is
\( A \cdot e \)
в. \( 4 € \)
\( c \cdot 2 e \)
D. \( 3 e \)
Subject: Physics
A bat flies at a constant speed of \( 0.04 V \)
toward a large tree trunk (where \( \boldsymbol{V} \)
denotes the speed of sound), the bat emits an ultrasonic pulse. The pulse is reflected off the tree and returns to the
bat, which can detect and analyse the returning signal. If the returning signal has a frequency of \( 61 k H z \), Find out the
frequency of the original ultrasonic
pulse?
\( \mathbf{A} .56 k H z \)
в. \( 62 k H z \)
\( c .68 k H z \)
D. \( 74 k H z \)
E \( .78 k H z \)
Subject: Physics
A satellite is moving very close to a planet of density \( 8 \times 10^{3} k g m^{-3} . \) If \( G= \)
\( 6.67 \times 10^{-11} N m^{2} k g^{-2}, \) then the time
period of the satellite is nearly.
A. \( 420 s \)
B. \( 4200 s \)
c. 1 hour
D. 1 day
Subject: Maths
n Fig 3.13
line \( D E \| \) line \( G F \) ray \( E G \) and ray \( F G \)
are bisectors of \( \angle D E F \) and \( \angle D F M \)
respectively. Prove that.
(i) \( \angle D E G=\frac{1}{2} \angle E D F \)
(ii) \( \boldsymbol{E} \boldsymbol{F}=\boldsymbol{F} \boldsymbol{G} \)
Subject: Physics
A source of sound producing wavelength \( 50 \mathrm{cm} \) is moving away from a stationary observer with \( \frac{1}{5}^{t h} \) speed of sound. Then what is the wavelength of sound heard by the observer?
\( \mathbf{A} \cdot 55 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
\( c .60 \mathrm{cm} \)
D. \( 70 \mathrm{cm} \)
Subject: Physics
A non conducting rod \( A B \) of length \( \sqrt{3} R \) uniformly distributed charge of linear charge density \( \lambda \) and.a non-conducting ring of uniformly distributed charge \( Q \) are placed as shown in the figure. Point
A is the centre of ring and line \( A B \) is the
axis of the ring, perpendicular to plane of ring. The electrostatic
interaction energy between ring and rod
is
A \( \cdot \frac{Q \lambda}{4 \pi \epsilon_{l}} \ln (2+\sqrt{3}) \)
c. \( \frac{Q \lambda}{4 \pi \epsilon} \ln (2-\sqrt{3}) \)
D・\frac{Q\lambda } \( {2 \pi \epsilon} \ln (2-\sqrt{3}) \)