AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
On the basis of following reactions, identify the correct matchings. \( \boldsymbol{A}_{(a q)}+\boldsymbol{A l} \stackrel{\text {heat}}{\longrightarrow} \boldsymbol{B}_{(\boldsymbol{g a s})} \) (colorless
combustible gas which is lightest) \( \boldsymbol{A}_{(\boldsymbol{a q})}+\boldsymbol{C} \stackrel{\text {heat}}{\longrightarrow} \boldsymbol{P} \boldsymbol{H}_{3(\boldsymbol{g a s})} \)
\( \boldsymbol{A}_{(a q)}+\boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{C l} \stackrel{\text {heat}}{\longrightarrow} \boldsymbol{D}_{(\boldsymbol{g} a s)}( \) turns red
litmus blue)
A. \( A=N a O H \) and \( C=P_{4} \)
в. \( A=C H_{3} C O O H \) and \( B=C H_{4} \)
C. \( A=K O H, D=N H_{3} \) and \( C=H_{3} P O_{4} \)
D. \( A=H C l, B=H_{2} \) and \( C=H_{3} P O_{4} \)
Subject: Chemistry
\( \boldsymbol{\Delta} \boldsymbol{H}^{0} \) for the raection \( \boldsymbol{X}_{(\boldsymbol{g})}+\boldsymbol{Y}_{(\boldsymbol{g})} \rightleftharpoons \)
\( Z_{(g)} \) is \( -4.6 \mathrm{Kcal} \), the value of \( \Delta U^{0} \) of the
reaction at \( 227^{\circ} \mathrm{C} \) is \( R= \)
\( 2 c a l m o l^{-1} K^{-1} \)
A. - -3.6kcal
B . - -5.6kcal
c. -4.6kcal
D. - -2.6kcal
Subject: Physics
\( N \) similar slabs of cubical shape of
edge \( b \) are lying on ground. Density of material of slab is \( \rho . \) Work done to arrange them one over the other is
A \( \cdot\left(N^{2}-1\right) b^{3} \rho g \)
B. \( (N-1) b^{4} \rho g \)
c. \( \frac{1}{2}\left(N^{2}-N\right) b^{4} \rho g \)
D. \( \left(N^{2}-N\right) b^{4} \rho g \)
Subject: Maths
Find the value of \( x \) for which \( f(x)= \)
\( \sqrt{\sin x-\cos x} \) is defined, \( x \epsilon[0,2 \pi] \)
\( ^{\mathbf{A}} \cdot_{x \epsilon}\left[\frac{\pi}{8}, \frac{5 \pi}{8}\right] \)
В \( \cdot x \in\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right] \)
\( ^{\mathbf{C}} \cdot_{x \epsilon}\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right] \)
D. \( x \in\left[\frac{\pi}{4}, \frac{5 \pi}{4}\right] \)
Subject: Biology
Assertion
Kidneys maintain the osmotic
concentration of the blood.
Reason
Kidneys eliminate either hypotonic or hypertonic urine according to the need of the body.
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
Value of v for which particle hit vertical
walls \( n \) times is \( \left(x n+\frac{5}{2}\right) \mathrm{m} / \mathrm{s} \) and
finally hit the point \( A \) which is the centre point between the two vertical walls (all collison are elastic) Find \( x \)
\( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
Subject: Chemistry
Complete the following chemical reactions:
\( \mathbf{i} \boldsymbol{S}(\boldsymbol{s})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
ii \( \boldsymbol{S O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \rightarrow \)
iii \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}(\boldsymbol{l})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)
Subject: Physics
The length and breadth of a rectangular sheet are \( 16.2 \mathrm{cm} \) and \( 10.1 \mathrm{cm} \) respectively. The area of the sheet in
appropriate significant figures and error is:
\( \mathbf{A} \cdot 164 \pm 3 c m^{2} \)
В. \( 163.62 \pm 2.6 \mathrm{cm}^{2} \)
c. \( 163.6 \pm 2.6 \mathrm{cm}^{2} \)
D. \( 163.62 \pm 3 c m^{2} \)
Subject: Maths
A non-zero vector \( \vec{a} \) is parallel to the line
of intersection of the plane determined by the vectors \( \hat{i}, \hat{i}+\hat{j} \) and the plane determined by the vectors \( \hat{i}-\hat{j}, \hat{i}+\hat{k} \) The angle between \( \vec{a} \) and \( \hat{i}-2 \hat{j}+2 \hat{k} \) is
A.
в.
c.
D. \( \frac{\pi}{2} \)
Subject: Physics
A tuning fork vibrating with a sonometer having \( 20 \mathrm{cm} \) wire produces 5 beats/s. The beat frequency does not
change, if the length of the wire is changed to \( 22 \mathrm{cm} . \) The frequency of the tuning fork (in Hz) must be
A . 200
B. 210
\( c \cdot 105 \)
D. 125
Subject: Maths
Show that if \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) and \( \boldsymbol{g}: \boldsymbol{B} \rightarrow \boldsymbol{C} \)
are \( 1-1, \) then \( g o f: A \rightarrow C \) is also 1
\( \mathbf{1} \)
Subject: Biology
Inorganic fertilizers are applied each year to fields bordering a lake. The fertilizers run off into the lake and
cause the following six changes which together cause high mortality of fishes.
(i) Aerobic bacteria feed on dead
plants.
(ii) Algae reproduce faster
(iii) Light cannot penetrate the water.
(iv) Oxygen level falls.
(v) Water becomes green.
(vi) Plants under water die.
Which of the following shows the correct order of the changes taking place?
A \( \cdot(\text { iv }) \rightarrow(v \text { i) } \rightarrow(i) \rightarrow(\text { ii }) \rightarrow(v) \rightarrow \) (iii)
B. (ii) \( \rightarrow(v) \rightarrow(\text { iii) } \rightarrow(v i) \rightarrow(i) \rightarrow \) (iv)
\( c \cdot(v) \rightarrow(i i) \rightarrow(\text { iii) } \rightarrow(v i) \rightarrow(i) \rightarrow(\text { iv }) \)
D. (ii) \( \rightarrow(\text { iii) } \rightarrow(v) \rightarrow(\text { iv }) \rightarrow(v \text { i) } \rightarrow(i) \)
Subject: Physics
Two protons and two neutrons combine to form a nucleus of \( _{2} H e^{4} . \) Find the energy released during the process. Take masses of proton, neutron and helium nuclues as
\( \mathbf{1 . 0 0 7 u}, \mathbf{1 . 0 0 9 u}, \mathbf{4 . 0 0 2 u} \) respectively
B. 84.67 MeV
c. 94.82 Mev
D. 24.12 Mev
Subject: Physics
A spaceship is released in a circular orbit near the Earth's surface. How
much additional velocity will have to be
given to the spaceship in order to escape out of this orbit?
\( \begin{array}{ll}\text { A. } 3.28 & \text { m/s }\end{array} \)
В. \( 3.28 \times 10^{3} \mathrm{m} / \mathrm{s} \)
C \( .3 .28 \times 10^{7} \mathrm{m} / \mathrm{s} \)
D. \( 3.28 \times 10^{-3} \mathrm{m} / \mathrm{s} \)
Subject: Physics
Four equal charges \( +Q \) are placed at the four corners of a body of side \( a \) each. Work done in removing a charge \( -\boldsymbol{Q} \) from its centre to infinity is
A. zero
В. \( \frac{\sqrt{2} Q^{2}}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{\sqrt{2} Q^{2}}{\pi \varepsilon_{0} a} \)
\( ^{\mathrm{D}} \cdot \frac{Q^{2}}{2 \pi \varepsilon_{0} a} \)
Subject: Physics
A disk has rotational inertia \( 1.22 \times 10^{-3} \)
\( \mathrm{kg}-\mathrm{m}^{2} \) and is attached to an electric drill whose motor delivers a torque of
\( 15.8 \mathrm{N}-\mathrm{m} \)
The angular momentum of the disk 33 ms after the motor is turned on is:
A. \( 0.256 \mathrm{kg}-\mathrm{m}^{2} / \mathrm{s} \)
B . 1.012 \( \mathrm{kg}-\mathrm{m}^{2} / \mathrm{s} \)
c. \( 0.158 \mathrm{kg}-\mathrm{m}^{2} / \mathrm{s} \)
D. 0.521 \( \mathrm{kg}-\mathrm{m}^{2} / \mathrm{s} \)
Subject: Chemistry
Metal carbonates decompose on
heating to give metal oxide and carbon dioxide. Which of the metal carbonates
is most stable thermally?
A. \( M g C O_{3} \)
в. \( C a C O_{3} \)
\( \mathrm{c} \cdot \operatorname{Sr} \mathrm{CO}_{3} \)
D. \( B a C O_{3} \)
Subject: Physics
A body is projected vertically up from a point on the ground. When it is at a height \( h \) above the ground, its kinetic
and potential energies are found to be in the ratio of \( 3: 2 . \) If the body rises to a
maximum height of \( H \) above the ground, then the ratio of \( \boldsymbol{H}: \boldsymbol{h} \) will be
A . 5: 3
B . 2: 1
c. 5: 2
D. 2: 5
Subject: Maths
Find the real values of \( x \) and \( y \) for which
the following equation is satisfied
\[
\frac{(1+i) x-2 i}{3+i}+\frac{(2-3 i) y+i}{3-i}=i
\]
A. \( x=3, y=-1 \)
B. \( x=-3, y=-1 \)
c. \( x=3, y=1 \)
D. \( x=-3, y=1 \)
Subject: Physics
A biconvex lens, \( f_{1}=20 c m, \) is placed 5
\( \mathrm{cm} \) in front of a convex mirror, \( \boldsymbol{f}_{2}= \)
15 \( c m . \) An object of length 2 cm is
placed at a distance \( 10 \mathrm{cm} \) from the lens. If overall magnification is \( X / 3 \) Then find out the value of \( X ? \)
Subject: Maths
In \( \Delta A B C, 4 \sin A \cos B=1 \) and
\( \tan B=3 \tan A . \) Then \( \sin C= \)
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.
Subject: Chemistry
The equilibrium constant of the following reactions are:
(।) \( \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \boldsymbol{K}_{\mathbf{1}} \)
(II) \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \boldsymbol{K}_{2} \)
\( (\| I) C O_{2}(g)+4 H_{2}(g) \rightleftharpoons C H_{4}(g)+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \boldsymbol{K}_{3} \)
Which of the following is true?
Subject: Physics
If I is the intensity of earth's magnetic
field, H its horizontal component and \( V \)
the vertical component, then these are
related as:
\( \mathbf{A} \cdot I=V+H \)
\( \mathbf{B} \cdot I=\sqrt{H^{2}+V^{2}} \)
\( \mathbf{C} \cdot I=\sqrt{H^{2}-V^{2}} \)
D \( \cdot I=H^{2}-V^{2} \)
Subject: Physics
Consider the cylindrical element as shown in the figure. Current flowing the through element is \( I \) and resistivity of
material of the cylinder is \( \rho . \) Choose the
correct option out the following
A. Power loss in first half is four times the power loss in second half
B. Voltage drop in first half is twice of voltage drop in second half
c. Current density in both halves are equal
D. Electric field in both halves is equal
Subject: Physics
A blackbox (BB) which may contain a
combination of electrical circuit
elements (resistor capacitor or
inductor) is connected with other
external circuit elements as shown
below in the figure (a).After the switch(s) is closed at time \( t=0, \) the
current (I) as a function of time (t) is
shown in the figure (b).
From this we can infer that the blackbox
contains
A. A resistor and a capacitor in series.
B. A resistor and a capacitor in parallel.
c. A resistor and an inductor in series
D. A resistor and an inductorin parallel.
Subject: Maths
Four different objects 1,2,3,4 are distributed at random in four places
marked \( 1,2,3,4 . \) What is the probability that none of the objects occupy the place corresponding to their number?
A \( \cdot \frac{17}{24} \)
в. \( \frac{3}{8} \)
c. \( \frac{1}{2} \)
D.
Subject: Physics
A ball of mass \( 400 g m \) is dropped from a height of 5 m. A boy on the ground hits the ball vertically upwards with a bat with an average force of \( 100 N \) so that it
attains a vertical height of 20 m. Find
the time for which the ball remains in
contact with the bat.
A. 0.12
B. 0.24
\( c \cdot 0.36 \)
D. 0.48
Subject: Maths
If \( t_{1}, t_{2} \) and \( t_{3} \) distinct. and the points
\( \left(t_{1} \cdot 2 a t_{1}+a t_{1}^{3}\right) \cdot\left(t_{2} \cdot 2 a t_{2}+a t_{2}^{3}\right),\left(t_{3} \cdot 2 a\right. \)
are collinear, then \( t_{1}+t_{2}+t_{3}= \)
A \( \cdot t_{1} t_{2} t_{3}=-1 \)
B \( \cdot t_{1}+t_{2}+t_{3}=t_{1} t_{2} t \)
\( \mathbf{c} \cdot t_{1}+t_{2}+t_{3}=0 \)
D. \( t_{1}+t_{2}+t_{3}=-1 \)
Subject: Physics
toppr
Q Type your question
time period is proportional to \( \sqrt{\frac{\boldsymbol{m}}{\boldsymbol{k}}}, \) as can be seen easily using dimensional analysis. However, the motion of a
particle can be periodic even when its
potential energy increases on both
sides of \( x=0 \) in a way different from
\( k x^{2} \) and its total energy is such that the
particle does not escape to infinity.
Consider a particle of mass m moving
on the \( x \) -axis. Its potential energy is
\( V(x)=\alpha x^{4}(\alpha>0) \) for \( |x| \) near the
origin and becomes a constant equal to
\( V_{0} \) for \( |x| \geq X_{0}(\text { see figure }) \)
The acceleration of this particle for
\( |\boldsymbol{x}|>\boldsymbol{X}_{0} \) is?
A. Proportional to \( V_{0} \)
B. Proportional to \( \frac{V_{0}}{m X_{0}} \)
C. Proportional to \( \sqrt{\frac{V_{0}}{m X_{0}}} \)
D. Zero
Subject: Chemistry
Identify the correct statement(s):
This question has multiple correct options
A. The oxidation number of \( C r \) in \( C r O_{5} \) is +6
B. \( \Delta H>\Delta U \) for the reaction \( N_{2} O_{4}(g) \rightarrow 2 N O_{2}(g) \)
provided both gases behave ideally.
C \( . \) pH of \( 0.1 N H_{2} S O_{4} \) is less than that of \( 0.1 \mathrm{N} \mathrm{HCl} \) at
\( 25^{\circ} C \)
D \( \cdot\left(\frac{R T}{F}\right)=0.0591 \) volt at \( 25^{\circ} \mathrm{C} \)
Subject: Physics
Two boys are standing at the ends \( A \) and
B of a ground where \( A B=a \). The boy at \( B \)
starts running in a direction
perpendicular to AB with velocity \( v_{1} . \) The
boy at A starts running simultaneously with velocity \( \mathbf{v} \) and catches the other in
a time \( t, \) where \( t \) is?
A \( \cdot \frac{a}{\sqrt{v^{2}+v_{1}^{2}}} \)
B. \( \frac{a}{v+v_{1}} \)
C. \( \frac{a}{v-v_{1}} \)
D. \( \sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}} \)
Subject: Physics
(a) Derive a relation for electric field
due to an electric dipole at a point on the equatorial plane of the electric dipole. Draw necessary diagram.
(b) An electric dipole of charge \( \pm 1 \mu C \) exists inside a spherical Gaussian
surface of radius \( 1 c m \). Write the value
of outgoing flux from the Gaussian
surface.
(c) Potential on the surface of a
charged spherical shell of radius \( 10 \mathrm{cm} \)
is \( 10 V . \) Write the value of potential at \( 5 c m \) from its centre.
Subject: Chemistry
When zinc is treated with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
an oxide of nitrogen is formed. The change in oxidation state of nitrogen during this reaction is:
A . +5 to 0
B. +5 to +2
\( c .+5 t o+4 \)
\( \mathbf{D} \cdot+5 \) to +1
Subject: Chemistry
Phosphorus separates, in the extraction of iron, as:
A \( \cdot \operatorname{slag}, C a_{3}\left(P O_{4}\right)_{2} \)
B. volatile \( P_{2} O_{5} \)
\( \mathbf{c} \cdot \operatorname{slag}, M g_{3}\left(P O_{4}\right)_{2} \)
D. \( C a_{3} P_{2} \)
Subject: Biology
The sequence of a reflex arc is
A. Receptor \( \rightarrow \) Sensory neuron \( \rightarrow \) Motor neuron \( \rightarrow \) Effector \( \rightarrow \) Response
B. Effector \( \rightarrow \) Sensory neuron \( \rightarrow \) Motor neuron \( \rightarrow \) Receptor \( \rightarrow \) Response
C. Effector \( \rightarrow \) Motor Neuron \( \rightarrow \) Interneuron \( \rightarrow \) Receptor \( \rightarrow \) Response
D. Receptor \( \rightarrow \) Motor neuron \( \rightarrow \) Sensory neuron \( \rightarrow \) Effector \( \rightarrow \) Response
Subject: Maths
The converse of "If \( x \) has courage, then \( x \)
will win", is
A. If \( x \) wins, then \( x \) has courage.
B. If \( x \) has no courage, then \( x \) will not win.
C. If \( x \) will not win, then \( x \) has no courage.
D. If \( x \) will not win, then \( x \) has courage.
Subject: Maths
If \( \sin \theta=\frac{8}{17} \) and \( 90^{\circ}<\theta<180^{\circ}, \) then
the value of the expression \( \frac{2 \sin \theta+\cos \theta}{3 \cos \theta+5 \sin \theta} \) is :
\( A \cdot \frac{1}{5} \)
B. \( -\frac{1}{5} \)
c. \( \frac{31}{85} \)
D. \( -\frac{31}{85} \)
Subject: Physics
Which of the following correctly presents the sequence of operations of isolator circuit breaker and earthing switch while closing a circuit :
A. Ensure circuit breaker is closed - close isolator - open earthing switch
B. Ensure circuit breaker is open - close isolator - open earthing switch if any close circuit breaker
C. Ensure circuit breaker is open - open isolator - open earthing switch if any close circuit breaker
D. None of the above
Subject: Chemistry
In terms of energy 1 u is equal to?
\begin{tabular}{l} 
A. \( 100 J \) \\
\hline
\end{tabular}
B. \( 931.1 k c a l \)
c. \( 931.1 \mathrm{MeV} \)
D. \( 10^{7} \) erg
Subject: Physics
The diagram shows three infinitely long uniform line charges placed on the \( x, Y \) and \( Y \), axis. The work done in moving a unit positive charge from (1,1,1) to \( (0,1, \)
1) is equal to
\( ^{A} \cdot \frac{(\lambda \ln 2)}{2 \pi \varepsilon_{0}} \)
B. \( \frac{(\lambda \ln 2)}{\pi \varepsilon_{0}} \)
c. \( \frac{(3 \lambda \ln 2)}{2 \pi \varepsilon_{0}} \)
D. None
Subject: Maths
Factorise \( \boldsymbol{x} \boldsymbol{y}\left(\boldsymbol{z}^{2}+\mathbf{1}\right)+\boldsymbol{z}\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right) \)
A \( .(x y+z)(y z+x) \)
B. \( (z x+y)(x y+z) \)
c. \( (y z+x)(z x+y) \)
D. \( \left(x^{2}+y^{2}\right)(z+x) \)
Subject: Physics
A boy weighing \( 25 k g f \) climbs up from
the first floor at height \( 3 m \) above the
ground to the third floor at height \( 9 m \)
above the ground. What will be the increase in the gravitational potential energy? Consider \( \boldsymbol{g}=10 m s^{-2} \)
\( \mathbf{A} \cdot 1 k J \)
B. \( 1.3 k J \)
c. \( 1.5 k J \)
D. None of these
Subject: Chemistry
Give the IUPAC names of the following compounds:
¡) \( \boldsymbol{C H}_{3} \boldsymbol{C H}(\boldsymbol{C l}) \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{3} \)
ii) \( C H F_{2} C B r C l F \)
iii) \( C l C H_{2} C \equiv C C H_{2} B r \)
iv) \( \left(C C l_{3}\right)_{3} C C l \)
v) \( \boldsymbol{C H}_{3} \boldsymbol{C}\left(\boldsymbol{p}-\boldsymbol{C l} \boldsymbol{C}_{6} \boldsymbol{H}_{4}\right)_{2} \boldsymbol{C H}(\boldsymbol{B r}) \boldsymbol{C H}_{3} \)
vi) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C C H}=\boldsymbol{C C l C}_{6} \boldsymbol{H}_{4} \boldsymbol{I}-\boldsymbol{p} \)
Subject: Chemistry
The best method to prepare neopenty chloride is:
A \( \cdot\left(C H_{3}\right)_{3} C C H_{2} O H \stackrel{P C l_{5},}{\longrightarrow} \)
в. \( \left(C H_{3}\right)_{3} C C H_{2} O H \stackrel{\text {НС}, \text {А}}{\longrightarrow} \)
C. \( \left(C H_{3}\right)_{3} C C H_{2} O H^{S_{o} C l_{2}, p y r i d i n e} \)
D. \( \left(C H_{3}\right)_{3} C C H_{3} \stackrel{C l_{2}, h \nu \Delta}{\longrightarrow} \)
Subject: Maths
If \( \int_{a}^{b} \frac{f(x)}{f(a)+f(a+b-x)} d x=10, \) then
This question has multiple correct options
A. \( b=22, a=2 \)
В. \( b=15, a=-5 \)
c. \( b=10, a=-10 \)
D. \( b=10, a=-2 \)
Subject: Physics
Two men ' \( A \) ' and ' \( B \) ' are standing on a
plank.' \( B^{\prime} \) is at the middle of the plank
and ' \( A \) ' is at the left end of the plank. Surface of the plank is smooth. System
is initially at rest and masses are as
shown in figure. ' \( \boldsymbol{A}^{\prime} \) and \( ^{\prime} \boldsymbol{B}^{\prime} \) start moving
such that the position of ' \( B \) ' remains
fixed with respect to ground and ' \( \boldsymbol{A}^{\prime} \)
meets ' \( B \) '. Then the point where \( A \)
meets \( B \) is located at
A. the middleof the plank
B. 30cm from the left end of the. plank
c. the right end of the plank
D. None of these
Subject: Maths
When the polynomial \( \left[6 x^{4}+8 x^{3}+\right. \)
\( \left.29 x^{2}+21 x+7\right] \) is divided by another
polynomial \( \left[3 x^{2}+4 x+1\right] \) the
remainder is in the form of \( (a x+b) \)
Find \( a \) and \( b \)
Subject: Physics
The focal length of an equiconvex lens is greater than the radius of curvature of any of the surfaces.Then the refractive index of the material of the lens is
A. greater than o but less than 1.5
B. greater than 1.5 but less than 2.0
c. greater than 2.0 but less than 2.5
D. greater than 2.5 but less than 3.0
Subject: Maths
The slope of the tangent to the curve \( y=\int_{0}^{x} \frac{d t}{1+t^{3}} \) at the point where \( x=1 \) is.
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. 1
Subject: Physics
Three charges \( 1 \mu C, 2 \mu C, \) and \( 3 \mu C \) are kept at vertices of an equilateral triangle of side \( 1 \mathrm{m} \). If they are brought nearer, so that they now form an
equilateral triangle of side \( 0.5 m, \) then
work done is :
A. \( 0.11 J \)
\( J \)
в. \( 11 J \)
c. \( 0.01 J \)
D. \( 1.1 \mathrm{J} \)
Subject: Maths
If \( A=\left|\begin{array}{l}1 \\ 3\end{array}\right| B=\left|\begin{array}{c}-1 \\ 4\end{array}\right| \) then \( 2 A+B= \)
\( A \cdot \mid 10 \)
9
B. \( \mid 10 \) 1
\( c \cdot\left|\begin{array}{l}1 \\ 10\end{array}\right| \)
D. \( \mid 1 \) 9
Subject: Chemistry
When photons of energy h fall on an
aluminium plate (of work function \( \mathrm{E}_{0} \) ), photoelectrons of maximum kinetic energy K are ejected. If the frequency of the radiation is doubled, then
the maximum kinetic energy of the
ejected photoelectrons will be:
\( A \cdot K+E_{0} \)
в. 2k
\( c \cdot k \)
\( D \cdot K+h \)
Subject: Chemistry
The arrangement of
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-,\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}-, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}- \)
when attached to benzene or an
unsaturated group in increasing order of inductive effect is
A \( \cdot\left(C H_{3}\right)_{3} C-<\left(C H_{3}\right)_{2} C H-<C H_{3} C H_{2}- \)
в. \( C H_{3} C H_{2}-<\left(C H_{3}\right)_{2} C H-<\left(C H_{3}\right)_{3} C- \)
c. \( \left(C H_{3}\right)_{2} C H-<\left(C H_{3}\right)_{4} C-<C H_{3} C H_{2}- \)
D. \( \left(C H_{3}\right)_{3} C-<C H_{3} C H_{2}-<\left(C H_{3}\right)_{2} C H- \)
Subject: Chemistry
\( R-C H_{2}-C H_{2} O H \) can be converted
into \( R C H_{2} C H_{2} C O O H \) by the following
sequence of steps:
\( \mathbf{A} \cdot P B r_{3}, K C N, H_{2} / P t \)
B. \( P B r_{3}, K C N, H_{3} O^{+} \)
c. \( H C N, P B r_{3}, H_{3} O^{+} \)
D. \( K C N, H_{3} O^{+} \)
Subject: Physics
A solid sphere of radius \( R \) and density \( \rho \) is attached to one end of a mass-less
spring of force constant \( k . \) The other end of the spring is connected to another solid sphere of radius \( \boldsymbol{R} \) and density \( \mathbf{3} \boldsymbol{\rho} \) The complete arrangement is placed in
a liquid of density \( 2 \rho \) and is allowed to
reach equilibrium. The correct
statement(s) is (are)

This question has multiple correct options
A \( \cdot \) the net elongation of the spring is \( \frac{4 \pi R^{3} \rho g}{3 k} \)
B. the net elongation of the spring is \( \frac{8 \pi R^{3} \rho g}{3 k} \)
c. the light sphere is partially submerged
D. the light sphere is completely submerged
Subject: Physics
80 g of water at \( 30^{\circ} \mathrm{C} \) are poured on a
large block of ice at \( 0^{\circ} \mathrm{C} \) The mass of ice that melts is
A. \( 30 g \)
в. 80 \( g \)
\( c \cdot 1600 g \)
D. \( 150 \mathrm{g} \)
Subject: Physics
A ball is dropped from a height \( h \) on a
floor of coefficient of restitution \( e \). The
total distance covered by the ball just before second hit is
A \( \cdot h\left(1-2 e^{2}\right) \)
B \( \cdot h\left(1+2 e^{2}\right) \)
c. \( h\left(1+e^{2}\right) \)
\( D \cdot h e^{2} \)
Subject: Chemistry
the mass of carbon anode consumed
(giving only carbon dioxide) in the production of \( 270 K g \) of aluminium metal from bauxite by the Hall's process is:
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3}+\mathbf{3} \boldsymbol{C} \rightarrow \mathbf{4} \boldsymbol{A} \boldsymbol{l}+\mathbf{3} \boldsymbol{C} \boldsymbol{O}_{2} \)
A. \( 180 \mathrm{Kg} \)
в. \( 270 K g \)
c. \( 240 K g \)
D. \( 90 K g \)
Subject: Chemistry
Which of the following substance is not present in clear water?
A \( \cdot \operatorname{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \)
в. \( M g C l_{2} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \)
D. \( C a C O_{3} \)
Subject: Physics
When a rod is heated from \( 25^{\circ} \mathrm{C} \) to
\( \mathbf{7 5}^{\circ} \boldsymbol{C}, \) it expands by \( \mathbf{1} \boldsymbol{m} \boldsymbol{m} . \) When a rod
of same material but with 4 times the
length is heated from \( 25^{\circ} C \) to \( 50^{\circ} C \) The increase in length is :
\( \mathbf{A} \cdot 1 m m \)
в. \( 1.5 \mathrm{mm} \)
\( \mathrm{c} .1 .6 \mathrm{mm} \)
D. \( 2 m m \)