AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If L and R denote inductance and
resistance, respectively, then the dimensions of L/R are
A \( \cdot M^{1} L^{0} T^{0} Q^{-1} \)
В. \( M^{0} L^{0} T Q^{0} \)
c. \( M^{0} L^{1} T^{-1} Q^{0} \)
D. \( M^{-1} L T^{0} Q^{-1} \)
Subject: Physics
The half life of a radioactive nucleus is
50 days.The time interval \( \left(t_{2}-t_{1}\right) \)
between the time \( t_{2} \) when \( \frac{2}{3} \) of it has
decayed and the time \( t_{1} \) when \( \frac{1}{3} \) of it
had delayed is-
A. 50 days
B. 60 days
c. 15 days
D. 30 days
Subject: Physics
A wire of length \( 1 m \) is made into a
circular loop and it carries a current of \( 3.14 A . \) The magnetic dipole moment of the current loop (in \( A m^{2} \) ) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0.5
c. 0.25
D. 0.314
Subject: Chemistry
In the following reactions, \( \boldsymbol{X}, \boldsymbol{Y} \) and \( \boldsymbol{Z} \)
are:
\( \mathbf{A} \cdot X=C H_{3} C l ; Y=a n h y d r o u s A l C l_{3} ; Z=H N O_{3}+ \)
\( H_{2} S O_{4} \)
B \( . X=C H_{3} C O C l ; Y= \) anhydrous \( A l C l_{3} ; Z=H N O_{3}+ \)
\( H_{2} S O_{4} \)
\( \mathbf{c} \cdot X=C H_{3} C l ; Y=c o n c . H_{2} S O_{4} ; Z=H N O_{3}+H_{2} S O_{4} \)
D. \( X=C H_{3} C l ; Y=d i l . H_{2} S O_{4} ; Z=H N O_{3} \)
Subject: Physics
Statement 1: The drift speed of electrons
in metals is small (in the order of a few
\( m m / s) \) and the charge of an electron is also very small \( \left(1.6 \times 10^{-19} C\right), \) yet we
can obtain a large current in a metal.
Statement 2: At room temperature, the thermal speed of electrons is very high
(about \( 10^{7} \) times the drift speed)
A. Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1
B. Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for statement
c. Statement 1 is True; Statement 2 is False
D. Statement 1 is False; Statement 2 is True
Subject: Physics
In above shown figure, the two plates of
the capacitor of charge \( +\mathrm{Q} \) and \( -\mathrm{Q}, \) which points lie on the same equipotential?
\( A \cdot 1 \) and 2 only
B. 1 and 3 only
C. 2 and 4 only
D. 3 and 4 only
E. \( 1,2,3, \) and 4 all lie on the same equipotential, since the electric field is uniform
Subject: Physics
The dependence of acceleration due to gravity g on the distance r from the centers of the earth assumed to be a
sphere of radius \( R \) of uniform density is as shown figure below.
The correct figure is
\( (i) \)
(ii)
(iii)
(iv)
\( A \cdot(i) \)
B. (ii)
\( c \)
D. Güvüù
Subject: Maths
\( \cos ^{2} \frac{3 \pi}{5}+\cos ^{2} \frac{4 \pi}{5} \) is equal to
A \( \cdot 4 / 5 \)
B. \( 5 / 2 \)
c. \( 5 / 4 \)
D. \( 3 / 4 \)
Subject: Maths
\( \left|\begin{array}{cc}\mathbf{2 x} & \mathbf{5} \\ \mathbf{8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{cc}\mathbf{6} & \mathbf{- 2} \\ \mathbf{7} & \mathbf{3}\end{array}\right|, \) write the value of
\( \boldsymbol{x} \)
Subject: Physics
Four pieces each of length \( l \) of a
conducting rod are joined as shown in the figure. The rod is placed in a downward magnetic field B. If the rod is
moved towards right with a uniform
velocity \( v, \) then the induced emf across the two ends of the rod is
\( A \). Blv
B. 4 Blv
C \( \cdot 2 \) Blv \( \sin (\theta / 2) \)
D \cdot 2 Blv (1+ sin\theta/2)
Subject: Chemistry
Which of the following statement is
incorrect:
A. On addition of catalyst the equilibrium constant value is not affected.
B. Equilibrium constant value for negative \( \Delta H \) value decreases as the temperature increases
C. In equilibrium mixture of ice and water, kept in insulated flask mass of ice and water does not change with time
D. The intensity of red colour increases when oxalic acid is added to the solution containing iron nitrate(III) and potassium thiocynate
Subject: Physics
the number of turn of primary and secondary coil of the transformer is 5 and 10 respectively ad the mutual inductance is 25 H. if the number \( f \)
turns of the primary and secondary is made 10 and \( 5, \) then the mutual
inductance of the coils will be
A . \( 6.25 \mathrm{H} \)
B. 12.5
c. 25
D. 50
Subject: Maths
If \( y=\sin ^{-1} x \operatorname{th} e n\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}= \)
A \( \cdot-x \frac{d y}{d x} \)
B.
c. \( _{x} \frac{d y}{d x} \)
D. \( x\left(\frac{d y}{d x}\right)^{2} \)
Subject: Physics
A bullet moving with a velocity of \( 200 \mathrm{cm} / \mathrm{s} \) penetrates a wooden block and comes to rest after traversing \( 4 \mathrm{cm} \) inside it. What velocity is needed for travelling distance of \( 9 \mathrm{cm} \) in same
block
A. \( 100 \mathrm{cm} / \mathrm{s} \)
B. \( 136.2 \mathrm{cm} / \mathrm{s} \)
c. \( 300 \mathrm{cm} / \mathrm{s} \)
D. \( 250 \mathrm{cm} / \mathrm{s} \)
Subject: Chemistry
The rate for a first order reaction is
\( 0.6932 \times 10^{-2} \) mol litre \( ^{-1} \min ^{-1} \) and
the initial concentration of the reactant
is \( 1 \mathrm{M}, t_{1 / 2} \) is equal to:
B. 100 minutes
c. \( 0.693 \times 10^{-3} \) minute
D. 6.932 minutes
Subject: Maths
If \( z_{1}, z_{2}, z_{3}, z_{4} \) be the vertices of
rhombus in argand palne and
\( \angle C B A=\pi / 3, \) then prove that
\( \mathbf{2} z_{2}=z_{1}(\mathbf{1}+i \sqrt{\mathbf{3}})+z_{3}(1-i \sqrt{\mathbf{3}}) \)
and \( 2 z_{4}=z_{1}(1-i \sqrt{3})+z_{3}(1+ \)
\( \boldsymbol{i} \sqrt{\boldsymbol{3}}) \)
Subject: Maths
If \( \int \frac{\boldsymbol{d x}}{\boldsymbol{a} e^{m x}+\boldsymbol{b} e^{-\boldsymbol{m} \boldsymbol{x}}}= \)
\( K \tan ^{-1}\left(P e^{m x}\right)+C, \) then \( K, P= \)
\( ^{\mathbf{A}} \cdot_{K}=\frac{1}{\sqrt{a b}}, P=\sqrt{\frac{a}{b}} \)
B. \( K=\frac{1}{m \sqrt{a b}}, P=\sqrt{\frac{a}{b}} \)
\( ^{\mathbf{c}} \cdot_{K}=m \sqrt{a b}, P=\sqrt{\frac{b}{a}} \)
D. \( \quad K=\frac{1}{m \sqrt{a b}}, P=\sqrt{\frac{b}{a}} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}x^{3}-x^{2}+10 x-5 \quad, x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-2\right), x>1\end{array} \) the set of \right.
values of \( b \) for which \( f(x) \) has greatest
value at \( x=1 \) is given by:
A. \( 1 \leq b \leq 2 \)
В . \( b=\{1,2\} \)
c. \( b \in(-\infty,-1) \)
D \( \cdot b \in[-\sqrt{130},-\sqrt{2}] \cup[\sqrt{2}, \sqrt{130}] \)
Subject: Physics
A horizontal overhead power line is at a height of \( 5 ~ m \) from the ground and carries a current of \( 100 A \) from east to
west. The magnetic field directly below it on the ground is
A \( \cdot 2.5 \times 10^{-6} T \) eastward
B . \( 4 \times 10^{-6} T \) eastward
c. \( 5 \times 10^{6} \) southward
D. \( 2 \times 10^{-6} \) westward
Subject: Physics
A convex lens forms a real image \( 9 \mathrm{cm} \)
long on a screen. Without altering the position of the object and the screen, the lens is displaced and we get again a real image \( 4 \mathrm{cm} \) long on the screen. Then the length of the object is
\( A \cdot 9 c m \)
в. 4 ст
\( c .6 c m \)
D. \( 36 \mathrm{cm} \)
Subject: Maths
Calculate the area of a regular pentagon
with sides of \( 2 \mathrm{cm} \) and apothem is 12
\( \mathrm{cm} \)
\( A \cdot 60 \mathrm{cm}^{2} \)
B. \( 61 \mathrm{cm}^{2} \)
\( c \cdot 62 c m^{2} \)
\( \mathrm{D} \cdot 63 \mathrm{cm}^{2} \)
Subject: Physics
A metal bar of \( 70 \mathrm{cm} \) long and \( 4 \mathrm{kg} \) in mass supported on two knife edges placed \( 20 \mathrm{cm} \) from each end. A \( 6 \mathrm{kg} \) load is suspended at \( 30 \mathrm{cm} \) from on end.
Find the normal reaction at the knife-
edge. (assume it to be of uniform cross
section and homogeneous)
\( A \cdot 55 \mathrm{N} \) at \( K_{1} \) and \( 33 \mathrm{N} \) at \( K_{2} \)
B. \( 45 \mathrm{N} \) at \( K_{1} \) and \( 53 \mathrm{N} \) at \( K_{2} \)
c. \( 55 \mathrm{N} \) at \( K_{1} \) and \( 43 \mathrm{N} \) at \( K_{2} \)
D. 43 N at \( K_{1} \) and \( 55 \mathrm{N} \) at \( K_{2} \)
Subject: Maths
If \( I_{n}=\int(\log x)^{n} d x, \) then \( I_{6}+6 I_{5}= \)
\( \mathbf{A} \cdot x(\log x)^{5} \)
B. \( -x(\log x)^{5} \)
\( \mathbf{c} \cdot x(\log x)^{6} \)
\( \mathbf{D} \cdot-x(\log x)^{6} \)
Subject: Maths
Let \( X \) be a random variable which
assumes values \( x_{1}, x_{2}, x_{3}, x_{4} \) such that
\( \mathbf{2} \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_{1}\right)=\mathbf{3} \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_{2}\right)=\boldsymbol{P}(\boldsymbol{X}= \)
\( \left.\boldsymbol{x}_{3}\right)=\mathbf{5} \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_{4}\right) \)
Find the probability distribution of \( \boldsymbol{X} \)
Subject: Chemistry
What is the order of basic nature of
hydrides of VA group elements?
A \( \cdot \mathrm{AsH}_{3}>\mathrm{SbH}_{3}>\mathrm{PH}_{3}>\mathrm{NH}_{3} \)
В. \( \mathrm{NH}_{3}>\mathrm{SbH}_{3}>\mathrm{PH}_{3}>\mathrm{AsH}_{3} \)
C. \( \mathrm{NH}_{3}>\mathrm{PH}_{3}>\mathrm{AsH}_{3}>\mathrm{SbH}_{3} \)
D. \( \mathrm{PH}_{3}>\mathrm{NH}_{3}>\mathrm{SbH}_{3}>\mathrm{AsH}_{3} \)
Subject: Physics
A transformer has 100 turns in the
primary coil and carries 8 A current. If input power is \( 1 \mathrm{kW} \), the number of turns
in secondary coil to have \( 500 \vee \) output will be:
A \( \cdot 100 \)
B. 200
\( c \cdot 400 \)
D. 300
Subject: Physics
Two stones are thrown up
simultaneously from the edge of a cliff \( 200 \mathrm{m} \) high with initial speeds of
\( 15 m s^{-1} \) and \( 30 m s^{-1} . \) Verify that the
graph shown in Fig.correctly represents the time variation of the relative
position of the second stone with
respect to the first. Neglect air
resistance and assume that the stones
do not rebound after hitting the ground.
Take \( \boldsymbol{g}=10 m s^{-2} . \) Give the equations
for the linear and curved parts of the
plot
Subject: Biology
A skull excavated from a place had large zygomatic arches, 2 pairs of large incisors, 2 pairs of premolars following a gap and 3 pairs of large molars. The foramen magnum was direction posterior. This skull belongs to a
A. Predatory mammal with bipedal locomotion
B. Predaceous dinosaur with bipedal locomotion
c. herbivorous mammal with Quadrupedal locomotion
D. Herbivorous dinosaur with Quadrupedal locomotion
Subject: Chemistry
Two substances \( A\left(t_{\frac{1}{2}}=5 \min \right) \) and \( B \) \( \left(t_{\frac{1}{2}}=15 \mathrm{min}\right) \) are taken in such a way that initially \( [\boldsymbol{A}]=\mathbf{4}[\boldsymbol{B}] . \) The time after
which both the concentrations will be
equal is:
A. 5 minutes
B. 15 minutes
c. 20 minutes
D. concentrations can never be equal
Subject: Chemistry
IUPAC name of \( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right] \) is:
A. Potassium dioxalatoferrate(1)
B. Potassium dioxalatoferrate(III)
c. Potassium trioxalatoferrate(III)
D. Potassium trioxalatoferate(II)
Subject: Chemistry
A solution containing \( \boldsymbol{N} \boldsymbol{a}^{\oplus}, \boldsymbol{N} \boldsymbol{O}_{3}^{\ominus}, \boldsymbol{C l}^{\ominus} \)
and \( S O_{4}^{2-} \) ions, all at unit concentrations, is electrolyzed between nickel anode and plantinum cathode. As the current is passed through the cell :
This question has multiple correct options
A. pH of the cathode increases
B. Oxygen is the major product at anode
c. Nickel is deposited at cathode
D. Chlorine is the maior product at anode
Subject: Maths
Find the direction cosines of a line that
pass through the point \( \boldsymbol{P}(\mathbf{1}, \mathbf{4}, \boldsymbol{6}) \) and
\( Q(5,1,11) \) and is so directed that it
make an acute angle with the positive direction of \( \boldsymbol{y}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s} \)
Subject: Maths
Divide the polynomial \( p(x) \) by the
polynomial \( g(x) \) and find the quotient and remainder in each of the following:
(i) \( p(x)=x^{3}-3 x^{2}+5 x-3, g(x)= \)
\( x^{2}-2 \)
(ii) \( p(x)=x^{4}-3 x^{2}+4 x+5, g(x)= \)
\( \boldsymbol{x}^{2}+\mathbf{1}-\boldsymbol{x} \)
(iii) \( p(x)=x^{4}-5 x+6, g(x)=2-x^{2} \)
Subject: Chemistry
Identify the equations involved in
bleaching action of \( \boldsymbol{S O}_{2}: \) This question has multiple correct options
A. \( S O_{2}+H_{2} O \rightarrow H_{2} S O_{3} \)
в. \( S O_{2}+O_{2} \rightarrow S O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{3}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}+2[\mathrm{H}] \)
\( \mathrm{D} \cdot S O_{3}+H_{2} O+H_{2} S O_{4} \)
Subject: Physics
A person throws balls into air vertically upward in regular intervals of time of one second. The next ball is thrown
when the velocity of the ball thrown earlier becomes zero. The height to which the balls rise is
(Assume, \( \left.g=10 m s^{-2}\right) \)
A. \( 5 m \)
B. \( 10 m \)
c. \( 7.5 m \)
D. \( 20 m \)
Subject: Maths
If \( A B C \) and DEF are similar triangles
such that \( \angle A=47^{\circ} \) and \( \angle B=83^{\circ} \)
then \( \angle \boldsymbol{F} \) is
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 70^{\circ} \)
\( c .50^{\circ} \)
D. \( 100^{\circ} \)
Subject: Maths
A person has Rs.30,000 to invest.He wants to invest some amount in the
fixed deposit and remaining in savings account.The interest rates are \( 7 \% \) and
\( 5 \% \) p.a for the fixed deposit and the saving account respectively. Find how he should divide the total amount
\( R s .30000 \) in two accounts if he wants to
get the annual interest as
(i) \( R s .1800 \)
(ii) \( R s .2000 \)
Subject: Physics
Q Type your question
consisting or two semıcircles eacn of
radius \( r \) is placed in such a way that
the centre \( C \) of the conducting wire is at
a distance \( 2 r \) from the end of
the wire.The rod AB moves with velocity
of \( 5 m s^{-1} \) along the direction of the
current flow as shown in the figure. If
the line joining the ends of the rod
makes an angle \( 30^{\circ} \) with the wire then,
This question has multiple correct options
A. the emf induced between the ends of the rod is
\( \ln 4) \mu V \)
B. the end \( A \) is at higher potential than end \( B \).
C. the end \( A \) is at lower potential than end \( B \)
D. the emf induced between the ends of the rod is \( \ln 3) \mu V \)
Subject: Maths
The area of the plane region bounded by the curves \( x+2 y^{2}=0 \) and \( x+3 y^{2}= \)
\( \mathbf{1} \) is
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{4}{3} \)
D.
Subject: Chemistry
Nernst equation is : \( \boldsymbol{E}=\boldsymbol{E}^{o}-\frac{\boldsymbol{R} \boldsymbol{T}}{\boldsymbol{n} \boldsymbol{F}} \boldsymbol{l} \boldsymbol{n} \boldsymbol{Q} \)
If \( Q=K_{c} \), then which one is not
correct?
A \( . E=E^{\circ} \)
в. \( \frac{R T}{n F} \ln Q=E^{c} \)
\( \mathbf{c} \cdot E=z e r o \)
D. \( _{K_{c}=e} \frac{n F E^{o}}{R T} \)
Subject: Maths
The side of a square is \( 2 \mathrm{cm} \)
Semicircles are constructed outside
the square on two sides of the square. Then area of the whole figure is
\( \mathbf{A} \cdot(4+\pi) \mathrm{cm}^{2} \)
в. \( (4+4 \pi) \mathrm{cm}^{2} \)
c. \( (4+2 \pi) c m^{2} \)
D. \( 4 \pi c m^{2} \)
Subject: Maths
A bag contains 15 red, 8 blue and
several green marbles. A marble is selected at random. The probability of drawing a blue marble is \( \frac{1}{5} \)
5 green marbles are now taken out from the bag. If a marble is now drawn at random, find the probability of drawing
a green marble
A \( \cdot \frac{3}{10} \)
В. \( \frac{12}{35} \)
c. \( \frac{23}{40} \)
D. \( \frac{17}{35} \)
Subject: Maths
What is the surface area of a cube
whose volume is \( 64 \mathrm{cm}^{3} \) ?
\( \mathbf{A} \cdot 16 \mathrm{cm}^{2} \)
B. \( 64 \mathrm{cm}^{2} \)
c. \( 96 \mathrm{cm}^{2} \)
D. \( 128 \mathrm{cm}^{2} \)
Subject: Biology
Select the correct option:
Identify the figures \( A, B, C \) showing
different types of muscle and select the correct option:
A. A- smooth muscle; B- Striated muscle; C- Cardiaç muscle
B. A-Cardiac muscle; B- - Smooth muscle; Striated muscle
c. A- striated muscle; B- Smooth muscle; C- Cardiaç muscle
D. A- Involuntary muscle; B- Voluntary muscle; C- Heat muscle
Subject: Physics
The value of current in two series \( L C R \)
circuits at resonance is same. Then
A. both circuits must be having same value of capacitance and inductance
B. in both circuits ratio of \( L \) and \( C \) will be same
c. for both the circuits \( X_{L} / X_{C} \) must be same at that frequency
D. both circuits must have same impedance at all frequencies
Subject: Maths
Evaluate the integral \( \int_{0}^{\pi} \frac{d x}{a+b \cos x} \) where \( a>b \)
A \( \cdot \pi \sqrt{a^{2}-b^{2}} \)
an \( \pi \sqrt{a^{2}-b^{a^{2}}} \)
в. \( \pi a b \)
c. \( \frac{\pi}{\sqrt{a^{2}+b^{2}}} \)
D. \( \frac{\pi}{\sqrt{a^{2}-b^{2}}} \)
Subject: Maths
If \( 1+\sin ^{2} \theta=3 \sin \theta \cos \theta \) then the
solution set in \( \left[0, \frac{\pi}{2}\right] \) is
A \( \cdot\left\{\frac{\pi}{4}, \cos ^{-1}(1 / 3)\right\} \)
B \( \cdot\left\{\frac{\pi}{4}, \tan ^{-1}(1 / 2)\right\} \)
c. \( \left\{\frac{\pi}{3}, \tan ^{-1}(1 / 3)\right\} \)
D \( \cdot\left\{\frac{\pi}{6}, \sin ^{-1}(1 / 3)\right\} \)
Subject: Physics
A person is throwing two balls in the air one after the other. He throws the
second ball when the first ball is at the
highest point. If he is throwing the balls every second, how high do they rise?
\( A \cdot 5 m \)
B. 3.75 m
c. \( 2.50 \mathrm{m} \)
D. 1.25 \( m \)
Subject: Physics
An aircraft, initially stationary on a
runway, takes off with a speed of \( 85 \mathrm{km} \)
\( h^{-1} \) in a distance of no more than 1.20
\( \mathbf{k m} \)
What is the minimum constant
acceleration necessary for the aircraft?
A \( \cdot 0.23 m s^{-2} \)
B. \( 0.46 \mathrm{ms}^{-2} \)
c. \( 3.0 m s^{-2} \)
D. \( 6.0 m s^{-2} \)
Subject: Maths
In an ellipse the distance between the foci is one third of the distance between
the directrices, then its \( e \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{\sqrt{3}} \)
\( c \cdot \frac{2 \sqrt{2}}{3} \)
D. \( \frac{1}{3} \)
Subject: Chemistry
A cell contains two hydrogen electrodes. The negative electrode is in
contact with a solution of \( 10^{-6} \mathrm{M} \)
hydrogen ions. The \( E M F \) of the cell is
\( 0.118 V \) at \( 25^{\circ} C . \) The concentration of
hydrogen ions at the positive electrode is:
A \( \cdot 10^{-4} M \)
В. \( 10^{-3} M \)
\( \mathrm{c} \cdot 10^{-1} M \)
D. None of these
Subject: Maths
\( \lim _{n \rightarrow \infty}\left[\frac{1}{n^{2}} \sec ^{2} \frac{1}{n^{2}}+\frac{2}{n^{2}} \sec ^{2} \frac{4}{n^{2}}+\ldots+\frac{1}{n}\right. \)
equals
A \( \cdot \frac{1}{2} \operatorname{cosec} 1 \)
B \( \cdot \frac{1}{2} \sec 1 \)
c. \( \frac{1}{2} \tan 1 \)
D. tan 1
Subject: Physics
Numerical Problems
Two stones \( A \) and \( B \) are dropped from the top of two different towers such that
they travel \( 44.1 \mathrm{m} \) and \( 63.7 \mathrm{m} \) in the last second of their motion respectively. Find the ratio of the heights of the two towers from where the stones were
dropped.
A . 25: 49
B. 45: 49
\( c \cdot 35: 49 \)
D. 125 : 49
Subject: Physics
Two small objects each with a net charge of \( +Q \) exert a force of magnitude Fon each other. We replace one of the objects with another whose net charge is \( +4 Q . \) We move the \( +Q \) and \( +4 Q \) charges to be 3 times as far apart as they were. What is the magnitude of the force on the \( +4 Q \) charge?
\( A \cdot F \)
B. 4F
\( c \cdot 4 F / 3 \)
D. 4F/9
E. F/3
Subject: Physics
Area of each of the conducting plates 1
2,3,4,5 and 6 is \( A . \) The system is kept
in air. Find the the capacitance between
\( A \) and \( B(1 \& 4,2 \& 5 \text { and } 3 \& 6 \) are pairs
of parallel plates)
A. \( \frac{3 \varepsilon_{0} A}{d} \)
B. \( \frac{2}{3} \frac{\varepsilon_{0} A}{d} \)
c. \( \frac{3}{2} \frac{\varepsilon_{0} A}{d} \)
D. \( \frac{\varepsilon_{0} A}{3 d} \)
Subject: Maths
If \( \frac{1+4 p}{4}, \frac{1-p}{2}, \frac{1-2 p}{2} \) are
probabilities of three mutually exclusive events, then
A \( \cdot \frac{1}{3} \leq p \leq \frac{1}{2} \)
в. \( \frac{1}{3} \leq p \leq \frac{2}{3} \)
c. \( \frac{1}{6} \leq p \leq \frac{1}{2} \)
D. None of these
Subject: Chemistry
Statement : If equal masses of sodium
metal and chlorine gas are allowed to
react, some sodium will be leftover after all the chlorine is used up.
Statement 2: The reaction required
twice as many atoms of chlorine as
Sodium.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.
Subject: Physics
A very small hole in an electrical
furnace used for treating metal acts nearly as black body. If the hole has an
area \( 100 m m^{2} \) and it is desired to
maintain the metal at \( 727^{\circ} C \), then how
much power travels through the hole?
A. zero
B. 5.7 \( w \)
c. \( 57 \mathrm{w} \)
D. 57 kw
Subject: Physics
A transmitter transmits at a
wavelength of \( 300 m . \) A condenser of
capacitance \( 2.4 \mu F \) is being used. The
value of the inductance for the resonant
circuit is approximately
В . \( 10^{-6} \) Н
\( \mathrm{c} \cdot 10^{-8} \mathrm{H} \)
D. \( 10^{-10} H \)
Subject: Physics
The nuclear radius of a nucleus with
nucleon number 16 is \( 3 \times 10^{-15} m \)
Then, the nuclear radius of a nucleus
with nucleon number 128 is :
A \( \cdot 3 \times 10^{-15} \mathrm{m} \)
B . \( 1.5 \times 10^{-15} m \)
\( \mathbf{c} \cdot 6 \times 10^{-15} m \)
D. \( 4.5 \times 10^{-15} \mathrm{m} \)
Subject: Chemistry
The correct order(s) is/are:
This question has multiple correct options
\( \mathbf{A} \cdot P h-C H_{2}-B r>P h-C l>P h-B r \)
\( \left(S_{N} \text { reaction with } N a O H\right) \)
\( \mathbf{B} \cdot C H_{3}-\underset{\|}{C}-B r>C H_{3}-\underset{\| \atop O}{C}-F>C H_{3}-C-O E t \)
\( _{O} \|_{O} \)
(Hydrolysis with \( N a O H) \)
\( \mathbf{c} \)
\( C H_{3} \)
\( C H_{3}-C H-C O O H>C H_{3}-C H_{2}-C O O H> \)
\( C H_{3}-C O O H \quad \) (rate of esterification)
D \( \left.\cdot \frac{a}{N H_{2}-N H-C_{O}^{b}-C N_{2}}(a>b>c) \quad \text { (Bascicity of } N\right) \)
Subject: Physics
If the length of Rough inclined plane is \( 10 m \) and the value of \( g \) is \( 10 m / s^{2} \) and
the Angle of Inclination is \( 30^{\circ} \) and
coefficient of friction is \( 0.2, \) then the
Acceleration of the block is
A . 4.13
B. 3.27
c. 1.43
D. 1.34
Subject: Maths
Write the decimals shown in the
following place value table:
\( \begin{array}{llll}\text { Thousands } & \text { Hundreds } & \text { Tens } \\ \text { (i) } & & & \\ \text { (ii) } & 9 & 5 & 4 \\ \text { (iii) } & & & \\ & & & \end{array} \)
Subject: Physics
Select the correct option given below:
When \( 1.5 k g \) of ice at \( 0^{\circ} C \) mixed with
\( 2 k g \) of water at \( 70^{\circ} C \) in a container, the
resulting temperature is \( 5^{\circ} \mathrm{C} \) the heat
of fusion of ice is \( \left(s_{w a t e r}=\right. \) \( \left.4186 J K g^{-1} K^{-1}\right) \)
A \( \cdot 1.42 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \)
В. \( 2.42 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \)
c. \( 3.42 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \)
D. \( 4.42 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \)
Subject: Physics
A convex spherical refracting surface
with radius \( R \) separates a medium
having refractive index \( 5 / 2 \) from air. As an object is moved towards the surface from far away from the surface along
the principle axis, its image
A. Changes from real to virtual when it is at a distance \( R \) from the surface
B. Changes from virtual to real when it is at a distance \( R \) from the surface
c. changes from real to virtual when it is at a distance \( 2 R / 3 \) from the surface
D. Changes from virtual to real when it is at a distance \( 2 R / 3 \) from the surface
Subject: Maths
The area between the curve \( y=2 x^{4}- \)
\( x^{2}, \) the \( x- \) axis and the ordinates of two
minima of the curve is:
A \( \cdot \frac{7}{120} \) sq.unit
B. \( \frac{9}{120} \) sq.unit
c. \( \frac{11}{120} \) sq.unit
D. \( \frac{13}{120} \) sq.unit