AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Pick the odd ones in each of the
following groups and select the correct
option.
(i) Renal pelvis, Medullary pyramid, Renal cortex, Renal papilla
(ii) Afferent arteriole, Henle's loop, Vasa
recta, Efferent arteriole
(iii) Glomerular filtration, Antidiuretic
hormone, Hypertonic urine, Collecting
duct
(iv) Proximal convoluted tubule, Distal
convoluted tubule, Henle's loop, Renal
corpuscle
A. (i)Renal pelvis (ii)Henle's loop (iii)Collecting duct tubule (iv)Distal convoluted tubule
B. (i)Renal papilla (ii)Afferent arteriole (iii)Antidiuretic hormone (iv)Henle's loop
C. (i)Medullary pyramid (ii)Efferent arteriole
(iii)Hypertonic urine (iv)Proximal convoluted tubule
D. (i)Renal cortex (ii)Vasa recta (iii)Glomerular filtration (iv)Renal corpuscle
Subject: Chemistry
Through what potential difference must an electron pass to have a wavelength of \( \mathbf{5 0 0} \boldsymbol{A} ? \)
A \( \cdot 6.03 \times 10^{-3} \) ev
В. \( 3.01 \times 10^{-4} \mathrm{ev} \)
\( c \cdot 6.03 \times 10^{-5} \mathrm{ev} \)
\( v \)
D. \( 3.01 \times 10^{-5} \mathrm{ev} \)
Subject: Physics
Assertion
Centre of mass of a rigid body always lies inside the body.
Reason
Centre of mass and centre of gravity coincide if gravity is uniform.
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: Maths
The adjacent sides of a parallelogram \( \operatorname{are} 2 \hat{i}+4 \hat{j}-5 \hat{k} \) and \( \hat{i}+2 \hat{j}+3 \hat{k} \) then
the unit vector parallel to a diagonal is
A \( \cdot \frac{-\bar{i}-2 \bar{j}+8 \bar{k}}{\sqrt{69}} \)
в. \( \frac{3 \bar{i}+6 \bar{j}-2 \bar{k}}{7} \)
c. \( \frac{\bar{i}+2 \bar{j}-8 \bar{k}}{\sqrt{69}} \)
D. All the above
Subject: Chemistry
The minus \( \operatorname{sign} \) in \( r a t e=-\frac{d[A]}{d t} \)
indicates the
concentration of the
time. The rate of a reaction is always quantity. The rate of reaction increases with
concentration of reactants. The blanks
in the question corresponds to:
A. decrease, products, positive, increase
B. increase, reactants, negative, decrease
c. decrease, reactants, positive, increase
D. increase, products, positive, increase
Subject: Maths
In the figure, the chord BD is
perpendicular to the diameter AC. Find
the measures of the following angles.
a. \( \angle B A C \)
b. \( \angle B C D \)
c. \( \angle \boldsymbol{A} \boldsymbol{D} \boldsymbol{C} \)
\( \mathrm{d} . \angle C D M \)
e. \( \angle B A P \)
Subject: Physics
Two identical smooth balls are
projected from points 0 and \( A \) on the horizontal ground with same speed of projection. the angle of projection in
each case is \( 30^{\circ} \) (see figure). The distance between 0 and \( A \) is 100 m. The
balls collide in mid-air and return to
their respective points of projection. If the coefficient of restitution is \( 0.7, \) find
the speed of projection of either ball (in
\( \mathrm{m} / \mathrm{s}) \) correct to nearest integer. (Take
\( \left.g=10 m s^{-2} \text {and } \sqrt{3}=1.7\right) \)
Subject: Maths
If \( a, b, c, d \) are non-negative real numbers where \( a+b+c+d=1, \) then
the maximum value of \( a b+b c+c d+ \)
\( a d \) is
A \( \cdot \frac{1}{4} \)
B. 3
\( c \cdot 4 \)
D. none of these
Subject: Physics
Which one of the following will make its way most easily through the tiny space between the fiber of the clothing:
A. glycerene at \( 10^{\circ} \mathrm{C} \)
B. water at \( 20^{\circ} \mathrm{C} \)
c. soap water at \( 20^{\circ} \mathrm{C} \)
D. water at \( 100^{\circ} \mathrm{C} \)
Subject: Physics
In a battery five dry cells each of 1.5 volt
have internal resistance of
0.2,0.3,0.4,0.5 and \( 0.6 \Omega \) are present in
series. The battery is connected to a \( 1 \Omega \) resistance. Identify the correct statement \( (s) \)
A. Current in the circuit will be \( 2.5 A \)
B. Current in the circuit will be \( 1.5 A \)
c. on short circuiting the battery 3.75 d current will flow
D. Both \( (A) \) and \( (C) \)
Subject: Physics
At \( 27^{0} \) C certain gas occupied a volume
Of 4 litres. If the volume of this is to be increased to 12 litres at
the same pressure, the gas is to be heated to a temperature
A. 300 K
B. \( 900 \mathrm{K} \)
\( \mathbf{C} .600 \mathrm{K} \)
D. \( 1200 K \)
Subject: Maths
If \( \cos ^{-1}\left(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\right)=k \) (a constant)
then \( \frac{d y}{d x}= \)
A. \( \frac{y}{x} \)
в. \( \frac{x}{y} \)
c. \( \frac{x^{2}}{y^{2}} \)
D. \( \frac{y^{2}}{x^{2}} \)
Subject: Maths
In the given figure \( A B \| C D \). find the
value of \( x \) and \( y \)
A \( \cdot x=35^{\circ}, y=65^{\circ} \)
B . \( x=95^{\circ}, y=65^{\circ} \)
C . \( x=85^{\circ}, y=65^{\circ} \)
D. \( x=25^{\circ}, y=65 \)
Subject: Maths
\( \forall \boldsymbol{n} \in \boldsymbol{N}, \mathbf{1}+\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}+\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}+\ldots \ldots+\frac{\mathbf{1}}{\sqrt{\boldsymbol{n}}} \) is
A \( \cdot \sqrt{n} \)
\( \mathbf{B} \cdot \leq \sqrt{n} \)
\( c \cdot>\sqrt{n} \)
D. none of these
Subject: Chemistry
Assertion
When an electric current is passed through an aqueous solution of sodium chloride, sodium ions move towards cathode and chloride ions move towards
anode.
Reason
Cathode is a negatively charged electrode and therefore attracts \( \boldsymbol{N} \boldsymbol{A}+ \)
ions. Anode is a positively charged
electrode and therefore attracts \( C l- \)
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. Assertion is incorrect but Reason is correct
Subject: Physics
(i) For a Searle's experiment, in the
graph shown, there are two readings a
and b that are not lying on the straight
line
(ii) Experiment is not performed
precisely
A. Both (i) and (ii) are true and (ii) is reason for (i)
B. Both (i) and (ii) are true but (ii) is not reason for (ii)
c. only (i) is true
D. only (ii) is true
Subject: Chemistry
An equilibrium mixture for the reaction
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{S}_{2}(\boldsymbol{g}) \) has
1 mole of \( H_{2} S, 0.2 \) mole of \( H_{2} \) and
0.8 mole of \( S_{2} \) in a 2 litre flask. The
value of \( \boldsymbol{K}_{c} \) in mol \( \boldsymbol{L}^{-1} \) is
\( \mathbf{A} \cdot 0.004 \)
B. 0.08
c. 0.016
D. 0.160
Subject: Maths
If \( f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^{2} & 2 x \\ \tan x & x & 1\end{array}\right|, \) then
\( \lim _{x \rightarrow 0} \frac{f^{\prime}(x)}{x} \)
A. Exists and is equal to -2
B. Does not exist
C. Exist and is equal to 0
D. Exists and is equal to 2
Subject: Maths
The area of the smaller part bounded by the semicircle \( \boldsymbol{y}=\sqrt{\mathbf{4}-\boldsymbol{x}^{2}}, \boldsymbol{y}=\boldsymbol{x} \sqrt{\mathbf{3}} \)
and x-axis is
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{4 \pi}{3} \)
D.
Subject: Physics
In a meter-bridge, the balancing length from the left end when standard
resistance of 1 is in right gap is found
to be \( 20 \mathrm{cm} \). The value of unknown
resistance is
A \( .0 .25 \Omega \)
B. \( 0.5 \Omega \)
\( c .0 .4 \Omega \)
D. 4\Omega
Subject: Physics
In the circuit shown in the fig the heat
produced in resistance \( R_{1} \) can be
measured by
A. connecting both voltmeter and an ammeter in parallel to \( R_{1} \)
B. connecting ammeter in series with \( R_{1} \) and voltmeter in parallel to both \( R_{1} \) and \( R_{2} \)
C. connecting ammeter in parallel to \( R_{1} \) and voltmeter in
series with \( R_{1} \)
D. connecting voltmeter in parallel to \( R_{1} \) and ammeter in
series with \( R_{1} \)
Subject: Chemistry
Two liters air formed \( 1915 \mathrm{ml} \) of ozonized
air when passed through Brodio's apparatus. The volume of ozone formed
is :
\( A \cdot 85 \mathrm{m} \)
B. 170 m1
c. 225 \( \mathrm{ml} \)
D. 42.5 m
Subject: Chemistry
Electromagnetic radiation having \( \lambda= \) \( 310 \dot{A} \) is subjected to a metal sheet having work function \( =12.8 \mathrm{eV} . \) What will be the velocity of photo electrons having maximum kinetic energy?
A \( \cdot 1.23 \times 10^{6} m / s \)
B . \( 2.28 \times 10^{6} \mathrm{m} / \mathrm{s} \)
c. \( 3.1 \times 10^{6} m / s \)
D. None of these
Subject: Chemistry
\( 10 m L \) of a solution of \( N a O H \) is found
to be completely neutralised by \( 8 m L \) of
a given solution of \( \boldsymbol{H} \boldsymbol{C l} \). If we take \( 20 m L \) of the same solution of \( N a O H \)
the amount \( H C l \) solution (the same
solution as before) required to neutralise it will be:
\( \mathbf{A} \cdot 4 m L \)
B. \( 8 m L \)
c. \( 12 m L \)
D. \( 16 m L \)
Subject: Physics
On rubbing a glass rod with silk cloth,
\( 6.84 \times 10^{16} \) electrons are transferred
from glass rod to silk cloth. Find the total charge transferred.
\( \mathbf{A} \cdot-1.09 \times 10^{-4} C \)
в. \( -1.09 \times 10^{-3} C \)
c. \( -1.09 \times 10^{-5} C \)
D. \( -1.09 \times 10^{-2} C \)
Subject: Physics
Match the following:
List

List 2
a)Reversible \( \quad \) 1)Temperature remains constant Process
b)Isothermal
2) Combustion reaction of Process \( \quad \) mixture of petrol and air
c) Irreversible
3)No heat flow between the Process \( \quad \) system and surrounding
d)Adiabatic
4) Temperature change in Process \( \quad \) atmosphere
\( A \cdot a-4, b-1, c-2, d-3 \)
B. a-3,b-2,c-4,d-1
c. a-3,b-1,c-2,d-4
D. a-2,b-3,c-1,d-4
Subject: Physics
How much heat energy in Joules is necessary to raise the temperature of
\( 5 k g \) of water from \( 20^{\circ} \) to \( 100^{\circ} ? \)
A. \( 1672 K J \)
в. \( 167200 J \)
c. \( 16720 J \)
D. \( 1672 J \)
Subject: Physics
A hammer exerts a force of 1.5 N on each
of the two nails \( A \) and \( B \). The area of
cross section of tip of nail is \( 2 m m^{2} \)
while that of nail \( \mathrm{B} \) is \( 6 \mathrm{mm}^{2} \). Calculate
pressure on each nail in pascal.
Subject: Physics
A capacitors has square plates each of
side \( l \) making an angle a with each
other as shown in the figure. Then, for
small value of a the capacitance \( C \) is
given by :
\( ^{\mathbf{A}} \cdot \frac{\epsilon_{0} I^{2}}{d}\left(1-\frac{a l}{2 d}\right) \)
В \( \cdot \frac{\epsilon_{0} I^{2}}{2 d}\left(1-\frac{a l}{d}\right) \)
c. \( \frac{\epsilon_{0} I^{2}}{d}\left(1-\frac{a l}{d}\right) \)
D \( \cdot \frac{\epsilon_{0} I^{2}}{2 d}\left(1+\frac{a l}{d}\right) \)
Subject: Maths
State whether True=1 or False=0
\( \int \frac{x^{2}}{\left(x^{2}+1\right)\left(x^{2}+4\right)} d x=\frac{-1}{3} \tan ^{-1} x+ \)
\( \frac{2}{3} \tan ^{-1}\left(\frac{x}{2}\right)+C \)
Subject: Chemistry
Molar heat capacity of water (liquid) in equilibrium with water vapour at
constant pressure is:
A. zero
B . \( \infty \)
c. 75.48 J mol \( ^{-1} \mathrm{k}^{-1} \)
D. 40.45 J mol \( ^{-1} \mathrm{K}^{-1} \)
Subject: Physics
\( R \) and \( r \) are the radii of the Earth and
the Moon respectively and \( \rho_{e} \) and \( \rho_{m} \) are
the densities of the Earth and Moon
respectively. The ratio of acceleration due to gravity on the surface of the
Earth to the Moon is:
A \( \cdot \frac{R}{r} \cdot \frac{\rho_{e}}{\rho_{m}} \)
в. \( \frac{r}{R} \cdot \frac{\rho_{e}}{\rho_{m}} \)
c. \( \frac{r}{R} \cdot \frac{\rho_{m}}{\rho_{e}} \)
D. \( \frac{R}{r} \cdot \frac{\rho_{m}}{\rho_{e}} \)
Subject: Physics
A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \( 15 \mathrm{cm} \) from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is :
A. \( 5 \mathrm{cm} \)
B. -10 cm
c. \( 20 \mathrm{cm} \)
D. -30 cm
Subject: Physics
In the figure a long uniform
potentiometer wire \( A B \) is having a
constant potential gradient along its
length. The null points for the two
primary cells of emfs \( \varepsilon_{1} \) and \( \varepsilon_{2} \)
connected in the manner shown are
obtained at a distance of \( 120 \mathrm{cm} \) and
\( 300 c m \) from the end \( A . \) Find (i) \( \varepsilon_{1} / \varepsilon_{2} \)
and (ii) position of null point for the cell
\( \varepsilon_{1} \)
How is the sensitivity of a
potentiometer increased?
Subject: Physics
toppr ०६
Q Type your question
In tigure. I nen the Key \( \mathbf{K} \) Is pressed to
complete the circuit. Finally the net
charge on upper plate and net charge the circuit. Finally the net charge on
upper plate and net charge on lower
plate of capacitor \( C \) is positive.

Reason : In a parallel plate capacitor
both plates always carry equal and
opposite charge.
A. If both Assertion arid Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
C. If Assertion is correct but Reason is incorrect
D. If Assertion is incorrect but Reason is correct.
Subject: Chemistry
Statements that are true of transition
and inner transition metals are :
This question has multiple correct options
A. osmium is the heaviest transition metal
B. \( C u^{+}\left(3 d^{10}\right) \) is more stable than \( C u^{2+}\left(3 d^{9}\right) \) in aqueous medium
C . actinides are generally strong reducing agents
D. \( Y, L a \) and \( A c \) exhibit variable valency
Subject: Maths
If \( \tan \alpha=K \cot \beta, \) then \( \frac{\cos (\alpha-\beta)}{\cos (\alpha-\beta)} \)
equals
A \( \cdot \frac{1+K}{1-K} \)
в. \( \frac{1-K}{1+K} \)
c. \( \frac{K+1}{K-1} \)
D. \( \frac{K-1}{K+1} \)
Subject: Maths
The velocity of a body varies with time
as \( V=3 t^{2}+2 . \) Find the instantaneous
acceleration \( t=3 \) sec
A \( \cdot 31 m / s^{2} \)
B . \( 18 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 3 m / s^{2} \)
D . \( -2 / 3 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
A source oscillates with a frequency 25
Hz and the wave propagates with 300 \( \mathrm{m} / \mathrm{s} . \) Two points \( \mathrm{A} \) and \( \mathrm{B} \) are located at distances \( 10 \mathrm{m} \) and \( 16 \mathrm{m} \) away from the
source. The phase difference between \( A \) and B is
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
\( c \)
D . 2 \( \pi \)
Subject: Chemistry
Which is not a disproportionation
reaction?
\( A \)
B.
\[
\begin{array}{l}
\mathrm{CHO} \\
\mathrm{COOH}
\end{array}+\mathrm{OH}^{-} \longrightarrow \begin{array}{l}
\mathrm{CH}_{2} \mathrm{OH} \quad \mathrm{COO}^{-} \\
\mathrm{COO}^{-}+\mid \\
\mathrm{COO}^{-}
\end{array}
\]
c. \( N a H+H_{2} O \longrightarrow N a O H+H_{2} \)
D. All of the above
Subject: Physics
A car is moving at a constant speed of \( 40 k m / h \) along a straight road which heads towards a large vertical wall and
makes sharp \( 90^{\circ} \) turn by side of the wall. A fly flying at a constant speed of
\( 100 k m / h, \) starts from the wall towards
the car at an instant when the car is
\( 20 k m \) away, flies until it reaches the glass pane of the car and returns to the wall at the same speed. It continues to fly between the car and the wall till the
car makes the \( 90^{\circ} \) turn. How many trips has it made between the car and the
wall?
A . 50
B. Infinite
\( c \cdot 66 \)
D. 150
Subject: Physics
In the following figure \( r_{1} \) and \( r_{2} \) are \( 5 \mathrm{cm} \) and \( 30 \mathrm{cm} \) respectively. If the moment of inertia of the wheel is
\( 5100 k g-m^{2} \) about the axis passing
through its centre and perpendicular to the plane of wheel, then what will be its angular acceleration?
Subject: Physics
The material of a wire has a density of
\( 1.4 \mathrm{g} / \mathrm{cm}^{3} . \) If it is not wetted by a liquid of
surface tension 44 dyne/cm, then the maximum radius of the wire which can
float on the surface of liquid is :
A \( \cdot \frac{10}{28} \mathrm{cm} \)
в. \( \frac{10}{14} \mathrm{cm} \)
c. \( \frac{10}{7} m m \)
D. 0.7 cm
Subject: Physics
A plane lamina has an area \( 2 m^{2} \) at
\( 10^{\circ} C \) then what is its area at \( 110^{\circ} C ? \)
It's co-efficient of superficial expansion
is \( 2 \times 10^{-5} / C \)
A \( .2 .002 \mathrm{m}^{2} \)
B . \( 2.004 \mathrm{m}^{2} \)
c. \( 2.02 m^{2} \)
D. \( 2.04 \mathrm{m}^{2} \)
Subject: Chemistry
Which one of the following statements
is correct?
A \( . \quad N a C l \) is a paramagnetic salt
B. \( C u S O_{4} \) is a diamagnetic salt
C. \( M n O \) is an example of ferromagnetic substance
D. \( C r O_{2} \) is an example of antiferromagnetic substance
E. Ferrimagnetic substance like \( Z n F e_{2} O_{4} \) becomes paramagnetic on heating
Subject: Maths
What is \( \frac{x^{2}-3 x+2}{x^{2}-5 x+6} \div \frac{x^{2}-5 x+4}{x^{2}-7 x+12} \)
equal to
A. \( \frac{x+3}{x-3} \)
B.
c. \( \frac{x+1}{x-1} \)
D.
Subject: Physics
Two radio stations broadcast their
program at the same amplitude \( A \) but
at slightly different frequencies \( n_{1} \) and \( n_{2} \) such that \( \left(n_{1}-n_{2}\right)=10^{3} H z . \)
detector receives signals from both the stations simultaneously but only when
intensity of signal is greater than \( 2 A^{2} \) The time interval between two
successive maxima will be :
в. \( 10^{-2} \) s
\( \mathrm{c} \cdot 10^{-3} s \)
D. \( 10^{\circ} \)
Subject: Physics
A semiconductor has equal number of
electron and hole concentration of \( 2 \times \)
\( 10^{8} m^{-3} . \) On doping with a certain
impurity, the electron concentration increases to \( 4 \times 10^{10} m^{-3} \), then the new
hole concentration of the
semiconductor is
A \( \cdot 10^{6} m^{-3} \)
B. \( 10^{8} m^{-3} \)
c. \( 10^{10} m^{-3} \)
D. \( 10^{12} m^{-3} \)
Subject: Maths
For a point \( \boldsymbol{P} \) in the plane, let \( \boldsymbol{d}_{1}(\mathrm{P}) \) and
\( \boldsymbol{d}_{2} \)
(P) be the distances of the point
from the lines \( x-y=0 \) and \( x+y=0 \)
respectively. The area of the region consisting of all points P lying in the first quadrant of the plane and
satisfying \( 2 \leq d_{1}(P)+d_{2}(P) \leq 4, \) is
A .4
B. 6
c. 10
D. 16
Subject: Biology
Match the columns.
\( \mathbf{A} \)
\( a-2, b-3, c-1, d-4 \)
B. \( a-1, b-4, c-2, d-3 \)
c. \( a-3, b-1, c-4, d-2 \)
D. \( a-2, b-4, c-1, d-3 \)
Subject: Chemistry
The numerical value of \( d / D \) when \( \alpha=0 \)
for \( \boldsymbol{P} \boldsymbol{C l}_{5} \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}+\boldsymbol{C l}_{2} ; \) where \( \boldsymbol{d} \) are
vapour density of equilibrium mixture
and \( D \) is vapour density of \( P C l_{5} \)
Subject: Maths
Is this possible \( a \neq \)
\( \mathbf{0} \cdot\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{a} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{a}^{2}\end{array}\right|=\mathbf{0} \)
represents a straight line parallel to the
y-axis
A. True
B. False
Subject: Chemistry
The molarity of \( 98 \% \)
\( \mathbf{H}_{2} \mathbf{S O}_{4}(\boldsymbol{d}=\mathbf{1} . \mathbf{8} \boldsymbol{g} / \boldsymbol{m} \boldsymbol{L}) \) by weight is:
A. 6 .
B. 18M
c. 10 м
D. 4 M
Subject: Maths
If \( A \) is a square matrix, then the value of
\( a d j A^{T}-(a d j A)^{T} \) is equal to
A. \( A \)
B. 2|A|I, where I is the identity matrix
c. null matrix whose order is same as that of \( A \)
D. unit matrix whose order is same as that of \( A \)
Subject: Maths
If \( R s .3,750 \) amount to \( R s .4,620 \) in 3 years at simple interest, then find the rate of interest.
A \( \cdot 7 \frac{11}{15} \% \)
в. \( 8 \frac{11}{15} \% \)
c. \( _{6} \frac{11}{15} \% \)
D. \( 5 \frac{11}{15} \% \)
Subject: Physics
The rotation of the Earth having radius \( \mathrm{R} \) about its axis speed upto a value
such that a man at latitude angle \( 60^{\circ} \)
feels weightless. The duration of the day in such case will be.
\( ^{\mathrm{A}} \cdot_{8 \pi} \sqrt{\frac{R}{g}} \)
в. \( 8 \pi \sqrt{\frac{g}{R}} \)
\( ^{c} \cdot \sqrt{\frac{R}{g}} \)
D. \( 4 \pi \sqrt{\frac{g}{R}} \)
Subject: Chemistry
The \( E_{M^{3+} / M^{2+}}^{0} \) values of \( \mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe} \) and
Co are \( -\mathbf{0 . 4 1},+\mathbf{1 . 5 7},+\mathbf{0 . 7 7} \) and
\( +1.97 \mathrm{V} \) respectively. For which one of these metals the change in oxidation
state from +2 to +3 is easiest?
A \( . C r \)
в. \( M n \)
c. \( F e \)
D. \( C o \)
Subject: Physics
A coil of radius \( \mathrm{R} \) carries a current I.
Another concentric coil of radius \( \boldsymbol{r}(\boldsymbol{r}<<\boldsymbol{R}) \) caries current \( \frac{\boldsymbol{I}}{2} . \) Initially
planes of the two coils are mutually perpendicular and both the coils are
free to rotate about common diameter.
They are released from rest from this
position. The masses of the coils are \( \mathbf{M} \)
and m respectively \( (\boldsymbol{m}<\boldsymbol{M}) . \) During
the subsequent motion let \( K_{1} \) and \( K_{2} \)
be the maximum kinetic energies of the
two coils respectively and let U be the
magnitude of maximum potential
energy of magnetic interaction of the system of the coils. Choose the correct
options.
A \( \cdot \frac{K_{1}}{K_{2}}=\frac{M}{m}\left(\frac{R}{r}\right)^{2} \)
B. \( \quad K_{1}=\frac{U m r^{2}}{m r^{2}+M R^{2}} K_{2}=\frac{U M R^{2}}{m r^{2}+M R^{2}} \)
\( ^{\mathbf{C}} U=\frac{\mu_{0} \pi I^{2} r^{2}}{4 R} \)
D. \( K_{2}>>K_{1} \)
Subject: Maths
Consider two curves \( C_{1}: y=\frac{1}{x} \) and \( C_{2} \)
\( \boldsymbol{y}=\ln x \) on the xy plane Let \( \boldsymbol{D}_{1} \) denotes
the region surrounded by \( C_{1}, C_{2} \) and the
line \( x=1 \) and \( D_{2} \) denotes the region
surrounded by \( C_{1}, C_{2} \) and the line \( x=a \)
If \( D_{1}=D_{2} \) then the value of 'a':
A \( \cdot \frac{e}{2} \)
в.
\( \mathbf{c} \cdot e-1 \)
D. \( 2(e-1) \)
Subject: Physics
A vibrator makes \( 150 \mathrm{cm} \) of a string to vibrate in 6 loops in the longitudinal arrangement when it is stretched by 150
N. The entire length of the string is then weighed and is found to weigh \( 400 \mathrm{mg} \)
Then
This question has multiple correct options
A. Frequency of the vibrator is 3 \( \mathrm{kHz} \)
B. Frequency of the vibrator is \( 1.5 \mathrm{kHz} \)
c. Distance between two nodes is \( 25 \mathrm{cm} \)
D. Distance between two nodes is 33 cm
Subject: Maths
Simplify the following into their lowest form: \( \frac{6 x^{2}+9 x}{3 x^{2}-12 x} \)
A \( \cdot \frac{2 x+3}{x-4} \)
в. \( \frac{2 x-3}{x-4} \)
c. \( \frac{2 x+3}{x+4} \)
D. None of these
Subject: Chemistry
A nuclide \( X \) undergoes \( \alpha \) -decay and
another nuclide undergoes \( \beta \) -decay.
Which of the following statements are
correct?
This question has multiple correct options
A. The \( \beta \) -particles emitted by \( Y \) may have widely different speed
B. The \( \alpha \) -particles emitted by \( X \) may have widely different speed
C. The \( \alpha \) -particles emitted by \( X \) will have almost the same speed
D. The \( \beta \) -particles emitted by \( Y \) will have the same speed
Subject: Physics
A uniform rod of length \( l=1 m \) is kept
as shown in the figure. \( \boldsymbol{H} \) is a horizontal
smooth surface and \( W \) is a vertical
smooth well. The rod is release from this
position. What is the angular angular acceleration of the rod just after the released?
A. \( \frac{6 g \cos \theta}{l} \)
B. \( \frac{3 g \cos \theta}{l} \)
\( c .6 g \cos \theta \)
D. \( \frac{2 g \cos \theta}{l} \)
Subject: Physics
Potential energy of a simple harmonic oscillator at its mean position is 0.4 J. If its kinetic energy at a displacement half of its amplitude from mean position is \( 0.6 \mathrm{J}, \) its total energy
is
A . \( 1.0 J \)
в. \( 1.2 J \)
c. \( 1.4 J \)
D. 1.6 .5
Subject: Physics
If the acceleration due to gravity inside
the earth is to be kept constant, then
the relation between the density \( d \) and the distance \( r \) from the centre of earth
will be
\( \mathbf{A} \cdot d \propto r \)
B. \( d \propto r^{1 / 2} \)
c. \( d \propto 1 / r \)
D. \( d \propto \frac{1}{r^{2}} \)