AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A conducting ring of radius \( r \) is rolling without slipping with a constant angular velocity \( \omega \) (figure). If the
magnetic field strength is \( B \) and is directed into the page then the emf induced across \( P Q \) is
A. \( B \omega r^{2} \)
в. \( \frac{B \omega}{2} \)
c. \( 4 B \omega r^{2} \)
D. \( \frac{B \omega}{4} \)
Subject: Physics
Two magnetic poles of equal pole strengths each of \( 1.732 A m \) should be
placed at \( _{---} c m s \) apart so that the
force of attraction between them is
0.5 dynes (nearly):
\( \mathbf{A} \cdot \mathbf{6} \)
в. 2.45
c. 24.5
D. \( \sqrt{3} \)
Subject: Chemistry
NaCN is sometimes added in the froth
flotation process as a depressant when ZnS and Pbs minerals are expected because
A. \( P b(C N)_{2} \) is precipitated while no effect on ZnS.
B. znS forms soluble complex \( N a_{2}\left[Z n(C N)_{4}\right] \) while PbS forms froth
C . PbS forms soluble complex \( N a_{2}\left[P b(C N)_{4}\right] \) while zns forms froth
D. NaCN is never added in froth flotation process
Subject: Maths
\( A, B \) and \( C \) start a business each
investing Rs 20000 After 5 months \( A \) withdraw Rs \( 5000, \) B withdraw Rs 4000 and \( C \) invests \( R s 6000 \) more \( A t \) the end
of the year a total profit of Rs 69900 was recorded Find the share of each
A. Rs. 20500, Rs.27200, Rs. 22200
B. Rs. 20500, Rs.25200, Rs. 24200
c. \( R s .20500, \) Rs.21200, Rs. 28200
D. Rs. 20500, Rs.23200, Rs. 26200
Subject: Chemistry
The rate constant for a zero order
reaction is \( 2 \times 10^{-2} \) mol \( L^{-1} s e c^{-1}, \) if
the concentration of the ractant after
\( 25 \sec \) is \( 0.25 M, \) calculate the initial concentration
A \( .0 .75 M \)
B. \( 1.5 M \)
c. 0.375
D. None of these
Subject: Maths
If \( \frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\ldots . . \) upto \( \infty=\frac{\pi^{2}}{6} \)
then \( \frac{1}{1^{2}}+\frac{1}{3^{2}}+\frac{1}{5^{2}}+\ldots= \)
A \( \cdot \frac{\pi^{2}}{12} \)
в. \( \frac{\pi^{2}}{24} \)
c. \( \frac{\pi^{2}}{8} \)
D. \( \frac{\pi^{2}}{4} \)
Subject: Physics
A circuit shown in Fig. has resistances
\( R_{1}=20 \Omega \) and \( R_{2}=30 \Omega . \) At what
value of the resistance \( R_{x} \) will the
thermal power generated in it be practically independent of small variations of that resistance. The
voltage between the points \( A \) and \( B \)
is supposed to be constant in this case.
Subject: Maths
The term independent of \( x \) in \( \left(\frac{1}{2} x^{\frac{1}{3}}+\right. \)
\( \left.\boldsymbol{x}^{\frac{-1}{5}}\right)^{8} \) is
A. \( \frac{35}{8} \)
B. 7
c. \( \frac{7}{2} \)
D . 28
Subject: Physics
toppr
Q Type your question
corresponding thermodynamic co-
ordinates are given. Here, the \( P \) and \( V \)
scales are so chosen that these cycles
on \( P-V \) diagram appear to be
circular.
Analyse these cycles on \( P-V \) diagram
and answer the following questions
about these processes.
What is the net work done in the given
process?
Cycle on System
\( \mathbf{A} \cdot \frac{\pi P_{0} V_{0}}{4} \)
\( \mathbf{B} \cdot-\frac{\pi P_{0} V_{0}}{4} \)
\( c \)
D.
Subject: Physics
A smooth track of incline of length \( l \) is
joined smoothly with circular track of
radius \( R . \) A mass of \( m \) kg is projected up from the bottom of the inclined
plane. The minimum speed of the mass
to reach the top of the track is given by,
\( \boldsymbol{v}= \)
\( \mathbf{A} \cdot[2 g(l \cos \theta+R)(1+\cos \theta)]^{1 / 2} \)
B - \( (2 g l \sin \theta+R)^{1 / 2} \)
\( \mathbf{c} \cdot[2 g\{l \sin \theta+R(1-\cos \theta)\}]^{1 / 2} \)
D. \( (2 g l \cos \theta+R)^{1 / 2} \)
Subject: Physics
At time \( t=0, \) two bodies \( A \) and \( B \) are at
the same point. A moves with constant
velocity \( V \) and \( B \) starts from rest and moves with constant acceleration. Relative velocity of B with respect to A when the bodies meet each other is:
A \( \cdot \frac{V}{2} \)
в. \( \frac{V}{3} \)
c. \( V \)
D. \( 2 V \)
Subject: Physics
Doppler's effect in sound in addition to
the relative velocity between source and
observer also depends on whether source and observer also depend on whether source or observer or both are
moving. Doppler effect in light depends only on the relative velocity of source and observer, the reason for this is:
A. Einstein's mass-energy relation.
B. Photoelectric effect.
c. the velocity of the observer with respect to the light velocity is negligible.
D. none of these
Subject: Chemistry
The vapour pressure of a moist gas at
\( 100^{\circ} \mathrm{C} \) is \( 750 \mathrm{mm} \) and the aqueous
tension at the same temperature is
10 mm. The vapour pressure of the dry
gas is :
\( A \cdot 750 \mathrm{mm} \)
B. 760 mm
c. \( 740 \mathrm{mm} \)
D. 720 mm
Subject: Chemistry
For an ideal binary liquid mixture:
A \( \cdot \Delta H_{(m i x)}=0 ; \quad \Delta S_{(\operatorname{mix})}<0 \)
B. \( \Delta S_{(\operatorname{mix})}>0 ; \quad \Delta G_{(\operatorname{mix})}<0 \)
\( \mathbf{c} \cdot \Delta S_{(m i x)}=0 ; \quad \Delta G_{(m i x)}=0 \)
D. \( \Delta V_{(\operatorname{mix})}=0 ; \quad \Delta G_{(\operatorname{mix})}>0 \)
Subject: Maths
Three sets of English, Hindi and Mathematics books have to be stacked
in such a way that all the books are
stored topic-wise and the height of each stack is the same. The number of
English books is \( 96, \) the number of Hindi books is 240 and the number of
Mathematics books is \( 336 . \) Assuming
that the books are of the same
thickness, determine the number of
stacks of English, Hindi and Mathematics books.
Subject: Physics
Two refracting media are separated by
a spherical interface as shown in figure.
PP' is the principle axis. \( \mu_{1} \) and \( \mu_{2} \) are
the refractive indices of medium of
incidence and medium of refraction
respectively. Then,
This question has multiple correct options
\( \mathbf{A} \cdot \) if \( \mu_{2}>\mu_{1} \) then there cannot be a real image of real object
\( \mathbf{B} \cdot \) if \( \mu_{2}>\mu_{1} \) then there cannot be a real image of virtual object.
\( \mathrm{C} \cdot \) if \( \mu_{1}>\mu_{2} \) then there cannot be a virtual image of virtual object
D. if \( \mu_{1}>\mu_{2} \) then there cannot be a real image of real
object
Subject: Maths
If 1 lies between the roots of the
equation \( y^{2}-m y+1=0 \) and \( [x] \) is
the GIF function,
then the value of \( \left[\left(\frac{4|x|}{|x|^{2}+16}\right)^{m}\right], \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of the above
Subject: Chemistry
Identify 'Z' in the following reaction \( \operatorname{series}, C H_{3} C H_{2} C H_{2} B r \stackrel{N a O H}{\longrightarrow} \)
\( (\boldsymbol{X}) \frac{A l_{2} O_{3}}{\Delta}(\boldsymbol{Y}) \stackrel{\boldsymbol{H O C l}}{\longrightarrow}(\boldsymbol{Z}) \)
\( A \)
Mixture of
в.
\( c \)
D.
Subject: Chemistry
The ion that has \( s p^{3} d^{2} \) hybridization for the central atom, is:
A \( \cdot\left[I C l_{2}\right]^{-} \)
B . \( \left[I F_{6}\right]^{-} \)
c. \( \left[I C l_{4}\right]^{-} \)
\( \mathbf{D} \cdot\left[B r F_{2}\right] \)
Subject: Biology
Which of the following statements is
false?
A. Oxygenated blood is pumped to all other parts of the body from left ventricle.
B. Gaseous exchange in the alveoli happens through capillaries.
C. Blood-from the right side of the heart enters into left side through right auricle and left auricle.
D. Lungs oxygenate the deoxygenated blood.
Subject: Maths
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional
probability that both are girls given that
(i) the youngest is a girl, (ii) at least one is a girl?
A. 0.33,0.34
В. 0.88,0.98
c. 0.78,0.67
D. 0.5,0.33
Subject: Physics
An LC circuit contains a \( 40 \mathrm{mH} \) inductor
and a \( 25 \mu \) F capacitor. The resistance of the circuit is negligible. The time is measured from the instant the circuit
is closed. The energy stored in the circuit is completely magnetic at times (in milliseconds)
A . 0,3.14,6.28
B. 0, 1.57, 4.71
c. 1.57,4.71,7.85
D. 1.57, 3.14, 4.71
Subject: Physics
A body of mass \( 1 k g \) is thrown with a
velocity of \( 10 m s^{-1} \) at an angle of \( 60^{\circ} \)
with the horizontal. Its momentum at
the highest point is:
\( \mathbf{A} \cdot 2 \mathrm{kg} \mathrm{ms}^{-1} \)
B. 3 \( k g m s^{-1} \)
\( \mathbf{c} \cdot 4 k g m s^{-1} \)
D. 5 kg \( m s^{-1} \)
Subject: Maths
If \( \frac{x^{2}+1}{x}=3 \frac{1}{3} \) and \( x>1 ; \) find the
value of
\( x-\frac{1}{x} \)
A \( \cdot 2 \frac{2}{3} \)
в. \( 1 \frac{2}{9} \)
c. \( 2 \frac{5}{7} \)
D. \( 1 \frac{1}{3} \)
Subject: Chemistry
Which of the following sets of reactants is used for preparation of paracetamol from phenol?
A \( \cdot H N O_{3}, H_{2} / P d,\left(C H_{3} C O\right)_{2} O \)
B \( \cdot H_{2} S O_{4}, H_{2} / P d,\left(C H_{3} C O\right)_{2} O \)
\( \mathrm{c} \cdot C_{6} H_{5} N_{2} C l, \operatorname{Sn} C l_{2} / H C l,\left(C H_{3} C O\right)_{2} O \)
D \( \cdot B r_{2} / H_{2} O, Z n / H C l,\left(C H_{3} C O\right)_{2} O \)
Subject: Chemistry
Formation of \( N i(C O)_{4} \) and its subsequent decomposition into Ni and CO (recycled) makes basis of Mond's
process. \( N i+4 C O \stackrel{T_{1}}{\longrightarrow} N i(C O)_{4} \stackrel{T_{2}}{\longrightarrow} N i+ \)
\( 4 C O \)
\( T_{1} \) and \( T_{2} \) are:
A \( \cdot 100^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)
в. \( 50^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C} \)
c. \( 50^{\circ} \mathrm{C}, 230^{\circ} \mathrm{C} \)
D. \( 230^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)
Subject: Physics
The radius and acceleration due to
gravity of the moon are \( \frac{1}{4} \) and \( \frac{1}{5} \) that of
the earth, the ratio of the mass of the
earth to mass of the moon is :
\( \mathbf{A} \cdot 1: 80 \)
B. 80: 1
c. 1: 20
D. 20:1
Subject: Biology
Assertion
The heart wood is more durable and
resistant to the attack of the micro
organisms and insects as compared to
the sap wood.
Reason
The heart wood contains organic
compounds like oils, aromatic
substance, gums, resin, tannins and
phenol etc.
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
A charge q is distributed over two spheres of radii \( R \) and \( r \) such that their surface densities are equal. What is the
ratio of the charges on the spheres?
A \( \cdot \frac{r}{R} \)
в. \( \frac{r^{2}}{R^{2}} \)
c. \( \frac{r^{3}}{R^{3}} \)
D. \( \frac{r^{4}}{R^{4}} \)
Subject: Chemistry
A reaction takes place in three steps. The rate constant of the three steps is
\( \boldsymbol{K}_{1}, \boldsymbol{K}_{2} \) and \( \boldsymbol{K}_{3} \) respectively. The overall rate constant \( \boldsymbol{K}=\frac{\boldsymbol{K}_{\mathbf{1}} \boldsymbol{K}_{\mathbf{3}}}{\boldsymbol{K}_{\mathbf{2}}} . \) If the energy
of activation for the three steps are
40,30 and \( 20 K J \) respectively, then :
This question has multiple correct options
A. overall energy of activation is \( 10 \mathrm{KJ} \)
B. overall energy of activation is \( 30 K J \)
C. the reaction mechanism is \( 2 A \rightleftharpoons A^{*}+A ; A^{*} \frac{K_{3}}{r d s} \)
product and overall order is one
D. the reaction mechanism is \( A \stackrel{K}{\rightarrow} B ; B \stackrel{K}{\longrightarrow} C ; C \stackrel{K_{3}}{\rightarrow} \)
product and overall order is one
Subject: Physics
A thin uniform rod \( A B \) of mass \( m= \)
1 kg moves translationally with
acceleration \( a=2 m / s^{2} \) due to two anti
parallel forces \( F_{1} \) and \( F_{2} \) The distance between the points at which these
forces are applied is equal to \( l=20 c m \)
Besides, it is known that \( F_{2}=5 N \). Find
the length of the rod (in meteres)
Subject: Maths
f matrix \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{4} & \mathbf{3}\end{array}\right] \) such that \( \boldsymbol{A} \boldsymbol{x}=\boldsymbol{I} \)
then \( \boldsymbol{x}= \)
\begin{tabular}{r}
\( \mathbf{A} \cdot \frac{1}{5}\left[\begin{array}{rr}1 & 3 \\
2 & -1\end{array}\right] \) \\
\hline
\end{tabular}
в. 1
\[
\begin{array}{ll}\overline{\overline{5}} & {\left[\begin{array}{ll}4 & -1\end{array}\right]}\end{array}
\]
c. \( 1\left[\begin{array}{ll}-3 & 2 \\ 5 & -1\end{array}\right] \)
D. \( \frac{1}{5}\left[\begin{array}{ll}-1 & 2 \\ -1 & 4\end{array}\right] \)
Subject: Physics
A cylinder of capacity \( 20 L \) is filled with
\( \boldsymbol{H}_{2} \) gas. The total average kinetic energy
of translatory motion of its molecules is
\( 1.5 \times 10^{5} J . \) The pressure of hydrogen in
the cylinder is
A \( .2 \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \)
в. \( 3 \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 4 \times 10^{6} N / m^{2} \)
D. \( 5 \times 10^{6} N / m^{2} \)
Subject: Physics
Two particles of masses \( 1 k g \) and \( 2 k g \) are placed at a distance at a distance of
\( 3 m . \) Moment of inertia of the particles about an axis passing through their centre of mass and perpendicular to the
line joining them is \( \left(\operatorname{in} k g-m^{2}\right) \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 9
c. 8
D. 12
Subject: Maths
If \( \vec{a}=4 \hat{i}-\hat{j}+\hat{k} \) and \( \vec{b}=2 \hat{i}-2 \hat{j}+\hat{k} \)
then find a unit vector parallel to the vector \( \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} \)
Subject: Chemistry
Convert \( 19200 \mathrm{kg} / \mathrm{m}^{3} \) into \( g \mathrm{cm}^{-3} \)
A \( \cdot 192 g c m^{-3} \)
В. \( 1.92 g \mathrm{cm}^{-3} \)
c. \( 19.2 g \mathrm{cm}^{-3} \)
D. \( 1920 \mathrm{g} \mathrm{cm}^{-3} \)
Subject: Maths
The points of intersection of the line \( 4 x-3 y-10=0 \) and the circle
\( x^{2}+y^{2}-2 x+4 y-20=0 \)
are....................and.
This question has multiple correct options
A \( .(4,2) \)
в. (-2,-6)
D. (-2,-4)
Subject: Chemistry
If \( v \) is rate corresponding to
\( P_{C H_{3} C H O}=P_{1}, \) what is the order of
reaction when \( \boldsymbol{P}_{C H_{3} C H O}=4 P_{1} ? \)
A .
в.
\( c \cdot 1.5 \)
\( D \ldots \)
Subject: Maths
Out of the total number of student who
opted for the given three subject, in the
year \( 2009,38 \% \) were girls. How many
boys opted for mathematics in the
same year?
\( \mathbf{7} \)
\( \mathbf{M}_{\mathbf{a}} \)
\( \mathbf{A} \cdot 1322 \)
B. 1332
\( \mathbf{c} \cdot 1312 \)
D. Cannot be determined
E. None of these
Subject: Maths
Chelsy spends \( 40 \% \) of her monthly
earnings on rent and \( 10 \% \) of the remaining amount on entertainment. If
she spends \( \$ 800 \) for rent, how much does she use for entertainment?
A. \( \$ 120 \)
B. \( \$ 180 \)
\( c . \$ 200 \)
D. \( \$ 800 \)
E . \( \$ 2,000 \)
Subject: Physics
The distance travelled by a body during last second of its upward journey is \( \boldsymbol{d} \) when the body is projected with certain velocity vertically up. If the velocity of projection is doubled, the distance travelled by the body during the last second of its upward journey is
A \( .2 d \)
B. \( 4 d \)
c. \( \frac{d}{2} \)
D. \( d \)
Subject: Physics
A ball is projected upwards from a height h above the surface of the earth with velocity v.The time at which the ball trikes the ground is This question has multiple correct options
A \( \cdot \frac{v}{g}+\frac{2 h g}{\sqrt{2}} \)
в. \( \frac{v}{g}[1-\sqrt{1+\frac{2 h}{g}}] \)
c. \( \frac{v}{g}[1+\sqrt{1+\frac{2 g h}{v^{2}}}] \)
D. \( \frac{v}{g}[1+\sqrt{v^{2}+\frac{2 g}{h}}] \)
Subject: Chemistry
Which of the following configurations represents the most electronegative
element?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{5} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
D \( \cdot 1 s^{2} 2 s^{2} 2 p^{4} \)
Subject: Chemistry
How many grams of \( 70 \% \) concentrated nitric acid solution should be used to
prepare \( 250 \mathrm{mL} \) of \( 2.0 \mathrm{M} ? \)
A \( \cdot 45.0 \mathrm{g} \) conc. \( \mathrm{H} \mathrm{NO}_{3} \)
B. 90.0 g conc. H \( \mathrm{NO}_{3} \)
c. 70.0 conc. \( H N O_{3} \)
D. 54.0 g conc. H NO
Subject: Chemistry
A weak acid \( H A \) is found to be \( 10 \% \)
ionized in \( 0.01 M \) aqueous solution. Calculate the pH of a solution which is
\( 0.1 M \) in \( H A \) and \( 0.05 M \) in \( N a A \)
\( \mathbf{A} \cdot 5.365 \)
B. 6.355
c. 3.653
D. 6.593
Subject: Chemistry
The electronic configurations of the first
four members of the actinoid series
cannot be written accurately in a
regular manner because of :
A. small difference in energy between \( 5 f \) and \( 6 d \) orbitals
B. large difference in energy between \( 5 f \) and \( 6 d \) orbitals
C. small difference in energy between \( 5 f \) and 6 s orbitals
D. violation of the Pauli exclusion principle
Subject: Physics
The dimensions of \( \epsilon_{0} \) (permittivity in
free space) is
\( \mathbf{A} \cdot M L^{2} T^{4} A^{2} \)
B. \( M L^{-3} T^{2} A^{2} \)
\( \mathbf{c} \cdot M^{-1} L^{3} T^{4} A^{2} \)
D. \( M L^{3} T^{2} A^{2} \)
E \( \cdot M^{-1} L^{-3} T^{4} A^{2} \)
Subject: Chemistry
Increasing basic properties of
\( T i O_{2}, Z r O_{2} \) and \( H f O_{2} \) are in order:
A. \( T i O_{2}<Z r O_{2}<H f O_{2} \)
в. \( H f O_{2}<Z r O_{2}<T i O_{2} \)
c. \( H f O_{2}<T i O_{2}<Z r O_{2} \)
D. \( Z r O_{2}<T i O_{2}<H f O_{2} \)
Subject: Physics
A ball is thrown vertically upwards (relative to the train) in a compartment
of a moving train. The face of the person sitting inside the compartment is towards engine of the train.
This question has multiple correct options
A. The ball will maintain the same horizontal velocity as that of the person (or the compartment) at the time of throwing.
B. If the train is accelerating then the horizontal velocity of the ball will be different from that of the train velocity, at the time of throwing.
C. If the ball appears to be moving backward to the person sitting in the compartment it means that speed of the train is increasing
D. If the ball appears to be moving ahead of the person sitting in the compartment it means the train's motion is retarding.
Subject: Chemistry
If an excess of \( A g N O_{3} \) solution is added to \( 100 \mathrm{ml} \) of \( 0.024 \mathrm{M} \) solution of dichlorobis (ethylene diamine) cobalt
(III) chloride, how many moles of \( A g C l \) will be precipitated?
A . 0.0012
B. 0.0016
c. 0.0024
D. 0.0048
Subject: Maths
If \( I=\int_{0}^{\frac{\pi}{2}} \log (\cos x \cos 2 n x) d x \) then 1
is same as
\( \int_{0}^{\frac{\pi}{2}} \cot x \cos (2 n x) d x \)
B. \( \int_{0}^{\frac{\pi}{2}} \cot x \sin (2 n x) d x \)
c. \( \int_{0}^{\frac{\pi}{2}} \tan x \cos (2 n x) d x \)
D \( \frac{1}{2 n} \int_{0}^{\frac{\pi}{2}} \tan x \sin (2 n x) d x \)
Subject: Maths
Construct a \( \triangle A B C \) in which \( A B= \) \( 4 \mathrm{cm}, B C=5 \mathrm{cm} \) and \( A C=6 \mathrm{cm} \)
Now, construct a triangle similar to
\( \triangle A B C \) such that each of its sides is
two-third of the corresponding sides of \( \triangle A B C . \) Also, prove your assertion.
Subject: Maths
Let \( z_{1} \) and \( z_{2} \) are two complex numbers
such that \( (1-i) z_{1}=2 z_{2} \) and \( \arg \left(z_{1} z_{2}\right)=\frac{\pi}{2} \) then \( \arg \left(z_{2}\right) \) is equals
to:
A \( \cdot \frac{3 \pi}{8} \)
B. \( \frac{\pi}{8} \)
c. \( \frac{5 \pi}{8} \)
D. \( \frac{-7 \pi}{8} \)
Subject: Maths
The circle drawn on the minor axis as
diameter passes through the foci of the ellipse \( \mathbf{S}=\mathbf{0}, \) then its eccentricity \( \mathbf{e}= \)
\( \mathbf{A} \cdot \sin 18^{0} \)
B. \( \sin 30^{\circ} \)
c. \( \cos 45^{\circ} \)
D. \( \cos 30^{\circ} \)
Subject: Physics
The acceleration due to gravity \( g \) and mean density of earth \( \rho \) are related by
which of the following relations? \( [G= \) gravitational constant and \( \mathrm{R}= \) radius of earth].
A \( \cdot \rho=\frac{4 \pi g R^{2}}{3 G} \)
В \( \cdot \rho=\frac{4 \pi g R^{3}}{3 G} \)
\( \mathbf{c} \cdot \rho=\frac{3 G}{4 \pi g R} \)
D. \( \rho=\frac{3 G}{4 \pi g R^{3}} \)
Subject: Chemistry
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{N}+\boldsymbol{Z} \boldsymbol{n} \longrightarrow \boldsymbol{A} \boldsymbol{g} \)
This method of extraction of Ag by
complex formation and then its displacement is called
A. Parke's method
B. Mac Arthur- Forrest method
c. Serpeck method
D. Hall's method
Subject: Maths
\( \lim _{x \rightarrow 0^{-}}\left\{\sin ^{-1}[\tan x]\right\}=l \) then \( l \) is equal
to
where \( [\text { and }\{\} \) denotes greatest the integer and fraction part function
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( -\sin ^{-1}(1) \)
\( c \cdot \sin 1 \)
D. \( 2-\frac{\pi}{2} \)
Subject: Chemistry
Select the correct statement.
A. If the critical micelle concentration (CMC) of a soap is \( 10^{-3} \mathrm{mol} / \mathrm{L} \) the \( 10^{-4} \mathrm{M} \) solution of soap is a colloidal
solution.
B. Charge of dispersed phase and dispersion medium in a colloidal solution can be identified by electrodialysis process.
C. Peptization is defined as the process of converting colloidal sol into precipitate by shaking it with dispersion medium in the small amount of electrolyte
D. The emulsion is water in oil (W/O) when some oil soluble dye is added to it and background becomes coloured.
Subject: Chemistry
Select correct statement(s):
This question has multiple correct options
A. \( C e, P r \) and \( N d \) are \( f \) -block elements
B. \( C u, P d \) and \( N i \) are d-block elements
\( \mathbf{c} \cdot C u\left([A r] 3 d^{10} 4 s^{1}\right) \) and \( K\left([A r] 4 s^{1}\right) \) have been placed in sblock.
D. \( S i, G e \) and \( A s \) are metalloids
Subject: Physics
In a hydraulic lift, the small piston has
an area of \( 2 \mathrm{cm}^{2} \) and the large piston
has an area of \( 80 \mathrm{cm}^{2} \). What is the
mechanical advantage of the hydraulic
lift?
A . 40
B. 42
c. 10
\( D .4 \)
Subject: Maths
Find the mean wage of the following distributions
\( \begin{array}{llllll}\text { Category } & \text { A } & \text { B } & \text { c } & \text { D } & \text { E } \\ \begin{array}{l}\text { Wages } \\ \text { per day }\end{array} & \text { 50 } & \text { 60 } & \text { 70 } & \text { 80 } & \text { 90 } \\ \begin{array}{l}\text { No. of } \\ \text { Workers }\end{array} & 2 & 4 & 8 & 12 & 10\end{array} \)
Subject: Physics
A spherical surface of radius of curvature \( R \) separates air (refractive
index 1.0 from glass (refractive index
1.5). The center of curvature is in the
glass.A point object \( \boldsymbol{P} \) placed in air is found to have a real image \( Q \) in the
glass. The line \( P Q \) cuts the surface at a point \( O, \) and \( P O=O Q . \) The distance
\( P Q \) is equal to
A . \( 5 R \)
в. \( 3 R \)
\( c .2 R \)
D. \( 1.5 R \)
Subject: Chemistry
Formation of a solution from two
components can be considered as
(i) Pure solvent \( \rightarrow \) separated solute
molecules, \( \triangle \boldsymbol{H}_{1} \)
(ii) Pure solute \( \rightarrow \) separated solute
molecules, \( \triangle \boldsymbol{H}_{2} \)
solution so formed will be ideal if
(iii) Separated solvent and solute
molecules \( \rightarrow \) solution, \( \triangle \boldsymbol{H}_{3} \)
Then:
\( \mathbf{A} \cdot \Delta H_{s o l n}=\Delta H_{1}+\Delta H_{2}+\Delta H_{3} \)
B. \( \triangle H_{\text {soln}}=\Delta H_{1}+\triangle H_{2}-\triangle H_{3} \)
C . \( \triangle H_{\text {soln}}=\Delta H_{1}-\triangle H_{2}-\triangle H_{3} \)
D. \( \triangle H_{\text {soln}}=\Delta H_{3}-\triangle H_{1}-\triangle H_{2} \)
Subject: Chemistry
Assertion
The solubility of ammonium chloride increases with increase in temperature
Reason In case of substances whose solubility increases with increase in temperature is due to the dissolution process being endothermic.
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
Products formed are:
\( \mathbf{2} N \boldsymbol{a} \boldsymbol{B} \boldsymbol{H}_{4}+\boldsymbol{I}_{2} \stackrel{\text {Polyether}}{\longrightarrow} \)
A. \( H I, N a l \) and \( H_{2} \)
в. \( B_{2} H_{6}, \) Nal and \( H I \)
c. \( B_{2} H_{6}, \) Nal and \( H_{2} \)
D. \( H_{3} B O_{3}+H_{2} \)