AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
toppr
Q Type your question
\( A \)
\( \mathrm{OH} \quad \mathrm{OCH}_{3} \)
\( X=Y=C H_{3}-C H-C\left(C H_{3}\right)_{2} \)
B.
\( \mathrm{OCH}_{3} \mathrm{OH} \)
\( X=Y=C H_{3}-C H-C\left(C H_{3}\right)_{2} \)
\( c \)
\( \mathrm{OH} \quad \mathrm{OCH}_{3} \)
\( \mathrm{I} \)
\( \mathrm{X}=\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2} \)
\( \mathrm{OCH}_{3} \mathrm{OH} \)
\( Y=C H_{3}-C H-C\left(C H_{3}\right)_{2} \)
\( D \)
\( \mathrm{OCH}_{3} \)
\( \mathrm{X}=\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2} \)
\( \mid \)
\( \mathrm{OH} \)
\( \mathrm{OH} \)
\( \mathrm{Y}=\mathrm{CH}_{3}-\mathrm{CH}-\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2} \)

\( \mathrm{OCH}_{3} \)
Subject: Chemistry
The \( p H \) of \( 0.1 \mathrm{M} \) acetic acid is \( 3, \) the
dissociation constant of acid will be:
A \( \cdot 1.0 \times 10^{-4} \)
В. \( 1.0 \times 10^{-5} \)
c. \( 1.0 \times 10^{-3} \)
D. \( 1.0 \times 10^{-8} \)
Subject: Chemistry
The reaction of \( \boldsymbol{C H}_{3} \boldsymbol{O C}_{2} \boldsymbol{H}_{5} \) with \( \boldsymbol{H} \boldsymbol{I} \)
gives:
\( \mathbf{A} \cdot C H_{3} I \)
в. \( C_{2} H_{5} O H \)
c. \( C H_{3} I+C_{2} H_{5} O H \)
D. \( C_{2} H_{5} I+C H_{3} O H \)
Subject: Maths
If \( a, b, c \) are positive and are the \( p \) th \( , q t h \)
and \( r t h \) terms, respectively, of a G.P. \( \operatorname{then} \Delta=\left|\begin{array}{lll}\log a & p & 1 \\ \log b & q & 1 \\ \log c & r & 1\end{array}\right| \) is
\( A \)
B. \( \log (a b c) \)
c. \( -(p+q+r) \)
D. none of these
Subject: Physics
\( 92 U^{238} \) absorbs a neutron. The product emits an electron. This product further emits an electron. The result is
\( A \cdot_{94} P u^{239} \)
В \( \cdot_{90} P u^{23} \)
\( \mathrm{c} \cdot_{93} \mathrm{Pu}^{237} \)
D \( \cdot \) \( _{94} P u^{23} \)
Subject: Chemistry
Which of the following resonating structures of 1 -methoxy-1, 3-butadiene
is least stable?
A \( \cdot \bar{C} H_{2}-C H=C H-C H=\dot{O}-C H_{3} \)
B. \( C H_{2}=C H_{2}-\bar{C} H_{2}-C H=\dot{O}-C H_{3} \)
\( \mathbf{c} \cdot \bar{C} H_{2}-C \dot{H}-C H=C H-O-C H_{3} \)
D. \( C H_{2}=C H-\stackrel{+}{C H}-\bar{C} H-O-C H_{3} \)
Subject: Maths
The coefficients of variation of two
series are \( 58 \% \) and \( 69 \% \). If their
standard deviations are 21.2 and 15.6
then their A.M's are
A \( .36 .6,22.6 \)
в. 34.8,22.6
c. 36.6,24.4
D. None of these
Subject: Maths
The solution of the differential equation,
\( \boldsymbol{e}^{\boldsymbol{x}}(\boldsymbol{x}+\mathbf{1}) \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{y} \boldsymbol{e}^{\boldsymbol{y}}+\boldsymbol{x} \boldsymbol{e}^{\boldsymbol{x}}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
with initial condition \( f(0)=0, \) is-
A \( \cdot x e^{x}+2 y^{2} e^{y}=0 \)
В \( \cdot 2 x e^{x}+y^{2} e^{y}=0 \)
C. \( x e^{x}-2 y^{2} e^{y}=0 \)
D. \( 2 x e^{x}-y^{2} e^{y}=0 \)
Subject: Chemistry
The pH of the solution obtained on
neutralisation of \( 40 m L \) of \( 0.1 M \)
NaOH with 40 m \( L \) of \( 0.1 M \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) is:
\( A \cdot 7 \)
B. 8
\( c \cdot 4 \)
D.
Subject: Physics
A candle placed \( 25 \mathrm{cm} \) form a lens
forms an image on a screen placed \( 75 \mathrm{cm} \) on the other side of the lens. The
focal length and type of the lens should
be
A. \( +18.75 \mathrm{cm} \) and convex lens
B. \( -18.75 \mathrm{cm} \) and concave lens
c. \( +20.25 \mathrm{cm} \) and convex lens
D. \( -20.25 \mathrm{cm} \) and concave lens
Subject: Physics
In a regular polygon of \( n \) sides, each corner is at a distance \( r \) from the
centre. Identical charges are placed at \( (n-1) \) corners. At the centre, the
intensity is \( \boldsymbol{E} \) and the potential is \( \boldsymbol{V} \)
The ratio \( V / E \) has magnitude.
\( \mathbf{A} \cdot r n \)
в. \( r(n-1) \)
\( c \cdot r \)
D. \( r(-1) / n \)
Subject: Physics
When a force \( F_{1} \) acts on a particle,
frequency \( 6 \mathrm{Hz} \) and when a force \( F_{2} \) acts frequency is 8 Hz. What is the frequency when both the force act simultaneously in same direction?
A . 12 нᅩ
в. 25нд
с. 10 н
D. \( 5 \mathrm{Hz} \)
Subject: Physics
Assertion(A): If one arm of a \( U \) -tube
containing a diamagnetic solution is placed in between the poles of a strong magnet with the level in line with the
field, the level of the solution falls Reason(R): Diamagnetic substances are repelled by the magnetic field
A. both \( A, R \) are true and \( R \) is the correct explanation of
B. both A,R are true and R is not correct explanation of A
c. A is true, R is false
D. A is false R is true
Subject: Biology
In the following dark reaction of photosynthesis,
\( 6 C O_{2}+6 H_{2} O+A+12 N A D P H+H \)
A and B stand for
A . 18 ADP, 18 ATP
B. 12 ATP, 18 ATP
c. 18 ATP, 18 ADP
D. 12 АтР, 12 АDP
Subject: Physics
A block of mass 2 kg is free to move along the \( x \) -axis. It is at rest and from
\( t=0 \) onwards it is subjected to a time-
dependent force \( F(t) \) in the \( x \) direction.
The force \( F(t) \) varies with \( t \) as shown in
the figure. The kinetic energy of the block after 4.5 seconds is:
в. 7.50 J
\( c .5 .06 \)
D. \( 14.06 \mathrm{J} \)
Subject: Chemistry
Assertion
lodine shows oxidation state of +1 and
+3 in the compounds ICl and \( I C l_{3} \)
respectively.
Reason
lodine coming below the halogens \( \mathrm{F} \), \( \mathrm{Cl} \) and Br in the halogen group of elements in the periodic table shows a higher degree of electropositive nature.
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
Displacement of a particle of mass \( 2 \mathrm{kg} \) varies with time as: \( s= \)
\( \left(2 t^{2}-2 t+10\right) m . \) Find total work done
on the particle in a time interval from \( t=0 \) to \( t=2 s \)
A . 16
B. 32 J
c. 48 J
D. 96 J
Subject: Chemistry
Assertion: Pure \( C H C l_{3} \) does not
give precipitate with \( A g N O_{3} \) solution.
Reason: \( C H C l_{3} \) is covalent compound.
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
The repeated factor of the determinant \( \left|\begin{array}{lll}\boldsymbol{y}+\boldsymbol{z} & \boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{z}+\boldsymbol{x} & \boldsymbol{z} & \boldsymbol{x} \\ \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{y} & \boldsymbol{z}\end{array}\right| \)
A. \( z-x \)
в. \( x-y \)
\( \mathbf{c} \cdot y-z \)
D. none of these
Subject: Physics
The volume of a gas is reduced adiabatically to \( \frac{1}{4} \) of its volume at \( 27^{\circ} C \) If \( \gamma=1.4 \) the new temperature is :
A \( \cdot(300) 2^{0.4} K \)
В . (300) \( 2^{1.4} K \)
c. \( 300(4)^{\text {) }-4} K \)
D. \( 300(2)^{0.4} K \)
Subject: Physics
A spherical soap bubble of radius \( 1 \mathrm{cm} \)
is formed inside another soap bubble of
radius \( 3 c m . \) The radius of a single soap
bubble which maintains the same
pressure difference as inside the
smaller and outside the larger soap
bubble as
A . \( 0.75 \mathrm{cm} \)
B. \( 0.75 m \)
c. \( 7.5 \mathrm{cm} \)
D. \( 7.5 \mathrm{m} \)
Subject: Physics
A proton (mass \( m \) ) accelerated by a
potential difference \( V \) files through a
uniform transverse magnetic filed \( \boldsymbol{B} \)
The field occupies a region of space by
width ' \( d^{\prime} . \) If \( ^{\prime} \alpha^{\prime} \) be the angle of deviation
of proton from initial direction of motion
(see figure), the value of \( \sin \alpha \) will be
A \( \cdot \frac{B}{2} \sqrt{\frac{e d}{m V}} \)
B. \( e V \sqrt{\frac{B d}{2 m}} \)
\( ^{c} \cdot \frac{B}{2} \sqrt{\frac{e}{2 m V}} \)
D \( \cdot B d \sqrt{\frac{e}{2 m V}} \)
Subject: Chemistry
Clemmensen's reduction reaction is:
\( A \)
в. \( C_{6} H_{5}-C O C H_{3}+ \)
\[
N H_{2} N H_{2} C_{2} H_{5} O N a C_{6} H_{5} C H_{2} C H_{3}
\]
c. \( C H_{3} C O C H_{3}+4 H I R e d \quad P_{>} C H_{3} C H_{2} C H_{3} \)
D. All the above
Subject: Physics
The path difference between the two
waves
\( \boldsymbol{y}_{1}=\boldsymbol{a}_{1} \sin \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{2} \boldsymbol{\pi} \mathbf{x}}{\boldsymbol{\lambda}}\right) \) and
\( \boldsymbol{y}_{2}=\boldsymbol{a}_{2} \cos \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{2} \boldsymbol{\pi} \mathbf{x}}{\boldsymbol{\lambda}}+\boldsymbol{\theta}\right) \)
\( A \cdot \frac{\lambda}{2 \pi} \)
в. \( \frac{\lambda}{2 \pi}\left(\theta+\frac{\pi}{2}\right) \)
c. \( \frac{\lambda}{2 \pi}\left(\theta-\frac{\pi}{2}\right) \)
D. \( \frac{2 \pi}{\lambda} \)
Subject: Chemistry
Assertion
SnCl \( _{2} \) is a reducing agent.
Reason
SnCl \( _{2} \) reduces \( F e C l_{3} \) to \( F e C l_{2} \) and
HgCl\( _{2} \) to \( H g \)
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
A running man has half the kinetic
energy of a running boy of half his mass. The man speeds up by \( 1 m / s \) and then
has \( K . E . \) as that of the boy. What were
the original speeds of man and the boy?
A \( \cdot \sqrt{2} m / s ;(2 \sqrt{2}-1) m / s \)
B . \( (\sqrt{2}-1) m / s ; 2(\sqrt{2}-1) m / s \)
c. \( (\sqrt{2}+1) m / s ; 2(\sqrt{2}+1) m / s \)
D. \( (\sqrt{2}+1) m / s ; \sqrt{2} m / s \)
Subject: Chemistry
Which one of the following reactions
does not form gaseous product?
A. \( P b O_{2}+H_{2} O_{2} \rightarrow \)
в. \( N a_{2} C O_{3}+H_{2} O_{2} \rightarrow \)
\( \mathbf{c} \cdot P b S+H_{2} O_{2} \rightarrow \)
D. \( C l_{2}+H_{2} O_{2} \rightarrow \)
Subject: Physics
An ant moves along a circle 5 times in 1
minute with a uniform speed and a
lizard moves in a straight line to and fro
5 times in 5 minutes. Then
A. The motion of the ant is uniformly accelerated but non periodic
B. The motion of the lizard is uniformly accelerated but non periodic
C. Both ant and lizard are periodic
D. Both ant and lizard are accelerated and their direction
is along the direction of velocity
Subject: Chemistry
Indicate whether each of the following
pairs are :
A. I- enantiomers, II- diastereomers, III- enantiomers
B. I- identical, II- enantiomers, III- enantiomers
c. I- enantiomers, II- diastereomers, III- identical
D. I- enantiomers, II- identical, III- identical
Subject: Physics
A body of mass \( 2 k g \) collides with a wall
with a speed of \( 100 \mathrm{ms}^{-1} \) are rebounds
with the same speed. If the time of
contact is \( 1 / 50 s, \) the force exerted on
the wall is
\( A \cdot 8 N \)
B . \( 2 \times 10^{4} N \)
c. \( 4 N \)
D. \( 10^{4} N \)
Subject: Maths
The value of \( (a+2 i)(b-i) \) is
\( \mathbf{A} \cdot a+b-i \)
B. \( a b+2 \)
c. \( a b+(2 b-a) i+2 \)
D. \( a b-2 \)
E \( . a b+(2 b-a) i-2 \)
Subject: Maths
\( \mathbf{f}\left[\begin{array}{rr}\boldsymbol{a}+\mathbf{4} & \mathbf{3} \boldsymbol{b} \\ \mathbf{8} & -\mathbf{6}\end{array}\right]=\left[\begin{array}{cc}\mathbf{2} \boldsymbol{a}+\mathbf{2} & \boldsymbol{b}+\mathbf{2} \\ \boldsymbol{8} & \boldsymbol{a}-\mathbf{8} \boldsymbol{b}\end{array}\right] \)
then write the value of \( a-2 b \)
Subject: Chemistry
\( 40 \% \) by weight solution will contain how much mass of the solute in 1 L solution?
Density of the solution is \( 1.2 \mathrm{g} / \mathrm{mL} \)
A. \( 480 g \)
B. \( 48 g \)
\( c \cdot 38 g \)
D. \( 380 g \)
Subject: Physics
A current source sends a current \( \boldsymbol{I}- \)
\( i_{0} \cos (\omega t) . \) when connected across an
unknown load, it gives a voltage output
of \( \boldsymbol{v}=\boldsymbol{v}_{0} \sin [\boldsymbol{\omega} \boldsymbol{t}+(\boldsymbol{\pi} / \mathbf{4})] \) across that
load. then the voltage across the current source may be brought in phase with the current through it by
A. Connecting an inductor in series with the load
B. Connecting a capacitor in series with the load
c. connecting an inductor in parallel with the loadd
D. connecting a capacitor in parallel with the load
Subject: Maths
\( (x+y-z)^{2}= \)
A \( \cdot x^{2}+y^{2}-z^{2}+2 x y+2 x z-2 y z \)
B \( \cdot x^{2}+y^{2}+z^{2}+2 x y-2 x z-2 y z \)
C \( \cdot x^{2}+y^{2}-z^{2}-2 x y+2 x z+2 y z \)
D. None of the above
Subject: Physics
If the terminal speed of a sphere of gold (density \( \left.=19.5 \quad k g / m^{3}\right) \) is \( 0.2 m / s \) in
a viscous liquid (density \( =1.5 \quad k g / m^{3} \)
), find the terminal speed of a sphere of silver (density \( \left.=10.5 \quad k g / m^{3}\right) \) of the
same size in the same liquid.
A. \( 0.4 m / s \)
в. \( 0.133 \mathrm{m} / \mathrm{s} \)
c. \( 0.1 m / s \)
D. \( 0.2 m / s \)
Subject: Chemistry
In the reaction :-
\[
\begin{array}{r}
\boldsymbol{C u} \boldsymbol{S O}_{4} \cdot \boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \mathbf{2} \boldsymbol{C u} \boldsymbol{S} \boldsymbol{O}_{4} \\
\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s})+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{v})
\end{array}
\]
Dissociation pressure is \( 7 \times 10^{-3} \) atm
at 25 and \( \Delta H=2700 \) cal. If the
dissociation pressure at 127 is \( X \times \)
\[
10^{-3} \text {atm, then } 100 X
\]
is
Subject: Maths
The values of \( \alpha, \) for which the system of
equation \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{1} \)
\( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{4} \boldsymbol{z}=\boldsymbol{\alpha} \)
\( x+4 y+10 z=\alpha \) is consistent, are
\( \mathbf{A} \cdot 1,-2 \)
в. -1,2
c. 1,2
D. None of these
Subject: Maths
A person sells a table at a profit of \( 20 \% \) If he had bought it at \( 10 \% \) less cost and
sold for Rs. 105 more, he would have
gained \( 35 \% \). The cost price of the table
is
A. Rs. 7000
B. Rs. 7350
c. Rs. 9200
D. Rs. 8140
Subject: Physics
If the electron concentration is \( \left(n_{e}\right) \) and
hole concentration is \( \left(n_{h}\right) \) in a semiconductor in thermal equilibrium
then
A \( \cdot n_{e} \times n_{h}= \) constant
B . \( \frac{n_{e}=\text { constant }}{n_{h}} \) to
C \( \cdot n_{e}^{2} n_{h}= \) constant
D. \( n_{h}^{2} n_{e}= \) constant
Subject: Chemistry
In a certain reaction, \( 10 \% \) of the
reactant decomposes in one hour, \( 20 \% \) in two hours, \( 30 \% \) in three hours and so
on. Dimension of the velocity constant
are:
A . hour \( ^{-1} \)
B. mole litre \( ^{-1} \) hour \( ^{-1} \)
c. litre mol- \( ^{1} \) hour \( ^{-1} \)
D. mole sec \( ^{-1} \)
Subject: Chemistry
Which of the following is true with respect to crystal field splitting in complexes?
\( \mathbf{A} \cdot \Delta_{0}=\Delta_{t} \)
B. \( \triangle_{0}=\frac{9}{4} \Delta_{t} \)
c. \( \Delta_{t}=\frac{9}{4} \Delta_{0} \)
D. \( \triangle_{t}=\frac{2}{3} \Delta_{0} \)
Subject: Maths
If \( \sec \theta=2 x \) and \( y \tan \theta=2, \) then the
value of \( 2\left[x^{2}-\frac{1}{y^{2}}\right] \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D.
Subject: Chemistry
For a reversible reaction \( \boldsymbol{a} \boldsymbol{A}+\boldsymbol{b} \boldsymbol{B} \rightleftharpoons \)
\( c C+d D ; \) the variation of \( K \) with
temperature is given by \( \log \frac{\boldsymbol{K}_{2}}{\boldsymbol{K}_{1}}=\frac{-\boldsymbol{\Delta} \boldsymbol{H}^{o}}{\mathbf{2 . 3 0 3} \boldsymbol{R}}\left[\frac{\mathbf{1}}{\boldsymbol{T}_{2}}-\frac{\mathbf{1}}{\boldsymbol{T}_{1}}\right] \) then
This question has multiple correct options
A \( \cdot K_{2}>K_{1} \) if \( T_{2}>T_{1} \) for an endothermic change
B. \( K_{2}<K_{1} \) if \( T_{2}>T_{1} \) for an endothermic change
C . \( K_{2}>K_{1} \) if \( T_{2}>T_{1} \) for an exothermic change
D. \( K_{2}<K_{1} \) if \( T_{2}>T_{1} \) for an exothermic change
Subject: Chemistry
Phosphide and phosphate ions are:
\( \mathbf{A} \cdot P O_{4}^{3-} \) and \( P^{3-} \)
B. \( P^{3-} \) and \( P O_{4}^{3-} \)
\( \mathrm{C} \cdot P O_{3}^{4-} \) and \( P^{4-} \)
D. \( P^{4-} \) and \( P O_{3}^{4-} \)
Subject: Maths
Let \( \boldsymbol{X} \) be the set of all persons living in a city. Persons \( x, y \) in \( X \) are said to be
related as \( x<y \) if \( y \) is at least 5 years
older than \( x \). Which one of the following
is correct?
A. The relation is an equivalence relation on \( X \)
B. The relation is transitive but neither reflexive nor symmetric
c. The relation is reflexive but neither nor symmetric
D. The relation is symmetric but neither transitive nor reflexive
Subject: Chemistry
Zeisse's salt is:
\( \mathbf{A} \cdot\left[P t\left(N H_{3}\right)_{2} C_{12}\right] \)
B \( \cdot K\left[P t C l_{3}\left(C_{2} H_{4}\right)\right] \)
\( \mathbf{C} \cdot F e\left(C_{5} H_{5}\right)_{2} \)
D. None of these
Subject: Physics
A person bring a mass of \( 1 k g \) from
infinite to point \( A \). Initially the mass was at rest but is moves a speed of \( 2 m / s \) as it reaches to \( A \). The workdone
by the person on mass is \( -3 J \) the gravitational potential at \( \boldsymbol{A} \) is
A. \( -3 J / k g \)
в. \( -2 J / k g \)
\( \mathbf{c} .-5 J / k g \)
D. \( -7 J / k g \)
Subject: Chemistry
What is the order of basicity of the
following compounds?
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H},\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N} \) (in
protic solvent)
A \( \cdot\left(C H_{3}\right)_{2} N H>C H_{3} N H_{2}>\left(C H_{3}\right)_{3} N \)
B . \( \left(C H_{3}\right)_{2} N H<C H_{3} N H_{2}<\left(C H_{3}\right)_{3} N \)
C. \( \left(C H_{3}\right)_{2} N H>\left(C H_{3}\right)_{3}>C H_{3} N H_{2} N \)
D. None of these
Subject: Chemistry
The chemical formula of \( X, Y \) and \( Z \)
are:
\[
\begin{array}{l}
\mathrm{X}+\mathrm{Na}_{2} \mathrm{CO}_{3} \longrightarrow \mathrm{Y}+\mathrm{Z} \\
\mathrm{CO}_{2}
\end{array}
\]
\( Z(\text { milky cloud }) \)
\( \mathbf{A} \cdot C a O, C a(O H)_{2}, N a O H \)
B. \( N a O H, C a O, C a C O_{3} \)
\( \mathbf{c} \cdot N a O H, C a(O H)_{2}, C a C O_{3} \)
D. \( C a(O H)_{2}, N a O H, C a C O_{3} \)
Subject: Maths
I: If \( \mathrm{f}^{\prime}(\mathrm{a})<0 \) then the function \( \mathrm{f} \) is
decreasing at \( \mathbf{x}=\mathbf{a} \)
Il: If \( f \) is decreasing at \( x=a \) then
\( \mathbf{f}^{\prime}(\mathbf{a})<\mathbf{0} \)
Which of the above statements are true
\( ? \)
A. only
B. only II
c. both land II
Subject: Physics
In Thomsons method, electric field of
intensity \( \boldsymbol{E}, \) magnetic field of induction
\( B \) and velocity \( V \) of the electrons were in mutually perpendicular directions. The condition for velocity is
A. \( V=E / B \)
в. \( V=B / E \)
c. \( V=B E \)
D. \( V=\sqrt{B / E} \)
Subject: Maths
A and \( \mathrm{B} \) are two points on the circle
\( \mathbf{x}^{2}+\mathbf{y}^{2}=1 . \) If the \( \mathbf{x} \) co-ordinates of \( \mathbf{A} \)
and \( \mathrm{B} \) are the roots of the equation
\( x^{2}+a x+b=0 \) and the \( y \)
coordinates of \( \mathbf{A} \) and \( \mathbf{B} \) are the roots of
the equation \( \mathbf{y}^{2}+\mathbf{b y}+\mathbf{a}=\mathbf{0} \) then the
equation of the line \( A B \) is
A \( \cdot a x+b y=0 \)
B. \( a x+b y+1=0 \)
c. \( b x+a y+a+b=0 \)
D. \( a x+b y+a+b+1=0 \)
Subject: Physics
An air bubble of radius \( 5 \times 10^{-4} \mathrm{m} \) rises
in a liquid of viscosity 0.1 Pas \( (g= \)
\( 10 m s^{-2} \) ) and density \( 900 \mathrm{kgm}^{-3} \). The
terminal velocity of the bubble is:
A \( \cdot 0.005 \mathrm{ms}^{-1} \)
B. \( 0.01 \mathrm{ms}^{-1} \)
c. \( 0.5 \mathrm{ms}^{-1} \)
D. \( 0.4 \mathrm{ms}^{-1} \)
Subject: Physics
A body of mass \( 6 k g \) is under a force of
\( 6 N \) which causes displacement in it given by \( S=\frac{t^{2}}{4} m \) where 't' is time. The
work done by the force in \( 2 s \) is :
A . \( 12 . J \)
в. \( 9 J \)
\( c .6 J \)
D. \( 3 J \)
Subject: Chemistry
The molar heat capacity of water at
constant pressure \( P, \) is \( 75 \mathrm{JK}^{-1} \mathrm{mol}^{-1} \) When \( 1.0 \mathrm{kJ} \) of heat is supplied to \( 100 \mathrm{g} \) of water which is free to expand, the increase in temperature of water is:
A . \( 1.2 k \)
B. 2.4 K
c. \( 4.8 \mathrm{k} \)
D. 6.6 K
Subject: Physics
An aeroplane is moving with horizontal velocity u at height h. The velocity of a packet dropped from it on the earth's surface will be (g is acceleration due to gravity
A \( \cdot \sqrt{u^{2}+h^{2}} \)
B . \( \sqrt{u^{2}+2 g h} \)
c. \( \sqrt{u^{2}-h^{2}} \)
D. Data Insufficient
Subject: Chemistry
The IUPAC name of \( \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is:
A. potassium ferricyanide
B. potassium ferrocyanide
c. potassium hexacyanoferrate (II)
D. potassium hexacyanoferrate (III)
Subject: Physics
If we place a solid hot metal in a cool liquid the metal and the liquid come to
some final temperature together. The specific heat of the liquid is five times as great as the specific heat of the
metal. The temperature change for the metal is twenty times as much as that for the liquid.
How does the mass of the liquid
compare to the mass of the solid metal?
Assume no heat is lost from the system.
A. The mass of the liquid is 100 times as much as the mass of the metal.
B. The mass of the liquid is 5 times as much as the mass of the metal.
c. The mass of the liquid is 20 times as much as the mass of the metal.
D. The mass of the liquid is \( 1 / 4 \) times as much as the mass of the metal.
E. The mass of the liquid is 4 times as much as the mass of the metal.
Subject: Physics
The frequency of a particle performing SHM is 12 Hz. Its amplitude is \( 4 \mathrm{cm} \). Its initial displacement is \( 2 \mathrm{cm} \) towards positive extreme position. Its equation for displacement is
A. \( x=0.04 \cos (24 \pi t+\pi / 6) \)
В. \( x=0.04 \sin (24 \pi t) \)
c. \( x=0.04 \sin (24 \pi t+\pi / 6) \)
D. \( x=0.04 \cos (24 \pi t) \)
Subject: Maths
Simplify : \( \left(\frac{3}{2} x-0.45 y\right)^{2} \)
A. \( 2.25 x^{2}-1.35 x y+0.2015 y^{2} \)
B. \( 2.15 x^{2}-1.35 x y+0.2025 y^{2} \)
c. \( 2.25 x^{2}-1.35 x y+0.2025 y^{2} \)
D. \( 2.25 x^{2}-1.25 x y+0.2025 y^{2} \)
Subject: Physics
In a potentiometer experiment, the
balancing length with a cell in the
secondary circuit is found to be \( 480 \mathrm{cm} \)
When a resistor of 8 ohm is connected
in parallel to the cell, the balancing length is found to be \( 420 \mathrm{cm} . \) The internal resistance of the cell is :
A . \( 1.14 \Omega \)
B. 2\Omega
c. \( 4.12 \Omega \)
D. \( 56 \Omega \)
Subject: Physics
The equation of a transverse wave
travelling on a rope is given by \( \boldsymbol{y}= \)
\( 10 \sin \pi(0.01 x-2 \pi t) \) where \( y \) and \( x \) are
in \( c m \) and \( t \) in seconds. The maximum
transverse speed of a particle in the rope is about.
A. \( 63 \mathrm{cm} / \mathrm{s} \)
B. \( 75 \mathrm{cm} / \mathrm{s} \)
c. \( 100 \mathrm{cm} / \mathrm{s} \)
D. \( 121 \mathrm{cm} / \mathrm{s} \)
Subject: Maths
If two parallel chords of length \( 8 \mathrm{cm} \) and
\( 6 \mathrm{cm} \) in a circle of radius \( 5 \mathrm{cm} \) are on
the opposite sides of the center then the
distance between the parallel chords is
A . \( 5 \mathrm{cm} \)
в. 6 ст
\( c .7 \mathrm{cm} \)
D. None of these
Subject: Physics
In figure the cylinder of mass \( 10 k g \) and
radius \( 10 \mathrm{cm} \) has a tape wrapped round
¡t. The pulley weighs \( 100 N \) and has a
radius \( 5 c m . \) When the system is
released, the \( 5 k g \) mass comes down
and the cylinder rolls without slipping.
Calculate the acceleration and velocity of the mass as a function of time.
Subject: Physics
A gardener waters a lawn with a hose ejecting \( 250 \mathrm{cc} \) of water per second through an orifice of area \( 2.5 \mathrm{sqcm} \)
Find the backward force on the
gardener.
A . \( 0.15 N \)
B. \( 1.25 N \)
c. \( 0.20 N \)
D. \( 0.25 N \)