AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
In acidic medium the rate of reaction
between \( \left(B r O_{3}\right)^{-} \) and \( B r^{-} \) ion is given by the expression \( \frac{\boldsymbol{d}\left[\boldsymbol{B r} \boldsymbol{O}_{3}^{-}\right]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}\left[\boldsymbol{B r O}_{3}^{-}\right]\left[\boldsymbol{B r}^{-}\right]\left[\boldsymbol{H}^{+}\right]^{2} \)
it means:
A. rate constant of overall reaction is 4 sec"
B. rate of reaction is independent of the conc. of acid
c. the change in pH of the solution will not attect the rate
D. doubling the conc. of \( H^{+} \) ions will increase the reaction rate by 4 times
Subject: Physics
(a) A conductor \( A \) with a cavity as
shown in Fig. \( (a) \) is given a charge \( Q \) Show that the entire charge must
appear on the outer surface of the
conductor.
(b) Another conductor \( B \) with charge \( q \)
is inserted into the cavity keeping \( \boldsymbol{B} \)
insulated from \( A . \) Show that the total
charge on the outside surface of \( \boldsymbol{A} \) is
\( \boldsymbol{Q}+\boldsymbol{q} \)
(c) A sensitive instrument is to be
shielded from the strong electrostatic fields in its environment.
Suggest a possible way.
\( (\mathbf{a}) \)
\( \mathbf{b} \)
Subject: Chemistry
The electronic configuration of the element with maximum electron
affinity is :
A \( \cdot 1 s^{2}, 2 s^{2} 2 p^{3} \)
B . \( 1 s^{2}, 2 s^{2} 2 p^{5} \)
C. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{5} \)
D. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{3} \)
Subject: Chemistry
Which facts are true when we use van't
Hoff equation \( P V=C S T \) for osmotic
pressure \( \mathrm{P} \) of dilute solutions?
This question has multiple correct options
A. The equation is identical to that of ideal gas equation
B. The solute particles in solution are analogous to the gas molecules and the solvent is analogous to the empty space between the gas molecules
C. Solute molecules are dispersed in the solvent, the way the gas molecules are dispersed in empty space
D. The equation is not identical to that of ideal gas equation
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{a} \boldsymbol{b}^{2} & \boldsymbol{a} \boldsymbol{c}^{2} \\ \boldsymbol{a}^{2} \boldsymbol{b} & \boldsymbol{0} & \boldsymbol{b} \boldsymbol{c}^{2} \\ \boldsymbol{a} \boldsymbol{c}^{2} & \boldsymbol{b}^{2} \boldsymbol{c} & \boldsymbol{0}\end{array}\right|= \)
\( \mathbf{A} \cdot a^{3} b^{3} c^{3}+a^{2} b^{3} c^{4} \)
B \( \cdot a^{3} b^{3} c^{3} \)
\( \mathbf{c} \cdot 2 a^{3} b^{3} c^{3} \)
D・ \( (2 a b c)^{3} \)
Subject: Chemistry
If average molecular wt. of air is 29
then assuming \( N_{2} \) and \( O_{2} \) gases are
there which options are correct regarding composition of air:
i) \( 75 \% \) by mass of \( N_{2} \)
ii) \( 75 \% \) by moles \( N_{2} \)
iii) \( 72.41 \% \) by mass of \( N_{2} \)
A. only (i) is correct
B. only (ii) is correct
c. both (ii) and (iii) are correct
D. both (i) and (ii) are correct
Subject: Maths
Edge of a cube whose volume is \( \frac{1}{125} \) cu \( \mathrm{m} \) is
A \( \cdot \frac{1}{15} \mathrm{m} \)
в. \( \frac{1}{5} \mathrm{m} \)
c. \( \frac{1}{25} \mathrm{m} \)
D. 125 \( \mathrm{m} \)
Subject: Chemistry
Each of the two platinum electrodes having area 64 mm of a conductivity
cell are separated by 8 mm. The resistance of the cell containing \( 7.5 \times \) \( \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \boldsymbol{K} \boldsymbol{C l} \) solution at \( \mathbf{2 9 8} \boldsymbol{K} \) is
1250 ohm. Calculate :
(i) Cell constant
(ii) Conductivity and
(iii) Molar conductivity
Subject: Physics
The equation \( \boldsymbol{y}=\mathbf{4}+\mathbf{2} \sin (\mathbf{6} \boldsymbol{t}-\mathbf{3} \boldsymbol{x}) \)
represents a wave motion with amplitude of
A. 6 units
B. 2units
c. 20 units
D. 8 units
Subject: Physics
Which of the following functions represent a travelling wave?
A \( \cdot(x-v t)^{2} \)
B \cdot \( \operatorname{Ln}(x+v t) \)
\( \mathbf{C} \cdot e^{-(x-\pi)^{2}} \)
D. \( \frac{1}{x+v t} \)
Subject: Physics
A long string under tension of \( 100 N \)
has one end at \( x=0 . \) A sinusoidal
wave is generated at \( x=0 \) whose
equation is given by
\( \boldsymbol{y}= \)
\( (0.01 c m) \sin \left[\left(\frac{\pi x}{10} m\right)-50 \pi t(s e c)\right] \)
Find the average power transmitted by
the wave.
Subject: Maths
A card is drawn from a well shuffled
pack of 52 cards. Events A and B are defined as follows:
\( A: \) Getting a card of spade
B : Getting an ace, then \( A \) and \( B \) are
A. mutually exclusive and independent events
B. not mutually exclusive but independent events
c. mutually exclusive and not independent events
D. neither mutually exclusive nor independent events
Subject: Chemistry
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{B r}_{2} \rightarrow \boldsymbol{C H}_{2} \boldsymbol{B r}- \)
\( C H_{2} B r, \) is an example of
A. addition reaction
B. substitution reaction
c. elimination reaction
D. molecular rearrangement
Subject: Physics
For the arrangement shown in figure,
pulleys and strings are ideal. Find out
the acceleration of \( 2 \mathrm{kg} \) block
A \( \cdot \frac{g}{3} \)
B. \( \frac{g \sqrt{2}}{3} \)
c. \( \frac{2 g}{3} \)
D. \( \frac{2 g}{\sqrt{2} g} \)
Subject: Chemistry
Match the Column I and Column II and
choose the correct code given below.
Column I
(A) Peroxyacetyl nitrile
(i) Waste incineration
(B) Indigo
(ii) Vat dye
(C) IR active
(iii) Global warming molecules
(D) Dioxins
(iv) Photochemical
\( \operatorname{smog} \)
\( A \cdot A-(i v) ; B-(i i) ; C-(i i i) ; D-(i) \)
B. A-(i); B-(ii); C-(iv); D-(iii)
C. \( A-(i i) ; B-(i) ; C-(i v) ; D-(i i i) \)
D. A-(iv); B-(i); C-(iii); D-(ii)
Subject: Maths
If the vectors \( \vec{A}=2 \hat{i}+4 \hat{j} \) and \( \vec{B}= \) \( \mathbf{5} \hat{\mathbf{i}}-\boldsymbol{P} \hat{\boldsymbol{j}} \) are parallel to each other, the
magnitude of \( \vec{B} \) is:
A \( 5 \sqrt{5} \)
5
B. 10
c. 15
D. \( 2 \sqrt{5} \)
Subject: Chemistry
Assertion: It is safe to stir \( 1 \mathrm{M} A g N O_{3} \)
solution with a copper spoon.
\[
\begin{aligned}
\text { Reason: } \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g} \oplus \mid \boldsymbol{A} \boldsymbol{g}}^{\ominus} &=\mathbf{0 . 8 0} \boldsymbol{V} \\
\boldsymbol{E}_{\boldsymbol{C u}^{2+} \mid \boldsymbol{C u}}^{\ominus} &=\mathbf{0 . 3 4} \boldsymbol{V}
\end{aligned}
\]
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Maths
What is \( \tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}\left(\frac{3}{5}\right) \) equal
to?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
D. \( \frac{\pi}{2} \)
Subject: Maths
If in two triangles \( P Q R \) and \( D E F \)
\( \boldsymbol{P R}=\boldsymbol{E F}, \boldsymbol{Q} \boldsymbol{R}=\boldsymbol{D} \boldsymbol{E} \) and \( \boldsymbol{P Q}=\boldsymbol{F D} \)
then \( \triangle \boldsymbol{P Q R} \cong \triangle_{---} \)
\( \mathbf{A} \cdot F D E \)
в. \( D E F \)
c. \( F E D \)
D. \( D F E \)
Subject: Maths
Identify a local maxima for:
\( \boldsymbol{y}=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2} \)
\( \mathbf{A} \cdot x=2 \)
B. \( x=1 \)
c. \( x=-2 \)
D. \( x=-1 \)
Subject: Physics
Two coherent waves are represented by
\( \boldsymbol{y}_{1}=\boldsymbol{a}_{1} \cos \omega t \) and \( \boldsymbol{y}_{2}=\boldsymbol{a}_{2} \sin \omega t . \) The
resultant intensity due to interference will be
B. \( \left(a_{1}^{2}+a_{2}^{2}\right) \)
c. \( \left(a_{1}-a_{2}\right) \)
and
D \( \cdot\left(a_{1}+a_{2}\right) \)
Subject: Maths
Assertion
The value of the determinant
\( \begin{array}{|ccc|}\tan ^{-1} x & \cot ^{-1} x & \pi / 2 \\ \sin ^{-1}(4 / 5) & \sin ^{-1}(3 / 5) & \sin ^{-1} 1 \\ \cos ^{-1}(3 / 5) & \cos ^{-1}(4 / 5) & 1\end{array} \)
equal to zero for all values of \( x \)
Reason
\( 2 \cos ^{-1} x=\cos ^{-1}\left(2 x^{2}-1\right) \) if \( -1 \leq \)
\( x \leq 1 \)
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: Chemistry
The potential of the cell at \( 25^{\circ} \mathrm{C} \) is Given
\( p K_{a} \) of \( C H_{3} C O O H \) and \( p K_{b} \) of
\( N H_{4} O H=4.74 \)
A . \( -0.04 V \)
В. \( 0.04 V \)
\( c .-0.189 V \)
\( V \)
D. \( 0.189 V \)
Subject: Chemistry
Let, paramagnetism is given by the relation \( \mu=2 \sqrt{s(s+1)} \) magnetons
where 's' is the total spin. On this basis,
the pramagnetism of \( C u^{+} \) ion is:
A . 3.88 magnetons
B. 2.83 magnetons
c. 1.41 magnetons
D. zero
Subject: Physics
A concave mirror forms the real image of an object which is magnified 4 times. The objects is moved 3 cm away, the magnification of the image is 3 times. What is the focal length of the mirror?
\( A \cdot 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. 36 cm
Subject: Chemistry
What sorts of informations can you
draw from the following reaction?
\( (\boldsymbol{C N})_{2}(\boldsymbol{g})+\mathbf{2 O H}^{-}(\boldsymbol{a q}) \rightarrow \)
\( \boldsymbol{C N}^{-}(\boldsymbol{a q})+\boldsymbol{C N O ^ { - }}(\boldsymbol{a q})+\boldsymbol{H}_{2} \boldsymbol{O}(l) \)
Subject: Chemistry
1 \( m L \) of methyl acetate was added to a
flask containing \( 20 m L \) of \( N / 20 H C l \)
maintained at \( 25^{\circ} \mathrm{C} .2 \mathrm{m} L \) of the
reaction mixture were withdrawn at
different intervals and titrated with a
standard alkali solution. The following
results were obtained:
Time
\( \mathbf{7 5} \)
\( \mathbf{1 1 9} \)
\[
(\min )
\]
\( \mathbf{0} \)
Alkali
\[
\begin{array}{l}
\text { used }( \\
m L)
\end{array} \quad \begin{array}{l}
19.24 \\
\qquad 24.20
\end{array} \quad 26.60
\]
Show that the reaction follows first
order kinetics.
Subject: Chemistry
Structure of ethanoic acid is:
A \( \cdot C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{3}-C-O H \)
॥
О
c. \( C H_{3}-O-C_{3} H_{7} \)
D. \( C H_{3}-C-C H_{3} \)
I
O
E \( \cdot C H_{3}-C H_{2}-N H_{2} \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\}, \boldsymbol{B}=\{\mathbf{2}, \mathbf{3}, \mathbf{6}, \mathbf{7}\} \)
Then the number of elements in
\( (\boldsymbol{A} \times \boldsymbol{B}) \cap(\boldsymbol{B} \times \boldsymbol{A}) \) is
A . 18
B. 6
\( c \cdot 4 \)
\( D \)
Subject: Maths
Consider the following groups \( A \) and \( B \) \( A: 3,4,5, \ldots . . \) upto n terms \( \mathrm{B}: 15,19,23, \ldots \ldots \) upto n terms
If the mean deviations of groups \( A \) and \( B \) about their means are \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \)
respectively then
A \( . \beta=5 \alpha \)
в. \( \beta=4 \alpha+3 \)
c. \( \beta=4 \alpha \)
D. None
Subject: Physics
In Fresnel's biprism expt., a mica sheet of refractive index 1.5 and thickness \( 6 x \)
\( 10^{-6} \mathrm{m} \) is placed in the path of one of interfering beams as a result of which the central fringe gets shifted through 5 fringe widths. The wavelength of light used is
A \( \cdot 6000 \stackrel{\circ}{A} \)
в. \( 8000 \stackrel{\circ}{A} \)
c. 4000 ,
D. \( 2000 \stackrel{\circ}{A} \)
Subject: Physics
Orbital acceleration of an electron is:
A \( \cdot \frac{n^{2} h^{2}}{4 \pi^{2} m^{2} r^{3}} \)
B. \( \frac{n^{2} h^{2}}{2 n^{2} r^{3}} \)
c. \( \frac{4 n^{2} h^{2}}{\pi^{2} m^{2} r^{3}} \)
D. \( \frac{4 n^{2} h^{2}}{4 \pi^{2} m^{2} r^{3}} \)
Subject: Chemistry
which has the maximum conductivity
in thier \( 0.1 \mathrm{M} \) solution?
\( A \)
A) \( \left[\operatorname{Co}\left(N H_{3}\right)_{3} C l_{3}\right]_{3} \)
B.
B) \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l\right] C l_{2} \)
c. \( \mathrm{c} \) ) \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} \)
\( D \)
D) \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
Subject: Maths
If \( g(x) \) is defined on [-1,1] and the area
of the equilateral triangle with two of its vertices (0,0) and \( (x, g(x)) \) is \( \frac{\sqrt{3}}{4}, \) then
A \( . g(x)=\pm \sqrt{\left(1-x^{2}\right)} \)
в. \( g(x)=-\sqrt{\left(1-x^{2}\right)} \)
c. \( g(x)=\sqrt{\left(1-x^{2}\right)} \)
D. \( g(x)=\sqrt{\left(1+x^{2}\right)} \)
Subject: Physics
Two small, identical spheres having \( +\boldsymbol{Q} \)
and \( -Q \) charge are kept at a certain
distance \( F \) force acts between the two
If in the middle of two spheres, another similar sphere having \( +Q \) charge is kept, then it experiences a force in magnitude and direction as
A. Zero having no direction
B. \( 8 F \) towards \( +Q \) charge
c. \( 8 F \) towards \( -Q \) charge
D. \( 4 F \) towards \( +Q \) charge
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}^{2}}, \) then what is \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}=\boldsymbol{\pi} \)
equal to?
\( \mathbf{A} \cdot(1+\pi) e^{\pi^{2}} \)
В . \( 2 \pi e^{\pi^{2}} \)
\( \mathbf{c} \cdot 2 e^{\pi^{2}}^{2} \)
D \cdot \( e^{\pi^{2}} \)
Subject: Physics
A square wire of side \( 3.0 \mathrm{cm} \) is placed \( 25 c m \) in front of a concave mirror of
focal length \( 10 c m, \) with its centre on the axis of the mirror and its plane normal to the axis. The area enclosed by the
image of the wire is :
A \( .7 .5 \mathrm{cm}^{2} \)
в. \( 6.0 \mathrm{cm}^{2} \)
\( c \cdot 4.0 \mathrm{cm}^{2} \)
D. 3.0 \( \mathrm{cm}^{2} \)
Subject: Physics
A metal sphere of \( 4 \mathrm{cm} \) radius is suspended within a hollow sphere of 6 cm radius. The inner sphere is charged
to potential 3 esu and the outer sphere is earthed. The charge on the inner sphere is
A . 54 esu
B. 1/4 esu
\( c . \) 30 esu
D. 36 esu
Subject: Chemistry
Assertion
Only one in 20000 of alpha particles deflected in Rutherford's experiment.
Reason

Most of the space in the atom is empty.
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
Arrange the following in order of decreasing \( N-O \) bond length :
\( N O_{2}^{+}, N O_{2}^{-}, N O_{3}^{-} \)
A \( \cdot N O_{3}^{-}>N O_{2}^{+}>N O_{2} \)
в. \( N O_{3}^{-}>N O_{2}^{-}>N O_{2}^{+} \)
c. \( N O_{2}^{+}>N O_{3}^{-}>N O_{2} \)
D. \( N O_{2}^{-}>N O_{3}^{-}>N O_{2} \)
Subject: Chemistry
If \( 684 g \) of sucrose \( (M M=342 g) \) is
dissolved in \( 2000 g \) of \( H_{2} O \) (essentially
\( 2 L), \) what will be the freezing point of this solution?
A . -0.51
B . -1.86
c. -3.72
D. - 6.58
Subject: Physics
Value of \( g \) on the surface of earth is
\( 9.8 m / s^{2} . \) Value of \( g \) on the surface of earth is \( 9.8 m / s^{2} . \) At height \( h=R \) from the surface the value of \( g \) is \( \frac{g}{x} . \) Find \( x \)
Subject: Physics
A current of \( 16 A \) is made to pass
through a conductor in which the
number density of free electrons is \( 4 x \) \( 10^{28} m^{-3} \) and its area of cross section
is \( 10^{-5} m^{2} . \) The average drift velocity of free electrons in the conductor is:
A \( .2 .5 \times 10^{-4} \mathrm{ms}^{-1} \)
B . \( 3.2 \times 10^{-4} \mathrm{ms}^{-1} \)
c. \( 6.4 \times 10^{-4} \mathrm{ms}^{-1} \)
D. \( 1.6 \times 10^{-4} \mathrm{ms}^{-1} \)
Subject: Physics
A wire of cross-sectional area \( 4 \times 10^{-4} m^{2} \)
modulus of elasticity \( 2 \times 10^{11} N / m^{2} \)
and length \( 1 m \), is stretched between two
vertical rigid poles. A mass of \( 1 \mathrm{kg} \) is suspended at its center. If the angle it makes with the horizontal is \( \frac{1}{2} \times 10^{-x} \) rad. Find \( x \)
Subject: Biology
Describe the structure of actin and
myosin filaments.
(The Length Sarcomere is 2.5 \( \mu \) m (.Actin \( \operatorname{rod}=1 \mu m,) \) myosin \( =1.5 \mu m \) 1Myosin
filament \& 1 Actin filament is
surrounded by 3 Myosin filament.)
Subject: Maths
As observed from the top of a \( 60 \mathrm{m} \) high lighthouse from the sea-level, the angles of depression of two ships are
\( 30^{\circ} \) and \( 45^{\circ} . \) If one ship is exactly behind the other on the same side of the
lighthouse. Find the distance between
the two ships.
A. \( 20 m \)
в. \( 46.5 \mathrm{m} \)
c. \( 54.9 m \)
D. \( 60.1 \mathrm{m} \)
Subject: Chemistry
Which of the following complex has five unpaired electrons?
\( \mathbf{A} \cdot\left[M n\left(H_{2} O\right)_{6}\right]^{2+} \)
B . \( \left[M n(C N)_{6}\right]^{3} \)
\( \mathbf{c} \cdot\left[C r C l_{3}\left(H_{2} O_{3}\right]\right. \)
D. \( \left[A g\left(N H_{3}\right)_{2}\right] \)
Subject: Physics
One mole of gas of specific heat ratio 1.5 being initially at temperature \( 290 K \) is adiabatically compressed to increase
its pressure 8 times. The temperature of the gas after compression will be
\( \mathbf{A} \cdot 580 K \)
B. \( 870 K \)
c. \( 290 \sqrt{2} K \)
D. \( 1160 K \)
Subject: Maths
If the direction ratios of two lines are
given by the equations \( 2 l+2 m-n= \)
0 and \( m l+n l+l m=0, \) then the angle
between the two lines is
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)
Subject: Chemistry
The gas \( A_{2} \) in the left flask allowed to
react with gas \( B_{2} \) present in right flask
\( \operatorname{at} \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{A} \boldsymbol{B}(\boldsymbol{g}), \boldsymbol{K}_{C}=\boldsymbol{4} \)
at \( 27^{\circ} C . \) What is the concentration of
\( A B \) when equilibrium is established?
A . 1.33 М
В. 0.66 М
c. 0.33 М
D. 2.66 М
Subject: Physics
A circular coil of radius \( 4 \mathrm{cm} \) and of 20
turns carries a current of 3 amperes. It is placed in a magnetic field of intensity
of 0.5 weber \( / m^{2} . \) The magnetic dipole moment of the coil is
A. 0.15 ampere \( -m^{2} \)
B. 0.3 ampere \( -m^{2} \)
c. 0.45 ampere \( -m^{2} \)
D. 0.6 ampere \( -m^{2} \)
Subject: Maths
The area of the plane region bounded by the curves \( x+2 y^{2}=0 \) and \( x+3 y^{2}= \)
1 is equal to
A \( \cdot \frac{5}{3}^{\operatorname{sq} . u n i t} \)
в. \( \frac{1}{3} \) sq.unit
c. \( \frac{2}{3} \) squnit
D \( \cdot \frac{4}{3} \) sq.unit
Subject: Physics
A cylindrical vessel contains a liquid of
density \( \rho \) upto a height \( h \). The liquid is closed by a piston of mass \( m \) and area of cross section A.There is a small hole
at the bottom of the vessel.The speed with which the liquid comes out of the vessel is:
A. \( \sqrt{2 g h} \)
в. \( \sqrt{2\left(g h+\frac{m g}{\rho A}\right)} \)
c. \( \sqrt{2\left(g h+\frac{m g}{A}\right)} \)
D. \( \sqrt{2 g h+\frac{m g}{A}} \)
Subject: Chemistry
A compound \( A \) of boron reacts with
\( N M e_{3} \) to give an adduct \( B \) which on hydrolysis gives a compound \( C \) and a
gas \( D . \) Compound \( C \) is an acid.
Compound \( \boldsymbol{C} \) is :
\( A \). diborane
B. boric acid
c. borate salt
D. none of these
Subject: Maths
\( f(x)=\left\{\begin{array}{c}a \sin \frac{\pi}{2}(x+1), x \leq 0 \\ \frac{\tan x-\sin x}{x^{3}}, x>0\end{array}\right. \)
continuous at \( x=0 . \) Find the value of
\( \boldsymbol{a} \)
Subject: Chemistry
Elevation in boiling point of \( \boldsymbol{C a}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
gives molar mass as \( 131.2 . \) The degree of
dissociation of \( \boldsymbol{C a}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) is:
A. \( 100 \% \)
B. \( 75 \% \)
\( c .50 \% \)
D. \( 12.5 \% \)
Subject: Physics
A car is moving on a circular road of curvature \( 300 \mathrm{m} . \) If the coefficient of
friction is 0.3 and acceleration due to
gravity is \( 10 \mathrm{m} / \mathrm{s}^{2} \), the maximum speed the car can have is:
\( A \cdot 30 \mathrm{km} / \mathrm{hr} \)
B. 81 km/hr
c. \( 108 \mathrm{km} / \mathrm{hr} \)
D. \( 162 \mathrm{km} / \mathrm{hr} \)
Subject: Chemistry
Among \( 0.1 ~ M \) solutions of
\( N a C l, C a C l_{2} \) and \( A l_{2}(S O)_{3}, \) the one with highest vapour pressure is:
A \( . N a C l \)
в. \( C a C l_{2} \)
c. \( A l_{2}(S O)_{3} \)
D. All have equal vapour pressure
Subject: Biology
Fill in the spaces \( a, b, c \) and \( d \) in the
following table of contraceptive devices
and the methods of contraception.
\begin{tabular}{|c|c|}
\hline Multiload 375 \( b \) \( c \) & \( a \) Non-medicated IUD Barier (mcthod) used by f fmales \( d \) \\
\hline Progestasert & \\
\hline
\end{tabular}
Subject: Chemistry
Indicate which nitrogen compound amongst the following would undergo Hofmann reaction (i.e., reaction with
\( \left.B r_{2}, \text { and strong } K O H\right) \) to furnish the
primary amine \( \left(\boldsymbol{R}-\boldsymbol{N} \boldsymbol{H}_{2}\right) \)
A. \( R C O N H C H_{3} \)
в. \( R C O O N H_{4} \)
\( \mathbf{c} \cdot R C O N H_{2} \)
D. \( R-C O-N H O H \)
Subject: Chemistry
The standard reduction potential
values, \( \boldsymbol{E}^{\circ}\left(\boldsymbol{B} \boldsymbol{i}^{3+} / \boldsymbol{B} \boldsymbol{i}\right) \) and
\( E^{\circ}\left(C u^{2+} / C u\right) \) are \( 0.226 \mathrm{V} \) and \( 0.344 \mathrm{V} \)
respectively. A mixture of salts of bismuth and copper at unit
concentration each is electrolysed at
\( 25^{\circ} \mathrm{C} . \) To what value \( \operatorname{can}\left[C u^{2+}\right] \) be
brought down before bismuth starts to
deposit, in electrolysis.
\( \mathbf{A} \cdot\left[C u^{2+}\right]=10^{-8} M \)
B. \( \left[C u^{2+}\right]=10^{-4} M \)
\( \mathbf{C} \cdot\left[C u^{2+}\right]=10^{-3} M \)
D. \( \left[C u^{2+}\right]=10^{-6} M \)
Subject: Physics
You throw a ball which a launch velocity of \( \overrightarrow{\boldsymbol{v}}=(\mathbf{3} \hat{\boldsymbol{i}}+\mathbf{4} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} \) the maximum
height attaind by the body is?
A. \( 0.8 m \)
в. \( 0.2 m \)
\( \mathrm{c} .2 .3 \mathrm{m} \)
D. \( 5.3 \mathrm{m} \)
Subject: Physics
A cord is wrapped around the rim of a
flywheel \( 0.5 m \) in radius and a steady
pull of \( 50 N \) in applied on the cord as shown in the figure. The wheel is mounted on a frictionless bearing on the horizontal shaft through its centre.
The moment of inertia of the wheel is
\( 4 k g m^{2} \)
(a) Compute angular acceleration of the whee
(b) If a mass having a weight \( 50 N \) hangs from the cord as shown in the figure. Compute the angular acceleration of the wheel. Why is this not the same as in part (a)?
Subject: Chemistry
For a chemical reaction, \( \Delta G \) will always
be negative if
A. \( \Delta H \) and \( T \Delta S \) both are positive
B. \( \Delta H \) and \( T \Delta S \) both are negative
c. \( \Delta H \) is negative and \( T \Delta S \) is positive
D. \( \Delta H \) is positive and \( T \Delta S \) is negative
Subject: Biology
Which of the following options shows the correct measurements of an adult
human kidney?
A. \( 10-12 \mathrm{cm} 5-7 \mathrm{cm} 2-3 \mathrm{cm} \)
\( 120-170 \mathrm{g} \)
B. \( 10-20 \mathrm{cm} 10-12 \mathrm{cm} 6-12 \mathrm{cm} \)
\( 40-50 \mathrm{g} \)
c. \( 2-6 \mathrm{cm} 8-10 \mathrm{cm} 5-10 \mathrm{cm} \)
\( 60-70 \mathrm{g} \)
D. \( 10-12 \mathrm{mm} 5-7 \mathrm{mm} 2-3 \mathrm{mm} \)
\( 120-170 \mathrm{mg} \)
Subject: Chemistry
Which of the following orders is not
correct with respect to the property indicated against each?
\( \mathbf{A} \cdot F>C l>B r>I \rightarrow \) electron gain enthalpy
B \( \cdot F^{-}>C l^{-}>B r>I^{-} \rightarrow \) enthalpy of hydration
\( \mathbf{C} \cdot F_{2}>C l_{2}>B r_{2}>I_{2} \rightarrow \) bond dissociation energy
\( \mathbf{D} \cdot F_{2}<C I_{2}<B r_{2}<I_{2} \rightarrow X-X \) bond lenght
Subject: Chemistry
A quantity of 9.8 g of \( F e S O_{4} \cdot\left(N H_{4}\right)_{2} S O_{4} \cdot x H_{2} O \) was
dissolved in \( 250 \mathrm{ml} \) of its solution.
Twenty millilitres of this solution
requires \( 20 \mathrm{ml} \) of \( K M n O_{4} \) solution
containing 3.53 g of \( 90 \% \) pure \( K M n O_{4} \) dissolved per litre. The value of 'x' is
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
D. 7