AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A body is dropped from height 8 m. After
striking the surface it rises to \( 6 m \)
what is the fractional loss in kinetic
energy during impact? Assuming the frictional resistance to be negligible.
A . \( 1 / 2 \)
в. \( 1 / 4 \)
c. \( 1 / 6 \)
D. \( 1 / 8 \)
Subject: Maths
The function \( \boldsymbol{f}:(-\infty,-1] \rightarrow\left(0, e^{5}\right) \)
defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}^{3}-\mathbf{3} \boldsymbol{x}+\mathbf{2}}, \) is
A. many-one and onto
B. many-one and into
c. one-one and onto
D. one-one and into
Subject: Chemistry
Which of the following statements(s)
is(are) true?
This question has multiple correct options
A. The two six-membered cyclic hemiacetal forms of \( D-(+)-g l u c o s e \) are called anomers
B. Hydrolysis of sucrose gives dextrorotatory glucose and laevorotatory fructose
C. Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones
D. Oxidation of glucose with bromine water gives glutamic acid
Subject: Physics
A thin uniform rod of mass m moves
translationally with acceleration a due to two antiparallel force of lever arm \( I \)
One force is of magnitude \( F \) and acts at one extreme end. The length of the rod is:
A \( \cdot \frac{2(F+m a) I}{m a} \)
B. \( _{I\left(1+\frac{F}{m a}\right)} \)
c. \( \frac{(F+m a) I}{2 m a} \)
D. \( \frac{m a I}{m a+F} \)
Subject: Chemistry
(a) Account for the following:
(i) \( C u^{+} \) is unstable in an aqueous
solution.
(ii) Transition metals form complex compounds.
(b) Complete the following equations:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}+\boldsymbol{8} \boldsymbol{H}^{+}+\boldsymbol{3} \boldsymbol{N} \boldsymbol{O}_{\overline{2}} \rightarrow \)
Subject: Physics
A non-conducting sphere has a total charge Q uniformly distributed throughout its volume. the centre of the sphere is at origin and its radius is \( \mathrm{R} \)
let \( U_{1} \) be the electrostatic potential energy in the region inside the sphere and \( U_{2} \) be the electrostatic potential energy in another imaginary spherical shell, having inner radius \( R \) and outer radius infinity, centred at origin. select the correct alternative(s)
\( ^{\mathrm{A}} \cdot U_{1}=\frac{Q^{2}}{8 \pi \varepsilon_{0} R} \)
в. \( U_{2}=\frac{Q^{2}}{8 \pi \varepsilon_{0} R} \)
c. \( U_{1}+U_{2}=\frac{3}{5} \times \frac{Q^{2}}{4 \pi \varepsilon_{0} R} \)
D. \( U_{1}=\frac{3 Q^{2}}{20 \pi \varepsilon_{0} R} \)
Subject: Chemistry
Select correct alternates(s).
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{In} N a H C O_{3}, \) the \( H C O_{3}^{-} \) ions are linked into infinite
chain
B. \( \ln K H C O_{3} \), a dimer is formed by H-bonding
C \( \cdot \ln N a H C O_{3}, \) a dimer is formed by H-bonding
D. \( \ln K H C O_{3} \), the \( H C O_{3}^{-} \) ions are linked into infinite chain
Subject: Chemistry
\( H_{2} O_{2} \) oxidises \( H_{2} S \) to :
A . \( S \)
в. \( H_{2} S O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \mathrm{O}_{8} \)
D. \( H_{2} S O_{5} \)
Subject: Chemistry
For the reaction: \( 2 H_{2(g)}+2 C l_{2(g)} \rightarrow \)
\( 4 H C l(g) ; \Delta H^{0}=-92.3 K J, \) choose
the correct statement(s) out of the
following:
(i) If the reaction equation is reversed,
the \( \Delta H^{0} \) value will become \( 92.3 K J \)
(ii) The \( 4(H-C l) \) bond in \( 4 H C l \) is
stronger than the \( 2(H-H) \) and
\( \mathbf{2}(\boldsymbol{C l}-\boldsymbol{C l}) \) bonds in \( \mathbf{2} \boldsymbol{H}_{2} \) and \( \mathbf{2} \boldsymbol{C l} \mathbf{l}_{\mathbf{2}} \)
respectively.
(iii) The \( \Delta H^{0} \) value will be \( -92.3 K J \), if
the \( H C l \) is produced as a liquid.
A. (i) only
B. (i) and (ii) only
C. (ii) and (iii) only
D. All of these
Subject: Chemistry
Match the List-I with List-II and select
the correct answer from the given
Codes.
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { (Compound) } & \text { (Oxidation state of nitrogen) } \\ N_{2} O_{5} & -2 \\ N a N_{3} & +5 \\ \text { NO } & -1 / 3 \\ N_{2} H_{4} & +2\end{array} \)
\( \mathbf{A} \cdot A-(i i), B(\text { iii) }, C-(i v), D-(i) \)
B. A-(i), B-(ii), C-(iii), D-(iv)
C. \( A-(i v), B-(i), C-(i i), D-(i i i) \)
D. A-(iii), B-(i), C-(iv), D-(ii)
Subject: Physics
In an hydrogen atom, the electron is making \( 6.6 \times 10^{15} \)rps. If the radius of
the orbit is \( 0.53 \times 10^{-10} m, \) then the
equivalent magnetic dipole moment is approximately
\( \mathbf{A} \cdot 10^{-29} A m^{2} \)
B . \( 10^{-27} \mathrm{Am}^{2} \)
c. \( 10^{-23} A m^{2} \)
D. \( 10^{-19} \mathrm{Am}^{2} \)
Subject: Physics
Two concentric hollow spherical shells have radii \( r \) and \( R(R>>r) . \) A charge
\( Q \) is distributed on them such that the
surface charge densities are equal. The electric potential at the centre is:
A \( \cdot \frac{Q(R+r)}{4 \pi \epsilon_{0}\left(R^{2}+r^{2}\right)} \)
B. \( \frac{Q\left(R^{2}+r^{2}\right)}{4 \pi \epsilon_{0}(R+r)} \)
c. \( \frac{Q}{R+r} \)
D.
Subject: Physics
Figure shows a LCR circuit connected
with a dc battery of emf \( \varepsilon \) and internal
resistance \( R \). Initially the capacitor was
uncharged. After a long time:
This question has multiple correct options
A \( \cdot \) current through the inductor is \( \frac{\varepsilon}{8 R} \)
B. charge stored in the capacitor is \( C \frac{^{2}}{4} \)
C. charge stored in the capacitor is \( C \frac{e}{2} \)
D. potential difference across the terminals of battery is
\( \frac{\varepsilon}{4} \)
Subject: Physics
If \( V_{0} \) be the potential at origin in an electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{\boldsymbol{x}} \hat{\boldsymbol{j}}+\boldsymbol{E}_{\boldsymbol{y}} \hat{\boldsymbol{j}}, \) then the
potential at point \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) is
\( \mathbf{A} \cdot V_{0}+x E_{x}+y E_{y} \)
B. \( V_{0}+x E_{x}-y E_{y} \)
C \( . V_{0}-x E_{x}-y E_{y} \)
D. \( \sqrt{\left(x^{2}+y^{2}\right)} \sqrt{E_{x}^{2}+E_{y}^{2}}-V_{0} \)
Subject: Maths
Area bounded by the curves \( \boldsymbol{y}= \)
\( e^{x}, y=e^{-x} \) and the straight line \( x=1 \)
is (in sq units)
A \( \cdot_{e+\frac{1}{e}} \)
B. \( e+\frac{1}{e}+2 \)
c. \( _{e+\frac{1}{e}-2} \)
D. \( _{e-\frac{1}{e}+2} \)
E \( e-\frac{1}{e} \)
Subject: Chemistry
Which among the following is not
correctly matched with their colour?
Compound

Colour
\( \mathbf{A} \cdot N a_{4}\left[F e(C N)_{5} N O S\right] \quad \) purple
\( \mathbf{B} \cdot F e_{4}\left[F e(C N)_{6}\right]_{3} \)
blue
\( \mathbf{c} \cdot F e(C N S)_{3} \)
blood red
D. \( A g C l \) light yellow
Subject: Maths
Prove that \( [\overrightarrow{\boldsymbol{a}} . \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}}+\overrightarrow{\boldsymbol{d}}]=[\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{c}}]+ \)
\( [\overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{b}} \cdot \overrightarrow{\boldsymbol{d}}] \)
Subject: Physics
n Fig., light is incident at an angle \( \theta \) is
incident at an angle \( \theta \) which is slightly greater than the critical angle. Now, keeping the incident angle fixed a
parallel slab of refractive index \( n_{3} \) is
placed on surface \( \boldsymbol{A B} \). Which of the
following statements are correct?
(a)
This question has multiple correct options
A. Total internal reflection occurs at \( A B \) for \( n_{3}<n \)
B. Total internal reflection occurs at \( A B \) for \( n_{3}>n_{1} \)
c. The ray will return back to the same medium for all
values of \( n_{3} \)
D. Total internal reflection occurs at \( C D \) for \( n_{3}<n_{1} \)
Subject: Chemistry
\( 40 \mathrm{mL} \) of \( 0.1 \mathrm{M} \) ammonia solution is
mixed with \( 20 \mathrm{mL} \) of \( 0.1 \mathrm{M} \) HCl
What is the \( p H \) of the mixture?
A . 5.74
B. 9.26
c. 4.56
D. 7.06
Subject: Physics
Calculate the ratio of the times taken by a uniform solid sphere and a disc of the same mass and the same diameter to
roll down through the same distance from rest on a smooth inclined plane.
A .15: 14
B. \( \sqrt{15}: \sqrt{14} \)
C. \( 15^{2}: 14^{2} \)
a \( .14^{2}: 14^{2} \)
D. \( \sqrt{14}: \sqrt{15} \)
Subject: Physics
What is the relation between resistance
\( \mathrm{R} \) and resistivity \( \rho \) of a wire \( ? \)
A \( \cdot R=\frac{\rho A}{l} \)
в. \( R=\frac{\rho l}{A} \)
c. \( R=\frac{A}{\rho l} \)
D. \( _{R}=\frac{l}{\rho A} \)
Subject: Chemistry
Two liquids \( A \) and \( B \) form ideal
solutions. At \( 300 K \), the vapour
pressure of a solution containing 1 mole of \( A \) and 3 moles of \( B \) is 550 mm
Hg. At the same temperature, if one
more mole of \( B \) is added to this
solution, the vapour pressure of the
solution increases by 10 mm \( H g \). The
vapour pressure of \( A \) and \( B \) in their
pure states are respectively:
A \( \cdot p_{A}^{o}=600 \mathrm{mm} \mathrm{Hg} \) and \( p_{B}^{o}=400 \mathrm{mm} \mathrm{Hg} \)
B . \( p_{A}^{o}=500 \mathrm{mm} \mathrm{Hg} \) and \( p_{B}^{o}=560 \mathrm{mm} \mathrm{Hg} \)
C \( \cdot p_{A}^{o}=450 \mathrm{mm} \mathrm{Hg} \) and \( p_{B}^{o}=650 \mathrm{mm} \mathrm{Hg} \)
D . \( p_{A}^{o}=400 \mathrm{mm} \mathrm{Hg} \) and \( p_{B}^{o}=600 \mathrm{mm} \mathrm{Hg} \)
Subject: Maths
If \( \lim _{x \rightarrow 0}\left(x^{-3} \sin 3 x+a x^{-2}+b\right) \) exists
and is equal to \( 0, \) then
\( ^{\mathbf{A}} \cdot_{a}=-3 \) and \( b=\frac{9}{2} \)
в. \( _{a=3} \) and \( b=\frac{9}{2} \)
c. \( _{a=-3 \text { and } b=-\frac{9}{2}} \)
D. \( _{a=3} \) and \( b=-\frac{9}{2} \)
Subject: Physics
The graph drawn between pressure and
volume in Boyle's law experiment is
shown in figure for different masses of
same gas at same temperature then
\( \mathbf{A} \cdot m_{2}>m_{1} \)
В \( \cdot m_{1}>m_{2} \)
\( \mathbf{c} \cdot m_{1}=m_{2} \)
\( \mathbf{D} \cdot m_{1}^{3}>m_{2} \)
Subject: Physics
Two particles having masses in \( \mathrm{m} \) and \( 2 \mathrm{m} \) are travelling along \( \mathrm{x} \) -axis on a
smooth surface with velocities \( u_{1} \) and
\( u_{2}, \) collide .If their velocities after
collision are \( v_{1} \) and \( v_{2}, \) then the ratio of
velocities of their centre of mass before
and after impact is
A. 2:
B. 2:3
\( c \cdot 1: \)
D. 1: 2
Subject: Biology
Assertion
The primitive atmosphere was reducing
one i.e., without oxygen.
Reason
In the primitive atmosphere, oxygen
was involved in forming ozone layer.
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: Maths
If \( \boldsymbol{y}=(\boldsymbol{A}+\boldsymbol{B} \boldsymbol{x}) e^{m \boldsymbol{x}}+(\boldsymbol{m}-\mathbf{1})^{-2} \boldsymbol{e}^{\boldsymbol{x}} \)
\( \operatorname{then} \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}-2 \boldsymbol{m} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{m}^{2} \boldsymbol{y} \) is equal to:
A \( \cdot e^{x} \)
B. \( e^{m} \)
\( \mathbf{c} \cdot e^{-m x} \)
D. \( e^{(1-m) x} \)
Subject: Chemistry
The unit of rate constant for zero order
reaction is:
A \( \cdot s^{-1} \)
B \( \cdot \operatorname{mol} L^{-1} s^{-1} \)
c. \( L m o l^{-1} s^{-1} \)
D. \( L^{2} m o l^{-2} s^{-1} \)
Subject: Chemistry
The rate of the elementary reaction
\( \mathbf{2} N \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \) at \( \boldsymbol{3} \boldsymbol{8} \boldsymbol{0}^{\circ} \boldsymbol{C} \)
is given by Rate \( =2.6 \times \)
\( \mathbf{1 0}^{-\mathbf{3}}[\mathbf{N O}]^{\mathbf{2}}\left[\mathbf{O}_{\mathbf{2}}\right] . \) The rate of the reverse
reaction is given by under identical conditions is given by Rate \( = \)
\( 4.1\left[N O_{2}\right]^{2} . \) Calculate equilibrium
constant.
Subject: Physics
The distance between the poles of a horse shoe magnet is \( 0.1 \mathrm{m} \) and its pole strength is \( 0.01 \mathrm{A} \) -m. The induction of magnetic field at a point mid way between the poles will be :
A. zero
В. \( 2 \times 10^{-5} T \)
C \( .4 \times 10^{-6} T \)
D. \( 8 \times 10^{-7} T \)
Subject: Physics
A car travelling with a velocity of
\( 80 k m / h \) slowed down to \( 44 k m / h \) in
15s. The retardation is
A \( \cdot 0.67 m / s^{2} \)
в. \( 1 m / s^{2} \)
\( \mathbf{c} \cdot 1.25 m / s^{2} \)
D. \( 1.5 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
the general solution of differential
equation \( \boldsymbol{x}^{4} \frac{d y}{d x}+\boldsymbol{x}^{3} \boldsymbol{y}+\operatorname{cosec} \boldsymbol{x} \boldsymbol{y}=\mathbf{0} \)
is
A \( \cdot 2 \cos (x y)+\frac{1}{x^{2}}=0 \)
B. \( 2 \cos (x y)+\frac{1}{y^{2}}=0 \)
\( c \cdot 2 \sin y+\frac{1}{x^{2}}=c \)
D. \( 2 \sin (x y)+\frac{1}{y^{2}}=c \)
Subject: Chemistry
Assertion
On cooling, the brown colour of nitrogen dioxide disappears.
Reason
On cooling, \( N O_{2} \) undergoes dimerisation resulting in the pairing of
odd electrons of \( N O_{2} \)
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: Maths
Prime factors of 140 are :
A. \( 2 \times 2 \times 7 \)
В. \( 2 \times 2 \times 5 \)
c. \( 2 \times 2 \times 5 \times 7 \)
D. \( 2 \times 2 \times 5 \times 7 \times 3 \)
Subject: Maths
If \( a, b \) and \( n \) are natural numbers then
\( a^{2 n-1}+b^{2 n-1} \) is divisible by
A \( \cdot a+b \)
в. \( a-b \)
\( \mathbf{c} \cdot a^{3}+b^{3} \)
D. \( a^{2}+b^{2} \)
Subject: Chemistry
Assertion
Bond angle of \( \boldsymbol{H}_{2} \boldsymbol{S} \) is smaller than \( \boldsymbol{H}_{2} \boldsymbol{O} \)
Reason
As the electronegativity of the central atom increases, bond angle decreases.
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: Maths
Find the order and degree of the
differential equations:
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\left[\boldsymbol{y}+\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)^{6}\right]^{1 / 4} \)
Subject: Maths
If the \( z x \) -plane divides the line segment
joining (1,-1,5) and (2,3,4) in the ratio \( \boldsymbol{p}: 1, \) then \( \boldsymbol{p}+\mathbf{1}= \)
A \( \cdot \frac{1}{3} \)
B.
\( c \cdot \frac{3}{4} \)
D. \( \frac{4}{3} \)
Subject: Maths
Find the solution of lines:
\[
\begin{array}{l}
\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{4} \\
\boldsymbol{2} \boldsymbol{x}-\boldsymbol{3} \boldsymbol{y}=\boldsymbol{3}
\end{array}
\]
Subject: Maths
In the given figure, \( a \) is greater than \( b \) by
two third of a right angle. The values of
\( a \) and \( b \) are
A \( \cdot 100^{\circ}, 80^{\circ} \)
B . \( 105^{\circ}, 75^{\circ} \)
\( \mathbf{c} \cdot 90^{\circ}, 90^{\circ} \)
D. \( 120^{\circ}, 60^{\circ} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{0}\end{array}\right] \)
then what is determinant of AB?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 10
D. 20
Subject: Chemistry
Barium ions, \( C N^{-} \) and \( C o^{2+} \) form an
ionic complex. If that complex is supposed to be \( 75 \% \) ionised in water with vant Hoff factor 'i' equal to four
then the coordination number of \( C o^{2+} \)
in the complex can be.
A. Six
B. Five
c. Four
D. six and Four both
Subject: Biology
Assertion
Electorcardiogram is record of electrical activity of the heart which shows certain waves called \( P, Q, R, S \)
and T waves.
Reason
It gives important information concerning the spread of excitation to the different parts of heart and it is of value in the diagnosis of cases of abnormal cardiac rhythm and myocardial damage
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Physics
The input characteristics of a transistor
in \( C E \) mode is the graph obtained by
plotting
\( \mathbf{A} \cdot I_{B} \) against \( V_{B E} \) at constant \( V_{C E} \)
B. \( I_{B} \) against \( V_{C E} \) at constant \( V_{B E} \)
C \( \cdot I_{B} \) against \( I_{C} \) at constant \( V_{C E} \)
D. \( I_{V} \) against \( I_{C} \) at constant \( V_{B E} \)
Subject: Physics
A bus driver is reversing his bus at a
speed \( 8 m s^{-1} . \) The rear view mirror of a
bus is a plane mirror. The driver sees in
his rear view mirror the image of a car
parked behind his bus. The speed at which the image of the car appears to approach the driver will be
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. \( 4 m s^{-1} \)
\( \mathrm{c} \cdot 8 \mathrm{ms}^{-1} \)
D. \( 16 m s^{-1} \)
Subject: Physics
A cubical block of mass \( m \) and side \( L \)
rests on a rough horizontal surface with
coefficient of friction \( \mu . \) A horizontal
force \( \boldsymbol{F} \) is applied on the block as shown in the figure. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is:
\( A \cdot \frac{m g}{4} \)
B. \( \frac{m g}{8} \)
\( c \cdot \frac{m g}{2} \)
D. \( m g(1-\mu) \)
Subject: Physics
The maximum intensity produced by
two coherent waves of intensity \( \boldsymbol{I}_{1} \) and
\( \boldsymbol{I}_{2} \) will be
A \( \cdot I_{1}+I_{2} \)
В \( \cdot I_{1}^{2}+I_{2}^{2} \)
\( \mathbf{c} \cdot I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \)
D. zero
Subject: Physics
Four dipoles each one having magnitudes of charges \( \pm \mathrm{e} \) are placed inside a sphere. The total flux of \( \vec{E} \) coming out of the sphere is :
A. zero
в. \( \frac{4 e}{\varepsilon_{0}} \)
\( c \cdot \frac{8 e}{\varepsilon_{0}} \)
D. None of these
Subject: Maths
Let \( \boldsymbol{A}=\left[\begin{array}{c}\mathbf{3} \boldsymbol{x}^{2} \\ \mathbf{1} \\ \mathbf{6} \boldsymbol{x}\end{array}\right], \boldsymbol{B}=[\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}] \) and \( \boldsymbol{C}= \)
\( \left[\begin{array}{ccc}(x+2)^{2} & 5 x^{2} & 2 x \\ 5 x^{2} & 2 x & (x+2)^{2} \\ 2 x & (x+2)^{2} & 5 x^{2}\end{array}\right] \)
three given matrices, where \( a, b, c \) and
\( \boldsymbol{x} \in \boldsymbol{R}, \) Given that \( \boldsymbol{t r} .(\boldsymbol{A B})=\boldsymbol{t r} .(\boldsymbol{C}) \vee \)
\( \boldsymbol{x} \in \boldsymbol{R}, \) where \( \boldsymbol{t r} .(\boldsymbol{A}) \) denotes trace of \( \boldsymbol{A} \)
Find the value of \( (\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}) \)
\( A \cdot 6 \)
B.
\( c \cdot 8 \)
D.
Subject: Physics
A volume of \( 2.5 ~ L \) of a sample of a gas
at \( 27^{\circ} \mathrm{C} \) and 1 bar pressure is
compressed to a volume of 500 ml keeping the temperature constant, the percentage increase in pressure is?
\( \mathbf{A} \cdot 100 \% \)
B. \( 400 \% \)
c. \( 500 \% \)
D. \( 80 \% \)
Subject: Physics
A double convex lens is made of glass which has refractive index 1.55 for violet
rays and 1.50 for red rays. If the focal length of violet rays is \( 20 \mathrm{cm}, \) the focal length for red rays is :
A. \( 9 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. 22 cm
Subject: Physics
In one dimensional motion,
instantaneous speed \( \boldsymbol{v} \) satisfies the
condition, \( 0 \leq v<v_{0}, \) when
A. The displacement in time T must always take nonnegative values.
B. The displacement x in time T satisfies - \( v_{0} T<x<v_{0} T \)
C. The acceleration is always a non-negative number
D. The motion has no turning points.
Subject: Physics
A small candle, \( 2.5 \mathrm{cm} \) in size is placed
at \( 27 \mathrm{cm} \) in front of a concave mirror of
radius of curvature \( 36 \mathrm{cm} . \) At what
distance from the mirror should a
screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the
screen have to be moved?
Subject: Maths
A sphere of constant radius \( 2 k \) passes
through the origin and meets the axes in \( A, B, C . \) The locus of the centroid of
the tetrahedron \( \boldsymbol{O} \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \) is
A \( \cdot x^{2}+y^{2}+z^{2}=4 k^{2} \)
B \cdot \( 9\left(x^{2}+y^{2}+z^{2}\right)=4 k^{2} \)
C . \( x^{2}+y^{2}+z^{2}=k^{2} \)
D. None of these
Subject: Chemistry
A reaction occurs spontaneously if
\( \mathbf{A} \cdot T \Delta S<\Delta H \) and both \( \Delta H \) and \( \Delta S \) are \( +v e \)
B. \( T \Delta S>\Delta H \) and both \( \Delta H \) and \( \Delta S \) are +ve
c. \( T \Delta S=\Delta H \) and both \( \Delta H \) and \( \Delta S \) are +ve
D. \( T \Delta S>\Delta H \) and both \( \Delta H \) and \( \Delta S \) are -ve
Subject: Chemistry
Match the colum:
\( \begin{array}{ll}\text { List - A } & \text { List - B } \\ \text { (Molecule) } & \begin{array}{l}\text { (Pure and hybrid } \\ \text { orbitals involved) }\end{array} \\ \text { A) } C_{2} H_{6} & \text { 1) } 12,18 \\ \text { B) } C_{2} H_{4} & \text { 2) } 6,4 \\ \text { C) } C_{2} H_{2} & \text { 3) } 6,6 \\ \text { D) } C_{6} H_{6} & \text { 4) } 6,8\end{array} \)
\( \mathbf{A} \)
B. A-2, B-3, C-4, D-1
c. \( A-3, B-4, C-2, D-1 \)
D. A-4, B-3, C-2, D-1
Subject: Maths
A medicine-capsule is in the shape of a cylinder of diameter \( 0.5 \mathrm{cm} \) with two hemispheres stuck to each of its ends. The length of entire capsule is \( 2 \mathrm{cm} . \) The capacity of the capsule is
A \( \cdot 0.36 c m^{3} \)
в. \( 0.35 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 0.34 \mathrm{cm}^{3} \)
D. \( 0.33 c m^{3} \)
Subject: Maths
\( P(-2,3), Q(3,7) . \) The point \( A \) on the \( x \) axis for which \( \mathbf{P A}+\mathbf{A Q} \) is least is
\( ^{\mathrm{A}} \cdot\left(\frac{-1}{2}, 0\right) \)
в. \( \left(\frac{1}{2}, 0\right) \)
c. \( \left(0, \frac{-1}{2}\right) \)
D. \( \left(0, \frac{1}{2}\right) \)
Subject: Chemistry
Consider the following statements for
micelles, which is/are correct?
This question has multiple correct options
A. At critical micelle concentration, several properties of solution of surfactants such as molar conductivity, surface tension and osmotic pressure change
B. Micelles from ionic surfactants can be formed only above a certain temperature called the Kraft temperature
C. Micelle formation is exothermic
D. Micelles are associated colloids
Subject: Chemistry
If the maximum concentration of \( \boldsymbol{P b C l}_{2} \)
in water is \( 0.01 M \) at \( 298 K \), Its
maximum concentration in
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \) will be:
A \( \cdot 4 \times 10^{-3} M \)
В. \( 0.4 \times 10^{-4} M \)
\( \mathbf{c} \cdot 4 \times 10^{-2} M \)
D. \( 4 \times 10^{-4} M \)
Subject: Maths
Assertion
Statement-1 If \( a_{1}, a_{2}, a_{3}, \dots \dots \dots, a_{24} \) are
\( \ln \) A. P. such that \( a_{1}+a_{5}+a_{10}+a_{15}+ \)
\( \boldsymbol{a}_{20}+\boldsymbol{a}_{24}=\mathbf{2 2 5} \) then \( \boldsymbol{a}_{\mathbf{1}}+\boldsymbol{a}_{\mathbf{2}}+\boldsymbol{a}_{3}+ \)
\( \ldots .+a_{23}+a_{24}=900 \) because
Reason
Statement-2 In any A.P. sum of the terms equidistant from begining and end is constant and is equal to
the sum of the first and the last term,
A. Statement-1 is true, Statement-2 Is true and statement-2 is correct explanation for Statement-
B. Statement-1 is true, Statement-2 Is true and Statement-2 is NOT correct explanation for Statement
c. statement-1 is true, statement-2 is false
D. statement-1 is false, Statement-2 Is true