AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Urethane is:
в.
\[
\mathrm{H}_{2} \mathrm{N}-\mathrm{C}-\mathrm{OH}
\]
c. \( H O-C \equiv N \)
D.
\[
\mathrm{H}_{2} \mathrm{N}-\underset{\mathrm{O}}{\|}-\mathrm{OC}_{2} \mathrm{H}_{5}
\]
Subject: Physics
A closely wound solenoid \( 80 \mathrm{cm} \) long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8
\( \mathrm{cm} . \) If the current carried is \( 8.0 \mathrm{A} \)
estimate the magnitude of B inside the solenoid near its centre.
Subject: Physics
Assertion
A charge moving in a circular orbit can
produce electromagnetic wave.
Reason
The source of electromagnetic wave
should be in accelerated motion.
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
The speci/species which do not support octet rule are:
\( (a) H_{2} O(b) C l_{2} O(c) N O \)
\( (d) P C l_{5} \)
\( A \cdot a, b \) and \( c \)
B. c and d
\( c . b, c \) and \( d \)
\( D . \quad b, d \) and \( a \)
Subject: Physics
Two particles \( A \) and \( B \) have de-Broglie's wavelengths \( 30 A \) and \( 20 A, \) combined to form a particle C. Momentum is conserved in this process. The possible de-Broglie's wavelength of C is :
(the motion is one dimensional)
A \( \cdot 12 \AA \)
в. 20 ,
\( c .10 \hat{A} \)
D. 22 a
Subject: Maths
If \( 4 x+4 y-k z=0 \) is the equation of
the plane through the origin that contains the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}+\mathbf{1}}{\mathbf{3}}=\frac{\boldsymbol{z}}{\mathbf{4}} \)
then \( \boldsymbol{k}= \)
A . 1
B. 3
\( c .5 \)
D.
Subject: Chemistry
The energy required to break \( 76 \mathrm{gm} \) gaseous fluorine into free gaseous
atom is 180 Kcal at \( 25^{0} C . \) The bond
energy of F-F bond will be:
A. 180 Kcal
B. 90 Kcal
c. 45 Kcal
D. 104 kcal
Subject: Physics
Assertion
The logic gate NOT can be built using diode
Reason
The output voltage and the input
voltage of the diode have \( 180^{\circ} \mathrm{C} \) phase difference.
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 square loop is placed in \( x-y \) plane
as shown in figure. Magnetic field in the region is \( \vec{B}=-B_{0} x \hat{k} . \) The induced
current in the loop is anticlockwise.
Reason
f inward magnetic field from such a loop increases, then current should be
anticlockwise
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 satellite S is moving in an elliptical orbit around the earth. The mass of the
satellite is very small compared to the
mass of the earth
A. the acceleration of S is always directed towards the centre of the earth
B. the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant
C. the total mechanical energy of S varies periodically with time
D. the linear momentum of S remains constant in magnitude
Subject: Physics
Statement 1: A large number of alpha particles were deflected in the Rutherford experiment. Statement 2: Alpha particles that came close to the nucleus of the gold atoms
were deflected.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct but statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct
Subject: Chemistry
Acidified \( K_{2} C r_{2} O_{7} \) solution turns
green when \( N a_{2} S O_{3} \) is added to it. This is due to the formation of:
A \( \cdot C r O_{4}^{2-} \)
В \( \cdot C r_{2}\left(S O_{3}\right)_{3} \)
\( \mathrm{c} \cdot \mathrm{CrSO}_{4} \)
D \( \cdot C r_{2}\left(S O_{4}\right)_{3} \)
Subject: Chemistry
Statement-1: In clarks process excess
of lime is not added to water sample to
remove temporary hardness. Statement-2: Addition of excess of milk
of lime causes permanent hardness.
A. Statement-1 is true, Statement-2 is true; Statementis a correct explanation for Statement-
B. Statement-1 is true, Statement-2 is true; Statement- is not a correct explanation for Statement-
c. Statement- 1 is true, Statement- 2 is false.
D. Statement-1 is false, Statement-2 is true
Subject: Chemistry
Decreasing order of size of various hybrid orbitals is :
A \( \cdot s p>s p^{2}>s p^{3} \)
B \( \cdot s p^{3}>s p^{2}>s p \)
C \( \cdot s p^{2}>s p>s p^{3} \)
\( \mathbf{D} \cdot s p>s p^{3}>s p^{2} \)
Subject: Physics
Assume that a molecule is moving with the root mean square speed at temperature \( 300 \mathrm{K} \). The de Broglie wavelength of nitrogen molecule is (Atomic mass of nitrogen \( =14.0076 \mathrm{u}, \mathrm{h} \) \( =\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{J} \boldsymbol{s}, \boldsymbol{k}_{\boldsymbol{B}}=\mathbf{1 . 3 8} \times \)
\( \mathbf{1 0}^{-\mathbf{2 3}} \boldsymbol{J} \boldsymbol{K}^{-\mathbf{1}}, \mathbf{1} \boldsymbol{u}=\mathbf{1 . 6 6} \cdot \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{k} \boldsymbol{g} \)
\( \mathbf{A} \cdot 2.75 \times 10^{-11} m \)
В. \( 2.75 \times 10^{-12} m \)
c. \( 3.24 \times 10^{-11} \mathrm{m} \)
D. \( 3.24 \times 10^{-12} \mathrm{m} \)
Subject: Chemistry
\( [\boldsymbol{X}]+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow[\boldsymbol{Y}] \) a colourless gas
with irritating burning smell of sulphur
\( [\boldsymbol{Y}]+\boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \operatorname{green} \)
solution.
\( [\boldsymbol{X}] \) and \( [\boldsymbol{Y}] \) are:
\( \mathbf{A} \cdot S O_{3}^{2-}, S O_{2} \)
в. \( C l^{-}, H C l \)
\( \mathbf{c} \cdot S^{2-}, H_{2} S \)
D. \( C O_{3}^{2-}, C O_{2} \)
Subject: Chemistry
Identify \( (\boldsymbol{E}) \) and \( (\boldsymbol{F}) \) in the following:
\( \boldsymbol{C a} \boldsymbol{C O}_{3} \rightarrow(\boldsymbol{A})+(\boldsymbol{B}) \)
\( (B)+H_{2} O \rightarrow(C) \stackrel{(A)}{\rightarrow}(D) \stackrel{(A) e x c e s s}{\rightarrow}(E) \)
\( (\boldsymbol{A})+\boldsymbol{N} \boldsymbol{H}_{3} \stackrel{\boldsymbol{\Delta}}{\rightarrow}(\boldsymbol{F}) \)
A \( \cdot(E) C a\left(H C O_{3}\right)_{2} ;(F) N H C O N H_{3} \)
B . \( (E) C a\left(H C O_{3}\right) ;(F) N H_{3} C O N H \)
C \( \cdot(E) C a\left(H C O_{3}\right)_{2} ;(F) N H_{2} C O N H_{2} \)
D. None of these
Subject: Chemistry
The secondary precursors of photochemical smog are:
A. \( S O_{2} \) and \( N O_{2} \)
B. \( N O_{2} \) and hydrocarbons
\( \mathrm{c} \cdot O_{3} \) and hydrocarbons
D. \( C O_{2} \) and \( O_{2} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\left(\frac{\boldsymbol{x}^{a}}{\boldsymbol{x}^{b}}\right)^{\boldsymbol{a}+\boldsymbol{b}} \cdot\left(\frac{\boldsymbol{x}^{b}}{\boldsymbol{x}^{c}}\right)^{b+c} \cdot\left(\frac{\boldsymbol{x}^{c}}{\boldsymbol{x}^{a}}\right)^{c+a} \)
then \( f^{\prime}(x) \) is equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( \mathbf{c} \cdot x^{a+b+c} \)
D. None of these
Subject: Physics
A semiconductor has equal electron
and hole concentration of \( 2 \times 10^{8} m^{-3} \)
On doping with a certain impurity, the electron concentration increases to \( 4 x \)
\( 10^{10} m^{-3}, \) then the new hole
concentration of the semiconductor is
A \( \cdot 10^{6} m^{-3} \)
B . \( 10^{8} m^{-3} \)
D. \( 10^{12} m^{-3} \)
Subject: Physics
A new temperature scale uses \( X \) as a
unit of temperature, where the
numerical value of the temperature \( t_{x} \)
in this scale is related to the
absolute temperature \( \mathrm{T} \) by \( t_{x}=3 \mathrm{T}+300 \)
If the specific heat of a material using
this unit is \( 1400 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \) its
specific heat in the S.1. system of units
is :
\( \mathbf{A} \cdot 4200 J k g^{-1} K^{-1} \)
B . \( 1400 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
c. \( 466.7 \mathrm{Jkg}^{-1} \mathrm{K}^{-1} \)
D. Impossible to determine from the information provided
Subject: Physics
A long copper wire is wound in the form
of a coil of radius \( r . \) A current of \( 2 A \) is
passed through this coil and the magnetic induction at the centre of this coil is noted. The same wire is now
folded end to end and coil of the same
radius \( r \) is prepared and the same current is passed through it. The magnetic induction at the centre
A. Will be doubled
B. Will be halved
c. will remain same
D. Will drop to zero
Subject: Physics
A \( 1 \mathrm{kg} \) body slides from the point \( \mathrm{A} \) along a horizontal track with an initial
speed of \( 6 m s^{-1} \) towards a weightless
horizontal spring of length \( 2 \mathrm{m} \) and force constant \( 4 N m^{-1} \).The part \( A B \) of the track is frictionless and the part
BC has the coefficients of static and
dynamic friction 0.22 and 0.2 respectively. Find the total distance through which the block moves before it comes to rest completely \( \left(g=10 m s^{-2}\right. \)
)
if \( A B=4 \mathrm{m} \) and \( B D=4.28 \mathrm{m} \)
Subject: Chemistry
The enthalpy of solution of anhydrous
\( C u S O_{4} \) is \( -16 k C a l \) and that of
\( \mathrm{CuSO}_{4} \cdot \mathrm{5H}_{2} \mathrm{O} \) is \( 3 \mathrm{kCal} \). Calculate \( \Delta \boldsymbol{H} \)
for the following reaction at \( 500 K \) and
constant pressure.
Subject: Physics
Two particles \( A_{1} \) and \( A_{2} \) of masses
\( \boldsymbol{m}_{1}, \boldsymbol{m}_{2}\left(\boldsymbol{m}_{1}>\boldsymbol{m}_{2}\right) \) have the same de
Broglie wavelength. Then
A. their momenta are the same
B. their energies are the same.
c. momentum of \( A_{1} \) is less than momentum of \( A_{2} \)
D. energy of \( A_{1} \) is more than the energy of \( A_{2} \)
Subject: Physics
A block of mass \( m \) is projected with velocity \( u \) forwards another identical
block with has a massless spring attached to its face. The spring constant of the spring is \( k \) and blocks are on smooth horizontal surface.

Maximum compression in the spring is:
A \( \cdot u \sqrt{\frac{2 m}{k}} \)
в. \( u \sqrt{\frac{m}{k}} \)
c. \( u \sqrt{\frac{m}{2 k}} \)
D. \( u \sqrt{\frac{m}{4 k}} \)
Subject: Maths
Laspeyres Price Index \( =? \)
\begin{tabular}{|c|c|c|c|c|}
\hline \multirow{2}{*} { Items } & \multicolumn{2}{|c|} {2005} & \multicolumn{2}{|c|} {2010} \\
\cline { 2 - 5 } & \( \mathrm{P}_{0}(₹) \) & \( \mathrm{Q}_{0} \) & \( \mathrm{P}_{1}(₹) \) & \( \mathrm{Q}_{1} \) \\
\hline \( \mathrm{A} \) & 2 & 5 & 3 & 4 \\
\( \mathrm{B} \) & 1 & 2 & 2 & 3 \\
\( \mathrm{C} \) & 3 & 1 & 4 & 1 \\
\hline
\end{tabular}
A. 157.33
B. 153.14
\( \mathbf{c} \cdot 153.33 \)
D. 157.14
Subject: Chemistry
When ethyl alcohol is heated with a
paste of bleaching powder, we get an intermediate compound. The formula of
that compound is:
\( \mathbf{A} \cdot C_{2} H_{5} C l \)
в. \( C C l_{3} C H O \)
\( \mathbf{c} \cdot C H_{3} I \)
D. \( C C l_{3} \) СОСН \( _{3} \)
Subject: Chemistry
Which solution would have the most
altered boiling point?
A \( \cdot 1 M L i_{2} S O_{4} \)
в. \( 1 \mathrm{M} \mathrm{CuSO}_{4} \)
\( \mathrm{c} \cdot 1 \mathrm{M} C_{6} \mathrm{H}_{12} \mathrm{O}_{6} \)
D. 1 \( M \) NaCl
Subject: Chemistry
Consider a hypothetical hydrogen like
atom. The wavelength in \( A^{\circ} \) for the
spectral lines for transition from \( \boldsymbol{n}=\boldsymbol{p} \)
to \( n=1 \) are given by:
\( \lambda=\frac{1500 p^{2}}{p^{2}-1}, \) where \( p>1 \)
Find the ionization potential of this element?
A. 16.56 ev
B. 8.28 ev
c. 4.14 ev
D. 22.4 ev
Subject: Physics
The magnification of the image when an object is placed at a distance \( x \) from the
principle focus of a mirror of focal length \( f \) is?
A \( \cdot \frac{x}{f} \)
B. \( 1+f / x \)
c. \( \frac{f}{x} \)
D. \( _{1-\frac{f}{x}} \)
Subject: Physics
The value of gravitation constant is \( \boldsymbol{G}=\mathbf{6 . 6 7} \times \mathbf{1 0}^{-\mathbf{1 1}} \boldsymbol{N}-\boldsymbol{m}^{2} / \boldsymbol{k g}^{2} \) in SI
units. Convert it into CGS system of
units.
A. Thus, value of G in CGS system of units is 6.67 x \( 10^{-8} \) dyne \( c m^{2} / g^{2} \)
B. Thus, value of G in CGS system of units is \( 6.67 \times \) \( 10^{-9} \) dyne \( c m^{2} / g^{2} \)
c. Thus, value of G in CGS system of units is 6.67 x \( 10^{-7} \) dyne \( c m^{2} / g^{2} \)
D. Thus, value of G in CGS system of units is 6.67 x \( 10^{-10} \) dyne \( c m^{2} / g^{2} \)
Subject: Maths
Each month a store owner can spend at
most \( \$ 100,000 \) on PC's laptops. A PC
costs the store owner \( \$ 1000 \) and \( a \)
laptop costs him \( \$ 1500 . \) Each PC is sold for a profit of \( \$ 400 \) while laptop is sold for a profit of \( \$ 700 . \) The store owner
estimates that at least 15 PC's but no
more than 80 are sold each month. He
also estimates that the number of
laptops sold is at most half the PC's. How many PC's and how many laptops should be sold in order to maximize the
profit?
Subject: Chemistry
For a reaction that has \( [\boldsymbol{A}] \) and \( [\boldsymbol{B}] \) both doubled, the rate goes up by a factor of
8. The rate law is: rate\( =\boldsymbol{k}[\boldsymbol{A}]^{m}[\boldsymbol{B}]^{2} \)
What is the rate order with respect to
\( [\boldsymbol{A}] ? \)
A. Third order
B. Second order
c. First order
D. Can not be determined with the given information
Subject: Chemistry
\( A l O_{2}^{-} \) ion in aqueous solution exists as
\( \mathbf{A} \cdot\left[A l(O H)_{4}\right]^{-} \)
в. \( \left[A l(O H)_{4}\left(H_{2} O\right)\right]^{-} \)
c. \( \left[A l(O H)_{4}\left(H_{2} O\right)_{2}\right] \)
D \( \cdot\left[A l(O H)_{6}\right]^{-} \)
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{x}: \boldsymbol{x} \in \boldsymbol{W}, \boldsymbol{3} \leq \boldsymbol{x}<\mathbf{6}\}, \boldsymbol{B}= \)
\( \{\boldsymbol{3}, \boldsymbol{5}, \boldsymbol{7}\} \) and \( \boldsymbol{C}=\{\mathbf{2}, \boldsymbol{4}\} ; \) find :
\( \boldsymbol{B}-\boldsymbol{C} \)
Subject: Physics
The water equivalent of a calorimeter is
10g and it contains 50g of water at \( 15^{\circ} \)
C. Some amount of ice, initially at \( -10^{\circ} \) \( \mathrm{C} \) is dropped in it and half of the ice melts till equilibrium is reached. What was the initial amount of ice that was
dropped (when specific heat of ice \( = \) 0.5cal \( g m^{-1} o^{-1} \), specific heat of
water \( =1.0 \) cal \( g m^{-1 o} C^{-1} \) and latest
heat of melting of ice \( =\mathbf{8 0} \) cal \( \boldsymbol{g m}^{-1} \) )?
A . 108
B. \( 18 g \)
\( \mathbf{c} \cdot 20 g \)
D. 30g
Subject: Maths
\( f\left(x-\frac{x^{2}}{4}+\frac{x^{3}}{4}-\dots \dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{4}+\frac{x^{6}}{4}-\ldots \ldots . . \infty\right)=\frac{\pi}{2} \)
and \( 0<x<\sqrt{2} \) then \( x= \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
D. -
Subject: Physics
A circular racetrack of radius \( 300 m \) is
banked at an angle of \( 15^{\circ} . \) If the
coefficient of friction between the
wheels of a race car and the road is 0.2
(a) What is the optimum speed of the race car to avoid wear and tear on its
tires?
(b) What is the maximum permissible speed to avoid slipping?
Subject: Physics
A small cube with mass \( M \) starts at
rest point 1 at a height \( 4 R, \) where \( R \) is
the radius of the circular part of the
track. The cube slides down the
frictionless track and around the loop.
The force that the track exerts on the
cube at point 2 is nearly
times the cube's
weight \( M g \)
\( A \)
в.
\( c .3 \)
D.
Subject: Chemistry
Benzene bums in \( O_{2} \) according to the equation:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(l)+\frac{\mathbf{1 5}}{\mathbf{2}} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{6} C O_{2}(\boldsymbol{g}) \)
If standard heat enthalpies of
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6}(\boldsymbol{l}), \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{\theta}_{2}(\boldsymbol{g}) \) are 11.7
-68.3 and -94.0 kcal respectively. The amount of heat liberated by burning 1 kg benzene in kcal is:
A. 10007.4
B. 1000
c. 500
D. None of these
Subject: Maths
Show that:
\( \left|\begin{array}{ccc}\boldsymbol{a}^{2} & \boldsymbol{b}^{2} & \boldsymbol{c}^{2} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right|=-(\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}- \)
\( \boldsymbol{a}) \)
Subject: Physics
Moving with uniform acceleration a
body covers \( 150 m \) in \( 10 s, \) so that it
covers \( 24 m \) during the tenth second. Then the acceleration of the body is
A \( \cdot 2 m / s^{2} \)
B . \( 3 m / s^{2} \)
\( \mathrm{c} \cdot 4 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 6 m / s^{2} \)
Subject: Physics
The rate of change of magnetic flux density through a circular coil of area 10
\( \mathrm{m} \) and number of turns 100 is \( 10^{3} \mathrm{Wb} / \mathrm{m} \)
2 /s. The value of induced emf will be
\( A \cdot 10^{-2} v \)
B. \( 10^{-3} v \)
\( c \cdot 10 v \)
\( D \cdot 10^{6} v \)
Subject: Chemistry
Which is not correct order for the
properties specified?
\( \mathbf{A} \cdot I>B r>C l>F \) (oxidising character)
B . \( K>M g>A l>B \) (metallic character)
C \( . L i<B<B e<C<O<N<F<N e \) (first
ionisation enthalpy)
D. None of these
Subject: Maths
Which of the following is a quadratic
equation?
\( \mathbf{A} \cdot x^{\frac{1}{2}}+2 x+3=0 \)
B. \( \left(x^{2}-1\right)(x+4)=x^{2}+1 \)
C \( \cdot x^{2}-3 x+5=0 \)
D. \( \left(2 x^{2}+1\right)(3 x-4)=6 x^{2}+3 \)
Subject: Physics
A flywheel is in the form of a uniform circular disc of radius \( 1 \mathrm{m} \) and mass 2
kg. The work which must be done on it to increase its frequency of rotation from 5 rev / \( s \) to 10 rev / s is
approximately
A \( \cdot 1.5 \times 10^{2} J \)
B. \( 3.0 \times 10^{2} J \)
c. \( 1.5 \times 10^{3} J \)
D. \( 3.0 \times 10^{3} J \)
Subject: Physics
The unit of rate constant for a zero order
reaction is:
A \( \cdot s^{-1} \)
B. \( m o l L^{-1} s^{-1} \)
c. \( L m o l^{-1} s^{-1} \)
D. \( L^{2} m o l^{-2} s^{-1} \)
Subject: Physics
Match the Following:
\begin{tabular}{lll|l} 
& Column - I & & Column \\
& & -II \\
A & Weight & p & Scalar \\
B & Mass & q & Vector \\
C & Force & r & kilogram \\
D & Quantity of matter in a body & s & Kgwt (or) kgf
\end{tabular}
\( A \cdot A-q, s ; B-p, r ; C-q, s ; D-p, r \)
B. A-r,s; B-p,q; C-q,s; D-p,r
C. \( A-q, s ; B-p, r ; C-q, r ; D-p, s \)
D. A-q,s; B-p,s; C-q,r; D-p,
Subject: Maths
\( \operatorname{Let} \boldsymbol{S}= \)
\( \left\{\frac{a^{2}+b^{2}+c^{2}}{a b+b c+c a}: a, b, c \epsilon R, a b+b c+c a\right. \)
where \( R \) is the set of real numbers. Then S equals.
A \( \cdot(-\infty,-1] \cup[1, \infty) \)
В . \( (-\infty, 0) \cup(0, \infty) \)
c. \( (-\infty,-1] \cup[2, \infty) \)
D \( \cdot(-\infty,-2] \cup[1, \infty) \)
Subject: Physics
An electron is moving with a speed of \( 10^{3} m / s \) in a straight line enters a
magnetic field where it experiences a
constant acceleration of \( 500 m / s^{2} \) in a direction opposite to its motion. The electron will come back to its initial
point after a time.
\( \mathbf{A} \cdot 2 \mathbf{s} \)
B. 4 s
c. \( 1 \mathrm{s} \)
D. 3s
Subject: Chemistry
Hybridization is the chemist's attempt to explain the observed molecular shape by constructing hybridized atomic orbitals with the appropriate
inter orbital angles. The molecule for
which deviation from a normal bond
angle is observed, \( V S E P R \) theory suggests electron pair repulsive interaction \( (l p-l p>l p-b p>b p) \)
While from hybridization point of view that is a departure from normal hybridization because the angle between any equivalent hybrid orbitals determines the fraction of \( s \) and \( p \)
characters of the hybrid and vice-versa. In which species number of lone pairs on iodine and number of d-orbitals used
in hybridization by iodine are the same?
A \( \cdot I C l_{2}^{+} \)
в. \( I C l_{2} \)
\( \mathrm{c} \cdot I F_{7} \)
D. \( I C l_{4} \)
Subject: Chemistry
The sodium salt of a certain weak
monobasic organic acid is hydrolysed
to an extent of \( 3 \% \) in its \( 0.1 ~ M \) solution
at \( 25^{0} C . \) Given that the ionic product of
water is \( 10^{-14} \) at this temperature,
what is the dissociation constant of the
acid?
A. \( \approx 1 \times 10^{-10} \)
0
В \( \cdot \approx 1 \times 10^{-9} \)
c. \( 3.33 \times 10^{-9} \)
D. \( 3.33 \times 10^{-10} \)
Subject: Physics
Assertion: A current flows in a
conductor only when there is an electric field within the conductor.

Reason : The drift velocity of electron in presence of electric field decreases.
A. Both (A) and (R) are true and
(R) is the correct explanation of
B. Both (A) and (R) are true but (R) is not the correct explanation of A
c. (A) is true but (R) is false
D. (A) is false but (R) is true
Subject: Maths
Let \( ^{*} \) be a binary operation on the set \( \boldsymbol{Q} \)
of rational numbers as follows:
\( \boldsymbol{a} * \boldsymbol{b}=\boldsymbol{a}^{2}+\boldsymbol{b}^{2} \)
Find which of the binary operations are commutative and which are
associative.
Subject: Maths
If \( z(1+a)=b+i c \) and \( a^{2}+b^{2}+c^{2}= \)
1, then \( \frac{1+i z}{1-i z}= \)
A \( \cdot \frac{a+i b}{1+c} \)
в. \( \frac{b-i c}{1+a} \)
c. \( \frac{a+i c}{1+b} \)
D. None of these
Subject: Physics
A ray of light travelling in the direction \( \frac{1}{2}(\hat{i}+\sqrt{3} \hat{j}) \) is incident on a plane mirror. After reflection, it travels along the direction \( \frac{1}{2}(\hat{i}-\sqrt{3} \hat{j}) . \) The angle of
incidence is \( 30^{\circ} \)
A. True
B. False
Subject: Biology
Which of the following statement(s)
is/are true?
This question has multiple correct options
A. The apoplastic movement of water occurs exclusively through the cell wall without crossing any membranes
B. Solutes present in a cell (or in any solution) increase the free energy of water or water potential.
C. The symplastic movements occurs from cell to cell through the plasmodesmata.
D. Membrane permeability depends on the membrane composition, as well as the chemical nature of the solute.
Subject: Physics
A current of \( 10 A \) is maintained in a
conductor of cross-section \( 1 \mathrm{cm}^{2} \). If the
number density of free electrons be \( 9 \times 10^{28} m^{-3}, \) the drift velocity of free
electrons is
A. \( 6.94 \times 10^{-6} \mathrm{m} / \mathrm{s} \)
B. \( 5.94 \times 10^{-2} \mathrm{m} / \mathrm{s} \)
c. \( 1.94 \times 10^{-3} \mathrm{m} / \mathrm{s} \)
D. \( 2.94 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
The number of \( S \) -S bonds in polythionic
\( \operatorname{acid}\left(\boldsymbol{H}_{2} \boldsymbol{S}_{n} \boldsymbol{O}_{6}\right) \)
\( A \cdot n \)
B. \( n-1 \)
c. \( n-2 \)
D. None of these
Subject: Physics
A \( 100 m \) long train at \( 15 m / s \) overtakes a man running on the platform in the same direction in \( 10 s . \) How long the
train will take top cross the man if he
was running in the opposite direaction?
A . \( 7 s \)
B. 5 s
\( c .3 s \)
D. \( 1 s \)
Subject: Maths
\( |\mathfrak{f}| \overline{\boldsymbol{a}}|=\mathbf{2},| \overline{\boldsymbol{b}} \mid=\mathbf{5} \) and \( |\overline{\boldsymbol{a}} \times \overline{\boldsymbol{b}}|=\mathbf{8}, \) then
\( |\bar{a} \cdot \bar{b}| \) is equal to
Subject: Physics
Assertion
Echo is produced only when sound is incident on hard and polished surface
Reason

Sound energy can be totally reflected by objects with soft and loose texture
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