AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be such that \( \boldsymbol{f}(\boldsymbol{2} \boldsymbol{x}- \)
1) \( =f(x) \) for all \( x \epsilon R \) fif \( f \) is continuous
\( \operatorname{at} x=1 \) and \( f(1)=1, \) then
This question has multiple correct options
A. \( f(2)=1 \)
B. \( f(2)=2 \)
c. \( f \) is continuous only at \( x=1 \)
D. \( f \) is continuous at all points
Subject: Chemistry
For the cell \( Z n(s)\left|Z n^{2+}\right|\left|C u^{2+}\right| C u(s) \)
the standard cell voltage, \( \boldsymbol{E}_{c e l l}^{\ominus} \) is \( 1.10 \mathrm{V} \) When a cell using these reagents was prepared in the lab, the measured cell voltage was \( 0.98 \mathrm{V} \). One possible explanation for the observed voltage is :
A. There were 2.00 mol of \( Z n^{2+} \) but only 1.00 mol of \( C u^{2} \)
B. The Zn electrode had twice the surface of the cu electrode
C. The \( \left[Z n^{2+}\right] \) was larger than the \( \left[C u^{2+}\right] \)
D. The volume of the \( \left[Z n^{2+}\right] \) solution was larger than the volume of the \( C u^{2+} \) solution
Subject: Physics
Unpolarised light is passed through a
polaroid \( P_{1} \).When this polarised beam
passes through another polaroid \( P_{2} \) and
if the pass axis of \( P_{2} \) makes angle \( \theta \)
with the pass axis of \( P_{1} \). then write the
intensity when \( \theta \) varies from 0 to \( 2 \pi \)
Subject: Chemistry
Ammonia is a weak base that reacts
with water according to the equation:
\( N H_{3}(a q)+2 H_{2} O(l) \quad \rightleftharpoons \)
\( N H_{4}^{+}(a q)+O H^{-}(a q) \)
Which of the following conditions will decrease the moles of ammonium in
water?
This question has multiple correct options
A. Addition of \( H C l \)
B. Addition of \( N a O H \)
c. Addtion of \( N H_{4} C l \)
D. Addition of \( H_{2} O \)
Subject: Physics
A particle tied to a string of negligible
weight and length \( L \) is rotated in a horizontal circular path with constant angular velocity having time period \( T . \) If
the string length is shortened by \( L / 2 \)
while the particle is in motion, the time
period is:
A . 47
в. 27
c. \( T / 2 \)
D. \( T / 4 \)
Subject: Maths
\( \int 32 x^{3}(\log x)^{2} d x \) is equal to
\( \mathbf{A} \cdot 8 x^{4}(\log x)^{2}+c \)
B . \( x^{4}\left\{8(\log x)^{2}-4 \log x+1\right\}+c \)
C. \( x^{4}\left\{8(\log x)^{2}-4 \log x\right\}+c \)
D. \( x^{3}\left\{(\log x)^{2}+2 \log x\right\}+c \)
Subject: Maths
One of the two boxes, box \( \boldsymbol{I} \) and box \( \boldsymbol{I} \boldsymbol{I} \)
was selected at random and balls are
drawn randomly out of this box. The ball was found to be red.If the probability
that this red ball was drawn from box \( I I \)
is \( \frac{1}{3}, \) then the correct option options
with the possible values of \( n_{1}, n_{2}, n_{3} \)
and \( n_{4} \) is (are)
This question has multiple correct options
\( \mathbf{A} \cdot n_{1}=3, n_{2}=3, n_{3}=5, n_{4}=15 \)
B . \( n_{1}=3, n_{2}=6, n_{3}=10, n_{4}=50 \)
C \( . n_{1}=8, n_{2}=6, n_{3}=5, n_{4}=20 \)
D \( \cdot n_{1}=6, n_{2}=12, n_{3}=5, n_{4}=20 \)
Subject: Physics
What is the nature of relation
betweenthe kinetic energy \( \left(\mathbf{E}_{\mathbf{k}}\right) \) and
their orbitalradius (r) of the satellites revolvingaround the Earth?
\( \mathbf{A} \cdot E_{k} \propto 1 \)
B . \( E_{k} \propto \frac{1}{r} \)
\( \mathrm{c} \cdot E_{k} \propto r^{2} \)
D. \( E_{k} \propto \frac{1}{r^{2}} \)
Subject: Physics
The loop shown moves with a velocity \( v \)
in a uniform magnetic field of
magnitude \( B \), directed into the paper. The potential difference between points
\( P \) and \( Q \) is \( e . \) Then
This question has multiple correct options
B. \( e=B l v \)
C. \( P \) is positive with respect to \( Q \)
D. \( Q \) is positive with respect to \( P \)
Subject: Chemistry
Calculate the internal energy at \( 298 \mathrm{K} \)
for the formation of one mole of
ammonia, if the enthalpy change at
constant pressure is \( -42.0 \mathrm{kJ} \) mol\( ^{-1} \)
\( \left[\text { Given: } \boldsymbol{R}=\mathbf{8 . 3 1 4} \mathbf{J} \boldsymbol{K}^{-\mathbf{1}} \boldsymbol{m o l}^{-1}\right] \)
Subject: Maths
If the middle term of \( \left(x+\frac{1}{x} \sin ^{-1} x\right)^{8} \)
is \( \frac{35 \pi^{4}}{8}, \) then value of \( x \) can be
A \( \cdot \frac{1}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D.
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \frac{\boldsymbol{H C l}}{\boldsymbol{Z n C l}_{2}} \)
Product
Find the correct statement.
This question has multiple correct options
A. Reaction is \( S_{N} 1 \), if higher concentration of \( Z n C l_{2} \) is used
B. Reaction is \( S_{N} 2 \), if higher concentration of \( Z n C l_{2} \) is used
c. Rearranged the product if higher concentration of \( Z n C l_{2} \) is used.
D. All of the above
Subject: Maths
f \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} \forall \boldsymbol{x} \in[\mathbf{0}, \boldsymbol{x} / 2], \boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{f}(\boldsymbol{\pi}-\boldsymbol{x})=\boldsymbol{2} \forall \boldsymbol{x} \in[\boldsymbol{x} / 2, \boldsymbol{\pi}] \) and
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{2} \boldsymbol{\pi}-\boldsymbol{x}) \forall \boldsymbol{x} \in[\boldsymbol{\pi}, \boldsymbol{2} \boldsymbol{\pi}] \) then
find the area bounded by \( y=f(x) \) and
the \( x- \) axis.
Subject: Maths
If \( |\overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}}|=\overrightarrow{\boldsymbol{A}} \cdot \overrightarrow{\boldsymbol{B}}, \) then \( |\overrightarrow{\boldsymbol{A}}+\overrightarrow{\boldsymbol{B}}| \) is:
\( \mathbf{A} \cdot|\vec{A}|+|\vec{B}| \)
B. \( \sqrt{|\vec{A}|^{2}+|\vec{B}|^{2}} \)
\( ^{\mathrm{c}} \cdot \sqrt{|\vec{A}|^{2}+|\vec{B}|^{2}+\frac{|\vec{A}||\vec{B}|}{\sqrt{2}}} \)
D \cdot \( \sqrt{|\vec{A}|^{2}+|\vec{B}|^{2}+\sqrt{2}|\vec{A}||\vec{B}|} \)
Subject: Chemistry
Which is correct about \( \Delta G ? \)
This question has multiple correct options
\( \mathbf{A} \cdot \Delta G=\Delta H-T \Delta G \)
B. at equilibrium, \( \Delta G^{\ominus}=0 \)
C . at equilibrium \( \Delta G=-R T l o g K \)
\( \mathbf{D} \cdot \Delta G=\Delta G^{\ominus}+R T \log K \)
Subject: Physics
A person moves \( 30 \mathrm{m} \) North and then \( 20 \mathrm{m} \) towards East and finally \( 30 \sqrt{2} \mathrm{m} \) in South-West direction. The
displacement of the person from the origin will be
A. \( 10 \mathrm{m} \) along North
B. \( 10 \mathrm{m} \) along south
c. \( 10 \mathrm{m} \) along west
D. zero
Subject: Maths
Solve the differential equation:
\( \left(x^{2}-1\right) \frac{d y}{d x}+2(x+2) y=2(x+1) \)
\( \frac{y(x+1)^{3}}{x+1}=\left\{\frac{(x+1)^{2}}{2}-4(x+1)+4 \log (x+1)\right\}+c \)
\( \frac{y(x-1)^{3}}{x+1}=\left\{\frac{(x+1)^{2}}{2}-4(x+1)+4 \log (x+1)\right\}+c \)
\( \frac{y(x-1)^{3}}{x-1}=\left\{\frac{(x+1)^{2}}{2}-4(x+1)+4 \log (x+1)\right\}+c \)
D. None of these
Subject: Maths
If \( \overline{D A}=\bar{a} ; \overline{A B}=\bar{b} \) and \( \overline{C B}=k \bar{a} \)
where \( k>0 \) and \( x, y \) are the midpoints
of \( D B \) and \( A C \) respectively such that \( |\overline{\boldsymbol{a}}|=\mathbf{1 7} \) and \( |\overline{\boldsymbol{X}} \boldsymbol{Y}|=\mathbf{4}, \) then \( \mathbf{k}= \)
A. \( \frac{8}{17} \)
в. \( \frac{9}{17} \)
c. \( \frac{11}{17} \)
D. \( \frac{4}{17} \)
Subject: Physics
A monochromatic beam of light is used for the formation of fringes on the screen by illuminating the two slits in the Youngs double-slit interference
experiment. When a thin film of mica is interposed in the path of the interference beams, then
A. The fringe width increases
B. The fringe width decreases
c. The fringe width remains the same but the pattern shifts
D. The fringe pattern disappears
Subject: Physics
You spin a globe at 2.5 rads/sec and
then give it a push to speed it up to 3 rads/ sec. If it takes 0.2 secs to change the speed of the globe, what is the
angular acceleration in \( r a d / s e c^{2} ? \)
A . 2.5
B. 3
\( c \cdot 5 \)
D. 10
Subject: Maths
Evaluate the integral \( \int_{-3}^{3} \log (\sqrt{x^{2}+1}+x) d x= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \log 2 \)
c. \( -\log 2 \)
D. \( 2 \log 2 \)
Subject: Chemistry
In Rutherford's \( \alpha \) -particle scattering
experiment, a very small fraction of \( \alpha \)
particles were deflected by \( 180^{\circ} . \) What did the conclude from this observation?
A. All the positive charge and mass of the atom occupy very little space.
B. Most of the space inside the atom is empty
c. All the positive charge and mass of the atom were concentrated in a very small volume.
D. Both A and B
Subject: Physics
Calculate energy needed for moving a mass of \( 4 k g \) from the centre of the earth
to its surface (in joule). If radius of the
earth is \( 6400 \mathrm{km} \) and acceleration due
to gravity at the surface of the earth is
\( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s e c ^ { 2 }} \)
A \( \cdot 1.28 \times 10^{8} J \)
в. \( 1.28 \times 10^{6} J \)
c. \( 2.56 \times 10^{8} J \)
D. \( 2.56 \times 10^{1} 0 J \)
Subject: Chemistry
Out of the following ores, how many ores
do not contain more than one metal in
their composition. Argentite, Barytes, Magnesite, Fluorspar, Carnalite, Dolomite, Chalcocite, Asbestos, Calamine.
\( A \cdot 6 \)
B. 4
\( c \cdot 5 \)
\( D \)
Subject: Maths
If the perpendicular distance of a point
\( P \) from the \( X \) -axis is 5 units and the
foot of the perpendicular lies on the
negative direction of \( X \) -axis, then the
point \( \boldsymbol{P} \) has
A. \( X \) -coordinate \( =-5 \)
B. Y-coordinate = - 5
c. \( Y \) -coordinate \( =-5 \) only
D. \( Y \) -coordinate \( =5 \) or -5
Subject: Chemistry
Which selection is an example of a combustion reaction?
A \( \cdot 2 K+F_{2} \rightarrow 2 K F \)
в. \( 2 A l+6 H C l \rightarrow 2 A l C l_{3}+3 H_{2} \)
c. \( C_{3} H_{8}+5 O_{2} \rightarrow 3 C O_{2}+4 H_{2} O \)
D. \( N a C l+A g N O_{3} \rightarrow A g C l+N a N O_{3} \)
Subject: Physics
Complete the following statements with an appropriate word /term be filled in the blank space(s).

The equivalent capacitance \( C \) for the parallel combination of three
capacitance \( C_{1}, C_{2} \) and \( C_{3} \) is given by
\( C=\dots \)
A \( \cdot C_{1}+C_{2}+C_{3} \)
B. \( \frac{1}{C_{1}+C_{2}+C_{3}} \)
\( ^{c}\left(\frac{1}{\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}}\right) \)
\( ^{\mathrm{D}} \cdot\left(\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}\right) \)
Subject: Physics
A fighter plane is flying horizontally at an altitude of \( 1.5 \mathrm{km} \) with speed 720
\( \mathrm{km} / \mathrm{h} . \) At what angle of sight (w.r.t. horizontal) when the target is seen should the pilot drop the bomb in order
to attack the target than?
A \( \cdot 23^{\circ} 4^{\prime} \)
B . \( 43^{\circ} 4^{\prime} \)
c. \( 33^{\circ} 4^{\prime} \)
D. \( 53^{\circ} 4^{\prime} \)
Subject: Physics
A particle executing simple harmonic motion has an angular frequency of \( 6.28 s^{-1} \) and an amplitude of \( 10 \mathrm{cm}, \) the speed when the displacement is \( 6 \mathrm{cm} \) from the mean position is:
A. \( 50.2 \mathrm{cm} / \mathrm{s} \)
в. \( 60.2 \mathrm{cm} / \mathrm{s} \)
c. \( 70.2 \mathrm{cm} / \mathrm{s} \)
D. \( 80.2 \mathrm{cm} / \mathrm{s} \)
Subject: Physics
Assertion
It is not possible for a system unaided
by an external agency to transfer heat
from a body at lower temperature to
another at a higher temperature.
Reason
It is not possible to violate the 2 nd law
of thermodynamics.
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
Five charges of equal values placed at
corners of a regular pentagon of side 'a'.
The force on \( q_{0} \) which is placed at
centroid 'O' is?
A. zero
B. \( \frac{2 k Q q \text { , along OE }}{r_{2}}, \) E
C. \( \frac{2 k Q q \text { , along }}{r_{2}} \) EO
\( \mathbf{D} \cdot \frac{k Q_{q 0}}{r_{2}}, \) along OE
Subject: Maths
A student noted that the number of cars
passing through the spot on the road for 200 periods each of 10 minutes and
summarized in a table given below. Find
the mode of the data.
Number \( \begin{array}{ll}5- & 1 \\ 10 & 1\end{array} \)
\( \mathbf{n} \)
5
\( 20- \)
of cars 15 20 25
frequency 12 1. If 24 \( 15 \quad 10 \)
A . 15.5
B. 20.50
c. 25.45
D. 19.4
Subject: Physics
Consider two satellites \( A \) and \( B \) of equal
mass \( \mathrm{m}, \) moving in the same circular
orbit about the earth, but in the
opposite sense as shown in Figure. The orbital radius is \( r \). The satellites
undergo a collision which is perfectly
inelastic. For this situation, mark out
the correct statement(s). [Take mass of
earth as \( \mathrm{M}] \)
(6)
A. The satellites starts falling towards center of the earth.
B. The total energy of the two satellites plus earth system just after collision is \( -2(G M m) / r \)
C. The total energy of two satellites plus earth system just after collision is \( -(G M m) / 2 r \)
D. The combined mass(two satellites) will fall towards the earth just after collision.
Subject: Chemistry
A compound contains equal masses of
the elements \( A, B \) and \( C . \) If the atomic
masses of \( A, B \) and \( C \) are 20,40 and 60
respectively, the empirical formula of the compound is
A \( . A_{3} B_{2} C \)
в. \( A B_{2} C_{3} \)
c. \( A B C \)
D. \( A_{6} B_{3} C_{2} \)
Subject: Physics
The operating temperature of the filament of lamp is \( 2000^{\circ} \mathrm{C} \). The temperature coefficient of the material
of filament is \( 0.005 /^{\circ} \mathrm{C} \). If the
atmospheric temperature be \( 0^{\circ} C, \) the current in the \( 100 \mathrm{W} \) and \( 2000 \mathrm{V} \) lamp when it is switched on its nearest to:
A. 2.5
B. 0.05 A
c. 4.5 A
D. \( 5.5 \mathrm{A} \)
Subject: Chemistry
Which is not correct about
monosaccharides?
This question has multiple correct options
A. Optically active polyhydroxy carbonyl compounds.
B. Fructose \& glucose can not be distinguish by \( B r_{2} / H_{2} O \)
c. Glucose and mannose are anomers.
D. Fructose \& glucose can be distuinguish by Fehling's solution
Subject: Maths
Range of the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}} \) is
\( A \cdot(-\infty, \infty) \)
В \cdot [-1,1]
\( c \cdot\left[-\frac{1}{2}, \frac{1}{2}\right] \)
D. \( [-\sqrt{2}, \sqrt{2}] \)
Subject: Chemistry
Among the following, identify the species with an atom in +6 oxidation
state
A. \( M n O_{4}^{\text {ह }} \)
В \( \cdot\left[C r(C N)_{6}\right]^{3-} \)
\( \mathbf{c} \cdot\left[N i F_{6}\right]^{2-} \)
D. \( \operatorname{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)
Subject: Physics
Water flows through the tube as shown
in figure. The areas of cross-section
of the wide and the narrow portions of
the tube are \( 5 c m^{2} \) and \( 2 c m^{2} \)
respectively. The rate of flow of water
through the tube is \( 500 \mathrm{cm}^{3} / \mathrm{s} \). Find the
difference of mercury levels in the U-
tube.
Subject: Maths
If \( \cos ^{-1}\left(\frac{1}{x}\right)=\theta \) then the value of \( \tan \theta \)
is
A \( \cdot \frac{1}{\sqrt{x^{2}-1}} \)
B. \( \sqrt{x^{2}-1} \)
c. \( \sqrt{1-x^{2}} \)
D. \( \sqrt{1+x^{2}} \)
Subject: Chemistry
Which of the following reactions will not
have fractional order for \( \boldsymbol{A}_{2} \) or \( \boldsymbol{B}_{2} ? \)
\( \mathbf{A} \cdot A_{2} \rightleftharpoons A+A(\text { fast }) \)
\[
\begin{array}{l}
A+B_{2} \rightleftharpoons A B+B \text { (slow) } \\
A+B \rightleftharpoons A B \text { (fast) }
\end{array}
\]
B \( \cdot A_{2} \rightleftharpoons C \) (slow)
\[
C+B_{2} \rightleftharpoons D \text { (fast) }
\]
\[
D+A_{2} \rightleftharpoons \text { Product }
\]
C. \( B_{2} \rightleftharpoons B+B \) (fast)
\[
\begin{array}{l}
A_{2}+B \rightleftharpoons A B+A \text { (slow) } \\
A B \longrightarrow \text { Products (fast) }
\end{array}
\]
D. None of the above
Subject: Chemistry
The \( C l-C-C l \) angle in \( 1,1,2,2- \)
tetrachloroethene and
tetrachloromethane will be about.
A \( \cdot 90^{\circ} \) and \( 109.5^{\circ} \)
B . \( 109.5^{\circ} \) and \( 90^{\circ} \)
C. \( 109.5^{\circ} \) and \( 120^{\circ} \)
D. \( 120^{\circ} \) and \( 109.5^{\circ} \)
Subject: Chemistry
Variation of \( \log _{10} K \) with \( \frac{1}{T} \) is shown by
the following graph in which straight
line is at \( 45^{\circ}, \) hence \( \Delta H \) is :
A \( .+4.606 \) cal
B . -4.606 ca
\( c .+2 \) cal
D. \( -2 \mathrm{ca} \)
Subject: Physics
Total mechanical energy \( \boldsymbol{E} \) of an object
of mass \( m \), at a height \( h \) above the
ground is given by the relation \( \boldsymbol{E}=\boldsymbol{m} \boldsymbol{g} \boldsymbol{h}+\frac{\boldsymbol{p}^{2}}{2 \boldsymbol{m}} \)
Find the dimension of \( \mathrm{p} .(g= \) acceleration due to gravity)
Subject: Physics
The water can be made to boil even at 0
if the pressure of surrounding is:
\( A .56 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. \( 5 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 0.1 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 4.6 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Chemistry
Assertion
Heat of hydrogenation of \( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \)
is greater than \( \boldsymbol{C H}_{3} \boldsymbol{C H}=\boldsymbol{C H}_{2} \)
Reason
\( C H_{3} \) give additional effect to double
bond
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
The flux linked with a coil at any instant
\( \mathrm{t}^{\prime} \) is given by \( \phi=10 t^{2}-50 t+250 . \) The
induced emf at \( t=3 s \) is
A . -190
B. -10 V
\( c \cdot 10 v \)
D. 190 V
Subject: Chemistry
Select correct statements about the
given reaction?
A. In the conversion of (C) to (D) attacking reagent is electron deficient.
B. If \( C C l_{4} \) is used in the reaction instead of \( C H C l_{3} \), the
product is soluble in \( N a H C O_{3} \) solution.
\( c \)
\[
\text { Product }(\mathrm{D}) \frac{\mathrm{AC}_{2} \mathrm{O}}{\mathrm{ACONa}} \rightarrow \stackrel{\mathrm{H}+}{\longrightarrow} \square
\]
D. Conversion of (B) to (C) is electrophilic aromatic substitution reaction
Subject: Maths
The value of \( [\sin x]+[1+\sin x]+2+ \)
\( [\sin x]+3+[\sin x] \) in \( \left(\pi, \frac{3 \pi}{2}\right] \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
\( c \cdot 2 \)
D. 3
Subject: Chemistry
For \( M^{2+} / M \) and \( M^{3+} / M^{2+} \) systems the \( E^{\ominus} \) values for some metals are as follows:
\( C r^{3} / C r^{2+} \)
\( \boldsymbol{C r}^{2+} / \boldsymbol{C r} \quad_{\boldsymbol{\$}}^{-\boldsymbol{0 . 9} \boldsymbol{V}} \)
\( / M n \quad-1.2 V \) \( M n^{3+} \) \( M n^{2+} \) \( / M n^{2+} \)
\( -0.4 V \)
\( F e^{3+} / F e^{2+} \)
Use this data to comment upon:
(i) the stability of \( F e^{3+} \) in acid solution
as compared to that of \( C r^{3+} \) or \( M n^{3+} \)
and
(ii) the ease with which iron can be
oxidised as compared to a similar process for either chromium or
manganese metal
Subject: Maths
Which of the following statements are
true for the function \( f(x) \) defined for
\( -1 \leq x \leq 3 \) in the figure shown?
This question has multiple correct options
A. \( \lim _{x \rightarrow-1^{+}} f(X)=1 \)
B. \( \lim _{x \rightarrow 2} f(X) \) does not exist
\( \mathbf{c} \cdot \lim _{x \rightarrow 1^{-}} f(X)=2 \)
D. \( \lim _{x \rightarrow 0^{+}} f(X)=\lim _{x \rightarrow 0^{-}} f(X) \)
Subject: Maths
Solve for \( x \) and \( y, \) if \( \left(\begin{array}{l}x^{2} \\ y^{2}\end{array}\right)+3\left(\begin{array}{c}2 x \\ -y\end{array}\right)= \)
\( \left(\begin{array}{c}-\mathbf{9} \\ \mathbf{4}\end{array}\right) \)
Subject: Maths
Let \( S \) be non-empty subset of \( \boldsymbol{R} \) then consider the following statement "Every number \( x \in S \) is an even
number."

Negation of the statement will be
A. There is no number \( x \in S \) which is even
B. There exists a number \( x \in S \) which is not even
C. There exists a number \( x \in S \) which is odd
D. \( (B) \) and \( (C) \) both
Subject: Maths
\( \mathrm{ff} \mathrm{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{0} \\ \mathbf{4} & \mathbf{1}\end{array}\right] \) and \( \mathrm{B}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{3} & \mathbf{1}\end{array}\right] \) find
BA. Can we find AB also?
Subject: Physics
Two parallel straight conductors carrying currents 5A each repel other
with a force of \( 25 \times 10^{-5} N m^{-1} . \) The
distance between the conductors is
A. \( 4 \mathrm{cm} \)
B. \( 0.4 \mathrm{cm} \)
\( c \cdot 2 \mathrm{cm} \)
D. \( 0.2 \mathrm{cm} \)
Subject: Physics
Two balls of equal mass are projected from a tower simultaneously with equal speeds. One at angle \( \theta \) above the
horizontal and the other at the same
angle \( \theta \) below the horizontal. The path of
the centre of mass of the two balls is
A. a vertical straight line
B. a horizontal straight line
c. a straight line at angle \( \alpha(<\theta) \) with horizontal
D. a parabola
Subject: Chemistry
Column 1
A) \( \wedge^{0}_{m}\left(N a N O_{3}\right) \)
(P) Can be
obtained by Kohlraush law
B) \( \wedge^{0}_{m} \)
(Q) Can be
obtained by
\( \left(\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C O O H}\right) \quad \) extrapolating
\( \wedge^{0} m \) vs
\( (\text {Molarity})^{1 / 2} \)
graph to zero molarity.
C) Ilonic conductance
(R) Contribution
by the ion to \( \wedge^{0}_{m} \)
D) \( \wedge^{0}_{m} \) of \( C H_{3} C O O H \)
(S) increases on
dilution
A. A-P,R: B-Q,S:C-S:D-S
B. A-P,Q: B-P,S:C-S:D-P,S
c. A-R: B-Q:C-R,S:D-P,Q
D a c. B-Q.R:C-P:D-Q
Subject: Physics
a parallel glass slab at a point \( A, \) as
shown in the given figure. It undergoes partial reflection and
refraction. At each reflection \( 25 \% \) of
incident energy is reflected. The rays
\( A B \) and \( A^{\prime} B^{\prime} \) undergo interference. The
1 max ratio \( \frac{\text { nunce is }}{\text { : }} \) is \( \boldsymbol{I}_{m i} \)
\( A \cdot 4: 1 \)
B. 8: 1
c. 7:
29
Subject: Chemistry
Which of the following is incorrect
statement?
A. The heats of hydration of the dipositive alkaline earth metal ions decrease with an increase in their ionic size
B. \( N a N O_{3} \) forms \( N a_{2} O \) on heating
C. Hydration energy of alkali metal ion is less than that of II \( A \)
D. Alkaline earth metal ions, because of their much large charge to size ratio, exert a much stronger electrostatic attraction on the oxygen of water molecule surrounding them
Subject: Chemistry
The number of sigma and pi bonds in benzene are:
\( \mathbf{A} \cdot 6 \sigma \) and \( 3 \pi \)
B. \( 12 \sigma \) and \( 3 \pi \)
\( \mathbf{c} \cdot 9 \sigma \) and \( 3 \pi \)
D. \( 6 \sigma \) and \( 6 \pi \)
Subject: Physics
In R-L-C series circuit, the potential differences across each element is \( 20 V \)
Now the value of the resistance alone is
doubled, then P.D. across \( \mathrm{R} \), L and \( \mathrm{C} \)
respectively.
A. \( 20 V, 10 V, 10 V \)
В. \( 20 V, 20 V, 20 V \)
c. \( 20 V, 40 V, 40 V \)
D. \( 10 V, 20 V, 20 V \)
Subject: Chemistry
For a sparingle soluble salt \( A_{p} B_{q} \). the relationship of its solubility product
\( \left(L_{s}\right) \) with its solubility (S) is:
A \( \cdot L_{s}=S^{p+q} p^{p} q^{q} \)
B \( \cdot L_{s}=S^{p+q} p^{q} q^{p} \)
c. \( L_{s}=S^{p q} p^{p} q^{q} \)
D. \( L_{s}=S^{p q}(p q)^{p+q} \)
Subject: Chemistry
Statement 1: Two isotopes of the same
element have the same mass number
Statement 2: Isotopes have the same number of protons.
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 Statement 1 and Statement 2 are not correct.