AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1} /\left(\mathbf{1}-\boldsymbol{e}^{-\mathbf{1} / \boldsymbol{x}}\right), \boldsymbol{x} \neq \mathbf{0}, \boldsymbol{f}(\mathbf{0})= \)
0 at \( x=0 \) Is function continuous at
\( x=0 ? \)
Subject: Chemistry
A system is taken along paths \( A \) and \( B \) as shown. If amounts of heat given in these processes are respectively \( Q A \) and
\( \mathrm{QB}, \) then:
A \( \cdot \mathrm{QA}=\mathrm{Q} \)
B. QA>QB
c. \( Q B<Q A \)
D. none of these
Subject: Maths
In a building there are 24 cylindrical pillars. The radius of each pillar is
\( 28 \mathrm{cm} \) and height is \( 4 \mathrm{cm} . \) Find the total
\( \operatorname{cost} \) of painting the curved surface area of all pillars at the rate of \( R s .8 \) per \( m^{2} \)
Subject: Chemistry
Which of the following is/are redox reactions?
This question has multiple correct options
A. \( B a O_{2}+H_{2} S O_{4} \rightarrow B a S O_{4}+H_{2} O_{2} \)
в. \( 2 B a O+O_{2} \rightarrow 2 B a O_{2} \)
\( \mathbf{c} \cdot 2 K C I O_{3} \rightarrow 2 K C l+3 O_{2} \)
D. \( S O_{2}+2 H_{2} S \rightarrow 2 H_{2} O+3 S \)
Subject: Maths
\( \int \frac{x^{2}-8 x+7}{\left(x^{2}-3 x-10\right)^{2}} d x= \)
\( \boldsymbol{P} \log |\boldsymbol{x}-\mathbf{5}|+\boldsymbol{Q} \frac{\mathbf{1}}{\boldsymbol{x}-\mathbf{5}}- \)
\( \boldsymbol{R} \cdot \log |\boldsymbol{x}+\mathbf{2}|-\boldsymbol{S} \cdot \frac{\mathbf{1}}{\boldsymbol{x}+\mathbf{2}}+\boldsymbol{c} . \) Then
A \( \cdot P=-\frac{45}{98} \)
в. \( Q=\frac{8}{49} \)
\( c \cdot R=\frac{15}{49} \)
D. All of these
Subject: Chemistry
What weight of \( C a C O_{3} \) must be decomposed to produce the sufficient quantity of carbon dioxide to convert
21.2 \( \mathrm{kg} \) of \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) completely into
\( N a H C O_{3} \)
[Atomic mass \( N a=23, C a=40] \)
\( \boldsymbol{C a C O}_{3} \rightarrow \boldsymbol{C a O}+\boldsymbol{C O}_{2} \)
\( \mathbf{N} \boldsymbol{a}_{2} \boldsymbol{C} \boldsymbol{O}_{3}+\boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{H} \boldsymbol{C} \boldsymbol{O}_{3} \)
\( A \cdot 100 \mathrm{kg} \)
B. 20 kg
c. \( 120 \mathrm{kg} \)
D. 30 kg
Subject: Maths
The normals to the curve \( y=x^{2}-x+ \)
1, drawn at the points with the abscissa
\( \boldsymbol{x}_{1}=\mathbf{0}, \boldsymbol{x}_{2}=-\mathbf{1} \) and \( \boldsymbol{x}_{3}=\frac{\mathbf{5}}{\mathbf{2}} \)
A. are parallel to each other
B. are pair wise perpendicular
c. are concurrent
D. are not concurrent
Subject: Physics
Steam is passed into 22 gm of water at \( 20^{\circ} \mathrm{C} . \) The mass of water that will be
present when the water acquires a
temperature of \( 90^{\circ} \mathrm{C} \) (Latent heat of
steam is 540 cal/g j is
A. \( 24.83 \mathrm{gm} \)
B. 24 gm
c. \( 36.6 \mathrm{gm} \)
D. 30 gm
Subject: Physics
During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at
\( 40.0 \mathrm{cm} \) using a standard resistance of
\( 90 \Omega, \) as shown in the figure. The least count of the scale used in the metre
bridge is 1 mm. The unknown
resistance is
A. \( 60 \pm 0.15 \Omega \)
B. \( 135 \pm 0.56 \Omega \)
c. \( 60 \pm 0.25 \Omega \)
D. \( 135 \pm 0.23 \Omega \)
Subject: Physics
An inductive coil has a resistance of 100
When an AC signal of frequency \( 1000 \mathrm{Hz} \) is applied to the coil, the voltage leads
the current by \( 45^{\circ} . \) The inductance of the coil is
A \( \cdot \frac{1}{10 \pi} \)
в. \( \frac{1}{20 \pi} \)
c. \( \frac{1}{40 \pi} \)
D. \( \frac{1}{60 \pi} \)
Subject: Maths
A parallelogram whose sides are \( 10 \mathrm{cm} \) and \( 5 \mathrm{cm} \) has one diagonal of \( 8 \mathrm{cm}, \) then the length of the other diagonal is
\( \mathbf{A} \cdot 12 \mathrm{cm} \)
B. \( 11 \mathrm{cm} \)
\( \mathrm{c} \cdot 14 \mathrm{cm} \)
D. None of these
Subject: Physics
There is a hole in the bottom of tank
having water. If total pressure at bottom
is 3 atm \( \left(1 \text { at } m=10^{5} N / m^{2}\right) \) then the velocity of water flowing from hole is:
\( \mathbf{A} \cdot \sqrt{400} m / s \)
B. \( \sqrt{600} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{60} m / s \)
D. None of these
Subject: Chemistry
In balancing the reaction \( \boldsymbol{x} \boldsymbol{Z} \boldsymbol{n}+ \) \( N O_{3}^{-}+y H^{+} \rightarrow x Z n^{2+}+N H_{4}^{+}+ \)
\( z H_{2} O, x, y \) and \( z \) are respectively:
A .4,10,3
в. 3,8,3
\( \mathrm{c} \cdot 3,10,3 \)
D. 4,3,10
Subject: Maths
Solve:
\( \mid \begin{array}{ccc}x^{2}-1 & x^{2}+2 x+1 & 2 x^{2}+3 x \\ 2 x^{2}+x-1 & 2 x^{2}+5 x-3 & 4 x^{2}+4 x \\ 6 x^{2}-x-2 & 6 x^{2}-7 x+2 & 12 x^{2}-5\end{array} \)
0. Let sum of all values of \( x \) be \( k \). Find
\( -2 k \)
Subject: Maths
Let there be a function \( f(x) \) that is
greater than the cube of \( x \) when
subtracted to the fourth root of the sum
of 2 and square of 2 multiplied with \( x \) Then the function id depicted by
A \( \cdot f(x)<\sqrt[4]{2+4 x^{2}}-x^{3} \)
B . \( f(x)>\sqrt[4]{2+4 x^{2}}-x^{3} \)
C \( \cdot f(x) \geq \sqrt[4]{2+4 x^{2}}-x^{3} \)
D. \( f(x) \leq \sqrt[4]{2+2 x^{2}}-x^{3} \)
Subject: Physics
8
asic
placed at a point \( O . \) The arrows show
the direction of the magnetic moment.
The other arrows show different
positions (and orientations of the
magnetic moment) of another identical
magnetised needle \( Q \). The dotted line
represent a circle centre at the
midpoint of \( \boldsymbol{P} \)
Which configuration in this system
corresponds to stable equilibrium?
\( \mathbf{A} \cdot P Q_{1}, P Q_{3} \)
B. \( P Q_{3}, P Q_{5} \)
\( \mathbf{c} \cdot P Q_{2}, P Q_{4} \)
D. \( P Q_{2}, P Q_{3} \)
Subject: Physics
If we assume only gravitational attraction between proton and electron in hydrogen atom and Bohr's quantization rule to be followed, then the expression for the ground state energy of the atom will be the mass of proton is \( \mathrm{M} \) and that of the electron is
\( m): \)
\( ^{\mathrm{A}} \cdot \frac{G^{2} M^{2} m^{2}}{h^{2}} \)
\( ^{\text {В }} \cdot \frac{2 \pi^{2} G^{2} M^{2} m^{3}}{h^{2}} \)
c. \( \frac{2 \pi^{2} G M^{2} m^{3}}{h^{2}} \)
D. None of these
Subject: Chemistry
A graph of concentration versus time
data for a second-order reaction gives a straight line in which of the following plots of the data?
A \( \cdot[A]_{t}=-k t+[A]_{0} \)
B \( \cdot \ln [A]_{t}=-k t+\ln [A]_{0} \)
c. \( \frac{1}{\left[A_{t}\right]}=k t+\frac{1}{\left[A_{0}\right]} \)
D. All of the above
E. None of the above
Subject: Maths
A chord \( A B \) of circle of radius \( 14 c m \)
makes an angle of \( 60^{\circ} \) at the centre of
the circle .The area of the minor
segment of the circle is \( \left(\text { Use } \pi=\frac{22}{7}\right) \)
A \( \cdot \frac{308}{3} c m^{2} \)
в. \( \frac{208}{3} \mathrm{cm}^{2} \)
c. \( \frac{108}{3} \mathrm{cm}^{2} \)
D. \( \frac{408}{3} \mathrm{cm}^{2} \)
Subject: Physics
A current loop consists of two identical
semicircular parts each of radius \( \mathrm{R} \), one
lying in the \( x \) -y plane and the other in \( x-z \)
plane. If the current in the loop is i. The
resultant magnetic field due to the two
semicircular parts at their common
centre is
A \( \cdot \frac{\mu_{0} i}{2 \sqrt{2} R} \)
B. \( \frac{\mu_{0} i}{2 R} \)
c. \( \frac{\mu_{0} i}{4 R} \)
D. \( \frac{\mu_{0} i}{\sqrt{2} R} \)
Subject: Physics
A bar magnet of magnetic moment \( 2 A m^{2} \) is free to rotate about a vertical axis passing through its center. The magnet is released from rest from east
west position. Then the KE of the magnet as it takes N-S position is
\( \left(B_{H}=25 \mu T\right) \)
A. \( 25 \mu J \)
в. \( 50 \mu J \)
c. \( 100 \mu J \)
D. \( 12.5 \mu J \)
Subject: Maths
A table cover \( 6 m \times 3 m \) is spread on a
table top. If \( 25 \mathrm{cm} \) of the cover hangs all
around the table then the cost of
polishing the table @ Rs \( 12 m^{2} \) is
A . \( R s 165 \)
B. \( R s 175 \)
c. \( R s 180 \)
D. \( R s 195 \)
Subject: Physics
A uniform chain of length \( 2 m \) is kept on
a table such that a length of \( 60 \mathrm{cm} \) hanging freely from the edge of the table. The total mass of the chain is
\( 4 k g . \) The work done is pulling the entire
chain on the table (Take \( \left.g=m s^{-2}\right) \)
A . \( 12.9 J \)
B. \( 6.3 J \)
c. \( 3.6 J \)
D . \( 2.0 J \)
Subject: Physics
The state of an ideal gas was changed
isobarically. The graph depicts three
such isobaric lines. Which of the
following is true about the pressures of
the gas????????
\( A \cdot P_{1}=P_{2}=P_{3} \)
в. \( P_{1}>P_{2}>P_{3} \)
\( c \cdot P_{1}<P_{2}<P_{3} \)
- \( P_{1} / P_{2}=P_{3} / P \)
\( P \)
Subject: Chemistry
Assertion: A solution of sodium acetate
and ammonium acetate can act as a
buffer.

Reason: A buffer solution consists of a
mixture of a weak acid and its
conjugate base or vice versa.
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: Physics
Two non-reactive monoatomic ideal
gases have their atomic masses in the
ratio 2:3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4: 3 The ratio of their densities is
\( A \cdot 1: 4 \)
B. 1: 2
\( c \cdot 6: 9 \)
D. 8: 9
Subject: Chemistry
Photosynthesis of a carbohydrate in plants is given by chemical equation:
\( 6 C O_{2}+6 H_{2} O \longrightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
If you have net result as:
\( 6 C O_{2}+6 H_{2} O \longrightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
Check whether this reaction is correct
or not.
Subject: Maths
The value of \( \lim _{n \rightarrow \infty} \Sigma_{i=1}^{n} \log \left(2+\frac{5 i}{n}\right) \frac{5}{n} \)
is equal to?
A \( \cdot \int_{2}^{5} \ln (x) d x \)
B. \( \int_{3}^{7} \ln (x) d x \)
c. \( \int_{2}^{7} \ln (x) d x \)
D \( \cdot \int_{2}^{7} \ln \left(x^{2}\right) d x \)
Subject: Maths
Which of the following is a
homogeneous differential equation?
\( \mathbf{A} \cdot(4 x+6 y+5) d y+(3 y+2 x+4) d x=0 \)
B. \( (x y) d x+\left(x^{3}+y^{3}\right) d y=0 \)
C \( \cdot\left(x^{3}+2 y^{2}\right) d x+2 x y d y=0 \)
D \( \cdot y^{2} d x+\left(x^{2}+x y+y^{2}\right) d y=0 \)
Subject: Physics
Two electrons are moving with the same velocity, one electron enters a region of uniform electric field while the other
enters a region of uniform magnetic field. Then, after sometime, if the de-
Broglie wavelength of two are \( \lambda_{1} \) and \( \lambda_{2} \) respectively, then
\( A \cdot \lambda_{1}=\lambda_{2} \)
в. \( \lambda_{1}>\lambda_{2} \)
c. \( \lambda_{1}<\lambda_{2} \)
D. \( \lambda_{1}>\lambda_{2} \) or \( \lambda_{1}<\lambda_{2} \)
Subject: Maths
In a conference there are 11 mechanical
engineers and 7 metallurgical engineers. In how many ways can they be seated in a row such that all the
metallurgical engineers do not sit together?
A. \( 18 !-(12 ! \times 7 !) \)
B. \( ^{18} P_{4}-2 ! \)
\( \mathbf{c} \cdot^{18} P_{4} \times 11 \)
D. \( 18 !-11 ! \)
Subject: Chemistry
A mixture of \( S O_{3}, S O_{2} \) and \( O_{2} \) gases is
maintained at equilibrium in 10 litre. flask at a temperature at which Kc for
the reaction, \( 2 S O_{2}(g)+ \)
\( O_{2}(g) \rightarrow \neg 2 S O_{3}(g) \) is \( 100 m o l^{-1} \) litre
At equilibrium.
A. If no. of mole of \( S O_{3}, S O_{2} \) in the flask are same, how many moles of \( O_{2} \) are present 0.1
B. If no. of mole of \( S O_{3} \) in the flask are twine the no.of
mole of \( S O_{2} \), how many moles of \( O_{2} \) are present \( 0 . \)
c. Both A and B
D. None
Subject: Chemistry
A solution prepared by dissolving a \( 2.50 g \) sample of an unknown compound dissolved in \( 34.0 g \) of benzene,
\( C_{6} H_{6} \) boils at \( 1.38^{\circ} C \) higher than pure benzene. Which expression gives the molar mass of the unknown compound
\( ? \)
Compound \( K_{b} \)
\( \boldsymbol{C}_{6} \boldsymbol{H}_{6} \quad \boldsymbol{2 . 5 3}^{\circ} \boldsymbol{C} \cdot \boldsymbol{m}^{-1} \)
A \( \cdot 2.53 \times \frac{2.50}{1.38} \)
в. \( _{1.38} \times \frac{34.0}{2.53} \times 2.50 \)
c. \( 2.50 \times 10^{3} \times \frac{2.53}{34.0} \times \frac{1}{1.38} \)
D. \( 2.50 \times 10^{3} \times \frac{1.38}{34.0} \times 2.53 \)
Subject: Maths
Find the point where the line of
intersection of the planes \( x-2 y+z= \)
1 and \( x+2 y-2 z=5 \) intersects the
plane \( 3 x+2 y+z+6=0 \)
A \( \cdot P(1,-2,-4) \)
B . \( P(1,2,-4) \)
c. \( P(1,-2,4) \)
D. None of these
Subject: Physics
Assertion
If we bend an insulated conducting wire, the resistance of the wire
increases.
Reason
The drift velocity of electrons in bent
wire 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: Physics
Assertion
In series \( \boldsymbol{L}-\boldsymbol{C}-\boldsymbol{R} \boldsymbol{A} \boldsymbol{C} \) circuit, current
and voltage are in same phase at
resonance.
Reason
In series \( \boldsymbol{L}-\boldsymbol{C}-\boldsymbol{R} \boldsymbol{A} \boldsymbol{C} \) circuit,
resonant frequency does not depend on the value of resistance. Hence current,
at resonance, does not depend on
resistance.
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
Sum of nine terms of the series \( \log a+ \)
\( \log \frac{a^{2}}{b}+\log \frac{a^{3}}{b^{2}}+\log \frac{a^{4}}{b^{3}}+\ldots . . i s- \)
A . \( 36 \log a-28 \log b \)
B. \( 45 \log a-36 \log b \)
c. \( 55 \log a-45 \log b \)
D. \( 66 \log a-55 \log b \)
Subject: Chemistry
The molarity of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) in a sample
which has density \( 1.4 \mathrm{g} / \mathrm{mL} \) and mass percentage of \( 63 \% \) is
[Molecular Weight of \( \left.\boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}=\boldsymbol{6 3}\right] \)
Subject: Physics
In instantaneous current in a metallic
wire is \( \mathrm{i}=(5+10 \mathrm{t}) \mathrm{A} \) then find amount of
charge flown through it from \( t=2 s \) to \( t=3 s \) is
A . 100
B. 24C
c. \( 30 c \)
D. 40C
Subject: Physics
An inverted vessel (bell) lying at the bottom of a lake, \( 50.6 \mathrm{m} \) deep has \( 50 \mathrm{cc} \) of air trapped in it. The bell is brought to
the surface of lake. The volume of the
trapped air will now be
A . 200 ç
B. 250 cc
c. 300 cc
D. 350 cc
Subject: Maths
If \( \lim _{x \rightarrow \infty}\left\{\frac{x^{3}+1}{x^{2}+1}-(a x+b)\right\}=2, \) then
A \( . a=1, b=1 \)
B. \( a=1, b=2 \)
c. \( a=1, b=-2 \)
D. None of these
Subject: Maths
Solve:
\( \left|\begin{array}{ccc}\mathbf{0} & -\mathbf{3} & \boldsymbol{x} \\ \boldsymbol{x}+\mathbf{1} & \mathbf{3} & \mathbf{1} \\ \mathbf{4} & \mathbf{1} & \mathbf{5}\end{array}\right|=\mathbf{0} \)
Subject: Chemistry
Which of the following is a normal salt:
A. \( \mathrm{NaH}_{2} \mathrm{PO}_{2} \)
в. \( \mathrm{NaH}_{2} \mathrm{PO}_{3} \)
\( \mathbf{c} \cdot \mathrm{NaH}_{2} \mathrm{PO}_{4} \)
D. \( \mathrm{Na}_{3} \mathrm{PO}_{4} \)
Subject: Chemistry
Which of the following reagents convert the acid chloride into aldehyde? \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C O}-\boldsymbol{C l} \rightarrow \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H O} \)
A. \( H_{2}, P d, B a S O_{4} \)
B . \( \left(C H_{3}-C H_{2}-C H_{2}-C H_{2}\right)_{3} \) SnH
c. LiAlH\( _{4} \)
D. Nah
Subject: Chemistry
2 mole each of \( S O_{3}, C O, S O_{2} \) and \( C O_{2} \)
is taken in a one lit. vessel. If \( \boldsymbol{K}_{c} \) for
\( \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
is \( 1 / 9 \) then:
A. Total no. of moles at equilibrium are less than 8
B . \( n\left(S O_{3}\right)+n\left(C O_{2}\right)=4 \)
\( \mathbf{c} \cdot\left[n\left(S O_{2}\right) / n(C O)\right]<1 \)
D. Both \( (B) \) and \( (C) \)
Subject: Physics
Two spherical bodies having masses \( M \) and \( 3 M \) and radii \( r \) and \( 4 r \) respectively are released in free space rest such that the initial separation between their
centres is \( 13 r \). If only force is gravitational attraction distance covered by the smaller bodyjust before collision is.
A \( \cdot 6 r \)
B . \( 2 r \)
c. \( \frac{9}{4 r} \)
D. \( \frac{39 r}{4} \)
Subject: Chemistry
Statement 1: While balancing equations, same number of atoms are
there on reactant side and the product
side.

Statement 2: For all regular chemical
equations, the conservation of matter holds good.
A. Both the statements 1 and 2 are correct and statement 2 is not correct explanation of statement 1
B. Both the statements 1 and 2 are correct and statement 2 is 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 statements 1 and 2 are not correct.
Subject: Physics
A ball collides with a fixed inclined
plane of inclination \( \boldsymbol{\theta} \) after falling
through a distance h. If it moves horizontallyjust after the impact, the coefficient of restitution is :
A \( \cdot \tan \theta \)
B \( \cdot \tan ^{2} \theta \)
c. \( \cot \theta \)
D. \( \cot ^{2} \theta \)
Subject: Physics
If a wire is stretched by applying force at one of its ends, then the elastic
potential energy density in terms of Young's modulus Y and linear strain \( \alpha \)
will be
\( ^{A} \cdot \frac{\alpha Y^{2}}{2} \)
в. \( \frac{Y \alpha}{2} \)
c. \( \frac{\alpha^{2} Y}{2} \)
D. \( 2 \alpha^{2} Y \)
Subject: Maths
For \( \boldsymbol{f}(\boldsymbol{x})=\sin ^{2} \boldsymbol{x}, \boldsymbol{x} \in(\mathbf{0}, \boldsymbol{\pi}) \) point of
inflection is
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{2 \pi}{4} \)
\( c \cdot \frac{3 \pi}{4} \)
D. \( \frac{4 \pi}{3} \)
Subject: Maths
\( \operatorname{In} \) an acute triangle \( A B C, \angle A B C= \) \( \mathbf{4 5}^{\circ}, \boldsymbol{A B}=\mathbf{3} \) and \( \boldsymbol{A C}=\sqrt{\mathbf{6}} . \) The angle
\( \angle B A C, \) is
A \( .60^{\circ} \)
B. 65
\( c \cdot 75 \)
D. \( 15^{\circ} \) or \( 75^{\circ} \)
Subject: Maths
A manufactacturer buys raw material
for Rs. 60,000 and pays \( 4 \% \) tax. He sells the ready stocks for Rs. 92,000 and charges \( 12.5 \% \) tax. Find the VAT paid by the manufacturer.
A . \( R s .13,870 \)
B. \( R s .12,160 \)
c. \( R s .10,370 \)
D. \( R s .9,100 \)
Subject: Chemistry
Among the following the most reactive towards alcoholic \( K O H \) is:
A. \( C H_{2}=C H B r \)
в. \( C H_{3} C O C H_{2} C H_{2} B r \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br} \)
D. \( C H_{3} C H_{2} C H_{2} B r \)
Subject: Maths
In a test an examinee either guesses or copies or knows the answer to a
multiple choice question with four choices. The probability that he make, a guess is \( \frac{1}{3} \) and the probability that he copies the answer is \( \frac{1}{6} . \) The probability that his answer is correct given that he copied it is \( \frac{1}{8} . \) Find the probability that he knew the answer to the question,
given that he correctly answered it.
Subject: Maths
This year, a salesman sells a total of
\( \$ 60,000 \) worth of steak knives by going door-to-door. This represents a \( 20 \% \)
increase from the year before. What was the value of his sales last year?
A. \( \$ 45,000 \)
в. \( \$ 48,000 \)
\( c . \$ 50,000 \)
D. \( \$ 52,000 \)
E. \( \$ 56,000 \)
Subject: Physics
In a collinear collision, a particular with
an initial speed \( v_{0} \) strikes a stationary
particle of the same mass. If the final
total kinetic energy is \( 50 \% \) greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is?
\( A \cdot \frac{v_{0}}{2} \)
в. \( \frac{v_{0}}{\sqrt{2}} \)
c. \( \frac{v_{0}}{4} \)
\( D \cdot \sqrt{2} v_{0} \)
Subject: Chemistry
Following table compares properties of
red phosphorus and white phosphorus.
Which is incorrect comparison?
A. Red- Nontoxic and has polymeric structure; White -
Toxic, waxy discrete tetrahedral \( P_{4} \) molecule
B. Red - Discrete tetrahedral \( P_{4} \) molecule; White -
Polymeric structure
C. Red - High m.p., less reactive; White - Low m.p., more reactive
D. Red - Shows no phosphorescence in air; White - Shows phosphorescence in air
Subject: Maths
\( \vec{A} \cdot(\vec{A} \times \vec{B}) \)
\( A \cdot \vec{A} \cdot \vec{B} \)
\( \mathbf{B} \cdot \underset{A}{\longrightarrow} \times \underset{B}{\longrightarrow} \)
\( c \cdot 0 \)
D. 1
Subject: Chemistry
Which of the following statements is/are incorrect for diamond?
(a) The refractive index of diamond is
highest among solids.
(b) Diamond is hard because all the
valence electrons of each carbon atom
are involved in bond formation.
(c) Diamond is thermodynamically more stable than graphite.
(d) One carat of diamond represents
its weight.
A. All are correct
B. a, b and c
c. a and b
D. conly
Subject: Physics
The time taken by a particle performing \( \boldsymbol{S H} \boldsymbol{M} \) to pass from point \( \boldsymbol{A} \) to \( \boldsymbol{B} \) where its velocities are same is 2
seconds.After another 2 seconds it
returns to \( B \). The time period of oscillation is (in seconds)
A \( .2 s \)
B. 8 s
\( c \cdot 6 s \)
D. \( 4 s \)
Subject: Biology
Aquaporins are integral proteins of the plasma membrane whose role is to
allow the passage of water molecules
down its concentration gradient. Recent observations have shown an
interesting arrangement of charged amino acid residues along the inner
surface of the channel resulting in the entry of water via its oxygen, then flipping to lead with its hydrogens half way through the channel. How might this explain aquaporins specificity for water and not cations or protons?
A. Cations such as \( K^{+} \) and \( N a^{+} \) would be repelled at the opening of the channel
B. Water gains access because it is electrically neutral.
c. Protons cannot cross since they do not interact with water
D. Water, being a small polar molecule, is able to interact with both negative and positive residues in the channel.
Subject: Maths
A circle is described with minor axis of
the ellipse as diameter. If the foci lie on the circle, then the eccentricty of the ellipse is
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\sqrt{5}} \)
Subject: Chemistry
pH of saturated solution of \( C a(O H)_{2} \) is
9. the solubility product \( \left(K_{s p}\right) \) of
\( \boldsymbol{C a}(\boldsymbol{O H})_{2} \) is:
A \( .0 .5 \times 10^{-15} \)
В. \( 0.25 \times 10^{-10} \)
\( c \cdot 0.125 \times 10^{-15} \)
5
D. \( 0.5 \times 10^{10} \)
Subject: Chemistry
Assertion (A) : The plants yield a milky suspension of crude rubber called latex.
Reason (R) : The latex contains about
\( 85 \% \) rubber
A. Both A and R are correct and R is the correct explanation of the A
B. Both A and R are correct but R is not the correct explanation of the \( A \)
c. A is correct but R is incorrect
D. A is incorrect but R is correct
Subject: Physics
A particle travels \( 10 \mathrm{m} \) in first 5 seconds
\( 10 \mathrm{cm} \) in next 3 seconds. Assuming constant acceleration what is the
distance travelled in next 2 second?
\( \mathbf{A} \cdot 8.3 \mathrm{m} \)
B. \( 9.3 \mathrm{m} \)
c. \( 10.3 \mathrm{m} \)
D. None of these
Subject: Physics
Three similar spheres of mass \( \mathrm{m} \) and
radius r are moving down along three
inclined planes \( A, B \) and \( C \) of similar
dimensions. Sphere on inclined plane \( A \) rolls down in pure rolling, on B it partially
rolls and partially slides down the plane
whereas on plane \( \mathrm{C} \) it slides down
without rolling, then at the bottom of
planes
A. Velocities of all sphere are same.
B. Velocities on A and C are same whereas that on B is less
C. Velocities of sphere on \( A \) is least and that on \( C \) is maximum
D. Velocities of sphere A is maximum