AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The sum of \( n \) terms of the series whose
\( \boldsymbol{n}^{t h} \) term is \( \boldsymbol{n}(\boldsymbol{n}+1) \) is equal to
A \( \frac{n(n+1)(n+2)}{3} \)
B. \( \frac{(n+1)(n+2)(n+3)}{12} \)
c. \( n^{2}(n+2) \)
D. \( n(n+1)(n+2) \)
Subject: Chemistry
Dimensions of equilibrium constant, \( \boldsymbol{K}_{c} \)
for the reaction \( 2 N H_{3} \rightleftharpoons N_{2}+3 H_{2} \)
are
A \( \cdot m o l L^{-2} \)
B \( \cdot m o l^{2} L^{-2} \)
\( \mathbf{c} \cdot m o l^{2} L^{-3} \)
D. \( m o l^{2} L^{-1} \)
Subject: Chemistry
\( \boldsymbol{F} \boldsymbol{e} \boldsymbol{C l}_{3} \) on reaction with \( \boldsymbol{K}_{\boldsymbol{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
in aqueous solution gives blue colour. These are separated by a
semipermeable membrane \( A B \) as
shown. Due to osmosis there is:
A. blue colour formation in side \( X \)
B. blue colour formation in side \( Y \).
c. blue colour formation in both of the sides \( X \) and \( Y \).
D. no blue colour formation
Subject: Physics
The momentum of a moving particle is vectorially given as \( \overrightarrow{\boldsymbol{p}}=\boldsymbol{p}_{0}(\cos \boldsymbol{t} \hat{\boldsymbol{i}}+ \)
\( \sin t \hat{j}), \) where \( t \) stands for time. choose
the correct option:
A. The applied force is constant
B. The momentum is constant
C. The applied force always remains perpendicular to the momentum.
D. The applied force is always parallel to the momentum
Subject: Physics
A certain radioactive material is known
to decay at a rate proportional to the amount present. Initially there is \( 50 \mathrm{kg} \) of thematerial present and after two hours it is observed that themateria
has lost \( 10 \% \) of its original mass, then
the
A \( \cdot \) mass of the material after four hours is \( 50\left(\frac{9}{10}\right)^{2} \)
B. mass of the material after four hours is \( 50 . e^{-0.51 n 9} \)
c. time at which the material has decayed to half of its initial mass (in hours) is \( \frac{\left(\ell n \frac{1}{2}\right)}{\left(-\frac{1}{2} \ell n 0.9\right)} \)
D. time at which the material has decayed to half of its initial mass (in hours) is \( \frac{2 \ln \frac{1}{2}}{\ln 0.99} \)
Subject: Chemistry
The specific conductance of a saturated
solution of silver bromide is \( \kappa \mathbf{S} \mathrm{cm}^{-1} \)
The limiting ionic conductivity of
\( A g^{+} \) and \( B r^{-} \) ions are \( x \) and \( y \)
respectively. The solubility of silver bromide in \( \mathrm{gL}^{-1} \) is:
[molar mass of \( \mathrm{AgBr}=188 \)
A. \( \frac{\kappa \times 100}{x-y} \)
B. \( \frac{\kappa}{x+y} \times 188 \)
c. \( \frac{\kappa \times 1000 \times 188}{x+y} \)
D. \( \frac{x \times y}{\kappa} \times \frac{1000}{188} \)
Subject: Physics
Two particles of masses \( m_{1} \) and \( m_{2} \) are
dropped from height \( h_{1} \) and \( h_{2} \). They
reach the earth after times \( t_{1} \) and \( t_{2} \)
respectively, Then:
A \( \cdot \frac{t_{1}}{t_{2}}=\sqrt{\frac{h_{1}}{h_{2}}} \)
B. \( \frac{t_{1}}{t_{2}}=\sqrt{\frac{h_{2}}{h_{1}}} \)
c. \( \frac{t_{2}}{t_{1}}=\frac{h_{2}}{h_{1}} \)
D. none of these
Subject: Physics
The velocity of a body at any instant is \( 10 \mathrm{m} / \mathrm{s} . \) After \( 5 \mathrm{sec}, \) velocity of the particle is \( 20 \mathrm{m} / \mathrm{s} \). The velocity at 3 seconds before is
(assume uniform accelaration)
A. \( 8 \mathrm{m} / \mathrm{sec} \)
B. 4 m/sec
c. \( 6 \mathrm{m} / \mathrm{sec} \)
D. \( 7 \mathrm{m} / \mathrm{sec} \)
Subject: Chemistry
The reaction between carbon and
oxygen can be represented as
\( C_{(s)}+O_{2(x)} \rightarrow C O_{2(g)}+ \)heat
In which of the following type(s), the above reaction can be classified?
I. Combustion reaction
Il. Displacement reaction
III. Endothermic reaction
IV. Combination reaction
\( A \). (I) and (III)
B. (I), (II) and (IV)
c. (I) and (IV)
D. (I) only
Subject: Chemistry
Assertion
According to Mendeleev, the properties of elements are a periodic function of their atomic weights.
Reason
Mendeleev left the gap under aluminium and a gap under silicon, and called these elements Eka-Aluminium
and Eka-Silicon.
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
In the equation of the motion of a particle \( \boldsymbol{y}=\mathbf{0 . 5} \sin (\mathbf{0 . 3} \boldsymbol{t}+\mathbf{0 . 1}), \) the
initial phase of motion is
A. \( (0.3 t+0.1) \)
B. 0.3
c. \( 0.3 t \)
D. \( 0 . \)
Subject: Chemistry
STATEMENT-1: Diethyl ether when boiled with water gives ethyl alcohol. STATEMENT-2: Diethyl ether is less dense than water.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Chemistry
\( 7.5 \mathrm{ml} \) of a gaseous hydrocarbon was
exploded with \( 36 \mathrm{ml} \) of \( \mathrm{O}_{2} . \) On cooling,
the volume of gases was found to be \( 28.5 \mathrm{ml}, 15 \mathrm{ml} \) of which was absorbed by KOH and the rest was absorbed in a
solution of alkaline pyrogallol. The formula of hydrocarbon is:
A. \( C_{2} H_{6} \)
в. \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{6} \)
Subject: Chemistry
The end-product in the reaction sequence would be:
Ethyl amine \( \frac{H N O_{2}}{\longrightarrow} A \stackrel{P C l_{5}}{\longrightarrow} B \stackrel{N H_{3}}{\longrightarrow} C \)
A. Ethyl cyanide
B. Ethyl amine
c. Methyl amine
D. Acetamide
Subject: Physics
A particle moves from \( A \) to \( B \) such that
\( \boldsymbol{x}=\boldsymbol{t}^{2}+\boldsymbol{t}-\mathbf{3} . \) Its average velocity from
\( t=2 s \) to \( t=5 s \) is
\( A \cdot 6 m s^{-1} \)
3. \( 8 m s^{-1} \)
\( c \cdot 8.5 m s^{-1} \)
D. \( 7 \mathrm{ms}^{-1} \)
Subject: Physics
A glass marble dropped from a certain height above the horizontal surface reaches the surface in time \( t \) and then
continues to bounce up and down. The time in which the marble finally comes to rest is:
\( \mathbf{A} \cdot e^{n} t \)
B . \( e^{2} t \)
\( ^{\mathbf{c}} \cdot t\left[\frac{1+e}{1-e}\right] \)
D. \( t\left[\frac{1-e}{1+e}\right] \)
Subject: Physics
Two point object of masses \( 10^{4} k g, 10^{6} k g \) are \( 1.2 \times 10^{3} m \) apart.
Find distance of point from smaller mass at which the net gravitational force due to them will be zero(in m)
A . 109
B. 1100
\( c \cdot 11 \)
D. 99
Subject: Biology
Which of the following statements are correct?
(i) Glucose has a high threshold value.
(ii) Urine is concentrated in Henle's
loop.
(iii) Haemodialyser removes urea, uric acid, glucose and plasma proteins.
(iv) In glomerulus, urea, uric acid, water, glucose and plasma proteins are filtered out.
A . (i), (iii) and (iv)
B. (ii), (iii) and (iv)
c. (i) and (ii)
D. (i) and (iii)
Subject: Chemistry
Total vapour pressure of mixture of
mol of \( A\left(P_{A}^{0}=150 \text { tor } r\right) \) and 2 mol of \( B \)
\( \left(P_{B}^{0}=240 \text { tor } r\right) \) is 200 torr. In this case
A. there is positive deviation from Raoult's law
B. there is negative deviation from Raoult's law
c. there is no deviation from Raoult's law
D. molecular masses of A and B are also required for calculating the deviation
Subject: Physics
The pd a cross terminals of a cell is
found to be 29 volt and 28 volt
respectively when it delivers a current of 1 ampere and 2 ampere respectively. The emf and internal resistance of a cell
are respectively
A. \( 30 \mathrm{V}, 2 \Omega \)
B. 30V,1\Omega
c. \( 29 v, 1 \Omega \)
D. \( 28 \mathrm{V}, 2 \Omega \)
Subject: Chemistry
The decomposition of dinitrogen monoxide gas occurs in two steps:
\( \operatorname{Step} 1: N_{2} O_{(g)} \rightarrow N_{2(g)}+O_{(g)} \) (slow)
Step \( \mathbf{2}: \mathbf{N}_{\mathbf{2}} \boldsymbol{O}_{(\boldsymbol{g})}+\boldsymbol{O}_{(\boldsymbol{g})} \rightarrow \boldsymbol{N}_{\mathbf{2}(\boldsymbol{g})}+\boldsymbol{O}_{\boldsymbol{2}(\boldsymbol{g})} \)
(fast)
What is the overall reaction?
A \( \cdot 2 N_{2} O_{(g)} \rightarrow 2 N_{2(g)}+O_{2(g)} \)
B \( \cdot 2 N_{2} O_{(g)}+O_{(g)} \rightarrow 2 N_{2(g)}+O_{2(g)} \)
C. \( 2 N_{2} O_{(g)}+O_{(g)} \rightarrow 2 N_{2(g)}+O_{2(g)}+O_{(g)} \)
D. \( N_{2} O_{(g)} \rightarrow N_{2(g)}+O_{2(g)} \)
Subject: Maths
If \( \boldsymbol{\alpha}=\mathbf{1} / \mathbf{4} \) and \( \boldsymbol{P}_{\boldsymbol{n}} \) denotes the
perimeter of the nth square then \( \sum_{n=1}^{\infty} P_{n} \) equals
A \( \cdot \frac{8}{3}(4+\sqrt{10}) \)
B. \( \frac{8}{3} \)
\( c \cdot \frac{16}{3} \)
D. None of these
Subject: Physics
The diagram below shows a cathode ray
tube in which the arrow indicates a
beam of charged particles approaching an electric field between the plates \( A \)
and B. State the amount of charge on each particle.
A \( \cdot 1.6 \times 10^{-19} \mathrm{C} \)
в. \( -1.6 \times 10^{-19} \mathrm{C} \)
\( c \)
D. \( -1.16 \times 10^{-19} C \)
Subject: Physics
Two charges of \( +10 \mu \mathrm{C} \) and \( +20 \mu \mathrm{C} \) are separated by a distance of 2 cm. The net potential (electric) due to the pair at the middle point of the line joining the two charges, is :
A . 27 MV
B. 18 MV
c. 20 MV
D. 23 MV
Subject: Chemistry
How can the conversion of (i) to (ii) be
brought about?
\( \mathbf{A} \cdot K B r \)
\( \mathbf{B} \cdot K B r+C H_{3} O N a \)
\( \mathbf{c} \cdot K B r+K O H \)
\( \mathbf{D} \cdot B r_{2}+K O H \)
Subject: Maths
Calculate the scalar product of the following vectors. Given three forces \( M= \)
\( \{3,-4,2\}, W= \)
\( \{2,3,-5\}, \) and \( P=\{-3,-2,4\} \)
applied to the same point. Calculate the work performed by the resultant of these three forces when the point of application of the resultant moves along a straight line and is displaced
from the position \( M_{1}\{5,3,-7\} \) to the
position \( M_{2}\{4,-1,-4\} \)
Subject: Physics
Figure shows a wedge of mass \( 2 k g \)
resting on a frictionless floor. A block of
mass \( 1 \mathrm{kg} \) is kept on the wedge and the
wedge is given an acceleration of 5
\( m / \sec ^{2} \) towards right. Then:
A. Block will remain stationary w.r.t. wedge
B. The block will have an acceleration of \( 1 \mathrm{m} / \mathrm{sec}^{2} \) w.r.t. the wedge
C. Normal reaction on the block is \( 11 N \)
D. Net force acting on the wedge is \( 2 N \)
Subject: Maths
Verify \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\} \)
\( \boldsymbol{B}=\{1,2,3,4\} C=\{5,6\} D= \)
\( \{5,6,7,8\} . \) Prove \( A \times(B \cap C)=(A \times \)
\( \boldsymbol{B}) \cap(\boldsymbol{A} \times \boldsymbol{C}) \)
Subject: Maths
The area of the quadrilateral formed by the tangents at the endpoints of the latus recta to the ellipse, \( \frac{x^{2}}{9}+\frac{y^{2}}{5}=1 \)
is
A \( \cdot \frac{27}{4} \)
B. 18
c. \( \frac{27}{2} \)
D. 27
Subject: Physics
Two parallel wires each of length \( 10 c m \)
are \( 0.5 \mathrm{cm} \) apart. A film of water is
formed between them. If the surface
tension of water is \( 0.072 N / m, \) then the work done in on increasing the distance between the wires by 1 mm is
A . \( 1.44 \times 10^{-5} \mathrm{J} \)
в. \( 1.72 \times 10^{-5} \mathrm{J} \)
c. \( 1.44 \times 10^{-4} J \)
D. \( 1.72 \times 10^{-4} J \)
Subject: Maths
\( \lim _{x \rightarrow \infty}\left(\frac{x^{2}+2 x-1}{2 x^{2}-3 x-2}\right)^{\frac{2 x+1}{2 x-1}} \) is equal
to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \infty \)
\( c \cdot \frac{1}{2} \)
D. None of these
Subject: Chemistry
Solubility of salt \( M_{2} X_{3} \) is \( y \operatorname{mol} d m^{-3} \)
The solubility product of the salt will be:
\( A \cdot 6 y^{4} \)
В . \( 64 y^{4} \)
\( c \cdot 36 y^{5} \)
D. \( 108 y^{5} \)
Subject: Chemistry
Chlorine is liberated when we heat:
A. \( K M n O_{4}+N a C l \)
В \( \cdot P b_{2}\left(N O_{3}\right)_{4}+M n O_{2} \)
c. \( K_{2} C r_{2} O_{7}+M n O_{2} \)
D. \( K_{2} C r_{2} O_{7}+H C l \)
Subject: Physics
Charges are placed on the vertices of a square as shown. Let \( \overrightarrow{\boldsymbol{E}} \) be the electric
field and \( V \) be the potential at the
centre. If the charges on \( A \) and \( B \) are interchanged with those on D and \( \mathbf{C} \)
respectively, then:
A \( . \vec{E} \) remains unchanged, \( V \) changes
B. Both \( \vec{E} \) and \( V \) change
C \( . \vec{E} \) and \( V \) remain unchanged
D. \( \vec{E} \) changes, \( V \) remains unchanged
Subject: Physics
In the circuit shown in figure, a
conducting wire \( H E \) is moved with a
constant speed \( \boldsymbol{v} \) toward left. The
complete circuit is placed in a uniform magnetic field \( \vec{B} \) perpendicular to the plane of the circuit inward. The current
in \( \boldsymbol{H} \boldsymbol{K} \boldsymbol{D} \boldsymbol{E} \) is
A . clockwise
B. anticloclwise
c. alternating
D. zero
E. answer required
Subject: Chemistry
Which is more stable in the below
given pair?
\( M n_{2} O_{7}_{-}-_{-}--R e_{2} O_{7} \)
A \( \cdot M n_{2} O_{7}=R e_{2} O_{7} \)
в. \( M n_{2} O_{7}<R e_{2} O_{7} \)
c. \( M n_{2} O_{7}>R e_{2} O_{7} \)
D. None of these
Subject: Maths
Let \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) and \( \boldsymbol{B}=\left[\boldsymbol{b}_{\boldsymbol{i} j}\right] \) be two \( \boldsymbol{3} \times \boldsymbol{3} \)
real matrices such that \( b_{i j}= \)
\( (3)^{(i+j-2)} a_{i j}, \) where \( i, j=1,2,3 . \) If the
determinant of \( B \) is 81 , then the
determinant of A is :
A. \( 1 / 3 \)
B. 3
c. \( 1 / 81 \)
D. \( 1 / 9 \)
Subject: Maths
Which of the following is the correct match with respect to the given
question? ABCD' is a rhombus such that
\( \angle A C B=40^{\circ} \) then \( \angle A D B= \)
\[
\begin{array}{ll}
\mathbf{7 0}^{o} & \text { As } \angle A D B=\mathbf{1} / \mathbf{2}\left(\mathbf{1 8 0}^{\circ}-\mathbf{4 0}^{\circ}\right) \\
45^{\circ} & \angle C+\angle D=90^{\circ}
\end{array}
\]
50
\[
\angle B C D=80^{\circ} \Rightarrow \angle A D C=100^{\circ} \therefore
\]
\[
\angle A D B=(1 / 2) x 100^{\circ}
\]
\( 60^{0} \quad \) All sides are equal
\( \mathbf{A} \cdot(a) \rightarrow(i) \)
B. \( (c) \rightarrow(i i i) \)
c. \( (d) \rightarrow(i i i) \)
D. \( (b) \rightarrow(i v) \)
Subject: Physics
When the temperature of a copper coin
is raised by \( 80^{0} \mathrm{C}, \) its diameter
increases by \( 0.2 \% \) This question has multiple correct options
A. percentage rise in the area of a face is \( 0.4 \% \)
B. percentage rise in the thickness is \( 0.4 \% \)
c. percentage rise in the volume is \( 0.6 \% \)
D. coefficient of linear expansion of copper is 0.25 x \( 10^{-4} /^{0} C \)
Subject: Maths
The degree of the differential equation \( \left(1+\left(\frac{d y}{d x}\right)^{2}\right)^{3 / 4}=\left(\frac{d^{2} y}{d x^{2}}\right)^{1 / 3} \) is:
\( A \)
B.
\( c \cdot 9 \)
\( D \)
Subject: Chemistry
Assertion
Ether can extract LiCl from the aqueous
solution of a mixture of LiCl, NaCl and
KCI.
Reason
Hydration of \( L i^{+} \) ion is greater than that
of \( N a^{+} \) and \( K^{+} \) ions.
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 long horizontal wire \( \boldsymbol{P} \) carries a
current \( 50 A \). It is rigidly fixed. Another
line wire \( Q \) is placed directly above and
parallel to \( P . \) The weight of wire \( Q \) is
\( 0.075 N m^{-1} \) and caries a current of
\( 25 A . \) Find the position of wire \( Q \) from \( P \) so that wire to remains suspended due to the magnetic repulsion-
A. \( 3.33 \mathrm{mm} \)
B. \( 33.3 \mathrm{mm} \)
c. 334 mm
D. 333 mm
Subject: Chemistry
Assertion
Some farmers feel that lightning helps
produce better crop.
Reason
Lighting forms No which is converted to
\( N o_{2}, H N O_{2} \) and \( H N O_{3} \) under
atomospheric condition. Thus, \( N O_{3}^{-} \) is a source of nutrients (fertilisers) to the
plant. Thus there are chances of better
crops when lightning occurs.

Read the above assertion and reason and choose the correct option regarding
¡t.
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
A cylinder has a diameter of \( 20 \mathrm{cm} \). The
area of curved surface is \( 1000 \mathrm{cm}^{2} \)
FindAthe height of the cylinder correct to one decimal place.The volume of the cylinder correct to one decimal place. (Take \( \boldsymbol{\pi}=\mathbf{3 . 1 4}) \)
Subject: Physics
The capacitance between adjacent plates shown in Fig \( 20.95(a) \) is 50 nF. \( A 1 \mu C \) charge is placed on the middle
plate. Find the charge on the outer surface of upper plate and the potential difference between upper and middle plates:
A. \( 0.5 \mu C, 10 V \)
B. \( 1 \mu C, 20 V \)
c. \( 0.5 \mu C, 20 V \)
D. \( 1.0 \mu, 40 V \)
Subject: Physics
In the reaction given below, at constant pressure, the work done by system on surrounding is?
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
A. positive
B. negative
c. no work is done
D. positive at temperatures above critical temperature
Subject: Chemistry
An experiment showed that in a lead chloride solution, 6.21 g of lead combined with 4.26 g of chlorine. The empirical formula of this chloride is:
\( \mathbf{A} \cdot P b C l_{2} \)
в. \( P b_{2} C l_{2} \)
c \( . P b C l \)
D. \( P b C l_{4} \)
Subject: Maths
Curved surface area of solid sphere is \( 24 c m^{2} . \) If the sphere is divided into two hemispheres, then the total surface area of one of the hemispheres is :
\( \mathbf{A} \cdot 12 c m^{2} \)
в. \( 8 c m^{2} \)
\( \mathbf{c} \cdot 16 \mathrm{cm}^{2} \)
D. \( 18 \mathrm{cm}^{2} \)
Subject: Physics
The velocity of a kerosene oil in a
horizontal pipe is \( 5 m / s . \) If \( g=10 m / s^{2} \)
then the velocity head of oil will be
\( \mathbf{A} \cdot 1.25 m \)
B. \( 12.5 m \)
c. \( 0.125 m \)
D. \( 125 m \)
Subject: Chemistry
The coefficient of \( \boldsymbol{I}^{-}, \boldsymbol{I} \boldsymbol{O}_{3}^{-} \) and \( \boldsymbol{H}^{+} \) in
the redox reaction, \( \boldsymbol{I}^{-}+\boldsymbol{I} \boldsymbol{O}_{3}^{-}+\boldsymbol{H}^{+} \rightarrow \)
\( I_{2}+H_{2} O, \) in the balanced form
respectively are:
\( \mathbf{A} \cdot 5,1,6 \)
в. 1,5,6
c. 6,1,5
D. 5,6,1
Subject: Chemistry
Assertion
The voltage of mercury cell remains constant for long period of time.
Reason
It is because net cell reaction does not
involve active species.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
An aqueous solution of a weak monobasic acid containing 0.1 g in 21.7 g of water freezes at \( 272.813 \mathrm{K} \). If the value
of \( K_{f} \) for water is \( 1.86 \mathrm{K} / \mathrm{m}, \) what is the molecular mass of the monobasic acid.
Subject: Physics
The mass of a gas molecules is \( 4 \times 10^{-30} \mathrm{kg} \)
If \( 10^{23} \) molecules strike per second at \( 4 \mathrm{m}^{2} \)
area with a velocity \( 10^{7} \mathrm{m} / \mathrm{s} \), then the
pressure exerted on the surface will be
A. 1 Pascal
B. 3 Pascal
c. 2 Pascal
D. 4 Pascal
Subject: Chemistry
Assertion
\( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) is generally preferred over
\( N a_{2} C r_{2} O_{7} \) in volumetric analysis
although both are oxidizing agents.
Reason
\( N a_{2} C r_{2} O_{7} \) is deliquescent in nature.
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
Assertion
If the matrices \( A, B,(A+B) \) are
nonsingular, then \( \left[\boldsymbol{A}(\boldsymbol{A}+\boldsymbol{B})^{-1} \boldsymbol{B}\right]^{-1}= \)
\( \boldsymbol{B}^{-1}+\boldsymbol{A}^{-1} \)
Reason
\( \left[\boldsymbol{A}(\boldsymbol{A}+\boldsymbol{B})^{-1} \boldsymbol{B}\right]^{-1}=\left[\boldsymbol{A}\left(\boldsymbol{A}^{-1}+\right.\right. \)
\( \left.\left.\boldsymbol{B}^{-1}\right) \boldsymbol{B}\right]^{-1}=\left[\left(\boldsymbol{I}+\boldsymbol{A} \boldsymbol{B}^{-1}\right) \boldsymbol{B}\right]^{-1}= \)
\( \left[\left(\boldsymbol{B}+\boldsymbol{A B}^{-1} \boldsymbol{B}\right)\right]^{-1}=[(\boldsymbol{B}+ \)
\( \boldsymbol{A I})]^{-1}=[(\boldsymbol{B}+\mathbf{1})]^{-1}=\boldsymbol{B}^{-1}+\boldsymbol{A}^{-1} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
A microscope is having objective of
focal length \( 1 \mathrm{cm} \) and eyepiece of focal
length \( 6 \mathrm{cm} \). If tube length is \( 30 \mathrm{cm} \) and image is formed at the least distance of distinct vision, what is the
magnification produced by the microscope? Take \( D=25 \mathrm{cm} \)
\( \mathbf{A} \cdot \mathbf{6} \)
в. 150
c. 25
D. 125
Subject: Chemistry
For the reaction
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \boldsymbol{\operatorname { S n }}(l) \)

Calculate \( \boldsymbol{K}_{\boldsymbol{p}} \) at \( \mathbf{9 0 0} \boldsymbol{K}, \) where the equilibrium steam - hydrogen mixture
was \( 45 \% H_{2} \) by volume.
A . 1.49
B. 1.22
c. 0.67
D. none of these
Subject: Maths
The set of points where the function
\( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]+|\mathbf{1}-\boldsymbol{x}|,-\mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3} \)
where [.] denotes the greatest integer
function, is not differentiable, is
A \( \cdot\{-1,0,1,2,3\} \)
B \( \cdot\{-1,0,2\} \)
c. \{0,1,2,3\}
D \( \cdot\{-1,0,1,2\} \)
Subject: Physics
A metal cube of length \( 10.0 \mathrm{mm} \) at \( 0^{\circ} \mathrm{C} \)
\( (273 \mathrm{K}) \) is heated to \( 200^{\circ} \mathrm{C}(473 \mathrm{K}) . \) Given
its coefficient of linear expansion is
\( 2 \times 10^{-5} K^{-1} . \) The percent change of its
volume is
A . \( 0 . \)
B. 0.2
\( c \cdot 0.4 \)
D. 1.2
Subject: Physics
The velocity of a particle executing a
simple harmonic motion is \( 13 m s^{-1} \)
when its distance from the equilibrium position \( (Q) \) is \( 3 m \) and its velocity is
\( 12 m s^{-1}, \) when it is \( 5 m \) away from \( Q \)
The frequency of the simple harmonic motion is:
\( \mathbf{A} \cdot \frac{5 \pi}{8} \)
В. \( \frac{5}{8 \pi} \)
c. \( \frac{8 \pi}{5} \)
D. \( \frac{8}{5 \pi} \)
Subject: Chemistry
Arrange the following in the increasing order of their ability as a leaving group:
\( \boldsymbol{C F}_{3} \boldsymbol{S O}_{3}^{-}, \boldsymbol{C H}_{3} \boldsymbol{S O}_{3}^{-} \boldsymbol{a n d} \boldsymbol{C H}_{3} \boldsymbol{C O O} \)
A \( \cdot C H_{3} S O_{3}^{-}>C F_{3} S O_{3}^{-}>C H_{3} C O O^{-} \)
в. \( C F_{3} S O_{3}^{-}>C H_{3} S O_{3}^{-}>C H_{3} C O O \)
c. \( C F_{3} S O_{3}^{-}>C H_{3} C O O^{-}>C H_{3} S O_{3}^{-} \)
D. \( C F_{3} S O_{3}^{-}<C H_{3} S O_{3}^{-}<C H_{3} C O O^{-} \)
Subject: Chemistry
Consider the following statements.
(I) Rutherford's name was associated
with the development of periodic table.
(II) A metal M having electronic configuration \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{1} \)
is d-block element.
(III) Diamond is an element.
(IV) The electronic configuration of the most electronegative element is \( 1 s^{2} 2 s^{2} 2 p^{5} \)
The correct statements are:
A. ।, ॥।, IV
B. ।, ॥, ॥ा, IV
c. ॥, IV
D. I, III, IV