AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The radius of a circular plate is
increased at \( 0.01 \mathrm{cm} / \) sec. If the area is
increased at the rate of \( \frac{\pi}{10} . \) Then its radius is
\( A \cdot 5 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)
Subject: Maths
f \( y=\tan ^{-1}\left[\frac{5 \cos x-12 \sin x}{12 \cos x+5 \sin x}\right] \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot-2 \)
D.
Subject: Chemistry
Assertion
The rate of reaction can also increase
w.r.t its product if one of the product act as catalyst.
Reason
A catalyst lowers the activation energy
of reactions.

Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are true Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Both Assertion and Reason are false
Subject: Biology
Identify the given figures \( A, B, C, D \) and
E.
\( E \)
A. A: Marginal, B: Axile, C: Free central, D: Parietal, E:
Basal
B. A: Marginal, B: Parietal, C: Free central, D: Axile, E: Basal
C . A: Marginal, B: Axile, C: Parietal, D: Free central, E:
Basal
D. A: Marginal, B: Axile, C: Parietal, D: Basal, E: Free central
Subject: Physics
"I is
smooth wall, as shown in the diagram,
making a variable angle \( \theta \) with the
horizontal floor. There is no friction with
the vertical wall.
At which angle \( \theta \) will the normal force
exerted by the floor upwards be at its
maximum?
Do not consider any motion by the plank (consider the forces exerted when the
plank is perfectly still for a given angle
\( \theta) \)
A. When \( \theta=0.00^{\circ} \) (the plank is horizontal)
B. When \( \theta=45.0^{\circ} \)
C. When \( \theta=90.0^{\circ} \) (the plank is vertical)
D. The angle \( \theta \) makes no difference
E. More information is needed
Subject: Maths
Solution of \( \boldsymbol{y}^{2} \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\mathbf{0} \) is
A \( \cdot \frac{y^{2}}{5}+\frac{y^{2}}{4 x^{2}}=c \)
в. \( \frac{x^{2}}{2}+\frac{x}{y}=C^{\prime} \)
c. \( \frac{y^{2}}{4}+\frac{y^{5}}{5 x^{4}}=c \)
D. \( \frac{x^{2}}{5}+\frac{x^{4}}{4 y^{4}}=c \)
Subject: Chemistry
Violet coloured complex obtained in the
detection of sulphur is :
\( \mathbf{A} \cdot N a_{2}\left[F e(N O)(C N)_{5}\right] \)
B . \( \operatorname{Na}_{3}\left[\mathrm{Fe}(\mathrm{ONSNa})(\mathrm{CN})_{5}\right. \)
c. \( N a_{4}\left[F e(C N)_{5} N O S\right. \)
D. Both (B) and (C)
Subject: Biology
Assertion
Coenzymes can be vitamins or
minerals.
Reason
NAD is an example of a coenzyme.
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
As shown in the figure, force of \( 105 N \)
each are applied in opposite directions,
on the upper and lower force of a cube of
side \( 10 \mathrm{cm}, \) shifting the upper face
parallel to itself by \( 0.5 \mathrm{cm} . \) If the side of
another cube of the same material is
\( 20 \mathrm{cm}, \) then under similar condition as
shown as above, the displacement will
be:
\( \mathbf{A} \cdot 0.25 \mathrm{cm} \)
B. \( 0.37 \mathrm{cm} \)
c. \( 0.75 \mathrm{cm} \)
D. \( 1.00 \mathrm{cm} \)
Subject: Physics
Assertion: By roughening the surface of
a glass sheet its transparency can be
reduced.

Reason: Glass sheet with rough surface absorbs more light.
A. Both assertion and reason are true and reason is the correct explanation of assertion
B. Both assertion and reason are true but the reason is not the correct explanation of assertion
c. Assertion is true but reason is false
D. Both the assertion and reason are false
E. Reason is true but assertion is false
Subject: Physics
Calculate \( Q \) value of the following nuclear reaction.
\[
_{13} A l^{27}+_{2} H e^{4} \longrightarrow_{14} S i^{30}+_{1} H^{1}+Q
\]
The exact mass of \( _{13} A l^{27} \) is \( \mathbf{2 6 . 9 8 1 5} \mathbf{a m u},_{\mathbf{1 4}} \mathbf{S i}^{\mathbf{3 0}} \mathbf{i s} \mathbf{2 9 . 9 7 3 8} \boldsymbol{a m u} \)
\( _{2} H e^{4} \) is \( 4.0026 a m u \) and \( _{1} H^{1} \) is
1.0078 amu.
Subject: Maths
The resultant of \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) is \( \boldsymbol{R} \) If \( \boldsymbol{Q} \) is
doubled, \( R \) is also doubled and if \( Q \) is
reversed, \( \boldsymbol{R} \) is again doubled. Then, \( \boldsymbol{P}^{2} \) :
\( Q^{2}: R^{2} \) given by
B. 3: 2: 2
c. 2: 3: 2
D. 2: 3: 1
Subject: Physics
Two electric charges of \( 9 \mu C \) and \( -3 \mu C \) are placed \( 0.16 m \) apart in air. There will be
a point \( \mathrm{P} \) at which electric potential is
\( z \) ero on the line joining the two charges
and in between them. The distance of \( \mathrm{P} \)
from \( 9 \mu C \) charge is:
A \( .0 .14 m \)
B. \( 0.12 m \)
c. \( 0.08 m \)
D. \( 0.06 m \)
Subject: Physics
Lis a circular ring made of a uniform
wire. Current enters and leaves the rind
through straight conductors which, if
produced, would have passed through
the centre \( C \) of the ring. The magnetic
field at \( C: \)
This question has multiple correct options
A. due to the straight conductors is zero
B. due to the loop is zero
C. due to the loop is proportional to \( \theta \)
D. due to the loop is proportional to \( (\pi-\theta) \)
Subject: Maths
If \( \frac{1}{k}=\frac{1}{3}+\frac{1}{4} \) then the value of \( K \) is
A \( \cdot 1 \frac{5}{7} \)
в. \( 2 \frac{5}{7} \)
\( \mathrm{c} \cdot_{3} \frac{5}{7} \)
D. \( _{4} \frac{5}{12} \)
Subject: Chemistry
From Bohr's model, radius of the orbit
and energy of the hydrogen atom are
calculated as:
This question has multiple correct options
A. the radius of the \( 1^{s t} \) orbit is \( 0.529 A^{\circ} \)
B. the energy of the \( 1^{s t} \) orbit is \( -13.6 e V \)
C. the energy of the \( 1^{s t} \) orbit is \( -21.72 \times 10^{-19} J \)
D. the radius of the \( 1^{s t} \) orbit is \( 1.06 A^{\circ} \)
Subject: Maths
If \( \int e^{x}(\operatorname{nn} x+x \operatorname{cn} x+1) d x=f(x)+ \)
cwhenf\( (1)=0, \) then \( f(e) \) is equal to
\( A \)
B \( \cdot e^{s} \)
\( \mathbf{c} \cdot e^{s-1} \)
D. \( e^{e+1} \)
Subject: Chemistry
Two particles \( A \) and \( B \) are in motion. If the wavelength associated with particle \( A \) is \( 5 \times 10^{-8} \) m. Calculate the
wavelength associated with particle B if its momentum is half of \( A \)
A. \( 5 \times 10^{-8} \mathrm{m} \)
B. \( 10^{-5} \mathrm{cm} \)
\( \mathrm{c} \cdot 10^{-6} \mathrm{cm} \)
D. \( 5 \times 10^{-8} \mathrm{cm} \)
Subject: Chemistry
Ratio of solubilities of gases \( N_{2} \& O_{2} \) in water from air at \( 25^{\circ} \) and 1 atm will
be if air is \( 20 \% \) by volume of \( O_{2} \) and \( 80 \% \)
by volume of \( N_{2} \) is:
\[
\begin{array}{c}
\text { Given }: \boldsymbol{K}_{\boldsymbol{H}}\left(\boldsymbol{N}_{\mathbf{2}}\right)=\mathbf{2} \times \mathbf{1 0}^{\mathbf{4}} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m} \\
\boldsymbol{K}_{\boldsymbol{H}}\left(\boldsymbol{O}_{2}\right)=\mathbf{1 0}^{4} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}
\end{array}
\]
\( A \cdot 8: 1 \)
B. 1: 8
c. 2: 1
D. 1: 2
Subject: Maths
Using the factor theorem it is found
that \( b+c, c+a \) and \( a+b \) are three
factors of the determinant \( \left|\begin{array}{ccc}-2 a & a+b & a+c \\ b+a & -2 b & b+c \\ c+a & c+b & -2 c\end{array}\right| . \) The other factor
in the value of the determinant is
A . 4
B. 2
\( \mathbf{c} \cdot a+b+c \)
D. none of these
Subject: Chemistry
The wave number for the shortest
wavelength transition in Paschal series of \( L i^{2+} \) lon is: \( \left(R: 109677 c m^{-1}\right) \)
A \( \cdot 27420 \mathrm{cm}^{-1} \)
B. \( 164515 \mathrm{cm}^{-1} \)
\( \mathbf{c} \cdot 219354 \mathrm{cm}^{-1} \)
D. \( 109677 \mathrm{cm}^{-1} \)
Subject: Maths
If a function \( f \) satisfy \( f\left(\frac{x+y}{3}\right)= \) \( \frac{\mathbf{2}+\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})}{\mathbf{3}} \) for real \( \mathbf{x} \) and \( \mathbf{y} \)
\( \boldsymbol{f}^{\prime}(2)=3 \) then \( \boldsymbol{f}(\boldsymbol{x}) \) is equal to
A \( \cdot-\frac{1}{12} x^{3}+x^{2} \)
B . \( 24 \log (3 x+2) \)
\( \mathbf{c} \cdot(3 x+2) \)
D. \( \frac{3}{4} x^{2}+2 \)
Subject: Maths
\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{lll}\boldsymbol{b}^{2}-\boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{b} \boldsymbol{c}-\boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b}-\boldsymbol{a}^{2} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{b}^{2}-\boldsymbol{a} \boldsymbol{b} \\ \boldsymbol{b} \boldsymbol{c}-\boldsymbol{a} \boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a} \boldsymbol{b}-\boldsymbol{a}^{2}\end{array}\right| \) then
\( \Delta \) equals
A \( \cdot(b-c)(c-a)(a-b) \)
B. \( a b c(b-c)(c-a)(a-b) \)
c. \( (a+b+c)(b-c)(c-a)(a-b) \)
D.
Subject: Chemistry
When 1 -pentyne \( (A) \) is treated with \( 4 N \)
alcoholic \( K O H \) at \( 175, \) it is converted
slowly into an equilibrium mixture of
1.3\% 1-pentyne (A) 95.2\% 2-pentyne (B)
and \( 3.5 \% \) of 1,2 -pentadiene \( (C) . \) The
equilibrium was maintained at 175 Calculate \( \Delta G \) for the following
equilibria.
\[
\begin{array}{l}
\qquad \boldsymbol{\Delta G}_{1}=? \\
\qquad \boldsymbol{B} \boldsymbol{G}_{2}=?
\end{array}
\]
From the calculate value of \( \Delta G_{1} \) and
\( \Delta G_{2} \) indicate the order of stability of \( A, B \) and \( C . \) Write a reasonable reaction mechanism showing all international leading to \( A, B \) and \( C \)
Subject: Physics
The surface that have zero flux are
\( \mathbf{A} \cdot S_{2}, S_{4}, \) and \( S_{5} \)
B. \( S_{1}, S_{3}, S_{4} \) and \( S_{6} \)
\( c \cdot S_{1}, S_{2}, \) and \( S_{3} \)
\( \mathrm{D} \cdot S_{2}, S_{3}, \) and \( S_{4} \)
Subject: Chemistry
If \( 9 g m H_{2} O \) is electrolysed completely with the current of \( 50 \% \) efficiency then :
A. 96500 charge is required
B. \( 2 \times 96500 C \) charge is required
c. \( 5.6 L \) of \( O_{2} \) at STP will be formed
D. \( 11.2 L \) of \( O_{2} \) at STP will be formed
Subject: Physics
A body is suspended from a spring balance kept in a satellite The reading
of the balance is \( W_{1} \) when the satellite
goes in an orbit of radius \( R \) and is \( W_{2} \)
when it goes in an orbit of radius \( 2 R \) Then
A. \( W_{1}=W_{2} \)
B. \( W_{1}<W_{2} \)
\( \mathbf{c} \cdot W_{1}>W_{2} \)
D. \( W_{1} \neq W_{2} \)
Subject: Maths
Construct a quadrilateral \( P Q R S \) in which \( \boldsymbol{P Q}=\mathbf{5} \boldsymbol{c m}, \boldsymbol{Q} \boldsymbol{R}=\mathbf{7 . 5 c m}, \boldsymbol{R S}= \)
\( P S=6.5 c m, \) and \( P R=10 c m \)
Measure the diagonal \( Q S \)
Subject: Chemistry
The equilibrium constant for a reaction
is \( K, \) and the reaction quotient is \( Q \). For a reaction mixture, the ratio \( \frac{K}{Q} \) is 0.33 This means that:
A. the reaction mixture will equilibrium to form more reactant species
B. the reaction mixture will equilibrium to form more product species
c. the equilibrium ratio of reactant to product concentrations will be 3
D. the equilibrium ratio of reactant to product concentrations will be 0.33
Subject: Maths
EFGH is a rhombus such the angle
EFG is \( 60^{\circ} . \) The magnitude of vectors \( \overrightarrow{F H} \) and \( \{m \overrightarrow{E G}\} \) are equal where \( m \) is a scalar. What is the value of \( m ? \)
\( A \cdot 3 \)
в. 1.5
\( c \cdot \sqrt{2} \)
D. \( \sqrt{3} \)
Subject: Physics
A ball is thrown from the top of a tower
with an initial velocityof \( 10 \mathrm{m} / \mathrm{s} \) at an
angle of \( 30^{\circ} \) above the horizontal. It hits
theground at a distance of \( 17.3 \mathrm{m} \) from the base of the tower.The height of the
tower \( \left(\mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2}\right) \) will be
A. \( 10 \mathrm{m} \)
B. \( 110 \mathrm{m} \)
\( c .12 \mathrm{m} \)
D. \( 100 \mathrm{m} \)
Subject: Chemistry
If copper is kept open in air, it slowly loses its shining brown surface and gains a green coating. It is due to the formation of:
A \( \cdot C u S O_{4} \)
в. \( C u C O_{3} \)
\( \mathbf{c} \cdot C u\left(N O_{3}\right)_{2} \)
D. \( C u O \)
Subject: Physics
An ideal monoatomic gas at \( 27^{\circ} \mathrm{C} \) is
compressed adiabatically to \( 8 / 27 \) times of its present volume. The increase in temperature of the gas is:
A \( .375^{\circ} \mathrm{C} \)
B . \( 402^{\circ} \mathrm{C} \)
c. \( 175^{\circ} \mathrm{C} \)
D. \( 475^{\circ} \mathrm{C} \)
Subject: Physics
A disc of mass \( \mathrm{m} \) and radius \( \mathrm{R} \) has a
concentric hole of a radius r. Its
moment of inertia about an axis
through its centre and perpendicular to its plane is :
A \( \cdot \frac{1}{2} m\left(R^{2}+r^{2}\right) \)
B . \( \frac{1}{2} m\left(R-r^{2}\right) \)
C \( \cdot \frac{1}{2} m\left(R^{2}-r^{2}\right) \)
D \( \cdot \frac{1}{2} m\left(R+r^{2}\right) \)
Subject: Maths
Let \( a, \beta, \gamma \) be distinct real numbers. The
points with position vectors ai \( +\beta j+ \) \( \gamma k, \beta i+\gamma j+a k, \gamma i+a j+\beta k \)
A. are collinear
B. form an equilateral triangle
c. form an scalene triangle
D. form a right angled triangle
Subject: Chemistry
A gaseous alkane is exploded with
oxygen. The moles of \( O_{2} \) for complete
combustion and \( C O_{2} \) formed is in the
ratio \( 7: 4 . \) Deduce the molecular
formula of alkane.
A \( \cdot C_{2} H_{6} \)
в. \( C H_{3} \)
\( \mathbf{c} \cdot C_{3} H_{6} \)
D. \( C_{2} H_{4} \)
Subject: Chemistry
Given below is a redox reaction. Which
of the following types the reaction belong to? \( \boldsymbol{C u}^{+\mathbf{2 + 6 - 2}} \boldsymbol{O}_{4(a q)}+\boldsymbol{Z} \boldsymbol{n}_{(s)} \rightarrow \boldsymbol{C u}_{(s)}+ \)
\( \underset{Z n S O_{4(a q)}}{+2+6+-2} \)
A. Combination reaction
B. Decomposition reaction
c. Metal displacement reaction
D. Non-metal displacement reaction
Subject: Maths
Volume and total surface area of a solid
hemisphere are equal in magnitude.
The volume is expressed in \( \mathrm{cm}^{3} \) and the
area is expressed in \( \mathrm{cm}^{2} \). Find the
radius of hemisphere.
A. \( 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
c. \( 4.5 \mathrm{cm} \)
D. \( 5.5 \mathrm{cm} \)
Subject: Physics
A block of mass \( 5 k g \) is released from rest when compression in spring is \( 2 m \)
Block is not attached with the spring and natural length of the spring is \( 6 m \) Maximum height of block from ground
is: \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
Subject: Chemistry
The reactivities of methanol (I), \( 1- \)
propanol (II), 2 - butanol (III) and 2 methyl-2- propanol (IV) towards sodium
metal follow the order:
\( A \cdot|>||>|||>\mid V \)
B. IV>|||> || > |
c. ।>IV> || > ||
D. IV > || > || > |
Subject: Maths
If \( \int \frac{\boldsymbol{f}(\boldsymbol{x})}{\log (\sin \boldsymbol{x})} \boldsymbol{d} \boldsymbol{x}=\log [\log \sin \boldsymbol{x}]+\boldsymbol{c} \)
\( \operatorname{then} f(x)=\dots \)
A . \( \cot x \)
B. \( \tan x \)
\( c . \sec x \)
D. \( \operatorname{cosec} x \)
Subject: Chemistry
Assertion: Thallium
(III) hydroxide is highly soluble in water.
Reason: Thallium
(III) hydroxide is the
most basic among 13th group
hydroxides.
A. Assertion is True, Reason is True, Reason is a correct explanation of Assertion
B. Assertion is True, Reason is True, Reason is not a correct explanation of Assertion
c. Assertion is True, Reason is False
D. Assertion is False, Reason is True
Subject: Physics
Assertion
For a particle performing SHM, its speed decreases as it goes away from the mean position.
Reason
In SHM, the acceleration is always
opposite to the velocity of the particle.
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
An aeroplane pilot wishes to fly due
west. A wind of \( 100 \mathrm{km} h^{-1} \) is blowing
towards south.
a. If the speed of the plane (its speed in
still air) is \( 300 \mathrm{km} h^{-1}, \) in which
direction should the pilot head?
What is the speed of the plane with respect to ground? IIlustrate with a vector diagram.
Subject: Maths
Two tailors, \( A \) and \( B \), earn Rs. 300 and
Rs. 400 per day, respectively. \( A \) can
stitch 6 shirts and 4 pairs of trousers while \( B \) can stitch 10 shirts and 4 pairs
of trousers per day. To find how many days should each of them work and if it
is desired to produce at least 60 shirts
and 32 pairs of trousers at a minimum
labour cost, formulate this as an LPP
and find the number of days \( A \) and \( B \) worked.
Subject: Maths
Expand:
\( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a}\end{array}\right| \)
Subject: Maths
A vector \( \vec{r} \) is equally inclined with the
coordinate axes. If the tip of \( \vec{r} \) is in the
positive octant and \( |\boldsymbol{r}|=\mathbf{6}, \) then \( \overrightarrow{\boldsymbol{r}} \) is
A \( \cdot 2 \sqrt{3}(\hat{i}-\hat{j}+\widehat{k}) \)
B \( \cdot 2 \sqrt{3}(-\hat{i}+\widehat{j}+\widehat{k}) \)
c. \( 2 \sqrt{3}(\hat{i}+\widehat{j}-\widehat{k}) \)
D \( \cdot 2 \sqrt{3}(\hat{i}+\hat{j}+\widehat{k}) \)
Subject: Maths
Fill in the blanks.
(i) Zero has
(ii) The numbers
and are their own
reciprocals.
(iii) The reciprocal of -5
is
(iv) Reciprocal of \( \frac{1}{x}, \) where \( x \neq 0 \)
is
(v) The product of two rational numbers is always a
(vi) The reciprocal of a positive rational number is
Subject: Maths
Find the distance between the lines \( 3 x+ \)
\( y-12=0 \) and \( 3 x+y-4=0 \)
A \( \cdot \frac{16}{\sqrt{10}} \)
в. \( \frac{12}{\sqrt{10}} \)
c. \( \frac{4}{\sqrt{10}} \)
D. \( \frac{8}{\sqrt{10}} \)
E. Answer Required
Subject: Physics
A solenoid of length 1 m, area of crosssection \( 4.0 \mathrm{cm}^{2} \) and having 4000 turns is placed inside another solenoid of 2000 turns having a cross-sectional \( \operatorname{area} 6 \mathrm{cm}^{2} \) and length 2 m. The mutual
inductance between the solenoids is
\( x \pi \times 10^{-5} H . \) Findout the value of \( x \)
Subject: Maths
In Figure \( 1, \) the ratio of \( A B \) to \( B C \) is 7:
5. If \( A C=1, \) calculate the distance
from \( A \) to the midpoint of \( B C \)
A \( \cdot \frac{5}{8} \)
B. \( \frac{2}{3} \)
c. \( \frac{19}{24} \)
D. \( \frac{3}{4} \)
Subject: Physics
A diverging electron beam enters a
region of varying potentials.
Intersection of equispaced
equipotential plane surfaces with the
plane of the paper are shown, with their
potentials mentioned in the figure. If
before entering this region, \( x \) and \( y \)
components of the velocity of electrons \( \operatorname{are} 3 \sqrt{\frac{2 e v}{m}} \) and \( \sqrt{\frac{e v}{m}}, \) respectively, where
\( m \) is the mass of an electron and \( e \) is
the electronic charge, then :
This question has multiple correct options
A. the electron beam is converged
B. the electron beam is diverged
C. the electric field is uniform and is directed towards negative x-axis
D. the electric field is uniform and is directed towards positive x-axis
Subject: Maths
In figure, \( \angle B A C=90^{\circ} \) and \( A D \perp B C \)
Then
\( \mathbf{A} \cdot B D \cdot C D=B C^{2} \)
B. \( A B . A C=B C^{2} \)
c. \( B D . C D=A D^{2} \)
D. \( A B . A C=A D^{2} \)
Subject: Physics
A drop of liquid having radius \( 2 \mathrm{mm} \) has
a terminal velocity \( 20 \mathrm{cms}^{-1} \), the
terminal velocity of a drop 1mm radius will be:
A. \( 40 \mathrm{cms}^{-1} \)
B. \( 20 \mathrm{cms}^{-1} \)
c. \( 10 \mathrm{cms}^{-1} \)
\( D \cdot 5 \mathrm{cms}^{-1} \)
Subject: Chemistry
Write the sum of geometrical isomers \( \operatorname{in}\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{N}-\mathrm{CH}\left(\mathrm{CH}_{3}\right)-\mathrm{COO}^{-}\right)_{2}\right] \) complex
and stereoisomers of \( \left[\mathrm{Pt}(\mathrm{gly})_{3}\right]^{+} \) complex.
Subject: Chemistry
A reaction \( A+B \rightarrow C \) is second order
with respect to \( A \) and independent of \( B \) The rate expression for the reaction is:
A. \( r a t e=K[A][B] \)
B . rate \( =K[A]^{2}[B] \)
c. \( r a t e=K[A]^{2}[B]^{2} \)
D. rate \( =K[A]^{2} \)
Subject: Maths
The distance travelled by the car, if a car travels \( 4 k m \) towards north at an
angle of \( 45^{\circ} \) to the east and then travels
a distance of \( 2 k m \) towards north at an
angle of \( 135^{\circ} \) to the east, is
\( \mathbf{A} \cdot 6 k m \)
в. \( 8 k m \)
\( c .5 k m \)
D. \( 2 \mathrm{km} \)
Subject: Physics
\( \boldsymbol{n} \) identical cells, each of emf \( \boldsymbol{E} \) and
internal resistance \( r, \) are joined in series to form a closed circuit. One of
the cell \( A \) is joined with reversed polarity. The potential difference across each cell except \( A \), is
A \( \cdot \frac{2 \varepsilon}{n} \)
в. \( \frac{n-1}{n} \)
c. \( \frac{n-2}{n} \)
D. \( \frac{2 n}{n-2} \)
Subject: Chemistry
Assertion
A small amount of acid or alkali is
added before electrolysis of water.
Reason
Pure water is weak electrolyte.
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: Maths
The sum of the infinite series \( 1+ \) \( \left(1+\frac{1}{5}\right)\left(\frac{1}{2}\right)+ \)
\( \left(1+\frac{1}{5}+\frac{1}{5^{2}}\right)\left(\frac{1}{2^{2}}\right)+\dots \dots \)
A \( \cdot \frac{20}{9} \)
в. \( \frac{10}{9} \)
\( c \cdot \frac{5}{9} \)
\( D \cdot \frac{5}{3} \)
Subject: Chemistry
Read the following passage and answer the questions at the end of it.
Dilute solution of alkali metals in
liquied \( N H_{3} \) is blue. It is the
ammoniated electron which is
responsible for the blue color of the
solution and the electrical conductivity is due to the ammoniated cation,
\( \left[\boldsymbol{M}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{x}\right]^{+} \) as well as the
ammoniated electron, \( \left[e\left(N H_{3}\right)_{y}\right]^{-} \)
values of \( x \) and \( y \) depend on the extent of
solvation \( \left(b y N H_{3}\right) . \) Dilute solutions are
paramagnetic due to free electrons.
What happens if alkali metal is allowed
to react with concentrated ammonia
solution?
A. Paramagnetic character of solvated electrons is retained
B. Solvated electrons associate to form electron-pairs and paramagnetic character decreases
C. Reducing character is increased
D. Reducing character is not affected
Subject: Chemistry
A compound of sodium does not give
\( C O_{2} \) when heated but it gives \( C O_{2} \)
when treated with dilute acids. A
crystalline compound is found to have
37.1\% Na and 14.52\% \( \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \). Hence, the
compound is :
A. \( N a H C O_{3} .10 H_{2} O \)
B. \( N a H C O_{3} .5 H_{2} O \)
c. \( N a_{2} C O_{3} .10 H_{2} O \)
D. \( N a_{2} C O_{3} . H_{2} O \)
Subject: Maths
Differentiate the following functions
with respect to \( \boldsymbol{x} \)
\[
\mathbf{f} \boldsymbol{y}=\cot ^{-1}\left\{\frac{\sqrt{\mathbf{1}+\sin \boldsymbol{x}}+\sqrt{\mathbf{1}-\sin \boldsymbol{x}}}{\sqrt{\mathbf{1}+\sin \boldsymbol{x}}-\sqrt{\mathbf{1}-\sin \boldsymbol{x}}}\right\}
\]
\( 0<x<\frac{\pi}{2}, \) show that \( \frac{d y}{d x} \) is
independent of \( \boldsymbol{x} \)
Subject: Physics
Two equal charges \( q \) are kept fixed at \( a \)
and \( +a \) along the \( x \) -axis. A particle of mass \( m \) and charge \( \frac{q}{2} \) is brought to the origin and given a small displacement along the \( x \) -axis, then:
A. the particle executes oscillatory motion
B. the particle remains stationary
c. the particle executes, SHM along x-axis
D. the particle executes SHM along y-axis