AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In Fig., \( A B C \) is the cross section of a
right-angled prism and \( A C D E \) is the
cross section of a glass slab. The value of \( \theta \) so that light incident normally on
the face \( A B \) does not cross the face \( A C \)
s (given \( \left.\sin ^{-1}(3 / 5)=37^{\circ}\right) \)
A \( \cdot \theta \leq 37 \)
В \( \cdot \theta<37 \)
\( c \cdot \theta \leq 53 \)
\( \theta<53 \)
3
Subject: Physics
Assertion
On polishing the surface the friction
decreases upto certain limit but
increases beyond that
Reason
On polishing the surface, the irregularities are cut off but beyond a certain limit the surface molecules
exert strong attractive forces on each
other
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The density of copper is \( 8.94 m L^{-1} \) Find out the number of coulombs
needed to plate an area \( 10 \times 10 \mathrm{cm}^{2} \) to
a thickness of \( 10^{-2} \mathrm{cm} \) using \( \mathrm{Cu} \) SO
solution as electrolyte. (At. mass of \( \boldsymbol{C u}=\mathbf{6 3 . 6}) \)
Subject: Physics
Two long straight wires are set parallel
to each other at separation \( r \) and each
carries a current \( i \) in the same
direction. The strength of the magnetic field at any point midway between the two wires is
A \( \cdot \frac{\mu_{0} i}{\pi r} \)
в. \( \frac{2 \mu_{0}}{\pi r} \)
c. \( \frac{\mu_{0} i}{2 \pi r} \)
D. zero
Subject: Chemistry
Ratio of \( C_{P} \) and \( C_{V} \) of gas ' \( X^{\prime} \) is 1.4. The
number of atoms of the gas ' \( X \) ' present
in 11.2 litres of at NTP will be:
A. \( 6.02 \times 10^{23} \)
B. \( 5.61 \times 10^{23} \)
c. \( 3.01 \times 10^{23} \)
D. \( 2.01 \times 10^{23} \)
Subject: Physics
Assertion
Induced potential across a coil and
therefore induced current is always
opposite to the direction of current due
to external source.
Reason
Lenz's law states that induced emf
always opposes the cause due to which it is being produced.
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
Work out the following divisions.
\( 96 a b c(3 a-12)(5 b+30) \div 144(a- \)
4)\( (b+6) \)
\( \mathbf{A} \cdot 96 a b c \)
B. \( 10 a b c \)
c. \( 144 a b c(b-12) \)
D. \( 24(a-b+c) \)
Subject: Physics
A truck starts from rest and accelerates
uniformly at \( 2.0 m s^{-2} . \) At \( t=10 s, \) a
stone is dropped by a person standing on the top of the truck (6 \( m \) high from the ground). What are the
(a) velocity, and (b) acceleration of the stone at \( t= \)
11 \( s \) ? (Neglect air resistance.)
Subject: Physics
Find the uncertainty in mass.
A \( \cdot 1.4 \times 10^{-35} \mathrm{kg} \)
в. \( 2.6 \times 10^{-11} \mathrm{kg} \)
c. \( 2.6 \times 10^{-13} k g \)
D. \( 8 \times 10^{-14} \mathrm{kg} \)
Subject: Chemistry
The two compounds
\( \left[\boldsymbol{C o}\left(\boldsymbol{S O}_{4}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\right] \boldsymbol{B r} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{S O}_{4}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\right] \boldsymbol{C l} \) represent
A. Linkage is isomerism
B. lonisation isomerism
c. co - ordination isomerism
D. No isomerism
Subject: Chemistry
The oxidation state of the most
electronegative element in the products
of the reaction between \( B a O_{2} \) and
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is:
A. 0 and -1
B. - - 1 and - 2
c. - - a and o
D. - 2 and +1
Subject: Chemistry
Calculate the frequency of the radiation emitted when an electronjumps from \( n=3 \) to \( n=2 \) in a hydrogen atom is:
A \( \cdot 4.57 \times 10^{14} s^{-1} \)
В. \( 4.57 \times 10^{16} s^{-1} \)
\( c \cdot 5.01 \times 10^{14} s^{-1} \)
-1
D. \( 5.01 \times 10^{16} s^{-1} \)
Subject: Maths
Find \( \frac{d y}{d x}, \) if \( x+y=\sin (x-y) \)
A \( \cdot \frac{\cos (x-y)-1}{\cos (x-y)+1} \)
B \( \cdot \frac{\cos (x-y)+1}{\cos (x-y)-1} \)
C \( \frac{\cos (x+y)+1}{\cos (x-y)-1} \)
D. \( \frac{\cos (x+y)-1}{\cos (x-y)+1} \)
Subject: Physics
Assertion
A cyclist always bends inwards while
negotiating a curve.
Reason
By bending he lowers his centre of
gravity.
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
The number of candy bars students
brought to school the day after Halloween are given in the table. What
is the mode?
\begin{tabular}{|c|c|}
\hline Number of Candy Bars & Number of Students \\
\hline 0 & 1 \\
\hline 1 & 1 \\
\hline 2 & 1 \\
\hline 3 & 3 \\
\hline 4 & 0 \\
\hline 5 & 4 \\
\hline 7 & 2 \\
\hline 8 & 2 \\
\hline
\end{tabular}
4
\( B \)
\( c \)
\( D \)
Subject: Physics
A dipole of moment p is placed in uniform electric field E then torque acting on it is given by : -
A.
\[
\vec{\tau}=\overrightarrow{\mathrm{p}} \cdot \overrightarrow{\mathrm{E}}
\]
в.
\[
\vec{\tau}=\vec{p} \times \vec{E}
\]
\( c \)
\[
\vec{\tau}=\vec{p}+\overrightarrow{\mathrm{E}}
\]
D.
\[
\vec{\tau}=\overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{E}}
\]
Subject: Maths
\( \ln \) a \( \triangle A B C, A(-2,3), B(2,1) \) and
\( C(1,2) . \) What is the foot of the altitude
from the vertex \( A \) of the triangle \( A B C ? \)
A \( .(1,4) \)
в. (-1,3)
c. (-2,4)
D. (-1,4)
Subject: Chemistry
Which of the following is incorrect
statement?
\( \mathbf{A} \cdot P b F_{4} \) is covalent in nature
B. \( S i C l_{4} \) is easily hydrolysed
\( \mathbf{c} \cdot \operatorname{Ge} X_{4}(X=F, C l, B r, I) \) is more stable than \( G e X_{2} \)
D. \( S n F_{4} \) is ionic in nature
Subject: Physics
A body of mass \( 2 k g \) initially at rest moves under the action of an applied
horizontal force of \( 7 N \) on a table with
coefficient of kinetic friction \( =\mathbf{0 . 1} \)
Compute the Work done by the applied force in \( 10 s \)
в. \( 890 J \)
c. \( 1000 J \)
D. \( 5000 J \)
Subject: Physics
If \( I \) is regarded as the fourth dimension, then the dimensional formula of charge
in terms of current \( \boldsymbol{I} \) is
\( \mathbf{A} \cdot\left[I T^{2}\right] \)
B . \( \left[I^{0} T^{0}\right] \)
c. \( \left[I^{-1} T^{0}\right] \)
D. [IT]
Subject: Chemistry
\( \begin{array}{ll}\text { List I } & \text { List II } \\ \text { a. Troposphere } & 1.11-50 \mathrm{Km} \\ \text { b. Stratosphere } & 2.85-500 \mathrm{Km} \\ \text { c. Mesosphere } & \text { 3. 0-11 Km } \\ \text { d. Thermosphere } & \text { 4. 50-85 Km } \\ \text { 5. Above 500 Km } & \text { 1) }\end{array} \)
The correct match is:
A. \( a-5, b-2, c-3, d-4 \)
B. \( a-1, b-2, c-3, d-4 \)
\( c \cdot a-3, b-1, c-4, d-2 \)
D. \( a-2, b-4, c-5, d-1 \)
Subject: Biology
Assertion
Wilting occurs due to loss in turgidity
Reason

Turgor pressure checks the excessive
entry of water into cells
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
Simplify:
\( \mathbf{2 0}(\boldsymbol{y}+\mathbf{4})\left(\boldsymbol{y}^{2}+\mathbf{5} \boldsymbol{y}+\mathbf{3}\right) \div \mathbf{5}(\boldsymbol{y}+\mathbf{4}) \)
A \( \cdot 5\left(y^{2}+5 y+3\right) \)
B \( \cdot 4\left(y^{2}-5 y+3\right) \)
\( \mathbf{c} \cdot 4\left(y^{2}+5 y-3\right) \)
D. \( 4\left(y^{2}+5 y+3\right) \)
Subject: Physics
Two waves \( Y_{1}=a \sin \omega t \) and \( Y_{2}= \)
\( \operatorname{asin}(\omega t+\delta) \) are producing
interference, then resultent intensity is:
A \( \cdot a^{2} \cos ^{2} \delta / 2 \)
B . \( 2 a^{2} \cos ^{2} \delta / 2 \)
c. \( 3 a^{2} \cos ^{2} \delta / 2 \)
D. \( 4 a^{2} \cos ^{2} \delta / 2 \)
Subject: Physics
Derive Lens maker formula \( \frac{\mathbf{1}}{\boldsymbol{f}}=\mathbf{( n}- \)
1) \( \left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) . \) The lower half of the concave mirror's reflecting surface is covered with an opaque material. What
will be the effect on the image formed by the mirror?
Subject: Physics
The time taken by a particle performing
SHM to pass from point \( A \) to \( B \) where
its velocities are same is 2 s. After
another \( 2 s \) it returns to \( B \). The ratio of
distance \( O B \) to its amplitude (where \( O \)
is the mean position) is :
A. \( 1: \sqrt{2} \)
B . \( (\sqrt{2}-1): 1 \)
c. 1: 2
D. \( 1: 2 \sqrt{2} \)
Subject: Chemistry
Polarisation is the distortion of the
shape of an anion by an adjacently
placed cation. Which of the following statements is correct?
This question has multiple correct options
A. Maximum polarisation is brought about by a cation of high charge
B. Maximum polarisation is brought about by a cation of low radius
c. A large cation is likely to bring about a large degree of polarisation
D. Polarising power of a cation is less than that of anion
Subject: Maths
Find the volume of a sphere whose
surface area is \( 55.44 \mathrm{cm}^{2} . \) (Take \( \pi=\frac{22}{7} \)
\( \mathbf{A} \cdot 38.808 \mathrm{cm}^{3} \)
B. \( 38.008 \mathrm{cm}^{3} \)
c. \( 32.808 \mathrm{cm}^{3} \)
D. \( 28.808 \mathrm{cm}^{3} \)
Subject: Maths
The distance of the point (1,-5,9) from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \) measured
along the line \( x=y=z \) is:
\( A \cdot 3 \sqrt{10} \)
в. \( 10 \sqrt{3} \)
c. \( \frac{10}{\sqrt{3}} \)
D. \( \frac{20}{3} \)
Subject: Maths
Solve the following simultaneous equations:
\( \frac{\mathbf{1 6}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{2}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{1} ; \quad \frac{\mathbf{8}}{\boldsymbol{x}+\boldsymbol{y}}- \)
\( \frac{12}{x-y}=7 \)
A \( . x=2, y=3 \)
B. \( x=6, y=1 \)
c. \( x=7, y=4 \)
D. \( x=3, y=5 \)
Subject: Maths
If \( z_{1} \) and \( z_{2} \) are two complex numbers satisfying the equation \( \left|\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\right|=1 \) then \( \frac{z_{1}}{z_{2}} \) is a number which is
A . Positive real
B. Negative real
c. zero or purely imaginary
D. none of these
Subject: Chemistry
Assertion
Coal is a fossil fuel.
Reason
It is formed due to compression of
inorganic material over millions of
years.
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
C. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect and the Reason is correct
Subject: Physics
Two thin infinite parallel sheets have uniform surface densities of charge \( +\sigma \)
and \( -\sigma . \) The value of \( E \) in the
space outside the sheets is:
A \( \cdot \frac{\sigma}{\epsilon_{0}} \)
в. \( \frac{\sigma}{2 \epsilon_{0}} \)
c. zero
D. \( \frac{2 \sigma}{\epsilon_{0}} \)
Subject: Physics
A block of mass \( 0.2 \mathrm{kg} \) is suspended
from the ceiling by a light string. \( \mathbf{A} \) second block of mass \( 0.3 \mathrm{kg} \) is
suspended from the first block through another string. Find the tensions in the
two strings. Take \( g=10 m / s^{2} \)
Subject: Physics
Two balls are dropped from different heights at different instants. Second
ball is dropped 2 sec after the first ball. If both balls reach the ground simultaneously after 5 sec. of dropping the first ball, the difference of initial
heights of the two balls will be: \( (g= \)
\( \left.9.8 m / s^{2}\right) \)
\( \mathbf{A} \cdot 58.8 \mathrm{m} \)
B. \( 78.4 \mathrm{m} \)
c. \( 98.0 \mathrm{m} \)
D. \( 117.6 \mathrm{m} \)
Subject: Physics
The radius of the curved part of the wire is \( R, \) the linear parts are assumed to be
very long. Find the magnetic induction of the field at the point \( O \) if a currentcarrying wire has the shape shown in
figure above.
A \( \cdot B=\frac{3 \mu_{0}}{4} \frac{i}{R} \)
В. \( B=\frac{\mu_{0}}{2} \frac{i}{R} \)
c. \( _{B}=\frac{2 \mu_{0}}{3} \frac{i}{R} \)
D. \( B=\frac{\mu_{0}}{4} \frac{i}{R} \)
Subject: Biology
Match the columns:
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { a. } & \text { Thymus gland } & \text { p. } & \text { Epinephrine } \\ \text { b. } & \begin{array}{l}\text { Adrenal } \\ \text { medulla }\end{array} & \text { q. } & \text { Thymosin } \\ \text { c. } & \begin{array}{l}\text { Parathyroid } \\ \text { gland }\end{array} & \text { r. } & \text { Calcitonin } \\ \text { d. } & \text { Thyroid gland } & \text { s. } & \begin{array}{l}\text { Bone } \\ \text { desorption }\end{array}\end{array} \)
\( A \cdot a-q, b-p, c-s, d-r \)
\( B \cdot a-s, b-r, c-q, d-p \)
\( \mathrm{C} \cdot \mathrm{a}-\mathrm{r}, \mathrm{b}-\mathrm{p}, \mathrm{c}-\mathrm{s}, \mathrm{d}-\mathrm{q} \)
D. \( a-p, b-q, c-q, d-s \)
Subject: Chemistry
Consider the following elementary
reaction
\[
\mathbf{2 A}+\boldsymbol{B}+\boldsymbol{C} \rightarrow \boldsymbol{\text {Products.}}
\]
All reactant are present in the gaseous
state and reactant \( C \) is taken in excess.
What is the unit of rate constant of the
reaction?
\( \mathbf{A} \cdot \operatorname{mol} L^{-1} \operatorname{tim} e^{-1} \)
B. \( \operatorname{time}^{-1} \)
\( \mathbf{c} \cdot m o l^{-1} L^{2} \operatorname{time}^{-1} \)
D. \( m o l^{-2} L^{2} \)time\( ^{-1} \)
Subject: Maths
The value of
\( \frac{\tan ^{2} 60^{0}-2 \tan ^{2} 45^{0}+\sec ^{2} 30^{0}}{3 \sin ^{2} 45^{0} \sin 90^{0}+\cos ^{2} 60^{0} \cos ^{3} 0^{0}} \)
A \( \cdot \frac{49}{12} \)
B. \( \frac{7}{3} \)
c. \( \frac{14}{9} \)
D.
Subject: Maths
Find the locus of the point, the sum of the squares of whose distances from
the planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{0}, \boldsymbol{x}-\boldsymbol{y}=\mathbf{0} \)
\( x+y-2 z=0 \) is 7
Subject: Physics
The velocity-time graph given shows the motion of a cyclist. Its velocity is given
by
A \( \cdot 20 m s^{-1} \)
B. \( 22.5 m s^{-1} \)
\( \mathrm{c} \cdot 19 \mathrm{ms}^{-1} \)
D. \( 21 m s^{-1} \)
Subject: Physics
A wire has non-uniform cross-section
as shown in figure. A steady current
flows through it. The drift speed of
electrons at points \( \boldsymbol{P} \) and \( \boldsymbol{q} \) is \( \boldsymbol{v}_{\boldsymbol{p}} \) and \( \boldsymbol{v}_{\boldsymbol{Q}} \)
A \( \cdot v_{p}=v_{Q} \)
В \( \cdot v_{p}<v_{Q} \)
с. \( v_{p}>v_{Q} \)
Data insufficient
Subject: Physics
Assertion
A vessel carrying water at room
temperature is kept on a flame. As a result, its heat increases.
Reason
Heat flows from higher temperature to
lower temperature
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
A two-step mechanism has been suggested for the reaction of nitric oxide and bromine. \( N O(g)+B r_{2}(g) \stackrel{K_{1}}{\longrightarrow} N O B r_{2}(g) \)
\( N O B r_{2}(g)+N O(g) \stackrel{K_{2}}{\longrightarrow} 2 N O B r(g) \)
The observed rate law is, rate \( = \)
\( \boldsymbol{k}[\boldsymbol{N} \boldsymbol{O}]^{2}\left[\boldsymbol{B} \boldsymbol{r}_{2}\right] . \) Hence, the rate
determining step is :
A \( \cdot N O(g)+B r_{2}(g) \rightarrow N O B r_{2}(g) \)
в. \( N O B r_{2}(g)+N O(g) \rightarrow 2 N O B r(g) \)
c. \( 2 N O(g)+B r_{2}(g) \rightarrow 2 N O B r(g) \)
D. none of these
Subject: Physics
Charges \( 5 \mu \mathrm{C} \) and \( 10 \mu \mathrm{C} \) are placed \( 1 \mathrm{m} \)
a part. Workdone to bring these charges
at a distance \( 0.5 \mathrm{m} \) from each other is
\( \left(k=9 \times 10^{9} S I\right) \)
\( \mathbf{A} \cdot 9 \times 10^{4} J \)
B . \( 18 \times 10^{4} J \)
c. \( 45 \times 10^{2} J \)
D. \( 9 \times 10^{-1} J \)
Subject: Biology
Assertion
More/s and Truffles are edible fungi
Reason
Ascocarps are edible
A. If both the assertion and the reason are true and the
reason
is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is
not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Maths
\( \operatorname{Given} \boldsymbol{A}(\mathbf{1},-\mathbf{1}, \mathbf{0}) ; \boldsymbol{B}(\mathbf{3}, \mathbf{1}, \mathbf{2}) ; \boldsymbol{C}(\mathbf{2},-\mathbf{2}, \mathbf{4}) \)
and \( D(-1,1,-1) \) which of the following
points neither lie on \( A B \) nor on \( C D \)
A \( .(2,2,4) \)
В. (2,-2,4)
c. (2,0,1)
D. (0,-2,-1)
Subject: Chemistry
In which compounds does vanadium
have an oxidation number of \( +4 ? \)
A. \( N H_{4} V O_{2} \)
B . \( K_{4}\left[V(C N)_{6}\right] \)
\( c \cdot v o s O_{4} \)
D. \( \operatorname{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)
Subject: Maths
\( A B C D \) is a quadrilateral, \( E \) is the point of intersection of the line joining the
middle points of the opposite sides. If \( \boldsymbol{O} \) is any point, then \( \hat{O} A+\hat{O} B+\hat{O C}+ \) \( \hat{O} D= \)
A \( \cdot 4 O E \)
в. 3 О
\( \mathrm{c} \cdot 2 O \hat{E} \)
D. \( O E \)
Subject: Maths
A bag contains some white and some
black balls, all of which are
distinguishable from each other, all combinations of balls being equally likely. The total number of balls in the
bag is \( 10 . \) If three balls are drawn at random and all of them are found to be
black, the probability that the bag contains 1 white and 9 black balls is :
A \( \cdot \frac{14}{55} \)
B. \( \frac{12}{55} \)
c. \( \frac{8}{55} \)
D. \( \frac{2}{11} \)
Subject: Chemistry
Find the incorrectly matched compounds with the functional group.
A. \( C H_{3} C O O H, \) hydroxy
B. \( C H_{3} O H, \) hydroxy
c. \( C H_{3} C H_{2} N H_{2} \), amine
D. \( C C l_{3} C O O H, \) carboxylic acid
E . \( C_{6} H_{5} C O O H, \) carboxylic acid
Subject: Maths
The value of \( \int \frac{d x}{x\left(x^{n}+1\right)} \) is
A \( \cdot \frac{1}{n} \log \left(\frac{x^{n}}{x^{n}+1}\right)+C \)
в. \( \log \left(\frac{x^{n}+1}{x^{n}}\right)+C \)
c. \( \frac{1}{n} \log \left(\frac{x^{n}+1}{x^{n}}\right)+C \)
D. \( \log \left(\frac{x^{n}}{x^{n}+1}\right)+C \)
Subject: Physics
A wire of cross section \( A \) is stretched
horizontally between two clamps located \( 2 l \) m apart. A weight \( W \) kg is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance \( x<1 \) the strain produced is
A \( \cdot \frac{2 x^{2}}{l^{2}} \)
в. \( \frac{x^{2}}{l^{2}} \)
c. \( \frac{x^{2}}{2 l^{2}} \)
D. None of these
Subject: Maths
The differential equation of the family of circles with fixed radius 5 units and
centre on the line \( y=2 \) is given by:
A \( \cdot(y-2)^{2} y^{\prime 2}=25-(y-2)^{2} \)
B . \( (x-2)^{2} y^{\prime 2}=25+(y-2)^{2} \)
c. \( (x-2) y^{\prime 2}=25-(y-2)^{2} \)
D . \( (y-2) y^{\prime 2}=25-(y-2)^{2} \)
Subject: Maths
Three lines \( \boldsymbol{p} \boldsymbol{x}+\boldsymbol{q} \boldsymbol{y}+\boldsymbol{r}=\mathbf{0}, \boldsymbol{q} \boldsymbol{x}+\boldsymbol{r} \boldsymbol{y}+ \)
\( \boldsymbol{p}=\mathbf{0} \) and \( \boldsymbol{r} \boldsymbol{x}+\boldsymbol{p} \boldsymbol{y}+\boldsymbol{q}=\mathbf{0} \) are
concurrent if
This question has multiple correct options
A \( . p+q+r=0 \)
B . \( p^{2}+q^{2}+r^{2}=p r+q r+p q \)
c. \( p^{3}+q^{3}+r^{3}=3 p q r \)
D. none of these
Subject: Maths
Assertion
If \( A \) is skew symmetric matrix of order 3 then its determinant should be zero
Reason

If \( A \) is square matrix, then \( d e t A= \)
\( \operatorname{det} A^{\prime}=\operatorname{det}\left(-A^{\prime}\right) \)
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
Determine the standard reduction
potential for the half reaction.
\[
\boldsymbol{C l}_{2}+\mathbf{2} e^{-} \rightarrow \mathbf{2} \boldsymbol{C l}^{-}
\]
Given: \( \boldsymbol{P t}^{2+}+\mathbf{2} \boldsymbol{C l}^{-} \rightarrow \boldsymbol{P t}+ \)
\[
\begin{array}{l}
\boldsymbol{C l}_{2}, \boldsymbol{E}_{c e l l}=-\mathbf{0 . 1 5} \boldsymbol{V} \\
\boldsymbol{P t}^{2+}+\boldsymbol{2} e^{-} \rightarrow \boldsymbol{P t}, \boldsymbol{E}=1.20 \boldsymbol{V}
\end{array}
\]
Subject: Chemistry
In a reaction involving one single reactant, the fraction of the reactant
consumed may be defined as \( \boldsymbol{f}= \) \( \left(1-\frac{C}{C_{0}}\right) \) where \( C_{0} \) and \( C \) are the concentrations of the reactant at the
after time, t. For a first order reaction:
A \( \cdot \frac{d f}{d t}=k(1-f) \)
B. \( -\frac{d f}{d t}=k f \)
c. \( -\frac{d f}{d t}=k(1-f) \)
D. \( \frac{d f}{d t}=k f \)
Subject: Physics
For the combination of gates shown
here, which of the following truth table
part is not true?
\( \mathbf{A} \cdot A=0, B=1, C=1 \)
B . \( A=0, B=0, C=0 \)
C \( . A=1, B=1, C=1 \)
D. \( A=1, B=0, C=1 \)
Subject: Physics
Angle of dip \( \delta \) and latitude \( \lambda \), on earth's
surface are related as
\( \mathbf{A} \cdot \tan \delta=2 \tan \lambda \)
B. \( \tan \delta=\cot \lambda \)
\( \mathbf{C} \cdot \tan \delta=\frac{\tan \lambda}{2} \)
D. \( \tan \delta=\tan \lambda \)
Subject: Physics
At a turn of track is banked for
optimum speed of \( 40 k m / h \). At the
instant shown in the figure a car is
travelling out of the plane of the figure. If the car travels at \( 60 k m / h, \) the net
frictional force acting on the wheels
must be :
A. static in nature and point downward along the bank of the track for safe driving
B. static in nature and point upward along the bank of the track for safe driving
c. kinetic in nature and points upward along the bank of the track for safe driving
D. kinetic in nature and points downwards along the bank of the track for safe driving
Subject: Maths
A rectangle with sides \( 2 m-1 \) and \( 2 n-1 \)
is divided into square of unit length by drawing parallel lines as shown in
diagram, then the number of rectangles possible with odd side length is
A \( \cdot(m+n-1)^{2} \)
B. \( 4^{m+n-1} \)
\( \mathbf{c} \cdot m^{2}-n^{2} \)
D. \( m(m+1) n(n+1) \)
Subject: Maths
Simplify: \( \left(8 m^{2}-9 m\right) \div 3 m \)
A \( \cdot \frac{1}{3}(8 m-9) \)
B. \( 8 m-9 \)
c. \( \frac{1}{3}(8 m-3) \)
D. \( 5 m-3 \)
Subject: Physics
two neighboring coils. A and B have mutual inductance of \( 20 \mathrm{mH} \). The
current flowing through A is given by \( i=3 t^{2}-4 t+6 . \) The induced emf at \( t= \)
2s is:
A . \( 100 m V \)
В. \( 160 m V \)
c. 260 \( \mathrm{mv} \)
D. 300 mv
Subject: Maths
The magnitude of the component of the \( \operatorname{vector}(2 \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}+\hat{\mathbf{k}}) \) along \( (\mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{k}}) \) is :
\( A \cdot 1 / 2 \)
B. 14/5
\( c \cdot 3 \)
D.
Subject: Physics
A hollow metal sphere of radius \( 5 \mathrm{cm} \) is charged such that the potential on its
surface is \( 10 V . \) The potential at a
distance of \( 2 \mathrm{cm} \) from the centre of the
sphere is:
A. zero
B. \( 10 V \)
\( c .4 V \)
D. \( 10 / 3 V \)
Subject: Maths
Assertion
Statement -1: If \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{c}\boldsymbol{x} \cos \boldsymbol{x} \cdot \sin \left(\frac{1}{\boldsymbol{x} \cos \boldsymbol{x}}\right), \quad \text { whenever de } \\ \mathbf{0}\end{array}\right. \)
then \( f(x) \) is continuous
Reason
Statement - \( 2: \lim _{x \rightarrow \infty} \frac{\sin x}{x}=0 \)
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-
c. Statement- -1 is True, Statement-2 is False
D. Statement- -1 is False, Statement-2 is True