AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Out of \( N O, N O_{2}, N_{2} O, N_{2} O_{4} \) and \( N_{2} O_{2} \)
the paramagnetic species
are
A. \( N_{2} O_{2} \) and \( N_{2} O_{4} \)
B. \( N O_{2} \) and \( N_{2} O_{4} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{2} \) and \( \mathrm{NO}_{2} \)
D. \( N O \) and \( N O_{2} \)
Subject: Maths
If \( f(x)=x^{2}-3 x+4 \), then find the
value of \( 3\left(x_{1}+x_{2}\right) \) if \( x_{1}, x_{2} \) satisfying
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{2} \boldsymbol{x}+\mathbf{1}) \)
Subject: Biology
Which of the following statements does
not apply to eutrophication.
A. It is natural ageing of a lake by nutrient enrichment of its water
B. In a young lake the water is cold and clear and supports less life
C. The nutrients such as sulphur and phosphorus encourage the growth of aquatic organisms in the lake
D. Pollutants released by man radically accelerate the ageing process of a lake
E . Overgrowth of algae leads to scum that depletes the level of dissolved oxygen in water
Subject: Maths
In the following case, use the remainder
theorem and find the remainder when
\( \boldsymbol{p}(\boldsymbol{x}) \) is divided by \( \boldsymbol{g}(\boldsymbol{x}) \cdot \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{4} \boldsymbol{x}^{3}- \)
\( 12 x^{2}+14 x-3 g(x)=2 x-1 \)
Subject: Chemistry
Blasting of TNT is done by mixing it with:
A . \( \mathrm{NH}_{4} \mathrm{Cl} \)
в. \( \mathrm{NH}_{4} \mathrm{NO}_{3} \)
c. \( \mathrm{NH}_{4} \mathrm{NO}_{2} \)
D. \( \left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \)
Subject: Physics
A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length \( 28 \mathrm{cm} \). When its
curved surface is silvered and the plane
surface is not silvered, it is equivalent
to a concave mirror of focal length 10 \( \mathrm{cm}, \) then the refractive index of the
material of the lens is:
\( \mathbf{A} \cdot \frac{9}{14} \)
B. \( \frac{14}{9} \)
c. \( \frac{17}{9} \)
D. None of these
Subject: Chemistry
Heptane and octane form ideal solution.
At \( 373 \mathrm{K} \), the vapour pressures of the two liquids are \( 105.2 \mathrm{kPa} \) and \( 46.8 \mathrm{kPa} \) respectively. What will be the vapour
pressure, in bar, of a mixture of 25 g heptane and 35 g of octane?
Subject: Chemistry
A storage battery contains a solution of
\( H_{2} S O_{4} 38 \% \) by weight. What will be the
Van't Hoff factor if the
\( \boldsymbol{\Delta} \boldsymbol{T}_{f \text {experiment}} \) is \( \mathbf{2 9 . 0 8} .\left[\text { Given } \boldsymbol{K}_{f}=\mathbf{1}\right. \)
B . \( i=2.5 \)
c. \( i=3 \)
D. \( i=3.5 \)
Subject: Maths
The difference of slopes of lines
represent by \( y^{2}-2 x y \sec ^{2} \alpha+ \)
\( \left(3+\tan ^{2} \alpha\right)\left(\tan ^{2} \alpha-1\right) x^{2}=0 \) is
\( A \cdot 3 \)
B. 4
\( c \cdot 0 \)
D.
Subject: Biology
Match the items of column I and
column II
\begin{tabular}{ccc|c} 
& Column I & & Column II \\
\( a \) & Auxin & \( p \) & \( G A_{3} \) \\
\( b \) & Gibberellin & \( q \) & Indole Acetic Acid \\
\( c \) & Cytokinin & \( r \) & Abscisic Acid \\
\( d \) & Dormin & \( s \) & Acetic acid \\
& & \( t \) & Zeatin
\end{tabular}
\( A \)
\( a-q, b-r, c-p, d-t \)
B. \( a-q, b-s, c-p, d-t \)
c. \( a-q, b-p, c-t, d-r \)
D. \( a-q, b-t, c-p, d-r \)
Subject: Physics
Two particles move in the same straight
line starting at the same moment from
the same point in the same
direction. The first moves with constant
velocity u and the second starts from
rest with constant acceleration \( f . \) Then
This question has multiple correct options
A. They will be at the greatest distance at the end of time Idfrac \( \{\mathrm{u}\}\{2 \mathrm{f}\} \$ \$ \) from the start
B. They will be at the greatest distance at the end of time Idfrac \( \{\mathrm{u}\}\{\mathrm{f}\} \$ \$ \) from the start
C their greatest distance is \( \frac{u^{2}}{2 f} \)
D. Their greatest distance is \( \frac{u^{2}}{f} \)
Subject: Chemistry
The uncertainty in position of an electron \( \left(\boldsymbol{m}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{2 8}} \mathbf{g m}\right) \) moving
with a velocity \( 3 \times 10^{4} \mathrm{cm} / \mathrm{s} \) accurate
upto \( 0.001 \% \) will be:
\( A . \quad 3.84 \mathrm{cm} \)
B. 1.92 \( \mathrm{cm} \)
c. \( 7.68 \mathrm{cm} \)
D. 5.76 cm
Subject: Physics
A parallel beam of light is incident on a
glass prism in the shape of a quarter
cylinder of radius \( R=0.05 m \) and
refractive index \( n=1.5 \) placed on a
horizontal table as shown in the figure.
Beyond the cylinder, a patch of light is
found whose nearest distance \( x \) from
the cylinder is
A \( \cdot(3 \sqrt{3}-4) \times 10^{-2} m \)
B \( \cdot(3 \sqrt{2}-2) \times 10^{-2} m \)
\( \mathbf{c} \cdot(3 \sqrt{5}-5) \times 10^{-2} m \)
D. \( (3 \sqrt{2}-3) \times 10^{-2} m \)
Subject: Maths
The given figure shows a solid formed of
a solid cube of side \( 40 \mathrm{cm} \) and a solid
cylinder of radius \( 20 \mathrm{cm} \) and height 50 \( \mathrm{cm} \) attached to the cubes as shown.
Find the volume and the total surface
area of the whole solid [Take \( \boldsymbol{\pi}=\mathbf{3 . 1 4}] \)
A \( \cdot 122700 \mathrm{cm}^{3} \) and \( 15880 \mathrm{cm}^{2} \)
B. \( 126800 \mathrm{cm}^{3} \) and \( 15880 \mathrm{cm}^{2} \)
c. \( 148900 \mathrm{cm}^{3} \) and \( 15880 \mathrm{cm}^{2} \)
D. \( 148800 \mathrm{cm}^{3} \) and \( 15880 \mathrm{cm}^{2} \)
Subject: Physics
Find the torque of a force \( \overrightarrow{\boldsymbol{F}}=-\mathbf{3} \hat{\mathbf{i}}+ \)
\( \hat{\boldsymbol{j}}+\boldsymbol{5} \widehat{\boldsymbol{k}} \) acting at the point \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{7} \hat{\boldsymbol{i}}+ \)
\( \mathbf{3} \widehat{\boldsymbol{j}}+\widehat{\boldsymbol{k}} \)
\( \mathbf{A} \cdot 14 \hat{i}-38 \hat{j}+16 \hat{k} \)
B . \( 4 \hat{i}-4 \widehat{j}+6 \hat{k} \)
c. \( \$ \$-13-16 \) lhat \( \{k\}-38 \) lhat \( \{j\}-16 \mid \) hat \( \{i\} \$ \$ \)
D. none of these
Subject: Maths
Which of the following points lie above X-axis
\( \boldsymbol{a}) \boldsymbol{A}(-\boldsymbol{3}, \boldsymbol{5}) \)
\( \boldsymbol{b}) \boldsymbol{B}(\boldsymbol{5},-1) \)
\( c) C(0,2) \)
\( \boldsymbol{d}) \boldsymbol{D}(\boldsymbol{0}, \boldsymbol{2}) \)
\( e) E(5,1) \)
\( \boldsymbol{f}) \boldsymbol{F}(\boldsymbol{3}, \mathbf{1}) \)
Subject: Maths
Find the latus rectum of the parabola \( \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{y}-\mathbf{3} \boldsymbol{x}+\mathbf{5}=\mathbf{0} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 4 \)
D.
Subject: Physics
A particle of ass \( \mathrm{m} \) and charge \( \mathrm{Q} \) is placed in an electric field E which varies
with time \( t \) ass \( E=E_{0} \) sin \( \omega t . \) It will undergo simple harmonic motion of amplitude
A \( \cdot \frac{Q E_{0}^{2}}{m \omega^{2}} \)
в. \( \frac{Q E_{0}}{m \omega^{2}} \)
c. \( \sqrt{\frac{Q E_{0}}{m \omega_{2}}} \)
D. \( \frac{Q E_{0}}{m \omega} \)
Subject: Chemistry
During the oxidation of \( M n^{2+} \) to
\( M n O_{4}^{-} \) by \( P b O_{2} \) in acid medium, the number of moles of acid consumed per
mole of \( M n^{2+} \) ion is
A .4
B. 1/2
\( c \cdot 2 \)
D. 1/4
Subject: Biology
A patient was administered a chemical agent called Guanfacine hydrochloride after the patient showed the symptoms like shortness of breath and headache.
Guantacme hydrochloride is a known
stimulant of central \( \alpha-2 \) -adrenergic
receptors of the medulla regulating the sympathetic nervous system. The patient in this case must be suffering from
A. Hypertension
B. Hyperslimulation
c. Hyperpolarization
D. None of the above
Subject: Maths
If \( \boldsymbol{A}=\int_{0}^{\pi} \frac{\cos \boldsymbol{x}}{(\boldsymbol{x}+\mathbf{2})^{2}} \boldsymbol{d} \boldsymbol{x}, \) then
\( \int_{0}^{\frac{\pi}{2}} \frac{\sin 2 x}{(x+1)} d x \) is equal to
A \( \cdot \frac{1}{2}+\frac{1}{\pi+2}-A \)
B. \( \frac{1}{\pi+2}-A \)
\( c \cdot 1+\frac{1}{\pi+2}-A \)
D. \( _{A-} \frac{1}{2}-\frac{1}{\pi+2} \)
Subject: Physics
The potential energy of the system of two identically charged spheres as shown in the figure is equal to (Assume the charge distribution to be uniform)
\( ^{\mathbf{A}} \cdot \frac{q^{2}}{4 \pi \varepsilon_{0}}\left[\frac{1}{R}+\frac{1}{r}\right] \)
в. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{(R+r)} \)
D. None of these
Subject: Maths
Complex number \( z \) satisfy the equation
\( |z-(4 / z)|=2 . \) Then the value of
\( \arg \left(z_{1} / z_{2}\right), \) where \( z_{1} \) and \( z_{2} \) are complex numbers with the greatest and the least moduli, can be
A . \( 2 \pi \)
в. \( \pi \)
\( c \cdot \frac{\pi}{2} \)
D. none of these
Subject: Maths
If \( z_{1}=a+i b \) and \( z_{2}=c+i d \) are
complex numbers such tat \( \left|z_{1}\right|= \)
\( \left|z_{2}\right|=1 \& R e\left(z_{1} \overline{z_{2}}\right)=0, \) then the pair
of complex numbers \( \boldsymbol{w}_{1}=\boldsymbol{a}+\boldsymbol{i} \boldsymbol{c} \) and
\( \boldsymbol{w}_{2}=\boldsymbol{b}+\boldsymbol{i} \boldsymbol{d} \) satisfies -
This question has multiple correct options
\( \mathbf{A} \cdot\left|w_{1}\right|=1 \)
B \( \cdot\left|w_{2}\right|=1 \)
\( \mathbf{c} \cdot \operatorname{Re}\left(w_{1} \overline{w_{2}}\right)=0 \)
D. None of these
Subject: Physics
A person is painting his house walls. He stands on a ladder with a bucket
containing paint in one hand and a brush in other. Suddenly the bucket slips from his hand and falls down on
the floor. If the bucket with the paint
had a mass of \( 0.6 k g \) and was at a
height of \( 2.0 m \) at the time it slipped,
how much gravitational potential energy is lost together with the paint?
Subject: Physics
A particle would take time \( t_{1} \) to move
down a straight tube from the surface of earth (supposed to be homogeneous sphere) to its centre. If gravitational acceleration were to remain constant
time would be \( t_{2} \). The ratio \( t / t^{\prime} \) will be
A \( \cdot \frac{\pi}{2 \sqrt{2}} \)
в. \( \frac{\pi}{2} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{\pi}{\sqrt{3}} \)
Subject: Maths
If \( a_{1}=1, a_{n+1}=\frac{1}{n+1} a_{n}, \forall n \geq 1, \) then
\( \boldsymbol{a}_{\boldsymbol{n}}= \)
A \( \cdot \frac{1}{n !} \)
в. \( \frac{1}{(n+2) !} \)
c. \( \frac{1}{(n+1) !} \)
D. none of these
Subject: Physics
The isothermal bulk modulus of
elasticity of a gas is \( 1.5 \times 10^{5} N m^{-2} \)
Its adiabatic bulk modulus of elasticity will be (if \( \gamma=1.4) \)
В. \( 2.1 \times 10^{5} \mathrm{Nm}^{-2} \)
c. \( 1.5 \times 10^{5} \mathrm{Nm}^{-2} \)
\( D \cdot \infty \)
Subject: Chemistry
Select the correct statement(s):
This question has multiple correct options
A. When temperature is reised, a point will be reached where the graph crosses the \( \Delta G=0 \) line. Below this temperature, the free energy of formatin of the oxide is negative, so the oxide is stable
B. When temperature is raised, a point will be reached where the graph crosses the \( \Delta G=0 \) line. Above this temperature, the free energy of formation of the oxide is positive, and the oxide becomes unstable, and should decompose into the metal and dioxygen.
C. Theoretically, all oxides can be decomposed to give the metal and dioxygen if.a sufficiently high temperature can be attained.
D. Theoretically, all oxides cannot be decomposed to give the metal and dioxygen if a sufficiently high temperature can he attaincd
Subject: Chemistry
\( \left[\boldsymbol{F} \boldsymbol{e} \boldsymbol{F}_{6}\right]^{3-} \) has Fe atom
hybridised with unpaired electrons.
A \( \cdot d^{2} s p^{3}, 4 \)
B \( \cdot d^{2} s p^{3}, 5 \)
\( \mathrm{c} \cdot s p^{3} d^{2}, \)
D. \( s p^{3} d^{2}, 3 \)
Subject: Maths
The number of \( A \) in \( T_{p} \) such that the
trace of \( A \) is not divisible by \( p \) but
\( \operatorname{det}(A) \) is divisible by \( p \) is? [Note: The trace of a matrix is the sum of its diagonal entries.
A \( \cdot(p-1)\left(p^{2}-p+1\right) \)
В . \( p^{3}-(p-1)^{2} \)
c. \( (p-1)^{2} \)
D. \( (p-1)\left(p^{2}-2\right) \)
Subject: Chemistry
Write the cell reaction and calculate the
emf of the cell
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{g}, \mathbf{1} \boldsymbol{a} \boldsymbol{t m})\right| \boldsymbol{H}^{+}(\mathbf{0 . 5} \boldsymbol{M}) \| \boldsymbol{K} \boldsymbol{C l}(\mathbf{1} \boldsymbol{M}) \)
\( \operatorname{at} 25^{\circ} C, E=0.28 V \)
Subject: Physics
In a motor, a rotor is fitted with the
armature that has current of 10 A. The
rotor rotates with angular speed of 3 rad/s.Magnetic field of magnitude 2 T varies in direction is such a way that it
is always perpendicular to the loop area If the rotor coil has \( N \) number of turns
and area of each loop is \( 0.45 m^{2} \) then
find the value \( N . \) Given that motor
consumes 2106 W power and there are
no losses.
Subject: Maths
f \( a+b+c=0 \), show that
\( \mathbf{6}\left(\boldsymbol{a}^{\mathbf{5}}+\boldsymbol{b}^{\mathbf{5}}+\boldsymbol{c}^{\mathbf{5}}\right)= \)
\( \mathbf{5}\left(\boldsymbol{a}^{3}+\boldsymbol{b}^{3}+\boldsymbol{c}^{3}\right)\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2}\right) \)
Subject: Physics
Amplitude of oscillation of a particle that executes S.H.M. is 2 cm. Its
displacement from its mean position in a time equal to \( 1 / 6 \) th of its time period
is
A \( \cdot \sqrt{2} \mathrm{cm} \)
B. \( \sqrt{3} \mathrm{cm} \)
c. \( 1 / \sqrt{2} \mathrm{cm} \)
D. \( 1 / \sqrt{3} \mathrm{cm} \)
Subject: Biology
Assertion
Xylem and, , phloem are also called as leptons and syndrome respectively
Reason

Xylem and phloem form conducting tissue of the plant
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: Chemistry
In complex hydrides, hydride ions act as ligand and are coordinated to metal
ions. These hydrides are good reducing agents. Which of the following hydrides is not a complex hydride?
A \( . \) Li \( A I H_{4} \)
в. \( N a B H_{4} \)
\( \mathrm{c} \cdot\left(A l H_{3}\right)_{n} \)
D. \( L i B H_{4} \)
Subject: Physics
The rear wheels of a car are turning at an angular speed of 60 rad/s. The brakes are applied for 5 s, causing a uniform angular retardation of
\( 8 r a d / s^{-2} . \) The number of revolutions turned by the rear wheels during the braking period is about:
A . 48
B. 96
\( c .32 \)
D. 12
Subject: Physics
In vacuum, to travel distance 'd', light takes time 't' and in medium to travel
distance \( ^{\prime} 5 d^{\prime}, \) it takes time 'T'. The
critical angle of the medium is.
A \( \cdot \sin ^{-1}\left(\frac{5 T}{t}\right) \)
в. \( \sin ^{-1}\left(\frac{5 t}{3 T}\right) \)
c. \( \sin ^{-1}\left(\frac{5 t}{T}\right) \)
D. \( \sin ^{-1}\left(\frac{3 t}{5 T}\right) \)
Subject: Physics
a concave mirror is shown by \( \boldsymbol{P} \boldsymbol{Q} \) while
directions in which the ray would travel
after reflection is shown by four rays
marked 1,2,3 and 4

Which of the four rays correctly shows
the direction of reflected ray?
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
Assertion
Acetone-Carbon disulphide solution shows positive deviation from Raoult's
law.
Reason
Acetone \( + \) Aniline solution shows
positive deviation from Raoult's law.
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
Among the four successive members of the first series of the transition metals
listed below in the options, which one has a positive standard potential \( \left(\boldsymbol{E}_{M^{2+} / M}^{0}\right) \) value?
A. \( N i(Z=28) \)
в. \( C u(Z=29) \)
c. \( F e(Z=26) \)
D. \( \operatorname{Co}(Z=27) \)
Subject: Chemistry
In the reaction between \( N O \) and \( H_{2} \) the
following data are obtained
Experiment \( 1: P_{H_{2}}= \) constant
\[
(\mathrm{mm} \text { of } \mathrm{Hg}) \quad \text { 359 } \quad \text { 300 }
\]
\( -\frac{P_{H_{2}}}{d t} \) 1.50 \( \quad 1.03 \quad \) 0.25
Experiment \( 2: P_{N O}= \) constant
\[
\boldsymbol{P}_{H_{2}}(\mathrm{mm} \text { of } \mathrm{Hg}) \quad 289 \quad 205
\]
\( -\frac{P_{H_{2}}}{d t} \) \( 1.60 \quad 1.10 \)
The orders with respect of \( \boldsymbol{H}_{2} \) and \( \boldsymbol{N} \boldsymbol{O} \)
are:
A \( \cdot 1 \) with respect to \( N O \) and 2 with respect to \( H_{2} \)
B. 2 with respect to \( N O \) and 1 with respect to \( H_{2} \)
c. 1 with respect to \( N O \) and 3 with respect to \( H_{2} \)
D. 2 with respect to \( N O \) and 2 with respect to \( H_{2} \)
Subject: Physics
\( \alpha \) and \( \beta \) - particles emitted when uranium nucleus \( _{92} U^{238} \) decay to \( 82 P b^{214} \) are
A. \( 6-\alpha \) particles and \( 2-\beta \) particles
B. 4 \( \alpha \) - particles and 2 \( \beta \) particles
c. \( 2-\alpha \) particles and \( 6 \beta \) particles
D. 2 \( \alpha \) -particles and 4 \( \beta \) -particles
Subject: Physics
A long solenoid with length \( l \) and a
radius \( R \) consists of \( N \) turns of
wire,Neglecting the end effects, find the self-inductance.
B . \( \mu_{0} N \pi R^{2} / l \)
c. \( \mu_{0} N^{2} \pi R^{3} l \)
D. \( \mu_{0} N^{3} \pi R^{2} l \)
Subject: Chemistry
Compound \( A \) and \( B \) are two oxides of
sulfur. Compound A is 50\% sulfur by
mass, while Compound B is \( 40 \% \) sulfur
by mass.

Given the atomic masses of sulfur and
oxygen are 32 amu and 16 am \( u \) respectively, which of the following statements is NOT a valid
interpretation of these data? This question has multiple correct options
A. Compound A could have the formula, \( S O_{2} \)
B. Compound B could have the formula, \( S O_{2} \)
C. Compound A and B illustrate Dalton's law of multiple proportions.
D. Compound A could have the formula, \( S O \).
Subject: Maths
If \( \sum_{r=1}^{n}(r)(r+1)(2 r+3)=a n^{4}+ \)
\( b n^{3}+c n^{2}+d n+e, \) then
This question has multiple correct options
A \( . a+c=b+d \)
В. \( e=0 \)
c. \( a, b-\frac{2}{3}, c-1 \) are in A.P
D. \( \frac{c}{a} \) is an integers
Subject: Physics
A vertical narrow smooth tube is bent
from it's diameter such that one
semicircular part of the tube is
horizontal and the other part is vertical
A smooth ball is released from the
highest point of the tube. If the
maximum speed of ball is \( \boldsymbol{x} \boldsymbol{m} / \boldsymbol{s}, \) then
the value of \( x \) is :
(neglect collision at bending) (take
\( \boldsymbol{R}=\mathbf{2 . 5 m} \) and \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)
Subject: Maths
A circular area having a radius \( 20 \mathrm{cm} \) is divided into two equal parts by a concentric circle of radius 'r'. The value
of 'r' will be
A. \( 5 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
\( \mathrm{c} \cdot 5 \sqrt{2} \mathrm{cm} \)
D. \( 10 \sqrt{2} \mathrm{cm} \)
Subject: Maths
State whether the following statement
is true or false.
Enter 1 for true and 0 for false If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] \) then the value of \( \mathrm{f} \) and \( \mathrm{g} \)
satisfying the matrix equation \( A^{2}+ \)
\( \boldsymbol{f} \boldsymbol{A}+\boldsymbol{g} \boldsymbol{I}=\boldsymbol{O} \) are equal to \( -\boldsymbol{t}_{\boldsymbol{r}}(\boldsymbol{A}) \) and
determinant of A respectively. Given a b, \( c, d \) are non zero reals and \( I= \) \( \left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] ; \boldsymbol{O}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{0}\end{array}\right] \)
Subject: Maths
Two players \( A \) and \( B \) toss a fair coin cyclically in the following order \( A, A, B, A, A, B, \ldots \) till a head shows. Let
\( \boldsymbol{\alpha}(\boldsymbol{\beta}) \) denote the probability that \( \boldsymbol{A}(\boldsymbol{B}) \)
gets the head first. Then
This question has multiple correct options
A \( \cdot \alpha=\frac{6}{7} \)
в. \( \alpha=\frac{5}{7} \)
c. \( _{\beta}=\frac{1}{7} \)
D. \( _{\beta}=\frac{2}{7} \)
Subject: Physics
A ball of mass \( m \) at rest receives an
impulse \( I_{1} \) in the direction of north.
After some time, it received another
impulse \( I_{2} \) in the direction of south. The
final kinetic energy of the ball is
A \( \cdot \frac{\left(I_{1}+I_{2}\right)^{2}}{2 m} \)
в. \( \frac{\left(I_{1}-I_{2}\right)^{2}}{2 m} \)
c. \( \frac{I_{1}^{2}+I_{2}^{2}}{2 m} \)
D. \( \frac{I_{1}^{2}-I_{2}^{2}}{2 m} \)
Subject: Physics
Average velocities for time intervals \( t= \)
0 to \( 2 s, t=2 \) to 4 s and \( t=0 \) to 4 s are
respectively equal to
A \( .2 .5 \mathrm{m} / \mathrm{s},-2.5 \mathrm{m} / \mathrm{s}, 2.5 \mathrm{m} / \mathrm{s} \)
B. \( 1.25 \mathrm{m} / \mathrm{s},-1.25 \mathrm{m} / \mathrm{s}, 0 \mathrm{m} / \mathrm{s} \)
\( c \cdot 5 m / s,-5 m / s, 0 m / s \)
D. \( 2.5 \mathrm{m} / \mathrm{s},-2.5 \mathrm{m} / \mathrm{s}, 0 \mathrm{m} / \mathrm{s} \)
Subject: Physics
When a resistor of \( 2 \Omega \) is connected
across the terminals of a battery a current of \( 2 A \) is found to flow. When a
second resistor of \( 8 \Omega \) is connected in
series with the first, the current is
reduced to \( 1 A . \) The emf and internal
resistance of the battery are
A \( .12 \%, 4 \Omega \)
B. 10V, 2\Omega
\( c \cdot 16 v, 6 \Omega \)
D. 16V, 4\Omega
Subject: Chemistry
Benzoyl chloride on reduction with
\( \boldsymbol{H}_{2} / \boldsymbol{P} \boldsymbol{d}-\boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \)
produces
A. Benzoic acid
B. Benzyl alcohol
c. Benzoyl sulphate
D. Benzaldehyde
Subject: Physics
A vertical wall of height \( a \) running from south to north has the height. A policeman of height \( b>a \) is standing
in front of the wall at a distance \( c \) from
it on the eastern side. What should be
the maximum distance of a crawling theif from the wall so that the thief can hide from the view of the policeman if the thief is on the other side of the wall
in the west of the policeman?
A \( \cdot \frac{a c}{b-a} \)
в. \( \frac{b c}{b-a} \)
c. \( \frac{a+b}{b-a} \cdot c \)
D. \( \frac{a c}{a+b} \)
Subject: Maths
Solution of the differential equation \( \frac{d y}{d x}+y \sec x=\tan x\left(\leq x<\frac{\pi}{2}\right) \) is
A \( \cdot y(\sec x-\tan x)=(\sec x+\tan x)-x+C \)
B \cdot \( y(\sec x+\tan x)=(\sec x-\tan x)-x+C \)
C \( \cdot y(\sec x+\tan x)=(\sec x+\tan x)-x+C \)
D. noneofthese
Subject: Physics
In the circuit shown, assume the diode
to be ideal. When \( V_{i} \) increases from \( 2 V \)
to \( 6 V \), the change in the current is (in
\( \boldsymbol{m} \boldsymbol{A}) \)
A . zero
B . 20
\( c \cdot 80 / 3 \)
D. 40
Subject: Physics
Two containers of equal volume
containing the same gas at pressure \( P_{1} \)
and \( P_{2} \) and absolute temperature \( T_{1} \) and
\( T_{2} \) respectively were connected with
narrow capillary tube. The gas reaches a
common pressure \( \mathrm{P} \) and a common
temperature T. The ratio P/T is equal to :
A \( \cdot \frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}} \)
B \( \cdot \frac{1}{2}\left(\frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}}\right) \)
c. \( \frac{P_{1} T_{2}+P_{2} T_{1}}{T_{1}+T_{2}} \)
D. \( \frac{P_{1} T_{2}-P_{2} T_{1}}{T_{1}-T_{2}} \)
Subject: Maths
If we plot \( \left|Z_{1}\right|=2 \) and \( \left|Z_{2}-6-8 i\right|=4 \)
on the argand plane, the locus of \( Z_{1} \)
and \( Z_{2} \) are
A. two circle touching each other
B. two circles neither touching nor intersecting
c. two circles intersecting
D. none of these
Subject: Maths
The solution of the equation \( 9 \cos ^{12} x+ \)
\( \cos ^{2} 2 x+1=6 \cos ^{6} x \cos 2 x+ \)
\( 6 \cos ^{6} x-2 \cos 2 x \) is/are:
\( \mathbf{A} \cdot \mathbf{x}=\mathbf{n} \pi+\frac{\pi}{2} ; \mathbf{n} \in \mathbf{I} \)
в. \( _{x}=n \pi+\cos ^{-1}(\sqrt[4]{\frac{2}{3}}), n \in I \)
c. \( _{x=n \pi-\cos ^{-1}}(\sqrt[4]{\frac{2}{3}}), n \in I \)
D. none of the above