AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find solution of following inequality, also show it graphically:
\[
\boldsymbol{x}+\mathbf{3} \leq \mathbf{5}, \boldsymbol{x} \in \boldsymbol{N}
\]
\( A \)
\begin{tabular}{rrrrrrrrrr}
\hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6
\end{tabular}
B.
\begin{tabular}{rrrrrr}
\hline & & & & & & \\
\hline-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
\( c \)
\( \underbrace{\longleftarrow}_{-2}-1 \quad_{0} \quad_{1} \quad_{2} \quad_{1} \)
\( D \)
\begin{tabular}{rrrrrr}
\hline & 1 & 1 & & & 1 \\
-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
Subject: Physics
If the electric flux entering and leaving
an enclosed surface respectively is \( \phi_{1} \)
and \( \phi_{2}, \) the electric charge inside the surface will be :
\( \mathbf{A} \cdot\left(\phi_{2}-\phi_{1}\right) \varepsilon_{0} \)
B. \( \frac{\left(\phi_{2}+\phi_{1}\right)}{\varepsilon_{0}} \)
c. \( \frac{\left(\phi_{2}-\phi_{1}\right)}{\varepsilon_{0}} \)
\( \mathbf{D} \cdot\left(\phi_{2}+\phi_{1}\right) \varepsilon_{0} \)
Subject: Physics
A particle moves in the \( x \) -y plane with
velocity \( v_{x}=8 t-2 \) and \( v_{y}=2 . \) If it
passes through the point \( x=14 \) and
\( \boldsymbol{y}=\mathbf{4} \) at \( \boldsymbol{t}=\mathbf{2 s}, \) the equation of the path
is?
A. \( x=y^{2}-y+2 \)
В. \( x=y^{2}-2 \)
c. \( x=y^{2}+y-6 \)
D. None of these
Subject: Chemistry
Which one of the following is true for an
exothermic reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} . \) If \( \boldsymbol{E}_{f} \) and
\( E_{b} \) are the activation energies of
forward and backward reactions
respectively?
\( \mathbf{A} \cdot E_{f}>E_{b} \)
B . \( E_{f}=E_{b} \)
\( \mathbf{c} \cdot E_{f}=-E_{b} \)
D \( \cdot E_{f}<E_{b} \)
Subject: Chemistry
\( 5.6 \mathrm{g} \) of an organic compound on burning with excess of oxygen gave 17.6
\( \mathrm{g} \) of \( \mathrm{CO}_{2} \) and \( 7.2 \mathrm{g} \mathrm{H}_{2} \mathrm{O} \). The organic
compound is:
A \( \cdot C_{6} H_{6} \)
в. \( C_{4} H_{8} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C H_{3} C O O H \)
E . \( C H_{3} C H O \)
Subject: Maths
Let \( \vec{A}, \vec{B} \) and \( \vec{C} \) be unit vectors. Suppose that \( \vec{A} \cdot \vec{B}=\vec{A} \cdot \vec{C}=0 \) and that the
angle between \( \vec{B} \) and \( \vec{C} \) is \( \frac{\pi}{6} \) then \( \overrightarrow{\boldsymbol{A}}= \)
A \( \cdot \pm 2(\vec{B} \times \vec{C}) \)
B \( \cdot \pm(\vec{B} \times \vec{C}) \)
c. \( \pm 2(\vec{B}+\vec{C}) \)
D. \( \pm(\vec{B}+\vec{C}) \)
Subject: Physics
The distance between an object and the
screen is \( 100 \mathrm{cm} . \) A lens produces an
image on the screen when placed at
either positions \( 40 \mathrm{cm} \) apart. The power
of the lens is :
\( A \cdot 3 D \)
B. 5D
\( c .70 \)
D. 90
Subject: Maths
There is flag-staff at the top of 10 metres high tower. If the flag-staff
makes an angle \( \tan ^{-1}(1 / 8) \) at a point
24 metres away from the tower, then the
height of the flag staff in metres is
A \( .26 / 7 \)
B. 27/8
c. \( 27 / 6 \)
D. 26 /3
Subject: Maths
The Rolle's theorem is applicable in the interval \( -1 \leq x \leq 1 \) for the function
\( \mathbf{A} \cdot f(x)=x \)
\( \mathbf{B} \cdot f(x)=x^{2} \)
\( \mathbf{c} \cdot f(x)=2 x^{3}+3 \)
\( \mathbf{D} \cdot f(x)=|x| \)
Subject: Physics
A body cools from \( 80^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in 5
minutes. Calculate the time it takes to
cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \). The temperature
of the surroundings is \( 20^{\circ} \mathrm{C} \)
Subject: Maths
If \( \cot ^{-1}\left[(\cos \alpha)^{1 / 2}\right]+ \)
\( \left[\tan ^{-1}(\cos \alpha)^{1 / 2}\right]=x, \) then \( \sin x \)
equals
A .
B \( \cdot \cot ^{2}\left(\frac{\alpha}{2}\right) \)
\( \mathbf{c} \cdot \tan \alpha \)
D. \( \cot \left(\frac{\alpha}{2}\right) \)
Subject: Maths
Find the derivative with respect to \( x \) of
the function
\( \left(\log _{\cos x} \sin x\right)\left(\log _{\sin x} \cos x\right)^{-1}+ \)
\( \sin ^{-1} \frac{2 x}{1+x^{2}} \) at \( x=\frac{\pi}{4} \)
A \( \cdot g\left(\frac{4}{\pi^{2}+16}-\frac{1}{\log 2}\right) \)
B. \( -8\left(\frac{4}{(\pi+4)^{2}}-\frac{1}{\log 2}\right) \)
\( ^{\mathbf{c}} \cdot_{8}\left(\frac{4}{\pi^{2}+16}+\frac{1}{\log 2}\right) \)
D \( \cdot g\left(\frac{4}{(\pi+4)^{2}}-\frac{1}{\log 2}\right) \)
Subject: Physics
Two spherical soap bubbles collapses. If \( V \) is the consequent change in volume of the contained air and \( S \) is the change
in the total surface area and \( T \) is the
surface tension of the soap solution,
then if relation between \( P_{0}, V, S \) and \( T \)
\( \operatorname{are} \lambda P_{0} V+4 S T=0, \) then find \( \lambda ?\left(\text { If } P_{0}\right. \)
is atmospheric pressure): Assume temperature of the air remain same in
all the bubbles.
Subject: Physics
A person carrying a whistle emitting
continuously a note of \( 272 H z \) is running towards a reflecting surface with a speed of \( 18 k m / \)hour. speed of
sound in air is \( 45 m / s . \) The number of
beats heard by him is:
A . 4
B. 6
\( c \cdot 8 \)
\( D \cdot 3 \)
Subject: Maths
If \( y=\frac{(1-x)^{2}}{x^{2}} \) where \( x \neq \)
\( 0, \) then \( \frac{d y}{d x} i s \)
A \( \cdot \frac{2}{x^{2}}+\frac{2}{x^{3}} \)
B. \( -\frac{2}{x^{3}}+\frac{2}{x^{2}} \)
\( c \cdot-\frac{2}{x^{2}}+\frac{2}{x^{3}} \)
D. \( -\frac{2}{x^{2}}-\frac{2}{x^{3}} \)
Subject: Chemistry
Identify the substance oxidised, reduced, oxidising agent and reducing agent for the following reaction.
\( \boldsymbol{H} \boldsymbol{C H O}_{(l)}+\mathbf{2}\left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]_{(a q)}^{+}+ \)
\( \mathbf{3} \boldsymbol{O} \boldsymbol{H}_{(\boldsymbol{a q})}^{-} \rightarrow \mathbf{2} \boldsymbol{A} \boldsymbol{g}_{(s)}+\boldsymbol{H} \boldsymbol{C O O}_{(\boldsymbol{a q})}^{-}+ \)
\( \mathbf{4} \boldsymbol{N} \boldsymbol{H}_{3(a q)}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} \)
Subject: Physics
A gas expands adiabatically from a
temperature \( T_{1} \) to a temperature
\( \boldsymbol{T}_{2}\left(\boldsymbol{T}_{1}>\boldsymbol{T}_{2}\right) . \) The work done in this
process is
A. \( C_{p}\left(T_{1}-T_{2}\right) \)
в. \( C_{v}\left(T_{1}-T_{2}\right) \)
c. \( R\left(T_{1}-T_{2}\right) \)
D. zero
Subject: Chemistry
The standard heat of formation of
sodium ions in aqueous solution from the following data:
Heat of formation of \( N a O H(a q .) \) at
\( 25^{\circ} C=-470.7 k J \)
Heat of formation of \( \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q} .) \) at
\( \mathbf{2 5}^{\circ} \boldsymbol{C}=-\mathbf{2 2 8 . 8 k J} \mathbf{i s} \)
\( \mathbf{A} \cdot-251.9 k J \)
в. 241.9k.
\( \mathbf{c} .-241.9 k J \)
D. \( 251.9 k J \)
Subject: Chemistry
Dehydrating agent and dehydrohalogenating agents among the following are respectively:
A. conc. \( H_{2} S O_{4}, A l_{2} O_{3} \)
B. \( A l_{2} O_{3}, \) сопс. \( H_{2} S O_{4} \)
c. conc. \( H_{2} S O_{4}, \) Alc. \( K O H \)
D. Alc. KOH, conc. \( H_{2} S O_{4} \)
Subject: Physics
A magnetic field of \( 100 \mathrm{G}\left(1 \mathrm{G}=10^{-4} \mathrm{T}\right) \) is required which is uniform in a region of linear dimension about \( 10 \mathrm{cm} \) and area
of cross-section about \( 10^{-3} m^{2} . \) The
maximum current-carrying capacity of a given coil of wire is 15 A and the
number of turns per unit length that can be wound round a core is at most
1000 turns \( m^{-1} . \) Suggest
some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.
Subject: Chemistry
Which one is most reactive towards \( S_{N} \)
reaction?
\( \mathbf{A} \cdot \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right) \mathrm{Br} \)
B. \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}\left(\mathrm{CH}_{3}\right) \) Br
\( \mathrm{c} \cdot \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{C}\left(\mathrm{CH}_{3}\right)\left(\mathrm{C}_{6} \mathrm{H}_{5}\right) \mathrm{Br} \)
D. \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{Br} \)
Subject: Chemistry
the blanks by choosing an appropriate
option.

In the given cell, hydrogen and oxygen
are bubbled through porous \( (i) \) electrodes into concentrated aqueous
\( (i i) \) solution. Catalysts like finely
divided \( (i i i) \) or \( (i v) \) metal are
incorporated into the electrodes for increasing the rate of electrode
reactions.
A. (i)- Hydrogen, (ii)-Potassium hydroxide, (iii)palladium, (iv)-platinum
B. (i)- Oxygen
(ii)- Hydrogen chloride
(iii)- Manganese, (iv)- Iron
c. (i)- Carbon
(ii)- sodium hydroxide
(iii)- Platinum, (iv) palladium
D. (i)- Graphite,
(ii)- Sodium Chloride
(iii)- Nickel, (iv)Platinum
Subject: Maths
Find the area of the region bounded by the curves \( x=\frac{1}{2}, x=2, y=\log x \) and
\( \boldsymbol{y}=\mathbf{2}^{\boldsymbol{x}} \)
\( ^{\mathbf{A}} \cdot \frac{4-\sqrt{2}}{\log 2}-\frac{5}{2} \log 2+\frac{3}{2} s q \cdot u n i t s \)
B. \( \frac{4+\sqrt{2}}{\log 2}-\frac{3}{2} \log 2+\frac{5}{2} \) sq.units
\( ^{\mathrm{c}} \cdot \frac{4-\sqrt{2}}{\log 2}-\frac{3}{2} \log 2+\frac{5}{2} s q \cdot u n i t s \)
D. \( \frac{4+\sqrt{2}}{\log 2}-\frac{5}{2} \log 2+\frac{3}{2} \) sq.units
Subject: Maths
If \( a>0, b>0, c>0 \) are respectively
the \( p^{t h}, q^{t h}, r^{t h} \) terms of a G.P., then the value of the deteminant \( \left|\begin{array}{lll}\log \boldsymbol{a} & \boldsymbol{p} & 1 \\ \log \boldsymbol{b} & \boldsymbol{q} & 1 \\ \log \boldsymbol{c} & \boldsymbol{r} & 1\end{array}\right| \) is
A . 1
B. 0
\( c \cdot-1 \)
D. None of these
Subject: Physics
A string of length \( 100 \mathrm{cm} \) and mass
\( 0.5 g m \) is streched with a force of \( 20 N \)
It is pulled at a distance of \( 12.5 \mathrm{cm} \) from one end. The frequency of the note emitted by it is
A . \( 100 \mathrm{Hz} \)
в. \( 200 H z \)
c. \( 400 H z \)
D. \( 800 H z \)
Subject: Physics
The conducting rod \( a b \), as shown in figure makes contact with metal rails
\( c a \) and \( d b . \) The apparatus is in a uniform magnetic field of \( 0.800 T \), perpendicular to the plane of the figure. If the
resistance of the circuit \( a b d c \) is \( 1.50 \Omega \)
(assumed to be constant), find the force (magnitude and direction) required to keep the rod moving to the right with a constant speed of \( 7.50 m / s . \) You can
ignore friction.
Subject: Physics
The radius \( R \) of the soap bubble is doubled under iso-thermal condition. If
\( \boldsymbol{T} \) be the surface tension of soap bubble The work done in doing so is given by:
\( \mathbf{A} \cdot 32 \pi R^{2} T \)
В . \( 24 \pi R^{2} T \)
c. \( 8 \pi R^{2} T \)
D. \( 4 \pi R^{2} T \)
Subject: Physics
An \( A C \) source rated \( 100 \vee(r m s) \)
supplies a current of \( 10 \mathrm{A}(\mathrm{rm} s) \) to a circiut. The average power delivered by the source. This question has multiple correct options
A. must be \( 1000 \mathrm{w} \)
B. may be \( 1000 \mathrm{w} \)
c. may be greater than 1000 w
D. may be less than 1000 w
Subject: Physics
A nucleus \( _{z}^{A} X \) emits an \( \alpha \) -particle with velocity \( v . \) The recoil speed of the daughter nucleus is:
A. \( \frac{A-4}{4 v} \)
в. \( \frac{4 v}{A-4} \)
\( c \)
D. \( \frac{v}{4} \)
Subject: Physics
Two balls are thrown with initial
velocities simultaneously at \( t=0 . \) They
will meet at \( t= \)
A. \( \frac{h}{u+u_{1}} \)
в. \( \frac{2 h}{u+u_{1}} \)
c. \( \frac{h}{u-u_{1}} \)
D. \( \frac{2 h}{u-u_{1}} \)
Subject: Physics
toppr
Q Type your question
insulted from each other. The entire loop
lies in the plane (of the paper). A uniform magnetic filed \( \vec{B} \) point into the
plane of the paper. At \( t=0 \), the loop
starts rotating about the common
diameter as axis with a constant
angular velocity \( \omega \) in the magnetic field.
Which of the following option is/are
correct?
A. The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the
paper
B. The net emf induced due to both the loops is proportional to cos \( \omega t \)
C. The emf induced in the loop is proportional to the sun of the areas of the two loops.
D. non of the above.
Subject: Chemistry
Which one of the following statements
about \( C_{2} \) molecule is wrong?
A. The bond order of \( C_{2} \) is 2 .
B. In vapour phase, \( C_{2} \) molecule is diamagnetic.
C. Double bond in \( C_{2} \) molecule consists of both \( \pi \) - bonds
because of the presence of 4 electrons in two \( \pi^{-} \) molecular orbitals.
D. Double bond in \( C_{2} \) molecule consists of one \( \sigma \) bond
and one \( \pi \) bond.
Subject: Physics
In the given graph an ideal gas change its state from A to state \( C \) by two paths ABC and AC. The internal energy of gas
at \( A \) is \( 10 \mathrm{J} \) and the amount of heat
supplied in path AC is 200 J. The
internal energy (in J) of gas at \( \mathrm{C} \) is \( 6 k^{2} \)
What is the value of \( k ? \)
Subject: Physics
In a compound microscope, the focal lengths of two lenses are \( 1.5 \mathrm{cm} \) and 6.25 \( \mathrm{cm} . \) If an object placed at \( 2 \mathrm{cm} \) from objective and the final image is formed at 25 from eye lens, the distance
between the two lenses is
A \( .6 .00 \mathrm{cm} \)
B. \( 7.75 \mathrm{cm} \)
\( \mathrm{c} .9 .25 \mathrm{cm} \)
D. \( 11.0 \mathrm{cm} \)
Subject: Physics
A light ray makes an angle of incidence
\( 60^{\circ}, \) when it falls on a plane reflecting
sheet
The angle of reflection will be.
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 90^{\circ} \)
Subject: Chemistry
The electronic configuration of the
element which is just above the
element with atomic number 43 in the
same periodic group is:
\( \mathbf{A} \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{5}, 4 s^{2} \)
B \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{5} \)
C \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{6}, 4 s^{1} \)
D. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{1} 4 p^{6} \)
Subject: Maths
Construct a quadrilateral \( A B C D, \) when
\( A B=3.2 \mathrm{cm}, B C=5.2 \mathrm{cm}, C D=6.2 \)
\( \mathbf{c m}, \boldsymbol{D} \boldsymbol{A}=\mathbf{4 . 2} \mathbf{c m} \) and \( \boldsymbol{B} \boldsymbol{D}=\mathbf{5} . \boldsymbol{2} \mathrm{cm} \)
Subject: Maths
Two digit numbers are formed using the
digits 0,1,2,3,4,5 where digits are not repeated.
\( P \) is the event that the number so
formed is even
\( Q \) is the event that the number so
formed is greater than 50
\( R \) is the event that the number so
formed is divisible by 3

Then write the sample space \( S \) and
events \( P, Q, R \) using set notation.
Subject: Maths
The \( p^{t h} \) term of an arithmetic
progression is \( \boldsymbol{q}, \) and the \( \boldsymbol{q}^{t h} \) term is \( \boldsymbol{p} \)
then the \( m^{t h} \) term is:
A. \( p+q-m \)
в. \( p-q-m \)
c. \( p+q+m \)
D. None of these
Subject: Maths
The sum n terms of two A Ps are in ratio \( \frac{7 n+1}{4 n+27} \) Find the ratio of their 11 th terms
A \( \cdot \frac{148}{111} \)
в. \( \frac{213}{311} \)
c. \( \frac{221}{343} \)
D. \( \frac{114}{157} \)
Subject: Maths
The mean deviation from the data
\( \mathbf{3}, \mathbf{1 0}, \mathbf{1 0}, \mathbf{4}, \mathbf{7}, \mathbf{1 0}, \mathbf{5} \)
\( \mathbf{A} \cdot \mathbf{3} \)
B . 2
c. 3.75
D. 2.57
E. None of these
Subject: Physics
Four large metal plates are given charges as shown in figure. The middle
two are then connected through a wire. Find the charge that will flow through
the wire:
A. \( 5 Q \) from A to B
B. \( \frac{5 Q}{2} \) from A to B
c. \( 5 Q \) from \( B \) to \( A \)
D. No charge will flow
Subject: Maths
Find the inverse of the matrix
\( \left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 0 & 2 \\ 2 & 1 & -3\end{array}\right] \) by elementary row
transformation. Hence solve the system
of equations \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{z}=\mathbf{4},-\boldsymbol{x}+ \)
\( \mathbf{2} z=\mathbf{0}, \mathbf{2} \boldsymbol{x}+\boldsymbol{y}-\mathbf{3} \boldsymbol{z}=\mathbf{0} \)
Subject: Chemistry
A white salt is readily soluble in water and gives a colourless solution with \( \boldsymbol{p} \boldsymbol{H} \)
of about \( 9 . \) The salt would be:
A. \( N H_{4} N O_{3} \)
в. \( C H_{3} \) СОО Na а
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{COONH}_{4} \)
D. \( C a C O_{3} \)
Subject: Maths
Evaluate \( \left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{x}^{2} & \boldsymbol{x}^{2} \\ \boldsymbol{y} & \boldsymbol{y}^{2} & \boldsymbol{y}^{2} \\ \boldsymbol{z} & \boldsymbol{z}^{2} & \boldsymbol{z}^{3}\end{array}\right| \)
Subject: Maths
Assertion
\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}1 & \text { if } 2 \leq x \leq 3 \\ 3 & \text { if } 3 \leq x \leq 5\end{array}\right. \)
The mean value of \( \boldsymbol{f} \) is attained
Reason
\( f \) is a bounded function but not
continuous on \( [\mathbf{2}, \mathbf{5}] \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
Under hydrolytic conditions, the
compounds used for preparation of linear polymer and for chain termination respectively are:
B. \( \left(C H_{3}\right)_{2} \) SiCl \( _{2} \) and \( \left(C H_{3} \text { ) }_{3} \) SiCl \right.
c. \( \left(C H_{3}\right)_{3} \) SiCl \( _{2} \) and \( C H_{3} \) SiCl \( _{2} \)
D. \( \operatorname{SiCl}_{4} \) and \( \left(C H_{3}\right)_{3} \)SiCl
Subject: Physics
Two small identical metal balls \( A \) and \( B \)
radius r are placed apart The distance
between centre of balls is \( a_{0} \) The net
potential of ball \( A \) is \( V_{1} \) and that of \( B \) is
\( V_{2} \) Let \( q_{1} \) and \( q_{2} \) are the charges on balls
A and B respectively Then the charge on
\( A \) and \( B \) are \( \left(\left(g i v e n r<<a_{0}\right)\right) \)
This question has multiple correct options
A \( \cdot q_{1}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{1} a_{0}-V_{2} r\right)}{a_{0}^{2}-r^{2}} \)
В. \( \quad q_{1}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{1} a_{0}+V_{2} r\right)}{a_{0}^{2}+r^{2}} \)
\( ^{\mathbf{C}} \cdot_{q_{2}}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{2} a_{0}+V_{1} r\right)}{a_{0}^{2}+r^{2}} \)
D. \( _{q_{2}}=4 \pi \varepsilon_{0} \frac{a_{0} r\left(V_{2} a_{0}-V_{1} r\right)}{a_{0}^{2}-r^{2}} \)
Subject: Maths
ff \( P(x)=\left[\begin{array}{cc}\cos x & \sin x \\ -\sin x & \cos x\end{array}\right] \) then
\( \boldsymbol{P}(\boldsymbol{x}) \cdot \boldsymbol{P}(\boldsymbol{y})= \)
This question has multiple correct options
A \( . P(x) . P(y)=P(x+y) \)
в. \( P(x) . P(y)=P(x y) \)
c. \( P(x) . P(y)=P(y) . P(x) \)
Subject: Biology
A scientist took 8 molecules of cytosoic aldolase into an enzyme reaction mixture to study its activity. After ten minutes of enzyme reaction, \( 60 \% \) of its
substrate was found converted into
2400 molecules of products. Then what is the TON of aldolase and number of
substrate molecules left over in the
reaction mixture?
A . 30,1440
B. 30,960
\( c .15,1280 \)
D. 15,800
Subject: Maths
\( \mathrm{f}\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{2} & \boldsymbol{x} \\ \boldsymbol{x}^{2} & \boldsymbol{x} & \boldsymbol{6} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{6}\end{array}\right|=\boldsymbol{a} \boldsymbol{x}^{4}+\boldsymbol{b} \boldsymbol{x}^{3}+\boldsymbol{c} \boldsymbol{x}^{2}+ \)
\( \boldsymbol{d} \boldsymbol{x}+\boldsymbol{e}, \) then \( \boldsymbol{5} \boldsymbol{a}+\boldsymbol{4} \boldsymbol{b}+\boldsymbol{3} \boldsymbol{c}+\boldsymbol{2} \boldsymbol{d}+\boldsymbol{e} \) is
equal to
A. 11
B. -11
c. 12
D. -12
E . 13
Subject: Physics
A current source sends a current i \( = \)
\( i_{0} \cos (\omega t) . \) When connected across an
unknown load gives a voltage output of,
\( \boldsymbol{v}=\boldsymbol{v}_{0} \sin (\omega t+\boldsymbol{\pi} / 4) \) across that load
Then voltage across the current source
may be brought in phase with the
current through it by
A. connecting an inductor in series with the load
B. connecting a capacitor in series with the load
C. connecting an inductor in parallel with the load
D. connecting a capacitor in parallel with the load.
Subject: Biology
Read the given statements that describe certain infectious particle.
(i) It was discovered by T.O. Diener and
was found to be smaller than viruses.
(ii) It causes potato spindle tuber
disease.
(iii) It is a free RNA particle which lacks the protein coat.
(iv) It has low molecular weight RNA as genetic material.
Which of the following is referred to here?
A. Virus
B. Viroid
c. virion
D. Bacteriophage
Subject: Chemistry
The strength of 11.2 volume solution of
\( H_{2} O_{2} \) is: \( [ \) Given that molar mass of
\( \boldsymbol{H}=\mathbf{1} \boldsymbol{g} \boldsymbol{m o l}^{-1} \) and \( \boldsymbol{O}=\mathbf{1 6} \boldsymbol{g} \boldsymbol{m o l}^{-1} \mathbf{j} \)
A . \( 13.6 \% \)
в. \( 3.4 \% \)
\( c .34 \% \)
D. \( 1.7 \% \)
Subject: Physics
The are of cross-section of steel wire is
\( 0.1 \mathrm{cm}^{2} \) and Young's modulus of steel is
\( 2 \times 10^{11} N \quad m^{-2} . \) The force required to
stretch by \( 0.1 \% \) of tis length is then
A . \( 1000 N \)
в. 2000N
c. \( 4000 N \)
D. \( 5000 N \)
Subject: Physics
Double convex lenses are to be
manufactured from a glass of refractive index \( 1.55, \) with both faces of same
radius of curvature. What is the radius
of curvature required if the focal length is to be \( 20 \mathrm{cm} ? \)
\( \mathbf{A} \cdot 11 \mathrm{cm} \)
B. 22 cm
\( c \cdot 7 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Biology
Two different plants associated with the
discovery of two different phytohormones having common biosynthetic precursor exhibit one of the following character each.
I- Versatile anthers
II- Compound spadix
III- Pentalocular ovary
IV- Trifoliate compound leaves
The correct answer is:
A . Il and III
B. I and III
c. ॥ and IV
D. I and IV
Subject: Chemistry
Within the list shown below, the correct
pair of structures of alanine in \( \boldsymbol{p} \boldsymbol{H} \)
range \( 2-4 \) and \( 9-11 \) is:
I. \( \boldsymbol{H}_{3} \boldsymbol{N}^{+} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C O}_{2} \boldsymbol{H} \)
II. \( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right) \boldsymbol{C} \boldsymbol{O}_{2}^{-} \)
III. \( \boldsymbol{H}_{3} \boldsymbol{N}^{+} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C O}_{2}^{-} \)
IV. \( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right) \boldsymbol{C} \boldsymbol{O}_{2} \boldsymbol{H} \)
A . ।, ॥
B. ।, III
c. ॥, ॥ ॥
D. III, IV
Subject: Physics
A nucleus \( _{Z}^{A} X \) has mass represented by \( \boldsymbol{m}(\boldsymbol{A}, \boldsymbol{Z}) . \) If \( \boldsymbol{m}_{\boldsymbol{p}} \) and \( \boldsymbol{m}_{\boldsymbol{n}} \) denote the mass
of proton and neutron respectively and BE the binding energy(in MeV) then.
A \( \cdot B E=\left[m\left(A_{1} Z\right)-Z m_{p}-(A-Z) m_{n}\right] C^{2} \)
B . \( B E=\left[Z m_{p}+(A-Z) m_{n}-m(A, Z)\right] C^{2} \)
C \( . B E=\left[Z m_{p}+A m_{n}-m(A, Z)\right] C^{2} \)
D. \( B E=m\left(A_{1} Z\right)-Z m_{p}-(A-Z) m_{N} \)
Subject: Maths
If \( P=\left[\begin{array}{lll}4 & 3 & 2\end{array}\right] \) and \( Q=\left[\begin{array}{lll}-1 & 2 & 3\end{array}\right] \) then
\( P-Q= \)
\( \left.\begin{array}{lll}\text { A } \cdot[6 & -1 & -4\end{array}\right] \)
B . \( \left[\begin{array}{lll}2 & -1 & -4\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{lll}6 & 1 & 4\end{array}\right] \)
D・[-4 -1 6]
Subject: Physics
A feather of mass \( m \) and a hammer of
mass \( 100 m \) are both released from rest
from the same height on the surface of the moon. Mass of moon is \( M \) and
radius of moon is \( R \). Both feather and
hammer are released simultaneously. What is the acceleration of the
hammer?
A \( \cdot \frac{m v^{2}}{r} \)
в. \( \frac{G M}{R^{2}} \)
c. \( \frac{G M m}{R^{2}} \)
D. \( _{100} \frac{G M}{R^{2}} \)
E \( \cdot_{100} \frac{G M m}{R^{2}} \)
Subject: Chemistry
Is \( 1.0 \mathrm{M} \boldsymbol{H}^{+} \) solution under \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) at
1.0atm capable of oxidising silver metal
in the prescence of \( 1.0 \mathrm{M} A g^{+} \) ion?