AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
The solution to the differential equation
\( \boldsymbol{y} \ln \boldsymbol{y}+\boldsymbol{x} \boldsymbol{y}^{\prime}=\mathbf{0} \) where \( \boldsymbol{y}(\mathbf{1})=\boldsymbol{e}, \) is:
A. \( x(\ln y)=1 \)
в. \( x y(\ln y)=1 \)
c. \( (\ln y)^{2}=2 \)
D. \( \ln y+\left(\frac{x^{2}}{2}\right) y=1 \)
Subject: Maths
Given \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}3-\left[\cot ^{-1}\left(\frac{2 x^{3}-3}{x^{2}}\right)\right] & \text { for } x>0 \\ \left\{x^{2}\right\} \cos \left(e^{1 / x}\right) & \text { for } x<0\end{array}\right. \)
where
\{\}\( \&[] \) denotes the fractional part and
the integral part functions respectively,
then which of the following statement
does not hold good -
This question has multiple correct options
\( \mathbf{A} \cdot f\left(0^{-}\right)=0 \)
B . \( f\left(0^{+}\right)=3 \)
C \( . f(0)=0 \Rightarrow \) continuity of \( f \) at \( x=0 \)
D. irremovable discontinuity of \( f \) at \( x=0 \)
Subject: Maths
If \( \tan ^{-1} x+\tan ^{-1} y=\frac{2 \pi}{3}, \) then
\( \cot ^{-1} x+\cot ^{-1} y \) is equal to
\( ^{A} \cdot \frac{\pi}{2} \)
в.
c.
D. \( \frac{\sqrt{3}}{2} \)
E . \( \pi \)
Subject: Physics
An electron tube was sealed off during
manufacture at a pressure of \( 1.2 \times \)
\( 10^{-7} \mathrm{mm} \) of mercury at \( 27^{\circ} \mathrm{C} \). Its
volume is \( 100 \mathrm{cm}^{3} . \) The number of
molecules that remain in the tube is
A \( .2 \times 10^{16} \)
В . \( 3 \times 10^{15} \)
c. \( 3.86 \times 10^{11} \)
D. \( 5 \times 10^{11} \)
Subject: Maths
\( \lim _{n \rightarrow \infty}(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \dots(1+ \)
\( \left.x^{2 n}\right),|x|<1, \) is equal to
A \( \cdot \frac{1}{x-1} \)
в. \( \frac{1}{1-x} \)
c. \( 1-x \)
\( D \)
Subject: Physics
A calorimeter of water equivalent 6 g has water of mass 64 gup to a certain volume. Another identical calorimeter
has liquid of mass 50 g and
specific heat \( 0.6 \mathrm{cal} / \mathrm{g}^{-0} \mathrm{C} \) up to same
level. If both of them cool in the same
surroundings through same range of temperature and the time taken for the water to cool is 140 s, then the time taken for the liquid to cool will be :
A. 72 s
B. 140 s
\( c \cdot 36 s \)
D. 120
Subject: Maths
A relation \( R \) is defined on the set \( z \) of
integers as follows. \( (x, y) \in R \Leftrightarrow x^{2}+ \)
\( \boldsymbol{y}^{2}=25 . \) Express \( \boldsymbol{R} \) and \( \boldsymbol{R}^{-1} \) as the set
of ordered pairs and hence find their respective domains.
Subject: Physics
A gold coin has a charge of \( +10^{-4} C . \) The
number of electrons removed from it is:
A \( \cdot 10^{6} \)
В. \( 625 \times 10^{12} \)
c. \( 1.6 \times 10^{-25} \)
D. \( 1.6 \times 10^{13} \)
Subject: Chemistry
The electrolyte in lead storage battery is dilute sulphuric acid. The concentration of sulphuric acid in a lead-storage battery must be between \( 4.8 \mathrm{M} \) and 5.3 M for most efficient functioning: A 5 mL sulphuric acid sample of a particular battery requires \( 50 \mathrm{mL} \) of \( 1.0 \mathrm{M} \) NaOH for complete neutralization. Which of the following statements about the functioning of battery is the, most appropriate?
A. The acid concentration in the battery is not in the mos effective range
B. The acid concentration in the battery is in the most effective range
c. The add concentration in the battery is hardly in the most effective range
D. only a good mechanic can tell whether or not the acid concentration in the battery is in the most effective range
Subject: Chemistry
suppose that a hypothetical atom gives a red, green,blue and violet line spectrum. Which jump according to figure would give off the red spectral
ine
A \( .3 \rightarrow 1 \)
В . \( 2 \rightarrow 1 \)
\( c \cdot 4 \rightarrow 1 \)
D. \( 3 \rightarrow 2 \)
Subject: Chemistry
Consider the cell:
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}), \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s})|\boldsymbol{K} \boldsymbol{C l}(\boldsymbol{0} \cdot \mathbf{1} \boldsymbol{M})| \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2}(\boldsymbol{s}) \)
The cell potential
This question has multiple correct options
A . increases on increasing concentration of \( C l^{-} \) ions
B. decreases on decreasing concentration of \( C l^{-} \) ions
c. is independent of concentration of \( C l^{-} \) ions.
D. is independent of amounts of \( A g C l \) and \( H g_{2} C l \)
Subject: Physics
\( \mathbf{A} \)
\( 24 V \) battery having internal resistor of \( X \Omega \) is connected to a \( 4 \Omega \) resistor,
causing a current of \( 5 A \). Find out the
value of \( \boldsymbol{X} \) ?
\( \mathbf{A} \cdot 0 W \)
B. \( 0.8 W \)
c. \( 0.4 W \)
D. \( 1.6 W \)
E . \( 1.2 W \)
Subject: Physics
A circuit containing a \( 20 \Omega \) resistor and
0.1 \( \mu F \) capacitor in series is connected to 230 V AC supply of angular frequency 100 rad \( s^{-1} . \) The impedance of the circuit is
A \( \cdot 10^{5} \Omega \)
B . \( 10^{4} \Omega \)
\( \mathbf{c} \cdot 10^{6} \Omega \)
D. \( 10^{10} \Omega \)
Subject: Physics
CE and DF are two walls of equal height
(20 meter) from which two particles \( A \) and \( \mathrm{B} \) of same mass are projected as
shown in the figure.A is projected
horizontally towards left while B is
projected at an angle \( 37^{0} \) (with horizontal towards left) with
velocity \( 15 ~ m / s e c \). If \( A \) always sees \( B \) to
be moving perpendicular to EF, then the range of A on ground is
A \( .24 m \)
в. \( 30 m \)
\( c .26 m \)
D. \( 28 m \)
Subject: Chemistry
For a reaction, \( \boldsymbol{A}(\boldsymbol{s})+\mathbf{2} \boldsymbol{B}^{+} \rightarrow \boldsymbol{A}^{2+}+ \)
\( 2 B, K_{c} \) has been found to be \( 10^{12} \). The
\( \boldsymbol{E}_{c e l l}^{o} \) is:
A. \( 0.138 V \)
\( V \)
в. \( 0.235 \mathrm{V} \)
c. \( 0.354 V \)
D. none of these
Subject: Physics
A given object takes \( n \) times more time
to slide down \( 45^{\circ} \) rough inclined plane
as it takes to slide down a perfectly
\( \operatorname{smooth} 45^{\circ} \) incline. The coefficient of
kinetic friction between the object and
the incline is:
A \( \cdot \frac{1}{2-n^{2}} \)
B. \( 1-\frac{1}{n^{2}} \)
c. \( \sqrt{1-\frac{1}{n^{2}}} \)
D. \( \sqrt{\frac{1}{1-n^{2}}} \)
Subject: Biology
Name the phenomenon that governs the
following-
A. Green beetels living in green bushes are not eaten by the crows
B. All tall plants are obtained in \( F_{1} \) generation, upon crossing pure tall and dwarf pea plant.
C. Tails of mice were surgically removed for several generation ; still mice have tails in the following generation
D. Numbers of blue beetles on green bushes increase in a fur distant location than green beetles on green bushes, isolated by a river.
E. A migrant beetle reproduces with the local population as a result genes of migrant beetle enter the new population.
Subject: Physics
A counterclockwise couple \( C(\theta) \) acts on
a uniform \( 1.5 \mathrm{kg} \) bar \( \mathrm{AB} \) as shown in Fig.
1. Given two cases:
Case (a) \( C(\theta)=5.4 \sin \theta \mathrm{N}-\mathrm{m} \)
Case (b) \( C(\theta) \) varies as shown in Fig. 2
The total work done on the bar as it
rotates in the vertical plane about \( \mathbf{A} \)
from \( \theta=0^{\circ} \) to \( \theta=180^{\circ} \) in the above two
cases are \( W_{a} \) and \( W_{b} \) respectively.
Then,
(Take \( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
This question has multiple correct options
\( A \cdot W_{a}=3.22 \mathrm{N}-\mathrm{m} \)
B. \( W_{a}=4.2 \mathrm{N}-\mathrm{m} \)
C \( . W_{b}=4.2 \mathrm{N}-\mathrm{m} \)
D. \( W_{b}=1.86 \mathrm{N}-\mathrm{m} \)
Subject: Physics
Assertion
A hydrogen-filled balloon stops rising after it has attained a certain height in the sky.
Reason
The atmospheric pressure decreases with height and becomes zero when the maximum height is attained.
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
If value of \( x \) which satisfy equation
\( \cos ^{-1} x<2 \) is \( x \epsilon(a, b] \)
Find the value of \( a+b \)
A. \( -1-\cos 2 \)
B. \( 1-\cos 2 \)
c. \( -1+\cos 2 \)
D. \( 1+\cos 2 \)
Subject: Physics
The ac generator in the Figure supplies
\( 150 V_{(\max )} \) at \( 50 \mathrm{Hz} . \) With the switch open as shown in the diagram, the
resulting current leads the generator
emf by \( 60^{\circ} . \) With the switch in position
1, the current lags the generator emf by
\( 30^{\circ} . \) When the switch is in
position \( 2, \) the maximum current is \( 3 A \)
Then, the value of R is:
A. \( 50 / \sqrt{3} \Omega \)
B. 83.3 \( \Omega \)
c. \( 133.3 \Omega \)
D. \( 50 \Omega \)
Subject: Physics
Current \( ^{\prime} i^{\prime} \) coming from the battery and ammeter reading are
A \( \cdot \frac{3}{8} A, \frac{1}{8} A \)
в. \( \frac{1}{8} A, \frac{1}{8} A \)
c. \( 2 A, \frac{2}{3} \)
' \( 2 A, \frac{1}{8} \)
Subject: Physics
The magnetic flux linked with a coil is
\( \phi \leq 8 t^{2}+3 t+5 \) Weber. The induced
emf in fourth second will be
\( \mathbf{A} \cdot 16 V \)
B. \( 139 V \)
\( c .67 V \)
D. \( 145 V \)
Subject: Physics
A train is moving forward at a velocity of \( 2.0 m / s . \) At the instant the train begins
to accelerate at \( 0.80 m / s^{2}, \) a passenger drops a coin which takes \( 0.50 s \) to fall
on the floor. Relative to a spot on the floor directly under the coin at release, the coin lands
A. \( 1.1 \mathrm{m} \) towards the rear of the train
B. \( 1.0 \mathrm{m} \) towards the rear of the train
c. \( 0.10 \mathrm{m} \) towards the rear of the train
D. \( 0.90 \mathrm{m} \) towards the front of the train
Subject: Physics
Charges of \( q \) coulomb but of alternately
opposite signs are placed along the \( x- \) axis at \( x=1, x=2, x=4, \ldots \) and so on. The
electric potential at the point \( x=0 \) due to
all these charges will be
A \( \cdot \frac{q}{2 \pi \epsilon_{0}} \)
в. \( \frac{q}{3 \pi \epsilon_{0}} \)
c. \( \frac{2 q}{3 \pi \epsilon_{0}} \)
D. \( \frac{q}{6 \pi \epsilon_{0}} \)
Subject: Chemistry
Which of the following is not s-block element?
В. \( 1 s^{2} 2 s^{2} 2 p^{1} \)
c. \( 1 s^{2} 2 s^{1} 2 p^{1} \)
D・ \( [A r] 4 s^{1} 4 p^{1} \)
Subject: Maths
Show that the function \( f \) given by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x}, \boldsymbol{x} \in \boldsymbol{R} \) is strictly
increasing.
Subject: Chemistry
The degree of dissociation of
\( C a\left(N O_{3}\right)_{2} \) in a dilute aqueous solution containing 7 gm of the salt per 100 gm
of water at \( 100^{\circ} \mathrm{C} \) is 70 per. If the vapour
pressure of water at \( 100^{\circ} \mathrm{C} \) is \( 760 \mathrm{mm} \)
Calculate the vapour pressure of the solution.
A. \( 373.12 \mathrm{mm} / \mathrm{Hg} \)
в. \( 524.89 \mathrm{mm} / \mathrm{Hg} \)
\( \mathbf{c} .746 .24 \mathrm{mm} / \mathrm{Hg} \)
D. \( 1049.6 \mathrm{mm} / \mathrm{Hg} \)
Subject: Chemistry
\( C_{6} H_{4} C l_{2}+C l_{2} \frac{F e}{(x)} C_{6} H_{5} C l_{3} \) Only one
structural isomer of \( Y \) is formed. Hence
\( (X) \) is:
(doclorobenzeme ) (Trichlorobenzeme)
A . o-isomer
B. p-isomer
c. m-isomer
D. any of this
Subject: Physics
A straight wire with a resistance of \( r \)
per unit length is bent to form an angle
2 \( \alpha \). A rod of the same wire
perpendicular to the angle bisector (of
\( 2 \alpha) \) forms a closed triangular loop. This loop is placed in a uniform magnetic
field of a induction \( B \). Calculate the
current in the wires when the rod moves
at a constant speed \( V \)
Subject: Physics
What is the value of magnetic potential,
at a distance of \( 1 \mathrm{cm} \) from the pole, of
pole strength 60 A-m?
A. \( 600 \mathrm{m} \) J/Am
B. 600 \( \mu \) /Ат
c. 600 MJ/Am
D. 600 KJ/Am
Subject: Maths
Mark the correct alternative of the
following.
In figure, \( A B|| C D \) and \( E F \) is a transversal
intersecting \( A B \) and \( C D \) at \( P \) and \( Q \)
respectively. The measure of \( \angle D P Q \) is
\( \mathbf{A} \cdot 100^{\circ} \)
B . \( 80^{\circ} \)
\( \mathbf{c} \cdot 110^{\circ} \)
D. \( 70^{\circ} \)
Subject: Physics
A charged particle having charge \( 10^{-6} C \) and mass of \( 10^{-10} k g \) is fired
from the middle of the plate making an
angle \( 30^{\circ} \) with plane of the plate. Length
of the plate is \( 0.17 \mathrm{m} \) and it is sperated
by 0.1 m.Electric field \( E=10^{-3} N / C \) is
present between the plates.Just outside the plates magnetic field is present. Find the velocity of projection of charged particle and magnitude of the magnetic field perpendicular to the plane of the figure,if it has to graze the plate at \( C \) and \( A \) parallel to the surface of the plate .(Neglect gravity)
Subject: Physics
An observer \( A \) fires a gun and another observer \( B \) at a distance \( 1650 m \) away
from \( A \) hears its sound. If the speed of
sound is \( 330 m s^{-1}, \) find the time when
\( B \) will hear the sound after firing by \( A \)
\( \mathbf{A} \cdot 5 s \)
в. \( 15 s \)
\( c .50 s \)
D. None of these
Subject: Maths
An alloy contains \( 15 \% \) zinc, \( 25 \% \) brass
and rest copper. How much copper is there in 75 kg of that alloy?
A. \( 20 \mathrm{kg} \)
в. \( 30 \mathrm{kg} \)
c. \( 45 \mathrm{kg} \)
D. \( 10 \mathrm{kg} \)
Subject: Chemistry
\( 60 \% \) of first order reaction was
completed in 60 min. The time taken for
reactants to decompose to half of their original amount will be :
\( \mathbf{A} \cdot \approx 30 \min \)
в. \( \approx 60 \) min
\( \mathbf{c} . \approx 90 \min \)
\( \mathbf{D} \cdot \approx 45 \min \)
Subject: Maths
\( f_{a, b, c, d} \) are positive real numbers, then show that \( (a+b+c+ \)
\( d)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}\right) \geq 16 . \) What happens
when the numbers are all equal?
Subject: Physics
bricks each. Aswin arranged his four
bricks as shown in figure A. Anwar arranged his bricks as shown in figure
B, in order to be a taller one.
Now let us complete the following
sentences by choosing the right option
below
(equal to, less than, more than)
a) The force of \( A \) on the ground is the force of \( B \) on the
ground.
b) The area that \( A \) occupies is
\( B \) on the ground.
c) The pressure exerted by \( A \) is the pressure exerted by B.
Subject: Physics
toppr
Q Type your question
4
\begin{tabular}{cc|c}
\( \mathbf{x} \) & \( \mathbf{y} \) & \( \mathbf{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
B. \begin{tabular}{cc|c}
\( \mathbf{x} \) & \( \mathbf{y} \) & \( \mathbf{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{0} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
\( c \)
\begin{tabular}{ll|l}
\( \mathbf{x} \) & \( \mathbf{y} \) & \( \mathbf{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \)
\end{tabular}
\( D \)
\begin{tabular}{ll|l}
\( \mathbf{x} \) & \( \mathbf{y} \) & \( \mathbf{z} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
& \( \mathbf{0} \) & \( \mathbf{1} \) \\
\( \mathbf{-} \) & \( \mathbf{1} \) & \( \mathbf{0} \)
\end{tabular}
Subject: Maths
\( \int \sec ^{2} x \log \left(1+\sin ^{2} x\right) d x= \)
\( \tan x \log \left(1+\sin ^{2} x\right)-2 x+ \)
\( \sqrt{k} \tan ^{-1} \sqrt{k} \tan x . \) Find the value of \( k \)
Subject: Maths
A store reported total sales of \( \$ 385 \)
million for February of this year. If the total sales for the same month last year
was \( \$ 320 \) million, approximately what was the percent increase in
sales?
A . \( 2 \% \)
B. \( 17 \% \)
c. \( 20 \% \)
D. \( 65 \% \)
E. \( 83 \% \)
Subject: Physics
In a Youngs interference experimental
arrangement the incident yellow light is composed of two wavelength \( 5890 A \) and 5895 A. The distance between the
slits is \( 10^{-3} m \) and the screen is-placed
1 \( m \) away. Upto what order can fringes be seen on the screen? And how far from
the centre of the screen does this
occur?
Subject: Physics
of the resistors in the circuit pictured
below?
A \( \cdot R_{1} \rightarrow 10 V ; R_{2} \rightarrow 4 V ; R_{3} \rightarrow 2 V ; R_{4} \rightarrow 4 V \)
B . \( R_{1} \rightarrow 1 V ; R_{2} \rightarrow 3 V ; R_{3} \rightarrow 2 V ; R_{4} \rightarrow 4 V \)
c. \( R_{1} \rightarrow 10 V ; R_{2} \rightarrow 2 V ; R_{3} \rightarrow 4 V ; R_{4} \rightarrow 4 V \)
D. \( R_{1} \rightarrow 1 V ; R_{2} \rightarrow 4 V ; R_{3} \rightarrow 4 V ; R_{4} \rightarrow 2 V \)
Subject: Maths
The length of two sides of a triangle are
\( 20 \mathrm{mm} \) and \( 29 \mathrm{mm} . \) Which of the
following can be the value of third side to form the triangle?
\( A \cdot 6 \mathrm{mm} \)
B. \( 7 \mathrm{mm} \)
\( c .23 \mathrm{mm} \)
D. \( 8 \mathrm{mm} \)
Subject: Maths
If \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi}, \) show that \( \sin \left(\frac{\boldsymbol{A}}{\mathbf{2}}\right)+ \)
\( \sin \left(\frac{B}{2}\right)+\sin \left(\frac{C}{2}\right)=1+ \)
\( 4 \sin \frac{\pi-A}{4} \sin \frac{\pi-B}{4} \sin \frac{\pi-C}{4} \)
Subject: Chemistry
The two particle \( A \) and \( B \) have de Broglie wavelengths 1 nm and 5 nm respectively. If mass of \( A \) is 4 times that of mass of \( B \)
the ratio of KE of \( A \) and \( B \) would be:
A . 5:
B. 25: 4
\( c \cdot 20: 1 \)
D. 5: 4
Subject: Chemistry
The \( K_{c} \) for the reaction \( A+B \Leftrightarrow C \) is 4
and \( K_{c} \) for \( 2 A+D \Leftrightarrow C \) is 6 the value
of \( \boldsymbol{K}_{c} \) for \( \boldsymbol{C}+\boldsymbol{D} \Leftrightarrow \mathbf{2} \boldsymbol{B} \) is:
Subject: Maths
Differentiate: \( \boldsymbol{x}^{\mathbf{1 0 0}}+\sin \boldsymbol{x}-\mathbf{1} \)
A \( \cdot 100 x^{99}-\cos x \)
\( x \)
B. \( 100 x^{99}+\cos x \)
c. \( x^{99}+\cos x \)
D. \( 100 x^{99}+\sin x \)
Subject: Maths
If \( \bar{a}, \bar{b} \) are the position vectors of \( A \) and
\( B \) then one of the following points lie on
\( A B \)
A \( \cdot \frac{2(\bar{a}+\bar{b})}{3} \)
в. \( \frac{(\bar{a}-\bar{b})}{3} \)
c. \( \frac{(\bar{a}+\bar{b})}{3} \)
\( ^{\mathrm{D}} \cdot \frac{2 \bar{a}+2 \bar{b}}{3} \)
E. None of these
Subject: Physics
A body of mass \( 3 \mathrm{kg} \) is under a force which causes a displacement in it, given by \( s=t^{2} / 3(\text { in } \mathrm{m}) . \) Find the work
done by the force in 2 second.
A . 2
B . 3.8
c. 5.2 J
D . 2.6
Subject: Physics
The rate of emission of radiation of a
black body at \( 273^{\circ} \mathrm{C} \) is \( E \), then the rate of
emission of radiation of this body at \( 0^{\circ} \mathrm{C} \)
will be
A \( \cdot \frac{E}{16} \)
в. \( \frac{E}{4} \)
c. \( \frac{E}{8} \)
D. 0
Subject: Physics
A ray incident at a point at an angle of
incidence \( 60^{\circ} \) enters a glass sphere of \( \mu=\sqrt{3} \) and is reflected and refracted
at the further surface of the sphere. The angle between the reflected
and refracted rays at this surface is :
A. \( 50^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 60 \)
\( D \cdot 40 \)
Subject: Chemistry
What is true for the equilibrium
reaction:
Acetic acid+ ethanol \( \stackrel{\boldsymbol{H}^{+}}{\rightleftharpoons} \) Ethyl acetate \( + \)
\( \boldsymbol{H}_{2} \boldsymbol{O} ? \)
This question has multiple correct options
A. The use of equimolar quantities of ethanol and acetic acid will give greatest yield of ester at equilibrium.
B. Removal of water will increase the amount of ester at equilibrium
C. Addition of water ester at equilibrium will cause formation of equal amount of water
D. Application of pressure increases the amount of ester at equilibrium
Subject: Chemistry
The molar conductance at infinite
dilution of \( A g N O_{3}, A g C l \) and \( N a C l \)
are 116.5,121.6 and 110.3 respectively.
The molar conductance of \( N a N O_{3} \) is:
\( \mathbf{A} \cdot 111.4 \)
B. 105.2
c. 130.6
D. 150.2
Subject: Biology
The inner ear also contains a complex
system called ....A... located above the
\( \dots .8 \dots \)
Fill the blank \( A \) and \( B \) with the correct
option.
A. A - Vestibular apparatus, B - Cochlea
B. A - Cochlea, B - Vestibular apperatus
c. A - otolith organ, B - Semicircular canal
D. A - Crista ampullaris, B - Semicircular canal
Subject: Maths
If \( f \) is a real-valued differentiable
function satisfying \( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})| \leq \)
\( (x-y)^{2}, \quad x, y \in R \) and \( f(0)=0, \) then
\( \boldsymbol{f}(\mathbf{1}) \) equals
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. 0
D. -
Subject: Maths
Equation of the parabola with its vertex at (1,1) and focus (3,1) is
A \( \cdot(x 1)^{2}=8(y-1) \)
B . \( (y-1)^{2}=8(x-3) \)
c. \( (y-1)^{2}=8(x-1) \)
D. \( (x-3)^{2}=8(y-1) \)
Subject: Maths
State whether the given list of numbers is an arithmetic progression or not.
\( a) 13,20,27,34, \dots \)
\( \boldsymbol{b}) \boldsymbol{6}, \boldsymbol{1} \boldsymbol{6}, \boldsymbol{2} \boldsymbol{6}, \boldsymbol{3} 5, \ldots \)
Subject: Maths
Prove the following identities
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2} \\ \boldsymbol{a}^{2} & \mathbf{1} & \boldsymbol{a} \\ \boldsymbol{a} & \boldsymbol{a}^{2} & \mathbf{1}\end{array}\right|=\left(\boldsymbol{a}^{3}-\mathbf{1}\right)^{2} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by
\( f(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} \) then
A. \( f \) is a bijection
B. \( f \) is an injection only
c. \( f \) is a surjection
D. \( f \) is neither an injection nor a surjection
Subject: Physics
Under isothermal condition, energy \( \boldsymbol{E} \) is supplied to a soap bubble of surface tension \( \sigma \) and radius \( r \) to double the
radius of the soap bubble. The value of
\( \boldsymbol{E} \) is:
A \( \cdot 16 \pi r^{2} \sigma \)
B. 24 \( \pi r^{2} \sigma \)
\( \mathbf{c} \cdot 8 \pi r^{2} \sigma \)
D. \( 12 \pi r^{2} \sigma \)
Subject: Physics
Assuming that the period of vibration of a tuning fork depends upon the length \( l \)
of its prongs density \( \rho \) of its material and the elastic constant \( \boldsymbol{E} \) of its
material what would be the formula for
the period of its vibration
A \( \cdot \frac{k}{l} \sqrt{\frac{y}{d}} \)
B. \( \frac{2 k}{l} \sqrt{\frac{y}{d}} \)
c. \( \frac{k}{2 l} \sqrt{\frac{2 y}{d}} \)
D. \( \frac{3 k}{l} \sqrt{\frac{y}{2 d}} \)
Subject: Chemistry
Metal carbonyls can have formula
\( \left.M(C O)_{x}\right), \) where \( x= \) number of \( C O \) units coordinated to metal \( M \)

What is the formula of the carbonyl of \( F e(26) \) if \( E A N \) of \( F e \) in metal carbonyl
is \( 36 ? \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Physics
The activity of a radioactive sample is measured as 9750 count \( / \) min at \( t=0 \)
and 975 count/min at \( t=5 \) min.The
decay constant is nearly
A. 0.922 min \( ^{-1} \)
B. \( 0.691 \mathrm{min}^{-1} \)
c. \( 0.461 \min ^{-1} \)
D. 0.230 \( \min ^{-1} \)
Subject: Maths
If \( \lim _{x \rightarrow c} \frac{f(x)-f(c)}{x-c} \) exists finitely, then
\( \mathbf{A} \cdot \lim _{x \rightarrow c} f(x)=f(c) \)
B. \( \lim _{x \rightarrow c} f^{\prime}(x)=0 \)
\( \mathbf{C} \cdot \lim _{x \rightarrow c} f(x) \) does not exist
D. \( \lim _{x \rightarrow c} f(x) \) may or may not exist
Subject: Physics
The density of \( O_{2} \) at \( \mathrm{NTP} \) is \( 1.429 \mathrm{g} / \mathrm{L} \) the standard molar volume:
\( \mathbf{A} \cdot 22.4 L \)
B. \( 11.2 L \)
c. \( 33.6 L \)
D. \( 5.6 L \)