AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
How many grams of \( C O_{2} \) gas is
dissolved in a 1 It bottle of carbonated
water if the manufacturer uses a
pressure of 2.4 atmosphere in the bottling process at \( 25^{\circ} \mathrm{C} \) ? \( \left(K_{H} \text { of } C O_{2}\right. \)
water \( \left.=29.76 a t m / m o l e / l \text { at } 25^{\circ} C\right) \)
A . 3.52
в. 4.2
\( c .3 .1 \)
D. 2.5
Subject: Chemistry
Which of the following is disproposination reaction?
A \( \cdot C a C O_{3}+2 H^{+} \rightarrow C a^{2+}+H_{2} O+C O_{2} \)
B . \( 2 \mathrm{CrO}_{4}^{2-}+2 \mathrm{H}^{+} \rightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+\mathrm{H}_{2} \mathrm{O} \)
c. \( C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow 2 C r O_{4}^{2-}+H_{2} O \)
D. \( C u_{2} O+2 H^{+} \rightarrow C u+C u^{2+}+H_{2} O \)
Subject: Physics
Match the following
Physical Quantity Unit in ¿uc is an a it \( \begin{array}{l}\text { a) Magnetic Moment } \\ \text { b) Magnetic Flux Density } \\ \text { c) Intensity of Magnetic Field } & \text { e) } A m p-m \\ \text { d) Pole strength } & \text { g) } N-m^{3} / W b \\ \text { h) Gauss }\end{array} \)
\( A \cdot a-e, b-f, c-g, d-h \)
B. \( a-g, b-h, c-f, d-e \)
\( \mathbf{C} \cdot a-g, b-f, c-h, d-e \)
D. a-e, b-f, c-h, d-g
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}, \boldsymbol{x} \in \boldsymbol{N} . \) Then \( \boldsymbol{f} \) is
A. one-one onto
B. many-one onto
c. one-one but not onto
D. none of these
Subject: Physics
A material \( B \) has twice the specific
resistance of \( A . \) A circular wire made of
\( B \) has twice the diameter of a wire
made of \( A \). Then for the two wires to
have the same resistance, the ratio \( l_{B} / \)
\( l_{A} \) of their respective lengths must be:
\( A \)
B. 1/2
\( c \cdot 1 / 4 \)
D.
Subject: Physics
A cannon ball of mass \( 5 \mathrm{kg} \) is discharged horizontally with a velocity of \( 500 m / s . \) If the cannon be free to move on the horizontal ground, what is the velocity with which it recoils? Mass of
the cannon is \( 100 \mathrm{kg} \)
A . \( 15 \mathrm{m} / \mathrm{s} \)
B. 25m/s
\( c \cdot 35 m / s \)
D. \( 45 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A cylinder of height \( 20 \mathrm{m} \) is completely filled with water. The velocity of efflux of water (in \( \mathrm{ms}^{-1} \) ) through a small hole on
the side wall or the cylinder near its bottom is:
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. 20 m/s
c. \( 25.5 \mathrm{m} / \mathrm{s} \)
D. \( 5 \mathrm{m} / \mathrm{s} \)
Subject: Physics
Specific heat capacity of a substance \( A \) is \( 3.8 J g^{-1} K^{-1} \) and of substance \( B \) is
\( 0.4 J g^{-1} K^{-1} \) is a good conductor of heat?
\( A \cdot A \)
B. B
c. both A \& B are equally good
D. cant say
Subject: Physics
The distance between the vertex and the
center of mass of a uniform solid planar
circular segment of angular size \( \theta \) and
radius \( \boldsymbol{R} \) is given by
\( A \)
\( B \frac{\sin (\theta / 2)}{\theta} \)
\( ^{\mathrm{c}} \cdot \frac{4}{3} R \cos \left(\frac{\theta}{2}\right) \)
D \( \cdot \frac{2}{3} R \cos (\theta) \)
Subject: Physics
A car of mass \( 500 \mathrm{kg} \), moving with the velocity of \( 4 \mathrm{m} / \mathrm{s} \) accelerates uniformly and attains the velocity of \( 8 \mathrm{m} / \mathrm{s} \) in 10
seconds. Calculate the initial and final
momentum of the object. find the magnitude of the force exerted on the car to provide this acceleration.
Subject: Physics
A particle of mass \( \mathrm{M} \) at rest decays into
two masses \( m_{1} \) and \( m_{2} \) with non-zero
velocities. The ratio \( \lambda_{1} / \lambda_{2} \) of de Broglie
wavelengths of particles is
A \( \cdot m_{2} / m_{1} \)
в. \( m_{1} / m_{2} \)
c. \( \sqrt{m_{1}} / \sqrt{m_{2}} \)
in
D. 1:
Subject: Maths
In a triangle \( A B C, \) right angled at the
vertex \( A, \) if the position vectors of \( A, B \) and \( C \) are respectively \( 3 \hat{i}+\hat{j}-\hat{k},-\hat{i}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}+\boldsymbol{p} \hat{\boldsymbol{k}} \) and \( \mathbf{5} \hat{\boldsymbol{i}}+\boldsymbol{q} \hat{\boldsymbol{j}}-\boldsymbol{4} \hat{\boldsymbol{k}}, \) then the
point \( (p, q) \) lies on a line:
A. Making an obtuse angle with the positive direction of x-axis
B. Making an acute angle with the positive direction of x axis
c. Parallel to x-axis
D. Parallel to y-axis
Subject: Maths
The closest distance of the origin from a curve given as \( \boldsymbol{a} \overline{\boldsymbol{z}}+\overline{\boldsymbol{a}} \boldsymbol{z}+\boldsymbol{a} \overline{\boldsymbol{a}}=\mathbf{0}(\boldsymbol{a} \) is a
complex number
A . 1
в. \( \frac{|a|}{2} \)
c. \( \frac{\operatorname{Re}(a)}{|a|} \)
D. \( \frac{\operatorname{Im}(a)}{|a|} \)
Subject: Maths
Simplify: \( \boldsymbol{x}^{2}\left(\boldsymbol{3}-\boldsymbol{5} \boldsymbol{y}^{2}\right)+ \)
\( \boldsymbol{x}\left(\boldsymbol{x} \boldsymbol{y}^{2}-\boldsymbol{3} \boldsymbol{x}\right)-\boldsymbol{2} \boldsymbol{y}\left(\boldsymbol{y}-\boldsymbol{2} \boldsymbol{x}^{2} \boldsymbol{y}\right) \)
A \( \cdot 6 x^{2}-2 y^{2}-3 x^{2} y \)
В. \( 6 x^{2} \)
\( \mathrm{c} \cdot 3 x^{2} y \)
D. \( -2 y^{2} \)
Subject: Physics
An electron, moving along the \( x \) -axis with an initial energy of \( 100 e V \), enters a region of magnetic field \( \vec{B}=(1.5 \times \)
\( \left.10^{-3} T\right) \hat{k} \) at \( S(\text { See figure }) . \) The field
extends between \( x=0 \) and \( x=2 c m \)
The electron is detected at the point \( Q \) on a screen placed \( 8 \mathrm{cm} \) away from the point S. The distance d between P and Q
(on the screen) is :
(electron's charge \( =1.6 \times 10^{-19} \mathrm{C}, \) mass
of electron \( \left.=9.1 \times 10^{-31} k g\right) \)
A \( .12 .87 \mathrm{cm} \)
В. \( 1.22 \mathrm{cm} \)
c. \( 11.65 \mathrm{cm} \)
D. \( 2.25 \mathrm{cm} \)
Subject: Maths
Evaluate \( \int e^{x}\left(\log (x)+\frac{1}{x^{2}}\right) d x \)
A. \( e^{x}\left(\log x+\frac{1}{x^{2}}\right) \)
B. \( \quad e^{x}\left(\log x+\frac{1}{x}\right) \)
c. \( \quad e^{x}\left(\log x-\frac{1}{x^{2}}\right) \)
D. \( \quad e^{x}\left(\log x-\frac{1}{x}\right) \)
Subject: Chemistry
The osmotic pressure of a dilute solution is given by :
A. \( P=P_{0} \times N_{1} \)
B . \( \pi V=n R T \)
c. \( \Delta P=P_{0} N_{2} \)
D. \( \frac{\Delta P}{P^{o}}=\frac{P^{o}-P_{S}}{P^{o}} \)
Subject: Physics
Two resister \( \boldsymbol{R}_{1}=\mathbf{4 0 0 \Omega} \) and \( \boldsymbol{R}_{2}=\mathbf{2 0 \Omega} \)
are connected in parallel to a battery. If
heating power developed in \( R_{1} \) in \( 25 \mathrm{W} \)
find the heating power developed in \( \boldsymbol{R}_{2} \)
Subject: Physics
A bullet of mass \( A \) and velocity \( B \) is fired
into a block of wood of mass \( C . \) If loss of
any mass and friction be neglected, the velocity of the system will be
\( ^{\text {A }} \cdot \frac{A B}{A+C} \)
в. \( \frac{A+C}{B+C} \)
c. \( \frac{A C}{B+C} \)
D. \( \frac{A+B}{A C} \)
Subject: Chemistry
Fourteen elements following
Lanthanum are called Lanthanoids:
(a) What is Lanthanoid contraction?
Give reason for it.
(b) \( K M n O_{4} \) is a purple coloured
crystal and it acts as an oxidant. How
will you prepare \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \) from \( \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2} ? \)
Subject: Physics
The magnetic flux through a coil perpendicular to the plane is varying according to the relation \( \varphi= \)
\( \left(5 t^{3}+4 t^{2}+2 t-5\right) \) wb. Calculate the
induced current through the coil at \( t= \)
2 sec, if the resistance of the coil is \( 5 \Omega \)
Subject: Physics
Assertion
Latent heat of fusion of ice is
\( 33600 J k g^{-1} \)
Reason
Latent heat refers to change of state without any change in 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
At \( 25^{\circ} C, \) the solubility product of \( C u C l \)
is \( 2.0 \times 10^{-7} \) and \( E_{C l^{-}|C u C l| C u}^{\circ} \) is
\( 0.128 V . \) The value of \( E_{C u^{+} / C u}^{\circ} \) is:
\( [(\log 2=0.3),(2.303 R T / F=0.06)] \)
A. \( -0.274 V \)
в. \( -0.402 \mathrm{V} \)
\( \mathbf{c} .+0.53 V \)
D. \( +0.402 \mathrm{V} \)
Subject: Physics
A solid sphere of mass \( M, \) radius \( R \) and
having moment of inertia about an axis passing through the centre of mass as
\( I, \) is recast into a disc of thickness \( t \)
whose moment of inertia about an axis
passing through its edge and perpendicular to its plane remains \( \boldsymbol{I} \) Then, radius of the disc will be:
A \( \cdot \frac{2 \mathrm{R}}{\sqrt{15}} \)
B \( \cdot R \sqrt{\frac{2}{15}} \)
c. \( \frac{4 \mathrm{R}}{\sqrt{15}} \)
D. \( \sqrt{\frac{2 R}{15}} \)
Subject: Physics
Water rises to a height of \( 10 \mathrm{cm} \) in a
capillary tube and mercury falls to a depth of the same capillary tube. If the density of water is \( 1 \mathrm{gm} / \mathrm{c} . \mathrm{c} \) and its
angle of contact is \( 0^{\circ}, \) then the ratio of
such of two liquids is \( \left(\cos 135^{\circ}=0.7\right) \)
Subject: Physics
Three similar cells, each of emf \( 2 V \) and
internal resistance \( r \) send the same
current through an external resistance of \( 2 \Omega, \) when connected in series or in
parallel. Then the magnitude of current flowing through the external resistance is :
\( \mathbf{A} \cdot 0.75 A \)
в. \( 1 A \)
\( c .1 .5 A \)
D. zero
Subject: Physics
A cylindrical vessel open at the top is \( 20 c m \) high and \( 10 c m \) in diameter. \( A \)
circular hole whose cross-sectional
\( \operatorname{area} 1 c m^{2} \) is cut at the centre of the
bottom of the vessel. Water flows from a
tube above it into the vessel at the rate
\( 100 \mathrm{cm}^{3} s^{-1} . \) The height of water in the
vessel under steady state (in cm) is
Subject: Physics
Assertion
Work done by friction force in case of pure rolling,is equal to change in rotational energy.
Reason
Ratio of kinetic energy of rotation to kinetic energy of translation is fixed for
every case.
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 plane \( a x+b y+c z+d=0 \) divides
the line joining the points \( \left(x_{1}, y_{1}, z_{1}\right) \)
and \( \left(x_{2}, y_{2}, z_{2}\right) \) in the ratio
A \( \cdot \frac{-\left(a x_{1}+b y_{1}+c z_{1}+d\right)}{\left(a x_{2}+b y_{2}+c z_{2}+d\right)} \)
B. \( \frac{\left(a x_{1}+b y_{1}+c z_{1}+d\right)}{\left(a x_{2}+b y_{2}+c z_{2}+d\right)} \)
c. \( \frac{a x_{1} x_{2}+b y_{1} y_{2}+c z_{1} z_{2}}{d^{2}} \)
D. None of these
Subject: Physics
Light rays of wavelengths \( 6000 A \) and of
photon intensity 39.6 watts \( / m^{2} \) incidents on a metal surface. If only \( 1 \% \) of photons incident on the surface emit photoelectrons, then the number of electrons emitted per second per
unit area from the surface will be
approximately:
[Planck constant \( \boldsymbol{h}=\mathbf{6 . 6 4} \times \mathbf{1 0}^{-\mathbf{3 4} \mathbf{J}} \boldsymbol{s} \)
Velocity of light \( \left.=\mathbf{3} \times \mathbf{1 0}^{\mathbf{8}} \boldsymbol{m} \boldsymbol{s}^{-\mathbf{1}}\right] \)
A \( \cdot 12 \times 10^{18} \)
В. \( 10 \times 10^{18} \)
C \( .12 \times 10^{17} \)
D. \( 12 \times 10^{15} \)
Subject: Chemistry
The measured resistance of a
conductance cell containing \( \mathbf{7 . 5} \times \) \( 10^{-3} M \) solution of \( K C l \) at \( 25^{\circ} C \) was
1005 ohms. Calculate molar
conductance \( \left(o h m^{-1} c m^{2} m o l^{-1}\right) \) of
the solution.
(Cell constant= \( 1.25 \mathrm{cm}^{-1} \) )
A . 16.587
B. 165.87
c. 1658.7
D. 1.6587
Subject: Maths
The value of \( (-3)^{0}-(-3)^{3}- \)
\( (-3)^{-1}+(-3)^{4}-(-3)^{-2} \) is
A \( \cdot_{109} \frac{2}{9} \)
в. \( _{109} \frac{9}{2} \)
\( c .109 \)
D. None of these
Subject: Physics
A ray of light moving along the vector \( (\hat{i}-\hat{\mathbf{2}} j) \) undergoes refraction at an interface of two media, which is \( x-z \)
plane. The refractive index for \( y>0 \) is 2 while for \( y<0 \) it is \( \frac{\sqrt{5}}{2} . \) The unit vector along the refracted ray is 2
\( ^{\mathbf{A}} \cdot \frac{-3 \hat{i}-5 \hat{j}}{\sqrt{34}} \)
\( \frac{(-4 \hat{i}-5 \hat{j})}{5} \)
\( ^{\mathbf{C}} \frac{-3 \hat{i}-4 \hat{j}}{5} \)
D. \( \frac{4 \hat{i}-3 \hat{j}}{5} \)
Subject: Maths
Three boxes numbered I, II, III contains
the balls as follows:
\( \begin{array}{llll}\text { White } & \text { Black } & \text { Red } \\ \text { I } & 1 & 2 & 3 \\ \text { II } & 2 & 1 & 1 \\ \text { "II } & 4 & 5 & 3\end{array} \)
One box is randomly selected and a ball is drawn from it. If the ball is red, then
find the probability that it is from box II
Subject: Physics
\( A 60 \mathrm{W} / 120 \mathrm{V} \) bulb is connected to a
\( 240 / 60 \mathrm{Hz} \) supply with an inductance in series. Find the value of inductance so
that bulb gets correct voltage.
A \( \cdot \frac{2.3}{\pi} \) н
в. \( 2 \sqrt{3} \) н
с. \( \pi \) н
D. \( \frac{2 \sqrt{3}}{\pi} \) н
Subject: Physics
The velocity and acceleration vectors of a particle undergoing circular motion \( \operatorname{are} \overrightarrow{\boldsymbol{v}}=2 \hat{\boldsymbol{i}} \boldsymbol{m} / \boldsymbol{s} \) and \( \overrightarrow{\boldsymbol{a}}=\boldsymbol{2} \hat{\boldsymbol{i}}+ \)
\( 4 \hat{j} m / s^{2} \) respectively at an instant of
time. The radius of the circle is
A . \( 1 m \)
B. \( 2 m \)
\( c .3 m \)
D. \( 4 m \)
Subject: Physics
Read the assertion and reason carefully to mark the correct option out of the
options given below:

Assertion: An astronaut in a satellite
feels weightlessness.
Reason: As observed by another
astronauts in the same satellite, force
of gravity and centrifugal force balance
each other.
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
C. If assertion is true but reason is false
D. If assertion is false but reason is true
Subject: Physics
A beam of incident light rays falls
onto the glass plate. Possible angles for
the reflected and refracted rays are
shown as \( \mathrm{E}, \mathrm{D}, \mathrm{C}, \mathrm{B} \& \mathrm{A} \) in the figure above dentify which of the following best
represents the reflected ray?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \cdot D \)
\( E . \)
Subject: Physics
An insect crawls up a hemispherical surface. The coefficient of friction
between the insect and the surface is
1/3. If the line joining the centre of the hemispherical surface to the insect
makes an angle \( \alpha \) with the vertical, the
maximum possible value of \( \alpha \) is given
by
A. \( \cot \alpha=3 \)
B. \( \tan \alpha=3 \)
c. \( \sec \alpha=3 \)
D. \( \operatorname{cosc} \alpha=3 \)
Subject: Maths
Factorise \( a^{2}(b+c)-(b+c)^{3} \)
A \( \cdot(b+c)\left(a^{2}-(b+c)^{2}\right. \)
В \( \cdot(b-c)\left(a^{2}-(b+c)^{2}\right. \)
c. \( (b+c)\left(a^{2}+(b+c)^{2}\right) \)
D. None of these
Subject: Physics
What is the work required to set up the four-charge configuration of the figure, assuming the charges are initially infinitely far apart?
A \( \cdot \frac{q^{2}}{4 \pi \epsilon_{0} a}(4+\sqrt{2}) \)
В \( \cdot \frac{q^{2}}{4 \pi \epsilon_{0} a}(4-\sqrt{2}) \)
c. \( \frac{q^{2}}{4 \pi \epsilon_{0} a}(-4+\sqrt{2}) \)
D. \( \frac{q^{2}}{4 \pi \epsilon_{0} a}(-4-\sqrt{2}) \)
Subject: Maths
If the range of \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2}+\sqrt[3]{\boldsymbol{x}},-\boldsymbol{3} \leq \)
\( \boldsymbol{x}<-1 \) is \( [\mathbf{0}, \sqrt[3]{\boldsymbol{n}}] \) where \( \boldsymbol{n} \in \boldsymbol{N} \) then \( n= \)
Subject: Physics
If the momentum of an electron is
changed by \( P, \) then the de-Broglie wavelength associated with it changes by \( 0.5 \% \). The initial momentum of
electron will be :
\( \mathbf{A} \cdot 400 P \)
в. \( \frac{P}{200} \)
\( c \cdot 100 P \)
D. 200P
Subject: Maths
f \( x_{1}, x_{2}, x_{3} \) and \( y_{1}, y_{2}, y_{3} \) are in GP with
same common ratio, then
\( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \)
A. lie on an ellipse
B. lie on a circle
c. are vertices of triangle
D. lie on a straight line
Subject: Chemistry
0.40 g of an organic compound containing phosphorous gave 0.555 g of \( M g_{2} P_{2} O_{7} \) by usual analysis.
Calculate the percentage of the phosphorous in the organic compound.
A . \( 38.75 \% \) \%
в. \( 31.56 \% \)
c. \( 25.99 \% \)
D. 63.45\%
Subject: Chemistry
In the dissociation of HI, 20\% of HI is dissociated at equilibrium. Calculate
\( \boldsymbol{K}_{\boldsymbol{p}} \) for
\( \mathrm{HI}(\mathrm{g}) \leftrightharpoons \frac{1}{2} H_{2}(g)+\frac{1}{2} I_{2}(g) \)
A . 1.25
B. 0.125
c. 12.5
D. 0.0125
Subject: Chemistry
\( \left[A u(C N)_{2}\right]^{\ominus} \) is a very stable
complex under certain conditions. The concentration of cyande ion which is required to keep 99 mol\% of the gold in
the form of the cyanide complex is: [Given \( \left.K_{f}\left[A u(C N)_{2}\right]^{\ominus}=4 \times 10^{28}\right] \)
A \( .2 \times 10^{-28} M \)
в. \( 3 \times 10^{-14} M \)
c. \( 5 \times 10^{-28} M \)
D. \( 5 \times 10^{-14} M \)
Subject: Maths
\( f \)
\( a, b, c \) are all different and if \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{a}^{2} & \mathbf{1}+\boldsymbol{a}^{3} \\ \boldsymbol{b} & \boldsymbol{b}^{2} & \mathbf{1}+\boldsymbol{b}^{3} \\ \boldsymbol{c} & \boldsymbol{c}^{2} & \boldsymbol{1}+\boldsymbol{c}^{3}\end{array}\right|=\mathbf{0} \) then \( -\boldsymbol{a} \boldsymbol{b} \boldsymbol{c}= \)
Subject: Physics
In an experiment, the refractive index of glass was observed to be
\( \mathbf{1 . 4 5}, \mathbf{1 . 5 6}, \mathbf{1 . 5 4}, \mathbf{1 . 4 4}, \mathbf{1 . 5 4}, \mathbf{1 . 4 4}, \mathbf{1 . 5 4} \)
and \( 1.53 . \) Calculate mean value of refractive index
Subject: Chemistry
In \( X e O_{3} F_{2}, \) the number of bond pair(s),
\( \pi \) -bond(s) and lone pair(s) on Xe atom
respectively are.
\( \mathbf{A} \cdot 5,3,0 \)
B. 5,2,0
c. 4,2,2
D. 4,4,0
Subject: Chemistry
Avogadro's number is?
\( \mathbf{A} \cdot 6.023 \times 10^{23} \)
B . \( 6.066 \times 10^{-19} \)
C \( \cdot 6.032 \times 10^{24} \)
D. \( 6.203 \times 10^{18} \)
Subject: Maths
A cylindrical gas container is closed at
the top and open at the bottom; if the iron plate of the top is \( 5 / 4 \) times as thick as the plate forming the cylindrical sides, find the radio of the radius to the height of the cylinder using minimum material for the same capacity.
A . 5 \( \bar{A} \)
в. \( \frac{4}{5} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{2}{5} \)
Subject: Maths
What is \( \sin ^{-1} \sin \frac{3 \pi}{5} \) equal to \( ? \)
\( \mathbf{A} \cdot \frac{3 \pi}{5} \)
B. \( \frac{2 \pi}{5} \)
\( c \cdot \frac{\pi}{5} \)
D. None of the above
Subject: Physics
If a coil of \( 20 \mathrm{cm} \times 20 \mathrm{cm} \) having 30
turns is making 3 rps in a magnetic field of induction \( 1 T, \) then the peak value of the induced emf is
approximately
\( \mathbf{A} \ldots 113 V \)
B. \( 150 V \)
\( \mathbf{c} \cdot 226 V \)
D. \( 339 V \)
Subject: Physics
A constant torque of \( 31.4 \mathrm{Nm} \) is exerted on a pivoted wheel. If the angular acceleration of the wheel is \( 4 \pi r a d / s e c^{2}, \) then the moment of
inertia will be
A \( \cdot 5.8 \mathrm{kg}-\mathrm{m}^{2} \)
в. \( 4.5 \mathrm{kg}-\mathrm{m}^{2} \)
c. \( 5.6 \mathrm{kg}-\mathrm{m}^{2} \)
D. \( 2.5 \mathrm{kg}-\mathrm{m}^{2} \)
Subject: Chemistry
According to the equation,
\( \boldsymbol{n} \boldsymbol{C} \boldsymbol{H}_{2}=\boldsymbol{C} \boldsymbol{H}_{2} \rightarrow\left(-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}-\right)_{n} \)
When \( 100 g \) of ethylene polymerises to polyethylene, then the weight of polyethylene produced will be:
A \( \cdot \frac{n}{2} \) g
в. \( 100 \mathrm{g} \)
c. \( \frac{100}{n} \mathrm{g} \)
D. \( 100 n \) g
Subject: Maths
Let \( x \in N \) Let \( x \) be a perfect square. Let
\( f(x)= \) the quotient when \( x \) is divided
by 5 and \( g(x) \) the remainder when \( x \) is divided by 5. Then \( \sqrt{\boldsymbol{x}}=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{x}) \)
holds for \( x \) equal to
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{0} \)
B . 16
c. 25
D. none of these
Subject: Physics
An air bubble rises from bottom to top of
a liquid of density \( 1.5 \mathrm{g} / \mathrm{cm}^{3} . \) If its volume is doubled, the depth of liquids is
A. \( 689 \mathrm{cm} \)
B. 398 \( \mathrm{cm} \)
\( c .760 \mathrm{cm} \)
D. 152 \( \mathrm{cm} \)
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( \vec{a} \times \) \( \overrightarrow{\boldsymbol{b}}=\overrightarrow{\boldsymbol{c}}, \overrightarrow{\boldsymbol{b}} \times \overrightarrow{\boldsymbol{c}}=\overrightarrow{\boldsymbol{a}}, \overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}}=\overrightarrow{\boldsymbol{b}} \) then prove
that \( |\overrightarrow{\boldsymbol{a}}|=|\overrightarrow{\boldsymbol{b}}|=|\overrightarrow{\boldsymbol{c}}| \)
Subject: Physics
Which of the following is Shell's law
A. \( n_{1} \) sini \( =n_{2} \) sinr
В \( \cdot n_{1} / n_{2}=\sin r \times \) constant
c. \( n_{2} / n_{1}=\sin r / \sin i \)
D. \( n_{2} \sin i= \) constant
Subject: Physics
The moment of inertia of a thin square
plate \( A B C D \) of uniform thickness about
an axis passing through the centre 0
and perpendicular to the plane of the
plate is :
This question has multiple correct options
A \( \cdot I_{1}+I_{2} \)
B \( \cdot I_{3}+I_{4} \)
\( \mathbf{c} \cdot I_{1}+I_{3} \)
\( \mathbf{D} \cdot I_{1}+I_{2}+I_{3}+I_{4} \)
Subject: Biology
Assertion
Thigh muscles can get tired but not the muscles of ventricle of heart.
Reason
Muscles of thigh are voluntary whereas that of heart are involuntary muscles.
A. If both the assertion and the reason are true and the reason is correct explanation of the assertion.
B. If both the assertion and the reason are true but the reason is not 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: Physics
A mass is attached to the end of a
string of which is tied to a fixed point 0 The mass is released from the initial
horizontal position of the string. Below the point 0 at what minimum distance a peg \( P \) be should fixed so that the mass
tums about \( P \) and can describe a
complete circle in the vertical plane?
A \( \cdot\left(\frac{3}{5}\right) l \)
B・(\frac{2 } { 5 } )
\( c \)
\( D \cdot \frac{2}{3} \)
Subject: Chemistry
Statement I: The entropy of a solid decreases when it is dissolved
Because
Statement II : It becomes less ordered
A. Statement 1 and Statement 2 are correct and
Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and
Statement 2 is not the correct explanation of Statement 1.
C. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.
Subject: Chemistry
Compound \( (D) \) is:
\( (\mathbf{D})\left(\mathbf{C}_{4} \mathbf{H}_{9} \mathbf{N} \mathbf{O}_{2} \mathbf{C l}_{2}\right) \)
\( A \)
B.
\( c \)
D. none of the above
Subject: Physics
A massless spring balance is attached to 2 kg trolley and is used to pull the trolley along a flat surface as shown in
the fig. The reading on the spring balance remains at \( 10 \mathrm{kg} \) during the motion. The acceleration of the trolley
is: (Use \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m s}^{-2} \) )
\( \mathbf{A} \cdot 4.9 \mathrm{ms}^{-2} \)
B. \( 9.8 m s^{-2} \)
\( \mathrm{c} \cdot 49 \mathrm{ms}^{-2} \)
D. \( 98 m s^{-2} \)
Subject: Chemistry
Nuclidic masses of \( _{7}^{14} \mathrm{N} \) and \( _{7}^{15} \mathrm{N} \) are mixed to give average atomic mass of
14.1. The ratio of \( 14 \mathrm{N} \) and \( 15 \mathrm{N} \) mixed is : 7 7