AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In a region an electric field \( \mathrm{E}=15 \mathrm{N} / \mathrm{C} \)
making an angle of \( 30^{\circ} \) with the horizontal plane is present. A ball having charge \( 2 \mathrm{C}, \) mass \( 3 \mathrm{kg} \) and coefficient of restitution with ground
\( 1 / 2 \) is projected at an angle of \( 30^{\circ} \) with the horizontal in the direction of electric field with speed \( 20 \mathrm{m} / \mathrm{s} \), the horizontal distance travelled by ball from first drop to the second drop is equal to \( 10 x \sqrt{3} m \) The value of \( x \) is:
Subject: Physics
In a Wheatstone's bridge, there resistances \( \mathbf{P}, \boldsymbol{O} \) and \( \mathbf{R} \) connected in
the three arms and the fourth arm is
formed by two resistances \( \mathbf{S}_{1} \) and \( \mathbf{S}_{\mathbf{2}} \)
connected in parallel. The condition for
bridge to be balanced will be
A \( \cdot \frac{P}{O}=\frac{R}{S_{1}+S_{2}} \)
B. \( \frac{P}{O}=\frac{2 R}{S_{1}+S_{2}} \)
c. \( \frac{P}{O}=\frac{R\left(S_{1}+S_{2}\right)}{S_{1} S_{2}} \)
D. \( \frac{P}{O}=\frac{R\left(S_{1}+S_{2}\right)}{2 S_{1} S_{2}} \)
Subject: Physics
A sphere of mass \( m \) moving with velocity \( v \) hits inelastically with another stationary sphere of same mass. The ratio of their final velocities will be (in
terms of \( e \) )
A \( \cdot \frac{v_{1}}{v_{2}}=\frac{1+e}{1-e} \)
B. \( \frac{v_{1}}{v_{2}}=\frac{1-e}{1+e} \)
c. \( \frac{v_{1}}{v_{2}}=\frac{1+e}{2} \)
D. \( \frac{v_{1}}{v_{2}}=\frac{1-e}{2} \)
Subject: Biology
Study the following statements about
ozone:
(a) It is essential for the breathing of living organisms.
(b) It is used to disinfect water.
(c) It absorbs ultraviolet rays.
(d) Its proportion of air is about \( 3 \% \) Which of these statements are correct?
\( A \cdot(a),(b) \) and \( (c) \)
B. (b) and (c)
c. (a) and (d)
D. All four
Subject: Maths
The displacement of a body varies with
the time as \( S=t^{3}+3 t^{2}+2 t-1 . \) If the
velocity at \( t=4 \sec \) is \( 2+12 K m / s \)
then find \( k \)
\( A \cdot 6 \)
B. 3
\( c \cdot 2 \)
D.
Subject: Chemistry
The ionization energy of hydrogen atom
is \( 13.6 \mathrm{eV} \). The energy required to excite the electron in a hydrogen atom from the ground state to the first excited state is:
A \( \cdot 1.69 \times 10^{-18} \mathrm{J} \)
В. \( 1.69 \times 10^{-23} \) 」
c. \( 1.69 \times 10^{23} \) 」
D. \( 1.69 \times 10^{25} \mathrm{J} \)
Subject: Maths
In the given Fig
f \( \boldsymbol{A B} \| \boldsymbol{C D}, \boldsymbol{E F} \perp \boldsymbol{C D} \boldsymbol{a n d} \angle \boldsymbol{G} \boldsymbol{E D}= \)
\( 126^{\circ}, \) Find \( \angle A G E, \angle G E F, \angle F G E \)
Subject: Maths
Which of the following is/are true regarding the following linear equation:
\( \boldsymbol{x}-\mathbf{3}=\frac{\mathbf{2}}{\mathbf{5}}(\boldsymbol{y}+\mathbf{1}) \)
A. It passes through (0,-2.5) and \( m=-8.5 \)
B. It passes through (0,-2.5) and \( m=8.5 \)
c. It passes through (0,8.5) and \( m=-2.5 \)
D. It passes through (0,-8.5) and \( m=2.5 \)
Subject: Biology
Identify the correct statement(s) in
relation to \( C_{4} \) photosynthesis.
A. Kranz anatomy is an essential feature for \( C_{4} \) plants
B. \( C_{4} \) plants have higher water use efficiency than \( C_{3} \) plants
C. Photorespiration can be minimized when \( C_{4} \) pathway is in operation
D. All of the above
Subject: Chemistry
Correct boiling point is:
\( \begin{array}{cc}\boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{I} & \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{B r}\end{array} \)
\( \begin{array}{cc}\boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{C l} & \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{F}\end{array} \)
A. \( I V>I I I>I I>I \)
В. \( I I>I I I>I V>I \)
c. \( I>I I>I I I>I V \)
D. \( I V>I I I>I>I I \)
Subject: Physics
A hollow metal sphere of radius \( R \) is
charged with a charge \( Q . \) The electric potential and intensity inside the sphere are respectively:
A \( \cdot \frac{Q}{4 \pi \epsilon_{0} R^{2}} \) and \( \frac{Q}{4 \pi \epsilon_{0} R} \)
B. \( \frac{Q}{4 \pi \epsilon_{0} R} \) and zero
c. zero and sero
D. \( \frac{4 \pi \epsilon_{0} Q}{R} \) and \( \frac{Q}{4 \pi \epsilon_{0} R^{2}} \)
Subject: Physics
At the first minimum adjacent to the central maximum of a single - slit diffraction pattern, the phase difference
between the Huygen's wavelet form the edge of the slit and the wavelet from the midpoint of the slit is:
A \( \cdot \frac{\pi}{8} \) radian
B . \( \frac{\pi}{4} \) radian
c. \( \frac{\pi}{2} \) radian
D. \( \pi \) radian
Subject: Physics
A triangle is formal using three wire \( A B, B C \) and \( C A \) and is placed in a vertical plane. Coefficient of friction for all three
wires is same. If \( \boldsymbol{w}_{1} \) and \( \boldsymbol{w}_{2} \) is the work
done by the friction in moving an object from \( A \) to \( B \) through \( C^{\prime} \) and \( C \)
respectively, then
A \( \cdot w_{1}=w_{2} \)
в. \( w_{1}<w_{2} \)
c. \( w_{1}>w_{2} \)
D. the relation depends on the length AC and BC
Subject: Chemistry
For the reaction:
\( \boldsymbol{I}^{-}+\boldsymbol{C l O}_{3}^{-}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{C l}^{-}+ \)
\( \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}^{-}+\boldsymbol{I}_{2} \)
A. stoichiometric coefficient of \( H S O_{4}^{-} \) is 6
B. iodide is oxidized
c. sulphur is reduced
D. \( H_{2} O \) is one of the products
Subject: Biology
Match and find the correct combination
\( \mathbf{A} \)
\( A-4, B-3, C-2, D-1 \)
B. \( A-3, B-4, C-1, D-2 \)
C \( \cdot A-4, B-2, C-1, D-3 \)
D. \( A-1, B-2, C-4, D-3 \)
Subject: Maths
\( \boldsymbol{i}^{3}=\frac{\mathbf{1}}{\boldsymbol{i}}=\frac{\mathbf{1}}{\boldsymbol{i}} \times \frac{\boldsymbol{i}}{\boldsymbol{i}}=\frac{\boldsymbol{u}}{\boldsymbol{1}}=-\boldsymbol{i} \)
Subject: Physics
Which of the following is not simple
harmonic function?
A \( \cdot y=a \sin 2 \omega t+b \cos ^{2} \omega t \)
B. \( y=a \sin \omega t+b \cos 2 \omega t \)
c. \( y=1-2 \sin ^{2} \omega t \)
D \( \cdot y=(\sqrt{a^{2}+b^{2}}) \sin \omega t \cos \omega t \)
Subject: Physics
An arc of a circle of radius \( R \) subtends
an angle \( \frac{\pi}{2} \) at the centre. It carries a
current \( i . \) The magnetic field at the centre will :
A \( \cdot \frac{\mu_{0} i}{2 R} \)
в. \( \frac{\mu_{0} i}{8 R} \)
c. \( \frac{\mu_{0} i}{4 R} \)
D. \( \frac{\mu_{0} i}{5 R} \)
Subject: Chemistry
Magnesium hydroxide is the white milky substance in milk of magnesia.
What mass of \( M g(O H)_{2} \) is formed when \( 15 m l \) of \( 0.2 M-N a O H \) is
combined with \( 12 \mathrm{ml} \) of \( 0.15 M- \)
\( M g C l_{2} ? \)
A. \( 0.087 g \)
в. \( 0.079 g \)
c. \( 0.1044 g \)
D. \( 0.522 g \)
Subject: Biology
Assertion
Prickles of last have a single role of
protection of plant
Reason
They are superficial in origin.
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: Physics
Choose the correct answer from the
alternatives given. An electromagnetic wave of frequency \( \nu=3 M H z \) passes from vacuum into
a dielectric medium with permittivity
\( \varepsilon=4 . \) Then
A. wavelength and frequency both become half.
B. wavelength is doubled and frequency remains unchanged
c. wavelength and frequency both remain unchanged.
D. wavelength is halved and frequency remains unchanged
Subject: Physics
Four identical plates \( 1,2,3, \) and 4 are
placed parallel to each other at equal
distance as shown in the figure. Plates
1 and 4 are joined together and the
space between 2 and 3 is filled with a
dielectric of dielectric constant \( k=2 \)
The capacitance of the system between
1 and \( 3 \& 2 \) and 4 are \( C_{1} \) and \( C_{2} \)
respectively. The ratio \( C_{1} / C_{2} \) is :
\( \mathbf{A} \cdot 5 \)
\( \overline{3} \)
B.
\( c \cdot \frac{3}{5} \)
D. 5 7
Subject: Physics
Two satellites of the same mass are
launched in the same orbit around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is
A. \( -\frac{2 G M m}{r} \)
в. \( -\frac{G M m}{r} \)
c. \( \frac{G M m}{2 r} \)
D. \( \frac{G M m}{4 r} \)
Subject: Physics
Two solid spheres \( A \) and \( B \) each of
radius \( ^{\prime} R^{\prime} \) are made of materials of
densities \( \rho_{A} \) and \( \rho_{B} \) respectively. Their moments of inertia about a diameter
\( \operatorname{are} I_{A} \) and \( I_{B} \) respectively. The value of \( \frac{\boldsymbol{I}_{A}}{\boldsymbol{I}_{B}} \) is:
A. \( \sqrt{\frac{\rho_{A}}{\rho_{B}}} \)
в. \( \sqrt{\frac{\rho_{B}}{\rho_{A}}} \)
c. \( \frac{\rho_{A}}{\rho_{B}} \)
D. \( \frac{\rho_{B}}{\rho_{A}} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \sqrt{\mathbf{4} \boldsymbol{a} \boldsymbol{x}-\boldsymbol{x}^{2}},(\boldsymbol{a}>\mathbf{0}) . . \) Then
\( f(x) \) is decreasing in:
This question has multiple correct options
A. \( (5 a, \infty) \)
)
в. \( (-\infty, 0) U(4 a, \infty) \)
c. Always increasing
D. None of the above
Subject: Maths
\( \lim _{x \rightarrow \sqrt{10}} \frac{\sqrt{7+2 x}-(\sqrt{5}+\sqrt{2})}{x^{2}-10} \) is equal to
A \( \cdot \frac{1}{\sqrt{40}(\sqrt{5}+\sqrt{2})} \)
B. \( \frac{-1}{\sqrt{10}[\sqrt{7+2 \sqrt{10}}+\sqrt{5}+2]} \)
c. 1
D. \( \frac{1}{\sqrt{10}(\sqrt{5}+\sqrt{2})} \)
Subject: Biology
Consider the following statements:
(a) High blood pressure is an infectious disease.
(b) Penicillin is effective against
bacteria because it inhibits their wall
formation.
(c) AlDS spreads, through sex, blood to blood contact and from mother to child.
Which of the above statements are
correct?
\( A \cdot(a) \) and \( (b) \)
B. (b) and (c)
\( c \cdot(a),(b) \) and \( (c) \)
D. None of the above
Subject: Physics
What is the dimensional formula of
universal gravitational'G'? The gravitational force of attraction between two objects of masses
\( m_{1} \) and \( m_{2} \) seperated by a distance \( \mathrm{d} \) is given by \( \boldsymbol{F}=\frac{\boldsymbol{G} \boldsymbol{m}_{1} \boldsymbol{m}_{2}}{\boldsymbol{d}_{2}} . \) Where 'G' is
the universal gravitational constant
B . \( \left[M^{-1} L^{2} T^{2}\right. \)
c. \( \left[M^{-1} L^{3} T^{-2}\right] \)
D. \( \left[M^{2} L^{2} T^{-2}\right. \)
Subject: Physics
A thin ring has mass \( 0.25 \mathrm{kg} \) and radius
\( 0.5 m . \) Its M.I. about an axis passing
through its centre and perpendicular to its plane is \( \ldots \)
\( \mathbf{A} \cdot 0.0265 g-c m^{2} \)
В. \( 0.0625 \mathrm{kg}-\mathrm{m}^{2} \)
c. \( 0.625 k g-m^{2} \)
D. \( 6.25 \mathrm{kg}-\mathrm{m}^{2} \)
Subject: Physics
Find the resultant of three vectors
\( \boldsymbol{O A}, \overrightarrow{\boldsymbol{O B}} \) and \( \overrightarrow{\boldsymbol{O C}} \) shown in figure.
Radius of circle is 'R'.
A \( \cdot R(1+\sqrt{2}) \)
B . \( R(1+\sqrt{3}) \)
c. \( R(2+\sqrt{3}) \)
D \cdot \( R(1+\sqrt{5}) \)
Subject: Physics
A spherical metal shell \( A \) of radius \( R_{A} \)
and a solid metal sphere \( B \) of radius
\( R_{8}\left(<R_{A}\right) \) are kept far apart and each
is given charge \( +Q . \) Now they are connected by a thin metal wire. Then This question has multiple correct options
\( \mathbf{A} \cdot E_{A}^{i n s i d e}=0 \)
в. \( \quad Q_{A}>Q_{B} \)
c. \( \frac{\sigma_{A}}{\sigma_{B}}=\frac{R_{B}}{R_{A}} \)
D. \( E_{A}^{\text {on surface}}<E_{B^{\text {B }}}^{\text {snj }} \)
Subject: Maths
f \( \sin ^{-1}\left(\frac{2 a}{1+a^{2}}\right)+\sin ^{-1}\left(\frac{2 b}{1+a^{2}}\right)= \)
\( 2 \tan ^{-1} x, \) then \( x \) is equal to
A \( \frac{a-b}{1+a b} \)
в. \( \frac{b}{1+a b} \)
c. \( \frac{b}{1-a b} \)
D. \( \frac{a+b}{1-a b} \)
Subject: Physics
Two point charge -q and +q/2 are situated at the origin and the point \( (a, 0,0) \) respectively. The point along the X-axis where the electric field vanishes
is
A \( \cdot x=\frac{a}{\sqrt{2}} \)
В. \( x=\sqrt{2} a \)
c. \( x=\frac{\sqrt{2} a}{\sqrt{2}-1} \)
D. \( x=\frac{\sqrt{2} a}{\sqrt{2}+1} \)
Subject: Maths
If \( y=\sqrt{\frac{1-x}{1+x}} \) then \( \frac{d y}{d x} \) equals-
A \( \cdot \frac{y}{1-x^{2}} \)
в. \( \frac{y}{x^{2}-1} \)
c. \( \frac{y}{1+x^{2}} \)
D. \( \frac{y}{y^{2}-1} \)
Subject: Physics
Three identical long solenoids \( P, Q, R \) are connected to each other as shown in
figure. If the magnetic field at the center of \( \boldsymbol{P} \) is \( 2.0 T, \) what would be the
field (in \( T \) ) at the center of \( Q \) ? Assume
that the field due to any solenoid is confined within the volume of that
solenoid only.
Subject: Physics
Consider the following statements \( (X \) and \( Y \) stand for two different elements)
(I) \( _{32} X^{65} \) and \( _{33} Y^{65} \) are isotopes.
(II) \( _{42} X^{86} \) and \( _{42} Y^{85} \) are isotopes.
(III) \( 85^{174} \) and \( _{88} Y^{177} \) have the same number of neutrons.
\( (\mid V)_{92} X^{235} \) and \( _{94} Y^{235} \) are isobars The correct statements are
A. Il and IV only
B. I, II and IV only
c. ॥, III and IV only
D. I, II, III and IV
Subject: Physics
The roadway bridge over a canal is in the form of an arc of a circle of radius
\( 20 m . \) What is the maximum speed with
which a car can cross the bridge without leaving the ground at the highest point.
A \( \cdot 10 \mathrm{ms}^{-1} \)
B. \( 12 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 14 \mathrm{ms}^{-1} \)
D. \( 16 \mathrm{ms}^{-1} \)
Subject: Maths
If \( \boldsymbol{f}(\mathbf{1})=\mathbf{1}, \boldsymbol{f}(\boldsymbol{n}+\mathbf{1})=\mathbf{2} \boldsymbol{f}(\boldsymbol{n})+\mathbf{1}, \boldsymbol{n} \geq \)
1, then \( f(n) \) is:
\( \mathbf{A} \cdot 2^{n+1} \)
в. \( 2^{\text {г }} \)
c. \( 2^{n}-1 \)
D. \( 2^{n-1}-1 \)
Subject: Chemistry
Consider the cell:
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}\left(\boldsymbol{p}_{1} \boldsymbol{a t m}\right)\right| \boldsymbol{H}^{\oplus}\left(\boldsymbol{x}_{1} \boldsymbol{M}\right) \| \boldsymbol{H}^{\oplus}\left(\boldsymbol{x}_{2} \boldsymbol{N}\right. \)
The cell reaction be spontaneous if This question has multiple correct options
\( \mathbf{A} \cdot p_{1}=p_{2} \) and \( x_{1}>x_{2} \)
B . \( p_{1}=p_{2} \) and \( x_{1}<x_{2} \)
C \( . x_{1}=x_{2} \) and \( p_{1}>p_{2} \)
D. \( x_{1}=x_{2} \) and \( p_{1}<p_{2} \)
Subject: Chemistry
Arrange the following in increasing
order of solubility in \( \boldsymbol{H}_{2} \boldsymbol{O} \)
\[
M g F_{2}, C a F_{2}, A g F
\]
A. \( C a F_{2}<M g F_{2}<A g F \)
в. \( M g F_{2}<C a F_{2}<A g F \)
c. \( C a F_{2}<A g F_{2}<M g F \)
D. None of these
Subject: Maths
The area bounded by \( y=\sec ^{-1} x, y= \)
\( \operatorname{cosec}^{-1} x \) and the line \( x-1=0 \) is:
\( \mathbf{A} \cdot \ln (3+2 \sqrt{2})-\frac{\pi}{2} \)
В \( \cdot \frac{\pi}{2}+\ln (3+2 \sqrt{2}) \)
\( c \cdot \pi-\ln 3 \)
D . \( \pi+\ln 3 \)
Subject: Maths
Calculate the mean of the following frequency distribution.
\( \begin{array}{llll}\text { Class } & \mathbf{9 0 -} & \mathbf{1 0 0 -} & \mathbf{1 1 0 -} \\ \mathbf{1 0 0} & \mathbf{1 1 0} & \mathbf{1 2 0}\end{array} \)
Frequency 8
78
Subject: Chemistry
The observed osmotic pressure for a
\( 0.10 M \) solution of \( F e\left(N H_{4}\right)_{2}\left(S O_{4}\right)_{2} \) at
\( 25^{\circ} C \) is 10.8 atm. The expected and experimental (observed) values of Van't Hoff factor (i) will be respectively:
\( \left(\boldsymbol{R}=\mathbf{0 . 0 8 2} \quad \boldsymbol{L} \quad \boldsymbol{a t m} \quad \boldsymbol{k}^{-} \boldsymbol{m o l}^{-1}\right) \)
A. 5 and 4.42
B. 4 and 4.00
c. 5 and 3.42
D. 3 and 5.42
Subject: Maths
Prove that \( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\mathbf{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}^{2}+\mathbf{1} & \boldsymbol{b} \boldsymbol{c} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c b} & \boldsymbol{c}^{2}+1\end{array}\right|= \)
\( \mathbf{1}+\boldsymbol{a}^{2}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2} \)
Subject: Maths
A four-digit number is formed by using the digits 1,2,4,8 and 9 without repitition. If one number is selected from those numbers, then what is the
probability that it will be an odd number
?
A \( \frac{1}{5} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{3}{5} \)
D. \( \overline{5} \)
Subject: Chemistry
Reactivity order of \( S_{N} 1 \) reaction for the
following compounds is:
\( \mathbf{c} \)
А. \( a>b>c>d \)
в. \( a>d>c>b \)
\( c \cdot c>d>b>a \)
\( . a>b>d>c \)
\( c \)
Subject: Chemistry
Assertion: In the calomel half-cell, the
reduction reaction to be considered is
\( \mathrm{Hg}_{2} \mathrm{Cl}_{2}(\mathrm{s})+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{Hg}(\mathrm{I})+2 \mathrm{Cl}^{-}(\mathrm{aq}) \)
Reason: The Saturated calomel
electrode (SCE) is a reference electrode
based on the reaction between
elemental mercury and mercury(l) chloride
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Physics
Two masses \( M_{1} \) and \( M_{2} \) are attached
to the ends of a string which passes
over a attached to the of a double
inclined plane of angles of inclination \( \alpha \)
and \( \beta . \) If \( \mathrm{M}_{2}>\mathrm{M}_{1} \) the acceleration a of
the system can be given by (neglect friction)
A \( \frac{M_{2} g(\sin \beta)}{M_{1}+M_{2}} \)
B. \( \frac{M_{1} \sin \alpha}{M_{q}+M_{2}} \)
\( c \)
D. zero
Subject: Maths
Find the value of \( \sin ^{-1} x+\sin ^{-1} \frac{1}{x}+ \)
\( \cos ^{-1} x+\cos ^{-1} \frac{1}{x} \)
A. \( -\pi \)
в. \( +\pi \)
\( c .-2 \pi \)
D. \( +2 \pi \)
Subject: Physics
Two particles each of the same mass move due north and due east
respectively with the same velocity \( ^{\prime} V^{\prime} \) The magnitude and direction of the velocity of the center of mass is:
A \( \cdot \frac{V}{\sqrt{2}} N E \)
в. \( \sqrt{2} V N E \)
c. \( 2 V S W \)
D. \( \frac{V}{2} S W \)
Subject: Chemistry
The number of sulphur atoms in one
mole molecule of sulphur \( \left(S_{8}\right) \) is:
A \( .5 \times 6.023 \times 10^{23} \)
B. \( 4 \times 6.023 \times 10^{23} \)
c. \( 8 \times 6.023 \times 10^{23} \)
D. \( 2 \times 6.022 \times 10^{22} \)
Subject: Physics
Two forces, each of magnitude \( F, \) act at
points \( V \) and \( W \) on an object.

The two forces form a couple. The shape
of the object is a right-angled triangle with sides of
lengths \( x \) and \( y, \) as shown.
Which expression gives the torque
exerted by the couple?
\( \mathbf{A} \cdot F x \)
B. \( F y \)
\( \mathbf{c} \cdot 2 F x \)
D. \( 2 F y \)
Subject: Maths
The solution of the differential equation \( \sec ^{2} x \cdot \tan y d x+\sec ^{2} y \cdot \tan x d y=0 \)
is
A. \( \tan x \cdot \cot y=C \)
B. \( \cot x \cdot \tan y=C \)
\( \mathbf{c} \cdot \tan x \cdot \tan y=C \)
\( \mathbf{D} \cdot \sin x \cdot \cos y=C \)
Subject: Maths
f \( y(n)=e^{x} e^{x^{2}} \ldots e^{x^{n}}, 0<x<1 \) then
\( \lim _{n \rightarrow \infty} \frac{\boldsymbol{d} \boldsymbol{y}(\boldsymbol{n})}{\boldsymbol{d} \boldsymbol{x}} \) at \( \frac{1}{2} \) is
\( A \)
B. \( 4 e \)
\( c \cdot 2 e \)
D. \( 3 e \)
Subject: Physics
Photoelectric effect supports the
quantum nature of light because
This question has multiple correct options
A. There is minimum frequency of light below which no photoelectrons are emitted
B. The maximum KE of photoelectrons depends only on the frequency of light and not on its intensity
C. Even when the metal surface is faintly illuminated by light of wavelength less than the threshold wavelength, the photoelectrons leave the surface immediately
D. Electric charge of photoelectrons is quantized
Subject: Physics
Use the mirror equation to deduce that:
(a) an object placed between \( f \) and \( 2 f \) of a concave mirror produces a real
image beyond \( 2 f \)
(b) a convex mirror always produces a virtual image independent of the location of the object.
(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus
and the pole.
(d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image. [Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.
Subject: Maths
The number of values \( k \) for which \( \left[x^{2}-\right. \)
\( \left.(k-2) x+k^{2}\right]\left[x^{2}+k x+(2 k-1)\right] \) is a
perfect square is
\( A \cdot 2 \)
B.
\( c \cdot 0 \)
D. None of these
Subject: Chemistry
For decolourisation of 1 mole of
\( K M n O_{4}, \) the moles of \( H_{2} O_{2} \) required
is:
A \( \cdot 1 / 2 \)
B. 3/2
\( c \cdot 5 / 2 \)
D. \( 7 / 2 \)
Subject: Physics
A block of mass \( 10 ~ k g \) is held at rest
against a rough vertical wall \( [\boldsymbol{\mu}=\mathbf{0 . 5}] \)
under the action a force \( F \) as shown in
figure. The minimum value of \( \boldsymbol{F} \)
required for it is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A .162 .6
B. \( 89.7 N \)
c. \( 42.7 N \)
D. 95.2
Subject: Maths
\begin{tabular}{c|ccc}
\( \mathbf{1} \) & \( \mathbf{s i n Q} \) & \( \mathbf{1} \) \\
\( -\mathbf{s i n Q} \) & \( \mathbf{1} \) & \( \mathbf{s i n Q} \) \\
\( \mathbf{- 1} \) & \( -\mathbf{s i n Q} \) & \( \mathbf{1} \)
\end{tabular}
Subject: Chemistry
Pick up the correct statement:
A. Boiling points of alkyl halides are greater than those of the corresponding alkanes.
B. In water, the solubility decreases as \( C H_{3} O H> \) \( C_{2} H_{5} O H>C_{6} H_{5} O H \)
C. Aniline is a weaker base than ammonia.
D. All of the above.
Subject: Chemistry
Two non-reactive gases A and B are present in a container with partial pressures 200 and \( 180 \mathrm{mm} \) of Hg. When
a third non - reactive gas \( C \) is added then total pressure becomes 1 atm then mole fraction of \( \mathrm{C} \) will be:
A . 0.225
B. 0.75
\( c \cdot 0.5 \)
D. none of these
Subject: Physics
A plane sound wave passes from medium 1 into medium \( 2 . \) The speed of
sound in medium 1 is \( 200 \mathrm{m} / \mathrm{s} \) and in
medium 2 is \( 100 \mathrm{m} / \mathrm{s} \). The ratio of
amplitude of the transmitted wave to that of incident wave is
A. \( \frac{3}{4} \)
в. \( \frac{4}{5} \)
c. \( \frac{5}{6} \)
D. \( \frac{2}{3} \)
Subject: Chemistry
The stable oxidation state of \( \boldsymbol{C} \boldsymbol{e}(\boldsymbol{Z}= \)
\( \mathbf{5 8} \) ) is:
\( A \cdot+4 \)
\( B \cdot+3 \)
\( c \cdot+2 \)
\( D \cdot+5 \)
Subject: Chemistry
For 'invert sugar', the correct statement(s) is(are).
(Given: specific rotations of \( (+) \)
sucrose, \( (+) \) -maltose, \( L-(-) \) -glucose
and \( L-(+) \) -fructose in aqueous solution
\( \operatorname{are}+66^{\circ},+140^{\circ},-52^{\circ} \) and \( +92^{\circ} \)
respectively)
This question has multiple correct options
A. 'Invert sugar' is prepared by acid catalyzed hydrolysis of maltose
B. 'Invert sugar' is an equimolar mixture of D-(+)-glucose and \( D-(-) \) -fructose
C. specific rotation of 'invert sugar' is \( -20^{\circ} \)
D. On reaction with \( B r_{2} \) water, 'invert sugar'forms
saccharic acid as one of the products
Subject: Chemistry
EMF of the cell
\( Z n\left|Z n S O_{4}(a=0.2)\right|\left|Z n S O_{4}\left(a_{2}\right)\right| Z n \)
is \( -0.0088 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \). Calculate the
value of \( a_{2} \)
A \( \cdot a_{2}=0.1006 \mathrm{M} \)
В . \( a_{2}=0.2012 M \)
\( \mathbf{c} \cdot a_{2}=0.3018 M \)
D. None of these
Subject: Chemistry
Identify \( A \)
A. \( H C H O \)
\( \mathbf{B} \cdot C H_{3} C H O \)
\( \mathbf{C} \cdot C_{6} H_{5} C H O \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{COCH}_{3} \)
Subject: Chemistry
Arrange the following compounds in the decreasing order of acidic character.
I. Butane II. But-1-ene III. But-1-yne IV.Butan-1-ol
\( A \cdot(|I\rangle(\mid I)>(\| I)>(I V) \)
B. \( (\mid V)>(||)>(|||\rangle>(\mid) \)
\( c \cdot(\mid V)>(\| \mid)>(||>||) \)
\( D \cdot(|D>(\| \mid)>(\mid D)(\mid V) \)