AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which of the following is/are peroxide(s)?
This question has multiple correct options
\( \mathbf{A} \cdot P b O_{2} \)
в. \( H_{2} O_{2} \)
\( \mathrm{c} \cdot \operatorname{Sr} \mathrm{O}_{2} \)
D. \( B a O_{2} \)
Subject: Physics
A thief in a stolen car passes through a police check post at his top speed of
\( 90 k m h^{-1} . \) A motorcycle cop, reacting after \( 2 s, \) accelerates from rest at \( 5 m s^{-2} . \) His top speed being \( 108 k m h^{-1} . \) Find the maximum
separation between policemen and
thief
\( \mathbf{A} \cdot-112.5 m \)
B. \( 115 \mathrm{m} \)
\( c .116 .5 m \)
D. None of these
Subject: Physics
Due to an impulse, the change in the momentum of a body is \( 1.8 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} . \) If the duration of the impulse is \( 0.2 \mathrm{s} \) then what is the force produced in it?
\( A \cdot 9 N \)
B. 8 N
\( c \cdot 7 N \)
\( D \cdot 6 N \)
Subject: Chemistry
A salt which in solution gives a bluish
white precipitate with \( N a O H \) solution
and a white precipitate with \( B a C l_{2} \) solution is:
A \( . C u S O_{4} \)
в. \( F e S O_{4} \)
c. \( F e_{2}\left(S O_{4}\right)_{3} \)
D. \( C u C l_{2} \)
Subject: Chemistry
Chloroethane, \( C_{2} H_{5} C l, \) does not react with methanol under mild conditions.
What reagent could be added to the reaction mixture to increase the rate of
substitution?
A. \( H C l \) (conc.)
в. \( N a O H \)
c. \( N H_{4} O H \)
D. \( A g N O_{3} \)
Subject: Chemistry
(a) Roasting and calcination are the two processes to reduce the metal oxides to
the respective metals.
(b) Magnesium is extracted from its ore by electrolytic reduction process.
(c) Cryolite is used in metallurgy of aluminium in order to increase the
fusibility and conductivity
(d) I Hall's process bauxite is leached
with the help of \( N a_{2} C O_{3} \)
Which of the following options regarding the above statements is
correct?
\( A \cdot a, b \) and \( c \)
B. b, c and d
\( c \cdot c \) and \( d \)
Subject: Physics
A uniform rod of length \( ^{\prime} L^{\prime} \) and density
\( \rho^{\prime} \) is being pulled along a smooth floor
with horizontal acceleration \( \alpha \) as shown
in the figure. The magnitude of the stress at the transverse cross-section
through the mid-point of the rod is
A \( \frac{\rho l \alpha}{4} \)
в. \( 4 \rho l \) d
\( c \cdot 2 \rho l \)
D. \( \frac{\rho l \alpha}{2} \)
Subject: Maths
Find the values of \( a \) and \( b \) so that the
function, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{1-\sin ^{2} x}{3 \cos ^{2} x}, \quad x<\pi / 2 \\ a, \quad x=\pi / 2 \\ \frac{b(1-\sin x)}{(\pi-2 x)^{2}}, \quad x>\pi / 2\end{array}\right. \)
continuous
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \equiv \boldsymbol{C} \) MgBr can be prepared by
the reaction of
A. \( C H_{3}-C \equiv C-B r \) with \( M g B r_{2} \)
B . \( C H_{3}-C \equiv C H \) with \( M g B_{2} \)
c. \( C H_{2}-C \equiv C H \) with KBr and Mg metal
D. \( C H_{3}-C \equiv C H \) with \( C H_{3} M g B r \)
Subject: Physics
A small ball of mass \( m \) and charge \( +q \)
tied with a string of length \( l \) is rotating in a vertical circle under gravity and a
uniform horizontal electric field \( \boldsymbol{E} \) as
shown. The tension in the string will be
minimum for:
A \( \cdot \quad \theta=\tan ^{-1}\left(\frac{q E}{m g}\right) \)
B . \( \theta=\pi \)
\( ^{\mathbf{c}} \cdot_{\theta}=\pi-\tan ^{-1}\left(\frac{q E}{m g}\right) \)
D.
Subject: Maths
Let \( A=\{5,6,7,8\} ; B=\{-11,4,7,-10,-7,-9, \)
-13\} and \( \boldsymbol{f}= \)
\( \{(x, y): y=3-2 x, x \epsilon A, y \epsilon B\} \)
(i) Write down the elements of \( f . \) (ii)
What is the co-domain?
(iii) What is the range?
(iv) Identify the type of function.
Subject: Physics
A smaller block of mass 'm' is placed on another block of mass M. When a
horizontal force \( F \) is applied on the block of mass \( \mathrm{M} \) as shown in the figure, the smaller block does not slide. If the
magnitude of friction between the
bigger block and ground is 'f',
determine the magnitude and direction
of friction between the two blocks.
A \( \cdot \frac{F}{M+m} \)
в. \( \frac{F-f}{M+m} \)
c. \( \frac{F+f}{M+m} \)
D. \( \frac{F-f}{m} \)
Subject: Maths
Let \( \boldsymbol{R}=\left\{\left(\boldsymbol{a}, \frac{\mathbf{1}}{\boldsymbol{a}}\right): \boldsymbol{a} \in \boldsymbol{N} \text { and } \mathbf{1}<\boldsymbol{a}<\right. \)
5 \( \} . \) Find the doman and range of \( R \)
Subject: Chemistry
Assertion
Only one out of every 20000 alpha particles rebound in Rutherford's experiment.
Reason
Most of the space in the atom is empty.
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: Physics
The value of acceleration due to gravity at a height \( R \) from surface of the earth is then(R=radius of the earth and
geacceleration due to gravity on earth surface
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \sqrt{g} \)
c. \( \frac{g}{4} \)
D. \( \frac{g}{2} \)
Subject: Maths
Construct a quadrilateral \( P Q R S \) with
\( Q R=8 \mathrm{cm}, R S=4 \mathrm{cm}, S P=9 \mathrm{cm} \)
\( \boldsymbol{P Q}=\mathbf{5 . 5} \mathrm{cm} \) and \( \boldsymbol{Q} \boldsymbol{S}=\boldsymbol{6} \mathrm{cm} \)
Subject: Physics
A magnetic field of flux density \( 1.0 \mathrm{Wb} \)
\( m^{-2} \) acts normal to a 80 tum coil of 0.01
\( m^{2} \) area. The e.m.f. induced in it, if this coil is removed from the field in 0.1
second is :
\( A \cdot 8 v \)
B. \( 4 v \)
c. \( 10 v \)
D. \( 6 v \)
Subject: Physics
If the acceleration due to gravity, \( g \), is \( 10 m / s^{2} \) at the surface of the earth
(radius \( 6400 k m \) ), then at a height of
1600 km the value of \( g \) will be? \( \operatorname{lin} m / s^{2} \)
A . 4
B. 5
\( c .7 .5 \)
D. 2.5
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cl}\frac{1-\sqrt{2} \sin x}{\pi-4 x}, & \text { if } x \neq \frac{\pi}{4} \\ a, & \text { if } x=\frac{\pi}{4}\end{array}\right. \)
is continuous at \( \frac{n}{4} \) then \( a= \)
\( A \)
B. 2
c. 1
\( 0 . \frac{1}{1} \)
Subject: Physics
In the circuit diagram of zener diode as
shown in figure, when the value of \( V_{0} \) is
8 volt, the current through zener diode s
\( i_{1} \) and when \( V_{0} \) is 16 volt, the
corresponding current is \( i_{2} . \) Find the
value of \( \left(i_{2}-i_{1}\right) . \) (Zener breakdown
voltage \( \left.=V_{2}=6 V\right) \)
A. zero
B. \( 5.0 \mathrm{mA} \)
C \( .1 .5 \mathrm{mA} \)
\( \mathbf{D} \cdot 8 m A \)
Subject: Physics
A unit vector along the incident ray of light is \( \hat{i} \). The unit vector for the
corresponding refracted ray of light is
\( \hat{\boldsymbol{r}} \cdot \hat{\boldsymbol{n}}, \) a unit vector normal to the
boundary of the medium and directed towards the incident medium. If \( \mu \) is the
refractive index of the medium, then
Snell's law (second law) of refraction is :
\( \mathbf{A} \cdot \hat{i} \times \hat{n}=\mu(\hat{n}+\hat{r}) \)
в. \( \hat{i} \cdot \hat{n}=\mu(\hat{r} \cdot \hat{n}) \)
c. \( \hat{i} \times \hat{n}=\mu(\hat{r} \times \hat{n}) \)
\( \mathbf{D} \cdot \hat{i} \cdot \hat{n}=\mu(\hat{r} \times \hat{n}) \)
Subject: Maths
Let \( A B C D \) be a quadrilateral with area
18, with side \( A B \) parallel to the side
\( C D \) and \( A B=2 C D . \) Let \( A D \) be
perpendicular to \( A B \) and \( C D . \) If a circle is drawn inside the quadrilateral \( A B C D \) touching all the sides, then its
radius is:
A . 3
B . 2
\( c \cdot \frac{3}{2} \)
\( D \)
Subject: Physics
Let \( \vec{F} \) be the force acting on a particle having position vector \( \vec{r} \) and \( \vec{\tau} \) be the torque of this force about the origin then:
\( \mathbf{A} \cdot \vec{r} \cdot \vec{\Gamma}=0 \) and \( \vec{F} \cdot \vec{\Gamma} \neq 0 \)
B . \( \vec{r} . \vec{\Gamma} \neq 0 \) and \( \vec{F} . \vec{\Gamma}=0 \)
c. \( \vec{r} . \vec{\Gamma} \neq 0 \) and \( \vec{F} \cdot \vec{\Gamma} \neq 0 \)
D. \( \vec{r} . \vec{\Gamma}=0 \) and \( \vec{F} \cdot \vec{\Gamma}=0 \)
Subject: Maths
The value of \( k \) for which the function
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\frac{1-\cos 4 x}{8 x^{2}} & , x \neq 0 \\ k & , x=0\end{array}\right. \)
continuous at \( \boldsymbol{x}=\mathbf{0}, \) is
\( \mathbf{A} \cdot k=0 \)
B. \( k=1 \)
c. \( k=-1 \)
D. None of the above
Subject: Physics
The velocity of a body of mass \( 20 \mathrm{kg} \) increases to \( 400 \mathrm{kgm} / \mathrm{s} \) in \( 5 \mathrm{s} \). If initia velocity was \( 10 \mathrm{m} / \mathrm{s} \), what is the
momentum before the force acts?
A. \( 200 k g . m / s^{2} \)
в. 300 kg.m / \( s \)
c. 200 kg.m \( / s \)
D. 100 kg.m \( / s \)
Subject: Maths
The ratio of the ratii of two circular
cones of hte same height is 1: 2 and height of each come is \( \sqrt{3} \) times the smaller radius then curved surface areas of two cones will be the ratio of
A . 2: 5
В. \( 10: 2 \sqrt{3} \)
c. \( 1: \sqrt{7} \)
D. 3:2
Subject: Maths
rume is the thupuric vi vectur \( \cup \boldsymbol{r} \)
and point \( Q \) is the endpoint of vector
OQ as shown in the above figure. When
the vectors \( \overline{O P} \) and \( \overline{O Q} \) are added,
calculate the length of the resultant
vector.
A . 1.41
B. 2.24
c. 2.65
D. 3.00
E . 8.6
Subject: Chemistry
Based upon M.O. theory state reason for the paramagnetic characater of \( \boldsymbol{C} \boldsymbol{N} \)
the diamagnetic character of \( C N \), the
stability of \( C N \) and calculate their respective bond orders.
A \( \cdot_{2} \frac{1}{2}, 2 \)
в. \( _{2 \frac{1}{2}, 3} \)
c. \( _{1 \frac{1}{2}, 3} \)
D. \( _{1} \frac{1}{2}, 2 \)
Subject: Physics
A man generates a symmetrical plus in a string by moving his hand up and down. At \( t=0 \) the point in his hand
moves downward. The pulse travels with speed \( 3 m / s \) on the string \( \& \) his hands
passes 6 times in eacgh seconds from the mean position. Then the point on the string at a distance \( 3 m \) will reach its upper extreme first time at time \( t= \)
A. 1.25 sec
в. 1 sec
\( \mathbf{c} \cdot \frac{13}{12} \sec \)
D. None
Subject: Physics
For a particle moving along X-axis if acceleration(constant) is acting along -
ve X-axis, then match the entries of
Column-I with entries of Column II
Column I Column II
A. Initial
P. Particle may move in +ve \( x \) velocity>
B. Initial Q.Particle may move in +ve x velocityく \( \quad \) direction with decreasing speed
R. Particle may move in-ve
C. \( x>0 \quad \) direction with increasing speed
S. Particle may move in -ve X
D.X \( <0 \)
\( A \cdot A->Q, R ; B \rightarrow Q, R ; C->Q, R ; D \rightarrow R \)
B. A -> Q; B -> Q, R; C-> R; D -> Q, R
C. \( A \) -> \( Q, R ; B \) -> \( R ; C \) -> \( Q, R ; D \rightarrow Q, R \)
D. A -> Q, R; B -> R; C->R; D -> R
Subject: Physics
A small hole is made at a height of \( \boldsymbol{h}= \)
\( \boldsymbol{m} \) from the bottom of a cylindrical
water tank and at a depth of \( \boldsymbol{h}=\mathbf{2 m} \)
from the upper level of water in the tank. The distance, where the water emerging from the hole strikes the ground, is:
A \( .22 m \)
в. \( 1 m \)
\( c .2 m \)
D. None of these
Subject: Chemistry
Assertion
For the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}), \) if the volume
of a vessel is reduced to half of its
original volume,equilibrium
concentration of all gases will be doubled.
Reason
According to Le Chatelier's principle, reaction shifts in a direction that tends
to minimize the effect of the stress.
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
Find the difference of the areas of two
segments of a circle formed by a chord of length \( 5 \mathrm{cm} . \) Subtending an angle of
\( 90^{\circ} \) till the centre.
A. 32.14 sq. \( \mathrm{cm} \)
в. 35.42 sq. \( \mathrm{cm} \)
c. 38.96 sq. \( \mathrm{cm} \)
D. 42.43 sq. \( \mathrm{cm} \)
Subject: Physics
A car traveled the total distance of \( x \) in three equal intervals, first at a speed of \( 10 \mathrm{km} / \mathrm{h} . \) The second at a speed of 20 \( \mathrm{km} / \mathrm{h} \) and the last third at a speed of 60 km/h. Determine the average speed of the car over the entire distance \( x \)
Subject: Chemistry
\( 2.2 \mathrm{g} \) of a compound of phosphorous and sulphur has 1.24 g of \( P \) in it. Its
empirical formula is :
A \( \cdot P_{2} S_{3} \)
в. \( P_{3} S_{2} \)
\( \mathrm{c} \cdot P_{3} S_{4} \)
D . \( P_{4} S_{3} \)
Subject: Physics
In the figure shown below the maximum
possible unknown resistance \( (X) \) that can be measured by the post office box
\( \operatorname{are} X_{\max } \) is given by \( R \times 10^{5} \Omega \) then \( \mathrm{R} \) is
(given that in this experiment we can
take out only one plug from arm \( A B \) and
only one plug from arm BC but from arm AD we can take out many plugs)
Subject: Chemistry
We can say that the energy of frequency \( \boldsymbol{v} \) is given by \( \boldsymbol{E}=\boldsymbol{h} \boldsymbol{v}, \) where \( \boldsymbol{h} \) is
Planck's constant. The momentum of a photon is \( p=\frac{h}{\lambda} \) where \( \lambda \) is the
wavelength of photon. Then we may conclude that velocity of light is
equal to:
A \( \cdot\left(\frac{E}{P}\right)^{1 / 2} \)
в.
c. Ep
D. \( \left(\frac{E}{P}\right)^{2} \)
Subject: Maths
Evaluate \( : \frac{\operatorname{cosec}^{2} \mathbf{6 3}^{\mathbf{0}}+\tan ^{2} \mathbf{2 4}^{\mathbf{0}}}{\cot ^{2} \mathbf{6 6}^{\mathbf{0}}+\mathbf{s e c}^{\mathbf{2}} \mathbf{2 7}^{\mathbf{0}}}+ \)
\( \frac{\mathbf{s i n}^{2} \mathbf{6 3}^{\mathbf{0}}+\cos \mathbf{6 3}^{\mathbf{0}} \sin \mathbf{2 7}^{\mathbf{0}}+\sin \mathbf{2 7}^{\mathbf{0}} \mathbf{s e c 6}}{\mathbf{2}\left(\operatorname{cosec}^{\mathbf{2}} \mathbf{6 5}^{\mathbf{0}}-\mathbf{t a n}^{\mathbf{2}} \mathbf{2 5}^{\mathbf{0}}\right)} \)
Subject: Physics
In a hydrogen atom, the binding energy
of the electron in the nth state is \( \boldsymbol{E}_{\boldsymbol{n}} \)
, then the frequency of revolution of the electron in the nth orbit is:
A \( \cdot 2 E_{n} / n h \)
в. \( 2 E_{n} n / h \)
c. \( E_{n} / n h \)
D. \( E_{n} n / h \)
Subject: Chemistry
Electromagnetic radiation of wavelength \( 242 \mathrm{nm} \) is just sufficient to ionise the sodium atom. What should
be ionization energy of sodium atom in
order of \( 10^{-19} ?\left(c=3 \times 10^{8} \mathrm{ms}^{-1}, h=\right. \)
\( 6.626 \times 10^{-34} \mathrm{Js} \)
A . 8.2
B. 8
c. 9
D. 9.2
Subject: Chemistry
Calculate the concentration of \( C O_{2} \) in a
soft drink that is bottled with a partial
pressure of 4 atm over the liquid at
\( 25^{\circ} \mathrm{C} . \) The Henry's law constant for \( C O_{2} \)
in water at \( 25^{\circ} \mathrm{C} \) is \( 3.1 \times \)
\( 10^{-2} \) atm / mole \( - \) litre.
A. 0.129 mol/litre
в. 129.03 mol/litre
c. 0.224 mol / litre
D. 224.3 mol/litre
Subject: Maths
Find the area of a trapezoid with bases of 21 and \( 17 \mathrm{mm}, \) and a height of \( 10 \mathrm{mm} \)
A \( .190 m^{2} \)
в. \( 190 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 190 m m^{3} \)
D. \( 190 \mathrm{mm}^{2} \)
Subject: Physics
A person with vibrating tuning fork of frequency \( 338 \mathrm{Hz} \) is moving towards a
vertical wall with a speed of \( 2 m s^{-1} \)
Velocity of sound in air is \( 340 m s^{-1} \). The
number of beats heard by that person per second is.
A . 2
B. 4
c. 6
D.
Subject: Physics
A particle executes \( S H M \) with time period \( T \) and amplitude \( A \), The maximum possible average velocity in time \( T / 4 \) is
A \( \cdot \frac{2 A}{T} \)
в. \( \frac{4 A}{T} \)
c. \( \frac{8 A}{T} \)
D. \( \frac{4 \sqrt{2 A}}{T} \)
Subject: Physics
thingy hanging from a spring. The system was set vibrating by pulling the
thingy down below its equilibrium position and then letting it go from
rest. If the initial displacement is
doubled what happens to the maximum
kinetic energy of the thing?
A. It is unchanged.
B. It is doubled
c. It is increased by a factor of \( 4 . \)
D. We can't tell from the information provided
Subject: Physics
A positively charged particle, having charge \( q, \) is accelerated by a potential difference V. This particle moving along the \( x \) -axis enters a region where an electric field \( \mathrm{E} \) exists. The direction of
the electric field is along positive y-axis. The electric field exists in the region
bounded by the line \( x=0 \) and \( x=a \)
Beyond the line \( x=a \) (i.e., in the region
\( x>a \) ), there exists a magnetic field of
strength B, directed along the positive y-axis. Find the pitch of the helix formed
after the particle enters the region \( x \geq \)
a. (Mass of the particle is \( m \) )
Subject: Chemistry
In the following which of the two are paramagnetic
\( (a) N_{2} \)
\( (b) C O \)
\( (c) B_{2} \)
\( (d) N O_{2} \)
Correct answer is:
A. a and c
B. b and c
\( c \cdot c \) and \( d \)
D. b and d
Subject: Physics
Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are \( +q \) and \( -q \) The potential difference between the centres of the two rings is -
A \( . Q R / 4 \pi \varepsilon 0 d^{2} \)
B. \( \frac{Q}{2 \pi_{c \theta}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+\alpha^{2}}}\right. \)
c. zero
D. \( \frac{Q}{4 \pi \varepsilon_{0}}\left[\frac{1}{R}-\frac{1}{\sqrt{R^{2}+\bar{d}^{2}}}\right] \)
Subject: Physics
At a place, the value of 'g' is less by \( 1 \% \) than its value on the surface of the Earth (Radius of Earth, \( \boldsymbol{R}=\mathbf{6 4 0 0 k m} \) ).
The place is:
A. \( 64 \mathrm{km} \) below the surface of the earth
B. \( 64 \mathrm{km} \) above the surface of the earth
c. \( 30 \mathrm{km} \) above the surface of the earth
D. 32 km below the surface of the earth
Subject: Physics
The equation of motion of a particle executing SHM is \( \left(\frac{d^{2} x}{d t^{2}}\right)+k x=0 . \) The time period of the particle will be ?
A \( \cdot \frac{2 \pi}{\sqrt{k} \pi} \)
в. \( 2 \pi \)
\( c \cdot 2 \pi k \)
D. \( 2 \pi \sqrt{k} \)
Subject: Physics
A particle starts from a point \( A \) and
travels along the solid curve shown
in figure. Find approximately the position B of the particle such that the
average velocity between the position \( A \)
and \( \mathrm{B} \) has the same direction as
the instantaneous velocity at B.
A \( . x=5 m, y=3 m \)
B. \( x=3 m, y=2 m \)
c. \( x=6 m, y=2 m \)
D. \( x=5 m, y=2 m \)
Subject: Chemistry
A sample of \( A g C l \) was treated with 5
\( \mathrm{mL} \) of \( 1.5 M N a_{2} C O_{3} \) solution to give
\( A g_{2} C O_{3} . \) The remaining solution
contained \( 0.0026 g \) of \( C l^{-} \) per litre. The
solubility product of \( A g C l \) is \( \left(\boldsymbol{K}_{\boldsymbol{s p}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C O}_{3}\right)}=\boldsymbol{8 . 2} \times \mathbf{1 0}^{-12}\right) \)
A \( \cdot K_{s p}=1.63 \times 10^{-10} M^{2} \)
B. \( K_{s p}=1.71 \times 10^{-10} M^{2} \)
C . \( K_{s p}=1.82 \times 10^{-10} M^{2} \)
D. None of these
Subject: Physics
The horizontal range of a projectile fired at an angle of \( 15^{\circ} \) is \( 50 \mathrm{m} \). If it is fired with the same speed at an angle of \( 45^{\circ} \) its range will be:
A. \( 60 \mathrm{m} \)
B. 71
c. \( 100 \mathrm{m} \)
D. \( 141 \mathrm{m} \)
Subject: Physics
The focal length of a convex mirror is
given as \( 2 \mathrm{cm} . \) Find the radius of
curvature, \( \boldsymbol{R} \), of the mirror?
A . \( 1.0 \mathrm{cm} \)
B. \( 2.0 \mathrm{cm} \)
c. \( 4.0 \mathrm{cm} \)
D. \( 8.0 \mathrm{cm} \)
Subject: Physics
A uniform chain of mass \( M \) and Length
\( \boldsymbol{L} \) is held vertically in such a way that its lower end just touches the horizontal floor. The chain is released from rest in
this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on
the floor, when a length \( x \) has reached
the floor.
Subject: Maths
If \( \cos y=x \cos (a+y) \) then prove that:
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\cos ^{2}(\boldsymbol{a}+\boldsymbol{y})}{\sin \boldsymbol{a}} \)
Subject: Chemistry
The number of water molecules
differing in molecular mass formed by hydrogen isotopes and \( ^{1} \boldsymbol{H},^{2} \boldsymbol{H},^{3} \boldsymbol{H} \) and
oxygen isotopes \( ^{16} \boldsymbol{O},^{17} \boldsymbol{O},^{18} \boldsymbol{O} \) is
\( A \cdot 6 \)
B. 9
c. 12
D. 18
Subject: Physics
For the four sets of three measured
physical quantities as given below. Which of the following options is
correct?
\( (i) A_{1}=24.36, B_{1}=0.0724, C_{1}= \)
\( \mathbf{2 5 6 . 2} \)
\( (i i) A_{2}=24.44, B_{2}=16.082, C_{2}= \)
\( \mathbf{2 4 0 . 2} \)
\( (i i i) A_{3}=25.2, B_{3}=19.2812, C_{3}= \)
\( \mathbf{2 3 6 . 1 8 3} \)
\( (i v) A_{4}=25, B_{4}=236.191, C_{4}= \)
19.5
A. \( A_{1}+B_{1}+C_{1}<A_{3}+B_{3}+C_{3}<A_{4}+B_{4}+C_{4}< \)
\( A_{2}+B_{2}+C_{2} \)
B . \( A_{4}+B_{4}+C_{4}<A_{1}+B_{1}+C_{1}<A_{3}+B_{3}+C_{3}< \)
\( A_{2}+B_{2}+C_{2} \)
c. \( A_{4}+B_{4}+C_{4}<A_{1}+B_{1}+C_{1}=A_{2}+B_{2}+C_{2}= \)
\( A_{3}+B_{3}+C_{3} \)
D. \( A_{1}+B_{1}+C_{1}=A_{2}+B_{2}+C_{2}=A_{3}+B_{3}+C_{3}= \)
\( A_{4}+B_{4}+C_{4} \)
Subject: Chemistry
What will be \( \Delta H \) for the reaction,
\( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2} \rightarrow \boldsymbol{C}+\mathbf{2} \boldsymbol{H}+\mathbf{2} \boldsymbol{C l} ? \)
(B.E. of \( C-H \) and \( C-C \) ) bonds are 416 kJ
\( m o l^{-1} \) and 325 kJmol \( ^{-1} \) respectively
A . 832 k
B . 1482 k
c. \( 650 \mathrm{kJ} \)
D. 1855 k
Subject: Maths
Find the range of each of the following
functions \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{6} \boldsymbol{x}+\mathbf{1 1}, \) all \( \boldsymbol{x} \in \)
\( \boldsymbol{R} \)
Subject: Physics
A water tap leaks such that water drops
fall at regular intervals. Tap is fixed \( 5 m \)
above the ground. First drop reaches the
ground and at that very instant third drop leaves the tap. At this instant the second drop is at a height of
\( A, 3 m \)
в. 4.5 т
\( \mathbf{c} .3 .75 \mathrm{m} \)
D. 2.5 .
Subject: Physics
A ball \( A \) is moving with velocity \( 5 m / s \) collides elastically with another identical ball \( B \) which is initially at rest
such that the velocity of \( B \) after the
collision makes an angle of \( 37^{\circ} \) with the
initial velocity of \( A \). Then the
INCORRECT statement is :
A. speed of \( A \) after collision is \( 3 m / s \)
B. Speed of \( B \) after collision is \( 4 m / s \)
c. Balls \( A \) and \( B \) move at right angle after collision
D. Kinetic energy is not conserved as the collision is not head on
Subject: Maths
The ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) passes
through the point (-3,1) and has the eccentricity \( \sqrt{\frac{2}{5}} . \) Then the major axis of the ellipse has the length:
\( ^{A} \cdot 4 \sqrt{\frac{2}{5}} \)
B. \( 8 \sqrt{\frac{2}{3}} \)
\( ^{c} \cdot 4 \sqrt{\frac{2}{3}} \)
D. \( 8 \sqrt{\frac{2}{5}} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{1}|, \) then
\( \mathbf{A} \cdot f\left(x^{2}\right)=(f(x))^{2} \)
B. \( f(x+y)=f(x)+f(y) \)
\( c . f(|x|)=\mid f(x) \)
D. None of these
Subject: Biology
Assertion
Every biological system resist a change and wants to remain in state of
equilibrium.
Reason
Climax communities of an ecosystem are produced after several changes it has gone through succession.
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: Physics
Find the In the circuit shown in Fig,
switch \( S_{1} \) was closed for a long time. At
time \( t=0 \) the switch is
opened. Angular frequency of oscillation of the charge on the capacitor:
A \( \cdot 100 \operatorname{rad} s^{-1} \)
B. 200 rads\( ^{-1} \)
c. 300 rads\( ^{-1} \)
D. 400 rads\( ^{-1} \)