AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
In the trapezium \( A B C D, \) side \( A B \| \) side
DC. Diagonals \( A C \) and DB intersect each other at \( 0 . \) If \( A B=15, D C=10 \) find \( \frac{O C}{O A} \)
A \( \cdot \frac{O C}{O A}=\frac{1}{3} \)
в. \( \frac{O C}{O A}=\frac{7}{3} \)
c. \( \frac{O C}{O A}=\frac{2}{3} \)
D. \( \frac{O C}{O A}=\frac{5}{3} \)
Subject: Maths
Find the angle between the following pair of lines:
(i) \( \vec{r}=2 \hat{i}-5 \hat{j}+\hat{k}+\lambda(3 \hat{i}-2 \hat{j}+6 \hat{k}) \)
and \( \vec{r}=\mathbf{7} \hat{\boldsymbol{i}}-\boldsymbol{6} \hat{\boldsymbol{k}}+\boldsymbol{\mu}(\hat{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}}) \)
(ii) \( \vec{r}=3 \hat{i}+\hat{j}-2 \hat{k}+\lambda(\hat{i}-\hat{j}-2 \hat{k}) \)
and \( \vec{r}=2 \hat{i}-\hat{j}-56 \hat{k}+ \)
\( \mu(\hat{\mathbf{3}} \mathbf{i}-\mathbf{5} \hat{\mathbf{j}}-\mathbf{4} \hat{\boldsymbol{k}}) \)
Subject: Physics
\( Q \) Type your ques
same material, A is solla but b is
hollow. These are connected by an idea
spring and this system is kept over a
smooth plank such that center of mass of two balls coincide with mid point of
the plank. Initially the spring is
compressed by a certain amount and
the plank is in horizontal position. Now
we release the system then,
A. Plank will rotate clock wise
B. Plank will rotate anti clock wise
C. Plank will not rotate
It will depend upon st
Subject: Maths
The sum of first \( n \) terms of an AP is
given by \( S_{n}=\left(1+T_{n}\right)(n+2) \) Then \( T_{2} \)
is
A \( \cdot-\frac{11}{6} \)
B. \( -\frac{-5}{3} \)
\( c \cdot-\frac{5}{3} \)
D. 2
Subject: Maths
If \( \bar{a} \) and \( \bar{b} \) include an angle of \( 120^{\circ} \) and their magnitudes are 2 and \( \sqrt{3} \) then \( \bar{a} . \bar{b} \) is
\( A \cdot 3 \)
B. \( -\sqrt{3} \)
\( c \cdot \sqrt{3} \)
D. - 3
Subject: Biology
Assertion
The presence of vessels is a
characteristic feature of Angiosperms.
Reason
Vessels are spindle primitive conducting elements
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 \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is a differentiable function
such that \( f^{\prime}(x)>2 f(x) \) for all \( x \in R \)
and \( f(0)=1, \) then
This question has multiple correct options
A \( \cdot f(x) \) is decreasing in \( (0, \infty) \)
B \( \cdot f^{\prime}(x)<e^{2 x} \) in \( (0, \infty) \)
C \( \cdot f(x) \) is increasing in \( (0, \infty) \)
D. \( f(x)>e^{2 x} \) in \( (0, \infty) \)
Subject: Chemistry
The depletion of ozone involves the following steps:
Step \( 1: O_{3} \frac{K_{1}}{k_{2}} O_{2}+O(\text { fast }) \)
\( \operatorname{step} 2: 0_{3}+O \longrightarrow 2 O_{2}(\text { slow }) \)
The predicted order of the reaction will be:
Subject: Physics
A sphere of mass m moving with velocity u h its another stationary sphere of same mass. If e is the coefficient of restitution, what is the
ratio of velocities of two spheres after
the collision?
A \( .1: e \)
в. \( \frac{1-e}{1+e} \)
c. \( \frac{1+e}{1-e} \)
D. \( 1: e^{2} \)
Subject: Chemistry
A chemical reaction proceeds into the following steps
Step \( \mid: 2 A \rightleftharpoons X \) (fast)
Step II: \( \boldsymbol{X}+\boldsymbol{B} \rightarrow \boldsymbol{Y}(\text { slow }) \)
Step III: \( Y+B \rightarrow \) Product(fast)
The rate low for the overall reaction \( ^{*} \) is:
Subject: Chemistry
Identify \( \mathbf{A}, \mathbf{B}: \)
\( \mathbf{A} \cdot A=N H_{3} ; B=N_{2} \)
B \( \cdot A=N O ; B=H N O_{3} \)
\( \mathbf{C} \cdot A=N_{2} ; B=N H_{3} \)
\( \mathbf{D} \cdot B=H N O_{3} ; A=N O \)
Subject: Physics
The emf of a Daniel cell is \( 1.08 V . \) When
the terminals of the cells are connected
to the resistance of \( 3 \Omega \), the potential difference across the terminals is found
to be \( 0.6 \% \). Then the internal resistance
of the cell is
A. \( 1.8 \Omega \)
в. 2.4\Omega
c. \( 3.24 \Omega \)
D. \( 0.2 \Omega \)
Subject: Maths
The middle term in the expansion of
\( (1+x)^{2 n} \) is
A. \( \frac{1.3 .5 \ldots(2 n-1) 2^{n}}{n !} \)
в. \( \frac{1.2 .3 \ldots(2 n-1) 2^{n} x^{n}}{n !} \)
c. \( \frac{1.3 .5 \ldots(2 n-1) x^{n}}{n !} \)
D. \( \frac{1.3 .5 \ldots .(2 n-1) 2^{n} x^{n}}{n !} \)
Subject: Chemistry
Assertion \( (\mathrm{A}): N H_{4} N O_{3} \) on gently
heating gives \( N_{2} O \) Reason(R): \( N_{2} O \) is acidic in nature
The correct answer is :
A. Both (A) and (R) are true and
(R) is the correct explanation of (A)
B. Both (A) and (R) are true and
(R) is not the correct explanation of (A)
c. (A) is true and
(R) is false
D. (A) is false but (R) is true
Subject: Chemistry
Select the incorrect statement from the
following:
A \( \cdot H^{+} \) can as \( H_{9} O_{4}^{+} \) in water
B. \( H_{2} \) is thermally stable
C. lonization of \( C H_{3} \mathrm{COOH} \) is slower than that of \( C H_{3} \)
COOD
D. Kinetic isotopic effect is observed when there is retardation in the rate if \( H_{2} O \) is replaced by \( D_{2} O \)
Subject: Physics
A bar magnet of magnetic moment
\( 0.4 A m^{2} \) is placed in the magnetic
meridian with its north pole pointing north. A neutral point is obtained at a
distance of \( 10 \mathrm{cm} \) from the centre of the
magnet.If the length of the magnet is
\( 20 \mathrm{cm}, \) then the value of horizontal
component of earth magnetic induction is:
A \( \cdot \sqrt{2} \times 10^{-5} T \)
B. \( \frac{1}{\sqrt{2}} \times 10^{-7} \)
c. \( 2 \times 10^{-7} T \)
D. \( \frac{1}{2} \times 10^{-7} T \)
Subject: Maths
Find the coordinates that was of the
equation \( \boldsymbol{x}^{3}-\boldsymbol{p} \boldsymbol{x}^{2}+\boldsymbol{q} \boldsymbol{x}-\boldsymbol{r}=\mathbf{0}, \) may
be in A.P. and hence solve the equation \( x^{3}-12 x^{2}+34 x-28=0 \)
Subject: Physics
If block \( A \) is moving with an
acceleration of \( 5 m s^{-2}, \) the acceleration
of B w.r.t ground is
\( A \cdot 5 m s^{-2} \)
B. \( 5 \sqrt{2} \mathrm{ms}^{-2} \)
\( c \cdot 5 \sqrt{5} m s^{-2} \)
D. \( 10 m s^{-2} \)
Subject: Chemistry
Pb is a very important element of carbon family. It forms a number of compounds which are very useful in
industries. The process of removal of base metals \( (\mathrm{Cu}, \mathrm{Sn}, \mathrm{Bi}, \mathrm{As}) \) from lead is called:
A. softening process
B. liquation
c. parke's process
D. cupellalion
Subject: Maths
Let \( \alpha \) be the distance between the lines
\( -x+y=2 \) and \( x-y=2, \) and \( \beta \) be the distance between the lines \( 4 x-3 y=5 \) and \( 6 y-8 x=1, \) then find \( \alpha \) and \( \beta \)
Subject: Physics
Q Type your question-
particle is attached to the cylinder by a
horizontal thread \( A B \) as shown in the
figure. The particle initially rest on
horizontal plane. A horizontal velocity \( \boldsymbol{v}_{0} \)
is imparted to the particle, normal to the threading during subsequent
motion. Point out the false statements:
This question has multiple correct options
A. Angular momentum of particle about \( O \) remains
constant
B. Angular momentum about \( B \) remains constant
c. Momentum and kinetic energy both remain constant
D. Kinetic energy remains consta
Subject: Physics
The maximum vertical distance
through which a full dressed astronaut canjump on the earth is \( 0.5 \mathrm{m} \)
Estimate the maximum vertical
distance through which he can jump on the moon, which has a mean density \( 2 / 3 \) rd that of the earth and radius one
quarter that of the earth.
A . \( 1.5 \mathrm{m} \)
B. 3 m
\( c \cdot 6 m \)
D. 7.5 \( m \)
Subject: Physics
The wavelength of a wave is \( \lambda=6000 A \)
then wave number will be
A \( \cdot 1.66 \times 10^{7} \mathrm{m}^{-1} \)
В . \( 1.66 \times 10^{6} \mathrm{m}^{-1} \)
c. \( 16.6 \times 10^{-1} \mathrm{m}^{-1} \)
D . 166 \( \times 10^{3} \mathrm{m}^{-1} \)
Subject: Physics
The velocity of a particle is \( \overrightarrow{\boldsymbol{v}}=\mathbf{6} \hat{\mathbf{i}}+ \)
\( 2 \hat{j}-2 \hat{k} . \) The component of the velocity parallel to vector \( \vec{a}=\hat{i}+\hat{j}+\hat{k} \) is :-
\( \mathbf{A} \cdot 6 \hat{i}+2 \hat{j}+2 \hat{k} \)
B . \( 2 \hat{i}+2 \hat{j}+2 \hat{k} \)
\( \mathbf{c} \cdot \hat{i}+\hat{j}+\hat{k} \)
D. \( 6 \hat{i}+2 \hat{j}-2 \hat{k} \)
Subject: Chemistry
The standard enthalpy of formation of carbon - di - sulphide ( \( l \) ) is:
Given the standard enthalpy of combustion of carbon (s), sulphur (s)
\& carbon - di - sulphide ( \( l \) ) are :
-393.3,-293.72 and
\( -1108.76 k J m o l^{-1} \) respectively.
A. \( 128.02 \mathrm{kJ} \)
J.
B. 456.21kJ
c. 232.56 kJ
D. 871.25 kJ
Subject: Physics
The inital velocity of a particle is \( u \) (at
\( t=0 \) ) and the acceleration \( a \) is given by
\( \alpha t^{3 / 2} . \) Which of the following relations is vaild?
A \( \cdot v=u+\alpha t^{3 / 2} \)
B. \( v=u+\frac{3 \alpha t^{3}}{2} \)
c. \( v=u+\frac{2}{5} \alpha t^{5 / 2} \)
D . \( v=u+\alpha t^{-5 / 2} \)
Subject: Physics
A current of \( 5 A \) is passing through a metallic wire of cross-sectional area
\( 4 \times 10^{-6} m^{2} . \) If the density of charge
carriers of the wire is \( 5 \times 10^{26} m^{-3}, \) the
drift velocity of the electrons will be :
A. \( 1 \times 10^{2} \mathrm{ms}^{-1} \)
В. \( 1.56 \times 10^{-2} \mathrm{ms}^{-1} \)
c. \( 1.56 \times 10^{-3} m s^{-1} \)
D. \( 1 \times 10^{-2} \mathrm{ms}^{-1} \)
Subject: Maths
\( \operatorname{Let} f(x)=3 x^{2} \cdot \sin \frac{1}{x}- \)
\( \boldsymbol{x} \cos \frac{1}{\boldsymbol{x}}, \boldsymbol{x} \neq \mathbf{0}, \boldsymbol{f}(\mathbf{0})=\mathbf{0} \boldsymbol{f}\left(\frac{\mathbf{1}}{\boldsymbol{\pi}}\right)=\mathbf{0} \)
then which of the following is/are not
correct.
This question has multiple correct options
A. \( f(x) \) is continuous at \( x=0 \)
B. \( f(x) \) is non-differentiable at \( x=0 \)
c. \( f(x) \) is discontinuous at \( x=0 \)
D. \( f(x) \) is differentiable at \( x=0 \)
Subject: Physics
A variable air capacitor has 11 movable plates and 12 stationary plates, The
area of each plate is \( 0.0015 m^{2} \) and
separation between opposite plates is \( 0.001 m . \) The maximum capacitance of
the capacitor is
A . \( 292.2 F \)
В. \( 292.2 \mathrm{mF} \)
c. \( 292 \mu F \)
D. 292 p
Subject: Chemistry
Which among the following is/ are
correct for a first order reaction?
This question has multiple correct options
A. The degree of dissociation is equal to \( \left(1-e^{-k t}\right) \)
B. A plot of reciprocal concentration of the reactant vs time gives a straight line.
C. The time taken for the completion of 75\% reaction is thrice the \( t_{1 / 2} \) of reaction.
D. The pre-exponential factor in the Arrhenius equation has the dimension of time, \( T^{-1} \)
Subject: Physics
In wheatstone's bridge \( \boldsymbol{P}=\mathbf{9} \) ohm, \( \boldsymbol{R}= \)
4 ohm and \( S=6 \) ohm. How much
resistance must be put in parallel to the resistance \( S \) to balance the bridge?
A .24 ohm
B. 13.5 ohm
c. 7.2 ohm
D. 18.7 ohm
Subject: Physics
The boiling point of mercury is \( 367^{\circ} \mathrm{C} . \) A mercury thermometer can be used to
measure a temperature of \( 500^{\circ} \mathrm{C} \)
A. by filling the space above mercury with oxygen at highh pressure
B. by filling the space above mercury with nitrogen at low pressure
c. by filling the space above mercury with nitrogen at high pressure
D. by keeping the space above mercury as vacuum
Subject: Physics
Equation of gas in terms of pressure \( p \)
absolute temperature \( T \) and density \( d \) is :
\( \mathbf{A} \cdot \frac{p_{1}}{d_{1} T_{1}}=\frac{p_{2}}{d_{2} T_{2}} \)
В \( \cdot \frac{p_{1} T_{1}}{d_{1}}=\frac{p_{2} T_{2}}{d_{2}} \)
\( \mathbf{c} \cdot \frac{p_{1} d_{2}}{T_{2}}=\frac{p_{2} d_{1}}{T_{1}} \)
D. \( \frac{p_{1} d_{1}}{T_{1}}=\frac{p_{2} d_{2}}{T_{2}} \)
Subject: Maths
If \( A \) and \( B \) are acute angles such that
\( \sin A=\sin ^{2} B, 2 \cos ^{2} A=3 \cos ^{2} B \)
then
This question has multiple correct options
A \( \cdot A=\frac{\pi}{6} \)
B. \( A=\frac{\pi}{2} \)
c. \( B=\frac{\pi}{4} \)
D. \( B=\frac{\pi}{3} \)
Subject: Physics
A certain number of spherical drops of a liquid of radius 'r' coalesce to form a
single drop of radius 'R' and volume 'V'. If 'T' is the surface tension of the liquid
then:
A . Energy \( =4 V T\left(\frac{1}{r}-\frac{1}{R}\right) \) is released
B . Energy \( =3 V T\left(\frac{1}{r}+\frac{1}{R}\right) \) is released
C. Energy \( =3 V T\left(\frac{1}{r}-\frac{1}{R}\right) \) is released
D. Energy is neither released nor absorbed
Subject: Physics
The temperature of a room is \( \mathbf{7 7}^{\circ} \boldsymbol{F} \) What would it be on the Celsius scale?
\( \mathbf{A} \cdot 25^{\circ} C \)
B. \( 45^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} \mathrm{C} \)
D. \( 350^{\circ} \mathrm{C} \)
Subject: Physics
A vernier callipers has its main scale of \( 10 \mathrm{cm} \) equally divided into 200 equal parts. Its vernier scale of 25 divisions
coincides with \( 12 \mathrm{mm} \) on the main
scale. The least count of the instrument
is -
\( A \cdot 0.020 \mathrm{cm} \)
B. \( 0.002 \mathrm{cm} \)
c. \( 0.010 \mathrm{cm} \)
D. \( 0.001 \mathrm{cm} \)
Subject: Maths
Select and write the most appropriate
answer from the given alternatives
for question:
The cartesian equation of the line passing through the points \( \boldsymbol{A}(\mathbf{4}, \mathbf{2}, \mathbf{1}) \) and \( \boldsymbol{B}(\mathbf{2},-\mathbf{1}, \mathbf{3}) \) is
A. \( \frac{x+4}{2}=\frac{y-2}{3}=\frac{z-1}{-2} \)
в. \( \frac{x-4}{-2}=\frac{y-2}{-3}=\frac{z-1}{-2} \)
c. \( \frac{x-4}{2}=\frac{y-2}{3}=\frac{z-1}{-2} \)
D. \( \frac{x-4}{-2}=\frac{y-2}{3}=\frac{z-1}{-2} \)
Subject: Maths
The lines \( \frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k} \& \)
\( \frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{k}}=\frac{\boldsymbol{y}-\boldsymbol{4}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\mathbf{5}}{\mathbf{1}} \) are coplanar if
A \( . k=0 \) or -1
B. \( k=1 \) or -1
c. \( k=0 \) or -3
D. \( k=3 \) or -3
Subject: Physics
Charges \( Q_{1} \) and \( Q_{2} \) lie inside and outside respectively of a closed surface
S. Let \( \mathrm{E} \) be the field at any point on \( \mathrm{S} \) and
\( \phi \) be the flux of E over \( S \)
This question has multiple correct options
A \( \cdot \) If \( Q_{1} \) changes, both \( \mathrm{E} \) and \( \phi \) will change
B . If \( Q_{2} \) changes, E will change but \( \phi \) will not change
C. If \( Q_{1}=0 \) and \( Q_{2} \neq 0, \) then \( E \neq 0 \) but \( \phi=0 \)
D. If \( Q_{1} \neq 0 \) and \( Q_{2}=0, \) then \( \mathrm{E}=0 \) but \( \phi \neq 0 \)
Subject: Chemistry
Following are the transition metal ions
of \( 3 d \) series:
\( \boldsymbol{T} \boldsymbol{i}^{4+}, \boldsymbol{V}^{2+}, \boldsymbol{M} \boldsymbol{n}^{3+}, \boldsymbol{C} \boldsymbol{r}^{3+} \)
(Atomic numbers: \( \boldsymbol{T} \boldsymbol{i}=\mathbf{2 2}, \boldsymbol{V}= \)
\( \mathbf{2 3}, \boldsymbol{M n}=\mathbf{2 5}, \boldsymbol{C r}=\mathbf{2 4}) \)
Answer the following:
(i) Which ion is most stable in an aqueous solution and why?
(ii) Which ion is a strong oxidising agent and why?
(iii) Which ion is colourless and why?
Subject: Chemistry
Among the following, in how many cases equilibrium \( C a C O_{3}(s) \rightleftharpoons \) \( \boldsymbol{C a O}(s)+\boldsymbol{C O}_{2}(\boldsymbol{g}) \) will shift in forward
direction?
(i) addition of \( C a C O_{3}(s) \)
(ii) addition of \( \operatorname{CaO}(s) \)
(iii) addition of \( C O_{2}(g) \)
(iv) addition of \( N_{2} \) at constant volume
(v) addition of \( N_{2} \) at constant pressure
(vi) increase in temperature
(vii) increase in pressure
(vii) addition of \( \boldsymbol{H} \boldsymbol{C l} \)
(ix) addition of \( N a O H \)
Subject: Physics
Two identical particles \( B \) and \( C \) each of
mass \( 50 g \) are connected by a light rod of length \( 30 C M . \) Another particle \( A \) of
same mass moving with a speed \( u= \)
\( 60 C M / s \) strikes \( B, \) in a direction
perpendicular to \( A B, \) and sticks to it.
The whole process takes place on a smooth horizontal plane. Find the
angular velocity \( \omega \) of the system about
its centre of mass, immediately after the impact.
Subject: Maths
The length, breadth and height of a room are \( 5 m, 4 m \) and \( 3 m \) respectively Find the cost of white washing the walls of the rooms and the ceiling at the rate
of \( R s .7 .50 \) per \( m^{2} \)
A . Rs.355
в. \( R s .505 \)
c. \( R s .455 \)
D. Rs.555
Subject: Maths
The ratio in which the plane \( \bar{r} .(\bar{i}-2 \bar{j}+ \) \( \mathbf{3} \bar{k})=17 \) divides the line joining the points \( -2 \bar{i}+4 \bar{j}+7 \bar{k} \) and \( 3 \bar{i}-5 \bar{j}+8 \bar{k} \)
is
A. 1: 10
B. 3: 10
\( c .3: 5 \)
D. 1: 5
Subject: Maths
Solve
\( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\mathbf{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}^{2}+\mathbf{1} & \boldsymbol{b} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{c} & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{c}^{2}+1\end{array}\right|=\boldsymbol{a}^{2}+\boldsymbol{b}^{2}+ \)
\( c^{2}+1 \)
Subject: Physics
A plank with a uniform sphere placed on it rests on a smooth horizontal plane.
The plank is pulled to the right by a constant force \( F \). If the sphere does not
slip over the plank, then This question has multiple correct options
A. both have the same acceleration
B. acceleration of the centre of sphere is less than that of the plank
c. work done by friction acting on the sphere is equal to its total kinetic energy
D. total kinetic energy of the system is equal to work done by the force \( F \)
Subject: Maths
The position vectors of the points \( A, B, C \) \( \operatorname{are} \bar{i}+2 \bar{j}-\bar{k}, \bar{i}+\bar{j}+\bar{k}, 2 \bar{i}+3 \bar{j}+2 \bar{k} \)
respectively. If \( A \) is chosen as the origin then the position vectors of \( \mathrm{B} \) and \( \mathrm{C} \) are
\( \mathbf{A} \cdot \bar{i}+2 \bar{k}, \bar{i}+\bar{j}+3 \bar{k} \)
B. \( \bar{j}+2 \bar{k}, \vec{i}+\bar{j}+3 \bar{k} \)
c. \( -\bar{j}+2 \bar{k}, \vec{i}-\bar{j}+3 \bar{k} \)
Subject: Maths
If two events \( A \) and \( B \) are such that
\( \boldsymbol{P}\left(\boldsymbol{A}^{\prime}\right)=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and
\( \boldsymbol{P}\left(\boldsymbol{A} \cap \boldsymbol{B}^{\prime}\right)=\mathbf{0 . 5}, \) then \( \boldsymbol{P}\left(\frac{\boldsymbol{B}}{\boldsymbol{A} \cup \boldsymbol{B}^{\prime}}\right) \)
equals
A \( \cdot \frac{3}{4} \)
в. \( \frac{5}{6} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Physics
The odometer of a car reads \( 2000 \mathrm{km} \) at
the start of a trip and \( 2400 \mathrm{km} \) at the
end of the trip. If the trip took \( 8 \mathrm{h} \)
calculate the average speed of the car in \( k m h^{-1} \) and \( m s^{-1} \)
\( A \cdot 50 \mathrm{km} / \mathrm{h} \) or \( 13.9 \mathrm{m} / \mathrm{s} \)
B. 40 km/h or 12.5 m/s
c. \( 50 \mathrm{km} / \mathrm{h} \) or \( 12.5 \mathrm{m} / \mathrm{s} \)
D. \( 40 \mathrm{km} / \mathrm{h} \) or \( 13.9 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A microscope has an objective of focal length \( 1.5 \mathrm{cm} \) and an eyepiece of focal length \( 2.5 \mathrm{cm} . \) If the distance between
objective and eyepiece is \( 20.5 \mathrm{cm}, \) what
is the magnification produced when the final image is at infinite distance
away?
A . 100
B. 75
\( c .110 \)
D. 120
Subject: Physics
Find the equivalent resistance between \( A \) and \( E \) (The resistance of each
resistor is \( R \).)
\( A \cdot \frac{7}{12} F \)
3. \( \frac{7}{13} \) f
\( c \cdot \frac{7}{15} \)
D. \( \frac{8}{13} R \)
Subject: Physics
A particle initially at rest starts moving from point \( A \) on the surface of a fixed
smooth hemisphere of radius r as
shown. The particle looses its contact
with hemisphere at point B. \( C \) is centre of the hemisphere. The equation
relating \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \) is:
A. \( 3 \sin \alpha=2 \cos \beta \)
B. \( 2 \sin \alpha=3 \cos \beta \)
\( c .3 \sin \beta=2 \cos \alpha \)
D. \( 2 \sin \beta=3 \cos \alpha \)
Subject: Physics
Three bodies a ring \( (R), \) a solid cylinder
\( (C) \) and a solid sphere \( (S) \) having same
mass and same radius roll down the
inclined plane without slipping. They
start from rest, if \( v_{R}, v_{C} \) and \( v_{S} \) are
velocities of respective bodies on reaching the bottom of the plane, then:
A \( \cdot v_{R}=v_{C}=v_{S} \)
в. \( v_{R}>v_{C}>v_{S} \)
c. \( v_{R}<v_{C}<v_{S} \)
D. \( v_{R}=v_{C}>v_{S} \)
Subject: Chemistry
An alkene \( A\left(C_{10} H_{20}\right) \) on oxidative
ozonolysis yields two molecules of
\( \left(C_{5} H_{10} O\right) B . B \) on treatment with
\( \boldsymbol{L} \boldsymbol{i} \boldsymbol{A} \boldsymbol{I} \boldsymbol{H}_{4} \) yields \( \mathbf{C}\left(\boldsymbol{C}_{5} \boldsymbol{H}_{12} \boldsymbol{O}\right) \) which can't
be resolved into enantiomers. Which of
following is correct?
A. A: 3,4-diethyl-3-hexene
B. B: 3-pentanone
c. \( c: 3 \) -pentanol
D. All of them are correct
Subject: Physics
Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of \( 14 \mathrm{m} / \mathrm{s} \) to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks
in the centre of mass frame after the
kick are, respectively:
A. \( 4 \mathrm{m} / \mathrm{s}, 4 \mathrm{m} / \mathrm{s} \)
B. \( 10 \mathrm{m} / \mathrm{s}, 4 \mathrm{m} / \mathrm{s} \)
\( c \cdot 4 m / s, 10 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s}, 10 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
A magnesium ribbon is burnt in oxygen
to give a white compound \( \boldsymbol{X} \) accompanied by the emission of light. If the burning ribbon is now placed in an atmosphere of nitrogen, it continues to
burn and forms a compound \( Y . \) Write
the chemical formula of \( X \) and \( Y: \)
A. \( x \rightarrow M g O ; y \rightarrow M g N \)
В. \( x \rightarrow 2 M g O ; y \rightarrow M g_{2} N_{3} \)
C \( . x \rightarrow M g O ; y \rightarrow M g_{3} N_{2} \)
D. None of these
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y}) \) for all \( \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R} \)
and suppose that \( f \) is differentiable at
0 and \( f^{\prime}(0)=4 . \) If \( f\left(x_{0}\right)=8 \) then
\( f^{\prime}\left(x_{0}\right) \) is equal to
Subject: Maths
If the distance between the points \( \boldsymbol{A}(\mathbf{4}, \boldsymbol{p}) \) and \( \boldsymbol{B}(\mathbf{1}, \mathbf{0}) \) is 5 units, then the
value(s) of \( p \) is are
A. 4 only
B. - 4 only y
\( c .\pm 4 \) only
D. 0
Subject: Physics
A thin horizontal disc of radius
\( \mathrm{R}=10 \mathrm{cm} \mathrm{R}=10 \mathrm{cm} \) is located within a
cylindrical cavity filled with oil whose
viscosity is \( \eta=0.08 P(\text { fig }) . \) The
clearance between the disc and the
horizontal planes of the cavity is equal
to \( h=1 \) mm. Find the power developed
by the angular velocity \( \omega=60 \) rad/s.
The end effects are to be neglected.
\( \mathbf{A} \cdot 8 W \)
В. \( 9 W \)
\( c \cdot 10 W \)
\( \mathbf{D} \cdot 19 W \)
Subject: Chemistry
For an elementary reaction \( \boldsymbol{X}(\boldsymbol{g}) \rightarrow \) \( \boldsymbol{Y}(\boldsymbol{g})+\boldsymbol{Z}(\boldsymbol{g}), \) the half-life period is \( \mathbf{1 0} \)
min. In what period would the concentration of \( X \) be reduced to \( 10 \% \)
of original concentration?
A . 20 Min
B. 33Min
c. 15Min
D. 25Min
Subject: Biology
Each thoracic segment of Periplaneta americana is enclosed by four
skeletal scleries: a dorsal
ventral and two lateral
The \( \quad \) of the
prothorax is also called pronotum,
which covers the neck and a part of the
head.
Complete the above paragraph by
selecting the correct sequence of words.
A. Chitinous, tergum, sternum, pleura, tergum
B. Proteinaceous, sternum, tergum, pleura, tergum
C. Chitinous, sternum, tergum, pleura, sternum
D. Proteinaceous, tergum, pleuron, sternum, tergum
Subject: Maths
A straight line passes through (1,-2,3) and perpendicular to the plane \( 2 x+ \) \( 3 y-z=7 . \) Find the direction ratios of
normal to plane
\( A \cdot<2,3,-1> \)
В. \( <2,3,1> \)
c. \( <-1,2,3> \)
D. None of the above