AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A particle is projected from the ground
with an initial velocity of \( 20 \mathrm{m} / \mathrm{s} \) at an
angle of \( 30^{\circ} \) with horizontal. The
magnitude of change in velocity in a time interval from \( t=0 \) to \( t=0.5 \mathrm{s} \) is
\( \left(g=10 m / s^{2}\right) \)
\( A \cdot 5 \mathrm{m} / \mathrm{s} \)
в. \( 2.5 \mathrm{m} / \mathrm{s} \)
\( c \cdot 2 m / s \)
D. \( 4 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
When treated with conc.\( H C l, M n O_{2} \)
yields a gas \( (X) \) which further reacts
with \( C a(O H)_{2} \) to generate a white
solid \( (Y) . \) The solid \( Y \) reacts with
dil.HCl to produce the same gas \( X \) The solid \( Y \) is :
A. \( C a O \)
в. \( C a C l_{2} \)
c. \( C a(O C l) C l \)
\( \mathrm{D} \cdot \mathrm{CaCO}_{3} \)
Subject: Chemistry
Find the values of \( A, B \) and \( C \) in the
following table for the reaction \( X+ \)
\( \boldsymbol{Y} \rightarrow Z . \) The reaction is of first order
w.r.t \( X \) and zero w.r.t. \( Y \)
Exp. \( [\boldsymbol{X}]\left(\boldsymbol{m o l} \boldsymbol{L}^{-1}\right) \quad[\boldsymbol{Y}]\left(\boldsymbol{m o l} \boldsymbol{L}^{-1}\right) \)
1
2
\begin{tabular}{ccc}
0.1 & 0.1 \\
\( A \) & 0.2 \\
0.4 & 0.4 \\
\( C \) & 0.2 \\
\hline
\end{tabular}
3
4
\( \mathbf{A} \cdot A=0.2 \mathrm{mol} L^{-1}, B=8 \times 10^{-2} \mathrm{mol} L^{-1} \mathrm{s}^{-1}, C= \)
\( 0.1 \mathrm{mol} L^{-1} \)
B . \( A=0.4 \) mol \( L^{-1}, B=4 \times 10^{-2} \) mol \( L^{-1} s^{-1}, C= \)
\( 0.2 \mathrm{mol} L^{-1} \)
C \( . A=0.2 \) mol \( L^{-1}, B=2 \times 10^{-2} \) mol \( L^{-1} s^{-1}, C= \)
\( 0.4 \mathrm{mol} L^{-1} \)
D. \( A=0.4 \) mol \( L^{-1}, B=2 \times 10^{-2} \) mol \( L^{-1} s^{-1}, C= \)
\( 0.4 \mathrm{mol} L^{-1} \)
Subject: Maths
Complete the following statements:
(i) Probability of an event \( \mathrm{E}+ \) Probability
of the event not \( \mathrm{E}= \)
(ii) The probability of an event that cannot happen is

Such an
event is called
(iii) The probability of an event that is
certain to happen is

Such an
event is called
(iv) The sum of the probabilities of all
the elementary events of an experiment
is
(v) The probability of an event is greater than or equal to and less than
or equal to
Subject: Physics
A force \( \overrightarrow{\boldsymbol{F}}=(3 \boldsymbol{t} \hat{\boldsymbol{i}}+\boldsymbol{5} \hat{\boldsymbol{j}}) \) N acts on a
particle whose position vector varies as \( \vec{S}=\left(2 t^{2} \hat{i}+5 \hat{j}\right) \mathrm{m}, \) where \( t \) is time in
seconds. The work done by this force
from \( t=0 \) to \( t=2 s \) is:
A . 23 J
B. 32 J
c. zero
D. can't be obtained
Subject: Maths
ABCD is a trapeziumin which AB is parallel to DC. If the diagonals intersect at \( 0, \) then which one of the following is
correct?
A \( \cdot \frac{O A}{O C}=\frac{O B}{O D} \)
в. \( \frac{A D}{B C}=\frac{A B}{D C} \)
c. \( \frac{O B}{O D}=\frac{B C}{C D} \)
D. \( \frac{O A}{O C}=\frac{D A}{D C} \)
Subject: Maths
Show that the four points \( A, B, C, D \) with position vectors \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) respectively such that \( 3 \vec{a}-2 \vec{b}+5 \vec{c}-6 \vec{d}=\overrightarrow{0}, \) are
coplanar. Also find the position vector of the point of intersection of the line
segments \( A C \) and \( B D \)
Subject: Physics
An rms voltage of \( 110 \mathrm{V} \) is applied across a series circuit having a resistance \( 11 \Omega \) and an impedance
\( 22 \Omega . \) The power consumed is
A \( .275 ~ W \)
в. \( 366 \mathrm{W} \)
\( c .550 W \)
D. \( 1100 W \)
Subject: Physics
If the mean free-path of gaseous
molecule is \( 60 \mathrm{cm} \) at a pressure of \( 1 \times \)
\( 10^{-4} \mathrm{mm} \) mercury, what will be its
mean free-path when the pressure is
increased to \( 1 \times 10^{-2} \mathrm{mm} \) mercury?
A \( \cdot 6.0 \times 10^{-1} \mathrm{cm} \)
B. \( 6.0 \mathrm{cm} \)
\( \mathbf{c} \cdot 6.0 \times 10^{-2} \mathrm{cm} \)
D. \( 6.0 \times 10^{3} \mathrm{cm} \)
Subject: Physics
Two astronauts, each of mass \( 75 k g \), are
floating next to each other in space, outside the space shuttle. They push each other through a distance of an arm's length \( =1 m \) each with a force of
\( 300 N \).If the final relative velocity of the
two, w.r.t each other is \( V_{0} m / s, \) find the value of \( \frac{\left(V_{0}\right)^{2}}{4}( \) Note that both astronauts are displaced by \( 1 \boldsymbol{m} \)
Subject: Chemistry
\( 40 \% \) of a mixture of 0.2 mole of \( N_{2} \) and
0.6 mole of \( H_{2} \) react to give \( N H_{3} \)
according to the equation, \( N_{2}(g)+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}) \) at constant
temperature and pressure. Then the
ratio of the final volume to the initial
volume of gases are:
A . 4: 5
B. 5: 4
c. 7: 10
D. 8: 5
Subject: Physics
The kinetic energy of \( 1 g \) molecule of a
gas at normal temperature and
pressure is :
\( \mathbf{A} \cdot 1.3 \times 10^{2} J \)
B . \( 2.7 \times 10^{2} J \)
c. \( 0.56 \times 10^{4} J \)
D. \( 3.4 \times 10^{3} J \)
Subject: Physics
Let there be a spherically symmetric
charge distribution with charge density \( \operatorname{varying} \operatorname{as} \rho(r)=\rho_{0}\left(\frac{5}{4}-\frac{r}{R}\right) \) upto \( r= \)
\( R, \) and \( \rho(r)=0 \) for \( r>R, \) where \( r \) is
the distance from the origin. Find the
electric field at a distance \( r(r<R) \)
from the origin.
A \( \cdot \frac{3 \rho_{0} r}{4 \epsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right) \)
В \( \cdot \frac{4 \rho_{0} r}{3 \epsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right) \)
C \( \cdot \frac{\rho_{0} r}{4 \epsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right) \)
D. \( \frac{3 \rho_{0} r}{4 \epsilon_{0}}\left(\frac{5}{4}-\frac{r}{R}\right) \)
Subject: Physics
A particle covers \( 150 \mathrm{m} \) in 8 thsecond
starting from rest, its acceleration is:
A \( \cdot 15 m / s^{2} \)
B. \( 20 m s^{2} \)
c. \( 10 m / s^{2} \)
D. \( 8 m / s^{2} \)
Subject: Physics
3
incident at an angle \( \alpha=30^{\circ} \) with the
normal to the slit plane in Young's double-slit experiment. Assume that
the intensity due to each slit at any
point on the scree is \( I_{0} . \) Point \( O \) is
equidistant from \( S_{1} \) and \( S_{2} \). The
distance between slits is 1 mm. Then
This question has multiple correct options
A. the intensity at \( O \) is \( I_{0} \)
B. the intensity at \( O \) is zero
C. the intensity at a point on the screen \( 1 m \) below \( O \) is \( I_{0} \)
D. the intensity at a point on the screen \( 1 m \) below \( O \) is
zero
Subject: Physics
\( A B C D \) is a quadrilateral. Forces \( \overrightarrow{B A}, \overrightarrow{B C}, \overrightarrow{C D} \) and \( \overrightarrow{D A} \) act at a point. Their resultant is:
A \( \cdot 2 A B \)
B. \( 2 D A \)
c. zero vector
D. \( 2 \overrightarrow{B A} \)
Subject: Maths
The point \( P(x, y, z) \) lies in the first octant and its distance from the origin
is 12 units. If the position vector of \( P \)
make \( 45^{\circ} \) and \( 60^{\circ} \) with the \( x \) -axis and \( y \)
axis respectively, then the coordinates of \( \boldsymbol{P} \) are
A \( \cdot(3 \sqrt{3}, 6,3 \sqrt{2}) \)
B. \( (4 \sqrt{3}, 8,4 \sqrt{2}) \)
c. \( (6 \sqrt{2}, 6,6,) \)
D. \( (6,6,6 \sqrt{2}) \)
E \( .(4 \sqrt{2}, 8,4 \sqrt{3}) \)
Subject: Chemistry
Assertion
Energy of electron in 1st orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) is
more than that in Hydrogen atom.
Reason
Nuclear charge is more in \( H e^{+} \) than in
Hydrogen.
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
A slit of width \( a \) is illuminated by white
light. The first minimum for red light \( (\lambda \)
\( =6500 A) \) will fall at \( \theta=30^{\circ} \) when \( a \) will
be
A \( \cdot \) з250 \( \stackrel{\circ}{A} \)
B. \( 6.5 \times 10^{-4} \)
c. 1.3 micron
D. \( 2.6 \times 10^{-4} \)
Subject: Maths
| vidnu nas decided to create a triangular
flower bed border. He plans to use 3
pieces of rectangular wooden plates
with lengths 4,5 and 6 feet, as shown in
the figure.

Manu plans to cut the 3 pieces of plate for the flower bed border from a single
piece of plate. If \( \frac{1}{8} \) inch wood is wasted
in every cut, calculate the shortest
single piece of plate which can be used
by Manu.
A . 178
B. 179
c. 180
D. 181
E . 182
Subject: Chemistry
Consider the reaction equilibrium Ice\( \rightleftharpoons_{\text {Lesservier}}-\boldsymbol{X k c a l} \)
Greatervolume
The favourable condition for forward
reaction are:
A. low temperature, high pressure and excess of ice
B. low temperature, low pressure and excess of ice
c. high temperature, low pressure and excess of ice
D. high temperature, high pressure and excess of ice
Subject: Chemistry
Select the most ionic and most covalent
compounds respectively from the following.
\( \boldsymbol{C r} \boldsymbol{O}_{5}, \boldsymbol{M n}_{2} \boldsymbol{O}_{7}, \boldsymbol{P b O}, \boldsymbol{P}_{4} \boldsymbol{O}_{10}, \boldsymbol{S n O}_{2} \)
A. \( C r O_{5}, M n_{2} O_{7} \)
в. \( P b O, M n_{2} O_{7} \)
\( \mathrm{c} \cdot \mathrm{Cr} \mathrm{O}_{5}, P_{4} \mathrm{O}_{1} \)
D. \( S n O_{2}, C r O_{5} \)
Subject: Chemistry
The equilibrium constant for the reaction \( N_{2}(g)+O_{2}(g) \leftrightharpoons 2 N O(g) \) is
\( 4 \times 10^{-4} \) at \( 2000 \mathrm{K} . \) In the presence of a
catalyst, the equilibrium is attained three times faster. The
equilibrium constant in the presence of the catalyst at \( 2000 \mathrm{K} \) is:
A. \( 40 \times 10^{-4} \)
B. \( 4 \times 10^{-4} \)
c. \( 4 \times 10^{-3} \)
D. \( 4 \times 10^{-8} \)
Subject: Maths
The value of \( \lim _{x \rightarrow 0} \frac{(1+x)^{1 / 4}-(1-x)^{1 / 4}}{x} \)
is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-1 \)
D. \( -\frac{1}{2} \)
Subject: Physics
\( 42000 J \) of heat energy is supplied to \( 175 g \) of iron at \( 30^{\circ} C, \) when the final temperature recorded is \( 430^{\circ} . \) Calculate
specific heat capacity of iron
A \( \cdot 600 J g^{-1} \circ C^{-1} \)
B. \( 0.6 J g^{-1} \) о \( C^{-1} \)
c. \( 60 J g^{-1} \) о \( C^{-1} \)
D. \( 6 J g^{-1} \) о \( C^{-1} \)
Subject: Physics
An object \( 2.4 ~ m \) in front of a lens forms
a sharp image on a film \( 12 \mathrm{cm} \) behind
the lens. A glass plate \( 1 \mathrm{cm} \) thick of
refractive index 1.50 is interposed between lens and film with its plane
faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?
\( \mathbf{A} \cdot 7.2 m \)
B. \( 2.4 m \)
c. \( 3.2 m \)
D. \( 5.6 m \)
Subject: Maths
If \( 0<A<\frac{\pi}{6} \) then \( A(\csc A) \) is:
\( A \cdot<\frac{\pi}{3} \)
в. \( >\frac{\pi}{3} \)
\( c \cdot=\frac{\pi}{3} \)
D. \( =\frac{\pi}{6} \)
Subject: Physics
In a series resonant circuit, the AC voltage across resistance \( R, \) inductor and capacitor \( C \) are \( 5 \vee, 10 \vee \) and \( 10 ~ V \) respectively. The AC voltage applied to the circuit will be
A . \( 10 v \)
B. 25
\( c \cdot 5 v \)
D. 20
Subject: Maths
The hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) passes
through the point \( (\sqrt{6}, 3) \) and the length
of the latusrectum is \( \frac{18}{5} . \) Then, the
length of the transverse axis is equal to
A . 5
B. 4
\( c \cdot 3 \)
D. 2
E . 1
Subject: Physics
\( |\overline{\mathbf{a}} \cdot \overline{\mathbf{b}}|^{2}-|\overline{\mathbf{a}} \times \overline{\mathbf{b}}|^{2}= \)
\( \mathbf{A} \cdot a b \cos \theta \)
B \( \cdot a^{2} b^{2} \cos \theta \)
C \( \cdot a^{2} b^{2} \cos 2 \theta \)
\( \mathbf{D} \cdot a b \cos 2 \theta \)
Subject: Chemistry
Atomic radius is of the order of \( 10^{-8} \mathrm{cm} \)
and nuclear radius is of the order of
\( 10^{-13} \mathrm{cm} . \) The fraction of atom occupied
by nucleus is:
A \( \cdot 10^{-5} \)
B . \( 10^{5} \)
\( \mathbf{c} \cdot 10^{-15} \)
D. none of these
Subject: Maths
Find the converse of the statement,"If
ABCD is square, then it is a rectangle".
\( A . \) If \( A B C D \) is a square, then it is .not a rectangle.
B. If \( A B C D \) is not a square, then i is a rectangle.
C. if ABCD is a rectangle, then it is square.
D. If \( A B C D \) is not a square, then it is not a rectangle.
Subject: Physics
A closed copper vessel contains water equal to half of its volume when the
temperature. Of the vessel is raised to
\( 447^{0} \mathrm{cthe} \) pressure of steam in the vessel
is (Treat steam as an ideal gas, \( \mathrm{R}=8310 \) \( \mathrm{J} / \mathrm{k} / \mathrm{mole}, \) density of water \( =1000 \mathrm{kg} / \mathrm{m}^{3} \)
molecular weight of water \( =18 \) )
\( A \cdot 33.24 \times 10^{7} \mathrm{pa} \)
B . 16.62 x 10 \( ^{7} \) pa
c. \( 10.31 \times 10^{7} \mathrm{pa} \)
D. \( 8.31 \times 10^{7} \mathrm{pa} \)
Subject: Physics
An ice cream truck travels around many circular curves at constant speeds.
Each table represents the speed of the truck and radii for some of these curves
During which curve is the magnitude of the truck's acceleration the greatest??
A. Radius of curve - Speed of Truck, \( 30 \mathrm{m}-5 \mathrm{m} / \mathrm{s} \)
B. Radius of curve - Speed of Truck, \( 60 \mathrm{m}-10 \mathrm{m} / \mathrm{s} \)
c. Radius of curve - Speed of Truck, \( 90 \mathrm{m}-15 \mathrm{m} / \mathrm{s} \)
D. Radius of curve - speed of Truck, \( 120 \mathrm{m}-20 \mathrm{m} / \mathrm{s} \)
E. The magnitude of the acceleration for the ice cream truck on all these curves is the same
Subject: Chemistry
a. Caprolactum\( \stackrel{\text {hydrolysis}}{ } \boldsymbol{A} \)
b. \( \boldsymbol{A}+\boldsymbol{G} \) lycine \( \rightarrow \boldsymbol{B}(\text { Polymer }) \)
Here, \( \boldsymbol{B} \) is :
I. Condensation Polymer
II. Addition Polymer
III. Polyamide Polymer
IV. Polyester Polymer
V. Biodegradable Polymer
A . I, III, v are corect
B. II, IV are correct.
c. ॥, ॥ा, IV are correct.
D. II, IV, V are correct.
Subject: Chemistry
Hydrogen chloride and \( S O_{2} \) are the side products in the reaction of ethanol with thionyl chloride. Which of the following is main product in this reaction?
A. \( C_{2} H_{5}-O-C_{2} H_{5} \)
в. \( C_{2} H_{6} \)
c. \( C H_{3} C l \)
D. \( C_{2} H_{5} C l \)
Subject: Physics
A ball moving with a speed \( v \) hits a
massive wall and returns with speed \( v \)
The impact lasts for time \( \Delta t, \) then
which of the following are correct:
This question has multiple correct options
A . average force acting on the ball is \( \frac{2 m v}{\Delta t} \)
B. average force acting on the ball is \( \frac{m v}{\Delta t} \)
c. kinetic energy of the ball becomes twice
D. kinetic energy of the ball remains the same
Subject: Physics
\( 40 g \) of ice at \( 0^{\circ} C \) is used to bring down
the temperature of certain mass of
water at \( 60^{\circ} \mathrm{C} \) to \( 10^{\circ} \mathrm{C} \). Find the mass
of water used.
[Specific heat capacity of water \( = \) \( 4200 J K g^{-1} C^{-1} \)
[Specific latent heat of fusion of ice \( = \)
\( \left.336 \times 10^{3} J k g^{-1}\right] \)
Subject: Chemistry
For the non-equilibrium process, \( \boldsymbol{A}+ \) \( B \rightarrow \) Products, the rate is first order
with respect to \( A \) and second-order with
respect to \( B \). If 1.0 mole each of \( A \) and
\( B \) are introduced into a 1 -litre vessel
and the initial rate was \( 1.0 \times 10^{-2} \)
mol/litre-sec. The rate (in mol
litre \( ^{-1} \) sec \( ^{-1} \) ) when half of the reactants
have been used:
A \( \cdot 1.2 \times 10^{-3} \)
В. \( 1.2 \times 10^{-2} \)
c. \( 2.5 \times 10^{-4} \)
D. none of these
Subject: Chemistry
Assertion
\( \beta \) -particles are deflected more than \( \alpha \) particles in a given electric field.
Reason
Charge on \( \alpha \) -particles is larger than on
\( \beta \) -particles.
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 the Reason is correct
Subject: Maths
Which square must be shaded so that
the figure has a line of symmetry?
\begin{tabular}{|l|l|l|l|}
\hline & & & \\
\hline & \( \mathbf{R} \) & & \\
\hline & \( \mathbf{P} \) & & \( \mathbf{Q} \) \\
\hline & & & \( \mathbf{S} \) \\
\hline
\end{tabular}
\( A \cdot P \)
в. \( Q \)
\( c . R \)
D.
Subject: Physics
An angled vector is shown in the
diagram above. What is the correct way to calculate the magnitude the
component of this vector in the \( x \)
direction?
\( \mathbf{A} \cdot 50 \times \sin (20) \)
B. \( 50 \times \cos (20) \)
\( \mathbf{c} \cdot 50 \div \sin (20) \)
D. \( 50 \div \cos (20) \)
Subject: Physics
When \( 1 g \) of water \( \operatorname{at} 0^{\circ} C \) and \( 1 \times \) \( 10^{5} N / m^{2} \) pressure is converted into
ice of volume \( 1.091 \mathrm{cm}^{3} \), the external
work done will be:
A. 0.0091 joule
B. 0.0182 joule
c. -0.0091 joule
D. - 0.0182 joule
Subject: Chemistry
Conductance of \( \boldsymbol{A l}^{+\mathbf{3}} \) is \( \boldsymbol{x} \boldsymbol{S} \boldsymbol{m}^{2} \boldsymbol{g} \boldsymbol{e q}^{-1} \)
and that of \( S O_{4}^{-2} \) is \( y S m^{2} g e q^{-1} . \) Molar conductance of Aliminium sulphate is \( \boldsymbol{S m}^{2} \boldsymbol{m} \boldsymbol{o l} \boldsymbol{e}^{-1} \)
A. \( \frac{x+y}{6} \)
B. \( x+y \)
c. \( 6(x+y) \)
D. \( 2 x+3 y \)
Subject: Maths
f \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{5}\end{array}\right] \) then \( \boldsymbol{A}+\boldsymbol{B} \)
Subject: Physics
A charge \( +q \) is placed at the origin 0 of
\( X-Y \) axes as shown in the figure. The
work done in taking a charge \( Q \) from \( A \)
to B along the straight line AB is:
A \( \cdot \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{a-b}{a b}\right) \)
В \( \cdot \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{b-a}{a b}\right) \)
c. \( \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{b}{a^{2}}-\frac{1}{b}\right) \)
D. \( \frac{q Q}{4 \pi \epsilon_{0}}\left(\frac{a}{b^{2}}-\frac{1}{b}\right) \)
Subject: Physics
The change in emitter current by \( 2.1 \mathrm{mA} \) results in change of \( 2 \mathrm{mA} \) in the collector current and a change of \( 0.05 V \) in the emitter base voltage. The input resistance is
A . \( 5 K \Omega \)
в. зкл
c. 1 К \( \Omega \)
D. 0.5к.
Subject: Physics
A right angled tube is fixed horizontally on a horizontal surface and an ideal
liquid of density p is flowing into the
tube at the rate of \( Q=4 m^{3} / s \) Cross
sectional area of the tube at intake and
outlet positions are \( A=2 m^{2} \) and \( S= \)
\( 1 m^{2} \) respectively. The magnitude of net
force exerted by liquid on the tube is (Given that the value of atmospheric
pressure \( \left.P_{o}=4 p N / m^{2}\right) \)
\( \mathbf{A} \cdot 3 \sqrt{12} p \)
B. \( 4 \sqrt{41} p \)
c. \( 5 \sqrt{21} p \)
D. None of there
Subject: Physics
A body is moving in a circle with a speed of \( 1 m s^{-1} . \) This speed increases
at a constant rate of \( 2 m s^{-1} \) every second. Assume that the radius of the
circle described is 25 m. The total
acceleration of the body after \( 2 s \) is:
\( \mathbf{A} \cdot 2 m s^{-2} \)
B. \( 25 m s^{-2} \)
c. \( \sqrt{5} m s^{-2} \)
D. \( \sqrt{7} m s^{-2} \)
Subject: Maths
In the given figure, \( \ln \Delta P Q R \quad X Y \| \)
\( Q R, P X: Q X=1: 3 Y R=4.5 \mathrm{cm} \) and \( Q R=9 \)
\( \mathrm{cm} . \) Find \( \mathrm{XY} \). Further if \( \operatorname{ar}(\Delta P X Y)=A \)
\( c m^{2}, \) find in terms of \( A \) the area of
\( \Delta P Q R \) and the area of trapezium
XYRQ.
Subject: Physics
An AC voltage source \( V=V_{0} \sin \omega t \) is
connected across resistance \( \mathrm{R} \) and
capacitance \( C \) as shown in figure. It is given that \( R=\frac{1}{\omega C} . \) The peak current is
\( I_{0} . \) If the angular frequency of the
voltage source is changed to \( \frac{\omega}{\sqrt{3}} \)
keeping \( R \) and \( C \) fixed, then the new peak current in the circuit is:
A \( \cdot \frac{I_{0}}{2} \)
в. \( \frac{I_{0}}{\sqrt{2}} \)
c. \( \frac{I_{0}}{\sqrt{3}} \)
D. \( \frac{I_{0}}{3} \)
Subject: Chemistry
The latent heat of fusion of ice is 80
calories per gram at \( 0^{\circ} \) C. What is the
freezing point of a solution of KCl in water containing 7.45 grams of solute 500 grams of water, assuming that the salt is dissociated to the extent of \( 95 \% ? \)
\( \mathbf{A} \cdot T_{f}=-0.73^{\circ} \mathrm{C} \)
B. \( T_{f}=-0.92^{\circ} \mathrm{C} \)
c. \( T_{f}=-1.46^{\circ} \mathrm{C} \)
\( \mathbf{D} \cdot T_{f}=-1.84^{\circ} \mathrm{C} \)
Subject: Maths
ff \( \left[\begin{array}{ll}\boldsymbol{x} & \mathbf{0} \\ \mathbf{1} & \boldsymbol{y}\end{array}\right]+\left[\begin{array}{cc}-\mathbf{2} & \mathbf{1} \\ \mathbf{3} & \mathbf{4}\end{array}\right]=\left[\begin{array}{ll}\mathbf{3} & \mathbf{5} \\ \mathbf{6} & \mathbf{3}\end{array}\right]- \)
\( \left[\begin{array}{ll}2 & 4 \\ 2 & 1\end{array}\right], \) then
A. \( x=-3, y=-2 \)
в. \( x=3, y=-2 \)
c. \( x=3, y=2 \)
D. \( x=-3, y=2 \)
Subject: Chemistry
Electrolysis of sea-water produces
\( C l_{2}(g) \) at the anode by the oxidation of
Cl (aq) ions. What volume of the gas will be produced at STP by current of \( 1.50 \mathrm{A} \) applied for 90.0 minutes?
B. 0.548 L
c. \( 0.94 \mathrm{L} \)
D. 0.470 L
Subject: Physics
A gun of mass M fires a bullet of mass \( \mathrm{m} \) with a velocity v relative to the gun. The average force required to bring the gun to rest in 0.5 sec. is
A \( \cdot \frac{2 M m V}{m+M} \)
в. \( \frac{M m V}{2(M+m)} \)
c. \( \frac{3 M m V}{2(M+m)} \)
D. \( \frac{M m V}{(M+m)} \)
Subject: Physics
A radioactive element decays by parallel path as given below:
\( \boldsymbol{A} \stackrel{\lambda_{1}}{\longrightarrow} \boldsymbol{B} \quad \boldsymbol{\lambda}_{1}=\mathbf{1 . 8} \times \mathbf{1 0}^{-2} \boldsymbol{s e c}^{-1} \)
\( \mathbf{2 A} \stackrel{\lambda_{2}}{\longrightarrow} \boldsymbol{B} \quad \boldsymbol{\lambda}_{2}=\mathbf{1 0}^{-\mathbf{3}} \boldsymbol{s e c}^{-\mathbf{1}} \)
Average life of radio-nuclide \( \boldsymbol{A} \) will be:
A .52 .63 sec
B. 500 sec
c. 50 sec
D. 120 sec
Subject: Maths
\( \lim _{n \rightarrow \infty}\left[\frac{1}{n^{2}} \sec ^{2} \frac{1}{n^{2}}+\frac{2}{n^{2}} \sec ^{2} \frac{4}{n^{2}}+\ldots+\frac{1}{r}\right. \)
A \( \cdot \frac{1}{2} \sec 1 \)
B \( \cdot \frac{1}{2} \csc 1 \)
\( c . \tan 1 \)
D. \( \frac{1}{2} \tan \)
Subject: Biology
Which combination is used in fruit
ripening?
A. \( 80 \% C H_{4}+20 \% O_{2} \)
в. \( 80 \% C_{2} H_{4}+20 \% \mathrm{CO}_{2} \)
c. \( 80 \% \mathrm{CO}_{2}+20 \% \mathrm{C}_{2} \mathrm{H}_{4} \)
D. \( 80 \% C H_{4}+20 \% C O_{2} \)
Subject: Maths
n fig, then \( \angle A+\angle B+\angle C+\angle D+ \)
\( \angle \boldsymbol{E}+\angle \boldsymbol{F}= \)
A \( \cdot 180^{\circ} \)
B. \( 270^{\circ} \)
\( c .360^{\circ} \)
D. \( 540^{\circ} \)
Subject: Chemistry
0.5 mole of \( H_{2} S O_{4} \) is mixed with 0.2
mole of \( \boldsymbol{C a}(\boldsymbol{O H})_{2} . \) The maximum
number of moles of \( \boldsymbol{C} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \) formed is:
A. 0.2
B. 0.5
\( c \cdot 0.4 \)
D. 1.5
Subject: Chemistry
Phosphorus trichloride, \( \boldsymbol{P} \boldsymbol{C l}_{3} \) undergoes hydrolysis to produce an oxoacid. The formula of oxoacid is :
A \( . H P O_{3} \)
в. \( H_{3} P O_{3} \)
\( \mathrm{c} \cdot H_{3} P O_{4} \)
D. \( H_{3} P O_{2} \)
Subject: Physics
Three charges \( Q,+q \) and \( +q \) are placed
at the vertices of a right-angled
isosceles triangle as shown.The net
electrostatic energy of the
configuration is zero if \( Q \) is equal to :
A \( \cdot \frac{-q}{1+\sqrt{2}} \)
B. \( \frac{-2 q}{2+\sqrt{2}} \)
\( c \cdot-2 q \)
\( D \cdot+a \)
Subject: Maths
Evaluate: \( \int(\boldsymbol{P}+\boldsymbol{Q}) \boldsymbol{d} \boldsymbol{x} \)
\( \mathbf{A} \cdot \int P d x+\int Q d x \)
в. \( \int P d x+Q+C \)
c. \( \int P d x-\int Q d x \)
D. None of the above