AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Draw a neat, labelled energy level diagram for H atom showing the transitions. Explain the series of spectral lines for H atom, whose fixed
inner orbit numbers are 3 and 4
respectively. The work functions for potassium and caesium are \( 2.25 \mathrm{eV} \) and
2.14eV respectively. Is the photoelectric effect possible for either of them if the
incident wavelength is \( 5180 A ? \) [Given: Planck's constant= 6.63 \( x \)
\( 10^{-34} \mathrm{J}_{. \mathrm{S}} \)
Velocity of light \( =3 \times 10^{8} m / s ; 1 e V= \)
\( \left.\mathbf{1} . \mathbf{6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{J}\right] \)
Subject: Chemistry
Assertion
The gases exert pressure.
Reason
Molecules exert pressure when they
collide with the walls of the container in
which they are taken.
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: Chemistry
Assertion
An endothermic reaction has a positive \( \Delta H \) value because
Reason
In an endothermic reaction, the total
enthalpy (heat content) of the products
is greater than that of the reactants.
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 \( 1 \mathrm{kg} \) block situated on a rough incline is connected to a spring of spring constant 100Nm-1100Nm-1 as shown
The block is released from rest with the
spring in the unstretched position. The
block moves \( 10 \mathrm{cm} \) down the incline
before coming to rest. Find the
coefficient of friction between the block
and the incline. Assume that the spring
has a negligible mass and the pulley is frictionless.
Subject: Maths
Find the shortest distance between the line \( \frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1} \) and the
line of intersection of the planes \( 2 x+ \)
\( 5 y-z+47=0 \) and \( 2 x+y+z+7= \)
\( \mathbf{0} \)
Subject: Chemistry
Assertion: Alcohols on dehydration can produce ether as well as alkene under different conditions.
Reason: Dehydration of alcohol proceeds through the formation of carbonium ion.
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Physics
A body is released from the top of the tower of height \( \boldsymbol{H} \). It takes \( \boldsymbol{t} \) time to reach the ground. The position of body \( \frac{t}{2} \)
time after release will be
A. at \( \frac{H}{2} \) metres from ground
B. at \( \frac{H}{4} \) metres from ground
c. at \( \frac{3 H}{4} \) metres from the ground
D. \( a t \frac{H}{6} \) metres from the ground
Subject: Maths
A plane meets the axes in \( A, B \) and \( C \)
such that centroid of the \( \triangle A B C \) is
\( (1,2,3) . \) The equation of the plane is
A \( \cdot x+\frac{y}{2}+\frac{z}{3}=1 \)
В \( \cdot \frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1 \)
c. \( x+2 y+3 z=1 \)
D. None of these
Subject: Maths
If \( A=\tan ^{-1} \frac{1}{7} \) and \( B=\tan ^{-1} \frac{1}{3} \) then
This question has multiple correct options
A \( \cdot \cos 2 A=\frac{24}{25} \)
B. \( \cos 2 B=\frac{4}{5} \)
c. \( \cos 2 A=\sin 4 B \)
D. \( \tan 2 B=\frac{3}{4} \)
Subject: Physics
The force of a required to row a boat at velocity is proportional to square of its speed of \( \mathbf{v} \mathrm{km} / \mathrm{h} \) requires \( 4 \mathrm{KW}, \) how many does a seepd of \( 2 \mathrm{V} \mathrm{km} / \mathrm{h} \) required
\( A \cdot 8 \mathrm{kW} \)
B. 16 kw
c. з२кw
D. 76kw
Subject: Maths
If \( g \) is the inverse function of \( f \) and \( f^{\prime}(x)=\frac{1}{1+x^{n}}, \) then \( g^{\prime}(x) \) is equal to
A \( \cdot 1+[g(x)]^{n} \)
в. \( 1-g(x) \)
c. \( 1+g(x) \)
D \( \cdot-g(x)^{n} \)
Subject: Chemistry
Ethylenediamine displaces \( H_{2} O \) in the
complex \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \) in three steps.
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+}+\boldsymbol{3} \boldsymbol{e n} \rightarrow\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{e n})_{3}\right]^{3+}+ \)
\( 6 H_{2} O \)
Stepwise formation constants are:
\( \log K_{1}=4.34 \)
\( \log K_{2}=3.31 \)
\( \log K_{3}=2.05 \)
Overall formation constant is \( \boldsymbol{A} \times \mathbf{1 0}^{\mathbf{2 B}} \)
\( B \) in question is:
Subject: Chemistry
Calculate the emf of the following
concentration cell at \( 25^{\circ} C \)
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \mid \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\mathbf{0} . \boldsymbol{0} \mathbf{1} \boldsymbol{M}) \)
\( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{0} . \boldsymbol{0} \boldsymbol{5} \boldsymbol{M}) \mid \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
A. \( -0.414 V \)
в. \( 0.828 V \)
c. \( 0.414 V \)
D. \( 0.0414 V \)
Subject: Chemistry
For which of the following reaction
\( \Delta \boldsymbol{H} \neq \Delta \boldsymbol{U}: \)
\( \mathbf{A} \cdot H_{2}(g)+C l_{2}(g) \rightarrow 2 H C I(g) \)
B. \( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
\( \mathbf{c} \cdot N H_{4} H S(s) \rightarrow N H_{3}(g)-H_{2} S(g) \)
D \( \cdot \operatorname{CaCO}_{3}(s) \rightarrow \operatorname{CaO}(s)+C O_{2}(g) \)
Subject: Chemistry
Enthalpy of formation of \( \boldsymbol{C}_{2} \boldsymbol{H}_{\mathbf{6}}= \)
\( -83 k J / m o l \)
Enthalpy of sublimation of graphite = \( \mathbf{7} 19 k J / m o l \)
Enthalpy of bond dissociation of \( \boldsymbol{H}_{2}= \) \( 435 k J / m o l \)
\( \mathrm{C}-\mathrm{H} \) bond enthalpy \( =414 k J / m o l \)
Calculate the bond enthalpy of \( C-C \)
Subject: Chemistry
The heat released in the neutralisation
of HCl and NaOH is 13.7 kcal/mol, the
heat
released on neutralisation of NaOH with
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) is 3.7 kcal/mol.
The \( \Delta H \) of ionisation of \( C H_{3} C O O H \)
is:
A. 10.2 kcal
B. 10 kcal
c. 3.7 kcal
D. 9.5 kcal
Subject: Chemistry
Fill in the blank.
If \( 100 \mathrm{mL} \) of \( S O_{2} \) solution requires 50 \( \mathrm{mL} \) of \( 0.01 \mathrm{M} C r_{2} O_{7}^{2-} \) in acidic
medium, then \( S O_{2} \) solution is
\[
\mathbf{1 0}^{-\mathbf{3}} \mathbf{M}
\]
Subject: Chemistry
Type of isomerism shown by
\( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{N} \boldsymbol{O}_{2}\right] \boldsymbol{C l}_{2} \) is
A. optical
B. ionisation
c. geometrical
D. linkage
Subject: Chemistry
A saturated solution of iodine in water
contains \( 0.33 \mathrm{g} \) iodine/L. More than this can dissolve in a \( K I \) solution because
of the following equilibrium: \( \boldsymbol{I}_{2}(\boldsymbol{a} \boldsymbol{q})+ \) \( \boldsymbol{I}^{-} \rightarrow \boldsymbol{I}_{3}-(\boldsymbol{a} \boldsymbol{q}) \cdot \mathbf{A} \mathbf{0} \cdot \mathbf{1} \boldsymbol{M} \boldsymbol{K} \boldsymbol{I} \) solution
\( \left(0.1 M I^{-}\right) \) actually dissolves 12.5 g of lodine/L, most of which is converted to
\( I_{3}^{-} . \) Assuming that the concentration of
\( I_{2} \) in all saturated solutions is the
same, calculate the equilibrium constant for the above reaction: (Mol. wt
of \( I=258 g m o l^{-1} \)
A. 709.3
B . 465.6
c. 287.4
D. 687.4
Subject: Chemistry
\( 40 \mathrm{ml} \) of ammonia gas was taken in a eudiometer tube and subjected to sparks till the volume did not further
change. The volume was found to increase by \( 40 \mathrm{ml} .40 \mathrm{ml} \) of oxygen gas then mixed and the mixture was further
exploded. The gases remaining were 30
ml. Deduce the formula of ammonia.
(Ammonia contains \( N \) and \( H \) only)
Subject: Physics
In the adjoining diagram,a wavelength
AB, moving in air is incident on a plane
glass surface XY. Its position CD after
refraction through a glass slab is shown also along with the normals drawn at \( A \)
and D. The refractive index of glass with
respect to air \( (\mu=1) \) will be equal to
A. \( \frac{\sin \theta}{\sin \theta^{\prime}} \)
B. \( \frac{\sin \theta}{\sin \phi^{\prime}} \)
c. \( \frac{\sin \phi^{\prime}}{\sin \theta} \)
\( D \)
Subject: Physics
Assertion
Static friction is a self adjusting force.
Reason

Coefficient of friction does not depend
upon mass of the body.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
The point which is equidistant from the points \( (\boldsymbol{a}, \boldsymbol{0}, \boldsymbol{0}),(\boldsymbol{0}, \boldsymbol{b}, \boldsymbol{0}),(\boldsymbol{0}, \boldsymbol{0}, \boldsymbol{c}) \) and
(0,0,0) is:
\( \mathbf{A} \cdot(a, b, c) \)
B . \( (\sqrt{a}, \sqrt{b}, \sqrt{c}) \)
c. \( (2 a, 2 b, 2 c) \)
D. \( \left(\frac{a}{2}, \frac{b}{2}, \frac{c}{2}\right) \)
Subject: Physics
If \( m_{2} \) again comes down and collides
with \( m_{1}, \) then after the collision:
\( \mathbf{A} \cdot m_{1} \) will rise the same height as risen by \( m_{2} \)
B. \( m_{1} \) will rise the less height as risen by \( m_{2} \)
\( \mathrm{C} \cdot m_{1} \) will rise the more height as risen by \( m_{2} \)
D. \( m_{1} \) and \( m_{2} \) will more in opposite directons
Subject: Physics
An electric heater which is connected to
a \( 220 \mathrm{V} \) supply line has two resistance
coils. \( A \) and \( B \) of \( 24 \Omega \) resistance each.
these coils can be used separately (one at a time), in series or in parallel.
calculate the current drawn when:
Only one coil A is used
coils \( A \) and \( B \) are used in series
Subject: Chemistry
In the reaction, \( 4 C r O_{5}+6 H_{2} S O_{4} \rightarrow \)
\( 2 C r_{2}\left(S O_{4}\right)_{3}+6 H_{2} O+7 O_{2}, \) which
statement is wrong?
A. It is a disproportionation reaction.
B. It is an intramolecular redox reaction
c. \( C r O_{5} \) acts as oxidant and reductant both.
D. cracts as oxidant and 0 acts as reductant
Subject: Chemistry
Density of a gas is found to be 5.46 \( \mathrm{gm} / \) lit at \( 27^{\circ} \mathrm{C} \) and 2 atm pressure. what will be its density at STP?
A. 3 gm/lit
B. 2 gm/lit
c. \( 1.5 \mathrm{gm} / \) lit
D. \( 1 \mathrm{gm} / \) lit
Subject: Physics
One litre of Helium gas at a pressure of 76
\( \mathrm{cm}-\mathrm{Hg} \) and temperature \( 27^{0} \mathrm{C} \) is heated till its pressure and volume are doubled. The final temperature attained by the gas is
A \( \cdot 900^{0} \mathrm{C} \)
B . \( 927^{\circ} \mathrm{C} \)
c. \( 627^{\circ} \mathrm{C} \)
D. 327 \( ^{0} \mathrm{c} \)
Subject: Physics
Assertion
Two different planets can have same escape velocity when their masses and
diameter are same.
Reason
Escape velocity is given as \( \sqrt{2 g R} \)
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 length of the largest side of a triangle is \( 12 \mathrm{cm} \) then other two sides of triangle
can be :
\( A \cdot 4.8 \mathrm{cm}, 8.2 \mathrm{cm} \)
B. 3.2 \( \mathrm{cm}, 7.8 \mathrm{cm} \)
c. \( 6.4 \mathrm{cm}, 2.8 \mathrm{cm} \)
D. \( 7.6 \mathrm{cm}, 3.4 \mathrm{cm} \)
Subject: Physics
The ratio of the concentration of electrons to that of holes in a semiconductor is \( \frac{7}{4}, \) then what is the ratio of their drift velocities:
A \( \cdot \frac{5}{8} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{5}{4} \)
\( D \cdot \frac{4}{7} \)
Subject: Maths
\( f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^{2} & 2 x \\ \tan x & x & 1\end{array}\right| \) then
\( \lim _{x \rightarrow 0} f(x)= \)
\( A \cdot O \)
B.
\( c \cdot-2 \)
\( D \)
Subject: Physics
On the basis of following features identify the correct option:
These rays travel in straight line. These rays consist of positively charged particles.

These rays are deflected by electric and magnetic fields. \( \mathrm{e} / \mathrm{m} \) values for the particles are not same
for all gases.
A. cathode rays
B. Anode rays
c. Both (1) and (2)
D. Neither (1) nor (2)
Subject: Physics
In a experiment to measure the height of a bridge by dropping a stone into water underneath,if the error in the
measurement of times is \( 0.1 s \) at the
end of \( 2 s \),then the error in the
estimation of the height of the bridge
will be
\( \mathbf{A} \cdot 0.49 m \)
B. \( 0.98 m \)
c. \( 1.96 m \)
D. \( 2.12 m \)
Subject: Maths
What is the length of the other sides of
the rectangle as shown in the figure, if
side \( A B=10 \) and \( B C=7 ? \)
\( A \cdot C D=10 \) and \( A D=5 \)
B. \( C D=10 \) and \( A D=7 \)
\( c \cdot C D=7 \) and \( A D=7 \)
D. \( C D=7 \) and \( A D=10 \)
0
Subject: Maths
The number of ways in which 10
candidates \( A_{1}, A_{2}, \dots, A_{10} \) can be
ranked so that \( A_{1} \) is always above \( A_{2} \)
is:-
A \( \cdot \frac{10 !}{2} \)
B . \( 2^{7} 3^{4} 5^{2} 7^{1} \)
\( \mathbf{c} \cdot 2^{8} 5^{2} \)
D. \( 3^{4} 5^{2} 7 \)
Subject: Physics
Q Type your question
of \( 0.7 m m \) diameter and suspended
vertically. The stone is now rotated in a horizontal plane at a rate such that wire
makes an angle of \( 85^{\circ} \) with the vertical
\( f Y=7 \times 10^{10} \mathrm{Nm}^{-2}, \sin 85^{\circ}=0.9962 \)
and \( \cos 85^{\circ}=0.0872, \) the increase in
length of wire is
\( A \cdot 1.67 \times 10^{-3} \mathrm{m} \)
B. \( 6.17 \times 10^{-3} \mathrm{m} \)
C \( \cdot 1.76 \times 10^{-3} \mathrm{m} \)
D. 7.16x10-3 \( m \)
Subject: Maths
\( \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \boldsymbol{C} \) parallelogram, \( \boldsymbol{Q} \boldsymbol{M} \) is the height
form \( Q \) to \( R C \) and \( Q N \) is the height from \( Q \) to \( P S . \) If \( R C=12 \mathrm{cm} \) and
\( Q M=7.6 \mathrm{cm} . \) Find
(a) the area of the parallegram \( P Q R C \)
\( (b) Q N \) if \( P S=8 c m \)
Subject: Physics
A particle is projected upwards. The times corresponding to height \( h \) while
ascending and while descending are \( t_{1} \)
and \( t_{2} \) respectively. The velocity of
projection will be
A \( \cdot g t \)
B. \( g t_{2} \)
c. \( g t\left(t_{1}+t_{2}\right) \)
D. \( \frac{g\left(t_{1}+t_{2}\right)}{2} \)
Subject: Physics
A particle oscillates as per the equation \( \boldsymbol{x}=\mathbf{7} \cos (\mathbf{0 . 5} \boldsymbol{\pi} \boldsymbol{t}) \mathrm{m}, \) the time taken by
the particle to move from the mean position to a point \( 3.5 \mathrm{m} \) away is:
A \( \cdot \frac{1}{3} s \)
в. \( \frac{1}{2} s \)
c. \( 1 s \)
D. \( \frac{2}{3} s \)
Subject: Physics
The radii of curvature of the surfaces of
a double convex lens are \( 20 \mathrm{cm} \) and 40
\( \mathrm{cm} \) respectively, and its focal length is \( 20 \mathrm{cm} . \) What is the refractive index of
the material of the lens?
A \( \cdot \frac{5}{2} \)
в. \( \frac{4}{3} \)
\( c \cdot \frac{5}{3} \)
D. \( \frac{4}{5} \)
Subject: Physics
A body of mass 3 kg hits a wall at an
angle of \( 600 \& \) returns at the same angle. The impact time was0.2 s. Calculate the force exerted on the wall:
A. \( 150 \sqrt{3} N \)
В. \( 50 \sqrt{3} N \)
c. \( 100 \mathrm{N} \)
D. \( 75 \sqrt{3} N \)
Subject: Physics
A sky laboratory of mass \( 2 \times 10^{3} K g \)
is raised from a circular orbit of radius
\( 2 \mathrm{R} \) to a circular orbit of radius \( 3 \mathrm{R} \). The
work done is (approximately):
\( \mathbf{A} \cdot 10^{16} J \)
В. \( 2 \times 10^{10} J \)
\( \mathbf{c} \cdot 10^{6} J \)
D. \( 3 \times 10^{10} J \)
Subject: Maths
The variable plane \( (2 \lambda+1) x+ \)
\( (3-\lambda) y+z=4 \) always passes
through the line
A \( \cdot \frac{x}{0}=\frac{y}{0}=\frac{x+4}{1} \)
в. \( \frac{x}{1}=\frac{y}{2}=\frac{z}{-3} \)
c. \( \frac{x}{1}=\frac{y}{2}=\frac{z-4}{-7} \)
D. none of these
Subject: Physics
A circular track of radius \( 100 \mathrm{m} \) is
designed for an average speed \( 54 \mathrm{km} / \mathrm{h} \) Find the angle of banking.
A \( \cdot \tan ^{-1}\left(\frac{3}{20}\right) \)
B. \( \tan ^{-1}\left(\frac{9}{40}\right) \)
c. \( \tan ^{-1}\left(\frac{3}{10}\right) \)
D. None of these
Subject: Maths
\( \int\left[\frac{1+\sin (\log x)}{1+\cos (\log x)}\right] d x= \)
A. \( \frac{x}{1+\cos (\log x)}+c \)
в. \( \quad x \tan \frac{\log x}{2}+c \)
c. \( \quad-x \cot \frac{\log x}{2}+c \)
D. \( \frac{x}{1+\sin (\log x)}+c \)
Subject: Chemistry
A mixture of 3.8 moles of \( \mathrm{NO} \) and 0.924
moles of \( C O_{2} \) was allowed to react in a \( 1.0 \mathrm{L} \) container.The equilibrium mixture
contains 0.124 mole of \( C O_{2} . \) Calculate
\( K_{c} \) for the reaction.
\( N O_{(g)}+C O_{2(g)} \rightleftharpoons N O_{2(g)}+C O_{(g)} \)
Subject: Maths
\( \text { Four points }\boldsymbol{A}(\mathbf{6}, \mathbf{3}), \boldsymbol{B})-\mathbf{3}, \mathbf{5}) \)
\( C(4,-2) \) and \( D(x, 3 x) \) are given such that \( \frac{\Delta D B C}{\Delta A B C}=\frac{1}{2}, \) find \( x \)
Subject: Physics
A thin iron ring with mean diameter
\( d=50 \mathrm{cm} \) supports a winding
consisting of \( N=800 \) turns carrying
current \( \boldsymbol{I}=\mathbf{3 . 0} \boldsymbol{A} . \) The ring has a cross
cut of width \( b=2.0 \) mm. Neglecting the
scattering of the magnetic flux at the gap edges, and using the plot shown in figure above, find the permeability of
iron under these conditions.
Subject: Maths
In the expansion of \( \left(\sqrt[3]{4}+\frac{1}{\sqrt[4]{6}}\right)^{20} \)
This question has multiple correct options
A. the number of rational terms \( =4 \)
B. the number of irrational terms \( =19 \)
C. the middle term is irrational
D. the number of irrational terms \( =17 \)
Subject: Maths
A solid sphere of diameter \( 12 \mathrm{cm} \) is melted and draw into a wire of radius \( \mathbf{1} \)
\( \frac{1}{5} c m \) then the length of the wire is
A . \( 108 \mathrm{m} \)
в. 72 \( \mathrm{m} \)
\( c \cdot 84 m \)
D. None
Subject: Maths
The equation of a line passing through
(2,-3) and inclined at an angle of \( 135^{\circ} \)
with the positive direction of \( x \) -axis is.
A. \( x+y-1=0 \)
в. \( x+y+1=0 \)
c. \( x-y-1=0 \)
D. \( -x+y+1=0 \)
Subject: Maths
\( \bar{a}, \bar{b} \) and \( \bar{c} \) are three vectors having magnitudes 1,1 and 2 respectively. If \( \bar{a} \times(\bar{a} \times \bar{c})+\bar{b}=0, \) then acute angle
between \( \overline{\boldsymbol{a}} \) \& \( \overline{\boldsymbol{c}} \) is
\( \mathbf{A} \cdot \pi / 6 \)
в. \( \pi / 4 \)
c. \( \pi / 3 \)
D. \( 5 \pi / 12 \)
Subject: Physics
A geostationary satellite is at a height
above the surface of earth. If earth
radius is \( \mathrm{R} \)
A. The minimum colatitude on earth upto which the satellite can be used for communication is \( \sin ^{-1}(\mathrm{R} / \mathrm{R} \)
\( +h) \)
B. The maximum colatitudes on earth upon which the satellite can be used for communication is \( \sin ^{-1}(R / R+h) \)
c. The area on earth escaped from this satellite is given as \( 2 \pi R^{2}(1+\sin \theta) \)
D. The area on earth escaped from this satellite is given as \( 2 \pi R^{2}(1+\cos \theta) \)
Subject: Maths
If \( 0 \leq x \leq 2 \pi, \) then the number of
solutions of the equation \( \sin ^{6} x+ \)
\( \cos ^{6} x=1 \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
E . 8
Subject: Chemistry
(A) Half-life of a first order reaction is
independent of the initial concentration of reactant
(R) \( t_{1 / 2} \) (first order) \( =\tau / 1.44 \)
where, \( \boldsymbol{\tau} \) =average life.
A. Both (R) and (A) are true and reason is the correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
c. Assertion
(A) is true but reason
(R) is false
D. Assertion
(A) and reason
(R) both are false
E. Assertion (A) is false but reason (R) is true
Subject: Maths
Gauri want to the stationers and bought things worth Rs 25 out of which 30
paise went on sale tax on taxable purchases If the tax rate was \( 6 \% \) then what was the cost of the tax free item?
\( \mathbf{A} \cdot \) Rs 15
B. Rs 15.70
c. Rs 19.70
D. Rs 20
Subject: Physics
When a p-n-p transistor is operated in
saturation region, then its
A. Base-emitter junction is forward biased and basecollector junction is reverse biased.
B. Both base-emitter and base-collector junctions are reverse biased
C. Both base-emitter and base-collector junctions are forward biased
D. Base-emitter junction is reverse biased and basecollector junction is forward biased.
Subject: Chemistry
\( 15 \mathrm{cc} \) of gaseous hydrocarbon required \( 45 \mathrm{cc} \) of oxygen for complete
combustion and \( 30 \mathrm{cc} \) of \( C O_{2} \) was
formed. The formula of the gaseous compound is:
A. \( C_{3} H_{16} \)
B. \( C_{2} H_{2} \)
\( \mathbf{c} \cdot C_{4} H_{10} \)
D. \( C_{2} H_{4} \)
Subject: Physics
For a new scale of temperature called
\( P \) scale (which is linear and total
division of the new scale is 200 ) the
freezing and boiling points of water are
\( 25^{\circ} P \) and \( 225^{\circ} P \) respectively. Then the
temperature on new scale
corresponding to \( 25^{\circ} \mathrm{C} \) on the celsius
scale is :
в. \( 75^{\circ} P \)
c. \( 50^{\circ} P \)
D \( .275^{\circ} \mathrm{P} \)
Subject: Chemistry
In which of the following pairs, first compound has larger bond angle than
another?
This question has multiple correct options
A. \( H_{2} O \) and \( N H_{3} \)
B. \( S F_{2} \) and \( B e F_{2} \)
\( \mathrm{c} . B F_{3} \) and \( B F_{4}^{-} \)
D. \( N H_{3} \) and \( N F_{3} \)
Subject: Chemistry
Calculate the standard oxidation
potentials of zinc electrode form the
following data. The EMF of the cell :
\( \boldsymbol{L} \boldsymbol{i}|\boldsymbol{L} \boldsymbol{i} \oplus(\mathbf{0 . 0 5} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{n}| \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{0} . \boldsymbol{5} \boldsymbol{M}), \boldsymbol{E} \)
\( -3.045 V, \) is \( 2.35 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \)
Subject: Chemistry
Which of the following is an anhydride
of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A \( . H_{2} S \)
в. \( H_{2} S_{2} \)
\( c \cdot S O_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)
Subject: Maths
The position vectors of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are \( \overline{\boldsymbol{i}}+ \)
\( \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}}, \boldsymbol{4} \overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}+\overline{\boldsymbol{k}}, \boldsymbol{4} \overline{\boldsymbol{i}}+\mathbf{5} \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}} . \) Then
the position vector of the circumcentre
of the triangle \( A B C \) is
\( \mathbf{A} \cdot 3 \hat{i}+2 \hat{j}+\hat{k} \)
B. \( \frac{1}{2}(6 \hat{i}+\hat{j}+\hat{k}) \)
c \( \cdot \frac{1}{2}(5 \hat{i}+6 \hat{j}+2 \hat{k}) \)
D. \( \frac{1}{2}(9 \bar{i}+7 \bar{j}+3 \bar{k}) \)
Subject: Physics
The magnetic flux linked with a coil
setisfies the relation \( \phi=4 t^{2}+6 t+ \)
\( 9 W b, \) where \( t \) is the time (in \( s \) ). The
emf indused in the coilat \( t=2 s \) is, (in
\( \mathbf{V}) \)
\( \mathbf{A} \cdot 22 \)
B . 18
c. 16
D. 40
Subject: Chemistry
The hybridization of \( X e \) -atom in \( X e O_{6}^{4-} \) is same with:
This question has multiple correct options
A \( \cdot x e \) in \( X e F_{6} \)
B. Te in \( T e O_{6}^{6} \)
\( \mathbf{c} \cdot \operatorname{Pin} P F_{6}^{-} \)
\( \mathbf{D} \cdot \sin S i F_{6}^{2} \)
Subject: Maths
The length of latus rectum of the
hyperbola \( \boldsymbol{x} \boldsymbol{y}-\mathbf{3} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{7}=\mathbf{0} \) is
A .4
B. 3
\( c \cdot 2 \)
D.
Subject: Physics
A \( 2.5 k g \) ball is dropped onto a concrete floor. It strikes the floor with a
momentum of \( 20 k g m / s \) and bounces away from the floor with a momentum
of \( 16 k g m / s . \) What is the magnitude of
change of momentum of the ball?
A. \( 4 k g . m / s \)
в. \( 8 k g m / s \)
c. \( 32 k g m / s \)
D. \( 36 k g m / s \)
E . \( 40 \mathrm{kgm} / \mathrm{s} \)