AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two block of mass \( m_{1} \) and \( m_{2} \) are
connected with the help of a spring
constant \( k \) initially the spring in its natural length as shown. A sharp
impulse is given to mass \( m_{2} \) so that it
acquires a velocity \( v_{0} \) towards right. If the system is kept on smooth floor then find
(a) the velocity of the centre of
mass,
(b) the maximum elongation that the spring will suffer?
Subject: Maths
If \( 0<x<\pi, \) then
\( \frac{\sin 8 x+7 \sin 6 x+18 \sin 4 x+12 \sin 2 x}{\sin 7 x+6 \sin 5 x+12 \sin 3 x} \)
is equal to
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
\( c \cdot 3 \)
D. 2
E . 8
Subject: Physics
A cell of negligible resistance and emf 2 volt is connected to a series
combination of 2,3 and 5 ohm. The
potential difference in volts between the terminals of 3 -ohm resistance will be:
A. \( 0.6 v o l t \)
B. \( \frac{2}{3} \) volt
c. \( 3 v o l t s \)
D. \( 6 v o l t s \)
Subject: Chemistry
In an organic compound \( P \) is estimated
as:
A. \( M g_{2} P_{2} O_{7} \)
в. \( M g_{3}\left(P O_{4}\right)_{2} \)
\( \mathrm{c} \cdot H_{3} P O_{4} \)
D. \( P_{2} O_{5} \)
Subject: Maths
The acute angle between two lines such
that the direction cosines \( I, m, n \) of each
of them satisfy the equations \( l+m+ \)
\( \boldsymbol{n}=\mathbf{0} \) and \( l^{2}+\boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \) is :
A . 30
B . 45
c. 60
D. 15
Subject: Physics
A series \( L C R \) circuit is connected to a
source of alternating emf \( 50 \mathrm{V} \) and if the potential differences across inductor and capacitor are \( 90 \mathrm{V} \) and
\( 60 V \) respectively, the potential
difference across resistor is:
\( \mathbf{A} \cdot 400 V \)
в. \( 40 V \)
\( c .80 V \)
D. \( 1600 V \)
Subject: Chemistry
A solution of \( N a_{2} S O_{4} \) in water is
electrolysed using inert electrodes. The
products at the cathode and anode respectively, are:
A. \( O_{2}, H_{2} \)
в. \( O_{2}, \) Na
c. \( H_{2}, O_{2} \)
D. \( O_{2}, S O_{2} \)
Subject: Physics
Three identical large metal plates of
area \( A \) are small at distances \( d \) and \( 2 d \)
from each other. Top metal plate is
uncharged, while the other metal plates
have charges \( +Q \) and \( -Q . \) Top and
bottom metal plates are connected by
switch \( S \) through a resistor of unknown
resistance. What energy (in mJ) is dissipated in the resistor when switch
is closed?
(given: \( \left.\frac{\epsilon_{0} A}{d}=6 \mu F, Q=60 \mu C\right) \)
Subject: Physics
A particle is executing SHM of period 4s.Then the time taken by it to move from thr extreme position to \( \frac{\sqrt{3}}{2} \) of the amplitude is:
A \( \cdot \frac{1}{3} s \)
в. \( \frac{2}{3} \) s
c. \( \frac{3}{4} \)
D. \( \frac{4}{3} \) s
Subject: Maths
Which one of the following is correct in respect of the equations \( \frac{x-1}{2}=\frac{y-2}{3} \)
and \( 2 x+3 y=5 ? \)
A. They represent two lines which are parallel
B. They represent two lines which are perpendicular
C. They represent two lines which are neither parallel nor perpendicular
D. The first equation does not represent a line
Subject: Maths
If \( \vec{a}=x \hat{i}+(x-1) \hat{j}+\hat{k} \) and \( \vec{b}= \)
\( (x+1) \hat{i}+\hat{j}+a \hat{k} \) always make an
acute angle with each other for every
value of \( x \in R, \) then
A \( . a \in(-\infty, 2) \)
B . \( a \in(2, \infty) \)
c. \( a \in(-\infty, 1) \)
D. \( a \in(1, \infty) \)
Subject: Physics
De Broglie wavelength of neutrons in
thermal equilibrium is (given \( \boldsymbol{m}_{\boldsymbol{n}}= \)
\( \left.1.6 \times 10^{-27} k g\right) \)
A \( \cdot 30.8 / \sqrt{T}_{A}^{\circ} \)
B \( \cdot 3.08 / \sqrt{T}_{A}^{o} \)
c. \( 0.308 / \sqrt{T}_{A}^{\circ} \)
D \( \cdot 0.0308 / \sqrt{T}^{\circ} \)
Subject: Chemistry
Assertion: If the activation energy of reaction is low, it proceeds at a faster rate.

Reason: Lowering activation energy increases the kinetic energy of molecules.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Maths
If \( f(x)=\int \frac{x^{2}+\sin ^{2} x}{1+x^{2}} \cdot \sec ^{2} x d x \) and
\( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) then \( \boldsymbol{f}(\mathbf{1})= \)
A \( \cdot 1-\frac{\pi}{4} \)
B. \( \frac{\pi}{4}-1 \)
c. \( \tan 1-\frac{\pi}{4} \)
D. None of these
Subject: Physics
For spherical symmetrical charge
distribution, variation of electric
potential with distance fro center is
given in diagram. Given that \( : V= \) \( \frac{\boldsymbol{q}}{\mathbf{4} \boldsymbol{\pi} \varepsilon_{0} \boldsymbol{R}_{0}} \) for \( \boldsymbol{r} \leq \boldsymbol{R}_{0} \) and \( \boldsymbol{v}=\frac{\boldsymbol{q}}{\boldsymbol{4} \boldsymbol{\pi} \varepsilon_{0} \boldsymbol{r}} \) for
\( \boldsymbol{r} \geq \boldsymbol{R}_{0} \)
Then which option (s) are correct:
This question has multiple correct options
A. Total charge within \( 2 R_{0} \) is 9
B. Total electrostatic energy for \( r \leq R_{0} \) is non-zer
c. \( A t r=R_{0} \) electric field is discontinuous
D. There will be no charge anywhere except at \( r<R_{0} \)
Subject: Maths
Using ruler and compasses only, construct a triangle \( A B C \). having \( A B=47 \)
\( \mathrm{cm}, \mathrm{AC}=34 \mathrm{cm} \) and \( \angle B A C=75^{\circ} . \) Draw
the perpendicular bisector of BC and the bisector of angle BAC. If the perpendicular bisector and the angle bisector meet at a point \( \mathrm{M} \), measure
\( \angle B M C \)
Subject: Maths
defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}k-2 x, \text { if } x \leq 1 \\ 2 x+3, \text { if } x>-1\end{array}\right\} \), if has a loca
minimum at \( x=-1, \) then a pair
Subject: Chemistry
A weak acid \( \boldsymbol{H} \boldsymbol{X}\left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{5}}\right) \) on
reaction with NaOH gives NaX. For \( 0.1 \mathrm{M} \) aqueous solution of NaX, the \% hydrolysis is:
A . 0.001\%
B . 0.01\%
c. \( 0.15 \% \)
D. 1\%
Subject: Chemistry
The energy of a photon of green light of wavelength \( 5000 A^{\circ} \) is
A . \( 3.459 \times 10^{-19} \) joule
в. \( 3.973 \times 10^{-19} \) joule
c. \( 4.132 \times 10^{-19} \) joule
D. \( 8453 \times 10^{-19} \) joule
Subject: Maths
Which option of linear equation is inconsistent?
\( \mathbf{A} \cdot x+y=1 \)
\( 2 x+y=0 \)
B. \( x-y=2 \)
\( 2 x-2 y=1 \)
c. \( 2 x-3 y=0 \)
\( 2 y+x=1 \)
D. 2x - 4 \( y=19 \) \( -2 x+y=0 \)
Subject: Physics
Refractive indices of water and glass
are \( 4 / 3 \) and \( 3 / 2 \) respectively. A ray of light travelling in water is incident on
the water-glass interface at \( 30^{0} \) Calculate the sine of angle of refraction.
A . 0.460
B. 0.585
c. 0.444
D. 0.623
Subject: Maths
Find \( |\vec{a} \times \vec{b}|, \) if \( \vec{a}=\hat{i}-7 \hat{j}+7 \hat{k} \) and \( \vec{b}= \)
\( \mathbf{3} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{2} \hat{\boldsymbol{k}} \)
Subject: Chemistry
The correct relationship between the
bond lengths \( a \) and \( b \) is:
\( \boldsymbol{O} \)
\( \boldsymbol{C H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C H}_{3} \)
\( \mathbf{A} \cdot a=b \)
В. \( b>a \)
\( c \cdot b<a \)
D. impossible to predict
Subject: Maths
\( \int_{0}^{\pi} x \cdot \log (\sin x) d x= \)
A \( \cdot \pi^{2} \log (2) \)
В. \( \frac{\pi^{2}}{2} \log (2) \)
c. \( \frac{\pi^{2}}{4} \)
D. \( -\frac{\pi^{2}}{2} \log (2) \)
Subject: Chemistry
Which one of the following is used in the extraction of aluminium by electrolytic process?
A. \( A l_{2} O_{3} \)
\( \mathbf{B} \cdot A l(O H)_{3} \)
c. \( A l C l_{3} \)
D. \( A l_{2}\left(S O_{4}\right)_{3} \)
Subject: Physics
\( ^{57} \) Co decays by electron capture. Its half life is 272 days. Find the activity left after a year if present activity is \( 2 \mu C i \)
A. \( 0.788 \mu \) Ci
B. \( 0.431 \mu C i \)
\( \mathbf{c} .0 .39 \mu \mathrm{Ci} \)
D. none of these
Subject: Chemistry
A compound consists of \( 47.8 \% \) zinc and
52\% chlorine by mass. The empirical
formula of the compound is \( Z n_{x} C l_{y} \)
where \( x \) and \( y \) can have the values:
A . 1 and 1
B. 1 and 2
c. 2 and 1
D. 2 and 3
Subject: Chemistry
Which of the following is general electron configuration of \( 4 d \) series?
\( \mathbf{A} \cdot 4 s^{1+o 2} 3 d^{1+t 01} \)
B. \( 4 s^{1 t o 2} 4 d^{1+t 01} \)
\( \mathbf{c} \cdot 5 s^{1 t o 2} 5 d^{1 t o 10} \)
D. \( 5 s^{1 \operatorname{to} 2} 4 d^{1 \text { lto } 10} \)
Subject: Chemistry
What mass of an organic compound
\( \left(M w_{0}=156\right) \) must be dissolved in 50
\( \mathrm{mL} \) of an organic solvent \( \left(\boldsymbol{d}=\mathbf{0 . 9 g c c}^{-1}\right) \)
water to lower the freezing point by \( 0.48^{\circ} \mathrm{C} . K_{f} \) of benzene \( =5.12 \)
Subject: Physics
Two balls are projected making an angle of 30 and 45 respectively with the horizontal. If both have the same
velocity at the highest points of their paths, then the ratio of their velocities of projection is
A. \( \sqrt{3}: \sqrt{2} \)
B. \( \sqrt{2}: 1 \)
c. \( \sqrt{2}: \sqrt{3} \)
D. \( \sqrt{3}: 2 \)
Subject: Physics
In Young's double slit experiment with monochromatic source of light of
wavelength \( 6000 A^{\circ}, \) if the path difference at a point on the screen is 6
\( \times 10^{-6} m \) the number of the bright band
formed at that point is:
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 10
Subject: Maths
Let \( z_{k}(k=0,1,2, \dots, 6) \) be the roots of
the equation \( (z+1)^{7}+z^{7}=0, \) then \( \sum_{k=0}^{6} R e\left(z_{k}\right) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{3}{2} \)
c. \( -\frac{7}{2} \)
D. \( \frac{7}{2} \)
Subject: Physics
Calculate the de Brogile wavelength of a photon whose linear momentum has a magnitude of \( 3.3 \times 10^{-23} k g m / s \)
A. 0.0002 nm
B. \( 0.002 \mathrm{nm} \)
c. \( 0.02 \mathrm{nm} \)
D. \( 0.2 \mathrm{nm} \)
\( E \cdot 2 \mathrm{nm} \)
Subject: Physics
cathode plate inside a vacuum tube as
shown in the figure. The work function
of the cathode surface is \( \phi \) and the
anode is a wire mesh of conducting
material kept at a distance d from the
cathode. A potential difference V is
maintained between the electrodes. If
the minimum de Broglie wavelength of
the electrons passing through the
anode is \( \lambda_{e}, \) which of the following
statement(s) is(are) true?
A \( \cdot \lambda_{e} \) increases at the same rate as \( \lambda_{p h} \) for \( \lambda_{p h}<h c / \phi \)
B. \( \lambda_{e} \) is approximately halved, if dis doubled
C. \( \lambda_{e} \) decreases with increase in \( \phi \) and \( \lambda_{p h} \)
D. For large potential difference \( (V>>\phi / e) \lambda_{e} \) is
pproximately halved if \( V \) is made four time
Subject: Physics
A calorimeter contains \( 70.2 g \) of water
at \( 15.3^{\circ} \mathrm{C} \). If \( 143.7 g \) of water \( \operatorname{at} 36.5^{\circ} \mathrm{C} \)
in mixed it with the common
temperature is \( 28.7^{\circ} \mathrm{C} \). The water
equivalent of the calorimeter is:
A. \( 15.6 g \)
в. \( 9.4 g \)
\( c .6 .3 g \)
D. \( 13.4 g \)
Subject: Chemistry
When 4.0 A of current is passed through a \( 1.0 \mathrm{L}, 0.10 \mathrm{M} F e^{3+}(a q) \) solution for 1.0
hour, it is partly reduced to \( \mathrm{Fe}(\mathrm{s}) \) and partly of \( \boldsymbol{F e}^{2+}(\boldsymbol{a q}) \). The correct statements(s) is/are:
This question has multiple correct options
A. 0.10 mol of electrons are required to convert all \( F e^{3} \)
to \( F e^{2+} \)
B. 0.025 mol of Fe(s) will be deposited.
c. 0.075 mol of iron remains as \( F e^{2+} \)
D. 0.050 mol of iron remains as \( F e^{2+} \)
Subject: Physics
If the length of a simple pendulum is recorded as \( (90.00 \pm 0.02) \mathrm{cm} \) and period as \( (1.90 \pm 0.02) \mathrm{s}, \) the
percentage of error in the measurement of acceleration due to
gravity is :
A . 4.2
B . 2.
c. 1.5
D. 2.8
Subject: Chemistry
The Molarity of \( 200 m l \) of \( H C l \) solution
which can neutralise \( 1.6 g \) of anhydrous
\( N a_{2} C O_{3} \) is:
\( \mathbf{A} \cdot 1 M \)
B. \( 0.1 M \)
c. \( 0.6 M \)
D. \( 0.75 M \)
Subject: Physics
Assertion
The frequencies of incident, reflected and refracted beam of monochromatic
light at the interface of two media are
same
Reason
The incident, reflected, refracted rays are coplanar.
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both assertion and reason are false
Subject: Chemistry
The reaction \( \boldsymbol{A}(\boldsymbol{g}) \longrightarrow \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{C}(\boldsymbol{g}) \) is
a first order reaction with rate constant
\( 2.772 \times 10^{-3} s^{-1} . \) Starting with 0.1 mole
of \( A \) in 2 litre vessel, find the
concentration of \( A \) after 250 sec when
the reaction is allowed to take place at
constant pressure at \( 300 K ? \)
\( \mathbf{A} \cdot 0.0125 M \)
В. 0.025 М
c. \( 0.05 M \)
D. none of these
Subject: Chemistry
Benzene and toluene form an ideal
solution over the entire range of
composition. The vapour pressure of pure benzene and toluene at \( 300 K \) are
\( 50.71 m m H g \) and \( 32.06 m m H g \)
respectively. Calculate the mole fraction
of benzene in vapour phase if \( 80 g \) of
benzene is mixed with \( 100 g \) of toluene.
Subject: Maths
\( f(x)=\left\{\begin{aligned} 4 x, & x<0 \\ 1, & x=0 \text { then } \lim _{x \rightarrow 0} f(x) \\ 3 x^{2}, & x>0 \end{aligned}\right. \)
equals
A .
B.
\( c \cdot 3 \)
D. does not exist
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \) then \( \boldsymbol{f} \)
is
A. only one-one
B. only into
c. one-one into
D. not a function
Subject: Chemistry
From the artg of the periodic table given, answer the following questions
\[
\begin{array}{l}
1 \\
\text { litium }
\end{array}
\]
\( 13 \quad \) carbon
\( \mathbf{1 5} \)
\[
X
\]
\( Y \)
\( Z \)
Name the family of \( L, Q, R, T \).
Subject: Physics
In the Young's double slit experiment two light beams of wavelengths \( \lambda= \)
\( 6000 A^{\circ} \) and \( \lambda=4800 A^{\circ} \) are used. The
distance between two slits is \( 2.5 m m \)
The distance between slits and the
screen is \( 1.5 m . \) The distance between
the central maxima obtained with two
beams will be
A . zero
B. \( 1.872 m m \)
c. \( 2.872 m m \)
D. \( 2.652 m m \)
Subject: Physics
A hollow dielectric sphere has \( R_{1} \) and
\( R_{2} \) as its inner and outer radii. The total
charge carried by the sphere is \( +\mathrm{Q} \) which is uniformly distributed throughout the dielectric sphere
between \( R_{1} \) and \( R_{2} \). The electric field
for \( R_{1}<r<R_{2} \) is given by :
\( ^{A} \cdot \frac{Q}{4 \pi r \in R_{1}} \)
в. \( \frac{Q}{4 \pi \epsilon r_{2}} \)
c. \( \frac{Q}{4 \pi \in R_{1}^{2}} \)
D. \( \frac{Q\left(r^{3}-R_{1}^{2}\right)}{4 \pi \in r^{2}\left(R_{2}^{3}-R_{1}^{3}\right)} \)
Subject: Physics
Two fixed charges separated by a distance \( \boldsymbol{d} \) experience a force \( \boldsymbol{F} \). \( \boldsymbol{A} \) dielectric medium of thickness \( \frac{d}{4} \) and dielectric constant 4 is introduced in
the space between them. Find the new
force between the charges.
A \( \cdot \frac{F}{4} \)
в. \( \frac{F}{3} \)
\( c . F \)
D. \( \frac{16 F}{25} \)
Subject: Chemistry
The correct order of enthalpy of vaporisation of noble gases is :
A. \( H e<N e<A r<K r<X e \)
в. \( H e>N e>A r>K r>X e \)
c. \( H e<A r<K r<N e<X e \)
D. \( H e<X e<A r<N e<K r \)
Subject: Maths
The number of solutions of the equation \( 1+\sin ^{4} x=\cos ^{2} 3 x, x \in\left[-\frac{5 \pi}{2}, \frac{5 \pi}{2}\right] \)
is?
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c \cdot 7 \)
\( D \)
Subject: Chemistry
In the preparation of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) we get \( \mathrm{NO} \)
gas by catalytic oxidation of ammonia. The moles of NO produced by the
oxidation of two moles of \( N H_{3} \) will be :
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 6
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{I}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a}+\boldsymbol{I}-\boldsymbol{C} \boldsymbol{H}_{3} \stackrel{\text {dryether}}{\longrightarrow} \)
A \( \cdot C_{2} H_{5}-C_{2} H_{5} \)
в. \( C H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C H_{3}-C H_{3} \)
Subject: Maths
The solution of differential equation
\( \left(e^{x}+1\right) y d y=(y+1) e^{x} d x \) is
A \( \cdot\left(e^{x}+1\right)(y+1)=C e^{y} \)
B . \( \left(e^{x}+1\right)|(y+1)|=C e^{-y} \)
C \( \cdot\left(e^{x}+1\right)(y+1)=\pm C e^{y} \)
D. None of these
Subject: Chemistry
Diazomethane was photolysed to
generate singlet carbine which was
treated with cis-2-butene. The main
product(s) of the reaction is/are:
A. cis-1, 2-dimethylcyclopropane
B. trans-1, 2-dimethylcyclopropane
c. mixture of \( (A) \) and \( (B) \)
D. Ethylcyclopropane
Subject: Physics
The specific charge of a proton is \( 9.6 \times \) \( 10^{7} C / k g . \) The specific charge of an
alpha particle will be:
\( \mathbf{A} \cdot 9.6 \times 10^{7} C / k g \)
B . \( 19.2 \times 10^{7} C / k g \)
\( \mathbf{c} \cdot 4.8 \times 10^{7} C / k g \)
D. \( 2.4 \times 10^{7} C / k g \)
Subject: Physics
Light of wave length \( 6.5 \times 10^{-7} \mathrm{m} \) is
made incident on two slits \( 1 \mathrm{mm} \) apart. The distance between third dark fringe and fifth bright fringe on a screen distant \( 1 \mathrm{m} \) from slits will be
A. \( 0.325 \mathrm{mm} \)
B. 0.65 mm
c. \( 1.625 \mathrm{mm} \)
D. 3.25 mm
Subject: Maths
The probability that, on the examination
day, the student \( S_{1} \) gets the previously
allotted seat \( R_{1} \) and NONE of the
remaining students gets the seat previously allotted to him/her is?
\( A \cdot \frac{3}{40} \)
B. \( \frac{1}{8} \)
c. \( \frac{7}{40} \)
D. \( \frac{1}{5} \)
Subject: Chemistry
The equilibrium of which of the
following reaction will not be disturbed by the addition of an inert gas
at constant volume?

This question has multiple correct options
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
B. \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
c. \( C O(g)+2 H_{2}(g) \rightleftharpoons C H_{3} O H(g) \)
D. \( C(s)+H_{2} O(g) \rightleftharpoons C O(g)+H_{2}(g) \)
Subject: Chemistry
Assertion(A): The temperature in
the stratosphere increases with
altitude.
Reason(R): Ozone present absorbs
ultraviolet radiation which is converted
into heat.
Choose the correct option from the
following:
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not correct explanation of Assertion
C. Assertion is true and Reason is false
D. Assertion is false and Reason is true
Subject: Maths
Let \( f \) be a twice differentiable such that
\( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})=-\boldsymbol{f}(\boldsymbol{x}) \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) . \) If
\( \boldsymbol{h}(\boldsymbol{x})=\{\boldsymbol{f}(\boldsymbol{x})\}^{2}+\{\boldsymbol{g}(\boldsymbol{x})\}^{2}, \) where
\( h(5)=11 . \) Find \( h(10) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 10
c. 11
D. 100
Subject: Maths
Range of the function \( \boldsymbol{f}(\boldsymbol{x}) \) \( \sqrt{\left|\sin ^{-1}\right| \sin x||-\cos ^{-1}|\cos x|} \)
\( A \cdot\{0\} \)
B. \( [0, \sqrt{\frac{\pi}{2}}] \)
c. \( [0, \sqrt{\pi}] \)
D. none of these
Subject: Maths
Find the degree of homogeneity of function \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y})=\boldsymbol{a} \boldsymbol{x}^{2 / 3}+\boldsymbol{h} \boldsymbol{x}^{1 / 3} \boldsymbol{y}^{1 / 3}+ \)
\( b y^{2 / 3} \)
\( A \cdot 2 / 3 \)
B. 2
\( c \cdot 3 \)
D. 3/2
Subject: Biology
Choose the correct statement(s).
A. Fermentation is the process of conversion of pyruvate into ethanol and \( C O_{2} \) under aerobic conditions.
B. Pyruvate breakdown into \( C O_{2} \), water and energy occurs in the mitochondria during anaerobic respiration.
C. Glycolysis is the breakdown of glucose into pyruvate by means of ten step reactions in the cytoplasm.
D. The common respiratory substrate is glycogen.
Subject: Maths
The sum of \( n \) terms of three
arithmetical progression are \( S_{1}, S_{2} \) and
\( S_{3} . \) The first term of each is unity and
the common differences are 1,2 and 3
respectively. Prove that \( \left(\boldsymbol{S}_{1}+\boldsymbol{S}_{3}=\boldsymbol{2} \boldsymbol{S}_{2}\right) \)
Subject: Chemistry
Assertion: Increasing the temperature increases the reaction rate.
Reason: At high temperatures, molecules or atoms tend to be further
apart.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Physics
What is the minimum and maximum
distance between the convex lens and
the object for the magnification of a real image to be greater than \( 1 . ? \)
A. o and f
B. \( f \) and \( 2 f \)
\( c \cdot f \) and \( \infty \)
\( D \cdot 2 f \) and \( \infty \)
Subject: Maths
The velocity of an object fired directly upward is given by \( V=80-32 t \), where \( t \)
is in seconds. When will the velocity be
between 32 and 64 feet per second?
A. The velocity will be between 32 and 64 feet per second between 0.8 seconds after launch and 1.5 seconds
after launch.
B. The velocity will be between 32 and 64 feet per second between 0.5 seconds after launch and 1.5 seconds after launch.
C. The velocity will be between 32 and 64 feet per second between 0.4 seconds after launch and 1.2 seconds
after launch.
D. None of the above
Subject: Biology
Refer the following diagram and identify
the parts of a kidney indicated.
A. A- Cortex, B- Nephron, C- Pelvis, D- Medulla, E- Ureter
B. A- Cortex, B- Medulla, C- Nephron, D- Pelvis, E- Ureter
C. A- Nephron, B- Cortex, C- Medulla, D- Ureter, E- Pelvis
D. A- Nephron, B- Cortex, C- Medulla, D- Pelvis, E- Ureter
E. A- Nephron, B- Ureter, C- Pelvis, D- Medulla, E- Cortex
Subject: Physics
Light of wavelength \( \lambda \) in the air enters a medium of refractive index \( \mu . \) Two
points in this medium, lying along the
path of this light are at a distance \( ^{\prime} x^{\prime} \) apart. The phase difference between these points is
A \( \cdot \frac{2 \pi}{\lambda}-\mu x \)
в. \( \frac{2 \pi}{\lambda} \cdot x \mu \)
c. \( (\mu-1) \cdot \frac{2 \pi}{\lambda} x \)
D. \( \frac{1}{(\mu-1)} \cdot \frac{2 \pi x}{\lambda} \)
Subject: Maths
Following are the weights (in \( \mathrm{kg} \) ) of 10 new born babies in a hospital on a particular day: 3.4,3.6,4.2,4.5,3.9,4.1
\( 3.8,4.5,4.4,3.6 . \) Find the mean \( \bar{X} . \) (in
kg)
Subject: Biology
Which among the following is the
correct sequence of prophase I of meiosis?
A. Leptotene, pachytene, zygotene, diplotene, diakinesis
B. Leptotene, diplotene, pachytene, zygotene, diakinesis
c. Leptotene, zygotene, pachytene, diplotene, diakinessis
D. Leptotene, zygotene, diakinesis, diplotene
Subject: Physics
A wheel of radius \( 10 \mathrm{cm} \) can rotate freely
about an axis passing through its centre. A force \( 20 N \) acts tangentially at
the rim of wheel. If moment of inertia of
wheel is \( 0.5 k g m^{2}, \) its
angular acceleration is:
A \( \cdot 2 \) rad/s^
B . \( 2.5 \mathrm{rad} / \mathrm{s}^{2} \)
C. 4 rad/s\( ^{2} \)
D. 5 rad/s\( ^{2} \)
Subject: Physics
Two frames, one stationary and the
other moving, are initially coincident. Two observers in the two frames
observe a body initially at rest in the coincident frame. A constant force \( \boldsymbol{F} \)
starts acting on the body along horizontal axis, when moving frame starts to separate from the fixed frame.
Work done \( W \) as observed by the
stationary frame and \( W^{\prime} \) as observed
from the moving frame are compared to the each other as:
A \( \cdot W=W^{\prime} \)
в. \( W \neq W^{\prime} \)
c. \( w=\frac{1}{2} W^{\prime} \)
D. \( W=2 W^{\prime} \)