AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find all functions \( f(x) \) defined on \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \) with real values and has a
primitive \( F(x) \) such that \( f(x)+ \) \( \cos x \cdot F(x)=\frac{\sin 2 x}{(1+\sin x)^{2}} . \) Then find
\( f(x) \)
A \( \cdot f(x)=-\frac{2 \cos x}{(1+\sin x)^{2}}-C e^{-\cos x} \cdot \sin x \)
B. \( f(x)=-\frac{2 \cos x}{(1+\sin x)^{2}}-C e^{-\sin x} \cdot \cos x \)
C \( \quad f(x)=-\frac{2 \cos x}{(1+\cos x)^{2}}-C e^{\sin x} \cdot \sin x \)
D. \( f(x)=-\frac{2 \cos x}{(1+\sin x)^{2}}-C e^{\cos x} \cdot \cos x \)
Subject: Maths
If \( \bar{x} \cdot \bar{y}=\bar{x} \cdot \bar{z} \) and \( \bar{x} \times \bar{y}=\bar{x} \times \bar{z} \) and
\( \bar{x} \neq \overline{0}, \) then prove that \( \bar{y}=\bar{z} \)
Subject: Chemistry
\( A+B \rightleftharpoons 2 C+D \)
II. \( 2 C+D \rightleftharpoons A+B \)
If the equilibrium constant for the reaction represented by equation I above is \( 4.0 \times 10^{-2} . \) What is the value
of the equilibrium constant for the
reaction represented by equation II?
\( \mathbf{A} \cdot 16 \times 10^{-4} \)
В. \( 4.0 \times 10^{-2} \)
c. \( \frac{1}{4.0} \)
D. \( \frac{1}{4.0 \times 10^{-2}} \)
E \( .4 .0 \times 10^{2} \)
Subject: Chemistry
(R)-2 -lodobutane is treated with Nal in
acetone and allowed to stand for a long
time.The product eventually formed is:
A \( \cdot(R)-2- \) iodobutane
B . \( (S)-2- \) iodobutane
C. \( (\pm)-2- \) iodobutane
D. (土) - 1,2 - diiodobutane
Subject: Physics
The temperature of a furnace is \( 2324^{\circ} \mathrm{C} \)
and the intensity is maximum in its
spectrum nearly at \( 12000 A^{\circ} . \) If the intensity in the spectrum of star is
maximum nearly at \( 4800 A^{\circ} \), then the
surface temperature of the star is :
A \( \cdot 8400^{\circ} \mathrm{C} \)
B. 6219 \( ^{\circ} \mathrm{C} \)
\( c \cdot 7200^{\circ} \mathrm{C} \)
D. \( 5900^{\circ} \mathrm{C} \)
Subject: Physics
A train of length \( 100 m \) travelling at \( 20 m / s \) overtakes another of length
\( 200 m \) travelling at \( 10 m / s . \) The time taken by the first train to pass the second train is
A . \( 30 s \)
в. \( 50 s \)
\( c \cdot 10 s \)
D. \( 40 s \)
Subject: Physics
Two circular coils 1 and 2 are made from
the same wire but the radius of 1st coil
is twice that of the 2 nd coil. What
potential difference in volts should be
applied across them so that the magnetic magnetic field at the centres is the same
A. 4 times of first coil
B. 6 times of first coil
c. 2 times of first coil
D. 3 times of first coil
Subject: Maths
The contentment obtained after
drinking \( x- \) units of a new drink at a
trial function is given by the function
\( C(x)=2 x^{3}-x^{2}+7 x+2 . \) If the
marginal contentment is defined as rate of change of \( C \) with respect to the number of units consumed at an
instant, then find the marginal contentment when 4 units of drink are
consumed
Subject: Biology
Match the wall components with the
type of tissues/ tissue system listed. Choose the answer which gives the correct combination of alphabets.
\begin{tabular}{llll} 
& List I & & List II \\
\cline { 8 - 5 } A & Suberin & 1 & Sclerenchyma \\
B & Lignin & 2 & Collenchyma \\
c & Pectin & 3 & Epidermis \\
D & Cutin & 4 & Phellem
\end{tabular}
A \( \cdot A-4, B-1, C-2, \)
B. A-1,B-4, C-2, D-3
c. \( A-4, \) В- \( 2, C-1, D-3 \)
D. A- 4, B-1, C-3
Subject: Maths
State whether the given statement is true or false.
If \( \boldsymbol{p}^{1-2 x} \times \sqrt{\boldsymbol{p}}=\boldsymbol{q}^{1-2 x} \times \sqrt{\boldsymbol{q}} ; \boldsymbol{p} \neq \boldsymbol{q} \) then
value of \( \boldsymbol{x} \) is \( \frac{\mathbf{3}}{\mathbf{4}} \)
A. True
B. False
Subject: Maths
Find \( a_{30} \) given that the first few terms of
a geometric sequence are given by \( -2,1,-\frac{1}{2}, \frac{1}{4} \dots \)
A \( \cdot \frac{1}{2^{27}} \)
в. \( \frac{1}{2^{2}} \)
c. \( \frac{1}{2^{28}} \)
D. \( \frac{1}{2^{29}} \)
Subject: Physics
On a friction less surface, a ball of mass
\( m \) moving at a speed \( v \) makes a headon collision with an identical ball at
rest. The kinetic energy of the balls after the collision is \( \frac{3}{4} t h \) of the original. Find the coefficient of restitution?
A \( \frac{1}{\sqrt{2}} \)
в. \( \frac{1}{\sqrt{3}} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{5}} \)
Subject: Maths
Find the coordinates of those points on the line \( \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}+\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{z}-\mathbf{3}}{\mathbf{6}} \) which
is at a distance of 3 units from the point
(1,-2,3)
Subject: Maths
The term independent of \( x \) in \( (1+ \)
\( x)^{n}\left(1+\frac{1}{x}\right)^{n} \) is
A \( \cdot C_{0}^{2}+2 \cdot C_{1}^{2}+3 \cdot C_{2}^{2}+\ldots \ldots \ldots+(n+1) \cdot C_{n}^{2} \)
B. \( \left(C_{0}+C_{1}+C_{2}+\ldots \ldots . .+C_{n}\right)^{2} \)
c. \( C_{0}^{2}+C_{1}^{1}+C_{2}^{2}+\ldots \ldots . .+C_{n}^{2} \)
D. None
Subject: Physics
A particle moving along \( x- \) axis whose position is given by \( \boldsymbol{x}=\mathbf{4}-\mathbf{9} \boldsymbol{t}+\frac{\boldsymbol{t}^{\mathbf{3}}}{\mathbf{3}} \)
then choose the correct statement(s)
for this motion-
This question has multiple correct options
A. Direction of motion is not changing at any of the instants
B. For \( 0<t<3 s \), the particle is slowing down
c. Direction of motion is changing at \( t=3 \)sec
D. For \( 0<t<3 s \) the particle is speeding up
Subject: Chemistry
What is the correct order of thermal
stability of carbonates of alkaline earth metals?
A \( \cdot B e C O_{3}>M g C O_{3}>C a C O_{3}>S r C O_{3}>B a C O_{3} \)
в. \( B e C O_{3}<M g C O_{3}<C a C O_{3}<S r C O_{3}<B a C O_{3} \)
c. \( B e C O_{3}<M g C O_{3}>C a C O_{3}>S r C O_{3}<B a C O_{3} \)
D. \( B e C O_{3}>M g C O_{3}<C a C O_{3}<S r C O_{3}<B a C O_{3} \)
Subject: Chemistry
Which of the following species has the ground state electron configuration of \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} ? \)
A . Sulfide ion, \( S^{2-} \)
в. \( H S O_{4}^{-} \)
c. \( K O H \)
D. \( H N O_{3} \)
E \( \cdot C_{2} O_{4}^{2} \)
Subject: Physics
A magnetizing field of \( 1600 \mathrm{A} / \mathrm{m} \) producers a magnetic flux of \( 2 \times 10^{-5} \) Wh in a bar of iron of cross section \( 0.2 x \)
\( 10^{-4} m^{2} . \) Calculate the susceptibility of
the bar.
A . 596.8
B . 288.9
\( c \cdot 2 \)
D. 1328
Subject: Chemistry
Statement 1: Excited tungsten atoms will give off light energy. Statement 2: As the excited electrons
return to their ground state, they emit energy in the form of light.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct
Subject: Maths
\( X \) and \( Y \) are independent binomial \( \operatorname{variates} \boldsymbol{A}\left(\mathbf{5}, \frac{\mathbf{1}}{\mathbf{2}}\right) \) and \( \boldsymbol{B}\left(\mathbf{7}, \frac{\mathbf{1}}{\mathbf{2}}\right) \) then
\( \boldsymbol{P}(\boldsymbol{X}+\boldsymbol{Y}=\boldsymbol{3}) \)
A \( \cdot \frac{45}{1024} \)
в. \( \frac{55}{1024} \)
c. \( \frac{65}{1024} \)
D. \( \frac{60}{1024} \)
Subject: Maths
Assertion
Vectors \( \vec{a}, \vec{b}, \vec{c} \) are coplanar.
Reason
\( (x \vec{a}+y \vec{b})=\overrightarrow{0} \Rightarrow x=0 \) and \( y=0 \)
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: Physics
The momentum of a \( 225 g \) ball moving at \( 35 m / s \) is
\( \mathbf{A} \cdot 7875 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. \( 3.5 N \)
\( c .5 .0 m / s \)
D. \( 7.875 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
Subject: Physics
The diameter of a sphere is measured with an instrument having least count \( 0.001 \mathrm{cm} . \) The diameter is \( 1.933 \mathrm{cm} . \) The
radius to correct significant figures will
be:
A . \( 0.9665 \mathrm{cm} \)
B. \( 0.966 \mathrm{cm} \)
c. \( 0.967 \mathrm{cm} \)
D. none of these
Subject: Maths
Three solid spheres of copper, whose
radii are \( 3 \mathrm{cm}, 4 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respestively are melted into a single
solid sphere of radius R. The value of R
is
A . \( 12 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c .4 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)
Subject: Physics
Ine elastıc collısıon between two
bodies, A and B, can be considered
using the following model. A and B are
free to move along a common line without friction. When their distance is
greater than \( d=1 \mathrm{m}, \) the interacting
force is zero; when their distance is less
than \( d, \) a constant repulsive \( F=6 N \) is
present. The mass of body \( A \) is \( m_{A}=1 \mathrm{kg} \)
and it is initially at rest; the mass of
body \( \mathrm{B} \) is \( m_{B}=3 \mathrm{kg} \) and it is
approaching body A head-on with a
speed \( v_{o}=2 \mathrm{m} / \mathrm{s} \). Find the minimum
distance between \( A \) and \( B \)
A. \( 0.25 \mathrm{m} \)
B. \( 0.50 \mathrm{m} \)
c. \( 0.75 \mathrm{m} \)
D. \( 2 \mathrm{m} \)
Subject: Chemistry
The correct order of atomic size of Na,
Be and Mg is:
\( A \cdot B e>M g>N a \)
в. \( \mathrm{Na}>\mathrm{Mg}>\mathrm{Be} \)
c. \( \mathrm{Mg}>\mathrm{Na}>\mathrm{Be} \)
D. \( N a=M g>B e \)
Subject: Physics
An object 0 is placed at a point
distance \( x \) from the focus \( F_{1} \) of a
convex lens of focal length \( f \) (both side
medium being same) and its image lis
formed at a distance \( x^{\prime} \) from \( F_{2} \) as
shown in the figure. the magnification is
A \( \cdot \frac{f}{x+x^{\prime}} \)
B. \( \frac{x^{\prime}}{x} \)
\( c \cdot \frac{f}{x} \)
D. none of these
Subject: Physics
The velocity \( v \) of sound can be assumed
as dependent on density of medium and modulus of elasticity of medium ,so which of the following can be considered as correct formula for
calculating velocity of sound, \( (\rho \) =density, \( E \) =modulus of elasticity
\( \mathbf{A} \cdot v=\rho^{0.5} \times E^{0.5} \)
В . \( v=\rho^{0.5} \times E^{-0.5} \)
C \( \cdot v=\rho^{-0.5} \times E^{0.5} \)
D. none of the above
Subject: Physics
Where should be a uniform rod of length
\( 10 m \) and weight \( 100 N \) and with a
weight of \( 100 N \) at an extreme point be
balanced?
A. \( 5 \mathrm{m} \) from that extreme
B. \( 2.5 \mathrm{m} \) from that extreme
\( \mathrm{c} .2 .5 \mathrm{m} \) from the other extreme
D. \( 5 m \) from the other extreme
Subject: Physics
A metal bullet moving at \( 400 \mathrm{ms}^{-1} \) strikes on a tree trunk and get
embedded inside it. Assuming total kinetic energy is converted to heat and \( 50 \% \) of heat is absorbed by the bullet,
find the increase in its temperature. (specific heat capacity of metal \( = \) \( 200 J k g^{-1} K^{-1} \) and bullet not melts
Subject: Maths
Which of the following algebraic operations with scalar and vector physical quantities are meaningful.
(i) adding any two vectors
(ii) adding a scalar to a vector of the same dimensions
(iii) multiplying any vector by any scalar
(iv) multiplying any two scalars
(v) adding any two scalars
(vi) adding a component of a vector to the same vector.
A. Only (iii) \& (iv) are permissible
B. Only (ii) \& (iv) are permissible
c. only (iii) \& (v) are permissible
D. Only (i) (iii) (iv) (v)\& (vi) are permissible
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{\mathbf{3}}+\mathbf{3} \boldsymbol{x} \forall \boldsymbol{x} \in \boldsymbol{R}, \) then
equation of tangent for \( y=f^{-1}(x) \) at
\( \boldsymbol{x}=\mathbf{5} \) will be
A \( \cdot 9 y-x=4 \)
В. \( 9 y-4 x=-19 \)
c. \( 49 y-9 x=4 \)
D. \( 9 y-2 x=-1 \)
Subject: Physics
A condenser of capacity \( C \) is charged to
a potential difference of \( V_{1} . \) The plates
of the condenser are the connected to
an ideal inductor of inductance \( L \). The
current through the inductor when the
potential difference across the
condenser reduces to \( V_{2} \) is
\( ^{\mathbf{A}} \cdot\left(\frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L}\right)^{1 / 2} \)
\( ^{\mathbf{B}} \cdot\left(\frac{C\left(V_{1}-V_{2}\right)}{L}\right)^{1 / 2} \)
\( ^{\mathbf{C}} \cdot \frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L} \)
D. \( \frac{C\left(V_{1}-V_{2}\right)}{L} \)
Subject: Maths
If \( \int \frac{d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)}=k \tan ^{-1} x+ \)
\( l \tan ^{-1} \frac{x}{2}+C, \) then
A \( \cdot \quad k=\frac{1}{3} \)
B \( \cdot l=\frac{2}{3} \)
c. \( \quad k=-\frac{1}{3} \)
D \( \cdot l=-\frac{1}{6} \)
Subject: Maths
If \( \boldsymbol{z}=\mathbf{1}+\boldsymbol{i}, \) then the multiplicative
inverse of \( \left.z^{2} \text { is (where } i=\sqrt{-1}\right) \)
\( \mathbf{A} \cdot 2 i \)
в. \( 1-i \)
c. \( -\frac{i}{2} \)
D.
Subject: Physics
Two monochromatic coherent point
sources \( S_{1} \) and \( S_{2} \) are separated by a
distance \( L \). Each source emits light of
wavelength \( \lambda \), where \( L>>\lambda \). The line
\( S_{1} S_{2} \) when extended meets a screen
perpendicular to it at a point \( \boldsymbol{A} \)
A. The interference fringes on the screen are circular in shape
B. The interference fringes on the screen are straight lines perpendicular to the line \( S_{1} S_{2} A \)
c. Point \( A \) is an intensity maxima if \( L=n \lambda \)
D. Point \( A \) is always an intensity maxima for any separation \( L \)
Subject: Physics
An electric alpole consists or small
charged objects \( A \) and \( B \) of charges \( -q \)
and \( +q \) and masses \( m \) and \( 4 m \)
respectively. They are connected by a light non -conducting rod of length \( L \) This system is hinged at \( A \) so that it
can rotate in vertical plane. A uniform
electric field of intensity \( \boldsymbol{E} \) is applied vertically downward. The rod is released
from horizontal position as shown in figure. The angular velocity of the rod
when the rod becomes vertical is.
A \( \cdot \sqrt{\frac{4 m g+q E}{2 m l}} \)
B. \( \sqrt{\frac{6 m g+q E}{2 m l}} \)
c. \( \sqrt{\frac{8 m g+q E}{6 m l}} \)
D. \( \sqrt{\frac{2 m g+q E}{2 m l}} \)
Subject: Physics
Two bottles \( A \) and \( B \) have radii \( R_{A} \) and
\( R_{B} \) and heights \( h_{A} \) and \( h_{B} \) respectively
with \( R_{B}=2 R_{A} \) and \( h_{B}=2 h_{A} . \) These
are filled with hot water at \( 60^{\circ} \mathrm{C} \)

Consider that heat loss for the bottles
takes place only from side surfaces. If the time the water takes to cool down to
\( 50^{\circ} \mathrm{C} \) is \( t_{A} \) and \( t_{B} \) for bottles \( \mathrm{A} \) and \( \mathrm{B} \)
respectively, then \( t_{A} \) and \( t_{B} \) are best
related as.
A \( \cdot t_{A}=t_{B} \)
B \( \cdot t_{B}=2 t_{A} \)
\( \mathbf{c} \cdot t_{B}=4 t_{A} \)
D. \( t_{B}=t_{A} / 2 \)
Subject: Maths
One mapping is selected at random from all the mappings of the set \( A= \) \( \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots, \boldsymbol{n} \) into itself. The probability
that the mapping selected is one to one, is given by
A \( \cdot \frac{1}{n^{n}} \)
в. \( \frac{1}{n !} \)
c. \( \frac{(n-1) !}{n^{n-1}} \)
D. None of these
Subject: Maths
Find the angle in radian though which a
pendulum swings if its length is \( 75 \mathrm{cm} \) and the tip describes an arc of length
(i) \( 10 \mathrm{cm} \)
(ii) \( 15 \mathrm{cm} \)
(iii) \( 21 \mathrm{cm} \)
Subject: Maths
The A.M. of the series \( 1,2,4,8,16, \dots . ., 2 \)
is
A \( \cdot \frac{2^{n}-1}{n} \)
B. \( \frac{2^{n+1}-1}{n+1} \)
c. \( \frac{2^{n}-1}{n+1} \)
\( \frac{2^{n+1}-1}{n} \)
Subject: Chemistry
A solution containing 0.5 g of naphthalene in 50 g \( C C l_{4} \) yield a
boiling point elevation of \( 0.4 \mathrm{K}, \) while a
solution of \( 0.6 \mathrm{g} \) of an unknown solute in the same mass of the solvent gives a
boiling point elevation of 0.65 K. Find
the molar mass of the unknown solute.
Subject: Maths
The arithmetic mean of the nine
numbers in the given set
\( \{9,99,999, \dots \dots . .999999999\} \) is a 9
digit number \( N, \) all whose digits are distinct, The number \( N \) does not
contain the digit
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
c. 5
D.
Subject: Physics
If we wish to represent the equation for the position of the mass in terms of a differential equation, which one of
these would be the most suitable?
A \( \cdot \quad m \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=0 \)
в. \( \quad_{m} \frac{d^{2} x}{d t^{2}}-b \frac{d x}{d t}+k x=0 \)
c. \( _{m} \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}-k x=0 \)
D. \( _{m} \frac{d^{2} x}{d t^{2}}-b \frac{d x}{d t}-k x=0 \)
Subject: Maths
The area enclosed between the curves
\( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}^{2} \) and \( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{y}^{2}(\boldsymbol{a}>\boldsymbol{0}) \) is
1 sq.unit. then \( a= \)
A \( \cdot \frac{1}{\sqrt{3}} \)
в. \( \frac{2}{\sqrt{3}} \)
c. \( \frac{4}{\sqrt{3}} \)
D. \( \sqrt{3} \)
Subject: Physics
calorie \( ^{\circ} \boldsymbol{C}^{-1}= \)
\( \mathbf{A} \cdot^{\circ} C^{-1} \)
\( 4.8 J K^{-1} \)
B . \( ^{\circ} C^{-1} \)
\( 4.2 J K^{-1} \)
c. \( 1000 C a l \)
D. All
Subject: Maths
\( \sqrt[*]{\frac{x}{1+x^{4}}} d x \)
\( \mathbf{A} \cdot \tan ^{-1} x^{2} \)
B. \( 2 \tan ^{-1} x^{2} \)
c. \( \frac{1}{2} \tan ^{-1} x^{2} \)
D. \( \frac{1}{2} \tan ^{-1} x \)
Subject: Physics
Two moles of an ideal monoatomic gas
occupies a volume \( V \) at \( 27^{\circ} \mathrm{C} \). The gas expands adiabatically to a volume \( 2 \mathrm{V} \) Calculate (a) the final temperature of the gas and (b) change on its internal
energy.
B. (a) \( 195 K \) (b) 2.7 k
\( c .(a) 189 K(b) 2.7 k J \)
D. (a) \( 195 \mathrm{k} \) (b) \( -2.7 \mathrm{kJ} \)
Subject: Physics
Assertion: Magnetic force between two short magnets, when they are co-axial follows inverse square law of distance. Reason : The magnetic forces between two poles do not follow inverse square
law of distance
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
Nitric acid is manufactured by the Ostwald process in which nitrogen dioxide reacts with water. The reaction
is as follows:
\( \boldsymbol{p} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightarrow \)
\( \boldsymbol{q} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{N} \boldsymbol{O} \)
Find the value of \( \boldsymbol{p}+\boldsymbol{q} \)
A . 8
B. 4
\( c .5 \)
D.
Subject: Chemistry
\( \boldsymbol{3} \boldsymbol{A} \longrightarrow \boldsymbol{B}+\boldsymbol{C} \)
It would be a zero-order reaction when:
A. The rate of reaction is proportional to square of concentration of \( A \)
B. The rate of reaction remains the same at any concentration of \( A \)
C. The rate remains unchanged at any concentration of \( B \) and \( C \)
D. The rate of reaction doubles if concentration of \( B \) is
increased to double
Subject: Maths
If \( f(x)=\frac{x}{\sqrt{1-x^{2}}}, g(x)=\frac{x}{\sqrt{1+x^{2}}} \)
\( \operatorname{then}(f o g)(x)= \)
\( A \)
В. \( \frac{x}{\sqrt{1+x^{2}}} \)
c. \( \sqrt{1+x^{2}} \)
D. 2x
Subject: Physics
Assertion
Suppose some reaction takes place in a container which has a movable
side,then if it is known that for that
particular reaction its entropy change is negative then we can necessarily say that that reaction is not possible.
Reason
For any process to undergo,its entropy change must be positive.
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 thin sheet of glass \( (\mu=1.5) \) of thickness 6 micron introduced in the
path of one of the interfering beams in a double slit experiment shifts the central fringe to a position previously occupied by fifth bright fringe. The the wavelength of light used is
A \( \cdot 6000 \stackrel{\circ}{A} \)
в. 3000 ,
\( c \cdot 4500 \stackrel{\circ}{A} \)
D・7500 \( \stackrel{\circ}{A} \)
Subject: Maths
In the diagram \( O \) is the centre of the
circle with diameter \( 20 \mathrm{cm} \)
The circle is the locus of a point \( \boldsymbol{X} \) State
the distance of \( X \) from \( O \)
\( A \cdot 5 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)
Subject: Maths
Which of the following indicates
ascending order of the fractions?
A. \( \frac{4}{13}, \frac{2}{7}, \frac{3}{11}, \frac{1}{5} \)
B. \( \frac{1}{5}, \frac{2}{7}, \frac{3}{11}, \frac{4}{13} \)
C. \( \frac{1}{5}, \frac{3}{11}, \frac{2}{7}, \frac{4}{13} \)
D. \( \frac{2}{7}, \frac{1}{5}, \frac{3}{11}, \frac{4}{13} \)
Subject: Maths
The area of a segment of a circle of
radius \( 21 \mathrm{cm} \) if the arc of the segment
has a measure of \( 60^{\circ} \) is
(Take \( \sqrt{\mathbf{3}}=\mathbf{1 . 7 3} \) )
A. 45.27 sq. \( \mathrm{cm} \)
B. 40.27 sq. \( \mathrm{cm} \)
c. 40.8 sq. \( \mathrm{cm} \)
D. none of these
Subject: Maths
What is the \( Y \) - intercept for the straight line \( 2 x-3 y=5 ? \)
A \( \cdot \frac{2}{5} \)
в. \( -\frac{5}{3} \)
c. \( -\frac{5}{2} \)
D. \( \frac{1}{2} \)
Subject: Maths
A cubic meter of copper weighing \( 9000 k g \) is rolled into a square bar \( 9 m \)
long. an exact cube is cut off from the bar. How much does it weight?
A. \( 333.3 \mathrm{kg} \)
в. \( 320.5 \mathrm{kg} \)
\( \mathrm{c} .349 .1 \mathrm{kg} \)
D. \( 312.9 \mathrm{kg} \)
Subject: Physics
Assertion
In the phenomenon of mutual induction,
self Induction of each of the coil
persists.
Reason
Self induction arises when strength of
current in one coil changes. In mutual induction, current is changing in both
the individual coils.
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
The integer next above \( (\sqrt{3}+1)^{2 n} \)
contains
\( \mathbf{A} \cdot 2^{n+1} \) as a factor
B. \( 2^{n+2} \) as a factor
\( \mathbf{c} \cdot 2^{n+3} \) as a factor
D. \( 2^{n} \) as a factor
Subject: Chemistry
We have all heard the phrase "opposites attract but like repels." This is especially true for ionic compounds. Which one of the following has the largest lattice energy as a result of this attraction?
A . Licl
в. \( N a C l \)
\( \mathrm{c} \cdot K_{2} \mathrm{O} \)
D. \( M g C l_{2} \)
Subject: Maths
Let the perpendiculars from any point on the line \( 2 x+11 y=5 \) upon the lines
\( 24 x+7 y-20=0 \) and \( 4 x-3 y-2= \)
0 have the lengths \( p_{1} \) and \( p_{2} \)
respectively. Then,
A \( \cdot 2 p_{1}=p_{2} \)
B . \( p_{1}=p_{2} \)
\( \mathbf{c} \cdot p_{1}=2 p_{2} \)
D. None of these
Subject: Maths
f \( A+B+C=\pi \), then
\( \left|\begin{array}{ccc}\sin (\boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}) & \sin \boldsymbol{B} & \cos \boldsymbol{C} \\ -\sin \boldsymbol{B} & \boldsymbol{0} & \boldsymbol{t a n} \boldsymbol{A} \\ \cos (\boldsymbol{A}+\boldsymbol{B}) & -\boldsymbol{t a n} \boldsymbol{A} & \boldsymbol{0}\end{array}\right| \)
equals
A .
B. 2 \( \sin B \tan A \cos C \)
\( c \)
D. none of these
Subject: Maths
The general solution of the differential
equation \( y d x-x d y+x^{2} \cdot \sin y d y+ \)
\( \left(1+x^{2}\right) d x=0, \) is equal to:
A \( \cdot x^{2}=(c+1) x+x \cdot \cos y-y \)
B . \( x^{2}=(c+1) x+x . \cos y+y \)
c. \( x^{2}=c x+x . \cos y+y-1 \)
D. \( x^{2}=c x+x . \cos y+y+1 \)