AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
To minimise parallax error, the observer
should place the object:
\( A \cdot \) as near to the scale of the ruler as possible and the eye must be directly above the scale
B. as far to the scale of the ruler as possible and the eye must be directly above the scale
C. as near to the scale of the ruler as possible and the eye must be to the right of the scale
D. as near to the scale of the ruler as possible and the eye must be to the left of the scale
Subject: Chemistry
In which of the following compounds iron
has the lowest oxidation state?
\( \mathbf{A} \cdot F e(C O)_{5} \)
\( \mathbf{B} \cdot F e_{2} O \)
\( \mathbf{c} \cdot K_{4}\left[F e(C N)_{6}\right] \)
D \( \cdot F e S O_{4} \cdot\left(N H_{4}\right) S O_{4} \cdot 6 H_{2} O \)
Subject: Physics
A uniform rod of mass \( \mathrm{m} \) and length Lis
suspended with two massless strings as shown in the figure. If the rod is at
rest in a horizontal position the ratio of
tension in the two strings \( T_{1} / T_{2} \) is
\( A \cdot 1: \)
B. 1: 2
\( c \cdot 2: 1 \)
\( D \)
Subject: Biology
Consider the following pairs.
Intake and utilization of
A. Nutrition
- nutrients for energy requirements
Derives nutrition from
B. Saprophytes - dead organic
matters
Animals and
c. Heterotrophs
D. Chemotrophic \( \mathrm{N}_{2} \) fixing bacteria
The correctly paired groups are given in
\( A \cdot A, B \) and \( C \)
B. B, C and D
C. \( A, B, C \) and \( D \)
D. \( A, C \) and \( D \)
Subject: Maths
\( \int \sec x \cdot \log (\sec x+\tan x) d x= \)
\( A \cdot[\log (\sec x+\tan x)]^{2}+c \)
B. \( \frac{[\log (\sec x+\tan x)]^{2}}{2}+c \)
c. \( -\log (\sec x+\tan x)+c \)
D. \( \log (\sec x+\tan x)+c \)
Subject: Chemistry
Choose the correct statements from the
following?
A. Rhombic sulphur is blue in colour.
B. Rhombic sulphur is soluble in water but insoluble in organic solvents
C. Rhombic and monoclinic sulphur have \( S_{6} \) molecules.
D. In Cyclo- \( S_{6} \) molecule, the ring adopts chair form.
Subject: Maths
The tangent to the curve \( x= \) \( a \sqrt{\cos 2 \theta} \cos \theta, y=a \sqrt{\cos 2 \theta} \sin \theta \) at
the point corresponding to \( \boldsymbol{\theta}=\boldsymbol{\pi} / \boldsymbol{6} \) is
A. parallel to the \( x \) -axis
B. parallel to the \( y \) -axis
c. parallel to line \( y=x \)
D. none of these
Subject: Physics
Two tuning folks with natural frequencies \( 340 \mathrm{Hz} \) each move relative
to a stationary observer. One fork moves away from the observer, while the other moves towards him at the same speed. The observer hears beats of frequency 3
Hz. Find the speed of the tuning fork. (Velocity of sound in air \( =330 \mathrm{m} / \mathrm{s} \) )
Subject: Physics
Which of the following represents the
relative penetrating power of the three types of radioactive emission in
decreasing order?
\( \mathbf{A} \cdot \beta>\alpha>\gamma \)
В \( \cdot \beta>\gamma>\alpha \)
\( \mathbf{c} \cdot \gamma>\alpha>\beta \)
D \( \cdot \gamma>\beta>\alpha \)
Subject: Maths
Three lines \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}-\mathbf{7}=\mathbf{0}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+ \)
\( \mathbf{3}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{4}=\mathbf{0} \) form \( \mathbf{3} \) sides
of two squares then equation of
remaining side of these squares is
A. \( 2 x+y+14=0 \)
В. \( 2 x-y-14=0 \)
c. \( 2 x-y+6=0 \)
D. \( 2 x-y+14=0 \)
Subject: Physics
The second's hand of a watch has length
6cm. Speed of end point and magnitude
of difference of velocities at two
perpendicular positions will be:
A \( .2 \pi \& 0 \mathrm{mm} / \mathrm{s} \)
B. \( 2 \sqrt{2} \pi \& 44 \mathrm{mm} / \mathrm{s} \)
\( \mathbf{c} \cdot 2 \sqrt{2} \pi \& 2 \pi \mathrm{mm} / \)
D. \( 2 \pi \& 2 \sqrt{2} \pi \mathrm{mm} / \mathrm{s} \)
Subject: Physics
Assertion : Every periodic motion is not simple harmonic motion.
Reason: The motion governed by the
force law
\( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \) is simple harmonic.
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: Maths
Find the coordinates of a point
equidistant from four points \( \boldsymbol{O}(\mathbf{0}, \mathbf{0}, \mathbf{0}), \boldsymbol{A}(\ell, \mathbf{0}, \mathbf{0}), \boldsymbol{B}(\mathbf{0}, \boldsymbol{m}, \boldsymbol{0}) \) and
\( \boldsymbol{C}(\mathbf{0}, \mathbf{0}, \boldsymbol{n}) \)
Subject: Maths
Let
\( |X| \) denote the number of elements in a set \( X \).let \( S=\{1,2,3,4,5,6\} \) be a
sample space,where each elements is equally likely to occur.If \( A \) and \( B \) are
independent events associated with \( S \) then the number of ordered pairs \( (A, B) \) such that \( 1 \leq|B|<|A| \) equals.
Subject: Physics
A ball falls from a height of \( 5 m \) and strikes the roof of a lift. If at the time of
collision, lift is moving in the upward direction with a velocity of \( 1 m / s, \) then the velocity with which the ball rebounds after collision will be :
A. \( 11 \mathrm{m} / \mathrm{s} \) downwards
B. 12 \( m / s \) upwards
c. \( 13 \mathrm{m} / \mathrm{s} \) upwards
D. 12 \( m / s \) downwards
Subject: Physics
A particular force propels a particle in such a way that the force can be
represented by the function \( \boldsymbol{F}(\boldsymbol{x})= \)
\( \sin 2 x, \) where \( x \) is in meters and \( F \) is in
Newtons (the proper conversion of input
and output units and dimensions is implied). When the particle moves from \( x=\frac{\pi}{2} \) to
\( x=\pi, \) by how much does its potential
energy change?
\( \mathbf{A} \cdot \mathbf{2} \)
B. 1
c. 0
D. -
E. -2
Subject: Physics
A stone tied to the end of a string which is \( 80 \mathrm{cm} \) long is whirled in a horizontal
circle with a constant speed. If the stone makes 14 revolutions in \( 25 s \), what is
the magnitude of
centripetal acceleration? \( \left(\operatorname{in} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A . 9.91
B . 2.36
c. 10.36
D. 12.69
Subject: Physics
The potential energy of a 1 kg particle free to move along the \( x \) -axis is given by \( V(x)=\left(\frac{x^{4}}{4}-\frac{x^{2}}{2}\right) J . \) The tota
mechanical energy of the particle 2 J. Then, the maximum speed (in \( \mathrm{m} / \mathrm{s} \) ) is
\( A \cdot 2 \)
B. \( 3 / \sqrt{2} \)
\( c \cdot \sqrt{2} \)
D. \( 1 / \sqrt{2} \)
Subject: Physics
A conducting sphere is enclosed by a
hollow conducting shell. Initially the
inner sphere has a charge \( Q \) while the
outer one is uncharged. The potential difference between the two spherical
surface is found to be \( V \). Later on the
outer shell is given a charge \( -4 Q \). The
new potential difference between the
two surface is:
A. \( V \)
B. \( -V \)
c. \( -2 V \)
D. \( 2 V \)
Subject: Chemistry
Which of the following statements are
incorrect?
This question has multiple correct options
A. For coagulation of \( A s_{2} S_{3} \) sol, tve ions are effective
B. For coagulation of aluminium hydroxide sol, \( B a^{2+} \)
ions are more effective than \( N a^{+} \)
C. Cellulose solution is an example of multimolecular colloid system
D. Colloidal sol of metals such as gold, silver etc. are prepared by Bredig's arc method
Subject: Physics
What is the did
charge \( q \) is projected towards an
infinitely long line of a charge (having linear density of charge \( +\lambda \) ) from a
distance \( t_{0} . \) The direction of initial
velocity \( v_{0} \) makes an angle \( 30^{\circ} \) with the
normal to the line of charge as shown in
figure. The minimum distance of
approach of the charge particle with the line of charge will be (neglect gravity). \( \operatorname{take} \lambda=\frac{\pi \varepsilon_{0} m v_{0}^{2}}{4 q} \)
\( A \cdot \frac{r_{0}}{e} \)
B. \( \frac{r_{0}}{e^{2}} \)
c. \( \frac{r_{0}}{e^{3}} \)
D. \( \frac{r_{0}}{2} \)
Subject: Physics
A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B represent the electric and magnetic fields respectively, this region of space may not have
A. \( E=0, B=0 \)
B. \( E=0, B \neq 0 \)
c. \( E \neq 0, B=0 \)
D. \( E \neq 0, B \neq 0 \)
Subject: Physics
A satellite close to the earth is in orbit
above the equator with a period of
revolution of 1.5 hours in the same
sense as that of the earth. If it is above a
point \( \boldsymbol{P} \) on the equator at some time, it will be above \( P \) again after a time.
A. 1.5 hours
B. 1.6 hours if it is rotating from west to east
c. \( \frac{24}{27} \) hours if it is rotating from west to east
D. none of these
Subject: Chemistry
Which of the following is not expected to show paramagnetism?
\( \mathbf{A} \cdot\left[N i\left(H_{2} O\right)\right]^{2+} \)
B. \( N i(C O)_{4} \)
\( \mathrm{c} \cdot\left[N i\left(N H_{3}\right)_{4}\right]^{2} \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{2} \)
Subject: Maths
Let \( A \) and \( B \) be two finite sets having \( m \)
and \( n \) elements respectively such that \( \boldsymbol{m} \leq \boldsymbol{n} . \) A mapping is selected at random from the set of all mappings from \( A \) to \( B \). The probability that the mapping selected is an injection, is
A. \( \frac{n !}{(n-m) ! m^{n}} \)
в. \( \frac{n !}{(n-m) ! n^{m}} \)
c. \( \frac{m !}{(n-m) ! n^{m}} \)
D. \( \frac{m !}{(n-m) ! m^{n}} \)
Subject: Chemistry
\( \boldsymbol{H}_{\alpha} \) line of Balmer series is \( \mathbf{6 5 0 0} \boldsymbol{A} \). The
wave length of \( \boldsymbol{H} \gamma \) is?
A. \( 4815 \AA \)
в. 4298 А
c. \( 7800 \hat{h} \)
D. 3800 月
Subject: Physics
Two long, thin, parallel conductors separated by a distance carry currents
\( i_{1} \) and \( i_{2} . \) The force per unit length on one of them is F. Then
This question has multiple correct options
\( \mathbf{A} \cdot F \propto\left(i_{1} i_{2}\right) \)
B . \( F \propto\left(i_{1} i_{2}\right)^{2} \)
\( \mathbf{c} \cdot F \propto \frac{1}{d^{2}} \)
\( D \cdot F \propto \frac{1}{d} \)
Subject: Physics
A ball is thrown vertically upwards. It returns \( 6 s \) later. Calculate: \( (i) \) the greatest height reached by the ball, and
\( (i i) \) the initial velocity of the ball. (Take \( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2} \mathbf{)} \)
A \( \cdot\left(\text { i) } 40 m, \text { (ii) } 30 m s^{-1}\right. \)
B. (i) \( 45 \mathrm{m}, \) (ii) \( 30 \mathrm{m} s^{-1} \)
\( \mathbf{c} \cdot(\mathbf{i}) 45 m,\left(\text { i) } 60 m s^{-1}\right. \)
D. (i) \( 45 m \), (ii) \( 20 m s^{-1} \)
Subject: Physics
A vehicle is moving with a speed \( v \) on a
curved smooth road of width \( b \) and
radius \( R \) For counteracting the centrifugal force on the vehicle, the difference in elevation required in
between the outer and inner edges of
the road is
A \( \cdot \frac{v^{2} b}{R g} \)
в. \( \frac{v b}{R g} \)
\( c \)
\( D \)
Subject: Physics
The position of a particle moving along \( \mathbf{x} \) -axis given by \( \boldsymbol{x}=\left(-\mathbf{2} \boldsymbol{t}^{3}+\mathbf{3} \boldsymbol{t}^{2}+\mathbf{5}\right) \boldsymbol{m} \)
The acceleration of particle at the instant its velocity becomes zero is
A \( \cdot 12 \mathrm{m} / \mathrm{s}^{2} \)
B . \( -12 \mathrm{m} / \mathrm{s}^{2} \)
c. \( -6 m / s^{2} \)
D. zero
Subject: Chemistry
A mixture of all isomers of pentane is allowed to react with chlorine
radicals(produced by photochemical
cleavage of \( C l_{2} \) ). How many different isomeric alkyl radicals can form by hydrogen abstraction in the following? Pentane\( (\text {all isomers})+\boldsymbol{C l}^{\bullet} \longrightarrow \)
Pentyl radicals (all isomers) \( + \) HCl
A. 5
B. 6
\( c \cdot 7 \)
D. 8
Subject: Maths
The value of
\( \int \frac{\boldsymbol{d} \boldsymbol{x}}{(\boldsymbol{x}-\boldsymbol{\beta}) \sqrt{(\boldsymbol{x}-\boldsymbol{\alpha})(\boldsymbol{\beta}-\boldsymbol{x})}}, \) is equal to
\( ^{\text {A }} \frac{-1}{\beta-\alpha} \sqrt{\frac{x-\alpha}{\beta-x}}+C \)
в. \( \frac{1}{\beta-\alpha} \sqrt{\frac{x-\alpha}{\beta-x}}+C \)
c. \( \frac{2}{\alpha-\beta} \sqrt{\frac{x-\alpha}{\beta-x}}+C \)
D. none of these
Subject: Physics
A material 'B' has twice the specific resistance of 'A'. A circular wire made of
B' has twice the diameter of wire made
of 'A' then for the two wires to have the same resistance, the ratio, \( \frac{\boldsymbol{I}_{B}}{\boldsymbol{I}_{A}} \) of their
respective length must be
\( A \)
B. 1/2
\( c \cdot 1 / 4 \)
D. 2
Subject: Physics
A reversible engine operates between
temperatures \( 900 \mathrm{K} \& T_{2}\left(T_{2}<900 \mathrm{K}\right) \)
\( \& \) another reversible engine between \( T_{2} \)
\( \& 400 \mathrm{K}\left(\mathrm{T}_{2}>400 \mathrm{K}\right) \) in series. What is
the value of \( T_{2} \) if work outputs of both
the engines are equal?
\( A \cdot 600 K \)
B. 625K
\( c .650 k \)
D. 675K
Subject: Physics
If a rubber ball is taken at the depth of \( 200 m \) in a pool, its voulme decreases by
\( 0.1 \% \). If the density of the water is \( 1 \times \) \( 10^{3} k g / m^{3} \) and \( g=10 m / s^{2}, \) then the
volume elasticity in \( N / m^{2} \) will be
A \( \cdot 10^{8} \)
B . \( 2 \times 10^{8} \)
\( c \cdot 10^{9} \)
D. \( 2 \times 10^{9} \)
Subject: Physics
\( \mathbf{1} \)
\( \boldsymbol{m} \) long wire is folded in the form of a
circular coil and 100 m \( A \) electric
current is flowing in it, then magnetic
field at a point \( 1 ~ m \) away from its centre
on its axis :
\( ^{\text {A }} \cdot \frac{10^{-5}}{4 \pi} T \)
в. \( \frac{10^{-8}}{2 \pi} T \)
\( ^{\text {c. }} \cdot \frac{10^{-5}}{2 \pi} T \)
D. \( \frac{10^{-8}}{4 \pi} T \)
Subject: Chemistry
Select the correct statement.
\( \mathbf{A} \cdot S F_{4}, C H_{4}, S i C l_{4} \) and \( C C l_{4} \) have tetrahedral structure
B. \( B F_{3}, C l F_{3} \) and \( I C l_{3} \) have trigonal planar structure
C \( . X e F_{2}, B e C l_{2} \) and \( I C l_{2}^{-} \) have linear structure
D. All are correct
Subject: Physics
A smooth block is released at rest on a
\( 45^{\circ} \) incline and then slides a distance \( d \)
The time taken to slide is \( n \) times as
much to slide on rough incline than on a
smooth incline. The coefficient of
friction is:
A
в. \( _{\mu_{k}}=\sqrt{1-\frac{1}{n^{2}}} \)
c. \( _{\mu_{s}=1-\frac{1}{n^{2}}} \)
D. \( _{\mu_{s}}=\sqrt{1-\frac{1}{n^{2}}} \)
Subject: Maths
The position vectors of four points \( \boldsymbol{P}, \boldsymbol{Q}, \boldsymbol{R}, \boldsymbol{S} \) are \( \boldsymbol{2} \overline{\boldsymbol{a}}+\boldsymbol{4} \overline{\boldsymbol{c}}, \boldsymbol{5} \overline{\boldsymbol{a}}+\boldsymbol{3} \sqrt{\boldsymbol{3} \boldsymbol{b}}+ \)
\( 4 \bar{c}),-2 \sqrt{3 b}+\bar{c} \) and \( 2 \bar{a}+\bar{c} \)
respectively, then
A. \( \overline{P Q} \) is parallel to \( \overline{R S} \)
B. \( \overline{P Q} \) is not parallel to \( \overline{R S} \)
c. \( \overline{P Q} \) is equal to \( \overline{R S} \)
D. \( \overline{P Q} \) is parallel and equal to \( \overline{R S} \)
Subject: Physics
Assertion
If refractive index of one medium is
equal to refractive index of second
medium, then beam does not bend at
all.
Reason
The bending of light does not depend on refractive indices of media.
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 one angle of a parallelogram is \( 65^{\circ} \)
What are the other angles?
A \( .50^{\circ}, 120^{\circ}, 50^{\circ} \)
в. \( 115^{\circ}, 65^{\circ} \), \( 115^{\circ} \)
\( \mathbf{c} \cdot 65^{\circ}, 115^{\circ}, 65^{\circ} \)
D. None of the above
Subject: Biology
Match the two lists. Choose the choice
which gives the correct combination of
the alphabets of the two columns.
List II
(Secretions) List I (Type of
cells) Lysozyme \( A \) \begin{tabular}{c|c}
\( ^{A} \) & \( B \) eta cells \\
\hline\( B \) & \( M \) astcells \\
\hline C & Paneth cells \\
\hline Acinarcells \\
\hline
\end{tabular} Mucus
\( r \) Histamine s \( \quad \) Insulin \( t \quad \) Pancreatic
enzymes
A. \( A-q, B-r, C-p, D-t \)
B. A-s, B-r, C- p, D-t
C. \( A-t, B-q, C-r, D-s \)
D. \( A-s, B-q, C-p, D-t \)
Subject: Maths
If the circumference of the inner edge of a hemispherical bowl is \( \frac{132}{7} c m, \) then what is its capacity?
\( \mathbf{A} \cdot 12 \pi c m^{3} \)
В. \( 18 \pi c m^{3} \)
\( \mathbf{c} \cdot 24 \pi c m^{3} \)
\( \mathrm{D} \cdot 36 \pi c m^{3} \)
Subject: Physics
Radius of curvature of a road is \( 60 \mathrm{m} \). It
is a to be banked so that no friction
force is required for a car travelling on the road at \( 25 \mathrm{mt} / \mathrm{sec} \). Find the angle of
banking?
A \( .47^{\circ} \)
B . \( 45^{\circ} \)
\( c .90 \)
D. \( 180^{\circ} \)
Subject: Physics
A body of mass 5 kg undergoes a change in speed from 20 to \( 0.20 \mathrm{m} / \mathrm{s} \)
The momentum of the body would:
A. increase by \( 99 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. decrease by \( 99 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. increase by \( 101 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. decrease by \( 101 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
Subject: Maths
If \( \frac{\mathbf{3} \boldsymbol{x}+\boldsymbol{a}}{\boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}+\mathbf{2}}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{2}}-\frac{\mathbf{1 0}}{\boldsymbol{x}-\mathbf{1}}, \) then
\( \boldsymbol{a}=\ldots \) and \( \boldsymbol{A}=\ldots \)
A \( \cdot a=7, A=13 \)
3
В. \( a=11, A=13 \)
c. \( a=13, A=7 \)
Subject: Physics
Figure represents a negatively charged
gold leaf electroscope. Of the parts \( A, B \) C, D and E, state whether they are an
insulator or a conductor:
\( A \cdot A, B \) and \( E \) are conductors while \( D \) and \( C \) are insulators
B. B, D and E are conductors while A and C are insulators
\( c . A, D \) and \( E \) are insulators while \( B \) and \( C \) are conductors
D. A, Dand E are conductors while B and C are insulators
Subject: Physics
A magnetic field directed along \( Z \) axis
varies as \( \boldsymbol{B}=\boldsymbol{B}_{0} \boldsymbol{x} / \boldsymbol{a}, \) where \( \boldsymbol{B}_{0}= \)
2 tesla and \( a=1 m . \) A conducting
square loop of side \( \ell=\frac{1}{2} m \) is placed
with its edges parallel to \( X \) and \( Y \) axes. If
the loop is made to move with a
constant velocity \( v_{0}=6 m / s \) directed
along \( X \) axis, the induced emf (in volts) in the loop is :
Subject: Physics
A charged particle (charge q) is moving in a circle of radius \( R \) with uniform
speed v. The associated magnetic
moment \( \mu \) is given by
A \( \cdot q v R \)
в. \( _{q v} \frac{R}{2} \)
\( \mathbf{c} \cdot q v R^{2} \)
D. \( _{q v} \frac{R^{2}}{2} \)
Subject: Physics
A wave of length \( 2 m \) is superposed on
its reflected wave to form a stationary wave. A node is located at \( x=3 m \) The
next node will be located at \( x= \)
A. \( 4 m \)
B. \( 3.75 m \)
\( c .3 .50 m \)
D. \( 3.25 m \)
Subject: Chemistry
The correct increasing order of melting point of alkali metal carbonates is:
A \( \cdot C s_{2} C O_{3}<N a_{2} C O_{3}<K_{2} C O_{3}<R b_{2} C O_{3}< \)
\( L i_{2} C O_{3} \)
в. \( L i_{2} C O_{3}<N a_{2} C O_{3}<K_{2} C O_{3}<R b_{2} C O_{3}< \)
\( C s_{2} C O_{3} \)
3
c. \( L i_{2} C O_{3}<R b_{2} C O_{3}<K_{2} C O_{3}<N a_{2} C O_{3}< \)
\( C s_{2} C O_{3} \)
D. None of these
Subject: Physics
Albert is riding his scooter at a velocity of \( 80 k m / h \) when he sees an old woman crossing the road \( 45 m \) away he immediately steps hard on the break to get the maximum deceleration of
\( 7.5 m / s^{2} . \) How far will he go before stopping, will he hit the old woman? (in
\( m) \)
A. \( 36.4, \) Yes
B. \( 35, \) No
c. \( 54.2, \) Yes
D. \( 32.9, \) No
Subject: Physics
One litre of water at \( 30^{\circ} C \) is mixed with
one litre of water at \( 50^{\circ} C . \) The
temperature of the mixture will be
A . \( 80 \mathrm{c} \)
B. more than 50c but less than 80C
\( c \cdot 20 c \)
D. between \( 30 c \) and 500
Subject: Maths
If pitqj is a unit vector perpendicular to \( 4 i+3 j, \) then
A. P= \( -3 / 5 \) and \( q=-4 / 5 \)
B. P=4/5 and q=3/5
c. \( P=2 / 5 \) and \( q=1 / 5 \)
D. None
Subject: Chemistry
The standard heat of combustion of
\( A l \) is \( -837.8 k J \) mol \( ^{-1} \) at \( 25^{\circ} \) C. If \( A l \)
reacts with \( O_{2} \) at \( 25^{\circ} C \), the formation of
0.150 mol of \( A l_{2} O_{3} \) release \( x k J \) of
heat. \( x \) is
Subject: Chemistry
For the equilibrium, \( \boldsymbol{L i C l} \cdot \mathbf{3 N H}_{3}(s) \rightleftharpoons \boldsymbol{L i C l} \cdot \boldsymbol{N} \boldsymbol{H}_{3}(s)+ \)
\( 2 N H_{3}(g) \quad K_{p}=9 a t m^{2} \) at \( 37^{\circ} C \)
A 5 litre vessel contains 0.1 mole of
\( L i C l \cdot 3 N H_{3} . \) How many moles of \( N H_{3} \)
should be added to the flask at this
temperature to derive the backward reaction for completion? \( \boldsymbol{R}=\mathbf{0 . 0 8 2} \boldsymbol{a t m . L / m o l K} \)
A . 0.2
в. 0.59
\( c \cdot 0.69 \)
D. 0.79
Subject: Physics
In terms of basic units of mass(M),
length(L), time(T) and charge(Q), the dimensions of magnetic permeability of
vacuum \( \left(\mu_{0}\right) \) would be?
\( \mathbf{A} \cdot\left[M L Q^{-2}\right] \)
B . \( \left[L T^{-1} Q^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1} Q^{-2}\right] \)
D \( \cdot\left[L T Q^{-1}\right] \)
Subject: Maths
After the first term in a sequence of
positive integers, the ratio of each term to the term immediately preceding it is
2 to \( 1 . \) What is the ratio of the \( 8^{t h} \) term
in this sequence to the \( 5^{t h} \) term?
\( A \cdot 6 \) to 1
B. 8 to 5
\( c \cdot 8 \) to 1
D. 64 to 1
E. 256 to 1
Subject: Maths
\( \mathrm{f}\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \\ \mathbf{2} \boldsymbol{x} & \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} & \boldsymbol{4} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{2} \boldsymbol{z} \\ \boldsymbol{3} \boldsymbol{x} & \boldsymbol{6} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y} & \boldsymbol{1} \mathbf{0} \boldsymbol{x}+\boldsymbol{6} \boldsymbol{y}+\boldsymbol{3} \boldsymbol{z}\end{array}\right|=\mathbf{6} \boldsymbol{4} \)
then find \( x \)
Subject: Physics
The disk has a weight of \( 100 \mathrm{N} \) and rolls without slipping on the horizontal surface as it oscillates about its
equilibrium position. If the disk is displaced, by rolling it counterclockwise 0.4 rad, determine the
equation which describes its oscillatory motion when it is released.
A \( \cdot \theta=-0.2 \cos (16.16 t) \)
B \( \cdot \theta=0.2 \cos (16.16 t) \)
c. \( \theta=-0.4 \cos (16.16 t) \)
Subject: Physics
A thin prism of angle \( 15^{\circ} \) made of glass
of refractive index \( \mu_{1}=1.5 \) is combined
with another prism of glass of refractive
index \( \mu_{2}=1.75 . \) The combination of the
prism produced dispersion without deviation. The angle of the second prism
should be :
A \( \cdot 5^{\circ} \)
B . \( 7^{\circ} \)
\( c \cdot 10^{\circ} \)
D. \( 12^{\circ} \)
Subject: Chemistry
The energy change accompanying the
equilibrium reaction \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \) is
\( -33.0 k J m o l^{-1} \)
Assuming that pre-exponential factor is
same for forward and backward
reaction. The equilibrium constant K for
the reaction at \( 300 \mathrm{K} \)
\( \mathbf{A} \cdot 5.55 \times 10^{5} \)
B . \( 5.67 \times 10^{3} \)
\( \mathbf{c} \cdot 5.55 \times 10^{6} \)
\( \mathbf{D} \cdot 5.67 \times 10^{2} \)
Subject: Biology
Match the followings and mark the
correct option.
Column I n Il
A. Sternum
(i) Synovial fluid ne
B. Glenoid d cavity
(ii) Vertebrae
(iii) Pectoral girdle
C. Freely movable joint
D. Cartilaginous joint
(iv) Flat bones \( t \) (i
\( A \cdot A-(i i), B-(i), C-(i i i), D-(i v) \)
B. \( A-(\text { iv }), B-(\text { iii) }, C-(i), D-(i i) \)
C \( \cdot A-(\text { ii) }, B-(i), C-(i v), D-(i i i) \)
D. \( A-(\text { iii) }, B-(i), C-(i i), D-(i v) \)
Subject: Physics
speed of \( 340 \mathrm{m} \mathrm{s}^{-1} \). The wavelength of
the wave is :
\( \mathbf{A} \cdot 1.5 \times 10^{5} m \)
B. 0.77 \( m \)
\( \mathbf{c} .1 .4 \mathrm{m} \)
D. 1.1