AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A lift starts from the top of a mine shaft
and descends with a constant speed of
\( 10 m / s .4 \) sec later a boy throws a stone
vertically upwards from the top of the shaft with a speed of \( 30 m / s . \) If stone
hits the lift at a distance \( x \) below the
shaft write the value of \( \frac{x}{3}(\text { in } m) \) \( \left[\text { Take }: \boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right]( \) given value of
\( \mathbf{2 0} \sqrt{\mathbf{6}}=\mathbf{4 9}) \)
Subject: Physics
The highest temperatures recorded in 4 different countries are listed below
What is the highest temperature listed
above?
A \( \cdot 127.6^{\circ} \)
B. \( 114.8^{\circ} \mathrm{F} \)
c. \( 136.4^{\circ} \mathrm{F} \)
D . 134.0 \( ^{\circ} \)
Subject: Maths
Find the slope of a line parallel to the line \( \boldsymbol{y}=\frac{\mathbf{2}}{\mathbf{3}} \boldsymbol{x}-\mathbf{4} \)
A . -4
в. \( -\frac{3}{2} \)
\( c \cdot 2 \)
D. \( \frac{3}{2} \)
\( E \cdot \frac{2}{3} \)
Subject: Chemistry
Which is the correct order of increasing energy of the listed orbitals in the atom
of titanium?
(At. no. \( Z=22) \)
\( \mathbf{A} \cdot 3 s 3 p 3 d 4 s \)
B. 3s 3p 4s 3d
c. \( 3 s \) 4s \( 3 p 3 d \)
D. \( 4 s 3 s 3 p 3 d \)
Subject: Chemistry
Hydrolysis of sucrose gives glucose and fructose. The reaction takes place as:
Sucrose \( +\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \) Glucose \( + \) Fructose
The equilibrium constant \( K_{c} \) for this
reaction is \( 2 \times 10^{13} \) at \( 300 K . \) The \( \Delta G^{\circ} \)
at \( 300 K \) is:
A . \( 7.64 \times 10^{4} \mathrm{J} \mathrm{mol}^{-} \)
В. \( 7.64 \times 10^{-4} \) Л то \( l^{-1} \)
c. \( -7.64 \times 10^{-4} \mathrm{J} \mathrm{mol}^{-1} \)
D. \( -7.64 \times 10^{4} \mathrm{J} \) mol \( ^{-1} \)
Subject: Physics
When a magnet M is pushed in and out
of a circular coil \( C \) connected to a very
sensitive galvanometer \( G \) as shown in
the figure with frequency f then which of
the following holds true?
A. constant deflection will be observed in the galvanometer.
B. visible small variation will be observed in the galvanometer if \( f \) is about 50 Hz
c. oscillation in the deflection will be seen clearly when \( f=1 \) or \( 2 \mathrm{Hz} \)
D. no variation in the deflection will be seen even when \( f=1 \) or 2 Hz.
Subject: Physics
The density of water is equal to:
A \( \cdot 10^{-3} \operatorname{kg} m^{-3} \)
B . \( 10^{-2} \mathrm{kgm}^{-3} \)
c. \( 10^{2} \mathrm{kgm}^{-3} \)
D. \( 10^{3} k g m^{-3} \)
Subject: Maths
A vector \( a=(x, y, z) \) of length \( 2 \sqrt{3} \)
which makes equal angles with the vectors \( b=(y,-2 z, 3 x) \) and \( c= \)
\( (2 z, 3 x,-y) \) and is perpendicular to
\( \boldsymbol{d}=(1,-1,2) \) and makes an obtuse angle with y-axis is
B. \( (1,1, \sqrt{10}) \)
D. none of these
Subject: Chemistry
According to Kohlrausch law, the limiting value of molar conductivity of
an electrolyte \( \boldsymbol{A}_{2} \boldsymbol{B} \)
\( \mathbf{A} \cdot \lambda_{A^{+}}+\lambda_{B^{2}} \)
в. \( \frac{1}{2} \lambda_{A+}+\lambda_{B^{2}} \)
c. \( _{2 \lambda_{A^{+}}+\frac{1}{2} \lambda_{B^{2}}} \)
D. \( 2 \lambda_{A^{+}}+\lambda_{B^{2}} \)
Subject: Physics
A block of mass of \( 1 k g \) is moving on the
x-axis. A force \( \boldsymbol{F} \) acting on the block
is shown. Velocity of the block at time
\( t=2 s \) is \( -3 m / s . \) What is the speed of
the block at time \( t=4 s ? \)
\( \mathbf{A} \cdot 8 m / s \)
B. \( 2 m / s \)
c. \( 3 m / s \)
D. \( 5 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A metal conductor of length \( 1 \mathrm{m} \) rotates vertically about one of its ends at angular velocity 5 radians per second. If
the horizontal component of earth's magnetic field is \( 0.2 \times 10^{-4} T \), then the
e.m.f developed between the two ends of
the conductor is
\( A \cdot 5 m v \)
B. \( 50 \mu V \)
c. \( 5 \mu V \)
D. 50 mv
Subject: Physics
The wave function of a pulse is given by \( y=\frac{5}{(4 x+6 t)^{2}} \) where \( x \) and \( y \) are in
meter and \( t \) is in second, then
determine the wave velocity of the
pulse.
A. \( 2 m / s \)
в. \( 1 \mathrm{m} / \mathrm{s} \)
c. \( -1.5 m / s \)
D. \( 2.5 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Order of number of revolution/sec
\( \gamma_{1}, \gamma_{2}, \gamma_{3} \) and \( \gamma_{4} \) for \( I, \) II, III and IV orbits
is:
A \( \cdot \gamma_{1}>\gamma_{2}>\gamma_{3}>\gamma_{4} \)
В \( \cdot \gamma_{4}>\gamma_{3}>\gamma_{2}>\gamma_{1} \)
C \( \cdot \gamma_{1}>\gamma_{2}>\gamma_{4}>\gamma_{3} \)
D. \( \gamma_{2}>\gamma_{3}>\gamma_{4}>\gamma_{1} \)
Subject: Physics
Magnetic field at point 'O' due to given current distribution. If 5 A current is
flowing in this system and the diameter of the loop is \( 10 \mathrm{cm} \)
A \( \cdot 2 \times 10^{-5} T, \otimes \)
B \( \cdot 10^{-5} T, \odot \)
\( \mathbf{c} \cdot 10^{-5} T, \otimes \)
D. \( 2 \times 10^{-5} T, \odot \)
Subject: Physics
A solid sphere of mass \( \mathrm{M} \& \) radius \( \mathrm{R} \) is divided in two parts of masses \( \frac{7 M}{8} \& \) \( \frac{M}{8}, \) and converted to a disc of radius \( 2 \mathrm{R} \)
\& solid sphere of radius 'r' resp. Find \( \frac{l_{1}}{l_{2}} \)
if \( l_{1} \& l_{2} \) are moment of inertia of disc
\& solid sphere respectively.
A . 200
в. 140
\( c \cdot 120 \)
D. 180
Subject: Physics
A machine gun fires a bullet of mass
\( 40 g \) with a velocity \( 1200 m / s . \) The man holding it can exert a maximum force of
\( 144 N \) on the gun. How many bullets can be fired per second at the most?
A. Only one
B. Three
c. can fire any number of bullets
D. \( 144 \times 48 \)
Subject: Physics
A police car with a siren of frequency \( 8 k H z \) is moving with uniform velocity \( 36 k m / h r \) towards a tall building which reflects the sound waves. The speed of sound in air is \( 320 m / s . \) The frequency
of the siren heard by the car driver is:
A. \( 8.50 k H z \)
B. \( 8.25 k H z \)
c. \( 7.75 k H z \)
D. \( 7.50 k H z \)
Subject: Maths
The mean deviation of the following data from mean is :
\( \begin{array}{llllll}\text { Class } & 0- & 5- & 10- & 15- & 20 \\ \text { interval } & 5 & 10 & 15 & 20 & 25\end{array} \) Frequency \( \quad 3 \quad 4 \quad 8 \quad 10 \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c \cdot 6 \)
D. 3
Subject: Chemistry
Assertion
If water is heated to \( 50^{\circ} \mathrm{C} \) then \( p H \) will
increase
Reason
\( K_{w} \) increases with decrease in
temperature
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
fthe matrix \( \left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{5} & -\mathbf{1}\end{array}\right]=\boldsymbol{A}+\boldsymbol{B}, \) where
A is symmetric and B is skew symmetric, then \( B= \)
A. \( \left[\begin{array}{cc}2 & 4 \\ 4 & -1\end{array}\right] \)
B. \( \left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right] \)
C \( \cdot\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right] \)
D. \( \left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right] \)
Subject: Chemistry
From the give options, which of the following compound will make best buffer solution?
A. \( H_{2} O, 1 M \) NaOH, 1 M \( H_{2} \) SO \( _{4} \),
в. \( H_{2} O, \) 1 \( M C H_{3} C O O H, 1 M N a^{+} C H_{3} C O O^{-} \)
c. \( H_{2} O, 1 M C H_{3} C O O H, 6 M N a^{+} C H_{3} C O O^{-} \)
D. \( H_{2} O, 1 M C H_{3} C O O H, 1 M N a O H \)
Subject: Physics
A parallel beam of white light is
incident normally on a water film \( 1.0 \times \)
\( 10^{-4} \mathrm{cm} \) thick. Find the wavelength in
the visible range \( (400 n m-700 n m) \)
which are strongly transmitted by the film. Refractive index of water \( =1.33 \)
\( A .538 n m \)
В. 534 пт
\( \mathrm{c} .532 \mathrm{nm} \)
D. 548 пт
Subject: Physics
Two stars each of one solar mass \( (= \)
\( \left.2 \times 10^{30} k g\right) \) are approaching each other
for a head on collision. When they are a
distance \( 10^{9} k m, \) their speeds are
negligible. What is the speed with which they collide? The radius of each star is \( 10^{4} k m . \) Assume the stars to remain
undistorted until they collide. (Use the
known value of \( G \) )
Subject: Physics
A aevice \( x \) is connectea to an ac
sources \( \boldsymbol{V}=\boldsymbol{V}_{0} \) sin \( \boldsymbol{\omega} \boldsymbol{t} . \) The variation of
voltage, current and power in one cycle is in the following graph:
(a) Identify the device 'X'.
(b) Which of the curves \( A, B \) and \( C \)
represent the voltage, current and the
power consumed in the circuit? Justify
your answer.
(c) How does its impedance vary with
frequency of the ac source? Show
graphically.
(d) Obtain an expression for the current
in the circuit and its phase relation with
ac voltage.
Subject: Chemistry
What is the minimum pH of a solution
\( 0.10 M \) in \( M g^{2+} \) from which \( M g(O H)_{2} \)
will not precipitate? \( \boldsymbol{K}_{s p} \boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}= \)
\( \mathbf{1} . \mathbf{2} \times \mathbf{1 0}^{-\mathbf{1 1}} \mathbf{M}^{\mathbf{3}} \)
Subject: Physics
Two cells of emf \( 4 V \) and \( 2 V \) and
internal resistance \( 2 \Omega \) and \( 1 \Omega \)
respectively are connected in parallel so
as to send the current in the same
direction through an external resistance of \( 10 \Omega \). Find the potential difference across \( 10 \Omega \) resistor.
Subject: Physics
A conducting circular loop of radius carries a constant current i. It is placed in a uniform mangetic field \( \vec{B}_{0} \) such
that \( \vec{B}_{0} \) is perpendicular to the plane of the loop. The magnetic force acting on the loop is
A . ir \( B_{0} \)
В . \( 2 \pi \) ir \( B_{0} \)
c. zero
\( \mathbf{D} \cdot \pi \) ir \( B_{0} \)
Subject: Physics
Figure shows two conducting spheres separated by large distance and of
radius \( 2 \mathrm{cm} \) and \( 3 \mathrm{cm} \) containing
charges \( 10 \mu \mathrm{C} \) arc \( 20 \mu \mathrm{C} \) respectively
When the spheres are connected by a conducting wire then find out following:
¡)Ratio of the final charge.
ii)Final charge on each sphere.
iii)Ratio of final charge densities.
Subject: Chemistry
The correct increasing covalent nature
is:
A. \( N a C l<L i C l<B e C l_{2} \)
в. \( B e C l_{2}<N a C l< \)LiСl
c. \( B e C l_{2}<L i C l<N a C l \)
D. \( L i C l<N a C l<B e C l_{2} \)
Subject: Maths
If \( p, q, r \) are positive and are in A.P., then the roots of the quadratic equation
\( p x^{2}+q x+r=0 \) are real for
A \( \cdot\left|\frac{r}{p}-7\right| \geq 4 \sqrt{3} \)
В \( \cdot\left|\frac{p}{r}-7\right|<4 \sqrt{3} \)
c. all \( p \) and \( r \)
D. no \( p \) and \( r \)
Subject: Chemistry
Arrange the following types of
interactions in order of increasing
stability (covalent, van der Waals' force,
hydrogen bonding).
A. Hydrogen bonding < covalent < van der Waals' force
B. Covalent \( < \) hydrogen bonding \( < \) van der Waals' force
C. Hydrogen \( < \) Van der Waals' force < covalent bonding
D. Van der Waals' force < hydrogen bonding < covalent
Subject: Physics
The binding energies of the atoms of
elements \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) are \( \boldsymbol{E}_{\boldsymbol{p}} \) and \( \boldsymbol{E}_{Q} \)
respectively. Three atoms of element \( \boldsymbol{Q} \)
fuse to form one atom of element \( P . \) In
this process, the energy released is \( e \)
The correct relation between \( \boldsymbol{E}_{\boldsymbol{P}}, \boldsymbol{E}_{\boldsymbol{Q}} \)
and \( e \) will be
\( \mathbf{A} \cdot E_{Q}=3 E_{P}+e \)
B . \( E_{Q}=3 E_{P}-e \)
\( \mathbf{c} \cdot E_{P}=3 E_{Q}+e \)
D. \( E_{P}=3 E_{Q}-e \)
Subject: Maths
Which of the given alternatives represent a point in Argand plane, equidistant from roots of the equation \( (z+1)^{4}=16 z^{4} ? \)
B \( \cdot\left(-\frac{1}{3}, 0\right) \)
\( ^{c} \cdot\left(\frac{1}{3}, 0\right) \)
D \( \cdot\left(0, \frac{2}{\sqrt{5}}\right) \)
Subject: Chemistry
An alkane with molecular formula
\( C_{5} H_{12} \) forms only one monochloro
product when heated with \( C l_{2} \). The
I \( \boldsymbol{U} \boldsymbol{A} \boldsymbol{C} \) name of this compound is:
A. \( 1, \) 1-dimethyl propane
B. 1,2-dimethyl propane
c. 2,2-dimethyl propane
D. none of the above
Subject: Maths
If
\( \int \frac{2 d x}{[(x-5)+(x-7)] \sqrt{(x-5)(x-7)}} \)
\( \boldsymbol{f}[\boldsymbol{g}(\boldsymbol{x})]+\boldsymbol{c}, \) then
A \( \cdot f(x)=\sin ^{-1} x, g(x)=\sqrt{(x-5)(x-7)} \)
B . \( f(x)=\sin ^{-1} x, g(x)=(x-5)(x-7) \)
C \( \cdot f(x)=\tan ^{-1} x, g(x)=\sqrt{(x-5)(x-7)} \)
D. \( f(x)=\tan ^{-1} x, g(x)=(x-5)(x-7) \)
Subject: Chemistry
A certain metal sulphide, \( M S_{2} \), is used
extensively as a high temperature lubricant. If \( M S_{2} \) is \( 40.06 \% \) by mass of
sulphur, metal \( M \) has atomic mass:
\( \mathbf{A} \cdot 160 \) amu
B. 64 amu
c. 40 amu
D. 96 amu
Subject: Chemistry
Bond dissociation enthalpies of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
and \( N_{2}(g) \) are \( 436.0 \mathrm{KJ} \) mol \( ^{-1} \) and
\( 941.8 \mathrm{mol}^{-1} \) and enthalpy of formation
of \( N H_{3}(g) \) is \( -46 \mathrm{KJ} \) mol \( ^{-1} . \) What is
enthalpy of atomization of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) ? \)
What is average bond enthalpy of \( N- \)
\( \boldsymbol{H} \) bond?
Subject: Chemistry
(A) When \( F e(C N)_{2} \) solution is treated with KCN solution, species formed does not give tests of \( F e^{2+} \) and \( C N^{-} \)
(B) When \( K_{2} S O_{4} \) solution is treated
with \( A l_{2}\left(S O_{4}\right)_{3} \) solution, species
formed gives tests of \( \boldsymbol{K}^{+}, \boldsymbol{A l}^{3+} \) and
\( \boldsymbol{S} \boldsymbol{O}_{4}^{2-} \)
Species formed in experiment A does
not give test of \( F e^{2+} \) and \( C N^{-} . \) It is due to formation of
A \( \cdot K_{2}\left[F e(C N)_{4}\right] \)
B . \( K_{3}\left[F e(C N)_{5}\right] \)
c. \( K_{3}\left[F e(C N)_{6}\right] \)
D. \( K_{4}\left[F e(C N)_{6}\right] \)
Subject: Maths
sleep. He classifies sleep activity in four stages: 1,2,3 and \( 4 . \) Stage 3 is the only stage considered to be deep sleep. Ajay goes to clinic for sleeping brainwashes analyzed. Doctor
monitored the person's brainwashes in \( 15- \) minute intervals, for 8 continuous
hours, and categorized them into one of the four stages. The graph above shows this study. fone \( 15- \) minute time period is chosen at random, then the probability that the patient was in deep sleep during that time is \( \frac{a}{b}, \) where \( a, b \) are co-primes. What is the value of \( a+b ? \)
Subject: Maths
If \( S \) is the circumcenter, \( O \) is the orthocenter of \( \triangle A B C, \) then \( \overrightarrow{S A}+ \) \( \overrightarrow{\boldsymbol{S B}}+\overrightarrow{\boldsymbol{S C}}= \)
A \( \cdot 2 \overrightarrow{O S} \)
B . 2 SO
\( c \cdot \partial s \)
D. \( \overrightarrow{S O} \)
Subject: Chemistry
In which of the following acid peroxy linkage is present? This question has multiple correct options
A. \( H_{2} S O_{3} \)
в. \( H_{2} S O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{CO}_{4} \)
D. \( H_{2} S_{2} O_{8} \)
Subject: Physics
The mass of block is \( m_{1} \) and that of
liquid with the vessel is \( m_{2} . \) The block is
suspended by a string(tension \( \boldsymbol{T} \) )
partially in the liquid. The reading of the weighing machine placed below the
vessel:
A \( \cdot \) can be \( \left(m_{1}+m_{3}\right) g \)
B. can be greater than \( \left(m_{1}+m_{2}\right) g \)
C . is equal to \( \left(m_{1} g+m_{5} g-T\right) \)
D. can be less than \( \left(m_{1}+m_{2}\right) g \)
Subject: Physics
For a body, angular velocity \( \vec{\omega}=\hat{i}- \) \( 2 \hat{j}+3 \hat{k} \) and radius vector \( \vec{r}=\hat{i}+\hat{j}+ \)
\( \hat{k}, \) then its velocity is :-
\( \mathbf{A} \cdot-5 \hat{i}+2 \hat{j}+3 \hat{k} \)
B. \( -5 \hat{i}+2 \hat{j}-3 \hat{k} \)
\( \mathbf{c} .-5 \hat{i}-2 \hat{j}+3 \hat{k} \)
D. \( -5 \hat{i}-2 \hat{j}-3 \hat{k} \)
Subject: Physics
The fraction of a radioactive material
which remains active after time \( t \) is
\( \mathbf{9} / \mathbf{1 6} . \) The fraction which remains active after time \( t / 2 \) will be
A. \( \frac{4}{5} \)
в. \( \frac{7}{8} \)
c. \( \frac{3}{5} \)
D.
Subject: Physics
A convex lens of focal length \( 20 \mathrm{cm} \) is placed coaxially with a convex mirror of radius of curvature \( 20 \mathrm{cm} . \) The two are
kept at \( 15 \mathrm{cm} \) apart from each other. \( \mathrm{A} \) point object lies \( 60 \mathrm{cm} \) in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and
position of the image formed.
Subject: Maths
The line \( \frac{x}{3}+\frac{y}{4}=1 \) meets the \( y- \) axis
and \( x- \) axis at \( A \) and \( B, \) respectively. square \( A B C D \) is constructed on the
line segment \( A B \) away from the origin. the coordinates of the vertex of the
square farthest from the origin are
A \( .(7,3) \)
в. (4,7)
c. (6,4)
(年. \( 6,4,4) \)
D. (3,8)
Subject: Maths
If \( n=^{m} C_{2}, \) then the value of \( ^{n} C_{2} \) is
given by
A. \( ^{m+1} C_{4} \)
в. \( ^{m-1} C_{4} \)
c. \( ^{m+2} C_{4} \)
D. \( 3 .^{m+1} C_{4} \)
Subject: Maths
If \( \cos ^{-1} x= \)
\( \left\{\begin{array}{r}a \pi-b \cos ^{-1}\left(2 x^{2}-1\right), i f-1 \leq x< \\ c \cos ^{-1}\left(2 x^{2}-1\right), \text { if } 0 \leq x \leq 1\end{array}\right. \)
Find the value of \( a+b+c \)
A . 1
B. 2
\( c .3 \)
D. 4
Subject: Maths
A point on the parabola \( y^{2}=18 x \) at
which the ordinate increases at twice
the rate of the absicca is
\( ^{A} \cdot\left(\frac{9}{8}, \frac{9}{2}\right) \)
в. (2,-4)
\( ^{\mathbf{c}} \cdot\left(\frac{-9}{8}, \frac{9}{2}\right) \)
D. (2,4)
Subject: Physics
The Binding energy per nucleon of \( _{3}^{7} L i \)
and \( _{2}^{4} H e \) nucleon are \( 5.60 M e V \) and
7.06 \( M e V \), respectively. In the nuclear
reaction \( _{3}^{7} L i+_{1}^{1} H \rightarrow_{2}^{4} H e+_{2}^{4} H e+Q \)
the value of energy \( Q \) released is
A. \( 19.6 \mathrm{MeV} \)
в. \( -2.4 \mathrm{MeV} \)
c. \( 8.4 \mathrm{MeV} \)
D. \( 17.3 \mathrm{MeV} \)
Subject: Physics
A faulty thermometer has its fixed
points marked as \( 3^{\circ} \) and \( 120^{\circ} . \) The
temperature of a body measured by the
faulty thermometer is \( 80^{\circ}, \) Find the
correct temperature of the body on Celsius scale:
A \( .36 .5^{\circ} \mathrm{C} \)
B. \( 77.8^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 25.8^{\circ} \mathrm{C} \)
D. \( 66.8^{\circ} \mathrm{C} \)
Subject: Physics
The projection of the vector \( A=\hat{i}-2 \hat{j}+ \) \( \hat{k} \) on the vector \( \mathrm{B}=4 \hat{i}-4 \hat{j}+7 \hat{k} \) is:
A . \( 19 / 9 \)
в. 38/9
\( c \cdot 8 / 9 \)
\( D \cdot 4 / 9 \)
Subject: Maths
Let \( S \) be a relation on \( \mathbb{R}^{+} \) defined by
\( \boldsymbol{x} \boldsymbol{S} \boldsymbol{y} \Leftrightarrow \boldsymbol{x}^{2}-\boldsymbol{y}^{2}=\boldsymbol{2}(\boldsymbol{y}-\boldsymbol{x}), \) then \( \boldsymbol{S} \) is
A. Only reflecxive
B. Only symmetric
c. only Trasitive
D. Equivalence
Subject: Maths
\( \underset{\boldsymbol{n} \rightarrow \infty}{\boldsymbol{L} \boldsymbol{t}} \sum_{\boldsymbol{r}=0}^{\boldsymbol{n}-\mathbf{1}} \frac{\boldsymbol{n}}{\boldsymbol{n}^{2}+\boldsymbol{r}^{2}} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot \frac{\pi}{2} \)
D. \( \frac{\pi}{4} \)
Subject: Physics
A uniform long rope is suspended from the roof. A transverse wave pulse is produced at its lower end. As the wave travels upward along the suspended rope, then the
1) velocity of wave increases
2) wavelength of wave increases
3) frequency of wave remains constant
A. only 1 and 2 are true
B. only 2 and 3 are true
c. only 1 and 3 are true
D. 1,2 and 3 all are true
Subject: Maths
The standard error of two means is
equal to
\( ^{\mathrm{A}} \cdot \sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n^{2}}} \)
в. \( \frac{\sigma}{\sqrt{n-1}} \)
c. \( \frac{\sigma}{\sqrt{n+1}} \)
D. \( \sqrt{\frac{P_{1} Q_{1}}{\sqrt{n_{1}}}+\frac{P_{2} Q_{2}}{n_{2}}} \)
Subject: Chemistry
Rate constant k varies with
temperature as given by equation:
\( \log k\left(\min ^{-1}\right)=5-\frac{2000 K}{T} . \) We can
conclude:
This question has multiple correct options
A. Pre-exponential factor A is 5.
B. \( E_{a} \) is 2000 kcal.
C. Pre-exponential factor A is \( 10^{5} \)
D. \( E_{a} \) is 9.152 kcal
Subject: Biology
In the processing of eukaryotic mRNA,
during protein synthesis, tailing
involves .............. of RNA.
A. Addition of adenylate residues at \( 3^{\prime} \) end
B. Addition of methyl guanosine triphosphate at \( 3^{\prime} \) end
C. Addition of methyl guanosine triphosphate at \( 5^{\prime} \) end
D. Removal of introns
Subject: Maths
\( a, b, c(a>c) \) are the three digits, from left to right of a three digit number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digit 4 in its unit's place. The other two digits
from left to right are -
A. 5 and 4
B. 5 and 9
c. 4 and 5
D. 9 and 5
Subject: Chemistry
A gas \( X \) bleaches the colour of flowers
by reduction while the other gas \( Y \) bleaches by oxidation. These two gases
\( X \) and \( Y \) are respectively:
A. \( C O \) and \( C O_{2} \)
B. \( N H_{3} \) and \( S O_{3} \)
\( \mathrm{c} \cdot \mathrm{CO}_{2} \) and \( \mathrm{Br}_{2} \)
D. \( S O_{2} \) and \( C l_{2} \)
Subject: Maths
Arrange the following in an ascending
order. \( -4,2,0,-\frac{5}{4}, 2.17,-3.7, \frac{22}{7}, 8 \)
A \( \cdot-4,-3.7,-\frac{5}{4}, 0,2,2.17, \frac{22}{7}, 8 \)
в. \( _{-4,0,-\frac{5}{4},-3.7,2,2.17, \frac{22}{7}, 8} \)
c. \( _{-4,-3.7,-\frac{5}{4}, 2,0,2.17, \frac{22}{7}, 8} \)
D. \( -4,-3.7,-\frac{5}{4}, 2.17,2,0, \frac{22}{7}, 8 \)
Subject: Chemistry
Which of the following contains the maxium number of atoms?
A \( \cdot 10 g \) of \( C a C O_{3} \)
B. \( 4 g \) of hydrogen
\( \mathbf{c} \cdot 9 g \) of \( N H_{4} N O_{3} \)
D. \( 1.8 g \) of \( C_{6} H_{12} O_{6} \)
Subject: Chemistry
Two flasks \( A \) and \( B \) of an equal volume
containing 1 mole and 2 moles of \( 0_{3} \)
respectively are heated to the same
temperature. When the reaction \( 2 O_{3} \rightleftharpoons \)
\( 30_{2} \) practically stops, then both the
flasks shall have
A \( . \) the same ratio: \( \left[O_{2}\right] /\left[O_{3}\right] \)
B. the same ratio: \( \left[O_{2}\right]^{3 / 2} /\left[O_{3}\right] \)
c. only \( O_{2} \)
D. the same time to reach equilibrium
Subject: Maths
If \( \boldsymbol{x}_{1}=\sqrt{\mathbf{3}} \) and \( \boldsymbol{x}_{\boldsymbol{n}+1}=\frac{\boldsymbol{x}_{\boldsymbol{n}}}{\mathbf{1}+\sqrt{\mathbf{1}+\boldsymbol{x}_{\boldsymbol{n}}^{2}}} \)
\( \forall n \epsilon N, \) then \( \lim _{n \rightarrow \infty} 2^{n} x_{n} \) equal to
A \( \cdot \frac{3}{2 \pi} \)
в. \( \frac{2}{3 \pi} \)
c. \( \frac{2 \pi}{3} \)
D. \( \frac{3 \pi}{2} \)
Subject: Physics
Consider a gravity- free hall in which an experimenter of mass \( 50 \mathrm{kg} \) is resting
on a \( 5 k g \) pillow, \( 8 f t \) above the floor of
the hall. He pushes the pillow down so that it starts falling at a speed of \( 8 f t / s \)
The pillow makes a perfectly elastic
collision with the floor, rebounds and
reaches the experimenter's head. Find the time elapsed in the process.
Subject: Physics
A block of a mass of \( 10 \mathrm{kg} \) rests on a horizontal table. The coefficient of
friction between the block and the table
is \( 0.05 . \) When hit by a bullet of mass 50 g moving with speed \( v \), that gets embedded in it, the block moves and
comes to rest after moving a distance of
\( 2 \mathrm{m} \) on the table. If a freely falling object were to acquire speed \( \frac{v}{10} \) after being dropped from height H, then neglecting energy losses and taking \( g=10 m s^{-2} \)
the value of \( \mathrm{H} \) is close to:
B. \( 0.05 k m \)
\( c .0 .02 k m \)
D. \( 0.03 k m \)
Subject: Physics
Consider a uniform disc of mass \( 4 \mathrm{kg} \) performing pure rolling with velocity 5 \( \mathrm{m} / \mathrm{s} \) on a fixed rough surface
A. Kinetic energy of upper half will be 37.5 J
B. Kinetic energy of upper half will be less than 37.5
c. Kinetic energy of upper half will be more than 37.5 j
D. Kinetic energy of upper half will be more than 75