AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
If \( \lambda_{1}, \lambda_{2}, \lambda_{3} \) are the wavelength of the
waves giving resonance to the fundamental, first and second overtone
modes respectively in a string fixed at both ends. The ratio of the wavelengths \( \boldsymbol{\lambda}_{1}: \boldsymbol{\lambda}_{2}: \boldsymbol{\lambda}_{3} \) is
A. 1: 2: 3
B. 1: 3: 5
c. \( 1: \frac{1}{2}: \frac{1}{3} \)
D. \( 1: \frac{1}{3}: \frac{1}{5} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{4} & \mathbf{1} & \boldsymbol{0} \\ \mathbf{1} & -\mathbf{2} & \mathbf{2}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{2} & \mathbf{0} & -\mathbf{1} \\ \mathbf{3} & \mathbf{1} & \mathbf{4}\end{array}\right], \boldsymbol{C}=\left[\begin{array}{c}\mathbf{1} \\ \mathbf{2} \\ -\mathbf{1}\end{array}\right] \) and
\( (\mathbf{3} \boldsymbol{B}-\mathbf{2} \boldsymbol{A}) \boldsymbol{C}+\mathbf{2} \boldsymbol{X}=\mathbf{0} \) then \( \boldsymbol{X}= \)
A \( \cdot \frac{1}{2}\left[\begin{array}{c}3 \\ 13\end{array}\right] \)
в. \( \frac{1}{2}\left[\begin{array}{c}3 \\ -13\end{array}\right] \)
c. \( \frac{1}{2}\left[\begin{array}{c}-3 \\ 13\end{array}\right] \)
D. \( \left[\begin{array}{c}3 \\ -13\end{array}\right] \)
Subject: Physics
A point moves with uniform
acceleration and \( \boldsymbol{v}_{1}, \boldsymbol{v}_{2} \) and \( \boldsymbol{v}_{3} \) denote
the average velocities in the three
successive intervals of time \( t_{1}, t_{2} \) and \( t_{3} \)
Which of the following relation is
correct?
\( \mathbf{A} \cdot\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}+t_{3}\right) \)
\( \mathbf{B} \cdot\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}+t_{3}\right) \)
\( \mathbf{c} \cdot\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{1}-t_{3}\right) \)
\( \mathbf{D} \cdot\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}-t_{3}\right) \)
Subject: Physics
A pulley fixed to the ceiling carries a
thread with bodies of masses \( m_{1} \) and
\( m_{2} \) attached to its ends. The masses of
the pulley and the thread are negligible, friction is absent. Find the acceleration
\( \boldsymbol{w}_{C} \) of the centre of mass of this system
A \( \cdot \frac{\left(m_{1} m_{2}\right)^{2} \vec{g}}{\left(m_{1}-m_{2}\right)^{2}} \)
B. \( \frac{\left(m_{1}+m_{2}\right)^{2} \vec{g}}{\left(m_{1}-m_{2}\right)^{2}} \)
c. \( \frac{\left(m_{1} m_{2}\right)^{2} \vec{g}}{\left(m_{1}+m_{2}\right)^{2}} \)
D. \( \frac{\left(m_{1}-m_{2}\right)^{2} \vec{g}}{\left(m_{1}+m_{2}\right)^{2}} \)
Subject: Physics
What is the minimum energy required
to lunch a satellite of mass \( m \) from the
surface of a planet of mass \( M \) and radius \( R \) In a circular orbit at an
altitude of \( 2 R ? \)
A \( \cdot \frac{2 G m M}{3 R} \)
в. \( \frac{G m M}{2 R} \)
c. \( \frac{G m M}{3 R} \)
D. \( \frac{5 G m M}{6 R} \)
Subject: Physics
The diameter of a solid disc is \( 0.5 \mathrm{m} \)
and its mass is \( 16 \mathrm{Kg} \). What torque will increase its angular velocity from zero to 120 rotation/minute in 8
seconds?
A \( \cdot \frac{\pi}{4} N / m \)
в. \( \frac{\pi}{2} N / m \)
c. \( \frac{\pi}{3} N / m \)
D. \( \pi N / m \)
Subject: Maths
Evaluate \( \int \frac{d x}{\left(a^{2}+x^{2}\right)^{3 / 2}} \)
\( \boldsymbol{I}=\frac{\boldsymbol{x}}{\boldsymbol{a}^{2}\left(\boldsymbol{x}^{2}+\boldsymbol{a}^{2}\right)^{\boldsymbol{K}}}+\boldsymbol{c} \)
What is K?
Subject: Chemistry
In the given reaction, the product \( (B) \) is
\( \boldsymbol{C H}_{3} \boldsymbol{C H O} \frac{(i) N a C N / \boldsymbol{H} C l}{(i i) \boldsymbol{H}_{2} \boldsymbol{O} / \boldsymbol{H} \oplus / \boldsymbol{\Delta}}(\boldsymbol{A}) \frac{\boldsymbol{F e n t o n}}{\text {reagent}} \)
\( (B) \)
A . acetic acid
B. oxalic acid
c. pyruvic acid
D. citric acid
Subject: Chemistry
Which of the following units is correctly
matched?
A. SI units of conductivity is \( S m^{-1} \)
B. \( S I \) units of molar conductivity is \( S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. \( S I \) unit of conductance is \( S^{-1} \)
D. All of these
Subject: Maths
The value of \( c \) in Lagrange's theorem for
the function in the interval [-1,1] is
\[
f(x)=\left\{\begin{array}{cl}
x \cos \left(\frac{1}{x}\right), & x \neq 0 \\
0, & x=0
\end{array}\right.
\]
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
\( c \)
\[
-\frac{1}{2}
\]
D. Non existent in the interva
Subject: Physics
To know the resistance \( G \) of a
galvanometer by half deflection method,
a battery of emf \( V_{E} \) and resistance \( R \) is
used to deflect the galvanometer by
angle \( \theta . \) If a shunt of resistance \( S \) is
needed to get half deflection the \( G, R \) and \( S \) are related by the equation:
A. \( S(R+G)=R G \)
B. \( 2 S(R+G)=R G \)
\( \mathrm{c} \cdot 2 G=S \)
D. \( 2 S=G \)
Subject: Chemistry
The correct statement is :
A. leaching of bauxite using concentrated \( N a O H \) solution gives sodium aluminate and sodium silicate
B. The blistered appearance of copper during the metallurgical process is due to the evolution of \( C O_{2} \)
C . pig iron is obtained from cast iron
D. the Hall-Heroult process is used for the prodeuction of aluminium and iron.
Subject: Maths
\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{5} & \mathbf{6} \\ \mathbf{0} & \mathbf{1} & \mathbf{7} \\ \mathbf{0} & \mathbf{0} & \mathbf{1}\end{array}\right| \) and \( \Delta^{\prime}=\left|\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{1} \\ \mathbf{3} & \mathbf{0} & \mathbf{3} \\ \mathbf{4} & \mathbf{6} & \mathbf{1 0 0}\end{array}\right| \)
then
A \( \cdot \Delta^{2}-3 \Delta^{\prime}=0 \)
B. \( \left(\Delta+\Delta^{\prime}\right)^{2}-3\left(\Delta+\Delta^{\prime}\right)+2=0 \)
c. \( \left(\Delta+\Delta^{\prime}\right)^{2}+3\left(\Delta+\Delta^{\prime}\right)+5=0 \)
D. \( \Delta+3 \Delta^{\prime}+1=0 \)
Subject: Biology
The characteristic that is shared by urea, uric acid and ammonia is /are
(A) They are nitrogenous wastes.
(B) They all need very large amount of water for excretion.
(C) They are all equally toxic.
(D) They are produced in the kidneys.
A . A and C
B. \( A, C \) and \( D \)
c. A and
D. A only
Subject: Chemistry
Calculate the potential of hydrogen electrode in contact with a solution of
\( 5 \times 10^{-3} M \) of \( B a(O H)_{2} \) at 1 atm
pressure and \( 298 \mathrm{K} \) temperature:
A . - \( 0.059 v \)
B. 0.059v
c. \( 0.59 v \)
D - -0.59V
Subject: Chemistry
Rate of disappearance of the reactant \( \boldsymbol{A} \)
at two different temperature is given by
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \)
\( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d t}}=\left(\boldsymbol{2} \times \mathbf{1 0}^{-2} \boldsymbol{S}^{-1}\right)[\boldsymbol{A}]-\boldsymbol{4} \times \)
\( \mathbf{1 0}^{-3} \boldsymbol{S}^{-\mathbf{1}}[\boldsymbol{B}], \boldsymbol{T}=\mathbf{3 0 0} \boldsymbol{K} \)
\( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d t}}=\left(\boldsymbol{4} \times \mathbf{1 0}^{-2} \boldsymbol{S}^{-1}\right)[\boldsymbol{A}]-\mathbf{1 6} \times \)
\( \mathbf{1 0}^{-\mathbf{4}}[\boldsymbol{B}], \boldsymbol{T}=\mathbf{4 0 0} \boldsymbol{K} \)
Calculate heat of reaction in the given temperature range, when equilibrium is
\( \operatorname{set} \) up.
A. \( 16.06 k J \)
в. \( 23.04 k J \)
c. \( 26.78 k J \)
D. \( 29.34 k J \)
Subject: Maths
Find the slope and \( y \) -intercept of the
line \( 0.2 x-y=1.2 \)
A. slope \( =0.2, y \) -intercept \( =-1.2 \)
B. slope \( =1.2, y \) -intercept \( =-1.2 \)
c. slope \( =0.2, y \) -intercept \( =-2.2 \)
D. slope \( =0.2, y \) -intercept \( =-1.3 \)
Subject: Maths
The equation of the circle with center (1,2) and tangent \( x+y-5=0 \) is
A \( \cdot x^{2}+y^{2}+2 x-4 y+6=0 \)
B . \( x^{2}+y^{2}-2 x-4 y+3=0 \)
c. \( x^{2}+y^{2}-2 x-4 y-8=0 \)
D. \( x^{2}+y^{2}-2 x-4 y+8=0 \)
Subject: Maths
STATEMENT - 1: The locus of the middle
points of equal chords of a circle with
centre at 0 is a circle with centre at 0
STATEMENT - 2 : The mid point of the equal chords are equidistant from the centre of the circle.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement- -
c. Statement - 1 is True, Statement - 2 is False
D. Statement-1 is False, Statement- - 2 is True
Subject: Maths
\( \Delta A B C \sim \Delta L M N \cdot \ln \Delta A B C, A B= \)
\( 5.1 \mathrm{cm}, \angle B=55^{\circ}, \angle C=65^{\circ} \) and
\( \frac{A C}{L N}=\frac{3}{5}, \) then construct \( \Delta L M N \)
Subject: Physics
Two long current carrying thin wires, both with current \( I \), are held by
insulating threads of length \( L \) and are in equilibrium as shown in the figure, with threads making an angle ' \( \boldsymbol{\theta}^{\prime} \) with
the vertical. If wires have mass \( \lambda \) per
unit length then the value of \( I \) is \( :(g= \)
gravitational acceleration)
A \( \cdot 2 \sqrt{\frac{\pi g L}{\mu_{0}} \tan \theta} \)
B. \( 2 \sin \theta \sqrt{\frac{\pi \lambda g L}{\mu_{0} \cos \theta}} \)
c. \( \sin \theta \sqrt{\frac{\pi \lambda g L}{\mu_{0} \cos \theta}} \)
D. \( \sqrt{\frac{\pi \lambda g L}{\mu_{0}}} \tan \theta \)
Subject: Chemistry
The correct order of decreasing acid strength of trichloroacetic acid (A), trifluoro acetic acid (B), acetic acid (C)
and formic acid (D) is
A. \( A>B>C>D \)
в. \( A>C>B>D \)
с. \( B>A>D>C \)
D. \( B>D>C>A \)
Subject: Chemistry
A sample of water is vaporized and tested in a mass spectrometer. There are 3 isotopes of hydrogen, \( 1 H,^{2} H \) and
3. H. There are 2 isotopes of oxygen, \( ^{15} \boldsymbol{O} \) and \( ^{16} \) O.

How many peaks would be expected to be found on the mass spectrum?
A . 3
B. 4
\( c .5 \)
D. 6
Subject: Physics
A lead bullet pertrates into a solid object and melts. Assuming that \( 50 \% \) of its kinetic energy was used to heat it, if the initial speed (in \( \mathrm{m} / \mathrm{s} \) ) of the bullet is \( 100 \times 100 \times J / K g \) and specific heat capacity of lead \( =125 \mathrm{J} / \mathrm{kg} \mathrm{K} \)
Subject: Physics
If a wire having initial diameter of \( 2 m m \)
produced the longitudinal strain of 0.1
\( \%, \) then the final diameter of wire is
\( (\sigma=\mathbf{0 . 5}) \)
A \( .2 .002 m m \)
B. \( 1.999 \mathrm{mm} \)
c. \( 1.998 \mathrm{mm} \)
D. \( 2.001 m m \)
Subject: Physics
The lengths of two wires made of same material are \( 2 \mathrm{m} \) and \( 1 \mathrm{m} . \) Their radii are
\( 1 \mathrm{mm} \) and \( 2 \mathrm{mm} . \) The ratio of their
specific resistances is
A. 2:
B. 1: 1
\( c \cdot 4: \)
D. 8: 1
Subject: Chemistry
The correct relationship between free
energy change in a reaction and the
corresponding equilibrium constant \( K_{c} \)
is:
\( \mathbf{A} \cdot-\Delta G=R T \ln K_{c} \)
\( \mathbf{B} \cdot \Delta G^{o}=R T \ln K_{c} \)
\( \mathbf{c} \cdot-\Delta G^{o}=R T \ln K_{c} \)
\( \mathbf{D} \cdot \Delta G=R T \ln K_{c} \)
Subject: Physics
The tro ends of a train moving with constant acceleration pass a certain
point with velocities \( u \) and \( 3 u \). The
velocity with which the middle point of the train passes the same point is
A \( .2 u \)
в. \( \frac{3}{2} u \)
c. \( \sqrt{5} u \)
D. \( \sqrt{10} u \)
Subject: Physics
Two monochromatic (wavelength \( =\boldsymbol{a} / \mathbf{5} \)
and coherent source of
electromagnetic waves are placed on the \( x \) -axis at the point \( (2 a, 0) \) and
\( (-a, 0) . \) A detector moves in a circle of radius \( R(>>2 a) \) whose Centre is at
the origin. The number of maximas detected during one circular revolution by the detector are:
A . 60
в. 15
c. 64
D. None
Subject: Chemistry
Assertion
In electrochemical cell, we can not use
KCl in the salt bridge if anodic or
cathodic compartment consists of \( \mathrm{Ag}^{+} \)
or \( P b^{2+} \) ion.
Reason
Salt bridge is employed to maintain the electrical neutrality and to minimize the liquid-liquid junction potential.
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 force between two electrons when
placedair is equal to 0.5 times the weight of an electrons find the distance between two electrons (masselectron
\( \left.=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
A . 7.2 m
B. 72cm
c. 72 m
D. 720m
Subject: Physics
Q Type your question.
smooth pulley as shown in figure. If the system is released from rest, find the
work done by tension on both \( 1 \mathrm{kg} \) and 2 kg blocks in 1 s. (Take \( g=10 m / s^{2} \) )
A \( \cdot \frac{200}{9} J,-\frac{200}{9} J \)
В. \( -\frac{200}{9} J,+\frac{200}{9} J \)
c. \( +\frac{200}{9} J,+\frac{200}{9} J \)
Subject: Physics
A planar object made up of a uniform square plate and four semicircular
discs of the same thickness and
material is being acted upon by four forces of equal magnitude as shown. The coordinates of point of application of forces is given by
A . \( (0, a) \)
в. \( (0,-a) \)
\( c .(a, 0) \)
D. \( (-a, 0) \)
Subject: Physics
A ray \( O P \) monochromatic light is
incident on the face \( A B \) of prism
\( A B C D \) near vertex \( B \) at an incident
angle of \( 60^{\circ} \) (see figure). If the refractive index of the material of the prism is \( \sqrt{3} \) which of the following is (are) correct?
rhis question has multiple correct options
A. The ray gets totally internally reflected at face \( c D \)
B. The ray comes out through face AD
c. The angle between the incident ray and the emergent ray is \( 90^{\circ} \)
D. The angle between the incident ray and the emergent
ray is \( 120^{\circ} \)
Subject: Physics
A satellite of mass \( m \) revolves around
the earth of radius \( R \) at a height \( x \) from its surface. If \( g \) is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
A . \( \sqrt{g x} \)
в. \( \sqrt{\frac{g R}{R-x}} \)
\( ^{\mathrm{c}} \cdot \sqrt{\frac{g R^{2}}{R-x}} \)
D. \( \sqrt{\frac{g R^{2}}{R+x}} \)
Subject: Chemistry
Which of the following is/are disproportionation reaction(s)? This question has multiple correct options
A \( \cdot 2 C C l_{3} C H O+N a O H \rightarrow C C l_{3} C O O N a+ \)
\( C C l_{3} C H_{2} O H \)
в. \( N H_{4} N O_{3} \rightarrow N_{2} O+2 H_{2} O \)
c. \( 2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} \)
D. \( 5 C l_{2}+6 O H^{-} \rightarrow C l O_{3}^{-}+5 C l^{-}+3 H_{2} O \)
Subject: Maths
\( A \) and \( B \) are events with \( P(A)= \)
\( \mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3} \)
Find the probability that neither \( A \) and \( B \) occurs.
Subject: Chemistry
Equilibrium constant for the following reaction is \( 1 \times 10^{-9}: C_{5} H_{5} N(a q)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \boldsymbol{C}_{5} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}+(\boldsymbol{a} \boldsymbol{q} \cdot)+ \)
\( O H^{-}(a q .) \) Determine the mole of
pyridirium chloride \( \left(C_{5} H_{5} N . H C l\right) \) that should be added to \( 500 m L \) solution of
\( 0.4 M \) pyridine \( \left(C_{5} H_{5} N\right) \) to obtain a
buffer solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{5} \)
Subject: Biology
Assertion
Archaebacteria are more similar to
eukaryotes rather than eubacteria.
Reason

Archaean genome is more similar to eukaryotic genome rather than
bacterial genome.
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
In a coil of area \( 10 \mathrm{cm}^{2} \) and 10 turns
with magnetic field directed perpendicular to the plane and is changing at the rate of \( 10^{4} \) gauss second. The resistance of the coil is 20
\( \Omega . \) The current in the coil will be
A . \( 0.5 A \)
в. \( 5 A \)
c. \( 50 A \)
D. \( 5 \times 10^{8} A \)
Subject: Physics
Find how the normal acceleration of the
balloon varies as a function of the
height of ascent.
\( \mathbf{A} \cdot \omega_{n}=\frac{a v_{0}}{\sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
B. \( \omega_{n}=\frac{2 a v_{0}}{\sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
\( ^{\mathbf{C}} \cdot_{\omega_{n}}=\frac{3 a v_{0}}{2 \sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
D \( \cdot \omega_{n}=\frac{a v_{0}}{2 \sqrt{1+\left(\frac{a_{y}}{v_{0}}\right)^{2}}} \)
Subject: Chemistry
Assertion
Metals of high impurity are obtained by zone-refining.
Reason
Impurities in the ore are more soluble in
the metal than in the pure metal
Choose the correct option.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Maths
Pankaj wants to create tests for SAT
students. He wants to make some
calculator and non calculator tests. He
figures that each non-calculator test
will take him 3 hours to create, and
each calculator test will take 4 hours to
create. Because of his time constraint,
he can at most devote at most 6 hours
per week of his time for the next 5
weeks to create the practice and he
wants to provide at least 8 practice
tests, which of the system of inequality represent how many of each type of test
he can create?
\( \mathbf{A} \cdot n+c \geq 8 \)
\( 3 n+4 c \leq 6 \)
B \( . n+c \geq 8 \)
\( 3 n+4 c \leq 30 \)
c. \( n+c \leq 8 \)
\( 3 n+4 c \geq 30 \)
D. \( n+c \geq 6 \)
\( 3 n+4 c \leq 8 \)
Subject: Maths
Arrange the following values of \( n \) in ascending order.
\( \boldsymbol{A}:^{n} \boldsymbol{P}_{5}=^{n} \boldsymbol{P}_{6} \Rightarrow \boldsymbol{n}= \)
\( \boldsymbol{B}:^{\boldsymbol{n}} \boldsymbol{P}_{12}=^{\boldsymbol{n}} \boldsymbol{P}_{\boldsymbol{8}} \Rightarrow \boldsymbol{n}= \)
\( \boldsymbol{C}:^{n} \boldsymbol{C}_{(\boldsymbol{n}-\mathbf{3})}=\mathbf{1 0} \Rightarrow \boldsymbol{n}= \)
\( \boldsymbol{D}:^{(\boldsymbol{n}+1)} \boldsymbol{P}_{5}:^{\boldsymbol{n}} \boldsymbol{P}_{6}=\mathbf{1}: \boldsymbol{2} \Rightarrow \boldsymbol{n}= \)
\( A \). САВ D
в. САDВ
c. АСВD
D. DBAC
Subject: Physics
You are driving along the street at the speed limit \( (35 m p h) \) and 50 meters before reaching a traffic light you notice it becoming yellow. You accelerate to make the traffic light within the 3 seconds it takes for it to turn red. What
is your speed as you cross the intersection? Assume that the
acceleration is constant and that there
is no air resistance.
A. \( 30 m p h \)
в. \( 40 \mathrm{mph} \)
c. \( 50 m p h \)
D. \( 60 m p h \)
Subject: Maths
Show that the straight lines \( \left(A^{2}-\right. \) \( \left.\mathbf{3} \boldsymbol{B}^{2}\right) \boldsymbol{x}^{3}+\mathbf{8} \boldsymbol{A} \boldsymbol{B} \boldsymbol{x} \boldsymbol{y}+\left(\boldsymbol{B}^{2}-\boldsymbol{3} \boldsymbol{A}^{2}\right) \boldsymbol{y}^{2}=\mathbf{0} \)
form with the line \( A x+B y+C=0 \) an equilateral triangle whose area is \( \frac{C^{2}}{\sqrt{3}\left(A^{2}+B^{2}\right)} \)
Subject: Chemistry
During the process of digestion, the protein present in food materials are hydrolysed to amino acids. The two enzymes involved in the process are:
Proteins

Enzyme \( \quad(A) \) Polypeptides
Enzyme\( ^{(B)} \) Amino acids
A. Invertase and zymase
B. Amylase and maltase
c. Diastase and lipase
D. Pepsin and trypsin
Subject: Chemistry
The energy of an electron in the ground
state of \( \boldsymbol{H} \) atom is \( -\mathbf{1 3 . 6 e V} \)
The negative sign indicates that:
A. electrons are negatively charged
B. \( H \) atom is more stable than a free electron
c. energy of the electron in the H atom is lower than that of a free electron
D. work must be done to make a \( H \) atom from a free electron and proton
Subject: Chemistry
The final product formed when silica reacts with hydrogen fluoride is :
A . \( S i F \)
в. \( H_{2} \) s \( s F_{6} \)
\( \mathrm{c} . \mathrm{H}_{2} \mathrm{SiF}_{4} \)
D. \( H_{2} \) sio \( _{3} \),
Subject: Maths
All the students of a batch opted
Psychology, Business, or both. \( 73 \% \) of
the students opted Psychology and \( 62 \% \) opted Business. If there are 220
students, how many of them opted for both Psychology and business?
\( \mathbf{A} \cdot 60 \)
в. 100
c. 77
D. 35
Subject: Physics
When 60 calories of heat are supplied to \( 15 \mathrm{g} \) of water, the rise in temperature is
A \( \cdot 75^{\circ} \mathrm{C} \)
В. \( 90^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 4^{\circ} C \)
D. \( 0.25^{\circ} \mathrm{C} \)
Subject: Physics
The intensity of central fringes in the interference pattern produced by two identical slits is \( I . \) When one of the slits
is closed then the intensity at the same
point is \( I_{o} . \) The relation between the \( I \)
and \( I_{o} \) is
A \( . I=4 I_{0} \)
B . \( I=2 I_{0} \)
c. \( I=I_{o} \)
D. \( I=\frac{I_{o}}{2} \)
Subject: Chemistry
How many coulombs of electricity are required for the oxidation of one mole of
water to dioxygen?
A \( .9 .65 \times 10^{4} C \)
в. \( 1.93 \times 10^{4} C \)
c. \( 1.93 \times 10^{5} \mathrm{C} \)
D. \( 19.3 \times 10^{5} C \)
Subject: Chemistry
The correct order of atomic radii is :
\( \mathbf{A} \cdot C e>S m>Y b>L u \)
в. \( S m>C e>L u>Y b \)
c. \( L u>Y b>S m>C e \)
\( \mathrm{D} \cdot S m>Y b>C e>L u \)
Subject: Physics
toppr
Q Type your question.
rumu ac shape ACB such that \( d<<l \). The
tension in the string is \( \mathrm{T} \) and the strain
produced in it is \( \varepsilon . \) If the Youngs modulus of the material of wire is \( Y \).
Then
This question has multiple correct options
A \( \cdot_{\varepsilon}=\frac{d}{2 l} \)
B. \( _{\varepsilon}=\frac{d^{2}}{2 l^{2}} \)
c. \( T=a Y\left(\frac{d}{2 l}\right) \)
D. \( T=a Y\left(\frac{d^{2}}{2 l^{2}}\right) \)
Subject: Physics
A sine wave of wavelength \( ^{\prime} \lambda^{\prime} \) is travelling in a medium. What is the minimum distance between two
particles of the medium which always have the same speed?
\( A \cdot \lambda \)
B. \( \frac{\lambda}{2} \)
\( c \cdot \frac{\lambda}{3} \)
D. \( \frac{\lambda}{4} \)
Subject: Physics
Light is incident at an angle \( \phi \) with the
normal to a plane containing two slits of
separation \( d . \) Select the expression that
correctly describes the positions of the
interference maxima in terms of the
incoming angle \( \phi \) and outgoing angle \( \theta \)
\( ^{\mathbf{A}} \cdot \sin \phi+\sin \theta=\left(m+\frac{1}{2}\right) \frac{\lambda}{d} \)
\( \mathbf{B} \cdot d \sin \theta=m \lambda \)
\( \mathrm{c} \cdot \sin \phi-\sin \theta=(m+1) \frac{\lambda}{d} \)
" \( \sin \phi+\sin \theta=m \frac{\lambda}{d} \)
Subject: Maths
A function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfies \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{f}(\boldsymbol{2} \boldsymbol{a}-\boldsymbol{x}) . \) Suppose \( \boldsymbol{f}(\boldsymbol{x}) \) is
differentiable at \( x=a \) then
This question has multiple correct options
A \( \cdot f^{\prime}(a)=0 \)
B . \( f^{\prime}\left(a^{+}\right)=-f^{\prime}\left(a^{-}\right) \)
c. \( f^{\prime}\left(a^{+}\right)=f^{\prime}\left(a^{-}\right)=0 \)
D. None of these
Subject: Chemistry
The dissociation energy of \( \boldsymbol{H}_{2} \) is
\( 482.5 K J / \) mol. If \( H_{2} \) is exposed to radiant energy of wavelength \( 124 \mathrm{nm} \) what \( \% \) of radiant energy will be converted into K.E?
\( \left(1 \frac{e v}{a t o m} 5=96 k J / m o l .\right) \)
Subject: Chemistry
Units of the rate constant of first and
zero order reactions in terms of molarity
M unit are respectively:
A \( \cdot \sec ^{-1}, \) M sec \( ^{-1} \)
B . \( \sec ^{-1}, \) М
c. \( M s e c^{-1}, s e c^{-1} \)
D. \( M, s e c^{-1} \)