AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Assertion If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{\pi} \\ \mathbf{0} & \mathbf{1}\end{array}\right], \) then \( \boldsymbol{A}^{100}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{1 0 0} \boldsymbol{\pi} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \)
Reason
If \( B \) is a \( 2 \times 2 \) matrix such that \( B^{2}=0 \)
then \( (I+B)^{n}=I+n B \) for each \( n \in \)
\( N \)
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: Chemistry
In a two-step exothermic reaction,
\( \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{3} \boldsymbol{C}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{D}(\boldsymbol{g}) \)
Steps 1 and 2 are favoured respectively
by:
A. high pressure, high temperature and low pressure, low temperature
B. high pressure, low temperature and low pressure, highh temperature
c. low pressure, high temperature and high pressure,high temperature
D. low pressure, low temperature and high pressure, low temperature
Subject: Physics
In a projectile motion from a point of horizontal surface to another point on
the same surface (Take \( \overrightarrow{\boldsymbol{a}}= \)
acceleration and \( \vec{v}= \) instantaneous
velocity) This question has multiple correct options
A. \( \vec{a} \cdot \vec{v}=0 \) at maximum height
B . \( \vec{a} \cdot \vec{v}=0 \) only if angle of projection is \( 90^{\circ} \)
c. \( \vec{a} \times \vec{v}= \) constant every where in air
D. None of these
Subject: Chemistry
A thermodynamical system is changed
from state \( \left(P_{1}, V_{1}\right) \) to \( \left(P_{2}, V_{2}\right) \) by two
different processes, the quantity which
will remain same will be
A. \( \Delta Q \)
в. \( \Delta W \)
c. \( \Delta Q+\Delta W \)
D. \( \Delta Q-\Delta W \)
Subject: Chemistry
RCOOH decomposes \( N a H C O_{3} \) to
liberate \( C O_{2} \) which comes
from
A \( . \) NaOH \( \mathrm{CO}_{3} \)
в. \( \operatorname{NaH} \mathrm{CO}_{3} \)
с. \( \operatorname{NaH} \mathrm{CO}_{2} \)
D. \( N a H C O \)
Subject: Maths
Given two functions \( f(x) \) and \( g(x) \) such that \( f(x)=\sin (a r c t a n x), g(x)= \)
\( \tan (\arcsin x), \) and \( 0 \leq x<\frac{\pi}{2} . \) The
value of the composite function \( f\left(g\left(\frac{\pi}{10}\right)\right) \) is:
\( \mathbf{A} \cdot 0.314 \)
в. 0.354
c. 0.577
D. 0.707
E . 0.866
Subject: Biology
The production of ATP through chemiosmosis is known to occur in
which of the following organisms?
A. All cells (prokaryotic and eukaryotic) are capable of respiration using either oxygen or other electron acceptors.
B. All cells (prokaryotic and eukaryotic), but only in the presence of oxygen.
C. Eukaryotic cells only, and only when oxygen is present.
D. All cells that possess mitochondria, and only when oxygen or other electron acceptors are present.
Subject: Chemistry
Oxime is the product of the following:
A. \( >C=O+ \) hydrazine
B. \( >C=O+ \) Phenylhydrazine
\( c \)
\[
-\mathrm{C}-\mathrm{O} \mathrm{H}+\mathrm{SOCl}_{2}
\]
D. >CO + Hydroxylamine
Subject: Maths
A rectangle plot of land measures \( 45 \mathrm{m} \) \( \times 30 \mathrm{m} . \) A boundary wall of height \( 2.4 \mathrm{m} \) is built all round the plot at a distance
of \( 1 \mathrm{m} \) from the plot. Find the area of the inner surface of the boundary wall.
A \( \cdot 226.2 m^{2} \)
В. \( 457.2 m^{2} \)
D. \( 291.2 m^{2} \)
Subject: Chemistry
Reaction, \( 5 C \longrightarrow 3 A+2 B . \) The rate of
formation of \( \boldsymbol{A} \) is \( \mathbf{0 . 0 2 7 m o l} \boldsymbol{L}^{-1} \boldsymbol{s e c}^{-1} \)
What will be the rate of disappearance
of \( C ? \)
A. \( 0.090 \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)
B. \( 0.027 \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)
c. \( 0.063 m o l L^{-1} s e c^{-1} \)
D. \( 0.045 \mathrm{molL}^{-1} \mathrm{sec}^{-1} \)
Subject: Physics
The angle of deviation by a prism is
\( \left(180^{\circ}-2 A\right) . \) Its critical angle will be
A \( \cdot \sin ^{-1}\left(\tan \frac{A}{2}\right) \)
B. \( \left(\cot \frac{A}{2}\right) \)
c. \( \cos ^{-1}\left(\cot \frac{A}{2}\right) \)
D. \( \cos ^{-1}\left(\tan \frac{A}{2}\right) \)
Subject: Maths
The sum of the series \( \frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !} \ldots \ldots . \)
upto infinity is-
A \( \cdot e^{-2} \)
B \( \cdot e^{-1} \)
\( c \cdot e^{-\frac{1}{2}} \)
D. \( e^{+\frac{1}{2}} \)
Subject: Physics
An unpolarised beam of intensity \( \boldsymbol{I}_{\mathbf{0}} \)
falls on a polaroid at an angle of \( 45^{0} . \) The intensity of the emergent light is
A \( \cdot \frac{I_{0}}{2} \)
в. \( I_{0} \)
c. \( \frac{I_{0}}{4} \)
D. zero
Subject: Maths
If the tangent at any point on the curve \( x^{4}+y^{4}=c^{4} \) cuts off intercepts \( a \) and \( b \)
on the coordinate axes, the value of
\( \boldsymbol{a}^{-\mathbf{4} / \mathbf{3}}+\boldsymbol{b}^{-\mathbf{4} / \mathbf{3}} \) is
A \( \cdot c^{-4 / 3} \)
B \( \cdot c^{-1 / 2} \)
c. \( c^{1 / 2} \)
D. \( c^{4 / 3} \)
Subject: Chemistry
Identify the condition necessary for the conversion of \( B \) and \( C \)
A. \( B \) - hot and conc. \( N a O H, C- \) cold and dil. \( N a O H \)
в. \( B \) - conc. \( N a O H, C- \) per chloric acid
c. \( B \) - per chloric acid, \( C- \) sodium chloride
D. \( B \) - sodium chloride, \( C- \) conc. NaOH
Subject: Physics
A block of mass \( 100 g \) slides on a rough horizontal surface. If the speed of the
block decreases from \( 10 \mathrm{m} / \mathrm{s}^{-1} \) to
\( 5 m / s^{-1}, \) the thermal energy developed
in the process is:
A . \( 3.75 J \)
B. 37.5 \( J \)
c. 0.375 J
D. \( 0.75 J \)
Subject: Physics
Flux \( \phi( \) in webers) in a closed circuit of resistance 10 ohm varies with time \( t \) (in
seconds according to the equation \( \phi=6 t^{2}-5 t+1 . \) What is the
magnitude of the induced current in 0.25 second :
A. \( 0.8 \mathrm{A} \)
B. 1.2 A
c. 0.6 A
D. \( 0.2 \mathrm{A} \)
Subject: Physics
Assertion
Assertion : If we perform an experiment in our laboratory today and repeat the
same experiment on the same objects under identical conditions after a year,
the results are found to be the same.
Reason
Reason : The laws of nature do not
change with time.
A. both assertion and reason are true and reason is the correct explanation of assertion.
B. both assertion and reason are true and reason is not the correct explanation of assertion.
c. assertion is true but reason is false.
D. both assertion and reason are false
Subject: Chemistry
Above reaction is known as:
\[
\begin{array}{c}
\mathrm{O} \\
\mathrm{H}-\mathrm{C}-\mathrm{D}-\mathrm{H}^{28} \mathrm{O}^{-}
\end{array} \mathrm{H}-\mathrm{N}^{-18} \mathrm{O}^{-}+\mathrm{CH}_{2} \mathrm{D}-\mathrm{OH}
\]
A. Cannizaro reaction, Disproportionation reaction
B. Tischenko reaction, Disproportionation reaction
C. Cross Cannizaro reaction, Redox reaction
D. Tischenko reaction, Redox reaction
Subject: Physics
Maximum P.E. of magnet of moment M situated in a magnetic field of induction
\( \mathrm{B}, \) is
\( ^{\mathbf{A}} \cdot \frac{1}{2} M B \)
в. \( \frac{M}{B} \)
\( \mathbf{c} .2 M B \)
D. \( M B \)
Subject: Physics
An inductance of \( 2 H \) carries a current
of \( 2 A . \) To prevent sparking when the circuit is broken a capacitor of \( 4 \mu F \) is connected across the inductance. The
voltage rating of the capacitor is of the order of :
B. \( 10 V \)
\( \mathbf{c} \cdot 10^{5} V \)
D. \( 10^{6} V \)
Subject: Physics
In a moving coil galvanometer, the deflection of the coil \( \theta \) is related to the
electric current \( i \) by the relation
A. \( i \propto \tan \theta \)
В \( . i \propto \theta \)
\( \mathbf{c} \cdot i \propto \theta^{2} \)
\( D \cdot i \propto \sqrt{\theta} \)
Subject: Chemistry
\( e+C H_{3} O H^{H C l(g)} \)
(1)Mannose Glucose 9)
\( \begin{array}{ll}\text {Sucrose }+H_{3} O^{+} \rightarrow & \text { (2) Galactose } \\ \text {Fructose} \stackrel{\text {Base}}{\rightarrow} & \text { (3) Glucose } \\ \text {Lactose}+H_{3} O^{+} \rightarrow & \text { (4) Fructose } \\ & \text { (5) Glucoside }\end{array} \)
\( \begin{array}{llll}\text { A. } A-5 ; & \text { B-3, 4; } & \text { C-1,3; } & \text { D-2,3 }\end{array} \) What is ; \( \quad \mathrm{C}-1,2 ; \)
B. A-4; B-4,5; ; \( \quad D-1,3 \) , an \( D-1,3 \)
C \( . A-5 ; \quad B-3,4 ; \)
4; \( \quad \) C-2,3; \( \quad D-1,2 \) ; \( \quad D-1,2 \) \( c-3.5 \) ; ; \( \quad \mathrm{B}-4,1 \)
D. \( A-3 \)
Subject: Maths
Show that the following poionts are
collinear
(i) \( \boldsymbol{A}(\mathbf{3}, \mathbf{2},-\mathbf{4}), \boldsymbol{B}(\mathbf{9}, \mathbf{8},-\mathbf{1 0}), \boldsymbol{C}(-\mathbf{2},-\mathbf{3}, \mathbf{1}) \)
(ii) \( P(4,5,2), Q(3,2,4), R(5,8,0) \)
Subject: Chemistry
Stability of the species \( L i_{2}, L i_{2}^{-} \) and
\( L i_{2}^{+} \) increases in the order of :
A \( \cdot L i_{2}<L i_{2}^{+}<L i_{2} \)
B . \( L i_{2}^{-}<L i_{2}<L i_{2}^{+} \)
C \( \cdot L i_{2}<L i_{2}^{-}<L i_{2}^{+} \)
D. \( L i_{2}^{-}<L i_{2}^{+}<L i_{2} \)
Subject: Chemistry
\( C N^{\ominus} \) ion is oxidised by a powerful
oxidising agent to \( N O_{3}^{\ominus} \) and \( C O_{2} \) or
\( C O_{3}^{2-} \) depending on the acidity of the
reaction mixture.
\( \boldsymbol{C N}^{\ominus} \longrightarrow \boldsymbol{C O}_{2}+\boldsymbol{N O}_{3}^{\ominus}+\boldsymbol{H}^{\oplus}+\boldsymbol{n} e^{-} \)
What is the number \( (n) \) of electrons
involved in the process?
Subject: Maths
Assertion
Derivative of \( 3 \cot x+5 \operatorname{cosec} x \) is
\( -\operatorname{cosec} x(3 \operatorname{cosec} x+5 \cot x) \)
Reason
\( \boldsymbol{f}^{\prime}(\boldsymbol{a})=\lim _{\boldsymbol{h} \rightarrow \mathbf{0}} \frac{\boldsymbol{f}(\boldsymbol{a}+\boldsymbol{h})-\boldsymbol{f}(\boldsymbol{a})}{\boldsymbol{h}} \)
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
If \( \boldsymbol{x}=\boldsymbol{c} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{z}, \boldsymbol{y}=\boldsymbol{a} \boldsymbol{z}+\boldsymbol{c} \boldsymbol{x}, \boldsymbol{z}=\boldsymbol{b} \boldsymbol{x}+ \)
\( a y, \) where \( x, y, z \) are not all zero, then
the value of \( a^{2}+b^{2}+c^{2}+2 a b c \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. -1
D. None of these
Subject: Chemistry
Polarisation of electrons in acrolein
may be written as:
A \( \cdot \stackrel{-\delta}{C} H_{2}=C H-C^{+\delta}=O \)
B. \( \stackrel{-\delta}{C H_{2}}=C H-C H=\stackrel{+}{O} \)
c. \( \frac{-\delta}{C H_{2}}=\stackrel{+\delta}{C H}-C H=O \)
D. \( _{C H_{2}}^{+\delta}=C H-C H=O^{-\delta} \)
Subject: Maths
A triangle is formed by joining three points whose coordinates are integers. If the \( x \) -unit and the \( y \) -unit are each 1 \( \mathrm{cm}, \) then the area of the triangle, in sq.
\( \mathrm{cm} \)
A. must be an integer
B. may be irrational
c. must be irrational
D. must be rational
E. will be an integer only if the triangle is equilatera
Subject: Maths
The range of \( \left|\tan ^{-1} x\right| \) is
\( \mathbf{A} \cdot\left[0, \frac{\pi}{2}\right] \)
В. \( \left[0, \frac{\pi}{2}\right) \)
c. \( \left(0, \frac{\pi}{2}\right) \)
D. \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \)
Subject: Physics
A spherical mirror produces an image of magnification -1 on a screen placed at a distance of \( 50 \mathrm{cm} \) from the mirror.
(a) Write the type of mirror.
(b) Find the distance of the image from
the object.
(c) What is the focal length of the mirror
\( ? \)
(d) Draw the ray diagram to show the image formation in this case.
Subject: Physics
Voltmeters \( V_{1} \) and \( V_{2} \) are connected in
series across a \( D . C . \) line. \( V_{1} \) reads \( 80 V \)
and has a per volt resistance of \( 200 \Omega \)
\( V_{2} \) has a total resistance of \( 32 k \Omega \). The
line voltage is
\( \mathbf{A} \cdot 120 V \)
в. \( 160 V \)
\( \mathbf{c} \cdot 220 V \)
D. \( 240 V \)
Subject: Chemistry
The decrease in the freezing point of an aqueous solution of a substance is
\( 1.395 k \) and that in the
freezing point of benzene solution of
the same substance is \( 1.280 k . \) Explain
the difference in \( \Delta T \).
The substance:
A. dissociates in the aqueous solutio as well as in the benzene solution
B. forms complex in solution
c. associates in the benzene solution
D. dissociates in the aqueous solution and not in the benzene solution
Subject: Chemistry
Which of the following statements related to the modern periodic table is incorrect?
(a) The p-block has 6 columns because a maximum of 6 electrons can occupy
all
the orbitals in a p-shell
(b) The d-block has 8 columns because
a maximum of 8 electrons can occupy
all the orbitals in a d-subshell
(c) Each block contains a number of
columns equal to the number of electrons that can occupy that subshell
(d) The block indicates value of
azimuthal quantum number (I) for the last subshell that received electrons
in building up the electronic configuration
Subject: Physics
The velocity of the particle at any time \( t \)
is given by \( \boldsymbol{v}=\mathbf{2} \boldsymbol{t}(\boldsymbol{3}-\boldsymbol{t}) \mathbf{m} \boldsymbol{s}^{-1} . \) At what
time is its velocity maximum?
A . 2 s
B. 6s
c. \( 1.5 \mathrm{s} \)
D. 1s
Subject: Chemistry
\( Z n \) Amalgam is prepared by the
electrolysis of aqueous \( Z n C l_{2} \) using \( H g \) cathode \( (9 \mathrm{gm}) . \) How much current
should be passed through \( Z n C l_{2} \) solution for 1000 seconds to prepare a
\( Z n \) amalgam with \( 25 \% Z n \) by weight ? \( (Z n \text { atomic weight }=65.4) \)
A . \( 5.6 \mathrm{A} \)
в. 7.2 A
\( c \cdot 8.85 A \)
D. 11.2 A
Subject: Physics
By suspending a mass of \( 0.50 \mathrm{kg} \), a spring is stretched by \( 8.20 \mathrm{m} . \) If a mass of \( 0.25 \mathrm{kg} \) is suspended, then its period of oscillation will be:
(Take \( g=10 m s^{-2} \) )
A . 0.137 s
B. 0.328 s
c. 0.628 s
D. 1.000
Subject: Physics
spheres of radii 'a' and 'b', respectively(see figure), has volume charge density \( \rho=\frac{A}{r}, \) where \( A \) is a
constant and \( r \) is the distance from the
centre. At the centre of the spheres is a
point charge \( Q . \) The value of \( A \) such that
the electric field in the region between
the spheres will be constant, is :
A \( \cdot \frac{Q}{2 \pi a^{2}} \)
В. \( \frac{Q}{2 \pi\left(b^{2}-a^{2}\right)} \)
c. \( \frac{2 Q}{\pi\left(a^{2}-b^{2}\right)} \)
\( D \cdot \frac{2 Q}{\pi^{2}} \)
Subject: Physics
Equations of a stationary wave and a
travelling wave are \( \boldsymbol{y}_{1}=\boldsymbol{a} \) sink \( \boldsymbol{x} \) coswt
and \( y_{2}=a \sin (\omega t-k x) . \) The phase
difference between two points \( \boldsymbol{x}_{1}= \) \( \frac{\pi}{3 k} \) and \( x_{2}=\frac{3 \pi}{2 k} i s \phi_{1} \) for the first
wave and \( \phi_{2} \) for the second wave. The
ratio \( \frac{\phi_{1}}{\phi_{2}} \) is :
A. 1
в. \( \frac{5}{6} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{6}{7} \)
Subject: Maths
The parabola \( y^{2}=4 x+1 \) divides the
\( \operatorname{disc} x^{2}+y^{2} \leq 1 \) into two regions with
\( \operatorname{areas} A_{1} \) and \( A_{2} . \) Then \( \left|A_{1}-A_{2}\right| \) equals
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
c.
D. \( \frac{\pi}{3} \)
Subject: Physics
Three men \( A, B, C \) of mass \( 40 \mathrm{kg}, 50 \mathrm{kg} \) and \( 60 \mathrm{kg} \) are standing on a plank of mass \( 90 \mathrm{kg} \) which is kept on a smooth
horizontal plane B sits in the middle of
the plane \( B \) sits in the middle of the plane \( A \) and \( C \) sit 2 meters away from opposite sides. If \( A \) and \( C \) exchange there positions then mass B will shift
Subject: Physics
After \( 10 s \) of the start of motion of both
objects \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) find the value of
velocity of \( \boldsymbol{A} \) if \( \boldsymbol{u}_{\boldsymbol{A}}=\boldsymbol{6} \boldsymbol{m} \boldsymbol{s}^{-1}, \boldsymbol{u}_{\boldsymbol{B}}= \)
\( 12 m s^{-1} \) and at \( T \) velocity of \( A \) is
\( 8 m s^{-1} \) and \( T=4 s \)
\( \mathbf{A} \cdot 12 m s^{-1} \)
\( \mathbf{B} \cdot 10 m s^{-1} \)
\( \mathbf{c} \cdot 15 m s^{-1} \)
D. None of these
Subject: Physics
An open vessel containing the liquid upto a height of \( 15 \mathrm{m} \). A small hole is
made at height of \( 10 \mathrm{m} \) from the base of the vessel, then the initial velocity of
efflux is \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B . \( 10 \sqrt{2} \mathrm{m} / \mathrm{s} \)
\( c \cdot 5 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)
Subject: Maths
A random variable \( X \) takes the values
\( \mathbf{0}, \mathbf{1} \) and \( \mathbf{2} . \) If \( \boldsymbol{P}(\boldsymbol{X}=\mathbf{1})=\boldsymbol{P}(\boldsymbol{X}=\mathbf{2}) \) and
\( P(X=0)=0.4, \) then the mean value
of the random variable \( \boldsymbol{X} \) is
A . 0.2
B. 0.5
\( c .0 .7 \)
D. 0.9
Subject: Chemistry
For a cell reaction involving a two-electron change, the standard emf of the cell is found to be \( 0.295 \mathrm{V} \) at \( 25^{\circ} \mathrm{C} \). The
equilibrium constant of the reaction at
\( 25^{\circ} \mathrm{C} \) will be :
A \( \cdot 1 \times 10^{-10} \)
B . \( 29.5 \times 10^{-2} \)
c. 10
D. \( 1 \times 10^{10} \)
Subject: Chemistry
A 2.00 g. of sample containing \( N a_{2} C O_{3} \) and \( N a H C O_{3} \) loses 0.248 g when
heated to \( 300^{\circ} \mathrm{C} \), the temperature at
which \( N a H C O_{3} \) decomposes.Find \%
composition of \( N a_{2} C O_{3} \) in the mixture
\( ? \)
Subject: Physics
An object of height \( 10 \mathrm{cm} \) is placed at a distance \( 100 \mathrm{cm} \) before the convex
mirror perpendicular below the principal axis. If the focal length of the mirror is \( 10 \mathrm{cm}, \) on applying the Cartesian sign convention. Find the signs of object distance, focal length and height of the object.
A. \( u=100 \mathrm{cm}, f=-10 \mathrm{cm}, h=-10 \mathrm{cm} \)
в. \( u=100 \mathrm{cm}, f=10 \mathrm{cm}, h=20 \mathrm{cm} \)
c. \( u=100 \mathrm{cm}, f=-10 \mathrm{cm}, h=10 \mathrm{cm} \)
D. \( u=-100 \mathrm{cm}, f=10 \mathrm{cm}, h=10 \mathrm{cm} \)
Subject: Chemistry
\( \boldsymbol{H O O C}-\boldsymbol{C H}_{2}-\underset{1}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C O O H} \)
COOH
What is the IUPAC name of the given
compound?
A. Propane-1,2,3-tricarboxylic acid
B. Propane -1,2,3 - trioic acid
c. 1,2,3 - tricarboxylic propane
D. Propanedioic carboxylic acid
Subject: Physics
A sphere of radius \( 10 \mathrm{cm} \) and mass
\( 25 k g \) is attached to the lower end of a
steel wire of length \( 5 m \) and diameter
\( 4 m m \) which is suspended from the ceiling of a room. The point of support is \( 521 \mathrm{cm} \) above the floor. When the
sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the
ball at its lowest position in \( \boldsymbol{m} / \boldsymbol{s} \) \( \left(\boldsymbol{Y}_{\text {steel}}=\mathbf{2} \times \mathbf{1 0}^{11} \boldsymbol{N} / \boldsymbol{m}^{2}\right) \)
Subject: Physics
A body weighs \( 160 N \) on the earth. Find
its weight on another planet whose mass is \( \frac{5}{2} \) times mass of earth and radius \( \frac{4}{5} \) times that of earth.
A . \( 125 N \)
B. \( 625 N \)
c. \( 225 N \)
D. 25 N
Subject: Chemistry
The oxidation states of central metal
ions of \( (A),(B) \) and \( (C) \) compounds are respectively:
A. \( +11,+ \) VI and \( + \) VII
B. \( +11,+ \) VI and \( +v \) I
c. \( +1 !,+ \) VII and \( + \) vII
D. \( +\mathrm{Vl} \), \( + \) VII and \( +\mathrm{V} \) I
Subject: Maths
The line \( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{y}-\mathbf{3}}{\mathbf{4}}=\frac{\boldsymbol{z}-\mathbf{4}}{\mathbf{5}} \) is
parallel to the plane.
A. \( 2 x+3 y+4 z=29 \)
B. \( 3 x+4 y-5 z=10 \)
c. \( 3 x+4 y+5 z=38 \)
D. \( x+y+z=0 \)
Subject: Maths
Find mean deviation from the mean for
the given data
\( \mathbf{8} \quad \mathbf{1 0} \quad \mathbf{1 2} \quad \mathbf{1 4} \) Item
Frequency \( \quad 10 \quad 5 \quad 11 \)
A .2 .12
в. 3.04
c. 10.45
D. 5.76
Subject: Chemistry
When acidified \( K_{2} C r_{2} O_{7} \) solution is
added to \( S n^{2+} \) salts, then \( S n^{2+} \) changes
to:
\( A \cdot S n \)
в. \( S n^{3} \)
\( c \cdot s n^{4} \)
D. \( S n^{+} \)
Subject: Chemistry
Calcium lactate is a salt of a weak
organic acid and represented as
\( \boldsymbol{C} \boldsymbol{a}(\boldsymbol{L} \boldsymbol{a} \boldsymbol{c})_{2} \cdot \boldsymbol{A} \) saturated solution of
\( C a(L a c)_{2} \) contains 0.13 mole of this
salt in 0.50 l litre solution. The pOH of
this solution is \( 5.60 . \) Assuming a complete dissociation of salt, calculate
\( K_{a} \) of the lactic acid.
Subject: Physics
A cyclotron's oscillator frequency is 10
MHz and the operating magnetic field is \( 0.66 \mathrm{T} . \) If the radius of its dees is \( 60 \mathrm{cm} \)
then the kinetic energy of the proton beam produced by the accelerator is?
\( \mathbf{A} \cdot 9 \mathrm{MeV} \)
B. 10 Mev
c. 7 Mev
D. 11 Mev
Subject: Maths
The value of \( \lim _{x \rightarrow-\infty}\left[\frac{x^{4} \sin \left(\frac{1}{x}\right)+x^{2}}{1+|x|^{3}}\right] \) is
equal to
\( A \cdot 1 \)
B. -
c. 0
\( D \cdot \alpha \)
Subject: Physics
In a horizontal pipe line of uniform cross-section,pressure falls by 5 Pa between two points separated by \( 1 k m \) The change in the kinetic energy per kg of the oil flowing at these points is :
(Density of oil \( =\mathbf{8 0 0} \) kgm \( ^{-3} \) )
A . \( 6.25 x 10^{-3} \mathrm{Jkg}^{-1} \)
B. \( 5.25 x 10^{-4} \mathrm{Jkg}^{-1} \)
c. \( 3.25 x 10^{-5} \mathrm{Jkg}^{-1} \)
D. \( 4.25 x 10^{-2} \mathrm{Jkg}^{-1} \)
Subject: Physics
A \( 120 V A C \) line transformer is to supply \( 13000 V \) for a neon sign. To reduce shock hazard a \( 8.5 \mathrm{mA} \) fuse is inserted. Find the
maximum input power that can be given to the transformer.
\( \mathbf{A} \cdot 120 W \)
B. \( 121 W \)
\( c \cdot 110 W \)
D. \( 104 W \)
Subject: Physics
the pulse in the figure shown has a speed of \( 0.1 m s^{-1} . \) the linear mass
density of the right string is 0.25 that of the left string. At what speed does the transmitted wave travel?
A \( .25 \mathrm{cms}^{-1} \)
B. 20cms-
\( \mathrm{c} \cdot 15 \mathrm{cms}^{-1} \)
D. \( 17.5 \mathrm{cms}^{-1} \)
Subject: Chemistry
1,3,5,7- Octatetraene contains \( \underline{X} \boldsymbol{\sigma}- \)
bonds and \( \underline{Y} \pi- \) bonds. \( X \) and \( Y \) are:
A .23,4
B. 17,4
\( \mathbf{c} \cdot 18,5 \)
D. 33, 2
Subject: Physics
The equation of a simple harmonic progressive wave is given by \( y=A \sin \) \( (100 \pi t-3 x) . \) Find the distance
between 2 particles having a phase difference of \( \frac{\boldsymbol{\pi}}{\mathbf{3}} \)
A \( \cdot \frac{\pi}{9} m \)
в. \( \frac{\pi}{18} m \)
c. \( \frac{\pi}{6} m \)
D. \( \frac{\pi}{3} m \)
Subject: Maths
In \( \triangle P Q R, P D \perp Q R \) such that \( D \) lies
on \( Q R \). If \( P Q=a, P R=b, Q D=c \) and
\( D R=d, \) then
A \( \cdot(a-d)(a+d)=(b-c)(b+c) \)
B . \( (a-c)(b-d)=(a+c)(b+d) \)
C \( \cdot(a-b)(a+b)=(c+d)(c-d) \)
D \( \cdot(a-b)(c-d)=(a+b)(c+d) \)
Subject: Maths
of the 1000 persons of a town, \( 60 \% \) are males of whom , \( 20 \% \) are literate. If of
all the person \( 25 \% \) are literate then what percentage of the female of the town are
literate?
A . 32.5\%
B. 22.5\%
c. \( 45 \% \)
D. 13\%
Subject: Maths
Find the slope of tangent of the curve
\( \boldsymbol{x}=\boldsymbol{a} \sin ^{3} \boldsymbol{t}, \boldsymbol{y}=\boldsymbol{b} \cos ^{3} \boldsymbol{t} \) at \( \boldsymbol{t}=\frac{\pi}{2} \)
A . cott
B. \( - \) tant
c. \( - \) cott
D. not defined at \( \frac{\pi}{2} \)
Subject: Maths
If \( \tan \theta=\frac{1}{\sqrt{5}} \) and \( \theta \) lies in the first
quadrant, the value of \( \cos \theta \) is
A \( \cdot \frac{1}{\sqrt{6}} \)
B. \( \frac{\sqrt{5}}{\sqrt{6}} \)
c. \( \frac{-1}{\sqrt{6}} \)
D. \( \frac{-\sqrt{5}}{\sqrt{6}} \)