AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The temperature at which the reaction given below is at equilibrium is \( A g_{2} O(s) \longrightarrow 2 A g(s)+\frac{1}{2} O_{2}(g) \)
Given that \( \Delta H^{o}=30.5 k J m o l^{-1} \) and
\( \boldsymbol{\Delta} \boldsymbol{S}^{o}=\mathbf{0 . 0 6 6} \boldsymbol{k} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
A. \( T=412.12 K \)
в. \( T=432.12 K \)
c. \( T=422.12 K \)
Subject: Maths
The equation of the line parallel to \( 5 x- \)
\( 12 y+26=0 \) and at a distance of 4
units from it, is
This question has multiple correct options
A. \( 5 x-12 y-26=0 \)
в. \( 5 x-12 y+26=0 \)
c. \( 5 x-12 y-78=0 \)
D. \( 5 x-12 y+78=0 \)
Subject: Physics
Which of the following is not the
characteristics of electromagnetic
wave?
A \( . \) The electric and magnetic fields \( \vec{E} \) and \( \vec{B} \) are always perpendicular to the direction in which the wave is travelling
B. The electric field is always perpendicular to the magnetic field
C. The cross product \( \vec{E} \times \vec{B} \) always gives the direction in which the wave travels
D. The fields do not vary simultaneously
Subject: Physics
Let \( p \) and \( E \) denote the linear
momentum and the energy of a photon. For another photon of smaller wavelength (in same medium)
A. Both \( p \) and \( E \) increase
B. \( p \) increases and \( E \) decreases
c. \( p \) decreases and \( E \) increases
D. Both \( p \) and \( E \) decrease
Subject: Maths
If \( A \times\left(\begin{array}{l}1 \\ 0\end{array}\right)=(12), \) then the order of \( A \) is
A \( .2 \times 1 \)
B. \( 2 \times 2 \)
c. \( 1 \times 2 \)
D. 3 \( \times 2 \)
Subject: Physics
\( \boldsymbol{I}=\boldsymbol{6} \cos \boldsymbol{w} \boldsymbol{t}+\boldsymbol{8} \sin \boldsymbol{w} \boldsymbol{t} \) is
applied across a resistor of \( 40 \Omega \). Find the potential difference across
the resistor
A . \( 660 v \)
B. 80
c. \( 330 v \)
D. 400
Subject: Maths
The tangent EF and EG are drawn from E
to the circle with centre 0. The diameter
Fl and the tangent EG, when produced,
intersect at H. If \( \angle \mathrm{IFG}=28^{\circ}, \) calculate
(a) \( \angle \mathrm{EFG} \)
(b) \( \angle \mathrm{FEG} \)
(c) \( \angle \mathrm{HGl} \)
Subject: Chemistry
An element has average atomic mass \( 20.426 u \) it has 2 isotopes with masses
\( \mathbf{2 2 . 1 8 2 4} \) and \( \mathbf{1 9 . 9 5 7 4 .} \) Calculate the
abundance of its isotopes \( X-22 \) and
\( X-20 \)
Subject: Chemistry
If \( K_{1} \) and \( K_{2} \) are the respective
equilibrium constants for the two reactions
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4}(\boldsymbol{g})+ \)
\( 2 H F(g) \)
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}(\boldsymbol{g})+\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4}(\boldsymbol{g})+ \)
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3} \boldsymbol{F}_{2}(\boldsymbol{g}) \)
the equilibrium constant of the
following reaction is:
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{4}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H} \boldsymbol{F}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3} \boldsymbol{F}_{2}(\boldsymbol{g})+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \) will be:
A \( . K_{1} / K_{2}^{2} \)
В. \( K_{1} \times K_{2} \)
c. \( K_{1} / K_{2} \)
Subject: Maths
A die is thrown twice. Each time the
number appearing on it is recorded. Describe the following events:
\( A= \) Both numbers are odd
\( B= \) Both numbers are even
\( C= \) Sum of the numbers is less than 6
Also, Find \( \boldsymbol{A} \cup \boldsymbol{B}, \boldsymbol{A} \cap \boldsymbol{B}, \boldsymbol{A} \cup \boldsymbol{C}, \boldsymbol{A} \cap \boldsymbol{C} \)
Which pairs of events are mutually exclusive
Subject: Physics
A body enters in MRI machine in 10 sec
If the magnetic field is \( 1.5 T \) and
circumference of MRI machine is \( 0.9 m \)
then find out emf induced in the body.
A . \( 0.96 V \)
B. \( 9.6 V \)
c. \( 9.6 m V \)
D. \( 96 m V \)
Subject: Chemistry
The solubility product of a sparingly soluble salt \( A X_{2} \) is \( 3.2 \times 10^{11} \). Its
solubility (moles/litre) is:
A \( .3 .1 \times 10^{-4} \)
B. \( 2 \times 10^{3} \)
c. \( 4 \times 10^{-4} \)
D. \( 5.6 \times 10^{-6} \)
Subject: Maths
\( \int \frac{x^{2}+\cos ^{2} x}{1+x^{2}} \csc ^{2} x d x \) is equal to:
This question has multiple correct options
\( \mathbf{A} \cdot \cot x-\cot ^{-1} x+c \)
B \( \cdot c-\cot x+\cot ^{-1} x \)
\( ^{\mathbf{C}}-\tan ^{-1} x-\frac{\csc x}{\sec x}+c \)
D. \( e^{\ln \tan ^{2} x}+\cos x+c \)
Subject: Physics
associated with electromagnetic radiations in different contexts in
physics. State the part of the electromagnetic spectrum to which
each belongs.
(a) \( 21 \mathrm{cm} \) (wavelength emitted by atomic hydrogen in interstellar space).
(b) 1057 MHz (frequency of radiation
arising from two close energy levels in hydrogen; known as Lamb shift).
(c) \( 2.7 \mathrm{K} \) [temperature associated with the isotropic radiation filling all space thought to be a relic of the big-bang origin of the universe].
\( (d) 5890 A-5896 \dot{A}[ \) double lines of
sodium]
(e) 14.4 ke \( V \) [energy of a particular transition in \( ^{57} \) Fe nucleus associated
with a famous high resolution spectroscopic method Mössbauer spectroscopy)].
Subject: Biology
Which of the following are true about the brain?
(a) The main thinking part of brain is hindbrain.
(b) Centres of hearing, smell, memory, sight etc., are located in forebrain.
(c) Involuntary actions like salivation, vomiting, blood pressure are controlled
by the medulla in the hindbrain.
(d) Cerebellum does not control posture
and balance of the body.
A. (a) and (b)
B. (a), (b) and (c)
\( c \cdot(b) \) and \( (c) \)
D. (c) and (d)
Subject: Chemistry
The acid dissociation constant of uric
\( \operatorname{acid} \) is \( \boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{4} \cdot \boldsymbol{0} \times \mathbf{1 0}^{-\boldsymbol{6}} \boldsymbol{M} \cdot \) The \( \boldsymbol{p} \boldsymbol{H} \) of
a sample is \( 6.0 . \) What is the ratio of urate ion to uric acid in the urine?
A . 2.0
в. 4.0
\( c .6 .0 \)
D. 0.25
Subject: Physics
If in a Young's double slit experiment, the slit width is \( 3 \mathrm{cm}, \) the separation between slits and screen is \( 70 \mathrm{cm} \) and
wavelength of light is \( 1000 \mathrm{A} \), then fringe width will be \( (\mu=1.5) \)
A \( .2 .3 \times 10^{-3} \mathrm{cm} \)
В. \( 2.3 \times 10^{-4} m \)
\( \mathbf{c} \cdot 2.3 \times 10^{-5} \mathrm{cm} \)
D . \( 2.3 \times 10^{-6} \mathrm{m} \)
Subject: Physics
The earth's radius is \( \mathrm{R} \) and acceleration
due to gravity at its surface is g. If a
body of mass \( m \) is sent to a height \( h= \) \( \boldsymbol{R} \)
\( \frac{i}{5} \) from the earth's surface, the
potential energy increases by
A . mgh
в. \( \frac{4}{5} m g h \)
c. \( \frac{5}{6} \) mgh
D. \( \frac{6}{7} \) mgh
Subject: Physics
Two radio frequency point sources
\( S_{1} \) and \( S_{2} \), separated by distance \( 2.5 \mathrm{m} \)
are emitting in phase waves of wavelength \( 1 \mathrm{m} . \) A detector moves in a large circular path around the two sources in a plane containing them. The number of maxima that will be detected
by it over the complete circular path,
are
A . 16
B. 12
\( c \cdot 10 \)
D. 8
Subject: Chemistry
Phosphine is obtained by This question has multiple correct options
A. \( C a_{3} P_{2}+H_{2} O \rightarrow \)
B . \( P_{4}+N a O H \rightarrow \)
c. \( C H C l_{3}+O_{2} \rightarrow \)
D. \( C C l_{4}+O_{2} \rightarrow \)
Subject: Physics
A body of mass \( 0.4 \mathrm{kg} \) moving with a constant speed of \( 10 \mathrm{m} / \mathrm{s} \) to the north is
subject to a constant force of \( 8 \mathrm{N} \)
direction toward the south for 30 s. Take
the instant the force is applied to be
\( t=0, \) the position of the body at the
time to be \( x=0, \) and predict its
position at \( t=-5 s, 25 s, 100 s \)
Subject: Physics
An object is lying at a distance of \( 90 \mathrm{cm} \) from a concave mirror of focal length
\( 30 \mathrm{cm} . \) The position and nature of image formed by it will be:
A. \( 45 \mathrm{cm} \), of the size to object
B. \( 95 \mathrm{cm} \), smaller than object
c. \( 35 \mathrm{cm} \), bigger than object
D. \( -45 \mathrm{cm}, \) smaller than object
Subject: Physics
A body of mass M was slowly hauled up a rough hill by a force \( F \) which at each point was directed along a tangent to the hill. Work done by the force.
This question has multiple correct options
A. Is independent of the shape of trajectory
B. Depends upon the vertical component of displacemen but is independent of horizontal component
c. Depends upon both the component
D. Does not depend upon the coefficient of friction
Subject: Biology
Match the Column-I with Column-II.
Column-I
(i) Depolarisation of
(a) P-wave
(ii) Repolarisation of
(b) QRS complex \( \quad \) ventricles
(iii) Coronary
(c) T-wave
(d) Reduction in the size
(iv) Depolarisation of of T-wave atria
(v) Repolarisation of atria
Select the correct option.
A. (a)-(iv), (b)-(i), (c)-(ii), (d)-(iii)
B. (a)-(iv), (b)-(i), (c)-(ii), (d)-(v)
\( c \cdot(a)-(i i),(b)-(i),(c)-(v),(d)-(i i i) \)
D. (a)-(ii), (b)-(iii), (c)-(v), (d)-(iv)
Subject: Physics
A cylinder of mass \( 10 \mathrm{kg} \) and radius 15 \( \mathrm{cm} \) is rolling perfectly on a plane of
inclination \( 30^{\circ} . \) The coefficient of static
friction \( \mu_{s}=0.25 \)
(a) How much is the force of friction
acting on the cylinder?
(b) What is the work done against friction during rolling?
(c) If the inclination \( \theta \) of the plane is
increased, at what value of \( \theta \) does the
cylinder begin to skid, and not roll
perfectly?
Subject: Maths
There are \( n \) points in a plane out of these points no three are in the same straight line except \( p \) points which are
collinear. Let " \( k \) " be the number of
straight lines and "m" be the number of
triangles.Then find \( m-k \) ?(Assume
\( \boldsymbol{n}=\boldsymbol{7} \boldsymbol{p}=\mathbf{5}) \)
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}\left(\boldsymbol{x}^{4}+\mathbf{1}\right)(\boldsymbol{x}+\mathbf{1})+\boldsymbol{x}^{4}+\mathbf{2}}{\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}}, \operatorname{then} \boldsymbol{f}(\boldsymbol{x}) \) is
A. one-one ito
B. many-one onto
c. one-one onto
D. many-one into
Subject: Physics
If e.m.f of cell is \( \boldsymbol{E} \) with internal
resistance \( r \) and external resistance is
\( \boldsymbol{R}, \) then terminal voltage will be :
A \( \cdot \frac{E r}{R+r} \)
в. \( \frac{E R}{R+r} \)
c. \( E \)
D. \( \frac{E r R}{R+r} \)
Subject: Physics
The surface of the metal is illuminated
with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be \( 1.68 \mathrm{eV} \), the work function of metal is :
A . \( 1.51 \mathrm{eV} \)
B. 1.42 ev
c. 3.0 ev
D. 1.68 ev
Subject: Maths
Let \( r^{t h} \) term of a series is given by, \( \boldsymbol{T}_{\boldsymbol{r}}= \) \( \frac{r}{1-3 r^{2}+r^{4}} \)
Then \( \lim _{n \rightarrow \infty} \sum_{r=1}^{n} T_{r} \) is
A \( \cdot \frac{3}{2} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{-1}{2} \)
D. \( \frac{-3}{2} \)
Subject: Physics
Suppose the loop in Exercise is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initia
value of \( 0.3 \mathrm{T} \) at the rate of \( 0.02 \mathrm{T} s^{-1} . \) If
the cut is joined and the loop has a resistance of 1.6 ohm , how much power is dissipated by the loop as heat? What is the source of this power?
Exercise :
I A rectangular wire loop of sides \( 8 \mathrm{cm} \) and \( 2 \mathrm{cm} \) with a small cut is moving out of a region of uniform magnetic field of magnitude \( 0.3 \mathrm{T} \) directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is \( 1 \mathrm{cm} \)
\( s^{-1} \) in a direction normal to the (a)
longer side,
(b) shorter side of the loop?
For how long does the induced voltage last in each case?
Subject: Physics
The atmospheric pressure at sea level is \( _{-}-_{-}- \) of \( \boldsymbol{H} \boldsymbol{g} \)
\( \mathbf{A} \cdot 76 k m \)
B. \( 76 \mathrm{cm} \)
\( \mathrm{c} .76 \mathrm{mm} \)
D. \( 76 m \)
Subject: Chemistry
When \( B a C l_{2} \) is added to an aqueous salt solution, a white precipitate is obtained. The anion among
\( C O_{3}^{2-}, S O_{3}^{2-} \) and \( S O_{4}^{2-} \) that was
present in the solution can be:
A \( \cdot C O_{3}^{2-} \) but not any of the other two
B. \( S O_{3}^{2-} \) but not any of the other two
c. \( S O_{4}^{2-} \) but not any of the other two
D. None of these
Subject: Chemistry
For a binary liquid solution obeying Raoult's law at \( 300 K \)
\( \boldsymbol{X}_{\boldsymbol{A}}=\mathbf{0 . 7 5}, \) Given: \( \boldsymbol{P}_{\boldsymbol{A}}^{\boldsymbol{o}}= \)
\( 400 m m H g ; P_{B}^{o}=600 m m H g \)
Then select correct statement
This question has multiple correct options
A. Vapour pressure of solution will be \( 450 \mathrm{mm} \mathrm{Hg} \)
B. In distillate mol fration of \( B \) will be \( 2 / 3 \)
c. If distillate is removed \( \& \) condensed then it is redistilled, then mole fraction of \( A \) in \( I I \) distillate is \( 4 / 7 \)
D. Normal boiling point of liquid solution should be more than \( 300 K \)
Subject: Physics
For reading small letters with a lens
A. one has to keep a convex lens at a distance between \( F \) and \( 2 \mathrm{F} \) from the book.
B. one has to keep a concave lens at a distance less than the focal length from the book
C. one has to keep concave lens at a distance between and \( 2 \mathrm{F} \) from the book
D. One has to keep a convex lens at a distance less than the an focal length from the book
E. None of these
Subject: Physics
An alternating voltage of \( 220 V, 50 H z \) frequency is applied across a capacitor of capacitance \( 2 \mu F \). The impedence of
the circuit is:
A \( \frac{\pi}{5000} \)
в. \( \frac{1000}{\pi} \)
\( c .500 \pi \)
D. \( \frac{5000}{\pi} \)
Subject: Chemistry
Arrange the following acids in
decreasing order of \( \left[\boldsymbol{H}^{+}\right] \) conc.
\( \mathrm{cH}_{2}=\mathrm{cHCH}_{2}-\mathrm{cooH} \quad \mathrm{cH}_{3} \mathrm{CH}_{2} \mathrm{coot} \)
(II
A \( . I>I I>I I I \)
В. \( I I>I I I>I \)
c. \( I I>I>I I I \)
D. \( I I I>I I>I \)
Subject: Maths
Find the median class for the following
data given below:
\( \begin{array}{llll}\text { Number } & \mathbf{0}- & \mathbf{1 0}- & \mathbf{2 0}- \\ \text { of cars } & \mathbf{1 0} & \mathbf{2 0} & \mathbf{3 0}\end{array} \)
Frequency 7 13
A . \( 30-40 \)
в. \( 40-50 \)
c. \( 50-60 \)
D. \( 60-70 \)
Subject: Chemistry
The molar enthalpy of vaporization benzene at its boiling point(350K) is \( 30.84 \mathrm{kJ} / \mathrm{mol} . \) What is the molar internal
energy change?For how long would a 12 volt source need to supply a \( 0.5 \mathrm{A} \) current in order to vaporize \( 7.8 g \) of sample at its boiling point?
Subject: Maths
The pair of complementary angles from the following options are:
A . \( 30^{\circ}, 150^{\circ} \)
В. \( 76^{\circ}, 14^{\circ} \)
\( \mathbf{c} \cdot 65^{\circ}, 65^{\circ} \)
D. \( 120^{\circ}, 30^{\circ} \)
Subject: Maths
Three distinct points \( A, B \) and \( C \) are given in the 2 -dimensional coordinate plane such that the ratio of the distance
of any one of them from the point (1,0) to the distance from the point (-1,0) is equal to \( \frac{1}{3} . \) Then the circumcentre of the triangle \( A B C \) is at the point:
\( ^{\text {A }} \cdot\left(\frac{5}{2}, 0\right) \)
в. \( \left(\frac{5}{3}, 0\right) \)
c. (0,0)
D. \( \left(\frac{5}{8}, 0\right) \)
Subject: Chemistry
Which compound amongst the following has the highest oxidation
number for \( M n ? \)
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}, \boldsymbol{K}_{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}, \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2} \) and
\( \boldsymbol{M} \boldsymbol{n}_{2} \boldsymbol{O}_{3} \)
Subject: Physics
If \( 13.6 e V \) energy is required to ionize
the hydrogen atom, then the energy required to remove an electron from
\( \boldsymbol{n}=\mathbf{2} \) is
A. \( 10.2 \mathrm{eV} \)
B. 0 eV
c. 3.4 eV
D. 6.8 eV
Subject: Physics
If the amplitude of waves at a distance
\( 10 \mathrm{cm} \) from a point source is \( A, \) the
amplitude at a distance \( 40 \mathrm{cm} \) will be
A. \( A / 2 \)
в. \( A / 4 \)
\( c . A \)
D. \( 2 A \)
Subject: Physics
Assertion
The decrease in speed of sound at high altitudes is due of fall in pressure at
this altitude.
Reason
The speed of sound is the same at all pressures and varies with temperature only.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Maths
The number of values of \( n \), for which
\( \boldsymbol{p}(\boldsymbol{n})=\mathbf{1} !+\mathbf{2 !}+\mathbf{3 !}+\mathbf{4} !+\cdots+\boldsymbol{n} ! \) is
the square of a natural number, is equal
to
\( A \cdot 0 \)
B. 1
\( c \cdot 2 \)
D. 3
Subject: Maths
Simplify using associative property :
\( \frac{7}{16} \times\left(\frac{-24}{49} \times \frac{28}{15}\right) \)
A \( \cdot \frac{28}{15} \)
B. \( \frac{2}{5} \)
c. \( \frac{-2}{5} \)
D. \( \frac{-3}{15} \)
Subject: Maths
The value of
\( \cos \left[\frac{1}{2} \cos ^{-1}\left[\cos \left[-\frac{14 \pi}{5}\right]\right]\right] \) is/are -
This question has multiple correct options
\( ^{A} \cdot \cos \left[-\frac{7 \pi}{5}\right] \)
B. \( \sin \left[\frac{\pi}{10}\right. \)
\( ^{\mathbf{c}} \cdot \cos \left[\frac{2 \pi}{5}\right] \)
D. \( -\cos \left[\frac{3 \pi}{5}\right] \)
Subject: Maths
The co-ordinates of the focus of
parabola \( \boldsymbol{y}^{2}=\mathbf{2 0} \boldsymbol{x} \) are
A. (5,5)
(年) 5,5,5
B. (3,5)
c. (0,5)
(年. (0,5)
D. (5,0)
Subject: Chemistry
On reaction with \( C l_{2} \), phosphorus forms
two types of halides 'A' and 'B'. Halide 'A' is yellowish-white powder but halide 'B' is colourless oily liquid. What would be the hydrolysis products of 'A' and 'B' respectively?
A. \( H_{3} P O_{4}, H_{3} P O_{3} \)
в. \( H O P O_{3}, H_{2} P O_{2} \)
\( \mathbf{c} \cdot H_{3} P O_{3}, H_{3} P O_{4} \)
D. \( H P O_{3}, H_{3} P O_{3} \)
Subject: Physics
Two \( 2 \Omega \) resistances are connected in
parallel in circuit \( X \) and in series in
circuit Y. The batteries in the two
circuits are identical and have zero
internal resistance. Assume that the
energy transferred to resistor A in
circuit \( X \) within a certain time is \( W \). The
energy transferred to resistor \( \mathrm{B} \) in
circuit \( Y \) in the same time will be:
A \( \cdot \frac{1}{4} w \)
B. \( \frac{1}{2} w \)
c. \( 2 w \)
D. \( 4 \mathrm{w} \)
Subject: Maths
Solve the following pair of equations by reducing them to a pair of linear equations: \( \frac{4}{x}+3 y=14, \frac{3}{x}-4 y=23 \)
B. \( x=-3, y=-1 \)
c. \( _{x}=\frac{1}{5}, y=-2 \)
D. \( x=\frac{7}{2}, y=7 \)
Subject: Physics
With due regard to significant figures, add the following:
a. 953 and 0.324
b. 953 and 0.625
c. 953.0 and 0.324
d. 953.0 and 0.374
A . a. \( 953 ; \) b. 954 c. 953.3 d. 953.4
B. a. \( 953 ; \) b. 955 c. 953.3 d. \( 953 . \)
c. a. \( 952 ; \) b. 954 с. 953.3 d. 953.4
D. a. \( 953 ; \) b. 954 c. 953.3 d. 952.4
Subject: Maths
\( \int \frac{1}{\sin ^{2} x+\sin 2 x} d x \)
A. \( \frac{1}{2} \log \frac{\tan x}{\tan x+2} \)
B. \( -\frac{1}{2} \log \frac{\tan x}{\tan x+2} \)
c. \( \frac{1}{2} \log \frac{\tan x}{\tan x-2} \)
D. \( \log \frac{\tan x}{\tan x+2} \)
Subject: Chemistry
Assuming the bond direction to the z-
axis, which of the overlapping of atomic orbitals of two atoms \( (A) \) and \( (B) \) will
result in bonding?
(I) \( s \) -orbital of \( A \) and \( p_{x} \) orbital of \( B \)
(II) \( s \) -orbital of \( A \) and \( p_{z} \) orbital of \( B \)
(III) \( p_{y} \) orbital of \( A \) and \( p_{z} \) orbital of \( B \)
(IV) \( s \) -orbital of both \( (A) \) and \( (B) \)
A. I and IV
B. I and II
c. Ill and IV
D. II and IV
Subject: Physics
A man of 60 kg gains 1000 cal of heat by eating 5 mangoes. His efficiency is \( 56 \% \) To what height he canjump by using
this energy?
\( \mathbf{A} \cdot 4 m \)
в. \( 20 m \)
\( c .28 m \)
D. \( 0.2 m \)
Subject: Physics
A particle of charge \( q \) and mass \( m \) starts moving from origin under the action of an electric field \( \vec{E}=E_{0} \vec{i} \) and magnetic field \( \vec{B}=B_{0} \vec{k} \). Its velocity at
\( (x, 3,0) \) is \( (4 i+3 i), \) the value of \( x \) is:
A \( \cdot \frac{36 E_{o} B_{0}}{q m} \)
В. \( \frac{25 m}{2 q E_{0}} \)
c. \( \frac{10 m}{q E_{o}} \)
D. \( \frac{25 E_{0} B_{0}}{m} \)
Subject: Chemistry
Hexa ammine nickel (II) hexa nitro
cobaltate (III) can be written as:
\( \mathbf{A} \cdot\left[N i\left(N H_{3}\right)_{6} C o\left(N O_{2}\right)_{6}\right] \)
B . \( \left[N i\left(N H_{3}\right)_{6}\right]_{3}\left[C o\left(N O_{2}\right)_{6}\right]_{2} \)
c. \( \left[N i\left(N H_{3}\right)_{6}\right]\left[C o\left(N O_{2}\right)_{6}\right]_{2} \)
D. \( \left[N i\left(N H_{3}\right)_{6}\left(N O_{2}\right)_{6}\right] C o \)
Subject: Chemistry
At \( 675 K, H_{2}(g) \) and \( C O_{2}(g) \) react to
form \( C O(g) \) and \( H_{2} O(g), K_{p} \) for the reaction is \( 0.16 . \) If a mixture of 0.25
mole of \( H_{2}(g) \) and 0.25 mole of \( C O_{2} \) is
heated at \( 675 \mathrm{K} \), mole percentage of
\( \boldsymbol{C O}(\boldsymbol{g}) \) in equilibrium mixture is:
A . 7.14
B. 14.28
c. 28.57
D. 33.33
Subject: Chemistry
Solid ammonium carbamate,
\( N H_{4} C O_{2} N H_{2}(s), \) dissociates into
ammonia and carbon dioxide, when it
evaporates as shown by:
\( N H_{4} C O_{2} N H_{2}(s) \rightleftharpoons 2 N H_{3}(g)+ \)
\( C O_{2}(g) . \) At \( 25^{\circ} C, \) the total pressure of
the gases in equilibrium with the solid
is 0.116 atm. If 0.1 atm of \( C O_{2} \) is introduced after equilibrium is reached,
then:
This question has multiple correct options
A. the final pressure of \( C O_{2} \) will be less than 0.1 atm
B. the final pressure of \( C O_{2} \) will be more than 0.1 atm
c. the pressure of \( N H_{3} \) will decrease due to addition of \( C O_{2} \)
D. the pressure of \( N H_{3} \) will increase due to addition of \( C O_{2} \)
Subject: Chemistry
Which of the following reactions involves the combination of two
elements?
A. \( C a O+C O_{2} \rightarrow C a C O_{3} \)
в. \( 4 N a+O_{2} \rightarrow 2 N a_{2} O \)
\( \mathrm{c} \cdot \mathrm{SO}_{2}+\frac{1}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{3} \)
D. \( N H_{3}+H C l \rightarrow N H_{4} C l \)
Subject: Maths
If \( x=a t^{2}, y=2 a t \) then \( \frac{d^{2} y}{d x^{2}}= \)
A. \( -\frac{1}{t^{2}} \)
B. \( \frac{1}{2 a t^{3}} \)
c. \( -\frac{1}{t^{3}} \)
D. \( -\frac{1}{2 a t^{3}} \)
Subject: Chemistry
A tetrapeptide has \( - \) COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary
structures) with \( N H_{2} \) group attached
to a chiral centre is :
\( A \cdot 4 \)
B. 3
\( c \cdot 6 \)
\( D \cdot 2 \)
Subject: Physics
An inductor of reactance \( X_{L}=4 \Omega \) and
resistor of resistance \( \boldsymbol{R}=\mathbf{3} \Omega \) are
connected in series with a voltage
source of emf \( \varepsilon= \)
\( (20 V)[\sin (100 \pi r a d / s) t] . \) The current in
the circuit at any time t will be?
A \( \cdot I=(4 A)\left[\sin (100 \pi r a d / s) t+37^{\circ}\right] \)
B . \( I=(4 A)\left[\sin (100 \pi r a d / s) t-37^{\circ}\right. \)
C \( \cdot I=(4 A)\left[\sin (100 \pi r a d / s) t+53^{\circ}\right. \)
D. \( I=(4 A)\left[\sin (100 \pi r a d / s) t-53^{\circ}\right. \)