AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
One mole of oxygen is expanded from a volume \( 1 \ell \) to \( 2 \ell \) at a constant
temperature \( \boldsymbol{T}=\mathbf{2 8 0} \boldsymbol{K} . \) Find the
change in internal energy of the gas.
\( \mathbf{A} \cdot 9.8 k J \)
B . \( 2.8 k J \)
\( c .0 k J \)
D. 12.8 k
Subject: Maths
For three events \( A, B \) and \( C, P( \) exactly
one of the events \( A \text { or } B \text { occurs })=P( \)
exactly one of the vents \( B \) or \( C \) occurs
\( =P(\text { exactly one of the events } C \text { or } A \) occurs \( )=p \) and \( P( \) all the three events
occur simultaneously \( )=p^{2}, \) where \( 0< \)
\( \boldsymbol{p}<\frac{1}{2} \)
Then the probability of atleast one of the three events \( A, B \) and \( C \) occurring is
A \( \cdot \frac{3 p+2 p^{2}}{2} \)
в. \( \frac{p+3 p^{2}}{2} \)
c. \( \frac{3 p+p^{2}}{2} \)
D. \( \frac{3 p+2 p^{2}}{4} \)
Subject: Maths
In the given figure, \( m \| n \) and \( \angle 1=50^{\circ} \)
then find \( \angle \mathbf{5} \)
A \( \cdot 130^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 180^{\circ} \)
Subject: Physics
What will be the electric flux through
the sphere \( S_{1} \) if a medium of dielectric
constant \( \epsilon_{r} \) is introduced in the
space inside \( S_{1} \) in place of air
A. \( \frac{20}{\epsilon \epsilon_{n}} \)
в. \( \frac{40}{\epsilon_{0} \epsilon_{r}} \)
c. \( \frac{20 \epsilon_{c}}{\epsilon_{0}} \)
D. \( \frac{406}{6} \)
Subject: Maths
The latus rectum of the hyperbola \( 16 x^{2}-9 y^{2}=144 \) is
A \( \cdot \frac{13}{6} \)
в. \( \frac{32}{3} \)
\( c \cdot \frac{8}{3} \)
D. \( \frac{4}{3} \)
Subject: Maths
A non-zero vector \( \vec{a} \) is parallel to the
line of intersection of plane \( \boldsymbol{p}_{\mathbf{1}} \)
determined by \( \hat{i}+\hat{j} \) and \( \hat{i} \) and plane \( P_{2} \) determined by vectors \( \hat{\mathbf{i}}-\hat{\mathbf{j}} \) and \( \hat{\mathbf{i}}+\hat{\boldsymbol{k}} \)
then angle between a and vector \( \hat{\mathbf{i}}- \) \( 2 \hat{j}+2 \hat{k} \) is
This question has multiple correct options
A \( \cdot \frac{\pi}{4} \)
B. \( \frac{\pi}{2} \)
c. \( \frac{\pi}{3} \)
D. \( \frac{3 \pi}{4} \)
Subject: Chemistry
Atoms of eight elements \( A, B, C, D, E, F \) G and H have the same number of
electronic shells but different number
of electrons in their outermost shell. It
was found that elements \( A \) and \( G \)
combine to form an ionic compound which can also be extracted from sea
water. This compound is added in a small amount to almost all vegetable dishes during cooking. Oxides of elements A and B are basic in nature
while those of \( \mathrm{E} \) and \( \mathrm{F} \) are acidic. The
oxide of \( \mathrm{D} \) is almost neutral. Based on
the above information answer the
following question.
To which group or period of the periodic table do the listed elements belong?
Subject: Physics
in a meter bridge, the balance point is found to be \( 40 \mathrm{cm} \) from one end (say end
A). if a resistance of \( 10 \Omega \) is connected
in series with \( R, \) a balance point is
obtained \( 60 \mathrm{cm} \) from end
A. What are
the values of \( R \) and \( S(S \) is other resistance in series with \( \boldsymbol{R} \) )?
Subject: Physics
An experiment needs to heat a small
sample to temperature \( 900 K, \) but the
only available large object has
maximum temperature of 600 \( K . \) Could
the experimenter heat the sample to
\( 900 K \) by using a large lens to concentrate the radiation from the large
object onto the sample as shown below?
A. Yes, if the front area of the large object is at least 1.5 times the area of the front of the sample
B. Yes, if the sample is placed at the focal point of the lens
c. It is not possible
D. Yes, if the volume of the large object is atleast 1.5 times the volume of the sample
Subject: Physics
A charge \( ^{\prime} \boldsymbol{q}^{\prime} \) is placed at the centre of the line joining two equal charges. The system will be in equilibrium if \( q \) is
equal to
A. \( -Q / 2 \)
в. \( -Q / 4 \)
\( c .-4 Q \)
D. \( +Q / 2 \)
Subject: Physics
The gravitational force which acts on a body of mass \( 1 \mathrm{kg} \) on the surface of the earth is
\( A \cdot 9.8 \mathrm{N} \)
B \cdot \( \frac{1}{9.8} \) N
c. \( 980 \mathrm{N} \)
D. \( \frac{1}{980} \mathrm{N} \)
Subject: Chemistry
How many atoms of hydrogen are
present in \( 7.8 g \) of \( A l(O H)_{3} ? \)
A. \( 6.0 \times 10^{22} \)
В. \( 1.8 \times 10^{23} \)
c. \( 1.7 \times 10^{23} \)
D. \( 5.1 \times 10^{22} \)
Subject: Chemistry
Cerium \( (Z=58) \) is an important
member of lanthanides. Which of the
following statements about cerium is
correct?
A. The common oxidation states of cerium are +3 and +4
B. The +3 oxidation states of cerium is more stable than the +4 state
c. The +4 oxidation states of cerium is not known in solutions
D. Cerium (IV) acts as an oxidising agent.
Subject: Chemistry
Which atoms in \( H_{2} O \) and \( C l F \) are
negatively charged?
A. \( O \) in \( H_{2} O \) and \( C l \) in \( C I F \)
B. \( H \) in \( H_{2} O \) and \( F \) in \( C I F \)
\( \mathrm{c} \cdot O \) in \( H_{2} \mathrm{O} \) and \( F \) in \( C I F \)
D. None of the above is correct.
Subject: Physics
The resistance of a carbon filament at
\( 0^{\circ} \mathrm{C} \) is \( 104 \Omega \). It is connected in series
with an iron wire. The temperature coefficients of resistivity of carbon and
iron are -0.0003 and 0.0052 per \( ^{o} C \) respectively. What must be the resistance of iron wire so that the
combined resistance does not change with temperature?
A \( .1 .8 \Omega \)
B. 3.7 \( \Omega \)
c. \( 6.0 \Omega \)
D. 15 \Omega
Subject: Chemistry
Assertion
The mass of a substance is constant
whereas its weight may vary from one place to another.
Reason
Mass of a substance is the amount of
matter present in it while weight is the force exerted by gravity on an object.
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: Chemistry
Polarisation of electron in acrolein
\( \left(\boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}=\boldsymbol{O}\right) \) or resonance
hybrid of acrolein can be written as:
\( A \)
\[
\stackrel{\partial^{+}}{\mathrm{CH}_{2}} \ldots \ldots \ldots \ldots \ldots
\]
B. \( \stackrel{\partial^{-}}{\mathrm{CH}}_{2} \cdots \ldots \ldots \ldots \ldots+\ldots 0^{+} \)
\( c \)
\( \partial^{-} \ldots \ldots \mathrm{CH}-\mathrm{CH} \cdots \cdot \mathrm{O}^{-} \)
\( \mathrm{CH}_{2} \cdots-\mathrm{O}^{-} \)
D. \( \stackrel{\partial^{+}}{\mathrm{CH}}_{2} \cdots \ldots+\cdots \cdot \mathrm{CH}=\ldots 0^{+} \)
Subject: Maths
ff \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is given by \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{3}- \)
\( \left.\boldsymbol{x}^{3}\right)^{1 / 3}, \) find \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{f}(\boldsymbol{x}) \)
Subject: Maths
Evaluate: \( \lim _{n \rightarrow \infty} \sum_{r=0}^{n-1} \frac{1}{n+r} \)
\( A \cdot \log 2 \)
B. \( 2 \log 2 \)
c. \( \frac{1}{2} \log 2 \)
D. \( \frac{1}{4} \log 2 \)
Subject: Physics
Two planets, \( A \) and \( B \), orbit a star. Planet A moves in an elliptical orbit whose semi major axis has length a. Planet B moves in an elliptical orbit whose semi major axis has a length of 9a. If planet \( A \) orbits with a period \( T, \) what is the period
of planet Bs orbit?
A. 7297
в. 27 T
\( c \cdot 3 T \)
D. \( T / 3 \)
E. т/27
Subject: Maths
If two sets \( A \) and \( B \) have 99 elements in
common, then the number of elements
common to each of the sets \( A \times B \) and
\( \boldsymbol{B} \times \boldsymbol{A} \) are
A . \( 2^{99} \)
B. \( 99^{2} \)
\( c \cdot 100 \)
D. 18
Subject: Biology
Consider the statements.
A. 'Oral Rehydration Solution' (ORS)
should be given to cholera or diarrhoea patients at regular intervals.
B. Poliovirus is transmitted through
food or water and ultimately affect
central nervous system.
C. E.coli and Shigella bacteria are responsible for diarrhoea disease.
D. Rhinoviruses are responsible for
common cold.
The correct statements are
A. A and D
B. A and B
\( c \cdot A, C \) and \( D \)
D. All of the above
Subject: Maths
Two vectors \( \vec{A} \) and \( \vec{B} \) have magnitude 3 each. \( \vec{A} \times \vec{B}=-5 \hat{k}+2 \hat{i} . \) Find the
angle between \( A \) and \( B \)
A \( \cdot \cos ^{-1} \frac{\sqrt{29}}{9} \)
B. \( \tan ^{-1}\left(\frac{-5}{2}\right) \)
\( ^{c} \cdot \sin ^{-1}\left(\frac{2}{5}\right) \)
D. \( \sin ^{-1}\left(\frac{\sqrt{29}}{9}\right) \)
Subject: Maths
If \( A \) and \( B \) are two square matrices such that \( B=-A^{-1} B A, \) then
\( (A+B)^{2}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( A^{2}+B^{2} \)
c. \( A^{2}+2 A B+B^{2} \)
D. \( A+B \)
Subject: Physics
Two resistances are connected in the
two gaps of a metre bridge. The balance point is \( 20 \mathrm{cm} \) from the zero end. When a resistance \( 15 \Omega \) is connected in series with the smaller of two resistances, the
null point shifts to \( 40 \mathrm{cm} . \) The smaller of
the two resistances has the value.
\( A \cdot 8 \Omega \)
B. \( 9 \Omega \)
\( c .10 \Omega \)
D. 12\Omega
Subject: Maths
Let \( \boldsymbol{f} \) be a function satisfying \( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})= \)
\( x^{-3 / 2}, f^{\prime}(4)=2 \) and \( f(0)=0 . \) Then
\( f(784) \) is equal to
Subject: Maths
In \( \triangle A B C, A B=5 c m, B C= \)
\( \mathbf{6} c \boldsymbol{m}, \boldsymbol{A C}=\mathbf{4} \boldsymbol{c m} . \) Identify the type of
triangle.
A. Right angled triangle
B. Isosceles triangle
c. Equilateral triangle
D. Scalene triangle
Subject: Maths
\( \sin ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right)+ \)
\( \cos ^{-1}\left(\sin \left(\cos ^{-1} x\right)\right) \) is equal to
\( A \cdot \frac{\pi}{2} \)
B.
\( c \cdot \frac{3 \pi}{4} \)
D.
Subject: Chemistry
In the following first-order competing reactions:
\( A+ \) Reagent \( \longrightarrow \)
Product; \( \quad B+ \) Reagent \( \longrightarrow \)
Product
The ratio of \( \frac{\boldsymbol{K}_{1}}{\boldsymbol{K}_{2}} \) if only \( 50 \% \) of \( \mathrm{B} \) will have been reacted when \( 94 \% \) of \( A \) has been
reacted is: (as nearest integer)
Subject: Biology
If the Neanderthals are not the direct
ancestors of humans, is it still possible for humans and Neanderthals to be
related?
A. Yes, because we share a common ancestor
B. Yes, but only if humans and Neanderthals could have interbred
c. No, because the human evolutionary tree is strictly linear and without branches
D. No, because this means that Neanderthals evolved from an entirely different branch of organisms than humans did
Subject: Physics
The velocity of a particle increases from \( u \) to \( v \) in a time \( t \) during which it covers a distances \( S \). If the particle has a uniform acceleration, which one of the following equations does not apply to the motion?
\( \mathbf{A} \cdot 2 S=(v+u) t \)
B. \( a=\frac{v-u}{t} \)
c. \( v^{2}=u^{2}-2 a S \)
D. \( s=\left(u+\frac{1}{2} a t\right) t \)
Subject: Maths
The length of a rectangle is \( 4 \mathrm{cm} \) more than the breadth, and the perimeter is
\( 11 \mathrm{cm} \) more than the breadth. Find the
length and breadth of the rectangle.
A. \( l=1, b=7 \mathrm{cm} \)
В. \( l=6, b=3 \mathrm{cm} \)
c. \( l=7, b=8 \mathrm{cm} \)
Subject: Physics
The flux of magnetic field through closed conducting loop of resistance 0.4 Whanges with time according to the
equation \( \phi=0.20 t^{2}+0.40 t+0.60 \) where
is time in seconds. Find
(i) the induced
emf at \( t=2 s . \) (ii) the average induced emf in \( t=0 \) to \( t=5 \) s. (iii) change passed through the loop in \( t=0 \) to \( t=5 s . \) (iv) average current in time interval \( t=0 \) to
\( t=5 s \)
(v) heat produced in \( t=0 \) to \( t=5 s \)
Subject: Chemistry
The Lassaigne's extract is boiled with
dil. \( H N O_{3} \) before testing for halogens
because
A. \( A g C N \) is soluble in \( H N O_{3} \)
B. Sliver halides are soluble in \( H N O_{3} \)
c. \( N a C N \) and \( N a_{2} S \) are decomposed by \( H N O_{3} \)
D. \( A g_{2} S \) is soluble in \( H N O_{3} \)
Subject: Chemistry
Calculate the average bond enthalpy of
the \( \boldsymbol{O}-\boldsymbol{H} \) bond in water at \( 298 \mathrm{K} \) using
the data / information given below :
\( \Delta_{f} \boldsymbol{H}^{0}[\boldsymbol{H}(\boldsymbol{g})]=\mathbf{2} \mathbf{1} \mathbf{8} \mathbf{k} \mathbf{J} / \mathrm{mol} \)
2. \( \Delta_{f} H^{0}[O(g)]=249.2 \mathrm{kJ} / \mathrm{mol} \)
3. \( \Delta_{f} H^{0}\left[H_{2} O(g)\right]=-241.8 \mathrm{kJ} / \mathrm{mol} \)
The average bond enthalpy of the \( - \) bond in water is defined as one - half of
the enthalpy change for
the reaction \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H}(\boldsymbol{g})+\boldsymbol{O}(\boldsymbol{g}) \)
Also, determine the \( \Delta U \) of the \( O-H \)
bond in water at 298 K. Assume ideal
gas behaviour.
A \( \cdot E(O-H)=462 \) kJ/mol; \( \Delta U=461 \) kJ/mol
B . \( E(O-H)=463.5 \) kJ/mol; \( \Delta U=463.5 \) kJ/mol
C \( \cdot E(O-H)=461 \mathrm{kJ} / \mathrm{mol} ; \Delta U=461 \mathrm{kJ} / \mathrm{mol} \)
D - \( E(O-H)=463.5 \mathrm{kJ} / \mathrm{mol} ; \Delta U=461 \mathrm{kJ} / \mathrm{mol} \)
Subject: Maths
f \( A+2 B=\left[\begin{array}{cc}2 & -4 \\ 1 & 6\end{array}\right], A^{\prime}+B^{\prime}= \)
\( \left[\begin{array}{cc}1 & 2 \\ 0 & -1\end{array}\right], \) then \( A= \)
Subject: Chemistry
\( H C l \) is prepared by heating \( N a C l \) with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) but \( \boldsymbol{H} \boldsymbol{I} \) cannot be
prepared by treating \( N a I \) with conc.
\( H_{2} S O_{4} \). Identify the reason.
A \( \cdot H_{2} S O_{4} \) is oxidised by \( H I \) and not oxidised by \( H C l \)
B. \( H I \) is oxidised by \( H_{2} S O_{4} \) and \( H C l \) is not oxidised by \( H_{2} S O_{4} \)
C. \( H I \) dissociates on treatment with \( H_{2} S O_{4} \) and \( H C l \) does not dissociate.
D. The reaction of \( H_{2} S O_{4} \) with \( H I \) Is reversible whereas with \( H C l \) is irreversible
Subject: Physics
The angle between two vectors \( \vec{P}= \) \( \mathbf{3} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{Q}}=\mathbf{2} \hat{\mathbf{i}}-\hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}} \) is:
A \( \cdot \cos ^{-1}\left[\frac{5}{\sqrt{77}}\right. \)
B. \( \cos ^{-1}\left[\frac{\sqrt{77}}{6.5}\right. \)
\( ^{\mathbf{C}} \cdot \cos ^{-1}\left[\frac{6.5}{\sqrt{77}}\right. \)
D. \( \sin ^{-1}\left[\frac{\sqrt{77}}{6.5}\right. \)
Subject: Chemistry
Find the number of photons of radiation of frequency \( 5 \times 10^{13} s^{-1} \) that must be
absorbed in order to melt one gm ice when the latent heat of fusion of ice is
\( \mathbf{3 3 0} \mathbf{J} \cdot\left(\mathbf{h}=\mathbf{6 . 6} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J} \times \mathbf{s e c} .\right) \)
Subject: Physics
The voltage and the current of an a.c circuit are \( V=100 \sin (100 t) \) volt and
\( \boldsymbol{i}=\mathbf{1 0 0} \sin (\mathbf{1 0 0} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{3}) \boldsymbol{m} \boldsymbol{A} \)
receptively. The power dissipated in the circuit is:
A \( \cdot 10^{4} W \)
в. \( 10 W \)
c. \( 2.5 W \)
D. \( 5.0 W \)
Subject: Physics
An ideal gas is initially at \( P_{l}, V_{1} \) is
expanded to \( P_{2}, V_{2} \) and then compressed adiabatically to the same
volume \( V_{l} \) and pressure \( P_{3} \).If \( W \) is the
net work done by the gas in complete process which of the
A. \( W>0 ; P_{3}>P_{1} \)
В. \( W<0 ; P_{3}>P_{1} \)
c. \( W<0 ; P_{3} \)
D. \( P_{2}>P_{1} ; W<0 \)
Subject: Maths
The unit vector perpendicular to both \( L_{1} \)
and \( \boldsymbol{L}_{2} \) is
\( ^{\mathbf{A}} \cdot \frac{-\hat{i}+7 \hat{j}+7 \hat{k}}{\sqrt{99}} \)
\( ^{\text {B. }} \frac{-\hat{i}-7 \hat{j}+5 \hat{k}}{5 \sqrt{3}} \)
\( \frac{-\hat{i}+7 \hat{j}+5 \hat{k} \hat{k}}{5 \sqrt{3}} \)
D. \( \frac{7 \hat{i}-7 \hat{j}-\hat{k}}{\sqrt{99}} \)
Subject: Physics
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The
mass of the wire is \( 3.5 \times 10^{-2} k g \) and
its linear mass density is \( 4.0 \times \) \( 10^{-2} k g m^{-1} . \) What is
(a) the speed of a
transverse wave on the string, and
the tension in the string?
Subject: Maths
Arjun wants to invest Rs 15,000 in two types of bonds. He earns \( 12 \% \) in the first type and \( 15 \% \) in the second. His
investment in \( 15 \% \) bond, if he has a total earning of Rs \( 1,950, \) is
A. Rs 10,000
B. Rs 5,000
c. \( R s 6,000 \)
D. Rs 7,000
Subject: Chemistry
The degree of dissociation of \( 0.1 M \)
\( H C N \) solution is:
A \( \cdot 6.4 \times 10^{-5} \)
B . \( 6.4 \times 10^{-3} \)
c. \( 6.4 \times 10^{-2} \)
D. \( 6.4 \times 10^{-6} \)
Subject: Physics
One end of a string of length L and cross-sectional area A is fixed to a
support and the other end is fixed to a
bob of mass \( \mathrm{m} \). The bob is revolved in a
horizontal circle of radius \( r, \) with an
angular velocity \( \omega, \) such that the string
makes an angle \( \theta \) with the vertical. The increase \( \Delta L \) in length of the string is
A \( \cdot \frac{M L}{A Y} \)
В. \( \frac{M g L}{A Y \cos \theta} \)
c. \( \frac{M g L}{A Y \sin \theta} \)
D. \( \frac{M g L}{A Y} \)
Subject: Chemistry
The change in pressure will not affect the equilibrium constant for:
A \( \cdot N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
B . \( P C l_{5}(s) \rightleftharpoons P C l_{3}(s)+C l_{2}(g) \)
C. \( H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
D. all of the above
Subject: Physics
A magnetic needle oscillates in a horizontal plane with a period T at a
place where the angle of dip is \( 60^{0} \) When the same needle is made to
oscillate in a vertical plane coinciding with the magnetic meridian, its period will be
A \( \cdot \frac{T}{\sqrt{2}} \)
B. T
c. \( \sqrt{2 T} \)
D. 2T
Subject: Physics
A choke coil has negligible resistance.
The alternating potential drop across it is 220 volts and the current is \( 5 \mathrm{mA} \). The
power consumed is
A \( \cdot 220 \times \frac{5}{1000} W \)
в. \( \frac{220}{5} W \)
c. zero
D. \( 2.20 \times 5 W \)
Subject: Physics
Two radioactive sources \( A \) and \( B \)
initially contain equal number of radioactive atoms. Source A has a half-
life of 1 hour and source \( \mathrm{B} \) has a half-life
of 2 hours. At the end of 2 hours, the
ratio of the rate of disintegration of \( A \) to that of B is :
A . 1: 2
B. 2:
\( c \cdot 1: 1 \)
D. 1:
Subject: Chemistry
The graph between \( \log \frac{x}{m} v / s \log P \) is
straight line inclined at an angle \( 45^{\circ} \) with intercept \( 0.30 . \) What will be rate of
adsorption at pressure 0.4 atm?
A . 0.4
B. 0.6
c. 0.8
D. 0.9
Subject: Maths
\( x^{2} \sqrt{1-x^{2}} d x= \)
A \( \cdot \frac{1}{8} \arcsin x-\frac{1}{8} x\left(1-2 x^{2}\right) \sqrt{1-x^{2}}+C \)
B \( \cdot \frac{1}{8} \arcsin x+\frac{1}{8} x\left(1-2 x^{2}\right) \sqrt{1+x^{2}}+C \)
C \( \cdot \frac{1}{8} \arcsin x+\frac{1}{8} x\left(1-x^{2}\right) \sqrt{1-x^{2}}+C \)
D. None of these
Subject: Physics
Assertion
In a meter bridge experiment, a high resistance is always connected in
series with a galvanometer.
Reason
As resistance increases, current
through the circuit increases.
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
A cathode ray tube has a potential difference of \( V \) volt between the cathode
and the anode. The speed of cathode rays is given by
\( \mathbf{A} \cdot 6 \times 10^{-5} \sqrt{V} \mathrm{cm} / \mathrm{s} \)
B . \( 6 \times 10^{5} \sqrt{V} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 6 \times 10^{7} \sqrt{V} \mathrm{cm} / \mathrm{s} \)
D \( \cdot 6 \times 10^{3} \sqrt{V} m / s \)
Subject: Chemistry
Arrange \( C e^{3+}, L a^{3+}, P m^{3+} \) and \( Y b^{3+} \) in
increasing order of their ionic radii
A \( \cdot Y b^{3+}<P m^{3+}<C e^{3+}<L a^{3+} \)
B. \( C e^{3+}<Y b^{3+}<P m^{3+}<L a^{3+} \)
c. \( Y b^{3+}<P m^{3+}<L a^{3+}<C e^{3+} \)
D. \( P m^{3+}<L a^{3+}<C e^{3+}<Y b^{3} \)
Subject: Physics
Determine the potential drop between
the points \( A \) and \( C \) in the following
circuit. Resistances \( 1 \Omega \) and \( 2 \Omega \) (internal
resistance of cell) :
A. \( \frac{4}{5} v \)
B . \( 1.75 V \)
c. \( 2.25 V \)
\( D \cdot \frac{5}{1} V \)
Subject: Chemistry
Nickel (atomic number \( =28 \) amu)
combines with a uninegative
monodentate ligand \( X^{-} \) to form a
paramagnetic complex \( \left[N i X_{4}\right]^{2-} . \) The number of unpaired electron(s) in nickel and the geometry of this complex ion are respectively:
A. two, square planar
B. one, tetrahedral
c. two, tetrahedral
D. one, square planar
Subject: Maths
If \( \boldsymbol{x}=\sin t, \boldsymbol{y}=\cos \boldsymbol{p} \boldsymbol{t}, \) then
B . \( \left(1-x^{2}\right) y_{2}+x y_{1}-p^{2} y=0 \)
C \( \cdot\left(1+x^{2}\right) y_{2}-x y_{1}+p^{2} y=0 \)
D. \( \left(1-x^{2}\right) y_{2}-x y_{1}+p^{2} y=0 \)
Subject: Physics
Choose the correct statement about
displacement d:
A. It is inversely proportional to the length a
B. It is directly proportional to the kinetic energy of incident particle \( \left(\frac{1}{2} m v_{0}^{2}\right) \)
c. It is directly proportional to the electric field E
D. For lesser \( \frac{q}{m} \) (charge to mass ratio), it is higher
Subject: Physics
The masses of three copper wires are in the ratio 1: 2: 3 and their lengths are
in the ratio \( 3: 2: 1 . \) The ratio of their
resistance is:
A. 27: 6: 1
B. 9: 3: 1
\( \mathrm{c} \cdot 6: 3: 2 \)
D. 1: 2: 3
Subject: Chemistry
Among the following which one is the formula for noncyclic, saturated
hydrocarbon?
\( \mathbf{A} \cdot C_{6} H_{12} \)
в. \( C_{7} H_{14} \)
с \( . C_{7} H_{16} \)
D. \( C_{7} H_{18} \)
E \( . C_{7} H_{12} \)
Subject: Chemistry
The \( p H \) at which \( M g(O H)_{2} \) begins to precipitate from a solution containing \( \mathbf{0 . 1 0} \boldsymbol{M} \boldsymbol{M} \boldsymbol{g}^{\mathbf{2 +}} \) ions. \( \boldsymbol{K}_{\boldsymbol{s} \boldsymbol{p}_{M g(O H)_{2}}}=\mathbf{1 0}^{-\mathbf{1 1}} \) is
Subject: Maths
Let \( A \) and \( B \) be two sets such that \( A \times \)
\( B \) Consists of 6 elements. If three
elements of \( A \times B \) are
(1,4),(2,6),(3,6) then \( B \times A . \) is \( = \)
\( \{(a, 1),(6,1),(4, d),(c, 2),(4,3)(b, 3)\} \)
Find \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}+\boldsymbol{d} \)
Subject: Physics
If
\( M_{e} \) is the mass of earth and \( M_{m} \) is
the mass of moon \( \left(M_{e}=81 M_{m}\right) \). The
potential energy associated with object of mass \( m \) situated at a distance \( R \)
from the centre of earth and \( r \) from
the centre of moon, will be :
\( ^{\mathbf{A}} \cdot_{-G m M_{m}}\left[\frac{R}{81}+r\right] \frac{1}{R^{2}} \)
в. \( -G m M_{m}\left[\frac{81}{r}+\frac{1}{R}\right] \)
\( ^{\mathrm{c}} \cdot_{-G m M_{m}}\left[\frac{81}{R}+\frac{1}{r}\right] \)
D. \( -G m M_{m}\left[\frac{81}{R}-\frac{1}{r}\right. \)
Subject: Chemistry
The IUPAC name of the following compound is:
\( \begin{aligned} \boldsymbol{C}_{2} \boldsymbol{H}_{5}-& \underset{\|}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \\ & \boldsymbol{C H}_{2} \quad \boldsymbol{C} \boldsymbol{H}_{3} \end{aligned} \)
A. 3-methyl-2-ethylbut-1-yne
B. 2-ethyl-3-methylbut-1-ene
c. 3-ethyl-3-methylbutene
D. ethylisopropylethane
Subject: Chemistry
Which does not represent correct
method?
\( \mathbf{A} \cdot T i C l_{4}+2 M g \stackrel{\Delta}{\longrightarrow} T i+2 M g C l_{2}: K \) roll process
B. \( N i(C O)_{4} \stackrel{\Delta}{\longrightarrow} N i+4 C O: \) Mond's process
\( \mathbf{c} \cdot P b I_{2} \stackrel{\Delta}{\longrightarrow} P b+I_{2}: \) Van arkel process
D. \( Z r I_{4} \stackrel{\Delta}{\longrightarrow} Z r+2 l_{2}: \) Van arkel process