AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A parallel plate capacitor contains a mica sheet \( \left(\text { thickness } 10^{-3} m\right) \) and \( a \)
sheet of fiber (thickness \( 0.5 \times 10^{-3} m \) ).
The dielectric constant of mica is 8 and
that of the fiber is \( 2.5 . \) Assuming that the fiber breaks down when subjected to an electric field of \( 6.4 \times 10^{6} V m^{-1} \)
find the maximum safe voltage (in
kV) that can be applied to the capacitor.
Subject: Biology
Arrange the following events of meiosis in the correct sequence.
(i) Crossing over
(ii) Synapsis
(iii) Terminalization of chiasma
(iv) The disappearance of the nucleolus.
A \( \cdot(i i),(i) .(i v) .(i i i) \)
B. \( (i i),(i) .(i i i) .(i) \)
c. \( (i),(i i) .(i i i) .(i v) \)
D. \( (i i),(i i i) . .(i v) . . i i) \)
Subject: Maths
A man running round a racecourse notes that the sum of the distances of
two flag-posts from him is always \( 10 m \) and the distance between the flag-posts
is \( 8 m . \) The area of the path he encloses
is
A. \( 18 \pi \) square metres
B. \( 15 \pi \) square metress
c. \( 12 \pi \) square metress
D. \( 8 \pi \) square metres
Subject: Physics
Given that there is a relationship between the orbital radius of a planet and its period of revolution and that the
periods of revolution of Mercury, Earth, Jupiter and Neptune are nearly 0.24,1 11.8 and 165 years. It follows that the period of revolution of
A. Venus is less than 0.24 years
B. Mars is less than 12 years.
C. Uranus is more than 165 years
D. Uranus is less than 165 years but
more than 12 years. Of these the correct statement(s) is 1
are :
A. A and C
B. D only
c. c only
D. B and D
Subject: Chemistry
Explain the terms Inductive and Electromeric effects. Which electron
displacement effect explains the
following correct orders of acidity of the carboxylic acids?
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H}> \)
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{C O O H}> \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C C O O H} \)
Subject: Maths
The side of a square sheet is increasing at the rate of \( 4 \mathrm{cm} \) per minute. The rate by which the area increasing when the side is \( 8 \mathrm{cm} \) long is.
\( \mathbf{A} \cdot 60 \mathrm{cm}^{2} / \mathrm{minute} \)
B. \( 66 \mathrm{cm}^{2} / \) minute
c. \( 62 \mathrm{cm}^{2} / \mathrm{minute} \)
D. \( 64 \mathrm{cm}^{2} / \mathrm{minute} \)
Subject: Physics
The diagram shows four charges
\( \boldsymbol{q}_{1}, \boldsymbol{q}_{2}, \boldsymbol{q}_{3} \) and \( \boldsymbol{q}_{4} \) all lying in the plane of
the page. The diagram also shows the dotted circle that represents the cross-
section of a spherical Gaussian surface
Point \( P \) is a single point on that surface Which of the charges contributes to the net electric flux through the sphere?
A \( \cdot q_{1} \) and \( q_{3} \)
B. \( q_{2} \) and \( q_{4} \)
\( \mathbf{c} \cdot q_{1} \) and \( q_{2} \)
\( \mathbf{D} \cdot q_{3} \) and \( q_{4} \)
E \( . q_{1}, q_{2}, q_{3}, \) and \( q_{4} \)
Subject: Chemistry
Hydrogen sulphide \( \left(\boldsymbol{H}_{2} \boldsymbol{S}\right) \) is a strong reducing agent. Which of the following reactions shows its reducing action?
A \( \cdot C d\left(N O_{3}\right)_{2}+H_{2} S \rightarrow C d S+2 H N O_{3} \)
B. \( C u S O_{4}+H_{2} S \rightarrow C u S+H_{2} S O_{4} \)
c. \( 2 \mathrm{FeCl}_{3}+\mathrm{H}_{2} \mathrm{S} \rightarrow 2 \mathrm{Fe} \mathrm{Cl}_{2}+2 \mathrm{HCI}+\mathrm{S} \)
D. \( P b\left(N O_{3}\right)_{2}+H_{2} S \rightarrow P b S+2 C H_{3} C O O H \)
Subject: Maths
In a school, \( 8 a^{2}+4 a+9 \) students
were enrolled. \( 2 a^{2}-9 a+2 \) students
were boys. How many girls were
enrolled?
A \( \cdot 6 a^{2}-13 a+7 \)
7
B . \( 4 a^{2}+13 a+7 \)
\( \mathbf{c} \cdot 6 a^{2}+13 a+7 \)
D. \( 4 a^{2}-13 a+7 \)
Subject: Maths
f DE \( \| \) BC and \( A D=1.7 c m, A B= \)
\( 6.8 c m \) and \( A C=9 c m . \) Then length of
AE is
A . \( 2.25 \mathrm{cm} \)
B. \( 4.5 \mathrm{cm} \)
\( c .3 .4 \mathrm{cm} \)
D. \( 5.1 \mathrm{cm} \)
Subject: Maths
When \( \left(x^{3}-2 x+p x-q\right) \) is divided by
\( \left(x^{2}-2 x-3\right), \) the remainder is \( (x-6) \)
What are the values of \( p, q \) respectively.
A . -2,-6
в. 2,-6
c. -4,12
D. 2,6
Subject: Physics
A step down transformer is connected
to 2400 volts line and 80 amperes of current is found to flow in output load.
The ratio of the turns in primary and secondary coil is \( 20: 1 . \) If the
transformer efficiency is \( 100 \% \), then the current flowing in the primary coil will be
\( \mathbf{A} \cdot 1600 \mathrm{amp} \)
B. 20 amp
c. 4 amp
D. 1.5 amp
Subject: Maths
If \( P_{n} \) denotes the product of all the coefficients in the expansion of
\( (1+x)^{n} \) and \( 9 ! P_{(n+1)}=10^{9} P_{n} . \) Then
\( \boldsymbol{n}= \)
A . 10
B. 9
c. 19
D. 11
Subject: Maths
Share of \( A, B \) and \( C \) respectively, are
if Rs. \( \mathbf{5 4 6 0} \) is divided in \( \frac{1}{2}: \frac{1}{3}: \frac{1}{4} \)
A . Rs. 1680 , Rs. 2520 , Rs. 1260
B. Rs. 2520, Rs. 1680, Rs. 1260
c. Rs. \( 1260, \) Rs. \( 2100, \) Rs. 2520
D. Rs. \( 2520, \) Rs. \( 1260, \) Rs. 1680
Subject: Chemistry
Enthalpy of the reaction \( : \boldsymbol{C H}_{4}+ \)
\( \frac{1}{2} O_{2} \longrightarrow C H_{3} O H \) is negative. If
enthalpy of combustion of \( C H_{4} \) and
\( C H_{3} O H \) are \( x \) and \( y \) respectively which relation is correct?
A \( . x>y \)
В. \( x<y \)
\( \mathbf{c} \cdot x=y \)
D. \( x \geq y \)
Subject: Chemistry
Assertion
\( \boldsymbol{T} e \boldsymbol{B} \boldsymbol{r}_{4} \) and \( \boldsymbol{P o} \boldsymbol{B r}_{4} \) are quite stable
while \( S B r_{4} \) and \( S e B r_{4} \) are unstable
Reason
Inert pair effect is greater in tetra bromides of \( S \) and \( S e \) than in \( T e \) and
Po.
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
Calculate the ratio of moles of \( 3.6 g \) of
water and \( 4.4 g \) of carbon dioxide.
Atomic mass of \( \boldsymbol{C}=\mathbf{1 2 u}, \boldsymbol{H}= \)
\( \mathbf{1} \boldsymbol{u}, \boldsymbol{O}=\mathbf{1 6} \boldsymbol{u} \)
Subject: Biology
Which of the following is the right match with the components of transport system of human beings with their functions?
\( \begin{array}{lll} & \text { Components } & \text { Functions } \\ 1 & \text { Heart } & O_{2} \text { transport } \\ 2 & \text { Fibrinogen } & \text { Blood clotting } \\ 3 & \text { RBC } & \text { Forms fibrin } \\ 4 & \text { Platelets } & \text { Pumps blood }\end{array} \)
\( A \)
B. 2
\( c \)
D.
Subject: Maths
Evaluate:
\( \lim _{x \rightarrow \infty} \frac{3 \sqrt{x}+5 \sin ^{2} x-10 \log x}{5 \sqrt{x}+7 \cos ^{2} x+100 \log x} \)
A . 3 5
в. \( \frac{5}{3} \)
c. 15
D. \( \frac{1}{15} \)
Subject: Physics
In a cyclotron, magnetic field of \( 1.4 W b / m^{2} \) is used. To accelerate
protons, how rapidly should the electric field between the Dees he reversed?
\( \left(\boldsymbol{\pi}=\mathbf{3 . 1 4 2}, \boldsymbol{M} \boldsymbol{p}=\mathbf{1 . 6 7} \times \mathbf{1 0}^{-\mathbf{2 7}} \mathbf{k g}, \boldsymbol{e}=\right. \)
\( \left.\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C}\right) \)
Subject: Chemistry
Calculate the equailibrium constant for
the reaction:
\[
\boldsymbol{C u}_{(s)}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+} \longrightarrow \boldsymbol{C u}_{(a q)}^{2+}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{(s)}
\]
Given that \( : \boldsymbol{E}_{A \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}^{0}= \)
\[
\mathbf{0 . 8 0 V}, \quad \boldsymbol{E}_{\mathbf{C u}^{2+} / \mathbf{C u}}^{\mathbf{0}}=\mathbf{0 . 3 4} \boldsymbol{V}
\]
Subject: Physics
The acceleration of block \( \mathrm{B} \) in the figure
will be:
\( \mathbf{A} \)
B.
c. \( \frac{2 M_{1} g}{\left(M_{1}+4 M_{2}\right)} \)
D. \( \frac{2 M_{1} g}{\left(M_{1}+M_{2}\right)} \)
Subject: Chemistry
A compound consists of \( 47.8 \% \) zinc and
52.2\% chlorine by mass. The empirical
formula is \( \mathrm{Zn}_{x} \mathrm{Cl}_{y} \) where \( x \) and \( y \) can have the values:
A . 1 and 1
B. 1 and 2
c. 2 and 1
D. 2 and 3 respectively
Subject: Maths
\( \operatorname{Let} \boldsymbol{I}_{n}=\int_{0}^{\pi} \frac{\sin ^{2}(\boldsymbol{n} \boldsymbol{x})}{\sin ^{2} \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x}, \boldsymbol{n} \in \boldsymbol{N}, \) then
A \( \cdot I_{n+2}+I_{n}=21_{n+1} \)
В. \( I_{n}=I_{n+1} \)
\( \mathbf{c} \cdot I_{n}=n \pi \)
D. \( I_{1}, I_{I}, I_{3}, \ldots \ldots I_{n} \) are in harmonic progression
Subject: Maths
What must be added to \( f(x)=4 x^{4}+ \)
\( 2 x^{3}+2 x^{2}+x-1 \) so that the resulting
polynomial is divisible by \( g(x)=x^{2}+ \)
\( 2 x-3 \)
A. \( -61 x+65 \)
в. \( 2 x-15 \)
c. \( -15 x+2 \)
D. None of these
Subject: Chemistry
The INCORRECT statement is:
A. The spin - only magnetic moments of \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+} \) and \( \left[C r\left(H_{2} O\right)_{6}\right]^{2+} \) are nearly similar
B. The spin-only magnetic moment of \( \left[N i\left(N H_{3}\right)_{4}\left(H_{2} O\right)_{2}\right]^{2+} \) is \( 2.83 B M \)
C. The gemstone, ruby, has \( C r^{3+} \) ions occupying the octahedral sites of beryl
D. The color of \( \left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right]^{2+} \) is violet as it absorbs the yellow light
Subject: Biology
of Helianthus leaf passing through the
midrib, certain parts have been
indicated by alphabets, choose the
answer in which these alphabets have been correctly matched with the parts
which they indicate.
A. A- Epidermis, B- Spongy parenchyma, C- Palisade parenchyma, D- Stomata, F - Phloem, G- Metaxylem, H Protoxylem
B. A- Epidermis, B- Palisade parenchyma, C- Spongy Parenchyma, D- Sub stomatal cavity, F- Phloem, GMetaxylem, H- Protoxylem
C. A- Epidermis, B- Palisade parenchyma, C- Spongy parenchyma, D- Stomata, F- Endodermis, G- Xylem, HPhloem
D. A- Epidermis, B- Palisade parenchyma, C- Spongy parenchyma, D- Stomata, F- Phloem, G- Metaxylem, HProtoxylem
Subject: Physics
A bulb of \( 100 \mathrm{W}-200 \mathrm{V} \) is connected to a
\( 160 \mathrm{V} \) supply. Find the power consumed.
A. \( 25 \mathrm{w} \)
B. 64 W
\( c \cdot 45 w \)
D. 20 W
Subject: Physics
A radioactive sample has \( 2.0 \times 10^{20} \)
active nuclei at a certain instant of
time. Then the the number of samples
in the same active state after three half-
lives is
A \( .2 .5 \times 10^{15} \)
B. \( 2.5 \times 10^{21} \)
c. \( 2.5 \times 10^{19} \)
D. \( 2.5 \times 10^{16} \)
Subject: Maths
Factorise:
\( \boldsymbol{p}^{3}(\boldsymbol{q}-\boldsymbol{r})^{3}+\boldsymbol{q}^{3}(\boldsymbol{r}-\boldsymbol{p})^{3}+\boldsymbol{r}^{3}(\boldsymbol{p}-\boldsymbol{q})^{3} \)
Subject: Chemistry
Set of molecules which are
isoelectronic is :
a) \( N_{2} \) and \( C O \)
b) \( C O_{2} \) and laughing gas \( \left(N_{2} O\right) \)
c) \( \mathrm{CaO} \) and \( \mathrm{MgS} \)
d) Benzene and Borazole \( \left(B_{3} N_{3} H_{6}\right) \)
\( A \cdot a, b, d \)
B. b, c, d
c. \( c, d \)
D. \( a, b, c, d \)
Subject: Maths
if \( \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon}[\mathbf{0}, \boldsymbol{2} \boldsymbol{\pi}] \) and \( \sin \boldsymbol{x}+\sin \boldsymbol{y}=\boldsymbol{2} \) then
the value of \( x+y \) is
A . \( \pi \)
в.
\( c .3 \pi \)
D. None of these
Subject: Physics
An isosceles right angle triangle of side d is placed in a horizontal plane. A point charge \( \mathrm{q} \) is placed at a distance \( \mathrm{d} \) vertically above from one of the corner as shown in the figure. Flux of electric
field passing through the triangle is
A \( \cdot \frac{q}{36 \varepsilon_{0}} \)
в. \( \frac{q}{18 \varepsilon_{0}} \)
c. \( \frac{q}{24 \varepsilon_{0}} \)
D. \( \frac{q}{48 \varepsilon_{0}} \)
Subject: Physics
Assertion
Meniscus is formed in case of confined
liquids.
Reason
It is not due to the force of surface
tension
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
n Fig., \( A B \) and \( C D \) are two diameters
of a circle with centre \( O, \) which are
perpendicular to each other. \( \boldsymbol{O B} \) is the
diameter of the smaller circle. If \( \boldsymbol{O A}= \)
\( \mathbf{7} \mathrm{cm}, \) find the area of the shaded region. \( \left[\boldsymbol{U s e} \boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right] \)
\( \mathbf{A} \cdot 60.5 \mathrm{cm}^{2} \)
B . \( 63.5 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 66.5 \mathrm{cm}^{2} \)
D. \( 56.5 \mathrm{cm}^{2} \)
Subject: Maths
\( P \) makes a bet with \( Q \) of 8 pounds to
120 pounds that three races will be won by the three horses \( A, B, C, \) against which the betting is 3 to 2,4 to \( 1, \) and 2 to 1 respectively. The first race having been a on by \( A \), and it being known that
the second race was won either by \( B \), or
by a horse \( D \) against which the betting
was 2 to 1 , find the value of \( P^{\prime} s \)
expectation.
Subject: Physics
A body is moving with velocity \( 30 m s^{-1} \)
towards east. After \( 10 s \) its velocity
becomes \( 40 m s^{-1} \) towards north. the
average acceleration of the body is
A \( .7 \mathrm{ms}^{-2} \)
В. \( \sqrt{7} \mathrm{ms}^{-2} \)
\( \mathrm{c} \cdot 5 \mathrm{ms}^{-2} \)
D. \( 1 \mathrm{ms}^{-2} \)
Subject: Maths
In the interval \( \boldsymbol{x} \epsilon\left(\boldsymbol{e}^{2 r \boldsymbol{\pi}+\boldsymbol{\pi} / 4}, \boldsymbol{e}^{2 \boldsymbol{r} \boldsymbol{\pi}+\boldsymbol{5} \boldsymbol{\pi} / \boldsymbol{4}}\right) \)
in which the function \( f(x)= \)
\( \sin \left(\log _{e} x\right)+\cos \left(\log _{e} x\right) \) is
A. decreasing
B. increasing
c. const.
D. no monotonicity
Subject: Maths
Two complex numbers are represented
by ordered pairs \( z_{1}: a+i b \& z_{2}: c+i d \)
which of the following is correct
representation for \( z_{1}-z_{2}=? \)
A \( \cdot(a-c)-i(b+d) \)
B . \( (a-c)+i(b-d) \)
c. \( (a+c)-i(b+d) \)
D. None of these
Subject: Maths
If \( f(x)=\left\{\begin{array}{ll}\frac{1-\cos x}{x^{2}}, & x<0 \\ \frac{1}{2} e^{x}, \quad x \geq 0\end{array} \) then at \right.
\( \boldsymbol{x}=\mathbf{0}, \boldsymbol{f} \) is
A. continuous
B. not continuous
\( c . \) differentiable
D. none of these
Subject: Physics
A particle starting with certain initial velocity and uniform acceleration covers a distance of \( 12 \mathrm{m} \) in first 3 s and
a distance of \( 30 \mathrm{m} \) in next 3 s. The initial velocity of the particle is
\( \mathbf{A} \cdot 3 m s^{-1} \)
B . \( 2.5 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 2 m s^{-1} \)
D. \( 1.5 \mathrm{ms}^{-1} \)
E \( \cdot 1 \mathrm{ms}^{-1} \)
Subject: Maths
The average ordinate of \( y=\sin x \) over the interval \( [\mathbf{0}, \boldsymbol{\pi}] \) is -
A. \( 1 / \pi \)
B. \( 2 / \pi \)
c. \( 4 / \pi^{2} \)
D. \( 2 / \pi^{2} \)
Subject: Maths
Factors of \( 8 x^{2}-18 x+9 \) are :
A. \( (4 x-3) \) and \( (2 x+3) \)
B. \( (8 x-1) \) and \( (x-9) \)
c. \( (8 x-3) \) and \( (x-3) \)
D. \( (2 x-3) \) and \( (4 x-3) \)
Subject: Physics
toppr
Q Type your question
battery has essentially no internal resistance, and all the wires are
essentially resistanceless, too. When a
light bulb is unscrewed, no current flows through that branch of the circuit.
For instance, if light bulb 2 is unscrewed, current flows only around
the lower loop of the circuit, which consist of the battery and light bulb 1. The more current flows through a light bulb, their equivalent resistance is
\( \boldsymbol{R}_{e q}=\boldsymbol{R}_{1}+\boldsymbol{R}_{2} . \) By contrast, when two
reisistors are wired in parallel, their net resisance is given by \( \frac{1}{R_{e q}}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \)
Bulb 2 is now screwed in as a result,
bulb 1:
A. turns off
B. becomes dimmer
C. stays about the same brightness
D. becomes brighter
Subject: Physics
You are given an arrangement of three point charges \( q, 2 q \) and \( x q \) separated by equal finite distances so that electric potential energy of the system is zero. then the values of \( x \) is:
\( A \cdot-2 / 3 \)
B. -1/3
\( c \cdot 2 / 3 \)
D. 3/2
Subject: Physics
A small metal ball of mass ' \( m \) ' is
dropped in a liquid contained in a
vessel, attains a terminal velocity ' \( V \) '. If a metal ball of same material but of
mass \( ^{\prime} 8 m^{\prime} \) is dropped in same liquid then the terminal velocity will be.
A. \( V \)
B. \( 2 V \)
\( c .4 V \)
D. 8V
Subject: Maths
Write the domain of the function
\( \boldsymbol{f}(\boldsymbol{x})=\log _{4}(1+\boldsymbol{x}) \)
\( A \cdot(-1, \infty) \)
B. \( (1, \infty) \)
c. \( (2, \infty) \)
D. None of these
Subject: Physics
A railway wagon of mass \( 10^{5} k g \) is
moving with a velocity of \( 0.5 m s^{-} 1 \) beneath a stationary coal dumper.
When \( 2 \times 10^{5} k g \) of coal is dropped into
it, the velocity of the wagon would be
A \( \cdot 0.333 m s^{-1} \)
В. \( 0.167 m s^{-1} \)
c. \( 0.233 m s^{-1} \)
D. \( 0.133 m s^{-1} \)
Subject: Chemistry
toppr
Q Type your question
Fill in the blanks by choosing an appropriate option.
At a particular spot of an object made of
iron, \( (i) \) of iron to ferrous ion takes
place and that spot behaves as \( (i i) \)
Electrons released at \( (i) \) spot move through the metal and \( \$ 0 \) to another
spot on the metal and reduce oxygen in
presence of \( \boldsymbol{H}^{+} . \) This spot behave as
(iiii). The ferrous ions are further
oxidised by atmospheric oxygen to ferric ions which come out as rust, \( (i v) \) and with further production of \( (v) \) ions.
\( A \cdot(i)- \) Oxidation
(ii)- Anode, (iii)-Cathode, (iv)\( F e_{2} O_{3} \cdot x H_{2} O,(v)-H y d r o g e n \)
B. (i)- Reduction, (ii)-Cathode, (iii)-Anode, (iv)- \( F e_{3} O_{4},(v) \)
Hydrogen
C . (i)-Oxidation, (ii)-Cathode, (iii)-Anode, (iv)\( F e_{2} O_{3} x H_{2} O,(v)-H y d r o g e n \)
D. (i)-Oxidation, (ii)-Anode, (iii)-Cathode, (iv)- \( F e_{2} O_{3} \) \( H_{2} O,(v) \) -Ferrous
Subject: Maths
Priya bent a plastic wire to form the given figure. The figure is made up of 4 squares and 4 equilateral triangles. Find the length of wire.
A. \( 110 \mathrm{cm} \)
B. \( 90 \mathrm{cm} \)
\( c .100 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)
Subject: Maths
Let \( \omega \) be a complex cube root of unity
with \( \omega \neq 1 . \) A fair die is thrown three
times. If \( r_{1}, r_{2} \) and \( r_{3} \) are the numbers
obtained on the die then the probability
that \( \omega^{r_{1}}+\omega^{r_{2}}+\omega^{r_{3}}=\mathbf{0} \) is
A \( \cdot \frac{1}{18} \)
в. \( \frac{1}{9} \)
\( c \cdot \frac{2}{9} \)
D. \( \frac{1}{36} \)
Subject: Maths
What is the value of \( \frac{m^{2}+m n}{m^{2}+n^{2}}+ \) \( \frac{m^{2}-m n}{m^{2}+n^{2}}+\frac{n^{2}+m}{m^{2}+n^{2}}+\frac{n^{2}-m n}{m^{2}+n^{2}} \)
\( A \)
B. 0
\( c \cdot 2 \)
\( D \)
Subject: Physics
An infinite number of charges each
equal to \( q \) are placed along the \( x \) -axis at \( \boldsymbol{x}=\mathbf{1}, \boldsymbol{x}=\mathbf{2}, \boldsymbol{x}=\mathbf{4}, \boldsymbol{x}=\mathbf{8} \) and \( \mathbf{s} \mathbf{o} \) on
Find the potential and electric field at the point \( x=0 \) due to this set of
charges.
A \( \cdot_{5 k q}, \frac{4 k g}{3} \)
в. \( 2 k q, \frac{4 k g}{3} \)
c. \( _{3 k q}, \frac{4 k g}{3} \)
D. \( 7 k q, \frac{4 k g}{4} \)
Subject: Chemistry
Raghav, Ajay and Nita were given three test tubes \( K, L \) and \( M \) respectively containing unknown substances They observed the following properties about their solutions
Substance Property
The components can be separated by filtration
Particles scatter the light
Particles size is \( 10^{-9} \) to \( 10^{-7} \mathrm{m} \)
On the basis of the above properties identify the solutions \( K, L \) and \( M \)
respectively
A. Ferrous sulphate solution, tonic, paints
B. Calcium carbonate solution, paints, milk
c. Muddy water, milk, calcium carbonate solution
D. Paints, ferrous sulphate solution, calcium carbonate solution
Subject: Physics
Two current carrying wires are a
distance \( a \) apart and experience a Force
\( F \) between them. The wires are moved a
distance \( 2 a \) apart. Which of the following is a possible value for the new force between the
wires?
A \( \cdot \frac{1}{4} F \)
в. \( \frac{1}{2} \)
\( c . F \)
D. \( 2 F \)
E . \( 4 F \)
Subject: Physics
The de Broglie wavelength of a particle
of mass 1 gram and velocity 100 ms \( ^{-1} \)
is:
A. \( 6.63 \times 10^{-35} \)
В. \( 6.63 \times 10^{-34} \)
c. \( 6.63 \times 10^{-33} \)
D. \( 6.63 \times 10^{-32} \)
Subject: Chemistry
\( C H_{3} C H_{2} O H \) can be converted into
\( \boldsymbol{C H}_{3} \boldsymbol{C H O} \) by:
A . catalytic hydrogenation
B. treatment with \( L i A l H_{4} \)
c. treatment with pyridinium chlorochromate
D. treatment with \( K M n O_{4} \)
Subject: Maths
The line \( (x-2) \cos \theta+(y-2) \sin \theta= \)
1 touches a circle for all value of \( \theta \), then
the equation of circle is
A \( \cdot x^{2}+y^{2}-4 x-4 y+7=0 \)
B . \( x^{2}+y^{2}+4 x+4 y+7=0 \)
c. \( x^{2}+y^{2}-4 x-4 y-7=0 \)
D. None of the above
Subject: Physics
Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of \( 444 m / s \) in 1.83 seconds, then
what is the acceleration? \( \left(\operatorname{in} m / s^{2}\right) \)
A. \( 243 m / s / s \)
B. \( 24 m / s / s \)
c. \( 23 m / s / s \)
D. \( 43 m / s / s \)
Subject: Physics
A uniform chain of mass \( m \) and length \( l \) is kept on a smooth horizontal surface such that \( 1 / 4 \) th of its length is hanging
from the edge of the table. If it slides
down, the change in kinetic energy when hanging length becomes
\( 3 l \)
\( \frac{w}{4} \) will be
\( \mathbf{A} \cdot \frac{m g l}{4} \)
в. \( \frac{m g l}{2} \)
\( \mathbf{c} \cdot \frac{m g l}{32} \)
D. \( \frac{9 m g l}{32} \)
Subject: Maths
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method?
\( 3 x-5 y=20,6 x-10 y=40 \)
A. No solutions
B. Unique solutions, \( x=0 \) and \( y=1 \)
c. Infinitely many solutions
D. Data insufficient
Subject: Chemistry
An acid with molecular formula
\( C_{7} H_{6} O_{3} \) forms three types sodium salts, i.e., \( C_{7} H_{5} O_{3} N a, C_{7} H_{4} O_{3} N a_{2} \)
and \( C_{7} H_{3} O_{3} N a_{3} . \) The basicity of the
acid is:
A. one
B. Two
c. Three
D. Four
Subject: Maths
Find the volume of a sphere whose radius is \( 7 \mathrm{cm} \)
A. \( _{1437} \frac{1}{3} c m^{3} \)
в. \( _{1437} \frac{1}{4} c m^{3} \)
c. \( _{1437} \frac{2}{3} c m^{3} \)
D. \( _{1437} \frac{1}{2} c m^{3} \)
Subject: Physics
Five forces \( \vec{F}_{1}, \vec{F}_{2}, \vec{F}_{3}, \vec{F}_{4} \) and \( \vec{F}_{5} \) are
acting on a particle of mass \( 2.0 \mathrm{kg} \) so that it is moving with \( 4 m / s^{2} \) in east direction. If \( \vec{F}_{1} \) force is removed, then
the acceleration becomes \( 7 \mathrm{m} / \mathrm{s}^{2} \) in north, then the acceleration of the block if only \( \vec{F}_{1} \) is acting will be :
A \( \cdot 16 m / s^{2} \)
B . \( \sqrt{65} \mathrm{ms}^{2} \)
c. \( \sqrt{260} \mathrm{ms}^{2} \)
D. \( \sqrt{3} 3 m s^{2} \)
Subject: Chemistry
Which of the following orders is true
regarding the acidic nature of \( C \) OOH?
A. Formic acid \( > \) Acetic acid \( > \) Propanoic acid
B. Formic acid \( > \) Acetic acid \( < \) Propanoic acid
C. Formic acid < Acetic acid < propanoic acid
D. Formic acid < Acetic acid >Propanoic acid
Subject: Chemistry
The electronic configuration of cerium is:
\( \mathbf{A} \cdot[X e] 4 f^{0} 5 d^{1} 6 s^{2} \)
B \( \cdot[X e] 4 f^{1} 5 d^{1} 6 s^{2} \)
\( \mathbf{c} \cdot\left[X e \mid 4 f^{2} 5 d^{0} 6 s^{2}\right. \)
D. Both 2 and 3
Subject: Physics
An object \( 2 \mathrm{cm} \) high is placed at a distance of \( 16 \mathrm{cm} \) from a concave
mirror, which produces a real image 3 \( \mathrm{cm} \) high. What is the focal length of the mirror?
A . - \( 9.6 \mathrm{cm} \)
B. -3.6 ст
\( c .-6.3 \mathrm{cm} \)
D. - 8.3 cm