AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A circular loop of radius \( 0.3 \mathrm{cm} \) lies
parallel to a much bigger circular loop of radius \( 20 \mathrm{cm} . \) The centre of the
smaller loop is on the axis of the bigger drop. The distance between their
centres is \( 15 \mathrm{cm} . \) If a current of \( 10 \mathrm{A} \)
flows through the bigger loop, then the flux linked with smaller loop is
A. \( 9.1 \times 10^{-11} \mathrm{Wb} \)
B. \( 6 \times 10^{-11} \mathrm{Wb} \)
c. \( 3.3 \times 10^{-11} W b \)
D. \( 6.6 \times 10^{-11} \mathrm{Wb} \)
Subject: Chemistry
The equilibrium constant for the
following reaction at \( 25^{\circ} \mathrm{C} \) is \( 2.9 \times 10^{9} \)
Calculate standard voltage of the cell.
\( \boldsymbol{C l}_{2(\boldsymbol{g})}+\boldsymbol{B r}_{(\boldsymbol{a q})}^{-} \rightleftharpoons \boldsymbol{2} \boldsymbol{C l}_{(\boldsymbol{a q})}^{-} \)
\( \mathbf{A} \cdot 0.18 \mathbf{V} \)
B. \( 0.22 v \)
c. \( 0.26 v \)
D. \( 0.28 \mathrm{v} \)
Subject: Maths
A flooring tile has the shape of a
parallelogram whose base is \( 24 \mathrm{cm} \) and
the corresponding height is \( 10 \mathrm{cm} . \) How
many such tiles are required to cover a
floor of area \( 1080 m^{2} ? \)
A . 20000
B. 35000
c. 45000
D. 65000
Subject: Chemistry
Which of the following is not a disproportionation reaction?
\( N H_{4} N O_{3} \stackrel{\Delta}{\longrightarrow} N_{2} O+H_{2} O \)
II. \( \boldsymbol{P}_{4} \stackrel{\Delta}{\longrightarrow} \boldsymbol{P} \boldsymbol{H}_{3}+\boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{2}^{\ominus} \)
III. \( \boldsymbol{P C l}_{5} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \boldsymbol{P C l}_{3}+\boldsymbol{C l}_{2} \)
IV. \( \boldsymbol{I} \boldsymbol{O}_{3}^{\ominus}+\boldsymbol{I}^{\ominus} \longrightarrow \boldsymbol{I}_{2} \)
A . ।, ॥
B. I, III, IV
c. ॥, IV
D. ।, II
Subject: Maths
The function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}3 x-1, & \text { if } x<1 \\ x^{2}, & \text { if } x>2\end{array} \) continuous on \right.
A \( \cdot(-\infty, 1) \)
B. \( (2, \infty) \)
C \( .(-\infty, 1) \cup(2, \infty) \)
D. (1,2)
Subject: Chemistry
Ashish took 4 test tubes \( P, Q, R \) and \( S \)
each containing \( 10 \mathrm{ml} \) of different solutions as shown in the figure. Few drops of methyl orange are added to each tube. The solution in which tube
will turn methyl orange to red?
'his question has multiple correct options
A . \( P \)
в. \( Q \)
\( c . R \)
D. \( S \)
Subject: Physics
If \( M_{0} \) is the mass of an oxygen isotope
\( \mathrm{s} \mathrm{O}^{17}, M_{p} \) and \( M_{n} \) are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is
\( \mathbf{A} \cdot\left(M_{O}-8 M_{p}\right) c^{2} \)
В \( \cdot\left(M_{O}-8 M_{p}-9 M_{n}\right) c^{2} \)
c. \( M_{O} c^{2} \)
D. \( \left(M_{O}-17 M_{n}\right) c^{2} \)
Subject: Physics
Q Type your question_
two charges is represented by the field
lines also shown in the diagram.
What signs do the two charges have,
and which charge is stronger?
A. Charge 1 is positive, Charge 2 is negative and the stronger charge is Charge 1
B. Charge 1 is positive, Charge 2 is negative, and both charges have the same strength.
C. Charge 1 is negative, Charge 2 is positive, and the stronger charge is Charge 1
D. Charge 1 is negative, Charge 2 is positive, and both charges have the same strength.
E. Charge 1 is positive, Charge 2 is negative, and the stronger charge is Charge 2
Subject: Physics
The radius of the sphere is \( 1.41 \mathrm{cm} . \) The volume of sphere to an appropriate number of significant figures will be:
A \( \cdot 11.7 c m^{3} \)
B. \( 11.74 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 12 c m^{3} \)
D. \( 11.736 \mathrm{cm}^{3} \)
Subject: Physics
An athlete completes one round of a circular track of radius \( \boldsymbol{R} \) in \( \mathbf{4 0} \boldsymbol{s} \). His
displacement at the end of 2 minutes will be
A \( .2 \pi R \)
в. \( 6 \pi R \)
\( c .2 R \)
D. Zero
Subject: Maths
An equation of sphere with centre at
origin and radius \( r \) can be represented
as
A \( \cdot x^{2}+y^{2}+z^{2}=r \)
B . \( x^{2}+y^{2}+z^{2}=r^{2} \)
c. \( x^{2}+y^{2}+z^{2}=2 r^{2} \)
D. None of the above
Subject: Maths
The mean deviation of the data
\( \mathbf{3}, \mathbf{1 0}, \mathbf{1 0}, \mathbf{4}, \mathbf{7}, \mathbf{1 0}, \mathbf{5} \) from the mean is
A . 2
в. 2.57
\( c .3 \)
D. 3.75
Subject: Physics
For traffic moving at \( 60 k m / h r \) along a smooth circular track of radius \( 0.1 k m \)
the correct angle of banking should be:
\( ^{\mathbf{A}} \cdot \tan ^{-1}\left[\frac{(100 \times 9.8)}{\left(\frac{50}{3}\right)^{2}}\right] \)
\( ^{\mathrm{B}} \tan ^{-1}\left[\frac{\left(\frac{50}{3}\right)^{2}}{(100 \times 9.8)}\right] \)
\( ^{\mathrm{c}} \tan ^{-1}\left(\frac{60^{2}}{0.1}\right) \)
D. \( \tan ^{-1} \sqrt{(60 \times 0.1 \times 9.8)} \)
Subject: Maths
The cost of setting up the type of a magazine is Rs. 1000 , the cost of running the printing machine is Rs. 120 per 100 copies, the cost of paper, ink and so on is 60 paise per copy. The magazines are sold at Rs. 2.75 each.
900 copies are printed, but only 784 copies are sole. What is the sum to be obtained from advertisements to give a
profit of \( 10 \% \) on the cost?
A. Rs. 730
B. Rs. 720
c. Rs. 726
D. Rs. 736
Subject: Physics
A photon of energy \( \mathrm{E}_{1} \) incident on a surface liberates electrons whose
energy is equal to the work function \( \mathbf{W} \) of the metal. When a photon of energy
2
is incident on the same surface, energy of the emitted electrons is \( 3 \mathrm{W} \)
The ratio \( \mathrm{E}_{1}: \mathrm{E}_{2} \) is
A . 1: 2
B. 2:
c. 1: 3
D. 3:
Subject: Physics
Two identical cylindrical vessels with their bases at the same level; contain
liquid of density \( \rho . \) The area of both is \( S \) but the height of liquid in one vessel is \( h_{1} \) and in other \( h_{2} . \) The work done when both cylinders are connected, by gravity in equalising levels is:
A \( \cdot \frac{1}{4} g \rho S\left(h_{2}-h_{1}\right)^{2} \)
в. \( g \rho S\left(h_{2}-h_{1}\right)^{2} \)
c. \( g \rho S\left(h_{2}-h_{1}\right) \)
D. \( \frac{1}{4} g \rho S\left(h_{2}-h_{1}\right) \)
Subject: Chemistry
Identify \( A \) and \( B \) the following reactions. \( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N}_{2} \boldsymbol{C l} \frac{\boldsymbol{H O H}}{\Delta} \boldsymbol{A} \stackrel{\boldsymbol{B r}_{2}}{\boldsymbol{B}} \boldsymbol{B} \)
Subject: Physics
A point charge \( Q \) is located at the center of the hollow spherical conductor of
inner radius \( \boldsymbol{R}_{1} \) and outer radius \( \boldsymbol{R}_{2} \)
the conductor being uncharged initially The potential at the inner surface will
be
A \( \cdot K Q\left[\frac{1}{R_{1}}+\frac{1}{R_{2}}\right] \)
В \( \cdot K Q\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right] \)
c. \( K Q\left[\frac{1}{R_{2}}-\frac{1}{R_{1}}\right] \)
D. None of these
Subject: Chemistry
Assertion
The \( 5^{t h} \) period of periodic table contains 18 elements not 32
Reason
\( \mathbf{n}=\mathbf{5}, \ell=\mathbf{0}, 1,2, \) 3. The order in which the
energy of available orbitals \( 4 \mathrm{d}, 5 \mathrm{s} \) and
\( 5 p \) increases is \( 5 s<4 d<5 p \) and the total number of orbitals available are 9
and thus 18 electrons can be
accommodated.
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
has the highest boiling
point.
A. \( 0.2 \mathrm{m} \mathrm{CaCl}_{2} \)
B. 0.2 \( \mathrm{m} \) NaCl
c. \( 0.1 \mathrm{m} \) Al \( C l_{3} \)
D. \( 0.2 \mathrm{m} \mathrm{CH}_{3} \mathrm{OH} \)
E. \( 0.2 \mathrm{m} \mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)
Subject: Physics
Two thin uniform circular rings each of
radius \( 10 \mathrm{cm} \) and mass \( 0.1 \mathrm{Kg} \) are
arranged such that they have common centre and their planes are perpendicular to each other. The moment of inertia of this system about an axis passing through their common centre and perpendicular to the plane of one of the rings in \( k g m^{2} \) is:
A \( \cdot 15 \times 10^{-3} \)
В . \( 5 \times 10^{-3} \)
c. \( 15 \times 10^{-4} \)
D. \( 18 \times 10^{-4} \)
Subject: Maths
Show that the function \( f(x) \) defined as
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \cos \frac{1}{x}, \boldsymbol{x} \neq \mathbf{0},=\mathbf{0}, \boldsymbol{x}=\mathbf{0} \) is
continuous at \( x=0 \) but not
differentiable at \( x=0 \)
Subject: Maths
The mode of the following data is 85.7
Find the missing frequency in it.
\( \begin{array}{ll}\text { Size } & \text { Frequency } \\ \text { 45-55 } & \text { 7 } \\ \text { 55-65 } & 12 \\ \text { 65-75 } & \text { 17 } \\ \text { 75-85 } & \text { f } \\ \text { 85-95 } & \text { 32 } \\ \text { 95-105 } & \text { 6 } \\ \text { 105-115 } & \text { 10 }\end{array} \)
A . 33
B. 31
\( c .30 \)
D. 32
Subject: Chemistry
5-litre vessel contains 2 moles of each
of gases \( A \) and \( B \) at equilibrium. If 1 mole each of \( A \) and \( B \) are removed.
Calculate \( K_{c} \) for the reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \) \( B(g) \)
Subject: Maths
\( \boldsymbol{y}=\sin ^{-1}\left[\log _{3}\left(\frac{\boldsymbol{x}}{\mathbf{3}}\right)\right] \Rightarrow-1 \leq \)
\( \log _{3}\left(\frac{\boldsymbol{x}}{\mathbf{3}}\right) \leq \mathbf{1} \)
Subject: Maths
\( A B C \) is a triangular park with \( A B= \) \( A C=100 \) metres. A vertical tower is
situated at the mid-point of \( B C . \) If the
angles of elevation of the top of the tower at \( A \) and \( B \) are \( \cos ^{-1}(3 \sqrt{2}) \) and \( \operatorname{cosec}^{-1}(2 \sqrt{2}) \) respectively, then the height of the tower (in metres is):
A. \( 10 \sqrt{5} \)
the \( 6 \sqrt{55} \)
в. \( \frac{100}{3 \sqrt{3}} \)
c. 20
D. 25
Subject: Chemistry
Given the following bond energies, \( \boldsymbol{C}-\boldsymbol{H}=\mathbf{4 1 4} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
\( \boldsymbol{C}-\boldsymbol{C l}=\mathbf{1 5 0} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
\( C l-C l=243 K J / m o l \)
\( \boldsymbol{H}-\boldsymbol{C l}=\mathbf{4 3 2} \boldsymbol{K} \boldsymbol{J} / \boldsymbol{m o l} \)
How much energy would be required in the reaction?
\( \boldsymbol{C H}_{4(\boldsymbol{g})}+\boldsymbol{2} \boldsymbol{C l}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{C H}_{2} \boldsymbol{C l}_{2(\boldsymbol{g})}+ \)
\( 2 H C l_{(g)} \)
A. -150 KJ
J
в. -130 Кл
с. -228 Кл
D. -571 Кл
Subject: Maths
n triangle \( A B C, \angle B A C=90^{\circ}, \) and
\( A D \) is its bisector. If \( D E \) is drawn
\( \perp A C, \) prove that \( D E \times(A B+A C)= \)
\( \boldsymbol{A B} \times \boldsymbol{A C} \)
Subject: Physics
The compressibility of water \( 4 \times 10^{-5} \)
per unit atmospheric pressure. The decrease in volume of 100 cubic
centimeter of water under a pressure of
100 atmosphere will be:
A \( .0 .4 c c \)
в. \( 4 \times 10^{-5} c c \)
c. \( 0.025 c c \)
D. \( 0.004 c c \)
Subject: Chemistry
\( \mu=\sqrt{15} \) is true for the pair:
A \( \cdot C o^{+2}, C r^{+3} \)
B. \( F e^{+2}, C r^{+3} \)
c. \( F e^{+3}, C r^{+2} \)
D. \( M n^{+2}, F e^{+2} \)
Subject: Maths
Subtract the sum of \( \left(5 x^{2}-7 x+4\right) \)
and \( \left(2 x-5 x^{3}+1\right) \) from
\( \left(3 x^{2}-1+5 x\right) \)
B. \( 5 x^{3}-2 x^{2}+10 x-6 \)
\( c \cdot 3 x^{3}+11 x^{2}+3 x+5 \)
5
D. \( 11 x^{3}+3 x^{2}+5 x-3 \)
Subject: Maths
For any two complex numbers \( z_{1}, z_{2} \) we
have \( \left|z_{1}+z_{2}\right|^{2}=\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}, \) then
A \( \cdot \operatorname{Re}\left(\frac{z_{1}}{z_{2}}\right)=0 \)
в. \( \operatorname{Im}\left(\frac{z_{1}}{z_{2}}\right)=0 \)
c. \( \operatorname{Re}\left(z_{1} z_{2}\right)=0 \)
D・Im \( \left(z_{1} z_{2}\right)=0 \)
Subject: Physics
In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases
\( 20 J \) of heat and \( 8 J \) of work is done on
the gas. If initial internal energy of the gas was \( 30 J \), what will be the fixed
internal energy?
\( \mathbf{A} \cdot 9 J \)
B. \( 27 J \)
c. \( 18 J \)
D. \( 12 J \)
Subject: Chemistry
Complete the structures of following hydrocarbons by placing hydrogens only
(i) \( \mathrm{C}-\mathrm{C}=\mathrm{C}-\mathrm{C} \quad \) (ii) \( \mathrm{C}=\mathrm{C}-\mathrm{C}_{\mathrm{I}} \)
co
(iv) \( C=C-C \)
(v) \( c-c-c-c-c \)
Subject: Physics
Four identical charges of charge \( q \) are
placed at the corners of a square of
sides r as shown above. Find the
magnitude of the net force acting on a
charge of magnitude \( 2 q \) placed in the
center of the square.
\( \mathbf{A} \cdot \mathbf{0} \)
\( \mathbf{B} \cdot \frac{2 k q^{2}}{r^{2}} \)
\( \mathbf{c} \cdot \frac{4 k q^{2}}{r^{2}} \)
D. \( \frac{16 k q^{2}}{r^{2}} \)
E \( \cdot \frac{\text { g } 2 k q^{2}}{r^{2}} \)
Subject: Chemistry
Assertion
In electrolyte refining of metal, impure metal is made cathode while a strip of
pure metal is used as anode.
Reason
The pure metal gets deposited at anode as anode mud.
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
The standard heats of formation at
\( 298 K \) for \( C C l_{4}(g), H_{2} O(g), C O_{2}(g) \)
and \( H C l(g) \) are -25.5,-57.8,-94.1
and \( -22.1 k c a l \) mol \( ^{-1} \) respectively
Calculate \( \Delta H_{298}^{o} \) for the reaction. \( \boldsymbol{C C l}_{4}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \longrightarrow \boldsymbol{C O}_{2}(\boldsymbol{g})+ \)
\( 4 H C l(g) \)
Subject: Chemistry
Buffer solution \( A \) of a weak monoprotic
acid and its sodium salt in the
concentration ratio \( \boldsymbol{x}: \boldsymbol{y} \) has \( \boldsymbol{p} \boldsymbol{H}= \)
\( (p H)_{1} . \) Buffer solution \( B \) of the same
acid and its sodium salt in the
concentration ratio \( \boldsymbol{y}: \boldsymbol{x} \) has \( \boldsymbol{p} \boldsymbol{H}= \)
\( (p H)_{2} . \) If \( (p H)_{2}-(p H)_{1}=1 \) unit and
\( (p H)_{1}+(p H)_{2}=9.5 \) units, then:
This question has multiple correct options
\( \mathbf{A} \cdot p K_{a}=4.75 \)
В. \( \frac{x}{y}=2.36 \)
c. \( \frac{x}{y}=3.162 \)
D \cdot \( p K_{a}=5.25 \)
Subject: Biology
Which of the following pairs are
correctly matched?
a. spirogyra Fragmentatio an -
Planaria
ponges
b. \( \quad \) Regeneration Hydra, Planari
and sponges
\( \mathrm{c} \)
Scion an \( - \) The part of the
plant that is
grafted to other
plant
Development of
d. Parthenogenesis organisms
from an
unfertilized degg
The correctly paired ones are given
\( A \cdot a, c \) and \( d \)
B. \( a, b, c \) and \( d \)
\( c . b, c \) and \( d \)
D. a, b and d
Subject: Physics
Consider the following statements:
\( A: p-p, p-n, n-n \) forces between
nucleons are not equal and charge
dependent
B: In nuclear reactor the fission reaction
will be in accelerating state if the value
of neutron reproduction factor \( k>1 \)
A. Both A and B are correct
B. Both A and B are wrongg
C. A is wrong and B is correct
D. A is correct and B is wrong
Subject: Chemistry
Which of the following statement(s)
is/are correct?
\( \mathbf{A} \cdot \operatorname{In}\left[\operatorname{CoBr} C l(e n)_{2}\right]^{+} \) geometrical isomerism exists,
while optical isomerism does not exist
B. Potassium aquadicyanosuperoxoperoxochromate(III) is IUPAC name of \( K_{2}\left[\mathrm{Cr}(\mathrm{CN})_{2} \mathrm{O}_{2}\left(\mathrm{O}_{2}\right)\left(\mathrm{H}_{2} \mathrm{O}\right)\right] \)
C. There are 3 geometrical and 15 stereisomers possible for \( \left[P t\left(N O_{2}\right)\left(N H_{3}\right)\left(N H_{2} O H\right)(p y)\right]^{+} \) and
\( \left[P t B r C l I\left(N O_{2}\right)\left(N H_{3}\right)(p y)\right] \) respectively
D. \( A \) cis and trans forms are not diastereomers to each
other
Subject: Physics
Four particles each of mass \( m \) are lying symmetrically on the rim of a disc of mass \( M \) and radius \( R \). The moment of
inertia of this system about an axis passing through one of the particles and perpendicular to the plane of the disc is :
A \( \cdot 16 m R^{2} \)
в. \( \quad(3 M+16 m) \frac{R^{2}}{2} \)
\( \mathrm{c} \cdot_{(3 m+16 M)} \frac{R^{2}}{2} \)
D. Zero
Subject: Chemistry
A sample of \( H e^{+} \) ions in a gaseous
state had all ions in \( n^{t h} \) excited state.
This sample on returning to ground state emits a total of 28 spectral lines.
Value of \( n \) is:
\( A \cdot 8 \)
B. 7
\( c \cdot 6 \)
D. 5
Subject: Maths
Find the values of \( p \) for which the
straight lines \( 8 p x+(2-3 p) y+1=0 \)
and \( p x+8 y-7=0 \) are perpendicular
to each other.
A \( . p=1,2 \)
в. \( p=2,2 \)
c. \( p=1,3 \)
D. None of these
Subject: Chemistry
Vapour pressure of chloroform
\( \left(C H C l_{3}\right) \) and dichloromethane
\( \left(C H_{2} C l_{2}\right) \) at \( 298 K \) are \( 200 m m H g \)
and 415 mm \( H g \) respectively.
(i) Calculate the vapour pressure of the solution prepared by mixing \( 25.5 g \) of
\( \boldsymbol{C H} \boldsymbol{C l}_{3} \) and \( \mathbf{4 0} \boldsymbol{g} \) of \( \boldsymbol{C H}_{2} \boldsymbol{C l}_{2} \) at \( \boldsymbol{2} \boldsymbol{9 0} \boldsymbol{K} \)
and
(ii) Mole fraction of each component in solution.
Subject: Chemistry
Which of the following statements
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) A plot of \( \log k_{p} \) versus \( 1 \backslash \mathrm{T} \) is linear
B. A plot of log [X] versus time is linear for a first order reaction, \( x \rightarrow p \)
C. A plot of log p versus 1/T is linear at constant volume.
D. A plot of p versus 1/V is linear at constant temperature
Subject: Physics
Q Type your question
chamber of volume \( V / 4 \) in the cube as
shown. The chamber is completely filled
by \( \mathrm{m} \) kg of water. Water leaks through a hole \( \mathrm{H} \) and spreads in the whole cube.
Then then work done by gravity in this
process assuming that the complete
water finally lies at the bottom of the
cube is
\( A \)
B. \( \frac{3}{8} m g \)
\( c \)
\( D \)
\( m g \)
Subject: Chemistry
Which of the following species has less number of protons than the number of
neutrons?
This question has multiple correct options
A \( \cdot \frac{12}{6} C \)
В . \( _{9}^{9} F \)
\( \mathbf{c} \cdot_{11}^{23} N a \)
D \( \cdot \frac{24}{12} M g \)
Subject: Chemistry
Give reasons for the following:
(i) \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{P}=\boldsymbol{O} \) exists but
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N}=\boldsymbol{O} \) does not.
(ii) Oxygen has less electron gain enthalpy with negative sign than sulphur.
(iii) \( H_{3} P O_{2} \) is a stronger reducing
agent than \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
Subject: Maths
\( \Delta S H R \sim \Delta S V U . \ln \Delta S H R, S H= \)
\( 4.5 \mathrm{cm}, H R=5.2 \mathrm{cm}, S R=5.8 \mathrm{cm} \)
and \( \frac{S H}{S V}=\frac{3}{5} \) Construct \( \Delta S V U \)
Subject: Physics
A solid ball of mass \( \mathrm{m} \) is made to fall
form a height \( \mathrm{H} \) on a pan suspended through a spring of spring constant \( \mathrm{K} \) as shown in figure. if the ball does not rebound and the pan is mass less, then
amplitude of oscillation is
\( A \cdot \frac{m g}{K} \)
\( ^{\mathrm{B}} \cdot \frac{m g}{K}\left(1+\frac{2 H K}{m g}\right)^{1 / 2} \)
\( ^{\mathrm{c}} \frac{m g}{K}+\left(\frac{2 H K}{m g}\right)^{1 / 2} \)
\( ^{\mathrm{D}} \cdot \frac{m g}{K}\left[1+\left(1+\frac{2 H K}{m g}\right)^{1 / 2}\right] \)
Subject: Maths
If \( 3 x^{2}+4 k x+1>0 \) for all real values
of \( x, \) then \( k \) lies in the interval.
A \( \cdot\left(\frac{-\sqrt{3}}{2}, \frac{\sqrt{3}}{2}\right) \)
в. \( \left(\frac{-1}{4}, \frac{1}{4}\right) \)
\( ^{c} \cdot\left[\frac{-\sqrt{3}}{2}, \frac{\sqrt{3}}{2}\right] \)
D. \( \left(\frac{-1}{2}, \frac{1}{2}\right) \)
Subject: Maths
If a continuous function \( f \) satisfies \( \int_{0}^{f(x)} t^{2} d t=x^{2}(1+x) \) for all \( x \geq 0 \)
then \( f(2) \) is equal to
A . 12
B. \( \sqrt[3]{36} \)
\( c .3 \)
D. \( \sqrt[3]{42} \)
Subject: Chemistry
Which is paramagnetic and coloured?
A. \( K_{2} C r_{2} O_{7} \)
B \( \cdot\left(N H_{4}\right)_{2}\left[T i C l_{6}\right] \)
\( c \cdot v O S O_{4} \)
D. \( K_{3}\left[C u(C N)_{4}\right] \)
Subject: Maths
A particle is moving in a straight line such that its distance at any time \( t \) is given by \( s=\frac{1}{4} t^{4}-2 t^{3}+4 t^{2}-7 . \) Find
twhen its velocity is maximum( \( t_{v} \) ) and
acceleration minimum(t \( _{a} \) ).
A \( \cdot t_{v}=2-2 / \sqrt{3}, t_{a}=4 \)
В \( \cdot t_{v}=2, t_{a}=1 \)
C \( \cdot t_{v}=2-2 / \sqrt{3}, t_{a}=2 \)
D. \( t_{v}=-2 / \sqrt{3}, t_{a}=2 \)
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{5} & \mathbf{7}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{4} \\ -\mathbf{1} & \mathbf{7}\end{array}\right] \boldsymbol{C}= \)
\( \left[\begin{array}{cc}\mathbf{1} & \mathbf{0} \\ \mathbf{- 1} & \mathbf{4}\end{array}\right] \)
find \( \boldsymbol{A} \boldsymbol{C}+\boldsymbol{B}^{2}-\mathbf{1 0 C} \)
Subject: Physics
In the circuit shown the resistance \( R \)
has a value that depends on the current.
Specifically, R is 20 ohms when I is zero and the increase in resistance in ohms
is numerically equal to one half of the
current in amperes. What is the value of current I in circuit?
A. 8.33 amp
B. 10 amp
c. 12.5 amp
D. 18.5 amp
Subject: Maths
A tangent to the hyperbola \( \boldsymbol{y}=\frac{\boldsymbol{x}+\mathbf{9}}{\boldsymbol{x}+\mathbf{5}} \)
passing though the origin is
A . \( x+25 y=0 \)
в. \( 5 x+y=0 \)
c. \( 5 x-y=0 \)
D. \( x-25 y=0 \)
Subject: Chemistry
\( \boldsymbol{C}_{5} \boldsymbol{H}_{12}+\boldsymbol{C l}_{2} \stackrel{\text {light}}{\rightarrow} \boldsymbol{C}_{5} \boldsymbol{H}_{11} \boldsymbol{C l}^{N \boldsymbol{a} / \text {ether}} \)
Only one structure of B is possible. (A),
(B) and (C) are?
\( A \)
B.
c. both are correct
D. none is correct
Subject: Maths
Rohit says to Ajay "Give me a hundred, I shall then become twice as rich as you." Ajay replies "If you give me ten, I shall be
six times as rich as you." How much does each have originally?
A. Rohit has Rs. 20 and Ajay has Rs. 90
B. Rohit has Rs. 50 and Ajay has Rs. 200
c. Rohit has Rs. 40 and Ajay has Rs. 170
D. Rohit has Rs. 56 and Ajay has Rs. 190
Subject: Physics
When current flows through a
conductor, then the order of drift
velocity of electrons will be:-
\( \mathbf{A} \cdot 10^{10} \mathrm{cms}^{-1} \)
B. \( 10^{-2} \mathrm{cms}^{-1} \)
\( \mathbf{c} \cdot 10^{4} c m s^{-1} \)
D. \( 10^{-1} \mathrm{cms}^{-1} \)
Subject: Physics
A car, starting from rest, accelerates at
the rate \( \boldsymbol{f} \) through a distance \( \boldsymbol{S}, \) then
continues at constant speed for time \( t \)
and then decelerates at the rate \( \frac{f}{2} \) to come to rest. If the total distance
traversed is \( 15 S, \) then
A \( \cdot S=\frac{1}{2} f t^{2} \)
B . \( S=\frac{1}{4} f t^{2} \)
\( \mathbf{c} \cdot S=\frac{1}{72} f t^{2} \)
D. \( S=\frac{1}{6} f t^{2} \)
Subject: Physics
n identical cells are joined in series with its two cells \( A \) and \( B \) in the loop with reversed polarities. EMF of each shell is \( \mathrm{E} \) and internal
resistance r. Potential difference across
cell \( A \) or \( B \) is:
A \( \cdot \frac{2 E}{n} \)
В \( \cdot 2 E \mid 1-\frac{1}{n} \)
c. \( \frac{4 E}{n} \)
D. \( 2 E \mid 1-\frac{2}{n} \)
Subject: Chemistry
\( S(s)+O_{2}(g) \rightarrow S O_{2}(g) \quad \Delta H^{\circ}= \)
\( -297 k J \)
\( 2 S O_{2}(g)+O_{2}(g) \rightarrow \)
\( 2 S O_{3}(g) \quad \Delta H^{\circ}=-198 k J \)
Given the above thermochemical
reactions, what is the heat of reaction
for the formation of \( S O_{3}(g) \) provided
below?
\( \boldsymbol{S}(\boldsymbol{s})+\boldsymbol{3} / 2 \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g}) \)
A \( .-495 \mathrm{kJ} \)
B . -396 k
c. -198 k
D . +99
E . +198 k