AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find the area bounded by the curve \( y= \)
\( x^{2}+x+1 \) and tangent to it at (1,3)
from \( \boldsymbol{x}=-\mathbf{1} \) to \( \boldsymbol{x}=\mathbf{1} \)
A \( \cdot \frac{2}{3} \)
в. \( \frac{5}{3} \)
c. \( -\frac{2}{3} \)
D. \( \frac{1}{3} \)
Subject: Physics
Weights of \( 20 \mathrm{kg} \) and \( 30 \mathrm{kg} \) are suspended from the ends of a light rod \( 5 \mathrm{m} \) long, so at which point the rod must be suspended by means of a string to keep it horizontal?
A. At \( 3 \mathrm{m} \) from 20kg weight
B. At \( 3 \mathrm{m} \) from 30kg weight
c. At \( 4 \mathrm{m} \) from 20kg weight
D. At \( 4 \mathrm{m} \) from 30 kg weight
Subject: Physics
An atom is initially at an energy level \( \boldsymbol{E}=-\mathbf{6 . 5 2} e \boldsymbol{V} . \) It absorbs a photon of
wavelength \( 860 n m . \) The internal energy
of atom after absorbing photon is
A . \( 5.08 e V \)
B. \( 1.44 e V \)
c. \( -1.44 e V \)
D. \( -5.08 e V \)
Subject: Physics
Assertion
A step up transformer can also be used as a step down transformer
Reason
This is because \( \frac{\boldsymbol{E}_{\boldsymbol{p}}}{\boldsymbol{E}_{\boldsymbol{s}}}=\frac{\boldsymbol{n}_{\boldsymbol{s}}}{\boldsymbol{n}_{\boldsymbol{p}}} \)
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
Separation of \( H_{2} O \) and \( D_{2} O \) by fractional distillation is possible
because \( D_{2} O \) has:
A . higher density than that of \( H_{2} O \)
B. higher boiling point than that of \( H_{2} O \)
C. higher freezing point than that of \( H_{2} O \)
D. lower dielectric constant than that of \( H_{2} O \)
Subject: Chemistry
The difference in the mass of 100 each
mole of sodium atoms and sodium ions
is 5.48002 g. Calculate the mass of an electron from the above data.
A \( \cdot 9.1 \times 10^{-28} \mathrm{kg} \)
В. \( 9.1 \times 10^{-31} k g \)
c. \( 5.4002 \times 6.022 \times 10^{-31} k g \)
D. \( 5.4002 \times 6.022 \times 10^{-28} \mathrm{kg} \)
Subject: Maths
Solve for \( x \) :
\( \mathbf{3} \boldsymbol{x}-\boldsymbol{4}>\boldsymbol{6}, \) where \( \boldsymbol{x} \in \boldsymbol{N} \)
A \( \cdot\{1,2,3, \ldots \ldots . . .\} \)
в. \( \{4,5,6, \dots . . . . . .\} \)
c. Data insufficient
D. None of these
Subject: Maths
Area enclosed between the curves \( y^{2}= \)
\( x \) and \( x^{2}=y \) is equal to
This question has multiple correct options
A \( \cdot_{2} \int_{0}^{1}\left(x-x^{2}\right) d x \)
B.
c. area of region \( \left\{(x, y): x^{2} \leq y \leq|x|\right\} \)
D. \( \frac{2}{3} \)
Subject: Chemistry
Heat of combustion of benzoic acid
\( \left(C_{6} H_{5} C O O H\right) \) at constant volume at
\( 25^{0} \) is \( 3233 \mathrm{KJ} / \) mole. When \( 0.5 \mathrm{g} \) of
benzoic acid is burnt in bomb
calorimeter, the temperature of
calorimeter increased by \( 0.53^{0} C . \) Now in the same bomb calorimeter 1g of
\( C_{2} H_{6} \) burnt then temperature
increased by \( 2.04^{0} C . \triangle H \) for
combustion of \( \boldsymbol{C}_{2} \boldsymbol{H}_{6} \) is?
Subject: Maths
Following is the distribution of the size of certain farms from a taluka (tehasil)
Find median size of farms.
\( \operatorname{size} \)
\( \begin{array}{ll}\text { of } & 5 \\ \text { farm } & -\end{array} \)
15
25
35
(in
25
\( 35 \quad 45 \)
\[
15
\]
acres
No. of
2
25
farms
A . 33.60 Acres
B. 37.60 Acres
c. 38.60 Acres
D. 40.60 Acres
Subject: Chemistry
Molar conductivities at infinite dilution
of \( N a C l, H C l \) and \( C H_{3} C O O N a \) are
126.4,425.9 and \( 91.0 \mathrm{Scm}^{2} \) mol \( ^{-1} \)
respectively. Molar conductivity for
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) will be:
Subject: Maths
\( \int \frac{2 x+3}{(2 x+1)(1-3 x)} d x= \)
A. \( \frac{2}{5} \log |2 x+1|-\frac{11}{15} \log |1-3 x|+c \)
B \( \cdot \frac{2}{5} \log |2 x+1|-\frac{11}{15} \log |1+3 x|+c \)
c. \( \frac{2}{3} \log |2 x-1|+\frac{11}{15} \log |1-3 x|+c \)
D. \( \frac{2}{5} \log |2 x+1|-\frac{21}{5} \log |1+3 x|+c \)
Subject: Physics
An automobile travelling with speed of
\( 60 k m / h, \) can brake to stop within a distance of 20 m. If the car is going
twice as fast, i.e. \( 120 \mathrm{km} / \mathrm{h} \), the
stopping distance will be:
A . \( 20 m \)
в. 40 т
\( c \cdot 60 m \)
D. \( 80 m \)
Subject: Physics
Four equal electric charges are arranged at the four corners of a square of side \( a . \) Out of these four charges, two
charges are positive and placed at the ends of one diagonal. The other two charges are positive and placed at the ends of the other diagonal. The energy of
the system is:
This question has multiple correct options
A. Negative
B. Positive
\( ^{\mathrm{C}} \). \( _{\text {Less than }} \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{2 q^{2}}{a}\right) \)
Deater than \( \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{2 q^{2}}{a}\right) \)
Subject: Physics
A beam of cathode rays is subjected to crossed.Electric (E) and Magnetic fields
(B). The fields are adjusted such that the beam is not deflected.The specific
charge of the cathode rays is given by -
(where \( V \) is the potential difference between cathode and anode)
A \( \cdot \frac{B^{2}}{2 V E^{2}} \)
B. \( \frac{2 V B^{2}}{E^{2}} \)
\( ^{\mathbf{C}} \cdot \frac{2 V E^{2}}{B^{2}} \)
D. \( \frac{E^{2}}{2 V B^{2}} \)
Subject: Maths
Multiply the given matrix:
\( \left[\begin{array}{cc}\boldsymbol{a} & \boldsymbol{b} \\ -\boldsymbol{b} & \boldsymbol{a}\end{array}\right]\left[\begin{array}{cc}\boldsymbol{a} & -\boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{a}\end{array}\right] \)
Subject: Chemistry
The temperature coefficient of a
reaction is:
A. ratio of rate constants at two temperature differing by \( 1^{o} C \)
B. ratio of rate constants at temperature \( 35^{\circ} \mathrm{C} \) and \( 25^{\circ} \mathrm{C} \)
C. ratio of rate constants at temperature \( 30^{\circ} \mathrm{C} \) and \( 25^{\circ} \mathrm{C} \)
D. specific reaction rate by \( 25^{\circ} \)
Subject: Chemistry
When the electric current is passed
through a cell having an electrolyte, the positive ions move towards cathode and negative ions towards the anode. If the cathode is pulled out of the solution
then
A. the positive and negative ions will be move towards anode
B. the positive ions will start moving towards the anode and while negative ions will stop moving
c. the negative ions will continue to move towards and while positive ions will stop moving
D. the positive and negative ions will start moving random
Subject: Physics
toppr
-०६ा॥
Q Type your question
Point \( P \) is located on the right side of the
sphere; and point \( \mathrm{T} \) is located somewhere on the inside of the sphere,
not necessarily in the center.

What happens to the charge density on
the hollow sphere at point \( P \) and to the
electric field at point \( T \) as the point
charge, \( +q, \) is brought closer to the
hollow sphere?
A. The charge density at P decreases. The electric field at T remains zero.
B. The charge density at P remains zero. The electric field at T remains zero
C. The charge density at P increases. The electric field at increases in magnitude and always points to the right
D. The charge density at P increases. The electric field at T remains zero
E. The charge density at P remains constant but nonzero. The electric field at T remains constant and points to the left.
Subject: Maths
Equation of the plane whose
intercepts are 1,2,3 is
A. \( 6 x+2 y+3 z=1 \)
в. \( x+y+z=6 \)
c. \( 6 x+3 y+2 z=6 \)
D. \( 6 x-3 y-2 z=1 \)
Subject: Physics
In an AC circuit we have a black box of
\( 200 \Omega, 60^{\circ} . \) Frequency of \( A C \) is \( 250 \mathrm{Hz} \)
When a capacitor of \( 2 n \mu F \) is added
maximum power is obtained. The values of components of black box are
A \( \cdot R=100 \Omega, X_{L}=100 \sqrt{3} \Omega \)
B. \( R=100 \sqrt{3} \Omega, X_{L}=100 \Omega \)
c. \( R=100 \Omega, X_{C}=100 \sqrt{3} \Omega \)
D. \( X_{C}=100 \Omega, R=100 \sqrt{3} \Omega \)
Subject: Maths
If \( \bar{z}_{1}=a \hat{i}+b \hat{j} \) and \( \bar{z}_{2}=c \hat{i}+d \hat{j} \) are two
vectors in \( \hat{i} \) and \( \hat{j} \) system where \( \left|\bar{z}_{1}\right|= \)
\( \left|\bar{z}_{2}\right|=r \) and \( \bar{z}_{1} \cdot \bar{z}_{2}=0, \) then \( \bar{\omega}_{1}=a \hat{i}+ \)
\( c \hat{j} \) and \( \bar{\omega}_{2}=b \hat{i}+d \hat{j} \) satisfy
\( \mathbf{A} \cdot\left|\bar{\omega}_{1}\right|=r \)
В \( \cdot\left|\bar{\omega}_{2}\right| \neq r \)
\begin{tabular}{l} 
c. \( \bar{\omega}_{1}, \bar{\omega}_{2}=0 \) \\
\hline
\end{tabular}
D. None of these
Subject: Physics
The diagram below (Fig.) shows a uniform bar supported at the middle
point \( O . A \) weight of \( 40 g f \) is placed at a
distance \( 40 \mathrm{cm} \) to the left of the point \( O \)
How can you balance the bar with a
weight of \( 80 g f ? \)
A. By placing the weight of \( 80 g f \) at a distance \( 10 \mathrm{cm} \) to the right of the point \( O \)
B. By placing the weight of \( 40 g f \) at a distance \( 20 \mathrm{cm} \) to the right of the point \( O \)
C. By placing the weight of \( 160 g f \) at a distance \( 10 \mathrm{cm} \) to the right of the point \( O \)
D. By placing the weight of \( 80 g f \) at a distance \( 20 \mathrm{cm} \) to the of the point \( O \)
Subject: Physics
A light is travelling from air into a medium. The velocity of light in a medium is reduced to 0.75 times the
velocity in air. Assume that angle of incidence \( i \) is very small, the deviation
of the ray is:
\( \mathbf{A} \cdot i \)
B. \( \frac{i}{3} \)
\( c \cdot \frac{i}{4} \)
D. \( \frac{3 i}{4} \)
Subject: Chemistry
The vapour pressure of water at \( 27^{\circ} \mathrm{C} \) is
\( 0.2463 a t m . \) Calculate the values of \( K_{p} \)
and \( K_{c} \) at \( 27^{\circ} C \) for the equilibrium
\( \boldsymbol{H}_{2} \boldsymbol{O}\left(\boldsymbol{l} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})\right. \)
Using the equilibrium constant Which of the following reactions goes almost all the way to completion, and which proceeds hardly.
Subject: Physics
A copper rod with length \( 1.4 \mathrm{m} \) and area
of cross-section of \( 2 \mathrm{cm}^{2} \) is fastened to a
steel rod with length L and cross-
sectional area \( 1 \mathrm{cm}^{2} . \) The compound rod
is subjected to equal and opposite pulls
of magnitude \( 6.00 \times 10^{4} \mathrm{N} \) at its ends.
What is the strain in each rod? \( \left[\boldsymbol{Y}_{\text {steel}}=\right. \) \( \left.\mathbf{2} \times \mathbf{1 0}^{11} \boldsymbol{P a} ; \boldsymbol{Y}_{C U}=\mathbf{1 . 1} \times \mathbf{1 0}^{\mathbf{1 1}} \boldsymbol{P a}\right] \)
Subject: Physics
400 g of vegetable oil of specific heat capacity \( 1.98 J g^{-1} o C^{-1} \) is cooled from
\( \mathbf{1 0 0}^{\circ} \boldsymbol{C} \). Find the final temperature, if the heat energy given out by oil is \( 47376 \mathrm{J} \)
A \( .30 .2^{\circ} \mathrm{C} \)
в. \( 40.2^{\circ} \mathrm{C} \)
c. \( 50.2^{\circ} \mathrm{C} \)
D. \( 43.2^{\circ} \mathrm{C} \)
Subject: Physics
If the rms current through a \( 6.8 k \Omega \)
resistor is \( 8 m A \), the rms voltage drop
across the resistor is
\( \mathbf{A} \cdot 5.44 V \)
в. \( 54.4 \mathrm{V} \)
c. \( 7.07 V \)
D. 8V
Subject: Physics
A wheel having a diameter of 3 m starts
from rest and accelerates uniformly to an angular velocity of 210 r.p.m.in 5 seconds. Angular acceleration of the wheel is
A \( \cdot 4.4 \pi \frac{r a d}{s^{2}} \)
В. \( _{3.3 \pi} \frac{r a d}{s^{2}} \)
c. \( _{2.2 \pi} \frac{r a d}{s^{2}} \)
D. \( _{1.1 \pi} \frac{r a d}{s^{2}} \)
Subject: Chemistry
Consider the following equilibrium
\( A g C l \downarrow+2 N H_{3} \rightleftharpoons\left[A g\left(N H_{3}\right)_{2}\right]^{+}+ \)
\( \boldsymbol{C l}^{-} . \) White precipitate of of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
appears on which of the following?
A \( \cdot N H_{3} \)
B. Aqueous NaCl
c. Aqueous \( H N O_{3} \)
D. Aqueous \( N H_{4} C l \)
Subject: Chemistry
Nitrogen is restricted to a maximum
covalency of 4 since only four (one s and three \( p \) ) orbitals are available for
bonding. The heavier elements have vacant d orbitals in the outermost shell
which can be used for bonding (covalency) and hence, expand their
covalence as in \( \boldsymbol{P} \boldsymbol{F}_{\mathbf{6}}^{-} \)
Subject: Chemistry
The correct rate of reaction of given
compounds towards electrophilic
aromatic substitution reaction is:
A \( \cdot(b)>(d)>(a)>(c) \)
B. \( (b)>(a)>(d)>(c) \)
C. \( (c)>(a)>(d)>(b) \)
D. \( (a)>(b)>(d)>(c) \)
Subject: Biology
Identify the wrong pair of statements.
I) During plant succession, some species colonise an area and
populations become more
numerous, whereas populations of other species decline and even disappear.
II) Both hydrarch and xerarch successions lead to mesic conditions.
III) Secondary succession is a slow
process when compared to primary
succession.
IV) In the successive seral stages, there is no change in the diversity of species
of organisms.
\( \mathbf{A} \cdot\|,\| \)
B. ।, ॥
c. ॥॥, IV
D. I, III
Subject: Chemistry
The white solid compound \( A \) decomposes quite rapidly on heating in the presence of a black substance \( X \) to form a solid compound B and a gas C. When an aqueous solution of compound B is reacted with silver nitrate solution, then a white precipitate of silver chloride is obtained along with potassium nitrate solution. Gas C does not burn itself but helps to burn other things.

What do you think that black substance \( \mathbf{X} \) and \( \mathrm{What} \) is its function?
Subject: Chemistry
Atomic numbers of Cr and Fe are
respectively 24 and \( 26 . \) Which of the following is paramagnetic with spin of electron?
A \( \cdot C r(C O)_{6} \)
в \( \cdot\left[F e(C O)_{5}\right] \)
c. \( \left[F e(C N)_{6}\right]^{4} \)
D. \( \left[C r\left(N H_{3}\right)_{6}\right]^{3+} \)
Subject: Chemistry
Number of molecules having non-zero
dipole moment
\( \boldsymbol{B} e C l_{2}, \boldsymbol{X} e \boldsymbol{F}_{2}, \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{P} C l_{3} \boldsymbol{F}_{2}, \boldsymbol{P} \boldsymbol{C l}_{2} \boldsymbol{F}_{3}, \boldsymbol{B} \)
Subject: Physics
A man pushes an \( 80 N \) crate a distance
of \( 5.0 m \) upward along a frictionless
slope that makes an angle of \( 30^{\circ} \) with the horizontal. The force he exerts is
parallel to the slope. If the speed of the crate is constant, then the work done by the man is:
A . \( -140 J \)
в. \( 140 J \)
\( c \cdot 200 J \)
D. \( -200 J \)
Subject: Chemistry
The incorrect statement pertaining to
the adsorption of a gas on a solid
surface is (are):
A. Adsorption is always exothermic
B. Physisorption may transform into chemisorption at high temperature
C. Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature
D. Chemisorption is more exothermic than physisorption, however, it is very slow due to higher energy of activation
Subject: Physics
A mass of \( 5 \mathrm{kg} \) is suspended from a spring of stiffness \( 46 \mathrm{kN} / \mathrm{m} . \) A dashpot is fitted between the mass and the
support with a damping ratio of 0.3.Calculate the critical damping coefficient in \( \mathrm{Ns} / \mathrm{m} \)
A . 939
B. 949
c. 959
D. 969
Subject: Maths
In a GP the sum of three numbers is 14
if 1 is added to first two numbers and
the third number is decreased by \( 1, \) the series becomes \( A P, \) find the geometric
sequence. This question has multiple correct options
\( \mathbf{A} \cdot 2,4,8 \)
в. 8,4,2
\( c .6,18,54 \)
D. 8,16,32
Subject: Maths
If \( |z|=5 \) and \( w=\frac{z-5}{z+5}, \) then the
\( \boldsymbol{R} e(\boldsymbol{w}) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{25} \)
c. 25
D.
Subject: Physics
The height of water in a capillary tube of
radius \( 2 c m \) is \( 4 c m . \) What should be the
radius of capillary, if the water rises to \( 8 c m \) in tube?
A . \( 1 c m \)
B. \( 2 c m \)
\( c .3 c m \)
D. \( 4 c m \)
Subject: Chemistry
Elements \( A, B \) and \( C \) belong to the same period in the long form of the periodic table. The nature of the oxides of \( A, B \)
and \( \mathrm{C} \) is amphoteric, basic and acidic respectively. The correct order of the
atomic numbers of these elements is:
A. \( C>B>A \)
в. \( C>A>B \)
c. \( A>B>C \)
D. \( B>A>C \)
Subject: Chemistry
If the solubility product of a sparingly
soluble salt \( M X_{2} \) at \( 25^{\circ} C \) is \( 1.0 \times \)
\( \mathbf{1 0}^{-11}, \) the solubility of the salt in moles
\( L^{-1} \) at this temperature will be:
A \( .2 .46 \times 10^{14} \)
B . \( 1.36 \times 10^{-4} \)
c. \( 2.60 \times 10^{-7} \)
D. \( 1.20 \times 10^{-10} \)
Subject: Physics
Two waves, each having a frequency of \( 100 H z \) and a wavelength of \( 2.0 \mathrm{cm} \) are travelling in the same direction on a string. What is the phase difference between the waves
\( (a) \) if the second wave was produced \( 0.015 s \) later than the first one at the same
place,
(b) if the two waves were produced at a same instant but the first one was produced a distance \( 4.0 \mathrm{cm} \) behind the second one?
\( (c) \) If each of
the waves has an amplitude of \( 2.0 m m \) what would be the amplitudes of the resultant waves in part
\( (a) \) and
\( (b) ? \)
Subject: Maths
If \( A=\left[\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 5 & 1\end{array}\right] \) whenever
\( \boldsymbol{A}^{2}=\boldsymbol{B} \)
then values of \( \boldsymbol{\alpha} \) is
A .
B. -
\( c \cdot 4 \)
D. no real value of \( \alpha \)
Subject: Physics
A heat engine absorbs \( Q_{1} \) heat from hot
reservoir and work produced by engine is \( W \), then:
A \( \cdot Q_{1} \) is always \( =W \)
B. only in some special cases \( Q_{1}=W \) otherwise \( Q_{1} \) is greater than \( W \)
c. \( Q_{1} \) is always less than \( W \)
D. \( Q_{1} \) is always greater than \( W \)
Subject: Physics
the thermal capacity of 40 g of aluminium \( \left(\text {specific } \quad \text {heat}=\frac{0.2 c a l}{g m \times C}\right) \)
is
A. \( 40 \mathrm{cal} / C \)
B. 160cal/C
c. 200 cal \( / C \)
D. 8cal/C
Subject: Physics
The de Broglie wavelength of 1 mg grain
of sand blown by a \( 20 m s^{-1} \) wind is:
A \( \cdot 3.3 \times 10^{-29} \mathrm{m} \)
В. \( 3.3 \times 10^{-21} \mathrm{m} \)
c. \( 3.3 \times 10^{-49} \mathrm{m} \)
D. \( 3.3 \times 10^{-42} \mathrm{m} \)
Subject: Chemistry
Which one of the following combinations is false?
A . Colloidal solution \( 10^{-5} \) to \( 10^{-7} \mathrm{cm} \)
B. True solution \( 10^{-7} \) to \( 10^{-8} \mathrm{cm} \)
C. Suspension \( 10^{-9} \) to \( 10^{-12} \) cm
D. All are correct combinations
Subject: Chemistry
Electronic configuration of Mg is:
\( \mathbf{A} \cdot 1 s^{2} 2 s^{1} p^{5} 3 s^{2} 3 d^{2} \)
B. \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} \)
C \( \cdot 1 s^{2} 2 s^{2} p^{7} 3 s^{1} \)
D. \( 1 s^{2} 2 s^{2} p^{6} 3 s^{2} p^{2} \)
Subject: Maths
PQRS is a parallelogram. QM is the
height from \( Q \) to \( S R \) and \( Q N \) is the height
from \( Q \) to PS. If \( S R=12 c m \) and \( Q M=7.6 \)
\( \mathrm{cm} . \) Find \( \mathrm{QN}, \) if \( \mathrm{PS}=8 \mathrm{cm} \)
Subject: Chemistry
Hybridised states of carbon in graphite and diamond are respectively:
\( \mathbf{A} \cdot s p^{3}, s p^{3} \)
в. \( s p^{3}, s p^{2} \)
c. \( s p^{2}, s p^{2} \)
D. \( s p^{2}, s p^{3} \)
Subject: Physics
A vessel full of hot water is kept in a
room and it cools from \( 80^{\circ} \mathrm{C} \) to \( 75^{\circ} \mathrm{C} \) in
\( T_{1} \) minutes, from \( 75^{\circ} \mathrm{C} \) to \( 70^{\circ} \mathrm{C} \) in \( T_{2} \)
minutes and from \( 70^{\circ} \mathrm{C} \) to \( 65^{\circ} \mathrm{C} \) in \( T_{3} \)
minutes. Then:
A. \( T_{1}=T_{2}=T_{3} \)
в. \( T_{1}>T_{2}>T_{3} \)
c. \( T_{1}<T_{2}=T_{3} \)
D. \( T_{1}<T_{2}<T_{3} \)
Subject: Maths
The distance formula between two
points \( A\left(x_{1}, y_{1}\right) \) and \( B\left(x_{2}, y_{2}\right) \) is given by
A \( \cdot\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2} \)
B . \( \left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2} \)
c. \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \)
D. None of the above
Subject: Physics
Two particles \( A \) and \( B \) are moving in a
horizontal place anticlockwise on two different concentric circles with
different constant angular velocities \( 2 \omega \)
and \( \omega \) respectively. Find the relative
velocity (in \( m s \) ) of \( B \) w.r.t \( A \) after time
\( \boldsymbol{t}=\boldsymbol{\pi} / \omega . \) They both start at the position
as shown in figure (Take \( \omega= \)
3 radsec, \( r=2 m \)
Subject: Physics
Four charges are placed at the
circumference of dial clock as shown in
figure. If the clock has only hour hand,
then the resultant force on a positive
charge \( q_{0} \) placed at the centre, points in
the direction which show the time as:
\( \mathbf{A} \cdot 1: 30 \)
B. 7: 30
\( c \cdot 4: 30 \)
D. 10: 30
Subject: Chemistry
The decreasing order for acidic strength
¡s:
\( \mathbf{A} \cdot N O_{2} C H_{2} C O O H>N C C H_{2} C O O H> \)
\( F C H_{2} C O O H>C l C H_{2} C O O H \)
B \( \cdot F C H_{2} C O O H>N C C H_{2} C O O H> \)
\( N O_{2} C H C O O H>C l C H_{2} C O O H \)
\( \mathrm{c} \cdot \mathrm{N} \mathrm{O}_{2} \mathrm{CH}_{2} \mathrm{COOH}>\mathrm{FCH}_{2} \mathrm{COOH}> \)
\( C N C H_{2} C O O H>C l C H_{2} C O O H \)
D. \( C N C H_{2} C O O H>O_{2} N C H_{2} C O O H> \)
\( F C H_{2} C O O H>C l C H_{2} C O O H \)
Subject: Maths
The value of \( \int \frac{\log x}{(x+1)^{2}} d x \) is
A \( \cdot \frac{-\log x}{x+1}+\log x-\log (x+1)+C \)
B. \( \frac{\log x}{x+1}+\log x-\log (x+1)+C \)
c. \( \frac{\log x}{x+1}-\log x-\log (x+1)+C \)
D. \( \frac{-\log x}{x+1}-\log x-\log (x+1)+C \)
Subject: Maths
Solve equations using substitution method:
\( 5 x-2 y=10 \) and \( 4 x-6 y=3 \)
A \( \cdot \frac{-27}{11} \) and \( \frac{25}{22} \)
B. \( \frac{27}{11} \) and \( \frac{-25}{22} \)
c. \( \frac{27}{11} \) and \( \frac{25}{22} \)
D. \( \frac{-27}{11} \) and \( \frac{-25}{22} \)
Subject: Physics
The position vector of a particle is given
by \( \vec{r}=\vec{r}_{0}(1-a t) t, \) where \( t \) is the time
and \( a \) as well as \( \vec{r}_{0} \) are constant. After
what time the particle returns to the
starting point?
\( A \cdot a \)
B. \( \frac{1}{a} \)
\( c \cdot A^{2} \)
D. \( \frac{a}{a^{2}} \)
Subject: Chemistry
The maximum number of \( 90^{0} \) angles
between bond pair-bond pair of electrons is observed in:
A. \( d s p^{3} \) hybridisation
B . sp \( ^{3} \) d hybridisation
c. \( d s p^{2} \) hybridisation
D. \( s p^{3} d^{2} \) hybridisation
Subject: Physics
A convex lens of focal length \( 0.2 \mathrm{m} \) and
made of glass \( \left(^{a} \mu_{g}=1.5\right) \) is immersed
in water \( \left(^{a} \mu_{w}=1.33\right) . \) Find the change in the focal length of the lens.
\( A \cdot 5.8 \mathrm{m} \)
B. 158 m
c. \( 0.58 \mathrm{m} \)
D. \( 5.8 \mathrm{cm} \)
Subject: Physics
An ac generator produced an output voltage \( \boldsymbol{E}=\mathbf{1 7 0} \sin \mathbf{3 7 7 t} \) volts, where \( t \)
is in seconds. The frequency of ac voltage is
\( \mathbf{A} \cdot 50 H z \)
в. \( 110 H z \)
\( \mathbf{c} \cdot 60 H z \)
D. \( 230 H z \)
Subject: Physics
The surface of a planet is found to be uniformly charged. When a particle of
mass \( m \) and no charge is thrown at an angle from the surface of the planet, it has a parabolic trajectory as in projectile motion with horizontal range \( L \). A particle
of mass \( m \) and charge \( q \) with the same initial conditions has a range \( \frac{L}{2} \). The range of particle of mass \( m \) and charge \( 2 q \)
with the same initial conditions is :
A. \( L \)
в. \( \frac{L}{2} \)
c. \( \frac{L}{3} \)
D. \( \frac{L}{4} \)
Subject: Physics
Assertion (A) : A freely falling body experiences a constant horizontal force due to wind velocity, its path is a straight line Reason (R) : The motion is decided by the unbalanced force acting on it
A. Both Assertion
(A) and Reason (R) are correct and R is the correct explanation
B. Both Assertion
(A) and Reason
(R) are correct but the reason does not give the correct explanation
c. Assertion
(A) is true but Reason
(R) is false
D. Assertion
(A) is false but Reason
(R) is true