AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If a and b are two unequal positive numbers, the:
A \( \cdot \frac{2 a b}{a+b}>\sqrt{a b}>\frac{a+b}{2} \)
B . \( \sqrt{a b}>\frac{2 a b}{a+b}>\frac{a+b}{2} \)
C \( \cdot \frac{2 a b}{a+b}>\frac{a+b}{2}>\sqrt{a b} \)
D \( \cdot \frac{a+b}{2}>\frac{2 a b}{a+b}>\sqrt{a b} \)
E \( \cdot \frac{a+b}{2}>\sqrt{a b}>\frac{2 a b}{a+b} \)
Subject: Maths
The principal value of \( \cos ^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\} \) is
A. \( -\frac{3 \pi}{20} \)
В. \( -\frac{7 \pi}{20} \)
c. \( -\frac{7 \pi}{10} \)
D. none of these
Subject: Physics
Two small loud speakers \( A \) and \( B \) are
driven by the same amplifier as shown in Fig and emit pure sinusoidal waves in phase. Speaker \( A \) is \( 1 \mathrm{m} \) away as
shown and speaker \( B \) is 2 m away from
the amplifier. The microphone is \( 4 \mathrm{m} \)
away from the amplifier in transverse direction as indicated in the Figure. For
what frequencies constructive interference will occur at \( \boldsymbol{P} \)
(microphone point)
B. 500 Нz, 1500 нz
c. 550 Нz, 1100 Н \( z_{\text {... }} \)
D. 500 нz, 1000 Нz,1500 нz
Subject: Maths
If \( y=\frac{f(x)}{\phi(x)} \) and \( z=\frac{f^{\prime}(x)}{\phi^{\prime}(x)}, \) then \( \frac{f^{\prime \prime}}{f}- \)
\( \frac{\phi^{\prime \prime}}{\phi}+\frac{2(y-z)}{f \phi}\left(\phi^{\prime}\right)^{2}= \)
A \( \cdot \frac{d^{2} y}{d x^{2}} \)
B. \( \frac{1}{y} \cdot \frac{d^{2} y}{d x^{2}} \)
c. \( y \cdot \frac{d^{2} y}{d x^{2}} \)
D. None of these
Subject: Chemistry
Which one of the following is wrongly
matched?
A. Saponification of \( C H_{3} C O O C_{2} H_{5} \) - second order reaction
B. Hydrolysis of \( C H_{3} C O O C H_{3} \) - pseudo unimolecular reaction
C. Decomposition of \( H_{2} O_{2} \) - first order reaction
D. Combination of \( H_{2} \) and \( B r_{2} \) to give \( H B r \) - first order
reaction
Subject: Physics
In a YDSE with two identical slits, when
the upper slit is covered with a thin, perfectly transparent sheet of mica, the intensity at the centre of screen reduces to \( 75 \% \) of the initial value.
Second minima is observed to be above
this point and third maxima below it. Which of the following can be a possible value of phase difference caused by the mica sheet
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{13 \pi}{3} \)
c. \( \frac{17 \pi}{3} \)
D. \( \frac{11 \pi}{3} \)
Subject: Physics
A voltage of peak value \( 283 \mathrm{V} \) and varying frequency is applied to series LCR combination in which \( R=3 \Omega, L=25 \)
\( \mathrm{mH} \) and \( \mathrm{C}=400 \mu \mathrm{F} \). Then the frequency (in \( \mathrm{Hz} \) ) of the source at which maximum power is dissipated in the above is
A . 51.5
B. 50.7
\( c . \) 51.
D. 50.3
Subject: Chemistry
\( A l F_{3} \) is soluble in \( H F \) only in presence
of \( K F \). It is due to the formation of :
A. \( A l H_{3} \)
B . \( K\left[A l F_{3} H\right] \)
c. \( K_{3}\left[A l F_{3} H_{3}\right] \)
D. \( K_{3}\left[A l F_{6}\right] \)
Subject: Maths
Box I contains 2 white and 3 red balls
and box II contains 4 white and 5 red
balls. One ball is drawn at random from
one of the boxes and is found to be red.
Then, the probability that it was from box \( \| \), is?
\( ^{\mathrm{A}} \cdot \frac{54}{44} \)
в. \( \frac{54}{14} \)
c. \( \frac{54}{104} \)
D. None of these
Subject: Physics
An object falls from a height of \( 15 \mathrm{m} \) in 0.5 sec. What is the average speed of the object?
A. \( 1.85 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
c. \( 2.45 \mathrm{m} / \mathrm{s} \)
D. 2.86 \( \mathrm{m} / \mathrm{s} \)
Subject: Physics
A positive charge \( +\mathrm{Q} \) is located at \( 5 \mathrm{cm} \)
on the positive y-axis. A negative charge
-Q is located at \( 5 \mathrm{cm} \) on the positive \( x \) -
axis. A positive test charge is at the origin where it feels a force "F" from the
positive charge above it. What is the net
force from both charges?
\( \mathbf{A} \cdot 2 F \)
B \( . F^{2} \)
\( c \cdot \frac{F}{2} \)
D. \( \sqrt{2} F \)
Subject: Maths
The roots of the equation \( \left|\begin{array}{ccc}\boldsymbol{x}-\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \boldsymbol{x}-\mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \boldsymbol{x}-\mathbf{1}\end{array}\right|=\mathbf{0} \operatorname{are} \)
A. 1,2
в. -1,2
c. -1,-2
D. 1,-2
Subject: Physics
On introducing a transparent \( \operatorname{slab}(\mu) \) the central fringe shifts to the point originally occupied by the fifth bright fringe. The thickness of the slab is
\( ^{\mathbf{A}} \cdot \frac{5 \lambda}{\mu-1} \)
в. \( \frac{4 \lambda}{\mu-1} \)
c. \( \frac{\mu-1}{4 \lambda} \)
D. \( \frac{\mu-1}{5 \lambda} \)
Subject: Biology
Match the hormones and its source.
(A) \( s \) Somatostatin
(1) \( \quad \) Pineal gland
(B) Melatonin
(2) Corpus luteum
(C) Aldosterone
(3) Placenta
(D) Progesterone
(4)
Adrenal cortex
(E) \( \mathrm{HCG} \)
(5)
Islets of
Langerhans
(6) \( \quad \) Adenohypophys
A. (A)- (5), (B)- (1), (C)- (6), (D)- (3), (E)- (2)
B. \( (A)-(1),(B)-(2),(C)-(4),(D)-(3),(E)-(5) \)
C. \( (A)-(2),(B)-(6),(C)-(4),(D)-(5),(E)-(3) \)
D. \( (A)-(5),(B)-(1),(C)-(4),(D)-(2),(E)-(3) \)
E. \( (A)-(1),(B)-(3),(C)-(4),(D)-(2),(E)-(5) \)
Subject: Chemistry
The solubility of anhydrous \( A l C l_{3} \) and
hydrous \( A l C l_{3} \) in diethyl ether are \( S_{1} \)
and \( S_{2} \) respectively, Then :
в. \( S_{1}>S_{2} \)
c. \( s_{1}<S_{2} \)
D. \( S_{1}<S_{1} \) but not \( S_{1}=S_{2} \)
Subject: Physics
For a planet revolving around sun, if \( a \) and \( b \) are the respective semi-major and semi-minor axes, then the square of its time period is proportional to
\( ^{\mathbf{A}} \cdot\left(\frac{a+b}{2}\right)^{3} \)
\( ^{\mathbf{B}} \cdot\left(\frac{a-b}{2}\right)^{3} \)
\( c \cdot b^{3} \)
D. \( a^{3} \)
Subject: Chemistry
If
\( \mathbf{1 0 0} \quad \mathbf{N} / \mathbf{5} \quad \mathbf{N H}_{4} \mathbf{O H} \) and HCl are
mixed. Find out the pH of the resultant
solution if \( p K_{b} \) for \( N H_{4} O H \) is \( 10^{-5} \)
Subject: Maths
If \( \boldsymbol{y}=\sin ^{-1}\left(\frac{\mathbf{5} \boldsymbol{x}+\mathbf{1 2} \sqrt{\mathbf{1}-\boldsymbol{x}^{2}}}{\mathbf{1 3}}\right), \) then
\( \frac{d y}{d x} \) is equal to
A. \( -\frac{1}{\sqrt{1-x^{2}}} \)
B. \( \frac{1}{\sqrt{1-x^{2}}} \)
c. \( \frac{3}{\sqrt{1-x^{2}}} \)
D. \( -\frac{x}{\sqrt{1-x^{2}}} \)
Subject: Physics
If the absolute errors in two physical
quantities \( A \) and \( B \) are \( a \) and \( b \) respectively, then the absolute error in
the value of \( A B \) is:
[Disclaimer: The options in the original question have been changed to match with the actual solution / answer.
\( \mathbf{A} \cdot b B-a A \)
B. \( a A+b B \)
\( \mathbf{c} \cdot a B+b A \)
\( \mathbf{D} \cdot a B-b A \)
Subject: Physics
If \( \vec{a}=2 \hat{i}+4 \hat{j}-5 \hat{k}, \vec{b}=\hat{i}+ \)
\( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}}, \) then the unit vectors
parallel to \( \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}} \) is
A \( \cdot \pm \frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k}) \)
в. \( (3 \hat{i}+6 \hat{j}-2 \hat{k}) \)
\( ^{\mathrm{C}} \pm \frac{1}{7}(3 \hat{i}+6 \hat{j}+2 \hat{k}) \)
D. \( (3 \hat{i}+6 \hat{j}+2 \hat{k}) \)
Subject: Chemistry
Account for the acidity of L-ascorbic
\( \operatorname{acid}\left(p K_{a}=4.21\right) . \) Which of the
following is most acidic \( H ? \) (Marked in
the structures as \( H^{a}, H^{b}, H^{c} \) and \( H^{d} \) )
A \( . H^{a} \)
В \( \cdot H^{b} \)
\( \mathbf{c} \cdot H^{c} \)
\( \mathbf{D} \cdot H^{d} \)
Subject: Physics
Which of the following statement(s)
is/are correct?
A. Conduction current obeys Ohm's law whereas displacement current does not.
B. Conduction current is the actual current whereas displacement current is the apparent
current produced by time varying electric field.
C . Conduction current density is represented by \( \overrightarrow{J_{c}}=\sigma \vec{E} \) whereas displacement current
density is given by \( \overrightarrow{J_{d}}=\frac{\overrightarrow{\delta E}}{\delta t} ; \sigma= \) conductivity of the element, \( \vec{E}= \) electric field
D. All of the above
Subject: Chemistry
Which of the following properly explains why the atomic radius decreases going cross a period from left to right?
A. As you cross the period from left to right, the number of electron orbital shells decreases as the number of protons remains constant
B. As you cross the period from left to right, the number of protons decreases as the number of electron orbitals remains constant.
C. As you cross the period from left to right, the number of electron orbital shells increases as the number of protons remains constant
D. As you cross the period from left to right, the number of protons increases as the number of electron orbitals remains constant
Subject: Physics
Which one of the following represents the correct dimensions of the quantity \( x=\frac{\eta}{\rho}, \) where \( \eta= \) coefficient of
viscosity and \( \rho= \) the density of a
liquid?
A \( \cdot\left[M L^{-2} T^{-1}\right] \)
B \( \cdot\left[M L^{-4} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{-5} T^{-2}\right] \)
D. \( \left[M^{0} L^{2} T^{-1}\right] \)
Subject: Maths
The image of the point \( 3 \hat{i}-2 \hat{j}+\hat{k} \) in the plane \( \bar{r} .(3 \hat{i}-\hat{j}+4 \hat{k})=2 \)
\( \mathbf{A} \cdot-\hat{j}+3 \hat{k} \)
B . \( \hat{j}-3 \hat{k} \)
\( \mathbf{c} .-\hat{j}-3 \hat{k} \)
D \( .-2 \hat{j}-3 \hat{k} \)
Subject: Chemistry
Consider the following steps. \( \boldsymbol{A}(\boldsymbol{g}) \overrightarrow{\boldsymbol{E}_{1}} \)
\( \boldsymbol{A}^{+}(\boldsymbol{g}) \underset{\boldsymbol{E}_{2}}{\longrightarrow} \boldsymbol{A}^{2+}(\boldsymbol{g}) \underset{\boldsymbol{E}_{3}}{\longrightarrow} \boldsymbol{A}^{3+}(\boldsymbol{g}) \) Third
ionization energy of \( \boldsymbol{A}(\boldsymbol{g}) \) is \( ? \)
A. \( E_{1}+E_{2} \)
B . \( E_{1}+E_{2}+E_{3} \)
\( \mathbf{c} \cdot\left(E_{1}+E_{2}+E_{3}\right)^{/ 3} \)
D. \( E_{3} \)
Subject: Physics
Calculate the amount of heat energy
required to raise the temperature of \( 100 g \) of copper from \( 20^{\circ} C \) to \( 70^{\circ} C \) Specific heat capacity of copper:
\( \mathbf{3 9 0} \boldsymbol{J k g}^{-1} \boldsymbol{K}^{-1} \)
A . \( 195 . J \)
в. \( 3900 J \)
c. \( 1950 J \)
D. \( 390 J \)
Subject: Physics
The coefficient of mutual inductance of
the two coils is \( 5 H . \) The current through the primary coil is reduced to zero value
from \( 3 A \) in 1 millisecond. The induced
emf in the secondary coils is
A. zero
в. 1.67 Кル
c. \( 15 K V \)
D. \( 600 V \)
Subject: Chemistry
Match the List I with List II and choose
the correct option from the codes given
below:
List - I List - II
\( (P) \)
Sky in blue
(Q) Peptisation
Delta
Formation Gold
number
\( \begin{array}{llll}\text { (R) } & \text { Tyndall effect } & \text { (3) } & \text { Coagulation }\end{array} \)
(s) Adsorption
of common
ion 1
A. \( P-3, Q-4, R-1, S-2 \)
B. P-2, Q-3, R-1, S-4
c. \( \mathrm{P}-3, \mathrm{Q}-1, \mathrm{R}-4, \mathrm{S}-2 \)
D. P-4, Q-3, R-1, S-2
Subject: Maths
A ball is tossed in the air in such a way
that the path of the ball is modeled by
the equation \( y=-x^{2}+6 x \) where \( y \)
represents the height of the ball in feet
and \( x \) is the time in seconds. At what
time \( x \) will the ball reach the ground
again?
\( \mathbf{A} \cdot \mathbf{6} \)
B. 2
\( c \cdot 3 \)
D. 4
E .
Subject: Chemistry
The numbers of iodine atoms present in
\( 1 \mathrm{ml} \) of its \( 0.1 \mathrm{M} \) solution is:
A. \( 6.02 \times 10^{23} \)
B . \( 6.02 \times 10^{22} \)
c. \( 6.02 \times 10^{19} \)
D. \( 1.204 \times 10^{20} \)
Subject: Chemistry
The total energy emitted when electrons
of \( 1.0 \mathrm{g} \) atom of hydrogen undergo transition giving the spectral line of lowest energy in the visible region of its atomic spectrum is:
\( \left[\text { Given }: \boldsymbol{E}_{\mathbf{1}(\boldsymbol{H})}=\mathbf{2 . 1 7 6} \times \mathbf{1 0}^{-\mathbf{1 8}}\right] \)
A . \( 1.82 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
В. \( 1.96 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
c. \( 2.01 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
D. \( 2.06 \times 10^{5} \mathrm{J} / \mathrm{mol} \)
Subject: Maths
A conic \( C \) satisfies the differential
equation \( \left(1+y^{2}\right) d x-x y d y=0 \) and
passes through the point (1,0) An ellipse \( \boldsymbol{E} \) which is confocal with \( \boldsymbol{C} \) having its eccentricity equal to \( \sqrt{2 / 3} \)
(a) Find the length of the latus rectum
of the conic \( C \)
(b) Find the equation of the ellipse \( \boldsymbol{E} \)
(c) Find the locus of the point of intersection of the perpendicular
tangents to the ellipse \( \boldsymbol{E} \)
Subject: Chemistry
The correct statement(s) about the
compound \( \boldsymbol{H}_{3} \boldsymbol{C}(\boldsymbol{H} \boldsymbol{O}) \boldsymbol{H} \boldsymbol{C}-\boldsymbol{C H}= \)
\( \boldsymbol{C H}-\boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}_{3}(\boldsymbol{X}) \) is(are):
This question has multiple correct options
A. The total number of stereoisomers possible for \( X \) is 6
B. The number of diastereomers possible for \( X \) is 3
c. If the stereochemistry about the double bond in \( X \) is trans, the number of enantiomers possible for \( X \) is 4
D. If the stereochemistry about the double bond in \( X \) is cis, the number of enantiomers possible for \( X \) is 2
Subject: Maths
If \( \mathbf{A} \) is \( 3 x 4 \) matrix \( B^{T} \) is a matrix such
that \( A^{T} B \) and \( B A^{T} \) are both defined
then \( B \) is of the type
\( A \cdot 3 \times 4 \)
B. \( 3 \times 3 \)
c. \( 4 \times 3 \)
D. \( 4 \times 4 \)
Subject: Physics
Consider the electric dipole moment \( (p=2 q a) \) shown in the figure. The
electric field at a point \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{0}) \) in the
polar coordinate system is :
A \( \cdot \frac{k_{e} p}{r^{3}}[(2 \cos \theta) \hat{r}-(\sin \theta) \hat{\theta}] \)
B. \( \frac{k_{e} p}{r^{3}}[(2 \cos \theta) \hat{r}+(\sin \theta) \hat{\theta} \)
c. \( \frac{k_{e} p}{r^{3}}[-(2 \cos \theta) \hat{r}+(\sin \theta) \hat{\theta} \)
D. \( \frac{k_{e} p}{r^{3}}[-(2 \cos \theta) \hat{r}-(\sin \theta) \hat{\theta} \)
Subject: Maths
\( \boldsymbol{p} \leftrightarrow \boldsymbol{q} \) is equivalent to
\( \mathbf{A} \cdot p \rightarrow q \)
\( \mathbf{B} \cdot q \rightarrow p \)
\( \mathbf{c} \cdot(p \rightarrow q) \vee(q \rightarrow p) \)
D. \( (p \rightarrow q) \wedge(q \rightarrow p) \)
Subject: Physics
A quantity of 10 g of a gas at 1 atm pressure is cooled from \( 273^{\circ} \mathrm{C} \) to \( 273 \mathrm{K} \)
keeping its volume constant, the final
pressure of the gas will be?
A. 273 atm
B. 0.5 atm
c. 0.2 atm
D. 0.1 atm
Subject: Physics
A carnot refrigeration cycle absorbs heat at270 Kand rejects heat at \( 300 K \)
If the cycle is absorbing \( 1260 K J / \) min at \( 270 K \), then work required per second
is :
A \( .2 .33 \mathrm{KJ} / \mathrm{sec.} \)
в. \( 4.66 K J / \)sec.
c. \( 1 K J / \) sec.
D. \( 4 K J / \)sec.
Subject: Chemistry
18g glucose and 6 g urea are dissolved
in 1 litre aqueous solution at \( 27^{\circ} C . \) The
osmotic pressure of the solution will be
\( \mathbf{A} \cdot 3.826 \mathrm{atm} \)
B. 4.926 atm
c. 2.92 atm
D. 9.42 atm
Subject: Maths
If the 7 th and 8 th term of the binominal
expansion \( (2 a-3 b)^{n} \) are equal, then \( \frac{2 a+3 b}{2 a-3 b} \) is to
A \( \cdot \frac{n-13}{n+1} \)
в. \( \frac{n+1}{13-n} \)
c. \( \frac{6-n}{13-n} \)
D. \( \frac{n-1}{13-n} \)
Subject: Physics
The number of neutrons in the element
Lin the following nuclear changes is
\( \boldsymbol{Y}^{\boldsymbol{X}} \boldsymbol{N} \rightarrow_{\boldsymbol{B}}^{\boldsymbol{A}} \boldsymbol{L}+\mathbf{2} \boldsymbol{\beta}^{+} \)
A. 146
в. 144
\( c .140 \)
D. 142
Subject: Physics
A simple camera with a converging lens of \( 60 \mathrm{mm} \) focal length is focused on very far objects. To focus the camera on a nearby object \( 1.5 \mathrm{m} \) away, the distance between the film and lens will have to
be
A. decreased by \( 2.5 \mathrm{mm} \)
B. increased by 2.5 mm
c. kept fixed as before, but aperture increased by a factor of 2.5
D. kept fixed as before, but aperture decreased by a factor of 2.5
Subject: Physics
A cylindrical vessel filled with water up to a height of \( 2 \mathrm{m} \) stands on a horizontal plane. The side wall of the vessel is a plugged circular hole touching the bottom. Find the minimum diameter of
the hole so that the vessel begins to move on the floor if the plug is removed. The coefficient of friction between the
bottom of the vessel and the plane is 0.4
and the total mass of water plus vessel
is \( 100 \mathrm{kg} \)
Subject: Physics
A bullet fired into a trunk of a tree loses
\( 1 / 4 \) of its kinetic energy in traveling a distance of \( 5 \mathrm{cm} . \) Assuming constant
retardation before stopping, it travels a further distance of
A. \( 150 \mathrm{cm} \)
B. \( 1.5 \mathrm{cm} \)
c. \( 1.25 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)
Subject: Maths
By graphical method solve the following linear programming problem for maximization.
Objective function \( z=1000 x+600 y \) Constraints \( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{2 0 0} \)
\( 4 x-y \leq 0 \)
\( x \geq 20, x \geq 0, y \geq 0 \)
Subject: Physics
A rectangle with its dimensions is as shown. A Magnetic mono pole of pole strength ' \( \mathrm{m}^{\prime} \) is placed at the point \( ^{\prime} \mathrm{A}^{\prime} \) and another pole of pole strength '5m' is
placed at the point 'B'. The magnetic force acting between them is 'F'.' If magnetic pole at the point 'B' is moved to the point 'C', Find final magnetic force acting between them.
A \( \cdot \frac{F}{10} \)
в. \( \frac{F}{17} \)
\( c \cdot \frac{F}{20} \)
\( \mathbf{D} \cdot F \)
Subject: Physics
A truck is carry a box of mass \( \boldsymbol{m}= \)
\( 50 k g \) on its flat horizontal rough
surface with coefficient of friction \( \boldsymbol{p}= \)
0.3. It is crossing a circular track of
radius 27 m. What is the maximum
speed of the truck to that the box does not slide from the muck while moving on the circular path?
\( \mathbf{A} \cdot 18 \mathrm{km} / \mathrm{hr} \)
B. \( 36 \mathrm{km} / \mathrm{hr} \)
c. \( 32.4 \mathrm{km} / \mathrm{hr} \)
D. \( 2.5 \mathrm{km} / \mathrm{hr} \)
Subject: Chemistry
\( \Delta H^{\ominus} \) for the cell reaction assuming
that these quantities remain
unchanged in the range \( 15^{\circ} C \) to \( 35^{\circ} \mathrm{C} \) is:
A. \( -99.97 k J \mathrm{mol}^{-1} \)
B. \( 99.97 k J \) mol \( ^{-1} \)
\( \mathbf{c} .-9.99 k J \mathrm{mol}^{-1} \)
D. \( 9.99 \mathrm{kJ} \mathrm{mol}^{-1} \)
Subject: Chemistry
Which of the following alkyl halides will
undergo \( S_{N} 1 \) reaction most readily?
A \( \cdot\left(C H_{3}\right)_{3} C-F \)
В \( \cdot\left(C H_{3}\right)_{3} C-C l \)
C \( \cdot\left(C H_{3}\right)_{3} C-B r \)
D \( \cdot\left(C H_{3}\right)_{3} C-I \)
Subject: Physics
There are two identical small holes on
the opposite sides of a tank containing liquid. The tank is open at the top. The
difference in height between the two
holes is \( h \). As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to:
A \( \cdot h^{1 / 2} \)
B.
\( c \cdot h^{3 / 2} \)
\( D \cdot h^{2} \)
Subject: Physics
A vertical circular coil of radius \( 0.1 m \)
and having 10 turns carries a steady current. When the plane of the coil is normal to the magnetic meridian, a neutral point is observed at the centre
of the coil. If \( \boldsymbol{B}_{\boldsymbol{H}}=\mathbf{0 . 3 1 4} \times \mathbf{1 0}^{-\mathbf{4}} \boldsymbol{T} \)
the current in the coil is :
\( \mathbf{A} \cdot 0.5 A \)
B. 0.25 A
\( c \cdot 2 A \)
D. \( 1 A \)
Subject: Physics
A body is lying on a piston which is executing vertical SHM. Its time period is 2 s. For what value of amplitude, the
body will leave the piston:
\( A \cdot 1 m \)
B. 0.248 m
c. \( 0.428 \mathrm{m} \)
D. \( 0.842 \mathrm{m} \)
Subject: Maths
Let \( f(x) \) be a function satisfying
\( f^{\prime}(x)=f(x)=e^{x} \) with \( f(0)=1 \) and
\( g(x) \) be a function that satisfies \( f(x)+ \)
\( g(x)=x^{2} . \) Then, the value of the integral \( \int_{0}^{1} f(x) g(x) d x \) is
\( ^{A} \cdot_{e}+\frac{e^{2}}{2}-\frac{3}{2} \)
B. \( _{e}-\frac{e^{2}}{2}-\frac{3}{2} \)
c. \( _{e}+\frac{e^{2}}{2}+\frac{5}{2} \)
D. \( _{e}-\frac{e^{2}}{2}-\frac{5}{2} \)
Subject: Physics
A sphere has a charge of \( +50 C . \) The absolute potential at a point at
distance of \( 10^{-12} \) m from the sphere is:
(Radius of the sphere is \( \left.<10^{-12} \text {m }\right) \)
A . \( 4500 \mathrm{V} \)
B . \( 45 \times 10^{23} \mathrm{V} \)
c. \( 4.5 \times 10^{23} V \)
D. \( 45 \times 10^{24} V \)
Subject: Physics
Assertion: Faraday's laws are consequences of conservation of energy Reason: In a purely resistive A.C. circuit
the current lags behind the e.m.f. in
phase
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E. If reason is true but assertion is false
Subject: Chemistry
Assertion
Van der Waals' forces are responsible
for chemisorption.
Reason
High temperature is favorable for chemisorption.
Read the above assertion and reason
and choose the correct option regarding
¡t.
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
Arrange the following elements in increasing order of their size.
\( \mathbf{V}, \mathrm{Nb}, \mathrm{Ta}, \mathrm{Db} \)
A. \( v<\mathrm{Nb}=\mathrm{Ta} \approx \mathrm{Db} \)
B. \( D b<N b= \) Ta \( \approx V \)
c. \( \mathrm{Ta}<\mathrm{Nb}=\mathrm{v} \approx \mathrm{Db} \)
D. None of these
Subject: Chemistry
The correct statement in respect of
structure of hypo phosphorous acid is:
A. 2 -OH groups, 2 -H atoms are attached directly
to \( P \)
B. One OH group and 2-H atoms are directly
attached to \( \mathrm{P} \)
C. One OH group and 3 - H atoms are directly
attached to \( \mathrm{P} \)
D. Three OH groups are attached directly to P
Subject: Physics
In LC oscillation resistance is \( 100 \Omega \) and
inductance and capacitance is \( 1 \mathrm{H} \) and
10 \( \mu F \). Find the half power of frequency.
\( \mathbf{A} \cdot 266.2 \)
B. 366.2
c. 166.2
D. 233.2
Subject: Physics
Assertion
Pulling a lawn roller is easier than
pushing it.
Reason
Pushing increases the apparent weight
and hence the force of friction.
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
The main difference in \( C-X \) bond of a
haloalkane and a haloarene is:
A. \( C-X \) bond in haloalkanes is shorter than haloarnes.
B. In haloalkanes, the \( C \) attached to halogen in \( C-X \)
bond is \( s p^{3} \) hybridised while in haloarenes it is \( s p^{2} \)
hybridised
C. \( C-X \) bond in haloarenes acquire a double bond
character due to the higher electronegativity of \( X \) than haloalkanes.
D. Haloalkanes are less reactive than haloarenes due to difficulty in \( C-X \) cleavage in haloalkanes
Subject: Physics
State clearly how an unpolarised light gets linearly polarised when passed through a polaroid.
(i) Unpolarised light of intensity \( I_{0} \) is
incident on a polaroid \( P_{1} \) which is kept
near another polaroid \( P_{2} \) whose pass
axis is parallel to that of \( \boldsymbol{P}_{1} \). How will the
intensities of light, \( \boldsymbol{I}_{1} \) and \( \boldsymbol{I}_{2} \)
transmitted by the polaroids \( P_{1} \) and \( P_{2} \)
respectively, change on rotating \( \boldsymbol{P}_{1} \)
without disturbing \( P_{2} ? \)
(ii) Write the relation between the
intensities \( I_{2} \) and \( I_{1} \)