AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature
on its equilibrium constant \( \boldsymbol{K} \) in terms of change in entropy is described by This question has multiple correct options
A. With increase in temperature, the value of \( K \) for exothermic reaction decreases because the entropy change of the system is positive
B. With increase in temperature, the value of \( K \) for endothermic reaction increases because unfavourable change in entropy of the surroundings decreases
c. with increase in temperature, the value of \( K \) for endothermic reaction increases because the entropy change of the system is negative
D. With increase in temperature, the value of \( K \) for exothermic reaction decrease because favourable change in entropy of the surroundings decreases
Subject: Chemistry
Change in entropy is negative for:
A. Bromine\( (I) \rightarrow \) Bromine\( (g) \)
B \( \cdot C(s)+H_{2} O(g) \rightarrow C O(g)+H_{2}(g) \)
\( \mathbf{C} \cdot N_{2}(g, 10 a t m) \rightarrow N_{2}(g, 1 a t m) \)
D. \( F e(a t 400 K) \rightarrow F e(a t 300 K) \)
Subject: Chemistry
Calculate the molality of a solution of
Ethanol \( \left(C_{2} H_{5} O H\right) \) in water in which
the mole fraction of ethanol is 0.040
A. \( 4.42 \mathrm{mol} / \mathrm{kg} \)
B. 2.31 mol/kg
c. \( 5.23 \mathrm{mol} / \mathrm{kg} \)
D. none of these
Subject: Chemistry
\( 100 \mathrm{mL} \) solution of \( 0.1 \mathrm{M} H C l \) was
titrated with 0.2 \( N a O H \) solution. The
titration was discontinued after the
addition of \( 30 \mathrm{mL} \) of \( \mathrm{NaOH.} \) The
remaining titration was completed with the addition of 0.5 M \( K O H . \) The volume
of \( K O H \) required for completing the titration is:
\( A \cdot 8 m L \)
в. \( 16 m L \)
c. \( 32 m L \)
D. \( 64 m L \)
Subject: Physics
The radius of the earth is \( R \) and
acceleration due to gravity at its surface is 'g'. If a body of mass ' \( m \) ' is
sent to a height of \( \boldsymbol{R} / \mathbf{4} \) from the earth's surface, the potential energy is:
\( A \cdot m g R / 3 \)
в. \( m g R / 4 \)
c. \( m g R / 5 \)
D. \( m g R / 16 \)
Subject: Maths
The value of \( \int \frac{1}{\sqrt{\sin ^{3} x \cos ^{5} x}} d x \) is
A \( \cdot \frac{-2}{\sqrt{\tan x}}+\frac{2}{3}(\tan x)^{3 / 2}+C \)
в. \( \frac{2}{\sqrt{\tan x}}-\frac{2}{3}(\tan x)^{3 / 2}+C \)
c. \( \frac{-2}{\sqrt{\tan x}}+\frac{2}{3}(\tan x)^{1 / 2}+C \)
D. None of these
Subject: Biology
Assertion
Arteries carry blood from various body
organs to heart.
Reason
Veins carry blood from various body
organ to heart.
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
A gas bulb is filled with \( N O_{2} \) gas and
immersed in an ice bath at \( 0^{\circ} \mathrm{C} \) which
becomes colourless after some time.
This colourless gas will be:
A \( \cdot N O_{2} \)
в. \( N_{2} \),
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \)
D. \( N_{2} O_{5} \)
Subject: Chemistry
Consider the following reactions:
\( C(s)+O_{2}(g) \rightarrow C O_{2}(g)+x k J \)
\( C O(g)+\frac{1}{2} O_{2}(g) \rightarrow C O_{2}(g)+y k J \)
The heat of formation of \( \mathrm{CO}(\mathrm{g}) \) is :
\( A \cdot-(x+y) k J / m o l \)
B. \( (x-y) \) kJ/mol
c. \( (y-x) \) k) \( \int m o \)
D. None of these
Subject: Maths
If the sum of maximum and minimum
values of \( \boldsymbol{E}=\left(\sin ^{-1} x\right)^{2}+ \)
\( 2 \pi \cos ^{-1} x+\pi^{2} \) is \( \frac{a \pi^{2}}{b}, \) where \( a \) and \( b \)
are coprime, then the value of \( (a-b) \) is
Subject: Physics
A hammer of mass 5 kg moving with a speed of \( 2 \mathrm{m} \mathrm{s}^{-1} \) strikes the head of a
nail driving it \( 20 \mathrm{cm} \) into the wall. Find the impulse.
A . \( 10 \mathrm{N} \) s
B. 20 N s
c. 30 N s
D. 40 N s
Subject: Physics
A physical quantity \( \times \) is calculated from the relation \( \boldsymbol{x}=\frac{\boldsymbol{a}^{2} \boldsymbol{b}^{3}}{\boldsymbol{c} \sqrt{\boldsymbol{d}}} \)
percentage error in \( a, b, c \) and \( d \) are \( 2 \%, 1 \%, 3 \% \) and \( 4 \% \) respectively. What
is the percentage error in \( x ? \)
Subject: Physics
Charges \( Q_{1} \) and \( Q_{2} \) are placed inside
and outside respectively of an
uncharged conducting shell. Their seperation is \( r \) This question has multiple correct options
A. The force on \( Q_{1} \) is zero
B. The force on \( Q_{1} \) is \( k \frac{Q_{1} Q_{2}}{r^{2}} \)
c. The force on \( Q_{2} \) is \( k \frac{Q_{1} Q_{2}}{r^{2}} \)
D. The force on \( Q_{2} \) is zero.
Subject: Physics
The driver of a train \( A \) running at
\( 25 m s^{-1} \) sights a train \( B \) on the same
track with \( 15 m s^{-1} . \) The driver of train \( A \)
applies brakes to produce a
deceleration of \( 1.0 m s^{-2} . \) If the trains
are \( 200 m \) apart, will the trains collide?
A . yes
B. no
c. collision just avoided
D. none of these
Subject: Maths
The equation to the altitude of the
altitude triangle formed by
\( (1,1,1) \cdot(1,2,3),(2,-1,1) \) through
(1,1,1) is
A \( \cdot \bar{r}=(\bar{i}+\bar{j}+\bar{k})+t(\bar{i}-\bar{j}-2 \bar{k}) \)
B \( \cdot \bar{r}=(\bar{i}-\bar{j}+\bar{k})+t(\bar{i}+\bar{j}-2 \bar{k}) \)
\( \mathbf{c} \cdot \bar{r}=(\bar{i}+\bar{j}+\bar{k})+t(\bar{i}-\bar{j}+2 \bar{k}) \)
D \( \cdot \bar{r}=(\bar{i}-\bar{j}-\bar{k})+t(\bar{i}+\bar{j}-2 \bar{k}) \)
Subject: Chemistry
toppr
Q Type your question
are taken in \( A \) and \( B \). How many of the following statement(s) is/are correct?
\( \mathbf{P}_{X}^{0}=\mathbf{2 0 0} \) tor \( r \)
\( \mathbf{P}_{Y}^{0}=\mathbf{5 0} \) tor \( r \)
(i) If \( \mathrm{NaCl} \) is added to vessel \( \mathrm{B} \), the
lowering of vapour pressure takes place.
(ii) If glucose is added to vessel \( A, \) the boiling point of the solution increases.
(iii) If the valve connecting \( A \) and \( B \) is
opened, then \( \mathbf{P}_{T} \) in both the vessel
becomes equal and is given by Raoult's law.
(iv) After opening the valve, the level of liquid in both the container decreases (even a slight decrease is to be considered)
(v) After opening the valve, the final pressure in vessel B is more than 50
torr.
(vi) After opening the valve, the final pressure in vessel \( A \) is more than 200
torr
\( A \cdot 2 \)
B. 3
\( c \)
\( D \)
Subject: Chemistry
Aluminium reacts with \( \boldsymbol{H} \boldsymbol{C l} \) to form \( \boldsymbol{H}_{2} \)
gas, but do not react with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) why?
A. \( A l \) with \( H N O_{3} \) forms \( A l_{2} O_{3} \) which is passive for further reaction
B. \( A l \) with \( H N O_{3} \) forms \( A l_{2} O_{7} \) which is passive for further reaction
c. \( A l \) with \( H N O_{3} \) forms \( A l_{2} O_{4} \) which is passive for further reaction
D. \( A l \) with \( H N O_{3} \) forms \( A l_{3} O_{2} \) which is passive for further reaction
Subject: Chemistry
The enthalpy changes at \( 298 \mathrm{K} \) in successive breaking of \( \boldsymbol{O}-\boldsymbol{H} \) bonds of
HOH are:
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{H}(\boldsymbol{g})+\boldsymbol{O} \boldsymbol{H}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{4} \boldsymbol{9} \boldsymbol{8} \)
kJ \( m o l^{-1} \)
\( \boldsymbol{O} \boldsymbol{H}(\boldsymbol{g}) \rightarrow \boldsymbol{H}(\boldsymbol{g})+\boldsymbol{O}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=\mathbf{4 2 8} \mathbf{k J} \)
\( m o l^{-1} \)
The bond enthalpy of the \( O-H \) bond is:
A . 498 k \( \operatorname{mol}^{-1} \)
B. 463 kJ \( m o l^{-1} \)
c. 428 ks \( m o l^{-1} \)
D. 70 kJ \( m o l^{-1} \)
Subject: Maths
Let three matrices \( A=\left[\begin{array}{ll}2 & 1 \\ 4 & 1\end{array}\right] ; B= \)
\( \left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{2} & \mathbf{3}\end{array}\right] \) and \( C=\left[\begin{array}{cc}\mathbf{3} & -\mathbf{4} \\ -\mathbf{2} & \mathbf{3}\end{array}\right] \) then
\( \boldsymbol{t}_{\boldsymbol{r}}(\boldsymbol{A})+\boldsymbol{t}_{\boldsymbol{r}}\left(\frac{A B C}{2}\right)+\boldsymbol{t}_{\boldsymbol{r}}\left(\frac{\boldsymbol{A}(\boldsymbol{B C})^{2}}{4}\right)+ \)
\( \boldsymbol{t}_{\boldsymbol{r}}\left(\frac{\boldsymbol{A}(\boldsymbol{B} C)^{3}}{\boldsymbol{8}}\right)+\ldots+\infty \)
\( A \cdot 6 \)
B.
c. 12
D. none of these
Subject: Maths
Let the discrete random variable \( \boldsymbol{X}=\boldsymbol{x} \)
has the probabilities given by \( \frac{x}{6} \) for \( x= \)
\( 0,1,2,3, \) then its mean is
A \( \cdot \frac{1}{3} \)
в. \( \frac{5}{3} \)
\( c \cdot \frac{7}{3} \)
D. \( \frac{9}{3} \)
Subject: Physics
A square of side L meters lies in the \( x-y \)
plane in a region where the magnetic field is given by \( \overline{\boldsymbol{B}}=\boldsymbol{B}_{0}(\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}+ \)
\( 4 \hat{k}) T, \) where \( B_{0} \) is constant. The magnitude of flux passing through the
square is:
\( \mathbf{A} \cdot 8 B_{0} L^{2} W b \)
B. \( 12 B_{0} L^{2} W b \)
c. \( 4 B_{0} L^{2} W b \)
D. \( \sqrt{4 \times 29} B_{0} W b \)
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{O}^{18}+\boldsymbol{N} \boldsymbol{a} \rightarrow \underset{(b a s e)}{(\boldsymbol{A})}+(\boldsymbol{B}) \)
\( o \)
\( \boldsymbol{C H}-\mathbf{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{3}+ \)
\( (A) \rightarrow(C)+(D) \) alcohol
Product \( (C) \) of the reaction is:
\( ^{\mathbf{A}} \cdot_{C H_{3}-C-_{18}^{\|}}^{0}-H \)
в. \( \quad \stackrel{o^{\prime 8}}{N}-O-H \)
\[
C H_{3}-C-O-H
\]
D.
\[
C H_{3}-C-O^{\ominus} N_{a}^{\oplus}
\]
Subject: Physics
A block of mass \( 10 k g \) is placed on rough
inclined plane of variable angle \( \theta \) and
friction coefficient \( \boldsymbol{\mu}_{s}=\boldsymbol{\mu}_{\boldsymbol{k}}=\mathbf{3} / \mathbf{4} \)
When \( \theta \) is \( 37^{\circ} \) net reaction force applied by inclined is \( \vec{N}_{1} \) and when \( \theta=53^{\circ} \) net
reaction force applied by inclined is \( \vec{N}_{2} \) find \( \left|\overrightarrow{\boldsymbol{N}}_{1}\right|-\left|\overrightarrow{\boldsymbol{N}}_{2}\right| \)
Subject: Maths
The value of \( \cos ^{-1}\left(\cos \frac{5 \pi}{4}\right) \) is?
A \( \cdot \frac{-3 \pi}{4} \)
в. \( \frac{3 \pi}{4} \)
c. \( \frac{-5 \pi}{4} \)
D. \( \frac{5 \pi}{4} \)
Subject: Physics
Assertion
An electric field \( \vec{E} \) is induced in a
closed loop where magnetic flux is varied.The induced \( \overrightarrow{\boldsymbol{E}} \) is not a
conservative field
Reason The line integral \( \vec{E} . \overrightarrow{d l} \) around the closed loop is nonzero
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: Maths
What is the mistake in computation of \( \mathbf{1}=\sqrt{\mathbf{1}}=\sqrt{(-\mathbf{1})(-\mathbf{1})}=\sqrt{-\mathbf{1}} \times \)
\( \sqrt{-\mathbf{1}}=\boldsymbol{i} \times \boldsymbol{i}=-\mathbf{1} \)
Subject: Chemistry
\( O_{2}^{+} P t F_{6}^{-} \) (an orange coloured compound) was prepared and thus,
formation of compound \( \boldsymbol{X} \boldsymbol{e}^{+} \boldsymbol{P} \boldsymbol{t} \boldsymbol{F}_{\boldsymbol{6}}^{-} \)
was feasible based on ionisation energy of Xe (which is very similar to that of \( \boldsymbol{O}_{2} \)
)
If true enter 1 , else enter 0
Subject: Chemistry
For complete combustion of ethanol
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l})+\boldsymbol{3} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \)
\( \mathbf{2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O}(l) \)
the amount of heat produced as measured in bomb calorimeter, is
\( 1364.47 k J \quad m o l^{-1} \) at \( 25^{\circ} C \)
Assuming ideality the enthalpy of
combustion, \( \Delta_{c} H \) for the reaction will
be:
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4 k J} \quad \boldsymbol{m o l}^{-1}\right) \)
\( \begin{array}{ll}\text { A. }-1366.95 k J & \text { mol }^{-1}\end{array} \)
B. \( -1361.95 k J \) mol\( ^{-1} \)
\( \begin{array}{ll}\text { c. }-1460.95 k J & \text { mol }^{-1}\end{array} \)
D. \( -1350.50 k J \) mol \( ^{-1} \)
Subject: Physics
A ship moves at \( 40 \mathrm{kmph} \) due north and
suddenly moves towards east through
\( 90^{0} \) and continues to move with the
same speed. Then the change in velocity
is
A. zero
B. 40 kmph North East
c. \( 40 \mathrm{kmph} \) south west
D. \( 40 \sqrt{2} \) kmph south East
Subject: Chemistry
Reagent (C) is:
\( \mathbf{A} \cdot O_{3} / P h_{3} P \)
\( \mathbf{B} \cdot O_{3} / N a B H_{4} \)
\( \mathbf{c} \cdot O_{3} / H_{2} O_{2} \)
D. \( K M n O_{4} / \) O \( H \)
Subject: Chemistry
Using Pt electrodes same quantity of electricity is passed in \( \mathbf{0 . 0 3} M A I C I_{3}, 0.01 M A I C I_{3}, 0.01 M A g \)
solutions. If 0.36 g silver is deposited what is the mass of Al deposited in two
\( A I C I_{3} \) solutions and volume of \( O_{2} \)
evolved at STP in NaOH solution?
Subject: Maths
\( \boldsymbol{f}:(-\infty, \infty) \rightarrow(-\infty, \infty) \) is defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} ; \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{R}(\boldsymbol{a} \neq \mathbf{0}) \) then \( \boldsymbol{f} \)
is
A. injective but not surjective
B. surjective but not injective
c. bijective
D. neither injective nor surjective
Subject: Physics
The resistance of the wire made of silver
at \( 27^{\circ} C \) temperature is equal to \( 2.1 \Omega \)
While at \( 100^{\circ} \mathrm{C} \) it is \( 2.7 \Omega \). Calculate the
temperature coefficient of the resistivity of the silver.Take the
reference temperature is equal to \( 20^{\circ} C \)
Subject: Chemistry
An organic compound \( \boldsymbol{A}\left(\boldsymbol{C}_{4} \boldsymbol{H}_{9} \boldsymbol{C l}\right) \) on
reaction with \( N a / \)diethyl ether gives a
hydrocarbon which on monochlorination gives only one chloro derivative. \( A \) is:
A. t-butyl chloride
B. sec-butyl chloride
c. isobutyl chloride
D. n-butyl chloride
Subject: Physics
If \( 1 \mathrm{g} \mathrm{cm}^{-3}=10^{3} \mathrm{kg} \mathrm{m}^{-3} \) then
\( 10^{6} k g m^{-3}= \)
A \( \cdot 10^{-3} g c m^{-3} \)
В \( \cdot 10^{6} g c m^{-3} \)
\( \mathbf{c} \cdot 10^{3} g c m^{-3} \)
D. \( 10^{-6} g c m^{-3} \)
Subject: Chemistry
The order of reactivity of the following
alcohols towards conc. H \( C l \) is:
\( \mathbf{A} \cdot I>I I>I I I>I V \)
В . \( I>I I I>I I>I V \)
\( \mathbf{C} \cdot I V>I I I>I I>I \)
D. \( I V>I I I>I>I I \)
Subject: Physics
Three bodies \( A, B \) and \( C \) of masses \( 1 k g \)
\( 2 k g \) and \( 3 k g \) are at rest on a horizontal
surface of coefficient of friction \( 0.5 . \) If
they are pulled with forces \( 20 N, 30 N \)
and \( 25 N \) respectively
their accelerations \( a_{A}, a_{B} \) and \( a_{C} \) will be in ascending order as follows:
A \( \cdot a_{A}, a_{B}, a_{C} \)
в. \( a_{C}, a_{B}, a_{A} \)
\( \mathbf{c} \cdot a_{B}, a_{A}, a_{C} \)
D. \( a_{B}, a_{C}, a_{A} \)
Subject: Physics
A smooth ball 'A' moving with velocity 'V' collides with another smooth initial ball
at rest. After collision both the balls
move the same speed with angle
between their velocities \( 60^{0} . \) No external
force acts on the systems of balls.
Choose the correct option(s).
A \( \cdot \) The speed of each ball after the collision is \( \frac{V}{\sqrt{3}} \)
B. The speed of each ball after the collision is \( \frac{2 V}{\sqrt{3}} \)
C. The magnitude of change in momentum of ball B is \( \left(\frac{m V}{\sqrt{3}}\right) \)
D. The magnitude of change in momentum of ball B is \( \left(\frac{2 m V}{\sqrt{3}}\right) \)
Subject: Chemistry
When \( 100 \mathrm{ml} \) of a \( O_{2}-O_{3} \) mixture was
passed through turpentine, there was the reduction of volume by \( 20 \mathrm{ml} \). If 100ml of such a mixture is heated, what
will be the increase in volume?
A. \( 10 \mathrm{ml} \)
B. \( 20 \mathrm{ml} \)
c. \( 30 m l \)
D. \( 25 \mathrm{ml} \)
Subject: Chemistry
Which of the following pairs of substances illustrate the law of multiple proportions?
A. \( C O \) and \( C O_{2} \)
B. \( H_{2} O \) and \( D_{2} O \)
c. \( N a C l \) and \( N a B r \)
D. \( M g O \) and \( M g(O H)_{2} \)
Subject: Maths
Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}\}, \) then
\( \boldsymbol{B} \times \boldsymbol{A}= \)
\{(2,1),(2,2),(3,1),(3,2),(4,1),(4,2)\}
If true enter 1 , or else enter 0 .
Subject: Physics
An object of mass \( m \) is tied to a string
of length \( l \) and a variable force \( F \) is
applied on it which brings the string
gradually at an angle \( \theta \) with the vertical
Find the work done by the force \( F \)
A. \( m g l(1-\cos \theta) \)
в. \( m g l(2-\cos \theta) \)
c. \( _{m g l}\left(1-\frac{\cos \theta}{2}\right) \)
D \( \cdot \operatorname{mgl}\left(2-\frac{\cos \theta}{2}\right) \)
Subject: Maths
The inequality \( \sin ^{-1} x>\cos ^{-1} x \) vholds
for
A. all values of \( x \)
B \( \cdot x \in\left(0, \frac{1}{\sqrt{2}}\right) \)
\( ^{c} \cdot_{x \in\left(\frac{1}{\sqrt{2}}, 1\right)} \)
D. no value of \( x \)
Subject: Physics
An ideal gas having initial pressures \( \boldsymbol{P} \)
volume \( V \) and temperature \( R \) is allowed
to expand adiabatically until its volume
becomes \( 5.66 V \) while its temperature falls to \( \boldsymbol{T} / \mathbf{2} \)
Obtain the work done by the gas during the expansion as a function of initial pressure \( \boldsymbol{P} \) and volume \( \boldsymbol{V} \)
Subject: Physics
The de-Broglie wavelength of a bus moving with speed 'v' is ' \( \lambda^{\prime} \). Some
passengers left the bus at a stoppage. Now when the bus moves with twice its initial speed, its kinetic energy is found to be twice its initial value. The de-
Broglie wavelength now is
\( A \cdot \lambda \)
B. \( 2 \lambda \)
c. \( \lambda / 2 \)
D. \( \lambda / 4 \)
Subject: Chemistry
Which of the following actions will help to reduce pollution?
Composting kitchen and garden waste
2. Using unleaded petrol in cars
3. Spraying pesticides on plants to kill
pests
4. Littering chocolates and biscuits
wrappers
A . 1 and 2
B. 3 and 4
C. 1,2 and 3
D. 1,2 and 4
Subject: Physics
Two blocks each of mass m is
connected to the spring of spring constant \( \mathrm{k} \) as shown in the figure.
If the blocks are displaced slightly in opposite directions and released, they
will execute simple harmonic motion.
The time period of oscillation is
A. \( 2 \pi \sqrt{\frac{m}{k}} \)
В \( .2 \pi \sqrt{\frac{m}{2 k}} \)
\( \mathbf{c} \cdot 2 \pi \sqrt{\frac{m}{4 k}} \)
D. \( 2 \pi \sqrt{\frac{2 m}{k}} \)
Subject: Maths
The letters of the word "INDEPENDENCE"
are arranged in all possible ways. The number of words in which the 'D's
do not come together is
A \( \cdot \frac{10 !}{4 ! 3 !} \)
B. \( \frac{10 !}{4 ! 3 !} \frac{10}{2 !} \)
c. \( \frac{10 !}{4 ! 3 !}^{10} P_{2} \)
D. \( \frac{10 !}{4 ! 3 !} \frac{11}{2 !} \)
Subject: Physics
A spherical \uparrow ole of radius \( \mathbf{R} / \mathbf{2} \) is
excavated from \( \mathbf{t} \uparrow \) e asteroid of mass
M as shown in fig. T Me gravitational
acceleration at a point on t \( \uparrow \mathbf{e} \)
surf ace of \( \mathbf{t} \uparrow \mathbf{e} \) asteroid just above \( \mathbf{t} \uparrow \)
excavation is :
A. GM/R \( ^{2} \)
B. \( \mathrm{GM} / 2 \mathrm{R}^{2} \)
c. \( \mathrm{GM} / 8 \mathrm{R}^{2} \)
D. \( 7 \mathrm{gW} 8 \mathrm{R}^{2} \)
Subject: Chemistry
Assertion
Tyrosine behave as a acidic at \( \boldsymbol{p} \boldsymbol{H}=\mathbf{7} \)
Reason
\( p K_{a} \) of phenol is more than 7
Select the correct option.
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
toppr
Q Type your question.
\( \left.\right|^{x \in L}\left|: \sin \left(\log _{e} \mid \overline{x-1}\right)\right|^{\operatorname{ls} a} \)
(Here, the inverse trigonometric
function \( \sin ^{-1} x \) assumes values in \( \left.\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\right) \)
Let \( \boldsymbol{f}: \boldsymbol{E}_{1} \rightarrow \mathbb{R} \) be the function define by \( f(x)=\log _{e}\left(\frac{x}{x-1}\right) \) and \( g: E_{2} \rightarrow \mathbb{R} \)
be the function defined by \( g(x)= \) \( \sin ^{-1}\left(\log _{e}\left(\frac{x}{x-1}\right)\right) \)
LIST-1
1. \( \left(-\infty, \frac{1}{1-e}\right] \)
The range of \( f \) is \( \quad\left[\frac{e}{e-1}, \infty\right) \)
Q. The range of \( g \)
contins
R. The domain of \( f \)
contains
\[
\begin{array}{ll}
\text { S. The domain of } g \text { is } & 4 .(-\infty, 0) \cup(0, \infty) \\
& 5 .\left(-\infty, \frac{e}{e-1}\right] \\
& \text { 6. }(-\infty, 0) \cup\left(\frac{1}{2}, \frac{e}{e-1}\right]
\end{array}
\]
The correct option is
A. \( P \rightarrow 4 ; Q \rightarrow 2 ; R \rightarrow 1 ; S \rightarrow 1 \)
в. \( P \rightarrow 3 ; Q \rightarrow 3 ; R \rightarrow 6 ; S \rightarrow 5 \)
c. \( P \rightarrow 4 ; Q \rightarrow 2 ; R \rightarrow 1 ; S \rightarrow 6 \)
D. \( P \rightarrow 4 ; Q \rightarrow 3 ; R \rightarrow 6 ; S \rightarrow 5 \)
Subject: Maths
(i) Quadrilateral \( A B C D \)
\( A B=4.5 c m \)
\( B C=5.5 \mathrm{cm} \)
\( C D=4 c m \)
\( A D=6 \mathrm{cm} \)
\( A C=7 c m \)
(ii) Quadrilateral \( J U M P \)
\( J U=3.5 c m \)
\( \boldsymbol{U} \boldsymbol{M}=\boldsymbol{4} \boldsymbol{c} \boldsymbol{m} \)
\( M P=5 c m \)
\( \boldsymbol{P J}=\mathbf{4 . 5 c m} \)
\( \boldsymbol{P U}=\mathbf{6 . 5 c m} \)
(iii) Parallelogram \( M O R E \)
\( \boldsymbol{O} \boldsymbol{R}=\boldsymbol{6} \boldsymbol{c m} \)
\( \boldsymbol{R} \boldsymbol{E}=\mathbf{4 . 5 c m} \)
\( E O=7.5 \mathrm{cm} \)
(iv) Rhombus \( B E S T \)
\( B E=4.5 c m \)
\( \boldsymbol{E T}=\mathbf{6} \boldsymbol{c m} \)
Subject: Chemistry
A hydrocarbon with formula \( \mathrm{C}_{8} \mathrm{H}_{18} \) gives
one mono chloro derivative. The
hydrocarbon can be :
A. n- Octane
B. 2-Methyl hepatane
c. 2,2,4 -Trimethyl butane
D. 2,2,3,3,- - Tetramethyl butane
Subject: Physics
In the following circuit, find the diode current when the diode potential is
\( 0.5 V . \) Also find the forward resistance of
the diode.
A. \( 0.5 A, 1 \Omega \)
B \( .1 A, 0.5 \Omega \)
c. \( 2 A, 1 \Omega \)
D. \( 5 A, 6 \Omega \)
Subject: Maths
If \( S=1^{2}-2^{2}+3^{2}-4^{2} \dots \) upto \( n \)
terms and \( n \) is even, then \( S \) equals
A \( \cdot \frac{n(n+1)}{2} \)
B. \( \frac{n(n-1)}{2} \)
c. \( \frac{-n(n+1)}{2} \)
D. \( \frac{-n(n-1)}{2} \)
Subject: Physics
In the circuit shown below, the key Kis
closed at \( t=0 . \) The current through the battery is:
A. \( \frac{\mathrm{VR}_{1} \mathrm{R}_{2}}{\sqrt{\mathrm{R}_{1}^{2}+\mathrm{R}_{2}^{2}}} \) at \( \mathrm{t}=0 \) and \( \frac{\mathrm{V}}{\mathrm{R}_{2}} \) at \( \mathrm{t}=\infty \)
\( \frac{V}{R_{2}} a t t=0 \) and \( \frac{V\left(R_{1}+R_{2}\right)}{R_{1} R_{2}} \) at \( t=\alpha \)
C \( \cdot \frac{\mathrm{V}}{\mathrm{R}_{2}} \mathrm{att}=0 \) and \( \frac{\mathrm{VR}_{1} \mathrm{R}_{2}}{\sqrt{\mathrm{R}_{1}^{2}+\mathrm{R}_{2}^{2}}} \) at \( \mathrm{t}=\infty \)
\( \frac{V\left(R_{1}+R_{2}\right)}{R_{1} R_{2}} a t t=0 \) and \( \frac{V}{R_{2}} \) at \( t=\infty \)
Subject: Physics
A particle of mass \( \mathrm{M} \) is moving in a
circle with constant speed \( v, \) between two position at the ends of a diameter, the particle's
A. Momentum changes by mv
B. kinetic energy changes by1/2mv \( ^{2} \)
c. Momentum changes by 2 mv
D. Kinetic energy changes by \( m v^{2} \)