AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A hammer exerts a force of \( 1.5 N \) on
each of the two nails \( A \) and \( B \). The area
of cross section of tip of nail \( \boldsymbol{A} \) is
\( 2 m m^{2} \) while that of nail \( B \) is \( 6 m m^{2} \)
Let the pressure on nail \( A \) be \( x \) and that on nail \( B \) be \( y, \) then find \( \frac{x}{y} \)
A \( \cdot \frac{1}{3} \)
в. 3
c. 9
D. \( \frac{1}{9} \)
Subject: Physics
In the experimental arrangement shown
in figure, the areas of cross-section of the wide and narrow portions of the tube
are \( 5 \mathrm{cm}^{2} \) and \( 2 \mathrm{cm}^{2} \) respectively. The
rate of flow of water through the tube is
\( 500 \mathrm{cm}^{3} \mathrm{s}^{-1} . \) The difference of
mercury levels in the U-tube is:
A. \( 0.97 \mathrm{cm} \)
в. 1.97 ст
\( \mathrm{c} .0 .67 \mathrm{cm} \)
D. \( 4.67 \mathrm{cm} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{2} & -\mathbf{3} \\ \mathbf{4} & \mathbf{1}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{3} \\ \mathbf{5} & \mathbf{0}\end{array}\right] \) and
\( \boldsymbol{C}=\left[\begin{array}{cc}-\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{5}\end{array}\right], \) then find \( \boldsymbol{A}(\boldsymbol{B}+\boldsymbol{C}) \)
Subject: Physics
Assertion
If optical density of a substance is more than that of water then the mass
density of substance can be less than
water
Reason
Optical density and mass density are not related.
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
Predict the products formed when cyclohexanecarbaldehyde reacts with the following reagents.
(i) PhMgBr and then \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
(ii) Tollens reagent
(iii) Semicarbazide and weak acid
(iv) Excess ethanol and acid
(v) Zinc amalgam and dilute
hydrochloric acid
Subject: Maths
The first and the last terms of an A.P are
5 and 45 respectively. If the sum of all its terms is \( 400, \) find its common
difference.
A. \( _{d=\frac{5}{3}} \)
B. \( d=\frac{8}{5} \)
c. \( _{d=\frac{8}{3}} \)
D. None of these
Subject: Physics
A solid cylinder starts rolling down on an inclined plane from its top and \( V \) is
the velocity of its centre of mass on reaching the bottom of inclined plane. If a block starts sliding down on an
identical inclined plane but smooth,
from its top, then the velocity of block on reaching the bottom of inclined plane is :
A \( \cdot \frac{V}{\sqrt{2}} \)
B. \( \sqrt{2} V \)
c. \( \sqrt{\frac{3}{2}} V \)
D. \( \sqrt{\frac{2}{3}} V \)
Subject: Maths
The determinant
\( \left|\begin{array}{lll}a^{2} & a^{2}-(b-c)^{2} & b c \\ b^{2} & b^{2}-(c-a)^{2} & c a \\ c^{2} & c^{2}-(a-b)^{2} & a b\end{array}\right| \) is divisible by
This question has multiple correct options
\( \mathbf{A} \cdot a+b+c \)
B . \( (a+b)(b+c)(c+a) \)
c. \( a^{2}+b^{2}+c^{2} \)
D. \( (a-b)(b-c)(c-a) \)
Subject: Maths
If \( \bar{a} \) is collinear with \( \bar{b}=3 \bar{i}+6 \bar{j}+6 \bar{k} \)
and \( \bar{a} \cdot \bar{b}=27 . \) Then \( \bar{a} \) is equal to?
A \( .3(\bar{i}+\bar{j}+\bar{k}) \)
B . \( \bar{i}+3 \bar{j}+3 \bar{k} \)
c. \( \bar{i}+2 \bar{j}+2 \bar{k} \)
D. \( 2 \bar{i}+2 \bar{j}+2 \bar{k} \bar{k}+2+2+2+2+2 \bar{k}+2 \bar{i}+2 \bar{i} \bar{i} \)
Subject: Physics
A car travels 1000 meters north and the
1000 meters south. The entire trip takes
200 seconds. What is the car's average velocity for the trip?
A. \( 10 \mathrm{m} / \mathrm{s} \)
в. \( 20 \mathrm{m} / \mathrm{s} \)
c. \( 100 m / s \)
D. \( 200,000 \mathrm{m} / \mathrm{s} \)
E . \( 0 m / s \)
Subject: Physics
Assertion
Mean free path of a gas molecules varies inversely as density of the gas.
Reason
Mean free path varies inversely as
pressure of the gas.
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
Add the given expression: \( 5 \sqrt{x}- \) \( 4 \sqrt{y}+2 ; 2 \sqrt{x}+7 \sqrt{y}-5 \)
A. \( 7 \sqrt{x}+3 \sqrt{y}-3 \)
В. \( 7 \sqrt{x}+3 \sqrt{y}-5 \)
c. \( 7 \sqrt{x}+3 \sqrt{y}-8 \)
D. \( 7 \sqrt{x}+2 \sqrt{y}-3 \)
Subject: Chemistry
(a) Silicone is a polymeric organo silicon compound which is chemically inert and thermally stable
(b) Silicon carbide can be used as a
lubricant.
(c) Silicon dioxide is the raw material
for the manufacture of cement as well
as glass.
(d) Hardness of \( S i O_{2} \) and \( S i C \) is due to
their regular tetrahedral structure.
Which of the following regarding silicon and its compounds is correct?
A. a and
B. b and c
\( c \cdot a, c \) and \( d \)
D. only d
Subject: Chemistry
Which among the following best describes the orbital overlap in
a molecule of :
\( \boldsymbol{H}-\underset{H}{_{H}}=\underset{H}{\boldsymbol{I}}-\boldsymbol{H} \)
i. s to s
ii. s to \( \mathrm{p} \)
iii. \( s p^{2} \) to \( s p^{2} \)
A. i only
B. ii only
c. i and iii only
D. ii and iii only
E. i, ii and iii
Subject: Maths
Find the solution of
(i) \( 10 \cos ^{3} x-16 \cos x=3 \cos 2 x+3, \) in
the interval \( [-\boldsymbol{\pi}, \boldsymbol{\pi}] \)
\( (i i) 2(\cos x+\cos 2 x)+\sin 2 x(1+ \)
\( 2 \cos x)=2 \sin x \) in the interval \( [-\pi, \pi] \)
Subject: Maths
na \( \Delta A B C \), the sides \( A B, B C \) and \( C A \) are
\( \mathbf{1 0 c m}, \mathbf{8 c m} \) and \( \mathbf{7 c m} \) respectively. In AB
a point \( P \) is taken such that \( A P=4 c m \).
If \( P Q \) is drawn parallel to \( B C \), then its
length is equal to
A. \( 4.0 \mathrm{cm} \)
В. \( 3.8 \mathrm{cm} \)
\( c .3 .5 \mathrm{cm} \)
\( 0.3 .2 \mathrm{cm} \)
Subject: Maths
The diagram shows two arcs, A and B.
Arc A is part of the circle with centre 0 and radius OP. Arc B is part of the circle
with centre \( \mathrm{M} \) and radius PM, where M is
the mid - point of PQ. Show that the area
enclosed by the two arcs is equal to 25 \( \left(\sqrt{3}-\frac{\pi}{6}\right) c m^{2} \)
Subject: Physics
Consider a spring that exerts the following restoring force: \( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \) for
\( \boldsymbol{x}>0 \) and \( \boldsymbol{F}=-4 \boldsymbol{k} \boldsymbol{x} \) for \( \boldsymbol{x}<\mathbf{0} \)
A mass m on a frictionless surface is
attached to the spring, displaced to \( x=A \) by stretching the spring and then
releasing:
This question has multiple correct options
A \cdot The period of motion will be \( T=\frac{3}{2} \pi \sqrt{\frac{m}{k}} \)
B. The most negative value, the mass \( m \) can reach will be \( x=-\frac{A}{2} \)
c. The time taken to move from \( x=A \) to \( x=-\frac{A}{\sqrt{2}} \) straight away will be equal to \( \frac{5 \pi}{8} \sqrt{\frac{m}{k}} \)
D. The total energy of oscillations will be \( \frac{5}{2} k A^{2} \)
Subject: Physics
If the capacity of a spherical conductor is 1 picofarad, then its diameter would
be
A \( \cdot 1.8 \times 10^{-3} \mathrm{m} \)
B . \( 18 \times 10^{-3} m \)
c. \( 1.8 \times 10^{-5} m \)
D. \( 18 \times 10^{-5} m \)
Subject: Chemistry
The product obtained in this reaction is:
A \( \cdot C H_{3} C H_{2} O H \)
в. \( \left(C H_{3}\right)_{2} \) СНОН
c. \( C H_{3} C H_{2} C H_{2} O H \)
D. \( H O-C H_{2}-C H_{2}-C H_{2}-C H_{2}-O H \)
Subject: Chemistry
The solubility of metal halides depends on their nature, lattice enthalpy and hydration enthalpy of the individual ions. Amongst fluorides of alkali metals, the lowest solubility of LiF in water is due to:
A. ionic nature of lithium fluoride
B. high lattice enthalpy
c. high hydration enthalpy for lithium ion
D. low ionisation enthalpy of lithium atom
Subject: Maths
Let \( \boldsymbol{A}=\{1,2,3,4,5,6\} . \) Let \( R \) be a relation on \( A \) defined by \( R=\{(a, b) \)
\( a, b \in A, b \text { is exactly divisible by a }\} \) Find
the range of \( R \)
Subject: Maths
Calculate the surface area of
hemisphere having the radius of \( 1.4 \mathrm{cm} \)
A \( \cdot 1.232 \mathrm{cm}^{2} \)
B . \( 12.32 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 123.2 \mathrm{cm}^{2} \)
D. \( 1232 c m^{2} \)
Subject: Chemistry
Choose the incorrect reaction.
\( \mathbf{A} \cdot 2 C_{2} H_{5} I+2 N a \frac{\left(C_{2} H_{5}\right)_{2} O}{\longrightarrow} C_{4} H_{10}+2 N a I \)
B \( \cdot 2 C_{2} H_{5} B r+Z n \stackrel{E t O H}{\longrightarrow}\left(C_{2} H_{5}\right)_{2} Z n+B r_{2} \)
\( \mathbf{c} \cdot_{2 C_{2}} H_{5} I+N a_{2} S \longrightarrow\left(C_{2} H_{5}\right)_{2} S+2 N a I \)
D \( \cdot 2 C_{2} H_{5} B r+N a I \frac{\left(C H_{3}\right)_{2} C=O}{\longrightarrow} C_{2} H_{5} I+N a B r \)
E. All are correct reations
Subject: Physics
If the ratio of the concentration of
electrons to that of hole in a semiconductor is \( \frac{7}{5} \) and the ratio of currents is \( \frac{7}{4} . \) Then, the ratio of their drift velocities is :
A \( \cdot \frac{4}{7} \)
B. \( \frac{4}{5} \)
\( c \cdot \frac{5}{8} \)
D.
Subject: Chemistry
The correct order of acidic character in
the above compounds is:
\( A \cdot a>b>c>d \)
\( B \cdot c>a>d>b \)
\( \mathbf{C} \cdot b>c>a>d \)
\( \mathrm{D} \cdot \mathrm{a}>\mathrm{c}>\mathrm{b}>\mathrm{d} \)
Subject: Maths
Differentiate \( e^{\sin x} \)
\( \mathbf{A} \cdot e^{\sin x} \cos x \)
B. \( -e^{\sin x} \cos x \)
\( \mathbf{c} \cdot e^{-\sin x} \cos x \)
\( \mathbf{D} \cdot e^{\cos x} \sin x \)
Subject: Physics
A power transmission line feeds input
power at \( 2400 \mathrm{V} \) to a step down transformer with its primary winding having 4000 turns. What should be the
number of turns in the secondary winding in order to get output power at \( 240 \vee ? \)
A . 400
B. 420
\( c \cdot 424 \)
D. 436
Subject: Biology
After forceful inspiration, the amount of air that can be breathed out by maximum forced expiration is equal to
A \( \cdot \operatorname{lRV}+\operatorname{ERV}+\operatorname{TV}+\operatorname{RV} \)
B. IRV + RV + ERV
C. \( \operatorname{IRV}+\mathrm{TV}+\mathrm{ERV} \)
D. \( T V+R V+E R V \)
Subject: Maths
f \( S_{1}, S_{2}, S_{3}, \dots . . S_{r} \) are the sums of \( n \) terms of arithmetic series whose first
terms are \( 1,2,3,4, \dots ; \) and whose common differences are \( 1,3,5,7, \dots \)
find the value of \( \boldsymbol{S}_{\mathbf{1}}+\boldsymbol{S}_{\mathbf{2}}+\boldsymbol{S}_{\mathbf{3}}+\ldots+ \)
\( \boldsymbol{S}_{\boldsymbol{r}} \)
Subject: Physics
\( 4 g m s \) of steam at \( 100^{\circ} \mathrm{C} \) is added to
\( 20 g m s \) of water at \( 46^{\circ} \mathrm{C} \) in a container
of negligible mass. Assuming no heat is lost to surrounding, the mass of water in container at thermal equilibrium is.
Latent heat of vaporisation \( = \)
\( \mathbf{5 4 0} \) cal / gm. Specific heat of water \( = \)
\( \mathbf{1} \boldsymbol{c a l} / \boldsymbol{g m}-^{\circ} \boldsymbol{C} \)
\( \mathbf{A} \cdot 18 g m \)
в. \( 20 g m \)
c. \( 22 g m \)
D. \( 24 g m \)
Subject: Chemistry
One mole of ideal gas whose adiabatic exponent \( \gamma=\frac{4}{3} \) undergoes process \( P= \) \( 200+\frac{1}{V} \) then change in internal energy
of gas when volume changes from \( 2 m^{3} \)
\( \operatorname{to} 4 m^{3} \) is?
A . 400
B. 800
c. 1200 J
D. 600
Subject: Maths
100 tickets are numbered as 00,01,02
\( \ldots .09,10,11,12, \ldots .99 . \) Out of them, one
ticket is drawn at random. The
probability that the sum of the digits of the number on the ticket is 9 is
A. \( \frac{7}{100} \)
в. \( \frac{9}{100} \)
c. \( \frac{1}{10} \)
D. \( \frac{1}{100} \)
Subject: Maths
Solve \( \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{2 4} \boldsymbol{x} \boldsymbol{y}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{2} \mathbf{1} \boldsymbol{x} \boldsymbol{y} \)
Subject: Physics
Assertion
Thermodynamic process in nature are irreversible.
Reason
Dissipative effect cannot be eliminated.
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: Physics
toppr
Q Type your question-
the rails is \( 1 m . \) A conducting rod of
mass \( 0.5 k g \) can slide on the rails
frictionlessly. The rod is tied at
midpoint to a light string passing over a smooth pulley fixed to the edge of the
table. A mass of 0.5kg tied to the other
end of the string hangs vertically as shown in the Figure. A uniform magnetic field of \( 0.5 T \) can be applied in
vertically downward direction. If the system is released from rest, then, point out incorrect statements from the
following:
I be the acceleration due to gravity]
This question has multiple correct options
A. When the magnetic field is put on, the acceleration of the system increases from \( \frac{g}{3} \) to \( \frac{g}{2} \)
B. Due to induction, the change in the acceleration of the system is same as that obtained by increasing the mass of the rod by \( 0.5 k g \) in the absence of the magnetic field.
c. Due to induction, the change in the acceleration of the system is same as that obtained by decreasing the mass of the rod by \( 0.25 \mathrm{kg} \) in the absence of magnetic field
D. When the magnetic field is put on, the acceleration of the system decreases from \( \frac{g}{2} \) to \( \frac{g}{3} \)
Subject: Physics
\( A \) tank of size \( 10 m \times 10 m \times 10 m \) is ful
of water and built on the ground. If \( g= \)
\( 10 m s^{-2}, \) the potential energy of the
water in the tank is:
A \( .5 \times 10^{7} \) J
В. \( 1 \times 10^{8} \) у
\( c \cdot 10^{4} \)
D. \( 10^{5} \) J
Subject: Maths
In the given figure, the diagonals \( A C \)
and BD intersect at point \( 0 . \) If \( O B=0 D \)
and AB//DC, show that:
Area \( (\Delta D O C)=A r e a(\Delta A O B) \)
f the \( A(\triangle D O C)=21 \) sq. units, then
\( \boldsymbol{A}(\triangle \boldsymbol{D} \boldsymbol{O} \boldsymbol{C})+\boldsymbol{A}(\triangle \boldsymbol{A} \boldsymbol{O} \boldsymbol{B}) \) is :
Subject: Chemistry
The IUPAC name of the given compound
¡s:
A. 2-methyl spiro [5.4] dec-1-ene
B. 2-Methyl spiro [4.5] dec-1-ene
c. 2 -methyl spiro [4.5] dec- 2 -ene
D. 2-methyl spiro [5.4] dec-2-ene
Subject: Maths
The slope and \( y \) -intercept of the
following line are respectively
\( \mathbf{5} \boldsymbol{x}-\mathbf{8} \boldsymbol{y}=-\mathbf{2} \)
A \( \cdot \) slope \( =m=-\frac{5}{8} \) and \( y \) -intercept \( =\frac{1}{4} \)
B. slope \( =m=\frac{5}{8} \) and \( y \) -intercept \( =-\frac{1}{4} \)
c. slope \( =m=-\frac{5}{8} \) and \( y \) -intercept \( =-\frac{1}{4} \)
D. slope \( =m=\frac{5}{8} \) and \( y \) -intercept \( =\frac{1}{4} \)
Subject: Physics
Taking the wavelength of first Balmer line in hydrogen spectrum \( (n=3 \) to \( \boldsymbol{n}=2) \) as \( 660 n m, \) the wavelength of the
2nd Balmer line \( (n=4 \text { to } n=2) \) will be:
\( \mathbf{A} \cdot 889.2 n m \)
B. \( 642.7 n m \)
\( \mathbf{c} .488 .9 n m \)
D. \( 388.9 n m \)
Subject: Chemistry
An aqueous solution of a non-volatile
solute boils as \( 100.17^{\circ} \mathrm{C} \). What is the
depression in the freezing point for the
solution in \( ^{\circ} \mathrm{C} \) ?
\( \left[K_{b} \text { and } K_{f} \text { for water is } 0.512 \) and \right.
\( \mathbf{1 . 8 6}^{\circ} \boldsymbol{C} / \boldsymbol{m} \) respectively
A . 0.93
B. 0.11
\( c \cdot 0.62 \)
D. 0.31
Subject: Physics
Four point charges, each of \( +q, \) are rigidly fixed at the four corners of a square planar soap film of side \( a \). The
surface tension of the soap film is \( \gamma \) The system of charges and planar film are in equilibrium, and \( \boldsymbol{a}=\boldsymbol{k}\left[\frac{\boldsymbol{q}^{2}}{\gamma}\right]^{1 / N}, \) where
\( k^{\prime} \) is a constant. Then \( N \) is:
\( A \cdot 3 \)
B. 2
\( c \cdot 4 \)
\( D \)
Subject: Maths
Derivative of which function is \( \boldsymbol{f}^{\prime}(\boldsymbol{x})= \)
\( x \sin x ? \)
This question has multiple correct options
A. \( x \sin x+\cos x \)
B. \( x \cos x+\sin x \)
c. \( x \sin \left(\frac{\pi}{2}-x\right)+\cos \left(\frac{\pi}{2}-x\right) \)
D. \( x \cos \left(\frac{\pi}{2}-x\right)+\sin \left(\frac{\pi}{2}-x\right) \)
Subject: Chemistry
Limiting molar conductivity of NaBr is:
\( \mathbf{A} \cdot \Lambda_{m}^{o} N a B r=\Lambda_{m}^{o} N a C l+\Lambda_{m}^{o} K B r \)
B. \( \Lambda_{m}^{o} N a B r=\Lambda_{m}^{o} N a C l+\Lambda_{m}^{o} K B r-\Lambda_{m}^{o} K C l \)
\( \mathbf{C} \cdot \Lambda_{m}^{o} N a B r=\Lambda_{m}^{o} N a O H+\Lambda_{m}^{o} N a B r-\Lambda_{m}^{o} N a C l \)
\( \mathbf{D} \cdot \Lambda_{m}^{o} N a B r=\Lambda_{m}^{o} N a C l-\Lambda_{m}^{o} N a B r \)
Subject: Physics
The mass of the earth is \( 6 \times 10^{24} \mathrm{kg} \) and
that of the moon is \( 7.4 \times 10^{22} \mathrm{kg} \)
distance between the earth and the
moon be \( 3.84 \times 10^{5} \mathrm{km}, \) calculate the
force exerted by the earth moon. \( (G= \) \( \left.6.7 \times 10^{-11} N m^{2} k g^{-2}\right) \)
Subject: Biology
With respect to Eichorrnia:
Statement \( X: \) It drains off oxygen from
water and is seen growing in standing
water.
Statement Y : It is an indigenous species of our country.
A. Both statements \( x \) and \( Y \) are correct
B. Both statements X and Y are wrong
c. only statement \( x \) is correct and \( Y \) is wrong
D. only statement Y is correct and X is wrong
Subject: Maths
A man 2 metres high walks at a uniform speed of \( 6 \mathrm{km} / \mathrm{h} \) away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases. (in
\( \boldsymbol{k} \boldsymbol{m} / \boldsymbol{h} \boldsymbol{r}) \)
Subject: Chemistry
a) A solution containing \( 18 g \) of nonvolatile non-electrolyte solute is dissolved in 200 g of water freezes at 272.07 K. Calculate the molecular mass
of the solute.
Given \( : \boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6} \mathrm{K} \mathrm{kg} / \mathrm{mol} \)
The freezing point of water \( =273 \mathrm{K} \)
b) Define the isotonic solution. What
happens when the blood cell is dipped in a solution containing more than normal saline concentration?
Subject: Maths
Three collinear points \( A, B \) and \( C \) ares
such that point \( B \) is between points \( A \) and \( C . \) The distance from \( A \) to \( B \) is 8
more than 4 times the distance from \( B \)
to \( C \) and the distance from \( A \) to \( C \) is 5
times the distance from \( B \) to \( C . \) What is
the distance from \( \boldsymbol{A} \) to \( \boldsymbol{C} \) ?
A .4
B . 20
c. 16
D. 24
Subject: Maths
If the origin is the centroid of the triangle whose vertices are \( \boldsymbol{A}(\mathbf{2}, \boldsymbol{p},-\mathbf{3}), \boldsymbol{B}(\boldsymbol{q},-\mathbf{2}, \mathbf{5}) \) and \( \boldsymbol{R}(-\mathbf{5}, \mathbf{1}, \boldsymbol{r}) \)
then find the values of \( \boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r} \)
Subject: Maths
ff \( (x)=x+\sin x ; g(x)=e^{-x} ; u= \)
\( \sqrt{\boldsymbol{c}+\mathbf{1}}-\sqrt{\boldsymbol{c}} ; \boldsymbol{v}=\sqrt{\boldsymbol{c}}-\sqrt{\boldsymbol{c}-\mathbf{1}} ;(\boldsymbol{c}>\mathbf{1}) \)
A \( . f o g(u) \geq f o g(v) \)
B. \( f o g(u) \leq f o g(v) \)
\( \mathbf{c} . f o g(u)>f o g(v) \)
D. \( f o g(u)<f o g(v) \)
Subject: Chemistry
What property of hydrogen chloride is demonstrated when it is collected by downward delivery. upward displacement].
A. Hydrogen chloride is highly reactive in nature and it has great affinity for water
B. Hydrogen chloride is less reactive in nature and it has great affinity for water
c. Hydrogen chloride is highly reactive in nature and it has low affinity for water
D. Hydrogen chloride is less reactive in nature and it has low affinity for water
Subject: Maths
\( \operatorname{Solve}\left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{p}-\boldsymbol{q} & \boldsymbol{p}-\boldsymbol{r} \\ \boldsymbol{q}-\boldsymbol{p} & \boldsymbol{0} & \boldsymbol{q}-\boldsymbol{r} \\ \boldsymbol{r}-\boldsymbol{p} & \boldsymbol{r}-\boldsymbol{q} & \boldsymbol{0}\end{array}\right|= \)
\( \mathbf{A} \cdot p+q+r \)
в. \( p q+q r+r p \)
\( c \cdot c \)
D. \( p^{2}+q^{2}+r^{2} \)
Subject: Chemistry
\( \operatorname{Gas}(\boldsymbol{A})+\boldsymbol{N a O H} \rightarrow \boldsymbol{B} \stackrel{\boldsymbol{A}^{+}}{\rightarrow} \boldsymbol{C} \stackrel{\boldsymbol{H}^{+}}{\rightarrow} \boldsymbol{D} \)
\( C \) and \( D \) decolorises acidified \( K M n O_{4} \) Identify \( C \) and \( D \)
A \( \cdot N a_{2} C O_{3}, N a O H \)
в. \( (C O O H)_{2},(C O O N a)_{2} \)
c. \( (C O O N a)_{2},(C O O H)_{2} \)
D. None of the above
Subject: Maths
The number of points at which the function \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{0 . 5}|+|\boldsymbol{x}-\mathbf{1}|+ \)
\( \tan x \) does not have a derivative in the
interval (0,2) is/are?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.
Subject: Maths
If \( y=e^{\left(x^{2}+2 \sin x\right)}, \) then \( \frac{d y}{d x} i s \)
\( \mathbf{A} \cdot e^{\left(x^{2}-2 \sin x\right)} \)
\( \mathbf{B} \cdot e^{\left(x^{2}+2 \sin x\right)} \times(2 x+2 \sin x) \)
C \( \cdot e^{\left(x^{2}+2 \sin x\right)} \times(2 x+2 \cos x) \)
\( \mathbf{D} \cdot e^{x} \)
Subject: Chemistry
How much time will it take for a
uniform current of \( 6.00 \mathrm{A} \) to deposit \( 78 \mathrm{g} \)
of gold from a solution of \( A u C l_{4}^{-} ? \) What mass of chlorine gas will be
formed simultaneously at the anode of the cell?
(Atomic mass of \( A u=197 \) )
A \( \cdot t=3010 \sec , w=35.50 g \)
B. \( t=20306 \sec , w=45.54 g \)
c. \( t=19500 \) sec \( , w=54.5 g \)
D. \( t=19139.16 \sec , w=42.24 g \)
Subject: Chemistry
The IUPAC name for the complex
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\right] \boldsymbol{C l} 2 ? \)
A. nitrito-N-pentamminecobalt
(III) chloride
(II) chlorid
B. nitrito-N-pentamminecobalt
c. pentammienenitrito-N-cobalt (II) chloride
D. none
Subject: Physics
A ball is dropped from a great height and the velocity of the ball as a function of time is given \( \boldsymbol{v}=\frac{\boldsymbol{m} \boldsymbol{g}}{\boldsymbol{K}}\left(\boldsymbol{1}-\boldsymbol{e}^{-(\boldsymbol{K} / \boldsymbol{m}) t}\right) \)
where \( m \) is mass of ball, \( K \) is a
constant and \( g \) is the acceleration due to gravity. Then, at a time when \( t \gg \) \( (\boldsymbol{m} / \boldsymbol{K}), \) the velocity of the ball becomes
A. \( v=g t \)
в. \( _{v}=\frac{m g}{K} \)
c. \( v=\frac{m g}{K} \)
D. \( v=0 \)
Subject: Biology
Assertion
Time taken for the completion of mitotic phase is \( 5-10 \% \) of the total cell cycle.
Reason
It is the shorter than the interphase.
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 radius of the orbit of a hydrogen atom is 0.85 nm. The velocity of an electron in this orbit is:
A \( .5 .44 \times 10^{5} \mathrm{m} / \mathrm{s} \)
В. \( 5.62 \times 10^{5} \mathrm{m} / \mathrm{s} \)
c. \( 5.48 \times 10^{5} \mathrm{m} / \mathrm{s} \)
D. \( 5.67 \times 10^{5} \mathrm{m} / \mathrm{s} \)
Subject: Physics
A hollow chaeged mental sphere has radius \( r . \) if the potential difference between its surface and a point at a distance \( 3 r \) from the center is 'v' then
electric field intensity at a distance 3 r
is
A \( \cdot \frac{v}{2 r} \)
B. \( \frac{v}{3 r} \)
c. \( \frac{v}{6 r} \)
D. \( \frac{v}{4 r} \)
Subject: Maths
A signal which can be green or red with probability \( \frac{4}{5} \) and \( \frac{1}{5}, \) respectively, is received at station \( A \) and then
transmitted to station B. The probability of each station receiving the signal correctly is \( \frac{3}{4} . \) If the signal received at station B is green, then the probability that the original signal was green is
\( A \cdot \frac{3}{5} \)
B. \( \frac{6}{7} \)
c. \( \frac{20}{23} \)
D. \( \frac{9}{20} \)