AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
In the relation, \( \boldsymbol{p}=\frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \boldsymbol{e}^{-} \frac{\boldsymbol{\alpha} \boldsymbol{Z}}{\boldsymbol{k} \boldsymbol{\theta}} \)
\( P \) is pressure, \( Z \) is distance, \( k \) is
Boltzmann's constant and \( \theta \) is the
temperature. The dimensional formula
of \( \boldsymbol{\alpha} \) will be:
\( \mathbf{A} \cdot\left[M L T^{-2}\right] \)
B \( \cdot\left[M L^{2} T\right] \)
\( \mathbf{c} \cdot\left[M L^{0} T^{-1}\right] \)
D \cdot \( \left[M^{0} L^{2} T^{-1}\right] \)
Subject: Maths
ff \( f(x)=\left\{\begin{array}{lll}\frac{e^{3 x}-1}{4 x} & \text { for } & x \neq 0 \\ \frac{k+x}{4} & \text { for } & x=0\end{array}\right. \)
continuous at \( x=0, \) then \( k= \)
\( A \cdot \)
B. 3
\( c \cdot 2 \)
\( D \)
Subject: Maths
The largest possible square is inscribed
in a circle of circumference \( 2 \pi \) units.
The area of the square in square units
is
\( \mathbf{A} \cdot 4 \pi \sqrt{2} \)
В. \( 2 \pi \sqrt{2} \)
\( c \cdot \sqrt{2} \)
\( D \)
Subject: Maths
Let \( A \) and \( B \) be two sets such that \( A \times \)
\( B \) consists of 6 elements.lf three
elements of \( \boldsymbol{A} \times \boldsymbol{B} \) are
\( \{(1,4),(2,6),(3,6)\} . \) Find \( A \times B \) and
\( \boldsymbol{B} \times \boldsymbol{A} \)
Subject: Maths
In the given figure, \( P \) is the center of the
circle. The area and perimeter
respectively, of the figure are
A \( \cdot 3256 c m^{2}, 234.2 c m \)
B. \( 2492 \mathrm{cm}^{2}, 229.2 \mathrm{cm} \)
\( \mathbf{c} \cdot 2942 c m^{2}, 234.2 \mathrm{cm} \)
D. \( 3256 c m^{2}, 229.2 c m \)
Subject: Physics
A ball after falling a distance of 5 meter
from rest hits floor of a lift and
rebounds. At the time of impact the lift was moving up with a velocity of 1 \( m / \) sec. The velocity with which the ball rebounds just after impact is- \( (g= \) \( \mathbf{1 0} \boldsymbol{m} / \boldsymbol{s e c}^{2} \)
A. \( 10 \mathrm{m} / \mathrm{sec} \)
B. \( 11 \mathrm{m} / \mathrm{sec} \)
c. \( 12 \mathrm{m} / \mathrm{sec} \)
D. \( 13 \mathrm{m} / \mathrm{sec} \)
Subject: Maths
If \( f(x)=\frac{2 x+1}{2 x^{3}+3 x^{2}+x} \) and
\( \{S=x: f(x)>0\} \) then \( S \)
\( A \cdot(-\infty,-3 / 2) \)
B . \( (-3 / 2,-1 / 4) \)
c. \( (-1 / 4,1 / 2) \)
D \( \cdot(-1 / 2,3) \)
Subject: Chemistry
The dissociation of \( N_{2} O_{4} \) takes place
as per the equation \( N_{2} O_{4}(g) \Leftrightarrow \)
\( 2 N O_{2}(g) . N_{2} O_{4} \) is \( 20 \% \) dissociated
while, the equilibrium pressure of mixture is \( 600 \mathrm{mm} \) of Hg. Calculate
\( K_{p} \) assuming the volume to be
constant.
A . 50
B. 100
\( c \cdot 166.8 \)
D. 600
Subject: Physics
An object shaped as a hemisphere rests with its flat surface on a table. The
object has radius \( r \) and density \( \rho \) The volume of a sphere is \( \frac{4}{3} \pi r^{3} \) Which average pressure does the object exert on the table?
\( A \)
B.
c. \( \frac{2}{3} \rho r \)
D. \( \frac{2}{3} \rho r g \)
Subject: Physics
In Young's double-slit experiment, the angular width of a fringe formed on
a distant screen is \( 1^{\circ} . \) The slit
separation is \( 0.01 \mathrm{mm} . \) The wavelength of the light is
A. \( 0.174 \mathrm{nm} \)
в. 0.174 А
c. \( 0.174 \mu m \)
D. \( 0.174 \times 10^{-4} \mathrm{m} \)
Subject: Maths
The image of the point (3,-1,11) w.r.t
the line \( \frac{\boldsymbol{x}}{\mathbf{2}}=\frac{\boldsymbol{y}-\boldsymbol{2}}{\boldsymbol{3}}=\frac{\boldsymbol{z}-\boldsymbol{3}}{\boldsymbol{4}} \) is
Subject: Maths
The expression \( 32 x^{3}+108 y^{3} \) can be
expressed in factor as
A \( \cdot(4 x+3 y)\left(4 x^{2}-6 x y+9 y^{2}\right) \)
B . \( (4 x-3 y)\left(4 x^{2}+6 x y+9 y^{2}\right) \)
C \( \cdot(4 x+3 y)\left(4 x^{2}+6 x y+9 y^{2}\right) \)
D. None of these
Subject: Physics
Figure shows a wheatstone bridge circuit.
Which of the following correctly shows
the currents \( I_{1}, I_{2} \) and \( I_{3} \) in the correct
decreasing order of magnitude?
\( \mathbf{A} \cdot I_{1}, I_{2}, I_{3} \)
B \( \cdot I_{2}, I_{3}, I_{1} \)
\( \mathbf{c} \cdot I_{2}, I_{1}, I_{3} \)
D. \( I_{3}, I_{2}, I_{1} \)
Subject: Maths
Given that \( 0 \leq x \leq \frac{1}{2} \) the value of
\( \tan \left[\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\sqrt{\frac{1-x^{2}}{2}}\right)-\sin ^{-1} x\right. \)
is
\( A \)
B.
\( c \cdot 1 \sqrt{3} \)
D. \( \sqrt{3} \)
Subject: Maths
If \( \boldsymbol{A}=\left\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x}^{2}-\mathbf{5}|\boldsymbol{x}|+\boldsymbol{6}=\mathbf{0}\right\} \)
\( \operatorname{then} n(A)= \)
\( A \cdot 2 \)
B.
\( c \cdot 1 \)
D.
Subject: Physics
Assertion : If the amplitude of a simple harmonic oscillator is doubled, its total
energy becomes double. Reason : The total energy is directly proportional to the amplitude of vibration of the harmonic oscillator.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false
Subject: Maths
In the binomial expansion of \( (a- \)
\( b)^{n}, n \geq 5, \) the sum of
5 th and 6 th terms is zero then a/b equal
to
A \( \cdot \frac{5}{n-4} \)
B. \( \frac{6}{n-5} \)
c. \( \frac{n-5}{6} \)
D. \( \frac{n-4}{5} \)
Subject: Maths
ff \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are given by
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}] \) for each \( \boldsymbol{x} \in \)
\( R, \) then
\( \{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{g}(\boldsymbol{f}(\boldsymbol{x})) \leq \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))\}= \)
A \( \cdot Z \cup(-\infty, 0) \)
В \( \cdot(-\infty, 0) \)
\( c . z \)
D. \( R \)
Subject: Maths
Four persons can hit a target correctly with probabilities \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \) and \( \frac{1}{8} \) respectively. If all hit at the target independently, then the probability that the target would be hit, is?
A \( \cdot \frac{25}{192} \)
в. \( \frac{1}{192} \)
c. \( \frac{25}{32} \)
D. \( \frac{7}{32} \)
Subject: Maths
Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) A player attempts to shoot a basketball. She/he shoots or misses the
shot
(iii) \( A \) trial is made to answer a true-
false question. The answer is right or
wrong.
(iv) A baby is born. It is a boy or a girl
Subject: Maths
A random variable \( X \) has the following probability distribution:
\[
\begin{array}{lllll}
\boldsymbol{X} & 0 & 1 & 2 & 3 \\
P(X= & \frac{1}{4} & 2 a & 3 a & 4 a
\end{array}
\]
Then \( P(1 \leq X \leq 4) \) is:
A. \( \frac{10}{21} \)
в.
c. \( \frac{1}{14} \)
D.
Subject: Maths
If \( \boldsymbol{d} \boldsymbol{x}+\boldsymbol{d} \boldsymbol{y}=(\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{d} \boldsymbol{x}-\boldsymbol{d} \boldsymbol{y}) \Rightarrow \boldsymbol{y}+ \)
\( \log (x+y)=x+C \) is the solution of
differential equation
Subject: Physics
A cube has a side \( l=1.2 \times 10^{-2} \mathrm{m} \)
Calculate its volume \( \left(\operatorname{in} m^{3}\right) \)
A \( \cdot 1.7 \times 10^{-6} \)
В. \( 1.728 \times 10^{-6} \)
c. \( 1.8 \times 10^{-6} \)
D. \( 2 \times 10^{-6} \)
Subject: Maths
\( f\left(a_{1}, a_{2}, a_{3}, \dots, a_{n-1}, a_{n} \) are in A.P., then \right.
show that \( \frac{1}{a_{1} a_{n}}+\frac{1}{a_{2} a_{n-1}}+\frac{1}{a_{3} a_{n-2}}+ \)
\( \ldots \cdot \frac{1}{a_{n} a_{1}}= \)
\( \frac{2}{\left(a_{1}+a_{n}\right)}\left[\frac{1}{a_{1}}+\frac{1}{a_{2}}+\dots \frac{1}{a_{n}}\right] \)
Subject: Physics
A metal sphere of diameter \( 7 \mathrm{cm} \) falls
through a liquid of coefficient of viscosity \( 0.8 P a . s . \) When its velocity is
\( 20 c m \cdot s^{-1} \) the viscous force acting on
it is nearly \( -\cdots-N \)
A . 0.11
B. 0.22
\( c .0 .3 \)
D. 0.01
Subject: Physics
Order of \( \frac{1}{8 \times 10^{9}} \) is:
\( \mathbf{A} \cdot 1.77 \times 10^{-10} \)
B \( .1 .25 \times 10^{-10} \)
C \( .1 .55 \times 10^{-10} \)
D. \( 1.95 \times 10^{-10} \)
Subject: Physics
\( 0.8 \mathrm{J} \) work is done in rotating a magnet
by \( 60^{\circ}, \) placed parallel to a uniform
magnetic field. How much work is done
in rotating it \( 30^{\circ} \) further?
A \( \cdot 0.8 \times 10^{7} \) erg
B. \( 0.8 e r g \)
\( c .8 J \)
D. 0.45
Subject: Maths
The equation of the plane which is equidistant from the two parallel planes \( 2 x-2 y+z+3=0 \) and \( 4 x-4 y+ \)
\( \mathbf{2} z+\mathbf{9}=\mathbf{0} \) is :
A. \( 8 x-8 y+2 z+15=0 \)
B. \( 8 x-8 y+4 z+15=0 \)
c. \( 8 x-8 y+4 z+3=0 \)
D. \( 8 x-8 y+4 z-3=0 \)
E \( .8 x-8 y+4 z+4=0 \)
Subject: Maths
What is \( i^{1000}+i^{1001}+i^{1002}+i^{1003} \) equal
to (where \( \boldsymbol{i}=\sqrt{-1} \) )?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-i \)
\( D \)
Subject: Physics
An object placed from a lens produces a virtual image at distance of \( 5 \mathrm{cm} \) in
front of the lens. Calculate the focal
length of lens.
A \( .6 .25 \mathrm{cm} \)
B. \( 0.16 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. None
Subject: Maths
If both roots of the equation \( a x^{2}+ \) \( 2 x a+1+a^{2}-16=0 \) are opposite in
\( \operatorname{sign}, \) then the range of \( a \) is
\( A \cdot(-\infty,-4) \cup(4, \infty) \)
B . (-4,4)
\( \mathbf{c} \cdot(-\infty,-4) \cup(0,4) \)
D \( \cdot(0,4) \)
Subject: Maths
\( \int \frac{\sqrt{\cot x}-\sqrt{\tan x}}{\sqrt{2}(\cos x+\sin x)} d x \) equals to
A \( \cdot \sec ^{-1}(\sin x+\cos x)+c \)
B. \( \sec ^{-1}(\sin x-\cos x)+c \)
c. \( \ln |(\sin x+\cos x)+\sqrt{\sin 2 x}|+c \)
D. \( \ln |(\sin x-\cos x)+\sqrt{\sin 2 x}|+c \)
Subject: Chemistry
Which one of the following ions is the most stable in aqueous solution?
\( [A t . \text { no.; } T i=22, V-23, C r=24 ; M n=25] \)
A \( \cdot C r^{3} \)
в. \( V^{3} \)
\( \mathrm{c} \cdot T i^{3} \)
\( \mathbf{D} \cdot M n^{3} \)
Subject: Physics
Which of the following is correct?
A. There are 78 neutrons in \( 78 P t^{192} \)
B \( \cdot_{84} P o^{214} \rightarrow_{82} P b^{210}+\beta \)
\( \mathbf{c} \cdot_{92} U^{238} \rightarrow_{90} T h^{234}+_{2} H e^{4} \)
D・ \( _{90} T h^{234} \rightarrow_{91} P a^{234}+_{2} H e^{4} \)
Subject: Maths
If \( \boldsymbol{E} \) and \( \boldsymbol{F} \) be events in a sample space
such that \( \boldsymbol{P}(\boldsymbol{E} \cup \boldsymbol{F})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F})= \)
0.3 and \( P(E)=0.5, \) then \( P(F) \) is
A . 0.6
B.
\( c .0 .8 \)
D. None
Subject: Maths
\( \int_{\alpha}^{\beta} \sqrt{(x-\alpha)(\beta-x)} d x \) equals
A \( \cdot \frac{\pi}{2}(\beta-\alpha) \)
В \( \cdot \frac{\pi}{8}(\beta-\alpha) \)
c. \( \frac{\pi}{8}(\beta-\alpha)^{2} \)
D. None of these
Subject: Chemistry
After doing experiment, it is found that
a saturated solution of \( B a S O_{4} \) at \( 25^{\circ} \mathrm{C} \)
contains \( 3.9 \times 10^{-5} \) mole / liter of \( B a^{2+} \)
ion. What is the value of \( K_{s p} \) of the
\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A \( .1 .5 \times 10^{-4} \)
В. \( 1.5 \times 10^{-9} \)
c. \( 1.5 \times 10^{-10} \)
D. \( 3.9 \times 10^{-10} \)
E \( .39 \times 10^{-9} \)
Subject: Chemistry
\( H-C-H \) bond angle in ethene and
ethane are \( _{-}-_{-}-_{-}- \) respectively
\( \mathbf{A} \cdot 120^{0} \) and \( 109.5^{0} \)
B. \( 180^{\circ} \) and \( 109.5^{\circ} \)
C . \( 109.5^{\circ} \) and \( 120^{\circ} \)
D. \( 120^{\circ} \) and \( 180^{\circ} \)
Subject: Chemistry
If \( 0.01 M \) solution of an electrolyte has a
resistance of 40 ohms in a cell having a cell constant \( 0.4 \mathrm{cm}^{-1} \) then its molar
conductance would be:
A \( \cdot 10^{4} \)
B . \( 10^{3} \)
\( c \cdot 10^{2} \)
D. 10
Subject: Maths
In an experiment with 15 observations the following results were available \( \sum x^{2}=2830, \quad \sum x=170 . \) One
observation that was 20 was found
wrong and was replaced by the correct value \( 30 . \) The corrected variance is
A . 8.33
B. 78.00
c. 188.66
D. 177.33
Subject: Chemistry
The number of hydrogen bonds formed
by a molecule each of \( \mathrm{H}_{2} \mathrm{O}, \mathrm{HF} \) and \( \mathrm{NH}_{3} \)
respectively are :
\( \mathbf{A} \cdot 2,2,3 \)
B. 4,2,3
c. 2,1,3
D. 4,4,3
Subject: Chemistry
"In moist air, copper corrodes to
produce a green layer on the surface". For this, the reaction is :
\( \boldsymbol{C u}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C O}_{2}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{C u} \boldsymbol{C O}_{3} \)
\( \boldsymbol{C u}(\boldsymbol{O} \boldsymbol{H})_{2} \)
If the statement is true enter 1 else
enter 0
Subject: Chemistry
Which of the following does not give ppt with \( \boldsymbol{C r} \boldsymbol{O}_{4}^{-2} \)
A \( \cdot C a^{+} \)
B. \( S r^{+} \)
\( c \cdot P b^{+2} \)
D. \( B a^{+2} \)
Subject: Physics
A plane mirror is placed along the \( x \)
axis facing negative y-axis. The mirror is fixed. A point object is moving with \( 3 \hat{i}+4 \hat{j} \) in front of the plane mirror. The
relative velocity of image with respect
to its object is
\( A \cdot-8 \hat{j} \)
B. \( 8 \hat{j} \)
c. \( 3 \hat{i}-4 \hat{j} \)
D. \( -6 \hat{i} \)
Subject: Physics
If a cathode ray tube has a potentia
difference \( V \) volt between the cathode
and anode, then the speed \( v \) of cathode
rays is given by:
A \( \cdot v \propto V^{2} \)
В. \( v \propto \sqrt{V} \)
\( ^{\mathrm{c}} \cdot_{v} \propto \frac{1}{V} \)
D. \( v \propto V \)
Subject: Physics
The difference between the wavelengths of the Stokes line and Anti-Stokes lines
in the Raman spectrum of \( \boldsymbol{H}-\boldsymbol{B} \boldsymbol{r} \)
molecule is \( 100 \dot{A} \). If the wavelength of the Anti-Stokes line is \( 5000 A \) the
wavelength of the incident radiation is:
В . \( 4950 \AA \)
c. \( 5100 \hat{h} \)
D. 4900 音
Subject: Chemistry
The specific conductance of a \( N / 10 \mathrm{KC} \)
solution at \( 18^{\circ} \mathrm{C} \) is \( 1.12 \times \)
\( 10^{-2} \) mho \( c m^{-1} . \) The resistance of the
solution contained in the cell is found to
be 65 ohms. Calculate the cell constant.
A \( \cdot 0.728 \mathrm{cm}^{-1} \)
B. \( 0.928 \mathrm{cm}^{-1} \)
c. \( 0.428 \mathrm{cm}^{-1} \)
D. \( 0.328 \mathrm{cm}^{-1} \)
Subject: Physics
Two rods \( A \) and \( B \). each of equal length
but different materials are suspended from a common support as shown in the figure. The roads \( A \) and \( B \) can support a
maximum load of \( W_{1}=600 \mathrm{N} \) and \( W_{2}= \) \( 6000 \mathrm{N}, \) respectively. If their cross-
sectional areas are \( A_{1}=10 m m^{2} \) and \( A_{2} \)
\( =1000 m m^{2}, \) respectively, then identify the stronger material.
Subject: Chemistry
Emf of the cell
\( \boldsymbol{P t . H}_{2}(\boldsymbol{1} \boldsymbol{a t m})\left|\boldsymbol{H}^{+}(\boldsymbol{a q} \cdot) \| \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}\right| \boldsymbol{A} \boldsymbol{g} \) is
\( 0.27 V \) and \( 0.26 V \) at \( 25^{\circ} C \) and \( 35^{\circ} C \)
Heat of reaction occuring inside the cell
\( \operatorname{at} 25^{\circ} \mathrm{C} \) is:
A \( .-54.8 k J \)
B . \( 26.05 k J \)
c. \( -26.05 k J \)
D. \( +54.8 k J \)
Subject: Chemistry
Indicate the correct statements.
This question has multiple correct options
A. Conductivity cells have cell constant values independent of the solution filled into the cell
B. DC (direct current) is not used for measuring the resistance of a solution
C. Kohlrausch law is valid both for strong and weak electrolytes
D. The k decreases but \( \lambda_{M} \) and \( \lambda_{E} \) increase on dilution
Subject: Physics
A ladder \( A B, 2.5 m \) long and of weight \( 150 N \) has its centre of gravity \( 1 m \) from \( A \) is lying flat on ground. \( A \) weight
of \( 40 N \) is attached to the end \( B \). The
work required (in joule) to raise the ladder from the horizontal position to vertical position so that the bottom end \( A \) is resting in a ditch 1 m below the ground level will be :
A . 60
B. 30
c. 20
D. 120
Subject: Physics
A thin brass sheet at \( 10^{\circ} C \) and thin
steel sheet at \( 20^{\circ} C \) have the same
surface area.The common temperature at which both would have the same area (Coefficient of linear expansion for
brass and steel are respectively \( 19 \times \)
\( \left.10^{-6} /^{\circ} \mathrm{C} \text { and } 11 \times 10^{-6} /^{\circ} \mathrm{C} .\right) \)
\( \mathbf{A} \cdot-3.75^{\circ} \mathrm{C} \)
B . \( -2.75^{\circ} \mathrm{C} \)
c. \( 2.75^{\circ} \mathrm{C} \)
D. \( 3.75^{\circ} \mathrm{C} \)
Subject: Maths
In figure \( 26, \overline{R T} \) is a diameter of the
semicircle. If \( \mathrm{RS}=2 \) and \( \mathrm{ST}=3, \) then the
area of the semicircle is
\( A \cdot \frac{13 \pi}{2} \)
B. \( \frac{13 \pi \pi}{4 \pi} \)
\( \mathbf{c} \cdot \frac{13 \pi}{6} \)
\( \mathbf{D} \cdot \frac{13 \pi}{8} \)
E. cannot be determined from the information given
Subject: Physics
A 10 m long potentiometer wire is
connected to a battery having a steady voltage. A Leclanche cell is balanced at
\( 4 m \) length of the wire. If the length is kept the same, but its cross-section is doubled, the null point will be obtained
at:
\( \mathbf{A} \cdot 8 m \)
в. \( 4 m \)
c. \( 2 m \)
D. None of these
Subject: Maths
Sum of all the values of \( x \) in the interval
\( [0,100 \pi] \) satisfying the equation
\( \sin x=0 \) is
\( \mathbf{A} \cdot 4950 \pi \)
B. \( 5050 \pi \)
c. \( 5151 \pi \)
D. none of these
Subject: Physics
The change in the value of \( g \) at a height
\( h \) above the surface of earth is the same
as at a depth \( d \) below the earth. When
both \( d \) and \( h \) are much smaller than the
radius of earth, then which one of the
following is correct?
\( ^{A} \cdot_{d}=\frac{h}{2} \)
B. \( d=\frac{3 h}{2} \)
c. \( d=2 h \)
\( \mathbf{D} \cdot d=h \)
Subject: Chemistry
In the reaction:
\( \mathbf{2} C O(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{C} \boldsymbol{O}(\boldsymbol{g}) \)
entropy_ -
A. decreases
B. increases
c. constant
D. none
Subject: Maths
Express \( \overrightarrow{A B} \) in terms of unit vectors \( \hat{i} \) and \( \hat{j}, \) when the points are:
\( A(4,-1), B(1,3) \)
Find \( |\overrightarrow{A B}| \) in each case.
A \( \cdot \overrightarrow{A B}=-3 \hat{i}-4 \hat{j},|\overrightarrow{A B}|=5 \)
B・方 \( =+3 \hat{i}+4 \hat{j},|A \vec{B}|=5 \)
c. \( \overrightarrow{A B}=-3 \hat{i}+4 \hat{j},|\overrightarrow{A B}|=5 \)
D. none of these
Subject: Maths
The equation of the circle, passing through the point \( (2,8), \) touching the \( \operatorname{lines} 4 x-3 y-24=0 \) and \( 4 x-3 y- \)
\( 42=0 \) and having \( x \) coordinate of the
center of the circle numerically less
then or equal to 8 , is
A \( \cdot x^{2}+y^{2}+4 x-6 y-12=0 \)
B. \( x^{2}+y^{2}-4 x+6 y-12=0 \)
C \( \cdot x^{2}+y^{2}-4 x-6 y-12=0 \)
D. None of these
Subject: Maths
Discuss the continuity of the following function at the indicated point(s):
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}
\frac{\boldsymbol{e}^{\boldsymbol{x}}-\mathbf{1}}{\log (\mathbf{1}+\mathbf{2} \boldsymbol{x})}, \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \neq \mathbf{0} \\
\boldsymbol{7}, \boldsymbol{i} \boldsymbol{f} \quad \boldsymbol{x}=\mathbf{0}
\end{array}\right.
\]
\( \boldsymbol{x}=\mathbf{0} \)
Subject: Chemistry
The haemoglobin from red corpuscles of most mammals contains
approximately \( 0.33 \% \) of iron by weight. The molecular weight of haemoglobin is \( 67,200 . \) The number of iron atoms in
each molecule of haemoglobin is :
A . 1
B. 2
\( c \cdot 3 \)
\( D \)
Subject: Chemistry
toppr
Q Type your question-
(i) \( \left.M_{(s)}+\frac{1}{2} O_{2(g)} \rightarrow M O_{(} s\right) \)
(ii) \( \frac{1}{2} C_{(s)}+\frac{1}{2} O_{2(g)} \rightarrow \frac{1}{2} C O_{2(g)} \)
(iii) \( C_{(s)}+\frac{1}{2} O_{2(g)} \rightarrow C O_{(g)} \)
\( \left(\text { iii) } C O_{(g)}+\frac{1}{2} O_{2(g)} \rightarrow C O_{2(g)}\right. \)
The temperature dependence of \( \Delta \) G of reaction (i) to (iv) is shown in the given
diagram. This is known as the Ellingham diagram. With the help of the Ellingham diagram, one can easily predict the most suitable reducing agent for the reduction of metal oxides.
\( A I_{2} O_{3} \) can be reduced by carbon at a
temperature of
\( A \cdot 30^{\circ} \mathrm{C} \)
B \( .500^{\circ} \mathrm{C} \)
\( \mathrm{D} \cdot>2500^{\circ} \mathrm{C} \)
Subject: Maths
\( \operatorname{Let} A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right] \) and \( 10 B= \)
\( \left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right] . \) If \( B \) is the inverse of
matrix \( A \), then \( \alpha \) is
\( A \)
в.
\( c \cdot 2 \)
\( D \)
Subject: Maths
A brass tray is in the shape of a parallelogram was polished at a total \( \operatorname{cost} \) pf \( R s 2250 \) at the rate of

Rs 2 per \( 10 \mathrm{cm}^{2} \). If the altitude of the
parallelogram is \( 45 \mathrm{cm}, \) find the length of its base.
Subject: Chemistry
Strongest hydrogen bond is present in:
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( C H C l_{3} \)
\( \mathbf{c} \cdot\left[C H_{3}\right]_{2} C H O H \)
D. \( \left[C H_{3}\right]_{3} C O H \)
Subject: Maths
A telephone company charges \( x \) cents for the first minute of a call and charges for any additional time at the rate of \( y \) cents per minute. If a certain call costs \( \$ 5.55 \) and lasts more than 1 minute, which of the following expressions represents the length of that call, in minutes?
\( ^{\text {A. }} \frac{555-x}{y} \)
B. \( \frac{555+x-y}{y} \)
c. \( \frac{555-x+y}{y} \)
D. \( \frac{555-x-y}{y} \)
E \( \frac{555}{x+y} \)
Subject: Maths
Solve \( 4 \cos \theta-3 \sec \theta=\tan \theta \)
A \( \cdot \theta=n \pi+(-1)^{n} \alpha, \theta=n \pi+(-1)^{n} \beta \)
B \( \cdot \theta=n \pi+(-1)^{n} \alpha, \theta=n \pi+(-1)^{n} 2 \beta \)
c. \( _{\theta=n \pi+(-1)^{n}} \alpha, \theta=n \pi+(-1)^{n} 3 \beta \)
D. \( \theta=n \pi+(-1)^{n} \alpha, \theta=n \pi+(-1)^{n} 4 \beta \)
Subject: Chemistry
Basic strength of the given compound is in order of:
(i) \( \boldsymbol{C H}_{3} \overline{\boldsymbol{C}} \boldsymbol{H}_{2} \)
(ii) \( \boldsymbol{H}_{2} \boldsymbol{C}=\stackrel{\Theta}{\boldsymbol{C}} \boldsymbol{H} \) and
(iii) \( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}^{\ominus} \)
A \( .(i i)>(i)>(i i i) \)
B. \( (i i i)>(i i i)>(i) \)
c. \( (i)>(i i i)>(i i) \)
D. \( (i)>(i i)>(i i i) \)
Subject: Physics
The work done in turning a magnet of magnetic moment \( M \) by an angle of \( 90^{\circ} \)
from the meridian is \( n \) times the
corresponding work done to turn it through an angle of \( 60^{\circ} \) from the
meridian, where \( n \) is given by :
A \( \cdot \frac{1}{2} \)
B. 2
\( c \cdot \frac{1}{4} \)
D.
Subject: Chemistry
When \( N_{2} O_{5} \) is heated at certain
temperature, it dissociates as \( N_{2} O_{5}(g) \rightleftharpoons N_{2} O_{3}(g)+ \)
\( O_{2}(g) ; \quad K_{c}=2.5 . \) At the same time
\( N_{2} O_{3} \) also decomposes as:
\( N_{2} O_{3}(g) \rightleftharpoons N_{2} O+O_{2}(g) . \) If initially
4.0 moles of \( N_{2} O_{5} \) are taken in 1.0 litre
flask and allowed to dissociation,
concentration of \( O_{2} \) at equilibrium is
\( \mathbf{2 . 5} \boldsymbol{M} \)
Equilibrium concentration of \( N_{2} O_{5} \) is:
A. \( 1.0 M \)
в. 1.5 М
c. \( 2.166 M \)
D. \( 1.834 M \)
Subject: Maths
A brass tray in the shape of a parallelogram was polished at a total \( \operatorname{cost} \) of \( \operatorname{Rs} 2,250 \) at the rate of Rs 20 per
\( 10 \mathrm{cm}^{2} . \) If the altitude of the
parallelogram is \( 45 \mathrm{cm}, \) find the length of its base.
Subject: Physics
When brakes are applied to a bus, the
retardation produced is \( 25 \mathrm{cm} \mathrm{s}^{-2} \) and
the bus takes 20 s to stop. Calculate the initial velocity of the bus.
A \( .500 \mathrm{m} \mathrm{s}^{-1} \)
B. \( 5 \mathrm{cm} \) s \( ^{-1} \)
c. \( 5 m s^{-1} \)
D. \( 12.5 \mathrm{m} \mathrm{s}^{-1} \)