AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Which one of the following relations on \( R( \) set of real numbers) is an
equivalence relation
\( \mathbf{A} \cdot a R_{1} b \Leftrightarrow|a|=|b| \)
в. \( a R_{2} b \Leftrightarrow a \geq b \)
\( \mathbf{c} \cdot a R_{3} b \Leftrightarrow a \) divides \( b \)
D \( \cdot a R_{4} b \Leftrightarrow a<b \)
Subject: Maths
Prove that the area of triangle with vertices \( (\boldsymbol{t}, \boldsymbol{t}-\mathbf{2}),(\boldsymbol{t}+\mathbf{2}, \boldsymbol{t}+\mathbf{2}),(\boldsymbol{t}+ \)
\( \mathbf{3}, \boldsymbol{t} \) ) is independent of \( \mathbf{t} \)
Subject: Maths
(Allocation problem) A cooperative
society of farmers has 50 hectare of
land to grow two crops \( X \) and \( Y . \) The
profit from crops \( X \) and \( Y \) per hectare
are estimated at \( R s .10,500 \) and

Rs.9, 000 respectively. To control weeds, a liquid herbicide has to be used for
\( \operatorname{crop} s X \) and \( Y \) at rates of 20 litres and
10 litres per hectare. Further, no more than 800 litres of herbicide should be
used in order to protect fish and wildlife using a pond which collects drainage from this land. How much land should
be allocated to each crop so as to maximise the total profit of the society?
Subject: Chemistry
Assertion
\( P \) orbital is dumb-bell shaped.
Reason
Electron present in p orbital can have any one of the three values of the magnetic quantum number, i.e 0,+1 or
-1
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. Both Assertion and Reason are incorrect
Subject: Maths
Differentiate the following w.r.t. \( x \)
\( \sin x \log x \)
A \( \cdot \frac{\sin x}{x}-\cos x \log x \)
B. \( \frac{\sin x}{x}+\cos x \log x \)
c. \( \frac{\cos x}{x}+\cos x \log x \)
D. \( \frac{\tan x}{x}+\cos x \log x \)
Subject: Maths
The construction of a \( \Delta A B C \) in which
\( B C=6 \mathrm{cm} \) and \( \angle B=50^{\circ}, \) is not
possible when \( (A B-A C) \) is equal to:
A \( .5 .6 \mathrm{cm} \)
в. \( 5 \mathrm{cm} \)
\( c \cdot 6 c m \)
D. \( 4.8 \mathrm{cm} \)
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{1} \)
then the values of \( \boldsymbol{f}^{-}(\mathbf{1 7}) \) and \( \boldsymbol{f}^{-}(-\mathbf{3}) \)
respectively are
\( \mathbf{A} \cdot \phi,\{4,-4\} \)
B \( \cdot\{3,-3\}, \phi \)
\( \mathbf{c} \cdot \phi,\{3,-3\} \)
\( \mathbf{D} \cdot\{4,-4\}, \phi \)
Subject: Maths
Which of the following equations
represents parametrically, parabolic
profile?
\( \mathbf{A} \cdot x=3 \cos t ; y=4 \sin t \)
B \( x^{2}-2=-\cos t ; y=4 \cos ^{2} \frac{t}{2} \)
\( \mathbf{c} \cdot \sqrt{x}=\tan t ; \sqrt{y}=\sec t \)
D. \( x=\sqrt{1-\sin t} ; y=\sin \frac{t}{2}+\cos \frac{t}{2} \)
Subject: Maths
The following table gives the distribution of 45 students across the
different levels of intelligent quotient. Draw the histogram for the data.
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline IQ Level & \( ^{60-70} \) & \( 70-80 \) & \( 80-90 \) & \( 90-100 \) & \( 100-110 \) & \( 110-120 \) & \( 120-130 \) \\
\hline No of Sudents & 2 & 5 & 6 & 10 & 9 & 8 & 5 \\
\hline
\end{tabular}
Subject: Physics
When the plane surface of a planoconvex lens of refractive index 1.5 is
silvered, it behaves like a concave mirror with \( \boldsymbol{f}=\mathbf{3 0} \) cm.When its convex
surface is silvered, it will behave like a
concave mirror of focal length:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 30 \mathrm{cm} \)
D. \( 45 \mathrm{cm} \)
Subject: Maths
toppr
Q Type your question
List I
The value of the determinant
A. \( \quad\left|\begin{array}{lll}x+2 & x+3 & x+5 \\ x+4 & x+6 & x+9 \\ x+8 & x+11 & x+15\end{array}\right| \) is
If one of the roots of the
equation
B. \( \left|\begin{array}{ccc}7 & 6 & x^{2}-13 \\ 2 & x^{2}-13 & 2 \\ x^{2}-13 & 3 & 7\end{array}\right|=0 \)
is \( x+2 \), then the sum of all other
five roots is
The value of
C. \( \quad\left|\begin{array}{ccc}\sqrt{6} & 2 i & 3+\sqrt{6} \\ \sqrt{12} & \sqrt{3}+\sqrt{8} i & 3 \sqrt{2}+\sqrt{6} i \\ \sqrt{18} & \sqrt{2}+\sqrt{12} i & \sqrt{27}+2 i\end{array}\right| \)
If \( f(\theta)= \)
D. \( \quad\left|\begin{array}{ccc}\cos ^{2} \theta & \cos \theta \sin \theta & -\sin \theta \\ \cos \theta \sin \theta & \sin ^{2} \theta & \cos \theta \\ \sin \theta & -\cos \theta & 0\end{array}\right| \)
then \( f(\pi / 3) \)
\( \mathbf{A} \cdot A-i v, B-i i i, C-i i, D-i \)
B . \( A-i, B-i i i, C-i i, D-i v \)
c. \( A-i i, B-i i i, C-i v, D-i \)
D. \( A-i i i, B-i v, C-i i, D-i \)
Subject: Maths
Find the centre and radius of the circle
\( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+2 \boldsymbol{a} \boldsymbol{x}-\boldsymbol{2} \boldsymbol{b} \boldsymbol{y}+\boldsymbol{b}^{2}=\mathbf{0} \)
Subject: Chemistry
How many moles of \( \boldsymbol{P t} \) may be deposited on the cathode when \( 0.80 \mathrm{F} \) of
electricity is passed through a \( 1.0 \mathrm{M} \)
solution of \( \boldsymbol{P} \boldsymbol{t}^{4+} \) ?
A. 0.1 mol
B. 0.2 mol
\( c .0 .4 \mathrm{mol} \)
D. 0.6 mo
Subject: Physics
One gram mol of helium at \( 27^{0} \mathrm{C} \) is
mixed with three gram mols of oxygen
at \( 127^{0} \mathrm{C} \) at constant pressure. If there is
no exchange of heat with the atmosphere then the final temperature will be
\( A \cdot 375 K \)
в. 175k
c. \( 475 \mathrm{k} \)
D. 575K
Subject: Physics
A proton of mass \( m \) charge \( e \) is released from rest in a uniform electric field of
strength \( E . \) The time taken by it to travel a distance \( d \) in the field is :
A \( \cdot \sqrt{\frac{2 d e}{m E}} \)
в. \( \sqrt{\frac{2 d m}{E e}} \)
c. \( \sqrt{\frac{2 d E}{m e}} \)
D. \( \sqrt{\frac{2 E e}{d m}} \)
Subject: Chemistry
\( 0.2595 \mathrm{g} \) of an organic substance, when treated by carius method, gave 0.25 g of \( B a S O_{4} \). Calculate the percentage of sulphur in the compound.
A . \( 9.08 \% \)
в. \( 12.75 \% \) \%
c. \( 15.96 \% \)
D . 13.23\%
Subject: Chemistry
Calculate the work done (in J) when 4.5 g
of \( H_{2} O_{2} \) reacts against a pressure of 1.0
\( \operatorname{atm} \operatorname{at} 2 H_{2} O_{2} \rightarrow O_{2}+2 H_{2} O \)
A . \( -1.63 \times 10^{2} \)
В. \( 4.5 \times 10^{2} \)
c. \( 3.2 \times 10^{2} \)
D. \( -6.1 \times 10^{2} \)
Subject: Maths
In a horse race there are 18 horses
numbered from 1 to 18. The probability that horse 1 would win is \( \frac{1}{6}, \) horse 2 is \( \frac{1}{10} \) and 3 is \( \frac{1}{8} . \) Assuming a tie is impossible, the chance that one of the
three horses wins the race, is
A. \( \frac{143}{420} \)
B. \( \frac{119}{120} \)
C. \( \frac{47}{120} \)
D. \( \frac{1}{5} \)
Subject: Physics
An inductor and a resistor are
connected to an ac supply of \( 50 V \) and
\( \mathbf{5 0} \boldsymbol{H} \boldsymbol{z} . \) If the voltage across the resistor
is \( 40 V \) the voltage across the inductor
will be:
A . \( 10 V \)
в. \( 20 V \)
\( c .30 V \)
D. \( 60 V \)
Subject: Maths
For \( \boldsymbol{r}=\mathbf{0}, \mathbf{1}, \ldots ., \mathbf{1 0}, \) let \( \boldsymbol{A}_{r}, \boldsymbol{B}_{r} \) and \( \boldsymbol{C}_{\boldsymbol{r}} \)
denote, respectively, the coefficient of
\( x^{r} \) in the expansions of \( (1+x)^{10},(1+x)^{20} \) and \( (1+x)^{30} . \) Then
\( \sum_{r=1}^{10} A_{r}\left(B_{10} B_{r}-C_{10} A_{r}\right) \) is equal to
A. \( B_{10}-C_{10} \)
B . \( A_{10}\left(B_{10}^{2}-C_{10} A_{10}\right) \)
c. 0
D. \( C_{10}-B_{10} \)
Subject: Physics
A series \( L C R \) circuit containing a
resistance of \( 120 \Omega \) has angular
resonance frequency \( 4 \times 10^{5} \) rad \( s^{-1} \)
At resonance the voltages across
resistance and inductance are \( 60 V \)
and \( 40 \mathrm{V} \), respectively. The value of
inductance \( L \) is
A. \( 0.1 \mathrm{mH} \)
в. \( 0.2 \mathrm{mH} \)
c. \( 0.35 \mathrm{mH} \)
D. \( 0.4 \mathrm{mH} \)
Subject: Chemistry
The coordination number and oxidation
number of the central metal ion in the
complex \( \left[\boldsymbol{P t}(\boldsymbol{e n})_{2}\right]^{+2} \) is:
A. C.N. \( =2, \) O.N. \( =+2 \)
B. C.N. \( =6, \) O.N. \( =+4 \)
c. \( \mathrm{c.N.}=4, \mathrm{O} . \mathrm{N}_{.}=+4 \)
D. C.N.= \( 4,0 . \) N. \( =+2 \)
Subject: Physics
A car travels the first half of the
distance between two places with a speed of \( 60 k m p . \) The speed of the car for
the rest of the distance so that its
average speed becomes \( 90 k m p h \)
A. \( 60 \mathrm{kmph} \)
в. \( 90 \mathrm{kmph} \)
c. \( 120 \mathrm{kmph} \)
D. \( 180 \mathrm{kmph} \)
Subject: Chemistry
A sample of hard water contains
0.005 moles of \( C a C l_{2} \) per litre. What is
the minimum concentration Of
\( N a_{2} S O_{4} \) which must be added for
removing \( C a^{2+} \) ions from the water
sample?
\( \left[K_{s p} \text { for } C a S O_{4} \text { is } 2.4 \times 10^{-5} \text {at } 25^{\circ} C\right] \)
A \( .2 .8 \times 0^{-5} M \)
В. \( 4.8 \times 10^{-3} M \)
c. \( 6.1 \times 10^{-3} M \)
D. \( 4.1 \times 10^{-5} M \)
Subject: Maths
The number of integer \( \boldsymbol{x} \) satisfying \( \sin ^{-1}|x-2|+\cos ^{-1}(1-|3-x|)=\frac{\pi}{2} \)
is
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
\( D \)
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. \( 1 \times 10^{8} J \)
c. \( 5 \times 10^{4} J \)
D. \( 5 \times 10^{5} J \)
Subject: Physics
resistances are connected as shown in
the figure. Initially resistance \( \boldsymbol{P}=4 \Omega \)
and the neutral point \( N \) is at \( 60 c m \)
from \( A . \) Now an unknown resistance \( \boldsymbol{R} \)
is connected in series to \( \boldsymbol{P} \) and the new
position of the neutral point is at \( 80 c m \)
from \( A \). The value of unknown
resistance \( \boldsymbol{R} \) is :
\( \mathbf{A} \cdot 6 \Omega \)
B. \( 7 \Omega \)
c. \( \frac{33}{5} \Omega \)
D. \( \frac{20}{3} \Omega \)
Subject: Physics
Three cell, \( (A, B \& C) \) each of emf \( E \)
and internal resistance \( (r) \) are
connected in series as shown in figure.
The potential difference across the cell
\( C^{\prime} \) is
A \( \cdot \frac{E r}{R} \)
B. \( \frac{E(R+r)}{R+3 r} \)
c. \( \frac{E(R+4 r)}{R+3 r} \)
D. \( \frac{E(R+3 r)}{R+4 r} \)
Subject: Maths
Find vector equation for the line passing through the points \( 3 \bar{i}+4 \bar{j}- \) \( \mathbf{7} \bar{k}, \overline{\boldsymbol{i}}-\overline{\boldsymbol{j}}+\mathbf{6} \overline{\boldsymbol{k}} \)
A \( . \bar{r}=(3-2 \lambda) \bar{i}+(4-5 \lambda) \bar{j}+(-7+13 \lambda) \bar{k} \)
B. \( \bar{r}=(2 \lambda) \bar{i}+(4+5 \lambda) \bar{j}+(-7-13 \lambda) \bar{k} \)
c. \( \bar{r}=(3-2 \lambda) \bar{i}-(4-5 \lambda) \bar{j}+(-7+13 \lambda) \bar{k} \)
D. \( \bar{r}=(3-2 \lambda) \bar{i}+(4-5 \lambda) \bar{j}-(-7+13 \lambda) \bar{k} \)
Subject: Chemistry
The unit of rate constant for a zero order
reaction is:
A \( \cdot \operatorname{mol} L^{-1} s^{-1} \)
B. \( L \) mol \( ^{-1} s^{-1} \)
c. \( L^{2} \) mol \( ^{-2} s^{-1} \)
D. \( s^{-1} \)
Subject: Maths
The domain of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\tan \pi[x]}{1+\sin \pi[x]+\left[x^{2}\right]} \) is (where [.] denotes
greatest integer function)
A. \( (0, \infty) \)
в. \( R \)
\( c \cdot(-\infty, 0) \)
D. \( z \)
Subject: Chemistry
Assertion
Aryl halides undergo electrophilic substitution less readily than benzene.
Reason

Aryl halide gives only meta product w.r.t. electrophilic substitution.
A. Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
c. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect but the Reason is correct
Subject: Physics
A cloud is at a potential of \( 8 \times 10^{9} V \)
relative to the ground. A charge of \( 40 C \) is transferred in a lightning stroke
between the cloud and the earth. The
energy released is:
A \( \cdot 3.2 \times 10^{11} J \)
B . \( 5 \times 10^{9} J \)
c. \( 2 \times 10^{9} J \)
D. \( 32 \times 10^{12} J \)
Subject: Chemistry
Solubility of \( A g B r \) will be minimum in:
A. pure water
в. \( 0.1 \mathrm{M} \) СаВг\( _{2} \)
c. \( 0.1 \mathrm{M} \) NaBr
D. \( 0.1 \mathrm{M} \) AgNO \( _{3} \)
Subject: Chemistry
Most oxidsing agent is:
\( \mathbf{A} \cdot\left[W O_{4}\right]^{2-} \)
B. \( \left[\mathrm{CrO}_{4}\right]^{2-} \)
c. \( \left[\mathrm{Ce} \mathrm{O}_{4}\right]^{2} \)
D. \( \left[M n O_{4}\right]^{2-} \)
Subject: Chemistry
The reaction that does not define
calcination is:
A \( . Z n C O_{3} \stackrel{\Delta}{\longrightarrow} Z n O+C O_{2} \)
B \( \cdot F e_{2} O_{3} \cdot x H_{2} O \stackrel{\Delta}{\longrightarrow} F e_{2} O_{3}+x H_{2} O \)
\( \mathbf{c} \cdot \mathrm{CaCO}_{3} \cdot \mathrm{MgCO}_{3} \stackrel{\Delta}{\longrightarrow} \mathrm{CaO}+\mathrm{MgO}+2 \mathrm{CO}_{2} \)
D \( \cdot 2 C u_{2} S+3 O_{2} \stackrel{\Delta}{\longrightarrow} 2 C u_{2} O+2 S O_{2} \)
Subject: Maths
f \( \sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2} \) then
\( a \) value of \( x \) is:
\( A \)
B. 3
\( c \cdot 4 \)
D. 5
Subject: Physics
The mass of object \( A \) is 5 kg,that of object B is \( 40 \mathrm{kg} \),that of object \( \mathrm{C} \) is 38 kg,and that of object D is 56 kg. Which object has the greatest inertia?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)
Subject: Physics
Calculate the frequency of beats produced in air when two sources of sound are activated, one emitting a
wavelength of \( 32 c m \) and the other of
\( 32.2 \mathrm{cm} . \) The speed of sound in air is
\( 350 m / s \)
\( A .3 H z \)
в. \( 5 H z \)
\( \mathrm{c} .7 \mathrm{Hz} \)
D. \( 2 H z \)
Subject: Physics
A hollow cylinder of mass \( M \) and radius
\( \boldsymbol{R} \) is pulled by a horizontal force \( \boldsymbol{F} \) acting at its centre of mass on a horizontal surface where the coefficient
of friction is \( \mu \)
If hollow cylinder is performing pure rolling then frictional force \( f \) will be :
A. \( F \)
в. \( \frac{F}{2} \)
c. \( \frac{F}{3} \)
D. \( 2 F \)
Subject: Maths
If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) and
\( \boldsymbol{f}(\mathbf{1})=\mathbf{1}, \boldsymbol{f}(\boldsymbol{p}+\boldsymbol{q})= \)
\( \boldsymbol{f}(\boldsymbol{p}) \cdot \boldsymbol{f}(\boldsymbol{q}) \quad \forall \boldsymbol{p}, \boldsymbol{q} \in \boldsymbol{R} \operatorname{th} \operatorname{en} \boldsymbol{x}^{f(1)}+ \)
\( \boldsymbol{y}^{f(2)}+\boldsymbol{z}^{f(\boldsymbol{3})}-\frac{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}}{\boldsymbol{x}^{f(1)}+\boldsymbol{y}^{f(2)}+\boldsymbol{z}^{f(3)}}= \)
\( A \cdot O \)
в.
\( c \cdot 2 \)
\( D \)
Subject: Biology
Watson and Crick model of DNA is a
A. \( B \) -form DNA with a spiral length of \( 34 \AA \) and a diameter of \( 20 \dot{A} \)
B. \( A \) -form DNA with a spiral length of 15 and a diameter of \( 20 \AA \)
C. \( Z \) -form DNA with a spiral length of \( 34 \AA \) and a diameter of \( 20 \dot{A} \)
D. \( B \) -form DNA with a spiral length of \( 28 \dot{A} \) and a diameter of \( 14 \dot{A} \)
Subject: Physics
A block of mass \( 50 \mathrm{kg} \) is projected
horizontally on a rough horizontal floor.
The coefficient of friction between the
block and the floor is \( 0.1 . \) The block
strikes a light spring of stiffness \( \boldsymbol{k}= \)
\( 100 N / m \) with a velocity \( 2 m / s . \) The
maximum compression of the spring is
\( A \cdot 1 m \)
3. \( 2 m \)
Subject: Physics
and mass m. A particle also of mass \( \mathrm{m} \) is fixed at a point \( A \) on the wedge of the disc as in fig. The disc can rotate freely
about a fixed horizontal chord PQ that is
at a distance \( \mathrm{R} / 4 \) from the centre \( \mathrm{C} \) of
the disc. The line AC is perpendicular to
PQ. Initially the disc is held vertical with
the point \( A \) at its highest position. It is
then allowed to fall so that it starts
rotating about PQ.
If the linear speed of the particle as it
reaches its lowest position is \( \boldsymbol{v}= \)
\( \sqrt{x g R} \) Find \( x \)
Subject: Physics
The electric potential due to charges \( 2 q \)
and \( -3 q, \) fixed at points \( (4 m, 0,0) \) and
\( (9 m, 0,0) \) respectively, is zero on:
A \( \cdot \) a spherical surface \( x^{2}+y^{2}+z^{2}=36 \)
B. a parabola \( y^{2}=36 z \)
c. an ellipsoidal \( \frac{x^{2}}{16}+\frac{y^{2}}{81}+z^{2}=1 \)
D. a spherical surface \( (x-4)^{2}+y^{2}+z^{2}=81 \)
Subject: Physics
Calculate the specific heat of the material if material of 10 kilograms
raises temperature \( 2^{\circ} C \) when 2000
joules of heat is added.
A \( \cdot 0.01 J / k g \cdot^{\circ} C \)
в. \( 0.2 J / k g \cdot^{\circ} C \)
\( \mathbf{c} \cdot 50 J / k g \cdot^{\circ} C \)
D. \( 100 J / k g \cdot^{\circ} C \)
E \( \cdot 200 J / k g \cdot^{\circ} C \)
Subject: Chemistry
Which of the following is an example for heterogeneous catalysis reaction?
\( \mathbf{A} \cdot 2 S O_{2}(g)+O_{2}(g) \quad N O(g) \quad 2 S O_{3}(g) \)
B. Hydrolysis of aqueous sucrose solution in the presence of a aqueous mineral acid
\( \mathbf{c} \cdot 2 H_{2} O_{2}(l) \quad P t(s) \quad 2 H_{2} O(l)+O_{2}(g) \)
D. Hydrolysis of liquid in the presence of aqueous mineral acid
Subject: Chemistry
Assertion:When \( Q_{c}=K_{c}, \) reaction is
at equilibrium
Reason : At equilibrium, \( \Delta G \) is 0
A. Both assertion and reason are true and reason is the correct explanation of assertion.
B. Both assertion and reason are true but reason is not the correct explanation of assertion
c. Assertion is true but reason is false
D. Both assertion and reason are false
Subject: Chemistry
A certain reaction occurs in the
following steps.
(i) \( C l_{(g)}+O_{3(g)} \rightarrow C l O_{(g)}+O_{2(g)} \)
(ii) \( C l O_{(g)}+O_{(g)} \rightarrow C l_{g}+O_{2(g)} \)
What is the molecularity of each of the elementary steps?
Subject: Maths
\( \lim _{x \rightarrow \frac{\pi}{2}}\left(\lim _{x \rightarrow \infty} \cos \frac{x}{2} \cos \frac{x}{2^{2}} \cos \frac{x}{2^{3}} \ldots \ldots \cos \frac{x}{2^{n}}\right) \)
equals to
Subject: Physics
A car driver going at a speed \( \mathbf{v} \) suddenly
find a wide wall at a distance.
(coefficient of friction is \( \mu \) )
A. If the apply breaks, he will come to rest after a distance \( \frac{v^{2}}{2 \mu g} \)
B. If he turn the cart in a circle to avoid hitting, then radius of the circle is \( \frac{v^{2}}{\mu g} \)
C. It is better to apply breaks rather than to turn the vehicle in a circle
D. It is better to turn the vehicle in a circle than to apply brakes
Subject: Physics
A charge of \( +2 Q \) resides inside of a conducting sphere with a hollow center If the net charge on the conducting
sphere is \( +5 Q, \) what is the amount of charge on the outer surface of the
conducting sphere?
\( A \cdot 2 Q \)
в. \( 3 Q \)
\( c .5 Q \)
D. \( 7 Q \)
Subject: Chemistry
Assertion
Two successive ionisation energies of Argon are \( 56.8 e V \) and \( 36.8 e V \)
respectively.
Reason
\( Z_{e f f} \) of \( \operatorname{Ar}\left(3 s^{2} 3 p^{6}\right) \) is greater than
\( A r^{+}\left(3 s^{2} 3 p^{5}\right) \)
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. Both Assertion and Reason are incorrect
Subject: Physics
Two copper wires, one of length \( 1 \mathrm{m} \) and the other of length \( 9 \mathrm{m}, \) are found to have the same resistance.
Their diameters are in the ratio:
A. 3:
B. 1: 9
\( c \cdot 9: \)
\( D \cdot 1: 3 \)
Subject: Chemistry
The recovery of silver from the solutions used in developing and fixing photographic film and prints present just such a problem. Silver is an expensive metal, and the recovery is profitable. Moreover, if not recovered, the silver ions would constitute and
undesirable pollutant in water supplies The equation in which silver recovered from such solution is \( : A g_{2} C O_{3} \stackrel{\Delta}{\rightarrow} \)
\( 2 A g+C O_{2}+\frac{1}{2} O_{2} \)
Subject: Maths
\( \sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} \frac{1}{2}\right)\right] \) is equal
to
A \( \cdot \frac{3 \sqrt{7}}{8} \)
B. \( \frac{5 \sqrt{7}}{8} \)
\( c \cdot \frac{5 \sqrt{7}}{2} \)
D. \( \frac{3 \sqrt{7}}{2} \)
Subject: Physics
In the fusion reaction \( _{1} H^{2}+_{1} H^{2} \longrightarrow_{2} \)
\( H e^{4}+_{0} n^{1}, \) the masses of deuteron
helium and neutron expresses in amu are 2.05,3.017 and \( 1.009, \) respectively. If
1 \( K g \) of deuterium undergoes complete
fusion, then find the amount of total
energy released
\( \mathbf{1} \boldsymbol{a} \boldsymbol{m} \boldsymbol{u}=\mathbf{9} \mathbf{3} \mathbf{1} . \mathbf{5} \boldsymbol{M} \boldsymbol{e} \boldsymbol{V} / \boldsymbol{c}^{2} \)
Subject: Physics
We sit in the room with windows open.
Then
A. Air pressure on the floor of the room equals the atmospheric pressure but the air pressure on the ceiling is eligible
B. Air pressure is nearly the same on the floor, the walls and ceiling
C. Air pressure on the floor equals the weight of the air coloumn inside the room (from floor to the ceiling) per unit area
D. Air pressure on the walls is zero since the weight of air acts downward
Subject: Chemistry
\( \beta \) -Elimination or anti-elimination
reaction is carried out with base \( \left(B^{\ominus}\right) \)
as shown.
The following bases are used. \( (I) \stackrel{\ominus}{O} H(I I) R O^{\ominus}(I I I) R C O O^{\ominus} \)
\( (I V) \stackrel{\ominus}{C} N(V) N O_{3}^{\ominus} \)
The decreasing order of reactivity for the above elimination is :
A. \( (I I)>(I)>(I V)>(I I I)>(V) \)
в. \( (V)>(I I I)>(I V)>(I)>(I I) \)
c. \( (I I)>(I)>(I I I)>(I V)>(V) \)
D. \( (I)>(I I)>(I I I)>(I V)>(V) \)
Subject: Physics
In the give velocity-time graph,
acceleration equals
\( A \cdot 4 m / s^{2} \)
B. \( 5 \mathrm{m} / \mathrm{s}^{2} \)
\( c \cdot 4.5 m / s^{2} \)
\( \mathbf{D} \cdot 3.5 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
The angles of dip at the poles and the equator respectively are :
A \( \cdot 30^{0}, 60^{\circ} \)
\( ^{0}, 66^{0} \)
В. \( 90^{0}, 0^{0} \)
c. \( 30^{0}, 90^{\circ} \)
D. \( 0^{0}, 0^{0} \)
Subject: Maths
If \( 6 \sin ^{2} \theta-\sin \theta=1 \) and \( 0 \leq \theta \leq \pi \)
calculate the value of \( \sin \theta \)
A \( \cdot \frac{1}{6} \)
B.
\( c \cdot \frac{1}{2} \)
D. 19
E . 30
Subject: Maths
For positive integers \( n_{1}, n_{2} \) the value of
the expression \( (1+i)^{n_{1}}+\left(1+i^{3}\right)^{n_{1}}+ \)
\( \left(1+i^{5}\right)^{n_{2}}+\left(1+i^{7}\right)^{n_{2}}, i=\sqrt{-1} \) is a
real number if and only if
\( \mathbf{A} \cdot n_{1}=n_{2}+1 \)
В . \( n_{1}=n_{2}-1 \)
c. \( n_{1}=n_{2} \)
D \( . n_{1}>0, n_{2}>0 \)
Subject: Maths
The marks in science of 80 students of
class \( X \) are given below. Find the mode of the marks obtained by the students in science
c... \( \begin{array}{llll}0- & 10- & 20- & 30- \\ 10 & 20 & 30 & 40\end{array} \)
Freq. 1 3
A. 17.36
B. 36.56
c. 53.17
D. 75.12
Subject: Chemistry
Assertion: Angular momentum of an
electron in any orbit is given by angular momentum \( =\frac{n . h}{2 \pi}, \) where \( n \) is the
principal quantum number. Reason: The principal quantum number, \( n, \) can have any integral value.
A. If both assertion and reason are true and the reason is
a correct explanation of the assertion.
B. If both assertion and reason are true but reason is not
a correct explanation of the assertion
C. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true
Subject: Physics
The angle of a prism is \( 6^{0} \) and its refractive index for green light is \( 1.5 . \) If a green ray passes through it, the deviation will be :-
A . \( 30^{\circ} \)
В. \( 15^{\circ} \)
\( c \cdot 9^{0} \)
D. \( 3^{\circ} \)