AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A block is attached to the end of an
ideal spring and moved from coordinate
\( x_{i} \) to coordinate \( x_{f} . \) The relaxed position
is at \( x=0 . \) The work done by spring is
positive if.
A \( \cdot x_{i}=2 c m \) and \( x_{f}=4 \mathrm{cm} \)
B . \( x_{i}=-2 \mathrm{cm} \) and \( x_{f}=4 \mathrm{cm} \)
C \( \cdot x_{i}=-4 \mathrm{cm} \) and \( x_{f}=4 \mathrm{cm} \)
D. \( x_{i}=4 \mathrm{cm} \) and \( x_{f}=-2 \mathrm{cm} \)
Subject: Physics
Which is not true for Second Law of
Thermodynamics?
A. The second law of thermodynamics states that the total entropy of an isolated system always increases over time, or remains constant in ideal cases where the system is in a steady state or undergoing a reversible process.
B. It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects
C. It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the raising of a weight and cooling of a heat reservoir.
D. The second law of thermodynamics states that the total energy of an isolated system is constant.
Subject: Chemistry
Amongst the following the lowest degree of paramagnetism per mol of the compound at \( 298 \mathrm{K} \) will be shown by:
A \( \cdot \) FeSO\( _{4} \cdot 6 H_{2} \) O
в. \( N i S O_{4} .6 H_{2} O \)
\( \mathrm{c} \cdot \mathrm{MnSO}_{4} \cdot 4 \mathrm{H}_{2} \mathrm{O} \)
D. \( C u S O_{4} .5 H_{2} O \)
Subject: Maths
If \( f(x)=5 \log _{5} x \) then \( f^{-1}(\alpha-\beta) \) where
\( \boldsymbol{\alpha}, \boldsymbol{\beta} \in \boldsymbol{R} \) is equal to
A \( \cdot f^{-1}(\alpha)-f^{-1}(\beta) \)
B. \( \frac{f^{-1}(\alpha)}{f^{-1}(\beta)} \)
c. \( \frac{1}{f(\alpha-\beta)} \)
D. \( \frac{1}{f(\alpha)-f(\beta)} \)
Subject: Chemistry
Moist hydrogen peroxide cannot be
dried over conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) because:
A. it can catch fire
B. it is reduced by \( H_{2} S O_{4} \)
C . it is oxidised by \( H_{2} S O_{4} \)
D. it is decomposed by \( H_{2} S O_{4} \)
Subject: Physics
If the distance is increased after
disconnecting the power source, then electric field inside the capacitor is:
A \( \cdot 6 \times 10^{3} V / m \)
B . \( 3 \times 10^{3} V / m \)
c. \( 12 \times 10^{3} V / m \)
D. \( 15 \times 10^{3} V / m \)
Subject: Maths
For \( -\frac{\pi}{2}<\theta<\frac{\pi}{2}, \) range of \( f(\theta)= \)
\( \frac{\sin \theta+\sin 2 \theta}{1+\cos \theta+\cos 2 \theta} \) is
A. \( (-\infty, \infty) \)
a
в. (-2,2)
\( c \cdot(0, \infty) \)
D. none of these
Subject: Chemistry
Calculate \( \Delta H^{o} \) for the reaction between
ethene and water to form ethyl alcohol from the following data
\( \Delta_{c} H^{o} C_{2} H_{5} O H_{(l)}=-1368 k J \)
\( \Delta_{c} H^{o} C_{2} H_{4(g)}=-1410 k J \)
Does the calculated \( \Delta H^{o} \) represent the enthalpy of formation of liquid ethanol?
Subject: Physics
A soap bubble of radius \( r \) is blown up to
form a bubble of radius 2r under
isothermal conditions. If \( T \) is the surface
tension of soap solution, the energy
spent in the blowing
\( \mathbf{A} \cdot 3 \pi T r^{2} \)
в. \( 6 \pi T r^{2} \)
\( \mathrm{c} \cdot 12 \pi T r^{2} \)
D. \( 24 \pi T r^{2} \)
Subject: Physics
Assertion
If a dielectric is placed in external field then field inside dielectric will be less
than applied field.
Reason
Electric field will induce dipole moment
opposite to field direction.
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
\( H C l O_{4}, H N O_{3} \) and \( H C l \) are all very
strong acids in aqueous solutions. In glacial acetic acid medium, their acid strength is such that:
A \( \cdot H C l O_{4}>H N O_{3}>H C l \)
в. \( H N O_{3}>H C l O_{4}>H C l \)
c. \( H C l>H C l O_{4}>H N O_{3} \)
D. \( H C l>H C l O_{4} \sim H N O_{3} \)
Subject: Maths
\( \mathbf{P} \) is the midpoint of the part of the line \( 3 x+y-2=0 \) intercepted between the
axes. Then the image of \( \mathbf{P} \) in origin is
\( \mathbf{A} \cdot\left(-1,-\frac{1}{3}\right) \)
B \( \cdot\left(-\frac{1}{3},-4\right) \)
\( ^{c} \cdot\left(-\frac{1}{3},-1\right) \)
D. (-2,-3)
Subject: Physics
A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The velocity of the shell is
A \( \cdot 102 \mathrm{ms}^{-1} \)
B. 82 \( m s^{-1} \)
\( \mathbf{c} \cdot \) 41 \( m s^{-} \)
D. \( 120 \mathrm{ms}^{-1} \)
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{(1-\cos 2 x)^{2}}{2 x \tan x-x \tan 2 x} \) is
\( A \cdot 2 \)
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \ldots-2 \)
Subject: Chemistry
Which of the following statement is
incorrect:
This question has multiple correct options
\( \mathbf{A} \cdot O_{2} \) is paramagnetic, \( O_{3} \) is also paramagnetic
B. \( O_{2} \) is paramagnetic, \( O_{3} \) is diamagnetic
\( \mathrm{C} \cdot B_{2} \) is paramagnetic, \( C_{2} \) is also paramagnetic
D. Different observation is found in their bond length when \( N O \rightarrow N O^{+} \) and \( C O \rightarrow C O^{+} \)
Subject: Physics
Equipotential surfaces are shown in the
figure. Find the magnitude and the
direction of the resultant electric field.
A. \( 200 \mathrm{V} / \mathrm{m} \) making an angle \( 60^{\circ} \) with the positive x-axis.
B. 200 V/m making an angle \( 120^{\circ} \) with the positive \( x \) axis
c. \( 200 \mathrm{V} / \mathrm{m} \) making an angle \( 120^{\circ} \) with the negative \( \mathrm{x} \) axis.
D. \( 100 \mathrm{V} / \mathrm{m} \) making an angle \( 60^{\circ} \) with the \( \mathrm{x} \) -axis
Subject: Chemistry
What is pH of \( 50 \mathrm{ml} \) 0.05 \( (\mathrm{M}) \) NaOH
and \( 50 \mathrm{ml} \) 0.1 \( (\mathrm{N}) \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H} \)
Subject: Physics
An oil drop is negatively charged and weights \( 5 \times 10^{-4} N \). The drop is
suspended in an electric field intensity of \( 2.6 \times 10^{4} N / C \). The number of
electrons the oil drop is in \( \boldsymbol{x} \times \mathbf{1 0}^{\mathbf{1 0}} \)
Then \( x \) is
A. 8
B. 10
\( c \cdot 16 \)
D. 12
Subject: Physics
A charged particle moves with a speed in a circular path of radius \( r \) around a long uniformly charged conductor then :
\( \mathbf{A} \cdot v \propto r \)
в. \( v \propto \frac{1}{r} \)
c. \( _{v \propto} \frac{1}{\sqrt{2}} r \)
D. \( v \) is independent of \( r \)
Subject: Maths
\( 2.4+4.7+6.10+\ldots(n-1) \) terms
A \( \cdot 2 n^{3}-2 n^{2} \)
B. \( \frac{n^{3}+3 n^{2}+1}{6} \)
c. \( 2 n^{3}+2 n \)
D. \( 2 n^{3}-n^{2} \)
Subject: Chemistry
The conductivity at infinite dilution of
\( N H_{4} C l, N a O H \) and \( N a C l \) are
\( 130,218,120 o h m^{-1} c m^{2} e q^{-1} . \) If
equivalent conductance of \( \frac{N}{100} \) solution
of \( N H_{4} O H \) IS \( 10, \) then degree of
dissociation of \( N H_{4} O H \) at this
dilution is:
A. 0.005
B. 0.043
c. 0.015
D. 0.025
Subject: Maths
\( A \) is known to tell the truth in 5 cases
out of 6 and he states that a white ball
was drawn from a bag containing 8
black and 1 white ball. The probability that the white ball was drawn, is
A \( \cdot \frac{7}{13} \)
B. \( \frac{5}{13} \)
\( c \cdot \frac{9}{13} \)
D. None of these
Subject: Maths
Places \( A \) and \( B \) are \( 80 k m \) apart from
each other on a highway. A car starts
from \( A \) and \( B \) other from \( B \) at the same
time. If they move in the some direction,
they meet in 8 hours and if they move in
opposite direction they meet in 1 hour
and 20 minutes Find the speeds of the
car
Subject: Chemistry
Consider following reactions:
\( \mathbf{l}: \boldsymbol{N}_{\mathbf{2}}+\boldsymbol{O}_{\mathbf{2}} \rightarrow \)
\[
\mathbf{2} \boldsymbol{N} \boldsymbol{O} \quad \triangle \boldsymbol{H}=\boldsymbol{X}_{\mathbf{1}}
\]
\( \|: 2 C O+O_{2} \rightarrow \)
\( 2 C O_{2} \)
\[
\triangle \boldsymbol{H}=\boldsymbol{X}_{2}
\]
\( \|: 2 H_{2} O+O_{2} \rightarrow \)
\[
\mathbf{2} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{2}} \quad \triangle \boldsymbol{H}=\boldsymbol{X}_{\mathbf{3}}
\]
\( \mathrm{IV}: \boldsymbol{P} \boldsymbol{C} \boldsymbol{I}_{3}+\boldsymbol{C} \boldsymbol{I}_{2} \rightarrow \)
\[
\boldsymbol{P C I}_{5}
\]
\[
\triangle \boldsymbol{H}=\boldsymbol{X}_{4}
\]
In which case \( (s), \triangle H_{f}=\frac{\Delta H}{2} ? \)
\( \mathbf{A} \cdot \) ।, ॥,।।
B. IV
c. ॥, ॥ ॥
\( D \)
Subject: Maths
\( \Delta A B C \) is an isosceles right triangle
with area \( P \).The radius of the circle that
passes through the point \( A, B \) and \( C \) is
\( A \cdot \sqrt{P} \)
B. \( \sqrt{\frac{P}{2}} \)
c. \( \frac{\sqrt{P}}{2} \)
D. \( \sqrt{2 P} \)
Subject: Maths
(iii) If \( f^{\prime \prime}(x)<0 \forall x \epsilon(a, b) \) and \( (c, f(c)) \)
is a point lying on the curve \( y=f(x) \)
where \( a<c<b \) and for that value of
\( c, F(c) \) has a maximum, then \( f^{\prime}(c) \)
equals
A \( \cdot \frac{f(b)-f(a)}{b-a} \)
в. \( \frac{2}{b-a}\{f(b)-f(a)\} \)
c. \( \frac{2 f(b)-f(a)}{2 b-a} \)
D.
Subject: Physics
Calculate the magnetic field induction B at the centre of a circular coil having \( \mathbf{5 0 0} \) turns, radius \( \pi \mathrm{cm} \) and carrying \( \mathbf{5} \mathbf{A} \) of current
\( \mathbf{A} \cdot 0.1 T \)
в. 0.005 न
c. 0.5 न
D. 0.05 न
Subject: Maths
The number of values of \( x \) for which
\[
\begin{array}{l}
\sin ^{-1}\left(x^{2}-\frac{x^{4}}{3}+\frac{x^{6}}{9} \dots\right)+ \\
\cos ^{-1}\left(x^{4}-\frac{x^{8}}{3}+\frac{x^{12}}{9} \dots\right)=\frac{\pi}{2}, \text { where } \\
0 \leq|x|<\sqrt{3}, \text { is }
\end{array}
\]
Subject: Physics
Q Type your question
shown in Fig. The cross sectional area of
\( A \) is half that of \( B \) and the Youngs
modulus of \( A \) is twice that of \( B . A \)
weight \( \mathrm{W} \) is hung as shown. The value of
\( x \) so that \( W \) produces equal stress in
wires \( A \) and \( B \) is
\( A \cdot \frac{L}{3} \)
в. \( L \) \( \overline{2} \)
c. \( \frac{2 L}{3} \)
D. \( \frac{3 L}{4} \)
Subject: Maths
How many 6-letter words with distinct
letters in each can be formed using the
letters of the word EDUCATION? How
many of these begin with I
A. \( ^{9} P_{6^{\prime}}^{8} P_{5} \)
в. \( ^{9} P_{6^{\prime}}^{9} P_{5} \)
\( \mathrm{c} \cdot^{8} P_{6^{\prime}}^{8} P_{5} \)
D. \( ^{8} P_{6^{\prime}}^{8} P_{4} \)
Subject: Chemistry
Copper sulphate dissolves in ammonia
due to the formation of:
\( \mathbf{A} \cdot C u_{2} O \)
B \( \cdot\left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \)
\( \mathbf{c} \cdot\left[C u\left(N H_{3}\right)_{4}\right] O H \)
D. \( \left[C u\left(H_{2} O\right)_{4}\right] S O_{4} \)
Subject: Maths
The equation to the normal to the hyperbola \( \frac{x^{2}}{16}-\frac{y^{2}}{9}=1 \) at (-4,0) is
A \( .2 x-3 y=1 \)
B. \( x=0 \)
\( \mathbf{c} \cdot x=1 \)
D. \( y=0 \)
Subject: Chemistry
A solution is one molar in each of
\( N a C l, C d C l_{2}, Z n C l_{2} \) and \( P b C l_{2} . \) To
this, tin metal is added. Which of the
following is true? Given:
\( \boldsymbol{E}_{\boldsymbol{P b}^{2+} / \boldsymbol{P b}}^{\circ}=-\mathbf{0 . 1 2 6} \boldsymbol{V}, \boldsymbol{E}_{\boldsymbol{S n}^{2+} / \boldsymbol{S} n}^{\circ}= \)
\( -\mathbf{0 . 1 3 6} \boldsymbol{V} \)
\( \boldsymbol{E}_{\boldsymbol{C d}^{2+} / \boldsymbol{C d}}^{\circ}=-\mathbf{0 . 4 0} \boldsymbol{V}, \boldsymbol{E}_{Z n^{2+} / Z n}^{\circ}= \)
\( -\mathbf{0 . 7 6 3} \boldsymbol{V}, \boldsymbol{E}_{N a^{+} / N a}^{\circ}=-\mathbf{2 . 7 1} \boldsymbol{V} \)
A. \( S n \) can reduce \( N a^{+} \) to \( N a \)
B. \( S n \) can reduce \( Z n^{2+} \) to \( Z n \)
\( \mathrm{c} \cdot \operatorname{Sn} \) can reduce \( C d^{2+} \) to \( C d \)
D. \( S n \) can reduce \( P b^{2+} \) to \( P b \)
Subject: Chemistry
n mole of \( P C l_{3} \) and n mole \( C l_{2} \) are
allowed to react at constant
temperature \( T \) to have a total
equilibrium pressure \( \boldsymbol{P}, \) as \( : \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) . \) If \( \mathbf{y} \) mole of \( \boldsymbol{P} \boldsymbol{C l}_{3} \) are
formed at equilibrium, find \( k_{p} \) for the
given reaction.
A \( \cdot \frac{(2 n-y) y}{(n-y)^{2} . P} \)
B. \( \frac{y}{(n-y)^{2}(2 n-y) P} \)
c. \( \frac{(n-y)^{2} \cdot P}{(2 n-y) y} \)
D. \( \frac{(n-y)^{2}(2 n-y) P}{y} \)
Subject: Chemistry
The main product obtained in the
reaction of acetamide and \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \) is:
A. \( C H_{3} C N \)
в. \( C H_{3} N C \)
\( \mathbf{c} \cdot C H_{3} N H_{2} \)
D. \( C H_{3} \) СООН
Subject: Chemistry
In solid state N205 exits as:
\( \mathbf{A} \cdot[N O 3]^{-}[N O 2]^{+} \)
в. \( [N O 2]^{-}[N O 3]^{+} \)
c. \( [N 2 O 4]^{+} O^{-} \)
D. \( [N O 3][N O 2] \)
Subject: Maths
If the scalar projection of the vector \( x \hat{i}-\hat{j}+\hat{k} \) on the vector \( 2 \hat{i}-\hat{j}+5 \hat{k} \) is
\( \frac{1}{\sqrt{30}}, \) then value of \( x \) is equal to
A \( \cdot \frac{-5}{2} \) units
B. 6 units
c. -6 units
D. 3 units
Subject: Physics
A block of mass 2 kg. is free to move
along the \( x \) -axis. It is at rest and from
\( t=0 \) onwards it is subjected to a time-
dependent force \( F(t) \) in the \( x \) direction. The force \( F(t) \) varies with \( t \) as shown in the figure. The kinetic energy of the block after 4.5 second is :
Subject: Maths
The value of \( \sum_{r=0}^{n-1}^{n} C_{r} /\left(^{n} C_{r}+^{n} C_{r+1}\right) \)
equals
\( \mathbf{A} \cdot n+1 \)
в. \( n / 2 \)
\( \mathbf{c} \cdot n+2 \)
D. none of these
Subject: Chemistry
The resistance of a conductivity cell
containing \( 0.001 M K C l \) solution at
\( 298 K \) is \( 1500 \Omega . \) What is the cell
constant (in \( \mathrm{mm}^{-1} \) ) if the conductivity
of \( 0.001 M K C l \) solution is \( 2 \times 10^{-3} \mathrm{s} \)
\( \mathrm{mm}^{-1} ? \)
Subject: Physics
Assertion
A disc rolls without slipping on a horizontal ground with uniform speed has 0 acceleration of lowest point.
Reason
velocity of the lowest point of the same
disc is zero
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Oxygen is more electronegative than
sulphur yet \( \boldsymbol{H}_{2} \boldsymbol{S} \) is acidic While \( \boldsymbol{H}_{2} \boldsymbol{O} \) is
neutral. This is because:
A. water is a highly associated
B. \( H-S \) bond is weaker than \( H-O \) bond
c. \( H_{2} S \) is a gas while \( H_{2} O \) is a liquid
D. The molecular weight of \( H_{2} S \) is more than that of \( H_{2} O \)
Subject: Physics
At a place the value of \( B_{H} \) and \( B_{V} \) are \( 0.4 \times 10^{-4} \) and \( 0.3 \times 10^{-4} \) respectively.
The resultant earths magnetic field is :
A \( .0 .5 \times 10^{-4} T \)
в. \( 10^{-4} T \)
c. \( 2 \times 10^{-4} T \)
D. \( 5 \times 10^{-4} T \)
Subject: Chemistry
Which of the following reaction is a part
of Hall's process?
\( \mathbf{A} \cdot A l_{2} O_{3}+2 N a O H \rightarrow 2 N a A l O_{2}+H_{2} O \)
B \( \cdot F e_{2} O_{3}+2 A l \rightarrow 2 F e+A l_{2} O_{3} \)
\( \mathbf{c} \cdot A l N+3 H_{2} O \rightarrow A l(O H)_{3}+N H_{3} \)
D. \( A l_{2} O_{3} .2 H_{2} O+2 N a_{2} C O_{3} \rightarrow 2 N a A l O_{2}+C O_{2}+2 H_{2} O \)
Subject: Physics
A body of mass \( m=1 k g \) is moving in a
medium and experiences a fractions
force \( F=-k v, \) where \( v \) is the speed of
the body. The initial speed is \( v_{0}= \)
\( 10 m s^{-1} \) and after \( , 10 s \) its energy
becomes half of initial energy. Then, the value of \( k \) is
A. \( 10 \ln \sqrt{2} \)
2 \( \ln \log 2 \)
B. \( \ln \sqrt{2} \)
\( c \cdot \frac{\ln 2}{20} \)
D. \( 10 \ln 2 \)
E . \( \ln 2 \)
Subject: Physics
A certain radioactive material can
undergo three different types of decay, each with a different decay constant \( \lambda, 2 \lambda \) and \( 3 \lambda . \) Then, the effective decay
constant \( \lambda_{e f f} \) is
\( A \cdot 6 \lambda \)
B. \( 4 \lambda \)
\( c \cdot 2 \lambda \)
D. \( 3 \lambda \)
Subject: Physics
If a magnet is suspended at an angle
\( 30^{\circ} \) to the magnetic meridian, the dip
needle makes angle of \( 45^{\circ} \) with the horizontal. The real dip is :
A \( \cdot \tan ^{-1}(\sqrt{3} / 2) \)
B. \( \tan ^{-1}(\sqrt{3}) \)
\( \mathbf{c} \cdot \tan ^{-1}(\sqrt{3} / \sqrt{2}) \)
D. \( \tan ^{-1}(2 / \sqrt{3}) \)
Subject: Maths
For the expression \( a x^{2}+7 x+2 \) to be
quadratic, the necessary condition is
\( \mathbf{A} \cdot a=0 \)
B. \( a \neq 0 \)
\( ^{c} \cdot_{a}>\frac{7}{2} \)
D. \( a<-1 \)
Subject: Maths
The height of a cuboid is \( 18 \mathrm{m} \). Its length is 3 times its height and 2 times its width. Find the surface area of the
cuboid.
\( \mathbf{A} \cdot 5280 m^{2} \)
В. \( 5832 m^{2} \)
c. \( 5313 m^{2} \)
D. \( 5188 m^{2} \)
Subject: Chemistry
The correct order of acidic strength of
oxides of nitrogen is :
A. \( N O<N O_{2}<N_{2} O<N_{2} O_{3}<N_{2} O_{5} \)
B. \( N_{2} O<N O<N_{2} O_{3}<N_{2} O_{4}<N_{2} O_{5} \)
c. \( N O<N_{2} \oslash<N_{2} O_{3}<N_{2} O_{5}<N_{2} O_{4} \)
D. \( N O<N_{2} O<N_{2} O_{5}<N_{2} O_{3}<N_{2} O_{4} \)
Subject: Physics
Two coils \( P \) and \( Q \) are kept near each other. When no current flows through coil \( P \) and current increases in coil \( Q \) at
the rate \( 10 A / s \), the e.m.f. in coil \( P \) is
\( 15 m V . \) When coil \( Q \) carries no current
and current of \( 1.8 A \) flows through coil
\( P, \) the magnetic flux linked with the coil
\( Q \) is
A. \( 1.4 \mathrm{m} \mathrm{Wb} \)
B . \( 2.2 \mathrm{m} \mathrm{Wb} \)
\( \mathbf{c} .2 .7 \mathrm{m} \mathrm{Wb} \)
D. \( 2.9 \mathrm{m} \mathrm{Wb} \)
Subject: Chemistry
Assertion
Physical adsorption of molecules on the surface requires activation energy.
Reason
Because the bonds of adsorbed
molecules are broken.
A. If both (A) and (R) are true and (R) is the correct explanation of (A).
B. If both (A) and (R) are true, but (R) is not the correct explanation of (A).
c. If (A) is correct, but (R) is incorrect.
D. If (A) and (R) are both incorrect
Subject: Physics
Three charges \( -q,+q \) and \( -q \) are
placed at the corners of an equilateral triangle of side a. The resultant electric force on a charge \( +\boldsymbol{q} \) placed at the centroid 0 of the triangle is:
A \( \cdot \frac{3 q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
в. \( \frac{q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
c. \( \frac{q^{2}}{2 \pi \varepsilon_{0} a^{2}} \)
D. \( \frac{3 q^{2}}{2 \pi \varepsilon_{0} a^{2}} \)
Subject: Maths
If \( \lim _{x \rightarrow-2} \frac{x^{p}+2^{p}}{x+2}=80 \) (where \( p \) is an odd
number), then \( p \) can be
\( A \cdot 3 \)
B. 5
\( c \cdot 7 \)
D. 9
Subject: Physics
The density of newly discovered planet is twice that of the earth. The
acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of
the earth is It the radius of the plane would be
A \( .2 . R \)
в. \( 4 R \)
c. \( \frac{1}{4} R \)
D・\( \frac{1}{2} R \)
Subject: Physics
Although Rutherford's planetary mode of the atom was a major step forward in understanding the structure of the atom, which of the following was a major problem for this model-one that Bohr's model attempted to fix?
A. Electrons cannot orbit in elliptical paths
B. Cometary electrons would interfere with the normal orbits of electrons
C. Gravity is too strong to allow stable electron orbits
D. orbiting electrons would emit electromagnetic energy and spiral into the nucleus
E. orbiting electrons are all the same size, unlike the planets
Subject: Physics
A ball is thrown horizontally from a point \( 100 \mathrm{m} \) above the ground with a speed of \( 200 \mathrm{m} / \mathrm{s} \). Find (a) the time it takes to reach the ground,
(b) the horizontal distance it travels before
reaching the ground,
(c) the velocity (direction and magnitude) with which it strikes the ground.
Subject: Chemistry
For an isomerization \( \boldsymbol{X}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{Y}(\boldsymbol{g}), \) the
temperature dependency of equilibrium constant is given by :
\( \mathbf{n}=2-\frac{\mathbf{1 0 0 0}}{\mathbf{T}} \)
The value of \( \Delta_{r} S^{o} \) at \( 300 K \) is :
\( \mathbf{A} \cdot 2 R \)
в. \( \frac{2}{R} \)
c. \( 1000 R \)
D. None of these
Subject: Maths
\( \lim _{n \rightarrow \infty}\left(\frac{2 n^{3}}{2 n^{2}+3}+\frac{1-5 n^{2}}{5 n+1}\right) \) is equal to.
A . 0
B. 1
\( c \cdot 1 / 5 \)
D.
Subject: Maths
Solve the following pair of equations by reducing them to a pair of linear equations:
\( \frac{1}{2 x}+\frac{1}{3 y}=2, \frac{1}{3 x}+\frac{1}{2 y}=\frac{13}{6} \)
A \( \cdot x=\frac{1}{4} \) and \( y=\frac{1}{7} \)
B. \( x=\frac{2}{5} \) and \( y=\frac{1}{3} \)
c. \( _{x}=\frac{3}{7} \) and \( y=\frac{1}{7} \)
D. \( x=\frac{1}{2} \) and \( y=\frac{1}{3} \)
Subject: Chemistry
In a first order reaction the
concentration of reactant decreases
from 800 mol \( / d m^{3} \) to \( 50 m o l / d m^{3} \) in
\( 2 \times 10^{4} \) sec. The rate constant of
reaction in \( \sec ^{-1} \) is:
A \( \cdot 2 \times 10^{4} \)
B. \( 3.415 \times 10^{-5} \)
c. \( 1.386 \times 10^{-4} \)
D. None of these
Subject: Chemistry
When 3 L of \( 0.5 ~ M \) NaCl is mixed with
\( 9 \mathrm{L} \) of \( 0.2777 M N a C l, \) determine the
concentration of the final solution, assuming that volumes are additive?
A. 0.33 M .
В. 0.39 М
c. \( 0.5777 M \)
D. \( 0.7777 M \)
E. None of the above
Subject: Maths
Let \( S \) be a square with sides of length \( x \)
If we approximate the change in size of the area of \( S \) by \( \left.h \cdot \frac{d A}{d x}\right|_{x=x_{0}}, \) when the sides are changed from \( x_{0} \) to \( x_{o}+h \)
then the absolute value of the error in
our approximation, is
\( \mathbf{A} \cdot h^{2} \)
B. \( 2 h x_{0} \)
c. \( x_{0}^{2} \)
D. \( h \)
Subject: Chemistry
State whether the given statement is True or False.
\( C u O \) can't be reduced by carbon but it
can be reduced by \( H_{2} \)
\( \operatorname{given}: \Delta G_{f}^{\circ} \) for \( C u O=-129.7 \mathrm{kJ} \mathrm{mol}^{-1} \)
\( C O=-137.2 \mathrm{kJ} \mathrm{mol}^{-1} \mathrm{H}_{2} \mathrm{O}=-237.2 \mathrm{kJ} \)
\( m o l^{1} \)
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{H} \) of \( \mathbf{1 0}^{-8} \mathbf{M} \boldsymbol{B} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \) solution will
be:
A . 6.96
B. 6.31
c. 7.04
D. 7.08
Subject: Maths
Solve the following pair of linear (simultaneous) equations by the method of elimination:
\( \boldsymbol{y}=\boldsymbol{4} \boldsymbol{x}-\mathbf{7} \)
\( 16 x-5 y=25 \)
A \( \cdot x=\frac{3}{2}, y=6 \)
B・ \( x=\frac{5}{2}, y=3 \)
c. \( _{x}=\frac{7}{4}, y=2 \)
D. \( x=\frac{9}{2}, y=0 \)
Subject: Physics
A \( 1500 k g \) car moving on a flat road negotiates a curve whose radius is \( 35 m . \) If the coefficient of static friction
between the tyres and the dry pavement is \( 0.5 . \) Find the maximum speed, the car can have in order to make the turn
successfully.
A. \( 13.1 \mathrm{m} / \mathrm{s} \)
В. \( 15.1 \mathrm{m} / \mathrm{s} \)
c. \( 20 m / s \)
D. \( 25 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Circles are described on the major axis and the line joining the foci of the ellipse \( 3 x^{2}+2 y^{2}=6 \) as diameters.
Then the radii of the circles are in the
ratio:
A \( \cdot \sqrt{2}: 1 \)
B. \( \sqrt{3}: 1 \)
\( c .3: 2 \)
D. 5: 4
Subject: Maths
\( \mathbf{f} A=\left\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{1} ; \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R}\right\} \)
and \( B=\left\{(x, y): x^{2}+y^{2} \geq 4 ; x, y \epsilon R\right\} \)
then
\( \mathbf{A} \cdot A-B=\phi \)
в. \( B-A=\phi \)
c. \( A \cap B \neq \phi \)
D. \( A \cap B=\phi \)