AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The moon is observed from two
diametrically opposite points on earth. The angle subtended at the moon by the
two directions of observations is \( 1^{\circ} 54^{\prime} \)
Given the diameter of the earth to be
about \( 2.276 \times 10^{7} m, \) compute the
distance of moon from the earth.
A \( \cdot 1 \times 10^{8} m \)
В. \( 6.84 \times 10^{8} \mathrm{m} \)
c. \( 6.84 \times 10^{10} m \)
D. \( 38.4 \times 10^{8} \mathrm{m} \)
Subject: Maths
The, sum of the radius of the base and
the height of a solid cylinder is 37 metres. If the total surface area of the
cylinder be 1628 sq. metres, its volume is :
A \( .3180 m^{3} \)
в. \( 4620 m^{3} \)
\( c .5240 m^{3} \)
D. None of these
Subject: Maths
If \( 2 A-\left[\begin{array}{ll}1 & 2 \\ 7 & 4\end{array}\right]=\left[\begin{array}{cc}3 & 0 \\ 0 & -2\end{array}\right], \) then \( A \) is
equal to
\( \mathbf{A} \cdot\left[\begin{array}{cc}2 & 1 \\ 7 / 2 & 1\end{array}\right] \)
В. \( \left[\begin{array}{cc}4 & 4 \\ 7 / 2 & 1\end{array}\right] \)
c. \( \left[\begin{array}{ll}3 & -1 \\ 7 & 2\end{array}\right] \)
D. None of these
Subject: Physics
When a resistor of \( 11 \Omega \) is connected in
series with an electric cell, the current
flowing in it is \( 0.5 A . \) Instead when a
resistor of \( 5 \Omega \) is connected to the same
electric cell in series, the current increases by \( 0.4 A . \) The internal resistance of the cell is
A. \( 1.5 \Omega \)
B. 2\Omega
\( c .2 .5 \Omega \)
D. 3.5\Omega
Subject: Physics
Two identical balls of equal masses \( A \)
and \( \mathrm{B} \), are lying on a smooth surface as shown in the figure. Ball A hits the ball B (which is at rest) with a velocity \( v= \) \( 16 m s^{-1} . \) What should be the minimum
value of coefficient of restitution
between \( A \) and \( B \) so that \( B \) just reaches the highest point of inclined plane?
\( \left(g=10 m s^{-2}\right) \)
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{3} \)
Subject: Chemistry
\( N_{2} F_{4}(g) \rightleftharpoons 2 N F_{2}(g) ; \Delta H^{o}=38.5 k J \)
Which of the following conditions will
favour the formation of \( N F_{2} ? \)
This question has multiple correct options
A. Adding He to the equilibrium mixture at constant temperature and volume
B. Increasing the temperature.
c. \( N F_{2} \) gas is removed from the reaction mixture.
D. Decreasing the pressure at constant temperature
Subject: Physics
Two isolated point poles of strength
\( 30 A m^{2} \) and \( 60 A m^{2} \) are placed at a
distance of 0.3 m. The force of repulsion
is:
A \( \cdot 2 \times 10^{-3} N \)
B . \( 2 \times 10^{-4} N \)
C \( .2 \times 10^{5} N \)
D. \( 2 \times 10^{-5} N \)
Subject: Physics
A bar magnet of pole strength \( 20 A-m \)
is cut into four equal parts breadth wise. Consider the following statements
A) Length becomes \( 1 / 4^{t h}, \) pole strength will be same. Intensity of magnetisation
will be same
B) Length becomes \( 1 / 4^{t h}, \) pole strength
will be \( 1 / 4^{t h} . \) Intensity of magnetisation
also becomes \( 1 / 4^{t h} \)
A . A is correct
B. B is correct
c. Both A and B are correct
D. Both A and B are false
Subject: Chemistry
The correct order of
pseudohalide,polyhalide and interhalogen are
\( \mathbf{A} \cdot B r I_{2}^{-}, O C N^{-}, I F_{5} \)
B \( \cdot I F_{5} \cdot B r I_{2}^{-}, O C N^{-} \)
\( \mathbf{c} \cdot O C N^{-}, I F_{5}, B r I_{2}^{-} \)
D. \( O C N^{-}, B r I_{2}^{-}, I F_{5} \)
Subject: Maths
The centre of two circles are \( 41 \mathrm{cm} \)
apart: The smaller circle has a radius of 4 inches and the larger one has ab radius of \( 5 \mathrm{cm} . \) The length of the common internal tangent is :
\( \mathbf{A} \cdot 41 \mathrm{cm} \)
в. \( 39 \mathrm{cm} \)
\( \mathrm{c} .39 .8 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)
Subject: Chemistry
Which of the following isomeric pairs
shows ionization isomerism?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]\left[\operatorname{Cr}(C N)_{6}\right] \) and \( \left[\operatorname{Cr}\left(N H_{3}\right)_{6}\right]\left[\operatorname{Co}(C N)_{6}\right] \)
\( \mathbf{B} \cdot\left[C r\left(H_{2} O\right)_{6}\right] C l_{3} \) and \( \left[C r\left(H_{2} O\right)_{5} C l\right] C l_{2} H_{2} O \)
\( \mathbf{C} \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \) and \( \left[P t\left(N H_{3}\right)_{4}\right]\left[P t C l_{4}\right] \)
\( \mathbf{D} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} B r\right] S O_{4} \) and \( \left[C o\left(N H_{3}\right)_{5} S O_{4}\right] B r \)
Subject: Chemistry
A metallic element has a cubic lattice.
Each edge of the unit cell is \( 2 \AA \). The
density of the metal is \( 2.5 \mathrm{cm}^{-3} \) The unit
cells in 200 g of metal are :
A \( .1 \times 10^{2} \)
В. \( 1 \times 10^{26} \)
\( c \cdot 1 \times 10^{2} \)
2
D. \( 1 \times 10^{25} \)
Subject: Physics
A gas is filled in a container at any
temperature and at pressure \( 76 \mathrm{cm} \) of Hg. If at the same temperature the
mass of gas is increased by \( 50 \% \) then the resultant pressure will be
\( A .38 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 76 \( \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 114 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 152 \mathrm{cm} \) of \( \mathrm{Hg} \)
Subject: Physics
3 mole of \( A g \) is heated from \( 300 K \) to
1000 \( K \). Calculate \( \Delta H \) when \( P=1 \) at \( m \)
and \( C_{p}=23+0.01 T \)
A. \( 62 k J / m o l \)
B. \( 45 \mathrm{kJ} / \mathrm{mol} \)
c. \( 38 k J / m o l \)
D. \( 54 ~ k J / m o l \)
Subject: Physics
A player kicks a football of mass \( 0.5 \mathrm{kg} \) and the football begins to move with a
velocity of \( 10 \mathrm{m} / \mathrm{s} \). If the contact
between the leg and the football lasts for \( \frac{1}{50} \) sec, then the force acted on the football should be
A \( .2500 N \)
в. \( 1250 N \)
c. \( 250 N \)
D. \( 625 N \)
Subject: Physics
For a cell, a graph is plotted between the potential difference \( V \) across the
terminals of the cell and the current \( I \)
drawn from the cell (see Figure). The
emf and the internal resistance of the
cell are \( E \) and \( r, \) respectively. Then :
A \( . E=2 V, r=0.5 \Omega \)
B. \( E=2 V, r=0.4 \Omega \)
c. \( E>2 V, r=0.5 \Omega \)
D. \( E>2 V, r=0.4 \Omega \)
Subject: Maths
If the sums of \( p, q \) and \( r \) terms of an A.P. be \( a, b \) and \( c \) respectively, then prove \( \operatorname{that} \frac{\boldsymbol{a}}{\boldsymbol{p}}(\boldsymbol{q}-\boldsymbol{r})+\frac{\boldsymbol{b}}{\boldsymbol{q}}(\boldsymbol{r}-\boldsymbol{p})+\frac{\boldsymbol{c}}{\boldsymbol{r}}(\boldsymbol{p}- \)
\( \boldsymbol{q})=\mathbf{0} \)
Subject: Physics
A liquid takes 5 minutes to cool from
\( 80^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} . \) How much time(in mins)
will it take to cool from \( 60^{\circ} \mathrm{C} \) to \( 30^{\circ} \mathrm{C} \) ?
The temperature of surrounding is \( 20^{\circ} \mathrm{C} \)
Use exact method.
Subject: Physics
Figure shows a capacitor made of two
circular plates each of radius \( 12 \mathrm{cm} \)
and separated by \( 5.0 \mathrm{cm} . \) The capacitor
is being charged by an external source (not shown in the figure). The charging
current is constant and equal to 0.15 A.
(a) Calculate the capacitance and the
rate of change of potential difference
between the plates.
\( (b) \)
Obtain the displacement current across
the plates.
\( (c) \)
Is
Kirchhoffs first rule (junction rule) valid
at each plate of
the capacitor Explain.
Subject: Maths
Area of the region bounded by the
curves, \( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}}, \boldsymbol{y}=\boldsymbol{e}^{-\boldsymbol{x}} \) and the straight
line \( x=1 \) is given by
A \( \cdot\left(e-e^{-1}+2\right) \) sq.unit
B \( \cdot\left(e-e^{-1}-2\right) \) sq.unit
c. \( \left(e+e^{-1}-2\right) \) sq.unit
D. None of the above
Subject: Maths
If \( I=\int_{8}^{15} \frac{d x}{(x-3) \sqrt{x+1}} \) then \( I \) equals
A \( \cdot \frac{1}{2} \log \frac{5}{3} \)
B. \( 2 \log \frac{1}{3} \)
c. \( \frac{1}{2}-\log \frac{1}{5} \)
D. \( 2 \log \frac{5}{3} \)
Subject: Physics
The wave number of energy emitted when electron jumps from fourth orbit to seconds orbit in hydrohen in \( 20,497 \mathrm{cm}^{-1} . \) The wave number of
energy for the same transition in \( \boldsymbol{H} \boldsymbol{e}^{+} \)
is
A \( .5,099 \mathrm{cm}^{-1} \)
B . \( 20,497 \mathrm{cm}^{-1} \)
c. \( 40,994 \mathrm{cm}^{-1} \)
D. \( 81,988 \mathrm{cm}^{-1} \)
Subject: Physics
A capillary tube when immersed vertically in a liquid records a rise of \( 3 c m . \) if the tube is immersed in the
liquid at an angle of \( 60^{\circ} \) with the vertical, then length of the liquid
column along the tube will be:
\( A \cdot 2 c m \)
в. 3 ст
c. \( 6 \mathrm{cm} \)
D. 9 cm
Subject: Maths
toppr
Q Type your question
\( \begin{array}{llllll}\text { Life } \bmod e & 0- & 20- & 40- & 60- & 80 \\ \text { Hrs.) } & 20 & 40 & 60 & 80 & 100\end{array} \)
No. of
electric
bulbs
\[
82
\]
\begin{tabular}{lll} 
31 & 36 & 38 & 42 \\
\hline
\end{tabular} Find the modal life of the electric bulbs.
Subject: Maths
Let \( \boldsymbol{f}:\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\} \rightarrow\{1,2,3\} \) be a one-one
mapping such that only one of the following three statements and remaining two are false : \( \boldsymbol{f}(\boldsymbol{x}) \neq \) \( \mathbf{2}, \boldsymbol{f}(\boldsymbol{y})=\mathbf{2}, \boldsymbol{f}(\boldsymbol{z}) \neq 1, \) then
A \( . f(x)>f(y)>f(z) \)
в. \( f(x)<f(y)<f(z) \)
c. \( f(y)<f(y)<f(z) \)
D. \( f(y)<f(z)<f(x) \)
Subject: Maths
Factorize:
\( 9 a^{2}+\frac{1}{9 a^{2}}-2-12 a+\frac{4}{3 a} \)
A \( \cdot\left(3 a-\frac{1}{3 a}\right)\left(3 a-\frac{1}{3 a}-4\right) \)
B. \( \left(a-\frac{1}{3 a}\right)\left(7 a-\frac{1}{3 a}-1\right) \)
c. \( \left(3 a-\frac{1}{3 a}\right)\left(2 a-\frac{1}{3 a}-4\right) \)
D. \( \left(3 a-\frac{1}{3 a}\right)\left(4 a-\frac{1}{3 a}-1\right) \)
Subject: Physics
What are the dimensions of \( \boldsymbol{K}=\frac{\mathbf{1}}{\mathbf{4} \boldsymbol{\pi} \boldsymbol{\epsilon}_{0}} ? \)
(Given, N is the unit of force, with
dimensions \( M L T^{-2} \) )
A \( \cdot C^{2} N^{-1} M^{-2} \)
в. \( N M^{2} C^{-2} \)
c. \( N M^{2} C^{2} \)
D. Unitless
Subject: Chemistry
Which of the following are physical changes?
(i) Melting of iron metal
(ii) Rusting of iron
(iii) Bending of an iron rod
(iv) Drawing a wire of iron metal
A. (i), (ii) and (iii)
B. (i), (ii) and (iv)
c. (i), (iii) and (iv)
D. (ii), (iii) and (iv)
Subject: Chemistry
What happens when a mixture of cobalt oxide and borax is heated in a flame on
a loop of platinum wire?
A. A transparent white bead is formed
B. A bright pink coloured \( N a B O_{2} \) bead is formed
C. A blue coloured \( C o\left(B O_{2}\right)_{2} \) bead is formed
D. A red coloured \( C o\left(B O_{2}\right)_{2} \) bead is formed
Subject: Chemistry
Applications of \( \boldsymbol{O}_{3} \) are:
(a) It absorbs UV light. It is used as a disinfectant to purify drinking water,
since it destroys bacteria and viruses.
(b) Its advantage over \( C l_{2} \) for this purpose is that it avoids the unpleasant smell and taste of chlorine since any
excess \( 0_{3} \) soon decompose to \( O_{2} \)
A. Both are true.
B. (a) is true \& (b) is false.
c. (a) is false \( \& \) (b) is true.
D. None of these
Subject: Chemistry
Assertion: The aqueous solution of
\( C F_{3} C O O^{-} N a^{+} \) is more basic than the
aqueous solution of \( \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-} \boldsymbol{N a}^{+} \)
for the same concentration of salt.
Reason: The salt derived from a weak
acid and strong base hydrolyses to
generate a basic solution.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct
Subject: Chemistry
For a zero order chemical reaction,
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \rightarrow \boldsymbol{N}_{2}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \)
rate of reaction \( =0.1 \) atm/sec. Initially
only \( N H_{3} \) is present and its pressure
\( =3 \) atm. Calculate total pressure at
\( t=10 \mathrm{sec} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{1-\sin 2 \boldsymbol{x}}, \) then \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \) is
equal to:
This question has multiple correct options
A. \( -(\cos x+\sin x) \), for \( x \in(\pi / 4, \pi / 2) \)
B. \( (\cos x+\sin x) \), for \( x \in(0, \pi / 4) \)
c. \( -(\cos x+\sin x) \), for \( x \in(0, \pi / 4) \)
D. None of these
Subject: Maths
If heads means one and tail means two,
then coefficients of quadratic equation
\( a x^{2}+b x+c=0 \) are chosen by tossing
three fair coins. The probability that roots of the equation are imaginary is
A \( \cdot \frac{5}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{7}{8} \)
D.
Subject: Physics
Assertion
A particle in \( x-y \) plane is related by
\( \boldsymbol{x}=\boldsymbol{a} \sin \omega \boldsymbol{t} \) and \( \boldsymbol{y}=\boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\omega} \boldsymbol{t}) \)
where \( a \) and \( \omega \) constants, then the
particle will have parabolic motion.
Reason

A particle under the influence of two perpendicular velocities has parabolic
motion.
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
Fill in the blanks in the following conversions:
¡) \( 1 k m=\dots \dots \dots . . m m=\dots \dots \dots . . p m \)
ii) \( 1 \boldsymbol{m} \boldsymbol{g}=\ldots \ldots \ldots \boldsymbol{k} \boldsymbol{g}=\ldots \ldots \ldots \boldsymbol{n} \boldsymbol{g} \)
iii) \( 1 m L=\dots \dots \dots . . L=\dots \dots \dots . d m^{3} \)
Subject: Maths
If \( x \) is so small that \( x^{3} \) and higher
powers of \( x \) may be neglected, then \( \frac{(1+x)^{3 / 2}-\left(1+\frac{1}{2} x\right)^{3}}{(1-x)^{1 / 2}} \) may be approximated
as
A \( \cdot \frac{x}{2}-\frac{3}{8} x^{2} \)
B. \( -\frac{3}{8} x^{2} \)
c. \( _{3 x+\frac{3}{8} x^{2}} \)
D. \( 1-\frac{3}{8} x^{2} \)
Subject: Maths
If \( S_{1}, S_{2} \) and \( S_{3} \). are the sums of first \( n \) natural numbers, their squares and
their cubes respectively, then
\( \boldsymbol{S}_{3}\left(\mathbf{1}+\mathbf{8} \boldsymbol{S}_{1}\right)= \)
\( A \cdot S_{2}^{2} \)
в. \( 9 S_{2} \)
\( \mathrm{c} \cdot 9 S_{2}^{2} \)
D. None
Subject: Maths
\( \int \frac{[\log (\log \boldsymbol{x})]^{\boldsymbol{m}}}{\boldsymbol{x} \log \boldsymbol{x}} \boldsymbol{d} \boldsymbol{x}= \)
\( \mathbf{A} \cdot \frac{[\log (\log (x))]^{m+1}}{m+1}+c \)
B. \( \frac{[\log (\log (x))]^{m}}{m}+c \)
c. \( \frac{[\log (\log (x))]^{m+1}}{m}+c \)
D. \( \frac{[\log (\log (x))]^{m}}{m+1}+c \)
Subject: Physics
Two masses \( A \) and \( B \) are moving in the same straight line, A moves with a
uniform velocity of \( 11 m / \)sec\( , B \) starts from rest at the instant when it is 52.5
metres ahead of \( A \), and moves with a
uniform acceleration \( 1 \mathrm{m} / \mathrm{sec}^{2} \). When
will \( A \) catch \( B ? \) Explain the reason for
two answers?
Subject: Chemistry
Assertion
The rate of reaction increases generally
by 2 to 3 times for every \( 10^{\circ} \mathrm{C} \) rise in temperature.
Reason
An increase in temperature increases the coliision frequency.
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
An ideal monoatomic gas undergoes
expansion according to \( \boldsymbol{P}=\boldsymbol{b} \boldsymbol{V}, \) Where
b' is a constant.Molar heat capacity of
gas in the process is
A \( \cdot \frac{3 R}{2} \)
в. \( 2 R \)
c. \( \frac{5 R}{2} \)
D. 3R
Subject: Physics
A ball is released from the top of a tower
of height h meters. It takes T seconds to reach the ground. What is the position of the ball in \( \frac{T}{3} \) seconds?
A \( \cdot \frac{h}{9} \) metres from the ground
B. \( \frac{7 h}{9} \) metres from the ground
c. \( \frac{8 h}{9} \) metres from the grounds
D. \( \frac{17 h}{18} \) metres from the ground
Subject: Chemistry
Find the ratio by mass of the combining
elements in the \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A. 1: 16: 32
B . 15: 16: 32
\( \mathbf{c} \cdot 1: 16: 16 \)
D. none of these
Subject: Physics
The electric field in a region of space is given by \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{0} \hat{\boldsymbol{i}}+\boldsymbol{2} \boldsymbol{E}_{\boldsymbol{o}} \hat{\boldsymbol{j}} \) where \( \boldsymbol{E}_{\boldsymbol{o}}= \)
\( \mathbf{1 0 0} N / C . \) The flux of this field through a
circular surface of radius \( 0.02 \mathrm{m} \)
parallel to the \( Y \) -Z plane is nearly:
A \( \cdot 0.125 \mathrm{Nm}^{2} / \mathrm{C} \)
B . \( 0.02 \mathrm{Nm}^{2} / \mathrm{C} \)
c. \( 0.005 \mathrm{Nm}^{2} / \mathrm{C} \)
D. \( 3.14 \mathrm{Nm}^{2} / \mathrm{C} \)
Subject: Maths
Show that the vectors \( 2 \hat{i}-\hat{j}+\hat{k}, \hat{i}- \) \( \mathbf{3} \hat{\boldsymbol{j}}-\mathbf{5} \hat{\boldsymbol{k}} \quad \) and \( \quad \mathbf{3} \hat{\mathbf{i}}-\mathbf{4} \hat{\boldsymbol{j}}-\mathbf{4} \hat{\boldsymbol{k}} \) form the
vertices of a right angled triangle.
Subject: Physics
If an electron and positron annihilate, then the energy released is
A . \( 3.2 \times 10^{-13} \mathrm{J} \)
В. \( 1.6 \times 10^{-13} \mathrm{J} \)
c. \( 4.8 \times 10^{-13} \mathrm{J} \)
D. \( 6.4 \times 10^{-13} \mathrm{J} \)
Subject: Physics
A current of \( 3.14 A \) flows in an infinitely long wire with cross section in the form of a semicircular ring of radius \( 5 \mathrm{cm} \) The magnitude of magnetic induction on its axis is :
A . \( 8.0 \times 10^{-6} T \)
В. \( 1.6 \times 10^{-5} T \)
c. \( 2.0 \times 10^{-5} T \)
D. \( 4.0 \times 10^{-6} T \)
Subject: Chemistry
What is the \( K_{b} \) for \( N H_{2} \) group in glycine?
\( \mathbf{A} \cdot 4 \times 10^{-3} \)
в. \( 1.6 \times 10^{-10} \)
c. \( 6.25 \times 10^{-5} \)
D. \( 2.5 \times 10^{-12} \)
Subject: Chemistry
An electron of a velocity \( x \) is found to have a certain wavelength. The velocity to be possessed by the neutron to have half the de Broglie wavelength possessed by electron is:
A \( \cdot \frac{x}{1840} \)
в. \( \frac{x}{920} \)
c. \( 3680 x \)
D. \( \frac{x}{3680} \)
Subject: Maths
The displacement of \( S \) of a particle at time \( t(O<t<\pi) \) is given by \( S= \)
\( \sin 2 t-6 \cos t . \) Then the acceleration for
the value of \( t \) for which its velocity is
zero is
A .0 unit/ \( \sec ^{2} \)
B. 3 unit/ sec \( ^{2} \)
c. 2 unit \( \mid \sec ^{2} \)
D. 4 unit/ \( \sec ^{2} \)
Subject: Physics
A car is moving in a circular track of radius \( 10 \mathrm{m} \) with a constant speed of 10 \( \mathrm{m} / \mathrm{s} . \mathrm{A} \) plumb bob is suspended from the roof of the car by a light weight rigid rod of \( 1 \mathrm{m} \) long.The angle made by the rod with track is:
A. 0
B. 30
\( c \cdot 45 \)
D. 60
Subject: Chemistry
\( A 26 \mathrm{ml} \) of \( N-N a_{2} C O_{3} \) solution is
neutralized by the solutions of acids \( A \) and \( \mathrm{B} \) in different experiments. The volumes of the acids \( A \) and \( B \) required
were \( 10 m l \) and \( 40 m l \), respectively. How
many volumes of \( A \) and \( B \) are to be mixed in order to prepare 1 litre of normal acid solution?
A \( .179 .4,820.6 \)
B. 820.6,179.4
c. 500,500
D. 474.3,525.7
Subject: Physics
Assertion (A): Nuclear fusion reactions
are considered as thermo-nuclear
reactions
Reason (R): The source of stellar energy
is nuclear fusion
A. Both A \& R are true and R is the correct explanation of \( A \)
B. Both A \& R are true and R is not correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. A is false but R is true
Subject: Chemistry
In an experiment during the analysis of
a carbon compound, 145 cc of \( H_{2} \) was collected at 760 mm of Hg pressure and
\( 27^{\circ} \mathrm{C} \) temperature. The mass of \( \boldsymbol{H}_{2} \) is
nearly:
A . \( 10 \mathrm{mg} \)
B. \( 12 \mathrm{mg} \)
c. \( 24 m g \)
D. \( 6 \mathrm{mg} \)
Subject: Maths
The area bounded by \( \boldsymbol{x}=\boldsymbol{a} \cos ^{3} \boldsymbol{\theta}, \boldsymbol{y}= \)
\( a \sin ^{3} \theta \) is:
A \( \cdot \frac{3 \pi a^{2}}{16} \)
в. \( \frac{3 \pi^{2}}{8} \)
c. \( \frac{3 \pi a^{2}}{32} \)
D. \( 3 \pi a^{2} \)
Subject: Physics
A manometer connected to a closed tap reads \( 3.5 \times 10^{5} N / m^{2} . \) When the value
is opened,the reading of manometer fall
to \( 3.0 \times 10^{5} N / m^{2}, \) then velocity of flow
of water is
A. \( 100 \mathrm{m} / \mathrm{s} \)
в. \( 1 \mathrm{m} / \mathrm{s} \)
\( c \cdot 10 m / s \)
D. \( 10 \sqrt{10} \mathrm{m} / \mathrm{s} \)
Subject: Maths
From a rectangular metal sheet of sides
\( 25 \mathrm{cm} \) and \( 20 \mathrm{cm} \) a circular sheet as
large as possible is cut off What is the area of the remaining metal sheet?
\( A \cdot 186 c m^{2} \)
В. \( 144 \mathrm{cm}^{2} \)
\( c \cdot 185 c m^{2} \)
\( \mathbf{D} \cdot 72 c m^{2} \)
Subject: Maths
Solve \( (\boldsymbol{x} \boldsymbol{y}-\mathbf{1}) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y}^{2}=\mathbf{0} \)
A. \( x y+\log x=C \)
в. \( x y+\log y=C \)
c. \( x y-\log y=C \)
D. \( x y-\log x=C \)
Subject: Physics
The distance between two consecutive
crests in a wave train produced in string is \( 5 \mathrm{m} \). If two complete waves pass through any point per second, the velocity of wave is:
A \( .2 .5 \mathrm{m} / \mathrm{s} \)
B. \( 5 \mathrm{m} / \mathrm{s} \)
c. \( 10 \mathrm{m} / \mathrm{s} \)
D. \( 15 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
10 L of hard water with temporary
hardness of \( \left[\boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2}\right] \) requires
\( 0.56 \mathrm{g} \) of lime. The reaction follows as:
\( \boldsymbol{C a}\left(\boldsymbol{H C O}_{3}\right)_{2}+\boldsymbol{C a O} \longrightarrow \boldsymbol{2} \boldsymbol{C a} \boldsymbol{C O}_{3}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Temporary hardness in terms of ppm of
\( \boldsymbol{C a} \boldsymbol{C O}_{3} \) is:
\( A .56 \) ppm
B. \( \frac{1}{2} \) ppm
c. 100 ppm
D. 200 ppm
Subject: Chemistry
There is \( 50 \% \) dimer formation of benzoic
\( \operatorname{acid}\left(C_{6} H_{5} C O O H\right) \) in benzene
solution.
\( 2 C_{6} H_{5} C O O H \rightleftharpoons\left(C_{6} H_{5} C O O H\right)_{2} \)
Hence the abnormal molecular weight of benzoic acid ( theoretical value \( =122 \)
\( \left.g m o l^{-1}\right) \) is:
A. \( 61 \mathrm{g} \) mol \( ^{-1} \)
B. 244 g mol-
c. \( 163 \mathrm{g} \) mol \( ^{-1} \)
D. 81 g \( m o l^{-1} \)
Subject: Chemistry
For which of the following equations is
the change in enthalpy at \( 25^{\circ} \mathrm{C} \) and 1
atm equal to \( \Delta H_{f}^{o} \) of \( C H_{2} O(l) \)
A \( \cdot C(s)+H_{2}(g)+1 / 2 O_{2}(g) \rightarrow C H_{2} O(l) \)
B. \( C(s)+2 H_{2}(g)+1 / 2 O_{2}(g) \rightarrow 2 C H_{2} O(l) \)
c. \( C(g)+2 H_{2}(g)+O(g) \rightarrow C H_{2} O(l) \)
D. \( C O(g)+2 H_{2}(g) \rightarrow C H_{2} O(l) \)
Subject: Maths
Find the coordinates of the point \( \boldsymbol{P} \)
which divides line segment \( Q R \)
internally in the ratio \( m: n \) in the
following example:
\( Q \equiv(-5,8), R \equiv(4,-4) \) and \( m: n=2: 1 \)
is (1,0)
If true then enter 1 and if false then
enter 0
Subject: Maths
If \( \boldsymbol{I}=\int_{0}^{1 / \sqrt{3}} \frac{\boldsymbol{d} \boldsymbol{x}}{\left(1+\boldsymbol{x}^{2}\right) \sqrt{1-\boldsymbol{x}^{2}}} \) then \( \boldsymbol{I} \) is
equal to
\( \mathbf{A} \cdot \pi / 2 \)
B. \( \pi / 2 \sqrt{2} \)
c. \( \pi / 4 \sqrt{2} \)
D . \( \pi / 4 \)
Subject: Physics
If two protons are moving with speed \( \boldsymbol{v}=\mathbf{4 . 5} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{m} / \mathrm{s} \) parallel to each other
then find the ratio of electrostatic and
magnetic force between them?
\( \mathbf{A} \cdot 4.4 \times 10^{5} \)
В. \( 2.2 \times 10^{5} \)
c. \( 3.3 \times 10^{5} \)
D. \( 1.1 \times 10^{5} \)