AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
An ideal gas is mixture of \( C_{2} H_{6} \) and
\( C_{2} H_{4} \) occupies 281 at 1 atm 8273 k. The
mixture reacts completely with 128 g of \( O_{2} \) to produce \( C O_{2} \) pf water vapour
Mole fraction of \( C_{2} H_{6} \) in the mixture
will be:
A. 0.4
B. 0.6
\( c \cdot 0.2 \)
D. 0.8
Subject: Physics
Four particles of masses \( \mathrm{m}, 2 \mathrm{m}, 3 \mathrm{m} \) and
\( 4 m \) are at the vertices of a
parallelogram in \( x \) y plane with one of the adjacent angle 60 and smaller side
a and larger side 2a. The mass m is at
the origin and mass \( 4 \mathrm{m} \) on the \( \mathrm{x} \) -axis. The centre of mass of the system is
A \( \cdot\left(\frac{33 \mathrm{a}}{20} ; \frac{5 \sqrt{3} \mathrm{a}}{2}\right) \)
B \( \cdot\left(\frac{a}{2} ; \frac{3 a}{2}\right) \)
\( ^{\mathrm{C}}\left(0.95 \mathrm{a} ; \frac{\sqrt{3 \mathrm{a}}}{4}\right) \)
D. \( \left(\frac{\sqrt{3 \mathrm{a}}}{2} ; 0.82 \mathrm{a}\right) \)
Subject: Physics
at a constant temperature of \( \theta \). Assume
that it obeys Newton's law of cooling. Its
temperature \( \theta \) is plotted against time \( t \)
Tangents are drawn to the curve at the
points \( \boldsymbol{P}\left(\boldsymbol{\theta}=\boldsymbol{\theta}_{1}\right) \) and \( \mathrm{Q}\left(\boldsymbol{\theta}=\boldsymbol{\theta}_{2}\right) . \) These
tangents meets the time axis at angles
of \( \phi_{2} \) and \( \phi_{1} \) as shown
\( \mathbf{A} \cdot \frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{1}-\theta_{0}}{\theta_{2}-\theta_{0}} \)
B. \( \frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{2}-\theta_{0}}{\theta_{1}-\theta_{0}} \)
c. \( \frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{1}}{\theta_{2}} \)
D. \( \frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{2}}{\theta_{1}} \)
Subject: Chemistry
Fire extinguisher's containing \( C O_{2} \) is
the best extinguisher.
A. Because \( C O_{2} \) being heavier than oxygen, covers the fire like a blanket
B. Because \( C O_{2} \) being heavier than oxygen, increase fire
C. Because \( C O_{2} \) being leighter than oxygen, covers the fire like a blanket
D. None of these
Subject: Chemistry
Which one of the following electrolytes is most effective for the coagulation of
\( \boldsymbol{F e}(\boldsymbol{O} \boldsymbol{H})_{3} \) sol?
A . \( N a C l \)
в. \( N a_{2} S O_{4} \)
\( \mathbf{c} \cdot N a_{3} P O_{4} \)
D. \( A s_{2} S_{3} \)
Subject: Maths
The graph of \( y=6 \) is a line:
A. parallel to \( x \) -axis \& at a distance of 6 units from the
\( x- \) axis
B. parallel to \( y \) -axis at a distance of 6 units from the origin
c. making an intercept 6 on the \( x \) -axis
D. making an intercept 6 on both the axes.
Subject: Physics
Two satellites \( A \) and \( B \) of equal mass
move in the equatorial plane of the earth, close to earth's surface. Satellite A moves in the same direction as that of
the rotation of the earth while satellite \( \mathrm{B} \)
moves in the opposite direction. Calculate the ratio of the kinetic energy of \( \mathrm{B} \) to that of \( \mathrm{A} \) in the reference frame
fixed to the earth. \( \left(g=9.8 m s^{-2} \) and \right.
radius of the earth \( =\mathbf{6 . 3 7} \times \mathbf{1 0}^{6} \mathbf{k m} \) ).
Subject: Biology
Consider the following statements \( (A- \)
C) each with one or two blanks.
(A)(1) are the most abundant cells (60-
\( 65 \text { per cent }) \) of the total WBCs and (2) are the least (0.5-1 per cent) among
them.
(B)Platelets are cell fragments produced from (3)
(C)During clot formation, fibrins are formed by the conversion of inactive in the plasma by the enzyme (5). Which one of the following options,
gives the correct fill ups for the respective blank numbers from
(1) to
(5)
in the statements?
A. (I)-Neutrophils, (2)-basophils, (4)-fibrinogens, (5) thrombin
B. (3)-mast cells, (4)-throm bo kinase, (5)prothrombin
c. (3)-megakaryocytes,
(4) prothrombin, (5)thrombin
D. (1)-Basophils, (2)-neutrophils, (3)-reticulocytes
Subject: Maths
\( A B \) and \( C D \) are two chords of a circle
which intersect each other internally at
\( \boldsymbol{P} . \) If \( \boldsymbol{C P}=\boldsymbol{4} \mathrm{cm}, \boldsymbol{A P}=\mathbf{8} \mathrm{cm}, \boldsymbol{P B}=\mathbf{2} \)
\( \mathrm{cm}, \) then find \( P D \)
Subject: Chemistry
Point out incorrect stability order.
\( \mathbf{A} \cdot\left[C u\left(N H_{3}\right)_{4}\right]^{2+}<\left[C u(e n)_{2}\right]^{2+}<[C u(\text {trien})]^{2+} \)
\( ^{\mathbf{B}} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{3+}<\left[F e\left(N O_{2}\right)_{6}\right]^{3-}<\left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
\( ^{\mathbf{C}} \cdot\left[\operatorname{Co}\left(H_{2} O\right)_{6}\right]^{3+}<\left[R h\left(H_{2} O\right)_{6}\right]^{3+}<\left[\operatorname{Ir}\left(H_{2} O\right)_{6}\right]^{3+} \)
\( ^{\mathrm{D}} \cdot\left[C r\left(N H_{3}\right)_{6}\right]^{+}<\left[C r\left(N H_{3}\right)_{6}\right]^{2+}<\left[C r\left(N H_{3}\right)_{6}\right]^{3+} \)
Subject: Maths
In a sequence, if \( S_{n} \) is the sum of the
first \( n \) terms and \( S_{n-1} \) is the sum of the
first \( (n-1) \) terms, then the \( n^{t h} \) term is
A. \( S_{n-2} \)
в. \( S_{n}-S_{n-1} \)
\( \mathbf{c} \cdot S_{n+1}-S_{n} \)
D. \( S_{n+1}-S_{n-1} \)
Subject: Physics
\( 146 k J \) work is performed in order to compress 1 kilomole of gas adiabatically and in this process the temperature of the gas increases by
\( \mathbf{7}^{o} \mathbf{C} . \) The gas is:
(Take \( \left.\boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{m} \boldsymbol{o l} \boldsymbol{e}^{-1} \boldsymbol{K}^{-1}\right) \)
A. monoatomic
B. diatomic
c. triatomic
D. a mixture of monoatomic and diatomic
Subject: Chemistry
Formalin \( 40 \% \) indicates:
A. \( 40 \% \) water, \( 6 \% \) formaldehyde
B. \( 40 \% \) water, \( 60 \% \) formaldehyde
C. \( 60 \% \) water, \( 40 \% \) formaldehyde
D. \( 4 \% \) water, \( 69 \% \) formaldehyde
Subject: Physics
The coefficient of superficial expansion of rod is \( 4 \times 10^{-5} /^{\circ} \mathrm{C} \). The percentage
increase in the volume of a cube of that
metal when it is heated from \( 0^{\circ} \mathrm{C} \) to
\( 100^{\circ} \mathrm{C} \) is :
A . 0.4\%
в. 0.8\%
c. 1.2\%
D. 0.6\%
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{x} \log |\boldsymbol{x}+\sqrt{\left(\mathbf{1}+\boldsymbol{x}^{2}\right)}|-\sqrt{\mathbf{1}+\boldsymbol{x}^{2}} \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
Subject: Physics
Two bodies of different masses
\( m_{1} \) and \( m_{2} \) are dropped from two
different heights \( h_{1} \) and \( h_{2} \). What is the ratio of time taken by the two to reach the ground?
\( \mathbf{A} \cdot \sqrt{h_{1}}: \sqrt{h_{2}} \)
B \( \cdot \sqrt{h_{2}}: \sqrt{h_{1}} \)
c. \( m_{1} h_{2}: m_{2} h_{1} \)
D. \( m_{1} h_{1}: m_{2} h_{2} \)
Subject: Chemistry
The reaction, \( A \stackrel{k}{\longrightarrow} \) Product, is zero order while the reaction, \( \boldsymbol{B} \stackrel{\boldsymbol{k}}{\longrightarrow} \)
Product, is first order reaction. For what
initial concentration of \( A \) are the half
lives of the two reactions equal?
\( \mathbf{A} \cdot(\ln 4) M \)
в. 2 М
c. \( (2 \log 2) M \)
D. \( (\ln 2) M \)
Subject: Physics
How much length of a very wire is required to obtain a solenoid of length \( I_{0} \) and inductance \( L: \)
A \( \cdot \sqrt{\frac{2 \pi L l}{\mu_{0}}} \)
в. \( \sqrt{\frac{4 \pi L l}{\mu_{0}^{2}}} \)
c. \( \sqrt{\frac{4 \pi L l}{\mu_{0}}} \)
D. \( \sqrt{\frac{8 \pi L l}{\mu_{0}}} \)
Subject: Physics
The position of a point in time 't' is given by \( \boldsymbol{x}=\boldsymbol{a}+\boldsymbol{b} \boldsymbol{t}-\boldsymbol{c t}^{2}, \boldsymbol{y}=\boldsymbol{a} \boldsymbol{t}+\boldsymbol{b} \boldsymbol{t}^{2} . \) Its
acceleration at time 't' is
A. \( b-c \)
в. \( b+c \)
c. \( 2 b-2 c \)
D. \( 2 \sqrt{b^{2}+c^{2}} \)
Subject: Chemistry
What is the mass of photon of sodium light having a wavelength of 5890 , i? \( \left(\text { Given } h=6.6 \times 10^{-27} \text {erg }-\text { sec }\right) \)
\( \mathbf{A} \cdot 3.735 \times 10^{-29} g \)
В. \( 3.735 \times 10^{-33} g \)
c. \( 1.57 \times 10^{-33} g \)
D. \( 3.735 \times 10^{-31} g \)
Subject: Biology
The basic difference between mitosis
and meiosis is that
A. Homologous chromosomes form tetrads in mitosis but not in meiosis
B. Homologous chromosomes form tetrads in meiosis but not in mitosis
C. The nuclear membrane disappears in mitosis but not in meiosis
D. A spindle forms in mitosis but not in meiosis
E. A spindle forms in meiosis but not in mitosis
Subject: Chemistry
A 0.004 M solution of \( N a_{2} S O_{4} \) is
isotonic with a \( 0.010 \mathrm{M} \) solution of
glucose at same temperature. The apparent degree of dissociation of
\( N a_{2} S O_{4} \) is:
A . \( 25 \% \)
B . 50\%
c. \( 75 \% \)
D. 85\%
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O A} \boldsymbol{g}+\boldsymbol{B r}_{2} \stackrel{\boldsymbol{C C l}_{4}}{\longrightarrow} \)
\( \boldsymbol{X} \stackrel{\boldsymbol{a q} \cdot \boldsymbol{K O H}}{\longrightarrow} \boldsymbol{Y} \stackrel{\boldsymbol{r e d} \boldsymbol{P}_{4} / \boldsymbol{B} \boldsymbol{r}_{2}}{\longrightarrow} \boldsymbol{Z} \)
\( Z \) is:
A \( \cdot C H_{3} C H_{2} C H_{2} B r \)
в. \( C H_{3} C H_{2} B r \)
c. \( C H_{3} B r \)
D. \( C H_{3} C H_{2} C H_{3} \)
Subject: Physics
Assertion
\( \mathbf{9} \mathbf{2} \mathbf{3} \mathbf{U}(\boldsymbol{I} \boldsymbol{I} \boldsymbol{I} \boldsymbol{B})-\boldsymbol{\alpha} \quad \boldsymbol{A} \)
\( \boldsymbol{B} \stackrel{-\boldsymbol{\beta}}{\longrightarrow} \boldsymbol{C} \)
Reason
Element \( \boldsymbol{B} \) will be of \( \boldsymbol{I} \boldsymbol{I} \boldsymbol{A} \) group.
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
A wheel takes \( \mathrm{m} \) rotations to travel a
certain distance while another whee
whose diameter is four times bigger than it takes n rotations to travel the
same distance. The relation between
A \( \cdot m=4 n \)
B. \( m=2 n \)
\( c \cdot 2 m=n \)
D. \( 4 \mathrm{m}=\mathrm{n} \)
Subject: Chemistry
Consider the following liquid-vapour equilibrium
Liquid \rightleftharpoons्<__ACCGRAVE__>ेvapour Which of the following relations is
correct?
\( \mathbf{A} \cdot \frac{d}{d T} \underbrace{I n}_{P}=\frac{-\Delta H_{v}}{R T} \)
в. \( \frac{d n \quad P}{d T^{2}}=\frac{-\triangle H_{v}}{T^{2}} \)
\( ^{\mathrm{c}} \cdot \frac{d \operatorname{In} P}{d T}=\frac{\Delta H_{v}}{R T^{2}} \)
D. \( \frac{d \text { In } G}{d T^{2}}=\frac{\Delta H_{v}}{R T^{2}} \)
Subject: Chemistry
Select the correct statement(s).
This question has multiple correct options
A. When the lead-silver alloy is rich in silver, lead is removed by the cupellation process.
B. When the lead-silver alloy is rich in lead, silver is removed by Parke's or Pattinson's process
C. Zinc forms an alloy with lead from which lead is separated.
D. zinc forms an alloy with silver from which zinc is separated by distillation.
Subject: Physics
If two balls each of mass \( 0.06 \mathrm{kg} \) moving in opposite directions with speed of \( 4 m s^{-4} \) collide and rebound
with same speed, then the impulse imparted to each ball due to other is:
A \( .0 .48 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} \)
в. 0.53 kg \( m s^{-1} \)
c. \( 0.8 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} \)
D. \( 0.92 \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} \)
Subject: Chemistry
The chemical reaction, \( 2 A g C l_{(s)}+ \)
\( \boldsymbol{H}_{2(g)} \rightarrow 2 \boldsymbol{H} \boldsymbol{C l}_{(a q)}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{(s)} \) taking
place in a galvanic cell is represented by the notation:
A \( \cdot P t_{(s)} \mid H_{2(g)}, 1 \) bar \( \left|1 M K C l_{(a)}\right| A g C l_{(s)} \mid A g_{(s)} \)
B . \( P t_{(s)} \mid H_{2(g)}, 1 \) bar \( \mid 1 \) M \( H C l_{(a q)}\left|1 M A g_{(a q)}^{+}\right| A g_{(s)} \)
C. \( P t_{(s)} \mid H_{2(g)}, 1 \) bar \( \mid 1 \) M \( H C l_{\left(a_{9}\right)}\left|A g C l_{(s)}\right| A g_{(s)} \)
D. \( P t_{s} \mid H_{2(g)}, 1 \) bar \( \left|1 M H C l_{(a q)}\right| A g_{(s)} \mid A g C l_{s} \)
Subject: Physics
Assertion
A disc-shaped magnet is deviated above a superconducting material that has been cooled by liquid nitrogen.
Reason

Superconductors repel a magnet.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
The vapour pressure of pure water at
\( 26^{\circ} \mathrm{C} \) is 25.21 torr. The vapour pressure
of a solution which contains 20.0 g glucose, \( C_{6} H_{12} O_{6}, \) in 70 g water is :
A .22 .5 torr
B . 23.4 torr
c. 24.4 torr
D. 24.5 torr
Subject: Physics
A block of mass \( 10 \mathrm{kg} \) is moving horizontally with a speed of \( 1.5 m s^{-1} \) on a smooth plane. If a constant vertical force \( 10 N \) acts on it, the displacement of the block from the point of application of the force at the end of 4
seconds is
A. \( 5 m \)
B. \( 20 m \)
c. \( 18 m \)
D. \( 10 m \)
Subject: Physics
(i) The cubical container ABCDEFGH
which is completely filled with an idea (nonviscous and incompressible) fluid,
moves in a gravity free space with a acceleration of \( \boldsymbol{a}=\boldsymbol{a}_{0}(\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \)
where \( a_{0} \) is a positive constant. Then
the only point in the container shown in
the figure where pressure is maximum,
is
\( A \cdot B \)
B.
\( c . E \)
\( D \)
Subject: Chemistry
Write the common name and IUPAC
name of the following.
(a) \( C H_{3} C H_{2} C H O \)
(b) \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
\( (c) C H_{3}-\underset{\mid O H}{C} H-C H_{3} \)
(d) \( C H_{3} C O O H \)
(e) \( H C H O \)
Subject: Chemistry
With excess of water, both \( P_{2} O_{5} \) and
\( \boldsymbol{P C l}_{5} \) give:
A \( . H_{3} P O_{3} \)
в. \( H_{3} P O_{2} \)
c. \( H_{3} P O_{4} \)
D. \( H_{4} P_{2} O_{7} \)
Subject: Maths
I.F. of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}}{\boldsymbol{x}+\mathbf{1}} \) is:
A. \( \frac{1}{y+1} \)
в. \( \frac{1}{x+1} \)
c. \( \log (x+1) \)
D. \( \log (y+1) \)
Subject: Chemistry
The valence configuration of a transition element is \( (n-1) d^{1 \rightarrow 10} n s^{1 \rightarrow 2} \)
The impossible values of \( n \) are:
\( A \cdot 4,5 \) and 6
B. 1 and 2
c. 2,4 and 6
D. 1,2 and 3
Subject: Physics
A force \( \mathbf{F}(-\hat{\mathbf{k}}) \) acts on the origin of the
co-ordinate system. The torque about the point (1,-1) is
A. \( \mathrm{F}(\hat{\mathrm{i}}-\hat{\mathrm{j}}) \)
B . \( -\mathrm{F}(\hat{\mathrm{i}}+\hat{\mathrm{j}}) \)
\( \mathbf{c} \cdot \mathbf{F}(\hat{\mathbf{i}}+\hat{\mathbf{j}}) \)
D. \( -\mathrm{F}(\hat{\mathrm{i}}-\mathrm{j}) \)
Subject: Maths
Find the number of values of \( x \) of the
form \( 6 n, \) where \( n \) is an integer, in the
domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \boldsymbol{x} \ln |\boldsymbol{x}-1|+\frac{\sqrt{\mathbf{6 4}-\boldsymbol{x}^{2}}}{\sin \boldsymbol{x}} \)
Subject: Maths
\( \boldsymbol{x}=\{4,5,6\} \) is the solution set for
A. \( x \geq 4 \) and \( x \leq 7 \)
B. \( x \geq 4 \) and \( x<7 \)
c. \( x>4 \) and \( x<7 \)
D. \( x>4 \) and \( x \leq 7 \)
Subject: Maths
A study was conducted to find out the
concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:
\( \begin{array}{cccccc}0.03 & 0.08 & 0.08 & 0.09 & 0.04 & 0.17 \\ 0.16 & 0.05 & 0.02 & 0.06 & 0.18 & 0.20 \\ 0.11 & 0.08 & 0.12 & 0.13 & 0.22 & 0.07 \\ 0.08 & 0.01 & 0.10 & 0.06 & 0.09 & 0.18 \\ 0.11 & 0.07 & 0.05 & 0.07 & 0.01 & 0.04\end{array} \) Using this table, find the probability of the concentration of sulphur dioxide in
the interval \( 0.12-0.16 \) on any of these
days.
Subject: Maths
Find the mean and variance for the
following frequency distrubution
\( \begin{array}{lllll}\text { classes } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}\text { 20- } \\ \text { 30 }\end{array} & \begin{array}{l}\text { 30 } \\ 40\end{array}\end{array} \)
Frequencies 5 8 3.
15
Subject: Physics
Two sources of equal emf are connected
to an external resistance R. The internal
resistance of the two sources are \( \boldsymbol{R}_{1} \)
\( \operatorname{and} R_{2}\left(R_{1}>R_{2}\right) . \) If the potential
difference across the source having
internal resistance \( \boldsymbol{R}_{2} \) is zero, then:
A. \( R=R_{2}-R_{1} \)
в. \( \quad R=\frac{R_{2}\left(R_{2}+R_{1}\right)}{R_{2}-R_{1}} \)
\( c \cdot R=\frac{R_{2} R_{1}}{R_{2}-R_{1}} \)
D. \( R=\frac{R_{2} R_{1}}{R_{1}-R_{2}} \)
Subject: Maths
If the tangents \( P A \) and \( P B \) are drawn
from the point \( \boldsymbol{P}(-1,2) \) to the circle \( x^{2}+y^{2}+x-2 y-3=0 \) and \( C \) is the
center of the circle, then the area of the
quadrilateral \( P A C B \) is
\( A \cdot 4 \)
B. 16
c. Does not exists
D. 8
Subject: Maths
\( \left[\begin{array}{lll}\mathbf{1} & \mathbf{1} & \boldsymbol{x}\end{array}\right]\left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{2} \\ \mathbf{0} & \mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{1} & \mathbf{0}\end{array}\right]\left[\begin{array}{l}\mathbf{1} \\ \mathbf{1} \\ \mathbf{1}\end{array}\right]=\mathbf{0}, \) then
find \( x \)
Subject: Maths
Evaluate the following limits. \( \lim _{x \rightarrow 1} \frac{\sqrt{5 x-4}-\sqrt{x}}{x^{3}-1} \)
A \( \cdot \frac{2}{5} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. None of these
Subject: Physics
The mass and density of a solid are
measured to be \( (12.4 \pm 0.1) \mathrm{kg} \) and
\( (4.6 \pm 0.2) k g / m^{3} . \) Calculate the
volume of the sphere with error limits.
\( \mathbf{A} \cdot \therefore V \pm \Delta V=(2.7 \pm 0.14) m^{3} \)
B \( \ldots V \pm \Delta V=(5.4 \pm 0.14) m^{3} \)
\( \mathbf{c} \cdot \therefore V \pm \Delta V=(2.7 \pm 0.28) m^{3} \)
D. None of these
Subject: Physics
section \( A \) and length \( 2 l \) is clamped
firmly at two points \( A \) and \( B \), which are
\( 2 l m \) apart and in the same plane. \( A \)
body of mass \( m \) is hung from
the middle point of the wire such that
the middle point sags by x lower from
the original position. If Young's modulus
is \( Y, \) then \( m \) is given by:
A \( \cdot \frac{1}{2} \frac{Y A x^{2}}{g l^{2}} \)
B \( \cdot \frac{1}{2} \frac{Y A l^{2}}{g x^{2}} \)
c. \( \frac{Y A x^{3}}{g l^{3}} \)
D \( \cdot \frac{Y A l^{2}}{g x^{2}} \)
Subject: Physics
The time period of oscillation of a particle, that executes SHM, is \( 1.2 s \). The time, starting from mean position, at which its velocity will be half of its velocity at mean position is?
A . \( 0.1 s \)
B. \( 0.2 s \)
\( c .0 .4 s \)
D. \( 0.6 s \)
Subject: Physics
The value of acceleration due to gravity,
at earth surface is \( g \). Its value at the
centre of the earth, which we assume as
a.sphere of radius \( R \) and of uniform mass density, will be:
\( \mathbf{A} \cdot 10 R m / s^{2} \)
B. zero
c. \( 5 R m / s \)
D. \( 20 R m / s^{2} \)
Subject: Maths
To construct a triangle similar to given \( \Delta A B C \) with its sides \( \frac{4}{5} \) of that of
\( \Delta A B C, \) locate points \( X_{1}, X_{2}, X_{3}, \dots . . \)
on ray \( B X \) at equal distances such that
\( \angle A B X \) is acute. The points to be joined
in the next step are:
A. \( X_{4}, C \)
в. \( X_{5}, C \)
c. \( x_{4}, A \)
D. \( X_{5}, A \)
Subject: Physics
In an experiment it was found that when a sonometer in its fundamental mode of
vibration and a tuning fork gave 5 beats when length of wire is 1.05 metre or 1 metre. The velocity of transverse waves in sonometer wire when its length is \( 1 \mathrm{m} \)
A. \( 400 \mathrm{m} / \mathrm{s} \)
B. 210 \( \mathrm{m} / \mathrm{s} \)
c. \( 420 \mathrm{m} / \mathrm{s} \)
D. \( 450 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A machine, which is 75 percent efficient uses 12 joules of energy in lifting up a 1 kg mass through a certain distance. The mass is then allowed to
fall through that distance. What will its
velocity be at the end of its fall?
A \( \cdot \sqrt{32} \mathrm{m} / \mathrm{s} \)
B. \( \sqrt{24} m / s \)
c. \( \sqrt{18} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{9} m / s \)
Subject: Physics
Two open pipes of length \( L \) are vibrated
simultaneously. If length of one of the
pipes is reduced by \( y, \) then the number of beats heard per second will nearly be (if the velocity of sound is \( v \text { and } y<L) \)
A \( \cdot \frac{v y}{2 L} \)
B. \( \frac{2 L^{2}}{V y} \)
c. \( \frac{v y}{2 L^{2}} \)
D. \( \frac{v y}{L^{2}} \)
Subject: Maths
If \( G \) is the centroid of the triangle \( A B C \) then \( \overrightarrow{G A}+\overrightarrow{G B}+\overrightarrow{G C} \) is equal to
\( \mathbf{A} \cdot \overrightarrow{A B} \)
в. \( \overrightarrow{B C} \)
\( c \cdot 4 \overrightarrow{G A} \)
D.
Subject: Physics
The magnetic flux linked with a coil at
any instant \( t \) is given by the equation
\( \phi=5 t^{3}-100 t+300 . \) The magnitude
of emf induced in the coil after \( 3 s \) is
A . \( 10 V \)
в. \( 20 V \)
\( c .35 V \)
D. \( 70 V \)
Subject: Physics
An electric circuit requires a total
capacitance of \( 2 \mu F \) across potential of
\( \mathbf{1 0 0 0} V \). Large number 1 \( \mu \boldsymbol{F} \)
capacitances are available each of which would breakdown if the potential is more than \( 350 V \) How many
capacitances are required to make the
circuit.
A .24
B . 20
c. 18
D. 12
Subject: Chemistry
Which of the following is the correct order of acidity of a carboxylic acid?
(i) \( C l_{3} C C O O H>C l_{2} C H C O O H> \)
\( \boldsymbol{C l C H}_{2} \boldsymbol{C O O H} \)
(ii) \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H}> \)
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{C O O H}> \)
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C C O O H} \)
(iii) \( F_{2} C H_{2} C O O H> \)
\( \boldsymbol{F C H}_{2} \boldsymbol{C O O H}>\boldsymbol{C l C H}_{2} \boldsymbol{C O O H} \)
A. (i) and (ii)
B. (ii) and (iii)
c. (i) and (iii)
D. (i), (ii) and (iii)
Subject: Chemistry
\( (\boldsymbol{A}) \)
\( (C) \stackrel{H_{3} O^{\oplus}}{\longrightarrow}(D) \)
Which statements are correct about the
reaction of maltose?
This question has multiple correct options
A. Product \( (C) \) is:
B. Product \( (C) \) is
c. Product \( (D) \) are
D. Products \( (D) \) are 2 mol \( \alpha \) - and \( \beta \) -D-glucose
Subject: Physics
In two figures
This question has multiple correct options
\( \mathbf{A} \cdot v_{1} / v_{2}=1 / 2 \)
\( \mathbf{B} \cdot t_{1} / t_{2}=2 / 1 \)
\( \mathbf{C} \cdot R_{1} / R_{2}=1 \)
\( \mathbf{D} \cdot v_{1} / v_{2}=1 / 4 \)
Subject: Physics
A charge of \( 10 \mathrm{C} \) is brought from infinity to a point near a charged body and in
this process, 200 J of work is done
Calculate the electric potential at that point near the charged body
A . \( 20 \mathrm{v} \)
B. \( 10 \mathrm{v} \)
\( c .5 v \)
D. 15 v
Subject: Chemistry
Which of the following statement is
incorrect about \( \boldsymbol{I F}_{\mathbf{7}} ? \)
A. The total number of \( 90^{\circ} F-I-F \) bond angles is 10
and the total number of \( 72^{\circ} F-I-F \) bond angles is
5
B. The axial \( F-I \) bond lengths are not longer than
equatorial \( F-I \) bond lengths
C. The molecular geometry is pentagonal bipyramidal
D. The hybridisation of central atom is \( s p^{3} d^{3} \)
Subject: Maths
Which of the following sets is not a
finite set?
\( \mathbf{A} \cdot\left\{(x, y): x^{2}+y^{2} \leq 1 \leq x+y, \quad x, y \in R\right\} \)
B \( \cdot\left\{(x, y): x^{2}+y^{2} \leq 1 \leq x+y, \quad x, y \in Z\right\} \)
\( \mathbf{c} \cdot\left\{(x, y): x^{2} \leq y \leq|x|, \quad x, y \in Z\right\} \)
D. \( \left\{(x, y): x^{2}+y^{2}=1, x, y \in Z\right\} \)