AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The cyclic process from \( X \) to \( Y \) is an isothermal process.
If the pressure of the gas at \( X \) is \( 4.0 \mathrm{kPa} \) and the volume is 6.0 cubic meters, and
if the pressure at \( Y \) is \( 8.0 \mathrm{kPa} \), what is the volume of the gas at \( Y ? \)
A . 12.0 cubic meters
B. 16.0 cubic meters
c. 3.0 cubic meters
D. 4.0 cubic meters
E . 2.0 cubic meters
Subject: Chemistry
\( C_{4} H_{9} C l \frac{N a}{_{\text {ether}}} A \)
\( \boldsymbol{A} \frac{\text {alcoholic}}{\boldsymbol{K O H}} \boldsymbol{B} \)
Identify the compound B.
A. 1-butene
B. cis but-2-ene
c. isobutene
D. trans but-2-ene
Subject: Physics
f current \( \boldsymbol{I}_{1}=\mathbf{3} \boldsymbol{A} \sin \omega \boldsymbol{t} \) and \( \boldsymbol{I}_{2}= \)
\( 4 A \cos \omega t, \) then \( I_{3} \) is
A \( \cdot 5 a \sin \left(\omega t+53^{\circ}\right) \)
B. \( 5 a \sin \left(\omega t+37^{\circ}\right) \)
c. \( 5 a \sin \left(\omega t+45^{\circ}\right) \)
D. \( 5 a \sin \left(\omega t+30^{\circ}\right) \)
Subject: Physics
The work done in bringing three
particles each of mass \( 10 g m \) from large distances to the vertices of an
equilateral triangle of side \( 10 \mathrm{cm} \) is
A \( \cdot 10^{-13} J \)
\( J \)
В. \( 2 \times 10^{-13} \mathrm{J} \)
c. \( 4 \times 10^{-11} J \)
D. \( 10^{-11} J \)
Subject: Maths
Using remainder theorem, find the reminder when \( x^{3}-a x^{2}+2 x-a \) is
divided by \( \boldsymbol{x}-\boldsymbol{a} \)
\( A \cdot a \)
B. \( a+2 \)
\( \mathbf{c} \cdot a+1 \)
D. \( a-2 \)
Subject: Maths
The area bounded by the curves \( y= \) \( \sin x, y=\cos x \) and the \( y \) -axis and the
first point of intersection is:
A \( \cdot \sqrt{2} \) sq,units
B. \( \sqrt{2}-1 \) sq. units
c. \( 2+\sqrt{2} \) sq. units
D. 0 sq, units
Subject: Maths
The value of \( \int \frac{10^{x / 2}}{\sqrt{10^{-x}-10^{x}}} d x \) is
A. \( \frac{1}{\log _{2} 10} \sin ^{-1}\left(10^{x}\right)+c \)
В. \( 2 \sqrt{10^{-x}+10^{x}}+c \)
c. \( \frac{1}{\log _{e} 10} \sin h^{-1}\left(10^{x}\right)+c \)
D. \( \frac{-1}{\log _{e} 10} \sin h^{-1}\left(10^{x}\right)+c \)
Subject: Physics
A real object is placed at a distance \( \frac{\boldsymbol{f}}{\mathbf{2}} \) in front of a concave mirror having focal length \( f . \) If object is shifted by a distance \( \frac{f}{4} \) away from the mirror. Find the ratio of final magnification to initial magnification.
A .4
B.
\( c \cdot \frac{1}{2} \)
D. 2
Subject: Maths
The direction cosine of a line which is
perpendicular to both the lines whose direction ratios are 1,2,2 and 0,2,1 are
A \( \cdot \frac{-2}{3}, \frac{1}{3}, \frac{2}{3} \)
B. \( \frac{2}{3}, \frac{-1}{3}, \frac{2}{3} \)
c. \( \frac{2}{3}, \frac{1}{3}, \frac{-2}{3} \)
D. \( \frac{2}{3}, \frac{-1}{3}, \frac{-2}{3} \)
Subject: Physics
A proton of charge \( e \) moving at speed \( v_{0} \) is placed midway between two parallel wires \( a \) distance a apart, each carrying
current \( I \) in the same direction.
The force on the proton is:
A . 0
в. \( \quad e v_{0} \frac{I_{0}}{2 \pi a} \)
\( ^{\mathrm{c}} \cdot \operatorname{ev}_{0} \frac{I_{0}}{2 \pi(2 a)} \)
D. \( _{e v_{0}} \frac{I_{0}}{2 \pi \frac{a}{2}} \)
E. Unable to be determined
Subject: Physics
Figure shows a square loop of side \( 1 m \)
and resistance 1\Omega. The magnetic field on left side of line PQ has a magnitude
\( B=1.0 T . \) The work done in pulling the
loop out of the field uniformly in \( 1 s \) is
4. 1
В. \( 10 J \)
\begin{tabular}{l}
\( .0 .1 .] \) \\
\hline
\end{tabular}
0.100
Subject: Physics
Match the following and choose the
correct option
\( \begin{array}{llll}\text { A } & \text { String vibration } & \text { 1. } & \text { Tabla } \\ \text { B } & \text { Membrane vibration } & \text { 2. } & \text { Cymbals } \\ \text { C } & \text { Vibration of air } & \text { 3. } & \text { Sitar } \\ \text { D } & \text { Vibration of plate } & \text { 4. } & \text { Flute }\end{array} \)
\( A \cdot A-1, B-2, C-3, D-4 \)
B. A-2, B-1, C-4, D-3
C. A-3, B-1, C-4, D-2
D. A-4, B-3, C-2, D-1
Subject: Maths
Unit vector perpendicular to the plane of the triangle \( A B C \) with position vectors of the vertices \( A, B, C, \) is (where \( \Delta \)
is the area of the triangle \( A B C \) ).
\( \frac{(\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a})}{\Delta} \)
B. \( \frac{(\vec{a} \times \vec{b}+\bar{b} \times \vec{c}+\vec{c} \times \vec{a})}{2 \Delta} \)
\( \overbrace{\frac{(\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a})}{3 \Delta}}^{\text {c. }} \)
\( \frac{(\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a})}{4 \Delta} \)
Subject: Physics
A plane wave of wavelength \( 6250 A \) is incident normally on a slit of width \( 2 \times \)
\( 10^{-2} \mathrm{cm} . \) The width of the principle
maximum of diffraction pattern on a
screen at a distance of \( 50 \mathrm{cm} \) will be:
A \( \cdot 312 \times 10^{-3} \mathrm{cm} \)
B . \( 312.5 \times 10^{-4} \mathrm{cm} \)
c. 312 ст
D. \( 312.5 \times 10^{-5} \mathrm{cm} \)
Subject: Chemistry
For which one of the following system
\( \Delta \boldsymbol{E}<\Delta \boldsymbol{H} ? \)
A \( \cdot 2 S O_{2(g)}+O_{2(g)} \rightarrow 2 S O_{3(g)} \)
B. \( N_{2(g)}+O_{2(g)} \rightarrow 2 N O_{(g)} \)
C. \( 2 N H_{3(g)} \rightarrow N_{2(g)}+3 H_{2(g)} \)
D. \( H_{2(g)}+I_{2(g)} \rightarrow 2 H I_{(g)} \)
Subject: Physics
Assertion - Sound wave is an example of longitudinal wave. Reason - In longitudinal waves, the
constituents of the medium oscillate
perpendicular to the direction of wave propagation.
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
If \( \boldsymbol{X}=\{1,2,3, \dots, 10\} \) and \( A= \)
\( \{1,2,3,4,5\} . \) Then, the number of
subsets \( B \) of \( X \) such that \( A-B=\{4\} \)
is
\( A \cdot 2^{5} \)
B \( \cdot 2^{4} \)
\( \mathbf{c} \cdot 2^{5}-1 \)
D.
E \( .2^{4}-1 \)
Subject: Physics
toppr
Q Type your question
densities \( d \) and \( 2 d \) each of height \( H / 2 \)
as shown in the figure. The lower density liquid is open to the
atmosphere having pressure \( \boldsymbol{P}_{0} \cdot \boldsymbol{A} \)
homogeneous solid cylinder of length
\( \boldsymbol{L}(\boldsymbol{L}<\boldsymbol{H} / 2), \) cross-sectional area \( \boldsymbol{A} / \mathbf{5} \)
is immersed such that it floats with its
axis vertical at the liquid-liquid
interface with length \( L / 4 \) in the denser
liquid.
The cylinder is then removed and the original arrangement is restored. A tiny hole of area \( s(s<<A) \) is punched on
the vertical side of the container at a
height \( h(h<H / 2) . \) As a result of this,
liquid starts flowing out of the hole with
a range \( x \) on the horizontal surface.
The horizontal distance traveled by the liquid, initially, is :
\( \mathbf{A} \cdot \sqrt{(3 H+4 h) h} \)
B \( \cdot \sqrt{(3 h+4 H) h} \)
\( \mathbf{c} \cdot \sqrt{(3 H-4 h) h} \)
D. \( \sqrt{(3 H-3 h) h} \)
Subject: Maths
Let \( \quad A=\left(\begin{array}{ccc}x^{2} & 6 & 8 \\ 3 & y^{2} & 9 \\ 4 & 5 & z^{2}\end{array}\right) \) and \( B= \)
\( \left(\begin{array}{ccc}2 x & 3 & 5 \\ 2 & 2 y & 6 \\ 1 & 4 & 2 z-3\end{array}\right) \) be two matrices
and if \( \operatorname{Tr}(\boldsymbol{A})=\boldsymbol{T} \boldsymbol{r}(\boldsymbol{B}), \) then the value of
\( (x+y+z) \) is equal to
(Note: \( \operatorname{Tr}(P) \) denotes trace of matrix \( P \) )
\( A \)
B.
\( c \)
\( D \)
Subject: Chemistry
Which of the following is the best
preparation of \( 2- \) methyl pentanoic
acid?
A \( \cdot \) 2 - chloropentane \( \stackrel{N a C N(a q)}{\longrightarrow} \stackrel{H^{+} / H_{2} O}{\longrightarrow} \)
B・ \( _{2-\text { pentanone }} \stackrel{N a C N(a q)}{\longrightarrow} \stackrel{H^{+} / H_{2} O}{\longrightarrow} \)
c. 2 - bromopentane \( \frac{M g}{\text {Ether}} \) (ii) (i) \( C O_{2} \) \( \overline{H C I} \) H \( _{2} \) O
D. \( 1- \) chloropentane \( \stackrel{N a C N(a q)}{\longrightarrow} \stackrel{H^{+} / H_{2}}{\longrightarrow} \)
Subject: Physics
A chain of mass \( M \) is placed on a
smooth table with \( 1 / n \) of its length \( L \) hanging over the edge. The work done in
pulling the hanging portion of the chain back to the surface of the table is:
A. \( M g L / n \)
в. \( M g L / 2 n \)
c. \( M g L / n^{2} \)
D. \( M g L / 2 n^{2} \)
Subject: Physics
The ray diagram could be correct
A \( \cdot \) If \( n_{1}=n_{2}=n_{g} \)
B. If \( n_{1}=n_{2} \) and \( n_{1}<n_{g} \)
\( \mathrm{c} \cdot \) If \( n_{1}=n_{2} \) and \( n_{1}>n_{g} \)
D. under no circumstances
Subject: Chemistry
A mixture of \( H C O O H \) and \( H_{2} C_{2} O_{4} \) is
heated with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} . \) The gas
produced is collected and on treating with \( K O H \) solution, the volume of the gas decreases by \( \frac{1}{6} \) th. The molar ratio of two acids in the original mixture is \( x: y \)
The value of \( \boldsymbol{x}+\boldsymbol{y} \) is :
Subject: Maths
Find the intersection of \( A \) and \( B, \) by
representing using Venn diagram:
\( \boldsymbol{A}=\{\mathbf{1}, \mathbf{3}, \mathbf{5}, \mathbf{7}\}, \boldsymbol{B}=\{\mathbf{2}, \mathbf{5}, \mathbf{7}, \mathbf{1 0}, \mathbf{1 2}\} \)
\( \mathbf{A} \cdot\{1,3,5,7\} \)
B \( \cdot\{5,7\} \)
\( \mathbf{c} \cdot\{1,2,3,5,7,10\} \)
D. None of these
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6} \\ \mathbf{7} & \mathbf{1} & \mathbf{0}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{4} & \mathbf{5}\end{array}\right] \)
\( , \operatorname{Tr}(\mathrm{BA})=\dots \)
A. 40
в. 45
\( c .39 \)
\( D \)
Subject: Physics
Which is the correct representation of
the net force \( f_{n e t} \) on the mass?
(k is the constant of oscillation and \( x \) is
the displacement about the mean
position)
A \( \cdot f_{n e t}=-k x+b v \)
B. \( f_{n e t}=k x+b v \)
C \( \cdot f_{n e t}=-k x-b v \)
\( \mathbf{D} \cdot f_{n e t}=k x-b v \)
Subject: Maths
There are two A.P.'s each of \( n \) terms
\( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}, \ldots \boldsymbol{L}, \boldsymbol{p}, \boldsymbol{p}+\boldsymbol{q}, \boldsymbol{p}+ \)
\( 2 q, \ldots . . L^{\prime} . \) These A.P.'s satisfy the
following conditions: \( \frac{\boldsymbol{L}}{\boldsymbol{p}}=\frac{\boldsymbol{L}^{\prime}}{\boldsymbol{a}}= \)
\( 4, \frac{S_{n}}{S_{n^{\prime}}}=2 ; \) find out \( 2\left(\frac{L}{L^{\prime}}\right) \)
Subject: Physics
A student is observing the diagram showing the path of a ray of light passing through a glass prism. He would find that for all angles of incidence the ray of light bends:
A. Towards the normal while entering into the prism and away from the normal while emerging out of the prism,
B. Away from the normal while entering into the prism and towards the normal while emerging out of the prism,
C. Away from the normal while entering as well as while emerging out of the prism,
D. Towards the normal while entering as well as while emerging out of the prism.
Subject: Chemistry
Which of these reactions are redox
reactions?
\( 16 N O(g)+4 N H_{3}(g) \rightarrow 5 N_{2}(g)+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)
\( 22 S O_{2}(g)+O_{2}(g) \rightarrow 2 S O_{3}(g) \)
3. \( \boldsymbol{S O}_{3}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}(\boldsymbol{g}) \)
A .1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct
Subject: Maths
Evaluate \( \int \frac{x^{2}-3 x+5}{\sqrt{x}} d x \)
A. \( \frac{2}{5} x^{\frac{5}{2}}-2 x^{\frac{3}{2}}+10 \sqrt{x}+c \)
B. \( \frac{5}{2} x^{\frac{5}{2}}-2 x^{\frac{3}{2}}+10 \sqrt{x}+c \)
c. \( \frac{2}{5} x^{\frac{3}{2}}+2 x^{\frac{3}{2}}+10 \sqrt{x}+c \)
D. \( \frac{2}{5} x^{\frac{3}{2}}-2 x^{\frac{3}{2}}-10 \sqrt{x}-c \)
Subject: Chemistry
Which of the following has been arranged in order of decreasing dipole
moment?
A. \( C H_{3} C l>C H_{3} F>C H_{3} B r>C H_{3} I \)
B. \( C H_{3} F>C H_{3} C l>C H_{3} B r>C H_{3} \)
c. \( C H_{3} C l>C H_{3} B r>C H_{3} I>C H_{3} F \)
D. \( C H_{3} F>C H_{3} C l>C H_{3} I>C H_{3} B r \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \mathbf{1 2} \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{x}^{2}=\tan \boldsymbol{x}+\cos \boldsymbol{x} \)
Subject: Chemistry
The empirical formula weight of a compound containing carbon and hydrogen is \( 13 . \) The molecule of the compound is 39 times heavier than a molecule of hydrogen. The molecular formula of the compound is:
A \( . C H \)
B. \( C_{3} H_{3} \)
c. \( C_{13} H_{13} \)
D. \( C_{6} H_{6} \)
Subject: Physics
Two object collides elastically mass \( 2 m \)
is moving with velocity \( U \) and mass \( m \) is initially at rest. After the collision, the
objects move away with velocities \( u \)
and \( v, \) as shown in above figure.
Find the relation between \( u \) and \( v ? \)
A \( \cdot 2 u \cos 30^{\circ}=v \cos 60^{\circ} \)
B \( \cdot u \cos 30^{\circ}=2 v \cos 60^{\circ} \)
c. \( 2 u \sin 30^{\circ}=v \sin 60^{\circ} \)
D. \( u \sin 30^{\circ}=2 v \sin 60^{\circ} \)
E \( \cdot u \sin 30^{\circ}=v \cos 60^{\circ} \)
Subject: Chemistry
ous' acid of a non-metal 'X' has 2 'O'
atoms. Per acid of the same non metal
has the formula
A. \( H X O_{2} \)
в. \( H_{2} X O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{XO}_{2} \)
D. \( H X O_{4} \)
Subject: Maths
Calculate \( \left(\frac{\mathbf{3} \boldsymbol{x}}{\boldsymbol{x}+\mathbf{5}}\right) \div\left(\frac{\mathbf{6}}{\mathbf{4} \boldsymbol{x}+\mathbf{2 0}}\right) \)
given that \( \boldsymbol{x} \neq-\mathbf{5} \)
\( \mathbf{A} \cdot 2 x \)
в. \( \frac{x}{2} \)
c. \( \frac{9 x}{2} \)
D. \( 2 x+4 \)
Subject: Physics
singly ionized helium(x), ionized deuteron(y), alpha(z) particles are projected into a uniform magnetic field \( \mathbf{3} \times \mathbf{1 0}^{-4} \) Tesla with velocities \( 10^{5} \boldsymbol{m} \boldsymbol{s}^{-1} \)
\( 0.4 \times 10^{4} m s^{-1} \) and \( 2 \times 10^{3} m s^{-1} \)
respectively. The correct relation between the ratio of the angular momentum to the magnetic moment of the particles is :
A. \( x>y=z \)
в. \( x<y<z \)
c. \( x<z<y \)
D. \( z>x>y \)
Subject: Maths
Find the centres of the circles passing through (-4,3) and touching the lines \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{2} \) and \( \boldsymbol{x}-\boldsymbol{y}=\boldsymbol{2} \)
A \( \cdot((-10 \pm \sqrt{54}), 0) \)
B. \( (10 \pm \sqrt{54}, 0) \)
c. \( (0,-10 \pm \sqrt{54}) \)
D. \( (0,10 \pm \sqrt{54}) \)
Subject: Chemistry
A study of chemical kinetics of the
reaction \( \mathbf{A}+\mathbf{B} \rightarrow \) products, gave the
following data at \( 25^{\circ} \mathrm{C} \)
Experiment
\( [\mathrm{A}] \)
\( [\mathrm{B}] \)
\[
\frac{\boldsymbol{d}[\boldsymbol{P r o d u c t s}]}{\boldsymbol{d t}}
\]
1.0
0.15
\( 4.20 \times 10^{-6} \)
2 \( \begin{array}{lll}\text { 2.0 } & \text { 0.15 } & 8.40 \times 10^{-6}\end{array} \)
3 1.0 0.20 \( \quad 5.60 \times 10^{-6} \)
Find:
(1) The order of reaction with respect to
\( \mathbf{A} \)
(2) The order of reaction with respect to
B.
(3) The rate law.
Subject: Physics
The resistance of a bulb filament is
\( 100 \Omega \) at a temperature of \( 100^{\circ} \mathrm{C} \). If its temperature coefficient of resistance
be 0.005 per \( ^{o} C, \) its resistance will
become \( 200 \Omega \) at a temperature of :
\( \mathbf{A} \cdot 200^{\circ} C \)
B. \( 300^{\circ} \mathrm{C} \)
c. \( 400^{\circ} \mathrm{C} \)
D. \( 500^{\circ} \mathrm{C} \)
Subject: Chemistry
Two elements M and X have electronic
configurations 2,8,3 and 2,8,6 respectively. Identify the correct formula of the compound formed.
\( A \cdot M x_{2} \)
B. \( M_{2} x \)
\( \mathrm{c} \cdot \mathrm{M}_{2} \mathrm{x}_{3} \)
D. \( M_{3} x_{2} \)
Subject: Maths
The real and imaginary parts of \( \log (1+i)= \)
\( ^{A} \cdot\left(\frac{1}{2}, \frac{\pi}{4}\right) \)
B \( \cdot\left(\log 2, \frac{\pi}{4}\right) \)
\( ^{\mathbf{c}} \cdot\left(\log \sqrt{2}, \frac{\pi}{4}\right) \)
\( ^{\mathrm{D}} \cdot\left(\log \frac{1}{2}, \frac{\pi}{4}\right) \)
Subject: Chemistry
\( y=-1 \)
\( \left.\langle\bigcirc\rangle-\mathrm{cH}_{2} \mathrm{Br}+\mathrm{Ho}-\bigcirc\right\rangle-\mathrm{Br} \)
\( \langle\bigcirc\rangle-_{\mathrm{o}_{\mathrm{H}}}^{\mathrm{cH}_{2}+\mathrm{B}_{\mathrm{r}}}\langle\bigcirc\rangle-\mathrm{B}_{\mathrm{r}} \)
\( \left.\langle\bigcirc\rangle-\mathrm{cH}_{2} \prec \bigcirc\right\rangle- \) ов
но \( \left.\langle\bigcirc\rangle-\text { сн }_{2} \prec \bigcirc\right\rangle \) в
Subject: Maths
If \( \vec{P}+\vec{Q}=\vec{P}-\vec{Q} \) and \( q \) is the angle between \( \vec{P} \) and \( \vec{Q}, \) then
A \( \cdot q=0^{\circ} \)
в. \( q=90^{\circ} \)
c. \( P=0 \)
D. \( Q=0 \)
Subject: Maths
Following are the marks obtained by 9 students in Mathematics test:
\( \mathbf{5 0 , 6 9}, \mathbf{2 0 , 3 3 , 5 3 , 3 9 , 4 0 , 6 5 , 5 9 \text { The }} \)
mean deviation from the median is
A . 9
B. 10.5
c. 12.67
D. 14.76
Subject: Physics
According to Joule's law of heating, heat produced \( \boldsymbol{H}=\boldsymbol{l}^{2} \boldsymbol{R} \boldsymbol{t}, \) where I is current
\( \mathrm{R} \) is resistance, and \( \mathrm{t} \) is time. If the
errors in the measurement of I,R and t
are \( 3 \%, 4 \% \) and \( 6 \%, \) respectively, find
error in the measurement of H.
Subject: Physics
A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base
inside the prism. If \( \mu \) is the refractive
index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is:
A \( \cdot \sin ^{-1}\left(\frac{1}{\mu}\right) \)
B. \( \tan ^{-1}\left(\frac{1}{\mu}\right) \)
c. \( \sin ^{-1}\left(\frac{\mu-1}{\mu}\right) \)
D \( \cdot \cos ^{-1}\left(\frac{1}{\mu}\right) \)
Subject: Chemistry
Given below are some elements of the
modern periodic table:
\( _{4} B e,_{26} F e,_{14} S i,_{19} K,_{20} C a \)
(i) Select the element that has one
electron in the outermost shell and
write its electronic configuration.
(ii) Select two elements that belong to the same group. Give reason for your
answer.
(iii) Select two elements that belong to the same period. Which one of the two
has bigger atomic size?
Subject: Maths
The coordinates of the point(s) on the
graph of the function \( f(x)= \) \( \frac{x^{3}}{3}-\frac{5 x^{2}}{2}+7 x-4 \) where the tangent
drawn cut off intercepts from the
coordinate axes which are equal in
magnitude but opposite in sign is
This question has multiple correct options
\( \mathbf{A} \cdot\left(2, \frac{8}{3}\right) \)
B. \( \left(3, \frac{7}{2}\right) \)
\( \mathbf{c} \cdot\left(1, \frac{5}{6}\right) \)
D. none
Subject: Chemistry
Equilibrium constants for four different
reactions are given as:
\( \boldsymbol{K}_{\mathbf{1}}=\mathbf{1 0}^{\mathbf{6}}, \boldsymbol{K}_{\mathbf{2}}=\mathbf{1 0}^{-\mathbf{4}}, \boldsymbol{K}_{\mathbf{3}}=\mathbf{1 0}, \boldsymbol{K}_{\mathbf{4}}= \)
1. Which reaction will take maximum
time to attain equilibrium?
A \( \cdot K_{1}=10^{6} \)
B \( \cdot K_{2}=10^{-4} \)
\( \mathbf{c} \cdot K_{3}=10 \)
D. can't predict
Subject: Chemistry
The following equilibrium are given
\( N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \quad K_{1} \)
\( N_{2}+O_{2} \rightleftharpoons 2 N O \)
\( H_{2}+\frac{1}{2} O_{2} \rightleftharpoons H_{2} O \)
The equilibrium constant of the reaction
\( \mathbf{2} N \boldsymbol{H}_{3}+\frac{\mathbf{5}}{\mathbf{2}} \boldsymbol{O}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}, \) in
terms of \( K_{1}, K_{2} \) and \( K_{3} \) is :
A. \( \frac{K_{1} K_{2}}{K_{3}} \)
B. \( \frac{K_{1} K_{3}^{2}}{K_{2}} \)
\( ^{\mathrm{C}} \cdot \frac{K_{2} K_{3}^{3}}{K_{1}} \)
D. \( K_{1} K_{2} K_{3} \)
Subject: Chemistry
Match the items in column I with the
item in column II.
Select the correct alternative.
\( \mathbf{A} \cdot|-A,| I-C,|I|-D, \mid V-B \)
B. I-B, II-D, III-C, IV-A
c. \( \mid-\mathrm{C}, \) । \( -\mathrm{A}, \) III-B, \( 1 \mathrm{V}-\mathrm{D} \)
D. I-D, II-B, III-A, IV-C
Subject: Physics
Arrange the following physical quantities in the increasing order of their magnitudes
I. 1 dyne
II. \( 1 N \)
III. \( 3 k g m s^{-2} \)
IV. \( 10^{7} g c m s^{-2} \)
\( \mathbf{A} \cdot \|, 1, \) ॥I \( , \) IV
B. IV, ।, ॥ᅵ, ॥
c. ॥, ॥ा, ।, IV
D. I, II, III, IV
Subject: Biology
In the DNA molecule
A. The proportion of adenine in relation of thymine varies with the organism.
B. There are two strands which run antiparallel one in \( 5^{\prime} \) \( \rightarrow 3^{\prime} \) direction and other in \( 3^{\prime} \rightarrow 5 \)
C. The total amount of purine nucleotides and pyrimidine nucleotides is not always equal.
D. There are two strands which run parallel in the \( 5^{\prime} \rightarrow 3^{\prime} \) direction.
Subject: Chemistry
The bond disssociation energies of
\( \operatorname{gases} H_{2}, C l_{2} \) and \( H C l \) are 104,58 and
\( \mathbf{1 0 3} \) kcal \( m o l^{-1} \) respectively.

Calculate the enthalpy of formation of \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) \)
Subject: Chemistry
Which of the following is/are true?
This question has multiple correct options
A. Van der Waals forces are responsible for the formation of molecular crystals
B. Branching lowers the boiling points of isomeric organic compounds due to decrease in van der Waals forces of attraction.
C. In graphite, van der Waals forces act between the carbon layers.
D. In diamond, van der Waals forces act between the carbon layers.
Subject: Maths
\( \frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)}= \)
A. \( -\frac{63}{25}+\frac{16}{25} i \)
в. \( -\frac{63}{25}-\frac{16}{25} i \)
c. \( \frac{63}{25}+\frac{16}{25} i . \)
D. \( \frac{63}{25}-\frac{16}{25} i \)
Subject: Maths
The value of \( \int \sqrt{2}\left(\frac{\sin x}{\sin \left(x-\frac{\pi}{4}\right)}\right) d x \)
is
\( ^{\mathbf{A}} \cdot_{x-\log }\left|\sin \left(x-\frac{\pi}{4}\right)\right|+c \)
B. \( x+\log \left|\cos \left(x-\frac{\pi}{4}\right)\right|+c \)
\( ^{\mathbf{C}} x-\log \left|\cos \left(x-\frac{\pi}{4}\right)\right|+c \)
D. \( x+\log \left|\sin \left(x-\frac{\pi}{4}\right)\right|+c \)
Subject: Maths
If \( x \sin y=3 \sin y+4 \cos y, \) then \( \frac{d y}{d x}= \)
\( \mathbf{A} \cdot \frac{-\sin ^{2} y}{4} \)
B. \( \frac{\sin ^{2} y}{4} \)
\( \mathbf{c} \cdot \frac{-\cos ^{2} y}{4} \)
D. \( \frac{\cos ^{2} y}{4} \)
Subject: Chemistry
Assertion
The mass number of hydrogen is equal
to its atomic number.
Reason
H-atom has no neutrons.
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 ice cube of edge length \( 20 \mathrm{cm} \) is
floating in a tank of base area \( 2500 \mathrm{cm}^{2} \)
filled with water to \( 22 c m \) height. The displacement of centre of mass of whole system (in \( \mathrm{cm} \) ), when ice cube melts completely will be
\( \left(\rho_{i c e}=900 k g / m^{3}, \rho_{\omega}=\right. \)
\( \left.\mathbf{1 0 0 0 k g} / \boldsymbol{m}^{3}, \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{\mathbf{2}}\right) \)
A . 1
в. 1.5
\( c \cdot 1.32 \)
D. 1.44
Subject: Chemistry
Which of the following aqueous solutions, when added to 100 ml of
\( 0.1 M H C l(a q) \) will cause no change in its \( p H ? \) Assume volumes to be additive.
A . \( 100 \mathrm{ml} \) distilled water
B. \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{HNO}_{3} \)
\( \mathrm{c} .50 \mathrm{ml} \) of \( 0.2 \mathrm{M} \) HCl
D. \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{AgNO}_{3} \)
Subject: Maths
Set the following vectors in the increasing order of their magnitudes.
a) \( 3 \hat{i}+4 \hat{j} \)
b) \( 2 \hat{i}+4 \hat{j}+6 \hat{k} \)
c) \( 2 \hat{i}+2 \hat{j}+2 \hat{k} \)
\( A \cdot b, a, c \)
B. \( c, a, b \)
\( c \cdot a, c, b \)
D. a, b, c