AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A cylinderical vessel is filled with equal
amount of weight of mercury and water.The overall height of the two layer is \( 29.2 \mathrm{cm}, \) specific gravity of mercury is 13.6.Then the pressure of the liquid at the bottom of the vessel is:
\( \mathbf{A} \cdot 29.2 \mathrm{cm} \) of water
в. \( \frac{29.2}{13.6} \mathrm{cm} \) of mercury
c. \( 4 c m \) of mercury
D. \( 15.6 \mathrm{cm} \) of mercury
Subject: Chemistry
\( N_{2}(g)+3 H_{2}(g)_{200-300} \frac{773 K}{b a r} 2 N H_{3}(g)+ \)
heat
Which of the following works as a catalyst?
\( \mathbf{A} \cdot A l_{2} O_{3} \)
в. \( K_{2} \),
c. \( F e \)
D. \( V_{2} O_{5} \)
Subject: Physics
The resistance of platinum wire is 2.4
ohms at \( 0^{\circ} \mathrm{C} \) and 3.4 ohms at \( 100^{\circ} \mathrm{C} \). If
the resistance at \( t^{\circ} C \) is 4 ohms then the
temperature \( t \) is equal to
A \( \cdot 160^{\circ} \mathrm{C} \)
В. \( 140^{\circ} \mathrm{C} \)
c. \( 180^{\circ} \mathrm{C} \)
D. \( 120^{\circ} \mathrm{C} \)
Subject: Physics
A charge of magnitude \( Q \) is placed at the origin. A second charge of magnitude \( 4 Q \) is placed at the position \( x=d \) along the \( x \) -axis.

Other than infinitely far away, at what position on the \( x \) -axis will a positive test charge experience a zero net force?
A \( . x=-d \)
B. \( x=-\frac{d}{2} \)
c. \( x=\frac{d}{3} \)
D. \( x=\frac{3 d}{2} \)
E. At no position other than infinitely far away will the positive test charge experience zero net force
Subject: Maths
If \( \mathbf{y}=\mathbf{c e}^{x /(x-a)}, \) then \( \frac{\mathbf{d y}}{\mathbf{d x}} \) equals
\( A \cdot a(x-a) \)
B. \( -\frac{\text { ay }}{(x-a)^{2}} \)
\( c \cdot a^{2}(x-a)^{2} \)
D.
Subject: Chemistry
What are the products formed when xenon hexafluoride react with silicon
dioxide?
A. \( \operatorname{XeSiO}_{4}+H F \)
B. \( X e F_{2}+S i F_{4} \)
\( \mathrm{c} \cdot \operatorname{Xe} \mathrm{OF}_{4}+\mathrm{SiF}_{4} \)
D. \( X e O_{3}+S i F_{2} \)
Subject: Maths
Identify the graph of the polynomial
function \( \boldsymbol{f} \)
\( f(x)=x^{4}+x^{3}-2 x^{2} \)
\begin{tabular}{|l|l|l|l|l|}
\hline 1 & 1 & & & \\
\hline & & & & \\
\hline & & & & \\
\hline & & & & \\
\hline & & & & \\
\hline & & & & \\
\hline
\end{tabular}
A. graph a
B. graph b
c. graph c
D. graph d
Subject: Physics
A hollow insulated conduction sphere is
given a positive charge of \( 10 \mu C . \) What
will be the electric field at the centre of
the sphere if its radius is 2 metres?
A. zero
в. \( 5 \mu C m^{-2} \)
\( c \cdot 20 \mu C m^{-2} \)
D. \( 8 \mu C m^{-2} \)
Subject: Maths
Evaluate : \( \int \frac{(4 x+1) d x}{x^{2}+3 x+2} \)
A.
\[
\begin{array}{l}\text { s. } \\ \begin{array}{l}\text { s. } 2 \log \left|x^{2}+5 x+2\right|-5 \log \left|\frac{x+1}{x+2}\right|+C \\ =2 \log \left|x^{2}+3 x+2\right|-5 \log \left|\frac{x+3}{x+2}\right|+C\end{array} \\ \text { 0. }=2 \log \left|x^{2}+3 x+2\right|-5 \log \left|\frac{x+1}{x+2}\right|+C\end{array}
\]
Subject: Chemistry
Which of the following statements is
wrong?
A. Acidified \( K M n O_{4} \) solution decolourises on the addition of sodium oxalate
B. In the reaction between \( B r_{2} \) and \( C s I, B r_{2} \) is an oxidising agent and \( C s I \) is a reducing agent
c. In the reaction \( 2 K_{2} S_{2} O_{3}+I_{2} \rightarrow 2 K I+K_{2} S_{4} O_{6} \), the
change in the oxidation number of \( S \) is 0.5
D. \( C \) has the same oxidation number in both \( C H_{4} \) and
\( C O_{2} \)
Subject: Chemistry
The crystal field splitting energy CFSE \( \left(\text {In } \Delta_{0} \text {units}\right) \) for \( \left[\text {Co} F_{6}\right]^{3-} \) will be:
A \( .-1.6 \Delta_{0} \)
в. \( -2.4 \Delta_{0} \)
\( c .-0.4 \Delta_{0} \)
D. \( +0.6 \Delta_{0} \)
Subject: Chemistry
The molecular formula of gypsum is :
A. \( \operatorname{CaSO}_{4} . \mathrm{H}_{2} \mathrm{O} \)
в. \( \operatorname{CaSO}_{4} .2 \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot 2 \operatorname{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( \operatorname{CaSO}_{4} .3 \mathrm{H}_{2} \)
Subject: Maths
Point \( P(6,6) \) lies on the circle with
center (2,3) and radius 5 coordinate
units. Find the co-ordinates of the
image of point \( \mathrm{P} \) after the circle is
rotated \( 90^{\circ} \) clockwise ( \( \circlearrowright \) ) about its
center.
A \( .(2,3) \)
B. (3,2)
\( c \cdot(5,-1) \)
\( D \cdot(6,0) \)
E. (7,3)
Subject: Physics
The force between two identical charges
placed at a distance of \( r \) in vacuum is
\( F . \) Now, a slab of dielectric of constant 4 is inserted between these two charges.
If the thickness of the slab is \( \frac{r}{2}, \) then the force between the charges will become:
A. \( F \)
в. 3
\( \overline{5}^{F} \)
c. \( _{\overline{9}}_{F} \)
D. \( \frac{F}{2} \)
Subject: Physics
We sit in the room with windows open,
then:
A. Air pressure on the floor of the room equals the atmospheric pressure but the air pressure on the ceiling is negligible
B. Air pressure is nearly the same on the floor, the walls and ceiling
C. Air pressure on the floor equals the weights of the air column inside the room (from floor to ceiling ) per unit area
D. Air pressure on the walls is zero since the weight of air acts downwards
Subject: Chemistry
The radius of \( L a^{3+} \) (Atomic number of \( \boldsymbol{L} \boldsymbol{a}=\mathbf{5} \mathbf{7}) \) is \( \mathbf{1 . 0 6} \boldsymbol{A} . \) Which one of the
following given values will be closest to
the radius of \( L u^{3+} \) (Atomic number of
\( \boldsymbol{L} \boldsymbol{u}=\mathbf{7} 1) ? \)
A \( .1 .40 \AA \)
В. 1.06 А
c. \( 0.85 \dot{A} \)
D. 1.60 月
Subject: Physics
Three wires \( A, B, C \) made of different
materials elongated by \( 1.5,2.5,3.5 \mathrm{mm} \) under a load of 5kg. If the diameters of the wires are the same,the most elastic material is that of
\( A \cdot A \)
B. B
\( c \cdot c \)
D. All
Subject: Maths
Assertion
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}1+x & x<0 \\ 1+[x]+\sin x & 0 \leq x \leq \pi / 2 \\ 3 & x \geq \pi / 2\end{array}\right. \)
is continuous on \( \mathrm{R}-\{1\} \)
Reason
The greatest integer function is
discontinuous at every integer.
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
\( \sin ^{-1}|\sin x|=\sqrt{\sin ^{-1}|\sin x|} \) then \( x= \)
This question has multiple correct options
A \( . n \pi-1 \)
в. \( n \pi \)
c. \( n \pi+1 \)
D. \( n \frac{\pi}{2}+1 \)
Subject: Maths
Factorize the following expression \( a^{3}+125 \)
A \( \cdot(a+5)\left(a^{2}-5 a+25\right) \)
B . \( (a+5)\left(a^{2}+5 a+25\right) \)
c. \( (a+5)\left(a^{2}-5 a-25\right) \)
D. None of these
Subject: Maths
Adj \( \left(A d j\left[\begin{array}{cc}2 & -3 \\ 4 & 6\end{array}\right]\right)= \)
A \( \cdot\left[\begin{array}{cc}2 & -3 \\ 4 & 6\end{array}\right] \)
в. \( \left[\begin{array}{cc}6 & 3 \\ -4 & 2\end{array}\right] \)
с. \( \left[\begin{array}{cc}-6 & 3 \\ -4 & -2\end{array}\right] \)
D \( \cdot\left[\begin{array}{cc}-6 & -3 \\ 4 & -2\end{array}\right] \)
Subject: Maths
Find the Standard Deviation of the
following data:
\( \mathbf{5}, \mathbf{9}, \mathbf{8}, \mathbf{1 2}, \mathbf{6}, \mathbf{1 0}, \mathbf{6}, \mathbf{8} \)
A . 2.14
B . 2.16
c. 2.15
D. 2.17
Subject: Physics
A particle hanging from a massless spring stretches it by \( 2 \mathrm{cm} \) at earths surface. How much will the same
particle stretch the spring at a height of \( 2624 \mathrm{km} \) from the surface of the earth? (Radius of earth \( =6400 \mathrm{km} \) ).
A \( .1 \mathrm{cm} \)
B. \( 2 \mathrm{cm} \)
\( \mathrm{c} .3 .3 \mathrm{cm} \)
D. 4 cm
Subject: Chemistry
toppr
\( Q \) туре
A large number of atoms/molecules (approximately \( 6.023 \times 10^{23} \) ) are
present in few grams of any chemical compound varying with their atomic/molecular masses. To handle
such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry, and radiochemistry. the following example illustrates a typical case, involving chemical/electrochemical reaction,
which requires a clear understanding of the mole concept.

A 4.0 molar aqueous solution of NaCl is prepared and \( 500 \mathrm{mL} \) of this solution is electrolyzed. This leads to the evolution of chlorine gas at one of the electrodes (atomic mass: \( \mathrm{Na}=23, \mathrm{Hg}=200 ; 1 \)
faraday =96500 coulombs) The total charge (coulombs) required for complete electrolysis is:
A . 24125
B. 48250
c. 96500
D. 193000
Subject: Maths
If \( x^{2}-b x+c=0 \) has equal integral
roots, then
This question has multiple correct options
A. \( b \) and \( c \) are integers
B. \( b \) and \( c \) are even integers
\( \mathrm{c} . b \) is an even integer and \( c \) is a perfect square of an integer
D. none of these
Subject: Physics
Pure \( S i \) at \( 500 K \) has equal number of
electron \( \left(\boldsymbol{n}_{e}\right) \) and hole \( \left(\boldsymbol{n}_{\boldsymbol{h}}\right) \)
concentration of \( 1.5 \times 10^{16} m^{-3} \)
Doping by indium increases \( n_{h} \) to \( 4.5 \times \)
\( 10^{22} m^{-3} . \) The doped semiconductor is
of
A \( \cdot n \) -type with electron concentration \( n_{e}=5 \times 10^{22} \mathrm{m}^{-3} \)
B . p-type with electron concentration \( n_{e}=2.5 \times 10^{10} \mathrm{m}^{-3} \)
C . \( n \) -type with electron concentration \( n_{e}=2.5 \times 10^{23} \mathrm{m}^{-3} \)
D. \( p \) -type having electron concentrations \( n_{e}=5 \times \) \( 10^{9} m^{-3} \)
Subject: Physics
The magnitude of electric field as a
function of the distance r inside the
sphere is given by :
\( ^{\mathbf{A}} \cdot_{E}=\frac{\rho_{0}}{\varepsilon}\left[\frac{r}{3}-\frac{r^{2}}{4 R}\right] \)
B. \( \quad E=\frac{\rho_{0}}{\varepsilon}\left[\frac{r}{4}-\frac{r^{2}}{3 R}\right] \)
\( ^{\mathrm{C}}=\frac{\rho_{0}}{\varepsilon}\left[\frac{r}{3}+\frac{r^{2}}{4 R}\right] \)
D. \( \quad E=\frac{\rho_{0}}{\varepsilon}\left[\frac{r}{4}+\frac{r^{2}}{3 R}\right. \)
Subject: Physics
A body is thrown vertically upwards and rises to a height of \( 10 \mathrm{m} \). The velocity with which the body was thrown
upwards is \( \left(g=9.8 m / s^{2}\right) \)
\( A \cdot 10 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 14 \mathrm{m} / \mathrm{s} \)
D. none of these
Subject: Chemistry
A solution of \( \boldsymbol{P h}_{3} \boldsymbol{C C O}_{2} \boldsymbol{H} \) in conc.
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) gives \( (\boldsymbol{X}) \) when poured into
methanol \( X \) is :
\( ^{\mathbf{A}} \cdot \operatorname{Ph}_{3} C-\stackrel{\mathbb{I}}{C}-O-C H_{3} \)
в. \( \quad P h_{2} C H-C \) I
\( \mathbf{c} \cdot P h_{3} C-O C H_{3} \)
D. \( P h_{3} C-C H_{3} \)
Subject: Maths
Of the students in a college, it is known that \( 60 \% \) reside in hostel and \( 40 \% \) are
day scholars (not residing in hostel) Previous year results report that \( 30 \% \) of all students who reside in hostel attain
\( A \) grade and \( 20 \% \) of day scholars attain
\( A \) grade in their annual examination. At
the end of the year, one student is chosen at random from the college and
he has an \( A \) grade, what is the probability that the student is a hosteller?
Subject: Maths
\( \operatorname{Let} f(x)=\left\{\begin{array}{cc}x^{2} & x<1 \\ x & 1<x<4, \text { then } \\ 4-x & x>4\end{array}\right. \)
This question has multiple correct options
A \( \cdot \lim _{x \rightarrow 1^{-}} f(x)=1 \)
B. \( \lim _{x \rightarrow 1^{+}} f(x)=1 \)
\( \mathbf{c} \cdot \lim _{x \rightarrow 4^{-}} f(x)=4 \)
D. \( \lim _{x \rightarrow+4^{+}} f(x)=4 \)
Subject: Chemistry
Carbon atoms in \( C_{2}(C N)_{4} \) are:
A. sp hybridizedd
B. \( s p^{2} \) hybridized
c. \( s p \) and \( s p^{2} \) hybridized
D. \( s p, s p^{2} \) and \( s p^{3} \) hybridized
Subject: Physics
A square loop, carrying a steady current
Is placed in a horizontal plane near a
long straight conductor carrying a
steady current \( I_{1} \) at a distance d from
the conductor as shown in figure. The loop will experience:
A. a net repulsive force away from the conductor
B. a net torque acting upward perpendicular to the horizontal plane
C. a net torque acting downward normal to the horizontal plane
D. a net attractive force towards the conductor
Subject: Chemistry
The electronic configuration of Gd (atomic number \( =\mathbf{6 4} \) amu) is:
\( \mathbf{A} \cdot[X e] 4 f^{8} 5 d^{9} 6 s^{2} \)
в. \( [X e] 4 f^{7} 5 d^{1} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{5} 5 d^{2} 6 s^{2} \)
\( \mathbf{D} \cdot[X e] 4 f^{3} 5 d^{3} 6 s^{2} \)
Subject: Physics
In a double slit experiment instead of taking slits of equal widths, one slit is made twice as wide as the other. Then,
in the interference pattern.
A. The intensities of both the maxima and the minima increase
B. The intensity of the maxima increases and the minima has zero intensity
c. The intensity of the maxima decrease and that of the minima increases
D. The intensity of the maxima decreases and the minima has zero intensity
Subject: Chemistry
In an organic compound with molar mass \( 108 \mathrm{g}, \mathrm{C}, \mathrm{H}, \) and \( \mathrm{N} \) are present in the ratio 9: 1: 3.5 by mass. Molecular formula of the compound is:
A \( \cdot C_{6} H_{8} N_{2} \)
В. \( C_{7} H_{10} N \)
\( \mathbf{c} \cdot C_{5} H_{6} N_{3} \)
D. \( C_{4} H_{5} N_{3} \)
Subject: Maths
If \( f(x)=\frac{x^{2}+2}{x-1} \) when \( x<3, f(x)= \)
\( \frac{\sin x}{x-3} \) when \( x>3, \) for what values of
is the function not defined
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6
Subject: Physics
\( \ln \) an \( A C \) generator, the rate of change of
magnetic flux through the coil is maximum when the angle between the
plane of the coil and the lines of force is
A . \( 0^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 90^{\circ} \)
Subject: Physics
The magnetic flux through the cross-
section of the toroidal solenoid is
A \( \cdot \frac{\mu_{0} N i h}{2 \pi} \)
В. \( \frac{\mu_{0} N i h(b-a)}{2 \pi r} \)
c. \( \frac{\mu_{0} N i h}{2 \pi} \log _{e} \frac{b}{a} \)
D. \( \frac{\mu_{0} N^{2} i h}{2 \pi} \log _{e} \frac{a}{b} \)
Subject: Physics
Assertion
A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal
Reason Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field \( \vec{B} \) in a direction perpendicular to \( \vec{B}, \) will describe circular trajectories of equal radii.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A coin placed on a rotating turn table just slips if it is at a distance of \( 40 \mathrm{cm} \)
from the centre if the angular velocity of the turntable is doubled, it will just slip at a distance of:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)
Subject: Maths
Three six-faced fair dice are thrown
together let \( P(k) \) denote the probability
that the sum of the numbers appearing
on the dice is \( k(9 \leq k \leq 4) \). Find 54 s where \( \boldsymbol{S}=\sum_{\boldsymbol{k}=\mathbf{9}}^{\mathbf{1 4}} \boldsymbol{P}(\boldsymbol{k}) \)
Subject: Maths
If \( \boldsymbol{x} \geq \mathbf{0} \)
\( 3 y-2 x \geq-12 \)
\( 2 x+5 y \leq 20 \)
The area of the triangle formed in the \( x y \) plane by the system of inequalities above is:
\( \mathbf{A} \cdot 60 \)
B . 30
c. 40
D. 50
Subject: Maths
The lines \( p\left(p^{2}+1\right) y-x+q=0 \) and
\( \left(p^{2}+1\right) x+\left(p^{2}+1\right)^{2} y+2 q=0 \) are
perpendicular to a common line for
A. exactly one value of \( p \)
B. exactly two values of \( p \)
c. more than two values of \( p \)
D. no value of \( p \)
Subject: Chemistry
A solution of glucose \( \left(\mathbf{C}_{6} \mathbf{H}_{\mathbf{1 2}} \mathbf{O}_{\mathbf{6}}\right) \) in
water is labelled as \( 10 \% \) by weight. What would be the molality of the solution?
(Molar mass of glucose \( =180 \mathrm{g} \mathrm{mol}^{-1} \) )
A. 0.4
B. 0.6
\( c .0 . \)
D. 0.5
Subject: Chemistry
Which one of the following sets of ions represent the collection of isoelectronic
species?
A \( \cdot K^{+}, C a^{2+}, S c^{3+}, C l^{-} \)
B. \( N a^{+}, M g^{2+}, A l^{3+}, C l^{-} \)
C \( \cdot K^{+}, C l^{-}, M g^{2+}, S c^{3+} \)
D. \( N a^{+}, C a^{2+}, S c^{3+}, F^{-} \)
Subject: Physics
A concave lens forms the image of an
object such that the distance between
the object and image is \( 10 \mathrm{cm} \) and the
magnification produced is \( 1 / 4 . \) The focal length of the lens will be
\( \mathbf{A} \cdot 8.6 \mathrm{cm} \)
B. \( 6.2 \mathrm{cm} \)
c. \( 10 \mathrm{cm} \)
D. \( 4.4 \mathrm{cm} \)
Subject: Physics
Three charges are placed at the vertices
of an equilateral triangle of side 'a' as shown in the following figure. The force experienced by the charge placed at the
vertex \( A \) in a direction normal to \( B C \) is
A \( \cdot Q^{2} /\left(4 \pi \epsilon_{0} a^{2}\right) \)
B \( \cdot-Q^{2} /\left(4 \pi \epsilon_{0} a^{2}\right) \)
\( c . \) Zero
D. \( Q^{2} /\left(2 \pi \epsilon_{0} a^{2}\right) \)
Subject: Physics
Assertion
Two bodies at different temperatures, if brought in thermal contact do not necessary settle to the mean temperature.
Reason
The two bodies may have different thermal capacities.
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: Chemistry
(1) 1,2 -dihydroxybenzene
(II) 1,3 -dihydroxybenzene
(III) 1,4 -dihydroxybenzene
(IV) Hydroxybenzene. The increasing order of boiling points of above mentioned alcohols is:
\( A \cdot|<||<|||<\mid V \)
c. IV < Is II <III
D. IV < || < |< ||
Subject: Physics
If wavelength of a wave is \( 100 \mathrm{m} \), then
100 waves will cover distance.
\( A \cdot 10 \mathrm{km} \)
B. \( 1 \mathrm{km} \)
\( c .100 \mathrm{km} \)
D. \( 100 \mathrm{m} \)
Subject: Maths
Let \( z=1+i b=(a, b) \) be any complex
number, \( a, b, \epsilon R \) and \( \sqrt{-1}=i . \) Let \( z \neq \) \( 0+0 i, a r g z=\tan ^{-1}\left(\frac{I m z}{R e z}\right) w h e r e \)
\( -\pi<\arg z \leq \pi \)
\( \arg (\bar{z})+\arg (-z)= \)
\( \left\{\begin{array}{c}\pi, \text { if } \arg (z)<0 \\ -\pi, \text { if } \arg (z)>0\end{array}\right. \)
Let \( z \& w \) be non-zero complex numbers such that they have equal modulus
values and \( \arg z-a r g \bar{w}=\pi, \) then \( z \)
equals
\( \mathbf{A} \cdot-u \)
B.
\( \mathrm{c} \cdot-\bar{w} \)
D. \( \bar{w} \)
Subject: Physics
If \( \vec{A}+\vec{B} \) is a unit vector along \( x \) -axis and \( \vec{A}=\hat{i}-\hat{j}+\hat{k} \) then what is \( \vec{B} ? \)
\( \mathbf{A} \cdot \hat{j}+\hat{k} \)
B. \( \hat{j}-\hat{k} \)
\( \mathbf{c} \cdot \hat{i}+\hat{j}+\hat{k} \)
D. \( \hat{i}+\hat{j}-\hat{k} \)
Subject: Physics
The equation of the displacement of two particles making SHM are represented by
\( \boldsymbol{y}_{1}=a \sin (\omega t+\phi) \& \boldsymbol{y}_{2}=a \cos (\boldsymbol{\omega} \boldsymbol{t}) \)
The phase difference of the velocities of the two particles is :
\( \mathbf{A} \cdot \frac{\pi}{2}+\phi \)
B. \( -\phi \)
c. \( \phi \)
D. \( \phi-\frac{\pi}{2} \)
Subject: Physics
The magnetic field normal to the plane
of a wire of \( n \) turns and radius \( r \) which
carries a current i is measured on the
axis of the coil at a small distance \( h \)
from the centre of the coil. This is
smaller than the magnetic field at the
centre by the fraction
\( \mathbf{A} \cdot(2 / 3) r^{2} / h^{2} \)
B. \( (3 / 2) r^{2} / h^{2} \)
c. \( (2 / 3) h^{2} / r^{2} \)
D. \( (3 / 2) h^{2} / r^{2} \)
Subject: Maths
Let \( \boldsymbol{P}(\boldsymbol{n}) \) be the statement \( \boldsymbol{2}^{\boldsymbol{n}}<\boldsymbol{n} ! \)
where \( n \) is a natural number, then \( P(n) \)
is true for:
A . all \( n \)
B. all \( n>2 \)
c. all \( n>3 \)
D. all \( n<3 \)
Subject: Physics
A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \( 15 \mathrm{cm} \) from the lens. If the lens is removed, the point where the rays meet will move \( 5 \mathrm{cm} \) closer to the mounting
that holds. Find the focal length \( (\text { in } \mathrm{cm}) \) of the lens without sign.
Subject: Physics
A hole is made at the bottom of the tank
filled with water (density \( 1000 k g / m^{3} \) ), If the total pressure at the bottom ofthe tankis 3 atmosphere
\( \left(1 \text { atmosphere }=10^{5} N / m^{2}\right), \) then the velocity of efflux is :
A \( . \sqrt{200} \mathrm{m} / \mathrm{s} \)
B. \( \sqrt{400} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{500} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{800} \mathrm{m} / \mathrm{s} \)
Subject: Maths
Two angles of triangle \( A B C \) are \( 85^{\circ} \) and
\( 65^{\circ} \) while the two angles of another
triangle DEF are \( 30^{\circ} \) and \( 65^{\circ} . \) Which of the statements is correct?
A. \( \triangle \) ABC is similar to \( \triangle \) DEF
B. \( \triangle \) ABC is congurent to \( \triangle \) DEF
c. \( \triangle \) ABC is equal to \( \triangle \) DEF
D. None of these
Subject: Maths
Area enclosed between the curves \( |\boldsymbol{y}|= \)
\( 1-x^{2} \) and \( x^{2}+y^{2}=1 \) is
A \( \cdot \frac{3 \pi-14}{3} \) sq.units
B. \( \frac{\pi-8}{3} \) sq.units
c. \( \frac{2 \pi-8}{3} \) sq.units
D. None of these
Subject: Physics
The Sl unit of specific latent heat is
A. cal \( g^{-1} \)
B . cal \( g^{-1} \mathrm{K}^{-1} \)
\( c \cdot J \operatorname{kg}^{-1} \)
D. J kg \( ^{-1} \mathrm{K}^{-1} \)
Subject: Physics
To get maximum current in a resistance
of \( 3 \Omega, \) one can use n rows of m cells
(connected in series) connected in
parallel. If the total number of cells is 24 and the internal resistance of a cell is
\( 0.5 \Omega, \) then
A \( . m=12, n=2 \)
в. \( n=3, m=8 \)
c. \( m=2, n=12 \)
D. \( m=6, n=4 \)
Subject: Physics
The magnetic field at the center of the
coil of radius \( r \) and carrying a current \( I \)
as shown in the figure is : (the wires crossing at \( P \) are insulated from each
other)
A \( \cdot \frac{\mu_{0}}{4 \pi} \frac{2 I}{r}(1+\pi) \)
в. \( \frac{\mu_{0}}{4 \pi} \frac{2 I}{r}(\pi-1) \)
c. \( \frac{\mu_{0}}{4 \pi} \frac{2 I}{r}\left(\pi^{2}+1\right) \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{2 \pi I}{r} \)
Subject: Physics
When an electric dipole \( \vec{p} \) is kept in a uniform electric field \( \vec{E} \) then for what of a value of the angle between \( \vec{p} \) and \( \vec{E} \),
torque will be maximum:
A \( .90^{\circ} \)
B. \( 0^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 45^{\circ} \)
Subject: Physics
Four wires \( P, Q, R \) and \( S \) of same
materials have diameters and
stretching forces as shown
below. Arrange their strains in the
decreasing order.
\( \begin{array}{lll}\text { Wire } & \text { Diameter } & \text { Stretching force } \\ \mathrm{P} & 2 \mathrm{mm} & 10 \mathrm{N} \\ \mathrm{Q} & 1 \mathrm{mm} & 20 \mathrm{N} \\ \mathrm{R} & 4 \mathrm{mm} & 30 \mathrm{N} \\ \mathrm{S} & 3 \mathrm{mm} & 40 \mathrm{N}\end{array} \)
\( A \)
\( \mathrm{Q}, \mathrm{S}, \mathrm{P}, \mathrm{R} \)
B. R,P,S,Q
\( \mathbf{c} . \) P,Q,R,S
D. \( P, R, Q, S \)
Subject: Maths
A hollow spherical shell is made of
metal of density \( 4.8 \mathrm{g} / \mathrm{cm}^{3} . \) If its
internal and external radii are \( 10 \mathrm{cm} \)
and \( 12 \mathrm{cm} \) respectively, find the weight of the shell
A. \( 15.24 \mathrm{kg} \)
B . \( 12.84 \mathrm{kg} \)
c. \( 14.64 \mathrm{kg} \)
D. None of these
Subject: Chemistry
If we know \( \Delta G^{\circ} \) of a reaction, which of
the following can be defined?
I. Cell potential, \( \boldsymbol{E}^{\circ} \)
II. Activation energy, \( \boldsymbol{E}_{\boldsymbol{a}} \)
III. Equilibrium constant, \( \boldsymbol{K}_{e q} \)
A. I and II only
B. I and III only
c. ॥ only
D. I, II, III
E. None of these