AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( 3 p+2 q=i+j+k \) and \( 3 p-2 q= \)
\( i-j-k, \) then the angle between \( p \) and
\( q \) is
A \( \cdot \frac{\pi}{6} \)
в.
c. \( \frac{\pi}{3} \)
D. \( \frac{\pi}{2} \)
\( E \)
Subject: Physics
The de Broglie wavelength of an electron having 80 eV of energy is nearly \( \left(1 e V=1.6 \times 10^{-19} J, \) Mass of electron \right.
\( =9 \times 10^{-31} k g \)
Planck's constant \( =\mathbf{6 . 6} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \)
(nearly)
A . \( 140 A^{\circ} \)
B. 0.14 \( A^{0} \)
\( \mathbf{c} \cdot 14 A^{0} \)
D. 1.4 \( A^{0} \)
Subject: Chemistry
Two moles of \( N_{2} \) and two moles of \( H_{2} \)
are taken in a closed vessel of \( 5 L \)
capacity and suitable conditions are provided. When the equilibrium is reached, it is found that 0.6 mole of \( N_{2} \)
is used up. The equilibrium
concentration of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is
A . 0.4
B. 0.08
\( c .0 .8 \)
D. 0.24
Subject: Chemistry
A mixture in which the mole ratio of \( \boldsymbol{H}_{2} \)
and \( O_{2} \) is 2: 1 is used to prepare water
by the reaction:
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \rightarrow \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \boldsymbol{O} \)
The total pressure in the container is
\( 0.8 \operatorname{atm} \) at \( 20^{\circ} \mathrm{C} \) before the reaction. The
final pressure (in atm) at \( 120^{\circ} \mathrm{C} \) after
the reaction, assuming \( 80 \% \) yield of water is (as nearest integer):
Subject: Physics
A horizontal force of \( 500 N \) pulls two
masses \( 10 k g \) and \( 20 k g \) connected by a light string and placed on a frictionless horizontal table. What is the tension in
the string if the force is applied on the \( 20 k g \) mass?
A. \( 333.3 N \)
N
в. \( 166.7 N \)
c. \( 233.3 N \)
D. \( 217 N \)
Subject: Physics
A ray of light is incident on a plane
mirror AB. The angle of incidence is \( 60^{\circ} \)
The ray is reflected from \( A B \) and strikes another plane mirror BC placed at right angles to mirror AB. The angle of reflection at BC is:
A . \( 135^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)
Subject: Physics
A small block slides with velocity
\( 0.5 \sqrt{g} r \) on the horizontal friction less
surface as shown in the figure. The
block leaves the surface at point \( C . \) The
angle \( \theta \) in the figure is:
\( \mathbf{A} \cdot \cos ^{-1}(4 / 9) \)
B \( \cdot \cos ^{-1}(3 / 4) \)
\( \mathbf{C} \cdot \cos ^{-1}(1 / 2) \)
D. none of the above
Subject: Chemistry
A graph between \( \log t_{1 / 2} \) and \( (\log \mathrm{a}) \)
(abscissa) a being the initial
concentration of \( A \) in the reaction. For
reaction \( A \rightarrow \) product, the rate law is:
A \( \cdot \frac{-d(A)}{d t}=k \)
B. \( \frac{-d(A)}{d t}=k[A] \)
\( \mathbf{c} \cdot \frac{-d(A)}{d t}=k[A]^{2} \)
D. \( \frac{-d(A)}{d t}=k[A]^{3} \)
Subject: Physics
A cylindrical tank stands on a frictionless surface.The seal over a
circular hole of radius \( 0.5 \mathrm{cm} \) in the wall
of the tank ruptures when the level of water above the hole is 1 metre. The
force that a person must apply on the cylinder to keep it from being set in motion is
A . \( 1.54 \times 10^{-3} N \) forward
B . \( 1.54 \times 10^{-3} N \) backward
c. \( 1.54 N \) forward
D. \( 1.54 N \) backward
Subject: Chemistry
Two electrochemical cells are
assembled in which following reactions
occur.
\( \boldsymbol{V}^{2+}+\boldsymbol{V} \boldsymbol{O}^{2+}+\boldsymbol{2} \boldsymbol{H}^{+} \rightarrow \boldsymbol{2} \boldsymbol{V}^{3+}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} ; \quad \boldsymbol{E}_{c e l l}^{o}=\mathbf{0 . 6 1 6} \boldsymbol{V} \)
\( \boldsymbol{V}^{3+}+\boldsymbol{A} \boldsymbol{g}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{V} \boldsymbol{O}_{2}+\boldsymbol{4} \boldsymbol{H}^{+}+ \)
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) ; \boldsymbol{E}_{c e l l}^{o}=\mathbf{0 . 4 3 9} \boldsymbol{V} \)
\( E^{o} \) for half reaction, \( V^{3+}+e \rightarrow V^{2+} \) is :
Given that \( \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}=\boldsymbol{0 . 7 9 9} \boldsymbol{V} \)
A. \( -0.256 v \)
B . - 0.216 V
c. \( -0.346 v \)
D. None of these
Subject: Physics
When two magnetic poles having same
pole strength are separated by a distance of \( 20 \mathrm{cm}, \) a force of \( 5 \mathrm{N} \) acts
between them. If the distance is halved, the force becomes
A . 20 N
B. 10 N
\( c .15 \mathrm{N} \)
D. 25 N
Subject: Maths
Let \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{Z} \text { and }(\boldsymbol{a}+\boldsymbol{b}) \) is
even \( \} \) Show that \( R \) is an equivalence relation on Z.
Subject: Physics
Assertion
An electric motor converts electrical
energy to mechanical energy.
Reason
The working of the motor is based on
mutual induction.
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
Draw the graph of the straight line given
by the equation \( 4 x-3 y+36=0 \)
Calculate the area of the triangle formed by the line drawn and the coordinate axes.
A. Area \( =45 \) sq. units
B. Area = 54 sq. units
c. Area \( =48 \) sq. units
D. Area = 58 sq. units
Subject: Chemistry
Reaction, \( 3 C l O^{-} \rightarrow C l O_{3}^{-}+2 C l \)
occurs in following two steps. I. \( C l O^{-}+C l O^{-} \stackrel{K_{1}}{\longrightarrow} C l O_{2}^{-}+C l^{-} \) (Slow
step)
\( \mathrm{Il.} \mathrm{ClO}_{2}^{+} \mathrm{ClO}^{-} \stackrel{k_{2}}{\longrightarrow} \mathrm{ClO}_{3}^{-}+\mathrm{Cl}^{-} \) (Fast
step) Then, the rate of given reaction is:
\( \mathbf{A} \cdot k_{1}\left[C l O^{-}\right] \)
B. \( k_{1}\left[C l O^{-}\right]^{2} \)
c. \( k_{2}\left[C l O_{2}^{-}\right]\left[C l O^{-}\right] \)
D. \( k_{2}\left[C l O^{-}\right]^{3} \)
Subject: Chemistry
The crystal fied stabilization energy
\( (C F S E) \) of \( \left[F e\left(H_{2} O\right)_{6}\right] C l_{2} \) and
\( \boldsymbol{K}_{2}\left[\boldsymbol{N} \boldsymbol{i} \boldsymbol{C l}_{4}\right], \) respectively, are:
A. \( -0.4 \Delta_{o} \) and \( -0.8 \Delta_{t} \)
B. \( -0.4 \Delta_{o} \) and \( -1.2 \Delta_{t} \)
c. \( -2.4 \Delta_{o} \) and \( -1.2 \Delta_{t} \)
D. \( -0.6 \Delta_{o} \) and \( -0.8 \Delta \)
Subject: Physics
A parallel plate capacitor (fig.) made of circular plates each of radius \( \boldsymbol{R}= \)
\( 6.0 \mathrm{cm} \) has a capacitance \( C=100 \mu \mathrm{F} \)
The capacitor is connected to a \( 230 V \)
ac supply with a (angular) frequency of 300 rad \( s^{-1} . \) Determine the amplitude of
\( B \) at a point \( 3.0 \mathrm{cm} \) from the axis
between the plates.?
Subject: Physics
Light rays (gold) are shown passing across the boundaries of different
colored transparent materials in three different cases below. The black dashed
line segments represent normal to the surfaces. Four different materials are
shown

Based on the way that the light moves through the materials, what is the ranking of the materials according to the values of their indices of refraction,
greatest first?
A. red, green. blue, purple.
B. purple, green, red, blue
c. blue, green, purple, red
D . . red, green, purple
E . green, purple, red, blue
Subject: Physics
For spherical symmetrical charge distribution, variation of electric
potential with distance from centre is
given in diagram. Given that:\( V=\frac{q}{4 \pi \varepsilon_{0} R_{0}} \) for \( r R_{0} \) and \( V=\frac{q}{4 \pi \varepsilon_{0} r} \)
for \( r \geq R_{0} \)
Then which option is incorrect:
A . Total charge within \( 2 R_{0} \) is \( q \)
B. Total electrostatic energy for \( r \leq R_{0} \) is zero
C. At \( r=R_{0} \) electric field is discontinuous
D. There will be no charge anywhere except at \( r=R_{0} \)
Subject: Maths
The plane through the intersection of the planes \( x+y+z=1 \) and \( 2 x+ \)
\( 3 y-z+4=0 \) and parallel to \( y \) -axis
also passes through the point.
A. (-3,0,1)
В. (3,3,-1)
c. (3,2,1)
D. (-3,1,1)
Subject: Chemistry
Assertion: Solution of \( A l C l_{3} \) in water is
neutral
Reason: \( \left[A l\left(H_{2} O\right)_{6}\right]^{3+} \) is formed
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
E. Both Assertion and Reason are incorrect
Subject: Chemistry
toppr
Q Type your question_
1.
of certain molarity was added gradually. The mass of precipitate produced (in g)
were measured and it was plotted
against volume of \( A g N O_{3} \) solution
added (in ml). Its known that \( A g I \) is
precipitated first. Precipitation of \( \boldsymbol{B} \boldsymbol{r} \)
does not start until the already
precipitating \( \boldsymbol{I}^{-} \) precipitates
completely. Find out the value of \( \boldsymbol{A B} \times \)
CD where:
\( A B= \) Atomic weight of metal \( M \)
\( C D= \) Mole percent of \( N a l \) in original
mixture.
\( \mathbf{A} \cdot 4994 \)
B . 2040
c. 3202
D. 3332
Subject: Chemistry
The electronic configurations of three elements \( X, Y \) and \( Z \) are given below. Which of the following is correct? \( x: 2,8 \)
\( Y: 2,8,7 \)
\( Z: 2,8,2 \)
A. \( x \) is a metal
B. Y is a metal
c. \( z \) is a non-metal
D. Y is a non-metal and \( z \) is a metal
Subject: Maths
f \( A \) and \( B \) are two events associated
with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B})=\mathbf{0 . 2}, \) find \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)
Subject: Physics
A linear object \( A B \) is placed along the axis of a concave mirror. The object is moving towards the mirror with speed
\( U . \) The speed of the image of the point \( A \)
is \( 4 U \) and the speed of the image of \( B \)
is also \( 4 U \) but in opposite direction. If
the center of the line \( A B \) is at a
distance \( L \) from the mirror then find out
the length of the object.
A \( \cdot \frac{3 L}{2} \)
в. \( \frac{5 L}{2} \)
\( c . L \)
D. None of these
Subject: Maths
Let \( A B C D \) be a square of side \( 2 a . \) Find
the coordinates of the vertices of this
square when
(i) A coincides with the origin and \( A B \)
and \( A D \) are along \( O X \) and \( O Y \)
respectively.
(ii) The centre of the square is at the
origin and coordinate axes are parallel
to the sides \( A B \) and \( A D \) respectivey.
Subject: Physics
An electric motor rotates a wheel at a
constant angular velocity \( \omega \) while
opposing torque is \( \tau \). The power of that
electric motor is :
A \( \cdot \frac{\pi}{2} \)
B. \( \pi \)
\( c \cdot 2 \tau \omega \)
D. \( \frac{\tau}{\omega} \)
Subject: Physics
A telephone cable at a place has four long straight horizontal wires carrying a current of \( 1.0 \mathrm{A} \) in the same direction
east to west. The earth's magnetic field at the place is \( 0.39 \mathrm{G}, \) and the angle of
dip is \( 35^{\circ} \).The magnetic declination is
nearly zero. What are the resultant magnetic fields at points \( 4.0 \mathrm{cm} \) below the cable?
Subject: Physics
An automobile engine absorbs \( 1600 J \) of heat from a hot reservoir and expel
\( 1000 J \) to a cold reservoir in each cycle.
What maximum work is done in each
cycle?
\( \mathbf{A} \cdot 400 J \)
B. \( 500 J \)
c. \( 600 J \)
D. \( 450 J \)
Subject: Maths
Show that \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \begin{array}{ll}\frac{\sin 3 x}{\tan 2 x}, & \text { if } x<0 \\ \frac{3}{2}, \quad \text { if } x=0 & \text { is contint } \\ \frac{\log (1+3 x)}{e^{2 x}-1}, & \text { if } x>0\end{array} \)
Subject: Maths
Tangents are drawn to the ellipse \( \frac{x^{2}}{9}+ \) \( \frac{y^{2}}{5}=1 \) at the ends of both latus
rectum. The area of the quadrilateral so formed is
A. 27 sq.units
B. \( \frac{13}{2} \) sq.units
c. \( \frac{15}{4} \) sq.units
D. 45 sq.units
Subject: Physics
There is a hole to the wall at the bottom
of a vessel filled with water to a height 10 \( c m . \) Water flows out completely in
5 sec. If the height of the water column above the hole is increased to \( 160 \mathrm{cm} \)
the total time taken for water flow is
A \( .2 .5 \mathrm{sec} \)
B. 5 sec
c. 10 sec
D. 20 sec
Subject: Chemistry
Calculate the formula unit mass (u) of
\( N a_{2} O \)
\( [\boldsymbol{N} \boldsymbol{a}=\mathbf{2 3}, \boldsymbol{O}=\mathbf{1 6}] \)
\( \mathbf{A} \cdot 60 \)
B. 62
c. 61
D. 59
Subject: Physics
Electric field in a region is given by \( \overrightarrow{\boldsymbol{E}}=-4 \boldsymbol{x} \hat{\boldsymbol{i}}+\boldsymbol{6} \boldsymbol{y} \hat{\boldsymbol{j}}, \) find the charge
enclosed in cube of side 1 m oriented as
shown in figure.
\( 4 \cdot 2 \varepsilon \)
B.
\( c \cdot \varepsilon \)
D. \( 6 \varepsilon \)
Subject: Maths
The probability that a man will be alive in 40 years is \( \frac{3}{5}, \) and the probability
that his wife will also survive 40 years is \( \frac{2}{3} . \) Find the probability that both will be alive
A
B. \( \frac{4}{5} \)
\( c \cdot \frac{2}{15} \)
D. \( \frac{6}{15} \)
Subject: Maths
For \( \boldsymbol{r}=\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots, \mathbf{1 0}, \) let \( \boldsymbol{A}_{r}, \boldsymbol{B}_{r}, \boldsymbol{C}_{\boldsymbol{r}} \)
denote respectively the coefficient of \( x^{r} \)
in the expansions of \( (1+x)^{10},(1+x)^{20} \)
and \( (1+x)^{30} . \) Then \( \sum_{r=1}^{10} A_{r}\left(B_{10} B_{r}-\right. \)
\( \left.C_{10} A_{r}\right) \) is equal to
\( \mathbf{A} \cdot B_{10}-C_{10} \)
B . \( A_{10}\left(B_{10}^{2}\right)-C_{10} A_{10} \)
c.
D. \( C_{10}-B_{10} \)
Subject: Physics
A positive charge \( Q \) is uniformly distributed along a circular ring of radius R. A small test charge q is placed
at the center of the ring figure. Then which statement is incorrect:
A. If \( q>0 \) and is displaced away from the centre in the plane of the ring,it will be pushed back towards the centr
B. if \( q<0 \) and is displaced away from the centre in the plane of the ring,it will never return towards the centre and will continue moving till it hits the ring
C. ifif q>0, it will perform SHM for small displacement along the axis
D. \( q \) at the centre of the ring is in an unstable equilibrium within the plane of the ring \( q>0 \)
Subject: Physics
Two cells of equal emf and of internal
resistances \( r_{1} \) and \( r_{2}\left(r_{1}>r_{2}\right) \) are
connected in series. On connecting this combination to an external resistance
\( \mathrm{R}, \) it is observed that the potential difference across the first cell becomes
zero. The value of R will be.
\( \mathbf{A} \cdot r_{1}+r_{2} \)
В. \( r_{1}-r_{2} \)
c. \( \frac{r_{1}+r_{2}}{2} \)
D. \( \frac{r_{1}-r_{2}}{2} \)
Subject: Physics
Assertion : Electric lines of force never
cross each other.
Reason: Electric field at a point superimpose to give one resultant electric field.
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both the assertion and reason are false.
E. If reason is true but assertion is false
Subject: Maths
\( \operatorname{Let} f(x)=\cos ^{-1}\left(\frac{x^{2}}{1+x^{2}}\right) . \) The range
of \( \boldsymbol{f} \) is
\( \mathbf{A} \cdot\left[0, \frac{\pi}{2}\right] \)
B. \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \)
c. \( \left[-\frac{\pi}{2}, 0\right] \)
D. none of these
Subject: Physics
The armature of de motor has \( 20 \Omega \)
resistance .It draws current of 1.5
ampere when run by 220 volts dc supply. The value of back e.m.f. induced in it will be
\( A \cdot 190 V \)
B. 150 V
c. \( 170 v \)
D. \( 120 \mathrm{V} \)
Subject: Physics
Two inclined planes intersect in a horizontal plane. their inclinations to
the horizontal being \( \alpha \) and \( \beta . \) If a particle is projected with velocity u at right angle to the former from a point on
it, find the time after which the velocity
vector will become perpendicular to the other inclined plane.
\( t_{t}=\frac{u \sin (\alpha+\beta)}{g \sin \beta} \)
B. \( t=\frac{u \cos (\alpha+\beta)}{g \cos \beta} \)
c. \( _{t}=\frac{u \cos (\alpha+\beta)}{g \sin \beta} \)
D. \( t=\frac{u \sin (\alpha+\beta)}{g \cos \beta} \)
Subject: Maths
The range of the function \( f(x)= \)
\( \log _{e}\left(3 x^{2}-4 x+5\right) \)
\( ^{A} \cdot\left(-\infty, \log _{e} \frac{11}{3}\right] \)
B. \( \quad\left[\log _{e} \frac{11}{3}, \infty\right) \)
c. \( \left[-\log _{e} \frac{11}{3}, \log _{e} \frac{11}{3}\right. \)
D. None of these
Subject: Physics
An aluminium measuring rod, which is
correct at \( 5^{\circ} \mathrm{C} \) measures the length of a
line as \( 80 \mathrm{cm} \) at \( 45^{\circ} \mathrm{C} \). If thermal
coefficient of linear expansion of aluminium is \( 2.50 \times 10^{-5} \) per \( ^{o} \) C.The
correct length of line is :
A \( .80 .08 \mathrm{cm} \)
B. \( 79.92 \mathrm{cm} \)
c. \( 81.12 \mathrm{cm} \)
D. \( 79.62 \mathrm{cm} \)
Subject: Physics
The dimensional formula of coefficient
of viscosity is
\( \mathbf{A} \cdot\left[M L T^{-1}\right] \)
B . \( \left[M^{-1} L^{2} T^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{-1} T^{-1}\right] \)
D. none
Subject: Maths
Determine the function which has a
domain of \( \boldsymbol{x} \leq \mathbf{3} \)
\( \mathbf{A} \cdot \)
\[
f(x)=(2-x)^{\frac{1}{2}}+\frac{x}{2}
\]
B. \( \quad f(x)=(3-x)^{\frac{1}{2}}+\frac{x}{2} \)
C
\[
f(x)=(x-3)^{\frac{1}{3}}+\frac{x}{4}
\]
D. \( \quad f(x)=(2-x)^{\frac{1}{4}}+\frac{x}{3} \)
E
Subject: Chemistry
The amount of \( \left(N H_{4}\right)_{2} S O_{4} \) to be added
to \( 500 \mathrm{mL} \) of \( 0.01 \mathrm{m} N H_{4} O H \) solution
\( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}} \) for \( \boldsymbol{N} \boldsymbol{H}_{4}^{+} \) is \( \boldsymbol{9} .2 \boldsymbol{6} \) ) prepare a buffer
of \( p H=8.26 \) is?
A. 0.05 mole
B. 0.025 mole
c. 0.10 mole
D. 0.005 mole
Subject: Physics
An object has an initial velocity \( u \) and an acceleration \( a \). The object moves in a straight line through a displacement s and has final velocity \( v \) The above quantities are related by the equation shown \( \boldsymbol{v}^{2}=\boldsymbol{u}^{2}+\mathbf{2} \boldsymbol{a} \boldsymbol{s} \)
Which condition must be satisfied in
order for this equation to apply to the motion of the object?
A. The direction of \( a \) is constant and the direction of \( a \) is the same as the direction of \( s \)
B. The direction of \( a \) is constant and the direction of \( a \) is the same as the direction of \( u \)
c. The magnitude of \( a \) is constant and the direction of \( a \) i constant
D. The magnitude of \( a \) is constant and the direction of \( a \) is the same as the direction of \( v \)
Subject: Maths
Let \( f(x) \) be a polynomial of degree four
having extreme values at \( x=1 \) and \( c=2 . \) If \( \lim _{x \rightarrow 0}\left[1+\frac{f(x)}{x^{2}}\right]=3, \) then \( f(2) \)
is equal to
A . -8
B. -4
c. 0
D. 4
Subject: Physics
\( \ln Y D S E, d=2 m m, D=2 m \) and
\( \lambda=500 n m . \) If intensity of two slits are
\( l_{0} \) and \( 9 l_{0}, \) then find the intensity at \( \boldsymbol{y}=\frac{1}{6} \boldsymbol{m m} \)
A \( .7 l_{0} \)
B. \( 10 l_{0} \)
c. \( 16 l_{0} \)
D. \( 4 l_{0} \)
Subject: Maths
If \( \boldsymbol{u}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2 b} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{c} \boldsymbol{y}^{2}, \boldsymbol{u}^{\prime}=\boldsymbol{a}^{\prime} \boldsymbol{x}^{2}+ \)
\( 2 b^{\prime} x y+c^{\prime} y^{2}, \) then prove that
\( \left|\begin{array}{ccc}\boldsymbol{y}^{2} & -\boldsymbol{x} \boldsymbol{y} & \boldsymbol{x}^{2} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{a}^{\prime} & \boldsymbol{b}^{\prime} & \boldsymbol{c}^{\prime}\end{array}\right|= \)
\( \left|\begin{array}{cc}\boldsymbol{a x}+\boldsymbol{b y} & \boldsymbol{b x}+\boldsymbol{c y} \\ \boldsymbol{a}^{\prime} \boldsymbol{x}+\boldsymbol{b}^{\prime} \boldsymbol{y} & \boldsymbol{b}^{\prime} \boldsymbol{x}+\boldsymbol{c}^{\prime} \boldsymbol{y}\end{array}\right|= \)
\( -\frac{1}{y}\left|\begin{array}{cc}u & u^{\prime} \\ a x+b y & a^{\prime} x+b^{\prime} y\end{array}\right| \)
Subject: Maths
f \( x, y, z \) are positive then minimum
value of
\( \boldsymbol{x}^{\log y-\log z}+\boldsymbol{y}^{\log z-\log x}+\boldsymbol{z}^{\log \boldsymbol{x}-\log \boldsymbol{y}} \) is
\( A \cdot 3 \)
B.
c. 9
D. 16
Subject: Maths
The difference between the greatest and
least value of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin 2 x-x \) on \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \) is
A \( \cdot \frac{\sqrt{3}+\sqrt{2}}{2} \)
B. \( \frac{\sqrt{3}+\sqrt{2}}{2}+\frac{\pi}{6} \)
c. \( \frac{\sqrt{3}}{2}+\frac{\pi}{3} \)
D. \( \frac{\sqrt{3}+\sqrt{2}}{2}-\frac{\pi}{3} \)
Subject: Chemistry
The actinoids exhibit more number of
oxidation states in general than the lanthanoids. This is because:
A. the \( 5 f \) orbitals are more buried than the \( 4 f \) orbitals
B. there is a similarity between 4 f and 5 f orbitals in their angular part of the wave function
c. the actinoids are more reactive than the lanthanoids
D. the 5 f orbitals extend further from the nucleus than the \( 4 f \) orbitals
Subject: Physics
A monochromatic beam of
electromagnetic radiation has an
intensity of \( 1 W / m^{2} . \) Then the average
number of photons per \( m^{3} \) for a \( 10 \mathrm{MeV} \)
\( \gamma \) ray is \( ? \)
A . 4166
B. 3000
c. 5000
D. 2083
Subject: Physics
A coil of area \( 500 \mathrm{cm}^{2} \) having 1000 turns
is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude \( 410^{-5} \)weber \( / m^{2} \). If it is
rotated by 180 degree about an axis passing through one of its diameter in
\( 0.1 \mathrm{sec}, \) find the average induced emf.
A. zero
в. \( 30 m V \)
\( \mathrm{c} .40 \mathrm{mV} \)
\( \mathbf{D} .50 \mathrm{mV} \)
Subject: Physics
The areal velocity of an object of mass \( \mathrm{m}=2 \mathrm{kg} \) revolving around another object
is given by \( 2 m^{2} / s, \) what is the angular momentum of the particle
A \( \cdot 6 k g-m^{2} / s \)
в. \( 8 k g-m^{2} / s \)
c. \( 4 k g-m^{2} / s \)
D. \( 2 k g-m^{2} / s \)
Subject: Maths
Vectors \( \overrightarrow{\boldsymbol{a}}=-\mathbf{4} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{k}} ; \overrightarrow{\boldsymbol{b}}=\mathbf{1 4} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}- \)
\( \mathbf{5} \hat{k} \) are laid from one point. Vector \( \overrightarrow{\boldsymbol{d}} \)
which is being laid off from the same point dividing the angle between vectors \( \vec{a} \) and \( \vec{b} \) in equal halves and having the magnitude \( \sqrt{\mathbf{6}} \) is
\( \mathbf{A} \cdot \hat{i}+\hat{j}+2 \hat{k} \)
B \( \cdot \hat{i}-\hat{j}+2 \hat{k} \)
c. \( \hat{i}+\hat{j}-2 \hat{k} \)
D . \( 2 \hat{i}-\hat{j}-2 \hat{k} \)
Subject: Chemistry
Which selection is the correct formula
for the chlorate ion?
A \( \cdot C l^{-} \)
B. \( C l O^{-} \)
\( \mathrm{c} \cdot \mathrm{ClO}_{2}^{-} \)
D. \( C l O_{3}^{-} \)
E \( \cdot C l O_{4}^{-} \)
Subject: Maths
Let \( a_{n} \) be the nth term of the G.P. of positive numbers. Let \( \sum_{n=1}^{100} a_{2 n}=\alpha \) and \( \sum_{n=1}^{100} a_{2 n-1}=\beta, \) such that \( \alpha \neq \beta . \) Prove
that the common ratio of the G.P. is \( \frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \)
Subject: Maths
Which of the following represents a linear polynomial?
A \( \cdot p(x)=3 x+4 \)
В \( \cdot p(x)=3 x^{3}+4 \)
C \( \cdot p(x)=4 x^{3}+3 \)
D \( \cdot p(x)=2 x^{2} \)
Subject: Physics
What will be the velocity of the electron when it just reaches the positive plate?
A \( \cdot \sqrt{\frac{2 V e d}{m}} \)
в. \( \sqrt{\frac{2 V e}{m}} \)
c. \( \sqrt{\frac{2 V e}{m d}} \)
D. \( \sqrt{\frac{V e d}{m}} \)