AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The hybridizations of \( N i(C O)_{4} \) and
\( \boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}^{2+}, \) respectively, are:
A \( \cdot s p^{3} \) and \( d^{3} s p^{2} \)
B. \( d s p^{2} \) and \( d^{2} s p^{3} \)
c. \( s p^{3} \) and \( d^{2} s p^{3} \)
D. \( d s p^{2} \) and \( s p^{3} d^{2} \)
Subject: Biology
Assertion
Environment signals such as light and gravity also affect phase or stage of growth
Reason
Gravity and light leads to differential auxin concentration which is
responsible for differential growth.
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
Which of the following statement is
wrong?
This question has multiple correct options
A. The stability of hydride increases from \( \mathrm{NH}_{3} \) to \( \mathrm{BiH}_{3} \) in group 15 of the periodic table.
B. Nitrogen cannot form \( \mathrm{d} \pi-\mathrm{p} \pi \) bond.
C. single \( \mathrm{N}-\mathrm{N} \) bond is weaker than the single P-P bond.
D. \( \mathrm{N}_{2} \mathrm{O}_{4} \) has two resonance structures.
Subject: Chemistry
The electronic configurations of three elements \( X, Y \) and \( Z \) are 2,\( 8 ; 2,8,7 ; \) and
2,8,2 respectively. Which of the following is correct?
A. \( X \) is a metal
B. \( Y \) is a metal
\( c \cdot Z \) is a non-metal
D. \( Y \) is a non-metal and \( Z \) is a metal
Subject: Physics
A non-uniform bar of weight \( W \) is
suspended at rest by two strings of
negligible weight as shown in fig. The angles made by the strings with the
vertical are \( 36.9^{\circ} \) and \( 53.1^{\circ} \)
respectively. The bar is \( 2 m \) long.
Calculate the distance d of the center of
gravity of the bar from its left end
Subject: Maths
The range of \( \mathbf{f}(\mathbf{x})=\frac{\sin \boldsymbol{\pi}\left[\mathbf{x}^{2}-\mathbf{1}\right]}{\mathbf{x}^{4}+\mathbf{1}} \) is
A. \( R \)
в. [-1,1]
c. \{0,1\}
D. \{0
Subject: Maths
Let \( \boldsymbol{A}=\mathbf{1 6}-\mathbf{4}+\mathbf{2}^{-\mathbf{4}}+\mathbf{3}^{-\mathbf{4}}+\mathbf{4}^{-\mathbf{4}}+\dots \)
and \( \boldsymbol{B}=\mathbf{1}^{-\mathbf{4}}+\mathbf{3}^{-\mathbf{4}}+\mathbf{5}^{-\mathbf{4}}+\mathbf{7}^{-\mathbf{4}}+\ldots \)
The ratio \( \frac{A}{B} \) in the lowest form is
A \( \cdot \frac{16}{15} \)
в. \( \frac{15}{14} \)
c. \( \frac{15}{16} \)
D. \( \frac{13}{12} \)
Subject: Physics
In a cyclotron, magnetic field of \( 3.5 W b / m^{2} \) is used to accelerate
protons.What should be the time interval in which the electric field
between the Dees be reversed?
(Mass of proton \( =1.67 \times 10^{-27} k g \)
charge on proton \( =\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C} \) ).
Subject: Maths
The inequality \( |z-4|<|z-2| \)
represents the following region.
\( \mathbf{A} \cdot \operatorname{Re}(z)>0 \)
B \( \cdot \operatorname{Re}(z)<0 \)
\( \mathbf{c} \cdot \operatorname{Re}(z)>2 \)
D. None of these
Subject: Physics
Mark out the correct statement(s)
This question has multiple correct options
\( A . \) in both fission and fusion processes, the mass of reactant nuclide is greater than the mass of product nuclide
B. in fission process, BE per nucleon of reactant nuclide is less than the binding energy per nucleon of product nuclide
C. in fusion process, BE per nucleon of reactant nuclide is less than the binding energy per nucleon of product nuclide
D. in fusion process, BE per nucleon of reactant nuclide is greater than the binding energy per nucloen of product nuclide
Subject: Maths
f \( a, b, c \epsilon R, \) find the number of real
roots of the equation given by \( \Delta=0 \)
where \( \boldsymbol{\Delta}=\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{c} & \boldsymbol{- b} \\ -\boldsymbol{c} & \boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{-} \boldsymbol{a} & \boldsymbol{x}\end{array}\right| \)
A . 0
B.
\( c \cdot 2 \)
D. 3
Subject: Maths
\( f_{f} A=\left[\begin{array}{lll}0 & 1 & 2 \\ 2 & 3 & 4 \\ 4 & 5 & 6\end{array}\right], B=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \)
Find \( 3 A-4 B \)
Subject: Biology
Match the terms to these definitions.
adipose tissue, blood, cardiac muscle, compact bone, connective tissue,
endocrine gland, epidermis, epithelial tissue, exocrine gland, fibroblast, homeostasis, lacuna, ligament, organ system, skeletal muscle, spongy bone, tendon tissue, nervous tissue, striated muscle.
A firm, white, fibrous inelastic cord
which attaches muscle to bone.
Subject: Physics
A particle of mass \( 1 \mathrm{kg} \) has a velocity of
\( 2 \mathrm{m} / \mathrm{s} . \) A constant force of \( 2 \mathrm{N} \) acts on
the particle for 1 s in a direction perpendicular to its initial velocity. Find the velocity and displacement of the particle at the end of 1 s.
Subject: Physics
A ball of mass \( 50 \mathrm{g} \) is dropped from a height \( h=10 \mathrm{m} . \) It rebounds losing 75 percent of its total mechanical energy. If it remains in contact with the ground
for \( \triangle \boldsymbol{t}=\mathbf{0 . 0 1} \) sec, find the impulse of
the impact force.
Subject: Maths
ox, oy are positive x-axis, positive \( y \) axis respectively where \( \boldsymbol{O}=(\mathbf{0}, \mathbf{0}, \mathbf{0}) \)
The \( d . c . s \) of the llne which bisects \( \angle x o y \)
are
\( \mathbf{A} \cdot 1,1,0 \)
B. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \)
c. \( \frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}} \)
D. 0,0,1
Subject: Chemistry
Assertion \( (A): \) Both \( H_{2} S_{2} O_{2} \) and
\( H_{2} S_{2} O_{3} \) contain \( S=S \) bonds
Reason (R): 'ic' acids are more acidic
than 'ous' acids
The correct answer is
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
Value of \( c \) of Lagranges mean theorem for
\[
\boldsymbol{f}(\boldsymbol{x})=\mathbf{2}+\boldsymbol{x}^{\mathbf{3}} \text { if } \boldsymbol{x} \leq \mathbf{1}
\]
\( =3 x \) if \( x>1 \) on [-1,2] is
\( A \cdot \pm \frac{\sqrt{5}}{3} \)
B. \( \pm \frac{\sqrt{3}}{2} \)
\( c \cdot \pm \frac{\sqrt{2}}{5} \)
\( D \cdot \pm \frac{3}{\sqrt{5}} \)
Subject: Chemistry
An organic compound \( \boldsymbol{A}\left(\boldsymbol{C}_{8} \boldsymbol{H}_{6}\right) \) gives brick red precipitate with ammoniacal
solution of \( C u_{2} C l_{2} . \) A on treatment with
ammoniacal solution of \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \boldsymbol{O}_{4} \) yields
\( B\left(C_{8} H_{8} O\right), \) B gives positive iodoform test \( \mathrm{B} \) can also be prepared by the reaction of benzene with acetic
anhydride in presence of \( A l C l_{3} \) identify \( A \) and \( B \)
Subject: Physics
The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of \( 10 \mathrm{m} / \mathrm{sec} \) is approximately:
A. \( 10^{-33} \mathrm{m} \)
.
В . \( 10^{-31} \mathrm{m} \)
c. \( 10^{-16} \mathrm{m} \)
.
D. \( 10^{-25} \mathrm{m} \)
Subject: Maths
A die is thrown. Let \( A \) be the event that
the number obtained is greater than 3
Let \( \mathrm{B} \) be the event that the number
obtained is less than 5. Then \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)
is
A . 1
B. \( \frac{2}{5} \)
c. \( \frac{3}{5} \)
D.
Subject: Physics
The emf of a cell is \( \epsilon \) and its internal
resistance is \( r . \) Its terminals are
connected to a resistance \( R \) The
potential difference between the terminals is \( 1.6 \mathrm{V} \) for \( \boldsymbol{R}=\mathbf{4} \Omega, \) and \( 1.8 \mathrm{V} \)
for \( \boldsymbol{R}=\mathbf{9} \Omega . \) Then
A. \( \epsilon=1 V, r=1 \Omega \)
В. \( \epsilon=2 V, r=1 \Omega \)
c. \( \epsilon=2 V, r=2 \Omega \)
D. \( \epsilon=2.5 V, r=0.5 \Omega \)
Subject: Maths
What is the angle between \( \vec{P} \times \vec{Q} \) and \( \vec{P}+\vec{Q} ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D. \( \frac{3 \pi}{2} \)
Subject: Chemistry
The order of reactivity of carboxylic acid
derivatives is:
A. Acid Chloride \( > \) Ester \( > \) Amide \( > \) Acid Anhydride
B. Acid Chloride \( > \) Acid Anhydride \( > \) Ester \( > \) Amide
C. Acid Chloride \( > \) Amide \( > \) Acid Anhydride \( > \) Ester
D. Acid Anhydride > Ester > Amide > Acid Chloride
Subject: Physics
Copper has one conduction electron per atom. Its density is \( 8.89 g / m^{3} \) and its
atomic mass is \( 63.54 \mathrm{g} / \mathrm{mol} \). If a copper wire of diameter \( 1.0 \mathrm{mm} \) carries a current
of 2.0 A. What is the drift speed of the electrons in the wire?
A \( \cdot 1.9 \times 10^{-4} \)
В. \( 2.9 \times 10^{-4} \)
\( \mathbf{c} \cdot 1.9 \times 10^{4} \)
D. \( 2.9 \times 10^{4} \)
Subject: Maths
The solution of \( \frac{d y}{d x}=|x| \) is :
A \( \cdot y=\frac{x|x|}{2}+c \)
В . \( y=\frac{|x|}{2}+c \)
C・ \( y=\frac{x^{2}}{2}+c \)
D・ \( y=\frac{x^{3}}{2}+c \)
Subject: Physics
A light ray travels at some angle (not head on) from water in a rectangular aquarium, through the glass side, and out into air. The indices if refraction for
water, glass, and air are \( 1.33, \) about 1.6 and \( 1.0, \) respectively.

Rank the material;s according to the angles of refraction made by the light ray with the normal in each, greatest
first.
A. air, water, glass.
B. air, glass, water.
C. water, air, glass.
D. water, glass, air
E. glass, water, air
Subject: Maths
A spherical ball of lead \( 5 \mathrm{cm} \) in diameter
is melted and recast into three
spherical balls. The diameters of two of these balls are \( 2 \mathrm{cm} \) and \( 2(14.5)^{1 / 3} \mathrm{cm} \) Find the diameter of the third ball.
A. \( 8 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .4 \mathrm{cm} \)
D. \( 1 \mathrm{cm} \)
Subject: Chemistry
Considering the elements \( F, C I, O \) and \( N \) the correct order of their chemical
reactivity in terms of oxidizing property is:
\( (a) F>C \mid>0>N \)
\( (b) F>0>C l>N \)
\( (c) C \mid>F>0>N \)
\( (d) O>F>N>C l \)
Subject: Chemistry
Assertion
\( \mathrm{CaCO}_{3} \) is prepared by passing carbon
dioxide gas through slaked lime.
Reason
Passing excess of \( C O_{2} \) through slaked lime leads to the formation of quick
lime.
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 \( f(x)+f\left(\frac{1}{1-x}\right)=x \) for all \( x \neq 0,1 \)
then
A \( \quad f(x)=\frac{1}{2}\left(x-1+\frac{1}{x}-\frac{1}{1-x}\right) \)
B. \( f(x)=\frac{1}{2}\left(1+x-\frac{1}{x}+\frac{1}{1-x}\right) \)
c. \( f(x)=\frac{1}{2}\left(1+x-\frac{1}{x}-\frac{1}{1-x}\right) \)
D \( f(x)=\frac{1}{2}\left(1-x+\frac{1}{x}-\frac{1}{1-x}\right) \)
Subject: Physics
In a meter bridge the length of the wire is \( 100 \mathrm{cm} . \) The point at which will the balance be obtained if the two
resistances are in the ratio 2: 3 is
A \( \cdot 1) \) 20cm
B. 2) 40cm
c. 3 ) \( 28.6 \mathrm{cm} \)
D. 4) 44.1cm
Subject: Chemistry
For the following electrochemical cell at
\( 298 K \)
\( \boldsymbol{P t}(s)\left|\boldsymbol{H}_{2}(\boldsymbol{g}, \mathbf{1} \boldsymbol{b a r})\right| \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}, \mathbf{1} \boldsymbol{M}) \| \boldsymbol{M}^{4+} \)
\( \boldsymbol{E}_{c e l l}=\mathbf{0 . 0 9 2 V} \) when \( \frac{\left[\boldsymbol{M}^{2+}(\boldsymbol{a} \boldsymbol{q})\right]}{\left[\boldsymbol{M}^{4+}(\boldsymbol{a q})\right]}=\mathbf{1 0}^{x} \)
Given \( : \boldsymbol{E}_{M^{4+} / M^{2+}}^{0}= \)
\( \mathbf{0 . 1 5 1} V ; \mathbf{2 . 3 0 3} \frac{\boldsymbol{R T}}{\boldsymbol{F}}=\mathbf{0 . 0 5 9} \boldsymbol{V} \)
The value of \( x \) is :
A . -2
B. -
\( c \cdot 1 \)
D.
Subject: Maths
State whether the statement is True or
False.
\( (\boldsymbol{m}+\boldsymbol{n})^{-1}\left(\boldsymbol{m}^{-1}+\boldsymbol{n}^{-1}\right)=(\boldsymbol{m} \boldsymbol{n})^{-1} \)
A. True
B. False
Subject: Maths
\[
\mathbf{f} \boldsymbol{a}_{\mathbf{1}} \boldsymbol{f}_{\mathbf{1}}(\boldsymbol{x})+\boldsymbol{a}_{\mathbf{2}} \boldsymbol{f}_{\mathbf{2}}(\boldsymbol{x})+\boldsymbol{a}_{\mathbf{3}} \boldsymbol{f}_{\mathbf{3}}(\boldsymbol{x})=\mathbf{0}
\]
where \( a_{1}, a_{2}, a_{3} \) are constants (not all
zero) and \( f_{1}, f_{2}, f_{3} \) are twice
differentiable functions.Then \( D= \)
\( \left|\begin{array}{ccc}\boldsymbol{f}_{1}(\boldsymbol{x}) & \boldsymbol{f}_{2}(\boldsymbol{x}) & \boldsymbol{f}_{3}(\boldsymbol{x}) \\ \boldsymbol{D} \boldsymbol{f}_{1}(\boldsymbol{x}) & \boldsymbol{D} \boldsymbol{f}_{2}(\boldsymbol{x}) & \boldsymbol{D} \boldsymbol{f}_{3}(\boldsymbol{x}) \\ \boldsymbol{D}^{2} \boldsymbol{f}_{1}(\boldsymbol{x}) & \boldsymbol{D}^{2} \boldsymbol{f}_{2}(\boldsymbol{x}) & \boldsymbol{D}^{2} \boldsymbol{f}_{3}(\boldsymbol{x})\end{array}\right| \) qual to \( D f_{1}(x)=\frac{d}{d x} f_{1} \)
Subject: Physics
sliding along its length on a horizontal
table whose top is partly smooth and
rest roughly with friction coefficient \( \mu . \) If
the rod after moving through the
smooth part enters the rough with
velocity \( \boldsymbol{v}_{\mathbf{0}} \)
(i) What will be the magnitude of the
friction force when its \( x \) length \( (<L) \)
lies in the rough part during sliding.
(ii) Determine the minimum velocity \( \boldsymbol{v}_{\mathbf{0}} \)
with which it must enter so that it lies
completely in a rough region before
coming to rest.
(iii) If the velocity is double the minimum velocity as calculated in part
(a) then what distance does its front
end \( A \) would have travelled in a rough region before rod comes to rest.
Subject: Maths
Solve the following pair of linear equations by the elimination method and the substitution method:
(i) \( x+y=5 \) and \( 2 x-3 y=4 \)
(ii) \( 3 x+4 y=10 \) and \( 2 x-2 y=2 \)
(iii) \( 3 x-5 y-4=0 \) and \( 9 x=2 y+7 \)
(iv) \( \frac{x}{2}+\frac{2 y}{3}=-1 \) and \( x-\frac{y}{3}=3 \)
Subject: Physics
A horizontal aluminium rod of diameter
\( 4.8 \mathrm{cm} \) projects \( 5.3 \mathrm{cm} \) from a wall. \( 1200 \mathrm{kg} \) object is suspended from the end of the rod. The shear modulus of
aluminium is \( 3.0 \times 10^{10} N / m^{2} \)
Neglecting the mass of the rod, find the
shearing stress on the rod.
A \( .6 .5 \times 10^{6} N m^{-2} \)
В. \( 9.5 \times 10^{6} \mathrm{N} \mathrm{m}^{-2} \)
c. \( 8.5 \times 10^{6} \mathrm{N} \mathrm{m}^{-2} \)
D. \( 7.5 \times 10^{6} \mathrm{N} \mathrm{m}^{-2} \)
Subject: Physics
Find the net flux through the cylinder.
\( \mathbf{A} \cdot-0.125 N m^{2} / C \)
B. \( -0.25 N m^{2} / C \)
\( \mathbf{C} \cdot 0.25 N m^{2} / C \)
D. \( 0.125 N m^{2} / C \)
Subject: Physics
The de Broglie wavelength of an electron
moving with a velocity \( 2.25 \times 10^{8} m s^{-1} \)
is equal to that of a photon. The ratio of the kinetic energy of the electron to that of the energy of photon is :
A \( \cdot \frac{3}{8} \)
B. 4
\( c \cdot \frac{1}{2} \)
D. \( 2-\sqrt{3} \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{A}(\mathbf{1}, \mathbf{3}), \boldsymbol{B}(\mathbf{0}, \mathbf{0}) \) and \( \boldsymbol{C}(\boldsymbol{k}, \boldsymbol{0}) \) be
vertices of a triangle \( A B C \) such that
area of \( \triangle A B C \) is \( 3 . \) Find the value of \( k \)
\( A \cdot \pm 2 \)
B. ±3
\( c .\pm 4 \)
D. ±1
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}-\{1,2,3\} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\mathbf{3} \) is
A. one-one only
B. onto only
c. bijective
D. neither one-one nor onto
Subject: Physics
A particle is performing oscillations with acceleration \( a=8 \pi^{2}-4 \pi^{2} x \)
where \( x \) is coordinate of the particle
w.r.t. the origin. The parameters are in
S.I. units. The particle is at rest at \( x=2 \) at \( t=0 . \) Find coordinates of the particle
w.r.t origin at any time.
A \( .4-2 \cos 2 \pi t \)
B. \( 2-2 \cos 2 \pi t \)
c. \( 4-4 \cos 2 \pi t \)
D. \( 2+4 \sin 2 \pi t \)
Subject: Physics
Two small metallic spheres each of
mass \( \mathrm{m} \) are suspended together with
strings of length \( l \) and placed together
When a quantum of charge \( \boldsymbol{q} \) is
transferred to each the strings make an
angle of \( 90^{\circ} \) with each other. The value
of \( q \) is
A \( \cdot l /\left(_{0} m g\right) \)
в. \( l /\left(16_{o} m g\right) \)
\( \mathbf{c} \cdot l /\left(2_{o} m g\right) \)
D. none of these
Subject: Physics
At what speed will the velocity head of
stream of water be equal to \( 40 \mathrm{cm} ? \)
\( A \cdot 280 \mathrm{ms}^{-1} \)
в. \( 2.80 \mathrm{cm} / \mathrm{s} \)
c. \( 280 \mathrm{cms}^{-1} \)
D. \( 0.280 \mathrm{m} / \mathrm{s} \)
Subject: Physics
A metal surface is illuminated by light
of two different wavelengths \( 248 n m \)
and \( 310 n m . \) The maximum speeds of
the photoelectrons corresponding to
these wavelengths are \( u_{1} \) and \( u_{2} \)
respectively. If the ratio \( u_{1}: u_{2}=2: 1 \)
and \( h c=1240 e V n m, \) the work
function of the metal is nearly:
\( \mathbf{A} \cdot 3.7 \mathrm{eV} \)
B. \( 3.2 e V \)
c. \( 2.8 e V \)
D. \( 2.5 e V \)
Subject: Physics
A container contains water up to a
height of \( 20 \mathrm{cm} \) and there is a point
source at the centre of the bottom of the
container. A rubber ring of radius \( r \) floats centrally on the water. The ceiling of the room is \( 2.0 m \) above the water
surface.
(a) Find the radius of the
shadow of the ring formed on the ceiling if \( r=15 \mathrm{cm} \)
(b) Find the maximum
value \( r \) for which the shadow of the ring
is formed on the ceiling. Refrective index of water \( =\mathbf{4} / \mathbf{3} \)
Subject: Maths
The probability distribution of a random variable \( X \) is given below:
\[
\begin{array}{lllll}
\mathrm{x}: & 0 & 1 & 2 & 3 \\
\mathrm{P}(\mathrm{x}): & \mathrm{k} & \frac{k}{2} & \frac{k}{4} & \frac{k}{8}
\end{array}
\]
Determine the value of \( X, \) if \( k=\frac{8}{X} \)
Subject: Physics
Two elastic wire \( A \& B \) having length
\( \ell_{A}=2 m \) and \( \ell_{B}=1.5 m \) and the ratio
of young's modules \( Y_{A}: Y_{B} \) is \( 7: 4 . \) If
radius of wire \( B\left(r_{B}\right) \) is \( 2 m m \) then
choose the correct value of radius of
wire \( A . \) Given that due to application of
the same force charge in length in both \( A \& B \) is same
A. \( 1.7 m m \)
в. \( 1.9 m m \)
\( c .2 .7 m m \)
D. \( 2 m m \)
Subject: Maths
A chord of a circle of radius \( 6 \mathrm{cm} \)
subtends a right angle at centre. The area of the minor segment \( (\pi=3.14) \)
is
A \( \cdot 9.82 \mathrm{cm}^{2} \)
B. \( 10.14 \mathrm{cm}^{2} \)
c. \( 10.26 \mathrm{cm}^{2} \)
D. \( 12.35 \mathrm{cm}^{2} \)
Subject: Physics
An unpolarized beam of light is incidents on a group of four polarizing sheets, which are arranged in such a way, that of the characteristic direction
of each polarizing sheet makes an
angle of \( 30^{0} \) with that of the preceding
sheet. The percentage of incident light transmitted by the first polarizered will be :
\( \mathbf{A} \cdot 100 \% \)
B. \( 50 \% \)
c. \( 25 \% \)
D. \( 12.5 \% \)
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{w} & \boldsymbol{w}^{2} \\ \boldsymbol{w} & \boldsymbol{w}^{2} & \mathbf{1} \\ \boldsymbol{w}^{2} & \boldsymbol{w} & \mathbf{1}\end{array}\right| \) Where \( \mathbf{w} \) is a complex
cube root of unity
Subject: Physics
Q Type your question
Nư.
between the plates. The battery is then
disconnected and a dielectric slab of
dielectric constant \( K \) is placed in between the plates of the capacitor as
shown.

Now, answer the following questions based on above information. The
electric field in the gaps between the
plates and the dielectric slab will is :
A \( \cdot \frac{\varepsilon A V}{d} \)
в. \( \frac{V}{d} \)
\( c \cdot \frac{K V}{d} \)
D. \( \frac{V}{d-t} \)
Subject: Maths
Assertion
\( f(x)=\frac{1}{x-7} \) is decreasing \( \forall x \epsilon R \)
\{7\}
Reason
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})<\mathbf{0} \forall \boldsymbol{x} \neq \mathbf{7} \)
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
An equilateral triangle and a square have equal perimeters. If side of the triangle is \( 9.6 \mathrm{cm} ; \) what is the length of
the side of the square?
\( \mathbf{A} \cdot 6.2 \mathrm{cm} \)
B. \( 3.2 \mathrm{cm} \)
\( c .5 .2 \mathrm{cm} \)
D. \( 7.2 \mathrm{cm} \)
Subject: Maths
A value of \( x \) satisfying the equation
\( \sin \left[\cot ^{-1}(1+x)\right]=\cos \left[\tan ^{-1} x\right], \) is.
A. \( -\frac{1}{2} \)
B. \( \frac{1}{2} \)
c. -1
\( D \)
Subject: Physics
A : The phase difference between any
two points on a wave front is zero
\( \mathrm{R}: \) From the source light, reaches every
point on the wave front in the same
time.
\( A . \) Both \( A \) and \( R \) are true, and \( R \) is correct explanation of \( A \)
B. Both A and R are true, and R is not correct explanation of \( A \)
C. A is true but R is false
D. A is false but R is true
Subject: Maths
The minimum \& maximum value of \( f(x)=\sin (\cos x)+\cos (\sin x) \forall-\frac{\pi}{2} \leq \)
\( x \leq \frac{\pi}{2} \) are respective
A. \( \cos 1 \) and \( 1+\sin 1 \)
1
B. \( \sin 1 \) and \( 1+\cos 1 \)
c. \( \cos 1 \) and \( \cos \left(\frac{1}{\sqrt{2}}\right)+\sin \left(\frac{1}{\sqrt{2}}\right) \)
D. None of these
Subject: Maths
If \( f(x)=x^{2}-6 x+8 \) and there exists
a point \( c \) in the interval [2,4] such that
\( \boldsymbol{f}^{\prime}(\boldsymbol{c})=\mathbf{0}, \) then what is the value of \( \boldsymbol{c} ? \)
A . 2.5
B. 2.8
\( c \cdot 3 \)
D. 3.5
Subject: Physics
A lens of power \( 6 D \) is put in contact
with a lens of power -4 D. The
combination will behave like a:
A. Divergent lens of focal length \( 25 \mathrm{cm} \)
B. Convergent lens of focal length 50 \( c m \)
c. Divergent lens of focal length \( 20 \mathrm{cm} \)
D. Convergent lens of focal length \( 100 \mathrm{cm} \)
Subject: Chemistry
Information about four hydrocarbons is
Shown.
number of \( \quad \) reaction carbon \( \quad \) with hydrocarbon atoms in the \( \quad \) water molecules
'D reaction
\( 2 \quad \) no reaction
decolourises 3
4 decolourises
\( z \)
it
Which statement is correct?
A. Hydrocarbon W has the formula \( C H_{4} \) and can be polymerised
B. Hydrocarbon x has the formula \( C_{2} H_{4} \) and can be polymerised
C. Hydrocarbon Y has the formula \( C_{3} H_{6} \) and can be polymerised
D. Hydrocarbon Y has the formula \( C_{4} H_{10} \) and can be polymerised
Subject: Biology
Which one of the following is the correct pathway for propagation of cardiac impulse?
A. SA node \( \rightarrow \) Bundle of his \( \rightarrow \) Purkinje fibres
B. AV node \( \rightarrow \) Bundle of his \( \rightarrow \) SA node \( \rightarrow \) Purkinje fibres
c. SA node \( \rightarrow \) Purkinje fibres \( \rightarrow \) AV node \( \rightarrow \) Bundle of his
D. Purkinje fibres \( \rightarrow \) AV node \( \rightarrow \) SA node \( \rightarrow \) Bundle of his
Subject: Physics
A \( 5 k g \) rod of square cross section 5 cm
on a side and 1 m long is pulled along a
smooth horizontal surface by a force
applied at one end. The rod has a
constant acceleration of \( 2 m / s^{2} \) Determine the elongation in the rod.
(Young's modulus of the material of the
\( \left.\operatorname{rod} \text { is } 5 \times 10^{3} N / m^{9}\right) \)
A. Zero, as for elongation to be there, equal and opposite forces must act on the rod
B. Non-zero but cannot be determine from the given situation
\( \mathbf{c} .4 \mu m \)
D. \( 16 \mu m \)
Subject: Physics
A stone projected vertically up from the ground reaches a height \( y \) in its path at
\( t_{1} \) seconds and after further \( t_{2} \) seconds
reaches the ground. The height \( y \) is
equal to
A \( \cdot \frac{1}{2} g\left(t_{1}+t_{2}\right) \)
B \( \cdot \frac{1}{2} g\left(t_{1}+t_{2}\right)^{2} \)
\( \mathbf{c} \cdot \frac{1}{2} g t_{1} t_{2} \)
D. \( g t_{1} t_{2} \)