AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Which reagent can be used to convert
ethanol to diethyl ether?
A. \( A l_{2} O_{3} \) at \( 250^{\circ} C \)
B. conc. \( H_{2} S O_{4} \) at \( 170^{\circ} C \)
c. conc. \( H_{2} S O_{4} \) at \( 130^{0}-140^{0} C \)
D. \( A l_{2} O_{3} \) at \( 350^{\circ} C \)
Subject: Physics
A conductor with a cavity is charged positively and its surface charge density is \( \sigma . \) If \( E \) and \( V \) represent the electric field and potential, then inside the cavity:
\( \mathbf{A} \cdot \) and \( V=0 \)
B. \( E=0 \) and \( V=0 \)
c. \( E=0 \) and \( \sigma= \) constant
D. \( V=0 \) and \( \sigma= \) constant
E . \( E=0 \) and \( V= \) constant
Subject: Chemistry
Assertion
Atomic size decreases in a period due
to increase of atomic number.
Reason
The nuclear charge is increasing and size of valence shell remains same as
we move from left to right. Hence, in any
period, the atomic size of the element decreases from left to right.
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 straight conductor of uniform cross-
section carries a current, \( I \). If \( ^{\prime} s^{\prime} \) is the
specific charge of an electron, the momentum of all the free electrons per unit length of the conductor, due to their drift velocity only, is
A . Is
в. \( \sqrt{\frac{I}{s}} \)
c. \( \frac{1}{s} \)
\( \left(\frac{I}{s}\right)^{2} \)
Subject: Maths
If \( \tan x+\tan \left(x+\frac{\pi}{3}\right)+ \)
\( \tan \left(x+\frac{2 \pi}{3}\right)=3, \) then
A \( \cdot \tan x=1 \)
B. \( \tan 2 x=1 \)
\( \mathbf{c} \cdot \tan 3 x=1 \)
D. None of these
Subject: Chemistry
Which of the following equations corresponds to the definition of
enthalpy of formation at \( 298 K ? \)
A . \( C(\text {graphite})+2 H_{2}(g)+1 / 2 O_{2}(l) \rightarrow C H_{3} O H(g) \)
B. \( C(\text { diamond })+2 H_{2}(g)+1 / 2 O_{2}(g) \rightarrow C H_{3} O H(l) \)
c. \( 2 C(\text { graphite })+4 H_{2}(g)+O_{2}(g) \quad \rightarrow 2 C H_{3} O H(l) \)
D. \( C(\text {graphite})+2 H_{2}(g)+1 / 2 O_{2}(g) \rightarrow C H_{3} O H(l) \)
Subject: Physics
A body executing S.H.M has a maximum
acceleration equal to \( 48 \mathrm{m} / \mathrm{sec}^{2} \) and maximum velocity equal to \( 12 \mathrm{m} / \mathrm{sec} \)
The amplitude of S.H.M is?
\( A \cdot 3 m \)
B. 3/32 m
c. \( 1024 / 9 \mathrm{m} \)
D. \( 64 / 9 \mathrm{m} \)
Subject: Chemistry
\( E^{o} \) values for the half cell reactions are
given:
\( \boldsymbol{C u}^{2+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}^{+} ; \boldsymbol{E}^{o}=\mathbf{0 . 1 5 V} \)
\( \boldsymbol{C u}^{2+}+\mathbf{2} e^{-} \rightarrow \boldsymbol{C u} ; \boldsymbol{E}^{o}=\mathbf{0 . 3 4} \mathbf{v} \)
What will be the \( E^{o} \) of the half-cell:
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} ? \)
A . \( +0.49 v \)
в. \( +0.19 v \)
\( c .+0.53 v \)
D. \( +0.30 v \)
Subject: Chemistry
I ne taple pelow laentıries triree energy
terms that must be considered in
discussing the energy involved in forming aqueous solutions of solid ionic electrolytes.
Term \( \quad \) Symbol
Lattice Energy of Solute
\[
\triangle H_{l a t t i c e}
\]
Enthalpy of Solution
\[
\triangle H_{\text {solution}}
\]
Enthalpy of Hydration
\[
\triangle H_{h y d r a t i o n}
\]
Which of the following equations
CORRECTLY expresses the relationship between the lattice energy of the solid
solute, the enthalpy of solution, and the
enthalpy of hydration of a solution of an electrolyte in water?
A \( . \triangle H_{\text {solution}}=\triangle H_{\text {lattice}}+\triangle H_{\text {hydration}} \)
B. \( \triangle H_{\text {hydration}}=\triangle H_{\text {solution}}+\triangle H_{\text {latice}} \)
C \( . \triangle H_{\text {lattice}}=\Delta H_{\text {solution}}+\triangle H_{\text {hydration}} \)
D. \( \triangle H_{\text {solution}}=\triangle H_{\text {hydration}}-\triangle H_{\text {lattice}} \)
Subject: Chemistry
Statement 1: The molecule \( S O_{2} \) has a net dipole. Statement 2: Oxygen has the higher electronegativity than sulfur.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of statement 1
B. Both Statement 1 and Statement 2 are correct, but Statement 2 is NOT the correct explanation of Statement 1.
c. Statement 1 is correct, but Statement 2 is not correct
D. Statement 1 is not correct, but Statement 2 is correct
Subject: Chemistry
1 mole of ice at \( 0^{\circ} \mathrm{C} \) and \( 4.6 \mathrm{mm} \) Hg
pressure is converted to water vapour at
a constant temperature and pressure Find \( \Delta H \) and \( \Delta E \) if the latent heat of
fusion of ice is 80 Cal/gm and latent heat of vaporisation of liquid water at
\( 0^{o} C \) is 596 Cal per gram and the volume of ice in comparison to that of water
vapour is neglected.
Subject: Chemistry
The concentration of a solution is
\( \mathbf{1 0}^{-4} \boldsymbol{M} \) for \( \boldsymbol{C l}^{-}, \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{M} \) for \( \boldsymbol{B r}^{-} \) and
\( 10^{-3} M \) for \( I^{-} . A g N O_{3}(s) \) is added slowly to the solution. The minimum
concentration of \( A g^{+} \) required to start precipitation of all three ions is:
\( \left[\text { Given, } \boldsymbol{K}_{s p(A g C l)}=\mathbf{1 0}^{-10}, \boldsymbol{K}_{s p(A g B r)}=\right. \)
\( \mathbf{1 0}^{-\mathbf{1 3}}, \mathbf{K}_{s p(A g I)}=\mathbf{1 0}^{-\mathbf{1 7}} \mathbf{]} \)
A \( \cdot 10^{-9} \)
B. \( 10^{-6} \)
\( \mathbf{c} \cdot 10^{-8} \)
D. \( 10^{-10} \)
Subject: Maths
The function
\( \boldsymbol{f}(\boldsymbol{x})\left\{\begin{array}{l}\frac{\sin \sqrt[3]{\boldsymbol{x}} \log (1+\boldsymbol{3} \boldsymbol{x})}{\left(\tan ^{-1} \sqrt{\boldsymbol{x}}\right)^{2}\left(\boldsymbol{e}^{\boldsymbol{5}} \sqrt[3]{\boldsymbol{x}}-\mathbf{1}\right)} \quad, \boldsymbol{x} \neq \mathbf{0} \\ \boldsymbol{a}, \quad \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
is continuous at \( \boldsymbol{x}=\mathbf{0}, \) if
\( \mathbf{A} \cdot a=0 \)
B. \( a=\frac{5}{3} \)
\( \mathbf{c} \cdot a=2 \)
D. \( a=\frac{3}{5} \)
Subject: Maths
If \( \boldsymbol{y}=\boldsymbol{e}^{2 x}(\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b}), \) show that \( \boldsymbol{y}_{2} \)
\( \mathbf{4} \boldsymbol{y}_{1}+\mathbf{4} \boldsymbol{y}=\mathbf{0} \)
Subject: Physics
A sphere of mass \( M \) and radius \( r \) slips
on a rough horizontal plane. At some
instant it has translation velocity \( \boldsymbol{v}_{0} \) and rotational velocity about the centre
\( v_{0} / 2 r . \) The translation velocity after the
sphere starts pure rolling
A \( \cdot 6 v_{0} / 7 \) in forward direction
B. \( 6 v_{0} / 7 \) in backward direction
\( c \cdot 7 v_{0} / 6 \) in forward direction
D. \( 7 v_{0} / 6 \) in backward direction
Subject: Chemistry
Which of the following options about the
oxidizing property of \( K M n O_{4} \) in acidic
medium is incorrect?
This question has multiple correct options
A \( \cdot H_{2} S \) can be oxidised to \( S O_{4}^{2} \)
B. \( H_{2} S \) can be oxidised to \( S \)
C. \( S O_{3}^{2-} \) can be oxidised to \( S O_{4}^{2} \)
D. \( C_{2} O_{4}^{2-} \) can be oxidised to \( C O_{3}^{2} \)
Subject: Maths
\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{- 1} \\ -\mathbf{1} & \mathbf{1} & \mathbf{2} \\ \mathbf{2} & \mathbf{- 1} & \mathbf{1}\end{array}\right], \) then
\( \operatorname{det}(\operatorname{adj}(\operatorname{adj} A)) \) is equal to
A \( \cdot 14^{4} \)
B. \( 14^{\text {? }} \)
\( c \cdot 14^{2} \)
D. 14
Subject: Maths
\( \mathbf{A} \mathbf{x}=\mathbf{0}, \mathbf{f}(\mathbf{x})=\cos \mathbf{x}-1+\frac{\mathbf{x}^{2}}{\mathbf{2}}-\frac{\mathbf{x}^{\mathbf{3}}}{\mathbf{6}} \)
A. Has a minimum
B. Has a maximum
c. Does not have an extremum
D. Is not defined
Subject: Chemistry
Pick out the correct statements
This question has multiple correct options
A. The ratio of vapour pressure over solution phase on mixing two immiscible liquids is equal to ratio of their moles in vapour phase
B. The ratio of vapour pressure over solution phase on mixing two miscible liquids is equal to ratio of their moles in liquid phase
C. The ratio of vapour pressure over solution phase on mixing two miscible liquids is equal to ratio of the product of their vapour pressure and their moles fraction in a liquid phase
D. The ratio of vapour pressure over solution phase on mixing two miscible liquids is equal to ratio of the product of their vapour pressure and their mole fraction in vapour phase
Subject: Chemistry
The IUPAC name of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2} \boldsymbol{B r} \) is
A. 1-bromopentane
B. 1-bromo-3-methylbutane
c. 2-methyl-4-bromobutane
D. 2-methyl-3-bromopropane
Subject: Chemistry
\( K F \) combines with \( H F \) to form \( K H F_{2} \)
The compound contains the species:
A \( \cdot K^{+}, F^{-} \) and \( H^{+} \)
B. \( K^{+}, F^{-} \) and \( H F \)
c. \( K^{+} \) and \( \left[H F_{2}\right]^{-} \)
D. \( [K H F]^{+} \) and \( F_{2} \)
Subject: Chemistry
A chemical A is used for the preparation of washing soda to recover ammonia.
When \( C O_{2} \) is bubbled through an aqueous solution of \( A, \) the solution turns milky. It is used in white washing due to disinfectant nature. What is the
chemical formula of \( A \) ?
A \( \cdot C a\left(H C O_{3}\right)_{2} \)
в. \( C a O O \)
\( \mathbf{c} \cdot C a(O H)_{2} \)
D. \( C a C O_{3} \)
Subject: Maths
Assertion
Let \( \bar{a}, \bar{b}, \bar{r} \) be the vectors such that \( \bar{r}+ \) \( \overline{\boldsymbol{r}} \times \overline{\boldsymbol{a}}=\overline{\boldsymbol{b}} \operatorname{then}|\overline{\boldsymbol{r}}|^{2}=\frac{(\overline{\boldsymbol{a}} \cdot \overline{\boldsymbol{b}})^{2}+|\overline{\boldsymbol{b}}|^{2}}{\mathbf{1}+|\overline{\boldsymbol{a}}|^{2}} \)
Reason
\( \overline{\boldsymbol{r}}=\frac{(\overline{\boldsymbol{a}} \cdot \overline{\boldsymbol{b}}) \overline{\boldsymbol{a}}+\overline{\boldsymbol{b}}+\overline{\boldsymbol{a}} \times \overline{\boldsymbol{b}}}{\mathbf{1}+|\overline{\boldsymbol{a}}|^{2}} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the correct (proper) explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
Q Type your question
One of the chief uses of sodium
carbonate has been in the conversion of
\( \operatorname{Ca}(O H)_{2}(s) \) to concentrated aqueous solution of NaOH which in turn was
used in the manufacture of soap.
\( \boldsymbol{C a}(\boldsymbol{O H})_{2}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a}^{+}(\boldsymbol{a q})+ \)
\( \boldsymbol{C O}_{3}^{2-}(\boldsymbol{a q}) \rightleftharpoons \boldsymbol{C a C O}_{3}(\boldsymbol{s})+ \)
\( \mathbf{2} N \boldsymbol{a}^{+}(\boldsymbol{a} \boldsymbol{q})+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
In \( 1775, \) in order to gain independence from the importation of natural
\( N a_{2} C O_{3}, \) the French government
offered a prize to anyone who could
devise a process to prepare \( N a_{2} C O_{3} \)
from NaCl

A more economical process but based
on the same principle was given by :
A. Solvay
B. Leblanc
c. williamson
D. Haber
Subject: Physics
An L-C-R circuit contains \( \boldsymbol{R}=\mathbf{5 0 \Omega} \)
\( \boldsymbol{L}=\mathbf{1} \boldsymbol{m} \boldsymbol{H} \) and \( \boldsymbol{C}=\mathbf{0 . 1} \boldsymbol{\mu} \boldsymbol{F} . \) The
impedence of the circuit will be minimum for a frequency of
\( ^{\mathbf{A}} \cdot \frac{10^{5}}{2 \pi} H z \)
в. \( \frac{10^{6}}{2 \pi} H z \)
c. \( 2 \pi \times 10^{5} H z \)
D. \( 2 \pi \times 10^{6} H z \)
Subject: Chemistry
Calculate \( K_{C} \) for the reaction:
\( 2 H_{2}(g)+S_{2}(g) \rightleftharpoons 2 H_{2} S(g) \) if \( 1.58 \mathrm{mol} \)
\( \boldsymbol{H}_{2} \boldsymbol{S}, 1.27 \mathrm{mol} \boldsymbol{H}_{2}, \) and \( \mathbf{2 . 7 8} \times \mathbf{1 0}^{-\mathbf{6}} \) mol
of \( S_{2} \) are in equilibrium in a flask of capacity \( 180 \mathrm{L} \) at \( 750 \mathrm{C} \)
A \( \cdot K_{C}=124 \times 10^{8} L \) mol \( ^{-1} \)
B. \( K_{C}=1 \times 10^{8} L \) mol\( ^{-1} \)
c. \( K_{C}=1 \times 10^{-8} L \mathrm{mol}^{-1} \)
D. \( K_{C}=1 \times 10^{7} L \mathrm{mol}^{-1} \)
Subject: Physics
whose hemispherical base is of
diameter \( 0.20 \mathrm{m} . \) The height of the flask
is \( 0.25 \mathrm{m} \). The flask is filled to the brim
with 2.5 litres \( \left(1 \text { litre }=10^{-3} m^{3}\right) \) of
water and sealed with a glass lid.
What is the approximate magnitude of
the total vertical force exerted by the
water on the curved surface of the
flask? (Take the acceleration due to
gravity, \( g, \) to be \( 10 m s^{-2} \) ).
\( A \cdot O N \)
B. 78.5
c. 53.5 N
D. 25.0
Subject: Maths
Evaluate : \( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\mathbf{3} \sin ^{2} \boldsymbol{x}+\sin \boldsymbol{x}} \cos \boldsymbol{x}+\mathbf{1} \)
A \( \cdot \frac{2}{\sqrt{15}} \tan ^{-1}\left(\frac{2(\cot x-2)}{\sqrt{15}}\right) \)
в. \( \frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{3 \tan x-1}{\sqrt{15}}\right)+c \)
c. \( \frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{3 \tan x+1}{\sqrt{15}}\right)+c \)
D. \( \frac{2}{\sqrt{15}} \tan ^{-1}\left(\frac{2(\cot x-2)}{\sqrt{15}}\right) \)
Subject: Maths
Solve \( \int_{0}^{h} x(h-x) d x \)
\( ^{A} \cdot_{I}=\frac{h^{3}}{3} \)
в. \( _{I=} \frac{h^{3}}{6} \)
\( ^{\mathrm{C}} \cdot_{I}=-\frac{h^{3}}{6} \)
D. None of these
Subject: Physics
A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function
of time t. Which of the following statements is true. Assume that the
particle started at \( t=0 \) at its mean position
A. P.E. is maximum when \( t=0 \)
B. T.E. is zero when \( t=0 \)
c. K.E. is maximum when \( t=0 \)
D. K.E. is minimum when t =
Subject: Chemistry
In certain polar solvents \( \boldsymbol{P} \boldsymbol{C l}_{5} \)
undergoes an ionisation reaction in
which \( C l^{-} \) ion leaves one \( P C l_{5} \)
molecule and attaches itself to another
\( 2 P C l_{5} \rightleftharpoons P C l_{4}^{+}+P C l_{6}^{-} \)
What are the changes in the geometrical shapes that occur in this ionisation?
A. Trigonal Bipyramidal to tetrahedral and octahedral
B. Trigonal Bipyramidal to pentagonal planar and square planar
c. Pentagonal planar to tetrahedral and octahedral
D. None of these
Subject: Physics
Choose the wrong statements from the following.

Two spheres made of the same material have the same diameter. One sphere is
hollow and the other is solid. If they are
heated through the same range of
temperature, Then:
This question has multiple correct options
A. Both spheres will expand equally.
B. Hollow sphere will expand more than solid one
c. solid sphere will expand more than hollow one
D. Solid sphere will expand three times that of hollow sphere
Subject: Chemistry
When the gases; sulphur dioxide and hydrogen sulphide mix in the presence
of water, the reaction \( S O_{2}+2 H_{2} S \rightarrow \)
\( 2 H_{2} O+3 S \) occurs
Here hydrogen sulphide is acting as:
A. an oxidizing agent
B. a reducing agent
c. a dehydrating agent
D. a catalyst
Subject: Chemistry
A student was given four unknown colourless samples labelled \( A, B, C \) and D and asked to test their pH using pH paper. He observed that the colour of pH paper turned to light green, dark red, light orange and dark blue with samples \( A, B, C \) and \( D \) respectively. the correct sequence of increasing order of
the pH value for samples is -
\( A \cdot A<B<C<D \)
B. \( A<D<C<B \)
\( c \cdot c<B<A<D \)
\( D \cdot B<C<A<D \)
Subject: Biology
Which among the following is correctly
categorized?
A. Troponin and Myosin \( \rightarrow \) Complex proteins in striated muscles
B. Calcitonin and Thymosin \( \rightarrow \) Thyroid hormones
C. Pepsin and Prolactin \( \rightarrow \) Digestive enzymes secreted in stomach
D. Secretin and Rhodopsin \( \rightarrow \) Polypeptide hormones
Subject: Physics
A convex lens of focal length \( 6.25 \mathrm{cm} \) is used as a simple microscope. To obtain maximum magnification, the object
distance should be
A \( .4 .25 \mathrm{cm} \)
в. \( 4.50 \mathrm{cm} \)
c. \( 5.00 \mathrm{cm} \)
D. \( 5.25 \mathrm{cm} \)
Subject: Maths
Draw a circle of radius \( 6 \mathrm{cm} \). Take an
external point \( \boldsymbol{P} \) at a distance of \( \mathbf{1 0} \boldsymbol{c m} \) from centre and construct tangents to
the circle from \( P . \) The sum of the
lengths of the tangent segments (in \( c m \)
is:
Subject: Maths
An integrating factor of the differential
equation \( x d y-y d x+x^{2} e^{x} d x=0 \) is
A \( \cdot \frac{1}{x} \)
B. \( \log \sqrt{1+x^{2}} \)
c. \( \sqrt{1+x^{2}} \)
D.
E \( \frac{1}{1+x^{2}} \)
Subject: Physics
In the given circuit diagram the ratio of
potential difference across 3 ohm and 4
ohm resistance is \( \frac{3}{4} . \) The unknown
resistance \( \boldsymbol{R} \) is:-
A. 8.0 ohm
B. 2.0 ohm
\( c .4 .5 \) ohm
D. 7.0 ohm
Subject: Chemistry
A chemical reaction was carried out at
\( 300 \mathrm{K} \) and \( 280 \mathrm{K} \). The rate constants
were found to be \( K_{1} \) and \( K_{2} \) at \( 300 \mathrm{K} \)
and \( 280 \mathrm{K} \) respectively. Then which of the following is true?
A. \( K_{1}=4 K_{1} \)
B . \( K_{2}=2 K_{1} \)
c. \( K_{2}=0.25 K_{1} \)
D. \( K_{2}=0.5 K_{1} \)
Subject: Physics
A particle having a charge \( 10 \mathrm{mC} \) is held fixed on a horizontal surface. A block of
mass 80 g and having charge stays in equilibrium on the surface at a distance of \( 3 \mathrm{cm} \) from the first charge. The coefficient of friction between the
surface and the block is \( \mu=0.5 . \) Find
the range within which the charge on the block may lie
A. \( -4 \times 10^{-12} \mathrm{C} \) to \( 4 \times 10^{-12} \mathrm{C} \)
B. \( -2 C \) to \( 2 \times 10^{2} C \)
\( \mathbf{c} .-4 \times 10^{-19} \mathrm{C} \) to \( 4 \times 10^{-19} \mathrm{C} \)
D. \( -2 \times 10^{-19} \mathrm{C} \) to \( 2 \times 10^{-19} \mathrm{C} \)
Subject: Physics
A single conservative force \( F(x) \) acts on a \( 1.0-k g \) particle that moves along the
x-axis. The potential energy \( U(x) \) is
\( \operatorname{given} \operatorname{by} U(x)=20+(x-2)^{2} \) where \( x \)
is in meters. At \( \boldsymbol{x}=\mathbf{5 . 0} \mathrm{m}, \) the particle
has a kinetic energy of 20 J.What is the
mechanical energy of the system?
A . \( 35 J \)
B. \( 64 J \)
c. \( 86 J \)
D. \( 49 J \)
Subject: Physics
Identify the gas filled in the container \( A \)
and B:
A \( . N_{2}, N e \)
в. \( \mathrm{He}, \mathrm{H}_{2} \)
\( \mathrm{c} \cdot O_{2}, A r \)
\( \mathrm{D} \cdot A r, O_{2} \)
Subject: Maths
A sphere of radius \( 3 \mathrm{cm} \) is dropped into a cylindrical vessel of radius \( 4 \mathrm{cm} \). If the sphere is submerged completely, then the height (in cm) to which the water
rises, is
A. \( 2.35 \mathrm{cm} \)
B . \( 2.30 \mathrm{cm} \)
c. \( 2.25 \mathrm{cm} \)
D. \( 2.15 \mathrm{cm} \)
Subject: Physics
The magnetic field at point \( C \) as shown in
the figure is:
\( A \)
\[
\frac{\mu_{0} M_{0}}{2 \pi r_{0}^{3}}
\]
B. \( \frac{\sqrt{2} \mu_{0} M_{0}}{2 \pi r_{0}^{3}} \)
C. zero
D. \( \frac{\sqrt{2} \mu_{0} M_{0}}{4 \pi r_{0}^{3}} \)
Subject: Chemistry
fin the mixed carbonyl, the other ligand is also pi acceptor, it would compete
with the ligand CO for gaining the metal
\( \boldsymbol{d}_{\pi} \) electron charge. The higher is the extent of back donation in \( \mathrm{CO} \), the lesser
will be the stretching vibration
frequency for \( C \) - 0 bond. If \( P F_{3} \) is better \( \pi \) -acceptor than \( \mathrm{CO} \), then answer the following.

Select the correct order of stretching vibration frequency \( C \) - 0 bond in the following molecules :
A \( \cdot\left[N i(C O)_{4}\right]>\left[N i\left(P F_{3}\right)(C O)_{3}\right] \)
B . \( \left[N i(C O)_{4}\right]<\left[N i(C O)_{3}\left(P F_{3}\right)\right] \)
c. \( \left[N i(C O)_{4}\right]=\left[N i\left(P F_{3}\right)(C O)_{3}\right. \)
D. can not predicted
Subject: Chemistry
Arrange the elements in increasing order of atomic radius \( \mathrm{Na}, \mathrm{Rb}, \mathrm{K}, \mathrm{Mg} \)
A. \( \mathrm{Na}<\mathrm{K}<\mathrm{Mg}<\mathrm{Rb} \)
B. \( K<N a<M g<R b \)
\( \mathrm{c} \cdot \mathrm{Mg}<\mathrm{Na}<\mathrm{K}<\mathrm{Rb} \)
D. \( R b<K<M g<N a \)
Subject: Biology
Match column i with column-ii and
select the correct answer.
\( \begin{array}{lll} & \text { Coloumn-1 } & \text { Column-2 } \\ \mathrm{A} & \text { Spring wood } & \text { Duramen } \\ \mathrm{B} & \text { Autumn wood } & \text { Alburnum } \\ \mathrm{c} & \text { Heartwood } & \text { Late wood } \\ \mathrm{d} & \text { Sap wood } & \text { Early wood }\end{array} \)
\( A \)
\( A-(i v), B-(i i i), C-(i), D-(i i) \)
B. \( A-(\text { iii) }, B-(i v), C-(i i), D-(i i) \)
\( c \)
\( A-(\text { iii) }, B-(i v), C-(i), D-(i i) \)
D. A-(iii), B - (iv), (ii), D-(i)
Subject: Maths
\( \lim _{\boldsymbol{x} \rightarrow \frac{\pi}{2}} \frac{\operatorname{cosec} \boldsymbol{x}-\cot \boldsymbol{x}}{\boldsymbol{x}}= \)
\( \mathbf{A} \cdot 1 \)
\( B \cdot \frac{2}{\pi} \)
\( c \cdot \frac{1}{2} \)
\( D \cdot \frac{1}{5} \)
Subject: Maths
In the figure, \( \angle A C B=90^{0} \) and radius
of big circle \( =2 c m, \) then the radius of
small circle is (in \( c m) \)
\( A \cdot 3-2 \sqrt{2} \)
B. \( 4-2 \sqrt{2} \)
c. \( 7-4 \sqrt{2} \)
D. \( 6-4 \sqrt{2} \)
Subject: Biology
How much amount of volume of air is in
lungs as FRC?
A. \( 1500 \mathrm{ml} \) to \( 1600 \mathrm{ml} \)
B. 2100 m| to 2500 m1
c. 2500 \( \mathrm{ml} \) । to \( 3000 \mathrm{ml} \)
D. 1600 \( \mathrm{ml} \) to \( 2100 \mathrm{ml} \)
Subject: Maths
Find the values of \( x \) satisfying \( [x]-1+ \)
\( x^{2} \geq 0 ; \) where [.] denotes the greatest
integer function.
A \( . x \in(-\infty,-\sqrt{3}] \cup[1, \infty) \)
B . \( x \in(-\infty,-\sqrt{2}] \cup[2, \infty) \)
c. \( x \in(-\infty,-3] \cup[3, \infty) \)
D. \( x \in(-\infty,-\sqrt{3}] \cup[3, \infty) \)
Subject: Maths
If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{\boldsymbol{m} \times \boldsymbol{n}^{\prime}} \boldsymbol{B}=\left[\boldsymbol{b}_{\boldsymbol{i} j}\right]_{\boldsymbol{m} \times \boldsymbol{n}^{\prime}} \) then the
element \( C_{23} \) of the matrix \( C=A+B \)
is:
A \( . C_{23} \)
В. \( a_{23}+b_{32} \)
\( \mathbf{c} \cdot a_{23}+b_{23} \)
D \( \cdot a_{32}+b_{23} \)
Subject: Maths
In any discrete series (when all the value are not same) the relationship between M.D. about mean and S.D. is
\( A \cdot M \cdot D=S \cdot D \)
в. \( M . D .> \) S.D.
c. \( M . D .<S . D \)
D. \( M . D . \leq S . D . \)
Subject: Chemistry
\( 1.00 \mathrm{g} \) of a hydrated salt contains \( 0.2014 \mathrm{g} \) of iron, \( 0.1153 \mathrm{g} \) of sulphur \( 0.2301 \mathrm{g} \) of oxygen and 0.4532 g of water of crystallisation. If its empirical formula \( (\boldsymbol{F e}=\mathbf{5 6} ; \boldsymbol{S}=\mathbf{3 2} ; \mathbf{0}=\mathbf{1 6}) \) is
\( F e S O_{x} \cdot y H_{z} O, \) then find the value of
\( x, y \) and \( z \)
A. \( x=4, y=7, z=2 \)
в. \( x=3, y=6, z=2 \)
c. \( x=4, y=6, z=3 \)
D. None of these
Subject: Physics
Eight drops of a liquid of density \( \rho \) and
each radius a are falling through air with a constant velocity \( 3.75 \mathrm{cm} s^{-1} \)
when the eight drops coalesce to from a single drop the terminal velocity of the
new drop will be
A. \( 2.4 \times 10^{-2} \mathrm{ms}^{-1} \)
В. \( 15 \times 10^{-2} \mathrm{ms}^{-1} \)
c. \( 0.75 \times 10^{-2} \mathrm{ms}^{-1} \)
D. \( 25 \times 10^{-2} \mathrm{ms}^{-1} \)
Subject: Chemistry
Concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) cannot be used to
prepare HBr or HI from KBr or KI because
it
A. reacts too slowly with KBr or KI
B. reduces HBr or H
c. oxidises KBror KI
D. oxidises KBr to \( K B r O_{3} \) or \( K \) I to \( K I O_{3} \)
Subject: Maths
Find the sum the infinite G.P.:
\( \frac{2}{3}-\frac{4}{9}+\frac{8}{27}-\frac{16}{21}+\dots \dots \)
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
c. \( \frac{19}{27} \)
D. 8