AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
At \( 27^{\circ} C \) a gas is compressed suddenly such that its pressure becomes \( \left(\frac{1}{8}\right) \) th of original pressure. Final temperature will be \( (\gamma=5 / 3) \)
\( \mathbf{A} \cdot 450 K \)
B. \( 300 K \)
c. \( -142^{\circ} \mathrm{C} \)
D. \( 327^{\circ} \)
Subject: Maths
If the function \( u=f(x) \) is continuous at
the point \( x=a \) and the
function \( y=g(u) \) is continuous at the
point \( u=f(a), \) then the
composite function \( \boldsymbol{y}=(\boldsymbol{g} \boldsymbol{o} \boldsymbol{f})(\boldsymbol{x})= \)
\( g(f(x)) \) is
A. continuous at the point \( x=f(a) \)
B. continuous at the point \( x=a \)
c. discontinuous at the point \( x=a \)
D. continuous at the point \( x=g(a) \)
Subject: Maths
Find \( \lim _{x \rightarrow(2 n+1) \pi^{+}} \sin \left([\sin x] \frac{\pi}{6}\right), \) where []
is a greatest integer function and \( n \epsilon I \)
A. 0
B. \( \frac{1}{2} \)
\( c \cdot-\frac{1}{2} \)
D. none of these
Subject: Chemistry
The correct set of quantum number for the unpaired electrons of chlorine atom is:
A \( \cdot_{3,1,1, \pm \frac{1}{2}} \)
в. \( _{2,1,-1,+\frac{1}{2}} \)
c. \( _{3,0,0, \pm} \frac{1}{2} \)
D. \( 2,0,0,+\frac{1}{2} \)
Subject: Physics
A solenoid of \( 1.5 \mathrm{m} \) length and \( 4.0 \mathrm{cm} \) diameter possesses 100 turns per meter. A current of 5 amperes is flowing through it. The magnetic induction at axis inside the solenoid is:
A \( \cdot 2 \pi \times 10^{-4} \mathrm{T} \)
В . \( 2 \pi \times 10^{-5} \) Т
c. \( 2 \pi \times 10^{-2} \) gauss
D. \( 2 \pi \times 10^{-5} \) gauss
Subject: Maths
Assertion
The number of real solution of the
equation \( \sin (\cos x)=\cos (\sin x) \) is
zero
Reason
\( \sin x>0, \) then \( 2 n \pi<x< \)
\( (2 n+1) \pi, n \epsilon I \)
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 false but Reason is true
Subject: Chemistry
An amount of 2 moles \( K C l O_{3} \) is
decomposed completely to produce \( \boldsymbol{O}_{2} \)
gas. How many moles of butane, \( C_{4} H_{2} \)
can be burnt completely by the \( O_{2} \) gas
produced?
A . 0.6
B. 1.0
\( c .2 .0 \)
D. 3.0
Subject: Physics
If a rigid body is subjected to two forces \( \vec{F}_{1}=2 \hat{i}+3 \hat{j}+4 \hat{k} \) acting at (3,3,4)
and \( \vec{F}_{2}=-2 \hat{i}-3 \hat{i}-4 \hat{k} \) acting at (1
0, 0) then which of the following is (are)
true?
A. The body maybe in equilibrium
B. The body is under the influence of a torque only
c. The body is under the influence of a single force.
D. The body is under the influence of a force together with torque
Subject: Maths
If \( I_{1}=\int_{1}^{2} x(\sqrt{x}+\sqrt{3-x}) d x \) and
\( \boldsymbol{I}_{2}=\int_{1}^{2}(\sqrt{\boldsymbol{x}}+\sqrt{\mathbf{3 - x}}) d \boldsymbol{x}, \) then \( \frac{\boldsymbol{I}_{1}}{\boldsymbol{I}_{2}}= \)
\( A \)
\( \overline{2} \)
B. \( \frac{3}{2} \)
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
In which of the following ionization processes, the bond order has increased and the magnetic behaviour has changed?
\( \mathbf{A} \cdot C_{2} \rightarrow C_{2}^{+} \)
в. \( N O \rightarrow N O^{+} \)
\( \mathbf{c} \cdot O_{2} \rightarrow O_{2}^{+} \)
\( \mathbf{D} \cdot N_{2} \rightarrow N_{2}^{+} \)
Subject: Physics
The velocity of a body moving with a uniform acceleration of \( 2 m / \sec ^{2} \) is 10 \( m / \) sec. Its velocity after an interval of \( 4 \sec \) is
\( A \cdot 12 \mathrm{m} / \mathrm{sec} \)
B. \( 14 \mathrm{m} / \mathrm{sec} \)
c. \( 16 \mathrm{m} / \mathrm{sec} \)
D. 18 m/sec
Subject: Maths
If \( a^{2}-a b=0, \) which of the following is
the correct conclusion?
\( \mathbf{A} \cdot a=0 \)
B . \( a=b \)
\( \mathbf{c} \cdot a^{2}=b \)
D. either \( a=0 \) or \( a=b \)
Subject: Physics
A capacitor of capacitance \( 1 \mu F \) is
charged to a potential of \( 1 V . \) It is
connected in parallel to an indicator of
inductance \( 10^{-3} \) H. The maximum
current that will flow in the circuit has
the value
A. \( \sqrt{1000} \mathrm{mA} \)
в. \( 1 \mathrm{mA} \)
\( c \cdot 1 \mu A \)
D. \( 1000 \mathrm{mA} \)
Subject: Biology
Assertion
Pulmonary circulation consists of flow of deoxygenated blood from right ventricle to the lungs and flow of oxygenated blood from lungs to the left atrium.
Reason
Systemic circulation consists of flow of
oxygenated blood from the left ventricle to all parts of the body and deoxygenated blood from different parts to right atrium.
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
A buffer solution of \( p H=9 \) can be
prepared by mixing:
A. \( C H_{3} C O O N a \) and \( C H_{3} C O O O H \)
B. \( N a C l \) and \( N a O H \)
c. \( N H_{4} C l \) and \( N H_{4} O H \)
D. \( K H_{2} P O_{4} \) and \( K_{2} H P O_{4} \)
Subject: Chemistry
The single electrode potential of metal \( E \)
of \( 0.1 \mathrm{M} \) solution of \( \mathrm{M}^{+} / \)Mions\( \left[E^{0}=\right. \)
\( -2.36 V] \) is nearly:
A . \( +2.41 V \)
в. \( -2.41 V \)
c. \( 4.82 V \)
D. \( +4.82 V \)
Subject: Maths
The sum of the outer angles of polygon is twice the sum of the inner angles.
(i) How many sides does it have?
(ii) What if the sum of outer angles is half the sum of inner angles?
(iii) If the sums are equal?
A. (i) 3 (ii) 4 (iii) 6
B. (i) 6 (ii) 4 (iii) 3
c. (i) 4 (ii) 3 (iii) 6
D. (i) 3 (ii) 6 (iii) 4
Subject: Physics
A magnetic field of flux density \( 1.0 W b m^{-2} \) acts normal to a 80 turn
coil of \( 0.01 m^{2} \) area. The e.m.f. induced
in it, if this coil is removed from the
field in 0.1 second is
A . \( 8 V \)
в. \( 4 V \)
\( c \cdot 10 V \)
D. \( 6 V \)
Subject: Physics
A Zener diode is connected to a battery
and a load as shown below: The current
\( \boldsymbol{I}, \boldsymbol{I}_{Z} \) and \( \boldsymbol{I}_{\boldsymbol{L}} \) are respectively :
A \( .12 .5 \mathrm{mA}, 735 \mathrm{mA}, 5 \mathrm{mA} \)
B. \( 12.5 \mathrm{mA}, 5 \mathrm{mA}, 7.5 \mathrm{mA} \)
c. \( 15 \mathrm{mA}, 7.5 \mathrm{mA}, 7.5 \mathrm{mA} \)
D. \( 15 \mathrm{mA}, 5 \mathrm{mA}, 10 \mathrm{mA} \)
Subject: Chemistry
Assertion
The Cl-ionCl-ion is formed, when 'Cl'
Cl' atom loses an electron.
Reason
Anion is form by accepting an electron.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect
Subject: Chemistry
\( C u^{+}(a q) \) is unstable in solution and
undergoes simultaneous oxidation and
reduction, according to the reaction \( \mathbf{2} C u^{+}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \boldsymbol{C} \boldsymbol{u}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C u}(s) \)
Choose correct \( E \) for above reaction if
\( \boldsymbol{E}_{C u^{2+} / C u}=\mathbf{0 . 3 4} \boldsymbol{V} \) and \( \boldsymbol{E}_{c u^{2+} / \boldsymbol{C u}^{+}}= \)
\( \mathbf{0 . 1 5} \boldsymbol{V} \)
A. \( -0.38 V \)
в. \( +0.49 V \)
\( \mathrm{c} \ldots+0.38 \mathrm{V} \)
D. - \( 0.19 V \)
Subject: Physics
The distances covered by a particle thrown in a vertical plane, in horizontal and vertical directions at any instant of
time 't' are \( x=3 t \) and \( y=4 t-5 t^{2} \)
.The acceleration due to gravity is
A \( .8 m / s^{2} \)
B . \( 9 m / s^{2} \)
\( \mathrm{c} \cdot 10 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 16 m / s^{2} \)
Subject: Maths
If \( f\left(x_{1}\right)-f\left(x_{2}\right)=f\left(\frac{x_{1}-x_{2}}{1-x_{1} x_{2}}\right) \) for
\( \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \in[-1,1] \) then \( \boldsymbol{f}(\boldsymbol{x}) \) is
This question has multiple correct options
\( ^{\mathbf{A}} \cdot \log \left(\frac{1-x}{1+x}\right) \)
B. \( \tan ^{-1}\left(\frac{1-x}{1+x}\right) \)
\( ^{\mathrm{c}} \cdot \log \left(\frac{1+x}{1-x}\right) \)
D. \( \tan ^{-1}\left(\frac{1+x}{1-x}\right) \)
Subject: Physics
The image of a candle flame formed by a lens is obtained on a screen placed on
the other side of the lens. If the image is
three times the size of the flame and
the distance between lens and image is \( 80 \mathrm{cm}, \) at what distance should the candle be placed from the lens?
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( -36.67 \mathrm{cm} \)
\( \mathbf{c} .-26.67 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)
Subject: Chemistry
Radius of nucleus may be given as \( \boldsymbol{R}_{N}=\boldsymbol{R}_{0} \boldsymbol{A}^{1 / 3}, \) where \( \boldsymbol{A}= \) mass
number and \( R_{0}= \) constant. Calculate
the density of nucleus of an atom if \( \boldsymbol{R}_{0}=\mathbf{1 . 2} \times \mathbf{1 0}^{-\mathbf{1 5}} \)
Subject: Physics
The table below shows the melting point of three liquids.
\( \begin{array}{lll}\text { Melting point } & \text { Boiling point } \\ \text { Alcohol } & -115^{\circ} \mathrm{C} & 78^{\circ} \mathrm{C} \\ \text { Mercury } & -39^{\circ} \mathrm{C} & 357^{\circ} \mathrm{C} \\ \text { Water } & 0^{\circ} \mathrm{C} & 100^{\circ} \mathrm{C}\end{array} \)
Which liquid is most suitable to be
used in a thermometer for measuring a
temperature range of \( -10^{\circ} \mathrm{C} \) to \( 95^{\circ} \mathrm{C} \)
Subject: Physics
How many sub-atomic particles are present in ana- particle used in
Rutherford's scattering experiment?
A. Protons - 4, Neutrons - 0, Electrons - 0
B. Protons - 2, Neutrons - 0, Electron - 2
c. Protons - 2, Neutron - 2, Electron - 0
D. Protons - 2, Neutron - 2, Electron - 1
Subject: Chemistry
Consider the following reaction:
\( \boldsymbol{H} \boldsymbol{C H O}+\mathbf{2}\left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]^{+}+\boldsymbol{3} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \)
\( \mathbf{2 A g}+\boldsymbol{H C O O}^{-}+\mathbf{4 N H}_{\mathbf{3}}+\mathbf{2 H}_{\mathbf{2}} \boldsymbol{O} \)
Which of the following statements
regarding oxidation and reduction is
correct?
\( \mathbf{A} \cdot H C H O \) is oxidised to \( H C O O^{-} \) and \( \left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is reduced to \( A g \)
B. \( H C H O \) is reduced to \( H C O O^{-} \) and \( \left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is oxidised to \( A g \)
\( \mathbf{C} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is reduced to \( A g \) while \( O H^{-} \) is oxidised to \( H C O O^{-} \)
\( \mathbf{D} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} \) is oxidised to \( N H_{3} \) while \( H C H O \) is reduced to \( H_{2} O \)
Subject: Chemistry
In which of the following, the chemical formula and the name are incorrectly
matched?
A \( \cdot_{K}\left[P t\left(N H_{3}\right) C l_{5}\right] \) - potassium
amminepentachloroplatinate(IV)
в. \( \left[A g(C N)_{2}\right]^{-}- \) dicyanoargentate (1) ion
\( c \)
\( K_{3}\left[C r\left(C_{2} O_{4}\right)_{3}\right] \) - potassium trioxalatochromate(II)
D. \( _{N a_{2}}[N i(E D T A)] \) - sodium
ethylenediaminetetraacetonickelate(IV)
Subject: Chemistry
The IUPAC name of
\( \boldsymbol{K}_{2}\left[\boldsymbol{C r}(\boldsymbol{C N})_{2} \boldsymbol{O}_{2}\left(\boldsymbol{O}_{2}\right) \boldsymbol{N} \boldsymbol{H}_{3}\right] \) is:
A. potassium amminedicyanotetraoxo chrominum (III)
B. potassium amminedicyanodioxygendioxo chromate \( (1 v) \)
c. potassium amminedicyanosuperoxoperoxo chromate
(III)
D. potassium amminedicyanodioxoperoxo chromate (VI)
Subject: Physics
The radius of curvature of a convex
mirror is \( 40 \mathrm{cm} . \) Find its focal length
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
\( \mathrm{c} \cdot 20 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
The magnetic flux through a circuit of resistance R changes by an amount \( \Delta \phi \) in time \( \Delta t . \) Then the total quantity of electric charges \( Q \) that passes any point in the circuit during the time \( \Delta t \) is represented by:
A \( \cdot Q=\frac{\Delta \phi}{R} \)
в. \( Q=\frac{\Delta \phi}{\Delta t} \)
c. \( Q=R \cdot \frac{\Delta \phi}{\Delta t} \)
D. \( Q=\frac{1}{R} \cdot \frac{\Delta \phi}{\Delta t} \)
Subject: Physics
Infinite number of cells having emfs and internal resistances \( (\boldsymbol{E}, \boldsymbol{r}),\left(\frac{\boldsymbol{E}}{\boldsymbol{n}}, \frac{\boldsymbol{r}}{\boldsymbol{n}}\right),\left(\frac{\boldsymbol{E}}{\boldsymbol{n}^{2}}, \frac{\boldsymbol{r}}{\boldsymbol{n}^{2}}\right),\left(\frac{\boldsymbol{E}}{\boldsymbol{n}^{3}}, \frac{\boldsymbol{r}}{\boldsymbol{n}^{3}}\right) \)
ara connected in series in same manner
\( \operatorname{across} \) an external resistance of \( \frac{\boldsymbol{n} \boldsymbol{r}}{\boldsymbol{n}-\mathbf{1}} \)
Current flowing through the external
resistor is:
A \( \cdot \frac{E}{2 r} \)
B. \( \frac{E}{(n+1) r} \)
c. \( \frac{(n-1) E}{r} \)
D. \( \frac{(n-1) E}{2 r} \)
Subject: Chemistry
Before: \( C u O+ \) porcelain boat \( =62.869 g \)
\( C a C l_{2}+U-t u b e=80.483 g \)
After:Porcelain boat+contents =
\( 54.869 g \)
CaCl \( _{2}+ \) U-tube \( =89.483 \mathrm{g} \)
Reactions: \( Z n(s)+2 H C l(a q) \rightarrow \)
\( Z n C l_{2}(a q)+H_{2}(g) \) then \( H_{2}(g)+ \)
\( \boldsymbol{C u} \boldsymbol{O}(\boldsymbol{s}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C u}(\boldsymbol{s}) \)
What type of reaction occurred in the
porcelain boat?
A . Electrolysis
B. Double displacement
c. Reduction and oxidation
D. Decomposition or analysis
E. Combination or synthesis
Subject: Physics
The source frequency for which a \( 5 \mu \mathrm{F} \)
capacitor has a reactance of \( 1000 \Omega \) is
A \( \cdot \frac{100}{\pi} \) Hz
в. \( \frac{1000}{\pi} \) Н \( z \)
\( c .200 H z \)
D. \( 5000 \mathrm{Hz} \)
Subject: Physics
A solid sphere of radius \( R \) made of
material of bulk modulus \( \boldsymbol{K} \), is
surrounded by a liquid in a cylindrical container. A massless piston of area \( \boldsymbol{A} \) floats on the surface of liquid. When a mass \( m \) is placed on the piston to compress the liquid, the fractional
change in the radius of the sphere \( \boldsymbol{\delta} \boldsymbol{R} / \boldsymbol{R} \) is :
A. \( m g / A K \)
в. \( m g / 3 A K \)
c. \( m g / A \)
D. \( m g / 3 A R \)
Subject: Biology
Assertion
Escherichia coli lives in a symbiotic relationship in the colon of the human body
Reason
The bacterium produces vitamins which are absorbed by the wall of colon into the blood stream
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 man weighing 100 kg carries a load of
\( 10 \mathrm{kg} \) on his head. He jumps from a tower with the load on his head. What
will be the weight of the load as experienced by the man?
A. zero
в. \( 10 \mathrm{kg} \)
c. slightly more than \( 10 \mathrm{kg} \)
D. \( 110 \mathrm{kg} \)
Subject: Chemistry
Among the following groups which represents the collection of isoelectronic species?
A \( \cdot N O^{+}, C_{2}^{2-}, O_{2}^{-}, C O \)
в. \( N_{2}, C_{2}^{2-}, C O_{2}^{-}, N O \)
c. \( C O, N O^{+}, C N^{-}, C_{2}^{2} \)
D. \( N O, C N^{-}, N_{2}, O_{2}^{-} \)
Subject: Physics
Two coils \( A \) and \( B \) have 200 and 400
turns respectively. A current of 1 A in coil
A causes a flux per turn of \( 10^{-3} \) Wh to
link with \( A \) and a flux per turn of \( 0.8 \times \) \( 10^{-3} \) Wh through B. The ratio of self-
inductance of \( A \) and the mutual
inductance of \( A \) and \( B \) is :
A. \( 5 / 4 \)
B. 1/1.6
c. 1.6
D.
Subject: Chemistry
Calculate the equilibrium constant for the redox reaction at \( 25^{\circ} \mathrm{C}, S r_{(s)}+ \) \( M g_{(a q)}^{2+} \rightarrow S r_{(a q)}^{2+}+M g_{(s)}, \) that occurs
in a galvanic cell. \( \boldsymbol{E}_{M g^{2+} / M g}^{o}=-2.37 \mathrm{V} \)
and \( \boldsymbol{E}_{\boldsymbol{S r}^{2}+/ \boldsymbol{S} \boldsymbol{r}}^{o}=-\boldsymbol{2} . \boldsymbol{8} \boldsymbol{9} \boldsymbol{V} \)
A \( \cdot 2.69 \times 10^{15} \)
В. \( 2.69 \times 10^{17} \)
D. \( 3.69 \times 10^{15} \)
Subject: Chemistry
Reduction of \( C H_{3} C H_{2} N C \) with
hydrogen in presence of \( \boldsymbol{N} \boldsymbol{i} \) or \( \boldsymbol{P} \boldsymbol{t} \) as catalyst gives:
A \( \cdot C H_{3} C H_{2} N H_{2} \)
B. \( C H_{3} C H_{2} N H C H_{3} \)
c. \( C H_{3} C H_{2} N H C H_{2} C H_{3} \)
D. \( \left(C H_{3}\right)_{3} N \)
Subject: Physics
A particle is travelling in a circular path of radius 4 m. At certain instant the
particle is moving at \( 20 \mathrm{m} / \mathrm{s} \) and its
acceleration is at an angle of \( 37^{\circ} \) from the direction to the centre of the circle
as seen from the particle.
(i) At what rate is the speed of the particle increasing?
(ii) What is the magnitude of the acceleration?
Subject: Chemistry
Given that \( N_{2}(g)+3 H_{2}(g) \rightarrow \)
\( \mathbf{2} N \boldsymbol{H}_{3}(\boldsymbol{g}) ; \boldsymbol{\Delta}_{r} \boldsymbol{H}=-\mathbf{9} 2 \boldsymbol{K} \boldsymbol{J}, \) the
standard molar enthalpy of formation in
\( \boldsymbol{K} \boldsymbol{J} \boldsymbol{m o l}^{-1} \) of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \) is :
A . -92
B. +46
\( c \cdot+92 \)
D. -46
Subject: Physics
A long coaxial cable consists of two thin-walled conducting cylinders with
inner radius \( 2 c m \) and outer radius \( 8 c m \)
The inner cylinder carries a steady current \( 0.1 A \), and the outer cylinder
provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the
magnetic field for length \( 5 m \) of the
cable. Express answer in \( n J \) (use
\( \ln 2=0.7) \)
Subject: Maths
n right triangle \( A B C \), right-angled at
\( C, M \) is the mid-point of hypotenuse
\( A B . C \) is joined to \( M \) and produced to a
point \( D \) such that \( D M=C M . \) Point \( D \)
is joined to point \( B \).Which of the
following is correct.

This question has multiple correct options
A. \( \Delta \mathrm{AMC} \cong \Delta \mathrm{BMD} \)
B. \( \angle D B C \) is a right angle.
c. \( \Delta D B C \equiv \Delta A B C \)
D. \( \mathrm{CM}=\frac{1}{2} \mathrm{AB} \)
Subject: Maths
Using integration, find the area of the triangle \( P Q R, \) whose vertices are at
\( \boldsymbol{P}(\mathbf{2}, \mathbf{5}), \boldsymbol{Q}(\mathbf{4}, \mathbf{7}) \) and \( \boldsymbol{R}(\mathbf{6}, \mathbf{2}) \)
Subject: Maths
Find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \quad \) If \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{\theta}-\sin \boldsymbol{\theta}), \boldsymbol{y}= \)
\( \boldsymbol{a}(1+\cos \boldsymbol{\theta}) \)
Subject: Maths
Let \( R= \) the set of real numbers, \( Z= \)
the set of integers, \( N= \) the set of
natural numbers. If \( S \) be the solution
set of the equation \( (x)^{2}+[x]^{2}=(x- \)
\( \mathbf{1})^{2}+[\boldsymbol{x}+\mathbf{1}]^{2}, \) where \( (\boldsymbol{x})= \) the least
integer greater than or equal to \( x \) and \( [x]= \) the greatest integer less than or
equal to \( x, \) then
A \( . S=R \)
в. \( S=R-Z \)
c. \( S=R-N \)
D. \( S=\phi \)
Subject: Chemistry
In which case first has higher solubility than second?
(I) Phenol, Benzene
(II) Nitrobenzene, Phenol
(III) o-Hydroxybenzaldehyde, p-Hydroxy benzaldehyde
\( (\mathrm{IV}) \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O}, \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{O}-\boldsymbol{C} \boldsymbol{H}_{3} \)
(V) o-Nitrophenol, p-Nitrophenol
A. Only I
B. ॥I,
\( c \cdot 1,1 v \)
D. II, IV
Subject: Maths
The formula to find variance is
This question has multiple correct options
\( \mathbf{A} \cdot \frac{\sum x^{2}}{n}-\left(\frac{\sum x}{n}\right) \)
\( ^{\mathrm{B}} \cdot \frac{\sum x^{2}}{n}-\left(\frac{\sum x}{n}\right)^{2} \)
C. \( \frac{\sum x^{2}}{n}-(\bar{x})^{2} \)
\( ^{\mathrm{D}} \cdot \frac{\sum x}{n}-\left(\frac{\sum x}{n}\right)^{2} \)
Subject: Maths
If \( P(A \cup B)=\frac{3}{4} \) and \( P(\bar{A})=\frac{2}{3}, \) then
find the value of \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B}) \)
A \( \cdot \frac{3}{2} \)
B. \( \frac{1}{2} \)
c. \( \frac{5}{12} \)
D. None of these
Subject: Maths
The point which does not belong to the feasible region of the LPP:
Minimize: \( Z=60 x+10 y \)
subject to \( 3 x+y \geq 18 \)
\( 2 x+2 y \geq 12 \)
\( x+2 y \geq 10 \)
\( x, y \geq 0 \) is
в. (4,2)
D. (10,0)
Subject: Chemistry
In which of the following, do all the \( C \) atoms not have the same hybridisation
\( ? \)
This question has multiple correct options
\( \mathbf{A} \cdot\left(C H_{3}\right)_{3} C^{\bullet} \)
в. \( _{C H_{3}-C H}^{\text {ต่ }}-C H_{3} \)
c. \( C H_{2}=C=C H_{2} \)
D. \( _{C H_{2}}=C_{H}^{\text {of }} \)
Subject: Maths
Consider \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \)
Parameters \( a, b, c \) are chosen,
respectively, by throwing a die three times. Then the probability that \( f(x) \) is
an increasing function is
A \( .5 / 12 \)
в. \( 2 / 9 \)
c. \( 4 / 9 \)
D. \( 1 / 3 \)
Subject: Chemistry
From the electronic configurations, one
can predict that the geometric configuration for which of the following
molecules is not correct?
\( \mathbf{A} \cdot P F_{3}, \) trigonal planar
B. \( C F_{4} \), tetrahedral
\( \mathbf{C} \cdot C H C l_{3}, \) irregular tetrahedron
D. \( O F_{2} \), bent (v-shaped)
E . \( H F \), linear
Subject: Chemistry
Which is more stable in the below
given pair?
\( M n O_{4}^{-} \) and \( R e O_{4}^{-} \)
\( \mathbf{A} \cdot M n O_{4}^{-}=R e O_{4}^{-} \)
B. \( M n O_{4}^{-}<R e O_{4}^{-} \)
\( \mathbf{c} \cdot M n O_{4}^{-}>R e O_{4} \)
D. None of these
Subject: Physics
A thin spherical insulating shell of radius R carries a uniformly distributed
charge such that the potential at its
surface is \( V_{0} . \) A hole with small area
\( \alpha 4 \pi R^{2}(\alpha<<1) \) is made on the shell
without affecting the rest of the shell. Which one of the following statement is
correct?
A. The ratio of the potential at the centre of the shell to that of the point at \( \frac{1}{2} R \) from center towards the hole
will be \( \frac{1-\alpha}{1-2 \alpha} \)
B. The potential at the centre of shell is reduced by \( 2 \alpha v_{0} \)
C. The magnitude of electric field at the centre of the shell is reduced by \( \frac{\alpha v_{0}}{2 R} \)
D. The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance \( 2 R \) from the center of the spherical shell will
be reduced by \( \frac{\alpha v_{0}}{2 R} \)
Subject: Physics
In a step-up transformer, if ratio of truns of primary to secondary is 1: 10 and primary voltage is \( 230 V \). If the load
current is \( 2 A \), then the current in
primary is
A . \( 20 A \)
в. \( 10 A \)
\( c . \$ 2 A \)
D. \( 1 A \)
Subject: Biology
Assertion
Anaerobic respiration sometimes occurs in our skeletal muscles during strenous exercise.
Reason
Pyruvic acid is reduced to lactic acid by lactate dehydrogenase in the absence of oxygen.
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 general electronic configuration for transition
elements is NOT correct?
This question has multiple correct options
A \( \cdot(n+1) s^{1-2} n d^{1-30} \)
B . \( \left.n s^{1-2}(n-1) d^{1-10} \text { (Where } n=2,3,4, \ldots \ldots\right) \)
C. \( n s^{1-2}(n-1) s^{2} p^{6} d^{1-10} \)
D \( \cdot(n-1) d^{1-10} n s^{0-2} \)
Subject: Maths
The triangle PQR is inscribed in the circle \( x^{2}+y^{2}=25 . \) If \( Q \) and \( R \) have
coordinates \( (\mathbf{3}, \mathbf{4}) \) and \( (-\mathbf{4}, \mathbf{3}) \)
respectively, then \( \angle Q P R \) is equal to
A \( \cdot \frac{\pi}{2} \)
в.
c.
D.