AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is a function which is
defined by \( f(x)=\max \left\{x, x^{3}\right\} . \) The set of all points on which \( f(x) \) is not differentiable
is
A \( \cdot\{-1,1\} \)
the
B. \{-1,0\}
\( c \cdot(0,1) \)
D. \{-1,0,1\}
Subject: Chemistry
The electronic configuration of \( G d^{2+} \) is (atomic number of \( G d \text { is } 64) \)
\( \mathbf{A} \cdot[X e] 4 f^{8} \)
\( \mathbf{B} \cdot[X e] 4 f^{7} \)
\( \mathbf{c} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)
D \( \cdot[X e] 4 f^{7} 5 d^{1} \)
Subject: Physics
The refractive index \( (\mu) \) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate percentage error.
A. \( 0.61 \% \)
B. \( 1.32 \% \)
c. \( 2.64 \% \)
D. \( 5.28 \% \)
Subject: Maths
Metal spheres, each of radius \( 2 \mathrm{cm}, \) are packed into a rectangular box of internal dimensions \( 16 \mathrm{cm} \times 8 \mathrm{cm} \times 8 \mathrm{cm} \)
When 16 spheres are packed the box is filled with preservative liquid. Find the
volume of this liquid (in \( c m^{3} \) ). Give your
answer to the nearest integer. [Use \( \boldsymbol{\pi}= \)
3.14]
Subject: Physics
A parachutist after bailing out falls \( \mathbf{5 0} \boldsymbol{m} \) without friction. When parachute opens, it decelerates at \( 2 m s^{-2} . \) He
reaches the ground with speed \( 3 m s^{-1} \)
At what height did he bail out?
\( \left(g=9.81 m / s^{2}\right) \)
A. \( 91 m \)
B. 182 m
c. 293 m
D. \( 111 m \)
Subject: Chemistry
Assertion
Millon's test is a test for identification
of proteins.
Reason Millon's reagent is a solution of mercurous nitrate and mercuric nitrate
in nitric acid containing little nitrous
acid.
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
Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?
\( ^{A} \cdot\left(y-x \frac{d y}{d x}\right)^{2}=1-\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{B}}\left(y+x \frac{d y}{d x}\right)^{2}=1+\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{c}}\left(y-x \frac{d y}{d x}\right)^{2}=1+\left(\frac{d y}{d x}\right)^{2} \)
\( ^{\mathrm{D} \cdot}\left(y+x \frac{d y}{d x}\right)^{2}=1-\left(\frac{d y}{d x}\right)^{2} \)
Subject: Maths
Given \( \boldsymbol{A}=\{\boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\} \) and \( \boldsymbol{B}=\{\boldsymbol{x}, \boldsymbol{y}\} \)
find element of \( \boldsymbol{A} \times \boldsymbol{B} \)
A \( \cdot\{b, x\} \)
в. \( \{b, y\} \)
c. \( \{c, x\} \)
D. All of the above
Subject: Maths
The Venn diagram shows the sets
\( \boldsymbol{\xi}, \boldsymbol{P}, \boldsymbol{Q} \) and \( \boldsymbol{R} \). Which of the following is
not true?
\( \mathbf{A} \cdot P \cap Q \neq \phi \)
в. \( R \subset Q \)
\( \mathbf{c} \cdot(P \cap R) \subset Q \)
D. \( (P \cap Q)=R \)
Subject: Physics
An insulated charged sphere of radius \( 5 c m \) has a potential of \( 10 V \) at the
surface. The potential at the centre will
be :
A. Same as that at \( 5 \mathrm{cm} \) from the surface
B. Same as that at \( 25 \mathrm{cm} \) from the surface
\( c .10 V \)
D. Zero
Subject: Physics
A machine gun is mounted on a \( 2000 k g \) vehicle on a horizontal smooth road
(friction negligible). The gun fires 10 bullets per sec with a velocity of \( 500 m / s . \) If the mass of each bullet be
\( 10 g, \) what is the acceleration produced
in the vehicle?
A \( \cdot 25 c m / s^{2} \)
B. \( 0.025 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.50 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 50 m / s^{2} \)
Subject: Physics
radii \( 2 R \) and \( 4 R \) respectively are kept at
distances \( x \) and \( 2 x \) from the point
charge \( q . \) A surface cutout of a non
conducting shell \( C \) is kept such that its
centre coincides with the point charge.
Each plate and the spherical surface
carries a surface charge density \( \sigma . \) If \( \phi_{1} \)
is flux through surface of \( (B) \) due to
electric field of \( (A) \) and \( \phi_{2} \) be the flux
through \( (A) \) due to electric field of \( (B) \)
then:
\( \mathbf{A} \cdot \phi_{1}=\phi_{2} \)
\( \mathbf{B} \cdot \phi_{1}>\phi_{2} \)
\( \mathbf{c} \cdot \phi_{1}<\phi_{2} \)
D. It depend \( R \)
Subject: Physics
Prove that work done by an ideal gas in
an adiabatic process is \( W= \) \( \frac{\boldsymbol{P}_{i} \boldsymbol{V}_{i}-\boldsymbol{P}_{f} \boldsymbol{V}_{f}}{\gamma-\mathbf{1}}, \) using the intergration
\( \int \boldsymbol{P} \boldsymbol{d} \boldsymbol{V} \)
Subject: Physics
If the displacement equation of a particle from its mean position is given as \( \boldsymbol{y}=\mathbf{0 . 2} \sin (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{t}+ \)
\( 1.5 \pi) \cos (10 \pi t+1.5 \pi) \) then, the
motion of particle is
A. Non-periodic
B. Periodic but not SHM
c. SHM with period 0.2
D. SHM with period 0.1 s
Subject: Chemistry
Using the cross-section image of an
iodine solid, which of the following
explains why it cannot conduct
electricity in the solid or molten states?
A. The molecular lattice points are too far away to conduct electricity
B. Only metallic solids conduct electricity
C. The electrons are tightly bound within the covalent bond of the \( I_{2} \) molecules.
D. The electrons are too polarizable to conduct electricity.
Subject: Chemistry
\( Z n(s) / Z n^{2+}(a q) \| C u^{2+}(a q) / C u(s) \)
\( \boldsymbol{E}^{0} z n^{2+} / Z n=-0.76 \mathrm{V} \)
\( \boldsymbol{E}^{0}_{C u^{2+} / C u}=+0.34 \mathrm{V} \)
Calculate \( \boldsymbol{E}_{c e l l}^{0} \) and equilibrium
constant \( \boldsymbol{K} \)
Subject: Chemistry
Which of the following is the correct
order for strength of \( C-X \) bond?
A. \( C H_{3} F<C H_{3} C l<C H_{3} B r<C H_{3} I \)
B. \( C H_{3} F>C H_{3} C l>C H_{3} B r>C H_{3} \)
c. \( C H_{3} I>C H_{3} F>C H_{3} C l>C H_{3} B r \)
D. \( C H_{3} C l>C H_{3} B r>C H_{3} F>C H_{3} \)
Subject: Chemistry
The \( p H \) of \( 10^{-6} \mathrm{M} H C l, 10^{-7} \mathrm{M} H C l \) and
\( 10^{-8} \) M \( H C l \) respectively is:
\( \mathbf{A} \cdot 6,7,8 \)
в. 6,6.79,6.98
c. 6,6.79,7.02
D. 6,6.98,8
Subject: Physics
A bead slide freely along a curve wire lying on a horizontal surface at
constant speed as shown in Fig.
a. Draw the vectors representing the force exerted by the wire on the bead at points \( A, B \) and \( C . \)
b. Suppose the bead in fig. speeds up with constant tangential acceleration as it moves towards the right. Draw the vectors representing the force on the bead at point \( A, B, \) and \( C \)
Subject: Physics
Two solenoids have identical
geometrical construction but one is made of thick wire and the other of thin
wire. Which of the following quantities are different for the two solenoids?
This question has multiple correct options
A. Self-inductance
B. Rate of Joule heating if the same current goes through them
c. Magnetic field energy if the same current goes through them
D. Time constant if one solenoid it connected to one battery and the other is connected to another battery
Subject: Maths
Assertion
If \( A, B, C \) are three events such that \( P(A)=\frac{1}{4}, P(B)=\frac{1}{6} \& P(C)=\frac{2}{3} \)
then events \( A, B, C \) are mutually exclusive.
Reason
If \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B} \cup \boldsymbol{C})=\boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})+ \)
\( \boldsymbol{P}(\boldsymbol{C}) \) then \( A, B, C \) are mutually
exclusive events.
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
The normal boiling of water is \( 373 K \) Vapour pressure of water at temperature \( \boldsymbol{T} \) is \( 19 \mathrm{mm} \) Hg. If enthalpy of evaporation is \( 40.67 k J / m o l, \) then
temperature \( \boldsymbol{T} \) would be:
(Use \( \log 2=\mathbf{0 . 3}, \boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{K}^{-1} \mathbf{)} \)
Subject: Maths
\( \operatorname{Let} h(x)=\min \left\{x, x^{2}\right\} \) for \( x \in R \) Then
which of the following is correct
A. \( h \) is continuous for all \( x \)
B. \( h \) is differentiable for all \( x \)
C \( \cdot h(x)=1 \) for all \( x>1 \)
D. \( h \) is not a differentiable at 2 values of \( x \)
Subject: Physics
Three identical balls each of mass \( \boldsymbol{m}= \)
\( 0.5 \mathrm{kg} \) are connected with each other as shown in Figure and rest over a smooth
horizontal table. At moment \( t=0, \) ball \( B \)
is imparted a horizontal velocity \( \boldsymbol{v}_{0}= \) \( 9 m s^{-1} . \) Calculate velocity of A just
before it collides with ball \( C \).
Subject: Physics
toppr
Q Type your question
velocity of the chain suddenly and without frictional resistance or
interference from the support or from
adjacent links Choose the incorrect
statement (when \( x=0, \text { then } v=0) \)
(length of the chain is L and p is the
mass per unit length of the chain)
A \( \cdot \) the velocity v of the chain as a function of \( x \) is \( \sqrt{\frac{2 g x}{3}} \)
B. the acceferation of a of the falling chain as a function
fris \( \frac{g}{3} \)
C. the energy Q lost from the system as the last link leaves the plafform is \( \frac{p g L^{2}}{6} \)
D. tension at the middle point of falling chain is \( \frac{p g x}{3} \)
Subject: Physics
Two point charges placed at a certain distance \( r \) in air exert a force \( F \) on each
other. The distance \( r \) at which these
charges will exert the same force in
medium if dielectric constant k is given by
\( A \)
в. \( \frac{r}{k} \)
c. \( \frac{r}{\sqrt{k}} \)
D. none of these
Subject: Physics
A uniform magnetic field \( \vec{B}=B_{0} \hat{j} \)
exists in a space. A particle of mass \( m \)
and charge q is projected towards
negative \( x \) -axis with speed \( v \) from the a
point \( (d, 0,0) . \) The maximum value v for
which the particle does not hit \( y \) -z plane is?
\( \mathbf{A} \cdot \frac{2 B q}{d m} \)
B. \( \frac{B q d}{m} \)
\( \mathbf{c} \cdot \frac{B q}{2 d m} \)
D. \( \frac{B q d}{2 m} \)
Subject: Biology
Critical count of platelet is
A \( \cdot 40,000 / \mathrm{mm}^{3} \)
B. 1 lac \( / \mathrm{mm}^{3} \)
c. \( 2 \operatorname{lac} / \mathrm{mm}^{3} \)
D. 4 lac / \( \mathrm{mm}^{3} \)
Subject: Chemistry
Which of the following statements is
not correct?
\( \mathbf{A} \cdot T i\left(N 0_{3}\right)_{4} \) is a colourless compound
B. \( \left.\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right)\right] \mathrm{Cl}_{3} \) is a coloured compound
\( \mathbf{C} \cdot K_{3}\left[V F_{6}\right] \) is a colourless compound
D \( \cdot\left[C u\left(N C C H_{3}\right)_{4}\right] B F_{4} \) is a colourless compound
Subject: Maths
Find \( \boldsymbol{f} \circ \boldsymbol{g} \) and \( \boldsymbol{g} \circ \boldsymbol{f}, \) if \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\mathbf{1} \)
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \)
Subject: Physics
in figure carrying current \( \boldsymbol{I} . \boldsymbol{A} \boldsymbol{B} \) and \( \boldsymbol{B} \boldsymbol{C} \)
parts are straight, long, and at right
angle. At \( D \) wire forms a circular turn
DM \( N D \) of radius \( R . A B, B C \) parts are
tangential to circular turn at \( N \) and \( D \)
The magnetic field at the centre of
circle is
A \( \cdot \frac{\mu_{0} I}{2 \pi R}\left(\pi-\frac{1}{\sqrt{2}}\right) \)
B. \( \frac{\mu_{0} I}{2 R} \)
c. \( \frac{\mu_{0} I}{2 \pi R}\left(\pi+\frac{1}{\sqrt{2}}\right) \)
\( ^{\mathrm{D}} \cdot \frac{\mu_{0} I}{2 \pi R}(\pi+1) \)
Subject: Physics
Three identical particles each of mass
1 kg are placed touching one another with their centres on a straight line. Their centres are marked \( A, B \) and \( C \)
respectively. The distance of centre of
mass of the system from \( \boldsymbol{A} \) is
\( ^{\text {A } \cdot \frac{A B+A C+B C}{3}} \)
в. \( \frac{A B+A C}{3} \)
c. \( \frac{A B+B C}{3} \)
D. \( \frac{A C+B C}{3} \)
Subject: Maths
If \( f(x)=\frac{x^{2}-10 x+25}{x^{2}-7 x+10} \) for \( x \neq 5 \) and \( f \) is
continuous \( a t x=5, \) then \( f(5) \) has the
value equal to-
A .
B. 5
c. 10
D. 25
Subject: Physics
Light is falling on surface \( \mathrm{S}_{1}, \mathrm{S}_{2}, \mathrm{S}_{3} \) as
shown in the figure. Surfaces on which the angle of incidence is equal to the angle of reflection is/are:
\( A \cdot S_{1} \) only
B. \( S_{1} \) and \( S_{2} \) only
\( c \cdot s_{2} \) and \( S_{3} \)
D. all the three surfaces
Subject: Biology
Rearrange the following stages of Calvin cycle in correct order.
1. Reduction during which carbohydrate
is formed at the expense of the
photochemically made ATP and NADPH.
2. Regeneration, during which the carbon dioxide acceptor ribulose- 1,5
biphosphate is formed.
3. Carboxylation during which carbon dioxide combines with ribulose- 1,5
biphosphate.
\( A \cdot 3-\rightarrow 1->2 \)
B. 3->>2
c. \( 1->2-\rightarrow 3 \)
D. \( 2-->1->3 \)
\( E \cdot 1-\rightarrow 3-\rightarrow>2 \)
Subject: Maths
Sum to infinite terms the following series:
\( \mathbf{1}+\mathbf{5} \boldsymbol{x}^{2}+\mathbf{9} \boldsymbol{x}^{4}+\mathbf{1} \mathbf{3} \boldsymbol{x}^{\mathbf{6}}+\ldots .,|\boldsymbol{x}|<\mathbf{1} \)
Subject: Maths
PQRS is a parallelogram. If \( L, M \) are
the midpoints of \( Q R \) and \( P S \)
respectively, and \( O \) is any point on \( L M \)
then the area of triangle \( O P Q \) is equal
to
A \( \cdot\left(\frac{1}{3}\right)^{r d} \) of the parallelogram \( P Q R S \)
B \( \cdot\left(\frac{1}{4}\right)^{t h} \) of the parallelogram \( P Q R S \)
C \( \cdot\left(\frac{1}{2}\right) \) of the parallelogram \( P Q R S \)
D \( \left(\frac{1}{6}\right)^{t h} \) of the parallelogram \( P Q R S \)
Subject: Maths
Given \( \tan (\pi \cos \theta)=\cot (\pi \sin \theta) \)
then the value of \( \cos \left(\theta-\frac{1}{4} \pi\right) \) will be
\( ^{A} \cdot \frac{1}{2 \sqrt{2}} \)
B. \( \frac{1}{\sqrt{2}} \)
c. \( \frac{1}{3 \sqrt{2}} \)
D. \( \frac{1}{4 \sqrt{2}} \)
Subject: Chemistry
Uncertainty in position of an electron
\( \left(m a s s=9.1 \times 10^{-28 g}\right) \) moving with a
velocity of \( 3 \times 10^{4} \mathrm{cm} / \mathrm{s} \) accurate upto
\( 0.001 \% \) will be: \( (U \text { se } h / 4 \pi \) in
uncertainty expression where \( h= \) \( \left.6.626 \times 10^{-27} \text {erg }-s\right) \)
A. \( 5.76 \mathrm{cm} \)
B . 7.68 \( \mathrm{cm} \)
\( c .1 .93 \mathrm{cm} \)
D. 3.84 \( \mathrm{cm} \)
Subject: Chemistry
The enthalpy change for the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C}_{2} \boldsymbol{H}_{4}(\boldsymbol{g}) \rightarrow \boldsymbol{C}_{2} \boldsymbol{H}_{6}(\boldsymbol{g}) \) is:
The bond energies are, \( \boldsymbol{H}-\boldsymbol{H}= \)
\( \mathbf{1 0 3}, \boldsymbol{C}-\boldsymbol{H}=\mathbf{9 9}, \boldsymbol{C}-\boldsymbol{C}=\mathbf{8 0} \) and
\( \boldsymbol{C}=\boldsymbol{C}=\mathbf{1 4 5} \boldsymbol{K} \boldsymbol{c a l} \boldsymbol{m o l}^{-1} \)
A. -10 Kcalmol\( ^{-1} \)
B. +10 K calmol\( ^{-1} \)
C. -30 K calmol\( ^{-1} \)
D. +30 Kcalmol-\( ^{-1} \)
Subject: Maths
The sides of a hexagon are produced in order. If the measures of exterior angles
so obtained are \( (6 x-1)^{\circ},(10 x+ \)
2) \( ^{\circ},(8 x+2)^{\circ},(9 x-3)^{\circ},(5 x+4)^{\circ} \) and
\( (12 x+6)^{\circ} ; \) Find each exterior angle
B . \( 41^{\circ}, 86^{\circ}, 56^{\circ}, 60^{\circ}, 39^{\circ}, 80^{\circ} \)
C \( \cdot 41^{\circ}, 72^{\circ}, 58^{\circ}, 60^{\circ}, 39^{\circ}, 90^{\circ} \)
D. \( 41^{\circ}, 82^{\circ}, 60^{\circ}, 60^{\circ}, 36^{\circ}, 100 \)
Subject: Chemistry
A silvery-white metal \( X \) reacts with
water at room temperature to produce a
water-soluble compound \( Y \) and a
colourless gas \( Z \). The reactions are
highly exothermic and the \( Z \) catches
fire immediately during the reaction. The solution of \( Y \) in the water on
reacting with a stoichiometric amount of dilute solution of hydrochloric acid gives a solution of \( \mathrm{pH}=7.0 . \) The
compounds \( X, Y \) and \( Z \) respectively
are:
A \( . A l, A l(O H)_{3} \) and \( H_{2} \)
B. \( A g, A g O H \) and \( H_{2} \)
c. \( K, K C l \) and \( H_{2} \)
D. \( N a, N a O H \) and \( H_{2} \)
Subject: Chemistry
The total number of moles of valence
electrons in \( 4.2 \mathrm{g} \) of \( N_{3}^{-} \) ion are:
A \( .2 .2 N_{A} \)
в. \( 4.2 N_{A} \)
c. \( 1.6 N_{A} \)
D. \( 3.2 N_{A} \)
Subject: Maths
The equation of the curve in which sub-
normal varies as the square of the ordinate is ( \( k \) is constant of
proportionality)
A \( \cdot y=A e^{2 k x} \)
B . \( y=e^{k x} \)
C \( \cdot y^{2} / 2+k x=A \)
D. \( y^{2}+k x^{2}=A \)
Subject: Physics
A uniform wire (Young's modulus \( 2 \times \) \( \left.10^{11} N m^{-2}\right) \) is subjected to
longitudinal tensile stress of \( 5 \times \)
\( 10^{7} N m^{-2} . \) If the overall volume change
in the wire is \( 0.02 \%, \) the frictional
decrease in the radius of the wire is
close to
A \( .1 .0 \times 10^{-4} \)
B. \( 1.5 \times 10^{-4} \)
c. \( 0.25 \times 10^{-4} \)
D. \( 5 \times 10^{-4} \)
Subject: Maths
In what ratio, does \( P(4,6) \) divide the
join of \( \boldsymbol{A}(-2,3) \) and \( \boldsymbol{B}(\boldsymbol{6}, \boldsymbol{7}) \)
A . 1: 2
B. 3: 1
c. 4: 1
D. 2: 1
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & -\mathbf{4} \\ \mathbf{1} & -\mathbf{1}\end{array}\right], \) then prove that \( \boldsymbol{A}- \)
\( A^{T} \) is a skew-symmetric matrix.
Subject: Maths
In figure, \( \boldsymbol{K} \boldsymbol{X} \boldsymbol{M} \) is a tangent to the
circumcircle \( C \) of \( \triangle X Y Z \) such that
\( \boldsymbol{L} \boldsymbol{M} \| \boldsymbol{Y} \boldsymbol{Z} . \) Show that \( \boldsymbol{X} \boldsymbol{Y}=\boldsymbol{X} \boldsymbol{Z} \)
Subject: Maths
For a positive numbers \( x, y \) and \( z \) the numerical value of the determinant \( \left[\begin{array}{ccc}1 & \log _{x} y & \log _{x} z \\ \log _{y} x & 1 & \log _{y} z \\ \log _{z} x & \log _{z} y & 1\end{array}\right] \) is:
A. 0
B. 1
\( \mathbf{c} \cdot \log _{e} x y z \)
\( \mathbf{D} \cdot-\log _{e} x y z \)
Subject: Physics
A circular current loop of magnetic moment M is in an arbitrary orientation in an external magnetic field \( \bar{B} \). The work done to rotate the loop by 30 about an axis perpendicular to its plane is:
\( A . M B \)
в. \( \sqrt{3} \frac{M B}{2} \)
c. \( \frac{M B}{2} \)
D. zero
Subject: Physics
At what temperature will the volume of a gas become twice the volume at \( 2700 \mathrm{C} \) at
a given pressure.
A. \( 327^{\circ} \mathrm{c} \)
B. \( 54^{\circ} \mathrm{C} \)
c. \( 127^{\circ} \mathrm{C} \)
D. \( 100^{\circ} \mathrm{C} \)
Subject: Physics
A horizontal wind is blowing with a velocity \( v \) towards north-east. A man starts running towards north with
acceleration \( a \). The time after which
man will feel the wind blowing towards east is
A \( \cdot \frac{v}{a} \)
B. \( \frac{\sqrt{2} v}{a} \)
c. \( \frac{v}{\sqrt{2} a} \)
D. \( \frac{2 v}{a} \)
Subject: Chemistry
The correct order of \( +I \) effect is
A \( \cdot-C O O^{-}>-\bar{O}>-\bar{N} H>-\bar{C} H_{2} \)
В. \( -\bar{C} H_{2}>-\bar{O}>-C O O^{-}>-C\left(C H_{3}\right)_{3} \)
\( \mathbf{c} \cdot-C\left(C H_{3}\right)_{3}>-\bar{O}>-C O O^{-}>-\bar{N} H \)
D \( -\bar{O}>-\operatorname{COO}^{-}>-C\left(C H_{3}\right)_{3}>-\bar{N} H \)
Subject: Maths
Determine the intervals over which the
function is decreasing, increasing, and
constant
A. Increasing \( [3, \infty) ; \) Decreasing \( (-\infty, 3] \)
B. Increasing \( (-\infty, 3] \); Decreasing \( [3, \infty) \)
c. Increasing \( (-\infty, 3] ; \) Decreasing \( (-\infty, 3 \)
D. Increasing [3
\( \infty) ; \) Decreasing \( [3, \infty) \)
Subject: Physics
A bar of iron is \( 10 \mathrm{cm} \) at \( 20^{\circ} \mathrm{C} \). At \( 19^{\circ} \mathrm{C} \) it
will be \( \left(\alpha_{F e}=11 \times 10^{-6} /^{o} C\right) \)
A. \( 11 x 10^{-6} \mathrm{cm} \) longer
B. \( 11 x 10^{-6} \) cm shorter
\( \mathrm{c} \cdot 11 x 10^{-5} \mathrm{cm} \) shorter
D. \( 11 x 10^{-5} \mathrm{cm} \) longer
Subject: Maths
If \( P=\left(\frac{-3}{4}\right)^{3}, Q=\left(\frac{-2}{5}\right)^{2}, R= \)
\( (0.3)^{2}, S=(-1.2)^{2} \) which of the
following is true?
A. \( P>Q>R>S \)
в. \( S>P>Q>R \)
c. \( S>Q>R>P \)
\( \mathbf{D} \cdot S>R>P>Q \)
Subject: Chemistry
A solution of weak acid \( \boldsymbol{H} \boldsymbol{A} \) was
titrated with base \( N a O H . \) The
equivalent point was reached when \( 40 m L \) of \( 0.1 M \) NaOH has been
added. Now 20 m \( L \) of \( 0.1 M \) HCl were
added to titrated solution, the \( p H \) was
found to be \( 5.0 . \) What will be the \( p H \) of
the solution obtained by mixing \( 20 m L \)
of \( 0.2 M N a O H \) and \( 20 m L \) of
\( \mathbf{0 . 2} \boldsymbol{M} \boldsymbol{H} \boldsymbol{A} ? \)
A . 7
B. 9
c. 11
D. None of the above
Subject: Chemistry
In the cyanide process for extraction of
gold and silver from ores, the cyanide
solution acts as a:
A. Reducing agent to reduce the gold and silver compounds present in the ores into the metallic states
B. Leaching agent to bring the gold and silver into solution as cyanide complexes and thus separate these metals from the ores
C. Leaching agent to dissolve all the other constituents of the ores leaving the gold and silver as metals
D. Leaching agent to bring the ores into solution
Subject: Maths
A line makes angles \( \alpha, \beta, \gamma \) with the
positive directions of the axes of
reference. The value of \( \cos 2 \alpha+ \)
\( \cos 2 \beta+\cos 2 \gamma \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot-1 \)
D. 0
Subject: Chemistry
For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in \( 100 \mathrm{g} \) of water, the elevation in boiling
point at 1 atm pressure is \( 2^{\circ} C \) Assuming concentration of solute is much lower than the concentration of
solvent, the vapour pressure (mm of Hg) of the solution is:
\( \left[\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 7 6} \boldsymbol{K} \boldsymbol{K} \boldsymbol{g} \boldsymbol{m o l}^{-1}\right] \)
A . 724
в. 740
\( c \cdot 736 \)
D. 718
Subject: Physics
A body of mass \( 5 k g \) moving on a horizontal surface with a velocity of
\( 10 m s^{-1} \) comes to rest in \( 2 s . \) The force
required to make this body move with a
velocity of \( 10 \mathrm{ms}^{-1} \) on the same surface
is:
A. zero
в. \( 10 N \)
c. \( 25 N \)
D. \( 50 N \)
Subject: Maths
\( I^{\prime} \) is the incentre of triangle of \( A B C \)
whose corresponding sides are \( a, b, c \) respectively, \( a \overrightarrow{I B}+b \overrightarrow{I B}+c \overrightarrow{I C} \) is
always equal to
A. 0
в. \( (a+b+c) \overrightarrow{B C} \)
c. \( (\vec{a}+\vec{b}+\vec{c}) \overrightarrow{A C} \)
D. \( (a+b+c) \overrightarrow{A B} \)
Subject: Biology
According to widely accepted, "Fluid
mosaic model" cell membranes are
semi-fluid, where lipids and integral proteins can diffuse randomly. In recent years, this model has been modified in
several respects. In this regard, which of
the following statements is incorrect?
A. Proteins in cell membranes can travel within the lipid bilayer.
B. Proteins can remain confined within certain domains of the memberane.
C. Proteins can also undergo flip-flop movements in the lipid bilayer.
D. Many proteins remain completely embedded within the lipid bilayer.
Subject: Chemistry
For a reaction \( 2 N O(g)+C l_{2}(g) \rightarrow \)
\( 2 N O C l(g), \) when concentration of \( C l_{2} \)
is doubled the rate of reaction becomes
two-times of the original. When the concentration of \( N O \) is doubled the
rate becomes four times. What is the
order of the reaction?
A . 1
B. 2
\( c .3 \)
D. 4
Subject: Maths
Show that \( \left(\frac{1}{a+} \frac{1}{b+} \frac{1}{c+} \dots\right)\left(c+\frac{1}{b+} \frac{1}{a+} \frac{1}{c_{1}} \dots .\right)= \)
\( \frac{1+b c}{1+a b} \)
Subject: Chemistry
If 10 g of liquid at \( 300 \mathrm{K} \) is heated to 350 K, the liquid absorbs 6 kcals. Determine the specific heat of the liquid in cal/
\( \boldsymbol{g}^{\circ} \boldsymbol{C} \)
A. 6
B. 12
\( c \cdot 60 \)
D. 120
E. 600