AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Consider the following anions.
When attached to \( s p^{3-} \) hybridized
carbon, their leaving group ability in nucleophilic substitution reactions
decreases in the order.
(II)
A. \( I>I I>I I I>I V \)
В. \( I>I I>I V>I I I \)
c. \( \quad I V>I>I I>I I I \)
D. \( I V>I I I>I I>I \)
Subject: Maths
A bag contains \( 6 \mathrm{R}, 4 \mathrm{W} \) and \( 8 \mathrm{B} \) balls. If 3 balls are drawn simultaneously at random determine the probability of the
event
(1) all 3 are red.
(2) all 3 are black
(3) at least 1 is red
(4) 1 of each colour are drawn
(5) the balls are drawn in the order of
red, white, black
(6) 2 are white and 1 is red.
Subject: Maths
Assertion
Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be any function. Define
\( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) by \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})| \) for all \( \boldsymbol{x} \)
Then, \( g \) is continuous is \( \boldsymbol{f} \) is
continuous.
Reason
Composition of two continuous functions is a continuous function
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
Seema invested an amount of Rs.
\( 16,000 /- \) for two years at C.I. and received an amount of Rs. 17640 on
maturity. What is the rate of interest?
A . \( 8 \% \)
B. \( 5 \% \)
c. \( 7 \% \)
D. \( 6 \% \)
Subject: Chemistry
The vapour pressure of two miscible
liquids \( (A) \) and \( (B) \) are 300 and
\( 500 m m \) of \( H g \) respectively. In a flask 10 mole of \( (A) \) is mixed with 12 mole
of \( (B) . \) However, as soon as \( (B) \) is added, \( (A) \) starts polymerising into a completely insoluble solid. The polymerisation follows first-order kinetics. After 100 minute, 0.525 mole of a solute is dissolved which arrests
the polymerisation completely. The final vapour pressure of the solution is
400 mm of \( H g . \) Estimate the rate
constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.
A . \( 1.3 \times 10^{-2} \)
B . \( 15 \times 10^{-3} \)
c. \( 2.0 \times 10^{-4} \)
D. \( 1.0 \times 10^{-4} \)
Subject: Biology
Assertion: Litter burning is not
suggested by ecologists.
Reason: Burning litter enhances 'CO
content of the air.
A. Both the Assertion and the Reason are true and the Reason is a correct explanation of the Assertion.
B. Both the Assertion and Reason are true but the Reason
is not a correct explanation of the Assertion.
C. The Assertion is true but the Reason is false.
D. Both the Assertion and Reason are false.
E. The Assertion is false but Reason is true.
Subject: Maths
\( \frac{1}{2}-\frac{1}{2.2^{2}}+\frac{1}{3.2^{3}}+\ldots \ldots= \)
A \( \cdot \)
\[
\begin{array}{l}\text { B } \cdot \frac{1}{2} \log _{2}\left(\frac{3}{2}\right) \\ \text { c. } \log _{e}\left(\frac{2}{3}\right) \\ \text { D } \cdot \frac{1}{2} \log _{e}\left(\frac{2}{3}\right)\end{array}
\]
Subject: Physics
A narrow tube is bent in the form of a
circle of radius \( R, \) as shown in the
figure. Two small holes \( S \) and \( D \) are made in the tube at the positions right
angle to each other. A source placed at
S generated a wave of intensity \( l_{0} \) which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point \( D \) where a detector is placed. If the minima is formed at the detector then,
the magnitude of wavelength \( \lambda \) of the wave produced is given by :
This question has multiple correct options
A. \( 2 \pi R \)
R
R. \( 2 \pi \)
в. \( \frac{3 \pi R}{2} \)
c. \( \frac{2 \pi R}{3} \)
D. \( \frac{2 \pi R}{5} \)
Subject: Physics
In
fig., \( L \) is a converging lens of focal length \( 10 c m \) and \( M \) is a concave mirror
of radius of curvature \( 20 \mathrm{cm} . \) A point
object \( \boldsymbol{O} \) is placed in front of the lens at
a distance of \( 15 \mathrm{cm} . A B \) and \( C D \) are
optical axes of the lens and mirror, respectively. Find the distance of the final image formed by this system from the optical center of the lens. The distance between \( C D \) and \( A B \) is \( 1 c m \).
Subject: Maths
The value of \( \lim _{n \rightarrow \infty} \sqrt{\frac{\mathbf{9}(i-1)}{n}} \cdot \frac{9}{n}=? \)
A \( \cdot \int_{0}^{9} \sqrt{x} d x \)
в. \( \int_{0}^{9} \sqrt{x}^{3} d x \)
\( \mathbf{c} \cdot \int_{0}^{9} \sqrt{9 x} d x \)
D. \( \int_{1}^{9} \sqrt{x} d x \)
Subject: Physics
A point charge \( q \) is palced on vertex of right circular cone. the semi-vertical
angle of cone
A. \( \frac{q}{\epsilon_{0}} \)
в. \( \frac{q}{2 \epsilon_{0}} \)
c. \( \frac{q}{3 \epsilon_{0}} \)
D. \( \frac{q}{4 \epsilon_{0}} \)
Subject: Physics
A Young's double slit experiment is conducted with slit separation \( 10 \mathrm{mm} \) where the screen is \( 2 \mathrm{m} \) away from the
slits. If wavelength of light used is \( 6000 \AA, \) then fringe width in 'mm' is
A . 0.12
B. 0.24
c. 0.36
D. 0.48
Subject: Physics
A current carrying loop is placed in a uniform magnetic field pointing in negative z direction. Branch PQRS is a tree quarter circle, while branch PS is straight. If force on branch PS is \( \mathrm{F} \), force on branch PQR is:
\( A \cdot \sqrt{2} F \)
в. \( \frac{F}{\sqrt{2}} \)
с. \( \frac{\pi F}{\sqrt{2}} \)
\( \mathbf{D} \cdot \sqrt{2} \pi F \)
Subject: Chemistry
For an ideal gas equation of a process for which the heat capacity of the gas varies with temperature as \( \mathrm{C}=\frac{\alpha}{T}(\alpha \) is a constant) is given by
A. \( V I n T= \) constant
в. \( \frac{1}{V T^{(\gamma-1)}} e^{\frac{\alpha}{R T}}= \) constant
c. \( \frac{1}{V^{(\gamma-1)}} T^{\frac{\alpha}{R T}}= \) constant
D. \( V^{\gamma-1} T= \) constant
Subject: Chemistry
IUPAC name of complex \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{A l}\left(\boldsymbol{C}_{\mathbf{2}} \boldsymbol{O}_{\mathbf{4}}\right)_{\boldsymbol{3}}\right] \)
is:
A. potassium alumino-oxalate
B. potassium trioxalatoaluminate (III)
c. potassium aluminium
(III) oxalate
D. potassium trioxalatoaluminate (IV)
Subject: Maths
Assertion
The matrix \( \left(\begin{array}{cccc}.1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 3 & 0\end{array}\right) \) is a
diagonal matrix
Reason
\( A=\left(a_{i j}\right)_{m \times m} \) is a square matrix such
that entry \( a_{i j}=0 \forall i \neq j, \) then \( A \) is
called diagonal matrix.
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A).
C. (A) is true but (R)is false,
D. (A) is false but (R ) is true.
Subject: Physics
A bullet leaves the rifle of mass one kg and the rifle recoils thereby with a velocity of \( 30 \mathrm{cm} / \mathrm{s} \). If the mass of bullet is \( 3 g, \) find the velocity of the bullet.
\( \mathbf{A} \cdot 10 m / s \)
в. \( 100 \mathrm{m} / \mathrm{s} \)
c. \( 200 m / s \)
D. \( 50 m / s \)
Subject: Maths
If \( \boldsymbol{x} \neq-\mathbf{5}, \) then the expression \( \frac{\mathbf{3} \boldsymbol{x}}{\boldsymbol{x}+\mathbf{5}} \div \)
\( \frac{6}{4 x+20} \) can be simplified to
A \( .2 x \)
в. \( \frac{x}{2} \)
c. \( \frac{9 x}{2} \)
D. \( 2 x+4 \)
Subject: Chemistry
Assertion
Dipole moment of \( N H_{3} \) is greater than
that of \( N F_{3} \)
Reason
Nitrogen is more electronegative than
fluorine.
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 parallel plate capacitor has plates
with area \( A \& \) separation \( d . A \) battery charges the plates to a potential
difference of \( V_{0} . \) The battery is then
disconnected \& a di-electric slab of
constant \( K \& \) thickness \( d \) is
introduced. Calculate the positive work done by the system (capacitor \( + \) slab) on the man who introduces the slab.
Subject: Maths
Suppose we know that \( f(x) \) is continuous and differentiable on the
interval \( [-7,0], \) that \( f(-7)=-3 \) and
that \( f^{\prime}(x) \leq 2 . \) What is the largest possible value for \( \boldsymbol{f}(\mathbf{0}) ? \)
A . 12
B. 22
c. 11
D . 24
Subject: Physics
A heavy uniform bar is being carried by two men on their shoulders. The weight
of the bar is \( w \). If one man lets it fall
from the end carried by him, what will be the weight experienced by the other person at the instant when the
other man releases the bar?
A. \( w / 4 \)
в. \( w / 2 \)
\( c . w \)
D. None of these
Subject: Maths
A point on the line \( \frac{\boldsymbol{x}+\mathbf{2}}{\mathbf{1}}=\frac{\boldsymbol{y}-\mathbf{3}}{-\mathbf{4}}= \)
\( \frac{z-1}{2 \sqrt{2}} \) at a distance 6 from the point \( (2, \)
3, 1) is
A \( \cdot(4-21,1+12 \sqrt{2}) \)
В. \( \left(\frac{-4}{5}, \frac{-9}{5}, 1\right) \)
C \( \cdot\left(\frac{-16}{5}, \frac{39}{5}, \frac{5-12 \sqrt{2}}{5}\right) \)
D. \( \left(\frac{-16}{5},-21,1+12 \sqrt{2}\right) \)
Subject: Maths
If the equation \( \sin ^{-1}\left(x^{2}+x+1\right)+ \)
\( \cos ^{-1}(\lambda x+1)=\frac{\pi}{2} \) has exactly two
solutions for \( \lambda \epsilon[a, b) \) then the value of
\( (a+b) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3
Subject: Maths
Given real numbers \( b \) and \( c \) such that
the product of 3 and \( c \) is \( b \). Which of the
following expressions represents, in terms of \( b \), the sum of \( c \) and \( 3 ? \)
A. \( b+3 \)
B. \( 3 b+3 \)
\( c \cdot 3(b+3) \)
D. \( \frac{b+3}{3} \)
E \( \frac{b}{3}+3 \)
Subject: Physics
The differential equation of a particle executing SHM along y-axis is
A \( \cdot \frac{d^{2} y}{d t^{2}}+\omega^{2} y=0 \)
B. \( \frac{d^{2} y}{d t^{2}}-\omega^{2} y=0 \)
\( ^{\text {C } \cdot \frac{d^{2} x}{d t^{2}}+\omega^{2} x=0} \)
D. \( \frac{d^{2} x}{d t^{2}}-\omega^{2} x=0 \)
Subject: Maths
\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{lll}\mathbf{5} & \mathbf{3} & \mathbf{8} \\ \mathbf{2} & \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}\end{array}\right|, \) write the minor of the
element \( a_{23} \)
Subject: Chemistry
The F-Xe-F bond angle in \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) is:
\( \mathbf{A} \cdot 109^{\circ} \)
B. \( 103^{\circ} \)
\( c .90^{\circ} \)
D. \( 60^{\circ} \)
Subject: Physics
A block of weight 15 N slides on a horizontal table the co-efficient of
sliding friction is \( 0.4 . \) The area of the
block in contact with the table is
\( 0.05 m^{2} . \) The shearing stress will be
B. \( 140 N m^{-2} \)
c. \( 160 N m^{-2} \)
D. \( 180 N m^{-2} \)
Subject: Chemistry
The efficiency of a fuel cell is \( 80 \% \) and the standard heat of reaction is
\( -300 k J . \) The reaction involves two
electrons in redox change. \( \boldsymbol{E}^{\ominus} \) for the
cell is:
A . \( 1.24 V \)
B . \( 2.48 V \)
c. \( 0 V \)
D. \( 0.62 V \)
Subject: Maths
Select the correct option given below:
n \( \triangle A B C, D, E \) and \( F \) are midpoint of \( A B, B C \) and \( A C \) respectively. If
perimeter of \( \triangle A B C=40 \) then find the
perimeter of \( \triangle D E F \)
4.10
в. \( \frac{40}{3} \)
\( c \cdot 20 \)
D.
Subject: Chemistry
Given a sample of one mole of the indicated gas at the following
conditions
Which of the following has the highest molecular speed?
A \( . H e \) at \( 100^{\circ} \mathrm{C} \) and 1 atm
B. \( H e \) at \( 25^{\circ} C \) and 1 atm
c. \( A r \) at \( 25^{\circ} C \) and 1 atm
D. \( A r \) at \( 25^{\circ} C \) and 2 atm
E. \( A r \) at \( 0^{\circ} C \) and 1 atm
Subject: Chemistry
List-I \( \quad \) List-II If \( r \)
\( (A) \)
, Angular
(1) \( 119.5^{\circ} \)
\( S_{O_{3}} \) anguiar
(B) \( 116.8^{\circ}, \) Angular (2) \( \mathrm{SO}_{2} \) 'Angular A
\( (C) \)
\( \mathrm{H}_{2} \mathrm{O} \)
(3) \( 120^{\circ} \), Trigonal pyramidal of The and dal
\( (D) \)
(4) \( 104.5^{\circ}, \) Angular \( \mathrm{O}_{3} \) \( 104.5^{\circ}, \mathrm{Ar} \) idr The correct match is:
\( A \cdot(A)-3,(B)-1,(C)-4,(D)-2 \)
B. \( (A)-2,(B)-3,(C)-1,(D)-4 \)
C \( \cdot(A)-4,(B)-2,(C)-3,(D)-1 \)
D. \( (A)-1,(B)-2,(C)-4,(D)-3 \)
Subject: Physics
Two waves are travelling in the same direction along a stretched string. The
waves are \( 90^{0} \) out of phase. Each wave
has an amplitude of \( 4.0 \mathrm{cm} . \) The amplitude of the resultant wave is
\( 5.66 \times 10^{-x} \) m. Find \( x \)
\( A \)
B. 2
\( c \cdot 8 \)
D. 4
Subject: Physics
Length, breadth and thickness of a rectangular slab are \( 4.234 \mathrm{m}, 1.005 \mathrm{m} \) and \( 2.01 \mathrm{m} \) respectively. Find volume of the slab to correct significant figures.
\( \mathbf{A} \cdot 8.55 m^{3} \)
в. \( 8.552 m^{3} \)
c. \( 8.6 m^{3} \)
D. None of the above
Subject: Physics
\( A 20 \mathrm{kg} \) block is in motion on a rough horizontal surface. A horizontal force of
\( 60 \mathrm{N} \) is required to keep the body moving with constant speed. Then find coefficient of kinetic friction? \( (\mathrm{g}=10 \mathrm{m} \)
\( \left.s^{-2}\right) \)
A. 0.4
B. 0.3
\( c \cdot 0.8 \)
D. 0.6
Subject: Chemistry
Addition of which of the following material to water does not make it
hard?
\( \mathbf{A} \cdot M g_{3}\left(P O_{4}\right)_{2} \)
B. \( \operatorname{Fe}\left(\mathrm{NO}_{3}\right)_{3} \)
c. \( V\left(N O_{3}\right)_{3} \)
D. \( T i\left(C l O_{4}\right)_{4} \)
Subject: Physics
A body is freely rolling down on an
inclined plane whose angle of inclination is \( \theta . \) If \( a \) is acceleration of
it's centre of mass then which of the
relation holds true? ( Given acceleration
due to gravity \( =g) \)
A \( . a=g \sin \theta \)
B. \( a<g \sin \theta \)
c. \( a>g \sin \theta \)
\( \mathbf{D} \cdot a=0 \)
Subject: Physics
The displacement of a particle of mass
\( 3 g m \) executing simple harmonic motion is given by \( y=3 \sin (0.2 t) \) in \( s \)
units. The kinetic energy of the particle at a point which is at a distance equal to \( \frac{1}{3} \) of its amplitude from its mean position is
A \( \cdot 12 \times 10^{-3} J \)
\( J \)
B . \( 25 \times 10^{-3} J \)
c. \( 0.48 \times 10^{-3} J \)
D. \( 0.24 \times 10^{-3} \mathrm{J} \)
Subject: Physics
Determine the pressure required to reduce the given volume of water by \( 2 \% \) Bulk modulus of water is \( 2.2 \times \)
\( 10^{4} N m^{-2} \)
A \( \cdot 4.4 \times 10^{7} \mathrm{Nm}^{-2} \)
В. \( 2.2 \times 10^{7} N m^{-2} \)
c. \( 3.3 \times 10^{7} \mathrm{Nm}^{-2} \)
D. \( 1.1 \times 10^{7} N m^{-2} \)
Subject: Maths
\( \lim _{n \rightarrow \infty} \frac{\left(1^{k}+2^{k}+3^{k}+\ldots . .+n\right.}{\left(1^{2}+2^{2}+\ldots . .+n^{2}\right)\left(1^{3}+2^{3}+\right.} \)
\( \boldsymbol{F}(\boldsymbol{k}), \) then \( (\boldsymbol{k} \in \boldsymbol{N}) \)
A. \( F(k) \) is finite for \( k \leq 6 \)
В. \( F(5)=0 \)
c. \( F(6)=\frac{12}{7} \)
D. \( F(6)=\frac{5}{7} \)
Subject: Chemistry
Assertion
\( P C l_{5} \) is a covalent in gaseous and
liquid states but ionic in solid state.
Reason
\( P C l_{5} \) in solid state consists of
tetrahedral \( P C l_{4}^{+} \) cation and octahedral
\( P C l_{6}^{-} \) anion
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
\( \ln S H M \) restoring force is \( F=-k x \)
where \( k \) is force constant, \( x \) is
displacement and \( a \) is amplitude of
motion, then total energy depends upon
A. \( k, a \) and \( m \)
в. \( k, x, m \)
c. \( k, a \)
D. \( k, x \)
Subject: Biology
The table given below shows a list of
organisms and their methods of
reproduction
What do \( P, Q \) and \( R \) repersent?
\begin{tabular}{|l|c|}
\hline Organism & Method of reproduction \\
\hline Sponge & \( \mathrm{P} \) \\
Planaria & \( \mathrm{Q} \) \\
Hydra & \( \mathrm{R} \) \\
\hline
\end{tabular}
A. P- Fission, Q - Budding,
R - Regeneration
B. P- Sporulation, Q - Regeneration,
\( \mathrm{R} \) - Budding
C. P- Binary fission,
Q- Sporulation,
R - Regeneration
D. P - Gemmules, Q - Regeneration,
R - Budding
Subject: Maths
If \( \bar{a}, \bar{b}, \bar{c} \) are position vectors of the noncollinear points \( A, B, C \) respectively, the shortest distance of \( A \) and \( B C \) is?
A. \( \bar{a} \cdot(\bar{b}-\bar{c}) \)
a)
в. \( \bar{b} \cdot(\bar{c}-\bar{a}) \)
c. \( |\bar{b}-\bar{a}| \)
D \( \cdot \sqrt{|\vec{b}-\vec{a}|^{2}-\left[\frac{(\vec{a}-\vec{b} \cdot(\vec{b}-\vec{c})}{|\vec{b}-\vec{c}|}\right)^{2}} \)
Subject: Chemistry
In
\( 0.1 \mathrm{M} \) solution, weak electrolyte,
\( C H_{3} C O O H \) is \( 1.3 \% \) dissociated. If 100
molecules of \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) are placed originally in the solution, how many acid molecules remain nonionized at
equilibrium?
Subject: Maths
If \( \sin ^{-1}(1-x)-2 \sin ^{-1} x=\frac{\pi}{2}, \) then \( x \)
is equal to
A \( \cdot 0, \frac{1}{2} \)
в. \( _{1, \frac{1}{2}} \)
\( c \cdot \frac{1}{2} \)
D.
Subject: Maths
Solve
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{a}(\boldsymbol{b}+\boldsymbol{c}) \\ \mathbf{1} & \boldsymbol{c} \boldsymbol{a} & \boldsymbol{b}(\boldsymbol{c}+\boldsymbol{a}) \\ \mathbf{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{c}(\boldsymbol{a}+\boldsymbol{b})\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot a b c \)
D. \( a b+b c+c a \)
Subject: Physics
A particle moves along positive branch of the curve, \( y=\frac{x}{2}, \) where \( x=\frac{t^{3}}{3}, x \) and
\( y \) are measured in maters and \( t \) in
second, then:
This question has multiple correct options
A ' the velocity of particle at \( t=1 s \) is \( \hat{i}+\frac{1}{2} \hat{j} \)
B \cdot The velocity of particle at \( t=1 s \) is \( \frac{1}{2} \hat{i}+\hat{j} \)
C. The acceleration of particle at \( t=2 s \) is \( 2 \hat{i}+\hat{j} \)
D. The acceleration of particle at \( t=2 s \) is \( \hat{i}+2 \hat{j} \)
Subject: Physics
Assuming \( i=i_{0} \) at \( t=0 ; \) The current at
any instant in the loop is after
the external field has stopped changing
A. \( _{i=i_{0} e^{\frac{-2 R t}{\mu_{0} \pi a}}} \)
в. \( \quad_{i=i_{0} e^{\frac{-R t}{\mu_{0} \pi a}}} \)
\( \mathrm{c} \cdot_{i=i_{0} e^{\frac{2 R t}{\mu_{0} \pi a}}} \)
D. \( _{i=i_{0} e^{\frac{-R t}{2 \mu_{0} \pi a}}} \)
Subject: Physics
Two blocks \( A \) and \( B \) of masses \( m \) and
\( 2 \mathrm{m} \) respectively placed on a smooth floor are connected by a spring. A third body \( C \) of mass \( m \) moves with velocity
\( \boldsymbol{v}_{0} \) along the line joining \( \mathbf{A} \) and \( \mathbf{B} \) and collides elastically with A. At a certain instant of time after collision it is found
that the instantaneous velocities of \( A \)
and \( \mathrm{B} \) are same then :
A. the common velocity of A and B at time to is \( v / 3 \).
в.
\[
\text { the spring constant is } \mathrm{k}=\frac{3 m v_{0}^{2}}{2 x_{0}^{2}}
\]
\( c \)
\[
\text { the spring constant is } \mathrm{k}=\frac{2 m v_{0}^{2}}{3 x_{0}^{2}}
\]
D. none of these
Subject: Maths
Arrange the following decimal numbers in ascending order.
5.5,0.55,0.055,0.005
A. 5.5,0.055,0.005,0.55
В. 0.55,0.005,0.055,5.5
c. 5.5,0.55,0.055,0.005
D. 0.005,0.055,0.55,5.5
Subject: Physics
Two point charges \( Q \) and \( -Q / 4 \) placed
along the \( x \) -axis are separated by a
distance \( r . \) Take \( -Q / 4 \) as origin and it
is placed at the right of \( Q . \) Then
the potential is zero.
\( \mathbf{A} \cdot \) at \( x=r / 3 \) only
B. at \( x=-r / 5 \) only
C. both at \( x=r / 3 \) and at \( x=-r / 5 \)
D. there exist two points on the axis where the electric field is zero
Subject: Maths
In the following figure, \( A B C D \) is a rhombus and \( D C E F \) is a square.
If \( \angle A B C=56^{\circ} \), find
\( \angle D A E \)
\( \angle \boldsymbol{F} \boldsymbol{E} \boldsymbol{A} \)
\( \angle E A C \)
\( \angle A E C \)
+ Option
Subject: Physics
A uniformly tapering vessel shown in figure, is filled with liquid of density
\( 900 k g / m^{3} . \) The force that acts on the base of the vessel due to liquid is :
\( A \cdot 3.6 \mathrm{N} \)
в. 7.2
\( c \cdot 9.0 \mathrm{N} \)
D. 12.6
Subject: Chemistry
Give the IUPAC name for the following alcohols. Classify as primary or secondary or teritiary alcohol \( \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
\( \boldsymbol{O H} \)
Subject: Chemistry
Arrange the following set of atoms in the order of increasing atomic radius:
\( \boldsymbol{F}, \boldsymbol{C l}, \boldsymbol{C}, \boldsymbol{O} \)
A. \( F, C l, O, C \)
в. \( C, O, F, C l \)
c. \( O, C, F, C l \)
D. \( F, O, C, C l \)
Subject: Chemistry
Choose the correct answer among the alternatives given :
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \stackrel{[a l c K O \boldsymbol{H}]}{\longrightarrow} \)
\( B r \)
\( \boldsymbol{X} \frac{\text {peroxide}}{\boldsymbol{H B r}} \boldsymbol{Y} \frac{\text {acetone}}{\boldsymbol{N a I}} \boldsymbol{Z} \)
In the given reaction what will be the final product?
A. \( C H_{3} C H_{2} C H_{2} I \)
в. \( C H_{3} C H_{2} I \)
c. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3} \)
D. \( C H_{3} C H_{2} C H I_{2} \)
Subject: Chemistry
Choose the correct answer among the
alternatives given :
In the following pairs of halogen
compounds, which compound
undergoes faster \( \boldsymbol{S}_{N} 1 \) reaction?
\( (\mathrm{i}) \)
\( A \)
(i)
(ii)
B.
(i)
(ii)
\( c \)
(i)
(ii)
\( D \)
(i)
(ii)
Subject: Physics
A body freely falls from a certain height
on to the ground in a time \( t . \) During the
first one third of the time interval it
gains a kinetic energy \( \Delta k_{1} \) and during the last one-third of the interval, it gains
a kinetic energy \( \Delta k_{2} \). The ratio \( \Delta k_{1} \)
\( \boldsymbol{\Delta} \boldsymbol{k}_{2} \) is:
A . 1: 1
B. 1: 3
c. 1: 4
D. 1: 5
Subject: Maths
To change \( (3 x+4 y+5)-(2 x+3 y+ \)
4) \( \frac{d y}{d x}=0 \) into homogeneous equation
origin is shifted to \( (\boldsymbol{h}, \boldsymbol{k}) \) then \( \boldsymbol{h}+\boldsymbol{k}= \)
\( A \cdot 3 \)
B.
c. -2
D. -
Subject: Maths
If \( \alpha \) and \( \beta \) are angles in the first quadrant \( \tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}} \) then
using the formula \( \sin (A+B)= \)
\( \sin A \cos B+\cos A \sin B \) one can find
the value of \( (\boldsymbol{\alpha}+\mathbf{2} \boldsymbol{\beta}) \) to be
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60 \)
D. \( 90^{\circ} \)
Subject: Physics
If \( X, F \) and \( U \) respectively denotes displacement, force acting on a particle and potential energy of a particle, then:
A \( . U=F \)
B. \( F=+\frac{d U}{d x} \)
c. \( F=-\frac{d U}{d x} \)
D. \( F=\frac{1}{x}\left(\frac{d U}{d x}\right) \)
Subject: Maths
\( \left(x^{2} y-2 x y^{2}\right) d x=\left(x^{3}-3 x^{2} y\right) d y \)
A \( \cdot k y^{3} e^{x / y}=x^{2} \)
B. \( k x^{3} e^{x / y}=x^{2} \)
c. \( k x^{3} e^{x / y}=y^{2} \)
D. \( k y^{3} e^{x / y}=y^{2} \)
Subject: Physics
If a diffraction peak is observed when
electrons are incident at an angle \( ^{\prime} \boldsymbol{i}^{\prime} \)
from the normal to the crystal planes
with distance ' \( d^{\prime} \) between them (see
figure), de-Broglie wavelength \( \lambda_{d B} \) of
electrons can be calculated by the
relationship \( (n \text { is an integer }) \)
\( \mathbf{A} \cdot d \sin i=n \lambda_{d B} \)
B . \( 2 d \cos i=n \lambda_{d B} \)
\( \mathbf{c} \cdot 2 d \sin i=n \lambda_{d B} \)
\( \mathbf{D} \cdot d \cos i=n \lambda_{d B} \)
Subject: Maths
\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left(\frac{\cos \boldsymbol{x}}{\mathbf{1}+\sin \boldsymbol{x}}\right) \)
A. \( -\frac{1}{2} \)
B. \( -\frac{1}{4} \)
\( c \cdot-\frac{1}{8} \)
D. 3