AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If the general solution of some
differential equation is \( \boldsymbol{y}=\boldsymbol{a}_{1}\left(\boldsymbol{a}_{2}+\right. \)
\( \left.\boldsymbol{a}_{3}\right) \cdot \cos \left(\boldsymbol{x}+\boldsymbol{a}_{4}\right)-\boldsymbol{a}_{5} \boldsymbol{e}^{x+\boldsymbol{a}_{6}} \quad \) then order
of differential equation is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 5
\( c \cdot 4 \)
D. 3
Subject: Chemistry
\( \boldsymbol{B e}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \rightarrow \boldsymbol{H}-\boldsymbol{C} \equiv \)
\( C-H \)
The reagents for the following conversion, is/are:
A. Alcoholic \( K O H \)
B. Alcoholic KOH followed by \( \operatorname{NaNH}_{2} \)
C. Aqueous KOH followed by NaNH
D. \( Z n / C H_{3} O H \)
Subject: Maths
The radius of two cylinders are in the ratio 2: 3 and their heights are in the
ratio \( 3: 5 . \) Find the ratio of their
volumes.
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{5} \)
c. \( \frac{4}{15} \)
D. \( \frac{3}{2} \)
Subject: Chemistry
What mass of \( H_{2} S O_{4} \) could be
produced in the process given below if \( 1.00 k g \) of \( F e S_{2} \) is used? The
unbalanced equations for the process
are:
\[
\begin{array}{l}
\boldsymbol{F e} \boldsymbol{S}_{2}+\boldsymbol{O}_{2} \longrightarrow \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{S} \boldsymbol{O}_{2} \\
\boldsymbol{S} \boldsymbol{O}_{2}+\boldsymbol{O}_{2} \longrightarrow \boldsymbol{S} \boldsymbol{O}_{3} \\
\boldsymbol{S} \boldsymbol{O}_{3}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7} \\
\boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}
\end{array}
\]
A . \( 1.55 \mathrm{kg} \)
в. \( 1.63 \mathrm{kg} \)
c. \( 3.26 \mathrm{kg} \)
D. \( 1.65 \mathrm{kg} \)
Subject: Physics
In a Rutherford scattering experiment
when a projectile of charge \( Z_{1} \) and
mass \( M_{1} \) approaches a target nucleus
of charge \( Z_{2} \) and mass \( M_{2} \), the
distance of closest approach is \( r_{0} . \) The
energy of the projectile is :
A . Directly proportional to mass \( M_{1} \)
B. Directly proportional to \( M_{1} \times M_{2} \)
C. Directly proportional to \( Z_{1} Z_{2} \)
D. Inversely proportional to \( Z_{1} \)
Subject: Physics
A particle of mass \( 1 g \) moving with a velocity \( \vec{v}_{1}=3 \hat{i}-2 \hat{j} m s^{-1} \) experiences
a perfectly in elastic collision with another particle of mass \( 2 g \) and velocity \( \vec{v}_{2}=4 \hat{j}-6 \hat{k} m s^{-1} . \) The velocity
of the particle is:
\( \mathbf{A} \cdot 2.3 \mathrm{ms}^{-1} \)
B . \( 4.6 \mathrm{ms}^{-1} \)
c. \( 9.2 \mathrm{ms}^{-1} \)
D. \( 6 m s^{-1} \)
Subject: Chemistry
The solubility of \( N_{2} \) in water at \( 300 \mathrm{K} \) and 500 torr, partial pressure is \( 0.01 \mathrm{g} \) \( L^{-1} . \) The solubility \( \left(\operatorname{in} g L^{-1}\right) \) at 750 torr partial pressure is:
A. 0.0075
B. 0.015
c. 0.02
D. 0.005
Subject: Chemistry
Hydrogen peroxide oxidises \( \left[\boldsymbol{F e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-} \) to \( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{3-} \) in acidic
medium but reduce \( \left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{3-} \) to
\( \left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{4-} \) in alkaline medium. The
other products formed are, respectively:
\( \mathbf{A} \cdot H_{2} O \) and \( \left(H_{2} O+O_{2}\right) \)
B. \( H_{2} O \) and \( \left(H_{2} O+O H^{-}\right) \)
\( \mathrm{c} \cdot\left(\mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\right) \) and \( \mathrm{H}_{2} \mathrm{O} \)
D. \( \left(H_{2} O+O_{2}\right) \) and \( \left(H_{2} O+O H^{-}\right) \)
Subject: Maths
Let \( A B \) and \( C D \) be two parallel lines and \( \stackrel{\leftrightarrow}{P Q} \) be a transversal. Let \( \stackrel{\leftrightarrow}{P Q} \)
intersect \( A^{\leftrightarrow} B \) in \( L . \) Suppose the bisector
of \( \angle A L P \) intersect \( C D \) in \( R \) and the bisector of \( \angle P L B \) intersect \( \stackrel{\leftrightarrow}{C D} \) in \( \mathrm{S} \)
Prove that
\( \angle \boldsymbol{L} \boldsymbol{R} \boldsymbol{S}+\angle \boldsymbol{R} \boldsymbol{S} \boldsymbol{L}=\boldsymbol{9} \boldsymbol{0}^{\boldsymbol{o}} \)
Subject: Maths
The real part of \( (1-\cos \theta+2 i \sin \theta)^{-1} \)
is
A. \( \frac{1}{3+5 \cos \theta} \)
B. \( \frac{1}{5-3 \cos \theta} \)
C. \( \frac{1}{3-5 \cos \theta} \)
D. \( \frac{1}{5+3 \cos \theta} \)
Subject: Chemistry
\( \boldsymbol{C a} \boldsymbol{C O}_{\boldsymbol{3}(\boldsymbol{s})} \rightarrow \boldsymbol{C a O}_{(s)}+\boldsymbol{C O}_{\boldsymbol{2}(\boldsymbol{g})} \boldsymbol{\Delta} \boldsymbol{H}= \)
\( +180 K J \)
If entropies of limestone, lime and carbon dioxide are 93,39 and
\( \mathbf{2 1 3} \boldsymbol{J} / \boldsymbol{m o l} / \boldsymbol{K} . \) Then \( \boldsymbol{\Delta} \boldsymbol{S}_{\boldsymbol{t o t a l}} \) in \( \boldsymbol{J} \boldsymbol{K}^{-1} \) at
\( \mathbf{3 0 0 K} \) is:
A. 159
в. -44
\( c .700 \)
D. - 650
Subject: Physics
When a liquid taken in along cylindrical vessel of material with linear coefficient
of expansion \( (\alpha) \) is heated, the level of
liquid did not change. The volume coefficient of expansion of liquid is :
A \( \cdot \frac{\alpha}{3} \)
B. \( 3 \alpha \)
\( c \cdot a \)
D. \( \alpha^{3} \)
Subject: Chemistry
The energy required to break one mole
of \( C l-C l \) bond in \( C l_{2} \) in
\( 242 k J \) mol \( ^{-1} . \) The longest wavelength
of light capable of breaking a single \( C l-C l \) bond is:
\( \left[c=3 \times 10^{4} m s^{-1} \text {and } N_{A}=6.02 \times\right. \)
\( \left.10^{23} m o l^{-1}\right] \)
A. 594 nm
B. 640 nm
c. 700 nm
D. 494 nm
Subject: Chemistry
Shape of \( N H_{3} \) is very similar to:
This question has multiple correct options
A \( \cdot \operatorname{Se} O_{3}^{2-} \)
B. \( C H_{3}^{-} \)
\( \mathbf{c} . B H_{3} \)
D. \( C H_{3}^{+} \)
Subject: Maths
\( \ln \) a rhombus \( \boldsymbol{A B C D}, \angle \boldsymbol{A}=\mathbf{6 0}^{\circ} \) and
\( A B=6 \mathrm{cm} . \) Then the diagonal \( B D \) is
A \( \cdot 2 \sqrt{3} c m \)
в. 6 ст
c. \( 12 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)
Subject: Physics
A prism having an apex angle 40 and
refractive index 1.5 is located in front of
a vertical plane mirror as shown in
figure. Through what total angle is the ray deviated after reflection from the
A \( \cdot 176^{\circ} \)
\( \mathbf{B} \cdot 4^{0} \)
\( c \cdot 178 \)
\( D \cdot 2 \)
Subject: Chemistry
Assertion
Ethane is a gas while ethyl alcohol is a
İiquid.
Reason
Ethyl alcohol has greater molecular
mass than ethane.
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
Find the mode of the following data.
\begin{tabular}{lllll}
\multirow{2}{*} { Number } & \( \mathbf{0}- \) & \( \mathbf{3}- \) & \( \mathbf{6}- \) & \( \mathbf{9}- \) \\
& \( \mathbf{3} \) & \( \mathbf{6} \) & \( \mathbf{9} \) & \( \mathbf{1 2} \)
\end{tabular}
Frequency \( \quad 4 \quad 18 \) 9
A . 19
B. 31
c. 26
D. 2
Subject: Maths
If \( \boldsymbol{A}-\boldsymbol{B}=\boldsymbol{\phi} \) and \( \boldsymbol{B}-\boldsymbol{A}=\boldsymbol{\phi} \) then \( \mathbf{A} \)
and B are
A. Overlapping
B. Equivalent
c. Dissiont
D. Equal
Subject: Chemistry
Which of the following molecule has
\( O-O \) bond?
This question has multiple correct options
\( \mathbf{A} \cdot H_{2} S_{2} O_{8} \)
\( \mathbf{B} \cdot H_{2} S_{2} O_{7} \)
\( \mathbf{c} \cdot H_{2} S O_{5} \)
\( \mathbf{D} \cdot H_{2} S_{2} O_{6} \)
Subject: Physics
Two parallel and opposite forces each \( \mathbf{5 0 0 0} N \) are applied tangentially to the upper and lower faces of a cubical
metal block of side \( 25 \mathrm{cm} . \) The angle of
shear is then
(The shear modulus of the metal is
\( 80 G P a) \)
A \( \cdot 10^{-4} x a d \)
B \( \cdot 10^{-5} r a d \)
c. \( 10^{-6} \)rad
D. \( 10^{-7} r a d \)
Subject: Physics
The Young's modulus of the material of a wire is \( 6 \times 10^{12} N / m^{2} \) and there is no
transverse in it, then its modulus of rigidity will be
A \( \cdot 3 \times 10^{12} N / m^{2} \)
В . \( 2 \times 10^{12} N / m^{2} \)
C \( \cdot 10^{12} N / m^{2} \)
D. None of the above
Subject: Physics
A mass \( \mathrm{M} \) is lowered with the help of a string by a distancex at a constant
acceleration \( \frac{\mathrm{g}}{2} . \) The magnitude of work doneby the string will be:
\( ^{\mathbf{A}} \cdot \frac{M g}{2} k \)
B - \( \frac{1}{2} M g x^{2} \)
\( \mathbf{c} \cdot \frac{1}{2} M g x \)
D. \( M g x^{2} \)
Subject: Physics
The component of vector \( \vec{a}=2 \hat{i}+3 \widehat{j} \)
along the vector \( \hat{\boldsymbol{i}}+\widehat{\boldsymbol{j}} \) is:
A \( \cdot \frac{5}{\sqrt{2}} \)
в. \( 10 \sqrt{2} \)
c. \( 5 \sqrt{2} \)
D.
Subject: Chemistry
When \( O_{2} \) is absorbed on a metallic
surface, electron transfer occurs from
the metal to \( O_{2} \). The true statement(s)
regarding this adsorption is(are):
This question has multiple correct options
A. \( O_{2} \) is physisorbed
B. heat is released
C. occupancy of \( \pi_{x_{p}^{*}} \) of \( O_{2} \) is increased
D. bond length of \( O_{2} \) is increased
Subject: Physics
In a series RLC circuit, the r.m.s. the
voltage across the resistor and the
inductor are respectively \( 400 \mathrm{V} \) and
\( 700 V . \) If the equation for the applied voltage is \( \varepsilon=500 \sqrt{2} \sin \omega t, \) then the
peak voltage across the capacitor is
B. \( 400 \sqrt{2} V \)
c. \( 400 V \)
D. \( 1200 \sqrt{2} \mathrm{V} \)
Subject: Maths
If \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{8}\}, \) then
\( (\boldsymbol{A} \cup \boldsymbol{B}) \times(\boldsymbol{A} \cap \boldsymbol{B}) \) is
A \( \cdot\{(3,1),(3,2),(3,3),(3,8)\} \)
B・ \{(1,3),(2,3),(3,3),(8,3)\}
c. \{(1,2),(2,2),(3,3),(8,8)\}
D \( \cdot\{(8,3),(8,2),(8,1),(8,8)\} \)
Subject: Physics
A rectangular loop PQRS, is being pulled
with constant speed into a uniform
transverse magnetic fieldby a force (as shown). E.m.f. induced in side PS
and potential difference between points
Pand S respectively are (Resistance of the \( \operatorname{loop}=r) \)
A \( \cdot \) zero, \( \frac{F r}{B \ell} \)
B. Zero, zero
c. zero, \( \frac{F r}{6 B \ell} \)
D. \( \frac{F r}{6 B \ell}, \frac{F r}{6 B \ell} \)
Subject: Chemistry
Assertion
The acid hydrolysis of ester takes place
more rapidly in \( D_{2} O \) than \( H_{2} O \)
Reason
\( D_{3} O^{+} \) is stronger acid than \( H_{3} O^{+} \)
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 is incorrect but Reason is correct
Subject: Physics
The number density of molecules of a
gas depends on their distance \( r \) from the origin as, \( n(r)=n_{0} e^{-\alpha r^{4}} . \) Then the
total number of molecules is
proportional to:
A \( \cdot n_{0} \alpha^{1 / 4} \)
B . \( n_{0} \alpha^{-3} \)
\( \mathbf{c} \cdot n_{0} \alpha^{-3 / 4} \)
D. \( \sqrt{n_{0}} \alpha^{1 / 2} \)
Subject: Maths
In the figure the boundary of the shaded region consists of four semicircular
\( \operatorname{arcs}, \) the smallest two being equal. If the
diameter of the largest is \( 14 \mathrm{cm} \) and of
the smallest is \( 3.5 \mathrm{cm}, \) find
1. The length of the boundary
2. The area of the shaded region
Subject: Maths
If \( a>0, b>0, c>0 \) and the minimum value
of \( \boldsymbol{a}\left(\boldsymbol{b}^{2}+\boldsymbol{c}^{2}\right)+\boldsymbol{b}\left(\boldsymbol{c}^{2}+\boldsymbol{a}^{2}\right)+\boldsymbol{c}\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right) \)
is \( \lambda a b c \), then \( \lambda \) is
\( A \cdot 2 \)
в.
\( c \cdot 6 \)
D.
Subject: Chemistry
In the reaction : \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]+ \)
\( K_{2} C O_{3} \rightarrow \) the product formed is :
A \( . F e C O_{3} \)
в. \( K C N \)
c. \( K F e C O_{3} \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)
Subject: Physics
Assertion
Peak value of current in \( \boldsymbol{A} \boldsymbol{C} \) through a
resistance of \( 10 \Omega \) is \( 2 A \). Then power
consumed by the resistance should be \( \mathbf{2 0} \boldsymbol{W} \)
Reason
Power in \( \boldsymbol{A C} \) is \( \boldsymbol{P}=\boldsymbol{I}_{r m s}^{2} \boldsymbol{R} \)
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
Solve the following puzzles using the
equations:

The present age of Beena is 2 years
more than Reeta.The present age of Teena is 3 years more than Beena.If the
sum of the ages of Reeta, Beena, and Teena is 79 years, find the present age of all the three of them.
A. Reeta 24 years, Beena 26 years, Teena 29 years
B. Reeta 24 years, Beena 21 years, Teena 29 years
c. Reeta 24 years, Beena 29 years, Teena 29 years.
D. Reeta 24 years, Beena 26 years, Teena 30 years
Subject: Maths
Determine the factors of \( 216 u^{3}+1 \)
A \( \cdot(6 u-1)\left(36 u^{2}-6 u+1\right) \)
B . \( (6 u+1)\left(36 u^{2}-6 u+1\right) \)
c. \( (6 u+1)\left(6 u^{2}-6 u+1\right) \)
D. \( (u+1)\left(6 u^{2}-6 u+1\right) \)
Subject: Chemistry
The number of electrons required to balance the given equation is
\( N O_{3}^{-}+4 H^{+}+e^{-} \longrightarrow 2 H_{2} O+N O \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 2
\( c \cdot 3 \)
D.
Subject: Maths
\( \sin h^{-1}\left(2^{3 / 2}\right)= \)
\( \mathbf{A} \cdot \log (2+\sqrt{8}) \)
B. \( \log (3+\sqrt{8}) \)
C \( \cdot \log (2-\sqrt{8}) \)
\( \mathbf{D} \cdot \log (\sqrt{8}+\sqrt{7}) \)
Subject: Chemistry
\( \boldsymbol{C}(\text {diamond})+\mathbf{2} \boldsymbol{H}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{C H}_{4}(\boldsymbol{g}) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
\( \mathbf{A} \cdot \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
\( \mathbf{c} \cdot \Delta H<\Delta U \)
D. None of these
Subject: Chemistry
Give the IUPAC name for the following alcohols. Classify as primary or secondary or teritiary alcohol \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\underset{\boldsymbol{o} \boldsymbol{H}}{\boldsymbol{C}} \boldsymbol{H}-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
Subject: Physics
A charge \( Q \) is to be divided into two parts such the force between them is
maximum. They should be divided as
A \( \cdot \frac{Q}{4}, \frac{3 Q}{4} \)
B . \( \frac{a}{3}, \frac{20}{3} \)
c. \( \frac{a}{8}, \frac{7 Q}{8} \)
D. \( \frac{Q}{2}, \frac{a}{2} \)
Subject: Maths
Let \( s_{1}(n) \) be the sum of the first n terms
of the arithmetic progression \( 8,12,16, \)
and let \( s_{2}(n) \) be the sum of the first \( n \)
terms of arithmetic progression 17,19,21
.... If for some value of \( n, s_{1}(n)=s_{2}(n) \)
then this common sum is
A. not uniquely determinable
B. 260
\( c \cdot 216 \)
D. 200
Subject: Physics
A particle is moving in \( x \) -y plane. At time \( t=0, \) particle is at \( (1 \mathrm{m}, 2 \mathrm{m}) \) and has velocity \( (4 \hat{i}+6 \hat{j}) \mathrm{m} / \mathrm{s}, \) At \( t=4 \mathrm{s} \)
particle reaches at \( (6 \mathrm{m}, 4 \mathrm{m}) \) and has velocity \( (2 \hat{i}+10 \hat{j}) \mathrm{m} / \mathrm{s} \). In the given time interval, find.
(a) average velocity,
(b) average acceleration and
(c) from the given data, can you find average speed?
Subject: Maths
Find the equation of the circle:
Centered at (3,-2) with radius 4
\( \mathbf{A} \cdot x^{2}+y^{2}+6 x-4 y=3 \)
B \( \cdot x^{2}+y^{2}-6 x+4 y=3 \)
C \( \cdot x^{2}+y^{2}-3 x+2 y=-3 \)
D. \( x^{2}+y^{2}+3 x-2 y=-3 \)
Subject: Maths
The value of \( \sin ^{-1}\left(\sin 5 \frac{\pi}{3}\right)= \)
A \( \cdot-\frac{\pi}{3} \)
B .
\( \mathbf{c} \cdot \frac{4 \pi}{3} \)
D. \( \frac{3 \pi}{3 \pi} \)
Subject: Maths
Below is given frequency distribution of driving speed (in kms/hour) of a vehicle of 400 college students.
Speed 20
in \( \begin{array}{llll}\operatorname{lm} s / h r) & -30 & 40 & 50 & 60 \\ & 40 & 50 & 60\end{array} \)
No. of \( \quad 6 \quad \) 80 \( \quad 156 \quad 98 \) students

Find modal driving speed of college students.
A. \( 41.67 \mathrm{kms} / \) hour
B. \( 45.67 \mathrm{kms} / \) hour
c. \( 49.67 \mathrm{kms} / \) hour
D. \( 53.67 \mathrm{kms} / \) hour
Subject: Physics
Two particles move parallel to \( x- \) axis
about the origin with same amplitude
\( a^{\prime} \) and frequency \( \omega . \) At a certain instant they are found at a distance \( a / 3 \) from
the origin on opposite sides but their velocities are in the same direction.
What is the phase difference between the two?
A \( \cdot \cos ^{-1} \frac{7}{9} \)
B. \( \cos ^{-1} \frac{5}{9} \)
\( ^{\mathbf{C}} \cdot \cos ^{-1} \frac{4}{9} \)
D. \( \cos ^{-1} \frac{1}{9} \)
Subject: Chemistry
\[
\begin{array}{c}
\boldsymbol{M} \boldsymbol{X}(\mathbf{s o l i d})+\boldsymbol{E}_{1} \rightarrow \boldsymbol{M}^{+}+\boldsymbol{X}^{-} ; \\
\boldsymbol{M}^{+}+\boldsymbol{n} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow\left[\boldsymbol{M}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{n}\right]^{+}+\boldsymbol{E}_{2} \\
\boldsymbol{X}^{-}+\boldsymbol{m} \boldsymbol{H}_{2} \boldsymbol{O} \rightarrow\left[\boldsymbol{X}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{m}\right]^{-}+\boldsymbol{E}_{3}
\end{array}
\]
\( E_{1}, E_{2} \) and \( E_{3} \) are energies, then correct
statement is :
A. Compound \( (M X) \) soluble in water if \( E_{3}-E_{2}>E_{1} \)
B. compound soluble in water \( E_{3}+E_{2}<E_{1} \)
C. compound soluble in water if \( E_{1}+E_{2}>E_{3} \)
D. compound soluble in water if \( E_{2}+E_{3}>E_{1} \)
Subject: Chemistry
\( \operatorname{In} \) a reaction \( \Delta H \) and \( \Delta S \) both are
positive. In which of the following cases, the reaction would not be spontaneous?
A \( . \Delta H>T \Delta S \)
в. \( T \Delta S>\Delta H \)
c. \( \Delta H=T \Delta S \)
D. All of these
Subject: Chemistry
Assertion
A reaction cannot become fast by itself unless a catalyst is added.
Reason
A catalyst always increases the speed
of a reaction.
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
Two identical masses each of mass \( m \)
are connected by a spring and placed on a smooth surface. A third identical
mass moving with speed \( v_{0} \) collides with one of the two masses perfectly inelastically. Choose the correct option.
A. Centre of mass of the given blocks moves with a constant speed \( \frac{v_{0}}{3} \) after collision
B. Maximum elongation in spring is \( \sqrt{\frac{m v_{0}^{2}}{6 k}} \)
c. Maximum compression in spring is \( \sqrt{\frac{m v_{0}^{2}}{2 k}} \)
D. Maximum compression in spring is \( \sqrt{\frac{m v_{0}^{2}}{6 k}} \)
Subject: Physics
A thin horizontal uniform rod \( A B \) of
mass \( M \) and length \( l \) can rotate freely about a vertical axis passing through
its end \( A \). At a certain moment the end
\( B \) starts experiencing a constant force
\( \boldsymbol{F} \) which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle \( \varphi \) counted relative to the initial position.
A \( \cdot \omega=\sqrt{\frac{6 F \sin \varphi}{M l}} \)
B. \( \omega=\sqrt{\frac{3 F \sin \varphi}{M l}} \)
c. \( \omega=\sqrt{\frac{6 F \cos \varphi}{M l}} \)
D. None of these
Subject: Maths
The relation \( R \) is defined in \( A= \)
\{1,2,3\} by \( a R b \) if \( \left|a^{2}-b^{2}\right| \leq 5 . \) Which
of the following is false?
A \( \cdot R=\{(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2)\} \)
В. \( R^{-1}=R \)
C. Domain of \( R=\{1,2,3\} \)
D. Range of \( R=\{5\} \)
Subject: Maths
The equation of electromotive force in
terms of current \( i \) for an electrical
circuit having resistance \( \boldsymbol{R} \) and condenser \( C \) in series is \( \boldsymbol{E}=\boldsymbol{R} \boldsymbol{i}+ \)
\( \int \frac{i}{c} d t . \) The current at any time \( t, \) when
\( \boldsymbol{E}=\boldsymbol{E}_{0} \sin \omega \boldsymbol{t} \) is?
A \( \cdot i=\frac{E_{0} \omega c}{\sqrt{1+R^{2} c^{2} \omega^{2}}} \sin (\omega t-\phi)+k e^{-t / R c} \)
B. \( i=\frac{E_{0} \omega c}{\sqrt{1+R^{2} c^{2} \omega^{2}}} \cos (\omega t-\phi)+k e^{-t / R c} \)
c. \( _{i}=\frac{E_{0} \omega c}{\sqrt{1+R^{2} c^{2} \omega^{2}}} \cosh (\omega t-\phi)+k e^{-t / R c} \)
D. \( i=\frac{E_{0} \omega c}{\sqrt{1+R^{2} c^{2} \omega^{2}}} \sinh (\omega t-\phi)+k e^{-t / R c} \)
Subject: Maths
On the parabola \( y=x^{2}, \) the point least
distant from the straight line \( y=2 x- \)
4 is
\( \mathbf{A} \cdot(1,1) \)
B \( \cdot(1,0) \)
c. (1,-1)
D \( \cdot(0,0) \)
Subject: Chemistry
Sequence of ond energy in \( N O, N O^{+} \)
and \( N O^{-} \) is:
A. \( N O>N O^{+}>N O^{-} \)
В. \( N O^{-}>N O^{+}> \) NO
c. \( N O^{+}>N O>N O^{-} \)
D. \( N O^{+}>N O^{-}>N O \)
Subject: Physics
A person is seeing two trains one of there is coming with speed of \( 4 \mathrm{m} / \mathrm{s} \) and another is going with same speed. If two trains blowing a whistle with frequency 243Hz . The beat frequency heard by stationary person will be (speed of sound in air \( =320 \mathrm{m} / \mathrm{s} \)
в. \( 3 H z \)
\( \mathrm{c} .6 \mathrm{Hz} \)
D. \( 12 H z \)
Subject: Physics
David is observing his image in a plane mirror. The distance between the mirror
and his image is \( 4 \mathrm{m} \). If he moves \( 1 \mathrm{m} \) towards the mirror, then the distance between David and his image will be:
\( A \cdot 3 m \)
B. \( 5 \mathrm{m} \)
\( c \cdot 6 m \)
D. 8 m
Subject: Physics
Which of the following statements are
true?
This question has multiple correct options
A. When the mass of a body is doubled then the momentum of a body is also doubled, provided the body maintains the same velocity.
B. We feel pain in the hand on hitting the wall, this is a consequence of Newton's third law of motion.
C. A table cloth can be pulled from a table without dislodging the dishes. This is due to inertia of rest.
D. Momentum is a vector quantity.
Subject: Biology
Botanical names of plants are treated in
Latin because
A. Rules of nomenclature were framed by Italian botanists they were speaking Latin.
B. It is very difficult to pronounce Latin names and they convey multiple meanings.
C. Latin was the natural language of many European countries.
D. Latin was a dead language, its word would convey precise meaning. It was the mother of all European languages and all the early botanical literature was in Latin.
Subject: Physics
A cylinder of radius \( R \) and length \( L \) is
placed in a uniform electric field \( \boldsymbol{E} \)
parallel to the cylinder axis. The total flux for the surface of the cylinder is given by :
\( \mathbf{A} \cdot 2 \pi R^{2} E \)
в. \( \frac{\pi R^{2}}{E} \)
c. \( \frac{R}{E} \)
D. zero
Subject: Maths
Cards marked with the numbers 2 to
101 are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is less than 14
A \( \cdot \frac{3}{27} \)
в. \( \frac{3}{29} \)
\( c \cdot \frac{3}{25} \)
D. \( \frac{3}{22} \)
Subject: Chemistry
Which of the following orbitals can not undergo hybridisation amongst themselves?
\( (I) 3 d, 4 s \)
\( (I I) 3 d, 4 d \)
\( (I I I) 3 d, 4 s \& 4 p \)
\( (I V) 3 s, 3 p \& 4 s \)
\( \mathbf{A} \cdot I I \)
B. II and III
c. \( I, I I \) and \( I V \)
D. II and \( I V \)