AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The de Broglie wavelength \( (\lambda) \) associated with a photoelectron varies
with the frequency ( \( v \) ) of the incident
radiation as, \( \left[v_{0} \text { is thrshold frequency }\right] \)
A \( \cdot \lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{3}{2}}} \)
B. \( \lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{1}{2}}} \)
c. \( a \lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{1}{4}}} \)
D. \( \lambda \propto \frac{1}{\left(v-v_{0}\right)} \)
Subject: Physics
If the area of a material is \( 4 m^{2} \) and
Iength \( 20 m . \) What will be the resistivity of that material when its resistance is
\( \mathbf{1 0 \Omega} ? \)
A. 12 mho
B. 20 mho
c. 4 mho
D. 2 mho
Subject: Maths
The value of \( c \) in lagrange's theorem for
the function \( f(x)=\log \sin x \) in the interval \( \left[\frac{\pi}{6}, \frac{5 \pi}{6}\right] \) is
A \( \cdot \frac{\pi}{4} \)
в.
c. \( \frac{2 \pi}{3} \)
D. None of these
Subject: Physics
A closed curve encircles several conductors.The line integral \( \int \overrightarrow{\boldsymbol{B}} \cdot \boldsymbol{d} \overrightarrow{\boldsymbol{l}} \)
around this curve is \( 3.83 \times 10^{-7} T-m \)
What is the net current in the
conductors?
A . \( 0.1 A \)
в. \( 0.2 A \)
\( c .0 .3 A \)
D. \( 0.4 A \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\sin 3 x+A \sin 2 x+B \sin x}{x^{5}}, x \neq 0 \)
is continous at \( x=0 \) then
This question has multiple correct options
A. \( A=-4 \)
B. \( B=5 \)
c. \( f(0)=1 \)
D. \( A=-3 \)
Subject: Physics
I ne IIgure snows lour palrs ol unılormıy
charged spheres. The red spheres are positively charged while the blue spheres are negatively charged. Each sphere has the same amount of charge. Assume each pair is isolated. For which pair there is a point between
them on the dotted line where the
magnitude of electric field is zero as well as the electric potential is also
zero?
A.
B. 2
\( c \cdot 3 \)
D. 4
E. None of the pairs has points that meet these conditions
Subject: Chemistry
Calculate the number of electrons lost
or gained the changes:
\( \mathbf{3} \boldsymbol{I}_{2}+\boldsymbol{6} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightarrow \boldsymbol{N} \boldsymbol{a} \boldsymbol{I} \boldsymbol{O}_{3}+\mathbf{5} \boldsymbol{N} \boldsymbol{a} \boldsymbol{I}+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}} \boldsymbol{O} \)
Subject: Physics
A particle of mass \( m \) is dropped from a height \( h \) above the ground. At the same
time another particle of the same mass is thrown vertically upwards from the ground with a speed of \( \sqrt{2 g h} \). If they collide head on completely inelastically, the time taken for the combined mass to reach the ground, in units of \( \sqrt{\frac{\boldsymbol{h}}{\boldsymbol{g}}} \) is:
A \( \cdot \sqrt{\frac{3}{4}} \)
B. \( \frac{1}{2} \)
c. \( \sqrt{\frac{1}{2}} \)
D. \( \sqrt{\frac{3}{2}} \)
Subject: Physics
Two cars of masses \( m_{1} \) and \( m_{2} \) are
moving along the circular paths of
radius \( r_{1} \) and \( r_{2} \) respectively. The speeds are such that they complete one round at the same time. The ratio of
angular speeds of two cars is
В. \( r_{1}: r_{2} \)
c. 1:
D. \( m_{1} r_{1}: m_{2} r_{2} \)
Subject: Physics
A steel rod of length \( I, \) area of cross
section \( A, \) Young's modulus \( E \) and linear
coefficient of expansion a is heated through \( t^{\circ} C . \) The work that can be
performed by the rod when heated is
A \( \cdot(E A a t) \times(l a t) \)
B \( \cdot \frac{1}{2}(E A a t) \times(l a t) \)
c. \( \frac{1}{2}(E A a t) \times \frac{1}{2}(l a t) \)
D. 2(EAat)(lat)
Subject: Maths
To find out the concentration of \( S O_{2} \) in
the air(in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:
concentration \( \begin{array}{llll}0.00 & 0.04 & 0.08\end{array} \)
of \( s o_{2} \) in 0.08 ppm \( 2^{11} \) 0.04 0.12
Frequency
The mean concentration of \( S O_{2} \) in the
\[
\operatorname{air} \mathbf{0 . 0 9 8 6 6 7}
\]
A. True
B. False
Subject: Physics
Two spheres of same size one of mass \( 2 k g \) and another of mass \( 4 k g \) are
dropped simultaneously from the top of Qutab Minar (height \( =\mathbf{7} 2 \boldsymbol{m} \) ). When
they are \( 1 m \) above the ground, the two
spheres have the same:
A. momentum
B. kinetic energy
c. potential energy
D. acceleration
Subject: Physics
In young's experiment, the fringe width at a distance of \( 50 \mathrm{cm} \) from the slits, of
light of wavelength \( 6000 \AA \) is \( 0.048 \mathrm{cm} \) The fringe width at the same distance for \( \lambda=5000 \AA \) will be :
A . \( 0.04 \mathrm{cm} \)
B. \( 0.4 \mathrm{cm} \)
\( c .0 .14 c m \)
D. \( 0.45 \mathrm{cm} \)
Subject: Maths
The value of \( \frac{1}{2} \times\left(\frac{1}{3}+\frac{4}{9}\right) \) is
A \( \cdot \frac{7}{18} \)
B. \( \frac{1}{2} \)
c. \( \frac{7}{12} \)
D. \( \frac{7}{24} \)
Subject: Maths
The area bounded by the curves \( x^{2}+ \)
\( y^{2} \leq 8 \) and \( y^{2} \geq 4 x \) lying in the first
quadrant is not equal to
A \( \cdot 32\left(\frac{\pi}{8}-\frac{1}{3}\right) \)
в. \( \frac{32}{3}\left(\frac{3 \pi}{8}-1\right) \)
c. \( _{4 \pi}-\frac{32}{3} \)
D. \( \frac{1}{3}(12 \pi-32) \)
Subject: Physics
Two bodies of masses \( m_{1} \) and \( m_{2} \) are
placed at distance X from each other.
IfX is kept constant and the masses of
the two bodies are increased to \( 2 m_{1} \)
and \( 2 m_{2}, \) then the value of gravitational force between them will become
A. 4 times
B. 2 times
c. 8 times
D. \( 1 / 4 \) times
Subject: Physics
Match the Column I with Column II
Column
(A) A body which regains its original shape after the removal of external forces
(B) A body which does not regain its original shape after the removal Elastic of external forces.
(C) A body which does not show any deformation on applying external forces
(D) The property of the body to regain
(s) Rigid its original configuration when the deforming forces are removed
A. A-q, B-r, C-s, D-p
B. A-p, B-q, C-r, D-s
\( c \cdot A-r, B-s, c-p, D-q \)
D. A-s, B-p, C-q, D-r
Subject: Physics
A particle of mass \( m \) strikes elastically
with a disc of radius \( R, \) with a velocity \( \vec{v} \)
as shown in the figure. If the mass of the
disc is equal to that of the particle and
the surface of the contact is smooth,
then the velocity of the disc just after the collision is:
A \( \cdot \frac{2 v}{3} \)
B. \( \frac{v}{2} \)
c. \( \frac{\sqrt{3} v}{2} \)
D.
Subject: Maths
What is the \( \sin (\boldsymbol{\alpha}+\boldsymbol{\beta})- \)
\( 2 \sin \alpha \cos \beta+\sin (\alpha-\beta) \) equal to?
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 2 \sin \alpha \)
\( c \cdot 2 \sin \beta \)
\( D \cdot \sin \alpha+\sin \beta \)
Subject: Physics
Recently, the phenomenon of superconductivity has been observed at
\( 95 K . \) This temperature is nearly equal
to.
\( \mathbf{A} \cdot-288^{\circ} F \)
B . \( -146^{\circ} F \)
c. \( -368^{\circ} F \)
\( \mathrm{D} \cdot+178^{\circ} \mathrm{C} \)
Subject: Maths
Assertion
The variance of first \( n \) natural numbers
is \( \frac{n^{2}-1}{6} \)
Reason
The sum of the first \( n \) odd natural
numbers is \( n^{2} \) and the sum of squares
of first \( n \) odd natural numbers is
\( \frac{n}{3}\left(4 n^{2}-1\right) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
If \( \mathrm{E}, \mathrm{m}, \mathrm{I} \) and \( \mathrm{G} \) denote energy, mass,
angular momentum and gravitational constant respectively, then the quantity \( \left(\frac{E l^{2}}{m^{5} G^{2}}\right) \) has the dimensions of then
A. mass
B. length
\( c . \) time
D. angle.
Subject: Physics
another in 2 hours time, its speed
during the motion is shown in graph above. The maximum acceleration
during the journey and distance covered during the time interval from
0.75 hour to 1.00 hour are
\( \mathbf{A} \cdot 60 \mathrm{kmhr}^{-2}, 100 \mathrm{km} \)
B. \( 160 \mathrm{kmhr}^{-2}, 10 \mathrm{km} \)
\( \mathbf{C} \cdot 10 \mathrm{kmhr}^{-2}, 10 \mathrm{km} \)
D. \( 260 \mathrm{kmhr}^{-2}, 1 \mathrm{km} \)
Subject: Physics
A wheel of radius \( 1 \mathrm{m} \) rolls forward half
a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is
A \( .2 \pi m \)
В. \( \sqrt{2} \pi m \)
\( \mathbf{c} \cdot \sqrt{\pi^{2}+4 m} \)
D. \( \pi m \)
Subject: Chemistry
\( 4 D_{2} O+3 F e \stackrel{r e d-h o t}{\longrightarrow} F e_{3} O_{4}+g a s . \) The gas
produced in the above reaction is:
\( A \cdot O_{2} \)
в. \( H_{2} \)
c. \( D_{2} \)
D. none
Subject: Maths
In which of the following functions is Rolle's theorem applicable
A \( , \quad f(x)=\left\{\begin{array}{l}x, 0 \leq x<1 \\ 0, x=1\end{array} \text { on }[0,1]\right. \)
в. \( \quad f(x)=\left\{\begin{array}{l}\frac{\sin x}{x},-\pi \leq x<0 \\ 0, x=0\end{array} \text { on }[-\pi, 0]\right. \)
c. \( f(x)=\frac{x^{2}-x-6}{x-1} \) on [-2,3]
D \( \quad f(x)=\left\{\begin{array}{l}\frac{x^{3}-2 x^{2}-5 x+6}{x-1}, \text { if } x \neq 1 \\ -6, \text { if } x=1\end{array}\right. \)
Subject: Chemistry
For 'invert sugar', the correct
statement(s) is (are)
(Given : specific rotations of \( (+)- \)
sucrose,
\( (+) \) -maltose, \( L-(-) \) -glucose and
L-(+)-fructose in aqueous solution are
\( +66^{0},+140^{0},-52^{0} \) and \( 92^{0} \)
respectively
A. 'invert sugar' is prepared by acid catalyzed hydrolysis of maltose
B. 'invert sugar' is an eqimolar mixture of D-(+)-glucose and D-(-)-fructose
C . specific rotation of 'invert sugar' is \( -20^{\circ} \)
D. on reaction with \( B r_{2} \) water, 'invert sugar' forms saccharic acid as one of the products
Subject: Chemistry
\( \ln C H_{3} C O O H \) molecule, the \( C-C \)
bond is formed by:
A \( \cdot s p^{3}-s p^{3} \) overlap
B. \( s p^{2}-s p^{2} \) overlap
c. \( s p^{3}-s p^{2} \) overlap
D. \( s p^{3}- \) sp overlap
Subject: Chemistry
The complex compound in which metal is not present in zero oxidation state?
\( \mathbf{A} \cdot M n_{2}(C O)_{10} \)
В \( \cdot\left[N i(C O)_{4}\right] \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(C_{6} H_{6}\right)_{2}\right] \)
D \( \cdot_{K}\left[P t C l_{3}\left(C_{2} H_{4}\right)\right] \)
Subject: Maths
State true or false:
The region of the z-plane for which \( \left|\frac{\boldsymbol{z}-\boldsymbol{a}}{\boldsymbol{z}+\overline{\boldsymbol{a}}}\right|=1(\boldsymbol{R} e \boldsymbol{a} \neq 0) \) is \( X \) -axis.
Subject: Physics
In the arrangement shown in figure the
mass \( M \) is very heavy compared to \( \boldsymbol{m}(\boldsymbol{M}>+>\boldsymbol{m}) . \) The tension \( \boldsymbol{T} \) in the
string suspended from the ceiling is
A. \( 4 m g \)
в. \( 2 m g \)
c. zero
D. None of the above
Subject: Physics
Under what conditions will the vectors \( \overrightarrow{\boldsymbol{A}}=3 \hat{\boldsymbol{i}}-\mathbf{5} \hat{\boldsymbol{j}}+\mathbf{5} \hat{\boldsymbol{k}} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \mathbf{5} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{b} \hat{\boldsymbol{k}} \) be
perpendicular to each other? Find the value of \( |b| ? \)
Subject: Physics
Two bars of masses \( m_{1} \) and \( m_{2} \)
connected by a non-deformed light spring rest on a horizontal plane. The coefficient of friction between the bars
and the surface is equal to \( k \). The minimum constant force that has to be
applied in the horizontal direction to the
bar of mass \( m_{1} \) in order to shift the other bar is \( F_{\min }=k g\left(m_{1}+\frac{m_{2}}{x}\right) \)
Find \( x \)
Subject: Chemistry
Which of the following statements is/are incorrect?
. Amylose does not give blue colour with
\( I_{2} \) solution.
II. Amylopectin gives blue colour with \( I_{2} \) solution.
III. Amylum is present in wheat, maize, rice, potatoes, barley, sorghum etc.
IV. Amylose is linear polymer of \( D \) glucose units.
A. I and II only
B. III and IV only
c. I and III only
D. II and III only
Subject: Chemistry
Compound \( A \) has how many functional
groups?
\[
\begin{array}{l}
\text { a-Amino acid (A) } \frac{\mathrm{MeOH} / \mathrm{HCl}}{\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NO}_{3}\right)} \\
\begin{array}{c}
\left.(\mathrm{D})\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{NO}_{2} \mathrm{Cl}\right) \quad \stackrel{\mathrm{H}_{3} \mathrm{O}^{\oplus}}{(\mathrm{Na}-\mathrm{Hg} / \mathrm{HCl}}\right) \\
& (\mathrm{D})\left(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{NO}_{2} \mathrm{Cl}_{2}\right)
\end{array}
\end{array}
\]
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
\( D \)
Subject: Chemistry
\( 100 \mathrm{ml} \) of tap water containing
\( \boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2} \) was titrated with \( \mathrm{N} / 50 \)
\( \boldsymbol{H} \boldsymbol{C l} \) with methyl orange as indicator. If
\( 30 \mathrm{ml} \) of \( H C l \) were required, calculate
the temporary hardness as part of \( \mathrm{CaCO}_{3} \) per \( 10^{6} \) parts of water.
A. 150 ppm
B. 300 ppm
c. 450 ppm
D. 600 ppm
Subject: Chemistry
The standard emf of a galvanic cell involving cell reaction with \( n=2 \) is found to be \( 0.295 \mathrm{V} \) at \( 25 \mathrm{C}^{\circ} \). The
equilibrium constant of the reaction would be
(Given, \( \boldsymbol{F}=\mathbf{9 6 5 0 0} \boldsymbol{C m o l}^{-1}, \boldsymbol{R}= \)
\( \left.8.314 J K^{-1} m o l^{-1}\right) \)
A \( .2 .0 \times 10^{11} \)
B . \( 4 \times 10^{12} \)
\( c \cdot 1 \times 10^{2} \)
D. \( 1 \times 10^{10} \)
Subject: Physics
The primary of a transformer has 40
turns and works on 100 volt and 100
watt. Then the number of turns in the
secondary to step up voltage to \( 400 \mathrm{V} \) and the current in the secondary and primary will be
A. \( 260,0.25 \mathrm{A}, 2 \mathrm{A} \)
B. 160, 0.25A, 1A
c. \( 360,0.55 \mathrm{A}, \) 1А
D. None of these
Subject: Maths
A solid iron pole consists of a cylinder of height \( 220 \mathrm{cm} \) and base diameter 24 \( \mathrm{cm}, \) which is surmounted by another
cylinder of height \( 60 \mathrm{cm} \) and radius 8
cm. Find the mass of the pole, given that \( 1 \mathrm{cm}^{3} \) of iron has approximately \( 8 \mathrm{g} \) mass. (Use \( \pi=3.14) \)
Subject: Physics
Number of electrons constituting \( 1 C \)
electric charge is
A \( \cdot 6.25 \times 10^{18} \) electrons
B. \( 1.6 \times 10^{-19} \) electrons
C. \( 6.25 \times 10^{-19} \) electrons
D. \( 1.6 \times 10^{-18} \) electrons
Subject: Physics
What is the angle between \( (\hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \)
and \( \hat{i} ? \)
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{\pi}{4} \)
\( c \cdot \frac{\pi}{3} \)
D. \( \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
Subject: Physics
Average kinetic energy in one time
period of a simple harmonic oscillator whose amplitude is \( A, \) angular velocity \( \omega \) and mass \( m, \) is
A \( \cdot \frac{1}{4} m \omega^{2} A^{2} \)
B \( \cdot \frac{1}{2} m \omega^{2} A^{2} \)
\( \mathrm{c} \cdot m \omega^{2} A^{2} \)
D. Zero
Subject: Chemistry
Several octahedral complexes are
possible from combinations of
\( C o^{3+}, C l^{-} \) and \( N H_{3} . \) The correct
statement(s) regarding the octahedral coordination entities having the formula \( \cdot\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{\boldsymbol{n}} \boldsymbol{C l}_{\boldsymbol{6}-\boldsymbol{n}}\right]^{(\boldsymbol{n}-\boldsymbol{3})+} \) with
\( \boldsymbol{n} \geq \mathbf{3}, \) is \( / \) are
This question has multiple correct options
A. At most six octahedral complexes are possible
B. One of the complexes is homoleptic
C. All the complexes are paramagnetic
D. Some of the complexes dissociate in water to give \( C o^{3+} \) and \( C l^{-} \) ions
Subject: Maths
Locus of a point \( \boldsymbol{P} \) which such that
\( \boldsymbol{P A}=\boldsymbol{P B} \) where \( \boldsymbol{A}=(\mathbf{0}, \boldsymbol{3}, \boldsymbol{2}) \) and \( \boldsymbol{B}= \)
(2,4,1) is
A. \( 2 x+y-z=4 \)
B. \( x-2 y+z+1=0 \)
c. \( 9 x-2 y+4 z-5=0 \)
D. None of these
Subject: Chemistry
The standard Gibbs free energy change,
\( \Delta G^{0} \) is related to equilibrium constant,
\( K_{p} \) as:
A \( . K_{p}=-R T \ln \Delta G^{0} \)
B. \( \quad K_{p}=\left[\frac{e}{R T}\right]^{\Delta G^{0}} \)
\( c \cdot_{K_{p}}=-\frac{\Delta G}{R T} \)
D. \( K_{p}=e^{-\Delta G^{0} / R T} \)
Subject: Maths
The number of points in
\( (-\infty, \infty) \) for which \( x^{2}-x \sin x- \)
\( \cos \boldsymbol{x}=\mathbf{0}, \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
\( c \cdot 2 \)
D. None of the above
Subject: Physics
An electrical technician requires a
capacitance of \( 2 \mu F \) in a circuit across
a potential difference of \( 1 \mathrm{kV} . \) A large number of \( 1 \mu F \) capacitors are available to him each of which can withstand a potential difference of not more than \( 400 \mathrm{V} . \) Suggest a possible arrangement that requires the minimum number of capacitors.
Subject: Physics
If the magnetic dipole moment of an atom of diamagnetic material,
paramagnetic material and ferromagnetic material are denoted by
\( \mu_{d}, \mu_{p} \) and \( \mu_{f} \) respectively, then
\( \mathbf{A} \cdot \mu_{p}=0 \) and \( \mu_{f} \neq 0 \)
B . \( \mu_{d} \neq 0 \) and \( \mu_{p}=0 \)
C \( \cdot \mu_{d} \neq 0 \) and \( \mu_{f} \neq 0 \)
D. \( \mu_{d}=0 \) and \( \mu_{p} \neq 0 \)
Subject: Chemistry
Reaction of calgon with hard water
containing \( C a^{2+} \) ions produces;
\( \mathbf{A} \cdot\left[N a_{2} C a P_{6} O_{18}\right]^{2-} \)
в. \( C a_{2}\left(P O_{4}\right)_{3} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( \operatorname{CaSO}_{4} \)
Subject: Maths
Assertion
The order of the differential equation
whose solution is \( \boldsymbol{y}=\boldsymbol{c}_{1} \boldsymbol{e}^{2 \boldsymbol{x}+\boldsymbol{c}_{2}}+ \)
\( c_{3} e^{2 x+c_{4}} \) is 4
Reason
Order of the differential equation is the order of the highest order derivative occurring in the differential equation.
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: Maths
State True or False
Let \( \boldsymbol{A}=\{1,2\} \) and \( \boldsymbol{B}=\{2,3,4\}, \) then \( \boldsymbol{A} \)
\( \times \mathrm{B}=\mathrm{B} \times \mathrm{A} ? \)
A. True
B. False
Subject: Chemistry
In a test tube, there is \( 18 g \) of glucose \( \left(C_{6} H_{12} O_{6}\right) 0.08 \) mole of glucose is taken out. Glucose left in the test tube
is:
A. \( 0.10 g \)
в. \( 0.02 g \)
c. 0.10 mole
D. 3.60 \( g \)
Subject: Maths
A student was asked to prove a statement by induction. He proved
(i) \( P(5) \) is true and
(ii) Trutyh of \( P(n) \Rightarrow \) truth of \( p(n+1), n \in \)
\( \mathbf{N} \)
On the basis of this, he could conclude that \( P(n) \) is true for
A. no \( n \in N \)
B. all n \in N
c. all \( n \geq 5 \)
D. None of these
Subject: Chemistry
\( \boldsymbol{p} \boldsymbol{K}_{a} \) of Quinoline base is \( 4.88 . \) What will
be the \( p K_{a} \) of \( 0.01 \mathrm{M} \) solution of it?
A . 4.88
B. 0.01
c. 9.12
D. 14
Subject: Maths
It is known that \( \sum_{r=1}^{\infty} \frac{1}{(2 r-1)^{2}}=\frac{\pi^{2}}{8} \)
Then \( \sum_{r=1}^{\infty} \frac{1}{r^{2}} \) is equal to
A \( \cdot \frac{\pi^{2}}{24} \)
в. \( \frac{\pi^{2}}{3} \)
c. \( \frac{\pi^{2}}{6} \)
D. none of these
Subject: Chemistry
Which of the following statements given below is incorrect?
A. \( O N F \) is isoelectronic with \( O_{2} N^{-} \)
B. \( O F_{2} \) is an oxide of fluorine
c. \( C l_{2} O_{7} \) is an anhhydride of perchloric acid
D. \( O_{3} \) molecule is bent.
Subject: Physics
A particle has initial velocity \( 4 i+ \) \( 4 j m s^{-1} \) and an acceleration
\( -0.4 i m s^{-2}, \) at what time will its speed
be \( 5 m s^{-1} ? \)
A . \( 2.5 s \)
B. \( 17.5 s \)
\( c \)
D. \( 8.5 s \)
Subject: Physics
A wire is wound on a long rod of
material of relative permeability \( \mu_{r}= \)
4000 to make a solenoid. If the current
through the wire is \( 5 A \) and number of
turns per length is 1000 per meter, then the magnetic field inside the solenoid is:
A. \( 25.12 \mathrm{mT} \)
B. \( 12.56 \mathrm{mT} \)
c. \( 12.56 T \)
D. 25.12 T
Subject: Chemistry
2
\( \boldsymbol{N} \equiv \boldsymbol{C}-\boldsymbol{C H}=\boldsymbol{C H}_{2} \)
What is the hybridization of carbons
marked as 1 and \( 2 ? \)
\( \begin{array}{lll}\text { A } \cdot s p^{2} & \text { and } & s p^{2}\end{array} \)
B . sp \( ^{3} \) and sp
c. sp and \( s p^{2} \)
D. sp and sp
Subject: Physics
A small object of mass \( m, \) on the end of
a light cord, is held horizontally at a distance \( r \) from a fixed support as
shown. The object is then released. What is the tension in the cord when the
object is at the lowest point of its
swing?
A. \( m g / 2 \)
в. \( m g \)
\( \mathbf{c} \cdot 2 m g \)
D. \( 3 m g \)
Subject: Chemistry
Which one of the following statements
concerning the ring strain in
cyclopropene is correct?
A. \( C-C=C \) angle is reduced by 30 degree compared to its normal value in propene
B. \( C-C=C \) angle is reduced by 40 degree compared to ¡ts normal value in propene
C. \( C-C=C \) angle is reduced by 50 degree compared to its normal value in propene
D. \( C-C=C \) angle is reduced by 60 degree compared to its normal value in propene
Subject: Chemistry
Find the weight of a substance if its molecular weight is 70 and in the
gaseous form it occupies \( 10 \mathrm{L} \) at \( 27^{\circ} \mathrm{C} \)
and \( 760 \mathrm{mm} \) Hg pressure.
A. 32.5 \( g \)
B. 35.5 g
c. \( 28.38 \mathrm{g} \)
D. None of the above
Subject: Chemistry
\( \boldsymbol{C H}_{3} \boldsymbol{O H} \stackrel{\boldsymbol{P}+\boldsymbol{I}_{2}}{\longrightarrow} \boldsymbol{A} \frac{M \boldsymbol{g} / \text {dryether}}{\boldsymbol{\}} \)
\( \boldsymbol{B} \stackrel{\boldsymbol{H C H O}}{\longrightarrow} \boldsymbol{C} \stackrel{\boldsymbol{H}^{+} / \boldsymbol{H}_{2} \boldsymbol{O}}{\longrightarrow} \boldsymbol{D} \)
What are \( B \& D \) respectively?
A. \( C H_{3} M g I, C H_{3} C H O \)
B. \( C H_{3} M g I, C H_{3} C H_{2} O H \)
c. \( C H_{3} M g I, C H_{3} C O O H \)
D. \( C H_{3} M g I, C H_{3} C O C H_{3} \)
Subject: Chemistry
Geometry as sulphur is bent in
\( \mathrm{I} \cdot \boldsymbol{S}_{8}\left\|\cdot \boldsymbol{S} \boldsymbol{F}_{2}\right\| \boldsymbol{S} \boldsymbol{O}_{2} \)
A . ।, ॥।, ॥।
B. ।, ॥
c. ॥, ॥ ॥
D. I, III
Subject: Physics
The coefficient of friction between the
block A of mass \( \mathrm{m} \) and the triangular
wedge B of mass M is \( \mu \). There is no friction between the wedge and the
plane. If the system (block \( A+\text { wedge B }) \) is released so that there is no sliding
between \( A \) and \( B \). Find the inclination \( \theta \)
Subject: Physics
The velocity \( v \) of a particle at timet is given by \( v=a t+\frac{b}{t+c} \) where \( a, b \) and \( c \) are constants. The dimensions of \( a, b \) and \( c \) are respectively:
\( \mathbf{A} \cdot L T^{-2}, L \) and \( T \)
B. \( L^{2}, T \) and \( L T^{2} \)
c. \( L T^{2}, L T \) and \( L \)
D. \( L, L T \) and \( T^{2} \)
Subject: Chemistry
Identify the type of polymer.
\( (i)-A-A-A-A-A-A \)
\( (i i)-A-B-B-A-A-A-B-A- \)
A. (i) Homopolymer, (ii) Copolymer
B. (i) Natural polymer, (ii) Synthetic polymer
C. (i) Linear polymer, (ii) Branched polymer
D. (i) Fibre, (ii) Elastomer
Subject: Chemistry
1 \( g \) of same non volatile solute is added
to \( 100 g \) o two different solvents \( A \) and \( B \)
\( \boldsymbol{K}_{\boldsymbol{b}} \) of \( \boldsymbol{A}: \boldsymbol{B}=\mathbf{1}: \mathbf{5} \)
find out \( \frac{\left(\Delta T_{b}\right)_{A}}{\left(\Delta T_{b}\right)_{B}} \)
\( \mathbf{A} \cdot 1: 10 \)
B. 1: 5
c. 1: 20
D. 2: 5