AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{2} & \mathbf{0} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{4}\end{array}\right], \boldsymbol{A}=\boldsymbol{B}+\boldsymbol{C}, \boldsymbol{B}= \)
\( \boldsymbol{B}^{\boldsymbol{T}}, \boldsymbol{C}=-\boldsymbol{C}^{\boldsymbol{T}}, \) then \( \boldsymbol{C}= \)
A. \( \left[\begin{array}{ccc}0 & 0.5 & 0 \\ -0.5 & 0 & 0 \\ 0 & 0 & 0\end{array}\right] \)
B. \( \left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 0.5 \\ 0 & -0.5 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ccc}0 & -0.5 & 0.5 \\ 0.5 & 0 & 0.5 \\ -05 & 0 & 0\end{array}\right] \)
D. \( \left[\begin{array}{ccc}0 & 0.5 & 0 \\ -0.5 & 0 & 0.5 \\ 0 & -0.5 & 0\end{array}\right] \)
Subject: Chemistry
Which of the following names is correct
for \( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{2} ? \)
\begin{tabular}{lll} 
CHO & CHO & CHO \\
\hline
\end{tabular}
A. 3- Formaldehyde-1,3-dial
B. 1,2,3- Triformaylpropane
c. 2-Formylmethylbutane-1,4-dial
D. Propane-1,2,3-tricarbaldehyde
Subject: Physics
Which of the following statements
is/are true?
This question has multiple correct options
A. Work done by kinetic friction on an object may be positive
B. A rigid body rolls up an inclined plane without sliding. The friction force on it will be up the incline. (only contact force and gravitational force is acting)
C. A rigid body rolls down an inclined plane without sliding. The friction force on it will be up the incline. (only contact force and gravitational force is acting)
D. A rigid body is left from rest and having no angular velocity from the top of a rough inclined plane. It moves down the plane with slipping. The friction force on it will be up the incline.
Subject: Maths
Given \( \boldsymbol{A}(\mathbf{0}, \mathbf{0}) \) and \( \boldsymbol{B}(\boldsymbol{x}, \boldsymbol{y}) \) with \( \boldsymbol{x} \in \)
(0,1) and \( y>0 . \) Let the slope of the line
\( A B \) equal to \( m_{1} . \) Point \( C \) lies on the line
\( x=1 \) such that the slope of \( B C \) equal
to \( m_{2} \) where \( 0<m_{2}<m_{1} . \) If the area of
the \( \triangle A B C \) can be expressed as \( \left(m_{1}-\right. \)
\( \left.m_{2}\right) f(x), \) then the largest possible
value of \( \boldsymbol{f}(\boldsymbol{x}) \) is
A.
в. \( \frac{1}{2} \)
c. \( \frac{1}{4} \)
D. \( \frac{1}{8} \)
Subject: Chemistry
The boiling point of a solution of 5 g sulphur in 100 g \( C S_{2} \) is \( 0.5^{\circ} C \) above
pure solvent. If the \( K_{b} \) of \( C S_{2} \) is 2.56
\( \mathrm{K} / \mathrm{m}, \) then find the atomicity of the sulphur in the solvent.
Subject: Physics
A sphere rolls down on an inclined plane of inclination \( \theta . \) What is the
acceleration as the sphere reaches bottom?
A \( \cdot \frac{5}{7} g \sin \theta \)
в. \( \frac{3}{5} g \sin \theta \)
c. \( \frac{2}{7} g \sin \theta \)
D. \( \frac{2}{5} g \sin \theta \)
Subject: Maths
\( \sim[(\sim p) \wedge q] \) is logically equivalent to
A \( . \sim(p \vee q) \)
В \( . \sim[p \wedge(\sim q)] \)
C \( . p \wedge(\sim q) \)
D. \( p \vee(\sim q) \)
E \( .(\sim p) \vee(\sim q) \)
Subject: Chemistry
\( \boldsymbol{C H}_{3}-\boldsymbol{C H O} \stackrel{\boldsymbol{O H}^{-}}{\longrightarrow} \boldsymbol{A} \)
The IUPAC name of \( \boldsymbol{A} \) is:
A. aldol
B. prop-1-ene-2-ol
c. 4 -hydroxy- 4 -methyl 2 -pentanone
D. 3-Hydroxybutanal
Subject: Physics
The orbit of Pluto is much more
eccentric than the orbits of the other
planets. That is, instead of being nearly
circular, the orbit is noticeably elliptical. The point in the orbit nearest
to the Sun is called the perihelion and
the point farthest from the Sun is called
the aphelion. At perihelion, the gravitational potential energy of Pluto
in its orbit has:
A. Its maximum value
B. Its minimum value
C. The same value as at every other point in the orbit
D. The value which depends on the sense of rotation
Subject: Chemistry
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{K}_{4}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) is \( 60 \% \) ionized
What will be its Van't Hoff factor?
A . 1.4
в. 3.4
c. 2.4
D. 4.
Subject: Physics
A body cools in 7 minutes from \( 60^{\circ} \mathrm{C} \) to
\( 40^{\circ} \mathrm{C} \). If the temperature of surrounding
is \( 10^{\circ} \mathrm{C}, \) the temperature after next 7
minutes will be :
\( \mathbf{A} \cdot 32^{\circ} C \)
B . \( 38^{\circ} \mathrm{C} \)
c. \( 22^{\circ} \mathrm{C} \)
D. None of these
Subject: Biology
Match the column I with column II and
choose the correct option.
\( \begin{array}{llll}\text { Column I } & & \text { Column II } \\ \begin{array}{l}\text { Synaptonemal } \\ \text { complex }\end{array} & \text { 1) } & \text { Zygotene } \\ \text { b) } & \begin{array}{l}\text { Recombination } \\ \text { nodules }\end{array} & \text { 2) } & \text { Pachytene } \\ \text { c) } & \begin{array}{l}\text { Activation of } \\ \text { recombinase } \\ \text { enzyme }\end{array} & \text { 3) } & \text { Diplotene } \\ \text { d) } & \begin{array}{l}\text { Termination of } \\ \text { chiasmata }\end{array} & \text { 4) } & \text { Diakinesis }\end{array} \)
\( A \cdot a-1, b-2, c-3, d-4 \)
\( B \cdot a-1, b-2, c-4, d-3 \)
\( c \cdot a-1, b-4, c-2, d-3 \)
\( D \cdot a-1, b-3, c-2, d-4 \)
Subject: Maths
Find the transpose of each of the following matrices:
\( (i)\left[\begin{array}{c}5 \\ \frac{1}{2} \\ -1\end{array}\right] \)
\( (i i)\left[\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right] \)
\( (i i i)\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right] \)
Subject: Physics
If the beads are released from rest, such
that the bead \( A \) is at the highest
position of ring at time \( t=0, \) the
magnitude of acceleration of the bead
\( B \) in the vertical direction at the same
instant is
\( A \). Zero
B. \( \frac{g}{4} \)
c. \( \frac{g}{2} \)
\( D \)
Subject: Maths
If \( S_{n}=\sum_{r=1}^{n} \frac{2 r+1}{r^{4}+2 r^{3}+r^{2}} \) then \( S_{20}= \)
A \( \cdot \frac{220}{2210} \)
в. \( \frac{420}{44} \)
c. \( \frac{439}{221} \)
D. \( \frac{440}{441} \)
Subject: Maths
The arithmetic mean of numbers
\( a, b, c, d, e \) is \( M . \) What is the value of \( (\boldsymbol{a}-\boldsymbol{M})+(\boldsymbol{b}-\boldsymbol{M})+(\boldsymbol{c}-\boldsymbol{M})+(\boldsymbol{d}- \)
\( M)+(e-M) ? \)
\( \mathbf{A} \cdot M \)
B. \( a+b+c+d+e \)
\( c \cdot 0 \)
\( D .5 M \)
Subject: Chemistry
If \( x \) is the ratio of currents it takes to
produce 4.5 g of platinum from molten
\( P t C l_{3} \) and \( P t C l_{5}, \) then \( 10 x \)
is
Electrolysis in each case is carried out for \( 1 \mathrm{min} 40 \) s. (Atomic Mass of \( \mathrm{Pt}= \)
195.0)
Subject: Physics
A beam of light converges at a point \( \mathrm{P} \) Now a lens is placed in the path of the convergent beam \( 12 \mathrm{cm} \) from P. At what
point does the beam converge if the lens
is
(a) a convex lens of focal length 20 \( \mathrm{cm}, \) and (b) a concave lens of focal
length \( 16 \mathrm{cm} ? \)
Subject: Physics
A homogeneous bar, as shown in the figure, has mass \( m \) and length L. The bar which is free to rotate in the vertical
plane about a pin at \( 0, \) is released from
rest in the position \( \theta=0 . \) The angular
acceleration, when \( \theta=60^{0} \) is:
A \( \cdot \frac{g}{2 L} \)
в. \( \frac{0.25 g}{L} \)
c. \( \frac{g}{L} \)
D. \( \frac{0.75 g}{L} \)
Subject: Physics
A satellite of mass m goes around the earth along a circular path of radius \( r \) (from the center of Earth), let me is the
mass of the earth and \( R \), its radius. Then
the linear speed of the satellite depends
on:
\( \mathbf{A} \cdot m_{e} \) and \( r \)
B . \( m_{e} \) only
\( \mathbf{c} \cdot \mu, m_{e}, V \)
D. \( m_{e}, R_{e} \) and \( r \)
Subject: Physics
A force \( \boldsymbol{F} \) is applied on free end of a
string such mass of \( 18 k g \) remain
stationary. Then value of \( \boldsymbol{F} \) will be:
\( \mathbf{A} \cdot 180 N \)
B. \( 90 N \)
c. \( 60 N \)
D. \( 30 N \)
Subject: Physics
In the figure shown, a T-shaped conductor moves with constant angular
velocity \( \omega \) in a plane perpendicular, to uniform magnetic field \( \vec{B} \). The potential
difference \( V_{A}-V_{B} \) is
A. zero
в.
\[
\frac{1}{2} B \omega l^{2}
\]
c. \( 2 B \omega l^{2} \)
D. B\omega \( l^{2} \)
Subject: Chemistry
Increasing order of reactivity of the
following compounds for \( \boldsymbol{S}_{N} \mathbf{1} \)
substitution is:
\( A \)
(B)
\( \mathbf{C} \)
\( \mathbf{D} \)
A \( \cdot(B)<(C)<(D)<(A) \)
В. \( (A)<(B)<(D)<(C) \)
C. \( (B)<(A)<(D)<(C) \)
D. \( (B)<(C)<(A)<(D) \)
Subject: Physics
A faulty thermometer has \( 90.5^{\circ} \mathrm{C} \) and
\( 0.5^{\circ} \mathrm{C} \) as upper and lower fixed points
respectively. What is the correct temperature if this faulty
thermometer reads \( 15.5^{\circ} \mathrm{C} \)
A \( \cdot 16.67^{\circ} \mathrm{C} \)
B . \( 16^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 15^{\circ} \mathrm{C} \)
D. \( 15.5^{\circ} \mathrm{C} \)
Subject: Maths
A circus is climbing a \( 20 m \) long rope, which is tightly stretched and tied from the top of vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level
is \( 30^{\circ} \)
A \( .24 m \)
в. 18 т
c. \( 28 m \)
D. \( 10 m \)
Subject: Maths
Let \( \alpha \) and \( \beta \) be any two positive values
of \( x \) for which \( 2 \cos x,|\cos x|, \) and \( 1- \)
\( 3 \cos ^{2} x \) are in G.P. The minimum value
of \( |\boldsymbol{\alpha}-\boldsymbol{\beta}| \) is
A \( \cdot \frac{\pi}{3} \)
в.
c. \( \frac{\pi}{2} \)
D. None of these
Subject: Maths
A metal sheet \( 27 \mathrm{cm} \) long, \( 8 \mathrm{cm} \) broad
and \( 1 \mathrm{cm} \) thick is melted to form a cube
The difference between the surface
areas of the two solids is
A \( \cdot 284 \mathrm{cm}^{2} \)
B . \( 286 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 296 \mathrm{cm}^{2} \)
D. \( 280 \mathrm{cm}^{2} \)
Subject: Physics
The diameter of a piston \( P_{2} \) is \( 50 \mathrm{cm} \)
and that of a piston \( P_{1} \) is \( 10 \mathrm{cm} \). What is
the force exerted on \( P_{2} \) when a force of
\( \mathbf{1} N \) is applied on \( \boldsymbol{P}_{1} ? \)
Subject: Chemistry
The solubility product of \( A g_{2} C r O_{4} \) is \( 32 \times 10^{-12} . \) What is the concentration
of \( C r O_{4}^{-} \) ions in that solution?
A \( \cdot 2 \times 10^{-4} m / s \)
В . \( 16 \times 10^{-4} \mathrm{m} / \mathrm{s} \)
c. \( 8 \times 10^{-4} m / s \)
D. \( 8 \times 10^{-8} \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
Match the following with the correct
answers.
(a) Scouring
(i) Yields silk
fibers
(b) Mulberry leaves
(ii) Cleaning sheared skin
(c) Sheep
(iii) Food of silk
worm.
(d) Cocoon
(iv) Wool yielding animal.
B . a - ->i, b- -> ii, c- -> iii, d- > iv
\( c \cdot a->-i v, b->>i i i, c-\rightarrow>i i, d->i \)
D. a->- ii, b- -> i, c- -> ii, d- - > iv
Subject: Maths
Given two independent events \( A, B \)
such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 6} \)
Determine
\( \boldsymbol{P}(\boldsymbol{A} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{B}) \)
Subject: Maths
Find the modulus, argument and the principal argument of the complex numbers.
\( z=1+\cos \frac{10 \pi}{9}+i \sin \left(\frac{10 \pi}{9}\right) \)
A . Principal Arg \( z=-\frac{4 \pi}{9} ;|z|=2 \cos \frac{4 \pi}{9} ; \operatorname{Arg} z=2 k \pi- \)
\( \frac{4 \pi}{9} k \epsilon l \)
B. Principal Arg \( z=-\frac{10 \pi}{9} ;|z|=2 \cos \frac{10 \pi}{9} ; \) Argz\( =2 k \pi- \)
\( \frac{10 \pi}{9} k \epsilon l \)
C . Principal Arg \( z=-\frac{-10 \pi}{9} ;|z|=2 \cos \frac{-10 \pi}{9} ; \) Argz\( = \)
\( 2 k \pi-\frac{4 \pi}{9} k \epsilon l \)
D. Principal Arg \( z=-\frac{-4 \pi}{9} ;|z|=2 \cos \frac{-4 \pi}{9} ; \) Argz\( =2 k \pi- \)
\( \frac{4 \pi}{9} k \epsilon l \)
Subject: Physics
A beaker containing liquid is placed on a table, underneath a microscope which can be moved along a vertical scale. The microscope is focused through the liquid on to a mark on the table when
the reading on the scale is \( h_{1} . \) It is next
focused on the upper surface of the
liquid and the reading is \( h_{2} . \) More liquid
is added and the observations are
repeated, the corresponding readings \( \operatorname{are} h_{1}^{\prime} \) and \( h_{2}^{\prime} . \) The refractive index of the liquid is
\( \mathbf{A} \)
\[
\frac{h_{2}^{\prime}-h_{2}}{h_{2}^{\prime}-h_{1}^{\prime}-h_{2}+h_{1}}
\]
B.
\[
\frac{h_{2}^{\prime}-h_{1}^{\prime}}{h_{2}^{\prime}-h_{1}^{\prime}-h_{2}+h_{1}}
\]
\( \mathbf{c} \)
\[
\frac{h_{1}^{\prime}-h_{2}}{h_{2}^{\prime}-h_{1}^{\prime}-h_{2}+h_{1}}
\]
D. None of these
Subject: Maths
Which of the following limits vanishes?
A \( \cdot \lim _{x \rightarrow \infty} x^{\frac{1}{4}} \sin \frac{1}{\sqrt{x}} \)
B. \( \lim _{x \rightarrow \pi^{2}}(1-\sin x) \cdot \tan x \)
C \( \lim _{x \rightarrow \infty} \frac{2 x^{2}+3}{x^{2}+x-5} \cdot \) sgn
D. \( \lim _{x \rightarrow 3^{\circ}} \frac{[x]^{2}-9}{x^{2}-9} \) where [] denotes greatest integer function
Subject: Chemistry
The progress of reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{x} \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{y} \boldsymbol{C}(\boldsymbol{g}) \) with time is presented
in figure. What is the value of \( \boldsymbol{K}_{c}^{0} \) at
\( \mathbf{3 0 0 K} ? \)
\( A \)
B.
\( c .3 \)
\( D \)
Subject: Physics
A resistance \( (R=12 \Omega), \) an inductor
\( \boldsymbol{L}=\mathbf{2} \boldsymbol{H}) \) and a capacitor \( (\boldsymbol{C}=\mathbf{5} \boldsymbol{\mu} \boldsymbol{F}) \)
are connected to an AC generator of
frequency \( 50 H z . \) Which of the following statement is correct?
A. At resonance, the circuit impedance is zero
B. At resonance, the circuit impedance is \( 12 \Omega \)
c. At resonance, the frequency of the circuit is \( 1 / 2 \pi \)
D. The inductive reactance is less than the capacitive reactance
Subject: Physics
A block of mass \( 0.5 k g \) is moving with a speed of \( 2.0 m / s \) on smooth surface. It
strikes another mass of \( 1.0 k g \) and then they move together as a single body. The energy loss during collision is (in J)
A . 0.16
B. 0.67
c. 1.0
D. 6.7
Subject: Chemistry
What is the density of solution of sulphuric acid used as an electrolyte in lead accumulator?
\( \mathbf{A} \cdot 1.5 \mathrm{gm} L^{-1} \)
B. \( 1.2 \mathrm{gm} L^{-1} \)
c. \( 1.8 \mathrm{gm} L^{-1} \)
D. \( 2.0 \mathrm{gm} L^{-1} \)
Subject: Maths
If \( |a|=5 .|\vec{b}|=4, \) and \( |c|=3 . \) then what will be the value of \( \vec{a} . \vec{b}+\vec{b} . \vec{c}+\vec{c} . \vec{a} \) given that \( \vec{a}+\vec{b}+\vec{c}=0 \)
A . 25
B. 50
c. -25
D. -50
Subject: Physics
If a conducting rod of length \( 4 l \) is
rotated about at point \( \boldsymbol{O} \) in a uniform
magnetic field \( B \) directed into the
paper and \( D E=l, E A=3 l \), then which
of the folowing is true?
\[
\begin{array}{rrrrrrrrrr}
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \multicolumn{1}{c} {\omega_{M}} & \times & \times & \times & \times & \times \\
\multicolumn{1}{c} {\times} & \times & \times & \times E_{\times} & & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times \\
\times & \times & \times & \times & \times & \times & \times & \times & \times & \times & \times
\end{array}
\]
A.
\[
V_{A}-V_{E}=\frac{9}{2} B \omega l^{2}
\]
B.
\[
V_{E}-V_{A}=\frac{9}{2} B \omega l^{2}
\]
\( \mathbf{c} \)
\[
V_{D}-V_{E}=\frac{B \omega l^{2}}{2}
\]
D. \( V_{A}-V_{E}=4 B \omega l^{2} \)
Subject: Chemistry
Complete and balance the following
compound \( \boldsymbol{C a}_{\mathbf{5}}\left(\boldsymbol{P O}_{4}\right)_{3} \boldsymbol{F}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \stackrel{\boldsymbol{H} e a t}{\rightarrow}-\ldots-\ldots-+\boldsymbol{C} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4} \)
\( 2 H_{2} O+_{-}-_{-}-- \)
Subject: Physics
The force required just to move a body up an inclined plane is double the force required just to prevent the body sliding down. If the coefficient of friction is 0.25
the angle of inclination of the plane is
A \( \cdot 36.8^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 42.6^{\circ} \)
Subject: Chemistry
In which of the following reactions the inversion of configuration takes place?
(I) pentan\( -2-o l+S O C l_{2} \rightarrow \)
(II) pentan\( -2-o l+C O C l_{2} \longrightarrow \)
(III) pentan \( -2-o l+(A)+S O C l_{2} \)
Pyridine
(IV) pentan\( -2-o l+ \)COCl\( _{2} \stackrel{\text {Pyridine}}{ } \)
\( \mathbf{A} \cdot(I),(I I I) \)
в. \( (I),(I I) \)
c. \( (I I I),(I V) \)
D. \( (I),(I V) \)
Subject: Physics
At a given place where acceleration due
to gravity is \( g m / s e c^{2}, \) a sphere of lead
of density \( d k g / m^{3} \) is gently released in
a column of liquid of density \( \rho k g / m^{3} . \). \( \boldsymbol{d}>\boldsymbol{\rho}, \) then immediately after the
sphere is released inside the liquid,
¡t will:
A . fall vertically with an acceleration of \( g \) m/ sec\( ^{2} \)
B. fall vertically with no acceleration
c. fall vertically with an acceleration \( g\left(\frac{d-\rho}{d}\right) \)
D. fall vertically with an acceleration \( (g \rho) / d \)
Subject: Physics
Find the maximum velocity of the bar over its motion.
A \( \cdot v_{\max }=\sqrt{\frac{g}{a} \cos \alpha \tan \alpha} \)
B. \( v_{\max }=\sqrt{\frac{2 g}{a} \sin \alpha \tan \alpha} \)
c. \( v_{m a x}=\sqrt{\frac{g}{a} \sin \alpha \tan \alpha} \)
D. \( v_{\max }=\sqrt{\frac{2 g}{a} \cos \alpha \tan \alpha} \)
Subject: Maths
Equation of a straight line passing through the point (2,3) and inclined at an angle of \( \tan ^{-1}\left(\frac{1}{2}\right) \) with the line \( y+ \) \( 2 x=5 \) is
This question has multiple correct options
\( \mathbf{A} \cdot y=3 \)
B. \( x=2 \)
c. \( 3 x+4 y-18-0 \)
D. \( 4 x+3 y-17=0 \)
Subject: Chemistry
toppr
Q Type your question.
radicals with almost equal ease, whereas bromine free radicals have a
clear preference for the formation of tertiary free radicals. So, bromine is
less reactive, and more selective
whereas chlorine is less selective and
more effective.
The relative rate of abstraction of
hydrogen by Br is \( \underset{(1600)}{3^{\circ}}>\underset{(82)}{2^{\circ}}>1^{\circ} \)
The relative rate of abstraction of
hydrogen by Cl is \( \mathbf{3}^{\circ}>\underset{(3.8)}{\mathbf{2}}^{\circ}>\mathbf{1}_{(1)}^{\circ} \)
\( (\mathbf{5}) \)
F. What would be the product ratio \( x / y \) in the chlorination of propane if all the
hydrogen were abstracted at equal rate
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \frac{C l_{2}}{h v} \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C H}_{3} \)
\( A \cdot 1 \)
3
B. 3 \( \overline{1} \)
\( c .9 \)
\( \overline{1} \)
\( D \)
Subject: Maths
If \( y=e^{m \sin ^{-1} x} \) then show that \( (1- \)
\( \left.\boldsymbol{x}^{2}\right) \boldsymbol{y}_{\boldsymbol{n}+\mathbf{2}}-(\boldsymbol{2} \boldsymbol{n}+\mathbf{1}) \boldsymbol{x} \boldsymbol{y}_{\boldsymbol{n}+\mathbf{1}}-\left(\boldsymbol{n}^{2}+\right. \)
\( \left.\boldsymbol{m}^{2}\right) \boldsymbol{y}_{n}=\mathbf{0} \)
Subject: Physics
The figure above represents some of the lower energy levels of the hydrogen atom in simplified form.
If the transition of an electron from \( \boldsymbol{E}_{\mathbf{4}} \)
to \( E_{2} \) were associated with the
emission of blue light, which one of the
following transitions could be
associated with the emission of red
light?
\( \mathbf{A} \cdot E_{4} \) to \( E_{1} \)
B \( . E_{3} \) to \( E_{1} \)
\( \mathbf{c} \cdot E_{3} \) to \( E_{2} \)
D. \( E_{1} \) to \( E_{3} \)
Subject: Physics
Two stationary objects are in
an equilibrium position on a seesaw.
The first object has a mass of \( 3 k g \) and
rests \( 10 m \) from the pivot. The other
rests \( 1 m \) from the pivot. Find out the
mass of the second object.
A. \( 0.3 k g \)
B. \( 3 k g \)
c. \( 10 k g \)
D. \( 30 k g \)
E . \( 50 k g \)
Subject: Physics
The volume of a gas at constant pressure increases by \( 2 \% \) when the temperature is increased by \( 5^{0} \) K, It's initial temperature
is
\( \mathbf{A} \cdot 100^{0} \mathbf{K} \)
B . 250^ K
\( c \cdot 500^{0} \mathrm{K} \)
D. \( 1000^{\circ} \) к
Subject: Physics
\( S_{1} \) and \( S_{2} \) are two coherent sources of
sound having no initial phase
difference. The velocity of sound is 330 \( \mathrm{m} / \mathrm{s} . \) No maxima will be formed on the
line passing through \( S_{2} \) and
perpendicular to the line joining
\( \boldsymbol{S}_{1} \) and \( S_{2} . \) If the frequency of both the
sources is :
A. 330 \( \mathrm{Hz} \)
в. 120 Н \( z \)
\( c \cdot 100 \mathrm{Hz} \)
D. 220 нz
Subject: Physics
A star initially has \( 10^{40} \) deuterons. It produces energy via the processes \( _{1} H^{2}+_{1} H^{2} \rightarrow_{1} H^{3}+p \) and \( _{1} H^{2}+_{1} \)
\( H^{3} \rightarrow_{2} H e^{4}+n . \) If the average power
radiated by the star is \( 10^{16} \mathrm{W} \), the deuteron supply of the star is exhausted in a time of the order of
[The mass of nuclei are as follows:
\( \boldsymbol{M}\left(\boldsymbol{H}^{2}\right)=\mathbf{2 . 0 1 4} \boldsymbol{a m} \boldsymbol{u}, \boldsymbol{M}(\boldsymbol{n})= \)
\( \mathbf{1 . 0 0 8 a m u} \)
\( M(p)=1.007 a m u, M\left(H e^{4}\right)= \)
\( 4.001 a m u\} \)
A \( \cdot 10^{6} s \)
B . \( 10^{8} \) s
\( c \cdot 10^{12} s \)
\( s \)
D. \( 10^{16} s \)
Subject: Chemistry
Which of the following reactions is not oxidation-reduction reaction?
\( \mathbf{A} \cdot H \oplus+O H^{\ominus} \rightarrow H_{2} O \)
B \( \cdot \frac{1}{2} H_{2}+\frac{1}{2} C l_{2} \rightarrow H C l \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \rightarrow \mathrm{CaO}+\mathrm{CO}_{2} \)
D. \( A \) and \( C \)
Subject: Maths
If \( \boldsymbol{A}=\tan ^{-1}\left(\frac{\boldsymbol{x} \sqrt{\mathbf{3}}}{\mathbf{2 K}-\boldsymbol{x}}\right) \) and \( \boldsymbol{B}= \)
\( \tan ^{-1}\left(\frac{2 x-K}{K \sqrt{3}}\right), \) then the value of
\( A-B \) is
\( A \)
B. 45
\( c .60 \)
D. 30
Subject: Physics
A body of mass \( 2 k g \) is thrown upward with initial velocity \( 20 m / s . \) After \( 2 s \) find its kinetic energy will be: \( (\boldsymbol{g}= \) \( \left.10 m / s^{2}\right) \)
A. \( 400 J \)
B. 200 J
c. \( 100 J \)
D. zero
Subject: Chemistry
Calculate the \( p H \) (nearest integer) of
\( \mathbf{0 . 0 1 0} M \mathbf{N a H C O}_{\mathbf{3}} \) solution. \( \boldsymbol{K}_{\mathbf{1}}= \)
\( 4.5 \times 10^{-7} \) and \( K_{2}=4.7 \times 10^{-11} \) for
carbonic acid.
Subject: Physics
rest on a inclined plane and are separated by a distance of 6.0 m as
shown in figure. The coefficient of
friction between each of the blocks and
the inclined plane is \( 0.25 . \) The \( 2 k g \) block
is given a velocity of \( 10.0 \mathrm{m} / \mathrm{s} \) up the
inclined plane. It collides with \( \boldsymbol{M} \)
comes back and has a velocity of \( 1.0 m / s \) when it reaches its initial
position. The other block \( M \) after the
collision moves \( 0.5 m \) up comes to rest.
calculated the coefficient [Take \( \sin \theta= \)
\( \left.\tan \theta=0.05 \text { and } g=10 m / s^{2}\right] \)
\( \mathbf{A} \cdot e=0.84, M=15 k g \)
в. \( e=4, M=5 k g \)
c. \( e=9, M=15 k g \)
D. \( e=84, M=17 k g \)
Subject: Physics
Two metallic wires \( A \) and \( B \) of equal
dimensions but made of different
materials, having resistivities \( \rho \) and \( 2 \rho \) temperature coefficients of resistivities \( 2 \alpha \) and \( \alpha \) are connected in series. The
temperature coefficient of resistance of the composite wire equals:
\( ^{\mathrm{A}} \rho_{e q}=\frac{3}{2} \rho \)
в. \( \quad \alpha_{e q}=\frac{3}{2} \)
\( c \cdot \rho_{e q}=3 \rho \)
D. \( _{\alpha_{e q}}=\frac{4}{3} \alpha \)