AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If in the determinant \( \Delta= \)
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \boldsymbol{c}_{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \boldsymbol{c}_{2} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & \boldsymbol{c}_{3}\end{array}\right|, \boldsymbol{A}_{i}, \boldsymbol{B}_{i}, \boldsymbol{C}_{i} \) etc. be the co-
factors of \( a_{i}, b_{i}, c_{i} \) etc., then which of the
following relations is incorrect?
A \( \cdot a_{1} A_{1}+b_{1} B_{1}+c_{1} C_{1}=\Delta \)
B . \( a_{2} A_{2}+b_{2} B_{2}+c_{2} C_{2}=\Delta \)
c. \( a_{3} A_{3}+b_{3} B_{3}+c_{3} C_{3}=\Delta \)
D. \( a_{1} A_{2}+b_{1} B_{2}+c_{1} C_{2}=\Delta \)
Subject: Physics
toppr
Q Type your question
can emit a \( \beta \) particle \( \left(\beta_{1}\right) \) and come to
ground state by either emitting one \( \gamma \)
ray \( \left(\gamma_{1}\right) \) or emitting two \( \gamma \) rays \( \left(\gamma_{3} \& \gamma_{4}\right) \)
(ii) it can emit one \( \beta \) particle \( \left(\beta_{2}\right) \) and
come to ground state by emitting \( \gamma_{2} \)
ray.
Atomic masses : \( ^{198} A u=197.9682 \) a.m.u.
\( ^{198} \boldsymbol{H} \boldsymbol{g}=\mathbf{1 9 7 . 9 6 6 2} \) amu \( , 1 \) amu \( = \)
\( 930 M e V / c^{2} \)
The energy levels of the nucleus are shown in figure. What is the maximum kinetic energy of
emitted \( \beta_{2} \) particles?
A. \( 1.44 \mathrm{MeV} \)
в. \( 0.59 \mathrm{MeV} \)
c. \( 1.86 \mathrm{MeV} \)
D. \( 1.46 M \)
Subject: Physics
A sphere contracts in volume by \( 0.01 \% \) when taken to the bottom of sea \( 1 \mathrm{km} \) deep. Find bulk modulus of the material
of sphere
A. \( 9.8 \times 10^{6} M / M^{2} \)
В. \( 1.2 \times 10^{10} N / M^{2} \)
c. \( 9.8 \times 10^{10} N / M^{2} \)
D. \( 9.8 \times 10^{11} N / M^{2} \)
Subject: Maths
Let
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}^{2} & \text { if } \boldsymbol{x} \leq \boldsymbol{x}_{0} \\ \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} & \text { if } \boldsymbol{x}>\boldsymbol{x}_{0}\end{array}\right. \)
The values of the coefficients a and b for which the function is continuous and
has a derivative at \( x_{0} \). are
A \( \cdot a=x_{0}, b=-x_{0} \)
B . \( a=2 x_{0}, b=-x_{0}^{2} \)
C \( . a=x_{0}^{2}, b=-x_{0} \)
D. \( a=x_{0}, b=-x_{0}^{2} \)
Subject: Physics
A body of mass \( \mathrm{M} \) is situated in a
potential field \( \boldsymbol{U}(\boldsymbol{x})=\boldsymbol{U}_{0}(\mathbf{1}-\cos \boldsymbol{d} \boldsymbol{x}) \)
where \( U_{0} \) and \( d \) are constants. The time
period of small oscillations will be
в. \( 2 \pi \sqrt{\frac{M}{U_{0} d^{2}}} \)
\( ^{\mathbf{C}} \cdot 2 \pi \sqrt{\frac{U_{0} d^{2}}{M}} \)
D. \( 2 \pi \sqrt{\frac{U_{0}}{M d^{2}}} \)
Subject: Physics
What is the number density of donor atoms which must be added to a pure
germanium semiconductor to produce an N-type semiconductor of
conductivity \( 6.4 X 10^{2} \) oh \( m^{-1} m^{-1} \) ? The mobility of electrons in N-type germanium is \( 4 X 10^{-1} m^{2} V^{-1} s^{-1} \)
Neglect contribution of holes to conductivity.
A \( \cdot 10^{20} m^{-3} \)
B. \( 10^{21} m^{-3} \)
\( \mathrm{c} \cdot 10^{22} \mathrm{m}^{-3} \)
D. \( 10^{23} \) s \( ^{-3} \)
Subject: Chemistry
Which among the following represent the conjugate acid/base pairs? This question has multiple correct options
A \( \cdot H_{3} O^{+} / H_{2} O \)
в. \( H_{2} S O_{4} / S O_{4}^{2} \)
c. \( H C O_{3}^{-} / C O_{3}^{2} \)
D. All are conjugate acid/ base pairs
Subject: Physics
Find at what height \( x_{m}, \) the ball will experience the maximum attraction.
A \( \cdot x_{m}=\frac{1}{\sqrt{a}} \)
B. \( x_{m}=\frac{1}{\sqrt{4 a}} \)
c. \( _{x_{m}}=\frac{1}{\sqrt{2 a}} \)
D. \( x_{m}=\frac{2}{\sqrt{a}} \)
Subject: Physics
Two particles having mass ratio \( n: 1 \)
are interconnected by a light in extensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of
mass of the system is :
A \( \cdot(n-1)^{2} g \)
\( ^{\text {B }}\left(\frac{n+1}{n-2}\right)^{2} \)
\( ^{\mathbf{c}} \cdot\left(\frac{n-1}{n+2}\right)^{2} \)
D. \( \left(\frac{n-1}{n+2}\right) g \)
Subject: Maths
If \( [\mathbf{x}] \) stands greatest integer \( \leq \mathbf{x} \) then
the value of \( \left|\begin{array}{ccc}{[\boldsymbol{e}]} & {[\boldsymbol{\pi}]} & {\left[\boldsymbol{\pi}^{2}-\boldsymbol{6}\right]} \\ {[\boldsymbol{\pi}]} & \boldsymbol{\pi}^{2}-\boldsymbol{6} & {[\boldsymbol{e}]} \\ {\left[\boldsymbol{\pi}^{2}-\boldsymbol{6}\right]} & {[\boldsymbol{e}]} & {[\boldsymbol{\pi}]}\end{array}\right| \) equals
\( A \cdot-8 \)
B. 8
\( c \cdot-1 \)
\( D \)
Subject: Maths
Given that \( x \) and \( y \) satisfy the relation. \( \boldsymbol{y}=\mathbf{3}[\boldsymbol{x}]+\mathbf{7} \)
\( \boldsymbol{y}=\mathbf{4}[\boldsymbol{x}-\mathbf{3}]+\mathbf{4} \) then find \( [\boldsymbol{x}+\boldsymbol{y}] \)
Subject: Physics
A ball of radius \( \boldsymbol{R}=\mathbf{1 0 . 0} \) cm rolls
without slipping on a horizontal plane
so that its centre moves with constant
acceleration \( a=2.50 \mathrm{cm} / \mathrm{s}^{2} ; t=2.00 s \)
after the beginning of motion its portion corresponds to that shown in Fig. Find:
(a) the velocities of the points \( A, B \) and
\( O \)
(b) the accelerations of these points.
Subject: Maths
Based on equations reducible to linear
equations Solve for \( x \) and \( y: \frac{24}{2 x+y}-\frac{13}{3 x+2 y}= \) \( 2 ; \frac{26}{3 x+2 y}+\frac{8}{2 x+y}=3 \)
A. \( x=-2, y=6 \)
в. \( x=-5, y=3 \)
c. \( x=3, y=2 \)
D. \( x=1, y=0 \)
Subject: Chemistry
Lead obtained from galena ore (PbS) by air reduction or carbon reduction
process contains base metal (Cu, Bi, As, Sn, \( Z n \) ) as impurities. Which of the following electrolyte is used for electrolysis of Pb?
\( \mathbf{A} \cdot P b S O_{4}+H_{2} S O_{4} \)
в. \( P b C l_{2}+H C l \)
\( \mathbf{c} \cdot P b S i F_{6}+H_{2} S i F_{6} \)
D. none of these
Subject: Maths
Assertion
No. of spherical balls that can be made out of a solid cube of lead whose edge is \( 44 \mathrm{cm}, \) each ball being \( 4 \mathrm{cm} \). in diameter, is 2541
Reason
Number of balls = (Volume of one
ball)/(Volume of lead)
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
Which one of the following relations is
true?
\( A \cdot \cos ^{2} \Theta-\sin ^{2} \Theta=1 \)
B. \( \operatorname{cosec}^{2} \Theta-\sec ^{2} \Theta=1 \)
\( \mathbf{c} \cdot \cot ^{2} \Theta-\tan ^{2} \Theta=1 \)
\( \mathrm{D} \cdot \sec ^{2} \Theta-\tan ^{2} \Theta=1 \)
Subject: Chemistry
For the reaction, \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \)
\( 2 H I(g), \) the equilibrium constant \( K_{p} \)
changes with:
A. total pressure
B. catalyst
C. the amounts of \( H_{2} \) and \( I_{2} \) present
D. temperature
Subject: Maths
The line \( 3 x+2 y=0 \)
A \( \cdot \) passes through (3,2) and \( m=-\frac{3}{2} \)
B. passes through (0,0) and \( m=\frac{3}{2} \)
c. passes through (2,3) and \( m=-\frac{3}{2} \)
D. passes through (0,0) and \( m=-\frac{3}{2} \)
Subject: Maths
Factorise:
\( (i) 25-4 x^{2}-12 x y-9 y^{2} \)
\( (i i) x^{2}-a^{2}+10 a b-25 b^{2} \)
\( (i i i) 6 x y+x^{2}+9 y^{2}-4 a^{2} \)
\( (i v) 9 x^{2}+4+12 x-a^{2}+2 a b-b^{2} \)
Subject: Physics
In an LCR circuit having \( \boldsymbol{L}=\mathbf{8 . 0 H}, \boldsymbol{C}- \)
\( 0.5 \mu F \) and \( R=100 \Omega \) in series, the
resonance frequency is:
A . 600 rad/sec
в. \( 600 H z \)
c. 500 rad/sec
D. \( 500 H z \)
Subject: Chemistry
Select the correct I.U.P.A.C. name for
\( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{NO})\right] \mathrm{SO}_{4} \)
A. Pentaaqua nitrosonium iron
(I) sulphate
B. Pentaaqua nitrosylium iron (I) sulphate
c. Pentaaqua nitrosylium iron
(II) sulphate
D. Pentaaqua nitrosonium ferrate
(II) sulphate
Subject: Maths
If the equation to the locus of points equidistant from the points (-2,3),(6,-5) is \( a x+b y+c=0 \)
where \( a>0 \) then, the ascending order
of \( a, b, c \) is
A. \( a, b, c \)
в. \( c, b, a \)
c. \( b, c, a \)
D. \( a, c, b \)
Subject: Physics
A bomb of mass 9 kg explodes into two pieces of masses \( 3 \mathrm{kg} \) and 6 kg. The velocity of mass \( 3 \mathrm{kg} \) is \( 16 \mathrm{ms}^{-1} \). The
kinetic energy of mass \( 6 \mathrm{kg} \) is
A . 96 J
B. 384 J
c. 192 J
D. 768 J
Subject: Physics
A metallic spherical shell has an inner
radius \( \boldsymbol{R}_{1} \) and outer radius \( \boldsymbol{R}_{2} . \) A charge
is placed at the centre of the spherical cavity. The surface charge density on
the outer surface is
A \( \cdot \frac{-q}{4 \pi R_{1}^{2}} \)
В. \( \frac{q}{4 \pi R_{2}^{2}} \)
c. \( \frac{q^{2}}{4 \pi R_{1}^{2}} \)
D. \( \frac{2 q}{4 \pi R_{2}^{2}} \)
Subject: Chemistry
The standard e.m.f. of the following cell
is \( 0.463 \mathrm{V} \)
\( \boldsymbol{C} \boldsymbol{u}\left|\boldsymbol{C} \boldsymbol{u}^{++} \| \boldsymbol{A} \boldsymbol{g}^{+}\right| \boldsymbol{A} \boldsymbol{g} \)
\( (s)^{\prime}(I M)^{\prime}(I M)^{\prime}(s) \)
If the standard potential of Ag electrode
is \( 0.800 \mathrm{V} \), what is the standard
potential of Cu electrode?
Subject: Maths
Construct \( \triangle L M N \) in which base
\( M N=7 \mathrm{cm}, \angle L M N=75^{\circ} \) and
\( \boldsymbol{L} \boldsymbol{M}+\boldsymbol{L} \boldsymbol{N}=\mathbf{9} \boldsymbol{c m} \)
Subject: Physics
Match the following.
\( \mathbf{A} \cdot A-H, B-G, C-E, D-F \)
\( \mathbf{B} \cdot A-G, B-H, C-E, D-F \)
\( \mathbf{c} \cdot A-E, B-H, C-G, D-F \)
\( \mathbf{D} \cdot A-F, B-G, C-H, D-F \)
Subject: Physics
Write the truth table for circuit given in the figure, consisting of NOR gates and identify the logic operation (OR, AND, NOT) which this circuit is performing. (Hint: \( A=0, B=1 \) then \( A \) and \( B \) inputs of
second NOR gate will be 0 and hence
\( Y=1 . \) Similarly work out the values of \( Y \) for other combinations of \( A \) and \( B \).
Compare with the truth table of OR,
AND, NOT gates and find the correct
one).
Subject: Maths
n \( \triangle A B C \),right angled at \( B, A B+ \) \( \boldsymbol{A C}=\mathbf{9} \) cm and \( \boldsymbol{B C}=\mathbf{3} \boldsymbol{c m} \)
The value of \( \sec C \) is
\( A \cdot \frac{4}{3} \)
B.
\( c \cdot \frac{1}{3} \)
D. none
Subject: Physics
In Young's double-slit experiment \( \boldsymbol{d} / \boldsymbol{D}=\mathbf{1 0}^{-4}(\boldsymbol{d}= \) distance between
slits, \( D= \) distance of screen from the
slits). At point \( P \) on the screen resulting intensity is equal to the intensity due to the individual slit \( \boldsymbol{I}_{0} \) Then, the distance of point \( P \) from the central maximum is \( (\boldsymbol{\lambda}=\mathbf{6 0 0 0} \boldsymbol{\boldsymbol { A }}) \)
\( \mathbf{A} \cdot 2 m m \)
B. \( 1 \mathrm{mm} \)
\( \mathrm{c} .0 .5 \mathrm{mm} \)
D. \( 4 \mathrm{mm} \)
Subject: Physics
When an iron cylinder of diameter \( 0.20 \mathrm{cm} \) and length \( 30 \mathrm{cm} \) is kept parallel to a magnetic field of intensity
\( 4800 A / m \) the cylinder acquires a pole
strength of \( 9 A m . \) Find the permeability
of the material of the rod?
A \( .0 .075222 \times 10^{-4} \mathrm{H} / \mathrm{m} \)
B . \( 9.522 \times 10^{-4} \mathrm{H} / \mathrm{m} \)
c. \( 75.22 \times 10^{-4} \mathrm{H} / \mathrm{m} \)
D. \( 7.522 \times 10^{-4} \mathrm{H} / \mathrm{m} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\boldsymbol{x}-\boldsymbol{2})(\boldsymbol{x}-\boldsymbol{4}), \mathbf{1} \leq \boldsymbol{x} \leq \mathbf{4} \)
then a number satisfying the conditions of the mean value theorem is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \frac{5}{2} \)
\( c .3 \)
D. \( \frac{7}{2} \)
Subject: Physics
What is the largest distance (in a straight line) that can be measured
with a meter scale of length \( 1 \mathrm{m} \) and smallest division of \( 1 \mathrm{mm} \) ?
\( \mathbf{A} \cdot 1 \mathrm{mm} \)
в. \( 1 \mathrm{m} \)
c. \( 100 \mathrm{m} \)
D. No upper limit exists for measurement of length with meter scale.
Subject: Physics
The radius of a flywheel is \( 10 \mathrm{cm} \). It is
rotated at the rate of 25 rads \( ^{-2} \). When a
constant force \( 40 N \) is applied on the rim of wheel along its tangent. The moment of inertia of wheel is:
\( \mathbf{A} \cdot 0.01 \mathrm{kgm}^{2} \)
B. \( 0.1 \mathrm{kgm}^{2} \)
\( \mathbf{c} \cdot 0.16 k g m^{2} \)
D. \( 1.6 k g m^{2} \)
Subject: Chemistry
\( A \) compound \( C \) (molecular formula,
\( \left.C_{2} H_{4} O_{2}\right) \) reacts with \( N a \) metal to form
a compound \( \boldsymbol{R} \) and evolves a gas which
burns with a pop sound. Compound \( C \)
on treatment with an alcohol \( A \) in
presence of an acid forms a sweet smelling compound \( S \) (molecular formula, \( C_{3} H_{6} O_{2} \) ). On addition of
NaOH to \( C, \) it also gives \( R \) and water.
S on treatment with \( N a O H \) solution
gives back \( \boldsymbol{R} \) and \( \boldsymbol{A} \)
Identify \( \boldsymbol{R} \) and \( \boldsymbol{A} \) ?
A . Compound \( R \) is \( C H_{3} C O O N a \) Compound \( A \) is \( C H_{3} O H \)
B. Compound \( A \) is \( C H_{3} O H \) Compound \( R \) is \( C H_{3} C O O C H_{3} \)
C. Compound \( A \) is \( C H_{3} C O O H \) compound \( R \) is \( C H_{3} C O O N a \)
D. Compound \( A \) is \( C H_{3} C O O N a \) Compound \( R \) is \( C H_{3} O H \)
Subject: Chemistry
A gas container observes Maxwellian
distribution law of speed. If the number
of molecules between the speed 5.0 and 5.1 km per sec at \( 298 \mathrm{K} \) is N, what would be number of molecules between this
range of speed if the total number of molecules in the vessel are doubled?
A . \( 2 N \)
в.
\( c \cdot 2 N^{2} \)
D. \( N^{2} / 2 \)
Subject: Maths
Let the number of elements of the sets
\( A \) and \( B \) be \( p \) and \( q \) respectively. Then
the number of relations from the set \( \boldsymbol{A} \)
to the set \( B \) is
\( \mathbf{A} \cdot 2^{p+q} \)
B. \( 2^{p q} \)
c. \( p+q \)
\( \mathbf{D} \cdot p q \)
Subject: Physics
A point charge of value \( 10^{-7} C \) is
situated at the centre of cube of \( 1 \boldsymbol{m} \)
side. The electric flux through its total
surface area is:
A. \( 113 \times 10^{4} \mathrm{Nm}^{2} / \mathrm{C} \)
в. \( 11.3 \times 10^{4} \mathrm{Nm}^{2} / \mathrm{C} \)
C. \( 1.13 \times 10^{4} \mathrm{Nm}^{2} / \mathrm{C} \)
D. none of these
Subject: Maths
A sum of Rs. 15500 was lent partly at \( 5 \% \)
and partly at \( 8 \% \) p.a. simple interest. The total interest received after 3 years was
Rs. \( 3000 . \) The ratio of the money lent at \( 5 \% \) at that lent at \( 8 \% \) is
\( A \cdot 8: 5 \)
B. 5: 8
\( c \cdot 31: 6 \)
D. 16 :15
Subject: Maths
If \( A B C D \) is a parallelogram whose diagonals intersect at \( O \) and \( \triangle B C D \) is
an equilateral triangle having each side of length \( 6 \mathrm{cm} \), then the length of diagonal \( \boldsymbol{A C} \) is
A \( \cdot 2 \sqrt{3} \mathrm{cm} \)
B. \( 6 \sqrt{3} \mathrm{cm} \)
c. \( 3 \sqrt{6} \mathrm{cm} \)
D. \( 12 \mathrm{cm} \)
Subject: Maths
Let \( \mathbf{f}(\mathbf{x})=(\mathbf{x}+\mathbf{1})^{2}-\mathbf{1}, \mathbf{x} \geq-\mathbf{1} \)
Statement-1: The set \( \left\{\mathbf{x}: \mathbf{f}(\mathbf{x})=\mathbf{f}^{-1}(\mathbf{x})\right\} \)
\( =\{\mathbf{0},-\mathbf{1}\} \)
Statement-2: \( f \) is a bijection
A. Statement 1 is true, Statement 2 is true,Statement 2 is correct explanation for statement
B. Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for statement 1
c. statement 1 is true, statement 2 is false.
D. Statement 1 is false, Statement 2 is true
Subject: Physics
Two waves are represented by the equations \( \boldsymbol{y}_{1}=\boldsymbol{a} \sin (\boldsymbol{\omega}+\boldsymbol{k} \boldsymbol{x}+\mathbf{0 . 5 7}) \boldsymbol{m} \) and
\( \boldsymbol{y}_{2}=\boldsymbol{a} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{k} \boldsymbol{x}) \boldsymbol{m} \)
where \( x \) is in meter and \( t \) in sec. The phase difference between them is
A. 0.57 radian
B. 1.0 radian
c. 1,25 radian
D. 1.57 radian
Subject: Physics
The percentage increase in magnetic
field B when the space within a current carrying toroid is filled with aluminium
\( \left(X=2.1 \times 10^{-5}\right) \) is
A \( .0 .2 \% \)
B. \( 2 \times 10^{-3} \% \)
c. \( 2 \times 10^{-2} \% \)
D. \( 2 \times 10^{-4} \% \)
Subject: Chemistry
The soluble complex formed during the extraction of silver from glance cyanide process is:
A \( \cdot \operatorname{Na}_{2}\left[\operatorname{Zn}(C N)_{4}\right] \)
В \( \cdot_{N a_{2}}\left[Z n(C N)_{6}\right] \)
c. \( _{N a_{4}}\left[Z n(C N)_{6}\right] \)
D. None of these
Subject: Chemistry
Assertion (A): Nitrogen cannot form pentahalides. Reason (R): Nitrogen cannot expand its octet configuration
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
c. (A) is true and (R) is false
D. (A) is false but (R) is true
Subject: Chemistry
The root mean square velocity of one mole of a monoatomic gas having molar
\( \operatorname{mass} M \) is \( U_{r m s} . \) The relation between
average kinetic energy \( (\boldsymbol{E}) \) of the gas
and \( U_{r m s} \) is :
\( ^{\mathrm{A}} \cdot U_{r m s}=\sqrt{\frac{3 E}{2 M}} \)
В. \( U_{r m s}=\sqrt{\frac{2 E}{3 M}} \)
c. \( \quad v_{r m s}=\sqrt{\frac{2 E}{M}} \)
D. \( U_{r m s}=\sqrt{\frac{E}{3 M}} \)
Subject: Physics
A certain mass of hydrogen gas is introduced into a vessel at room
temperature, the final pressure of the gas
in the vessel is
\( A \cdot 85 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 78 cm of Hg
\( c \cdot 63 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 58 \mathrm{cm} \) of \( \mathrm{Hg} \)
Subject: Physics
Four particles each of mass ' \( m^{\prime} \) are
placed at the corners of a square of side
\( L^{\prime \prime} . \) The radius of gyration of the system
about an axis normal to the square and
passing through its centre.
A \( \cdot \frac{L}{2} \)
в. \( \frac{L}{\sqrt{2}} \)
\( c . L \)
\( D . \sqrt{2} L \)
Subject: Maths
A survey regarding the heights (in cm) of 51 girls of Class \( X \) of a school
was conducted and data was obtained
as shown in table. Find their median.
\( \begin{array}{ll}\text { Height (in cm) } & \text { Number of girls } \\ \text { Less than } 140 & 4 \\ \text { Less than } 145 & 11 \\ \text { Less than } 150 & 29 \\ \text { Less than } 155 & 40 \\ \text { Less than } 160 & 46 \\ \text { Less than } 165 & 51\end{array} \)
Subject: Chemistry
Among the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?
A \( \cdot(n-1) d^{8} n s^{2} \)
B . \( (n-1) d^{8} n s^{1} \)
c. \( (n-1) d^{5} n s^{\text {। }} \)
D. \( (n-1) d^{5} n s^{2} \)
Subject: Physics
A block of mass \( M_{1}=10 \mathrm{kg} \) is placed
on a slab of mass \( M_{2}=30 \mathrm{Kg} \). The slab
lies on a frictionless horizontal surface
as shown in figure. The coefficient of
static friction between the block and
slab is \( \mu_{s}=0.25 \) and that of dynamic
friction is \( \mu_{k}=0.12 . \) A force \( F=40 \mathrm{N} \) acts
on block \( M_{1} \). The acceleration of the
slab will be \( \left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
A \( \cdot 0.5 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 0.4 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 1 \mathrm{m} / \mathrm{s}^{2} \)
D. \( \frac{5}{6} m / s^{2} \)
Subject: Maths
The area of the region bounded by the curve \( \sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}}=\sqrt{\boldsymbol{a}}(\boldsymbol{x}, \boldsymbol{y} \geq 0) \) and the
coordinate axes is
A \( \cdot a^{2} / 6 \)
в. \( a^{2} / 2 \)
c. \( a^{2} / 3 \)
D. \( a^{2} \)
Subject: Physics
Q Type your question.
orbiting some star. The planet is closer to the star as it moves from point 1 to
point 2 than it is when it moves from
point 3 to point 4 in its orbit. The dotted
ine shows the orbital path.
If the time it takes the planet to get from point 1 to point 2 is equal to the time it takes the planet to get from point 3 to point 4 then which of the following statements is true, according to Kepler's laws of planetary motion?
A. The average speed as the planet travels from 1 to 2 is the same as when it travels from 3 to 4
B. Area 1 in the diagram is equal to Area 2
C. Area 1 in the diagram is smaller than Area 2
D. The planet moves further from 3 to 4 from 1 to 2
E. The average speed as the planet moves from 3 to 4 is greater than when the planet moves from 1 to
Subject: Physics
A ball moving with velocity \( \hat{i} \) collides
with a stationary wall and returns with a velocity \( \hat{j} / 2 . \) The coefficient of restitution for this collision is :
A. \( 1 / 2 \)
B. \( 1 / 3 \)
c. \( 1 / 4 \)
D. \( 1 / 5 \)
Subject: Physics
A point-charge of \( 6.0 \times 10^{-8} \mathrm{C} \) is
situated at the coordinate origin. How much work will be done in taking an electron from the point \( x=3 \mathrm{m} \) to \( x=6 \)
\( \mathrm{m} ? \)
B . \( 1.44 \times 10^{-27} \) J
c. \( 1.44 \times 10^{-37} \) J
D. \( 1.44 \times 10^{-7} \).
Subject: Physics
A filled shopping cart (30.0kg) is being pushed rapidly toward the back of a store so that its velocity is \( 2.0 \mathrm{m} / \mathrm{s} \)
What is the momentum of the cart. and
what is the kinetic energy of the cart?
A. \( 90 k g m / s \) and \( 60 J \)
B. \( 60 k g m / s \) and \( 90 J \)
c. \( 60 k g m / s \) and \( 60 J \)
D. \( 90 k g m / s \) and \( 90 J \)
Subject: Maths
The D.E of the family of ellipse with centre at the origin and having co ordinate axes as axes is
A \( . x\left[y y_{2}+y_{1}^{2}\right]=y y_{1} \)
B . \( x^{2} y_{2}+y_{1}^{2}=y \)
\( \mathbf{c} \cdot x y y_{2}+y_{1}^{2}=y \)
D. \( x y y_{2}+y_{1}^{2}+y=0 \)
Subject: Physics
The magnetic field existing in a region is given by \( \overrightarrow{\boldsymbol{B}}=\boldsymbol{B}_{0}\left(1+\frac{\boldsymbol{x}}{\boldsymbol{l}}\right) \hat{\boldsymbol{k}} \)
A square loop of edge I and carrying a
current i, is placed with its edges parallel to the \( X \) -Y axes, Find the magnitude of the net magnetic force experienced by the loop.
Subject: Maths
\( \int \frac{\boldsymbol{a}}{\boldsymbol{b}+\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{a}{b}\left[x-\log \left(b+c e^{x}\right)\right] \)
B \( \cdot \frac{a}{b}\left[x+\log \left(b+c e^{x}\right)\right] \)
c. \( \frac{a}{b}\left[x-\log \left(c e^{x}\right)\right] \)
D. \( \frac{a}{c}\left[x+\log \left(b+c e^{x}\right)\right] \)
Subject: Chemistry
Which of the following
statements about bonding is correct?
A. Only van der Waals forces exist between polar molecules
B. Dipoles are the result of the equal sharing of electrons
C \( . C u(s) \) is a network covalent solid
D. Hydrogen bonds exist between the molecules of \( H C l \)
E . \( N a C l(a q) \) has attraction between the molecules and the ions
Subject: Chemistry
A constant current of \( 30 A \) is passed
through an aqueous solution of \( N a C l \)
for a time of \( 1.00 h \). What is the volume
of \( C l_{2} \) gas at STP produced?
A . \( 30.00 L \)
B . \( 25.08 L \)
c. \( 12.54 L \)
D. \( 1.12 L \)
Subject: Maths
In the figure shown, if the area of the
shaded region is 3 times the area of the
smaller circular region, then the
circumference of the larger circle is how many times the circumference of the
smaller circle?
A .4
B. 3
\( c \cdot 2 \)
\( D \cdot \sqrt{3} \)
\( E \cdot \sqrt{2} \)
Subject: Maths
If the lines \( x+2 y+3=0, x+2 y- \)
\( \mathbf{7}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}-\mathbf{4}=\mathbf{0} \) are the sides
of a square, then equation of the remaining sides of the square can be This question has multiple correct options
A. \( 2 x-y+6=0 \)
В. \( 2 x-y+8=0 \)
c. \( 2 x-y-10=0 \)
D. \( 2 x-y-14=0 \)
Subject: Physics
What is the momentum of an object of
mass \( m, \) moving with a velocity \( v ? \)
A \( \cdot(m v)^{2} \)
a) \( ^{\infty} \)
B. \( m v^{2} \)
c. \( 1 / 2 m v^{2} \)
D. \( m v \)