AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( f(x)=x^{2}+2 b x+2 c^{2} \) and \( g(x)= \)
\( -x^{2}-2 c x+b^{2} \) are such that min
\( f(x)>\max g(x), \) then the relation
between \( b \) and \( c \) is
A. no relation
в. \( 0<c<b / 2 \)
C \( \cdot|c|<|b| \sqrt{2} \)
D \( \cdot|c|>|b| \sqrt{2} \)
Subject: Maths
For a certain value of \( c, \lim _{x \rightarrow \infty}\left[\left(x^{5}+\right.\right. \)
\( \left.\left.7 x^{4}+2\right)^{c}-x\right] \) is finite \( \& \) non zero. The
value of \( c \) and the value of the limit is
A \( \cdot \frac{1}{5}, \frac{7}{5} \)
B. 0,1
c. \( _{1,} \frac{7}{5} \)
D. none
Subject: Chemistry
Elements \( X, Y \) and \( Z \) have atomic numbers 19,37 and 55 respectively. Which of the following statements are true about them?
A. Their ionization potential would increase with increasing atomic number
B. Y would have an ionization potential between those of \( x \) and \( z \)
c. z would have the highest ionization potential
D. \( \mathrm{r} \) would have the highest ionization potential
Subject: Physics
Which of the following equations does not represent the kinematic equations
of motion?
\( \mathbf{A} \cdot v=u+a t \)
B. \( S=u t+\frac{1}{2} a t^{2} \)
c. \( S=a t+\frac{1}{2} a t^{2} \)
D. \( v^{2}-u^{2}=2 a S \)
Subject: Maths
The value of \( k \) for which the system of
equations
\( 2 x+3 y=5 \)
\( 4 x+k y=10 \)
has an infinite number of solutions, is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 6 \)
D. 0
Subject: Chemistry
Identify the compound \( \boldsymbol{A} \)
\( \mathbf{A} \cdot C_{6} H_{5} O H \)
B \( \cdot C_{6} H_{5} C O C H_{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} C l \)
\( \mathbf{D} \cdot C_{6} H_{5} C H O \)
Subject: Chemistry
Fusion of \( M n O_{2}, \) with \( K O H \) in
presence of \( \boldsymbol{O}_{2} \) produces a salt \( \boldsymbol{W} \)
Alkaline solution of \( W \) upon
electrolytic oxidation yields another salt
\( X . \) The manganese containing ions
present in \( W \) and \( X, \) respectively are \( Y \)
and \( Z . \) Correct statement(s) is (are)
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{In} \operatorname{both} Y \) and \( Z, \alpha- \) bonding occurs between \( p- \)
orbitals of oxygen and d-orbitals of manganese
B. Both \( Y \) and \( Z \) are coloured and have tetrahedral shape
C. In aqueous acidic solution, \( Y \) undergoes disproportionation reaction to give \( Z \) and \( M n O_{2} \)
D. \( Y \) is diamagnetic in nature while \( Z \) is paramagnetic
Subject: Biology
Which of the following is the correct ord
er of evolutionary history of man?
A. Peking man, Heidelberg man, Neanderthal, CroMagnon
B. Peking man, Homo sapiens, Cro-Magnon, Neanderthal
C. Peking man, Neanderthal, Homo sapiens, Heidelberg
D. Peking man, Cro-Magnon, Homo sapiens, Neanderthal
Subject: Maths
Value of \( c \) of Rolles theorem for \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sin x-\sin 2 x \) on \( [0, \pi] \)
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left(\frac{1+\sqrt{33}}{8}\right) \)
B. \( \cos ^{-1}\left(\frac{1+\sqrt{35}}{8}\right) \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left(\frac{1-\sqrt{38}}{5}\right) \)
D. does not exist
Subject: Maths
The negative of the statement "If a
number is divisible by 15 then it is
divisible by 5 or \( 3^{\prime \prime} \)
A. If a number is not divisible by \( 15, \) then it is not divisible by 5 and 3
B. A number is divisible by 15 and it is not divisible by 5 or 3
C. A number is not divisible by 15 or it is not divisible by 5 and 3
D. A number is divisible by 15 and it is not divisible by 5 and 3
Subject: Physics
A single slit of width \( a \) is illuminated by violet light of wave length 400 nm and
width of the diffraction pattern is measured as \( y \). Half of the slit is
covered and illuminated with 600 nm.
The width of the diffraction pattern will be
A \( \cdot \frac{y}{3} \)
B. pattern vanishes and width is zero
c. \( 3 y \)
D. none of these
Subject: Chemistry
The enery of loss of an electron from \( N e \)
and \( N a^{+} \) ion(both isoelectronic) are:
A \( \cdot 4562 \) k) \( m o l^{-1}, 2081 \) k) \( m o l^{-1} \)
-
B . 2081 kJ mol-1, 4562 kJ mol-1
\( \mathbf{c} .2081 \mathrm{kJ} \mathrm{mol}^{-1} \) each
D. 4562 kJ \( m o l^{-1} \) each
Subject: Maths
Equation of chord \( \mathrm{AB} \) of circle \( x^{2}+ \)
\( \boldsymbol{y}^{2}=\boldsymbol{2} \) passing through (2,2) such
that \( \boldsymbol{P B} / \boldsymbol{P A}=\mathbf{3}, \) is given by
A \( . x=3 y \)
В. \( y-2=\sqrt{3}(x-2) \)
c. \( x=y \)
D. none of these
Subject: Physics
Two identical conducting rings \( A \) and \( B \)
of radius \( R \) are rolling over a horizontal
conducting plane with same speed \( v \) but in opposite direction. A constant magnetic field \( B \) is present pointing
into the plane of the paper. Then the
potential difference between the highest points of the two rings is
\( A \)
в. \( 2 B v R \)
c. \( 4 B v R \)
D. none of these
E. answer require
Subject: Physics
A current of \( 0.5 A \) flows through a resistance of \( 10 \Omega \) for \( \frac{1}{2} \) hour. And the amount of electrical energy consumed by the resistance.
\( \mathbf{A} \cdot 4500 J \)
в. \( 500 J \)
c. \( 250 k J \)
D. \( 2.6 k J \)
Subject: Maths
A particle moves along the y-axis so that its position at time \( 0 \leq t \leq 20 \) is
\( \operatorname{given} \operatorname{by} y(t)=5 t-\frac{t^{2}}{3} \cdot \) At what time
does the particle change direction?
A. 5 seconds
B. 7.5 seconds
c. 10 seconds
D. 15 seconds
E. 18 seconds
Subject: Physics
ABCD is a square of 1 metre side of a
non-conducting material. Four metallic spheres of 4,5,8 and \( 10 \mathrm{cm} \) diameters are placed at the four corners. All of
them are connected by a fine metallic wire and charge of 540 units is imparted to the system. The potential at the centre of the square is :
(in cgs system)
A \( \cdot \frac{540 \sqrt{2}}{400} \)
B. \( \frac{540 \sqrt{2}}{200} \)
c. \( \frac{540 \sqrt{2}}{100} \)
D. \( \frac{540 \sqrt{2}}{10} \)
Subject: Chemistry
For the reaction
\( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
A. \( \Delta H=\Delta E+R T \)
в. \( \Delta H=\Delta E-R T \)
c. \( \Delta H=\Delta E+2 R T \)
D. \( \Delta H=\Delta E-2 R T \)
Subject: Maths
Let \( \vec{a}, \vec{b}, \vec{c} \) be vectors of length 3,4 and 5 respectively. Let \( \vec{a} \) be perpendicular to \( (\vec{b}+\vec{c}), \vec{b} \) to \( (\vec{c}+\vec{a}) \) and \( \vec{c} \) to \( (\vec{a}+\vec{b}) \)
Find the length of the vector \( \vec{a}+\vec{b}+\vec{c} \).
Subject: Maths
Which term of the A.P., \( 84,80,76, . . \) is \( 0 ? \)
A \( \cdot 18^{\text {th}} \) term
B. \( 20^{\text {th }} \) term
c. \( 22^{\text {nd }} \) term
D. \( 24^{t h} \) term
Subject: Maths
\( f \frac{x}{a}+\frac{y}{b}=1 \) and \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\frac{a b}{a+b} \)
then prove that \( \frac{\boldsymbol{x}^{\boldsymbol{n}+\mathbf{1}}}{\boldsymbol{a}}+\frac{\boldsymbol{y}^{\boldsymbol{n}+\mathbf{1}}}{\boldsymbol{b}}= \)
\( \left(\frac{a b}{a+b}\right)^{n} \)
Subject: Physics
1 TORR is equal to
A. \( 1 \mathrm{mm} \) of \( \mathrm{Hg} \)
B. \( 10 \mathrm{mm} \) of \( \mathrm{Hg} \)
\( \mathrm{c} .0 .5 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. \( 5 \mathrm{mm} \) of \( \mathrm{Hg} \)
Subject: Chemistry
\( \begin{array}{cc} & C H_{3} \\ C H_{3}-C H-C H_{2}- & C \\ _{I} H_{3} & C H_{3}\end{array}-C H_{3} \)
How many primary, secondary, tertiary and quaternary carbon atoms are present in the following compound?
A. One primary, two secondary and one tertiary
B. Five primary, three secondary
C. Five primary, one secondary, one tertiary, and one Quaterrnary
D. Four primary, two secondary and two quaternary
Subject: Maths
The following real numbers have decimal expansions as given below. In each case, decide whether they are
rational or not. If they are rational and of
the form \( p \), you say about the prime
factors of \( q ? \)
(i) 43.123456789 (ii)
\( 0.120120012000120000 \ldots \)
\( 43 . \overline{123456789} \)
Subject: Physics
The image of an object placed on the principal axis of a concave mirror of focal length \( 12 \mathrm{cm} \) is formed at a point which is \( 10 \mathrm{cm} \) more distance from the mirror than the object. The magnification of the image is
\( \mathbf{A} \cdot \underline{\mathbf{s}} \)
B. 2.5
\( c \cdot 2 \)
D. -1.5.
Subject: Chemistry
\( \boldsymbol{C o}^{2+}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{S C N}^{-}(\boldsymbol{a q}) \rightarrow \) Complex
\( (\boldsymbol{X}) \)
\( N i^{2+}(a q)+ \) dimethylglyoxime Complex \( (\boldsymbol{Y}) \) The coordination number of cobalt and
nickel in both the complexes \( (X) \) and \( (Y) \)
is four. The IUPAC names of the
complexes \( (X) \) and \( (Y) \) are respectively:
A. tetrathiocyanato-S-cobalt(II) and bis(dimethylglyoximate)nickel(II)
B. tetrathiocyanato-S-cobaltate(II) and bis(dimethylglyoximato)nickel(II)
C. tetrathiocyanato-S-cobaltate(II) and bis(dimethylglyoximato)nickelate(II)
D. tetrathiocyanato-S-cobaltate(III) and bis(dimethylglyoximato)nickel(II)
Subject: Chemistry
\( 10 \mathrm{ml} \) of a compound containing 'N' and
'O' is mixed with \( 30 \mathrm{ml} \) of \( \mathrm{H}_{2} \) to
produce \( H_{2} O(\mathrm{l}) \) and \( 10 \mathrm{ml} \) of \( N_{2} \)
(g). Molecular formula of compound if both reactants reacts completely, is:
A. \( N_{2} O \)
в. \( N O_{2} \)
c. \( \quad N_{2} O_{3} \)
D. \( N_{2} O_{5} \)
Subject: Chemistry
The \( r . m . s . \) velocity of hydrogen is \( \sqrt{7} \) times the \( r . m . s . \) velocity of nitrogen. If
\( \boldsymbol{T} \) is the temperature of the gas:
\( \mathbf{A} \cdot T\left(H_{2}\right)=T\left(N_{2}\right) \)
B \( \cdot T\left(H_{2}\right)>T\left(N_{2}\right) \)
C \( \cdot T\left(H_{2}\right)<T\left(N_{2}\right) \)
D. \( T\left(H_{2}\right)=\sqrt{7} T\left(N_{2}\right) \)
Subject: Maths
\( \boldsymbol{P}(\mathbf{0}, \mathbf{5}, \mathbf{6}), \boldsymbol{Q}(\mathbf{1}, \mathbf{4}, \mathbf{7}), \boldsymbol{R}(\mathbf{2}, \mathbf{3}, \mathbf{7}) \) and
\( S(3,5,16) \) are four points in the space.
The point nearest to the origin \( \boldsymbol{O}(\mathbf{0}, \mathbf{0}, \mathbf{0}) \)
is
A. \( P \)
B. \( Q \)
\( c . R \)
D. \( S \)
Subject: Physics
A hemispherical body is placed in a
uniform electric field E. What is the flux
linked with curved surface, if field is
perpendicular to base in figure.
\( \mathbf{A} \cdot 2 \pi R^{2} E \)
\( \mathbf{B} \cdot \pi R^{2} E / 2 \)
\( \mathbf{C} \cdot \pi R^{2} E \)
D. Zero
Subject: Maths
Consider the function \( g(x)= \) \( \left\{\begin{array}{ll}\frac{1+a^{x}+x a^{x} \ln a}{a^{x} x^{2}} & x<0 \\ \frac{2^{x} a^{x}-x \ln 2-x \ln a-1}{x^{2}} & x>0\end{array}\right. \)
where \( a>0 \)
Find the value of \( a \& g(0) \) so that the function \( g(x) \) is continuous at \( x=0 \)
\( ^{A} \cdot a=\frac{1}{\sqrt{2}}, g(0)=\frac{(\ln 2)^{2}}{8} \)
B. \( a=-\frac{1}{\sqrt{2}}, g(0)=\frac{(l n 2)^{2}}{8} \)
c. \( a=-\frac{1}{\sqrt{2}}, g(0)=\frac{-}{(l n 2)^{2}} 8 \)
D. \( a=\frac{1}{\sqrt{2}}, g(0)=-\frac{(l n 2)^{2}}{8} \)
Subject: Chemistry
Arrange the alkyl in decreasing order of
their mass.
A \( \cdot C H_{3} C l>H_{2} O>C H_{3} B r \)
в. \( C H_{3} C l>C H_{3} B r>H_{2} O \)
\( \mathrm{c} \cdot C H_{3} B r>C H_{3} C l>H_{2} O \)
D. \( H_{2} O>C H_{3} C l>C H_{3} B r \)
Subject: Physics
A car was travelling at a speed of 10 \( \mathrm{m} / \mathrm{s} . \) After the brakes were applied, it start to decelerate at a rate of \( 2 m / s^{2} \) and finally came to rest. Find the distance traveled by the car before coming to rest.
A. \( 10 \mathrm{m} \)
B. 15 \( m \)
c. \( 25 \mathrm{m} \)
\( D \cdot 35 \mathrm{m} \)
Subject: Physics
In a room where the temperature is
\( 30^{\circ} \mathrm{C} \) a body cools from \( 61^{\circ} \mathrm{C} \) to \( 59^{\circ} \mathrm{C} \) in
4 minutes. The time taken by the body
to cool from \( 51^{\circ} \mathrm{C} \) to \( 49^{\circ} \mathrm{C} \) will be about
A. 5 minutes
B. 8 minutes
c. 4 minutes
D. 6 minutes
Subject: Physics
A sonometer wire, \( 100 \mathrm{cm} \) in length has a fundamental frequency of 330 Hz. The velocity of propagation of transverse waves along this wire is :
A \( .330 \mathrm{ms}^{-1} \)
B. \( 660 \mathrm{ms}^{-1} \)
C. \( 115 \mathrm{ms}^{-1} \)
D. \( 990 \mathrm{ms}^{-1} \)
Subject: Physics
If \( \mathrm{M} \) is the mass of the earth and \( \mathrm{R} \) its
radius, the ratio of the gravitational acceleration and the gravitational constant is given by:
A \( \cdot \frac{R^{2}}{M} \)
в. \( \frac{M}{R^{2}} \)
c. \( M R^{2} \)
D. \( \frac{M}{R} \)
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{C} \boldsymbol{N}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
According to above reaction, the Hydrocyanic acid dissociates, find the
acid dissociation constant for \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) ?
\( ^{\mathbf{A}} \cdot \frac{\left[H^{+}\right]\left[C N^{-}\right]}{[H C N]} \)
в. \( \left[H^{+}\right]\left[C N^{-}\right][H C N] \)
c. \( \frac{[H C N]}{\left[H^{+}\right]\left[C N^{-}\right]} \)
D. \( \frac{\left[H^{+}\right]}{[H C N]\left[C N^{-}\right]} \)
E \( \frac{1}{[H C N]\left[H^{+}\right]\left[C N^{-}\right]} \)
Subject: Chemistry
Use the relationship \( \Delta G^{\circ}=-n F E_{\text {cell }}^{\circ} \) to
estimate the minimum voltage required
to electrolyse \( A l_{2} O_{3} \) in the Hall-Heroult
process. \( \Delta G_{f}^{\circ}\left(A l_{2} O_{3}\right)=-1520 k J m o l^{-1} \)
\( \Delta G_{f}^{\circ}\left(C O_{2}\right)=-394 k J m o l^{-1} \)
The oxidation of the graphite anode to
\( C O_{2} \) permits the electrolysis to occur at a
lower voltage than if the electrolysis
reactions were:
\( A l_{2} O_{3} \rightarrow 2 A l+3 O_{2} \)
What is the approximate value of low
voltage?
\( A \cdot 2 V \)
B. 3 V
\( c \cdot 4 v \)
D. \( 5 v \)
Subject: Physics
In a one dimensional collision between
two identical particles \( A \) and \( B, B \) is stationary and \( A \) has momentum \( p \)
before impact. During impact, \( B \) gives impulse \( J \) to \( A \) This question has multiple correct options
A. The total momentum of the \( A+B \) system is \( p \) before and after the impact, and \( (p-J) \) during the impact
B. During the impact \( A \) gives impulse of magnitude \( J \) to \( B \)
c. the coefficient of restitution is \( \frac{2 J}{p}-1 \)
D. The coefficient of the restitution is \( \frac{J}{p}+1 \)
Subject: Maths
A function \( \boldsymbol{f}:(-\mathbf{3}, \mathbf{7}) \rightarrow \boldsymbol{R} \) is defined as
follows:
\( f(x)=\left\{\begin{array}{cc}4 x^{2}-1 ; & -3 \leq x<2 \\ 3 x-2 ; & 2 \leq x \leq 4 \\ 2 x-3 ; & 4<x \leq 6\end{array}\right. \)
Find: \( \boldsymbol{f}(\boldsymbol{5})+\boldsymbol{f}(\boldsymbol{6}) \)
Subject: Maths
15th term of the series \( 243,81,27, \ldots \) is This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left(\frac{1}{3}\right)^{9} \)
\( ^{\text {B }}\left(\frac{1}{3}\right)^{10} \)
\( ^{\text {c. }}\left(\frac{1}{3}\right)^{10}\left(\frac{1}{3}\right)^{-1} \)
\( ^{\mathrm{D} \cdot}\left(\frac{1}{3}\right)^{10}\left(\frac{1}{3}\right) \)
Subject: Maths
Find the mean salary of 80 workers of a
factory from the following tables:
\( \begin{array}{ll}\text { Salary (in Rs) } & \text { Numbers of workers } \\ 5000 & 22 \\ 6000 & 18 \\ 7000 & 15 \\ 8000 & 10 \\ 9000 & 8 \\ 10000 & 7\end{array} \)
Subject: Chemistry
The \( C-C \) and \( S i-C \) inter-atomic
distance are \( 154 p m \) and \( 188 p m \). the
atomic radius of \( \boldsymbol{S} \boldsymbol{i} \) is:
\( \mathbf{A} \cdot 77 p m \)
B . 94 pm
\( c .114 p m \)
D. \( 111 p m \)
Subject: Physics
Two wires of equal length, one of aluminium and the other of copper have
the same resistance. Which of the two
wires is lighter? Hence explain why aluminium wires are preferred for
overhead power cables. \( \left(\rho_{A I}=2.63 \times\right. \)
\( 10^{-8} \Omega m, \rho_{C u}=1.72 \times 10^{-8} \Omega m \)
Relative density of \( A I=2.7, \) of \( C u=8.9 . \)
Subject: Physics
The length of two wires are in the ratio
\( 3: 4 . \) Ratio of the diameters is 1: 2
young's modulus of the wires are in the
ratio \( 3: 2 ; \) If they are subjected to same
tensile force, the ratio of the elongation produced is
A . 1:
B. 1: 2
c. 2: 3
\( D \cdot 2: \)
Subject: Maths
The mean and median of 100 items are
50 and 52 respectively. The value of largest item is \( 100 . \) If was later found that it it 110 and not \( 100 . \) The true mean
and median are:
A. 50.10,51.5
B . 50.10,52
\( c .50,51.5 \)
D. none of these
Subject: Chemistry
Which of the following will have
maximum electron affinity?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{5} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \)
\( \mathbf{C} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
Subject: Chemistry
The magnetic moment of
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+} \) was found to be 1.73 B.M.
The number of unpaired electrons in the complex is:
\( A \cdot O \)
B.
\( c \cdot 2 \)
\( D \cdot 3 \)
Subject: Chemistry
Select incorrect reduction process:
\( \mathbf{A} \cdot 2\left[A g(C N)_{2}\right]^{-}+Z n \rightarrow\left[Z n(C N)_{4}\right]^{2-}+2 A g \)
в. \( C u O+H_{2} \rightarrow C u+H_{2} O \)
c. \( Z n O H_{2} \rightarrow Z n+H_{2} O \)
D. \( M g O+C \rightarrow M g+C O \)
Subject: Physics
Which of the following statement is true about the relation between electric field
and potential?
A. Electric field in the direction in which the potential decreases steepest
B. Magnitude of electric field is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at that point.
C. In the region of strong electric field, equipotentia
D. Both the statements
(a) and
(b) are correct.
Subject: Maths
Wher
distribution of 2 black and 2 white balls
in two containers are as shown.Which
of the following statements is true?
A. (iv) has the maximum possibility of picking a black ball
B. (i) and (iv) has equal probability of picking a white ball
C. (iii) has the maximum possibility of picking a white ball
D. (ii) has the maximum possibility of picking a white ball
Subject: Physics
A piece of lead falls from a height of 100m on a fixed non-conducting slab which brings it to rest. The temperature of the lead piece immediately after collision increases by (Sp.heat of lead
is \( 30.6 \mathrm{cal} / \mathrm{kg} /^{0} C \) and \( g=9.8 m / s e c^{2} . \)
\( A \cdot \) ок
в. \( 27^{\circ} \mathrm{C} \)
c. \( 7.62 k \)
D. 4.2k
Subject: Chemistry
Which of the following reactions shows
reducing nature of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} ? \)
A. \( P b S+4 H_{2} O_{2} \rightarrow P b S O_{4}+4 H_{2} O \)
B. \( A g_{2} O+H_{2} O_{2} \rightarrow 2 A g+H_{2} O+O_{2} \)
c. \( 2 H C H O+H_{2} O_{2} \rightarrow 2 H C O O H+H_{2} O \)
D. \( N a_{2} S O_{3}+H_{2} O_{2} \rightarrow N a_{2} S O_{4}+H_{2} O \)
Subject: Physics
A person pushing a stroller starts from rest, uniformly accelerating at a rate of
\( 0.5 m / s^{2} 1 . \) What is the velocity of the stroller after it has travelled \( 4.75 \mathrm{m} \) ?
A . \( 2.18 \mathrm{m} / \mathrm{s} \)
в. \( 5.18 m / s \)
c. \( 9.18 m / s \)
D. \( 1.28 \mathrm{m} / \mathrm{s} \)
Subject: Maths
Divide 1000 into 2 parts such that 10
\( \% \) of one part equals \( 20 \% \) of the other Find the bigger part.
A \( \cdot \frac{2000}{3} \)
в. \( \frac{1000}{3} \)
c. \( \frac{150}{3} \)
D. None of the above
Subject: Chemistry
A gaseous mixture enclosed in a vessel
of volume \( V \) consists of one mole of gas
\( \mathbf{A} \) with \( \gamma\left(=C_{P} / C_{V}\right)=5 / 3 \) and another
gas \( \mathrm{B} \) with \( \gamma=7 / 5 \) at a certain
temperature T. The relative molar
masses of the gas \( A \) and \( B \) are 4 and 32 respectively. The gases \( A \) and \( B \) do not react with each other and are assumed
to be ideal. The gaseous mixture follows the equation \( P V^{19 / 13}= \) constant, in
adiabatic processes. Compute the speed of sound in the
gaseous mixture at \( \boldsymbol{T}=\mathbf{3 0 0 K} \)
A. \( v=501 \mathrm{m} / \mathrm{s} \)
в. \( v=401 \mathrm{m} / \mathrm{s} \)
c. \( v=701 \mathrm{m} / \mathrm{s} \)
D. \( v=801 \mathrm{m} / \mathrm{s} \)
Subject: Chemistry
What will be the reduction potential for the following half-cell reaction at \( 298 \mathrm{K} ? \)
(Given: \( \left[\boldsymbol{A} \boldsymbol{g}^{+}\right]=\mathbf{0 . 1} \mathbf{M} \) and \( \boldsymbol{E}_{c e l l}^{o}=+\mathbf{0 . 8 0} \)
\( \mathbf{V}) \)
A . \( 0.741 \mathrm{v} \)
B. \( 0.80 v \)
c. \( -0.80 v \)
D. \( -0.741 \mathrm{V} \)
Subject: Chemistry
Indicate the types of isomerism exhibited by the following complex and
draw the structure of this isomer.
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)\left(\boldsymbol{H}_{2} \boldsymbol{O}\right) \boldsymbol{C l}_{2}\right] \)
Subject: Maths
If \( \boldsymbol{\alpha} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \) then \( \sqrt{\mathbf{x}^{2}+\mathbf{x}}+\frac{\tan ^{2} \boldsymbol{\alpha}}{\sqrt{\mathbf{x}^{2}+\mathbf{x}}} \)
is always greater than or equal to
\( A \cdot 2 \tan \alpha \)
B.
\( c \cdot 2 \)
\( D \cdot \sec ^{2} \alpha \)
Subject: Physics
The number of independent constituent simple harmonic motions yielding a resultant displacement equation of the
periodic motion as \( \boldsymbol{y}= \)
\( 8 \sin ^{2}\left(\frac{t}{2}\right) \sin (10 t) \) is:
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
\( D .3 \)
Subject: Physics
Assertion
In a series \( L C R \) circuit, at resonance
condition power consumed by circuit is
maximum.
Reason
At resonance condition, the effective
resistance of circuit is maximum.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Physics
A small uncharged metallic sphere is positioned exactly at a point midway between two equal and opposite point charges separated by very small distance. If the spheres is slightly displaced towards the positive charge and released, then
This question has multiple correct options
A. It will oscillate about it's original position.
B. It will move further towards the positive charge.
c. Its potential energy will decrease and kinetic energy will increase
D. The total energy remains constant but is non-zero
Subject: Maths
\( \cot ^{-1} \frac{x y+1}{x-y}+\cot ^{1} \frac{y z+1}{y-z}+ \)
\( \cot ^{-1} \frac{x z+1}{z-x} \)
\( A \)
B. -
\( c \cdot 0 \)
D. none of these
Subject: Chemistry
The IUPAC name of the Wilkinsons
catalyst \( \left[R h C l\left(P P h_{3}\right)_{3}\right] \) is
A. Chlorotris (triphenylphopshine) rhodium (I)
B. Chlorotris (triphenylphosphine) rhodium (IV)
C. Chlorotris (triphenylphosphine) rhodium (0)
D. Chlotrotris (triphenylphosphine) rhodium (VI)
Subject: Chemistry
The protective power of the lyophilic colloids is expressed in terms of gold number a term introduced
by Zsigmondy. The gold number is the number of milligrams of the protective colloid which prevents the
coagulation of \( 10 \mathrm{mL} \) of red gold sol.
When \( 1 ~ m L \) of a 10 percent solution of
sodium chloride is added to it. Thus, the smaller the gold number of lyophilic colloids, the greater is the protective
power.

Which of the following statement(s) is/are correct
This question has multiple correct options
A. Higher the gold number, more protective power of colloid
B. Lower the gold number, more the protective power
c. Higher the coagulation value, more the coagulation power
D. Lower the coagulation value, higher the coagulation power
Subject: Physics
A string of mass \( \mathrm{m} \) is fixed at both ends. The fundamental tone oscillations are excited in the strong with angular frequency \( \omega \) and maximum
displacement amplitude A. Find the total energy curtained in the string.
\( \mathbf{A} \cdot \frac{1}{2} m \omega^{2} A^{2} \)
B \( \cdot \frac{1}{4} m \omega^{2} A^{2} \)
\( \mathbf{C} \cdot \frac{1}{6} m \omega^{2} A^{2} \)
D. \( \frac{1}{8} m \omega^{2} A^{2} \)