AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
\( E C \) of \( G d(64) \) is written as:
A \( \cdot[X e]_{54} 4 f^{7} 5 d^{1} 6 s^{2} \)
В \( \cdot[X e]_{54} 4 f^{8} 8 s^{2} \)
\( \mathbf{c} \cdot[X e]_{54} 4 f^{9} 6 s^{1} \)
D. \( [X e]_{54} 4 f^{10} \)
Subject: Chemistry
The equilibrium constant \( \left(\boldsymbol{K}_{c}\right) \) for the
reaction, \( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \) at
room temperature \( \boldsymbol{T} \) is \( \boldsymbol{4} \times \mathbf{1 0}^{-4} \). The
value of \( \boldsymbol{K}_{c} \) for \( \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{N}_{2}(\boldsymbol{g})+ \)
\( \frac{1}{2} O_{2}(g) \) at the same \( T \) is:
A .0 .02
B . 50
C \( .4 \times 10^{-4} \)
D. \( 2.5 \times 10^{-2} \)
Subject: Chemistry
Which one will have highest boiling
point, if 1 mole of each of the following substances was discovered in 1,000
grams of water?
A. Nacı
в. кс।
c. \( C a C l_{2} \)
D. \( C_{6} H_{10} O_{5} \)
E \( \cdot C_{12} H_{22} O_{11} \)
Subject: Physics
Two long parallel conductors are placed
at right angles to a metre scale at the \( 2 c m \) and \( 4 c m \) marks, as shown in the
figure. They carry currents of \( 1 A \) and \( 3 A \)
respectively. They will produce zero magnetic field at the
(ignore the Earth's magnetic field)
A. \( 0.5 \mathrm{cm} \) mark
B. \( 2.5 \mathrm{cm} \) mark
c. \( 1 \mathrm{cm} \) mark
D. \( 8 \mathrm{cm} \) mark
Subject: Chemistry
Which of the following statement is
incorrect?
A. Sodium and potassium are soft and silvery white metals.
B. Sodium and potassium in air get tarnished due to the formation of a layer of oxide or carbonates.
C. Sodium and potassium burn in dry oxygen (excess) gives peroxides.
D. Sodium and potassium are kept under kerosene to avoid contact with air and moisture.
Subject: Physics
Air filled capacitor of capacitance \( 2 \mu \boldsymbol{F} \)
is filled with three dielectric material of
dielectric constants \( \boldsymbol{K}_{\mathbf{1}}=\mathbf{4}, \boldsymbol{K}_{\mathbf{2}}= \)
4 and \( K_{3}=6 \) as shown in the figure.
The new capacitance of the capacitors
is
\( \mathbf{A} \cdot 50 \mu F \)
в. \( 2 \mu F \)
\( c \cdot 20 \mu F \)
D. \( 10 \mu F \)
Subject: Chemistry
The frequency of light emitted for the
transition \( n=4 \) to \( n=2 \) of \( H e^{+} \) is
equal to the transition in \( \mathrm{H} \) atom
corresponding to which of the following?
A \( . n=3 \) to \( n=1 \)
в. \( n=2 \) to \( n=1 \)
c. \( n=3 \) to \( n=2 \)
D. \( n=4 \) to \( n=3 \)
Subject: Chemistry
When \( 1.20 g \) of sulphur is melted with \( 15.00 g \) of naphthalene, the solution
freezes at \( 77.2^{\circ} \mathrm{C} \).. What is the molar
mass of this form of sulphur?
Data for Naphthalene:
Melting point, \( \mathrm{M} . \mathrm{P}=80^{\circ} \mathrm{C} \)
Freezing point depression constant, \( k_{f}=6.80^{\circ} \mathrm{C} \boldsymbol{m}^{-1} \)
A . \( 180 g \) mol \( ^{-1} \)
B. \( 194 g \) mol \( ^{-1} \)
c. \( 260 g \) mol \( ^{-1} \)
D. \( 450 \mathrm{g} \) mol \( ^{-1} \)
Subject: Maths
\( \operatorname{Let} g(x)=2 f\left(\frac{x}{2}\right)+f(x-2) \) and
\( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})<\mathbf{0} \forall \boldsymbol{x} \in(\mathbf{0}, \mathbf{2}), \) then \( \boldsymbol{g}(\boldsymbol{x}) \)
increases in
A \( \cdot\left(\frac{1}{2}, 2\right) \)
в. \( \left(\frac{4}{3}, 2\right) \)
c. (0,2)
(年. \( 0,2,2) \)
D. \( \left(0, \frac{4}{3}\right) \)
Subject: Physics
Which statement is wrong from the
following?
A. The earthing wire is green coloured.
B. In India, current flowing through wire is \( A C \) and its frequency is \( 50 \mathrm{Hz} \)
C. In India, voltage between two wires is \( 110 V \)
D. T.V., Tublight, bulbs are connected with \( 5 A \) line.
Subject: Maths
\( R \) is a relation on \( N \) given by \( R= \)
\( \{(x, y) \mid 4 x+3 y=20\} . \) Which of the
following doesnot belong to \( R \) ?
A \( .(-4,12) \)
B . (5,0)
c. (3,4)
(年. \( (3,4)) \)
D. (2,4)
Subject: Physics
A current in a 240 turn solenoid varies
at \( 0.8 A / s . \) Find emf induced if the
length of the solenoid is \( 12 \mathrm{cm} \) and
radius \( 2 c m \)
A \( \cdot 6.14 \times 10^{-4} V \)
в. \( 6.4 \times 10^{-3} V \)
\( \mathrm{c} .3 .07 \times 10^{-3} \mathrm{V} \)
D. \( 3.07 \times 10^{-4} V \)
Subject: Maths
Find the value of \( \mathbf{x}, \mathbf{y}, \mathbf{z}\left[\begin{array}{cc}\boldsymbol{x}+\mathbf{2} & \mathbf{6} \\ \mathbf{3} & \mathbf{5} z\end{array}\right]= \)
\( \left[\begin{array}{cc}\mathbf{3} & \boldsymbol{y}^{2}+\mathbf{4} \\ \mathbf{3} & \mathbf{2 0}\end{array}\right] \)
Subject: Chemistry
Let the solubility of an aqueous solution
of \( M g(O H)_{2} \) be \( x \) then its \( K_{s p} \) is
\( \mathbf{A} \cdot 4 x^{3} \)
B . \( x^{3} \)
\( c \cdot 27 x^{4} \)
D. \( 9 x \)
Subject: Physics
If a vector \( 2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to the vector \( 4 \hat{j}-4 \hat{i}+\alpha \hat{k} . \) Then, the
value of \( \alpha \) is :
A \( \cdot \frac{-1}{2} \)
B. - -
\( c \cdot \frac{1}{2} \)
D. 1
Subject: Physics
A uniform wire of resistance \( 50 \Omega \) is cut
into five equal parts. These parts are now connected in parallel. Then the equivalent resistance of the combination is:
A . \( 2 \Omega \)
B. \( 12 \Omega \)
\( \mathbf{c} \cdot 250 \Omega \)
D. \( 6250 \Omega \)
Subject: Chemistry
select correct statement(s):
This question has multiple correct options
A. Alkali metals ozonides are coloured and
paramagnetic.
B. Alkali metal-ozonides are colourless and diamagnetic
C. Sesquioxides of alkali metal are peroxides disuperoxides \( \left(M^{+}\right)_{4}\left(O_{2}^{2-}\right)\left(O_{2}^{-}\right)_{2} \)
D. Sesquioxides are paramagnetic due to presence of superoxide ion \( O_{2}^{-} \)
Subject: Chemistry
At a given temperature, total vapour pressure (in torr) of a mixture of volatile
components \( A \) and \( B \) is given by \( P_{T o t a l}=120-75 X_{B} \) hence, the vapour
pressure of pure \( A \) and \( B \) respectively (in Torr) are:
A .120,75
в. 120,195
c. 120,45
D. 75,45
Subject: Chemistry
Consider following complexes:
I: \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{2+} \)
\( \|:\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-} \)
\( \| I:\left[N i(C O)_{4}\right] \)
\( \mid V:\left[N i\left(H_{2} O\right)_{4}\right]^{2+} \)
\( \mathbf{V}:\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right]^{2-} \)
Out of this, select the complex with equal number of unpaired electrons:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{2+} \)
B \( \cdot\left[N i(C O)_{4}\right] \)
c. \( \left[N i\left(H_{2} O\right)_{4}\right]^{2+} \)
D. None of these
Subject: Physics
A helicopter rises vertically with a speed of \( 100 \mathrm{m} / \mathrm{s} \). If helicopter has length \( 10 \mathrm{m} \) and horizontal component
of earth's magnetic field is \( 5 \times \)
\( 10^{-3} W b / m^{2}, \) then the induced emf
between the tip of nose and tail of helicopter is:
A. \( 50 v \)
B. 0.5 \( v \)
\( c \cdot 5 v \)
D. 25 V
Subject: Chemistry
The de-brogile wavelength of an electron in the ground state of hydrogen atom is:
\( [\boldsymbol{K} . \boldsymbol{E} .=\mathbf{1 3 . 6} e \boldsymbol{V} ; \mathbf{1} e \boldsymbol{V}=\mathbf{1 . 6 0 2} \times \)
\( \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{J} \)
A. \( 33.28 n m \)
B. \( 3.328 n m \)
\( \mathbf{c} .0 .3328 n m \)
D. \( 0.0332 n m \)
Subject: Maths
If \( \sin ^{-1}(6 x)+\sin ^{-1}(6 \sqrt{3} x)=-\frac{\pi}{2} \)
then the value of \( x \) is
A \( \cdot \frac{1}{12} \)
B. \( -\frac{1}{12} \)
c. \( -\frac{1}{4 \sqrt{3}} \)
D. \( \frac{1}{4 \sqrt{3}} \)
Subject: Maths
If \( |z|=1 \) and \( w=\frac{z-1}{z+1}(z \neq-1) \) then
\( \operatorname{Re}(w) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{-1}{|z+1|^{2}} \)
c. \( \frac{1}{|z+1|^{2}} \)
D. \( \frac{\sqrt{2}}{|z+1|^{2}} \)
Subject: Chemistry
A reaction is represented as \( 2 A+B \mapsto \)
\( 2 C+3 D . \) The concentration of \( C \) at 10 s
is 4 moles \( l^{-1} \). The concentration of \( C \) at
20 seconds is 5.2 moles \( l^{-1} . \) The rate of
reaction of \( \mathrm{B} \) in the same time interval
could be :
A. -0.12 mole \( l^{-1} S^{-1} \)
B. -0.6 mole \( l^{-1} S^{-1} \)
c. -0.06 mole \( l^{-1} S^{-1} \)
D. -1.2 mole l" \( S^{-1} \)
Subject: Maths
The solution of the differential equation \( \left(\frac{d y}{d x}\right)^{2}-3 x\left(\frac{d y}{d x}\right)-2 y=8 \)
A \( \cdot y=2 x^{2}+4 \)
B . \( y=2 x^{2}-4 \)
\( \mathbf{c} \cdot y=2 x+4 \)
D. \( y=2 x-4 \)
Subject: Maths
A sphere of radius \( 100 \mathrm{mm} \) shrinks to radius \( 98 \mathrm{mm} \), then the approximate decrease in its volume is
A. \( 12000 \pi m m^{3} \)
В. \( 800 \pi m m^{3} \)
c. \( 80000 \pi m m^{3} \)
D. \( 120 \pi m m^{3} \)
Subject: Chemistry
Predict the sign of \( \Delta S \) for each of the following processes, which occur at
constant temperature:
I. The volume of 2 mol of \( O_{2}(g) \)
increases from \( 44 L \) to \( 54 L \)
II. The pressure of 2 mil of \( O_{2}(g) \)
increases from 1 atm to 1.2 atm.
A \( \cdot(I) \rightarrow \Delta S=-v e ;(I I) \rightarrow \Delta S=-v e \)
в. \( (I) \rightarrow \Delta S=-v e ;(I I) \rightarrow \Delta S=+v e \)
c. \( (I) \rightarrow \Delta S=+v e ;(I I) \rightarrow \Delta S=-v e \)
D. \( (I) \rightarrow \Delta S=+v e ;(I I) \rightarrow \Delta S=+v e \)
Subject: Maths
Find the distance of the point (2,12,5) from the point of intersection of the line \( \overrightarrow{\boldsymbol{r}}=2 \hat{\hat{\boldsymbol{i}}}-\mathbf{4} \hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}}+\boldsymbol{\lambda}(\boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}}) \)
and the plane \( \vec{r} \cdot(\hat{\boldsymbol{i}}-\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}})=\mathbf{0} \)
Subject: Chemistry
The ionization constant of ammonium
hydroxide is \( 1.77 \times 10^{-5} \) at \( 298 K \)
Hydrolysis constant of ammonium chloride is
A \( .5 .65 \times 10^{-12} \)
B . \( 5.65 \times 10^{-10} \)
c. \( 6.50 \times 10^{-12} \)
D. \( 5.65 \times 10^{-13} \)
Subject: Physics
If \( \mu_{0} \) is absolute permeability of
vacuum and \( \mu_{r} \) is relative magnetic permeability of another medium, then permeability \( \mu \) of the medium is
A . \( \mu_{0} \mu_{r} \)
B. \( \mu_{0} / \mu_{r} \)
\( \mathbf{c} \cdot \mu_{r} / \mu_{0} \)
D. \( I / \mu_{0} \mu_{r} \)
Subject: Chemistry
Let there be as first-order reaction of the
type, \( \boldsymbol{A} \rightarrow \boldsymbol{B}+\boldsymbol{C} \). Let us assume that
only \( A \) is gaseous. We are required to calculate the value of rate constant
based on the following date.
\[
\begin{array}{lcc}
\text { Time } & \text { o } & \text { T } \\
\text { Partial pressure of A } & P_{0} & P_{t}
\end{array}
\]
Calculate the expression of rate
constant.
A \( \cdot k=\frac{1}{t} \ln \left(\frac{P_{0}}{T_{l}}\right) \)
B . \( k=\frac{1}{t} \ln \left(\frac{P_{t}}{T_{D}}\right) \)
C . \( k=\frac{1}{t} \ln \left(\frac{2 P_{0}}{P_{t}}\right) \)
D・ \( k=\frac{1}{t} \ln \left(\frac{P_{F}}{2 P_{0}}\right) \)
Subject: Physics
Two metal spheres of radius \( r \) are kept
in contact. If \( ^{\prime} d^{\prime} \) is the density of each sphere material, the gravitational force between them is proportional to
\( \mathbf{A} \cdot d^{2} r^{6} \)
B. \( d^{2} r^{4} \)
c. \( \frac{d^{2}}{r^{4}} \)
D. \( \frac{r^{4}}{d^{2}} \)
Subject: Physics
A stationary ball weighing \( 0.25 k g \) acquires a speed of \( 10 \mathrm{m} / \mathrm{s} \) when hit by a hockey stick. The impulse imparted to the ball is :
A. \( 0.25 \mathrm{N} \) s
B. 2.5 N s
c. \( 2.0 \mathrm{N} \) s
D. \( 0.5 \mathrm{N} \) s
Subject: Maths
A water tank has the shape of a right circular cone with its vertex down. Its
altitude is \( 10 \mathrm{cm} \) and the radius of the
base is \( 15 \mathrm{cm} \). Water leaks out of the
bottom at a constant rate of
1 \( c u \) cm / sec. Water is poured into the
\( \operatorname{tank} \) at a constant rate of \( C \) cu.cm / sec.
Compute \( C \) so that the water level will
be rising at the rate of \( 4 \mathrm{cm} / \) sec at the
instant when the water is \( 2 \mathrm{cm} \) deep.
Subject: Physics
When an electronjumps from \( n_{1} \) th orbit
to \( n_{2} \) th orbit then the formula for energy
radiated out is
A \( . E_{1}-E_{2}=h v \)
в. \( E_{2}-E_{1}=h v \)
c. \( h v=\frac{E_{1}+E_{2}}{2} \)
D. \( h v=\frac{E_{1}}{E_{2}} \)
Subject: Chemistry
Which of the following statement is true for graphite?
(a) In graphite, each carbon atom is bonded to four other carbon atoms.
(b) Graphite is very hard.
(c) It is a good conductor of electricity.
(d) It is bad conductor of electricity.
\( A \cdot a, b \) and \( d \)
B. only c
\( c . \) a and d
D. a and c
Subject: Chemistry
ampere current is passed for 60 seconds into an electrolytic cell. Number
of electrons that pass through the
solution is :
A. \( 6.0 \times 10^{23} \)
B. \( 1.2 \times 10^{24} \)
c. \( 37.5 \times 10^{19} \)
D. \( 7.48 \times 10^{21} \)
Subject: Chemistry
\( 25 \mathrm{ml} \) of \( H_{2} O_{2} \) solution were added to
excess of acidified \( K I \) solution. The
iodine so liberated required \( 20 \mathrm{ml} \) of
\( 0.1 \mathrm{N} N a_{2} S_{2} O_{3} \) for titration
Calculate strength of \( H_{2} O_{2} \) in terms of
normality and percentage?
A. \( 0.04 \mathrm{N}, 0.136 \% \)
В. \( 0.08 \mathrm{N}, 0.136 \% \)
c. \( 0.04 \mathrm{N}, 0.163 \% \)
D. \( 0.02 \mathrm{N}, 0.163 \% \)
Subject: Chemistry
Pick the correct name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{C l}\right] \boldsymbol{C l}_{2} \)
a) Chloropentammine cobalt (III)
b) Pentammine cobalt (III) chloride
c)Chloropentammine cobalt (III) chloride
d)Pentaamminechloridocobalt(III)dichl
oride.
Subject: Chemistry
Assertion
\( H_{3} P O_{2} \) can act as strong reducing agent and gives disproportionation reaction on heating.
Reason
Due to presence of one \( -O H \) group and
\( \boldsymbol{P}-\boldsymbol{H} \) group, \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) is a monobasic
bronsted acid.
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: Chemistry
Which amongst the following reactions cannot be used for the preparation of the halogen acid?
A \( \cdot 2 K B r+H_{2} S O_{4}(\text { Conc. }) \rightarrow K_{2} S O_{4}+2 H B r \)
В. \( 2 \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{SO}_{4}(\text { Conc. }) \rightarrow \mathrm{NaHSO}_{4}+\mathrm{HCl} \)
c. \( N a H S O_{4}+N a C l \rightarrow N a_{2} S O_{4}+H C l \)
D. \( C a F_{2}+H_{2} S O_{4}(\text {conc.}) \rightarrow C a S O_{4}+2 H F \)
Subject: Physics
In an electromagnetic wave in free space the root mean square value of the electric filed is \( \boldsymbol{E}_{r m s}=\boldsymbol{6} \boldsymbol{V} / \boldsymbol{m} . \) The peak
value of the magnetic field is:
A \( \cdot 4.23 \times 10^{-8} T \)
B. \( 1.41 \times 10^{-8} T \)
c. \( 2.83 \times 10^{-8} T \)
D. \( 0.70 \times 10^{-8} T \)
Subject: Maths
The constant \( c \) of Rolle's theorem for the
function \( \boldsymbol{f}(\boldsymbol{x})=\log \frac{\boldsymbol{x}^{2}+\boldsymbol{a} \boldsymbol{b}}{(\boldsymbol{a}-\boldsymbol{b}) \boldsymbol{x}} \) in \( [\boldsymbol{a}, \boldsymbol{b}] \)
where \( \mathbf{0} \notin[\boldsymbol{a}, \boldsymbol{b}] \) is
A. \( \sqrt{a b} \)
в. \( \frac{a+b}{2} \)
c. \( \frac{a-b}{2} \)
D. \( \frac{b-a}{2} \)
Subject: Maths
Applying mean value theorem on \( \boldsymbol{f}(\boldsymbol{x})=\log \boldsymbol{x} ; \boldsymbol{x} \in[\mathbf{1}, \boldsymbol{e}] \) the value of \( \boldsymbol{c}= \)
\( \mathbf{A} \cdot \log (e-1) \)
в. \( e-1 \)
\( \mathbf{c} \cdot 1-e \)
\( D \)
Subject: Chemistry
\( \mathbf{A} \mathbf{5} . \mathbf{8 5} \%(\mathbf{w} \mathbf{t} / \mathbf{v} \text { ol }) \mathbf{N} \boldsymbol{a} \boldsymbol{C l} \) solution will
exert an osmotic pressure closet to which one of the following.
A. \( 5.85 \% \) (wt/vol) sucrose solution
B. \( 5.85 \% \) (wt/vol) glucose solution
c. 2 m sucrose solution
D. \( 1 \mathrm{m} \) glucose solution
Subject: Physics
Assertion
The diamond shines due to multiple
total internal reflections
Reason
The critical angle for diamond is \( 24.4^{\circ} \)
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
The distance between a north pole of
strength \( 6 \times 10^{-3} A m \) and south pole of
strength \( 8 \times 10^{-3} \mathrm{Am} \) is \( 10 \mathrm{cm} . \) The poles
are separated in air. The force between
them:
A \( \cdot 4.8 \times 10^{-11} N \)
В. \( 24 \times 10^{-11} N \)
\( \mathbf{c} \cdot 48 \times 10^{-11} N \)
D. \( 24 \times 10^{-12} N \)
Subject: Biology
Read the given statements and select
the correct option.

Statement 1: Mammals can eat while breathing.

Statement 2 : Mammals have negative-
pressure breathing.
A. Both statements 1 and 2 are Correct
B. Statement 1 is correct but statement 2 is incorrect
c. Statement 1 is incorrect but statement 2 is correct
D. Both statements 1 and 2 are incorrect.
Subject: Biology
After examining the blood groups of husband and wife, the doctor advised them not to have more than one child.
The blood groups of the couple are likely
to be
A. Male Rh" and female Rh
B. Male Rht and female Rht
C. Female \( \mathrm{Rh}^{-} \) and male \( \mathrm{Rh}^{+} \)
D. Male Rh - and female Rh
Subject: Physics
In an LCR circuit having \( \mathrm{L}=\mathbf{8 H}, \mathbf{C}= \)
\( 0.5 \mu F \) and \( R=100 \Omega \) in series, the
resonance frequency rad/s is?
A. 600
в. 200
c. \( 250 / \pi \)
D. 500
Subject: Maths
\( \tan ^{-1}\left[\frac{\cos x}{1+\sin x}\right] \) is equal to
A \( \cdot \frac{\pi}{4}-\frac{x}{2}, \) for \( x \epsilon\left(-\frac{\pi}{2}, \frac{3 \pi}{2}\right) \)
B. \( \frac{\pi}{4}-\frac{x}{2}, \) for \( x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
\( ^{\mathbf{C}} \cdot \frac{\pi}{4}-\frac{x}{2}, \) for \( x \in\left(\frac{3 \pi}{2}, \frac{5 \pi}{2}\right) \)
D \( \cdot \frac{\pi}{4}-\frac{x}{2}, \) for \( x \in\left(-\frac{3 \pi}{2},-\frac{3 \pi}{2}\right) \)
Subject: Chemistry
Which of the following molecular formulae represent the ore carnallite?
A. \( N a_{2} A l_{2} O_{4} \)
в. \( N a_{3} A l F_{6} \)
c. \( K C l M g C l_{2} \cdot 6 H_{2} O \)
D. \( F e_{3} O_{4} \)
Subject: Chemistry
Which of the following will not give halo benzene by reacting with benzene diazonium chloride?
\( \mathbf{A} \cdot C u_{2} B r_{2} / H B r \)
в. \( K I \)
c. \( S n C l_{2}+H C l \)
D. \( C u \) powder \( +H C l \)
Subject: Chemistry
Which of the following is used as desiccant for absorbing water in Leibigs method for estimation of \( \mathrm{C} \) and \( \mathrm{H} \) ?
\( \mathbf{A} \cdot M g S O_{4} \cdot 7 H_{2} O \)
в. \( C u S O_{4} .5 H_{2} O \)
c. Anhydrous \( \mathrm{CaCl}_{2} \)
D. КОН
Subject: Chemistry
Arrange the following in increasing
order of oxidation states of \( M n \)
\( \boldsymbol{K}_{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}, \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2}, \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
Subject: Physics
If \( \vec{E}=E_{0} \cos (k z) \cos (\omega t) \hat{i} \) then \( \vec{B} \) for
electromagnetic wave is:
A \( \cdot \vec{B}=\frac{E_{0}}{C} \hat{k} \)
B・ \( \vec{B}=\frac{E_{0}}{C} \sin (k z) \sin (\omega t) \hat{\imath} \)
\( \mathbf{c} \cdot \vec{B}=\frac{E_{0}}{C} \sin (k z) \cos (\omega t) \hat{\jmath} \)
D・ \( \vec{B}=\frac{E_{0}}{C} \cos (k z) \sin (\omega t) \hat{\jmath} \)
Subject: Physics
n Fig, \( P Q \) and \( P R \) are the two light rays
emerging from an object \( \boldsymbol{P} \). The ray \( \boldsymbol{P Q} \)
is refracted as \( Q \) S. The ray \( P R \) suffers
partial reflection and refraction on the water-air interface. This is because:
A. the angle of incidence is more than the critical angle
B. the angle of incidence is equal to the critical angle
c. the angle of incidence is less than the critical angle
D. the angle of incidence is \( 90^{\circ} \)
Subject: Chemistry
The electronic configuration of an element is \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} 3 p^{3} . \) What is
the atomic number of the element
which is just below the given element in the periodic table?
\( \mathbf{A} \cdot 34 \)
B . 49
c. 33
D. 31
Subject: Physics
Which one of the following is a property of a monochromatic, plane
electromagnetic wave in free space?
A. Electric and magnetic fields have a phase difference of \( \pi / 2 \)
B. The energy contribution of both electric and magnetic fields are equal
c. The direction of propagation is in the direction of \( \bar{B} \) x \( \bar{E} \)
D. The pressure exerted by the wave is the product of its speed and energy density
Subject: Physics
A \( 10.0 \mathrm{W} \) electrical heater is used to
heat a container filled with \( 0.5 \mathrm{kg} \) of water. It is found that the temperature
of the water and the container rose by 3 K in 15 minutes. The container is then
emptied, dried, and filled with \( 2 \mathrm{kg} \) of an oil. It is now observed that the same
heater raises the temperature of the container-oil system by 2 Kin 20 minutes. Assuming no other heat losses in any of the processes, the specific
heat capacity of the oil is??
A \( .2 .5 \times 10^{3} J K^{-1} k g^{-1} \)
B. \( 5.1 \times 10^{3} J K^{-1} k g^{-1} \)
c. \( 3.0 \times 10^{3} J K^{-1} k g^{-1} \)
D. \( 1.5 \times 10^{3} J K^{-1} k g^{-1} \)
Subject: Physics
A small body of super dense material, with mass equal to half of that of earth
but whose size is very small compared
to that of earth, starts from rest at the
height h<
\( A \cdot \sqrt{\frac{2 h}{q}} \)
в. \( \sqrt{\frac{4 h}{3 g}} \)
c. \( \sqrt{\frac{2 h}{3 g}} \)
D. \( \sqrt{\frac{h}{g}} \)
Subject: Physics
A body of mass 5 kg falls from a height of 20 metres on the ground and it
rebounds to a height of 0.2 If the loss in Potential energy is used up by the body then what will be the temperature
rise? (specific heat of material = 0.09 \( \left.\operatorname{cal} \mathfrak{g m}^{-1 \circ} \boldsymbol{C}^{-1}\right) \)
\( \mathbf{A} \cdot 0^{\circ} C \)
B . \( 4^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 8^{\circ} C \)
D. None of these
Subject: Maths
If \( \boldsymbol{n}(\boldsymbol{A})=\boldsymbol{4}, \boldsymbol{n}(\boldsymbol{B})=\boldsymbol{3}, \boldsymbol{n}(\boldsymbol{A} \times \boldsymbol{B} \times \)
\( \boldsymbol{C})=\boldsymbol{2} 4, \) then \( \boldsymbol{n}(\boldsymbol{C})= \)
Subject: Chemistry
The ion \( A^{n+} \) is oxidised to \( A O_{3}^{-} \) by
\( M n O_{4}^{-} \) changing to \( M n^{2+} \) in acid
solution. Given that \( 2.68 \times 10^{-3} \) mol of
\( A^{n+} \) requires \( 1.61 \times 10^{-3} \) mol of
\( M n O_{4}^{-} \)
What is the weight of one gram
equivalent of \( A C l_{n} \) for the above
reaction if the atomic mass of \( A \) is \( 97 ? \)
Subject: Chemistry
By which way you can dispose the
useless chemicals?
A. The rule is to add concentrated acid to water slowly
B. Dispose of chemicals in the proper places following posted procedures. Do not return them to their original containers
C. Carefully replace unused or excess chemicals into their properly labeled containers from which they
came
D. Flush eyes with water at the eyewash fountain for at least 15 minutes, and then report the accident for further help
E. The rule is to add water to the concentrated acid slowly
Subject: Maths
The diagram shows part of the curve \( y=\frac{1}{16}(3 x-1)^{2}, \) which touches the \( x \)
axis at the point P. The point \( Q(3,4) \) lies
on the curve and the tangent to the
curve at \( Q \) crosses the \( x \) -axis at \( R \)
State the \( x \) -coordinate of \( P \)
Subject: Physics
A particle starts from the origin of coordinates at time \( t=0 \) and moves in
the \( x y \) plane with a constant
acceleration \( \alpha \) in the \( y \) -direction. Its
equation of motion is \( y=\beta x^{2} \). Its
velocity component in the x-direction is
A. variable
B. \( \sqrt{\frac{2 \alpha}{\beta}} \)
c. \( \frac{\alpha}{\beta} \)
D. \( \sqrt{\frac{\alpha}{2 \beta}} \)