AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Through a fixed point \( (h, k) \) secants are
drawn to the circle \( x^{2}+y^{2}=r^{2} \) Then
the locus of the midpoints of the chords
intercepted by the circle is
A \( \cdot x^{2}+y^{2}=h x+k y \)
B . \( x^{2}-y^{2}=h x+k y \)
C. \( x^{2}+y^{2}=h x-k y \)
D. \( x^{2}-y^{2}=h x-k y \)
Subject: Chemistry
\( X e F_{n}(n=2,4,6) \) are oxidising agents
and thus estimation of Xe salts can be
determined by suitable methods.
\[
\boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4}+\boldsymbol{4} \boldsymbol{K} \boldsymbol{I} \longrightarrow \boldsymbol{X} \boldsymbol{e}+\boldsymbol{2} \boldsymbol{I}_{2}+\boldsymbol{4} \boldsymbol{K} \boldsymbol{F}
\]
Write the increasing order of oxidising power of xenon compounds?
A. \( X e F_{2}<X e F_{4}<X e F_{6} \)
в. \( X e F_{2}<X e F_{6}<X e F_{4} \)
c. \( X e F_{6}<X e F_{4}<X e F_{2} \)
D. \( X e F_{6}=X e F_{4}=X e F_{2} \)
Subject: Chemistry
How many Faradays of electricity are required to deposit 10 g of calcium from molten calcium chloride using inert
electrodes? (molar mass of calcium =
\( \left.40 \text { g } m o l^{-1}\right) \)
A . \( 0.5 \mathrm{F} \)
B. 1
c. \( 0.25 \mathrm{F} \)
D. 2
Subject: Maths
\( X \) follows a binomial distribution with
parameters \( n \) and \( p, \) and \( Y \) follows a binomial distribution with parameters
\( \boldsymbol{m} \) and \( \boldsymbol{p} . \) Then, if \( \boldsymbol{X} \) and \( \boldsymbol{Y} \) are independent \( \boldsymbol{P}\left(\frac{\boldsymbol{X}=\boldsymbol{r}}{\boldsymbol{X}+\boldsymbol{Y}=\boldsymbol{r}+\boldsymbol{s}}\right)= \)
A \( \cdot \frac{\left(^{m} C_{r}\right)\left(^{n} C_{s}\right)}{m+n C_{r+s}} \)
В. \( \frac{\left(^{m} C_{s}\right)\left(^{n} C_{r}\right)}{m+n C_{r+s}} \)
c. \( \frac{\left(^{m} C_{s}\right)}{m+n C_{r}} \)
D. none of these
Subject: Physics
Two uniform rods of equal lengths \( \left(l_{0}\right) \) and equal masses have coefficient of linear expansion \( \alpha \) and \( 2 \alpha \) are placed in contact on a smooth horizontal surface
as shown. The temperature of system is
\( \theta^{0} C . \) Now the temperature is increased by \( \Delta \theta^{0} C \) The junction of the rods will shift from its initial position by?
initial temperature \( =\theta^{\circ} \mathrm{C} \)
A \( \cdot \frac{\log _{2} \Delta \theta}{2} \)
B. \( \frac{\log _{3} \Delta \theta}{3} \)
\( c \cdot \frac{\log _{4} \Delta \theta}{_{4}} \)
D. \( \frac{\log _{6} \Delta \theta}{6} \)
Subject: Chemistry
Match items of Column I with the items
of Column II and assign the correct code
with respect to Column I:
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { (a) } & \begin{array}{l}\text { Cyanide } \\ \text { process }\end{array} & \text { (i) } & \begin{array}{l}\text { Ultrapure } \\ \text { Ge }\end{array} \\ \text { (b) } & \begin{array}{l}\text { Froth } \\ \text { floatation } \\ \text { process }\end{array} & \text { (ii) } & \begin{array}{l}\text { Dressing of } \\ Z n S\end{array} \\ \text { (c) } & \begin{array}{l}\text { Electrolytic } \\ \text { reduction }\end{array} & \text { (iii) } & \begin{array}{l}\text { Extraction } \\ \text { of } A l\end{array} \\ \text { (d) } & \text { Zone refining } & \text { (iv) } & \begin{array}{l}\text { Extraction } \\ \text { of } A u\end{array} \\ & \text { (v) } & \begin{array}{l}\text { Purification } \\ \text { of } N i\end{array}\end{array} \)
\( \mathbf{A} \cdot(i v),(i i),(i i i),(i) \)
B. (ii), (iii), (i), (v)
\( \mathbf{C} \cdot(\mathrm{i}),(\mathrm{ii}),(\mathrm{iii}),(\mathrm{iv}) \)
D. (iii),(iv),(v), (i)
Subject: Chemistry
The \( K_{a} \) values for \( H P O_{4}^{2-} \) and \( H S O_{3}^{-} \)
\( \operatorname{are} 4.8 \times 10^{-13} \) and \( 6.3 \times 10^{-8} \)
respectively. Therefore, it follows that \( H P O_{4}^{2-} \) is a acid
\( \operatorname{than} H S O_{3}^{-} \) and \( P O_{4}^{3-} \) is a
base than \( \boldsymbol{S O}_{3}^{2-} \)
A. weaker, stronger respectively
B. stronger, weaker respectively
c. weaker, weaker respectively
D. stronger, stronger respectively
Subject: Physics
The electric current in a circular coil of
two turns produced a magnetic induction of \( 0.2 T \) at its centre. The coil
is unwound and is rewound into a
circular coil of four turns. The magnetic induction at the centre of the coil now
is, in \( T: \)
(if same current flows in the coil)
A . 0.2
B. 0.4
\( c .0 .6 \)
D. 0.8
Subject: Maths
If \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar vector and \( \lambda \) is
a real number, then the vectors \( \vec{a}+ \) \( 2 \vec{b}+3 \vec{c}, \lambda \vec{b}+\mu \vec{c} a n d(2 \lambda-1) \vec{c} \) are
coplanar when
\( \mathbf{A} \cdot \mu \epsilon R \)
B \( \cdot \lambda=\frac{1}{2} \)
c. \( \lambda=0 \)
D. All value are correct
Subject: Physics
A \( 200 M e V \) proton enters a region of the magnetic field of intensity 5 T. The
magnetic field points from south to north and the proton in moving along the vertical. The value of the force
acting on the proton will be
A. zero
В. \( 1.8 \times 10^{-10} N \)
c. \( 3.2 \times 10^{-18} N \)
D. \( 1.6 \times 10^{-6} N \)
Subject: Chemistry
Which of the following statements
is/are wrong?
This question has multiple correct options
A. Sulphur is estimated by Carius method as \( B a S O_{4} \)
B. Victor Meyer's method is used for the determination of molecular mass of a non-volatile compound
C. Kjeldahl's method is used for all nitrogen-containing organic compounds
D. Phosphorous is estimated by Carius method as \( M g\left(N H_{4}\right) \cdot P O_{4} \)
Subject: Physics
The radii and Young's modulus of two uniform wires \( A \& B \) are in the ratio
2: 1 and 1: 2 respectively. Both the
wires are subjected to the same longitudinal force. If increase in the length of wire \( A \) is \( 1 \% \). Then the
percentage increase in length of wire \( B \) is :
A . 1
в. 1.5
\( c \cdot 2 \)
\( D \)
Subject: Physics
A hollow spherical conductor of radius
\( R \) is given a charge \( Q . \) Work done in
moving a charge \( q \) from its centre to surface is :
A \( \cdot \frac{Q q}{4 \pi \varepsilon_{0} R} \)
в. \( \frac{Q q}{2 \pi \varepsilon_{0} R} \)
c. \( \frac{Q q}{\pi \varepsilon_{0} R} \)
D. zero
Subject: Physics
An atom initially at an energy level \( \boldsymbol{E}= \)
\( -6.52 e V . \) It absorbs a photon of
wavelenght \( 860 n m . \) What is the interna energy of atom after absorbing photon.
A . \( 5.08 e V \)
B. \( 1.44 e V \)
c. \( -1.44 e V \)
D. \( -5.08 e V \)
Subject: Chemistry
Which complex compound possesses \( s p^{3} d^{2} \) hybridisation?
A \( \cdot\left[F e\left(N H_{3}\right)_{6}\right]^{3+} \)
B . \( \left[F e(C N)_{6}\right]^{4-} \)
c. \( \left[F e(C N)_{6}\right]^{3} \)
D \cdot \( \left[F e(C l)_{6}\right]^{3-} \)
Subject: Chemistry
2mol of \( N_{2} \) is mixed with 6 mol of \( H_{2} \) in
a closed vessel of one litre capacity. If
\( 50 \% N_{2} \) is converted into \( N H_{3} \) at
equilibrium, the value of \( K_{c} \) for the
reaction.
\( N_{2}(g) 3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \) is:
A . 4/27
B. 27/4
c. 2/27
D. 20
Subject: Physics
Choose the correct options -
This question has multiple correct options
A. In a nuclear reactor, the function of the moderator, is to slow down neutrons
B. 1 MeV energy is \( 1.6 \times 10^{-13} J \)
C . A nucleus \( _{Z}^{A} X \) emits an \( \alpha- \) particle. The resultant nucleus emits a \( \beta^{+}- \) particle. The respective atomic
and mass nos. of the final nucleus will be \( z-3, A-4 \)
D. The mass equivalent of 931 MeV energy is \( 1.66 \times \) \( 10^{-27} k g \)
Subject: Chemistry
Foe the electrochemical cell:
\[
\begin{array}{c}
\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s}) \mid \boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{a} \boldsymbol{q}) \| \\
\boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q})\left|\boldsymbol{C l}_{2}(\boldsymbol{g})\right| \boldsymbol{P} \boldsymbol{t}(\boldsymbol{s}) \\
\text { Given }: \boldsymbol{E}_{\boldsymbol{Z n}^{2+} / Z \boldsymbol{n}}^{o}=-\mathbf{0 . 7 6} \boldsymbol{V} \boldsymbol{o l t} \\
\boldsymbol{E}_{\boldsymbol{C l}^{\prime} / \boldsymbol{C l}_{2}(\boldsymbol{g})}=-\mathbf{1 . 3 6} \boldsymbol{V} \boldsymbol{o l t} \boldsymbol{t}
\end{array}
\]
From these data one can deduce that:
A \( \cdot Z n+C l_{2} \rightleftharpoons Z n^{2+}+2 C l^{-} \) is a non-spontaneous
reaction at standard conditions
B . \( Z n^{2+}+2 C l^{-} \rightleftharpoons C l_{2}+Z n \) is a spontaneous reaction at
standard conditions with \( E_{c e l l}^{o}=2.12 \) volt.
C. \( Z n+C l_{2} \longrightarrow Z n^{2+}+2 C l^{-} \) is a spontaneous reaction
at standard conditions with \( E_{c e l l}^{o}=2.12 \) volt.
D. \( Z n+C l_{2} \longrightarrow Z n^{2+}+2 C l^{-} \) is a spontaneous reaction
at standard conditions with \( E_{c e l l}^{o}=0.60 \) volt.
Subject: Chemistry
On moving from left to right in a period what is the order of acidic character of
hydrides?
A. \( N H_{3}<H_{2} O<H F \)
в. \( H F<H_{2} O<N H_{3} \)
c. \( H_{2} O<H F<N H_{3} \)
D. \( H_{2} O<N H_{3}<H F \)
Subject: Maths
Given the function \( f(x) \) such that \( 2 f(x)+x f\left(\frac{1}{x}\right) \)
\( 2 f\left(\left|\sqrt{2} \sin \pi\left(x+\frac{1}{4}\right)\right|\right)= \)
\( 4 \cos ^{2} \frac{\pi x}{2}+x \cos \left(\frac{\pi}{x}\right), \) then which one
of the following is correct? This question has multiple correct options
A \( \cdot f(2)+f\left(\frac{1}{2}\right)=1 \)
B. \( f(1)=-1, \) but the values of \( f(2), f\left(\frac{1}{2}\right) \) cannot be determined
c. \( f(2)+f(1)=f\left(\frac{1}{2}\right) \)
D. \( f(2)+f(1)=0 \)
Subject: Chemistry
Which one has same Van't Hoff factor \( ' i^{\prime} \)
as that of \( \boldsymbol{H} \boldsymbol{g}_{2} \boldsymbol{C l}_{2} \) ?
A . \( N a C l \)
в. \( N a_{2} S O_{4} \)
c. \( A l\left(N O_{3}\right)_{3} \)
D. \( A l_{2}\left(S O_{4}\right)_{3} \)
Subject: Maths
Let a sequence \( \left\{a_{n}\right\} \) be defined by
\( \boldsymbol{a}_{\boldsymbol{n}}=\frac{\mathbf{1}}{\boldsymbol{n}+\mathbf{1}}+\frac{\mathbf{1}}{\boldsymbol{n}+\mathbf{2}}+\frac{\mathbf{1}}{\boldsymbol{n}+\mathbf{3}}+\dots \dots+ \)
\( \frac{1}{3 n}, \) then
This question has multiple correct options
A \( a_{2}=\frac{7}{12} \)
B. \( a_{2}=\frac{19}{20} \)
\( ^{\mathbf{C}} \cdot a_{n+1}-a_{n}=\frac{9 n+5}{(3 n+1)(3 n+2)(3 n+3)} \)
D. \( a_{n+1}-a_{n}=\frac{-2}{3(n+1)} \)
Subject: Maths
If the mean of following frequency distribution. is \( 2.6, \) then the values of
is
\( \begin{array}{llllll}x_{i} & 1 & 2 & 3 & 4 & 5\end{array} \)
\( f_{i} \quad 5 \quad 4 \quad \) f \( \quad 2 \quad 3 \)
\( A \cdot 3 \)
B.
c. 8
D. None of these
Subject: Maths
The number of points where the
function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}\mathbf{1}+\left[\cos \frac{\pi x}{2}\right], & \mathbf{1}<\boldsymbol{x} \leq \mathbf{2} \\ \mathbf{1}-\{\boldsymbol{x}\}, & \mathbf{0} \leq \boldsymbol{x}<\mathbf{1} \\ |\boldsymbol{s i n} \boldsymbol{\pi} \boldsymbol{x}|, & -\mathbf{1} \leq \boldsymbol{x}<\mathbf{0}\end{array} \) and \right.
\( f(1)=0 \) is continuous but nondifferentiable is/are (where [.] and \{
represent greatest integer and fractional part functions, respectively)
\( A \cdot O \)
в.
\( c \cdot 2 \)
D. none of these
Subject: Chemistry
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{3} \stackrel{\boldsymbol{\Delta}}{\rightarrow} \boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3}+\boldsymbol{6} \boldsymbol{N} \boldsymbol{O}_{3}+ \)
\( \mathbf{1 . 5 0}_{\mathbf{2}} \)
If reaction is correct enter 1 else 0
Subject: Physics
Assertion: Two forces \( 7 \mathrm{N} \) and \( 5 \mathrm{N} \) are
acting at a point and their resultant can
be \( 3 N \)
Reason: If two vectors \( \vec{P} \) and \( \vec{Q} \) are
acting at a point their resultant can have a value between \( \vec{P}-\vec{Q} \) to \( \vec{P}+\vec{Q} \).
A. Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.
c. Assertion is true, but the Reason is false.
D. Assertion is false, but the Reason is true.
Subject: Maths
Q Type your question
Leagur Iuuchan a vaic, yuu unotive someone who is clearly supporting
Manchester United in the game. What is the probability that they were actually born within 25 miles of Manchester?
Assume that:
\( \Longrightarrow \) the probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is \( \frac{1}{20}, \) and
\( \Longrightarrow \) the chance that a person born within 25 miles of Manchester
actually supports United is \( \frac{7}{10} \)
\( \Longrightarrow \) the probability that a person not born within 25 miles of
Manchester supports United with probability \( \frac{1}{10} \)
A \( \cdot \frac{7}{26} \)
в. \( \frac{8}{26} \)
c. \( \frac{9}{26} \)
D. \( \frac{10}{26} \)
Subject: Physics
The current flowing in the primary circuit of potentiometer is \( 2 A \) and the resistance of its wire is \( 0.2 \Omega / m . \) If a one ohm standard coil gets balanced at \( 250 \mathrm{cm} \) length of the wire, then the
current flowing in the coil will be
A . \( 0.1 \mathrm{A} \)
B. 1A
c. \( 1.5 \mathrm{A} \)
D. 0.05A
Subject: Chemistry
Which statements are correct about the
reaction?
\[
\mathbf{R}-\|^{*}_{\mathbf{M e}}^{\mathbf{O}} \underbrace{\mathbf{D}}_{\mathbf{O}} \ddot{\mathbf{N}} \mathbf{H}_{2} \frac{\mathbf{B r}_{2}+\stackrel{\Theta}{\mathbf{O H}}}{\Delta} \begin{array}{c}
\text { Mixture of } \\
\mathbf{1}^{\circ} \text { amines }
\end{array}
\]
This question has multiple correct options
A. A mixture of two amines is formed, which suggests that rearrangement is intramolecular
B. If \( R \) is chiral, it migrates with retention of configuration.
\( c \)
\[
\left[\begin{array}{c}
0 \\
R-C \\
\| \\
\dot{N}
\end{array}\right]
\]
A mixture of four different amines is formed, which suggests that a free acyl nitrene (diag) intermediate is formed.
D. A mixture of two different amines and a free acyl nitrene intermediate is formed.
Subject: Physics
A long string under tension of \( 100 N \) has one end at \( x=0 . \) A sinusoidal wave
is generated at \( x=0 \) whose equation is
given by
\( \boldsymbol{y}= \)
\( (0.01 c m) \sin \left[\left(\frac{\pi x}{10} m\right)-50 \pi t(s e c)\right] \)
Sketch the shape of the string at \( t= \) \( \frac{1}{50} s e c \)
Subject: Maths
The integrating factor of the differential equation \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y}=\boldsymbol{x}^{3} \boldsymbol{y}^{\boldsymbol{6}} \) is
A \( \cdot-\frac{5}{x^{5}} \)
в. \( \frac{5}{y^{5}} \)
\( c \cdot-\frac{1}{x^{5}} \)
D. \( \frac{1}{x^{5}} \)
Subject: Physics
A network of four \( 10 \mu F \) capacitors is
connected to a \( 500 V \) supply, as shown
in fig. Determine
(a) the equivalent
capacitance of the network and
(b) the
charge on each capacitor.(Note, the
charge on a capacitor is the charge on
the place with higher potential, equal
and opposite to the charge on the plate
with lower potential)
Subject: Chemistry
\( 250 m l \) of a sodium carbonate solution
contains 2.65 grams of \( N a_{2} C O_{3} .10 m l \)
of this solution is added to \( ^{\prime} x^{\prime} m l \) of
water to obtain \( 0.001 M N a_{2} C O_{3} \)
solution.
What is the value of \( ^{\prime} x^{\prime} \) in \( m l \) ?
[Molecular weight of \( \left.\boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3}=\mathbf{1 0 6}\right] \)
A. 1000
в. 990
c. 9990
D. 90
Subject: Chemistry
The numbers of \( \boldsymbol{F} \hat{\boldsymbol{I}} \boldsymbol{F} \) angle equal to \( \boldsymbol{9 0}^{\boldsymbol{o}} \)
and less than \( 90^{\circ} \) in \( I F_{7} \) are and
respectively.

If the answer is 15 and 9 then represent as 159
Subject: Maths
In a certain shop, which stocks four types of caps, there are \( 1 / 3 \) as many red caps as blue and \( 1 / 2 \) as many green caps as red caps. There are equal
numbers of green caps and yellow caps. If there are 42 blue caps, then what
percent of the total caps in the shop are
blue?
A . \( 70 \% \)
B. \( 28 \% \)
\( c \cdot 60 \% \)
D. \( 14 \% \)
Subject: Maths
Make h the subject of the formula given
above.
A \( \quad h=\frac{s+2 \pi r^{2}}{2 \pi r} \)
B. \( h=\frac{s-2 \pi r^{2}}{2 \pi r} \)
c. \( h=\frac{s-2 \pi r^{2}}{4 \pi r} \)
D. none of the above
Subject: Physics
In the shown figure, there are four point
charges each with a charge of \( +\mathrm{Q} \) and
situated at the four corners of a square
with a side of length \( \mathrm{D} \) What is the electric potential at the
center of the square? (k is the coulomb constant)
A \( \cdot \frac{4 k Q}{D} \)
B.
c.
D.
\( E \)
Subject: Physics
The top of the atmosphere is at about \( 400 k V \) with respect to the surface of
the earth, corresponding to an electric field that decreases with altitude. Near
the surface of the earth, the field is
about \( 100 V m^{-1} . \) Why then do we not \( \operatorname{get} \) an electric shock as we step out of
our house into the open? (Assume the house to be a steel cage so there is no field inside
Subject: Physics
Assertion
If the earth suddenly stops rotating about its axis, the n acceleration due to gravity will become the same at all
places.
Reason
The value of acceleration due to gravity is independent of rotation of the earth.
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: Chemistry
Assertion
On cooling, the brown colour of nitrogen dioxide disappears.
Reason
On cooling, \( N O_{2} \) undergoes
dimerisation resulting in the pairing of
the odd electrons in \( N O_{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
An inverted T-shaped object is placed on a smooth horizontal floor as shown in
figure
A force \( \boldsymbol{F} \) is applied on the system as
shown in figure. The value of \( x \) so that
the system performs pure transional motion is
A \( \cdot \frac{L}{4} \)
в. \( \frac{3 L}{4} \)
c. \( \frac{L}{2} \)
D. \( \frac{2 L}{2} \)
Subject: Maths
If \( \alpha, \beta, \gamma \) be the direction angles of a vector and \( \cos \alpha=\frac{14}{15}, \cos \beta=\frac{1}{3}, \) then
\( \cos \gamma= \)
This question has multiple correct options
\( A \cdot \pm \frac{2}{15} \)
в. \( \frac{1}{5} \)
\( c \cdot \pm \frac{1}{15} \)
D. None of these
Subject: Chemistry
Study the \( C_{1} \) bonding in the image
above. How does the strength of the \( C=O \) bond compare to the \( C-O H \)
bond?
A. The \( C=O \) bond is a stronger than the \( C-O H \) bond
B. The \( C=O \) bond is a weaker than the \( C-O H \) bond
C. The \( C=O \) bond and the \( C-O H \) bonds are of equal
strength.
D. The strength cannot be determined without knowing the average bond enthalpies.
Subject: Chemistry
The total number of stereoisomers of
\( \left(\boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{2}\right)_{3} \boldsymbol{C H} \) is:
\( A \cdot 6 \)
B. 4
\( c \cdot 3 \)
D. 5
Subject: Chemistry
The energy of the second Bohr orbit of hydrogen atom is - 3.41 eV. The energy of
the second orbit of \( \boldsymbol{H} \boldsymbol{e}^{+} \) would be:
A . - \( 0.85 \mathrm{ev} \)
B . -13.6ev
c. -1.70ev
D. - \( 6.82 \mathrm{eV} \)
Subject: Physics
An observer moves towards a stationary source of sound with a speed \( 1 / 5^{t h} \) of the speed of sound. The wavelength and frequency of the source emitted are \( \lambda \)
and \( f \) respectively. The apparent frequency and wavelength recorded by the observer are respectively:
A. \( 1.2 f, 1.2 \lambda \)
B. \( 1.2 f, \lambda \)
c. \( f, 1.2 \lambda \)
D. \( 0.8 f, 0.8 \lambda \)
Subject: Physics
The value of acceleration due to gravity
near the earth's surface is
A \( \cdot 8.9 m / s^{2} \)
в. \( 7.9 m / s^{2} \)
\( \mathrm{c} \cdot 9.8 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 19.8 m / s^{2} \)
Subject: Physics
There are 5 tube-lights each of \( 40 W \) in a house. These are used on an average
for 5 hrs / day. In addition, there is an immersion heater of \( 1500 W \) used on
an average for 1 h \( / \) day. The number of
units of electricity that are
consumed in a month of 30 days is:
A. 25 units
B. 50 units
c. 75 units
D. 100 units
Subject: Physics
A zener diode voltage regulator
operated in the range \( 120-180 V \)
produces a constant supply of \( 110 V \)
and \( 250 m A \) to the load. If the
maximum current is to be equally
shared between the load and zener, then
the values of series resistance \( \left(R_{S}\right) \) and
load resistance \( \left(R_{L}\right) \) are:
\( \mathbf{A} \cdot R_{L}=70 \Omega ; R_{S}=280 \Omega \)
B . \( R_{L}=440 \Omega ; R_{S}=140 \Omega \)
C \( . R_{L}=140 \Omega ; R_{S}=440 \Omega \)
\( \mathbf{D} \cdot R_{L}=280 \Omega ; R_{S}=70 \Omega \)
Subject: Chemistry
A current of \( 19.3 \mathrm{mA} \) is passed for 9375 seconds through \( 500 \mathrm{ml} \) of \( 2 \mathrm{mM} \)
\( Z n S O_{4} \) solution. If the final molarity of
\( Z n^{2+} \) is \( 0.5 \mathrm{mM} \), then the current efficiency of the source is (assume volume remains constant during this process):
A . 80\%
B. 75\%
c. 72\%
D. 65\%
Subject: Physics
\( A B C \) is a right-angled triangle, where \( A B \) and \( B C \) are \( 25 \mathrm{cm} \) and \( 60 \mathrm{cm} \)
respectively. A metal sphere of \( 2 \mathrm{cm} \)
radius charged to a potential of \( 9 \times 10^{5} \)
Vis placed at \( B \) as shown in Fig. Find the amount of work done in carrying a
positive charge of 1 coulomb from \( C \) to
\( \boldsymbol{A}: \)
\( A \cdot 21 k J \)
В. \( 42 k J \)
\( c \cdot 14 k J \)
D. \( 52 k J \)
Subject: Maths
The function \( f(x)=\frac{\tan \left\{\pi\left[x-\frac{\pi}{2}\right]\right\}}{2+[x]^{2}} \)
where \( [x] \) denotes the greatest integer
\( \leq x, \) is
A. continuous for all values of \( x \)
B. Discontinuous at \( x=\frac{\pi}{2} \)
c. Not differentiable for some values of \( x \)
D. Discontinuous at \( x=-2 \)
Subject: Chemistry
The wrong statements about \( N H_{3} \) is :
A. it is oxidised with oxygen at \( 700^{\circ} \mathrm{C} \) in the presence of platinum
B. it gives black precipitate with calomel
\( \mathbf{C} \cdot \) it can be dried by \( P_{2} O_{5}, H_{2} S O_{4} \) and \( C a C l_{2} \)
D. it gives white fumes with HCI
Subject: Biology
Optimum temperature of photosynthesis is
\( \mathbf{A} \cdot 10-15^{\circ} \mathrm{C} \)
В. \( 20-25^{\circ} \mathrm{C} \)
c. \( 20-35^{\circ} \mathrm{C} \)
D. \( 35-50^{\circ} \mathrm{C} \)
Subject: Chemistry
Mention the type of reaction to obtain \( \boldsymbol{A} \boldsymbol{u}(\mathbf{s} 0 I) \)
Reaction:
\( \mathbf{2} \boldsymbol{A} \boldsymbol{u} \boldsymbol{C l}_{3}+\mathbf{3} \boldsymbol{H} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O}+\mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \)
\( \mathbf{2} \boldsymbol{A} \boldsymbol{u}(\boldsymbol{s} \boldsymbol{o l})+\boldsymbol{3} \boldsymbol{H} \boldsymbol{O O H}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l} \)
A. Hydrolysis
B. Oxidation
c. Reduction
D. Double decomposition
Subject: Maths
Find the mode of the following
frequency table:
\( \begin{array}{ll}\text { Class Interval } & \text { Frequency } \\ 140-150 & 4 \\ 150-160 & 6 \\ 160-170 & 10 \\ 170-180 & 12 \\ 180-190 & 9 \\ 190-200 & 3\end{array} \)
Subject: Maths
Direction cosines of ray from
\( \boldsymbol{P}(\mathbf{1},-\mathbf{2}, \mathbf{4}) \) to \( \boldsymbol{Q}(-\mathbf{1}, \mathbf{1},-\mathbf{2}) \) are
в. 2,-3,6
\( \mathbf{c} \cdot 2,3,6 \)
D. \( \frac{-2}{7}, \frac{3}{7}, \frac{-6}{7} \)
Subject: Maths
If \( f^{\prime \prime}(x)<0 \) for all \( x \in(a, b), \) then
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\mathbf{0} \)
A. exactly once in \( (a, b) \)
B. at most once in \( (a, b) \)
c. at least once in \( (a, b) \)
D. none of these