AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A conducting ball is given a certain charge and fixed at point \( P . \) An another
charge of mass \( 1 g m \) and charge \( 20 \mu C \)
when kept at \( Q(3 m, 9 m) \) starts moving with acceleration \( \overrightarrow{\boldsymbol{a}}=(1.08 \hat{\boldsymbol{i}}+ \)
1.44 \( \hat{\boldsymbol{j}} \) ) \( \boldsymbol{m} \boldsymbol{s}^{-2} \). The potential at \( \boldsymbol{Q} \) is \( +\mathbf{7 2 0} \)
volt. Calculate
(a) charge given to ball
(b) position of the ball
\( \mathbf{A} \cdot 6.4 \times 10^{-7} C(\mathrm{b})(-1.8 m, 4 m) \)
B . \( 6.4 \times 10^{-7} C(\text { b ) }(-2.8 m, 2 m) \)
C \( .7 .4 \times 10^{-7} C(\mathrm{b})(-1.8 m, 2 m) \)
D. \( 6.4 \times 10^{-7} C \) (b) \( (-1.8 m, 2 m) \)
Subject: Maths
\( \left[\begin{array}{ll}\boldsymbol{x}-\boldsymbol{y} & \boldsymbol{4} \\ \boldsymbol{z}+\boldsymbol{6} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right]=\left[\begin{array}{ll}\boldsymbol{8} & \boldsymbol{w} \\ \boldsymbol{0} & \boldsymbol{6}\end{array}\right], \) write the
value of \( (\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}) \)
Subject: Physics
A metal ball of radius \( 2 \mathrm{mm} \) and
density \( 10.5 \mathrm{gmcm}^{-3} \) is dropped in glycerine of coefficient of viscosity 9.8 poise and density \( 1.5 \mathrm{gm} \mathrm{cm}^{-3} \). The
terminal velocity of the ball in \( \mathrm{cm} s^{-1} \) is:
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. 8
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}\} \) and \( \boldsymbol{B}=\{\boldsymbol{y}, \boldsymbol{x}\} ; \) then
\( \boldsymbol{A} \times \boldsymbol{B}=? \)
What are the number of elements of
such set?
Subject: Maths
Two persons \( A \) and \( B \) are throwing an
unbiased six faced die alternatively, with the condition that the person who
throws 3 first wins the game. If \( A \) starts the game, the probabilities of \( A \) and \( B \) to win the same are respectively
A \( \cdot \frac{6}{11}, \frac{5}{11} \)
в. \( \frac{5}{11}, \frac{6}{11} \)
c. \( \frac{8}{11}, \frac{3}{11} \)
D. \( \frac{3}{11}, \frac{8}{11} \)
Subject: Physics
toppr
Q туре уо
inductance to determine the height of the liquid level in the tank. The inductance of the tank changes from a
value of \( L_{0} \) corresponding to a relative permeability of 1 when the tank is
empty to value \( L_{f} \) corresponding to a
relative permeability \( \boldsymbol{X}_{m} \) (relative permeability of liquid) when the tank is full. The appropriate electronic circuit can determine the inductance
correct upto 5 significant figures and thus the effective relative permeability of the combined air and liquid within the rectangular has height \( D \). The
height of the liquid level in the tank is \( d \) Ignore the fringing effects. Assume tank is fitted with \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{X}_{\boldsymbol{H} \boldsymbol{g}}=\boldsymbol{2} . \boldsymbol{9} \times \mathbf{1 0}^{5} \)
Express \( d \) as a function of \( L \), inductance corresponding to a certain liquid height
\( \boldsymbol{L}_{0}, \boldsymbol{L}_{f} \) and \( \boldsymbol{D} \)
A \( \cdot d=\frac{\left(L-L_{0}\right) D}{L_{f}-L_{0}} \)
в. \( _{d}=\frac{L D}{L_{f}-L_{0}} \)
c. \( _{d=} \frac{\left(L-L_{0}\right) D}{L_{f}} \)
D. None of these
Subject: Chemistry
\( \mathrm{CaSO}_{4} \) is somewhat soluble in water.
I. When \( H_{2} S O_{4} \) is added to a solution
of \( C a S O_{4}, \) the solubility of the \( C a S O_{4} \)
will be increased.
II. The addition of \( H_{2} S O_{4} \) will lower the
\( p H \) of the solution
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement \( I I \) is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false
Subject: Physics
A particle goes from \( A \) to \( B \) with a speed of \( 40 \mathrm{km} / \mathrm{h} \) and \( \mathrm{B} \) to \( \mathrm{C} \) with a speed of 60 \( \mathrm{km} / \mathrm{h} \). If \( \mathrm{AB}=6 \mathrm{BC} \), the average speed in km/h between \( A \) and \( C \) is
A. \( 42 \mathrm{km} / \mathrm{h} \)
B. 50km/h
c. \( 60 \mathrm{km} / \mathrm{h} \)
D. \( 40 \mathrm{km} / \mathrm{h} \)
Subject: Chemistry
If a monovalent metal ion carries \( 1.6 \times \)
\( 10^{-19} \) coulomb of electricity, what is the
amount of electricity carried by one gram molecular mass of the metal
ions?
\( \mathbf{A} \cdot 9.6336 \times 10^{4} \)coulomb
B. \( 10.6336 \times 10^{4} \) coulomb
c. \( 95.336 \times 10^{4} \) coulomb
D. \( 96.336 \times 10^{4} \) coulomb
Subject: Chemistry
A gaseous hydrocarbon upon
combustion gives 0.72 g of \( H_{2} O \) and \( 3.08 \mathrm{g} \) of \( C O_{2} . \) The empirical formula of the hydrocarbon is :
A. \( C_{6} H_{5} \)
в. \( C_{7} H_{8} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{3} H_{4} \)
Subject: Chemistry
Assertion
Sulphuric acid is more viscous than
water.
Reason
Concentrated sulphuric acid has a
great affinity for water.
A. If both assertion and reason are correct and the reason
is the correct explanation of the assertion.
B. If both assertion and reason are correct, but the reason is not the correct explanation of the assertion.
C. If assertion is correct, but reason is incorrect
D. If assertion is incorrect, but reason is correct.
Subject: Chemistry
For a gas deviation from ideal behaviour is maximum at:
\( \mathbf{A} \cdot 0^{0} C \) and \( 1.0 a t m \)
B. \( 100^{\circ} \mathrm{C} \) and 2.0 atm
c. \( -13^{0} \mathrm{C} \) and 1.0 atm
D. \( -13^{0} C \) and 2.0 atm
Subject: Chemistry
The following some statements about
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} \) are :
i)It acts as both oxidising and reducing
agent.
ii) It is a strong acid.
iii) Its anhydride in pure state exists as pale blue liquid The correct combination is :
A. All are correct
B. i, iii are correct
c. ii, iii are correct
D. i, ii are correct
Subject: Physics
A gas at temperature \( 27^{\circ} \mathrm{C} \) and pressure
30 atmospheres is allowed to expand to one atmospheric pressure. If the volume becomes 10 times its initial volumes, the
final temperature becomes:
\( A \cdot 100^{\circ} \mathrm{C} \)
в. з7з к
c. \( 373^{\circ} \mathrm{C} \)
D. \( -173^{\circ} \mathrm{C} \)
Subject: Maths
If
(i) \( A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right], \) then verify
that \( \boldsymbol{A}^{\prime} \boldsymbol{A}=\boldsymbol{I} \)
(ii) \( A=\left[\begin{array}{cc}\sin \alpha & \cos \alpha \\ -\cos \alpha & \sin \alpha\end{array}\right], \) then verify
that \( \boldsymbol{A}^{\prime} \boldsymbol{A}=\boldsymbol{I} \)
Subject: Chemistry
0.2 mol sample of hydrocarbon, \( C_{X} H_{Y} \) yields after complete combustion with
excess \( \boldsymbol{O}_{2} \) gas, 0.8 mol of \( \boldsymbol{C} \boldsymbol{O}_{2} \) and \( \mathbf{1 . 0} \)
mol of \( \boldsymbol{H}_{2} \boldsymbol{O} . \) Hence, the hydrocarbon is :
A. \( C_{4} H_{10} \)
в. \( C_{4} H_{8} \)
c. \( C_{4} H_{6} \)
D. \( C_{8} H_{16} \)
Subject: Maths
f \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}=\boldsymbol{x} \boldsymbol{y} \boldsymbol{z}, \) prove that
\( \frac{2 x}{1-x^{2}}+\frac{2 y}{1-y^{2}}+\frac{2 z}{1-z^{2}}= \)
\( \frac{2 x}{1-x^{2}} \frac{2 y}{1-y^{2}} \frac{2 z}{1-z^{2}} \)
Subject: Maths
To construct a triangle similar to given \( \triangle A B C \) with its sides \( \frac{2}{3} \) of that of
\( \Delta A B C, \) locate points on ray \( B X \) at
equal distances as \( B_{1}, B_{2}, B_{3}, \ldots \) such
that \( \angle C B X \) is acute. The points to be
joined in the next step are:
A. \( B_{4}, C \)
в. \( B_{3}, C \)
c. \( B_{1}, C \)
D. \( B_{2}, C \)
Subject: Physics
Assertion
Smaller the orbit of the planet around
the sun, shorter is the time it takes to
complete one revolution
Reason
According to Kepler's third law of
planetary motion, square of time period is proportional to cube of mean distance from sun
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: Biology
There are two opposing views about origin of modern man. According to one view, Homo erectus in Asia was ancestor
of modern man. A study of variations of DNA, however suggested African origin of modern man.
What kind of observation of DNA
variations could suggest this?
A. Greater variation in Asia than in Africa
B. Greater variation in Africa than in Asia
c. similar variation in Africa and Aisa
D. Variation only in Asia and no variation in Africa
Subject: Physics
Assertion (A): Propagation of light through an optical fibre is due to total internal reflection taking place at the core-cladding interface. Reason (R) : Refractive index of the material of the core of the optical fibre is greater than that of air.
A. Both (A) and (R) are true and
(R) is the correct explanation of (A)
B. Both (A) and (R) are true but (R) is not the correct explanation of (A)
c. (A) is true and (R) is false
D. (A) is false and (R) is true
Subject: Chemistry
Assertion
Heavy water is used as amoderator in
nuclear reactors.
Reason
Heavy water is made of an isotope of
helium.
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
Out of the two concentric circles, the
radius of the outer circle is \( 5 \mathrm{cm} \) and
the chord \( A C \) of length \( 8 \mathrm{cm} \) is a tangent to the inner circle. Find the radius of
the inner circle.
\( A .3 c m \)
B. \( 6 \mathrm{cm} \)
\( c .5 \mathrm{cm} \)
D. 7 cm
Subject: Maths
Prove that the points \( \boldsymbol{A}(\mathbf{1}, \mathbf{7}), \boldsymbol{B}(\mathbf{4}, \mathbf{2}), \boldsymbol{C}(-\mathbf{1},-\mathbf{1}) \) and
\( D(-4,4) \) are the vertices of a square.
Subject: Chemistry
Which of the following statements are
correct about \( \boldsymbol{S} \boldsymbol{F}_{4} ? \)
A. It is prepared by reacting sulphur directly with fluorine
B. Sulphur tetrafluoride hydrolyzed by water to give \( S O_{2} \) and нF
\( \mathrm{c} . S F_{4} \) has a square planar shape with \( \mathrm{S} \) having two lone pair of electrons
D. S-atom has a expanded octet.
Subject: Maths
The function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{e^{1 / x}-1}{e^{1 / x}+1}, \quad x \neq 0 \\ 0, \quad x=0\end{array}\right. \)
A. is continuous at \( x=0 \)
B. is not continuous at \( x=0 \)
c. is not continuous at \( x=0, \) but can be made continuous at \( x=0 \)
D. None of these
Subject: Chemistry
The solubility product of \( A g B r \) is \( 4.9 \times \)
\( 10^{-9} . \) The solubility of AgBr will be:
A. \( 7 \times 10^{-4} \) mole /litre
B. \( 7 \times 10^{-5} g / \)litre
c. \( 1.316 \times 10^{-2} g / \)litre
D. \( 1 \times 10^{-3} \) mole \( / \)litre
Subject: Physics
The total radiant energy per unit area, normal to the direction of incidence, received at a distance \( \mathrm{R} \) from the center
of a star of radius \( r, \) whose outer surface
radiates as a black body at a temperature \( T \) Kelvin is given by:
(Where \( \sigma \) is Stefan's Constant)
\( ^{\text {A } \cdot \frac{\sigma r^{2} T^{4}}{R^{2}}} \)
в. \( \frac{\sigma r^{2} T^{4}}{4 \pi r^{2}} \)
c. \( \frac{\sigma r^{4} T^{4}}{r^{4}} \)
D. \( \frac{4 \pi \sigma r^{2} T^{4}}{R^{2}} \)
Subject: Physics
The angle between the two vectors \( \vec{A}= \) \( \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=-\hat{\mathbf{i}}+\hat{\boldsymbol{j}}-\mathbf{2} \hat{\boldsymbol{k}} \) is:
A \( \cdot 90^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
Subject: Maths
\( f\left|\begin{array}{lll}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}+\boldsymbol{2} & \boldsymbol{x}+\boldsymbol{a} \\ \boldsymbol{x}+\mathbf{2} & \boldsymbol{x}+\boldsymbol{3} & \boldsymbol{x}+\boldsymbol{b} \\ \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\boldsymbol{4} & \boldsymbol{x}+\boldsymbol{c}\end{array}\right|=\mathbf{0} \) then show
that \( a, b, c \) are in \( A . P \)
Subject: Chemistry
\( \mathrm{Zn}(s)\left|\mathrm{ZnCl}_{2}(\mathrm{aq})\right| \mathrm{Cl}^{-}(\mathrm{aq})\left|\mathrm{Cl}_{2}(g)\right| \mathrm{C}(s) \)
According to the above cell diagram the electrochemical cell described, the
reaction at anode is :
A \( \cdot z n \rightarrow z n^{2+}+2 e^{-} \)
B. \( z n^{2+}+2 e^{-} \rightarrow \) Zn
c. \( \mathrm{cl}_{2}+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cl}^{-} \)
D . 2CI- \( \rightarrow \mathrm{Cl}_{2}+2 \mathrm{e}^{-} \)
E. \( z n+C l_{2} \rightarrow Z n C l_{2} \)
Subject: Chemistry
The number of coulombs required to deposit \( 5.4 g \) of Aluminium when the
given electrode reaction is represented
as \( A l^{3+}+3 e^{-} \rightarrow A l \)
A \( \cdot 1.83 \times 10^{5} C \)
в. \( 57900 C \)
\( \mathbf{c} \cdot 5.86 \times 10^{5} C \)
D. \( 3 F \)
Subject: Chemistry
From 2 moles of \( K C l O_{3} \) by
decomposition of all the \( K C l O_{3}, \) how
many liters of \( \boldsymbol{O}_{2} \) can be produced at
STP?
A . 11.2
в. 22.4
c. 33.6
D. 44.8
E . 67.2
Subject: Chemistry
Which of the following statements is
correct about the water-gas shift
reaction used for the commercial
preparation of hydrogen gas?
A. It involves the selective oxidation of \( \mathrm{CO} \) of water gas to
\( C O_{2} \) with the help of steam in the presence of iron chromate as catalyst
B. It involves the separation of \( \mathrm{CO} \) and \( \mathrm{H}_{2} \) by solvent extraction method
C. It involves the absorption of \( \mathrm{CO} \) in aqueous copper (I) chloride solution
D. It involves the removal of \( H_{2} \) through occlusion with
\( P d \)
Subject: Maths
Differentiate the following functions
with respect to \( x: \) \( \mathbf{f} \boldsymbol{y}=\mathbf{s e c}^{-1}\left(\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{1}}\right)+ \)
\( \sin ^{-1}\left(\frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{x}+\mathbf{1}}\right), \boldsymbol{x}>\mathbf{0} . \) Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)
Subject: Physics
If the constant forces \( 2 \hat{i}-5 \hat{j}+6 \hat{k} \) and \( -\hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) act on a particle due to
which it is displaced from a point \( A(4,-3,-2) \) to a point \( B(6,1,-3) \) then the work done is
A . 15 unit
B. 9 unit
c. -15 unit
D. - 9 unit
Subject: Maths
Show that: \( \left|\begin{array}{ccc}\mathbf{1} & -\mathbf{2} \boldsymbol{i} & \mathbf{- 1} \\ \mathbf{3} \boldsymbol{i} & \boldsymbol{i}^{\mathbf{3}} & -\mathbf{2} \\ \mathbf{1} & \mathbf{- 3} & -\boldsymbol{i}\end{array}\right|=-\mathbf{7}+ \)
\( \mathbf{1 8 i}, \) where \( \boldsymbol{i}=\sqrt{-\mathbf{1}} \)
Subject: Maths
Evaluate: \( \lim _{x \rightarrow 0}\left(\frac{a^{x}+b^{x}+c^{x}}{3}\right)^{2 / x} \)
A \( . a+b+c \)
В \( \cdot(a b c)^{1 / 3} \)
c. \( (a b c)^{2} \)
D. \( (a b c)^{2 / 3} \)
Subject: Chemistry
Which of the following conclusions
could not be derived from Rutherford's
\( \alpha \) -particles scattering experiment?
A. Most of the spaces in the atom is empty.
B. The radius of the atom is about \( 10^{-10} \mathrm{m} \) while that of
nucleus is \( 10^{-15} \mathrm{m} \)
C. Electrons move in a circular path of fixed energy called orbits
D. Electrons and the nucleus are held together by electrostatic force of attraction
Subject: Chemistry
For joining railway tracks, ferric oxide is reacted with aluminium to produce aluminium oxide and iron. The balanced
chemical equation for the given reaction is \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3(x)}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{l}_{(x)} \rightarrow \)
Ferricoxide
\( \begin{array}{cc}\boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{\boldsymbol{3}(\boldsymbol{x})} & \boldsymbol{+} \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}_{(\boldsymbol{x})} \\ \text {Aluminium oxide} & \text {Iron}\end{array} \)
Which of the following substances is oxidized in the given reaction?
A \( \cdot A l_{2} O_{3} \)
в. \( F e_{2} O_{3} \)
\( c . A l \)
D. \( F e \)
Subject: Maths
The circumference of the base of a
circular cylinder is \( 6 \pi \mathrm{cm} . \) The height of
the cylinder is equal to the diameter of the base. How many litres of water can it hold?
A . \( 0.54 \pi \) litres
B. \( 0.6 \pi \) litres
c. \( 0.5 \pi \) litres
D. \( 0.4 \pi \) litres
Subject: Physics
Three particles, each of mass \( 10^{-2} \mathrm{kg} \)
are brought from infinity to the vertices of an equilateral triangle of side \( 0.1 m \) the work done is:
A \( .2 \times 10^{-8} \mathrm{J} \)
В. \( 2 \times 10^{-11} J \)
c. \( 2 \times 10^{-12} J \)
D. \( 2 \times 10^{-13} \mathrm{J} \)
Subject: Physics
The displacement of the particle varies with time \( x=12 \sin \omega t-16 \sin ^{3} \omega t . \) If its
motion is SHM, then maximum
acceleration is
A \( \cdot 12 \omega^{2} \)
B. 36 \( \omega^{2} \)
c. \( 144 \omega^{2} \)
D. \( \sqrt{192} \omega^{2} \)
Subject: Physics
A rod of length \( L \) rotates in the form of a
conical pendulum with an angular velocity \( \omega \) about its axis as shown in
figure. The rod makes an angle \( \boldsymbol{\theta} \) with the axis. The magnitude of the motional emf developed across the two ends of
the rod is
\( A \)
в.
\( ^{\mathrm{c}} \cdot \frac{1}{2}^{B \omega L^{2} \cos ^{2} \theta} \)
D.
E. answer required
Subject: Chemistry
\( D_{2} O \) will have maximum density at :
\( \mathbf{A} \cdot 9^{\circ} C \)
B. \( 11.5^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 15.9^{\circ} \mathrm{C} \)
D. \( 20^{\circ} \mathrm{C} \)
Subject: Chemistry
If \( 9 g \) of \( H_{2} O \) is electrolyzed completely with \( 50 \% \) current efficiency:
A. \( 1 F \) of electricity will be needed
B. \( 3 F \) of electricity is needed
c. 5.6 L of \( O_{2} \) at \( S T P \) will be formed
D. \( 11.2 L \) of \( O_{2} \) at \( S T P \) will be formed
Subject: Chemistry
The complex that can show fac- and
mer- isomers is :
A \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{3}\left(N O_{2}\right)_{3}\right] \)
B \( \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right] \)
c. \( \left[\operatorname{CoCl}_{2}(e n)_{2}\right] \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right]^{+} \)
Subject: Maths
Find \( k, \) if the given function is
continuous at \( x=2 \) \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\mathbf{3} \boldsymbol{x}-\mathbf{4} \text { for } \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{2} \\ \mathbf{2} \boldsymbol{x}+\boldsymbol{k} \text { for } \mathbf{2} \leq \boldsymbol{x} \leq \mathbf{4}\end{array}\right. \)
Subject: Physics
A beaker containing water weighs 100 \( g m \). It is placed on the pan of a balance and a piece of metal weighing \( 70 g m \) and having a volume of \( 10 c c \) is placed inside the water in the beaker
The weigh of the beaker and the metal would be
A. \( 170 g m \)
в. \( 160 g \) m
c. \( 100 g m \)
D. \( 30 g m \)
Subject: Physics
A conducting circular loop is placed in a uniform magnetic field, \( B=.025 \) T with its plane perpendicular to the loop. The
radius of the loop is made to shrink at a
constant rate of \( 1 \mathrm{mm} \) s1. The induced
e.m.f. when the radius is \( 2 \mathrm{cm} \), is
\( A \cdot 2 \mu V \)
в. \( 2 \pi \mu V \)
\( c . \pi \mu V \)
D \( \cdot \frac{\pi}{2} \mu V \)
Subject: Chemistry
Assertion
Liquefication of a gas is a continuous
process with increase in pressure below
\( \boldsymbol{T}_{\boldsymbol{c}} \)
Reason
Liquefication of a gas is a
discontinuous process with increase in
pressure below \( \boldsymbol{T}_{\boldsymbol{c}} \)
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
Why covalent character of lithium
halides follow the following order? \( \boldsymbol{L} \boldsymbol{i} \boldsymbol{I}>\boldsymbol{L} \boldsymbol{i} \boldsymbol{B} \boldsymbol{r}>\boldsymbol{L} \boldsymbol{i} \boldsymbol{C l}>\boldsymbol{L} \boldsymbol{i} \boldsymbol{F} \)
Subject: Maths
Let \( \boldsymbol{A}=\{-2,-1,0,1,2\} \) and \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \)
\( Z \) be given by \( f(x)=x^{2}-2 x-3 . \) Find
the pre-image of 6,-3 and 5
Subject: Physics
Find the magnitude of the angular
acceleration of the cone
A \( .3 .3 \mathrm{rad} / \mathrm{s}^{2} \)
B . \( 2.6 \mathrm{rad} / \mathrm{s}^{2} \)
c. 2.3 rad / \( s^{2} \)
D. \( 3.6 \mathrm{rad} / \mathrm{s}^{2} \)
Subject: Physics
A spherical conducting shell of inner
radius \( r_{1} \) and outer radius \( r_{2} \) has a
charge \( Q . A \) charge \( -q \) is placed at the
center of the shell. The surface of the
shell will be
A \( \cdot \frac{q}{4 \pi r_{1}^{2}} \) and \( \frac{Q}{4 \pi r_{2}^{2}} \)
В. \( \frac{-q}{4 \pi r_{1}^{2}} \) and \( \frac{Q+q}{4 \pi r_{2}^{2}} \)
c. \( \frac{q}{4 \pi r_{1}^{2}} \) and \( \frac{Q-q}{4 \pi r_{2}^{2}} \)
D. 0 and
Subject: Maths
Let \( f \) be a function defined on \( R \) (the set
of all real numbers) such that \( \mathbf{f}^{\prime}(\mathbf{x})= \) \( 2010(x-2009)(x-2010)^{2}(x- \)
2011)\( ^{3}(x-2012)^{4}, \) for all \( x \in R \). If \( g \) is a
function defined on \( \mathbf{R} \) with values in the
interval \( (0, \infty) \) such that \( f(x)= \) \( \ln (\mathrm{g}(\mathrm{x})), \) for all \( \mathrm{x} \in \mathrm{R}, \) then the number
of points in \( \mathbf{R} \) at which \( \mathbf{g} \) has a local maximum is
A .
B.
\( c \cdot 2 \)
D. 3
Subject: Maths
The centre, vertex, focus of a conic are
\( (0,0),(0,5),(0,6) . \) Its length of latus rectum is
A \( \cdot \frac{11}{5} \)
в. \( \frac{7}{5} \)
c. \( \frac{14}{5} \)
D. \( \frac{22}{5} \)
Subject: Chemistry
Assertion
\( H N O_{3} \) is stronger acid than \( H N O_{2} \)
Reason
\( \ln H N O_{3} \) there are two nitrogen to
oxygen bonds where as in \( H N O_{2} \) there
is only one.
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
A metal, M forms chlorides in its +2 and +4 oxidation states. Which of the
following statements about these chlorides is correct?
A \( \cdot M C l_{2} \) is more ionic than \( M C l_{4} \)
B. \( M C l_{2} \) is more easily hydrolysed than \( M C l \)
c. \( M C l_{2} \) is more volatile than \( M C l_{4} \)
D. \( M C l_{2} \) is more soluble in anhydrous ethanol than \( M C l \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{1} \\ -\mathbf{1} & \mathbf{2}\end{array}\right], \) show that \( \boldsymbol{A}^{2}-\mathbf{5} \boldsymbol{A}+ \)
\( \mathbf{7} \boldsymbol{I}=\boldsymbol{O} . \) Hence find \( \boldsymbol{A}^{-1} \)
Subject: Chemistry
Encircle whichever of the following:
a) is the stronger nucleophile (aprotic
solvent) : \( \boldsymbol{F}^{-} \) or \( \boldsymbol{I}^{-} \)
b) is the stronger nucleophile (protic
solvent) \( : \boldsymbol{F}^{-} \) or \( \boldsymbol{I}^{-} \)
c) is the stronger base \( : \boldsymbol{F}^{-} \) or \( \boldsymbol{I}^{-} \)
d) is the stronger nucleophile (protic solvent): \( N H_{3} \) or \( N H_{2} N H_{2} \)
e) is the better leaving group:
\( \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-} \boldsymbol{o r} \boldsymbol{C H}_{2} \boldsymbol{S O}_{3}^{-} \)
Subject: Maths
A batsman scores runs in 10 innings as \( \mathbf{3 8}, \mathbf{7 0}, \mathbf{4 8}, \mathbf{3 4}, \mathbf{4 2}, \mathbf{5 5}, \mathbf{6 3}, \mathbf{4 6}, \mathbf{5 4}, \mathbf{4 4 .} \) The
mean deviation about mean is :
A. 8.6
B. 6.4
c. 10.6
D. 7.6
Subject: Physics
The separation between two coherent
point sources is \( 3 \lambda . \) On a line
perpendicular to \( S_{1} S_{2} \) and passing
through \( S_{2} \). Find the smallest distance
where minimum of intensity occurs:
A \( \cdot \frac{11 \lambda}{20} \)
B. \( \frac{\lambda}{2} \)
c. \( \frac{9 \lambda}{20} \)
D. \( \frac{35 \lambda}{4} \)