AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
I: The area bounded by the line \( y=x \)
and the curve \( y=x^{3} \) is \( 1 / 2 \) sq. units.
II: The area bounded by the curves \( \boldsymbol{y}= \)
\( x^{3} \) and \( y=x^{2} \) and the ordinates \( x=1 \)
\( x=2 \) is \( \frac{7}{12} \) sq. units.
Which of the above statement is
correct?
A. onlyı
c. Both I and II
D. Neither I nor II.
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{5} \sin ^{2} \boldsymbol{x} \) be
an increasing function on the set \( R \)
Then, \( a \) and \( b \) satisfy
A \( \cdot a^{2}-3 b-15>0 \)
B . \( a^{2}-3 b+15>0 \)
c. \( a^{2}-3 b+15<0 \)
D. \( a>0 \) and \( b>0 \)
0
Subject: Chemistry
The number of electrons in an element
\( X \) is 15 and the number of neutrons is
16. The element can be represented as:
A. \( 31_{X} \)
\( 15^{X} \)
в. \( 31_{X} \)
\[
16^{\text {月 }}
\]
D. 15
\( 16^{X} \)
Subject: Maths
If \( A B C D \) is parallelogram. E is mid-point of \( A B \) and \( C E \) bisects \( \angle B C D, \) then
\( \angle D E C \) is
A \( \cdot 60^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 100^{\circ} \)
D. 120
Subject: Physics
When brakes are applied to a bus, the
retardation produced is \( 25 \mathrm{cm} \mathrm{s}^{-2} \) and
the bus takes \( 20 s \) to stop. Calculate the initial velocity of the bus.
\( \mathbf{A} \cdot 5 m s^{-1} \)
B. \( 10 m s^{-1} \)
\( \mathbf{c} \cdot 15 m s^{-1} \)
D. \( 20 m s^{-1} \)
Subject: Physics
A convex lens of focal length \( 1.5 \mathrm{m} \) is
placed in a system of coordinate axis
such that its optical centre is at origin and principal axis coinciding with the x-axis. An object and a plane mirror are arranged on the principal axis as shown n fig. Find value of \( d \) (in \( m \) ) so that \( y \) coordinate of image (after refraction and reflection) is \( 0.3 \mathrm{m} . \) (Take \( \tan \theta= \)
\( \mathbf{0 . 3}) \)
Subject: Maths
\( S \) and \( T \) are the foci of an ellipse and \( B \)
is an end of the minor axis. If \( \triangle \boldsymbol{S T B} \) is
an equilateral triangle, the eccentricity of the ellipse is equals to:
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{2}{3} \)
E. None of these
Subject: Chemistry
The volume of a monoatomic ideal gas
increases linearly with pressure as
shown in the diagram. What is the
increase in internal energy?
A \( .4 .8 \times 10^{5} J \)
B \( .3 .6 \times 10^{5} J \)
c. \( 2.9 \times 10^{5} J \)
D. \( 5.6 \times 10^{5} J \)
Subject: Maths
Prove that:
\[
\frac{3^{-3} \times 6^{2} \times \sqrt{98}}{5^{2} \times \sqrt[3]{1 / 25} \times(15)^{-4 / 3} \times 3^{1 / 3}}=
\]
\( 28 \sqrt{2} \)
Subject: Chemistry
Assertion
According to Rutheford's atomic model, electron should fall into the nucleus
Reason

Electron is a charged particle and it emits radiation while in motion and
lose energy
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
The element having electronic configuration.
\( [\boldsymbol{K} \boldsymbol{r}] \boldsymbol{4} \boldsymbol{d}^{10} \boldsymbol{4} \boldsymbol{f}^{14} \boldsymbol{5} \boldsymbol{s}^{2} \boldsymbol{5} \boldsymbol{p}^{6} \boldsymbol{5} \boldsymbol{f}^{2} \boldsymbol{6} \boldsymbol{s}^{2} \) belongs
to
A. s-block
B. p-block
c. d-block
D. f-block
Subject: Chemistry
If for the following half-cell reactions:
\( \boldsymbol{C u}^{2+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}^{\oplus} \)
\( \boldsymbol{E}^{\oplus}=\mathbf{1 . 7 7} \boldsymbol{V} \)
\( \boldsymbol{C u}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} \)
\( \boldsymbol{E}^{\ominus}=-\mathbf{0 . 3 4} \)
The \( E^{\ominus} \) of the half-cell reaction will be
\( (\text { in } V) \)
\( \boldsymbol{C u}^{\oplus}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u} \)
Subject: Physics
Let \( \boldsymbol{v}_{\boldsymbol{K}_{\alpha}}, \boldsymbol{v}_{\boldsymbol{K}_{\beta}}, \) and \( \boldsymbol{v}_{\boldsymbol{L}_{\alpha}} \) are the
frequencies of \( \boldsymbol{K}_{\boldsymbol{\alpha}}, \boldsymbol{K}_{\boldsymbol{\beta}} \) and \( \boldsymbol{L}_{\boldsymbol{\alpha}} . \mathbf{X} \)
raylines of a material, then
\( \mathbf{A} \cdot v_{K_{\alpha}}+v_{K_{\beta}}=v_{L_{\alpha}} \)
В . \( v_{K_{a}}-v_{K_{\beta}}=v_{l_{d}} \)
\( \mathbf{c} \cdot v_{L_{\alpha}}+v_{K_{\alpha}}=v_{K_{\beta}} \)
D. \( v_{K_{\alpha}}-v_{L_{\alpha}}=v_{K_{\beta}} \)
Subject: Physics
A \( 15 \Omega \) resistor, a \( 220 \mu \mathrm{H} \) coil, and a \( 60 p F \) capacitor are in series across an
ac source. What is the bandwidth of the
circuit?
\( \mathbf{A} \cdot 138 M H z \)
в. \( 10,866 \mathrm{Hz} \)
\( \mathbf{c} .1,907 H z \)
D. \( 138 k H z \)
Subject: Chemistry
Assertion
Equilibrium Constant of a reaction increases if temperature is increased.
Reason

The forward reaction becomes faster
with increase of temperature.
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
In solid state \( P C l_{5} \) exist as an ionic
solid \( \left[\boldsymbol{P C l}_{4}\right]^{+}\left[\boldsymbol{P C l}_{6}\right]^{-} \) hybridisation
state of cation and anion respectively:
\( \mathbf{A} \cdot d s p^{2}, s p^{3} d^{2} \)
B \( \cdot s p^{3}, s p^{3} d^{2} \)
\( \mathbf{c} \cdot s p^{3} d^{2}, s p^{3} \)
D. \( s p^{3} d^{2}, d s p^{2} \)
Subject: Maths
\( A=(2,4,5) \) and \( B=(3,5,-4) \) are two
points. If the \( x y \) -plane, \( y z \) -plane divide \( A B \) in the ratios \( a: b, p: q \) respectively then \( \frac{a}{b}+\frac{p}{q}= \)
A. \( \frac{7}{15} \)
в. \( \frac{-7}{12} \)
c. \( \frac{7}{12} \)
D. \( \frac{22}{25} \)
Subject: Physics
If pressure of an ideal gas contains in a closed vessel is increased by \( 0.5 \% \) the
increase in temperature is \( 20 \mathrm{k} \) the initial temperature of the gas is
A \( \cdot 27^{\circ} \mathrm{C} \)
B. \( 127^{\circ} \mathrm{C} \)
\( c \cdot 300^{0} c \)
D. \( 400^{\circ} \mathrm{C} \)
Subject: Chemistry
Number of revolution per second made by electron in Bohr orbit is called orbital
frequency. If \( \boldsymbol{u}_{n}, \boldsymbol{r}_{n}, \boldsymbol{E}_{n} \) are velocity,
radius and energy level of \( n \) th orbit respectively?
A \( \cdot \frac{u_{n}}{2 \pi r_{n}} \)
B. \( -\frac{2 E_{n}}{n h} \)
c. \( -\frac{2 E_{1}}{n^{3} h} \)
D. either of these
Subject: Chemistry
The oxidation state of Fe in browns ring
complex \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{NO}^{+}\right] \mathrm{SO}_{4} \) is:
\( A \cdot+1 \)
\( B \cdot+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)
Subject: Chemistry
\( 2 H I(g) \longrightarrow H_{2}(g)+I_{2}(g) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. None of these
Subject: Maths
Let \( L \) denote the set of all straight lines
in a plane, Let a relation \( R \) be defined by
\( l R m, \) iff \( l \) is perpendicular to \( m \) for all
\( l \in L . \) Then, \( R \) is
A . reflexive
B. symmetric
c. transitive
D. none of these
Subject: Physics
A particle moves such that its acceleration is given by \( \boldsymbol{a}=-\boldsymbol{\beta}(\boldsymbol{x}-\boldsymbol{2}) \)
Here \( \beta \) is a positive constant and \( x \) is
the position from origin. Time period of oscillations is
A. \( 2 \pi \sqrt{\beta} \)
в. \( 2 \pi \sqrt{\frac{1}{\beta}} \)
\( \mathbf{c} \cdot 2 \pi \sqrt{\beta}+2 \)
D. \( 2 \pi \sqrt{\frac{1}{\beta+2}} \)
Subject: Chemistry
For the reaction \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B}^{+} \rightleftharpoons \boldsymbol{A}^{2+}+ \)
\( 2 B ; K_{c} \) has been found to be \( 10^{12} \). The
\( \boldsymbol{E}_{c e l l}^{o} \) is:
A . 0.354
в. 0.708
c. \( 0.0098 \mathrm{v} \)
D. 1.36 \( v \)
Subject: Maths
If vectors \( a \) and \( b \) be respectively equal \( \operatorname{to} 3 \hat{i}-4 \hat{j}+5 \hat{k} \) and \( 2 \hat{i}+3 \hat{j}-4 \hat{k} . \) Find
the unit vector parallel to \( \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} \)
Subject: Physics
When a silver foil (Z=47) was used in an
\( \alpha \) -ray scattering experiment, the
number of \( \alpha \) partied scattered at \( 30^{\circ} \)
aws found to be 200 per minute. If the silver foil is replaced by aluminium \( (z=13) \) foil of same thickness, the
number of \( \alpha \) -particles scattered per
minute at \( 30^{\circ} \) is nearly equal to
A . 15
B. 30
c. 10
D. 26
Subject: Maths
Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose elements \( a_{i j} \) are given by:
\( \boldsymbol{a}_{\boldsymbol{i} j}=\left|\frac{\boldsymbol{3} \boldsymbol{i}-\boldsymbol{j}}{\boldsymbol{2}}\right| \)
Subject: Maths
The locus of the mid points of the chord
of the circle \( x^{2}+y^{2}=4, \) which
subtended a right angle at the origin is
A. \( x+y=1 \)
B . \( x^{2}+y^{2}=1 \)
c. \( x+y=2 \)
D. \( x^{2}+y^{2}=2 \)
Subject: Physics
Magnetic filed at point \( ^{\prime} \boldsymbol{P}^{\prime} \) due to both
infinite long current carrying wires is :-
\( ^{A} \cdot \frac{\mu_{0}}{2 \pi} \)
в. \( \frac{5 \mu_{0}}{6 \pi} \)
\( c \cdot \frac{5 \mu_{0}}{6 \pi} \mathrm{c} \)
' \( \frac{\mu_{0}}{2 \pi} \) с
Subject: Maths
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are
functions defined by \( f(x)=3 x- \)
\( \mathbf{1} ; \boldsymbol{g}(\boldsymbol{x})=\sqrt{\boldsymbol{x}+\boldsymbol{6}}, \) then the value of \( (\boldsymbol{g} \circ \)
\( \left.\boldsymbol{f}^{-1}\right)(\mathbf{2 0 0 9}) \) is
A . 26
B . 29
c. 16
D. 15
Subject: Physics
Two persons each of mass m are
standing at the two extremes of a
railroad ear of mass \( M \) resting on a smooth track. The person on left jumps to the left with a horizontal speed \( u \) with
respect to the state of the car before the jump. Thereafter, the other person jumps to the right, again with the same horizontal speed \( u \) with respect to the
state of the car before his jump. Find the velocity of the car after both the
persons have jumped off
Subject: Maths
\( \operatorname{If}\left(1+3 x+3 x^{2}\right)^{20}=a_{0}+a_{1} x+ \)
\( \boldsymbol{a}_{2} \boldsymbol{x}^{2}+\boldsymbol{a}_{3} \boldsymbol{x}^{3}+\boldsymbol{a}_{4} \boldsymbol{x}^{4}+\boldsymbol{a}_{5} \boldsymbol{x}^{5}+\ldots \ldots+ \)
\( a_{40} x^{40}, \) then find the value of \( 2 a_{2}- \)
\( 6 a_{3}+12 a_{4}-20 a_{5} \dots \dots+1560 a_{40} \)
A . 3450
B. 3350
\( c .3540 \)
D. 2150
Subject: Maths
In the given figure, if \( E \) and \( F \) are the
midpoints of \( A B \) and \( C D \) of
parallelogram \( A B C D, \) which one is
true?
A \( . C E \) trisects \( B D \)
B. \( A F \) trisects \( B D \)
c. \( \Delta A D F \cong \Delta C B E \)
D. All of these
Subject: Biology
How are the modes of reproduction
different in unicellular and
multicellular organisms?
A. Unicellular organisms reproduce mainly by asexual method, multicellular organisms reproduce by sexual and asexual methods.
B. Unicellular organisms reproduce mainly by sexual method, multicellular organisms reproduce mainly by asexual methods
C. Unicellular organisms reproduce mainly by propagation, multicellular organisms reproduce mainly by asexual methods.
D. None of these
Subject: Maths
5 pencils and 7 pens together cost Rs.
\( 50, \) whereas 7 pencils and 5 pens
together cost Rs. \( 46 . \) Find the cost of one
pencil and that of one pen by graphical
method.
A. cost of one pencil \( =\mathrm{Rs} .2 \) and that of one pen \( =\mathrm{Rs} .4 \)
B. cost of one pencil \( =\mathrm{Rs} .3 \) and that of one pen \( =\mathrm{Rs} . \)
C. \( \operatorname{cost} \) of one pencil \( =\operatorname{Rs} .5 \) and that of one pen \( =\operatorname{Rs} .6 \)
D. cost of one pencil \( = \) Rs. 2 and that of one pen \( = \) Rs. 6
Subject: Physics
The time taken by the current to rise to 0.63 of its maximum value in a d.C
circuit containing inductance \( (\boldsymbol{L}) \) and
resistance \( (\boldsymbol{R}) \) depends on
A. \( L \) only
B. \( R \) only
c. \( \frac{L}{R} \) only
D. \( L R \) only
Subject: Biology
Which of the following true for an
offspring formed as a result of sexual
reproduction?
A. The offspring gets a full set of genes from the mother and from the father.
B. The offspring gets half the genes from the mother and half the genes from the father.
C. The offspring gets all of its genes from the father.
D. The offspring gets a random mixture of genes from the mother and father
E. The offspring gets all of its genes from the mother.
Subject: Maths
Let \( A, B, C, D \) be (not necessarily
square) real matrices such that \( \boldsymbol{A}^{\boldsymbol{T}}= \)
\( \boldsymbol{B C D} ; \boldsymbol{B}^{\boldsymbol{T}}=\boldsymbol{C D A} ; \boldsymbol{C}^{\boldsymbol{T}}=\boldsymbol{D A B} \) and
\( D^{T}=A B C \) for the matrix \( S=A B C D \)
then which of the following is/are true This question has multiple correct options
A \( \cdot S^{3}=S \)
B. \( S^{2}=S^{4} \)
c. \( S=S^{2} \)
D. none of these
Subject: Maths
The value of \( \left(^{7} C_{0}+^{7} C_{1}\right)+ \)
\( \left(^{7} C_{1}+^{7} C_{2}\right)+\ldots+\left(^{7} C_{6}+^{7} C_{7}\right) \) is
\( \mathbf{A} \cdot 2^{8}-2 \)
B . \( 2^{8}-1 \)
\( \mathbf{c} \cdot 2^{8}+1 \)
D. \( 2^{8} \)
Subject: Chemistry
Balance the following redox reaction \( \left(\boldsymbol{C r}_{2} \boldsymbol{O}_{7}\right)_{(a q)}^{2-}+\boldsymbol{F} \boldsymbol{e}_{(a q)}^{2+} \rightarrow \boldsymbol{C r}_{(a q)}^{3+}+\boldsymbol{F} \boldsymbol{e}_{(a q)}^{3+} \)
(acidic medium)
Subject: Maths
Find the value of \( x \) such that
\( \frac{(x+\alpha)^{2}-(x+\beta)^{2}}{\alpha+\beta}=\frac{\sin 2 \theta}{\sin ^{2} \theta} . \) when \( \alpha \)
and \( \beta \) are the roots of \( t^{2}-2 t+2=0 \)
A. \( x=i \)cot \( \theta-1 \)
B. \( x=-(i \text { cot } \theta+1) \)
\( \mathbf{c} \cdot x=i \cot \theta \)
D. \( x= \) itan \( \theta-1 \)
Subject: Chemistry
Equal weight of \( \boldsymbol{X} \) (At. wt. \( =36 \) ) and \( \boldsymbol{Y} \) (At. wt. \( =24) \) are reacted to form the
compound \( \boldsymbol{X}_{2} \boldsymbol{Y}_{3} . \) Then:
A. \( X \) is the limiting reagent
B. \( Y \) is the limiting reagent
c. no reactant is left over and mass of \( X_{2} Y_{3} \) formed is double the mass of \( X \) taken
D. none of these
Subject: Maths
If \( \boldsymbol{\alpha}=\mathbf{3} \sin ^{-1} \frac{\mathbf{6}}{\mathbf{1 1}} \) and \( \boldsymbol{\beta}=\mathbf{3} \cos ^{-1} \frac{\mathbf{4}}{\mathbf{9}} \)
where the inverse trigonometric functions take only the principal values then the correct option(s) is(are) This question has multiple correct options
\( \mathbf{A} \cdot \cos \beta>0 \)
B. \( \sin \beta<0 \)
\( \mathbf{c} \cdot \cos (\alpha+\beta)>0 \)
D. \( \cos \alpha<0 \)
Subject: Maths
The area of a side of a box is 120 sq. \( \mathrm{cm} \) The area of the other side of the box is
72 sq. \( \mathrm{cm} . \) If the area of the upper surface of the box is 60 sq. \( \mathrm{cm} \), then find the volume of the box.
\( \mathbf{A} \cdot 259200 \mathrm{cm}^{3} \)
B. \( 84000 \mathrm{cm}^{3} \)
c. \( 86400 c m^{3} \)
D. \( 720 \mathrm{cm}^{3} \)
Subject: Chemistry
In an experiment, 18.0 g of mannitol was dissolved in 100 g of water. The vapour pressure of solution at \( 20^{\circ} \mathrm{C} \) was 17.226
mm of mercury. Calculate the molecular mass of mannitol. The vapour pressure
of water at \( 20^{\circ} \mathrm{C} \) is \( 17.535 \mathrm{mm} \) of
mercury.
A. Molecular mass of mannitol = 171.02
B. Molecular mass of mannitol = 181.02
c. Molecular mass of mannitol = 161.02
D. Molecular mass of mannitol = 121.02
Subject: Physics
In the figure, identical capacitors are
connected in the given three
configurations.The ratio of the total capacitancies in (i), (ii) and (iii)
respectively, is :
\( \mathbf{A} \cdot 3: 5: 5 \)
B. 3: 3: 5
\( \mathbf{c} \cdot 5: 4: 4 \)
\( \mathbf{D} \cdot 5: 5: 3 \)
Subject: Physics
A condenser and a \( 30 \Omega \) resistance are
connected in series. When they are
connected to 120 V A.C. source then the
current flowing in the circuit is 1A The
p.d. across the ends of the condenser
will be nearly
\( A \cdot 1 v \)
B. 116 \( v \)
c. zero
D. 220
Subject: Biology
A student is given two samples of nucleotides. One sample contains DNA nucleotides and the other sample contains RNA nucleotides, but the two samples have not been labeled.
What information would assist the
student in identifying which sample contained the DNA nucleotides versus
the RNA nucleotides?
A. The sugar in DNA nucleotides contains six carbon atoms and the sugar in an RNA molecule contains five carbon atoms.
B. The sugar in DNA nucleotides is an aldehyde sugar anc the sugar in RNA nucleotides is a ketone sugar
c. The sugar in DNA nucleotides contains one less oxyger atom than the sugar in RNA nucleotides
D. The sugar in DNA nucleotides is in the alpha configuration and the sugar in RNA nucleotides is in the beta configuration
Subject: Maths
If \( \boldsymbol{P}=\left[\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{b} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{c}\end{array}\right] \) then, \( \operatorname{det}\left(\boldsymbol{P}^{-1}\right) \)
A \( . a b c \)
B. \( a^{2} b^{2} c^{2} \)
c. \( \frac{1}{a b} \)
D. \( \frac{1}{a^{2} b^{2} c^{2}} \)
Subject: Chemistry
\( 4.4 C O_{2} \) gas and 2.24 litre of \( H_{2} \) gas at
S.T.P are taken in a 1 litre container at
27. The total pressure of gases in container will be ?
\( A \cdot 4.926 \) atm
B. 3743.76 mm of Hg
c. \( 1871.88 \mathrm{mm} \) of \( \mathrm{Hg} \)
D. 2.463 atm
Subject: Maths
The first of two samples has 100 items with mean 15 and \( S . D .3 . \) If the whole
group has 250 items with mean 15.6 and \( s . d=\sqrt{13.44}, \) find the standard
deviation of the second group.
A . 5
B. 4
\( c \cdot 6 \)
D. 3.52
Subject: Physics
A uniform cylinder rests on a cart as shown. The coefficient a static friction
between the cylinder and the cart is 0.5 fthe cylinder is \( 4 \mathrm{cm} \) in diameter and
\( 10 \mathrm{cm} \) in height, then what is the minimum acceleration \( \left(\text { in } m s^{-2}\right) \) of the cart needed to cause the cylinder to tip
over?
Subject: Chemistry
Dissolving \( 120 g \) of urea in \( 1000 g \) of water gave a solution of density \( \mathbf{1 . 1 5} g / \boldsymbol{m} \boldsymbol{L} . \) The molarity of the solution is:
A \( .1 .79 M \)
в. \( 2 M \)
\( c .2 .05 M \)
D. 2.22 \( M \)
Subject: Physics
A charged particle initially at rest is kept
in an electric field (choose the most
appropriate option)
A. will always move perpendicular to the line of force.
B. will always move along the line of force in the direction of the field.
C. will always move along the line of force opposite to the direction of the field.
D. will always move along the line of force in the direction of the field or opposite to the direction of the field depending on the nature of the charge.
Subject: Chemistry
Select the incorrect statement(s):
This question has multiple correct options
A. Magnesium can be burnt in the atmosphere of \( C O_{2} \)
and \( S O_{2} \)
B. Magnesium reacts with alkyl halides to form Grignard's reagent
C. Out of \( M g \) and \( C a \), only \( M g \) reacts with \( N_{2} \) to form magnesium nitride
D. Calcium is less reactive than magnesium
Subject: Maths
If the three points with position vectors \( \bar{a}-2 \bar{b}+3 \bar{c}, 2 \bar{a}+\lambda \bar{b}-4 \bar{c},-7 \bar{b}+10 \bar{c} \)
are collinear, then \( \lambda= \)
\( A \)
B. 2
\( c .3 \)
D. none of these
Subject: Chemistry
The molar conductivities of \( \wedge_{N a O A c}^{\circ} \) and \( \wedge_{H C l}^{\circ} \) at infinite dilution in water at
\( 25^{\circ} \mathrm{C} \) are 91 and \( 426.2 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
respectively. To calculate, \( \wedge_{H O A c}^{\circ}, \) the additional value required
is
\( \mathbf{A} \cdot \wedge_{H_{2} O}^{\circ} \)
в. \( \wedge_{K C l}^{\circ} \)
c. \( \wedge_{N a O H}^{\circ} \)
\( \mathbf{D} \cdot \wedge_{N a C l}^{\circ} \)
Subject: Physics
A square loop of side a lying a perpendicular magnetic field to its plane is changed to a circle. If change occusrs in \( t \) seconds in magnetic field \( B \) tesla, the induced emf is
A \( \cdot \frac{4}{\pi} \frac{B a^{2}}{t} \)
B. \( \frac{B a^{2}}{t} \)
c. \( \frac{B a^{2}}{t}\left[\frac{4}{\pi}-1\right] \)
D. zero
Subject: Maths
Write the marks wise frequencies in the following frequency distribution table.
Marks \( \begin{array}{cccc}\text { Up } & \text { Up } & \text { Up } & \text { Up } \\ \text { to } & \text { to } & \text { to } & \text { to } \\ \mathbf{5} & \mathbf{6} & \mathbf{7} \$ & \mathbf{8}\end{array} \)
No of
11
student
Subject: Physics
A charge \( q \) is placed at the centre of the line joining two equal charges \( Q \). The system of three charges will be in equilibrium if \( q \) is equal to:
A \( \cdot-\frac{Q}{2} \)
в. \( -\frac{Q}{4} \)
\( c \cdot+\frac{Q}{4} \)
D. \( +\frac{Q}{2} \)
Subject: Physics
Assertion
A transistor amplifier in common emitter configuration has a low input impedance.
Reason
The base to emitter region is forward
biased.
A. Assertion is true, Reason is true; Reason is a correct explanation for Assertion
B. Assertion is true, Reason is true; Reason is not a correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true
Subject: Physics
The half life of a radioactive isotope is 3 hours.What is the value of its
disintegration constant?
A. 0.3 hour \( ^{-1} \)
B. 0.693 hour \( ^{-1} \)
c. 0.231 hour \( ^{-1} \)
D. \( 0.231 \min ^{-1} \)
Subject: Chemistry
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -242 k J m o l^{-1} \)
Bond energy of \( H_{2} \) and \( O_{2} \) are 436 and
\( \mathbf{5 0 0} k J \mathrm{mol}^{-1} \) respectively. The bond
energy of \( 0-H \) bond is :
A \( \cdot 434 k J \mathrm{mol}^{-1} \)
B. \( 464 k J \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 452 k J \mathrm{mol}^{-1} \)
D. \( 485 k J \) mol \( ^{-1} \)
Subject: Chemistry
\( \mathbf{3} C l_{2}+\boldsymbol{x} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \longrightarrow \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l}+ \)
\( \boldsymbol{N a C l O _ { 3 }}+\boldsymbol{H}_{2} \boldsymbol{O}, \) then \( \mathbf{x} \) is
Subject: Maths
If \( \sqrt{\frac{\boldsymbol{v}}{\boldsymbol{\mu}}}+\sqrt{\frac{\boldsymbol{\mu}}{\boldsymbol{v}}}=\boldsymbol{6}, \) then \( \frac{\boldsymbol{d} \boldsymbol{v}}{\boldsymbol{d} \boldsymbol{\mu}}= \)
A. \( \frac{17 \mu-v}{\mu-17 v} \)
в. \( \frac{\mu-17 v}{17 \mu-v} \)
c. \( \frac{17 \mu+v}{\mu-17 v} \)
D. \( \frac{\mu+17 v}{17 \mu-v} \)
Subject: Physics
The optical path of a monochromatic light is same if it goes through \( 4.0 \mathrm{cm} \) of glass of \( 4.5 \mathrm{cm} \) of water. If the
refractive index of glass is 1.53 , the refractive index of the water is:
A . 1.30
B. 1.36
c. 1.42
D. 1.46
Subject: Chemistry
The enthalpy of combustion of methane,
graphite and dihydrogen at \( 298 K \) are \( -890.3 k J m o l^{-1},-393.5 \)
\( k J m o l^{-1},-285.8 k J m o l^{-1} \)
respectively. Enthalpy of formation of \( \boldsymbol{C H}_{4(g)} \) will be:
A \( .-74.8 k J m o l^{-1} \)
В. \( -52.27 k J \) mol \( ^{-1} \)
c. \( +74.8 k J m o l^{-1} \)
D. \( +52.26 k J m o l^{-1} \)
Subject: Maths
The domain of the function \( f(x)= \) \( \left\{\begin{array}{l}\left(x^{2}-9\right) /(x-3), \text { if } x \neq 3 \\ 6, \quad \text { if } x=3\end{array}\right. \)
A \( .(0,3) \)
в. \( (-\infty, 3) \)
\( \mathbf{C} \cdot(-\infty, \infty) \)
D \cdot \( (3, \infty) \)
E \( .(-3,3) \)
Subject: Maths
Find whether the lines representing the following pair of linear equation
intersect at a point, are parallel or coincident \( \cdot \frac{3 x}{2}-\frac{5 y}{3}=-2 ; \frac{x}{3}+\frac{y}{2}= \)
\( \mathbf{1 3} \)
\( \mathbf{6} \)