AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
When magnesium burns in steam, the formulae of the products are:
A \( \cdot M g(O H)_{2}, H_{2} \)
\( \mathbf{B} \cdot \mathrm{MgO}, H_{2} \)
с. \( M g O_{2}, H_{2} \)
D. \( M g(O H)_{2}, O_{2} \)
Subject: Physics
Find \( V_{b a} \) if \( 12 J \) of work has to be done
against an electric field to take a
charge of \( 10^{-2} C \) from \( a \) to \( b \)
A . \( 1000 V \)
B. 1200V
c. \( 1100 V \)
D. 2400V
Subject: Maths
Equation of the plane passing through the point of intersection of \( x+2 y+=0 \) and \( 2 x+y=0 \) and which is perpendicular to
\( 5 x+6 z=0 \)
This question has multiple correct options
A. \( x=0 \)
B. \( y=0 \)
\( c \cdot z=0 \)
D. x+y=0
E. \( x+z=0 \)
Subject: Physics
Two copper rods \( P \) and \( Q \) of thickness in
the ratio 2: 5 are taken. If both the rods
\( P \) and \( Q \) of length \( 10 \mathrm{cm} \) are heated to same temperature rise, then the ratio of the linear expansions of \( P \) to that of rod
Q is :
A .2: 5
B. 5: 2
c. 1: 1
D. 4: 1
Subject: Chemistry
Among the following, the correct
statement is:
\( \mathbf{A} \cdot \) Between \( N H_{3} \) and \( P H_{3}, N H_{3} \) is better electron donor
because the lone pair of electrons occupies spherical s orbital and is less directional
B. Between \( N H_{3} \) and \( P H_{3}, P H_{3} \) is better electron donor
because the lone pair of electrons occupies \( s p^{3} \) orbital and is more directional
C. Between \( N H_{3} \) and \( P H_{3}, N H_{3} \) is a better electron donor
because the lone pair of electrons occupies \( s p^{3} \) orbital and is more directional
D. Between \( N H_{3} \) and \( P H_{3}, P H_{3} \) is better electron donor because the lone pair of electrons occupies spherical s orbital and is less directional
Subject: Physics
A body cools from \( 50^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \) in 5
minutes. The surrounding temperature
is \( 20^{\circ} \mathrm{C} . \) By how many \( ^{\circ} \mathrm{C} \) does the temperature decrease in the next 5 minutes? Round your answer to the nearest integer.
Subject: Maths
The value of
\( \lim _{|x| \rightarrow \infty} \cos \left(\tan ^{-1}\left(\sin \left(\tan ^{-1} x\right)\right)\right) \) is equal
to
A . -1
B. \( \sqrt{2} \)
\( c \cdot-\frac{1}{\sqrt{2}} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Maths
If \( \boldsymbol{A}= \)
\( \frac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1}(\pi x) & \tan ^{-1}\left(\frac{\pi}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x)\end{array}\right], B= \)
\( \frac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x)\end{array}\right], \) then
\( A-B \) is equal to
\( A \)
B.
\( c .2 \)
\( D \cdot \underline{1} \)
Subject: Chemistry
The reaction taking place is:
\( \mathbf{A} \cdot H g_{2} C l_{2}(s)+2 A g(s) \rightarrow 2 A g C l(s)+2 H g(l) \)
B \( \cdot 2 H g_{2} C l_{2}(s)+2 A g(s) \rightarrow 4 A g C l(s)+2 H g(l) \)
\( \mathbf{c} \cdot H g_{2} C l_{2}(s)+3 A g(s) \rightarrow A g C l(s)+2 H g(l) \)
D. None of these
Subject: Physics
Which of the following statements can
help you to determine the direction of
induced current in Electromagnetic
Induction?
A. Induced current flows such that it increase the total
value of current
B. Induced current flows such that it reduces the total value of current
C. Induced current flows such that direction of magnetic field produced from induced current opposes change in external magnetic field
D. Induced current flows such that direction of magnetic field produced from induced current opposes external magnetic field
Subject: Physics
If to a stationary observer the apparent frequency appear to be \( 6 / 5 \) times the actual frequency of the moving source then the speed and direction of the sound source is : (velocity of sound = \( 360 \mathrm{m} / \mathrm{sec}) \)
A. \( 60 \mathrm{m} / \mathrm{s} \) towards the observer
B. 60 m/s away from the observer
c. \( 55 \mathrm{m} / \mathrm{s} \) towards the observer
D. 55 m/s away from the observer
Subject: Chemistry
\( \boldsymbol{C} \boldsymbol{a}_{\boldsymbol{4}}\left(\boldsymbol{P} \boldsymbol{O}_{\boldsymbol{4}}\right)_{2} \boldsymbol{O} \) is:
This question has multiple correct options
A. thomas slag
B. formed in manufacturing of steel iron
C. used in manufacture of phosphorus fertilizer
D. used as a refractory material
Subject: Chemistry
A compound contains \( 38.8 \% C, 16 \% H \)
and \( 45.2 \% N . \) The formula of the
compound would be:
A. \( C H_{3} N H_{2} \)
в. \( C_{2} H_{5} C N \)
c. \( C H_{3} C N \)
D. \( C H_{2}\left(N H_{2}\right)_{2} \)
Subject: Physics
An object \( A \) is dropped from rest from the top of a \( 30 \mathrm{m} \) high building and at the same moment another object B is projected vertically upwards with an initial speed of \( 15 \mathrm{m} / \mathrm{s} \) from the base of
the building. Mass of the object A is 2 kg while mass of the object B is 4 kg. The maximum height above the ground level attained by the center of mass of
the \( A \) and \( B \) system is \( (\text {take } g= \)
\( \left.10 m / s^{2}\right) \)
\( \mathbf{A} \cdot 15 \mathrm{m} \)
B. 25 m
c. 30 \( m \)
D. 35 m
Subject: Maths
If radii of two concentric circles are 4
\( \mathrm{cm} \) and \( 5 \mathrm{cm}, \) then the length of each chord of one circle which is tangent to the circle is
A. \( 3 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c .9 \mathrm{cm} \)
D. \( 1 \mathrm{cm} \)
Subject: Chemistry
The energy required to melt 1 g ice is \( 33 J . \) The number of quanta of radiation
of frequency \( 4.67 \times 10^{13} \) sec \( ^{-1} \) that
must be absorbed to melt \( 10 \mathrm{g} \) ice is:
A \( \cdot 1.065 \times 10^{22} \)
B. \( 3.205 \times 10^{23} \)
c. \( 9.076 \times 10^{20} \)
D. none of the above
Subject: Physics
The correct relation between
interatomic force constant \( K, \) Young
modulus \( Y \) and interatomic distance \( r_{0} \)
is
A. \( K=Y r_{0} \)
в. \( K=\frac{r_{0}}{Y} \)
\( c \cdot K=\frac{Y}{r_{0}} \)
D. \( K=r_{0}^{2} Y^{2} \)
Subject: Maths
The lines \( \frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k} \) and
\( \frac{\boldsymbol{x}-\mathbf{1}}{\boldsymbol{k}}=\frac{\boldsymbol{y}-\boldsymbol{4}}{\mathbf{2}}=\frac{\boldsymbol{z}-\mathbf{5}}{\mathbf{1}} \) are coplanar if
A. \( k=1 \) or -1
B. \( k=0 \) or -3
c. \( k=3 \) or -3
D. \( k=0 \) or -1
Subject: Physics
Current in a coil is increased at a
constant rate. The current in the second
coil is also increased at the same rate.
At a certain instant of time, the power given to the two coils is the same. At that time the current, the induced
voltage and the energy stored in the
first coil are \( I_{1}, V_{1}, \) and \( W_{1} \) respectively. Corresponding values for
the second coil at the same instant are
\( I_{2}, V_{2} \) and \( W_{2} \) respectively. Then
A. \( \frac{W_{2}}{W_{1}}=8 \)
в. \( \frac{W_{2}}{W_{1}}=\frac{1}{8} \)
c. \( \frac{W_{2}}{W_{1}}=4 \)
D. \( \frac{W_{2}}{W_{1}}=\frac{1}{4} \)
Subject: Chemistry
In the reaction, \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{I})= \)
\( N H_{4}^{+}+O H^{-} \) the water is a
A. bronsted acid
B. bronsted base
c. conjugate acid
D. conjugate base
Subject: Chemistry
The rusting of iron takes place as follows:
\( \mathbf{2} \boldsymbol{H}^{\oplus}+\mathbf{2} e^{-}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2} \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) ; \boldsymbol{E}^{\ominus}=+\mathbf{1} \cdot \boldsymbol{2} \boldsymbol{3} \boldsymbol{V} \)
\( \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}(s) ; \boldsymbol{E}^{\ominus}= \)
\( -0.44 V \)
Calculate \( \Delta G^{\ominus} \) for the net process.
B. \( -152 k J \) mol\( ^{-1} \)
c. \( -76 k J \) mol \( ^{-1} \)
D. - \( 161 k J \) mol \( ^{-1} \)
Subject: Maths
If the angle of elevation of a cloud from a point h meters above a lake is \( \alpha \) and
the angle of depression of its reflection in the lake is \( \beta \) then height of the cloud is \( h\left(\frac{1+r}{1-r}\right) \) where \( r=\frac{\text { tan } \alpha}{\tan \beta} \)
A. True
B. False
Subject: Chemistry
Which of the following is the electron
configuration of a transition metal?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{5} \)
D \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{2} \)
Subject: Maths
The distance (in metre) travelled by a
vehicle in time \( t \) (in seconds) is given by the equation \( s=t^{3}+2 t^{2}+t+1 . \) The
difference in the acceleration between
\( \boldsymbol{t}=\boldsymbol{2} \) and \( \boldsymbol{t}=\boldsymbol{4} \) is
A \( \cdot 12 m / s^{2} \)
B . \( 18 m / s^{2} \)
c. \( 16 m / s^{2} \)
D. \( 14 m / s^{2} \)
Subject: Maths
\( \lim _{\mathbf{x} \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(\mathbf{x}-\mathbf{2})\}}}{\mathbf{x}-\mathbf{2}}\right) \)
A. does not exist
B. equals \( \sqrt{2} \)
c. equals \( -\sqrt{2} \)
D. equals \( \frac{1}{\sqrt{2}} \)
Subject: Physics
Assertion
When current is represented by a straight line, the magnetic field will be circular.
Reason
According to Fleming's left hand rule, direction of force is parallel to the magnetic field
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
Select the IUPAC name for the following
complex.
A. Tetraamminecobalt (III)- \( \mu \) dihydroxidobis(ethylenediamine) cobalt (III) chloride
B. \( \mu \) -Dihydroxidotetraamminebis(ethylenediamine) dicobalt(III) chloride
c. Tetraammine cobaltate (III)- \( \mu \) -dihydroxidobis(ethane-
1, 2-diamine) cobalt
(III) chloride
D. Tetraamminecobalt (III)- \( \mu \) dihydroxidobis(ethylenediamine) cobalt(II) tetrachloride
Subject: Chemistry
Assertion
\( \operatorname{gmof} S O_{2} \) and \( 1 \mathrm{gm} \) of \( C O_{2} \) contains the same number of molecules under
similar conditions.
Reason
\( 64 \mathrm{gm} \) of \( S O_{2} \) and \( 44 \mathrm{gm} \) of \( C O_{2} \) contains the same number of atoms
under similar conditions.
Choose the correct option.
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
A smooth sphere (mass \( 10 \mathrm{kg} \)
negligible radius) moves on a smooth
curved surface from the point with a
speed of \( 10 \mathrm{m} / \mathrm{s} \) as shown in figure. The
sphere reaches the point D passing
through point B. If the ground is taken
as reference, Then \( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
This question has multiple correct options
A. The total mechanical energy of the sphere at point A is zero
B. The total mechanical energy of the sphere at the point A is 2500 J
C. The kinetic energy at point B is 2500 J
D. The notential energy at point B is 0 J
Subject: Chemistry
One element has atomic weight \( 39 . \) Its electronic configuration is
\( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2}, 3 p^{6} 4 s^{1} . \) The true
statement for that element is:
A. more I.E
B. transition element
C. isotone with \( _{18} A r^{36} \)
D. stable oxide \( M_{2} O \)
Subject: Maths
If \( \vec{a}=x \hat{i}-y \hat{j} \) and \( \vec{b}=y \hat{i}+x \hat{j}, \mid \vec{a} \times \)
\( \vec{b} \mid=5 \) then locus of \( (x, y) \) is
A. Hyperbola
B. Parabola
c. Ellipse
D. Circle
Subject: Chemistry
One gram sample of \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{O}_{3} \) is
decomposed in a bomb calorimeter, the temperature of the calorimeter
increases by \( 6.12 K . \) The heat capacity of the system is \( 1.23 \mathrm{kJ} / \mathrm{g} / \) deg. What is the molar heat of decomposition for
\( N H_{4} N O_{3} ? \)
B. \( +398.1 k J / \) mol
c. \( -16.1 k J / \) mol
D. \( +602 k J / m o l \)
Subject: Physics
The fraction of atoms of radioactive
element that decays in 6 days is \( 7 / 8 \) The fraction that decays in 10 days will
be :
A. \( 77 / 80 \)
B. \( 71 / 80 \)
c. \( 31 / 32 \)
D. \( 15 / 16 \)
Subject: Maths
The D. \( E \) of the family of parabolas having their focus at the origin and axis along the \( x \) -axis is
A \( \cdot y_{1}\left[y y_{1}-2 x\right]=y \)
B . \( y_{1}\left(y_{1}\right)^{2}=2 x y_{1}+y \)
\( \mathbf{c} \cdot y y_{1}^{2}+2 x y_{1}=y \)
D. \( y y_{1}+2 x=y \)
Subject: Biology
Given below are the steps of protein synthesis. Arrange them in. correct sequence and select the correct option.
(j) Codon-anticodon reaction between mRNA and aminoacyl tRNA complex.
(ii) Attachment of mRNA and smaller
sub-unit of ribosome.
(iii) Charging or aminoacylation of tRNA.
(iv) Attachment of larger sub unit of ribosome to the mRNA-tRNAMet
complex.
(v) Linking of adjacent amino acids.
(vi) Formation of polypeptide chain.
A \( \cdot(\text { ii }) \rightarrow(i) \rightarrow(\text { iii }) \rightarrow(v) \rightarrow(\text { iv }) \rightarrow(v \) i)
B. (v) \( \rightarrow \) (ii) \( \rightarrow(\text { i) } \rightarrow \text { (iii) } \rightarrow \text { (iv) } \rightarrow \) (vi)
\( c \cdot(\text { iii) } \rightarrow(\text { ii) } \rightarrow(\text { iv }) \rightarrow(i) \rightarrow(v) \rightarrow(v i) \)
D. (iii) \( \rightarrow(\text { ii }) \rightarrow(i) \rightarrow(\text { iv } v \rightarrow(v) \rightarrow(v i) \)
Subject: Chemistry
At \( 25^{\circ} \mathrm{C}, \) the solubility product of
\( M g(O H)_{2} \) is \( 1.0 \times 10^{-11} . \) At which \( p H \)
will \( \mathrm{Mg}^{2+} \) ions start precipitating in
the form of \( \mathrm{Mg}(\mathrm{OH})_{2} \) from a solution of
\( 0.001 \mathrm{M} \mathrm{Mg}^{2+} \) ions?
\( A \cdot 9 \)
B. 10
\( c \cdot 11 \)
D. 8
Subject: Physics
As shown in fig. if a charge \( +q \) is
carried from a point \( \boldsymbol{A}\left(\boldsymbol{r}, \mathbf{1} \mathbf{3 5}^{\circ}\right) \) to point
\( B\left(r, 45^{\circ}\right) . \) If dipole moment is \( p \) then the
work done by the external agent is then
going to be
A . 0
В. \( \frac{q p}{4 \pi \epsilon_{0} r^{2}} \)
\( c \cdot \frac{1}{4 \pi \epsilon_{0}} \frac{\sqrt{2} q p}{r^{2}} \)
D. \( \frac{1}{4 \pi \epsilon} \frac{q p}{r^{2}} \)
Subject: Physics
In a p-njunction the depletion region is \( 400 n m \) wide and electric field of \( 5 \times \)
\( 10^{5} V m^{-1} \) exists in it. The minimum
energy of a conduction electron, which can diffuse from n-side to the p-side is:
A . \( 4 e V \)
в. \( 5 e V \)
c. \( 0.4 e V \)
D. \( 0.2 e V \)
Subject: Physics
The surface tension of soap solution is \( 0.03 N / m . \) The work done in blowing to form a soap bubble of surface area
\( 40 c m^{2}, \) in Joules, is:
A \( \cdot 1.2 \times 10^{-4} \)
B. \( 2.4 \times 10^{-4} \)
c. \( 12 \times 10^{-4} \)
D. \( 24 \times 10^{-4} \)
Subject: Physics
A force vector is acting on a unit length
of a thin wire, carrying a current \( \boldsymbol{I}= \)
\( 80 A, \) at a point \( O . \) Find the magnitude
and direction of the force vector, if the
wire is bent as shown in figure above, the distance between the long parallel
segments of the wire being equal to \( l= \)
\( \mathbf{2 0} \boldsymbol{c m} \)
A. \( 1.3 N \)
B. \( 0.26 N \)
c. \( 2.6 N \)
D. \( 0.013 N \)
Subject: Chemistry
Consider the following gas phase
reaction:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{B r}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}(\boldsymbol{g}) \)
The concentrations of \( \boldsymbol{H}_{2}, \boldsymbol{B} \boldsymbol{r}_{2}, \) and
HBr are \( 0.05 M, 0.03 M, \) and \( 500.0 M \)
respectively. The concentration equilibrium constant for this reaction
\( \operatorname{at} 400^{\circ} \mathrm{C} \) is \( 2.5 \times 10^{3} . \) Is this system at
equilibrium?
A. Yes, the system is at equilibrium.
B. No, the reaction must shift to the right in order to reach equilibrium.
c. No, the reaction must shift to the left in order to reach equilibrium.
D. It cannot be determined
Subject: Physics
An unknown resistance \( R_{1} \) is connected
in series with a resistance of 10 ohm.
This combination is connected to one
gap of a metre bridge, while other gap is
connected to another resistance \( \boldsymbol{R}_{2} \)
The balance point is at \( 50 \mathrm{cm} . \) Now, when the 10 ohm resistance is removed, the balance point shifts to \( 40 \mathrm{cm} . \) Then,
the value of \( \boldsymbol{R}_{1} \) is
A. \( 60 \Omega \)
B. 40\Omega
c. \( 20 \Omega \)
D. \( 10 \Omega \)
Subject: Chemistry
For the following statements. write T for True and F for False
(a) J.J. Thomson proposed that the nucleus of an atom contains only
nucleons.
(b) A neutron is formed by an electron and a proton combining together. Therefore, it is neutral.
(c) The mass of an electron is about
\( \mathbf{1} \)
\( \mathbf{2 0 0 0} \)
times that of proton.
Subject: Physics
The work done to transport \( 20 C \) charge
from points \( A \) to another point \( B \) over distance of \( 0.2 m \) is 2 joule The
potential difference across \( A B \) is
A \( \cdot 2 \times 10^{-2} V \)
В. \( 4 \times 10^{-1} \mathrm{V} \)
c. \( 1 \times 10^{-1} \mathrm{V} \)
D. 10V
Subject: Physics
A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of
10cm. The separation between the two
lenses is \( 2 \mathrm{cm} \). The focal lengths of the
component lenses
A. \( 18 \mathrm{cm}, 20 \mathrm{cm} \)
в. \( 10 \mathrm{cm}, 12 \mathrm{cm} \)
c. \( 12 \mathrm{cm}, 14 \mathrm{cm} \)
D. \( 16 \mathrm{cm}, 18 \mathrm{cm} \)
Subject: Chemistry
How many coordination isomer are
possible for the following compound? (excluding the given structure of molecule)
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+}\left[\boldsymbol{C r}\left(\boldsymbol{N O}_{2}\right)_{6}\right]^{3+} \)
Subject: Physics
The torque required to hold a small
circular coil of 10 turns, are \( 1 m m^{2} \) and
carrying a current of \( \left[\frac{21}{44}\right] \) A in the middle
of a long solenoid of \( 10^{3} \) turns/m
carrying a current of \( 2.5 \mathrm{A} \), with its axis perpendicular to the axis of the solenoid
is:
A \( .1 .5 \times 10^{-6} N m \)
в. \( 1.5 \times 10^{-8} N m \)
c. \( 1.5 \times 10^{6} \mathrm{Nm} \)
D. \( 1.5 \times 10^{8} \mathrm{Nm} \)
Subject: Maths
If \( f(x)=x^{2} e^{-x^{2} / a^{2}} \) is an increasing
function then (for \( a>0 \) ), x lies in the
interval
\( \mathbf{A} \cdot[a, 2 a] \)
в. \( (-\infty,-a) \cup(0, a) \)
c \( .(-a, 0) \)
D. None of these
Subject: Chemistry
\( \boldsymbol{H}_{2}+\boldsymbol{I}_{2}=2 \boldsymbol{H} \boldsymbol{I} . \) What will be the
instantaneous rate of the reaction in
terms of product?
A \( \cdot \frac{1}{2} \frac{d[H I]}{d t} \)
B. \( -\frac{1}{2} \frac{d[H I]}{d t} \)
c. \( \frac{d[H I]}{d t} \)
D. \( -\frac{d[H I]}{d t} \)
Subject: Maths
toppr
Q Type your question
Minimum value of \( y= \)
\( A \)
\( 4 \sec ^{2} x+\cos ^{2} x \) for
permissible real values of \( x \) is equal to
If \( m, n \) are positive
integers and \( m+n \sqrt{2}= \)
B. \( \quad \sqrt{41+24 \sqrt{2}} \), then \( (m+ \)
to
\( n) \) is equal
Number of solutions of then equation
\( \mathrm{C} \)
\( \log _{\left(\frac{3 x-x^{2}-14}{7}\right)}(\sin 3 x-\sin x) \) 3. \( =\log _{\left(\frac{9 x-x^{2}-14}{7}\right)} \cos 2 x \) is
equal to
Consider arithmetic sequence of positive the integers. If the sum of first ten terms is al to
D. equal 4. the \( 58^{n} \) term, then the e of the least possible value first term is equal to
5.
\( \mathbf{A} \cdot A-4, B-5, C-1, D-3 \)
\( \mathbf{B} \cdot A-4, B-5, C-3, D-1 \)
\( \mathbf{c} \cdot A-5, B-4, C-1, D-3 \)
D . \( A-1, B-5, C-4, D-3 \)
Subject: Maths
A rectangle DEFG is plotted in \( X Y \) plane. The co-ordinates of D , E , F and G \( \operatorname{are}(2,2),(9,2),(9,10) \) and (2,10)
Find the new co-ordinates of F when
DEFG is rotated \( 270^{\circ} \) around origin.
This question has multiple correct options
A \( \cdot(-10,9) \)
B. (-10,-9)
c. (10,9)
D. (10,-9)
Subject: Physics
A fuse wire with a radius of \( 0.1 m m \)
blows up at \( 5 A \). The radius of another
fuse wire made of the same material
which will blow up at \( 40 A \) is
\( \mathbf{A} \cdot 0.8 m m \)
B. \( 0.6 m m \)
\( \mathrm{c} .0 .45 \mathrm{mm} \)
D. \( 0.4 m m \)
Subject: Physics
A circular coil of cross-sectional area
\( 200 c m^{2} \) and 20 turns is rotated about
the vertical diameter with angular
speed of 50 rads\( ^{-1} \) in a uniform
magnetic field of magnetic \( 3.0 \times 10^{-2} \) T
Calculate the maximum value of the
current in the coil.
Subject: Physics
If \( \overrightarrow{\boldsymbol{u}}=\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}} ; \overrightarrow{\boldsymbol{v}}=\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}} \) and \( |\overrightarrow{\boldsymbol{a}}|=|\overrightarrow{\boldsymbol{b}}|= \)
2 then \( |\vec{u} \times \vec{v}| \) is equal to
\( \sqrt[A \cdot]{2\left(16-(\vec{a} \cdot \vec{b})^{2}\right)} \)
в. \( 2 \sqrt{\left(16-(\vec{a} . \vec{b})^{2}\right)} \)
\( ^{\mathrm{c}} \sqrt[2]{\left(4-(\vec{a} \cdot \vec{b})^{2}\right)} \)
D . \( \left[4-(\vec{a} . \vec{b})^{2}\right] \)
Subject: Maths
Prove that the Greatest integer function \( \boldsymbol{f}: \mathbb{R} \rightarrow \mathbb{R} \) given by \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}], \) is neither
one-one nor onto, where \( [x] \) denotes the
greatest integer less than or equal to \( x \)
Subject: Chemistry
The value of Bohr radius for hydrogen
atom is:
A \( .0 .529 \times 10^{-8} \mathrm{cm} \)
B . \( 0.529 \times 10^{-10} \mathrm{cm} \)
c. \( 0.529 \times 10^{-6} \mathrm{cm} \)
D. \( 0.529 \times 10^{-12} \mathrm{cm} \)
Subject: Maths
The image of the point with position vector \( \hat{i}+3 \hat{k} \) in the plane \( r \cdot(\hat{i}+\hat{j}+ \)
\( \hat{\boldsymbol{k}})=\mathbf{1} \) is
\( \mathbf{A} \cdot \hat{i}+2 \hat{j}+\hat{k} \)
B \( \cdot \hat{i}-2 \hat{j}+\hat{k} \)
c. \( -\hat{i}-2 \hat{j}+\hat{k} \)
D. \( \hat{i}+2 \hat{j}-\hat{k} \)
Subject: Chemistry
What is IUPAC name of the following
compound?
\( \mathbf{C H}_{3}-\mathbf{C H}_{2}-\mathbf{C H}_{2}-\mathbf{O H} \)
A. Propane-1-ol
B. Propane-2-ol
c. Ethane-1-ol
D. Ethane-2-ol
Subject: Chemistry
For the reaction \( A+B \rightleftharpoons 3 C \) at \( 25^{0} C \)
A 3 Lvessel contains \( 1,2, \) and 4 moles of
A, \( B, \) and \( C \) respectively. Predict the direction of reaction if:
a) \( K_{C} \) for the reaction is 10
b) \( K_{C} \) for the reaction is 15
c) \( K_{C} \) for the reaction is 10.66
A. a) Backward direction
b) Forward direction \( c \) ) At equilibrium
B. a) Forward direction b) Backward direction c) Forward direction
c. a) Backward direction b) Forward direction c) Back direction
D. a) Backward direction
b) Backrward direction c) At equilibrium
Subject: Physics
A rocket is moving in a gravity free space with a constant acceleration of
\( 2 m s^{-2} \) along \( +x \) direction (see figure). The length of a chamber inside the
rocket is \( 4 \mathrm{m} \). A ball is thrown from the
left end of the chamber in \( +x \) direction
with a speed of \( 0.3 m s^{-1} \) relative to the rocket. At the same time, another ball is thrown in \( -x \) direction with a speed of
\( 0.2 m s^{-1} \) from its right end relative to the rocket. The time in seconds when the two balls hit each other is
Subject: Physics
A ray of light is incident on a plane
mirror and the angle of reflection is \( 50^{\circ} \)
Calculate the angle between the incident and the reflected ray.
A \( .50^{\circ} \)
B . \( 25^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 100^{\circ} \)
Subject: Physics
The pressure on a swimmer \( 10 \mathrm{m} \) below the surface lake is:(Atmospheric
pressure \( =1.01 \times 10^{5} \) Pa,Density of
water \( \left.=1000 k g / m^{3}\right) \)
A . 10 atm
B. 5 atm
c. 15 atm
D. 2 atm