AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Biology
Join properly Column-I and Column-II.
Column I Column II
\( (A) \)
(1)
Lysin A) UUU \( 6^{G C} \)
(B)
(2)
Stop codon
\( (C) \)
(3) Phenyl Alanine AAA
(D)
(4)
UAA Glycine ne
\( A \cdot a-2, b-3, c-4, d-1 \)
B. \( a-4, b-3, c-1, d-2 \)
c. \( a-1, b-4, c-3, d-2 \)
D. \( a-3, b-4, c-1, d-2 \)
Subject: Physics
Derive the formula \( \frac{\boldsymbol{F}}{\boldsymbol{l}}=\frac{\boldsymbol{\mu}_{o}}{\mathbf{2} \boldsymbol{\pi}} \cdot \frac{\boldsymbol{i}_{1} \boldsymbol{i}_{2}}{\boldsymbol{r}} \) as
the force per unit length between two parallel wires each of length I meter,
carrying currents \( i_{1} \) and \( i_{2} \) amperes and separated by a distance r meters. Define ampere with the help of this formula.
Subject: Maths
If \( \{x\} \) denotes fractional part of \( x, \) then \( \lim _{x \rightarrow 1} \frac{x \sin \{x\}}{x-1}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
c. 1
D. does not exist
Subject: Maths
Match the points on the curve \( 2 y^{2}= \)
\( x+1 \) with the slope of normals at those
points and choose
the correct answer.
A \( . i-b, i i-d, i i i-c, i v-a \)
B . \( i-b, i i-a, i i i-d, i v-c \)
c. \( i-b, i i-c, i i i-d, i v-a \)
D. \( i-b, i i-d, i i i-a, i v-c \)
Subject: Physics
The upper and lower fixed points of a thermometer are separated by \( 180 \mathrm{mm} \) What is the temperature in Celcius if the length of the mercury thread is 90 \( \mathrm{mm} \) above the lower fixed point?
\( \mathbf{A} \cdot 90^{\circ} C \)
B . \( 50^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 45^{\circ} C \)
D. \( 58^{\circ} \mathrm{C} \)
Subject: Physics
A capacitor 'C', a variable resistor'R' and
a bulb 'B' are connected in series to the
ac mains in circuit as shown. The bulb
glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between
the plates of the capacitor, keeping resistance \( R \) to be the same; (ii) the
resistance \( R \) is increased keeping the
same capacitance?
Subject: Physics
Two slits are separated by a distance of \( 0.5 m m \) and illuminated with light of wavelength \( \lambda=6000 A \). If the screen is
placed at 2.5 m from the slits. The
distance of the third bright fringe from the centre will be
A. \( 1.5 \mathrm{mm} \)
B. \( 3 m m \)
\( c .6 m m \)
D. \( 9 \mathrm{mm} \)
Subject: Physics
Q Type your question-
uniformly distributed over its
circumference is hanging by a
insulated thread with the help of a
small smooth ring (not rigidly fixed with bigger ring). A time varying magnetic
field \( B=B_{0} \sin \omega t \) is switched on at \( t \)
\( =0 \) and the ring is released at the
same time.The average magnetic
moment of Ring in time interval 0 to
is
A \( \cdot \frac{B_{0} q^{2} R^{2}}{2 \pi m} \)
B. \( \frac{B_{0} q^{2} R^{2}}{4 \pi m} \)
c. \( \frac{B_{0} q^{2} R^{2}}{\pi m} \)
D. zer
Subject: Maths
Given two functions
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}+\mathbf{1 0 0} \)
\( \boldsymbol{g}(\boldsymbol{x})=\mathbf{3}^{\boldsymbol{x}} \)
Calculate at what minimum integral value of \( \boldsymbol{x}, \boldsymbol{g}(\boldsymbol{x})>\boldsymbol{f}(\boldsymbol{x}) \)
A . 5
B. 3
\( c \cdot 4 \)
D. 6
Subject: Chemistry
Referring to the molecular sketch and table above, choose the option that best describes the percentage of carbon in the molecule, in terms of both atomic
composition and mass-percent composition.
A. Carbon makes up approximately \( 25 \% \) of the atoms and \( 25 \% \) of the mass
B. Carbon makes up approximately 40\% of the atoms, and \( 40 \% \) of the mass
c. carbon makes up approximately 25\% of the atoms, and \( 40 \% \) of the mass
D. carbon makes up approximately \( 40 \% \) of the atoms. and \( 25 \% \) of the mass
Subject: Physics
An electron is in an excited state in a
hydrogen like atom. It has a total energy of \( -3.4 e V . \) The kinetic energy of the
electron is \( \boldsymbol{E} \) and its de Broglie
wavelength is \( \lambda \)
A \( . E=6.8 \mathrm{eV}, \lambda=-6.6 \times 10^{-10} \mathrm{m} \)
B . \( E=3.4 \mathrm{eV}, \lambda=-6.6 \times 10^{-10} \mathrm{m} \)
C . \( E=3.4 \mathrm{eV}, \lambda=-6.6 \times 10^{-11} \mathrm{m} \)
D. \( E=6.8 e V, \lambda=-6.6 \times 10^{-11} \mathrm{m} \)
Subject: Physics
If Velocity of flow is \( 4 \mathrm{m} / \mathrm{s} \), then velocity
head is
A. \( 0.2 m \)
в. \( 0.4 m \)
\( \mathrm{c} .0 .6 \mathrm{m} \)
D. \( 0.8 m \)
Subject: Chemistry
The formula of the calcium ion is \( C a^{2+} \)
and that of the acetate ion is
\( C H_{3} C O O^{-} . \) What is the formula of
calcium acetate?
\( \mathbf{A} \cdot C a\left(C H_{3} C O O\right)_{2} \)
в. \( C a C H_{3} C O O \)
\( \mathrm{c} \cdot \mathrm{Ca}_{2}\left(\mathrm{CH}_{2} \mathrm{COO}\right)_{2} \)
D. \( C a_{2} C H_{3} \) COO
Subject: Chemistry
Assertion
Concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) reacts with \( \boldsymbol{K} \boldsymbol{C l} \)
to give \( C l_{2} \) gas.
Reason
\( H C l \) cannot be oxidised by
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
A. Both assertion and reason are CORRECT and reason is the CORRECT explanation of the assertion,
B. Both assertion and reason are CORRECT, but reason is NOT THE CORRECT explanation of the assertion
c. Assertion is CORRECT, but reason is INCORRECT
D. Assertion is INCORRECT, but reason is CORRECT
Subject: Maths
Let \( T_{r} \) be the rth term of an A.P.
whose first term is \( a \), and common
difference is \( d \). If for some positive integers \( \boldsymbol{m}, \boldsymbol{n}, \boldsymbol{T}_{\boldsymbol{m}}=\frac{\mathbf{1}}{\boldsymbol{n}} \) and \( \boldsymbol{T}_{\boldsymbol{n}}=\frac{\mathbf{1}}{\boldsymbol{m}} \)
then \( \boldsymbol{a}-\boldsymbol{d}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{m}+\frac{1}{n} \)
c. \( \frac{1}{m n} \)
D.
Subject: Maths
Tell if the following statement is true or
false. In case give a valid reason for
saying so
\( p: \) If \( x \) and \( y \) are integers such that \( x> \)
\( \boldsymbol{y} \cdot \) then \( -\boldsymbol{x}<-\boldsymbol{y} \)
A. True
B. False
Subject: Chemistry
What is the formula to find the value of
\( t_{1 / 2} \) for a zero order reaction?
A. \( \frac{k}{[R]_{0}} \)
в. \( \frac{2 k}{[R]_{0}} \)
c. \( \frac{[R]_{0}}{2 k} \)
D. \( \frac{0.693}{k} \)
Subject: Maths
In the following figure, \( M \) is midpoint of
BC of a parallelogram ABCD. DM intersects the diagonal \( A C \) at \( P \) and
AB produced at E. Then
\( \mathbf{A} \cdot P E=3 P D \)
B. \( P E=2 P D \)
c. \( P E=P D \)
\( D . P E=4 P D \)
Subject: Physics
A uniform disc of mass \( m \) is fitted
(pivoted smoothly) with a rod of mass
\( m / 2 . \) If the bottom of the rod is pulled
with a velocity \( v, \) it moves without changing its angle of orientation and the disc rolls without sliding. Find the
kinetic energy of the system \( (r o d+ \)
\( \operatorname{disc} \)
Subject: Physics
Choose the correct statement from the
following options.
This question has multiple correct options
A. If the zeroeth division of the vernier and main scales of
a standard vernier callipers coincide then measured length is equal to the actual length.
B. The least count of vernier scale is \( 0.9 \mathrm{mm} \)
C. The length of a one vernier scale division is greater than that of one main scale division.
D. The internal jaws are used for measuring the internal diameter of a hollow cylinder
Subject: Physics
There are \( 8.4 \times 10^{22} \) free electrons per
\( c m^{3} \) in copper, the current in the wire is
\( \mathbf{0 . 2 1} \boldsymbol{A}\left(\boldsymbol{e}=\mathbf{1 . 6} \times \mathbf{1 0}^{-\mathbf{1 9}} \boldsymbol{C}\right) . \) Then the
drifts velocity of electrons in a copper
wire of \( 1 \mathrm{mm}^{2} \) cross section will be:
A \( .2 .12 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
B . \( 0.78 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
c. \( 1.56 \times 10^{-5} \mathrm{m} / \mathrm{s} \)
D. none of these
Subject: Chemistry
Nitrogen reacts with a metal \( M \) to
produce a compound \( X . \) This compound
\( X, \) when dissolved in water forms
pungent gas \( Y \) which can be identified easily by the formation of white fumes in the presence of \( \boldsymbol{H} \boldsymbol{C l} \)
Identify the metal \( M \)
A. Calcium
B. Sodium
c. cobalt
D. Iron
Subject: Chemistry
Molecules of benzoic acid
\( \left(C_{6} H_{5} C O O H\right) \) dimerise in benzene. g of the acid dissolved in 30 g of benzene
shows a depression in freezing point
equal to \( 2 \mathrm{K} \). If the percentage association of the acid to form a dimer
in the solution is \( 80, \) then \( w \) is:
(Given that \( \boldsymbol{K}_{f}=\mathbf{5} \mathrm{K} \) kg \( \boldsymbol{m o l}^{-1} \), Molar
mass of benzoic acid \( =122 \) g \( m o l^{-1} \)
A . \( 1.8 g \)
в. 2.4g
c. \( 1.0 g \)
D. \( 1.5 \mathrm{g} \)
Subject: Physics
Two light waves of intensities \( ^{\prime} I_{1}^{\prime} \) and \( ^{\prime} I_{2}^{\prime} \) having same frequency pass through
same medium at a time in same
direction and interfere. The sum of the
minimum and maximum intensities is
\( \mathbf{A} \cdot\left(I_{1}+I_{2}\right) \)
B \( \cdot 2\left(I_{1}+I_{2}\right) \)
C \( \cdot\left(\left(\sqrt{I}_{1}+\sqrt{I}_{2}\right)\right) \)
D. \( \left(\left(\sqrt{I}_{1}-\sqrt{I}_{2}\right)\right) \)
Subject: Physics
A cubical room is formed with 6 plane
mirror. An insect moves along diagonal of the floor with uniform speed. The velocity of its image in two adjacent walls are \( 20 \sqrt{2} \mathrm{cm} / \mathrm{s} \). Then the velocity of image formed by the roof is
\( \mathbf{A} \cdot 20 \mathrm{cm} / \mathrm{sec} \)
B. \( 40 \mathrm{cm} / \mathrm{sec} \)
\( \mathrm{c} \cdot 9 \mathrm{cm} / \mathrm{sec} \)
D. \( 45 \mathrm{cm} / \mathrm{sec} \)
Subject: Physics
A body is vibrating 7200 times in one minute. If the velocity of sound is 360 \( \mathrm{m} / \mathrm{s}, \) find (i) frequency of the vibration
in \( \mathrm{Hz}, \) (ii) the wavelength of the sound
produced.
A. \( 120 \mathrm{Hz}, 3 \mathrm{m} \)
в. \( 140 H z, 3 \) т
c. \( 120 H z, 4 m \)
D. \( 140 H z, 4 m \)
Subject: Maths
\( \boldsymbol{p}(\boldsymbol{y})=\mathbf{5} \boldsymbol{y}^{3}-\boldsymbol{2} \boldsymbol{y}^{2}+\boldsymbol{y}+\mathbf{1 0} \) is a
polynomial in \( y \) of degree
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
D. 3
Subject: Chemistry
The IUPAC name of \( \boldsymbol{X} \boldsymbol{e}\left[\boldsymbol{P} \boldsymbol{t} \boldsymbol{F}_{6}\right] \) is
A. hexafluoridoplatinate (VI) xenon
B. xenon hexafluoridoplationate (V)
c. xenon hexafluoridoplatinate (VI)
D. xenonium hexfluoridoplatinum (V)
Subject: Physics
An air chamber of volume \( V \) has a neck
of cross-sectional area a into which a
light ball of mass \( \mathrm{m} \) just fits and can move up and down without friction. The
diameter of the ball is equal to that of
the neck of the chamber. The ball is
pressed down a little and released. If the bulk modulus of air is \( \mathrm{B} \), the time period
of the oscillation of the ball is
A \( \cdot T=2 \pi \sqrt{\frac{B a^{2}}{m V}} \)
B \( \cdot T=2 \pi \sqrt{\frac{B V}{m a^{2}}} \)
\( \mathbf{c} \cdot T=2 \pi \sqrt{\frac{m B}{V a^{2}}} \)
\( \mathbf{D} \cdot T=2 \pi \sqrt{\frac{m V}{B a^{2}}} \)
Subject: Maths
If \( \cos ^{-1}\left(4 x^{3}-3 x\right)=2 \pi-3 \cos ^{-1} x \)
then \( x \) lies in interval
A \( \cdot\left[-1,-\frac{1}{2}\right] \)
в. \( |x|<\frac{1}{2} \)
\( \mathbf{c} \cdot\left[\frac{1}{2}, 1\right. \)
D. None of these
Subject: Biology
Assertion
Smaller the organism higher is the rate of metabolism per gram weight.
Reason
The heart rate of a six month old baby is much higher than that of an old person.
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: Maths
ff \( f(x)= \)
\( f(x-a)(x-b)(x-c)(x-d) \) then
prove that
\( \Delta=\left|\begin{array}{cccc}\boldsymbol{a} & \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{b} & \boldsymbol{x} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{c} & \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{x} & \boldsymbol{d}\end{array}\right|=\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{x} \boldsymbol{f}^{\prime}(\boldsymbol{x}) \)
Subject: Physics
f a vector \( 2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to the vector \( 4 \hat{j}-4 \hat{i}+\alpha \hat{k}, \) then the
value of \( \alpha \)
A . -
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \)
Subject: Maths
The expression \( \frac{5-x}{x^{2}-x-20} \) when simplified equals
A \( \cdot \frac{1}{(x+4)} \)
в. \( \frac{1}{(x-4)} \)
c. \( -\frac{1}{(x+4)} \)
D. \( \frac{1}{(x-5)} \)
Subject: Physics
If the electric field at all points on a
closed Gaussian surface is zero, does
this mean that the net charge enclosed
by the surface is zero?
A. Yes; zero field everywhere means zero flux everywhere.
B. Yes; zero electric field means that there are no charges of any kind in the region.
C. No; there may be some positive and some negative charges enclosed within the surface.
D. No; zero field could be caused by charges outside of the surface as well as inside the surface.
E. No; it is impossible for charges to exist and yet electric field to be zero everywhere.
Subject: Physics
A \( 10 \mu F \) condenser is charged to a potential of 100 volt. It is now connected to another uncharged condenser. The common potential reached is 40 volt. The capacitance of second condenser is
A \( .2 \mu F \)
в. \( 10 \mu F \)
c. \( 15 \mu F \)
\( \mathbf{D} \cdot 22 \mu F \)
Subject: Chemistry
Fill the blank.
\( \$ \$ 2\{\text { Ca }\}_{-}\{3\}\left\{\text { lleft }\left(P\{0\}_{-}\{4\} \mid \text { right }\right)\right. \)
3. \( \{2\}+6 \operatorname{si}\{0\}_{-}\{2\}+10 C \) lrightarrow \( \{P \)
\( -\{4\}+\mid \) text \( \{-\} \operatorname{casi}\{0\}_{-}\{3 \)
\( 3+10 \cos \$ \)
\( A \cdot 2 \)
B. 4
\( c .5 \)
D. 6
E . 8
Subject: Physics
A square metal loop of side \( 10 \mathrm{cm} \) and
resistance \( 1 \Omega \) is moved with a
constant velocity partly inside a uniform magnetic field of \( 2 W b m^{-2} \)
directed into the paper, as shown in the
figure. The loop is connected to a
network of five resistors each of value
\( 3 \Omega \). If a steady current of 1 m \( A \) flows in
the loop, then the speed of the loop is
A \( \cdot 0.5 \mathrm{cms}^{-1} \)
B. \( 1 \mathrm{cms}^{-1} \)
\( \mathrm{c} \cdot 2 \mathrm{cms}^{-1} \)
D. \( 4 \mathrm{cms}^{-1} \)
Subject: Physics
The temperature coefficient of
resistance of a wire at \( 0^{\circ} \mathrm{C} \) is
\( 0.00125^{\circ} \mathrm{C}^{-1} . \) At \( 25^{\circ} \mathrm{C} \) its resistance is
one ohm. The resistance of the wire will
be 1.2 ohm at
A . \( 225 K \)
B . \( 190^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 260^{\circ} C \)
D. \( 185 K \)
Subject: Chemistry
Among
\( \boldsymbol{B}_{2} \boldsymbol{H}_{6}, \boldsymbol{B}_{3} \boldsymbol{N}_{3} \boldsymbol{H}_{6}, \boldsymbol{N}_{2} \boldsymbol{O}, \boldsymbol{N}_{2} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{3} \)
and \( H_{2} S_{2} O_{8}, \) the total number of
molecules containing covalent bond between two atoms of the same kind is
Subject: Maths
If \( \frac{1}{2}<|x|<1, \) then which of the following are real? This question has multiple correct options
\( A \cdot \sin ^{-1} x \)
B. \( \tan ^{-1} x \)
\( \mathrm{c} \cdot \sec ^{-1} x \)
D. \( \cos ^{-1} x \)
Subject: Physics
In a clockwise system:
\( \mathbf{A} \cdot \hat{j} \times \hat{k}=\hat{i} \)
\( \mathbf{B} \cdot \hat{i} \hat{i}=0 \)
\( \mathbf{c} \cdot \hat{j} \times \hat{j}=1 \)
D. \( \hat{k} . \hat{i}=1 \)
Subject: Maths
If \( y=\frac{\log _{e} x}{x} \) and \( z=\log _{e} x, \) then
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} z^{2}}+\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} z}= \)
A \( \cdot e^{-} \)
B. \( 2 e^{-2} \)
\( \mathrm{c} \cdot z e^{-} \)
D. \( -e^{-z} \)
Subject: Chemistry
A neutron breaks into a proton and an electron. This decay of neutron is
accompanied by the release of energy. Assuming that \( 50 \% \) of the energy is produced in the form of electromagnetic radiation, what will be the frequency of radiation produced. Will this photon be sufficient to cause ionization of aluminum? In case it is
able to do so what will be the energy of the electron ejected from the aluminum
atom
\( \boldsymbol{I} \boldsymbol{E}_{1} \) of \( \boldsymbol{A l}=\mathbf{5 7 7} \mathrm{KJ} / \mathrm{mol} \)
Subject: Physics
A \( 20 \mathrm{cm} \) tall object is placed
perpendicular to the principal axis of a convex lens of focal length \( 10 \mathrm{cm} \). If
object distance is \( 15 \mathrm{cm} . \) Find the
image distance.
A. \( -30 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathrm{c} \cdot 15 \mathrm{cm} \)
D. -15 cm
Subject: Physics
The linear momentum of a particle is given by \( \boldsymbol{P}=(\boldsymbol{a} \sin \boldsymbol{t} \hat{\boldsymbol{i}}-\boldsymbol{a} \cos \boldsymbol{t} \hat{\boldsymbol{j}}) \) kg-
\( \mathrm{m} / \mathrm{s} \) A force \( \overrightarrow{\boldsymbol{F}} \) is acting on the particle Select correct alternative/s
A. Linear momentum \( \vec{P} \) of particle is always parallel to
B. Linear momentum \( \vec{P} \) of particle is always perpendicular to \( \vec{F} \)
c. Linear momentum \( \vec{P} \) is always constant
D. Magnitude of linear momentum is constant with respect to time
Subject: Chemistry
Match the following
Set-I (Cl-O bond length) \( \quad \operatorname{Set}-\|\left(\mathbf{A}^{0}\right) \)
A) \( \boldsymbol{H} \mathbf{C l O} \)
1)1.64
\( \mathbf{B}) \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{2} \)
2)1.70
\( \mathbf{C}) \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{3} \)
3) 1.45
D) \( \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{\boldsymbol{4}} \)
4) 1.57
The correct matching is:
B. A-2, B-3, C-4, D-1
c. A-2, B-1, C-4, D-3
D. A-2, B-1, C-3, D-4
Subject: Chemistry
Increasing order of magnetic moment among the following species is:
\( N a^{+}, F e^{+3}, C o^{+2}, C r^{+2} \)
A. \( N a^{+}<C o^{2+}<C r^{2+}<F e^{3+} \)
B. \( N a^{+}<F e^{3+}<C r^{2+}<C o^{2+} \)
c. \( C r^{2+}<C o^{2+}<N a^{+}<F e^{3+} \)
D. \( C o^{2+}<N a^{+}<C r^{2+}<F e^{3+} \)
Subject: Maths
\( \boldsymbol{A}= \)
\( \{x: x \text { is a perfect square, } x<50, x \in \lambda \)
\( \boldsymbol{B}= \)
\( \{x: x=8 m+1, \text { where } m \in W, s<5 \)
then find \( A \cap B \) and display it with
Venn diagram.
Subject: Physics
I ne rollowıng table represents the
velocity of a moving body at different
instants of time.
Times
\( (s) \)
Velocity
\( \left(m s^{-1}\right) \)
\( 20 \quad 20 \)
The velocity-time graph is as shown in
figure. For which interval of time the
body has a uniform motion? Find the
velocity in this time interval?
\( A \cdot \) from \( t=0 \) s to \( t=5 s ; 10 m / s \)
B. from \( t=5 \) s to \( t=10 s ; 20 m / s \)
C. from \( t=10 \) s to \( t=15 s ; 20 \mathrm{m} / \mathrm{s} \)
D. from \( t=15 \) s to \( t=25 s ; 30 m / s \)
Subject: Chemistry
If 0.80 mol of \( M n O_{2} \) and 146 g of \( H C l \) react, then number of moles of \( C l_{2} \)
formed is (as nearest integer):
\( M n O_{2}+4 H C l \longrightarrow M n C l_{2}+C l_{2}+ \)
\( 2 H_{2} O \)
Subject: Maths
If \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) are the arguments of \( z_{1} \) and
\( \bar{z}_{2}, \) then the value of \( \arg \left(z_{1} z_{2}\right) \) is
A \( \cdot \frac{5 \pi}{12} \)
в. \( \frac{\pi}{12} \)
c. \( \frac{7 \pi}{12} \)
D. None of these
Subject: Maths
If \( z_{1} \) and \( z_{2} \) are two complex numbers
such that \( \left|z_{1}\right|=\left|z_{2}\right| \) and \( \arg \left(z_{1}\right)+ \)
\( \operatorname{rag}\left(z_{2}\right)=\pi, \) then show that \( z_{1}=-\bar{z}_{2} \)
Subject: Maths
Let \( \boldsymbol{P} \) be an \( \boldsymbol{m} \times \boldsymbol{m} \) matrix such that
\( \boldsymbol{P}^{2}=\boldsymbol{P} . \) Then \( (\boldsymbol{I}+\boldsymbol{P})^{n} \) equals.
\( \mathbf{A} \cdot I+P \)
B. \( I+n P \)
c. \( I+2^{n} P \)
D. \( I+\left(2^{n}-1\right) P \)
Subject: Maths
\( \int x \sin \left(-x^{2}\right) d x= \)
A \( \cdot \frac{1}{2} \sin \left(x^{2}\right)+c \)
B \( \cdot \frac{1}{2} \cos \left(x^{2}\right)+c \)
c. \( \frac{1}{8} \cos \left(x^{2}\right)+c \)
D. \( \frac{1}{2} x \sin x^{2}+c \)
Subject: Physics
When two bodies move uniformly towards each other, the distance
decreases by \( 6 m s^{-1} \). If both bodies
move in the same direction with the
same speed as above the distance
between them increases by \( 4 m s^{-1} \)
Then the speed of the two bodies are
\( \mathbf{A} \cdot 3 m s^{-1} \) and \( 3 m s^{-1} \)
B. \( 4 m s^{-1} \) and \( 2 m s^{-1} \)
\( \mathbf{c} \cdot 5 m s^{-1} \) and \( 1 m s^{-1} \)
D. \( 7 m s^{-1} \) and \( 3 m s^{-1} \)
Subject: Physics
Figure shows a Wheatstone bridge
circuit. Which of the following correctly
shows the currents \( I_{1}, I_{2} \) and \( I_{3} \) in the
decreasing order of magnitude?
\( A \cdot I_{1}, I_{2}, I_{3} \)
В \( \cdot I_{2}, I_{3}, I_{1} \)
\( \mathrm{c} \cdot I_{2}, I_{1}, I_{3} \)
D \( \cdot I_{3}, I_{2}, I_{1} \)
Subject: Physics
\( \ln \operatorname{an} A C \) circuit \( V \) and \( I \) is given by
\( \boldsymbol{V}=\mathbf{1 0 0 0} \sin (\mathbf{1 0 0 0} \boldsymbol{t}) \) volt
\( \boldsymbol{I}=\mathbf{1 0 0} \sin \left(\mathbf{1 0 0 0} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\mathbf{6}}\right) \boldsymbol{m} \boldsymbol{A} \)
The power dissipation in the circuit in one complete cycle is.
\( \mathbf{A} \cdot 25 W \)
B. \( 25 \sqrt{3} \)
c. \( 100 \mathrm{W} \)
D. 10 W
Subject: Chemistry
Number of spectral lines that are emitted by atomic hydrogen excited to
the \( n t h \) energy level is:
A \( \cdot \frac{1}{2} n(n-1) \)
B . \( \frac{1}{4} n(n-1) \)
c. \( \frac{1}{2} n(n+1) \)
D \( \cdot \frac{1}{2} n(n-2) \)
Subject: Biology
Select the correct option:Fermentation
is represented by the equation
\( \mathbf{A} \cdot C_{6} H_{12} O_{6}+6 O_{2} \rightarrow 6 C O_{2}+6 H_{2} O+686 K c a l \)
B \( \cdot C_{6} H_{12} O_{6} \rightarrow 2 C_{2} H_{5} O H+2 C O_{2}+59 K c a l \)
\( \mathbf{c} \cdot 6 C O_{2}+12 H_{2} O \frac{\text {Light}}{\text {Chlorophyll}} C_{6} H_{12} O_{6}+6 H_{2} O+6 O_{2} \)
D. \( 6 C O_{2}+6 H_{2} O \rightarrow C_{6} H_{12} O_{6}+6 O_{2} \)
Subject: Biology
Match the scientist and their
discoveries given in Column I and I
correctly and choose the correct
combination from the following.
\( \mathbf{A} \)
\( A-p, B-q, C-r, D-t \)
B. \( A-q, B-p, C-s, D-t \)
C. \( A-q B-p, C-r, D-t \)
D. \( A-q, B-p, C-t \)
\( D \)
Subject: Physics
The coefficients of self induction of two
inductance coils arc \( 0.01 \mathrm{H} \) and \( 0.03 \mathrm{H} \)
respectively. When they are connected in series so as to support each other then the resultant self inductance
becomes 0.06 Henry. The value of coefficient of mutual induction will be-
A . \( 0.02 \mathrm{H} \)
B. 0.05
c. \( 0.01 \mathrm{H} \)
D. ZERO
Subject: Physics
A point charge \( q \) is located at the point \( (0,0,-a) . \) Consider a hemispherical surface of radius 'a' with its centre at
the origin and \( z \geq 0 . \) The modulus of the electric flux through the hemispherical
surface is:
A \( \cdot q / €_{0} \)
B \( \cdot q /\left(2 \sqrt{2} \in_{0}\right) \)
\( ^{\mathbf{c}} \cdot\left(1-\frac{1}{\sqrt{2}}\right) q / \epsilon_{0} \)
D \( \left(1-\frac{1}{\sqrt{2}}\right) q /\left(2 \in_{0}\right) \)
Subject: Maths
If \( f \) and \( g \) are differentiable functions in
\( [\mathbf{0}, \mathbf{1}] \) satisfying \( \boldsymbol{f}(\mathbf{0})=\mathbf{2}= \)
\( g(1), g(0)=0 \) and \( f(1)=6, \) then for
some \( \boldsymbol{c} \in[\mathbf{0}, \mathbf{1}] \)
A \( \cdot 2 f^{\prime}(c)=g^{\prime}(c) \)
B \( \cdot 2 f^{\prime}(c)=3 g^{\prime}(c) \)
c. \( f^{\prime}(c)=g^{\prime}(c) \)
D. \( f^{\prime}(c)=2 g^{\prime}(c) \)
Subject: Physics
Light of wavelength \( 5000 \dot{A} \) and intensity \( 3.96 \times 10^{-3} W / c m^{2} \) is
incident on the surface of a
photosensitive material. If 1 percent of incident photons only emit
photoelectrons, then the number of electrons emitted per unit area from the surface will be
A \( \cdot 10^{16} \)
B. \( 10^{18} \)
\( c \cdot 10^{20} \)
D. \( 10^{2} \)