AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A uniform solid cylinder of mass \( 2 k g \)
and radius \( 0.2 m \) is released from the
rest at the top of a semicircular track of
radius \( 0.7 m \) cut in block of mass \( M= \)
\( 3 k g \) as shown. The block is resting on a
smooth horizontal surface and the
cylinder rolls down without slipping. The
distance moved by the block when the cylinder reaches the bottom of the track is:
\( \mathbf{A} \cdot 0.3 m \)
B. \( 0.5 m \)
c. \( 0.7 m \)
D. \( 0.2 m \)
Subject: Maths
Find the value of \( x \) which satisfy equation \( \cos \left(2 \sin ^{-1} x\right)=\frac{1}{3} \)
A \( \cdot x=\frac{1}{\sqrt{5}} \) and \( x=\frac{-1}{\sqrt{5}} \)
B . \( x=\frac{1}{\sqrt{3}} \) and \( x=\frac{-1}{\sqrt{3}} \)
c. \( x=\frac{1}{\sqrt{2}} \) and \( x=\frac{-1}{\sqrt{2}} \)
D. None of these
Subject: Maths
Q Type your question
brand \( Q \).The amounts (in \( \mathrm{kg} \) ) of nitrogen, phosphoric acid, potash, and
chlorine in a bag of each brand are
given in the table. Tests indicate that
the garden needs at least \( 240 k g \) of
phosphoric acid, at least 270 kg of
potash and at most \( 310 k g \) of chlorine.
If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum
amount of nitrogen added in the
garden?
\( \begin{array}{llll}\text { Kg per bag } & & & \\ & & \text { Brand } P & \text { Brand } Q \\ & & & \\ \text { Nitrogen } & 3 & 3.5 & \\ \text { Phosphoric acid } & 1 & 2 & \\ \text { Potash } & 3 & 1.5 & \\ \text { Chlorine } & 1.5 & 2 & \end{array} \)
Subject: Physics
At a moment in a progressive wave, the phase of a particle executing \( \mathrm{SHM} \) is \( \frac{\pi}{3} \) Then the place of the particle \( 15 \mathrm{cm} \) ahead and at time \( \frac{T}{2} \) will be, if the wavelength is \( 60 \mathrm{cm} \)
A. zero
в. \( \frac{\pi}{2} \)
c. \( \frac{5 \pi}{6} \)
D. \( \frac{2 \pi}{3} \)
Subject: Biology
A trihybrid cross is made between two plants with genotypes \( \mathrm{A} / \mathrm{a} \) B/b \( \mathrm{C} / \mathrm{c} \), how many offsprings of such cross will have a genotype a/a b/b c/c?
A . \( 1 / 64 \)
B. \( 1 / 4 \)
\( c \cdot 1 / 16 \)
D. 1/32
Subject: Chemistry
The most favourable conditons for
the formation of \( S O_{3} \) via the equation
\( \boldsymbol{S O}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{S} \boldsymbol{O}_{3}, \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -95 k J m o l^{-1} \) are
A. Low concentration of reactants and high presure
B. High concentration of reactants and atmospheric pressure
C. High concentration of reactants and high pressure
D. Low concentration of reactants and atmospheric presure
Subject: Maths
\( f(x)=\frac{\cos x}{\left[\frac{2 x}{\pi}\right]+\frac{1}{2}}, \) where \( x \) is not an
integral multiple of \( \pi \) and [.] denotes the
greatest integer function, is
A. an odd function
B. an even function
c. neither odd nor even
D. none of these
Subject: Maths
Calculate Mean deviation about median
for the given data
\( \begin{array}{llll}\text { Marks } & \begin{array}{l}100- \\ 110\end{array} & \begin{array}{l}110- \\ 120\end{array} & \begin{array}{l}120- \\ 130\end{array}\end{array} \)
Frequency 4
A . 10.5
в. 31.5
c. 12.5
D. 66.16
Subject: Chemistry
A cylinder containing an ideal gas is in a vertical position and has a piston of
mass \( M \) that is able to move up or
down without friction. If the
temperature is increased, then :
A. Both \( P \) and \( V \) of the gas will change
B. Only \( P \) will increase according to Charles's law
c. \( V \) will change but not \( P \)
D. \( P \) will change but not \( V \)
Subject: Maths
Find mode for the following data:
\( \begin{array}{llllll}\mathbf{x} & \mathbf{2}- & \mathbf{4}- & \mathbf{6}- & \mathbf{8}- & \mathbf{1 0} \\ \mathbf{4} & \mathbf{6} & \mathbf{8} & \mathbf{1 0} & \mathbf{1 2} \mathbf{2}\end{array} \)
2 2 1
A . 11
в. 12
c. 13
D. 14
Subject: Physics
A point particle of mass \( 0.1 k g \) executing SHM with amplitude of \( 0.1 m \) When the particle passes through the mean position is \( \mathrm{KE} \) is \( 8 \times 10^{-3} \mathrm{J} \)
Obtain the equation of motion of this particle if the initial phase of oscillation
is \( 45^{\circ} \)
Subject: Physics
A constant force \( \boldsymbol{F} \) is applied in
horizontal direction as shown. Contact
force between \( M \) and \( m \) is \( N \) and
between \( m \) and \( M^{\prime} \) is \( N^{\prime} \) then:
A \( . N=N^{\prime} \)
B. \( N>N^{\prime} \)
C \( . N^{\prime}>N \)
D. Cannot be determined
Subject: Biology
Assertion
Most of the secretions released by
laticiferous tissue is of no use to plants.
Reason
They are by products of physiological reactions useful for mankind.
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: Physics
A grind-stone starts revoiving from rest,
it its angular acceleration is 4.0 rad / sec \( ^{2} \) (uniform) then after 4 sec.
What is its angular displacement \& angular velocity respectively -
A. 32 rad, 16 rad/sec
B. 16 rad, 32 rad/sec
c. 64 rad, 32 rad/sec
D. 32 rad, 64 rad/sec
Subject: Physics
Suppose a current carrying wire has a cross-sectional area that gradually
become smaller along the wire has the shape of a very long cone as shown in
figure:
A. Electric current is different in different portions of wire
B. Electric field at point \( A \) is same as that of point \( B \)
C. Drift speed of electrons at point \( A \) is lesser than that of at point \( B \)
D. Drift speed of electrons at point \( A \) is same as that of at point \( B \)
Subject: Maths
\[
\begin{aligned}
\boldsymbol{f}(\boldsymbol{x})=& \boldsymbol{x}, \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \leq 1 \\
\boldsymbol{5}, & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \geq 1
\end{aligned}
\]
Check whether \( f(x) \) is continuous at
\[
\boldsymbol{x}=\mathbf{0} ? \boldsymbol{x}=\mathbf{1} ? \boldsymbol{x}=\mathbf{2} ?
\]
Subject: Maths
If \( \boldsymbol{x}^{\boldsymbol{y}}=\boldsymbol{e}^{\boldsymbol{x}-\boldsymbol{y}}, \) then find \( \frac{d \boldsymbol{y}}{d \boldsymbol{x}} \) at \( \boldsymbol{x}=\mathbf{1} \)
Subject: Physics
toppr LOGIN JolN Now
Q Type your question
Which table gives the correct directions
for the magnetic field at the two
positions around the wire?
wire field on right side of
(6)
wire head on with conventional
current flow out of page
\( A \)
\begin{tabular}{|l|l|}
\hline & Direction of Field \\
\hline Right of the Wire & toward right side of page \\
Below the Wire & toward bottom of page \\
\hline
\end{tabular}
B. \begin{tabular}{|l|c|}
\hline & Direction of Field \\
\hline Right of the Wire & toward left of page \\
Below the Wire & toward top of page \\
\hline
\end{tabular}
\( \mathbf{c} \)
\begin{tabular}{|l|l|}
\hline & Direction of Field \\
\hline Right of the Wire & toward top of page \\
Below the Wire & toward right side of page \\
\hline
\end{tabular}
D.
\begin{tabular}{|l|l|}
\hline & Direction of Field \\
\hline Right of the Wire & toward bottom of page \\
Below the Wire & toward left side of page \\
\hline
\end{tabular}
\( E \)
\begin{tabular}{|l|l|}
\hline & Direction of Field \\
\hline Right of the Wire & toward lower left portion of page \\
Below the Wire & toward upper right portion of page \\
\hline
\end{tabular}
Subject: Maths
The Venn diagram shows sets \( \xi, P \) and
\( Q \)
The shaded region in the Venn diagram
represents set
\( A \cdot P \cap Q \)
в. \( P^{\prime} \cap Q \)
c. \( P \cap Q^{\prime} \)
D. \( P^{\prime} \cap Q^{\prime} \)
Subject: Physics
Consider a plane flying due West at 200 MPH. The co-pilot is firing a gun in the opposite direction the plane is flying due East. If the co-pilot clocks the bullets at \( 500 \mathrm{MPH} \), how fast would the
bullets be clocked from the ground?
A. 300 MPH East
в. 700 МРн Еазн
c. 500 MPH West
D. 200 MPH West
E. cannot determine with information provided
Subject: Physics
Figure shows some equipotential lines distributed in space. A charged object
is moved from point \( A \) to point \( B \)
A. The work done in figure (i) is the greatest.
B. The work done in figure (ii) is the least.
C. The work done is the same in figure (i), (ii) and (iii)
D. The work done is the same in figure (iii) is greater than figure
(ii) but equal to that in figure (i).
Subject: Maths
For \( \boldsymbol{O} \) being the origin and 3 points \( \boldsymbol{P}, \boldsymbol{Q} \) and \( R \) lie on a plane. If \( \overrightarrow{P O}+\overrightarrow{O Q}= \) \( \overrightarrow{Q O}+\overrightarrow{O R}, \) then \( P, Q, R \) are
A. the vertices of an equilateral triangle
B. the vertices of an isoceles triangle
c. collinear
D. none of these
Subject: Chemistry
toppr
Q Type your question
(A)
\( (\mathrm{C}) \)
This question has multiple correct options
A \( \cdot(B) \) and \( (D) \) are the same product as given
B. \( (B) \) is as shown in figure
C. \( (D) \) is as shown in figure
D. The above reaction is called ipso substitution
Subject: Chemistry
Which of the following compounds is stable?
\( \mathbf{A} \cdot C H_{3} C H(O H)_{2} \)
B. \( \left(C H_{3}\right)_{2} C H(O H)_{2} \)
\( \mathbf{c} \cdot C C l_{3} C H(O H)_{2} \)
D. None of these
Subject: Physics
If a cell of constant E.M.F. produces the same amount of the heat during the same time in two independent resistors
\( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}, \) when they are separately connected across the terminals of the
cell, one after the another, the internal resistance of the cell is \( \sqrt{x R_{1} R_{2}} \). Find \( x \)
Subject: Chemistry
\( Z n+H_{2} S O_{4} \rightarrow A \)
If we bring a burning splinter near the gas produced in the given reaction,it burns with a pop sound. The gas \( A \) is:
\( A \cdot O_{2} \)
в. \( N_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \)
D. \( C O_{2} \)
Subject: Physics
Assertion
If no external force acts on a system of
particles, then the centre of mass will
not move in any direction.
Reason
If net external force is zero, then the
linear momentum of the system
changes.
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: Physics
In a magnetic field of \( 0.05 T \) area of coil
changes from \( 101 c m^{2} \) to \( 100 c m^{2} \)
without changing the resistance which is \( 2 \Omega . \) The amount of charge that flow during this period is
A \( \cdot 2.5 \times 10^{-6} C \)
B . \( 2 \times 10^{-6} C \)
c. \( 10 \times 10^{-6} C \)
D. \( 8 \times 10^{-6} C \)
Subject: Chemistry
Balance the reaction of copper sulphide
with dilute hydrochloric acid.
\( \mathbf{A} \cdot C u_{2} S+2 H C l \rightarrow 2 C u C l+H_{2} S \)
B \( \cdot C u_{2} S+H C l \rightarrow C u C l+H_{2} S \)
\( \mathbf{c} \cdot C u_{2} S+H C l \rightarrow C u C l_{2}+H_{2}+S \)
D. \( 2 C u_{2} S+2 H C l \rightarrow 2 C u C l_{2}+S_{2}+H_{2} S \)
Subject: Chemistry
A flask of \( 4.48 \mathrm{L} \) capacity contains a
mixture of \( N_{2} \) and \( H_{2} \) at \( 0^{\circ} \mathrm{C} \) and 1 atm
pressure. If the mixture is made to react
to form \( N H_{3} \) gas at the same temperature, the pressure in the flask reduces to 0.75 atm. The partial pressure of \( N H_{3} \) gas in the final mixture is?
A. 0.33 atm
B. 0.50 atm
c. 0.66 atm
D. 0.25 atm
Subject: Physics
A stone is thrown upwards from a tower with a velocity \( 50 m s^{-1} \). Another stone
is simultaneously thrown downwards from the same location with a velocity \( 50 m s^{-1} . \) When the first stone is at the
highest point, the relative velocity of the second stone with respect to the first stone is (assume that second stone has
not yet, reached the ground
A. zero
B. \( 50 m s^{-1} \)
\( c \cdot_{100 m s^{-}} \)
D. \( 150 \mathrm{ms}^{-1} \)
Subject: Physics
A new system of unit is evolved in which
the values of \( \mu_{0} \) and \( \varepsilon_{0} \) are 2 and 8
respectively. Then the speed of light in this system will be \( (\text { in } \mathrm{m} / \mathrm{s}) \)
A . 0.25
B. 0.5
c. 0.75
\( D \)
Subject: Maths
The order and degree of the differential
equation
\( \left[\left\{x-\left(\frac{d y}{d x}\right)^{2}\right\}^{\frac{3}{2}}\right]^{2}=\left(a^{2} \frac{d^{2} y}{d x^{2}}\right) \)
\( A \)
B. 1,2
\( c .2,2 \)
D. \( 1, \)
Subject: Chemistry
\( 9 \mathrm{gm} \) of \( A l \) (at. \( \mathrm{Wt} \). = 27 ) will react
completely with an acid to give :
A. one mole of \( H_{2} \)
B. one half mole of \( H_{2} \)
c. one-third mole of \( H_{2} \)
D. none of these
Subject: Chemistry
(1) 1,2 -dihydroxybenzene \( (\|) 1,3- \) dihydroxybenzene (III) \( 1,4^{-} \) dihydroxybenzene (IV) Hydroxybenzene The increasing order of boiling points of above-mentioned alcohols is:
A. \( I<I I<I I I<I V \)
в. \( I<I I<I V<I I I \)
c. \( I V<I<I I<I I I \)
D. \( I V<I I<I<I I I \)
Subject: Physics
A wheel has moment of inertia \( 5 x \)
\( 10^{-3} k g m^{2} \) and is making 20 rev/sec.
The torque needed to stop it in 10 sec is
\[
\mathbf{x} \mathbf{1 0}^{-\mathbf{2}} \mathbf{N}-\boldsymbol{m}:
\]
A . \( 2 \pi \)
в. \( 2.5 \pi \)
c. \( 4 \pi \)
D. \( 4.5 \pi \)
Subject: Biology
Which part of the atmosphere is called
homosphere?
A. Atmosphere up to \( 70 \mathrm{km} \) from the surface of the earth
B. Atmosphere up to \( 80 \mathrm{km} \) from the surface of the earth
C. Atmosphere up to \( 90 \mathrm{km} \) from the surface of the earth
D. Atmosphere up to \( 110 \mathrm{km} \) from the surface of the earth
Subject: Physics
Which of the following is the infrared wavelength?
A \( \cdot 10^{-4} \mathrm{cm} \)
B \( \cdot 10^{-5} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-6} c m \)
D. \( 10^{-7} \mathrm{cm} \)
Subject: Maths
Which of the following options is correct?
(1) Every integer and fraction is a rational number.
(2) A rational number \( \frac{p}{q} \) is positive if \( p \)
and \( q \) are either both positive or both negative.
(3) A rational number \( \frac{p}{q} \) is negative if one of \( p \) and \( q \) is positive and other is
negative.
(4) If there are two rational numbers
with same denominator, then the one
with the larger numerator is larger numerator is larger than the other.
A. Both 1 and 4 are incorrect
B. Both 2 and 3 are incorrect
c. only 1 is correct
D. All are correct
Subject: Physics
The edge of a cube is measured using a vernier callipers. \( [9 \) divisions of the main scale is equal to 10 divisions of vernier scale and 1 main scale division
is \( 1 \mathrm{mm} \) ]. The main scale division reading is 10 and 1 division of vernier scale was found to be coinciding with the main scale. The mass of the cube is
2.736 gm. Calculate the density in \( \mathrm{gm} / \mathrm{cm}^{3} \) up to correct significant figures.
Subject: Physics
A one litre sphere and a two litre sphere are connected with a capillary tube of negligible volume. They contain an ideal \( \operatorname{gas} \) at \( 27^{\circ} \mathrm{C} \) at a pressure of \( 100 \mathrm{cm} \) of \( \mathrm{Hg} \)
Keeping the temperature of one litre sphere constant at \( 27^{\circ} \mathrm{C} \), if
temperature of two litre sphere is
increased to \( 127^{0} \mathrm{C} \), then the final pressure
is
A. \( 110 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. 120 cm of Hg
c. \( 150 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. 200 cm of Hg
Subject: Physics
A person driving a car with a speed 72 \( \mathrm{km} / \mathrm{h}, \) suddenly sees a boy crossing the road. If the distance moved by a car, before the person applies brakes is \( 5 \mathrm{m} \) the reaction time of the person is:
A . 0.5 s
B. 0.10
\( c \cdot 10 s \)
D. 0.25 s
Subject: Physics
A body executes S.H.M. under the action of a force \( \boldsymbol{F}_{1} \) with a time period \( \mathbf{4} / \mathbf{5} \)
seconds. If the force is changed to \( \boldsymbol{F}_{2}, \) it
executes S.H.M. with a time period \( 3 / 5 \)
seconds. If both the forces \( F_{1} \) and \( F_{2} \) act
simultaneously in the same direction on the body, then its time period in seconds is:
A . \( 12 / 25 \)
в. \( 24 / 25 \)
c. \( 25 / 24 \)
D. 25/12
Subject: Physics
The declaration experienced by a moving motor boat, after its engine is cut-off is given by \( \frac{\mathrm{dv}}{\mathrm{dt}}=-\mathrm{kv}^{3} \) where \( \mathrm{k} \)
is constant If \( \mathbf{v}_{\mathbf{0}} \) is the magnitude of the velocity at cut-off, the magnitude of the velocity at a time \( t \) after the cut off is
\( A \cdot \frac{v_{0}}{2} \)
B . v
c. \( \mathrm{v}_{0} \mathrm{e}^{-\mathrm{ti}} \)
D. \( \frac{v_{0}}{\sqrt{\left(2 v_{v}^{2} \mathrm{kt}+1\right)}} \)
Subject: Physics
There is a uniform electrostatic field in
a region. The potential at various points on a small sphere central at \( P \), in the region, is found to vary between the limits \( 589.0 \mathrm{V} \) to \( 589.8 \mathrm{V} \). What is the
potential at a point on the sphere whose
radius vector makes an angle of \( 60^{\circ} \)
with the direction of the field?
A . \( 589.5 \mathrm{v} \)
B. \( 589.2 v \)
c. \( 589.4 \mathrm{v} \)
D. 589.6
Subject: Physics
Lets consider a thermodynamic system.
If \( \Delta U \) represents the increase in its
internal energy and \( W \) the work done by the system, which of the following statements is true?
A. \( \Delta U=-W \) is an adiabatic process
B. \( \Delta U=W \) in an isothermal process
c. \( \Delta U=-W \) in an isothermal process
D. \( \Delta U=W \) in an adiabatic process
Subject: Physics
The length of a simple pendulum is determined by measuring the length of thread / by meter scale and radius of bob r by Vernier callipers. The effective length \( L \) is obtained by adding the two i.e., \( \boldsymbol{L}=\boldsymbol{l}+\boldsymbol{r} . \) If \( \boldsymbol{l}=\mathbf{1 0 2 . 4} \mathrm{cm} \) and \( \boldsymbol{r}= \)
\( 2.24 \mathrm{cm}, \) how would you use quote \( L \) in proper significant figures?
\( A \cdot 104.64 \mathrm{cm} \)
B. 104.6 cm
\( c .105 \mathrm{cm} \)
D. \( 1.0464 \mathrm{cm} \)
Subject: Physics
The angles which the vector \( \vec{A}=3 \hat{i}+ \) \( 6 \widehat{j}+2 \widehat{k} \) makes with the co-ordinate
axes are:
A \( \cdot \cos ^{-1} \frac{3}{7}, \cos ^{-1} \frac{4}{7}, \cos ^{-1} \frac{1}{7} \)
B. \( \cos ^{-1} \frac{3}{7}, \cos ^{-1} \frac{6}{7}, \cos ^{-1} \frac{2}{7} \)
C \( \cdot \cos ^{-1} \frac{4}{7}, \cos ^{-1} \frac{5}{7}, \cos ^{-1} \frac{3}{7} \)
D. None of these
Subject: Physics
Assertion
Two cylinders, one hollow (metal) and the other solid (wood), with the same
mass and identical dimensions are
simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane
first.
Reason
By the principle of conversation of
energy the total kinetic energies of both the cylinders are identical when they
reach the bottom of the incline.
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
Twelve cells, each having an e.m.f of \( \mathrm{E} \)
volt are connected in series and are
kept in a closed box. Some of these cells
are wrongly connected with positive and negative terminals reversed. This 12 cell battery is connected in series with
an ammeter, an external resistance \( \mathrm{R} \)
ohms and a two-cell battery (two cells of the same type used earlier, connected perfectly in series). The current in the
circuit when the 12 -cell battery and 2 cell battery aid each other is \( 3 A \) and is
2A when they oppose each other. Then the number of cells in 12-cells
battery that are connected wrongly is:
A . 14
B. 3
\( c \cdot 2 \)
D.
Subject: Maths
If \( z_{1}, z_{2} \) are the complex numbers such
that \( \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| \) then arg \( z_{1}- \)
\( \arg z_{2} \) is
A . \( -\pi \)
в. \( \frac{-\pi}{2} \)
\( c \cdot 0 \)
D.
Subject: Physics
For an isochoric process the temperature
at which the pressure of a gas will be
double that of its pressure at \( 270^{0} \mathrm{C} \) is
A \( .543^{\circ} \mathrm{C} \)
B. \( 813^{0} \) C
\( c \cdot 3^{0} c \)
D. 270 \( ^{0} \) С
Subject: Maths
In the given figure, \( A B \| \) EF \( \| \) CD. If \( A B= \)
\( 22.5 \mathrm{cm}, \mathrm{EP}=7.5 \mathrm{cm}, \mathrm{PC}=15 \mathrm{cm} \) and DC
\( =27 \mathrm{cm} . \) Find \( \mathrm{AC} \)
\( A \cdot A C=37.5 \mathrm{cm} \)
B. AC = 22.5 cm
\( c \cdot A C=13.5 \mathrm{cm} \)
D. \( A C=27 \mathrm{cm} \)
Subject: Maths
\( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\cos \boldsymbol{x}-\sin \boldsymbol{x}}= \)
A. \( \frac{1}{\sqrt{2}} \log \left|\tan \left(\frac{x}{2}-\frac{\pi}{8}\right)\right|+c \)
в. \( \frac{1}{\sqrt{2}} \log \left|\tan \left(\frac{x}{2}+\frac{3 \pi}{8}\right)\right|+c \)
c. \( \frac{1}{\sqrt{2}} \log \left|\tan \left(\frac{x}{2}-\frac{3 \pi}{8}\right)\right|+c \)
D. \( \frac{1}{\sqrt{2}} \log \left|\cot \left(\frac{x}{2}\right)\right|+c \)
Subject: Physics
Find the components of vector \( \overrightarrow{\boldsymbol{a}}=\mathbf{3} \hat{\mathbf{i}}+ \)
\( 4 \hat{j} \) along the direction of vectors \( \hat{i}+\hat{j} \& \) \( \hat{\mathbf{i}}-\hat{\boldsymbol{j}} \)
A \( \cdot \frac{7}{2}(\hat{i}+\hat{j}),-\frac{1}{2}(\hat{i}-\hat{j}) \)
B \( \cdot \frac{1}{2}(\hat{i}+\hat{j}),-\frac{7}{2}(\hat{i}-\hat{j}) \)
c. \( \frac{-7}{2}(\hat{i}+\hat{j}),-\frac{1}{2}(\hat{i}-\hat{j}) \)
D \( \cdot \frac{7}{2}(\hat{i}+\hat{j}), \frac{1}{2}(\hat{i}-\hat{j}) \)
Subject: Maths
\( \int \frac{\boldsymbol{x}+\sqrt[3]{\boldsymbol{x}^{2}}+\sqrt[6]{\boldsymbol{x}}}{\boldsymbol{x}(1+\sqrt[3]{\boldsymbol{x}})} \boldsymbol{d} \boldsymbol{x} \) is equal to
A \( \cdot \frac{3}{2} x^{2 / 3}+6 \tan ^{-1} x^{1 / 6}+c \)
B. \( \frac{3}{2} x^{2 / 3}-6 \tan ^{-1} x^{1 / 6}+c \)
c. \( -\frac{3}{2} x^{2 / 3}+6 \tan ^{-1} x^{1 / 6}+c \)
D. None of these
Subject: Chemistry
The oxidation of \( S O_{2} \) by \( O_{2} \) to \( S O_{3} \) is an
exothermic reaction. The yield of \( \boldsymbol{S O}_{3} \)
will be increased for the exothermic
reaction if:
A. temperature is increases and pressure is kept constant
B. temperature is reduced and pressure is increased
c. both temperature and pressure are increses
D. both temperature and pressure are decreased
Subject: Maths
If the distances of \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) from \( \boldsymbol{A}(-1,5) \) and \( \boldsymbol{B}(\mathbf{5}, 1) \) are equal, then
A \( .2 x=y \)
в. \( 3 x=2 y \)
c. \( 3 x=y \)
D. \( 2 x=3 y \)
Subject: Biology
Examine the data showing the percent identity of the GAPDH gene and protein sequences between humans and the
three species shown below.
Species G
lo \( \begin{array}{ll}\text { Gene } & \text { Protein } \\ \text { ldentity } & \text { ldentity }\end{array} \)
99.6\% \( \quad 100 \% \) Chimpanzee
Fruit Fly 72.4\% 76.7\%
Roundworm \( 68.2 \% \) 74.3\%
Provide a possible reason for why the percent identity between gene sequences is lower than the percent identity of protein sequences.
A. Multiple codons code for the same amino acid
B. Introns are likely to have different sequences.
c. Differences in DNA sequences are edited when the mRNA is transcribed
D. Amino acids cannot be substituted without consequence
Subject: Maths
If \( a \) and \( b \) are two variables and \( (a, b)= \)
\( (b, a), \) then
\( \mathbf{A} \cdot a=0 \)
В. \( b=0 \)
\( \mathbf{c} \cdot a=b \)
\( \mathbf{D} \cdot a \pm b \)
Subject: Chemistry
Compound \( X \) react with sodium
phosphate in presence of conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{\boldsymbol{3}} \)
from a yellow ppt, than \( \boldsymbol{X} \) is:
A \( \cdot M n O_{4}^{2} \)
в. \( M o C l_{4} \)
c. \( M o O_{4}^{2} \)
D. \( A I O_{2}^{-} \)
Subject: Physics
Can you find at least one vector perpendicular to \( 3 \hat{i}-4 \hat{j}+7 \hat{k} ? \)
A \( \cdot \hat{i}+2 \hat{j}+\frac{6}{7} \hat{k} \)
B・ \( _{\hat{i}+2 \hat{j}}+\frac{5}{7} \hat{k} \)
\( \mathbf{c} \cdot \hat{i}+3 \hat{j}+\frac{5}{7} \hat{k} \)
D・ \( \hat{i}+2 \hat{j}+\frac{5}{6} \hat{k} \)