AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
"The final Agent Orange raid in Vietnam took place in 1970 areas
have begun to bloom in 1970. But 19
years after the war's end, it seem plain that Agent Orange is killing and maiming human beings, something it never intended to do. The apparent toxic fallout from those clouds \( _{---} \) is a crop
of human miseries including cancers, miscarriages and birth defects - that
may persist for decades." The offensive substance referred to in
this quotation is
A. A complex minute of DDT and other insecticides used as aerial sprays for protection against malaria and other tropical diseases
B. A complex mixture of herbicides and weedicides used to increase agricultural output in the South Vietnam under the U.S. aid programme
c. Dot used as an insecticide
D. Dioxin used as defoliants
Subject: Maths
A committee of 4 students is selected
at random from a group consisting of 8 boys and 4 girls. Given that there is at least one girl in the committee, the
probability that there are exactly 2 girls in the committee is
A \( \cdot \frac{168}{4558} \)
B. \( \frac{85}{99} \)
\( \mathbf{c} \cdot \frac{_{5}}{165} \)
D. \( \frac{14}{999} \)
Subject: Maths
In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good
in all three subjects. What is the number of students who are good in either Hindi or Mathematics but not in
English?
A . 99
в. 107
c. 125
D. 130
Subject: Biology
RNAI prevents translation of copies of
RNA that appear viral in nature.
Which of the following describes an
instance in which it would be beneficial
to insert a copy of a gene that would
trigger RNAi?
A. To improve immune response by producing more white blood cells
B. To reduce overgrowth of blood vessels in certain types of glaucoma
C. To develop a more vivid flower color by increasing pigment production.
D. To transform bacteria so they will produce specific proteins.
Subject: Maths
f \( \sin ^{-1}\left(\tan \frac{17 \pi}{4}\right)-\sin ^{-1}(\sqrt{\frac{3}{x}}) \)
\( \left(\frac{\pi}{6}\right)=0, \) then \( x \) is a root of the
equation
A \( \cdot x^{2}-x-6=0 \)
B . \( x^{2}+x-6=0 \)
c. \( x^{2}-x-12=0 \)
D. \( x^{2}+x-12=0 \)
Subject: Maths
If \( f(x)=\frac{x}{\sqrt{1-x^{2}}}, \) then \( (f o f)(x)= \)
A \( \cdot \frac{x}{\sqrt{1-x^{2}}} \)
в. \( \frac{x}{\sqrt{1-2 x^{2}}} \)
c. \( \frac{x}{\sqrt{1-3 x^{2}}} \)
D.
Subject: Chemistry
(A) Define the following terms:
(i) Limiting molar conductivity
(ii) Fuel cell
(B) Resistance of a conductivity cell filled with 0.1 mol \( L^{-1} \) KCl solution is
100\Omega. If the resistance of the same cell
when filled with 0.02 mol \( L^{-1} \) KCl
solution is \( 540 \Omega \), calculate the
conductivity and molar conductivity of 0.02 mol \( L^{-1} K C l \) solution. The
conductivity of 0.1 mol \( L^{-1} \) KCl solution is \( 1.29 \times 10^{-2} \Omega^{-1} \mathrm{cm}^{-1} \)
Subject: Chemistry
Which of the following reaction is an example of a redox reaction?
A. \( X e F_{2}+P F_{5} \rightarrow[X e F]^{+}+P F_{6} \)
в. \( X e F_{6}+H_{2} O \rightarrow X e O F_{4}+2 H F \)
c. \( X e F_{6}+2 H_{2} O \rightarrow X e O_{2} F_{2}+4 H F \)
D. \( X e F_{4}+O_{2} F_{2} \rightarrow X e F_{6}+O_{2} \)
Subject: Chemistry
Which of the following statements
concerning fluorine and chlorine is
incorrect?
A. Fluorine is more electronegative than chlorine
B. The atomic radius of the fluorine atom is less than
that of the chlorine atom.
C. Fluorine is stronger oxidizing agent than chlorine
D. Both fluorine and chlorine commonly exist in positive and negative oxidation states
E. Both fluorine and chlorine are diatomic gases at room conditions.
Subject: Physics
Calculate the total positive or negative
charge on a \( 3.11 g \) copper penny. Given
Avogadro number \( =6.02 \times 10^{23} \)
atomic number of copper \( =29 \) and
atomic mass of copper \( =\mathbf{6 3 . 5} \)
A \( \cdot 3.37 \times 10^{5} \mathrm{C} \)
B . \( 2.37 \times 10^{5} \mathrm{C} \)
c. \( 1.37 \times 10^{5} C \)
D. \( 0.37 \times 10^{5} C \)
Subject: Chemistry
The \( K_{a} \) values of \( C a C O_{3} \) and \( C a C_{2} O_{4} \)
in water are \( 4.7 \times 10^{-9} \) and \( 1.3 \times 10^{-9} \)
respectively, at \( 25^{\circ} \mathrm{C} \). If a mixture of
two is washed with \( H_{2} O, \) what is \( C a^{2+} \)
ion concentration in water?
A \( .7 .746 \times 10^{-5} \)
В. \( 5.831 \times 10^{-5} \)
c. \( 6.856 \times 10^{-5} \)
D. \( 3.606 \times 10^{-5} \)
Subject: Chemistry
The solubility product of \( P b B r_{2} \) is
\( K_{s p}=6.3 \times 10^{-6} \) at room temperature.
If \( 50 \mathrm{ml} \) of \( 0.02 M P b\left(N O_{3}\right)_{2} \) are mixed
with \( 50 \mathrm{ml} \) of \( 0.01 M C a B r_{2}, \) then
A. \( P b B r_{2} \) will precipitate and excess \( B r^{-} \) will remain in
B. \( C a\left(N O_{3}\right)_{2} \) will precipitate
c. \( P b B r_{2} \) will precipitate and excess \( P b^{2+} \) will remain in
D. no precipitate will form
Subject: Chemistry
Which is the volatile covalent liquid at
\( 25^{\circ} \mathrm{C} \) and 1 atm \( ? \)
\( A \cdot N_{2} \)
B. KI
\( c \cdot c c l_{4} \)
D. AgNO
E \( . \mathrm{caCO}_{3} \)
Subject: Physics
The mixture of \( X \) and \( Y \) were taken in a
condenser flask and were then heated.
After keepint it for cooling, crystals of \( Y \) were found on the walls of the flask and
X was present as such at the bottom of
flask. Identify \( X \) and \( Y: \)
A. \( X=N a C l, Y=K C l \)
B. \( X= \) Anthracene, \( Y= \) Naphthalene
c. \( X=N a C l, Y= \) Naphthalene
D. \( X= \)Anthracene, \( Y=N a C l \)
Subject: Maths
Let \( n \) be a positive integer and \( \Delta_{r}= \) \( \left|\begin{array}{ccc}2 r-1 & n & C_{r} & 1 \\ n^{2}-1 & 2^{n} & n+1 \\ \cos ^{2}\left(n^{2}\right) & \cos ^{2} n & \cos ^{2}(n+1)\end{array}\right| \) then
\( \sum_{r=0}^{n} \Delta_{r}=\dots \)
\( A \cdot 0 \)
B.
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
On strong heating, 3.64 g of a silver salt of an organic dibasic acid yield 2.16 g of silver. If the weight percentage of carbon in it is 8 times the weight
percentage of hydrogen and one-half the weight percentage of oxygen, then the molecular formula of the acid is:
[Atomic weight of \( \boldsymbol{A} \boldsymbol{g}=\mathbf{1 0 8}] \)
A \( \cdot C_{4} H_{6} O_{4} \)
в. \( C_{4} H_{6} O_{6} \)
\( \mathrm{c} \cdot C_{2} H_{6} \mathrm{O}_{2} \)
D. \( C_{5} H_{10} O_{5} \)
Subject: Chemistry
The energy of the electron in the first orbit of \( \boldsymbol{H} \boldsymbol{e}^{-} \) is \( -\mathbf{8 7 1 . 6} \times \mathbf{1 0}^{-\mathbf{2 0}} \quad \boldsymbol{J} . \) The
energy of the electron in the first orbit of hydrogen would be:
\( \begin{array}{ll}\text { A } . & -871.6 \times 10^{-20}\end{array} \)
B . \( -435 \times 10^{-20} J \)
c. \( -217.9 \times 10^{-20} \mathrm{J} \)
D. - \( 108.9 \times 10^{-20} \mathrm{J} \)
Subject: Physics
A liquid is flowing in a horizontal uniform capillary tube under a constant
pressure difference p. The value of pressure for which the rate of flow of the
liquid is doubled when the radius and length both are doubled, is
\( A \cdot \rho \)
в. \( \frac{3 \rho}{4} \)
c. \( \frac{\rho}{2} \)
D. \( \frac{\rho}{4} \)
Subject: Maths
If \( a+b+c=12 \) and \( a^{2}+b^{2}+c^{2}= \)
\( \mathbf{5 0} ; \) find
\( \boldsymbol{a} \boldsymbol{b}+\boldsymbol{b} \boldsymbol{c}+\boldsymbol{c} \boldsymbol{a} \)
\( \mathbf{A} \cdot 47 \)
B. 55
\( c \cdot 72 \)
D. 32
Subject: Chemistry
The optical rotation of the \( \alpha- \) form of
a pyramose is \( +150.7^{\circ}, \) that of the \( \beta- \)
form is \( +52.8^{\circ} . \) In solution an
equilibrium mixture of these anomers
has an optical rotation of \( +80.2^{\circ} . \) The percentage of the \( \alpha \) form in equilibrium
mixture is:
A . \( 28 \% \)
B. \( 32 \% \)
c. \( 68 \% \)
D. 72\%
Subject: Physics
Two stereo speakers are separated by a
distance of \( 2.4 \mathrm{m} . \) A person stands at a
distance of \( 3.2 \mathrm{m} \) as shown directly in
front of one of the speakers. Find the
frequencies in audible range for which
the listener will hear a minimum sound
intensity:

Speed of the sound in air is \( 320 m s^{-1} \)
\( \mathbf{A} \cdot 160(2 n+1) \)
B. \( 320(2 n+1) \)
\( \mathbf{c} \cdot 200(2 n+1) \)
D. \( 100(2 n+1) \)
Subject: Physics
A body projected vertically up has a displacement of \( 20 \mathrm{m} \) in the first ' \( \mathrm{n}^{\prime} \) seconds while it was moving up. Find its magnitude of displacement in the last n' seconds while falling down.
A. \( 40 \mathrm{m} \)
B. 10 \( m \)
\( c \cdot 20 m \)
D. 30 m
Subject: Chemistry
Assertion: The rate at which sugar
dissolves in water increases with
stirring
Reason: Stirring exposes the surface of a solute crystal to a less concentrated
layer of solution.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct
Subject: Physics
Resultant of two vectors \( \vec{P} \) and \( \vec{Q} \) is
inclined at \( 45^{\circ} \) to either of them. What
is the magnitude of the resultant?
\( \mathbf{A} \cdot \sqrt{P^{2}+Q^{2}} \)
B . \( \sqrt{P^{2}-Q^{2}} \)
\( c \cdot P+Q \)
D. \( P-Q \)
Subject: Maths
Which of the following relations are false?
This question has multiple correct options
A \( \cdot \tan \left|\tan ^{-1} x\right|=x \)
B . \( \cot \left|\cot ^{-1} x\right|=|x| \)
c. \( \tan ^{-1}|\tan x|=|x| \)
D \( \cdot \sin \left|\sin ^{-1} x\right|=|x| \)
Subject: Physics
How watt is related to the fundamental
units?
A \( \cdot \mathrm{kg} \mathrm{m}^{2} s^{-3} \)
B. \( \mathrm{kg} \mathrm{m}^{2} s^{-2} \)
\( \mathrm{c} \cdot \mathrm{Nm} s^{-1} \)
D. Nm
Subject: Chemistry
The equilibrium constant for a reaction
\( N_{2}(g)+O_{2}(G)=2 N O(g) \) is \( 4 \times 10^{-4} \)
at \( 2000 \mathrm{K} . \) In the presence of catalyst, the equilibrium constant is attained 10 times faster. The equilibrium constant in the presence of catalyst, at \( 2000 \mathrm{K} \) is
\( \mathbf{A} \cdot 40 \times 10^{-4} \)
В. \( 4 \times 10^{-4} \)
C \( .4 \times 10^{-2} \)
D. incomplete data
Subject: Physics
A physical parameter a can be determined by measuring the parameters b, \( c, d \) and e using the relation \( a=b^{\alpha} c^{\beta} d^{\gamma} e^{\delta} . \) If the maximum
errors in the measurement of \( b, c, d \) and
e are \( b_{1} \%, c_{1} \%, d_{1} \% \) and \( e_{1} \%, \) then find
the maximum error in the value of a
determined by the experiment.
Subject: Chemistry
Select incorrect statement:
A \( \cdot C l O_{2} \) and \( C l_{2} O \) are used as bleaching agents for paper pulp and textiles.
B. \( O C l^{-} \) (hypohalites) salts are used as detergent.
C . \( O C l^{-} \) disproportionates in alkaline medium.
D. \( B r O_{3}^{-} \) is oxidised to \( B r_{2} \) by \( B r^{-} \) in acidic medium.
Subject: Chemistry
Read the given observations for four elements \( \begin{array}{l}A_{1} P A_{2} \\ Z_{1} P, Z_{2}\end{array}, \begin{array}{l}A_{3} \\ Z_{3}\end{array} \boldsymbol{R} \) and \( A_{4} \)
\( Z_{4} S \)
carefully. Here Z represents atomic
number and A represents mass number.
(i) Elements P and R shows similar
chemical properties.
(ii) Elements \( Q \) and \( S \) belong to different
groups.
(iii) For elements \( \mathrm{P} \) and \( \mathrm{R}, Z_{1}=Z_{3} \) and
\( \boldsymbol{A}_{1} \neq \boldsymbol{A}_{3} \)
(iv) For elements \( \mathrm{Q} \) and \( \mathrm{S}, Z_{2} \neq Z_{4} \) and
\( \boldsymbol{A}_{2}=\boldsymbol{A}_{4} \)
Which of the following statements is
correct?
\( A . P \) and \( R \) are isobars while \( Q \) and \( S \) are isotopes
B. P and S are isobars while Q and R are isotopes
c. \( P \) and \( Q \) are isotopes while \( R \) and \( S \) are isobar
D. \( P \) and \( R \) are isotopes while \( Q \) and \( S \) are isobar
Subject: Physics
A body of mass \( 6 \mathrm{kg} \) is moving with uniform velocity along a straight line when a force of \( 12 \mathrm{N} \) is acting on it. If \( \boldsymbol{g}=\mathbf{1 0 m} \boldsymbol{s}^{-2}, \) find the frictional
force acting on the body.
\( A \cdot 6 N \)
B. 12 N
\( c \cdot 18 N \)
D. 24 N
Subject: Chemistry
Equal volumes of \( 0.1 M A g N O_{3} \) and
\( 0.2 M N a C l \) are mixed. The
concentration of \( N O_{3}^{-} \) ion in the mixture will be:
A . \( 0.1 M \)
B. \( 0.05 M \)
c. \( 0.2 M \)
D. 0.15 М
Subject: Maths
Consider the function \( \boldsymbol{y}= \)
\( \log _{a}(x+\sqrt{x^{2}+1}), a>0, a \neq 1 . \) The
inverse of the function
A. does not exist
B \cdot is \( x=\log _{a}(y+\sqrt{y^{2}+1}) \)
\( \mathbf{c} \cdot \) is \( x=\sin (y \ln a) \)
D \( \quad \) is \( x=\cosh \left(-y \ln \frac{1}{a}\right) \)
Subject: Physics
A particle moving horizontally. collides
perpendicularly at one end of a rod having equal mass and placed on a
smooth horizontal surface.
This question has multiple correct options
A. Particle comes to rest if collision is perfectly elastic and centre of rod starts to move with the same velocity
B. Particle continues to move along the same direction, whatever is the value of e.
C . Particle may get rebound back.
D. Velocity of mid-point of the rod will be less than \( v_{0} / 2 \) i the particle gets stuck.
Subject: Physics
A torque of \( 0.5 N m \) is required to drive a screw into a wooden frame with the help of a screw driver. If one of the two forces
of couple produced by screw driver is
\( \mathbf{5 0} N, \) the width of the screw driver is:
\( \mathbf{A} \cdot 0.5 \mathrm{cm} \)
B. \( 0.75 \mathrm{cm} \)
\( c \cdot 1 c m \)
D. \( 1.5 \mathrm{cm} \)
Subject: Physics
The conductor \( A D \) moves to the right in
a uniform magnetic field directed into the plane of the paper.
This question has multiple correct options
A. The free electron in \( A D \) will move toward \( A \)
B. Dd will acquire a positive potential with respect to
c. \( A \) current will flow from \( A \) to \( D \) in \( A D \) in closed loop
D. The current in \( A D \) flows from lower to higher potential
E. answer required
Subject: Physics
The escape velocity of a body thrown vertically upwards from the surface of
earth is
\( 11.2 \mathrm{Km} / \mathrm{s} . \) If it is thrown in a
direction making an angle of \( 30^{0} \) from the vertical, the new escape velocity will
be
\( \mathbf{A} \cdot 5.6 \mathrm{Km} / \mathrm{s} \)
B. \( 11.2 \mathrm{Km} / \mathrm{s} \)
c. \( 11.2 \times \sqrt{2} \mathrm{km} / \mathrm{s} \)
D. \( _{11.2} \times \frac{\sqrt{3}}{2} \mathrm{km} / \mathrm{s} \)
Subject: Maths
\( A B C \) is a right-angle triangle, right angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are \( 6 \mathrm{cm} \) and \( 8 \mathrm{cm} \) then radius of the circle is :
\( A \cdot 3 \mathrm{cm} \)
B. \( 2 \mathrm{cm} \)
\( c \cdot 4 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)
Subject: Chemistry
\( \mathrm{H}_{2} \mathrm{O} \) is a liquid where as \( \mathrm{H}_{2} \mathrm{S} \) is a gas.
This is due to
A. the molecular mass of \( \mathrm{H}_{2} \mathrm{S} \) is more than that of \( \mathrm{H}_{2} \mathrm{O} \)
B. the molecular mass of \( \mathrm{H}_{2} \mathrm{S} \) is less than that of \( \mathrm{H}_{2} \mathrm{O} \)
C . Presence of hydrogen bond in \( \mathrm{H}_{2} \mathrm{S} \)
D. absence of hydrogen bond in \( \mathrm{H}_{2} \mathrm{S} \)
Subject: Chemistry
Identify the correct statement from the
given alternatives.
A. Intra molecular hydrogen bonding is not found to occur in \( 2- \) hydroxy benzaldehyde
B. The boiling point of hydrogen iodide \( (H I) \) is more that hydrogen fluoride \( (H F) \)
C. The dipole moment of \( C H_{3} C l \) is not equal to zero
D. \( C H_{3} F \) has a larger dipole moment that \( C H_{3} C l \)
Subject: Physics
It is possible to project a particle with a given speed in two possible ways so
that it has the same horizontal range \( \boldsymbol{R} \) The product of the times taken by it in the two possible ways is
A \( \cdot \frac{R}{g} \)
в. \( \frac{2 R}{g} \)
c. \( \frac{3 R}{g} \)
D. \( \frac{4 R}{g} \)
Subject: Physics
liquid is kept on a table in a vacuum. The force exerted by the liquid on the
base of the flask is \( W_{1} \). The force exerted
by the flask on the table is \( W_{2} \)
This question has multiple correct options
A \( . W_{1}=W_{2} \)
\( \mathbf{B} \cdot W_{1}>W_{2} \)
c. \( W_{1}<W_{2} \)
D. The force exerted by the liquid on the walls of the flask
is \( \left(W_{1}-W_{2}\right) \)
Subject: Physics
A certain color of light towards the purple end of the visible spectrum has a
wavelength of 420 nm in a vacuum.
What is the frequency of this light? The speed of light in a vacuum is
\( 3.00 \times 10^{8} m / s \)
\( \mathbf{A} \cdot 126 H z \)
В . \( 1.26 \times 10^{11} \mathrm{Hz} \)
c. \( 7.1 \times 10^{14} \mathrm{Hz} \)
D. \( 1.4 \times 10^{-15} \mathrm{Hz} \)
E \( \cdot 1.4 \times 10^{-6} \mathrm{Hz} \)
Subject: Maths
If \( \alpha \) and \( \beta \) are zeroes of the polynomial \( 2 x^{2}+3 x+7 . \) Find a quadratic
polynomial whose zeroes are \( \frac{1}{\alpha^{2}} \& \frac{1}{\beta^{2}} \)
A \( \cdot 49 x^{2}+18 x+4 \)
B . \( 49 x^{2}-18 x+4 \)
c. \( 49 x^{2}-23 x-4 \)
D. \( 49 x^{2}-21 x+4 \)
Subject: Biology
Mark the incorrect statement.
A. The building blocks of lipids are amino acids.
B. Majority of enzymes contain a non-protein part called the prosthetic group.
C. The thylakoids are arranged one above the other like a stack of coins forming a granum.
D. Crossing-over occurs at pachytene stage of meiosis I.
E. Steroids are complex compounds commonly found in cell membranes and animal hormones.
Subject: Physics
For a common-emitter transistor, input
current is \( 5 \mu A, \beta=100 . \) Circuit is
operated at load resistance of \( 10 k \Omega \). The
voltage across collector emitter will be
A. \( 5 v \)
B. 10 \( v \)
c. \( 12.5 \mathrm{v} \)
D. 7.5 \( v \)
Subject: Maths
Consider a triangle \( A B C, \) whose vertical
\( \operatorname{are} A(-2,1), B(1,3) \) and \( C(x, y) \).ff \( C \) is
a moving point such that area of
\( \Delta A B C \) is constant,then locus of \( C \) is:
A. staight line
B. Circle
c. Ray
D. Parabola
Subject: Physics
A body moves in a plane so that the displacements along the \( x \) and \( y \) axes are given by \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}^{3} \) and \( \boldsymbol{y}=\mathbf{4} \boldsymbol{t}^{3} . \) The
velocity of the body is :
A \( .10 t \)
B . 15
\( c \cdot 15 t^{2} \)
D. \( 25 t^{2} \)
Subject: Chemistry
Turnbull's blue is:
\( \mathbf{A} \cdot F e_{3}\left[F e(C N)_{6}\right]_{2} \)
\( \mathbf{B} \cdot K_{4} F e(C N)_{6} \)
\( \mathbf{C} \cdot K_{3} F e(C N)_{6} \)
D. \( N a_{4} F e(C N)_{6} \)
Subject: Maths
Three numbers are chosen at random
withput replacement from \( \{1,2, \ldots, 15\} \)
Let \( E_{1} \) be the event that minimum of
the chosen numbers is 5 and \( E_{2} \) their
maximum is 10 then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot P\left(E_{1}\right)=\frac{9}{91} \)
\( ^{\mathrm{B}} \cdot P\left(E_{2}\right)=\frac{36}{455} \)
\( ^{\mathbf{C}} \cdot P\left(E_{1} \cap E_{2}\right)=\frac{4}{455} \)
\( P\left(E_{1} \mid E_{2}\right)=\frac{1}{9} \)
Subject: Physics
Magnitude of change of linear
momentum of the ball between \( t=0 \)
and \( t=t^{\prime}, t^{\prime} \) being the instant when the
ball hits the wall, is nearly
A. \( 3.2 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
в. \( 2.8 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 4.6 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. \( 1.4 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
Subject: Maths
If the line \( y=x \sqrt{3}-3 \) cuts the
parabola \( \boldsymbol{y}^{2}=\boldsymbol{x}+\boldsymbol{2} \) at \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) and if
\( A \) be the points \( (\sqrt{3}, 0), \) then \( A P . A Q \) is
A \( \cdot \frac{2}{3}(\sqrt{3}+2) \)
B. \( \frac{4}{3}(\sqrt{3}+2) \)
c. \( \frac{4}{3}(2-\sqrt{3}) \)
D. \( \frac{4}{6-3 \sqrt{3}} \)
Subject: Maths
If \( f(x)=|\cos x| \) then \( f^{\prime}\left(\frac{3 \pi}{4}\right) \) is equal to
\( ^{\mathbf{A}} \cdot-\frac{1}{\sqrt{2}} \)
в. \( \frac{1}{\sqrt{2}} \)
c. 1
D. None of these
Subject: Maths
If \( a, b \) are constants then, \( V a r(a+b X) \)
is
A. \( \operatorname{Var}(a)+\operatorname{Var}(X) \)
B. \( \operatorname{Var}(a)-\operatorname{Var}(X) \)
\( \mathbf{c} \cdot b^{2} \operatorname{Var}(X) \)
D. None of these
Subject: Chemistry
\( K_{c} \) for the synthesis of \( \mathrm{Hl}(\mathrm{g}) \) from \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
and \( I_{2}(g) \) is \( 50 . \) The degree of dissociation of HI is:
A . 0.10
B. 0.14
c. 0.18
D. 0.22
Subject: Physics
A particle is moving with velocity \( 5 \mathrm{m} / \mathrm{s} \) towards the east and its velocity changes to \( 5 \mathrm{m} / \mathrm{s} \) north in 10 sec. Find the acceleration.
A \( \cdot \sqrt{2} m / s^{2} \mathrm{N}-\mathrm{w} \)
B. \( \frac{1}{\sqrt{2}} m / s^{2} \) N-w
\( ^{\mathrm{c}} \cdot \frac{1}{\sqrt{2}} m / s^{2} \mathrm{N}-\mathrm{E} \)
D. \( \sqrt{2} m / s^{2} \) N-E
Subject: Chemistry
\( \mathrm{CoCl}_{3} \cdot 3 \mathrm{NH}_{3} \) does not form any
precipitate with excess \( A g N O_{3} \) solution, whereas 1 mole of
\( \mathrm{CoCl}_{3} \cdot 5 \mathrm{NH}_{3} \) gives two moles of \( \mathrm{AgCl} \)
with excess \( A g N O_{3} . \) The van't Hoff factor for both the compounds
respectively are:
A. 0 and 2
B. O and 3
\( c \cdot 1 \) and 3
D. 1 and 2
Subject: Physics
An electron is moving in \( 2^{n d} \) excited orbit of H-atom Radius of orbit in terms
of de-Broglie wavelength \( \lambda \) of electron can be given as
\( A \cdot \frac{\lambda}{\pi} \)
в. \( \frac{2 \lambda}{\pi} \)
c. \( \frac{3 \lambda}{2 \pi} \)
D. \( \frac{\lambda}{2 \pi} \)
Subject: Maths
Consider the linear inequations and
solve them graphically:
\( \mathbf{3} \boldsymbol{x}-\boldsymbol{y}-\mathbf{2}>\mathbf{0} ; \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{4} ; \boldsymbol{x}> \)
\( \mathbf{0} ; \boldsymbol{y} \geq \mathbf{0} \)
Which of the following are corner points of the convex polygon region of the
solution?
A. (0,0)
(年) \( 0,0,0,0,0,1, \)
B. (2,3)
c. (0,4)
(年. \( (0,4)) \)
D \( \cdot\left(\frac{3}{2}, \frac{5}{2}\right) \)
Subject: Maths
Draw the graph for the equation given below. Hence find the co-ordinates of
the points where the graph drawn meets the co-ordinate axes:
\( \frac{1}{3} x+\frac{1}{5} y=1 \)
\( \mathbf{A} \cdot(6,3) \) and (5,0)
B \( \cdot(3,5) \) and (2,0)
c. (3,0) and (0,5)
\( \mathbf{D} \cdot(2,0) \) and (0,7)
Subject: Maths
\( \operatorname{Show}\left|\begin{array}{ccc}\boldsymbol{a x} & \boldsymbol{b y} & \boldsymbol{c z} \\ \boldsymbol{x}^{2} & \boldsymbol{y}^{2} & \boldsymbol{z}^{2} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right|=\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{y} \boldsymbol{z} & \boldsymbol{z} \boldsymbol{x} & \boldsymbol{x} \boldsymbol{y}\end{array}\right| \)
Subject: Physics
A point moves on the \( x-y \) plane
according to the law \( x=a \sin \omega t \) and
\( \boldsymbol{y}=\boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\omega} \boldsymbol{t}) \) where \( \boldsymbol{a} \) and \( \boldsymbol{\omega} \) are
positive constants and \( t \) is in seconds.
Find the distance covered in time \( t_{0} \)
A \( . a \omega t_{0} \)
B. \( \sqrt{2 a^{2}+2 a^{2} \cos \omega t_{0}} \)
\( ^{\mathrm{C}} 2 a \sin \frac{\omega t_{0}}{2} \)
D. \( 2 a \cos \frac{\omega t_{0}}{2} \)
Subject: Physics
A mass \( \boldsymbol{m}=\mathbf{1 4 k g} \) performing \( \boldsymbol{S H} \boldsymbol{M} \) as
displacement, \( \boldsymbol{x}=(\mathbf{0 . 5 m}) \sin (\boldsymbol{6} \boldsymbol{t}+\boldsymbol{\pi}) \)
Determine maximum K.E. of the mass
during its motion \( (\text { in } \boldsymbol{J}) \)
A. \( \frac{7 \pi^{2}}{4} \)
B . 49
c. 63
D. Data insufficient
Subject: Chemistry
Which of the following orders is correct regarding the basicity of aliphatic amines?
A \( \cdot C H_{3} N H_{2}>\left(C H_{3}\right)_{2} N H>\left(C H_{3}\right)_{3} N \)
B . \( C H_{3} N H_{2}<\left(C H_{3}\right)_{2} N H<\left(C H_{3}\right)_{3} N \)
c. \( C H_{3} N H_{2}>\left(C H_{3}\right)_{2} N H<\left(C H_{3}\right)_{3} N \)
D. \( C H_{3} N H_{2}<\left(C H_{3}\right)_{2} N H>\left(C H_{3}\right)_{3} N \)