AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
\( A 2 k g \) copper block is heated to \( 500^{\circ} \mathrm{C} \) and then it is placed on a large block of
ice at \( 0^{\circ} \mathrm{C} \). If the specific heat capacity of copper is \( 400 \mathrm{J} / \mathrm{kg} / \mathrm{C} \) and latent heat of water is \( 3.5 \times 10^{5} J / k g . \) The amount
of ice that can melt is:
\( A \cdot 7 / 8 \mathrm{kg} \)
B. 7/5 kg
c. \( 8 / 7 \mathrm{kg} \)
\( D \cdot 5 / 7 \mathrm{kg} \)
Subject: Chemistry
One litre of \( C O_{2} \) ia passed through red hot coke. The volume become 1.4 litres
at same temperature and pressure The composition of product is
A. 0.8 litre of \( C O_{2} \) and 0.6 litre of \( C O \)
B. 0.7 litre of \( C O_{2} \) and 0.7 litre of \( C O \)
c. 0.6 litre of \( C O_{2} \) and 0.8 litre of \( C O \)
D. 0.4 litre of \( C O_{2} \) and 1.0 litre of \( C O \)
Subject: Physics
Two cells of emf \( E_{1} \) and \( E_{2} \) are to be
compared in a potentiometer \( \left(\boldsymbol{E}_{\mathbf{1}}>\boldsymbol{E}_{2}\right) \)
When be the cells are used in series
correctly, the balancing length obtained is \( 400 \mathrm{cm} . \) When they are used in series
but \( E_{2} \) is connected with reverse
polarities, then find the balancing length obtained is 200 of emf of cells....
Subject: Maths
If \( A \) and \( B \) are two mutually exclusive
events, then?
\( \mathbf{A} \cdot P(A) \leq P\left(B^{\prime}\right) \)
в. \( P(A) \leq P(B) \)
\( \mathbf{c} \cdot P(A) \geq P\left(B^{\prime}\right) \)
D. None of these
Subject: Biology
Q Type your question.
according to the balanced equation:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}+\boldsymbol{6} \boldsymbol{O}_{2}+\boldsymbol{3} \boldsymbol{0} \boldsymbol{A} \boldsymbol{D} \boldsymbol{P}+\boldsymbol{3} \boldsymbol{0} \boldsymbol{P}_{i} \rightarrow \)
\( 6 H_{2} O+6 C O_{2}+30 A T P \)
ATP is then hydrolyzed by cells for a variety of biochemical processes. Changes in free energy between glucose oxidation and ATP hydrolysis were compared. The table below illustrates the data collected:
Reaction Change in Free Energy \( (\triangle G \)
Glucose \( \quad-686 \mathrm{kcal} / \mathrm{mol} \)
Oxidation
ATP Hydrolysis
-13 kcal/mol
Which statement best explains the
data?
A. Both glucose oxidation and ATP hydrolysis, are exergonic because they have negative \( \triangle G \) values
B. Both glucose oxidation and ATP hydrolysis, are exergonic because their products have more free energy than their reactants
c. Both glucose oxidation and ATP hydrolysis, are endergonic because they have negative \( \triangle G \) values
D. Both glucose oxidation and ATP hydrolysis, are endergonic because their products have less free energy than their reactants
Subject: Physics
Two blocks \( A \) and \( B \), each of mass \( m \), are
connected by a massless spring of natural length L and spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring
at its natural length as shown in Fig. A
third identical block \( C \), also of mass \( m \)
moves on the floor with a speed \( \mathbf{v} \) along the line joining \( A \) and \( B \) and collides with \( A, \) then
This question has multiple correct options
A. The KE of the AB system at maximum compression of the spring is zero.
B. The KE of the AB system at maximum compression of the spring is \( (1 / 4) m v^{2} \)
c. The maximum compression of the spring is \( v \sqrt{\frac{m}{k}} \)
D. The maximum compression of the spring is \( v \sqrt{\frac{m}{2 k}} \)
Subject: Maths
Equation of two equal sides of a triangle are the lines \( 7 x-y+3=0 \) and \( x+ \)
\( y-3=0 \) and the third side passes
through the point \( (1,-10), \) then the equation of the third side can be
This question has multiple correct options
A . \( x-3 y=31 \)
B. \( 3 x+y+7=0 \)
c. \( x+3=0 \)
\( \mathbf{D} \cdot y=3 \)
Subject: Physics
\( \mathbf{4}_{\mathbf{1}} \boldsymbol{H}^{\mathbf{1}} \rightarrow_{\mathbf{2}} \boldsymbol{H} \boldsymbol{e}^{\mathbf{4}}+\mathbf{2} \boldsymbol{e}^{+}+\mathbf{2} \mathbf{6} \boldsymbol{M} \boldsymbol{e} \boldsymbol{V} \)
The above reaction represents
A. Fusion
B. Fission
c. \( \beta \) -decay
D. \( \gamma \) -decay
Subject: Physics
A gas thermometer measures the temperature from the variation of
pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure
measured at the triple point of water
find the melting point of lead.
\( \mathbf{A} \cdot 600 K \)
B. \( 420 K \)
\( \mathbf{c} .790 K \)
D. \( 510 K \)
Subject: Biology
Assertion
In India, IUDs like placement of copper-T is one of most widely accepted method of contraception.
Reason
Sterilisation, procedure in the male is called vasectomy.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
Pick the group which does not contain a neutral oxide.
A. \( N O_{2}, P_{4} O_{10}, A l_{2} O_{3}, N O \)
в. \( M g O, N_{2} O_{5}, S O_{3}, N_{2} O \)
\( \mathrm{c} \cdot \mathrm{CO}_{2}, \mathrm{SO}_{3}, \mathrm{CaO}, \mathrm{XeO}_{3} \)
D. \( C O, S i O_{2}, S n O_{2}, N a_{2} O_{3} \)
Subject: Physics
Magnetic flux during time interval \( \tau \) varies through a stationary loop of
resistance \( \boldsymbol{R}, \) as \( \boldsymbol{\phi}_{\boldsymbol{B}}=\boldsymbol{a} \boldsymbol{t}(\boldsymbol{\tau}-\boldsymbol{t}) . \) Find
the amount of heat generated during
that time. Neglect the inductance of the
loop.
\( ^{\text {A }} \cdot \frac{a^{2} \tau^{3}}{R} \)
в. \( \frac{a^{2} \tau^{2}}{2 R} \)
c. \( \frac{a^{2} \tau^{3}}{3 R} \)
D. \( \frac{a^{2} \tau^{3}}{4 R} \)
Subject: Physics
A thin plano-convex lens fits exactly into a thin plano-concave lens. Their plane surfaces are \( \mathrm{R} \), for to each other. If the lensps parpenoley of different materials of refractive indices \( \mu_{1} \) and
\( \mu_{2} \) and \( R \) is the radiuts of curvature of
the curved surfaces of the lenses, then the focal length of the combination is:
A \( \frac{R}{\mu_{2}-\mu_{1}} \quad \begin{array}{l}\text { Get } 30 \% \text { scholarship } \\ \text { onanysubscription }\end{array} \) LAST DAY
B. \( \frac{2 R}{\mu_{2}-\mu_{1}} \quad \) use cooe \( \quad \) FathER 30 DAY
C. \( \frac{R}{2\left(\mu_{1}-\mu_{2}\right)} \quad \) UPGRADE NOW
D. \( \frac{R}{2-\left(\mu_{1}+\mu_{2}\right)} \quad \) Web \( _{\text {ไingage }}^{\text {povereaby }} \)
Subject: Chemistry
1 L of \( 0.15 M H C l \) and 1 L of \( 0.3 M \)
\( H C l \) is given. What is the maximum
volume of \( 0.2 M H C l \) which one can
make from these two solutions? No
water is added.
\( \mathbf{A} \cdot 1.2 L \)
B. \( 1.5 L \)
c. \( 1.3 L \)
D. \( 1.4 L \)
Subject: Physics
A solid sphere of radius \( 20 \mathrm{cm} \) is
subjected to a uniform pressure of \( 10^{6} \)
\( N m^{-2} . \) If the bulk modulus is \( 1.7 \times \)
\( 10^{11} N m^{-2}, \) the decrease in the volume
of the solid is approximately equal to:
A \( \cdot 0.2 \mathrm{cm}^{3} \)
В. \( 0.3 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 0.4 \mathrm{cm}^{3} \)
D. \( 0.5 \mathrm{cm}^{3} \)
Subject: Maths
If \( \boldsymbol{x}=\frac{\mathbf{1}}{\mathbf{1}^{2}}+\frac{\mathbf{1}}{\mathbf{3}^{2}}+\frac{\mathbf{1}}{\mathbf{5}^{2}}+\ldots ., \boldsymbol{y}=\frac{\mathbf{1}}{\mathbf{1}^{2}}+ \)
\( \frac{3}{2^{2}}+\frac{1}{3^{2}}+\frac{3}{4^{2}}+\ldots \) and \( z=\frac{1}{1^{2}}- \)
\( \frac{1}{2^{2}}+\frac{1}{3^{2}}-\frac{1}{4^{2}}+\ldots ., \) then
A. \( x, y, z \) are in A.P.
B. \( \frac{y}{6}, \frac{x}{3}, \frac{z}{1} \) are in A.P.
c. \( \frac{y}{6}, \frac{x}{3}, \frac{z}{2} \) are in A.P
D. \( 6 y, 3 x, 2 z \) are in H.P
Subject: Chemistry
A balloon contains 14.0 L of air at 760
torr. What will be the volume of the
balloon when it is taken to a depth of 10 ft. in a swimming pool? Assume that the temperature of the air and water are equal. (Density: \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \mathrm{g} / \mathrm{mL} . \)
A . 47.5
B . 42.5
c. 44.5
D. 50
Subject: Maths
If \( I=\int \frac{d x}{\sqrt{(1-x)(x-2)}}, \) then \( I \) is
equal to
\( A \cdot \sin ^{-1}(2 x-3)+C \)
B. \( \sin ^{-1}(2 x+5)+C \)
\( c \cdot \sin ^{-1}(3-2 x)+C \)
D \( \cdot \sin ^{-1}(5-2 x)+C \)
Subject: Physics
A \( 1.5 m \) wide by \( 2.5 m \) long water bed
weighs \( 1025 N \). Find the pressure that
the water bed exerts on the floor.

Assume that the entire lower surface of
the bed makes contact with the floor.
A. \( 273.3 P a \)
в. \( 373.5 P a \)
\( \mathbf{c} .173 .3 P a \)
D. \( 473.3 P a \)
Subject: Maths
Sushant has a vessel, of the form of an inverted cone, open at the top, of height \( 11 c m \) and radius of top as \( 2.5 \mathrm{cm} \) and is
full of water. Metallic spherical balls each of diameter \( 0.5 \mathrm{cm} \) are put in the
vessel due to which \( \left(\frac{2}{5}\right) \) th of the water in the vessel flows out. Find how many
balls were put in the vessel. Sushant
made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by
Sushant?
Subject: Physics
Two identical rods are joined to form the shape of \( X \). the smaller angle between rods is \( \theta \). The moment of inertia of the
system about an axis passing through the point of intersection of the rod and perpendicular to their plane is
\( \mathbf{A} \cdot I \propto \theta \)
B. \( I \propto \sin ^{2} \theta \)
\( \mathbf{c} \cdot I \propto \cos ^{2} \theta \)
D. Independent of \( \theta \)
Subject: Maths
A company has two plants to manufacture televisions. The plant
manufacture \( 70 \% \) of televisions and
plant II manufacture \( 30 \% . \) At plant 1,80 \( \% \) of the televisions are rated as of
standard quality and at plant II, \( 90 \% \) of
the televisions are rated as of standard
quality. A television is chosen at random and is found to be of standard
quality. The probability that it has come from plant II is
Subject: Biology
Study given chart and select the option
which incorrectly identifies any of the
animals, \( P, Q, R \) and \( S \)
A. P is Aurelia and Q is Ascaris
B. Q is Ascaris and R is Nereis
C. \( R \) is Ascaris and \( S \) is Cockroach
D. S is Periplaneta and P is Spongilla
Subject: Physics
Assertion
Liquids and gases are largely incompressible and densities are therefore, nearly constant at all
pressures.
Reason
Liquids exhibits large variation in
densities with pressure but gases do
not.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Chemistry
\( \boldsymbol{R}-\underset{\boldsymbol{O}}{\|}-\boldsymbol{C l} \frac{\boldsymbol{H}_{2}}{\boldsymbol{P} \boldsymbol{d}-\boldsymbol{B a S O}_{4}} \boldsymbol{P} \)
In the following reaction, product ' \( P \) ' is
A \( \cdot R C H_{2} O H \)
в. \( R C O O H \)
c. \( R C H O \)
D. \( R C H_{3} \)
Subject: Maths
What is the mode from the following
table \( ? \)
\( \begin{array}{ll}\text { Marks obtained } & \text { Frequency } \\ & \\ 3 & 7 \\ 1 & 11 \\ 23 & 15 \\ 33 & 8 \\ 43 & 3\end{array} \)
\( \mathbf{A} \cdot 13 \)
B. 43
c. 33
D. 23
Subject: Physics
A body is gently on a conveyor belt moving \( 3 \mathrm{m} / \mathrm{s} \). If \( \mu=0.5 \) how far will the body move relative to the belt befour
coming to rest \( ?\left(g=10 \mathrm{m} / \mathrm{s}^{2}\right) \)
\( A \cdot 0.3 \mathrm{m} \)
B. 0.6 \( m \)
c. \( 0.9 \mathrm{m} \)
D. \( 0.8 \mathrm{m} \)
Subject: Physics
A broad source of light \( (1=680 \mathrm{nm}) \) illuminates normally two glass plates \( 120 \mathrm{mm} \) long that touch at end and are separated by a wire \( 0.048 \mathrm{mm} \) in diameter at the other end. The total
number of bright fringes that appear over the \( 120 \mathrm{mm} \) distance is:
A . 50
B. 100
\( c \cdot 141 \)
D. 400
Subject: Chemistry
Which of the following bond angles are
correct?
A. Ammonia : 107 \( ^{\circ} \); methylamine : \( 108^{\circ} \)
B. Ammonia : \( 108^{\circ} \); methylamine : 107 \( ^{\circ} \)
C. Ammonia : 107 \( ^{\circ} \); methylamine : \( 110^{\circ} \)
D. Ammonia : \( 110^{\circ} \); methylamine : 105 \( ^{\circ} \)
Subject: Physics
In a meter bridge experiment the null deflection is obtained at a length of 25cm. When a standard resistance of 5
ohm is employed. The value of resistance in the left gap is
A . \( 2 \Omega \)
B. \( 1.66 \Omega \)
\( c \cdot 4 \Omega \)
D. \( 1.2 \Omega \)
Subject: Maths
ff \( y=4 x-5 \) is a tangent to the curve
\( \boldsymbol{y}^{2}=\boldsymbol{p} \boldsymbol{x}^{3}+\boldsymbol{q} \) at \( (\boldsymbol{2}, \boldsymbol{3}), \) then \( (\boldsymbol{p}+\boldsymbol{q}) \) is
equal to
A . -5
B. 5
\( c .-9 \)
D.
E .
Subject: Physics
Two simple harmonic motions are
denoted as \( \mathbf{S}_{1} \) and \( \mathbf{S}_{2} \) as below
\( \mathbf{S}_{1}: \mathbf{x}=\mathbf{6} \sin ^{2} \boldsymbol{\pi} \boldsymbol{t} \)
\( \mathbf{S}_{2}: \mathbf{x}(\boldsymbol{x}-\mathbf{2})=\cos \mathbf{3} \boldsymbol{\pi} \boldsymbol{t} \)
where \( x \) is displacement (In \( c m \) ) and \( t \) is time (In second)
Subject: Maths
For the conic \( 9 x^{2}-16 y^{2}+18 x+ \)
\( 32 y-151=0, \) find \( e \)
A \( \cdot \frac{5}{4} \)
в. \( \frac{4}{5} \)
\( c \cdot \frac{1}{2} \)
D. None of these
Subject: Chemistry
Complete and balance the following chemical equations:
(i) \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+\boldsymbol{K} \boldsymbol{I}+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \)
\( t \)
(ii) \( K_{2} C r_{2} O_{7}+H_{2} S O_{4}+H_{2} S \rightarrow \)
(iii) \( K M n O_{4}+H_{2} S O_{4}+F e S O 4 \rightarrow \)
Subject: Chemistry
\( 1 \times 10^{-3} \) mole of \( H C l \) is added to a
buffer solution made up of \( 0.01 M \)
acetic acid and \( 0.10 M \) sodium acetate.
The final pH of the buffer will be: (given
\( \boldsymbol{p} \boldsymbol{K}_{a} \) of acetic acid is \( \boldsymbol{4} . \boldsymbol{7} \boldsymbol{5} \) at \( \boldsymbol{2} \boldsymbol{5}^{\boldsymbol{o}} \boldsymbol{C} \boldsymbol{)} \)
A . 4.60
B. 4.66
c. 4.75
D. 4.8
Subject: Physics
A missile of mass \( M \) moving with velocity \( v=200 m / s \) explodes in midair
breaking into two parts of mass \( M / 4 \) and \( 3 M / 4 . \) If the smaller piece flies off
at an angle of \( 60^{\circ} \) with respect to the original direction of motion with an initial speed of \( 400 \mathrm{m} / \mathrm{s} \), what is the magnitude and direction of the initia
velocity of the other piece.
Subject: Chemistry
The following acids have been arranged in order of decreasing acid strength. Identify the correct order \( \mathrm{ClOH}(\mathrm{l}) \) \( \mathrm{BrOH}(\mathrm{II}), \mathrm{IOH}(\mathrm{III}) \)
B. ॥>1>111
\( c \cdot\|\mid>\|>1 \)
Subject: Maths
n fig, chord \( A B \| C D \) of a circle
with centre \( O \) and radius 5 cm such
that \( A B=6 \mathrm{cm} \) and \( C D=8 \mathrm{cm} . \) if \( O P \)
\( \perp A B, O Q . \perp C D, \) then \( P Q \) in cm is
\( \mathbf{A} \cdot 4 \mathrm{cm} \)
\( \mathbf{B} \cdot 7 \mathrm{cm} \)
\( c \cdot 1 \mathrm{cm} \)
D. \( 3 \mathrm{cm} \)
Subject: Maths
If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right], \boldsymbol{i}, \boldsymbol{j}=1,2 \) where \( \boldsymbol{a}_{i j} \) is
defined as \( a_{i j}=i^{2}+j^{2} \) then write the
sum of the elements of the matrix \( \boldsymbol{A} \)
Subject: Physics
A given resistor has the following colour scheme of the various strips on it:
Brown, black, green and silver. Its value in ohm is :
A \( \cdot 1.0 \times 10^{4} \pm 10 \% \)
В. \( 1.0 \times 10^{5} \pm 10 \% \)
C. \( 1.0 \times 10^{6} \pm 10 \% \)
D. \( 1.0 \times 10^{7} \pm 10 \% \)
Subject: Physics
An iron rod of length \( 2 \mathrm{m} \) and cross sectional area of \( 50 \mathrm{mm}^{2} \) stretched by
0.5mm, when a mass of 250 kgis hung from its lower end. Young's modulus of
iron rod is
\( \mathbf{A} \cdot 19.6 \times 10^{20} N / m^{2} \)
B . \( 19.6 \times 10^{18} N / m^{2} \)
C \( \cdot 19.6 \times 10^{10} N / m^{2} \)
D. \( 19.6 \times 10^{15} N / m^{2} \)
Subject: Physics
The distance traveled by 5 identical particle is given below in the options \( A \) B, \( C, D \) and \( E \) respectively at specific time interval. Which object is moving with a constant velocity?
в. \( 2 m, 2 m, 4 m 4 m, 6 m \)
\( \mathbf{c} .2 m, 4 m, 6 m, 8 m, 10 m \)
D. \( 6 m, 11 m, 15 m, 18 m, 20 m \)
E. \( 4 m, 9 m, 15 m, 22 m, 29 m \)
Subject: Chemistry
The equilibrium constant for the
reaction \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightleftharpoons \)
\( C O_{2}(g)+H_{2}(g) \) is 3 at \( 500 K . \ln a 2 \)
litre vessel \( 60 \mathrm{gm} \) of water gas
[equimolar mixture of \( \left.\mathrm{CO}(\mathrm{g}) \text { and } \boldsymbol{H}_{2}(\boldsymbol{g})\right] \)
and \( 90 \mathrm{gm} \) of steam is initially taken.
What is the equilibrium concentration of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) at equilibrium (mole/L)?
A . 1.75
в. 3.5
\( c \cdot 1.5 \)
D. 0.75
Subject: Maths
In a certain town, \( 25 \% \) families own a
phone and \( 15 \% \) own a car, \( 65 \% \) families
own neither a phone nor a car. 2000 families own both a car and a phone. Consider the following statements in this regard.
1) \( 10 \% \) families own both a car and a
phone
Il) \( 35 \% \) families own either a car or a
phone
III) 40,000 families live in the town.
Which of the above statements are
correct ?
A . \( I \& I I \)
в. I \& III
c. II \& III
D. I,II \& III
Subject: Physics
In one second, a particle goes from
point \( A \) to point \( B \) moving in a semicircle. Find the magnitude of the
average velocity.
\( A \cdot 1 \mathrm{m} / \mathrm{s} \)
B. 2 m/s
c. \( 0.5 \mathrm{m} / \mathrm{s} \)
D. None of the above
Subject: Chemistry
\( \ln \) a system \( \boldsymbol{A}(\boldsymbol{s}) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g})+\boldsymbol{3} \boldsymbol{C}(\boldsymbol{g}) \)
the concentration of \( C \) at equilibrium is
increased by a factor \( 2, \) it will cause the equilibrium concentration of \( B \) to change to:
A. two times of its original value
B. one half of its original value
c. \( 3 \sqrt{2} \) times of its original value
D. \( \frac{1}{2 \sqrt{2}} \) times of its original value
Subject: Chemistry
The geometries of the ammonia
complexes of \( N i^{2+}, P t^{2+} \) and \( Z n^{2+} \)
respectively, are:
A. octahedral, square planar and tetrahedral
B. square planar, octahedral and tetrahedral,
C . tetrahedral, square planar and octahedral
D. octahedral, tetrahedral and square planar
Subject: Physics
Rohan wants to test whether a white
object or a black object would heat up faster in the Sun. The given picture shows you his experiment. These thermometers were left out in the Sun
for 30 minutes.

Which of the following statements is
true?
A. Thermometer 1 reads the same as thermometer
B. Thermometer 2 shows a higher temperature than thermometer
c. Thermometer 3 shows a higher temperature than thermometer
D. Thermometer 1 reads the same as thermometer
Subject: Biology
Assertion
Contraceptive pills are rich in only
progesterone and estrogen.
Reason
This will stop menstrual cycle for
Sometime.
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: Maths
Show that the points \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{2},-\boldsymbol{4}), \boldsymbol{B}(\boldsymbol{5}, \boldsymbol{4},-\boldsymbol{6}) \) and
\( C(9,8,-10) \) are collinear, find the ratio in which \( B \) divides \( \overline{A C} \).
Subject: Physics
In a Geiger Marsden experiment, calculate the distance of closest
approach to the nucleus of \( Z=\mathbf{7 5} \)
when an \( \alpha \) -particle of \( 5 M e V \) energy impinges on it before it comes momentarily to rest and reverse its direction.
How will the distance of closest
approach be affected when the kinetic energy of the \( \alpha \) -particle is doubled?
Subject: Maths
The slope of one of the lines given by \( a x^{2}+2 h x y+b y^{2}=0 \) is \( k \) times the
other, then
A \( \cdot 4 k^{2} h=a b(1+k) \)
B . \( k h^{2}=4 a b(1+k)^{2} \)
C. \( k h^{2}=2 a b(1+k)^{2} \)
D. \( 4 k h^{2}=a b(1+k)^{2} \)
Subject: Physics
Average torque on a projectile of mass
\( m, \) initial speed \( u \) and angle of
projection \( \theta \) between initial and final positions \( \mathrm{P} \) and \( \mathrm{Q} \) as shown in the figure about the point of projection is:
A \( \cdot \frac{m u^{2} \sin 2 \theta}{2} \)
в. \( m u^{2} \cos \theta \)
c. \( \mu^{2} \sin \theta \)
D. \( \frac{m u^{2} \cos \theta}{2} \)
Subject: Chemistry
The correct order of magnitude of bond
angles among the compounds \( \boldsymbol{C H}_{4} \)
\( N H_{3} \) and \( H_{2} O \) is:
A. \( C H_{4}>H_{2} O<N H_{3} \)
B. \( H_{2} O<N H_{3}<C H_{4} \)
c. \( N H_{3}<C H_{4}<H_{2} O \)
D. \( N H_{3}<H_{2} O<C H_{4} \)
Subject: Chemistry
When \( C O_{2} \) dissolves in water, the
following equilibrium is establishes, \( \boldsymbol{C O}_{2}+\mathbf{2 H}_{\mathbf{2}} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}_{3} \boldsymbol{O}^{+}+\boldsymbol{H} \boldsymbol{C O}_{3}^{-}, \) for
which the equilibrium constant is
\( 3.8 \times 10^{-7} \) and \( p H=6.0 . \) The ratio of
\( \left[\boldsymbol{H} \boldsymbol{C O}_{3}^{-}\right] /\left[\boldsymbol{C O}_{2}\right] \) is
A . \( 3.8 \times 10^{-18} \)
в. 3.8
c. 0.38
D. 13.8
Subject: Physics
A long straight cable of length I is placed symmetrically along z-axis and has radius \( a(<<l) \). the cable consists
of a thin wire and co-axial conducting tube. An alternating current I(t) =
\( I_{0} \sin (2 \pi \nu t) \) flows down the central
thin wire and returns along the co-axial
conducting tube. The induced electric field at a distance s from the wire inside
the cable is \( E(s, t)= \) \( \mu_{0} I_{0} \cos (2 \pi \nu t) \ln \left(\frac{s}{a}\right) \hat{k} ., \) the ratio of
conduction current and displacement
current is
A \( \cdot\left(\frac{a \pi}{\pi}\right)^{2} \)
B \cdot \( \left(\frac{a \pi}{\lambda}\right) \)
\( ^{c} \cdot\left(\frac{\lambda}{a \pi}\right)^{2} \)
D \( \cdot\left(\frac{\lambda}{a \pi}\right) \)
Subject: Physics
A car is moving with a velocity of \( 10 \mathrm{m} / \mathrm{s} \) The driver sees a wall ahead of him and
applied brakes. The car stops after
covering \( 10 m \) distance. If the car was
moving with a speed pf \( 20 m s^{-1}, \) it
would have stopped in \( 30 m \) distance. The reaction of the driver is
A . \( 0.5 s \)
B. \( 0.6 s \)
\( c .0 .7 s \)
D. \( 1 s \)
Subject: Maths
Let \( f \) and \( g \) be differential functions
satisfying \( \boldsymbol{g}^{\prime}(\boldsymbol{a})=\mathbf{2}, \boldsymbol{g}(\boldsymbol{a}) \boldsymbol{b} \) and \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{g}=\boldsymbol{I} \)
(identify function) then \( \boldsymbol{f}^{\prime}(\boldsymbol{b})= \)
A \( \cdot 1 / 2 \)
B . 2
\( c \cdot 2 / 3 \)
D. None of these
Subject: Chemistry
A quantity of electrical charge that brings about the deposition of \( 4.5 g A l \)
from \( A l^{3+} \) at the cathode will also
produce the following volume at \( (\boldsymbol{S T P}) \)
of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \) from \( \boldsymbol{H}^{+} \) at the cathode
A . \( 44.8 L \)
B. 22.4 L
c. \( 11.2 L \)
D. \( 5.6 L \)
Subject: Chemistry
The increasing order of base strength of
\( \boldsymbol{C l}^{-} \boldsymbol{C H}_{3} \boldsymbol{C O O}^{-},^{-\boldsymbol{O H}} \) and \( \boldsymbol{F}^{-} \) is
A \( \cdot C l^{-}<F^{-}<C H_{3} C O O^{-}<^{-} O H \)
в. \( C l^{-}>F^{-}>C H_{3} C O O^{-}>^{-} O H \)
c. \( C H_{3} C O O^{-}<C l^{-}<F^{-}<^{-} O H \)
D. None of these
Subject: Physics
The intensity of gamma radiation from
a given source is \( l . \) On passing through \( 36 m m \) of lead, it is reduced to \( l / 8 . \) The thickness of lead which will reduce the
intensity to \( l / 2 \) will be:
\( \mathbf{A} \cdot 18 m m \)
B. \( 12 m m \)
\( \mathbf{c} .6 m m \)
\( \mathbf{D} \cdot 9 m m \)