AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \vec{a}=\hat{i}+\hat{j}-\hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+2 \hat{k} \& \)
\( \vec{c}=-\hat{i}+2 \hat{j}-\hat{k}, \) find a unit vectors normal to the vectors \( \vec{a}+\vec{b} \) and \( \vec{b}+\vec{c} \).
\( ^{\mathbf{A}} \cdot \frac{-\hat{i}-2 \hat{j}+6 \hat{k}}{\sqrt{40}} \)
B. \( \frac{-\hat{i}-2 \hat{j}+6 \hat{k}}{\sqrt{41}} \)
c. \( \frac{\hat{i}-2 \hat{j}+6 \hat{k}}{\sqrt{41}} \)
D. \( \frac{-\hat{i}+2 \hat{j}+6 \hat{k}}{\sqrt{41}} \)
Subject: Chemistry
A solution containing 10 g per \( \mathrm{dm}^{3} \) of urea (m.w. = 60) is isotonic with a 5\%
solution of a non-volatile solute. The
molecular mass of this non-volatile
solute is:
A . \( 250 \mathrm{g} \mathrm{mol}^{-1} \)
B . 300 g mol-
c. \( 350 \mathrm{g} \) mol \( ^{-1} \)
D. \( 200 \mathrm{g} \mathrm{mol}^{-1} \)
Subject: Physics
A ray of light passes through an equilateral prism (refractive index \( = \)
1.5) such that the angle of incidence is
equal to the angle of emergence and the latter is equal to \( 3 / 4 \) th the angle of the prism. The angle of deviation is:
A \( .20^{\circ} \)
B. \( 39^{\circ} \)
c. \( 5^{\circ} \)
D. \( 30^{\circ} \)
Subject: Physics
Find the distance scovered by the
particle during the first 4.0 and \( 8.0 s \)
A. \( 3 c m \)
B. \( 5 \mathrm{cm} \)
\( \mathrm{c} \cdot 10 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)
Subject: Chemistry
The correct order for reducing nature of
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) is :
A. \( H_{3} P O_{2}<H_{3} P O_{3}<H_{3} P O_{4} \)
в. \( H_{3} P O_{4}<H_{3} P O_{3}<H_{3} P O_{2} \)
c. \( H_{3} P O_{3}<H_{3} P O_{4}<H_{3} P O_{2} \)
D. \( H_{3} P O_{4}<H_{3} P O_{2}<H_{3} P O_{3} \)
Subject: Maths
If \( f(x) \) is the integral of \( \frac{2 \sin x-\sin 2 x}{x^{3}}, x \neq 0 . \) Find
\( \lim _{x \rightarrow 0} f^{\prime}(x), \) where \( f^{\prime}(x)=\frac{d f(x)}{d x} \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
\( D \)
Subject: Maths
A real valued function \( f(x) \) satisfies the functional equation \( \boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y})-\boldsymbol{f}(\boldsymbol{a}-\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{a}+\boldsymbol{y}), \) where \( \boldsymbol{a} \)
is a given constant and \( f(0)=1, \) then
A. \( f(2 a-x)=f(x), f(x) \) is symmetric about \( x=a \)
B. \( f(2 a-x)=0=f(x), f(x) \) is symmetric about \( x=a \)
c. \( f(2 a-x)+f(x)=0, f(x) \) is not symmetric about \( x= \)
D. \( f(x)=0, f(x) \) is symmetric about \( x=a \)
Subject: Chemistry
The oxidation number of underlined
element in \( \left[\boldsymbol{F e}(\boldsymbol{N O})\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}\right] \boldsymbol{S} \boldsymbol{O}_{4} \)
compound is :
\( A \cdot+1 \)
B. +3
\( c .+5 \)
D. None of these
Subject: Physics
A maglev train is gradually taking a \( 45^{\circ} \) turn while moving with constant-speed
of \( \pi m s^{-1} . \) For a special compartment
of train, turning process takes \( 220 m \) length on the track. Magnitude of centripetal acceleration of the train is:
A \cdot Is constant and \( \frac{\pi}{88} m s^{-2} \) (approximately)
B. Is variable
c. zero, as speed is constant
D. Either (2) or (3)
Subject: Biology
Assertion
TIBA \( (2,3,5 \) -triiodobenzoic acid) functions as antiauxin.
Reason
It blocks transport of auxin.
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
Value of
\( \lim _{x \rightarrow 0} \frac{x+2 \sin x}{\sqrt{x^{2}+2 \sin x+1}-\sqrt{x-\sin ^{2} x}} \)
is
\( A \cdot 2 \)
B.
\( c \cdot 6 \)
D. - 2
Subject: Maths
Let \( A \) be a real matrix such that \( A^{67}= \)
\( A^{-1}, \) then
\( \mathbf{A} \cdot|A|=\pm 1 \)
B . \( |A|=1 \)
C. \( A=I, I \) being unit matrix
D. \( A \) is diagonal matrix
Subject: Physics
A small satellite revolves around a
planet in an orbit just above planet's surface. Taking the mean density of the planet \( 8000 \mathrm{kg} m^{-3} \) and \( G=6.67 \times \)
\( 10^{-11} \mathrm{N} m^{-2} / k g^{-2}, \) find the time period
of the satellite.
Subject: Chemistry
The maximum number of \( 90^{\circ} \) angles
between bond pair of electrons is
observed in:
A. \( d s p^{2} \) hybridization
B. \( s p^{3} d \) hybridization
c. \( d s p^{3} \) hybridization
D. \( s p^{3} d^{2} \) hybridization
Subject: Physics
An ac generator consists of a coil of 200 turns, \( 100 \mathrm{cm} \) in diameter. If the coil
rotates at 500 rpm in a magnetic field of \( 0.25 \mathrm{T} \), then the maximum induced
emf
A . 20.6 \( v \)
B. 51.7
c. 4.1
D. None of the above
Subject: Physics
A particle is projected vertically upwards and it attains maximum
height \( \boldsymbol{H} . \) If the ratio of times to attain
height \( h(h<H) \) is \( 1 / 3, \) then \( h \) equals
\( A \cdot 2 / 3 H \)
B. 3H
c. 5/9. म
D. 3/.
Subject: Chemistry
Correct arrangement of the following
acids in correct \( \boldsymbol{K}_{3} \) order is :
\( (\boldsymbol{I}) \boldsymbol{H} \mathbf{3} \boldsymbol{N} \oplus \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C O O H}(\boldsymbol{I I}) \boldsymbol{N C C H} \mathbf{2 C} \)
A \( .|>||>|||>|V| \)
\( V \)
B. || >|>॥|> |V
c. \( |>|||>||>\mid V \)
D. IV>||| > || > |
Subject: Chemistry
Study the following table.
Compound Compound Mass of the wmpound Compound Mass
(mol. mass)
\( C O_{2}(44) \) 4.4
॥. \( N O_{2}(46) \) 2.3
\( \| \)
\( H_{2} O_{2}(34) \) 6.8
\( V \)
\( S O_{2}(64) \)
Which two compounds have least mass
of oxygen? (Molecular masses of compounds are given in brackets)
A. II and IV
B. I and III
c. I and II
D. III and IV
Subject: Maths
If \( \frac{\boldsymbol{S}-\boldsymbol{8}}{\boldsymbol{3}}=\frac{\boldsymbol{S}-\boldsymbol{3}}{\boldsymbol{2}}, \) then the value of \( \boldsymbol{S} \) is
\( \mathbf{A} \cdot \mathbf{5} \)
B. -7
\( c \cdot 7 \)
D. None of these
Subject: Chemistry
Which of the following statements on the atomic wave function \( \Psi \) is not
correct?
A. \( \Psi \) may be a real valued wave function
B. \( \Psi \) may be in some cases be a complex function
c. \( \Psi \) has a mathematical significance only
D. \( \Psi \) is proportional to the probability of finding an electron
Subject: Maths
For two events \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) if \( \boldsymbol{p}(\boldsymbol{A})= \)
\( \boldsymbol{p}(\boldsymbol{A} \mid \boldsymbol{B})=\frac{1}{4} \) and \( \boldsymbol{p}(\boldsymbol{B} \mid \boldsymbol{A})=\frac{1}{2}, \) then
\( P\left(\frac{\bar{B}}{\bar{A}}\right)=\frac{m}{n} \) where \( m+n= \)
Subject: Physics
What is \( \mu_{\max } \) equal to?
A \( \cdot \mu_{\max } \approx 1.0 \times 10^{4} \)
B . \( \mu_{\max } \approx 2.0 \times 10^{4} \)
C \( \cdot \mu_{\max } \approx 1.0 \times 10^{3} \)
D. \( \mu_{\max } \approx 2.0 \times 10^{3} \)
Subject: Chemistry
Which one of the following sets of quantum numbers represents the highest energy level in an atom?
B. \( n=3, l=1, m=1, s=+1 / 2 \)
c. \( n=3, l=2, m=-2, s=+1 / 2 \)
D. \( n=3, l=0, m=0, s=+1 / 2 \)
Subject: Chemistry
(a) Explain the following
(i) Henry's law about a dissolution of a gas in a liquid.
(ii) Boiling paint elevation constant for a solvent.
(b) A solution of glycerol \( \left(C_{3} H_{8} O_{3}\right) \) in
water was prepared by dissolving some glycerol in 500 g of water. This solution
has a boiling point of \( 100.42^{\circ} \mathrm{C} \). What
mass of glycerol was dissolved to make
this solution? \( \left(K_{b} \text { for water }=0.512 \mathrm{K} \mathrm{kg}\right. \)
\( \left.\operatorname{mol}^{-1}\right) \)
Subject: Maths
Solve:
\( \int e^{x}\left(\tan ^{-1} x+\frac{1}{1+x^{2}}\right) d x \)
A \( \cdot e^{x} \tan ^{-1} x+c \)
B. \( \frac{e^{x}}{1+x^{2}}+c \)
\( \mathbf{c} \cdot e^{x} \tan x+c \)
D. None of these
Subject: Maths
The distance of the point (1,-2,3)
from the plane \( \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
measured parallel to the line whose direction cosines are proportional to
2,3,-5 is
A \( \cdot \frac{9}{7} \)
B. \( \frac{11}{7} \)
c. \( \frac{15}{7} \)
D. None of these
Subject: Maths
\( \Delta B A C \cong \Delta D E C, A B \| D E, \) if \( \angle B \) is
\( 90^{\circ} \) and \( \angle C \) is \( 50^{\circ} \)
Find \( \angle A \) and \( \angle D=\dots \)
A . \( 35^{\circ} \)
В \( \cdot 50^{\circ} \)
\( \mathbf{c} \cdot 40^{\circ} \)
D. \( 55^{\circ} \)
Subject: Chemistry
\( \boldsymbol{C C l}_{3} \boldsymbol{C H}(\boldsymbol{O H})_{2} \) is stable. It's
extraordinary stability is due to the presence of:
A. two \( O H \) groups on the same carbon
B. hydrogen bonding with \( C l \)
c. \( -C H O \) group present
D. all of the above
Subject: Chemistry
Find the equilibrium constant for the reaction \( I n^{2+}+C u^{2+} \rightarrow I n^{3+}+C u^{+} \) at
298 K. Given, \( E^{o} \mathrm{Cu}^{2+} / \mathrm{Cu}^{+}= \)
\( 0.15 V, E_{I n^{3+} / I n^{+}}^{o}=-0.42 V E^{o}_{I n^{2+} / I n^{+}}= \)
\( -0.40 V \) is approximately:
A \( \cdot 10^{10} \)
B. \( 10^{11} \)
c. \( 10^{12} \)
D. \( 10^{14} \)
Subject: Physics
Q Type your question-
than Segment \( 2, \) but both segments are
centered on point \( P \)

The segments are connected by straight
wires as shown, and an unseen source
of EMF creates a constant
counterclockwise current in the wire.
Which wire segment creates a stronger
magnetic field at point P?
A. segment 1 creates stronger magnetic field because Segment 1 is longer
B. Segment 2 creates stronger magnetic field becaus Segment 2 is closer
C. Both segments create the same strength magnetic field because both segments have the same angle
D. Both segments create the same strength magnetic field because both segments have the
Subject: Chemistry
There are two colourless solutions \( (A) \)
and (B), both give white ppt with
\( A g N O_{3} \) which dissolves in \( a q N H_{3} \) Also (A) on reaction with \( H_{2} O \) gives orange turbidity while
(B) gives white turbidity. Identify (A) and (B).
\( \mathbf{A} \cdot(A) S b C I_{3} \)
(В) \( B i C I_{3} \)
B . (A) \( B i C I_{3} \);
(В) \( S b C I_{3} \)
C \( . \) (A) \( S e C I_{3} \);
(В) \( B i C I_{3} \)
D. (A) \( B i C I_{3} \);
(В) \( S e C I_{3} \)
Subject: Physics
One end of a steel rectangular girder is embedded into a wall (figure shown above). Due to gravity it sags slightly. Find the radius of curvature of the
neutral layer (see the dotted line in the figure above) in the vicinity of the point
\( O \) if the length of the protruding section
of the girder is equal to \( l=6.0 m \) and
the thickness of the girder equals \( h= \)
\( 10 \mathrm{cm} \)
Subject: Physics
Find the angle between \( \overrightarrow{\boldsymbol{A}}=\mathbf{4} \hat{\mathbf{i}}+\hat{\mathbf{j}}+ \)
\( \mathbf{3} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}+\mathbf{3} \hat{\boldsymbol{j}}+\boldsymbol{4} \hat{\boldsymbol{k}} \)
Subject: Maths
In \( \triangle A B C, \overline{X Y} \) is paralled to \( \overline{A C} \) and
divides the triangle into two parts of equal area, Then the \( \frac{A X}{A B} \) equals
A \( \cdot \frac{\sqrt{2}+1}{2} \)
B. \( \frac{2-\sqrt{2}}{2} \)
c. \( \frac{2+\sqrt{2}}{2} \)
D. \( \frac{\sqrt{2}-1}{2} \)
Subject: Physics
The work-energy theorem states that
the change in:
A. kinetic energy of a particle is equal to the work done on it by the net force
B. kinetic energy of a particle is equal to the work done by one of the forces acting on it
C. potential energy of a particle is equal to the work done on it by the net force
D. potential energy of a particle is equal to the work done by one of the forces acting on it
E. total energy if a particle is equal to the work done on it by the net force
Subject: Physics
An elevator is going up vertically with a
constant acceleration of \( 2 \mathrm{m} / \mathrm{s}^{2} \). at the
instant when its velocity is \( 4 \mathrm{m} / \mathrm{s} \) a ball is projected from the floor of the elevator with a speed of \( 4 \mathrm{m} / \mathrm{s} \) relative to the floor with an angular elevation of
\( 30^{\circ} . \) the time taken by te ball to return
to the floor is : (take \( g=10 m / s^{2} \) )
A \( \cdot \frac{1}{3} \mathrm{sec} \)
B. \( \frac{1}{\sqrt{3}} \sec \)
c. \( \frac{2}{\sqrt{3}} \sec \)
D. \( \sqrt{3} \mathrm{sec} \)
Subject: Chemistry
Mark the incorrect relation.
A \( \cdot N_{0}=N E^{\lambda t} \)
B . \( \tau=1.44 t_{0.5} \)
\( ^{\mathrm{c}} N=N_{0}\left(\frac{1}{2}\right)^{n} \)
D. \( t_{1 / 2}=2.303 \lambda \log 2 \)
Subject: Physics
A straight conductor \( 0.1 \mathrm{m} \) long moves in a uniform magnetic field 0.1 T. The velocity of the conductor is \( 15 \mathrm{m} / \mathrm{s} \) and is directed perpendicular to the field. The emf induced between the two ends
of the conductor is:
A . \( 0.10 \mathrm{v} \)
B. 0.15 \( v \)
c. \( 1.50 v \)
D. 15.00
Subject: Physics
The given figure shows the velocity-time
graph of an object. Find the acceleration
during the last \( 15 s \)
\( \mathbf{A} \cdot-2 m / s^{2} \)
B \( \cdot-4 m / s^{2} \)
\( \mathrm{C} \cdot-8 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{D} \cdot-16 m / s^{2} \)
Subject: Physics
The diagram below shows a hydraulic lift. A force is applied at side 1 and an output force is generated at side 2
Which of the following is true.?
A. the force at the side lis greater than the force at side 2
B. The force at the side lis less than the force at side 2 .
C. The pressure at side 1 is greater than the force at side
2
D. The pressure at side 1 is less than the pressure at side
2
Subject: Physics
As the electron in the Bohr Orbit of
hydrogen atom passes from state \( \boldsymbol{n}=\mathbf{2} \)
to \( n=1, \) the \( K E(K) \) and \( P E(U) \)
change as
A. \( K \) two-fold, \( U \) also two-fold
B. \( K \) four-fold, \( U \) also four-fold
c. \( K \) four-fold, \( U \) two-fold
D. \( K \) two-fold, \( U \) four-fold
Subject: Physics
A film of water is formed between two
straight parallel wires each \( 10 \mathrm{cm} \) long and at separation 0.5cm. Calculate the work required to increase \( 1 \mathrm{mm} \) distance between the wires. Surface
tension of water \( =\mathbf{7 2} \times \mathbf{1 0}^{-\mathbf{3}} \mathbf{N} / \mathbf{m} \)
A \( \cdot 1.44 \times 10^{-3} \)
В. \( 1.44 \times 10^{-7} \)
c. \( 1.44 \times 10^{-5} \)
D. \( 1.44 \times 10^{-4} \)
Subject: Maths
The following observations have been arranged in ascending order, if the median of data is 63
Find the value of \( x: \)
\( \mathbf{2 9}, \mathbf{3 2}, \mathbf{4 8}, \mathbf{5 0}, \boldsymbol{x}, \boldsymbol{x}+\mathbf{2}, \mathbf{7 2}, \mathbf{7 8}, \mathbf{8 4}, \mathbf{9 5} \)
Subject: Maths
If \( S \) is a sample space \( P(A)=\frac{1}{3} P(B) \)
and \( S=A \cup B \) where \( A \) and \( B \) are two
mutually exclusive events, then
\( \boldsymbol{P}(\boldsymbol{A})= \)
A \( \cdot \frac{1}{4} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.
Subject: Maths
The variance of the series
\( \boldsymbol{a}, \boldsymbol{a}+\boldsymbol{d}, \boldsymbol{a}+\boldsymbol{2} \boldsymbol{d}, \ldots \ldots \boldsymbol{a}+(\boldsymbol{2} \boldsymbol{n}-\mathbf{1}) \boldsymbol{d}, \boldsymbol{a}+ \)
2nd is
\( ^{\text {A } \cdot} \frac{n(n+1)}{2} d^{2} \)
\( ^{\text {В }} \cdot \frac{n(n-1)}{6} d^{2} \)
c. \( \frac{n(n+1)}{6} d^{2} \)
D. \( \frac{n(n+1)}{3} d^{2} \)
Subject: Chemistry
The reagents / conditions K, L and M are
respectively:
\( \mathbf{A} \cdot B a(O H)_{2}, K C N \) and \( C H C l_{3} / N a O H \) heat, \( H_{3} O^{+} \)
B. \( H_{2} O \) boil, \( C O_{2} / K O H \) and \( A c_{2} O-A c O N a \), heat
c. steam \( ; C H C l_{3} / N a O H, \) heat, \( H_{3} O^{+} \) and \( A c_{2} O- \) \( A c O N a, \) heat
D. \( C u_{2} C l_{2} / H C l, N a O H / h i g h \quad P \) and \( C O_{2} \mid N a O H, \) heat
E. Blank
Subject: Physics
A man has a concave shaving mirror of focal length \( 0.2 \mathrm{m} \). How far should the mirror be held from his face in order to
give an image of two fold magnification?
\( \mathbf{A} \cdot 0.1 \mathrm{m} \)
B. \( 0.2 \mathrm{m} \)
c. \( 0.3 \mathrm{m} \)
D. \( 0.4 \mathrm{m} \)
Subject: Chemistry
Assertion
The density of nucleus is about \( 2.3 \times \) \( 10^{17} k g m^{-3} \) and all nucleus have
approximately same density.
Reason
The density of nucleus is independent of
mass present in it.
A. Assertion is correct but Reason is wrong
B. Assertion is wrong but Reason is correct
c. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
D. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
Subject: Maths
If \( 9.2 \mathrm{cm} \) is the diameter of a circle then
its radius is
A \( .4 .1 \mathrm{cm} \)
в. \( 4.6 \mathrm{cm} \)
c. \( 4.8 \mathrm{cm} \)
D. \( 4.3 \mathrm{cm} \)
Subject: Physics
An oil drop, carrying six electronic
charges and having a mass of \( 1.6 \times \)
\( 10^{-12} g, \) falls with some terminal
velocity in a medium. What magnitude of vertical electric field is required to make the drop move upward with the same speed as it was formerly moving downward with? Ignore buoyancy
A \( \cdot 10^{5} N C^{-1} \)
B . \( 10^{4} N C^{-1} \)
c. \( 3.3 \times 10^{4} N C^{-1} \)
D. \( 3.3 \times 10^{5} N C^{-1} \)
Subject: Maths
A circus tent is cylindrical to a height of \( 4 \mathrm{m} \) and conical above it If its diameter
is \( 105 \mathrm{m} \) and the slant height of the cone is \( 80 \mathrm{m} \) then the total surface area of the canvas required is
A. \( 15540 m^{2} \)
В. \( 30880 m^{2} \)
c. \( 46020 m^{2} \)
D. \( 14520 m^{2} \)
Subject: Physics
A series LCR circuit with \( \mathrm{R}=22 \Omega, \mathrm{L}=1.5 \)
\( \mathrm{H} \) and \( \mathrm{C}=40 \mu \mathrm{F} \) is connected to a variable frequency \( 220 \mathrm{V} \) ac supply.
When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one
complete cycle?
A. 2000
B. 2200 W
c. 2400 \( w \)
D. 2500 W
Subject: Physics
A block of mass \( 2 k g \) is moving with a velocity of \( 2 \hat{i}-\hat{j}+3 \hat{k} m / s . \) Find the
magnitude and direction of momentum of the block with the \( x- \) axis.
A \( \cdot_{2 \sqrt{14}} \operatorname{kg} m / s, \tan ^{-1}(\sqrt{\frac{5}{7}}) \)
B. \( _{2 \sqrt{7}} k g m / s, \tan ^{-1}(\sqrt{\frac{2}{7}}) \)
c. \( _{2 \sqrt{14}} k g m / s, \tan ^{-1}(\sqrt{\frac{2}{7}}) \)
D. \( 2 \sqrt{9} \) kg \( m / s, \tan ^{-1}(\sqrt{\frac{3}{7}}) \)
Subject: Physics
The inductance of a resistanceless coil
is 0.5 henry. In the coil, the value of alternating current is \( 0.2 \mathrm{A} \) whose frequency is 50 Hz. The reactance of circuit is
\( A \cdot 15.7 \Omega \)
в. \( 157 \Omega \)
c. \( 1.57 \Omega \)
D. 757\Omega
Subject: Maths
If \( \mathrm{A}=\left[a_{i j}\right]_{2 \times 2} \) such that \( a_{i j}=i-j+3 \)
then find \( \boldsymbol{A} \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}2 & 3 \\ 4 & 2\end{array}\right] \)
в. \( \left[\begin{array}{ll}3 & 4 \\ 2 & 3\end{array}\right] \)
c. \( \left[\begin{array}{ll}4 & 2 \\ 2 & 3\end{array}\right] \)
D. \( \left[\begin{array}{ll}3 & 2 \\ 4 & 3\end{array}\right] \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) where \( \left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right)^{2}=\boldsymbol{x} \boldsymbol{y} \)
Subject: Physics
\( N^{\prime} \) atoms of a radioactive element
emit \( ^{\prime} \boldsymbol{n}^{\prime} \) alpha particles per second at an instant. Then the half-life of the element is :
A \( \cdot \frac{n}{N} \) sec.
в. \( 1.44 \frac{n}{N} \) sec
c. \( 0.69 \frac{n}{N} \) sec.
D. \( 0.69 \frac{N}{n} \) sec.
Subject: Chemistry
Assertion
Statement -1: White phosphorus is
less stable where as red phosphorus is
more stable.
Reason
Statement -2: White phosphorus exist
as individual \( P_{4} \) having more strained
geometery while red phosphorus has \( \boldsymbol{P}_{\mathbf{4}} \) tetrahedron structure linked together.
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1.
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. Statement -1 is true, Statement -2 is false
D. Statement - 1 is false, Statement - 2 is true
Subject: Chemistry
In the reaction,
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{3}(\boldsymbol{g}) \) the
amounts of \( \boldsymbol{P C l}_{5}, \boldsymbol{P C l}_{3} \) and \( \boldsymbol{C l}_{2} \) are \( \boldsymbol{2} \)
mole each at equilibrium and the total
pressure is 3 atmospheres. The
equilibrium constant, \( \boldsymbol{K}_{\boldsymbol{p}} \) is:
\( A \cdot 1 \) atm
B. 2 atm
\( c .3 \) atm
D. 1.5 atm
Subject: Maths
n the figure, \( l \| \boldsymbol{m} \) and \( \boldsymbol{n} \| \boldsymbol{p} \). If \( \angle \mathbf{1}=\mathbf{6 0}^{\circ} \)
then \( \angle 2=3 \times \angle 1 \)
4 . True
3. False
Subject: Maths
Consider the function \( \boldsymbol{f}:(-\infty, \infty) \rightarrow \)
\( (-\infty, \infty) \) defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{x^{2}-a x+1}{x^{2}+a x+1}, 0<a<2 \)
Which of the following is true?
A. \( f(x) \) is decreasing on (1,1) and has a local minimum at \( x=1 \)
B. \( f(x) \) is increasing on (1,1) and has a local maximum at \( x=1 \)
c. \( f(x) \) is increasing on (1,1) but has neither a local maximum nor a local minimum at \( x=1 \)
maximum nor a local minimum at \( x=1 \)
Subject: Maths
The equation of the lines passing through the point (1,0) and at a distance \( \frac{\sqrt{3}}{2} \) from the origin are This question has multiple correct options
B. \( x+\sqrt{3} y-\sqrt{3}=0 \)
c. \( \sqrt{3} x-y-\sqrt{3}=0 \)
D. \( x-\sqrt{3} y-\sqrt{3}=0 \)
Subject: Physics
A plank fitted with a gun is moving on a horizontal surface with speed of \( 4 \mathrm{m} / \mathrm{s} \) along the positive x-axis. The z-axis is in vertically upward direction. The mass of the plank including the mass of the mass of the gun is 50 kg. When the plank reaches the origin, a shell of
mass \( 10 \mathrm{kg} \) is fired at an angle of \( 60^{\circ} \) with the positive x-axis with a speed of \( \mathbf{v}=20 \mathrm{m} / \mathrm{s} \) with respect to the gun \( \mathrm{n} \mathbf{x}-\mathrm{z} \)
plane. Find the position vector of the shell at \( t=2 \) s after firing it. Take \( g= \) \( 9.8 m / s^{2} \)
A. \( [15 \hat{i}-24 \hat{k}] m \)
в. \( [28 \hat{i}+15 \hat{k}] m \)
c. \( [15 \hat{i}-18 \hat{k}] m \)
D. \( [14 \hat{i}-15 \hat{k}] m \)
Subject: Maths
\( \cot B=2 \tan (A-B)=>2 \tan B+ \)
\( \cot B \) is equal to
\( \mathbf{A} \cdot \tan A \)
B. \( \cot A \)
\( c \cdot 2 \tan A \)
D. \( 2 \cot A \)
Subject: Maths
Use remainder theorem to find
remainder when \( p(x) \) is divided by \( q(x) \) in the following questions: \( p(x)=x^{4}+ \)
\( \boldsymbol{x}^{3}+\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\mathbf{1}, \boldsymbol{q}(\boldsymbol{x})=\boldsymbol{x}+\mathbf{1} \)
Subject: Physics
A ray of light passing from glass of water is incident on the glass-water interface at \( 65^{0} . \) If the critical angle for
the pair of media is \( 63^{0}: \)
A. the ray will emerge into water with a deviation of \( 2^{\circ} \) from the normal
B. the ray will be refracted into water with a deviation of \( 2^{0} \)
c. the ray will be totally internally reflected back into glass with a deviation of \( 50^{\circ} \)
D. the ray will be totally internally reflected back into glass with a deviation of \( 2^{0} \)
Subject: Physics
A dielectric in the form of a sphere is
introduced into a homogeneous electric
field. \( A, B \) and \( C \) are three points as
shown in Fig. Then
A. Intensity at \( A \) increases while that at \( B \) and \( C \) decreases
B. Intensity at \( A \) and \( B \) decreases whereas intensity at \( C \) increases
c. Intensity at \( A \) and \( C \) increases and that at \( B \) decreases
D. Intensity at \( A, B \) and \( C \) decreases