AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The oxidation state of the most
electronegative element in the products
of the reaction between \( B a O_{2} \) and
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) are
A. 0 and -1
B. -1 and -2
c. -2 and 0
D. -2 and +1
Subject: Physics
The wire shown in figure carries a
current of \( 40 A . \) If \( r=3.14 c m \) the
magnetic field at point p will be :
A \( .1 .6 \times 10^{-3} T \)
В. \( 3.2 \times 10^{-3} T \)
c. \( 6 \times 10^{-4} T \)
D . \( 4.8 \times 10^{-3} T \)
Subject: Physics
There is a small black dot at the centre
C of a solid glass sphere of refractive index \( \mu . \) When seen from outside, the
dot will appear to be located:
A. Away from C for all values of \( \mu \)
B. At C for all values of \( \mu \)
c. At \( \mathrm{C} \) for \( \mu=1.5 \), but away from \( \mathrm{C} \) for \( \mu \neq 1.5 \)
D. At C only for \( \sqrt{2} \leq \mu \leq 1.5 \)
Subject: Physics
A vehicle is moving with a velocity \( v \) on
a curved road of width \( b \) and radius of
curvature \( R \). For counteracting the centrifugal force on the vehicle, the
difference in elevation required in
between the outer and inner edge of the
road is
A \( \cdot \frac{v^{2} b}{R g} \)
B. \( \frac{v b}{R g} \)
c. \( \frac{v b^{2}}{R g} \)
D. \( \frac{v b}{R^{2} g} \)
Subject: Physics
Two loud speakers \( L_{1} \) and \( L_{2}, \) driven by a common oscillator and amplifier, are arranged as shown. The frequency of the oscillator is gradually increased from
zero and the detector at D records a
series of maxima and minima. If the
speed of sound is \( 330 \mathrm{m} / \mathrm{s} \) then the
frequency at which the first maximum is observed is :
A . \( 165 \mathrm{Hz} \)
в. ззо нz
c. 495 нz
D. 660 нz
Subject: Maths
If \( b>a, \) and \( I=\int_{a}^{b} \sqrt{\frac{x-a}{b-x}} d x, \) then \( I \)
equals
A \( \cdot \frac{\pi}{2}(b-a) \)
в. \( \pi(b-a) \)
c. \( \pi / 2 \)
D. \( 2 \pi(b-a) \)
Subject: Physics
The figure shown depicts the distance
travelled by a body as a function of time.

The average speed and maximum
speed between 0 and \( 20 s \) are
A. \( 1 m / s, 2.0 m / s \) respectively
B. \( 1 m / s, 1.6 m / s \) respectively
c. \( 2.0 m / s, 2.6 m / s \) respectively.
D. \( 1.3 m / s, 2.0 m / s \) respectively
Subject: Physics
The magnetic induction at a point at a large distance d on the axial line of
circular coil of small radius carrying
current is \( 120 \mu T . \) At a distance 2 d the
magnetic induction would be:
A. \( 60 \mu T \)
в. зод \( T \)
\( c \cdot 15 \mu T \)
D. 240\muT
Subject: Chemistry
Tyndall effect is applicable when:
This question has multiple correct options
A. the diameter of the dispersed particles is not much smaller than the wavelength of the light used
B. the diameter of the dispersed particles is much smaller than the wavelength of the light used
C. the refactive indices of the dispersed phase and the dispersion medium must be same
D. the refractive indices of the dispersed phase and the dispersion medium must differ greatly in magnitude
Subject: Chemistry
Which out of following hydrocarbons undergo addition reaction? \( \boldsymbol{C}_{2} \boldsymbol{H}_{6}, \boldsymbol{C}_{3} \boldsymbol{H}_{8}, \boldsymbol{C}_{3} \boldsymbol{H}_{6}, \boldsymbol{C}_{2} \boldsymbol{H}_{2} \) and \( \boldsymbol{C} \boldsymbol{H}_{4} \)
A. \( C_{2} H_{6} \) and \( C_{3} H_{8} \)
B. \( C_{3} H_{6} \) and \( C_{2} H_{2} \)
c. \( C H_{4} \) and \( C_{2} H_{6} \)
D. \( C_{3} H_{8} \) and \( C_{2} H_{2} \)
Subject: Physics
A copper wire of cross-section A is under a tension \( \mathrm{T} \). Find the decrease in
the cross-section area. Young's
modulus is \( Y \) and Poisson's ratio is \( \sigma \)
\( ^{\text {A }} \cdot \frac{\sigma T}{2 A Y} \)
в. \( \frac{\sigma T}{A Y} \)
c. \( \frac{2 \sigma T}{A Y} \)
D. \( \frac{4 \sigma T}{A Y} \)
Subject: Maths
Consider the following events for a family with children
\[
A=\{o f \text { both sexes }\} ; B=
\]
\( \{a t \text { most one boy }\} \)
In which of the following (are/is) the events \( A \) and \( B \) are independent
(a)If a family has 3 children
(b) If a
family has 2 children Assume that the birth of a boy or a girl is equally likely mutually exclusive and exhaustive
Subject: Chemistry
Match the column - I with Column - II
and pick up the correct answer:
\( \begin{array}{ll}\text { Column - - } & \text { Column -II } \\ \text { (I) Nickel } & \text { A. Conversion }\end{array} \)
(II) ZSM-5 \( \quad \) B. Alkylation of benzene I) ZSM-5
(III) \( S i O_{2} \quad \) C. Hydrogenation 'on
A.
B. I-A II - B III - C
c. \( 1-\mathrm{C} \) ॥ \( -\mathrm{B} \) III \( -\mathrm{A} \)
D. I - B II - C III - B
Subject: Maths
ABCD is a square of length a, \( a \epsilon N, a>1 \)
Let \( L_{1}, L_{2}, L_{3}, \dots \) be points on BC such
that \( B L_{1}=L_{1} L_{2}=L_{2} L_{3}=\ldots=1 \) and
\( M_{1}, M_{2}, M_{3}, \ldots \) be points on CD such
that \( \boldsymbol{C M}_{\mathbf{1}}=\boldsymbol{M}_{\mathbf{1}} \boldsymbol{M}_{\mathbf{2}}=\boldsymbol{M}_{\mathbf{2}} \boldsymbol{M}_{\mathbf{3}}=\ldots=\mathbf{1} \)
Then \( \sum_{n=1}^{a-1}\left(A L_{n}^{2}+L_{n} M_{n}^{2}\right) \) is equal to
A \( \cdot \frac{1}{2} a(a-1)^{2} \)
в. \( \frac{1}{2} a(a-1)(4 a-1) \)
c. \( \frac{1}{2} a(a-1)(2 a-1)(4 a-1) \)
D. none of these
Subject: Physics
Current of 10 ampere and 2 ampere are passed through two parallel wires A and
B, respectively in opposite directions. If the wire \( A \) is infinitely long and the length of the wire \( \mathrm{B} \) is \( 2 \mathrm{m} \), the force on the conductor \( B \) which is situated at 10
\( \mathrm{cm} \) distance from A will be
\( \mathbf{A} \cdot 8 \times 10^{-5} N \)
B \( \cdot 4 \times 10^{-5} N \)
c. \( 8 \pi \times 10^{-7} N \)
D. \( 4 \pi \times 10^{-7} N \)
Subject: Chemistry
The lattice energy of NaCl is
\( 788 k J \) mol \( ^{-1} . \) This means that \( 788 k J \)
of energy is required:
A. to separate one mole of solid \( N a C l \) into one mole of \( N a(g) \) and one mole of \( C l(g) \) to infinite distance
B. to separate one mole of solid \( N a C l \) into one mole of \( N a^{+}(g) \) and one mole of \( C l^{-}(g) \) to infinite distance
C. to convert one mole of solid \( N a C l \) into one mole of
gaseous \( N a C l \)
D. to convert one mole of gaseous \( N a C l \) into one mole of solid \( N a C l \)
E. to separate one mole of gaseous \( N a C l \) into one mole of \( N a^{+}(g) \) and one mole of \( C l^{-}(g) \) to infinite distance
Subject: Physics
Fig. \( 29.17(a) \) shows two coherent
sources \( S_{1} \) and \( S_{2} \) which emit light of
wavelength \( \lambda \) in phase. The phase
separation between the sources is \( 3 \lambda . \) A
circular wire of radius \( \boldsymbol{R}>>\boldsymbol{I} \) is
placed symmetrically to \( S_{1} \) and \( S_{2} \) as
illustrated. Find the angular positions \( \theta \)
on the wire for which constructive
interference occurs.
Subject: Chemistry
Which of the following element is expected to have highest electron gain enthalpy:
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{3} \)
c. \( 1 s^{2} 2 s^{2} 2 p^{4} \)
D \( \cdot 1 s^{2} 2 s^{2} 2 p^{5} \)
Subject: Chemistry
The rms speed of hydrogen is \( \sqrt{7} \) times the rms speed of nitrogen. If T is the temperature of the gas, then :
\( \mathbf{A} \cdot T_{H_{2}}=T_{N_{2}} \)
\( \mathbf{B} \cdot T_{H_{2}}>T_{N_{2}} \)
\( \mathbf{c} \cdot T_{H_{2}}<T_{N_{2}} \)
D. \( T_{H_{2}}=\sqrt{7} T_{N_{N}} \)
Subject: Physics
A potentiometer consists of a wire of length \( 4 \mathrm{m} \) and resistance \( 10 \Omega \). It is connected to a cell of e.m.f. 3V. The
potential gradient of wire is
A. \( 0.75 \mathrm{V} / \mathrm{m} \)
B. 2 V /m
\( c \cdot 6 v / m \)
D. \( 10 \mathrm{V} / \mathrm{m} \)
Subject: Physics
If the momentum of an electron is
changed by \( p_{m}, \) then the de Broglie wavelength associated with it
increased by \( 0.5 \% \). The initial momentum of electron will be
A \( \cdot p_{m} / 200 \)
в. \( p_{m} / 100 \)
c. \( 201 p_{m} \)
D. \( 100 p_{m} \)
Subject: Physics
An accumulator of emf 2 Volt and
negligible internal resistance is
connected across a uniform wire of
length \( 10 \mathrm{m} \) and resistance \( 30 \Omega \). The
appropriate terminals of a cell of emf
\( \mathbf{1 . 5} V \) olt and internal resistance \( 1 \Omega \) is
connected to one end of the wire, and
the other terminal of the cell is
connected through a sensitive galvanometer to a slider on the wire. If the length of the wire which is required to produce zero deflection of the galvanometer is \( \frac{x}{2} m . \) Find \( x \)
Subject: Biology
The given figure represents locations in human female reproductive system that are affected by different birth control measures. Identify them and
select the correct option
A. P-Copper T, Q - Birth control pills, R Tubectomy, S condom
B. P - Birth control pills, Q Copper T, R Tubectomy, S -
C. P- Birth control pills, Q Diaphragm, R Ovariectomy, copper \( T \)
D. P Copper T, Q - Birth control pills, R Ovariectomy, S -
Subject: Maths
solve:-
\( 1+\cos 2 x+\cos 4 x+\cos 6 x= \)
A \( .2 \cos x \cos 2 x \cos 3 x \)
B. 2 \( \cos x \sin 2 x \cos 3 x \)
\( \mathrm{c} \cdot 4 \cos x \cos 2 x \cos 3 x \)
D. \( 4 \cos x \sin 2 x \sin 3 x \)
Subject: Physics
The average energy in one time period in simple harmonic motion is.
A \( \cdot \frac{1}{2} m \omega^{2} A^{2} \)
B \( \cdot \frac{1}{4} m \omega^{2} A^{2} \)
\( \mathrm{c} \cdot m \omega^{2} A^{2} \)
D. zero
Subject: Maths
f \( \boldsymbol{y}=\sin \boldsymbol{p} \boldsymbol{x} \) prove that
\( \boldsymbol{\Delta}=\left|\begin{array}{lll}\boldsymbol{y} & \boldsymbol{y}_{1} & \boldsymbol{y}_{2} \\ \boldsymbol{y}_{3} & \boldsymbol{y}_{4} & \boldsymbol{y}_{5} \\ \boldsymbol{y}_{6} & \boldsymbol{y}_{7} & \boldsymbol{y}_{8}\end{array}\right|=0 \)
where \( y_{r}, \) means \( r-t h \) differential
coefficient of \( \boldsymbol{y} \)
Subject: Chemistry
The compound (C) is:
(D) \( \quad(\mathrm{C})+\mathrm{CO}_{2} \)
\[
\begin{array}{ll}
\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{2}\right) & \left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right) \\
\text { Acid } &
\end{array}
\]
\( A \)
B.
\( c \)
D.
Subject: Chemistry
(1) \( N_{2}+2 O_{2} \leftrightarrow 2 N O_{2} ; K_{e}=2 \times 10^{-31} \)
(2) \( 2 N O^{+} \leftrightarrow N_{2}+O_{2} ; K_{e}=2.2 \times \)
\( \mathbf{1 0}^{-\mathbf{3 1}} \)
(3) \( 2 N_{2} O_{5} \leftrightarrow 2 N_{2}+5 O_{2} ; K_{e}=3.8 \times \)
\( 10^{-32} \)
(4) \( 2 N_{2}+O_{2} \leftrightarrow 2 N_{2} O ; K_{e}=4 \times \)
\( 10^{-32} \)
From the above data, the most stable
oxide is:
A. \( N O_{2} \)
B. \( N O \)
\( \mathbf{c} \cdot N_{2} O_{5} \)
D. \( N_{2} O \)
Subject: Chemistry
Match the following
List -I \( \quad \) List -II
(Products) (Reactants-Reaction)
(1) Sabatier - Senderens reaction of
A) Methane propylene
B) Ethane
(2) Wurtz reaction of methyl iodide
(3) Decarboxylation of sodium
C) Propane \( \quad \) acetate
(4) Sodium butanoate by Kolbes
D) Butane \( \quad \) electrolysis
(5) Sodium propanoate by Kolbes electrolysis
The correct match is :
\( A \cdot A-2 B-3 C-1 D-5 \)
B. \( A-4 B-2 C-1 D-5 \)
C \( \cdot A-3 B-2 C-1 D-5 \)
D. \( A-2 B-3 C-1 D-4 \)
Subject: Maths
If \( A=(6,7,8,9), B=(4,6,8,10) \) and \( C=\{x \)
\( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{N}: \boldsymbol{2}<\boldsymbol{x} \leq \mathbf{7}\} ; \) find :
\( A-B \)
A \( \cdot\{6,8\} \)
в. \{7,9\}
c. \{6,9\}
D. \{6,7,9,10\}
Subject: Maths
A marketing firm determined that, of
200 households surveyed, 80 used
neither Brand A nor Brand B soap, 60
used only Brand A soap, and for every household that used both brands of
soap, 3 used only Brand B soap. How
many of the 200 households surveyed used both brands of soap?
A . 15
B. 20
c. 30
D. 40
E . 45
Subject: Chemistry
Decreasing order of stability of \( \boldsymbol{O}_{2}, \boldsymbol{O}_{2}^{-} \)
\( O_{2}^{+}, \) and \( O_{2}^{2-} \) is:
A \( \cdot O_{2}>O_{2}^{+}>O_{2}^{2-}>O_{2}^{-} \)
B. \( O_{2}^{-}>O_{2}^{2-}>O_{2}^{+}>O_{2} \)
\( \mathrm{c} \cdot O_{2}^{+}>O_{2}>O_{2}^{-}>O_{2}^{2} \)
D. \( O_{2}^{2-}>O_{2}^{-}>O_{2}>O_{2}^{+} \)
Subject: Physics
A particle executes simple harmonic motion between \( \boldsymbol{x}=-\boldsymbol{A} \) and \( \boldsymbol{x}=+\boldsymbol{A} \)
The time taken for it to go from 0 to \( A / 2 \)
is \( T_{1} \) and to \( \operatorname{gofrom} A / 2 \) to \( A \) is \( T_{2} \). Then
A \( \cdot T_{1}<T_{2} \)
в. \( T_{1}>T_{2} \)
c. \( T_{1}=T_{2} \)
D. \( T_{1}=2 T_{2} \)
Subject: Chemistry
Atoms of eight elements \( A, B, C, D, E, F \) \( G \) and \( H \) have the same number of
electronic shells but different number
of electrons in their outermost shell. It
was found that elements \( A \) and \( G \)
combine to form an ionic compound which can also be extracted from sea
water. This compound is added in a small amount to almost all vegetable dishes during cooking. Oxides of elements A and B are basic in nature
while those of \( \mathrm{E} \) and \( \mathrm{F} \) are acidic. The
oxide of \( \mathrm{D} \) is almost neutral. Based on
the above information answer the
following question.

Which two of these elements could
definitely be metals.
Subject: Physics
A body is dropped from certain height H. If the ratio of the distances travelled by
it in \( (n-3) \) seconds to \( (n-3)^{r d} \) second
is \( \left.4: 3, \text { find } H . \text { (Take } g=10 \mathrm{m} s^{-2}\right) \)
A. \( 75 \mathrm{m} \)
B. 100 \( m \)
c. \( 125 \mathrm{m} \)
D. 150 \( m \)
Subject: Physics
Assertion
In a simple electric circuit, positive terminal of the battery is a point of lowest potential
Reason
The electronic current flow in a circuit
is from a point of highest potential to a point of lowest potential
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
Solution of \( |4 x+3|+|3 x-4|=12 \) are
A \( \cdot x=-\frac{7}{3}, \frac{3}{7} \)
в. \( x=-\frac{5}{2}, \frac{2}{5} \)
c. \( _{x=-\frac{11}{7}}, \frac{13}{7} \)
D. \( x=-\frac{13}{7}, \frac{11}{7} \)
Subject: Chemistry
Assertion
Molecular nitrogen is less reactive than
molecular oxygen.
Reason
The bond length of \( N_{2} \) is shorter than
that of oxygen.
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not a correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
Subject: Maths
The D.E whose solution is \( y=c(x-c)^{2} \)
is
\( ^{\mathbf{A}} \cdot\left(\frac{d y}{d x}\right)^{3}=4 y\left(x \frac{d y}{d x}-2 y\right) \)
В. \( y_{1}^{3}=2 y\left(x y_{1}-y\right) \)
\( ^{\mathbf{c}}\left(\frac{d y}{d x}\right)^{3}=4 y\left(2 x \frac{d y}{d x}-y\right) \)
D. \( \left(\frac{d y}{d x}\right)^{3}=2 y\left(x \frac{d y}{d x}-4 y\right) \)
Subject: Physics
The fraction of ice that melts by mixing
equal masses of ice at \( -10^{\circ} \mathrm{C} \) and
water at \( 60^{\circ} \mathrm{C} \) is :
A \( \cdot \frac{6}{11} \)
в. \( \frac{11}{16} \)
c. \( \frac{5}{16} \)
D. \( \frac{11}{15} \)
Subject: Chemistry
Increasing order of metallic characteristic of \( \mathrm{C}, \mathrm{Sb}, \mathrm{As}, \mathrm{Bi}, \) Si is
shown by :
A. \( c, \) si, \( A s, \) sb, Bi
B. \( C, \) Si, Bi, Sb, As
c. \( c, \) si \( , \) sb, Bi, As
D. \( c, \) si, As, Bi, Sb
Subject: Physics
A double convex lens of focal \( 30 \mathrm{cm} \) is made of glass of refractive index 1.6 When it is immersed in a liquid, the focal length becomes \( 126 \mathrm{cm} \). The refractive index of the liquid is :
A . 1.4
B. 1.5
\( c \cdot 1.33 \)
D. 1.6
Subject: Maths
A polynomial \( p(x) \) when divided by \( x^{2}- \)
\( 3 x+2 \) leaves remainder \( 2 x-3 . \) Then
A. \( p(x) \) must have a root between 1 and 2
B. \( p(x) \) cannot have a root between 0 and 3
c. \( p(x) \) must have a real root but mayor may not be between o and 3
D. \( p(x) \) need not have a real root
Subject: Physics
A particle moves rectilinearly. its displacement \( x \) at time \( t \) is given by
\( x^{2}=t^{2}+1 . \) Its acceleration at time \( t \) is
proportional to
A \( \cdot \frac{1}{x^{3}} \)
B. \( \frac{1}{x}-\frac{1}{x^{2}} \)
\( c \cdot-\frac{t}{x^{2}} \)
D. \( \frac{1}{x}-\frac{t^{2}}{x^{3}} \)
Subject: Maths
A mirror and a source of light are situated at the origin \( \mathrm{O} \) and at a point on \( \mathrm{O} X, \) respectively. A ray of light from the source strikes the mirror and is
reflected. If the direction ratios of the
normal to the plane are \( 1,-1,1, \) then find the DCs of the reflected ray.
A \( \cdot \frac{1}{3}, \frac{2}{3}, \frac{2}{3} \)
в. \( -\frac{1}{3}, \frac{2}{3}, \frac{2}{3} \)
\( c \cdot-\frac{1}{3},-\frac{2}{3},-\frac{2}{3} \)
D. \( -\frac{1}{3},-\frac{2}{3}, \frac{2}{3} \)
Subject: Physics
Two square metal plates \( A \) and \( B \) are of
the same thickness and material. The
side of \( B \) is twice that of \( A \). If the
resistances of \( A \) and \( B \) are denoted by \( \boldsymbol{R}_{A} \) and \( \boldsymbol{R}_{B}, \) Then \( \left(\frac{\boldsymbol{R}_{\boldsymbol{A}}}{\boldsymbol{R}_{\boldsymbol{B}}}\right) \) is
\( A \cdot \frac{1}{2} \)
B. 2
\( c .1 \)
\( D \)
Subject: Maths
The equation of the latusrecta of the ellipse \( 9 x^{2}+4^{2}-18 x-8 y-23=0 \)
are
A \( . y=\pm \sqrt{5} \)
В. \( x=\pm \sqrt{5} \)
c. \( y=1 \pm \sqrt{5} \)
D. \( x=1 \pm \sqrt{5} \)
Subject: Physics
AB IS a resistanceless conaucting roa
which forms a diameter of a conducting
ring of radius \( r \) rotating in a uniform
magnetic field \( B \) as shown in figure.
The resistors \( R_{1} \) and \( R_{2} \) do not rotate.
Then the current through the resistor
\( \boldsymbol{R}_{1} \)
\( ^{\mathbf{A}} \cdot \frac{B \omega r^{2}}{2 R_{1}} \)
B. \( \frac{B \omega r^{2}}{2 R_{2}} \)
\( ^{\mathbf{C}} \frac{B \omega r^{2}}{2 R_{1} R_{2}}\left(R_{1}+R_{2}\right) \)
D. \( \frac{B \omega r^{2}}{2\left(R_{1}+R_{2}\right)} \)
E. answer required
Subject: Maths
Find a unit vector perpendicular to each of the vectors \( \vec{a}+\vec{b} \) and \( \vec{a}-\vec{b} \) where \( \vec{a}=3 \hat{i}+2 \hat{j}+2 \hat{k} \) and \( \vec{b}=\hat{i}+2 \hat{j}-2 \hat{k} \)
Subject: Physics
Assertion
A brass tumbler feels much colder than
a wooden tray on a chilly day.
Reason
The thermal conductivity of brass is more than the thermal conductivity of
wood.
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
The radius of an atom is of the order of:
A \( \cdot 10^{-10} \mathrm{cm} \)
B . \( 10^{-13} \mathrm{cm} \)
\( c \cdot 10^{-15} \mathrm{cm} \)
\( D \cdot 10^{-8} \mathrm{cm} \)
Subject: Maths
Factorize \( 3 a^{5}-108 a^{3} \)
A \( \cdot 3 a^{3}(a-6)(2 a-6) \)
В \( \cdot 2 a^{3}(a+6)(7 a-6) \)
c. \( 2 a^{3}(a-6)(3 a+6) \)
D. \( 3 a^{3}(a+6)(a-6) \)
Subject: Maths
Assertion
A vector cannot be divided by other
Vector.
Reason
A vector can be dived by a scalar.
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
A random variable \( \boldsymbol{X} \) has the following probability distribution:
Determine
(i) \( k \)
(ii) \( \boldsymbol{P}(\boldsymbol{X}<\mathbf{3}) \)
(iii) \( \boldsymbol{P}(\boldsymbol{X}>\boldsymbol{6}) \)
(iv) \( \boldsymbol{P}(\mathbf{0}<\boldsymbol{X}<\mathbf{3}) \)
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline \( \mathrm{X} \) & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline \( \mathrm{P}(\mathrm{X}) \) & 0 & \( k \) & \( 2 k \) & \( 2 k \) & \( 3 k \) & \( k^{2} \) & \( 2 k^{2} \) & \( 7 k^{2}+k \) \\
\hline
\end{tabular}
Subject: Physics
Match List - I (Event) with List - II (Order
of the time interval for happening of the
event) and select the correct option from the options given below the lists.
List - 1
(a) Rotation period of
(i) earth
Revolution period of
(ii)
(b) earth
\( (c) \)
Period of a light
(iii) wave
\( (d) \)
Period of a sound
iv wave
A \( \cdot(a)-(i),(b)-(i i),(c)-(i i i),(d)-(i v) \)
B. (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
\( c \cdot(a)-(i),(b)-(i i),(c)-(i v),(d)-(i i i) \)
D. (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
Subject: Physics
A uniform charged solid sphere of radius \( R \) has potential \( V_{0} \) (measure with respect to \( \infty \) ) on its surface. For this sphere the equipotential surfaces with potentials \( \frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4}, \frac{V_{0}}{4} \) have
radius \( R_{1}, R_{2}, R_{3} \) and \( R_{4} \) respectively.
Then
A. \( R_{1}=0 \) and \( R_{2}>\left(R_{4} R_{3}\right) \)
B. \( R_{1} \neq 0 \) and \( \left(R_{2} R_{1}\right)>\left(R_{4} R_{3}\right) \)
c. \( R_{1}=0 \) and \( R_{2}<\left(R_{4} R_{3}\right) \)
D . \( 2 R<R_{4} \)
Subject: Physics
A thermodynamic system is taken from an original state to an intermediate
state by the linear process shown in the
figure. Its volume is then reduced to the
original value from \( \boldsymbol{E} \) to \( \boldsymbol{F} \) by an
isobaric process. Calculate the total
work done by the gas from \( D \) to \( E \) to \( F \)
A .225 J
D. 600
Subject: Maths
Find the distance of point (-2,3,-4) from the line \( \frac{\boldsymbol{x}+\mathbf{2}}{\mathbf{3}}=\frac{\mathbf{2} \boldsymbol{y}+\mathbf{3}}{\mathbf{4}}=\frac{\mathbf{3} \boldsymbol{z}+\mathbf{4}}{\mathbf{5}} \)
measured parallel to the plane \( 4 x+ \) \( 12 y-3 z+1=0 \)
Subject: Maths
The sum of 'n' terms of series \( 1^{2}+ \)
\( \left(1^{2}+2^{2}\right)+\left(1^{2}+2^{2}+3^{2}\right)+\left(1^{2}+\right. \)
\( \left.\mathbf{2}^{2}+\mathbf{3}^{2}+\mathbf{4}^{2}\right)+\ldots \ldots . \) will be
A \( \cdot \frac{1}{4} n(n+1)^{2}(n+2) \)
B \( \cdot \frac{1}{3} n(n+1)^{2}(n+2) \)
c. \( \frac{1}{12} n(n+1)(n+2)^{2} \)
D. \( \frac{1}{12} n(n+1)^{2}(n+2) \)
Subject: Biology
Choose the correct answer from the
alternatives given:

Identify the labels \( A, B, C \) and Din the
given structure of tRNA and select the
correct option.
A. A - Anticodon loop, B T \( \Psi \mathrm{C} \) loop, \( \mathrm{C} \) - AA binding site, D DHU loop
B. A - AA binding site, B - T\PsiC loop, C - Anticodon loop, D DHU loop
C. \( A-M \) binding site, \( B \) - DHU loop, \( C \) - Anticodon loop, \( D \) T \( \Psi \) C loop
D. A - M binding site, B - DHU loop, C - T\PsiC loop, D Anticodon loop
Subject: Physics
(a) Find the angle of incidence.
(b) Find the angle between the incident
and reflected rays.

Figure shows an incident ray \( A O \) and
the normal \( O N \) on a plane mirror. The
angle which the incident ray \( A O \) makes
with a mirror is \( 30^{\circ} \)
\( \mathbf{A} \cdot(a) 60^{\circ},(b) 60^{\circ} \)
B . \( (a) 120^{\circ},(b) 120^{\circ} \)
\( \mathbf{c} \cdot(a) 60^{\circ},(b) 120^{\circ} \)
D. \( (a) 120^{\circ},(b) 60^{\circ} \)
Subject: Chemistry
The exact mathematical expression of Raoult's law is:
\( ^{\text {A }} \cdot \frac{P_{0}-P_{s}}{P_{0}}=\frac{n}{N} \)
в. \( \frac{P_{0}-P_{s}}{P_{0}}=\frac{N}{n} \)
c. \( \frac{P_{0}-P_{s}}{P_{s}}=\frac{n}{N} \)
D. \( \frac{P_{0}-P_{s}}{P_{0}}=n \times N \)
Subject: Chemistry
particular orbit, the electron does not lose its energy. Therefore, these orbits are called stationary orbits and the electrons are said to be in stationary energy states.
(b) Each orbit or shell is associated with
a definite amount of energy. Hence these are also called energy levels.
(c) An electron jumps from a lower energy level to a higher energy level, by absorbing energy. It jumps from a higher energy level to a lower energy level, by emitting energy in the form of electromagnetic radiation.
(d) Electrons move around the nucleus
in specified circular paths called orbits or shells or energy levels and are designated as \( \mathrm{K}, \mathrm{L}, \mathrm{M}, \mathrm{N} \) shells
respectively.
Arrange the above postulates of Bohr's theory in a correct sequence.
A. \( d \) a cb
B. \( d b \) a c
c. \( d \) a b c
D. b da c