AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The following data were obtained during the first order thermal decomposition of
\( S O_{2} C l_{2} \) at a constant volume.
\[
\boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g})
\]
Total pressure/
atm Experiment A Time \( / s^{-1} \)
100
Calculate the rate of the reaction when
total pressure is 0.65 at \( m \)
Subject: Chemistry
Specialised cells in the stomach
release \( H C l \) to aid digestion. If they
release too much \( H C l \), the excess can
be neutralized by antacid tablets.
Which of the following should be more effective ingredient of antacid tablets?
\( \mathbf{A} \cdot M g(O H)_{2} \)
в. \( A l(O H) \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2} \)
D. \( H_{2} S O_{4} \)
Subject: Maths
The order the matrix is \( \left[\begin{array}{lll}2 & 3 & 4 \\ 9 & 8 & 7\end{array}\right] \) is
\( \mathbf{A} \cdot 4 \times 3 \)
B. \( 3 \times 2 \)
\( c \cdot 2 \times 3 \)
D. \( 3 \times 1 \)
Subject: Chemistry
Four metals and their methods of
refinement are given :
(i) \( N i, C u, Z r, G a \)
(ii) Electrolysis, van Arkel process, Zone
refining, Monds process

Choose the right method for each metal.
A. \( N i: \) Electrolysis, \( C u: \) van Arkel process, \( Z r: \) zone refining \( G a: \) Monds process
B. \( N i: \) Monds process, \( C u \) : Electrolysis, \( Z r: \) van Arkel process, \( G a: \) Zone refining
C. \( N i: \) Monds process, \( C u \) : van Arkel process, \( Z r: \) Zone refining, \( G a \) : Electrolysis
D. \( N i \) : Electrolysis, \( C u \) : Zone refining, \( Z r \) : van Arkel process, \( G a: \) Monds process
Subject: Chemistry
The monomer that undergo radical
polymerisation most easily is:
\( \mathbf{A} \cdot C H_{2}=C H_{2} \)
\( \mathbf{B} \cdot C_{6} H_{5} C H=C H_{2} \)
\( \mathbf{c} \cdot C_{6} H_{6} \)
D. \( C H_{3}-C H=C H_{2} \)
Subject: Physics
A spring of spring constant \( 5 \times 10^{3} \frac{N}{m} \)
is stretched initially by \( 5 \mathrm{cm} \) from the unstretched position. The work required to further stretch the spring by another \( 5 \mathrm{cm} \) is
\( \mathbf{A} \cdot 6.25 N m \)
B . \( 12.50 \mathrm{Nm} \)
c. \( 18.75 N m \)
D. \( 25.00 \mathrm{Nm} \)
Subject: Maths
Find the values of a and b so that the
function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}x^{2}+3 x+a, & \text { if } & x \leq 1 \\ b x+2, & \text { if } & x>1\end{array} \) is \right.
differentiable at each \( \boldsymbol{x} \in \boldsymbol{R} \)
\( \mathbf{A} \cdot a=1, b=3 \)
В. \( a=5, b=3 \)
c. \( a=3, b=5 \)
D. \( a=3, b=1 \)
1
Subject: Physics
\( \ln \beta^{+} \) decay process, the following changes take place inside the nucleus
A \( \cdot \frac{A}{Z} X \longrightarrow_{Z-1}^{A} Y+e^{+}+\gamma \)
B . \( _{Z} X \longrightarrow_{Z+1}^{A} Y+e^{-}+\gamma \)
\( \mathbf{c} \cdot_{Z}^{A} X \longrightarrow_{Z}^{A} Y+e^{-}+\gamma \)
D \( \cdot \frac{A}{Z} X \longrightarrow_{Z}^{A} Y+e^{-}+\bar{\gamma} \)
Subject: Physics
A girl having mass of 35 kg sits on a trolley of mass 5 kg. The trolley is
given an initial velocity of \( 4 m s^{-1} \) by applying a force. The trolley comes to rest after traversing a distance of \( 16 \mathrm{m} \) How much work is done on the
trolley?
A. ०
B. 320 J
c. \( 120 \mathrm{J} \)
D. 250 J
Subject: Maths
The number of cubic polynomials \( \boldsymbol{P}(\boldsymbol{x}) \) satisfying \( P(1)=2, P(2)=4, P(3)=6 \)
\( P(4)=8 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. more than one but finitely manyt
D. infinitely many
Subject: Chemistry
\( N_{2}+O_{2} \leftrightharpoons 2 N O, K_{1} ; \quad \frac{1}{2} N_{2}+ \)
\( \frac{1}{2} O_{2} \leftrightharpoons N O, K_{2} \)
\( \mathbf{2} N \boldsymbol{O} \rightleftharpoons \boldsymbol{N}_{2}+\boldsymbol{O}_{2}, \boldsymbol{K}_{3} ; \quad \boldsymbol{N} \boldsymbol{O} \rightleftharpoons \)
\( \frac{1}{2} N_{2}+\frac{1}{2} O_{2}, K_{4} \)
Correct relation(s) between \( \boldsymbol{K}_{1}, \boldsymbol{K}_{2}, \boldsymbol{K}_{3} \)
and \( \boldsymbol{K}_{4} \) is/are:
This question has multiple correct options
A \( \cdot K_{1} \times K_{3} \)
в. \( \sqrt{\left(K_{1}\right)} \times K_{4}=1 \)
c. \( \sqrt{\left(K_{3}\right)} \times K_{2}=1 \)
D. None of the above
Subject: Maths
Let the interval \( I[-1,4] \) and \( f: I \rightarrow R \)
be a function such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{\boldsymbol{3}}- \)
\( 3 x \). Then the range of the function is
A . [2,52]
в. [-2,2]
\( \mathbf{c} \cdot[-2,52] \)
D. none of these
Subject: Chemistry
Specify the coordination geometry and
hybridisation of \( N \) and \( B \) atoms in a 1:
1 complex of \( B F_{3} \) and \( N H_{3} \)
\( \mathbf{A} \cdot N: \) tetrahedral, \( s p^{3} ; B: \) planar, \( s p^{2} \)
B. \( N: \) pyramidal, \( s p^{3} ; B: \) pyramidal, \( s p^{3} \)
C. \( N: \) pyramidal, \( s p^{3} ; B: \) planar, \( s p^{3} \)
D. \( N: \) tetrahedral, \( s p^{3} ; B: \) tetrahedral, \( s p^{3} \)
Subject: Chemistry
What is the standard reduction
potential \( \left(\boldsymbol{E}^{o}\right) \) for \( \boldsymbol{F} \boldsymbol{e}^{\mathbf{3}+} \rightarrow \boldsymbol{F} \boldsymbol{e} \)
Given that:
\( \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e} \boldsymbol{6}-\rightarrow \boldsymbol{F} \boldsymbol{e} ; \boldsymbol{E}_{\boldsymbol{F}}^{o} \boldsymbol{e}_{\boldsymbol{F} e^{2+} / \boldsymbol{F} e}= \)
\( -0.47 V \)
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+} ; \boldsymbol{E}_{\boldsymbol{F} e^{3+} / \boldsymbol{F} e^{2+}}^{o}= \)
\( +0.77 V \)
A \( .+0.057 V \)
в. \( +0.30 V \)
c. \( -0.30 V \)
D. \( -0.057 V \)
Subject: Chemistry
When 0.01 mole of a cobalt complex is treated with excess silver nitrate
solution, 4.305 g silver chloride is precipitated. The formula of the complex is:
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)
В . \( \left[C o\left(N H_{3}\right)_{6} C l_{3}\right] \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right] C l_{2} \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] N O_{3} \)
Subject: Maths
In the year 2000 , rice formed \( 20 \% \) of the total food gain production in a country. In the next year, the total food grain production increased by \( 20 \% \) and the rice production was \( 25 \% \) of the total food grain production. What is the increase in the production of rice from
\( \mathbf{2 0 0 0} \) to \( \mathbf{2 0 0 1} \) ?
Subject: Maths
\( \mathbf{1}+\mathbf{3}+\mathbf{6}+\mathbf{1 0}+\ldots+\frac{(\boldsymbol{n}-\mathbf{1}) \boldsymbol{n}}{\mathbf{2}}+ \)
\( \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})}{\mathbf{2}}= \)
A. \( \frac{n(n+1)(n+2)}{3} \)
B. \( \frac{(n+1)(n+2)}{6} \)
c. \( \frac{n(n+1)(n+2)}{6} \)
D. \( \frac{(n+2)(n+1)^{2}}{3} \)
Subject: Physics
The volume(V) of a monatomic gas
varies with its temperature (T), as
shown in the graph. The ratio of work
done by the gas, to the heat absorbed by
it, when it undergoes a change from
state \( A \) to state \( B \), is?
A \( \cdot \frac{1}{3} \)
B. 2 \( \overline{5} \)
\( c \cdot 2 \)
7
D. 2
3
Subject: Maths
Let \( \hat{a} \) and \( \hat{b} \) be two unit vectors. If the vectors \( \vec{c}=\hat{a}+2 \hat{b} \) and \( \vec{d}=5 \hat{a}-4 \hat{b} \) are
perpendicular to each other, then the angle between \( \hat{a} \) and \( \hat{b} \) is
A. \( \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{3} \)
D. \( \frac{\pi}{4} \)
Subject: Physics
Two metallic rings of radius \( R \) are
rolling on a metallic rod. A magnetic
field of magnitude \( B \) is applied in the
region. The magnitude of potential
difference between points \( A \) and \( C \) on
the two rings (as shown), will be:
\( A \)
в. \( 4 B \omega R^{2} \)
\( \mathbf{c} \cdot 8 B \omega R^{2} \)
\( D \cdot 2 B \omega R^{2} \)
Subject: Physics
Q Type your question
y \( D-D_{0}\lfloor\bar{a} / \) \kappa.
bo 14
\( d \) is placed with it's edges on the \( x \) and \( y \)
axis. The loop is moved with a constant velocity \( \vec{v}=v_{0} \hat{i} . \) The emf induced in
the loop is :
A \( \cdot B_{0} v_{0} d \)
B. \( \frac{B_{0} v_{0} d^{2}}{2 a} \)
c. \( \frac{B_{0} v_{0} d^{3}}{a^{2}} \)
D. \( \frac{B_{0} v_{0} d^{2}}{a} \)
Subject: Maths
In one shop, an article is marked 75\% above the cost price but the purchaser is allowed a discount of \( 20 \% \) on the
marked price. In another shop, a similar article is sold for \( \mathrm{Rs} .58 \) at a gain of \( 45 \% \) What did the purchased pay for this article in the first shop?
A . \( R s .69 \)
B. \( R s .56 \)
c. \( R s .62 \)
D. Rs.65
Subject: Chemistry
Which of the following acids, listed with
their ionization constant at \( 25^{\circ} C \), is the
strongest?
A . Nitrous acid \( \left(H N O_{2}\right) K_{i}=4.5 \times 10^{-4} \)
B. Formic acid \( \left(H C H O_{2}\right) K_{i}=1.8 \times 10^{-4} \)
C . Benzoic acid \( \left(H C_{7} H_{5} O_{2}\right) K_{i}=6.3 \times 10^{-5} \)
D. Acetic acid \( \left(H C_{2} H_{3} O_{2}\right) K_{i}=1.8 \times 10^{-5} \)
E . Hydrocyanic acid (H \( C N \) ) \( K_{i}=4.0 \times 10^{-10} \)
Subject: Physics
A thin circular ring of mass \( M \) and
radius \( r \) is rotating about its axis with
a constant angular velocity \( \omega . \) Two
objects, each of mass \( \boldsymbol{m}, \) are attached gently to the opposite ends of the
diameter of the ring. The wheel now rotates with an angular velocity
\( \mathbf{A} \cdot \frac{\omega M}{(M+m)} \)
B. \( \frac{\omega(M-2 m)}{(M+2 m)} \)
\( ^{\mathbf{c}} \cdot \frac{\omega M}{(M+2 m)} \)
D. \( \frac{\omega(M+2 m)}{M} \)
Subject: Chemistry
What is the minimum pH necessary to
cause a precipitate of
\( \boldsymbol{P b}(\boldsymbol{O} \boldsymbol{H})_{2}\left(\boldsymbol{K}_{s p}=1.2 \times 10^{-5}\right) \) to form
in a \( 0.12 M P b C l_{2} \) solution?
A . 12.4
B. 10.0
c. 12.0
D. 11.1
Subject: Physics
Assertion
If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies.
Reason
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.
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
Statement-1:
The point \( A(1,0,7) \) is the mirror image of the point \( B(1,6,3) \) in the line \( \frac{x}{1}= \) \( \frac{y-1}{2}=\frac{z-2}{3} \)
Statement-2:
The line: \( \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) bisects the
line segment joining \( A(1,0,7) \) and \( B(1,6,3) \)
A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement- -1
B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-
c. Statement-1 is true, Statement-2 is false
D. Statement-1 is false, Statement-2 is true
Subject: Chemistry
A 0.1 molal solution of a monobasic
acid is \( 45 \% \) ionized. Calculate the
depression in freezing point:
(Molecular weight of the acid \( =300 \)
\( \left.\mathrm{g} / \mathrm{mol}, \boldsymbol{K}_{f}=\mathbf{1 . 8 6} \boldsymbol{K} \boldsymbol{m o l}^{-1} \boldsymbol{k g}\right) \)
A \( .--0.199^{\circ} \mathrm{C} \)
B . \( 2.00^{\circ} \mathrm{C} \)
\( \mathrm{c} \cdot 0^{\circ} \mathrm{C} \)
D. \( 0.269^{\circ} \mathrm{C} \)
Subject: Maths
\( * \) is a binary operation on \( Z \) such that:
\( \boldsymbol{a} * \boldsymbol{b}=\boldsymbol{a}+\boldsymbol{b}+\boldsymbol{a} \boldsymbol{b} \)
The solution of \( (3 * 4) * x=-1 \) is
A . 1
B. -
\( c \cdot 4 \)
D. 3
Subject: Physics
A string of mass \( 3 \mathrm{kg} \) is under tension of 400N. The length of the stretched string
is \( 25 \mathrm{cm} . \) If the transverse jerk is stuck
at one end of the string find the
velocity?
A \( \cdot 25 \pi^{2} m s^{-2} \)
B. \( -5 \pi^{2} m s^{-2} \)
\( \mathbf{c} \cdot 5 \pi^{2} m s^{-2} \)
D. \( -25 \pi^{2} m s^{-2} \)
Subject: Maths
Evaluate the integral \( \int_{\pi / 4}^{\pi / 2} \log (1+\cot x) d x \)
A \( \cdot \frac{\pi}{4} \log 2 \)
в. \( \frac{\pi}{8} \log 2 \)
c. \( \pi \log 2 \)
D.
Subject: Maths
The unit vector along \( 2 i-3 j+k \) is
A. \( \frac{2 i-3 j+k}{\sqrt{14}} \)
в. \( \frac{2 i-3 j+k}{\sqrt{5}} \)
c. \( \frac{2 i-3 j+k}{\sqrt{15}} \)
D. None of these
Subject: Chemistry
Match the column I with column II and
mark the appropriate choice.
" Column I
An element which
\( (A) \)
\( 1+8 \) can show
(i) oxidation state
An element with \( 7+ \)
(B) as the most stable
(ii) \( P m \) oxidation state in
its oxides
Radioactive
(iii) 0
\( \mathcal{D}_{\mathcal{S}} \)
(C) Ianthanoid
Lanthanoid which
(D) shows shows +4 oxidation state 4
(iv) \( M n \)
\( \mathbf{A} \cdot(A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
B \( \cdot(A) \rightarrow(i i),(B) \rightarrow(i i i),(C) \rightarrow(i v),(D) \rightarrow(i) \)
C \( \cdot(A) \rightarrow(i v),(B) \rightarrow(i),(C) \rightarrow(i i),(D) \rightarrow(i i i) \)
D. \( (A) \rightarrow(i i i),(B) \rightarrow(i v),(C) \rightarrow(i i),(D) \rightarrow(i) \)
Subject: Maths
In the given figure given below \( P Q \) is a
diameter chord \( S R \) is parallel to \( P Q \)
Given \( \angle P Q R=58^{\circ}, \) calculate \( \angle R P Q \)
\( A \cdot 30^{\circ} \)
B. 32
\( c \cdot 34 \)
\( D .36 \)
Subject: Physics
A photon of energy \( 4 e V \) is incident on a
metal surface whose work function is
\( 2 e V . \) The minimum reverse potential to be applied for stopping the emission of electrons is:
\( \mathbf{A} \cdot 2 V \)
B. \( 4 V \)
c. \( 6 V \)
D. \( 8 V \)
Subject: Physics
Fill in the blank.
The length of the vocal chords in men and women is approximately and \( _{--}-_{-} \) respectively
A. \( 15 \mathrm{mm}, 20 \mathrm{mm} \)
B. 20 \( \mathrm{mm}, 30 \mathrm{mm} \)
c. \( 20 \mathrm{mm}, 15 \mathrm{mm} \)
D. 25 mm, 15 mm
Subject: Maths
If \( A \) is an invertible matrix of order \( n \)
then the determinant of adj \( A \) is equal
to:
\( \mathbf{A} \cdot|A|^{n} \)
В \( \cdot|A|^{n+1} \)
c. \( |A|^{n-1} \)
D. \( |A|^{n+2} \)
Subject: Physics
The height of mercury barometer is \( h \)
when the atmospheric pressure is
\( 10^{5} P a, \) The pressure at \( x \) in the shown
diagram is
\( \mathbf{A} \cdot 10^{5} P a \)
В \( .0 .8 \times 10^{5} \mathrm{Pa} \)
c. \( 0.2 \times 10^{5} P a \)
D. \( 120 \times 10^{5} \mathrm{Pa} \)
Subject: Physics
Assertion
A ladder is more likely to slip when a person is near the top than when he is
near the bottom.
Reason
The friction between the ladder and the
floor decreases as he climbs up.
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
If \( A \) and \( B \) are two events, the
probability that exactly one of them occurs is given by
This question has multiple correct options
A. \( P(A)+P(B)-2 P(A \cap B) \)
В \( \cdot P\left(A \cap B^{\prime}\right)+P\left(A^{\prime} \cap B\right) \)
c. \( P(A \cap B)-P(A \cap B) \)
D. \( P\left(A^{\prime}\right)+P\left(B^{\prime}\right)-2 P\left(A^{\prime} \cap B^{\prime}\right) \)
Subject: Physics
Assertion
Displacement \( (S) \) -time
(t) graph of a
particle moving in a straight line is
shown in figure. Work done by all the
forces is equal to change in kinetic
energy.
Reason
Work done by all the forces between
time interval \( t_{1} \) and \( t_{2} \) is definitely zero.
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
Two thick plates having same charges (same charge density \( \sigma \) ) are placed side by side. Consider the case of infinite plate. Find the difference between the electric field present
between the plate and remaining space of the plate, \( (\varepsilon=\text { permittivity }) \)
A \( \cdot \frac{\sigma}{\varepsilon} \)
в. \( 2 \frac{\sigma}{\varepsilon} \)
c. \( \frac{\sigma}{2 \varepsilon} \)
D.
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{i} & \mathbf{0} \\ \mathbf{0} & \boldsymbol{i}\end{array}\right], \boldsymbol{n} \in \boldsymbol{N}, \) then \( \boldsymbol{A}^{4 n} \) equals
\( A \cdot\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \)
в. \( \left[\begin{array}{ll}i & 0 \\ 0 & i\end{array}\right] \)
c. \( \left[\begin{array}{ll}0 & i \\ i & 0\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \)
Subject: Physics
The principle section of a glass prism is isosceles triangle \( A B C \) with \( A B=A C, \) the face \( A C \) is silvered. A ray of light is incident normally on the face \( A B \) and after two reflections, it emerges from the base BC perpendicular to the base.
Angle of BAC of the prism is
\( A \cdot 30 \)
B. 36
\( c \cdot 18 \)
\( D \cdot 72 \)
Subject: Maths
Given: \( z_{1}+z_{2}+z_{3}=A ; z_{1}+z_{2} w+ \)
\( z_{3} w^{2}=B ; z_{1}+z_{2} w^{2}+z_{3} w=C \) where
\( \boldsymbol{w} \) is cube rott of unity
Prove: \( |\boldsymbol{A}|^{2}+|\boldsymbol{B}|^{2}+|\boldsymbol{C}|^{2}= \)
\( \left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}+\left|z_{3}\right|^{2}\right) \)
Subject: Physics
A uniform string of length \( l \) is fixed at both ends such that tension \( T \) is
produced in it. The string is excited to vibrate with maximum displacement
amplitude \( a_{o} . \) The maximum kinetic
energy of the string for its fundamental tone is given as \( \frac{a_{o}^{2} \pi^{2} T}{x l} . \) Find \( x \)
Subject: Chemistry
Which of the following is incorrect?
A. \( M g \) burns in air releasing dazzling light rich in \( U V \)
rays
B. \( C a C l_{2} \cdot 6 H_{2} O \) when mixed with ice gives freezing
mixture
c. \( M g \) cannot form complexes
D. \( B e \) can form complexes due to its very small size
Subject: Physics
Find the relation between potential
difference V and separation between the
plates z:
\( ^{\mathrm{A}} \cdot_{V^{2}}=\frac{K_{z}\left(z_{0}-z\right)^{2}}{A \varepsilon_{0}} \)
B. \( V^{2}=\frac{2 K_{z}\left(z_{0}-z\right)^{2}}{A \varepsilon_{0}} \)
c. \( V^{2}=\frac{4 K_{z}\left(z_{0}-z\right)^{2}}{A \varepsilon_{0}} \)
D. \( V^{2}=\frac{K_{z}\left(z_{0}-z\right)^{2}}{4 A \varepsilon_{0}} \)
Subject: Chemistry
Extraction of aluminium from
aluminium oxide \( \left(A l_{2} O_{3}\right) \) is best done
by :
A . electrolytic reduction of \( A l_{2} O_{3} \)
B. reduction of \( A l_{2} O_{3} \) with carbon
c. reduction of \( A l_{2} O_{3} \) wilh sodium
D. reduction of \( A l_{2} O_{3} \) with \( c o \)
Subject: Chemistry
A mixture of \( 1.65 \times 10^{21} \) molecules of \( x \)
and \( 1.85 \times 10^{21} \) molecules of \( Y \) weighs
0.688 g. If molecular mass of Y is 187 what is the molecular mass of \( X ? \)
A .41 .35
B. 42.35
c. 41.65
D. 41.75
Subject: Physics
There is a uniform (in spatial districution) magnetic filed B in a circular region of radius \( R \) as shown in
the figure whose magnitude varies uniformly a the rate \( \beta \) w.r.t. time. The emf induced across the ends of a
circular concentric conducting arc of
radius \( R_{1} \) having an agle \( \theta \) as shown
\( \left(<\boldsymbol{O} \boldsymbol{A} \boldsymbol{O}^{\prime}=\boldsymbol{\theta}\right) \) is
\( ^{\mathrm{A}} \cdot \frac{\theta}{2 \pi} R_{1}^{2} \cdot \beta \)
B. \( \frac{\theta}{2} R^{2} \cdot \beta \)
c. \( \frac{\theta}{2 \pi} R^{2} . \).
D. zero
Subject: Chemistry
The rate law for a reaction between the
substances \( A \) and \( B \) is given by:
Rate \( =\boldsymbol{K}[\boldsymbol{A}]^{n}[\boldsymbol{B}]^{m} . \) On doubling the
concentration of \( A \) and having concentration of \( B \) the ratio of new rate
law to the earlier rate of the reaction will
be as
\( \mathbf{A} \cdot n-m \)
B \( \cdot 2^{(n-m)} \)
c. \( \frac{1}{2^{m+n}} \)
D. \( m+n \)
Subject: Maths
Let \( \boldsymbol{f}: \mathbb{R} \rightarrow(0,1) \) be a continuous
function. Then, which of the following function(s) has (have) the value zero at
some point in the interval (0,1)\( ? \) This question has multiple correct options
\( \mathbf{A} \cdot f(x)+\int_{0}^{\frac{\pi}{2}} f(t) \sin t d t \)
B . \( e^{x}-\int_{0}^{x} f(t) \sin t d t \)
C \( \cdot x-\int_{0}^{\frac{\pi}{2}-x} f(t) \cos t d t \)
D. \( x^{9}-f(x) \)
Subject: Physics
A ray of light travelling in a transparent medium of refractive index \( \mu, \) falls on a
surface separating the medium from
air at an angle of incidence of \( 45^{\circ} . \) For
which of the following value of \( \mu \) the ray can undergo total internal reflection?
A. \( \mu=1.33 \)
в. \( \mu=1.40 \)
c. \( \mu=1.50 \)
D. \( \mu=1.25 \)
Subject: Maths
If \( l_{1}=\frac{d}{d x}\left(e^{\sin x}\right), l_{2}= \)
\( \lim _{h \rightarrow 0} \frac{e^{\sin (x+h)}-e^{\sin x}}{h} \) and \( l_{3}= \)
\( \int e^{\sin x} \cos x d x, \) then which one of the
following is correct?
A. \( l_{1} \neq l_{2} \)
в. \( \frac{d}{d x}\left(l_{3}\right)=l_{2} \)
\( \mathbf{c} \cdot \int l_{3} d x=l_{2} \)
D. \( l_{2}=l_{3} \)
Subject: Maths
Choose the correct answer from the
alternatives given:
The sum of \( \frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+ \)
\( \frac{1}{\sqrt{4}+\sqrt{3}}+\ldots . .+\frac{1}{\sqrt{100}+\sqrt{99}} \) is
\( \mathbf{A} \cdot \mathbf{9} \)
B . 10
c. 11
D. None of these
Subject: Chemistry
In a 20 litre vessel initially 1,1,1 mole
of \( C O, H_{2} O, C O_{2} \) are present, then for
the equilibrium of \( \boldsymbol{C O}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \)
\( C O_{2}+H_{2} . \) Which of the following is
true?
A. \( H_{2} \) more then 1 mole
B. \( C O, H_{2} O, H_{2} \) less then 1 mole
c. \( C O_{2} \) and \( H_{2} O \) both more than 1 mole
D. All of these
Subject: Chemistry
Assertion
White phosphorus is more reactive than
red phosphorus.
Reason
Red phosphorus contains tetrahedral units linked to one another to form
linear chains.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Physics
A planet of mass \( m \) moves around the
sun of mass \( M \) in an elliptical orbit. The
maximum and minimum distances of
the planet from the sun are \( r_{1} \) and \( r_{2} \) respectively. The time period of the planet is proportional to:
\( \mathbf{A} \cdot r_{1}^{3 / 2} \)
B \( \cdot r_{2}^{3 / 2} \)
c. \( \left(\frac{r_{1}+r_{2}}{2}\right)^{3 / 2} \)
D. \( \frac{\left(r_{1}-r_{2}\right)^{3 / 2}}{2} \)
Subject: Physics
An ideal gas is initially at \( P_{1}, V_{1} \) is
expanded to \( P_{2}, V_{2} \) and then
compressed adiabatically to the same
volume \( V_{1} \) and pressure \( P_{3} \). If \( W \) is the
net work done by the gas in the complete process which of the following
is true.
A. \( W>0 ; P_{3}>P_{1} \)
В. \( W<0 ; P_{3}>P_{1} \)
\( \mathbf{c} \cdot W>0 ; P_{3}<P_{1} \)
D. \( W<0 ; P_{3}<P_{1} \)
Subject: Physics
A vertical spring with force constant \( k \)
is fixed on a table. A ball of mass \( \mathrm{m} \) at a
height h above the free upper end of the
spring falls vertically on the spring so that the spring is compressed by a
distance d. The net work done in
the process is
\( ^{\mathbf{A}} \cdot m g(h+d)-\frac{1}{2} k d^{2} \)
B . \( m g(h-d)-\frac{1}{2} k d^{2} \)
c. \( m g(h-d)+\frac{1}{2} k d^{2} \)
D \( m g(h+d)+\frac{1}{2} k d^{2} \)
Subject: Maths
In a factory which manufactures bolts, machines \( A, B \) and \( C \) manufacture \( 30 \%, 50 \% \) and \( 20 \% \) of the bolts
respectively. Of their output \( 3 \%, 4 \% \) and \( 1 \% \) respectively are defective bolts. bolt is drawn at random from the
product and is found to be defective Find the probability that this is not manufactured by machine B.