AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
The number of neutrons accompanying the formation of \( _{54}^{139} X e \) and \( _{38}^{94} S r \) from the absorption of a slow neutron by \( _{92}^{235} U \) followed by nuclear fission is:
\( \mathbf{A} \cdot \mathbf{0} \)
B . 2
c. 1
D. 3
Subject: Physics
A person can see objects clearly only upto a maximum distance of \( 60 \mathrm{cm} \). His
eye defect nature of the corrective lens
and its focal length are respectively
A. Myopia, convex, \( 60 \mathrm{cm} \)
B. Myopia, concave, \( 60 \mathrm{cm} \)
c. Hypermetropia, concave, \( 60 \mathrm{cm} \)
D. Contract, convex, \( 60 \mathrm{cm} \)
Subject: Physics
A copper block of mass \( 50 \mathrm{g} \) is heated to
\( 100^{\circ} \) and placed on a block of ice at \( 0^{\circ} \mathrm{C} \)
The specific heat of copper is \( 0.1 \mathrm{cal} \)
\( g^{-1} \cdot C^{-1} \) and latent heat of ice is
\( 80 c a l g^{-1} . \) The amount of ice melted is
A. \( 6.15 \mathrm{g} \)
B. \( 6.2 \mathrm{g} \)
c. \( 6.25 \mathrm{g} \)
D. \( 6.3 \mathrm{g} \)
Subject: Physics
Two forces are such that the sum of
their magnitude is \( 18 N \) and their
resultant is \( 12 N \) and it is
also perpendicular to the smaller force.Then the magnitude of the forces
are
A \( .12 N, 6 N \)
B . \( 13 N, 5 N \)
c. \( 10 N, 8 N \)
D. \( 16 N, 2 N \)
Subject: Chemistry
Among the following, identify the species with an atom in +6 oxidation
state.
\( \mathbf{A} \cdot\left[M n O_{4}\right]^{-} \)
B . \( \left[\operatorname{Cr}(C N)_{6}\right]^{3-} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( \operatorname{Cr} \mathrm{O}_{2} \mathrm{Cl}_{2} \)
Subject: Maths
In an ellipse, the distance between its focii is 6 and minor axis is \( 8 . \) Then its'
eccentricity is
A \( \cdot \frac{3}{5} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{4}{5} \)
D. \( \frac{1}{\sqrt{5}} \)
Subject: Physics
Two bodies of masses \( 0.1 k g \) and \( 0.4 k g \) move towards each other with velocities
\( 1 m / s \) and \( 0.1 m / s \) respectively. After
collision they stick together. In \( 10 s \) the combined mass travels a distance of :
A. zero
B. \( 12 m \)
c. \( 0.12 m \)
D. \( 1.2 m \)
Subject: Chemistry
Consider the following statements.
\( S_{1}: \) The percentage of s-character in the
orbital forming \( S-S \) bonds and \( P-P \)
bonds in \( S_{8} \) and \( P_{4} \) molecules respectively are same.
\( S_{2}: \ln S F_{4} \) the bond angles, instead of
being \( 90^{\circ} \) and \( 180^{\circ} \) are \( 89^{\circ} \) and \( 177^{\circ} \) respectively due to the repulsions between lone pair and bond pairs of electrons.
\( S_{3}: \) Aqueous \( H_{3} P O_{4} \) is syrupy (i.e more viscous than water)
\( S_{4}: S i O_{2} \) crystal maybe considered as giant molecule in which eightmembered rings are formed with alternate silicon and oxygen atoms of these:
A. \( S_{1} \& S_{4} \) are correct only
B . \( S_{2}, S_{3} \& S_{4} \) are correct only.
c. \( S_{1}, S_{2}, S_{3} \& S_{4} \) are correct
D. \( S_{1}, S_{2} \& S_{3} \) are correct only.
Subject: Maths
Consider the function \( y=|x-1|+ \)
\( |x-2| \) in the interval [0,3] and discuss
the continuity and differentiability of
the function in this interval.
This question has multiple correct options
A. continuous everywhere
B. differentiable everywhere except at \( x=1 \) and \( x=2 \)
c. differentiable everywhere
D. continuous everywhere except at \( x=1 \) and \( x=2 \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & -\mathbf{2} \\ \mathbf{4} & \mathbf{5}\end{array}\right] \) and \( \boldsymbol{f}(\boldsymbol{t})=\boldsymbol{t}^{2}-\boldsymbol{3} \boldsymbol{t}+\mathbf{7} \)
then \( \boldsymbol{f}(\boldsymbol{A})+\left[\begin{array}{cc}\mathbf{3} & \mathbf{6} \\ -\mathbf{1 2} & -\mathbf{9}\end{array}\right]= \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cc}0 & 0 \\ 0 & 0\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}0 & 1 \\ 1 & 0\end{array}\right] \)
\( \mathbf{D} \cdot\left[\begin{array}{cc}1 & 1 \\ 0 & 0\end{array}\right] \)
Subject: Physics
An airplane is flying at a height of
\( \mathbf{1 9 6 0} \mathbf{m} \) in the horizontal direction with
a velocity of \( 360 \mathrm{km} / \mathrm{hr} \). It drops a bomb. The bomb strikes a point on the ground, then the time took \( t \) by the bomb to reach the ground is:
A. \( 20 \sqrt{2} \) sec
B. 20 sec
c. \( 10 \sqrt{2} \mathrm{sec} \)
D. 10 sec
Subject: Physics
Two convex lenses of focal lengths \( f_{1} \)
and \( f_{2} \) form images with magnification
\( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2}, \) when used individually for an object kept at the same distance
from the lenses. Then \( f_{1} / f_{2} \) is:
A \( \cdot \frac{m_{1}\left(1+m_{2}\right)}{m_{2}\left(1+m_{2}\right)} \)
в. \( \frac{m_{1}\left(1+m_{2}\right)}{m_{2}\left(1+m_{1}\right)} \)
c. \( \frac{m_{2}\left(1+m_{1}\right)}{m_{1}\left(1+m_{2}\right)} \)
D. \( \frac{m_{2}\left(1+m_{2}\right)}{m_{1}\left(1+m_{1}\right)} \)
Subject: Maths
There are n different object \( 1,2,3, \ldots n \)
distributed at random in n boxes
\( A_{1}, A_{2}, A_{3}, \cdots A_{N} . \) Find the probability
that two objects are placed in the boxes corresponding to their number.
A .
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{2}{3} \)
Subject: Chemistry
What is the hybridization state of
carbon number 2 and 3 in the following
compound \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C} \equiv \boldsymbol{C H} \)
A. sp and \( s p^{2} \)
B. \( s p^{2} \) and \( s p \)
\( \mathbf{c} \cdot s p^{3} \) and \( s p \)
D. \( s p \) and \( s p \)
Subject: Chemistry
Choose the correct option:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is a
acid,
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) is a
acid and
\( H_{3} P O_{2} \) is a
acid
A. dibasic, tribasic, monobasic
B. tribasic, monobasic, dibasic
c. monobasic, dibasic, tribasic
D. tribasic, dibasic, monobasic
Subject: Maths
The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) given by
\( f(x)=\cos x \) for all \( x \in R, \) is :
A. surjective bu nor injective
B. injective but nor surjective
c. neither injective nor surjective
D. injective
Subject: Physics
The distance between the vertex and the
center of mass of a uniform solid planar
circular segment of angular size \( \boldsymbol{\theta} \) and
radius R is given by
A \( \cdot \frac{4}{3} R \frac{\sin (\theta / 2)}{\theta} \)
B. \( R \frac{\sin (\theta / 2)}{\theta} \)
c. \( \frac{4}{3} R \cos \left(\frac{(\theta)}{2}\right) \)
D \( \cdot \frac{2}{3} R \cos (\theta) \)
Subject: Physics
As per the diagram a point charge \( +q \) is placed at the origin 0. work done in
taking another point charge - \( \mathrm{Q} \) from the point \( A[\text { coordinates }(0, a)] \) to another point \( \mathrm{B}[\text { coordinates }(\mathrm{a}, 0)] \) along the
straight line \( A B \) is:
A. zero
B. \( \left(\frac{q Q}{4 \pi \varepsilon_{0}} \frac{I}{a^{2}}\right) \sqrt{2} a \)
c. \( \left(\frac{-q Q}{4 \pi \varepsilon_{0}} \frac{I}{a^{2}}\right) \sqrt{2} a \)
D. \( \left(\frac{q Q}{4 \pi \varepsilon_{0}}-\frac{I}{a^{2}}\right)\left(\frac{a}{\sqrt{2}}\right) \)
Subject: Physics
the density of cooking oil is \( 0.6 g / c m^{3} \)
What is the mass of \( 18 \mathrm{cm}^{3} \) of the
cooking oil?
A . \( 0.5 g \)
в. \( 10.8 g \)
c. \( 18.9 g \)
D. \( 20.0 g \)
Subject: Physics
The equations of two displacement sound waves propagating in a medium are given by \( s_{1}=2 \sin (200 \pi t) \) and
\( s_{2}=5 \sin (150 \pi t) \) The ratio of
intensities of sound produced is :
A . 4: 25
B. 9: 100
c. 8: 15
D. 64:225
Subject: Chemistry
A mixed solution of potassium hydroxide and sodium carbonate required \( 15 \mathrm{mL} \) of \( \frac{N}{20} H C l \) solution when titrated with phenolphthalein as an indicator. But the same amount of
the solution when titrated with methyl orange as an indicator required \( 25 \mathrm{ml} \) of
the same acid. The amount of \( K O H \)
present in the solution is :
A. \( 0.014 \mathrm{g} \)
B. \( 0.14 \mathrm{g} \)
c. \( 0.028 \mathrm{g} \)
D. \( 1.4 \mathrm{g} \)
Subject: Maths
If \( x^{3}-y^{3}+3 x y^{2}-3 x^{2} y+1=0, \) then
\( \operatorname{at}(0,1) \frac{d y}{d x} \) equals
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 2 \)
D.
Subject: Maths
In a triangle \( A B C, \) bisector of angle \( C \)
meets the side \( A B \) at \( D \) and
circumcentre at E. The maximum value
of CD.DE is equal to
A \( \cdot a^{2} / 4 \)
B . \( b^{2} / 4 \)
c. \( c^{2} / 4 \)
D. \( (a+b)^{2} / 4 \)
Subject: Maths
Assertion
If \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2})(\boldsymbol{x}-\mathbf{3}), \) then
area enclosed by \( |\boldsymbol{f}(\boldsymbol{x})| \) between the
lines \( x=2.2, x=2.8 \) and \( x- \) axis is equal to \( \int_{2.2}^{2.8}(x-1)(x-2)(x-3) d x \)
Reason
\( (x-1)(x-2)(x-3) \leq 0 \) for all \( x \in \)
[2.2,2.8]
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: Chemistry
\( \mathbf{P} \mathrm{Cl}_{3} \) is prepared by the action of \( \mathbf{C l}_{2} \)
on:
\( \mathbf{A} \cdot \mathrm{P}_{2} \mathrm{O}_{3} \)
в. \( \mathrm{P}_{2} \mathrm{O}_{5} \)
c. white \( \mathrm{P} \)
D. \( \mathrm{H}_{3} \mathrm{PO}_{3} \)
Subject: Chemistry
Assertion (A): Stability of \( N H_{3} \) is
greater than \( \boldsymbol{P H}_{3} \)
Reason (R): M - H bond energy increases down the group in the hydrides of pnicogens.
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
\( c \cdot(A) \) is true and
(R) is false
D. (A) is false but (R) is true
Subject: Chemistry
Calculate the \( \Delta \boldsymbol{H}_{f}^{o} \) of \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{12} \boldsymbol{O}_{6}(\boldsymbol{s}) \) from
the following data:
\( \Delta \boldsymbol{H}_{c o m b}\left[\boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}(\boldsymbol{s})\right]= \)
\( -2816 k J / m o l \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{f}^{o} \quad \) of \( \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})=-\boldsymbol{3} \boldsymbol{9} \boldsymbol{3} . \boldsymbol{5} \boldsymbol{k} \boldsymbol{J} / \boldsymbol{m} \boldsymbol{l} \)
\( \Delta H_{f}^{o} \quad \) of \( H_{2} O(l)=-285.9 k J / m o l \)
A. \( -126.0 k J / m o l \)
В. \( -1260 k J / m o l \)
c. \( -1220 k J / m o l \)
D. \( -160 k J / \) mol
Subject: Physics
A police van moving on a highway with a speed of \( 30 \mathrm{km} / \mathrm{hr} \) fires a bullet at a
thief's car speeding away in the same
direction with a speed of \( 192 k m / h r \) If the muzzle speed of the bullet is \( 150 m / s, \) with what speed does the bullet hit the thief's car? (Note:Obtain
that speed which is relevant for
damaging the thief's car)
Subject: Maths
If a polynomial \( f(x)=4 x^{4}-a x^{3}+ \)
\( b x^{2}-c x+5,(a, b, c \epsilon R) \) has four
positive real roots \( r_{1}, r_{2}, r_{3}, r_{4} \) such that
\( \frac{r_{1}}{2}+\frac{r_{2}}{4}+\frac{r_{3}}{5}+\frac{r_{4}}{8}=1 \) Then value of \( a \)
will be
A . 20
B . 21
\( c \cdot 19 \)
D. 22
Subject: Chemistry
Assertion
Large number of organic compounds
are formed with long carbon-chain.
Reason
Maximum catenation occurs in carbon
atoms.
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
The side of a regular hexagon is \( \boldsymbol{p} \boldsymbol{c m} \)
then its area is
A \( \cdot \frac{\sqrt{3}}{2} p^{2} \mathrm{cm}^{2} \)
B. \( \frac{3 \sqrt{3}}{2} p^{2} \mathrm{cm}^{2} \)
c. \( 2 \sqrt{3} p^{2} c m^{2} \)
D. \( 6 p^{2} \mathrm{cm}^{2} \)
Subject: Maths
Show that the equation of normal at any point on the curve \( x=3 \cos t-\cos ^{3} t \)
\( \boldsymbol{y}=\mathbf{3} \sin t-\sin ^{3} \boldsymbol{t} \) is
\( 4\left(y \cos ^{3} t-x \sin ^{3} t\right)=3 \sin 4 t \)
Subject: Physics
Figure shows three circular arcs, each of radius \( R \) and total charge as
indicated. The net electric potential at
the center of curvature is :
\( ^{A} \cdot \frac{Q}{2 \pi \varepsilon_{0} R} \)
\( B \)
c. \( \frac{3 Q}{32 \pi \varepsilon_{0} R} \)
D. none of these
Subject: Maths
How many numbers between 5000 and
10,000 can be formed using the digits \( \mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9} \) each digit
appearing not more than once in each number
\( A \cdot 5 \times^{8} P_{3} \)
В. \( 5 \times^{8} C_{3} \)
c. \( 5 ! \times^{8} P_{3} \)
D. \( 5 ! \times^{8} C_{3} \)
Subject: Physics
An astronomical telescope and a Galilean telescope use identical objective lenses. They have the same magnification, when both are in normal adjustment. The eyepiece of the astronomical telescope has a focal length \( \mathrm{f} \). This question has multiple correct options
A. The tube length of the two telescope differ by f.
B. The tube length of the two telescopes differ by 2 f
c. The Galileans telescope has shorter tube length
D. The Galileans telescope has longer tube length.
Subject: Chemistry
Statement-1: Lithium chloride is
predominately covalent compound. Statement-2: Electronegativity difference between Li and Cl is small.
A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-
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
For the cell (at \( 298 \mathrm{K} \) ), which of the
following is correct?
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})|\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s})| \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q}) \| \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{a} \boldsymbol{q}) \mid \boldsymbol{A} \)
A. The cell emf will be zero when ( \( \left.\left[\mathrm{Ag}^{+}\right]\right) \) in anodic compartment \( =\left[\mathrm{Ag}^{+}\right] \) in cathodic compartment
B. The amount of AgCl(s) precipitate in anodic compartment will decrease will the working of the cell
C. The concentration of \( \left[\mathrm{Ag}^{+}\right]= \) constant, in anodic compartment during working of cell
D. \( E_{\text {cell}}=E_{A g^{+} \mid A g}^{0}-E_{C l^{-}|A g C l| A g}^{0}-\frac{0.059}{1} \log \frac{1}{\left[C l^{-}\right]_{a}} \)
Subject: Maths
Given \( 3 x-4 y=7 \) and \( x+c y=13 \) for what value of "c" will the two equation not have a solution?
A \( \cdot \frac{3}{4} \)
B. \( \frac{4}{3} \)
\( c \cdot-4 \)
D. \( \frac{-4}{3} \)
Subject: Chemistry
At \( 672^{\circ} \mathrm{C} \) and one atmosphere, \( S O_{3} \) is
partially dissociated into \( S O_{2} \) and \( O_{2} \)
\( \boldsymbol{S} \boldsymbol{O}_{3(g)} \leftrightharpoons \boldsymbol{S} \boldsymbol{O}_{2(g)}+\frac{1}{2} \boldsymbol{O}_{2(g)} . \) If the
density of the equilibrium mixture is 0.925 g/litre, then what is the degree of dissociation?
A . 0.74
B. 0.34
c. 0.68
D. 0.64
Subject: Maths
ABCD is a parallelogram where
\( \mathbf{A}(\boldsymbol{x}, \boldsymbol{y}), \mathbf{B}(\mathbf{5}, \mathbf{8}), \mathbf{C}(\mathbf{4}, \mathbf{7}) \) and \( \mathbf{D}(\mathbf{2},-\mathbf{4}) \)
Find
(i) the coordinates of \( A \)
(ii) the equation of the diagonal \( B D \)
Subject: Maths
Find the mean of the following data
using shortcut method.
\begin{tabular}{|c|c|c|c|c|}
\hline Class interval & \( 10-15 \) & \( 15-20 \) & \( 20-25 \) & \( 25-30 \) \\
\hline Frequenuy & 7 & 12 & 8 & 10 \\
\hline
\end{tabular}
A. 19.781
B . 20.836
c. 20.337
D. 21.005
Subject: Chemistry
Examples of few compounds in a particular oxidation state are given Mark the example which is not correct.
A. Phosphorus in + 1 oxidation state - \( H_{3} P O_{2} \)
B. Chlorine in +7 oxidation state - \( H C l O \)
c. Chromium in +6 oxidation state \( -C r O_{2} C l_{2} \)
D. Carbon in 0 oxidation state \( -C_{12} H_{22} O_{1} \)
Subject: Maths
Prove that: \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{y}+\boldsymbol{z} \\ \mathbf{1} & \boldsymbol{y} & \boldsymbol{z}+\boldsymbol{x} \\ \mathbf{1} & \boldsymbol{z} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right|=\mathbf{0} \)
Subject: Physics
A rubber cord catapult has cross-
sectional area \( 25 \mathrm{mm}^{2} \) and initial
length of rubber cord is \( 10 \mathrm{cm} . \) It is stretched to \( 5 \mathrm{cm} \) and then released to
project a missile of mass 5 g. Taking \( \boldsymbol{Y}_{r u b b e r}=\mathbf{5} \times \mathbf{1 0}^{8} \boldsymbol{N} \boldsymbol{m}^{-2}, \) velocity of
projected missile is:
A. \( 20 \mathrm{ms}^{-1} \)
B. \( 100 \mathrm{ms}^{\wedge}(-1) \$ \$ \)
c. \( 250 \mathrm{ms}^{-1} \)
D. \( 200 \mathrm{ms}^{-1} \)
Subject: Physics
In the shown circuit, \( \boldsymbol{R}_{1}=\mathbf{1 0 \Omega}, \boldsymbol{L}= \)
\( \frac{\sqrt{3}}{10} H, R_{2}=20 \Omega, C=\frac{\sqrt{3}}{2} \) milli
farad and \( t \) is time in seconds. Then at
the instant current through
\( \boldsymbol{R}_{1} \boldsymbol{i} \boldsymbol{s} \mathbf{1} \boldsymbol{0} \sqrt{\boldsymbol{2}} \boldsymbol{A} \)
find the current through resistor \( \boldsymbol{R}_{2} \) in
amperes.
Subject: Physics
For common emitter configuration of a
transistor, the collector voltage \( V_{c}= \)
\( 2 V \) and, base current changes from
\( 100 \mu A t o 200 \mu A, \) and collector
current changes from \( 5 \mathrm{mA} \) to \( 10 \mathrm{mA} \) The current gain is
A . 100
B. 25
\( c \cdot 125 \)
D. 50
Subject: Maths
\( \left(\begin{array}{l}n \\ 0\end{array}\right)+2\left(\begin{array}{l}n \\ 1\end{array}\right)+2^{2}\left(\begin{array}{l}n \\ 2\end{array}\right)+\ldots .+2^{n}\left(\begin{array}{l}n \\ n\end{array}\right) \)
is equal to
A \( \cdot 2^{n} \)
B.
\( c \cdot 3^{n} \)
D. None of these
Subject: Chemistry
Which statements are correct?
This question has multiple correct options
A. Phenol and aniline give coupling reaction with diazonium salt.
B. Phenol couples with diazonium salt in mild basic conditions \( (p H=8-10) \)
C. Aniline couples with diazonium salt in mild acidic condition \( (p H=4-6) \)
D. Both phenol and aniline couple with diazonium salt in neutral condition \( (p H=7) \)
Subject: Chemistry
\( \boldsymbol{C H} \equiv \boldsymbol{C}-\boldsymbol{C H}_{3} \frac{40 \% \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{1 \% \boldsymbol{H g S O}_{4}} \boldsymbol{B} \)
Then, \( B \) is :
A. acetone
B. trichloroacetone
c. acetaldehyde
D. chloral
Subject: Maths
If \( p \) is \( T \) and \( q \) is \( F, \) then which of the
following have the truth value \( T \) ?
\( (i) p \vee q \)
\( (i i) \sim p \vee q \)
\( (i i i) p \vee(\sim q) \)
\( (i v) p \wedge(\sim q) \)
A \( \cdot(i),(i i),(i i i) \)
B. \( (i),(i i),(i v) \)
c. \( (i),(i i i),(i v) \)
D. \( (i i),(i i i),(i v) \)
Subject: Physics
The binding energies of nuclei \( X \) and \( Y \)
are \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2}, \) respectively. Two atoms of \( X \) fuse to give one atom of \( Y \) and an energy \( Q \) is released. Then,
A \( \cdot Q=2 E_{1}-E_{2} \)
в. \( Q=E_{2}-2 E_{1} \)
c. \( Q<2 E_{1}-E_{2} \)
D. \( Q>E_{2}-2 E_{1} \)
Subject: Maths
If the angle between the vectors \( \vec{A} \) and \( \vec{B} \) is \( \theta, \) the value of the product \( (\vec{B} \times \)
\( \vec{A}) \cdot \vec{A} \) is equal to:
A. \( B A^{2} \cos \theta \)
B. \( B A^{2} \sin \theta \)
c. \( B A^{2} s \) in \( \theta \cos \theta \)
D.
Subject: Chemistry
The chemical composition of slag formed during the smelting process in the extraction of copper is:
A \( \cdot C u_{2} O+F e S \)
в. Fesi Оз\( _{3} \)
\( \mathbf{c} \cdot \mathrm{CuFeS}_{2} \)
D. \( C u_{2} S+ \) Fe\( O \)
Subject: Physics
If the time taken. by a hot body to cool
from \( 50^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \) is 10 min when the
surrounding temperature is \( 25^{\circ} \mathrm{C} \), then
the time taken for it to cool from \( 40^{\circ} \mathrm{C} \)
to \( 30^{\circ} C \) when the surrounding
temperature is \( 15^{\circ} \mathrm{C} \), is
A. 40 min
B. 10 min
c. \( 4 \min \)
D. 15 min
E. 20 min
Subject: Chemistry
At \( 25^{\circ} C \) and one atmospheric pressure
the partial pressures in an equilibrium
mixture of \( N_{2} O_{4} \) and \( N O_{2} \) are 0.7 and
0.3 atmosphere, respectively. Calculate the partial pressures of these gases
when they are in equilibrium at \( 25^{\circ} \mathrm{C} \)
and at a total pressure of 10
atmospheres.
Subject: Maths
\( \mathbf{A}=\left|\begin{array}{ccc}\cos \frac{\theta}{2} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \cos \frac{\theta}{2} & -\cos \frac{\theta}{2} \\ -\cos \frac{\theta}{2} & \mathbf{1} & -\mathbf{1}\end{array}\right| \)
the minimum of \( \Delta \) is \( m_{1} \) and
maximum of \( \Delta \) is \( m_{2} \) then \( \left[m_{1}, m_{2}\right] \) are
related to
A. [4, 2]
B. [2,4]
\( c \cdot[4,0] \)
D. [0,2]
Subject: Maths
The equation of one of the tangents to the curve \( \boldsymbol{y}=\cos (\boldsymbol{x}+\boldsymbol{y}),-2 \boldsymbol{\pi} \leq \boldsymbol{x} \leq \)
\( 2 \pi ; \) that is parallel to the line \( x+2 y= \)
\( 0, \) is
A. \( x+2 y=1 \)
B. \( x+2 y=\frac{\pi}{2} \)
c. \( x+2 y=\frac{\pi}{4} \)
D. None of these
Subject: Physics
In a fission process, nucleus A divides into two nuclei B and C, their binding
energies being \( \mathbf{E}_{\mathbf{a}^{*}} \quad \boldsymbol{E}_{\boldsymbol{b}} \) and \( \boldsymbol{E}_{\boldsymbol{c}} \)
respectively. Ihen
A \( \cdot \mathbf{E}_{\mathrm{b}}+\mathrm{E}_{\mathrm{c}}=\mathrm{E}_{\mathrm{a}} \)
в. \( \mathrm{E}_{\mathrm{b}}+\mathrm{E}_{\mathrm{c}}>\mathrm{E}_{\mathrm{a}} \)
c. \( \mathrm{E}_{\mathrm{b}}+\mathrm{E}_{\mathrm{e}}<\mathrm{E}_{\mathrm{a}} \)
D. \( \mathrm{E}_{\mathrm{b}} \mathrm{E}_{\mathrm{c}}=\mathrm{E}_{\mathrm{a}} \)
Subject: Physics
Four solid spheres each of diameter \( \sqrt{5} \)
\( \mathrm{m} \) and mass \( 0.5 k g \) are placed with their
centres at the corners of a square of
side \( 4 c m \). The moment of inertia of the
system about the diagonal of the square is \( N \times 10^{-4} k g m^{2} \) then \( N \) is
Subject: Physics
A point dipole is located at the origin in
some orientation. the electric field at
the point \( (10 \mathrm{cm}, 10 \mathrm{cm}) \) on the \( \mathrm{x} \) -y plane is measured to have a magnitude \( 1.0 \times \)
\( 10^{-3} \mathrm{V} / \mathrm{m} . \) What will be the magnitude
of the electric field at the point(20 \( \mathrm{cm} \)
\( 20 \mathrm{cm}) ? \)
A. \( 5.0 \times 10^{-4} \mathrm{V} / \mathrm{m} \)
В. \( 2.5 \times 10^{-4} \mathrm{V} / \mathrm{m} \)
c. It will depend on the orientation at the dipole
D. \( 1.25 \times 10^{-4} \mathrm{V} / \mathrm{m} \)
Subject: Chemistry
What will be the molarity of a solution which contains \( 5.85 g \) of \( N a C l(s) \) per \( \mathbf{5 0 0} \mathrm{ml} ? \)
A. 4 mol \( L^{-1} \)
B. 20 mol \( L^{-1} \)
c. 0.2 mol \( L^{-1} \)
D. 2 mol \( L^{-1} \)
Subject: Physics
In the pulley-block arrangement shown
in figure. Find relation between \( \boldsymbol{a}_{\boldsymbol{A}}, \boldsymbol{a}_{\boldsymbol{B}} \)
and \( \boldsymbol{a}_{C} \)
\( \mathbf{A} \cdot a_{A}+2 a_{B}+a_{C}=0 \)
в. \( 2 a_{A}+a_{B}+a_{C}=0 \)
c. \( a_{A}+a_{B}+2 a_{C}=0 \)
D. \( a_{A}+a_{B}+a_{C}=0 \)
Subject: Physics
Two charges - \( q \) and \( +q \) are located at points \( (0,0,-a) \) and \( (0,0, a) \) respectively.
(a) What is the electrostatic potential at the points \( (0,0, z) \) and \( (x, y, 0) ? \)
(b) Obtain the dependence of potential on the distance r of a point from the origin when \( r / a>>1 \)
(c) How much work is done in moving a small test charge from the point (5,0,0) to (-7,0,0) along the \( x \) -axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?