AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
If the Gibbs free energy change when 1 mole of \( N a C l \) is dissolved in water at
\( 298 \mathrm{K} \) is \( x \mathrm{kJ}, \) then \( -1000 x \) is
Given that,
(a) Lattice energy of \( N a C l= \) \( 778 k J m o l^{-1} \)
(b) Hydration energy of \( N a C l= \) \( -774.3 k J m o l^{-1} \)
(c) Entropy change at \( 298 K= \)
43 Jmol\( ^{-1} \)
A. 9117
B. 9441
c. 9114
D. 9141
Subject: Chemistry
The products of combustion of an
aliphatic thiol (RSH) at \( 298 K \) are
A \( \cdot C O_{2}(g), H_{2} O(g), \) and \( S O_{2}(g) \)
B . \( C O_{2}(g), H_{2} O(l), \) and \( S O_{2}(g) \)
c. \( C O_{2}(l), H_{2} O(l), a n d S O_{2}(g) \)
D. \( C O_{2}(g), H_{2} O(l), \) and \( S O_{2}(l) \)
Subject: Chemistry
An electrolyte \( A \) gives 3 ions and \( B \) is a non- electrolyte. If \( 0.1 ~ M \) solution of \( B \)
produces an osmotic pressure \( P, \) then \( 0.05 M \) solution of \( A \) will produce an osmotic pressure, assuming that the electrolyte is completely ionised:
A . \( 1.5 P \)
в. \( P \)
\( c .0 .5 P \)
D. \( 0.75 P \)
Subject: Chemistry
\( x, y, \) and \( z \) in the following processes are respectively:-
(i) \( P_{2} O_{5}+x \rightarrow C a_{3}\left(P O_{4}\right)_{2} \)
(ii) \( 2 C u_{2} O+C u_{2} S \rightarrow y+S O_{2} \)
(iii) \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3}+\boldsymbol{3} \boldsymbol{C O} \rightarrow \boldsymbol{z}+\boldsymbol{3} \boldsymbol{C O}_{2} \)
A. 3 Ca, \( C u S O_{4} \), Fe
B . \( 3 C a(O H)_{2}, \) 6Си,Fео
c. \( 3 C a O, 6 C u, 2 F e \)
D. \( 3 \mathrm{CaO}_{2} \), cus, Feo
Subject: Physics
Water drops fall at regular intervals from a tap \( 5 \mathrm{m} \) above ground. The \( 3 \mathrm{rd} \) drop is leaving tap when first drop reaches ground. The distance of 2 nd drop at the instant is
A . \( 2.5 \mathrm{m} \)
B. 3.75 m
\( c \cdot 4 m \)
D. 1.25 \( m \)
Subject: Chemistry
If the empirical formula of potash alum
is \( K A l\left(S O_{4}\right)_{x}, 12 H_{2} O, \) then the value
of 'x' in \( \boldsymbol{K} \boldsymbol{A l}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{x}, \boldsymbol{1} \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \) is:
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Physics
A solenoid \( 30 c m \) long is made by
winding 2000 loops of wire on an iron
rod whose cross-section is \( 1.5 \mathrm{cm}^{2} \). If
the relative permeability of the iron is
6000. What is the self-inductance of the
solenoid?
\( \mathbf{A} \cdot 15 H \)
в. 25H
\( c .35 H \)
D. \( 5 H \)
Subject: Physics
Determine the energy released during the fusion of \( _{1} H^{1} \) to form a \( _{2} H e^{4} \) nucleus, if the total mass of the
products is \( 4.001506 u, \) mass of proton
is \( 1.0078 u \) and mass of neutron is
\( 1.00878 u \)
\( \mathbf{A} \cdot 27.67 M e V \)
в. \( 27.67 J \)
c. \( 127.67 J \)
D. 127.67 MeV
Subject: Chemistry
Which of the following halides undergoes nucleophilic substitution most readily?
A \( \cdot p-H_{3} C C_{6} H_{4} C l \)
в. \( O-M e O C_{6} H_{4} C l \)
c \( \cdot p-C l C_{6} H_{4} C l \)
D. \( C_{6} H_{5} C H(C l) C H_{3} \)
Subject: Maths
While preparing the progress reports of the students, the class teacher found
that \( 70 \% \) of the students passed in
Hindi, \( 80 \% \) passed in English and only \( 65 \% \) passed in both the subjects. Find
out the percentage of students who
failed in both the subjects.
A . \( 15 \% \)
B. 20\%
c. \( 30 \% \)
D. \( 35 \% \)
Subject: Chemistry
A proton is accelerated to one-tenth of the velocity of light. If its velocity can be measured with a precision \( \pm 1 \% \), then its uncertainty in position is:
A \( \cdot 1.05 \times 10^{-13} m \)
В. \( 1.13 \times 10^{-13} \mathrm{m} \)
c. \( 1.15 \times 10^{-13} \mathrm{m} \)
D. \( 1.25 \times 10^{-13} \mathrm{m} \)
Subject: Physics
A coil has resistance 30 ohm and
inductive reactance 20 Ohm at \( 50 \mathrm{Hz} \) frequency. If an ac source, of 200 volt, \( 100 \mathrm{Hz}, \) is connected across the coil, the current in the coil will be :
\( \mathbf{A} \cdot 4 \cdot 0 \mathrm{A} \)
B. \( 8.0 \mathrm{A} \)
c. \( \frac{20}{\sqrt{13}} \) A
D. 2.0 A
Subject: Chemistry
The correct order of ionic radii of
\( \boldsymbol{Y} \boldsymbol{b}^{3+}, \boldsymbol{L} \boldsymbol{a}^{3+}, \boldsymbol{E} \boldsymbol{u}^{3+} \) and \( \boldsymbol{L} \boldsymbol{u}^{3+} \) is:
\( \mathbf{A} \cdot Y b^{3+}>L u^{3+}>E u^{3+}>L a^{3+} \)
B. \( L u^{3+}<Y b^{3+}<E u^{3+}<L a^{3+} \)
c. \( L u^{3+}<E u^{3+}<L a^{3+}<Y b^{3+} \)
D. \( L a^{3+}<E u^{3+}<L u^{3+}<Y b^{3+} \)
Subject: Physics
Which of the following is the dimension of compressibility?
\( \mathbf{A} \cdot\left[M^{-1} L^{1} T^{2}\right] \)
B . \( \left[M^{1} L^{-1} T^{-2}\right] \)
c. \( \left[M^{-1} L^{-1} T^{-2}\right. \)
D・ \( \left[M^{-1} L^{-1} T^{2}\right] \)
Subject: Physics
The blocks are connected as shown in
figure on a horizontal frictionless table.
if \( \boldsymbol{m}_{1}=\mathbf{1} \mathbf{k g} \boldsymbol{m}_{2}=\mathbf{8} \mathbf{k g} \boldsymbol{m}_{3}=\mathbf{2 7 k g} \) and
\( \boldsymbol{T}_{3}=\boldsymbol{6} \boldsymbol{4} \boldsymbol{N}, \boldsymbol{T}_{2} \)
\( A \cdot 18 N \)
в. 9 N
c. 3. 375 N
D. 1.75 N
Subject: Maths
\( \frac{\boldsymbol{x}-\boldsymbol{y}}{\sqrt{\boldsymbol{x}}+\sqrt{\boldsymbol{y}}}=\ldots \ldots \)
\( \mathbf{A} \cdot \sqrt{x-y} \)
B. \( \sqrt{x}+\sqrt{y} \)
c. \( -(\sqrt{x}+\sqrt{y}) \)
D. \( \sqrt{x}-\sqrt{y} \)
Subject: Chemistry
Which of the following diazonium salt is
relatively stable at \( 0-5^{0} C ? \)
A. \( \left.C H_{3}-N \equiv N\right\}^{\oplus} C l^{-} \)
В \( \left.\cdot\left(C H_{3}\right)_{2} C H-N \equiv N\right\} \oplus C l^{-} \)
c. \( \left.C_{6} H_{5}-N \equiv N\right\}^{\oplus} C l^{-} \)
D \( \left.\cdot\left(C H_{3}\right)_{3} C-N \equiv N\right\}^{\oplus} C l \)
Subject: Physics
A stone is dropped from a tower. It was
found that it covered a distance of \( 45 m \)
during its last second of the fall.
Calculate the time of the fall and the
height of the tower? \( \left(g=10 m s^{-2}\right) \)
\( A \cdot 5 s, 45 m \)
B . \( 10 s, 90 m \)
\( \mathbf{c} .5 s, 125 m \)
D. \( 10 s, 100 m \)
Subject: Chemistry
\( \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{q}) \rightleftharpoons \)
A \( \cdot K^{-}+O H^{+} \)
B. \( K^{+}+O H^{+} \)
\( \mathbf{c} \cdot K^{-}+O H^{-} \)
\( \mathbf{D} \cdot K^{+}+O H^{-} \)
Subject: Maths
Let \( E^{c} \) denote the complement of an
event Let \( E, F, G \) be pairwise
independent events with \( P(G)>0 \) and
\( \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F} \cap \boldsymbol{G})=\mathbf{0} \operatorname{then} \boldsymbol{P}\left(\boldsymbol{E}^{c} \cap \boldsymbol{F}^{c} \mid \boldsymbol{G}\right) \)
equals
\( \mathbf{A} \cdot P\left(E^{c}\right)+P\left(F^{c}\right) \)
B . \( P\left(E^{c}\right)-P\left(F^{c}\right) \)
\( \mathbf{c} \cdot P\left(E^{c}\right)-P(F) \)
D. \( P(E)-P\left(F^{c}\right) \)
Subject: Maths
Find the value of \( x \) which satisfy
euqation \( : \tan ^{-1} 2 x+\tan ^{-1} 3 x=\pi / 4 \)
A. \( x=-1 / 6 \)
В. \( x=+1 / 6 \)
c. \( x=-1 \)
D. \( x=+1 \)
Subject: Chemistry
The chemical name for melamine is:
A . 1,3,5 -Triamino- 2,4,6 -triazine
B. 1,3,5-Triazine-2,4,6-triamine
c. 2-Amino-1,3,5-triazine
D. 2,4-Diamino 1,3,5-triazine
Subject: Chemistry
Calculate the volume of carbondioxide
produced by the combustion of \( 40 \mathrm{ml} \) of acetone vapours in presence of excess of oxygen?
\( A \cdot 12 \mathrm{m} \)
B. 1.20 \( m \)
c. \( 120 \mathrm{ml} \)
D. 11.2 m1
Subject: Physics
Which of the following order is correct?
A. Sound \( \rightarrow \) ear \( \rightarrow \) inner ear \( \rightarrow \) vibration of eardrum \( \rightarrow \)
brain \( \rightarrow \) hearing
B. Ear \( \rightarrow \) Vibration of eardrum \( \rightarrow \) Inner ear \( \rightarrow \) hearing \( \rightarrow \) brain \( \rightarrow \) vibration
C. Sound \( \rightarrow \) ear \( \rightarrow \) inner ear \( \rightarrow \) vibration of eardrum \( \rightarrow \) hearing \( \rightarrow \) brain
D. Sound \( \rightarrow \) ear \( \rightarrow \) vibration of eardrum \( \rightarrow \) inner ear \( \rightarrow \) brain \( \rightarrow \) hearing
Subject: Maths
Find \( \mathrm{k} \) so that the function
\[
\begin{array}{cc}
\boldsymbol{f}(\boldsymbol{x})=\left\{1-\cos 2 \boldsymbol{x} / 2 \boldsymbol{x}^{2}\right. & \boldsymbol{x} \neq \mathbf{0} \\
\{\boldsymbol{k} & \boldsymbol{x}=\mathbf{0}
\end{array}
\]
is coutinous at \( x=0 \)
Subject: Chemistry
Choose the correct observation.
This question has multiple correct options
A. The orbital diagram in which Aufbau principle is obeyed
11 11111
B. The spectra of \( H e \) and \( L i^{+} \) will be similar
C. Following is the violation of Pauli's exclusion principle
11
D. The \( d \) -orbit involved in \( s p^{3} d \) hybridisation is \( d_{x^{2}-y^{2}} \)
Subject: Physics
A parallel plate capacitor having plates
of area \( \mathrm{S} \) and plate separation \( \mathrm{d}, \) has
capacitance \( C_{1} \) in air. When two
dielectrics of different relative
permittivities \( \left(\varepsilon_{1}=2 \text { and } \varepsilon_{2}=4\right) \) are
introduced between the two plates as
shown in the figure, the capacitance becomes \( C_{2} . \) The ratio \( \frac{C_{2}}{C_{1}} \) is
A . \( 6 / 5 \)
B. \( 5 / 3 \)
\( c \cdot 7 / 5 \)
\( 0.7 / 3 \)
Subject: Physics
A cylinder contains a gas at temperature
of \( 27^{0} \mathrm{C} \) and a pressure 1 MPa. If the temperature of the gas
is lowered to \( -23^{0} \mathrm{C} \), the change in pressure
is
A. \( 1 \mathrm{MPa} \)
B. \( 5 / 6 \) MPa
C . \( 1 / 6 \mathrm{MPa} \)
D. \( 5 \mathrm{MPa} \)
Subject: Physics
What should be the ratio of area of
cross section of the master cylinder and wheel cylinder of a hydraulic brake so that a force of \( 15 N \) can be obtained at
each of its brake shoe by exerting a
force of \( 0.5 N \) on the pedal?
\( \mathbf{A} \cdot 1: 60 \)
B. 1: 30
c. 1: 15
D. 1: 45
Subject: Physics
Two small blocks of charges \( 5 \mu C \) and
\( 3 \mu C \) are kept on a rough surface \( (\mu= \)
0.5) at a separation of 0.1 m. Find the
separation between the blocks when
they come to rest.
A . \( 0.27 \mathrm{m} \)
в. 0.6 т
c. \( 0.72 m \)
D. 1.27 m
Subject: Chemistry
\( P \) and \( Q \) are two elements which form
\( P_{2} Q_{3} \) and \( P Q_{2} \) compounds. If 0.15
moles of \( \boldsymbol{P}_{2} \boldsymbol{Q}_{3} \)
\& \( P Q_{2} \) weigh 15.9 g and \( 9.3 \mathrm{g} \) respectively, then the atomic mass of \( 6 Q \) is \( Y \). Then \( Q \) is:
Subject: Physics
A wire of length \( 60 \mathrm{cm} \) is bent into a
circle with a gap of \( 1 \mathrm{cm} . \) At its ends, on heating it by \( 100^{\circ} \mathrm{C} \), the length of the gap increases to \( 1) 02 \mathrm{cm} . \alpha \) of material
of wire is
A \( \cdot 2 \times 10^{-4} /^{\circ} \mathrm{C} \)
B . \( 4 \times 10^{-4} /^{\circ} \mathrm{C} \)
c. \( 6 \times 10^{-4} /^{\circ} \mathrm{C} \)
D. \( 1 \times 10^{-4} /^{\circ} \mathrm{C} \)
Subject: Chemistry
Select pair of compounds in which both have different hybridization but have same molecular geometry.
A. \( B F_{3}, B r F_{3} \)
B . \( I C I_{2}^{\ominus}, B e C l_{2} \)
c. \( B e C l_{3}, P C l_{3} \)
D. \( P C l_{3}, N C l_{3} \)
Subject: Maths
If \( \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{j}-\hat{k}, \) then find a
vector \( \vec{c} \) such that \( \vec{a} \times \vec{c}= \)
\( \overrightarrow{\boldsymbol{b}} \quad \) and \( \quad \overrightarrow{\boldsymbol{a}} \cdot \overrightarrow{\boldsymbol{c}}=\mathbf{3} \)
Subject: Biology
The chronological order of human
evolution from early to the recent is
A. Ramapithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Australopithceus \( \rightarrow \) Homo erectus
B. Australopithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Ramapithecus \( \rightarrow \) Homo erectus
C. Australopithecus \( \rightarrow \) Ramapithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo erectus
D. Ramapithecus \( \rightarrow \) Australopithceus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo erectus
Subject: Physics
A person who is moving parallel to the
charge and at the same velocity as the
charge will measure.
A. A magnetic field and an electric field due to the moving charge.
B. A magnetic field, but not an electric field due to the moving charge.
C. An electric field, but not a magnetic field due to the moving charge.
D. Neither an electric field nor a magnetic field due to the moving charge.
E. A decrease in the amount of charge.
Subject: Chemistry
Which of the following is a
decomposition reaction?
\( \mathbf{A} \cdot 3 N a(s)+F e B r_{3}(a q) \rightarrow 3 N a B r(a q)+F e(s) \)
B. \( N a O H(a q)+H N O_{3}(a q) \rightarrow N a N O_{3}(a q)+H_{2} O(l) \)
\( \mathbf{c} \cdot 2 N a H C O_{3}(s) \rightarrow N a_{2} C O_{3}(s)+C O_{2}(g)+H_{2} O(l) \)
D. \( 3 H_{2}(g)+N_{2}(g) \rightarrow 2 N H_{3}(g) \)
Subject: Biology
Assertion
Angina pectoris means "pain in the chest".
Reason
It results due to carrying of extra blood to the heart muscle.
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: Biology
Examine the figures \( A, B, C \) and \( D . \) In
which one of the four options all the
items \( A, B, C \) and \( D \) are correct?
A. \( A \) - Selaginella, \( B \) - Equisetum, \( C \) - Salvinia, D - Ginkgo
B. A - Equisetum, B - Ginkgo, C - Selaginella, D Lycopodium
C. A - Chara, B - Marchantia, C - Fucus, D - Pinus
D. A - Funaria,B - Adiantum,
C - Salvinia
D - Riccia
Subject: Physics
Inner and outer radii of a spool are \( r \) and
\( R \) respectively. A thread is wound over
its inner surface and placed over a
rough horizontal surface. Thread is
pulled by a force \( F \) as shown in fig. then
in case of pure rolling:
A. Thread unwinds, spool rotates anticlockwise and friction act leftwards.
B. Thread winds, spool rotates clockwise and friction acts leftwards
C. Thread winds, spool moves to the right and friction act rightwards.
D. Thread winds, spool moves to the right and friction does not come into existence
Subject: Chemistry
Deep sea divers use \( \left(O_{2}+H e\right) \) mixture
as preference to \( \left(O_{2}+N_{2}\right) \) mixture.
This is because:
A. helium is lighter than nitrogen
B. helium is less soluble in blood than nitrogen
c. helium is more soluble in blood.
D. helium provides a better inert atmosphere than nitrogen.
Subject: Physics
What are the changes in ciliary muscle
when nearby objects and distant
objects are viewed?
A. When objects near the eyes are viewed,the ciliary muscles contract and while viewing distant objects ciliary muscles relax.
B. When objects near the eyes are viewed,the ciliary muscles relax and while viewing distant objects ciliary muscles contract
C. Cilliary muscle is not related to the functioning of the lens and provides mechanical support only.
D. Ciliary muscles contract or relax depending on the intensity of the light and not hte distance of the object.
Subject: Chemistry
The value of \( \Delta H_{O-H} \) is \( 109 k c a l m o l^{-1} \) The formation of one mole of water in
gaseous state from \( H(g) \) and \( O(g) \) is accompanied by:
A \( .218 \mathrm{kcal} \)
B . -109 kcal
c. -218 kcal
D. Unpredictable
Subject: Physics
Atomic number (Z) of a neutral atom and mass number (A) of an atom are
equal to:
(Here \( n= \) number of neutrons and \( p= \)
number of protons)
\( A \cdot Z=n \) and \( A=n+p \)
B. \( z=e \) and \( A=n+e \)
c. \( z=p \) and \( A=n+p \)
D. \( z=n \) and \( A=p+e \)
Subject: Chemistry
For the reaction \( 2 A+B \rightarrow C+ \)
\( D,-\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}]^{2}[\boldsymbol{B}] . \) The expression
for \( \frac{-\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d} \boldsymbol{t}} \) will be:
\( \mathbf{A} \cdot K[A]^{2}[B] \)
B . \( 1 / 2 K[A]^{2}[B] \)
\( \mathbf{c} \cdot K[A]^{2}[2 B] \)
D. \( K[2 A]^{2}[B] \)
Subject: Biology
Glycosidic linkage present between adjacent glucose units of starch or glycogen is generally
A. \( \beta 1 \longrightarrow 4 \)
B . \( \alpha 1 \longrightarrow 4 \)
c. \( \alpha 2 \rightarrow 1 \)
D. \( \beta 2 \longrightarrow 1 \)
Subject: Maths
If displacement \( s \) at time \( t \) is \( s=t^{3}- \) \( 3 t^{2}-15 t+12, \) then acceleration at
time \( t=1 \) sec is
A \( \cdot \) 6units \( / \) sec \( ^{2} \)
B. - 6units/sec \( ^{2} \)
\( c \cdot 0 \)
D. 4units \( / \)sec\( ^{2} \)
Subject: Biology
Study the given statements about gymnosperms and select the correct
option.
(i) Mode of fertilisation is siphonogamy.
(ii) Male and female cones are borne on same tree in Pinus
(iii) Endosperm represents female gametophyte.
A. Statements (i) and (ii) are correct
B. Statements (ii) and (iii) are correct
c. Statements (i) and (iii) are correct.
D. Statements (i), (ii) and (iii) are correct.
Subject: Chemistry
Assertion
A solution of sucrose in water is
dextrortatory while on hydrolysis in pressence of little hydrochloric acid, it becomes laveorotatory
Reason
Sucrose on hydrolysis gives unequal amounts of glucose and fructose as a result of which change in sign of
rotation is observed.
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
If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}, \) if
\( \boldsymbol{x}>2 ; \boldsymbol{f}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}-\boldsymbol{2} \) if \( \boldsymbol{x} \leq 2 \) then \( \boldsymbol{f} \) is
A. an identity function
B. one one
c. onto
D. one one and onto
Subject: Physics
A ball weighing 15 g is tied to a string 10 cm long. Initially the ball is held in the position such that the string is
horizontal. The ball is now released. A
nail N is situated vertically below the support at a distance

The minimum value of L such that the
string will be wound round the nail is
A \( .2 \mathrm{cm} \)
в. 4 ст
\( c .6 \mathrm{cm} \)
D. \( 8 \mathrm{cm} \)
Subject: Maths
The value of \( K \) which the Function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}
\frac{\tan 4 \boldsymbol{x}}{\tan 5 x}, & 0<x<\frac{\pi}{2} \\
\boldsymbol{k}+\frac{2}{5}, & \boldsymbol{x}=\frac{\pi}{2}
\end{array}\right.
\]
continuous at \( x=\frac{\pi}{2}, \) is
Subject: Chemistry
Which of the following statement(s)
is/are true for the process of anodizing?
A. Anodizing is an electrochemical process
B. It converts the metal surface into a decorative, durable, corrosion-resistant, anodic oxide finish.
C. Aluminum is ideally suited to anodizing, although other nonferrous metals, such as magnesium and titanium, also can be anodized.
D. All of the above
Subject: Chemistry
Which of the following statements about Radioactive pollution are correct?
1. It causes genetic changes in the animals.
2. It causes disbalance among different minerals in the soil.
3. It hinders blood circulation.
4. It causes cancers.
Select the correct answer from the
codes given below:
A . 1 and 2
B. 1 and 4
c. 1,3 and 4
D. 2, 3 and 4
Subject: Maths
Match the elements of list I, which have differential equations, with elements of list II, which have solutions of
differential equations:
List I
\[
\text { A) } y y_{1}=\sec ^{2} x
\]
1) \( y \sec ^{2} x=\sec x+c \)
В) \( y_{1}=x \sec y \)
2) \( x y=\cos y+c \)
C) \( y_{1}+(2 y \tan x)=\sin x \)
3) \( x y=\sin x+c \)
D) \( x y_{1}+y=\cos x \)
\[
\text { 4) } y^{2}=2 \tan x+c
\]
\[
\text { 5) } x^{2}=2 \sin y+c
\]
Then, the correct order for \( \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \boldsymbol{D} \) is:
\( \mathbf{A} \cdot 3254 \)
B. 4123
c. 4513
D. 3512
Subject: Maths
\( \int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x \) is
A \( \cdot e^{x} \tan \left(\frac{x}{2}\right)+C \)
B \cdot \( \tan \left(\frac{x}{2}\right)+C \)
\( \mathbf{c} \cdot e^{x}+C \)
D. \( e^{x} \sin x+C \)
Subject: Maths
Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) where \( \boldsymbol{x}^{\mathbf{3}}+\boldsymbol{y}^{\mathbf{3}}+\mathbf{3} \boldsymbol{x} \boldsymbol{y}=\mathbf{7} \)
Subject: Chemistry
The products formed when an aqueous solution of \( N a B r \) is electrolysed in a
cell having inert electrodes are :
A. \( N a \) and \( B r_{2} \)
B. \( N a \) and \( O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2}, \mathrm{Br}_{2} \) and \( \mathrm{NaOH} \)
D. \( H_{2} \) and \( O_{2} \)
Subject: Maths
The number of \( A \) in \( T_{p} \) such that the trace of \( A \) is not divisible by \( p \) but \( \operatorname{det}(A) \) divisible by p is ?[Note: The trace of matrix is the sum of its diagonal entries].
A \( \cdot(p-1)\left(p^{2}-p+1\right) \)
B . \( p^{3}-(p-1)^{2} \)
c. \( (p-1)^{2} \)
D. \( (p-1)\left(p^{2}-2\right) \)
Subject: Physics
"14
incline. A device on the cart launches a
ball, forcing the ball perpendicular to
the incline, as shown above. Air
resistance is negligible. Where will the
ball land relative to the cart, and why?
A. The ball will land in front of the cart, because the balls acceleration component parallel to the plane is greater than the carts acceleration component parallel to the plane
B. The ball will land in front of the cart, because the ball has a greater magnitude of acceleration than the cart
C. The ball will land in the cart, because both the ball and
the cart have the component of acceleration parallel to the plane
D. The ball will land in the cart, because both the ball and the cart have the same magnitude of acceleration
Subject: Maths
(a) If \( x \) be real, then the expression \( \frac{2 a(x-1) \sin ^{2} \theta}{x^{2}-\sin ^{2} \theta} \) does not lie between
\( 2 a \sin ^{2}(\theta / 2) \) and \( 2 a \cos ^{2}(\theta / 2) \)
(b) A function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \) where \( \mathrm{R} \) is the
set of real numbers, is defined by \( f(x)=\frac{\alpha x^{2}+6 x-8}{\alpha+6 x-8 x^{2}} \) Find the interval of
values of \( \alpha \) for which \( f \) is onto.

Is the function one-to-one for \( \boldsymbol{\alpha}=\mathbf{3} ? \)
Justify yout answer.
Subject: Chemistry
The value of \( K_{c} \) for the reaction
\( \mathbf{3} \boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{O}_{\mathbf{3}}(\boldsymbol{g}) \) is \( \mathbf{2} . \mathbf{0} \times \mathbf{1 0}^{-\mathbf{5 0}} \mathbf{a} \mathbf{t} \)
\( 25^{\circ} \mathrm{C} . \) If the equilibrium concentration
of \( O_{2} \) in air at \( 25^{\circ} C \) is \( 1.6 \times 10^{-2} \mathrm{M} \)
what is the concentration of \( O_{3} \) ?
Subject: Physics
It is observed in a potentiometer
experiment that no current passes through the galvanometer across when
the terminals of a cell are connected
across a certain length of the potentiometer wire. On shuting the cell by a \( 2 \Omega \) resistance, the balancing length is reduced to half. The internal resistance of the cell is :-
A . \( 4 \Omega \)
B. 2\Omega
c. \( 1 \Omega \)
D. 8\Omega
Subject: Maths
The area bounded by two branches of the curve \( (\boldsymbol{y}-\boldsymbol{x})^{2}=\boldsymbol{x}^{3} \& \boldsymbol{x}=\mathbf{1} \) equals
A . \( 3 / 5 \)
B. \( 5 / 4 \)
\( c \cdot 6 / 5 \)
D. \( 4 / 5 \)
Subject: Chemistry
What is the final product \( ^{\prime} C^{\prime} \) in the following reaction? \( \boldsymbol{C H}_{3} \boldsymbol{C H O} \stackrel{\boldsymbol{H C N}}{\longrightarrow} \boldsymbol{A}^{\prime} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}^{+}}{\longrightarrow} \)
\( ' \boldsymbol{B}^{\prime} \frac{\text {sodalime}}{\longrightarrow} \boldsymbol{C}^{\prime} \)
A. Propane
B. Propanol
c. Ethanol
D. Propanoic acid
Subject: Biology
National Forest Policy of India has recommended (i) forest cover for the plains and (ii) for the hills.
\( A \cdot \) (i) 33\% (ii) 67\%
B. (i) 67\% (ii) 33\%
c. (i) 50\% (ii) 50\%
D. (i) 40\% (ii) 60\%