AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Prove that
\( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{0}), \boldsymbol{B}(\mathbf{3}, \mathbf{1}, \mathbf{1}), \boldsymbol{C}(\mathbf{7},-\mathbf{1}, \mathbf{3}) \) are
collinear.
Subject: Chemistry
The reaction between which of the
following reactants produces hydrogen?
\( \mathbf{A} \cdot Z n+H C I \)
B \( . B a O_{2}+H C I \)
\( \mathbf{c} \cdot K_{2} S_{2} O_{8}+H_{2} O \)
D. \( N a_{2} O_{2}+H C I \)
Subject: Physics
Which of the following is a necessary
condition for a process to be reversible?
A. The substance undergoing a reversible change must at all instances be in thermodynamic equilibrium with its surroundings.
B. All the processes taking place in the cycle of operation must be infinitely slow.
C. There should not be any loss of energy due to conduction, convection or radiation during the cycle of operation.
D. All of the above.
Subject: Physics
\( \boldsymbol{E}_{\boldsymbol{g}}(\boldsymbol{T})=\boldsymbol{E}_{\boldsymbol{g}}(\boldsymbol{m})-\frac{\boldsymbol{\alpha} \boldsymbol{T}^{2}}{\boldsymbol{T}+\boldsymbol{\beta}} \) is
the Varshni's empirical expression,then
the value of \( m \) is
Subject: Physics
M g of ice at \( 0^{\circ} \mathrm{C} \) is to be converted to
water at \( 0^{\circ} \mathrm{C} \). If \( \mathrm{L} \) is the latent heat of
fusion of ice, the quantity of heat required for the above operation would
be:
A . \( M L \) cal
в. \( \frac{M^{2}}{L} \)
\( ^{\mathrm{c}} \cdot \frac{M}{L} \mathrm{cal} \)
D. none of these
Subject: Chemistry
When soap or detergent dissolves in
water, which of the following is true?
A. The polar water soluble ( hydrophilic) head is on the surface of the micelle whereas non polar oil soluble (hydrophobic) tail is in the center of the micelle.
B. The polar water soluble ( hydrophilic) head is in the center of the micelle whereas non polar oil soluble (hydrophobic) tail is on the surface of the micelle
C. The polar water soluble ( hydrophilic) head is in the center of the micelle.
D. Non polar oil soluble (hydrophobic) tail is on the surface of the micelle.
Subject: Chemistry
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{O} \boldsymbol{H} \stackrel{\boldsymbol{C H} C l_{3}+\boldsymbol{K} \boldsymbol{O} \boldsymbol{H}}{\longrightarrow} \quad \) Product
About the above reaction the incorrect
statement is:
A. the name of reaction is Riemer teimann's reaction
B. the intermediate in the reaction dichloro carbene
c. the final major product is o-hydroxy benzaldehyde
D. the final major product is benzyl chloride
Subject: Chemistry
The solubility product of \( B a S O_{4} \) is
\( 1.5 \times 10^{-9} . \) The precipitation in a
\( 0.01 M B a^{2+} \) solution will start on
adding \( H_{2} S O_{4} \) of concentration:
A \( \cdot 1 \times 10^{-9} M \)
в. \( 1.5 \times 10^{-7} M \)
c. \( 2 \times 10^{-7} M \)
D. \( 1 \times 10^{-6} M \)
Subject: Physics
A gas at pressure \( p \) has volume \( V \). It is adiabatically compressed to volume \( V / 32 . \) If \( (32)^{1.4}=128, \) what is the
current pressure of the gas?
A . \( 128 p \)
B. \( 63 p \)
c. \( 32 p \)
D. \( 16 p \)
Subject: Physics
Four different circuit components are
given in each situation of List 1 and al the components are connected across
an ac source of same angular frequency \( \omega=200 \mathrm{rad} s^{-1} . \) The information of
phase difference between the current
source voltage in each situation of List 1 is given in List \( 2 . \) Match the circuit components in List 1 with the corresponding List 2
Subject: Chemistry
An inorganic mixture gives yellow
precipitate on boiling with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
and ammonium molybdate
\( \left.\left(\left(N H_{4}\right)\right)_{2} M o O_{4}\right) . \) Thus, inorganic
mixture can be :
This question has multiple correct options
A \( \cdot\left(N H_{4}\right)_{3} P O_{4} \)
B. \( \left(N H_{4}\right)_{3} A s O_{4} \)
\( \mathbf{c} \cdot p b\left(N O_{3}\right)_{2} \)
D. \( \left(N H_{4}\right)_{3} C_{2} O_{4} \)
E. None of the above
Subject: Physics
A charge ' \( Q \) ' is placed at each corner of a cube of side 'a'. The potential at the
centre of the cube is :
A \( \cdot \frac{8 Q}{\pi \varepsilon_{0} a} \)
в. \( \frac{4 Q}{4 \pi \varepsilon_{0} a} \)
c. \( \frac{4 Q}{\sqrt{3} \pi \varepsilon_{0} a} \)
D. \( \frac{2 Q}{\pi \varepsilon_{0} a} \)
Subject: Chemistry
How many moles of \( N a O H \) are required to neutralize 1.2 moles of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. 0.6 mole
B. 1.2 mole
c. 2.4 mole
D. 3.6 mole
E . 4.8 mole
Subject: Maths
\( A \) and \( B \) are two sets having 3 and 4
elements respectively and having 2 elements in common. The number of
relations which can be defined from \( \boldsymbol{A} \)
to \( B \) is
A \( \cdot 2^{5} \)
B. \( 2^{10}-1 \)
\( \mathbf{c} \cdot 2^{12}-1 \)
D. None of these
Subject: Biology
The most accepted line of descent in
human evolution is
A. Australopithecus\( \rightarrow \) Ramapithecus\( \rightarrow \)
Homo sapiens \( \rightarrow \) Homo habilis
B. Homo erectus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo sapiens
C . Ramapithecus \( \rightarrow \) Homo habilis \( \rightarrow \) Homo erectus \( \rightarrow \)
Homo sapiens
D. \( \$ \$ \) Australopithecus lrightarrow Ramapithecus |rightarrow Homol erectus Irightarrow Homol habilis Irightarrow Homo sapiens
Subject: Chemistry
Match List-I with List-II
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { A. Molarity } & \text { i) no units } \\ \text { B. Molality } & \text { ii) gm.equivalents/lit } \\ \text { C. Normality } & \text { iii) mol/lit } \\ \text { D. Mole fraction } & \text { iv) moles/kg. solvent }\end{array} \)
\( \mathbf{A} \)
B. A-iv, B-v, C-ii, D-i
C . A-iii, B-iv, C-i, D-i
D-i
D. A-iii, B-iv, C-ii,
Subject: Physics
The speed of sound in a gas is given by \( \boldsymbol{v}=\sqrt{\frac{\gamma \boldsymbol{R} \boldsymbol{T}}{\boldsymbol{M}}} \)
\( R= \) universal gas constant
\( \boldsymbol{T}= \) temperature
\( M= \) molar mass of gas The dimensional formula of \( \gamma \) is
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right. \)
B . \( \left[M^{0} L T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L T^{-2}\right] \)
D \cdot \( \left[M^{0} L^{0} T^{-1}\right] \)
Subject: Maths
The polynomial \( p(x)=x^{4}-2 x^{3}+ \)
\( 3 x^{2}-a x+3 a-7 \) when divided by \( x+ \)
1 leaves the remainder 19
Find the value of \( a \). Also find the
remainder when \( p(x) \) is divided by \( x+ \)
2
A \( . a=5 ; 62 \)
В. \( a=4 ; 62 \)
c. \( a=5 ; 60 \)
D. \( a=4 ; 60 \)
Subject: Chemistry
According to the ideal gas law, what is the approximately volume that will be occupied by 0.5 mole of an ideal gas at
\( 30^{\circ} \mathrm{C} \) and 3 atm pressure (gas constant
\( \boldsymbol{R}=\mathbf{0 . 0 8 2 1} \mathrm{L} \operatorname{atm} \mathrm{mol}^{-1} \mathrm{K}^{-1} \) )?
A. Less than 1 L
в. 5 L
\( c .10 L \)
D. 15 L
E. More than \( 20 L \)
Subject: Chemistry
\( 100 \mathrm{mL} \) of \( 0.20 M \) weak acid \( H A \) is
completely neutralized by \( 0.20 M \) NaOH. \( K_{b} \) for \( A^{-} \) is \( 10^{-5} \), the \( p H \) at
the equivalence point is
A . 1
B. 7
c. 10
D. none of these
Subject: Maths
Let \( \boldsymbol{f}_{\boldsymbol{p}}(\boldsymbol{a})=\boldsymbol{e}^{\frac{i a}{p^{2}}} \cdot \boldsymbol{e}^{\frac{2 i a}{p^{2}}} \cdot \boldsymbol{e}^{\frac{3 i a}{p^{2}}} \ldots \cdot \boldsymbol{e}^{\frac{i a}{p}} \)
(Where \( i=\sqrt{-1} \) and \( p \in \)
\( N) \) then \( \lim _{n \rightarrow \infty} f_{n}(\pi) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c. -1
D. \( -i \)
Subject: Physics
The equiconvex lens has a focal length
'f. If the lens is cut along the line perpendicular to principal axis and passing through the pole, what will be the focal length of any half part?
A \( \cdot \frac{f}{2} \)
B . \( 2 f \)
\( c \cdot \frac{3 f}{2} \)
D. \( f \)
Subject: Maths
\( \left|\begin{array}{cc}4 \sin ^{2} \theta & \cos ^{2} \theta \\ 3 \sec ^{2} \theta & \operatorname{cosec}^{2} \theta\end{array}\right|= \)
\( A \cdot 8 \sin ^{2} \theta \cos ^{2} \theta \)
B. \( 4 \sin 2 \theta \cos 2 \theta \)
c.
\( \mathbf{D} \cdot 4 \cos ^{3} \theta-3 \cos \theta \)
Subject: Physics
At. N.T.P. \( 28 ~ g \) of Nitrogen occupies 22.4 litres. What is the mass of 5.6 litres of Nitrogen at \( 38 \mathrm{cm} \) Hg pressure and \( 273^{0} C \) temperature is then
A \( .1 .87 \mathrm{g} \)
в. 48 g
c. \( 1.75 \mathrm{g} \)
D. \( 1.5 \mathrm{g} \)
Subject: Chemistry
Assertion
When KI solution is added to \( A g N O_{3} \)
solution, negatively charged sol results.
Reason
Negative charge of sol is due to preferential adsorption of iodide ions from the dispersion medium.
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: Chemistry
The number of atoms in \( 67.2 \mathrm{L} \) of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
\( (g) \) at \( S T P \) is:
\( A \cdot 9 N_{A} \)
B . \( 12 N_{A} \)
c. \( 3 N_{A} \)
D. \( 4 N_{A} \)
Subject: Maths
Let \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{4} \\ \mathbf{3} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ -\mathbf{2} & \mathbf{5}\end{array}\right] \) and
\( \boldsymbol{C}=\left[\begin{array}{cc}\mathbf{- 2} & \mathbf{5} \\ \mathbf{3} & \mathbf{4}\end{array}\right] . \) Find:
\( \boldsymbol{B}-\mathbf{4} \boldsymbol{C} \)
Subject: Chemistry
Calculate the e.m.f of the following cell reaction at \( 298 K: \)
\( \boldsymbol{M} \boldsymbol{g}_{(s)}+\boldsymbol{C u}^{2+}(\mathbf{0 . 0 0 0 1 M}) \rightarrow \)
\( M g^{2+}(0.001 M)+C u_{(s)} \)
The standard potential \( \left(\boldsymbol{E}^{o}\right) \) of teh cell
is \( 2.71 V \)
Subject: Physics
The angle made by the vector \( \vec{A}=\hat{i}+\hat{j} \)
with \( x- \) axis is
A \( \cdot 90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 22.5^{\circ} \)
D. \( 30^{\circ} \)
Subject: Physics
Choose the correct statements:
This question has multiple correct options
A. It is easier to fabricate 10000 AND gates using circuit components than on an integrated chip.
B. It is easier to fabricate 10000 AND gates on an integrated chip than fabricating them using circuit components.
C. It is easier to fabricate a single AND gate using circuit components as compared to on an IC.
D. It is easier to fabricate a single AND gate on an IC as compared to using circuit components.
Subject: Chemistry
An aqueous solution freezes at
\( -\mathbf{0 . 1 8 6}^{\circ} \boldsymbol{C}\left(\boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6}^{\boldsymbol{o}} ; \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5 1 2}^{\boldsymbol{o}}\right) \)
What is the elevation in boiling point?
A. 0.186
в. 0.512
c. \( \frac{0.512}{1.86} \)
D. 0.0512
Subject: Physics
The component of vector \( 3 \hat{i}+4 \hat{j} \) along vector \( \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}} \) is
A \( \cdot \frac{1}{2}(\hat{j}+\hat{i}) \)
B \( \cdot \frac{3}{2}(\hat{j}+\hat{i}) \)
c. \( \frac{5}{2}(\hat{j}+\hat{i}) \)
D. \( \frac{7}{2}(\hat{j}+\hat{i}) \)
Subject: Chemistry
Assertion
Copper obtained after bessemerization
is known as blister copper.
Reason
Blisters are produced on the surface of the metal due to escaping of dissolved
\( \boldsymbol{S O}_{2} \)
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
Which of the following is practical
applications of the law of conservation
of linear momentum?
This question has multiple correct options
A. When a manjumps out of a boat on the shore, the boat is pushed slightly away from the shore
B. A person left on a frictionless surface can get away from it by blowing air out of his mouth or by throwing some object in a direction opposite to the direction in which he wants to move.
C. Recoiling of a gun
D. None of these
Subject: Maths
Consider the following parallelograms. ind the values of the unknowns \( x, y, z \)
A \( . X=60^{\circ}, Y=100^{\circ}, Z=20^{\circ} \)
B . \( X=28^{\circ}, Y=112^{\circ}, Z=28^{\circ} \)
c. \( X=65^{\circ}, Y=105^{\circ}, Z=20^{\circ} \)
Subject: Physics
If the intensities of two interfering
waves be \( I_{1} \) and \( I_{2} \), the contrast between maximum and minimum
intensity is maximum, when
A \( \cdot I_{1}>>I_{2} \)
В . \( I_{1}<<I_{2} \)
c. \( I_{1}=I_{2} \)
D. either \( I_{1} \) or \( I_{2} \) is zero
Subject: Chemistry
The reaction which gives Borazole as a
major product is ?
\( \mathbf{A} \cdot L i H+B_{2} H_{6}^{2 m o l e s L i H_{\rightarrow} 1 m o l e B_{2} H_{6}} \)
\( \mathbf{B} \cdot B_{2} H_{6}+N H_{3} \frac{2 m o l e s B_{2} H_{6} 1 m o l e N H_{3}}{l o w t e m p} \)
\( \mathbf{c} \cdot B_{2} H_{6}+N H_{3} \frac{1 m o B_{2} H_{6} .2 m o l e s N H_{3}}{l o w t e m p} \)
D. \( B_{2} H_{6}+N H_{3} \frac{1 m o B_{2} H_{6} .2 \text { moles } N H_{3}}{\text {hightemp}} \)
Subject: Physics
When in going east at \( 10 \mathrm{km} / \mathrm{h} \) a train moving with constant velocity appears to be moving exactly north - east. when my velocity is increased to \( 30 \mathrm{km} / \mathrm{h} \)
east it appears to be moving north. At what speed (in Kmph) should I move North so that train appears to be moving exactly South-East?
\( A \cdot 30 \mathrm{km} / \mathrm{h} \)
B. 20 km/h
\( c .50 \mathrm{km} / \mathrm{h} \)
D. \( 10 \mathrm{km} / \mathrm{h} \)
Subject: Chemistry
Heat energy of \( 2100 \mathrm{J} \) is given to a gas at a constant pressure of \( 10^{5} \) Pa. The increase in internal energy, if the change in volume is \( 5 \times 10^{-3} m^{3}, \) is:
A . 1500
B. 1400 J
c. 1600 J
D. 800 J
Subject: Maths
ff \( \vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}, \) then the value of
\( (a \times i)^{2}+(a \times j)^{2}+(a \times k)^{2}= \)
\( A \cdot 2 \)
B. 4
\( c .6 \)
D. 18
Subject: Chemistry
For the decomposition,
\( N H_{2} C O O N H_{4}(s) \rightleftharpoons 2 N H_{3}(g)+ \)
\( \boldsymbol{C O}_{2}(\boldsymbol{g}) ; \boldsymbol{K}_{\boldsymbol{p}}=\boldsymbol{2} \cdot \boldsymbol{9} \times 10^{-5} \boldsymbol{a} \boldsymbol{t m}^{3} \)
The total pressure of gases at equilibrium when 1.0 mol of
\( N H_{2} C O O N H_{4}(s) \) was taken to start
with, would be :
A. 0.0194 atm
B. 0.0388 atm
c. 0.0582 atm
D. 0.0776 atm
Subject: Physics
The relation between voltage sensitivity
\( \sigma_{v} \) and the current sensitivity \( \sigma_{i} \) of \( a \)
moving coil galvanometer is (Given that
\( G \) is the resistance of the
galvanometer)
A \( \cdot \sigma_{v}=G \sigma_{i} \)
в. \( \sigma_{v}=\frac{\sigma_{i}}{G} \)
\( \mathbf{c} \cdot \sigma_{v} \sigma_{i}=G \)
D. \( \sigma_{v} \sigma_{i}=\frac{1}{G} \)
Subject: Physics
A convex lens of focal length \( 30 \mathrm{cm} \) is placed in front of a luminous point object. The separation between the object and the lens is \( 90 \mathrm{cm} . \) A glass slab of thickness \( t \) is placed between the object and the lens. A real image of the object is formed at the shortest
possible distance from the object. The refractive index of the slab is \( \frac{t}{t-k} \) Find \( k \)
Subject: Physics
In passing through a boundary,
refraction will not take place if
This question has multiple correct options
A. light is incident normally on the boundary
B. the indices of refraction of the two media are same
C. the boundary is not visible
D. angle of incidence is lesser than angle of refraction but greater than \( \sin ^{-1}\left(\frac{\mu_{R}}{\mu_{D}}\right) \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{\alpha} & \boldsymbol{2} \\ \boldsymbol{2} & \boldsymbol{\alpha}\end{array}\right] \) and \( |\boldsymbol{A}|^{3}=125 \) then the
value of \( \boldsymbol{\alpha} \) is
A. ±1
B. ±2
\( c .\pm 3 \)
D. ±5
Subject: Biology
Categories the given equations under
respective phases and select the
correct option.
\[
\begin{array}{r}
\text { "I. } C_{6} \mathrm{H}_{12} \mathrm{O}_{6}+2 \mathrm{NAD}^{+}+2 \mathrm{ADP}+2 \mathrm{Pi} \rightarrow \\
\qquad 2 \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}_{3}+2 \mathrm{ATP}+2 \mathrm{NADH}+2 \mathrm{H}^{+}
\end{array}
\]
Il. Pyruvic acid + \( 4 \mathrm{NAD}^{+}+\mathrm{FAD}^{+}+2 \mathrm{H}_{2} \mathrm{O}+\mathrm{ADP}+\mathrm{Pi} \rightarrow \)
\[
3 \mathrm{CO}_{2}+4 \mathrm{NADH}+4 \mathrm{H}^{+}+\mathrm{ATP}+\mathrm{FADH}_{2}
\]
A. I-Glycolysis ; II-Fermentation ; III-Krebs' cycle
B. I-Krebs' cycle ; II - Fermentation ; III -Glycolysis
C. I-Krebs' cycle ;II- Glycolysis ; III- Fermentation
D. I- Glycolysis ; II- Krebs' cycle ; III-Fermentation
Subject: Physics
A current passing through a circle coil of two turns produces a magnetic field \( B \) as its centre. The coil is then rewound
so as to have four turns and the same
current is passed through it. The magnetic field at its centre now is
A \( .2 B \)
B. \( B / 2 \)
\( c \cdot B / 4 \)
D. \( 4 B \)
Subject: Maths
fthe binomial distribution whose mean
is 5 and variance \( \frac{10}{3} \) is \( P(X=r)= \)
\( ^{15} C_{r}\left(\frac{1}{a}\right)^{r}\left(\frac{2}{a}\right)^{15-r}, r=0,1,2, \dots, 15 \)
then the value of \( a \) is
Subject: Chemistry
The ratio of the molar amounts of \( \boldsymbol{H}_{2} \boldsymbol{S} \)
needed to precipitate the metal ions
from \( 20 \mathrm{ml} \) each of \( 1 \mathrm{M} C d\left(N O_{3}\right)_{2} \) and
\( \mathbf{0 . 5} \boldsymbol{M} \boldsymbol{C u} \boldsymbol{S O}_{4} \) is:
A . 1:
B. 2:1
\( c \cdot 1: 2 \)
D. indefinite
Subject: Chemistry
Select the correct order of boiling point:
A. diethyl ether \( >n \) -butyl alcohol \( >n \) -butaraldehyde \( >n- \) pentane
B. n-butyl alcohol > n-butaraldehyde > n-pentane> diethylether
C. n-pentane \( >n \) -butaraldehyde \( >n \) -butyl alcohol \( > \) diethylether
D. n-butyl alcohol > n-butaraldehyde > diethylether > npentane
Subject: Maths
If \( a^{2}, b^{2}, c^{2} \) are in A.P. then the following
are also in A.P. True or False? If true
write 1 otherwise write 0 \( \frac{\boldsymbol{a}}{\boldsymbol{b}+\boldsymbol{c}}, \frac{\boldsymbol{b}}{\boldsymbol{c}+\boldsymbol{a}}, \frac{\boldsymbol{c}}{\boldsymbol{a}+\boldsymbol{b}} \)
Subject: Physics
If \( F \) is the force between two bodies of
masses \( m_{1} \) and \( m_{2} \) at certain
separation, then the force between \( \sqrt{2} m_{1} \) and \( \sqrt{3} m_{2} \) at same separation
is:
A \( \cdot \sqrt{6} F \)
в. \( \sqrt{26} F \)
\( c .6 F \)
D. \( \sqrt{216} F \)
Subject: Physics
A body weighing \( 8 g \) when placed in one pan and \( 18 g \) when placed on the other pan of a false balance. If the beam is horizontal when both the pans are
empty, then the true weight of the body is
A . \( 13 g \)
в. \( 9 g \)
c. \( 22 g \)
D. \( 12 g \)
Subject: Chemistry
For a reaction \( : A+B \rightarrow \) Products, the
rate of the reaction at various
concentrations are given below:
Expt
[А] \( \quad \) [В] rate (mol Io \( \left.d m^{-3} s^{-1}\right) \)
\( \begin{array}{lll}\text { 0.2 } & \text { 0.2 } & \text { 2. }\end{array} \)
\( 0.2 \quad 0.4 \)
\( \begin{array}{ll}0.4 & 36\end{array} \)
The rate law for the above reaction is :
A \( \cdot r=K[A]^{2}[B] \)
B . \( r=K[A][B]^{2} \)
c . \( r=K[A]^{3}[B] \)
D . \( r=K[A]^{2}[B]^{2} \)
Subject: Maths
\( \int e^{\tan ^{-1} x}\left[\frac{1+x+x^{2}}{1+x^{2}}\right] d x= \)
A \( \cdot x^{2} e^{\tan ^{-1} x}+c \)
B . \( x e^{\tan ^{-1} x}+c \)
C \( \cdot e^{\tan ^{-1} x}+c \)
D. \( \frac{1}{2} e^{\tan ^{-1} x}+c \)
Subject: Physics
Imagine a new planet having the same density as that of the earth but it is 3 times bigger than the earth is size. If
the acceleration due to gravity on the surface of the earth is \( g \) and that on the
new planet is \( g^{\prime} \), then what is the value of g'lg?
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
D. 6
Subject: Physics
A train runs along an unbanked circular
track of radius \( 30 m \) at a speed of
\( \mathbf{5 4 k m / h .} \) The mass of the train is \( 10^{6} k g \) What provides the centripetal force
required for this purpose-the engine or the rails? What is the angle of banking required to prevent wearing out of the rail?
Subject: Maths
If \( |\vec{a}|=|\vec{b}|=|\vec{c}|=1, \vec{a} \cdot \vec{b}=\vec{b} \cdot \vec{c}= \)
\( \vec{c} \cdot \vec{a}=\frac{1}{2} \operatorname{then}[\vec{a}, \vec{b}, \vec{c}]= \)
A . 1
B. \( \frac{1}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{\sqrt{3}}{2} \)
Subject: Physics
A. Current flow inside the capacitor due to accumulation of charges on the capacitor walls is called displacement
current.
B. Current due to the flow of electrons
due to some potential difference is called as conduction current.
C. Displacement current came into existence when Maxwell observed that
if a magnetic compass is placed between the capacitors the needle gets deflected which signifies presence of magnetic fields which would possibly caused due to some changing current.
D. Displacement current change the actual motion of electric charges. Which of the above statement(s) is/are
correct?
A. A and B only
B. A, B and C only
c. \( c \) only
D. \( A, B, C \) and \( D \)
Subject: Physics
Which of the following statement is true on a scattering of atom according to Rutherfords experiments on the alpha particle ?
A. Atoms are roughly spherical with a radius of about \( 10^{-10} m \)
B. The electrons occupy quantized energy levels absorbing or emitting energy only when they make a quantum jump between these levels
c. The density of positive charge within an atom is not uniform throughout the atoms volume
D. Allowed electron orbits must have a circumference equal to a whole number times the electrons de Broglie wavelength
E. Alpha particles are positively charged
Subject: Chemistry
The standard reduction potential for \( C u^{2+} / C u \) is +0.34 V. What will be the
reduction potential at \( \mathrm{pH}=14 ?[ \) Given:
\( \left.\boldsymbol{K}_{s p} \text { of } \boldsymbol{C u}(\boldsymbol{O H})_{2} \text { is } \mathbf{1 . 0} \times \mathbf{1 0}^{-\mathbf{1 9}}\right] \)
A . \( 2.2 v \)
в. 3.4v
c. \( -0.22 v \)
D . \( -2.2 v \)
Subject: Chemistry
an organic liquid (A), containing C,H
and 0 with boiling point \( 78^{\circ} \mathrm{C} \) and possessing a rather pleasant odour or heating with concenterated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
gives a gaseous product (B) with the
empirical formula \( C H_{2} . \) B decolourises
bromine water as well as alkaline
\( K M n O_{4} \) solution and takes up one
mole of \( \boldsymbol{H}_{2}(\text { per mole of } \mathrm{B} \) ) in the presence of finely divided nickle at high
temperature. A and B are:
\( \mathbf{A} \cdot C_{2} H_{5} O H, C_{2} H_{2} \)
в. \( C H_{3} O H, C_{2} H_{2} \)
c. \( C_{2} H_{5} \) OH \( , C_{2} H_{4} \)
D \( \cdot\left(C H_{3}\right)_{2} C H O H, C_{3} H_{6} \)
Subject: Physics
A sphere of mass \( M \) and radius \( r \)
shown in the figure, slips on rough
horizontal plane. At some instant it has
translational velocity \( v_{0} \) and rotational
velocity about centre \( \boldsymbol{v}_{\mathbf{0}} / 2 \boldsymbol{r} . \) The
percentage change of translational
velocity after the sphere start pure
rolling:
A. \( 14.28 \% \)
B . \( 7.14 \% \)
c. \( 21.42 \% \)
D. None
Subject: Maths
The solution of the differential equation
\( \boldsymbol{y}^{\prime}=\frac{\mathbf{1}}{e^{-\boldsymbol{y}}-\boldsymbol{x}}, \) is
\( \mathbf{A} \cdot x=e^{-y}(y+c) \)
B . \( y+e^{-y}=x+c \)
C \( . x=e^{y}(y+c) \)
D. \( x+y=e^{-y}+c \)
Subject: Physics
Four charges \( 10^{-8},-2 \times 10^{-8},+3 x \)
\( 10^{-8} \) and \( 2 \times 10^{-8} \mathrm{C} \) are placed at the
four corners of a square of 1 meter
\( \mathbf{1} / \mathbf{4} \boldsymbol{\pi} \varepsilon_{\mathbf{0}}=\mathbf{9} \times \mathbf{1 0}^{\mathbf{9}} \mathbf{N}-\boldsymbol{m}^{2} / \boldsymbol{C}^{\mathbf{2}} \) its
potential at the centre Of the square is
A . 206
B. 308
c. \( 360 \sqrt{2} \mathrm{V} \)
D. 90
Subject: Chemistry
\( 40 m l \) of hydrocarbon on combustion
gave \( 120 m l C O_{2} \) and \( 80 m l \) water vapour. The molecular formula of
hydrocarbon is:
\( \mathbf{A} \cdot C_{2} H_{6} \)
в. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{4} \)