AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
Both \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) have the same
number of hydrogen atoms but \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \)
is a tribasic acid and \( H_{3} P O_{3} \) is a
dibasic acid
Reason
mole of \( H_{3} P O_{3} \) is neutralised by 2
moles of \( N a O H \) while 1 mole of \( H_{3} P O_{4} \)
is neutralised by 3 moles of \( N a O H \)
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: Biology
Choose the correct answer from the
alternatives given :
Watson and Crick (1953) proposed DNA
double helix model and won the Nobel
Prize; their model of DNA was based on
(i) X-ray diffraction studies of DNA done by Wilkins and Franklin
(ii) Chargaffs base equivalence rule
(iii) Griffiths transformation
experiment
(iv) Meselson and Stahls experiment.
A. (i), (ii) and (iv)
B. (i) and (ii)
c. (iii) and (iv)
D. (i), (ii), (iii) and (iv)
Subject: Maths
\[
\begin{aligned}
\operatorname{Let} A &=\left\{\theta: 2 \cos ^{2} \theta+\sin \theta \leq 2\right\} \text { and } \\
B &=\{\theta: \pi / 2 \leq \theta \leq 3 \pi / 2\} . \text { Then }
\end{aligned}
\]
find the value of \( \boldsymbol{A} \cap \boldsymbol{B} \)
Subject: Chemistry
Which of the following is/are correct statement(s)?
This question has multiple correct options
A. p-nitrophenol and o-nitrophenol can be separated by steam distillation
B. p-nitrophenol is less acidic than o-nitrophenol
c. p-hydroxybenzonic acid is less acidic than ohydroxybenzonic acid
D. \( C C l_{4} \) does not give reaction with aq. \( A g N O_{3} \) solution
Subject: Maths
Find an equation of the line through the points (-3,5) and (9,10) and write it in standard form \( A x+B y=C, \) with \( A> \)
0
A \( .6 x-10 y=-75 \)
B. \( 5 x-12 y=-75 \)
c. \( 4 x-11 y=-65 \)
D. \( x-6 y=-15 \)
Subject: Maths
The value of \( \frac{(\boldsymbol{n}+\mathbf{2}) !-(\boldsymbol{n}+\mathbf{1}) !}{\boldsymbol{n} !} \) is:
A \( \cdot(n+2) ! \)
в. \( (n+1) ! \)
c. \( (n+2)^{2} \)
D. \( (n+1)^{2} \)
\( E \)
Subject: Maths
If \( n \) is a positive integer, then the value
of the determinant \( \left|\begin{array}{ccc}\boldsymbol{a}^{n}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+1}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\mathbf{2}}-\boldsymbol{x} \\ \boldsymbol{a}^{\boldsymbol{n}+\mathbf{3}}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\mathbf{4}}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\mathbf{5}}-\boldsymbol{x} \\ \boldsymbol{a}^{\boldsymbol{n}+\mathbf{6}}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\mathbf{7}}-\boldsymbol{x} & \boldsymbol{a}^{\boldsymbol{n}+\boldsymbol{8}}-\boldsymbol{x}\end{array}\right|= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c .-1 \)
D. None of these
Subject: Physics
The wave function (in S.I. units) for an
electromagnetic wave is given as-
\( \psi(x, t)=10^{3} \sin \pi\left(3 \times 10^{6} x-9 x\right. \)
\( \left.10^{14} t\right) \) The speed of the wave is:
A \( \cdot 9 \times 10^{14} \mathrm{m} / \mathrm{s} \)
В. \( 3 \times 10^{8} \mathrm{m} / \mathrm{s} \)
c. \( 3 \times 10^{6} m / s \)
D. \( 3 \times 10^{7} m / s \)
Subject: Maths
For \( \boldsymbol{x} \in(\mathbf{0}, \boldsymbol{\pi}), \) the equation \( \sin \boldsymbol{x}+ \)
\( 2 \sin 2 x-\sin 3 x=3, \) has
A. infinitely many solutions
B. three solutions
c. one solution
D. no solution
Subject: Maths
In the following figure, \( X Y \) is parallel to \( B C, A X=9 c m, X B=4.5 \mathrm{cm} \) and
\( B C=18 \mathrm{cm} . \) Find the value of \( x y \)
\( A \cdot 14 \)
3. 12
\( c .16 \)
D. 18
Subject: Maths
Examine the continuity of the function \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}(\sin \boldsymbol{x}-\cos \boldsymbol{x}) \text { for } \boldsymbol{x} \neq 0 \\ -\mathbf{1} \text { for } \boldsymbol{x}=\mathbf{0}\end{array}\right. \)
at the point \( \boldsymbol{x}=\mathbf{0} \)
Subject: Physics
If strength of magnetic field \( \vec{B}=2 \hat{i}+ \) \( \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and area vector is \( \overrightarrow{\boldsymbol{A}}=\mathbf{3} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}} \)
then find the magnetic flux link with
area vector
A. 4 wber
B. 6 weber
c. 7 weber
D. 5 weber
Subject: Maths
The variance of the following data is :
\[
\begin{array}{llll}
\text { Length } & \mathbf{7 2 . 0 -} & \mathbf{7 4 . 0 -} & \mathbf{7 6 . 0 -} \\
\text { of rod } & \mathbf{7 3 . 9} & \mathbf{7 5 . 9} & \mathbf{7 7 . 9}
\end{array}
\]
No. of
Rods
A .2
B. 13.45
c. 13.54
D. 13.40
Subject: Maths
Get the area of \( \triangle A B C \) for
\( \boldsymbol{A}(\mathbf{1}, \mathbf{1}, \mathbf{2}), \boldsymbol{B}(\mathbf{2}, \mathbf{3}, \mathbf{5}), \boldsymbol{C}(\mathbf{1}, \mathbf{3}, \mathbf{4}) \) by use of
vectors.
Subject: Maths
For a polynomial \( \boldsymbol{p}(\boldsymbol{x}), \) the value of \( \boldsymbol{p}(\boldsymbol{3}) \)
is \( -2 . \) Which of the following must be
true about \( p(x) ? \)
A \( \cdot x-5 \) is a factor of \( p(x) \)
B . \( x-2 \) is a factor of \( p(x) \)
c. \( x+2 \) is a factor of \( p(x) \)
D. The remainder when \( p(x) \) is divided by \( x-3 \) is -2
Subject: Chemistry
A sample of coconut oil weighing
\( 1.573 g \) is mixed with \( 25 m L \) of
\( 0.4210 M K O H \) is used in
saponification of coconut oil. After the
saponification is complete, \( 8.46 m L \) of
\( 0.2732 M H_{2} S O_{4} \) is required to
neutralize excess \( K O H . \) The
saponification number of peanut oil is:
A . 209.6
B. 98.9
c. 108.9
D. 218.9
Subject: Maths
Given 3 identical boxes \( 1,2, \& 3 . \) Each containing 2 coins. \( \ln \) box 1 , both are gold coins \( \& \) in box 2 both are silver
coins and in box 3 there is 1 silver and 1
gold coin. A person chooses a box at random and takes out the coin. If the
coin is gold then what is the probability that it is coming from the first box?
Subject: Physics
A small metal sphere of radius \( a \) is
falling with a velocity \( v \) through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid
is \( \eta \), then the sphere encounters an opposing force of:
A \( \cdot 6 \pi \eta a^{2} v \)
в. \( \frac{6 \eta v}{\pi a} \)
c. \( 6 \pi \eta a v \)
D. \( \frac{\pi \eta v}{6 a^{3} v} \)
Subject: Physics
The work done by electric field in
carrying a point charge of \( 5 \mu C \) from a
point \( A \) to point \( B \) is 10 mJ. The potential
difference \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}} \) is the:
\( A \cdot+2 k V \)
B. -2 kV
\( c \cdot+2000 v \)
D. -2000V
Subject: Physics
An element \( A \) decays into element \( C \) by
the following two step processes:
\( \boldsymbol{A} \longrightarrow_{2} \boldsymbol{H} \boldsymbol{e}^{\boldsymbol{4}}+\boldsymbol{B} \)
\( \boldsymbol{B} \longrightarrow \mathbf{2}\left(_{-1} \boldsymbol{e}^{0}\right)+\boldsymbol{C} \)
Select pair for isobars from elements
\( A, B \) and \( C \)
Subject: Maths
\( \frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+1}= \)
\( \mathbf{A} \cdot \frac{\cos \theta}{1+\sin \theta} \)
B. \( \frac{1+\cos \theta}{\sin \theta} \)
\( \mathbf{C} \cdot \frac{1+\sin \theta}{\cos \theta} \)
D. \( \frac{1-\sin \theta}{\cos \theta} \)
Subject: Maths
If \( x=2+2^{\frac{1}{3}}+2^{\frac{2}{3}}, \) then the values of
\( \boldsymbol{x}^{3}-\mathbf{6} \boldsymbol{x}^{2}+\boldsymbol{6} \boldsymbol{x} \) is
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
\( c \cdot-2 \)
D.
Subject: Physics
toppr
Q Type your question
decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic
energy has a continuous spectrum. Considering a three-body decay
process, i.e. \( \boldsymbol{n} \rightarrow \boldsymbol{p}+\boldsymbol{e}^{-}+\overline{\boldsymbol{v}}_{e}, \) around
1930, Pauli explained the observed electron energy spectrum. Assuming
the anti-neutrino \( \left(\bar{v}_{e}\right) \) to be massless
and possessing negligible energy, and the neutron to be at rest, momentum
and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron
is \( 0.8 \times 10^{6} e V . \) The kinetic energy
carried by the proton is only the recoil
energy. f the anti-neutrino had a mass of 3
\( e V / c^{2}(\text { where } c \) is the speed of light) instead of zero mass, what should be
the range of the kinetic energy, \( \boldsymbol{K}, \) of the
electron?
A. \( 0 \leq K \leq 0.8 \times 10^{6} e V \)
B . \( 3.0 e V \leq K \leq 0.8 \times 10^{6} c V \)
c. \( 3.0 e V \leq K<0.8 \times 10^{6} e V \)
D. \( 0 \leq K<0.8 \times 10^{6} e V \)
Subject: Chemistry
Carbon reduction process is not commercially applicable for which of the following set of oxides to extract the respective metal?
(I) \( Z n O \)
\( (\|) \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3} \)
\( (\| I) A l_{2} O_{3}(I V) \)
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2}(\vee) \boldsymbol{M} \boldsymbol{g} \boldsymbol{O} \)
A. \( Z n O, F e_{2} O_{3}, S n O_{2} \)
в. \( Z n O, S n O_{2}, M g O \)
\( \mathrm{c} \cdot \mathrm{Mg} \mathrm{O}, \mathrm{Al}_{2} \mathrm{O}_{3} \)
D. \( M g O, S n O_{2}, A l_{2} O_{3} \)
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{e^{x^{2}}-\cos x}{\sin ^{2} x} \) is equal to :
\( A \cdot 2 \)
B. \( \frac{3}{2} \)
\( c \cdot 3 \)
\( D \cdot \frac{5}{4} \)
Subject: Chemistry
The Vant Hoff factor (i) for a dilute
solution of \( \boldsymbol{K}_{\mathbf{3}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \) is (Assuming
\( 100 \% \text { ionsation }) \)
A . 10
B. 4
c. 5
D. 0.25
Subject: Physics
A wire loop formed by joining two semi-
circular wires of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) carries
a current as shown in the adjoining
diagram. The magnetic induction at
the center \( \boldsymbol{O} \) is
A \( \cdot \frac{\mu_{0} I}{4 R_{1}} \)
B. \( \frac{\mu_{0} I}{4 R} \)
c. \( \frac{\mu_{0} I}{4}\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \)
D. \( \frac{\mu_{0} I}{4}\left(\frac{1}{R_{1}}+\frac{1}{R_{2}}\right) \)
Subject: Biology
The enzyme polynucleotide phosphorylase randomly assembles nucleotides into a polynucleotide phosphorylase to a solution of adenosine triphosphate and guanosine triphosphate, how many types artificial
\( m R N A 3 \) nucleotide codons would be
possible?
\( \mathbf{A} \cdot \mathbf{3} \)
B. 4
c. 8
D. 16
Subject: Chemistry
The correct order of boiling points of the
following isomeric amines is:
\( \boldsymbol{C}_{\mathbf{4}} \boldsymbol{H}_{\mathbf{9}} \boldsymbol{N} \boldsymbol{H}_{\mathbf{2}} \cdot\left(\boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}}\right)_{\mathbf{2}} \boldsymbol{N} \boldsymbol{H}, \boldsymbol{C}_{\mathbf{2}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{N}\left(\boldsymbol{C} \boldsymbol{H}_{\mathbf{3}}\right. \)
\( \mathbf{A} \cdot C_{2} H_{5} N\left(C H_{3}\right)_{2}>\left(C_{2} H_{5}\right)_{2} N H>C_{4} H_{9} N H_{2} \)
\( \mathbf{B} \cdot\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N\left(C H_{3}\right)_{2}>C_{4} H_{9} N H_{2} \)
\( \mathbf{c} \cdot C_{4} H_{9} N H_{2}>\left(C_{2} H_{5}\right)_{2} N H>C_{2} H_{5} N\left(C H_{3}\right)_{2} \)
D. \( \left(C_{2} H_{5}\right)_{2} N H>C_{4} H_{9} N H_{2}>C_{2} H_{5} N\left(C H_{3}\right)_{2} \)
Subject: Chemistry
Hess' Law and bond energy data can be used to calculate the enthalpy change of a reaction. Bromoethane
\( C H_{2} C H_{2} B r, \) can be made by reacting ethene with hydrogen bromide.
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H B r} \rightarrow \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{B r} \)
What is the enthalpy change for this
reaction?
A. \( -674 \mathrm{kJ} \mathrm{mol}^{-} \)
B. -64 kJ \( m o l^{-1} \)
c. +186 k \( \mathrm{mol}^{-1} \)
D. +346 k \( \mathrm{mol}^{-1} \)
Subject: Maths
The area common to the cardioids \( r= \)
\( \boldsymbol{a}(\mathbf{1}+\cos \boldsymbol{\theta}) \) and \( \boldsymbol{r}=\boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\theta}) \) is:
\( ^{A} \cdot\left(\frac{3 \pi}{2}+4\right) a^{2} \)
в. \( \left(\frac{3 \pi}{2}-4\right) a^{2} \)
c. \( \left(\frac{\pi}{2}+4\right) a^{2} \)
D \( \cdot\left(\frac{\pi}{2}-4\right) a^{2} \)
Subject: Physics
Statement-1: When two vibrating tuning
forks having frequencies 256 Hz and 512
Hz are held near each other, beats
cannot be heard.
Statement-2: The principle of
superposition is valid only if the
frequencies of the oscillations are
nearly equal.
A. Both the statements are true and statement- 2 is the correct explanation of statement-
B. Both the statements are true but statement-2 is not the correct explanation of statement-
c. Statement-1 is true and statement-2 is false
D. Statement-1 is false and statement-2 is true
Subject: Physics
A diatomic ideal gas is compressed adiabatically to \( \frac{1}{32} \) of its initial volume.
If the initial temperature of the gas is \( \mathbf{T}_{\mathbf{i}} \) (in Kelvin) and the final temperature is
\( a T_{i}, \) the value of a is
\( A \cdot 4 \)
B. 5
\( c \cdot 2 \)
D. 3
Subject: Biology
Match the following (column I with column II).
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { (a) Chlamydomonas } & \text { (i) Moss } \\ \text { (b) cycas } & \text { (ii) Pteridophyta } \\ \text { (c) Selaginella } & \text { (iii) Algae } \\ \text { (d) Sphagnum } & \text { (iv) Gymnosperm }\end{array} \)
Subject: Chemistry
A black powder when heated with conc.
HCl gives a greenish yellow gas. The gas acts as an oxidizing and a bleaching agent. When it is passed over slaked lime, a white powder is formed which is a ready source of gas. The black powder
and white powder respectively are:
A \( . K C l O_{3} \) and \( N a C l O_{3} \)
B. \( M n O_{2} \) and \( C a(O C l)_{2} \)
\( \mathrm{c} \cdot \mathrm{M} n \mathrm{O}_{2} \) and \( \mathrm{KClO}_{3} \)
D. \( M n C l_{4} \) and \( C O C l_{2} \)
Subject: Maths
If there are ' \( n \) ' arithmetic means
between \( a \) and \( b \), then the common
difference \( (\boldsymbol{d})= \)
A \( \cdot \frac{a-b}{n+1} \)
в. \( \frac{b-a}{n+1} \)
c. \( \frac{a+b}{n-1} \)
D. \( \frac{b-a}{n-1} \)
Subject: Physics
If the displacement of a particle executing SHM is given by \( \boldsymbol{y}= \)
\( 0.30 \sin (220 t+0.64) \) in metre, then the
frequency and maximum velocity of the particle are
A \( .35 H z, 66 m / s \)
B. \( 45 H z, 66 m / s \)
\( \mathbf{c} .58 H z, 113 m / s \)
D. \( 35 H z, 132 m / s \)
Subject: Physics
A Carnot refrigerator extracts heat from
water at \( 0^{\circ} \mathrm{C} \) and rejects it to a room at
\( 24.4^{\circ} \mathrm{C} . \) The work required by the
refrigerator for every \( 1 \mathrm{kg} \) of water converted into ice is
(Latent heat of ice \( =336 \mathrm{kj} \mathrm{kg}^{-1} \) )
A . \( 24.4 k j \)
в. \( 30 k j \)
c. \( 336 k j \)
D. \( 11.2 k j \)
Subject: Physics
A circular thin disc of mass 5 kg has a diameter \( 1 \mathrm{m} . \) The moment of inertia
about an axis passing through the edge and perpendicular to the plane of the disc is
A \( \cdot(8 / 15) k g-m^{2} \)
В \( \cdot 8 k g-m^{2} \)
\( \mathbf{c} \cdot(15 / 8) k g-m^{2} \)
D. \( 1 k g-m^{2} \)
Subject: Chemistry
The correct \( I . U . P . A . C \) name for
\( \boldsymbol{H}_{2}\left[\boldsymbol{P t C l}_{6}\right] \) complex:
A. Hexachloridoplatinic (IV) acid
B. Hexachloridoplatinate (IV) acid
c. Hydrogenhexachloridoplatinate (IV) acid
D. Di hydrogenhexachloridoplatinate (IV) acid
Subject: Physics
A cricket ball of mass \( \mathrm{m} \) is hitted at the
angle \( 45^{\circ} \) to the horizontal with velocity
v.lts kinetic energy at the topmost point is
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot \frac{1}{2} m v^{2} \)
c. \( \frac{m v^{2}}{4} \)
D. \( \frac{m v^{2}}{2 \sqrt{2}} \)
Subject: Physics
There are two concentric spherical
shells of radii \( r \) and \( 2 r . \) Initially a
charge \( Q \) is given to the inner shell and
both the switches are open. If switch \( S_{1} \) is closed and then opened, charge on
the outer shell will be
\( A \cdot Q \)
в. \( \frac{Q}{2} \)
c. \( -Q \)
D. \( \frac{-Q}{2} \)
Subject: Physics
Match column - -I with column-II and
select the correct answer using the
codes given below:
Column-I Column
(A)
The rate of change \( \quad(p) \quad \) Accelera of momentum
The ratio of the total
(B) distance travelled to
(q) Velocity
the total time taken
\( (C) \)
The time rate of \( \quad \) (r) \( \quad \) Average
\( (r) \)
change of velocity \( \quad \) '(') \( \quad \) speed
Displacement per \( \quad(s) \quad \) Force
(D) \( \quad \) unit time
\( \mathbf{A} \cdot(A) \rightarrow(s),(B) \rightarrow(r),(C) \rightarrow(p),(D) \rightarrow(q) \)
B \( .(A) \rightarrow(p),(B) \rightarrow(r),(C) \rightarrow(q),(D) \rightarrow(s) \)
\( \mathbf{c} \cdot(A) \rightarrow(s),(B) \rightarrow(p),(C) \rightarrow(r),(D) \rightarrow(q) \)
D. \( (A) \rightarrow(q),(B) \rightarrow(r),(C) \rightarrow(p),(D) \rightarrow(s) \)
Subject: Physics
\( 2 \mu F \) capacitance has P.D across its two terminals of \( 200 \mathrm{V} . \) It is disconnected
from the battery and when another uncharged capacitance is connected in parallel to it, P.D becomes 20 V. The capacity of another capacitance will be:
A \( .2 \mu F \)
в. \( 4 \mu F \)
c. \( 10 \mu F \)
\( \mathbf{D} \cdot 16 \mu F \)
Subject: Physics
The primary coil of an idea step up transformer has 100 turns and
transformation ratio is also \( 100 . \) The
input voltage and power are respectively \( 220 V \) and \( 1100 W \)
calculate \( (2 M) \)
1. Number of turns in secondary
2. Current in primary
3. Voltage across secondary
4. Current in secondary
5. Power in secondary
Subject: Physics
A point mass \( m \) is rigidly attached at
the circumference of uniform Ring of same mass. It is at same horizontal
position as centre of ring. The minimum coefficient of friction between ring and
ground so that there is pure rolling of
ring on surface just after system is
released is:
A . \( 3 / 5 \)
B. 2/3
\( c \cdot 1 / 3 \)
D. \( 2 / 7 \)
Subject: Chemistry
A gas mixture \( 3.67 L \) in volume contain
\( C_{2} H_{4} \) and \( C H_{4} \) is proportion of 2: 1 by
moles and is at \( 25^{\circ} \mathrm{C} \) and 1 atm. If the
\( \Delta H_{C}\left(C_{2} H_{4}\right) \) and \( \Delta H_{C}\left(C H_{4}\right) \) are
-1400 and \( -900 k J / m o l, \) find heat evolved on burning this mixture:
в. \( 50.88 k J \)
c. \( 201 k J \)
D. 160kJ
Subject: Maths
\( \int \frac{d x}{(x-b) \sqrt{(x-a)(b-x)}}= \)
A \( -\frac{(b-a)}{2} \sqrt{\frac{b-x}{x-a}}+c \)
В. \( -(b-a) \sqrt{(b-x)(x-a)}+c \)
c. \( -\frac{2}{(b-a)} \sqrt{\frac{x-a}{b-x}}+c \)
D. \( (b-a) \sqrt{(x-b)(x-a)}+c \)
Subject: Chemistry
Which of the following are chiral (optically active)?
A. Benzoic acid
B. Pent-2,3-diene \( \left(C H_{3}-C H=C=C H-C H_{3}\right) \)
c. Hex- 2,3,4 -triene \( \left(C H_{3}-C H=C=C=C H-C H_{3}\right) \)
D. 1,1,3,3 - tetrachloroprop- 1,2 -diene \( \left(C C I_{2}=C=C I_{2}\right) \)
E. 2-(2-Carboxy-6-Nitrobenzyl)-3-Nitrobenzoicacid
Subject: Maths
Let \( x_{1}, x_{2}, \ldots . . \) be positive integers in
A.P., such that \( x_{1}+x_{2}+x_{3}=12 \) and
\( \boldsymbol{x}_{4}+\boldsymbol{x}_{6}=\mathbf{1 4} . \) Then \( \boldsymbol{x}_{5} \) is
This question has multiple correct options
A. A prime number
B. 11
\( c \cdot 13 \)
D. 7
Subject: Physics
A body has a weight of \( 10 k g \) on the
surface of the Earth. What will be its
mass and weight when taken to the centre of the Earth?
A. \( 10 \mathrm{kg} \), zero
B. zero, zero
c. \( 10 \mathrm{kg}, 10 \mathrm{g} \)
D. zero, \( 10 g \)
Subject: Chemistry
A buffer solution, \( 0.080 M \) in \( N a_{2} P O_{4} \)
and \( 0.020 M \) in \( N a_{3} P O_{4} \) is prepared. The electrolytic oxidation of 1.0 mmol of
the organic compound \( R N H O H \) is carried out in \( 100 \mathrm{m} L \) of the buffer. The
reaction is as follows:
\( \boldsymbol{R} \boldsymbol{N} \boldsymbol{H} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{R} \boldsymbol{N} \boldsymbol{O}_{2}+ \)
\( 4 H^{+}+4 e \)
Calculate the approximate \( p H \) of the solution after the oxidation is complete.
A . 6.19
B. 7.81
c. 10.34
D. 12.45
Subject: Maths
If \( z_{1}, z_{2}, z_{3} \) are the solutions of \( z^{2}+ \)
\( \bar{z}=z, \) then \( z_{1}+z_{2}+z_{3} \) is equal to
(where \( z \) is a complex number on the
argand plane and \( i=\sqrt{-1}) \)
\( \mathbf{A} \cdot 2+2 i \)
B . \( 2-2 i \)
c. 0
D. 2
Subject: Maths
Direction cosines \( l, \boldsymbol{m}, \boldsymbol{n} \) of two lines are
connected by the equation \( l-5 m+ \)
\( \mathbf{3} n=\mathbf{0} \) and \( \mathbf{7 l}^{2}+\mathbf{5 m}^{\mathbf{2}}-\mathbf{3 n}^{\mathbf{2}}=\mathbf{0 .} \) The
direction cosines of one of the lines are
в. \( 2 / \sqrt{6}, 1 / \sqrt{6},-1 / \sqrt{6} \)
D. \( 1 / \sqrt{6}, 1 / \sqrt{6}, 2 / \sqrt{6} \)
Subject: Maths
\( \left[\begin{array}{cc}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right]\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{1}\end{array}\right]\left[\begin{array}{ll}\mathbf{1} & \mathbf{3} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \cdot\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{n}-\mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right]= \)
\( \left[\begin{array}{cc}\mathbf{1} & \mathbf{7 8} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \)
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{n} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \operatorname{then} \boldsymbol{A}^{-\mathbf{1}}=? \)
A \( \cdot\left[\begin{array}{cc}1 & 12 \\ 0 & 1\end{array}\right] \)
B \( \cdot\left[\begin{array}{cc}1 & -13 \\ 0 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}1 & -12 \\ 0 & 1\end{array}\right] \)
D. \( \left[\begin{array}{cc}1 & 0 \\ -13 & 1\end{array}\right] \)
Subject: Maths
If
\( [x] \) denotes the greatest integer \( \leq x \)
then the system of linear equations \( [\sin \theta] x+[-\cos \theta] y=0[\cot \theta] x+y=0 \)
A \( \cdot \) Have infinitely many solutions if \( \theta \epsilon\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right) \cup \) \( \left(\pi, \frac{7 \pi}{6}\right) \)
B. Have infinitely many solutions if \( \theta \epsilon\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right) \) and has unique solution if \( \theta \epsilon\left(\pi, \frac{7 \pi}{6}\right) \)
c. Has a unique solution if \( \theta \epsilon\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right) \) and have nfinitely many solutions if \( \theta \epsilon\left(\pi, \frac{7 \pi}{6}\right) \)
D. Has a unique solution if \( \theta \epsilon\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right) \cup\left(\pi, \frac{7 \pi}{6}\right) \)
Subject: Chemistry
Which of the following statements is
not correct for \( \boldsymbol{S O}_{2} \) gas?
A. It acts as bleaching agent in moist conditions.
B. Its dilute solution is used as disinfectant.
C. Its molecules have linear geometry.
D. Acidified \( K M n O_{4} \) is decolourised when \( S O_{2} \) is passed through it
Subject: Maths
Let \( T \) be the set of all triangles in the
Euclidean plane, and let a relation \( R \) on \( T \) be defined as \( a R b, \) if \( a \) is congruent to
\( b \) for all \( a, b \in T . \) Then, \( R \) is
A. reflexive but not symmetric
B. transitive but not symmetric
c. equivalence
D. none of these
Subject: Physics
An insect is sitting in front of a plane
mirror at a distance 1 m from it.
(a) Where is the image of the insect
formed?
(b) What is the distance between the
insect and its image?
\( \mathbf{A} \cdot(a) 2 m \) behind the mirror \( (b) 1 m \)
B. \( (a) 2 m \) infront of the mirror
\( (b) 1 m \)
C \( .(a) 1 m \) infront of the mirror
\( (b) 2 m \)
D. \( (a) 1 m \) behind the mirror
\( (b) 2 m \)
Subject: Maths
In a given figure,ABCD is a trapezium in
which the parallel sides \( A B \) and \( C D \) are
both perpendicular to BC.If \( \boldsymbol{A B}= \)
\( \mathbf{1 6}, \boldsymbol{A D}=\mathbf{1 7} \) and \( \boldsymbol{C D}=\mathbf{8}, \) then \( \mathbf{B C} \) is
A .15
B. 25
\( c .25 .5 \)
0.39