AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Following reaction,
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C B r}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \)
\( \left(C H_{3}\right)_{3} C O H+H B r \) is an example of
A. elimination rection
B. free radical substitution
c. nucleophilic substitution
D. electrophilic substitution
Subject: Chemistry
Oxygen occurs in nature as a mixture of isotopes \( ^{1} 60,17 O \) and \( ^{1} 8 O \) having
atomic masses of 15.995 u, 16.999 u and
\( 17.999 \mathrm{u} \) and relative abundance of
\( 99.763 \%, 0.037 \%, \) and \( 0.200 \% \)
respectively. What is the average atomic mass of oxygen?
A . 15.999 u
B . 16.999 u
c. 17.999 u
D. 18.999 u
Subject: Chemistry
Match the column.
List -
\( \| \)
A) Rayon Cationic Polymerisation
B) Glass
Organic Polymers
C) Polystyrene Inorganic polymers
D) Polyisoprene Anionic polymerisation
A. \( A-2, B-3, C-4, D-1 \)
в. \( A-3, B-2, C-4, D-1 \)
c. \( A-2, B-1, C-3, D-4 \)
D. \( A-2, B-3, C-1, D-4 \)
Subject: Chemistry
A certain weak acid has \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 0} \times \)
\( 10^{-4} . \) The equilibrium constant for tis
reaction with a strong base is \( \boldsymbol{K}_{e q}= \) \( 10^{5 X} . \) Value of \( X \) is
Subject: Physics
Find the nature and order of the
interference at 0
\( A \cdot 20^{t h} \operatorname{minimal} \)
B. \( 20^{\text {th }} \) maxima
\( \mathrm{c} \cdot 10^{t h} \) maxima
\( D \cdot 10^{t h} \operatorname{minimaa} \)
Subject: Chemistry
If \( \Delta H_{f}^{\circ} \) of \( H_{2} S_{(g)} \) and \( H_{2} S_{(a q)} \) are -4.5 and -9.5 kcal. The amount of heat
required for the change is
\[
\boldsymbol{H}_{2} \boldsymbol{S}_{(a q)} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{S}_{(g)}
\]
Subject: Physics
A capacitor of capacitance \( 15 n F \)
having dielectric slab of \( \varepsilon r=2.5 \)
dielectric strength \( 30 \mathrm{MV} / \mathrm{m} \) and potential difference \( =30 \) volt. Calculate
the area of plate.
В. \( 4.2 \times 10^{-4} \mathrm{m}^{2} \)
c. \( 8.0 \times 10^{-4} \mathrm{m}^{2} \)
D. \( 9.85 \times 10^{-4} m^{2} \)
Subject: Maths
If \( A=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right], \) then the general
solution of \( \sin \theta=\left|A^{2}-4 A+3 I\right| \) is
A \( . n \pi \)
B \( \cdot 2 n+1 \frac{\pi}{2} \)
c. \( n \pi+(-1)^{n} \frac{\pi}{2} \)
D. \( 2 n \pi, n \epsilon z \)
Subject: Chemistry
Complete and balance the following
compound \( \boldsymbol{A l} \boldsymbol{B} \boldsymbol{r}_{3}+\boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}+ \)
\[
\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \rightarrow \boldsymbol{K}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{A} \boldsymbol{l} \boldsymbol{P} \boldsymbol{O}_{4}+
\]
Subject: Physics
Consider the following reaction \( ^{1} \boldsymbol{H}_{2}+^{1} \)
\( \boldsymbol{H}_{2} \rightarrow_{2} \boldsymbol{H} \boldsymbol{e}^{4}+\boldsymbol{Q} \)
If \( \boldsymbol{m}\left(_{1} \boldsymbol{H}^{2}\right)=\mathbf{2 . 0 1 4 1} \boldsymbol{u}, \boldsymbol{m}\left(_{2} \boldsymbol{H} \boldsymbol{e}^{4}\right)= \)
\( 4.0024 u, \) then the energy \( Q \) released (in
MeV) in this fusion reaction is
A . 12
B. 6
c. 24
D. 48
Subject: Physics
The binding energies per nucleon of
deutreron \( \left(_{1} H^{2}\right) \) and helium \( \left(_{2} H e^{4}\right) \) atoms are \( 1.1 \mathrm{MeV} \) and \( 7 \mathrm{MeV} \). If two
deuteron atoms react to form a single
helium atom, then the energy released
is
A. \( 13.9 \mathrm{MeV} \)
в. \( 26.9 \mathrm{MeV} \)
c . \( 23.6 \mathrm{MeV} \)
D. \( 19.2 \mathrm{MeV} \)
Subject: Maths
If the matrix \( A B \) is a zero matrix, then
which one of the following is correct?
A. \( A \) must be equal to zero matrix or \( B \) must be equal to zero matrix
B. \( A \) must be equal to zero matrix and \( B \) must be equal to zero matrix
c. It is not necessary that either \( A \) is zero matrix or \( B \) is zero matrix
D. None of the above
Subject: Maths
Find \( \frac{d y}{d x} \) if
(a) \( x^{3}+2 x^{2} y+3 x y^{2}+4 y^{3}=5 \)
(b) \( x=2 \cos ^{3} \theta, y=2 \sin ^{3} \theta \)
(c) \( y=\sin ^{-1}(2 x \sqrt{1-x^{2}}) ;-1 \leq x \leq 1 \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{5} \\ \mathbf{7} & \mathbf{- 9}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{6} & \mathbf{- 4} \\ \mathbf{2} & \mathbf{3}\end{array}\right], \) find
\( (4 A-3 B) \)
Subject: Physics
A thermometer graduated according to
a linear scale reads a value \( x_{0} \) when in
contact with boiling water, and \( \boldsymbol{x}_{\mathbf{0}} / \mathbf{3} \) when in contact with ice. What is the
temperature of an object in \( 0^{\circ} \mathrm{C} \), if this thermometer in the contact with the
object reads \( \boldsymbol{x}_{0} / 2 ? \)
A . 35
B . 25
c. 60
D. 40
Subject: Maths
\( \operatorname{Let} a, b, c, \epsilon R \) If \( f(x)=a x^{2}+b x+c \) is
such that \( a+b+c=3 \) and \( f(x+ \)
\( \boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})+\boldsymbol{x} \boldsymbol{y}, \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R}, \) the
\( \sum_{n=1}^{10} f(n) \) is equal to
A . 330
в. 165
c. 190
D. 255 55
Subject: Chemistry
Hybridization of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \) is:
\( A \cdot s p^{3} \)
В . \( d s p^{2} \)
c. \( s p^{3} d^{2} \)
D. \( s p^{3} d \)
Subject: Maths
Draw the histogram of the following
frequency distribution:
\( \begin{array}{ll}\text { Class-Interval } & \text { Frequency } \\ 0-9 & 5 \\ 10-19 & 8 \\ 20-29 & 12 \\ 30-39 & 18 \\ 40-49 & 22 \\ 50-59 & 10\end{array} \)
Subject: Physics
The following truth table corresponds to the logic gate
\( \begin{array}{ccc}\mathbf{A} & \mathbf{B} & \mathbf{X} \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1\end{array} \)
A. NAND
B. OR
C . AND
D. xor
Subject: Maths
For all positive value of \( x \) and \( y, \) the value of \( \frac{\left(1+x+x^{2}\right)\left(1+y+y^{2}\right)}{x y} \) is
\( A . \leq 9 \)
в. \( <9 \)
\( c \cdot \geq 9 \)
\( D \cdot>9 \)
Subject: Physics
Calculate the mass of ice required to
lower the temperature of \( 300 g \) of water at \( 40^{\circ} \mathrm{C} \) to water at \( 0^{\circ} \mathrm{C} \). (Specific latent heat of ice \( =336 \mathrm{J} / \mathrm{g}, \) Specific heat capacity of water \( \left.=4.2 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C}\right) \)
Subject: Maths
Let the complex number \( z_{1}, z_{2}, z_{3} \) be the
vertices of an equilxeral triangle. let \( z z_{0} \) be the circumcentre of the triangle,
then \( z_{1}^{2}+z_{2}^{2}+z_{3}^{2}- \)
A. \( z_{0}^{2} \)
an \( ^{2} \cdot \frac{z^{2}}{2}_{2}^{2} \)
B. \( -z_{0}^{2} \)
\( c \cdot 3 z_{0}^{2} \)
D. \( -3 z_{0}^{2} \)
Subject: Physics
Two balls of same mass are dropped from the same height \( h, \) on to the floor. The first ball bounces to a height \( h / 4 \) after the collision and the second ball to a height \( h / 16 . \) The impulse applied by the first and second ball on the floor are
\( I_{1} \) and \( I_{2} \) respectively. Find the ratio \( \frac{I_{1}}{I_{2}} \)
Subject: Maths
If \( \operatorname{cosec} \theta-\cot \theta=p, \) then \( \operatorname{cosec} \theta+ \)
\( \cot \theta= \)
\( A \cdot 1 / p \)
B. -1/p
\( c \cdot-p \)
D \( \cdot p^{2} \)
Subject: Maths
All x satisfying the inequality
\( \left(\cot ^{-1} x\right)^{2}-7\left(\cot ^{-1} x\right)+10>0, \) lie in
the interval:-
A \( \cdot(-\infty, \cot 5) \cup(\cot 4, \cot 2) \)
B. (cot \( 5, \) cot 4 ) \( \$ \$ \)
c. \( (\cot 2, \infty) \)
D. \( (-\infty, \cot 2) \cup(\cot 5, \infty) \)
Subject: Physics
A charged particle \( X \) moves directly towards another charged particle Y. For
the \( X \) plus \( Y \) system, the total
momentum is \( \mathrm{p} \) and the total energy is
E.
This question has multiple correct options
\( A \cdot p \) and \( E \) are conserved if both \( X \) and \( Y \) are free to move.
B. (a) is true only if \( X \) and \( Y \) have similar charges.
C. If \( Y \) is fixed, \( E \) is conserved but not \( P \)
D. If \( Y \) is fixed, neither \( E \) nor \( P \) is conserved
Subject: Chemistry
The oxidation state of \( A, B, \) and \( C \) in a
compound are +2,+5 and -2 respectively. The compound is :
\( \mathbf{A} \cdot A_{2}(B C)_{2} \)
B \( \cdot A_{2}(B C)_{3} \)
\( \mathbf{c} \cdot A_{3}\left(B C_{4}\right)_{2} \)
D. \( A_{2}\left(B C_{4}\right)_{3} \)
Subject: Chemistry
A quantity of \( \mathrm{PCl}_{5} \) was heated in \( 10 \mathrm{dm}^{3} \)
vessels \( 250^{\circ} \mathrm{C} \)
\( \mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \)
At equilibrium, the vessel contains \( 0 . \)
moles of \( \mathrm{PCl}_{5} \) and 0.2 moles of \( \mathrm{Cl}_{2} \). The
equilibrium constant of the reaction is :
Subject: Physics
In a moving coil galvanometer, the
deflection \( (\Phi) \) on the scale by a pointer attached to the spring is
\( ^{\mathrm{A}} \cdot\left(\frac{N A}{k B}\right) I \)
в. \( \left(\frac{N}{k A B}\right) I \)
\( ^{\mathbf{c}} \cdot\left(\frac{N A B}{k}\right) I \)
D. \( \left(\frac{N A B}{k I}\right) \)
Subject: Physics
In the circuit shown in the figure, ammeter and voltmeter are ideal. If
\( E=4 V \) and \( R=15 \Omega \) and \( r=1 \Omega, \) then
the reading of the ammeter is
A \( \cdot \frac{1}{3} A \)
\( B \cdot \frac{2}{3} A \)
\( c \cdot 1 A \)
D. \( \frac{1}{4} A \)
Subject: Maths
When a right triangle of area 3 is
rotated \( 360^{\circ} \) about its shorter leg, the
solid that results has a volume of 30 Calculate the volume of the solid if
the same right triangle is rotated about
its longer leg.
A . 0.99
B. 7.90
c. 8.88
D. 31.42
E . 41.12
Subject: Maths
If \( \Delta_{r}=\left|\begin{array}{ccc}r-1 & n & 6 \\ (r-1)^{2} & 2 n^{2} & 4 n-2 \\ (r-1)^{3} & 3 n^{3} & 3 n^{2}-3 n\end{array}\right| \)
Subject: Maths
If \( \boldsymbol{y}=\log \left(1+2 t^{2}+\boldsymbol{t}^{4}\right), \boldsymbol{x}=\tan ^{-1} \boldsymbol{t} \)
find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \)
Subject: Chemistry
Which of the following is true
statement?
A. The boiling point of aldehydes and ketones is higher than less polar ethers and non polar hydrocarbons of comparable molecular masses.
B. The boiling point of aldehydes and ketones is higher than less polar ethers but lower boiling points than non polar hydrocarbons of comparable molecular masses.
C. The boiling point of aldehydes and ketones is lower than less polar ethers but higher boiling points than non polar hydrocarbons of comparable molecular
masses.
D. The boiling point of aldehydes and ketones is lower than less polar ethers and non polar hydrocarbons of comparable molecular masses.
Subject: Chemistry
Assertion
\( X e F_{4} \) may be estimated by titrating the
\( I_{2} \) by reaction with \( K I \)
Reason
Equivalent weight of \( N a_{2} S_{2} O_{3} \) can be determined by iodimetric titration.
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 true but Reason is false
D. Assertion is false but Reason is true
Subject: Chemistry
The option(s) with only amphoteric oxides is (are):
This question has multiple correct options
A. \( C r_{2} O_{3}, B e O, S n O, S n O_{2} \)
в. \( C r_{2} O_{3}, C r O, S n O, P b O \)
c. \( Z n O, A l_{2} O_{3}, P b O, P b O_{2} \)
D. \( N O, B_{2} O_{3}, P b O, S n O_{2} \)
Subject: Physics
For the Bohr's first orbit of
circumference \( 2 \pi r, \) the de-Broglie wavelength of revolcing electron will be.
A \( .2 \pi r \)
B . \( \pi r \)
c. \( \frac{1}{2 \pi r} \)
D. \( \frac{1}{4 \pi r} \)
Subject: Biology
Assertion
Bacterial cell wall is characterised by
having mucopolysaccharidies.
Reason
Acetylmuramic acid is an example of mucopolysaccharide.
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
Assertion
Red algae contribute in producing coral reef
Reason
Some red algae secrete and deposit calcium carbonate our their walls
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
Subject: Physics
Consider earth to be a homogeneous
sphere. Scientist \( \boldsymbol{A} \) goes deep down in a
mine and scientist \( B \) goes high up in a
balloon. The gravitational field measured by
A. \( A \) goes on decreasing and that by \( B \) goes on increasing
B. \( B \) goes on decreasing and that by \( A \) goes on increasing
c. Each decreases at the same rate
D. Each decreases at different
Subject: Physics
Mankind has existed for about \( 10^{6} \)
years whereas the universe is about
\( 10^{10} \) years old. If the age of universe is taken to be one day, for how many seconds has the mankind existed?
A . \( 10 \mathrm{sec} \)
B. 8 sec
c. 8.64 sec
D. 64 sec
Subject: Maths
Find the median from the following
data.
\( \begin{array}{lllll}\text { Marks } & 0- & 10- & 30- & 60- \\ & 10 & 30 & 60 & 80\end{array} \)
No. of
students , an a 15 30
A . 10
B . 20
c. 30
D. 40
Subject: Physics
A proton of mass ' \( m^{\prime} \) moving with a
speed ' \( v_{0}^{\prime} \) approaches a stationary proton that is free to move. Assume impact parameter to be zero, i.e. headon collision. How close will the incident
proton go to other proton?
A \( \cdot \frac{\epsilon^{3}}{\pi \epsilon_{0} m^{2} v_{0}} \)
В. \( \frac{\epsilon^{3}}{\pi \epsilon_{0} m v_{0}} \)
\( ^{\mathrm{C}} \frac{\epsilon^{2}}{\pi \epsilon_{0} m v_{0}^{2}} \)
D. None of the above
Subject: Chemistry
Which statements are correct?
This question has multiple correct options
A. Lactose is a disaccharide and is a reducing sugar
B. \( \alpha-D- \) glucopyranoside has an acetal structure and is
non-reducing sugar
c. Methyl\( -\alpha-D- \)glucopyranose has an acetal
structure and is a non-reducing sugar
D. \( \alpha-D- \) Glucopyranose has a hemiacetal structure and
is a reducing sugar
Subject: Maths
Let \( A=R \times R \) and \( * \) be the binary
operation on A defined by \( (a, b) * \) \( (c, d)=(a+b, b+d) . \) Prove that \( * \) is
commutative and associative find the
identity element for \( * \) on \( \boldsymbol{A} \)
Subject: Maths
Let \( \cos ^{-1}\left(4 x^{3}-3 x\right)=a+b \cos ^{-1} x \)
\( x \in\left(\frac{1}{2}, 1\right], \) then the value of \( \lim _{y \rightarrow a} b \cos (y) \)
is
A. \( -\frac{1}{3} \)
в. -3
\( c \cdot \frac{1}{3} \)
D. 3
Subject: Maths
\( f(x)=\frac{3}{2} x+b \)
In the function above, \( b \) is a constant. If
\( \boldsymbol{f}(\boldsymbol{6})=\mathbf{7}, \) what is the value of \( \boldsymbol{f}(-\mathbf{2}) ? \)
A . -
B . - -
\( c . \)
\( D \)
Subject: Maths
The eccentricity of the conic \( 9 x^{2}+ \)
\( 5 y^{2}-54 x-40 y+116=0 \) is:
A \( -\frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{4}{9} \)
D. \( \frac{2}{\sqrt{5}} \)
Subject: Physics
During "inelastic collision "
a) There is a loss of kinetic energy.
b) Some of the kinetic energy is used to
deform the body.
c) Some of the kinetic energy is
liberated as heat.
d) There is a loss of mass energy.
A. Only a is true
B. Only b and c are true
\( c \cdot a, b \& c \) are true
D. b, c \& d are true
Subject: Physics
Statement-1: The angular velocity of all the points on the rigid body as seen
from any other point on it is the same. Statement-2: The distance between any
2 points on the rigid body remains
constant.
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- -
c. Statement-1 is true, statement-2 is false.
D. Statement-1 is false, statement-2 is true
Subject: Chemistry
Following reactions are taking place in
a Galvanic cell, \( Z n \rightarrow Z n^{2+}+ \)
\( \mathbf{2} e^{-} ; \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g} \)
Which of the given representations is the correct method of depicting the
cell?
A \( \cdot Z n_{(s)}\left|Z n_{(a q)}^{2+}\right|\left|A g_{(a q)}^{+}\right| A g_{(s)} \)
B . \( Z n^{2+}|Z n \| A g| A g^{+} \)
c. \( Z n_{(a q)}\left|Z n_{(s)}^{2+}\right|\left|A g_{(s)}^{+}\right| A g_{(a q)} \)
D. \( Z n_{(s)}\left|A g_{(a q)}^{+}\right|\left|Z n_{(a q)}^{2+}\right| A g_{s s} \)
Subject: Chemistry
Find the product of:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{O}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{O}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}}+\underset{(\boldsymbol{e} \boldsymbol{x} \boldsymbol{c} \boldsymbol{e} \boldsymbol{s} \boldsymbol{s})} \rightarrow ? \)
\( \mathbf{A} \cdot O H-C H_{2} C H_{2} O H, C_{6} H_{5} C H_{2}-I, C H_{3} C H_{2}-I \)
B \( \cdot C_{6} H_{5} C H_{2}-O H, C H_{3} C H_{2}-I, I-C H_{2} C H_{2}-O H \)
\( \mathbf{c} \cdot I-C H_{2} C H_{2}-I, C_{6} H_{5} C H_{2}-I, C H_{3} C H_{2}-O H \)
D. \( H O-C H_{2} C H_{2}-O H, C_{6} H_{5} C H_{2}-I, C H_{3} C H_{2}- \)
\( O H \)
Subject: Maths
The number of permutations that can be made out of the letters of the word
"MATHEMATICS" When all vowels come
together is:
A \( \cdot \frac{8 ! 4 !}{2 !} \)
в. \( \frac{8 ! 4 !}{(2 !)^{2}} \)
c. \( \frac{7 ! 4 !}{2 !} \)
D. 7!4!
Subject: Maths
The ratio between the sum of \( n \) terms of
two A.P.'s is \( 3 n+8: 7 n+15 \).Find the
ratio between their 12 th terms.
A \( \cdot \frac{7}{12} \)
в. \( \frac{7}{16} \)
c. \( \frac{7}{20} \)
D. \( \frac{7}{18} \)
Subject: Maths
The D.E whose solution is \( y=C^{2}+\frac{C}{x} \)
is:
A \( \cdot y=x^{4} y_{1}-x y_{1}^{2} \)
B . \( y=x^{4} y_{1}^{2}-x^{2} y_{1} \)
C \( \cdot y=x^{4} y_{1}^{2}-x y_{1} \)
D. \( y=x^{4} y_{1}^{2}+x y_{1} \)
Subject: Chemistry
Which of the following compounds can form \( \boldsymbol{H} \) -bonding with each other?
A. \( C H_{3} C O O H \) and \( H_{2} O \)
B. Phenol and \( C H_{4} \)
\( \mathrm{c} \cdot C H F_{3} \) and acetone
D. \( P H_{3} \) and \( H F \)
Subject: Physics
\( \begin{array}{ccc}\boldsymbol{A} & \boldsymbol{B} & \boldsymbol{Q} \\ 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1\end{array} \)
The truth table is given above for which of the following gates is correct
A. NAND gate
B. OR gate
c. AND gate
D. NOT gate
Subject: Maths
An urn contains 11 balls numbered from
to \( 11 . \) If a ball is selected at random,
what is the probabiloity of having a ball with a number which is mutliple of either 2 or \( 3 ? \)
A \( \cdot \frac{7}{11} \)
в. \( \frac{8}{11} \)
c. \( \frac{4}{11} \)
D. \( \frac{6}{11} \)
Subject: Physics
The speed of a longitudinal wave in a mixture of hellium and neon at \( 300 \mathrm{k} \)
was found to be \( 758 \mathrm{m} / \mathrm{s} \). The
composition of the mixture would then
be
\( \mathbf{A} \cdot 13: 3 \)
B . 4: 3
c. 2: 1
D. 4: 1
Subject: Maths
If \( A \) is a scalar matrix \( k I \) with scalar
\( k \neq 0 \) of order \( 3, \) the \( A^{-1} \) is:
A \( \cdot \frac{1}{k^{2}} I \)
B. \( \frac{1}{k^{3}} \)
c. \( \frac{1}{k} I \)
D. \( k I \)
Subject: Maths
Minimize \( Z=7 x+y \) subject to
\( \mathbf{5} \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{5}, \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{3}, \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Chemistry
Identify the substance oxidised, reduced, oxidising agent and reducing
agent for each of the following reactions
\( \boldsymbol{P b}_{(s)}+\boldsymbol{P b O}_{2(s)}+\mathbf{2 H}_{2} \boldsymbol{S O}_{4(a q)} \rightarrow \)
\( 2 P b S O_{4(s)}+2 H_{2} O_{(l)} \)
Subject: Biology
Which of the following set of three items are true, as each set belongs to the category mentioned against them?
A. Lysine, glycine, thiamine - Amino acids
B. Myosin, oxytocin and gastrin - Hormones
c. Rennin, helicase and hyaluronidase - Enzyme
D. optic nerve, oculomotor, vagus - sensory nerves
Subject: Maths
Prove the following identities:
\( \boldsymbol{a b c}\left(\sum \boldsymbol{a}\right)^{3}-\left(\sum \boldsymbol{b c}\right)^{3}=\boldsymbol{a b c} \sum \boldsymbol{a}^{3}- \)
\( \sum b^{3} c^{2}=\left(a^{2}-b c\right)\left(b^{2}-c a\right)\left(c^{2}-a b\right) \)
Subject: Maths
Consider the two quadratic
polynomials:
\( C_{a}: y=\frac{x^{2}}{4}-a x+a^{2}+a-2 \) and
\( C: y=2-\frac{x^{2}}{4} \)
If the origin lies between the zeroes of
the polynomial \( C_{a}, \) then the number of
integral value(s) of \( ^{\prime} \boldsymbol{a}^{\prime} \) is
A.
B. 2
\( c .3 \)
D. more than 3
Subject: Chemistry
Which of the following reagents are used as primary standard?
\( \boldsymbol{I}: \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} ; \boldsymbol{I} \boldsymbol{I}: \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} ; \boldsymbol{I} \boldsymbol{I} \boldsymbol{I} \)
\( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \)
\( \boldsymbol{I} \boldsymbol{V}: \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}\left(\boldsymbol{N} \boldsymbol{H}_{4}\right)_{2} \boldsymbol{S} \boldsymbol{O}_{4} \cdot \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} ; \boldsymbol{V} \)
\( \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \cdot \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
A. All except II, \( I V \)
B. All except I, II
C. All except \( I \), II, III
D. only \( I V \)
Subject: Maths
What is \( \int(x \cos x+\sin x) d x \) equal to?
Where \( c \) is an arbitrary constant
\( \mathbf{A} \cdot x \sin x+c \)
B. \( x \cos x+c \)
\( c \cdot-x \sin x+c \)
D. \( -x \cos x+c \)
Subject: Chemistry
What is the \( H^{+} \) ion concentration in
ammonium acetate solution?
\( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}, \boldsymbol{K}_{\boldsymbol{v}}\right. \)
Subject: Maths
For \( a>0, \) all the real roots of the
equation \( \boldsymbol{x}^{2}-\mathbf{3} \boldsymbol{a}|\boldsymbol{x}-\boldsymbol{a}|-\mathbf{7} \boldsymbol{a}^{2}=\mathbf{0} \) are
\( \mathbf{A} \cdot 4 a, 5 a \)
в. \( -4 a, 5 a \)
\( \mathbf{c} .-4 a,-5 a \)
D. \( 4 a,-5 a \)
Subject: Chemistry
\( 1.525 g \) of an organic compound was kjeblahlised and the ammonia so produced was passed through \( 30 m l \) of 1 \( N \) HCl.The remaining \( H C l \) was
further neutralised by 120 ml of \( \frac{N}{10} N a O H \) solution. Calculate the \( \% \) nitrogen in the compound.
Subject: Maths
If \( z_{1}, z_{2}, \ldots, z_{n} \) lie on the circle \( |z|=2 \)
then the value of \( \mid z_{1}+z_{2}+\dots+ \)
\( z_{n}|-4| \frac{1}{z_{1}}+\frac{1}{z_{2}}+\ldots+\frac{1}{z_{n}} \mid \) is
A . 0
в.
c. \( -n \)
D.
Subject: Physics
Three resistor of \( 10 \Omega, 20 \Omega, \) and \( 30 \Omega \) are
connected in parallel in a circuit. Calculate the equivalent resistance.
A. \( 6000 \Omega \)
в. \( 0.017 \Omega \)
\( c \cdot 1 \Omega \)
D. \( 60 \Omega \)
E. \( 5.45 \Omega \)
Subject: Biology
The following is the scheme showing the path of reflex arc. Identify the different labeling \( A, B, C, D, E, F \) in the
reflex arc.
A. A- stimulus, B- Effector, C- Motor nerve, D- sensory nerve, E- Receptor, F- Response
B. A- Stimulus, B- Receptor, C- Motor nerve, D- Sensory nerve, E- Effector, F- Response
c. A- stimulus, B- Effector, C- - Sensory nerve, D- Motor nerve, E- Receptor, F- Response
D. A- Stimulus, B- Receptor, C- - Sensory nerve, D- Motor nerve, E- Effector, F- Response
Subject: Chemistry
\( \mathrm{R}, \mathrm{S} \) and \( \mathrm{T}, \) respectively are:
\( \mathbf{A} \cdot \mathrm{SO}_{2} \mathrm{Cl}_{2}, \mathrm{PCl}_{5} \) and \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
B. \( \mathrm{SO}_{2} \mathrm{Cl}_{2}, \mathrm{PCl}_{3} \) and \( \mathrm{H}_{3} \mathrm{PO}_{3} \)
\( \mathrm{c} \cdot \mathrm{OCl}_{2}, \mathrm{PCl}_{3} \) and \( \mathrm{H}_{3} \mathrm{PO}_{2} \)
D. \( \operatorname{SOCl}_{2}, \mathrm{PCl}_{5} \) and \( \mathrm{H}_{3} \mathrm{PO}_{4} \)