AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
The formula for \( \% \) composition of \( a \)
compound is:
A. molar mass of a compound/mass due to specific component \( \times 100 \)
B. mass due to specific component \( \times 100 \)
C. mass due to specific component/molar mass of a compound \( \times 100 \)
D. molar mass of a specific component/temperature \( x \) 100
Subject: Physics
A transistor has \( \alpha=0.95 . \) If the emitter
current is \( 10 m A \), then the collector
current will be
A . \( 9.5 \mathrm{mA} \)
в. \( 10 \mathrm{mA} \)
c. \( 0.95 \mathrm{mA} \)
D. \( 95 \mathrm{mA} \)
Subject: Physics
Which of the following conversions is
correct?
\( A \cdot 1 a t m=1.01 \times 10^{4} \mathrm{Pa} \)
B. \( 1 \mathrm{mm} \) of \( \mathrm{Hg}=133 \mathrm{Pa} \)
c. 1 bar \( =10^{7} \) Pa
D. 1 torr \( =10^{2} \) Pa
Subject: Physics
The notation for an isotope of sodium
\( _{11}^{23} N a . \) Which row gives the composition
of a neutral atom of this isotope of
sodium?
\( \begin{array}{lll}\text { number } & \text { number } & \text { number } \\ \text { of } & \text { of } & \text { of } \\ \text { protons } & \text { neutrons } & \text { electrons } \\ \text { A } & 11 & 12 & 11 \\ \text { B } & 11 & 12 & 12 \\ \text { C } & 11 & 23 & 11 \\ \text { D } & 12 & 11 & 12\end{array} \)
\( A \)
B. B
\( c \cdot c \)
\( D . \)
Subject: Chemistry
An organic compound contains \( 69 \% \)
carbon and 4.85 hydrogen, the remainder being oxygen. The masses of carbon dioxide and water produced when 0.20 g of this substance is subjected to complete combustion?
A. \( 0.506 g \) and 0.0864 g
в. \( 0.678 \mathrm{g} \) and \( 0.0234 \mathrm{g} \)
c. \( 0.786 g \) and 0.0128 g
D. None
Subject: Chemistry
Assertion
Atoms with completely filled and half filled subshells are stable.
Reason
Completely filled and half-filled subshells have the symmetrical distribution of electrons and have
maximum exchange energy
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
Copper matte contains
\( \mathbf{A} \cdot C u_{2} O, C u_{2} S \)
\( \mathbf{B} \cdot C u_{2} O, F e S \)
\( \mathbf{c} \cdot C u_{2} S, F e S \)
D. \( C u_{2} S, F e O \)
Subject: Maths
Let \( \boldsymbol{A}=\boldsymbol{R}-\{\mathbf{3}\} \) and \( \boldsymbol{B}=\boldsymbol{R}-\{\mathbf{1}\} \)
Then, \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B}: \boldsymbol{f}(\boldsymbol{x})=\frac{(\boldsymbol{x}-\boldsymbol{2})}{(\boldsymbol{x}-\boldsymbol{3})} \) is?
A. One-one and into
B. One-one and onto
c. Many-one and into
D. Many-one and onto
Subject: Physics
In Searle's experiment to find Young's
modulus, the diameter of wire is
measured as \( D=0.05 \mathrm{cm}, \) the length of
wire is \( L=125 c m, \) and when a weight,
\( \boldsymbol{m}=20 k g \) is the put, extension in wire
was found to be \( 0.100 \mathrm{cm} \). Find the
maximum permissible error in Young's modulus \( (Y) \)
Subject: Chemistry
For an equilibrium \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{O}(\ell) \)
which of the following statement is
true?
A. The pressure changes do not affect the equilibrium
B. More of ice melts if pressure on the system is increased
c. More of liquid freezes if pressure on the system is increase
D. The pressure changes may increase or decrease the degree of advancement of the reaction depending upon the temperature of the system.
Subject: Chemistry
The IUPAC name of \( N C-C H_{2}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C O O H} \) is:
A. 3 - carboxy propanenitrile
B. 4- cyanobutanoic acid
c. 2 - cyanomethane Carboxylic acid
D. 3- cyanopropanoic acid
Subject: Chemistry
Write the \( I U P A C \) names of the
following ketones and aldehydes. Wherever possible, give also common
names.
A \( \cdot C H_{3} C O\left(C H_{2}\right)_{4} C H_{3} \)
в. \( C H_{3} C H_{2} C H B r C H_{2} C H\left(C H_{3}\right) C H O \)
c. \( C H_{3}\left(C H_{2}\right)_{5} C H O \)
D. \( P h-C H=C H-C H O \)
Subject: Physics
Two rods \( A \) and \( B \) made up of same metal have same length. The ratio of their resistances is \( 1: 2 . \) If these rods are
immeresed in water then loss in weight will be :-
\( A . \) more in \( A \)
B. more in B
c. same is A and B
D. in the ratio 1: 2
Subject: Maths
Let I be the purchase value of an equipment and \( V(t) \) be the value after it has been used for t years. The value \( V(t) \) depreciates at a rate given by differential equation \( \frac{\boldsymbol{d} \boldsymbol{V}(\boldsymbol{t})}{\boldsymbol{d} \boldsymbol{t}}=-\boldsymbol{k}(\boldsymbol{T}- \)
\( t), \) where \( k>0 \) is a constant and T is
the total life in years of the equipment. Then the scrap value \( V(t) \) of the
equipment is?
A \( \cdot_{I-\frac{k(T-t)^{2}}{2}} \)
\( \frac{k(T-t)^{2}}{2}+I \)
\( c \cdot T^{2}-\frac{I}{k} \)
D. \( _{I-\frac{k T^{2}}{2}} \)
Subject: Physics
If a star can convert all the \( H e \) nuclei
completely into oxygen nuclei, the energy released per oxygen nuclei is [Mass of \( H e \) nucleus is \( 4.0026 a m u \) and
mass of oxygen nucleus is \( 15.9994 a m u \)
A. \( 7.6 \mathrm{MeV} \)
B. 56.12 MeV
c. \( 10.24 \mathrm{MeV} \)
D. \( 23.9 \mathrm{MeV} \)
Subject: Maths
The value of \( \int_{0}^{\pi / 2} \frac{x \sin x \cos x}{\sin ^{4} x+\cos ^{4} x} d x \) is
A \( \cdot \pi^{2} / 8 \)
B . \( \pi^{2} / 16 \)
c. \( 3 \pi^{2} / 4 \)
D. \( \pi^{2} / 2 \)
Subject: Chemistry
The \( p K_{a} \) of acetylsalicylic acid (aspirin) is 3.5 The pH of gastric juice in human stomach is about \( 2-3 \) and the pH in
the same intestine is about \( 8 . \) Aspirin will be
A. Unionised in the small intestine and in the stomach
B. Completely ionised in the small intestine and in the stomach
c. lonised in the stomach and almost unionised in the samılı intestine
D. lonised in small intestine and almost unionised in the stomach
Subject: Chemistry
Which of the following is not correct?
A. \( A l \) reacts with \( N a O H \) and liberate \( H_{2} \)
B. \( A l C l_{3} \) is a lewis acid
C. \( A l \) is used in the manufacture of electrical cables
D. \( N a O H \) is used during Hall's process of purification of bauxite
Subject: Physics
There is a current of 1.344 amp in a
copper wire whose area of cross-section
normal to the length of the wire is
\( 1 m m^{2} . \) If the number of free electrons
per \( c m^{3} i s 8.4 \times 10^{2} 2, \) then the drift
velocity would be
A . \( 1.0 \mathrm{mm} / \mathrm{sec} \)
B. 1.0 \( \mathrm{m} / \mathrm{sec} \)
c. \( 0.1 \mathrm{mm} / \mathrm{sec} \)
D. 0.01 \( \mathrm{mm} / \mathrm{sec} \)
Subject: Maths
ff \( \boldsymbol{y}=\boldsymbol{y}(\boldsymbol{x}) \) satisfies the differential equation \( 8 \sqrt{x}(\sqrt{9+\sqrt{x}}) d y= \)
\( (\sqrt{4+\sqrt{9+\sqrt{x}}})^{-1} d x, x>0 \) and
\( \boldsymbol{y}(\mathbf{0})=\sqrt{\mathbf{7}}, \) then \( \boldsymbol{y}(\mathbf{2 5 6})= \)
\( A \)
B.
c. 16
D. 80
Subject: Physics
Which of the following is not true
for Universal law of gravitation?
A. It is the gravitational force between the sun and the earth, which makes the earth move around the sun.
B. The tides formed in sea are because of gravitational pull exerted by the sun and the moon on the surface of water.
C. It is the gravitational pull of the earth which keeps us and other bodies firmly on the ground.
D. The gravitational force exerted by sun on earth is larger than that exerted by earth on sun.
Subject: Physics
What are possible speeds of two objects, if they move uniformly towards each other, they get \( 4 m \) closer in each second and if they move uniformly in the same direction with the original
speeds they get \( 4.0 m \) closer in each \( 10 s \)
A. \( 2.8 m / s \) and \( 1.2 m / s \)
B. \( 5.2 m / s \) and \( 4.6 m / s \)
c. \( 3.2 m / s \) and \( 1.2 m / s \)
D. \( 2.2 m / s \) and \( 1.8 m / s \)
Subject: Chemistry
Concentrated sulphuric acid cannot be
used to prepare \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \) from \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{B} \boldsymbol{r} \)
because it :
A. reacts slowly with \( N a B r \)
B. oxidises \( H B r \)
c. reduces \( H B r \)
D. none of the above
Subject: Chemistry
\( \ln 20 \) minutes of \( 80 \% \) of \( N_{2} O_{5} \) is
decomposed. Rate constant is:
\[
\begin{array}{l}
\mathrm{N}_{2} \mathrm{O}_{5} \stackrel{\mathrm{Keq}}{\longleftarrow} \mathrm{NO}_{2}+\mathrm{NO}_{3}(\text { fast equilibrium }) \\
\mathrm{NO}_{2}+\mathrm{NO}_{3} \frac{\mathrm{k}_{1}}{ } \mathrm{NO}_{2}+\mathrm{NO}+\mathrm{O}_{2}(\text { slow }) \\
\mathrm{NO}+\mathrm{NO}_{3} \frac{\mathrm{k}_{2}}{\longrightarrow} 2 \mathrm{NO}_{2}(\text { fast })
\end{array}
\]
A . 0.08
B. 0.05
c. 0.12
D. 0.2
Subject: Maths
If the sum of first \( 2 n \) terms of \( A . P .2,5 \)
\( 8, \ldots \) is equal to the sum of the first \( n \) terms of the A.P.57,59, 61, ...., then n
equals-
A . 10
B. 12
\( c \cdot 11 \)
D. 13
Subject: Chemistry
\( 10 \mathrm{ml} \) of \( \mathrm{KMnO}_{4} \) Solution is required it completely oxidise acidic solution of 30
\( \mathrm{ml} \) of 1.5 Volume strength \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
Calculate normality of \( K M n O_{4} \) Solution:
A. 0.4
B. 0.65
\( c \cdot 0.8 \)
D. 0.19
Subject: Chemistry
The correct relation between \( \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{K}_{\boldsymbol{c}} \) for the given reaction is:
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{l}_{1}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{H} \boldsymbol{l}(\boldsymbol{g}) \)
\( \mathbf{A} \cdot K_{p}=K_{c}(R T)^{2} \)
В . \( K_{p}=K_{c} \)
c. \( \frac{K_{p}}{R T}=K_{c} \)
D. \( K_{p}=K_{c}(R T)^{-2} \)
Subject: Physics
For ordinary terrestrial experiments, which of the observers below are inertial
and which are non-inertial?
a) a child revolving in a giant wheel
b) a driver in a sports car moving with a constant high speed of \( 200 \mathrm{km} / \mathrm{h} \) on a straight road
c) the pilot of an airplane which is taking off
d) a cyclist negotiating a sharp turn
e) the guard of a train which is slowing down to stop at a station
Subject: Maths
find the value of the following:
\( (i) \sin ^{-1}\left(\frac{-1}{2}\right) \)
\( (i i) \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
\( (i i i) \operatorname{cosec}^{-1}(2) \)
\( (i v) \tan ^{-1}(-\sqrt{3}) \)
\( (v) \cos ^{-1}\left(\frac{-1}{2}\right) \)
\( (v i) \tan ^{-1}(-1) \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\cos ^{-1} \sin (\boldsymbol{x}+\boldsymbol{\pi} / \mathbf{3})} \) Then
This question has multiple correct options
\( \mathbf{A} \cdot f\left(\frac{5 \pi}{9}\right)=e^{5 \pi / 18} \)
B \( \cdot f\left(\frac{8 \pi}{9}\right)=e^{13 \pi / 18} \)
\( ^{\mathbf{C}} \cdot f\left(-\frac{7 \pi}{4}\right)=e^{\pi / 12} \)
D \( \quad f\left(-\frac{7 \pi}{4}\right)=e^{11 \pi / 12} \)
Subject: Maths
\( P \) is a point on the line through the point \( A \) whose position vector is \( \vec{a} \) and the line is parallel to the vector \( \vec{b} \). If
\( \boldsymbol{P A}=\mathbf{6}, \) the position vector of \( \boldsymbol{P} \) is
A \( \cdot \vec{a}+6 \vec{b} \)
B \( \cdot \vec{a}+\frac{6}{|\vec{b}|} \vec{b} \)
c. \( \vec{a}-6 \vec{b} \)
D \( \cdot \vec{b}+\frac{6}{|\vec{a}|} \vec{a} \)
Subject: Maths
\( \operatorname{Given}|z|=4 \) and \( A r g z=\frac{5 z}{6}, \) then \( z \) is
A \( \cdot 2 \sqrt{3}+2 i \)
B. \( 2 \sqrt{3}-2 i \)
c. \( -2 \sqrt{3}+2 i \)
D. \( -\sqrt{3}+i \)
Subject: Chemistry
Select correct statement(s).
A. Hydrophilic colloid is a colloid in which there is a strong attraction between the dispersed phase and water.
B. Hydrophobic colloid is a colloid in which there is a lack of attraction between the dispersed phase and water.
C. Hydrophobic sols are often formed when a solid crystallises rapidly from a chemical reaction or a supersaturated solution.
D. All of the above.
Subject: Maths
The number of real roots of the equation
\( \mathbf{5}+\left|\mathbf{2}^{x}-\mathbf{1}\right|=\mathbf{2}^{x}\left(\mathbf{2}^{x}-\mathbf{2}\right) \) is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \)
Subject: Physics
A spherical ball of density \( \rho \) and radius
\( 0.003 m \) is dropped into a tube
containing a viscous fluid up to the
\( 0 \mathrm{cm} \) mark as shown in the figure.
Viscosity of the fluid \( =1.26 N-s / m^{2} \)
and its density \( \rho_{L}=\frac{\rho}{2}=1260 k g / m^{3} \)
Assume the ball reaches a terminal
speed at \( 10 c m \) mark. The time taken by
the ball to travel the distance between
the \( 10 c m \) and \( 20 c m \) mark is \( (g= \)
\( \left.\mathbf{1} \mathbf{0} \boldsymbol{m} / \boldsymbol{s}^{\mathbf{2}}\right) \)
A \( .2 s \)
B. \( 1 s \)
c. \( 0.5 s \)
D. \( 5 s \)
Subject: Chemistry
Which of the following is not a conjugate acid-base pair?
\( \mathbf{A} \cdot H P O_{3}^{2-}, P O_{3}^{3-} \)
B . \( H_{2} P O_{4}^{-}, H P O_{4}^{2-} \)
c. \( H_{2} P O_{4}^{-}, H_{3} P O_{4} \)
D. \( H_{2} P O_{4}^{-}, P O_{3}^{3-} \)
Subject: Physics
A boy a wagon along a horizontal surface for a distance of 10.0 meters.
The boy applies a force of 15 N straight along the handle while the wagon moves, and the handle makes an angle of 35 degrees with the horizontal.

How much work does the boy do on the wagon?
A. 150 Joules
B. 120 Joules
c. 86 Joules
D. 1.5 Joules
E. 0.67 Joules
Subject: Physics
A current of \( 5 A \) passes through a copper conductor (resistivity \( =1.7 \times \)
\( 10^{-8} \Omega m \) ) of radius of cross-section
5 \( m \) m. Find the mobility of the charges if
their drift velocity is \( 1.1 \times 10^{-3} m / s \)
A \( \cdot 1.3 m^{2} / V s \)
B. \( 1.5 \mathrm{m}^{2} / \mathrm{Vs} \)
\( \mathbf{c} \cdot 1.8 m^{2} / V s \)
D. \( 1.0 m^{2} / V s \)
Subject: Chemistry
The specific conductance of a \( 0.1 \mathrm{N} \mathrm{KC} \) solution is 0.012 ohm \( ^{-1} c m^{-1} \). The
resistance of the cell containing the
same solution is 55 ohms. Then the
cell constant is :
\( \begin{array}{lll}\text { A } \cdot 0.918 & c m^{-1}\end{array} \)
B. \( 0.66 \mathrm{cm}^{-1} \)
\( \begin{array}{lll}\text { C } \cdot & 1.142 & c m^{-1}\end{array} \)
D. 1.12 cm \( ^{-1} \)
Subject: Chemistry
Which of the following is/are correct?
This question has multiple correct options
A. Acid hydrolysis of an ester follows pseudo first order kinetics
B. Inversion of cane sugar follows pseudo first order kinetics
C. Decomposition of varous gases on the surface of metallic catalysts, such as decomposition of \( H I \) on gold surface also exhibits zero roder kinetics
D. Radioactivity follows first order kinetics
Subject: Maths
The direction cosines of the line
passing through \( \mathbf{P}(\mathbf{2}, \mathbf{3},-\mathbf{1}) \) and the origin are
A \( \cdot \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)
B. \( \frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)
c. \( \frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}} \)
D. \( \frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{-1}{\sqrt{14}} \)
Subject: Physics
A length \( L=15 m \) if flexible tape is
tightly wound. It is then allowed to unwinding as it rolls down a fixed
incline that makes and angle \( \boldsymbol{\theta}=\mathbf{3 0}^{\circ} \)
with the horizontal, the upper end of the
tape being fixed. Find the time taken (in
second) by the tapes to unwind completely. Neglect radius at any time
w.r.t. the length of the rope.
Subject: Maths
Let \( \boldsymbol{d} \in \boldsymbol{R}, \) and \( \boldsymbol{A}= \)
\( \left[\begin{array}{ccc}-2 & 4+d & (\sin \theta)-2 \\ 1 & (\sin \theta)+2 & d \\ 5 & (2 \sin \theta)-d & (-\sin \theta)+2+2 d\end{array}\right. \)
\( \boldsymbol{\theta} \in[\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] . \) If the minimum value of
\( \operatorname{det}(A) \) is \( 8, \) then a value of d is?
A . -7
B. \( 2(\sqrt{2}+2) \)
\( c .-5 \)
D. \( 2(\sqrt{2}+1) \)
Subject: Maths
The mean of a finite set \( X \) of numbers is
14, the median of this set of numbers is
\( 12, \) and the standard deviation is \( 1.8 . A \) new set Y is formed by multiplying each
member of the set \( \$ \) by \( 3 . \) Determine the correct statements w.r.t. set \( Y: \)
I. The mean of the numbers is set Y is 42
II. The median of the numbers in set Y is
\( \mathbf{3 6} \)
III. The standard deviation of the
numbers is set Y is 5.4
A. I only
B. II only
c. I and II only
D. I and III only
E. ।, ॥।, and ॥|
Subject: Biology
Assertion
In humans, the gamete contributed by the male determines whether the child
produced will be male or female.
Reason
Sex in humans in a polygenic trait
depending upon a cumulative effect of
some genes on \( X \) chromosome and
some on Y chromosome.
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: Physics
A body is dropped from a height \( h \), if it acquires a momentum p, then the mass of the body is:
A \( \cdot \frac{p}{\sqrt{2 g h}} \)
в. \( \frac{P^{2}}{2 g h} \)
c. \( \frac{2 g h}{p} \)
D. \( \sqrt{2 g h / p} \)
Subject: Maths
The equation of the base of an equilateral triangle is \( x+y=2 \) and
the vertex is \( (2,-1) . \) Length of its side
is
A \( \cdot \sqrt{\frac{1}{2}} \)
в. \( \sqrt{\frac{3}{2}} \)
c. \( \sqrt{\frac{2}{3}} \)
D. \( \sqrt{2} \)
Subject: Maths
Assertion
For a singular square matrix \( \mathbf{A}, \boldsymbol{A} \boldsymbol{B}= \)
\( \boldsymbol{A C} \Rightarrow \boldsymbol{B}=\boldsymbol{C} \)
Reason
If \( |A|=0, \) then \( A^{-1} \) does not exist.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
Subject: Chemistry
An element \( X \) which occurs in the
second period has an outer electronic
structure \( s^{2} p^{2} . \) The formula and acidbase character of its oxide, respectively
are
A. \( X O_{3} \), basic
B. \( X_{2} O_{3} \), basic
c. \( X_{2} O_{3} \), amphoteric
D. \( X O_{2} \), acidic
Subject: Chemistry
Assertion
The metals of group 2 (except Be) form
ionic compounds.
Reason
Electropositive character and the
reducing property increase on moving
down the group.

Read the above assertion and reason and
choose the correct statement regarding
it.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
The price of a scooter is \( R s .14000 . \) If it
depreciates by \( 2 \% \) of its value at the beginning of each year. Find the sale value after 4 years.
A . \( R s 1213.154 \)
в. \( R s 12000.154 \)
c. \( R s 12913.154 \)
D. None of these
Subject: Maths
Find the value of \( k \) for which the given
system of equations has infinite number of solutions.
\( \mathbf{5} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{2} \boldsymbol{k} \) and \( \mathbf{2}(\boldsymbol{k}+\mathbf{1}) \boldsymbol{x}+\boldsymbol{k} \boldsymbol{y}= \)
\( (3 k+4) \)
A . 4
B. 7
\( c \cdot 3 \)
D. 6
Subject: Maths
Let \( \boldsymbol{R}=(\boldsymbol{a}, \boldsymbol{a}),(\boldsymbol{b}, \boldsymbol{c}),(\boldsymbol{a}, \boldsymbol{b}) \) be a relation
on a set \( A=a, b, c . \) Then the minimum
number of ordered pairs which when added to make it an equivalence
relation are
Subject: Maths
The line \( P Q \) whose equation is \( x-y= \)
2 cuts the \( x- \) axis at \( P \) and \( Q \) and
passes through \( (4,2) . \) The line \( P Q \) is
rotated about \( P \) through \( 45^{\circ} \) in the
anticlockwise direction. The equation of the line \( P Q \) in the new position is
A. \( y=-\sqrt{2} \)
B. \( y=2 \)
\( \mathbf{c} \cdot x=2 \)
D. \( x=-2 \)
Subject: Physics
Give the range of wavelength of the electromagnetic waves visible to us.
A . \( 1000 A^{\circ} \) to \( 4000 A^{\circ} \)
B . \( 4000 A^{\circ} \) to \( 8000 A^{\circ} \)
c. \( 8000 A^{\circ} \) to \( 9000 A^{\circ} \)
D. \( 400 A^{\circ} \) to \( 800 A^{\circ} \)
Subject: Maths
f an isosceles \( \triangle A B C \) in which \( A B= \)
\( A C=6 \mathrm{cm} \) is inscribed in a circle of
radius \( 9 \mathrm{cm} . \) Find area of the triangle.
\( \mathbf{A} \cdot 8 c m^{2} \)
B. \( 8 \sqrt{2} c m^{2} \)
\( c \cdot 6 c m^{2} \)
D. none
Subject: Physics
Two equal point charges are fixed at \( x= \)
\( -a \) and \( x=+a \) on the \( x \) -axis. Another
point charge \( Q \) is placed at the origin. The change in the electrical potential energy of \( \mathrm{Q}, \) when it is displaced by a smal distance \( x \) along the \( x \) -axis, is approximately proportional to :
\( A \cdot x \)
B . \( x^{2} \)
c. \( x^{3} \)
D. \( 1 / x \)
Subject: Physics
In uniform electric field, \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{N} \boldsymbol{C}^{-1} \)
as shown in figure.
Find. \( (\mathrm{i}) \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}} \)
(ii) \( V_{B}-V_{C} \)
A . -10,20
B. 30,50
\( c .-20,30 \)
D. 40,50
Subject: Physics
The figure shows a square loop[ of resistance \( 1 \Omega \) side \( 1 m \) being moved
towards right at a constant speed of
1 \( m / s \). The front edge enters the \( 3 m \) wide magnetic field \( (B=1 T) \) at \( t=0 \)
draw the graph of current induced in the loop as time passes. (Take the anticlockwise direction of current as
positive)
\[
\begin{array}{l}
x \times x \times x \times \\
x \times \times \times \times \times \\
\times \times \times \times \times \times \\
\times \times \times \times \times \times \\
\times \times \times \times \times \times
\end{array}
\]
Subject: Physics
Why are transmission losses so crucial
that electrical power systems are
designed to work on Alternating
currents?
A. Electrical power systems are not very efficient for transmission of power
B. It is a practice to use AC over DC
C. AC networks are easier to handle than DC Networks and constructional setup cost is really high in DC
D. since, power stations are very far away from destinations, transmission has to be done over long distances and losses add up over the distance
Subject: Chemistry
\( 10 m L \) of a strong acid solution of
\( \boldsymbol{p} \boldsymbol{H}=\boldsymbol{2} \) are mixed with \( \boldsymbol{9} \boldsymbol{9} \boldsymbol{m} \boldsymbol{m} \)
another acid solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{4} . \) The
\( \boldsymbol{p} \boldsymbol{H} \) of the following solution will be:
\( A \cdot 3 \)
в. 3.3
\( c .3 .7 \)
D. none of the above
Subject: Maths
For any two events \( A \) and \( B \) in a sample
space
This question has multiple correct options
\( ^{\mathbf{A}} \cdot p(A / B) \geq \frac{P(A)+P(B)-1}{P(B)}, P(B) \neq 0, \) is always true
B \( \cdot P(A \cap B)=P(A)-P(\bar{A} \cap \bar{B}) \) does not hold.
\( \mathbf{c} \cdot P(A \cup B)=1-P(\bar{A}) P(\bar{B}), \) if \( A \) and \( B \) are independent
D \( \cdot P(A \cup B)=1-P(\bar{A}) P(\bar{B}) \), if \( A \) and \( B \) are disjoint.
Subject: Physics
An infinite number of charges each equal to q are placed along the \( X- \) axis at \( x= \) \( 1, x=2, x=4, x=8 \ldots \ldots \) and so on. The
potential and field respectively due to this set of charges at the origin is :
A \( \cdot \frac{q}{3 \pi \epsilon_{0}} \) and \( \frac{q}{2 \pi \epsilon_{0}} \)
в. \( \frac{q}{2 \pi \epsilon_{0}} \) and \( \frac{q}{3 \pi \epsilon_{0}} \)
c. \( \frac{q}{4 \pi \epsilon_{0}} \) and \( \frac{q}{3 \pi \epsilon_{0}} \)
D. \( \frac{q}{2 \pi \epsilon_{0}} \) and \( \frac{q}{4 \pi \epsilon_{0}} \)
Subject: Maths
The principal value of \( \sin ^{-1}\left\{\cos \left(\sin ^{-1} \frac{\sqrt{3}}{2}\right)\right\} \)
A. \( \frac{\pi}{6} \)
в. \( \frac{\pi}{3} \)
\( c \cdot-\frac{\pi}{3} \)
D. none of these
Subject: Chemistry
According to Bohr theory, the angular momentum of electron in 5 th orbit is:
A \( \cdot_{25} \frac{h}{\pi} \)
в. \( _{1} \frac{h}{\pi} \)
\( \mathrm{c} \cdot_{10} \frac{h}{\pi} \)
D. \( _{2.5} \frac{h}{\pi} \)