AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
For motion of an object along the \( x \) -axis,
the velocity v depends on the
displacement \( x \) as \( v=3 x^{2}-2 x, \) then
what is the acceleration at \( x=2 m \)
A. \( 48 \mathrm{ms}^{-2} \)
B . \( 80 \mathrm{ms}^{-2} \)
c. \( 18 m s^{-2} \)
D. \( 10 m s^{-2} \)
Subject: Physics
The expression for mean free path is :
A \( \cdot \lambda=\frac{K T}{\sqrt{2} \pi d^{2} P} \)
B. \( \lambda=\frac{\pi d P}{k T} \)
c. \( _{\lambda}=\frac{\pi d^{2} P}{k T} \)
D. \( \lambda=\frac{k T}{\pi d P} \)
Subject: Maths
The value of the integral \( \int_{-a}^{a} \frac{x e^{x^{2}}}{1+x^{2}} d x \)
is
A \( \cdot e^{a^{2}}^{2} \)
B.
\( \mathbf{c} \cdot e^{-a^{2}}^{2} \)
D. \( a \)
Subject: Physics
The water drops fall at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at the
instant the first drop touches the ground. How far above the ground is the second drop at the instant?
\( \mathbf{A} \cdot 1.25 m \)
B. \( 2.50 m \)
\( c .3 .75 m \)
D. \( 4.00 m \)
Subject: Physics
A bob is suspended by a string of length
I. The minimum horizontal velocity imparted to the ball for reaching it to the height of suspension is
\( \mathbf{A} \cdot \sqrt{l / g} \)
B . \( \sqrt{2 g l} \)
c. \( \sqrt{g / l} \)
D. \( 2 \sqrt{g l} \)
Subject: Chemistry
Assertion
Alkaline earth metals have lower
densities than alkali metals.
Reason
Atomic radii of alkaline earth metals
are larger than that of corresponding alkali metals.
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
\( \mathbf{f} \overrightarrow{\boldsymbol{A}}=\widehat{\boldsymbol{j}}+\widehat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{B}}=2 \hat{\boldsymbol{i}}-\widehat{\boldsymbol{j}}+\boldsymbol{4} \widehat{\boldsymbol{k}} \) then
the unit vector of \( \vec{A}+\vec{B} \) is
\( A \cdot \frac{3 i+5 \hat{k}}{\sqrt{24}} \)
B. \( \frac{3 \hat{i}-5 \vec{k}}{\sqrt{34}} \)
C. \( \frac{3 \hat{i}+5 \vec{k}}{\sqrt{34}} \)
D. None of these
Subject: Maths
The given distribution shows the
number of runs scored by some top batsmen of the world in one-day
international cricket matches.
Runs scored \( \quad \) Number of batsmen tsmen \( 3000-4000 \) Is \( ^{4000}-5000 \) \( \begin{array}{lll}5000-6000 & 9 \\ 6000-7000 & 7 \\ 7000-8000 & 6 \\ 8000-9000 & 3 \\ 9000-10000 & 1 \\ 10000-11000 & 1\end{array} \) and
Find the mode of the data.
Subject: Maths
\( \frac{2}{5} \) of total students in a class have opted
Maths.Find the percentage of students
opting Maths
A \( \cdot \frac{2}{5} \times 100 \)
В. \( \frac{5}{2} \times 100 \)
\( \mathbf{c} \cdot \frac{2}{5} \times \frac{1}{100} \)
D. \( \frac{5}{2} \times \frac{1}{100} \)
Subject: Maths
On one page of a telephone directly, there were 200 telephone numbers. The frequency distribution of their unit place digit (for example in the number 25828573
the unit place digit is 3 ) is given in table
below :
Digit
Frequency 22 26 22 22
Without looking at the page, the pencil is placed on one of these numbers, i.e., the
number is chosen at random. What is the
probability that the digit in its unit place is more than \( 7 ? \)
\( A \)
\[
0.15
\]
в. 0.17
\( c \)
0.18
D. None of these
Subject: Maths
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \mathbf{1} \\ \boldsymbol{\omega}^{2} & \mathbf{1} & \boldsymbol{\omega}\end{array}\right] \) Find Det \( \mathbf{A} \)
Subject: Maths
Find the centroid of Triangle whose
vertices are
\( \boldsymbol{A}(\mathbf{1}, \mathbf{2}, \mathbf{3}), \boldsymbol{B}(\mathbf{2},-\mathbf{1}, \mathbf{6}), \boldsymbol{C}(\mathbf{3}, \mathbf{2},-\mathbf{3}) \)
A \( .(2,1,2) \)
В. (2,-1,2)
c. (-2,-2,-2)
D. (1,2,1)
Subject: Chemistry
A blueliquid among the following is :
A. \( \mathrm{N}_{2} \mathrm{O}_{3} \)
в. \( \mathrm{N}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \)
D. NO
Subject: Maths
The solution of differential equation
\( \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{x}-\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
\( \mathbf{A} \cdot e^{\frac{y}{x}}=\sin x+c \)
B. \( y=c x \log x \)
c. \( x=\frac{y^{2}}{3}+\frac{c}{y} \)
D. \( \cos \left(\frac{y-2}{x}\right)=a \)
Subject: Maths
\( \operatorname{Let} f(x)=\sin \frac{1}{x}, x \neq 0 . \) Then \( f(x) \) can
be continuous at \( 4 x=0 \)
A. If \( f(0)=1 \)
B. If \( f(0)=0 \)
c. If \( f(0)=-1 \)
D. For no definite value of \( f(0) \)
Subject: Physics
A bullet of mass \( m \) moving with a horizontal velocity \( v \) strikes a stationary
block of mass \( M \) suspended by a string
of length \( L \). The bullet gets embedded in the block. What is the maximum angle made by the string after impact?
A \( \cdot \theta=\cos ^{-1}\left(\frac{M}{m}\right) \)
в. \( \theta=\cos ^{-1}\left(\frac{m}{M}\right) \)
c. \( _{\theta}=\cos ^{-1}\left(\frac{m V}{M+m}\right) \)
" \( \quad \theta=\cos ^{-1}\left(1-\frac{1}{2 g L}\left(\frac{m v}{m+M}\right)^{2}\right) \)
Subject: Maths
Assertion
The value \( \int_{-4}^{-5} \sin \left(x^{2}-3\right) d x+ \)
\( \int_{-2}^{-1} \sin \left(x^{2}+12 x+33\right) \) is zero
Reason
\( \int_{-a}^{a} f(x) d x=0 \) if \( f(x) \) is an odd function.
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
Assertion
In the refrigerator, the evaporator is located in the freezer section.
Reason
In the heat pump, the evaporator is located outside the room which is to be
heated.
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
In which of the following reactions, the oxidation state of nitrogen is not changed?
A . Action of very dilute \( H N O_{3} \) on magnesium.
B. Action of dilute \( H N O_{3} \) on zinc.
c. Action of conc. \( H N O_{3} \) on copper.
D. Action of very dilute \( H N O_{3} \) on zinc.
Subject: Maths
The sum of first \( n \) terms of an G.P. is
A \( \cdot s_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r} \)
B. \( s_{n}=\frac{a_{1}\left(1+r^{n}\right)}{1-r} \)
\( ^{\mathbf{c}} \cdot_{S_{n}}=\frac{a_{1}\left(1-r^{n}\right)}{1+r} \)
D. \( _{S_{n}}=\frac{a_{1}\left(1-r^{n}\right)}{r-1} \)
Subject: Physics
Assertion
The number of electrons in a p-type
silicon semiconductor is less than the
number of electrons in a pure silicon semiconductor at room temperature
Reason
It is due to law of mass action.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
Subject: Maths
If \( A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 2 & -3 & 0\end{array}\right] \) and \( B=\left[\begin{array}{ccc}3 & 4 & -2 \\ 1 & 0 & 0\end{array}\right] \)
then the order of \( A B^{T} \) is
\( A \cdot 2 \times 3 \)
B. \( 3 \times 3 \)
\( c \cdot 3 \times 2 \)
D. \( 2 \times 2 \)
Subject: Maths
\( A B \) and \( C D \) are two parallel chords of a circle such that \( A B=10 \mathrm{cm} \) and \( \mathrm{CD}=24 \)
\( \mathrm{cm}, \) If the chords are on the opposite sides of the centre and the distance
between them is \( 17 \mathrm{cm} \), the radius of the circle is:
A . \( 14 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
\( c \cdot 13 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)
Subject: Physics
A charge \( Q \) is placed at a distance \( a / 2 \)
above the centre of the square surface
of edge a as shown in the figure. The
electric flux through the square surface
is :
A \( \cdot \frac{Q}{3 \epsilon_{0}} \)
в. \( \frac{Q}{6 \epsilon_{0}} \)
c. \( \frac{Q}{2 \epsilon_{0}} \)
D. \( \frac{Q}{\epsilon_{0}} \)
Subject: Physics
The accompanying graph of position \( x \)
versus time represents the motion of a
particle. If \( p \) and \( q \) are positive
constants, the expression that best
describes acceleration \( a \) of the particle
is
A. \( a=-p-q t \)
B \( . a=-p+q t \)
\( \mathbf{c} \cdot a=p+q t \)
D. \( a=p-q t \)
Subject: Biology
Match the following
\( \mathbf{A} \)
(i) \( -a,(i i)-b,(i i i)-c,(i v) d \)
B. (i) \( -b,(i i)-c,(i i i)-a,(i v)-d \)
C. (i) - b, (ii) - a, (iii) - d, (iv) c
D. (i) - d, (ii) - c, (iii) - b, (iv) - a
Subject: Maths
\( \int x \sec ^{2} 2 x d x \)
A. \( \frac{1}{4} x \tan 2 x-\frac{1}{2} \log \sec 2 x \)
B. \( \frac{1}{2} x \tan 2 x+\frac{1}{4} \log \sec 2 x \)
C \( \frac{1}{4} x \tan 2 x-\frac{1}{4} \log \sec 2 x \)
D. \( \frac{1}{2} x \tan 2 x+\frac{1}{4} \log \cos 2 x \)
Subject: Maths
The solution set of \( 6 x-1>5 \) is
\( \mathbf{A} \cdot\{x \mid x<1, x \in R\} \)
B . \( \{x \mid x<1, x \in N\} \)
\( \mathbf{c} \cdot\{x \mid x>1, x \in W\} \)
D \cdot \( \{x \mid x>1, x \in R\} \)
Subject: Maths
If focii of \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) coincide with the focii of \( \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 \) and eccentricity of
the hyperbola is \( 2, \) then
A \( \cdot a^{2}+b^{2}=14 \)
B. There is a director circle of the hyperbola
c. centre of the director circle is (0,0)
D. Length of latus rectum of the hyperbola is 12
Subject: Physics
A current passes through a resistor. If \( \mathrm{K} \)
and \( \mathrm{K}_{2} \) represent the average kinetic
energy of the conduction electrons and
the metal ions respectively then
\( \mathbf{A} \cdot K_{1}<K_{2} \)
B \( . K_{1}=K_{2} \)
\( \mathbf{c} \cdot K_{1}>K_{2} \)
D. Any of these three may occur
Subject: Physics
In the Newton's gravitational law, \( \boldsymbol{F}= \) \( \frac{G M m}{d^{2}}, \) the quantity \( G \)
A. depends on the value of \( g \) at the place of observation
B. is used only when the earth is one of the two masses
c. is greatest at the surface of the earth
D. is universal constant in nature
Subject: Maths
\( \int_{0}^{1} \tanh x d x= \)
\( A \cdot \log (e+1 / e) \)
B. \( \log (e-1 / e) \)
\( \mathbf{c} \cdot \log (\mathrm{e} / 2+1 / 2 \mathrm{e}) \)
D. \( \log \left(\frac{e}{2}-\frac{1}{e}\right) \)
Subject: Chemistry
Consider the reaction \( : 2 C O(g)+ \)
\( O_{2}(g) \rightleftharpoons 2 C O_{2}(g)+H e a t \)
Under what conditions shift is
undeterminable?

This question has multiple correct options
A. addition of \( O_{2} \) and decrease in volume
B. Addition of \( C O \) and removal of \( C O_{2} \) at constant volume
c. Increase in temperature and decrease in volume.
D. Addition of \( C O \) and increase in temperature at constant volume
Subject: Maths
\( \operatorname{Let} f(x)=\cos 2 x \cdot \cot \left(\frac{\pi}{4}-x\right) \) If \( f \) is
continuous at \( x=\frac{\pi}{4} \) then the value of \( f\left(\frac{\pi}{4}\right) \) is equal to
A . 2
B. -
c. \( \frac{-1}{2} \)
D.
Subject: Maths
What is the value of \( a \) in terms \( b, \) if \( \frac{a}{b}+ \) \( \frac{a+2}{3 b}=\frac{1}{4} ? \)
A. \( \frac{b+4}{2} \)
в. \( \frac{b-4}{2} \)
c. \( \frac{3 b-2}{4} \)
D. \( \frac{3 b+8}{16} \)
E \( \cdot \frac{3 b-8}{16} \)
Subject: Physics
In Young's double slit eperiment two disturbances arriving at a point P have phase difference of \( \frac{\pi}{3} . \) The intensity of this point expressed as a fraction of
maximum intensity \( I_{0} \) is then
A \( \cdot \frac{3}{2} I_{0} \)
в. \( \frac{1}{2} I_{0} \)
c. \( \frac{4}{3} I_{0} \)
D. \( \frac{3}{4} I_{0} \)
Subject: Physics
Sound waves of frequency \( 600 \mathrm{Hz} \) fall normally on perfectly reflecting wall. The distance from the wall at which the air
particles have the maximum amplitude of vibration is
(speed of sound in air \( =330 \mathrm{m} / \mathrm{s} \) )
\( A \cdot 13.75 \mathrm{cm} \)
B. \( 40.25 \mathrm{cm} \)
\( c .70 .5 \mathrm{cm} \)
D. \( 60.75 \mathrm{cm} \)
Subject: Biology
Assertion
Conversion of 1,3 -biphosphoglycerate (BPGA) to 3-phosphoglyceric acid (PGA) is an energy-yielding step.
Reason
This energy is trapped in the form of
ATP.
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
If torques of equal magnitudes are applied to a hollow cylinder and a solid sphere both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its center. Which of the two will acquire a greater angular speed after a given time?
A \( \cdot \omega_{1}>\omega_{2} \)
в. \( \omega_{1}=\omega_{2} \)
\( \mathrm{c} \cdot \omega_{2}>\omega \)
D. None of these
Subject: Physics
A parallel plate capacitor having plates
of area \( S \) and plate separation \( d, \) has
capacitance \( C_{1} \) in air. When two
dielectrics of different relative
permittivities \( \left(\epsilon_{1}=1 \text { and } \epsilon_{2}=4\right) \) are
introduced between the two plates as
shown in the figure, the capacitance
become \( C_{2} . \) The ratio \( \frac{C_{2}}{C_{1}} \) is
\( A \cdot 6 / 5 \)
В. \( 5 / 3 \)
\( c .7 / 5 \)
\( D \)
Subject: Maths
If \( f(x)=\log _{e}\{\log (x)\}, \) then \( f^{\prime}(x) \) at
\( \boldsymbol{x}=\boldsymbol{e} \) is :
\( A \)
B. \( -c \)
\( c \cdot e^{2} \)
D. \( e^{-1} \)
Subject: Maths
The \( 3 r d, 4 t h, \) and 5 th terms in the
expansion \( (x+a)^{n} \) are respectively
\( 84,280, \) and \( 560, \) find the values of \( x, a \)
and \( n \)
A. \( x=1, a=2, n=6 \)
B. \( x=1, a=6, n=7 \)
c. \( x=3, a=2, n=7 \)
D. \( x=1, a=2, n=7 \)
Subject: Physics
If the angle between incident ray and
normal is \( 30^{\circ}, \) choose the correct option:
A. Angle between incident ray and mirror \( =60^{\circ} \)
angle between reflected ray and mirror \( =60^{\circ} \)
Angle between normal and the mirror \( =90^{\circ} \)
B. Angle between incident ray and mirror \( =30^{\circ} \)
angle between reflected ray and mirror \( =30^{\circ} \)
Angle between normal and the mirror \( =30^{\circ} \)
C. Angle between incident ray and mirror \( =120^{\circ} \)
angle between reflected ray and mirror \( =30^{\circ} \)
Angle between normal and the mirror \( =30^{\circ} \)
D. Angle between incident ray and mirror \( =60^{\circ} \)
angle between reflected ray and mirror \( =30^{\circ} \)
Angle between normal and the mirror \( =120^{\circ} \)
Subject: Physics
A condenser of capacity \( 2 \mu F \) is charged
to a potential of \( 200 \mathrm{V} \). It is now connected to an uncharged condenser of capacity \( 3 \mu F \). The common potential is :
A . 200
B. \( 100 \mathrm{V} \)
c. \( 80 v \)
D. 40
Subject: Chemistry
In the diagram above, what is the half
reaction that occurs at the cathode?
A \( \cdot A l \rightarrow A l^{3+}+3 e^{-} \)
B. \( N i^{2+}+2 e^{-} \rightarrow N i \)
\( \mathbf{C} \cdot N i \rightarrow N i^{2+}+2 e^{-} \)
\( \mathbf{D} \cdot 2 A l^{3+}+6 e^{-} \rightarrow 2 A l \)
E. None of these
Subject: Chemistry
In the manufacture of hydrogen from
water gas \( \left(C O+H_{2}\right), \) which of the
following is correct statement?
A. Hydrogen is isolated by diffusion
B. \( H_{2} \) is removed by occlusion with pd
c. co and \( H_{2} \) are separated based on difference in their densities
D. co is oxidized to \( C O_{2} \) with steam in the presence of a catalyst followed by absorption of \( C O_{2} \) in alkali
Subject: Physics
A source of sound produces waves of wavelength \( 20 \mathrm{cm} \) in air. It is moving with a velocity one-fourth the velocity of sound towards east. The apparent wavelength noted by a man moving in the same direction with velocity equal to \( 2 / 3 \mathrm{rd} \) of velocity of sound wave and at the back of source is :
A . \( 15 \mathrm{cm} \)
B. 50 cm
c. \( 75 \mathrm{cm} \)
D. 80 cm
Subject: Chemistry
\( \begin{array}{lll}\text { Element } & \text { Reaction with water } & \triangle \boldsymbol{T}\left(^{\circ} \boldsymbol{C}\right) \\ \mathrm{A} & \text { small bubbles formed } & -2 \\ \mathrm{B} & \text { vigorous bubbling } & +10 \\ \mathrm{C} & \text { dissolves, no bubbles } & 0 \\ \mathrm{D} & \text { small bubbles formed } & 0\end{array} \) Which electron configuration would
match the laboratory data for Element
\( \mathrm{B} ? \)
\( \mathbf{A} \cdot[N e] 3 s^{2} \)
\( \mathbf{B} \cdot[X e] 6 s^{2} \)
\( \mathbf{C} \cdot[A r] 4 s^{2} 3 d^{10} \)
D. \( [N e] 3 s^{2} 3 p^{3} \)
Subject: Chemistry
In an ideal solution of non-volatile
solute \( \mathrm{B} \) in solvent \( \mathrm{A} \) in 2: 5 molar ratio
has vapour pressure \( 250 \mathrm{mm} \). If another solution in ratio 3: 4 prepared then vapour pressure above this solution is:
\( A \cdot 200 \mathrm{mm} \)
B. 250 mm
c. 350 \( \mathrm{mm} \)
D. \( 400 \mathrm{mm} \)
Subject: Chemistry
At \( 25^{\circ} C, K_{p} \) for the reaction:
\( N_{2} O_{4}(g) \leftrightharpoons 2 N O_{2}(g) \)
has a value of 0.14 atm. Calculate the
value of \( K_{c} \) in which the concentrations
are measured in mol \( \boldsymbol{L}^{-1} \)
Subject: Chemistry
Among the electrolytes
\( N a_{2} S O_{4}, C a C l_{2}, A l_{2}\left(S O_{4}\right)_{3} \) and
\( N H_{4} C l, \) the most effective coagulating
agent for \( \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3} \) sol is :
A \( \cdot N a_{2} S O_{4} \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot A l_{2}\left(S O_{4}\right) \)
D. \( N H_{4} C l \)
Subject: Physics
A battery of e.m.f. \( \boldsymbol{E} \) has an internal resistance 'r'. A variable resistance \( \boldsymbol{R} \) is
connected to the terminals of the
battery. A current \( I \) is drawn from the
battery. \( V \) is the terminal P.D. If \( R \) alone
is gradually reduced to zero, which of
the following best describes \( I \) and \( V ? \)
A. I approaches \( E / r, V \) approaches \( E \)
B. I approaches infinity, \( V \) approaches \( E \)
c. \( I \) approaches zero, Vapproaches \( E \)
D. I approaches \( E / r, V \) approaches zero
Subject: Chemistry
Which of the following is correct regarding Ellingham diagram?
A \( \cdot \) It is plot of \( \Delta G_{f} \) per mole of metal versus temperature
B. Reduction of a metal oxide is difficult if the metal formed is in liquid state at the temperature of reduction
c. Plot is a straight line except when some change in phase.
D. Ellingham diagram deals with both the feasibility as well as the rate of the reduction process
Subject: Physics
If \( \overline{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and \( \overline{\boldsymbol{B}}=-\hat{\boldsymbol{i}}+\mathbf{3} \hat{\boldsymbol{j}}+ \)
\( 4 \hat{k}, \) then projection of \( \bar{A} \) on \( \bar{B} \) will be:
A \( \cdot \frac{3}{\sqrt{13}} \)
в. \( \frac{3}{\sqrt{26}} \)
c. \( \sqrt{\frac{3}{26}} \)
D. \( \sqrt{\frac{3}{13}} \)
Subject: Maths
Given \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
Form all possible ordered pairs and write the total number of ordered pairs formed so that the first component is from set \( A \) and second component is
from set B.
What is the total number of such pairs?
Subject: Maths
Find the equation of the quadratic function \( \boldsymbol{f} \) whose graph increases over the interval \( (-\infty,-2) \) and decreases over the interval \( (-2,+\infty), f(0)=23 \)
and \( \boldsymbol{f}(\mathbf{1})=\mathbf{8} \)
A \( \cdot f(x)=3(x+2)^{2}+35 \)
B. \( f(x)=-3(x+2)^{2}-35 \)
C. \( f(x)=-3(x-2)^{2}+35 \)
D. \( f(x)=-3(x+2)^{2}+35 \)
Subject: Chemistry
Le-Chatelier principle is not applicable
to:
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
В. \( F e(s)+S(s) \rightleftharpoons F e S(s) \)
C. \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
D. \( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \)
Subject: Physics
On a two-lane road, car A is travelling
with a speed of \( 36 \mathrm{km} h^{-1} . \) Two cars \( \mathrm{B} \) and \( C \) approach car \( A \) in opposite
directions with a speed of \( 54 \mathrm{km} h^{-1} \) each. At a certain instant, when the
distance \( A B \) is equal to \( A C, \) both being 1
\( \mathrm{km}, \mathrm{B} \) decides to overtake \( \mathrm{A} \) before \( \mathrm{C} \) does. The minimum required
acceleration of car \( \mathrm{B} \) to avoid an
accident is
A \( \cdot 1 \mathrm{m} \mathrm{s}^{-2} \)
B. \( 1.5 \mathrm{m} s^{-2} \)
\( \mathbf{C} \cdot 2 \mathrm{m} s^{-2} \)
D. 3 \( \mathrm{m} \mathrm{s}^{-2} \)
Subject: Maths
If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sin \{[\boldsymbol{x}+\mathbf{5}]+\{\boldsymbol{x}-\{\boldsymbol{x}-\{\boldsymbol{x}\}\}\}\} \) for
\( \boldsymbol{x} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{4}}\right) \) is invertible, where \( \{.\} \)
and [.] represent fractional part and greatest integer functions respectively,
then \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \) is
This question has multiple correct options
\( \mathbf{A} \cdot \sin ^{-1} x \)
в. \( \frac{\pi}{2}-\cos ^{-1} x \)
\( c \cdot \sin ^{-1}\{x\} \)
D \( \cdot \cos ^{-1}\{x\} \)
Subject: Physics
A prism has a refractive index \( \sqrt{\frac{3}{2}} \) and
refracting angle \( 90^{\circ} \). Find the minimum
deviation produced by prism.
\( A \cdot 40^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 49^{\circ} \)
Subject: Chemistry
Which of the following produces
colorless gas with dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
This question has multiple correct options
A \( \cdot N a_{2} S_{2} O_{3} \)
в. \( \operatorname{NaH} \mathrm{CO}_{3} \)
c. \( C H_{3} C O_{2} N H_{4} \)
D. All
Subject: Maths
If \( f(x)=\frac{4-7 x}{7 x+4}, \lim _{x \rightarrow 0} f(x)=l \) and
\( \lim _{x \rightarrow \infty} f(x)=m \) the quadratic equation
having roots as \( \frac{1}{l} \) and \( \frac{1}{m} \) is
A \( \cdot x^{2}-1=0 \)
B. \( x^{2}-x+1=0 \)
c. \( x^{2}-\frac{1}{2}=0 \)
D. \( x^{3}-1=0 \)
Subject: Maths
The sum of the inner and the outer
curved surfaces of a hollow metallic
cylinder is \( 1056 \mathrm{cm}^{2} \) and the volume of
material in it is \( 1056 \mathrm{cm}^{3} \). Find the sum
of its internal and external radii. Given
that the height of the cylinder is \( 21 \mathrm{cm} \)
Subject: Chemistry
In a particular isomer of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right], \) the \( \boldsymbol{C l}-\boldsymbol{C o}-\boldsymbol{C l} \)
angle is \( 90^{\circ}, \) the isomer is known as:
A. Linkage isomer
B. Optical isomer
c. Cis-isomer
D. Position isomer
Subject: Maths
Determine the compound amount and
compound interest on Rs. 1,000 at \( 6 \% \)
compounded semi-annually for 6 years.
Given that \( (1+i)^{n}=1.42576 \) for \( i= \)
\( 3 \% \) and \( n=12 \)
A . 16,000
B. 630.50
c. 425.76
D. 1,640
Subject: Maths
Find the value of \( x \) and \( y \) using elimination method:
\( \frac{x}{2}+\frac{y}{3}=1 \) and \( \frac{x}{4}+\frac{y}{7}=2 \)
A. (44,-63)
В . (-41,63)
c. (44,63)
D. (-44,-63
Subject: Physics
An ideal gas has an initial pressure of 3 pressure units and an initial volume of 4 volume units. The table gives the final pressure and volume of the gas (in those same units) in four processes.
Which processes start and end on the same isotherm
\[
\begin{array}{llll}
A & B & C & D \\
5 & 4 & 12 & 6
\end{array}
\]
\( A \cdot A \)
B. B
\( c \cdot c \)
D.
Subject: Chemistry
Conjugate base of \( \boldsymbol{H} \boldsymbol{S O}_{\boldsymbol{4}}^{-} \) is:
A \( \cdot H_{2} S O_{4} \)
B. \( S O_{4}^{2-} \)
\( c \cdot s o_{4} \)
D. \( H_{2} S O_{4}^{-} \)