AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
Two sound sources are moving in
opposite direction with velocity \( v_{1} \) and
\( v_{2}\left(v_{1}>v_{2}\right) . \) Both are moving away from
a stationary observer.the frequency of
both the source is 900 Hz.What is the
value of \( v_{1}-v_{2} \) so that the beat
frequency observed will be \( 6 H z ? \)
Speed of sound \( =300 m s^{-1} \)
A \( \cdot 1 \mathrm{ms}^{-1} \)
B. \( 4 m s^{-1} \)
c. \( 3 m s^{-1} \)
D. \( 2 m s^{-1} \)
Subject: Physics
What is de Broglie wavelength
associated with an \( e^{-} \) accelerated
through potential difference \( =100 \mathrm{kV} ? \)
\( A \cdot 3.88 \mathrm{pm} \)
B. 4.23 pm
c. \( 4.78 \mathrm{pm} \)
D. \( 5.03 \mathrm{pm} \)
Subject: Physics
In a series resonant L-C-R circuit, the
voltage across \( \mathrm{R} \) is \( 100 \mathrm{V} \) and \( \boldsymbol{R}=\mathbf{1} \boldsymbol{k} \boldsymbol{\Omega} \)
with \( C=2 \mu F . \) The resonant frequency
is 200 rads \( ^{-1} \). At resonance the voltage
across Lis:
A . \( 2.5 \times 10^{-2} V \)
В. \( 4 \times 10^{-8} V \)
c. \( 250 V \)
D. \( 4 \times 10^{-3} V \)
Subject: Maths
The area of an ellipse is \( 8 \pi \) sq. units. Its distance between the foci is \( 4 \sqrt{3} \), then
\( \mathbf{e}= \)
\( \mathbf{A} \cdot \sin 30^{\circ} \)
B. \( \sin 45^{\circ} \)
c. \( \sin 60^{\circ} \)
\( \mathbf{D} \cdot \sin 75^{\circ} \)
Subject: Chemistry
For a reaction, \( 2 H I \rightleftharpoons H_{2}+I_{2} \) at
equilibrium, \( 7.8 \mathrm{g}, 203.2 \mathrm{g} \) and \( 1638.4 \mathrm{g} \)
of \( \boldsymbol{H}_{2}, \boldsymbol{I}_{2} \) and \( \boldsymbol{H} \boldsymbol{I} \) respectively
were found. Calculate \( \boldsymbol{K}_{\boldsymbol{C}} \)
A. \( K_{C}=2.1 \)
В. \( K_{C}=0.019 \)
c. \( K_{C}=0.005 \)
D. \( K_{C}=0.27 \)
Subject: Chemistry
Which one of the following statements
is not correct?
A. Oxidation state of \( S \) in \( \left(N H_{4}\right)_{2} S_{2} O_{8} \) is +6
B. Oxidation number of \( O s \) in \( O s O_{4} \) is +8
C. Oxidation state of \( S \) in \( H_{2} S O_{5} \) is +8
D. oxidation number of \( O \) in \( K O_{2} \) is \( -\frac{1}{2} \)
Subject: Maths
Let \( \boldsymbol{f}: \boldsymbol{N} \rightarrow \boldsymbol{N}(\boldsymbol{N} \) being the set of
positive integers) be a function defined by \( f(x)= \) the biggest positive integer
obtained by reshuffling the digits of \( x \) For example, \( \boldsymbol{f}(\mathbf{2 9 6})=\mathbf{9 6 2} \)
\( f \) is
A. One-one and onto
B. One-one and into
c. Many-one and onto
D. Many-one and into
Subject: Chemistry
Which one of the following is a tertiary alcohol?
A. \( C H_{3} C H_{2} C H_{2} O H \)
в. \( C H_{3} C H(O H) C H_{3} \)
c. \( \left(C H_{3}\right)_{2} \) СНСН\( _{2} \) ОН
D. \( \left(C H_{3}\right)_{3} C O H \)
Subject: Chemistry
For preparing a buffer solution of \( \mathrm{pH}= \) 7.0, which buffer system you will
choose:
A \( \cdot H_{2} P O_{4}, H_{2} P O_{4}^{-} \)
B . \( H_{2} P O_{4}^{-}, H P O_{4}^{2-} \)
\( \mathbf{c} \cdot H P O_{4}^{2-}, P O_{4}^{3} \)
D. \( H_{3} P O_{4}, P O_{4}^{3-} \)
Subject: Maths
Which of the following functions are
identity functions?
This question has multiple correct options
\( \mathbf{A} \cdot f: R \rightarrow R, f(x)=x \)
\( \mathbf{B} \cdot g: N \rightarrow Z, g(p)=3 \)
C \( . h: z \rightarrow z, h(y)=y \)
\( \mathbf{D} \cdot g: N \rightarrow N, g(z)=z \)
Subject: Maths
Lucy invested \( \$ 10,000 \) in a new mutual fund account exactly three years ago. The value of the account increased by
10 percent during the first year,increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
A. \( \$ 10,350 \)
в. \( \$ 10,395 \)
c. \( \$ 10,500 \)
D. \( \$ 11,500 \)
E. \( \$ 12,705 \)
Subject: Chemistry
Which one of the following is a simple
ether?
A. \( C H_{3}-O-C_{2} H_{5} \)
в. \( C_{6} H_{5}-O-C H_{3} \)
c. \( C_{2} H_{5}-O-C_{2} H_{5} \)
D. \( C_{3} H_{7}-O-C_{2} H_{5} \)
Subject: Maths
\( \mathbf{f} A^{\prime}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{4} \\ -\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}\end{array}\right] \)
then verify that:
\( (i)(A+B)^{\prime}=A^{\prime}+B^{\prime} \)
\( (i i)(A-B)^{\prime}=A^{\prime}-B^{\prime} \)
Subject: Physics
A metal disc of radius \( a \) rotates with a
constant angular velocity \( \omega \) about its axis. The potential difference between the center and the rim of the disc is \( \boldsymbol{m}= \) mass of electron, \( \boldsymbol{e}= \) charge on
electron)
\( ^{\mathrm{A}} \cdot \frac{m \omega^{2} a^{2}}{e} \)
B. \( \frac{1 m \omega^{2} a^{2}}{2} \)
\( ^{\mathrm{c}} \cdot \frac{e \omega^{2} a^{2}}{2 m} \)
D. \( \frac{e \omega^{2} a^{2}}{m} \)
Subject: Physics
Assertion
Though air is a bad conductor yet a
body kept in air loses heat quickly.
Reason
The heat loss is mainly due to radiation.
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
\( X \) and \( Y \) are two elements which form
\( X_{2} Y_{3} \) and \( X_{3} Y_{4} . \) If 0.2 mol of \( X_{2} Y_{3} \)
weighs 32 g and 0.4 mole of \( X_{3} Y_{4} \) weighs \( 92.8 \mathrm{g} \), the atomic weights of \( \boldsymbol{X} \)
and \( Y \) respectively are :
A. 16,56
B. 16,16
\( \mathbf{c} \cdot 56,16 \)
D. 56,56
Subject: Physics
An small object is kept at \( 18 \mathrm{cm} \) from combination of a convex lens and plane
mirror to get the image on object itself. Now the space between lens and mirror is filled with liquid of refractive index
\( \mu L . \) Now we need to keep the object at
\( 27 \mathrm{cm} \) to get the image on object. Find
\( \mu L \)
\( A \)
B.
\( c \)
2
\( D \)
Subject: Maths
Using section formula show that the
points \( \boldsymbol{A}(\mathbf{2},-\mathbf{3}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1}, \mathbf{2}, \mathbf{1}) \) and
\( C\left(0, \frac{1}{3}, 2\right) \) are collinear.
Subject: Physics
Three rods of the same mass are placed as shown in the figure. What will be the
coordinate of centre of mass of the
system?
A \( \cdot\left(\frac{a}{2}, \frac{a}{2}\right) \)
в. \( \left(\frac{a}{\sqrt{2}}, \frac{a}{\sqrt{2}}\right) \)
c. \( \frac{2 a}{3}, \frac{2 a}{3} \)
D. \( \left(\frac{a}{3}, \frac{a}{3}\right) \)
Subject: Maths
In a right angled \( \Delta B A C, \angle B A C=90^{\circ} \)
segment \( A D, B E \) and \( C F \) are the medians
Prove that \( 2\left(A D^{2}+B E^{2}+C F^{2}\right)= \)
\( 3 B C^{2} \)
Subject: Maths
ff \( \left[\begin{array}{cc}\boldsymbol{\alpha} & \boldsymbol{\beta} \\ \boldsymbol{\gamma} & -\boldsymbol{\alpha}\end{array}\right] \) is to be the square root of \( \mathbf{a} \)
two -rowed unit matrix, then \( \alpha, \beta \) and \( \gamma \)
should satisfy the relation.
A. \( 1+\alpha^{2}+\beta \gamma=0 \)
B . \( 1-\alpha^{2}-\beta \gamma=0 \)
C \( \cdot 1-\alpha^{2}+\beta \gamma=0 \)
D. \( 1+\alpha^{2}-\beta \gamma=0 \)
Subject: Maths
Two cards are drawn simultaneously
(without replacement) from a well-
shuffled pack of 52 cards. Find the
mean and variance of the number of red
cards.
\( \mathbf{A} \cdot \) Mean \( =0.1 \) and Variance \( =0.7 \)
B. Mean \( =0.6 \) and Variance \( =0.3 \)
C . Mean \( =0.49 \) and Variance \( =0.37 \)
D. Mean \( =0 \) and Variance \( =0.45 \)
Subject: Physics
A sphere of mass m moving with a constant velocity collides with another stationary sphere of same mass. The ratio of velocities of two spheres after collision will be, if the co-efficient of
restitution is e:
A \( \cdot \frac{1-e}{1+e} \)
в. \( \frac{e-1}{e+1} \)
c. \( \frac{1+e}{1-e} \)
D. \( \frac{e+1}{e-1} \)
Subject: Maths
A plane meet the co-ordinate axes in
\( A, B, C \) such that the centroid of
triangle \( A B C \) is \( (a, b, c) . \) If equation of plane \( \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=k(k \neq 0), \) then the
value of \( k \) equals
A . 2
B. 3
\( c \cdot 4 \)
D. 5
Subject: Maths
If \( \vec{a}=\hat{i}+\widehat{j}+\widehat{k}, \vec{b}=4 \hat{i}+3 \widehat{j}+4 \widehat{k} \) and
\( \vec{c}=\hat{i}+\alpha \hat{j}+\beta \widehat{k} \) are linearly dependent
vectors and \( |\overrightarrow{\boldsymbol{c}}|=\sqrt{\mathbf{3}}, \) then
B. \( a=1, b=\pm 1 \)
c. \( \alpha=-1, \beta=\pm 1 \)
D. \( \alpha=\pm 1, \beta=1 \)
Subject: Chemistry
Consider p-aminophenol
Which positions are activated for electrophilic aromatic substitution
reaction in acidic and basic media
respectively?
A. \( \alpha^{\prime} \) in A and \( \beta \) in B
B. \( \alpha^{\prime} \) in \( A \) and \( \alpha \) in \( B \)
c. \( \beta^{\prime} \) in \( A \) and \( \alpha \) in \( B \)
\( D \cdot \beta^{\prime} \) in \( A \) and \( \beta \) in \( B \)
Subject: Chemistry
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H}_{2} \stackrel{N i}{\rightarrow} \boldsymbol{C H}_{3}-\boldsymbol{C H}_{3} \) is
an addition reaction. \( \boldsymbol{C H} \equiv \boldsymbol{C H}+\boldsymbol{H}_{2} \stackrel{N i}{\rightarrow} ? \)
Predict and write the products.
Subject: Physics
For the circuit shown in the figure. The
equivalent resistance between point \( \mathbf{A} \)
and \( \mathrm{B} \) for the two cases \( (\mathrm{i}) \boldsymbol{V}_{\boldsymbol{A}}>\boldsymbol{V}_{\boldsymbol{B}} \)
(ii) \( V_{B}>V_{A} \quad \) respectively is
\( \mathbf{\Omega} \) and
respectively \( \left(D_{1} \text { and } D_{2} \) are ideal \right.
diodes)
\( A \cdot 25, \infty \)
B. \( 50, \infty \)
\( \mathrm{c} \cdot \infty, 25 \)
D. 50.5
Subject: Physics
In the radioactive transformation \( z^{\boldsymbol{X}}^{\boldsymbol{A}} \frac{\boldsymbol{\beta}^{-}}{\boldsymbol{X}} \boldsymbol{z}+\mathbf{1} \boldsymbol{X}_{\mathbf{1}}^{\boldsymbol{A}} \)
\( z-1 X_{2}^{A-4} \longrightarrow Z_{-3} X_{3}^{A-3} \)
which are successively emitted radioactive radiations?
A \( \cdot \beta^{-}, \alpha, \beta^{-} \)
в. \( \alpha, \beta^{-}, \beta^{-} \)
\( \mathrm{c} \cdot \beta^{-}, \alpha, \alpha \)
D \( \cdot \alpha, \beta^{-}, \alpha \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}-1 & -2 & -1 \\ 6 & 12 & 6 \\ 5 & 10 & 5\end{array}\right], \) then which of the
following is/are correct?
1. \( A \) and \( B \) commute.
2. AB is null matrix.
Select the correct answer using the
code given below:
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2
Subject: Chemistry
The rate constant for the forward
reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{B}(\boldsymbol{g}) \) is \( 1.5 \times \)
\( 10^{-3} s^{-1} \) at \( 100 \mathrm{K} \). If \( 10^{-5} \) moles of \( \mathrm{A} \) and
100 moles of \( \mathrm{B} \) are present in a 10 litre
vessel at equilibrium then rate
constant for the backward reaction at
this temperature is:
\( \begin{array}{ll}\text { A } \cdot 1.50 \times 10^{4} L & \text { mol- }^{-1} s^{-1}\end{array} \)
В. \( 1.5 \times 10^{11} L \quad \) mol \( ^{-1} s^{-1} \)
C. \( 1.5 \times 10^{10} L \quad \) mol \( ^{-1} s^{-1} \)
D. \( 1.5 \times 10^{-11} L \quad \) mol \( ^{-1} s^{-1} \)
Subject: Physics
The diagram shows two magnets and
two iron rods placed in a line.

Which magnetic poles are induced at the ends \( J \) and \( K \) of the iron rods?
A. Pole induced at end \( J-N \), pole induced at end \( K-N \)
B. Pole induced at end \( J-N \), pole induced at end \( K-S \)
C. Pole induced at end \( J-S \), pole induced at end \( K-N \)
D. Pole induced at end \( J-S \), pole induced at end \( K-S \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{ll}-\boldsymbol{b} & -\boldsymbol{a}\end{array}\right] \) and \( \boldsymbol{C}= \)
\( \left[\begin{array}{c}\boldsymbol{a} \\ -\boldsymbol{a}\end{array}\right], \) then the correct statement is
A. \( A=-B \)
В. \( A+B=A-B \)
c. \( A C=B C \)
D. \( C A=C B \)
Subject: Maths
\( \mathbf{1 0} \)
\( \mathbf{2 0} \)
\( \mathbf{3 0} \)
40
\( f \quad 5 \quad 7 \quad 15 \quad 13 \)
From the given distribution, calculate
mean deviation about mean.
A .1 .021
B. 11.231
c. 10.256
D. 12.214
Subject: Physics
A drop of liquid of density \( \rho \) is floating
half-immersed in a liquid of density \( d \). If
\( \rho \) is the surface tension the diameter of
the drop of the liquid is
A \( \cdot \sqrt{\frac{\sigma}{g(2 \rho-d)}} \)
в. \( \sqrt{\frac{3 \sigma}{g(2 \rho-d)}} \)
c. \( \sqrt{\frac{6 \sigma}{g(2 \rho-d)}} \)
D. \( \sqrt{\frac{12 \sigma}{g(2 \rho-d)}} \)
Subject: Maths
If \( \sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \)
then \( \frac{\sum_{k=1}^{2}\left(x^{100 k}+y^{106 k}\right)}{\sum x^{207} \cdot y^{207}} \) is
A \( \cdot \frac{1}{3} \)
B. \( \frac{4}{3} \)
\( c \cdot \frac{2}{3} \)
D. None of these
Subject: Physics
Three identical blocks each having a
mass \( \mathrm{m} \) are pushed by a force \( \mathrm{F} \) on a
friction less table. what is the
acceleration of the blocks? what is the
net force on the block P? hat force does
p apply on \( Q . \) what forces \( Q \) apply on \( R ? \)
\( A \cdot \frac{3 F}{8} \)
B. \( \frac{F}{7} \)
\( \mathbf{c} \cdot \frac{F}{3} \)
D. \( \frac{2 F}{4} \)
Subject: Biology
Match the theories given with the names of scientists. Choose the answer
which gives the correct combination of
the alphabets.
Names of Names of theories \( \quad \) scientists
A. Relay pump theory
p. Schleiden
B. Cohesion tension theory
q. Sir J.C. Bose
C. Mass flow theory Godlewski
D. Pulsation theory
s. Dixon and Jolly
t. Ernst Munch
A \( \cdot \) A- \( q, \) B- \( p, C-t, D-r \)
B. A-r, B- q, C- t, D- q
c. \( A-s, B-r, C-p, D-q \)
D. A- r, B- s, C- t, D- q
Subject: Chemistry
Which of the following statements is
not correct for chemisorption and
physisorption?
A. Physical adsorption occurs at a low temperature and chemisorption occurs at high temperatures
B. Magnitude of chemisorption decreases with rise in temperature while physisorption increases with rise in temperature.
C. Chemisorption is irreversible and physisorption is reversible.
D. In physisorption activation energy is low while in chemisorption it is high.
Subject: Physics
A woman dancing in high-heeled shoes accidentally steps on her partner's foot with the heel of her shoe. Even though her partner outweighs her by \( 400 \mathrm{N} \) and can easily lift her off the floor, he feels pain because:
A. her weight is concentrated into a small area
B. her small foot has a large momentum
c. her foot has a large inertia
D. his foot has no inertia
Subject: Chemistry
For a reaction \( \boldsymbol{P} \rightarrow \boldsymbol{Q} \), the half-life of the
reaction was \( 3 h, \) when the initial
concentration of \( P \) was 0.5 M. As the
concentration of \( P \) was increased to
1.0 \( \mathrm{M} \), half life changes to \( 6 \mathrm{h} \). The order of reaction with respect to P is:
A . zero
B. one
c. two
D. three
Subject: Physics
A hollow conducting spherical shell of radius \( R \) is charged with \( Q \) coulomb.
The amount of work done for moving any
charge \( q \) from the centre to the surface of the shell will be
A \( \cdot \frac{q Q}{4 \pi \epsilon_{0} R} \)
B. Zero
c. \( \frac{Q q}{\pi \epsilon_{0} R} \)
D \( \frac{2 Q q}{\pi \epsilon_{0} R} \)
Subject: Chemistry
Cadmium amalgam is prepared by
electrolysis of a solution of \( C d C l_{2} \) using a mercury cathode. Find how long a current of 5 ampere should be passed in order to prepare \( 12 \% C d-H g \)
amalgam on a cathode of \( 2 g \) mercury.
At. mass of \( C d=112.40 \)
Subject: Physics
The earth has volume 'V' and surface
area 'A'; then its capacitance would be:
A \( \cdot_{4 \pi \in_{0}} \frac{A}{V} \)
в. \( _{4 \pi \in_{0}} \frac{V}{A} \)
c. \( _{12 \pi \in_{0} \frac{V}{A}} \)
D. \( _{12 \pi \in_{0}} \frac{A}{V} \)
Subject: Chemistry
Which of the following statement is not
true?
\( \mathbf{A} \cdot C H_{3} C H_{2} N H_{2} \) is ethanamine
B. \( C H_{2} C H_{2} O H \) is an ether
C . Cyclopentane and 2-pentene have a molecular formula of \( C_{5} H_{10} \)
D. Alkenes an alkynes are unsaturated
Subject: Maths
Let \( \mathbf{f}=\left\{\begin{array}{ll}\mathbf{a x}^{2}+\mathbf{1} & \text { for } \mathbf{x}>\mathbf{1} \\ \mathbf{x}+\mathbf{a} & \text { for } \mathbf{x} \leq \mathbf{1}\end{array} \text { then } \mathbf{f}\right. \)
is derivable at \( x=1 \) if
\( \mathbf{A} \cdot \mathbf{a}=0 \)
B. \( a=\frac{1}{2} \)
\( \mathbf{c} \cdot \mathbf{a}=1 \)
\( \mathbf{D} \cdot \mathbf{a}=\mathbf{2} \)
Subject: Chemistry
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s}) \rightarrow \boldsymbol{Z} \boldsymbol{n} \boldsymbol{C l}_{2}(\boldsymbol{a q})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
In the reaction above, which term best
describes the role of \( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a} \boldsymbol{q}) ? \)
A. Bronsted acid
B. Oxidizing agent
c. Reducing agent
D. Precipitate
E. Cathode
Subject: Chemistry
How many of the following reactions goes almost all the way to completion?
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) ; K_{c}=2.7 \times \)
\( \mathbf{1 0}^{-18} \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
Subject: Chemistry
For a given reaction, energy of
activation for forward reaction
\( \left(\boldsymbol{E}_{\boldsymbol{a} f}\right) \boldsymbol{i s} \boldsymbol{8 0 k} \boldsymbol{J} \cdot \boldsymbol{m o l}^{-1} \cdot \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -40 k J . \) mol \( ^{-1} \) for the reaction. \( A \)
catalyst lowers \( E_{a f} \) to \( 20 k J . m o l^{-1} \) Find out the ratio of energy of activation for reverse reaction before and after
addition of catalyst.
Subject: Maths
If the price of an article is increased by per cent \( p, \) then the decrease in per cent
of sales must not exceed \( d \) in order to
yield the same income. The value of \( d \) is
A \( \cdot \frac{1}{1+p} \)
в. \( \frac{1}{1-p} \)
c. \( \frac{p}{1+p} \)
D. \( \frac{p}{p-1} \)
E \( \cdot \frac{1-p}{1+p} \)
Subject: Physics
A solid sphere is rolling without slipping on a level surface at a constant
speed of \( 2.0 m s^{-1} . \) How far can it roll up
a \( 30^{\circ} \) ramp before it stops?
\( \mathbf{A} \cdot 56 \mathrm{cm} \)
B . \( 26 \mathrm{cm} \)
\( c .53 \mathrm{cm} \)
D. 84
Subject: Physics
Match the following.
\( \begin{array}{llll}\text { I } & \text { Isothermal process } & \mathbf{1} & \boldsymbol{\Delta} \boldsymbol{Q}=\mathbf{0} \\ \text { II } & \text { Isobaric process } & 2 & \Delta V=0 \\ \text { III } & \text { Isochoric process } & 3 & \Delta P=0 \\ \text { IV } & \text { Adiabatic process } & 4 & \Delta T=0\end{array} \)
\( A \)
\( |-4,||-3,|||-2, \mid V-1 \)
B. \( \mid-3, \) । \( -2, \) II \( -1, \) IV- 4
c. \( |-1,| \mid-2, \) ।I \( -3, \) ।V -4
D. \( |-4,||-2,| 1|-3,| V-1 \)
E . \( |-1,||-4,|||-2, \mid v-3 \)
Subject: Chemistry
A measured temperature on the Fahrenheit scale is \( 200^{0} \) F.What will
this reading be on the Celsius scale?
A \( \cdot 40^{\circ} \mathrm{C} \)
В \( \cdot 94^{\circ} \mathrm{C} \)
c. \( 93.3^{\circ} \mathrm{C} \)
D. \( 30^{\circ} \mathrm{C} \)
Subject: Maths
The distance of the point \( ,(-1,-5,-10) \) from the point intersection of the line,
\( \frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12} \) and the plane \( x- \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{5}, \) is
\( A \cdot 13 \)
B. 1
c. 12
D. none of these
Subject: Chemistry
Using electron-transfer concept, identify the oxidant and reductant in
the following redox reactions.
(a) \( Z n(s)+2 H^{+}(a q) \longrightarrow \)
\( Z n^{2+}(a q)+H_{2}(g) \)
(b) \( 2\left[F e(C N)_{6}\right]^{3-}(a q)+2 O H^{-}(a q)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right]^{4-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
(c) \( 2\left[F e(C N)_{6}\right]^{3-}(a q)+2 O H^{-}(a q)+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{2}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{4-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) \)
Subject: Chemistry
Electromagnetic radiation of wavelength \( 242 \mathrm{nm} \) is just sufficient to ionise the sodium atom. Calculate the
ionisation of sodium \( \mathrm{kn} \mathrm{kJ} \mathrm{mol}^{-1} \)
A. \( 8.8266 \times 10^{-35} \mathrm{m} \)
B. 8.8266 \( \times 10^{35} \mathrm{m} \)
c. \( 8.8266 \times 10^{-36} \mathrm{m} \)
D. 8.8266 \( \times 10^{-34} \mathrm{m} \)
Subject: Maths
Factorise: \( 8 a^{3}+b^{3}+12 a^{2} b+6 a b^{2} \)
A \( \cdot(2 a+b)(2 a+b)(2 a+b)(2 a+b)(2 a+b)(2 a+b) \)
B. (2ab)(2a+b)(2a+b)(2ab)(2a+b)(2a+b)
\( c \cdot(2 a-b)(2 a+b) \)
\( D \cdot(2 a+b)(2 a+b) \)
Subject: Maths
If \( i=\sqrt{-1}, \) then select from the
following having the greatest value.
A \( \cdot i^{4}+i^{3}+i^{2}+i \)
B . \( i^{8}+i^{6}+i^{4}+i^{2} \)
\( \mathbf{c} \cdot i^{12}+i^{9}+i^{6}+i^{3} \)
D. \( i^{16}+i^{12}+i^{8}+i^{4} \)
E . \( i^{20}+i^{15}+i^{10}+i^{5} \)
Subject: Maths
On the Cartesian plane, \( Q \) is the
midpoint of the straight line \( \boldsymbol{P} \boldsymbol{R} \)
Find the values of \( x \) and \( y \)
A \( . x=3, y=2 \)
B. \( x=4, y=2 \)
c. \( x=4, y=3 \frac{1}{2} \)
D. \( x=8, y=3 \)
Subject: Maths
Derivative of \( \tan ^{3} \theta \) with respect to \( \sec ^{3} \theta \) at \( \theta=\frac{\pi}{3} \) is
A \( \cdot \frac{3}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{1}{2} \)
D. \( -\frac{\sqrt{3}}{2} \)
Subject: Physics
An electron at rest has a charge of
\( 1.6 \times 10^{-19} C . \) It starts moving with a
velocity \( \boldsymbol{v}=\boldsymbol{c} / 2, \) where \( \boldsymbol{c} \) is the speed of
light, then the value the new charge on
it is
\( \mathbf{A} \cdot 1.6 \times 10^{-19} \) Coulomb
B. \( _{1.6} \times 10^{-19} \sqrt{1-\left(\frac{1}{2}\right)^{2}} \) Coulomb
c. \( _{1.6} \times 10^{-19} \sqrt{\left(\frac{1}{2}\right)^{2}-1 \text { Coulomb }} \)
\( \frac{1.6 \times 10^{-19}}{\sqrt{1-\left(\frac{1}{2}\right)^{2}}} \) Coulom
Subject: Physics
Two liquids of densities \( d_{1} \) and \( d_{2} \) are
flowing in identical capillaries under
same pressure difference. If \( t_{1} \) and \( t_{2} \)
are the time taken for the flow of equal quantities of liquids, then the ratio of coefficients of viscosities of liquids
must be
\( \mathbf{A} \cdot \frac{d_{1} d_{2}}{t_{1} t_{2}} \)
B. \( \frac{d_{1} t_{1}}{d_{2} t_{2}} \)
\( \mathbf{c} \cdot \frac{d_{1} t_{2}}{d_{2} t_{1}} \)
D \( \sqrt{\left(\frac{d_{1} t_{1}}{d_{2} t_{2}}\right)} \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{F}(\boldsymbol{x})=\left|\begin{array}{ccc}\sin \boldsymbol{x} & \cos \boldsymbol{x} & \sin \boldsymbol{x} \\ \cos \boldsymbol{x} & -\sin \boldsymbol{x} & \cos \boldsymbol{x} \\ \boldsymbol{x} & \boldsymbol{1} & \boldsymbol{1}\end{array}\right| \)
Which of the following statement hold true?
This question has multiple correct options
A \( \cdot \) Range of \( F(x) \) is \( (-\infty, \infty) \)
B \( \cdot F^{\prime}\left(\frac{\pi}{2}\right)= \)
c. \( F(x) \) is bounded
D. \( F(x) \) is continuous and differentiable every where in its domain
Subject: Physics
Two particles \( A \) and \( B \), initially at rest, moves towards each other under a
mutual force of attraction. At the instant
when the speed of \( A \) is \( u \) and the speed of
\( \mathrm{B} \) is \( 2 u, \) the speed of centre of mass is
A. zero
в. \( u \)
\( c .1 .5 u \)
D. \( 3 u \)
Subject: Maths
A parallelogram and rhombus are equal in area. The diagonals of the rhombus
measures \( 120 m \) and 44 m. If one of the
side of the parallelogram measures \( 66 m, \) find its corresponding altitude (in
\( \boldsymbol{m}) \)
A . 40
B. 45
c. 48
D. 55