AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Assertion
Reaction quotient is defined in the same way as equilibrium constant at any stage of the reaction.
Reason
If \( Q_{c} \) (reaction quotient) \( <K_{c} \)
(equilibrium constant reaction moves in direction of reactants).
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 coil of area \( 5 \mathrm{cm}^{2} \) with 20 turns is
kept under the magnetic field of \( 10^{3} \) Gauss. Normal to the plane of coil
makes an angle \( 30^{\circ} \) with the magnetic field. The flux through the coil is
A \( \cdot 6.67 \times 10^{-4} \mathrm{Wb} \)
B. \( 3.2 \times 10^{-5} \mathrm{Wb} \)
\( \mathbf{c} \cdot 5.9 \times 10^{-4} W b \)
D. \( 8.65 \times 10^{-4} W b \)
Subject: Physics
A force \( \overrightarrow{\boldsymbol{F}}=(-\boldsymbol{y} \hat{\boldsymbol{i}}+\boldsymbol{x} \hat{\boldsymbol{j}}) \boldsymbol{N} \) acts on a
particle as it moves in an anticlockwise
circular motion in \( x \) -y plane. The centre of the circle is at the origin. If the work done by the force is \( 32 \pi J \) in one
complete revolution then assuming \( x, y \)
to be in meters, find the radius of the
path
A. 5
B. 4
\( c \cdot 6 \)
D.
Subject: Chemistry
Units of the properties measured are given. Which of the properties has not been matched correctly?
A. Molar conductance \( =\mathrm{S} m^{2} m o l^{-1} \)
B. Cell constant \( =m^{-1} \)
C. Specific conductance \( =\mathrm{S} m^{2} \)
D. Equivalent conductance \( =\operatorname{Sm}^{2}(g e q)^{-1} \)
Subject: Chemistry
The formula of Haematite is:
\( \mathbf{A} \cdot F e_{3} O_{4} \)
в. \( F e O_{4} \)
\( \mathrm{c} \cdot \mathrm{Fe}_{2} \mathrm{O}_{3} \)
\( \mathrm{D} \cdot \mathrm{Fe}_{3} \mathrm{O}_{2} \)
Subject: Chemistry
The coefficient B in the virial equation
of state has unit:
\( \boldsymbol{P} \boldsymbol{V}_{\boldsymbol{m}}=\boldsymbol{R} \boldsymbol{T}\left(\boldsymbol{1}+\frac{\boldsymbol{B}}{\boldsymbol{V}_{m}}+\frac{\boldsymbol{C}}{\boldsymbol{V}_{\boldsymbol{m}}^{2}}+\ldots . .\right) \)
A. mole
B. L/mole
c. L-mole
\( D \)
Subject: Physics
A solenoid has 2000 turns wound over a
length of \( 0.3 m . \) Its cross-sectional area is equal to \( 1.2 \times 10^{-3} m^{2} \). Around its
central cross-section, a coil of 300
turns is wound. If an initial current of
\( 2 A \) flowing in the solenoid is reversed in
\( 0.25 s, \) the emf induced in the coil is
A \( .0 .6 m V \)
B. \( 60 m V \)
c. \( 40.2 m V \)
D. \( 0.48 m V \)
Subject: Chemistry
The product obtained by heating diethyl ether with \( \boldsymbol{H} \boldsymbol{I} \) is:
A. \( C_{2} H_{5} I \)
В \( \cdot C_{2} H_{5} O H \)
\( \mathbf{c} \cdot C_{2} H_{5} O H+C_{2} H_{5} \)
D. \( C_{2} H_{5}-C_{2} H_{5} \)
Subject: Maths
\( \lim _{x \rightarrow \infty} \sin ^{-1} \sin \left(\frac{x^{2}+2}{x^{2}+1}\right) \) is equal to
(where [.] and \( \{.\} \) denote greatest integer and fractional part function respectively) This question has multiple correct options
A \( \cdot \lim _{x \rightarrow \infty}\left[\frac{x^{2}+2}{x^{2}+1}\right] \)
B. \( \lim _{x \rightarrow \infty} \frac{x^{2}+2}{x^{2}+1} \)
\( ^{\mathbf{C}} \lim _{x \rightarrow \infty}\left\{\frac{x^{2}+2}{x^{2}+1}\right\} \)
D. \( \lim _{x \rightarrow \infty}\left\{\frac{x^{2}}{x^{2}+1}\right\} \)
Subject: Chemistry
The volume occupied by one molecule of
water (density \( 1 g / c m^{3} \) ) is:
\( \mathbf{A} \cdot 18 \mathrm{cm}^{3} \)
В. \( 22400 \mathrm{cm}^{3} \)
c. \( 6.023 \times 10^{-23} \mathrm{cm}^{3} \)
D. \( 3.342 \times 10^{-23} \mathrm{cm}^{3} \)
Subject: Physics
Assertion
A rectangular current loop is in an arbitrary orientation in an external
uniform magnetic field. No work is
required to rotate the loop about an axis
perpendicular to its plane.
Reason
All positions represent the same level of
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
Which is correct about the reaction
between \( H_{2} O \) and \( O_{2} ? \)
\( \mathbf{A} \cdot \) It is a case of mutual reduction
B. \( O_{3} \) will oxidize \( H_{2} O_{2} \) into \( O_{2} \)
C. It is not a redox reaction
D. \( H_{2} O_{2} \) being a stronger oxidizing agent will decompose ozone into oxygen
Subject: Physics
Two blocks \( A \) and \( B \) each of 20 kg lying on a frictionless table are connected by
a light string. The system is pulled horizontally with an acceleration of
\( 2 m s^{-2} \) by a force \( F \) on \( B . \) The tension in the string will be:
A. \( 10 N \)
в. \( 40 N \)
c. \( 100 N \)
D. \( 120 N \)
Subject: Maths
\( \boldsymbol{O} \) is the centre of the circle having
radius \( 5 \mathrm{cm} . A B \) and \( A C \) are two chords
such that \( A B=A C=6 \mathrm{cm} . \) If \( 0 \mathrm{A} \)
meets \( B C \) at \( M, \) then \( O M \) is equal to
A . \( 3.6 \mathrm{cm} \)
B. \( 1.4 \mathrm{cm} \)
\( c \cdot 2 c m \)
\( 0.3 \mathrm{cm} \)
Subject: Chemistry
The correct statement(s) about the
compound is/are:
This question has multiple correct options
A. The total number of meso compounds possible for \( x \) are 2
B. R,R-cis stereo isomer of \( X \) is enantiomer of \( S \), S-cis stereo isomer of the same compound.
c. If the stereo chemistry about the double bond in \( x \) is trans, the number of enantiomers possible for \( x \) is 4
D. If the stereo chemistry about the double bond in \( x \) is cis, the number of enantiomers possible for \( x \) is 2
Subject: Chemistry
I. An endothermic reaction process
cannot occur spontaneously.
II. The enthalpy change for an
endothermic process is negative.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement II is false
Subject: Chemistry
The speed of the electron in the 1 st orbit of the hydrogen atom in the ground state is: \( (c \) is the velocity of light)
A \( \cdot \frac{c}{1.37} \)
в. \( \frac{c}{1370} \)
c. \( \frac{c}{13.7} \)
D. \( \frac{c}{137} \)
Subject: Maths
If \( P \) is a \( 3 \times 3 \) matrix such that \( P^{T}= \)
\( 2 P+I, \) where \( P^{T^{\prime}} \) is the transpose of \( P \)
and \( I \) is the \( 3 \times 3 \) identity matrix, then
there exists a column matrix \( \boldsymbol{X}= \)
\( \left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y} \\ \boldsymbol{z}\end{array}\right] \neq\left[\begin{array}{l}\mathbf{0} \\ \mathbf{0} \\ \mathbf{0}\end{array}\right] \) such that
\( ^{\mathbf{A}} \cdot \operatorname{PX}=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)
в. \( P X=X \)
c. \( P X=2 X \)
D. \( P X=-X \)
E.
\[
P X=\left[\begin{array}{l}2 \\ 0 \\ 0\end{array}\right]
\]
F. \( P X=3 X \)
G. \( P X=5 X \)
H. \( P X=-3 X \)
Subject: Maths
\( \mathbf{y}=\sin \mathbf{x}, \boldsymbol{y}_{n}=\frac{\boldsymbol{d}^{n}(\sin \boldsymbol{x})}{\boldsymbol{d} \boldsymbol{x}^{n}} \)
\( \operatorname{then}\left|\begin{array}{lll}\boldsymbol{y} & \boldsymbol{y}_{1} & \boldsymbol{y}_{2} \\ \boldsymbol{y}_{3} & \boldsymbol{y}_{4} & \boldsymbol{y}_{5} \\ \boldsymbol{y}_{6} & \boldsymbol{y}_{7} & \boldsymbol{y}_{8}\end{array}\right|=? \)
\( A \cdot-\sin x \)
B.
\( c \cdot \sin x \)
D. \( \cos \)
Subject: Maths
Solve the differential equation \( \frac{d y}{d x}+ \)
\( \frac{y}{x}=x^{2} \)
A. \( x=\frac{x^{4}}{4}+C \)
в. \( _{y}=\frac{x^{4}}{4}+C \)
c. \( _{x y}=\frac{x^{4}}{4}+C \)
D. None of these
Subject: Chemistry
Given;
(i) \( C u^{2+}+2 e^{-} \rightarrow C u, E^{\circ}=0.337 V \)
(ii) \( \boldsymbol{C u}^{2+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}^{+}, \boldsymbol{E}^{\circ}=\mathbf{0 . 1 5 3} \boldsymbol{V} \)
Electrode potential \( \boldsymbol{E}^{\circ} \) for the reaction,
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C u}, \) will be:
A . \( 0.38 V \)
в. \( 0.52 \mathrm{V} \)
c. \( 0.90 V \)
D. \( 0.30 V \)
Subject: Maths
Construct a quadrilateral ABCD, if \( A B=4.5 \mathrm{cm}, \mathrm{BC}=5.5 \mathrm{cm}, \mathrm{CD}=5 \mathrm{cm}, \mathrm{DA}=4.8 \)
\( \mathrm{cm}, \) and \( \angle A B C=60^{\circ} \)
Subject: Chemistry
Which of the following compounds is most widely used as an oxidizing agent in the volumetric analysis?
A. \( C e O_{2} \)
B. \( \left(N H_{4}\right)_{2}\left[C e\left(N O_{3}\right)_{6}\right] \)
\( \mathrm{c} \cdot \mathrm{Ce}\left(\mathrm{SO}_{4}\right)_{2} \)
D. \( C e F_{3} \)
Subject: Chemistry
The given figure shows the colour
changes in test tubes I, II and III, when
China rose indicator is added to them.
The respective solutions in test tubes I,
II and III are
A. Sugar solution, Lime water, Baking powder
B. Sugar solution, Lemonjuice, Vinegar
C. lime water, Sugar solution, Lemon juice
D. Lemon juice, Sugar solution, lime water
Subject: Maths
If \( a^{2}+b^{2}+c^{2}=-2 \) and \( f(x)= \)
\( \left|\begin{array}{ccc}\mathbf{1}+\boldsymbol{a}^{2} \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{b}^{2}\right) \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{c}^{2}\right) \boldsymbol{x} \\ \left(\mathbf{1}+\boldsymbol{a}^{2}\right) \boldsymbol{x} & \mathbf{1}+\boldsymbol{b}^{2} \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{c}^{2}\right) \boldsymbol{x} \\ \left(\mathbf{1}+\boldsymbol{a}^{2}\right) \boldsymbol{x} & \left(\mathbf{1}+\boldsymbol{b}^{2}\right) \boldsymbol{x} & \mathbf{1}+\boldsymbol{c}^{\mathbf{2}} \boldsymbol{x}\end{array}\right| \) then
\( f(x) \) is a polynomial of degree
\( A \cdot \)
B.
\( c .3 \)
\( D \)
Subject: Maths
A triangle \( A B C \) is placed so that the
midpoints of its sides are on the \( \boldsymbol{x}, \boldsymbol{y} \)
and \( z \) axes respectively. Lengths of the
intercepts made by the plane containing the triangle on these axes
\( \operatorname{are} \) respectively \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}, \) then
the coordinates of the centroid of the
triangle \( A B C \) are
A \( \cdot\left(-\frac{\alpha}{3}, \frac{\beta}{3}, \frac{\gamma}{3}\right) \)
В \( \cdot\left(\frac{\alpha}{3},-\frac{\beta}{3}, \frac{\gamma}{3}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{\alpha}{3}, \frac{\beta}{3},-\frac{\gamma}{3}\right) \)
D \( \cdot\left(\frac{\alpha}{3}, \frac{\beta}{3}, \frac{\gamma}{3}\right) \)
Subject: Maths
\[
\mathbf{A}=\left[\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}\right]
\]
The new matrix formed after
interchanging \( 2^{n d} \) and \( 3^{r d} \) rows will be
\( A \)
\[
-\left[\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}\right]
\]
в.
\[
\left[\begin{array}{lll}
4 & 5 & 6 \\
1 & 2 & 3 \\
7 & 8 & 9
\end{array}\right]
\]
c.
\[
-\left[\begin{array}{lll}
1 & 2 & 3 \\
7 & 8 & 9 \\
4 & 5 & 6
\end{array}\right]
\]
D.
\[
\left[\begin{array}{lll}
1 & 2 & 3 \\
7 & 8 & 9 \\
4 & 5 & 6
\end{array}\right]
\]
Subject: Chemistry
Assertion
Addition of \( H C l(a q .) \) to \( H C O O H(a q .) \) decrease the ionization of
HCOOH(aq.).
Reason
Due to common ion effect of \( \boldsymbol{H}^{+} \)
ionization of \( H C O O H \) decrease.
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
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3} \boldsymbol{x}^{5}+\mathbf{1} \mathbf{1} \boldsymbol{x}^{4}+\mathbf{9} \mathbf{0} \boldsymbol{x}^{2}-\mathbf{1} \mathbf{9} \boldsymbol{x}+\mathbf{5} \mathbf{3} \)
is divided by \( x+5, \) then the remainder
is:
A. 100
B . -100
\( c \cdot-102 \)
D. 102
Subject: Physics
A bullet of mass \( 0.01 \mathrm{kg} \) is fired from a gun of mass \( 5 \mathrm{kg} \) with velocity of \( 250 \mathrm{m} / \mathrm{s} \) calculate the speed with which the gun
recoils.
A. \( 0.50 \mathrm{m} / \mathrm{s} \)
B. \( 0.25 \mathrm{m} / \mathrm{s} \)
c. \( 0.05 \mathrm{m} / \mathrm{s} \)
D. \( 0.025 \mathrm{m} / \mathrm{s} \)
Subject: Physics
The electric field in a region is radially
outward with magnitude \( \boldsymbol{E}=\boldsymbol{\alpha} \boldsymbol{r} \)
Calculate the charge contained in a sphere of radius \( R \) centered at the
origin. Calculate the value of the charge
if \( \alpha=100 V m^{-2} \) and \( R=0.30 \mathrm{m} \)
A \( \cdot 3 \times 10^{-7} C \)
В. \( 12 \times 10^{-10} \mathrm{C} \)
c. \( 3 \times 10^{-10} C \)
D. \( 7 \times 10^{-10} C \)
Subject: Chemistry
The rate constant for the forward
reaction \( \boldsymbol{A}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{B}(\boldsymbol{g}) \) is \( 1.5 \times \)
\( 10^{-3} s^{-1} \) at 100 K. If \( 10^{-5} \) moles of \( A \) 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:
A. \( 1.50 \times 10^{4} L \) mol \( ^{-1} s^{-1} \)
B . \( 1.5 \times 10^{11} L \) mol \( ^{-1} s^{-1} \)
c. \( 1.5 \times 10^{10} L m o l^{-1} s^{-1} \)
D. \( 1.5 \times 10^{-11} L \) mol \( ^{-1} s^{-1} \)
Subject: Maths
If all the words, with or without
meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position
of the word QUEEN is.
\( \mathbf{A} \cdot 45^{t h} \)
B. \( 46^{\text {th }} \)
\( \mathbf{c} \cdot 44^{t h} \)
D. \( 47^{t h} \)
Subject: Physics
Th circular arc (in \( x-y \) plane) shown in
figure rotates (about \( z- \) axis ) with a
constant angular velocity \( \omega . \) Time in a
cycle for which there will be induced
emf in the loop is:
A \( \cdot \frac{\pi}{2 \omega} \)
B. \( \frac{\pi}{\omega} \)
c. \( \frac{2 \pi}{3 \omega} \)
D. \( \frac{3 \pi}{2 \omega} \)
Subject: Chemistry
Fluorobenzene \( \left(C_{6} H_{5} F\right) \) can be
synthesised in the lab:
A. by heating phenol with HF and KF
B. from aniline by diazotization followed by heating the diazonium salt with \( H B F_{4} \)
C. by direct fluorination of benzene with \( F_{2} \) gas
D. by reacting bromo benzene with NaF solution
Subject: Physics
A tester is used to check the conduction
of electricity through two liquids, labeled \( A \) and \( B \). It is found that the
bulb of the tester glows brightly for
liquid \( \boldsymbol{A} \) while it glows very dimly for liquid \( B \). You would conclude that:
A. liquid \( A \) is a better conductor than liquid \( B \)
B. liquid \( B \) is a better conductor than liquid \( A \)
c. both liquids are equally conducting
D. conducting properties of liquid cannot be compared in this manner
Subject: Physics
A uniform rod of mass \( 6 M \) and length
\( 6 l \) is bent to make an equilateral
hexagon. Its mutual inductance about an axis passing through the centre of mass and perpendicular to the plane of hexagon is
\( A \cdot 5 m l^{2} \)
В \( .6 m l^{2} \)
\( \mathrm{c} \cdot 4 m l^{2} \)
\( \mathbf{D} \cdot 12 m l^{2} \)
Subject: Maths
The differential equation, which represents the family if plane curves
\( \boldsymbol{y}=\boldsymbol{e}^{c \boldsymbol{x}}, \) is
A \( \cdot y^{\prime}=c y \)
B. \( x y^{\prime}-\log y=0 \)
c. \( x \log y=y y^{\prime} \)
D. ylogy = \( x y^{\prime} \)
Subject: Maths
The area bounded by \( y=\cos x, y= \)
\( \boldsymbol{x}+\mathbf{1}, \boldsymbol{y}=\mathbf{0} \) is
A \( \cdot \frac{3}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{5}{2} \)
Subject: Physics
The unit vector perpendicular to the plane containing \( \overrightarrow{\boldsymbol{A}}, \overrightarrow{\boldsymbol{B}} \) such that \( \overrightarrow{\boldsymbol{A}}= \)
\( 4 \hat{i}-\hat{j}-\hat{k} \) and \( \vec{B}=4 \hat{i}+\hat{j}-4 \hat{k} \) is:
\( \frac{5 \hat{i}-5 \hat{j}+5 \hat{k}}{\sqrt{3}} \)
B. \( \frac{5 \hat{i}+12 \hat{j}+8 \hat{k}}{\sqrt{233}} \)
c. \( \frac{\hat{i}+3 \hat{j}+\hat{k}}{11} \)
D. \( 5 \hat{i}-5 \hat{j}+5 \hat{k} \)
Subject: Physics
A car travels along a circular path of radius \( \left(\frac{50}{\pi}\right) \mathrm{m} \) with a speed of \( 10 \mathrm{m} / \mathrm{s} \)
Then what is its displacement after 17.5 seconds.
\( A \cdot \frac{50 \sqrt{2}}{\pi} \)
B. \( \frac{50 \sqrt{3}}{\pi} \)
c. \( \frac{100 \sqrt{2}}{\pi} \)
D. 175
Subject: Physics
A toy cart is tied to the end of an
unstretched string of length 'L'. When revolved, the toy card moves in
horizontal circle with radius '2 \( l \) ' and
time period \( T . \) If it is speeded until it moves in horizontal circle of radius '3 \( l^{\prime} \)
with period \( T_{1}, \) relation between \( T \) and
\( T_{1} \) is (Hooke's law is obeyed)
\( ^{\mathbf{A}} \cdot_{T_{1}}=\frac{2}{\sqrt{3}} T \)
в. \( T_{1}=\sqrt{\frac{3}{2}} T \)
\( ^{\mathbf{c}} \cdot_{T_{1}}=\sqrt{\frac{2}{3}} T \)
\( T_{1}=\frac{\sqrt{3}}{2} T \)
Subject: Chemistry
A \( 0.5 g \) sample of \( K H_{2} P O_{4} \) is titrated with \( 0.1 M \) NaOH.The volume of base
required to do this is \( 25.0 m l \) The
reaction is represented as:
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-}+\boldsymbol{H}_{2} \boldsymbol{O} \)
The percentage purity of \( K H_{2} P O_{4} \) is \( (\boldsymbol{K}=\mathbf{3 9}, \boldsymbol{P}=\mathbf{3 1}) \)
A . \( 68 \% \)
B. 34\%
c. \( 85 \% \)
D. 51\%
Subject: Chemistry
What is the structural formula of
lithium tetrahydrido aluminate?
\( \mathbf{A} \cdot A l\left[L I H_{4}\right] \)
B. \( A l_{2}\left[L i H_{4}\right]_{3} \)
c. \( L i\left[A l H_{4}\right] \)
D. \( L i\left[A l H_{4}\right]_{2} \)
Subject: Chemistry
For two ionic solids \( C a O \) and \( K I \) which
of the following statement(s) is false?
A. Lattice enthalpy of \( C a O \) is much higher than that of \( K I \)
B. \( C a O \) has high melting point
c. \( K I \) has low melting point
D. \( C a O \) is not soluble in benzene
Subject: Physics
An electron is moving in an orbit of a hydrogen atom from which there can be
a maximum of six transitions. An
electron is moving in an orbit of another
hydrogen atom from which there can be
a maximum of three transitions. The
ratio of the velocity of the electron in these two orbits is
\( \mathbf{A} \cdot \frac{1}{2} \)
B. \( \frac{2}{1} \)
\( \mathbf{c} \cdot \underline{5} \)
D. \( \frac{3}{4} \)
Subject: Maths
Write the sum of first five terms of the
following Arithmetic Progressions where, the common difference \( d \) and the
first term \( a \) are given,
\( \boldsymbol{a}=\mathbf{2}, \boldsymbol{d}=\mathbf{2 . 5} \)
A .32
B. 33
\( c .34 \)
D. 35
Subject: Physics
A radioactive substance X decays into another radioactive substance Y.

Initially, only \( X \) was present. \( \lambda_{x} \) and \( \lambda_{y} \) are the disintegration constants of \( \mathbf{X} \)
and Y. \( N_{y} \) will be maximum when \( \left(N_{y} \) is \right.
atoms of \( Y \) )
A \( \cdot \frac{N_{y}}{N_{x}-N_{y}}=\frac{\lambda_{y}}{\lambda_{x}-\lambda_{y}} \)
В. \( \frac{N_{x}}{N_{x}-N_{y}}=\frac{\lambda_{x}}{\lambda_{x}-\lambda_{y}} \)
c. \( \lambda_{y} N_{y}=\lambda_{x} N_{x} \)
D. \( \lambda_{y} N_{x}=\lambda_{x} N_{y} \)
Subject: Physics
Two parallel wires are suspended in vacuum. When the potential difference between the wires is 30 V then the
charge on the wires is \( 140 \mu C \). The capacitance of the system of wires will be:
A \( .4 .66 \mu F \)
в. \( 5 \mu F \)
c. \( 10.21 \mu F \)
\( \mathbf{D} \cdot 50 \mu F \)
Subject: Physics
The torque equation for a physical
pendulum making an angle \( \theta \) with the vertical is given by
A \( \cdot d^{2} \theta / d t^{2}=-(m g L / I) \cos \theta \)
B . \( d^{2} \theta / d t^{2}=-(m g L / I) \sin \theta \)
C \( \cdot d^{2} \theta / d t^{2}=-(m g L / 2 I) \sin \theta \)
D \( \cdot d^{2} \theta / d t^{2}=-(m g L / 2 I) \cos \theta \)
Subject: Maths
If \( \boldsymbol{A}=\left(\begin{array}{cc}1 & -2 \\ -\mathbf{3} & 4\end{array}\right) \) and \( \boldsymbol{A}+\boldsymbol{B}=\boldsymbol{O}, \) then \( \mathbf{B} \) is
A \( \cdot\left(\begin{array}{cc}1 & -2 \\ -3 & 4\end{array}\right) \)
B. \( \left(\begin{array}{c}-1 \\ 3\end{array}\right) \)
c. \( \left(\begin{array}{cc}-1 & -2 \\ -3-4\end{array}\right) \)
D. \( \left(\begin{array}{c}1 \\ 0 \\ 0\end{array}\right) \)
Subject: Physics
A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)
This question has multiple correct options
A. The emf induced in the loop is zero if the current is constant
B. The emf induced in the loop is finite if the current is constant
c. The emf induced in the loop is zero if the current decreases at a steady rate.
D. The emf induced in the loop is finite if the current decreases at a steady rate
Subject: Maths
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be such that
\( |\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})|^{2} \leq|\boldsymbol{x}-\boldsymbol{y}|^{3} \) for all \( \boldsymbol{x}, \boldsymbol{y} \in \)
\( R \) then the value of \( f^{\prime}(x) \) is
A \( \cdot f(x) \)
B. constant possibly different from zero
c. \( (f(x))^{2} \)
D.
Subject: Maths
It is not possible to construct a triangle
with which of the following sides?
A. \( 8.3 \mathrm{cm}, 3.4 \mathrm{cm}, 6.1 \mathrm{cm} \)
B. \( 5.4 \mathrm{cm}, 2.3 \mathrm{cm}, 3.1 \mathrm{cm} \)
c. \( 6 \mathrm{cm}, 7 \mathrm{cm}, 10 \mathrm{cm} \)
D. \( 3 \mathrm{cm}, 5 \mathrm{cm}, 5 \mathrm{cm} \)
Subject: Physics
A physical quantity is measured and the result is expressed as \( n u \) where \( u \) is
the unit used and \( n \) is the numerical
value. If the result is expressed in
various units then
A \( . n \propto \) size of \( u \)
В . \( n \propto u^{2} \)
c. \( n \propto \sqrt{u} \)
D. \( n \propto \frac{1}{u} \)
Subject: Chemistry
The empirical formula of a compound containing 47.9 \% potassium, 5.5 \% beryllium and \( 46.6 \% \) fluorine by mass is
[At. weight of \( \mathrm{Be}=9 ; \mathrm{F}=19 ; \mathrm{K}=39] \)
A. \( K_{2} B e F_{2} \)
в. \( K B e F_{4} \)
\( \mathrm{c} \cdot K_{2} B e_{2} F_{4} \)
D. \( K_{2} B e F_{4} \)
Subject: Biology
In which of the following situations, is there a risk factor for children of
incurring erythroblastosis foetalis?
A. Mother is Rh-ve and father is Rh-ve
B. Mother is Rh-ve and father is Rh +ve
c. Mother is Rh tve and father is Rh +ve
D. Mother is Rh \( + \) ve and father is Rh-ve
Subject: Physics
A helicopter is flying south with a speed
of \( 50 \mathrm{kmh}^{-1} \). A train is moving with the
same speed towards east. The relative
velocity of the helicopter as seen by the passengers in the train will be \( 50 \sqrt{2} \mathrm{kmh}^{-1} \) towards
A. northwest
B. southwest
c. northeast
D. southeast
Subject: Physics
A plane electromagnetic wave in a non magnetic dielectric medium is given by \( \overline{\boldsymbol{E}}=\overline{\boldsymbol{E}}_{0}\left(\mathbf{4} \times \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{x}-\mathbf{5 0} \boldsymbol{t}\right) \) with
distance being in meter and time in seconds. The dielectric constant of the
medium is:
A . 5.8
B. 2.4
c. 1.6
D. 3.5
Subject: Maths
The set of all real numbers satisfying \( e^{\left(\frac{1}{x}-1\right)}<1 \)
A. \( (0, \infty) \)
)
B . \( (-\infty, 0) \cup(1, \infty) \)
\( c \cdot(-\infty, \infty) \)
D. (0,1)
Subject: Physics
A particle of mass \( m \) is allowed to
oscillate on a smooth parabola: \( \boldsymbol{x}^{2}= \)
\( 4 a y, a>1 \) as shown in the figure. The
angular frequency \( (\omega) \) of small
oscillations is
A \( \cdot \omega=\sqrt{\frac{g}{4 a}} \)
B. \( \omega=\sqrt{\frac{g}{2 a}} \)
c. \( \omega=\sqrt{\frac{2 g}{a}} \)
\( \omega=\sqrt{\frac{g}{a}} \)
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}) \) be defined on \( [-2,2], \) and is
given by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}-1,-2 \leq x \leq 0 \\ x-1,0 \leq x \leq 2\end{array} \text { and } g(x)=\right. \)
\( \boldsymbol{f}(|\boldsymbol{x}|)+|\boldsymbol{f}(\boldsymbol{x})|, \) then find \( \boldsymbol{g}(\boldsymbol{x}) \)