AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A uniform circular loop of radius \( a \) and resistance \( R \) is placed perpendicular to
a uniform magnetic field \( B \). One half of
the loop is rotated about the diameter
with angular velocity \( \omega \) as shown in
figure. Then, the current in the loop is:
This question has multiple correct options
A. zero, when \( \theta \) is zer
B. \( \frac{\pi a^{2} B \omega}{2 R}, \) when \( \theta \) is zero
c. zero, when \( \theta=\pi / 2 \)
\( \stackrel{\pi a^{2} B \omega}{2 R}, \) when \( \theta=\frac{\pi}{2} \)
Subject: Maths
f \( a \neq b \neq c \) Then one value of \( x \) which
satisfies the equation \( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{x}-\boldsymbol{a} & \boldsymbol{x}-\boldsymbol{b} \\ \boldsymbol{x}+\boldsymbol{a} & \boldsymbol{0} & \boldsymbol{x}-\boldsymbol{c} \\ \boldsymbol{x}+\boldsymbol{b} & \boldsymbol{x}+\boldsymbol{c} & \boldsymbol{0}\end{array}\right|=0 \) is given by
A \( \cdot x=a \)
B. \( x=b \)
\( c \cdot x=c \)
D. x =
Subject: Chemistry
\( \ln H_{3} P O_{4} \) which of the following is true?
This question has multiple correct options
A \( \cdot K_{a}=K_{a_{1}} \times K_{a_{2}} \times K_{a_{3}} \)
B . \( K_{a_{1}}<K_{a_{2}}<K_{a_{3}} \)
C \( \cdot K_{a_{1}}>K_{a_{2}}>K_{a_{3}} \)
D. \( K_{a_{1}}=K_{a_{2}}=K_{a_{3}} \)
Subject: Chemistry
Atoms of eight elements \( A, B, C, D, E, F \) G and H have the same number of
electronic shells but different number
of electrons in their outermost shell. It
was found that elements \( A \) and \( G \) combine to form an ionic compound which can also be extracted from sea
water. This compound is added in a small amount to almost all vegetable dishes during cooking. Oxides of elements A and B are basic in nature
while those of \( \mathrm{E} \) and \( \mathrm{F} \) are acidic. The
oxide of \( \mathrm{D} \) is almost neutral. Based on
the above information answer the
following question.
What would be the nature of compound formed by a combination of elements B
and F?
Subject: Chemistry
The lanthanide element that has the
electronic configuration \( [\boldsymbol{X} \boldsymbol{e}] \boldsymbol{4} \boldsymbol{f}^{7} \boldsymbol{5} \boldsymbol{d}^{1} \boldsymbol{6} \boldsymbol{s}^{2} \)
is:
A. Lutetium
B. Terbium
c. Ytterbium
D. Gadolinium
Subject: Maths
An unbiased normal coin is tossed \( n \)
times. Let \( E_{1}: \) event that both heads and
tails are present in \( n \) tosses. \( E_{2} \) :event that the coin shows up heads at most
once. The value of \( n \) for which \( E_{1} \) and \( E_{2} \)
are independent is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Physics
A particle of mass \( 4 m \) initially at rest
explodes into three fragments. If two fragments each of mass \( m \) move mutually perpendicular to each other
with speed \( v, \) then the total energy released in the process of explosion will
be
\( ^{\mathrm{A}} \cdot \frac{3}{2}^{m v^{2}} \)
B. \( \frac{2}{3} m v^{2} \)
\( \mathrm{c} \cdot 4 m v^{2} \)
D. \( v^{2} \)
Subject: Physics
A single slit Fraunhoffer diffraction pattern is formed with white light. For what wavelength of light the third secondary maximum in the diffraction pattern coincides with the second
secondary maximum in the pattern for red light of wavelength 6500 A?
B . \( 4642 A^{\circ} \)
c. \( 4100 A^{\circ} \)
D. \( 4400 A^{\circ} \)
Subject: Chemistry
When 1 mole of \( N_{2} \) and 1 mole of \( H_{2} \) is
enclosed in \( 3 L \) vessel and the reaction
is allowed to attain equilibrium .it is found that at equilibrium there is 'x'
mole of \( \boldsymbol{H}_{2} \) The number of moles of
\( N H_{3} \) formed would be?
\( A \cdot \frac{2 x}{3} \)
B. \( \frac{2(1+x)}{3} \)
c. \( \frac{2(1-x)}{3} \)
D. \( \frac{(1+x)}{2} \)
Subject: Physics
A resistor of \( 6 k \Omega \) with tolerance \( 10 \% \)
and another of \( 4 k \Omega \) with tolerance \( 10 \% \)
are connected in series.The tolerance of
combination is about
\( A \cdot 5 \% \)
B. \( 10 \% \)
\( c \cdot 12 \% \)
D. \( 15 \% \)
Subject: Chemistry
Assertion
Addition of \( \boldsymbol{H} \boldsymbol{C l} \) to \( \boldsymbol{3}, \boldsymbol{3}, \boldsymbol{3} \) -trifuoro-1
propene gives 1 -chloro-3, 3,3 -trifluoro
propane as major product.
Reason
Addition follow Markownikoff's rule.
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
\( f(x)=\left\{\begin{array}{lc}\frac{x^{2}}{a} \quad ; & 0 \leq x<1 \\ -1 & 1 \leq x<\sqrt{2} \\ \frac{2 b^{2}-4 b}{x^{2}} & ; \sqrt{2} \leq x<\infty\end{array}\right. \)
then find the value of \( a \) and \( b \) if \( f(x) \) is
continuous in \( [\mathbf{0}, \infty) . \) Find \( \boldsymbol{a}+\boldsymbol{b} \)
Subject: Maths
If \( f(x)=x^{4}-2 x^{3}-a x+b \) is a
polynomial such that when it is divided by \( x-1 \) and \( x+1 \),the remainders are
respectively 45 and \( 19 . \) Determine the remainder when \( f(x) \) is divided by \( (x- \)
2
Subject: Biology
Match the columns and choose the
correct combination.
Growth
Regulator Action
\( (a) \)
Abscisic
acid
(1)
Delays leaf
abscission
\( (b) \)
Ethylene \( \quad(2) \quad \begin{array}{l}\text { Inhibits seed } \\ \text { germination }\end{array} \)
\( (c) \)
cytokinin
(3)\( \quad \) Herbicide
\( (d) \)
Auxin \( \quad(4) \quad \begin{array}{l}\text { Hastens fruit } \\ \text { ripening }\end{array} \)
A \( . a-2, b-4, c-1, d-3 \)
в. \( a-1, b-2, c-3, d-4 \)
c. \( a-2, b-3, c-4, d-1 \)
D. \( a-2, b-1, c-3, d-4 \)
E . \( a-3, b-4, c-1, d-2 \)
Subject: Maths
Reshma wishes to mix two types of food \( P \) and \( Q \) in such a way that the
vitamin contents of the mixture contain
at least 8 units of vitamin \( A \) and
11 units of vitamin B. Food \( P \) costs
Rs. \( 60 / k g \) and Food \( Q \operatorname{costs} R s .80 / k g \)
Food \( P \) contains 3 units/kg of Vitamin
\( A \) and 5 units / kg of Vitamin \( B \) while
food \( Q \) contains 4 units/kg of Vitamin
\( A \) and 2 units / kg of vitamin \( B \) Determine the minimum cost of the
mixture.
Subject: Physics
For a transistor, the current
amplification factor is \( 0.8 . \) The transistor is connected in
common emitter configuration, the change in collector current when the
base current changes by \( 6 m A \) is
\( \mathbf{A} \cdot 6 m A \)
в. \( 4.8 \mathrm{mA} \)
c. 24 m
D. \( 8 m A \)
Subject: Maths
Let \( \boldsymbol{f}:\{\mathbf{1}, \mathbf{3}, \mathbf{4}\} \rightarrow\{\mathbf{1}, \mathbf{2}, \mathbf{5}\} \) and \( \boldsymbol{g} \)
\{1,2,5\}\( \rightarrow\{1,3\} \)
given by \( \boldsymbol{f}=\{(\mathbf{1}, \mathbf{2}),(\mathbf{3}, \mathbf{5}),(\mathbf{4}, \mathbf{1})\} \) and
\( \boldsymbol{g}=\{(1, \mathbf{3}),(\mathbf{2}, \mathbf{3}),(\mathbf{5}, \mathbf{1})\} \) write down
gof
Subject: Physics
If the time period of a pendulum is \( 25 s \)
What is the frequency of the pendulum?
A \( \cdot 4 \times 10^{-2} \mathrm{Hz} \)
в. \( 4 \times 10^{-1} \mathrm{Hz} \)
c. \( 25 \times 10^{-2} \mathrm{Hz} \)
D. \( 2 \times 10^{-2} \mathrm{Hz} \)
Subject: Physics
A disc of radius \( R \) is rolling without sliding on a horizontal surface with a velocity of center of mass \( v \) and angular
velocity \( \omega \) in a uniform magnetic field \( B \) which is perpendicular to the plane of
the disc as shown in figure. \( O \) is the
center of the disc and \( P, Q, R \) and \( S \) are
the four points on the disc. Which of the
following statements is true?
This question has multiple correct options
A. Due to translation, induced emf across \( P S=B v r \)
B. Due to rotation, induced emf across \( Q S=0 \)
c. Due to translation, induced emf across \( R O=0 \)
D. Due to rotation, induced emf across \( O Q=B v r \)
Subject: Physics
f the brass wire were replaced by
another brass wire of diameter 1 m \( m \)
where should the mass be suspended
so that \( A B \) would remain horizontal?
\( \mathbf{A} \cdot x=0.06 m \)
В . \( x=0.12 \) т
c. \( x=0.24 m \)
D. \( x=0.48 m \)
Subject: Maths
ff \( \boldsymbol{y}=\frac{a}{2}\left(e^{\frac{x}{a}}+e^{\frac{-x}{a}}\right) \) and \( \frac{d^{2} y}{d x^{2}}=y, \) then a
equals
A .
в.
\( c \cdot \frac{1}{3} \)
D. \( \frac{1}{\sqrt{2}} \)
Subject: Chemistry
For the following three reactions \( a, b, c \) equilibrium constants are given:
1. \( \boldsymbol{C O}(\mathbf{g})+\mathbf{H}_{2} \mathbf{O}(\mathbf{g}) \rightleftharpoons \mathbf{C} \mathbf{O}_{2}(\mathbf{g})+\mathbf{H}_{2}(\mathbf{g}) \)
\( ; \mathbf{K}_{\mathbf{1}} \)
2. \( \mathbf{C H}_{4}(\mathbf{g})+\mathbf{H}_{2} \mathbf{O}(\mathbf{g}) \rightleftharpoons \mathbf{C O}(\mathbf{g})+ \)
\( \mathbf{3} \mathbf{H}_{\mathbf{2}}(\mathbf{g}) ; \mathbf{K}_{\mathbf{2}} \)
3. \( \mathbf{C H}_{4}(\mathbf{g})+\mathbf{2} \mathbf{H}_{\mathbf{2}} \mathbf{O}(\mathbf{g}) \rightleftharpoons \mathbf{C} \mathbf{O}_{\mathbf{2}}(\mathbf{g})+ \)
\( \mathbf{4} \mathbf{H}_{\mathbf{2}}(\mathbf{g}) ; \mathbf{K}_{\mathbf{3}} \)
Which of the following relations is
correct?
A \( \cdot \mathrm{K}_{3}=\mathrm{K}_{1} \mathrm{K}_{2} \)
в. \( \mathrm{K}_{3} \cdot \mathrm{K}_{2}^{3}=\mathrm{K}_{1}^{2} \)
c. \( \mathrm{K}_{1} \sqrt{\mathrm{K}_{2}}=\mathrm{K}_{3} \)
D. \( \mathrm{K}_{2} \mathrm{K}_{3}=\mathrm{K}_{1} \)
Subject: Maths
PQ and PR are the tangents to a circle with centre \( O . \) If \( \angle P=\frac{4}{5} \angle O . \) Find
\( \angle Q P R \)
A \( \cdot 100^{\circ} \)
B. \( 180^{\circ} \)
\( c .80^{\circ} \)
D. None of these
Subject: Maths
\( \operatorname{Given} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{6} \\ -\mathbf{2} & -\mathbf{8}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{1 6}\end{array}\right] \)
find the matrix \( \boldsymbol{X} \) such that \( \boldsymbol{X} \boldsymbol{A}=\boldsymbol{B} \)
A \( \cdot\left[-\frac{4}{3}-3\right] \)
в. \( \left[\frac{4}{3} 3\right] \)
\( ^{\mathbf{c}} \cdot\left[\begin{array}{ll}\frac{4}{3} & -3\end{array}\right] \)
D. \( \left[-\frac{4}{3} \quad 3\right] \)
Subject: Physics
A cell can be balanced against \( 110 \mathrm{cm} \) and \( 100 \mathrm{cm} \) of potentiometer wire, respectively with and without being short circuited through a resistance of 10\Omega. Its internal resistance is
A . \( 1 \Omega \)
B. \( 0.5 \Omega \)
c. \( 2 \Omega \)
D. none
Subject: Physics
Fill in the blank.
The following truth table with \( A \) and \( B \)
as inputs is for \( _{-}- \) gate.
\( \begin{array}{lll}\text { A } & \text { B } & \text { Output } \\ & & \\ 1 & \text { 0 } & 1 \\ \text { 1 } & 1 & \text { 0 } \\ \text { 0 } & 1 & 1 \\ \text { 0 } & \text { 0 } & \text { 0 }\end{array} \)
A. AND
B. OR
c. хок
D. NOR
Subject: Chemistry
The reaction(s) which (do) not occur in
the reduction zone in the extraction of
iron from haematite ore is (are):-
This question has multiple correct options
A. \( F e_{2} O_{3}+C O \rightarrow 2 F e O+C O_{2} \)
в. \( F e O+C O \rightarrow F e+C O_{2} \)
\( \mathbf{c} \cdot F e_{2} O_{3}+3 C \rightarrow 2 F e+3 C O \)
D. \( C a O+S i O_{2} \rightarrow C a S i O_{3} \)
Subject: Maths
How many different words can be
fanned by jumbling the letters of the word MISSISSIPPI in which no two 's' are
adjacent
A \( \cdot 7 \cdot^{6} C_{2} \cdot^{8} C_{4} \)
B . \( 6 \cdot 7 \cdot^{8} C_{4} \)
\( \mathbf{c} \cdot 6 \cdot 8 \cdot^{7} C_{4} \)
D. \( 8 \cdot^{6} C_{4} \cdot^{7} C_{4} \)
Subject: Maths
The line \( b x+a y=3 a b \) cuts the
coordinate axes at \( A \) and \( B \), then
centroid of \( \triangle O A B \) is -
\( \mathbf{A} \cdot(b, a) \)
B \( \cdot(a, b) \)
c. \( \left(\frac{a}{3}, \frac{b}{3}\right) \)
D \cdot \( (3 a, 3 b) \)
Subject: Maths
\( \operatorname{Let} f(x)=\frac{x^{2}-4}{x^{2}+4} \) for \( |x|>2, \) then the
function \( \boldsymbol{f}:(-\infty,-2) \cup[\mathbf{2}, \infty) \rightarrow \)
(-1,1) is
A. One-one into
B. One-one onto
c. Many one into
D. Many one onto
Subject: Chemistry
Strongest hydrogen bond is present in:
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( C H_{4} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C H O H \)
D. \( \left(C H_{3}\right)_{3} C O H \)
Subject: Chemistry
Which of the following which has the
highest molar conductivity?
\( \mathbf{A} \cdot\left[C o\left(N H_{3}\right)_{5} C l\right] B r \)
в. \( \left[C o\left(N H_{3}\right)_{5} C l\right] S O_{4} \)
\( \mathbf{c} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right] N O_{2} \)
D. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l\right] \cdot 2 H_{2} O \)
Subject: Physics
A person wear normal spectacles in which the distance of glasses and eyes is approximately \( 2 \mathrm{cm}, \) then power required is \( -5 D . \) If he wears contact
lens, then the required power is?
A . -5.2 D
B. -4.54 D
c. \( +5.2 \mathrm{D} \)
D. +4.7 D
Subject: Chemistry
Which of the following is the least volatile?
A \( \cdot C H_{3}-C H_{2}-C H_{2}-F \)
в. \( C H_{3}-C H_{2}-C H_{2}-C l \)
c. \( C H_{3} C H-C H \)
D. \( C H_{3}-C H_{2}-C H_{2}-B r \)
Subject: Physics
If we take some water at \( 0^{\circ} \mathrm{C} \) and start
heating it,we find that in the
temperature range \( 0^{\circ} \mathrm{C} \) to \( 4^{\circ} \mathrm{C} \)
A. It expands on heating
B. It contracts on heating
c. Both
D. None
Subject: Physics
Mark the option which correctly
differentiates between solar and lunar
eclipse:
A. When the moon comes in between the earth and the
sun and if all the three are in same straight line, solar eclipse occurs. And when the earth comes in between the sun and the moon and if all the three are in same straight line, lunar eclipse occurs.
B. When the earth comes in between the sun and the
moon and if all the three are in same straight line, solar eclipse occurs. And, when the earth comes in between the sun and the moon and if all the three are
in same straight line, lunar eclipse occurs.
C. Both A and B are wrong.
D. Sun's shadow causes solar eclipse and moon's shadow causes lunar eclipse.
Subject: Chemistry
IUPAC name of \( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{C H}= \)
\( \boldsymbol{C H}-\boldsymbol{C H O} \)
A. 4,4,4 -trimethyl but- - -en- -1-al
B. 4, 4-Dimethylpent-2-enal
c. 2, 2-dimethylpent-3- 3n-4-al
D. 3-tert. butyl prop-2-en-1-al
Subject: Chemistry
For the redox reaction
\( M n O_{4}^{\ominus}+C_{2} O_{4}^{2-}+H^{\oplus} \longrightarrow M n^{2+}+ \)
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
the correct coefficients of the reactions
for the balanced reaction are:
\( \begin{array}{lll}\text { A. } M n O_{4}^{\ominus} & C_{2} O_{4}^{2-} & H^{\oplus}\end{array} \)
\( 2 \quad 5 \quad 16 \)
B. \( M n O_{4}^{\ominus} \quad C_{2} O_{4}^{2-} \quad H^{\oplus} \)
\( 16 \quad 5 \quad 2 \)
\( \begin{array}{lll}\text { c. } M n O_{4}^{\ominus} & C_{2} O_{4}^{2-} & H^{\oplus}\end{array} \)
16
D. \( M n O_{4}^{\ominus} \quad C_{2} O_{4}^{2-} \quad H^{\oplus} \)
Subject: Maths
\( \begin{array}{lllll}\mathbf{0} & & \mathbf{c o s} \boldsymbol{\alpha} & \mathbf{c o s} & \boldsymbol{\beta} \\ \mathbf{c o s} & \boldsymbol{\alpha} & \mathbf{0} & \mathbf{c o s} & \gamma \\ \mathbf{c o s} & \boldsymbol{\beta} & \mathbf{c o s} \boldsymbol{\gamma} & \mathbf{0} & \end{array} \mid= \)
A \( \cdot \cos \alpha+\cos \beta+\cos \gamma \)
\( \mathbf{B} \cdot \cos \alpha \cos \beta \cos \gamma \)
c. \( 2 \cos \alpha \cos \beta \cos \gamma \)
D. \( 2 \sum \cos \alpha \cos \beta \)
Subject: Chemistry
Match List I with List II and select the
correct answer using the codes given
below the lists-
List List II
(1) Muscle contraction
(i) Zinc
(2) Blue-green algae
(ii) Cobalt
(3) Carboxypeptidase
(iii) Calcium
(4) Cyanocobalamine
(iv) Molybdenum
A. (1)-iv; (2)-iii; (3)-i; (4)-ii
B. (1)-iii; (2)-iv; (3)-ii; (4)-
c. (1)-iv; (2)-iii; (3)-ii; (4)-ii
D. (1)-iii; (2)-iv; (3)-i; (4)- -
Subject: Maths
\( A B C \) is an isosceles triangle inscribed in a circle of radius \( r . \) If \( A B=A C \) and \( h \)
is the altitude from \( A \) to \( B C, \) then evaluate \( \lim _{h \rightarrow 0} \frac{\Delta}{P^{3}}, \) where \( \Delta \) is area of the triangle and \( P \) its perimeter.
A \( \cdot \frac{1}{128 r} \)
в. \( \frac{1}{64 r} \)
c. \( \frac{1}{32 r} \)
D. \( \frac{1}{256 r} \)
Subject: Chemistry
In a hydrogen atom, an electronjumps from the second orbit to the first orbit
Find out
The wavelength of the radiation is :
A \( \cdot 1.325 \times 10^{3} \mathrm{A} \)
в. \( 2.430 \times 10^{3} \) А
c. \( 1.215 \times 10^{3} \) A
D. \( 2.255 \times 10^{3} \) A
Subject: Physics
Assertion
Isotopes of an element can be separated by using a mass spectrometer.
Reason
Separation of isotopes is possible because of difference in electron
number of isotopes.
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
Identify the correct statement of Work-
Energy Theorem:
A. Work done by all the forces on a particle to displace it is equal to its change in kinetic energy.
B. Work done by all the forces on a particle is equal to its change in mechanical energy
C. Work done by all the forces acting on a particle is equal to change in its potential energy.
D. Work done by a force on a particle is equal to change in its kinetic energy.
Subject: Physics
Four electric charges \( +\boldsymbol{q},+\boldsymbol{q},-\boldsymbol{q} \) and
\( -q \) are placed at the corners of a square
of side \( 2 L \) (see figure). The electric
potential at point \( A, \) midway between
the two charges \( +\boldsymbol{q} \) and \( +\boldsymbol{q} \), is
A \( \cdot \frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{L}(1+\sqrt{5}) \)
в. \( \frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{L}\left(1+\frac{1}{\sqrt{5}}\right) \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{L}\left(1-\frac{1}{\sqrt{5}}\right) \)
D. zero
Subject: Physics
Magnetic field at the center (at nucleus) of the hydrogen-like atoms (atomic number \( =Z \) ) due to the motion
of electron in \( n^{t h} \) orbit is proportional to
A \( \cdot \frac{n^{3}}{z^{5}} \)
B. \( \frac{n^{4}}{z} \)
c. \( \frac{z^{2}}{n^{3}} \)
D. \( \frac{z^{3}}{n^{5}} \)
Subject: Chemistry
List- -
List- II
A) \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
-3,+5 oxidation state
B) \( N H_{4} N O_{3} \)
\( \frac{-1}{3} \) oxidation state
C) \( N_{3} H \)
+5 oxidation state
D) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)
+3 oxidation state
5)
oxidation state
The correct match is :
A. A-3, B-1, C-2, D-4
B. A-5, B-2, C-3, D-4
c. A-1, B-2, C-3, D-4
D. A-4, B-3, C-2, D-5
Subject: Maths
if \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \mathbf{0} \\ \boldsymbol{0} & \boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{b} & \boldsymbol{0} & \boldsymbol{a}\end{array}\right|=\mathbf{0} \) then
A. \( a \) is a cube root of 1
B. \( b \) is a cube root of 1
c. \( \frac{a}{b} \) is a cube root of 1
D. \( \frac{a}{b} \) is a cube root of -1
Subject: Physics
Two boys are standing at the ends \( A \) and B of a ground, where \( A B=a \). The boy at \( B \) starts running in a direction perpendicular to AB with velocity \( v_{1} \). The boy at A starts running simultaneously with velocity \( v \) and catches the other boy in a time \( t, \) where \( t \) is
A. \( \frac{a}{\sqrt{v^{2}+v_{1}^{2}}} \)
в. \( \sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}} \)
c. \( \frac{a}{\left(v-v_{1}\right)} \)
D. \( \frac{a}{\left(v+v_{1}\right)} \)
Subject: Physics
In classical physics the force \( F \) acting on a body is assumed to be the product of mass \( \mathrm{m} \) and acceleration a.lf \( \mathrm{m}=2.31 \)
\( \mathrm{kg} \) and acceleration is \( 3.123 \mathrm{m} / \mathrm{s}^{2} \), then taking into account significant figures the force \( F \) should be reported as
A. \( 7.21413 \mathrm{N} \)
B. 7.2141
c. 7.214 N
D. 7.21 N
Subject: Maths
The internal bisectors of \( \angle Q \) and \( \angle R \) of
\( \triangle P Q R \) meet at \( C . \) If \( \angle P=70^{\circ}, \) then
\( \angle P=70^{\circ} \) is
A \( \cdot 110^{\circ} \)
B . \( 125^{\circ} \)
\( \mathbf{c} \cdot 130^{\circ} \)
D. \( 140^{\circ} \)
Subject: Physics
A uniform capillary tube of length \( l \) and
inner radius \( r \) with its upper end sealed
is submerged vertically into water. The
outside pressure is \( p_{0} \) and surface
tension of water is \( \gamma \). When a length \( x \) of
the capillary is submerged into water, it is found that water levels inside and
outside the capillary coincide, the value
of \( x \) is
A.
\[
\frac{l}{\left(l+\frac{p_{0} r}{4 \gamma}\right)}
\]
B. \( l\left(l-\frac{p_{0} r}{4 \gamma}\right) \)
\( ^{\mathbf{c}} \cdot_{l}\left(l-\frac{p_{0} r}{2 \gamma}\right) \)
D.
\[
\left(l+\frac{p_{0} r}{2 \gamma}\right)
\]
Subject: Physics
Two Nicole prisms are kept perpendicular. One of them is illuminated with a light intensity
(natural) \( I_{o} \). Two more nicol prisms are introduced in between symmetrically. Find the light intensity emitted from the last nicol prism.
A \( \cdot \frac{27 I_{0}}{64} \)
в. \( \frac{27 I_{o}}{128_{o}} \)
c. \( _{9} \frac{I_{o}}{32} \)
D. \( \frac{9 I_{0}}{64} \)
Subject: Maths
On approximately what percent of the
days was the 2 p.m temperature above
\( 40^{\circ} F \) but less than \( 70^{\circ} F ? \)
a
A. Approx. \( 50 \% \)
B. Approx. \( 70 \% \)
c. Approx. \( 60 \% \)
D. None of these
Subject: Physics
In the nuclear reaction
\( \frac{14}{7} \boldsymbol{N}+_{2}^{4} \boldsymbol{H} e \rightarrow_{8}^{17} \boldsymbol{O}+\ldots \ldots \ldots \ldots \)
What is the missing particle?
A \( \cdot \frac{4}{2} \mathrm{He} \)
B . \( _{1}^{1} H \)
c. \( _{0}^{1} n \)
\( D \)
Subject: Maths
Let \( A \) and \( B \) are two matrices of same
order \( 3 \times 3 \) given by \( A= \) \( \left[\begin{array}{ccc}1 & 3 & \lambda+2 \\ 2 & 4 & 6 \\ 3 & 5 & 8\end{array}\right] B=\left[\begin{array}{lll}3 & 2 & 4 \\ 3 & 2 & 5 \\ 2 & 1 & 4\end{array}\right] \) If
\( t r(A B)^{t}+t r(B A)^{t}=t r(A B) \) then the
value of \( 2 \lambda \) equals
A . 103
в. 206
\( c .-103 \)
D. -206
Subject: Chemistry
Which of the following is an example of
heterogeneous catalysis?
\( \mathbf{A} \cdot 4 N H_{3(g)}+5 O_{2(g)} \stackrel{\left.P t_{s}\right)}{\leftrightarrow} 4 N O_{(g)}+6 H_{2} O_{(g)} \)
B \( \cdot 2 S O_{2}+O_{2} \stackrel{N O_{(g)}}{\rightarrow} 2 S O_{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{3} \mathrm{COOCH}_{3(l)}+\mathrm{H}_{2} \mathrm{O} \stackrel{\mathrm{HClaa}}{\rightarrow} \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{CH}_{3} \mathrm{OH} \)
D. \( C_{12} H_{22} O_{11}+H_{2} O^{H_{2} S O_{4}} C_{6} H_{12} O_{6}+C_{6} H_{12} O_{6} \)
Subject: Chemistry
Express the rate for the following
reaction in terms of concentration of
reactants and products.
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
Subject: Maths
The value of \( c \) in the lagranges mean
value theorem for \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}, \boldsymbol{a}= \)
\( 1, h=\frac{1}{2} \) is
A \( \cdot \frac{1}{3} \)
в. \( \sqrt{\frac{19}{56}} \)
c. \( \sqrt{\frac{19}{3}}+2 \)
D. \( \sqrt{\frac{19}{3}}-2 \)
Subject: Maths
In a geometric progression with common ratio 'q', the sum of the first 109 terms exceeds the sum of the first
100 terms by \( 12 . \) If the sum of the first nine terms of the progression is \( \frac{\boldsymbol{\lambda}}{\boldsymbol{q}^{100}} \) then the value of \( \lambda \) equals to
A . 10
B. 14
c. 12
D. 22
Subject: Chemistry
The following is an example of a single displacement reaction:
\( \boldsymbol{M} \boldsymbol{g}_{(s)}+\boldsymbol{Z} \boldsymbol{n}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2(a q)} \rightarrow \boldsymbol{Z} \boldsymbol{n}_{(s)}+ \)
\( M g\left(N O_{3}\right)_{2(a q)} \)
How else can this reaction be
classified?
A. A precipitate reaction
B. An acid-base reaction
c. A neutralization reaction
D. A redox reaction
Subject: Maths
If the primitive of \( \frac{e^{x}\left(1+e^{x}\right)}{\sqrt{1-e^{2 x}}} \) is \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{g}(\boldsymbol{x})-\sqrt{\boldsymbol{h}(\boldsymbol{x})}+\boldsymbol{C} \) then
This question has multiple correct options
A \( \cdot f(x)=\sin ^{-1} x \)
B \( \cdot g(x)=e^{2 x} \)
\( \mathbf{c} \cdot g(x)=e^{x} \)
D. \( h(x)=1-e^{2 x} \)