AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Assertion
Statement-1: \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\{\boldsymbol{x}\}} \) is
discontinuous for integral values of \( \boldsymbol{x} \) where \( \vartheta \) denotes the fractional part
function.
Reason
Statement-2: For integral values of \( \boldsymbol{x} \) \( f(x) \) is not defined.
A. Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1
B. Statement-1 is true, Statement-2 is true and Statement-2 is NOT the correct explanation for Statement-1
c. statement-1 is true, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true.
Subject: Physics
A ray of light passes through four transparent media with refractive
indices \( \mu_{1}, \mu_{2}, \mu_{3} \) and \( \mu_{4} \) as shown in the
figure. The surfaces of all media are
parallel. If the emergent ray CD is parallel to the incident ray AB, we must
have:
A \( \cdot \mu_{1}=\mu_{2} \)
в. \( \mu_{2}=\mu_{3} \)
\( \mathbf{c} \cdot \mu_{3}=\mu_{4} \)
D. \( \mu_{4}=\mu_{1} \)
Subject: Physics
An object is thrown between two tall
buildings \( 180 \mathrm{m} \) from each other. The
object thrown horizontally from a
window \( 55 \mathrm{m} \) above the ground from one
building strikes a window \( 10 \mathrm{m} \) above the tom ground in another building.
Find out the speed of projection.
A. 60
B. 80
\( c .70 \)
D. 90
Subject: Chemistry
Assertion
\( C O \) is toxic.
Reason
CO forms complex with haemoglobin in the blood, and this complex is more stable than oxy-haemoglobin.
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
Distance between \( \boldsymbol{A}(\mathbf{4}, \mathbf{5}, \mathbf{6}) \) from origin
\( \boldsymbol{O} \) is
A \( \cdot 25 \sqrt{3} \)
B. \( \sqrt{77} \)
c. \( 3 \sqrt{5} \)
D. Data Insufficient
Subject: Maths
If \( \cos \theta=\frac{8}{10} \) and \( \theta \) is acute, what is the
value of \( \operatorname{cosec} \theta ? \)
A \( \cdot \frac{10}{6} \)
в. \( \frac{8}{10} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{10}{7} \)
Subject: Maths
In right triangle \( A B C, B C=7 c m \)
\( \boldsymbol{A C}-\boldsymbol{A B}=\mathbf{1 c m} \) and \( \angle \boldsymbol{B}=\mathbf{9 0}^{\circ} . \) The
value of \( \cos A+\cos B+\cos C \) is
A \( \cdot \frac{1}{7} \)
в. \( \frac{32}{24} \)
c. \( \frac{31}{25} \)
D. \( \frac{25}{31} \)
Subject: Physics
Which of the following is not the standard from of a sine wave? (Here,
symbols have their usual meaning)
A \( \cdot y=A \sin 2 \pi\left(\frac{t}{T}-\frac{x}{\lambda}\right) \)
B. \( y=A \sin (v t-k x) \)
c. \( y=A \sin \omega\left(t-\frac{x}{v}\right) \)
D. \( y=A \sin k(v t-x) \)
Subject: Physics
A closed vessel contains a mixture of two
gases Neon \& Argon the total mass of mixture is 28 gm.The partial pressure due to Argon and neon are 4 atm and 12atm respectively.The mass of individual gases in vessel is \( \left(M_{\text {neon}}=\right. \)
\( \left.20, M_{\text {argon}}=40, R=8.3 \mathrm{J} / \mathrm{mol}-\mathrm{k}\right) \)
A. \( 4 \mathrm{gm}, 24 \mathrm{gm} \)
B . \( 1 \mathrm{gm}, 27 \mathrm{gm} \)
\( \mathrm{c} \cdot 6 \mathrm{gm}, 22 \mathrm{gm} \)
D. \( 2 g \mathrm{m}, 26 \mathrm{gm} \)
Subject: Maths
Mark the correct alternative of the
following. In figure, AOB is a straight line such that \( \angle A O C=(3 x+10)^{o}, \angle C O D= \)
\( \mathbf{5 0}^{\circ} \) and \( \angle B O D=(x-8)^{\circ} . \) The value of
\( x \) is?
\( A \cdot 32 \)
B. 36
\( c \cdot 42 \)
D. 52
Subject: Physics
As shown in the figure, light is incident normally on one face of the prism. A liquid of refractive index \( \$ \$ 1 \mathrm{my} \$ \$ \) is
placed on the horizontal face \( A C \). The
refractive index of prism is \( 3 / 2 \). If total
internal reflection taken place on face
\( A C, m \) should be less than \( \$ \$ \) ldfrac
Illsrat \( \{3\}\}\{4\} \$ \$, \) where \( I \) is an integer
Find the value of \( \boldsymbol{I} \)
Subject: Physics
Two runners start simultaneously from
the same point on a circular \( 200 m \)
track in the same direction. Their
speeds are \( 6.2 m s^{-1} \) and \( 5.5 m s^{-1} . \) How
far from the starting point the faster and the slower runner would be side by
side again?
A. \( 150 \mathrm{m} \) away from the starting point
B. \( 170 m \) away from the starting point
c. \( 120 m \) away from the starting point
D. none
Subject: Chemistry
A gas has a volume of \( \mathrm{V} \mathrm{cm}^{3} \) at \( 10^{\circ} \mathrm{C} \). If
the pressure is doubled, at what temperature will the volume still be \( \mathbf{V} \)
\( c m^{3} ? \)
A \( \cdot 273^{\circ} \mathrm{C} \)
B. \( 300^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 283^{\circ} \mathrm{C} \)
D. \( 293^{\circ} \mathrm{C} \)
Subject: Maths
Show that the function \( f \) in \( A=R=\frac{2}{3} \) defined by \( f(x)=\frac{3 x+2}{5 x+3}, \neq \frac{-3}{5} \) is
one-one and onto.Hence find \( \boldsymbol{f}^{-1}(\boldsymbol{x}) \)
Subject: Chemistry
At \( 300 \mathrm{K} \), the vapour pressure of an ideal solution containing 3 mole of \( A \) and 2 mole of \( \mathrm{B} \) is 600 torr. At the same
temperature, if 1.5 mole of \( A \& 0.5 \) mole of \( \mathrm{B} \) (non-volatile) are added to this solution the vapour pressure of solution increases by 30 torr. What is the value
of \( P_{B}^{\circ} ? \)
A . 150
в. 405
c. 90
D. none of these
Subject: Chemistry
Aluminium and copper are extracted from their oxide and sulphide ores
respectively. Which of the following is
correct?
I. Copper is extracted by the auto reduction of copper oxide by copper sulphide.
II. Aluminium cannot be obtained by
chemical reduction due to its strong
affinity for oxygen.
III. In electrometallurgy of \( A l \), graphite is used as cathode to avoid reoxidation
of \( A l \) into \( A l_{2} O_{3} \) by preventing
formation of \( \boldsymbol{O}_{2} \)
IV. Sulphide ores of copper are difficult
to be reduced than the oxide ores.
A. \( I, I I, I V \)
B. II and III
c. \( I I I \)
D. II and \( I V \)
Subject: Physics
Two spherical stars \( A \) and \( B \) emit
blackbody radiation. The radius of \( A \) is
400 times that of \( B \) and \( A \) emits \( 10^{4} \)
times the power emitted from \( B \). The ratio \( \left(\frac{\boldsymbol{\lambda}_{\boldsymbol{A}}}{\boldsymbol{\lambda}_{\boldsymbol{B}}}\right) \) of their wavelengths \( \boldsymbol{\lambda}_{\boldsymbol{A}} \)
and \( \lambda_{B} \) at which the peaks occur in their respective radiation curves is
Subject: Maths
Let \( A=\{1,2,3,4,6\} \) and \( R \) be the relation on \( \boldsymbol{A} \) defined by \( \{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}, \boldsymbol{b} \in \)
\( A, b \text { is exactly divisible by } a\} \)
(i) Write \( R \) in roster form
(ii) Find the domain of \( \boldsymbol{R} \)
(iii) Find the range of \( \boldsymbol{R} \)
Subject: Physics
A spring of spring constant k placed horizontally on a rough horizontal
surface is compressed against a block
of mass \( \mathrm{m} \) placed on the surface so as to store maximum energy in the spring. If the coefficient of friction between the
block and the surface is \( \mu, \) the potential
energy stored in the spring is:
A \( \cdot \frac{\mu^{2} m^{2} g^{2}}{k} \)
B. \( \frac{2 \mu^{2} g^{2}}{k} \)
\( ^{\mathrm{C}} \cdot \frac{\mu^{2} m^{2} g^{2}}{2 k} \)
D. \( \frac{3 \mu^{2} m g^{2}}{k} \)
Subject: Physics
The potential energy between two atoms in a molecule is given by, \( U_{(x)}=\frac{a}{x^{12}}- \) \( \frac{B}{X^{6}}, \) where a and b are positive
constants and \( x \) is the distance
between the atoms. The system is in stable equilibrium when -
\( \mathbf{A} \cdot x=0 \)
B \( \cdot x=\frac{a}{2 b} \)
c. \( x=\left(\frac{2 a}{b}\right)^{1 / 6} \)
D. \( x=\left(\frac{11 a}{5 b}\right) \)
Subject: Maths
\( \left|\begin{array}{ccc}\mathbf{2}^{3} & \mathbf{3}^{3} & \mathbf{3 . 2}^{\mathbf{2}}+\mathbf{3 . 2}+\mathbf{1} \\ \mathbf{3}^{\mathbf{3}} & \mathbf{4}^{\mathbf{3}} & \mathbf{3 . 3}^{\mathbf{2}}+\mathbf{3 . 3}+\mathbf{1} \\ \mathbf{4}^{\mathbf{3}} & \mathbf{5}^{\mathbf{3}} & \mathbf{3 . 4}^{\mathbf{2}}+\mathbf{3 . 4}+\mathbf{1}\end{array}\right| \) is equal to
\( A \)
B.
\( c \cdot 2 \)
D. 3
Subject: Physics
Two wheels \( A \) and \( B \) are mounted on the
same axle. moment of inertia of \( A \) is 6
\( \mathrm{kg} \boldsymbol{m}^{2} \) ans it is rotating at \( 600 \mathrm{rpm} \)
when \( \mathrm{B} \) is at rest. What is moment of inertia of \( \mathrm{B} \), if their combined speed ids
400 rpm?
\( A \cdot 9 \mathrm{kg} m^{2} \)
B. 4 kg \( m^{2} \)
\( \mathrm{c} \cdot 3 \mathrm{kg} \mathrm{m}^{2} \)
\( D \cdot 5 \mathrm{kg} m^{2} \)
Subject: Chemistry
Predict the product (T) for the following
reaction sequence. \( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{C H}=\boldsymbol{O} \stackrel{\boldsymbol{K C N} / \boldsymbol{O H}^{-}}{\longrightarrow} \)
\( \boldsymbol{R} \frac{\boldsymbol{C r} \boldsymbol{O}_{2} / \boldsymbol{H}^{\oplus}}{\longrightarrow} \boldsymbol{S} \frac{(i) \operatorname{conc} K \boldsymbol{O} \boldsymbol{H}}{(i i) \text { Acidification }} \boldsymbol{T} \)
A. cinnamic acid
B. Mandelic acid
c. Benzilic acid
D. Benzoic acid \& Benzyl alcohol
Subject: Physics
A pulse of sound is produced at the
bottom of a boat. The sound travels
through the water and is
reflected from the sea-bed. The sound
reaches the boat again after 1.3 s. The
sea-bed is \( 1000 m \) below the boat
Using this information, what is the speed of sound in the water?
A. \( 769 \mathrm{m} / \mathrm{s} \)
в. \( 1300 \mathrm{m} / \mathrm{s} \)
c. \( 1538 \mathrm{m} / \mathrm{s} \)
D. \( 2600 \mathrm{m} / \mathrm{s} \)
Subject: Physics
In periscopes, the parallel rays entering the cylindrical tube from the upper end from an object, strike the plane mirror at an angle of and hence are
reflected through an angle of
A \( .30^{\circ}, 30^{\circ} \)
\( ^{0} \)
B . \( 45^{\circ}, 45^{\circ} \)
\( \mathbf{c} \cdot 45^{0}, 30^{0} \)
D. \( 90^{0}, 90^{0} \)
Subject: Physics
A light string passes over a frictionless
pulley. To one of its ends a mass of \( 6 k g \) is attached to the other end a mass of
10 \( k g \) is attached. The tension of the thread is:
A . \( 24.5 N \)
B . \( 2.45 N \)
\( c .79 N \)
D. \( 73.5 N \)
Subject: Physics
For PN junction, the intensity of electric field is \( 1 \times 10^{6} \mathrm{V} / \mathrm{m} \) and the width of
depletion region is 5000 A. The value of
potential barrier=
V.
A . 0.05
B. 0.005
\( c .0 .5 \)
D. 5
Subject: Chemistry
An element X has 7 electrons in its shell. What is true about the element \( x \)
\( ? \)
I. It belongs to period 9 of modern periodic table.
II. Its atom contains 9 protons.
III. It has a valency of 1
IV. Its atoms can accept an electron to acquire noble gas configuration.
\( A \cdot(1) \) and (11)
B. (II), (III), (IV)
c. (III) and (IV)
D. (II) and (IV)
Subject: Maths
A non zero polynomial with real coefficients has the property that
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{g}^{\prime}(\boldsymbol{x}) \cdot \boldsymbol{g}^{\prime \prime}(\boldsymbol{x}) \cdot \) Let the leading
coefficient of \( g(x) \) be \( a \). Then \( 36 a= \)
\( A \cdot 6 \)
B. 4
\( c .3 \)
D.
Subject: Maths
Solve the given differential equation
\( \left(x y^{2}+x\right) d x+\left(y x^{2}+y\right) d y=0 \)
\( \mathbf{A} \cdot\left(x^{2}+1\right)\left(y^{2}+1\right)=c \)
B \( \cdot \log \left(x^{2}+1\right) \log \left(y^{2}+1\right)=c \)
c. \( \left(x^{2}+1\right)+\left(y^{2}+1\right)=c \)
D. none of these
Subject: Physics
A body is projected vertically upwards with a velocity of \( 19.6 ~ m / s . \) The total time for which the body will remain in
the air is (Take \( \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)
A . \( 4 s \)
B. \( 6 s \)
\( \mathrm{c} .9 \mathrm{s} \)
D. 12 s
Subject: Chemistry
Upon mixing \( 45.0 m L \) of \( 0.25 M \) lead
nitrate solution with \( 25 m L \) of \( 0.1 M \)
chromic sulphate solution, precipitation of lead sulphate takes
place. How many moles of lead
sulphate are formed? Also, calculate the
molar concentrations of the species left behind in the final solution. Assume
that lead sulphate is completely insoluble.
Subject: Chemistry
One fermi is?
A \( \cdot 10^{-15} \mathrm{cm} \)
B. \( 10^{-13} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-10} \mathrm{cm} \)
D. \( 10^{-12} \mathrm{cm} \)
Subject: Chemistry
What is the product formed when
hydrated \( C a S O_{4} \) is heated to \( 125^{\circ} C \)
instead of \( 200^{\circ} \mathrm{C} ? \)
\( \mathbf{A} \cdot\left(C a S O_{4}\right) \frac{1}{2} H_{2} O \)
в. \( \operatorname{CaSO}_{4} \frac{3}{4} \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \)
D. \( C a O+S O_{3} \)
Subject: Physics
For three non-zero vectors \( \vec{a}, \vec{b}, \vec{c} \) the elation \( |(\vec{a} \times \vec{b}) \cdot \vec{c}|=|\vec{a}||\vec{b}||\vec{c}| \) will hold
true if and only if:
\( \mathbf{A} \cdot \vec{a} \cdot \vec{b}=0, \vec{b} \cdot \vec{c}=0 \)
В . \( \vec{c} . \vec{a}=0, \vec{a} . \vec{b}=0 \)
C \( . \vec{a} . \vec{c}=0, \vec{b} . \vec{c}=0 \)
D. \( \vec{a} . \vec{b}=\vec{b} . \vec{c}=\vec{c} . \vec{a}=0 \)
Subject: Physics
A wave travelling along the x-axis is described by the equation \( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})= \)
\( 0.005 \cos (\alpha x-\beta t) \) if the wavelength
and the time period of the wave are \( 0.08 m \) and \( 2.0 s \) respectively, then \( \alpha \)
and \( \beta \) in appropriate units are
A. \( \alpha=25.00 \pi, \beta=\pi \)
B. \( \alpha=\frac{0.08}{\pi}, \beta=\frac{2.0}{\pi} \)
c. \( \alpha=\frac{0.04}{\pi}, \beta=\frac{1.0}{\pi} \)
D. \( \alpha=12.50 \pi, \beta=\frac{\pi}{2.0} \)
Subject: Chemistry
Which will contain undissociated
aqueous particles?
A. A 0.01-molar solution of HNO
B. A 0.01-molar solution of \( \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)
c. A 0.01-molar solution of \( \operatorname{Cu}\left(\mathrm{NO}_{3}\right)_{2} \)
D. A 0.01-molar solution of NaNO
E. A 0.01-molar solution of NaOH
Subject: Chemistry
Assertion: The absolute value of
standard electrode potential can be determined experimentally. Reason: Standard electrode potentials are measured using a hydrogen halfcell reference electrode whose potential is known.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false
Subject: Chemistry
For which reaction will \( \Delta \boldsymbol{H}=\Delta \boldsymbol{U} ? \)
Assume each reaction is carried out in
an open container.
\( \mathbf{A} \cdot H_{2}(g)+B r_{2}(g) \longrightarrow 2 H B r(g) \)
B \( \cdot C(s)+2 H_{2} O(g) \longrightarrow 2 H_{2}(g)+C O_{2}(g) \)
\( \mathbf{c} \cdot 4 C O(g)+2 O_{2}(g) \longrightarrow 4 C O_{2}(g) \)
D. \( 2 P C l_{5}(g) \longrightarrow 2 P C l_{3}(g)+2 C l_{2}(g) \)
Subject: Chemistry
If the \( p K_{a} \) of a weak acid \( H A \) is 4.80
and the \( p K_{b} \) of a weak base \( B O H \) is
4.78. Then, the \( p H \) of an aqueous
solution of the corresponding salt, \( \boldsymbol{B A} \)
will be:
A. 8.23
B. 9.41
c. 7.01
D. 5.91
Subject: Physics
A current \( I=1.00 A \) circulates in a
round thin-wire loop of radius \( \boldsymbol{R}= \)
100 \( m m \). Find the magnetic
induction at the centre of the loop.
A. \( 7.3 \mu T \)
B. \( 3.7 \mu T \)
c. \( 3.6 \mu T \)
D. \( 6.3 \mu T \)
Subject: Biology
Which of the following type of movement are seen in human body?
A. Amoeboid
B. Ciliary
C. Flagellar
D. Muscular
\( A \cdot A, b \) and \( c \)
B. \( A, b \) and \( d \)
C. \( A, \) c and \( d \)
D. \( A, b, \) c and \( d \)
Subject: Physics
In the given figure, what is the
magnetic field at the point '0'?
A \( \cdot \frac{\mu_{0} I}{4 \pi r}+\frac{\mu_{0} I}{2 \pi r} \)
\( B \cdot \frac{\mu_{0}}{1 \pi} \)
C. \( \frac{\mu_{0} I}{4 r}+\frac{\mu_{0} I}{4 \pi r} \)
D. \( \frac{\mu_{0} I}{4 r}-\frac{\mu_{0} I}{4 \pi r} \)
Subject: Maths
Let \( \quad A=\{x:-1 \leq x \leq 1\} \) and \( f \)
\( \boldsymbol{A} \rightarrow \boldsymbol{A} \) such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}|\boldsymbol{x}| \), then \( \boldsymbol{f} \) is
A. a bijection
B. injective but not surjective
c. surjective but not injective
D. neither injective nor surjective
Subject: Chemistry
Identify the correct statement for
change of Gibbs energy for a system \( (\Delta \)
\( \left.\mathrm{G}_{\text {system}}\right) \) at constant temperature and
pressure:
\( \mathbf{A} \cdot \) If \( \Delta \mathrm{G}_{\text {system}}>0, \) the process is spontaneous
B. If \( \Delta G_{s y s t e m}=0, \) the system has attained equilibrium
C. If \( \Delta G_{\text {system}}=0, \) the system is still moving in a particular direction
D. If \( \Delta \mathrm{G}_{\text {system}}<0 \), the process is not spontaneous
Subject: Maths
\( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{3} \boldsymbol{z}-\mathbf{1}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+ \)
\( \mathbf{3} \boldsymbol{z}+\mathbf{3}=\mathbf{0} \)
Subject: Physics
The work done in increasing the size of
a soap film from \( 10 \mathrm{cm} \times 6 \mathrm{m} \) to
\( 10 c m \times 11 c m \) is \( 3 \times 10^{-4} J . \) The
surface tension of the film is:
A \( \cdot 1.0 \times 10^{-2} N / m \)
B . \( 6.0 \times 10^{-2} \mathrm{N} / \mathrm{m} \)
c. \( 3.0 \times 10^{-2} N / m \)
D. \( 1.5 \times 10^{-2} N / m \)
Subject: Chemistry
The oxidation state of sulphur in the
anions \( S O_{3}^{2-}, S_{2} O_{4}^{2-} \) and \( S_{2} O_{6}^{2-} \) follows the order:
A \( \cdot S_{2} O_{6}^{2-}<S_{2} O_{4}^{2-}<S O_{3}^{2} \)
B. \( S O_{3}^{2-}<S_{2} O_{4}^{2-}<S_{2} O_{6}^{2} \)
c. \( S_{2} O_{4}^{2-}<S O_{3}^{2-}<S_{2} O_{6}^{2-} \)
D. \( S_{2} O_{4}^{2-}<S_{2} O_{6}^{2-}<S O_{3}^{2} \)
Subject: Biology
During anaerobic respiration in yeast
A. Water and \( C O_{2} \) are end products
в. \( C O_{2}, C_{2} H_{5} O H \) and energy are end products
C. \( H_{2} S, C_{6} H_{12} O_{6} \) and energy are the end products
D. \( H_{2} O, C O_{2} \) and energy are the only end products
Subject: Physics
Assertion
The back emf in a dc motor is
maximum when the motor has just been switched on.
Reason
When motor is switched on it has
maximum speed.
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 stone tied to the end of a string \( 80 \mathrm{cm} \) long is whirled in a horizontal circle with a constant speed. If the stone
makes 14 revolutions in \( 22 s \) then the
acceleration of the stone is :
A \( \cdot 5 m / s^{2} \)
B . \( 10 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 12.8 m / s^{2} \)
D. \( 14.8 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Maths
Let \( A \) be the matrix of order \( 3 \times 3 \) such
that \( |\boldsymbol{A}|=\mathbf{1}, \boldsymbol{B}=\mathbf{2} \boldsymbol{A}^{-1} \) and \( \boldsymbol{C}=\frac{(\boldsymbol{a} d \boldsymbol{j} \boldsymbol{A})}{\sqrt[3]{2}} \)
then the value of \( \left|A B^{2} . C^{3}\right| \) is [Note : \( |A| \) represent determinant value of matrix A.]
Subject: Maths
Given that \( 2 a-3 b=c ;-3 a+5 b=d \)
expressing \( a \) and \( b \) as linear
combinations of \( c \) and \( d \) we get \( a= \)
\( k c+m d \) and \( b=h c+r d . \) Find \( k+ \)
\( \boldsymbol{m}+\boldsymbol{h}+\boldsymbol{r} ? \)
Subject: Chemistry
Which of the following properties can be assigned to water?
I. It has a permanent dipole moment attributed to its molecular structure.
Il. It is a very good conductor of
electricity.
III. It has its polar covalent bonds with hydrogen on opposite sides of the oxygen atom, so that the molecule is
linear
A. I only
B. III only
c. I and II only
D. II and III only
E . I, II and III
Subject: Maths
Let \( \boldsymbol{f}(\boldsymbol{x}) \) be polynomial in \( \boldsymbol{x} \) of degree
not less than 1 and \( ^{\prime} a^{\prime} \) be a real number.
If \( f(x) \) is divided by \( (x-a), \) then the
remainder is \( \boldsymbol{f}(\boldsymbol{a}) \). If \( (\boldsymbol{x}-\boldsymbol{a}) \) is a factor
of \( f(x), \) then \( f(a)=0 . \) Find the remainder of \( x^{4}+x^{3}-x^{2}+2 x+3 \)
when divided by \( \boldsymbol{x}-\mathbf{3} \)
A. 108
B. 98
c. 165
D. 170
Subject: Physics
A body is thrown vertically upwards and takes 5 seconds to reach maximum height. The distance travelled by the body will be same in:
A \( \cdot 1^{s t} \) and \( 10^{t h} \) second
B. \( 2^{n d} \) and \( 8^{t h} \) second
\( \mathrm{c} \cdot 4^{\operatorname{th}} \) and \( 6^{t h} \) second
D. Both (2) and (3)
Subject: Maths
The coordinates of a point which divides the line joining the points \( P(2,3,1) \) and \( Q(5,0,4) \) in the ratio 1: 2 are
\( ^{\mathbf{A}} \cdot\left(\frac{7}{3}, 1, \frac{5}{3}\right) \)
в. (4,1,3)
c. (3,2,2)
D. (1,-1,1)
Subject: Physics
A cylinder of height \( h \) is filled with water and is kept on a block of height h/2. The level of water in the cylinder is kept
constant. Four holes numbered 1,2,3 and 4 are at the side of the cylinder and at heights \( 0, h / 4, h / 2 \) and \( 3 h / 4 \) respectively.When all four holes are opened together, the hole from which water will reach farthest distance is
\( A \)
B. 2
\( c \cdot 3 \)
D. 4
Subject: Maths
The chances of defective screws in three
boxes \( A, B \) and \( C \) are \( \frac{1}{5}, \frac{1}{6}, \frac{1}{7} \) respectively. A box is selected at
random and a screw drawn from it at
random, is found to be defective.

The probability that it came from the
box'A' is
A \( \cdot \frac{16}{29} \)
B. \( \frac{1}{15} \)
c. \( \frac{27}{59} \)
D. \( \frac{42}{107} \)
Subject: Physics
A converging lens of focal length \( f_{1} \) is
placed in front of and coaxially with a
convex mirror of focal length \( f_{2} \). Their
separation is d and whole arrangement
is in air. A parallel beam of light
incident on the lens returns as a
parallel beam from the arrangement.
Then
This question has multiple correct options
A. The diameter of incident and emergent beam is the same
B. The distance d can be \( f_{1} \)
C. The distance d can be \( f_{2} \)
D. The distance d can be \( f_{1}-2 f_{2} \)
Subject: Physics
Two identical conductors \( P \) and \( Q \) are
placed on two frictionless rails \( R \) and \( S \)
in a uniform magnetic field directed
into the plane. If \( P \) is moved in the
direction shown in figure with a
constant speed, then rod \( Q \)
\begin{tabular}{c|c|c} 
& \( P \) & \( Q \) \\
& & \\
\( \times \) & \( \times \) & \( \times \) \\
\hline\( \times \) & \( \widehat{V} \) & \( \times \) & \( \times \) \\
\hline\( s \) & & & \\
\hline\( \times \) & \( \times \) & \( \times \) \\
\hline
\end{tabular}
A. will be attracted toward \( P \)
B. will be repelled away from \( P \)
c. will remain stationary
D. may be repelled away or attracted toward \( P \)
E. answer required
Subject: Maths
If the four letter words(need not be meaningful) are to be formed using the
letters from the word "MEDI

TERRANEAN" such that the first letter is
\( \mathrm{R} \) and the fourth letter is \( \mathrm{E} \), then the
total number of such words, is?
A \( \cdot \frac{11 !}{(2 !)^{3}} \)
B . 59
c. 110
D. 56
Subject: Maths
Solve the given pair of equations by substitution method:
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \)
\( \boldsymbol{y}-\boldsymbol{x}=\boldsymbol{6} \)
A. (2,7)
(i)
в. (-3,3)
c. (4,9)
(年. (4,9)
D. (-6,2)
Subject: Physics
The force \( \boldsymbol{f} \) acting after time \( t \) on the
bottom of a beaker of area \( A \) when
water of density \( \rho \) falls from a tap at a
height \( h \) at uniform rate \( v \) is:
\( ^{\mathbf{A}} \cdot_{v \rho}\left[g t+2 g A\left(h-\frac{v t}{A}\right)\right] \)
B \( \cdot v \rho[g t+\sqrt{2 g h}] \)
c. v\( \rho g h \)
D \( \cdot \operatorname{ve}[g t+\sqrt{2 g\left(h+\frac{v t}{A}\right)}] \)