AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
If \( \boldsymbol{x}^{p} \cdot \boldsymbol{y}^{\boldsymbol{q}}=(\boldsymbol{x}+\boldsymbol{y})^{\boldsymbol{p}+\boldsymbol{q}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A. \( \frac{y}{x} \)
B. \( -\frac{y}{x} \frac{y}{x} \)
c. \( \frac{x}{y} \)
D. \( -\frac{x}{y} \)
Subject: Physics
Match the following:
Quantity Formula
x linked a coil
1) Magnetic c flux with
a) \( -N \frac{d \phi}{d t} \)
2)
Induced emf
b) \( \mu_{r} \mu_{0} n_{1} n_{2} \pi r_{1}^{2} l \)
3) Force on a charged particle
\( \cdots \) moving in a electric and
c) \( B A \cos \theta \)
magnetic field
\( f a \) 4) Mutual inductance of
solenoid d)
\[
q(\bar{E}+\bar{v} \times \bar{B})
\]
\( A \cdot 1-c, 2-d, 3-b, 4-a \)
B. \( 1-c, 2-a, 3-d, 4-b \)
\( \mathbf{C} \cdot 1-\mathbf{b}, 2-\mathbf{a}, \mathbf{3}-\mathbf{c}, \mathbf{4}-\mathbf{d} \)
D. \( 1-a, 2-b, 3-d, 4-c \)
Subject: Chemistry
We have four substances \( \mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S} \)
Substance \( P \) is dark coloured violet
solid having diatomic molecules.
Solution of \( P \) in alcohol is an Antiseptic 'T' Substance 'Q'is a white solid usually
recovered from sea on a large scale.
Substance 'R' is also a white solid
insoluble in water and used in the form
of small balls for safe storage of woolen
clothes. Substance 'S' is a white solid
too used in dry cell. P,Q,R,S,T, may be (choose correct option)
A. P-lodine, Q-Napthalene,R- \( R-N H_{4} C I \) S-Nacl, T-lodin
tincture
B. P-NaCI,Q-Napthalene, \( R-N H_{4} C I \)
S-lodine, T-lodine tincture
C. P-lodine tincture, Q- \( R-N H_{4} C I R \) - lodine, S-
Napthalene, T-NaCl
D. P-lodine, Q-Nacl, R- Napthalene
S- \( R-N H_{4} C I, \) T-lodine tincture
Subject: Maths
Mark the correct alternative of the
following. If the measures of the angles of a
triangle are \( (2 x)^{o},(3 x-5)^{o} \) and \( (4 x- \)
13) \( ^{\circ} . \) Then the value of \( x \) is?
A . 22
B . 18
c. 20
D. 30
Subject: Physics
In the context of accuracy to
measurement and significant figures in expressing results of experiment, which of the following is/are correct?
(1) Out of the measurements \( 50.14 \mathrm{cm} \) and 0.00025 ampere, the first one has greater accuracy.
(2) If one travels \( 478 \mathrm{km} \) by rail and 397
m. by road, the total distance traveled is
\( 478 \mathrm{km} \)
A. Only (1) is correct
B. only (2) is correct
c. Both are correct
D. None of these is correct
Subject: Chemistry
Acid buffer can be prepared by mixing solutions of:
A \( . \quad N a C l+N a O H \)
в. \( H_{2} S O_{4}+N a_{2} S O_{4} \)
c. \( N H_{4} O H+N H_{4} C l \)
D. \( C H_{3} C O O N a+C H_{3} C O O H \)
Subject: Physics
Six capacitors each of capacitance of
\( 2 \mu F \) are connected as shown in the
figure. The effective capacitance
between \( A \) and \( B \) is
\( \mathbf{A} \cdot 12 \mu F \)
B. \( -\mu F \)
\( F F \)
\( c .3 \mu F \)
D. \( 6 \mu F \)
Subject: Maths
If \( \bar{A}=3 \hat{i}+5 \hat{j}-2 \hat{k}, \) and vector \( \bar{B}= \)
\( -3 \hat{j}+6 \hat{k} . \) Find a vector \( \bar{C} \) such that 2 \( \bar{A}+7 \bar{B}+4 \bar{C}=0 \)
\( \mathbf{A} \cdot-6 \hat{i}+11 \hat{j}-38 \hat{k} \)
B . \( 11 \hat{j}-4 \hat{k} \)
c. \( -1.5 \hat{i}+2.75 \hat{j}-9.5 \hat{k} \)
D. \( 4 \hat{j}-6 \hat{k} \)
Subject: Physics
Assertion
A beam of protons is moving towards east in vertically upward magnetic field.Then,this beam will deflect
towards south.
Reason
A constant magnetic force will act on the proton beam.
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
Measure of two quantities along with the precision of respective measuring instrument is
\( \boldsymbol{A}=\mathbf{2 . 5 m s}^{-1} \pm \mathbf{0 . 5 m s}^{-1}, \boldsymbol{B}=\mathbf{0 . 1 0 s} \pm \)
\( \mathbf{0 . 0 1 s} \)
The value of \( A B \) will be
\( \mathbf{A} \cdot(0.25 \pm 0.08) m \)
в. \( (0.25 \pm 0.8) m \)
c. \( (0.25 \pm 0.05) m \)
D. \( (0.25 \pm 0.135) m \)
Subject: Maths
What is the value of a for which the
system of linear equations \( a x+3 y=a \) \( 3 ; 12 x+a y=a \) has no solution
\( \mathbf{A} \cdot a=6 \)
B . \( a=-3 \)
\( \mathbf{c} \cdot a=3 \)
D. \( a=-6 \)
Subject: Biology
Which of the following statement(s) is
(are) true about heart?
A. The left atrium receives oxygenated blood from different parts of the body, while right atrium receives deoxygenated blood from lungs.
B. The left ventricle pumps oxygenated blood to different body parts, while right ventricle pumps deoxygenated blood to lungs.
C. The left atrium transfers oxygenated blood to the right ventricle, which sends it to different body parts.
D. The right atrium receives oxygenated blood from different parts of the body, while left ventricle pumps oxygenated blood to different parts of the body.
Subject: Biology
Match the terms listed with the
structures where they occur. Choose the
answer, which gives the correct
combination of alphabets of the two
columns.
\( \begin{array}{ll}\text { Structure } & \text { Occurrence } \\ \text { A. Haversian canal } & \text { p. Kidney } \\ \text { B. Dendrites } & \text { q. Cartilage } \\ \text { C. Sarcolemma } & \text { r. Muscle } \\ \text { D. Chondrocytes } & \text { s. Nerve cells } \\ & \text { t. Bone }\end{array} \)
\( A \)
\( A-q, B-r, C-s, D-t \)
c. \( A-t, B-s, C-r, D-q \)
D. A-s.B-t. C- a \( D- \)
Subject: Maths
The value of \( 3^{7} C_{0}+4^{7} C_{1}+5^{7} C_{2}+ \)
\( -----------10^{7} C_{7} \) is
A \( \cdot 10(2)^{6} \)
B . \( 13(2)^{7} \)
c. \( 14(2)^{6} \)
D. \( 13(2)^{6} \)
Subject: Physics
Assertion
The photoelectrons produced by a
monochromatic light beam incident on
a metal surface, have a spread in their
kinetic energies.
Reason
The work function of the metal varies as
a function of depth from the surface.
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: Physics
Three charges \( -q_{1},+q_{2} \) and \( -q_{3} \) are placed
as shown in the figure. The \( x \) -component
of the force on \( -q_{1} \) is proportional to:
A \( \cdot \frac{q_{2}}{b^{2}}-\frac{q_{3}}{a^{2}} \cos \theta \)
B \( \cdot \frac{q_{2}}{b^{2}}+\frac{q_{3}}{a^{2}} \sin \theta \)
C \( \cdot \frac{q_{2}}{b^{2}}+\frac{q_{3}}{a^{2}} \cos \theta \)
D. \( \frac{q_{2}}{b^{2}}-\frac{q_{3}}{a^{2}} \sin \theta \)
Subject: Chemistry
A measured mass of an unreactive
metal was dropped into a small
graduated cylinder half filled with water. The following measurement were
made:
Mass of metal \( =25.200 g \)
Volume of water before addition of
metal \( =12.5 m L \)
Volume of water after addition of metal
\( =15.0 m L \)
The density of the metal should be reported as:
A. \( 10.0800 g / m L \)
\( L \)
в. \( 10.080 g / m L \)
c. \( 10.08 g / m L \)
D. \( 10.1 g / m L \)
Subject: Chemistry
Which of the above compounds will not
show enolisation?
\( (\mathbf{A}) \)
(B)
\( (\mathrm{C}) \)
\( (\mathbf{D}) \)
his question has multiple correct options
\( A \cdot(A) \)
в. \( (B) \)
\( c \cdot(C) \)
D. \( (D) \)
Subject: Biology
Match the following with correct
combination
\begin{tabular}{lll|l} 
& Column-I & & Column-II \\
a. & Anthoceros & 1. & Walkin fern \\
b. & Asplenium & 2. & Alga \\
c. & Sargassum & 3. & Inferae \\
d. & Prothallus & 4. & Gametophyte \\
e. & Asterales & 5. & Hornwort \\
& 6. & Livewort
\end{tabular}
\( A \)
\( a-6, b-5, c-1, d-3, e-4 \)
\( B \cdot a-5, b-4, c-3, d-2, e-1 \)
\( C \cdot a-5, b-1, c-2, d-4, e-3 \)
D. \( a-3, b-2, c-1, d-5, e-4 \)
\( E \cdot a-1, b-4, c-3, d-5, e-2 \)
Subject: Chemistry
An isotope of helium is represented by the symbol \( _{2}^{3} H e . \) How many protons, neutrons and electrons are there in an
atom of the isotope?
A. 1 proton, 2 neutrons, 1 electron
B. 1 proton, 3 neutrons, 2 electrons
C. 2 protons, 1 neutron, 2 electrons
D. 2 protons, 3 neutrons, 2 electrons
Subject: Physics
The adjoining curve represents the
velocity-time graph of a particle, its
acceleration values along \( \mathrm{O} \mathrm{A}, \mathrm{AB} \) and \( \mathrm{BC} \)
in \( m \cdot / \sec ^{2} \) are respectively:
A. 1,0,-0.5
В. 1,0,0.5
c. 1,1,0.5
D. \( 1,0.5 . \)
Subject: Physics
Conisder a block of conducting material
of resistivity \( \rho \) shown in fig., Current
enters at \( A \) and leaves at \( D \)

For current entering at \( A, \) the electric
field at a distance 'r' from A is??
A \( \cdot \frac{\rho l}{8 \pi r^{2}} \)
B. \( \frac{\rho l}{r^{2}} \)
c. \( \frac{\rho l}{2 \pi r^{2}} \)
D. \( \frac{\rho l}{4 \pi r^{2}} \)
Subject: Physics
A thin convergent glass lens \( \mu=1.5 \) has a power of \( +5 D . \) When this lens is
immersed in a liquid of refractive index
\( \mu \) it acts as a diverging lens of focal length \( 100 \mathrm{cm} . \) The value of \( \mu \) must be :
\( A \cdot 5 / 3 \)
B. \( 4 / 3 \)
c. \( 5 / 4 \)
D. \( 6 / 5 \)
Subject: Chemistry
Write balanced redox reactions of the
following:
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \) reduces \( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}(\boldsymbol{a} \boldsymbol{q}) \) to
green coloured \( C r^{3+}(a q) \) in acidic
medium.
A \( \cdot C r_{2} O_{7}^{2-}+3 H_{2} O_{2}+8 H^{+} \rightarrow 2 C r^{3+}+3 O_{2}+7 H_{2} O \)
B . \( C r_{2} O_{9}^{2-}+3 H_{2} O_{2}+4 H^{+} \rightarrow 2 C r^{3+}+3 O_{2}+7 H_{2} O \)
c. \( C r_{2} O_{7}^{2-}+3 H_{2} O_{2}+8 H^{+} \rightarrow 2 C r^{3+}+3 O_{2}+9 H_{2} O \)
D. None of these
Subject: Physics
A hammer of mass \( M \) falls from a
height \( h \) repeatedly to drive a pile of
mass \( m \) into the ground. The hammer
makes the pile penetrate in the ground
to a distance \( d \) in single blow.

Opposition to penetration is given by:
A \( \cdot \frac{m^{2} g h}{M+m d} \)
B. \( \frac{m^{2} g h}{(M+m) d}+(M+m) g \)
c. \( \frac{M^{2} g h}{M+m d} \)
D. \( \frac{m^{2} g h}{(m+M) d}-(M+m) g \)
Subject: Chemistry
\( X e O_{3} \) has
\( \mathbf{A} \cdot \) one \( p \pi-p \pi \) and two \( p \pi-d \pi \)
B. three \( p \pi-p \pi \) bonds
\( \mathbf{C} \cdot \) four \( p \pi-d \pi \) bonds
D. three \( p \pi-d \pi \) bonds
Subject: Physics
An electric field can just support a
water droplet \( 1.0 \times 10^{-6} \mathrm{m} \) in diameter
carrying one electron charge. The magnitude of electric field strength is
A \( \cdot 3.21 \times 10^{4} V / m \)
В. \( 2.31 \times 10^{4} V / m \)
C \( .1 .32 \times 10^{4} V / m \)
D. \( 6.42 \times 10^{4} V / m \)
Subject: Physics
Assertion
The average and instantaneous velocities have same value in a uniform
motion
Reason
In uniform motion, the velocity of an
object increases uniformly.
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
Assertion
Catalyst is a substance which takes
part in a chemical reaction, undergoes chemical change and alters the rate of a
reaction
Reason
Catalyst is a substance which does not
take part in a chemical reaction, but changes the rate of reaction
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 one of the following statements
is not correct?
A. Oxidation number of \( \sin \left(N H_{4}\right)_{2} S_{2} O_{8} \) is +6
B. Oxidation number of 0 s in \( O s O_{4} \) is +8
C. Oxidation number of \( \sin H_{2} S O_{5} \) is +8
Dexidation number of 0 in \( K O_{2} \) is \( -\frac{1}{2} \)
Subject: Maths
A certain vector in the xy-plane has an
x-component of \( 4 \mathrm{m} \) and a y-component of \( 10 \mathrm{m} . \) It is then rotated in the xy-plane so that its \( x \) -component is doubled Then, its new y-component is (approximately)
A. \( 20 \mathrm{m} \)
B. 7.2 \( m \)
c. \( 5.0 \mathrm{m} \)
D. \( 4.5 \mathrm{m} \)
Subject: Chemistry
Assertion
Oxidation involves loss of electrons and
reduction involves gain of electrons.
Reason
The overall reaction in which oxidation
and reduction occurs simultaneously is called redox reaction.
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
What is the electronic configuration of the ground state of the magnesium
cation, \( M g^{2+} ? \)
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{4} 3 s^{2} \)
Subject: Maths
From a square metal sheet of side \( 28 \mathrm{cm}, \) a circular sheet is cut off. Find the radius of the largest possible
circular sheet that can be cut. Also find
the area of the remaining sheet.
A \( .14 \mathrm{cm}, 148 \mathrm{cm}^{2} \)
B. \( 14 \mathrm{cm}, 168 \mathrm{cm}^{2} \)
c. \( 12 \mathrm{cm}, 168 \mathrm{cm}^{2} \)
D. \( 14 \mathrm{cm}, 164 \mathrm{cm}^{2} \)
Subject: Physics
Given a uniform electric field \( \overrightarrow{\boldsymbol{E}}=\mathbf{2} \times \)
\( 10^{3} \hat{i} \mathrm{N} / \mathrm{C} \). Find the flux of this field
through a square of side \( 20 \mathrm{cm}, \) whose plane is parallel to the \( y \) -z plane. What would be the flux through the same square, if the plane makes an angle of
\( 30^{\circ} \) with the \( x \) -axis?
Subject: Physics
Assertion
For nuclear reactor, it is desirable to
have (Multiplication Factor) \( k=1 \)
Reason
Sustained chain reaction occur at this
critical condition.
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
The masses of \( 10 k g \) and \( 20 k g \) respectively are connected by a
massless spring. A force of \( 200 N \) acts
on the \( 20 k g \) mass. At the instant shown
the \( 10 k g \) mass has an acceleration of
\( 12 m s^{-2}, \) what is the acceleration of
\( 20 k g \) mass \( ? \)
A \( \cdot 12 m s^{-2} \)
B. \( 4 m s^{-2} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-2} \)
D. \( 20 m s^{-2} \)
Subject: Chemistry
If the same element is forming oxides in different oxidation states then:
A. that oxide will be neutral in nature in which element will be in its highest oxidation state
B. the oxide will be highest acidic in nature in which element will be in its highest oxidation state
c. that oxide will be amphoteric in nature in which element will be in its highest oxidation state
D. that oxide will be highly basic in nature in which element will be in its highest oxidation state
Subject: Maths
Prove the following \( \left[\begin{array}{llll}1 & 3 & 2 & 0 \\ 4 & 1 & 5 & 9 \\ 3 & 2 & 1 & 3\end{array}\right] \pm \)
\( \left[\begin{array}{cccc}1 & 0 & 5 & 8 \\ 2 & 3 & 5 & 8 \\ 1 & -5 & 2 & 3\end{array}\right] \)
\( =\left[\begin{array}{cccc}2 & 3 & 7 & 8 \\ 6 & 4 & 9 & 14 \\ 4 & -3 & 3 & 6\end{array}\right] \) for plus
\( =\left[\begin{array}{cccc}0 & 3 & -3 & -8 \\ 4 & 2 & 1 & 4 \\ 0 & 7 & -1 & 0\end{array}\right] \) for minus
Subject: Physics
The mass of \( U^{234} \) of radioactivity 1 curie
is
A . 3.7 \( \times 10^{10} g \)
B. 3.7 \( \times 10^{-10} g \)
c. \( 6.25 \times 10^{-34} g \)
D . 1.438 \( \times 10^{-11} g \)
Subject: Physics
Magnetic field in a region is given by \( \vec{B}=B_{o} x \hat{k} . \) Two loops each of side a is
placed in this magnetic region in the \( x \) y plane with one of its sides on x-axis. If
\( F_{1} \) is the force on loop 1 and \( F_{2} \) be the
force on loop 2 then:
A \( . F_{1}=F_{2}=0 \)
B. \( F_{1}>\left\{F_{3},\{2\} \$ \$\right. \)
\( \mathbf{c} \cdot F_{2}>F_{1} \)
D. \( F_{1}=F_{2} \neq 0 \)
Subject: Physics
Two charges of \( -2 Q \) and \( Q \) are located at points \( (a, 0) \) and \( (4 a, 0) \) respectively. What is the electric flux through a sphere of radius \( 3 a \) centred at the
origin?
A \( \cdot \frac{Q}{\epsilon_{0}} \)
в. \( \frac{-Q}{\epsilon_{0}} \)
c. \( \frac{-2 Q}{\epsilon_{0}} \)
D. \( \frac{3 Q}{\epsilon_{0}} \)
Subject: Physics
From a motorboat moving downstream
with a velocity \( 2 m / s \) with respect to
river, a stone is thrown. The stone falls
on an ordinary boat at the instant when
the motorboat collides with the ordinary boat. The velocity of the ordinary boat with respect to the river is equal to zero.
The river flow velocity is given to be \( \mathbf{1} \boldsymbol{m} / \boldsymbol{s} . \) The initial velocity vector of the stone with respect to earth is
A \( .2 \hat{i}+20 \hat{j} \)
B . \( 3 \hat{i}+40 \hat{j} \)
c. \( 3 \hat{i}+50 \hat{j} \)
D . \( 2 \hat{i}+50 \hat{j} \)
Subject: Physics
Two blocks of masses \( m_{1} \) and \( m_{2} \) are
connected by spring constant \( \boldsymbol{K} \) Initially the spring is at its natural length. The coefficient of friction between the bars and the surface is \( \mu \)
What minimum constant force has to
be applied in the horizontal direction on
the block of mass \( m_{1}, \) in order to shift
the other block?
\( A \)
\[
F=\mu\left(2 m_{1}+\frac{m_{2}}{2}\right) g
\]
В \( \cdot F=\mu\left(2 m_{1}+m_{2}\right) g \)
\( ^{\mathbf{c}} \cdot_{F}=\mu\left(m_{2}+\frac{m_{1}}{2}\right) g \)
\( ^{\mathrm{D}} F=\mu\left(m_{1}+\frac{m_{2}}{2}\right) g \)
Subject: Maths
Show that the Modulus Function \( \boldsymbol{f} \) \( \boldsymbol{R} \rightarrow \boldsymbol{R}, \) given by \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|, \) is neither
one-one nor onto, where \( |x| \) is \( x, \) if \( x \) is
positive or 0 and \( |x| \) is \( -x, \) if \( x \) is
negative.
Subject: Maths
Simplify \( \tan ^{-1}\left[\frac{\boldsymbol{a} \cos \boldsymbol{x}-\boldsymbol{b} \sin \boldsymbol{x}}{\boldsymbol{b} \cos \boldsymbol{x}+\boldsymbol{a} \sin \boldsymbol{x}}\right], \) if
\( \frac{\boldsymbol{a}}{\boldsymbol{b}} \tan \boldsymbol{x}>-1 \)
Subject: Chemistry
What will be the uncertainty in velocity
of an electron when the uncertainty in its position is 1000 , i?
A. \( 5.79 \times 10^{2} \mathrm{ms}^{-1} \)
В. \( 5.79 \times 10^{8} \mathrm{ms}^{-1} \)
c. \( 5.79 \times 10^{4} m s^{-1} \)
D. \( 5.79 \times 10^{-10} \mathrm{ms}^{-1} \)
Subject: Maths
The area bounded by the curve \( y= \) \( (x+1)^{2}, y=(x-1)^{2} \) and the line \( y= \)
0 is
A \( \cdot \frac{1}{6} \)
в. \( \frac{2}{3} \)
\( c \cdot \frac{1}{4} \)
D.
Subject: Maths
Let \( X \) be a set of 5 elements. The number
d of ordered pairs \( (A, B) \) of subsets of \( X \) such that \( \boldsymbol{A} \neq \mathbf{\Phi}, \boldsymbol{B} \neq \mathbf{\Phi}, \boldsymbol{A} \cap \boldsymbol{B}=\mathbf{\Phi} \)
satisfies.
A \( .50 \leq d \leq 100 \)
в. \( 101 \leq d \leq 150 \)
c. \( 151 \leq d \leq 20 \)
D. \( 201 \leq d \)
Subject: Chemistry
Which one of the following pairs of
solution is not an acidic buffer?
A. \( H_{2} C O_{3} \) and \( N a_{2} C O_{3} \)
B. \( H_{3} P O_{4} \) and \( N a_{3} P O_{4} \)
c. \( H C l O_{4} \) and \( N a C l O_{4} \)
D. \( C H_{2} \) COOH and \( C H_{3} \) COONa
Subject: Physics
\( (\overline{\mathbf{A}}+\overline{\mathbf{B}}) \times(\overline{\mathbf{A}}-\overline{\mathbf{B}}) \) is:
A \( \cdot\left(\bar{A}^{2}-\bar{B}^{2}\right) \)
в. \( 2 \overline{\mathrm{AB}} \)
c. \( 2(\overline{\mathrm{A}} \times \overline{\mathrm{B}}) \)
D. \( 2(\overline{\mathrm{B}} \times \overline{\mathrm{A}}) \)
Subject: Physics
A weightless string passes through a slit over a pulley. The slit offers
frictional force \( \boldsymbol{f} \) to the string. The
string carries two weights having
masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} \) where \( \boldsymbol{m}_{2}>\boldsymbol{m}_{1} \)
then acceleration of the weights is:
A \( \cdot \frac{\left(m_{2}-m_{1}\right) g-f}{m_{1}+m_{2}} \)
B. \( \frac{f-\left(\left(m_{2}-m_{1}\right) g\right.}{\left(m_{1}+m_{2}\right)} \)
C \( \cdot \frac{\left(m_{1}+m_{2}\right) g-f}{m_{1}-m_{2}} \)
D. \( \frac{m_{2} g-f}{\left(m_{1}+m_{2}\right)} \)
Subject: Chemistry
The concentration of \( K^{+} \) in interior and
exterior of a Nerve cell are \( 500 \mathrm{mM} \) and
\( 25 \mathrm{mM} \) respectively. The electrical potential (in volt) that exists across the
membrane is : \( \left[\log _{10} 2=\right. \) \( \mathbf{0 . 3}, \mathbf{2 . 3 0 3} \boldsymbol{R} \boldsymbol{T} / \boldsymbol{F}=\mathbf{0 . 0 6}] \) (Given answer
be multiplying with 1000)
Subject: Physics
Two simple harmonic motions are
represented by the equations \( \boldsymbol{Y}_{1}=\mathbf{1 0} \sin \left(\boldsymbol{3} \boldsymbol{\pi} \boldsymbol{t}+\frac{\boldsymbol{\pi}}{\boldsymbol{4}}\right) \) and \( \boldsymbol{Y}_{2}= \)
\( 5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t) \)
Their amplitudes are in the ratio of
A . 2:
B. 3:
c. 1: 3
D. 1:
Subject: Physics
When the following bodies of same radius starts rolling down on same inclined plane, identify the decreasing order of their time of descent:
I) Solid cylinder
II) Hollow cylinder
III) Hollow sphere
IV) Solid sphere
A. \( I V, I, I I I, I I \)
в. \( I I, I I I, I, I V \)
c. \( I, I V, I I I, I I \)
D. II, III, IV,
Subject: Maths
If \( \overline{\boldsymbol{p}}=\hat{\boldsymbol{i}}-\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \overline{\boldsymbol{q}}=\hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}-\boldsymbol{2} \hat{\boldsymbol{k}} \)
are position vectors of points \( \boldsymbol{P} \) and \( \boldsymbol{Q} \)
find the position vector of the point \( \boldsymbol{R} \) which divides segment \( P Q \) internally in
the ratio 2: 1
Subject: Chemistry
The wave number for the shortest
wavelength transition in the Balmer series of atomic hydrogen is :
A . \( 8225714 \mathrm{m}^{-1} \)
В. \( 1523693 m^{-1} \)
\( \mathbf{c} \cdot 5333 c m^{-1} \)
D. \( 27419 \mathrm{cm}^{-1} \)
Subject: Physics
A wire as a parabola \( y=4 x^{2} \) is located
in a uniform magnetic field of inductance B perpendicular to the XY plane. At t=0 a connection starts
translation wise from the parabola apex
with constant acceleration \( \alpha \). The
induced emf in the loop, thus formed, as a function of y is:
A \( e=\sqrt{2 \alpha} \cdot B y \)
\( y \)
в. \( e=B y \sqrt{\frac{\alpha}{2}} \)
c. \( e=\frac{B y \sqrt{a}}{2 \sqrt{2}} \)
D. \( e=\frac{B y \sqrt{\alpha}}{4} \)
Subject: Physics
A man, of mass \( m \), standing at the bottom of the staircase, of height \( \boldsymbol{L} \)
climbs it and stands at its top.
This question has multiple correct options
A. Work done by all forces on man is equal to the rise in potential energy mgL
B. Work done by all forces on man is zero
c. work done by the gravitational force on man is mgL
D. The reaction force from a step does not do work because the point of application of the force does not move while the force exists
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right] \) then show
that for all the positive integers \( n A^{n}= \) \( \left[\begin{array}{cc}\cos n \theta & \sin n \theta \\ -\sin n \theta & \cos n \theta\end{array}\right] \)
Subject: Chemistry
The pH of an aqueous solution of
\( B a(O H)_{2} \) is \( 10 . \) If the \( K_{s p} \) of \( B a(O H)_{2} \)
is \( 1 \times 10^{-9} \), then the concentration of
\( B a^{2+} \) ions in the solution in mol \( L^{-1} \) is:
A. \( 1 \times 10^{-2} \)
B. \( 1 \times 10^{-4} \)
C \( .1 \times 10^{-1} \)
D. \( 1 \times 10^{-5} \)
Subject: Maths
If \( A \) is the coefficient of the middle term
in the expansion of \( (1+x)^{2 n} \) and \( B \) and
\( \mathrm{C} \) are the coefficients of two middle
terms in the expansion of \( (1+x)^{2 n-1} \)
then
A. \( A+B=C \)
в. \( B+C=A \)
c. \( C+A=B \)
D. \( A+B+C=0 \)