AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
In physics, the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties. In which of the following mean free path is used ?
A. to estimate the resistivity of a material
B. to design a chemical apparatus
c. It can be used in optics and in acoustics
D. All of the above
Subject: Chemistry
The composition of mischmetal is:
A. \( 5 \% \) of a lanthanoid metal, \( 95 \% \) of iron and traces of \( S, C, C a \) and \( A l \)
B. \( 95 \% \) of an actinoid metal, \( 5 \% \) of iron and traces of \( S, C, C a \) and \( A l \)
C. \( 95 \% \) of a lanthanoid metal, \( 5 \% \) of iron and traces of \( S, C, C a \) and \( A l \)
D. \( 95 \% \) of a transition metal, \( 5 \% \) of iron and traces of \( S, C, C a \) and \( A l \)
Subject: Biology
Which of the following enzymes has/have heme as a prosthetic group?
(i) Catalase
(ii) Carboxypeptidase
(iii) Succinic dehydrogenase
(iv) Peroxidase
\( A \cdot( \) i) only
B. (i) and (ii)
c. (ii) and (iii)
D. (iii) and (iv)
E. (i) and (iv)
Subject: Physics
A bus travels \( 30 \mathrm{km} \) at a uniform speed of \( 40 \mathrm{km} / \mathrm{h} \) and the next \( 30 \mathrm{km} \) at a
uniform speed of \( 20 \mathrm{km} / \mathrm{h} \).The average speed of the bus is
\( \mathbf{A} \cdot 26.6 \mathrm{km} / \mathrm{h} \)
B. 36.8 km/h
c. \( 25 \mathrm{km} / \mathrm{h} \)
D. 28.9 km/h
Subject: Physics
Which of the following set ups represent a second class lever?
\( A \)
\[
\frac{L F E}{\Delta}
\]
в.
\[
\begin{array}{lll}
F & L & E \\
\hline \Delta
\end{array}
\]
\( c \)
\[
\frac{L}{L} E \frac{F}{\Delta}
\]
D.
\[
\frac{F}{\Delta} E L
\]
Subject: Physics
A solid copper sphere has a charge of
\( +Q \) on it. Identify the correct statement
about the charge distribution of solid
sphere?
A. \( +Q \) at the center of the sphere
B. \( Q / 2 \) at the center of the sphere and \( Q / 2 \) on the outer surface
c. \( -Q \) at the center of the sphere and \( +2 Q \) on the outer surface
D. \( +Q \) on the outer surface
E. The charge is spread evenly throughout the sphere
Subject: Maths
\( \operatorname{Let} f(x)=\frac{x^{2}-4}{x^{2}+4} \) for \( |x|>2, \) then the
function \( \boldsymbol{f}:(-\infty,-2] \cup[2, \infty) \rightarrow \)
(-1,1) is
A. One-one into
B. One-one onto
c. Many one into
D. Many one onto
Subject: Chemistry
The \( \pi \) acid ligands donate their lone pairs to the metal to form a normal
bond with the latter in addition to it, the
vacant orbitals accept e- from the filled metal orbitals to form a type of \( \pi \) -bond which supplements the \( \sigma \) bond.

Which of the following has lowest C-O bond length?
A \( \cdot\left[N i(C O)_{4}\right] \)
в. \( \left[\operatorname{Co}(C O)_{4}\right]^{-} \)
c. \( \left[F e(C O)_{4}\right]^{2} \)
D. \( \left[M n(C O)_{6}\right]^{+} \)
Subject: Chemistry
Statement 1: The addition of \( \boldsymbol{H}_{2} \) to
ethene will form an unsaturated
compound called ethane Statement 2: Ethane, has as many
hydrogen atoms bonded to the carbon atoms as possible
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement'
c. statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct
Subject: Physics
A physical quantity \( A \) is related to four observable \( a, b, c \) and \( d \) as follows, \( A= \) \( \frac{a^{2} b^{3}}{c \sqrt{d}}, \) the percentage errors of
measurement in \( a, b, c \) and \( d \) are \( 1 \%, 3 \% \) \( 2 \% \) and \( 2 \% \) respectively. What is the percentage error in the quantity \( \boldsymbol{A} \) ?
A . \( 12 \% \)
B . \( 7 \% \)
c. \( 5 \% \)
D. 14\%
Subject: Maths
Solution set of \( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{3} & \boldsymbol{5} \\ \boldsymbol{2} & \boldsymbol{6} & \boldsymbol{1 0} \\ \boldsymbol{7} & \boldsymbol{2 1} & \boldsymbol{3 5}\end{array}\right|=0 \)
\( A \cdot \phi \)
B. (1)
\( c . R \)
D. (0)
Subject: Chemistry
How many molecules of \( C O_{2} \) are
present in one litre of air containing
\( 0.03 \% \) by volume of \( C O_{2} \) at STP?
A . \( 8.066 \times 10^{10} \)
в. \( 8.066 \times 10^{-10} \)
\( c \cdot 8.066 \times 10^{-18} \)
D. \( 8.066 \times 10^{18} \)
Subject: Chemistry
What is the total number of sigma bonds and pi bonds in the following
molecules? \( \boldsymbol{C}_{2} \boldsymbol{H}_{3} \boldsymbol{C l}, \boldsymbol{C H}_{2} \boldsymbol{C l}_{2}, \boldsymbol{H}_{3} \boldsymbol{C}-\dot{\boldsymbol{C}}=\stackrel{\boldsymbol{H}}{\boldsymbol{C}}- \)
\( \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H} \)
Subject: Maths
\( \lim _{x \rightarrow \infty}\left\{\left(e^{x}+\pi\right)^{\frac{1}{x}}\right\} \) ( where \{\} denotes the
fractional part of \( x \) ) is equal to:
\( \mathbf{A} \cdot \pi-e \)
B . \( \pi-3 \)
\( \mathbf{c} \cdot e-2 \)
D. \( 3-e \)
Subject: Chemistry
The compound in which all the bond
angles around every atom are 109.28 is:
\( \mathbf{A} \cdot H C O O H \)
B \( \cdot\left(N H_{2}\right)_{2} C O \)
с. \( \left(C H_{3}\right)_{3} C O H \)
D. \( \left(C H_{3}\right)_{3} C C H O \)
Subject: Maths
The vertices of \( \triangle A B C \) are
\( \boldsymbol{A}(\mathbf{1}, \mathbf{8}), \boldsymbol{B}(-\mathbf{2}, \mathbf{4}), \boldsymbol{C}(\mathbf{8},-\mathbf{5}) . \) If \( \boldsymbol{M} \) and \( \boldsymbol{N} \)
are the midpoints of \( A B \) and \( A C \)
respectively, find the slope of \( M N \) and
hence verify that \( M N \) is parallel to \( B C \).
A \( \cdot-\frac{9}{10} \)
в. \( \frac{9}{10} \)
\( c \cdot-\frac{9}{5} \)
D. None of these
Subject: Physics
A chain \( A B \) of mass \( m \) and length \( L \) is
hanging on a smooth horizontal table as shown in the figure. If it is released from
the position shown then the displacement of centre of mass of chain
in magnitude, when end \( A \) moves a
distance \( \frac{L}{2} i s X \sqrt{2} m \)
Find \( \boldsymbol{X} .(\boldsymbol{L}=\mathbf{3} 2 \boldsymbol{m}) \)
A \( \cdot \frac{m g l}{4} \)
в. \( \frac{m g}{8} \)
c. \( \frac{m g}{24} \)
D. \( \frac{m g}{32} \)
Subject: Physics
A uniform wire of length \( 1 ~ m \) and radius
\( 0.028 \mathrm{cm} \) is employed to raise a stone of
density \( 2500 \mathrm{kg} / \mathrm{m}^{3} \) immersed in water. Find the change in elongation of wire when the stone is raised out of
water.
\( [\text {massofstone}=\mathbf{5} k g, \) Yofmaterialo
Subject: Physics
Assertion
Space rockets are usually launched in the equatorial line from west to east
Reason
The acceleration due to gravity is minimum at the equator.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True
Subject: Chemistry
ASSERTION: \( C u F e S_{2} \) is concentrated
by froth floatation method.

REASON: \( C u F e S_{2} \) is the main ore of
copper.
A. If both assertion and reason are CORRECT, and reason is the CORRECT explanation of the assertion
B. If both assertion and reason are CORRECT, but reason is NOT the CORRECT explanation of the assertion
c. If assertion is CORRECT but reason is INCORRECT
D. If assertion is INCORRECT but reason is CORRECT
Subject: Maths
\( \mathbf{f}\left[\begin{array}{cc}\boldsymbol{x}-\boldsymbol{y} & \boldsymbol{z} \\ \mathbf{2} \boldsymbol{x}-\boldsymbol{y} & \boldsymbol{w}\end{array}\right]=\left[\begin{array}{cc}-\mathbf{1} & \mathbf{4} \\ \mathbf{0} & \mathbf{5}\end{array}\right], \) find the
value of \( \boldsymbol{x}+\boldsymbol{y} \)
Subject: Physics
An alternating potential \( V=V_{0} \sin \omega t \)
is applied across a circuit. As a result, the current \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{\pi}}{2}\right) \) flows
in it. The power consumed in the circuit per cycle is:
A . zero
в. \( 0.5 I_{0} V_{0} \)
с. \( 0.707 I_{0} V_{0} \)
D. \( 1.414 I_{0} V_{0} \)
Subject: Chemistry
Draw Werner's structure of the
following:
(a) \( C o C l_{3} .6 N H_{3} \)
(b) \( C o C l_{3} .5 N H_{3} \)
(c) \( C o C l_{3} .4 N H_{3} \)
(d) \( C o C l_{3} .3 N H_{3} \)
Subject: Chemistry
The molar mass of \( N_{2} O \) as well as \( C O_{2} \)
is \( 44 g m o l^{-1} . A t 25^{o} C \) and 1 atm
pressure, \( 1 \mathrm{L} N_{2} \mathrm{O} \) contains \( \mathrm{n} \) molecules
of gas. The number of \( C O_{2} \) molecules in
2 L under same conditions will be:
\( A \)
B. \( 2 n \)
\( c \cdot \frac{n}{2} \)
\( D \cdot \frac{n}{n} \)
Subject: Maths
Prove that
\( \left|z_{1}\right|+\left|z_{2}\right|=\left|\frac{1}{2}\left(z_{1}+z_{2}\right)+\sqrt{z_{1} z_{2}}\right|+ \)
\( \left|\frac{1}{2}\left(z_{1}+z_{2}\right)-\sqrt{z_{1} z_{2}}\right| \)
Subject: Physics
Two circular rings of equal mass \( (\boldsymbol{m}) \) and radius \( (r) \) are placed side by side, touching each other. The moment of inertia of the system about tangential axis in the plane of system passing through point of contact of the rings is:
A \( \cdot \frac{3}{2} m r^{2} \)
B. \( 6 m r^{2} \)
c. \( \frac{5}{2} m r^{2} \)
\( D \cdot 3 m r^{2} \)
Subject: Maths
A parallelogram \( A B C D \) has sides \( A B=24 \mathrm{cm}, A D=16 \mathrm{cm} . \) The
distance between the sides \( A B \) and
DC is \( 10 \mathrm{cm} . \) Find the distance
between the sides \( A D \) and \( B C= \)
\( \mathbf{A} \cdot 16 \mathrm{cm} \)
B. \( 18 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 26 \mathrm{cm} \)
Subject: Physics
When a charge of amount \( Q \) is given to an isolated metal plate \( X \) of surface area \( A, \) its surface charge density
becomes \( \sigma_{1} . \) When an isolated identical
plate \( Y \) is brought close to \( X, \) the surface charge density on X becomes
\( \sigma_{2} . \) When \( y \) is earthed, the surface
charge density becomes \( \sigma_{3} \)
This question has multiple correct options
A \( \cdot \sigma_{1}=\frac{Q}{A} \)
В. \( \sigma_{1}=\frac{Q}{2 A} \)
\( \mathbf{C} \cdot \sigma_{1}=\sigma_{2} \)
D. \( _{\sigma_{3}}=\frac{Q}{A} \)
Subject: Physics
Potential difference between centre and
the surface of sphere of \( R \) and having uniform volume charge density. p with it will be :
A \( \cdot \frac{p R^{2}}{6 \epsilon_{0}} \)
в. \( \frac{p R^{2}}{4 \epsilon_{0}} \)
\( c \cdot 0 \)
D. \( \frac{p R^{2}}{2 \epsilon_{0}} \)
Subject: Maths
Find the modulus and the principal value of the argument of the number
\( 1-i \)
A \( \cdot \sqrt{2}, \pi / 4 \)
B \( \cdot \sqrt{2},-\pi / 4 \)
c. \( \sqrt{2},-\pi / 3 \)
D. \( \sqrt{2}, 3 \pi / 4 \)
Subject: Chemistry
A silver electrode is immersed in
saturated \( A g_{2} S O_{4}(a q .) . \) The potential
difference between silver and the
standard hydrogen electrode is found to
be \( 0.711 V . \) Determine \( K_{s p}\left(A g_{2} S O_{4}\right) \)
\( \left(\text { Given, } \boldsymbol{E}_{A \boldsymbol{g}^{+} / A \boldsymbol{g}}^{\circ}=\mathbf{0 . 7 9 9} \boldsymbol{V}\right) \)
Subject: Chemistry
A first order reaction was commenced
with \( 0.2 \mathrm{M} \) solution of the reactants. If
the molarity of the solution falls to \( 0.02 M \) after 100 minutes the
rate constant of the reaction is:
A \( \cdot 2 \times 10^{-2} \min ^{-1} \)
В. \( 2.3 \times 10^{-2} \min ^{-1} \)
c. \( 4.6 \times 10^{-2} \min ^{-1} \)
D. \( 2.3 \times 10^{-1} \min ^{-1} \)
Subject: Physics
An observer is moving with half the speed of light toward a stationary microwave source emitting waves frequency \( 10 \mathrm{GHz} \). What is the frequency of the microwave measured by the observer? (speed of the light=3 \( x \) \( 10^{8} m s^{-1} \)
A. \( 17.3 \mathrm{GHz} \)
B . 15.3 GHz
c. 10.1 Gн
D. 12.1 GHz
Subject: Chemistry
According to Werner's theory the primary valency and secondary valency in complex \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl} \) is
respectively:
\( A \cdot 3,3 \)
B. 3,6
\( c \cdot 6,3 \)
\( D \cdot 4,2 \)
Subject: Biology
Assertion
Muscles fibres of SA node possess the lowest rhythmicity among all cardiac
muscles.
Reason
Due to this fact, it can initiate excitory waves at the highest rate
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
A silver article generally turns black when kept in the open for a few days. The article when rubbed with
toothpaste again starts shining. Name the black substance formed and give its chemical formula:
A . silver oxide, \( \left(A g_{2} \text { , } \) ) \right.
B. Silver chloride, \( (A g C l) \)
C. Silver sulphide, \( \left(A g_{2} S\right) \)
D. silver iodide,( \( (A g I) \)
Subject: Physics
The radius of the circular conducting
loop shown in figure is \( \boldsymbol{R} \). Magnetic field
is decreasing at a constant rate \( \alpha \) Resistance per unit length of the loop is
\( \rho . \) Then, the current in wire \( A B \) is \( (A B \)
is one of the diameters)
\( ^{\mathbf{A}} \cdot \frac{R \alpha}{2 \rho} \) from \( A \) to \( B \)
в. \( \frac{R \alpha}{2 \rho} \) from \( B \) to \( A \)
\( ^{c} \cdot \frac{R \alpha}{\rho} \) from \( B \) to \( A \)
D.
E . answer required
Subject: Physics
A particle of mass \( \mathrm{m} \) is moving in a
circular path of constant radius r such
that its centripetal acceleration \( a_{c} \) is
varying with time \( t \) as \( a_{c}=k^{2} r t^{2} \) where
\( k \) is a constant. The power delivered to the particle by the forces acting on it, is?
A. zero
B. \( m k^{2} r^{2} t^{2} \)
\( \mathbf{c} \cdot m k^{2} r^{2} t \)
\( \mathbf{D} \cdot m k^{2} r t \)
Subject: Maths
If \( \tan A=\frac{5}{12}, \) find the value of \( (\sin A+ \)
\( \cos A) \times \sec A: \)
A \( \cdot \frac{6}{13} \)
в. \( \frac{7}{12} \)
c. \( \frac{17}{12} \)
D. \( \frac{12}{17} \)
Subject: Physics
A string is clamped at both the ends and it is vibrating in its 4 th harmonic. The equation of the stationary wave is \( \boldsymbol{Y}=\mathbf{0 . 3} \sin (\mathbf{0 . 1 5 7} \boldsymbol{x}) \cos (\mathbf{2 0 0} \boldsymbol{\pi} \boldsymbol{t}) . \) The
length of the string is: (All quantities are in SI units)
A \( .20 m \)
в. \( 80 m \)
c. \( 60 m \)
D. \( 40 m \)
Subject: Chemistry
Which of the following is tetrahedral paramagnetic complex?
A \( \cdot K_{2}\left[P t C l_{4}\right] \)
в. \( K_{2}\left[M n C l_{4}\right] \)
c. \( _{K_{2}}\left[Z n C l_{4}\right] \)
D \( \cdot K_{2}\left[H g l_{4}\right] \)
Subject: Physics
When load is applied to a wire, the extension is 3 mm. The extension in the
wire of same material and length but
half the radius extended by the same load is :
A. \( 0.75 \mathrm{mm} \)
B. \( 6 m m \)
\( c .1 .5 m m \)
D. \( 12.0 m m \)
Subject: Physics
Force acting between two small magnets, placed in end on position
\( 0.1 m \) apart from their centres is
(Given magnetic moment of each
magnet is \( \left.5 A m^{2}\right) \)
A . \( 0.6 N \)
B. \( 0.8 N \)
c. \( 0.15 N \)
D. \( 0.2 N \)
Subject: Physics
Efficiency of a heat engine whose sink is at a temperature of \( 300 K \) is \( 40 \% \). To
increase the efficiency to \( 60 \% \), keeping the sink temperature constant, the source temperature must be increased
by :
\( \mathbf{A} \cdot 750 K \)
B. \( 500 K \)
c. \( 250 K \)
D. \( 1000 K \)
Subject: Maths
Solve: \( \int \frac{d x}{\sqrt{x^{2}+2 x+5}} \)
A \( \cdot \ln |\sqrt{x^{2}+2 x+5}-x+1|+C \)
B \( \cdot \ln |\sqrt{x^{2}+2 x+5}+x+1|+C \)
c. \( \ln |\sqrt{x^{2}+2 x+5}-x|+C \)
D. None of these
Subject: Physics
A spherical planet far out in space has a
\( \operatorname{mass} M_{0} \) and diameter \( D_{0} . \) A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to:
A \( \cdot \frac{G M_{0}}{D_{0}^{2}} \)
в. \( \frac{4 m G M_{0}}{D_{0}^{2}} \)
c. \( \frac{4 G M_{0}}{D_{0}^{2}} \)
D. \( \frac{G m M_{0}}{D_{0}^{2}} \)
Subject: Maths
For positive numbers \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \) the
numerical value of the determinant \( \left|\begin{array}{ccc}\mathbf{1} & \log _{x} \boldsymbol{y} & \log _{\boldsymbol{x}} \boldsymbol{z} \\ \log _{\boldsymbol{y}} \boldsymbol{x} & \boldsymbol{3} & \log _{\boldsymbol{y}} \boldsymbol{z} \\ \log _{\boldsymbol{z}} \boldsymbol{x} & \log _{\boldsymbol{z}} \boldsymbol{y} & \boldsymbol{5}\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \log x \log y \log z \)
\( c .1 \)
D. 8
Subject: Chemistry
Yasmeen wrote few series of
hydrocarbon and left blanks in between.
Look at the chemical formula in the
series of hydrocarbon carefully. Answer
the following questions accordingly.
\( \begin{array}{cccc}1 & \mathrm{II} & \mathrm{III} \\ C H_{4} & C_{2} H_{4} & \mathrm{X} \\ C_{2} H_{6} & C_{3} H_{6} & C_{3} H_{4} \\ \mathrm{Y} & C_{4} H_{8} & C_{4} H_{6} \\ C_{4} H_{10} & \mathrm{z} & C_{5} H_{8}\end{array} \)
X and Y respectively are:
\( \mathbf{A} \cdot C_{2} H_{2} \) and \( C_{3} H_{8} \)
B. \( C_{2} H_{2} \) and \( C_{4} H_{10} \)
\( \mathbf{c} \cdot C_{2} H_{2} \) and \( C_{3} H_{6} \)
\( \mathbf{D} \cdot C_{2} H_{4} \) and \( C_{3} H_{8} \)
Subject: Physics
A small ball (menu) falling under
gravity in a viscous medium
experiences a drag force proportional to the instantaneous speed u such that
\( F_{d r a g}= \) Ku. Then the terminal speed of the ball within the viscous medium is:
A \( \cdot \frac{K}{m g} \)
в. \( \frac{m g}{K} \)
c. \( \sqrt{\frac{m g}{K}} \)
D. \( \left(\frac{m g}{K}\right)^{2} \)
Subject: Physics
Two identical cylinders \( A \) and \( B \) with frictionless pistons contain the same
ideal gas at same temperature and the same volume \( V \). The mass of gas \( A \)
is \( m_{A} \) and that of \( B \) is \( m_{B} . \) The gas in
each cylinder is allowed to expand isothermally to the same final volume
2V. The change in the pressure in \( A \) and B are found to be \( \Delta P \) and \( 1.5 \Delta P \)
respectively. Then
\( \mathbf{A} \cdot 4 m_{A}=9 m_{B} \)
B. \( 3 m_{A}=3 m_{B} \)
\( \mathbf{c} \cdot 3 m_{A}=2 m_{B} \)
D. \( 9 m_{A}=4 m_{B} \)
Subject: Maths
Assertion
The maximum value of
\( (\sqrt{-3+4 x-x^{2}}+4)^{2}+(x-5)^{2} \)
(where \( 1 \leq x \leq 3 \) ) is 36
Reason
The maximum distance between the
point (5,-4) and the point on the circle
\( (x-2)^{2}+y^{2}=1 \) is 6
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 wire of resistance \( 40 \Omega \) is bent into a
square. Then consider the following
statements:
a) resistance between opposite corners
is \( 20 \Omega \)
b) resistance between adjucent corners
is \( 7.5 \Omega \)
c) resistance between mid points of
opposite sides is \( 10 \Omega \)
d) resistance between mid points of
adjacent sides is \( 15 \Omega \)
A. a and dare correct
B. b and d are correct
C. \( b \) and \( c \) are correct
D. a and b are correct
Subject: Physics
A \( 50 H z \) alternating current of crest value \( 2.0 . A \) flows through the primary of a transformer. If the mutual inductance
between the primary and secondary is \( 0.25 H . \) The crest voltage induced in the
secondary is
A . \( 50 V \)
B. \( 100 V \)
c. \( 200 V \)
D. 300V
Subject: Maths
The number of solutions of the equation \( \mathbf{1}+\sin \boldsymbol{x} \cdot \sin ^{2} \frac{\boldsymbol{x}}{\mathbf{2}}=\mathbf{0}[-\boldsymbol{\pi}, \boldsymbol{\pi}] \) is
A . zero
B.
\( c \cdot 2 \)
\( D \)
Subject: Chemistry
A buffer solution can be prepared from a
mixture of:
(i) Sodium acetate and acetic acid in
water
(ii) Sodium acetate and hydrochloric
acid in water
(iii) Ammonia and ammonium chloride
in water
(iv) Ammonia and sodium hydroxide in
water
\( A \cdot(i),(\text { ii }) \)
B . (ii), (iii)
c. (iii), (iv)
D. (i), (iii)
Subject: Physics
A block of mass 2 kg slides down an
incline plane of inclination \( 30^{0} . \) The coefficient of friction between block and
plane is \( 0.5 . \) The contact force between block and plank is:
A. 20 N
B. \( 10 \sqrt{3} \) N
c. \( 5 \sqrt{7} \) N
D. \( 5 \sqrt{15} \) N
Subject: Chemistry
Which of the following compounds is
not colored?
A. \( N a_{2} C u C l_{4} \)
в. \( N a_{2} C d C l_{4} \)
\( \mathbf{c} \cdot N a_{3}\left[F e(C N)_{6}\right] \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)
Subject: Maths
ff \( a_{1}, a_{2}, a_{3}, b_{1}, b_{2}, b_{3} \in R \) and are such
\( \operatorname{that} a_{i} b_{j} \neq 1 \) for \( 1 \leq i, j \leq 3, \) then
\( \begin{array}{|lll|}\frac{1-a_{1}^{3} b_{1}^{3}}{1-a_{1} b_{1}} & \frac{1-a_{1}^{3} b_{2}^{3}}{1-a_{1} b_{2}} & \frac{1-a_{1}^{3} b_{3}^{3}}{1-a_{1} b_{3}} \\ \frac{1-a_{2}^{3} b_{1}^{3}}{1-a_{2} b_{1}} & \frac{1-a_{2}^{3} b_{2}^{3}}{1-a_{2} b_{2}} & \frac{1-a_{2}^{3} b_{3}^{3}}{1-a_{2} b_{3}} \\ \frac{1-a_{3}^{3} b_{1}^{3}}{1-a_{3} b_{1}} & \frac{1-a_{3}^{3} b_{2}^{3}}{1-a_{3} b_{2}} & \frac{1-a_{3}^{3} b_{3}^{3}}{1-a_{3} b_{3}}\end{array} \)
either \( a_{1}<a_{2}<a_{3} \) and \( b_{1}<b_{2}<b_{3}, \) or
\( a_{1}>a_{2} a_{3} \) and
\( \boldsymbol{b}_{1}>\boldsymbol{b}_{2}>\boldsymbol{b}_{3} \)
then show \( \left(a_{1}-a_{2}\right)\left(a_{2}-a_{3}\right)\left(a_{3}-\right. \)
\( \left.\boldsymbol{a}_{1}\right)\left(\boldsymbol{b}_{1}-\boldsymbol{b}_{2}\right)\left(\boldsymbol{b}_{2}-\boldsymbol{b}_{3}\right)\left(\boldsymbol{b}_{3}-\boldsymbol{b}_{1}\right)<\mathbf{0} \)
Subject: Physics
A coil of inductance \( 8.4 m H \) and
resistance \( 4.2 \Omega \) is connected to \( 10 V \)
battery. The time constant of the circuit
is
\( \mathbf{A} \cdot 2 m s \)
в. \( 0.5 m s \)
c. \( 4 m s \)
D. \( 0.25 \mathrm{ms} \)
Subject: Maths
The value of \( \lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^{2} x\right)}{x^{2}} \) is
A. \( -\pi \)
в. \( \frac{\pi}{2} \)
c. \( \pi \)
D. \( \frac{3 \pi}{2} \)
Subject: Chemistry
Assertion
\( N O_{2} \) is reddish brown and its dimer
\( N_{2} O_{4} \) is colourless
Reason
There is a dative bond formation
between two \( N O_{2} \) molecules
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
If \( \boldsymbol{x}=\boldsymbol{2} \boldsymbol{p}, \) then find the value of \( \boldsymbol{p} \) from
the equation \( : 2(3 p+3)-\frac{2}{5}(3+ \)
\( 4 x)=\frac{9}{2} \)
Subject: Maths
Suppose \( \boldsymbol{f}:[\mathbf{0}, \boldsymbol{\pi}] \rightarrow \mathbb{R} \) satisfied \( \boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{f}(\boldsymbol{\pi}-\boldsymbol{x})=1 \) for all \( \boldsymbol{x} . \) Then
\( \int_{0}^{\pi} f(x) \sin x d x \) is
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.
Subject: Maths
The diagram below shows part of the \( \operatorname{graph} \) of \( y=\frac{b-x}{c x+d} \)
The \( x \) intercept is (6,0)
The vertical asymptote is \( \boldsymbol{x}=-3 \)
The horizontal asymptote is \( y=-1 \)
Find the value of \( \boldsymbol{d} \)
Subject: Maths
\( \operatorname{Let} z_{k}(k=0,1,2, \dots \dots \dots .6) \) be the roots
of the equation \( (z+1)^{7}+z^{7}=0, \) then
\( \sum_{k=0}^{6} R e\left(z_{k}\right) \) is equal to
\( A \cdot 0 \)
B. \( \frac{3}{2} \)
c. \( -\frac{7}{2} \)
D. \( \frac{7}{2} \)
Subject: Maths
Calculate the scalar product of the following vectors \( \boldsymbol{a}=\mathbf{3} \boldsymbol{i}+\mathbf{2} \boldsymbol{j}+\mathbf{2} \boldsymbol{k} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{b}=\mathbf{1} \mathbf{8} \boldsymbol{i}- \)
\( 22 j-5 k \)
Subject: Maths
If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\alpha} & \sin \boldsymbol{\alpha} \\ -\sin \boldsymbol{\alpha} & \cos \boldsymbol{\alpha}\end{array}\right], \) then verify that
\( \boldsymbol{A}^{\boldsymbol{T}} \boldsymbol{A}=\boldsymbol{I}_{2} \)