AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Physics
A particle with mass 2.0 mg and charge \( 3.0 \mu C \) is in a region with uniform electric field of \( (\mathbf{3} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}) \boldsymbol{N} / \boldsymbol{C} \). The
acceleration of the particle will be:
A \( \cdot(3 \hat{i}+4 \hat{j}) m / s^{2} \)
B \( \cdot(1.5 \hat{i}+2 \hat{j}) m / s^{2} \)
\( \mathbf{c} \cdot(4.5 \hat{i}+6 \hat{j}) m / s^{2} \)
D. \( (2 \hat{i}+3 \hat{j}) m / s^{2} \)
Subject: Physics
A uniform wire of length \( 4 m \) and area of
\( \operatorname{cross} \operatorname{section} 2 m m^{2} \) is subjected to
longitudinal force produced an
elongation of 1 mm.lf \( Y=0.2 \times 10^{11} \mathrm{NM}^{-2} \)
elastic potential energy stored in the body is
A. \( 0.5 J \)
\( J \)
в. \( 0.05 J \)
c. \( 0.005 J \)
D. \( 5.0 J \)
Subject: Physics
A conductor wire, having \( 10^{29} \) free
electrons per \( m^{3} \) carries a current of
\( 20 A . \) If the cross-section of the wire is
\( 1 m m^{2}, \) then the drift velocity of
electrons will be of the order of:
A \( \cdot 10^{-5} m s^{-1} \)
B. \( 10^{-3} \mathrm{ms}^{-1} \)
c. \( 10^{-4} m s^{-1} \)
D. \( 10 m s^{-1} \)
Subject: Chemistry
The vapour pressure of a pure liquid \( \mathbf{A} \) is \( 40 \mathrm{mm} \) of \( \mathrm{Hg} \) at \( 310 \mathrm{K} \). The vapour pressure of this liquid in a solution with liquid B is 32 mm of Hg. The mole fraction of \( A \) in the solution, if it obey's Raoult's law, is?
A . 0.8
B. 0.5
\( c \cdot 0.2 \)
D. 0.4
Subject: Physics
Charges \( Q, 2 Q \) and \( 4 Q \) are uniformly distributed in three dielectric solid
spheres 1,2 and 3 of radii \( \mathrm{R} / 2, \mathrm{R} \) and \( 2 \mathrm{R} \) respectively. If magnitudes of the electric fields at point \( P \) at a distance \( R \) from the centre of spheres 1,2 and 3 are
\( E_{1}, E_{2}, \) and \( E_{3} \) respectively, then:
A. \( E_{1}>E_{2}>E_{3} \)
в. \( E_{3}>E_{1}>E_{2} \)
c. \( E_{2}>E_{1}>E_{3} \)
D. \( E_{3}>E_{2}>E_{1} \)
Subject: Physics
A student performs an experiment for determination of \( g\left(=\frac{4 \pi^{2} l}{T^{2}}\right), l \approx 1 m \)
and he commits an error of \( \Delta l \). For T he
takes the time of n oscillations with the
stop watch of least count \( \Delta T \) and the
commits a human error of 0.1 sec. For
which of the following data, the measurement of \( g \) will be most
accurate?
A. \( \Delta l-5 m m, \Delta T-0.2 \sec , n-10 \), Amplitude of oscillation \( 5 \mathrm{mm} \)
B. \( \Delta l=5 m m, \Delta T-0.2 \) sec \( , n-20, \) Amplitude of oscillation-
\( 5 \mathrm{mm} \)
c. \( \Delta l-5 m m, \Delta T-0.1 \sec , n- \)
\( 20, \) Amplitude of oscillation \( 1 \mathrm{mm} \)
D. \( \Delta l \) -1mm, \( \Delta T \) -0.1sec, \( n-50 \), Amplitude of oscillation-
\( \mathrm{mm} \)
Subject: Physics
A light ray is incident perpendicular to
one face of a \( 90^{0} \) prism and is totally intemally reflected at the glass-air
interface. If the angle of reflection is \( 45^{\circ} \)
we conclude that the refractive index n
4
B \( . n>\sqrt{2} \)
\( c \cdot n>\frac{1}{\sqrt{2}} \)
D. \( n<\sqrt{2} \)
Subject: Maths
Find the area bounded by \( \boldsymbol{y}= \) \( \cos ^{-1} x, y=\sin ^{-1} x \) and \( y- \) axis
A \( \cdot(2-\sqrt{2}) \) sq. units
B \( \cdot(\sqrt{2}-2) \) sq. units
c. \( 2 \sqrt{2} \) sq. units
D. \( \sqrt{2} \) sq. units
Subject: Maths
Function \( f(x)=\left\{\begin{array}{ll}5 x-4 & \text { for } 0<x \leq 1 \\ 4 x^{2}-3 x & \text { for } 1<x<2 \\ 3 x+4 & \text { for } x \geq 2\end{array}\right. \)
A. continuous at \( x=1 \) and \( x=2 \)
B. continuous at \( x=1 \) but not derivable at \( x=z \)
c. continuous at \( x=2 \) but not derivable at \( x=1 \)
D. none of these
Subject: Maths
which of the following function(s) is/are Transcendental?
This question has multiple correct options
\( \mathbf{A} \cdot f(x)=5 \sin \sqrt{x} \)
B. \( f(x)=\frac{2 \sin 3 x}{x^{2}+2 x-1} \)
C. \( f(x)=\sqrt{x^{2}+2 x-1} \)
D. \( f(x)=\left(x^{2}+3\right) 2^{x} \)
Subject: Maths
Assertion
Points
\( \boldsymbol{A}(\boldsymbol{4}, \boldsymbol{0}, \boldsymbol{4}), \boldsymbol{B}(\boldsymbol{1}, \boldsymbol{2}, \boldsymbol{3}), \boldsymbol{C}(-\boldsymbol{2}, \boldsymbol{4}, \boldsymbol{2}) \) are
collinear
Reason
Three points \( A, B, C \) are collinear if
\( \boldsymbol{A B}+\boldsymbol{B C}=\boldsymbol{A C} \) and \( \boldsymbol{A B}, \boldsymbol{B C}<\boldsymbol{A C} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true
Subject: Maths
Find the value of limit
\( \lim _{x \rightarrow \frac{\pi}{6}} \frac{2 \sin ^{2} x+\sin x-1}{2 \sin ^{2} x-3 \sin x+1}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 3
\( c .-3 \)
D.
Subject: Physics
Find out the points on the line joining two charges \( +\boldsymbol{q} \) and \( \boldsymbol{3} \boldsymbol{q} \) (kept at a
distance of \( 1.0 m \) in that order), where
electric potential is zero. This question has multiple correct options
A. \( 0.5 m \) to the left of \( q \)
B. \( 0.5 m \) to the right of \( q \)
c. \( 0.25 m \) to the right of \( q \)
D. \( 0.75 m \) to the right of \( q \)
Subject: Chemistry
Sulphuric acid is \( 95.8 \% \) by mass.
Calculate mole fraction of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) of
density \( 1.91 \mathrm{cm}^{-3} .(H=1, S= \)
\( \mathbf{3 2}, \boldsymbol{O}=\mathbf{1 6}) \)
A . 0.8950
B. 0.2982
c. 0.2056
D. 0.8075
Subject: Physics
The wavefront of a light beam is given by the equation \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\boldsymbol{c} \)
(where \( c \) is arbitrary constant) then what is the angle made by the direction of light with the y-axis?
A \( \cdot \cos ^{-2} \frac{2}{\sqrt{14}} \)
B. \( \cos ^{-1} \frac{2}{\sqrt{14}} \)
\( \mathrm{c} \cdot \cos ^{-3} \frac{2}{\sqrt{14}} \)
D. \( \cos ^{-4} \frac{2}{\sqrt{14}} \)
Subject: Chemistry
The \( p H \) of a 0.1 molar solution of the
acid \( H A \) is \( 3 . \) The value of the
ionization constant, \( \boldsymbol{K}_{(a)} \) of the acid is:
A. \( 3 \times 10^{-10} \)
В. \( 1 \times 10^{-3} \)
c. \( 1 \times 10^{-5} \)
D. \( 1 \times 10^{-7} \)
Subject: Chemistry
If the elevation in boiling point of a solution of 10 g of solute (mol.wt. \( =100 \) ) in 100 g of water is \( \triangle \boldsymbol{T}_{\boldsymbol{b}}, \) the ebullioscopic constant of water is :
A . 10
в. \( 100 T_{b} \)
c. \( \triangle T_{b} \)
D. \( \frac{\Delta T_{b}}{10} \)
Subject: Chemistry
(i) What type of isomers are
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{B r}\right] \boldsymbol{S} \boldsymbol{O}_{4} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{S O}_{4}\right] \boldsymbol{B r} ? \) Give a chemical
test to distinguish between them.
(ii) Write the structures of optical isomers of the complex ion
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2} \boldsymbol{C l}_{2}\right]^{+} \)
Subject: Chemistry
Assertion
\( C_{p}-C_{V}=R \) for an ideal gas.
Reason \( \left[\frac{\partial \boldsymbol{E}}{\partial \boldsymbol{V}}\right]_{T}=\mathbf{0} \) for an ideal gas.
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
The values of current(l) flowing through a given resistor of resistance (R), for the corresponding values of potential difference (V) across the resistor are as
given
\( \begin{array}{lll}\mathbf{0 . 5} & \mathbf{1 . 0} & \mathbf{1 . 5}\end{array} \) V(volts) 2.0
0.1 0.3 I(amperes) 0.2
Plot a graph between current(l) and
potential difference (V) and determine the resistance (R) of the resistor.
Subject: Chemistry
Assertion: Formula mass (in grams) of
magnesium chloride has \( 12.044 \times 10^{23} \)
magnesium ions. Reason: One formula
mass of an ionic compound has \( 6.022 \times 10^{23} \) ions of each type.
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
E. Both assertion and reason are incorrect
Subject: Maths
The length of common chords of circles \( x^{2}+y^{2}+p x=0 \) and \( x^{2}+y^{2}+g y=0 \) is
\( A \cdot \frac{2 p q}{\sqrt{p^{2}+q^{2}}} \)
c. \( \frac{p q}{\sqrt{p^{2}+q^{2}}} \)
D. \( \frac{2 p q}{p^{2}+q^{2}} \)
Subject: Physics
The lengths of two wires made of the same material are in the ratio \( 2: 1 . \) If
the masses of the two wires are in the
ratio \( 1: 8, \) find the ratio of their
resistances
\( \mathbf{A} \cdot 1: 16 \)
B. 32: 1
\( \mathbf{c} \cdot 16: 1 \)
D. 1: 32
Subject: Physics
If a graph is plotted between \( T^{2} \) and \( r^{3} \)
for a planet, then its slope will be
A \( \cdot \frac{4 \pi^{2}}{G M} \)
в. \( \frac{G M}{4 \pi^{2}} \)
\( \mathrm{c} .4 \pi G M \)
D. zero
Subject: Chemistry
\( N_{2} O_{5} \) decomposes to \( N_{2} O_{4} \) and \( O_{2} \) as :
\( N_{2} O_{5} \rightarrow N_{2} O_{4}+\frac{1}{2} O_{2} \)
The pressure \( P_{1} \) at any stage is related
to \( p_{0} \) and \( x, \) the fraction of dissociation,
as:
\( \mathbf{A} \cdot p_{0} \)
B. \( \left(1+\frac{1}{2} x\right) p_{0} \)
c. \( _{1-\frac{3}{2} p_{0}} \)
D. \( \frac{3}{2} x p_{0} \)
Subject: Chemistry
The complex used as an anticancer
agent is :
A . \( \operatorname{trans}-\left[\operatorname{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right. \)
B . \( \operatorname{cis}-\left[P t C l_{2}\left(N H_{3}\right)_{2}\right] \)
c. \( \operatorname{cis}-K_{2}\left[P t C l_{2} B r_{2}\right. \)
D. \( N a_{2} C O_{3} \)
Subject: Chemistry
Which will have graded property
particular to \( \boldsymbol{E} \cdot \boldsymbol{C} \cdot \boldsymbol{1} \boldsymbol{s}^{2} \boldsymbol{2} \boldsymbol{s}^{2} \boldsymbol{2} \boldsymbol{p}^{6} \boldsymbol{3} \boldsymbol{s}^{2} \boldsymbol{3} \boldsymbol{p}^{\boldsymbol{6}} \boldsymbol{4} \boldsymbol{s}^{1} \) ?
\( \mathbf{A} \cdot[A r] 3 d^{10} 4 s^{1} \)
B . \( [K r] 4 d^{10} 5 s^{1} \)
c. \( [K r] 5 s^{1} \)
D. all of these
Subject: Chemistry
If a current of 1.5 ampere flows through a metallic wire for 3 hours, then how many electrons would flow through the wire?
A \( \cdot 2.25 \times 10^{22} \) electrons
B. \( 1.13 \times 10^{23} \) electrons
C \( \cdot 1.01 \times 10^{23} \) electrons
D. \( 4.5 \times 10^{23} \) electrons
Subject: Maths
Let \( G \) and \( G^{1} \) be the centroids of the
triangles \( A B C \) and \( A^{1} B^{1} C^{1} \)
respectively, then \( \boldsymbol{A} \boldsymbol{A}^{1}+\boldsymbol{B} \boldsymbol{B}^{1}+\boldsymbol{C} \boldsymbol{C}^{1} \)
is equal to
\( \mathbf{A} \cdot 2 G G^{1} \)
B. \( 3 G^{1} G \)
\( \mathbf{c} \cdot 3 G G^{1} \)
D. \( \frac{3}{2} G G^{1} \)
Subject: Maths
The domain of the relation \( R= \)
\( \{(x, y): x, y \epsilon N \text { and } x+y \leq 3\} \)
is
\( A \cdot\{1,2,3\} \)
B. \{1,2\}
\begin{tabular}{l} 
c. \( (\ldots-1,0,1,2,3] \) \\
\hline
\end{tabular}
D. None of these
Subject: Maths
Solve:
¡) \( \boldsymbol{y}=\boldsymbol{e}^{2 x}(\boldsymbol{a}+\boldsymbol{b} \boldsymbol{x}) \quad \boldsymbol{y}= \)
\( e^{x}(a \cos x+b \sin x) \)
ii) Form the differential equation of the family of circle touching the y-axis at origin.
Subject: Maths
Use graphical method
Maximize: \( \boldsymbol{z}=\mathbf{2} \boldsymbol{x}+\mathbf{3} \boldsymbol{y} \)
Subject to:
\( x+2 y \leq 40 \)
\( 6 x+5 y \leq 150 \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)
Subject: Maths
The solution of \( \frac{d^{2} y}{d x^{2}}=x e^{x}+1 \) is:
A \( \cdot y=(x-1) e^{x}+\frac{1}{2} x^{2}+C_{1} x+C_{2} \)
B. \( y=(x-2) e^{x}+\frac{1}{2} x^{2}+C_{1} x+C_{2} \)
c. \( y=(x+2) e^{x}+\frac{1}{2} x^{2}+C_{1} x+C_{2} \)
D. \( y=(x+2) e^{x}+C_{1} \)
Subject: Physics
A rectangular coil of single turn, having
area \( A, \) rotates in a uniform magnetic
field B with an angular velocity \( \omega \) about an axis perpendicular to the field. If
initially the plane of the coil is perpendicular to the field, then the average induced emf when it has
rotated through \( 90^{\circ} \) is:
\( \mathbf{A} \cdot \frac{\omega B A}{\pi} \)
в. \( \frac{\omega B A}{2 \pi} \)
c. \( \frac{\omega B A}{4 \pi} \)
D. \( \frac{2 \omega B A}{\pi} \)
Subject: Maths
Find the derivative of \( \sec ^{-1}\left(\frac{x+1}{x-1}\right)+ \)
\( \sin ^{-1}\left(\frac{x-1}{x+1}\right) \)
A .
B.
\( c \cdot-1 \)
D. \( \frac{x+1}{x-1} \)
Subject: Physics
A cell of emf \( \boldsymbol{E} \) Volt with no internal
resistance is connected to a wire whose
cross section changes. The wire has
three sections of equal length. The
middle section has a radius \( a \), whereas
the radius of the outer two sections is
2a. The ratio of the potential difference
across section \( A B \) to the potential
difference across section \( C A \) is :
\( A \)
B. 4
\( c \cdot \frac{1}{2} \)
D.
Subject: Physics
A car moves from \( A \) to \( B \) with a speed of \( 30 k m p h \) and from \( B \) to \( A \) with a speed of 20kmph. What is the average speed of
the car?
A. \( 25 k m p h \)
в. \( 24 k \) три
\( c .50 k m p h \)
D. \( 10 k m p h \)
Subject: Maths
Solve :
\( \int \frac{1+x \cos x}{x\left(1-x^{2} e^{2 \sin x}\right)} d x= \)
\( k \ell n \sqrt{\frac{x^{2} e^{2 \sin x}}{1-x^{2} e^{2 \sin x}}}+C \) then \( k \) is equal
to
Subject: Maths
The angle between lines joining the original to the point of intersection of the line \( \sqrt{\mathbf{3}} x+\boldsymbol{y}=\mathbf{2} \) and the curve
\( y^{2}-x^{2}=4 \) is
A \( \cdot \tan ^{-1} \frac{2}{\sqrt{3}} \)
B. \( \frac{\pi}{6} \)
\( ^{\mathrm{c}} \tan ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
D. \( \frac{\pi}{2} \)
Subject: Physics
A \( 50 k g \) skydiver falls through the air and reaches terminal velocity after
some time. The drag force is a function of velocity given by
\[
\boldsymbol{F}_{d r a g}=-\boldsymbol{b} \boldsymbol{v}^{2}
\]
where the negative sign denotes that the drag force is opposite to the direction of the velocity. What is the terminal velocity of the
skydiver (assuming the drag constant \( b \)
is \( 0.2 k g / m \) )?
A \( \cdot 5 \frac{m}{s} \)
B.
\[
50 \frac{m}{s}
\]
\( c \)
\[
100 \frac{m}{s}
\]
D.
\[
250 \frac{m}{s}
\]
E
\[
2500 \frac{m}{s}
\]
Subject: Maths
ABCD is a parallelogram with sides \( A B=12 \mathrm{cm}, B C=10 \mathrm{cm} \) and
diagonal \( \boldsymbol{A C}=\mathbf{1 6} \mathrm{cm} . \) Find the
approximate area of the parallelogram.
\( \mathbf{A} \cdot 119.8 \mathrm{cm}^{2} \)
B. \( 103.7 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 15.7 \mathrm{cm}^{2} \)
D. None of these
Subject: Physics
A surface is hit elastically and normally by n balls per unit time. All the balls
have same mass \( \mathrm{m} \) and moves with the
same velocity u. The force on the
surface is :
A \( \cdot 1 / 2 \) mnu \( ^{2} \)
B. mnu \( ^{2} \)
\( c \cdot 2 m n u^{2} \)
D. 2 mnu
Subject: Chemistry
Match column I with column II.
Column I
P. Non-stick coating
(i). Melamine
Q. Flame resistant
(ii). Polystyrene
R. First fully synthetic fibre
(iii). Teflon
S. Thermoplastic
(iv). Nylon
Choose the correctly matched option.
\( A \cdot(P)-(i i),(Q)-(i),(R)-(i i i),(S)-(i v) \)
B. (P) - (iii), (Q) - (i), (R) - (iv), (S) - (ii)
c. (P) - (ii), (Q) - (iii), (R) - (iv), (S) - (i)
D. (P) - (iii), (Q) - (iv), (R) - (ii), (S) - (i)
Subject: Physics
Fig. shows the time acceleration graph for a particle in rectilinear motion. The
average acceleration in first twenty
seconds is
\( A \cdot 45 \mathrm{m} / \mathrm{s}^{2} \)
\( 3 \cdot 40 \mathrm{m} / \mathrm{s}^{2} \)
\( c \cdot 30 m / s^{2} \)
20
Subject: Biology
plate \( 1 ? \)
Well water and nutrient agar
Well water and nutrient agar-antibiotic (tetracycline)
A. Bacteria 2 produces an antibiotic to which bacteria 1,3, and 4 are susceptible.
B. Bacteria 2 produces an antibiotic to which bacteria 4 is susceptible.
C. Bacteria 2 produces an antibiotic to which bacteria 1 and 4 is susceptible.
D. Bacteria 4 require a protein produced by bacteria 1.
E. Bacteria 4 require a protein produced by bacteria 3.
Subject: Physics
(a) Three point charges \( q,-4 q \) and \( 2 q \) are placed at the vertices of an
equilateral triangle \( A B C \) of side \( ^{\prime} l^{\prime} \) as
shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the
charge \( \boldsymbol{q} \)
(b) Find out the amount of the work done to separate the charges at infinite
distance.
Subject: Maths
ff \( \boldsymbol{y}=\boldsymbol{x}+\frac{1}{\boldsymbol{x}+\frac{1}{\boldsymbol{x}+\frac{1}{\boldsymbol{x}+\cdots}}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{d y}{d x}=\frac{x}{2 x-y} \)
в. \( \frac{d y}{d x}=\frac{y}{2 y-x} \)
c. \( \frac{d y}{d x}=\frac{2 y}{2 x-y} \)
D. None of these
Subject: Physics
The focal lengths of the objective and eye-piece of a compound microscope are \( 1 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. An
object is placed at a distance of \( 1.1 \mathrm{cm} \) from the objective has its final image formed at least distance of distinct
vision, then the magnifying power is
A . 20
B. 30
c. 50
D. 60
Subject: Chemistry
The reaction, \( C_{2} H_{6}(g) \rightleftharpoons C_{2} H_{4}(g)+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \) is at equilibrium in a closed
vessel at \( 1000 K . \) The enthalpy change
\( (\Delta H) \) for the reaction is 137.0 \( k J . m o l^{-1} . \) Which one of the following
actions would shift the equilibrium to the right?
A. Decreasing the volume of the closed reaction vessel
B. Decreasing the temperature at which the reaction is performed
c. Adding an inert gas to the closed reaction vessel
D. Increasing the volume of the closed reaction vessel
Subject: Physics
If in a wire of Young's modulus \( Y \) longitudinal strain \( X \) is produced then the potential energy stored in its unit volume will be :
\( \begin{array}{l}\text { A } .0 .5 Y X^{2} \\ ^{2}\end{array}^{.0 .5 Y X X^{2}} \)
в. \( 0.5 Y^{2} X \)
\( \mathbf{c} \cdot 2 Y X^{2} \)
D. \( Y X^{2} \)
Subject: Physics
A vibrating string of certain length \( \ell \) under a tension \( T \) resonates with a
mode corresponding to the first overtone (third harmonic) of an air column of length \( 75 \mathrm{cm} \) inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be \( 340 \mathrm{m} / \mathrm{s}, \) the frequency nof the tuning fork in \( \mathrm{Hz} \) is
\( A \cdot 344 \)
в. ззб
\( c . \) 117.
D. 109.
Subject: Maths
If \( \frac{\sin ^{3} \theta-\cos ^{3} \theta}{\sin \theta-\cos \theta}-\frac{\cos \theta}{\sqrt{1+\cot ^{2} \theta}}- \)
\( 2 \tan \theta \cot \theta=-1, \theta \in[0,2 \pi], \) then
A \( \cdot \theta \in\left(0, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4}\right\} \)
в. \( _{\theta} \in\left(\frac{\pi}{2}, \pi\right)-\left\{\frac{3 \pi}{4}\right\} \)
c. \( _{\theta \in\left(\pi, \frac{3 \pi}{2}\right)-\left\{\frac{5 \pi}{4}\right\}} \)
D. \( \theta \in(0, \pi)-\left\{\frac{\pi}{4}, \frac{\pi}{2}\right\} \)
Subject: Chemistry
A solution containing 3.3 g of a substance in 125 g of benzene (b.pt. \( = \) \( 80^{\circ} \mathrm{C} \) ) boils at \( 80.66^{\circ} \mathrm{C} \). If \( \mathrm{K}_{b} \) for
benzene is \( 3.28 \mathrm{K} \mathrm{kg} \) mol\( ^{-1} \) the
molecular mass of the substance will
be:
A . 130.20
B. 129.20
c. 132.20
D. 131.20
Subject: Maths
The vectors \( \vec{a}(x)=\cos x \hat{i}+\sin x \hat{j} \) and
\( \vec{b}(x)=x \hat{i}+\sin (x) \hat{j} \) are collinear for
A \cdot Unique value of \( x, 0<x<\frac{\pi}{6} \)
B. Unique value of \( x, \frac{\pi}{6}<x<\frac{\pi}{3} \)
c. No value of \( x \)
D \cdot Infinite values of \( x, 0<x<\frac{\pi}{2} \)
Subject: Chemistry
Alkyl isocyanides \( \left(R N \oplus \equiv C^{\ominus}\right) \) are
reduced to \( 2^{\circ} \) amines \( \left(R-N H-C H_{3}\right. \)
with:
\( \mathbf{A} \cdot L A H \)
в. \( N a B H_{4} \)
c. \( H I+P \)
D. \( H_{2} / P t \)
Subject: Chemistry
Reaction \( \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{H}+\boldsymbol{H} \boldsymbol{O C l} \rightarrow \)
product, here product will be:
A. \( C l C H_{2}-C H O \)
в. \( C H O-C H O \)
c. \( C H-C l=C H C l \)
D. \( C H C l_{2}-C H C l_{2} \)
Subject: Maths
If the angles of a triangle are in the ratio
\( 2: 3: 4, \) find the three angles.
A \( \cdot 80^{\circ}, 120^{\circ}, 160^{\circ} \)
\( ^{\circ} 00^{\circ}, 166^{\circ} 0^{\circ} \)
В. \( 20^{\circ}, 30^{\circ}, 40^{\circ} \)
c. \( 40^{\circ}, 60^{\circ}, 80^{\circ} \)
D. None of these
Subject: Biology
Which of the following statement
regarding \( C_{4} \) plants is false?
A. The primary \( C O_{2} \) acceptor is a 5 carbon molecule.
B. The initial carboxylation reaction occurs in mesophyll.
C . The leaves that fix \( C O_{2} \) have two cell types.
D. The chloroplasts are dimorphic.
E. The Calvin pathway does not take place in the mesophyll cells but does so only in the bundle sheath cells.
Subject: Maths
A metal box with a square base and
vertical height is to contain \( 1024 \mathrm{cm}^{2} \)
The material for the top and the bottom
\( \operatorname{costs} \mathrm{Rs} .5 / \mathrm{cm}^{2} \) and the material for the
sides costs Rs. \( 2.50 / c m^{2} \). Find the least
\( \operatorname{cost} \) of the box.
Subject: Chemistry
For a process to be spontaneous at
constant \( \boldsymbol{T} \) and \( \boldsymbol{P}: \)
\( \mathbf{A} \cdot \$ \$(1 \text { Delta } G)_{-}\{\text {system }\} \) must be negative
B. \( \$ \$ \) (IDelta G) \( _{-}\{\text {system }\} \) must be positive
\( \mathbf{C} . \$ \$(1 \mathrm{Delta} \)
S) \( _{-}\{\text {system }\} \) must be positive
D. \( \$ \$ \) ( ( Delta S) \( _{-} \) (system) must be negative
Subject: Maths
Equation of a straight line passing through the origin and making with \( x- \) axis an angle twice the size of the angle
made by the line \( y=0.2 x \) with the \( x- \)
axis, is :
A. \( y=4.0 x \)
В. \( y=\frac{5}{12} x \)
c. \( 6 y-5 y=0 \)
D. none of these
Subject: Chemistry
Which of the following is a formula of
methanides : \( (a) B e_{2} C(b) C a C_{2}(c) \)
\( \boldsymbol{M} \boldsymbol{g}_{2} \boldsymbol{C}_{3}(\mathrm{d}) \boldsymbol{A} \boldsymbol{l}_{4} \boldsymbol{C}_{3} \)
A. Only \( a, d \)
B. Only \( a, b \)
c. only \( c, d \)
D. only \( b, d \)
Subject: Physics
A neutron travelling with a velocity \( v \) and kinetic energy E collides perfectly elastically head on with the nucleus of an atom of mass number \( A \) at rest. The
fraction of total energy retained by the neutron is:
\( ^{A} \cdot\left(\frac{A-1}{A+1}\right)^{2} \)
\( ^{\text {B. }}\left(\frac{A+1}{A-1}\right)^{2} \)
\( ^{c}\left(\frac{A-1}{A}\right)^{2} \)
\( ^{\mathrm{D}}\left(\frac{A+1}{A}\right)^{2} \)
Subject: Physics
A physical quantity \( Q \) is found to depend on observables \( x, y \) and \( z \) obeying relation \( Q=\frac{x^{2 / 5} z^{3}}{y} . \) The
percentage error in the measurements of \( x, y \) and \( z \) are \( 1 \%, 2 \% \) and \( 4 \% \)
respectively. What is percentage error in the quantity \( Q \) will be :
\( A \cdot 5 \% \)
в. \( 4.5 \% \)
c. \( 11 \% \)
D. \( 7.75 \% \)
Subject: Physics
Two cells of internal resistances \( r_{1} \) and
\( r_{2} \) and of same emf are connected in
series, across a resistor of resistance \( \mathrm{R} \)
If the terminal potential difference
across the cells of internal resistance \( r_{1} \)
is zero, then the value of \( R \) is?
A \( \cdot R=2\left(r_{1}+r_{2}\right) \)
B. \( R=r_{2}-r_{1} \)
c. \( R=r_{1}-r_{2} \)
D. \( R=2\left(r_{1}-r_{2}\right) \)
Subject: Physics
An object is placed at a distance of 1.5 \( \mathrm{m} \) from a screen and a convex lens is interposed between them. The
magnification produced is 4. The focal length of the lens is then
\( A \cdot 1 m \)
B. 0.5 \( m \)
c. \( 0.24 \mathrm{m} \)
D. \( 2 \mathrm{m} \)