AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Maths
Find DF, if \( \mathrm{CG}=11 \mathrm{cm} \)
A. \( 5.6 \mathrm{cm} \)
B. \( 5.5 \mathrm{cm} \)
\( c \cdot 0.55 \mathrm{cm} \)
D. \( 55 \mathrm{cm} \)
Subject: Physics
The potential at a point \( (x, 0,0) \) is given by \( V=\left(\frac{1000}{x}+\frac{1500}{x^{2}}+\frac{500}{x^{3}}\right) . \) The
intensity of the electric field at \( x=1 \)
will be
A. \( 550 V / m \)
B. \( 55 V / m \)
\( \mathbf{c} .55000 V / m \)
D. \( 5500 V / m \)
Subject: Chemistry
A buffer solution is prepared by mixing \( 10 \mathrm{ml} \) of \( 1.0 \mathrm{M} \) acetic acid \( \& 20 \mathrm{ml} \) of 0.5
M sodium acetate and then diluted to
\( 100 \mathrm{ml} \) with distilled water. If the \( p K_{a} \) of
\( C H_{3} C O O H \) is \( 4.76 . \) What is the pH of the buffer solution prepared? (1998)
A . 3.84
B. 4.76
\( c \cdot 4.34 \)
D. 5.21
Subject: Physics
If Bohr radius is \( r_{0}, \) the corresponding de Broglie wavelength of the electron is
\( ^{\mathbf{A}} \cdot\left(\frac{2 \pi}{r_{o}}\right) \)
В \( \cdot\left(\frac{r_{o}}{2 \pi}\right) \)
c. \( \left(\frac{1}{2 \pi r_{o}}\right) \)
D. \( 2 \pi r_{o} \)
Subject: Maths
The coordinates of the point on the
curve \( \left(x^{2}+1\right)(y-3)=x \) where a
tangent to the curve has the greatest slope are given by This question has multiple correct options
A \( \cdot(\sqrt{3}, 3+\sqrt{3} / 4) \)
B \( \cdot(-\sqrt{3}, 3-\sqrt{3} / 4) \)
c. (0,3)
D. none of these
Subject: Chemistry
During bleaching action, \( \mathbf{S O}_{2} \) converts
into
\( A \cdot S O_{3} \)
в. \( \mathrm{H}_{2} \mathrm{SO}_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
Subject: Physics
Find the magnetic field intensity due to
a thin wire carrying current \( I \) in the
figure :
A \( \cdot \frac{\mu_{0} i}{2 \pi R}(\pi-a+\tan a) \)
в. \( \frac{\mu_{0} i}{2 \pi R}(\pi-a) \)
c. \( \frac{\mu_{0} i}{2 \pi R}(\pi+a) \)
D. \( \frac{\mu_{0}}{2 \pi R}(\pi+a-\text { tana }) \)
Subject: Maths
The function \( f(x) \) is defined on the interval \( [0,1] . \) Find the domain of the function:
\( \boldsymbol{f}(\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}) \)
\( ^{A} \cdot-\frac{3}{2} \leq x \leq-1 \)
в. \( -\frac{3}{2} \leq x \leq \frac{3}{2} \)
\( ^{\mathrm{c}}-1 \leq x \leq \frac{3}{2} \)
D. \( -1 \leq x \leq 1 \)
Subject: Physics
A wave pulse traveling on a two piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to incident one. If the
incident wave has wavelength \( \lambda \) and
transmitted wave has \( \lambda^{\prime}, \) then
\( A \cdot \lambda^{\prime}>\lambda \)
B . \( \lambda^{\prime}=\lambda \)
c. \( \lambda^{\prime}<\lambda \)
D. none
Subject: Chemistry
Assertion
\( 35 C l \) and \( 37 C l \) do not differ in their \( 17^{17} \) chemical reactions.
Reason
Isotopes contain identical numbers of electrons, equal to the atomic number of the atom.
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
Assertion
The magnetic field produced by a
current carrying solenoid Is
independent of its length and cross-
sectional area.
Reason
The magnetic field inside the solenoid
is uniform.
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
When a metal wire is stretched by a load, the fractional change in its volume \( \Delta V / V \) is proportional to?
\( ^{\mathrm{A}} \cdot-\frac{\Delta l}{l} \)
\( ^{\mathrm{B}}\left(\frac{\Delta l}{l}\right)^{2} \)
c. \( \sqrt{\Delta l / l} \)
D. None of these
Subject: Physics
Calculate \( \theta_{1} \) and \( \theta_{2} \) in shown situation
\begin{tabular}{|cccc|}
\hline \( 200^{\circ} \mathrm{C} \) & \( \theta_{1} \) & \( ^{\theta_{2}} \) & \( 19^{\circ} \mathrm{C} \) \\
\hline \( \mathrm{K} \) & \( 2 \mathrm{K} \) & \( 1.5 \mathrm{K} \) \\
\hline
\end{tabular}
Subject: Maths
\( A B \) is parallel to \( Q R, \) such that \( \frac{P A}{A Q}= \) \( \frac{P B}{B R} \cdot P B=2 \mathrm{cm}, E C=4 \mathrm{cm} \) and
\( Q R=9 \mathrm{cm}, \) then find the length of \( A B \)
Subject: Physics
The weight of a man is \( 750 \mathrm{N} \) The total
area of the soles of his shoes is \( 250 \mathrm{cm}^{2} \)
Find the pressure he applies on the floor
\( \mathbf{A} \cdot 30,000 P a \)
B. \( 15,000 P a \)
c. \( 60,000 P a \)
D. \( 90,000 P a \)
Subject: Maths
The image of the point (1,2,3) through
the plane \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{4} \boldsymbol{z}=\boldsymbol{0} \) is
A \( \cdot\left(\frac{-2}{3}, \frac{1}{3}, \frac{-11}{3}\right) \)
в. \( \left(\frac{3}{7},-\frac{6}{7}, \frac{19}{7}\right) \)
\( ^{\mathbf{c}} \cdot\left(\frac{2}{3}, \frac{1}{3}, \frac{11}{3}\right) \)
D. \( \left(\frac{-2}{3}, \frac{-1}{3}, \frac{11}{3}\right) \)
Subject: Physics
Six particles are situated at the corners
of a regular hexagon of side \( a \), they
move at a constant speed \( v \). Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet
each other:
A \( \cdot 2 \) a/v
B. 3 a/v
\( c \cdot 5 a / v \)
D. 6 a/v
Subject: Chemistry
Which substance does not possess a
peroxy cyclic ring?
\( \mathbf{A} \cdot \mathrm{CrO}_{5} \)
\( \mathbf{B} \cdot B a O_{2} \)
\( \mathbf{c} \cdot H_{2} S_{2} O_{8} \)
D. All have peroxy linkage
Subject: Biology
Choose the correct answer from the
alternatives given. In an experiment, oat (Avena sativa) seedlings were grown under the same conditions of temperature, moisture and light. Their tips were removed and divided into four groups. Each group was given different treatments and the growth was measured carefully after keeping them in dark for 16 Firs. Which of the following groups had the most growth?
A. In Group I, the tip was put back on each seedling
B. In Group II, a block of agar gel containing juice of 10 tips was placed on top of each seedling
c. In Group III, nothing was placed on top of each seedling
D. In Group IV, a drop of water was placed on top of each seedling
Subject: Chemistry
The compound Y is:
\( A \)
B. \( \quad C H_{3} \)
\( C H_{2}-C H=C-C H_{2}-C O O H \)
\( O H \)
\( c \)
\( \mathbf{D} \cdot C H_{2}=C H-C H-C H_{2}-C O O H \)
Subject: Physics
Two concentric shells of radii \( d \) and \( 2 d \)
respectively are placed far away from a parallel plate capacitor. Each plate of the capacitor is a square of side \( d \) and
separation between the plates is \( d / 4 \pi \)
The charge on the plates are \( q \) and \( -q \)
Then the keys \( k_{1} \) and \( k_{2} \) are closed, find
the charges on the shells and electric
potential energy left in the parallel plate capacitor in equilibrium.
Subject: Chemistry
Column chromatography involves separation of a mixture over a column of adsorbent (stationary phase) packed in a glass tube. Depending upon the degree of adsorption complete
separation takes place. In the given column, three coloured bands \( x, y, z \) are
formed. Identify the correct statement
A. \( x, y \) and \( z \) are adsorbed to the same extent
B. The most readily adsorbed component is retained nea the top (x)
c. The most readily absorbed component comes \( \operatorname{down}(z) \)
D. \( x, y, z \) layers are formed according to the wavelengths of the colours not on the basis of adsorption
Subject: Maths
Represent the following data using a suitable graphical representation.
\( \begin{array}{lllll}\text { class- } & 0- & 5- & 10- & 1 \\ \text { intervals } & 5 & 10 & 15 & 2\end{array} \)
Frequency \( \begin{array}{ll}\text { 1. } & 5\end{array} \) 6
Subject: Physics
In order to increase the resistance of a
given wire of uniform cross-section to four times its value, a fraction of its
length is stretched uniformly till the full length of the wire becomes \( \frac{3}{2} \) times the original length.What is the value of this
fraction?
\( A \cdot \frac{1}{4} \)
B. \( \frac{1}{8} \)
\( c \cdot \frac{1}{16} \)
D. \( \frac{1}{6} \)
Subject: Physics
An ideal gas can be expanded from an initial state to a certain volume through
two different processes
(i) \( P V^{2}= \)
constant and \( (i i) P=K V^{2} \) where \( K \) is
a positive constant. Based on the given situation, choose the correct
statements
This question has multiple correct options
A. Final temperature in
(ii) will be greater than in (i)
B. Final temperature in (ii) will be less than in (i)
c. Total heat given to the gas in case (ii) is greater than in
(i)
D. Total heat given to the gas in case (ii) is less than in (i)
Subject: Physics
Displacement of a particle executing simple harmonic motion is represented by \( \boldsymbol{Y}=\mathbf{0 . 0 8} \sin \left(3 \pi t+\frac{\pi}{4}\right) \) metre.
Then calculate:-
(a) Time period.
(b) Initial phase
(c) Displacement from mean position at \( t=\frac{7}{36} \) sec.
Subject: Physics
\( m_{1} \) and diameter \( A O C \) has mass \( m_{2} \)
Here, axis passes through mid-point of
diameter and the axis is perpendicular
to plane \( \boldsymbol{A B C} \)
Here, \( \boldsymbol{A O}=\boldsymbol{O C}=\boldsymbol{R} \). The moment of
inertia of this composite system about
the axis is:
\( \mathbf{A} \cdot \frac{m_{1} R^{2}}{2}+\frac{m_{2} R^{2}}{3} \)
B. \( \frac{m_{1} R^{2}}{2}+\frac{m_{2} R^{2}}{6} \)
\( \mathrm{c} \cdot_{m_{1} R^{2}+} \frac{m_{2} R^{2}}{3} \)
D \( \quad m_{1} R^{2}+\frac{m_{2} R^{2}}{12} \)
Subject: Chemistry
Consider the following figure,
The correct relationship between
fahrenheit and celsius scale is:
\( \mathbf{A} \cdot^{0} F=^{0} C+273.15 \)
\( \mathbf{B} \cdot^{0} F=\frac{2}{5}^{0} C+16 \)
\( \mathbf{c} \cdot^{0} F=\frac{9}{5} C+32 \)
D. \( ^{0} F=\frac{1}{3}^{0} C+32 \)
Subject: Maths
Standard Deviation of n observations
\( a_{1}, a_{2}, a_{3} \dots \dots a_{n} \) is \( \sigma \) Then the standard
deviation of the observations
\( \lambda a_{1}, \lambda a_{2}, \dots, \lambda a_{n} \) is
\( A \cdot \lambda \sigma \)
B. - \( \lambda \sigma \)
c. \( |\lambda| \sigma \)
D. \( \lambda^{n} \sigma \)
Subject: Chemistry
For the reaction, \( \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \)
\( O_{3}(g) ; \Delta H^{o}=-107.2 k J . \) Hence, the
average bond energy in \( \boldsymbol{O}_{3} \) is:
(Assume \( \boldsymbol{O}=\boldsymbol{O} \) bond energy
\( \left.498.8 k J m o l^{-1}\right) \)
A \( \cdot 606.0 k J \) mol\( ^{-1} \)
B. \( 107.2 \mathrm{kJ} \mathrm{mol}^{-1} \)
c. \( 391.6 \mathrm{kJ} \mathrm{mol}^{-1} \)
D. 303.0 kJ mol-1
Subject: Chemistry
If two subshells have equal value of
\( (n+1) \) and one of them has \( n=4, l=3, \) while
second subshell has dumbbellshape.
Then which of the bfollowing statement is/are correct?
This question has multiple correct options
A. Second subshell has value of \( n=6 \)
B. One of the orbitals of second subshell has one nodal plane
c. second subshell is d-subshell.
D. First subshell is f-subshell
Subject: Chemistry
Assign number 1 for least to 4 for most to indicate the relative base strength of the following.
\( \mathbf{C}_{6} \mathbf{H}_{5}^{\mathbf{I}} \mathbf{N} \mathbf{H}_{\mathbf{2}} \)
\( \mathbf{p}-\mathbf{N} \mathbf{O}_{2} \mathbf{C}_{6} \mathbf{H}_{4} \mathbf{N} \mathbf{H}_{\mathbf{2}} \)
\( \mathbf{m}-\mathbf{N} \mathbf{O}_{2} \mathbf{C}_{6} \mathbf{H}_{4} \mathbf{N} \mathbf{H}_{\mathbf{2}} \)
\( \mathbf{m}-\mathbf{C} \mathbf{H}_{3} \mathbf{O} \mathbf{O}_{6} \mathbf{H}_{\mathbf{4}} \mathbf{N} \mathbf{H}_{\mathbf{2}} \)
A. III IIIIV
3124
в. IIIIIIIV
1234
c. ।॥ III IV
2 3 4 1
D. III IIIIV
4132
Subject: Physics
A bullet of mass \( 20 \mathrm{g} \) is fired from a rifle with a velocity of \( 800 m s^{-1} . \) After passing through a mud wall \( 100 \mathrm{cm} \)
thick, velocity drops to \( 100 \mathrm{ms}^{-1} \). What
is the average resistance of the wall? (Neglect friction due to air and work of
gravity)
Subject: Maths
If \( f(x)=3 x-2 \) and \( g(x)= \)
\( \mathbf{7}, \boldsymbol{f}[\boldsymbol{g}(\boldsymbol{x})]= \)
A . \( 21 x-2 \)
B. 7
c. 19
D. \( 7 x-2 \)
E . 13
Subject: Chemistry
A reversible reaction \( A \rightleftharpoons C \) takes
place in two steps \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} ; \boldsymbol{B} \rightleftharpoons \boldsymbol{C} \)
which are also equilibrium steps. If the equilibrium constants of the two steps
are \( K_{1} \) and \( K_{2} \) respectively, the overall equilibrium constant \( \boldsymbol{K} \) is equal to:
\( ^{\text {A }} \cdot \frac{K_{1}}{K_{2}} \)
в. \( \frac{K_{2}}{K_{1}} \)
\( \mathbf{c} \cdot K_{1} \times K_{2} \)
D. \( K_{1}-K_{2} \)
Subject: Chemistry
Extraction of gold (Au) involves the formation of complex ions \( X \) and \( Y \) Gold ore \( \frac{\text { Roasting }}{C N^{-}, H_{2} O, O_{2}} H O^{-}+X \stackrel{Z n}{\longrightarrow} \)
\( \boldsymbol{Y}+\boldsymbol{A} \boldsymbol{u} \)
X and Y respectively are :
A \( \cdot A u(C N)_{2}^{-} \) and \( Z n(C N)_{4}^{2} \)
B . \( A u(C N)_{4}^{3-} \) and \( Z n(C N)_{4}^{2} \)
c. \( A u(C N)_{3}^{-} \) and \( Z n(C N)_{6}^{4} \)
D. \( A u(C N)_{4}^{-} \) and \( Z n(C N)_{3} \)
Subject: Maths
Show that the function \( f \) fiven below by:
\( \left\{\begin{array}{ll}\frac{e^{1 / x}-1}{e^{1 / x}+1} & , \text { if } x \neq 0 \\ -1 & , \text { if } x=0\end{array} \) is discontinuous at \right.
\( \boldsymbol{x}=\mathbf{0} \)
Subject: Maths
The differential equation of all nonhorizontal lines in a plane is:
A \( \cdot \frac{d^{2} y}{d x^{2}}=0 \)
B. \( \frac{d^{2} x}{d y^{2}}=0 \)
c. \( \frac{d y}{d x}=0 \)
D. \( \frac{d x}{d y}=0 \)
Subject: Chemistry
Assertion
When a crystal is added to a supersaturated solution of itself, the
crystal does not appear to change.
Reason
The supersaturated solution is holding more solute than its normal solubility
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
In a cyclic process shown in the figure
an ideal gas is adiabatically taken from
\( A \) to \( B, \) the work done on the gas during
the process \( A \rightarrow B \) is \( 80 J, \) when the
gas is taken from \( B \) to \( A \) the heat
absorbed by the gas is 40 J. What will
be work done by the gas in process
\( \boldsymbol{B} \rightarrow \boldsymbol{A} ? \)
Subject: Chemistry
The structure shown has:
\( \mathbf{A} \cdot 1^{o}, 2^{o} \) and \( 3^{o} \) carbon atoms
B. \( 1^{\circ} \) and \( 2^{\circ} \) carbon atoms only
C \( \cdot 1^{\circ} \) and \( 3^{\circ} \) carbon atoms only
D. \( 2^{\circ} \) and \( 3^{\circ} \) carbon atoms only
Subject: Physics
A solid conducting sphere having a charge \( Q \) is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the
solid sphere and that of the outer
surface of the hollow shell be V. If the
shell is now given a charge of \( -3 Q, \) the new potential difference between the same two surface is :
A. \( V \)
B. \( 2 V \)
\( c .4 V \)
D. \( -2 V \)
Subject: Chemistry
Identify the correct sets of entries that
are rightly matched.

Column A
\( B \)
(A) Bridge elements Elements of group IA-VIIA
(B) Representative elements
(b) 2nd-
period elements
(C) Typical elements
(c) 7 th-
period elements
(D) Transition elements
(d) \( 3 r d- \)
period elements
(E) Transuranic elements
(e) Present
in 4 th, 5 th and 6 th periods
\( \mathbf{A} \cdot A-b, B-a, C-d, D-e, E-c \)
B . \( A-c, B-a, C-b, D-d, E-e \)
c. \( A-a, B-c, C-d, D-e, E-b \)
D. \( A-c, B-e, C-d, D-b, E-a \)
Subject: Physics
A nuclear transformation is denoted by
\( X(n, \alpha)_{3}^{7} L i . \) Which of the following is
the nucleus of element \( \boldsymbol{X} \) ?
A \( \cdot^{12} C_{6} \)
В \( \cdot \frac{10}{5} B \)
\( c \cdot_{5}^{9} B \)
\( \mathrm{D} \cdot_{4}^{11} \mathrm{Be} \)
Subject: Maths
\( A \) is of order \( m \times n \) and \( B \) is of order \( p \times \)
\( q, \) addition of \( A \) and \( B \) is possible only if
A \( . m=p \)
B . \( n=q \)
c. \( n=p \)
D. \( m=p, n=q \)
Subject: Chemistry
Ni is metal but dissolved in \( C O \) gas
due to formation of \( A . A \) decomposes
into metal.
(a)What is \( A \) ?
(b) \( A \) is formed at what temperature
(c) \( A \) decomposes into metal at what
temperature
A \( \cdot(\text { a }) N i(C O)_{4} ;(b) 28^{0} C\left(\text { c) } 230^{0} C\right. \)
B . (a) \( N i(C O)_{4} ;(b) 48^{0} C \) (с) \( 330^{0} C \)
C \( \cdot \) (a) \( N i(C O)_{2} ;(b) 14^{0} C \) (c) \( 230^{0} C \)
D. (a) \( N i\left(C O_{2} ; \text { (b) } 56^{\circ} C \text { (с) } 125^{\circ} C\right. \)
Subject: Maths
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \\ \mathbf{2} \boldsymbol{x} & \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} & \boldsymbol{4} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{2} \boldsymbol{z} \\ \boldsymbol{3} \boldsymbol{x} & \boldsymbol{6} \boldsymbol{x}=\boldsymbol{3} \boldsymbol{y} & \boldsymbol{1} \boldsymbol{0} \boldsymbol{x}+\boldsymbol{6} \boldsymbol{y}+\boldsymbol{3} \boldsymbol{z}\end{array}\right|=\mathbf{6 4} \)
then the real value of \( x \) is
Subject: Chemistry
A battery jar contained a solution of
copper sulfate. Two electrodes. one
made of copper the other a metal object to be copper plated, were placed in the jar and connected to a source of direct current. Which of the following statements concerning this system is correct?
A. The object to be placed is the anode
B. Oxidation occurs at the anode
c. The sulfate ions migrate toward the cathode
D. The concentration of the copper sulfate solution increases as electrolysis proceeds
E. The copper electrode increases in mass
Subject: Physics
A flat car is pulled with a constant
acceleration \( 2 m / s^{2} . \) The mass of the
block is \( 50 \mathrm{kg} \). There is friction between
the flat car surface and the block. The
wheels of the car are rolling without slipping. Then
This question has multiple correct options
A. tension in the string is \( 350 \mathrm{N} \)
B. frictional force is 150 N
C. acceleration of the block is \( 4 m / s^{2} \)
D. acceleration of center of the weel is \( 1 \mathrm{m} / \mathrm{s}^{2} \)
Subject: Physics
Two particles \( X \) and \( Y \) having equal charges, after being accelerated through the same potential differences, enter in a region of uniform magnetic field and describe circular paths of radii
\( R_{1} \) and \( R_{2} \) respectively. The ratio of the mass of \( X \) to that of \( Y \) is :
\( ^{A} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{1 / 2} \)
\( ^{\text {в. }}\left(\frac{R_{1}}{R_{2}}\right)^{-1} \)
\( ^{c} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{2} \)
D. \( \left(\frac{R_{1}}{R_{2}}\right) \)
Subject: Physics
A soap bubble of radius \( r_{1} \) is placed on
another soap bubble of radius \( r_{2}\left(r_{1}<\right. \)
\( r_{2} \) ). The radius \( R \) of the soapy film
separating the two bubbles is:
\( \mathbf{A} \cdot r_{1}+r_{2} \)
B . \( \sqrt{r_{1}^{2}+r_{1}^{2}} \)
c. \( \left(r_{1}^{2}+r_{1}^{2}\right) \)
D. \( \frac{r_{2} r_{1}}{r_{2}-r_{1}} \)
Subject: Maths
The mode from the following table will
be:
Term \( \quad \mathbf{2 5} \quad \mathbf{3 5} \quad \mathbf{4 5} \) Frequency \( \quad 14 \quad 16 \quad 24 \quad 20 \)
A . 24
B. 45
c. 65
\( D \)
Subject: Maths
\( \lim _{x \rightarrow 0} \frac{27^{x}-9^{x}-3^{x}+1}{\sqrt{2}-\sqrt{1+\cos x}}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B . \( 8 \sqrt{2}(\log 3)^{2} \)
c. \( 8(\log 3)^{2} \)
D.
Subject: Physics
A travelling of frequency \( 30 \mathrm{Hz} \) and velocity \( 300 \mathrm{m} / \mathrm{s} \) enters a water surface
and the speed of the wave becomes 400 \( \mathrm{m} / \mathrm{s} . \) What is the new frequency of the
wave
\( A \cdot 40 \mathrm{Hz} \)
B. 30 Нz
c. 22.5 нz
D. 10 Hz
Subject: Chemistry
The plot of \( \frac{1}{X_{A}} \) vs \( \frac{1}{Y_{A}} \) (where \( X_{A} \) and
\( \boldsymbol{Y}_{A} \) are the mole fractions of liquid \( \mathrm{A} \) in liquid and vapour phase, respectively) is linear. The slope and intercept of this plot are respectively:
\( ^{\mathrm{A}} \cdot \frac{P_{d}^{0}}{P_{B}^{0}} \) and \( \frac{P_{A}^{0}-P_{B}^{0}}{P_{B}^{0}} \)
в. \( \frac{P_{d}^{0}}{P_{B}^{0}} \) and \( \frac{P_{B}^{0}-P_{A}^{0}}{P_{B}^{0}} \)
c. \( \frac{P_{B}^{0}}{P_{A}^{0}} \) and \( \frac{P_{A}^{0}-P_{B}^{0}}{P_{B}^{0}} \)
D. \( \frac{P_{B}^{0}}{P_{A}^{0}} \) and \( \frac{P_{B}^{0}-P_{A}^{0}}{P_{B}^{0}} \)
Subject: Maths
Xavier, Yvonne, and Zelda each try
independently to solve a problem. If their individual probabilities for success are \( \frac{1}{4}, \frac{1}{2} \) and \( \frac{5}{8} \) respectively, what is the probability that Xavier and Yvonne, but not Zelda,
will solve the problem?
A \( \cdot \frac{11}{8} \)
в. \( \frac{7}{8} \)
c. \( \frac{9}{64} \)
D. \( \frac{5}{64} \)
E \( \cdot \frac{3}{64} \)
Subject: Chemistry
Enough \( N a_{2} S O_{4} \) is dissolved in water
at \( 40^{\circ} C \) to saturated the solution. When
this occurs heat is given off. All of the following statements are true EXCEPT:
A. The enthalpy change of this process is negative
B. The boiling point of the solution is higher than that of pure water
C. The freezing point of the solution is lower than that of pure water
D. If the temperature of the water is lowered, then the solubility of \( N a_{2} S O_{4} \) decreases
Subject: Physics
A region in space has a total charge \( Q \)
distributed spherically such that the
volume charge density \( \rho(r) \) is given by
\( \boldsymbol{\rho}(\boldsymbol{r})=\boldsymbol{3} \boldsymbol{a} \boldsymbol{r}(\boldsymbol{2} \boldsymbol{R}) \)
for \( r \leq \frac{R}{2} \)
\( \boldsymbol{\rho}(\boldsymbol{r})=\boldsymbol{a}\left[\mathbf{1}-\left(\frac{r}{R}\right)^{2}\right] \quad \) for \( \frac{R}{2} \leq r \leq \)
\( \boldsymbol{R} \)
\( \rho(r)=0 \)
for \( r>R \)
Find the electric field at \( \rho\left(\frac{R}{2}<x<R\right) \)
Subject: Physics
Which of the following statements are true for hypermetropia?
a. The near point is farther away from
25cm.
b. The image of the object is formed behind the retina.
c. It arises due to decreased power of
accommodation.
d. It can be corrected by diverging lens.
A. b and c
B. c and d
\( c . \) a and \( b \)
D. a and d
Subject: Physics
Let \( U_{a} \) and \( U_{d} \) be the energy densities in air and in a dielectric of constant k for
same field. Then
\( \mathbf{A} \cdot U_{a}=U_{d} \)
в. \( U_{a}=k U_{d} \)
\( \mathbf{c} \cdot U_{d}=k U_{a} \)
D. \( U_{a}=(k-1) U_{d} \)
Subject: Chemistry
Calculate \( \left[\boldsymbol{H}^{+}\right] \) in a \( \mathbf{0 . 2 0} \boldsymbol{M} \) solution of
dichloroacetic acid \( \left[\boldsymbol{K}=\mathbf{5} \times \mathbf{1 0}^{-\mathbf{2}}\right] \)
that also contains \( 0.1 ~ M \) sodium
dichloroacetate. Neglect hydrolysis of sodium salt.
A. \( 0.078 M \)
В. 0.05 М
c. \( 0.06 M \)
D. \( 0.04 M \)
Subject: Biology
Assertion: In prokaryotes, there are three initiation factors used for protein synthesis.

Reason: All the initiation factors have
their own functions.
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true
Subject: Chemistry
The thermal decomposition of
HCOOH is a first-order reaction with
a rate constant of \( 2.4 \times 10^{-3} s^{-1} \) at
certain temperature. How long will it take for three-fourths of the initial
quantity of \( H C O O H \) to decompose?
A. 578 sec
B. 225 sec
\( c .436 \mathrm{sec} \)
D. 57.8 sec
Subject: Maths
There are 100 tickets in a raffle
(Lottery). There is 1 prize each of Rs. \( \mathbf{1 0 0 0} /-, \) Rs. \( \mathbf{5 0 0} /- \) and Rs. \( \mathbf{2 0 0} /- \)
Remaining tickets are blank. Find the
expected price of one such ticket.