AkshitPareek2004/jee-question-analyzer-data huggingface dataset:
Subject: Chemistry
Polarization may be called the distortion of the shape of an anion by an
adjacently placed cation. Which of the following statements is/are incorrect? This question has multiple correct options
A. Minimum polarization is brought about by a cation of low radius
B. A large cation is likely to bring about a large degree of polarization.
c. Maximum polarization is brought about by a cation of high charge.
D. A small anion is likely to undergo a large degree of polarization.
Subject: Physics
The \( (x, y) \) coordinates of the corners of
a square plate are \( (0,0),(L, 0),(L, L) \)
and \( (0, L) . \) The edge of the plate are
clamped and transverse standing
waves are set up in it. If \( u(x, y) \) denotes
the displacement of plate at \( (x, y) \) at some instant of time, the possible expression(s) for \( u \) is (are)
\( \mathbf{A} \cdot a \cos \left(\frac{\pi x}{2 L}\right) \cos \left(\frac{\pi y}{2 L}\right) \)
B. \( a \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{2 \pi y}{L}\right) \)
\( ^{\mathbf{c}} \cdot a \cos \left(\frac{2 \pi x}{L}\right) \sin \left(\frac{\pi y}{L}\right) \)
D. none of these
Subject: Chemistry
Select the correct I.U.P.A.C. name for
\( \left[\boldsymbol{C r}\left(\boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\mathbf{6}}\right)_{2}\right] \)
\( \mathbf{A} \cdot \) bis \( \left(\eta^{5} \text { -benzene }\right) \) chromium (0)
B. bis( \( \eta^{6} \) -benzene) chromate (O)
C. bis \( \left(\eta^{5} \text { -benzene }\right) \) chromate (O)
D. bis( \( \eta^{6} \) -benzene) chromium (0)
Subject: Physics
In a cylindrical vessel containing liquid of density \( \rho, \) there are two holes in the
side walls at heights of \( h_{1} \) and \( h_{2} \)
respectively such that the range of efflux at the bottom of the vessel is
same. Find the height of a hole, for which the range of efflux would be maximum
A \( \cdot \frac{h_{2}+h_{1}}{2} \)
B. \( \frac{h_{2}-h_{1}}{2} \)
\( c \cdot \frac{h_{2} h_{1}}{2} \)
D. \( \frac{h_{2}}{h_{1}} \)
Subject: Chemistry
Acid rain is produced by:
A. excessive release of CO in air
B. excessive release of \( S O_{2} \) and \( H_{2} S \) in air
C . excessive release of \( N O_{2} \) and \( S O_{2} \) in air
D. excessive release of \( N H_{3} \) and \( C O_{2} \) in air
Subject: Chemistry
Assertion
\( H_{2} S \) reacts with oxygen under standard
conditions in acid medium to give \( \boldsymbol{H}_{2} \boldsymbol{O} \)
and sulphur.
Reason
\( \boldsymbol{E}_{\boldsymbol{H}^{+} / \boldsymbol{O}_{2} / \boldsymbol{P t}}>\boldsymbol{E}_{\boldsymbol{H}^{+} / \boldsymbol{H}_{2} \boldsymbol{S} / \boldsymbol{S}}^{\boldsymbol{o}} \)
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: Maths
The marks in the science of 80 students
of class \( X \) are given below: Find the mode of the marks obtained by the students in science.
\( \begin{array}{lllll}\text { Marks: } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}\text { 20- } \\ \text { 30 }\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array}\end{array} \)
Frequency: \( \quad 3 \quad 5 \) 16 12
Subject: Physics
Three aluminium rods of equal length
form an equilateral triangle \( A B C \). Take \( O \)
(mid point of \( \operatorname{rod} B C \) ) as the origin. The
increase in Y-coordinate of center
of mass per unit change in temperature of the system is given as \( x \times 10^{-6} \mathrm{m} /^{\circ} \mathrm{C} \)
Find \( x \). Assume the length of each rod is
\( 2 m, \) and \( \alpha_{a l}=4 \sqrt{3} \times 10^{-6} /^{\circ} \mathrm{C} \)
Subject: Maths
If \( \tan ^{-1} \frac{1-x}{1+x}=\frac{1}{2} \tan ^{-1} x, \) then \( x= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \sqrt{3} \)
c. \( \frac{1}{\sqrt{3}} \)
D. None of these
Subject: Physics
Current \( i \) is flowing in a coil of area \( A \& \)
number of turns \( N, \) then magnetic
moment of the coil is \( M \) is equal to
A. \( N i A \)
в. \( \frac{N i}{A} \)
c. \( \frac{N i}{\sqrt{A}} \)
D. \( N^{2} A i \)
Subject: Chemistry
Diborane is a potential rocket fuel which undergoes combustion according to the reaction \( B_{2} H_{6(g)}+3 O_{2(g)} \rightarrow \)
\( B_{2} O_{3(s)}+3 H_{2} O(g) \) Form the following dada, calculation the enthalpy change for the combustion of diborane.
\( 2 B(s)+(3 / 2) O_{2(g)} \rightarrow B_{2} O_{3(s)} \)
\( \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 2 7 3} \boldsymbol{k J} \boldsymbol{m o l}^{-1} \boldsymbol{H}_{2(g)}+ \)
\( (1 / 2) O_{2(g)} \rightarrow H_{2} O(1) \quad \Delta H= \)
\( -286 k J m o l^{-1} H_{2} O_{(1)} \rightarrow H_{2} O_{(g)} \)
\( \Delta H=44 k J m o l^{-1} \)
\( 2 B(s)+3 H_{2(g)} \rightarrow B_{2} H_{6(g)} \)
\( \Delta \boldsymbol{H}=\mathbf{3 6 K J m o l}^{-1} \)
Subject: Physics
Light moves from air into water. The
light makes an angle of \( 47^{0} \) with the
normal in the air. What angle will it
make with the normal in the water?
The index of refraction for air is 1.00
The index of refraction for water is 1.33
A \( \cdot 47^{\circ} \)
В. \( 77^{\circ} \)
\( c \cdot 43^{\circ} \)
D. 25
E \( .33^{\circ} \)
Subject: Maths
If \( S_{n} \) denotes the sum of \( n \) terms of \( g . p \)
whose common ratio is \( r, \) then
\( (r-1) \frac{d S_{n}}{d r} \) is equal to
A \( \cdot(n-1) S_{n}+n S_{n-1} \)
B . \( (n-1) S_{n}-n S_{n-1} \)
\( \mathbf{c} \cdot(n-1) S_{n} \)
D. None of these
Subject: Maths
A plane intersects the co ordinate axes
at \( A, B, C . \) If \( O=(0,0,0) \) and (1,1,1) is
the centroid of the tetrahedron \( O A B C \)
then the sum of the reciprocals of the
intercepts of the plane
\( \mathbf{A} \cdot 12 \)
B. \( \frac{4}{3} \)
c. 1
\( D \cdot \frac{3}{4} \)
Subject: Maths
If \( \boldsymbol{P}=\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right), \boldsymbol{Q}=\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}\right) \) and \( \boldsymbol{R}= \)
\( \left(x_{3}, y_{3}\right) \) are three points of a triangle in
\( \mathbb{R}^{2} . \) Then, area of a \( \triangle P Q R \) in terms of determinant of matrix \( M= \) \( \left[\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \boldsymbol{x}_{\mathbf{1}} & \boldsymbol{x}_{\mathbf{2}} & \boldsymbol{x}_{\boldsymbol{3}} \\ \boldsymbol{y}_{\boldsymbol{1}} & \boldsymbol{y}_{\boldsymbol{2}} & \boldsymbol{y}_{\boldsymbol{3}}\end{array}\right] \) is
A. \( -\mid \operatorname{det}(M) \)
B. |det(M)||
\( ^{\mathbf{c} \cdot \frac{1}{2} \mid \operatorname{det}(M)} \)
D. \( 2|\operatorname{det}(M)| \)
Subject: Chemistry
Which transition in \( L i^{2+} \) would have the
same wavelength as the \( 2 \rightarrow 4 \)
transition in \( \boldsymbol{H} \boldsymbol{e}^{+} \) ion?
\( A \cdot 4 \) to 6
B. 4 to 3
\( c \cdot 5 \) to 6
D. 5 to 4
Subject: Chemistry
Out of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one?
A \( \cdot(n-1) d^{8} n s^{2} \)
B . \( (n-1) d^{5} n s^{2} \)
c. \( (n-1) d^{3} n s^{2} \)
D・ \( (n-1) d^{5} n s^{1} \)
Subject: Biology
Fermentation is a type of anaerobic respiration that occurs in yeast and bacteria.What is the function of
fermentation?
I. Regenerate \( \boldsymbol{N} \boldsymbol{A} \boldsymbol{D}^{+} \) from \( \mathrm{NADH} \)
II. Produce oxygen as a waste product
III. Produce ATP
A. I only
B. II only
c. ॥ only
D. I and II only
E. I and III only
Subject: Maths
The angles of a pentagon in degrees are \( \boldsymbol{y}^{o},\left(\boldsymbol{y}+\mathbf{2 0}^{o}\right),\left(\boldsymbol{y}+\mathbf{4 0}^{o}\right),\left(\boldsymbol{y}+\mathbf{6 0}^{o}\right) \) and
\( \left(y+80^{\circ}\right) . \) The smallest angle of the
pentagon is
\( A \cdot 88^{\circ} \)
B. \( 78^{\circ} \)
\( c \cdot 68^{\circ} \)
\( D \cdot 58^{\circ} \)
Subject: Maths
D.E. whose solution is \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \)
A \( . x y y_{2}+x y_{1}^{2}=y y_{1} \)
В. \( x y y_{2}+y_{1}=y \)
C \( . x^{2} y_{2}+x y_{1}=y \)
D. \( x^{2} y_{2}+2 x y_{1}=y_{1}^{2} \)
Subject: Physics
A point charge \( \boldsymbol{q}=\mathbf{1 0 0} \mu \boldsymbol{C} \) is located in
the \( x \) -y plane at the point with position vector \( \vec{r}_{0}=2 \hat{i}+3 \hat{j}+\hat{k} . \) What is the
electric field vector(in \( \mathrm{kV} / \mathrm{m} \) ) at the
point with position vector \( \vec{r}=8 \hat{i}- \) \( \mathbf{5} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} ? \)
\( \mathbf{A} \cdot 4 \cdot 2 \hat{i}-5.6 \hat{j} \)
в. \( 6 \hat{i}-8 \hat{j} \)
c. \( 54 \hat{i}-72 \hat{j} \)
D. \( 5.4 \hat{i}-7.2 \hat{j} \)
Subject: Chemistry
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g)+22 \)
kcal. The activation energy for the
forward reaction 50 kcal. What is the
activation energy for the backward reaction?
A . 72 kcal
B. 28 kcal
c. -72 kcal
D. -28 kcal
Subject: Maths
In a \( \Delta A B C, \angle A B C=\angle A C B \) and the
bisectors of \( \angle A B C \) and \( \angle A C B \)
intersect at 0 such that \( \angle B O C=120^{\circ} \)
Show that \( \angle A=\angle B=\angle C=60^{\circ} \)
Subject: Physics
A circular disc of mass \( 10 \mathrm{kg} \) and radius
\( 0.2 \mathrm{m} \) is set into rotation about an axis
passing through its centre and perpendicular to its plane by applying torque \( 10 \mathrm{Nm} \). Calculate angular velocity of the disc that it will attain at the end
of 6 s from the rest.
Subject: Maths
If \( f(x)=\left\{\begin{array}{l}2 x+b(x<\alpha) \\ x+d(x \geq \alpha)\end{array} \) is such \right.
that
\( \lim _{x \rightarrow \alpha} f(x)=L, \) then \( L= \)
\( \mathbf{A} \cdot 2 d-b \)
B. \( b-d \)
c. \( d+b \)
D. \( b-2 d \)
Subject: Maths
In a school, \( 14 \% \) of students take computer classes and \( 67 \% \) take drama classes.What is the probability that a
student neither takes computer class nor takes drama class?
A \( \frac{8}{100} \)
в. \( \frac{29}{100} \)
c. \( \frac{53}{100} \)
D. \( \frac{19}{100} \)
Subject: Physics
A full wave p-n diode rectifier uses a
load resistance of \( 1300 \Omega \). No filter is
used. If the internal resistance of each
diode is \( 9 \Omega \), then the efficiency of this full wave rectifier is
A. \( 80.64 \% \)
B . \( 40.6 \% \)
c. \( 13.9 \% \)
D. \( 100 \% \)
Subject: Physics
The moment of inertia of a square plate
about a diagonal is \( I_{d} \) and that about a
side in its plane is \( I_{s} \) then
A \( \cdot I_{s}=I_{d} \)
в. \( I_{s}<I_{d} \)
\( \mathrm{c} \cdot I_{s}>I_{d} \)
D. None of these
Subject: Physics
An object mass \( 10 \mathrm{kg} \) falls from rest through a vertical distance of \( 10 \mathrm{m} \) and acquires a velocity of \( 10 \mathrm{m} / \mathrm{s} \). The work done by the push of air on the object is \( \left(g=10 m / s^{2}\right) \)
A. 500 J
B . -500 J
c. 250
D . -250J
Subject: Chemistry
The concentration of \( \mathrm{CO}_{2} \) in a soft drink
bottled with a partial pressure of \( \mathrm{CO}_{2} \) of
4.0 atm over the liquid at \( 25^{\circ} \mathrm{C} \) is \( 1.2 \times \)
\( 10^{-1} \) M. The Henry's law constant for
\( C O_{2} \) at this temperature is
A \( \cdot 3.0 \times 10^{-2} \mathrm{mol} / \mathrm{L}- \) atm
B . \( 4.5 \times 10^{-3} \) mol \( / L- \) atm
c. \( 5.6 \times 10^{-3} \mathrm{mol} / \mathrm{L}- \) atm
D. \( 2.3 \times 10^{-2} \mathrm{mol} / \mathrm{L}- \) atm
E. More information is needed to solve the problem.
Subject: Physics
A man is going in a topless car with a velocity of \( 10.8 k m / h . \) It is raining vertically downwards. He has to hold the
umbrella at an angle of \( 53^{\circ} \) to the vertical to protect himself from rain. The
actual speed of the rain is \( \left(\cos 53^{\circ}=\right. \) \( \left.\frac{3}{5}\right) \)
A \( .2 .25 \mathrm{ms}^{-1} \)
B. \( 3.75 \mathrm{ms}^{-1} \)
c. \( 0.75 \mathrm{ms}^{-1} \)
D. \( 2.75 \mathrm{ms}^{-1} \)
Subject: Maths
If \( \boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{W}: \boldsymbol{5}<\boldsymbol{x}<\mathbf{1 0}\}, \boldsymbol{B}= \)
\( \{\mathbf{3}, \boldsymbol{4}, \mathbf{5}, \boldsymbol{6}, \boldsymbol{7}\} \) and \( \boldsymbol{C}=\{\boldsymbol{x}=\boldsymbol{2} \boldsymbol{n} ; \boldsymbol{n} \in \boldsymbol{N} \)
and \( \boldsymbol{n} \leq \mathbf{4}\}, \) Find \( :(\boldsymbol{A} \cap \boldsymbol{B}) \cup(\boldsymbol{A} \cap \boldsymbol{C}) \)
Subject: Maths
If \( A=\{a, b, c, d\}, B=\{1,2,3\}, \) find whether
or not the following sets of ordered pairs are relations from \( A \) to \( B \) or not
(a) \( R_{1}=\{(a, 1),(a, 3)\} \)
(b) \( R_{2}=\{(b, 1),(c, 2),(d, 1)\} \)
\( (c) R_{3}=\{(a, 1),(b, 2),(3, c)\} \)
Subject: Maths
\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{3} \boldsymbol{x}-\mathbf{4}, & \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{2} \\ \mathbf{2} \boldsymbol{x}+\boldsymbol{\lambda}, & \mathbf{2}<\boldsymbol{x} \leq \mathbf{3}\end{array} . \text { If } \boldsymbol{f} \) is \right.
continuous at \( x=2, \) then \( \lambda \) is
\( A \)
B.
c. -2
\( D \)
Subject: Chemistry
In which of the following reactions, the equilibrium remains unaffected on addition of small amount of argon at
constant volume?
\( \mathbf{A} \cdot H_{2(g)}+I_{2(g)} \rightleftharpoons 2 H I_{(g)} \)
B. \( P C l_{5(g)} \rightleftharpoons P C l_{3(g)}+C l_{2(g)} \)
C. \( N_{2(g)}+3 H_{2(g)} \rightleftharpoons 2 N H_{3(g)} \)
D. The equilibrium will remain unaffected in all the three cases
Subject: Maths
The angles of a pentagon in degrees are \( x, x+20, x+40, x+60 \) and \( x+80, \) then
the smallest angle of the pentagon is
\( \mathbf{A} \cdot 50^{\circ} \)
B. \( 68^{\circ} \)
\( c \cdot 78^{\circ} \)
D. \( 85^{\circ} \)
Subject: Maths
The fraction, \( \frac{1}{3} \)
A. equals 0.33333333
B. is less than 0.33333333 by \( \frac{1}{3.10^{8}} \)
c. is less than 0.33333333 by \( \frac{1}{3.10^{9}} \)
D ' is greater than 0.33333333 by \( \frac{1}{3.10^{8}} \)
E \( \cdot \) is greater than 0.33333333 by \( \frac{1}{3.10^{9}} \)
Subject: Physics
Find the change in internal energy in
joule when \( 10 g \) of air heated from \( 30^{\circ} C \) to \( 40^{\circ} \mathrm{C} \)
\( \left(c_{v}=\mathbf{0 . 1 7 2} k c a l / k g / K J=\right. \)
\( 4200 J / k c a l) \)
\begin{tabular}{l} 
A \( .62 .24 \mathrm{J} \) \\
\hline
\end{tabular}
в. 72.24
\( \mathrm{c} .52 .24 \mathrm{J} \)
D. \( 82.24 \mathrm{J} \)
Subject: Chemistry
Calgon used as water softner is:
\( \mathbf{A} \cdot N a_{2}\left[N a_{4}\left(P O_{3}\right)_{6}\right] \)
B. \( N a_{4}\left[N a_{2}\left(P O_{3}\right)_{6}\right] \)
\( \mathbf{c} \cdot N a_{2}\left[N a_{4}\left(P O_{4}\right)_{5}\right] \)
D. none of the above
Subject: Chemistry
Calculate the molality of a \( 1 \mathrm{M} \) solution of sodium nitrate. The density of the
solution is \( 1.25 g c m^{-3} \)
A . 0.66 mol \( k g^{-1} \)
B. 0.86 mol \( k g^{-} \)
c. 0.46 mol \( k g^{-1} \)
D. None of these
Subject: Chemistry
\( \boldsymbol{C} \boldsymbol{a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2}(\boldsymbol{s}) \leftrightharpoons \boldsymbol{3} \boldsymbol{C} \boldsymbol{a}^{2+}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \mathbf{2} \boldsymbol{P} \boldsymbol{O}_{4}^{3-}(\boldsymbol{a} \boldsymbol{q}) \)
What is the equilibrium expression for
the dissolution of \( C a_{3}\left(P O_{4}\right)_{2} \) where the above is true?
\( \mathbf{A} \cdot K_{s p}=\left[C a^{2+}\right]^{3}\left[P O_{4}^{3-}\right]^{2} \)
B. \( K_{s p}=\left[C a^{2+}\right]^{3}\left[P O_{4}^{3-}\right]^{3} \)
C \( \cdot K_{s p}=\left[C a^{2+}\right]\left[P O_{4}^{3-}\right] /\left[C a_{3}\left(P O_{4}\right)_{2}\right. \)
D. \( K_{s p}=\left[C a^{2+}\right]^{3}\left[P O_{4}^{3-}\right]^{2} /\left[C a_{3}\left(P O_{4}\right)_{2}\right] \)
E \( \cdot K_{s p}=\left[C a^{2+}\right]^{2}\left[P O_{4}^{3-}\right]^{3} /\left[C a_{3}\left(P O_{4}\right)_{2}\right. \)
Subject: Chemistry
The three elements \( A, B \) and \( C \) with
similar properties have atomic masses
\( x, Y \) and \( z \) respectively. The mass of \( Y \) is approximately equal to the average mass of \( X \) and \( Z . \) Such an
arrangement of elements called as:
A. Dobereiner triad
B. Mendeleev triad
c. Modern triad
D. none of the above
Subject: Maths
Use Venn diagrams to verify De Morgan's law for set difference \( \boldsymbol{A} \backslash \)
\( (\boldsymbol{B} \cap \boldsymbol{C})=(\boldsymbol{A} \backslash \boldsymbol{B}) \cup(\boldsymbol{A} \backslash \boldsymbol{C}) \)
Subject: Chemistry
A heat engine operating between 227 \( \operatorname{deg} \mathrm{C} \) and 27 deg \( \mathrm{C} \) absorbs 1 kcal of heat from the 227 deg \( C \) reservoir per cycle. Calculate
(1) the amount of heat discharged into
the low temperature reservoir.
(2) the amount of work done per cycle.
(3) the efficiency of cycle.
A. 0.4 kcal, 0.6 kcal, 40\%
B. 0.6 kcal, 0.4 kcal, 40\%
c. 0.4 kcal, 0.6 kcal, \( 60 \% \)
D. 0.7 kcal, 0.4 kcal, 40\%
Subject: Chemistry
Carbon suboxide has the formula \( C_{3} O_{2} \)
\( \mathrm{C}-\mathrm{C} \) ditance are found to be \( 130 \mathrm{pm} \) and
\( \mathrm{C}-\mathrm{O} \) distances are \( 120 \mathrm{pm} . \) Lewis structures is \( \boldsymbol{O}=\boldsymbol{C}=\boldsymbol{C}=\boldsymbol{C}= \)
\( \boldsymbol{O}, \overline{\boldsymbol{O}}-\boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C} \equiv \boldsymbol{O}^{+} \)
If true enter 1 , else enter 0 .
Subject: Physics
A particle moves on the curve \( y=\frac{x^{4}}{4} \)
where \( \boldsymbol{x}=\boldsymbol{t} / 2, \mathbf{x} \) and \( \mathbf{y} \) are measured in
metre and \( t \) in second. At \( t=4 s, \) find
the velocity of particle.
Subject: Chemistry
What is the density of \( \boldsymbol{P} \boldsymbol{C l}_{3} \) ?
A \( 2.0 g / c c \)
\( c c \)
в. \( 2 . g / c c \)
c. \( 1.57 g / c c \)
D. \( 3.0 g / c c \)
Subject: Maths
In the following figure, the area of the
shaded region is \( 20 \% \) of the area of the
whole circle centered at P. The angle
shown measures d degrees. What is its
measurement in radians?
\( A \cdot 1 \)
\( B \cdot \frac{2}{5} \pi \)
\( c \cdot \frac{4}{5} \pi \)
\( D \cdot \frac{2}{15} \pi \)
E \( \cdot \frac{4}{15} \pi \)
Subject: Physics
A 5 V zener diode is used to regulate the
voltage across load resistor \( \boldsymbol{R}_{L} \) and the
input voltage varies in between \( 10 \mathrm{V} \) to \( 15 \mathrm{V} . \) The load current also varies from 5
\( \mathrm{mA} \) to \( 50 \mathrm{mA} \). Find the value of series
resistance R.
Given, \( \boldsymbol{I}_{Z}(\boldsymbol{m} \boldsymbol{i} \boldsymbol{n})=\boldsymbol{2} \boldsymbol{0} \boldsymbol{m} \boldsymbol{A} \)
A . \( 70 \Omega \)
B. \( 90.91 \Omega \)
c. \( 142.86 \Omega \)
D. \( 71.43 \Omega \)
Subject: Chemistry
Backward reaction is favoured by
increase in the pressure of which of the following equilibrium?
A \( \cdot 2 S O_{2}+O_{2} \leftrightharpoons 2 S O_{3} \)
в. \( N_{2}+O_{2} \leftrightharpoons 2 N O \)
c. \( N_{2}+3 H_{2} \leftrightharpoons 2 N H_{3} \)
D. \( P C l_{5} \leftrightharpoons P C l_{3}+C l \)
Subject: Physics
Figure shown a DC voltage regulator
circuit, with a Zener diode of breakdown
voltage \( =6 V . \) If the unregulated input
voltage varies between \( 10 V \) to \( 16 V \)
then what is the maximum Zener
current?
A. \( 2.5 \mathrm{mA} \)
B. \( 3.5 \mathrm{mA} \)
c. \( 7.5 m A \)
D. \( 1.5 \mathrm{mA} \)
Subject: Physics
A proton takes \( 10^{-12} \) seconds to
complete one revolution in uniform
magnetic field. The time taken in another orbit of double the radius in
the same field is
B . \( 2 \times 10^{-12} \) seconds
c. \( 4 \times 10^{-12} \) seconds
D. \( 10^{-12} \) seconds
Subject: Maths
If \( \theta \) is the angle between the pair of
straight lines \( x^{2}-5 x y+4 y^{2}+3 x- \)
\( 4=0, \) then \( \tan ^{2} \theta \) is equal to
\( A \cdot \frac{9}{16} \)
в. \( \frac{16}{25} \)
c. \( \frac{9}{25} \)
D. \( \frac{21}{25} \)
E \( \cdot \frac{25}{9} \)
Subject: Maths
Find the value of \( k \) for which the
equation \( x^{2}-6 x+k=0 \) has distinct
roots.
\( \mathbf{A} \cdot k>9 \)
B. \( k=6,7 \) only
c. \( k<9 \)
\( \mathbf{D} \cdot k=9 \)
Subject: Chemistry
The binding energy of an electron in the ground state of an atom is equal to \( 24.6 e V . \) Find the energy required to
remove both the electrons from the
atom.
\( \mathbf{A} \cdot 79 e V \)
B. 89 eV
\( \mathbf{c} \cdot 99 e V \)
\( \mathbf{D} \cdot 69 \mathrm{eV} \)
Subject: Maths
Let \( x \) be a real number \( [x] \) denotes the
greatest integer function, and \( \{x\} \)
denotes the fractional part and \( (x) \)
denotes the least integer function,then
solve the following. \( [x]^{2}+2[x]= \)
\( 3 x, 0 \leq x \leq 2 \)
\( \mathbf{A} \cdot\{0,1\} \)
B . \{-1,1\}
c. \{0,-1\}
D \( \cdot\{2,1\} \)
Subject: Chemistry
(a) Calculate the radii of the first three
Bohr orbits for hydrogen. (Planck's constant \( \boldsymbol{h}=\mathbf{6 . 6 2 6 2} \times \mathbf{1 0}^{-\mathbf{3 4}} \)
Js; mass of electron \( \boldsymbol{m}=\mathbf{9 . 1 0 9 1} \times \)
\( 10^{-31} \mathrm{kg} ; \) charge on electron \( e= \)
\( \mathbf{1 . 6 0 2 1 0} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C} ; \) permittivity of
vacuum \( \epsilon_{0}=8.854185 \times \)
\( \left.10^{-12} C^{2} N^{-1} m^{-2} .\right) \)
(b) Use these radii to calculate the
velocity of an electron in each of these
three orbits.
Subject: Physics
There are two uncharged identical metallic spheres 1 and 2 of radius \( r \)
separated by a distance \( d(d>>r) . A \) charged metallic sphere of same radius having charge \( q \) is touched with one of the sphere. After sometime it is moved
away from the system. Now the uncharged sphere is earthed. Charge on earthed sphere is :
\( A \cdot+\frac{q}{2} \frac{q}{2} \)
B. \( -\frac{q}{2} \)
c. \( -\frac{q r}{2 d} \)
D. \( -\frac{q d}{2 r} \)
Subject: Maths
The vector \( \boldsymbol{T}+\mathbf{2} \overline{\boldsymbol{y}}+\boldsymbol{2} \boldsymbol{k} \) restated
through an angle \( \theta \) and doubled in
magnitude then it becomes \( 2 T+ \)
\( (2 x+2)\}+(6 x-2) k \) values of \( x \) are
A \( \cdot 1, \frac{1}{3} \)
B. \( -1, \frac{1}{3}= \)
c. \( 1, \frac{-1}{3} \)
D. (0,3)
() (0,3)
Subject: Maths
Factorise the following: \( 2 a^{3}-54 b^{3} \)
\( \mathbf{A} \cdot 2(a b+3 b)\left(a^{2}+3 b+9 a b^{2}\right) \)
B \( \cdot 2(a+2 b)\left(a^{3}+3 a b-9 b^{3}\right) \)
C \( \cdot(a-3 b)\left(a^{2}+3 b+9 a b^{2}\right) \)
D \( \cdot 2(a-3 b)\left(a^{2}+3 a b+9 b^{2}\right) \)
Subject: Physics
\( \boldsymbol{L} \)
If length of potentiometer wire is \( \frac{-}{2} \) and
resistance is \( x \) then value of unknown
emf \( \boldsymbol{E} \) is:
A \( \cdot \frac{2 E_{0} x \ell}{r_{1}+x} \)
B. \( \frac{2 E_{0} x \ell}{2 r_{1}+x} \)
c. \( \frac{4 E_{0} x \ell}{2 r_{1}+x} \)
D. \( \frac{4 E_{0} x \ell}{r_{1}+x} \)
Subject: Physics
consists of isosceles triangular frame
of base length \( l_{1} \) and expansivity \( \alpha_{1} \) and side length \( \frac{l_{1}}{l_{2}} \) and expansivity \( \alpha_{2} . \) The pendulum is supported as shown in the
figure. What is the correct ratio of
lengths, so that the length of the
pendulum remains unchanged at all
temperatures?
A \( \cdot l_{1} \alpha_{1}=l_{2} \alpha_{2} \)
B. \( \frac{l_{1}}{l_{2}}=2 \sqrt{\frac{a_{2}}{a_{1}}} \)
\( \mathbf{c} \cdot l_{1}^{2} \alpha_{1}=l_{2}^{2} \alpha_{2} \)
D. \( l_{1} l_{2}=\alpha_{1} \alpha_{2} \)
Subject: Maths
ff \( y \sqrt{1-x^{2}}+x \sqrt{1-y^{2}}=1 \) then \( \frac{d y}{d x}= \)
A \( \cdot-\sqrt{\frac{1-y^{2}}{1-x^{2}}} \)
B. \( \sqrt{\frac{1-y^{2}}{1-x^{2}}} \)
c. \( \sqrt{\frac{1-x^{2}}{1-y^{2}}} \)
D. None of these
Subject: Chemistry
\( \boldsymbol{H}_{2} \boldsymbol{C}=\boldsymbol{C} \boldsymbol{H}_{2}+\boldsymbol{H}_{2} \frac{N i / 300^{0} C}{\longrightarrow} \boldsymbol{C}_{2} \boldsymbol{H}_{6} \)
to get back the ethene, ethane must be:
A. dehydrogenated in the presence of \( C u \) at \( 300^{\circ} \mathrm{C} \)
B. heated to \( 450^{\circ} \mathrm{C} \) in the presence of \( \mathrm{H} \mathrm{NO}_{3} \) vapoar
c. heated \( 170^{\circ} \mathrm{C} \) in the presence of conc. \( \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. heated to \( 750^{0} C \)