In Young's double slit experiment the intensity of the maxima is \( I . \) If the width of each slit is doubled, the intensity of
the maxima will be:
\( \mathbf{A} \cdot I / 2 \)
B. \( 2 I \)
c. \( 4 I \)
D. \( I \)


Calcium carbonate decomposes on heating according to the equation
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightarrow \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \)
The volume of \( C O_{2} \) obtained by thermal
decomposition of 50 g of \( C a C O_{3} \) at STP will be:
A. 22.4 litre
B. 44 litre
c. 11.2 litre
D. 1 litre


In the given figure, \( O A C B \) is a
quadrant of a circle. The radius \( \boldsymbol{O A}= \)
\( 3.5 \mathrm{cm}, O D=2 \mathrm{cm} . \) Calculate the area
of the shaded portion.
A \( \cdot 6.225 \mathrm{cm}^{2} \)
В \( \cdot 6.25 \mathrm{cm}^{2} \)
c. \( 6.116 \mathrm{cm}^{2} \)
D. \( 4.25 \mathrm{cm}^{2} \)


The graph of \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{4} \boldsymbol{x}+\boldsymbol{3} \)
represents
A. a line segment
B. parabola
c. a line
D. a ray


A particle initially at rest starts moving from point \( A \) on the surface of a fixed
smooth hemisphere of radius r as
shown. The particle looses its contact
with hemisphere at point B. \( C \) is centre of the hemisphere. The equation
relating \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \) is:
A. \( 3 \sin \alpha=2 \cos \beta \)
B. \( 2 \sin \alpha=3 \cos \beta \)
\( c .3 \sin \beta=2 \cos \alpha \)
D. \( 2 \sin \beta=3 \cos \alpha \)


Determine a point which divides a line
segment of length \( 12 \mathrm{cm} \) internally in
the ratio \( 2: 3 . \) Also, justify you
construction.


A particle executes \( \boldsymbol{S} \boldsymbol{H} \boldsymbol{M} \) of
amplitude \( 25 c m \) and time period \( 3 s \)
What is the minimum time required for the particle to move between two points
\( 12.5 \mathrm{cm} \) on either side of the mean
position?
A . \( 0.5 s \)
B. \( 1.0 s \)
c. \( 1.5 s \)
D. 2.0


A ray of light parallel to principal axis
after reflection from concave mirror
passes through


A resistor and a capacitor are connected to an ac supply of \( 200 V, 50 H z \) in series. The current in the circuit is \( 2 A \). If the power consumed in the circuit is \( 100 W \) then
the resistance in the circuit is
\( \mathbf{A} \cdot 100 \Omega \)
в. 25 \( \Omega \)
c. \( \sqrt{125 \times 75} \Omega \)
D. \( 400 \Omega \)


Which one of the following has the lowest boiling point?
A \( . C H_{3} C l \)
B \( \cdot C_{2} H_{5} C l \)
c. \( C_{2} H_{5} B r \)
D. \( C_{2} H_{5} I \)


Taking \( O^{\prime} \) as origin and the position vectors of \( \boldsymbol{A}, \boldsymbol{B} \) are \( \overrightarrow{\boldsymbol{i}}+\boldsymbol{3} \overrightarrow{\boldsymbol{j}}-\boldsymbol{2} \overrightarrow{\boldsymbol{k}}, \boldsymbol{3} \overrightarrow{\boldsymbol{i}}+ \)
\( \vec{j}-2 \vec{k} . \) The vector \( \overrightarrow{O C} \) is bisecting the
angle \( A O B \) and if \( C \) is a point on line \( A B \) then \( C \) is
A \( \cdot 4(\vec{i}+\vec{j}-\vec{k}) \)
В . \( 2(\vec{i}+\vec{j}-\vec{k}) \)
c. \( (\vec{i}+\vec{j}-\vec{k}) \)
D. \( 6(\vec{i}+\vec{j}-\vec{k}) \)


The ratio of oxygen atom having -2 and
-1 oxidation numbers in \( S_{2} O_{8}^{2-} \) is
three
If true enter 1 , else enter 0
A.


How are \( \mathrm{C}_{1} \) and \( \mathrm{C}_{2} \) related?
A \( \cdot C_{1}=C_{2} \)
в. \( C_{1}>C_{2} \)
c. \( C_{1}<C_{2} \)
D. Insufficient data to reply


Initially \( (l=0), \) the force on the cart is equal to:
A . \( 20 N \)
B. \( 40 N \)
\( c .80 N \)
D. zero


If \( R \) is an equivalence relation in a set \( A \)
then \( R^{-1} \) is
A. Reflexive but not symmetric
B. Symmetric but not transitive
c. An equivalence relation
D. None of these


Check whether \( 4^{n} \) can end with 0 or not.


Two sides of a triangle are \( 6 \mathrm{cm} \) and 8 cm. If height of the triangle corresponding to \( 6 \mathrm{cm} \) side is \( 4 \mathrm{cm}, \) find height of triangle corresponding to 8 cm side.


A ray of light passes from air into a liquid The glancing angle is 30 The deviation produced in the ray of light is 15 The refractive index of liquid is;


How do bats locate their prey? Explain in detail.


Assertion
Gold and silver are extracted from their
native ores by leaching.
Reason
Both silver and gold particles dissolve in dilute solution of sodium cynide in
presence of oxygen.
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


A power transformer (step-up) with an 1: 8 turn ratio has \( 60 H z, 120 V \) across
the primary; the load in the secondary is
\( 10^{4} \Omega . \) The current in the secondary is
\( \mathbf{A} \cdot 96 A \)
B . \( 0.96 A \)
\( c .9 .6 A \)
D. \( 96 m A \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{3} \\ \mathbf{2} & -\mathbf{5}\end{array}\right] \)
\( \& \boldsymbol{K} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{0} & \mathbf{4} \boldsymbol{a} \\ -\mathbf{8} & \mathbf{5} \boldsymbol{b}\end{array}\right] \)
then find the value of a and


Which of the following pairs has both members from the same group of the periodic table?
A. \( N a, C a \)
в. \( N a, C l \)
c. \( C a, C l \)
D. \( C l, B r \)


The action of cleaning of oily dirt by soap is based on
A. Solubility in water
B. Hydrophilic property
c. Hydrophobic property
D. Presence of both hydrophilic and hydrophobic groups


Find the value of \( \cot \left(-\frac{15 \pi}{4}\right) \)


The sum of two complex numbers \( a+ \)
ib and \( c+i d \) is purely imaginary if
A \( \cdot a+c=0 \)
B . \( a+d=0 \)
c. \( b+d=0 \)
D. \( b+c=0 \)


Statement 1: The magnitude of velocity of two boats relative to river is same.
Both starts simultaneously from same point on one bank and they may reach opposite bank simultaneously moving along different paths.
Statement 2: For boats to cross the
river in same time.The component of their velocity relative to river in direction normal to flow should be
same.
A. Statement-1 is false, Statement- 2 is true
B. Statement-1 is true, Statement-2 is true, Statementis a correct explanation for statement- -
c. statement-1 is true, statement- 2 is true; statementis not a correct explanation for statement-
D. Statement-1 is true, Statement-2 is false.


Which of the following is nucleophilic
addition reaction?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O C l \frac{C H_{3} M g B r(1 e q)}{ } C H_{3} C O C H_{3} \)
\( \mathbf{B} \cdot C H_{3} C O C H_{3} \frac{I_{2} / O H^{-} / \Delta}{\longrightarrow} C H_{3} C O O^{-}+C H I_{3} \)
\( \mathbf{c} \cdot \operatorname{Ph} C H O \frac{K C N / H^{\oplus}}{\longrightarrow} \operatorname{Ph} C H(O H)(C N) \)
\( \mathbf{D} \cdot C H_{3} C \equiv C M g B r \frac{C H_{3} B r}{\longrightarrow} C H_{3} C \equiv C C H_{3} \)


Two metals \( X \) and \( Y \) have 3 and 2
electrons in their valence shells \( ^{\prime} M^{\prime} \)
and ' \( N^{\prime} \) respectively. These metals can
form binary compounds \( A \) and \( B \) with the same non-metal carbon. Both \( A \) and
\( B \) can undergo hydrolysis forming
hydrocarbons \( C \) and \( D \). Identify \( C \) and
\( D \)
A. \( C_{6} H_{6}, C_{3} H_{4} \)
в. \( C_{3} H_{6}, C_{3} H_{4} \)
c. \( C H_{4}, C_{2} H_{2} \)
D. \( C_{4} H_{10}, C_{3} H_{6} \)


The maximum angular deflection of the
rod from the vertical after the collision
is
\( ^{\mathbf{A}} \cdot_{\theta}=\cos ^{-1}\left(1-\frac{5 v_{0}^{2}}{16 g l}\right) \)
B. \( \quad \theta=\sin ^{-1}\left(1-\frac{3 v_{0}^{2}}{16 g l}\right) \)
\( \mathbf{c} \cdot_{\theta}=\cos ^{-1}\left(1-\frac{3 v_{0}^{2}}{16 g l}\right) \)
D \( \quad \theta=\sin ^{-1}\left(1-\frac{5 v_{0}^{2}}{16 g l}\right) \)


Which one of the following nutrients is not available in fertilizers?
A. Nitrogen
B. Phosphorus
\( c . \) Iron
D. Potassium


The temperature to which a gas must be cooled before it can be liquefied by pressure alone is called its
A. Critical temperature
B. Saturation point
c. Boiling point
D. Freezing point


Some of the substances used in
making of a modern safety match box are listed below:-
a) Antimony trisulphide
b) Glass powder
c)Potassium chlorate
d) Red phosphorous The head of a modern safety match stick contains:
A. A and D
B. B and C
\( c \cdot c \) and \( D \)
D. c and A


Explain why pulling is easier than
pushing with a neat sketch on a rough horizontal plane.


The tolerance for silver color in color
coding of a resistor is:
A . \( 10 \% \)
B. 5\%
c. \( 1 \% \)
D. 15\%


Find the value of \( x \) which satisfy
equation \( : 2 \tan ^{-1}(\cos x)= \)
\( \tan ^{-1}(2 \csc x) \)
A \( \cdot x=n \pi+\frac{\pi}{4} \)
B \cdot \( x=n \pi-\frac{\pi}{4} \)
c. \( x=n \pi+\frac{\pi}{2} \)
D. \( x=n \pi-\frac{\pi}{2} \)


What is the formal charge on carbon
atom in the following two structures?
A .0,-2
В. 0,0
\( c \cdot+2,-2 \)
\( \mathbf{D} \cdot+1,- \)


Initially 480 particles per minute are being emitted by a radioactive substance. This number reduces to 240
after 2 hours. The number of particles being emitted per minute after next 4 hour will be
A . 0
B. 60
c. 80
D. 120


The domain of Function \( \sqrt{9-x^{2}} \)


Which of the following parts of caterpillar swings side to side during the formation of cocoon around the
caterpillar?
A. Head moves
B. Neck moves
c. Abdomen moves
D. Thorax moves


A ball falls off a table and reaches the
ground in 1 s. Assuming \( g=10 m / s^{2} \)
calculate its speed on reaching the ground and the height of table.


Which one of the following is not a property of physical adsorption?
A. Lower the temperature, more the adsorption
B. Greater the surface area, more the adsorption
c. Higher the pressure, more the adsorption
D. Unilayer adsorption occurs


Three numbers are in arithmetic
progression. Their sum is 21 and the product of the first number and the
third number is \( 45 . \) Then the product of these three number is
A . 315
B. 90
\( c .180 \)
D. 270


passing through a spot on a road for 100 periods each of 3 minutes and
summarised it in the table given below.
Find the mode of the data.
\( \begin{array}{ll}\text { No. of cars } & \text { Frequency } \\ 0-10 & 7 \\ 10-20 & 14 \\ 20-30 & 13 \\ 30-40 & 12 \\ 40-50 & 20 \\ 50-60 & 11 \\ 60-70 & 15 \\ 70-80 & 8\end{array} \)
A. \( 44 . \)
B. 45.8
c. \( 46 . \)
D. 42


\( \boldsymbol{B C l}_{3}+\boldsymbol{L i A l H _ { 4 }} \rightarrow \boldsymbol{A}+\boldsymbol{L i C l}+\boldsymbol{A l C l}_{3} \)
\( \boldsymbol{A}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{B}+\boldsymbol{H}_{2} \)
\( \boldsymbol{B} \rightarrow \boldsymbol{C} \)
in this reaction sequence \( A, B, \) and \( C \) compounds respectively are?
в. \( B_{2} H_{6}, H_{3} B O_{3}, B_{2} O_{3} \)
c. \( B_{2} H_{6}, H_{3} B O_{3}, B \)
D. \( H B F_{4}, H_{3} B O_{3}, B_{2} O_{3} \)


A glass vessel of volume \( 100 \mathrm{cm}^{3} \) is
filled with mercury and is heated from
\( 25^{\circ} \mathrm{C} \) to \( 75^{\circ} \mathrm{C} \). What volume of mercury
will overflow? Coefficient of linear
expansion of glass \( =1.8 \times 10^{-6} /^{\circ} \mathrm{C} \)
and coefficient of volume expansion of
mercury is \( 1.8 \times 10^{-4} /^{\circ} C \)
A \( \cdot 0.67 \mathrm{cm}^{3} \)
B. \( 0.87 \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 1.74 \mathrm{cm}^{3} \)
D. \( 0.98 \mathrm{cm}^{3} \)


The apparent wavelength of light from a star moving away from the earth is \( 0.02 \% \) more than actual wavelength. What is the velocity of the star.
\( \mathbf{A} \cdot 30 k m s^{-1} \)
B . \( 60 k m s^{-1} \)
c. \( 90 k m s^{-1} \)
D. None of these


Inspite of mutual repulsion between the
protons and no electric force between
neutrons, a number of protons and
neutrons do stay together to form stable nuclei. Which of the following are
reasons for this?
1. Another type of force, called nuclear
force works between these particles
when they are very close to each other
2. The neutrons keep the protons apart so that there is no repulsion between them
3. The nuclear force is always attractive
and does not depend on the charge of
the particles
Select the correct answer from the
codes given.
\( A \cdot 2 \) and 3 only
B. 1 and 2 only
c. 1,2 and 3
D. 1 and 3 only


The number of trees in different parks of a city are 33,38,48,33,34,33 and 24 The mode of this data is
A .24
B. 34
\( c .33 \)
D. 48


During the period \( 2007-2010 \), the
minimum rate of increase in sales is in
the case of?
A. Dove
3. Himalayas
c. Detto
D. Lux


In the electric field of charge \( Q, \) another charge is carried from \( A \) to \( B . A \) to \( C, A \) to
Dand A to E, then work done will be
A. minimum along path AB
B. minimum along path AD
c. minimum along path AE
D. zero along all the paths


A gas that follows Boyle's law, Charles law and Avogadro's law is called an ideal gas. Under what conditions a real
gas would behave ideally?
A. High pressure \& low temperature
B. Low pressure \& high temperature
c. Low pressure \& low temperature
D. High pressure \& high temperature


\( \sum_{r=1}^{n} r(n-r) \)
\( \mathbf{A} \cdot \frac{1}{6} n(n+1)(2 n+1) \)
B \( \cdot\left(\frac{n(n+1)}{2}\right)^{2} \)
C \( \cdot \frac{n^{2}(n+1)}{6} \)
D. \( \frac{n\left(n^{2}-1\right)}{6} \)


Give IUPAC name:
A. n-Butylcyclohexane
B. Butylcyclohexane
C. 1 -Cyclohexanylbutane
D. 4 -Cyclohexanylbutane


If the period of oscillation of a simple pendulum is 4 second and we want to convert it into a second pendulum, then
we have to
A. Make the length of the pendulum one fourth of the previous length
B. Double the length of the pendulum
c. Make the length of the pendulum half of the previous length
D. Double the mass of the bob


Highly pure dilute solution of sodium in liquid ammonia:
This question has multiple correct options
A. shows blue color
B. exhibits electric conductivity
c. produces sodium amide
D. produces hydrogen gas


If the reading in voltmeter \( V_{1} \) is \( 40 V \)
then what is the reading of voltmeter \( V_{2} \)


Suppose \( A_{1}, A_{2}, \dots, A_{30} \) are thirty sets each having 5 elements and
\( B_{1}, B_{2}, \dots, B_{n} \) are n sets each with 3 elements. Let \( \bigcup_{i=1}^{30} A_{i}=\bigcup_{j=1}^{n} B_{j}=S \) and
each elements of \( S \) belongs to exactly 10
of the \( A_{i} \) and exactly 9 of the \( B_{j} . \) Then \( n \)
is equal to-
A . 35
B. 45 5
\( c .55 \)
D. 65


Assertion
Statement-1: In the case of a stationary
wave, a person hear a loud sound at the
pressure nodes as compared to the
antinodes.
and
Reason
Statement-2: In a stationary wave all
the particles of the medium vibrate in
phase.
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-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True.


A force of \( 50 k g f \) is applied to the smaller piston of a hydraulic machine. Neglecting friction, find the force exerted on the large piston, the diameters of the piston being \( 5 \mathrm{cm} \) and
\( 24 c m \) respectively


The volume of \( 1.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} \) required to
completely neutralize \( 150 \mathrm{mL} \) of \( 2 \mathrm{M} \) NaOH solution is
A . 150 \( \mathrm{mL} \)
B. 200 mL
\( c .100 \mathrm{mL} \)
D. 250 mL


Find the frequency of osculation of an underdamped harmonic oscillator of
mass \( m \) in terms of its natural
frequency \( \omega_{0} \) and damping constant \( \gamma \) (where - \( \boldsymbol{v} \boldsymbol{y} \) is the damping force, \( \boldsymbol{v} \) being the velocity)


Which of the following reproduces by fragmentation?
A. Spirogyra
B. chlamydomonas
c. Bryophyllum
D. All of the above


If \( \boldsymbol{x} \sqrt{\boldsymbol{y}}+\boldsymbol{y} \sqrt{\boldsymbol{x}}=1, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) equals
\( \mathbf{A} \cdot-\frac{y+2 \sqrt{x y}}{x+2 \sqrt{x y}} \)
B. \( -\sqrt{\frac{x}{y}}\left(\frac{y+2 \sqrt{x y}}{x+2 \sqrt{x y}}\right) \)
\( \mathbf{c} \cdot-\sqrt{\frac{y}{x}}\left(\frac{y+2 \sqrt{x y}}{x+2 \sqrt{x y}}\right) \)
D. None of these


The IUPAC name of :
A. 1 -Cyclohexyl-3-methylpent-1-ene
B. 3-methyl-5-cyclohexypentene
C. 1 -cyclohexyl-3-ethyl-butene
D. 1 -cyclohexyl-3,4-dimethylbutene


Draw a frequency polygon of the following data using histogram.
\( \begin{array}{llll}\text { class } & \mathbf{0}- & \mathbf{1 0}- & \mathbf{2 0}- \\ \text { interval } & \mathbf{1 0} & \mathbf{2 0} & \mathbf{3 0}\end{array} \) 一年
Frequency 5
10
25


The moment of a force about a given axis depends:
A. only on the magnitude of force
B. only on the perpendicular distance of force from the axis
c. neither on the force nor on the perpendicular distance of force from the axis
D. both on the force and its perpendicular distance from the axis


The number of real solutions of
\( \cos ^{-1} x+\cos ^{-1} 2 x=\frac{\pi}{4} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. infinitely many


Sum of interior angle of quadrilateral
equals
A . \( 300^{\circ} \)
B. \( 180^{\circ} \)
\( c .360^{\circ} \)
D. \( 540^{\circ} \)


Muscular force is a type of
A . Gravitational force
B. contact force
c. Non contact force
D. Frictional force


In a mixture of concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
and \( H N O_{3} \) intermediate formed is:
A \( \cdot H_{2} S O_{4}^{+} \)
B. \( S O_{4}^{2-} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{N} \mathrm{O}_{3}^{-} \)
D. \( H_{2} N O_{3}^{+} \)


The two functional groups present in a typical carbohydrate are :
A. \( -C H O \) and \( -C O O H \)
B. \( -C O \) and \( -O H \)
c. \( -O H \) and \( -C H O \)
D. - \( O H \) and \( -C O O H \)


Smallest man like ape is
A. Chimpanzee
B. Orangutan
c. sloth
D. Gibbon


\( P \) and \( Q \), respectively, are the sodium salts of:
A. hypochlorus and chloric acids
B. hypochlorus and chlorous acids
c. chloric and perchloric acids
D. chloric and hypochlorous acids


The compounds \( A \) and \( B \) shows which
isomerism ?
A. Ligand isomerism
B. Coordination position isomerism
c. Position isomerism
D. Ionisation isomerism


The function of part labelled as \( C \) is
A. Storage of blood
B. Storage of urine
c. Storage of water
D. None of the above


write the general electric configure in periodic table.with example


The sum of the series
\( 2\left[7^{-1}+3^{1} .7^{-1}+5^{1} .7^{-1}+\ldots\right] \) upto 20
twenty terms is
A. \( \frac{800}{7} \)
B. \( \frac{580}{7} \)
c. \( \frac{780}{9} \)
D. \( \frac{680}{7} \)


The geometry of the molecule having sand p-characters equal to \( 25 \% \) and \( 75 \% \) respectively is:
A. trigonal
B. linear
c. tetrahedral
D. octahedral


The momentum of electron is:
A. directly proportional to wavelength
B. inversly proportional to wave number
C. inversly proportional to wavelength
D. cannot be determined


A 2 meter long aluminum pipe at \( 27^{\circ} \mathrm{C} \)
is heated until it is 2.0024 at \( 77^{\circ} \) C. The
coefficient of linear expansion of aluminum is :
A . \( 12 \times 10^{-6} /^{\circ} \mathrm{C} \)
B . \( 24 \times 10^{-6} /^{\circ} \mathrm{C} \)
c. \( 6 \times 10^{-6} /^{\circ} \mathrm{C} \)
D \( .20 \times 10^{-2} \)


The geometric mean if the series
\( 1,2,4, \dots .2^{n} \) is
\( \mathbf{A} \cdot 2^{n+(1 / 2)} \)
B. \( 2^{(n+1) / 2} \)
\( \mathrm{c} \cdot 2^{n-(1 / 2)} \)
\( D \cdot 2^{n / 2} \)


\( A B \) is chord of a circle with centre \( O \)
and radius \( 17 \mathrm{cm} . \) If \( O M \perp A B \) and
\( \boldsymbol{O} \boldsymbol{M}=\mathbf{8} \mathrm{cm} . \) The length of chord \( \boldsymbol{A B} \) is
A . \( 12 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 24 \mathrm{cm} \)


The resistance of a \( 240 \vee, 200 \mathrm{W} \)
electric bulb when hot is 10 times the
resistance when cold.The resistance at
room temperature and the temperature coefficient of the filament are
(given working temperature of the filament is \( \left.2000^{0} \mathrm{C}\right) \)
A \( \cdot 28.8 \Omega, 4.5 \times 10^{-3} /^{0} C \)
В . \( 14.4 \Omega, 4.5 \times 10^{-3} /^{0} C \)
c . \( 28.8 \Omega, 3.5 \times 10^{-3} /^{0} C \)
D. \( 14.4 \Omega, 3.5 \times 10^{-3} /^{0} C \)


Heat change in a chemical reaction, at
constant temperature and pressure is
called
A. entropy
B. enthalpy
c. internal energy
D. free energy


A point charge \( q \) is palced on vertex of right circular cone. the semi-vertical
angle of cone
A. \( \frac{q}{\epsilon_{0}} \)
в. \( \frac{q}{2 \epsilon_{0}} \)
c. \( \frac{q}{3 \epsilon_{0}} \)
D. \( \frac{q}{4 \epsilon_{0}} \)


Draw the electron dot formula of
\( \boldsymbol{H}_{\mathbf{4}} \boldsymbol{P}_{2} \boldsymbol{O}_{\mathbf{7}} \)


The ore that contains both iron and
copper is:
A. malachite
B. dolomite
c. azurite
D. copper pyrites


Which of the following mixtures is used in the preparation of tips of match
sticks?
\( \mathbf{A} \cdot S+K \)
B. \( S b_{2} S_{3}+S \)
c. \( K_{2} C r_{2} O_{7}+S+P \)
D. \( P+K \)


have higher lung capacities than humans.
A. Elephants
B. Birds
c. cheetahs
D. Both A and C


In case of a real and inverted image, the magnification of a mirror is:
A. Positive
B. Negative
c. zero
D. Infinity


Ocean currents are caused by the
setting up of in water
A. convection current
B. heat current
c. electric current
D. wave current


Evaluate each of the following:
\( \frac{\sin 60^{\circ}}{\cos ^{2} 45^{\circ}}-\cot 30^{\circ}+15 \cos 90^{\circ} \)


If \( \boldsymbol{x}>1, \) then the value of \( 2 \tan ^{-1} x+\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right) \) is
\( ^{A} \cdot \frac{2 \pi}{4} \)
в.
\( c \)
D. \( \frac{3 \pi}{2} \)


A particle of mass \( 2 \mathrm{kg} \) is moving on a straight line under the action of force \( \mathrm{F}= \) \( (8-2 x) \) newton along the \( x \) -axis where \( x \) is the coordinates on \( x \) -axis If a particle
is released from \( x=7 \) m then for the
subsequent motion match the following (all values in Column II are in S.I units)


A plane lamina has an area \( 2 m^{2} \) at
\( 10^{\circ} C \) then what is its area at \( 110^{\circ} C ? \)
It's co-efficient of superficial expansion
is \( 2 \times 10^{-5} / C \)
A \( .2 .002 \mathrm{m}^{2} \)
B . \( 2.004 \mathrm{m}^{2} \)
c. \( 2.02 m^{2} \)
D. \( 2.04 \mathrm{m}^{2} \)


Select incorrect statement(s).
A. Ionisation energies of 5d-elements are greater than those of \( 3 d \) and \( 4 d \) elements
B. Cu(l) is diamagnetic while Cu(II) is paramagnetic
\( \mathbf{c} \cdot\left[T i\left(H_{2} O\right)_{6}\right]^{3+} \) is coloured while \( \left[S c\left(H_{2} O\right)_{6}\right]^{3+} \)
colourless
D. Transition elements cannot form complexes


Which of the following is a plant hormone?
A . Insulin
B. Thyroxine
c. Oestrogen
D. cytokinin


Metal used in electroplating is:
This question has multiple correct options
A. Zinc
B. Iron
c. gold
D. None of these


Write the negative of the following
statement:

All the students completed their homework.


Write the degree of the following polynomial:
\( 5 y+\sqrt{2} \)


What does LED stand for?
A. Light emitting display
B. Light energy display
C. Light emitting diode
D. Light emitting detector


The \( A s-C l \) bond distance in \( A s C l_{3} \) is
\( 2.20 A \). If radius of chlorine atom is \( C \)
then radius of \( A s \) atom is:
A \( .2 .24 \AA \)
В. \( 3.19 \dot{A} \)
c. \( 1.21 \dot{h} \)
D. \( 2.09 \dot{A} \)


An atom can neither release nor accept
electrons when it has:
\( A \cdot 4-5 \) electrons in its outermost shell
B. 5 - 6 electrons in its outermost shell
c. \( 2-3 \) electrons in its outermost shell
D. \( 3-4 \) electrons in its outermost shell


Side BC of a \( \Delta A B C \) is produced in both
the directions. Prove that the sum of the
two exterior angles so formed is greater
\( \operatorname{than} 180^{\circ} \)


The minimum value of \( 4 e^{x}+9 e^{-x} \) is
A. 5
B. 25
\( c \cdot 12 \)
D. 13


Identify the process to which the
following reaction belongs:
\( A l_{2} O_{3} \cdot 2 H_{2} O+N a_{2} C O_{3} \longrightarrow \)
\( \mathbf{2} N \boldsymbol{a} \boldsymbol{A} \boldsymbol{l} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{O}_{2} \)
\( \mathbf{2} N \boldsymbol{a} \boldsymbol{A} \boldsymbol{l} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( C O_{2} 50-60^{\circ} C A l_{2} O_{3} .2 H_{2} O+ \)
\( N a_{2} C O_{3} \)
A. Hall's process
B. Baeyer's process
C. Serpeck's process
D. None of these


The ovary is half inferior in the flowers of
A. Peach
B. Cucumber.
c. cotton
D. Gauva.


In the Venn diagram, the numbers
represent the number of elements in the
subsets. Given that
\( \boldsymbol{\xi}=\boldsymbol{F} \cup \boldsymbol{G} \cup \boldsymbol{H} \) and \( \boldsymbol{n}(\boldsymbol{\xi})=\mathbf{4 2}, \) find
\( n\left(G^{\prime} \cup H\right) \)
\( A \cdot 18 \)
3. 28
\( c .30 \)
0.38


Arrange the following compounds in the increasing order of their densities.
\( (\mathbf{I}) \)
\( (\mathrm{II}) \)
\( (\mathbf{I I I}) \)
\( (\mathbf{I V}) \)
\( A \cdot(1)<(11)<(111)<(1 \vee) \)
\( B \cdot(1)<(111)<(11 V)<(11) \)
\( c \cdot(\mid V)<(|| \mid)<(\text { ii) }<(1) \)
\( D \cdot(\|)<(\mid V)<(\| I)<(1) \)


Integrate \( \int_{a}^{b} e^{x} d x \)


The pH of the gastric juices released during digestion is :
A. less than 7
B. more than 7
c. equal to 7
D. equal to 0


If the incident ray falls on a surface normally, then the angle of reflection is degree
A . 90
B.
\( c . \) 30
D. 60


\( \int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x=\dots \)
A \( \cdot(a+x) \tan ^{-1} \sqrt{x / a}+\sqrt{a x}+c \)
B. \( (a+x) \tan ^{-1} \sqrt{x / a}-\sqrt{a x}+c \)
C. \( (a+x) \cot ^{-1} \sqrt{x / a}+\sqrt{a x}+c \)
D. \( (a-x) \cot ^{-1} \sqrt{x / a}-\sqrt{a x}+c \)


The \( E^{o} \) values for \( \mathrm{Mn} \) and \( \mathrm{Zn} \) are more
negative than expected because:
A. they have either half-filled and fully-filledd configurations
B. they can easily donate electrons
c. it is quite easy to remove electrons from their orbitals
D. none of the above


toppr 5
Q Type your question
its length in the direction of flow \( (x- \) direction), is best depicted by which of
the following graphs
4
B.
\( c \)
\( D \)


Write short notes on the following:
(i) Carbylamine reaction Diazotisation
(iii) Hofmanns
bromamide reaction
(iv) Coupling reaction Ammonolysis
(vi) Acetylation
(vii) Gabriel phthalimide synthesis.


Two sources \( A \) and \( B \) are sounding notes of frequency \( 660 \mathrm{Hz} \) A listener moves from \( A \) to \( B \) with a constant
velocity \( u . \) If the speed of sound is
\( 330 \mathrm{m} / \mathrm{s} \) what must be the value of \( u \)
so that he hears 8 beats per second?
A \( .2 .8 \mathrm{m} / \mathrm{s} \)
в. \( 2 m / s \)
c. \( 3.0 \mathrm{m} / \mathrm{s} \)
D. \( 3.5 \mathrm{m} / \mathrm{s} \)


For what instant of time, does potential energy becomes equal to kinetic energy for a particle executing SHM with a time period \( T \)
A. \( T / 4 \)
в. \( T / 8 \)
c. \( T / 2 \)
D. \( T \)


opo \( E \)
voe
gnored?


The reaction can be classified as:
A. williamson ether synthesis reaction
B. alcohol formation reaction
C. dehydration reaction
D. williamson alcohol synthesis reaction


Rate constant k varies with
temperature as given by equation:
\( \log k\left(\min ^{-1}\right)=5-\frac{2000 K}{T} . \) We can
conclude:
This question has multiple correct options
A. Pre-exponential factor A is 5.
B. \( E_{a} \) is 2000 kcal.
C. Pre-exponential factor A is \( 10^{5} \)
D. \( E_{a} \) is 9.152 kcal


Arrange the following in the descending order of their role in soil erosion
(I) Wind erosion
(ii) Chemical degradation
(iii) Physical degradation
(iv) Water erosion
\( \mathbf{A} \cdot \mathbf{i v} \rightarrow \mathbf{i} \rightarrow \mathbf{i i} \rightarrow \) iii
B. \( i v \rightarrow i i \rightarrow \) ii \( \rightarrow i \)
\( \mathrm{c} \cdot \mathrm{i} \rightarrow \mathrm{ii} \rightarrow \) iii \( \rightarrow \) iv
D. iv \( \rightarrow \) ii \( \rightarrow \) ii \( \rightarrow \) i


Calculate the mean deviation about the
mean of the set of first \( n \) natural
numbers when \( n \) is an odd number


Correct formula of
tetraamminechloronitroplatinum (IV) sulphate can be written as:
A \( \cdot\left[P t\left(N H_{3}\right)_{4}(O N O) C l\right] S O_{4} \)
B . \( \left[P t\left(N H_{3}\right)_{4} C l_{2} N O_{2}\right]_{2} S O_{4} \)
\( \mathrm{c} \cdot\left[\operatorname{Pt}\left(N H_{3}\right)_{4}\left(\mathrm{NO}_{2}\right) \mathrm{Cl}\right] \mathrm{SO}_{4} \)
D \cdot \( \left[P t C l(O N O) N H_{3}\left(S O_{4}\right)\right] \)


The circle of radius \( 5 \mathrm{cm} \) has the area
as.


Why does hydrogen resemble both
group \( I \) and group 17 elements?


The projection of \( \bar{a}=3 \hat{i}-\hat{j}+5 \hat{k} \) on \( \overline{\boldsymbol{b}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) is
A \( \cdot 8 / \sqrt{(35)} \)
B . \( 8 / \sqrt{(39)} \)
c. \( 8 / \sqrt{(14)} \)
D. \( \sqrt{(14)} \)


Which of the following statements is
not correct about \( X e F_{2} ? \)
A. It can be obtained by direct reaction between \( F_{2} \) and Xe at high pressure.
B. \( X e F_{2} \) undergoes alkaline hydrolysis to give \( O_{2} \) and \( X \) e.
C \( . X e F_{2} \) is a powerful reducing agent.
D. \( X e F_{2} \) contains two bond pairs and three lone pairs.


waters off the Eastern coast of the
United States was examined by
scientists. The results are depicted in
the graph which shows the algal count at 6 different locations. The control was
also carried out without the addition of
nutrients.
The greatest increase in algae in
response to phosphorus addition is shown by location
Control Nitrogen
Phosphorus
\( A \)
\( B .2 \)
\( c \cdot 3 \)
\( D \cdot 4 \)
\( E \)


What is the following parabola's axis of
symmetry?
\( \boldsymbol{y}=\boldsymbol{x}^{2}-\boldsymbol{4} \boldsymbol{x}+\mathbf{5} \)
A. \( x=-2 \)
B. \( x=2 \)
c. \( y=-2 \)
D. None of these


Any vector in an arbitrary direction can always be replaced by two (or three):
A. Parallel vectors which have the original vector as their resultant
B. Mutually perpendicular vectors which have the original vector as their resultant
c. Arbitrary vectors which have the original vector as their resultant
D. It is not possible to resolve a vector


In a common emitter transistor
amplifier \( \beta=60, R_{0}=5000 \Omega \) and
internal resistance of a transistor is
500\Omega. The voltage amplification of amplifier will be
A . 500
в. 460
c. 600
D. 560


Find \( \frac{d y}{d x} \) of \( 2 x+3 y=\sin x \)


Choose the correct mRNA sequence for
the given DNA sequence.
AGTTCG
A. TCUUGC
B. UCAACG
c. AGTTCG
D. TCAACG
E. UCAAGC


The element with atomic number 16
belongs to which period?
A .2
B. 3
\( c \cdot 4 \)
D.


In DNA replication, the primer is
A. A small deoxyribonucleotide polymer.
B. A small ribonucleotide polymer.
C . Helix destabilizing protein.
D. Enzyme taking part in joining nucleotides of new strand.


The average kinetic energy of a simple harmonic oscillator with respect to
mean position will be:
A \( \frac{k a^{2}}{6} \)
в. \( \frac{k a^{2}}{4} \)
c. \( \frac{k a^{2}}{3} \)
D. \( \frac{k a^{2}}{2} \)


In a region of space the electronic field is given by \( \vec{E}=(8 \hat{i}+4 \hat{j}) N / C . \) The electric
flux through a surface of area \( 10 \mathrm{m}^{2} \) in the
x-y plane is
A. 80 units
B. 40 units
c. 120 units
D. zero


The value of \( \int_{0}^{2 \pi} \frac{d x}{e^{\sin x}+1} \)
A . \( \pi \)
B.
\( c \cdot 2 \pi \)
D.


Consider a titration of potassium
dichromate solution with acidified
Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is:
A . 3
B. 4
c. 5
D. 6


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{\boldsymbol{i j}}\right] \) is a square matrix of even
order such that \( \left[a_{i j}\right]=i^{2}-j^{2}, \) then
A \( \cdot A \) is a skew-symmetric matrix and \( |A|=0 \)
B. \( A \) is symmetric matrix and |A| is a square
C. \( A \) is symmetric matrix and \( |A|=0 \)
D. none of these


Assertion
If \( \boldsymbol{F}(\boldsymbol{\alpha})=\left[\begin{array}{ccc}\cos \boldsymbol{\alpha} & -\sin \boldsymbol{\alpha} & \boldsymbol{0} \\ \boldsymbol{s i n} \boldsymbol{\alpha} & \boldsymbol{\operatorname { c o s } \boldsymbol { \alpha }} & \boldsymbol{0} \\ \boldsymbol{0} & \boldsymbol{0} & \boldsymbol{1}\end{array}\right], \) then
\( [\boldsymbol{F}(\boldsymbol{\alpha})]^{-1}=\boldsymbol{F}(-\boldsymbol{\alpha}) \)
Reason For matrix \( G(\beta)=\left[\begin{array}{ccc}\cos \beta & 0 & \sin \beta \\ 0 & 1 & 0 \\ -\sin \beta & 0 & \cos \beta\end{array}\right] \)
we have \( [G(\beta)]^{-1}=G(-\beta) \)
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


What is the vital capacity of our lungs?
A. Inspiratory reserve volume plus functional residual capacity.
B. Total lung capacity minus expiratory reserve volume.
C. Inspiratory reserve volume plus expiratory reserve volume
D. Total lung capacity minus residual volume.


Write the place value of 3 in the following decimal numbers.
\( \mathbf{3 2 . 4 6} \)


Choose the correct statements:
This question has multiple correct options
A. For a closed surface, the surface integration \( \oint \vec{B} \cdot \overrightarrow{d s} \) is always zero, where \( \vec{B} \) is magnetic field
B. A current carrying circular loop is in a uniform external magnetic field and is free to rotate about its
diametrical axis will be in stable equilibrium when flux of total magnetic field (external field + field due to the
loop itself) is maximum.
C . Spectral energy distributed graph of a black body is shown in figure. If temperature (in \( \mathrm{K} \) ) of the black body is
doubled and surface area is halved, the area under the
graph will be eight times.
D. In keplers third law, \( \frac{T^{2}}{R^{3}} \) depends on the mass of the
Sun, around which a planet is revolving.


A cylindrical vessel of cross-sectional
area \( 1000 \mathrm{cm}^{2}, \) is fitted with a
frictionless piston of mass \( 10 k g \), and filled with water completely. A small
hole of cross-sectional area \( 10 m m^{2} \) is
opened at a point \( 50 c m \) deep from the lower surface of the piston. The velocity of efflux from the hole will be
A. \( 10.5 \mathrm{m} / \mathrm{s} \)
в. \( 3.4 m / s \)
c. \( 0.8 m / s \)
D. \( 0.2 m / s \)


Assertion
Dust particles generally settle down in a
closed room.
Reason
The terminal velocity is inversely proportional to the square of their radii.
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


A wire \( 28 \mathrm{m} \) long is bent into \( \mathrm{N} \) turns of circular coil of diameter \( 14 \mathrm{cm} \) forming a solenoid of length \( 60 \mathrm{cm} \). Calculate the magnetic field inside it when a current of 5 amp passed through it. \( \left(\mu_{0}=12.57 \times 10^{-7} m^{-1}\right) \)
A \( \cdot 6.67 \times 10^{-1} T \)
\( T \)
в. \( 6.67 \times 10^{-4} T \)
c. \( 6.67 \times 10^{4} T \)
D. \( 2.67 \times 10^{-4} T \)


What is true for the equilibrium
reaction:
Acetic acid+ ethanol \( \stackrel{\boldsymbol{H}^{+}}{\rightleftharpoons} \) Ethyl acetate \( + \)
\( \boldsymbol{H}_{2} \boldsymbol{O} ? \)
This question has multiple correct options
A. The use of equimolar quantities of ethanol and acetic acid will give greatest yield of ester at equilibrium.
B. Removal of water will increase the amount of ester at equilibrium
C. Addition of water ester at equilibrium will cause formation of equal amount of water
D. Application of pressure increases the amount of ester at equilibrium


Q 1 ) If the polynomial \( a z^{3}+4 z^{2}+3 z- \)
4 and \( z^{3}-4 z+a \) leave the same
remainder when divided by \( z-3, \) find
the value of \( a \)
\( Q \) 2) If both \( x-2 \) and \( x-\frac{1}{2} \) are the
factors of \( p x^{2}+5 x+r, \) show that \( p=r \)
Q 3) Without actually division prove that \( 2 x^{4}-5 x^{3}+2 x^{2}-x+2 \) is
divisible by \( x^{2}-3 x+2 \)


In double-slit experiment using light wavelength \( 600 n m \), the angular width of a fringe formed on a distant screen is
\( 0.1^{\circ} . \) What is the spacing between the two slits?


a) Is it correct to say that only red colour is given out from the water droplets situated on the outer edge of a rainbow? Justify your answer.
b) Write a situation in which a rainbow can be viewed as a full circle instead of
an arc.


In an A.C. circuit, the current flowing in
inductance is \( \boldsymbol{I}=\mathbf{5} \sin (\mathbf{1 0 0} \boldsymbol{t}-\boldsymbol{\pi} / \mathbf{2}) \)
ampers and the potential difference is \( =200 \sin (100 \mathrm{t}) \) volts. The power
consumption is equal to
A. 1000 watt
B. 40 watt
c. 20 watt
D. zero


State True or False.
\( C_{2} H_{5} O H \) and cyclohexane mixture shows positive deviation from Raoult's law.
A. True
B. False


A mixture of \( C a_{3} P_{2} \) and \( C a C_{2}, \) is used in making Holmes signal. Explain.


Explain how groundwater is recharged.


What is translation called as?
A. Formation of RNA from DNA
B. Formation of DNA from DNA
c. Formation of DNA from RNA
D. Protein formation


Breeding ground for migratory flamingo
is
A. Area of Gulf of Kachch (Kutch)
B. Area between Khadir and Paccham islands in great Rann of Kachch
C. Area of great Rann of Kachch (Kutch) and little Rann of Kachch (Kutch)
D. Area of Nal Sarovar Bird Sanctuary


Q Type your question
\( +\sigma \) and \( -\sigma \) respectively are separated by a small distance. The medium
between the plates is vacuum. If \( \varepsilon_{0} \) is
the dielectric permittivity of vacuum then the electric field in the region
between the plates is :
A \( \cdot 0 \mathrm{Vm}^{-1} \)
В \( \cdot \frac{\sigma}{2 \varepsilon_{0}} V m^{-1} \)
c. \( \frac{\sigma}{\varepsilon_{0}} V m^{-1} \)
D. \( \frac{2 \sigma}{\varepsilon_{0}} V m^{-1} \)


Find each of the following ratios in the simplest form.
48 minutes to 1 hour


Define the following:
(a) 1 volt \( P D \)
(b) Electric power


A homogeneous chain of length \( L \) lies
on a table. Some part of chain is
hanging down the table. The coefficient of friction between the chain and the
table is \( \mu . \) The maximum length which can hangover the table in equilibrium is
A \( \cdot \frac{\mu L}{1+\mu} \)
в. \( \left(\frac{1-\mu}{\mu}\right) L \)
\( ^{C}\left(\frac{1-\mu}{1+\mu}\right)^{2} \)
D. \( \left(\frac{2 \mu}{1+2 \mu}\right) \)


Both, hydrarch and xerarch successions
lead to
A. Medium water conditions
B. Xeric conditions
c. Highly dry conditions
D. Excessive wet conditions


Which of the following is not a feature of quantum mechanical model?
This question has multiple correct options
A. The exact location and velocity of electron can be easily determined
B. orbitals can have more than two electrons
C. Energy of electrons is quantised
D. All of the above


\( \int \frac{1}{e^{x}+e^{-x}} d x \)
\( A \cdot \tan ^{-1} x \)
B. \( \tan ^{-1} e^{x} \)
\( \mathbf{c} \cdot \cot ^{-1} e^{x} \)
D. \( \frac{1}{2} \cot ^{-1} e^{x} \)


Which one of the following ores is known as Malachite?
\( \mathbf{A} \cdot C u_{2} O \)
в. \( C u_{2} S \)
c. \( C u F e S_{2} \)
D. \( C u(O H)_{2} . C u C O_{3} \)


During the discharge of a lead storage
battery, the density of \( 40 \% H_{2} S O_{4} \) by weight fell from 1.225 to 0.98 (which is \( 20 \% \) by weight). The change in
molarities of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is:
\( A \cdot 6 M \)
в. \( 5 M \)
\( c .3 M \)
D. None of these


On which conservation principle is
Kirchoff's Second Law of electrical
networks based?


The degree of dissociation of \( \boldsymbol{P C l}_{5} \) will
be more at
A. constant pressure
B. low pressure
c. high pressure
D. none of these


Two atoms of elements \( X \) and \( Y \)
contribute an electron each during the bond formation and both \( X \) and \( Y \) have
equal tendency to attract the shared electron pair. The type of bond formed between \( X \) and \( Y \)
is
A. polar covalent bond
B. ionic bond
c. coordinate covalent bond
D. non-polar covalent bond


Find:
(i) \( 9^{\frac{3}{2}} \)
(ii) \( 32^{\frac{2}{5}} \)
(iii) \( 16^{\frac{3}{4}} \)
(iv) \( 125^{\frac{-1}{3}} \)


If \( A \) and \( B \) are whole numbers such that
\( 9 A^{2}=12 A+96 \) and \( B^{2}=2 B+3, \) find
the value of \( 5 A+7 B \)
A . 31
B. 37
c. 41
D. 43


Scientist who discovered the role of
light in photosynthesis was
A. Sachs
B. Jan Ingenhousz
c. Senebier
D. Priestley


There are \( n \) distinct white and \( n \)
distinct black balls. The number of ways of arranging them in a row so that neighbouring balls are of different colours is:
A \( \cdot n+1 C_{2} \)
B \( \cdot(2)(n !)^{2} \)
c. \( \frac{(n !)}{2} \)
D. none of these


\( A 5^{0} C \) rise is temperature is observed in
a conductor by passing a current, when the current is doubled, the rise in
temperature will be nearly
A \( \cdot 10^{0} \mathrm{C} \)
B . \( 16^{\circ} \mathrm{C} \)
\( c \cdot 20^{0} c \)
D. \( 12^{\circ} \mathrm{C} \)


Which of the following compound(s) is/are peroxyacids? This question has multiple correct options
A \( . H C l O_{4} \)
в. \( H_{2} S O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{8} \)
D. \( H_{3} P O_{5} \)


Give equations for effect of heat on red lead and lead dioxide.


If strength of magnetic field \( \vec{B}=2 \hat{i}+ \) \( \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and area vector is \( \overrightarrow{\boldsymbol{A}}=\mathbf{3} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}} \)
then find the magnetic flux link with
area vector
A. 4 wber
B. 6 weber
c. 7 weber
D. 5 weber


Assertion
The third law of motion concludes that
the forces occur in pairs of action and
reaction.
Reason
The action force is more than the
reaction force.
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


Nodulated roots occur in
A. Pea
B. Wheat
C. Mustard
D. Rice


The resistor in which maximum heat
will be produced is :
\( A \cdot 6 \Omega \)
3. \( 2 \Omega \)
\( c .5 \Omega \)
D. \( 4 \Omega \)


Find the derivative by first principle
(1) \( 3 x^{2}+4 \)
(2) \( \frac{1}{2 x+3} \)


For hypothetical chemical reaction \( \mathbf{A} \rightarrow \)
I it is found that the reaction is third
order in A. What happens to the rate of reaction when the concentration of \( A \) is
doubled?
A. Rate increases by a factor 2
B. Rate decreases by a factor 3
c. Rate increases by a factor 8
D. Rate remains unaffected


Convert \( \frac{22}{17} \) into a mixed number


\( \frac{d}{d} \)


Express the complex number \( 1+i \sqrt{3} \)
in modulus amplitude form.


Primary, Secondary and Tertiary alkyl halides belongs to :
A. monohalogen derivative
B. dihalogen derivative
c. trihalogen derivative
D. tetrahalogen derivative


\( \int_{\pi^{2} / 16}^{\pi^{2} / 4} \frac{\sin \sqrt{x}}{\sqrt{x}} d x= \)
A \( \cdot \sqrt{2} \)
B. \( 1 / \sqrt{2} \)
\( c \cdot 2 \sqrt{2} \)
D. \( \pi / 2 \)


had Rs. 200 with me. I gave Rs. \( x \) to Anwar, Rs. \( \frac{x}{2} \) to Vidhu and I am left with Rs \( \frac{x}{2} . \) The amount I gave to vidhu is
A . Rs. 50
B. Rs. 40
c. Rs. 30
D. Rs. 15


The SI on a sum of money for 3 years is
Rs. 9600 and the \( C \) l on the sum at the
same rate for 2 years is Rs. 6800 . The rate \( \% \) p.a. is:
A . 12.5
в. 13.5
c. 14.5
D. 15.5


Carbogen is:
A. Pureform of \( C \)
\( \mathbf{B} \cdot C O C l_{2} \)
C. Mixture of \( C O \) and \( C O_{2} \)
D. Mixture of \( O_{2} \) and \( C O_{2} \)


Find the sum of first \( n \) term of an \( A . P \) is
\( c n^{2}, \) which \( n t h \) term is \( t_{n}=5+6 n n \in \)
\( N \)
A \( \cdot \frac{n\left(4 n^{2}-1\right) c^{2}}{6} \)
B. \( 3 n^{2}+8 n \)
c. \( \frac{n\left(4 n^{2}-1\right) c^{2}}{3} \)
D. \( \frac{n\left(4 n^{2}+1\right) c^{2}}{6} \)


Yarn can be converted into fabrics by
the process of spinning.
A . True
B. False


Which of the following is INCORRECT?
\( \mathbf{A} \cdot p(x)=5 x+5, \) degree \( =1 \)
B \( \cdot p(x)=4 x^{4}+4, \) degree \( =4 \)
\( \mathbf{C} \cdot p(x)=x^{8}, \) degree \( =8 \)
D \( . p(x)=9, \) degree \( =9 \)


In order for glucose to be used as an energy source, it is necessary that
A. Glucose be formed from fructose
B. Glucose be degraded to \( \mathrm{CO}_{2} \)
c. 2 molecules of ATP be invested in the system
D. None of these


\( = \)
\( \frac{n}{n} \)
\( d \)
\( d x \)


The action and reaction force referred to
in the third law
A. must act on the same object
B. must act on different object
c. may act on different object
D. act in the same direction


For the principal value:
\( \tan ^{-1}\left\{2 \sin \left(4 \cos ^{-1} \frac{\sqrt{3}}{2}\right)\right\} \)


A person standing between two parallel
hills fores a gun. He hears the first echo after \( 3 / 2 \) s, and second echo after \( 5 / 2 \) s.
If speed of sound is \( 332 \mathrm{m} / \mathrm{s} \), calculate the distance between the hills. When
will hear the third echo?


If any of the mirrors is removed, will he
be able to see the objects?


Two uniform stretched strings \( A \) and \( B \), made of steel, are vibrating under the same tension. If the first overtone of \( A \) is
equal to the second overtone of B and if
the radius of \( A \) is twice that of \( B \), the
ratio of the lengths of the strings is:
A .2: 3
B. 1: 2
c. 1: 3
D. 1: 4


The electric field of an electromagnetic wave traveling through the vacuum is given by the equation \( \boldsymbol{E}= \)
\( \boldsymbol{E}_{0} \sin (\boldsymbol{K} \boldsymbol{x}-\boldsymbol{\omega} \boldsymbol{t}) . \) The quantity that is
independent of wavelength is:
A . \( k \omega \)
в. \( \frac{k}{\omega} \)
\( \mathbf{c} \cdot k^{2} \omega \)
\( D \)


Diamond is a crystalline form of carbon which is good conductor of electricity.
A. True
B. False


Consider the following statements:
1. The Government of India had launched
an initiative to study the phenomenon of black carbon, commonly known as
soot.
2. Black carbon is a form of particulate air pollution, produced from incomplete combustion of biomass burning,
cooking with solid fuels and diesel
exhaust.
3. The National Black Carbon
Programme is the joint effort of the Ministry of Environment, Earth
Sciences, Science end Technology and
ISRO.

Which of the statements given above is/are correct?
\( A \cdot 1,2 \) and 3
B. 1 and 2
c. only 1
D. only 2


Most of the plants are seasonal due to
A. Photoperiodism
B. Phototropism
c. Photosynthesis
D. Photolysis


1 Joule \( = \)
\( \mathbf{A} \cdot 10^{8} \)ergs
B. \( 10^{6} \) ergs
\( \mathbf{c} \cdot 10^{7} \)ergs
D. \( 10^{10} \) ergs


Sequence of acidic character
is
\( \mathbf{A} \cdot S O_{2}>C O_{2}>C O>N_{2} O_{5} \)
B \( \cdot S O_{2}>N_{2} O_{5}>C O>C O_{2} \)
\( \mathrm{c} \cdot N_{2} \mathrm{O}_{5}>S \mathrm{O}_{2}>\mathrm{CO}>\mathrm{CO}_{2} \)
\( \mathrm{D} \cdot N_{2} O_{5}>S O_{2}>C O_{2}>C O \)


Consider the following changes:
\( \boldsymbol{A} \rightarrow \boldsymbol{A}^{+}+\boldsymbol{e}^{-}: \boldsymbol{E}_{1} \) and \( \boldsymbol{A}^{+} \rightarrow \boldsymbol{A}^{2+}+ \)
\( e^{-}: E_{2} \)
The energy required to pull out the two
electrons are \( E_{1} \) and \( E_{2} \) respectively. The correct relationship between two energies would be:
A \( \cdot E_{1}<E_{2} \)
B \( . E_{1}=E_{2} \)
c. \( E_{1}>E_{2} \)
D. \( E_{1} \neq E_{2} \)


The range of the function
\( f(x)=\sin \cos \left(\ln \left(\frac{x^{2}+1}{x^{2}+e}\right)\right) \) is
A \( \cdot[\sin \cos 1,1) \)
B. \( [\sin \cos 1, \cos 1) \)
c. \( [\sin \cos 1, \sin 1) \)
D. \( (\sin \cos 1, \sin 1] \)


Select Redox reaction from the
following:
A \( . Z n+C u S O_{4} \rightarrow Z n S O_{4}+C u \)
в. \( C a O+2 H C l \rightarrow C a C l_{2}+H_{2} O \)
c. \( N a O H+2 H C l \rightarrow N a C l+H_{2} O \)
D. \( C a C O_{3} \rightarrow C a O+C O_{2} \)


For a body, angular velocity \( \vec{\omega}=\hat{i}- \) \( 2 \hat{j}+3 \hat{k} \) and radius vector \( \vec{r}=\hat{i}+\hat{j}+ \)
\( \hat{k}, \) then its velocity is :-
\( \mathbf{A} \cdot-5 \hat{i}+2 \hat{j}+3 \hat{k} \)
B. \( -5 \hat{i}+2 \hat{j}-3 \hat{k} \)
\( \mathbf{c} .-5 \hat{i}-2 \hat{j}+3 \hat{k} \)
D. \( -5 \hat{i}-2 \hat{j}-3 \hat{k} \)


Indicate the relation which can hold in
their respective domain for infinite
values of \( x \)
This question has multiple correct options
\( \mathbf{A} \cdot \tan \left|\tan ^{-1} x\right|=|x| \)
B \cdot \( \cot \left|\cot ^{-1} x\right|=|x| \)
C \( \cdot \tan ^{-1}|\tan x|=|x| \)
D \( \cdot \sin \left|\sin ^{-1} x\right|=|x| \)


Integrate:
\( \int \sin ^{4} x d x \)


The distance of point \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}, \boldsymbol{z}_{1}\right) \) to
the plane \( a x+b y+c z+D=0 \) is
given by
A \( \cdot \frac{\left|a x_{1}+b y_{1}+c z_{1}-d\right|}{\sqrt{a+b+c}} \)
B. \( \frac{\left|a x_{1}+b y_{1}+c z_{1}\right|}{\sqrt{a^{2}+b^{2}+c^{2}}} \)
c. \( \frac{\left|a x_{1}+b y_{1}+c z_{1}-d\right|}{\sqrt{a^{2}+b^{2}+c^{2}}} \)
D. None of these


A power line lies along the east-west direction and carries a current of 10
ampere. The force per metre due to the
earth's magnetic field of \( 10^{-4} \) tesla is:
\( \mathbf{A} \cdot 10^{-5} \mathbf{N} \)
B. \( 10^{-4} \) N
\( \mathbf{c} \cdot 10^{-3} \mathbf{N} \)
D. \( 10^{-2} \) N


Differentiate the function with respect
to \( x \)
\( 2 \sqrt{\cot \left(x^{2}\right)} \)


Afforestation and reforestation is a
measure mainly to control
A. soil pollution
B. water pollution
c. thermal pollution
D. none of above


A parallel plate condenser with oil between the plates (dielectric constant of oil \( K=2 \) ) has a capacitance \( C . \) If the oil is removed, then capacitance of the capacitor becomes:
A \( \cdot \sqrt{2} C \)
в. \( 2 C \)
c. \( \frac{C}{\sqrt{2}} \)
D. \( \frac{c}{2} \)


The axes being inclined at an angle of
\( 60^{\circ}, \) the angle between the two straight
lines \( y=2 x+5 \) and \( 2 y+x+7=0 \) is
\( \mathbf{A} \cdot 90 \)
B. \( \tan ^{-1} \frac{5}{3} \)
\( ^{\mathrm{C}} \cdot \tan ^{-1} \frac{\sqrt{3}}{2} \)
D. \( \tan ^{-1} \frac{5}{\sqrt{3}} \)


An \( \alpha \) -particle is moving along a circle of
radius \( R \) with a constant angular
velocity \( \omega . \) Point \( A \) lies in the same
plane at a distance \( 2 R \) from the center.
Point \( A \) records magnetic field
produced by the \( \alpha \) -particle. If the
minimum time interval between
successive times at which \( A \) records
zero magnetic field is \( t \), the angular
speed \( \omega, \) in terms of \( t, \) is :
A. \( \frac{2 \pi}{t} \)
в. \( \frac{2 \pi}{3 t} \)
c. \( \frac{\pi}{3 t} \)
D.


Find the smallest positive integer \( n \)
such that \( t_{n} \) of the arithmetic sequence \( 20,19 \frac{1}{4}, 18 \frac{1}{2}, \ldots . \) is negative?


Which of the following halides is least stable and has doubtful existence?
\( \mathbf{A} \cdot C I_{4} \)
в. \( G e I_{4} \)
\( \mathrm{c} \cdot \operatorname{SnI}_{4} \)
D. \( P b I_{4} \)


Saturated solution of \( K N O_{3} \) is used to
make salt bridge because:
A. velocity of \( K^{+} \) ion is greater than that of \( N O_{3}^{-} \) ion
B. velocity of \( N O_{3}^{-} \) ion is greater than that of \( K^{+} \) ion
C. velocities of both \( K^{+} \) and \( N O_{3}^{-} \) ions are nearly the
same
D. \( K N O_{3} \) is highly soluble in water


What is the value of \( \angle \boldsymbol{R} \) ?
A. 100
on
В. \( 110^{\circ} \)
\( c \cdot 120 \)
0.130


Clinical thermometers are made up of glass. The important characteristic(s) considered for this selection is/are:
A. it is a bad conductor of heat
B. it is transparent
\( c \cdot \operatorname{both} A \& B \)
D. it is strong


The value of \( \sin \left(2 \sin ^{-1} 0.8\right) \) is equal to.
\( \mathbf{A} \cdot \sin ^{-1} 1.2 \)
B. \( \sin ^{-1}(0.96) \)
c. \( \sin ^{-1}(0.48) \)
D. sin \( 1.6^{\circ} \)


\( 1 g \) of \( ^{12} C \) contains \( 6.022 \times 10^{23} \) atoms
of the isotope.
A. True
B. False


Carnassial teeth are modified for
A. Crushing
B. Tearing
c. Grinding
D. cutting


Which of the following statement is
true?
A . Cold and very diluted \( H N O_{3} \) forms \( N H_{4} N O_{3} \) with \( Z n \) or \( S n \)
B. Concentrated \( H N O_{3} \) forms \( H_{2} S n O_{3} \) with \( S n \)
C . Cold and concentrated \( H N O_{3} \) forms \( N O_{2} \) with \( C u \)
D. All the above statements are correct


Based on equations reducible to linear
equations Solve for \( x \) and \( y: \frac{24}{2 x+y}-\frac{13}{3 x+2 y}= \) \( 2 ; \frac{26}{3 x+2 y}+\frac{8}{2 x+y}=3 \)
A. \( x=-2, y=6 \)
в. \( x=-5, y=3 \)
c. \( x=3, y=2 \)
D. \( x=1, y=0 \)


If uncertainty principle is applied to an object of mass 1 microgram, the uncertainty value of velocity and position will be :
A \( \cdot 0.2 \times 10^{-4} m^{2} s^{-1} \)
В. \( 0.52 \times 10^{6} m^{2} s^{-1} \)
D. \( 2 \times 10^{-34} \mathrm{m}^{2} s^{-1} \)


The horizontal component \( N_{x} \) and
vertical component \( N_{y} \) of the reaction
at end \( P \) are given by:
A \( \cdot \mathrm{N}_{\mathrm{x}}=1300 \mathrm{N}, \mathrm{N}_{\mathrm{y}}=960 \mathrm{N} \)
B. \( \mathrm{N}_{\mathrm{x}}=960 \mathrm{N}, \mathrm{N}_{y}=140 \mathrm{N} \)
C. \( \mathrm{N}_{\mathrm{x}}=960 \mathrm{N}, \mathrm{N}_{\mathrm{y}}=960 \mathrm{N} \)
D. \( \mathrm{N}_{\mathrm{x}}=1300 \mathrm{N}, \mathrm{N}_{\mathrm{y}}=1300 \mathrm{N} \)


An angle which is equal to \( 360^{\circ} \) is called \( _{\text {一一一一一一一 }} \) angle.
A. Right
B. Complete
c. Acute
D. obtuse


Q Type your question-
\( s p^{2} \) hybridized carbon atom of an aromatic ring. It is more acidic than an alcohol, but less acidic than
a carboxylic acid. It is even less acidic
than carbonic acid but more acidic
than water. Thus, phenol is unable to
protonate \( H C O_{3}^{-} \) anion but easily
protonates \( \boldsymbol{O H}^{-} \) anion. The \( \boldsymbol{O H}^{-} \) group activates the benzene ring so much that electrophilic substitution takes place readily.
The correct order of acidity of the
following substituted phenols is:
A \( . I>I I>I I I>I V \)
в. \( I>I I I>I V>I I \)
с. \( I>I I>I V>I I I \)
I I \( I>I I I>I I>I V \)
\( V \)


From the figure, identify a sector


The radius of a circular plate is increasing at the ratio of 0.20 cm/sec.At what rate is the area
increasing when the radius of the plate
is \( 25 \mathrm{cm} \)


A gas that cannot be collected over
water is:
A \( . P H_{3} \)
в. \( S O_{2} \)
\( c \cdot O_{3} \)
D. \( N_{2} \)


Which one of the following will reduce the rate of transpiration?
A. Increase in wind velocity
B. Rise in temperature
c. Increase in water uptake by plants
D. Decrease in light intensity


How much \( B a C l_{2} \) would be needed to
make 250 ml of a solution having the
same concentration of \( C l^{-} \) as one
containing \( 3.78 g N a C l \) per 100 ml?
\( (B a=137) \)
A. \( 22.4 g \)
в. \( 16.8 g \)
c. \( 67.2 g \)
D. 33.6 \( g \)


Find \( A \triangle B \) and draw Venn diagram when:
\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\} \) and \( \boldsymbol{B}=\{\boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}\} \)


Study the graph carefully and answer
the question:
The number of people who prefer
playing Tennis in 2006 is how many millions less than the number of people
who prefer playing Tennis in \( 2005 ? \)
A . 110
B . 105
\( c .100 \)
D. 95


In Bohr's theory of Hydrogen atom, the electronjumps from higher orbit 'n' to lower orbit 'p'. The wavelength will be minimum for the transition
\( A \cdot n=5 \) to \( p=4 \)
B. \( n=4 \) to \( p=3 \)
\( c \cdot n=3 \) to \( p=2 \)
\( D \cdot n=2 \operatorname{top}=1 \)


The element in the first row and third
column of the inverse of the matrix
\( \left[\begin{array}{ccc}1 & 2 & -3 \\ 0 & 1 & 2 \\ 0 & 0 & 1\end{array}\right] \) is
A . -2
B.
\( c \cdot 1 \)
D. 7


Let \( A=\{10,15,20,25,30,35,40,45\} 50 \)
\( B=\{1,5,10,15,20,30\} \) and \( C=\{1,5,15 \)
\( 20,35,45,3 . \) Verify \( A \backslash(B \cap C)=(A \backslash \)
\( \boldsymbol{B}) \cup(\boldsymbol{A} \backslash \boldsymbol{C}) \)


Which of the following is an elastomer?
\( A \). Buna - N
B. Buna - S
C. Neoprene
D. All


Based on equation \( \boldsymbol{E}=\mathbf{2 . 1 7 8} \times \mathbf{1 0}^{\mathbf{1 8}} \mathbf{J} \)
\( \left(\frac{Z^{2}}{n^{2}}\right), \) certain conclusions are written Which of them is not correct?
A. The negative sign in equation simply means that the energy of electron bound to the nucleus is lower than i would be if the electrons were at the infinite distance from the nucleus
B. Larger the value of n, the larger is the orbit radius
c. Equation can be used to calculate the change in energy when the electron changes orbit
D. For \( n=1 \), the electron has a more negative energy that it does for \( n=6 \) which means that the electron is more loosely bound in the smallest allowed orbit


The table gives the probability distribution of a random variable \( \boldsymbol{X} \)
\[
\begin{array}{lll}
x & 1 & 2 \\
P(X= & &
\end{array}
\]
\( x) \)
0.2 0.1
\[
\begin{array}{ll}
0.3 & 0.3
\end{array}
\]
(i) Find \( P \)
(ii) Find the mean of \( \boldsymbol{X} \)
(iii) Find the variance of \( \boldsymbol{X} \)


In the figure shown here, \( A \) is a
conducting sphere and \( \mathrm{B} \) is a closed
spherical surface. If a-q change is
placed at \( C \) near \( A \), then the electric flux
through the closed surface is -
A . zero
B. positive
c. negative
D. none of the above can be predicted


It is required to seat 5 men and 4 women in a row so that the women
occupy the even places. How many such arrangements are possible?
A .24
в. 120
\( c \cdot 720 \)
D. 2880


At \( 27^{\circ} C, \) most probable speed of
methane gas is \( X \mathrm{m} / \mathrm{s} \), then select the
correct statement.
A. R.M.S speed of \( O_{2} \) at 300 K is \( x \) m/s
B. R.M.S speed of \( O_{2} \) at \( 400 \mathrm{K} \) is \( \mathrm{Xm} / \mathrm{s} \)
C. R.M.S speed of \( O_{2} \) at 500 K is \( x \) m/s
D. R.M.S speed of \( O_{2} \) at \( 600 \mathrm{K} \) is \( \mathrm{Xm} / \mathrm{s} \)


Find the sum of square of the following
number:
\( \mathbf{3 9} \)


In an experiment, 18.0 g of mannitol was dissolved in 100 g of water. The vapour pressure of solution at \( 20^{\circ} \mathrm{C} \) was 17.226
mm of mercury. Calculate the molecular mass of mannitol. The vapour pressure
of water at \( 20^{\circ} \mathrm{C} \) is \( 17.535 \mathrm{mm} \) of
mercury.
A. Molecular mass of mannitol = 171.02
B. Molecular mass of mannitol = 181.02
c. Molecular mass of mannitol = 161.02
D. Molecular mass of mannitol = 121.02


A charged particle moves in a gravity
free space where an electric field of
strength \( \mathrm{E} \) and a magnetic field of induction B exist. Which of the following
statement is/are correct?
This question has multiple correct options
A. If \( E \neq 0 \) and \( B \neq 0, \) velocity of the particle may remain constant
B. if \( E=0 \), the particle cannot trace a circular path
c. if \( E=0 \), kinetic energy of the particle remains constant
D. none of these


The total area enclosed by the lines \( y= \)
\( |x|,|x|=1 \) and \( y=0 \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot \frac{1}{2} \)
D. 4


\( \underbrace{n}_{n} \)


\( \Delta=\left|\begin{array}{ccc}0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0\end{array}\right| \)


Which would most likely cause a greater burn would if applied to someone's skin:
A: 100 grams of water at the boiling point
or
B: 100 grams of steam at the boiling
point and why?
A. B: 100 grams of steam would most likely cause a greater wound because it is at a lower temperature
B. A: 100 grams of water would most likely cause a greater wound because it is more dense
c. в: 100 grams of steam would most likely cause a greater wound because it is at a higher temperature
D. A: 100 grams of water would most likely cause a greater wound because it has not yet "boiled away" its heat
E. B: 100 grams of steam would most likely cause a greater wound because it gives heat to the skin in changing to liquid; then it gives heat in lowering temperature to that of the skin


If \( \boldsymbol{x}=\sec \boldsymbol{\theta}-\cos \boldsymbol{\theta} \) and \( \boldsymbol{y}=\sec ^{n} \boldsymbol{\theta}- \)
\( \cos ^{n} \theta, \) then \( \left(\frac{d y}{d x}\right)^{2} \) is equal to
A \( \cdot \frac{n^{2}\left(y^{2}+4\right)}{x^{2}+4} \)
\( ^{\text {В } \cdot} \frac{n^{2}\left(y^{2}-4\right)}{x^{2}} \)
\( ^{\mathbf{c}} \cdot_{n}\left(\frac{y^{2}-4}{x^{2}-4}\right) \)
D. \( \left(\frac{n y}{x}\right)^{2}-4 \)


What is derived name of Neopentyl alcohol?
A. Isopropyl carbinol
B. n-Butyl carbinol
c. Tertiary butyl carbinol
D. Ethyl methyl carbinol


Cell surface receptors are integral membrane proteins and possess regions that contribute to which of the
basic domains?
A. Extracellular domains
B. Transmembrane domain
c. Intracellular domain
D. All of the above


A 3.4 g sample of \( H_{2} O_{2} \) solution containing \( \boldsymbol{x} \% \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) by mass requires
\( x \) mL of a \( K M n O_{4} \) solution for complete oixidation under acidic
condition.The molarity of \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
solution is:
\( A \)
B. 0.5
\( c \cdot 0.4 \)
D. 0.2


The weight of one hydrogen atom is:
\( \mathbf{A} \cdot 1.66 \times 10^{-27} k g \)
В. \( 2.66 \times 10^{-27} k g \)
C \( \cdot 1.76 \times 10^{-27} \mathrm{kg} \)
D. \( 1.66 \times 10^{-37} k g \)


One mole of \( \boldsymbol{H}_{2}, \boldsymbol{2} \) moles of \( \boldsymbol{I}_{2} \) and \( \boldsymbol{3} \)
moles of \( H I \) are injected in a one litre flask. What will be the concentration of
\( \boldsymbol{H}_{2}, \boldsymbol{I}_{2} \) and \( \boldsymbol{H} \boldsymbol{I} \) at equilibrium when \( \boldsymbol{K}_{\boldsymbol{c}} \)
is \( 45.9 ? \)


In an experiment, addition of \( 5.0 \mathrm{mL} \) of
\( 0.006 \mathrm{M} \mathrm{BaCl}_{2} \) to \( 10.0 \mathrm{mL} \) of arsenic
sulphite sol just causes the complete coagulation in 34 hours. The flocculating value of the effective ion is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Let \( \boldsymbol{A}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{j}}-\hat{\boldsymbol{k}}, \boldsymbol{B}=\mathbf{4} \hat{\mathbf{i}}+\mathbf{5} \hat{\mathbf{j}}+\hat{\boldsymbol{k}} . \) If
the centroid \( G \) of the triangle \( A B C \) is \( \mathbf{3} \hat{\mathbf{i}}+\mathbf{5} \hat{\mathbf{j}}-\hat{\boldsymbol{k}}, \) then the position vector of
\( C \) is
\( \mathbf{A} \cdot 3 \hat{i}-6 \hat{j}+3 \hat{k} \)
B . \( 3 \hat{i}-6 \hat{j}-3 \hat{k} \)
c. \( 3 \hat{i}-6 \hat{j}+2 \hat{k} \)
D. \( 3 \hat{i}+6 \hat{j}-3 \hat{k} \)


Which of following does not give white precipitate of \( A g C l \) on heating with silver nitrate.
A. \( C H_{3} C H_{2} C l \)
B. \( \left(C H_{3}\right)_{2} C H_{2} C l \)
c. \( \left(C H_{3}\right)_{3} C C l \)
D. \( C C l_{4} \)


The magnification produced by a plane mirror is \( +1 . \) What does this mean?


Ratio of angle in 5: 3: 1 find the angle.


Which does not have conjugate system?
A \( \cdot C H_{2}=C H C l \)
в. \( C H_{2}=C H C H O \)
c. \( C H_{3} C H=C H_{2} \)
D.


Rahul takes 6 hours more than than
Pathak to cover a distance of \( 540 k m \). If
instead, Rahul doubles his speed, he
would reach the destination one and a
half hours before Pathak. Find Pathak's
speed.
A. \( 36 \mathrm{kmph} \)
B. \( 60 \mathrm{kmph} \)
c. \( 45 \mathrm{kmph} \)
D. \( 40 \mathrm{kmph} \)


Which of the following has lowest boiling point?
A. Helium
B. Neon
c. xenon
D. Argon


If \( 50 m L \) of \( 0.2 M K O H \) is added to
\( 40 m L \) of \( 0.5 M H C O O H . \) The \( p H \) of
the resulting solution is:
\( \left(\boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{4}}\right) \)
A. 3.74
B. 5.6
\( c .7 .5 \)
D. 3.4


Hydrogen sulphide gets reduced to sulphur.
A . True
B. False


Take small amounts of salt and add it to
large amounts of water. \( X \) is formed.
The substance present in small amount
is called \( Y \) whereas the substance
present in large amounts is called \( Z \)
and the salt solution formed is called \( A \)
The solution in which more of the solute
can be dissolved at a given temperature
is called \( B \) solution. The solution which
cannot be dissolved any more of the solute at a given temperature is \( C \) solution.
What is \( B \) ?
A. Salt solution
B. Unsaturated
c. Saturated
D. Super saturated solution


gigameter is \( 10^{-a} \) exameter. What is
value of a?


A current \( I \) flows through a uniform
wire of diameter \( d \) when the mean
electron drift velocity is \( v . \) The same
current will flow through a wire of diameter \( \frac{d}{2} \) made of the same material if the mean drift velocity of the electron
is
A. \( \frac{v}{4} \)
в. \( \frac{v}{2} \)
\( c \cdot 2 v \)
D. \( 4 v \)


\( \mathrm{IF} \mathrm{A}=\left|\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{0}\end{array}\right| \) And \( \mathrm{B}=\left|\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right| \) then \( \mathbf{A}+\mathbf{B}= \)
\( A \cdot A \)
B. B
c. \( \mid \begin{array}{ll}2 & 0 \\ 1 & 1\end{array} \)
D. \( \left|\begin{array}{ll}0 & 2 \\ 2 & 2\end{array}\right| \)


What are the necessary conditions for
autotrophic nutrition and what are its
by-products?


If \( \boldsymbol{O P}=2 \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) and \( \boldsymbol{O} \boldsymbol{Q}=\boldsymbol{3} \hat{\boldsymbol{i}}- \)
\( 4 \hat{j}-2 \hat{k} \) then the modulus \( \bar{P} Q \) is
A \( \cdot \sqrt{13} \)
B. \( \sqrt{51} \)
c. \( \sqrt{39} \)
D. \( \sqrt{67} \)


Find mode for the following data.
\( \begin{array}{lllll}\text { Employees } & 0- & 10- & 20- & 30 \\ \text { salary } & 10 & 20 & 30 & 40\end{array} \)
No. of
employees


A hypothetical magnetic field existing in a region is given by \( \vec{B}=B_{0} \vec{e}_{r}, \) where
\( \vec{e}_{r} \) denotes the unit vector along the
radial direction. A circular loop of radius \( \alpha, \) carrying a current \( i, \) is placed
with its plane parallel to \( X-Y \) plane
and the centre at \( (0,0, d) . \) Find the magnitude of the magnetic force acting on the loop.
A \( \cdot \frac{i 2 \pi b_{o} a^{3}}{\sqrt{a^{2}+d^{4}}} \)
B. \( \frac{i 2 d_{o} a^{2}}{\sqrt{a^{2}+b^{2}}} \)
c. \( \frac{\pi b_{o} a^{2}}{\sqrt{a+d^{2}}} \)
D. \( \frac{i 2 \pi b_{a} a^{2}}{\sqrt{a^{2}+d^{2}}} \)


If \( S_{1} \) and \( S_{2} \) are respectively the sets of local minimum and local maximum
points of the functions, \( f(x)=9 x^{4}+ \)
\( 12 x^{3}-36 x^{2}+25, x \in R, \) then
A \( . S_{1}=\{-2,1\} ; S_{2}=\{0\} \)
B. \( S_{1}=\{-2,0\} ; S_{2}=\{1\} \)
c. \( S_{1}=\{-2,\} ; S_{2}=\{0,1\} \)
D. \( S_{1}=\{-1\} ; S_{2}=\{0,2\} \)


At a given place on earth's surface the horizontal component of earths
magnetic field is \( 2 \times 10^{-5} T \) and
resultant magnetic field is \( 2 \times 10^{-5} \mathrm{T} \)
and resultant magnetic field is \( 4 \times \)
\( \mathbf{1 0}^{-5} \mathrm{T} . \) The angle of dip at this place is
A \( .30^{\circ} \)
В. \( 60^{\circ} \)
\( c \cdot 90^{0} \)
D. \( 45^{\circ} \)


What is the probability of obtaining
total outcome in the multiple of 12 if
two die is tossed together once.


In an experiment of verification of
Ohm's law, following observations are obtained:
Potential difference
1.
\[
v \operatorname{cin}
\]
0.5
volt'
Current in
\( 0.4 \quad 0.6 \)
per
What will be the potential difference \( \mathbf{V} \) when the current I is 0.5 A ?
A. \( 1.25 V \)
в. \( 0.5 V \)
c. \( 2 V \)
D. \( 1 V \)


Solve \( \sin ^{2} \theta-\cos \theta=\frac{1}{4} .0 \leq \theta \leq 2 \pi \)


In \( N i-C d \) storage cell, anode consists
of:
A. cadmium oxide
B. nickel oxide
c. cadmium metal plate
D. nickel metal plate


\( \left[\begin{array}{ll}\boldsymbol{x}-\boldsymbol{y} & \boldsymbol{4} \\ \boldsymbol{z}+\boldsymbol{6} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right]=\left[\begin{array}{ll}\boldsymbol{8} & \boldsymbol{w} \\ \boldsymbol{0} & \boldsymbol{6}\end{array}\right], \) write the
value of \( (\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}) \)


Four particle of mass \( 5,3,2,4 k g \) are at
the points \( (1,6),(-1,5),(2,-3),(-1,-4) . \) Find
the coordinates of their center of mass.


Least energetic conformation of cyclohexane is :
A. chair conformation
B. boat conformation
c. cis conformation
D. \( E-Z \) form


A capacitors is charged to store an
energy \( U . \) The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in
parallel. The energy in each of the capacitors is
A \( \cdot \frac{U}{2} \)
в. \( \frac{3 U}{2} \)
c. \( U \)
D. \( \frac{U}{4} \)


A person suffering from frequent episodes of nasal discharge, nasal
congestion, reddening of eyes and watery eyes. These are the symptoms of
A. Cyanosis
B. Bronchitis
c. Rhinitiss
D. Bronchial carcinoma


Write the molecular formula of
novestrol.


After electrolysis of a sodium chloride
solution with inner electrodes for a
certain period of time, \( 600 \mathrm{mL} \) of the \( 1 \mathrm{N} \)
solution was left which was found to be
NaOH. During the same time 31.80 g of Cu was deposited in copper voltameter in series with the electrolytic cell. The \% yield of NaOH obtained will be:
(Atomic mass of \( C u=63.6 .) \)


What are hydrocarbons? Write the name and general formula of
(i) saturated
hydrocarbons,
(ii) unsaturated
hydrocarbons and draw the structure of one hydrocarbon of each type. How can an unsaturated hydrocarbon be made
saturated?


Calculate the depression in the freezing
point of water when \( 10 g \) of
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H C l C O O H} \) is added to
\( 250 g \) of water
\( \left[\boldsymbol{K} \boldsymbol{a}=\mathbf{1 . 4} \times \mathbf{1 0}^{-\mathbf{3}}, \boldsymbol{K}_{\boldsymbol{f}}=\right. \)
1.86 \( \left.\boldsymbol{K} \boldsymbol{k g} \boldsymbol{m o l}^{-1}\right] \)


Assertion
Cell wall is not found in an animal cell.
Reason
Animal cells are covered by cell
membrane.
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.


The graph of any Quadratic polynomial is such that the chord joining the points \( x=a \) and \( x=b \) is parallel to the
tangent line at \( \boldsymbol{x}=? \)
A. A.M. of \( a \) and \( b \)
B. G.M. of \( a \) and \( b \)
C . H.M. of \( a \) and \( b \)
D. AGP


What does an enzyme do in terms of
energy requirement of a reaction? What would happen if the enzyme did not play this role?


How many distinct sets of three positive integers have a mean of \( 6, \) a
median of 7 and no mode?
A . 1
B . 2
\( c .3 \)
D.


The fastest reaction with aqueous
acetone solution is given by:
A. \( C H_{3}-C H_{2}-C l \)
в. \( C H_{3}-O-C H_{2}-C l \)
c. \( O=C H-C H_{2}-C l \)
D. \( C H_{2}=C H-C l \)


The radius of a circle is \( 14 \mathrm{m} \), then the
circumference of a circle is
\( \mathbf{A} \cdot 616 \mathrm{m} \)
в. 88 m
c. \( 154 \mathrm{m} \)
D. None of the above


The angle made by the tangent line at (1
3) on the curve \( y=4 x-x^{2} \) with \( O X \) is
A \( \cdot \tan ^{-1}(2) \)
B. \( \tan ^{-1}(1 / 3) \)
c. \( \tan ^{-1}(3) \)
D. \( \pi / 4 \)


When an organic compound containing nitrogen is heated with copper oxide,nitrogen is obtain in its:
A. oxide form
B. nitride form
C. free form
D. azide form


Heavy metals like Ni can be separated
from water by
A. Carbomethyl enitosan
B. Biological treatment
c. Ultrafiltration
D. Sedimentation


If \( f \) is a continuous function on the real
line. Given that \( x^{2}+(f(x)-2) x- \) \( \sqrt{3} \cdot f(x)+2 \sqrt{3}-3=0 . \) Then the value
of \( f(\sqrt{3}) \)
A. can not be determined
B. \( 2(1-\sqrt{3} \)
c. zero
D. \( \frac{2(\sqrt{3}-2)}{\sqrt{3}} \)


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{1 . \cos x+5 \cos 3 x+\cos 5 x}{\cos 6 x+6 \cos 4 x+15 \cos 2 x+10} \) then
\( \boldsymbol{f}(\mathbf{0})+\boldsymbol{f}^{\prime}(\mathbf{0})+\boldsymbol{f}^{\prime \prime}(\mathbf{0})= \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
\( D \)


In the figure above (not to scale) ABCD
is trapezium in which \( \overline{\boldsymbol{A B}} \| \overline{\boldsymbol{C D}}, \mathbf{A D}= \)
\( \mathrm{CD} \) and \( \mathrm{AB}=2 \mathrm{CD} \)
If \( \angle A D C=100^{\circ} \) then find \( \angle A B C \)
A \( \cdot 40^{\circ} \)
B .50
\( c \cdot 60^{\circ} \)
D. 70


Calculate the work done (in J) when 4.5 g
of \( H_{2} O_{2} \) reacts against a pressure of 1.0
\( \operatorname{atm} \operatorname{at} 2 H_{2} O_{2} \rightarrow O_{2}+2 H_{2} O \)
A . \( -1.63 \times 10^{2} \)
В. \( 4.5 \times 10^{2} \)
c. \( 3.2 \times 10^{2} \)
D. \( -6.1 \times 10^{2} \)


A person is seeing two trains one of there is coming with speed of \( 4 \mathrm{m} / \mathrm{s} \) and another is going with same speed. If two trains blowing a whistle with frequency 243Hz . The beat frequency heard by stationary person will be (speed of sound in air \( =320 \mathrm{m} / \mathrm{s} \)
в. \( 3 H z \)
\( \mathrm{c} .6 \mathrm{Hz} \)
D. \( 12 H z \)


Only rotating bodies can have angular
momentum
A . True
B. False


A ray of light is incident on a thin film.
As shown in the figure, \( M \) and \( N \) are
two reflected rays while \( P \) and \( Q \) are two
transmitted rays. Rays \( N \) and \( Q \)
undergo a phase change of \( \pi \). correct
ordering of the refracting indices is
A \( \cdot n_{2}>n_{3}>n_{1} \)
в. \( n_{3}>n_{2}>n_{1} \)
\( \mathbf{c} \cdot n_{3}>n_{1}>n_{2} \)
D. none of these, the specified changes cannot occu


\( \boldsymbol{P}^{\boldsymbol{\ell}} \) is an intinite current carryıng
conductor. \( A B \) and \( C D \) are smooth
conducting rods on which a conductor
\( E F \) moves with constant velocity \( V \) as shown. The force needed to maintain
constant speed of \( \boldsymbol{E F} \) is -
\( ^{\mathrm{A}} \frac{1}{V R}\left[\frac{\mu_{0} I V}{2 \pi} \ln \left(\frac{b}{a}\right)\right]^{2} \)
\( ^{\mathrm{B}}\left[\frac{\mu_{0} I V}{2 \pi} \ln \left(\frac{b}{a}\right)\right]^{2} \frac{1}{2 V R} \)
\( ^{\mathbf{c}} \cdot\left[\frac{\mu_{0} I V}{2 \pi} \ln \left(\frac{b}{a}\right)\right]^{2} \frac{V}{R} \)
\( \stackrel{2 V}{R}\left[\frac{\mu_{0} I V}{2 \pi} \ln \left(\frac{b}{a}\right)\right]^{2} \)


For which of the following the total internal reflection of light is possible?
A. Angle of incidence = Critical angle
B. Angle of incidence is less than critical angle
c. Angle of incidence is more than critical angle
D. None of the above


In the given Fischer Projection, which
group/s is/are oriented away from you?
A. Carboxylic
B. Ethyl
\( c . \) Both carboxylic and ethy
D. Hydroxyl


Using vector method, prove that the following points are collinear:
\( A(6,-7,-1), B(2,-3,1) \) and
\( \boldsymbol{C}(\mathbf{4},-\mathbf{5}, \mathbf{0}) \)


The value of magnetic field induction which is uniform, is 2T. What is the flux
passing through a surface of area
\( 1.5 m^{2} \) perpendicular to the field.
A. 3 Tesla
В \( \cdot 1 W b / m^{2} \)
c. 2 Tesla
D. None


The transpose of a rectangular matrix is
\( \mathbf{a} \)
A. rectangular matrix
B. diagonal matrix
c. square matrix
D. scalar matrix


Using properties of sets, prove that \( \boldsymbol{A} \cup \) \( (\boldsymbol{A} \cap \boldsymbol{B})=\boldsymbol{A} \)


The above electron-dot formulas for
carbon dioxide both satisfy the octet
rule for all of the atoms. Which of these
structures is the better structure and
why is this the case?
\[
\begin{array}{cc}
: \mathrm{O}=\mathrm{C}=\mathrm{o} & : \mathrm{O} \equiv \mathrm{C}-\ddot{\mathrm{O}}: \\
\mathbf{A} & \mathbf{B}
\end{array}
\]
A. "A" is the better structure because there is no formal charge on any of the atoms.
B. "B" is the better structure because the bond energies of a single bond and a triple bond are higher than the bond energies of two double bonds.
C. "A" is the better structure because all the bonds and non-bonding electron pairs are arranged in a symmetrical pattern.
D. "B" is the better structure because there are opposite formal charges on the two oxygen atoms which attract each other and give the molecule a lower energy.


Grittiness of fruit wall is due to the
present of
A. Scleride
B. Sclerenchyma fibres
c. Trecheids
D. collenchyma


The domain of \( \sin ^{-1}[x], \) where \( [x] \) is greatest integer function, given by
A \( \cdot[-1,1] \)
B . [-1,2)
\( \mathbf{c} \cdot\{-1,0,1\} \)
D. None of these


If the smog density of an area increases, it indicates
A. Increase in agricultural waste
B. Increase in noise pollution
c. Vehicles of area is not under PUC norms
D. None of the above


For the equation given below, find the slope and the y-intercept:
\( \boldsymbol{x}=\mathbf{5} \boldsymbol{y}-\boldsymbol{4} \)
A \( \cdot \frac{1}{5} \) and \( \frac{4}{5} \)
B. \( \frac{4}{5} \) and \( \frac{4}{5} \)
c. \( \frac{4}{5} \) and \( \frac{1}{5} \)
D. \( \frac{1}{5} \) and \( \frac{1}{5} \)


Evaluate \( \int_{0}^{\pi / 2} \frac{d x}{2+\sin 2 x} \)
A \( \cdot \frac{2 \pi}{3} \)
в.
\( c \cdot \frac{2 \pi}{5} \)
D. None of these


The number of rational terms in the expansion of \( \left(3 \frac{1}{4}+7 \frac{1}{6}\right)^{144} \)
A . 33
B. 23
\( c \cdot 12 \)
D. 13


If \( \tan ^{-1}\left(\frac{x}{\sqrt{a^{p}-x^{q}}}\right)= \)
\( \sin ^{-1}\left(\frac{x}{a}\right), a>0 . \) Find the value of
and \( q \)
\( \mathbf{A} \cdot p=1, q=1 \)
\( \mathbf{B} \cdot p=1, q=2 \)
\( \mathbf{c} \cdot p=2, q=1 \)
D \( . p=2, q=2 \)


This question has Statement I and Statement II. Of the four choices given
after the Statements, choose the one
that best describes the two Statements.
Statement - I: A point particle of mass
\( m \) moving with speed \( v \) collides with
stationary point particle of mass \( M . \) If the maximum energy loss possible is \( \operatorname{given} \operatorname{as} f\left(\frac{1}{2} m v^{2}\right) \) then \( f= \)
\( \left(\frac{m}{M+m}\right) \)
Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.
A. Statement I is true, Statement II is true, Statement II is not a correct explanation of Statement!
B. Statement I is true, Statement II is false.
c. Statement l is false, Statement II is true
D. Statement I is true, Statement II is true, Statement II is correct explanation of Statement


Resolve \( \frac{x}{(1+x)\left(1+x^{2}\right)^{2}} \) into partial
fractions.
A \( \cdot \frac{-1}{4(1+x)}+\frac{(x-1)}{4\left(1+x^{2}\right)}+\frac{(x+1)}{2\left(1+x^{2}\right)^{2}} \)
B. \( \frac{1}{4(1+x)}+\frac{(x-1)}{4\left(1+x^{2}\right)}+\frac{(x+1)}{\left(1+x^{2}\right)^{2}} \)
C \( \frac{1}{2(1+x)}+\frac{(x-1)}{2\left(1+x^{2}\right)}+\frac{(x+1)}{2\left(1+x^{2}\right)^{2}} \)
D \( \frac{1}{4(1+x)}-\frac{(x-1)}{4\left(1+x^{2}\right)}+\frac{(x+1)}{2\left(1+x^{2}\right)^{2}} \)


Explain the purification of sulphide ore by Froth floatation method.


Which of the following sequences lists the relative sizes of particles in a water mixture from smallest to largest?
A. Solutions, suspensions, colloids
B. Solutions, colloids, suspensions
c. colloids, solutions, suspensions
D. Colloids, suspensions, solutions
E. Suspensions, colloids, solutions


Electromagnetic theory suggests that the light consists of
A. Magnetic vector only
B. Electric vector only
C. Electric and magnetic vector perpendicular to each other
D. Perpendicular electric and magnetic vector


A current I flows in a rectangularly shaped wire whose center lies at
\( \left(x_{0}, 0,0\right) \) and whose vertices are located
at the point \( \boldsymbol{A}\left(\boldsymbol{x}_{0}+\boldsymbol{d},-\boldsymbol{a},-\boldsymbol{b}\right), \boldsymbol{B}\left(\boldsymbol{x}_{0}-\right. \)
\( \boldsymbol{d}, \boldsymbol{a},-\boldsymbol{b}), \boldsymbol{C}\left(\boldsymbol{x}_{0}-\boldsymbol{d}, \boldsymbol{a}, \boldsymbol{+} \boldsymbol{b}\right), \) and \( \boldsymbol{D}\left(\boldsymbol{x}_{0}+\right. \)
\( \boldsymbol{d},-\boldsymbol{a},+\boldsymbol{b}) \) respectively. Assume that \( \mathbf{a} \)
b, \( d<<x_{0} \). Find the magnitude of
magnetic dipole moment vector of the rectangular wire frame in J/T. (Given:
\( \boldsymbol{b}=\mathbf{1 0 m}, \boldsymbol{I}=\mathbf{0 . 0 1 A}, \boldsymbol{d}=\mathbf{4 m}, \boldsymbol{a}=\mathbf{3 m .} \)


The sum of odd integers from 1 to 2001
is
A. \( 1001^{2} \)
B. \( 1000^{2} \)
\( \mathbf{c} \cdot 1002^{2} \)
D. \( 1003^{2} \)


Fill in the blanks with approriate words.
Left auriculo-ventricular valve is also
known as ...........valve.


Two plano convex lenses of same material and of focal lengths \( 20 \mathrm{cm} \& 5 \) cm should be arranged such that the combination is free from chromatic
aberration. Then effective focal length of the combination will be:
A. \( 20 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
c. \( 12.5 \mathrm{cm} \)
\( D \cdot 8 \mathrm{cm} \)


For matrix \( \mathbf{A} \)
\( (\boldsymbol{\alpha}+\boldsymbol{\beta}) \boldsymbol{A}= \)
A \( . \alpha A \)
B. \( \alpha A+\beta B \)
\( \mathbf{c} \cdot \alpha A+\beta A \)
D. \( \alpha^{2} A+\beta^{2} A \)


The adjoint of the matric \( \boldsymbol{A}= \) \( \left[\begin{array}{lll}1 & 0 & 2 \\ 2 & 1 & 0 \\ 0 & 3 & 1\end{array}\right] \) is
A. \( \left[\begin{array}{ccc}-1 & 6 & 2 \\ -2 & 1 & -4 \\ 6 & 3 & 1\end{array}\right] \)
B.
\[
\left[\begin{array}{ccc}
1 & 6 & -2 \\
-2 & 1 & 4 \\
6 & -3 & 1
\end{array}\right]
\]
\( c \)
\[
\left[\begin{array}{ccc}
6 & 1 & 2 \\
4 & -1 & 2 \\
6 & 3 & -1
\end{array}\right]
\]
D.
\[
\left[\begin{array}{ccc}
-6 & 2 & 1 \\
4 & -2 & 1 \\
3 & 1 & -6
\end{array}\right]
\]


State true or false:
The graph of the linear equation \( x+ \)
\( 2 y=7 \) passes through the point (0,7)
A . True
B. False


Which of the following is not true about the advantages of electromagnet over permanent magnet?
A. Small electromagnets are used in electronic lock
B. Scrapyard cranes have powerful electromagnets that lift metal car bodies with ease
c. Magnetic Resonance Imaging machines use very powerful electromagnets to produce highly detailed images of the human body
D. None of the above


One part of an element A combines with two parts of B (another element). Six parts of element C combine with four
parts of element B. If \( A \) and \( C \) combine together, the ratio of their masses will
be governed by:
A. law of definite proportions
B. law of multiple proportions
c. law of reciprocal proportions
D. law of conservation of mass


Left hand derivative and right hand
derivative of a function \( f(x) \) at a point \( x=a \) are defined as
\( f^{\prime}\left(a^{-}\right)=\lim _{h \rightarrow 0^{+}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{h \rightarrow 0^{-}} \frac{f(a)-f(a-h)}{h}= \)
\( \lim _{x \rightarrow a^{+}} \frac{f(a)-f(x)}{a-x} \) respectively
Let \( f \) be a twice differentiable function.
We also know that derivative of an even
function is odd function and derivative
of an odd function is even function.
If \( f \) is odd, which of the following is Lefthand derivative of \( f \) at \( x=a \)
A \( \cdot \lim _{h \rightarrow 0^{-}} \frac{f(a-h)-f(a)}{-h} \)
в. \( \lim _{h \rightarrow 0^{-}} \frac{f(a-h)-f(a)}{h} \)
c. \( \lim _{h \rightarrow 0^{+}} \frac{f(a)+-f(a-h)}{-h} \)
D. \( \lim _{h \rightarrow 0^{-}} \frac{f(-a)-f(-a-h)}{-h} \)


In the quadrilateral (2) given below, \( \boldsymbol{A B}\|\boldsymbol{D C}\| \boldsymbol{E G}, \) If \( \boldsymbol{E} \) is mid point of \( \boldsymbol{A} \boldsymbol{D} \)
respectively. Prove that
\( 2 E G=A B+C D \)
(2)


The equilibrium mixture for the
reaction \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2(g)}+ \)
\( \boldsymbol{H}_{2(g)} \) contains 2,3,4,6 moles
respectively at \( 500 \mathrm{K} \) in a 2 litre vessel. Now this mixture is transferred in a 4 lit
vessel. What is the new equilibrium constant?
\( A \cdot 4 \)
B. 2
c. 8
D. 6


Karyokinesis differ from cytokinesis because it involves
A. Division of cytoplasm
B. Division of the nucleus and cytoplasm
c. Division of the nucleus
D. Division of the cell


A shop-keeper sells a badminton racket
marked Rs. 30 at \( 15 \% \) discount and
gives a shuttle cock costing Rs. 1.50 free with each racket. He then makes a
profit of \( 20 \% \). His cost price per racket is
A . Rs. 15
B. Rs. 16
c. Rs. 18
D. Rs. 20


Which colour of light travels fastest in any medium except air?
A . Red
B. Violet
c. Blue
D. orange


In a square \( A B C D, \angle A B D=3 x= \)
\( \angle A D B, \) then \( \angle B D C ? \)
\( \mathbf{A} \cdot 6 x^{\circ} \)
B. \( (90-6 x)^{\text {d }} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. None


A PN-junction has a thickness of the order of :
A \( .1 g m \)
B. \( 1 \mathrm{mm} \)
\( \mathrm{c} \cdot 1 \mu \mathrm{m} \)
D. \( 1 p \) m


The mobile electron carrier of
mitochondria membrane is
A. \( C y t \alpha_{3} \)
B. Fes
\( c \cdot \cos \)
D. \( C y t c_{1} \)


Calculate \( \Delta H_{f}^{o} \) for chloride ion from the following data:
\[
\begin{array}{l}
\frac{1}{2} H_{2}(g)+\frac{1}{2} C l_{2}(g \longrightarrow H C l(g) ; \Delta H= \\
-92.4 k J \quad m o l^{-1} \\
H C l(g)+n H_{2} O \longrightarrow H^{+}(a q .)+ \\
C l^{-}(a q .) ; \Delta H=-74.8 k J \quad m o l^{-1} \\
\quad \Delta H_{f\left(H^{+}(a q .)\right.}^{o}=0.0 k J \quad m o l^{-1}
\end{array}
\]
A \( .-167 k J \mathrm{mol}^{-} \)
в. 267 k \( J \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 167 k J \operatorname{mol}^{-1} \)
D. \( -267 k J \mathrm{mol}^{-1} \)


If the same photograph is printed in different sizes, we say it is
A. Not similar
B. Similar
c. common
D. None


The ionization enthalpies, \( (I E)_{1} \) and
the \( (I E)_{2} \) in \( \mathrm{kJ} \mathrm{mol}^{-1} \) of a few elements designated by Roman numerals are shown below:
\( \begin{array}{lll}\text { Element } & (I E)_{1} & (I E)_{2} \\ \text { A } & \text { 2372 } & 5251 \\ \text { B } & 520 & 7300 \\ \text { c } & 900 & \text { 1760 } \\ \text { D } & \text { 1680 } & \text { 3380 }\end{array} \)
Which of the above elements form a
stable binary halide of the formula
\[
\boldsymbol{M} \boldsymbol{X}_{2} ?
\]
A. \( A \)
в. \( B \)
c. \( C \)
D. \( D \)


Which of the following statement(s)
is/are not correct?
\( \mathbf{A} \cdot L a(O H)_{3} \) is less basic than \( L u(O H)_{3} \)
B. In lanthanide series, ionic radius of \( L n^{3+} \) ion
decreases.
C. \( L a \) is actually an element of transition series rather than lanthanides.
D. Atomic radii of \( Z r \) and \( H f \) are same because of lanthanide contraction.


Consider the curves \( y=\sin x \) and \( y= \)
\( \cos x \)
What is the area of the region bounded by the above two curves and the lines \( x=\frac{\pi}{4} \) and \( x=\frac{\pi}{2} ? \)
B. \( \sqrt{2}+1 \)
\( c \cdot 2 \sqrt{2} \)
\( D \)


In a Lassaigine's test for sulphur in the
organic compound with sodium nitroprusside solution the
purple colour formed is due to:
A \( \cdot N a_{4}\left[F e(C N)_{5} N O S\right] \)
B \( \cdot N a_{3}\left[F e(C n)_{5} S\right] \)
c. \( N a_{2}\left[F e(C N)_{5} N O S\right. \)
D. \( \operatorname{Na}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \)


Identify the electrolyte which deposits maximum amount of cathodic product for the passage of 1 faraday of electricity.
A. \( F e C l_{2} \)
B. FeBr \( _{3} \)
c. \( A g N O_{3} \)
D. \( C u S O_{4} \)


A paste of substance \( A \) is used to
decorate the ceiling of your home. State the name of the product in the
above reaction.


If the distinct points on the curve \( y= \) \( 2 x^{4}+7 x^{3}+3 x-5 \) are collinear, then
find the arithmatic mean of \( x- \)
coordinates of the aforesaid points


The monomer for the given compound
is:
\[
\left[\begin{array}{l}
\mathrm{CH}_{3} \\
\mathrm{I} \\
\mathrm{fH}_{3}
\end{array}\right]_{n_{2}}
\]
A. 2-methylpropene
B. Styrene
c. Propylene
D. Ethene


\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{lll}\boldsymbol{a}_{11} & \boldsymbol{a}_{12} & \boldsymbol{a}_{13} \\ \boldsymbol{a}_{21} & \boldsymbol{a}_{22} & \boldsymbol{a}_{23} \\ \boldsymbol{a}_{31} & \boldsymbol{a}_{32} & \boldsymbol{a}_{33}\end{array}\right| \) and \( \boldsymbol{c}_{i j}= \)
\( (-1)^{i+j} \) (determinant obtained by
deleting ith row and jth column), then \( \left|\begin{array}{lll}c_{11} & c_{12} & c_{13} \\ c_{21} & c_{22} & c_{23} \\ c_{31} & c_{32} & c_{33}\end{array}\right|=\Delta^{2} \)
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{x}^{2} \\ \boldsymbol{x} & \boldsymbol{x}^{2} & \mathbf{1} \\ \boldsymbol{x}^{2} & \boldsymbol{1} & \boldsymbol{x}\end{array}\right|=\mathbf{7} \) and \( \boldsymbol{\Delta}= \)
\( \left|\begin{array}{ccc}x^{3}-1 & 0 & x-x^{4} \\ 0 & x-x^{4} & x^{3}-1 \\ x-x^{4} & x^{3}-1 & 0\end{array}\right|, \) then
A \( . \Delta=7 \)
B. \( \Delta=343 \)
c. \( \Delta=-49 \)
D. \( \Delta=49 \)


The value of
\( \frac{(1.5)^{2}+(4.7)^{3}+(3.8)^{3}-3 \times 1 .}{(1.5)^{2}+(4.7)^{2}+(3.8)^{2}-1.5 \times 4.7-4} \)
\( A \cdot 8 \)
B. 9
c. 10
\( D \)


A concave mirror forms the real image of an object which is magnified 4 times. The objects is moved 3 cm away, the magnification of the image is 3 times. What is the focal length of the mirror?
\( A \cdot 3 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. 36 cm


The narrow band of land, water and air
where all kinds of life is possible is
known as
A. Atmosphere
B. Biosphere
c. Lithosphere
D. Hydrosphere


If \( f: R \rightarrow R \) be a differentiable function and \( f(0)=0 \) and \( f^{\prime}(0)=1 \) then
\( \lim _{x \rightarrow 0} \frac{1}{x}\left[f(x)+f\left(\frac{x}{2}\right)+\ldots+f\left(\frac{x}{100}\right)\right] \)
equals
A . 1
B \cdot \( 1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{100} \)
D. Does not exist


If three unit vector \( \hat{a}, \hat{b}, \hat{c} \) satisfy \( \hat{a}+ \) \( \hat{\boldsymbol{b}}+\hat{\boldsymbol{c}}=\hat{\mathbf{0}}, \) then the angle between \( \hat{\boldsymbol{a}} \) and
\( \hat{b} \) is
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{\pi}{6} \)
D. \( \frac{5 \pi}{6} \)


Four charges, all of same magnitude are placed at the four corners of a
square. At the centre of the square, the
potential is \( V \) and the field is \( E . B y \) suitable choices of the signs of the four charges, which of the following can be obtained?
This question has multiple correct options
A. \( V=0, E=0 \)
B. \( V=0, E \neq 0 \)
c. \( V \neq 0, E=0 \)
D. \( V \neq 0, E \neq 0 \)


If \( f(x)=\frac{x^{2}-1}{x^{2}+1}, \) for every real \( x, \) then
the minimum value of \( \boldsymbol{f} \) is
A. does not exist because fis unbounded
B. is not attained even through f is bounded
c. is equal to 1
D. is equal to -1


Which one of the following shows the presence of cell wall and absence of chloroplast?
A. Amoeba
B. Chordate
c. Plant
D. Fungus
E. Bacteria


Pyrimidine bases present in RNA are:
A. Adenine and Guanine
B. Thymine and Uraci
c. Uracil and Cytosine
D. Thymine and Cytosine


A radioactive nuclide is produced at the constant rate of \( ^{\prime} \boldsymbol{n}^{\prime} \) per second (say, by bombarding a target with neutrons)
The expected number' \( N^{\prime} \) of nuclei in
existence \( t \) s after the number is \( N_{0} \) is
given by
A. \( N=N_{0} e^{-\lambda t} \)
B. \( N=\frac{n}{\lambda} N_{0} e^{-\lambda} \)
c. \( N=\frac{n}{\lambda}+\left(N_{0}-\frac{n}{\lambda}\right) e^{-\lambda t} \)
D. \( N=\frac{n}{\lambda}+\left(N_{0}+\frac{n}{\lambda}\right) e^{-\lambda t} \)


Explain the reasons that you feel are behind such embarrassment amongst
some parents to freely discuss such issues with their growing children.


Parto of the uranium decay series is shown
\( 92^{2}-90 T h^{234} \rightarrow 91 P a^{234} \rightarrow \)
\( 92 U^{234} \rightarrow_{90} T h^{230} \rightarrow_{88} R a^{226} \)
How many pairs of isotopes are there in the above series:
A \( . \)
B. 2
\( c \cdot 3 \)
D.


A student measures the terminal
potential difference (V) of a cell ( of emf
\( \mathrm{E} \text { and internal resistance } r) \) as a
function of the current
(I) flowing through it. The slope and intercept of the graph between \( V \) and \( I \), then respectively equal
A. -rand E
B. rand-E
c. - - and R
D. E and -r


The osmotic pressure of the solution obtained by mixing \( 200 \mathrm{cm}^{3} \) of \( 2 \% \) (mass-volume) solution of urea with
\( 200 \mathrm{cm}^{3} \) of \( 3.42 \% \) solution of sucrose at
\( \mathbf{2 0} \) is?
A \( .421 P a \)
в. \( 267 P a \)
\( c .5240 P a \)
D. \( 153 P a \)


Differentiate between minerals and
ores.


Salt can be obtained by of sea water.
A. sublimation
B. cooling
c. evaporation
D. heating


If the tangents \( P A \) and \( P B \) are drawn
from the point \( \boldsymbol{P}(-1,2) \) to the circle \( x^{2}+y^{2}+x-2 y-3=0 \) and \( C \) is the
center of the circle, then the area of the
quadrilateral \( P A C B \) is
\( A \cdot 4 \)
B. 16
c. Does not exists
D. 8


The graph represent a current-voltage behaviour of a water-voltameter. spot
the correct explanation.
A. Dissociation takes place at \( E_{1} \) and it obeys Ohm's law
thereafter.
B. Ohm's law is not valid for low voltages
C. Ohm's law is obyed but only for potential difference larger than back emf.
D. Electrolyte does not obey Ohm's law.


In triangle \( A B C, \) the bisector of angle
\( B A C \) meets opposite side \( B C \) at point
D. If \( B D=C D, \) prove that \( \Delta A B C \) is
isosceles.


Exchange of genetic material takes
place in
A. Vegetative reproduction
B. Asexual reproduction
c. Sexual reproduction
D. Budding


Which of the following patterns of reproduction involves both the parents?
A. Sexual reproduction
B. Asexual reproduction
c. Both A and B
D. None of these


Which conformation of \( C_{6} H_{6} C l_{6} \) is the
most powerful insecticide?
A . aaeeee
B. aaaeee
c. aaaaee
D. aaaaaa


The heat of combustion of methane is
\( -880 k J \) mol\( ^{-1} . \) The quantity of heat
liberated in the combustion of \( 3.2 g \)
methane is:
A . \( -88 k J \)
в. \( +88 k J \)
\( \mathbf{c} .+176 k J \)
D. \( -176 k J \)


The number of reflexive relation in \( \operatorname{set} A \)
\( =\{a, b, c\} \) is equal to
A \( \cdot 2^{9} \)
B \( \cdot 2^{4} \)
\( c \cdot 2^{7} \)
D. \( 2^{\text {6 }} \)


Which of the following factors are
responsible for origination of van der
Waals forces?
This question has multiple correct options
A. Instantaneous dipole-induced dipole interaction.
B. Dipole-induced dipole interaction and ion-induced dipole interaciton.
C. Dipole-dipole interaction and ion-induced dipole interaction.
D. Small size of molecule.


If the given statement is true enter 1 , if
false enter 0
\( O_{3} \) is absorbed by turpentine oil.


\( \operatorname{lt} \frac{x}{a}+\frac{y}{b}=a^{2}+b^{2} \) and \( \frac{x}{a^{2}}+\frac{y}{b^{2}}=a+ \)
\( \boldsymbol{b} \) then \( \boldsymbol{x}=? \)
\( \mathbf{A} \cdot a \)
B \( \cdot a^{2} \)
\( c \cdot a^{3} \)
D. \( a^{4} \)


Borax is actually made of two tetrahera
and two triangular units joined together
and should be written as:
\[
N a_{2}\left[B_{4} O_{5}(O H)_{4}\right] .8 H_{2} O
\]
Consider the following statements about borax.
This question has multiple correct options
A. Each boron atom has four \( B-O \) bonds
B. Each boron atom has three \( B-O \) bonds
C. Two boron atoms have four \( B-O \) bonds while other
two have three \( B-O \) bonds
D. Each boron atom has one \( -O H \) groups


In young's double slit experiment the
maximum intensity is \( I_{0} . \) When one slit is closed, the intensity becomes:
A \( \cdot \frac{I_{0}}{2} \)
B. \( \frac{I_{0}}{8} \)
c. \( \frac{I_{0}}{4} \)
D. \( I_{0} \)


Give the structural formula for : Ethanal
A. \( C H_{3} C H O \)
в. \( C H_{3} C H_{2} O \)
\( \mathbf{c} \cdot C H_{2} C O \)
D. \( H C H O \)


A thin rod of negligible mass and area of cross-section \( 4 \times 10^{-6} m^{2} \)
suspended vertically from one end, has
a length of \( 0.5 \mathrm{m} \) at \( 100^{\circ} \mathrm{C} \). The rod is
cooled to \( 0^{\circ} \mathrm{C} ; \) but prevented from
contracting by attaching a mass at the
lower end. Find (i) this mass, and (ii)
the energy stored in the rod. Given for
the rod, Young's modulus \( =10^{11} N / m^{2} \)
coefficient of linear expansion \( 10^{-5} K^{-1} \)
and \( g=10 m / s^{2} \)
A . (i) \( 60 \mathrm{kg} \), (ii) \( 0.1 \mathrm{J} \)
B. (i) 40kg, (ii) 0.1J
c. (i) 560kg, (ii) 0.1]
D. (i) \( 490 \mathrm{kg}, \) (ii) 10.1


During estimation of nitrogen in the organic compound by Kjeldahls method, the ammonia evolved from 0.5 g of the compound in Kjeldahls estimation of nitrogen, neutralised 10 mL of 1 IM
\( H_{2} S O_{4} . \) Find out the percentage of nitrogen in the compound?
A . 14\%
в. 28\%
c. 56\%
D. 68\%


Assertion
Carbon dioxide is a gas but silicon dioxide is an in-fusible solid.
Reason
Carbon dioxide has a linear \( \pi- \) bonded
structure
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


Initially interference is observed with the entire experimental set up inside a chamber filled with air, Now the
chamber is evacuated. With the same
source of light used, a careful observer
will find that.
A. The interference pattern is almost absent as it is very much diffused
B. There is no change in the interference pattern
c. The fringe width is slightly decreased
D. The fringe width is slightly increased


Which of the following statements is
correct?
(i) Copper is extracted by hydrometallurgy from low-grade ores.
(ii) In the electrolytic reduction of alumina, graphite is acting as an anode
and steel vessel with the lining of carbon acts as an anode.
(iii) In Hall-Heroult process, aluminium
is obtained at anode and \( \mathrm{CO} \) and \( \boldsymbol{C O}_{2} \)
are produced at the cathode.
A. (i) only
B. (i) and (ii) only
C . (ii) and (iii) only
D. All of these


Which of the following is wrong about ethylene?
A. Inhibit growth of root
B. Ripening of fruits
c. Elongation of stem in paddy
D. Promote senescence of leaves \& flowers


\( \frac{\boldsymbol{A} \boldsymbol{x}-\mathbf{1}}{\left(\mathbf{1}-\boldsymbol{x}+\boldsymbol{x}^{2}\right)(\boldsymbol{x}+\mathbf{2})}=\frac{\boldsymbol{x}}{\mathbf{1}-\boldsymbol{x}+\boldsymbol{x}^{2}}- \)
\( \frac{1}{x+2} \Rightarrow A= \)
\( A \cdot 3 \)
B. 2
\( c \cdot 4 \)
\( D \)


\( 2 S O_{2}+O_{2} \rightarrow 2 S O_{3} \)
Rate of formation of \( \boldsymbol{S} \boldsymbol{O}_{3} \) according to
the reaction is \( 1.6 \times 10^{-3} \mathrm{kg} \) min \( ^{-1} \)
Hence rate at which \( S O_{2} \) reacts is:
A \( \cdot 1.6 \times 10^{-3} \mathrm{kg} \min ^{-1} \)
B. \( 8.0 \times 10^{-4} \mathrm{kg} \min ^{-1} \)
c. \( 3.2 \times 10^{-3} \mathrm{kg} \min ^{-1} \)
D. \( 1.28 \times 10^{-3} \) kg \( \min ^{-1} \)