If \( s=\sqrt{t^{2}+1}, \) then \( \frac{d^{2} s}{d t^{2}} \) is equal to
A \( \cdot \frac{1}{s} \)
в. \( \frac{1}{s^{2}} \)
c. \( \frac{1}{s^{3}} \)
D. \( \frac{1}{s^{4}} \)


Draw a circle and mark a sector.


A gas has
A. definite volume and no definite shape
B. definite shape and no definite volume
C. definite shape and definite volume
D. no definite shape and no definite volume


toppr
Q Type your question
Nucleus
\( \sqrt{c} \)
es
Yes

Yes res
The three cell types were grown in separate cultures with plenty of oxygen and nutrients available. Figure 1 shows
their rates of growth. At time 1 , oxygen was no longer available to the cells.
Given below are three equations.
(।) \( C_{6} H_{12} O_{6}+6 O_{2} \rightarrow 6 C O_{2}+ \)
\( 6 H_{2} O+A T P \)
(II) \( \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{l i g h t} \rightarrow \boldsymbol{O}_{2}+\boldsymbol{A} \boldsymbol{T} \boldsymbol{P}+ \)
\( N A D P H \)
(III) \( 6 \mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O}+\mathrm{ATP}+\mathrm{NADPH} \rightarrow \)
\( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O} \)
Cell type \( C \) would show equation
A. I only
B. II only
c. I and III only
D. II and III only
E. I, II and III


If \( \bar{E} \) and \( \bar{F} \) are the complementary
events of events \( \boldsymbol{E} \) and \( \boldsymbol{F} \) respectively
and if \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{F})<\mathbf{1}, \) then
\( ^{\mathbf{A}} \cdot_{P}\left(\frac{E}{F}\right)+P\left(\frac{\bar{E}}{F}\right)=1 \)
в. \( \quad P\left(\frac{E}{F}\right)+P\left(\frac{E}{\bar{F}}\right)=1 \)
\( ^{\mathbf{c}} \cdot_{P}\left(\frac{\bar{E}}{F}\right)+P\left(\frac{E}{\bar{F}}\right)=1 \)
\( P\left(\frac{E}{\bar{F}}\right)+P\left(\frac{\bar{E}}{\bar{F}}\right)=1 \)


The main difference in \( C-X \) bond of a
haloalkane and a haloarene is:
A. \( C-X \) bond in haloalkanes is shorter than haloarnes.
B. In haloalkanes, the \( C \) attached to halogen in \( C-X \)
bond is \( s p^{3} \) hybridised while in haloarenes it is \( s p^{2} \)
hybridised
C. \( C-X \) bond in haloarenes acquire a double bond
character due to the higher electronegativity of \( X \) than haloalkanes.
D. Haloalkanes are less reactive than haloarenes due to difficulty in \( C-X \) cleavage in haloalkanes


What is isomerism? Name the isomers
of butane.


Which of the following is a unit of nucleic acid?
A. Phosphoric acid
B. Nitrogenous bases
c. Pentose Sugar
D. Nucleotides


The moss which form dense extensive
mats on the soil prevents
A. Uprooting of trees
B. Soil erosion
c. Evaporation of water from the soil
D. Both B and C


If we apply the mean value theorem to
\( f(x)=2 \sin x+\sin 2 x \) then \( c= \)
This question has multiple correct options
A . \( \pi \)
в. \( \pi / 4 \)
c. \( \pi / 2 \)
D. \( \pi / 3 \)


In froth floatation process, gangue
particles are wetted by pine oil
A. True
B. False


Factorise
(i) \( a^{4}-b^{4} \)
(ii) \( p^{4}-81 \)
(iii) \( x^{4}- \)
\( (y+z)^{4} \)
\( \left(\text { iv ) } x^{4}-(x-z)^{4}\right. \)
\( a^{4}-2 a^{2} b^{2}+b^{4} \)


Clay has \( _{--} \) permeability and porosity.
A. High - high
B. High - low
c. Low - high
D. Low - low


Find the smallest number that must be
added to 400 to make it a perfect cube
A . 108
в. 112
c. 18
D. 12


The sum of two numbers is 11 and the
sum of their reciprocals is \( \frac{11}{28} \) Find the
numbers.


A thunder cloud and the earth's surface
may be regarded as a pair of charged
parallel plates separated by a distance
\( h \) and the capacitance of the system is
C. When a flash of mean current ' \( i \) '
occurs for a time duration 't', the
electric field strength between the cloud and earth is:
\( \mathbf{A} \cdot \frac{i t}{C} \)
B. Cit
c. \( \frac{i t}{C h} \)
D. \( \frac{\text { Cit }}{h} \)


At breakdown voltage, the rate of creation of hole-electron pairs is
leading to the in
current.
A. increased, decrease
B. increased, increase
c. decreased, increase
D. decreased, decrease


For the four sets of three measured
physical quantities as given below. Which of the following options is
correct?
\( (i) A_{1}=24.36, B_{1}=0.0724, C_{1}= \)
\( \mathbf{2 5 6 . 2} \)
\( (i i) A_{2}=24.44, B_{2}=16.082, C_{2}= \)
\( \mathbf{2 4 0 . 2} \)
\( (i i i) A_{3}=25.2, B_{3}=19.2812, C_{3}= \)
\( \mathbf{2 3 6 . 1 8 3} \)
\( (i v) A_{4}=25, B_{4}=236.191, C_{4}= \)
19.5
A. \( A_{1}+B_{1}+C_{1}<A_{3}+B_{3}+C_{3}<A_{4}+B_{4}+C_{4}< \)
\( A_{2}+B_{2}+C_{2} \)
B . \( A_{4}+B_{4}+C_{4}<A_{1}+B_{1}+C_{1}<A_{3}+B_{3}+C_{3}< \)
\( A_{2}+B_{2}+C_{2} \)
c. \( A_{4}+B_{4}+C_{4}<A_{1}+B_{1}+C_{1}=A_{2}+B_{2}+C_{2}= \)
\( A_{3}+B_{3}+C_{3} \)
D. \( A_{1}+B_{1}+C_{1}=A_{2}+B_{2}+C_{2}=A_{3}+B_{3}+C_{3}= \)
\( A_{4}+B_{4}+C_{4} \)


Brine has a density of \( 1.2 g / c c .40 c c \) of it
are mixed with \( 30 c c \) of water. The
density of solution is
A \( .2 .11 g / c c \)
в. \( 1.11 g / c c \)
c. \( 12.2 g / c c \)
D. \( 20.4 g / c c \)


While preparing soap, a small quantity of common salt is generally added to the reaction mixture of vegetable oil and sodium hydroxide. Which one of the following may be the purpose of adding
common salt?
A. To reduce the basic nature of the soap
B. To make the soap neutral
c. To enhance the cleansing power of the soap
D. To favour the precipitation of the soap


When aqueous solution of potassium fluoride is added to the blue coloured
aqueous \( \boldsymbol{C u} \boldsymbol{S O}_{4} \) solution, a green precipitate is formed. This observation can be explained as follows:
A. on adding \( K F, H_{2} O \) being weak field ligand is replaced by \( F^{-} \) ions forming \( \left[C u F_{4}\right]^{2-} \) which is green in colour.
B. potassium is coordinated to \( \left[C u\left(H_{2} O\right)_{4}\right]^{2+} \) ion present in \( C u S O_{4} \) and gives green colour
C. on adding \( K F, C u^{2+} \) are replaced by \( K^{+} \) forming a green complex.
D. blur colour of \( C u S O_{4} \) and yellow colour of \( K \) f form green colour on mixing


If an inductor of inductance \( L \), radius \( r \)
current changes from \( I_{1} \) to \( I_{2} \). Find work
done.


A flat coil, \( C \) of \( n \) turn, area \( A \) and
resistance \( R \), is placed in a uniform
magnetic field of magnitude \( B \). The plane of the coil is initially perpendicular to \( B \). The coil is rotated by an angle \( \theta \) about a diameter and
charge of amount \( Q \) flows through it. Choose the correct alternatives.
This question has multiple correct options
A \( \cdot \theta=90^{\circ}, Q=(B A n / R) \)
B . \( \theta=180^{\circ}, Q=(2 B A n / R) \)
c. \( \theta=180^{\circ}, Q=0 \)


If \( \boldsymbol{A}=\{\mathbf{3}, \boldsymbol{4}\} \quad \) and \( \quad \boldsymbol{B}=\{1,2\} \) then of
\( \boldsymbol{A} \times \boldsymbol{B} \) is


In tall plants, because of which factor,
continuous water column extends
upward?
A. Atmospheric pressure
B. Osmotic pressure
c. suction pull
D. Root pressure


Which of the following is a characteristics of coke?
A. Grayish-black residue
B. Blue residue
c. Pale white residue
D. Brown residue


Find the eccentricity of the conic represented by \( \boldsymbol{x}^{2}-\boldsymbol{y}^{2}-\boldsymbol{4} \boldsymbol{x}+\boldsymbol{4} \boldsymbol{y}+ \)
\( \mathbf{1 6}=\mathbf{0} \)
A \( \cdot \sqrt{2} \)
B. \( \sqrt{3} \)
\( c \cdot-\sqrt{2} \)
D. \( -\sqrt{3} \)


Monadelphous androecium occurs in
A. Pea
B. Hibiscus
C . Brassica
D. Helianthus


A \( _{-1}-\ldots_{\text {diol has two hydroxyl }} \)
groups on C atoms.
This question has multiple correct options
A. vicinal, adjacent
B. geminal, adjacent
c. vicinal, same
D. geminal, same


Upper reaches of a river does not possess many living beings because of
A. Low temperature
B. High speedd
c. Both low temperature and high speed
D. Little depth


An object \( 5 \mathrm{cm} \) tall is placed \( 1 \mathrm{m} \) from a concave spherical mirror which has a
radius of curvature of \( 20 \mathrm{cm} . \) The size of the image is:
A. \( 0.11 \mathrm{cm} \)
B. \( 0.50 \mathrm{cm} \)
c. \( 0.55 \mathrm{cm} \)
D. \( 0.60 \mathrm{cm} \)


The order of differential equation of all
circles of given radius \( ^{\prime} a^{\prime} \) is
A . 4
B. 2
\( c \cdot 1 \)
D. 3


Pick the correct statement.
A. Contraction of internal intercostal muscles lifts up the ribs and sternum.
B. RBCs transport oxygen only.
C. Thoracic cavity is anatomically an air tight chamber.
D. Healthy man can inspire approximately 500 mL of air per minute.
E. During expiration the interpleural pressure is slightly below the surrounding atmospheric pressure.


A road is 10 mwide. Its radius of
curvature is \( 50 m \). The outer edge is above the lower edge by a distance of
1./5m. This road is most suited for the
velocity
A. \( 2.5 \mathrm{m} / \mathrm{sec} \)
B. \( 4.5 \mathrm{m} \) sec
c. \( 6.5 m \) sec
D. \( 8.5 m \) sec


\( \mathbf{1 0} C l^{-}(a q)+2 M n O_{4}^{-}(a q)+ \)
\( \mathbf{1 6} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \mathbf{5} \boldsymbol{C l}_{2}(\boldsymbol{g})+ \)
\( 2 M n^{2+}(a q)+8 H_{2} O(l) \)
The value of \( E^{o} \) for the above reaction at
\( 25^{\circ} \mathrm{C} \) is \( 0.15 \mathrm{V} \). Hence, the value of \( \mathrm{K} \) for
this reaction is :
A . \( 2.4 \times 10^{25} \)
B . \( 4.9 \times 10^{12} \)
c. \( 1.2 \times 10^{15} \)
D. \( 3.4 \times 10^{20} \)


If torques of equal magnitudes are applied to a hollow cylinder and a solid sphere both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its center. Which of the two will acquire a greater angular speed after a given time?
A \( \cdot \omega_{1}>\omega_{2} \)
в. \( \omega_{1}=\omega_{2} \)
\( \mathrm{c} \cdot \omega_{2}>\omega \)
D. None of these


Oxygen as a super oxide is in the form of:
\( A \cdot O_{2}^{-2} \)
B. \( O^{-2} \)
\( c \cdot O_{2}^{-} \)
D. \( O^{-} \)


The function \( \boldsymbol{f}(\boldsymbol{x})=\frac{1+\sin \boldsymbol{x}-\cos \boldsymbol{x}}{1-\sin \boldsymbol{x}-\cos \boldsymbol{x}} \)
is not defined at \( x=0 . \) The value of
\( f(0) \) so that \( f(x) \) is continuous at \( x= \)
\( 0, \) is
\( A \)
B. -
\( c \cdot 0 \)
D. none of these


The strength of an electromagnet can be increased by.
A. increasing the current in the coil
B. decreasing the current in the coil
c. decreasing the number of turns in the coil
D. increasing the length of air gap between its poles


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


The role of coke in the electrolytic reduction of alumina is to
A. provide heat for melting of alumina
B. prevent loss of heat
c. prevent burning of carbon rods
D. reduce alumina to metal


If an atom loses an electron, it forms a
A. cation
B. anion
c. it remains neutral
D. none of the above


A body dropped from a height reaches
the ground in \( 5 s . \) The velocity with which it reaches the ground is \( (g= \)
\( \left.9.8 m s^{-2}\right) \)
A \( .0 m s^{-1} \)
в. \( 49 \mathrm{ms}^{-1} \)
c. \( 4.9 \mathrm{ms}^{-1} \)
D. \( 9.8 \mathrm{ms}^{-1} \)


If for the half-cell reactions
\( \boldsymbol{C u}^{2+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u}^{+} \boldsymbol{E}^{o}=\mathbf{0 . 1 5} \boldsymbol{V} \)
\( \boldsymbol{C u}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u} \quad \boldsymbol{E}^{o}=\mathbf{0 . 3 4} \boldsymbol{V} \)
Calculate \( E^{o} \) of the half cell reaction
\( \boldsymbol{C u}^{+}+\boldsymbol{e}^{-} \longrightarrow \boldsymbol{C u} \)
Also predict whether \( C u^{+} \) undergoes
disproportionation or not


If \( a+b+c=8 \) and \( a b+b c+c a=20 \)
find the value of \( a^{3}+b^{3}+c^{3}-3 a b c \)


Which of the following statements are
correct regarding the galvanic cell?
This question has multiple correct options
A. A reaction is spontaneous from left to right if \( E_{\text {cell}}>0 \)
B. A reaction occurs from right to left if \( E_{\text {cell}}<0 \)
C. If the system is at equilibrium no net reaction occurs
D. \( E_{\text {cell}} \) is temperature-independent


The moment of inertia of a ring about its geometrical axis is \( I \), then its moment of inertia about its diameter
will be :
A . \( 2 I \)
в. \( \frac{1}{2} \)
c. \( I \)
D. \( \frac{I}{4} \)


There is increase in boiling point of
takes place for each carbon atom added to the chain.
A \( \cdot 10^{0} \) to \( 20^{0} \)
B . \( 20^{0} \) to \( 30^{0} \)
\( \mathbf{c} \cdot 30^{0} \) to \( 40^{0} \)
D. \( 5^{0} \) to \( 10^{0} \)


An enzyme that converts starch to disaccharides is known as
A. Amylase
B. Gastrin
c. secretin
D. Pepsin
E. Maltase


Explain how the separation of oxygenated and deoxygenated blood is useful in humans.


A square conducting coil of area \( = \)
\( 100 \mathrm{cm}^{2} \) is placed normally inside a
uniform magnetic field of \( 10^{3} W b m^{-2} \) The magnetic flux linked with the coil is
Wh.
A . 10
B . \( 10^{-5} \)
\( c \cdot 10^{5} \)
D. 0


Three variable Boolean expression \( \boldsymbol{P Q}+\boldsymbol{P Q R}+\overline{\boldsymbol{P}} \boldsymbol{Q}+\boldsymbol{P} \overline{\boldsymbol{Q}} \boldsymbol{R} \operatorname{can} \mathrm{be} \)
written as
A. \( \bar{Q}+\bar{P} R \)
в. \( \bar{P}+\bar{Q} R \)
c. \( Q+P R \)
D. \( Q+\sqrt{P} R \)
E . \( P+Q R \)


On heating metal plate having two holes at certain separation the distance
between the centres of the holes
A. Increases
B. Decreases
c. Remains same
D. Cannot be said


A scientist performed an experiment as shown in the picture above. What happened as air was pumped out of the jar and he rang the bell?
A. The sound became louder
B. The sound became fainter first and then louder once all the air was pumped out
c. The sound could not be heard anymore
D. The sound was the same as before


Prove that: \( \sin ^{2}\left(\frac{\pi}{8}+\frac{A}{2}\right) \)
\( \sin ^{2}\left(\frac{\pi}{8}-\frac{A}{2}\right)=\frac{1}{\sqrt{2}} \sin A \)
Find the general solution of the equation.


Health hazards related to nuclear
radiations are:
A. They can cause cancer
B. They can cause deformity in the body
c. They can damage the genes of a person.
D. All of the above.


\( f(1,2,3,4,5\}, B=\{3,4,7,8\} \) then find \( A \cup \)
\( B \) and \( A \cap B \)


Dichloroacetic acid \( \left(\boldsymbol{C H} \boldsymbol{C l}_{2} \boldsymbol{C O}_{2} \boldsymbol{H}\right) \) is
oxidized to \( C O_{2}, H_{2} O \) and \( C l_{2} \) by 1.2 equivalents of an oxidizing agent. Same amount of the acid can neutralize 'X'
moles of \( N H_{2} \) to give ammonium
dichloroacetate.' \( X^{\prime} \) is
A. 0.4
B. 0.3
\( c \cdot 0.2 \)
D. 0.1


A power (set up) transformer 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
A . \( 96 A \)
B. \( 0.96 A \)
\( \mathbf{c} .9 .6 A \)
D. 96 m \( A \)


The equilibrium constant is 10 at \( 100 K \) Hence, \( \Delta G \) will be negative.
A. True
B. False


The label of a bottle containing a dilute aqueous solution of an acid become damage Only its concentration was
readable \( A \) pH meter was nearby, and a quick measurement showed that the
hydrogen ion concentration is equal to the value on the label. Which of the
following four acids that could have been the solution if the pH changed one unit after a tenfold dilution?
This question has multiple correct options
\( \mathbf{A} \cdot H C l O_{4} \)
B. \( H_{3} B O_{3} \)
с. \( C H_{3} \) СООН
D. \( H N O_{3} \)


At \( 300 \mathrm{K} \) and 1 atmospheric pressure, 10
mL of a hydrocarbon required 55 mL of
\( O_{2} \) for complete combustion and \( 40 \mathrm{mL} \)
of \( C O_{2} \) is formed. The formula of the
hydrocarbon is:
A \( \cdot C_{4} H_{8} \)
в. \( C_{4} H_{7} \) С \( l \)
\( \mathbf{c} \cdot C_{4} H_{10} \)
D. \( C_{4} H_{6} \)


\( A \) took 15 seconds to cross a
rectangular field diagonally walking at the rate of \( 52 \mathrm{m} / \mathrm{min} \) and \( \mathrm{B} \) took the
same time to cross the same field along
its sides, walking at the rate of 68 \( \mathrm{m} / \mathrm{min.} \) The area of the field is:
A \( \cdot 30 m^{2} \)
в. \( 40 \mathrm{m}^{2} \)
\( \mathbf{c} \cdot 50 m^{2} \)
D. \( 60 m^{2} \)


The maximum kinetic energy of photoelectrons is directly proportional
to of the incident radiation.
The missing word can be:
This question has multiple correct options
A. intensity
B. wavelength
c. wave number
D. frequency


Find the coordinates of the points which divides the line joining the points (2,-4,3),(-4,5,-6) in the ratio
\( (i) 1:-4 \)
\( (i i) 2: 1 \)


The molar conductivities of \( \wedge_{N a O A c}^{\circ} \) and \( \wedge_{H C l}^{\circ} \) at infinite dilution in water at
\( 25^{\circ} \mathrm{C} \) are 91 and \( 426.2 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
respectively. To calculate, \( \wedge_{H O A c}^{\circ}, \) the additional value required
is
\( \mathbf{A} \cdot \wedge_{H_{2} O}^{\circ} \)
в. \( \wedge_{K C l}^{\circ} \)
c. \( \wedge_{N a O H}^{\circ} \)
\( \mathbf{D} \cdot \wedge_{N a C l}^{\circ} \)


Differentiate the following function with
respect to \( x \)
\( \boldsymbol{x}^{-4}\left(\boldsymbol{3}-\boldsymbol{4} \boldsymbol{x}^{-\boldsymbol{5}}\right) \)
A . \( -12 x^{-6}+36 x^{-10} \)
B. \( -12 x^{-5}+36 x^{-11} \)
c. \( -12 x^{-5}+36 x^{-10} \)
D. \( -12 x^{5}+36 x^{-10} \)


Isotopes are identified by:
A. positive ray analysis
B. Astons' mass spectrograph
C. Dempster's mass spectrograph
D. all of the above


A cell develops the same power across
two resistance \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) seprarately.The internal resistance of the cell is :
A \( \cdot R_{1}+R_{2} \)
в. \( \frac{R_{1}+R_{2}}{2} \)
c. \( \sqrt{R_{1} R_{2}} \)
D. \( \frac{\sqrt{R_{1} R_{2}}}{2} \)


On one page of a telephone directly, there were 200 telephone numbers. The frequency distribution of their unit place digit (for example in the number 25828573
the unit place digit is 3 ) is given in table
below :
Digit
Frequency 22 26 22 22
Without looking at the page, the pencil is placed on one of these numbers, i.e., the
number is chosen at random. What is the
probability that the digit in its unit place is more than \( 7 ? \)
\( A \)
\[
0.15
\]
в. 0.17
\( c \)
0.18
D. None of these


Consider the following two statements A and B and identify the correct option:
A) When a rigid body is rotating about its own axis at a given instant, all particles of body possess same angular velocity
B) When a rigid body is rotating about its own axis, the linear velocity of a particle is directly proportional to its perpendicular distance from axis.
A . A is true but B is false
B. A is false but B is true
c. Both A and B are true
D. Both A and B are false


The critical temperature and pressure
of \( C O_{2} \) gas are \( 304.2 K \) and 72.9 at \( m \)
respectively.what is the radius of \( C O_{2} \)
molecules assuming it to behave as Vander Waal's gas?


toppr LOGIN JolN Now
Q Type your question
What happens to the charge on the
plates, the voltage across the plates,
and the capacitance of the capacitor as
a result of moving the plates closer
together?
\( A \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \\
\hline Charges on Plates & same \\
Voltage Across Plates Capacitance & larger larger \\
\hline
\end{tabular}
B. \begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \\
\hline Charges on Plates & same \\
Voltage Across Plates & smaller \\
Capacitance & larger \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \\
\hline Charges on Plates & larger \\
Voltage Across Plates Capacitance & same same \\
\hline
\end{tabular}
D. \begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \\
\hline Charges on Plates & larger \\
Voltage Across Plates & same \\
Capacitance & larger \\
\hline
\end{tabular}
E \begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|} { Capacitor } & Values after Plates are Moved Closer Together \\
\hline Charges on Plates & larger \\
Voltage Across Plates Capacitance & larger larger \\
\hline
\end{tabular}


Acetophenone cannot be prepared
easily starting from:
A \( \cdot C_{6} H_{5} C H_{3} \)
B . \( C_{6} H_{6} \)
\( \mathbf{c} \cdot C_{6} H_{5} C H(O H) C H_{3} \)
D. \( C_{6} H_{5} C \equiv C H \)


Find four number forming a \( G . P . \) in
which the third term is greater than the
first by \( 9, \) and the second term is
greater than the fourth by \( 18 . \) Write the largest of the four numbers.


If \( x=a t^{2}, y=2 a t \) then \( \frac{d^{2} y}{d x^{2}}= \)
A. \( -\frac{1}{t^{2}} \)
B. \( \frac{1}{2 a t^{3}} \)
c. \( -\frac{1}{t^{3}} \)
D. \( -\frac{1}{2 a t^{3}} \)


Silk is a natural fibre, with continuous
filaments which can stretch upto \( 1 k m \)
A. True
B. False


Twenty people sit around at random at a round table. Find the probability that two people \( A, B \) sit with four people between them.
A \( \cdot \frac{1}{19} \)
в. \( \frac{2}{19} \)
c. \( \frac{1}{38} \)
D. \( \frac{3}{19} \)


State whether true or false.
Fuses should be connected to the
neutral wire.
A. True
B. False


A shopkeeper buys an article for Rs.
1,500 and spends \( 20 \% \) of the cost on its packing, transportation, etc. Then he marks the article at a certain price. If he sells the article for Rs. 2,452.50 including \( 9 \% \) Sales Tax on the price marked, find his profit as per cent.
A . \( 13 \% \)
B. \( 18 \% \)
\( c .25 \% \)
D. \( 30 \% \)


If \( \vec{a}=3 \hat{i}-6 \hat{i}-\hat{k}, \vec{b}=-1 \hat{i}+4 \hat{i}- \)
\( \mathbf{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\mathbf{3} \hat{\boldsymbol{i}}-\mathbf{4} \hat{\boldsymbol{i}}-\mathbf{1 2} \hat{\boldsymbol{k}}, \) then the length
of projection of \( \vec{a} \times \vec{b} \) on \( \bar{c} \) is
A \( \cdot \frac{250}{13} \)
B. \( 5 \sqrt{2} \)
c. \( \frac{250}{\sqrt{13}} \)
D. 14


In a Young's double slit experiment, constructive interference is produced at
a certain point \( P . \) The intensities of
light at \( \boldsymbol{P} \) due to the individual sources
are 4 and 9 units. The resultant
intensity at point \( \boldsymbol{P} \) will be-
A. 13 units
B. 25 units
c. \( \sqrt{97} \) units
D. 5 units


Find the area of \( \| g m A B C D \) if the area
of shaded region is \( 12 \mathrm{cm}^{2} \)


Two wires \( A \) and \( B \) of same dimensions
are stretched by same amount of force. Young's modulus of \( A \) is twice that of \( B \).
Which wire will get more elongation? Enter 1 for \( A \) and 2 for \( B \)


Assertion
Phase of cell division is also known as
formative phase.
Reason
In formative phase new cells are produced from pre-existing cells through meiosis.
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 electrons revolving close to the nucleus of an atom are called
electrons.
A . free
B. positive charge
c. bound
D. attract


Which element has highest electronegativity?
A.
в. не
c. Ne
D. Na


Boron rods in a nuclear reactor are used
to
A. absorb excess neutrons
B. absorb alpha particle
c. slow down the reaction
D. speed up the reaction


The sides of an \( 8 \times 8 \) square are cut by
certain points into pieces of length and 7,2 and 6,3 and 5 and 4 and 4 as
shown in the figure above. The area of
the quadrilateral determined by these
four points are
\( A \cdot 28 \)
в. 36
\( c \cdot 48 \)
\( D \)


A system in thermodynamic equilibrium will have the minimum value for-?
This question has multiple correct options
A. Helmholtz free energy
B. Gibb's free energy
C. Entropy
D. Temperature


In two figures
This question has multiple correct options
\( \mathbf{A} \cdot v_{1} / v_{2}=1 / 2 \)
\( \mathbf{B} \cdot t_{1} / t_{2}=2 / 1 \)
\( \mathbf{C} \cdot R_{1} / R_{2}=1 \)
\( \mathbf{D} \cdot v_{1} / v_{2}=1 / 4 \)


\( D_{2} O \) will have maximum density at :
\( \mathbf{A} \cdot 9^{\circ} C \)
B. \( 11.5^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 15.9^{\circ} \mathrm{C} \)
D. \( 20^{\circ} \mathrm{C} \)


A conducting hollow sphere of radius
\( 0.1 \mathrm{m} \) is given a charge of \( 10 \mu C . \) The
electric potential on the surface of
sphere will be :
A . zero
B . \( 3 \times 10^{5} V \)
\( \mathbf{c} \cdot 9 \times 10^{5} V \)
\( \mathbf{D} \cdot 9 \times 10^{9} V \)


Chlorine is 2.5 times havier than air.
A. True
B. False


A particle performs SHM given by the
equation \( \boldsymbol{x}= \)Asinwt. Where is the
particle at \( t=3 T / 8 \)
A. The particle is at a distance of \( A / \sqrt{(} 2) \) moving away from the mean position to its extreme
B. The particle is at a distance of \( A / \sqrt{(} 2) \) moving towards the mean position to its extreme
C. The particle is at a distance of \( A(1-1 / \sqrt{(} 2)) \) moving away from the mean position to its extreme
D. None of these


Which of the following statement(s) is/are not correct?
A \( \cdot L a_{2}(O H)_{3} \), is less basic than \( L u_{2}(O H)_{3} \)
B. In Lanthanoid series ionic radius of \( \operatorname{Ln} \) n \( 3^{\wedge} \) + ions decreases
c. La is actually an element of transition series rather than Lanthanoid series
D. Atomic radii of Zr and Hf are same because of Lanthanide contraction


A particle moving horizontally. collides
perpendicularly at one end of a rod having equal mass and placed on a
smooth horizontal surface.
This question has multiple correct options
A. Particle comes to rest if collision is perfectly elastic and centre of rod starts to move with the same velocity
B. Particle continues to move along the same direction, whatever is the value of e.
C . Particle may get rebound back.
D. Velocity of mid-point of the rod will be less than \( v_{0} / 2 \) i the particle gets stuck.


Identify the product obtained when following acid prolonged heating.
\( \boldsymbol{P H}-\stackrel{\|}{C}-\boldsymbol{C H}_{2}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O} \boldsymbol{H} \)


The ratio Q/P will be
A .2 .1: 1 \)
3. 1.005: 1
\( c .1 .5: 1 \)
D. 1.25: 1


An airplane in which the distance
between the tips of the wings is 50 meter is flying horizontally with a speed of 360 km/hour over a place where the vertical
component of earths magnetic field is \( 2.0 \times 10^{-4} \) Testa. The potential difference
between the tips of the wings would be:-
A . 0.1
B. 1.0
c. \( 0.2 v \)
D. \( 0.0 \mathrm{v} \)


Find the area bounded on the right by
the line \( x+y=2, \) on the left by the
parabola \( y=x^{2} \) and below by the \( x- \)
axis.


The greatest value of \( f(x)=x-2 \ln x \)
in \( [1, e] \) is attained at \( x= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( \sqrt{e} \)
\( c \cdot 2 \)
D.


Isotones possess which of the following
properties?
A. They have different number of electrons
B. They have same number of neutrons but different number of nucleons
c. Both A and B
D. None of the above


A \( 2 m \) long wire of resistance 4 ohm and
diameter 0.64 mm is coated with
plastic insulation of thickness 0.06 mm. When a current of \( 5 A \) flows
through the wire, find the temperature
difference across the insulation in
steady state. If \( \boldsymbol{K}=\mathbf{0 . 1 6} \times \mathbf{1 0}^{-\mathbf{2}} \mathbf{c a l} / \mathbf{c m}^{\circ} \mathbf{C} \mathbf{s e c} \)


Discuss with your teacher about
(i) Haploid insects and lower plants where cell-division occurs and
(ii) Some haploid cells in higher plants where cell-division does not occur?


In the binary number system \( 100+1011 \)
is equal to:
A. 1000
B. 1011
c. 1110
D. 111


A cylindrical conducting rod is kept with its axis along positive z-axis, where a uniform magnetic field exists parallel to z-axis. The current induced in
the cylinder is
A. zero
B. clockwise as seen from +z-axis
c. anti-clockwise as seen from +z-axis
D. opposite to the direction of magnetic field


In Neurospora, the arrangement of ascospore after meiosis is found to be
2a : 4A : 2a. What can be concluded?
A. First reductional then equational division
B. First equational and then reductional division
c. Both occur simultaneously


Sound waves of frequency \( 600 \mathrm{Hz} \) fall normally on perfectly reflecting wall. The distance from the wall at which the air
particles have the maximum amplitude of vibration is
(speed of sound in air \( =330 \mathrm{m} / \mathrm{s} \) )
\( A \cdot 13.75 \mathrm{cm} \)
B. \( 40.25 \mathrm{cm} \)
\( c .70 .5 \mathrm{cm} \)
D. \( 60.75 \mathrm{cm} \)


Which of the following ions does not have S-S linkage?
A. \( S_{2} O_{8}^{2} \)
B. \( S_{2} O_{6}^{2-} \)
\( \mathrm{c} \cdot S_{2} O_{5}^{2} \)
D. \( S_{2} O_{3}^{2} \)


Two bodies have masses in the ratio 3 :
4. When a force is applied on the first body, it moves with an acceleration of
\( 6 m s^{-2} . \) How much acceleration will the
same force produce in the other body?
A . 0
в. 4.5
\( c .5 \)
D. 10


(i) \( A \) lot of 20 bulbs contain 4 defective
ones. One bulb is drawn at random from
the lot. What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in
(i) is not
defective and not replaced. Now bulb is drawn at random from the rest. What is
the probability that thisbulb is not defective?


If \( f(x) \) is continuous in [0,1] and \( f\left(\frac{1}{3}\right)=1 \) then \( \lim _{n \rightarrow \infty} f\left(\frac{n}{\sqrt{9 n^{2}+1}}\right) \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
c. \( \frac{1}{3} \)
D. none of these


A particle is revolving in a circle, clockwise in the plane of the circle. The angular acceleration in directed
A. Towards the center in the plane of the paper.
B. Radially outwards in the plane of the paper
c. Perpendicular to the plane of the paper.
D. Veertically in the plane of the paper.


What amount of \( C a C l_{2}(i=2.47) \) is
dissolved in 2 litres of water so that its
osmotic pressure is 0.5 at \( m \) at \( 27^{\circ} C \)
A. \( 3.42 g \)
B. \( 9.24 g \)
c. \( 2.834 g \)
D. \( 1.820 g \)


The IUPAC name of the given compound
is :
A. 4 -ethyl-3-methyloctene
B. 4 -ethyl-3-methyloctane
c. 3 -ethyl- 4 -methyloctane
D. 3 -ethyl-3-methyloctane


\( f_{f} A=\left[\begin{array}{lll}0 & 1 & 2 \\ 2 & 3 & 4 \\ 4 & 5 & 6\end{array}\right], B=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \)
Find \( 3 A-4 B \)


1 Curie is:
A. Activity of \( 1 g \) of Uranium
B. 1 disintegration / second
C \( .3 .7 \times 10^{10} \) becquerel
D. \( 1.6 \times 10^{12} \) disintegration / second


If \( a^{2}(b+c), b^{2}(c+a), c^{2}(a+b) \) are in
AP, then \( a, b, c \) are in
\( A \cdot A P \)
в. GР
\( c . \) не
D. None of these


Sound waves need an .......... (elastic, rigid) medium for propagation.


What is the formula of ammonium
aquapentafluoronickelate(IV)?
\( \mathbf{A} \cdot\left[\operatorname{Ni}\left(N H_{3}\right)\left(H_{2} O\right) F_{5}\right]^{+1} \)
B . \( \left[N i\left(N H_{3}\right)\left(H_{2} O\right) F_{5}\right] \)
\( \mathbf{c} \cdot\left(N H_{4}\right)_{2}\left[N i\left(H_{2} O\right) F_{5}\right] \)
D. \( N H_{4}\left[N i\left(H_{2} O\right) F_{5}\right] \)


The distance of the closest approach of an alpha particle fired at a nucleus with
kinetic energy \( \boldsymbol{K} \) is \( \boldsymbol{r}_{0} . \) The distance of
the closest approach when the \( \alpha \) particle is fired at the same nucleus
with kinetic energy \( 2 K \) will be
A \( .4 r_{n} \)
B. \( \frac{r_{0}}{2} \)
c. \( \frac{r_{0}}{4} \)
D. \( 2 r_{0} \)


Expand \( \left(2 y-\frac{3}{y}\right)^{3} \)
A \( \cdot 8 y^{3}-36 y+\frac{54}{y}-\frac{27}{y^{3}} \)
в. \( 8 y^{3}+36 y+\frac{54}{y}-\frac{27}{y^{3}} \)
c. \( 8 y^{3}-36 y-\frac{54}{y}-\frac{27}{y^{3}} \)
D. None of these


The tribasic acid is:
\( \mathbf{A} \cdot H_{3} P O_{4} \)
\( \mathbf{B} \cdot H_{3} P O_{3} \)
\( \mathbf{c} \cdot H_{3} P O_{2} \)
\( \mathbf{D} \cdot H P O_{3} \)


The carboxylic acid includes the functional group:
A. carboxyl and amine group
B. carboxyl and amide group
c. carboxyl and hydroxyl group
D. carboxyl and amine functional group


toppr
Q Type your question
This chart shows the relative
abundance of different groups of
echinoderms throughout geologic time.
The width of the band indicates the
number of species for each group.
Identify the time periods showed a
boom in all echinoderm groups?
A. Ordovician
B. Silurian
C. Mississippian
D. Permian
E . Jurassic


Which of the following belongs to actinoid series of elements?
A. Nd
B.
\( c . \mathrm{sm} \)
D. Al


2,2'-dinitro-6,6'-disulfonic acid biphenyl
is non-resolvable. If true enter 1 and if
false enter 0


Using commutativity and associativity of addition of rational numbers, express each of the following as a rational
number:
\( \frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9} \)


There are two A.P.s whose common
differences differ by unity, but sum of the three consecutive terms in each is
15. If \( P \) and \( P_{1} \) be the products of these terms such that \( \frac{\boldsymbol{P}}{\boldsymbol{P}_{1}}=\frac{\mathbf{7}}{\mathbf{8}}, \) then find the
two A.P.'s.


The oxidation number of arsenic atom
\( \operatorname{in} H_{3} A s O_{4} \) is:
A . -1
B. -3
\( c \cdot+3 \)
D. +5


If \( p(t)=t^{3}-1, \) find the values of
\( \boldsymbol{p}(\mathbf{1}), \boldsymbol{p}(-\mathbf{2}) \)


Sweet tooth may lead to decay'.Explain
why? What is the role of tooth paste in preventing cavities?


An observer whose least distance of
distinct vision is 'd', views his own face
in a convex mirror or radius or
curvature 'r'. The magnification produced cannot exceed \( \frac{\boldsymbol{k} \boldsymbol{r}}{\boldsymbol{d}+\sqrt{\boldsymbol{d}^{2}+\boldsymbol{r}^{2}}} \)
Find \( k \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Assertion
In cyanide process for the extraction of gold and silver from their native ores,
the cyanide solution acts as a reducing agent to reduce the gold and silver compounds present in the ores into the metallic states.
Reason
In the extraction of gold and silver, the cyanide solution acts as complexing reagent in the presence of air and form their respective soluble complexes.
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


\( \mathbf{1}^{o} \boldsymbol{A} \) is
A. \( 10 n m \)
B. \( 0.1 n m \)
c. 100 n \( m \)
D. \( 1 n m \)


A small mass \( \mathrm{m} \) is attached to the
inside of a rigid ring of the same mass \( \mathrm{m} \) and radius R. The ring rolls without slipping over a horizontal plane. At the moment when the mass m gets into the lowest position, the centre of the ring
moves with velocity \( \boldsymbol{v}_{0} . \) If \( \left(\boldsymbol{v}_{0}\right)_{\max }= \)
\( \sqrt{\mathrm{ngR}}, \) when the ring moves without bouncing, find \( n \)


Define trait


Define negative of a vector.


A solution of \( \boldsymbol{P h}_{3} \boldsymbol{C C O}_{2} \boldsymbol{H} \) in conc.
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) gives \( (\boldsymbol{X}) \) when poured into
methanol \( X \) is :
\( ^{\mathbf{A}} \cdot \operatorname{Ph}_{3} C-\stackrel{\mathbb{I}}{C}-O-C H_{3} \)
в. \( \quad P h_{2} C H-C \) I
\( \mathbf{c} \cdot P h_{3} C-O C H_{3} \)
D. \( P h_{3} C-C H_{3} \)


Which product is obtained when bleaching powder is distilled with acetone?
A \( \cdot C C l_{4} \)
в. \( C H C l_{3} \)
c. \( C H_{2} C l_{2} \)
D. \( C H_{3} C l \)


ff \( f(x) \) is a function such that \( f(x y)= \) \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y}): \boldsymbol{x}, \boldsymbol{y}[\boldsymbol{R}, \text { then } \boldsymbol{f}(\mathbf{1} / \boldsymbol{e}) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Why is parallel arrangement used in
domestic wiring?
A. For getting same potential difference across each electrical appliance.
B. For getting different potential difference across each electrical appliance.
C. For getting high potential difference across each electrical appliance.
D. For getting low potential difference across each electrical appliance.


The figure given below shows the
cooling curve of pure wax material after
heating. It cools from \( A \) to \( B \) and
solidifies along \( B D . \) If \( L \) and \( C \) are respective values of latent heat and the
specific heat of the liquid wax, the ratio
\( \boldsymbol{L} / \boldsymbol{C} \) is \( \boldsymbol{v} \)
A . 40
B. 80
c. 100
D. 20


A machine gun fires a bullet of mass
\( 40 g \) with a velocity of \( 1200 m s^{-1} . \) The
man holding it can exert a maximum force of \( 144 N \) on the gun. How many
bullets can he fire per second at the
most?
A
B. 3
\( c \cdot 2 \)
\( D \)


\( \int e^{\tan ^{-1} x}\left(\frac{1+x+x^{2}}{1+x^{2}}\right) d x \) is equal to
A \( \cdot-e^{\tan ^{-1} x}+c \)
B . \( e^{\tan ^{-1} x}+c \)
\( \mathrm{c} \cdot-x e^{\tan ^{-1} x}+c \)
D. \( x e^{\tan ^{-1} x}+c \)


What are the oxidation number of the
underlined elements in each of
the following and how do you rationalise your results?
\( \boldsymbol{K} \underline{\boldsymbol{I}}_{\mathbf{3}} \)


A convex lens of focal length fis cut into
two halves as shown. Light rays parallel to the principal axis are incident on one
half of the lens \( \left(\operatorname{say} L_{1}\right) \) This will form an image at
\( A \)
B. f/2
\( c \cdot 2 \)
D. \( f / 4 \)


Dipole moment of chlorobenzene is less then cyclohexylchloride
A. True
B. False


The correct IUPAC name for \( \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H C H}_{2} \boldsymbol{N H C H}_{3} \) is:
A. allylmethylamine
B. 2-amino-4-pentene
c. 4 -aminopent- - ene
D. N-methylprop-2-en-1-amine.


An electron is confined in the region of
width \( 1 A^{\circ} \). Estimate its K.E.
A. 3.4 ev
B. 3.8 ev
c. 13.6 ev
D. 10.2 ev


A man can row \( 9 \frac{1}{3} k m p h \) in still water and finds that it takes him thrice as
much time to row up then as to row
down the same distance in the river.
Find the speed of the current.


Which of the following pair is not proper?
A. Food preservative - Sodium meta bi-sulphate
B. Anti oxidant - Sorbic acid
c. Food colour - Arneto
D. Artificial sweetening agent- Alitame


if \( \cos ^{-1} x+\cos ^{-1} y=\theta, \) show that \( x^{2}-2 \)


The balance chemical equations for the following:
The preparation of ethyne from 1,2 dibromoethane.
A \( \cdot C H_{2} B r-C H_{2} B r \stackrel{\text {alc.KOH}}{\longrightarrow} C H_{2}=C H B r \)
B . \( C H_{2}=C H B r \stackrel{N a N H_{2}}{\longrightarrow} C H_{2}=C H_{2} \)
c. \( C H_{2} B r-C H_{2} B r \stackrel{\text {alc.KOH}}{\longrightarrow} C H_{2}=C B r_{2} \stackrel{N a N H_{2}}{\longrightarrow} \)
\( C H \equiv C H \)
D. \( C H_{2} B r-C H_{2} B r \stackrel{\text {alc.KOH}}{\longrightarrow} C H_{2}=C H B r \stackrel{N a N H_{2}}{\longrightarrow} \)
\( C H \equiv C H \)


The pace setter of the endocrine system in the human body is the endocrine hormone called:
A. thyroxin
B. insulin
c. adrenaline
D. secretin


Choose the correct answer from the
alternatives given Which one of the following hormones has a stimulatory effect on heart?
A. Thyroxine
B. Gastrin
c. Adrenaline
D. Thymosin


A radioactive element gets spilled over the floor of a room. Its half life period is
30 days. If the initial activity is ten times the permissible value, after how may days will it be safe to enter the room?


Which of the following is a way to dispose non-biodegradable materials?
A. Recycling
B. Land fill
c. Incineration
D. All of above


Apply Euclid"s theorem for 17,5
A. \( 17=5 \times 3+2 \)
В. \( 17=5 \times 2+7 \)
\( \mathbf{c} \cdot 17=5 \times 4-3 \)
D. None of the above


What can be observed when sunlight is
passed through a colloidal solution?
A. Adsorption
B. Coagulation
c. Tyndall effect
D. Brownian motion


Metallic calcium is prepared by:
A. displacement of calcium by iron from calcium sulphate solution
B. electrolysis of molten calcium chloride
C. reduction of lime by coke
D. electrolysis of aqueous solution of calcium nitrate


A stone is thrown from a bridge at an
angle of \( 30^{\circ} \) down with the horizontal
with a velocity of \( 25 m / s \). If the stone
strikes the water after 2.5 seconds, then calculate the height of the bridge from
the water surface.


In the reaction the major product formed is:
\( A \)
B.
\( c \)
D.


If \( l^{2}+m^{2}=1, \) then find the maximum
value of \( l+m \)


A fair coin is tossed four times. The
probability that the tails exceed the heads in number is
\( ^{\mathbf{A}} \cdot_{\frac{4}{3} C}\left(\frac{1}{2}\right)^{4} \)
\( ^{\mathbf{B}} \cdot_{3}^{4} C\left(\frac{1}{2}\right)^{4}+\left(\frac{1}{2}\right)^{4} \)
\( ^{c} \cdot\left(\frac{1}{2}\right)^{4} \)
\( ^{\mathrm{D}} \cdot_{3}^{4} C\left(\frac{1}{3}\right)^{2}\left(\frac{2}{3}\right)^{1} \)


Find probability of bag chosen out random contains more than \( 5 \mathrm{kg} \)
A . 0.7
B. 0.8
\( c .0 .9 \)
D. 0.6


A ball reaches a wall at \( 60 \mathrm{m} / \mathrm{s} \) along +ve X direction, and leaves the wall in
the opposite direction with the same speed. Assuming that the mass of the ball as \( 50 \mathrm{gm} \) and the contact time is 0.02 second, the force exerted by the wall on the ball is
A. 300 N along + X direction
B. 300 N along - X direction
c. \( 3,00,000 \mathrm{N} \) along \( +\mathrm{x} \) direction
D. 3,00,000 N along - X direction


The value of \( ^{6} C_{4} \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 9
c. 15
D. 240


If the mean free-path of gaseous
molecule is \( 60 \mathrm{cm} \) at a pressure of \( 1 \times \)
\( 10^{-4} \mathrm{mm} \) mercury, what will be its
mean free-path when the pressure is
increased to \( 1 \times 10^{-2} \mathrm{mm} \) mercury?
A \( \cdot 6.0 \times 10^{-1} \mathrm{cm} \)
B. \( 6.0 \mathrm{cm} \)
\( \mathbf{c} \cdot 6.0 \times 10^{-2} \mathrm{cm} \)
D. \( 6.0 \times 10^{3} \mathrm{cm} \)


If \( x^{2}+y^{2}=a^{2} \) and \( k=1 / a, \) then \( k \) is
equal to?
A \( \cdot \frac{y \prime}{\sqrt{1+y^{\prime}}} \)
B. \( \frac{|y \prime \prime|}{\sqrt{\left(1+y^{\prime 2}\right)^{3}}} \)
c. \( \frac{2 y \prime}{\sqrt{1+y \prime}} \)
D. \( \frac{y \prime}{2 \sqrt{\left(1+y^{\prime 2}\right)^{3}}} \)


Which of the following reason is correct about the statement "All members of Group IA have similar reactivity"?
A. They have the same number of protons
B. They have the same number of electrons
c. They have similar outer-shell electron configurations
D. They have valence electrons with the same quantum numbers
E. They have the same number of neutrons


Silk fiber is obtained from the stem of a
plant.
A . True
B. False


Which has maximum value of mean
free path?
A. \( C O_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( N_{2} \)


If a polynomial \( \boldsymbol{f}(\boldsymbol{x}) \) is divided by \( \boldsymbol{x}^{2}- \) 16 then remainder is \( 5 x+3 \), what will
be the remainder when the same
polynomial is divided by \( (x+4) ? \)


A stone tied to the end of a string \( 80 \mathrm{cm} \) long is whirled in a horizontal circle with a constant speed. If the stone
makes 14 revolutions in \( 22 s \) then the
acceleration of the stone is :
A \( \cdot 5 m / s^{2} \)
B . \( 10 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 12.8 m / s^{2} \)
D. \( 14.8 \mathrm{m} / \mathrm{s}^{2} \)


Appendicular skeleton includes
A. Girdles and limbs
B. Vertebrae
c. Skull and vertebral column
D. Ribs and sternum


If direction cosines of two lines are
proportional to (2,3,-6) and (3,-4,5) then the acute angle between them is
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left(\frac{49}{36}\right) \)
B. \( \cos ^{-1}\left(\frac{18 \sqrt{2}}{35}\right) \)
\( c \cdot 96^{\circ} \)
D. \( \cos ^{-1}\left(\frac{18}{35}\right) \)


The string of a Sonometer is plucked so as to make it to vibrate in one segment The frequency produced in called.
\( A \). first Harmonic
B. first Overtone
c. second Harmonic
D. second Overtone


Assertion
The equation \( a \sin x+\cos 2 x=2 a-7 \)
possesses a solution if \( \boldsymbol{a} \in[\mathbf{2}, \mathbf{6}] \)
Reason
\( -1 \leq \sin x \leq 1 \forall x \in R \)
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


If an external force and the frictional
force are acting on a body, which is in rest on the floor, and are equal and opposite, then the frictional force is:
A. rolling friction.
B. sliding friction.
C. static friction.
D. Both B and C


What is the source of centripetal force that a planet requires to revolve around
the Sun?
A . Gravitational force
B. Electrical force
c. Magnetic force
D. Atomic force


Give the significance of fertilization.


Assertion
A light-year is a distance that light
travels with velocity of \( 3 \times 10^{8} m s^{-1} \) in
one year.
Reason
Light year is the unit for measuring time.
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


Draw the structural isomer of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{N} \boldsymbol{O}_{2}\right] \boldsymbol{C l}_{2} \) and name the type
of isomerism?


The energy of the electron in the second and third Bohr orbits of the hydrogen atom is \( -5.42 \times 10^{-12} \) erg and \( -2.41 \times 10 \)
-12 erg, respectively. The wavelength of the emitted radiation when the electron
drops from third to second orbit is:
A \( .4 .6 \times 10^{6} \)
B . \( 6.6 \times 10^{3} \)
c. \( 0.66 \times 10^{6} \)
D. none of these


Evaluate :
\( \int \frac{(1+\log x)^{2}}{x} d x \)


A rope brake is fitted to a flywheel of
diameter \( =1 \mathrm{m} . \) The flywheel runs at 220
r.p.m. It is required to absorp \( 5.25 \mathrm{kW} \) of
brake power. Difference in the two pulls \( (T-S) \) is :
\( \mathbf{A} \cdot 456 N \)
B. \( 654 N \)
\( c .564 N \)
D. \( 465 N \)


In Millikan's oil drop experiment, a charged drop of mass \( 1.8 \times 10^{-14} k g \) is
stationary between the plates. The distance between the plates is \( 0.90 \mathrm{cm} \) and potential difference between them is \( 2.0 \mathrm{kV} \). The number of electrons on the
drop is
A. 500
B. 50
\( c \cdot 5 \)
D.


A non-planar closed loop of arbitrary shape carrying a current \( I \) is placed in uniform magnetic field.The force acting on the loop
A. is zero only for one orientation of loop in magnetic field
B. is zero for two symmetrically located positions of loop in magnetic field
c. is zero for all orientations
D. is never zero


The potential energy of a particle in a space is given by \( U=x^{2}+y^{2} \). Find the
force associated with this potential
energy:
A \( .-2 x \hat{i}-2 y \hat{j} \)
B . \( 2 x \hat{i}-2 y \hat{j} \)
c. \( -2 x \hat{i}+2 y \hat{j} \)
D. \( 2 x \hat{i}+2 y \hat{j} \)


In the estimation of sulphur in an organic compound, fuming nitric acid is used to convert sulphur into:
\( A \cdot S O_{2} \)
в. \( H_{2} \).
c. \( H_{2} S O_{3} \)
D. \( H_{2} S O_{4} \)


Polymer of \( \alpha \) -D glucose is
A. Cellulose
B. Glycogen
c. Inulin
D. Chitin


The cost of 2 kg of Apples and 1 kg
grapes on a day was bound to be Rs. 160 After a moth the lost of 4 kg grapes and 2 kg graps is Rs. 300. Represent this situation algebraicallyand geometrically.


In which of the following does sulphur has the lowest oxidation state?
A. \( H_{2} S O_{4} \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{SO}_{3} \)
D. \( H_{2} S_{S} \)


Arrange the following physical quantities in the increasing order of their magnitudes
I. 1 dyne
II. \( 1 N \)
III. \( 3 k g m s^{-2} \)
IV. \( 10^{7} g c m s^{-2} \)
\( \mathbf{A} \cdot \|, 1, \) ॥I \( , \) IV
B. IV, ।, ॥ᅵ, ॥
c. ॥, ॥ा, ।, IV
D. I, II, III, IV


If we consider no mixing of '2s' and '2p' orbitals, then the bond order and
magnetic nature of the diatomic
molecule \( \mathrm{C}_{2} \) would be:
B. 2.5 and diamagnetic
c. 2 and diamagnetic
D. 2 and paramagnetic


Ozone is present as a chief constituent in which region of the atmosphere?
A. Troposphere
B. Stratosphere
c. Mesosphere
D. Thermosphere


In a gas equation, \( P V=R T, V \) refers to the
volume of:
A. any amount of a gas
B. one gram mass of a gas
C. one gram mole of gas
D. one litre of gas


What type of bond would exist between this soap and oil?
A. Hydrogen bonds
B. Dispersion forces
c. covalent bonds
D. Dipole-dipole forces


A resistor of \( 100 \Omega \), a pure inductance coil of \( L=0.5 \mathrm{H} \) and capacitor are in series in a circuit containing an a.c sources of \( 200 \mathrm{V}, 50 \mathrm{Hz} \). In the circuit, current is added is ahead of the voltage
by \( 30^{0} . \) Find the value of the capacitance
A . 1.46
B. 3
\( c \cdot 4 \)
D. 5


Let \( z \neq 1 \) be a complex number and let \( \omega=x+i y \neq 0 . \) If \( \frac{\omega-\omega z}{1-z} \) is purely
real, then | \( z \mid \) is equal to :
\( A \cdot|\omega| \)
B . |\omega| \( ^{2} \)
c. \( \frac{1}{|\omega|^{2}} \)
D. \( \frac{1}{|\omega|} \)
\( E \)


Without using tables evaluate
\( 3 \cos 80^{\circ} \cdot \operatorname{cosec} 10^{\circ}+2 \sin 59^{\circ} \cdot \sec 31^{\circ} \)


Alkanes undergo addition reactions.
A. True
B. False


Solve: \( \frac{\mathbf{2 0}}{\boldsymbol{x}+\boldsymbol{y}}+\frac{\mathbf{3}}{\boldsymbol{x}-\boldsymbol{y}}=\mathbf{7} \) and
\( \frac{8}{x-y}-\frac{15}{x+y}=5 \)
A. \( x=3 \) and \( y=2 \)
B. \( x=2 \) and \( y=7 \)
c. \( x=9 \) and \( y=4 \)
D. \( x=1 \) and \( y=9 \)


The number of moles of water present in
90 grams of water are:
\( A \cdot 9 \)
B. 6
\( c \cdot 5 \)
\( D \cdot 0.5 \)


Consider the linear inequalities \( 2 x+3 y \leq 6,2 x+y \leq 4, x \geq 0, y \geq 0 \)
(a) Mark the feasible region.
(b) Maximise the function \( z=4 x+5 y \)
subject to the given constraints.


If true enter 1 , else enter 0
All the \( A l-C l \) bonds in \( A l_{2} C l_{6} \) are
equivalent.


Which of the following is the vegetative part of Jasmine plant?
A. Stem
B. Root
c. Flower
D. Leaf


Lateral roots arise from primordia developed by division of
A. Pericycle cells in between two protoxylem points
B. Pericycle cells opposite protoxylem points
C. Endodermis cells in between two protoxylem points
D. Endodermis opposite protoxylem points


If \( 12+\frac{3 \sqrt{x-5}}{2}=18, \) find the value of
\( x ? \)
A . 21
B . 20
\( c \cdot 26 \)
D. 18


In the fig. the potentiometer wire \( A B \) of
length \( L \& \) resistance \( 9 r \) is joined to
the cell \( D \) of e.m.f. \( \varepsilon \) and internal
resistance \( r . \) The cell \( C s \) e.m.f. is \( \varepsilon / 2 \)
and its internal resistance is \( 2 r . \) The
galvanometer \( G \) will show no deflection
then find length \( A J: \)


Given standard \( E^{\ominus}: \)
\( F e^{3+}+3 e^{-} \rightarrow F e ; E^{\ominus}=-0.036 V \)
\( F e^{2+}+2 e^{-} \rightarrow F e ; E^{\ominus}=-0.440 V \)
The \( E^{\ominus} \) of \( F e^{3+}+e^{-} \rightarrow F e^{2+} \) is:
A. \( 0.476 V \)
\( V \)
в. \( 0.404 V \)
c. \( 0.604 V \)
D. \( 0.772 V \)


Indira Gandhi canal brought water to large areas of
A. Himachal Pradesh
B. Bihar
c. Kerala
D. Rajasthan


Which of the following enzymes is present in animals like cows, buffaloes,
etc to digest compound like paper cloth, etc.?
A . Uraze
B. Cellulase
c. silicones
D. sucrase


The function \( \mathbf{f}(\mathbf{x})=\frac{\cos \boldsymbol{x}-\sin \boldsymbol{x}}{\cos \mathbf{2} \boldsymbol{x}} \) is not
defined at \( x=\frac{\pi}{4} \) The value of \( f\left(\frac{\pi}{4}\right) \) so that \( \mathbf{f}(\mathbf{x}) \) is continuous at \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\mathbf{4}} \) is
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
\( c \cdot-\sqrt{2} \)
D.


The chemical system in equilibrium is not affected by:
A. addition of a catalyst
B. change in the concentration of products
c. changing the temperature
D. all of these


The product \( B \) can be:
\( \mathbf{A} \)
B. \( H C H O \)
\( \mathbf{c} \cdot C H_{3} H_{8} \)
\( \mathbf{D} \cdot C H_{4} \)


If first dissociation of \( \boldsymbol{X}(\boldsymbol{O} \boldsymbol{H})_{3} \) is \( \mathbf{1 0 0 \%} \)
whereas second dissociation is \( 50 \% \)
and third dissociation is negligible then the \( p H \) of \( 4 \times 10^{-3} M X(O H)_{3} \) is :
A. 11.78
B. 10.78
c. 2.5
D. 2.22


The ionisation potential of \( \boldsymbol{H} \) -atom is
\( 13.6 V . \) When it is excited from ground state by monochromatic radiations of \( \$ \$ 970.6 / \) buildrel \( _{-} \) lcirc lover \( \mathrm{~ I l m a t h r m \{ A \} 3 \$ \$ , ~ t h e ~ n u m b e r ~ o f ~} \)
emission lines will be (according to Bohr's theory)
A . 10
B. 8
c. 6
\( D \)


Two spheres of radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \) have
densities \( \rho_{1} \) and \( \rho_{2} \) and specific heat \( C_{1} \)
and \( C_{2} . \) If they are heated to the same
temperature, the ratio of their rates of cooling will be
A \( \cdot \frac{R_{2} \rho_{2} C_{2}}{R_{1} \rho_{C} C_{1}} \)
В. \( \frac{R_{1} \rho_{2} C_{2}}{R_{2} \rho_{1} C_{1}} \)
c. \( \frac{R_{2} \rho_{1} C_{2}}{R_{1} \rho_{2} C_{1}} \)
D. \( \frac{R_{2} \rho_{2} C_{1}}{R_{1} \rho_{1} C_{2}} \)


Dalton's theory fails to determine the existence of
A. molecules
B. compounds
c. allotropes
D. All of the above


Solve for \( \boldsymbol{\lambda} \) if
\( \left|\begin{array}{ccc}\boldsymbol{a}^{2}+\boldsymbol{\lambda} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a c} \\ \boldsymbol{a b} & \boldsymbol{b}^{2}+\boldsymbol{\lambda} & \boldsymbol{b c} \\ \boldsymbol{a c} & \boldsymbol{b c} & \boldsymbol{c}^{2}+\boldsymbol{\lambda}\end{array}\right|=\mathbf{0} \)


toppr
Q Type your question-
(i) \( \left.M_{(s)}+\frac{1}{2} O_{2(g)} \rightarrow M O_{(} s\right) \)
(ii) \( \frac{1}{2} C_{(s)}+\frac{1}{2} O_{2(g)} \rightarrow \frac{1}{2} C O_{2(g)} \)
(iii) \( C_{(s)}+\frac{1}{2} O_{2(g)} \rightarrow C O_{(g)} \)
\( \left(\text { iii) } C O_{(g)}+\frac{1}{2} O_{2(g)} \rightarrow C O_{2(g)}\right. \)
The temperature dependence of \( \Delta \) G of reaction (i) to (iv) is shown in the given
diagram. This is known as the Ellingham diagram. With the help of the Ellingham diagram, one can easily predict the most suitable reducing agent for the reduction of metal oxides.
\( A I_{2} O_{3} \) can be reduced by carbon at a
temperature of
\( A \cdot 30^{\circ} \mathrm{C} \)
B \( .500^{\circ} \mathrm{C} \)
\( \mathrm{D} \cdot>2500^{\circ} \mathrm{C} \)


The value of \( K_{p} \) is \( 1 \times 10^{-3} \) at \( m^{-1} \) at
\( 25^{\circ} C \) for the reaction \( 2 N O(g)+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons 2 N \boldsymbol{O} \boldsymbol{C l} . \) A flask contains \( \boldsymbol{N O} \)
at 0.02 at \( m \) and at \( 25^{\circ} C . \) Calculate the
mole of \( C l_{2} \) that must be added if \( 1 \% \) of
the \( N O \) is to be converted to \( N O C l \) at
equilibrium. The volume of the flask is such that 0.2 mole of gas produces
1 atm pressure at \( 25^{\circ} \mathrm{C} \). (lgnore
probable association of \( \left.N O \text { in } N_{2} O_{2}\right) \)


If \( P \) is a \( 3 \times 3 \) matrix such that \( P^{T}= \)
\( 2 P+I, \) where \( P^{T^{\prime}} \) is the transpose of \( P \)
and \( I \) is the \( 3 \times 3 \) identity matrix, then
there exists a column matrix \( \boldsymbol{X}= \)
\( \left[\begin{array}{l}\boldsymbol{x} \\ \boldsymbol{y} \\ \boldsymbol{z}\end{array}\right] \neq\left[\begin{array}{l}\mathbf{0} \\ \mathbf{0} \\ \mathbf{0}\end{array}\right] \) such that
\( ^{\mathbf{A}} \cdot \operatorname{PX}=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)
в. \( P X=X \)
c. \( P X=2 X \)
D. \( P X=-X \)
E.
\[
P X=\left[\begin{array}{l}2 \\ 0 \\ 0\end{array}\right]
\]
F. \( P X=3 X \)
G. \( P X=5 X \)
H. \( P X=-3 X \)


Oxygen atom has an atomic mass of 16
u and eight neutrons in its nucleus. What is its atomic number?
\( A \cdot 4 \)
B. 12
\( c \cdot 8 \)
D. 6


Which of the following motions is not simple harmonic?
A. Vertical oscillations of a spring
B. Motion of a simple pendulum
c. Motion of planet around the sun
D. oscillation of liquid in a U-tube


How many gram of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) would be needed to neutralise 100 gm of
\( M g(O H)_{2} ? \)
A. \( 66.7 \mathrm{gm} \)
B. 252 gm
c. \( 112.6 \mathrm{gm} \)
D. 168 gm


A linear object of height \( 10 \mathrm{cm} \) is kept in front of a concave mirror of radius of
curvature \( 15 \mathrm{cm}, \) at a distance of \( 10 \mathrm{cm} \)
The image formed is
A. Magnified and erect
B. Magnified and inverted
c. Diminished and erect
D. Diminished and inverted


The increasing non-metallic character
is:
A. \( F<O<C<B e<L i \)
в. \( L i<B e<C<O<F \)
c. \( O<F<C<B e<L i \)
D. \( F<O<B e<C<L i \)


The specific conductance of a saturated solution of AgCl in water is \( 1.826 \times \) \( 10^{-6} \Omega^{-1} \mathrm{cm}^{-1} \) at \( 25^{\circ} \mathrm{C} \) calculate its
solubility in water at \( 25^{\circ} \mathrm{C} \)
Given that \( :-\lambda^{\circ}\left(A g^{+}\right)=61.92 \)
\[
\boldsymbol{\lambda}^{\circ}\left(\mathbf{C l}^{-}\right)=\mathbf{7 6 . 3 4}
\]


In the dichlorination reaction of propane
mixture of products are obtained. How many isomers the mixture contains?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Two objects of masses \( m_{1} \) and \( m_{2} \) having the same size are dropped simultaneously from heights
\( h_{1} \) and \( h_{2} \) respectively. Find out the ratio of time they would take in reaching the ground.
A \( \cdot \sqrt{\frac{h_{1}}{h_{2}}} \)
B. \( \sqrt{\frac{h_{2}}{h_{1}}} \)
c. \( \frac{h_{1}}{h_{2}} \)
D. \( \frac{h_{2}}{h_{1}} \)


Value Based Questions:
The role of ATP can be compared with that of a battery Explain this statement.


opp


The diameter of a sphere is 4.24 m. Its
surface area with due regard to significant figures is :
A \( .5 .65 \mathrm{m}^{2} \)
в. \( 56.5 \mathrm{m}^{2} \)
\( c .565 m^{2} \)
D. \( 5650 m^{2} \)


An electric dipole when placed in a uniform electric field \( \boldsymbol{E} \) will have a
minimum potential energy if the dipole moment makes the following angle with
\( \boldsymbol{E} \)
\( A \)
В. \( \pi / 2 \)
c. zero
D. \( 3 \pi / 2 \)


Write the number of significant figures
for 1.0076


Find equation of line joining (1,2) and
(3,6) using determinants.


In a balanced wheat stone bridge,
current in the galvanometer is zero. It
remains zero when
\( [1] . \) battery emf is increased
\( [2] . \) all resistances are increased by 10 ohms
\( [3] . \) all resistances are made five times
\( [4] . \) the battery and the galvanometer are interchanged
A . only [1] is correct
B. [1],[2] and [3] are correct
c. [1],[3] and [4] are correct
D. [1] and [3] are correct


Two waves of frequencies \( 20 \mathrm{Hz} \) and 30
Hz travels out from a common point. The phase difference between them after 0.6
\( \sec \) is
A . \( 12 \pi \)
B.
\( c . \pi \)
\( D \cdot \frac{3 \pi}{4 \pi} \)


Which has highest specific charge?
A \( . N a^{+}(\text {mass } n o=23) \)
В. \( M g^{2+}(\text { mass } \text {по}=24) \)
C \( . A l^{+3}(\text {mass } n o=27) \)
D. \( S i^{+4}(\text {mass } n o=28) \)


Which of the following induces cell division in a cell?
A. Cytokinin
B. Gibberellins
c. Auxins
D. ABAA


Cardiac muscle cells are
A. Uninucleate and voluntary
B. Uninucleate and involuntary
C. Multinucleate and voluntary
D. Multinucleate and involuntary


1 L of a solution containing 10 g of
\( C u S O_{4} \) is to be electroyzed by a current strength of 48.25 A for 200 s. The weight of the final solution and pH of the
solution at the end of electrolysis are :
(assume that the volume remains
constant during electrolysis)
A. \( 6.825 g, p H=1 \)
в. \( 6.325 g, p H=10 \)
c. \( 6.795 g, p H=7 \)
D. none of the above


Assertion
Power of a glass convex lens in air is
\( +6 D, \) then power of the same convex lens in water will be \( +2 D \)
Reason \( \boldsymbol{P}=\left(\frac{\boldsymbol{\mu}_{l}}{\boldsymbol{\mu}_{\boldsymbol{m}}}-\mathbf{1}\right)\left(\frac{\mathbf{1}}{\boldsymbol{R}_{\mathbf{1}}}-\frac{\mathbf{1}}{\boldsymbol{R}_{2}}\right) \)
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


Carboxylic acids can be prepared from alcohols, nitriles or esters. Which statements are correct?
1. Both primary and secondary alcohols can be oxidised to carboxylic acids.
2. Carboxylic acids can be made from nitriles by hydrolysis.
3. Ethyl propanoate gives propanoic acid when reacted with hydrochloric
acid.
A .1,2 and 3 are correct
B. 1 and 2 only are correct
c. 2 and 3 only are correct
D. 1 only is correct


The maximum number of jets generally employed in an impulse turbine without jet interference are
\( A \cdot 6 \)
B. 5
\( c \cdot 7 \)
D. 8


The angular momentum of a disc of radius R about an axis, passing through its centre of mass perpendicular to the plane and rotating
with an angular velocity \( \omega \) will be
\( \mathbf{A} \cdot m R^{2} \omega \)
B. \( 2 m R^{2} \omega^{\text {( }} \)
\( \mathbf{c} \cdot 1 / 2 m R^{2} \omega \)
D. \( m R^{2} / 4 \omega \)


The weight of the body immersed in a liquid appears to be than its actual
weight.


Find the values of \( x \) satisfying \( [x]-1+ \)
\( x^{2} \geq 0 ; \) where [.] denotes the greatest
integer function.
A \( . x \in(-\infty,-\sqrt{3}] \cup[1, \infty) \)
B . \( x \in(-\infty,-\sqrt{2}] \cup[2, \infty) \)
c. \( x \in(-\infty,-3] \cup[3, \infty) \)
D. \( x \in(-\infty,-\sqrt{3}] \cup[3, \infty) \)


Write \( \tan \theta \) in terms of \( \sin \theta \)


A printer can print 54,000 pages in 24 hours. then the function \( f(x)=2,250 x \)
represents
A. The number of pages the printer can print in \( x \) days
B. The number of pages the printer can print in \( x \) hours
c. The number of days it takes the printer to print \( x \) pages
D. The number of hours it takes the printer to print \( x \) pages


A sinusoidal voltage \( V=200 \sin 314 t \)
is appiled to a \( 10 \Omega \) resistor. Find (i)
rms voltage
(ii) rms current and (iii)
power dissipated as heat.


Collectors are the substances which
combine with sulphide ore and make
them water repellant. Which of the following substance can act as collector?
A. Sodium ethyl xanthate
B. Sodium xenate
c. Sodium pyrophosphate
D. Adsorption


The element having most stable oxidation state +2 is
A. \( Q \)
B.
\( c \cdot s \)
D. T


The sum of all integers between 81 and
719 which are divisible by 5 is
\( \mathbf{A} \cdot 51800 \)
B. 50800
c. 52800
D. None of these


The value of the integral \( \int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\left(\frac{1+\sin 2 x+\cos 2 x}{\sin x+\cos x}\right) d x \) is equal
to
A . 16
B. 8
\( c \cdot 4 \)
\( D \)


Two strings \( A \) and \( B \) have lengths \( i_{A} \)
and \( l_{B} \) and carry pendulum of masses
\( M_{A} \) and \( M_{B} \) at their lower ends the
upper ends being supported by rigid
supports. If \( n_{A} \) and \( n_{B} \) are their
frequencies of their oscillations and
\( \boldsymbol{n}_{\boldsymbol{A}}=\boldsymbol{2} \boldsymbol{n}_{\boldsymbol{B}}, \) then :
A \( . l_{A}=4 l_{B} \), regardless of masses
B . \( l_{B}=4 l_{4}, \) regardless of masses
C . \( M_{A}=2 M_{B}, l_{A}=2 l_{B} \)
D. \( M_{B}=2 M_{A}, l_{B}=2 l_{A} \)


Which of the following could act as a propellant for rockets?
A. liquid hydrogen + liquid nitrogen
B. liquid oxygen + liquid argon
c. liquid hydrogen + liquid oxygen
D. liquid nitrogen + liquid oxygen


Which of the following mixtures in aqueous solution of equimolar concentration acts as a buffer solution?
A. \( H N O_{3}+N a O H \)
в. \( H_{2} S O_{4}+K O H \)
c. \( N H_{4} O H(\text {excess})+H C l \)
D. \( C H_{3} C O O H+N a O H(e x c e s s) \)


A point \( P \) moves in counter-clockwise
direction on a circular path as shown in
the figure. The movement of \( ^{\prime} \boldsymbol{P}^{\prime} \) is such
that it sweeps out a length \( s=t^{3}+5 \)
where \( s \) is in metres and \( t \) is in seconds.
The radius of the path is 20 m. The
acceleration of \( ^{\prime} \boldsymbol{P}^{\prime} \) when \( \boldsymbol{t}=\mathbf{2} \boldsymbol{s} \) is
nearly.
A \( \cdot 13 m / s^{2} \)
B \( \cdot 12 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 7.2 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 14 \mathrm{m} / \mathrm{s}^{2} \)


Centre of gravity of geometrical shaped objects will lie:
A. At its periphery
B. At its centre
c. outside it
D. None


The magnetic field around a currentcarrying coil lasts.
A. For three hours
B. As long as current flows thorugh it
c. Till its half-life period
D. Field is permanent


ABC represents the principal cross-
section of an equilateral prism made
with a transparent material. If PQRS
indicates the path of a light ray, find the refractive index of the material.
A \( \cdot \frac{1}{\sqrt{2}} \)
B. \( \frac{2}{\sqrt{3}} \)
\( c \cdot \sqrt{2} \)
D. \( \frac{\sqrt{3}}{2} \)


In each of the exercises 1 to 3 , form a
differential equation representing the given family of curves by eliminating arbitrary constants \( a \) and \( b \)
1. \( \frac{x}{a}+\frac{y}{b}=1 \)
2. \( y^{2}=a\left(b^{2}-x^{2}\right) \)
3. \( \boldsymbol{y}=\boldsymbol{a} e^{3 x}+\boldsymbol{b} e^{2 x} \)


The natural rubber is the polymer of
A . 1,3 -butadiene
B. polyamide
c. isoprene
D. none of the above


Find the value of \( \sum_{n=0}^{100} i^{n !}(\text {where}, i= \)
\( \sqrt{-1}) \)


When potassium ferrocyanide crystals
are heated with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) the gas
evolved is:
\( A \cdot S O_{2} \)
B. \( N H_{3} \)
\( c \cdot C O_{2} \)
D. \( C O \)


The current does not rise immediately
in a circuit containing inductance
A. because of induced emf
B. because of high voltage drop
c. because of low power consumption
D. because of joule heating


\( \int 7^{7^{7^{x}}} \cdot 7^{7^{x}} \cdot 7^{x} d x= \)
\( ^{\mathbf{A}} \cdot \frac{7^{7^{7^{x}}}}{(\log 7)^{3}}+C \)
в. \( \frac{7^{7^{7}}}{(\log 7)^{2}}+C \)
C \( \cdot 7^{7^{7^{x}}} \cdot(\log 7)^{3}+C \)
D・ \( 7^{7^{7}} \)


When photons of energy \( 4.25 e V \) strike
the surface of a metal \( A \), the ejected
photo-electrons have maximum kinetic
energy, \( \boldsymbol{T}_{A}(\text { expresses in } \boldsymbol{e} \boldsymbol{V}) \) and de
Broglie wavelength \( \lambda_{A} \). The maximum
kinetic energy of photoelectrons liberated from another metal \( B \) by
photons of energy \( 4.70 e V \) is \( T_{B}=T_{A}- \)
1.50 \( e V \). If the de-Broglie wavelength of
these photo-electrons is \( \lambda_{B}=2 \lambda_{A}, \) then
which is not correct?
A. The work function of \( A \) is \( 2.25 e V \)
B. The work function of \( B \) is \( 1.20 e V \)
\( \mathbf{c} \cdot T_{A}=2.00 e V \)
D. \( T_{B}=0.5 e V \)


When an object is accelerated:
A. its direction must be constant
B. its velocity is necessarily changing
c. its velocity is constant
D. its speed is necessarily changing


Which of the following is a redox reaction?
A . Reaction of \( H_{2} S O_{4} \) with \( N a O H \)
B. In atmosphere, formation of \( O_{3} \) from \( O_{2} \) by lightening
c. Formation of oxides of nitrogen from nitrogen and oxygen by lightening
D. Evaporation of \( H_{2} O \)


Balanced chemical equations for the following:
Monochloro ethane is hydrolysed with
aqueous KOH:
A \( \cdot C H_{3} C H_{2} C l+K O H \rightarrow C_{2} H_{5} O H+H C l+K_{2} O \)
в. \( C H_{3} C H_{2} C l+K O H \rightarrow C_{2} H_{3} O H+K C l+H_{2} O \)
c. \( C H_{3} C H_{2} C l+K O H \rightarrow C_{2} H_{3} C l+K O H+H_{2} \)
D. \( C H_{3} C H_{2} C l+K O H \rightarrow C_{2} H_{5} O H+K C l+H_{2} O \)


Assuming that \( m \ll M, \) find at what
distance \( x \) from the upper end of the rod
the bullet must strike for the
momentum of the system "bullet-rod" to remain constant during the impact.
A \( \cdot x \approx \frac{1}{3} l \)
в. \( x \approx \frac{4}{3} l \)
c. \( _{x} \approx \frac{4}{5} l \)
D. \( _{x} \approx \frac{2}{3} l \)


A load of \( 10 k N \) is supported from a
pulley which in turn is supported by a rope of sectional area, \( 1 \times 10^{3} m m^{2} \)
and modulus of elasticity \( 10^{3} N m m^{-2} \) as shown in Fig. 5.18. Neglecting the friction at the pulley, determine the deflection of the load is \( x+0.75 m m \)
Find \( \boldsymbol{x} \)


Formation of anion from a neutral atom
\( X \) is favoured by :
A. high electron affinity
B. large size of \( X \)
c. low ionisation potential
D. high charge on anion \( X \)


A particle of mass \( M \) at rest decays
into two particles of mass \( m_{1} \) and \( m_{2} \)
having non-zero velocities. The ratio of
the de-Broglie wavelength of the
particles, \( \lambda_{1} / \lambda_{2} \) is:
\( \mathbf{A} \cdot m_{1} / m_{2} \)
в. \( m_{2} / m_{1} \)
\( c .1 .0 \)
D. none of these


A pulse of light of duration 100 ns is
absorbed completely by a small object initially at rest. Power of the pulse is
\( 30 m W \) and the speed of light \( 3 x \)
\( 10^{8} m / s . \) The final momentum of the
object is
В . \( 1.0 \times 10^{-17} \mathrm{kg} \mathrm{ms}^{-1} \)
c. \( 3 \times 10^{-17} k g m s^{-1} \)
D. \( 9.0 \times 10^{-17} \) в \( g \) ms \( ^{-1} \)


Does the value of resistance of a
conductor depend upon the potential difference applied across it or current
passes through it?


Select the cells that transports
potassium ions and water in the presence of sunlight and low concentrations of carbon dioxide and
make them rigid.
A. Tracheids and vessel elements
B. Guard cells
c. Parenchyma cells
D. sieve tube members and companion cells
E. Sclerenchyma cells


Which of the following sets of quantum numbers is correct for an electron in \( 4 f \)
orbital?
A \( . n=4, l=3, m=+4, s=+1 / 2 \)
в. \( n=4, l=4, m=-4, s=-1 / 2 \)
c. \( n=4, l=3, m=+1, s=+1 / 2 \)


\( \boldsymbol{\alpha}- \) Helix structure of
polypeptide contains:
A. intermolecular hydrogen bonds
B. intramolecular hydrogen bonds
\( c . \) both \( A \) and \( B \)
D. none of these


A telescope makes use of
A. convex lenses
B. concave lenses
C. either convex or concave lenses
D. neither convex nor concave lenses


An open box of height \( 1 m \) is placed near
a \( 2 m \) high table as shown. Marble
rolling on the table leaves the table and
are collected in the box \( u_{\max } \) and \( u_{\text {min }} \)
are the minimum and maximum values
of velocity of marbles to fall into the box.
Find the value of \( u_{\max }-u_{\min }(\text { in } \boldsymbol{m} / \boldsymbol{s}) \)


A wheel rotating at an angular speed of
\( 20 \mathrm{rad} s^{-1}, \) is brought to rest by a constant torque in 4s.If the M.l is 0.2 kg \( m^{2}, \) the work done in first \( 2 s \) is:
\begin{tabular}{l}
A \( .50 \mathrm{J} \) \\
\hline
\end{tabular}
в. \( 30 J \)
\( c .20 J \)
D. 10 J


In a nuclear reactor, what is the
function of the control rods?


Give reasons
All masses cannot be measured in
Kilogram.


On which day is the whole disc of the Moon visible?
A. New moon day
B. Full moon day
c. Half moon day
D. crescent moon day


Which action of prism is used in a
slide projector
A. it deviate a ray of light through \( 180^{\circ} \)
B. it erect the inverted image without deviation
C . it deviate a ray of light through \( 90^{\circ} \)
D. All


A bulb is connected to an ideal battery
of emf \( 10 \mathrm{V} \) so that the resulting current is \( 10 \mathrm{mA} \). When the bulb is connected to
\( 220 \mathrm{V} \) mains (ideal), the current is 50
mA. choose the correct alternative
A. the resistance of the bulb is 1 k ohm and in the second case, it is \( 4.4 \mathrm{k} \) ohm
B. it is not possible since ohm's law is not followed
c. the increase in resistance is due to heating of the filament of the bulb when it is connected to \( 220 \mathrm{v} \) main
D. none of these


The correct sequence of involvement of the following in non-cyclic electron transport
(i) PC (ii) PQ (iii) Pheo (d) Fd is
\( \mathbf{A} \cdot \) ii, i, i, iii, iv
B. iii, ii, iv, i
c. iv , i, ii, iii
D. iii, ii, i, iv


Q Type your question
wire \( A C \) is \( 100 \mathrm{cm} . X \) is a standard
resistor of \( 4 \Omega \) and \( Y \) is a coil. When Y is
immersed in melting ice the null point
is at \( 40 \mathrm{cm} \) from point A. When the coil
Yis heated to \( 100^{\circ} \mathrm{C}, \) a \( 78 \Omega \) resistor has
to be connected in parallel with Y in order to keep the bridge balanced at the
same point. Temperature coefficient of resistance ofthe coil is
A \( \cdot 6.3 \times 10^{4} K^{1} \)
B . \( 4.3 \times 10^{4} K^{1} \)
c. \( 8.3 \times 10^{4} K^{1} \)
D \( .2 .3 \times 10^{4} K^{1} \)


Explain the mechanism of sexdetermination in humans.


In Thomson's experiment, prove that the ratio of charge to the mass \( (e / m) \) of an
electron is given by:
\( \frac{e}{m}=\frac{1}{2 V} \cdot \frac{E^{2}}{B^{2}} \)
where the terms have their usual
meaning


If \( \int \frac{d x}{x^{2}+a x+1}=f(g(x))+c, \) then
This question has multiple correct options
A \( \cdot f(x) \) is inverse trigonometric function for \( |a|>2 \)
B . \( f(x) \) is logarithmic function for \( |a|<2 \)
C . \( g(x) \) is quadratic function for \( |a|>2 \)
D \( \cdot f(x) \) is logarithmic function for \( |a|>2 \)


The half-life of a radio-isotope is \( 4 h r . \) If
initial mass of the isotope was \( 200 g \), then mass remaining after \( 24 h r \) will be
A . \( 1.042 g \)
в. \( 2.084 g \)
c. \( 3.125 g \)
D. \( 4.167 g \)


\( \operatorname{In} \) a trapezium \( \boldsymbol{A B C D}, \boldsymbol{A B} \| \boldsymbol{D C} \) and
\( D C=2 A B . E F \) drawn parallel to \( A B \)
cuts \( A D \) in \( F \) and \( B C \) in \( E \) such that \( \frac{B E}{E C}=\frac{3}{4} . \) Diagonal \( D B \) intersects \( E F \)
at \( G . \) Prove that \( \mathbf{7 F E}=\mathbf{1 0 A B} \)


The gyromagnetic ratio of an electron in
sodium atom is:
A. depending upon the atomic number of the atom
B. depending upon the shell number of the atom
C. independent of that orbit it is in
D. having positive value


Given that \( \boldsymbol{K}_{c}=\mathbf{1 3 . 7} \) at \( \mathbf{5 4 6 K} \) for
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
calculate what pressure will develop in a 10 litre box at equilibrium at \( 546 K \)
when 1.00 mole of \( P C l_{5} \) is injected into
the empty box?


Sometimes you see a fountain of water rucshing out of the leaking joints (or holes) in the pipes of main water supply line in the city. Why does it happen?


Calculate the wavelength and energy of radiation emitted for the electronic
transition from infinity to stationary state of the hydrogen.
B. 3.142 \( \times 10^{18} \) 」
C . \( 1.021 \times 10^{18} \mathrm{J} \)
D . 0.536 \( \times 10^{18} \) 」


The figure represents a displacement
time graph of a body moving in a
straight line. The instantaneous velocity
of the body at \( 3 s \) is :
A \( \cdot 4 m s^{-1} \)
B. \( 3 m s^{-1} \)
\( c \)
D. \( 1 \mathrm{ms}^{-1} \)


Find the value of \( 12 x^{3}+x^{3}+x . \) If \( x=3 \)


Boiling point of petrol is:
A. below \( 20^{\circ} \mathrm{C} \)
B . \( 170-120^{\circ} \mathrm{C} \)
c. \( 35-70^{\circ} \mathrm{C} \)
D. 270 - 340 \( ^{\circ} \mathrm{C} \)


\( x, y, \) and \( z \) in the following processes are respectively:-
(i) \( P_{2} O_{5}+x \rightarrow C a_{3}\left(P O_{4}\right)_{2} \)
(ii) \( 2 C u_{2} O+C u_{2} S \rightarrow y+S O_{2} \)
(iii) \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3}+\boldsymbol{3} \boldsymbol{C O} \rightarrow \boldsymbol{z}+\boldsymbol{3} \boldsymbol{C O}_{2} \)
A. 3 Ca, \( C u S O_{4} \), Fe
B . \( 3 C a(O H)_{2}, \) 6Си,Fео
c. \( 3 C a O, 6 C u, 2 F e \)
D. \( 3 \mathrm{CaO}_{2} \), cus, Feo


Find the distance between (8,3) and (3,2)


Which of the following material(s) is/are used in making a solar cell? This question has multiple correct options
A. Silicon
B. Polycrystalline Thin Films
c. Gallium Arsenide
D. Both A and B


Which of the following statement(s) is correct while conducting electricity through vegetable oil?
A. The liquid (vegetable oil) allows the electric current to pass through. since, it is a good conductor of electricity.
B. The circuit of the tester is complete but the bulb does not glow.
c. The circuit of the tester is not complete and hence the bulb does not glow.
D. Both A and B


Photosynthesis is an example of
A. Anabolism
B. Endergonic reactions
c. Both A and B
D. Exergonic reactions


Cis- decalin has lower energy than trans
decalin
What is the reason behind the above
statement?


If the area of a semicircle is \( 84 \mathrm{cm}^{2} \)
then the area of the circle is
A \( \cdot 144 \mathrm{cm}^{2} \)
B. \( 42 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 168 \mathrm{cm}^{2} \)
D. \( 288 \mathrm{cm}^{2} \)


Gas exerts pressure on the walls of
container because the molecules-
A. Are loosing the kinetic energy
B. Are getting stuck to the walls
C. Are transferring their momentum to walls
D. Are accelerated toward walls.


What do you meant by ecosystem?


What do you call the compounds having the same molecular formula but
different structural arrangements of atoms?


A radioactive isotope \( \boldsymbol{X} \) with half life \( 1.5 \times 10^{9} y r \) decays into a stable
nucleus \( Y . A \) rock sample contains both
elements \( X \) and \( Y \) in ratio \( 1: 15 . \) Find
the age of the rock


What is the domain of function \( g \)
defined by a set of ordered pairs as
follows: \( \boldsymbol{g}= \)
\{(3,2),(5,9),(6,9),(11,0)\}
\( \mathbf{A} \cdot\{2,9,9,0\} \)
B \( \cdot\{3,5,6,11\} \)
c. \{3,9,9,11\}
D \( \cdot\{2,5,6,11\} \)


A rectangle DEFG is plotted in \( X Y \) plane. The co-ordinates of D , E , F and G \( \operatorname{are}(2,2),(9,2),(9,10) \) and (2,10)
Find the new co-ordinates of G when
DEFG is rotated \( 270^{\circ} \) around origin. This question has multiple correct options
A \( \cdot(-10,2) \)
B. (10,-2)
c. (10,-1)
D. (10,2)


The plane \( 2 x-(1+\lambda) y+3 z=0 \)
passes through the intersection of the
planes
A. \( 2 x-y=0 \) and \( y+3 z=0 \)
в. \( 2 x-y=0 \) and \( y-3 z=0 \)
c. \( 2 x+3 z=0 \) and \( y=0 \)
D. None of the above


Choose the correct statement(s).
This question has multiple correct options
A. pH of an acidic buffer increases if more salt is added.
B. \( \mathrm{pH} \) of a basic buffer decreases if more salt is added.
C. In a saturated solution, ionic product is equal to its solubility product
D. The term solubility product is only for sparingly soluble salts


A gas 'X', when dissolved in water heat, is evolved. Then solubility of 'X' will increase at:
A. low pressure, high temperature
B. low pressure, low temperature
c. high pressure, high temperature
D. high pressure, low temperature


State biot-savart law in vector from
along with expression.


A charged \( 30 \mu \mathrm{F} \) capacitor is connected to a \( 27 \mathrm{mH} \) inductor. The
angular frequency of free oscillations of the circuit is
A \( \cdot 1.1 \times 10^{3} r a d s^{-1} \)
B. \( 2.1 \times 10^{3} r a d s^{-1} \)
c. \( 3.1 \times 10^{3} r a d s^{-1} \)
D. \( 4.1 \times 10^{3} r a d s^{-1} \)


Choose the correct answer among the alternatives given :
Reproductive health in society can be improved by;
(I) Introduction of sex education in
schools
(II) Increased medical assistance
(III) Awareness about contraception and
STDS
(IV) Equal opportunities to male and female child
(V) Encouraging myths and misconceptions
\( A \cdot(i),(\text { ii) },(i i i),(i v),(v) \)
B. (i), (ii), (iv), (v)
c. (i), (ii), (iii), (iv)
D. (ii), (v)


Which of the following is a volatile liquid at room temperature?
A. Ethanal
B. Ethane
c. Ethene
D. None of these


The number of lines of symmetry in a regular hexagon is
A . 4
B. 5
\( c .6 \)
D. 7


Which of the following phosphorus oxyacids can act as reducing agent?
A. \( H_{3} P O_{3} \)
в. \( H_{3} P O_{4} \)
c. \( H_{2} P_{2} O_{6} \)
D. \( H_{4} P_{2} O_{7} \)


The number of \( P-O H \) bonds and the
oxidation state of phosphorus atom in
pyrophosphoric acid \( \left(\boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}\right) \)
respectively are:
A. Four and five
B. Four and four
c. Five and five
D. Five and four


Preformation's are not found in cell wall
of the following cells.
A. Tracheid
B. Companion cells
c. sieve tube
D. vessels


Hyperconjugation involves overlap of which of the following orbitals?
\( \mathbf{A} \cdot \sigma-\sigma \)
в. \( \sigma-p \)
c. \( p-p \)
D . \( \pi-\pi \)


Stethescope works on the principle of of sound.
A. Refraction
B. Echo
c. Multiple reflection
D. None of the above


The ratio of mean distances of three
planets from the sun are \( 0.5,1,1.5, \) then the square of time periods are in the ratio of:
A. 1: 4: 9
B. 1: 9: 4
c. 1: 8: 27
D. 2: 1: 3


Through the neuron, information travels
as an
A. Electrical impulse
B. Mechanical impulse
c. chemical impulse
D. None of the above


The ratio in which the line joining
(2,-4,3) and (-4,5,-6) is divided by the plane \( 3 x+2 y+z-4=0 \) is
A .2: 1
B. 4: 3
\( c \cdot 1: 4 \)
D. 2: 3


Find the area enclosed between the curves \( \boldsymbol{y}^{2}-\mathbf{2} \boldsymbol{y} e^{s i n^{-1} \boldsymbol{x}}+\boldsymbol{x}^{2}-\mathbf{1}+[\boldsymbol{x}]+ \)
\( e^{2 \sin ^{-1} x}=0 \)
and line \( x=0 \) and \( x=\frac{1}{2} \) is (where [.]
denotes greatest integer function)
A. \( \frac{\sqrt{3}}{4}+\frac{\pi}{6} \)
B. \( \frac{\sqrt{3}}{2}+\frac{\pi}{6} \)
c. \( \frac{\sqrt{3}}{4}-\frac{\pi}{6} \)
D. \( \frac{\sqrt{3}}{2}-\frac{\pi}{6} \)


A vector \( \vec{A} \) points vertically upward and \( \vec{B} \) points towards north. The vector product \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{B}} \) is:
A. null vector
B. along west
c. along east
D. vertically downward


Isopropyl alcohol is heated with suspension of bleaching powder \( \left(-C a O C l_{2}\right) \) with water. The products are:
A. ethane and propane
B. ethyne and ethene
C. trichloromethane and calcium acetate
D. carbon tetrachloride


The value of \( K_{c}=4.24 \) at \( 800 \mathrm{K} \) for the
reaction
\( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \)
Calculate equilibrium concentrations of
\( C O_{2}, H_{2}, C O \) and \( H_{2} O \) at \( 800 \mathrm{K}, \) if any
\( C O \) and \( H_{2} O \) are present initially at
concentration of \( 0.10 \mathrm{M} \) each?


Assertion
Assertion: In a nuclear process mass
gets converted into energy.
Reason Reason: According to Einstein's mass energy equivalence relation, mass m is equivalent to energy \( \mathrm{E} \), given be the
relation \( \boldsymbol{E}=\boldsymbol{m} \boldsymbol{c}^{2} \) where \( c \) is the speed
of light in vacuum.
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
C. If assertion is true but reason is false
D. If both assertion and reason are false.


For certain first-order reaction, \( 75 \% \) of
the reaction complete in 30 min. How much time did it require to complete
\( 99.9 \% \) of the reaction?
A. 150 min
B. 100 min
c. 90 min
D. 300 min


The temperature of 5 mol of a gas which was held at constant volume was
changed from \( 100^{\circ} \mathrm{C} \) to \( 120^{\circ} \mathrm{C} \). The
change in internal energy was found to be 80 . \( J \). The total heat capacity of the gas at constant volume will be equal to
\( \mathbf{A} \cdot 8 J / K \)
в. \( 0.8 \mathrm{J} / \mathrm{K} \)
c. \( 4 J / K \)
D. \( 0.4 J / K \)


Which is responsible for the formation of nucleolus?
A. SAT chromosome
B. Nuclear membrane
c. Endoplasmic reticulum
D. Ribosomes


A bomb of mass 2 kg which is at rest
explodes into three fragments of equal
masses. Two of the fragments are found to move with a speed of \( 1 \mathrm{m} / \mathrm{s} \) each in mutually perpendicular direction. The total energy released during explosion is then
A . 1.5
B. 2 J
c. 4 J
D. 5 J


\( \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C} \boldsymbol{H} \frac{(i) \mathbf{2} \boldsymbol{N} \boldsymbol{a}}{(i i) \mathbf{2} C \boldsymbol{O}_{2}}(\boldsymbol{A}) \frac{\boldsymbol{H}_{2} / \boldsymbol{P} \boldsymbol{d}}{\boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}}(\boldsymbol{B}) \)
What is B?
\( \mathbf{A} \cdot H_{2} C=C H-C O O^{-} N a^{+} \)
\( \mathbf{B} \cdot: H_{3} C-C H_{2}-C O O^{-} N a^{+} \)
\( \mathbf{c} \cdot H_{2} C=C H-C H_{2} O H \)
\( \mathbf{D} \cdot H_{3} C-C H_{2}-C H_{2} O H \)


Let \( \boldsymbol{a}=\overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}-\overline{\boldsymbol{k}}, \overline{\boldsymbol{b}}=\overline{\mathbf{5}} \boldsymbol{i}-\overline{\mathbf{3}} \boldsymbol{j}- \)
\( \mathbf{3 k}, \overline{\boldsymbol{c}}=\overline{\mathbf{3}} \mathbf{i}-\boldsymbol{j}-\mathbf{2} \overline{\mathbf{k}} . \) If collinear with \( \overline{\boldsymbol{c}} \)
and \( |\overline{\boldsymbol{r}}|=|\overline{\boldsymbol{a}}+\overline{\boldsymbol{b}}| . \) Then \( \overline{\boldsymbol{r}} \) equals:
\( \mathbf{A} \cdot \pm 3 c \)
B \( \cdot \pm \frac{3}{2} \sqrt[3]{c} \)
\( c \cdot \pm 2 c \)
\( \mathbf{D} \cdot \pm \frac{3}{2} \overline{4 c} \)


A projectile is fired with the a speed \( u \)
at an angle \( \theta \) above the horizontal field. The coefficient of restitution be tween
the projectile and filed is e. Find the position from the starting point when the projectile will land at its second
collision
A \( \cdot \frac{e^{2} u^{2} \sin 2 \theta}{g} \)
B. \( \frac{\left(1+e^{2}\right) u^{2} \sin 2 \theta}{g} \)
\( ^{\mathbf{C}} \cdot \frac{\left(1+e^{2}\right) u^{2} \sin \theta \cos \theta}{g} \)
D. \( \frac{(1+e) u^{2} \sin 2 \theta}{g} \)


In which of the following animal, post anal tail is found?
A. Earthworm
B. Lower invertebrate
c. Scorpion
D. snake


\( \boldsymbol{a}+\boldsymbol{i} \boldsymbol{b}=(\mathbf{1}+\boldsymbol{i} \sqrt{\boldsymbol{3}})^{300} \) then \( \boldsymbol{a}= \)
and \( b= \)
A .0,1
B . \( 2^{300}, 0 \)
\( c .0,0 \)
D. none of these


If \( D \) is a point on side \( A B \) of \( A B C \) and \( D E \) is a line through D meeting \( A C \) at \( E \) such that \( \Delta A D E \sim \Delta A C B . \) Then \( A B \)
AD is equal to
A . AE. AC
B. AC. DE
c. AE. BC
D. AB. BC


Construct a \( \triangle A B C \) in which \( A B= \)
\( 6 \mathrm{cm}, \angle A=30^{\circ} \) and \( \angle B=60^{\circ} \)
Construct another \( \triangle A B^{\prime} C^{\prime} \) similar to
\( \triangle A B C \) with base \( A B^{\prime}=8 \mathrm{cm} \)


Hari bought \( 20 \mathrm{kg} \) of rice at
Rs.36 per kg and 25 kg of rice at
Rs.32 per kg. He mixed the two verities
and sold the mixture at \( R s .38 \) per \( k g \)
Find his gain per cent in the whole transition.


is the red colour pigment found in algae.


If \( \cos A=\frac{4}{5}, \cos B=\frac{12}{13}, \frac{3 \pi}{2}< \)
\( A, B<2 \pi, \) find the values of the
following.
\( (\mathrm{i}) \cos (\boldsymbol{A}+\boldsymbol{B}) \)
(ii) \( \sin (A-B) \)


Calculate the Avogadro's number using
the charge on the electron \( 1.60 \times \) \( 10^{-19} C \) and the fact that \( 96500 C \)
deposit \( 107.9 g \) silver from its solution.


The dispersed phase and dispersion medium in soap lather are respectively:
A. gas and liquid
B. liquid and gas
c. solid and gas
D. solid and liauid


If \( \boldsymbol{x}=\boldsymbol{p} \sec \boldsymbol{\theta} \) and \( \boldsymbol{y}=\boldsymbol{q} \tan \boldsymbol{\theta}, \) then
\( \mathbf{A} \cdot x^{2}-y^{2}=p^{2} q^{2} \)
B . \( x^{2} q^{2}-y^{2} p^{2}=p q \)
c. \( x^{2} q^{2}-y^{2} p^{2}=\frac{1}{p^{2} q^{2}} \)
D . \( x^{2} q^{2}-y^{2} p^{2}=p^{2} q^{2} \)


Assertion
In a 'tug-of-war' game, both teams exert force on the other through the rope.
Reason

The team that pulls the rope harder wins.
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 roots of the equation \( a x^{2}+b x+ \)
\( c=0 \) will be imaginary if
A. \( a>0, b=0, c<0 \)
В. \( a>0, b=0, c>0 \)
c. \( a=0, b>0, c>0 \)
D. \( a>0, b>0, c=0 \)


The emf of the cell involving the following reaction, \( 2 A g^{+}+H_{2} \longrightarrow \)
\( 2 A g+2 H^{+} \) is 0.80 volt. The standard
oxidation potential of silver electrode is:
B. \( 0.50 \mathrm{v} \)
c. \( -0.30 v \)
D. \( 0.40 \mathrm{v} \)


A student tested the \( p H \) of distilled
water and found that the colour of \( p H \) paper changed to green. He checked the \( p H \) again after dissolving a pinch of
common salt in water. The colour of the
\( \boldsymbol{p} \boldsymbol{H} \) paper this time was:
A. green
B. yellow
c. red
D. blue


In the third energy level, the number of orbtials are:
A. 7
B. 8
\( c \cdot 9 \)
\( D \)


In the power assisted kind of brake the bellows applies force to master cylinder
piston
A. Through diaphragm linkage
B. Directly
c. Through mechanical linkage
D. Through kinetic linkage


Which one is correct about bulliform/
motor cell?
A. It is seen in grasses
B. It is large-sized, colorless, vacuolate cells on the adaxial surface of monocot leaf
c. Both of the above
D. None of the above


By selling a scooter for Rs.9, \( 200, \) a man gains \( 15 \% \). Find the cost price of the
scooter


In hydrogen atom electron of charge \( -e \) and mass m revolves round the nucleus
in a circular orbit of radius r. The
electrostatic potential energy of the electron is \( \frac{1}{4 \pi \varepsilon_{0}} \) times
A \( \cdot \frac{-e}{r} \)
B. \( \frac{-e^{2}}{r} \)
c. \( \frac{e^{2}}{r} \)
D. \( \frac{-m e^{2}}{r} \)


Surface tension is responsible for
A. Lower layer of water has lower veocity
B. A small needle can be made to float on the surface of water
C. Higher layer of water has lower veocity
D. None of these


The outermost electronic configuration of the most electronegative element is:
\( \mathbf{A} \cdot n s^{2} n p^{3} \)
В \( \cdot n s^{2} n p^{4} \)
c. \( n s^{2} n p^{5} \)
D. \( n s^{2} n p^{6} \)


A reflecting telescope has a large mirror for its objective with radius of curvature equal to \( 80 \mathrm{cm} . \) The magnifying power of this telescope if eye piece used has a focal length of \( 1.6 \mathrm{cm} \) is:
A . 100
B. 50
\( c \cdot 25 \)
D. 5


\( \frac{C_{1}}{C_{0}}+2 \cdot \frac{C_{2}}{C_{1}}+3 \cdot \frac{C_{3}}{C_{2}}+\dots+n \cdot \frac{C_{n}}{C_{n-1}}= \)
A. \( \frac{n(n+1)}{2} \)
в. \( \frac{n(n-1)}{2} \)
c. \( \frac{(n-1)(n+1)}{2} \)
D. \( \frac{n(n+2)}{2} \)


Loss of reproductive capacity in women after age of 45 years is called
A. Mensturation
B. Ageing
c. Menopause
D. Menarche


A mirror faces the negative x-axis. (Normal to its reflecting surface is \( -\hat{\mathbf{i}} \) )
While a particle starts moving such that its image is formed in the mirror.
At a certain instant the velocity of the particles is \( 3 \hat{i}+4 \hat{j}+5 \hat{k} \) and that of the mirror is \( \hat{\mathbf{1}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) Choose the correct
options.
This question has multiple correct options
A. Magnitude of relative velocity of the image w.r.t mirrror is \( \sqrt{45} \)
B. Magnitude of relative velocity of image w.r.t object is 4
C. Magnitude of relative velocity of image w.r.t mirrror is \( \sqrt{45} \)
D. Absolute velocity of the image w.r.t ground is \( \sqrt{42} \)


The cells named podocytes occur in
A. Inner wall of Bowman's capsule
B. Outer wall of Bowmans capsule
C . Large intestine
D. Neck region of nephrons


Two galvanometers \( A \) and \( B \) require
\( 3 m A \) and \( 6 m A \) respectively, to produce the same deflection of 10 divisions.
Then is,
A. \( A \) is more sensitive than \( B \)
B. \( B \) is more sensitive than \( A \)
c. \( A \) and \( B \) are equally sensitive
D. Sensitiveness of \( B \) is twice that of \( A \)


Which of the following can be made
passive?
¡) Fe
ii) Co
iii) Ni
iv) \( \mathrm{Cr} \)
A . i, ii, iii and iv
B. Only i and ii
c. only iii and iv
D. only i, ii and iii


Which one of the following is wrong for
fungi?
A. They are heterotrophic.
B. They are both unicellular and multicellular.
C. They are eukaryotic.
D. All fungi posses a purely cellulosic cell wall.


Carbon monoxide is more effective
reducing agent than carbon below 983 K but above this temperature the
reverse is true. If true enter 1 else 0
A


For a certain distribution, \( M . D . \) about
mean is \( 77 . \) If each item is reduced by
\( \mathbf{2 0}, \) what effect would this have on mean
deviation?


Using differentials, find the approximate value of \( \left(\frac{17}{81}\right)^{\frac{1}{4}} \)


Find the area of the region bounded by
the curves \( \boldsymbol{y}=\boldsymbol{x}^{2}, \boldsymbol{y}=\mathbf{2}-\boldsymbol{x} \) and \( \boldsymbol{y}=\mathbf{1} \)


A rectangular carbon block has
dimensions \( 1.0 \mathrm{cm} \times 1.0 \mathrm{cm} \times 50 \mathrm{cm} \)
Resistance are measured first across
two square ends and then across two
rectangular ends, respectively. If
resistivity carbon is \( 3.5 \times 10^{-5} \Omega m \)
then value of measured resistances
respectively are
\( \mathbf{A} \cdot 17.5 \times 10^{-2} \Omega, 7 \times 10^{-5} \Omega \)
B . \( 7 \times 10^{-5} \Omega, 7.5 \times 10^{-2} \Omega \)
C. \( 17.5 \times 10^{-4} \Omega, 7 \times 10^{-7} \Omega \)
D. \( 7.5 \Omega, 7 \times 10^{-2} \Omega \)


Convert speed into \( k m / h \)
\( 7.5 m / s \)


Represent \( \frac{-3}{4} \) on number line


Which of the following is a solid at room temperature?
A \( \cdot \mathrm{Cl}_{2} \)
B. Bra
\( \mathbf{c} \cdot I_{2} \)
D. \( \mathrm{F}_{2} \)


If the roots of the equation \( x^{2}+p x+ \)
\( c=0 \) are (2,-2) and the roots of the
equation \( \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{q}=\mathbf{0} \) are \( (-\mathbf{1},-\mathbf{2}) \)
then the roots of the equation \( x^{2}+ \)
\( b x+c=0 \) are
A \( .-3,-2 \)
в. -3,2
c. 1,-4
D. -5,1


Which of the following connects to bone to a bone?
A. Cartilage
B. Ligament
c. Tendon
D. Interstitial fluid


If \( \sqrt{3} \tan \theta=3 \sin \theta, \) find the value of
\( \sin ^{2} \theta-\cos ^{2} \theta \)


Which one of the four hexagons is not
similar to the other three?
\( A \)
B. B
\( c \cdot c \)
D.


A copper rod with length \( 1.4 \mathrm{m} \) and area
of cross-section of \( 2 \mathrm{cm}^{2} \) is fastened to a
steel rod with length L and cross-
sectional area \( 1 \mathrm{cm}^{2} . \) The compound rod
is subjected to equal and opposite pulls
of magnitude \( 6.00 \times 10^{4} \mathrm{N} \) at its ends.
What is the strain in each rod? \( \left[\boldsymbol{Y}_{\text {steel}}=\right. \) \( \left.\mathbf{2} \times \mathbf{1 0}^{11} \boldsymbol{P a} ; \boldsymbol{Y}_{C U}=\mathbf{1 . 1} \times \mathbf{1 0}^{\mathbf{1 1}} \boldsymbol{P a}\right] \)


All triploblastic animals are?
A. Eucoelomated
B. Bilateral symmetry
c. schizocoelomates
D. Pseudocoelomates


The reduction potential of a hydrogen electrode at \( p H 10 \) at \( 298 K \) is \( :(P= \)
1 \( (a t m) \)
A. 0.51 volt
B. 0 volt
c. 0.591 volt
D. 0.059 volt


\( A \) and \( B \) are friends and their ages differ
by 2 years. A's father D is twice as old as A and B is twice as old as his sister \( C \).
The age of \( D \) and \( C \) differ by 40 years. Find the ages of \( A \) and \( B \)


A racemic mixture has:
A. \( (+) \) effect on the plane polarised light
B. (-) effect on the plane polarised light
C. no effect on the plane polarised light
D. may be any of (A) or (B)


\( \sec A=\frac{12}{5} \) for some value of angle \( A \)
A. True
B. False


A hollow hemispherical bowl of thickness \( 1 \mathrm{cm} \) has an inner radius of 6
\( \mathrm{cm} . \) Find the volume of metal required to make the bowl.


If \( A=\operatorname{diag}(1,-1,2) \) and \( B= \)
\( \operatorname{diag}(2,3,-1) \operatorname{then} 3 A+4 B= \)
\( \operatorname{diag}(a, b, c) . \) Then \( a-b-c= \)


If the velocity of sound in a gas is 360 \( \mathrm{m} / \mathrm{s} \) and the distance between
compression and the nearest rarefraction is \( 1 \mathrm{m} \), then the frequency of sound is
\( A \cdot 90 \mathrm{Hz} \)
в. 180 Н \( z \)
c. 360 нz
D. 720 нz


Explain why objects moving in fluids must have special shapes.


In a primary coil 5 A current is flowing on 220 volts. In a primary coil 5 A current is flowing on 220 volts. the ratio of number of turns in secondary coil and primary coil will be :
A .1: 10
B. 10:
\( c \cdot 1: 1 \)
D. 11:


What is binomial system of nomenclature? Who proposed this
system?


A solenoid of length \( 1 m \) and \( 0.05 m \)
diameter has 500 turns. If a current of
\( 2 A \) passes through the coil, calculate
the co-efficient of self induction of the
coil.


If \( \angle R P Q=45^{\circ}, \) then find \( \angle P Q R \)
\( \mathbf{A} \cdot 15^{\circ} \)
B \( .30^{\circ} \)
\( c \cdot 60^{\circ} \)
D \( .45^{\circ} \)


If \( \boldsymbol{K}_{s p} \) for \( \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \boldsymbol{O}_{4} \) is \( \boldsymbol{6} . \boldsymbol{4} \times 10^{-5}, \) then
solubility of this substance in mole per
\( \boldsymbol{m}^{3} \) is
A \( .8 \times 10^{3} \)
В. \( 6.4 \times 10^{3} \)
c. \( 8 \times 10^{6} \)
D. none of these


Charge is distributed within a sphere of
radius R with a volume charge density \( \rho(r)=\frac{A}{r^{2}} e^{-2 r / a}, \) where \( A \) and a are
constants. If \( Q \) is the total charge of this
charge distribution, the radius R is:
A \( \cdot \frac{a}{2} \log \left(1-\frac{Q}{2 \pi a A}\right) \)
B. \( \operatorname{alog}\left(1-\frac{Q}{2 \pi a A}\right) \)
\( ^{\mathbf{C}} \operatorname{alog}\left(\frac{1}{1-\frac{Q}{2 \pi a A}}\right) \)
\( ^{\mathrm{D}} \cdot_{\overline{2}}^{a} \log \left(\frac{1}{1-\frac{Q}{2 \pi a A}}\right) \)


The property of catenation is strongest in carbon because?
A. Its ionisation potential is low
B. Its electronegativity is low
c. The C-C bond energy is high
D. Its atomic radius is smal


Predict conditions under which \( \boldsymbol{A l} \)
might be expected to reduce \( M g O \)


Which of the following groups contains metals, non-metals and metalloids?
A. Group 17
B. Group 14
c. Group 13
D. Group 12


Gravitational force is a/an
force
A. repulsive
B. attractive
c. contact
D. neutral


Divide \( 6 x^{4}+13 x^{3}+39 x^{2}+37 x+45 \)
by \( 3 x^{2}+2 x+9 \)


There are n different objects, \( 1,2,3,4, \ldots \)
\( n, \) distributed at random in n places
marked \( 1,2,3, \ldots, \) n. If \( p \) is the probability that at least three of the objects occupy
places corresponding to their number, find \( 6 p \)


State Modern periodic law.


Draw electron dot representation for the formation of \( \boldsymbol{H} \boldsymbol{C l} \)


A vector is inclined at \( \frac{\pi}{4} \) rad with \( x \) -axis
\( \& \frac{\pi}{3} \) rad with \( y \) -axis then find angle of vector with z-axis.
\( ^{A} \cdot \frac{2 \pi}{3} r a d \)
в. \( \frac{5 \pi}{3} \) rad
c. \( \frac{\pi}{4} \) rad
D. \( \frac{\pi}{2} \) rad