The emf \( \left(E^{\circ}\right) \) of the following cells are:
\( \boldsymbol{A} \boldsymbol{g} / \boldsymbol{A} \boldsymbol{g}^{+}(\mathbf{1} \boldsymbol{M}) \| \)
\( \boldsymbol{C u}^{2+}(\mathbf{1} \boldsymbol{M}) \mid \boldsymbol{C u} ; \boldsymbol{E}^{\circ}=-\mathbf{0 . 4 6} \boldsymbol{v o l t} \)
\( \boldsymbol{Z} \boldsymbol{n} / \boldsymbol{Z} \boldsymbol{n}^{\boldsymbol{2}+}(\boldsymbol{1} \boldsymbol{M}) \| \)
\( \boldsymbol{C u}^{2+}(\mathbf{1} \boldsymbol{M}) \mid \boldsymbol{C u} ; \boldsymbol{E}^{\circ}=+\mathbf{1 . 1 0} \boldsymbol{v o l t} \)
Calculate the emf of the cell:
\( \boldsymbol{Z} \boldsymbol{n}\left|\boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{1} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{g}^{+}(\boldsymbol{1} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{g} \)


Why does \( H^{+} \) ion always get
associated with other atoms or
molecules?
A. Ionisation enthalpy of hydrogen resembles that of alkali metals.
B. Its reactivity is similar to halogens
C. It resembles both alkali metals and halogens
D. Loss of an electron from hydrogen atom results in a nucleus of very small size as compared to other atoms or ions. Due to small size it cannot exist free


Explain Rosenmund's reduction of benzoyl chloride.


In the circuit, \( 5 \Omega \) resistor develops
\( 45 \mathrm{J} / \mathrm{s} \) due to current flowing through it.
The power developed per second across
\( 12 \Omega \) resistor is:
\( A \cdot 16 w \)
B. 192W
\( c \cdot 36 w \)
D. \( 64 w \)


Addition of non-metals like \( B \) and \( C \) to
the interstitial sites of a transition
metal results the metal:
This question has multiple correct options
A. of more ductability
B. of less ductability
c. Less malleable
D. of more hardness


Let \( a, b, c \) are non zero constant number
then the value of
\( \lim _{r \rightarrow \infty} \frac{\cos \frac{a}{r}-\cos \frac{b}{r} \cos \frac{c}{r}}{\sin \frac{b}{r} \sin \frac{c}{r}} \) is?
\( ^{\mathbf{A}} \cdot \frac{a^{2}+b^{2}-c^{2}}{2 b c} \)
B. \( \frac{c^{2}+a^{2}-b^{2}}{2 b c} \)
c. \( \frac{b^{2}+c^{2}-a^{2}}{2 b c} \)
D. Independent of \( a, b \) and \( c \)


A good absorber is a good
A. Emitter
B. Radiator
C. Emitter and Absorber both
D. None


Coracoid is component of
\( A \). Fore limb
B. Skull
C . Pectoral girdle
D. Pelvic girdle


If the eccentricity of an ellipse is \( \frac{5}{8} \) and
the distance between its foci is \( 10, \) then
find the latus rectum of the ellipse.


Name two factors on which the internal
resistance of a cell depends.
This question has multiple correct options
A. separation between plates
B. emf of cell
c. area of plates
D. external resistance.


(i) State Ohm's law.
(ii) A metal wire of resistance \( 6 \Omega \) is
stretched so that its length is increased to twice its original length. Calculate its new resistance.


Electric force \( \quad \) on the nature of
the medium between the charges.
A. depends
B. does not depend
c. sometimes depends
D. None of these


STATEMENT -1: Roots of the quadratic equation \( 3 x^{2}-2 \sqrt{6}+2=0 \) are same
STATEMENT -2: A quadratic equation
\( a x^{2}+b x=c=0 \) has two distinct real
roots, if \( b^{2}-4 a c>0 \)
A. Statement - 1 is True, Statement- - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement- -
c. statement- 1 is True, Statement - 2 is False
D. Statement-1 is False, Statement- - 2 is True


Write the equation of reaction of chlrobenzene:
Alkylation


I: Physical properties of ice, water, and
steam are very different.
2: Chemical composition of water is different in all three states. Explain.
A . only 1 is true
B. only 2 is true
c. both are true
D. both are false


State the difference between: acid
radical and basic radical


A point on the line \( \frac{\boldsymbol{x}+\mathbf{2}}{\mathbf{1}}=\frac{\boldsymbol{y}-\mathbf{3}}{-\mathbf{4}}= \)
\( \frac{z-1}{2 \sqrt{2}} \) at a distance 6 from the point \( (2, \)
3, 1) is
A \( \cdot(4-21,1+12 \sqrt{2}) \)
В. \( \left(\frac{-4}{5}, \frac{-9}{5}, 1\right) \)
C \( \cdot\left(\frac{-16}{5}, \frac{39}{5}, \frac{5-12 \sqrt{2}}{5}\right) \)
D. \( \left(\frac{-16}{5},-21,1+12 \sqrt{2}\right) \)


The catalyst used for olefin polymerisation is:
A. zieger-Natta Catalyst
B. Raney Nickel Catalyst
c. wilkinson Catalyst
D. Merrifield Resin


Range of \( f(x)=\frac{\sec x+\tan x-1}{\tan x-\sec x+1} \)
\( \boldsymbol{x} \epsilon\left(\mathbf{0}, \frac{\pi}{2}\right) \) is
A \( .(0,1) \)
B. \( (0, \infty) \)
c. (-1,0)
D. \( (-\infty,-1) \)


In an electromagnetic wave
A. Power is equally transferred along the electric and magnetic fields
B. Power is transmitted in a direction perpendicular to both the fields
C. Power is transmitted along electric field
D. Power is transmitted along magnetic field


What are real and virtual images? How will you find out whether an image is
real or virtual ? Can a virtual image be obtained on a screen?


The cross-section of a canal is
trapezium in shape. The canal is \( 12 m \) wide at the top and \( 8 m \) wide at the
bottom. If the area of the cross-section
is \( 840 s q . m, \) the depth of the canal is:
\( \mathbf{A} \cdot 8.75 m \)
в. \( 42 m \)
\( c .63 m \)
D. \( 84 m \)


Which of the following is/are correct? This question has multiple correct options
A. Warm air rises
B. Cold air rises
c. cold air sink
D. Both A and B


\( \ln \) a G.P., \( t_{2}=\frac{3}{5} \) and \( t_{3}=\frac{1}{5} . \) Then the
common ratio is
A \( \cdot \frac{1}{5} \)
B. \( \frac{1}{3} \)
c. 1
D.


In how many different ways can the letters of the word I KURUKSHETRA' be
arranged?


Find the centre of mass of a triangular lamina.


Two forces act at the vertex \( \mathbf{A} \) of
quadrilateral ABCD represented by \( A B, \overline{A D} \) and two at \( C \) represented by \( C D \) and \( \overline{C B} . \) If \( \mathrm{E}, \mathrm{F} \) are mid points of \( A C \) and \( \overline{B D} \) respectively, then their resultant is
A. \( \overline{E F} \)
в. \( 2 \overline{E F} \)
c. \( \frac{3}{2} \overline{E F} \)
D. \( 4 \overline{E F} \)


Match the methods of nutrition of
special organs with suitable examples.
cuscuta Autotrophs Mycorrhiza Parasites Chlorophyll Monotropa Saprophytes \( \quad \) Haustoria Hibiscus 1


A body is thrown vertically up to reach its maximum height in \( t \) seconds. The
total time from the time of projection to reach a point at half of its maximum height while returning ( in seconds) is
A \( \cdot \sqrt{2} t \)
B. \( \left[1+\frac{1}{\sqrt{2}}\right] t \)
c. \( \frac{3 t}{2} \)
D. \( \frac{t}{\sqrt{2}} \)


Which of the following test cannot be used for identifying amino acids?
A. Biuret test
B. xanthoproteic test
c. Barfoed test
D. Ninhydrin test


Average atomic weight of boron is 10.10 and boron exists in two isotopic forms
\( B^{10} \) and \( B^{11} . \) The percentage abundance
of \( B^{10} \) is?
A . \( 10 \% \)
B. \( 90 \% \)
c. \( 50 \% \)
D. 20\%


\( k g m s^{-1} \) is the Sl unit of
A. Impulse
B. Force
c. Angular velocity
D. None of these


Which of the following equimolar solution have highest vapour pressure?
A. Glucose
B. \( N a C l \)
c. \( K_{2} S O_{4} \)
D. \( K_{4} \) Fe \( (C N)_{6} \)


Given two characteristics of EM waves.


If the whole bi-prism experiment is immersed in water then the fringe width becomes, if the refractive indices
of bi-prism material and water are 1.5 and 1.33 respectively,
A. 3 times
B. \( \frac{3}{4} \) times
c. \( \frac{4}{3} \) times
D. \( \frac{1}{3} \) times


The value of \( 4 \cos ^{2} \frac{\pi}{3}+\sec ^{2} \frac{\pi}{6}-\sin ^{2} \frac{\pi}{4} \)
is
A \( \cdot \frac{13}{6} \)
в. \( \frac{11}{6} \)
\( c \cdot \frac{7}{6} \)
D.


Find the value of \( k \) so that
\( \boldsymbol{f}(\boldsymbol{x})\left\{\begin{array}{ll}\boldsymbol{k} \boldsymbol{x}+\mathbf{1} & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x} \leq \boldsymbol{\pi} \\ \cos \boldsymbol{x} & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x}>\pi\end{array}\right. \)
continuous at \( \boldsymbol{x}=\boldsymbol{\pi} \)


Which of the following statements is
true?
\( \mathbf{A} \cdot F-N-F \) angle in \( N F_{3} \) is greater than \( H-N-H \)
angle in \( N H_{3} \)
B. \( F-N-F \) angle in \( N F_{3} \) is smaller than \( H-N-H \)
angle in \( N H_{3} \)
\( \mathbf{c} \cdot H-O-H \) angle in \( H_{2} O \) is greater than \( H-N-H \)
angle in \( N H_{3} \)
D. \( F-O-F \) angle in \( F_{2} O \) is greater than \( H-O-H \)
angle in \( H_{2} O \)


Which of the following gas is lightest?
A. Dihydrogen
B. Helium
c. Dinitrogen
D. Dioxygen


Assertion
n electrolysis, the quantity of electricity needed for depositing 1 mole of silver is different from that required for 1 mole
of copper.
Reason
The molecular weights of silver and
copper are different.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A long horizontally fixed wire carries a
current of 100 ampere. Directly above and parallel to it is a fine wire that
carries a current of 20 ampere and
weights 0.04 newton per meter. The distance between the two wires for
which the upper wire is just supported by magnetic repulsion is:
\( \mathbf{A} \cdot 10^{-2} m m \)
B. \( 10^{-2} \mathrm{cm} \)
\( \mathrm{c} \cdot 10^{-2} \mathrm{m} \)
D. \( 10^{-2} k m \)


Which of the following statements are true (T) and which are false (F)?
In a parallelogram, the diagonals intersect each other at right angles.
A . True
B. False


A man getting down a running bus, falls
forward because:
A. due to inertia of rest, road is left behind and man reaches forward
B. due to inertia of motion upper part of body continues to be in motion in forward direction while feet come to
rest as soon as they touch the road
C. he leans forward as a matter of habit
D. of the combined effect of all the three factors stated in
(A), (B) and (C)


Two particles are moving along two long straight lines, in the same plane with
same speed \( 20 \mathrm{cm} / \mathrm{s} \). The angle
between the two lines is \( 60^{\circ} \) and their
intersection point is \( O . A t \) a certain
moment, the two particles are located at distance \( 3 m \) and 4 m from \( O \), and
are moving towards \( 0 . \) Subsequently,
the shortest distance between them will
be
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( 40 \sqrt{2} \mathrm{cm} \)
\( \mathbf{c} \cdot 50 \sqrt{2} \mathrm{cm} \)
D. \( 50 \sqrt{3} \mathrm{cm} \)


In which group of fungi, the zoospores possess two oppositely directed flagella, one whiplash and another
tinsel type?
A. Ascomycetes
B. Zygomycetes
c. oomycetes
D. Deuteromycetes


Atoms of different elements having the same mass number are known as:
A. isotopes
B. isobars
c. isotones
D. isomers


\( \lim _{n \rightarrow \infty}\left[\frac{1}{2 n}+\frac{1}{\sqrt{4 n^{2}-1}}+\frac{1}{\sqrt{4 n^{2}-4}}+. .\right. \)
is equal to
A \( \cdot \frac{\pi}{4} \)
в. \( \frac{\pi}{2} \)
c.
D.


For a certain value of \( c, \lim _{x \rightarrow \infty}\left[\left(x^{5}+\right.\right. \)
\( \left.\left.7 x^{4}+2\right)^{c}-x\right] \) is finite \( \& \) non zero. The
value of \( c \) and the value of the limit is
A \( \cdot \frac{1}{5}, \frac{7}{5} \)
B. 0,1
c. \( _{1,} \frac{7}{5} \)
D. none


An inductive coil has resistance of
100\Omega. When an ac signal of frequency 1000 \( H z \) is fed to the coil, the applied
voltage leads the current by \( 45^{\circ} . \) What
is the inductance of the coil?
\( \mathbf{A} \cdot 2 m H \)
в. 3.3 тН
c. \( 16 m H \)
D. \( \sqrt{5} \) m Н


The device used to observe stars and
other heavenly bodies is
A. periscope
B. microscope
c. telescope
D. compound microscope


The yearly change in the yield of cotton over consecutive years was as follows as increase in \( x \% \) in each of the first 2
years, followed by decrease of \( x \% \) in
each of the next 2 years. Assume that at least some cotton was produced during
the period and 0
A. Increased
B. Decreased
c. Remain Unchanged
D. Data insufficient


Write the nature of the lines
representing the linear equation \( 2 x- \)
\( \boldsymbol{y}=\mathbf{3} \) and \( \mathbf{4} \boldsymbol{x}-\boldsymbol{y}=\mathbf{5} \)


Solid \( N_{2} O_{5} \) is:
A . ionic
B. covalent
c. coordinate covalent
D. metallic


Complete the given table.
\( r \)


A weightless rod is acted on by upward parallel forces of \( 2 N \) and \( 4 N \) ends \( A \)
and \( B \) respectively.; The total length of
the rod \( A B=3 m . \) To keep the rod in
equilibrium a force of \( 6 N \) should act in
the following manner.
A. Downwards at any point between \( A \) and \( B \).
B. Downwards at mid point of \( A B \).
c. Downwards at a point \( C \) such that \( A C=1 m \).
D. Downwards at a point \( D \) such that \( B D=1 m \).


The value of \( \int \frac{e^{x}}{x}(x \log x+1) d x \) is
equal to
A \( \cdot \frac{e^{x}}{x}+C \)
B . \( x e^{x} \log |x|+C \)
c. \( e^{x} \log |x|+C \)
D・ \( x\left(e^{x}+\log |x|\right)+C \)
E \( \cdot x e^{x}+\log |x|+C \)


The force that a magnetic field exerts on a current is always perpendicular to
A. Field
B. Velocity
c. current
D. All of the above


Product of the given reaction:
A. Salicylic acid
B. 2-Hydroxybenzoic acidd
\( c . \) Both A and B
D. None of these


In what ratio, does \( P(4,6) \) divide the
join of \( \boldsymbol{A}(-2,3) \) and \( \boldsymbol{B}(\boldsymbol{6}, \boldsymbol{7}) \)
A . 1: 2
B. 3: 1
c. 4: 1
D. 2: 1


Which one of the following is a greenhouse gas?
A. oxygen
B. Methane
c. Sulphur dioxide
D. Nitrogen


According to an accepted model of plasma membrane, transport during 'symport' or 'co-transport' of sugar or amino acids through cell membrane is when
A. Nat ions move in both directions irrespective of concentration gradient
B. Nat ions moves in the direction of its concentration gradient.
c. \( \mathrm{Na}^{+} \) ions moves against the direction of its concentration gradients.
D. No movement of Nat ions is involved.


An electrical appliance is rated
\( \mathbf{1 5 0 0} W, \mathbf{2 5 0} V . \) This appliance is
connected to \( 250 V \) mains. Calculate
the current drawn.
A . \( 5 A \)
в. \( 10 A \)
\( c \cdot 6 A \)
D. 2A\$


A block of mass \( m=0.1 \mathrm{kg} \) is released from a height of \( 4 \mathrm{m} \) on a curved smooth surface. On the horizontal surface, path
AB is smooth and path BC offers
coefficient of friction \( \mu=0.1 . \) If the impact of block with the vertical wall at
C be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be :
\( \left(\operatorname{take} g=10 m / s^{2}\right) \)
A. \( 29 \mathrm{m} \)
B. 49 \( \mathrm{m} \)
c. \( 59 \mathrm{m} \)
D. \( 109 \mathrm{m} \)


A particle is executing S.H.M with a frequency 'f', the frequency with which is K.E. oscillates is?
\( \mathbf{A} \cdot \mathbf{f} \)
B. \( f / 2 \)
c. \( 2 f \)
D. \( 4 f \)


Ammonia is converted into urea in
A. Kidney
B. Spleen
c. Liver
D. Nephron


Hardness is the resistance of a metal to
the penetration of another harder body
which does not
A. have poisson's ratio less than 0
B. receive a permanent set.
c. have low young's modulus
D. have high elastic point


The ratio of the actual value of a
colligative property to the value calculated, assuming the substance to be a nonelectrolyte, is referred to as
A. Henry's law
B. vapor pressure lowering
c. the van't Hoff factor
D. freezing point depression
E . osmotic pressure


Consider the reaction at 300 K.
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow 2 \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( -185 k J \)
If 2 mole of \( H_{2} \) completely react with 2
mole of \( C l_{2} \) to form HCl. What is \( \Delta U^{\circ} \)
for the reaction?
\( \mathbf{A} \cdot \mathbf{0} \)
B . -185 kJ
c. 370 k.
D. None of these


Solve the following and find \( x \) \( \mathbf{3} \boldsymbol{x}+\mathbf{9} \geq-\boldsymbol{x}+\mathbf{1} \mathbf{9} \)


Solve the following equation using the
trial and error method.
\( 2 x+4=8 \)


Which facts are true when we use van't
Hoff equation \( P V=C S T \) for osmotic
pressure \( \mathrm{P} \) of dilute solutions?
This question has multiple correct options
A. The equation is identical to that of ideal gas equation
B. The solute particles in solution are analogous to the gas molecules and the solvent is analogous to the empty space between the gas molecules
C. Solute molecules are dispersed in the solvent, the way the gas molecules are dispersed in empty space
D. The equation is not identical to that of ideal gas equation


The Sl unit of heat is
A. joul
B. kilojoule
c. both a and
D. None of these


The basic group of an organic ester
looks like:
A . \( -C O- \)
B. \( -C O O- \)
c. \( -C H O \)
D. \( - \) COOH
E . \( -O- \)


The pathogens for leaf spot disease in Arachis hypogea is
A. Fusarium verticillioides
B. Cercospora arachidieola
c. Alternaria celosiae
D. Helminthosporium solani


Q Type your question.
questions
(i) Label parts 1,2,3 and 4
(ii) State the reason for the high hydrostatic pressure in the glomerulus.
(iii) Name the blood vessel which
contains the least amount of urea in
this diagram.
(iv) Name the two main stages of urine
formation.
(v) Name the part of the nephron which
lies in the renal medulla.


A greenish yellow gas of halogen family turns moist blue litmus paper red.
A. True
B. False


The radioactive material A and B have
decay constant \( 5 \lambda \) and \( \lambda \)
respectively.Initially both A and B have
the same number of nuclei.The ratio of
the number of nuclei of \( A \) and \( B \) will be \( \frac{1}{e}, \) after the time is \( \frac{x}{8 \lambda} \) then \( x \) is


The measured resistance of a
conductance cell containing \( \mathbf{7 . 5} \times \) \( 10^{-3} M \) solution of \( K C l \) at \( 25^{\circ} C \) was
1005 ohms. Calculate molar
conductance \( \left(o h m^{-1} c m^{2} m o l^{-1}\right) \) of
the solution.
(Cell constant= \( 1.25 \mathrm{cm}^{-1} \) )
A . 16.587
B. 165.87
c. 1658.7
D. 1.6587


Find whether \( f(x)=\frac{a^{x}+1}{a^{x}-1} \) is even
odd or neither odd nor even.


Assertion
Ramenta are scales which cover
young rhizome and leaves of Dryopteris
Reason
Pteridium lacks ramenta
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Magnetic field of earth is identical to
magnetic field of a giant magnet held
\( 20^{\circ} \) west of geographic \( N-S \) at the
centre of earth. At equator, horizontal
component of earth is \( 0.32 G \). Vertical
component can be calculated from the
relation \( V=H \) tan \( \delta, \) where \( \delta \) is angle
of dip at the place. The value of \( \boldsymbol{\delta}=\mathbf{0}^{\boldsymbol{o}} \) at
equator and \( \delta=90^{\circ} \) at poles. What is
the order of magnetic declination at a place on earth :
A \( \cdot 20^{\circ} \) East
B . \( 10^{\circ} \) East
c. \( 20^{\circ} \) west
D. \( 10^{\circ} \) west


If \( \boldsymbol{A}=\left(\begin{array}{c}4-2 \\ 5-9\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}8 & 2 \\ -1 & -3\end{array}\right) \) find \( 6 A \)
3B.


\( \boldsymbol{n} \) balls each of mass \( \boldsymbol{m} \) impinge elastically each second on a surface
with velocity \( u \). The average force experienced by the surface will be
A . \( m n u \)
B. 2 mnu
c. 4 mnu
D. \( m n u / 2 \)


Arrange the following basic forces in the increasing order of relative strength.
1. Gravitational force
2. Electromagnetic force
3. Weak nuclear force
4. Strong nuclear force
A .1,2,3,4
в. 1,3,2,4
c. \( 4,2,3, \)
D. 4,1,2,3


Triangle \( X Y Z \) is right-angled at vertex
\( Z . \) Calculate the length of \( Y Z, \) if \( X Y= \)
\( 13 \mathrm{cm} \) and \( X Z=12 \mathrm{cm} \)


\( X O Z \) plane divides the join of (2,3,1) and (6,7,1) in the ratio
A . 3: 7
B. 2: 7
c. -3: 7
D. -2: 7


In which of the following pairs, first compound has larger bond angle than
another?
This question has multiple correct options
A. \( H_{2} O \) and \( N H_{3} \)
B. \( S F_{2} \) and \( B e F_{2} \)
\( \mathrm{c} . B F_{3} \) and \( B F_{4}^{-} \)
D. \( N H_{3} \) and \( N F_{3} \)


If \( \frac{a x}{\cos \theta}+\frac{b y}{\sin \theta}=a^{2}-b^{2} \) and
\( \frac{a x \sin \theta}{\cos ^{2} \theta}-\frac{b y \cos \theta}{\sin ^{2} \theta}=0 \) then \( (a x)^{2 / 3}+ \)
\( (b y)^{2 / 3}=\left(a^{2}-b^{2}\right)^{2 / 3} ? \)
A. True
B. False


In a first order reaction the
concentration of reactant decreases
from 800 mol \( / d m^{3} \) to \( 50 m o l / d m^{3} \) in
\( 2 \times 10^{4} \) sec. The rate constant of
reaction in \( \sec ^{-1} \) is:
A \( \cdot 2 \times 10^{4} \)
B. \( 3.415 \times 10^{-5} \)
c. \( 1.386 \times 10^{-4} \)
D. None of these


Evaluate: \( \int_{e}^{e^{2}} \frac{d x}{x \log x} \)


Assertion
In the shop there are five types of ice-
creams available, a child buys six ice-
creams.
Reason
The number of different ways the child
can buy the six ice-creams is \( ^{10} C_{3} \)
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


Sulphur in +3 oxidation state is
present in:
A. dithionous acid
B. sulphurous acid
c. thionous acid
D. pyrosulphuric acid


A police party is moving in a jeep at a
constant speed \( V . \) They saw a thief at a
distance \( x \) on a motorcycle which is at
rest. The moment the police saw the
thief, the thief started at constant
acceleration \( a . \) Which of the following
relations is true if the police is able to catch the thief?
A \( \cdot V^{2}<a x \)
B. \( V^{2}<2 a x \)
\( \mathbf{c} \cdot V^{2} \geq 2 a x \)
D. \( V^{2}=a x \)


A cell that has 36 chromosomes, at the
start of interphase will have at the
conclusion of meiosis.
A. 18 singular chromosomes
B. 36 singular chromosomes
c. 18 replicated chromosomes
D. 9 chromosomes, one in each of the four gametes produced


Match the column:
\( \begin{array}{ll}\text { Column-I } & \text { Column-II } \\ \text { (a) }\left[A g\left(N H_{3}\right)_{2}\right]^{+} & \text {(p) Octahedral } \\ \text { (b) }\left[C u\left(N H_{3}\right)_{4}\right]^{2+} & \text { (q) Tetrahedral } \\ \text { (c) }\left[C r\left(H_{2} O\right)_{6}\right]^{2+} & \text { (r) Trigonal bipyramidal } \\ \text { (d) }\left[F e(C O)_{5}\right] & \text { (s) Square planar } \\ & \text { (t) Linear }\end{array} \)
\( A \)
\( (a) t ;(b) s ;(c) p ;(d) r \)
\( \mathbf{B} \cdot(\mathbf{a}) \mathbf{t} \)
\( ;(b) s ;(c) r ;(d) p \)
\( c \cdot(a) t ;(b) q ;(c) r ;(d) p \)
\( \mathbf{D} \cdot(a) q_{i}(b) s_{j} \)
\( (\mathrm{c}) \mathrm{p} \) (d)


\( 4,9,25,49, \dots \)
\( A \cdot 64 \)
B. 81
\( c \cdot 12 \)
D. 125


In the following, the coordinates of the three vertices of a rectangle \( A B C D \) are given. By plotting the given points; find, the coordinates of the fourth vertex:
\( A(-4,-6), C(6,0) \) and \( D(-4,0) \)
Claim: The co-ordinates of the fourth
vertex are \( (x,-6) \)
Find \( \boldsymbol{x} \)


The reactions that occur during the
preparation of \( \boldsymbol{C H} \boldsymbol{C l}_{3} \) from \( \boldsymbol{C}_{2} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{O} \boldsymbol{H} \)
and bleaching powder is:
i) oxidation
ii) disproportionation
iii) hydrolysis
iv) chlorination
\( A \). i, iii, iv
B. iii, iv only
c. ii, i, iv
D. all are correct


\( \frac{\boldsymbol{x}^{2}+\mathbf{5}}{\left(\boldsymbol{x}^{2}+\mathbf{2}\right)^{2}}=\frac{\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{2}}+\frac{\boldsymbol{k}}{\left(\boldsymbol{x}^{2}+\mathbf{2}\right)^{2}} \Rightarrow \)
\( \boldsymbol{k}= \)
\( A \)
B.
\( c \cdot 3 \)
D. 5


Shweta is competing in a group stairclimbing relay challenge with two of her friends. They will take turns climbing the stairs of two of the tallest buildings
of the city. The three of them each plan to climb an equal number of stairs, and
Shweta will go first. The first building
has \( s \) stairs, and the second building
has 3639 stairs. During the race, Shweta faces anaemia and is only able
to complete \( 75 \% \) of her goal. What is the total number of stairs that she climbs?
A \( \cdot 0.75\left(\frac{1}{3} s+1213\right) \)
В. \( 0.75\left(\frac{1}{3} s+3639\right) \)
c. \( 75\left(\frac{1}{3} s+1213\right) \)
D \( \cdot 75\left(\frac{1}{3} s+3639\right) \)


The value of \( \frac{\mathbf{3 6}}{\boldsymbol{\pi}} \int_{\boldsymbol{\pi} / \boldsymbol{6}}^{\boldsymbol{\pi} / \boldsymbol{3}} \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{1}+\sqrt{\cot \boldsymbol{x}}} \) is


Corolla is papilionaceous in
A. Fabaceae
B. Asteraceae
c. Poaceae
D. Solanaceae


A particle falling down freely under the influence of gravity covers a distance of \( 20 \mathrm{m} \) in 4 secs. Find its acceleration
A \( \cdot 9.8 m / s^{2} \)
B . \( 15 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 5 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 3 m / s^{2} \)


Two bodies are said to be in the state of
thermal equilibrium if there is no transfer of heat taking place between them. True or false.
A . True
B. False


Oblique ovary is found in
A. Liliaceae
B. Solanaceae
c. Asteraceae
D. Poaceae


The slope of kinetic energy vs. displacement curve of a particle in motion is:
A. inversely proportional to acceleration of the particle.
B. directly proportional to acceleration of the particle.
c. equal to acceleration of particle.
D. none of the above


A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral
A. A potential difference appears between the two cylinders when a charge density is given to the inner cylinder
B. A potential difference appears between the two cylinders when a charge density is given to the outer cylinder
c. No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.
D. No potential difference appears between the two cylinders when same charge density is given to both the cylinders.


Which of the following statements
is/are correct?
This question has multiple correct options
A. The bleaching action of chlorine is due to oxidation and so permanent, while the bleaching action of sulphurdioxide is due to reduction and so temporary.
B. \( H I \) cannot be prepared by heating an ionic iodide with conc. \( H_{2} S O_{4}, \) but \( H C l \) can be prepared by the same
way.
C. The oxidising power of halogens follow the order:
\( C l_{2}>F_{2}>B r_{2}>I_{2} \)
D. On reaction of \( X e F_{2} \) with water, no redox change
takes place.


The monomer of Buna-S are:
A. styrene and butadiene
B. isoprene and butadiene
C. vinyl chloride and Sulphur
D. butadiene.


Turnip (Brassica rapa) belongs to family
A . Cruciferae
B. Malvaceae
c. Liliaceae
D. cucurbitaceae


The \( Q \) - factor of a resonant circuit is
equal to
\( ^{\mathbf{A}} \cdot \frac{1}{L} \sqrt{\frac{R}{C}} \)
в. \( \frac{1}{R} \sqrt{\frac{L}{C}} \)
c. \( \frac{1}{R L} \sqrt{C} \)
D. \( \frac{1}{C} \sqrt{\frac{R}{L}} \)


The colour of \( C u_{2} C r_{2} O_{7} \) solution in
water is :
A. green
B. blue
c. orange
D. black


Calculate the scalar product of the following vectors. Two points \( A \) and \( B \) are given in the rectangular Cartesian system of coordinates Oxy on the curve \( \boldsymbol{y}=\mathbf{2}^{\boldsymbol{x}+\mathbf{2}} \)
the points being such that \( \overrightarrow{\boldsymbol{O A}} \cdot \boldsymbol{i}= \)
-1 and \( \overrightarrow{O B} \cdot i=2, \) where 1 is a unit
vector of the \( 0 x \) axis. Find the length of the vector \( \overline{-4 O A}+\overrightarrow{O B} \)


In the figure, \( O \) is the centre of a circle
such that diameter \( A B=13 \mathrm{cm} \) and
\( A C=12 \mathrm{cm} . B C \) is joined. Find the
area of the shaded region. (Take \( \pi= \)
\( \mathbf{3 . 1 4}) \)


If \( \vec{A}=5 \hat{i}+7 \hat{j}-3 \hat{k} \) and \( \vec{B}=2 \hat{i}+2 \hat{j}+ \)
\( a \hat{k} \) are perpendicular vectors then the
value of \( \boldsymbol{a} \) is:
\( A \cdot-2 \)
B. 8
\( c \cdot-7 \)
\( D \cdot-8 \)


Assertion \( f(x)=\frac{2}{\pi} x \sin x+x^{3}, \) where \( x \in \)
\( \left[0, \frac{\pi}{2}\right] \)
Statement-1: \( f(x)=\frac{\pi}{2} \) has exactly one solution in \( \boldsymbol{x} \in\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right] \)
and
Reason
Statement-2: \( \boldsymbol{f}(\boldsymbol{x}) \geq \mathbf{0} \) for all \( \boldsymbol{x} \) in
\( \left[0, \frac{\pi}{2}\right] \)
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
c. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.


Find the cube root of a given number by prime factorization method.
27000


The orbital radius of moon around the
earth is \( 3.8 \times 10^{8} \) meter and its time
period is 27.3 days. The centripetal acceleration of moon will be
A. \( -2.4 \times 10^{-3} \mathrm{m} / \mathrm{s}^{2} \)
B. \( 11.2 m / s^{2} \)
c. \( 2.7 \times 10^{-3} \mathrm{m} / \mathrm{s}^{2} \)
D. \( 9.8 m / s^{2} \)


The incorrect statement(s) among
the following is (are):
¡) Primary valency of a transition metal
ion in complex represent its oxidation
number.
ii) \( Z n^{2+} \) is colourless.
iii) \( M n C l_{2} \) exhibits green color in aqueous
solution.
iv) \( F e, C o, N i \) complexes are diamagnetic
in nature.
A. i and ii
B. ii only
c. iii and iv
D. iv only


Equilibrium constant depends on:
A. the actual quantities of reactants and products
B. the presence of a catalyst
C . temperature
D. the presence of inert material


which of the following is/are not
proportional to the inverse square of the
distance \( \times ? \)
This question has multiple correct options
A. The potential at a distance \( x \) from an isolated point charge
B. the electric field at a distance \( x \) from an isolated point charge
C. The force per unit length between two thin, straight, infinitely long current carrying conductors, parallel to each other, separated by a distance \( x \)
D. The gravitational attraction between two small bodies kept at a distance x apart


A rectangular coil placed in a region having a uniform magnetic field perpendicular to the plane of the coil. An
e.m.f. will not be induced in the coil if
the:
A. magnetic field increases uniformly
B. coil is rotated about an axis perpendicular to the plans of the coil and passing through its centre 0 , the coil remaining in the same plane
c. coil is routed about the axis \( 0 x \)


Ratio of maximum to minimum
ntensities at \( P \) is
\( A, 2: 1 \)
3.4: 1
\( c \cdot 8: 1 \)
0.16: 1


Find the coordinates of a point on \( y \) -axis which are at a distance of \( 5 \sqrt{2} \) from the
point \( \boldsymbol{P}(\boldsymbol{3},-\boldsymbol{2}, \boldsymbol{5}) \)


If \( E_{f} \) and \( E_{b} \) are in the ration \( 20: 31 E_{f} \)
and \( E_{b} \) at \( 30 \mathrm{K} \) respectively are:
A. 60 kJ and 93 kJ
B. -44 kJ and 93 kJ
c. 13 ks and -63 k
D. none of these


A bag contains \( n+1 \) coins. It is known that one of these coins has heads on
both sides, whereas the other coins are fair. One coin is selected at random and
tossed. If the probability that the toss results in heads is \( 7 / 12, \) find \( n \)


In a non-leap year the probability of
getting 53 Sundays or 53 Tuesdays or
53 Thursdays is.
A \( \cdot \frac{1}{7} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{3}{7} \)
D. \( \frac{4}{7} \)


Pickout among the following:
\( \mathrm{LI}^{-}, \mathrm{Be}^{-}, \mathrm{C}^{-}, \) species which is least
stable?


A \( 100 W / 200 V \) bulb and an inductor are connected in series to a
\( 220 V / 50 H z \) supply. Find the power
consumed by the bulb.
\( \mathbf{A} \cdot 100 W \)
в. \( 92 W \)
\( \mathrm{c} .84 \mathrm{W} \)
D. \( 74 W \)


Electromotive force represents
A . force
B. energy
C. energy per unit charge
D. current


The eight group of Mendeleev's periodic table is divided into how many subgroups?
A .2
B. 0
\( c \cdot 4 \)
D.


Calculate the 15 th term of the A.P.
\( -3,-4,-5,-6,-7 \dots \)
A . -13
в. -15
\( c .-17 \)
D. -19


The reaction, \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) \) is carried out in a \( 1 d m^{3} \)
vessel and \( 2 d m^{3} \) vessel respectively.
The ratio of the reaction velocities will
be:
\( A \cdot 1: 4 \)
B. 2:4
c. 1: 8
D. 8: 1


Which is not aromatic?
\( \mathbf{A} \)
B.
\( c \)
D.


Two sphere's are isolated from each other. They each have an identical net positive charge and have the same radius, however, one sphere is solid and insulating, while the other is a hollow conducting sphere whose charge is uniformly distributed. For which sphere is the electric field the
greatest distance \( x \) from the center of
the spheres? Assume \( x \) is less than the radius of the
spheres.
A. The conducting hollow sphere has a greater E-field.
B. The insulating solid sphere has a greater E field
c. Both spheres have the same E field
D. Neither sphere would cause there to be an Electric field


A person was complaining of excessive thirst and excretion of large amounts of urine. The treating doctor gave some medicines but did not advise him to
stop taking sugar in his food. Name the disease and explain what happens in it?


If a source of power \( 4 k W \) produces \( 10^{20} \) photons/second, the radiation belongs to a part of the spectrum called:-
A . \( \gamma \) -rays
B. \( X \) -rays
c. Ultraviolet rays
D. Microwave


State one appropriate observation for
each of the following. Copper sulphide is treated with dilute hydrochloric acid.


Find the Cartesian equation of the curve whose parametric equations are \( \boldsymbol{x}= \) \( \boldsymbol{t}^{2}+\boldsymbol{t}+\mathbf{1}, \boldsymbol{y}=\boldsymbol{t}^{2}-\boldsymbol{t}+\mathbf{1} \)


Check the continuity of \( f \) given by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ccc}\left(x^{2}-9\right) /\left(x^{2}-2 x-3\right) & \text { if } & 0<x< \\ 1.5 & \text { if } & x=\varepsilon\end{array}\right. \)
and \( x \neq 3 \) at the point 3


Molecules of ethanoic acid dimerises in
benzene due to \( H- \) bonding if al molecules of ethanoic acid associated
in benzene then:
A. boiling boiling of ethanoic acid become half of norma value
B. freezing point of ethanoic acid become twice of normal value
c. molar mass become twice of normal value
D. vapour pressure of solution decreases due to dimerisation


\( f\left|\begin{array}{lll}\boldsymbol{x} & \boldsymbol{2} & \boldsymbol{8} \\ \boldsymbol{2} & \boldsymbol{8} & \boldsymbol{x} \\ \boldsymbol{8} & \boldsymbol{x} & \boldsymbol{2}\end{array}\right|=\left|\begin{array}{lll}\boldsymbol{3} & \boldsymbol{x} & \boldsymbol{7} \\ \boldsymbol{x} & \boldsymbol{7} & \boldsymbol{3} \\ \boldsymbol{7} & \boldsymbol{3} & \boldsymbol{x}\end{array}\right|= \)
\( \left|\begin{array}{ccc}\mathbf{5} & \mathbf{5} & \boldsymbol{x} \\ \mathbf{5} & \boldsymbol{x} & \mathbf{5} \\ \boldsymbol{x} & \mathbf{5} & \mathbf{5}\end{array}\right|=\mathbf{0} \) then \( \boldsymbol{x} \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. -10
\( c .3 \)
D. None of these


An article is marked at Rs. \( 2,250 . \) By selling it at a discount of \( 12 \%, \) the dealer makes a profit of \( 10 \% \). Find the cost price of the article for the dealer
A . Rs. 1,500
B. Rs. 1, 600
c. Rs. 1,700
D. Rs. 1, 800


Which of the following is a redox
reaction?
\( \mathbf{A} \cdot 2 C r O_{4}^{2-}+2 H^{+} \rightarrow C r_{2} O_{7}^{2-}+H_{2} O \)
В \( \cdot \quad C u S O_{4}+4 N H_{3} \rightarrow\left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \)
\( \mathbf{c} \cdot N a_{2} S_{2} O_{3}+I_{2} \rightarrow N a_{2} S_{4} O_{6}+N a I \)
D. \( C r_{2} O_{7}^{2-}+2 O H^{-} \rightarrow 2 C r O_{4}^{2-}+H_{2} O \)


The molecular formula of Copper (II) bromide is:
\( \mathbf{A} \cdot C u B r \)
в. \( C u B r_{3} \)
c. \( C u B r_{2} \)
D. \( C u_{2} \) В \( r_{3} \)


Write the multiplicate inverse \( o \) \( -5-\frac{1}{-5} \)


Fill in the blank:
The colour of a star is a measure of its:
A . age
B. temperature
\( c . \) size
D. distance from the Earth


A lift is moving down with acceleration
\( a . A \) man in the lift drops a ball inside
the lift. The acceleration of the ball as
observed by the man in the lift and a man standing stationary on the ground are respectively.
A \( \cdot g, g \)
в. \( g-a, g-a \)
\( \mathbf{c} . g-a, g \)
D. \( a, g \)


The potential of outer shell is
\( A \cdot \frac{q}{32 \pi \epsilon 0^{a}} \)
B. \( \frac{q}{16 \pi \epsilon a} \)
\( c \cdot \frac{q}{8 \pi \cos ^{a}} \)
\( D \cdot \frac{q}{4 \pi \varepsilon a a} \)


In a school, \( 30 \% \) of students play chess,
\( 60 \% \) play carrom and the rest play other games. If the total number of students
in the school is \( 900, \) find the exact
number of students who play each
game.


What are brittle bodies.??


Let \( v_{1} \) be the frequency of the series
limited of the Lyman series, \( v_{2} \) be the frequency of the first line of the Lyman
series, and \( v_{3} \) be the frequency of the
series limited of the Balmer series.
Then:
A. \( v_{1}-v_{2}=v_{3} \)
В. \( v_{2}-v_{1}=v_{3} \)
C \( \cdot v_{3}=\frac{1}{2}\left(v_{1}+v_{3}\right) \)
D. \( v_{1}+v_{2}=v_{3} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{1})^{\boldsymbol{m}}(\boldsymbol{2}-\boldsymbol{x})^{n} ; \boldsymbol{m}, \boldsymbol{n} \boldsymbol{\epsilon} \boldsymbol{N} \)
and \( \boldsymbol{m}, \boldsymbol{n}>2 \)


The real part of \( (1-\cos \theta+2 i \sin \theta)^{-1} \)
is:
A \( \frac{2 \sin \theta}{(1-\cos \theta)^{2}+4 \sin ^{2} \theta} \)
B. \( \frac{1+\cos \theta}{(1-\cos \theta)^{2}+4 \sin ^{2} \theta} \)
c. \( \frac{(1-\cos \theta)-2 i \sin \theta}{(1-\cos \theta)^{2}+4 i^{2} \sin ^{2} \theta} \)
D. \( \frac{1-\cos \theta}{(1-\cos \theta)^{2}+4 \sin ^{2} \theta} \)


In our society the women are often
blamed for giving birth to daughters. Can you explain why this is not correct?


Assertion
In humans the gamete contributed by the male determines whether the child
produced will be male or female.
Reason

Sex in humans is polygenic trait
dependent upon the cumulative effect
of some genes on X-chromosome and
some on Y-chromosome.
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.


Let \( S_{n} \) denote the sum of first \( n \) terms of
an AP and \( 3 S_{n}=S_{2 n} . \) What is \( S_{3 n}: S_{2 n} \)
equal to?
A .2: 1
B. 3: 1
c. 4: 1
D. 5: 1


Solve for \( x \) and \( y \) if \( \left(\begin{array}{l}2 x+y \\ x-3 y\end{array}\right)=\left(\begin{array}{c}5 \\ 13\end{array}\right) \)


Which of the following has strongest hydrogen bonding?
A. \( O-H \ldots N \)
B. \( O-H \ldots O \)
c. \( F-H \ldots F \)
D. \( O-H \ldots F \)


The resting tidal volume to vital capacity ratio should be
A . 1: 5
B. 1:10
c. 1: 20
D. 1: 40


Consider an YDSE that has different
slits width, as a result, amplitudes of
waves from two slits are \( A \) and \( 2 A \)
respectively. If \( I_{0} \) be the maximum
intensity of the interference pattern,
then intensity of the pattern at a point
where phase difference between waves
is \( \phi \) is :
\( \mathbf{A} \cdot I_{0} \cos ^{2} \phi \)
B. \( \frac{I_{0}}{3} \sin ^{2} \frac{\phi}{2} \)
c. \( \frac{I_{0}}{9}[5+4 \cos \phi] \)
D \( \cdot \frac{I_{0}}{9}[5+8 \cos \phi] \)


If \( y= \)
\( (x+\sqrt{x^{2}-a^{2}})^{n} \quad \) then \( \quad\left(x^{2}-a^{2}\right)\left(\frac{d y}{d x}\right. \)
A \( \cdot n^{2} y \)
B. \( -n^{2} y \)
\( c \cdot n y^{2} \)
D \cdot \( n^{2} y^{2} \)


5 bullets, each of mass 10 gm are fired per second, vertically upwards, such that a plate of mass 200 gm floats in air. If the bullets rebound with the same
velocity back vertically downwards, the velocity with which each bullet is fired
in \( \mathrm{ms}^{-1} \) is:
(Take \( \left.g=10 m s^{-2}\right) \)
A . 10
B. 30
c. 20
D. 40


Boron has two stable isotopes, \( ^{10} B(19 \%) \) and \( ^{11} B(81 \%) . \) Average
atomic weight for boron in the periodic table is:
A . 10.8
B. 10.2
c. 11.2
D. 10.0


Graphite powder is used in machines to
A. Enhance friction
B. Enhance profit
c. Reduce friction
D. Reduce efficiency


The valencies of p block elements are
equal to group number or 8 minus the group number. Therefore they show one
lower valency and one higher valency. However, if we go to the bottom elements of any group, the compounds with lower valency are predominant whereas higher valency becomes rather
uncommon. Explain.


\( \left|\begin{array}{ccc}x^{2}+x & x+1 & x-2 \\ 2 x^{2}+3 x-1 & 3 x & 3 x-3 \\ x^{2}+2 x+3 & 2 x-1 & 2 x-1\end{array}\right|= \)
\( A x+B \) then
A. A and B are independent of \( x \)
B. A and B are dependent of \( x \)
C. A dependent on x but B does not depend on x
D. B depends on x but A does not depend on x


Two charges \( 5 \times 10^{-8} C \) and \( -3 x \)
\( 10^{-8} C \) are located \( 0.16 m \) apart. At what
point(s) on the line joining the two charges in the electric potential zero? Take the potential at infinity to be zero.


ff \( \bar{a}, \bar{b}, \bar{c}, \bar{d} \) are the position vectors of four points \( \mathbf{A}, \mathbf{B}, \mathbf{C}, \mathbf{D} \) in a plane such that \( |\overline{\boldsymbol{a}}-\overline{\boldsymbol{d}}|=|\overline{\boldsymbol{b}}-\overline{\boldsymbol{d}}|=|\overline{\boldsymbol{c}}-\overline{\boldsymbol{d}}| \) then the
point \( \mathbf{D} \) is the \( \cdots \) of \( \Delta \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \)
A. centroid
B. circumcentre
c. orthocentre
D. incentre


Five particles each of mass ' \( m \) ' are kept
at five vertices of a regular pentagon. A sixth particle of mass ' \( M^{\prime} \) is kept at
centre of the pentagon' \( O \) '. Distance
between ' \( M \) ' and ' \( m \) ' is 'a'. Find
(i) net force on \( ^{\prime} \boldsymbol{M}^{\prime} \)
(ii) magnitude of net force on ' \( M^{\prime} \) if any one particle is removed from one of the vertices.


The length of conductor ab carrying
current \( I_{2} \) is \( l . \) The force acting on it due
to a long current carrying conductor as shown in figure. The midpoint of wire ab is distance \( x \) apart from long wire. The magnitude of the force on the wire is:
A \( \cdot \frac{\mu_{0} I}{2 \pi} \log _{e} \frac{x+l / 2}{x-l / 2} \)
В. \( \frac{\mu_{0} I}{2 \pi x} \)
c. \( \frac{\mu_{0} I}{2 \pi} \log _{e} \frac{x-l / 2}{x+l / 2} \)
D. \( _{\mu_{0} \text { Ilog }_{e}} \frac{x-l / 2}{x+l / 2} \)


Give the absolute and gauge pressure of the gas in the enclosure for cases (a)
and (b)in units of cm of mercury


If \( \bar{A}=3 \hat{i}+5 \hat{j}-2 \hat{k}, \) and vector \( \bar{B}= \)
\( -3 \hat{j}+6 \hat{k} . \) Find a vector \( \bar{C} \) such that 2 \( \bar{A}+7 \bar{B}+4 \bar{C}=0 \)
\( \mathbf{A} \cdot-6 \hat{i}+11 \hat{j}-38 \hat{k} \)
B . \( 11 \hat{j}-4 \hat{k} \)
c. \( -1.5 \hat{i}+2.75 \hat{j}-9.5 \hat{k} \)
D. \( 4 \hat{j}-6 \hat{k} \)


A ray of light traveling in a transparent medium falls on a surface separating the medium from the air at an angle of incidence of \( 45^{\circ} . \) The ray undergoes
total internal reflection. If \( n \) is the
refractive index of the medium with
respect to air, select the possible value(s) of \( n \) from the following. This question has multiple correct options
A . 1.3
в. 1.4
c. 1.5
D. 1.6


The bond angle in \( N F_{3}\left(102.3^{\circ}\right) \) is
smaller than \( N H_{3}\left(107.2^{\circ}\right) . \) This is
because of
A. large size of \( F \) compared to \( H \)
B. large size of \( N \) compared to \( F \)
c. opposite polarity of \( N \) in the two molecules
D. small size of \( H \) compared to \( N \)


(a) Write IUPAC names of the following
compounds:
(i) \( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \)
(ii) \( \boldsymbol{C H}_{2}-\boldsymbol{C H}-\boldsymbol{C H}_{2} \)
\( \begin{array}{ccc}1 & 1 & 1 \\ o_{H} & o_{H} & o_{H}\end{array} \)
(b) Write equations of the following chemical reactions:
(i) Phenol reacts with \( B r_{2} \) in
presence of \( \boldsymbol{C S}_{\mathbf{2}} \)
(ii) Ethanol is heated at \( 573 \mathrm{K} \) in
presence of Cu.


instrument is used to find the
quantity of electricity of different bodies.


The range of a clinical thermometer is
A \( \cdot 0-100^{\circ} \mathrm{C} \)
B. 32-214 \( ^{0} \) F
c. \( 0-1273^{\circ} \mathrm{C} \)
D. 35-42 \( ^{0} \mathrm{C} \)


A graph of concentration versus time
data for a second-order reaction gives a straight line in which of the following plots of the data?
A \( \cdot[A]_{t}=-k t+[A]_{0} \)
B \( \cdot \ln [A]_{t}=-k t+\ln [A]_{0} \)
c. \( \frac{1}{\left[A_{t}\right]}=k t+\frac{1}{\left[A_{0}\right]} \)
D. All of the above
E. None of the above


The fluid present in the membranous labyrinth of ear is
A. Plasma
B. Endolymph
c. Perilymph
D. Blood


There are two groups of subjects one of which consists of 5 science subjects and 3 engineering subjects and the
other consists of 3 science and 5
engineering subjects. An unbaised die
is cast. If number 3 or number 5 turns
up, a subject is selected at random
from the first group, other wise the
subject is selected at random from the
second group. Find the probability that an engineering subject is selected ultimately.
A \( \cdot \frac{13}{24} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{11}{24} \)


Define the following terms with a
suitable example:
Fibrous protein


Evaluate : \( \underset{n \rightarrow \infty}{L t} \frac{1}{2^{n}} \)


\( s p^{3} d^{2} \) hybridisation is present in:
\( \mathbf{A} \cdot\left[C o F_{6}\right]^{-3} \)
B. \( \left[N i(C o)_{4}\right] \)
C. \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right]^{+2} \)
D. All


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \sin \boldsymbol{x}, \) find \( \boldsymbol{f}^{\prime}(\boldsymbol{\pi}), \) using first
principle.


Socket in pelvic girdle in which head of femur articulates is formed by fusion of
A. Ischium and pubis
B. Ilium and pubis
c. llium, and ischium
D. Ileum, ischium and pubis


The equivalent weights of an element of variable valency are 21 and \( 14 . \) The atomic mass of the element may be :
A . 35
B. 42
c. 70
D. 126


The botanist would like to increase the
number of plants that the environment can support so that the population of the species will increase more rapidly. If the botanists goal is that the number of plants will increase from 3000 this year
to 3360 next year, how many plants must the modified
environment support?


In a bank, principal increases
continuously at the rate of \( 5 \% \) per year. An amount of \( R s .1000 \) is deposited
with this bank, how much will it worth
after 10 years\( \left(e^{0.5}=1.648\right) \)


A gaseous mixture contains four gases \( A, B, C \) and \( D . \) The mole fraction of \( B \)
is \( 0.5 . \) the mole fraction of \( \boldsymbol{A} \) is:
A . 0.525
B. 0.375
c. 0.625
D. 0.732


Which of the following pairs of ions makes the water hard?
A . \( N a^{\text {t }} \)
B. \( C s^{ } \)
\( \mathbf{c} \cdot R b^{+} \)
D. \( B a^{+2} \)


Match the column


The molecular formula of the compound which gives two moles of acetone during ozonolysis:
A. \( C_{2} H_{4} \)
в. \( C_{3} H_{6} \)
\( \mathbf{c} \cdot C_{4} H_{8} \)
D. \( C_{6} H_{12} \)


A body of mass \( 5 k g \) under the action of constant force \( \overrightarrow{\boldsymbol{F}}=\boldsymbol{F}_{\boldsymbol{x}} \hat{\boldsymbol{i}}+\boldsymbol{F}_{\boldsymbol{y}} \hat{\boldsymbol{j}} \) has
velocity at \( t=0 s \) as \( \vec{v}=(6 \hat{i}-2 \hat{j}) m / s \) and \( \operatorname{at} t=10 s \) as \( \vec{v}=+6 \hat{j} m / s . \) The
force \( \overrightarrow{\boldsymbol{F}} \) is:
A \( \cdot(-3 \hat{i}+4 \hat{j}) N \)
В \( \cdot\left(-\frac{3}{5} \hat{i}+\frac{4}{5} \hat{j}\right) N \)
c. \( (3 \hat{i}-4 \hat{j}) N \)
D \( \cdot\left(\frac{3}{5} \hat{i}-\frac{4}{5} \hat{j}\right) N \)


Find the right option among the following concerning "At equilibrium".
A. The forward reaction will continue
B. A change in reaction conditions may shift the equilibriumm
c. The reverse reaction will not continue
D. Both A and B


If \( \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}}=\mathbf{0},|\overrightarrow{\boldsymbol{a}}|=\mathbf{3},|\overrightarrow{\boldsymbol{b}}|=\mathbf{5},|\overrightarrow{\boldsymbol{c}}|=\mathbf{7} \)
then the angle between \( \vec{a} \) and \( \vec{b} \) is
A \( . \pi / 6 \)
в. \( 2 \pi / 3 \)
c. \( 5 \pi / 3 \)
D . \( \pi / 3 \)


For spontaneous reaction, \( \Delta G \) is:
A . -ve
B. +ve
c. zero
D. None of these


Identify the reagent from the following list which can easily distinguish between 1-butyne and 2-butyne.
\( A \). Bromine water
B. Baeyer's reagent
c. Dilute \( H_{2} S O_{4}+H g S O_{4} \)
D. Ammoniacal \( C u_{2} C l_{2} \)


The diagonal of a square formed by the points (1,0)(0,1)(-1,0) and (0,-1) is
A .2
B. 4
\( c \cdot \sqrt{2} \)
D.


In a first order reaction, the initial conc.
of the reactant was \( M / 10 . \) After 8 minutes 20 seconds the conc. becomes
\( M / 100 \)
What is the rate constant?
A. \( 5 \times 10^{-3} \) second \( ^{-1} \)
B. \( 2.303 \times 10^{-5} \) second\( ^{-1} \)
c. \( 2.303 \times 10^{-4} \) second\( ^{-1} \)
D. \( 4.606 \times 10^{-3} \) second \( ^{-1} \)


In a given reaction \( z^{\boldsymbol{A}^{A}} \longrightarrow z_{+1} \boldsymbol{Y}^{\boldsymbol{A}} \longrightarrow z_{-1} \)
\( \boldsymbol{K}^{\boldsymbol{A}-\boldsymbol{4}} \longrightarrow \boldsymbol{z}-\mathbf{1} \boldsymbol{K}^{\boldsymbol{A}-\boldsymbol{4}} \)
Radioactive radiations are emitted in
the sequence of
\( \mathbf{A} \cdot \alpha, \beta, \gamma \)
в. \( \gamma, \alpha, \beta \)
\( \mathbf{c} \cdot \beta, \alpha, \gamma \)
D. \( \gamma, \beta, \alpha \),


In the given figure of square plate, possible axis of rotation is shown,if in
each case we give same angular
impulse parallel to the axis shown then
A. angular momentum about axis 1 and 2 will be same
B. angular momentum about axis 1 and 3 will be same
C . angular momentum about axis 1 and 4 will be same
D. none of the above


\( C_{p}-C_{v} \) for an ideal gas is


Water flows through a cylindrical pipe of internal diameter \( 7 \mathrm{cm} \) at \( 5 \mathrm{m} / \mathrm{s} \)
Calculate:
(i) the volume, in litres, of water
discharged by the pipe in 1 minute
(ii) the time, in minutes, the pipe would take to fill an empty rectangular tank
\( 4 m \) by \( 3 m \) by \( 2.31 m \)


The value of \( \sin ^{-1}\left(\sin 2010^{0}\right)+ \)
\( \cos ^{-1}\left(\cos 2010^{0}\right)+\tan ^{-1}\left(\tan 2010^{0}\right) \) is
\( A \cdot \frac{\pi}{6} \)
B .
\( \mathbf{c} \cdot \frac{2 \pi}{3} \)
D. \( \frac{5 \pi}{6} \)


An AND gate is followed by a NOT gate in series. With two inputs \( \boldsymbol{A} \& \boldsymbol{B} \), the
Boolean expression for the out put \( Y \) will be :
A. \( A . B \)
B. \( A+B \)
\( c \cdot \overline{A+B} \)
D. \( \overline{A . B} \)


Polymer formation form monomers
starts by:
A. condensation reaction between monomers
B. conversion of monomer to monomer ions by protons
C. coordination reaction between monomers
D. hydrolysis of monomers


The radius of the sphere is measured
\( \operatorname{as}(10 \pm 0.02) c m . \) The error in the
measurement of its volume is
A \( .25 .1 c c \)
B. 25.21cc
c. \( 2.51 c c \)
D. \( 251.2 c c \)


The value of \( \int x(\operatorname{cosec} x \cot x) d x= \) is
A. \( x \operatorname{cosec} x-\log |\tan x / 2|+c \)
B. \( 2-x \operatorname{cosec} x+\log \left|\tan \frac{x}{2}\right|+c \)
c. \( x \operatorname{cosec} x-2 \log |\tan x / 2|+c \)
D. \( x \) cot \( x-\log \left|\tan \frac{x}{2}\right|+c \)


Geometry of central atom in \( S N F_{3} \) is:


Explain the process of sex determination in honey bees.


For a reaction \( 2 A+3 B \rightarrow \) Products
the rate law expression is given by rate
\( =K(A)^{1}(B)^{2} . \) The order of the reaction
with respect to \( A, B \) and overall order of
reaction are:
\( \mathbf{A} \cdot 2,1,3 \)
в. 1,2,3
c. 0,1,2
D. 2,1,0


The compound extracted from the plant
Rauwolfia Serpentina is:
A. aspirin
B. bithional
C. quinine
D. reserpine


An astronaut is looking down on earth's
surface from a space shuttle an altitude of \( 400 \mathrm{km} \) Assuming that the astronaut's pupil diameter is \( 5 \mathrm{mm} \) and the wavelength of visible light is \( 500 \mathrm{nm}, \) the astronaut will be able to resolve linear objects of the size of
about :
A . \( 0.5 \mathrm{m} \)
B. 5 m
\( c . \) 50m
D. 500m


What is chemical equilibrium?
A. A state of balance in a reaction where the forward and reverse reaction speed is equal and the concentrations of the products and reactants remain unchanged.
B. Equilibrium involving chemicals.
C. A state of balance in a reaction where the forward and reverse reaction speed is unequal
D. Equilibrium between two substances that does not involve a change in the chemical makeup of a substance.
E. A state where the reaction is unbalanced


Sun light filtering through the tree leaves often makes circular patches on
the ground because:
A. the sun is round
B. the space through which light penetrates is round
c. light is transverse in nature
D. of diffraction effects


Solve:-
\( \int t \sqrt{\frac{t^{2}+1}{t^{2}-1}} d t \)


The elements present in fluorapatite
are:
A. \( C a, N, O \)
в. \( C a, P \)
c. \( C a, P, F, O \)
D. \( C a, N, O, F \)


The combination of atoms occurs
because they want:
A. to decrease number of electrons in the outer most
orbit
B. to attain an inert gas configuration
c. to increase number of electrons in the outer most orbit
D. to attain 18 electrons in the outermost orbit


If a current carrying wire carries 10 A
current then the magnetic field is
X. Now the current in the wire increases
to 100 A, them magnetic field in the wire becomes
\( A \cdot>x \)
B.
D. all
December 27, 2019
Yashassvi Padigala
\( B \)
Share Save


The area bounded by the curve \( y= \)
\( x^{4}-2 x^{3}+x^{2}+3 \) with \( x \) -axis and
ordinates corresponding to the minima of y is :
\( \mathbf{A} \cdot \mathbf{1} \)
B . \( \frac{91}{30} \)
\( c \cdot \frac{30}{9} \)
D. 4


Ropes made of are used in
cranes and lifts.
A. rayon
B. nylon
c. acrylic
D. spandex


On reaching puberty, a woman's ovaries usually release egg each month.
A. one
B. Two
c. Three
D. Many


Atoms of two elements \( P \) and \( Q \) have 5
electrons in \( 2^{n d} \) shell and \( 3^{r d} \) shell
respectively. What could be the geometric representations of \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) ?
What will be the atomic numbers of
these elements?


The volume of a monoatomic ideal gas
increases linearly with pressure as
shown in the diagram. What is the
increase in internal energy?
A \( .4 .8 \times 10^{5} J \)
B \( .3 .6 \times 10^{5} J \)
c. \( 2.9 \times 10^{5} J \)
D. \( 5.6 \times 10^{5} J \)


The error in the measurement of radius
of a sphere is \( 2 \% . \) What will be the error in the calculation of its surface area? (surface area \( \left.A=4 \pi r^{2}\right) \frac{\Delta A}{A}=\frac{2 \Delta r}{r} \)


The conductivity of saturated solution
of \( A g C l \) is found to be \( 1.86 \times \) \( 10^{-6} \) ohm \( ^{-1} c m^{-1} \) and that of water is
\( 6 \times 10^{-8} o h m^{-1} c m^{-1} . \) If \( \lambda^{0} A g C l \) is 138
\( o h m^{-1} c m^{2} e q^{-1} \) the solubility product
of \( A g C l \) is:
A \( \cdot 1.3 \times 10^{-5} \)
В. \( 1.69 \times 10^{-10} \)
C \( .2 \times 10^{-10} \)
D. \( 2.7 \times 10^{-10} \)


Which of the following organisms requires a medium through which male
gametes move?
A. Algae, Bryophyta and Gymnosperm
B. Pteridophyta, and Angiosperm
c. Bryophytea and Pteridophyta only
D. Algae, Bryophyta, and Pteridophyta


A metal ball immersed in water weighs
\( \boldsymbol{w}_{1} \) at \( 5^{\circ} \boldsymbol{C} \) and \( \boldsymbol{w}_{2} \) at \( \mathbf{5 0 ^ { \circ }} \boldsymbol{C} \). The
coefficient of cubical expansion of
metal is less than that of water. Then
A. \( w_{1}>w_{2} \)
В. \( w_{1}<w_{2} \)
\( \mathbf{c} \cdot w_{1}=w_{2} \)
D. Insufficient information


A speaks truth in \( 75 \% \) of the cases and \( \mathrm{B} \) in \( 80 \% \) of the cases. In what
percentage of cases are they likely to
contradict each other in stating the same fact?


The tendency of one object to force another adjoining or interconnected object into vibration motion is referred
to as a
A. forced vibration
B. damped vibration
c. loudness
D. pitch


For the structure of nucleic acid, which
of the following statements is wrong?
A. DNA can be single stranded in some viruses.
B. RNA can be double stranded occasionally.
C. There are as many as 12 bases per turn in Z DNA.
D. The length of one helix is \( 45 \AA \) in B-DNA and in Z-DNA.


Consider the following statements:
1. Global Warming is a phenomenon in which lower atmosphere traps more terrestrial radiation and thus the mean
global temperature of the earth rises beyond \( 14^{\circ} \mathrm{C} \)
2. Global Warming takes place because of rise in the concentration of gases
known as greenhouse gases namely-
water, vapour, \( C O_{2}, C H_{4}, \) oxides of
Nitrogen and man-made gases like
\( \boldsymbol{C F C s} \)
3. Among the greenhouse gases, \( C O_{2} \) is primarily responsible for Global Warming. Which of the statements given above is/are correct?
\( A \cdot 1,2 \) and 3
B. 2 and 3
c. only 2
D. only 3


The book "Origin of species" was written by
A. Darwin
B. Beagle
c. Mendel
D. None of the above


Why are wires coated with plastic
coverings:
\( A \). to make it a bit decorative
B. to make it more durable
C. it order to make them distinguishable
D. to make it shock free


Bartholinus discovered:
A. Interference by splitting the wave front
B. Polarisation by reflection
C. Polarisation by refraction
D. Polarisation by double refraction


Combination of proteins with nucleic acids give
A. enzymes
B. polypeptides
c. nucleo proteins
D. dipeptides


Light moves at velocity of roughly kms in every second.
A. 300,000
B. 500000
\( c \cdot 100000 \)
D. 400000


A body falls from a height of 16 m and
rebounds to a height of 4 m. The coefficient of restitution is
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.


State whether the following statement is True or False. The instrument that is used to see
things of celestial bodies like stars and planets is called as gyroscope
A. True
B. False


Bases common to RNA and DNA are?
A. adenine, guanine, cytosine
B. adenine, uracil, cytosine
c. adenine, guanine, thymine
D. guanine, uracil, thymine


Goitre is related to which of the
following glands of human body?
A. Thymus
B. Thyroid
c. Parathyroid
D. Pancreas


Add the following rational numbers:
\( \frac{5}{8} \) and \( \frac{-7}{12} \)


Write the reactions of \( F_{2} \) and \( C l_{2} \) with
water


One end of a steel rod \( (k= \) \( \left.45 J s^{-1} m^{-1} C^{-1}\right) \) of length \( 1.0 \mathrm{m} \) is kept
in ice at \( 0^{0} C \) and the other end is kept
in boiling water at \( 100^{0} C . \) The are aof \( \operatorname{cross} \) section of the rod is \( 0.04 \mathrm{cm}^{2} \)
Assuming no heat loss to the atmosphere, find the mass of the ice
melting per second. Latent heat of fusion of ice \( =\mathbf{3 . 3 6} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{J k g}^{-1} \)


When a current carrying coil is placed in a uniform magnetic field of induction
\( B, \) then a torque \( \tau \) acts on it. If \( I \) is the current, \( n \) is the number of turns and \( A \)
is the face area of the coil and the
normal to the coil makes an angle \( \theta \)
with \( \boldsymbol{B}, \) Then
A \( \cdot \tau=B I n A \)
B. \( \tau=B \) In \( A \sin \theta \)
\( \mathbf{c} \cdot \tau=B \operatorname{In} A \cos \theta \)
\( \mathbf{D} \cdot \tau=B I n A \tan \theta \)


Factorise
\( 2 a^{2}+10 a-28=0 \)


The product of \( x^{1 / 2} \cdot x^{1 / 4} \cdot x^{1 / 8} \dots \infty \)
equals
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( x \)
\( D \cdot \infty \)


Find solution of following inequality, also show it graphically.
\( \boldsymbol{x}-\mathbf{5} \geq-\mathbf{7}, \boldsymbol{x} \in \boldsymbol{R} \)
\( A \)
\( \begin{array}{cccccc} & 1 & 1 & 1 & & & 1 \\ -2 & -1 & 0 & 1 & 2 & 3\end{array} \)
B.
\begin{tabular}{lllllll}
\hline-2 & -1 & 0 & 1 & 2 & 3
\end{tabular}
\( c \)
\begin{tabular}{lllllll}
& & & & & & & \( \bullet \) \\
\hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4
\end{tabular}
\( D \)
\( \longleftrightarrow \)\begin{tabular}{ccccccc}
& & & & & \( \rightarrow \) & \( \rightarrow \) \\
\hline-2 & -1 & 0 & 1 & 2 & 3 & 4
\end{tabular}


A solid sphere of mass \( M, \) radius \( R \) and having moment of inertia about an axis passing through the centre of mass as \( I, \) is recast into a disc of thickness \( t \)
whose moment of inertia about an axis
passing through its edge and perpendicular to its plane remains \( \boldsymbol{I} \)
Then, radius of the disc will be:
A \( \cdot \frac{2 R}{\sqrt{15}} \)
B. \( R \sqrt{\frac{2}{15}} \)
c. \( \frac{4 R}{\sqrt{15}} \)
D. \( \frac{R}{4} \)


Find the distance of point (-2,3,-4) from the line \( \frac{\boldsymbol{x}+\mathbf{2}}{\mathbf{3}}=\frac{\mathbf{2} \boldsymbol{y}+\mathbf{3}}{\mathbf{4}}=\frac{\mathbf{3} \boldsymbol{z}+\mathbf{4}}{\mathbf{5}} \)
measured parallel to the plane \( 4 x+ \) \( 12 y-3 z+1=0 \)


An object will continue accelerating
until:
A. Resultant force on it begins to decrease
B. Its velocity changes direction
C. The resultant force on it is zero
D. The resultant force is at right angles to its direction of motion


An \( \alpha \) -particle of energy \( 5 M e V \) is
scattered through \( 180^{0} \) by a fixed
uranium nucleus. The closest distance
is in the order of
\( \mathbf{A} \cdot 1 A^{0} \)
B . \( 10^{-10} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-12} \mathrm{cm} \)
D. \( 10^{-16} \mathrm{cm} \)


\( \frac{4}{25} \) Coulomb of charge contains
electrons:
\( \mathbf{A} \cdot 10^{15} \)
B . \( 10^{18} \)
\( \mathbf{c} \cdot 10^{20} \)
D. None of these


Solve
\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{a}(\boldsymbol{b}+\boldsymbol{c}) \\ \mathbf{1} & \boldsymbol{c} \boldsymbol{a} & \boldsymbol{b}(\boldsymbol{c}+\boldsymbol{a}) \\ \mathbf{1} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{c}(\boldsymbol{a}+\boldsymbol{b})\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot a b c \)
D. \( a b+b c+c a \)


When a body is charged by induction, then the body
A. Becomes neutral
B. Does not lose any charge


A uniform electric field and uniform
magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron
A. will turn towards right of direction of motion
B. speed will decrease
c. speed will increase
D. will turn towards left direction of motion


Evaluate:
\( \int \frac{x^{4}+4}{x^{2}-2 x+2} d x \)
A \( \cdot \frac{x^{3}}{2}+x^{2}+2 x+C \)
B. \( \frac{x^{3}}{3}+x^{2}+2 x+C \)
c. \( \frac{x^{3}}{3}+x^{2}+x+C \)
D. \( \frac{x^{3}}{3}+x^{2}-2 x+C \)


For the reaction \( A+B \rightarrow \) Products, it is
found that the order of the reactions \( A \)
and \( \mathrm{B} \) are 1 and \( 2, \) respectively. When the concentration of \( A \) is halved and that of
\( \mathrm{B} \) is doubled, the rate increases by a factor of:


A quadratic polynomial is exactly divisible by \( (x+1) \&(x+2) \) and leaves the remainder 4 after division by \( (x+3) \) then that polynomial is
A \( \cdot x^{2}+6 x+4 \)
B. \( 2 x^{2}+6 x+4 \)
c. \( 2 x^{2}+6 x-4 \)
D. \( x^{2}+6 x-4 \)


Name the principle on the basis of which optical fibres work.


An incandescent filament emits a
spectrum which is :
A. line spectrumm
B. band spectrum
c. continuous spectrum
D. characteristic spectrum


Identify compounds in which the central atom has incomplete octet.
\( B F_{3}, A l C l_{3}, G a C l_{2}, M g C l_{2}, B e C l_{2} \)


\( \boldsymbol{L} \)
If length of potentiometer wire is \( \frac{-}{2} \) and
resistance is \( x \) then value of unknown
emf \( \boldsymbol{E} \) is:
A \( \cdot \frac{2 E_{0} x \ell}{r_{1}+x} \)
B. \( \frac{2 E_{0} x \ell}{2 r_{1}+x} \)
c. \( \frac{4 E_{0} x \ell}{2 r_{1}+x} \)
D. \( \frac{4 E_{0} x \ell}{r_{1}+x} \)


Find the vertex focus, equation of directrix and equation of axis of the \( \boldsymbol{y}^{2}-\boldsymbol{x}+\mathbf{4} \boldsymbol{y}+\mathbf{5}=\mathbf{0} \)


The \( \left[\boldsymbol{O H}^{-}\right] \) of \( \mathbf{0 . 0 0 5} \boldsymbol{M} \boldsymbol{H}_{2} \boldsymbol{S O}_{4} \) is:
A \( \cdot 2 \times 10^{-2} M \)
В. \( 5 \times 10^{-3} M \)
\( \mathrm{c} \cdot 10^{-2} M \)
D. \( 10^{-12} M \)


Show that the function \( f: R \rightarrow R \) given
by \( f(x)=x^{3} \) is injective


Assertion
lonisation potential of Be(atomic number 4 ) is less than B(atomic
number 5 ).
Reason
The first electron released from Be is of
p orbital but that form B is of s orbital.
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 area of the region bounded by \( y= \)
\( \boldsymbol{x}^{2}+\mathbf{2}, \boldsymbol{y}=-\boldsymbol{x}, \boldsymbol{x}=\mathbf{0} \) and \( \boldsymbol{x}=\mathbf{1} \) is
A \( \cdot \frac{17}{6} \)
в. \( \frac{17}{3} \)
c. \( \frac{10}{3} \)
D. \( \frac{8}{3} \)


\( \begin{array}{ccc}\sin ^{2} x & \cos ^{2} x & 1 \\ \cos ^{2} x & \sin ^{2} x & 1 \\ -10 & 12 & 2\end{array} \mid= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 12 \cos ^{2} x-10 \sin ^{2} x \)
c. \( 12 \sin ^{2} x-10 \cos ^{2} x-2 \)
D. \( 10 \sin 2 x \)


If \( \boldsymbol{x} \in \boldsymbol{W}, \) find the number of values of \( \boldsymbol{x} \) in the solution set of \( \frac{3}{5} x-\frac{2 x-1}{3}>1 \)


The resistance of carbon filament at
\( 0^{0} C \) is \( 104 \Omega . \) It is connected in series to
an iron wire. The temperature coefficient of resistivity of carbon and
iron are -0.0003 and +0.0052 per degree Celsius respectively. What must be the resistance of iron wire so that the
combined resistance does not change with temperature?
A . 15
B. 6
c. 1.5
D. 156


A house is on built on the top of a hill
with \( 45^{0} \) slope. Due to the sliding of material and sand from top to the
bottom of hill, the slope angle has been reduced.
If the coefficient of static friction
between sand particles is \( 0.75, \) what is the final angle attained by hill?
\( \left.\tan ^{-1} 0.75=37^{0}\right) \)
\( \mathbf{A} \cdot 8^{0} \)
B. \( 45^{\circ} \)
\( c \cdot 37^{0} \)
D. \( 30^{\circ} \)


What is the difference between concave
and convex mirrors? Choose the correct
statement?
A. Convex mirror is curved outwards and concave mirror is curved inwards
B. Focal point is in front of convex mirror and for a concave mirror, it is behind
c. centre of curvature is in front of convex mirror and for concave mirror, it is behind
D. None of these


Two capacitors of unknown
capacitances \( C_{1} \) and \( C_{2} \) are connected
first in series and then in parallel across a battery of \( 100 \mathrm{V} \). If the energy stored in two combinations is 0.045
and 0.25 J respectively, determine the
value of \( C_{1} \) and \( C_{2} . \) Also calculate the
charge on each capacitor in parallel combination.


If \( S_{1}, S_{2}, S_{3} \) be respectively the sums of \( n, 2 n, 3 n \) terms of a \( G . P ., \) then prove that

If the series \( a_{1}, a_{2}, a_{3}, a_{n} \) be a \( G . P . \) of
common ratio \( r, \) then prove that \( \frac{1}{a_{1} m+a_{2} m}+\frac{1}{a_{2} m+a_{3} m}+\dots+ \)
\( \frac{1}{a_{n-1}^{m}+a_{n-1}^{m}}=\frac{1-r^{m(1-n)}}{a_{1}^{m}\left(r^{m}-r^{-m}\right)} \)


\( \mathbf{5 0} \boldsymbol{V} \) battery is supplying current of \( \mathbf{1 0} \) amp when connected to a resistor. If the
efficiency of battery at this current is 25
\%. Then internal resistance of battery
is:-
A . \( 2.5 \Omega \)
B. \( 3.75 \Omega \)
c. \( 1.25 \Omega \)
D. \( 5 \Omega \)


Arrange the following carboxylic acids in increasing order of reactivity towards thermal decarboxylation reaction:
\( A \cdot|<||<|||<\mid V \)
c. \( |<| V<\|<\| \)


Which one of the following is not normally excreted in urine?
A. Uric acid
B. Haemoglobin
c. Ketone bodies
D. Hippuric acid


Name the following reaction.
\( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{B r}+\boldsymbol{A} \boldsymbol{g} \boldsymbol{F} \rightarrow \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{F}+ \)
\( A g B r \)


Which of the following is the main purpose of respiration in plants?
A. Breaking of complex food into simple ones
B. Production of energy
c. Exchange of gases
D. Both A and B


The amount of DNA in a mammalian
cell in early prophase I is \( x \)
What is the amount of DNA in the same
cell in anaphase I of meiosis?
A \( \cdot \frac{x}{4} \)
в. \( \frac{x}{2} \)
\( c \cdot x \)
D. \( 2 x \)


The tRNA anticodon 3-UAC-5 will pair
with the mRNA codon
A. 5-AUU-3
B. 5-UAC-3
c. 5-AUG-3
D. 3-GUA-5


Which statement about a \( 3 p \) orbital is
correct?
A. It can hold a maximum of 6 electrons
B. It has the highest energy of the orbitals with principal quantum number 3
C. It is at a higher energy level than a 3 s orbital but has the same shape
D. It is occupied by one electron in an isolated phosphorous atom


Mesangial cells are located
A. In endothelium of glomerulus
B. Between endothelium and basal lamina
C. Infiltration slit
D. Sub podocytic space


If \( M \) denotes the maximum value of
\( \left(1+\sec ^{-1} x\right)\left(1+\cos ^{-1} x\right) \& m \)
denotes the maximum value of
\( \left(1+\operatorname{cosec}^{-1} x\right)\left(1+\sin ^{-1} x\right), \) then
\( \left[\frac{M}{m}\right] \) is (where [.] denotes greatest integer function)


The work-energy theorem states that
the change in
A. Kinetic energy of a particle is equal to the work done on it by the net force
B. Kinetic energy of a particle is equal to the work done by one of the forces acting on it
C. Potential energy of a particle is equal to the work done on it by the net force
D. Potential energy of a particle is equal to the work done by one of the forces acting on it


A spherical mirror has radius of curvature equal to \( 50 \mathrm{cm} \). Find the value
of focal length.
\( \mathbf{A} \cdot 50 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
\( \mathrm{c} \cdot 25 \mathrm{cm} \)
D. \( 100 \mathrm{cm} \)


Which of the following minerals activates the enzymes involved in respiration?
A. Nitrogen and phosphorus
B. Magnesium and manganese
c. Potassium and calcium
D. Sulphur and iron
E. copper and boron


Draw a labelled diagram of an electric
generator


Assertion
Magnetic force on a moving charge is always perpendicular to the magnetic field.
Reason
Electric force on a charge is along the direction of electric field.
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


Which is the best description of a
covalent bond?
A. Electrons are simultaneously attracted by more than one nucleus.
B. Filled orbitals of two or more atoms overlap one another.
C. Unoccupied orbitals of two or more atoms overlap one another.
D. Oppositely charged ions attract one another.


Examine the following curve for continuity and differentiability: \( \boldsymbol{y}=\boldsymbol{x}^{2} \)
for \( \boldsymbol{x} \leq \mathbf{0} ; \boldsymbol{y}=\mathbf{1} \) for \( \mathbf{0} \boldsymbol{x} \leq \mathbf{1} \) and \( \boldsymbol{y}=\mathbf{1} / \boldsymbol{x} \)
for \( x>1 . \) Also draw the graph of the
function.


The reaction of elemental \( P_{4} \) in aqueous
NaOH gives:
A. \( P H_{3}, N a H_{2} P O_{2} \)
в. \( P H_{3}, N a_{3} P O_{4} \)
c. \( N a H_{2} P O_{4}, N a_{3} P O_{4} \)
D. \( N a_{3} P, N a_{3} P O_{4} \)


Show that in an arithmetical
progression \( a_{1}, a_{2}, a_{3} \)
\( \boldsymbol{S}=\boldsymbol{a}_{1}^{2}-\boldsymbol{a}_{2}^{2}+\boldsymbol{a}_{3}^{2}-\boldsymbol{a}_{4}^{2}+_{--} \)
\( \boldsymbol{a}_{2 k}^{2} \)
\( =\frac{k}{2 k-1}\left(a_{1}^{2}-a_{2 k}^{2}\right) \)


In the figure shown, cylinder'A' has
pump piston, whereas \( \mathrm{B} \) and \( \mathrm{C} \) cylinders
have lift pistons. If the maximum weight that can be placed on the pump
piston is 50 kgwt what is the maximum
weight that can be lifted by the piston in the cylinder'B'. Find the total
mechanical advantage. (Take \( \boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)


The polymer used for post operative stitches is:
A. glycolic acid
B. poly lactic acid
c. Nylon-2 - Nylon- -
D. PHBV


The sum of 49 consecutive integers is
\( 7^{5} . \) What is their median?
\( A \cdot 7 \)
B \( \cdot 7^{2} \)
\( c \cdot 7^{3} \)
\( D \cdot 7^{4} \)


If different class of compounds are present it is termed as:
A. chain isomerism
B. position isomerism
c. ring chain isomerism
D. metamerism


The period of element having three shells with three electrons in valence
shell is:
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


An inductor is connected to a battery
through \( e_{1} \) switch induced emf is a
when the switch is pressed and \( e_{2} \) when
the switch is opened. Then:
A \( \cdot e_{1}=e_{2} \)
в. \( e_{1}>e_{2} \)
c. \( e_{1}<e_{2} \)
D. \( e_{1}>\mid<e_{2} \)


Integrate:
\( \int \frac{2+\sin 2 x}{1+\cos 2 x} e^{2} d x \)


A box contains 6 red marbles numbers
from 1 through 6 and 4 white marbles
12 through 15. Find the probability that a marble drawn 'at random' is white and
odd numbered
A . 5
B. \( \frac{1}{5} \)
\( c \cdot 6 \)
D.


A radioactive element \( \boldsymbol{A} \) on
disintegration gives two elements \( B \) and \( C . \) If \( B \) is helium and \( C \) is the
element of atomic number 90 and
atomic mass 234 , the element \( A \) is:
\( A \cdot \frac{238}{92} U \)
B \( \cdot_{88}^{24} R a \)
\( \mathbf{c} \cdot_{90}^{24} T h \)
D・ \( 23372 a \)


FeCl \( _{3} .4 H_{2} O \) is actually:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{4}\right] C l_{3} \)
\( \mathbf{B} \cdot\left[F e\left(H_{2} O\right)_{3} C l\right] C l_{2} \cdot H_{2} O \)
\( \mathbf{c} \cdot\left[F e\left(H_{2} O\right)_{4} C l_{2}\right] C l \)
D. \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3} \mathrm{Cl}_{2}\right] \mathrm{Cl} . \mathrm{H}_{2} \mathrm{O} \)


If \( f(x)=x^{2}-x+5, x>\frac{1}{2}, \) and \( g(x) \) is
its inverse function, then \( g^{\prime}(7) \) equals:
A. \( -\frac{1}{3} \)
в. \( \frac{1}{13} \)
c. \( \frac{1}{3} \)
D. \( -\frac{1}{13} \)


A particle of mass \( m \) is executing S.H.M If amplitude is a and frequency \( n \), the value of its force constant will be:
\( \mathbf{A} \cdot m n^{2} \)
B. \( 4 m n^{2} a^{2} \)
\( \mathrm{c} \cdot m a^{2} \)
D. \( 4 \pi^{2} m n^{2} \)


In a school, there are 1000 student, out
of which 430 are girls. It is known that out of \( 430,10 \% \) of the girls study in class \( X I I . \) What is the probability that
a student chosen randomly studies in
class \( X I I \) given that the chosen
student is a girl?.


Which of them is released on heating
\( \boldsymbol{P b}\left(\boldsymbol{N O}_{3}\right)_{2} ? \)
A . \( N O \)
в. \( N_{2} \),
c. \( N_{2} O_{3} \)
D. \( N O_{2} \)


Linear momentum and angular
momentum have the same dimensions
in:
A. mass and length
B. length and time
c. mass and time
D. mass, length and time


A body is projected upwards with a velocity \( u \). It passes through a certain
point above the ground after \( t_{1} \) second The time after which the body passes through the same point during the return journey is
A. \( \frac{u}{g}-t_{1}^{2} \)
В \( \cdot 2\left[\frac{u}{g}-t_{1}\right] \)
c. \( _{3} \frac{u^{2}}{g}-t_{1} \)
D. \( _{3} \frac{u^{2}}{g^{2}}-t_{1} \)


Sketch the graph for \( y=1+ \)
\( \mathbf{3}(\log |\sin \boldsymbol{x}|+\log |\mathbf{c s c} \boldsymbol{x}|) \)


The focal length of a convex lens when placed in air and then in water will :
A. increase in water with respect to air
B. increase in air with respect to water
c. decrease in water with respect to air
D. remain the same


Find the Odd one among : 49, 121, 169,
225,289,361
A . 225
B. 121
\( c \cdot 49 \)
D. 36


The first term of the G.P. is 25 and 6 th
term is \( 800 . \) Find the seventh term.


Equation of a straight line on which length of perpendicular from the origin is four units and the line makes an
angle of \( 120^{\circ} \) with \( x- \) axis is
A \( . x \sqrt{3}+y+8=0 \)
в. \( x+\sqrt{3} y=8 \)
c. \( x \sqrt{3}-y=8 \)
D. \( x-\sqrt{3} y+8=0 \)


Which oxide is formed when potassium is heated in excess of oxygen?
\( A \cdot K_{2} O \)
B. KO
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{O}_{2} \)
D. \( K O_{2} \)


Lymph is responsible for removal of
A. Antigens
B. Toxins
c. Interstitial fluid
D. All of the above


The logic circuit in the figure represents characteristics of which logic gate?
A . NOR
B. OR
c. NAND
D. NOT


The end product of anaerobic respiration, in plants, is
A. Pyruvic acid
B. Malic acid
c. Ethyl alcohol
D. Methyl alcohol


The spreading of white light into its component colours is known as.
A. Dispersion
B. Deviation
c. Refraction
D. Diffraction


If \( \boldsymbol{y}=\boldsymbol{x}^{n}, \) then the ratio of relative
errors in \( y \) and \( x \) is
A . 1: 1
B . 2: 1
\( c \cdot 1: n \)
D. \( n: 1 \)


Both organs of which set secretes hormones?
A. spleen- Brain
B. Intestine- Eye
c. spleen- Liver
D. Testes- Placenta


The only non-metal, which is a liquid at
room temperature is:
\( A \cdot O_{2} \)
B. \( \mathrm{F}_{2} \)
\( c \cdot N_{2} \)
D. Bra


What is active glucose?
A. FAD glucose
B. NAD glucose
c. Glucose-6-Phosphate
D. Glycerophosphate


Find the ratio between the depths where the pressures are \( 3 \times 10^{5} N m^{-2} \) and
\( \mathbf{5} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{N} \boldsymbol{m}^{-\mathbf{2}} \cdot\left(\boldsymbol{P}_{\boldsymbol{A}}=\mathbf{1 0}^{\mathbf{5}} \boldsymbol{N} \boldsymbol{m}^{-\mathbf{2}}\right) \)


Potential due to a point mass \( m \) at a distance \( r \) is \( V=-\frac{G M}{r} \)


The translocation of organic solutes in sieve tube members is supported by
A. Mass flow involving a carrier and ATP
B. Cytoplasmic streaming
c. Root pressure and transpiration pull
D. P-proteins


A convex mirror with a radius of
curvature of \( 3 m \) is a used as rear view
mirror for a vehicle. If a bus is located at
\( 5 m \) from this mirror, find the position, nature and size of the image.


A field of strength \( \frac{\mathbf{5} \times \mathbf{1 0}^{\mathbf{4}}}{\boldsymbol{\pi}} \) ampere
turns /meter acts at right angles to a coil of 50 turns of area \( 10^{-2} m^{2} . \) The coil
is removed from the field in 0.1 second.
Then, the induced e.m.f in the coil is:
A . \( 0.1 \mathrm{v} \)
B. 0.2 \( v \)
c. \( 1.96 v \)
D. 0.98


Among the following mixtures, dipoledipole as the major interaction is
present in :
A . \( K C l \) and water
B. benzene and carbon tetrachloride
c. benzene and ethanol
D. acetonitrile and acetone


In the arrangement shown in figure,
dielectric constant \( k_{1}=2 \) and \( K_{2}=3 . \) If
the capacitance across \( \mathrm{P} \) and \( \mathrm{Q} \) are \( C_{1} \) and \( C_{2} \) respectively, then \( \frac{C_{1}}{C_{2}} \) will be (the gaps shown are negligible)
A . 1:
B. 2:
\( c .9: 5 \)
D. 25: 24


it strikes the rod normally,


The force on a charged particle moving through a magnetic field is maximum when
A. Moving with the field
B. Moving against the field
C. Moving at a \( 45^{\circ} \) angle to the field
D. Moving at a \( 90^{\circ} \) angle to the field
E. The particle will not be affected


During waste water treatment, trickling filter is used for
A. Primary treatment
B. Secondary aerobic treatment
c. Secondary anaerobic treatment
D. Tertiary treatment


n figure, \( \boldsymbol{k}=\mathbf{1 0 0} \boldsymbol{N} / \boldsymbol{m}, \boldsymbol{M}= \)
1 kgand \( F=10 N . \) Write the potential
energy of the spring when the block is at the right extreme during simple harmonic motion
If your answer is \( x \) write the value of \( 4 x \)


Prove that
\( \frac{\sin A+\sin B}{\cos A+\cos B}=\tan \frac{A+B}{2} \)


Let the three digit numbers \( A 28,3 B 9 \)
and \( 62 C, \) where \( A, B, C \) are integers
between 0 and 9 , be divisible by a fixed integer \( k, \) Show that the determinant \( \left|\begin{array}{lll}\boldsymbol{A} & \boldsymbol{3} & \boldsymbol{6} \\ \boldsymbol{8} & \boldsymbol{9} & \boldsymbol{C} \\ \boldsymbol{2} & \boldsymbol{B} & \boldsymbol{2}\end{array}\right| \) is also divisible by the
same integer \( \boldsymbol{k} \)


Very short answer type.
Who raised the fungi to the status of an
independent kingdom?


Ozone higher up in the atmosphere acts as a shield to prevent UV rays from reaching the Earth's surface These UV
rays are responsible for which of the following diseases?
(i) Skin cancer
(ii) Eye damage
(iii) Lung cancer
(iv) Damage to immune system Colour blindness
A . (i), (ii) \& (iii)
B. (i), (ii), (iv) \& (v)
\( c \cdot(i),(\text { iii) },(v) \)
D. (i), (ii), (iii), (iv) \& (v)


\( \operatorname{Let} \overline{\boldsymbol{a}}=\mathbf{2} \overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}+\overline{\boldsymbol{k}}, \overline{\boldsymbol{b}}=\overline{\boldsymbol{i}}+\mathbf{2} \overline{\boldsymbol{j}}-\overline{\boldsymbol{k}} \) and
a unit vector \( \bar{c} \) be coplanar. If \( \bar{c} \) is
perpendicular to \( \bar{a} \), then \( \bar{c} \) is


Assertion
The burning of a candle is both a
physical and a chemical change.
Reason
Burning of candle melts the wax and hence physical state of wax has changed from solid to liquid. Again the wax combines with the atmosphere oxygen and changes to carbon dioxide, heat and light.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A torch converts
energy to energy.
A. chemical, heat
B. electrical, chemical
c. chemical, light
D. light, electrical


In which of the following is the \( O \)
\( N-O \) bond angle highest ?
A \( . N O_{2} \)
B. \( N O_{2}^{+} \)
\( \mathbf{c} \cdot N O_{2} \)
D. \( N O_{3}^{-} \)


To measure atmospheric pressure,
Torricelli in 1643 made an instrument,
which is called:
A. hygrometer
B. barometer
c. anemometer
D. none of these


In the residential area at night, the standard limit of sound intensity is decibel.
A . 55
B. 70
c. 45
D. 40


Which of the following are negative colloids?
This question has multiple correct options
A \( \cdot \operatorname{Fe}(O H)_{3} \) sol
в. \( A s_{2} S_{3} \) sol
c. Blood
D. Gold sol


It is first face of a prism which disperses white light. The statement is
A. True
B. False


Select the correct IUPAC name for
\( \left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+} \) complex ion
A. Tetraammineplatinum(II) ion
B. Tetraammineplatinum(2+) ion
c. Tetraammineplatinate(II) ion
D. Tetraammineplatinate(2+) ion


Differentiate between
Hygroscopic Water and capillary Water


\( \lim _{\boldsymbol{x} \rightarrow \frac{\pi}{2}} \frac{\operatorname{cosec} \boldsymbol{x}-\cot \boldsymbol{x}}{\boldsymbol{x}}= \)
\( \mathbf{A} \cdot 1 \)
\( B \cdot \frac{2}{\pi} \)
\( c \cdot \frac{1}{2} \)
\( D \cdot \frac{1}{5} \)


Write object of Dacisson and Germer's experiment. Draw a labelled diagram of its parctical arrangement.


If \( \sin x+\cos x=\sqrt{y+\frac{1}{y}}, x \epsilon[0, \pi] \) and
\( \boldsymbol{y}>0, \) then
A . \( x=\pi / 4 \)
B. \( x=\frac{\pi}{2} \)
c. \( x=\frac{\pi}{6} \)
D. \( x=3 \pi / 4 \)


Fill in the blank:
During one synodic month, the Moon
takes \( _{--}-_{-}- \) complete revolution around the Earth with respect to the background stars.
A . 1
B. 0.5
c. 2
D. 0.25


Consider the following statements in respect of the determinant \( \left|\begin{array}{cc}\cos ^{2} \frac{\alpha}{2} & \sin ^{2} \frac{\alpha}{2} \\ \sin ^{2} \frac{\beta}{2} & \cos ^{2} \frac{\beta}{2}\end{array}\right| \) where \( \alpha, \beta \) are
complementary angles
1. The value of the determinant is \( \frac{1}{\sqrt{2}} \cos \left(\frac{\alpha-\beta}{2}\right) \)
2. The maximum value of the determinant is \( \frac{\mathbf{1}}{\sqrt{\mathbf{2}}} \)
Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


A large number of particles are placed around the origin, each at a distance \( \boldsymbol{R} \)
from the origin. The distance of the
centre of mass of the system from the origin is:
\( \mathbf{A} \cdot=R \)
в. \( \geq R \)
\( c \cdot>R \)
\( \mathrm{D} \cdot \leq R \)


Which of the following statements about friction is true?
A. Frictional force can accelerate a body
B. Friction can be reduced to zero
C. Frictional force is proportional to the area of contact between the two surfaces
D. Sliding friction is always greater than rolling friction


Peptization denotes:
A. digestion of food
B. hydrolysis of proteins
C. breaking and dispersion into colloidal state
D. precipitation of solid from colloidal dispersion


Replace the blank with an integer to
make it a true statement.
\( 5 \times-----=-35 \)


\( N a O H+C H_{3} C O O H \longrightarrow \)
\( C H_{3} C O O N a+H_{2} O \)
This reaction is called:
A. oxidation reaction
B. hydrogention reaction
c. neutralisation reaction
D. addition reaction


Wind currents are generated due to:
A. Uneven heating between the equator and the poles
B. Change in atmospheric pressure
c. Thunderstorm
D. Cyclone


A bead of mass \( \mathrm{m} \) kept at the top of a
smooth hemispherical wedge of mass M and radius R, is gently pushed
towards right. As a result, the wedge slides due left. Find the a. speed of the
wedge
b. magnitude of velocity of the bead relative to the wedge


What are the advantages and disadvantages of water level controller and indicator?


A block of mass \( M \) with a semicircular
track of radius \( R \) rests on a horizontal
frictionless surface. A uniform cylinder
of radius \( r \) and mass \( m \) is released
from rest from the top point \( \boldsymbol{A} \). The
cylinder steps on the semicircular frictionless track. The distance travelled
by the block when the cylinder reaches
the point \( \boldsymbol{B} \) is :
A \( \cdot \frac{M(R-r)}{M+m} \)
В \( \cdot \frac{m(R-r)}{M+m} \)
c. \( \frac{(M+m) R}{M} \)
D. None of the above


Assertion
The calculated value of dipole moment
of \( L i I=11.5 D \) in the gaseous state is
more than its experimental value
\( (3.25 D) \)
Reason
In \( L i I \) the electron charge cloud of \( I^{-} \)
ion is polarized by \( L i^{+} \) ion; hence the
flow of electric charge occurs from \( \boldsymbol{I}^{-} \) to
\( \boldsymbol{L} \boldsymbol{i}^{+} \) ion.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Assertion is true, Reason is true and Reason is correct explanation for Assertion
B. Assertion is true, Reason is true and Reason is NOT the correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true


To increase de-Broglie wavelength of an electron from \( 0.5 \times 10^{-10} \mathrm{m} \) to \( 10^{-10} \mathrm{m} \)
its energy should be
A. Increased to 4 times
B. Halvedd
c. Doubled
D. Decreases to fourth parttt


If \( x \) is a random variable with
probability distribution \( \boldsymbol{p}(\boldsymbol{x}=\boldsymbol{k})= \)
\( \frac{(\boldsymbol{k}+\mathbf{1}) \boldsymbol{C}}{\mathbf{2}^{k}}, \boldsymbol{k}=\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots \dots \dots \dots, \) then
find \( C \)


A bomb explodes on the moon. How long will it take for the sound to reach the
earth?
A . 10 seconds
B. 1000 seconds
c. 1 day
D. None of these


The correct increasing order of melting point of alkali metal carbonates is:
A \( \cdot C s_{2} C O_{3}<N a_{2} C O_{3}<K_{2} C O_{3}<R b_{2} C O_{3}< \)
\( L i_{2} C O_{3} \)
в. \( L i_{2} C O_{3}<N a_{2} C O_{3}<K_{2} C O_{3}<R b_{2} C O_{3}< \)
\( C s_{2} C O_{3} \)
3
c. \( L i_{2} C O_{3}<R b_{2} C O_{3}<K_{2} C O_{3}<N a_{2} C O_{3}< \)
\( C s_{2} C O_{3} \)
D. None of these


Amongst \( L i C l, R b C l, B e C l_{2} \) and
\( M g C l_{2}, \) the compounds with the
greatest and the least ionic character
respectively are:
\( \mathbf{A} \cdot L i C l \) and \( R b C l \)
в. \( R b C l \) and \( B e C l_{2} \)
c. \( M g C l_{2} \) and \( B e C l_{2} \)
D. \( R b C l \) and \( M g C l_{2} \)


Explain why:
\( C u^{+} \) is diamagnetic but \( C u^{2+} \) is paramagnetic. \( (Z=29) \)


The number of arrangements in which
the letters of the word DEEDS be
arranged such that neither the two D's nor the two E's are together is
A . 10
B. 12
c. 18
\( D \)


Let \( Y_{S} \) and \( Y_{A} \) represent Young's modulus for steel and aluminium
respectively lt is said that steel is more elastic than aluminium. Therefore, it
follows that
A. \( Y_{S}=Y_{A} \)
в. \( Y_{S}<Y_{A} \)
c. \( Y_{S}>Y_{A} \)
\( \stackrel{Y_{S}}{Y_{A}}=0 \)


For a real number \( \boldsymbol{y},[\boldsymbol{y}] \) denotes the
greatest integer less than or equal to \( y \) then \( f(x)=\frac{\tan (\pi[x-\pi])}{1+[x]^{2}} \) is
A. discontinuous at some \( x \)
B. continuous at all \( x \), but \( f^{\prime}(x) \) does not exist for same \( x \)
\( \mathbf{C} \cdot f^{\prime}(x) \) exists for all \( x \) but \( f^{\prime}(x) \) does not exist
D. \( f^{\prime}(x) \) exists for all \( x \)


If the inertial mass \( m_{i} \) of the bob of a
simple pendulum of length \( ; l^{\prime} \) is not
equal to the gravitational mass \( m_{g} \) then its time period is:
\( ^{\mathrm{A}} \cdot_{T}=2 \pi \sqrt{\frac{m_{i} l}{m_{g} \cdot g}} \)
В \( \cdot T=2 \pi \sqrt{\frac{m_{g} \cdot l}{m_{i \cdot g}}} \)
\( ^{\mathbf{c}} \cdot_{T}=2 \pi \sqrt{\frac{l}{g}} \)
\( ^{\mathrm{D}} \cdot_{T}=2 \pi \sqrt{\frac{\left(m_{i}+m_{g}\right)}{\left(m_{i}-m_{g}\right)} \cdot \frac{l}{g}} \)


Why is sexual reproduction considered to be superior to asexual reproduction in terms of evolution?


Find the cost price / Selling price
\begin{tabular}{llll}
cost price & Selling price & Profit & Loss \\
\hline (i) 7,282 & & 208 & \\
(ii) & 572 & 72 & \\
(iii) 9,684 & & & 684 \\
(iv) & 1,973 & 273 & \\
(v) & & & \\
6,76,000 & & & 18,500 \\
& & &
\end{tabular}


The addition of two negative numbers is \( -108 . \) If one of the number is \( -79, \) find
the other number
A . -29
B . -187
c. 29
D. 187


The internal and external diameter of a
hollow hemi-spherical vessel is \( 24 \mathrm{cm} \)
and \( 25 c m \) respectively. The cost of paint
one sq.cm of the surface is paise. Find
the total cost to paint the vessel all over


Distance travelled by body from \( (n- \)
1) \( ^{t h} \sec \) to \( n^{t h} \) secis :


Formation of volatile \( N i(C O)_{4} \) and
its subsequent heating gives pure Ni This process is called
A . Hall
B. Dow
c. serpeck
D. Mond


A thin copper wire of length \( 100 \mathrm{m} \) is wound as a solenoid of length \( l \) and radius \( r . \) Its self-inductance is
found to be L. Now if the same length of wire is wound as a solenoid of length \( l \)
but of radius \( r / 2, \) then its self-
inductance will be :
A . \( 4 L \)
B. 2L
\( c \cdot L \)
D. L/2


Which of the compound is both paramagnetic and coloured?
A. \( C u F_{2} \)
в. \( K_{3}\left[C u(C N)_{4}\right] \)
c. \( K_{2}\left[T i C l_{6}\right] \)
D. \( K_{2} C r O_{4} \)


Natural rubber is a:
A. polyester
B. polyamide
c. polyisoprene
D. polysaccharide


The freezing point of 0.02 mol fraction of acetic acid in benzene is \( 277.4 K \)
Acetic acid exists partly as a dimer. Calculate the equilibrium constant for dimerization. (approximately)
(Freezing point of \( C_{6} H_{6}=278.4 K \) and
\( \boldsymbol{K}_{f} \) of \( \boldsymbol{C}_{6} \boldsymbol{H}_{6}=\mathbf{5} \boldsymbol{K} \boldsymbol{m}^{-1} \mathbf{)} \)
A . 2.6
в. 3.
c. 4.3
D. 5.8


In a first order reaction, \( 75 \% \) of the reactants disappeared in 1.386 hr. What
is the rate constant?
A \( \cdot 3.6 \times 10^{-3} s^{-1} \)
В. \( 2.7 \times 10^{-4} s^{-1} \)
c. \( 72 \times 10^{-3} s^{-1} \)
D. \( 1.8 \times 10^{-3} s^{-1} \)


A matrix has 16 elements Which of the
following can be the order of the matrix?
A . \( 1 \times 16 \)
B. \( 2 \times 8 \)
\( c \cdot 4 \times 4 \)
D. All of these


When \( O_{2} \) is absorbed on a metallic
surface, electron transfer occurs from
the metal to \( O_{2} \). The true statement(s)
regarding this adsorption is(are):
This question has multiple correct options
A. \( O_{2} \) is physisorbed
B. heat is released
C. occupancy of \( \pi_{x_{p}^{*}} \) of \( O_{2} \) is increased
D. bond length of \( O_{2} \) is increased


The dissociation equilibrium of a gas
\( A B_{2} \) can be represented as:
\[
\begin{array}{r}
\mathbf{2 A B}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2 A B}(\boldsymbol{g})+ \\
\boldsymbol{B}_{2}(\boldsymbol{g})
\end{array}
\]
The degree of dissociation is \( x \) and is
small compared to 1. The expression relating the degree of dissociation \( x \)
with equilibrium constant \( \boldsymbol{K}_{\boldsymbol{p}} \) and total
pressure \( p \) is:
\( A \)
\[
\left(2 K_{p} / p\right)
\]
В \( \cdot\left(2 K_{p} / p\right)^{1 / 3} \)
c. \( \left(2 K_{p} / p\right)^{1 / 2} \)
D. \( \left(K_{p} / p\right) \)


\( \widehat{n} \)
Q Type your question
and function
\( A \cdot a \)
\( B . \)
\( \mathbf{C} \)
D.


Air is a bad conductor of heat because:
A. it's molecules are in continuous contact with each
other.
B. it's molecules are not in continuous contact with each
other
C. it's molecules absorb all the heat
D. it's molecules are moving randomly due to Brownian motion


Ten small planes are flying at a speed of \( 150 \mathrm{km} h^{-1} \) in total darkness in an air
space that is \( 20 \times 20 \times 1.5 k m^{3} \) in
volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with your plane. Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius 10
\( \mathrm{m} \)
A. 125 h
в. 220h
c. 432 h
D. 225h


A man travels \( 600 \mathrm{km} \) by train at 800 \( \mathrm{km} / \mathrm{hr}, 800 \mathrm{km} \) by ship at \( 40 \mathrm{km} / \mathrm{hr} \)
\( 500 \mathrm{km} \) by aeroplane at \( 400 \mathrm{km} / \mathrm{hr} \) and \( 100 \mathrm{km} \) by car at \( 50 \mathrm{km} / \mathrm{hr} . \) What is the
average speed for the entire distance?
\( \mathbf{A} \cdot 60 \mathrm{km} / \mathrm{hr} \)
в. \( 60 \frac{5}{123} \mathrm{km} / \mathrm{hr} \)
c. \( 62 \mathrm{km} / \mathrm{hr} \)
D. \( 83 \frac{1}{3} \mathrm{km} / \mathrm{hr} \)


A hypothetical planet has density \( \rho \) radius \( R, \) and surface gravitational acceleration g. If the radius of the
planet were doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet's surface would be?


Chlorine atom in \( N a C l \) gets a unit
negative charge:
A. its nucleus has 17 protons, 18 electrons
B. its nucleus has 18 protons, 17 electrons
c. its nucleus has 8 protons, 7 electrons
D. none of the above


Find \( \boldsymbol{A}+\boldsymbol{B} \)
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{3} & \mathbf{- 1} \\ \mathbf{2} & \mathbf{- 5} & \mathbf{4} \\ \mathbf{3} & \mathbf{2} & \mathbf{- 6}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{2} & \mathbf{4} & \mathbf{0} \\ \mathbf{3} & \mathbf{- 4} & \mathbf{5} \\ \mathbf{2} & \mathbf{3} & \mathbf{- 5}\end{array}\right] \)


\( C O_{2} \) is removed from the blood in the
A . ovaries
B. Heart
c. Kidney
D. Lungs


Which of the following is not correct about sulphuric acid?
A. Reducing agent
B. Dehydrating agent
c. Sulphonating agent
D. Highly viscous


Which of the following will have a mesoisomer also?
A . 2- chlorobutane
B. 2,3 - dichlorobutane
c. 2,3 - dichloropentane
D. 2 - hydroxypropanoic acid


Two trains depart from one station, one
going north at 30.00 miles per hour, and another going west, steadily accelerating with a rate of 0.3333 miles per minute How many minutes after departure would the two trains be 50.00 miles
apart?
A. 10.96 min
B. 76.28 min
c. 89.54 min
D. 120.0 min
E . 240.0 min


In which of the compound given below contains more than one kind of
hybridization \( \left(s p, s p^{2}, s p^{3}\right) \) for carbon:
A \( \cdot C H_{3} C H_{2} C H_{2} C H_{3} \)
в. \( C H_{3}-C H=C H-C H_{3} \)
\( \mathrm{c} \cdot C H_{2}=C H-C H=C H_{2} \)
D. \( H-C \equiv C-H \)


Botanical name of Radish is
B. Brassica oleracea
c. Raphanus sativa
D. None of the above


Which of the following antibiotics was first discovered?
A. Ampicillin
B. Amoxycilline
c. Panicilline
D. None of the above


Each of the following is true for white and red phosphorus except that they:
A . are both soluble in \( C S_{2} \)
B. can be oxidized by heating in air
c. consist of the same kind of atoms
D. can be converted into one another


Find the locus of a point which moves in
such a way that the sum of its distances from(4,3) and (4,1) is 5.


\( N_{2} \) gas is assumed to behave ideally \( A \)
given volume of \( N_{2} \) originally at \( 373 \mathrm{k} \)
and 0.1013 M pa pressure is adiabatically compressed due to which
its temperature rises to \( \mathbf{6 7 3} \boldsymbol{K}\left(\boldsymbol{C v}=\frac{\mathbf{5}}{\mathbf{2}} \boldsymbol{R}\right) \)
Which of the following statement(s) is/are correct?
This question has multiple correct options
A. The change in internal energy is 6235.5 J mole \( ^{-1} \)
B. In this case the final internal pressure is equal to the external pressure
C. The final pressure of \( N_{2} \) is approximately 0.38 MPa
D. The final pressure of \( N_{2} \) is approximately 0.02 Mpa


Give the main sources of Vitamins \( \boldsymbol{A}, \boldsymbol{C} \)
and \( D \). Write down the names of
diseases caused by their deficiency.


For \( \boldsymbol{x} \in(\mathbf{0}, \boldsymbol{\pi} / \mathbf{2}) \)
\( \sin ^{-1}(\cos x)=? \)
A. \( \pi-x \)
B \( \cdot \frac{\pi}{2}-x \)
c. \( \pi-\frac{x}{2} \)
D . \( \pi-2 x \)


find the equation of a line passing
through the point (1,2,-4) and
perpendicular to two lines. \( \vec{r}= \) \( (8 \hat{i}-19 \hat{j}+10 \hat{k})+ \)
\( \boldsymbol{\lambda}(\boldsymbol{3} \hat{\boldsymbol{i}}-\boldsymbol{1 6} \hat{\boldsymbol{j}}+\boldsymbol{7} \hat{\boldsymbol{k}}) \) and \( \overrightarrow{\boldsymbol{r}}= \)
\( (15 \hat{i}+29 \hat{j}+5 \hat{k})+ \)
\( \boldsymbol{\mu}(\mathbf{3} \hat{\boldsymbol{i}}+\quad \boldsymbol{8} \hat{\boldsymbol{j}}-\boldsymbol{5} \hat{\boldsymbol{k}}) \)


Euchlorine is a mixture of:
A. \( C l_{2} \) and \( S O_{2} \)
B. \( C l_{2} \) and \( C l O_{2} \)
c. \( C l_{2} \) and \( C O \)
D. \( C l_{2} \) and \( C O_{2} \)