If \( a \) and \( b \) are two non-zero non-collinear
vectors then \( a+3 b \) and \( a-3 b \) are:
A. Linearly independent.
B. Linearly dependent
c. May be both
D. None of these


Antony secured 384 marks out of 500
marks. Find the percentage of marks secured by Antony


Two plastic drinking straws are vigorously rubbed with a piece of wool
Then they are brought near each other as shown above. What observation con
you make?
A. They attract eachother
B. They repel eachother
c. nothing will happen
D. can't say


When the glandular cells breakdown completely, the gland is known as
A. Holocrine gland
B. Apocrine gland
c. Merocrine gland
D. None of these


Transition metals are less reactive than
alkali metals because they have:
A. high ionisation potential and low melting point
B. high ionisation potential and high melting point
c. low ionisation potential and low melting point
D. low ionisation potential and high melting point


Correct the mistakes, if any, in the
following statements.
i) One newton is the force that produces
an acceleration of \( 1 \mathrm{ms}^{-2} \) in an object
of 1 gram mass.
ii) Action and reaction always act on the same body


An enclosed fluid under pressure exerts that pressure throughout its volume and against any surface containing it. Is the statement true or false
A . True
B. False


State whether true or false.
A ball thrown upwards in a train moving with uniform velocity returns to the
thrower
A. True
B. False


Explain with suitable diagram and appropriate examples why some nonideal solution show positive deviation from ideal behavior:


The modulus of elasticity of a material
does not depend upon
A. shape
B. temperature
c. nature of material
D. impurities mixed


Define chemotaxonomy in a sentence.


Which one is a broad spectrum antibiotic?
A. Chloramphenicol
B. Plasmoquin
c. xylocaine
D. None of these


Which of the following is a weak acid?
A. \( \mathrm{H}_{2} \mathrm{Te} \)
в. \( \mathrm{H}_{2} \mathrm{Se} \)
c. \( \mathrm{H}_{2} \)
D. \( \mathrm{H}_{2} \mathrm{Po} \)


The bleaching action of the bleaching powder is due to liberation of :
A. nascent chlorine
B. nascent oxygen
c. nascent hydrogen
D. atomic hydrogen


Multiple Choice Questions Eutrophication of water bodies leading to killing of fishes is mainly due to nonavailability of.
A. Food
B. Light
c. Essential minerals
D. oxygen


The IUPAC name of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{2} \boldsymbol{B r} \) is
A. 1-bromopentane
B. 1-bromo-3-methylbutane
c. 2-methyl-4-bromobutane
D. 2-methyl-3-bromopropane


Describe the principle involved in each
of the following processes.
(i) Mond process for refining of nickel
(ii) Column chromatography for purification of rare relements


If \( n(A)=1000, n(B)=500 \) and if
\( \boldsymbol{n}(\boldsymbol{A} \cap \boldsymbol{B}) \geq 1 \) and \( \boldsymbol{n}(\boldsymbol{A} \cup \boldsymbol{B})=\boldsymbol{p}, \) then
A. \( 500 \leq p \leq 1000 \)
B . \( 1001 \leq p \leq 1498 \)
c. \( 1000 \leq p \leq 1498 \)
D. \( 999 \leq p \leq 1499 \)
E . \( 1000 \leq p \leq 1499 \)


If \( \Delta G \) standard is zero, this means:
A. the reaction is both spontaneous and at equilibrium
B. the system is at equilibrium at standard conditions
C. the reaction is non spontaneous at standard conditions
D. the reaction is spontaneous at standard conditions
E. the reaction is both non spontaneous and at equilibrium


Aluminium exhibits +3 oxidation state.
As we move down the group, +1 oxidation states get more stable. This is
a consequence of :
A. increasing size of the atom
B. inert pair effect
c. electron deficient nature
D. \( p \pi \) - \( p \pi \) bonding


\( 0_{3} \) with \( K I \) solution produces:
A \( \cdot K_{2} O \)
В. \( I_{2} \)
c. \( H I \)
D. \( H I O_{3} \)


Find the sum of first \( n \) terms and the
sum of first 5 terms of the geometric series \( 1+\frac{2}{3}+\frac{4}{9}+\dots \)


The value of a new bike is Rs. 50,000 . If
the value depreciated by \( 5 \% \) in two years, find the value of the bike after 2
years


Which one of the following pairs of reactants does not produce oxygen when they react with each other?
A \( \cdot F_{2}, \) NaOH solution (hot, conc.
В. \( F_{2}, H_{2} O \)
c. \( C l_{2}, \) NaOH solution (cold, dilute)
D. \( C a O C l_{2}, H_{2} S O_{4} \) (dilute, small amount)


Which of the following is the cause of weightlessness experienced while orbiting around earth on a spaceship?
A. Inertia
B. Zero gravity
c. Acceleration
D. Centre of gravity


Which one of the following pairs is
correctly matched?
A. Streamlined body - Aquatic adaptation
B. Excessive perspiration - Xeric adaptation
C. Parasitism - Intra specific relationship
D. Uricotelism - Aquatic habitat


Show that the function \( f(x) \) defined as
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \cos \frac{1}{x}, \boldsymbol{x} \neq \mathbf{0},=\mathbf{0}, \boldsymbol{x}=\mathbf{0} \) is
continuous at \( x=0 \) but not
differentiable at \( x=0 \)


Two projectile \( A \) and \( B \) thrown with
speed in the ratio acquired the same heights.If A is thrown at an angle of projection of B will be.


The products of \( (A) \) on ozonolysis
followed by reduction with LAH are:
\( \mathbf{A} \)
\( B \)
\( C \)
\( D \)


Monochromatic light passes through a prism. Compares to that in air, inside the prism the light's.
A. Speed and wavelength are different but frequency remains same
B. Speed and frequency are different but wavelength remains same
c. Frequency and wavelength are different but speed remains same
D. speed, wavelength and frequency are all different


Evaluate \( \sum_{k=1}^{11}\left(2+3^{k}\right) \)


An electric tea kettle has two electric
heating coils. When one of the coil is switched on the tea begins to boil in 6 minutes. When the other is switched on
the boiling begins in 8 minutes If both the coils are now arranged in series and switched on, boiling starts in
A . \( 24 / 7 \) minutes
B. 12 minutes
c. 14 minutes
D. 4 minutes


Area of each of the conducting plates 1
2,3,4,5 and 6 is \( A . \) The system is kept
in air. Find the the capacitance between
\( A \) and \( B(1 \& 4,2 \& 5 \text { and } 3 \& 6 \) are pairs
of parallel plates)
A. \( \frac{3 \varepsilon_{0} A}{d} \)
B. \( \frac{2}{3} \frac{\varepsilon_{0} A}{d} \)
c. \( \frac{3}{2} \frac{\varepsilon_{0} A}{d} \)
D. \( \frac{\varepsilon_{0} A}{3 d} \)


What are hydrocarbons?


The water equivalent of a body, whose mass is 'm' g and specific heat is 's' \( \operatorname{cal} g^{-1} C^{-1} \) is given by


Refrigerators and freezers works by:
A. Converting hot air to cold air
B. Keeping hot air out with cold air pressure
C. Removing heat from inside themselves
D. Blowing cold inside them
E. Producing cold air


Structurally, cellulose is a linear polymer of :
A. \( \beta \) -D-glucose units
B. sucrose molecules
c. \( \alpha \) -D-glucose units
D. glucose and fructose units


Find the ratio of the edge of a cube to
the radius of a sphere, if the volume of the cube is equal to the volume of the
sphere
A . 1.61
в. 2.05
c. 2.33
D. 2.45
E . 2.65


The magnitude of induced current in a closed coil increases with the increase
in the \( \ldots \ldots . . . . . . . . . . \) of magnetic lines of force.
A. strength
B. alternating
c. magnetic field
D. less


Two metallic wires \( A \) and \( B \) of equal
dimensions but made of different
materials, having resistivities \( \rho \) and \( 2 \rho \) temperature coefficients of resistivities \( 2 \alpha \) and \( \alpha \) are connected in series. The
temperature coefficient of resistance of the composite wire equals:
\( ^{\mathrm{A}} \rho_{e q}=\frac{3}{2} \rho \)
в. \( \quad \alpha_{e q}=\frac{3}{2} \)
\( c \cdot \rho_{e q}=3 \rho \)
D. \( _{\alpha_{e q}}=\frac{4}{3} \alpha \)


Select the correct statement(s):
This question has multiple correct options
A. When Al is added to potassium hydroxide solution,hydrogen gas is evolved
B. \( H_{2} S i F_{6} \) is formed when silica reacts with hydrogen fluoride followed by hydrolysis
C. Phosphine gas is formed when red phosphorus is heated with NaOH
D. \( \left(N H_{4}\right)_{2} S O_{4} . F e S O_{4} .6 H_{2} O \) is called alums


Evaluate \( \sin ^{-1}(\cos x) \)


Which of the following has the highest molar conductivity?
A. Diamminedichloroplatinum (II)
B. Tetramminedichlorocobalt(III) chloride
c. Potassium hexacyanoferrate (II)
D. Hexaaquochromium
(III) bromide


\( \boldsymbol{Y} \stackrel{\boldsymbol{N a}}{\longleftrightarrow} \boldsymbol{X} \stackrel{\boldsymbol{c o n c . H}_{2} \boldsymbol{S O}_{4}, \boldsymbol{4 1 3} \boldsymbol{K}}{\longrightarrow}\left(\boldsymbol{C}_{2} \boldsymbol{H}_{5}\right)_{2} \boldsymbol{O} \)
What are \( X \) and \( Y \) in the above reactions
\( ? \)
\( \mathbf{A} \cdot X-H_{3} C O H, Y-H_{3} C O N a \)
B \( \cdot X-C_{4} H_{9} O H, Y-C_{4} H_{9} O N a \)
\( \mathbf{c} \cdot X-C_{2} H_{5} O H, Y-C_{2} H_{5} O N a \)
D. \( X-C_{3} H_{7} O H, Y-C_{3} H_{7} O N a \)


In a half-wave rectifier circuit operating
from \( 50 \mathrm{Hz} \) mains frequency, the fundamental frequency in the ripple would be
A. \( 10 \mathrm{Hz} \)
B. 25 Hz
c. 50 нz
D. 100 нz


The time required for a first-order reaction for \( 99 \% \) completion is \( x \) times
for the time required for \( 90 \% \)
completion. \( \boldsymbol{x} \) is:


A car of mass \( m \) is taking a circular
turn of radius ' \( r^{\prime} \) on a fictional level road
with a speed \( v . \) In order that the car
does not skid
A \( \cdot \frac{m v^{2}}{r} \geq \mu m g \)
B . \( \frac{m v^{2}}{r} \leq \mu m g \)
c. \( \frac{m v^{2}}{r}=\mu m g \)
D. \( \frac{v}{r}=\mu m g \)


When zinc reacts with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}(60 \%) \)
the oxidation state of nitrogen changes
from :
\( \mathbf{A} \cdot+5 t o+1 \)
B. +5 to -3
\( \mathbf{c} \cdot+5 t o+4 \)
\( \mathbf{D} \cdot+5 t o+3 \)


The solubility of \( C a F_{2} \) is \( 2 \times 10^{-4} \)
mole/litre. Its solubility product is:
A \( .2 .0 \times 10^{-4} \)
B . \( 4.0 \times 10^{-8} \)
c. \( 8.0 \times 8.0 \times 10^{-12} \)
D. \( 3.2 \times 10^{-11} \)


In an irreversible process, system goes from an initial state \( A \) to a final state \( B \)
Which of the following is true?
A. Work done from state A to state B is zero
B. Heat required from state A to state B is non-zero
c. Heat required from state A to state B and back to state \( A \) is non-zero.
D. Heat required from state A to state B and back to state A may be non-zero


A Zener diode, having breakdown
voltage equal to \( 15 V \) is used in a
voltage regulator circuit shown in
figure. The current through the diode is
\( A \cdot 10 m A \)
B. \( 15 m A \)
\( c \cdot 20 m A \)
\( \mathbf{D} \cdot 5 m A \)


The animals possessing the following type of germ layers \( (A \text { and } B) \) are calbed
and
respectively.
A. diploblastic, triploblastic
B. triploblastic, diploblastic
C. diploblastic, diploblastic
D. triploblastic, triploblastic


One of these is not associated with
termination of protein synthesis
A. UAA
B. UAG
c. UGA
D. AUGGGGGGGGG


J.J.Thomson for the first time identified
electron as a particle and his son
G.P.Thomson first time identified
electron as a wave and both were
awarded Nobel Prize in different years.
A. True
B. False


Natural aging of a lake by nutrient enrichment of its water
A. Eutrophication
B. Carrying capacity
c. Photophosphorylation
D. None of the above


Match the correct atomic radius with
the element:
\( \begin{array}{ll}\text { Element } & \text { Atomic radius }(\mathrm{pm}) \\ \text { (a) } B e & \text { (p) } 74 \\ \text { (b) } C & \text { (q) } 88 \\ \text { (c) } O & \text { (r) } 111 \\ \text { (d) } B & \text { (s) } 77 \\ \text { (e) } N & \text { (t) } 66\end{array} \)


In the equilibrium, \( C a C O_{3}(s) \rightleftharpoons \)
\( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}), \) the number of
moles of \( C O_{2} \) is increased by
This question has multiple correct options
A. Increasing the volume of the vessel
B. Removing some \( C a C O_{3} \) from the mixture
c. Adding a few drops of NaOH to the reaction mixture.
D. Adding a few drops of HCI to the reaction mixture


If the segments joining the points \( A(a, b) \) and \( B(c, d) \) studends an angle
at the origin, prove that \( \cos \theta= \) \( \frac{\boldsymbol{a c}+\boldsymbol{b} \boldsymbol{d}}{\sqrt{\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}\right)\left(\boldsymbol{c}^{2}+\boldsymbol{d}^{2}\right)}} \)


For phenol, which of the following
statements is correct?
A. It is insoluble in water
B. It has higher boiling point than toluene
C. It does not shows acidic property
D. It has lower melting point compared to aromatic hydrocarbons of comparable molecular weight


The rate of Sales Tax
A. 8\%
B . 10\%
c. 12\%
D. 14\%


\( 0.4 g \) of \( N a O H \) present in one litre solution, then the \( p H: \)
A . 12
B. 2
\( c \cdot 6 \)
D. 10


Two tuning folks with natural frequencies \( 340 \mathrm{Hz} \) each move relative
to a stationary observer. One fork moves away from the observer, while the other moves towards him at the same speed. The observer hears beats of frequency 3
Hz. Find the speed of the tuning fork. (Velocity of sound in air \( =330 \mathrm{m} / \mathrm{s} \) )


The device used to detect the presence
of static electric charges on a body is
called:
A. ammeter
B. gold leaf electroscope
c. voltmeter
D. microscope


Work done in blowing a soap bubble of radius \( R \) is \( W \). The additional amount
of work done to increase its radius to
\( \sqrt{3 R} \) is :
\( \mathbf{A} \cdot 3 W \)
B. \( 2 W \)
c. \( W \)
D. \( \frac{W}{3} \)


The dimensions of a room are \( 10 \mathrm{m} \times 7 \)
\( \mathrm{m} \times 5 \mathrm{m} . \) There are 2 doors and 3
windows in the room. The dimensions of
the doors are \( 1 \mathrm{m} \times 3 \mathrm{m} \). One window is
of the size \( 2 \mathrm{m} \times 1.5 \mathrm{m} \) and other two
windows are size \( 1 \mathrm{m} \times 1.5 \mathrm{m} \). The cost
of painting the walls at Rs. 3 per \( m^{2} \) is
A. Rs. 474.00
B. Rs. 578.00
c. Rs. 648.00
D. Rs. 849.00


Total number of atoms present in 34 g of \( N H_{3} \) is:
A \( .4 \times 10^{23} \)
B . \( 4.8 \times 10^{21} \)
C \( .2 \times 10^{23} \)
D. \( 48 \times 10^{23} \)


On treatment of the following compound with a strong acid, the most susceptible
site for bond cleavage is:
A. \( C 1-O 2 \)
в. \( O 2-C 3 \)
c. \( C 4-O 5 \)
D. \( O 5-C 6 \)


The intercept on x-axis made by tangent to the curve, \( y=\int_{0}^{x}|t| d t, x \in R, \) which
are parallel to the line \( y=2 x, \) are equal
to
A . ±1
B. ±2
\( c .\pm 3 \)
\( \mathrm{D} \cdot \pm 4 \)


The addition of two numbers is \( -72 . \) If
one number is thrice the another
number. Find the greater number
A. -9
B. -18
c. -54
D. -11


Solve: \( \int \frac{\ln \frac{x}{e}}{(\ln x)^{2}} d x \)


Among the compounds \( I-I V \), the
compound having the lowest boiling
point is:
\( A \cdot I \)
B. II
c. \( I I I \)
D. \( I V \)


In a double-stranded DNA, the sequence
of base pairs in one strand is

AGCTAAGC. What is the complementary sequence on the other strand?
A. TCGATTCG
B. UCGAUUCG
c. АGСТААGС
D. сАUтАUСG


Neutralization is a:
A. physical change
B. chemical change
C. sometimes physical and sometimes chemical change
D. neither physical nor chemical change


Select correct statement(s).
This question has multiple correct options
A. Stabilities of variable oxidation states can be explained by standard electrode potential
B. \( C r^{2+} \) is unstable and \( C r^{3+} \) is stable in aqueous solution
C \( \cdot F e^{2+} \) is stable and \( F e^{3+} \) is unstable is aerated water
D. All of the above


In the active absorption, movement of
water is through
A. Symplast
B. Free spaces
c. Apoplast
D. All of the above


Largest number of cell bodies of neuron
in our body are found in
the
A. Retina
B. Spinal cord
c. Brain
D. Tongue


\( \boldsymbol{Y} \stackrel{\text {excess } H C l}{ } \boldsymbol{H} \boldsymbol{C} \equiv \boldsymbol{C} \boldsymbol{H} \stackrel{\boldsymbol{O}_{3} / Z n, \boldsymbol{H}_{2} \boldsymbol{O}}{\boldsymbol{N}} \boldsymbol{X} \)
\( X, Y \) respectively are :
A \( \cdot C O_{2}, C H_{3} C H C l \)
B. \( \mathrm{CO}_{2}, \quad_{\mathrm{Cl}}^{\mathrm{CH}_{2}-\mathrm{CH}_{2}} \mathrm{Cl} \)
\( c \)
\( \mathrm{H}_{\mathrm{O}}^{\mathrm{C}-\mathrm{C}}_{\mathrm{O}}^{-\mathrm{H},}, \mathrm{CH}_{3}-\mathrm{CHCl}_{2} \)
D.
\( \underset{\|}{\|}_{\mathrm{O}}^{\mathrm{C}-\mathrm{C}-\mathrm{H},} \underbrace{\mathrm{CH}_{2}-}_{\mathrm{O}} \frac{\mathrm{CH}_{2}}{\mathrm{Cl}} \mathrm{Cl} \)


Convert \( 25^{0} \) into Radian measure.


The AFC Curve passes through the Origin statement is -
A. True
B. False
c. Partially True
D. Nothing can be said


What is the use of platelets? \( (\boldsymbol{A} \boldsymbol{S} \boldsymbol{I}) \)


The \( C-C \) and \( S i-C \) inter-atomic
distance are \( 154 p m \) and \( 188 p m \). the
atomic radius of \( \boldsymbol{S} \boldsymbol{i} \) is:
\( \mathbf{A} \cdot 77 p m \)
B . 94 pm
\( c .114 p m \)
D. \( 111 p m \)


The electron revolves only in the orbits
in which
A \( \cdot m v r=\frac{n h}{2 \pi} \)
B. \( m v r \geq \frac{n h}{2 \pi} \)
c. \( m v r>\frac{n h}{2 \pi} \)
D. \( _{m v r}<\frac{n h}{2 \pi} \)


In all its properties, hydrogen resembles:
A. alkali metals only
B. halogens only
c. both alkali metals and halogens
D. neither alkali metals nor halogens


Earthworm is friend of farmers, because
it
A. Produces humus
B. Eats soil bacteria
c. Increases fertility of soil
D. Eats the plant


Semi molten rocks which together made up third layer of Earth Mantle are
known as:
A . ores
B. rust rocks
c. crust
D. magma


Which of the following systems of units is not based on units of mass, length and time alone?
A. s
в. мкя
c. cas
D. FPS


Ethyl alcohol reacts with thionyl chloride to give:
A \( \cdot C H_{3} C H_{2} C l+H C l \)
в. \( C H_{3} C H_{2} C l+H_{2} O+S O_{2} \)
c. \( C H_{3} C H_{2} C l+H C l+S O_{2} \)
D. \( C H_{3} C H_{2} C l+S O_{2}+C l_{2} \)


1 mole of ice at \( 0^{\circ} \mathrm{C} \) and \( 4.6 \mathrm{mm} \) Hg
pressure is converted to water vapour at
a constant temperature and pressure Find \( \Delta H \) and \( \Delta E \) if the latent heat of
fusion of ice is 80 Cal/gm and latent heat of vaporisation of liquid water at
\( 0^{o} C \) is 596 Cal per gram and the volume of ice in comparison to that of water
vapour is neglected.


At a depth of \( 1000 \mathrm{m} \) in the ocean,what
is the gauge pressure when density of sea water is given \( 1.03 \times 10^{3} \mathrm{kgm}^{-3} \) ?
Take \( \boldsymbol{g}=\mathbf{1 0 m s}^{-\mathbf{2}} \)
A. 675 atm
B. 103 atm
c. 203 atm
D. 244 atm


Explain with examples:
(i) Atomic number
(ii) Mass
number,
(iii) Isotopes and
(iv) Isobars.
Give any two uses of isotopes.


A conduction loop of area \( 5 \mathrm{cm}^{2} \) is
placed in a magnetic field which varies sinusoidally with time as \( B= \)
\( 0.2 \sin 300 t . \) The normal to the coil
makes an angle of \( 60^{\circ} \) with the field. The emf induced at \( t=(\pi / 900) \) s is?
A \( .7 .5 \times 10^{-3} \mathrm{v} \)
B. zero
c. \( 15 \times 10^{-3} v \)
D. \( 20 \times 10^{-3} \mathrm{V} \)


When \( 1 g \) liquid naphthalene \( \left(C_{1} 0 H_{8}\right) \)
solidifies, \( 149 J \) of heat is evolved. The
enthalpy of fusion of naphthalene is :
A. \( 14532 J \)
B. \( 15882 J \)
\( \mathrm{c} .198925 \)
D. \( 19072 . J \)


Which element is monoatomic gas at
room temperature?
A . \( N e \)
в. \( F \)
\( c \cdot O_{2} \)
D. \( N_{2} \)


Let \( f(x)=7 e^{\sin ^{2} x}-e^{\cos ^{2} x}+2, \) then the
value of \( \sqrt{7 f_{m i n}+f_{m a x},} \) is


Assertion
Except sciophyte and plants of dense forest, light is rarely a limiting factor in
nature.
Reason
Light saturation occurs at 10 percent of full summer sunlight.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( \boldsymbol{A}=\left[\begin{array}{cc}2 & 3 \\ \mathbf{5} & -2\end{array}\right] \) be such that \( \boldsymbol{A}^{-1}=\boldsymbol{k} \boldsymbol{A} \)
then find the value of \( k \)


Wavelengths of the first lines of the Lyman series, Paschen series and Balmer series in hydrogen spectrum are
denoted by \( \lambda_{L}, \lambda_{P} \) and \( \lambda_{B} \) respectively Arrange these wavelength in increasing order.


Which group is always taken as a
substituent in the IUPAC system of
nomenclature?
A. \( -N O_{2} \)
B. \( -C \equiv N \)
c. \( -N \equiv C \)
D. \( -N H_{2} \)


About how much saliva does a person
produce each day?
A . \( 100 \mathrm{ml} \)
B. 1 to 2 litre
c. \( 500 \mathrm{ml} \)
D. 250 m1


In a square \( \boldsymbol{P Q R S} \), an equilateral
triangle \( \triangle \boldsymbol{T} \boldsymbol{Q} \boldsymbol{R} \) is formed, then
\( \boldsymbol{m} \angle \boldsymbol{P T S}-? \)
A \( .75^{\circ} \)
В. \( 90^{\circ} \)
\( c \cdot 120^{\circ} \)
D. \( 150^{\circ} \)


The pair of equations \( \boldsymbol{x}=\boldsymbol{a} \) and \( \boldsymbol{y}=\boldsymbol{b} \)
graphically represents lines which are
A. parallel
B. intersecting at \( (b, a) \)
c. coincident
D. intersecting at \( (a, b) \)


Conversion of phenol to salicylic acid and to salicyaldehyde are known as? (respectively)
A. Reimer - Tiemann reaction and Kolbe's reaction
B. Williamson's synthesis and Hydroboration-oxidation
c. Kolbe's reaction and Williamson's synthesis
D. Kolbe's reaction and Reimer - Tiemann reaction


The dimensional formula for Magnetic
induction is :
\( \mathbf{A} \cdot M T^{-1} A^{-1} \)
B. \( M T^{-2} A^{-1} \)
\( \mathrm{c} \cdot M L A^{-1} \)
D. \( M T^{-2} A \)


An organic compound whose functional group is carboxyl is :
A. ethyne
B. ethanol
c. acetic acid
D. ethanone


International Code of Botanical
Nomenclature is applicable to
A. Plants
B. Animals
c. species
D. All of the above


In the following which has highest boiling point:
A. \( H I \)
в. \( H F \)
\( \mathbf{c} \cdot H B r \)
D. \( H C l \)


A car of mass \( 100 \mathrm{kg} \) moves on a circular track of radius \( 20 \mathrm{m} \). If the coefficient of friction is \( 0.64, \) then the maximum
velocity with which the car can move is
A. \( 22.4 \mathrm{m} / \mathrm{s} \)
B. \( 5.6 \mathrm{m} / \mathrm{s} \)
c. \( 11.3 \mathrm{m} / \mathrm{s} \)
D. 20 \( \mathrm{m} / \mathrm{s} \)


White light reflected from a soap film(Refractive Index=1.5) has a
maxima at 600 nm and a minima at 450
nm with no minimum in between. Then
the thickness of the film is
\( \times 10^{-7} \mathrm{m} \)
A . 1
B. 2
\( c \cdot 3 \)
D. 4


Integrating factor of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\frac{\mathbf{1}}{\boldsymbol{x} \log \boldsymbol{x}} \boldsymbol{y}= \)
\( \frac{2}{x^{2}} \) is:
A \( \cdot e^{x} \)
B. \( \log x \)
\( c \cdot \frac{1}{x} \)
D \( \cdot e^{-x} \)


The area enclosed between the curves
\( \mathbf{y}=\mathbf{a x}^{2} \) and \( \mathbf{x}=\mathbf{a y}^{2}(\mathbf{a}>\mathbf{0}) \) is 1 sq. unit,
then the value of a is
A. \( 1 / \sqrt{3} \)
в. \( 1 / 2 \)
c. 1
D. \( 1 / 3 \)


The name of the compound is bicylo[2.2.1]heptane.
If true enter 1 , else enter 0 .


\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{lll}{[\boldsymbol{x}]+[-\boldsymbol{x}],} & \boldsymbol{w} \boldsymbol{h} e \boldsymbol{n} & \boldsymbol{x} \neq \boldsymbol{2} \\ \boldsymbol{\lambda} & , & \boldsymbol{w} \boldsymbol{h} \boldsymbol{e} \boldsymbol{n} & \boldsymbol{x}=\boldsymbol{2}\end{array}\right. \)
If \( f(x) \) is continuous at \( x=2 \) then, the
value of \( \lambda \) will be
A . -1
B.
c.
\( D \)


An experiment is known to be random if the results of the experiment.
A. cannot be predicted
B. Can be predicted
c. can be split into further experiments
D. can be selected at random


Which metals does not corrode easily?
A . Gold
B. Iron
c. Aluminium
D. zinc


The product formed in absorption tower during the manufacturing of sulphuric acid in contact process is
A. \( S O_{3} \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
D. All of the above


The upper and lower fixed points of a thermometer are separated by \( 180 \mathrm{mm} \) What is the temperature in Celcius if the length of the mercury thread is 90 \( \mathrm{mm} \) above the lower fixed point?
\( \mathbf{A} \cdot 90^{\circ} C \)
B . \( 50^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 45^{\circ} C \)
D. \( 58^{\circ} \mathrm{C} \)


An aircraft is flying at a height of
\( 3400 m \) above the ground. If the angle subtended at a ground observation
point by the aircraft positions \( 10 s \) apart
is \( 30^{\circ}, \) then the speed of the aircraft is:
\( \mathbf{A} \cdot 10.8 \mathrm{ms}^{-1} \)
В. \( 1963 \mathrm{ms}^{-1} \)
c. \( 108 \mathrm{ms}^{-1} \)
D. 196.3 \( m s^{-1} \)


A hemisphere body of radius \( R \) is
placed in a uniform electric field \( \boldsymbol{E} \)
What is the flux linked with the curved surface if the field is perpendicular to
the base?
\( A \cdot 2 \pi R^{2} E \)
\( \mathbf{B} \cdot \pi R^{2} E \)
c. \( \pi R^{2} E / 2 \)
D.


Find the distance scovered by the
particle during the first 4.0 and \( 8.0 s \)
A. \( 3 c m \)
B. \( 5 \mathrm{cm} \)
\( \mathrm{c} \cdot 10 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


The reaction, is an example of reaction
of:
\( 2 M n S O_{4}+2 K M n O_{4}+8 H_{2} S O_{4} \rightarrow \)
\( \mathbf{2} M n S O_{4}+5 F e_{2}\left(S O_{4}\right)_{3}+K_{2} S O_{4}+ \)
\( 8 H_{2} O \)
A. disproportionation
B. intermolecular redox
c. intramolecular redox
D. none of these


The impedance of a circuit, when a
resistance \( R \) and an inductor of
inductance \( L \) are connected in series in
an AC circuit of frequency \( f \), is
A \( \cdot \sqrt{R+2 \pi^{2} f^{2} L^{2}} \)
B . \( \sqrt{R+4 \pi^{2} f^{2} L^{2}} \)
c. \( \sqrt{R^{2}+4 \pi^{2} f^{2} L^{2}} \)
D. \( \sqrt{R^{2}+2 \pi^{2} f^{2} L^{2}} \)


Assertion \( (\mathrm{A}): H_{2} S \) acts only as
reducing agent.
Reason \( (\mathrm{R}): \boldsymbol{H}_{2} \boldsymbol{S} \) is a dibasic acid.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


The graph of \( x+2=0 \) is a line parallel
to \( \ldots \ldots . . . \) axis.
This question has multiple correct options
A . \( x \)
B. \( y \)
c. \( x-2=0 \)
D. None of these


The radius of potassium atom is 0.203 nm. The radius of the potassium ion in nano-meter will be:
\( \mathbf{A} \cdot 0.133 \)
B. 0.231
c. 0.234
D. 0.251


Which polymer is used in the preparation of hose-pipe?
A. Orlon
B. Polystyrene
c. Teflon
D. Altame


What do you understand by the term glycosidic linkage?


Find the number of delta bonding molecular orbital from the following set if \( z \) is the inter-nuclear axis :
\( \boldsymbol{d}_{\boldsymbol{x}^{2}-\boldsymbol{y}^{2}} \) and \( \boldsymbol{d}_{\boldsymbol{x} z}, \boldsymbol{d}_{\boldsymbol{x}^{2}-\boldsymbol{y}^{2}} \) or \( \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{z}} \)


There are \( _{---} \) isotopes of chlorine.
A. 0
B.
\( c \cdot 2 \)
D.


Radiation of two photon energies twice and five times the work function of
metal are incident successively on the metal surface. The ratio of the
maximum velocity of photoelectrons emitted is the two cases will be :
A .1: 2
B . 2: 1
c. 1: 4
D. 4: 1


If \( \boldsymbol{d} \boldsymbol{x}+\boldsymbol{d} \boldsymbol{y}=(\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{d} \boldsymbol{x}-\boldsymbol{d} \boldsymbol{y}) \Rightarrow \boldsymbol{y}+ \)
\( \log (x+y)=x+C \) is the solution of
differential equation


\( (+)- \) sucrose is made up of :
A. D - glucose and L - fructose
B. D - glucose and D - fructose
c. \( D \) - fructose and \( L \) - glucose
D. L- fructose and L- glucose


Find the derivatives of the following functions at the indicated points.
\( \boldsymbol{y}=\ln (2-\sqrt{2 x+1}), y^{\prime}(0)=? \)


How individuals can help to prevent acid rains?
A. By using public transportation
B. Using the electrical energy efficiently
c. simply walking wherever possible
D. All


If \( \boldsymbol{y}^{\prime}-\mathbf{3} \boldsymbol{y}^{\prime}+\mathbf{2} \boldsymbol{y}=\mathbf{0} \) where \( \boldsymbol{y}(\mathbf{0})= \)
1 \( , y^{\prime}(0)=0, \) then the value of \( y \) at \( x= \)
\( \log 2 \) is
A .
B. - -
\( c \cdot 2 \)
D.


Identify correct acidic strength order in
the following compounds:
A . i > ii > ii
B. ii> sii's


Differentiate \( \sqrt{e^{\sqrt{x}}}, x>0 \)


Differentiate w.r.t \( \mathbf{x} \) \( \boldsymbol{y}=\boldsymbol{x}^{2} \ln (\sqrt{\frac{\boldsymbol{x}^{2}+\mathbf{9}}{\boldsymbol{x}^{2}+\boldsymbol{4}}} \)


How does ozone react with following?
(i) PbS
(ii) Moist \( \mathrm{K} \)
(iii) \( \mathrm{Hg} \)
(iv) \( C_{2} H_{4} \)


In Lassaigne's test, sodium metal is
used because:
A . it is very reactive.
B. its melting point is low.
c. its compounds are soluble in water.
D. All of the above


Read the following passage and answer the questions at the end of it.
Dilute solution of alkali metals in
liquied \( N H_{3} \) is blue. It is the
ammoniated electron which is
responsible for the blue color of the
solution and the electrical conductivity is due to the ammoniated cation,
\( \left[\boldsymbol{M}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{x}\right]^{+} \) as well as the
ammoniated electron, \( \left[e\left(N H_{3}\right)_{y}\right]^{-} \)
values of \( x \) and \( y \) depend on the extent of
solvation \( \left(b y N H_{3}\right) . \) Dilute solutions are
paramagnetic due to free electrons.
What happens if alkali metal is allowed
to react with concentrated ammonia
solution?
A. Paramagnetic character of solvated electrons is retained
B. Solvated electrons associate to form electron-pairs and paramagnetic character decreases
C. Reducing character is increased
D. Reducing character is not affected


Column II gives the area of triangles whose vertices are given in column I match them correctly.


A beam of cross section area \( A \) is made
of a material of Young modulus Y. The beam is bent into the arc of a circle of
radius R. The bending moment is proportional to
A \( \cdot \frac{Y}{R} \)
в. \( \frac{Y}{R A} \)
c. \( \frac{R}{Y} \)
D. \( Y R \)


Match the columns and choose the
correct option.
\( (a) \)
\( (b) \)
\( (c) \)
\( (e) \)
\( (d) \)
\( \mathbf{A} \cdot a-3, b-5, c-4, d-1, e-2 \)
B \( \cdot a-2, b-5, c-1, d-3, e-4 \)
\( \mathbf{c} \cdot a-2, b-4, c-1, d-3, e-5 \)
D \( . a-3, b-1, c-5, d-2, e-4 \)
E \( . a-5, b-4, c-2, d-1, e-3 \)


Pick the correct statement.
A. Home range of members of a species has larger area than that of territory.
B. Many insects mainly honey bees communicate among themselves by secreting pheromones.
C. The last succession in series of biotic succession is called as climax community.
D. Number of individuals of particular species present in a unit area at a given time is known as population size.


Due to some force \( \boldsymbol{F}_{1}, \) a body oscillates with period \( 4 / 5 \) second and due to other
force \( F_{2} \) it oscillates with the period of \( 3 / 5 \) sec. If both forces act simultaneously new period will be
A . 0.72 s
B. 0.64 s
c. 0.48 s
D. 0.36 s


If the volume of a right circular cylinder with its height equal to the radius is \( 25 \frac{1}{7} c m,^{3}, \) then the radius of the cylinder is equal to
A . \( \pi \)
B. 3 cm
c. \( 4 c m \)
D. \( 2 c m \)


Calculate the volume occupied by 40 g. of a \( C H_{4} \) at \( \mathrm{S.T.P} \) if its \( \mathrm{V} . \mathrm{D} \). is 8
A. 24 litres
B. 46 litres
c. 34 litres
D. 56 litres


Maximum refraction of light rays entering the eye takes place from
A. Cornea
B. Iriss
c. Retina
D. Eye lens


Match the column.


The remainder when \( f(x)=3 x^{4}+ \)
\( 2 x^{3}-\frac{x^{2}}{3}-\frac{x}{9}+\frac{2}{27} \) is divided by
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}+\frac{\boldsymbol{2}}{\boldsymbol{3}} \) is
\( A \)
B. 1
c. 0
D. -


Which of the following is an example of elastic deformation?
A. stretching a rubber band
B. stretching saltwater taffy
\( c . \) both
D. none


Arrange the following compounds in the decreasing order of their solubility in
water

Ethyl amine, diethyl amine and triethyl amine


Evaluate the integral \( \int_{-1}^{1} \frac{d x}{x^{2}+2 x+5} \) using substitution


rolling on a smooth horizontal surface
with velocity \( V \) and angular velocity \( \omega \)
(where \( V=\omega r) . \) The sphere collides
with a sharp edge on the wall as shown
in the figure. The coefficient of friction
between the sphere and the edge \( \mu= \)
1/5. Just after the collision the angular
velocity of the sphere becomes equal to
zero. The linear velocity of the sphere
just after the collision is equal to:
\( \mathbf{A} \cdot V \)
B. \( \underline{V} \) \( \overline{5} \)
c. \( \frac{3 V}{5} \)
D. \( \frac{V}{6} \)


Light year is the unit of the
A. distance
B. time
c. speed
D. intensity of light


For \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{-2}+\mathbf{1 4} \boldsymbol{H}^{+}+\boldsymbol{6} \boldsymbol{e}^{-} \rightarrow \)
\( \mathbf{2} \boldsymbol{C r}^{+\mathbf{3}}+\mathbf{7 H}_{\mathbf{2}} \boldsymbol{O} ; \quad \boldsymbol{E}^{\boldsymbol{o}}=\mathbf{1 . 3 3} \boldsymbol{V} \)
At \( \left[\boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{-2}\right]=\mathbf{4 . 5} \) millimole, \( \left[\boldsymbol{C r}^{+3}\right]= \)
15 millimole, \( \boldsymbol{E} \) is 1.067 V. The pH of the
solution is nearly equal to :
A . 3
B. 4
\( c \cdot 2 \)
D. 5


at a constant temperature of \( \boldsymbol{\theta}_{\boldsymbol{o}} \)
Assume that it obeys Newtons law of
cooling. Its temperature \( \boldsymbol{\theta} \) is plotted
against time ' \( t \). Tangents are drawn to
the curve at the points \( P\left(\theta-\theta_{1}\right) \) and
\( Q\left(\theta-\theta_{2}\right) . \) These tangents meet
the time axis at angles of \( \phi_{2} \) and \( \phi_{1} \) as
shown. Then
A \( \cdot \frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{1}-\theta_{o}}{\theta_{2}-\theta_{o}} \)
B. \( \frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{2}-\theta_{o}}{\theta_{1}-\theta_{o}} \)
\( \mathbf{c} \cdot \frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{1}}{\theta_{2}} \)
D. \( \frac{\tan \phi_{1}}{\tan \phi_{2}}=\frac{\theta_{2}}{\theta_{1}} \)


Meteorites are useful because:
A. those can be stored in the museum
B. those help the scientists in studying the material from which the solar system was formed
C. those cause destruction
D. those are only rocks


Find the net amount of heat absorbed
by the system for the cyclic process.


A material \( B \) has twice the specific
resistance of \( A . \) A circular wire made of
\( B \) has twice the diameter of a wire
made of \( A \). Then for the two wires to
have the same resistance, the ratio \( l_{B} / \)
\( l_{A} \) of their respective lengths must be:
\( A \)
B. 1/2
\( c \cdot 1 / 4 \)
D.


Number of which two chemical species will be same in the given procedure?
A. \( M n O_{2} \)
в. \( I_{2} \)
c. \( I^{-} \)
D. \( S_{2} O_{3}^{2} \)


If \( \boldsymbol{x} \cos \boldsymbol{\theta}=\boldsymbol{y} \cos \left(\boldsymbol{\theta}+\frac{\boldsymbol{2} \boldsymbol{\pi}}{\boldsymbol{3}}\right)= \)
\( z \cos \left(\theta+\frac{4 \pi}{3}\right), \) then the value of \( x y+ \)
\( \boldsymbol{y} \boldsymbol{z}+\boldsymbol{z} \boldsymbol{x}= \)
\( A \)
B.
c.
D.


Let \( \boldsymbol{A}=\left[\begin{array}{c}-\mathbf{1} \\ \mathbf{2} \\ \mathbf{3}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{lll}-\mathbf{2} & -\mathbf{1} & -\mathbf{4}\end{array}\right] \)
The skew symmetric part of \( A B \) is?
\( \mathbf{A} \cdot\left(\begin{array}{ccc}0 & 5 / 2 & 5 \\ -5 / 2 & 0 & -5 / 2 \\ -5 & 5 / 2 & 0\end{array}\right) \)
В. \( \left(\begin{array}{ccc}0 & 5 & 10 \\ -5 & 0 & 11 \\ -10 & -11 & 0\end{array}\right) \)
\( \mathbf{c} \cdot\left(\begin{array}{ccc}0 & 3 & 5 \\ -3 & 0 & 11 \\ -5 & -11 & 0\end{array}\right) \)
D. None of these


Find the value \( (s) \) of \( k \) so that the
equation \( x^{2}-11 x+k=0 \) and \( x^{2}- \)
\( 14 x+2 k=0 \) may have a common root.


Evaluate :
\[
\lim _{y \rightarrow 0} \frac{(x+y)}{y} \sec (x+y)-x \sec x
\]


Assertion: Litter burning is not
suggested by ecologists.
Reason: Burning litter enhances 'CO
content of the air.
A. Both the Assertion and the Reason are true and the Reason is a correct explanation of the Assertion.
B. Both the Assertion and Reason are true but the Reason
is not a correct explanation of the Assertion.
C. The Assertion is true but the Reason is false.
D. Both the Assertion and Reason are false.
E. The Assertion is false but Reason is true.


The function 'f' is defined by \( f(x)= \)
\( \boldsymbol{x}^{p}(\mathbf{1}-\boldsymbol{x})^{\boldsymbol{q}} \) for all \( \boldsymbol{x} \in \boldsymbol{R}, \) where \( \mathbf{p}, \boldsymbol{q} \) are
positive integers, has a maximum value, for x equal to
A. \( \frac{p q}{p+q} \)
B.
c. \( \frac{p}{p+q} \)
D. 0


If the light moving in a straight line bends by a small but fixed angle, it may
be a case of
(i) reflection
(ii) refraction
(iiii) diffraction
\( (i v) \) dispersion
A. only ( \( i \) ) and ( \( (i) \)
B. (ii) and (iii)
C . \( (i),(i i) \) and \( (i v) \)
D. only \( (i v) \)


An atom of the element is \( _{17}^{35} \mathrm{Cl} \) Complete the following table.
\begin{tabular}{llll}
Element & Mass number & Atomic number & No. of protons \\
\hline
\end{tabular}


Which method is used to degrade the waste by microorganism in the absence of oxygen?
A. Dumping
B. Composting
c. Digesting
D. Incineration


A fair coin is tossed 99 times. Let \( X \) be
the number of times heads occurs. Then
\( P(X=r) \) is maximum when \( r \) is
A . 49
B. 52
\( c .51 \)
D. None of these


Calculate the pH of the buffer solution prepared by mixing, \( 50 \mathrm{ml} \) of \( 0.1 \mathrm{M} \)
\( N H_{4} O H \) and \( 25 \mathrm{ml} \) of \( 2 \mathrm{M} N H_{4} C I \)
\( \left(p K_{b} \text { of } N H_{4} O H \text { is } 4.8\right) \)
A . 5.8
B. 4.8
\( c \cdot 9.2 \)
D. 8.2


Fill in the blanks:
During the development of a thunder-
storm, the air currents move
while the water droplets
move
A. downward, upward
c. downward, downward
D. upward, upward


Boric acid \( \left(\boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3}\right) \) has:
A. trigonal structure
B. tetrhedral structure
C. layer structure, in which \( B O_{3} \) units are linked by oxygen
D. layer structure, in which planar \( B O_{3} \) units are linked by hydrogen bondining


Explain body cavity or coelom in animals.


For a stationary wave \( \boldsymbol{y}= \) \( 4 \sin \left(\frac{\pi x}{15}\right) \cos (96 \pi t), \) the distance
between a node and the next antinodes
is.
A . 7.5
B . 15
c. 22.5
D. 30


The ac generator in the Figure supplies
\( 150 V_{(\max )} \) at \( 50 \mathrm{Hz} . \) With the switch open as shown in the diagram, the
resulting current leads the generator
emf by \( 60^{\circ} . \) With the switch in position
1, the current lags the generator emf by
\( 30^{\circ} . \) When the switch is in
position \( 2, \) the maximum current is \( 3 A \)
Then, the value of R is:
A. \( 50 / \sqrt{3} \Omega \)
B. 83.3 \( \Omega \)
c. \( 133.3 \Omega \)
D. \( 50 \Omega \)


Assertion
Ammonia gas collected over water by the downward displacement of air.
Reason

Ammonia is not collected over water
since it is highly soluble in water
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


During amphibolic pathway, acetyl Co-A can perform the biosynthesis of
A. Amino acid
B. Gibberellic acid
c. Fatty acid
D. All of the above


The selling price of an article is \( 96 \% \) of
its cost price. Find the loss or the gain
as percent on the whole.


The energy equivalent to \( 1 k g \) of matter in (in Joule)
\( \mathbf{A} \cdot 10^{17} \)
B. \( 19^{20} \)
\( c \cdot 10^{11} \)
D. \( 10^{14} \)


A positively charged rod is touched with the brass disc of a positively charged gold leaf electroscope. State the effect on divergence of the leaves.
A. Divergence increases
B. Divergence decreases
c. Divergence remains same
D. none


Is the given equation quadratic? Enter 1 for True and 0 for False.
\( \boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x}=\mathbf{1 1} \)


Surface tension of liquid is 70
dyne/cm. Its value in Sl unit is
A . \( 70 \mathrm{N} / \mathrm{m} \)
В. \( 7 \times 10^{-2} N / m \)
C. \( 7 \times 10^{2} N / m \)
D. \( 7 \times 10^{3} N / m \)


Sum of the first \( p, q \) and \( r \) terms of an
A.P. are \( a, b \) and \( c, \) respectively. Prove that \( \frac{\boldsymbol{a}(\boldsymbol{q}-\boldsymbol{r})}{\boldsymbol{p}}+\frac{\boldsymbol{b}(\boldsymbol{r}-\boldsymbol{p})}{\boldsymbol{q}}+ \)
\( \frac{c(p-q)}{r}=0 \)


What should be the minimum work
function of a metal so that visible light
is able to cause emission?
(visible light=400-700 \( n m \) )
A .1 .77 eV
B. 1.87 \( e V \)
c. 1.97 eV
D. None of these


Modulus of elasticity for a perfectly elastic body is
A. zero
B. Infinity
\( c \)
D. can have any value


Which method should be used to
separate a mixture of two liquids?
A. Crystallisation
B. Electrolysis
c. Filtration
D. Fractional distillation


In Kranz anatomy, the bundle sheath
cells have
A. Thin walls, no intercellular spaces and several mitochondria
B. Thin walls, many intercellular spaces and few chloroplast
c. Thin walls, many intercellular spaces and no chloroplast
D. Thik walls, no intercellular spaces and large number of chloroplast


Hydrazine is a constitutent of drugs
that are used for the treatment of:
A. cholera
B. tuberculosis
c. typhoid
D. malaria


The temperatures of two bodies
measured by a thermometer are \( t_{1}= \)
\( \mathbf{2 0}^{o} \boldsymbol{C} \pm \mathbf{0 . 5}^{o} \boldsymbol{C} \) and \( \boldsymbol{t}_{2}=\mathbf{5 0}^{o} \boldsymbol{C} \pm \)
\( 0.5^{\circ} \mathrm{C} . \) The temperature difference and
the error there is
\( \mathbf{A} \cdot 30^{\circ} C \pm 1^{\circ} C \)
B \( \cdot 70^{\circ} \mathrm{C} \pm 0.5^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 30^{\circ} C \pm 0.5^{\circ} \mathrm{C} \)
D. \( 70^{\circ} \mathrm{C} \pm 1^{\circ} \mathrm{C} \)


Assertion: In a movie, ordinarily 24 frames are projected per second from one end to the other of the complete
film.
Reason: The image formed on retina of eye is sustained upto \( 1 / 10 \) second after the removal of stimulus.
A. Both assertion and reason are true but the reason is the correct explanation of assertion
B. Both assertion and reason are true but the reason is not the correct explanation of assertion
c. Assertion is true but reason is false
D. Both the assertion and reason are false
E. Reason is true but assertion is false


\( \boldsymbol{C H}_{3}-\underset{C l}{\boldsymbol{C}} \boldsymbol{H}-\underset{\boldsymbol{B} \boldsymbol{r}}{\boldsymbol{C} \boldsymbol{H}}-\underset{\boldsymbol{O} \boldsymbol{H}}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C H}_{3} \)
The IUPAC name of the compound is
A. 3 - Bromo - 4 - chloropentan - 2 - ol
B. 3 - Bromo - 2 - chloro- 4 hydroxypentane
c. 3 - Bromo - 2 - chloropentan - 4 - - о।
D. none of these


Why are crop fields known as artificial
ecosystems?
A. Crop fields are man made.
B. Some biotic and abiotic components are manipulated by humans for the production of crop.
C. Both A and B.
D. None of the above


Find the minimum and maximum
values of the function \( y=x^{3}-3 x^{2}+6 \)
Also find the values of \( x \) at which these
occur.


The first man - made polymer is :
A. PVC
B. Teflon
c. Bakelite
D. Nylon


If uncertainties in the measurement of
position and momentum of an electron are equal, calculate uncertainty in the measurement of velocity.


An element belongs to the 3 rd period and Group II of the periodic table.
Name of the element is
A. magnesium
B. sodium
c. aluminium
D. calcium


An iron ball and a wooden ball of the
same radius are released from the
same height in vacuum. The times
taken by both of them to reach the
grounds are
A . exactly equal
B. roughly equal
c. unequal
D. nothing can be decided


At \( 25^{\circ} \mathrm{C} \), the dissociation constant for
pure water is given by :-
\( \mathbf{A} \cdot\left(55.4 \times 10^{14}\right)^{-1} \)
B . \( 1 \times 10^{-14} \)
c. \( \frac{1 \times 10^{-14}}{18} \)
D. none of these


What are the changes in ciliary muscle
when nearby objects and distant
objects are viewed?
A. When objects near the eyes are viewed,the ciliary muscles contract and while viewing distant objects ciliary muscles relax.
B. When objects near the eyes are viewed,the ciliary muscles relax and while viewing distant objects ciliary muscles contract
C. Cilliary muscle is not related to the functioning of the lens and provides mechanical support only.
D. Ciliary muscles contract or relax depending on the intensity of the light and not hte distance of the object.


Draw a labelled diagram of an ac generator. Obtain the expression for the emf induced in the rotating coil of \( \mathrm{N} \)
turns each of cross-sectional area \( A \), in
the presence of a magnetic field \( \vec{B} \).


State True or False.
In association of solute, the Van't Hoff
factor is greater than unity.
A. True
B. False


State True or False.
Sn \( C l_{2} \) is non-linear molecule.


When an athlete takes part in a long
jump he runs for a while and then jumps. This is because:
A. inertia of motion helps him to take a longer jump
B. running for a time makes him alert
c. it helps him to focus on the point of jump
D. he can apply more force for the jump after running


What is the role of depressants in the forth floatation process?


Prove that a diagonals of a parallelogram divides it into two congruent triangles.


Write the expression for the
equillibrium constant \( \left(\boldsymbol{K}_{c}\right) \) for the
following reactions.
(i) \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{2} \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
(ii) \( 4 N H_{3}(g)+5 O_{2}(g) \leftrightharpoons 4 N O(g)+ \)
\( \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \)


A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes
are in the ratio 1: 2: 3


What is redox reaction? Explain with one example.


Name any two contraceptive methods used by human female.


The number of ordered pairs \( (a, b) \) of positive integers such that \( \frac{\mathbf{2 a - 1}}{\mathbf{b}} \) and \( \frac{2 b-1}{a} \) are both integers is
A . 1
B . 2
\( c .3 \)
D. more than 3


In lanthanum, the differentiating
electron enters into:
\( \mathbf{A} \cdot d \) sub shel
B. \( f \) sub shell
c. \( s \) sub shell
D. \( p \) sub shell


The plant of arid regions with flat green stem carrying out photosynthesis is
A. Euphorbia
B. opuntia
c. citrus
D. Bougainvillea
E . colocasia


If 36 men can do a piece of work in 25 days, in how many days will 15 men do it
\( ? \)


When a ray of light is incident normally on one refracting surface of an equilateral prism (Refractive index of the material of the prism \( =1.5 \) )
A . emerging ray is deviated by \( 30^{\circ} \)
B. emerging ray is deviated by 45
c. emerging ray just grazes the second refracting surface
D. The ray undergoes total internal reflection at the second refracting surface


Which of the following takes place during Calvin cycle?
A. Photophosphorylation
B. Replication
c. Reduction and carboxylation
D. None of the above


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin ^{-1}\left(\log _{2} \frac{x^{2}}{2}\right) \) is \( ? \)
A \( \cdot[-2,2]-(-1,1) \)
B . \( [-1,2]-\{0\} \)
c. [1.2]
D \cdot \( [-2,2]-\{0\} \)


Which of the following is/are correct?
This question has multiple correct options
A. Enthalpy (numerical value) of physisorption is greater than that of chemisorption.
B. Physisorption is not very specific but chemisorption is highly specific.
C. Chemisorption takes place at relatively high temperatures.
D. In physisorption, generally multi - molecular layers are formed on the adsorbent.


Which of the following is not the main function of lymph glands?
A. Forming WBC
B. Forming RBC
c. Forming antibodies
D. Destroying bacteria


In the figure, the center of the circle is \( A \)
and ABCDEF is a regular hexagon
of side \( 6 \mathrm{cm} \)
Find :
: (i) Area of segment BPF
(ii) Area of shaded portion


Ionic hydrides are formed by:
A. transition metals
B. elements of very high electropositivity
C . elements of very low electropositivity
D. metalloids


The rate of a reaction expressed in terms of change in concentration of
reactants at two different times, that is
the average rate in terms of reactants, can be written as ?
This question has multiple correct options
A \( \cdot \frac{x_{2}-x_{1}}{t_{2}-t_{1}} \)
B. \( +\Delta x / \Delta t \)
c. \( -\frac{x_{2}-x_{1}}{t_{2}-t_{1}} \)
D. \( -\Delta x / \Delta t \)


The molecular formula of Calcium
cyanamide is :
A. \( C a C N_{2} \)
в. \( \operatorname{CaCH} N H_{2} \)
c. \( C a C_{2} N_{2} \)
D. \( \operatorname{Ca}(C N)_{2} \)


For some data \( M+\bar{X}=22 \) and \( M- \)
\( \bar{X}=2, \) then \( Z=\dots \)
A . 14
B . 15
c. 16
D. 12


Deficiency of insulin in human beings
causes:
A. Blood coagulation
B. Beri Beri
c. Diabetes
D. Dermatitis


The quantum number 'm' of a free
gaseous atom is associated with:
A. the effective volume of the orbital
B. the shape of the orbital
C. the spatial orientation of the orbital
D. the energy of the orbital in the absence of a magnetic field


"Pheromones" in insects are secreted
from
A. Endocrine glands
B. Exocrine glands
c. corpus allatum
D. Digestive tract


For the reaction \( A+B \rightleftharpoons 3 C \) at \( 25^{0} C \)
A 3 Lvessel contains \( 1,2, \) and 4 moles of
A, \( B, \) and \( C \) respectively. Predict the direction of reaction if:
a) \( K_{C} \) for the reaction is 10
b) \( K_{C} \) for the reaction is 15
c) \( K_{C} \) for the reaction is 10.66
A. a) Backward direction
b) Forward direction \( c \) ) At equilibrium
B. a) Forward direction b) Backward direction c) Forward direction
c. a) Backward direction b) Forward direction c) Back direction
D. a) Backward direction
b) Backrward direction c) At equilibrium


Assertion
Be \( (\text { O } H) \) a dissolves in excess NaOH
solution.
Reason
Be \( (O H) \) a is an acidic compound.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


What kind of compound is \( C a O \) or Calcium Oxide.
A. Covalent compound
B. Electrovalent compound
c. Co-ordinate covalent compound
D. None of these


The oxide of iodine used in the
estimation of carbon monoxide is:
A \( \cdot I_{2} O_{4} \)
в. \( I_{2} O_{6} \)
\( \mathrm{c} \cdot I_{2} \mathrm{O}_{7} \)
D. \( I_{2} O_{5} \)


Assertion
The size of the mirror affect the nature
of the image.
Reason
Small mirrors always form a virtual
image.
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


(i) What happens to the resistivity of semi-conductors with the increase of
temperature?
(ii) For a fuse, higher the current rating is the fuse wire. (Thicker / Thinner)


Penicillin was discovered by:
A. Graham Bell
B. Alexander Flemming
c. Paul Elrich
D. Lister


STATEMENT-1: Diethyl ether when boiled with water gives ethyl alcohol. STATEMENT-2: Diethyl ether is less dense than water.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Which is not a disproportionation
reaction?
\( A \)
B.
\[
\begin{array}{ll}
\text { CHO } & \text { CH }_{2} \text { OH } \quad \text { COO }^{-} \\
\text {COOH } & \text { COO }^{-}+\mid
\end{array}
\]
c. \( N a H+H_{2} O \rightarrow N a O H+H_{2} \)
D. All of the above


Which of the following is pseudounimolecular reaction?
A. \( 2 H_{2} O_{2} \rightarrow 2 H_{2} O+O_{2} \)
в. \( C_{6} H_{5} N_{2} C l+H O H \longrightarrow C_{6} H_{5} O H+N_{2}+H C l \)
c. \( C H_{3} C O O C_{2} H_{5}+N a O H \rightarrow C H_{3} C O O N a+ \)
\( C_{2} H_{5} O H \)
D. \( 20_{3} \rightarrow 30_{2} \)


If \( \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}=\mathbf{0} \) and \( |\boldsymbol{a}|=\mathbf{3} ;|\boldsymbol{b}|= \)
\( \mathbf{5} ;|\boldsymbol{c}|=\mathbf{7}, \) find the angle between a
vector and
A \( \cdot 60^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 45^{\circ} \)
D. none of these


Two identical particles of mass \( m \) carry
charge \( Q \) each. Initially one is at rest on
a smooth horizontal plane and the other
is projected along the plane directly towards the first from a large distance
with an initial speed \( V \). Find the closest
distance of approach.


The nuclear charge of \( L i \) is:
\( A \cdot 3 \)
B. 5
\( c \cdot 4 \)
D. 2


Which of the following statement is incorrect?
A. All algae are microscopic
B. All algae are thalloid in nature.
C. Algae are most primitive plants
D. Algae possess both unicellular and multicellular eukaryotes


\( \lim _{x \rightarrow 2} \frac{x^{8}-256}{x-2} \)


A dipole of moment p is placed in uniform electric field E then torque acting on it is given by : -
A.
\[
\vec{\tau}=\overrightarrow{\mathrm{p}} \cdot \overrightarrow{\mathrm{E}}
\]
в.
\[
\vec{\tau}=\vec{p} \times \vec{E}
\]
\( c \)
\[
\vec{\tau}=\vec{p}+\overrightarrow{\mathrm{E}}
\]
D.
\[
\vec{\tau}=\overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{E}}
\]


A radio active nucleus (initial mass number A and atomic number Z emits 4
\( \alpha \) - particles and 3 positrons).The ratio
of numbers of neutrons to that of
protons in the final nucleus will be
A \( \cdot \frac{A-Z-4}{Z-8} \)
B. \( \frac{A-Z-3}{Z-2} \)
c. \( \frac{A-Z-2}{Z-3} \)
D. \( \frac{A-Z-5}{Z-11} \)


Which of the following is true for electrolytic refining?
A. Pure metal is used at anode and impure metal at cathode
B. Pure metal is used at cathode and impure metal at anode
c. Both can be possible A and B
D. None of these


In a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of the
longitudinal strain \( \sigma \) and modulus of
elasticity \( \boldsymbol{Y} \) is
A \( \cdot \frac{Y \sigma^{2}}{2} \)
в. \( \frac{Y \sigma}{2} \)
\( ^{\text {c. }} \frac{2 Y \sigma^{2}}{2} \)
D. \( \frac{Y^{2} \sigma}{2} \)


Which of the following is bacteriostatic?
A. Penicillin
B. Erythromycinn
c. Amnioglycoside
D. ofloxacin


\( f(x-1)(x+2)(x-3)=A+ \)
\( \frac{B}{(2 x-1)}+\frac{C}{(x+2)}+\frac{D}{(x-3)} \) then
\( \mathbf{A}= \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{-1}{50} \)
\( c \cdot \frac{-8}{25} \)
D. \( \frac{27}{25} \)


Assertion \( P h N_{2} B r^{\ominus} \) is more acidic than
\( N H_{4} B r \)
Reason
\( P h N H_{3} \) (anilinium ion) is resonance
stabilised.
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


Portland cement does not contain :
A \( . \) Casio \( _{4} \)
в. \( \operatorname{casi} 0_{3} \)
\( \mathbf{c} \cdot C a_{3} A l_{2} O_{6} \)
D. \( C a_{3}\left(P O_{4}\right)_{2} \)


\( f \)
\( a, b, c \) are all different and if \( \left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{a}^{2} & \mathbf{1}+\boldsymbol{a}^{3} \\ \boldsymbol{b} & \boldsymbol{b}^{2} & \mathbf{1}+\boldsymbol{b}^{3} \\ \boldsymbol{c} & \boldsymbol{c}^{2} & \boldsymbol{1}+\boldsymbol{c}^{3}\end{array}\right|=\mathbf{0} \) then \( -\boldsymbol{a} \boldsymbol{b} \boldsymbol{c}= \)


The triangle with vertices \( A(4,4), B(-2, \)
-6) and \( \mathrm{C}(4,-1) \) is shown in the diagram
The area of \( \Delta \) ABC is
A . 5 sq. units
B. 12 sq. units
c. 15 sq. units
D. 20 sq. units


If the distance between the Sun and
Earth is increased by three times then attraction between two will:
A. decreases by \( 11 \% \)
B. decreases by 33\%
c. decreases by 66\%
D. decreases by 89\%


What is mastication? Explain about the teeth used in mastication


Let \( f(x) \) be a derivable function,
\( f^{\prime}(x)>f(x) \) and \( f(0)=0 . \) Then?
A. \( f(x)>0 \) for all \( x>0 \)
B. \( f(x)<0 \) for all \( x>0 \)
c. No sign of \( f(x) \) can be ascertained
D. \( f(x) \) is a constant function


Cortisone, Somatotropin, Adrenocorticotropic hormone,
Vasopressin.


The area bounded by the curve \( y= \)
\( 2 x^{4}-x^{2}, x \) -axis and the two ordinates
corresponding to the minima of the function is \( \frac{8}{a} . \) Find \( a \)


The number of different words that can
be formed using all the letters of the letters of the word \( C \)OCACOLA with
start and ends with \( O \) is
A. 840
в. 420
\( c \cdot 120 \)
D. 60


In the primary circuit of potentiometer
the rheostat can be varied from 0 to
10\Omega. Initially it is at minimum
resistance (zero).The rheostat is put at
maximum resistance \( (10 \Omega) \) and the
switch \( S \) is closed. New balancing
length is found to be 8 m. Find the
internal resistance \( r(\text { in ohms }) \) of the
\( 4.5 V \) cell.


Fill in the blank.
\( 13+_{-1}-\dots \)


A student tests the \( p H \) of pure water
using a \( p H \) paper. It shows the green
color. If a \( p H \) paper is used after adding lemon juice to water, what color will be observed?
A. Green
B. Red
c. Yellow
D. purple


The phenomenon in which light that strikes a surface is thrown back into
the same medium is called -
A. reflection
B. reflex action
c. refraction
D. regression


Match the columns
\begin{tabular}{ll|l}
& I & \\
(a) & Physical change & (I) & Curdling of milk \\
(b) & Chemical change & (ii) & Demagnetisation of magnets \\
& (iii) & Digestion of food \\
& (iv) & Crystallisation of substance \\
& (v) & Rusting of iron
\end{tabular}
\( A \cdot a-i, i i, \) iii, \( b-i v, v \)
B. \( a-i i, \) iv, \( b-i, \) iii, iv
\( \mathbf{C} \cdot a-i i, i v, b-i, \) iii, \( v \)
\( \mathbf{D} \cdot a-i i i, v, b-i, \) ii, iv


The coefficient of \( x^{9} \) in the expansion of \( \left(x^{3}+\frac{1}{2^{t}}\right)^{11}, \) where \( t=\log _{\sqrt{2}}\left(x^{\frac{3}{2}}\right) \)
A . -5
в. 330
\( c .520 \)
D. \( 5+\log _{\sqrt{2}}(3) \)


Two soap bubbles \( A \) and \( B \) are kept in a
closed chamber where the air is
maintained at pressure \( 8 N / m^{2} . \) The radii of bubble \( A \) and \( B \) are 2 cm and
\( 4 \mathrm{cm}, \) respectively. Surface tension of the soap water used to make bubbles is \( 0.04 N / m . \) Find the ratio \( n B / n A \) where \( n A \) and \( n B \) are the number of
moles of air in bubbles \( A \) and \( B \)
respectively. (Neglect the effect of gravity).


The degree of hydrolysis for a salt of strong acid and weak base
This question has multiple correct options
A. Is independent of dilution
B. Increases with dilution
C . Increases with decrease in \( K_{b} \) of the bases
D. Decreases with decrease in temperature


Production of new individual from
parent is called as
A. Reproduction
B. Formation
c. cloning
D. None of the above


the value of \( g \) at the surface of the earth
is \( 9.8 m / s^{2} . \) then the value of \( g \) at the place \( 480 k m \) above the surface of the
earth will be nearly? (Radius of the earth is \( 6400 k m \)


Expand the following binomial \( \left(x^{2}+x\right)^{5} \)


1 unified atomic mass unit (1 \( u \) ) is equal
to the
A \( \cdot 1.66 \times 10^{-25} \mathrm{kg} \)
B . \( 1.66 \times 10^{-27} \mathrm{kg} \)
C \( .1 .66 \times 10^{-29} \mathrm{kg} \)
D. \( 1.66 \times 10^{-31} \mathrm{kg} \)


Meiosis is also called as haplosis as
A. Meiosis occurs in haploid cell
B. Meiosis nullify the effect of fertilization
C. Meiosis reduce the number of chromosome to half
D. None of the above


Statement-1: The variance of first n
even natural numbers is \( \frac{n^{2}-1}{4} \) Statement-2: The sum of first n natural
numbers is \( \frac{n(n+1)}{2} \) and The sum of
squares first n natural numbers is \( \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})(\boldsymbol{2} \boldsymbol{n}+\mathbf{1})}{\boldsymbol{6}} \)
A. Statement-1 is true, Statement-2 is true ;Statement-2 is not a correct explanation for Statement-
B. Statement-1 is true, Statement-2 is false
c. Statement-1 is false, Statement-2 is true
D. Statement-1 is true, Statement-2 is true ;Statement-2 is a correct explanation for Statement-


Figure shows a diode connected to an
external resistance and a battery.
Assuming the barrier potential developed in the diode to be \( 0.5 \mathrm{V} \), find the value of current in the circuit in \( \mathrm{mA} \)


Find the total surface area of the cuboid
with \( l=4 m, b=3 m \) and \( h=1.5 m \)


Assertion: Aryl halides undergo electrophilic substitution more readily than benzene.

Reason: Aryl halide gives a mixture of
\( o-, p- \) products when they undergo electrophilic substitution.
A. Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is true and Reason is false
D. Assertion is false and Reason is true


A narrow pencil of parallel light is
incident normally on a solid transparent sphere of radius \( r . \) What should be the
refractive index if the pencil is to be focussed
(a) at the surface of the
sphere
(b) at the centre of the sphere.


Assertion
The main reason of ozone layer
depletion is believed to be the release of
chlorofluorocarbon compounds known
as freons.
Reason
CFCs are transporting agents for continuously generating chlorine radicals into the stratosphere.
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 constituents of the electrolyte for the extraction of aluminium is
A. 40 parts cryolite +40 parts fluorspar +20 parts pure \( A l_{2} O_{3} \)
B. 60 parts cryolite +30 parts fluorspar +10 parts pure \( A l_{2} O_{3} \)
C. 30 parts cryolite +30 parts fluorspar +40 parts pure \( A l_{2} O_{3} \)
D. 60 parts cryolite +20 parts fluorspar +20 parts pure \( A l_{2} O_{3} \)


The number of points in
\( (-\infty, \infty) \) for which \( x^{2}-x \sin x- \)
\( \cos \boldsymbol{x}=\mathbf{0}, \) is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
\( c \cdot 2 \)
D. None of the above


Which of the following is correct about measure of dispersion?
A. It does not measure direction of the variation
B. Dispersion measures the extent to which the items vary from some central value
c. Measures only degree of variation
D. All of the above


A satellite is in a circular orbit around a planet, Its period of revolution is \( \mathrm{T} \), radius of the orbit is \( R \), orbital velocity \( V \)
and acceleration 'a', then:
A \( \cdot V=a t \) and \( a=\frac{V^{2}}{R} \)
B. \( V=\frac{2 \pi R}{T} \) and \( V=a T \)
c. \( V=\frac{2 \pi R}{T} \) and \( a=\frac{V^{2}}{R} \)
D. \( V=\frac{1}{2} a T^{2} \)


A source of sound is travelling with a velocity \( 40 \mathrm{km} / \mathrm{hr} \) towards an observer and emits sound of frequency 2000 Hz. If velocity of sound is \( 1220 \mathrm{km} / \mathrm{hr} \), then what is the apparent frequency heard by an observer?
A. 2210 нᅩ
в. 1920 нz
c. 2068 Нz
D. 2086 Нz


A torch bulb rated \( 4.5 \mathrm{W}, 1.5 \mathrm{V} \) is
nnected as in figure. The emf of the ell needed to make the bulb glow at ntensity i


In the reduction of \( H N O_{3} \) to \( N_{2} O \) the
no.of moles of electrons involved per
mole of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) is :
\( A \cdot 8 \)
B. 4
\( c \cdot 3 \)
D. 6


The correct IUPAC name of the
compound is


From the diagram, relation between \( A \)


If \( f(x)=x^{2}-7, \) then find the value
\( \boldsymbol{f}(\boldsymbol{a}-\boldsymbol{3}) \)
A \( \cdot a^{2}-6 a-16 \)
B . \( a^{2}-10 \)
\( \mathbf{c} \cdot a^{2}+21 \)
D. \( a^{2}-6 a+2 \)
E . \( 2 a-13 \)


Which one of the following differentiates Pteridophytes from
Mosses?
A. Prothallus
B. Homosporous spores
c. Haplontic life cycle
D. All of the above


The volume of blood pumped by heart in one minute is called?
A. Heart rate
B. systole
c. cardiac output
D. Diastols


Assertion
In natural tris chelating complex,
\( \left[\boldsymbol{C o}(\boldsymbol{a c a c})_{3}\right], \) in each ring the two \( \mathrm{M}-\mathrm{O} \)
bonds are equal to length, as are two \( \mathrm{C} \) O and the two C-C bonds because,
Reason

In each ring resonance takes place.
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


Name the following:
The property of elements by virtue of which atoms of the element can link to
each other in the form of a long chain or
ring structure


Consider a triangle \( A B C, \) whose vertical
\( \operatorname{are} A(-2,1), B(1,3) \) and \( C(x, y) \).ff \( C \) is
a moving point such that area of
\( \Delta A B C \) is constant,then locus of \( C \) is:
A. staight line
B. Circle
c. Ray
D. Parabola


A solution is \( 25 \% \) water, \( 25 \% \) ethanol
and \( 50 \% \) acetic acid by mass. Calculate the mole fraction of each component.


\( f\left[\begin{array}{cc}\cos ^{2} \alpha & \cos \alpha \sin \alpha \\ \cos \alpha \sin \alpha & \sin ^{2} \alpha\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{cc}\cos ^{2} \beta & \cos \beta \sin \beta \\ \cos \beta \sin \beta & \sin ^{2} \beta\end{array}\right] \) are two
matrices such that the product \( A B \) is
null matirx, then \( \alpha-\beta \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. Multiple of \( \pi \)
c. An odd number of \( \frac{\pi}{2} \)
D. None of the above


Given in the diagram \( \mathrm{OB}=\mathrm{BA} \). The time
taken to cover \( \mathrm{OB} \) is \( T_{1} \) and the time
take to cover BA is \( T_{2} \), then the ratio
\( \boldsymbol{T}_{1} / \boldsymbol{T}_{2} \) is
\( A_{1}=1 \)
B. >1
\( c .<1 \)
D. cannot be determined


Which of the following alkenes on reductive ozonolysis will give a mixture of ketones?
\( \mathbf{A} \cdot C H_{3} C H=C H C H_{3} \)
в. \( \left(C H_{3}\right)_{2} C=C H C H_{3} \)
\( \mathbf{c} \cdot\left(C H_{3}\right)_{2} C=C\left(C H_{3}\right)_{2} \)
D. None of these


When 13546 is rounded off to four
significant figures, it becomes:
This question has multiple correct options
A . 1355
B. 13550
C. \( 1355 \times 10^{1} \)
D. 135.5


The Antherozoids of Bryophytes possess
A. 2 flagella
B. 1 flagella
c. Multiflagella
D. No flagella


A microscope consists of an objective with a focal length \( 2 \mathrm{mm} \) and an eye piece with a focal length \( 40 \mathrm{mm} \). The distance between the foci(which are
between the lenses) of objective and eyepiece is \( 18 \mathrm{cm} . \) The total
magnification of the microscope is(Consider normal adjustment and \( \operatorname{take} D=25 \mathrm{cm} \)
A. 562.5
В. 625
c. 265
D. 62.5


Which of the following is a synthetic polymer?
A. Starch
B. Cellulose
c. \( R N A \)
D. Terylene


Factorise:
\( 36 a^{2}+12 a b c-15 b^{2} c^{2} \)


The IUPAC name for \( \left[N i(C O)_{4}\right] \) is :
A. Tetracarbonylnickel (II)
B. Tetracarbonylnickel (O)
c. Tetracarbonylnickelate (II)
D. Tetracarbonylnickelate (0)


\( A \) and \( B \) are two independent witnesses
is a case. The probability that \( A \) will speak truth is \( x \) and the probability that \( B \) will speak the truth is \( y . A \) and \( B \) agree in a certain statement. The
probability that the statement is true is
A \( \cdot \frac{x y}{1-x y} \)
в. \( \frac{x y}{1-x-y+2 x y} \)
c. \( \frac{2 x y}{x-y} \)
D. \( \frac{x y}{1-x-y} \)


In the following figure, \( X Y \) is parallel to \( B C, A X=9 c m, X B=4.5 \mathrm{cm} \) and
\( B C=18 \mathrm{cm} . \) Find the value of \( x y \)
\( A \cdot 14 \)
3. 12
\( c .16 \)
D. 18


Choose the correct statement for the
given structure shown in figure.
A. It is found in the small intestine
B. It is part of the large intestine.
C. It is necessary for protein digestion
D. It is part of the hepatic system
E. It is a flame cell.


\( \operatorname{Let} g(x)=f(\log x)+f(2-\log x) \) and
\( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})<\mathbf{0} \forall \boldsymbol{x} \in(\mathbf{0}, \boldsymbol{3}) . \) Then find the
interval in which \( g(x) \) increases.
\( ^{\mathrm{A}} \cdot\left(0, \frac{1}{e}\right) \)
B. \( \left(\frac{1}{e}, e\right) \)
\( c \cdot(0, e) \)
D. None of these


A smooth washer impinges at a velocity v on a group of three smooth identical
blocks resting.
on a smooth horizontal surface as
shown in fig. The mass of each block is
equal to the washer. The diameter of the
washer and its height are equal to the edge of the block.
Determine the velocities of all the
bodies after the impact


Which is stronger acid in the following
pair?
3-Chlorophenol and 2-Ethylphenol.


What constitutes the central nervous
system ? How are the components of central nervous system protected? What are the constituents of peripheral
nervous systems?


Is \( a \leq a^{2}, a \in R \) true? Why or why not?


What are earth heating gases?


\( \boldsymbol{x}^{\frac{1}{2}}+\mathbf{1}=\boldsymbol{t} \)
differentiate w.r.t. \( \mathbf{x} \)
\( \mathbf{A} \cdot \frac{d t}{d x}=\frac{1}{2 \sqrt{x}} \)
B. \( \frac{d t}{d x}=\frac{1}{4 \sqrt{x}} \)
\( \mathbf{C} \cdot \frac{d t}{d x}=\frac{1}{8 \sqrt{x}} \)
D. \( \frac{d t}{d x}=\frac{1}{16 \sqrt{x}} \)


After the secondary growth, the oldest layer of secondary phloem in a dicot stem is located
A. Just outside the vascular cambium
B. Just inside the vascular cambium
c. Just inside the vascular primary phloem
D. Just outside the secondary xylem


A hemispherical tank full of water is
emptied by a pipe at the rate of 5 litres per second. How much time will it take
to empty half of the tank, if it is \( 3.5 m \) in diameter?


The work done in rearranging a system of 3 identical particles of mass 1kg on a right angled triangle to an equilateral triangle is (length of the side in both the configuration is \( 1 \mathrm{m} \) )
A. \( W=G(1+1 \sqrt{2}) \)
в. \( W=G(1-1 \sqrt{(} 2)) \)
c. \( W=G(1-2 \sqrt{(} 2)) \)
D. \( W=G(1+2 \sqrt{(} 2)) \)


A reduction in atomic size with increase
in atomic number is a characteristics of
which elements?
A. d-block
B. f-block
c. radioactive series
D. high atomic masses


Find inverse?
\( \left[\begin{array}{ccc}2 & -1 & 4 \\ 4 & 0 & 2 \\ 3 & -2 & 7\end{array}\right] \)


If \( f(x)=\cos ^{-1}\left[\frac{1-(\log x)^{2}}{1+(\log x)^{2}}\right], \) then
\( \boldsymbol{f}^{\prime}(\boldsymbol{e})= \)
\( A \cdot \frac{1}{e} \)
B. \( \frac{2}{e^{2}} \)
\( c \cdot \frac{2}{e} \)
D. None of these


After watching a programme on TV about the adverse effects of junk food and soft drinks on the health of school
children, Sonali, a student of Class XII,
discussed the issue with the school
principal. The principal immediately instructed the canteen contractor
to replace the fast food with the fiber and vitamins rich food like sprouts, salad, fruits etc. This decision was welcomed by
the parents and the students. After
reading the above passage, answer the following questions:
(a) What values are expressed by Sonali and the Principal of the school?
(b) Give two examples of water-soluble
vitamins.


Construct the truth table for the
statement \( (\boldsymbol{p} \wedge \boldsymbol{q}) \vee \boldsymbol{r} \)


Structural isomerism only should be considered with answering this question. All the isomeric alcohols with the
molecular formula \( C_{5} H_{12} O \) are added
separately to warm alkaline aqueous iodine.

How many of the isomers give a yellow
precipitate?
A . 0
B. 1
\( c \cdot 2 \)
D. 3


Find a point of inflation for the curve \( y=\frac{x+1}{x^{2}+1} \)


Three charges, each \( +q, \) are placed at the corners of an isosceles triangle \( A B C \)
of sides \( \mathrm{BC} \) and \( \mathrm{AC}=2 \mathrm{a} \). D and \( \mathrm{E} \) are the
midpoints of BC and CA, as shown in the
figure. The work done in taking a charge
\( Q \) from \( D \) to \( E \) is
A \( \cdot \frac{q Q}{8 \pi \varepsilon_{0} a} \)
в. \( \frac{q Q}{4 \pi \varepsilon_{0} a} \)
\( c . \) zero
D. \( \frac{3 q Q}{4 \pi \varepsilon_{n} a} \)


Pulsars are.
Source of radio-waves.
II. Rapidly rotating neutron stars with intense magnetic field.
III. So compressed that electrons and
protons are forced to combine to form neutrons.
Which combinations is correct?
A. I and III only
B. I and II only
c. I only
D. I, II and III


Assertion
Carbon has 2 crystalline forms.
Reason
This is due to tetravalency of carbon.
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


A beaker contains a liquid of density \( \rho \)
upto a height \( h \), such that \( P \) is the
atmospheric pressure and \( g \) is the acceleration due to gravity. Answer the following questions:
a) What is the pressure at the free surface of the liquid?
b) What is the pressure at the base of the beaker?
c) What is the lateral pressure at the base on the inner walls of beaker?


Tritium is used as:
A. light sources for watches and instruments
B. with deuterium, as a fuel for nuclear fusion reactions
C . as a radioactive tracer
D. all of them


If standard entropies of \( N_{2}, H_{2} \) and
\( N H_{3} \) are \( 60,40,50 J /(K . m o l) \)
respectively and enthalpy of formation of \( N H_{3} \) is \( -30 k J . m o l^{-1}, \) then the
temperature at which reaction for formation of ammonia will be at
equilibrium is:
\( \mathbf{A} \cdot 227^{\circ} C \)
В. \( 477^{\circ} \mathrm{C} \)
c. \( 750^{\circ} \mathrm{C} \)
D. \( 900^{\circ} \mathrm{C} \)


Temperature is measured in degree


Atomic size of \( N e>F e \)
A. True
B. False


Two conducting plates \( x \) and \( y \) each of area \( A \) are placed parallel to each other at a small separation \( \boldsymbol{d} . \boldsymbol{X} \) is given a charge \( 3 q \) and \( Y \) is given a charge \( q \) The potential difference between the plates is
A \( \cdot \frac{q d}{2 \varepsilon_{0} A} \)
в. \( \frac{q d}{\varepsilon_{0} A} \)
c. \( \frac{3 q d}{2 \varepsilon_{0} A} \)
D. \( \frac{2 q d}{\varepsilon_{0} A} \)


The price of a commodity is increased
by \( 40 \% . \) By what percent shuld a consumer reduce his consumption so that his expenditure on the commodity remains constant?


In a building there are 24 cylindrical pillars. The radius of each pillar is
\( 28 \mathrm{cm} \) and height is \( 4 \mathrm{cm} . \) Find the total
\( \operatorname{cost} \) of painting the curved surface area of all pillars at the rate of \( R s .8 \) per \( m^{2} \)


Find the slope and \( y \) -intercept of the
line \( \boldsymbol{x}-\boldsymbol{y}=\mathbf{3} \)
A. slope \( =2, y \) -intercept \( =-3 \)
B. slope \( =0, y \) -intercept \( =-3 \)
c. slope \( =1, y \) -intercept \( =-3 \)
D. slope \( =1, y \) -intercept \( =3 \)


The Lassaigne's extract is boiled with
dil. \( H N O_{3} \) before testing for halogens because :
A. silver halides are soluble in \( H N O_{3} \)
B. \( N a_{2} S \) and \( N a C N \) are decomposed by \( H N O_{3} \)
\( \mathrm{c} \cdot A g_{2} S \) is soluble in \( \mathrm{HNO}_{3} \)
D. \( A g C N \) is soluble in \( H N O_{3} \)


If the instantaneous emf and the
instantaneous current equations of an
A.C. circuit are respectively
\( e=E_{0} \sin (\omega t-\pi / 6), i=I_{0} \sin (\omega t+ \)
\( \boldsymbol{\pi} / \boldsymbol{6}), \) then the phase difference
between voltage and current is :
A \( \cdot \frac{\pi}{3} \)
B. zero
\( c \cdot \frac{\pi}{2} \)
D.


Parasexual cycle occurs in
A. Phycomycetes
B. Deuteromycetes
C . Ascomycetes
D. Basidiomycetes


Find the median from the following
data.
\( \begin{array}{lllll}\text { Marks } & 0- & 10- & 30- & 60- \\ & 10 & 30 & 60 & 80\end{array} \)
No. of
students , an a 15 30
A . 10
B . 20
c. 30
D. 40


Application of a forward bias to a \( \mathrm{p}-\mathrm{n} \)
junction
A. widens the depletion zone
B. increases the potential difference across the depletion
zone
C. increases the number of donors on the n side
D. increases the electric field in the depletion zone


Let \( E_{D}, E_{P}, E_{S} \) denote efficiency of a
diesel, a petrol and a steam engine respectively. which of the following is
correct?
A. \( E_{D}<E_{P}>E_{S} \)
В. \( E_{D}<E_{P}<E_{S} \)
\( \mathbf{c} \cdot E_{P}>E_{D}>E_{S} \)
D. \( E_{P}<E_{S}<E_{D} \)


A bag contains 40 balls out of which some are red, some are blue and
remaining are black. If the probability of drawing a red ball is \( \frac{11}{20} \) and that of blue ball is \( \frac{1}{5}, \) then the number of black ball is?
\( \mathbf{A} \cdot \mathbf{5} \)
B . 25
c. 10
D. 30


A particle of mass \( m \) is made to move
with uniform speed \( v \) along the perimeter of a regular polygon of \( 2 n \) sides. The magnitude of impulse applied at each corner of the polygon is:
A \( \cdot_{2 m v \sin } \frac{\pi}{2 n} \)
B. \( _{m v \sin } \frac{\pi}{2 n} \)
\( ^{\mathrm{c}} 2 m v \cos \left(\frac{\pi}{2 n}\right) \)
D. \( _{m v \cos } \frac{\pi}{2 n} \)


At what height from the surface of the earth (in terms of the radius of earth) the acceleration due to gravity will be \( \frac{g}{100} ? \)
A. \( 10 R \)
\( R \)
в. \( 9 R \)
c. \( 100 R \)
D. \( R / 100 \)


On the basis of Rutherford's particle scattering experiment, he stated that:
A. there is positively charged center in an atom which was termed as nucleus
B. the electrons revolve around the nucleus is well defined orbits
c. the size of nucleus is very small relative to the size of the atom
D. all of the above


Maximum prescribed limit of Fe in drinking water is:
A. 0.1 ppm
B. 0.2 ppm
c. 0.5 ppm
D. \( 0.2 \mathrm{ppb} \)


Divide \( :-24 x^{2} y^{2}-4 x y \) by \( 2 x y \)


Pitch-Blende is the source of some
metals. Find the total No. of such metals
among these:
\( [\boldsymbol{H} \boldsymbol{g}, \boldsymbol{R} \boldsymbol{a}, \boldsymbol{U}, \boldsymbol{T} \boldsymbol{h}, \boldsymbol{Z} \boldsymbol{n}, \boldsymbol{T} \boldsymbol{c}] \)


Indium impurity in germanium makes
A. n-type
B. p-type
c. insulator
D. intrinsic


For real \( \boldsymbol{x} \), let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\mathbf{5} \boldsymbol{x}+\mathbf{1}, \) then
A. \( f \) is onto \( R \) but not one-one
B. \( f \) is one-one and onto \( R \)
c. \( f \) is neither one-one nor onto \( R \)
D. \( f \) is one-one but not onto \( R \)


Vehicular standard based on European regulation was first introduced in in India.
A. 2000
B . 1999
\( c .200 \)
D. 1997


\( \ln C u X_{2}, X \) belongs to which group?
A. group IA
B. group IIA
c. group IIIA
D. group VIA
E. group VIIA


Assertion
When a charge is brought near a
conductor then a very small value
current is established in the conductor
Reason
since electric field inside the conductor
has to be zero so to overcome the
electric field of the external charge,
internal charge of conductor is
collected all accross the surface.
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


There is a series \( L-C-R \) circuit.An
alternating source of emf having voltage \( V=V_{0} \sin \omega t \) is applied between M and N Here \( \boldsymbol{V}_{M}-\boldsymbol{V}_{N}=\boldsymbol{V}_{0} \sin \omega \boldsymbol{t} \) and \( \frac{\mathbf{1}}{\boldsymbol{\omega} \boldsymbol{C}}- \)
\( \omega L=R \)
A \( \cdot \theta=\frac{\pi}{2} \)
в. \( \theta=0 \)
c. \( \theta=\frac{\pi}{4} \)
D. \( \theta=\pi \)


For the cleavage of ethers by halogen
acids, the order of reactivity of halogen acids is:
A. \( H I>H B r>H C l \)
в. \( H B r>H I>H C l \)
c. \( H C l>H B r>H I \)
D. ethers do not undergo cleavage


Find the sum of the rational numbers \( \frac{-4}{9}, \frac{15}{12} \) and \( \frac{-7}{18} \)


Isomers which can be interconverted
through rotation about \( C-C \) single
bond are:
A. diastereomers
B. enantiomers
c. conformers
D. chain isomers
E. position Isomers


Example of life processes is
A. Excretion
B. Respiration
c. Photosynthesis
D. All of the above


Study the graph which shows results of three different experiments \( P, Q \) and \( R \)
Which factor has been changed to
produce the difference(s) you can see between curves P and Q?
A. Temperature is higher in
B. Temperature is lower in \( Q \)
c. Temperature is higher in \( Q \)
D. Temperature is lower in


If \( g \) is the acceleration due to gravity on
the earth's surface, the gain in the potential energy of an object of mass \( \boldsymbol{m} \)
raised from the surface of the earth to a
height equal to the radius \( R \) of the earth
is
\( ^{\mathbf{A}} \cdot \frac{1}{2}^{m g R} \)
в. \( 2 m g R \)
\( ^{\mathrm{c}} \cdot \frac{1}{4}^{m g R} \)
D. \( m g R \)


The mechanism of the reaction:
\( N u^{-}+R-X \rightarrow R-N u+X^{-} \) is:
\( N u^{-}+R-X \rightarrow[\text { Transition state }] \)
(slow) [Transition state] \( \rightarrow N u-R+ \)
\( X^{-}(\text {fast }) \) The rate of reaction can be
increased by:
A. increasing the cone, of \( N u^{-} \) only
B. increasing the core, of \( R-X \) only
c. increasing the cone, of both \( N u^{-} \) and \( R-X \)
D. decreasing the cone, of both \( N u^{-} \) and \( R-X \)


Unburnt carbon particles causes:
A. stomach infections
B. respiratory problems
C. throat problems
D. none of these


Catalytic converters are fitted into automobiles to reduce emission of
harmful gases. Catalytic converters change unburnt hydrocarbons into
A. Carbon dioxide and Water
B. Carbon monooxide
c. Methane
D. Carbon dioxide and Methane


What is the least number by which 8640 is divided, the quotient as a
complete cube number?
\( A \cdot 6 \)
B. 7
\( c \cdot 5 \)
D. 8


Evaluate \( \int\left(\frac{x^{6}-1}{1+x^{2}}\right) d x \) for \( x \in R \)


Saheli, a female antifertility pill is used
A . Daily
B. weekly
c. Quarterly
D. Monthly


A students plots a graph between inverse of magnification \( 1 / \mathrm{m} \) produced by a convex thin lens and the object
distance \( u \) as shown in figure. What
was the focal length of the lens used?
\( A \cdot \frac{b}{c^{2}} \)
в. \( b c c \)
\( c \)
\( b \)
\( D \)


Distance between focus and optical centre of a lens is called
A. Focal plane
B. Focal length
c. Focus
D. Principal axis


Can a body have energy without having momentum ? Explain?


Sex is determined by different factors in various species.
A . True
B. False


A person traveling on a straight line
moves with a uniform velocity \( v_{1} \) for a
distance \( x \) and with uniform velocity \( v_{2} \)
for the next equal time. The average velocity \( v \) is given by
A \( \cdot v=\frac{v_{1}+v_{2}}{2} \)
B. \( v=\sqrt{v_{1} v_{2}} \)
c. \( v=\frac{v_{1} v_{2}}{v_{1}+v_{2}} \)
D. \( v=\frac{v_{1}+v_{2}}{v_{1} v_{2}} \)


A point \( P \) is \( 13 \mathrm{cm} \) from the centre of
the circle. The length of the tangent
drawn from \( P \) to the circle is 12 cm.
Find the radius of the circle.


In a group of 950 persons, 750 can
speak Hindi and 460 can speak English.
Find how many can speak English only.


Which oil is used as frother in froth
floatation process?
A. Mustard oil
B. coconut oil
c. Olive oil
D. Pine oil


Rub a piece of ebonite across a piece of
animal fur. What happens?
A. the fur has a slightly positive charge and the ebonite is slightly negative
B. the fur has a slightly positive charge and the ebonite is also slightly positive
C. the fur has a slightly negative charge and the ebonite is also slightly negative
D. the fur has a slightly negative charge and the ebonite is slightly positive


Assertion \( f_{i=1}^{2 n} \sin ^{-1} x_{i}=n \pi \forall n \epsilon N \) then \( \sum_{i=1}^{2 n} x_{i}= \)
\( \sum_{i=1}^{2 n} x_{i}^{2}=\sum_{i=1}^{2 n} x_{i}^{n}=2 n \)
Reason \( -\frac{\pi}{2} \leq \sin ^{-1} x \leq \frac{\pi}{2} \forall x \epsilon[-1,1] \)
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 false but Reason is true


Find \( \boldsymbol{A}-\boldsymbol{B} \)
\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{2} & \mathbf{2} & \mathbf{0} \\ \mathbf{3} & \mathbf{- 4} & \mathbf{5} \\ \mathbf{2} & \mathbf{3} & \mathbf{- 7}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\mathbf{3} & \mathbf{3} & \mathbf{1} \\ \mathbf{4} & \mathbf{- 5} & \mathbf{4} \\ \mathbf{3} & \mathbf{2} & \mathbf{- 4}\end{array}\right] \)


If the radius of a circle is increased by
\( 10 \% \) then corresponding increase in the
area of the circle is \( \ldots . .(\boldsymbol{\pi}=\mathbf{3 . 1 4}) \)
A . 19 \%
B . 10 \%
c. 21 \%
D. 20 \%


You are provided with a mixture of naphthalene and ammonium chloride by your teacher. Suggest an activity to separate them with well labelled
diagram.


toppr
Q Type your question
The final product \( (C) \) of the above
reaction is
\( A \)
3
\( c \)
\( D \)


Which of the following shows the side
elevation?
\( \mathbf{A} \)
B.
\( c \)
D.


toppr
Q Type your question
\( \int_{0}^{1} \frac{1}{1} \)
\( A \)
\begin{tabular}{|c|c|c|}
\hline \( \mathbf{A} \) & \( \mathbf{B} \) & \( \mathbf{Y} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\hline \( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\hline \( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{0} \) \\
\hline
\end{tabular}
\( B \)
\begin{tabular}{|c|c|c|}
\hline \( \mathbf{A} \) & \( \mathbf{B} \) & \( \mathbf{Y} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{0} \) \\
\hline \( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\hline \( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\hline
\end{tabular}
\( c \)
\begin{tabular}{|c|c|c|}
\hline \( \mathbf{A} \) & \( \mathbf{B} \) & \( \mathbf{Y} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\hline \( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\hline \( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{0} \) \\
\hline
\end{tabular}
\( D \)
\begin{tabular}{|c|c|c|}
\hline \( \mathbf{A} \) & \( \mathbf{B} \) & \( \mathbf{Y} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{0} \) & \( \mathbf{1} \) \\
\hline \( \mathbf{0} \) & \( \mathbf{1} \) & \( \mathbf{0} \) \\
\hline \( \mathbf{1} \) & \( \mathbf{0} \) & \( \mathbf{0} \) \\
\hline \( \mathbf{1} \) & \( \mathbf{1} \) & \( \mathbf{1} \) \\
\hline
\end{tabular}


The perpendicular distance from the point of intersection of the lines \( 3 x+ \) \( 2 y+4=0,2 x+5 y-1=0 \) to the line
\( 7 x+24 y-15=0 \) is
A \( \cdot \frac{2}{3} \)
B.
\( c \cdot \frac{1}{5} \)
D.


Assertion
The refractive index of a prism depends only on the kind of glass of which it is made of and the colour of light.
Reason
The refractive index of a prism depends on the refracting angle of the prism and the angle of minimum deviation.
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 uniform disc is rolling on a horizontal surface. At a certain instant \( B \) is the
point of contact and \( A \) is a stationary
point at height \( 2 R \) from ground, where
\( R \) is radius of disc :
This question has multiple correct options
A. The magnitude of the angular momentum of the disc about \( B \) is thrice that about \( A \).
B. The angular momentum of the disc about \( A \) is anticlockwise
C. The angular momentum of the disc about \( B \) is clockwise.
D. The angular momentum of the disc about \( A \) is equal to that about \( B \).


If some coins each of diameter \( 1.5 \mathrm{cm} \)
and thickness \( 0.2 \mathrm{cm} \) are melted and a
right circular cylinder of height \( 10 \mathrm{cm} \)
and diameter \( 4.5 \mathrm{cm} \) is made, then find
the number of coins required to make the right circular cylinder
A . 336
в. 450
c. 512
D. 545


An object is thrown into space horizontally under the action of earth's gravity. Then the object is said to be a :
A. projectile
B. trajectory
c. spaceship
D. none of these


Two charges \( -10 C \) and \( +10 C \) are placed 10cm apart. Potential at the center of
the line joining the two charges is
A. zero
B. \( 2 V \)
\( c .3 V \)
D. None of these


The balanced chemical reaction with
\( \boldsymbol{C l}_{2} \) is
A \( \cdot C l_{2}+2 N a_{2} S_{2} O_{3} \rightarrow 2 N a C l+N a_{2} S_{4} O_{6} \)
в. \( C l_{2}+H_{2} O+N a_{2} S_{2} O_{3} \rightarrow N a_{2} S O_{4}+2 H C l+S \)
c. \( C l_{2}(g)+S_{2} O_{3}^{2-} \rightarrow S O_{4}^{2-}+S+C l \)
D. None of the above


Solve the equation \( z^{2}=\bar{z} \)


Which of the following compounds gives
blood red colouration when its
Lassaignes extract is treated with alkali and ferric chloride?
A. Thiourea
B. Diphenyl sulphide
c. Phenyl hydrazine
D. Benzamide


The country that lies to the south-west of India is
A. Maldives
B. Pakistan
c. srilanka
D. Bangladesh


The standard reduction potential
values, \( \boldsymbol{E}^{\circ}\left(\boldsymbol{B} \boldsymbol{i}^{3+} / \boldsymbol{B} \boldsymbol{i}\right) \) and
\( E^{\circ}\left(C u^{2+} / C u\right) \) are \( 0.226 \mathrm{V} \) and \( 0.344 \mathrm{V} \)
respectively. A mixture of salts of bismuth and copper at unit
concentration each is electrolysed at
\( 25^{\circ} \mathrm{C} . \) To what value \( \operatorname{can}\left[C u^{2+}\right] \) be
brought down before bismuth starts to
deposit, in electrolysis.
\( \mathbf{A} \cdot\left[C u^{2+}\right]=10^{-8} M \)
B. \( \left[C u^{2+}\right]=10^{-4} M \)
\( \mathbf{C} \cdot\left[C u^{2+}\right]=10^{-3} M \)
D. \( \left[C u^{2+}\right]=10^{-6} M \)


The light velocity of revolving electrons is conquered by ........... force of attraction of nucleus on an electron in
Rutherford's model.
A. electrostatic
B. gravitational
c. magnetic
D. van der waals


If \( \boldsymbol{a}+\boldsymbol{b}=\mathbf{7} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{a} \boldsymbol{b}=\boldsymbol{6}, \boldsymbol{f} \boldsymbol{i} \boldsymbol{n} \boldsymbol{d} \boldsymbol{a}^{2}-\boldsymbol{b}^{2} \)
\( \mathbf{A} \cdot \pm 35 \)
B. ±12
\( c .\pm 22 \)
\( \mathrm{D} \cdot \pm 39 \)


Show that \( f(x)=\frac{1}{x} \) is decreasing
function on \( (\mathbf{0}, \infty) \)


The number of valence electrons across
a period and down the group:
A. increases, same
B. decreases, same
c. same, increases
D. increase, decreases


In a current-carrying solenoid, the magnetic field direction is given by the
right hand rule such that the
A. Encircling fingers indicate the direction of electric current
B. Encircling fingers indicate the direction of magnetic field
C. Extended right thumb will point in the direction of the axial magnetic field
D. Both (2) and (3)


Match the list 1 (mixtures) with list 2 (solution used for separation).


For the elementary reaction \( 2 S O_{2(g)}+ \)
\( O_{2(g)} \rightarrow 2 S O_{3(g)}, \) identify the correct among the following relaitons.
A \( \cdot \frac{-d\left[S O_{2(g)}\right]}{d t}=\frac{-d\left[O_{2(g)}\right]}{d t} \)
\( ^{\mathbf{B}} \cdot \frac{+1}{2} \frac{d\left[S O_{3(g)}\right]}{d t}=\frac{d\left[S O_{2(g)}\right]}{d t} \)
c. \( \frac{+d\left[S O_{3(g)}\right]}{d t}=\frac{-2 d\left[O_{2(g)}\right]}{d t} \)
D. \( \frac{+d\left[S O_{2(g)}\right]}{d t}=\frac{-d\left[O_{2(g)}\right]}{d t} \)


According to binomial nomenclature system, scientific name includes two
terms. They are
A. Genus and species
B. Class and order
c. Genus and phylum
D. Species and order


Describe an experiment to show that equal volumes of different liquids expand by different amounts for the
same rise in temperature.


Nikhil calculates the change in gravitational potential energy at a height of \( 5 \mathrm{km} \) from the surface of earth using the equation \( U=-G M m / r \) and Varun calculates this energy using the formula \( U= \) mgh. The energies
calculated have different numerical
values.
A . True
B. False


A metallic ball strikes a wall and falls
down whereas a tennis bail having the same mass and velocity bounces back.
The reason for this is that:
A. both suffer equal change in momentum.
B. the tennis ball suffers a greater change in momentum
c. metallic ball suffers a greater change in momentum.
D. the momentum of the tennis ball is less than that of the metallic ball


Fill in the blank:
Air is a/an conductor of
electricity.
A. good
B. poor
c. extremely good
D. neutral


Kupffer cells are present in
A . Liver
B. Pancreas
c. Small intesine
D. Large intestine


The particles which can be added to the nucleus of an atom, without changing properties, are called.
A. Neutrons
B. Electrons
c. Protons
D. None of these


Function \( f(x)=\log _{10} \cos x \) is
function in \( \left(0, \frac{\pi}{2}\right) \)
A. Decreasing
B. Increasing
c. constant
D. Increasing and decreasing


If we divide a positive integer by another positive integer, what is the resulting
number?
A. Always a natural number
B. Always an integer
c. A rational number
D. An irrational number


A cationic colloidal electrolyte forms
micelles at \( 10^{-4} \) M concentration in
water. If \( 1 \mathrm{mm}^{3} \) solution contains \( 10^{12} \)
micelle structure, then the number of
cations involved in one micelle is:
A . 20
B . 40
c. 60
D. 80


A white solid \( X \) reacts with dil. \( H C l \) to
give colourless gas which is used in fire extinguishers. The solid \( \boldsymbol{X} \) is:
A \( . \) NaCl
в. \( C H_{2} \) СОО \( N a \)
\( \mathbf{c} \cdot N a_{2} C O_{3} \)
D. \( \operatorname{NaH} \mathrm{CO}_{3} \)


Find the value of \( \sin ^{-1}\left(\sin \frac{3 \pi}{5}\right) \)


The value of equivalent capacitance of
the combination shown in figure,
between the points \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) is
A. \( 3 C \)
B. \( 2 C \)
\( c . C \)
D. \( C / 3 \)


Evaluate \( \lim _{x \rightarrow 0} \frac{a^{\sin x}-1}{\sin x} \)


Write any one linear equation using the
variables ' \( x \) ' and ' \( y \) '.


If \( A \) is a skew-symmetric matrix of
order \( 3, \) then prove that det \( A=0 \)


Find the distance between two complex
nymbers \( z_{1}=2+3 i \) and \( z_{2}=7-9 i \) on
the complex plane.


if \( a, b, c \) are distinct and the roots of
\( (b-c) x^{2}+(c-a) x+(a+b)=0 \) are
equal, then \( a, b, c \) are in
A. Arithmetic progression
B. Geometric progression
c. Harmonic progression
D. Arithmetico-Geometric progression


A weighing machine measures:
A. weight only
B. mass only
c. mass and weight
D. none of these


top
Q Type your question
codes given below:
Column\( \mathbf{1} \)
Bond order
(a) \( N_{2} \rightarrow \quad \) increases and
\( N_{2}^{+} \)
(p) magnetic property is changed
Bond order
\( (b) \)
\( O_{2}^{+} \rightarrow \quad \) decreases and
(q) magnetic property \( O_{2}^{2+} \quad \) is not changed
Bond order
(c)
\( B_{2} \rightarrow \) \( B_{2}^{+} \)\( \quad \) (r) \( \quad \) increases and magnetic property is not changed
Bond order
(d)
\( \begin{array}{l}\begin{array}{l}N O^{-} \rightarrow \\ N O\end{array} \rightarrow & \text { (s) } \quad \begin{array}{l}\text { decreases and } \\ \text { magnetic property } \\ \text { is changed }\end{array}\end{array} \) 1 Note: Here change in magnetic property refers to change from diamagnetic to
paramagnetic or paramagnetic to diamagnetic.
\( A \cdot A-s, B-p, C-r, D-q \)
B. \( A-s, B-p, C-q, D-r \)
\( C \cdot A-r, B-q, C-s, D-p \)
D. \( A-p, B-s, C-q, D-r \)


In physical adsorption, the molecules of adsorbate are held by chemical forces.
A. True
B. False


Which of the following metal is present in the anode mud during the electrolytic refining of copper?
A. \( N a \)
в. \( A l \)
c. \( A u \)
D. \( f e \)


Salts of sulphuric acid are called
A. sulphates
B. sulphites
c. silicates
D. sulphides


Resistors are generally colour coded to:
A. Indicate the type of the circuit in which they are to be used
B. Identify whether they are ohmic or non-ohmic
C. Determine their values in ohm
D. Determine whether they are wire wound or composition resistors


Calculate the average bond enthalpy of
the \( \boldsymbol{O}-\boldsymbol{H} \) bond in water at \( 298 \mathrm{K} \) using
the data / information given below :
\( \Delta_{f} \boldsymbol{H}^{0}[\boldsymbol{H}(\boldsymbol{g})]=\mathbf{2} \mathbf{1} \mathbf{8} \mathbf{k} \mathbf{J} / \mathrm{mol} \)
2. \( \Delta_{f} H^{0}[O(g)]=249.2 \mathrm{kJ} / \mathrm{mol} \)
3. \( \Delta_{f} H^{0}\left[H_{2} O(g)\right]=-241.8 \mathrm{kJ} / \mathrm{mol} \)
The average bond enthalpy of the \( - \) bond in water is defined as one - half of
the enthalpy change for
the reaction \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{H}(\boldsymbol{g})+\boldsymbol{O}(\boldsymbol{g}) \)
Also, determine the \( \Delta U \) of the \( O-H \)
bond in water at 298 K. Assume ideal
gas behaviour.
A \( \cdot E(O-H)=462 \) kJ/mol; \( \Delta U=461 \) kJ/mol
B . \( E(O-H)=463.5 \) kJ/mol; \( \Delta U=463.5 \) kJ/mol
C \( \cdot E(O-H)=461 \mathrm{kJ} / \mathrm{mol} ; \Delta U=461 \mathrm{kJ} / \mathrm{mol} \)
D - \( E(O-H)=463.5 \mathrm{kJ} / \mathrm{mol} ; \Delta U=461 \mathrm{kJ} / \mathrm{mol} \)


Two identical \( +v e \) charges are at the ends of a straight line AB. Another identical \( +v e \) charge is placed at 'C' such that
\( A B=B C . \) (A, B and C being on the same
line). Now the force on 'A' will :
\( A \). increase
B. decrease
c. remain same
D. cannot be predicted


The determination of sex of the child
depends on the chromosome of
A. Female
в. Male
c. The child itself
D. None of the above


Looming' in polar region
\( A \cdot \) Is an optical illusion
B. Arise due to the veriation of refractive index of atmosphere
C. Is an example of total internal reflection
D. All of the above


The displacement of a particle is
represented by the equation \( y=\sin ^{3} \omega t \)
the motion is
A. Non-periodic
B. Simple harmonic with period \( \pi / \omega \)
c. simple harmonic with period \( 2 \pi / \omega \)
D. Periodic but not simple harmonic


State True or False.
Kohlrausch law is valid for weak
electrolytes only.
A. True
B. False