Which is used in making of thermocol?
A. Polypropylene
B. Polyethylene
c. Polystyrene
D. High density polyethylene


Blister Cu contains about:
A. \( 60 \% \) Cu
B. 90\% Cu
c. \( 98 \% \) си
D. \( 100 \% \) Cu


If the 7 th and 8 th term of the binominal
expansion \( (2 a-3 b)^{n} \) are equal, then \( \frac{2 a+3 b}{2 a-3 b} \) is to
A \( \cdot \frac{n-13}{n+1} \)
в. \( \frac{n+1}{13-n} \)
c. \( \frac{6-n}{13-n} \)
D. \( \frac{n-1}{13-n} \)


Match the entries of Column- I and
Column - II.
A . a-4, b-3, c-2, d-
B. \( a-1, b-3, c-2, d-4 \)
C. \( a-4, b-3, c-1, d-2 \)
D. \( a-3, b-4, c-2, d-1 \)


Which of the following pair is correct?
A. Rutherford; X-rays
B. Roentgen;electron
c. chadwick;neutron
D. J-J-Thomson;photon


In which of the following reactions new carbon-carbon bond is not formed?
A. Cannizzaro reaction
B. Wurtz reaction
c. Aldol condensation
D. Friedel-Crafts reaction


An extensive property is
A. a property that changes when the size of the sample changes
B. a property that doesn't change when you take away some of the sample.
\( c \cdot \) both
D. none


An equation whose maximum degree of variable is two is called \( \ldots \). equation.


Ten positively charged particles are
kept fixed on the \( x- \) axis at points \( x= \)
\( 10 \mathrm{cm}, 20 \mathrm{cm}, 30 \mathrm{cm}, \ldots ., 100 \mathrm{cm} . \) The
first particle has a charge \( 1.0 \times 10^{-8} C \)
the second \( 8 \times 10^{-8} C, \) the third \( 27 \times \)
\( 10^{-8} C \) and so on. The tenth particle has
a charge \( 1000 \times 10^{-8} C . \) Find the
magnitude of the electric force acting on a \( 1 C \) charge placed at the origin.
\( \mathbf{A} \cdot 5.94 \times 10^{5} N \)
B . \( 5.49 \times 10^{5} N \)
c. \( 9.45 \times 10^{5} N \)
D. \( 4.95 \times 10^{5} N \)


The quantity of heat required to raise the temperature of unit mass of a given body through \( 1^{\circ} C \) is known as specific
heat.
A. True
B. False


A man projects a coin upwards from the gate of a uniform moving train. The path of coin for the man will be


\( 9 / 16 \) of a number is 51 greater than \( 50 \% \) of the number. Then, that number is
A . 832
B. 704
c. 960
D. 816


A force \( F \) acting on an object varies
with distance \( x \) as shown in the figure.
The work done by the force in moving
the object from \( x=0 \) and \( x=20 m \) is
A . \( 500 J \)
B. \( 1000 J \)
c. \( 1500 J \)
D. \( 2000 J \)


A \( 20 g \) bullet passes through a plate of
mass \( 1 k g \) and finally comes to rest
inside another plate of mass \( 2980 g \). It
makes the plates move from rest to
same velocity. The percentage loss in velocity of bullet between the plate is:
\( A \)
B . \( 50 \% \)
\( c .75 \% \)
D. \( 25 \% \)


If \( A \) is square matrix such that \( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})=\left(\begin{array}{ccc}\mathbf{4} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{4} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{4}\end{array}\right) \) then det \( (\mathbf{A} \mathrm{d} \)
\( A)= \)
\( A \cdot 4 \)
B. 16
\( c \cdot 64 \)
D. 256


Who is considered as the founding father of chemistry?
A. Boyle
B. Aristotle
c. sir Francis
D. John Mayow


The heat capacity of a material depends
upon.
A. density of matter
B. specific heat of matter
c. temperature of matter
D. structure of matter


A ray of light undergoes deviation of \( 30^{\circ} \) when incident on an equilateral prism of refractive index \( \sqrt{2} . \) The angle made
by the ray inside the prism with the base of the prism is:


"Law of Priority" is applicable after the
yearr
A . 1720
B. 1753
\( c \cdot 1853 \)
D. 1845


According to carrier concept, the transport of ions across the membrane
is
A. Passive process
B. Active process
c. osmotic proces
D. None of the above


Kabaddi players rub their hands with
soil so that they can:
A. make their skin dry
B. moisture the hands
c. get a better grip while holding the opponent
D. soil the opponent


\( \operatorname{Let} f(x)=\frac{a x+b}{c x+d}, \) then \( f o f(x)=x \)
provided
A \( . d=-a \)
B. \( d=a \)
c. \( a=b=c=d=1 \)
D. \( a=b=1 \)


Differentiate with respect to \( x \) :
\( \boldsymbol{y}=\boldsymbol{e}^{-\mathbf{3} \boldsymbol{x}}+\sin \mathbf{2} \boldsymbol{x} \)


A transition element containing only one electron in \( 4 s \) -orbital is:
A \( \cdot_{21} \mathrm{Se} \)
В. \( _{23} M n \)
\( \mathbf{c} \cdot_{26} F e \)
D・ \( _{29} C u \)


A number \( x \) when divided by 7 leaves a
remainder 1 and another number \( y \)
when divided by 7 leaves the remainder
2. What will be the remainder if \( x+y \) is
divided by \( 7 ? \)
A .
B. 2
\( c .3 \)
D. 4


A moving charge will produce
A. No field
B. An electric field only
C. A magnetic field only
D. Both (b) and (c)


What is mucus membrane?


When a piece of zinc metal is added to a solution of hydrochloric acid, a reaction occurs. The products are aqueous zinc chloride and hydrogen gas. Which of the following conditions would
result in the fastest rate of reaction
with \( 1.00 g \) of zinc?
\( \mathbf{A} \cdot 0.010 M H C l \) at \( 10^{\circ} C \)
B . \( 0.010 M \) HCl at \( 80^{\circ} \mathrm{C} \)
c. \( 0.10 M \) HCl at \( 10^{\circ} \) C
D. \( 0.10 M H C l \) at \( 80^{\circ} C \)


Which substance forms cell wall in
fungi?
A. Chitin or fungal cellulose
B. Pectin
c. Lignin
D. Suberin


What is the frequency of photon whose
momentum is \( 1.1 \times 10^{-23} k g m s^{-2} ? \)
\( \mathbf{A} \cdot 5 \times 10^{13} H z \)
В. \( 5 \times 10^{17} \mathrm{Hz} \)
c. \( 0.5 \times 10^{18} \mathrm{Hz} \)
D . \( 5 \times 10^{18} \mathrm{Hz} \)


The field of polymer chemistry was revolutionised by :
This question has multiple correct options
A. Kharasch in USA
B. Kael Ziegler in Germany
c. Giulio Natta in Italyy
D. Barton in England


If \( 4 \cos ^{-1} x+\sin ^{-1} x=\pi, \) then the
value of \( x \) is.
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{\sqrt{2}} \)
\( c \cdot \frac{\sqrt{3}}{2} \)
D. \( \frac{2}{\sqrt{3}} \)


In the following figure potential
difference between \( A \) and \( B \) is
\( A \)
B. 5 volt
\( c \cdot 10 \) volt
D. 15 volt


If light intensity increases the first
limiting factor is
\( A \cdot C O_{2} \)
B. Starch
\( c \cdot O_{2} \)
\( D \cdot s O_{2} \)


The dimensions of \( \frac{v^{2}}{\mu g} \) where \( \mu= \)
coefficient of friction, \( \boldsymbol{v}= \) the velocity
\( g= \) acceleration due to gravity is same
as that of
\( ^{A} \cdot \frac{F}{B q} \)
в. \( \mu F \)
c. \( \frac{F}{m} \)
D. None


What is the nature of relation
betweenthe kinetic energy \( \left(\mathbf{E}_{\mathbf{k}}\right) \) and
their orbitalradius (r) of the satellites revolvingaround the Earth?
\( \mathbf{A} \cdot E_{k} \propto 1 \)
B . \( E_{k} \propto \frac{1}{r} \)
\( \mathrm{c} \cdot E_{k} \propto r^{2} \)
D. \( E_{k} \propto \frac{1}{r^{2}} \)


What is inheritance


If \( \boldsymbol{A}=\cos ^{2} \boldsymbol{x}+\frac{\mathbf{1}}{\cos ^{2} \boldsymbol{x}}, \boldsymbol{B}=\cos \boldsymbol{x}- \)
\( \frac{1}{\cos x} \forall x \neq(2 n \pm 1) \frac{\pi}{2}, \) then the
minimum value of \( \frac{\boldsymbol{A}}{\boldsymbol{B}} \) is
A \( \cdot \sqrt{2} \)
B. \( 2 \sqrt{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. None of these


A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it.
By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?


The atmospheric pressure is due to the:
A. sky above our head
B. air mass surrounding earth
c. gravitational force of sun and other planets
D. mass of the earth


\( \mathbf{2} \boldsymbol{C} \boldsymbol{a}_{3}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2}+\boldsymbol{6} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2}+\mathbf{1 0} \boldsymbol{C} \rightarrow \boldsymbol{P}_{4}+ \)
\( \boldsymbol{C a} \boldsymbol{S i O}_{3}+\mathbf{1 0 C O} \)
Which coefficient balances the reaction
given above?
A . 2
B. 4
c. 5
D. 6


Is it possible for an accelerating body to have zero velocity? Explain.


In a windmill:
A. the translational motion of the windmill is used to turn the turbine of the electric generator.
B. the rotatory motion of the windmill is used to turn the turbine of the electric generator.
C. the upward motion of wind is the primary source of energy.
D. slow winds are more efficient for energy production.


An impure sample of sodium chloride
that weighed 0.50 g gave 0.90 g of silver chloride as precipitate on treatment with excess of silver nitrate solution.
Calculate the percentage purity of the sample:
A . \( 72 \% \)
B. \( 78 \% \)
\( c .80 \% \)
D. None of the above


For prism of refractive index \( 1.732, \) the angle of minimum deviation is equal to the angle of the prism. The angle of the
prism is
\( A \cdot 80^{\circ} \)
B. 70
\( c \cdot 60 \)
D. 50


Evaluate \( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\sqrt{\mathbf{8}+\mathbf{3} \boldsymbol{x}-\boldsymbol{x}^{2}}} \)


In a rotational motion of a rigid body, all
particles move with
A. same linear velocity and same angular velocity
B. same linear velocity and different angular velocity
C. different linear velocities and same angular velocities
D. different linear velocities and different angular velocities


If a couple has two boys and one girl, the probability of the next girl child to be born is
A \( \cdot \frac{1}{4} \)
B.
\( c \cdot \frac{1}{2} \)
D. \( \frac{2}{3} \)
E.


Metals can produce sound when struck, this property of metals is known as sonority.
A. True
B. False


In the potentiometer arrangement
shown in figure, the driving cell D has emf \( \mathrm{E} \) and internal resistance r. The cell
C, whose emf is to measured, has emf \( \boldsymbol{E} \)
\( \overline{2} \) and internal resistance 2r. The
potentiometer wire is \( 100 \mathrm{cm} \) long. If balance is obtained, the length AJ is
A . equal to \( 50 \mathrm{cm} \)
B. more than \( 50 \mathrm{cm} \)
c. less than \( 50 \mathrm{cm} \)
D. balance will be obtained only if resistance of AB is more than


Which group of elements was missing from Mendeleev's original periodic table?


The volume of perhydrol which on
decomposition gives 1.5 lit of \( O_{2} \) gas at
STP is:
\( \mathbf{A} \cdot 25 \mathrm{ml} \)
B. \( 15 \mathrm{ml} \)
c. \( 10 \mathrm{ml} \)
D . 20 m


The probability of an event is
A. always more than 1
B. always less than 1
c. always equal to
D. always negative


Which of the following is absorbed efficiently in colloidal forms?
A. Colloidal sulphur
B. Colloidal gold
c. colloidal copper
D. Colloidal mercury


Given \( \boldsymbol{C}(\boldsymbol{s})+\boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( \mathbf{9 4 . 2 K c a l} \)
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(l)+ \)
\( \mathbf{6 8 . 3 K c a l} \)
\( \boldsymbol{C H}_{4}(\boldsymbol{g})+\mathbf{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 2 H_{2} O(l)+210.8 K c a l \)
The heat of formation of methane in
kcal will be:
A . - 45.9
в. -47.8
c. - 20.0
D. -47.3


If the \( H^{+} \) concentration decreased from
\( 1 \mathrm{M} \) to \( 10^{-4} \mathrm{M} \) at \( 25^{\circ} \mathrm{C} \) for the couple
\( M n O_{4}^{-} / M n^{2+}, \) then the oxidising
power of the \( M n O_{4}^{-} / M n^{2+} \) couple decreases by
A . -0.18v
B. 0.18V
c. \( 0.38 v \)
D. -0.38V


Vapour pressure of pure benzene at any
temperature is 640 mm \( H g . \) A non volatile, non-electrolyte solid whose
weight is \( 2.75 g m, \) is added to \( 39.0 g m \) of benzene. Vapour pressure of solution is 600 mm \( H g \). Calculate the molecular weight of the solid?


\( \boldsymbol{L} \boldsymbol{t}_{n \rightarrow \infty} \boldsymbol{n} \cos \left(\frac{\boldsymbol{\pi}}{\boldsymbol{n}}\right) \sin \left(\frac{\boldsymbol{2} \boldsymbol{\pi}}{\mathbf{3} \boldsymbol{n}}\right)= \)
A \( \cdot \frac{2 \pi}{3} \)
B.
\( c . \pi \)
D.


The temperature of an object is observed to rise during a period. In this period:
This question has multiple correct options
A. heat is certainly supplied to it
B. heat is certainly not supplied to it
c. heat may have been supplied to it
D. work may have been done on it it


The angle between the normal and
refracted ray is called:
A. angle of deviation
B. angle of incidence
c. angle of refraction
D. none of these


What will be the products of combustion of a hydrocarbon at \( 398 K ? \)
A \( \cdot C O_{2}(g), H_{2} O(g) \)
B. \( C O_{2}(l), H_{2} O(g) \)
\( \mathrm{c} \cdot \mathrm{CO}_{2}(g), \mathrm{H}_{2} \mathrm{O}(l) \)
D. None of these


Prove that: \( \frac{1}{\operatorname{cosec} A-\cot A}-\frac{1}{\sin A}= \)
\( \frac{1}{\sin A}-\frac{1}{\operatorname{cosec} A+\cot A} \)


Solve for \( x \) and \( y \)
\( \boldsymbol{m} \boldsymbol{x}-\boldsymbol{n} \boldsymbol{y}=\boldsymbol{m}^{2}+\boldsymbol{n}^{2}, \boldsymbol{x}-\boldsymbol{y}=\boldsymbol{2} \boldsymbol{n} \)
A. \( x=m+n ; y=m-n \)
в. \( x=m-n ; y=m n-n \)
c. \( x=m+m n ; y=m+n \)
D. \( x=m n-n ; y=m-n \)


Find the \( 21^{s t} \) term of an A.P. whose \( 1^{s t} \)
term is 8 and the \( 15^{t h} \) term is 120
A . 167
в. 165
c. 168
D . 169


For the following arithmetic progressions write the first term \( a \) and
the common difference \( d \) :
\( \mathbf{0 . 3}, \mathbf{0 . 5 5}, \mathbf{0 . 8 0}, \mathbf{1 . 0 5}, \ldots \)


Active transport occurs
A. Against concentration gradient and requires ATP
B. Against concentration gradient but does not require ATP
C. Along concentration gradient but requires ATP
D. Along concentration gradient but does not require ATP


If \( \alpha=\cos \theta+i \sin \theta, \) then \( \frac{1+\alpha}{1-\alpha} \) is
equal to
A \( \cdot \cot \frac{\theta}{2} \)
B. \( \cot \theta \)
\( \mathrm{c} \cdot_{i \cot \frac{\theta}{2}} \)
D. \( i \tan \frac{\theta}{2} \)


If a body placed at the origin is acted upon by a force \( \overline{\boldsymbol{F}}=(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\sqrt{\mathbf{2}} \hat{\boldsymbol{k}}) \)
then which of the following statements are correct?
1.Magnitude of \( \overline{\boldsymbol{F}} \) is \( (2+\boldsymbol{s} \boldsymbol{q} \boldsymbol{r} \boldsymbol{t} \boldsymbol{2}) \)
2.Magnitude of \( \overline{\boldsymbol{F}} \) is 2
3. \( \bar{F} \) makes an angle of \( 45^{0} \) with the \( Z \) -
axis.
4. \( \bar{F} \) makes an angle of \( 30^{0} \) with the \( Z \)
axis.
Select the correct answer using the codes given below.
A . 1 and 3
B. 2 and 3
c. 1 and 4
D. 2 and 4


Using an A.C. voltmeter the potential
difference in the electrical line in a
house is read to be 234 volts. If the line
frequency is known to be 50 cycles/second, the equation for the line voltage is
A. \( V=165 \sin (100 \pi t) \)
B. \( V=331 \sin (100 \pi t) \)
c. \( V=220 \sin (100 \pi t) \)
D. \( V=420 \sin (100 \pi t) \)


A cuboid has
A. 4 edges
B. 8 edges
c. 12 edges
D. 16 edges


A metallic rod falls under gravity with
its ends pointing east and west. Then
A. an emf is induced in it as it cuts the magnetic lines of force
B. no emf is induced at all
C. two emf of equal nut opposite signs are induced, giving no emf is
D. its acceleration is equal to the product of \( g \) and the radius of the rod.


The atomic numbers of two elements A
and B are 11 and 12 respectively. Which element exhibits highest metallic property ? Write the molecular formula of the compounds formed when theses elements combine with the element 'Z'
having atomic number 8


One ampere hour charge is equivalent
to :
A. 36 coulombs
B. 360 coulombs
c. 3600 coulombs
D. 36000 coulombs


Assertion: Different colours travel with
different speed in vacuum.

Reason: Wavelength of light depends on refractive index of medium.
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


A square matrix can always be
expressed as a
A. Sum of a symmetric matrix and a skew-symmetric matrix
B. Sum of a diagonal matrix and a symmetric matrix
C. Skew-matrix
D. Skew-symmetric matrix


The mass of the earth is \( 6 \times 10^{22} k g \)
and that of the moon is \( 7.4 \times 10^{22} \) kg. If
the distance between the earth and the
moon is \( 3.84 \times 10^{5} k m, \) calculate the
force exerted by the earth on the moon. \( G=6.7 \times 10^{-11} N m^{2} k g^{-2} \)


Find the net capacitance between \( A \) and
B in Fig:
\( \mathbf{A} \cdot 5 / 2 \mu F \)
B . \( 2 / 5 \mu F \)
\( \mathbf{c} \cdot 9 / 22 \mu F \)
D. \( 22 / 9 \mu F \)


Which of the following are
concentration cells?
This question has multiple correct options
\( \mathbf{A} \cdot P t\left|H_{2}(g)\right| H C l\left|H_{2}(g)\right| P t \)
B. \( P t: P t: / \begin{array}{l}H C l / / H C l / H_{2}: P t \\ \left(P^{H}=4\right)^{\prime} /\left(P^{H}=2\right)\end{array} \)
\( \mathbf{c} . A g / A g C l / / A g B r / A g \)
\( (1 M) \quad 1 M \)
\( \mathbf{D} \cdot A g|A g C l| C_{c_{1}}^{-}(a q)|| B_{c_{2}}^{-}(a q)|A g B r| A g \)


Mendel's first law is
A. Law of dominance
B. Law of variation
C. Law of independent assortment
D. Law of segregation


Find the areas of the triangles the
coordinates of whose angular points are
respectively. \( \left\{\begin{array}{c}a m_{1}, \frac{a}{m_{1}} \\ a m_{3}, \frac{a}{m_{3}}\end{array}\right\},\left\{a m_{2}, \frac{a}{m_{2}}\right\} \) and


What is Latent Heat?
A. It is the heat given to a body and simultaneously the body releases it to the atmosphere
B. It is the heat given to a body to heat it by \( 1^{\circ} \mathrm{C} \)
C. It is the heat given to body to change its state at constant temperature
D. None of the above


Three charges each of value q are placed at the corners of an equilateral triangle. A fourth charge \( Q \) is placed at the center of the triangle.
a. If \( Q=-q, w i \| \) the charges at the corners move toward the center or fly away from it
b. For what value of \( Q \) at 0 will the
charges remain stationary?


Increase in bleeding time and delay in blood coagulation is due to the deficiency of which hormone?
A. Thyroxine
B. Adrenaline
c. Noradrenaline
D. Parathormone


Explain series combination of Capacitors. Derive the formula for equivalent capacitance.


The solubility products of \( \mathrm{MA}, \mathrm{MB}, \mathrm{MC} \) and MD are \( 1.8 \times 10^{-10}, 4 \times 10^{-3}, 4 \times \)
\( 10^{-8} \) and \( 6 \times 10^{-5} \) respectively. If a 0.01
M solution of MX is added dropwise to a mixture containing \( A^{\ominus}, B^{\ominus}, C^{\ominus}, \) and \( D^{\ominus} \) ions, then the one to be precipitated first will be:
A. MA
в. мв
c. мс
D. MD


The oxidation of oxalic acid by acidified
\( K M n O_{4} \) is an example of
autocatalysis. It is due to which of the following?
A. \( S O_{4}^{2-} \)
в. \( M n O_{4}^{2} \)
\( \mathbf{c} \cdot M n^{2+} \)
D. \( K^{\oplus} \)


Cane Sugar, Glucose and Starch are Carbohydrates.
(a) Represent the structure of Glucose.
(b) Write a method to prepare Glucose
from Starch. Write the chemical
equation of the reaction.
(c) Suggest any two uses of Carbohydrates.


In the estimation of nitrogen by Kjeldahl's method. 2.8 gm of an organic compound required 20 millimole of
\( H_{2} S O_{4} \) for the complete neutralisation
of \( N H_{3} \) gas evolved. The percentage of nitrogen in the sample is:
A . 20\%
B . 10\%
c. 40\%
D. 30\%


\( \lim _{n \rightarrow \infty} n\left[\frac{1}{(n+1)(n+2)}+\frac{1}{(n+2)(n+}\right. \)
is equal to
\( ^{A} \cdot \log \left(\frac{3}{2}\right) \)
в. \( \log \left(\frac{5}{2}\right) \)
c. \( \log \left(\frac{1}{2}\right) \)
D. \( \log \left(\frac{7}{4}\right) \)


A step up transformer is used to:
A. increase the current and increase the voltage
B. decrease the current and increase the voltage
C. increase the current and decrease the voltage
D. decrease the current and decrease the voltage


Evaluate \( \int_{0}^{2}\left(x^{2}-3 x+2\right) d x \)


Clemmensen's reduction reaction is:
\( A \)
в. \( C_{6} H_{5}-C O C H_{3}+ \)
\[
N H_{2} N H_{2} C_{2} H_{5} O N a C_{6} H_{5} C H_{2} C H_{3}
\]
c. \( C H_{3} C O C H_{3}+4 H I R e d \quad P_{>} C H_{3} C H_{2} C H_{3} \)
D. All the above


Consider the functions defined
implicitly by the equation \( \mathbf{y}^{3}-\mathbf{3 y}+ \) \( \mathbf{x}=\mathbf{0} \) on various intervals in the real line. If \( \boldsymbol{x} \in(-\infty,-2) \cup(2, \infty), \) the
equation implicitly defines a unique real valued differentiable function \( \mathbf{y}= \)
\( \mathbf{f}(\mathbf{x}) . \) If \( \boldsymbol{x} \in(-\mathbf{2}, \mathbf{2}), \) the equation
implicitly defines a unique real valued differentiable function \( \mathbf{y}=\mathbf{g}(\mathbf{x}) \) satisfying \( \mathbf{g}(\mathbf{0})=\mathbf{0} \)
\( \int_{-1}^{1} \mathbf{g}^{\prime}(\mathbf{x}) \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot 2 g(-1) \)
B. 0
c. \( -2 g(1) \)
D. \( 2 \mathrm{g}(1) \)


An alga rich in proteins is
A. Chlorella
B. Oscillatoria
c. Ulothrix
D. Spirogyra


If \( Q, E, \) and \( W \) denote respectively the heat added, change in internal energy and the work done by a closed cycle
process, then :
\( A \cdot E=0 \)
B. \( Q=0 \)
c. \( w=0 \)
D. \( Q=W=0 \)


Which reagent should be used for
following conversion?
A. \( N H_{2}-N H_{2} / O H^{-} \)
B . \( H_{2}-P d / C \)
\( \mathbf{c} . Z n-H g / \)Conc \( H C l \)
D. Both (A) and (C)


If \( \frac{x-1}{3}=k \) and \( k=3, \) what is the value of \( x ? \)
\( A \cdot 2 \)
B. 4
c. 9
D. 10


Match the list I with list II.
List I List II
A) \( C l F \)
1) \( s p^{3} d \)
B) \( C l F_{3} \)
2) T- shape
C) \( C l F_{5} \)
3) linear
4) \( s p^{3} d^{2} \)
5) one lone
pair
6)
pentagonal Bi-pyramidal
B. \( A-3 ; B-1,2 ; C-5,6 \)
c. \( A-3 ; \quad B-1,6 ; \quad C-4,5 \)
D. \( A-3 ; B-3,4 ; C-5,6 \)


A satellite close to the earth is in orbit
above the equator with a period of
revolution of 1.5 hours in the same
sense as that of the earth. If it is above a
point \( \boldsymbol{P} \) on the equator at some time, it will be above \( P \) again after a time.
A. 1.5 hours
B. 1.6 hours if it is rotating from west to east
c. \( \frac{24}{27} \) hours if it is rotating from west to east
D. none of these


The first Nobel prize in chemistry was awarded to:
A. Hoffman
B. Van't Hoff
c. Beeyer
D. Madam curie


Which of the following statements is/are correct for internal forces?
A. They are always balancedd
B. They are never balanced
c. They may or may not be balanced
D. none of these


At the boiling point of water the saturated vapour pressure will be (in mm of \( \mathrm{Hg} \) )
A. 750
B. 760
\( c \cdot 850 \)
D. 860


A gas mixture consists of 2moles of
oxygen and 4 moles of Ar at temperature
T. Neglecting all vibrational modes, the total internal energy of the system is
A . 4 RT
B. 15 RT
\( c .9 \) RT
D. 11 RT


"Nitric oxide reacts with oxygen to form reddish brown nitrogen dioxide gas"" Choose the correct equation for the
above reaction
A \( \cdot 2 N O+O_{2} \rightarrow 2 N O_{2} \)
в. \( N_{2} O+O_{2} \rightarrow N O_{2}+N O \)
C. \( N a N O_{3} \stackrel{\text {heat}}{\longrightarrow} 2 \mathrm{NaNO}_{2}+\mathrm{O}_{2} \)
D. \( 2 N O_{3}+O_{2} \rightarrow 2 N O_{2}+2 O_{2} \)


Compute \( \boldsymbol{P}(\boldsymbol{A} \mid \boldsymbol{B}), \) if \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \) and
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 3 2} \)
\( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \)


3.2 moles of \( H I(g) \) were heated in a sealed bulb at 444 till the equilibrium was reached. Its degree of dissociation
was found to be \( 20 \% \). Calculate the
number of moles of hydrogen iodide, hydrogen and iodine present at the equilibrium point and determine the value of equilibrium constant for the
reaction \( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
Considering the volume of the container \( 1 L \)


dentify \( A, B \) and \( C \) in following
reactions.


Which of the following represent(s) the correct order of electron affinities?
This question has multiple correct options
\( A \cdot F>C \mid>B r>1 \)
B. \( c<N<C I<F \)
c. \( N<c<0<F \)
\( D \cdot c<\operatorname{sic} P<N \)


A body of mass \( 5 k g \) is cut into two
parts of masses
(a) \( \frac{m}{4} ; \frac{3 m}{4} \)
(b) \( \frac{m}{7} ; \frac{5 m}{7} \)
(c) \( \frac{\boldsymbol{m}}{2} ; \frac{\boldsymbol{m}}{\boldsymbol{2}} \)
(d) \( \frac{\boldsymbol{m}}{\mathbf{5}} ; \frac{\boldsymbol{4} \boldsymbol{m}}{\mathbf{5}} . \) When these two
pieces are kept apart by certain distance; In which case the gravitational force acting is maximum?
A. In case a
B. In case \( c \)
c. In case d
D. In case b


An aeroplane at an altitude of
960 meters flying horizontally at \( \mathbf{7} 20 k m / h r . \) passes directly over an observer. The rate at which it is
approaching the observers when it is
1600 meters directly away from him is
A. \( 576 \mathrm{km} / \mathrm{hr} \)
B. \( 676 \mathrm{km} / \mathrm{hr} \)
c. \( 720 \mathrm{km} / \mathrm{hr} \)
D. \( 570 \mathrm{km} / \mathrm{hr} \)


The voltage across the capacitor as a
function of time is given by \( 10^{x} t^{2} V \)
then find \( x \)
A. 7
B. 6
\( c \cdot-5 \)
D. 4


In photorespiration, peroxisome helps
in
A. Synthesis of PGA
B. Reduction of glyoxylate
c. oxidation of glycolate
D. oxygenation of glycolate


Let \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\boldsymbol{x}-\mathbf{1}}+ \)
\( \sqrt{x+24-10 \sqrt{x-1}} ; 1<x<26 \) be
real valued function. Then \( f^{\prime}(x) \) for \( 1< \)
\( \boldsymbol{x}<26 \) is
\( A \cdot 0 \)
в. \( \frac{1}{\sqrt{x-1}} \)
c. \( 2 \sqrt{x-1}-5 \)
D. none of these


A button cell used in watches functions
as following:
\( Z n(s)+A g_{2} O(s)+H_{2} O(l) \rightleftharpoons \)
\( 2 A g(s)+Z n^{2+}(a q)+2 O H^{-}(a q) \)
If half cell potentials are:
\( Z n^{2+}(a q)+2 e^{-} \rightarrow Z n(s) ; E^{\circ}= \)
\( -0.76 V \)
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{O}(\boldsymbol{s})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})+ \)
\( \mathbf{2 O H}^{-}(\boldsymbol{a q}), \boldsymbol{E}^{\circ}=\mathbf{0 . 3 4} \boldsymbol{V} \)
The cell potential will be:
A. \( 1.10 v \)
B. 0.42
c. \( 0.84 \mathrm{v} \)
D. 1.34


The 17 th term of an AP exceeds its 10 th
term by \( 7 . \) Find the common difference
A \( \cdot \frac{3}{7} \)
B. \( \frac{-3}{7} \)
\( c \cdot \frac{7}{3} \)
D. \( \frac{-7}{3} \)


An electric lamp of resistance \( 20 \Omega \) and
a conductor of resistance \( 4 \Omega \) re
connected to a \( 6 \mathrm{V} \) battery as shown in
the circuit Calculate:
(a) The total resistance of the circuit
(b) The current through the circuit
(c)The potential difference across the
(i) Electric lamp and
(ii) Conductor, and
(d) Power of the lamp.


A chelating 'agent is a chemical that catches' a metal ion (charged particle) in its 'claw'. Penicillin can remove
excesses of a metal by chelation in the
ailment known as Wilson's disease. The
metal chelated by penicillin is?
A . Nickel
B. copper
c. Iron
D. Molybdenum


Match the following reactions:
\( (\boldsymbol{A})_{4} \boldsymbol{B} \boldsymbol{e}^{9}+_{2} \boldsymbol{H} \boldsymbol{e}^{4} \rightarrow_{\boldsymbol{6}} \boldsymbol{C}^{12}+\cdots \)
\( (i)_{2} H e^{4} \)
\( (B)_{6} C^{12}+\cdots \rightarrow_{5} B^{10}+_{2} H e^{4} \)
\( (i i)_{0} n^{1} \)
\( (C)_{7} N^{14}+\cdots \rightarrow_{8} O^{17}+_{1} H^{1} \)
\( (i i i i)_{1} D^{2} \)
\( (D)_{20} C a^{40}+\cdots \rightarrow_{19} K^{37}+_{2} H e^{4} \)
\( (i v)_{1} H^{1} \)
\( \mathbf{A} \cdot A-i, B-i i, C-i i i, D-i v \)
\( \mathbf{B} \cdot A-i i, B-i i i, C-i, D-i v \)
\( \mathbf{c} \cdot A-i v, B-i i, C-i i i, D-i \)
\( \mathbf{D} \cdot A-i i i, B-i i, C-i, D-i v \)


Water at normal atmospheric pressure
boils at :
\( \mathbf{A} \cdot 0^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
c. \( 250 K \)
D. \( 50^{\circ} \mathrm{C} \)


Nickel forms a compound with carbon
monoxide, \( N i_{x}(C O)_{y} . \) To determine its formula, you carefully heat a \( 0.0973 \mathrm{g} \) sample in air to convert the nickel to \( 0.0426 \mathrm{g} \) of \( N i O \) and the \( C O \) to
\( 0.100 g C O_{2} \). If the empirical formula is
of the form \( N i_{x}(C O)_{y}[N i=58.7], \) then
\( x+y \) is :


Draw two angles of \( 90^{\circ} \) at the ends of a line segment. Extend these rays. Do you get a triangle. Join these 2 rays by another line segment which shape can yo get? What will be the measure of all the angles?


If \( \tan A+\sec A=3, \) Find the value of \( \sin \)
\( \mathbf{A} \)


A student while performing an experiment was surprised to find that when two identical cells are either
connected in series or in parallel across
a \( 2 \Omega \) resistor, the same current passes through the resistor. What is the
internal resistance of each cell?
A . \( 2 \Omega \)
B. \( 4 \Omega \)
\( c \cdot 1 \Omega \)
D. 3\Omega


From the stability constant
hypothetical values \( ), \) given below,
predict which is the strongest ligand?
\( \mathbf{A} \)
\[
C u^{2+}+4 N H_{3} \rightleftharpoons\left[C u\left(N H_{3}\right)_{4}\right]^{2+}, K=4.5 \times 10^{11}
\]
\( B \)
\[
C u^{2+}+4 C N^{-} \rightleftharpoons\left[C u(C N)_{4}\right]^{2-}, K=2.0 \times 10^{27}
\]
\( \mathbf{c} \)
\[
C u^{2+}+2 e n \rightleftharpoons\left[C u(e n)_{2}\right]^{2+}, K=3.0 \times 10^{15}
\]
D.
\[
C u^{2+}+4 H_{2} O \rightleftharpoons\left[C u\left(H_{2} O\right)_{4}\right]^{2+}, K=9.5 \times 10^{8}
\]


The volume of a sphere is \( 1.76 \mathrm{cm}^{3} \). The
volume of 25 such spheres according to the idea of significant figures in \( \mathrm{cm}^{3} \) is
A . 44.00
B. 44.0
\( c \cdot 44 \)
D. 4.4


Which of the following complexes will give a white precipitate on treatment with a solution of barium nitrate?
\( \mathbf{A} \cdot\left[\operatorname{Cr}\left(N H_{3}\right)_{4} S O_{4}\right] C l \)
в. \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] N O_{2} \)
c. \( \left[\operatorname{Cr}\left(N H_{3}\right)_{4} C l_{2}\right] S O_{4} \)
D. \( \left[C r C l_{2}\left(H_{2} O\right)_{4}\right] C l \)


The polynomial \( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{3}+\boldsymbol{4} \boldsymbol{x}^{2}+ \)
\( 3 x-4 \) and \( q(x)=x^{3}-4 x+a \) leave
same remainder when divided by
\( (x-3) . \) Find \( a \) and hence find the
remainder when \( p(x) \) is divided by
\( (x-2) \)


If \( A=(6,7,8,9), B=(4,6,8,10) \) and \( C=\{x \)
\( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{N}: \boldsymbol{2}<\boldsymbol{x} \leq \mathbf{7}\} ; \) find :
\( A-B \)
A \( \cdot\{6,8\} \)
в. \{7,9\}
c. \{6,9\}
D. \{6,7,9,10\}


State Huygen's principle.


Osmotic pressure is maintained by blood colloid
A. Albumin
B. Thrombin
c. Fibrinogen
D. Globulin


Which compound amongst the following has the highest oxidation
number for \( M n ? \)
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}, \boldsymbol{K}_{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}, \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2} \) and
\( \boldsymbol{M} \boldsymbol{n}_{2} \boldsymbol{O}_{3} \)


Find the integral of the function \( \frac{\cos x-\sin x}{1+\sin 2 x} \)


The distance travelled by a body started
with a velocity of \( 20 m s^{-1}, \) and moving
with an acceleration of \( 2 m s^{-2}, \) in the
8th second in metres:
A . 35
B. 20
\( c \cdot 120 \)
D. 10


What is vapour pressure?


If the circumference of a circle exceeds
its diameter by \( 30 \mathrm{cm}, \) find the radius of the circle.


Assertion
the power in an ac circuit is minimum
if the circuit has only a resistor
Reason
Power of a circuit is independent of the
phase angle
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 relation \( 3 t=\sqrt{3 x}+6 \) describes
the displacement of a particle in one direction where \( x \) is in meters and \( t \) in
seconds. The displacement when velocity is zero is:
A \( .24 m \)
B. \( 12 m \)
\( c .5 m \)
D. zero


What kind of a molecule is \( \boldsymbol{P C l}_{3} \) ?
A. lonic
B. Polar covalent
c. Non polar covalent
D. none of these


Enriched air if inhaled for long time
causes
A . Allergy
B. Bronchitis
c. Disturbance of psychomotor function
D. Diarrhoea


Differentiate the following function with
respect to \( x \) \( \frac{4 x+5 \sin x}{3 x+7 \cos x} \)


Longitudinal strain is possible in
A. Liquid
B. Gases
c. Solid
D. All of these


A function \( f \) has domain [-1,2] and range \( [0,1] . \) The domain and range respectively of the function \( g \) defined by \( \boldsymbol{g}(\boldsymbol{x})=\mathbf{1}-\boldsymbol{f}(\boldsymbol{x}+\mathbf{1}) \) is?
A \( \cdot[-1,1] ;[-1,0] \)
B \cdot [-2,1]\( ;[0,1] \)
c. [0,2]\( ;[-1,0] \)
D \cdot [1,3]\( ;[-1,0] \)


Calculate the amount (in milligrams)
of \( S e O_{3}^{2-} \) in solution on the basis of following data:
\( 20 \mathrm{mL} \) of \( \frac{M}{60} \) solution of \( K B r O_{3} \) was added to a definite volume of \( S e O_{3}^{2-} \) solution. The bromine evolved was
removed by boiling and excess of
\( K B r O_{3} \) was back titrated with 5 mL of
\( M \) solution of \( N a A s O_{2} . \) The reactions \( \overline{\mathbf{2 5}} \)
are given below.
1) \( S e O_{3}^{2-}+B r O_{3}^{-}+H^{-} \rightarrow \)
\( \boldsymbol{S} \boldsymbol{e} \boldsymbol{O}_{\boldsymbol{4}}^{2-}+\boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
2) \( B r O_{3}^{-}+A s O_{2}+H_{2} O \rightarrow B r^{-}+ \)
\( \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4}^{3-}+\boldsymbol{H}^{+} \)
(Atomic mass of \( \boldsymbol{K}=\mathbf{3 9}, \boldsymbol{B r}= \)
\( \mathbf{8 0}, \boldsymbol{A s}=\mathbf{7 5}, \boldsymbol{N a}=\mathbf{2 3}, \boldsymbol{O}=\mathbf{1 6}, \boldsymbol{S e}= \)
\( \mathbf{7} 9 \)
A .84
в. 95
\( c \cdot 42 \)
D. None of the above


A game of chance consists of spinning
an arrow which is equally likely to come to rest pointing to one of the number
\( 1,2,3, \dots .12 \) as shown in Fig. What is the probability that it will point to:
(i) 10
(ii) an odd number (iii) a
number which is a multiple of 3 (iv) an
even number.


Solve \( \int x \sqrt{x+2} d x \)


A spherical ball of diameter \( 1 \mathrm{cm} \) and
density \( 5 \times 10^{3} \mathrm{kg} m^{-3} \) is dropped
gently in a large tank containing viscous liquid of density \( 3 \times 10^{3} \mathrm{kg} m^{-3} \)
and coefficient of viscosity \( 0.1 \mathrm{Ns} m^{-2} \)
The distance, the ball moves in 1 s after
attaining terminal velocity is \( (\boldsymbol{g}= \) \( \left.10 m s^{-2}\right) \)
A \( \cdot \frac{10}{9} \mathrm{m} \)
в. \( \frac{2}{3} \) m
c. \( \frac{4}{9} \mathrm{m} \)
D. \( \frac{4}{5} \mathrm{m} \)
E \( \cdot \frac{9}{10} \mathrm{m} \)


f \( 25025=p_{1}^{x_{1}} \cdot p_{2}^{x_{2}} \cdot p_{3}^{x_{3}} \cdot p_{4}^{x_{4}} \) find the value
of \( p_{1}, p_{2}, p_{3}, p_{4} \) and \( x_{1}, x_{2}, x_{3}, x_{4} \)


State whether true or false.
The equations of motion are applicable only when the body moves with constant
acceleration.
A. True
B. False


Find the argument of \( \frac{1+\sqrt{3} i}{\sqrt{3}+i} \)
A \( \cdot \frac{\pi}{3} \)
в. \( \frac{\pi}{6} \)
c. \( \frac{\pi}{2} \)
D.


The intensity of gamma radiation from
a given source is \( l . \) On passing through \( 36 m m \) of lead, it is reduced to \( l / 8 . \) The thickness of lead which will reduce the
intensity to \( l / 2 \) will be:
\( \mathbf{A} \cdot 18 m m \)
B. \( 12 m m \)
\( \mathbf{c} .6 m m \)
\( \mathbf{D} \cdot 9 m m \)


Assertion
When super charged particles enter the earth's atmosphere from the solar wind, they spiral around the magnetic field lines of the earth.
Reason
They tend to be channelled toward the poles by magnetic forces.
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


\( \boldsymbol{V}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)+\boldsymbol{V}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)+\boldsymbol{V}(\boldsymbol{C l}) \) is
divisible by :
\( (V(X) \text { shows valency of } X) \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


A ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and the latter is equal to \( \frac{3^{t h}}{4} \) angle of prism. What will be the
deviation?
A \( \cdot 45^{\circ} \)
В. \( 37^{\circ} \)
\( c \cdot 20^{0} \)
D. 30


Which of the following statements is
true?
A. Normal is always perpendicular to the mirror
B. Incident ray is always on the left side of the normal
c. Both A and B
D. None


A charge of 10 e.s.u is placed at the distance of \( 2 \mathrm{cm} \) from a charge of 40
e.s.u and \( 4 \mathrm{cm} \) from another charge of
20 e.s.u.The potential energy of charged
10 e.s.u is?
A. 87.5
B. 112.5
c. 150
D. 250


An endothermic reaction \( A \rightarrow B \) have
an activation energy 15 kcal/mol and the heat of reaction is 5 kcal/mol. The
activation energy of the reaction \( \boldsymbol{B} \rightarrow \)
\( \boldsymbol{A} \) is:
A . 20 kcal/mol
B. 15 kcal/mol
c. 10 kcal/mol
D. zero


Coating used on raincoat are waterproof
because
A. water is absorbed by the coating
B. cohesive force becomes greater
C. water is not scattered away by the coating
D. angle of contact decreases


The photoelectric threshold of a certain metal is 3000 A. If the radiation of \( 2000 A \) is incident on the metal
A. electrons will be emitted
B. positrons will be emitted
c. protons will be emitted
D. electrons will not be emitted


When potassium chloride is dissolved in
water
A. Entropy increases
B. Entropy decreases
C. Entropy increases and then decreases
D. Free energy increases


Suppose that \( f(0)=-3 \) and \( f^{\prime}(x) \leq 5 \)
for all values of \( x \). Then the largest value
which \( f(2) \) can attain is
A. 7
B. -7
c. 13
D.


The bulk modulus of an ideal gas at
constant temperature is :
A. Equal to its pressure
B. Equal to its volume
c. Equal to \( p / 2 \)
D. Cannot be determined


Rajendra and Rehana own a business. Rehana receives \( 25 \% \) of the profit in
each month. If Rehana received Rs. 2080
in particular month, what is the total profit in that month


A charge particle enters into a magnetic field with a velocity vector
making an angle of \( 30^{\circ} \) with respect to the direction of magnetic field. The path of the particle is:
A. circular
B. helical
c. elliptical
D. straight line


A body executes S.H.M. under the action of a force \( \boldsymbol{F}_{1} \) with a time period \( \mathbf{4} / \mathbf{5} \)
seconds. If the force is changed to \( \boldsymbol{F}_{2}, \) it
executes S.H.M. with a time period \( 3 / 5 \)
seconds. If both the forces \( F_{1} \) and \( F_{2} \) act
simultaneously in the same direction on the body, then its time period in seconds is:
A . \( 12 / 25 \)
в. \( 24 / 25 \)
c. \( 25 / 24 \)
D. 25/12


The displacement of a particle from its mean position (in metre) is given by \( \boldsymbol{Y}=\mathbf{0 . 2} \sin (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{t}+\mathbf{1 . 5} \boldsymbol{\pi}) \cos (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{t}+ \)
1.5 \( \pi \) ), the motion of the particle is:
A. periodic but not SHM
B. non periodic
c. simple harmonic motion with period 0.1 s
D. simple harmonic motion with period 02.


If two electric charges \( q \) and \( -2 q \) are
placed at distance \( 6 a \) apart, then locus
of point in the plane of charges, where electric potential is zero is: (Take
charge \( q \) at origin and \( -2 q \) lies on positive \( x \) -axis
A. \( x^{2}+y^{2}+4 a x-6 a^{2}=0 \)
B . \( x^{2}+y^{2}+4 a x-12 a^{2}=0 \)
c. \( x^{2}+y^{2}+2 a x-12 a^{2}=0 \)
D. \( x^{2}+y^{2}-4 a x+12 a^{2}=0 \)


Electrons in a TV tube move horizontally
South to North. Vertical component of earth's magnetic field points down. The electron is deflected towards which
direction? \( [\boldsymbol{F}=\boldsymbol{q}(\overrightarrow{\boldsymbol{v}} \times \overrightarrow{\boldsymbol{B}})] \)
A. west
B. No deflection
c. East
D. North to South


The forbidden energy gap for
germanium crystal at \( 0 K \) is
A. \( 0.071 e V \)
в. \( 0.71 e V \)
c. \( 2.57 e V \)
D. \( 6.57 e V \)


A sphere of mass m moving with a constant velocity collides with another stationary sphere of same mass. The ratio of velocities of two spheres after collision will be, if the co-efficient of
restitution is e:
A \( \cdot \frac{1-e}{1+e} \)
в. \( \frac{e-1}{e+1} \)
c. \( \frac{1+e}{1-e} \)
D. \( \frac{e+1}{e-1} \)


At \( 27^{0} \) C certain gas occupied a volume
Of 4 litres. If the volume of this is to be increased to 12 litres at
the same pressure, the gas is to be heated to a temperature
A. 300 K
B. \( 900 \mathrm{K} \)
\( \mathbf{C} .600 \mathrm{K} \)
D. \( 1200 K \)


A transformer consists of 500 turn in
the primary coil and 10 turns in a
secondary coil with the load of \( 10 \Omega \) Find out current in the primary coil when the voltage across the secondary
coil is \( \mathbf{5 0} \boldsymbol{V} \)
A . \( 5 A \)
в. \( 1 A \)
\( c \cdot 10 A \)
D. \( 2 A \)


Evaluate \( \int_{-1}^{1} 5 x^{4} \sqrt{x^{5}+1} d x \)


A machine gun fires a bullet of mass \( 40 g \) with a velocity \( 1200 m s^{-1} \). The man
holding it can exert a maximum force of
\( 144 N \) on the gun. How many bullets can he fire per second at the most?
A .2
B. 4
\( c . \)
D. 3


The sum of \( n \) terms of the
\( G \cdot P .3,6,12, \ldots \) is \( 381 . \) Find the value of
\( \boldsymbol{n} \)


Choose the rational number which does
not lie between rational numbers \( -\frac{2}{5} \)
and \( -\frac{1}{5} \)
\( A \cdot-\frac{1}{4} \)
B. \( -\frac{3}{10} \)
c. \( \frac{3}{10} \)
D. \( -\frac{7}{20} \)


If the line segment joining the midpoint of the consecutive side of quadrilateral ABCD form a rectangle then ABCD must
be
A. Rhombus
B. Square
c. Kite
D. All of the above


State True or False.
Magnetic lines of force are closed
continuous curves.


Compute the modal class of the scores of the students in a Mathematics VIII
test.
21 \( \begin{array}{llll}\text { class } & 12- & 15- & 1 \\ \text { score } & 15 & 18 & 2\end{array} \) 21 24
frequency 2
A . \( 15-18 \)
в. \( 24-27 \)
c. \( 27-30 \)
D. \( 30-33 \)


If \( I_{n}=\int_{0}^{\pi / 4} \tan n x d x \) then
\( \lim _{n \rightarrow \infty} n\left(I_{n}+I_{n-2}\right)= \)
\( A \)
B. 1/2
\( c \cdot \alpha \)
D.


The number of \( \sigma \) -bonds in aspirin is:
4.19
3. 20
\( c .21 \)
0.2


Assertion: At infinite dilution, both strong and weak electrolyte have degree of ionization equal to unity. Reason: At infinite dilution of an
electrolyte, the equivalent conductance
of cations and anions are
independent of each other.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


A long dielectric cylinder of radius \( \boldsymbol{R} \) is
statically polarized so that at all its points the polarization is equal to \( \vec{P}= \) \( \alpha \vec{r}, \) where \( \alpha \) is a positive constant, and
\( \vec{r} \) is the distance from the axis.

The cylinder is set into rotation about
its axis with an angular velocity \( \omega . \) Find
the magnetic induction \( B \) at the centre
of the cylinder


Find the sum of all even integers between 101 and 999
A .246950
B . 249650
c. 256950
D. 276950


A uniform conducting wire \( A B C \) lying in \( X Y \) plane has a mass of \( 10 g . A \)
current of \( 2 A \) flows through it. The wire
is kept in a uniform magnetic field \( B=2 T \) which acceleration of the wire
is
A. Zero
B \( \cdot 12 m / s^{2} \) and along postive \( Y \) -axis
C. \( 12 \times 10^{-3} \mathrm{m} / \mathrm{s}^{2} \) along postive \( Y \) -axis
D. \( 12 m / s^{2} \) and along postive \( X \) -axis


Let the eccentricity of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) be reciprocal to that of the
ellipse \( x^{2}+4 y^{2}=4 . \) If the hyperbola
passes through a focus of the ellipse, then
This question has multiple correct options
A the equation of the hyperbola is \( \frac{x^{2}}{3}-\frac{y^{2}}{2}=1 \)
B. a focus of the hyperbola is (2,0)
c. the eccentricity of the hyperbola is \( \sqrt{\frac{5}{3}} \)
D. the equation of the hyperbola is \( x^{2}-3 y^{2}=3 \)


Choose the INCORRECT relation among the following:
A \( \cdot \) Ampere \( =\frac{\text { Coulomb }}{\text { Second }} \)
B. \( \mathrm{v}_{\text {olt }}=\frac{\text { Coulomb }}{\text { Joule }} \)
\( ^{\mathbf{c}} \cdot \mathrm{O}_{\mathrm{hm}}=\frac{\mathrm{V}_{\mathrm{olt}}}{\mathrm{Ampere}} \)
D. 1 Coulomb = 6.25 \( \times 10^{18} \) electron charge


Two wires each of radius of cross
section \( r \) but of different materials are
connected together end to end (in series). If the densities of charge carriers in the two wires are in the
ration \( 1: 4, \) the drift velocity of
electrons in the two wires will be in the
ratio:
A .1: 2
B . 2: 1
c. 4: 1
D. 1: 4


Number of teeth in man which grow
twice are
\( A \cdot 4 \)
B. 8
c. 12
D. 28
E. 20


Integrate \( \sec ^{3} x \) w.r.t. \( x \)


Differentiate \( \frac{x^{2} \sin x}{1-x} \) w.r.t \( x \)


Which of the following statements about angular momentum is correct?
A. It is moment of inertia
B. It is directly proportional to moment of inertia
c. . tis a scalar quantity
D. All of these


Write \( \left[\sqrt{2}\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right]^{2} \) in the
form \( a+b i \)
A \( .2+i \sqrt{3} \)
B . \( \frac{3}{2}+\frac{1}{2} i \)
\( \mathrm{c} \cdot 1-i \sqrt{3} \)
D. \( \frac{3}{2}-\frac{1}{2} i \)
\( E \cdot 1+i \sqrt{3} \)


The line spectrum of two elements is
not identical because:
A. they do not have same number of neutrons
B. they have dissimilar mass number
C. they have different energy level schemes
D. they have different number of valence electrons


What is rate?
A. Change / Time
B. Time / Concentration
C. Time / Change
D. Rate / Time
E. Concentration / Time


The combination of haemoglobin with
oxygen in blood can be promoted by:
A. increasing oxygen concentration in the blood
B. increasing carbon dioxide concentration in the blood
C. decreasing oxygen concentration in the blood
D. increasing carbon monoxide concentration in the blood


The number of sulphur atoms in one
mole molecule of sulphur \( \left(S_{8}\right) \) is:
A \( .5 \times 6.023 \times 10^{23} \)
B. \( 4 \times 6.023 \times 10^{23} \)
c. \( 8 \times 6.023 \times 10^{23} \)
D. \( 2 \times 6.022 \times 10^{22} \)


Physics is sometimes referred to as
exact science. Because.
A. Physics interacts with almost all the sciences
B. Due important is given for the measurement of quantities
C. It involves philosophy
D. Physics is related more closely to mathematics than any other science


In many cultivated ornamental flowers,
number of petal whorls is higher than the one in wild type. Extra petals are generally modified
A. Sepals
B. Petals
c. stamens
D. Pistils


For the reaction \( 2 A \rightarrow B+3 C \); if
\( -\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} t}=\boldsymbol{k}_{1}[\boldsymbol{A}]^{2} ; \frac{\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d} t}= \)
\( \boldsymbol{k}_{2}[\boldsymbol{A}]^{2} ; \frac{\boldsymbol{d}[\boldsymbol{C}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}_{3}[\boldsymbol{A}]^{2} \) the correct
relation between \( k_{1}, k_{2} \) and \( k_{2} \) is:
A \( \cdot k_{1}=k_{2}=k_{2} \)
B. \( 2 k_{1}=k_{2}=3 k_{2} \)
\( \mathbf{c} \cdot 4 k_{1}=k_{2}=3 k_{2} \)
D. \( \frac{k_{1}}{2}=k_{2}=\frac{k_{3}}{3} \)


A man can row a boat with \( 4 k m / h \) in
still water. If he is crossing a river where the current is \( 2 k m / h . \) Width of river is 4 k \( m \). In what direction should he head
the boat if he wants to cross the river in
shortest time and what is this
minimum time?
A. Parallel to river current, 2 hrs
B. Perpendicular to river current, 2 hrs
C. Parallel to river current, 1 hrs
D. Perpendicular to river current, 1 hrs


Solve :-
\[
x^{2}-2 \cos \alpha+\cos 2 \alpha=0
\]


If \( a S H M \) is given by \( y=(\sin \omega t+ \)
\( \cos \omega t) m, \) Which of the following
statements are true?
A. The amplitude is \( 1 m \)
B. The amplitude is \( (\sqrt{2}) m \)
c. Time is considered from \( y=1 m \)
D. Time is considered from \( y=0 m \)


When the current changes from \( +2 A \) to
\( -2 A \) in 0.05 second, an e.m.f. of \( 8 V \) is
induced in a coil. The coefficient of self-
induction of the coil is
\( \mathbf{A} \cdot 0.2 H \)
в. \( 0.4 \mathrm{H} \)
c. \( 0.8 H \)
D. \( 0.1 H \)


A dip circle, lying initially in the magnetic meridian is rotated through an angle \( \theta \) in the horizontal plane, then the tangent of the angle of dip is increased in the ratio
of :
A. \( 1: \cos \theta \)
B. \( 1: \tan \theta \)
c. \( 1: \cot \theta \)
D. \( 1: \sin \theta \)


Which of the following is NOT a true statement about the entropy of a
system?
A. Entropy is a measure of the randomness in a system.
B. The entropy of an amorphous solid is greater than that of a crystalline solid.
C. The entropy of a spontaneous reaction cannot decrease
D. The entropy of an isolated system will spontaneously increase or remain constant


The products of combustion of an
aliphatic thiol (RSH) at \( 298 K \) are
A \( \cdot C O_{2}(g), H_{2} O(g), \) and \( S O_{2}(g) \)
B . \( C O_{2}(g), H_{2} O(l), \) and \( S O_{2}(g) \)
c. \( C O_{2}(l), H_{2} O(l), a n d S O_{2}(g) \)
D. \( C O_{2}(g), H_{2} O(l), \) and \( S O_{2}(l) \)


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a}, \boldsymbol{a} \in \boldsymbol{R}, \) then
\( \mathbf{A} \cdot \nabla f(x)=0 \)
B \( \cdot \nabla f(x)=a \)
\( \mathbf{c} \cdot \nabla f(x)=2 a \)
D. \( \nabla f(x)=a^{2} \)


A hemispherical bowl has diameter 9 cm. The liquid is poured into cylindrical bottles of diameter \( 3 \mathrm{cm} \) and height 3
cm. If a full bowl of liquid is filled in the bottles, find how many bottles are required.


If the length of the filament of a heater is reduced by \( 25 \% \), the power of the heater will
A. increase by about \( 25 \% \)
B. increase by about \( 33 \% \)
c. decrease by about \( 25 \% \)
D. decrease by about \( 33 \% \)


Force between two plates of a capacitor
is :
A. \( \frac{Q}{\epsilon_{0} A} \)
В. \( \frac{Q^{2}}{2 \epsilon_{0} A} \)
c. \( \frac{Q^{2}}{\epsilon_{0} A} \)
D. none of these


List and explain any two advantages associated with water harvesting at community level


Lactic acid molecule has:
A. one chiral carbon atom
B. two chiral carbon atom
c. no chiral carbon atom
D. asymmetric molecule


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{2} \\ \mathbf{1} & \mathbf{4}\end{array}\right], \) then \( \boldsymbol{A}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \cdot \boldsymbol{A}) \) equals-
A. \( \left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right] \)
В. \( \left[\begin{array}{cc}0 & 10 \\ 10 & 0\end{array}\right] \)
c. \( \left[\begin{array}{ll}10 & 1 \\ 1 & 10\end{array}\right] \)
D. none of these


\( \mathbf{\Psi}^{2}=\mathbf{0} \) represents:
A . a node
B. an orbital
c. angular wave function
D. wave function


If the number of elements in a matrix is
60 then how many different order of matrix are possible
A . 12
B. 6
\( c \cdot 24 \)
D. none of these


A redox reaction is one in which:
A. both the substances are reduced
B. both the substances are oxidized
c. an acid is neutralized by the base
D. one substance is oxidized, while the other is reduced


The melting point of pure ice is


Show that


Differentiate between :
Biotic and abiotic components of an
ecosystem


Acid hydrolysis of ester is first order reaction and rate constant is given by \( \boldsymbol{k}=\frac{\mathbf{2 . 3 0 3}}{\boldsymbol{t}} \log \frac{\boldsymbol{V}_{\infty}-\boldsymbol{V}_{\mathbf{0}}}{\boldsymbol{V}_{\infty}-\boldsymbol{V}_{\boldsymbol{t}}} \) where, \( \boldsymbol{V}_{0}, \boldsymbol{V}_{\boldsymbol{t}} \)
and \( V_{\infty} \) are the volume of standard
NaOH required to neutralise acid
present at a given time, if ester is \( 50 \% \) neutralised then:
\( \mathbf{A} \cdot V_{\infty}=V_{t} \)
В \( \cdot V_{\infty}=\left(V_{t}-V_{0}\right) \)
C \( . V_{\infty}=2 V_{t}-V_{0} \)
D. \( V_{\infty}=2 V_{t}+V_{0} \)


Factorise the given polynomial:
\( 4 a^{2}-12 a b+9 b^{2}+4 a-6 b \)
A. \( (2 a-3 b)(2 a-3 b+2) \)
B. \( (2 a+3 b)(2 a-3 b+2) \)
c. \( (2 a-3 b)(2 a+3 b-2) \)
D. \( (2 a+3 b)(2 a-3 b-2) \)


The percentage efficiency of nuclear fission is \( _{-}-_{-}-_{-}- \) that of nuclear
fusion.
A. higher than
B. lower than
c. same as
D. may be higher, lower or same


In a reaction, \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}, \mathbf{2 . 0} \) mole of
\( A 3.0 \) mole of \( B \) and 2.0 mole of \( C \) are
placed in a \( 2.0 L \) flask and the
equilibrium concentration of \( \boldsymbol{C} \) is 0.5 mole \( / L . \) The equilibrium constant
\( K \) for the reaction is
\( \mathbf{A} \cdot 0.073 \)
B. 0.147
\( c .0 .05 \)
D. 0.026


An element \( M \) has an atomic number 9
and atomic mass \( 19 . \) Its negative ion will be represented by:
\( \mathbf{A} \cdot M \)
В. \( M^{2} \)
\( c \cdot M^{-} \)
D. \( M^{2} \)


Which one of the following carbohydrates is a monosaccharide?
A. Ribose
B. Arabinose
c. Lyxose
D. All of these


What is the role of concave lens in
flashlights?
A. It helps in magnifying light produced by the bulb
B. It helps in reflecting light produced by the bulb
c. It helps in removing light from the bulb
D. None


Derivative of an odd function.
A. May be even or may be odd
B. Is always odd
C. Is always even
D. None of these


If the first minima in Young's double-slit experiment occurs directly in front of the slits (distance between slit and
\( \operatorname{screen} D=12 c m \) and distance
between slits \( d=5 c m \) ), then the
wavelength of the radiation used can be
\( A \cdot 2 c m \)
в. 4 ст
c. \( _{\overline{3}^{c m}} \)
\( \stackrel{-4}{3}^{c m} \)


Under what conditions will the vectors \( \overrightarrow{\boldsymbol{A}}=3 \hat{\boldsymbol{i}}-\mathbf{5} \hat{\boldsymbol{j}}+\mathbf{5} \hat{\boldsymbol{k}} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \mathbf{5} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\boldsymbol{b} \hat{\boldsymbol{k}} \) be
perpendicular to each other? Find the value of \( |b| ? \)


A wave travelling in air falls on a glass plate, It is partly reflected and partly refracted. The phase difference between
the reflected and refracted waves is
A. zero
в. \( \frac{\pi}{2} \)
\( c \)
D. \( 2 \pi \)


Write the formulae of area and volume
of different solid shapes. Find out the variables and constants in them


What is the density of \( \boldsymbol{P} \boldsymbol{C l}_{3} \) ?
A \( 2.0 g / c c \)
\( c c \)
в. \( 2 . g / c c \)
c. \( 1.57 g / c c \)
D. \( 3.0 g / c c \)


From the figure
\[
F_{1} \sqrt{\longleftarrow} d_{1} \longrightarrow d_{2} \longrightarrow
\]
\( \mathbf{A} \cdot \frac{f_{1}}{d_{1}}=\frac{f_{2}}{d_{2}} \)
\( \mathbf{B} \cdot f_{1} \times d_{2}=f_{2} \times d_{1} \)
\( \mathbf{C} \cdot f_{1} \times d_{1}=f_{2} \times d_{2} \)
D. All


The radii of two of the first four Bohr's
orbits of the hydrogen atom are in the
ratio \( 1: 4 . \) The energy difference
between them may be:
A. either \( 12.09 e V \) or \( 3.4 e V \)
B. either \( 2.55 e V \) or \( 10.2 e V \)
c. either \( 13.6 e V \) or \( 3.4 e V \)
D. either \( 3.4 e V \) or \( 0.85 e V \)


White crystalline solid (A) reacts with
\( H_{2} \) to form a highly associated liquid
(B) and a monoatomic colorless gas (C). The liquid (B) is used for etching glass. Compound (A) undergoes hydrolysis slowly to form (C), (B) and a diatomic \( \operatorname{gas}(D) \) whose IE is almost similar to that of (C). (B) forms an addition
compound with KF to form (E) which is electrolyzed in the molten state to form a most reactive gas (F) which combines
with
(C) in a 1: 1 ratio to produce \( (A) \)
The molecule of compound E contains which of the following types of bonds?
A. lonic
B. lonic and Covalent both
c. lonic, covalent and Metallic
D. Ionic, Covalent and H-bonds


Solve: \( 37 x+29 y=45 ; 29 x+37 y=21 \)


Two metals \( X \) and \( Y \) belong to the
second group of the periodic table. \( \boldsymbol{X} \) forms insoluble oxide but soluble
sulphate. \( Y \) forms a soluble oxide but
insoluble sulphate. The hydroxide of
metal \( X \) is soluble in \( N a O H \) while that
of metal \( Y \) is insoluble in \( N a O H . \) What
are metals \( X \) and \( Y ? \)
A. \( X=B e, Y=B a \)
в. \( X=M g, Y=C a \)
c. \( X=C a, Y=S r \)
D. \( X=B a, Y=M g \)


The maximum stress that can be
applied to the material of a wire
employed to suspend an elevator is \( \frac{3}{\pi} \times 10^{8} N / m^{2} . \) If the mass of the
elevator is \( 900 \mathrm{kg} \) and it moves up with
an acceleration of \( 2.2 m / s^{2} \) then calculate the minimum radius of the
wire.


Methane can not be prepared by :
This question has multiple correct options
A. Wurtz reaction
B. Decarboxylation
C. Kolbes reaction
D. Sabatier - senderens reaction


An \( A P \) consists of 21 terms. The sum of
the three terms in the middle is \( 129 \& \)
of the last three is 237 . Find \( A P \)


Which combination is odd with respect
to oxidation number?
\( \mathbf{A} \cdot H_{2} S O_{4}, H_{2} S_{2} O_{8}, K_{2} C r_{2} O_{7}, S F_{6} \)
B. \( K_{2} C r_{2} O_{7}, K_{2} C r O_{4}, C r O_{5}, C r O_{2} C l_{2} \)
\( \mathbf{C} \cdot N H_{3}, N H_{4}^{+}, N_{3} H, N O_{2}^{-} \)
\( \mathbf{D} \cdot C a H_{2}, B a H_{2}, B e H_{2}, M g H_{2} \)


Terrestrial animals must
A. Excrete large amounts of urine
B. Conserve water
C. Actively pump out salts through skin
D. Excrete large amount of salts in urine


An arc of a bridge is semi- elliptical with major axis horizontal. The length of
the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal. The best approximation of the pillar 2 meter form the center of the base is
A \( \cdot \frac{11}{4} m \)
в. \( \frac{8}{3} m \)
c. \( \frac{7}{2} m \)
D. \( 2 m \)


A circular coil of closely wound N turns
and radius r carries a current I. If the
expressions of The magnetic field at its centre is \( \frac{\mu_{0} N i}{x R} . \) Find \( x \)


These antiseptics can also be used as disinfectants, which depends on the concentration of the compound.
A. True
B. False


Equal volumes of molar hydrochloric acid and sulphuric acid are neutralized
by dilute NaOH solution and \( \boldsymbol{x} \) kcal
and \( y k c a l \) of heat are liberated
respectively. Which of the following is
true?
A \( . x=y \)
B・ \( x=\frac{y}{2} \)
c. \( x=2 y \)
D. None of these


Eye is the only organ to visualise the colourful world around us. This is
possible due to accommodation of eye lens. Prepare a six line stanza
expressing your wonderful feelings.


The moment of inertia of a circular disc
about an axis passing through the circumference perpendicular to the plane of the disc is
\( \mathbf{A} \cdot M R^{2} \)
B. \( \frac{3}{2} M R^{2} \)
c. \( \frac{M R^{2}}{2} \)
D. \( \frac{5}{4} M R^{2} \)


Which of the following is the most stable ecosystem?
A. Mountain
B. Desert
c. Forest
D. Ocean


A cube of side \( 20 \mathrm{cm} \) is kept in a region
as shown in the figure. An electric field
\( \vec{E} \) exists in the region such that the
potential at a point is given by \( \boldsymbol{V}= \)
\( 10 x+5, \) where \( V \) is in volt and \( x \) is in \( m \)
Find the electric flux through the cube


A capacitor acts as an infinite resistance for
A . \( D C \)
B. \( A C \)
c. \( D C \) as well as \( A C \)
D. neither \( A C \) nor \( D C \)


Which of the following is an example of a direct band gap
intrinsic semiconductor?
A. Silicon
B. Germanium
c. Gallium Arsenide
D. none of these


Show that in a first order reaction, time
required for completion of \( 75 \% \) is twice of half life of the reaction. \( (\log 2= \)
\( \mathbf{0 . 3 0 1 0} \)


A piece of cloth looks red in sun light. If it is held in the blue portion of a solar spectrum, it will appear
A. Red
B. Black
c. Вlue
D. white


The element with highest electronegativity value is :
A. carbon
B. Chlorine
c. Fluorine
D. oxygen


Assertion
A hollow metallic closed container
maintained at a uniform temperature can act as a source of a black body radiation.
Reason
All metals act as a black body.
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. If Assertion is incorrect but Reason is correct


Show that the function \( \boldsymbol{f}: \boldsymbol{Z} \rightarrow \boldsymbol{Z} \)
defined by \( f(x)=x^{2}+x \forall x \in Z, \) is a
many-one function.


The equation that represents van't Hoff general solution equation is :
A \( \cdot \pi=\frac{n}{V} R T \)
В . \( \pi=n R T \)
c. \( \pi=\frac{V}{n} R T \)
D. \( \pi=n V R T \)


\( f(x)=\left\{\begin{array}{cl}m x+1, & x \leq \frac{\pi}{2} \\ \sin x+n, & x>\frac{\pi}{2}\end{array} \) is \right.
continuous at \( x=\frac{\pi}{2}, \) then
A \( . m=1, n=0 \)
B. \( m=\frac{n \pi}{2}+1 \)
c. \( n=\frac{m}{2} \)
D. \( m=n=\frac{n \pi}{2} \)


The unit of mass in SI system is and the unit of weight in \( \mathrm{S} \) I system is
A. kg, Newton
B. m, Ampere
c. seconds, Joule
D. ergs, Newton


A quantity of \( \mathrm{PCl}_{5} \) was heated in \( 10 \mathrm{dm}^{3} \)
vessels \( 250^{\circ} \mathrm{C} \)
\( \mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \)
At equilibrium, the vessel contains \( 0 . \)
moles of \( \mathrm{PCl}_{5} \) and 0.2 moles of \( \mathrm{Cl}_{2} \). The
equilibrium constant of the reaction is :


Find the degree of the polynomial \( \left(x^{2}+\right. \)
\( \mathbf{9})\left(\mathbf{5}-\boldsymbol{x}^{2}\right) \)


Simplify: \( (-\sqrt{3}+\sqrt{-2})(2 \sqrt{3}-i) \)


How many kinds of \( \mathrm{N}_{2} \) bases in nucleic
acids are?
A. Three
B. Four
c. Five
D. Eight


Define a polygon.


Which one of the following ancestors of man first time showed bipedal
movement?
A. Australopithecus
B. Cro-Magnon
c. Java ape man
D. Peking man


Show dimensionally that the frequency
(a) of transverse wanes in a string of
length / and mass per unit length \( \boldsymbol{m} \)
under a tension T is given by, \( \boldsymbol{n}= \) \( \boldsymbol{k} \sqrt{\boldsymbol{T}} / \boldsymbol{l} \sqrt{\boldsymbol{m}} \)


Write \( S I \) units of luminous intensity
and temperature


Choose the correct statement from the
following options.
This question has multiple correct options
A. If the zeroeth division of the vernier and main scales of
a standard vernier callipers coincide then measured length is equal to the actual length.
B. The least count of vernier scale is \( 0.9 \mathrm{mm} \)
C. The length of a one vernier scale division is greater than that of one main scale division.
D. The internal jaws are used for measuring the internal diameter of a hollow cylinder


Identify the pair in which the two species are isostructural.
A. \( S i F_{4} \) and \( S F_{4} \)
B. \( I O_{3}^{-} \) and \( X e O_{3} \)
c. \( B H_{4}^{-} \) and \( N H_{4}^{+} \)
D. \( P F_{6}^{-} \) and \( S F_{6} \)


A powerful oxidant in the list given below is :
A. \( H N O_{2} \)
в. \( H N O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{4} \)
D. \( H_{3} P O_{3} \)


\( \int_{a}^{b} \cos x d x \)
Obtain the definite integral as a limit of
d sum.


The reaction of toluene with chlorine in
the presence of iron and in the absence of light yields:
\( A \)
в.
\( c \)
D. mixture of (B) and (c)


Find the acceleration of the block of
mass \( \mathrm{M} \) in the arrangement shown in the figure. The coefficient of friction
between the two blocks is \( \mu_{1} \) and that
between the bigger block and the
ground is \( \mu_{2} \)


A conductor is moving with the velocity v in the magnetic field and induced current is I. If the velocity of conductor becomes double, the induced
current will be
A. \( 0.5 I \)
B. 1.5 \( I \)
\( c \cdot 2 I \)
D. 2.5 I


How would you account the lower atomic radius of \( G a \) as compared to \( A l \)


If the decay constant of radium is
\( 4.28 \times 10^{-4} \) per year, then its half life
will be approximately be
A. 1240 years
B. 1620 years
c. 2000 years
D. 2260 years


The vapour pressure of pure benzene
and toluene at a particular temperature are \( 100 m m \) and 50 mm respectively. Then the mole fraction of benzene in
vapour phase in contact with equimolar solution of benzene and toluene is :
A . 0.67
B. 0.75
c. 0.33
D. 0.50
E . 0.20


A conducting rod of length \( ^{\prime} l^{\prime} \) is moving
with constant linear speed ' \( v^{\prime} \) in a
uniform magnetic field ' \( B \) '. This arrangement is mutually perpendicular Obtain the expression of motional electromotive force


How do you expect the metallic hydrides to be useful for hydrogen storage? Explain.


Which of the following statements in
relation to the hydrogen atom is
correct?

This question has multiple correct options
A. \( 3 s \) -orbital is lower in energy than \( 3 p \) -orbital
B. \( 3 p \) -orbital is lower in energy than \( 3 d \) -orbital
C. \( 3 s \) -and \( 3 p \) -orbitals are of lower energy than \( 3 d \) -orbital
D. \( 3 s, 3 p \) -and \( 3 d \) -orbitals all have the same energy


Using identities, find the square of 101


Hydrogenation of vegetable ghee at
\( 25^{\circ} C \) reduces the pressure of \( H_{2} \) from 2 atm to 1.2 atm in 50 minutes.

The rate of reaction in terms of change of molarity per second is:
A. \( 1.6 \times 10^{-2} \) at \( m \) min \( ^{-1} \)
В. \( 3.3 \times 10^{-2} \) atm \( \min ^{-1} \)
c. \( 2.6 \times 10^{-3} \)atm \( \min ^{-1} \)
D. None of these


Ethanoic acid has a
A. Rotten eggs
B. Pungent
c. vinegar-like
D. Mild


Q Type your question
\( A \)
B
\( c \)
\( D \)


Solve:
\( \frac{m^{2}-3 m-108}{m+9}=0, \) then \( m=? \)


A boy is executing Simple Harmonic Motion. At a displacement \( x \), its
potential energy is \( E_{1} \) and at a
displacement \( y, \) its potential energy is \( \boldsymbol{E}_{2} . \) The potential energy \( \boldsymbol{E} \) at
displacement \( (\boldsymbol{x}+\boldsymbol{y}) \) is:
A \( \cdot \sqrt{E}=\sqrt{E_{1}}-\sqrt{E_{2}} \)
B. \( \sqrt{E}=\sqrt{E_{1}}+\sqrt{E_{2}} \)
c. \( E=E_{1}+E_{2} \)
D. \( E=E_{1}-E_{2} \)


If \( 3 x^{2}+10=11 x, \) then \( x=2, \frac{5}{3} \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


Which of the following is not explained by Rutherford in his Rutherford nuclear model of atom?
A. It could not explain about the nucleus
B. It could not explain the line spectra of hydrogen and discontinuous spectrum nature
c. It could not explain about the stability of atom
D. A and B


According to classical theory of
Rutherford, atom is
A. unstable
B. stable
C. positive
D. partially stable


\( \int_{-3}^{3} \frac{x^{2} \sin ^{3} x}{1+x^{8}} d x \) equals \( g(x) \) then \( g(x) \)
equal to
A . 6
B. 3
\( c \cdot 0 \)
\( D \)


The solution with the highest boiling point temperature is:
в. \( 0.1 \mathrm{M} \) НС \( \mathrm{CO}_{4} \)
c. \( 0.1 \mathrm{M} \mathrm{NH}_{4} \mathrm{OH} \)
D. 0.1 М КОН
E. \( 0.1 \mathrm{M} \) LiNO \( _{3} \)


In which of the following compounds oxygen exhibits an Oxidation state of
\( +2 ? \)
A \( \cdot H_{2} O \)
в. \( H_{2} O_{2} \)
c. \( O F_{2} \)
D. \( H_{2} S O_{4} \)


Alternating current is one which
changes in its :
A. direction
B. magnitude
c. magnitude and direction both
D. none


Assertion If \( A=\left(\begin{array}{ll}\cos \alpha & \sin \alpha \\ \cos \alpha & \sin \alpha\end{array}\right) \) and \( B= \)
\( \left(\begin{array}{cc}\cos \alpha & \cos \alpha \\ \sin \alpha & \sin \alpha\end{array}\right) \) then \( A B \neq I \)
Reason
The product of two matrices can never be equal to an identity matrix
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Let \( S \) be the set of points whose abscissas and ordinates are natural
numbers. Let \( \boldsymbol{P} \in \boldsymbol{S} \) such that the sum
of the distance of \( \boldsymbol{P} \) from (8,0) and (0,12) is minimum among all elements
in
S. Then the number of such points \( P \)
in \( \boldsymbol{S} \) is
\( A \cdot 1 \)
B. 3
\( c .5 \)
D. 11


The coordinates of two consecutive
vertices \( A \) and \( B \) of a regular hexagon
\( A B C D E F \) are (1,0) and (2,0)
respectively. The equation of the diagonal \( C E \) is
A. \( \sqrt{3} x+y=4 \)
B . \( x+\sqrt{3} y+4=0 \)
c. \( x+\sqrt{3} y=4 \)
D. None of these


Let
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\boldsymbol{x}^{2} & \text { if } \boldsymbol{x} \leq \boldsymbol{x}_{0} \\ \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} & \text { if } \boldsymbol{x}>\boldsymbol{x}_{0}\end{array}\right. \)
The values of the coefficients a and b for which the function is continuous and
has a derivative at \( x_{0} \). are
A \( \cdot a=x_{0}, b=-x_{0} \)
B . \( a=2 x_{0}, b=-x_{0}^{2} \)
C \( . a=x_{0}^{2}, b=-x_{0} \)
D. \( a=x_{0}, b=-x_{0}^{2} \)


The dielectric strength of air is \( 3 \times 10^{6} v \)
\( / \mathrm{m} . \) A parallel plate air capacitor has
\( \operatorname{area} 20 c m^{2} \) and plate separation \( 1 \mathrm{mm} \)
Then maximum r.m.s. voltage of an A.C. source which can be safely connected to this capacitor is
A . 212.2
B. 21.22
c. \( 2.122 \mathrm{v} \)
D. 2122 V


The lymph vessel which aids in absorption and distribution of fats is
A. Lacteal
B. Vill
c. Rugae
D. Vene cava


The compound which is not isomeric
with diethyl ether is:
A. n-propylmethylether
B. butan-1-ol
c. 2- methylpropan-2-ol
D. butanone


A concaved lens has focal length of 15 cms. At what distance should the object
from the lens is placed so that it forms an erect and virtual image at \( 10 \mathrm{cm} \) from the lens?
\( \mathbf{A} \cdot 30 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( c .60 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


What is the maximum \( p H \) of \( 0.10 M \)
solution in \( M g^{2+} \) from which
\( M g(O H)_{2} \) will not precipitate. Given :
\( \boldsymbol{K}_{s p}\left(\boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2}\right)=\mathbf{1 . 2} \times \mathbf{1 0}^{-11} \)


Interpret \( \mathrm{K}^{\prime}-\mathrm{K} \)


During adolescence, several changes occur in the human body. Find out the change which is associated with sexual maturation in boys.
A. Loss of milk teeth
B. Increase in height
c. cracking of voice
D. weight gain


The length of the latus rectum of the \( \operatorname{conic} \frac{5}{r}=3-2 \cos \theta \) is
A \( \cdot \frac{3}{5} \)
B. \( \frac{5}{3} \)
\( c \cdot \frac{6}{5} \)
D. \( \frac{10}{3} \)


Draw any circle and mark an arc.


Evaluate \( : \int_{-\pi / 4}^{\pi / 4} x^{5} \cos ^{2} x d x \)


A force \( (10 \hat{i}-3 \hat{j}+6 \hat{k}) \) newton acts on a body of mass \( 100 g \) and displaces it from \( (6 \hat{i}-5 \hat{j}-3 \hat{k}) \) metre to \( (10 \hat{i}-2 \hat{j}+7 \hat{k}) m \)
The work done is
\( \mathbf{A} \cdot 21 J \)
в. \( 361 J \)
c. \( 121 J \)
D. \( 1000 J \)


A right triangle has a hypotenuse of length \( p c m \) and one side of length \( q c m \)
\( \mathbf{f} p-\boldsymbol{q}=1, \) find the length of the third
side of the triangle if \( p=5 \) and \( q=4 \)


Assertion \( (A): \) Bulk modulus of
elasticity (K) represents
incompressibility of the material.
Reason \( (\mathrm{R}): K=-\frac{\Delta P}{\Delta V / V}, \) where
symbols have their standard meaning.
A. Both assertion and reason are true and the reason is
correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
C. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true


A man of height \( 170 \mathrm{cm} \) wants to see his complete image in a plane mirror (while standing). His eyes are at a height of \( 160 \mathrm{cm} \) from the ground.
A. minimum length of the mirror \( =80 \mathrm{cm} \)
B. minimum length of the mirror = 85 cm
c. bottom of the mirror should be at a height 80 cm or
more
D. bottom of the mirror should be at a height \( 85 \mathrm{cm} \)


The general configuration \( (n-1) d^{3} n s^{2} \)
indicates that the particular element belongs to \( _{-}- \) - - \( - \) group.
A . II B
B. IB
c. \( \vee \) в
D. III B


Which of the following is wrong of Bohr's
model?
A. It establishes stability of atom
B. It is inconsistent with Heisenberg uncertainty principle
C. It explains the concept of spectral lines for hydrogen like species
D. Electrons behave as particle and wave


The equation to the altitude of the
altitude triangle formed by
\( (1,1,1) \cdot(1,2,3),(2,-1,1) \) through
(1,1,1) is
A \( \cdot \bar{r}=(\bar{i}+\bar{j}+\bar{k})+t(\bar{i}-\bar{j}-2 \bar{k}) \)
B \( \cdot \bar{r}=(\bar{i}-\bar{j}+\bar{k})+t(\bar{i}+\bar{j}-2 \bar{k}) \)
\( \mathbf{c} \cdot \bar{r}=(\bar{i}+\bar{j}+\bar{k})+t(\bar{i}-\bar{j}+2 \bar{k}) \)
D \( \cdot \bar{r}=(\bar{i}-\bar{j}-\bar{k})+t(\bar{i}+\bar{j}-2 \bar{k}) \)


Vasopressin is a
A. peptide hormone
B. steroid hormone
c. amine hormone
D. vitamin


The IUPAC name of the Wilkinson's
catalyst
\( \left[\boldsymbol{R h C l}\left(\boldsymbol{P P h}_{3}\right)_{3}\right] \) is:
A. Chlorotris (triphenylphosphine) rhodium (I)
B. Chlorotris (triphenylphosphine) rhodium (IV)
C. Chlorotris (triphenylphosphine) rhodium (0)
D. Chlorotris (triphenylphosphine) rhodium (VI)


State True or False.
In recharging of lead storage cell, sulphuric acid is produced.
A. True
B. False


A point source of light is kept at a depth of h in water of refractive index 4/3. The
radius of the circle at the surface of
water through which light emits is
A \( \cdot \frac{3}{\sqrt{7}} h \)
в. \( \frac{\sqrt{7}}{3} h \)
c. \( \frac{\sqrt{3}}{7} \)
D. \( \frac{7}{\sqrt{3}} h \)


If the p.d.f of a continuous random variable \( \boldsymbol{x} \) is \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}k x^{2}(1-x) & , 0<x<1 \\ 0 & , \text { otherwise }\end{array}\right. \)
then value of \( k \) is
A . 12
B. 10
c. -12
D.


toppr DG
Q Type your question_
\( x \)
light string of length \( l \), whose other end
is attached to the circumference of the
disc. Initially string is just taut and
tangential to the disc, particle \( A \) is at
rest. In the same horizontal plane
another particle \( B \) of same mass \( m \)
moving with velocity \( v_{0} \) perpendicular
to string collides elastically with \( A \). Just
after impact which of the following
statements will be true.
This question has multiple correct options
A tension in the string is \( \frac{2 m v_{0}^{2}}{5 l} \)
B. acceleration of the centre of the disc is \( \frac{v_{0}^{2}}{5 l} \)
C tension in the string is \( \frac{m v_{0}^{2}}{5 l} \)
Deceleration of the centre of the disc is \( \frac{2 v_{0}^{2}}{5 l} \)


Show that -
(i) \( (2 a+3 b)^{2}-(2 a-3 b)^{2}=24 a b \)
(ii) \( (4 x+5)^{2}-80 x=(4 x-5)^{2} \)


Meibomian gland are associated with
A. Eyes
B. Ears
c. Reproductive organ
D. skin


When hydrogen combines with oxygen,
it produces water and hydrogen peroxide. This illustrates:
A. Law of constant composition
B. Law of constant volume
c. Law of reciprocal proportion
D. Law of multiple proportion


Two elastic wire \( A \& B \) having length
\( \ell_{A}=2 m \) and \( \ell_{B}=1.5 m \) and the ratio
of young's modules \( Y_{A}: Y_{B} \) is \( 7: 4 . \) If
radius of wire \( B\left(r_{B}\right) \) is \( 2 m m \) then
choose the correct value of radius of
wire \( A . \) Given that due to application of
the same force charge in length in both \( A \& B \) is same
A. \( 1.7 m m \)
в. \( 1.9 m m \)
\( c .2 .7 m m \)
D. \( 2 m m \)


Evaluate the following integral as limit
of sum:
\( \int_{0}^{5}(x+1) d x \)


A point on the parabola \( y^{2}=18 x \) at
which the ordinate increases at twice
the rate of the absicca is
\( ^{A} \cdot\left(\frac{9}{8}, \frac{9}{2}\right) \)
в. (2,-4)
\( ^{\mathbf{c}} \cdot\left(\frac{-9}{8}, \frac{9}{2}\right) \)
D. (2,4)


Patterns of stars in the sky are called
A. Confrontations
B. Comprehensions
c. configurations
D. constellations


A ball moving with a momentum of
5kgm/s strikes against a wall at an
angle of \( 45^{\circ} \) and is reflected at the
same angle. The change in momentum will be \( (\mathrm{kg}-\mathrm{m} / \mathrm{s}): \)
A . 7.07
B. 14.14
c. 8.00
D. 7.5


Identify the correct type of food chain which is as follows:

Dead animal \( \rightarrow \) blow fly maggots \( \rightarrow \)
common frog \( \rightarrow \) snake
A. Grazing food chain
B. Detrital food chain
c. Decomposer food chain
D. Predator food chain


Compute the molar solubility of water
that is saturated with air.
\( \left[\text { Given: } k=0.00105 \mathrm{M} / \mathrm{atm}, P_{N e} \text { in air }=\right. \)
\( 0.0341 \mathrm{atm}] \)
A \( .2 .56 \times 10^{-2} M \)
в. \( 3.58 \times 10^{-5} M \)
c. \( 4.44 \times 10^{-6} M \)
D. \( 2.78 \times 10^{-4} M \)


The green scum seen in the freshwater
bodies is
A. Blue green algae
B. Red algae
c. Green algae
D. Both A and C


Shown in the figure is a meter-bridge set up with null deflection in the
galvanometer. The value of the unknown resistance R is?
A . \( 55 \Omega \)
B. \( 13.75 \Omega \)
c. \( 220 \Omega \)
D. \( 110 \Omega \)


In a parallel circuit of bulbs,
A. same current exists in all the bulbs
B. voltage across each bulb remains the same
C. failure of any bulb leads to a break in the circuit
D. all the above


No. of double bond(s) present in the Lewis structure of \( C_{3}^{4-} \) is


Which of the following commonly forms ionic compounds as a -1 anion?
A. \( C \)
в. \( N \)
\( c \cdot O \)
D. \( F \)
E . \( N e \)


\( \infty-3^{-5} \)
What is


Given a function \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} ; \) where \( \boldsymbol{A}= \)
\{1,2,3,4,5\} and \( B=\{6,7,8\} \)
The number of mappings of \( g(x): B \rightarrow \)
\( A \) such that \( g(i) \leq g(j) \) whenever \( i<j \)
is
A . 55
в. 140
c. 10
D. 35 5


The diameter of a copper sphere is \( 6 \mathrm{cm} \) It is beaten and drawn into a wire of
diameter \( 0.2 \mathrm{cm} . \) The length of wire is
\( \mathbf{A} \cdot 36 \mathrm{cm} \)
в. \( 360 \mathrm{cm} \)
c. \( 3600 \mathrm{cm} \)
D. None


Prove that:
\( \int \tan ^{3} 2 x \sec 2 x d x \)


For which region is \( f(x)=3 x^{2}-2 x+ \)
1 strictly increasing?
This question has multiple correct options
\( \mathbf{A} \cdot(2,5) \)
B. \( \left(\frac{1}{3}, \infty\right) \)
c. \( \left(-1, \frac{1}{3}\right] \)
D. \( \left(-\infty, \frac{1}{3}\right) \)


\( \boldsymbol{A} \boldsymbol{s}_{2} \boldsymbol{S}_{3} \) sol is :
A . positive colloid
B. negative colloid
c. neutral colloid
D. none of the above


State the characteristics required in a
material to be used as an effective fuse
wire


Assertion
Pascal's law is the working principle of
hydraulic lift.
Reason
Pressure \( =\frac{\text { Thrust }}{\text { Area }} \)
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


Write these as a per cent.
11 out of 100
98 out of 100


Which of the following expressions
is/are not true?
\( \mathbf{A} \cdot\left[H^{+}\right]=\left[O H^{-}\right]=\sqrt{K_{w}} \) for a neutral solution at al
temperatures
B \( \cdot\left[H^{+}\right]>\sqrt{K_{w}} \&\left[O H^{-}\right]<\sqrt{K_{w}} \) for an acidic solution
\( \mathbf{C} \cdot\left[H^{+}\right]<\sqrt{K_{w}} \&\left[O H^{-}\right]>\sqrt{K_{w}} \) for an alkaline solution
D \( \cdot\left[H^{+}\right]=\left[O H^{-}\right]=10^{-7} M \) for a neutral solution at all
temperatures


The distance between points \( (5 \sin 90,0) \) and \( (0,6 \cos 90) \) is
A. 5 units
B. 6 units
c. 1 units
D. None of the above


Which of the following statement(s)
is/are true?
This question has multiple correct options
\( \mathbf{A} \cdot \) In metal carbonyl complexes \( d_{C-O} \) increases compared to that in CO molecule
B. The pair of compounds \( \left[C r\left(H_{2} O\right)_{6}\right] C l_{3} \) and \( \left[C r C l_{3}\left(H_{2} O\right)_{3}\right] \cdot 3 H_{2} O \) show hydrate isomerism.
\( \mathrm{C} \cdot d_{z 2} \) orbital of central metal atom/ion is used in \( d s p^{2} \) hybridisation.
D. Facid and Meridional isomers associated with
\( \left[M a_{3} b_{3}\right]^{n \pm} \) type complex compound, both are optically inactive.


Assertion
Enzyme differ from man-made catalysts as the enzymes affect fewer substrates
Reason
Enterokinase is activator for pepsin.
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 diverging meniscus lens of 1.5 refractive index has concave surface of
radii 3 and 4 cm.The position of the
image, if an object is placed \( 12 \mathrm{cm} \) in front of the lens, is
A. \( 7 \mathrm{cm} \)
B. - 8 cm
\( c .9 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


According to the Rutherford's atomic model, the electrons inside the atom are
A. stationary
B. not stationary
c. centralized
D. None of these


Assertion
Optical fibres are used for
telecommunication.
Reason
Optical fibres are based on the
phenomenon of total internal reflection.
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 transition of electron in H-atom that
will emit maximum energy is :
A \( \cdot n_{3} \rightarrow n_{2} \)
В . \( n_{4} \rightarrow n_{3} \)
\( \mathbf{c} \cdot n_{5} \rightarrow n_{4} \)
D. all have same energy


Zinc is used to protect iron from
corrosion because:
\( \mathbf{A} \cdot E_{r e d} \) of \( Z n<E_{r e d} \) of iron
B. \( E_{\text {oxidation}} \) of \( Z n<E_{\text {oxidation}} \) of iron
C . \( E_{\text {oxidation}} \) of \( Z n=E_{\text {oxidation}} \) of iron
D. zinc is cheaper than iron


A light of wavelength \( 1218 \mathrm{A}^{\circ} \) is emitted when the electron of a hydrogen atom
drops from fifth to third quantum level. Find the wavelength of the photon emitted when electron falls fro third to
ground level?
A \( .1025 A^{0} \)
B . 2050 \( A^{0} \)
c. \( 1320 A^{\circ} \)
D. 2460 \( A^{0} \)


Which of the following is the failure of Bohr's atomic model
A. Electrons revolve round the nucleus with definite velocities in concentric circular orbits situated at definite distances from the nucleus
B. The energy of an electron in a certain orbit remains constant
c. As long as it remains in that orbit, it neither emits no absorbs energy. These are termed stationary states or main energy states.
D. None of these


If an iron ball and a wooden ball of the
same radius are released from a height \( h \) in vaccum then time taken by both of them to reach ground will be:-
A. unequal
B. exactly equal
c. roughly equal
D. zero


The form of energy that water stored in a dam primarily has is :
A. muscular energy
B. kinetic energy
c. potential energy
D. magnetic energy


The product obtained on fusion of
\( B a S O_{4} \) and \( N a_{2} C O_{3} \) is:
A. \( B a C O_{3} \)
в. Ва О
\( \mathbf{c} \cdot B a(O H)_{2} \)
D. \( B a H S O_{4} \)


There are circumstances in which two
objects exert forces on one another even though they are not touching. Such forces are called (Mark the most
appropriate answer)
A. non-contact forces
B. contact forces
c. electric forces
D. attractive forces


Weed killers have properties similar to
A. Hormones
B. Enzymes
c. Insecticides
D. Vitamins


f \( a=1 \) and \( b=-1, \) find the value of
the following:
\( \left(a^{2}+b^{2}\right)\left(-a^{2}+b^{2}\right) \)


What is the name given to the atoms whose nuclei contain the same number
of proton but different number of
neutrons?


Which of the following possesses Potential energy?
A. Moving leaf on the road
B. A running athlete
c. Stone on the road
D. A stretched rubber band


A cart travels a distance d on a straight
road in two hours and then returns to
the starting point in next three hours. Its average speed is:
A \( \cdot \frac{d}{5} \)
в. \( \frac{2 d}{5} \)
c. \( \frac{d}{2}+\frac{d}{3} \)
D. none of these


The part labelled as 1 in the given
structure of nephron is
A. Glomerulus
B. Bowman's capsulel
c. Proximal convoluted tubule
D. Loop of Henle
E. Distal convoluted tubule


The \( \boldsymbol{f}(\boldsymbol{x})=(3-\boldsymbol{x}) e^{2 x}-4 \boldsymbol{x} e^{x}-\boldsymbol{x} \) has
\( \mathbf{A} \cdot \) a maximum at \( x=0 \)
B. a minimum at \( x=0 \)
C. neither of two at \( x=0 \)
D. \( f(x) \) is not differentiable at \( x=0 \)


Equation of a straight line passing
through (1,4) if the sum of its positive intercepts on the coordinate axis is the smallest is
A. \( 2 x+y-6=0 \)
B . \( x+2 y-9=0 \)
c. \( y+2 x+6=0 \)
D. none


Two moles of \( N H_{3} \) gas are introduced
into a previously evacuated one litre vessel in which it partially dissociates
at high temperature as \( 2 N H_{3}(g) \leftrightharpoons \) \( N_{2}(g)+3 H_{2}(g) . \) At equilibrium, one
mole of \( \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g}) \) remain. The value of
\( \boldsymbol{K}_{\boldsymbol{C}} \) is:
A . 3
B. \( 27 / 16 \)
c. \( 3 / 2 \)
D. \( 27 / 64 \)


In the cyanide extraction process of
silver from argentite ore, the oxidizing
and reducing agents used are:
A. \( O_{2} \) and \( C O, \) respectively
B. \( O_{2} \) and \( Z n \) dust, respectively
c. \( H N O_{3} \) and \( Z n \) dust, respectively
D. \( H N O_{3} \) and \( C O, \) respectively


Express the following as a fraction and simplify:
\( \mathbf{0 . 0 0 8} \)
A \( \cdot \frac{1}{25} \)
в. \( \frac{1}{125} \)
c. \( \frac{2}{25} \)
D. \( \frac{4}{125} \)


Two particles are moving along a straight line as shown. The velocity of approach between \( A \) and \( B \) is
A \( \cdot V_{A}+V_{B} \)
в. \( \left|V_{A}-V_{B}\right| \)
c. \( V_{A}-V_{B} \)
D. \( V_{B}-V_{A} \)


Pseudoparenchyma occurs in some
A. Fungi
B. Bryophyta
C. Bacteria
D. Angiosperms


benzene derivatives would furnish only
three isomers in significant amount, when one more substituents is
introduced?
\( \mathbf{A} \)
B.
\( c \)
D.


Let \( \mathbf{f}: \mathbf{R} \rightarrow \mathbf{R} \) be any function. Define
\( \mathbf{g}: \mathbf{R} \rightarrow \mathbf{R} \) by \( \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})| \) for all \( \boldsymbol{x} \)
Then \( g \) is
A. \( g \) may be bounded even if \( f \) is unbounded
B. one-one if fis one
c. continuous if \( f \) is continuous
D. differentiable if f is differentiable


Three solid spheres of copper, whose
radii are \( 3 \mathrm{cm}, 4 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respestively are melted into a single
solid sphere of radius R. The value of R
is
A . \( 12 \mathrm{cm} \)
B. \( 8 \mathrm{cm} \)
\( c .4 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


An Ideal gas undergoes an isobaric
process. If its heat capacity is \( C_{v} \) at
constant volume and number of mole \( n \)
then the ratio of work done by gas to heat given to gas when temperature of gas changes by \( \Delta \boldsymbol{T} \) is:
\( ^{A} \cdot\left(\frac{n R}{c_{v}+R}\right) \)
в. \( \left(\frac{R}{c_{v}+R}\right) \)
\( ^{\mathrm{c}} \cdot\left(\frac{n R}{c_{v}-R}\right) \)
\( ^{D \cdot}\left(\frac{R}{c_{v}-R}\right) \)


Impulse is
A. a scalar quantity
B. a vector quantity
C. neither a scalar nor a vector
D. sometimes a scalar and sometimes a vector


Antimicrobial drugs that are derived
from the natural processes of some microorganisms and that can inhibit or destroy other microorganisms, are specifically known as:
A. synthetic drugs
B. chemotherapeutic drugs
c. antibiotics
D. prophylactic drugs


A body of mass \( 2 \mathrm{kg} \) is floating in the liquid of density \( 900 \mathrm{kgm}^{-3} \). The weight of liquid displaced by it is
A . 20 dyne
B. \( 20 N \)
\( c \cdot 2 N \)
D. None of the above


From which of the following case, the
induced current in the loop will not be
obtained?
A. The loop is moved in the direction of the magnet
B. The loop and magnet are moved in the opposite direction with the same speed
C. The magnet is moved in the direction of the loop
D. The loop and magnet are moved in one direction with the same speed


Two inductors of inductance L each are
connected in series with opposite
magnetic fluxes. The resultant inductance is (Ignore mutual inductance)
A. zero
B.
c. 2L
D. 3L


In aqueous environment, the
microscopic organisms are collectively called as
A. Herbivores
B. Carnivores
c. Planktons
D. Fauna and flora


According to five kingdom system, the unicellular algae like Dinoflagellates, Diatoms and Euglenoids are included in
kingdom
A. Monera
B. Protista
c. Plantae
D. Animalia


Put the following in the form \( A+i B: \) \( \frac{(a+i b)^{2}}{(a-i b)}-\frac{(a-i b)^{2}}{(a+i b)} \)


Find the number of arrangements of the letters of the word INDEPENDENCE. In
how many of these arrangements.
Do the vowels never occur together?


Keeping the angle of banking same, if the radius of curvature is made four
times, the percentage increase in the
maximum speed with which a vehicle can travel on a circular road is:
A . 25\%
B. 50\%
c. 75\%
D. 100\%


Who is given the credit for creation of first nuclear reactor.
A. Fermi
B. Niels Bohr
c. Einstein
D. oppenheimer


Very short answer type.
What structures in the ovary contain endocrine tissue and what hormones do
they secrete?


Let \( ^{*} \) be a binary operation on the set \( \boldsymbol{Q} \)
of rational numbers as follows:
\( \boldsymbol{a} * \boldsymbol{b}=(\boldsymbol{a}-\boldsymbol{b})^{2} \)
Find which of the binary operations are commutative and which are
associative.


As the height of the liquid column increases, the pressure exerted by a liquid at a point


A satellite is moving in a circular orbit at a certain height above the
earth's surface. It takes \( 5.26 \times 10^{3} s \) to
complete one revolution with a centripetal acceleration equal to 9.32
\( \mathrm{m} / \mathrm{s}^{2} . \) The height of satellite orbiting
above the earth is
(Earth's radius \( \left.=\mathbf{6 . 3 7} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m}\right) \)
A. \( 220 \mathrm{km} \)
B. 160 km
c. 70 \( \mathrm{km} \)
D. 120 km


Find \( \int a^{x} \cdot e^{x} d x \)


Find the number of photons of radiation of frequency \( 5 \times 10^{13} s^{-1} \) that must be
absorbed in order to melt one gm ice when the latent heat of fusion of ice is
\( \mathbf{3 3 0} \mathbf{J} \cdot\left(\mathbf{h}=\mathbf{6 . 6} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J} \times \mathbf{s e c} .\right) \)


A spring gun has a spring constant of
\( 80 N / m . \) The spring is compressed \( 12 \mathrm{cm} \) by a ball of mass \( 15 \mathrm{gm} \). How much is potential energy of the spring and what will be the velocity of the ball,
if the trigger is pulled:
A. \( 57.6 \mathrm{J}, 87.6 \mathrm{m} / \mathrm{s} \)
в. \( 67.6 \mathrm{J}, 97.6 \mathrm{m} / \mathrm{s} \)
c. \( 0.576 J, 76.8 \mathrm{m} / \mathrm{s} \)
D. none of these


If the area of the triangle formed by \( (0,0),(a, 0) \) and \( \left(\frac{1}{2}, a\right) \) is equal to \( \frac{1}{2} s q \) unit, then the values of \( a \) are :
\( A \ldots \pm 2 \)
B. ±3
\( c .\pm 1 \)
D. ±4
\( \mathrm{E} \cdot \pm 5 \)


If linear magnification for a spherical mirror is \( \frac{3}{2}, \) then we may write: (symbols have their usual meanings)
A \( \cdot f=\frac{u}{2} \)
B. \( f=\frac{3 u}{2} \)
\( c \cdot f=\frac{3 u}{5} \)
D. None of these


How many \( 1^{\circ}, 2^{\circ}, 3^{\circ} C \) atoms does 1,3,5
Trimethyl cyclohexane have?
\( A \cdot 3,6,0 \)
B. 3,4,2
c. 0,3,6
D. 3,3,3


Find the area bounded by \( \boldsymbol{y}= \) \( \cos ^{-1} x, y=\sin ^{-1} x \) and \( y- \) axis
A \( \cdot(2-\sqrt{2}) \) sq. units
B \( \cdot(\sqrt{2}-2) \) sq. units
c. \( 2 \sqrt{2} \) sq. units
D. \( \sqrt{2} \) sq. units


Which among the following carbonyl compound is most polar?
B.
\( c \)
D.


Which of the following alkyl halides is used as a methylating agent?
A. \( C_{2} H_{5} B r \)
B . \( C_{6} H_{5} C l \)
c. \( C H_{3} C l \)
D. \( C_{2} H_{5} C l \)


Most vertebrates show
A. Bilateral symmetry
B. Radial symmetry
C. Biradial symmetry
D. Spherical symmetry


Which physical properties of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
enable separation of \( \boldsymbol{N} \boldsymbol{H}_{3} \) from a
mixture of \( \boldsymbol{N} \boldsymbol{H}_{3}, \boldsymbol{N}_{2} \) and \( \boldsymbol{H}_{2} ? \)
A. Ammonia is easily liquefied
B. Ammonia is highly soluble
c. Both A and B
D. None of these


What is the value of 1 fermi in \( m ? \)
A \( \cdot 10^{-3} \)
3
B. \( 10^{-6} \)
\( c \cdot 10^{15} \)
D. \( 10^{-15} \)


Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January?
A . 39
в. 400
\( c \cdot 410 \)
D. 423
E . 445


Assertion
Two persons on the surface of moon
cannot talk to each other.
Reason
There is no atmosphere on moon.
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


Evaluate using identities \( 6^{3}-9^{3}+3^{3} \)
\( \mathbf{A} \cdot-486 \)
в. 486
\( c .-86 \)
D. None of these


Two spheres of masses \( 2 \mathrm{M} \) and \( \mathrm{M} \) are kept at a distance R apart. Due to mutual force of attraction, they
approach each other. When they are at a separation R/2. Find the acceleration of centre of mass.


An electric motor operates on a 50 volt supply and a current of 12A. If the efficiency of the motor is \( 30 \% \), what is
the resistance of the winding of the
motor
A. \( 3.4 \Omega \)
в. 2.19
\( c .3 .9 \Omega \)
D. 2.9\Omega


Which statement is linked with the idea
that two identical containers filled with
different gases will contain the same number of particles?
A. Mosely
B. Avagadro
c. Dalton
D. Mendeleev


The standard deviation of 5 items is
found to be \( \$ \$ 15 \$ . \) What will be the
standard deviation if the values of al
the items are increased?
A . 15
B . 20
c. 10
D. None of the above


Solve \( \sin 2 x+\cos 4 x=2 \)


Two points charges placed at a distance
\( r, \) in the air experience a certain force then the distance at which they will experience the same force in the
medium off dielectric constant K is
A. \( K r \)
в. \( \frac{r}{K} \)
c. \( \frac{r}{\sqrt{K}} \)
D. \( r \sqrt{K} \)


The standard heat of formation of
sodium ions in aqueous solution from the following data:
Heat of formation of \( N a O H(a q .) \) at
\( 25^{\circ} C=-470.7 k J \)
Heat of formation of \( \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q} .) \) at
\( \mathbf{2 5}^{\circ} \boldsymbol{C}=-\mathbf{2 2 8 . 8 k J} \mathbf{i s} \)
\( \mathbf{A} \cdot-251.9 k J \)
в. 241.9k.
\( \mathbf{c} .-241.9 k J \)
D. \( 251.9 k J \)


Which of the following material has lowest resistivity?
A. Manganin
B. Copper
c. constantan
D. Silver


A solution contains \( 15 \% \) glucose
\( \left[\boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}\right] \) in water and has density \( \mathbf{1 . 5} \)
\( \mathrm{g} / \mathrm{ml} . \) Find the molarity and molality of this solution \( [\boldsymbol{C}=\mathbf{1 2}, \boldsymbol{H}=\mathbf{1}, \boldsymbol{O}=\mathbf{1 6}] \)


Calculate the electrostatic potential
energy of an electron-proton system of hydrogen atom. In the first Bohr orbit of hydrogen atom, the radius of the orbit is \( 5.3 \times 10^{-11} m \)
A. \( -4.35 \times 10^{-18} \mathrm{J} \)
В. \( -2.175 \times 10^{-18} \mathrm{J} \)
c. \( -4.35 \times 10^{-19} J \)
D. \( -2.175 \times 10^{-19} \mathrm{J} \)


The first formed nitrogenous waste of
vertebrates is
A \( . N H_{2} \)
B. Urea
c. \( N H_{3} \)
D. \( N H_{4} \)


Is larger surface area break on a bicycle wheel more effective than small surface
area brake? Explain?


Unpolarized light of intensity \( \boldsymbol{I}_{\mathbf{0}} \) is incident on a polarizer and the emerging light strikes a second polarizing filter with its axis at
\( 45^{\circ} \) to that of the first. The intensity of
the emerging beam:
A \( \cdot \frac{I o}{2} \)
в. \( \frac{\text { Io }}{4} \)
\( c \cdot I_{o} \)
D. \( \frac{\text { Io }}{3} \)


Ultrasound has frequency of vibration
A. between \( 20 \mathrm{Hz} \) and \( 20000 \mathrm{Hz} \)
B. below 20 Hz.
c. above 20000 Hz.
D. between \( 500 \mathrm{Hz} \) and \( 10000 \mathrm{Hz} \)


A stone is dropped into a quiet lake. If
the waves moves in circle at the rate of
\( 30 \mathrm{cm} / \mathrm{sec} \) when the radius is \( 50 \mathrm{m} \), the
rate of increase of enclosed area is
A \( .30 \pi m^{2} / \) sec
B. \( 30 m^{2} / \)sec
c. \( 3 \pi m^{2} / \)sec
D. none of these


A ray of light passes from air into water. The angle of refraction will be
A. Equal to the angle of incidence
B. Smaller than the angle of incidence
c. Greater than the angle of incidence
D. Equal to 45


\( \frac{d}{d x}[\log \sqrt{\frac{1-\cos x}{1+\cos x}}]= \)
A . sec
B. \( \csc x \)
c. \( \operatorname{cosec} \frac{x}{2} \)
D. \( \sec \frac{x}{2} \)


The number of mesostructure in the
following compound is:
HOOC \( \cdot \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \cdot \boldsymbol{C H}(\boldsymbol{O H}) \)
\( \boldsymbol{C H}(\boldsymbol{C l}) \cdot \boldsymbol{C H}(\boldsymbol{O H}) \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \)
COOH
\( A \cdot 3 \)
B. 4
\( c \cdot 8 \)
D. 16


The acceleration of blocks B is:
A. zero
B. \( 3.336 m / s^{2} \)
c. \( 4.11 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 2.943 m / s^{2} \)


where \( X, Y, Z \) are atoms of different
elements with different
electronegativities, are shown below.
The molecules are regular
tetrahedral species. Assume the bond
lengths in all the structures to be the
same.
Identify the pair(s) of structures of
molecules in which both the members
have the same magnitude of dipole
moment.
A. I and III
B. Il and v
c. IV and vı
D. I and \( V \)


Mother gives birth to a baby but the baby has characters of both parents. How is this possible?
A. In sexual reproduction, zygote forms by fertilization of both male and female gametes
B. By parental care
c. By vegetative methodd
D. Characters come asexually