The process which are subjected to action of heat in absence of air is called
A. Extraction
B. Polishing
c. Calcination
D. None of these


The ratio in which the line \( 3 x+y=9 \)
divides the line sequent joining the
points (1,3) and (2,7) is given by
A .4: 3
B. 3: 4
\( c \cdot 2: 3 \)
D. 3: 2


Draw a triangle \( P Q R \), right angled at \( Q \)
such that \( P Q=3 \mathrm{cm}, Q R=4 \mathrm{cm} . \) Now
construct \( \triangle A Q B \) similar to \( \triangle P Q R \) each of whose sides is \( \frac{7}{5} \) times the
corresponding side of \( \triangle \boldsymbol{P} Q \boldsymbol{R} \)


If the direction of the initial velocity of the charged particle is perpendicular to the magnetic field, the orbit of charged particle will be
A. a straight line
B. a cycloid
c. a circle
D. a helix


Find the area of a body which
experiences a pressure of \( 50,000 P a \) by
a thrust of \( 100 N \)


The plates of a parallel plate capacitor are charged to \( 200 \mathrm{V} \) and then, the charging battery is disconnected. Now, a dielectric
slab of dielectric constant 5 and
thickness \( 4 \mathrm{mm} \) is inserted between the
capacitor plates. To maintain the original
capacity, the increase in the separation between the plates of the capacitor is:
A. \( 1.6 \mathrm{mm} \)
B. \( 3.2 \mathrm{mm} \)
\( \mathrm{c} .0 .8 \mathrm{mm} \)
D. \( 4.8 \mathrm{mm} \)


Which of the following transition element shows the highest oxidation
state?
\( \mathbf{A} \cdot M n \)
в. \( F e \)
\( c \cdot V \)
D. \( C r \)


The ionisation enthalpy of \( H e^{+} \) ion is
\( 19.60 \times 10^{-18} J \) atom \( ^{-1} . \) The ionisation
enthalpy of \( L i^{2+} \) ion will be:
A. \( 84.2 \times 10^{-18} \) Jatom\( ^{-1} \)
B. \( 44.10 \times 10^{-18} \) Jatom \( ^{-1} \)
c. \( 63.20 \times 10^{-18} \) Jatom \( ^{-1} \)
D. \( 21.20 \times 10^{-18} \) Jatom \( ^{-1} \)
E \( .2 .17 \times 10^{-19} \mathrm{Jatom}^{-1} \)


What is the percentage dissociation of
\( 0.1 \mathrm{M} \) solution of acetic acid? \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\right. \)
\( \left.10^{-5}\right) \)
A . \( 10 \% \)
B. \( 100 \% \)
\( c \cdot 1 \% \)
D. \( 0.01 \% \)


The number of significant figures in the numbers 672.9 and \( 2.520 \times 10^{7} \) are
A .4,4
в. 3,4
c. 4,3
D. 3,3


The normal electric flux per unit area is
called
This question has multiple correct options
A. Electric field intensity
B. Electric force
c. Electric flux density
D. Electric potential


Assertion \( f(x)=\sin ^{2} x+\sin ^{2}\left(x+\frac{\pi}{3}\right)+ \)
\( \cos x \cos \left(x+\frac{\pi}{3}\right) \) then \( f^{\prime}(x)=0 \)
Reason Derivative of a constant function is
always zero
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 rate of reaction between two
reactants \( A \) and \( B \) decreases by a
factor of 4 if the concentration of
reactant B is doubled. The order of this
reaction with respect to reactant B is:


A small magnet M is allowed to fall
through a fixed horizontal conducting ring R. Let \( g \) be the acceleration due to gravity. The acceleration of M will be This question has multiple correct options
A. \( <g \) when it is above \( R \) and moving towards \( R \)
B. > g when it is above R and moving towards R
c. < g when it is below R and moving away from R
D. \( >g \) when it is below \( R \) and moving away from \( R \)


The gravitational force between two masses kept in air at a certain distance
is \( x \) N. The same two masses are now
kept in water and the distance between
them are same. The gravitational force
between these masses in water is \( y \) N.
Then
A. \( x>y \)
в. \( x<y \)
c. \( x=y \)
D. can't say


The eccentricity of an ellipse \( 9 x^{2}+ \)
\( 16 y^{2}=144 \) is
A \( \frac{\sqrt{3}}{5} \)
B. \( \frac{\sqrt{5}}{3} \)
c. \( \frac{\sqrt{7}}{4} \)
D.


Find area of triangle with vertices at the point given in each of the following
\( (\mathrm{i})(1,0),(6,0),(4,3) \)
\( (i i)(2,7),(1,1),(10,8) \)
\( (\text { iii) }(-2,-3),(3,2),(-1,-8) \)


Which of the following is illustration of pyrosilicate?
A. Zircon
B. Hemimorphite
c. Bery!
D. Asbestos


Phosphorylation of glucose during glycolysis is catalysed by
A. Phosphoglucomutase
B. Phosphoglucoisomerase
c. Hexokinase
D. Phosphorylase


If \( R \) and \( S \) are transitive relations on a
set \( A, \) then prove that \( R \cup S \) may not be
transitive relation on \( \boldsymbol{A} \)


A group of similar organisms, which freely breeds among themselves is


When the metal terminal of a gold-leaf electroscope is touched with a charged
object,
A. the gold leaves spread apart in a "v:
B. the gold leaves close together.
c. the gold leaves remain unaffected.
D. None of these


An isotropic point source emits light with wavelength 500nm. The radiation
power of the source is \( \boldsymbol{P}=\mathbf{1 0} \boldsymbol{W} \). Find
the number of photons passing through unit area per second at a distance of
\( 3 m \) from the source
A \( .5 .92 \times 10^{17} / m^{2} s \)
B . \( 2.23 \times 10^{17} / m^{2} s \)
c. \( 2.23 \times 10^{18} / m^{2} s \)
D. \( 5.92 \times 10^{18} / m^{2} s \)


A number is chosen at random from
among the 1 st 50 natural numbers. The probability that the number chosen is either a prime number or a multiple of 5 is
A \( \cdot \frac{12}{25} \)
B. \( \frac{1}{2} \)
c. \( \frac{14}{25} \)
D.


How many seconds are there in 3 days?
A. 259200 s
B. 172800 s
c. 24800 s
D. 72000 s


Find the angle between the curves given below:
\( \boldsymbol{y}^{2}=\boldsymbol{4} \boldsymbol{x}, \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\mathbf{5} \)


If \( \boldsymbol{E} \) and \( \boldsymbol{F} \) are events such that \( \boldsymbol{P}(\boldsymbol{E})= \) \( \frac{1}{4}, P(F)=\frac{1}{2} \) and \( P(E a n d F)=\frac{1}{8} \) find
(i) \( P(E \text { or } F) \)
(ii) \( P(\text { not } E \text { and } \operatorname{not} F) \)


Which plant hormone is named anti-
ageing hormone?


Decide using factor theorem, whether
\( (x-2) \) is a factor of \( x^{3}-4 x^{2}-4 \)


Let \( \mathbf{f}: \mathbf{R} \rightarrow\left[\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right) \) be defined by \( \mathbf{f}(\mathbf{x})= \)
\( \tan ^{-1}\left(x^{2}+x+a\right) \cdot \) Then the set of
values of 'a' for which \( f \) is onto is
B. [2,1]
c. \( \left\{\frac{1}{4}\right. \)
D. \( \left[\frac{1}{4}, \infty\right) \)


For a first order reaction with rate
constant \( k \) and initial concentration a
the half-life period is given by:
This question has multiple correct options
A \( \cdot \frac{\ln 2}{k} \)
B. \( \frac{1}{k} \)
c. \( \frac{0.693}{k} \)
D. \( \frac{2.303}{k} \log 2 \)


What is \( p H \) Scale? Explain that \( p H \)
change of the mouth is the cause of tooth decay


Very short answer type. Observe the relationship between the first two words and then fill in the fourth
place
angiosperms : roots, rhodophyta:


Which of the following sets of atomic masses do not correspond to Dobernier traid?
This question has multiple correct options
A .7,23,39
в. 20,38,56
c. 47,91,178
D. 54,95,183


Fast neutrons can easily be slowed down by
A. the use of lead shielding
B. passing them through water
c. elastic collision with heavy nuclei
D. applying a strong electric field


The shape of \( X e F_{5}^{+} \) ion is :
A. Pentagonal
B. Octahedral
c. Square pyramidal
D. Trigonal bipyramidal


The mode of the following series is 36 Find the missing frequency in it
\( \begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 30- \\ \text { interval } & 10 & 20 & 30 & 40\end{array} \)
Frequency 1 8 10 \( \dots \)
A . 10
B. 15
c. 16
D. 12


Sound can travel through
A. solids and liquids
B. liquids and gases
c. solids and gases
D. all of these


In Rutherford's alpha-ray scattering experiment, a screen is used to detect the alpha particles which is coated by
A. carbon black
B. platinum black
c. zinc sulphide
D. poly tetrafluoro ethylene


Consider the following statements:
(a) All hydrocarbons show phenomena of isomerism.
(b) The members of a homologous series have similar chemical and
physical properties.
(c) Cyclic hydrocarbons are saturated or unsaturated organic compounds that contain ring of carbon atoms.
(d) Synthetic detergents are sodium or potassium salts of long chain carboxylic acids. Which of the above statement(s) is/are
correct?
A. only (c)
B. only (d)
\( c \cdot(a),(b) \) and \( (c) \)
D. \( (a),(c) \) and \( (d) \)


The boiling point of \( 95 \% \) ethanol is higher than that of absolute ethanol.
A. True
B. False


A \( 1500 k g \) car moving on a flat road negotiates a curve whose radius is \( 35 m . \) If the coefficient of static friction
between the tyres and the dry pavement is \( 0.5 . \) Find the maximum speed, the car can have in order to make the turn
successfully.
A. \( 13.1 \mathrm{m} / \mathrm{s} \)
В. \( 15.1 \mathrm{m} / \mathrm{s} \)
c. \( 20 m / s \)
D. \( 25 \mathrm{m} / \mathrm{s} \)


In Holmes signal contains \( C a C_{2} \) along
with :
A. \( C a C l_{2} \)
в. \( C a_{3} P_{2} \)
c. \( C a_{3} N_{2} \)
D. \( C a C O_{3} \)


One end of a uniform rope of length and of weight \( w \) is attached rigidly to a
point in the roof and a weight \( \mathbf{w}_{1} \) is suspended from its lower. If s is the area
of cross-section of the wire, the stress in the wire at a height \( \frac{3 L}{4} \) from its lower end is:
A \( \cdot \frac{w}{s} \)
B. \( \frac{w_{1}+\frac{w}{4}}{s} \)
c. \( \underbrace{w_{1}+\frac{2 w}{4}}_{s} \)
D. \( \frac{w_{1}+w}{s} \)


"Emphysema" is a condition in which
A. Respiratory centre is inhibited
B. Lots of fluid in the lungs
C. The walls separating the alveoli break
D. Lungs have excess \( O_{2} \)


Prove that \( \int x^{2} a^{x} d x= \)
\( \frac{a^{x}}{(\log a)^{3}}\left[x^{2}(\log a)^{2}-2 x(\log a)+2\right] \)


Explain Watson and Crick's model of
DNA.


See the figure above
Find its perimeter.


Which food chain directly depends on solar radiations?
A. Predator
B. Grazing
c. Detritus
D. None of the above


If cube of \( 1 \frac{2}{3}, \) is of the form \( \frac{a}{b}, \) then \( a+ \)
\( b \) is equal to:


Find the degree of each of the polynomials given below \( 5 t-\sqrt{3} \)


Two long, thin, parallel conductors separated by a distance carry currents
\( i_{1} \) and \( i_{2} . \) The force per unit length on one of them is F. Then
This question has multiple correct options
\( \mathbf{A} \cdot F \propto\left(i_{1} i_{2}\right) \)
B . \( F \propto\left(i_{1} i_{2}\right)^{2} \)
\( \mathbf{c} \cdot F \propto \frac{1}{d^{2}} \)
\( D \cdot F \propto \frac{1}{d} \)


If a line makes an angle \( \theta_{1}, \theta_{2}, \theta_{3} \) which
the axis respectively, then \( \cos 2 \theta_{1}+ \)
\( \cos 2 \theta_{2}+\cos 2 \theta_{3}=? \)
A . -4
B . 2
\( c .3 \)
D. -


The volume of air remaining in the lungs even after a forceful expiration is
A. Tidal volume
B. Residual volume
c. Inspiratory reserve volume
D. Expiratory reserve volume


A simple formula to calculate the
standard error is
A \( . S_{y x}=\sigma_{y} \sqrt{1-r^{2}} \)
B . \( S_{x y}=\sigma_{x} \sqrt{1-r^{2}} \)
\( \mathbf{c} \cdot S_{y x}=\mathrm{S.E.} \)
D. Both (A) and (B)


Assertion
HClO is stronger acid than HBro.
Reason
Greater is the electronegativity of the halogen, greater will be attraction of electron pair towards it and hence more
easily the \( \boldsymbol{H}^{+} \) ion will be released.
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 equation \( 7 y^{2}-9 x^{2}+54 x-28 y- \)
\( 116=0 \) represents
A. a hyperbola
B. a parabola
c. an ellipse
D. a pair of straight lines


Find the value of the unknown interior
angle \( x \) in the following figure.


Name four appliances wherein an electric motor, a rotating device that converts electrical energy to
mechanical energy, is used as an important component. In what respect motors are different from generators?


The type of bond between atoms of potassium and chloride in a crystal of potassium chloride is :
A. hydrogen bond
B. ionic bond
c. polar covalent bond
D. pure covalent bond
E. metallic bond


If \( z \) is a non-real complex number, then the minimum value of \( \frac{\operatorname{Im} z^{5}}{(\operatorname{Im} z)^{5}} \) is
\( A \cdot-2 \)
B . - -
\( c \cdot-5 \)
D. -


\( \mathbf{f} A^{\prime}=\left[\begin{array}{cc}\mathbf{3} & \mathbf{4} \\ -\mathbf{1} & \mathbf{2} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}\end{array}\right] \)
then verify that:
\( (i)(A+B)^{\prime}=A^{\prime}+B^{\prime} \)
\( (i i)(A-B)^{\prime}=A^{\prime}-B^{\prime} \)


A pebble is thrown vertically upwards
with a speed of \( 20 m s^{-1} . \) How high will
it be after \( \left.2 s ? \text { (Take } g=10 m s^{-2}\right) \)
A. \( 40 \mathrm{m} \)
B. 10 \( \mathrm{m} \)
\( c \cdot 20 m \)
D. 25 m


How much energy must be imparted to
the proton so as to start the reaction? \( ^{7} L i_{3}+^{1} H_{1} \rightarrow_{4} B e^{7}+_{0} \eta^{1} \)
Given the mass of the atoms;
\( _{3}^{7} L i-7.01600_{, 1}^{1} H-1.00783_{, 4}^{7} B e- \)
\( \mathbf{7 . 0 1 6 9 3}_{.0} \mathbf{n}-\mathbf{1 . 0 0 8 6 6} \)


Which of the following is a proper fraction?
A \( \cdot 1 \frac{1}{3} \)
B. \( \frac{5}{4} \)
\( c \cdot \frac{2}{3} \)
D. None of these


The important principles that do not help in assigning electronic configuration to atoms are:
A. Aufhau rule
B. Hund's rule
c. Heisenberg uncertainty principle
D. Pauli's exclusion principle


Photoelectric effect supports the
quantum nature of light because
This question has multiple correct options
A. There is minimum frequency of light below which no photoelectrons are emitted
B. The maximum KE of photoelectrons depends only on the frequency of light and not on its intensity
C. Even when the metal surface is faintly illuminated by light of wavelength less than the threshold wavelength, the photoelectrons leave the surface immediately
D. Electric charge of photoelectrons is quantized


On which factors does the heat
produced depend when the current is flown through a conducting wire and explain it.


The average induced emf in the circuit
is
\( \mathbf{A} \cdot 0.2 V \)
B. \( 0.1 V \)
\( \mathbf{c} \cdot 1 V \)
D. \( 10 V \)


A conductor of non uniform cross
section is connected across a potentia
difference \( V \) as shown in the figure,

Choose the correct option regarding the
conductor
This question has multiple correct options
A. current at \( B \) is same as that of \( A \)
B. current density near at the end A inside the conductor is more than the current density near the end B inside the conductor
C. resistance of thickness dx near the end B is less than
the resistance near the end
D. electric field near the end \( A \) is more than at \( B \)


Which one is correct
A. Oxidizing property along a period - Decreases. Down the group - Increases. Reducing property along a period - Decreases. Down the group - Increases
B. Oxidizing property along a period - Increases. Down the group - Decreases. Reducing property along a period - Increases. Down the group - Decreases
C. Oxidizing property along a period - Increases. Down the group - Increases. Reducing property along a period - Decreases. Down the group - Increases
D. Oxidizing property along a period - Increases. Down the group - Decreases. Reducing property along a period - Decreases. Down the group - Increases


According to Curie's law, the magnetic susceptibility of a substance
at an absolute temperature T is proportional to -
A. \( 1 / T \)
в. \( T \)
c. \( 1 / T^{2} \)
D. \( T^{2} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) of \( \boldsymbol{x}^{3}+\boldsymbol{x}^{2} \boldsymbol{y}+\boldsymbol{x} \boldsymbol{y}^{2}+\boldsymbol{y}^{3}=\boldsymbol{8} \mathbf{1} \)


Two hail stones iron the form of a sphere
with radii in the ratio \( 1: 2, \) fall from a great height through the atmosphere. What will be the ratio of their momenta when they
attain their respective terminal
velocities?
A . 1: 16
B . \( 1 ; 32 \)
\( c \cdot 1: \)
D. \( 1 ; 4 \)


Which of the following pair of elements do not resemble according to Newlands
arrangement?
A. Lithium and sodium
B. Beryllium and magnesium
c. Boron and silicon
D. Oxygen and selenium


Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. The variance of the number of aces is
A \( .24 / 169 \)
B . \( \sqrt{24 / 169} \)
c. \( \sqrt{24 / 173} \)
D. \( 24 / 173 \)


Prove \( \frac{b c}{a}+\frac{c a}{b}+\frac{a b}{c} \geq a+b+c, \) for
\( a, b, c>0 \)


A catalyst is used:
A. Only for increasing the velocity of a reaction
B. For altering the velocity of a reaction
C. Only for decreasing the velocity of a reaction
D. All (a), (b), and
(c) are correct


The Lewis dot diagram representing ammonia molecule is:


A counter consists of a cylindrical cathode of radius \( 1 c m \) and an anode
wire of radius \( 0.01 c m \) which is placed along the axis of the cathode. A voltage of \( 2.3 k V \) is applied between the
cathode and anode. The electric field on
the anode surface must be:
A \( \cdot 2.3 \times 10^{5} V m^{-1} \)
B. \( 5 \times 10^{6} V m^{-1} \)
\( \mathbf{c} \cdot 4.6 \times 10^{5} \mathrm{Vm}^{-1} \)
D. \( 2.5 \times 10^{6} \mathrm{Vm}^{-1} \)


Which of the following statements is
correct?
A. LPG is a mixture of butane and propane.
B. LPG is liquefied methane.
C . LPG is liquefied propane.
D. LPG is a mixture of methane and ethane.


The oxidation state of \( S \) in \( N a_{2} S_{4} O_{6} \) is:
A . +2.5
B. +2 and +3 (two \( S \) have +2 and two \( S \) have +3 )
\( \mathrm{c} \cdot+2 \) and +3 (three \( S \) have +2 and one \( S \) has +3
D. +5 and 0 (two \( S \) have +5 and the other two \( S \) have 0 )


\( 0.23 \mathrm{g} \) of an organic compound gave 0.332 g of \( B a S O_{4} . \) Determine the \( \% \) of sulphur in the compound.
A . \( 32.61 \% \)
в. \( 8.5 \% \)
c. \( 19.77 \% \)
D. None of these


Tuning fork \( C \) of frequency 305 Hz gives 5 beats/sec with tuning fork D when sounded together. When prongs of D are filled a little they produce 3 beats/s. The frequency of tuning fork D before filling is:
A . 310 \( \mathrm{Hz} \)
в. зоо нz
c. 295 н
D. 315 нz


Given \( \mathbf{A}=\left[\begin{array}{cc}\mathbf{2} & \mathbf{- 6} \\ \mathbf{2} & \mathbf{0}\end{array}\right], \mathbf{B}= \)
\( \left[\begin{array}{cc}-\mathbf{3} & \mathbf{2} \\ \mathbf{4} & \mathbf{0}\end{array}\right], \boldsymbol{C}=\left[\begin{array}{ll}\mathbf{4} & \mathbf{0} \\ \mathbf{0} & \mathbf{2}\end{array}\right] . \) Find the matrix
\( x \) such that \( \boldsymbol{A}+\mathbf{2} \boldsymbol{X}=\mathbf{2} \boldsymbol{B}+\boldsymbol{C} \)


Two plane mirror are inclined as shown in figure an object is placed at origin. Ist reflection takes place from \( M_{1} \) and
then from \( M_{2} \). Calculate the
coordinates of final image.


Express the square matrix \( A \) as the
sum of a symmetric and a skewsymmetric matrix.


A reaction which is of first order w.r.t
reactant \( A, \) has a rate constant 6
\( \boldsymbol{m} \boldsymbol{i n}^{-1} . \) If we start with \( [\boldsymbol{A}]=\mathbf{0 . 5 m o l} \)
\( \boldsymbol{L}^{-1}, \) when would \( [\boldsymbol{A}] \) reach the value of
\( 0.05 m o l L^{-1} ? \)
\( \mathbf{A} \cdot 0.384 \mathrm{min} \)
B. 0.15 min
c. 3 min
D. 3.84 min


\( 2.33 \mathrm{g} \) of compound \( \mathrm{X} \) (empirical formula
\( \left.C o H_{12} N_{4} C l_{3}\right) \) upon treatment with
excess \( A g N O_{3} \) solution produces 1.435 \( g \) of a white precipitate. The primary and secondary valences of cobalt in
compound \( X, \) respectively, are. [Given : Atomic mass: \( \boldsymbol{C o}=\mathbf{5 9}, \boldsymbol{C l}= \)
\( \mathbf{3 5 . 5}, \boldsymbol{A} \boldsymbol{g}=\mathbf{1 0 8}] \)
\( A \cdot 3,6 \)
в. 3,4
\( c \cdot 2,4 \)
D. 4,3


Select the correct statement(s).
This question has multiple correct options
A. In hydrometallurgy, \( Z n \) is used as oxidizing agent in the purification of \( A g \) from \( \left[A g(C N)_{2}\right]^{\circ} \)
B. When pine oil or eucalyptus oil is added into the water, it lowers down the surface tunsion by which froth is formed
C. Sodium ethyl xanthate is used as collector
D. Basic copper carbonate or \( P b S O_{4} \) is concentrated by froth floatation method by using an activator


Sex of the child is determined by the type of \( \ldots \) provided by the father.
A. Sperm
B. Ovum
c. Embryo
D. Placenta


Evaluate the following integral by expressing them as a limit of a sum. \( \int_{1}^{2}(3 x-2) d x \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{7}{2} \)


Silica gel is a very useful:
A. raw material for soap
B. drying agent
c. wetting agent
D. solvent


Explain Equilibrium in chemical processes - Dynamic Equilibrium.


Find the area of rhombus if the base is
\( 20 c m \) and height is \( 45 c m \)


A particle is thrown vertically upwards. Its velocity at one fourth of the
maximum height is \( 20 \mathrm{m} \mathrm{s}^{-1} \). Then, the maximum height attained by it is
A . \( 16 \mathrm{m} \)
B. \( 10 \mathrm{m} \)
\( c \cdot 8 m \)
D. 18


Evaluate \( \int \frac{x^{2}-3 x+5}{\sqrt{x}} d x \)
A. \( \frac{2}{5} x^{\frac{5}{2}}-2 x^{\frac{3}{2}}+10 \sqrt{x}+c \)
B. \( \frac{5}{2} x^{\frac{5}{2}}-2 x^{\frac{3}{2}}+10 \sqrt{x}+c \)
c. \( \frac{2}{5} x^{\frac{3}{2}}+2 x^{\frac{3}{2}}+10 \sqrt{x}+c \)
D. \( \frac{2}{5} x^{\frac{3}{2}}-2 x^{\frac{3}{2}}-10 \sqrt{x}-c \)


Which of the following steps is/are involved in roasting?
This question has multiple correct options
A. remove water of hydration
B. remove arsenic and sulphur impurities
C . convert sulphide to oxide and sulphate
D. None of these


ff \( y=-8 x-5 \) and \( \operatorname{SD} \) of \( x \) is \( 3, \) then \( S D \)
of \( \boldsymbol{y} \) is:
A . 8
B . 24
\( c .3 \)
D. None of these


If \( C E \) is parallel to \( B D \) in the given
figure, then the value of \( x \) will be
A . 45
В. 75
\( c .30 \)
D. 85


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) when \( \boldsymbol{y}=\boldsymbol{x}^{\boldsymbol{x} \cos \boldsymbol{x}}+\left(\frac{\boldsymbol{x}^{2}+\mathbf{1}}{\boldsymbol{x}^{2}-\mathbf{1}}\right) \)


What atomic number of an element \( \boldsymbol{X} \)
would have to become so that the \( 4 t h \)
orbit around \( X \) would fit inside the 1 st
Bohr orbit of \( \boldsymbol{H}- \) atom?
\( A \cdot 3 \)
B. 4
\( c \cdot 16 \)
D. 25


In a \( \triangle A B C, \angle A-\angle B=30^{\circ} \) and \( \angle B- \)
\( \angle C=42^{\circ} ; \) find \( \angle A \)
A \( \cdot 84^{\circ} \)
B. \( 94^{\circ} \)
\( c \cdot 32^{0} \)
D. none of the above


Trace the following central conics. \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{a}(\boldsymbol{x}+\boldsymbol{y}) \)


\( A B C D \) is a rectangle with \( \angle A B D= \)
\( 40^{\circ} . \) Determine \( \angle D B C \)


The solution set of the equation \( \sin ^{-1} \sqrt{1-x}+\cos ^{-1} x= \)
\( \cot ^{-1}\left(\frac{\sqrt{1-x^{2}}}{x}\right)-\sin ^{-1} x \)
A \( \cdot[-1,1]-\{0\} \)
B . (0,1]\( \cup\{-1\} \)
c. [-1,0)\( \cup\{1\} \)
D. \{1\}


Assertion
In a free fall, weight of a body becomes
effectively zero.
Reason
Acceleration due to gravity acting on a body having free fall is zero.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If in a moderately asymmetrical
distribution mean and mode are \( 9 a, 6 a \)
respectively then median is equals,
\( \mathbf{A} \cdot 6 a \)
B. \( 9 a \)
\( c \cdot 8 a \)
D. \( 15 a \)


In the secondary coil of a step up transformer, the number of turns of the copper wire are :
A. More and the wire is thick
B. More and the wire is thin
c. Less and the wire is thick
D. Less and the wire is thin


Define:
(a) Photon
(b) Quantum \( (c) C_{3} \) plant \( (d) \)
\( C_{4} \) plant
(e) Light Reaction (f)
Photorespiration
(g)Limiting Factor.


What is the mass of one molecule of
yellow phosphorus? (Atomic mass, \( \boldsymbol{P}= \)
30)
A \( \cdot 1.993 \times 10^{-22} k g \)
B . \( 1.993 \times 10^{-19} \mathrm{mg} \)
C \( .4 .983 \times 10^{-20} \mathrm{mg} \)
D. \( 4.983 \times 10^{-23} \mathrm{kg} \)


Which of the following statements are
correct
A. Collision does not require physical contact
B. Collision between sub atomic particles is elastic
c. Collision between macroscopic bodies is generally inelastic
D. None of these


(i) \( \boldsymbol{C H} \equiv \boldsymbol{C H} \stackrel{(\boldsymbol{A})}{\longrightarrow}(\boldsymbol{B}) \stackrel{(\boldsymbol{O})}{\longrightarrow} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \stackrel{(\boldsymbol{C})}{\longrightarrow} \boldsymbol{C H}_{2} \boldsymbol{C l C O O H} \)
Complete the given reactions:


Find the distance of the point (2,12,5) from the point of intersection of the line \( \overrightarrow{\boldsymbol{r}}=2 \hat{\hat{\boldsymbol{i}}}-\mathbf{4} \hat{\boldsymbol{j}}+\mathbf{2} \hat{\boldsymbol{k}}+\boldsymbol{\lambda}(\boldsymbol{3} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}}) \)
and the plane \( \vec{r} \cdot(\hat{\boldsymbol{i}}-\boldsymbol{2} \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}})=\mathbf{0} \)


The correct relationship between free energy change in a reaction and the
corresponding equilibrium constant, \( \boldsymbol{K} \)
is:
A \( \cdot \Delta G^{o}=-R T \ln K \)
В. \( \Delta G=R T l n K \)
c. \( \Delta G=-R T \ln K \)
D. \( \Delta G^{o}= \) R TlnK


From the following 3 solids of the same shape and same volume which one has
the highest inertia?
A. steel
B. Woodd
c. Aluminium
D. None of the above


The grid below is shaded to represent fraction. What fraction of the grid is
shaded?
A \( \cdot \frac{1}{20} \)
B. 1 5
\( c \cdot \frac{1}{4} \)
D. 1


In the following circuit the value of total resistance between \( X \) and \( Y \) in ohm is
A. \( (1+\sqrt{3}) R \)
B. \( (\sqrt{3}-1) R \)
\( c \)
D. 50


Four equal circles each of radius \( a \)
units touch one another. the area
enclosed between them in square units,
is \( \left(\operatorname{take} \pi=\frac{22}{7}\right) \)
\( A \cdot 3 a^{2} \)
B. \( \frac{6 a^{2}}{7} \)
c. \( \frac{41 a^{2}}{7} \)
D. \( \frac{a^{2}}{7} \)


The secondary alkyl halide is called as
secondary because:
A. the functional group attached to primary carbon atom
B. the functional group attached to secondary carbon atom
C. the functional group attached to tertiary carbon atom
D. the functional group is attached to secondary noncarbon atom


Assertion
Following is not a suitable technique for
the preparation of shown alkane
product.
\[
\mathbf{2} \boldsymbol{H}_{3} \boldsymbol{C}-\underset{\boldsymbol{C} \boldsymbol{H}_{3}}{\boldsymbol{C}-\boldsymbol{C l}}+\boldsymbol{N a} \frac{\boldsymbol{T} \boldsymbol{H} \boldsymbol{F}}{\boldsymbol{H e a t}} \boldsymbol{H}_{3} \boldsymbol{C}-
\]
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{3} \)
\[
\begin{array}{l}
c-C-C H_{3} \\
C H_{3} C H_{3}
\end{array}
\]
Reason
Above mentioned reaction involves a
highly unstable tertiary carbanion
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 wrong but reason is correct


Form the differential equation
corresponding to \( \boldsymbol{y}=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x},(\boldsymbol{a}, \boldsymbol{b}) \)


Water in a closed tube is heated with
one arm vertically placed above a lamp. Water will begin to circulate along the tube in counter-clockwise direction.
A. True
B. False


11
İ Compound (C) [ Isomer of (A)]
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)


A capacitor of capacitance \( 0.1 \mu F \) is
connected to a battery of emf \( 8 \mathrm{V} \) (as shown in Figure) under the steady-state
condition.


An organic acid \( \boldsymbol{A}\left(\boldsymbol{C}_{5} \boldsymbol{H}_{10} \boldsymbol{O}_{2}\right) \) reacts
with \( B r_{2} \) in presence of phosphorus to produce a resolvable compound B. B on dehydrobromination yields C. C does not show geometrical isomerism and on decarboxylation gives an alkene D. D on ozonolysis gives \( \mathrm{E} \) and \( \mathrm{F} \). Compound \( \mathrm{E} \) gives positive Schiff's test but F does not. Give structures of \( A \) to \( F \)


If \( z \) is uni modular complex number \( \frac{1+z}{1+\bar{z}} \) is equal to?
A. \( \bar{z} \)
в. \( y+i x \)
c. \( y-i x \)
D.


\( \mathbf{f}\left(\mathbf{1}+\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{x}^{2}\right)^{4}=\boldsymbol{a}_{\mathbf{0}}+\boldsymbol{a}_{1} \boldsymbol{x}+ \)
\( a_{2} x^{2}+\ldots \ldots . .+a_{8} x^{8}, \) where
\( a, b, a_{0}, a_{1}, \dots \dots a_{8} \in R \) such that \( a_{0}+ \)
\( a_{1}+a_{2} \neq 0 \) and \( \left|\begin{array}{lll}a_{0} & a_{1} & a_{2} \\ a_{1} & a_{2} & a_{0} \\ a_{2} & a_{0} & a_{1}\end{array}\right|=0, \) then
the value of \( \frac{\mathbf{5} a}{b} \) is


At a certain location in Africa, a
compass points \( 12^{\circ} \) west of the
geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian
points \( 60^{\circ} \) above the horizontal. The
horizontal component of the earth's field is measured to be 0.16 G. Specify the direction and magnitude of the earth's field at the location.


Penicillin is a/an:
A. hormone
B. antibiotic
c. antipyretic
D. vitamin


Find the square of \( 3 a+7 b \)
\( \mathbf{A} \cdot 9 a^{2}+42 a b+49 b^{2} \)
B \( \cdot 9 a^{2}+40 a b+49 b^{2} \)
C \( \cdot 18 a^{2}+42 a b+98 b^{2} \)
D. \( 18 a^{2}+40 a b+98 b^{2} \)


\( \boldsymbol{f}(\boldsymbol{x})=(\sin \boldsymbol{x}+\cos \boldsymbol{x}) \) Find \( \boldsymbol{f}^{\prime}(\boldsymbol{x}) \)


Dead space air in man is
A. \( 500 \mathrm{mL} \)
B. 150 \( \mathrm{mL} \)
c. 250 \( \mathrm{mL} \)
D. 1.5 L


The electric field just outside the surface of conductor of area \( \boldsymbol{A} \) and
surface charge density \( \sigma \) is given by
A \( \cdot \frac{\sigma}{3 \epsilon_{0}} \)
в. \( \frac{\sigma}{2 \epsilon_{0}} \)
c. \( \frac{\sigma}{\epsilon_{0}} \)
D. \( \frac{2 \sigma}{\epsilon_{0}} \)


A first order reaction was commenced
with \( 0.2 \mathrm{M} \) solution of the reactants. If
the molarity of the solution falls to \( 0.02 M \) after 100 minutes the
rate constant of the reaction is:
A \( \cdot 2 \times 10^{-2} \min ^{-1} \)
В. \( 2.3 \times 10^{-2} \min ^{-1} \)
c. \( 4.6 \times 10^{-2} \min ^{-1} \)
D. \( 2.3 \times 10^{-1} \min ^{-1} \)


Form the differential equation
corresponding to \( y=e^{m x} \) by
eliminating \( \boldsymbol{m} \)


Which of the following combination are
correct?
A . Fluorspar, \( F e C O_{3} \)
B. Zinc blende, ZnO
c. Magnesite, Oxide ore
D. cryolite, Halide ore


The angle between the incident ray and the reflecting surface is known as:
A. glancing angle of incidence
B. angle of incidence
c. glancing angle of reflection
D. angle of reflection


3
incident at an angle \( \alpha=30^{\circ} \) with the
normal to the slit plane in Young's double-slit experiment. Assume that
the intensity due to each slit at any
point on the scree is \( I_{0} . \) Point \( O \) is
equidistant from \( S_{1} \) and \( S_{2} \). The
distance between slits is 1 mm. Then
This question has multiple correct options
A. the intensity at \( O \) is \( I_{0} \)
B. the intensity at \( O \) is zero
C. the intensity at a point on the screen \( 1 m \) below \( O \) is \( I_{0} \)
D. the intensity at a point on the screen \( 1 m \) below \( O \) is
zero


The total number of sigma bonds in
\( \left(C_{2} H_{6}\right) \) is
A. Four
B. Five
c. \( \operatorname{six} \)
D. Seven


Assertion
Bond dissociation energy of \( \boldsymbol{F}_{2} \)
molecule is less than that of \( C l_{2} \)
molecule.
Reason
Due to inter-electronic repulsion
between \( F \) atom \( , F- \) - \( F \) bond length in \( F_{2} \)
molecule is higher than Cl- -Cl bond
Iength in \( C l_{2} \) molecule

Read the above assertion and reason
and choose the correct option regarding
it.
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


Ortho-nitrophenol is less soluble in
water than para and meta-nitrophenols
because:
A. o- nitrophenol is more volatile in steam than those of \( \mathrm{m}- \) and \( \mathrm{p}- \) isomers.
B. o- nitrophenol shows intramolecular \( H \) -bonding.
C. o-nitrophenol shows intermolecular \( H \) -bonding.
D. none of these


Within the list shown below, the correct
pair of structures of alanine in \( \boldsymbol{p} \boldsymbol{H} \)
range \( 2-4 \) and \( 9-11 \) is:
I. \( \boldsymbol{H}_{3} \boldsymbol{N}^{+} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C O}_{2} \boldsymbol{H} \)
II. \( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right) \boldsymbol{C} \boldsymbol{O}_{2}^{-} \)
III. \( \boldsymbol{H}_{3} \boldsymbol{N}^{+} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C O}_{2}^{-} \)
IV. \( \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{C} \boldsymbol{H}\left(\boldsymbol{C} \boldsymbol{H}_{3}\right) \boldsymbol{C} \boldsymbol{O}_{2} \boldsymbol{H} \)
A . ।, ॥
B. ।, III
c. ॥, ॥ ॥
D. III, IV


Potentiometer measures potential
more accurately because
A. it measures potential in the open circuit.
B. it uses sensitive galvanometer for null deflection.
C. it uses high resistance potentiometer wire.
D. it measures potential in the closed circuit.


Which of the following is/are not
correct?
\( \mathbf{A} \cdot S i O_{2} \) is used as acid flux
B. The distance between the layers in graphite is \( 3.35 \times \) \( 10^{-8} \mathrm{cm} \)
C \( . S i O_{2} \) reacts with \( N a_{2} C O_{3} \) and liberates CO.
D. The hybridization of \( C \) in graphite is \( S p^{2} \).


In laboratory, \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is prepared by the
action of:
A \( \cdot \) cold \( H_{2} S O_{4} \) and \( B a O_{2} \)
B. aqueous alkali on \( N a_{2} O_{2} \)
c. \( M n O_{2} \) and cold \( H_{2} S O_{4} \)
D. dilute \( H C l \) and \( M n O_{2} \)


A liquid enter at point \( A_{1} \) with speed 3.5
\( \mathrm{m} / \mathrm{s} \) and leaves at point \( A_{2} . \) Then find out the height attained by the liquid
above point \( \boldsymbol{A}_{\mathbf{2}} \)
A \( .61 .25 \mathrm{cm} \)
B. \( 51.25 \mathrm{cm} \)
c. \( 41.25 \mathrm{cm} \)
D. \( 71.25 \mathrm{cm} \)


The pair, that referred as 'chemical
twins' is.
\( A \cdot A c, C f \)
B. Hf, Ta
c. Tc, Re
D. La, Acc


Let \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|, \) then
\( \mathbf{A} \cdot f^{\prime}(0)=0 \)
B. \( f(x) \) has a maximum at \( x=0 \)
\( \mathbf{c} \cdot f(x) \) has a minimum at \( x=0 \)
D. \( f(x) \) has no maximum and not minimum


Brain Nurtures
Why do nonmetals not conduct electricity?


The position vector of a particle is \( \vec{r}= \) \( \boldsymbol{a}[\cos \omega \boldsymbol{t} \hat{\boldsymbol{i}}+\sin \omega \boldsymbol{t} \hat{j}] . \) The velocity of the
particle is
A. parallel to position vector
B. directed towards origin
c. directed away from origin
D. perpendicular to position vector


Two copper rods \( P \) and \( Q \) of thickness in
the ratio 2: 5 are taken. If both the rods
\( P \) and \( Q \) of length \( 10 \mathrm{cm} \) are heated to same temperature rise, then the ratio of the linear expansions of \( P \) to that of rod
Q is :
A .2: 5
B. 5: 2
c. 1: 1
D. 4: 1


A stone is dropped into a quiet lake an waves move in circles at the speed of 5 \( \mathrm{cm} / \mathrm{sec} . \) At the instant when the radius of the circular wave is \( 8 \mathrm{cm}, \) how fast is the enclosed area increasing?


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 :
A. \( 0.2 H \)
в. \( 0.4 H \)
\( c .0 .8 H \)
D. \( 0.1 H \)


\( (-8) \times(-4)= \)
\( A \cdot-8 \)
B. -32
\( c \cdot-4 \)
\( D \cdot+32 \)


A source emitting wavelengths \( 480 \mathrm{nm} \) and \( 600 \mathrm{nm} \) is used in YDSE. The
separation between the slits is 0.25 mm. The interference is observed \( 1.5 \mathrm{m} \) away from the slits. The linear separation between first maxima of the
two wavelengths is :
A. \( 0.72 \mathrm{mm} \)
в. 0.72 ст
c. \( 7.2 \mathrm{cm} \)
D. \( 7.2 \mathrm{mm} \)


Inside a hollow conducting sphere:
A. electric field is zero
B. electric field is a non zero constant
C . electric field changes with magnitude of the charge given to the conductor
D. electric field changes with distance from the center of the sphere


Two waves are travelling and
superimposed as a result of this
constructive interference occur
between waves, the two waves
amplitude are:
A. added to produce a larger amplitude
B. subtracted to produce a smaller amplitude.
C . added to produce a smaller amplitude.
D. cancelled out by each other
E. in opposite directions.


Succinate is oxidised to fumarate in
Krebs cycle by
A. Removal of hydrogen
B. Loss of electrons
c. Addition of oxygen
D. Removal of oxygen


Find the value \( : \frac{d}{d x}\left\{\cos x^{0}\right\}=? \)


Assertion
Assertion: A solution of \( N H_{4} C l \) in
water is acidic in nature.
Reason
Reason : Ammoniun ions undergo
hydrolysis to form \( N H_{4} O H \)
A. If both the assertion and reason are true and reason is the correct explanation of assertion.
B. If both the assertion and reason are true but reason is not the correct explanation of assertion
c. If assertion is true but reason is false
D. If both assertion and reason are false


Find \( 10 t h \) and 16 th terms of the G.P.
\( 256,128,64, \dots \dots \)


I ne aata glven in the table snows species richness of mosses, shrubs and trees calculated for one hectare
\( \left(10,000 m^{2}\right) \) of land every 50 years for
200 years based on a long running
ecological study.
\( \begin{array}{llll}\text { Year } & \text { Mosses } & \text { Shrubs } & \text { Trees } \\ 1800 & 16 & 2 & 0 \\ 1850 & 21 & 7 & 4 \\ 1900 & 10 & 5 & 3 \\ 1950 & 13 & 12 & 6 \\ 2000 & 17 & 28 & 14\end{array} \) The ecological process occurring
according to the data is
A. Evolution
B. Succession
c. Destabilization
D. Primary growth
E . Artificial selection


Evaluate:
\( \int_{0}^{\frac{\pi}{2}} \frac{\sin x}{\sin x+\cos x} d x \)


If \( \bar{a}, \bar{b}, \bar{c} \) are unit vectors satisfying the relation \( \bar{a}+\bar{b}+\sqrt{3} \bar{c}=0, \) then the
angle between \( \bar{a} \) and \( \bar{b} \) is
\( ^{A} \cdot \frac{\pi}{6} \)
в.
\( c \cdot \frac{\pi}{3} \)
D.


If \( a, b, c \) are unit vectors, then the
maximum value of \( |\boldsymbol{a}+\mathbf{2 b}|^{2}+\mid \boldsymbol{b}+ \)
\( \left.3 c\right|^{2}+|c+4 a|^{2} \) is
A . 50
B . 21
c. 48
D. 58


The mass of a body
\( \mathbf{A} \cdot \) is slightly different at different places on earth.
B. is independent of the free-fall acceleration.
C. is the same for all bodice of the same volume.
D. can be measured most accurately on a spring scale.


As the electron in the Bohr Orbit of
hydrogen atom passes from state \( \boldsymbol{n}=\mathbf{2} \)
to \( n=1, \) the \( K E(K) \) and \( P E(U) \)
change as
A. \( K \) two-fold, \( U \) also two-fold
B. \( K \) four-fold, \( U \) also four-fold
c. \( K \) four-fold, \( U \) two-fold
D. \( K \) two-fold, \( U \) four-fold


The bleaching agent in paper and textile industry:
A . \( \mathrm{NH}_{3} \)
в. \( \mathrm{H}_{2} \mathrm{O}_{2} \)
\( c \cdot \mathrm{sO}_{3} \)
D. \( \mathrm{Cl}_{2} \)


For the determination of the coefficient
of viscosity of a given liquid, a graph between square of the radius of the spherical steel balls and their terminal
velocity is plotted. The slope of the graph is given by
A \( \cdot \frac{r^{2}}{v} \)
в. \( \frac{v^{2}}{r} \)
c. \( _{\frac{v}{r}} \)
D. \( \frac{v}{r^{2}} \)


The range of \( f(x)=\cos ^{2} x+\sec ^{2} x \) is
\( [a, \infty] \) Find a


Give the decreasing order of nucleophilic addition reaction of the
following:
(i) \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \)
PhCHO
(iii) Chloral \( \left(\mathbf{C l}_{3} \mathbf{C}-\mathbf{C H}=\mathbf{O}\right) \)
Acetophenone
A \( .(i i i)>(i)>(i i)>(i v) \)
B. \( (i v)>(i i)>(i)>(i i i) \)
C. \( (i)>(i i i)>(i i)>(i v) \)
D. \( (i i i)>(i)>(i v)>(i i) \)


To which of the following the angular velocity of the electron in the n-th Bohr orbit is proportional?
\( \mathbf{A} \cdot n^{2} \)
в. \( \frac{1}{n^{2}} \)
c. \( \frac{1}{n^{\frac{3}{2}}} \)
D. \( \frac{1}{n^{3}} \)


Flowering in pineapple is promoted by
A. NAA
B. GA \( _{3} \)
c. short days
D. Cytokinin


Assertion
The conversion of diamond into
graphite is an endothermic reaction.
Reason
The conversion of diamond into
graphite is kinetically very slow.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


How many total number of optically
active products are formed? The given
compound is (S)-2-chloro-2-
methylbutane


Electric current arises from the flow of
charged particles. Now
This question has multiple correct options
A. In metals it is dominant due to flow of electrons
B. In semiconductors it is jointly due to flow of holes and electrons
C. In electrolytes it is due to flow of negative ions only
D. In discharge tubes containing gases at low pressure it is due to flow of positive ions only


A ball of mass \( 50 g \) moving at a speed of \( 2.0 m / s \) strikes a plane surface at an
angle of incidence \( 45^{\circ} \) The ball is
reflected by the plane at equal angle of reflection with the same speed.
Calculate
(a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the
momentum of the ball


Solve.
(i) \( (-7) \times(-3)= \)
(ii) \( \frac{16}{(-8)}= \)


What is the chemical formula of plaster
of paris?


Find the moment of inertia of a hollow
sphere about a chord that is at a distance of \( 3 \mathrm{m} \) from the centre of the
sphere. The radius of the sphere is \( 5 \mathrm{m} \) and mass \( =10 \mathrm{kg} \)
A. \( 257 k g-m^{2} \)
B . \( 57 k g-m^{2} \)
c. \( 27 k g-m^{2} \)
D. \( 157 k g-m^{2} \)


What happen when water enter into
tissue without being retained in
kidney?


\( 4.6 \mathrm{cm}^{3} \) of methyl alcohol is dissolved in \( 25.2 \mathrm{g} \) of water. Calculate mole fraction of methyl alcohol and water. (Given density of methyl alcohol = \( \mathbf{0 . 7 9 5 2 g c m}^{-\mathbf{3}} \) and \( \boldsymbol{C}=\mathbf{1 2}, \boldsymbol{H}=\mathbf{1}, \boldsymbol{O}= \)
\( \mathbf{1 6}) \)


Show that the middle term in the
expansion of \( (1+x)^{2 n} \) is \( \frac{1.3 .5 \ldots . . .(2 n-1)}{n !} \)
\( 2^{n} x^{n} ; \) where \( n \) is a positive integer.


Which one of the following planets has the largest number of natural
satellites?
A. Jupiter
B. Neptune
c. saturn
D. Uranus


If the ratio of areas of two similar
triangle is 16: 81 find the ratio of their
corresponding sides.


A small rod of bismuth is suspended
freely between the poles of a strong magnet. It is found to arrange itself at right angles to the magnetic field. What is established by the observation?


The ground state electronic
configuration of \( C O \) molecule is:
\( \mathbf{A} \cdot 1 \sigma^{2} 2 \sigma^{2} 1 \pi^{4} 3 \sigma^{2} \)
B \( \cdot 1 \sigma^{2} 2 \sigma^{2} 3 \sigma^{2} 1 \pi^{2} 2 \pi^{2} \)
C \( \cdot 1 \sigma^{2} 2 \sigma^{2} 1 \pi^{2} 3 \sigma^{2} 2 \pi^{2} \)
D. \( 1 \sigma^{2} 1 \pi^{4} 2 \sigma^{2} 3 \sigma^{2} \)


Assertion
Iron is protected from corrosion by connecting magnesium metal with it.
Reason

Iron acts as cathode and magnesium as anode which gradually disappears.
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


Fill in the blank:
When angle of incidence increases, glancing angle of incidence
A. decreases
B. increases
c. remains same
D. becomes zero


Which of the following exhibit covalency only upto \( 4 ? \)
A. Boron
B. Aluminium
c. Thallium
D. Indium


The type of bonds present in \( \boldsymbol{P} \boldsymbol{H}_{4} \boldsymbol{I} \) are:
A . ionic
B. covalent
c. coordinate
D. \( H- \) bond


When \( 25 g \) of \( N a_{2} S O_{4} \) is dissolved in
\( 10^{3} k g \) of solution, its concentration will
be :
A . 2.5 ppm
в. 25 ррт
c. 250 ppm
D. 100 ppm


The value of \( \mu \) is \( 4 \pi \times 10^{-7} H m^{-1} \)
A. True
B. False


Dimension of specific heat is:
A \( \cdot M L T^{-1} K^{-1} \)
B. \( M L^{2} T^{-2} K^{-1} \)
c. \( M^{0} L^{2} T^{-2} K^{-1} \)
D. \( M^{-1} L^{2} T^{-2} K^{-1} \)


Protonsil is converted to a compound
called:
A. sulphapyridine
B. arsphenamine
c. salvarsan
D. sulphanilamide


\( \lim _{x \rightarrow o} \cos (\sqrt{1+x})-\cos \sqrt{x} \)


Which of the following amides will give ethylamine on reaction with sodium hypobromide?
A. Butanamide
B. Propanamide
c. Acetamide
D. Benzamide


Which has the smallest size?
A . \( N a^{+} \)
в. \( M g^{2+} \)
c. \( A l^{3} \)
D. \( P^{5} \)


Balanced chemical equation imply which of the following?
A. Numbers of atoms are conserved in a chemica change
B. Numbers of molecules are conserved in a chemica change
c. volume is conserved in a chemical change
D. 'A' and 'B'
E . 'B' and 'C'


A ball is thrown vertically upward with a speed of \( 25.0 \mathrm{m} / \mathrm{s} \). How long does the ball take to hit the ground after it reaches its highest point?
A . \( 2.5 s \)
B. \( 3 s \)
c. \( 4 s \)
D. \( 2 s \)


The value of \( \lim _{n \rightarrow \infty} \frac{(n !) \frac{1}{n}}{n} \) is?
\( \mathbf{A} \cdot \mathbf{1} \)
в. \( \frac{1}{e^{2}} \)
c. \( \frac{1}{2 e} \)
D.


Assertion: For the extraction of iron,
haematite ore is used.

Reason: Haematite is a carbonate ore
of iron.
A. Only the reason is correct.
B. Both the assertion and reason are correct and the reason is the correct explanation for the assertion.
C. Only the assertion is correct.
D. Both the assertion and reason are correct, but the
reason is not the correct explanation for the assertion.


Which of the following is/are the reason of the irreversibility of process? This question has multiple correct options
A. Friction
B. Heat transfer through a finite temperature difference
c. Spontaneous mixing of matter of varying composition/states
D. Viscosity and other dissipative effects


The eye can be regarded as a single refracting surface. The radius of this surface is equal to that of cornea (7.8 \( \mathrm{mm} \) ). This surface separates two media of refractive indices 1 and 1.34 . Calculate
the distance from the refracting surface
at which a parallel beam of light will
come to focus.
A . \( 2 \mathrm{cm} \)
B. \( 1 \mathrm{cm} \)
c. \( 3.1 \mathrm{cm} \)
D. 4.0 \( \mathrm{cm} \)


If \( (a, b)(c, d) \) and \( (a-c, b-d) \) are collinear
then
A \( \cdot \frac{a}{b}=\frac{c}{d} \)
в. \( \frac{a}{d}=\frac{b}{c} \)
c. \( \frac{a}{c}=\frac{d}{b} \)
D. \( \frac{a}{b}=\frac{b}{c} \)


When a graph is plotted between \( \log x / m \) and \( \log p, \) it is a straight line
with an angle \( 45^{\circ} \) and intercept 0.3010
on y-axis. If the initial pressure is 0.3
atm, what will be the amount of gas adsorbed per gram of the adsorbent?
A . 0.4
B. 0.6
c. 0.8
D. \( 0 . \)


In the synthesis of n-alkyl tert-alkyl ether by Williamson's method the reactants used are:
B. \( 1^{\circ} R X \) and \( 3^{\circ} \)RONa
\( \mathrm{c} \cdot 3^{\circ} R X \) and \( 3^{\circ} R O N a \)
D. \( 1^{\circ} R X \) and \( 1^{\circ} R O N a \)


The transition from from the state \( n= \)
5 to \( n=1 \) in a hydrogen atom results in
\( U V \) radiation. Infrared radiation will be
obtained in the transition.
\( \mathbf{A} \cdot 2 \rightarrow 1 \)
B . \( 3 \rightarrow 2 \)
c. \( 4 \rightarrow 3 \)
\( \mathbf{D} \cdot 6 \rightarrow 2 \)


Plagioclimax is climax of plagiosere
which means
A. Sere of marine plants
B. Deflected sere resulting in deviation of plant succession from natural course due to human activity
c. Sere where plant succession deviates from its natural course due to human activity
D. Both B and C


Shapes of certain interhalogen
compounds are stated below. Which one of them is not correctly stated?
A. \( B r F_{3} \) : Planar T-shaped
B. \( I C l_{3}: \) Planar dimeric
C. \( I F_{7} \) : Pentagonal bipyramid
D. \( B r F_{5} \) : Trigonal bipyramid


toppr 5
Q Type your question_
\( \mathbf{A} \)
Reactance
\( B \)
Reactance
\( c \)
Reactance
D. Reactance


Find the amount on a deposit of Rs. \( 2100, \) earning \( 4 \% \) interest compounded
quarterly for 2 years.


If all the vegetation in the pond died,
what effects would it have on the
animals? Why?


How many '\alpha' and' \( \beta \) '-particles will be emitted when \( _{90} T h^{234} \) changes into \( 84 P o^{218} ? \)


Which of the following statements are
correct?
A. Poisson's ratio can be greater than 0.5
B. Poisson's ratio is a characteristic property of the material of the body
C. Poisson's ratio of a body depends upon its shape and size
D. None of these


If \( n \epsilon N>1 \), then the sum of real part of
roots of \( z^{n}=(z+1)^{n} \) is equal to
A \( \cdot \frac{n}{2} \)
в. \( \frac{(n-1)}{2} \)
\( c \cdot-\frac{n}{2} \)
D. \( \frac{(1-n)}{2} \)


The cost price of 30 chairs is equal to
the selling price of 25 chairs. Find the gain percent.


The characteristic spectrum of an atom is observed as
A. Pure line spectrum
B. Emission band spectrum
c. Absorption line spectrummmmmm
D. Absorption band spectrum


Evaluate: \( \int \frac{\sec ^{8} x}{\operatorname{cosec} x} d x \)


A current-carrying ring is placed in a magnetic field. The direction of the field is perpendicular to the plane of the ring This question has multiple correct options
A. there is no net force on the ring
B. the ring will tend to expand
c. the ring will tend to contract
D. either
(b) or
(c) depending on the directions of the current in the ring and the magnetic field


Two long thin parallel conductors of the
shape shown in figure above carry
direct currents \( I_{1} \) and \( I_{2} \). The separation
between the conductors is \( a \), the width
of the right-hand conductor is equal to \( b \)
With both conductors lying in one
plane, the magnetic interaction force between them reduced to a unit of their length is given as \( F_{1}=\frac{\mu_{0} I_{1} I_{2}}{x \pi b} \ln \frac{a+b}{a} \)
Find \( \boldsymbol{x} \)


For a very dilute aqueous solution of
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right], \) van't Hoff factor is :
\( \mathbf{A} \cdot i=11 \)
в. \( i=5 \)
\( c \cdot_{i}=\frac{1}{11} \)
D. \( i=10 \)


An element has electronic configuration \( (2,8,8,1), \) then the element will be:
A. non-metal
B. metal
c. metalloid
D. noble gas


Which one of following statements
related to center of gravity is incorrect?
A. The center of gravity of an object is defined as point through which its whole weight appears to act.
B. The center of gravity is sometimes confused with center of mass.
C. The center of gravity always lies inside object.
D. For an object placed in a uniform gravitational field, center of gravity coincides with center of mass.


Product \( (A) \) is?
\( A \)
\( B \)
\( c \)
\( D \)


Number of increasing permutations of
\( m \) symbols are there from the \( n \)
set numbers \( \left\{a_{1}, a_{2}, \ldots, a_{n}\right\} \) where
the order among the numbers is given
by \( \boldsymbol{a}_{1}<\boldsymbol{a}_{2}<\boldsymbol{a}_{3}<\ldots \boldsymbol{a}_{n-1}<\boldsymbol{a}_{n} \) is :


Which contains the greatest number of
oxygen atoms?
A. \( 1 g m \) of oxygen atom
в. \( 1 g \) m of \( O_{2} \)
\( \mathbf{c} \cdot \lg m \) of \( O_{3} \)
D. All have same number of atoms


Five solutions \( A, B, C, D, E \) when
tested with universal indicator showed
\( p H \) as 4,1,11,7 and 9 respectively. Which solution is weakly acidic?
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D . \) D


Correct order of reactivity of following compounds towards Grignard reagent.
\( \mathbf{A} \cdot \mid>\|>\| 1 \)
B. \( \|>1>\| 1 \)
c. \( \|>\|>1 \)
D. \( \mid>\| 1>11 \)


Prove that: \( \cos ^{2} A+\cos ^{2} B+\cos ^{2} C= \)
\( 1-2 \cos A \cos B \cos C \)


The d.r's of the line of intersection of the
planes \( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z}-\mathbf{1}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}+ \)
\( 3 y+4 z-7=0 \) are
A .1,2,-3
в. 2,1,-3
c. 4,2,-6
D. 1,-2,1


Electric flux through a surface of area
100 \( m^{2} \) lying in the xy plane is (in \( V \) m) if \( \overrightarrow{\boldsymbol{E}}=\hat{\boldsymbol{i}}+\sqrt{\boldsymbol{2}} \hat{\boldsymbol{j}}+\sqrt{\boldsymbol{3}} \hat{\boldsymbol{k}} \)
A. 100
B. 141.4
c. 173.2
D. 200


Find the value of \( x \)
\( A, x=6 \)
B . \( x=7 \)
c. \( x=8 \)
\( x=9 \)


If angles of a triangle are in the ratio 2 :
\( 4: 9, \) then the difference of the two
smaller exterior angles of the triangle is:
A \( \cdot 24^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 44^{0} \)
D. \( 60^{\circ} \)


How many of the given below features are associated with members of
chrysophyta?
(a) chief 'producers' in the oceans
(b) Shows photoautrophic nutrition
(c) Zygote develops into an auxospore
(d) From gritty soil
(e) Diatoms may be pennate type or centric type depending upon the
symmetry
A. Three
B. Five
c. Four
D. Two


State whether given statement is True or False :

In conductors electric current can flow
freely.
A. True
B. False


Carbon tetrachloride is inflammable.
A. True
B. False


How \( \boldsymbol{S} \boldsymbol{O}_{2} \) turns lime water milky?


Find the interval of increase and
decrease of the following functions. \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}+\ln (1-\boldsymbol{4} \boldsymbol{x}) \)


The distance between two points
differing in phase by \( 60^{\circ} \) on a wave
having a wave velocity \( 360 m / s \) and frequency \( 500 H z \) is
A . \( 0.72 \mathrm{m} \)
B. \( 0.18 m \)
c. \( 0.12 m \)
D. 0.36 m


In Ruscus, the stem is a
A. Phyllode
B. Cladode
c. offset
D. sucker


One of the soil pollutants is
A. radioactive substances
B. pesticides
C. herbicides
D. all of above


\begin{tabular}{|c|c|}
\hline 0 \\
\( -5 \mathrm{V} \) \\
\hline
\end{tabular}
\( 5 \mathrm{V} \)
0
0
\( -10 \mathrm{V} \)
\( 10 \mathrm{V} \)
\( \log _{10} 10 \)


A biconvex lens made of a transparent material of refractive index 1.25 is
immersed in water of refractive index
1.33. Will the lens behave as a
converging or a diverging lens? Give
reason.


If \( A \) is a diagonal matrix of order \( 3 \times 3 \)
is a commutative with every square
matrix of order \( 3 \times 3 \) under
multiplication and \( \operatorname{tr}(A)=12, \) then the value of \( |\boldsymbol{A}| \) is


A carbohydrate which cannot be hydrolysed to simpler compounds is called:
A. monosaccharide
B. disaccharide
c. polysaccharide
D. oligosaccharide


The number of electrons in the
outermost orbit of carbon atom is
\( A \cdot 3 \)
B. 4
\( c \cdot 6 \)
\( D \)


Write whether the given statement is true or false : The magnetic
susceptibility \( \left(X_{m}\right) \) of a paramagnetic substance has a small negative value.


Base strength of -
\( (i) H_{3} C C H_{2} \)
\( (i i) H_{2} C=C H \)
and \( (\boldsymbol{i} \boldsymbol{i} \boldsymbol{i}) \boldsymbol{H}-\boldsymbol{C} \equiv \boldsymbol{C} \)
is in the order of :
\( A \cdot(\text { i) }>(\text { iii })>(\text { ii }) \)
B. (i) > (ii) > (iii)
\( c . \) (ii) > (i) > (iii)
D. (iii) > (ii) > (i)


Two small beads having positive
charges \( 3 q \) and \( q \) are fixed at the
opposite ends of a horizontal, insulating
rod, extending from the origin to the
point \( \boldsymbol{x}=\boldsymbol{d} . \) As shown in figure, a third
small charged bead is free to slide on
the rod. At what position is the third
bead in equilibrium? Can it be in stable equilibrium?
A \( \cdot \frac{\sqrt{3} d}{(1+\sqrt{3})} \) from \( +3 q \) charge, yes
B. \( \frac{\sqrt{5} d}{(1+\sqrt{3})} \) from \( +3 q \) charge, yes
C \( \frac{\sqrt{3} d}{(1+\sqrt{2})} \) from \( +3 q \) charge, yes
D. \( \frac{\sqrt{2} d}{(1+\sqrt{3})} \) from \( +3 q \) charge, yes


Identify the name of sheep of indian breed shown in image?
A. Deccani sheep breedd
B. Mandya sheep breed
C. Nellore sheep
D. Bakra


Which of the following is not a function of ground tissue in plants?
A. Production of other tissues
B. Supporting the plant
c. storage of water and carbohydrates
D. Transport of materials
E. None of the above


Find the nth term of the A.P.'s:
\( 1.2,2.3,3.4,4.5, \ldots . \)


A wheel with 4 spokes is placed with its
plane perpendicular to a uniform
magnetic field B of magnitude 0.5 T. The
field is directed into the plane of the
paper and is present over the entire
region of the wheel as shown in fig.
When the switch \( \mathrm{S} \) is closed, there is
initial current of 6 A between the axis
and the rim and the wheel begins to
rotate. Resistances of the spokes are 1
2, 4 and \( 8 \Omega \), respectively. Resistance of
rim is negligible. Radius of the wheel is
0.2 \( \mathrm{m} . \) The initial torque acting on the
wheel is \( 6 \times 10^{-x} \) Nm. Find \( x \) than


To move at same speed, a car with flat face and another with streamlined body
will require different amount of force from the engine. The engine of the streamline bodied car will:
A. exert less force
B. exert more force
c. exert zero force
D. exert no force


What is E in the outer region of the second plate?
\( \mathbf{A} \cdot 2 \times 10^{-15} N / C \)
B . \( 5 \times 10^{-10} N / C \)
c. \( 9 \times 10^{-9} N / C \)
D. 0


Which of the following points lie in the solution set?
A \( .(1,1) \)
в. (1,2)
c. (2,1)
()
D. (3,2)


To make \( 50 \mathrm{mL} \) solution of \( K C l \) of \( 1 \mathrm{M} \)
how many grams of \( K C l \) are required to add to this solution?
A \( .1 .00 \mathrm{g} \)
В. \( 1.86 \mathrm{g} \)
c. \( 3.73 \mathrm{g} \)
D. 7.45 g
E . \( 1.49 \mathrm{g} \)


Who first indicated that water is
electron donor in photosynthesis?
A. Arnon
B. Calvin
c. Blakeslee
D. Van Niel.


Which of the following gases released during the preparation of phenol from benzene diazonium chloride:
A. \( N_{2}, C l_{2} \)
в. \( N_{2}, H C l \)
c. \( N O_{2}, C l_{2} \)
D. \( N_{2} O, C l_{2} \)


In a hydrogen atom, the electronjumps from 3 to 2 energy level, the energy released is:
A \( \cdot 3.03 \times 10^{-19} \) Jatom \( ^{-1} \)
В. \( 1.03 \times 10^{-19} \) Jatom\( ^{-1} \)
c. \( 3.03 \times 10^{-18} \) Jatom \( ^{-1} \)
D. \( 6.06 \times 10^{-19} \) Jatom \( ^{-1} \)


Bilirubin and biliverdin are derived from
A. Globin
B. Heme
\( c . \) Iron
D. Fatt


Moses deposited Rs. 850 into the bank in July. From July to December, the amount of money he deposited into the
bank increase by \( 25 \% \) per month. Whats the total amount of money in his
account after December?
A . 6570
в. 7570
\( c .8570 \)
D. 9570


To reverse bias a photo-diode:
A. cathode of the detector is set at a higher electric potential than the anode.
B. anode of the detector is set at a higher electric potential than the cathode.
C. cathode and anode are set at the same electric
potential.
D. none of the above.


Chemically boraxis?
A. sodium metaborate
B. sodium orthoborate
C . sodium tetraborate decahydrate
D. sodium hexaborate.


Give examples for the following
processes.
(i) Condensation
(ii) Evaporation
(iii) Transfer of heat
(iv) Sublimation


Using properties of determinants, prove
the following:
\( \left(\begin{array}{ccc}\mathbf{1} & \boldsymbol{x} & \boldsymbol{x} \\ \mathbf{2} \boldsymbol{x} & \boldsymbol{x}(\boldsymbol{x}-\mathbf{1}) & \boldsymbol{x}(\boldsymbol{x} \boldsymbol{x} \\ \mathbf{3} \boldsymbol{x}(\mathbf{1}-\boldsymbol{x}) & \boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}-\mathbf{2}) & \boldsymbol{x}(\boldsymbol{x}+\mathbf{1})\end{array}\right. \)
\( 6 x^{2}\left(1-x^{2}\right) \)


Which of the following orbitals has the lowest energy?
A . \( 4 d \)
B. \( 4 f \)
c. \( 5 s \)
D. \( 5 p \)


Find the solution of \( \left(\frac{\boldsymbol{x}+\boldsymbol{y}-\boldsymbol{a}}{\boldsymbol{x}+\boldsymbol{y}-\boldsymbol{b}}\right) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{a}}{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{b}} \)
\( ^{\mathbf{A}} \cdot(b-a) \log \left\{(x+y)^{2}-a b\right\}=2(x-y)+k \)
в. \( (b-a) \log \left\{(x-y)^{2}-a b\right\}=2(x+y)+k \)
c. \( (b-a) \log \left\{(x-2 y)^{2}-a b\right\}=2(x-y)+k \)
D. \( (b-a) \log \left\{(x+y)^{2}-a b\right\}=2(x+2 y)+k \)


Arrange the following force of friction in correct ascending order.
A. rolling < sliding < static
B. sliding < static < rolling
c. static < sliding < rolling
D. static < rolling < sliding


How many different nine-digit numbers can be formed from the digits of the number 223355888 by rearrangement of the digits so that the odd digits
occupy even places?

This question has multiple correct options
A . 16
B. 36
c. 60
D. 180


The bar graph as shown in above fig. represents the circulation of
newspapers in 10 languages.
study the bar graph and answer the
following question:
What is the total number of newspapers
published in Hindi, English,Urdu, Punjabi and Bengali?


\( \begin{array}{cc}\boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) \\ 1 & 1 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7 \\ 5 & 9 \\ 6 & 11\end{array} \) For the function in the table above,
calculate \( \boldsymbol{f}(\boldsymbol{3}) \)
A . 5
B. 4
\( c .3 \)
D. 6


During the production of bread, it becomes porous due to the release of
\( C O_{2} \) formed by the action of
A. Yeast
B. Bacteria.
c. virus.
D. Protozoa.


Give reasons for the following. Split rings are used instead of slip rings to construct DC dynamo.


How do you find the valency of chlorine,
sulphur \( \& \) magnesium


What is the shape of each face of a cuboid?
A. Rectangular
B. Circular
c. Hyperbolic
D. Eliptical


Two balls are drawn at random with
replacement from a box containing 10 black and 8 red balls. Find the
probability that both balls are red


Which of the following hydrides is electron deficient?
\( \mathbf{A} \cdot N a H \)
в. \( C a H_{2} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( B_{2} H_{6} \)


Integrate the function \( x \log 2 x \)


Horse head Nebula in Orion are dense
clouds of molecular hydrogen which partially or completely absorb the light from the stars behind them. These are
called
A. planetary nebula
B. dark nebula
c. reflection nebula
D. emission nebula


Find the equation of the line perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive \( x \) -axis
is \( 30^{\circ} \)


A thin spherical conducting shell has
radius \( R \) and charge \( q \). Another charge
\( Q \) is placed at the centre of the shell. The electric potential at a point \( \boldsymbol{P} \) at \( \mathbf{a} \)
distance \( 0.5 d \) from the centre of the
shell is :
A \( \cdot \frac{2(q+Q)}{4 \pi \epsilon_{0} R} \)
в. \( \frac{2(Q-q)}{4 \pi \epsilon_{0} R} \)
c. \( \frac{2 Q+q}{4 \pi \epsilon_{0} R} \)
D. \( \frac{2 Q}{4 \pi \epsilon_{0} R} \)


If \( I \) is the moment of inertia of a
circular ring about a tangent of ring in its plane then the moment of inertia of the same ring about a tangent of ring perpendicular to its plane is:
A \( \cdot \frac{2 I}{3} \)
в. \( \frac{3 I}{2} \)
c. \( \frac{4 I}{3} \)
D. \( \frac{3 I}{4} \)


In the case of the waves from two
coherent sources \( S_{1} \) and \( S_{2}, \) there will
be constructive interference at an
arbitrary point \( P \), the path difference
\( \boldsymbol{S}_{1} \boldsymbol{P}-\boldsymbol{S}_{2} \boldsymbol{P} \) is then
A \( \cdot\left[n+\frac{1}{2}\right] \lambda \)
B. \( n \lambda \)
c. \( \left[n-\frac{1}{2}\right] \lambda \)
D. \( \frac{\lambda}{2} \)


Isomers of pentane:
A. isopentane
B. n-pentane
c. neopentane
D. all of the above


Two concentric thin metallic spheres of
radii \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}\left(\boldsymbol{R}_{1}>\boldsymbol{R}_{2}\right) \) bear charges
\( Q_{1} \) and \( Q_{2} \) respectively. Then the
potential at a radius \( r \) between \( R_{1} \) and
\( \boldsymbol{R}_{2} \) will be \( 1 / 4\left(\pi \varepsilon_{0}\right) \) times:
A. \( \frac{Q_{1}+Q_{2}}{4} \)
в. \( \frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{r} \)
c. \( \frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{R_{2}} \)
D. \( \frac{Q_{1}}{R_{2}}+\frac{Q_{2}}{R_{1}} \)


An AC voltage source \( V=V_{0} \sin \omega t \) is
connected across resistance \( \mathrm{R} \) and
capacitance \( C \) as shown in figure. It is given that \( R=\frac{1}{\omega C} . \) The peak current is
\( I_{0} . \) If the angular frequency of the
voltage source is changed to \( \frac{\omega}{\sqrt{3}} \)
keeping \( R \) and \( C \) fixed, then the new peak current in the circuit is:
A \( \cdot \frac{I_{0}}{2} \)
в. \( \frac{I_{0}}{\sqrt{2}} \)
c. \( \frac{I_{0}}{\sqrt{3}} \)
D. \( \frac{I_{0}}{3} \)


Enlargement of \( \ldots \ldots . . \) causes change in voice in children.
A . Larynx
B. Pharynx
c. Throat
D. Epiglottis


How many molecules of \( C O_{2} \) are
present in one litre of air containing
\( 0.03 \% \) by volume of \( C O_{2} \) at STP?
A . \( 8.066 \times 10^{10} \)
в. \( 8.066 \times 10^{-10} \)
\( c \cdot 8.066 \times 10^{-18} \)
D. \( 8.066 \times 10^{18} \)


A mass of \( 10 k g \) is suspended by a rope
of length \( 4 m, \) from the ceiling. A force \( F \) is applied horizontally at the mid-point of the rope such that the top half of the
rope makes an angle of \( 45^{\circ} \) with the
vertical. Then F equals: (Take \( \boldsymbol{g}= \)
\( 10 m s^{-2} \) and the rope to be massless)
A . \( 70 N \)
B. \( 75 N \)
c. \( 100 N \)
D. \( 90 N \)


Select the mis-matched pair in the
following.
(a) Biomagnification- Accumulation of chemicals at the successive trophic
levels of a food
chain.
(b) Ecosystem- Biotic components of environment
(c) Aquarium- A man-made ecosystem.
(d) Parasites- Organisms which obtain
food from other living organisms.
\( A \cdot(a) \) and \( (b) \)
B. Only (b)
c. \( (a),(b) \) and \( (c) \)
D. Only (d)


The choices below are some of the
proposed steps of a reaction mechanism.
Which step is least likely to be the ratedetermining step of the mechanism?
A. \( J+K \rightarrow J K \)
B. \( 2 J K+4 L \rightarrow 2 J L+2 K L \)
c. \( K L+M N \rightarrow K M+M L \)
D. \( 2 K M \rightarrow K_{2}+2 M \)


Figure shows a potentiometer circuit
for comparison of two resistances. The
balance point with a standard resistor
\( R=10.0 \Omega \) is found to be \( 58.3 \mathrm{cm}, \) while
that with the unknown resistance \( X \) is
\( 68.5 \mathrm{cm} . \) Determine the value of \( \mathrm{X} \). What
might you do if you failed to find a balance point with the given cell of emf
\( \epsilon ? \)


lodine is a non-metal which has
metallic lusture.
A . True
B. False


Image formed by convex mirror is?
A. Virtual
B. Real
c. Enlarged
D. Inverted


\( \underbrace{=}_{i=0} \)


A bus travels \( 120 \mathrm{km} \) in 4 hrs The distance that can be travelled by the
bus in 6 hrs is \( _{-} \)
\( \mathbf{A} \cdot 18 \mathrm{km} \)
B. 140 km
\( c .180 \mathrm{km} \)
D. 120 km


How many histogens are present at the apex of root?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


The value of \( 2 \int \sin x \operatorname{cosec} 4 x d x \) is
equal to:
\( ^{\mathbf{A}} \cdot \frac{1}{2 \sqrt{2}} \ln \left|\frac{1+\sqrt{2} \sin x}{1-\sqrt{2} \sin x}\right|-\frac{1}{4} \ln \left|\frac{1+\sin x}{1-\sin x}\right|+c \)
\( \frac{1}{2 \sqrt{2}} \ln \left|\frac{1+\sqrt{2} \sin x}{1-\sqrt{2} \sin x}\right|-\frac{1}{2} \ln \left|\frac{1+\sin x}{\cos x}\right|+c \)
\( \frac{1}{2 \sqrt{2}} \ln \left|\frac{1-\sqrt{2} \sin x}{1+\sqrt{2} \sin x}\right|-\frac{1}{4} \ln \left|\frac{1+\sin x}{1-\sin x}\right|+c \)
\( \frac{1}{2 \sqrt{2}} \ln \left|\frac{1-\sqrt{2} \sin x}{1+\sqrt{2} \sin x}\right|+\frac{1}{2} \ln \left|\frac{1+\sin x}{\cos x}\right|+c \)


An important reaction of acetone is autocondensation in presence of concentrated sulphuric acid to give the aromatic compound
A . Mesitylene
B. Mesityl oxide
c. Trioxan
D. Phorone


The ion formed when excess ammonia
is added to cupric salt solution is


\( \int \frac{e^{x}}{e^{2 x}+5 e^{x}+6} d x= \)
A \( \cdot \log \left|\frac{e^{x}+2}{e^{x}+3}\right|+c \)
в. \( \log \left|\frac{e^{x}+3}{e^{x}+2}\right|+c \)
c. \( \log \left|\frac{e^{x}-2}{e^{x}-3}\right|+c \)
D. \( \log \left|\frac{e^{x}-3}{e^{x}-2}\right|+c \)


Match the following
\( \begin{array}{ll}\text { A } & \text { B } \\ \text { a. Kingdom } & \text { (i) Amphibia } \\ \text { b. Phylum } & \text { (ii) Animalia } \\ \text { c. Class } & \text { (iii) Chordata } \\ & \text { (iv) Frog }\end{array} \)
ii
\( A \cdot a-i, b-i i, c- \)
B. a- ii, b- iii, c- -i
D. a- ii, b-i, c-iii


Calculate the standard enthalpy for the given reaction.
\( \boldsymbol{C a C O}_{3} \rightarrow \boldsymbol{C a O}+\boldsymbol{C O}_{2} \)
\( \triangle \boldsymbol{H}_{f} \boldsymbol{C a C O}_{3}=\mathbf{1 2 0 6 . 9} \)
\( \triangle \boldsymbol{H}_{f} \boldsymbol{C a O}=-\mathbf{6 3 5 . 1} \boldsymbol{k J m o l} \)
\( \triangle \boldsymbol{H}_{f} \boldsymbol{C O}_{2}=-\mathbf{3 9 3 . 5} \)


The formation of \( S O_{2} \) and \( S O_{3} \)
illustrates the law of:
A. conservation of Mass
B. definite proportions
c. multiple proportions
D. gaseous volumes


For what value of \( \lambda \) is the line
\( (8 x+3 y-15)+\lambda(3 x-8 y+12)=0 \)
parallel to the X-axis?


Match the polymers given in column
with the monomers in column II and
mark the appropriate choice.
\( \mathbf{A} \)
\( (A) \rightarrow(i i),(B) \rightarrow(i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
B. \( (A) \rightarrow(\text { iii) },(B) \rightarrow(i v),(C) \rightarrow(i),(D) \rightarrow( \text { ii) } \)
, (C) \( \rightarrow \) (ii), (D) \( \rightarrow \) (iv)
\( c \)
\( (A) \rightarrow(i),(B) \rightarrow(i i i) \)
\( (A) \rightarrow(i v) \)
\( D \)
\( (\mathrm{B}) \rightarrow(\mathrm{ii}) \)
\( (C) \)
\( \rightarrow \) (iii) (D) \( \rightarrow \) (i)


Draw \( \angle A B C \) of measure \( 120^{\circ} \) and
bisect it.


Which is not an electron carrier?
A. \( \operatorname{col} \)
B. cyt
c. cyt a
D. \( H_{2} O \)


Find the area of the pentagonal park
shown in figure in two different ways.
A \( .600 m^{2} \)
B. \( 800 m^{2} \)
\( c \cdot 60 m^{2} \)
D. \( 600 \mathrm{cm}^{2} \)


Functional kidney of tadpole in Frog is
A. Pronephros
B. Mesonephros
c. Metanephros
D. Archinephros


Assertion
Dipole moment of \( N H_{3} \) is greater than
that of \( N F_{3} \)
Reason
Nitrogen is more electronegative than
fluorine.
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 work done in an adiabatic change in a particular gas depends only upon
A. change in volume
B. change in temprature
c. change in pressure
D. none of these


Find the number of molecules in \( 1 \mathrm{cm}^{3} \)
of an ideal gas at \( 0^{0} C \) and at a
pressure of \( 10^{-5} \) mm of mercury.


Find conjugate: \( -i(9+6 i)(2-i)^{-1} \)


Name the scientist
A) Who discovered the process of
fermentation?
B) Who discovered Germ theory of
disease?
C) Who discovered penicillin?
D) Who developed Vaccine?


Which one of the following does not form sodium bisulphite addition
product with sodium bisulphite
solution?
A. \( C H_{3} C O C H_{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} C H O \)
D. \( C H_{3} C H O \)


Number of elements in 6 th period are:
A . 28
B. 26
\( c \cdot 34 \)
D. 32


\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C O C H}_{3} \) and \( \boldsymbol{C H}_{3} \boldsymbol{O C}_{2} \boldsymbol{H}_{5} \) are
treated with hydroiodic acid.The fragments obtained after reactions are respectively:
A \( \cdot\left(C H_{3}\right)_{3} C I+C H_{3} O H ; C H_{3} I+C_{2} H_{5} O H \)
B. \( \left(C H_{3}\right)_{3} C I+C H_{3} O H ; C H_{3} O H+C_{2} H_{5} I \)
c. \( \left(C H_{3}\right)_{3} C O H+C H_{3} I ; C H_{3} O H+C_{2} H_{5} I \)
D. \( C H_{3} I+\left(C H_{3}\right)_{3} C O H ; C H_{3} I+C_{2} H_{5} O H \)


Among the following, the diamagnetic compound is/ are:
This question has multiple correct options
A. \( N a_{2} O_{2} \)
в. \( O_{3} \)
\( c \cdot N_{2} O \)
D. \( K O_{2} \)


The vector sum of (N) coplanar forces, each of magnitude \( F, \) when each force is making an angle of
\( \frac{2 \pi}{N} \) with that preceding one, is :
\( A \cdot F \)
B. \( \frac{N F}{2} \)
c. \( \mathrm{NF} \)
D. zero


Water evaporates into air from oceans, rivers and lakes but not from the soil.
A. True
B. False


Find \( x, \) If \( \left(\tan ^{-1} x\right)^{2}+\left(\cot ^{-1} x\right)^{2}=\frac{5 \pi^{2}}{8} \)
A . -1
B.
\( c \cdot 0 \)
\( D \)


Solve the following differential equation:
\( \left(y-x y^{2}\right) d x-\left(x+x^{2} y\right) d y=0 \)
A \( \cdot x=c y e^{x y} \)
В. \( y=c x e^{x y} \)
c. \( y=-c x e^{x y} \)
D. \( x=c y e^{-x y} \)


Write the IUPAC name of the following amine.
\( \boldsymbol{H}_{2} \boldsymbol{N}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C}=\boldsymbol{0}-\boldsymbol{C H}_{3} \)


The backbone of DNA is made up of?
A. Sugar only
B. Lipid and phosphate
C. Protein and phosphate
D. Sugar and phosphate


Using properties of deteminants, prove
\[
\operatorname{that}\left|\begin{array}{ccc}
\frac{(\boldsymbol{a}+\boldsymbol{b})^{2}}{\boldsymbol{c}} & \boldsymbol{c} & \boldsymbol{c} \\
\boldsymbol{a} & \frac{(\boldsymbol{b}+\boldsymbol{c})^{2}}{\boldsymbol{a}} & \boldsymbol{a} \\
\boldsymbol{b} & \boldsymbol{b} & \frac{(\boldsymbol{c}+\boldsymbol{a})^{2}}{\boldsymbol{b}}
\end{array}\right|
\]
\( 2(a+b+c)^{3} \)


In chemistry lab class, your teacher asks you to find magnesium oxide, \( M g O, \) to use in the experiment. When you go to the stockroom, you realized there is no magnesium oxide available. Which of the following would be the
most suitable replacement?
A. Sodium oxide, \( N a_{2} O \)
B. Calcium oxide, \( C a O \)
c. carbon dioxide, \( C O_{2} \)
D. silicon dioxide, \( S i O_{2} \)


Assertion
Hydrogen is a diatomic molecule.
Reason
Hydrogen atom has a single electron in its outermost shell.
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 electric current in a circular coil of
two turns produced a magnetic induction of \( 0.2 T \) at its centre. The coil
is unwound and is rewound into a
circular coil of four turns. The magnetic induction at the centre of the coil now
is, in \( T: \)
(if same current flows in the coil)
A . 0.2
B. 0.4
\( c .0 .6 \)
D. 0.8


Which of the following reactions is used to prepare isobutane?
A. Wurtz reaction of \( C_{2} H_{5} B r \)
B. Hydrolysis of n-butylmagnesium iodide
c. Reduction of propanol with red phosphorus and \( H I \)
D. Decarboxylation of 3-methylbutanoic acid


In the circuit diagram shown, \( X_{C}= \)
\( \mathbf{1 0 0 \Omega}, \boldsymbol{X}_{L}=\mathbf{2 0 0 \Omega} \& \boldsymbol{R}=\mathbf{1 0 0 \Omega} . \) The
effective current through the source is:
\( A \cdot 2 A \)
B. \( 2 \sqrt{2} A \)
\( c \cdot 0.5 \mathrm{A} \)
D. \( \sqrt{0.4 A} \)


Statement-1: Both sodium and hydrogen
have outer electronic configuration \( \boldsymbol{n} \boldsymbol{s}^{1} \)
but hydrogen is less reactive than sodium

Statement-2: Hydrogen has greater ionisation energy.
A. Statement-1 is true, Statement-2 is true; Statementis a correct explanation for Statement-
B. Statement-1 is true, Statement-2 is True; Statementis not a correct explanation for Statement-
c. statement-1 is true, statement-2 is false
D. Statement-1 is false, Statement-2 is true


The human body does not produce:
A. Enzymes
B. DNA
c. Vitamins
D. Hormones


What are electrons deficient and
electron rich compounds of hydrogen? Give examples.


(a) Calculate the radii of the first three
Bohr orbits for hydrogen. (Planck's constant \( \boldsymbol{h}=\mathbf{6 . 6 2 6 2} \times \mathbf{1 0}^{-\mathbf{3 4}} \)
Js; mass of electron \( \boldsymbol{m}=\mathbf{9 . 1 0 9 1} \times \)
\( 10^{-31} \mathrm{kg} ; \) charge on electron \( e= \)
\( \mathbf{1 . 6 0 2 1 0} \times \mathbf{1 0}^{-\mathbf{1 9}} \mathbf{C} ; \) permittivity of
vacuum \( \epsilon_{0}=8.854185 \times \)
\( \left.10^{-12} C^{2} N^{-1} m^{-2} .\right) \)
(b) Use these radii to calculate the
velocity of an electron in each of these
three orbits.


Though same current flows the wire and the filament of a bulb, yet only the filament glows.Why?


Find the density of lattice, A compound
AB has a rock type structure with \( A: B= \)
1 : 1. The formula mass of AB is 6.023 Y
amu and the closed \( A \) -B distance is
\( \boldsymbol{Y}^{1 / 3} \mathrm{nm} \)
A \( \cdot 4 \mathrm{kg} / m^{3} \)
в. \( 5 \mathrm{kg} / \mathrm{m}^{3} \)
c. \( 40 \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 50 \mathrm{kg} / \mathrm{m}^{3} \)


When the momentum of a body increases by \( 100 \% \), its K.E. increases by
A . 20\%
B. 40\%
\( c \cdot 100 \% \)
D. 300\%


Evaluate \( \left|\begin{array}{cc}2 \cos \theta & -2 \sin \theta \\ \sin \theta & \cos \theta\end{array}\right| \)


An electric heater is connected to the
voltage supply. After a few seconds,
current get its steady value then its initial current will be?
A. Equal to its steady current
B. Slightly higher than its steady current
c. Slightly less than its steady current
D. zero


The straight chain polymer is formed by
\( \mathbf{A} \cdot \) hydrolysis of \( \left(C H_{3}\right)_{2} S i C l_{2} \) followed by condensation polymerization
B. hydrolysis of \( \left(C H_{3}\right)_{3} \) SiCl followed by condensation polymerization
C . hydrolysis of \( C H_{3} S i C l_{3} \) followed by condensation polymerization
D. hydrolysis of \( \left(C H_{3}\right)_{4} \) Si followed by addition polymerization


The image formed in a periscope is :
A. real with lateral inversion
B. virtual with lateral inversion
c. real without lateral inversion
D. virtual without lateral inversion


What is sexual and asexual
reproduction?


The angle of dip is the angle between:
A. the vertical component of earth's magnetic field and magnetic meridian
B. the vertical component of earth's magnetic field and geographical meridian
C . earth's magnetic field direction and horizontal direction
D. the magnetic meridian and the geographic meridian


Choose the word that is different from
the others in the following and give
reason.
A. Clavicle
B. Skull
c. Femur
D. Ball and socket


The appropriate reagent for the
transformation:
\( \mathbf{A} \cdot Z n(H g), H C l \)
\( \mathbf{B} \cdot N H_{2} N H_{2}, O H^{-} \)
\( \mathbf{C} \cdot H_{2}, N i \)
\( \mathbf{D} \cdot N a B H_{4} \)


State true or false.
Animals like camels walk easily in the desert as broad feet exert great
pressure on the sandy ground.


\( \frac{d \sin x^{2}}{d x} \)
A. \( 2 x \cos x^{2} \)
B . \( 4 x \cos x^{2} \)
c. \( 2 x \sin x^{2} \)
D. \( -2 x \sin x^{2} \)


The displacement of a particle executing simple harmonic motion is
given by \( \boldsymbol{y}=\boldsymbol{A}_{0}+\boldsymbol{A} \sin \omega \boldsymbol{t}+\boldsymbol{B} \cos \boldsymbol{\omega} \boldsymbol{t} \)
Then the amplitude of its oscillation is given by :
\( \mathbf{A} \cdot A_{0}+\sqrt{A^{2}+B^{2}} \)
B. \( \sqrt{A^{2}+B^{2}} \)
c. \( \sqrt{A_{0}^{2}+(A+B)^{2}} \)
D. \( A+B \)


One gram of charcoal adsorbs \( 100 m L \)
of \( 0.5 M C H_{3} C O O H \) to form a
monolayer and thereby the molarity of acetic acid is reduced to \( 0.49 M \)
Calculate the surface area of the
charcoal adsorbed by each molecule of acetic acid. Surface area of charcoal \( = \)
\( 3.01 \times 10^{2} m^{2} / g m \)


A tennis ball hits a vertically well horizontally at \( 10 \mathrm{m} / \mathrm{s} \) bounces back at
\( 10 m / s \)
A \( \cdot \) There is no acceleration because \( 10 \frac{20 m}{s}-10 \frac{20 m}{s}=0 \)
B. There may be an acceleration becouse its initial direction is horizontal
C. There is an acceleration because there is a momentum change
D. Even through there is no change in momentum there is a change in direction. hence it has an acceleration


An obligate anaerobe is
A. Ulothrix
B. Spirogyra
c. Methane bacteria
D. Onion


What are the advantages of water stored in the ground than pond water?
A. It does not evaporate.
B. It spreads out to recharge wells
c. Provides moisture for vegetation over a wide area
D. All of the above.


Which of the following statements
is/are true?
This question has multiple correct options
A. The strength of \( H- \) bond depends upon the polarity of the bond.
B. The extent of \( H- \) bond depends upon the number of sites available for \( H- \) bond.
C. The extent of \( H- \) bond in \( H_{2} O_{2} \) is greater than that in
\( H_{2} O \)
D. The strength of \( H- \) bond in \( H_{2} O_{2} \) is greater than that in \( H_{2} O \)


If \( \left(p^{2}+q^{2}\right)^{3}=\left(p^{3}+q^{3}\right)^{2} \) and \( p q \neq 0 \)
then the value of \( \frac{\boldsymbol{p}}{\boldsymbol{q}}+\frac{\boldsymbol{q}}{\boldsymbol{p}} \) is


Helium is subjected to electrical discharge. The following species is not present in the discharge tube:
\( \mathbf{A} \cdot \mathrm{He}^{+} \)
B. \( \mathrm{He}_{2}^{+} \)
c. \( \mathrm{He}_{2} \)
D. He


If \( A \) and \( B \) are two disjoint sets and \( N \) is
the universal set then \( \boldsymbol{A}^{c} \cup \)
\( \left[(\boldsymbol{A} \cup \boldsymbol{B}) \cap \boldsymbol{B}^{c}\right] \) is
\( A \cdot \phi \)
B. A
\( c . \) в
D.


Assertion
Two different planets can have same escape velocity when their masses and
diameter are same.
Reason
Escape velocity is given as \( \sqrt{2 g R} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A ray of light passing through an equilateral triangular prism gets
deviated at least by \( 30^{\circ} . \) Then, the
refractive index of the material of the
prism must be
\( A \cdot \leq \sqrt{2} \)
B. \( \geq \sqrt{2} \)
\( c \cdot \leq \sqrt{3} \)
\( D \cdot \geq \sqrt{3} \)


Choose the correct answer from the
alternatives given Blood pressure is high in and lowest in
A. Arteries; veins
B. Arteries; ventricles
C. Arteries; relaxed atria
D. Arterioles; veins


What is the secondary suffix for aldehyde?
A . -al
B. - -one
c. - -oic acid
D. -oate


Find standard deviation 50,56,59,60
63,67,68


Let \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{3}, \mathbf{4}\}, \) then
\( \boldsymbol{A} \times \boldsymbol{A}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{1}),(\mathbf{2}, \mathbf{2})\} . \) If
true enter \( 1, \) or else enter 0


Which of the following causes electric
sparks?
A. Wind blowing and shaking electric poles.
B. When amber rubbed with fur.
C. When we take off woollen and polyester clothes.
D. All of the above.


Power of regeneration is lowest in
\( \mathbf{A} \). Brain cell
B. Liver cell
c. Bone cell
D. Muscle cell


How do you calculate the \( p H \) of a
buffered solution?
A. By determining \( K a \), then using \( K a \) to determine the
\( \mathrm{pH} \)
B. By using the equation \( K a=\left[H 3 O^{+}\right]\left[X^{-}\right] /[H X] \)
C. By determining the \( O H^{-} \) concentration.
D. By using the equation \( K a=\left[H 3 O^{+}\right]\left[X^{-}\right] \)
E . By using the equation \( K a=\left[H X^{+}\right]\left[X^{-}\right] /\left[H 3 O^{+}\right] \)


Match the above given table
4. A-3, B-1, C-5, D-2
B. A-1, B-2, C-3, D-4
c. \( A-4, B-1, C-5, D-2 \)
D. A-2, B-1, C-3, D-4


Find the distance of the point (36,15) from origin.


The roots of \( a x^{2}+b x+c=0, \) where
\( a \neq 0, b, c \epsilon R \) are non real complex and
\( a+c<b \). Then
\( \mathbf{A} \cdot 4 a+c>2 b \)
B . \( 4 a+c<2 b \)
c. \( 4 a+c=2 b \)
D. None of these


If the minimum deviation produced by a prism of refracting angle 60 is \( 30, \) then calculate the refractive index of the
material of the prism.
A .2
B. 1.414
c. \( \sqrt{13} \)
D. 4


Distance of chord \( A B \) from the centre of
a circle is \( 8 \mathrm{cm} \). Length of the chord \( A B \)
is \( 12 \mathrm{cm} . \) Find the diameter of the circle


The potential difference between points
\( A \) and \( D \) in the given circuit is:-
\( A \cdot \frac{2}{V} \)
\( B \cdot \frac{8}{0} V \)
\( c \cdot \frac{4}{3} v \)
D. \( 2 V \)


\( C O_{2} \) is not iso-structural with:
A. \( H g C l_{2} \)
в. \( \operatorname{Sn} C l_{2} \)
c. \( C_{2} H_{2} \)
D. \( Z n C l_{2} \)


The atom is indivisible was proposed
by :
A. Rutherford
B. Dalton
\( c . \) Bohr
D. Einstein


Match the columns.
\( \begin{array}{llll}\text { A. } & \begin{array}{l}\text { Obligate stem } \\ \text { parasite }\end{array} & \text { 1. } & \begin{array}{l}\text { Ochroma } \\ \text { lagopus }\end{array} \\ \text { B. } & \text { Erythrina } & \text { 2. } & \text { Coral tree } \\ \text { C. } & \text { Butea } & \text { 3. } & \text { Cuscuta } \\ \text { D. } & \text { Lightest wood } & \text { 4. } & \begin{array}{l}\text { Flame of } \\ \text { the forest }\end{array} \\ & \text { 5. } & \text { Guiacum }\end{array} \)
A. \( A-5, B-4, C-2, D-3 \)
B. \( A-3, B-4, C-3, D-2 \)
C. \( A-3, B-2, C-4, D-1 \)
D. \( A-3, B-2, C-4, D-5 \)


An element \( X \) which occurs in the
second period has an outer electronic
structure \( s^{2} p^{2} . \) The formula and acidbase character of its oxide, respectively
are
A. \( X O_{3} \), basic
B. \( X_{2} O_{3} \), basic
c. \( X_{2} O_{3} \), amphoteric
D. \( X O_{2} \), acidic


Plasma membrane is a semipermeable membrane.
A. True
B. False


The first emission line in the atomic
spectrum of hydrogen in the Balmer series appears at:
A \( \cdot \frac{9 R}{400} c m^{-1} \)
B. \( \frac{7 R}{144} \mathrm{cm}^{-1} \)
\( ^{\mathrm{C}} \cdot \frac{3 R}{4} c m^{-1} \)
D. \( \frac{5 R}{36} c m^{-1} \)


The Bose-Einstein condensate is formed
by:
A. heating a gas of extremely low density, about onehundred-thousandth the density of normal air, to super low temperatures
B. cooling a gas of extremely high density, about onehundred-thousand times the density of normal air, to super low temperatures
C. heating a gas of extremely low density, about onehundred-thousandth the density of normal air, to super high temperatures
D. cooling a gas of extremely low density, about onehundred-thousandth the density of normal air, to super low temperatures


Determine the range of the function \( \boldsymbol{f}(\boldsymbol{x}) \) defined as \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{R}, \boldsymbol{f}(\boldsymbol{x})= \)
\( \boldsymbol{x}^{3}+\mathbf{1}, \) where \( \boldsymbol{A}=\{-\mathbf{1}, \mathbf{0}, \boldsymbol{3}, \mathbf{7}, \boldsymbol{9}\} \)


Find \( : \int \frac{\sin ^{6} x}{\cos ^{8} x} d x \)


What will be the products formed when \( P H_{3} \) reacts with \( A g^{+}(\text {aq.) } ? \)


The given statements describe a group
of organisms.
(i) Instead of a cell wall they have a
protein rich pellicle making their body flexible.
(ii) They have 2 flagella, a short and a
long one.
(iii) They show mixotrophic nutrition.
(iv) They are connecting link between
plants and animals. Which of the following groups is
referred to here?
A. Dinoflagellates
B. Slime moulds
c. Desmids and diatoms
D. Euglenoids


Assertion
When a plane wave passes through a thin prism, the emerging wavefront gets titled.
Reason
Speed of light is less in glass than in air.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


Number of \( K^{+} \) ions and number of
moles of \( K^{+} \) ions present in \( 1 L \) of \( \frac{N}{5} K M n O_{4} \) solution respectively, in acidic medium are :
A \( \cdot 0.04 \) and \( 2.4 \times 10^{2} \)
B . 2.4 \( \times 10^{22} \) and 0.04
c. 200 and \( 6.023 \times 10^{23} \)
D. \( 6.023 \times 10^{23} \) and 200


\( \cos ^{-1}\left\{\cos \left(\frac{5 \pi}{4}\right)\right\} \) is given by
\( ^{\text {A }} \cdot \frac{5 \pi}{4} \)
в. \( \frac{3 \pi}{4} \)
c. \( \frac{-\pi}{4} \)
D. none of these


In an isosceles triangle, the base angles
are equal and the vertex angle is \( 100^{\circ} \) Find the measure of the base angle.


If a magnet is dropped through a vertical hollow copper tube, then?
A. The time taken to reach the ground is longer than the time taken, if the tube was made out of plastic
B. The magnet will get attracted and stick to the copper tube
C. The time taken to reach the ground is longer than the time taken, if the tube was made out of stainless steel
D. The time taken to reach the ground does not depend on the radius of the copper tube
E. The magnet will be repelled away by the tube


What is the effect on the thermion
beam in a cathode ray tube if the anode voltage value is reduced but remains
above zero?


Which of the following statements
about radioactivity is/are true?
This question has multiple correct options
A. It involves outer electrons activity
B. It is not affected by temperature or pressure
C. It is an exothermic process
D. The radioactivity of an element is not affected by any other element compounded by it


The energy taken by system is \( \delta Q, \) work
done by system is \( \delta W \) and increase in
internal energy is \( d U, \) the quantity which does not depend on path is :
\( \mathbf{A} \cdot d U \)
B. \( \delta Q \)
\( \mathbf{c} \cdot \delta Q \& \delta W \)
D. \( \delta W \)


The pH pf a solution is 10 and that of
another is 12. When equal volumes of
these two are mixed, the pH of the resulting solution is
A . 10
B. 12
\( c \cdot 11 \)
D. 10.3010


Equation of a straight line passing through the origin and making an acute
angle with \( x- \) axis twice the size of the
angle made by the line \( y=(0.2) x \) with
the \( x- \) axis, is:
A \( . y=(0.4) x \)
В. \( y=(5 / 12) x \)
c. \( 6 y-5 x=0 \)
D. \( 6 y+5 x=0 \)


Match the hominids with their correct
brain size:
(a) Homo habilis
(i) 900 cc
(b) Homo neanderthalensis
(ii) 1350 сс
(c) Homo erectus
(iii) \( 650-800 \) сс
(d) Homo sapiens
(iv) \( 1400 \mathrm{cc} \)
Select the correct option.
\( A \cdot(a)-(i i i),(b)-(i),(c)-(i v),(d)-(i i) \)
B. (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
c. (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
D. (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)


Rahim takes out all the hearts from the
cards. What is the probability of

Picking out a card that is not a heart.


Catalyst used in dimerisation of
acetylene to prepare chloroprene is:
A. \( H g S O_{4}+H_{2} S O_{4} \)
в. \( C u_{2} C l_{2} \)
c. \( C u_{2} C l_{2}+N H_{4} C l \)
D. \( C u_{2} C l_{2}+N H_{4} O H \)


In the figure given, 0 is the center of the
circle. If \( \angle O B C=37^{\circ}, \) the \( \angle B A C \) is
equal to
A \( \cdot 74^{\circ} \)
B . \( 106^{\circ} \)
\( c \cdot 53^{\circ} \)
D. 37


What is the process of joining together different DNA fragments often referred as?
A. Transcription
B. Cloning
c. Gene splicing
D. DNA amplification


Find the length and foot of the perpendicular from the point \( (\mathbf{7}, \mathbf{1 4}, \mathbf{5}) \) to the plane \( 2 x+4 y-z=2 \)


Four solid rigid balls each of mass \( m \)
and radius \( r \) are fixed on a rigid-ring of
radius \( 2 r \) and mass \( 2 m . \) The system is
whirled about \( ^{\prime} O^{\prime} \) as shown. The radius
of gyration of the system is
\( 128 m r^{2} / 30 . \) how?
A \( \cdot \sqrt{\frac{128}{5}} \)
B.
c. \( r \sqrt{\frac{128}{3}} \)


Phloem loading is
A. Translocation of starch in high concentration in sieve tubes
B. Translocation of raffinose along with only solvents through sieve tubes by apoplastic operation
C. Presence of solutes in sieve tubes without any turgor
pressure
D. Symplastic operation transporting raffinose or stachyose in addition to sucrose


Find \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}, \) where \( \boldsymbol{y}=\log \left(\frac{\boldsymbol{x}^{2}}{\boldsymbol{e}^{2}}\right) \)


Draw an angle of measure \( 135^{\circ} \) and
bisect it.


Write IUPAC name of the given
compound:
\[
\mathbf{C H}_{3}-\underset{\mathbf{C} \mathbf{H}_{3}}{\mathbf{I}} \mathbf{U}-\mathbf{C}_{\mathbf{O H}}-\frac{\mathbf{C} \mathbf{H}_{3}}{\mathbf{C} \mathbf{H}_{3}}-\mathbf{C H}_{3}
\]


At constant pressure, the ratio of
increase in volume for an ideal gas per degree rise in kelvin temperature to its
original volume is :
\( A \)
в. \( \frac{1}{\alpha} \)
c. \( \frac{1}{\sqrt{\alpha}} \)
\( D \cdot \sqrt{\alpha} \)


Why does the bulb glow, when the electric current passes through it?
A. Due to the lighting effect of electric current
B. Due to the magnetic effect of electric current.
c. Due to the chemical effect of electric current
D. Due to the heating effect of electric current


The +3 ion of which one of the following has half filled \( 4 f \) subshell:
A . \( L a \)
в. \( L u \)
\( c . G d \)
D. \( A c \)


The linear density of rod of length \( L \) and placed along x-axis with the lighter and at origin, is given by \( \lambda=B x^{2} \) where \( B \)
is a constant. The the c-ordinates of
centre of mass are
A \( \cdot\left(\frac{3 L}{4}, 0\right) \)
B \( \cdot\left(0, \frac{3 L}{4}\right) \)
c. \( \left(\frac{4 L}{3}, 0\right) \)
D. \( \left(\frac{0,4 L}{3}\right) \)


A wire had a resistance of \( 12 \Omega \). It is bent
in the form ofa circle.The effective resistance between two points on any diameter is
A . \( 3 \Omega \)
B. \( 6 \Omega \)
\( c .12 \Omega \)
D. \( 24 \Omega \)


The compound which is responsible for
the green colour formed when \( S O_{2} \) is
bubbled through acidified potassium dichromate solution is:
A. Nitroso iron \( [I I] \) sulphate
B. Iron \( [I I I] \) chloride
c. Chromium sulphate
D. Lead \( [I I] \) chloride


\( \forall \boldsymbol{n} \in \boldsymbol{N}, \mathbf{1}+\frac{\mathbf{1}}{\sqrt{\mathbf{2}}}+\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}+\ldots \ldots+\frac{\mathbf{1}}{\sqrt{\boldsymbol{n}}} \) is
A \( \cdot \sqrt{n} \)
\( \mathbf{B} \cdot \leq \sqrt{n} \)
\( c \cdot>\sqrt{n} \)
D. none of these


If \( T_{B} \) and \( T_{S} \) are the temperatures of the body and the surroundings and
\( T_{B}-T_{S} \) is of very high value, then the
rate of cooling in natural convection is
proportional to
A \( \cdot T_{B}^{4} \)
в. \( T_{S}^{4} \)
c. \( \quad\left(T_{B}-T_{s}\right)^{\frac{5}{4}} \)
\( ^{\mathrm{D}}\left(T_{B}^{\frac{5}{4}}-T_{S}^{\frac{5}{4}}\right) \)


Optical isomerism arises from the
presence of :
A. A centre of symmetry
B. A line of symmetry
C. An asymmetric carbon atom
D. None of these


is a decrease in the
response to an ongoing stimulus.
A. perception
B. visual accommodation
c. sensory adaptation
D. both (b) and (c)


Terminalisation is related with
A. Mitosiss
B. Meiosiss
c. Diakinesis
D. Telophase


In the following figure, \( \square A B C D \) is a
parallelogram. \( D L \perp A B \) and \( A B=13 \)
\( \mathrm{cm}=A D . \) If the area of parallelogram
is \( 156 \mathrm{cm}^{2} \). Find \( A L \)
\( A \cdot 5 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 7 \mathrm{cm} \)
\( 0.8 \mathrm{cm} \)


There are two opposing views about the origin of modern man. According to one view, Homo erectus in Asia was the
ancestor of modem man. A study of variations of DNA, however, suggested African origin of modern man. What
kind of observation on DNA variations
could suggest this
A. Greater variation in Asia than in Africa
B. Greater variation in Africa than in Asia
c. similar variation in Africa and Asia
D. Variation only in Asia and no variation in Africa


\( O \) is the centre of the circle having
radius \( 5 \mathrm{cm} . O M \perp \) chord \( A B . \) If
\( \boldsymbol{O} \boldsymbol{M}=\mathbf{4} \mathrm{cm}, \) then the length of the
chord \( A B \) is
A. \( 6 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c \cdot 8 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Which of the following statements
¡IIIustrates the law of multiple
proportions?
A. An element forms two oxides, \( \mathrm{XO} \) and \( \mathrm{XO}_{2} \) containing \( 50 \% \) and \( 60 \% \) oxygen respectively. The ratio of masses of oxygen which combines with 1 g of element is 2: 3
B. Hydrogen sulphide contains \( 5.89 \% \) hydrogen, water contains \( 11.1 \% \) hydrogen and sulphur dioxide contains \( 50 \% \) oxygen
C. 3.47 g of \( B a C l_{2} \) reacts with 2.36 g of \( N a_{2} S O_{4} \) to give 3.88 \( \mathrm{g} \) of \( \mathrm{BaSO}_{4} \) and \( 1.95 \mathrm{g} \) of NaCl
D. 20 \( \mathrm{mL} \) of ammonia gives 10 volumes of \( \mathrm{N}_{2} \) and 30
volumes of \( H_{2} \) at constant temperature and pressure


Which of the following metal is famous with magicians for its melting properties?
A. Tellurium
B. Gallium
c. Dysprosium
D. Rhodium


State condition when magnitude of
force on a current carrying conductor placed in a magnetic field is maximum.
A. When current in conductor is parallel to the magnetic field
B. When current in conductor is normal to the magnetic field
c. When current in conductor is acute angled to the magnetic field
D. When current in conductor is obtuse angled to the magnetic field


\( \Delta A B C \) is right angle at \( A(\text { figure }) . A D \) is
perpendicular to BC. if \( \boldsymbol{A B}= \)
\( 5 c m, B C=13 c m, A C=12 c m, \) Find
the area of \( \Delta A B C . \) Also find the length
of AD.


In an L-C-R a.c. circuit at resonance, the
current:
A. is always in phase with the voltage
B. always leads the voltage
C . always lags behind the voltage
D. may lead or lag behind the voltage


Suppose the concentration of hydroxide ion in the cell is doubled, then the cell
voltage will be:
A. Reduced by half
B. Increased by a factor of 2
c. Increased by a factor of 4
D. Unchanged


How many isomers are possible in
\( C_{3} H_{4} C l_{2} \) (including stereo-isomers)?
A .4
B. 6
\( c \cdot 8 \)
D. 10


The following reaction occurs in the Blast Furnace where ion ore is reduced
to iron metal:
\( \boldsymbol{F e}_{2} \boldsymbol{O}_{3}(\boldsymbol{s})+\boldsymbol{3} \boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{2} \boldsymbol{F} \boldsymbol{e}(l)+ \)
\( 3 C O(g) \)
Using Le Chatelier's principle, predict which of the following will not disturb
the equilibrium?
A. Addition of \( F e_{2} O_{3} \)
B. Removal of \( C O_{2} \)
c. Removal of \( \mathrm{CO} \)
D. Addition of \( C O_{2} \)