Two forces each of \( 10 N \) act at an angle
\( 60^{\circ} \) with each other. The magnitude \( \& \) direction of the resultant with respect
to one of the vectors is


Ornithorhynchus is a
A. A fossil bird
B. Duck
C. Monotreme mammal
D. Dinosaur


Which of the following statement is incorrect about order of reaction?
A. Order of reaction is determined experimentally
B. It is the sum of power of concentration terms in the rate law expression
c. It does not necessarily depend on stoichiometric coefficients
D. Order of the reaction can not have fractional value


What is the ethanol ethanoic acid ratio
if the breathalyzer records 1.33 V and other species are at 1 M?
A \( \cdot 10^{4} \)
B . \( 10^{-4} \)
\( c \cdot 10^{12} \)
\( \mathbf{D} \cdot 10^{-12} \)


Which one of the following group of
fungi is sometimes known as "fungal
waste basket".
A. Phycomycetes
B. Ascomycetes
c. Basidiomycetes
D. Deuteromycetes


Draw the tangents to the circle from the
point \( L \) with radius 3 cm. Point \( L \) is at a
distance of \( 8 \mathrm{cm} \) from the centre \( M \)


In the given circuit diagram calculate
the current \( I_{2} \) through the resistor of
\( \mathbf{1 0 \Omega} \)


\( \frac{\mathbf{2} \boldsymbol{x}+\mathbf{1}}{(\boldsymbol{x}-\mathbf{1})\left(\boldsymbol{x}^{2}+\mathbf{1}\right)}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{1}}+\frac{\boldsymbol{B} \boldsymbol{x}+\boldsymbol{c}}{\boldsymbol{x}^{2}+\mathbf{1}} \Rightarrow \frac{\boldsymbol{A}-\boldsymbol{B}}{\boldsymbol{C}}= \)
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
D. 2


The diameter of a solid metallic sphere
is \( 16 \mathrm{cm} . \) The sphere is melted and
recast into 8 equal solid spherical balls. Determine the radius of the ball.


The standard deviation of
1,2,3,4,5,6,7 is?
\( A \cdot 4 \)
B . 2
\( c \cdot \sqrt{7} \)
D. None of the above


Number of simple eyes found in Cockroach is
A. one
B. Two
c. Three
D. Numerous


Monazite sample contains \( 9 \% T h O_{2} \)
and \( 0.35 \% U_{3} O_{8} . P b^{208} \) and \( P b^{208} \) are
the stable end products in the radioactive decay series of \( \boldsymbol{T} \boldsymbol{h}^{238} \boldsymbol{q u a d a n d} \quad \mathbf{2 3 8} \) respectively. All
the lead in monazite is of radiogenic origin.

The isotopic ratio of \( P b^{208} T h^{232} \) was
found to be 0.104 . The half lives of Th
and \( U \) are \( 1.4 \times 10^{10} \) years and \( 4.47 \times \)
\( 10^{9} \) years, respectively. The time elapsed since the formation of monazite sample will be :
A. \( 1.34 \times 10^{9} \) years
B . \( 2.01 \times 10^{9} \) years
c. \( 1.41 \times 10^{10} \) years
D. \( 4.47 \times 10^{9} \) years


Find the median for the following data given below:
\( \begin{array}{llll}\text { class } & 11- & 21- & 31- \\ \text { interval } & 21 & 31 & 41\end{array} \)
Frequencies
A . 35.28
B . 45.28
c. 55.28
D. 65.28


What is green chemistry? Write one importance of green chemistry.


\( A \) is a set containing \( n \) elements. subset \( P \) of \( A \) is chosen at random. The
set \( A \) is reconstructed by replacing the elements of the subset P.A subset Q of
A is again chosen at random. The probability that where \( |\boldsymbol{X}|= \) number of elements in \( \mathbf{X} \)


\( \boldsymbol{n}^{2}+\mathbf{2}^{\boldsymbol{n}} \)


Match the following columns.
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { A. Opuntia } & \text { 1. Stem thorns } \\ \text { B. Asparagus } & \text { 2. Phylloclades } \\ \text { C. Citrus } & \text { 3. Cladodes }\end{array} \)
\( A \cdot A-1, B-2, C-3 \)
B. A- 2, B-3, C-1
C. \( A-3, B-2, C-1 \)
D. A- 2, B-1, C-3


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{lll}\boldsymbol{k}-\boldsymbol{2} \boldsymbol{x}, & \boldsymbol{i} \boldsymbol{f} & \boldsymbol{x} \leq-1 \\ 2 \boldsymbol{x}+\boldsymbol{3}, & \boldsymbol{i f} & \boldsymbol{x}>-1\end{array}\right. \)
If \( f \) has a local minimum at \( x=-1 \)
then the possible value of \( k \) is
A. \( -1 / 2 \)
B. -
\( c \cdot 1 \)
\( D \)


The burning of a piece of magnesium ribbon in air is a chemical change.
Explain.


From Rutherford's \( \boldsymbol{\alpha}- \) particle
scattering experiment give the experimental evidence for deriving the conclusion that:
most of the space inside the atom is
empty.


Three equal charges each \( +q \) are placed (fixed) on the corners of an equilateral triangle of side a. Then, the Coulomb force experienced by one charge due to the rest of the two is :
\( ^{A} \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{a^{2}} \)
В. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{2 q^{2}}{a^{2}} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{\sqrt{3} q^{2}}{a^{2}} \)
D. zero


PQ is the diameter of given circle and
\( \angle P R O=35^{\circ} . \) Then \( \angle R O Q \) equals
being the center):
A \( \cdot 40^{\circ} \)
B. \( 35^{\circ} \)
\( c \cdot 105^{\circ} \)
D. 70


Which reagent is used for the following
conversion?
\( \boldsymbol{R}-\boldsymbol{C H}_{2}-\begin{array}{c}\boldsymbol{C l} \\ \dot{\boldsymbol{C}}-\boldsymbol{R} \longrightarrow \boldsymbol{R}-\boldsymbol{C} \equiv \boldsymbol{C}- \\ \boldsymbol{C l}\end{array}-\boldsymbol{C} \longrightarrow \)
\( \boldsymbol{R} \)
A. Na
в. ая. кон
c. alcoholic KOH followed by NaNHa
D. zn


A string of negligible thickness is
wrapped several times around a
cylinder kept on a rough horizontal
surface. A man standing at a distance \( l \)
from the cylinder holds one end of the string and pulls the cylinder towards him (fig). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is
\( A \)
B . \( 2 l \)
\( c .3 l \)
D. \( 4 l \)


Assertion
A magnetic field exert a force on a
moving charge in the same direction as the direction of field itself
Reason
The direction of force is given by Fleming's left hand rule.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


8
8
0


Cyclopentane belongs to:
A. aromatic compounds
B. heterocyclic compounds
C . alicyclic compounds
D. unsaturated aliphatic compounds


Which of the following statements is
true?
A. Cations are smaller in size than neutral atoms.
B. Horizontal rows in the table are called periods.
C. On going across the periods atomic size of the element decreases.
D. All to the above


Indicate the point of the complex plane
\( z \) which satisfy the following equation. \( z^{2}+|z|=0 \)


In two right triangles one side and an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are
congruent.


In aqueous solution, amino acids
mostly exist as:
A. \( H_{2} N-C H(R)-C O O H \)
в. \( H_{2} N-C H(R)-C O O \)
c. \( H_{3} N^{+}-C H(R)-C O O H \)
D. \( H_{3} N^{+} C H(R)-C O O^{-} \)


Assertion
In case of electric bell if AC power supply is used then its amplitude of the supply must be sufficiently high.
Reason
Due to AC supply there will be continuous magnetization and demagnetization of the magnet
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 Joule) in carrying a charge of 100 coulomb between two points having a potential difference of 10 volt is:
A . \( 0 . \)
B. 10
\( c \cdot 100 \)
D. 1000


Evaluate \( \int_{1}^{2} \frac{2}{x} d x \)


Check whether 13,19,25,31 form
an A.P.


Which of the following statements is
true?
A. The angle of incidence is twice the angle of reflection
B. Angle of incidence + Glancing angle of incidence \( =90^{\circ} \)
C. Some types of virtual images can be caught on the screens.
D. A convex mirror forms real image


Answer the following:
Name the types of Hydrocarbons.


A magnetic needle of negligible breadth
and thickness compared to its length, oscillates in a horizontal plane with a period T. The period of oscillation of each part obtained on breaking the magnet into n equal parts and perpendicular to the length is
A. \( T \)
B. T/n
\( c . T n \)
D. \( 1 / \) Th


The inertia of a moving body makes it:
A. stop due to friction
B. increase its speed
c. decrease its speed
D. resist a change in its state of motion


Choose the correct answers from the
alternatives given :
During protein synthesis, an anticodon on transfer RNA (tRNA) pairs with
A. messenger RNA (mRNA) nucleotide bases
B. ribosomal RNA (rRNA) nucleotide bases
c. other tRNA nucleotide bases
D. DNA nucleotide bases


The number of solutions of
\( \sin ^{-1}\left(1+b+b^{2}+\ldots . \infty\right)+\cos ^{-1}(a- \)
\( \left.\frac{a^{2}}{3}+\frac{a^{3}}{9}+\ldots \infty\right)=\frac{\pi}{2} \)
\( A \)
B . 2
\( c .3 \)
\( D \)


Ptyxis in Cycasis
A. Simple
B. Circular
c. circinate
D. None of the above


Why is the gas with higher critical temperature easily adsorbed on activated alumina?


What will be the loss in potential energy
of chain (mass \( m \) ) when half of its
length is grounded.


A letter is known to have come form
TATANAGAR or CALCUTTA. On the
envelope just two consecutive letters TA are visible. The probability that the letter has come from CALCUTTA is
A \( \cdot \frac{4}{11} \)
в. \( \frac{7}{11} \)
c. \( \frac{1}{22} \)
D. \( \frac{21}{22} \)


The specific latent heat of fusion of
water is :
A. 80 cal \( g^{-1} \)
В. \( 2260 \mathrm{J} g^{-1} \)
c. \( 80 J g^{-1} \)
D. \( 3366 J g^{-1} \)


By how much will the kinetic energy of a body increase if its speed is doubled?
A. 4 times
B. 2 times
c. 8 times
D. 16 times


What is the oxidation state of nitrogen
in \( N_{2} O_{5} ? \)
A. 5
B. 10
\( c \cdot 4 \)
D.


A cathode ray tube has a potential difference of \( V \) volt between the cathode
and the anode. The speed of cathode rays is given by
\( \mathbf{A} \cdot 6 \times 10^{-5} \sqrt{V} \mathrm{cm} / \mathrm{s} \)
B . \( 6 \times 10^{5} \sqrt{V} \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 6 \times 10^{7} \sqrt{V} \mathrm{cm} / \mathrm{s} \)
D \( \cdot 6 \times 10^{3} \sqrt{V} m / s \)


Calgon removes hardness by forming
complex compounds with the \( C a^{2+} \) and
\( M g^{2+} \) ions of hard water or by adsorption.
A. True
B. False


If \( 0<x<y, \) then
\( \lim _{n \rightarrow \infty}\left(y^{n}+x^{n}\right)^{1 / n} \) is equal to:
\( A \)
B.
\( c \cdot y \)
D. None of these


The gate for which output is high, if at least one input is low is
A. NAND
в. NOR
c. AND
D. or


Passive absorption of water from the soil by the root is mainly effected by
A. Typical tissue organisation
B. Respiratory activity of root
c. Tension on cell sap due to transpiration
D. None of the above


An overhead tank having some water
possesses \( \ldots \) mergy.
A. Kinetic
B. Potential
c. Thermal
D. Electrical


Choose the correct answers from the
alternatives given Ectotrophic mycorrhiza is found in
A . Pinus
B. orchids
c. Riccia
D. Ocimum


The hottest region of Bunsen flame shown in the figure below is:
A. region 2
B. region 3
c. region 4
D. region


Enthalpy change of a reaction will be
equal to:
\( \mathbf{A} \cdot \Delta U+P \Delta V \)
B. \( \Delta U+V \Delta P \)
c. \( \Delta U+\Delta(P V) \)
D. \( \Delta U+\left(\Delta n_{g}\right) \Delta(P V) \)


In Lassaignes test when both nitrogen
and
sulphur is present, blood red colour
obtained
is due to the formation
of
A. ferric ferrocyanide
B. ferric thiocyanate
c. ferric cyanide
D. sodium cyanide


If \( y=x^{2} \tan x, \) find \( \frac{d y}{d x} \)


Write the balanced reaction of
ammonia with sulphuric acid.


Determine whether the product of the matrices is defined in each case. If \( s 0 \)
state the order of the product. MN,
where \( \boldsymbol{M}=\left[\boldsymbol{m}_{i j}\right]_{3 \times 1}, \boldsymbol{N}=\left[\boldsymbol{n}_{i j}\right]_{1 \times 5} \)


What is true about the statement "If two
angles are right angles the angles have equal measure" and its converse "If two angles have equal measure then the two angles are right angles"?
A. The statement is true but its converse is false
B. The statement is false but its converse is true
c. Both the statement and its converse are false
D. Both the statement and its converse are true


Let \( S \) be the set of all real numbers
except -1 and let \( ^{\prime} *^{\prime} \) be an operation defined by \( a * b=a+b+a b \) for al
\( a, b \in S . \) Determine whether \( ^{\prime} *^{\prime} \) is a
binary operation on \( S . \) If yes, check its commutativity and associativity. Also, solve the equation \( (2 * x) * 3=7 \)


Another name for a strong electrostatic interaction is :
A. metallic
B. ionic
c. covalent
D. van der Waal


Study the bar graph representing the
number of persons in various age
groups in a town shown in Fig. Observe
the bar graph and answer the following
questions:
What is the total number of persons
living in the town in the age-group 50
\( 55 ? \)


The parallel sides of a trapezium are \( 15 c m \) and \( 9 c m . \) The distance between
them is \( 5 c m \). A rectangle has same area as the trapezium. If its length is \( 10 \mathrm{cm} \) what is its breadth?
A \( .6 \mathrm{cm} \)
в. 3 ст
\( c .5 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Which of the following is not a cyclic compound?
A. Anthracene
B. Pyrrole
c. Phenol
D. Isobutylene


The rating of a fuse connected in the general household lighting circuit is:
\( A \cdot 15 \mathrm{A} \)
B. 5 A
\( c \cdot 10 A \)
D. zero


If the points \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}), \boldsymbol{B}(-\boldsymbol{a},-\boldsymbol{b}) \) and
\( P\left(a^{2}, a b\right) \) are collinear then the ratio in
which \( P \) divides \( \overline{A B} \) is
A \( .1+a: 1-a \)
B. \( 1: a \)
\( c \cdot a: 1 \)
D. \( 1-a: 1+a \)


Histones are present in
A. Cell membrane
B. Lysosomes
c. Nucleosomes
D. Sphaerosomes


Borax is not used?
A. as a styptic to stop bleeding
B. in making enamel and pottery glazes
C . as a flux in soldering
D. in making optical glasses.


Angle inscribed in a semi-circle is
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 3 \)
c. \( \pi / 4 \)
D.


A straight conductor of uniform cross-
section carried a current I. Let
s=specific charge of an electron. The momentum of all the free electrons per
unit length of the conductor, due to their drift velocities only, is
A . Is
B. \( 1 / s \)
c. \( \sqrt{I / s} \)
D. \( (I / s)^{2} \)


The oxidation potential of hydrogen
electrode at \( \mathrm{pH}=10 \) and \( \mathrm{P}_{H_{2}}=1 \) atm is
A . \( 0.51 V \)
в. \( 0.00 \mathrm{V} \)
\( \mathbf{c} .+0.59 V \)
D. \( -0.059 V \)


A compound is a substance composed
of two or more different types of chemically combined in a fixed
proportion.
A. Element
B. Compound
c. Molecule
D. Ion


The vapour pressure of a dilute aqueous
solution of glucose is \( 750 \mathrm{mm} \) Hg at
\( \mathbf{3 7 3} \mathbf{K} \)
Calculate (i) molality, (ii) mole fraction of the solute.
в. 0.078,0.02
\( c .0 .0729,0.0187 \)
7
D. 0.0779,0.3


If one penetrates a uniformly charged solid sphere, the electric field \( E \)
A . increases
B. decreases
c. is zero at all points
D. remains same as at the surface


A simple pendulum with bob of mass \( m \)
and conducting wire of length \( L \) swings
under gravity through an angle \( 2 \theta \). The
earth's magnetic field component in the direction perpendicular to swing is \( B \) The maximum potential difference
induced across the pendulum is:
\( ^{\mathrm{A}} \cdot_{2 B L} \sin \left(\frac{\theta}{2}\right) \sqrt{g L} \)
B. \( \quad B L \sin \left(\frac{\theta}{2}\right) \sqrt{g L} \)
\( ^{\mathrm{c}} \cdot_{B L \sin }\left(\frac{\theta}{2}\right)(g L)^{3 / 2} \)
D. \( \quad B L \sin \left(\frac{\theta}{2}\right)(g L)^{2} \)


Renal physiology was described by
A. Ludwiggsgigg
B. Krebs
c. walter
D. Claude


A car of mass \( 1000 \mathrm{kg} \) moves on a
circular track of radius \( 40 \mathrm{m} \). If the
coefficient of friction is 1.28 then the
maximum velocity with which the car can be moved is:
A. \( 22.4 \mathrm{m} / \mathrm{s} \)
B. \( 112 \mathrm{m} / \mathrm{s} \)
c. \( \frac{(0.64 \times 40)}{(1000 \times 100)} \) m/s
D. \( 1000 \mathrm{m} / \mathrm{s} \)


Calculate the missing frequency \( f \) from
the following distribution, it is being given that the median of the distribution is 24
class \( \begin{array}{ll}0- & 10- \\ 10 & 20\end{array} \) 30 40
25 Frequency


The IUPAC name for given hydrocarbon
is:
A. neononane
B. tetraethylcarbon
c. 2 -ethylpentane
D. 3,3 -diethylpentane


A solution is
\( \mathbf{1 0}^{-4} \mathbf{M} \) in \( \boldsymbol{C l}^{-}, \mathbf{1 0}^{-\mathbf{5}} \boldsymbol{M} \) in \( \boldsymbol{B r}^{-}, \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} \)
is added slowly to the solution. The
minimum concentration of \( \boldsymbol{A} \boldsymbol{g}^{+} \) required to start precipitation of all
three ions is \( 10^{-x} \) then the value of \( x \) is:
\( \left[\text { Given }, \boldsymbol{K}_{s p(A g C l)}=\mathbf{1 0}^{-10}, \boldsymbol{K}_{s p(A g B r)}=\right. \)
\( \left.\mathbf{1 0}^{-\mathbf{1 3}}, \boldsymbol{K}_{s p(\boldsymbol{A g I})}=\mathbf{1 0}^{-\mathbf{1 7}}\right] \)
\( A \cdot 8 \)
B. 14
\( c \cdot 5 \)
D.


Let \( a \) denote the element of the \( i^{t h} \) row
and \( j^{t h} \) column in a \( 3 \times 3 \) matrix and let
\( \boldsymbol{a}_{i j}=-\boldsymbol{a}_{j i} \) for every i and j then this
matrix is an -
A. Orthogonal matrix
B. singular matrix
c. matrix whose principal diagonal elements are all zero
D. skew-symmetric matrix


The reactance of inductance at \( 10^{4} H z \)
is \( 10^{4} \Omega . \) Its reactance at \( 2 \times 10^{4} H z \) will
be:
A \( \cdot 10^{4} \Omega \)
B \( \cdot 2 \times 10^{4} \Omega \)
\( \mathbf{c} \cdot 3 \times 10^{4} \Omega \)
D. \( 4 \times 10^{4} \Omega \)


Find a vector in the direction of a vector
\( \vec{a}=\hat{i}-\widehat{j}+\widehat{k}, \) which has magnitude 8
units.


What is the order of reactivity of the following compounds towards nucleophilic substitution?
\( \langle-\mathbf{C l} \leqslant-\mathbf{C l}(-\mathbf{l})-\mathbf{C l} \)
(I)
\( (\mathbf{I I}) \)
\( (\mathrm{III}) \)
\( (\mathbf{I V}) \)
A. \( I<I I<I I I<I V \)
в. \( I V<I I I<I I<I \)
c. \( I V<I<I I<I I I \)
D. \( I V<I I<I<I I I \)


\( A \) tower of \( x \) meters high has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant
\( y \) meters from the foot of the tower then
the length of the flagstaff in meters is
A \( \frac{y\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} \)
B. \( \frac{x\left(y^{2}+x^{2}\right)}{y^{2}-x^{2}} \)
c. \( \frac{x\left(x^{2}+y^{2}\right)}{x^{2}-y^{2}} \)
D. \( \frac{x\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}} \)


Center of gravity is usually located where
A. less mass is concentrated
B. less weight is concentrated
c. more mass is concentrated
D. more weight is concentrated


Using the method of integration find the area bounded by the curve \( |\boldsymbol{x}|+|\boldsymbol{y}|=\mathbf{1} \)


Ethyl alcohol is treated with chlorine.
The final product obtained is:
A. \( C H_{3} C H O \)
в. \( C C l_{3}- \) СНО
c. \( C H C l_{3} \)
D. \( C C l_{4} \)


Non-metal conducting electicity:
A. diamond
B. graphite
c. lead
D. iron


Emission transitions in the Paschen
series end at orbit \( n=3 \) and start from
orbit \( n \) and can be represented as \( v= \)
\( \mathbf{3} . \mathbf{2 9} \times \mathbf{1 0}^{\mathbf{1 5}}(\mathbf{H z})\left[\mathbf{1} / \mathbf{3}^{\mathbf{2}}-\mathbf{1} / \mathbf{n}^{\mathbf{2}}\right] \)
Calculate the value of \( n \) if the transition
is observed at 1.285 nm. Find the region
of the spectrum.


The study of chemical kinetics becomes highly complicate if there occurs:
This question has multiple correct options
A. reversible reaction
B. side reaction
c. surface reaction
D. none of these


The temperature coefficient of resistance of a wire is \( 0.00125 K^{-1} \). The
resistance of the wire is 1 ohm at \( 300 \mathrm{K} \)
The resistance at \( 1100 \mathrm{K} \) will be:
\( A \cdot 2 \) ohm
B. 2.1 ohm
\( c \cdot 1.4 \) on
D. 1.2 ohm


Write the properties that the relation "is greter that" satisfies in the set of all
positive integers
A. Reflexive
B. Symmetric
c. Antisymmetric
D. Transitive


is prepared on a large seals from water gas.
A. Methanol
B. Ethanal
c. Methane
D. Ethanol


Identify the matrix given below:
\( \left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 2\end{array}\right] \)


Dalton said that elements are
distinguished from each other by :
A. the charge on their ions
B. the density of their solid forms
c. the weights of their atoms
D. the shapes of their atoms


mRNA coded language is known as
A. Cryptogam
B. Cryptoanalysis
c. cryptogram
D. codogens


In given figure \( A B C \) is a triangle in
which \( A B=A C \) and \( D \) is a point on \( A C \)
such that \( B C^{2}=A C \times C D . \) Prove that
\( \mathrm{BD}=\mathrm{BC} \)


For artificial ripening of fruit, which of the following is used?
A. Testosterone
B. Insulin
c. Ethylene
D. Estrogen


Which of the following reactions
proceed at low pressure
\( \mathbf{A} \cdot N_{2}+3 H_{2} \rightleftharpoons 2 N H_{3} \)
\( \mathbf{B} \cdot H_{2}+I_{2} \rightleftharpoons 2 H I \)
\( \mathbf{c} \cdot P C l_{5} \rightleftharpoons P C l_{3}+C l_{2} \)
D. \( N_{2}+O_{2} \rightleftharpoons 2 N O \)


Match the Structure in column-I with
their Common name given in column
II. Matching can be one or more than one.


Consider the below shown reaction.
\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{N} \longrightarrow(\boldsymbol{A}) \)
\( (A)+Z n \longrightarrow(B) \)
If \( (B) \) is a metal, then \( (A) \) and \( (B) \) are, respectively:
A \( \cdot N a_{2}\left[Z n(C N)_{4}\right] \) and \( Z n \)
В. \( \operatorname{Na}\left[A g(C N)_{2}\right] \) and \( A g \)
c. \( N a_{2}\left[A g(C N)_{4}\right] \) and \( A g \)
D. \( N a_{3}\left[A g(C N)_{4}\right] \) and \( A g \)


A heavy particle hanging from a string of length/ is projected horizontally with speed \( \sqrt{g l} . \) The speed of particle at the point where the tension in the string equals weight of the particle is
A \( \cdot \sqrt{2 g l} \)
B. \( \sqrt{3 g l} \)
c. \( \sqrt{g l l 2} \)
D. \( \sqrt{g l / 3} \)


Consider the following nuclear
reactions:
\( 238 M \longrightarrow_{y}^{x} N+2_{2}^{4} H e \)
\( 92^{B} M \)
\( \boldsymbol{y}^{\boldsymbol{x}} \boldsymbol{N} \longrightarrow_{\boldsymbol{B}}^{\boldsymbol{A}} \boldsymbol{L}+\boldsymbol{2} \boldsymbol{\beta}^{+} \)
the number of neutrons present in the
element ' \( L^{\prime} \) is:
A .142
в. 144
c. 140
D. 146


Why oxide \( n \) is a gas but sulphur is solid?


Find the direction cosines of the line:
\( \frac{x-1}{2}=-y=\frac{z+1}{2} \)


Many forests in Jatray's village did not
agree to move away their land and forest. Why? They had to leave even though they did not want to?


Among the oxides of nitrogen:
\( N_{2} O_{3}, N_{2} O_{4} \) and \( N_{2} O_{5} ; \) the
molecule(s) having nitrogen-nitrogen bond is/are:
A. Only \( N_{2} O_{5} \)
B. \( N_{2} O_{3} \) and \( N_{2} O_{4} \)
c. \( N_{2} O_{3} \) and \( N_{2} O_{5} \)
D. \( N_{2} O_{4} \) and \( N_{2} O_{5} \)


\( \mathrm{XeF}_{4} \) and \( \mathrm{XeF}_{6} \) are expected to
be
A. oxidizing
B. reducing
c. unreactive
D. strongly basic


In expansion of \( (1+x)^{3}, \) the second
term is \( 240, \) find \( x \)


\( p H \) of the rain is increased in heavy industrial area due to:
\( A \cdot \) acid rain
B. land pollution
c. water pollution
D. none of the above


The Andromeda Galaxy is
A. 2.3 million light years
B. 3.5 million light years
c. 2 million light years
D. 5.6 million light years


What is Green Chemistry?


In \( P-f \) curve the half power
frequencies are those at which
A \( \cdot P=\frac{P_{\max }}{\sqrt{2}} \)
B. \( P=\frac{P_{\text {max }}}{2} \)
c. \( \quad P=\frac{P_{\max }}{4} \)
D. \( P=P_{\max } \)


The gas \( A_{2} \) in the left flask is allowed to
react with gas \( B_{2} \) presence in right
flask as \( A_{2}(g)+B_{2}(g) \rightleftharpoons \)
\( 2 A B(g) ; K_{c}=4 \) at \( 27^{\circ} C . \) What is the
concentration of \( A B \) when equilibrium is established?
A. 1.33 м
в. 2.66
\( c .0 .66 \)
\( 0.0 .33 \mathrm{m} \)


Zinc sulphate contains \( 22.65 \% \mathrm{Zn} \) and
\( 43.9 \% H_{2} O . \) If the law of constant
proportions is true, then the mass of zinc required to give 40 g crystals will be:
A. 90.68
B. \( 9.06 g \)
c. \( 0.906 \mathrm{g} \)
D. 906 g


Which one of the following methods is
used to prepare \( M e_{3} \) COEt with a good
yield?
A . Mixing EtONa with \( M e_{3} C C l \)
B. Mixing \( M e_{3} C O N a \) with \( E t C l \)
C. Heating a mixture of \( (1: 1) E t O H \) and \( M e_{3} C O H \) in the presence of \( \operatorname{conc} . H_{2} S O_{4} \)
D. Treatment of \( M e_{3} C O H \) with \( E t M g I \)


The vein that does not directly open into the heart is:
A. Pulmonary vein
B. postcaval vein
c. Precaval vein
D. Posterior mesentric vein


Which molecule pair do not have
identical structure
\( \mathbf{A} \cdot I_{3}^{-}, B e F_{2} \)
в. НС го\( , \) \( , \)О О\( _{2} \)
\( \mathbf{c} \cdot B F_{3}, I C l_{3} \)
D. \( B r F_{4}^{-}, X e F_{4} \)


A uniform rod of mass \( m \), length \( L \), area
of cross-section \( A \) is rotated about an
axis passing through one its ends and perpendicular to its length with constant angular velocity \( \omega \) in a
horizontal plane. If \( Y \) is the Young's modulus of the material of rod, the
increase in its length due to rotation of
rod is:
\( ^{A} \cdot \frac{m \omega^{2} L^{2}}{A Y} \)
в. \( \frac{m \omega^{2} L^{2}}{2 A Y} \)
\( ^{\mathbf{C}} \cdot \frac{m \omega^{2} L^{2}}{3 A Y} \)
D. \( \frac{2 m \omega^{2} L^{2}}{A Y} \)


Rest mass of a \( \beta \) particle is
A \( \cdot 1.6 \times 10^{-19} k g \)
В . \( 9.1 \times 10^{-31} k g \)
C. \( 2 \times 10^{2} k g \)
D. \( 1 \times 10^{5} \mathrm{kg} \)


Which one of the following is a unicellular, non-motile desmid?
A. Chromatium
B. cosmarium
c. chlorobium
D. clostridium


Find the perimeter of trapezium if The length of sides of trapezium are
\( 25,11,15,13 c m \)


A girl of mass \( 50 \mathrm{kg} \) standing on a rail road car of mass \( 75 \mathrm{kg} \) moving with velocity \( 20 \mathrm{m} / \mathrm{s} \). Now, the girl begins to run with velocity of \( 10 \mathrm{m} / \mathrm{s} \) with respect to the car in the same direction. as that
of the car. Velocity of the car at this instant will be
A. \( 20 \mathrm{m} / \mathrm{s} \)
B. 24 m/s
\( c \cdot 16 m / s \)
D. \( 18 \mathrm{m} / \mathrm{s} \)


Anodic oxidation of ammonium
hydrogen sulphate produces ammonium persulphate. \( N H_{4} H S O_{4} \rightarrow N H_{4} S O_{4}^{-}+H^{+} \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{S} \boldsymbol{O}_{4}^{-} \rightarrow\left(\boldsymbol{N} \boldsymbol{H}_{4}\right)_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8}+\boldsymbol{2} \boldsymbol{e}^{-} \)
(Anodic oxidation)
\( 2 H^{+}+2 e^{-} \rightarrow H_{2} \) (Cathodic reduction)
Hydrolysis of ammonium persulphate
forms \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
\( \left(N H_{4}\right)_{2} S_{2} O_{8}+2 H_{2} O \rightarrow \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
Current efficiency inn electrolytic process is \( 60 \% \). Calculate the amount of
current required to produce \( 85 g \) of
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) per hour
Hydrolysis reaction shows \( 100 \% \) yield.


f \( 1.0 k \) cal of heat is added to \( 1.2 L \) of \( O_{2} \)
in a cylinder at constant pressure of 1 atm, the volume increase to \( 1.5 L \)
Calculate \( \Delta U \) and \( \Delta H \) of the process
\( (1 L-a t m=100 J) \)


The y-coordinate of second order bright
(maxima) formed on the screen is
A \( .250 \mu m \)
B. \( 500 \mu m \)
\( \mathbf{c} .-250 \mu m \)
\( \mathbf{D} \cdot-500 \mu m \)


A piece of water melon stays cool for a longer time than sandwitches when
both of them are taken out from the
refrigerator on a hot day. Why?


A bacterial colony is produced from
A. A single bacterium by its repetitive division
B. Multiple bacterium without replication
C . Clumping of two to three bacteria
D. A single bacterium without cell division


The given figure shown the Maxwell
distribution of molecular speeds of gas
at three different temperatures \( \boldsymbol{T}_{1}, \boldsymbol{T}_{2} \)
and \( T_{3} . \) The correct order of temperature
is :
\( \mathbf{A} \cdot T_{1}>T_{2}>T_{3} \)
В. \( T_{1}>T_{3}>T_{2} \)
\( \mathbf{c} \cdot T_{3}>T_{2}>T_{1} \)
D. \( T_{2}>T_{3}>T_{1} \)


A man 1.5 m tall walks away from a
lamp post \( 4.5 ~ m \) high at a rate fo \( 4 k m / h r . \) How fast is the farther end of shadow moving on the pavement?
A. \( 4 \mathrm{km} / \mathrm{hr} \)
B. \( 2 \mathrm{km} / \mathrm{hr} \)
\( \mathrm{c} .6 \mathrm{km} / \mathrm{hr} \)
D. \( 5 \mathrm{km} / \mathrm{hr} \)


A person standing on the escalator
takes time \( t_{1} \) to reach the top of a tower
when the escalator is moving. He takes
time \( t_{2} \) to reach the top of the tower
when the escalator is standing. How long will he take if he walks up a moving escalator?
A \( \cdot t_{2}-t_{1} \)
B . \( t_{1}+t_{2} \)
c. \( t_{1} t_{2} /\left(t_{1}-t_{2}\right) \)
D. \( t_{1} t_{2} /\left(t_{1}+t_{2}\right) \)


To some extent viability of pollen grains depends on prevailing temperature and humidity.
A. True
B. False


Assertion
Activity of an enzyme is \( p H \) dependent.
Reason

Changes in \( p H \) affect the solubility of the enzyme in water.
A. If both (A) and (R) are true and (R) is the correct explanation of (A).
B. If both (A) and (R) are true, but (R) is not the correct explanation of \( (A) \)
c. If (A) is correct, but (R) is incorrect.
D. If (A) and (R) are both incorrect


You are required to draw blood from a
patient and to keep it in a test tube for
analysis of blood corpuscles and plasma. You are also produced with the following four types of test tubes. Which of them will you not use for the
purpose?
A. Test tube containing calcium bicarbonate
B. Chilled test tube
c. Test tube containing heparin
D. Test tube containing sodium oxalate


The relation among \( u, v \) and \( f \) for a mirror is:
A \( \cdot f=\frac{u v}{u+v} \)
в. \( v=\frac{f u}{u+f} \)
c. \( _{u=\frac{f v}{f+v}} \)
D. all of these


A conducting sphere of radius r has a
charge. Then:
A. The charge is uniformly distributed over its surface, if there is an external electric field.
B. Distribution of charge over its surface will be non uniform if no external electric field exist in space.
C. Electric field strength inside the sphere will be equal to zero only when no external electric field exists.
D. Potential at every point of the sphere must be same.


Which of the following is not the
characteristics of electromagnetic
wave?
A \( . \) The electric and magnetic fields \( \vec{E} \) and \( \vec{B} \) are always perpendicular to the direction in which the wave is travelling
B. The electric field is always perpendicular to the magnetic field
C. The cross product \( \vec{E} \times \vec{B} \) always gives the direction in which the wave travels
D. The fields do not vary simultaneously


Heavy water violence is formed on
combining \( _{-}--_{-}- \) with


In case of Hall's process applied on
reduction of \( A l_{2} O_{3} \) to \( A l \) can be done by
using:
A. Cathode - Al, Anode - Graphite
B. Cathode - Graphite, Anode - Graphite
c. cathode - Graphite, Anode - steel
D. Cathode - Steel, Anode - Graphite


How are fuels classified ? Give two
examples of each.


Graphite fluoride and graphite oxide are electrically conducting compounds.
A. True
B. False


If \( \theta \) is the angle between two lines
whose d.c.s are \( l_{1}, m_{1}, n_{1} \) and \( l_{2}, m_{2}, n_{2} \)
then the d.cs of one of the angular bisectors of the two lines are
\( ^{\text {A }} \cdot \frac{l_{1}+l_{2}}{2}, \frac{m_{1}+m_{2}}{2}, \frac{n_{1}+n_{2}}{2} \)
B. \( \frac{l_{1}+l_{2}}{2 \cos \left(\frac{\theta}{2}\right)}, \frac{m_{1}+m_{2}}{2 \cos \left(\frac{\theta}{2}\right)}, \frac{n_{1}+n_{2}}{2 \cos \left(\frac{\theta}{2}\right)} \)
c. \( \frac{l_{1}+l_{2}}{\cos \left(\frac{\theta}{2}\right)}, \frac{m_{1}+m_{2}}{\cos \left(\frac{\theta}{2}\right)}, \frac{n_{1}+n_{2}}{\cos \left(\frac{\theta}{2}\right)} \)
D. \( \frac{l_{1}+l_{2}}{2 \sin \left(\frac{\theta}{2}\right)} \frac{m_{1}+m_{2}}{2 \sin \left(\frac{\theta}{2}\right)} \frac{n_{1}+n_{2}}{2 \sin \left(\frac{\theta}{2}\right)} \)


\( o \)
The molecules \( \boldsymbol{C} \boldsymbol{H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C} \boldsymbol{H}_{2}-\stackrel{\boldsymbol{V}}{\boldsymbol{C}}- \)
\( \boldsymbol{O}-\boldsymbol{C}_{2} \boldsymbol{H}_{3} \)
\( \begin{array}{cc}\boldsymbol{O H} & \boldsymbol{o} \\ \text { and } \boldsymbol{C H}_{3}-\dot{\boldsymbol{C}}=\boldsymbol{C H}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\end{array} \)
\( C_{2} H_{5} \) are:
A. geometrical isomers
B. tautomers
c. diastereomers
D. metamers


State whether the statement is true or
false:
Boyle's law is applicable only when mass and temperature are made
variable.


The value of \( \left|\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{b}-\boldsymbol{c} & \boldsymbol{2} \boldsymbol{a} & \boldsymbol{2} \boldsymbol{a} \\ \boldsymbol{2} \boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}-\boldsymbol{a} & \boldsymbol{2} \boldsymbol{b} \\ \boldsymbol{2} \boldsymbol{c} & \boldsymbol{2} \boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a}-\boldsymbol{b}\end{array}\right| \) will
n \( \mathbf{2 C} \)
A \( \cdot(a+b+c)^{2} \)
B \( \cdot(a+b+c)^{3} \)
c. \( (a-b-c)^{2} \)
D \( \cdot(a+b-c)^{2} \)


We feel sleepy just after taking meals because
A. Blood flow increases in the brain
B. Blood flow decreases in the brain
c. Body weight increases
D. we feel lethargic


If \( C u \) reacts with conc. \( H_{2} S O_{4}, \) then
what reactions take place:
A \( . C u \) is oxidised to \( C u^{2} \)
B. \( S O_{4}^{2-} \) is reduced to \( S O_{2} \)
c. Both of the above reactions take place
D. None of the above reaction take place


Let \( \boldsymbol{f}(\boldsymbol{x}) \) be a polynomial in \( \mathbf{x} . \) The
second derivative of \( f\left(e^{x}\right) \) at \( x=1 \) is
\( \mathbf{A} \cdot e f^{\prime \prime}(e)+f^{\prime}(e) \)
В \( \cdot\left(f^{\prime \prime}(e)+f^{\prime}(e)\right) e^{2} \)
c. \( e^{2} f^{\prime \prime}(e) \)
D. \( \left(f^{\prime \prime}(e) e+f^{\prime}(e)\right) e \)


Sulphuric acid is a stronger Bronsted
acid than nitric acid.
If true enter 1 , else enter 0 .


fthree or more parallel lines are intersected by two transversals prove
that the intercepts made by them on the
transversals are proportional


The compound with highest lattice
energy is:
A. \( K B r \)
в. \( N a B r \)
\( \mathbf{c} \cdot L i B r \)
D. \( R b B r \)


A block of mass \( m \) moves with constant
speed down the inclined plane of
inclination \( \theta \). Find the coefficient of
kinetic friction.


The rate of reaction increase by the
increase of temperature because:
A. collision frequency is increased.
B. energy of products decreases.
C. the fraction of molecules possessing energy \( \geq E_{T} \)
(threshold energy) increases.
D. mechanism of a reaction is changed.


Assertion
Ammonium hydroxide solution is added to zinc nitrate solution slowly and then in excess we see white precipitates are soluble
Reason
Ammonium hydroxide solution is added to zinc nitrate solution slowly white precipitates of ammonium nitrate is formed and when ammonium hydroxide is added in excess then the white
precipitates are soluble in 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


Consider the following statements and arrange in the order of true/false as
given in the codes.
\( \mathrm{S}_{1}: \mathrm{Mn}^{2+} \) compounds more stable than
\( \mathrm{Fe}^{2+} \) towards oxidation to their +3
states.
\( \mathrm{S}_{2}: \) Titanium and copper both in the first series of transition metals exhibits
+1 oxidation state most frequently.
\( \mathbf{S}_{3}: \mathbf{C u}^{+} \) ion is stable in aqueous
Solution
A. TTF
B. T F F
\( \mathbf{c} . \) T \( F T \)
D. F FT


The bark of woody plant is dead but the
inner layers inside the bark are living. How do these inner layers get oxygen and release carbon dioxide?
A. Lenticels
B. Stomata
c. Pneumatophores
D. Tendrils


Why are objects electroplated?
A. To protect it from corrosion.
B. To prevent spoilage of objects.
C. To make it appear shining.
D. All of the above


another prism of refractive index \( n_{2} \) are
struck together without a gap as shown,
\( \boldsymbol{n}_{1} \) and \( \boldsymbol{n}_{2} \) depend upon \( \boldsymbol{\lambda} \) the wave
length of light according ton \( _{1}=1.2+ \) \( \frac{10.8 \times 10^{4}}{\lambda^{2}} \) and \( n_{2}=1.45+\frac{1.8 \times 10^{4}}{\lambda^{2}} \)
where \( \lambda \) is in nanometer.
(a)Calculate the wave length \( \lambda_{0} \) for
which rays incident at any angle on the
interface pass through without bending
a the interface.
(b)For light of wave length \( \lambda_{0} \) for which
rays incident on the face \( A C \) such that
the deviated produced by the
combination of the prism is minimum.


\( \begin{array}{ll}\text { List - I } & \text { List - II } \\ \text { 1) Solid in gas } & \text { A) Brass } \\ \text { 2) Solid in solid } & \text { B) Amalgam } \\ \text { 3) Liquid in solid } & \text { C) Camphor in air } \\ \text { 4) Liquid in liquid } & \text { D) Alcohol in water }\end{array} \)
Which of the following is correct?
\( A \cdot 1-C, 2-A, 3-B, 4-D \)
B. \( 1-A, 2-C, 3-D, 4-B \)
C \( \cdot 1-C, 2-B, 3-A, 4-D \)
D. \( 1-D, 2-A, 3-B, 4-C \)


If \( \sin \theta+\sin ^{2} \theta+\sin ^{3} \theta=1, \) then the
value of \( \cos ^{6} \theta-4 \cos ^{4} \theta+8 \cos ^{2} \theta \)
must be-


If true enter 1 , else enter 0
Number of electron pairs in \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \) at
the corners of the square are four
\( A \)


Select the correct statement from the
following.
A. Activated sludge-sediment in settlement tanks of sewage treatment plant is a rich source of aerobic bacteria
B. Biogas is produced by the activity of aerobic bacteria on animal waste.
C. Methanobacterium is an aerobic bacterium found in
rumen of cattle.
D. Biogas, commonly called as gobar gas, is pure methane.


\( B e^{2+} \) is isoelectronic with which of the
following ions?
A . \( H^{+} \)
B . \( L i^{+} \)
\( c \cdot N a^{+} \)
D. \( M g^{2+} \)


Which among the following reactions is an example of instantaneous reaction under normal condition?
A \( .2 H_{2}+O_{2} \rightarrow 2 H_{2} O \)
в. \( N_{2}+O_{2} \rightarrow 2 N O \)
c. \( N a O H+H C l \rightarrow N a C l+H_{2} O \)
D. \( C_{12} H_{22} O_{11}+H_{2} O \rightarrow C_{6} H_{12} O_{6}+C_{6} H_{12} O_{6} \)


The outer proteinaceous coat of a virus
is known as the
A. capsid
B. Viron
c. Cell wall
D. Plasmalemma


Consider the reaction: \( \boldsymbol{F e}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( \boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \)
If the number of electrons lost or gained
during the changes is \( x \). Then, the value
of \( x \) is :


The side of a square is \( 2 \mathrm{cm} \)
Semicircles are constructed outside
the square on two sides of the square. Then area of the whole figure is
\( \mathbf{A} \cdot(4+\pi) \mathrm{cm}^{2} \)
в. \( (4+4 \pi) \mathrm{cm}^{2} \)
c. \( (4+2 \pi) c m^{2} \)
D. \( 4 \pi c m^{2} \)


An ideal transformer has 500 and 5000
turns in primary and secondary winding respectively. If the primary coil is connected to a 6 V battery then
the secondary voltage is :
A. \( 60 v \)
B. Zero
\( c \cdot 0.6 v \)
D. \( 6.0 \mathrm{V} \)


A \( 1-k W \) radio transmitter operates at a
frequency of 880 Hz. How many photons per second does it emit?
A. \( 1.71 \times 10^{21} \)
the \( 1.71 \times 10^{1.11} \)
B . \( 1.71 \times 10^{30} \)
c. \( 6.02 \times 10^{23} \)
D. \( 2.85 \times 10^{26} \)


The correct expression for the rate of
reaction of elementary reaction, \( \boldsymbol{A}+ \)
\( B \rightarrow C \) is :
\( \mathbf{A} \cdot \frac{d[C]}{d t}=K[A] \)
\( \mathbf{B} \cdot \frac{d[C]}{d t}=K[B] \)
\( \mathbf{C} \cdot \frac{-d[A]}{d t}=K[A][B] \)
\( \mathbf{D} \cdot \frac{-d[A]}{d t}=K[A] \)


Show that \( \boldsymbol{A} \cup \boldsymbol{B}=\boldsymbol{A} \cap \boldsymbol{B} \) implies \( \boldsymbol{A}= \)
\( \boldsymbol{B} \)


The radius of the base of a cone is
increasing at the rate of \( 3 \mathrm{cm} / \mathrm{minute} \) and the altitude is decreasing at the rate of \( 4 \mathrm{cm} / \mathrm{minute} . \) The rate of change
of lateral surface when the radius is
\( \mathbf{7} c \boldsymbol{m} \) and altitude \( \mathbf{2 4 c m} \) is
A \( .54 \pi c m^{2} / \) min
B. \( 7 \pi c m^{2} / \) min
\( \mathbf{c} \cdot 27 c m^{2} / \min \)
D. none of these


Removal of top fertile layer of soil by wind or water is called as
A. Leaching
B. Erosion
c. Siltation
D. Weathering


What happens when an inert gas is added to an equilibrium keeping volume unchanged?
A. More product will form
B. Less product will form
c. More reactant will form
D. Equilibrium will remain unchanged


The sounds having frequency of \( 20 \mathrm{Hz} \) to \( 20,000 \mathrm{Hz} \) are
A . Ultrasound
B. Infrasonics
c. Hypersonics
D. Audible Sounds


ff \( i^{2}=-1 \) then the value of \( \sum_{n=1}^{200} i^{2 n} \) is:
A . 50
B . 10
\( c \cdot 0 \)
D. 100


In a horse race there are 18 horses
numbered from 1 to 18. The probability that horse 1 would win is \( \frac{1}{6}, \) horse 2 is \( \frac{1}{10} \) and 3 is \( \frac{1}{8} . \) Assuming a tie is impossible, the chance that one of the
three horses wins the race, is
A. \( \frac{143}{420} \)
B. \( \frac{119}{120} \)
C. \( \frac{47}{120} \)
D. \( \frac{1}{5} \)


List three problems which arise due to construction of big dams. Suggest a
solution for these problems.


Endocrine gland for combating
emergency is
A. Adrenal cortex
B. Adrenal medulla
c. Pancreas
D. Parathyroid


The de Broglie wave present in fifth Bohr orbit is
\( A \)
в.
\( c \)
D.


The pigment found in rods is
A. Rhodopsin
B. Melanin
c. Photosin
D. Keratin


(1) 1,2 -dihydroxybenzene
(II) 1,3 -dihydroxybenzene
(III) 1,4 -dihydroxybenzene
(IV) Hydroxybenzene. The increasing order of boiling points of above mentioned alcohols is:
\( A \cdot|<||<|||<\mid V \)
c. IV < Is II <III
D. IV < || < |< ||


The Brownian movement is due to:
A. temperature fluctuations within the liquid phase
B. attraction and repulsion between charges on colloidal particles
C. impact of molecules of the dispersion medium on colloidal particles
D. convection currents


A species which is capable of showing subvarieties, race or demes is known
as
A. Monotypic
B. Allopatric
c. Polytypic
D. All of the above


Match the following:
What is and


A measuring jar is graduated in \( \mathrm{ml} \) from bottom to top.
A. True
B. False


Which stage of silkworm secretes silk?
A. Adult
B. Larva
c. cocoon
D. Pupa


\( \left|\begin{array}{lll}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \mathbf{1} \\ \boldsymbol{\omega}^{2} & \mathbf{1} & \boldsymbol{\omega}\end{array}\right|=\ldots \)
\( A \)
B.
\( c \cdot 2 \)
D. -1


Lymph drains excess fluid from extracellular space back into
A. Bloodd
B. Lymph node
c. Lymphatic channel
D. Lymph gland


Does short-sightedness (myopia) or long-sightedness (hypermetropia) imply necessarily that the eye has partially lost its ability of accommodation? If not, what might cause these defects of vision?


If three altitudes of a triangle are equal then the triangle is
A . Right angled
B. Equilateral
c. Isosceles
D. Scalene


Out of \( H C l O, H B r O \) and \( H I O \) which
one is most acidic:
A. \( H B r O \)
в. НС СО
c . \( H I O \)
D. All are equally acidic


For hydrogen-oxygen fuel cell at 1 atm
and \( 298 K \)
\( \boldsymbol{H}_{2(\boldsymbol{g})}+\frac{1}{2} \boldsymbol{O}_{2(\boldsymbol{g})} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)} ; \quad \boldsymbol{\Delta} \boldsymbol{G}^{o}= \)
\( -240 k J \)
\( E^{o} \) for the cell is approximately:
\( [\text { Given: } \boldsymbol{F}=\mathbf{9 6}, \mathbf{5 0 0} \boldsymbol{C}] \)
A . \( 1.24 V \)
B . \( 1.26 V \)
c. \( 2.48 V \)
D. \( 2.5 V \)


Gibberellins can promote seed germination because of their influence
on
A. Rate of cell division
B. Production of hydrolyzing enzymes
c. synthesis of abscisic acid
D. Absorption of water through hard seed coat


\( \begin{array}{cc}C_{4} H_{6} O_{4} \stackrel{\Delta}{\longrightarrow} C_{3} H_{6} O_{2} \frac{\text {sodalime}}{\Delta} & C \\ A & B\end{array} \)
Compound ' \( C^{\prime} \) is a hydrocarbon,
occupying approx \( 0.75 L \) volume per
gram. Identify \( ^{\prime} A^{\prime} \) and \( ^{\prime} B^{\prime} \)
A. tartaric acid, propanoic acid
B. Succinic acid, succinic anhydride
C . Maleic anhydride, maleic acid
D. Methyl malonic acid, propanoic acid


Find the angle between the incident ray
and reflected ray.
A \( \cdot 60^{\circ} \)
B. \( 90^{\circ} \)
\( c .80^{\circ} \)
\( D .50 \)


A plane travelling at \( 300 m / s \) banks its wings to enter into a horizontal circular
turn. The circular path has a radius of \( 2.7 k m \)
Which of these values best represents the angle of the wings relative to the horizontal if the plane experiences no change in its altitude during the turn?
A \( \cdot 8^{\circ} \)
B. 16
\( c \cdot 20^{\circ} \)
D. \( 25^{\circ} \)
E \( .32^{\circ} \)


Find five terms in A.P. whose sum is \( 12 \frac{1}{2} \) and the ratio of first to the last
term is 2: 3


A clot of blood contains
A. Prothrombin
B. Fibrinogen
c. Fibrin
D. Thrombin


A wire in the form of a circular loop of radius \( 10 \mathrm{cm} \) lies in a plane normal to a
magnetic field of \( 100 T . \) If this wire is pulled to take a square shape in the same plane in \( 0.1 s, \) find the average induced emf in the loop.
\( \mathbf{A} \cdot 8.99 V \)
B. \( 4.33 V \)
c. \( 7.77 V \)
D. \( 6.74 V \)


A hollow metal sphere of radius \( 5 \mathrm{cm} \) is
charged such that the potential on its surface is 10 volts. The potential at the
centre of the sphere will be:
A . zero
B. 5 volts
c. 10 volts
D. 0.2 volts


\( \frac{3}{4} \) part of radioactive compound undergoes decay in 2h. Calculate its half-life time.
A. 60 min
B. 45 min
\( c .30 \) min
D. 15 min


Which of the following statements are
true? For a particle on the surface of the
earth.
This question has multiple correct options
A. The linear speed is minimum at the equator
B. The angular speed is maximum at the equator
C. The linear speed is minimum at the poles
D. The angular speed is \( 7.3 \times 10^{-5} \) rad \( s^{-1} \) at the equator


Lets consider a thermodynamic system.
If \( \Delta U \) represents the increase in its
internal energy and \( W \) the work done by the system, which of the following statements is true?
A. \( \Delta U=-W \) is an adiabatic process
B. \( \Delta U=W \) in an isothermal process
c. \( \Delta U=-W \) in an isothermal process
D. \( \Delta U=W \) in an adiabatic process


The ratio of densities of two bodies is 5:
6 and their specific heat in the ratio 3 :
5. The ratio of their thermal capacities per unit volume is:
\( A \cdot 25: 18 \)
B. 1:
c. 2:
D. 1:


Let \( \boldsymbol{A}=(\mathbf{1}, \mathbf{2}, \mathbf{2}), \boldsymbol{B}=(\mathbf{2}, \mathbf{3}, \mathbf{6}) \) and \( \boldsymbol{C}= \)
\( (3,4,12) . \) The direction cosines of a line
equally inclined with \( O A, O B \) and \( O C \)
where \( \boldsymbol{O} \) is the origin, are
A \( \cdot \frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, 0 \)
B. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \)
c. \( \frac{1}{\sqrt{3}}, \frac{-1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \)
D. \( \frac{1}{\sqrt{3}}, \frac{-1}{\sqrt{3}}, \frac{-1}{\sqrt{3}} \)


Choose the correct combination of
labelling of stomatal apparatus of dicot
and monocot leaves.
A. a- epidermal cells, b- subsidiary cells, c- chloroplast
d- guard cells, e- stomatal aperture
B. a- epidennal cells, b- guard cells, c- chloroplast, dsubsidiary cells, e- stomatal aperture
C. a- epidermal cells, b- subsidiary cells, c- chloroplast
d- stomatal aperture, e- guard cells
D. a- subsidiary cells, b- epidermal cells, c- chloroplast
d- stomatal aperture, e- guard cells
E. a- guard cells, b- epidennal cells, c- stomatal aperturet, d- subsidiary cells, e- chloroplast


Name the two important groups into
which Kingdom Monera has been divided


\( (\boldsymbol{A})\left(\boldsymbol{C}_{10} \boldsymbol{H}_{6}\right) \frac{\text {Reductiveoroxidative}}{\text {ozonolysis}} \)
\( (B)\left(C_{5} H_{8} O\right) \)
(A) reacts with one equivalent of \( \boldsymbol{H}_{2} / \mathrm{Pd} \) Give all the possible structures of \( (A) \) and (B) if :
Both (A) and (B) are resolvable.


A long-jumper runs before jumping because
A. He covers a greater distance
B. He maintains momentum conservation
c. He gains energy by running
D. He gains momentum


A particle starts from a point \( \boldsymbol{P} \) at a
distance of \( A / 2 \) from the mean position
O \& travels towards left as shown in the
figure. If the time period of \( \mathrm{SHM} \)
executed about \( O \) is \( T \) and amplitude \( A \)
then the equation of motion of particle
is :
\( \mathbf{A} \cdot_{x}=A \sin \left(\frac{2 \pi}{T} t+\frac{\pi}{6}\right) \)
В. \( x=A \sin \left(\frac{2 \pi}{T} t+\frac{5 \pi}{6}\right) \)
\( ^{\mathbf{C}} \cdot_{x}=A \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{6}\right) \)
D. \( x=A \cos \left(\frac{2 \pi}{T} t+\frac{\pi}{3}\right) \)


Ram was going through a forest and found many similar plants. What
amongst the given below could be
reason for the observed phenomenon?
The plants are
A. Of many genera
B. Of only one species
C. Capable of interbreeding
D. Capable of crossbreeding. Select the correct alternative from the
following.
A. A and B
B. B and C
c. \( c \) and \( D \)
D. A and D


2, 2-dimethyl propanol primary alcohol of molecular formula \( C_{5} H_{12} O \) cannot
be prepared from an alkene. If true enter else 0.


Two rings of the same radius \( R \) and
mass \( M \) are placed such that their centres coincide and their planes are perpendicular to each other. The moment of inertia of the system
about an axis passing through the common centre and perpendicular to the plane of one of the rings is:
\( ^{A} \cdot \frac{M R^{2}}{2} \)
в. \( M R^{2} \)
c. \( \frac{3 M R^{2}}{2} \)
D. \( 2 M R^{2} \)


Construct a quadrilateral \( L I F T, \) when:
\( \boldsymbol{L} \boldsymbol{I}=\boldsymbol{4} \boldsymbol{c m}, \boldsymbol{I} \boldsymbol{F}=\boldsymbol{3} \boldsymbol{c m}, \boldsymbol{T} \boldsymbol{L}= \)
\( 2.5 \mathrm{cm}, L F=4.5 \mathrm{cm}, I T=4 \mathrm{cm} \)


The correct floral formula of soyabean is
\( A \)
\( \% \oplus \mathbf{K}_{5} \mathbf{C}_{\mathbf{1}+(2)+2} \mathbf{A}_{(9)+\mathbf{1}} \mathbf{G}_{\underline{\mathbf{1}}} \)
B. \( \% \oplus \mathbf{K}_{(5)} \mathbf{C}_{1+2+(2)} \mathbf{A}_{(9)+1} \mathbf{G}_{\underline{1}} \)
c. \( \% \oplus \mathbf{K}_{(5)} \mathbf{C}_{\mathbf{1}+2+(\mathbf{2})} \mathbf{A}_{\mathbf{1}+(\mathbf{9})} \mathbf{G}_{\underline{\mathbf{l}}} \)
D. \( \% \oplus \mathbf{K}_{(5)} \mathbf{C}_{\mathbf{1}+(2)+2} \mathbf{A}_{(9)+\mathbf{1}} \mathbf{G}_{\mathbf{1}} \)


Find the radius of that circle whose area
is \( 616 \mathrm{cm}^{2}(\text { in } \mathrm{cm} .) \)


Major pollution causing agent is
\( A \cdot \) Man
B. Animals
C. Hydrocarbon gases
D. None of the above


When \( H_{2} S \) is passed into aqueous \( S O_{2} \)
\( \mathbf{A} \cdot H_{2} S \) is converted to yellow precipitate of sulphur
B. \( S O_{2} \) is converted to yellow precipitate of sulphur
C \( . \) a clear solution of \( H_{2} S O_{4} \) is formed
D. \( S O_{2} \) as well as \( H_{2} S \) are converted into a yellow precipitate of sulphur


You invested Rs. 1500 and received Rs.
\( \mathbf{5 0 0 0} \) after three years. What had been
the interest rate?
A. \( 111.11 \% \)
B . \( 222.22 \% \)
c. \( 333.33 \% \)
D. \( 77.77 \% \)


Compare \( \frac{\mathbf{1 9}}{\mathbf{2 0}} \) and \( \frac{\mathbf{1 4}}{\mathbf{2 0}} \)
A \( \cdot \frac{19}{20}=\frac{14}{20} \)
в \( \cdot \frac{19}{20}>\frac{14}{20} \)
c. \( \frac{19}{20} \geq \frac{14}{20} \)
D. \( \frac{19}{20} \leq \frac{14}{20} \)


Let the equation of the plane through
the points (-1,1,1) and (1,-1,1) and
perpendicular to the plane \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+ \)
\( \mathbf{2} z=\mathbf{7} \) be \( \boldsymbol{k} \boldsymbol{x}+\boldsymbol{m} \boldsymbol{y}-\boldsymbol{n} \boldsymbol{z}+\boldsymbol{p}=\mathbf{0} . \) Find
\( \boldsymbol{k}+\boldsymbol{m}+\boldsymbol{n}+\boldsymbol{p} ? \)


The heat absorbed by the system in
going through the cyclic process as
shown in figure is
4.30 .4
3,31,4
c. 32.4
334


An electrical conductor has a
resistance of \( 5.6 k \Omega . \) A potential
difference (p.d.) of \( 9.0 V \) is applied
across its ends.
How many electrons pass a point in the conductor in one minute?
A \( \cdot 6.0 \times 10^{20} \)
В. \( 1.0 \times 10^{19} \)
\( \mathbf{c} \cdot 6.0 \times 10^{17} \)
D. \( 1.0 \times 10^{16} \)


Hardest substance of the body is
A. Bone
B. Enamel
c. Cartilage
D. Tendon


If the de-Broglie wavelength of a particle of mass \( m \) is 100 times its velocity then
its value in terms of its mass \( (m) \) and Planck's constant \( (\boldsymbol{h}) \) is:
A \( \cdot \frac{1}{10} \sqrt{\frac{m}{h}} \)
в. \( 10 \sqrt{\frac{h}{m}} \)
\( c \cdot \frac{1}{10} \sqrt{\frac{h}{m}} \)
D. \( 10 \sqrt{\frac{m}{h}} \)


The term genetics was coined by
A. Mendel
B. Bateson
c. Strasburger
D. All of the above


Give the oxidation state of underlined.
\( N a_{2} S_{4} O_{6} \)


Find the range of \( \boldsymbol{f}(\boldsymbol{x})= \) \( \cos ^{-1} \sqrt{\log _{[x]} \frac{|x|}{x}}, \) where [.]denotes the
greatest integer.
A \( \cdot\left\{\frac{\pi}{2}\right\} \)
в. \( \left\{\frac{\pi}{4}\right\} \)
\( c \cdot\left\{\frac{\pi}{6}\right\} \)
D. \( \left\{\frac{\pi}{8}\right\} \)


One Volt is equal to:
A . 1 Joule
B. 1 Newton/Coulomb
c. 1 Joule/Coulomb
D. 1 Coulomb/Newton


Find the area of trapezium \( \boldsymbol{A B C D} \)


Find \( m \) if the point on the \( x \) -axis which
is equidistant from (7,6) and (3,4) is \( \left(\frac{m}{2}, 0\right) \)


Which of the following statements are true for Mohr's salt?
This question has multiple correct options
A . it decolourizes \( K M n O_{4} \) solution
B. it is a double salt
\( \mathrm{c} \). it is a colourless salt
D. it is primary standard substance


Which is the class of phylum Chordata to which, bat belongs?
A. Mammalia
B. Chiroptera
c. Prototheria
D. Aves


Find the \( C I \) on \( R s .7000 \) at \( 10 \% p . a \)
compounded annually for 4 years.


The solar spectrum in general is:
A. radiation spectrum
B. absorption spectrum
c. emission spectrum
D. continuous spectrum


A body of mass \( m \) was slowly hauled up the hill (figure shown above) by a force \( \vec{F} \) which at each point was directed along a tangent to the trajectory. Find the work performed by this force, if the height of the hill is \( h \), the length of its
base \( l \), and the coefficient of friction \( k \).


A sine wave of wavelength \( ^{\prime} \lambda^{\prime} \) is travelling in a medium. What is the minimum distance between two
particles of the medium which always have the same speed?
\( A \cdot \lambda \)
B. \( \frac{\lambda}{2} \)
\( c \cdot \frac{\lambda}{3} \)
D. \( \frac{\lambda}{4} \)


An object starts from rest, and moves under the acceleration \( \overrightarrow{\boldsymbol{a}}=\mathbf{4} \hat{\mathbf{i}} \). Its
position after \( 3 s \) is given by \( \vec{r}= \) \( (7 \hat{i}+4 \hat{j}) . \) What is its initial position?


A monochromatic source of light
operating at \( 200 \mathrm{W} \) emits \( 4 \times 10^{20} \)
photons per second. Find the
wavelength of the light \( \left(i n \times 10^{-7} m\right) \)


The oxidation number of oxygen
changes in the given reaction:
\( \mathbf{3} \boldsymbol{O}_{\mathbf{2}} \longrightarrow \mathbf{2} \boldsymbol{O}_{\mathbf{3}} \)
If true enter 1 , else enter 0 .


The area of a trapezium is \( 300 m^{2} \). The
perpendicular distance between the two parallel sides is 15 m. If the difference
of the parallel side is \( 16 m, \) find the
length of the parallel sides.


As compared to spring wood, autumn
wood has
A. more number of xylary elements with wider vessels
B. more number of xylary elements with narrow vessels
C. fewer xylary elements with wider vessels
D. fewer xylary elements with narrow vessels


During the disproportionation of lodline to iodide and iodate ions, the ratio of iodate and iodide ions formed in
alkaline medium is:
A . 1: 5
B. 5:
\( c .3: \)
D. 1:3


Percentage of oxygen in the earth's atmosphere is
A . 21\%
в. 78\%
c. 20.94\%
D. 10\%


Find the number of molecules(s) among
the following which is/are planar and have dipole moment.
\( \boldsymbol{S} \boldsymbol{F}_{4}, \quad \boldsymbol{P} \boldsymbol{C l}_{3} \boldsymbol{F}_{2}, \quad \boldsymbol{P C l}_{2} \boldsymbol{F}_{3}, \quad \boldsymbol{I}_{3}^{-} \)


Assertion
Statement -1: White phosphorus is
less stable where as red phosphorus is
more stable.
Reason
Statement -2: White phosphorus exist
as individual \( P_{4} \) having more strained
geometery while red phosphorus has \( \boldsymbol{P}_{\mathbf{4}} \) tetrahedron structure linked together.
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1.
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1
c. Statement -1 is true, Statement -2 is false
D. Statement - 1 is false, Statement - 2 is true


Dimensions of impulse are:
A \( . M L T^{-2} \)
В. \( M^{2} L T^{-1} \)
\( \mathrm{c} \cdot M L T^{-1} \)
D. \( M L^{2} T^{-1} \)


State whether the following statements are true or false.

Accessory glands like seminal vesicles
contribute to the fluid substance of the
seminal fluid.
A. True
B. False


Which of the following statement(s)
is/are correct?
This question has multiple correct options
A. Primary valency of the central metal of a complex is always satisfied by anions.
B. Secondary valency of the central metal of a complex may be satisfied by either negative ions or neutral molecules.
C . Species which show primary valencies in a complex compound can be precipitated out
D. None of the above


Consider the following first order competing reactions:
\( \boldsymbol{X} \stackrel{\boldsymbol{k}_{1}}{\rightarrow} \boldsymbol{A}+\boldsymbol{B} \quad \) and \( \quad \boldsymbol{Y} \quad \underline{k}_{2} \quad \boldsymbol{C}+ \)
\( D \)
If \( 50 \% \) of the reaction of \( X \) was
completed when \( 96 \% \) of the reaction of \( Y \) was completed, the ratio of their rate
constants \( \left(k_{2} / k_{1}\right) \) is:
A . 4.0
B. 6.8
c. 3.
D. 4.6


Salivary glands of cockroach open on
A . Maxilla
B. Hypopharnyx
c. Labium
D. Labrum


Burning of a meteorite in the earth's atmosphere is an example of change of
A. heat energy into kinetic energy
B. kinetic energy into heat energy
c. kinetic energy into poential energy
D. potential energy into heat energy


Find the multiplicative of \( 2-3 i a=2 \)
\( \boldsymbol{b}=-\mathbf{3} \)


If \( \mathrm{B} \) be the exterior angle of a regular
polygon of \( n \) sides and \( A \) is any constant, then prove that \( \sin A+\sin (A+B)+\sin (A+2 B)+ \)
\( . . n \) terms \( =0 \)


The door of an almirah is \( 6 f t \) high, \( 1.5 f t \) wide and weighs 8 kg. The door is supported by two hinges situated at a
distance of \( 1 \mathrm{ft} \) from the ends. If the
magnitudes of the forces exerted by the hinges on the door are equal, find this magnitude


Use of chlorofluorocarbons is not
encouraged because:
A. they are harmful to the eyes of people that use it
B. they damage the refrigerators and air conditioners
C. they eat away the ozone in the atmosphere
D. they destroy the oxygen layer


Which of the following radiations are not emitted by electron transitions in
atoms ?
A. Ultra-violet.
B. Infra-red radiations
c. visible rays.
D. \( \alpha \) -rays


The distance moved by a particle in
time \( t \) seconds is given by \( s=t^{3}- \)
\( 6 t^{2}-15 t+12 . \) The velocity of the
particle when acceleration becomes
zero is
A . 15
в. -27
\( c \cdot 6 / 5 \)
D. none of these


When equal volumes of the following solutions are mixed, precipitation of
\( A g C l\left(K_{s p}=1.8 \times 10^{-10}\right) \) will occur
only with:
A \( \cdot 10^{-4} M A g^{+}+10^{-4} M C l^{-} \)
B . \( 10^{-5} M A g^{+}+10^{-5} M C l^{-} \)
C. \( 10^{-6} M A g^{+}+10^{-6} M C l \)
D. \( 10^{-10} M A g^{+}+10^{-10} M C l \)


\( \ln \) a \( \triangle A B C, \) the sides \( A B, B C \) and \( C A \)
are \( 10 \mathrm{cm}, 8 \mathrm{cm} \) and \( 7 \mathrm{cm} \) respectively.
\( \ln A B \) a point \( P \) is taken such that
\( \boldsymbol{A P}=\mathbf{4} \mathrm{cm} . \) If \( \boldsymbol{P Q} \) is drawn parallel to
\( D C, \) then its length is equal to
A \( .4 .0 \mathrm{cm} \)
B. \( 3.8 \mathrm{cm} \)
c. \( 3.5 \mathrm{cm} \)
D. \( 3.2 \mathrm{cm} \)


ox, oy are positive x-axis, positive \( y \) axis respectively where \( \boldsymbol{O}=(\mathbf{0}, \mathbf{0}, \mathbf{0}) \)
The \( d . c . s \) of the llne which bisects \( \angle x o y \)
are
\( \mathbf{A} \cdot 1,1,0 \)
B. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \)
c. \( \frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}} \)
D. 0,0,1


A lorry and a car moving with the same
K.E. are brought to rest by applying the same retarding force, then?
A. Lorry will come to rest in a shorter distance
B. Car will come to rest in a shorter distance
c. Both come to restin a same distance
D. None of the above


\( \boldsymbol{C u} \boldsymbol{C O}_{3} \cdot \boldsymbol{C u}(\boldsymbol{O H})_{2} \) is also known
as Malachite (green). State True or
False.
A. True
B. False
c. Cannot be determined
D. None of the above


\( \frac{87}{20} \)


The total value of \( m_{s} \) for all electrons in
\( N \) atom is:


Calculate the M.I. of a thin uniform ring about an axis tangent to the ring and in a plane of the ring, if its M.I. about an axis passing through the centre and
perpendicular to plane is \( 4 k g m^{2} \)
A \( \cdot 12 k g m^{2} \)
B. \( 3 k g m^{2} \)
c. \( 6 k g m^{2} \)
D. \( 9 k g m^{2} \)


The velocity of plane \( P \) relative to \( Q \) is
magnitude nearly in \( \boldsymbol{m} / \boldsymbol{s} \)
4.124
3. 283
\( c .506 \)
0.362


Assertion
A mangrove tree growing in marshy
place has pneumatophores.
Reason
Pneumatophores helps in better
anchorage to marshy soil.
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.


An electric dipole of moment \( \overrightarrow{\boldsymbol{p}} \) is placed at the origin along the \( x \) -axis. The angle made by electric field with \( x \) axis at a point \( P, \) whose position vector makes an angle \( \theta \) with \( x \) -axis, is (where \( \left.\tan \alpha=\frac{1}{2} \tan \theta\right) \)
\( A \cdot \alpha \)
B. \( \theta \)
\( c \cdot \theta+\alpha \)
D. \( \theta+2 \alpha \)


A particle performing SHM with a frequency of \( 5 \mathrm{Hz} \) and amplitude \( 2 \mathrm{cm} \) is initially in the positive extreme position. The equation for its displacement is
A. \( x=0.02 \sin 10 \pi t \mathrm{m} \)
B. \( x=0.02 \sin 5 \pi t \mathrm{m} \)
c. \( x=0.02 \cos 10 \pi t \mathrm{m} \)
D. \( x=0.02 \cos 5 \pi t \mathrm{m} \)


Which one of the following does not increase while moving down the group of the periodic table?
A. Atomic radius
B. Metallic character
c. Valence electrons
D. None of the above


Choose the correct answer from the
alternatives given. If \( x-\frac{1}{x}=3 \) then find the value of \( x^{3}+\frac{1}{x^{3}} \)
A. \( 10 \sqrt{13} \)
(3) 5
B. \( 100 \sqrt{3} \)
c. \( 13 \sqrt{10} \)
D. \( 130 \sqrt{10} \)


Statement 1: The hybrid orbital form of carbon in acetylene is believed to be the
sp form.
Statement \( 2: C_{2} H_{2} \) is a linear compound with a triple bond between the carbons.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


Deep black soil is considered to be
highly productive due to high proportion of
A. silt and earthworm
B. Clay and humus
c. Gravel and Catt
D. sand and zn


Choose the correct statements with
regard to human respiration.
(A) Inspiration is facilitated by the contraction of phrenic and external inter-costal muscles
(B) Healthy human can inhale or exhale about 2000 to \( 3000 \mathrm{ml} \) of air per
minute
(C) Functional residual capacity represent the volume of left out air in lungs after expiration
(D) Total lung capacity is the total volume of air that could be accomodated in the lungs after forced inspiration.
A \( . \) A, \( c, \),
в. в, D,
\( c \cdot c, D, B \)
D. A, BCC


A solid sphere of mass \( 1 \mathrm{kg} \) rolls on a table with linear speed \( 2 \mathrm{m} / \mathrm{s} \), find its total kinetic energy.


\( \sigma_{\sigma^{\prime}}^{\sigma_{0}} \)


A ray of light striking a plane mirror at an angle of 35 degrees with the normal. Find out the angle of reflection with normal.
A. 35 degrees.
B. 55 degrees.
c. 10 degrees
D. 90 degrees
E. 125 degrees


A uniform but time varying magnetic
field \( \mathrm{B}=\boldsymbol{K}_{1} \boldsymbol{K}_{2} \boldsymbol{t} \) where \( \boldsymbol{K}_{1} \& \boldsymbol{K}_{2} \) are
positive constants and t is time (in seconds), is applied perpendicular to the plane of a circular loop of radius a and resistance R.Find the total charge (in coulomb) that will pass through any point of the loop by the time \( \mathrm{B} \)
becomes zero. [Given a \( =2 \mathrm{m}, \mathrm{R}=\pi \Omega, K_{1} \) \( =2 T] \)


Which of the following is an autoimmune disorder?
A. Myasthenia graviss
B. osteoporosis
c. Muscular dystrophy
D. Gout


\( \sin h^{-1}\left(2^{3 / 2}\right)= \)
\( \mathbf{A} \cdot \log (2+\sqrt{8}) \)
B. \( \log (3+\sqrt{8}) \)
C \( \cdot \log (2-\sqrt{8}) \)
\( \mathbf{D} \cdot \log (\sqrt{8}+\sqrt{7}) \)


For which of the pair Newland octave
rule is not applicable?
A. \( L i, N a \)
в. \( C, S i \)
c. \( M g, C a \)
D. \( C l, B r \)


Find the principal value of:
\( \sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)-2 \sec ^{-1}\left(2 \tan \frac{\pi}{6}\right) \)


There are two concentric spherical shells of radii \( r \) and \( 2 r . \) Initially a
charge \( Q \) is given to the inner shell and
both the switches are open. Now \( S_{2} \) is closed and opened, The charge flowing
through the switch \( S_{2} \) in the process is
A. \( Q \)
в. \( \frac{Q}{4} \)
\( c \cdot \frac{Q}{2} \)
D. \( \frac{2 Q}{3} \)


Aloe barbadensis belongs to family of
A. xanthorrhoeaceae
B. Apocynaceae
C. Gramineae
D. None of the above


Which is not true of enzymes?
A. They are specific
B. They are made of globular proteins
C. Enzymes are most active at maximum temperature
D. They are most active at optimum temperature


Correct order of bond angles for the following is:
A. \( N H_{3}>P C l_{3}>B C l_{3} \)
В. \( B C l_{3}>C H_{4}>P C l_{3} \)
c. \( B C l_{3}>P C l_{3}>N H_{3} \)
D. \( P C l_{3}>B C l_{3}>N H_{3} \)


On what factors does the induced
electromotive force depend?


A ball is dropped from the height if it
takes one second to cross last \( 55 m \)
before hitting the ground. Find the height from which it was drop.


Antiparallel strands of a DNA molecule
means that
A. One strand turns clockwise.
B. One strand turns anti-clockwise.
C. The phosphate groups of two DNA strands at their ends share the same position.
D. The phosphate groups at the start of two DNA strands are in opposite position (pole)


Four bulbs marked \( 40 W, 250 V \) are
connected in series with \( 250 V \) mains,
the total power consumed is
A. \( 10 W \)
в. \( 40 W \)
c. \( 320 W \)
D. \( 160 W \)


Least boiling point is of:
A. ethylene glycol
B. ether
c. water
D. phenol


A point source or IIgnt b is placea at a
distance \( L \) in front of the centre of a
mirror of width d hung vertically on a
wall. A man walks in front of the mirror
along a line parallel to the mirror at a
distance \( 2 L \) from it as shown. The
greatest distance over which he can see
the image of the light source in the
mirror is
A \( \cdot d / 2 \)
B.
\( c \cdot 2 d \)
D. 3d


Which of the following have same significant figures?

This question has multiple correct options
A \( \cdot 6.02 \times 10^{23} \)
В. \( 7.70 \times 10^{-20} \)
c. 7.50
D. 0.75


Which terms for \( P, Q, R, S, T, U, \) and \( V \) will
make the following paragraph true?
The human excretory system consists
of kidneys, ureters, \( _{-}-P_{--} \) and \( _{-}-Q \) The \( _{--} R_{--} \) brings the dirty blood into kidneys. Kidneys remove the poisonous substances urea, salt and extra water
from the body. The cleaned blood is
carried away from the kidneys by \( S_{--} \cdot_{--} T_{--} \) is the tube that carries
urine from the kidney to the \( _{--} U_{--} \) The urine collected in the bladder is
passed out of the body through the
\( \mathbf{V}_{--} \)
A. P- -bladder; Q-urethra; R_renal artery; S-renal vein; Tureters; U-bladder; V-urethra
B. P- bladder; Q-urethra; R_renal vein; S-renal artery; Tureters; U-bladder; V-urethra
c. P- bladder; Q-urethra; R_renal artery; S-venacava; Tureters; U-bladder; V-urethra
D. None of these


A mixed solution of potassium hydroxide and sodium carbonate required \( 15 \mathrm{mL} \) of \( \frac{N}{20} H C l \) solution when titrated with phenolphthalein as an indicator. But the same amount of
the solution when titrated with methyl orange as an indicator required \( 25 \mathrm{ml} \) of
the same acid. The amount of \( K O H \)
present in the solution is :
A. \( 0.014 \mathrm{g} \)
B. \( 0.14 \mathrm{g} \)
c. \( 0.028 \mathrm{g} \)
D. \( 1.4 \mathrm{g} \)


Which of the following is a statement?
A. Rani is a beautiful girl.
B. Shut the door.
c. Yesterday was Friday.
D. If its raining then there must be cloud in the sky


The \( \% \) by weight of hydrogen in \( H_{2} O_{2} \) is :
A . 50
B . 25
c. 6.25
D. 5.88


The ratio of maximum and minimum
magnitudes of the resultant of two vectors \( \vec{a} \) and \( \vec{b} \) is \( 3: 1 . \) Now, \( |\vec{a}| \) is equal
to
\( \mathbf{A} \cdot \mid \vec{b} \)
в. \( 2 \mid \vec{b} \)
c. \( 3|\vec{b}| \)
D. \( 4 \mid \vec{b} \)


Choose the correct answer from the
alternatives given.

Glucose \( \left(C_{6} H_{12} O_{6}\right) \) can exist as both
an open chain form and a dosed ring form Earlier, it was thought that
glucose occurs in the closed ring form
What possible difference between these forms would give scientists a clue
that the open chain form was not
present
A. Only open chain forms can undergo condensation, which does not occur with glucose
B. An open chain presents ends with functional groups (in this case aldehyde), and glucose failed to undergo typical aldehyde reactions, a phenomenon that could be explained by having no end functional group in a ring structure
C. Because glucose is solid at room temperature, it must have saturated hydrocarbon chains
D. Glucose could not be denatured so it must be a tight chain


In the vapour state, alkali metals may
exist as atoms or diatomic molecules. If
sodium forms a diatomic molecule,
what will be its bond order?


Consider these sentences regarding the structure and nature of DNA.
I. DNA has two pyrimidine bases that contain single ring structure.
II. In DNA, composition of bases should be \( \frac{\boldsymbol{A}+\boldsymbol{T}}{\boldsymbol{G}+\boldsymbol{C}}=\mathbf{1} \)
III. Each base pair of DNA is \( 3.4 A \) apart from other base pairs.
IV. The nucleosome model DNA
packaging was proposed by Kornberg and Thomas.

Choose the correct statements from the
given options.
A. I and III
B. I, II and III
c. ॥, ॥ा and IV
D. I, III and IV


An electron makes a transition from
\( \boldsymbol{n}=\mathbf{2} \) to \( \boldsymbol{n}=\mathbf{1} \) state in a hydrogen like
atom
This question has multiple correct options
A. magnetic field at the site of nucleus is decreased by 16 times
B. magnetic field at the site of nucleus is increased by 32 times
c. angular momentum of electron is changed
D. none of these


Hydrogen gas is:
A. has high molecular weight.
B. a medium for storage of energy
C. excellent fuel
D. both B and C


Conversion of Glucose- 6 -phosphate to fructose- 6 -phosphate is a
A. Anabolic reaction
B. Catabolic reaction
c. Isomerization
D. None of the above


\( \frac{\cos (90-\theta) \sec (90-\theta) \tan \theta}{\operatorname{cosec}(90-\theta) \sin (90-\theta) \cot (90-\theta)} \)
\( \frac{\tan (90-\theta)}{\cot \theta}=\dots \)
\( A \)
B. -
\( c \cdot 2 \)
D. -2


A particle executes simple harmonic motion along a straight line with mean position at \( x=0 \) and period of \( 20 s \) and amplitude of \( 5 \mathrm{cm} . \) The shortest time taken by the particle to go from \( \boldsymbol{x}=\mathbf{4 c m} \) to \( \boldsymbol{x}=-\mathbf{3 c m} \) is
A . \( 4 s \)
B. 7 s
\( c .5 s \)
D. \( 6 s \)


Splitting of spectral lines in electric
field is called stark effect.
A. True
B. False


The average \( K E \) of molecules in a gas at temperature \( T \) is \( \frac{3}{2} k T . \) Find the temperature at which the average KE of molecules equal to binding energy of its
atoms.
A . \( 1.05 \times 10^{5} K \)
В. \( 1.05 \times 10^{4} K \)
c. \( 1.05 \times 10^{3} K \)
D. none of these


If the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}^{2}-(\boldsymbol{A}+\mathbf{2}) \boldsymbol{x}+\boldsymbol{A}}{\boldsymbol{x}-\mathbf{2}}, \) for \( \boldsymbol{x} \neq \mathbf{2} \) and
\( f(2)=2, \) is continuous at \( x=2, \) then
find the value of \( \boldsymbol{A} \) ?


\( \left|\begin{array}{ccc}a^{2}+1 & a b & a c \\ a b & b^{2}+1 & b c \\ a c & b c & c^{2}+1\end{array}\right|= \)
A . abc
B. atb+c
c. \( 1+a^{2}+b^{2}+c^{2} \)
\( D \cdot a b c(1+a+b+c) \)


Explain the following terms:
(i) Electrophoresis
(ii) Coagulation (iii) Dialysis (iv) Tyndall effect


A NOR gate and a NAND gate are
connected as shown in the figure. Two different sets of inputs are given to this set up. In the first case, the input to the
gates are \( A=0, B=0, C=0 . \) In the second
case, the inputs are \( A=1, B=0, C=1 . \) The output D in the first case and second case respectively are
A. 0 and 0
B. O and 1
c. 1 and 0
D. 1 and 1


The ultimate end parts of the
respiratory system in humans are known as
A. alveoli
B. bronchioles
c. tracheoles
D. bronchíi


Silver is purified by the distillation
process.
A . True
B. False


What are ethers? How are they
classified?


The density of mercury is \( 13.6 g m / c c \) Convert it into S.I. units:
A \( \cdot 13.6 \times 10^{3} k g / m^{3} \)
B. \( 13.6 \times 10^{2} k g / m^{3} \)
c. \( 13.6 \times 10^{4} k g / m^{3} \)
D. \( 13.6 \times 10^{5} \mathrm{kg} / \mathrm{m}^{3} \)


The cube as shown in Fig. has sides of
length \( L=10.0 \mathrm{cm} . \) The electric field is
uniform, has a magnitude \( \boldsymbol{E}=\mathbf{4 . 0 0} \times \)
\( 10^{3} N C^{-1}, \) and is parallel to the \( x y- \)
plane at an angle of \( 37^{\circ} \) measured from
the \( +x-a x i s \) towards the \( +y-a x i s \)
Electric flux passing through surface \( \boldsymbol{S}_{1} \)
is
A \( .-24 N m^{2} C^{-1} \)
B. \( 24 N m^{2} C^{-1} \)
\( \mathbf{c} \cdot 32 N m^{2} C^{-1} \)
D. \( -32 N m^{2} C^{-1} \)


Which group hydrogen has resemblance?
This question has multiple correct options
A. I-A
в. Il-A
c. IV-A
D. VII-A


If mass-energy equivalence is taken into account, when water is cooled to
form ice, the mass of water should
\( A \). increase
B. remain unchanged
c. decrease
D. first increase then decrease


Differentiate with respect to \( x \) :
\( \log \left(\cos x^{2}\right) \)


Calculate the pH of \( \frac{N}{1000} \) sodium hydroxide (NaOH) solution assuming complete ionisation.


Find matrix \( \boldsymbol{X} \) so that \( \boldsymbol{X}\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6}\end{array}\right]= \)
\( \left[\begin{array}{ccc}-\mathbf{7} & -\mathbf{8} & -\mathbf{9} \\ \mathbf{2} & \mathbf{4} & \mathbf{6}\end{array}\right] \)


Assertion
A sinusoidal wave is created in a thick
rope by moving hand holding the rope up \& down. If the hand is moved up and
down with greater frequency, the wave reached the other end more quickly.
Reason
Wave velocity is product of frequency \& wavelength for a sinusoidal wave.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Potato tuber is modified/edible part of
potato is
A. Stem
B. Bulb
c. stolon
D. Root


What happens when \( H_{2} S \) gas is passed
through nitric acid?


A firm readymade garments makes both men's and women's shirts. Its
average profit it \( 6 \% \) of sales. Its profits in men's shirts average is \( 8 \% \) of sales and women's shirt comprise \( 60 \% \) of
output. The average profit per sales rupee in women's shirts is
A . 0.0466
B. 0.0666
c. 0.0166
D. None of these


What is true about Nereis, scorpion,
cockroach and silver fish?
A. They all possess dorsal heart.
B. None of them is aquatic
C. They all belong to the same phylum.
D. They all have jointed paired appendages.


A machine gun is mounted on a \( 2000 k g \) vehicle on a horizontal smooth road
(friction negligible). The gun fires 10 bullets per sec with a velocity of \( 500 m / s . \) If the mass of each bullet be
\( 10 g, \) what is the acceleration produced
in the vehicle?
A \( \cdot 25 c m / s^{2} \)
B. \( 0.025 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 0.50 \mathrm{cm} / \mathrm{s}^{2} \)
D. \( 50 m / s^{2} \)


Give reasons for following:
Dry \( H C l \) does not change the colour of
the dry blue litmus paper

Antacid tablets are used by a person suffering from stomach pain. Toothpaste is used for cleaning teeth


Calculate the mass percentage of
benzene \( \left(C_{6} H_{6}\right) \) and carbon
tetrachloride \( \left(C C l_{4}\right) \) if \( 22 g \) of benzene
is dissolved in \( 122 g \) of carbon
tetrachloride.


Column II Column (Monosaccharide units on hydrolysis)


Following reaction is spontaneous at \( 300 K \)
\( 2 C u O(s) \longrightarrow C u_{2} O(s)+I / 2 O_{2}(g) \)
\( \boldsymbol{\Delta} \boldsymbol{H}=-\mathbf{1 4 4 . 6 k} \boldsymbol{J m o l}^{-1} ; \boldsymbol{\Delta} \boldsymbol{S}= \)
\( 0.116 k J m o l^{-1} \) if true enter 1 else 0
\( A \)


In the following check the given value is a solution of the given equation or not \( \boldsymbol{x}^{2}-\boldsymbol{x}+\mathbf{1}=\mathbf{0}, \boldsymbol{x}=\mathbf{1}, \boldsymbol{x}=-\mathbf{1} \)
A . True
B. False


The function \( f(x)=4-3 x+3 x^{2}-x^{3} \)
is
A. decreasing on \( R \)
B. increasing on \( R \)
c. strictly decreasing on \( R \)
D. strictly increasing on \( R \)


Which of the following is an example of atmospheric electricity?
A. Auroras
B. Lightening
c. Ionospheric currents
D. All of the above


The approximate value of quantum
number ' \( n^{\prime} \) for the circular orbit of
hydrogen of 0.0001 mm in diameter is
A. 1000
B. 60
c. 10000
D. 31


A, \( \mathrm{B} \) are two inaccurate arithmeticians
whose chances of solving a given question correctly are \( (1 / 8) \) and \( (1 / 12) \) respectively. They solve a problem and obtained the same result. If it is 1000 to
1 against their making the same mistake, find the chance that the result
is correct
\( \mathbf{A} \cdot \frac{13}{14} \)
B. \( \frac{2}{7} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{11}{12} \)


Define regeneration and fragmentation.


Find the mean and variance for the data
\[
\begin{array}{lll}
92 & 93 & 97
\end{array}
\]
98
\( \boldsymbol{x}_{i} \)
\( f_{i} \quad 3 \quad 2 \) 3 2


\( \left\{\boldsymbol{a} \boldsymbol{m}_{1} \boldsymbol{m}_{2}, \boldsymbol{a}\left(\boldsymbol{m}_{1}+\boldsymbol{m}_{2}\right)\right\},\left\{\boldsymbol{a} \boldsymbol{m}_{2} \boldsymbol{m}_{3}, \boldsymbol{a}(\boldsymbol{m}\right. \)


Choose the odd one in the following. Sperm, implantation, fertilization, ovum, afterbirth


Which one of the following is a partial heterotroph?
A . Rafflesia
B. Eucalyptus
c. Drosera
D. Hydrilla


\( \operatorname{Let} \tan ^{-1} y=\tan ^{-1} x+ \)
\( \tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right) \) where \( |x|<\frac{1}{\sqrt{3}} . \) Then
a value of y is
A \( \cdot \frac{3 x-x^{3}}{1-3 x^{2}} \)
В. \( \frac{3 x+x^{3}}{1-3 x^{2}} \)
c. \( \frac{3 x+x^{3}}{1+3 x^{2}} \)
D. \( \frac{3 x-x^{3}}{1+3 x^{2}} \)


Evaluate \( : \int_{0}^{\log _{e} 5} \frac{e^{x} \sqrt{e^{x}-1}}{e^{x}+3} d x \)


How many significant digits does the
measurement \( 0.5873 g \) possess?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
E . 5


If \( a^{2}+b^{2}+c^{2}=1, x^{2}+y^{2}+z^{2}=1 \)
where \( a, b, c, x, y, z \) are real, prove that \( \boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+\boldsymbol{c} \boldsymbol{z} \leq \mathbf{1} \)


The difference of two numbers is 3 and
the difference of their square is \( 69 . \) Find
the numbers.
A. 3 and 9
B. 13 and 10
c. 11 and 18
D. 5 and 2


An adaption for better gaseous exchange in plant leaves is
A. Hair on lower surface
B. Multiple epidermis
c. waxy cuticle
D. Stomata on lower surface away from direct sun rays


State True or False.
Mixture of \( H N O_{3} \) and \( H C l \) is an
example of maximum boiling point
azeotrope
A. True
B. False


Find four consecutive terms of an A.P.
whose sum is 88 and sum of first and
third term is 40


During dark reaction 2 PGA are derived
from
\( A \cdot C O_{2} \) and \( R U B P \)
B. \( \mathrm{cO}_{2} \)
c. RUBP
D. \( \mathrm{cO}_{2} \), PEP and RUBP


What voltage on \( y \) -plate will give such a
deflection
A \( .0 .11 V \)
B. \( 1.1 V \)
\( \mathbf{c} \cdot 11 V \)
D. none


The refractive index \( (\mu) \) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate the absolute error in each
measurement.


Draw number lines and locate the
points on them:
\( \frac{2}{5}, \frac{3}{5}, \frac{8}{5}, \frac{4}{5} \)


What is the atomic mass (u) of Sodium
\( ? \)
A . 22
B. 23
c. 23.5
D. 24


List- List-II
\( (\mathrm{A}) \mathrm{O}_{3} \)
(1) Turns benzidine paper to brown
(B) Hypo
(2) Turns anhydrous \( C u S O_{4} \) to blue
(C) \( H_{2} O \)
(3) Violet colour with \( \mathrm{FeCl}_{3} \)
(D) \( H_{2} S \)
(4) Rotten egg smel
The correct match is :
A. A-2, B-3, C-1, D-4
B. A-4, B-2, C-3, D-1
C. \( A-1, B-3, C-2, D-4 \)
D. A-3, B-4, C-2, D-1


A proton and an electron are accelerated by same potential difference starting from rest have de-
Brogile wavelength \( \lambda_{p} \) and \( \lambda_{e^{*}} \)
A \( \cdot \lambda_{e}=\lambda_{p} \)
B . \( \lambda_{0}<\lambda_{p} \)
c. \( \lambda_{e}>\lambda_{p} \)
D. none of these


The sum of the intercepts of the tangent to the curve \( \sqrt{x}+\sqrt{y}=3 \) on the coordinate axes where it meets the curve
\( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}} \)
\( A \cdot S \)
B. 10
\( c \cdot 11 \)
D. 12


Ecosystems have
A. energy inputs and outputs
B. nutrient cycling but not outputs
C . one trophic level
D. both
(a) and (b)


toppr
Q Type your question_
force, but otherwise the sled will not
have external forces interacting with its horizontal motion).
In order to push the sled without
making it rotate, where should you
push?
Refer to the diagram to help you conceptualize the situation. All objects
in the system you are about to push
have some mass, through their
quantities are unknown. The sled is
motionless initially and the surface is
completely flat. Assume you are going
to push on the side that is closer to you,
as shown in the diagram.
A. Directly between the two dogs depicted in the diagram
B. Somewhere closer to the black dog
c. Somewhere closer to the white dog
D. At the center of mass of the two dogs
E. More information is needed


Find the area of the closed figure bounded by the following curve \( y=x^{2}, y=2 x-x^{2} \)


Photochemical smog is generally formed:
A. in early hours of winters
B. around mid day in summer months
c. when intensity of solar radiations is very low
D. when concentration of particulate matter is very low


Fill in the blanks:
kg coal can light up 1 bulb for hours.
\( A \cdot 6 \)
B. 8
c. 7
D. 5


A counterclockwise couple \( C(\theta) \) acts on
a uniform \( 1.5 \mathrm{kg} \) bar \( \mathrm{AB} \) as shown in Fig.
1. Given two cases:
Case (a) \( C(\theta)=5.4 \sin \theta \mathrm{N}-\mathrm{m} \)
Case (b) \( C(\theta) \) varies as shown in Fig. 2
The total work done on the bar as it
rotates in the vertical plane about \( \mathbf{A} \)
from \( \theta=0^{\circ} \) to \( \theta=180^{\circ} \) in the above two
cases are \( W_{a} \) and \( W_{b} \) respectively.
Then,
(Take \( \left.\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
This question has multiple correct options
\( A \cdot W_{a}=3.22 \mathrm{N}-\mathrm{m} \)
B. \( W_{a}=4.2 \mathrm{N}-\mathrm{m} \)
C \( . W_{b}=4.2 \mathrm{N}-\mathrm{m} \)
D. \( W_{b}=1.86 \mathrm{N}-\mathrm{m} \)


Short / Long answer type questions. Is swallowing a voluntary or involuntary
action?


The repetition of reflected sound from a distant object is called
A . echo
B. transformation
c. eddy currents
D. string


Noble gases do not react because they have electrons in their
valence shell.
\( A \cdot 3 \)
B. 6
\( c \)
D. 8


The length of a steel wire is \( l_{1} \) when the
stretching force is \( T_{1} \) and \( l_{2} \) when the
stretching force is \( T_{2} \) The natural length of the wire is
\( ^{\text {A } \cdot \frac{l_{1} T_{1}+l_{2} T_{2}}{T_{1}+T_{2}}} \)
в. \( \frac{l_{2} T_{1}+l_{2} T_{2}}{T_{1}+T_{2}} \)
c. \( \frac{l_{2} T_{1}+l_{2} T_{2}}{T_{1}-T_{2}} \)
D. \( \frac{l_{2} T_{1}-l_{1} T_{2}}{T_{1}-T_{2}} \)


Given compounds are:
Methylcyclopropane
A. functional isomers
B. optical isomers
C . geometrical isomers
D. ring chain isomers


Hardness of water is mainly due to the
dissolved salts of calcium and
magnesium.
A. True
B. False


A particle of mass \( M, \) charge \( q>0 \) and
initial kinetic energy \( K \) is projected from infinity towards a heavy nucleus of charge \( Q \) assumed to have a fixed
position.
(a) If the aim is perfect, how close to the center of the nucleus is the particle when it comes instantaneously to rest?
(b) With a particular imperfect aim, the particle's closest approach to nucleus is twice the distance determined in (a)
Determine speed of particle at the closest distance of approach.


The domain of the function
\( \sin ^{-1}\left(\log _{2}\left(\frac{x}{3}\right)\right) \) is
A \( \cdot \frac{1}{2}, 3 \)
B. \( \frac{1}{2}, 4 \)
c. \( \frac{3}{2}, 6 \)
D. \( \frac{1}{2}, 2 \)


The IUPAC name of the given compound
is :
A. 3-Bromo-5-chloro-1-methylcyclohexanol
B. 5-Bromo-3-chloro-1-methyl-cyclohexanol
C. 1-Bromo-5-chloro-3-methyl-3-cyclohexanol
D. 5-Bromo-1-chloro-3-methyl-3-cyclohexanol


Name the smallest cell and the largest
cell in the human.


Let \( f \) and \( g \) be differentiable functions
on \( R \) such that fog is the identify
function. If for some \( a, b, \epsilon R, g^{\prime}(a)=5 \)
and \( g(a)=b, \) then \( f^{\prime}(b) \) is equal to
A \( \cdot \frac{1}{5} \)
B. 5
\( c \cdot 1 \)
D.


The polymer, which is the constituent of
cotton is:
A . cellulose
B. ester
c. rayon
D. nylon


Mixtures on separation can give
A. elements
B. compounds
c. both elements and compounds
D. impure substances


What are the coordinates of the center
of the circle represented by the
equation \( (x+3)^{2}+(y-4)^{2}=25 ? \)
\( A \cdot(3,4) \)
B. (3,-4)
c. (-3,4)
D. (-3,-4)


For a sample of perfect gas when its pressure is changed isothermally from
\( p_{i} \) to \( p_{f}, \) the entropy change is given by:
A \( \cdot \Delta S=n R \ln \left(\frac{p_{f}}{p_{i}}\right) \)
в. \( \Delta S=n R \ln \left(\frac{p_{i}}{p_{f}}\right) \)
\( \mathbf{c} \cdot \Delta S=n R T \ln \left(\frac{p_{f}}{p_{i}}\right) \)
D. \( \Delta S=R T \ln \left(\frac{p_{i}}{p_{f}}\right) \)


An electric bulb is marked \( 200 \vee, 100 W \)
Calculate electrical resistance of its
filament. If five such bulbs are
connected in series to a \( 200 \mathrm{V} \) supply, how much current will flow through them?


The radius of \( _{13}^{27} \) Al is 3.6 Fermi. Find the radius of \( _{52}^{125} \mathrm{Te} \)
A. 6 Fermi
B. 8 Fermi
c. 4 fermi
D. 5 Fermi


An electroscope is used:
A. to detect presence of charge on a body.
B. to determine the nature of charge on a body.
C. to measure the exact amount of charge on a body.
D. for both \( A \) and \( B \).


Find area of trapezium whose parallel
sides \( 9 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively and
the distance between these sides is
\( \mathbf{8} c \boldsymbol{m} \)


Which of the following arylamines will
not form a diazonium salt on reaction
with sodium nitrite in hydrochloric
acid?
This question has multiple correct options
A. m-Ethylaniline
B. p-Aminoacetophenone
c. 4 -chloro-2-nitroaniline
D. N-Ethyl-2-methylaniline


The ratio in which the area bounded by the curves \( y^{2}=12 x \) and \( x^{2}=12 y \) is
divided by the line \( x=3 \) is
A . 15: 16
B. 15: 49
\( c \cdot 1: 2 \)
D. None of these


Using the relationship between
moments of inertia as \( \boldsymbol{I}_{\boldsymbol{x}}+\boldsymbol{I}_{\boldsymbol{y}}=\boldsymbol{I}_{\boldsymbol{z}} \)
where sub indices \( x, y, \) and \( z \) define three mutually perpendicular axes passing through one point, with axes 1 and 2 lying in the plane of the plate, the moment of inertia of a thin uniform
round disc of radius \( R \) and mass \( m \)
relative to the axis coinciding with one of its diameters is \( I=\frac{m R^{2}}{x} . \) Find the
value of \( \boldsymbol{x} \)


Write the IUPAC name of the compound shown in the figure.


"Forestry of the people, by the people and for the people" is
A. Agroforestry
B. Social forestry
c. Urban forestry
D. all


How many bonds are there in the
compound shown?
4,13
3.23
\( c \cdot 20 \)
0.26


A gas obeys the Van der Waals equation
The approximate value of the constants
a' and 'b' for this gas are:
\( \mathbf{A} \cdot 1.88 \times 10^{6} c c^{2} a t m / m o l e^{2}, 120 c c / m o l e \)
B . \( 3.16 \times 10^{6} c c^{2} a t m / \) mole \( ^{2}, 30 \mathrm{cc} / \mathrm{mole} \)
C. \( 3.16 \times 10^{6} \mathrm{cc}^{2} \) atm \( / \mathrm{mole}^{2}, 50 \mathrm{cc} / \mathrm{mol} \)
D. \( 0.86 \times 10^{5} \mathrm{cc}^{2} \) atm / mole \( ^{2}, 30 \mathrm{cc} / \mathrm{mole} \)


Distinguish between Myopia and Hypermetropia.


The force which is responsible for circular motion of electrons around the
nucleus is
A. Van der Waals
B. Electrostatic forces
c. centrifugal and Centripetal
D. Intermolecular forces


Which of the following is tertiary alkyl
halide?
A \( \cdot(C H)_{3} C H C l \)
в. \( C H C l_{3} \)
c. \( (C H)_{3} C C l \)
D. \( C H_{3} C l \)


Identify the type of polymer.
\( (i)-A-A-A-A-A-A \)
\( (i i)-A-B-B-A-A-A-B-A- \)
A. (i) Homopolymer, (ii) Copolymer
B. (i) Natural polymer, (ii) Synthetic polymer
C. (i) Linear polymer, (ii) Branched polymer
D. (i) Fibre, (ii) Elastomer


A circular disc \( D_{1} \) of mass \( \mathrm{M} \) and radius
R has two identical discs \( D_{2} \) and \( D_{3} \) of
the same mass \( \mathrm{M} \) and radius \( \mathrm{R} \)
attached rigidly at its opposite ends(see figure). The moment of inertia of the system about the axis 00 ',
passing through the centre of \( D_{1}, \) as
shown in the figure, will be?
\( \mathbf{A} \cdot 3 M R^{2} \)
B. \( \frac{2}{3} M R^{2} \)
c. \( M R^{2} \)
D. \( \frac{4}{5} M R^{2} \)


Which of the following processes makes the ore porous?
A. Distillation
B. Reduction
c. calcination
D. All of these


If for all \( x, y \) the function \( f \) is defined by
\( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})+\boldsymbol{f}(\boldsymbol{x}) \cdot \boldsymbol{f}(\boldsymbol{y})=1 \) and
\( \boldsymbol{f}(\boldsymbol{x})>\mathbf{0}, \) then
A \( \cdot f^{\prime}(x) \) does not exist
B \( \cdot f^{\prime}(x)=0 \) for all \( x \)
c. \( f^{\prime}(0)<f^{\prime}(1) \)
D. None of these


The term independent of \( x \) in the expansion of \( \left(\sqrt{\frac{x}{3}}+\frac{3}{2 x^{2}}\right)^{10} \) will be
\( ^{A} \cdot \frac{3}{2} \)
в.
\( c \cdot \frac{5}{2} \)
D. None of these


The variance of first \( n \) natural numbers
is
A \( \frac{n^{2}+1}{12} \)
в. \( \frac{n^{2}-1}{12} \)
c. \( \frac{n(n+1)(2 n+1)}{6} \)
D. none of these


Three letters, to each of which
corresponds an envelope, are placed in the envelopes at random. The
probability that all the letters are not placed in the right envelopes, is
A \( \cdot \frac{1}{6} \)
в. \( \frac{5}{6} \)
\( c \cdot \frac{1}{3} \)
D.


If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] \) and \( \boldsymbol{B}=\left[\begin{array}{ll}\boldsymbol{k} & \boldsymbol{l} \\ \boldsymbol{m} & \boldsymbol{n}\end{array}\right] \) then
find \( \boldsymbol{A B} \)


In Sulphur estimation 0.157 grams of
an organic compound gave 0.4813 gram of barium sulphate. what is the percentage of Sulphur in the compound?


Out of soft iron and steel which has
more coercivity, less retentivity.
A . iron
B. steel
c. both are equal
D. can't say


The most stable free radical among the
following is:
\( A \)
\( (a) \)
в.
(b)
\( c \)
\( (c) \)
\( D \)
\( (d) \)


Give the major product of the above
reaction sequence:
\( A \)
B.
\( c \)
\( D \)


Two battery having unequal emf:
A. cannot be connected in parallel.
B. cannot be connected in series.
C. can be connected in series only.
D. may be connected in parallel or series.


The shaded part of the given figure is
represented as
\( A \cdot A \cap B \)
в. \( A \cup B \)
\( c \cdot A-B \)
D. All of the above


Which of the following can be negative?
A \( \cdot 4 \pi r^{2} \Psi^{2} \)
B . \( 4 \pi r^{2} \Psi^{2} d r \)
\( c . \Psi \)
D. \( \Psi^{2} \)


The diameters of two planets are in ratio \( 4: 1 . \) Their mean densities have
ratio \( 1: 2 . \) The ratio of 'g' on the planets
will be:
A .1: 2
B. 1: 4
c. 2: 1
D. 4: 1


The emf of a Daniel cell is \( 1.08 V . \) When
the terminals of the cells are connected
to the resistance of \( 3 \Omega \), the potential difference across the terminals is found
to be \( 0.6 \% \). Then the internal resistance
of the cell is
A. \( 1.8 \Omega \)
в. 2.4\Omega
c. \( 3.24 \Omega \)
D. \( 0.2 \Omega \)


Assertion
Activated charcoal is used for
decolourising sugar solution.
Reason

Activated charcoal absorbs the
impurities on its surface.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A particle starts from rest and moves with an acceleration of \( \boldsymbol{a}=\mathbf{2}+(\boldsymbol{t}- \)
2) \( \mid m / s^{2}, \) the velocity of the particle at
\( t=4 \sec \) is
\( A \cdot 2 m / s \)
B. \( 4 \mathrm{m} / \mathrm{s} \)
c. zero
D. \( 12 \mathrm{m} / \mathrm{s} \)


Three consecutive natural numbers are
such that the square of the middle number exceeds the difference of
squares of the other, two by \( 60 . \) Find the numbers.


The law of octaves was proposed by :
A. Newlands
B. Dobereiner
c. Lavoisier
D. Mendeleev


As shown in figure, a particle of mass \( m \) a performing vertical circular motion.
The velocity of the particle is increased, then at which point and the string break


Use division method of contradiction to
show that \( \sqrt{3} \) and \( \sqrt{5} \) are irrational numbers. Also find the value of \( \sqrt{15} \times \) \( \sqrt{3} \times \sqrt{5} \)


\( \lim _{x \rightarrow 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x} \) is equal to:
A \( \cdot \frac{1}{2} \)
B. 1
c. 2
D. \( -\frac{1}{4} \)


Consider the triangle OAB in the xyplane where \( 0=(0,0) A=(6,0), B= \)
\( (\sqrt{2}, 3) . \) A sqare PQRS is inscribed in
the square with \( P, Q \) on \( O A, R \) on \( A B \) and Son BO. Then the side of the square
equals
A. \( 3 / \sqrt{2} \)
B. \( \frac{9}{4} \)
c. \( \frac{3}{2} \sqrt{\frac{5}{2}} \)
D.


The internal energy U of an ideal gas depends only on its temperature \( T, \) not on its pressure or volume.


Genes do not occur in pairs in
A. Zygote
B. Somatic cell
C. Endosperm cells
D. Gametes


Find the smallest number which should
be multiplied to 100 to get a perfect
cube.


Composition of gunpowder is :
A. \( S+ \) Charcoal \( +K N O_{3} \)
B. \( S+ \) Coke \( +K N O_{3} \)
c. \( S+ \) Coal \( +K N O_{3} \)
D. all of the above


In an intrinsic semiconductor,
conductivity is due to
A. doping
B. breaking of covalent bonds
c. free electrons
D. holes


Plant classification based on floral
characters are preferred because
A. The floral characters are less affected by environment than vegetative characters
B. flowers are coloured and more attractive
C. Flower can be preserved in herbaria than vegetative parts.
D. Linnaeus classified plants based on flower characters like the number of stamens


Which of the following relations hold for units of activity?
A. \( 1 B q=1 \) decay \( / s \)
В . \( 1 C l=3.7 \times 10^{10} B q^{4} \)
C \( .1 R d=10^{6} B q \)
D. All of the above


Which of the following is/are more reactive towards nucleophilic addition
reactions?
A. \( C H_{3} C O C H_{3} \)
в. НСНО
c. \( C H_{3} C H O \)
D. \( C_{2} H_{5} C H O \)


Simplify:
\( \mathbf{3 6} \times(-\mathbf{3})+(-\mathbf{3 6}) \times \mathbf{7} \)


Evaluate: \( \int_{0}^{2}\left(x^{2}+3\right) d x \) as limit of
sums


The gaseous phase neutralisation reaction can be explained only on the basis of:
A. Arrhenius theory
B. Lowry -Bronsted theory
c. Lewis theory
D. Bohrs theory


Higher the refractive index of a medium
A. Less it will change the direction of a beam of light passing through it
B. More it will change the direction of a beam of light passing through it
c. No bending occurs
D. All


The angle of dip at a place on the earth
gives
A. The horizontal component of the earth's magnetic field
B. The location of geographical meridian
C. The vertical component of the earth's magnetic field
D. The direction of the earth's magnetic field


Tangents are drawn from the point \( (a, a) \) to the circle \( x^{2}+y^{2}-2 x-2 y- \)
\( 6=0 . \) If the angle between the tangents lies in the range \( \left(\frac{\pi}{3}, \pi\right), \) then the exhaustive range of values of \( a \) is
B. (-5,-3)\( \cup(3,5) \)
c. \( (-\infty, 2 \sqrt{2}) \cup(2 \sqrt{2}, \infty) \)
D. (-3,-1)\( \cup(3,5) \)


Most metallic element in the fifth
period is?
A . silver
B. rubidium
c. gold
D. rhodium