Show that \( x+1 \) and \( 2 x-3 \) are factors of
\( 2 x^{3}-9 x^{2}+x+12 \)


Obtain the angle between \( \vec{A}+\vec{B} \) and \( \vec{A}-\vec{B} \) if \( \vec{A}=2 \hat{i}+3 \hat{j} \) and \( \vec{B}=\hat{i}-2 \hat{j} \)
\( ^{A} \cdot \cos ^{-1}\left(\frac{4}{\sqrt{65}}\right) \)
в. \( \pi-\cos ^{-1}\left(\frac{4}{\sqrt{65}}\right) \)
\( ^{\mathrm{c}} \cdot \sin ^{-1}\left(\frac{4}{\sqrt{65}}\right) \)
D. \( -\sin ^{-1}\left(\frac{4}{\sqrt{65}}\right) \)


Assertion
Transition metal compounds are often colored.
Reason
They frequently possess partially filled \( d \) orbitals.
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


Coke is a fuel.
A. ashless
B. renewable
C. smokeless
D. harmless


Two wires of the same material (young's modules \( Y \) ) and same length \( L \) but radii
\( R \) and \( 2 R \) respectively are joined end to
end and a weight \( W \) is suspended from
the combination as shown in the figure.
the elastic potential energy in the system in equilibrium is
A \( \cdot \frac{3 W^{2} L}{4 \pi R^{2} Y} \)
В \( \cdot \frac{3 W^{2} L}{8 \pi R^{2} Y} \)
\( ^{\mathbf{C}} \cdot \frac{5 W^{2} L}{8 \pi R^{2} Y} \)
\( ^{\mathrm{D}} \cdot \frac{W^{2} L}{\pi R^{2} Y} \)


A condenser of capacity \( C \) is charged to
a potential difference of \( V_{1} . \) The plates of the condenser are then connected to
an ideal inductor of inductance \( L \). The
current through the inductor when the
potential difference across the
condenser reduces to \( V_{2} \) is
\( \left(\frac{C\left(V_{1}-V_{2}\right)^{2}}{L}\right)^{\frac{1}{2}} \)
в. \( \frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L} \)
c. \( \frac{C\left(V_{1}^{2}+V_{2}^{2}\right)}{L} \)
\( \left(\frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L}\right)^{\frac{1}{2}} \)


The part of the atmosphere above the 90 km from the earth is called
A. homosphere
B. heterosphere
c. ozone layer
D. mesosphere


The methods chiefly used for the
extraction of lead and tin from their ores
are respectively
A. self reduction and carbon reduction
B. self reduction and electrolytic reduction
C. carbon reduction and self reduction
D. cyanide process and carbon reduction


Write the degree of the differential
equation \( \left(\frac{d y}{d x}\right)^{4}+3 x \frac{d^{2} y}{d x^{2}}=0 \)


For a particular reversible reaction at
temperature \( \mathbf{T}, \boldsymbol{\Delta} \mathbf{H} \) and \( \Delta \mathbf{S} \) were found
to be both +ve. If \( \mathbf{T}_{\mathbf{e}} \) is the temperature at equilibrium, the reaction would be
spontaneous when:
A \( \cdot \mathrm{T}_{\mathrm{e}}>\mathrm{T} \)
в. \( \mathrm{T}>\mathrm{T}_{\mathrm{e}} \)
\( \mathrm{c} \cdot \mathrm{T}_{\mathrm{e}} \) is 5 times \( \mathrm{T} \)
D. \( \mathrm{T}=\mathrm{T}_{\mathrm{e}} \)


If the MP is \( 30 \% \) above \( \mathrm{CP} \) and a
discount of \( 10 \% \) is given for cash payments, what is the profit?
A . \( 10 \% \)
B. \( 15.5 \% \)
c. \( 17 \% \)
D. \( 18.5 \% \)


The reaction, \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}+\boldsymbol{D} \) was
studied using an initial concentration
of \( B \) which was 1.5 times that of \( A \). But
the equilibrium concentration of \( A \) and
\( C \) were found to be equal. The \( K_{c} \) for the
equilibrium is:
A .4
B. 8
\( c \cdot 6 \)
D. 0.32


Nitrogen reaction with oxygen to form nitrogen (III) oxide

What will be the volume ratio of the
reactants and products of the given reaction?
A \( \cdot 2: 3: 2 \)
B. 2:3:4
\( c \cdot 1: 3: 2 \)
D. 2:1:2


A defective eye cannot see close objects clearly because their image is formed:
A. On the eye lens
B. Between eye lens and retina
c. on the retina
D. Beyond retina


A line is perpendicular to \( 3 x+y=3 \)
and passes through a point \( (2,2) . \) Its \( y \) intercept is
A \( \cdot 2 / 3 \)
в. \( 1 / 3 \)
c. 1
D. \( 4 / 3 \)


The image of our face in a plane mirror
is :
A . real
B. magnified
c. diminished
D. virtual


Chipko Andolan originated in Haridwar during 1980s.
A . True
B. False
c. Nither
D. Either


The probability that atleast one of the
events \( A, B \) happens is \( 0.6 . \) If probability of their simultaneously happening is \( 0.5, \) then \( \boldsymbol{P}(\overline{\boldsymbol{A}})+\boldsymbol{P}(\overline{\boldsymbol{B}})= \)
A . 0.4
B. 0.8
c. 0.9
D. 1.


Which of the following has the maximum number of unpaired delectrons?
A \( \cdot F e^{2} \)
в. \( C u^{+} \)
\( c \cdot Z n \)
D. \( N i^{3} \)


If a magnet of pole strength \( \mathrm{m} \) is divided into four parts such that the length and width of each part is half that of the
initial one, then the pole strength of each
part will be
\( A \cdot m / 4 \)
B. m/2
\( c \cdot m / 8 \)
D. \( 4 \mathrm{m} \)


Solve for \( x ; \cos ^{-1} \sqrt{x}>\sin ^{-1} \sqrt{x} \)


Find the principal value of:
\( \sin ^{-1}\left(\cos \frac{3 \pi}{4}\right) \)


Sum \( 1+2 a+3 a^{2}+4 a^{3}+\dots \) to \( n \)
terms.
A \( \cdot \frac{1+\left(a^{n}\right)}{(a-1)^{2}}-\frac{n a^{n}}{1+a} \)
в. \( \frac{1-2\left(a^{n}\right)}{(a-1)^{2}}+\frac{n a^{n}}{1-2 a} \)
c. \( \frac{1-\left(a^{n}\right)}{(a-1)^{2}}-\frac{n a^{n}}{1-a} \)
D. none of these


The point equidistant from the points (0,0,0),(1,0,0),(0,2,0) and (0,0,3) is
A \( .(1,2,3) \)
B \( \cdot\left(\frac{1}{2}, 1, \frac{3}{2}\right) \)
\( ^{c} \cdot\left(-\frac{1}{2},-1,-\frac{3}{2}\right) \)
D. (1,-2,3)


A square frame with side \( a \) and a long
straight wire carrying a current \( i \) are located in the same plane as shown in figure. The frame translates to the right
with constant velocity \( v . \) Find the emf induced in the frame as a function of
distance \( \boldsymbol{x} \)
A \( \cdot \frac{\mu_{0}}{7 \pi} \frac{2 i a^{3} v}{x(x+a)} \)
В. \( \frac{\mu_{0}}{4 \pi} \frac{2 i a^{2} v}{x(x+a)} \)
c. \( \frac{\mu_{0}}{2 \pi} \frac{2 i a^{4} v}{x(x+a)} \)
D. \( \frac{\mu_{0}}{3 \pi} \frac{7 i a^{2} v}{x(x+a)} \)


The electric intensity E current density
and resistance k are related to each
other through the relation


An organic compound \( (X) \) with
molecular formula \( C_{3} H_{6} O \) is not
readily oxidised. On reduction, it gives
\( C_{3} H_{8} O(Y) \) which react with \( H B r \) to
give a bromide \( (Z) \) which is converted
to Grignard's reagent. Grignard's
reagent reacts with \( (X) \) to give 2,3
dimethylbutan-2-ol. \( (X),(Y) \) and \( (Z) \) respectively are:
A \( \cdot C H_{3} C O C H_{3}, C H_{3} C H_{2} C H_{2} O H, C H_{3} C H(B r) C H_{3} \)
B. \( C H_{3} C H_{2} C H O, C H_{3} C H=C H_{2}, C H_{3} C H(B r) C H_{3} \)
c. \( C H_{3} C O C H_{3}, C H_{3} C H(O H) C H_{3}, C H_{3} C H(B r) C H_{3} \)
D. \( C H_{3} C H_{2} C H O, C H_{3} C H_{2} C H_{2} O H, C H_{3} C H_{2} C H_{2} B r \)


A hydrocarbon gas decolourises alkaline potassium permanganate and gives precipitate with ammonical silver
nitrate. The gas is :
A \( . C H_{4} \)
в. \( C_{2} H_{4} \)
c. \( C_{2} H_{2} \)
D. \( C_{2} H_{6} \)


Maltose is converted to 'A' by Maltase. The mole fraction of 'A' in \( 10 \% \) (w/w) aq solution is approximately.
\( \mathbf{A} \cdot 0.989 \)
B. 0.012
c. \( 0 . \)
D. 0.017


A water sample contains 81 ppm of
\( \boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2}, 73 \) ppm of \( \boldsymbol{M} \boldsymbol{g}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2} \)
68 ppm of \( C a S O_{4} \) and 60 ppm of
\( M g S O_{4} . \) What is the hardness of the
Water sample? (Atomic weights of calcium, magnesium and sulphur are respectively 40,24 and 32 ).
A. 50 ppm
B. 100 ppm
c. 150 ppm
D. 200 ppm


At constant pressure, which of the
following graph best shows the relationship between temperature and volume of a gas?
\( A \cdot A \)
в. \( B \)
\( c . C \)
D. \( D \)
E. \( E \)


Evaluate: \( \int \frac{\boldsymbol{d x}}{\boldsymbol{x}^{2}\left(\boldsymbol{x}^{3}+\mathbf{1}\right)^{\frac{2}{3}}} \)
A.
B.
\( -\left(1-\frac{1}{x^{3}}\right)^{1 / 3}+c \)
c. \( \quad-\left(1-\frac{1}{x^{2}}\right)^{2 / 3}+c \)
D \( \cdot\left(1+\frac{1}{x^{3}}\right)^{1 / 3}+c \)
\( -\left(1+\frac{1}{x^{2}}\right)^{2 / 3}+c \)


A gold coin has a charge of \( +10^{-4} C . \) The
number of electrons removed from it is:
A \( \cdot 10^{6} \)
В. \( 625 \times 10^{12} \)
c. \( 1.6 \times 10^{-25} \)
D. \( 1.6 \times 10^{13} \)


The electric flux passing through a hemispherical surface of radius \( \mathrm{R} \)
placed in an electric field E with its axis parallel to the filed is :
\( \mathbf{A} \cdot \pi R^{2} E \)
В. \( 2 \pi R^{2} E \)
c. \( 2 \pi R E \)
\( \mathbf{D} \cdot 2 \pi R^{3} E \)


In right angled \( \Delta A B C \angle B= \)
\( 90^{\circ} B D \perp A C, A B=b, B D=c, B C= \)
\( \boldsymbol{a}, \boldsymbol{A} \boldsymbol{D}=\boldsymbol{8} \boldsymbol{D} \boldsymbol{C}=\mathbf{1 0} . \) Then find \( ^{\boldsymbol{}} \boldsymbol{b}^{\prime} \)
A \( \cdot \sqrt{5} \)
B. 12
\( c \cdot 6 \sqrt{6} \)
D. \( \sqrt{18} \)


Assertion
\( \boldsymbol{S} \boldsymbol{O}_{2} \) gas is easily liquefied while \( \boldsymbol{H}_{2} \)
gas is not
Reason
\( \boldsymbol{S} \boldsymbol{O}_{2} \) has low critical temperature while
\( \boldsymbol{H}_{2} \) has high critical temperature.
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


Which of the following set ups represent a second class lever?
\( A \)
\[
\frac{L F E}{\Delta}
\]
в.
\[
\begin{array}{lll}
F & L & E \\
\hline \Delta
\end{array}
\]
\( c \)
\[
\frac{L}{L} E \frac{F}{\Delta}
\]
D.
\[
\frac{F}{\Delta} E L
\]


\( \int \frac{x d x}{1+x^{4}} \) is equal to
A. \( \tan ^{-1} x^{2}+k \)
B. \( \frac{1}{2} \tan ^{-1} x^{2}+k \)
C \( \cdot \log \left(1+x^{4}\right)+k \)
D. none of these


The mean deviation of the data
\( \mathbf{2}, \mathbf{9}, \mathbf{9}, \mathbf{3}, \mathbf{6}, \mathbf{9}, \mathbf{4} \) from the mean is
A . 2.23
в. 2.57
c. 3.23
D. 3.57


The equilibrium of which of the
following reaction will not be disturbed by the addition of an inert gas
at constant volume?

This question has multiple correct options
A \( \cdot H_{2}(g)+I_{2}(g) \rightleftharpoons 2 H I(g) \)
B. \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
c. \( C O(g)+2 H_{2}(g) \rightleftharpoons C H_{3} O H(g) \)
D. \( C(s)+H_{2} O(g) \rightleftharpoons C O(g)+H_{2}(g) \)


Two different vectors having same
magnitude:
\( \mathbf{A} \cdot \hat{i}+2 \hat{j}+3 \widehat{k}, 3 \hat{i}+2 \hat{j}+\widehat{k} \)
в. \( \hat{i}+\widehat{j}-\widehat{k}, 2 \hat{i}-\widehat{j}-\bar{k} \)
c. \( \hat{i}-2 \hat{j}+2 \widehat{k}, \hat{i}+\widehat{j}+\widehat{k} \)
D. None


The mutual inductance between two
coils when a current of 5 A changes to \( 10 \mathrm{A} \) in \( 1 \mathrm{s} \) and induces an emf of \( 100 \mathrm{m} \)
Vin the secondary is
A . \( 20 \mathrm{m} \) н
B. \( 10 \mathrm{mH} \)
c. \( 30 \mathrm{mH} \)
D. \( 15 \mathrm{mH} \)


The reaction;
\( \mathbf{9 2} \boldsymbol{U}^{\mathbf{2 3 8}}+\mathbf{0} \boldsymbol{n}^{\mathbf{1}} \rightarrow \mathbf{9 2} \boldsymbol{U}^{\mathbf{2 3 9}} \rightarrow \mathbf{9 3} \boldsymbol{N} \boldsymbol{p}^{\mathbf{2 3 9}}+ \)
\( -1 e^{0} \)
is an example of:
A. \( \alpha \) -emission
B. \( \beta \) -emission
C \( . \gamma \) -emission
D. none of these


Plot a graph showing the variation of current \( I \) versus resistance \( R \)
connected to a cell of emf \( E \) and
internal resistance \( r \)


Using \( (\boldsymbol{x}+\boldsymbol{a})(\boldsymbol{x}+\boldsymbol{b})=\boldsymbol{x}^{2}+(\boldsymbol{a}+ \)
\( b) x+a b, \) find
\( 12.1^{2}-7.9^{2} \)
A . 97
B. 65
\( c \cdot 34 \)
\( D \cdot 84 \)


System A is in thermal equilibrium with
B and B is separately in thermal equilibrium with C. Then A and C are in thermal equilibrium, from which law of thermodynamics it follows?
A. zeroth
B. First
c. second
D. Third


What is the remainder if \( \boldsymbol{p}^{11}+\boldsymbol{p}^{9}+ \)
\( p^{7}+p^{5}+p^{3}+p^{2} \) divided by \( p+1 \)


Which statement is not true?
A. The casparian strips prevent water from moving.
B. The endodermis is a cell layer in the cortex.
C. The symplast is a meshwork consisting of the (connected) living cells.
D. Water can enter the stele without entering the symplast.


The properties or physical constants which are lower for hydrogen than that of deuterium are:
This question has multiple correct options
A. Abundance
B. Boiling point
c. Latent heat of fusion
D. Activation energy


Offspring formed as a result of sexual reproduction exhibits more variations
because
A. Sexual reproduction is a lengthy process.
B. Genetic material comes from two parents of the same species.
c. Genetic material comes from two parents of different species
D. Genetic material comes from many parents


Some students, during a study, caught marked and released 80 fish in a pond.
Later 100 fishes were caught at random. Among these 40 were found to be marked. What is the approximate number of fishes in the pond?
A . 50
B. 100
\( c \cdot 200 \)
D. 4000


The ratio of \( x_{1} / x_{2} \) is
\( A \cdot 2 \)
B. \( \frac{1}{2} \)
\( c \cdot \sqrt{2} \)
D. \( \frac{1}{\sqrt{2}} \)


The torque required to hold a small
circular coil of 10 turns, are \( 1 m m^{2} \) and
carrying a current of \( \left[\frac{21}{44}\right] \) A in the middle
of a long solenoid of \( 10^{3} \) turns/m
carrying a current of \( 2.5 \mathrm{A} \), with its axis perpendicular to the axis of the solenoid
is:
A \( .1 .5 \times 10^{-6} N m \)
в. \( 1.5 \times 10^{-8} N m \)
c. \( 1.5 \times 10^{6} \mathrm{Nm} \)
D. \( 1.5 \times 10^{8} \mathrm{Nm} \)


ECG method is the way to detect
A. Heart attack
B. Heart block
C. Coronary thrombosis
D. All of the above


Which of the following is not a postulate
of Dalton's atomic theory?
A. All matter is made of very tiny particles called atoms
B. Atoms of a given element are not identical in mass and chemical properties
C. Atoms combine in a ratio of small whole numbers to
form compounds
D. The relative number and kinds of atoms are constant in a given compound


Which of the following statements
regarding diamond is (are) correct?
This question has multiple correct options
A. diamond does not refract light
B. when proper cut and polished, a diamond reflects light in an array of many colours
C. diamond is less stable than graphite
D. Impure sample of diamond is often black and are used in abrasives


In figure, \( B C \) represents a body moving
A. Backward with uniform velocity
B. Forward with uniform velocity
C. Backward with non-uniform velocity
D. Forward with non-uniform velocity


Aerosol decrease primary productivity
by
A. Decreasing \( O_{2} \) concentration
B. Competing with \( C O_{2} \)
C. Preventing \( N_{2} \) fixation
D. Reducing photosynthesis


The image of an object, formed by a plano-convex lens at a distance of \( 8 m \) behind the lens, is real and is one-third
the size of the object. The wavelength of light inside the lens is \( \frac{2}{3} \) times the wavelength in free space. The radius of the curved surface of the lens is:
A . \( 1 \mathrm{m} \)
B. 2 \( m \)
\( c \cdot 3 m \)
D. \( 6 \mathrm{m} \)


A body is allowed to fall from a height of \( 98 \mathrm{m} \) before hitting the ground the distance travelled by it in the last
second of motion \( \left(\boldsymbol{g}=\mathbf{9} . \mathbf{8 m} \boldsymbol{s}^{-2}\right) \) is
\( A .38 m \)
в. \( 40 m \)
\( c .50 m \)
D. \( 29 m \)


Which of the following has the shortest carbon-carbon bond length?
\( A \cdot C_{2} H_{2} \)
B. \( c_{2} \) Hata
\( c \cdot c_{2} H_{6} \)
D. All have the same bond length


In which of the following solvent, the solubility of \( N a C l \) is maximum?
A. Methanol
B. water
c. Formic acid
D. Formamide


The method of extraction of Ag by cyano complex formation followed by metal displacement is called
A. Parke's method
B. McArthur-Forest method
c. serpeck method
D. Hall's method


The edge of a cube is \( a=1.2 \times 10^{-2} m \)
Then its volume will be recorded as :
A \( \cdot 1.7 \times 10^{-6} m^{3} \)
В. \( 1.70 \times 10^{-6} m^{3} \)
C. \( 1.70 \times 10^{-7} m^{3} \)
D. \( 1.78 \times 10^{-6} m^{3} \)


A particle is projected horizontally from
the top of a tower with a velocity \( v_{0} . \) If \( v \)
be its velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to
\( \mathbf{A} \cdot v^{3} \)
B \( \cdot v^{2} \)
c.
D. \( \frac{1}{v} \)


Check whether \( 3 x-10=0 \) is
a quadratic equation.


If s.d,of \( X \) is \( \sigma \), then s.d.of the variable \( U=\frac{a X+b}{c} \) where \( a, b, c \) are constants
is
A \( \cdot\left|\frac{c}{a}\right| \sigma \)
B \( \cdot\left|\frac{a}{c}\right| \sigma \)
\( c \cdot\left|\frac{b}{c}\right| \)
D. \( \frac{c^{2}}{a^{2}} \sigma \)


Identify the correct statement regarding
enzymes.
A. Enzymes are specific biological catalysts and their action is independent of \( p H \)
B. Enzymes are normally heterogeneous catalyst that are very specific in their action
C. Enzymes are specific biological catalyst that cannot be poisoned
D. Enzymes are specific biological catalysts that can normally function at very high temperature \( (T=1000 \) \( K) \)


In tissue culture, differentiation of
shoot is controlled by
A . Light Intensity
B. Temperature shock
c. Low Auxin and high ck \( \left(\text {High} \frac{\text { Cyto }}{\text {Auxin}} \text { Ratio} \) ) \right.
D. None of the above


Identify incorrect for electric charge \( \boldsymbol{q} \)
A. Quantised
B. Conserved
C. Additive
D. Non-transferable


\( \operatorname{Let} z=x+i y \& \operatorname{amp}\left(e^{z^{2}}\right)=\operatorname{amp} \)
\( \left(e^{(z+i)}\right) . \) If \( y=(x) \) is a function, then
\( \boldsymbol{y}(\mathbf{3}) \) is equal to
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{4} \)
D.


The conversion of vinyl allyl ether to
pent-4-enol follows a certain kinetics. The following plot is obtained for such
reaction.The order for the reaction is:
4. zercor
B.
\( c \)
2


According to whose atomic model,
electrons are embedded in a gel of positive charge?
A. Dalton's model
B. Bohr's model
c. Thomson's model
D. Rutherford's model


In a reaction of acidified hydrogen
peroxide with potassium iodide, the concentration of iodine formed rises from 0 to \( 10^{-5} \) mol \( d m^{-3} \) in 10 seconds.
What is the rate of reaction?
A \( \cdot 10^{-6} \) mold \( m^{-3} s^{-1} \)
B \( \cdot 10^{6} \) mol \( d m^{-3} s^{-1} \)
c. \( 10^{-5} \) mold \( m^{-3} s^{-1} \)
D. \( 10^{4} \) mol \( d m^{-3} s^{-1} \)


The solution of \( \frac{d y}{d x}=\frac{x+x^{2}}{y+y^{2}} \) is:
A \( \cdot x^{3}-y^{3}-y^{2}-x^{2}=c \)
B . \( 2\left(x^{3}-y^{3}\right)+3\left(x^{2}-y^{2}\right)=c \)
c. \( x^{2}+y^{2}+x+y=c \)
D. \( x^{2} y+x y^{2}=c \)


The force of attraction between two
bodies at a certain separation is \( 10 N \)
What will be the force of attraction
between them if the separation between them is reduced to half?
\( \mathbf{A} \cdot 2.5 N \)
B. \( 5 N \)
\( c .20 N \)
D. \( 40 N \)


After surgical removal of an infected
gall bladder, a person must be especially careful to restrict dietary
intake of
A. Starch
B. Protein
c. sugar
D. Fatt


\( \int x \sqrt{x} d x= \)
A \( \cdot \frac{3}{2} x^{3 / 2}+c \)
B \( \cdot \frac{2}{5} x^{5 / 2}+c \)
c. \( \frac{5}{2} x^{5 / 2}+c \)
D. \( \frac{3}{2} \sqrt{x}+c \)


Unit of \( \boldsymbol{K}_{\boldsymbol{p}} \) for \( \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{4}} \boldsymbol{C O O} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{2}(s)} \rightleftharpoons \)
\( N H_{3(g)}+C O_{2(g)} \) is:
A. No units
B. \( a t m^{2} \)
\( c \cdot a t m^{3} \)
D. none


airplane shaped cars attached to steel
rods. Each rod has a length of \( 20.0 \mathrm{m} \)
and a cross-sectional area of \( 8.00 \mathrm{cm}^{2} \)
Young's modulus for steel is \( 2 \times \)
\( 10^{11} N / m^{2} \)
When operating, the ride has a
maximum angular speed of \( \sqrt{19 / 5} \) rad/s. How much is the rod stretched (in
\( \mathrm{mm} \) ) then?
A . \( 0.38 \mathrm{mm} \)
B. \( 0.55 \mathrm{mm} \)
\( c \cdot 0.45 \mathrm{mm} \)
D. 0.34


Which of the following reaction is most
exothermic?
\( A \)
B.
\( c \)
D. \( \dot{C H}_{3}+C H_{3} C H_{2} C H_{3} \rightarrow C H_{4}+C H_{3} \dot{C} H C H_{3} \)


With the help of a neat labelled diagram, describe the Geiger- Marsden experiment. What is mass defect? The photoelectric work function for a metal surface is \( 2.3 \mathrm{eV} \). If the light of wavelength \( 6800 A^{\circ} \) is incident on the
surface of metal find threshold
frequency and incident frequency. Will there be an emission of photoelectrons or not?
[Velocity of light \( c=3 \times 10^{8} m / s \)
Planck's constant, \( \boldsymbol{h}=\mathbf{6} \cdot \mathbf{6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \)


How would you convert?
Aniline to chlorobenzene


The compounds shown below have similar weights but significantly different boiling points. Match the compound with its boiling point.
(Boiling points \( \left.\left(^{o} C\right) 28,57,100,141\right) \)
A. Methyl acetate=100, 2-butanol=141, 2-methyl butane=28, Propanoic acid=57
B. Methyl acetate=57, 2-butanol=100, 2-methyl butane=28, Propanoic acid=141
c. Methyl acetate=28, 2-butanol=100, 2-methyl butane=57, Propanoic acid=141
D. Methyl acetate=141, 2-butanol=57, 2-methy butane=28, Propanoic acid=100


Assertion
An object from a greater height reaches a steady terminal velocity.
Reason
The viscous forces on a body depends upon its velocity. The greater the velocity the greater is the viscous force.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following is safest way to protect yourself from lightning?
A. To run to an open field.
B. To open an umbrella for cover.
c. To take shelter under a tree.
D. To squat low on ground.


Describe the structure of interstitial
and substitutional alloys and outline the factor determining which is formed.


Chl a, Chl d and phycoerythrin occur in
A. Chlorophyceae
B. Bacillariophyceae
c. cyanophyceae
D. Rhodophyceae


\( \lim _{x \rightarrow 0} \frac{\cos a x-\cos b x}{x^{2}}= \)


Equation of the plane through the midpoint of the line segment joining the points \( \boldsymbol{P}(\mathbf{4}, \mathbf{5},-\mathbf{1 0}), \boldsymbol{Q}(-\mathbf{1}, \mathbf{2}, \mathbf{1}) \) and
perpendicular to \( \boldsymbol{P} \boldsymbol{Q} \) is
A \( \cdot r .\left(\frac{1}{3} 2 \hat{i}+\frac{7}{2} \hat{j}-\frac{9}{2} \widehat{k}\right)=45 \)
B \( \cdot r .(-\hat{i}+2 \hat{j}+\widehat{k})=\frac{135}{2} \)
c. \( r .(5 \hat{i}+3 \hat{j}-11 \widehat{k})+\frac{135}{2}=0 \)
D. \( r .(4 \hat{i}+5 \widehat{j}-10 \widehat{k})=85 \)
E \( \cdot r_{\cdot}(5 \hat{i}+3 \hat{j}-11 \widehat{k})=\frac{135}{2} \)


For all numbers a and ,b let \( a \odot b \) be
defined by \( a \odot b=a b+a+b . \) For all
numbers \( x, y \) and \( z, \) which of the following must be true?
I. \( \boldsymbol{x} \odot \boldsymbol{y}=\boldsymbol{y} \odot \boldsymbol{x} \)
Il. \( (x-1) \odot(x+1)=(x \odot x)-1 \)
III. \( \boldsymbol{x} \odot(\boldsymbol{x}+\boldsymbol{z})=(\boldsymbol{x} \odot \boldsymbol{y})+(\boldsymbol{x} \odot \boldsymbol{z}) \)
A. I only
B. II only
c. ॥ only
D. I and II only
E. I, II and III


What is the product formed?
\[
\mathrm{CH}_{2}=\mathrm{CH}-\left(\mathrm{CH}_{2}\right)_{3}-\mathrm{CH}_{2}-\mathrm{OH} \stackrel{\mathrm{PCC}}{\longrightarrow}
\]


The artery can be distinguished from vein in having
A. Thicker walls
B. More blood cells
c. More plasma
D. Larger cavity


The half life of a radioactive substance
is 5000 years. The number of years after which its activity will decrease to 0.2
times of its initial value is:
\( \left(\log _{10} 5=0.6990\right) \)
A \( \cdot 1.02 \times 10^{5} \) years
B . \( 2.34 \times 10^{6} \) years
C. \( 2.06 \times 10^{2} \) years
D. \( 1.16 \times 10^{4} \) years


2mol of \( N_{2} \) is mixed with 6 mol of \( H_{2} \) in
a closed vessel of one litre capacity. If
\( 50 \% N_{2} \) is converted into \( N H_{3} \) at
equilibrium, the value of \( K_{c} \) for the
reaction.
\( N_{2}(g) 3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \) is:
A . 4/27
B. 27/4
c. 2/27
D. 20


Haplodiploidy is found in
A. Grasshoppers and cockroaches
B. Birds and reptiles
C. Butterflies and moths
D. Honeybees, ants and wasps


Which of the following is not a water borne disease?
A. Asthma
B. Cholera
c. Amoebiasis
D. None of the above


Solve the following pair of linear equations by the elimination method and the substitution method:
(i) \( x+y=5 \) and \( 2 x-3 y=4 \)
(ii) \( 3 x+4 y=10 \) and \( 2 x-2 y=2 \)
(iii) \( 3 x-5 y-4=0 \) and \( 9 x=2 y+7 \)
(iv) \( \frac{x}{2}+\frac{2 y}{3}=-1 \) and \( x-\frac{y}{3}=3 \)


How many \( S-S \) bonds are there in
\( \boldsymbol{S}_{3} \boldsymbol{O}_{9} ? \)


There are ............ rational numbers
between two rational numbers.
A . infinite
B. two
c. one
D. none of these


\( \frac{\boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}+\mathbf{7}}{(\boldsymbol{x}-\mathbf{3})^{3}}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{3}}+\frac{\boldsymbol{B}}{(\boldsymbol{x}-\mathbf{3})^{2}}+ \)
\( \frac{C}{(x-3)^{3}} \Rightarrow A= \)
\( A \cdot 2 \)
B . - -
\( c \)
\( D \)


Voltage induced in the secondary coil of a transformer is mainly due to :
A. The iron core of the transformer
B. The vibrations of the primary coil
c. A varying induced electric field
D. A varying induced magnetic field


Show that \( n^{2}-1 \) is divisible by 8 , if \( n \) is
an odd positive integer.


Match the interhalogen compounds of
column I with the geometry in column II
and assign the correct code.
Column I
\( \begin{array}{ll}\text { (a) } & X X^{\prime}\end{array} \)
(i) \( \quad \) T-shape
Pentagona
\( \begin{array}{ccccc}(b) & X X_{3}^{\prime} & ( \text { ii) } & \text { bipyramida }\end{array} \)
\begin{tabular}{ll}
(с) & \( X X_{5}^{\prime} \) \\
\\
\hline
\end{tabular}
(iii) \( \quad \) Linear
Square -
\( \begin{array}{llll}\text { (d) } & X X_{7}^{\prime} & \text { (iv) } & \text { pyramidal }\end{array} \)
\( (v) \)
Tetrahedral
A \( \cdot(a)-(i v),(b)-(i i i),(c)-(i i),(d)-(i) \)
B. \( (a)-(i i i),(b)-(i v),(c)-(i),(d)-(i i) \)
C \( .(a)-(i i i),(b)-(i),(c)-(i v),(d)-(i i) \)
D. \( (a)-(v),(b)-(i v),(c)-(i i i),(d)-(i i) \)


In a group, basic nature from
top to bottom.
A. decreases
B. increases
c. constant
D. none of these


Find equivalent capacitance between
points \( A \) and \( B: \)
\( ^{A} \cdot \frac{5 C}{3} \)
в. \( \frac{4 C}{3} \)
\( c \cdot 2 C \)
\( D . C \)


Total number of possible alkyl chlorides
with the formula \( C_{4} H_{9} C l \) is/are:


Time period of oscillation of a spring is
12s on earth. What shall be the time
period if it is taken to moon?
A . \( 6 s \)
B. 12s
c. \( 36 s \)
D. 72 s


At what temperature would the resistance of a copper conductor be
double its resistance at \( 0^{\circ} \mathrm{C} ? \) Given \( \alpha \)
for copper is \( 3.9 \times 10^{-3}^{\circ} C^{-1} \)
A \( \cdot 256.4^{\circ} \mathrm{C} \)
в. \( 512.8^{\circ} \mathrm{C} \)
\( c \cdot 100^{\circ} \mathrm{C} \)
D. 256.4k


Lungs are made up of air-filled sacs, the alveoli. They do not collapse even after forceful expiration, because of
A. Expiratory Reserve Volume
B. Residual Volume
c. Inspiratory Reserve Volume
D. Tidal Volume


The momentum of a moving particle is vectorially given as \( \overrightarrow{\boldsymbol{p}}=\boldsymbol{p}_{0}(\cos \boldsymbol{t} \hat{\boldsymbol{i}}+ \)
\( \sin t \hat{j}), \) where \( t \) stands for time. choose
the correct option:
A. The applied force is constant
B. The momentum is constant
C. The applied force always remains perpendicular to the momentum.
D. The applied force is always parallel to the momentum


When electron remains between orbits,
its momentum is :
A. quantized
B. dequantized
c. emitted
D. changed always


A piezo - electric quartz plate is vibrating to produce wavelength of \( 10^{-2} m . \) Find the frequency, if for quartz,
\( \boldsymbol{E}=\mathbf{8} \times \mathbf{1 0}^{\mathbf{1 0}} \mathbf{N m}^{-\mathbf{2}} \) and \( \boldsymbol{\rho}=\mathbf{2 . 6 5} \times \)
\( 10^{3} k g m^{-3} \)


In halogenation of aromatic hydrocarbon, a halogen carrier is used which is generally a Lewis acid. The
main function of this reagent is to generate the species:
\( \mathbf{A} \cdot X \)
B. \( X \)
\( c \cdot x^{+} \)
D. \( x^{\text {. }} \)


A line passing through \( \mathbf{P}(-2,3) \) meets the axes in \( A \) and \( B \). If \( P \) divides \( A B \) in
the ratio of 3: 4 then the perpendicular
distance from (1,1) to the line is
A \( \cdot \frac{9}{\sqrt{5}} \)
B. \( \frac{7}{\sqrt{5}} \)
c. \( \frac{8}{\sqrt{5}} \)
D. \( \frac{6}{\sqrt{5}} \)


If a mixture containing 3 moles of
hydrogen and 1 mole of nitrogen is converted completely into ammonia, then the ratio of initial and final volume
under same temperature and pressure would be :
A. 3:
B. 1: 3
c. 2: 1
D. 1: 2


Select the correct statement(s):
This question has multiple correct options
A. When temperature is reised, a point will be reached where the graph crosses the \( \Delta G=0 \) line. Below this temperature, the free energy of formatin of the oxide is negative, so the oxide is stable
B. When temperature is raised, a point will be reached where the graph crosses the \( \Delta G=0 \) line. Above this temperature, the free energy of formation of the oxide is positive, and the oxide becomes unstable, and should decompose into the metal and dioxygen.
C. Theoretically, all oxides can be decomposed to give the metal and dioxygen if.a sufficiently high temperature can be attained.
D. Theoretically, all oxides cannot be decomposed to give the metal and dioxygen if a sufficiently high temperature can he attaincd


\( \underbrace{L}_{L} \)


The volume of thin brass and the
volume of a solid cube made of same
material is both equal to \( 1 m^{3} \) at \( 0^{0} C \).
What will be the ratio of change in volumes of vessel and the cube on being heated to \( 25^{0} \) C? Given \( \alpha \) for brass \( = \) \( \mathbf{1} . \mathbf{9} \times \mathbf{1 0}^{-\mathbf{5}} /^{0} \mathbf{C} \)


If \( 2^{2 x-y}=32 \) and \( 2^{x+y}=16 \) then \( x^{2}+ \)
\( y^{2} \) is equal to
\( \mathbf{A} \cdot \mathbf{9} \)
B. 10
c. 11
D. 13


In the following case, use the remainder
theorem and find the remainder when
\( \boldsymbol{p}(\boldsymbol{x}) \) is divided by \( \boldsymbol{g}(\boldsymbol{x}) \cdot \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{4} \boldsymbol{x}^{3}- \)
\( 12 x^{2}+14 x-3 g(x)=2 x-1 \)


A plane electromagnetic wave in a non magnetic dielectric medium is given by \( \overline{\boldsymbol{E}}=\overline{\boldsymbol{E}}_{0}\left(\mathbf{4} \times \mathbf{1 0}^{-\mathbf{7}} \times-\mathbf{5 0} \boldsymbol{t}\right) \) with
distance being in meter and time in seconds. The dielectric constant of the
medium is:
A . 2.4
в. 5.8
\( c \cdot 8.2 \)
D. 4.8


If \( A \) is symmetric and \( B \) is skew
symmetric matrix, then which of the following is/are correct? This question has multiple correct options
A \( \cdot A B A^{T} \) is skew symmetric matrix
B. \( A B^{T}+B A^{T} \) is symmetric matrix
c. \( (A+B)(A-B) \) is symmetric
D. \( (A+I)(B-I) \) is skew symmetric


The length and breadth of a rectangular sheet are \( 16.2 \mathrm{cm} \) and \( 10.1 \mathrm{cm} \) respectively. The area of the sheet in
appropriate significant figures and error is:
\( \mathbf{A} \cdot 164 \pm 3 c m^{2} \)
В. \( 163.62 \pm 2.6 \mathrm{cm}^{2} \)
c. \( 163.6 \pm 2.6 \mathrm{cm}^{2} \)
D. \( 163.62 \pm 3 c m^{2} \)


The enzyme which can cut molecules of
DNA into segments is known as
A. DNA polymerase
B. DNA ligase
c. Restriction enzyme
D. DNA gyrase


Which of the following reaction is a fast reaction at laboratory temperature?
A . Reaction between \( K M n O_{4} \) and oxalic acid
B. Reaction between \( K M n O_{4} \) and mohr's salt
c. Hydrolysis of ethyl acetate
D. Thermal decomposition of \( N_{2} O_{5} \)


A hemispherical container with radius \( 6 \mathrm{cm} \) contains \( 325 \mathrm{ml} \) of milk. Calculate
the volume of milk that is needed to fill
the container completely. \( (\pi=3.142) \)
A. \( 147.45 \mathrm{ml} \)
B. \( 127.45 \mathrm{ml} \)
c. \( 137.45 \mathrm{ml} \)
D. None


\( \ln P C l_{5}, \) how many \( (C l-P-C l) \) are
inclined at \( 120^{\circ} \) with one each :


Which is the strongest oxidising agent out of the following?
A \( \cdot I_{2} \)
B. \( C l_{2} \)
c. \( B r_{2} \)
D. \( F_{2} \)


Three equal resistors, connected across a source of e.m.f. together dissipate 10 watt of power. What will be the power
dissipated in watts if the same resistors are connected in parallel across the same source of e.m.f.
A . \( 10 V \)
в. \( 10 / 3 V \)
c. \( 30 V \)
D. \( 90 V \)


Simplify \( 2 x^{2}+y^{2}+2 x y=5 \) where,
\( x=(2 \cos \theta-\sin \theta) \) and \( y=(\cos \theta) \)
\( 3 \sin \theta) \)


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{cc}\sin \boldsymbol{\theta} & \mathbf{0} \\ \mathbf{0} & -\boldsymbol{\operatorname { s i n } \boldsymbol { \theta }}\end{array}\right] \cdot \). If \( \boldsymbol{A}+\boldsymbol{A}^{\boldsymbol{T}} \) is a
null matrix, then the number of values
of \( \boldsymbol{\theta} \) in \( [\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] \) is
A . 4
B. 3
\( c \cdot 2 \)
D.


Q Type your question
\( \left(p+\frac{a}{V^{2}}\right)(V-b)=R T \)
undergoes the quasi-static cyclic
process which is shown in the p-V
diagram. The net heat absorbed by the gas in this process is:
\( ^{A} \cdot \frac{1}{2}\left(p_{1}-p_{2}\right)\left(V_{1}-V_{2}\right) \)
B \( \cdot \frac{1}{2}\left(p_{1}+p_{2}\right)\left(V_{1}-V_{2}\right) \)
c. \( \frac{1}{2}\left(p_{1}+\frac{a}{V_{1}^{2}}-p_{2}-\frac{a}{V_{2}^{2}}\right)\left(V_{1}-V_{2}\right) \)
\( \cdot \frac{1}{2}\left(p_{1}+\frac{a}{V_{1}^{2}}+p_{2}+\frac{a}{V_{2}^{2}}\right)\left(V_{1}-V_{2}\right) \)


For matrices \( A \) and \( B ; \) if \( A B=4 I, \) then
\( A^{-1} \) is \( = \)
A \( .4 B \)
в. \( 4 B^{-1} \)
c. \( \frac{1}{4} \)
D. \( \frac{1}{4} B^{-1} \)


A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The
change in potential energy of body will be -
A. \( \mathrm{mg} \) २R
в. \( \frac{2}{3} m g R \)
c. \( 3 \mathrm{mgR} \)
D. \( \frac{1}{3} m g R \)


Two identical glass bulbs are
interconnected by a thin glass tube. A
gas is filled in these bulbs at N.T.P. If
one bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes 1.5 times.
The temperature of hot bath will be
\( \mathbf{A} \cdot 100^{\circ} C \)
B. \( 182^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 256^{\circ} \mathrm{C} \)
D. \( 546^{\circ} \mathrm{C} \)


Assertion
If \( \lim _{x \rightarrow 0}\left\{f(x)+\frac{\sin x}{x}\right\} \) does not exist
then \( \lim _{x \rightarrow 0} f(x) \) does not exist.
Reason
\( \lim _{x \rightarrow 0} \frac{\sin x}{x} \) exists and has value 1
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


\( \int \frac{\operatorname{cosec} x}{\cos ^{2}\left(1+\log \tan \frac{x}{2}\right)} d x \) is equal to
\( A \cdot \sin ^{2}\left[1+\log \tan \frac{x}{2}\right]+C \)
B \cdot \( \tan \left[1+\log \tan \frac{x}{2}\right]+C \)
c. \( \sec ^{2}\left[1+\log \tan \frac{x}{2}\right]+C \)
D. \( -\tan \left[1+\log \tan \frac{x}{2}\right]+C \)


Solve:
\( 28-31 x-5 x^{2}=0 \)


Identify the matrix given below:
\( \left[\begin{array}{cccc}1 & 0 & 0 & 0 \\ 0 & 4 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -3\end{array}\right] \)
A. diagonal matrix
B. zero matrix
c. scalar matrix
D. unit matrix


The mass number of \( H e \) is 4 and that
for sulphur is \( 32 . \) The radius of sulphur nuclei is larger than that of helium by
A. \( \sqrt{8} \)
B. 4
\( c \cdot 2 \)
D. 8


The hybrid state of \( S \) in \( S O_{3} \) is similar
to that of:
A. \( C \) in \( C_{2} H_{2} \)
в. \( C \) in \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C \) in \( C H_{4} \)
D. \( C \) in \( C O_{2} \)


The number of gram-atoms in 8 g of He
are:
A .2
B . \( 1.204 \times 10^{24} \)
c. \( 3.10 \times 10^{23} \)
D. 4


the slant height of a right cone is given as \( 10 \mathrm{cm} . \) if the volume of cone is
maximum, then the semi- vertical angle
is:
A \( \cdot_{-\cos \frac{1}{\sqrt{3}}} \)
B. \( \tan ^{-1} \sqrt{2} \)
c.
D.


A vector \( \vec{B} \) which has a magnitude 8.0 is added to a vector \( \vec{A} \) which lie along
the \( x \) -axis. The sum of these two vectors
is a third vector which lie along the \( y \)
axis and has a magnitude that is twice the magnitude of \( \vec{A} . \) The magnitude of
\( \vec{A} \) is:
A. \( \frac{8}{\sqrt{5}} \)
B. \( \frac{10}{\sqrt{5}} \)
c. \( \frac{8}{\sqrt{3}} \)
D. \( \frac{8}{\sqrt{6}} \)


An insulating loop has one side charged positively and the other side charged negatively. An electron is placed in the middle of the loop. What would be the direction of the net force on the electron
due to the charges in the ring?
A. Toward the top of the loop
B. Toward the right of the loop
c. Toward the left of the loop
D. There is no net force on the loop


Draw electron dot structure of
\( \boldsymbol{C O}_{2}, \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{F}_{2}, \boldsymbol{N}_{2} \)


\( \sim[(\sim p) \wedge q] \) is logically equivalent to
A \( . \sim(p \vee q) \)
В \( . \sim[p \wedge(\sim q)] \)
C \( . p \wedge(\sim q) \)
D. \( p \vee(\sim q) \)
E \( .(\sim p) \vee(\sim q) \)


spheres of radii 'a' and 'b', respectively(see figure), has volume charge density \( \rho=\frac{A}{r}, \) where \( A \) is a
constant and \( r \) is the distance from the
centre. At the centre of the spheres is a
point charge \( Q . \) The value of \( A \) such that
the electric field in the region between
the spheres will be constant, is :
A \( \cdot \frac{Q}{2 \pi a^{2}} \)
В. \( \frac{Q}{2 \pi\left(b^{2}-a^{2}\right)} \)
c. \( \frac{2 Q}{\pi\left(a^{2}-b^{2}\right)} \)
\( D \cdot \frac{2 Q}{\pi^{2}} \)


Find the value of the polynomial \( y^{3}- \)
\( 5 y-2 y^{2}+3 \) when, \( y=-b \)
A. \( -b^{3}-2 b^{2}+5 b+3 \)
3
В. \( b^{2}-2 b^{3}+b+1 \)
C. \( -b^{3}-2 b^{2}-b+3 \)
D. \( b^{3}-2 b^{2}+b-3 \)


Fill in the blanks with the correct
word/symbol to make it a true
statement:
A triangle whose one angle is more than
\( 90^{\circ} \) is known as


State True or False.
Non-metals have lustre.
A. True
B. False


The number of real solutions of the
equation \( \left(\frac{\mathbf{9}}{\mathbf{1 0}}\right)^{\boldsymbol{x}}=-\mathbf{3}+\boldsymbol{x}-\boldsymbol{x}^{2} \) is
A .2
B.
\( c \cdot 0 \)
D. None of these


China wares are wrapped in straw or
paper before packing.What is the basis of this application?
A. Impulse
B. Momentum
c. Acceleration
D. Force


Fill in the blanks.
A horizontal pipeline carries water in streamline flow. At a point along the pipe, where the cross-sectional area is \( 10 \mathrm{cm}^{2}, \) the water velocity is \( 1 \mathrm{ms}^{-1} \)
and the pressure is 2000 Pa. The
pressure of water at another point
where the cross-sectional area is \( 5 \mathrm{cm}^{2} \)
is
\( \left.10^{3} k g m^{-3}\right) \)


There are 42 hemispherical bowls, each
of radius \( 3.5 \mathrm{cm} \). Find the quantity of water in litres which is just sufficient to
fill these 42 bowls. (Take \( \pi=\frac{22}{7} \) )
A . 3.773 litres
B. 3.553 litres
c. 3.223 litres
D. 4.773 litres


Select the wrong statement:
A. There is no convection in zero gravity environment
B. Entire radiation emitted by a hot body falls in the infrared region of the electromagnetic spectrum
C. Blue flame is at higher temperature than a yellow flame
D. Diathermanous substance means it neither absorbs
nor reflects any fraction of the radiation incident on it


Solve the following equation:
\( \sin x+\sin ^{2} x+\cos ^{2} x=0 \)


On
\( \mathbf{2 9} \) October there was a difference of
hour and minute in the
time of the moon rise (as compared to
28 October)


Which of the following is not a postulate
given by Rutherford?
A. The positively charged particles are present in the nucleus of atom
B. Size of nucleus is very small as compare to the size of atom
c. The whole mass of the atom is concentrated in the
center of atom called nucleus
D. An atom consists of a positively charged sphere, with electrons set within the sphere


Assertion
The relation among \( u, v \) and \( f \) for the spherical mirror is valid only for mirrors
whose sizes are very small compared to
their radii of curvature.
Reason
The laws of reflection are strictly valid
for plane surfaces but not for large spherical surfaces.
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


Which statement is incorrect for a
catalyst?
A. It does not affect the equilibrium constant
B. It increases the proportion of products in less time
C. It decreases the activation energy of a reaction
D. It increases the free energy change for the reaction


Which of these best describes a
coenzyme?
A. An inorganic molecule that reduces enzyme activity
B. An organic molecule that reduces enzyme activity
C. An inorganic molecule that enhances enzyme activity
D. An organic molecule that enhances enzyme activity
E. An organic molecule that competes for the active site of an enzyme


Two satellites \( A \) and \( B \) go round the planet \( \boldsymbol{P} \) in circular orbits having radii \( 4 R \) and \( R \) respectively. If the speed of
the satellite \( A \) is \( 3 v, \) then the speed of
satellite \( \boldsymbol{B} \) will be
A . \( 6 v \)
в. \( 12 v \)
c. \( \frac{3 v}{2} \)
D. \( \frac{4 v}{3} \)


Batsman \( A \) gets and average of 64 runs per innings with standard deviation of
18 runs, while batsman \( B \) get an
average score of 43 runs with standard
deviation of 9 runs in an equal number of innings. Discuss the efficiency and consistency of both the batsmen


A particle is moving in a straight line such that its distance at any time \( t \) is given by \( s=\frac{1}{4} t^{4}-2 t^{3}+4 t^{2}-7 . \) Find
twhen its velocity is maximum( \( t_{v} \) ) and
acceleration minimum(t \( _{a} \) ).
A \( \cdot t_{v}=2-2 / \sqrt{3}, t_{a}=4 \)
В \( \cdot t_{v}=2, t_{a}=1 \)
C \( \cdot t_{v}=2-2 / \sqrt{3}, t_{a}=2 \)
D. \( t_{v}=-2 / \sqrt{3}, t_{a}=2 \)


The displacement - time graph for a
particle executing SHM is as shown in
figure
Which of the following statement is
correct?
A \( \cdot \) the velocity of the particle is maximum at \( t=\frac{3}{4} T \)
B. The velocity of the particle is maximum at \( t=\frac{T}{2} \)
C the acceleration of the particle is maximum at \( t=\frac{T}{4} \)
D. The acceleration of the particle is maximum at \( t=\frac{3}{4} T \)


Assertion (A): More the turns more is
the
resistance
Reason(R): Impedance of primary and secondary in a transformer is directly proportional
to number
of turns in the coils.
A. Both Assertion and Reason are true and Reason is the correct explanation for Assertion
B. Assertion and Reason are true but Reason is not the correct explanation for Assertion
C. Assertion is true, Reason is false
D. Assertion is false, Reason is true


Explain the terms Inductive and Electromeric effects. Which electron
displacement effect explains the
following correct orders of acidity of the carboxylic acids?
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C O O H}> \)
\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{C O O H}> \)
\( \left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C C O O H} \)


Which out of the following has smel similar to that of vinegar?
A. Methanol
B. Ethanol
c. Ethanoic acid
D. Formic acid


Cell of emf \( X \) is connected across a
resistor R. The potential difference across the wire is measured as Y. The internal resistance of'the cell should be
A. \( x-Y / R \)
B. (X - Y)R/Y
c. \( (x-y) Y / R \)
\( D \cdot(x-y) R \)


The population of a village is \( 10000 . \) If the population increases by \( 10 \% \) in the first year, by \( 20 \% \) in the second year and due to mass exodus, it decreases by \( 5 \% \) in the third year, what will be its population after 3 years?
A . 10,540
B. 11,540
c. 12,540
D. 13,540


Which of the following is path function?
A. Work
B. Specific volume
c. Pressure
D. Temperature


The magnetic flux through a circular
carrying a current of \( 2.0 A \) is 0.8 weber.
If the current reduces to \( 1.5 A \) in \( 0.1 s \)
the induced emf be
A . \( 2.0 V \)
в. \( 4.0 V \)
\( c .8 .0 V \)
D. None of the above


A particle at \( x=0 \) and \( t=0 \) starts
moving along +ve X-direction with velocity v then x varies with time as?
\( \mathbf{A} \cdot \mathbf{t} \)
в. \( t^{3} \)
\( c \cdot t^{2} \)
D. \( t^{1 / 2} \)


Which of the following is a neutral oxide
\( ? \)
A . \( N O \)
в. \( N O_{2} \)
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{3} \)
D. \( N_{2} O_{5} \)


\( \frac{k}{L} \)


\( \boldsymbol{f}: \boldsymbol{B} \rightarrow \boldsymbol{B}, \) if \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}, \) then the
function \( \boldsymbol{f} \) is


Compared to K for the dissociation, \( 2 H_{2} S \rightleftharpoons 2 H^{+}+2 H S^{-}, \) then \( K \) for the
\( \boldsymbol{H}^{+}+\boldsymbol{H} \boldsymbol{S}^{-} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{S} \) would have :
A \( \cdot \frac{1}{\sqrt{K}} \)
в. \( \frac{1}{K} \)
c. \( \frac{1}{K^{2}} \)
D. \( \frac{1}{K^{3}} \)


Solve \( : 2 x=100 \)


\( M L^{2} T^{-2} \) is the dimensional formula for
A. moment of inertia
B. pressure
c. elasticity
D. couple acting on a body


What happens when:
(i) \( P C l_{5} \) is heated?
(ii) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) is heated?
Also write the reactions involved.


A body is acted upon by force which is inversely proportional to the distance covered. The work done will be
proportional to:
\( A \)
B \( \cdot s^{2} \)
c. \( \sqrt{s} \)
D. None of the above


The number of values of b for which
there is an isosceles triangle with sides of lengths \( b+5,3 b-2 \) and \( 6-b \) is/are
A.
B.
\( c \cdot 2 \)
D. 3


Puberty is preceded by
A. Increased levels of androgen.
B. Increased levels of thyroxine.
C. Increased levels of insulin.
D. None of the above.


The botanical name for 'Kattha' is
A . Acacia concinna
B. Acacia catechu
c. Acacia senegal
D. Acacia nilotica


Nucleus of mass number \( A \), originally
at rest, emits the \( \alpha \) particle with speed
v. The daughter nucleus recoils with a
speed of :
A \( .2 v(A+4) \)
B. \( 4 v(A+4) \)
c. \( 4 v /(A-4) \)
D. \( 2 v /(A-4) \)


Find the mode of the following data
\( \begin{array}{ll}\text { Class Interval } & \text { Frequency } \\ 10-20 & 7 \\ 20-30 & 12 \\ 30-40 & 20 \\ 40-50 & 11 \\ 50-60 & 8\end{array} \)


Construct a triangle \( P Q R \) in which \( Q R=6 c m, \angle Q=60^{\circ} \) and \( P R- \)
\( \boldsymbol{P Q}=\boldsymbol{2} \boldsymbol{c m} \)


A 50 kg girl wearing heel shoes balances on a single heel. The heel is circular with a diameter \( 1 \mathrm{cm} \) The pressure exerted by the heel on the horizontal floor is then (Take \( g=10 \mathrm{m} \) s -2)
A \( \cdot 6.4 \times 10^{4} \) Pa. . \( . \). 6.4 .
B. \( 6.4 \times 10^{5} \) pa
c. \( 6.4 \times 10^{6} \) Ра
D. 6.4 \( \times 10^{7} \) Ра


Unpolarised light is incident from air on
a plane surface of a material of
refractive index' \( \mu^{\prime} . \) At a particular
angle of incidence \( ^{\prime} \boldsymbol{i}^{\prime}, \) it is found that the reflected and refracted rays are
perpendicular to each other. Which of the following options is correct for this situation?
A \( \cdot i=\sin ^{-1}\left(\frac{1}{\mu}\right) \)
B. Reflected light is polarised with its electric vector parallel to the plane of incidence
C. Reflected light is polarised with its electric vector perpendicular to the plane of incidence
D. \( i=\tan ^{-1}\left(\frac{1}{\mu}\right) \)


The brilliance of diamonds is due to the
internal reflection of light the light is slowed down and bent away from its original path because it strikes:
A. tightly-bound nucleus
B. the nucleus (centre) of carbon atoms
c. loosely-held mobile electrons
D. layers of carbon atoms


If \( \frac{1}{p+q}, \frac{1}{r+p}, \frac{1}{q+r} \) are in A.P., then
A \( \cdot p^{2}, q^{2}, r^{2} \) are in A.P.
B . \( q^{2}, p^{2}, r^{2} \) bare in A.P.
c. \( q^{2}, r^{2}, p^{2} \) are in A.P.
D. \( p, q, r \) are in A.P.


If \( z \in C, \) the minimum value of \( |z|+ \)
\( |z-5| \) is attained by
This question has multiple correct options
\( \mathbf{A} \cdot z=0 \)
B . \( z=5 \)
c. \( z=5 / 2 \)
D. For all \( z \in[0,5] \)


Let \( \bar{X} \) and M.D. be the mean and the
mean deviation about \( \bar{X} \) of \( n \)
observations \( x_{i}, i=1,2, \ldots . ., n . \) If each
of the observations is increased by 5
then the new mean and the mean
deviation about the new mean, respectively, are :
A. \( \bar{X}, \) М.D.
в. \( \bar{X}+5, M . D \)
c. \( \bar{X}, M . D .+5 \)
D. \( \bar{X}+5 m, M . D .+5 \)


radii \( 2 R \) and \( 4 R \) respectively are kept at
distances \( x \) and \( 2 x \) from the point
charge \( q . \) A surface cutout of a non
conducting shell \( C \) is kept such that its
centre coincides with the point charge.
Each plate and the spherical surface
carries a surface charge density \( \sigma . \) If \( \phi_{1} \)
is flux through surface of \( (B) \) due to
electric field of \( (A) \) and \( \phi_{2} \) be the flux
through \( (A) \) due to electric field of \( (B) \)
then:
\( \mathbf{A} \cdot \phi_{1}=\phi_{2} \)
\( \mathbf{B} \cdot \phi_{1}>\phi_{2} \)
\( \mathbf{c} \cdot \phi_{1}<\phi_{2} \)
D. It depend \( R \)


Fusion reaction takes place at very
high temperature because
A. atoms are ionised at high temperatures
B. molecules breakup at high temperature
C . nuclei break up at high temperature
D. kinetic energy is high enough to overcome repulsion between nuclei


If \( f(x y)=f(x) . f(y) \forall x, y \in R \) If the
function is continuous at one point \( \boldsymbol{x}= \)
\( a, \) then \( f(x) \) is:
A. continuous for all \( x \in R-\{0\} \)
B. continuous forall \( x \in R \)
c. discontinuous on
D. continuous at \( x=0 \)


What is the normality of aqueous
solution of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) having \( \boldsymbol{p} \boldsymbol{H}=\mathbf{1} ? \)
A. \( 1 N \)
B. \( 0.05 N \)
\( c \cdot 0.1 N \)
D. \( 0.5 N \)


Number of irrational terms in the expansion of \( (\sqrt{2}+\sqrt{3})^{15} \) is equal to
A . 16
B. 7
c. 12
D. 15


The wavelength of light from the spectral emission line of sodium is 589
nm. Find the kinetic energy at which
(a) an electron, and
(b) a neutron would have the same de
Broglie wavelength.


Explain biomagnification of DDT in an aquatic food chain. How does it affect the bird population?


Maximum number of \( \boldsymbol{P}-\boldsymbol{H} \) bond \( (\boldsymbol{s}) \)
are there in a molecule of?
A. Orthophosphorous acid
B. Pyrophosphoric acid
c. Pyrophosphorous acid
D. Hypophosphoric acid


Two numbers are in the ratio \( 1 \frac{1}{2}: 2 \frac{2}{3} \)
But if each number is increased by 15 then the ratio becomes \( 1 \frac{2}{3}: 2 \frac{1}{2} . \) The
numbers are
\( \mathbf{A} \cdot 27,42 \)
B . 36,48
c. 27,48
D. 27,36


A short magnet is allowed to fall from
rest along the axis of a horizontal conducting ring. The distance fallen by the magnet in one second may be
\( A \cdot 5 m \)
в. \( 6 m \)
\( c .4 m \)
D. None of these


n figure, \( x: y: z=5: 4: 6 . \) If \( x \) OY is a
straight line then the values of \( x, y \) and \( z \)
are
This question has multiple correct options
A . \( x=60^{\circ} \)
В . \( y=48^{\circ} \)
\( \mathbf{c} . z=72^{\circ} \)


For a given reaction, \( \triangle \boldsymbol{H}= \)
\( 35.5 k J m o l^{-1} \) and \( \triangle S= \)
\( 83.6 J K^{-1} \) mol \( ^{-1} . \) The reaction is
spontaneous at: (Assume that \( \triangle \boldsymbol{H} \) and
\( \triangle S \) do not vary with temperature)
\( \mathbf{A} \cdot T>298 K \)
В. \( T<425 K \)
c. \( T>425 K \)
D. All temperatures


The basic unit of neoprene
is
A. chloroprene
B. isoprene
c. styrene
D. butadiene


Predict the direction in which the
following equilibrium will shift backward
\( N_{2}+3 H_{2} \Leftrightarrow 2 N H_{3} \Delta H= \)
\( (g) \)
\( (g) \)
\( -100 J \) oule
A. increasing Temperature
B. increasing pressure
c. addition of catalyst
D. on addition of \( N H_{3} \)


Acceleration of 3 rd maxima w.r.t 3 rd
maxima on other side of central
maxima at \( t=3 s \) is
A \( \cdot 0.02 m s^{-2} \hat{i} \)
B. \( 0.03 m s^{-2} \hat{i} \)
\( \mathbf{c} \cdot 10 m s^{-2 \hat{i}} \)
D. \( 0.6 m s^{-2} \hat{i} \)


State the role of silica in the metallurgy
of copper.


The current in the given circuit is:
(Given barrier potential of the diode =
\( 0.5 V) \)
\( \mathbf{A} \cdot 4 m A \)
B. \( 4 A \)
c. \( 4 \mu A \)
D. \( 40 \mu A \)


\( \frac{\sqrt{2}}{8} \)


Who is responsible for the sex of
offspring-male of female? Why?


Incident parallel rays make an angle \( 5^{\circ} \)
with the axis of a diverging lens of focal
length \( 20 \mathrm{cm} . \) Then image will be :
\( \left(\tan 5^{\circ}=0.0875\right) \)
A. Real and in focal plane at a distance of \( 1.75 \mathrm{cm} \) from the optical axis
B. Real but not in focal plane
C. Virtual and in focal plane at a distance of \( 1.75 \mathrm{cm} \) from the optical axis
D. Image will be virtual but not in focal plane


Metals can gain electrons to form negative ion.
A . True
B. False


No. of elements in 1st period are:
\( A \cdot 2 \)
B. 6
\( c \cdot 8 \)
D. 18


Among the following, which will not help
to reduce air pollution?
A. Burn household rubbish in incinerators
B. Use catalytic converters on motor vehicles
C. Fix electric precipitators to factory chimneys
D. Ban smoking in public places such as in offices


If \( \mu_{O} \) and \( \mu_{e} \) are the refractive indices
of a double
refracting crystal, then
1) \( \mu_{O}<\mu_{e} \) for quartz crystal
2) \( \mu_{O}>\mu_{e} \) for calacite crystal
A. both 1 and 2 are true
B. 1 is true 2 is false
c. 1 false 2 is true
D. both 1 and 2 are false


A conducting body 1 has some initial charge \( Q, \) and its capacitance is \( C . \) There are two other conducting bodies, 2 and \( 3, \) having capacitances: \( C_{2}=2 C \)
and \( C_{3} \rightarrow \infty . \) Bodies 2 and 3 are
initially uncharged. "Body 2 is touched with body \( 1 . \) Then, body 2 is removed from body 1 and touched with body 3 and then removed". This process is
repeated \( N \) times. Then, the charge on
body 1 at the end must be :
A \( \cdot Q / 3^{N} \)
B . \( Q / 3^{N-1} \)
c. \( Q / N^{3} \)
D. None


In a given DNA segment, the number of nucleotides of guanine is 75 and those of thymine is \( 75 . \) What will be the total
number of nucleotides in the segment?
A . 75
B. 750
c. 225
D. 300


A thin tube of uniform cross-section is
sealed at both ends. It lies horizontally.
The middle \( 5 c m \) contains \( \mathrm{Hg} \) and two equal ends contain air at the same
pressure \( P_{0} . \) When the tube is held at an
angle of \( 60^{\circ} \) with the vertical, the length of the air column above and below the
Hg are \( 46 \mathrm{cm} \) and \( 44.5 \mathrm{cm} \). Calculate
pressure \( P_{0} \) in cm of Hg. Assume
temperature of the system to be
constant.
A. \( 55 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. \( 65 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 70.4 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 75.4 \mathrm{cm} \) of \( \mathrm{Hg} \)


14 12
connected by a string which passes
over a frictional pulley. If \( \mathrm{M}_{1}, \mathrm{M}_{2} \) and the
table are frictionless, the acceleration
of the masses would be
\( \mathbf{A} \cdot \frac{M_{1} g}{M_{1}+M_{2}} \)
B. \( \frac{M_{1}+M_{2}}{M_{1} g} \)
c. \( \frac{M_{2} g}{M_{1}+M_{2}} \)
D. none of these


A cois
B. Happy Father's Day
\( c \)
D.


The catalytic promoter used in Haber's
process is :
A. Mo
B. Ni
\( c \cdot P t \)
D. \( \mathrm{v}_{2} \mathrm{O}_{5} \)


In the given figure if \( V_{I N} \) increases then
\( \boldsymbol{I}_{z} \) will
A. change
B. decrease
\( c . \) increase
D. does not change


A lot of contains 20 articles. The
probability that the lot contains exactly
2 defective articles is 0.4 and the
probability that the lot contains exactly 3 defective articles is \( 0.6 . \) Articles are
drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is
the probability that the testing procedure ends at the twelfth testing?
A \( \cdot \frac{99}{1900} \)
в. \( \frac{99}{950} \)
c. \( \frac{198}{1900} \)
D. \( \frac{99}{1000} \)


The selling price and cost price of an article differ by Rs. \( 240 . \) If the profit percentage is \( 20, \) then selling price is:
A. Rs. 1440
B . Rs. 1200
c. Rs.1420
D. None of these


The converse of \( \boldsymbol{p} \rightarrow(\boldsymbol{q} \rightarrow \boldsymbol{r}) \) is
\( \mathbf{A} \cdot(q \wedge \sim r) \vee p \)
в. \( (\sim q \vee r) \vee p \)
\( c \cdot(q \wedge \sim r) \wedge \sim p \)
\( p \)
D. \( (q \wedge \sim r) \wedge p \)


What are the major products in the
following reactions:


Which of the following is detected by carbylamine test?
A. \( C O N_{2} H_{4} \)
В . \( C_{6} H_{5} N H_{2} \)
c. \( C H_{3} C O N H_{2} \)
D. \( C_{2} H_{5} C N \)


lonic species are stabilised by the dispersal of charge, which of the following carboxylate ions is the most positive charge?
A. O
\( C H_{3}-C-\bar{O} \)
в. \( C l-C H_{2}-C-\bar{O} \)
c. O
\( F-C H_{2}-C-\bar{O} \)
D. \( F-C H_{2}-C-\bar{O} \)
\( _{\mathrm{F}} \)


Four solid spheres each of diameter \( \sqrt{5} \)
\( \mathrm{m} \) and mass \( 0.5 k g \) are placed with their
centres at the corners of a square of
side \( 4 c m \). The moment of inertia of the
system about the diagonal of the square is \( N \times 10^{-4} k g m^{2} \) then \( N \) is


Carbon forms bonds with another
element by :
A. transferring of electrons.
B. sharing of electrons.
c. Both A and B
D. None of the above


An electric dipole has a pair of equa and opposite point charges \( +\mathrm{Q} \) and \( \mathrm{Q} \) separated by a distance 2x. The axis of the dipole is defined as
A. the line joining positive charge to -ve charge
B. the line making angle of \( 45^{\circ} \) with line joining two charges
c. perpendicular to the line joining the two charges drawn at the centre and pointing upward direction
D. perpendicular to the line joining the two charges drawn at the centre and pointing downward direction


\( \ln L C R \operatorname{series} A C \) circuit
A. If \( R \) is increased current will decrease
B. If \( L \) is increased current will decrease
c. If \( C \) is increased current will increase.
D. If \( C \) is increased current will decrease.


The value of \( K \) which the Function
\[
\boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}
\frac{\tan 4 \boldsymbol{x}}{\tan 5 x}, & 0<x<\frac{\pi}{2} \\
\boldsymbol{k}+\frac{2}{5}, & \boldsymbol{x}=\frac{\pi}{2}
\end{array}\right.
\]
continuous at \( x=\frac{\pi}{2}, \) is


Edge of a cube whose volume is 27 cu.
cm. is
A \( \cdot \frac{1}{9} c m \)
в. \( \frac{1}{3} c m \)
\( c \cdot 3 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)


The potentiometer wire of length has
\( 100 \mathrm{cm} \) has a resistance of \( 10 \Omega \).It is
connected in series with a resistance of
\( 5 \Omega \) and an acceleration of emf \( 3 V \)
having magnitude resistance. A source A source of \( 1.2 \mathrm{V} \) is balanced against
ength I' Of the potential wire. Find the
value of L.


Which of the following procedures will give you water free from all impurities?
A. Adding chlorine tablets
B. Distillation
c. Boiling
D. Filtration


For the preparation of alkanes, aqueous solution of sodium or potassium salt of carboxylic acid is subjected to:
A. Electrolysis
B. Oxidation
c. Hydrogenation
D. Hydrolysis


The correct name of the given
compound:
\( \boldsymbol{C H}_{3}-\underset{\boldsymbol{O} \boldsymbol{H}}{\boldsymbol{C}}-\boldsymbol{C O O H} \)
A. glycoxal
B. lactic acid
c. glycine
D. glyceraldehyde


Identify the organisms.
A. Cnidarian - A, Yeast - B showing budding
B. Cnidarian - A, Protozaon - B showing budding
C. Cnidarian - A showing binary fission, Protozaon - B showing budding
D. Cnidarian - A showing budding, Protozaon - B showing binary fission


Define the following term limiting
reagent.


A mixture of \( C_{3} H_{8} \) and \( C H_{4} \) exerts a
pressure of \( 320 \mathrm{mm} \) Hg at temperature \( \boldsymbol{T}(\boldsymbol{K}) \) in a \( \boldsymbol{V} \) litre flask. On complete combustion, gaseous mixture contains
\( C O_{2}, \) only and exerts a pressure of 448 \( \mathrm{mm} \) Hg under identical condition.
Hence, mole fraction of \( C_{3} H_{8} \) in the mixture is :
A . 0.2
B. 0.8
c. 0.25
D. 0.75


Ethylenediamine is an example of:
A. monodentate ligand
B. bidentate ligand
c. tridentate ligand
D. polydentate ligand


When \( A \) is given its first impulse at the
moment:
\( A . A, B \) and centre of earth are in same straight line
B. \( B \) is ahead of \( A \) angularly
\( \mathrm{c} . B \) is behide \( A \) angularly
D. None of these


Assertion
If three points \( P, Q \) and \( R \) have position vectors \( \vec{a}, \vec{b} \) and \( \vec{c}, \) respectively, and \( 2 \vec{a}+3 \vec{b}-5 \vec{c}=0, \) then the points \( P, Q \)
and \( R \) must be collinear.
Reason
If for three points \( A, B \) and \( C, A B= \) \( \lambda \overrightarrow{A C}, \) then points \( A, B \) and \( C \) must be
collinear.
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


Why is a car or a bus safe place during lightening?
A. Because it does not rain inside the bus
B. Because lightening cannot travel through the glass.
c. Because a car or a bus is insulated from the Earth.
D. None of the above


Arrange the following in order of decreasing boiling point:
(1) n-Butane
(II) n-Butanol
(III) n-Butyl chloride
(IV) Isobutane
A. \( I>V>I I I>I I \)
в. \( I V>I I>I I I>I \)
c. \( I>I I>I I I>I V \)
D. \( I I>I I I>I>I V \)


The force acting on a mass of 1 g due to the gravitational pull on the earth is called 1 g wt. One \( g \) wt equals
A . \( 1 \mathrm{N} \)
B. 9.8N
c. 980 dyne
D. None of these


Give the increasing order of \( p K_{a} \) value of the following compounds?
I. \( \mathrm{C}_{9} \mathrm{H}_{10} \)
A. \( (I)<(I I I)<(I I) \)
в. \( (I)<(I I)<(I I I) \)
c. \( (I I)<(I I I)<(I) \)
D. \( (I I I)<(I I)<(I) \)


The operating magnetic field for accelerating protons in a cyclotron oscillator having frequency of 12 MHz is \( \left(q=1.6 \times 10^{-19} \mathrm{C}, m_{p}=1.67 \times 10^{-27}\right. \)
kg and \( \left.1 \mathrm{MeV}=1.6 \times 10^{-13} \mathrm{J}\right) \)
A . 0.69 न
B . 0.79 न
c. 0.59 न
D. 0.49 \( T \)


When \( \mathbf{S O}_{2} \) is passed through acidified
solution of \( \mathbf{H}_{2} \mathbf{S} \)
A \( \cdot \mathrm{H}_{2} \mathrm{SO}_{3} \) is formed
B. \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is formed
c. sulphur is precipitated
D. \( \mathrm{H}_{2} \mathrm{SO}_{5} \) is formed


Where on the phase diagram is there an equilibrium between liquids and
gases?
A. Graph between \( A \) and \( B \)
B. Graph \( A \)
c. Graph between \( B \) and \( C \)
D. Graph \( A, B \), and \( C \)


\( \frac{-}{8} \)
\( d \)
\( \frac{6}{6} \)
0


How much heat energy in Joules is necessary to raise the temperature of
\( 5 k g \) of water from \( 20^{\circ} \) to \( 100^{\circ} ? \)
A. \( 1672 K J \)
в. \( 167200 J \)
c. \( 16720 J \)
D. \( 1672 J \)


Which one of the following substances is formed by the reaction of potassium permanganate on concentrated by hydrochloric acid?
\( \mathbf{A} \cdot H_{2} O_{2} \)
в. НОС\( l \)
\( \mathrm{c} \cdot H_{2} \)
D. \( C l_{2} \)


Which of the following electronic configurations are associated with the formation of a molecule with expanded
octet?
This question has multiple correct options
A \( \cdot[H e] 2 s^{2} 2 p^{1} \)
B . \( [H e] 2 s^{2} 2 p^{2} \)
C . \( [N e] 3 s^{2} 3 p^{3} \)
D \cdot \( [N e] 3 s^{2} 3 p^{4} \)


Why do nails have pointed tips?
A. It enhances their look.
B. It reduces the force required to fix it in the wall.
C . It increases the strength.
D. It makes it easy to handle.


The empirical formula of an organic
compound is \( C H_{2} O . \) Its vapour density
is \( 45 . \) The molecular formula of the
compound is:
A \( \cdot C_{2} O \)
в. \( C_{2} H_{4} O_{2} \)
\( \mathbf{c} \cdot C_{3} H_{6} O_{3} \)
D. \( C_{6} H_{12} O_{6} \)


The frequency of vibration is less than the natural frequency in
A. Forced vibrations
B. Free vibration
c. Damped vibrations
D. All


Which one of the following statements
is correct?
A. Flower of tulip is a modified shoot
B. In a tomato, fruit is a capsule
c. Seeds of orchids have oil-rich endosperms
D. Placentation in primrose basal


Which of the following is not characteristic of all divisions of
vascular plants?
A. Development of seeds
B. An alternation of generations
c. Differentiation into roots, stems, and leaves
D. xylem and phloem for transporting materials between roots and leaves


Identify the electronic transition among the consecutive orbits in a hydrogen atom that results in the emission of the
electromagnetic relation of the highest frequency. Explain.


Calculate mode of the following data.
\( \begin{array}{lllll}\text { Marks } & 0- & 20- & 40- & 60- \\ & 20 & 40 & 60 & 80\end{array} \)
Number
of
students \( \quad 8 \quad \begin{array}{ll}8 & 10 \\ \text { students }\end{array} \)


If foci are points (0,1)(0,-1) and minor axis is of length \( 1, \) then equation of ellipse is
A \( \cdot \frac{x^{2}}{1 / 4}+\frac{y^{2}}{5 / 4}=1 \)
В. \( \frac{x^{2}}{5 / 4}+\frac{y^{2}}{1 / 4}=1 \)
c. \( \frac{x^{2}}{3 / 4}+\frac{y^{2}}{1 / 4}=1 \)
D. \( \frac{x^{2}}{1 / 4}+\frac{y^{2}}{3 / 4}=1 \)


The mean deviation of the data
\( \mathbf{3}, \mathbf{1 0}, \mathbf{1 0}, \mathbf{4}, \mathbf{7}, \mathbf{1 0}, \mathbf{5} \) from the mean is
A . 2
в. 2.57
\( c .3 \)
D. 3.75


An organic compound with molecular
formula \( C_{4} H_{10} O \) does not react with
sodium. With excess of HI it gives only one type of alkyl halide. The compound
is:
A. \( C_{2} H_{5} O C_{2} H_{5} \)
B \( . C H_{3} \) \( H_{3} C_{\} H C H_{3} \)
\( O C H_{3} \)
c. \( C H_{3} C H_{2} C H_{2} O C H_{3} \)
D. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)


In our country, vast tracts of forests are cleared and a single species of plant is
cultivated. This practice promotes
A. Biodiversity in the area
B. Monoculture in the area
c. Growth of natural forest
D. Preserves the natural ecosystem in the area


Solve the
\( 2 \frac{1}{5}-\frac{-1}{3} \)


Let \( \mathbf{S}_{\mathbf{n}}=\sum_{\mathbf{k}=1}^{\mathbf{n}} \frac{\mathbf{n}}{\mathbf{n}^{2}+\mathbf{k} \mathbf{n}+\mathbf{k}^{2}} \) and \( \mathbf{T}_{\mathbf{n}}= \)
\( \sum_{\mathbf{k}=0}^{\mathbf{n}-1} \frac{\mathbf{n}}{\mathbf{n}^{2}+\mathbf{k} \mathbf{n}+\mathbf{k}^{2}} \) for \( \mathbf{n}=\mathbf{1}, \mathbf{2}, \mathbf{3}, \dots \)
Then, This question has multiple correct options
A \( \cdot \mathrm{S}_{\mathrm{n}}<\frac{\pi}{3 \sqrt{3}} \)
В \( \cdot \mathrm{s}_{\mathrm{n}}>\frac{\pi}{3 \sqrt{3}} \)
\( \mathrm{c} \cdot \mathrm{T}_{\mathrm{n}}<\frac{\pi}{3 \sqrt{3}} \)
D. \( \mathrm{T}_{\mathrm{n}}>\frac{\pi}{3 \sqrt{3}} \)


Three large plates are arranged as shown. How much charge will flow
through the key \( K \) if it is closed?
\( A \cdot \frac{5 Q}{6} \)
в. \( \frac{4 Q}{3} \)
\( c \cdot \frac{3 Q}{2} \)
D. None of these


The Fahrenheit temperature \( \boldsymbol{F} \)
decreased by 32 is equal to nine-fifths of the centigrade temperature \( C . \) The correct formula framed for the above
statement will be :
A \( \cdot F+32=\frac{5}{9} C \)
В \( \cdot F-32=\frac{5}{9} C \)
c. \( _{F}+32=\frac{9}{5} C \)
D. \( _{F-32}=\frac{9}{5} C \)


A rectangle DEFG is plotted in \( X Y \) plane. The co-ordinates of D , E , F and G \( \operatorname{are}(2,2),(9,2),(9,10) \) and (2,10)
Find the new co-ordinates of F when
DEFG is rotated \( 270^{\circ} \) around origin.
This question has multiple correct options
A \( \cdot(-10,9) \)
B. (-10,-9)
c. (10,9)
D. (10,-9)


If a hemi-spherical dome has an inner diameter of \( 28 m, \) then its volume (in
\( \boldsymbol{m}^{3} \) ) is:
A . 6186.60
в. 5749.33
c. 7099.33
D. 7459.33


As we go down in the electro-chemical
series of metals, the reactivity
A. decreases and then increases
B. increases and then decreases
c. decreases
D. increases


A tendril of a pea plant and phylloclade of Opuntia are homologous.
A. True
B. False


If a particle moves in a circle with
constant speed, its velocity :
A. remains constant
B. changes in magnitude
c. changes direction
D. changes both in magnitude and directions


The monthly salaries in rupees of 30
workers in a factory are given below:
\( \mathbf{5 0 0 0}, \mathbf{7 0 0 0}, \mathbf{3 0 0 0}, \mathbf{4 0 0 0}, \mathbf{4 0 0 0}, \mathbf{3 0 0 0}, \mathbf{3} \)
4000,9000,3000,5000,4000,4000,3
\( 8000,3000,3000,6000,7000,7000, \)
Find the mean of monthly salary.


A cylindrical gas container is closed at
the top and open at the bottom; if the iron plate of the top is \( 5 / 4 \) times as thick as the plate forming the cylindrical sides, find the radio of the radius to the height of the cylinder using minimum material for the same capacity.
A . 5 \( \bar{A} \)
в. \( \frac{4}{5} \)
\( c \cdot \frac{5}{2} \)
D. \( \frac{2}{5} \)


Suppose we have four boxes \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
and \( D \) containing colored marbles as
given :

One of the boxes has been selected at
random and a single marble is drawn
from it. If the marble is red, what is the
probability that it was drawn from box
\( A, \) box \( B, \) box \( C ? \)
\begin{tabular}{cc|cc}
BOX & \multicolumn{3}{c} { Marbles Color } \\
\hline & Red & White & Black \\
\hline \( \mathrm{A} \) & 1 & 6 & 3 \\
\( \mathrm{B} \) & 6 & 2 & 2 \\
\( \mathrm{C} \) & 8 & 1 & 1 \\
\( \mathrm{D} \) & 0 & 6 & 4 \\
\hline
\end{tabular}


A simple pendulum is suspended from
a peg on a vertical wall.The pendulum is
pulled away from the wall to a
horizontal position (see fig) and released.The ball hits the wall, the coefficient of restitution being \( \frac{2}{\sqrt{5}} \)
What is the minimum number of
collisions after which the amplitude of
oscillations becomes less than 60
degrees?


Mark the correct alternative of the
following. n figure, \( A B|| C D \) and \( E F \) is a transversal intersecting \( A B \) and \( C D \) at \( P \) and \( Q \)
respectively. The measure of \( \angle D Q P \) is?
\( A \cdot 65 \)
В. 25
\( c .115 \)
0.105


The speed of electromagnetic waves in
air is
A \( \cdot 2 \times 10^{5} \mathrm{km} / \mathrm{s} \)
B . \( 2 \times 10^{6} \mathrm{km} / \mathrm{s} \)
\( c \cdot 2 \times 10^{7} \mathrm{km} / \mathrm{s} \)
D. \( 2 \times 10^{8} \mathrm{km} / \mathrm{s} \)


A tyre manufacturing company kept a record of the distance covered before a
tyre needed to be replaced. The table
show the result of 1000 cases :
Distance in \( K m \quad \) Frequency
Less than 4000 20
4000 to 9000 210
9000 to 14000 325
More than 14000 445
If you buy a tyre of this company what is the probability that it will need to be replaced after it has covered somewhere between \( 4000 \mathrm{km} \) and \( 14000 \mathrm{km} \) ?
A . 0.65
B. 0.625
c. 0.125
D. None of these


For given logic diagram, output \( \boldsymbol{F}=\mathbf{1} \)
then inputs are:
\( \mathbf{A} \cdot A=0, B=0, C=0 \)
\( \mathbf{B} \cdot A=0, B=1, C=0 \)
\( \mathbf{c} \cdot A=1, B=1, C=1 \)
\( \mathbf{D} \cdot A=0, B=0, C=1 \)


If a soap bubble, having radius \( r, \) is
charged to a charge density \( \sigma \) and its
increased to \( R \), then \( R \) equals to
\( [T \) is the surface tension]
A \( \cdot R=\frac{9 \varepsilon_{0} T}{\sigma^{2}} \)
в. \( \quad R=\frac{8 \varepsilon_{0} T}{\sigma^{2}} \)
c. \( R=\frac{10 \varepsilon_{0} T}{\sigma^{2}} \)
D. \( R=\frac{11 \varepsilon_{0} T}{\sigma^{2}} \)


If \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x})=4 \boldsymbol{x}^{3}-\frac{\boldsymbol{3}}{\boldsymbol{x}^{4}} \) such that \( \boldsymbol{f}(\boldsymbol{2})= \)
0. Then \( f(x) \) is


The number of electrons in an element
with atomic number \( A \) and mass
number B will be
A \( \cdot A-B \)
B. B-A
\( c . \) в
D. A


Amino acids show amphoteric behaviour. Why?


Formula of glucose is :
A. \( C_{5} H_{12} O_{6} \)
в. \( C_{6} H_{12} O_{16} \)
\( \mathbf{c} \cdot C_{6} H_{12} O_{7} \)
D. \( C_{6} H_{12} O_{6} \)


Which harmonics are these?
\( A \cdot 2 \)
B. 8
\( c \cdot 5 \)
D. 4


The compound Y is:
\( A \)
B. \( \quad C H_{3} \)
\( C H_{2}-C H=C-C H_{2}-C O O H \)
\( O H \)
\( c \)
\( \mathbf{D} \cdot C H_{2}=C H-C H-C H_{2}-C O O H \)


Which type of overlapping is shown by \( \boldsymbol{p} \)
\( \left(p_{x}, p_{y} \text { and } p_{z}\right) \) -orbitals?
A. Two end to end and one sidewise overlap
B. Two sidewise and one end to end overlap
c. Three sidewise overlaps
D. Three end to end overlaps


If \( A, B \) are symmetric matrices of the same order then \( \mathbf{A B}-\mathbf{B A} \) is
A. symmetric matrix
B. skew symmetric matrix
c. Diagonal matrix
D. identity matrix


What is Iymph? How is composition of lymph different from blood plasma?


The decomposition of \( N H_{3} \) gas on a
heated tungsten surface gave the following results:
Initial
pressure \( \quad 65 \quad 105 \) (mm of \( \boldsymbol{H} \boldsymbol{g} \)
Half-life
\( \begin{array}{ll}290 & x=670\end{array} \)
\( (\mathrm{sec}) \)
Calculate approximately the values of \( x \)
and \( y \)


With increase in distance from the
nucleus, energy of electron. increases
though velocity of electron decreases.
How do you account for this?


A metal M (specific heat 0.16 ) forms a metal chloride with \( \approx 65 \% \) chlorine
present in it. The formula of the metal
chloride will be
A . MCI
в. \( M C l_{2} \)
c. \( M C l_{3} \)
D. \( M C l_{4} \)


The number of turns in primary and secondary coils of a transformer is 50 and 200 respectively. If the current in
the primary coil is \( 4 A \), then the current in the secondary coil is
A . \( 1 A \)
в. \( 2 A \)
\( c .4 A \)
D. \( 5 A \)


Write the additive inverse of each of the
following rational numbers:
\( \frac{-2}{17} \)


One gram atomic weight of metal of the following can be deposited by one Faraday:
\( \mathbf{A} \cdot \) AuCl \( _{3} \)
B. Bacla
c. Nacı
D. cuso


Draw a circle with center \( \boldsymbol{O} \) and radius
6cm. Take a point \( \boldsymbol{P} \) outside the circle
at a distance of \( 10 \mathrm{cm} \) from \( O . \) Draw
tangents to the circle from point \( P . \) Let
the tangents intersect the circle in points \( A \) and \( B . \) Find the approximate
value of \( \angle B O P \) in degrees.
A \( .37^{\circ} \)
B. \( 53^{\circ} \)
\( c \cdot 45^{\circ} \)
D. None of these


Find \( 4 t h \) and \( 8 t h \) terms of the G.P.
\( \mathbf{0 . 0 0 8}, \mathbf{0 . 0 4}, \mathbf{0 . 2}, \dots \dots \dots \)


... ray is the ray of light reflected from a
surface.


The molecular mass of any two adjacent homologous differ by amu.


If \( \frac{2+5+8+\ldots n \text { terms }}{7+11+15+\ldots . n \text { terms }}=\frac{23}{35} \)
then \( n \) value is
A . 17
B . 15
c. 18
D. 23


Role of calciferous glands in stomach of earthworm is to
A. Neutralise the humic acid in the humus
B. Produce HC
c. Emulsify fats
D. Increase absorptive area
E. secrete slime


\( P Q: D B \) is equal to
A \( \cdot \frac{2}{3} \)
в. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{4} \)


Use of ICs has lead to an increase in
speed of PCs. Current processor speeds
in personal computers is of the order of:
A. \( k H z \)
B. \( M H z \)
\( \mathrm{c} . G H z \)
D. \( T H z \)


If \( \left|\mathbf{z}^{2}-\mathbf{1}\right|=|\mathbf{z}|^{2}+\mathbf{1}, \) then \( \mathbf{z} \) lies on
A. the real axis
B. the imaginary axis
c. a circle
D. an ellipse


\( " N a_{2} C O_{3} \) is more thermally stable than
\( \boldsymbol{L} \boldsymbol{i}_{2} \boldsymbol{C} \boldsymbol{O}_{3} \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


During extraction of \( N a C l \), chlorine is deposited at :
A. anode
B. cathode
c. Depends on sodium
D. None of the above


Form the differential equation representing the family of ellipses
having centre at the origin and foci on \( x \) axis.


Below is given distribution of profit (in
Rs.) per day of a shop in a certain town. Calculate median profit of shops.
Profit 500 \( \quad 1000 \quad 1500 \quad 2000 \)
in
Rs.) \( \quad 1000 \quad \) 1500 \( \quad 2000 \)
\[
\begin{array}{l}
\text { No. of } \\
\text { shops }
\end{array}
\]
18
A. Rs. 1867
B. Rs. 196
c. Rs. 2167
D. Rs.2567


Find the zeroes of the polynomial in
each of the following:
\( h(y)=2 y \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 2 y \)
c. \( y \)
D. -


Find the following integrals:
\( \int\left(\sqrt{\boldsymbol{x}}-\frac{1}{\sqrt{x}}\right)^{2} d x \)


A plane is at a distance of 5 units from the origin and perpendicular to the vector \( 2 \hat{i}+\hat{j}+2 \hat{k} . \) The equation of the
plane is
A \( . \vec{r} .(2 \hat{\imath}+\hat{j}-2 \hat{k})=15 \)
в. \( \vec{r} .(2 \hat{i}+\hat{j}-\hat{k})=15 \)
c. \( \vec{r} .(2 \hat{i}+\hat{j}+2 \hat{k})=15 \)
D. \( \vec{r} .(\hat{i}+\hat{j}+2 \hat{k})=15 \)
E \( . \vec{r} .(2 \hat{i}-\hat{j}+2 \hat{k})=15 \)


Assertion
Many great rivers flow towards the equator. The sediments that they carry
increase the time of rotation of the
earth about its own axis.
Reason
The angular momentum of the earth about its rotation axis is conserved.
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) Rutherford's alpha parcticle scattering experiment led to the discovery of the
B) Isotopes have same but
different
C) Neon and chlorine have atomic numbers 10 and 17
respectively. Their valencies will be and
D) An atom with 3
protons and 4 neutrons will have a
valency of


By the end of 2002 , the public transport
of Delhi switched over to a new fuel.
Name the fuel. Why is this fuel considered better? Explain.


Which among the following can be a chiral center?
\( A \cdot C^{+} \) of a cabocation
B. Carbon of a radical
c. \( A n s p^{2} \) carbon
D. An sp \( ^{3} \) carbon


Which of the following is the most basic in character?
A \( . H_{2} O \)
в. \( C H_{3} C H_{2} O H \)
\( \mathbf{c} \cdot C H_{3} O C H_{3} \)
D. \( C H_{3} O H \)


Let \( A \) and \( B \) be two events such that
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\boldsymbol{P}(\boldsymbol{A})+\boldsymbol{P}(\boldsymbol{B})- \)
\( \boldsymbol{P}(\boldsymbol{A}) \boldsymbol{P}(\boldsymbol{B}) . \) If \( \boldsymbol{0}<\boldsymbol{P}(\boldsymbol{A})<1 \) and \( \boldsymbol{0}< \)
\( \boldsymbol{P}(\boldsymbol{B})<1, \) then \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})^{\prime} \) is equal to
A \( \cdot 1-P(A) \)
B . \( 1-P\left(A^{\prime}\right) \)
c. \( 1-P(A) P(B) \)
D \cdot \( [1-P(A)] P\left(B^{\prime}\right) \)
\( E \)


When a star of mass \( 9 \times 10^{30} \) kg ends
as a black hole, the
Schwarzschild radius of the star is
\( \left(G=6.7 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{kg}^{-2}\right) \)
A . \( 13.4 \mathrm{m} \)
B. 6.7 \( m \)
\( c \cdot 13.4 \mathrm{km} \)
D. \( 26.8 \mathrm{km} \)


Assertion
Complexity of classification increases from kingdom to species.
Reason
Common characters increase from
kingdom to species.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A wheel is rotating at \( 900 ~ r . p . m, \) about its axis. When power is cut off it comes
to rest in 1 minute. The angular
retardation in \( r a d / s^{2} \) is:
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 4 \)
c. \( \pi / 6 \)
D. \( \pi / 8 \)


Which of the following compound is used as froth stabliser?
A. Fatty acid
B. Aniline
c. xanthates
D. Phosphoric acid


\( \mathbf{A} \)
0.1 molal aqueous solution of a weak
acid is \( 30 \% \) ionized. If \( K_{f} \) for water is
\( 1.86^{\circ} \mathrm{C} / \mathrm{m}, \) the freezing point of the solution will be:
B \( .-0.18^{\circ} \mathrm{C} \)
c. \( -0.54^{\circ} \mathrm{C} \)
D. \( -0.36^{\circ} \mathrm{C} \)


Find the net flux through the cylinder.
\( \mathbf{A} \cdot-0.125 N m^{2} / C \)
B. \( -0.25 N m^{2} / C \)
\( \mathbf{C} \cdot 0.25 N m^{2} / C \)
D. \( 0.125 N m^{2} / C \)


When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle
is \( n, \) the frequency of the kinetic energy
is:
A \( \cdot n / 2 \)
в. \( n \)
\( c \cdot 2 n \)
D. \( 4 n \)


Assertion: Substances with hydrogen
bonding tend to have unusually low boiling points.
Il : Extra energy is necessary to break the hydrogen bonds.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both the Assertion and Reason are not correct


Simplify, using trigonometric tables \( \sin 50^{\circ} 26^{\prime}+\cos 18^{\circ}+\tan 70^{\circ} 12^{\prime} \)


If a Carnot engine works between \( 127^{0} C \)
and \( 527^{0} C, \) then the efficiency is:
A . 25\%
B . 37.5\%
c. 50\%
D. 75\%


A small metal ball of diameter 4 mm
and density \( 10.5 g / c m^{3} \) in dropped in glycerine of density \( 1.5 g / c m^{3} . \) The ball attains a terminal velocity of \( 8 \mathrm{cm} / \mathrm{sec} \)
The coefficient of viscosity of glycerine
is
A. 4.9 poise
B. 9.8 poise
c. 98 poise
D. 980 poise


Calculate the amount of work done in
carrying a charge of \( 5 \mathrm{mC} \) against a potential difference of \( 100 V \)
A. \( 0.5 . \)
J
в. \( 50 J \)
c. \( 5 J \)
D. None


The value of pre-expotential factor is :
A . \( A=1.25 \times 10^{18} s^{-1} \)
B. \( A=1.95 \times 10^{18} s^{-1} \)
c. \( A=1.56 \times 10^{18} s^{-1} \)
D. None of these


Styrofoam is obtained from
A. polymethylene
B. polyesters
c. cellulose
D. styrene


Potential Energy \( (U) \) of a body of unit mass moving in a one-dimension conservative force field is given by \( U= \)
\( \left(x^{2}-4 x+3\right) . \) All units are in S.I.
(i) Find the equilibrium position of the body
(ii) Show that oscillations of the body
about this equilibrium position is simple harmonic motion and find its time period.
(iii) Find the amplitude of oscillations if the speed of the body at equilibrium position is \( 2 \sqrt{6} m / s \)


The coefficients of \( x^{p} \) and \( x^{q} \) (p and q are positive integers) in the expansion of
\( (1+x)^{p+q} \) are
A. Equal
B. Equal with opposite signs
c. Reciprocals to each other
D. None of these


The low electron affinity value of nitrogen is due to:
A. small size
B. high nuclear charge
c. half-filled 2p subshell
D. high metallic character


A sample of a radioactive substance has a half-life of 20 minutes. If the
sample's activity is 200 counts/second. Find out the number of counts/second
after one hour passes?
A . 6.25 counts/sec
B. 12.5 counts/sec
C. 25 counts/sec
D. 50 counts/sec
E. 100 counts/sec


Two events \( A \) and \( B \) will be
independent, if
\( \mathbf{A} . A \) and \( B \) are mutually exclusive
B \( \cdot P\left(A^{\prime} B^{\prime}\right)=[1-P(A)][1-P(B)] \)
\( \mathbf{c} \cdot P(A)=P(B) \)
D \( \cdot P(A)+P(B)=1 \)


How many rational numbers exist between any two distinct rational numbers?
A .2
B. 3
c. 10
D. Infinite


Which one of the following is not the
characteristic of Planck's quantum
theory of radiation?
A. The energy is not absorbed or emitted in whole number multiple of quantum
B. Radiation is associated with energy
C. Radiation energy is not emitted or absorbed continuously but in the form of small packets called quanta
D. This magnitude of energy associated with a quantum is proportional to the frequency


Which of the following compounds has hexagonal structure?
A. Diamond
в. \( N a C l \)
c. \( K C l \)
D. Graphite


The reaction:
\[
\mathbf{2} \boldsymbol{C}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{2} \boldsymbol{C} \boldsymbol{O}
\]
is carried out by taking \( 24 g \) of carbon
and \( 96 ~ g O_{2} . \) The amount of other
reactant in grams that should be taken
so that nothing is left at the end of the
reaction is :


The area of a circle and a square are
equal, the ratio of the sides of the
square to the radius of the circle is
A \( .2: \sqrt{\pi} \)
B. \( \sqrt{\pi}: 1 \)
c. \( \sqrt{2}: 1 \)
D. \( 1: \sqrt{2} \)
E . None of these


The non-metal having shining surface is:
A. sulphur
B. phosphorus
c. iodine
D. carbon


\( H_{2} O_{2} \) solution of \( 0.2 \mathrm{N} \) is prepared and
after 5 hours it is titrated with \( K M n O_{4} \)
solution. If the volume of the \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
solution taken is half of the volume of
\( K M n O_{4} \) used (in acidic medium), find
the molarity of \( K M n O_{4} \) solution?
\( \mathbf{A} \cdot 0.4 \mathrm{M} \)
в. 0.01 М
c. 0.02 М
D. 0.2 M


\( \left|\frac{1}{2}\left(z_{1}+z_{2}\right)+\sqrt{z_{1} z_{2}}\right|+ \)
\( \left|\frac{1}{2}\left(z_{1}+z_{2}\right)-\sqrt{z_{1} z_{2}}\right|= \)
A \( \cdot \mid z_{1}+z_{2} \)
B . \( \left|z_{1}-z_{2}\right| \)
\( \mathbf{c} \cdot\left|z_{1}\right|+\left|z_{2}\right| \)
D. \( \left|z_{1}\right|-\mid z_{2} \)


Classify the following into monosaccharides,oligosaccharides and
polysaccharides.
(1) starch,
(2) glucose,
(3) stachyose,
maltose,
(5) raffinose,
(6) cellulose, (7)sucrose,
(8) lactose.


The atmospheric pressure at is 100,000 pascal.
A . \( 10.34 \mathrm{m} \)
B. torcellian
c. sea level
D. none


Hydraulic press is based upon:-
A. Archimede's principle
B. Bernoulli's theorem
c. Pascal's law
D. Reynold's number


Silver, gold, platinum, iron, copper and titanium are part of the:
A. minerals
B. transition element
c. salts
D. all of these


If the area of a rectangle is equal to the area of a square and length of the rectangle is equal to the perimeter of
the square, then the breadth of rectangle is
A. side \( \div 2 \)
B. \( (\text {side})^{2} \div 2 \)
\( c \cdot \operatorname{side} \div 4 \)
D. side \( \div 3 \)


The intensity of an earthquake is
measure on the \( -? \)
A. Righter scale
B. Richter scale
c. Seismic scale
D. None of the above


The number of real solutions of the
equation \( \tan ^{-1} \sqrt{x(x+1)}+ \)
\( \sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{2} \) is
A. One
B. Four
c. Two
D. Infinitely many


If a set contains \( m \) elements and \( B \)
contains \( n \) elements, then find the
number of elements in \( \boldsymbol{A} \times \boldsymbol{B} \)


f there is no change in concentration, why is the equilibrium state considered dynamic?


if \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is given by \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{4}^{\boldsymbol{x}}}{\boldsymbol{4}^{\boldsymbol{x}}+\mathbf{2}} \)
for all \( x \epsilon R \) then \( f\left(\frac{1}{1997}\right)+ \) \( \boldsymbol{f}\left(\frac{\mathbf{2}}{\mathbf{1 9 9 7}}\right)+---+\boldsymbol{f}\left(\frac{\mathbf{1 9 9 6}}{\mathbf{1 9 9 7}}\right)= \)
\( \mathbf{A} \cdot 997.5 \)
в. 998
c . 998.5
D. 999


A particle moves in such a way that its position vector at any time \( t \) is \( \vec{r}=t \hat{i}+ \) \( \frac{1}{2} t^{2} \hat{j}+t \hat{k} . \) Find as a function of time
(i) the velocity \( \left(\frac{d \vec{r}}{d t}\right) \)
(ii) the speed \( \left(\left|\frac{d \vec{r}}{d t}\right|\right) \)
(iii) the acceleration \( \left(\frac{\boldsymbol{d} \overrightarrow{\boldsymbol{v}}}{\boldsymbol{d} \boldsymbol{t}}\right) \)
(iv) the magnitude of the acceleration
(v) the magnitude of the component of acceleration along velocity (called tangential acceleration)
(vi) the magnitude of the component of acceleration perpendicular to velocity (called normal acceleration).


The spectrum of molecular form the substance is called:
A. band spectrum
B. line spectrum
c. absorption spectrum
D. continuous spectrum


Total number of bones in a hindlimb of a
man is
A . 14
B. 21
\( c \cdot 24 \)
D. 30


There is a pentagonal shaped park as shown in figure. For finding its area jyot and kavita divided it into two different
ways. Find the area of the park using both the ways.


White phosphorus on reaction with
NaOH gives \( P H_{3} \) as one of the products. This is a :
A. dimerization reaction
B. disproportionation reaction
c. condensation reaction
D. precipitation


pKb of fluoride ions at 25 deg celcius is
10.83, the ionisation const of
hydrofluoric acid in water at this temp. is?


Sound from the outside world reach the
inner ear through:
A. pinna
B. cochlea
c. auditory canal
D. labyrinth


Which of the following process determines the breathing rate?
A. Inhalation
B. Exhalation
c. Respiration
D. Both A and B


The fraction of a radioactive material
which remains active after time \( t \) is
\( \mathbf{9} / \mathbf{1 6} . \) The fraction which remains active after time \( t / 2 \) will be
A. \( \frac{4}{5} \)
в. \( \frac{7}{8} \)
c. \( \frac{3}{5} \)
D.


Compared to the mass of lightest nucleus the mass of an electron is only:
A \( \cdot \frac{1}{80} \)
B . \( \frac{1}{360} \)
\( c \cdot \frac{1}{1800} \)
D. \( \frac{1}{1000} \)


An electron is projected at an angle \( \theta \) with a uniform magnetic field. If the pitch of the helical path is equal to its radius, then the angle of projection is
\( \mathbf{A} \cdot \tan ^{-1} \pi \)
В \( \cdot \tan ^{-1} 2 \pi \)
\( \mathbf{c} \cdot \cot ^{-1} \pi \)
D. \( \cot ^{-1} 2 \pi \)


If two bodies of different masses \( m_{1} \)
and \( m_{2} \) are dropped from different
heights \( h_{1} \) and \( h_{2} \), then ratio of the
times taken by the two to drop through these distances is
B. \( h_{2} / h_{1} \)
c. \( \sqrt{h_{1}}: \sqrt{h_{2}} \)
D. \( h_{1}^{2}: h_{2}^{2} \)


Fire extinguisher's containing \( C O_{2} \) is
the best extinguisher.
A. Because \( C O_{2} \) being heavier than oxygen, covers the fire like a blanket
B. Because \( C O_{2} \) being heavier than oxygen, increase fire
C. Because \( C O_{2} \) being leighter than oxygen, covers the fire like a blanket
D. None of these


The conjugate surd of \( 2-\sqrt{3} \) is


A hypothetical planet has density \( \rho \) radius \( \mathrm{R} \), and surface gravitational acceleration \( g \). If the radius of the
planet were doubled, but the planetary density stayed the same, find the acceleration due to gravity at the planet's surface.
A \( .4 g \)
в. \( 2 g \)
\( c . g \)
D. \( g / 2 \)


If \( \boldsymbol{A}=\{1,2,3\}, \) then a relation \( \boldsymbol{R}= \)
\{(2,3)\} on \( A \) is
A. symmetric and transitive only
B. symmetric only
C. transitive only
D. none of these


Draw the diagram of mercury
barometer.


The relationship between enthalpy and internal energy change is
A. \( \Delta U=\Delta H+P \Delta V \)
в. \( \Delta H=\Delta U+P \Delta V \)
c. \( \Delta H=\Delta U-P \Delta V \)
D. \( P \Delta V=\Delta U+\Delta H \)


You are required to make an electromagnet from a soft iron bar by using a cell, an insulated coil of copper
wire and a switch. Label the poles of the electromagnet.


The point \( P(3,4) \) is reflected to \( P^{\prime} \) in the
\( x \) -axis and \( O^{\prime} \) is the image of 0 (the
origin) when reflected in the line \( P P^{\prime} \) Using Graph paper give :
1) The coordinates of \( P^{\prime} \) and \( O^{\prime} \)
2) The length of segments \( P P^{\prime} \) and \( O O^{\prime} \)
3) The perimeter of the quadrilateral POP' \( O^{\prime} \)
4) Geometrical name of the figure POP' \( \boldsymbol{O}^{\prime} \)


Bohr's theory is applicable to
This question has multiple correct options
\( \mathbf{A} \cdot H e^{+} \) ion
B. \( L i^{2+} \) ion
C . Tritium \( _{1} H^{3} \)
\( \mathbf{D} \cdot_{1} H^{1} \)


\( K_{c} \) for \( \frac{3}{2} H_{2}+\frac{1}{2} N_{2} \rightleftharpoons N H_{3} \) are 0.0266
and 0.0129 at \( m^{-1} \) respectively at \( 350^{\circ} C \)
and \( 400^{\circ} \mathrm{C} . \) Calculate heat of formation
of \( \boldsymbol{N} \boldsymbol{H}_{3} \)
A . 12.140 Kcal
B. 1.214 Kcal
c. \( -12.140 \mathrm{Kcal} \)
D. -1.214 Kcal


f \( \alpha, \beta, \gamma \) are non-constant terms in G.P
and equations \( \alpha x^{2}+2 \beta x+\gamma=0 \)
and \( x^{2}+x-1=0 \) has a common root
then \( (\gamma-\alpha), \beta \) is
\( A \cdot \alpha \beta \)
в. \( \beta \gamma \)
c. \( \gamma \alpha \)
D.


A bullet of mass \( A \) and velocity \( B \) is fired
into a block of wood of mass \( C . \) If loss of
any mass and friction be neglected, the velocity of the system will be
\( ^{\text {A }} \cdot \frac{A B}{A+C} \)
в. \( \frac{A+C}{B+C} \)
c. \( \frac{A C}{B+C} \)
D. \( \frac{A+B}{A C} \)


Find the following:
\( \sin \left[\frac{\pi}{2}-\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)\right] \)


A man standing on a platform holds
weights in his outstretched arms. The
system rotates freely about a central
vertical axis. If he now draws the
weights inwards close to his body,
This question has multiple correct options
A. the angular velocity of the system will increase.
B. the angular momentum of the system will decrease.
C. the kinetic energy of the system will increase.
D. he will have to expend some energy to draw the weights in.


Cetyltrimethyl ammonium bromide is a
popular:
A. anionic detergent
B. cationic detergent
c. sweetener
D. non-ionic detergent


A resistance of \( 600 \Omega \) has the color code
given by 3 steps. The color of strips (from left to right) is given by
A. blue, black \& brown
B. blue, brown \& black
c. brown, blue \& black
D. brown, black \& blue


The temperature of a room is \( \mathbf{7 7}^{\circ} \boldsymbol{F} \) What would it be on the Celsius scale?
\( \mathbf{A} \cdot 25^{\circ} C \)
B. \( 45^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 60^{\circ} \mathrm{C} \)
D. \( 350^{\circ} \mathrm{C} \)


The molarity of \( \boldsymbol{H} \boldsymbol{C l} \) solution containing 0.4 moles in 200 ml of the
solution is:
A. 2 M
в. 1
\( c \cdot 3 M \)
D. 4 M


Nu Which
pictured, moving northeast through a
magnetic field that points straight up. What is the direction of the force on the
negatively charged particle at the
moment it is pictured?
North
west
\( - \)
East
South
A. Northeast
B. Southeast
c. Southwest
D. Northwest
E. Up


A magnet is moved towards a coil, first
quickly and then slowly. The induced
e.m.f. produced is:
A. Larger in first case
B. Smaller in first case
C. Equal in both cases
D. Larger or smaller, depending upon resistance of the coil


The domain of function \( f(x)=\sin ^{-1} 5 x \)
is
A \( \cdot\left(-\frac{1}{5}, \frac{1}{5}\right) \)
B. \( \left[-\frac{1}{5}, \frac{1}{5}\right] \)
c. \( R \)
D. \( \left(0, \frac{1}{5}\right) \)


\( \boldsymbol{y}=\log \boldsymbol{x} \) satisfies for \( \boldsymbol{x}>1, \) the
equality
This question has multiple correct options
A. \( x-1>y \)
B. \( x^{2}-1>y \)
c. \( y>x-1 \)
D. \( \frac{x-1}{x}<y \)


Peroxisomes are involved in the
synthesis of
A. Glucose
B. Fatty acids
c. Glycine and serine
D. Nucleotides


The Sl units of potential is


What transition in the hydrogen spectrum would have the same
wavelength as the Balmer transition, \( n= \)
4 to \( n=2 \) of \( H e^{+} \) spectrum?


The mass of the earth is \( 6.00 \times 10^{24} k g \)
and that of the moon is \( 7.40 \times 10^{22} k g \)
The constant of gravitation \( G= \)
\( 6.67 \times 10^{-11} N m^{2} k g^{-2} \). calculate
gravitational force of attraction.
\( \mathbf{A} \cdot 38 \times 10^{18} \)
В. \( 20.2 \times 10^{19} \)
c. \( 7.60 \times 10^{8} \)
D. \( 1.90 \times 10^{8} \)


Gives an example of a metal which:
a)liquid at room temperature
b) can be cut with a knife
c)is the best conductor of heat
d)is a poor conductor of heat


Estimate the change in the density of
water in ocean at a depth of \( 400 \mathrm{m} \)
below the surface. The density of water
at the surface \( =1030 \mathrm{kg} m^{-3} \) and the
bulk modulus of water \( =2 \times 10^{9} \mathrm{N} m^{-2} \)


Complete reduction of benzene-
diazonium chloride with \( Z n / H C l \)
gives:
A. azobenzene
B. phenylhydrazine
c. hydrazobenzene
D. aniline


A liquid is allowed to flow in a tube of truncated cone shape. Identify correct statement from the following.
A. The speed is high at the wider end and low at the narrow end
B. The speed is low at the wider end and high at the narrow end
c. The speed is same at both ends in a stream line flow
D. The liquid flows with uniform velocity in the tube


Vascular tissues of flowering plant
develop from
A. Dermatogen
B. Periblem
c. Plerome
D. Phellogen


Benzene is used as solvent for which
type of chemical compound?
A. fats
B. resin
c. rubbers
D. all of these


The principle upon which a lactometer works is
A. Viscosity
c. Surface tension
D. Presence of protein


For three number \( a, b, c \) product of the average of the number \( a^{2}, b^{2}, c^{2} \) and \( \frac{1}{a^{2}} \) \( \frac{1}{b^{2}}, \frac{1}{c^{2}} \) can not be less than
\( A \)
B. 3
\( c \cdot 9 \)
D. none of these


Is 184 a term of the sequence \( 3,7,11, \ldots \)
\( ? \)


A metallic rod \( C D \) rests on a thick
metallic wire \( P Q R S \) with arms \( P Q \) and
\( R S \) parallel to each other, at a distance
\( l=40 \mathrm{cm}, \) as shown in following figure.
A uniform magnetic field \( B=0.1 T \)
acts perpendicular to the plane of this paper, pointing inwards (i.e., aways
from the reader). The rod is now made to
slide towards right, with a constant
velocity of \( \boldsymbol{v}=\mathbf{5 . 0} \boldsymbol{m} \boldsymbol{s}^{-1} \)
How much emf is induced between the
two ends of the rod \( C D ? \)


Let \( \boldsymbol{A}=\mathbf{1 6}-\mathbf{4}+\mathbf{2}^{-\mathbf{4}}+\mathbf{3}^{-\mathbf{4}}+\mathbf{4}^{-\mathbf{4}}+\dots \)
and \( \boldsymbol{B}=\mathbf{1}^{-\mathbf{4}}+\mathbf{3}^{-\mathbf{4}}+\mathbf{5}^{-\mathbf{4}}+\mathbf{7}^{-\mathbf{4}}+\ldots \)
The ratio \( \frac{A}{B} \) in the lowest form is
A \( \cdot \frac{16}{15} \)
в. \( \frac{15}{14} \)
c. \( \frac{15}{16} \)
D. \( \frac{13}{12} \)


The number of reflexive relations of a
set with four elements is equal to
A \( \cdot 2^{16} \)
B. 2 \( ^{12} \)
\( c \cdot 2^{8} \)
\( D \cdot 2^{4} \)


For formation of ethanol, pyruvic acid is
first changed to acetaldehyde by
enzyme
A. Pyruvate dehydrogenase
B. Pyruvate decarboxylase
c. Alcohol oxidase
D. Alcohol dehydrogenase


State true false:
It is possible to have a polygon whose
sum of interior angles is \( 630^{\circ} \)
A. True
B. False


In which one of the following parts of the female reproductive system fertilization takes place?
A. Uterus
B. oviduct
c. vagina
D. Ovary
E. None of these