The direction of induced current in the
case lis
A. from a to b and from c to d
B. from a to b and from fto e
\( c . \) from b to a and from d to c
D. from b to a and from e to b


If \( \sin ^{2} \theta=\frac{1}{4}, \) then the general solution
of \( \boldsymbol{\theta} \)
A \( \cdot 2 n \pi \pm(-1)^{n} \frac{\pi}{6} \)
в. \( \frac{n \pi}{2} \pm(-1)^{n} \frac{\pi}{6} \)
c. \( n \pi \pm \frac{\pi}{6} \)
D. \( 2 n \pi \pm \frac{\pi}{6} \)


The rate of disappearance of \( A \) at two temperatures is given by \( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \)
i. \( \frac{-d[A]}{d t}=2 \times 10^{-2}[A]-4 \times 10^{-3}[B] \) at
\( 300 \mathrm{K} \)
ii. \( \frac{-d[A]}{d t}=4 \times 10^{-2}[A]-16 \times 10^{-4}[B] \)
at \( 300 \mathrm{K} \)
From the given values of heat of reaction which are incorrect
This question has multiple correct options
A. \( 3.86 k c a l \)
B. 6.93 kcal
c. \( 1.68 k c a l \)
D. \( 1.68 \times 10^{-2} k c a l \)


\( \operatorname{Let} f(x)=\int \frac{e^{x}}{x} d x \) and
\( \int \frac{\left(e^{x-1}\right)(2 x)}{x^{2}-5 x+4} d x=\alpha f(x-4)+ \)
\( \beta f(x-1)+\gamma, \) then
This question has multiple correct options
\( \mathbf{A} \cdot \ln 3 \alpha=3 \)
B. \( 4+3 \beta=\ln 3 \alpha \)
c. \( 3 \beta+2=0 \)
D. \( \ln 3 \alpha=3+\ln 8 \)


Gametic meiosis occurs in Protists,
which are
A. Diploid
B. Haploid
c. Tetraploid
D. Mesokaryotic


In contact process, sulfur is burned to
produce sulfur dioxide which is then oxidized to sulfur trioxide using oxygen
in the presence of a catalyst called
A. vanadium pentaoxide
B. oleum oxide
c. vanadium dioxide
D. oleum pentaoxide


What is recycling?
A. Burning of material
B. Break down the material by natural process
C. Recovering and reprocessing the material into useful products
D. Burying the products in land


What structural feature distinguishes proline from other natural \( \alpha \) -amino
acids?
A. It is optically inactive
B. It contains aromatic group
c. It is a di carboxylic acid
D. It has a secondary amine


State whether the following statements
are true of false
Circles with same radii are equal
A. True
B. False


If \( \boldsymbol{A}=\{1,2,3, \ldots, 9\} \) and \( \boldsymbol{R} \) be the
relation in \( A \times A \) defined by
\( (a, b) R(c, d) . \) If \( a+d=b+c \) for
\( (a, b),(c, d) \) in \( A \times A . \) Prove that \( R \) is an
equivalence relation. Also, obtain the
equivalence class [(2,5)]


In amalgam of mercury with sodium, solvent is;
A. mercury
B. sodium
c. amalgam
D. none of these


The centre of mass of a system of two particles divides. The distance between them is
A. In inverse ratio of square of masses of particles
B. In direct ratio of square of masses of particles
c. In inverse ratio of masses of particles
D. In direct ratio of masses of particles.


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


The figure shows a square loop \( L \) of side
\( 5 c m \) which is connected to a network of
resistances. The whole setup is moving
towards right with a constant speed of
\( 1 \mathrm{cm} s^{-1} . \) At some instant, a part of Lis
in a uniform magnetic field of \( 1 T \)
perpendicular to the plane of the loop. If
the resistance of \( L \) is \( 1.7 \Omega \), the current
in the loop at that instant will be close
to
A . \( 115 \mu A \)
в. 170 иА
\( c \cdot 60 \mu A \)
D. \( 150 \mu A \)


A man buys 400 , twenty-rupee shares at a premium of Rs. 4 each and receives a dividend of 12\%. Find his total income
from the shares.


Which of the following bond angles are
correct?
A. Ammonia : 107 \( ^{\circ} \); methylamine : \( 108^{\circ} \)
B. Ammonia : \( 108^{\circ} \); methylamine : 107 \( ^{\circ} \)
C. Ammonia : 107 \( ^{\circ} \); methylamine : \( 110^{\circ} \)
D. Ammonia : \( 110^{\circ} \); methylamine : 105 \( ^{\circ} \)


A coil made of insulated copper wire is
connected to a galvanometer. What will
happen if a bar magnet is held stationary inside the coil?
outside
opposite


The position of the center of gravity of the pot before filling it with water will be
at its base.
A. True
B. False


A solid maintained at \( t_{1}^{o} C \) is kept in an evacuated chamber at temperature
\( t_{2}^{o} C\left(t_{2}<<t_{1}\right) . \) The rate of heat
absorbed by the body is proportional to:
A \( \cdot t_{2}^{4}-t_{1}^{4} \)
B . \( \left(t_{2}^{4}+273\right)-\left(t_{1}^{4}+273\right) \)
c. \( t_{2}-t_{1} \)
D \( \cdot t_{2}^{2}-t_{1}^{2} \)


With the help of circuit diagram, explain the V-1 characteristics of p-n junction diode in forward biasing.


Hypanthodium inflorescence is found
in?
A. Coriander
B. Sunflower
c. Cauliflower
D. Figg


Choose the correct answer form the
alternatives given

Match column I with column II and
mark the appropriate choice.
\( \begin{array}{llll} & \text { Column I } & & \text { Column II } \\ \text { (A) } & \text { Li } & \text { (i) } & M_{2} O_{2} \\ \text { (B) } & \text { Na } & \text { (ii) } & M O_{2} \\ \text { (C) } & \text { Rb } & \text { (iii) } & M_{2} O\end{array} \)
\( A \)
\( (A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i) \)
в. \( (A) \rightarrow(i i i),(B) \rightarrow(i i),(C) \rightarrow(i) \)
\( c \)
\( (A) \rightarrow(i i i),(B) \rightarrow(i),(C) \rightarrow(i i) \)
\( D \)
\( (A) \rightarrow(i i),(B) \rightarrow(i i i),(C) \rightarrow(i) \)


Write the IUPAC name of the following
(i) \( P t C l_{4} \cdot 5 N H_{3} \) (gives 4 ions in
solution)
(ii) \( P t C l_{4} \cdot 2 K C l \) gives 3 ions in
solution)
(ii) \( \operatorname{Ir} C l_{3} \cdot 3 N H_{3}\left(\text { no } C l^{-} \) ion is \right.
precipitated)
(iv) \( C o C l_{3} \cdot 4 N H_{3} \mathrm{m} \) (one \( C l \) is
precipitated by \( A g N O_{3} \)


A coil has resistance 30 ohm and
inductive reactance 20 Ohm at \( 50 \mathrm{Hz} \) frequency. If an ac source, of 200 volt, \( 100 \mathrm{Hz}, \) is connected across the coil, the current in the coil will be :
\( \mathbf{A} \cdot 4 \cdot 0 \mathrm{A} \)
B. \( 8.0 \mathrm{A} \)
c. \( \frac{20}{\sqrt{13}} \) A
D. 2.0 A


If \( 2^{x}-2^{x-1}=4, \) then what is the value
of \( 2^{x}+2^{x-1} ? \)
A . 8
B. 12
c. 10
D. 16


\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{C} \boldsymbol{N} \rightarrow \boldsymbol{A} \)
\( \boldsymbol{A}+\boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{B} \)
\( B \) is a metal. Hence, \( A \) and \( B \) are
respectively:
A \( \cdot N a_{2}\left[\operatorname{Zn}(C N)_{4}\right], Z n \)
B. \( \operatorname{Na}\left[A g(C N)_{2}\right], A g \)
c. \( \operatorname{Na}\left[A g(C N)_{4}\right], A g \)
D. \( N a_{3}\left[A g(C N)_{4}\right], A g \)


From the graph pick out the correct one:
\( \mathbf{A} \cdot \Delta E \) for forward reaction is \( B-A \)
\( \mathrm{B} \cdot \Delta E \) for the forward reaction \( C-A \)
\( \mathrm{C} \cdot \Delta E \) reverse is greater than forward
\( \mathbf{D} \cdot \Delta E \) for forward reaction is \( A+B \)


Assertion (A): The points on the curve
\( y=x^{3}-3 x \) at which the tangent is
parallel to \( x \) -axis are (1,-2) and (-1,2)
Reason (R): The tangent at \( \left(x_{1}, y_{1}\right) \) on the curve \( y=f(x) \) is vertical then \( \frac{d y}{d x} \)
\( \operatorname{at}\left(x_{1}, y_{1}\right) \) is not defined
A. Both A and R are true and R is the correct explanation for A
B. Both A and R are true but R is not the correct explanation for \( A \)
C. A is true but R is false
D. A is false but R is true


\( X \) is any point inside a \( \triangle D E F \) and is joined to all vertices. From point \( \boldsymbol{P} \) on \( D X, P Q \| D E \) is drawn which meets \( \boldsymbol{E} \boldsymbol{X} \) at \( \boldsymbol{Q} \) and from \( \boldsymbol{Q}, \boldsymbol{Q} \boldsymbol{R} \| \boldsymbol{E} \boldsymbol{F} \) is drawn
which meets \( X F \) at \( R \) Prove that
\( \boldsymbol{P R} \| \boldsymbol{D} \boldsymbol{F} \)


8 students are participating in a competition. In how many ways can the first three prizes be won?


Which one of the following methods is most appropriate to check soil erosion on steep slopes?
A. Shelter belts
B. Mulching
c. Terrace cultivation
D. Multi-river project


Arrange the following events of meiosis in the correct sequence.
(i) Crossing over
(ii) Synapsis
(iii) Terminalization of chiasma
(iv) The disappearance of the nucleolus.
A \( \cdot(i i),(i) .(i v) .(i i i) \)
B. \( (i i),(i) .(i i i) .(i) \)
c. \( (i),(i i) .(i i i) .(i v) \)
D. \( (i i),(i i i) . .(i v) . . i i) \)


Why are the tyres of automobiles grooved?
A. To improve the design
B. To increase friction
c. To make it durable
D. To make it strong


Gemmule formation in sponges is helpful in
A. Parthenogenesis
B. Sexual reproduction
c. only dissemination
D. Asexual reproduction


\( f f=\{(4,5),(5,6),(6,-4) \text { and } g=\{(4,-4) \)
(6,5),(8,5)\} then find
\( \boldsymbol{A}) \boldsymbol{f}+\boldsymbol{g} \quad \boldsymbol{B}) \boldsymbol{f}-\boldsymbol{g} \)
\( \boldsymbol{C}) \mathbf{2} \boldsymbol{f}+ \)
\( \begin{array}{ll}\mathbf{4} \boldsymbol{g} & \boldsymbol{D}) \boldsymbol{f}+\end{array} \)
\( \begin{array}{lll}\boldsymbol{4} & \boldsymbol{E}) \boldsymbol{f} \boldsymbol{g} & \boldsymbol{F}) \boldsymbol{f} / \boldsymbol{g}\end{array} \)
\( \boldsymbol{G})|\boldsymbol{f}| \quad \boldsymbol{H}) \sqrt{\boldsymbol{f}} \quad \boldsymbol{I}) \boldsymbol{f}^{2} \)


A light beam is being reflected by using two mirrors,as in a periscope used in submarines.if one of the mirrors rotates
by an angle \( \theta \), the reflected light will deviate from its original path by the angle
\( \mathbf{A} \cdot 2 \theta \)
B. \( 3 \theta \)
\( c \cdot \theta \)
D. \( 4 \theta \)


Find the cube root of each of the
following cube numbers through
estimation.
\( \mathbf{5 9 3 1 9} \)


The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is?
A. benzoic acid
B. salicylaldehyde
c. salicylic acid
D. phthalic acid


In a circuit inductance \( L \) and
capacitance \( C \) are connected as shown
in figure. \( A_{1} \) and \( A_{2} \) are ammeters

When key \( K \) is pressed to complete the
circuit, then just after closing key \( (\boldsymbol{K}) \)
the readings of \( A_{1} \) and \( A_{2} \) will be
A. zero in both \( A_{1} \) and \( A_{2} \)
B. maximum in both \( A_{1} \) and \( A_{2} \)
C. zero in \( A_{1} \) and maximum in \( A_{2} \)
D. maximum in \( A_{1} \) and zero in \( A_{2} \)


Give reason why a chemical equation needs to be balanced?


Why do we need to classify drugs in
different ways?


If two vertices of an isosceles triangle \( \operatorname{are}(2,0) \) and (2,5) and length of the equal sides is 3 then the third vertex is
A \( .(2,6) \&(-5,3) \)
B. (8,3)\( \&(5,1) \)
\( ^{\mathbf{C}} \cdot\left(2 \pm \frac{\sqrt{11}}{2}, \frac{5}{2}\right) \)
D. \( \left(3 \pm \frac{\sqrt{14}}{2}, \frac{7}{2}\right) \)


Find the particular solution of the differential equation
\( \left(1-y^{2}\right)(1+\log x) d x+2 x y d y=0 \)
given that \( y=0 \) when \( x=1 \)


If the curves \( y=x^{3}+a x \) and \( y= \)
\( b x^{2}+c \) pass through the point (-1,0)
and have common tangent line at this
point, then the value of \( a+b \) is?
\( \mathbf{A} \cdot \mathbf{0} \)
в. -2
c. -3
D. -


f \( a, b, c \) are in G.P., then
A \( \cdot a\left(b^{2}+a^{2}\right)=c\left(b^{2}+c^{2}\right) \)
B . \( a\left(a^{2}+c^{2}\right)=c\left(a^{2}+b^{2}\right) \)
C \( \cdot a^{2}(b+c)=c^{2}(a+b) \)
D. None of these


\( 28 g \) of \( N_{2} \) gas is contained in a flask at
a pressure 10 atm and at a
temperature of \( 57^{0} C . \) It is found that
due to leakage in the flask, the pressure is reduced to half and the temperature
reduced to \( 27^{0} \) C.The quantity of \( N_{2} \) gas
that leaked out is:
\( \mathbf{A} \cdot \frac{11}{20} \mathrm{g} \)
B. \( \frac{80}{11} \) g
c. \( \frac{5}{63} \) g
D. \( \frac{63}{5} g \)


Draw parallelogram \( A B C D \) with the following measurements and calculate
its area
\( A B=7 \mathrm{cm}, A C=10 \mathrm{cm} \) and \( \angle \mathrm{AOB}= \)
\( 100^{\circ} \) where \( \overline{A C} \) and \( \overline{B D} \) intersect at 0


Ibuprofen is a:
A. propionic acid derivative
B. benzoic acid derivate
C. nephthoic acid derivative
D. sulphanilic acid derivative


Teflon is an example of polymer which is a/an:
A. polyamide
B. addition polymer
c. polyester
D. formaldehyde resin


Two fixed point charges \( +4 e \) and \( +e \) are
separated by a distance a. Where should the third point charge be placed
from \( +4 e \) charge for it to be in equilibrium?
A \( \cdot \frac{2}{3} a \)
в. \( \frac{4}{3} a \)
\( c \cdot \frac{1}{3} a \)
D. None of these


The figure given below shows a container \( C \) partially filled with water There is a plane mirror \( \mathrm{M} \) at the bottom of the container. A light ray AB incidents on the surface of water at angle of
incidence \( 30^{\circ} . \) Copy and complete the ray diagram. Mark the ray emerging from the water surface. Refractive index
of water \( =\frac{4}{3} \)


Write any two major reasons for the population explosion in India.


In Young's double slit experiment, a
glass plate is placed before a slit which
absorbs half the intensity of light. Under
this case:
A. The brightness of fringes decreases
B. The fringes width decrease
C. No fringes will be observed
D. The bright fringes become fainter and the dark fringes have finite light intensity


A sphere of radius \( 1.00 \mathrm{cm} \) is placed in
the path of a parallel beam of light of large aperture. The intensity of the light is \( 0.50 W \mathrm{cm}^{-2} . \) If the sphere
completely absorbs the radiation falling on it, find the force exerted by the light beam on the sphere.


Looking at the pattern, fill in the gaps in the following
\( \mathbf{3} \)
\( 4 \quad-5 \)
, and
\( \begin{array}{cccc}2^{3}= & 3^{3}= & \ldots= & \ldots \ldots \\ 8 & \ldots \ldots & 64 & \ldots\end{array} \)


If a coil of \( 20 \mathrm{cm} \times 20 \mathrm{cm} \) having 30
turns is making 3 rps in a magnetic field of induction \( 1 T, \) then the peak value of the induced emf is
approximately
\( \mathbf{A} \ldots 113 V \)
B. \( 150 V \)
\( \mathbf{c} \cdot 226 V \)
D. \( 339 V \)


Solve the equation:\( \int_{0}^{2}\left[x^{2}-x+1\right] d x \)


Determine the energy released during the fusion of \( _{1} H^{1} \) to form a \( _{2} H e^{4} \) nucleus, if the total mass of the
products is \( 4.001506 u, \) mass of proton
is \( 1.0078 u \) and mass of neutron is
\( 1.00878 u \)
\( \mathbf{A} \cdot 27.67 M e V \)
в. \( 27.67 J \)
c. \( 127.67 J \)
D. 127.67 MeV


How the linear velocity 'v' of an electron in the Bohr orbit is related to its
quantum number 'n'?
A \( \cdot v \propto \frac{1}{n} \)
в. \( v \propto \frac{1}{n^{2}} \)
c. \( _{v} \propto \frac{1}{\sqrt{n}} \)
D. \( v \propto n \)


The time period of an earth satellite close to the surface of the earth is 83
minutes. The time period of another
earth satellite in an orbit at a distance
of the earth's radius from its surface
will be
A. 83 minutes
B. \( 83 \sqrt{8} \) minutes
c. 664 minutes
D. 249 minutes


If the dipole of moment \( 2.57 \times \)
\( 10^{-17} \mathrm{C} . \mathrm{m} \) is placed into an electric
field of magnitude \( 3.0 \times 10^{4} N / C \) such
that the fields lines are aligned at \( 30^{\circ} \) with the line joining the dipole, what torque will act on the dipole?
A. \( 7.7 \times 10^{-13} \mathrm{Nm} \)
B . \( 3.855 \times 10^{-13} \mathrm{Nm} \)
\( \mathbf{c} \cdot 3.855 \times 10^{-15} \mathrm{Nm} \)
D. \( 7.7 \times 10^{-15} \mathrm{Nm} \)


Compute the enthalpy of formation of liquid methyl alcohol in kJ \( m o l^{-1}, \) using
the following data. Enthalpy of vaporization of liquid \( \boldsymbol{C H}_{3} \boldsymbol{O H}= \) \( 38 k J / \) mol.

Enthalphy of formation of gaseous
atoms from the elements in their
standard states are enthalpy of
formation of gaseous atoms from the elements in their standard states are
\( \boldsymbol{H} \rightarrow 218 \mathrm{kJ} / \mathrm{mol} ; \boldsymbol{C} \rightarrow 715 \mathrm{kJ} / \mathrm{mol} ; \boldsymbol{O} \)
\( \rightarrow 249 \mathrm{kJ} / \mathrm{mol} \)
Bond Enthalpies \( \boldsymbol{C}-\boldsymbol{H} \rightarrow 415 \mathrm{kJ} / \mathrm{mol} ; \boldsymbol{C}-\boldsymbol{O} \rightarrow 356 \mathrm{kJ} \)
\( \mid \mathrm{mol} ; \boldsymbol{O}-\boldsymbol{H} \rightarrow \mathbf{4 6 3} \mathrm{kJ} / \mathrm{mol} \)


A ferromagnetic material is heated above its curie temperature. Which one of a correct statement?
A. Ferromagneitc domains are perfectly arranged
B. Ferromagnetic domains become random
c. Ferromagnetic domains are not influenced
D. Ferromagnetic material changes into diamagnetic material


\( \frac{\sqrt{2}}{\frac{1}{n}} \)


A beam of natural light falls on a
system of 6 Polaroids, which are arranged in succession such that each
of the Polaroid is turned through \( 30^{\circ} \) with respect to the proceeding the one. The percentage of incident intensity that passes through the system will be:
\( \mathbf{A} \cdot 100 \% \)
B. \( 50 \% \)
\( c .30 \% \)
D. \( 12 \% \)


The diagram given represents a stage during cell division. Study the same and answer the question that follow. Name the type of cell division that occurs during.
1. Replacement of old leaves by new
ones.
2. Formation of gametes.


Assertion
\( P H \) of a buffer solution does not
change on dilution.
Reason
On dilution, the ratio of concentration of salt and acid (or base) remains
unchanged.
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 cyclotron is used to accelerate charged particles. Then the time period
under the influence of 17 magnetic
field of a proton:-
A \( .20 \pi n s \)
в. \( 40 \pi n s \)
c. \( 10 \pi n s \)
D. \( 5 \pi n s \)


The equation of the normal to the curve
\( \boldsymbol{y}=(1+\boldsymbol{x})^{y}+\sin ^{-1}\left(\sin ^{2} \boldsymbol{x}\right) \boldsymbol{a t} \quad \boldsymbol{x}=\mathbf{0} \)
is
A. \( x+y=1 \)
B. x-y+1=0
c. \( 2 x+y=2 \)
D. 2x-y+


Three wires are carrying same constant current \( i \) indifferent directions. Four
loops enclosing the wires in different
manners are shown in figure. The direction of \( d \vec{l} \) is shown in figure.


The component of a vector r along x-axis
will have maximum value if:
\( A \cdot r \) is along positive \( y \) -axis
B. r is along positive x-axis
C . r makes an angle of \( 45^{\circ} \) with the x-axis
D. r is along negative y-axis


Chaeta of Pheretima is about
A. \( 0.025 \mathrm{mm} \) long
B. 0.25 mm long
c. \( 0.5 \mathrm{mm} \) long
D. 2.5 mm long


By using elementary transformation find the inverce of \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{2}-\mathbf{1}\end{array}\right] \)


If \( A \) and \( B \) are independent events such
\( \operatorname{that} \boldsymbol{P}(\boldsymbol{A})>\mathbf{0}, \boldsymbol{P}(\boldsymbol{B})>\mathbf{0}, \) then
A. \( A \) and \( B \) are mutually exclusive
B. \( A \) and \( \bar{B} \) are dependent
c. \( \bar{A} \) and \( B \) are dependent
\( P\left(\frac{A}{B}\right)+P\left(\frac{\bar{A}}{B}\right)=1 \)


Which of the following is responsible for transporting food (mainly sugars) made during photosynthesis throughout the plant body?
A. Xylem
B. Phloem
c. vascular cambium
D. Mesophyll
E. Pith


Point the odd one out
Hydrometer, density bottle, physical balance
A. physical balance
B. density bottle
c. hydrometer
D. NONE


Expanded octets result in substances with more than an octet of valence
electrons resulting in non-traditional geometries of molecular compounds. Which of the following elements cannot form an expanded octet as the central atom?
A. Nitrogen
B. Phosphorus
c. sulfur
D. Chlorine


Water is a neutral substance what
coloure will you get when you add few drops of universal indicator to a test
tube containing distilled water.


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


Why is ferric hydroxide colloid positively charged when prepared by adding ferric chloride to hot water?
A. Due to precipitation of ferric hydroxide there is an excess of \( F e^{3+} \) ions.
B. Due to preferential adsorption of \( F e^{3+} \) ions by the sol of \( F e(O H)_{3} \)
c. Due to absence of any negatively charged ion.
D. Due to adsorption of \( O H^{-} \) and \( C I^{I} \) ions, the remaining sol has only \( F e^{3+} \) ions


The decreasing order of acidic character of the following is:
(I) EtOH (II) Me- \( \mathrm{COOH} \) (III) \( M e O O C- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C O O M e}(\mathrm{IV}) \mathrm{MeCOMe} \)
B. \( \|>\|>>1>1 v \)
c. ।>IV> |||> ||


If \( y=\left(\tan ^{-1} x\right)^{2} \) and \( \left(x^{2}+1\right)^{2} \frac{d^{2} y}{d x^{2}}+ \)
\( 2 x\left(x^{2}+1\right) \frac{d y}{d x}=k, \) then the value of \( k \)
is
A . 3
B. 2
c. 1
D.


In the four numbers first three are in
G.P. and last three are in A.P. whose
common difference is \( 6 . \) If the first and
last numbers are same, then first will
be


\( \boldsymbol{H} \boldsymbol{O}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{C} \boldsymbol{H}_{2}-\underset{_{O H}}{_{I}}-\boldsymbol{C} \boldsymbol{H}_{2}- \)
\( \boldsymbol{O H} \frac{\boldsymbol{H I O}_{4}}{\boldsymbol{\Delta}} \)
Identify the product of the above reaction.


A few organisms are known to grow and
multiply at temperatures of \( 100^{0} \mathrm{C} \)
\( 105^{0} \mathrm{C} . \) They belong to
A. Thermophilic sub aerial fungi
B. Marine archaebaderia
C. Thermophilic sulphur bacteria
D. Hot spring blue-green algae


A rope ladder with a length \( l \) carrying a man with a mass \( m \) at its end is
attached to the basket of a balloon with
a mass \( M . \) The entire system is in equilibrium in the air. As the man climbs up the ladder into the balloon,
the balloon descends by a height \( h \). The change in potential energy of the man is:
A \( . m g l \)
в. \( M g(l-h) \)
\( c \cdot 1 / 2 m g l \)
D. \( m g(l-h) \)


Presence of \( \mathrm{CO}_{2} \) in natural water
facilitate rusting of iron.
If true enter 1 , else enter 0


The two parts of a bimetallic strip are supposed to expand equally on heating. State whether true or false.
A. True
B. False


Consider the integrals \( A=\int_{0}^{\pi} \frac{\sin x d x}{\sin x+\cos x} \) and \( B= \)
\( \int_{0}^{\pi} \frac{\sin x d x}{\sin x-\cos x} \)
Which one of the following is correct?
A. \( A=2 B \)
в. \( B=2 A \)
c. \( A=B \)
D. \( A=3 B \)


A sure test of electrification is:
A . attraction
B. repulsion
c. friction
D. induction


For a reversible equilibrium reaction
\( K_{C}>K_{P} \) at \( 298 K \) and \( \Delta H=+200 \)
\( K J, \) the forward reaction is favoured if:
(i) Pressure is increased
(ii) Temperature is increased
(iii) Temperature is decreased
(iv) Increasing the concnetration of reactants
A . i, i i, iv
B. i, ii
c. ii, iv
D. i, iii, iv


A metallic solid sphere is rotating about is diameter as axis of rotation. If
the temperature is increased by \( 200^{\circ} \mathrm{C} \)
the percentage increased in its moment
of inertia is (Coefficient of linear
expansion of the metal \( =10^{-5} /^{\circ} \mathrm{C} \)
A . \( 0 . \)
B. 0.2
c. 0.3
D. 0.4


Find the position vector of the mid point of the vector joining the points \( \boldsymbol{P}(\mathbf{2}, \mathbf{3}, \mathbf{4}) \) and \( \boldsymbol{Q}(\mathbf{4}, \mathbf{1}, \mathbf{2}) \)


A large sheet carries uniform surface charge density \( \sigma . \) A rod length \( 2 l \) has a linear charge density \( \lambda \) on one half and \( -\lambda \) on the second half. The rod is hinged at the midpoint 0 and makes and angle \( \theta \) with the normal to the sheet. The
torque experienced by the rod is:
\( A \cdot O \)
B. \( \frac{\sigma \lambda l^{2}}{2 \varepsilon_{0}} \sin \theta \)
\( ^{\text {c. }} \frac{\sigma \lambda l^{2}}{\varepsilon_{0}} \sin \theta \)
D. \( \frac{\sigma \lambda l}{2 \varepsilon_{0}} \)


If \( A \) is a square matrix, then \( a d j A^{T}- \)
\( (a d j A)^{T} \) is equal to
A \( \cdot 2|A| \)
B . \( 2|A| I \)
c. null matrix
D. unit matrix


\( \ln \triangle A B C, \angle B=90^{\circ}, B C=7 \) and
\( A C-A B=1, \) then \( \cos C=\dots \)
A \( \cdot \frac{3}{25} \)
в. \( \frac{6}{25} \)
\( c \cdot \frac{7}{25} \)
D. \( \frac{8}{25} \)


Qualitative analysis of nitrogen is done by which test/ method?
A. Duma's method
B. Kjeldahl's method
c. Lassaigne's test
D. silver mirror test


Velocity-time graph of a particle moving
in a straight line is as shown in figure.
Mass of the particle is \( 2 k g . \) Work done
by all the forces acting on the particle in
time interval between \( t=0 \) to \( t=10 \) is
A. \( 300 J \)
в. \( -300 J \)
\( c .400 \)
D. \( -400 J \)


The work done by the force \( \overrightarrow{\boldsymbol{F}}=\mathbf{2} \hat{\mathbf{i}}- \)
\( \hat{j}-\hat{\mathbf{k}} \) in moung an object along the vector \( 3 \hat{i}+2 j-5 \hat{k} \) is
A. -9 units
B. 9 units
c. -15 units
D. None of these


The radius of the circle with centre at
the origin is 10 units. Write the
coordinates of the point where the circle intersects the axes. Find the distances
between any two of such points.
A \( . \) Co-ordinates \( =(10,0)(-10,0)(0,10)(0,-10) \) Distance \( =20,10 \sqrt{2} \) units
B. \( C o- \) ordinates \( =(10,0)(-10,0)(0,10)(0,-10) \) Distance \( =10,10 \sqrt{2} \) units
c. \( C o- \) ordinates \( =(10,0)(-10,0)(0,10)(0,-10), 0 \) Distance \( =20 \sqrt{2} \) or \( 10 \sqrt{2} \) units
D. none


Six charges are placed at the corner of a
regular hexagon as shown. If an electron
is placed at the centre \( 0, \) force on it will
be:
A. zero
B. along OF
c. along oc
D. none of these


Explain why respiration is said to be the reverse of photosynthesis.


What is green house effect? Write its two
control measures.


An object placed at a distance of \( 16 \mathrm{cm} \)
from a convex lens produces an image
of magnification \( \boldsymbol{m}(\boldsymbol{m}>\mathbf{1}) . \) If the
object is moved towards the lens by
\( 8 c m \) then again an image of magnification \( m \) is obtained. Find the numerical value of focal length of the
lens.


A cube of side b has a charge q at each of its vertices. Determine the potential
and electric field due to this charge array at the centre of the cube.


What is red shift?


Find the work done to take a particle of mass \( \mathrm{m} \) from surface of the earth to a
height equal to \( 2 R \)
\( \mathbf{A} \cdot 2 m g R \)
в. \( \frac{m g R}{2} \)
c. \( 3 m g R \)
D. \( \frac{2 m g R}{3} \)


Find \( A \triangle B \) and draw Venn diagram when:
\( A=\{a, b, c, d, e\} \) and \( B=\{a, c, e, g\} \)


The urine is
A. Hypotonic to blood and isotonic to medullary fluid
B. Hypertonic to blood and isotonic to medullary fluid
C. Isotonic to blood and hypotonic to medullary fluid
D. Isotonic to blood and hypertonic to medullary fluid


When the electron of \( C a \) is excited,then
the electron will move upto which of the orbital first?
\( \mathbf{A} \cdot 4 p \)
B. \( 3 d \)
\( c .5 s \)
D. None of these


Binomial Nomenclature means
A. A scientific name comprising of a generic and specific epithet
B. One name given by two different botanists
C. A latinised name
D. Scientific name given to a piece of vegetation


Two particles \( A \) and \( B \) start
simultaneously from the same point
and move in a horizontal plane. \( A \) has
an initial velocity \( u_{1} \) due east and
acceleration \( a_{1} \) due north. \( B \) has an
initial velocity \( u_{2} \) due north and
acceleration \( a_{2} \) due east. Which of the
following statements is(are) correct? This question has multiple correct options
A. Their paths must intersect at some point
B. They must collide at some point.
C. They will collide only if \( a_{1} u_{1}=a_{2} u_{2} \)
D. If \( u_{1}>u_{2} \) and \( a_{1}<a_{2} \), the particles will have the same speed at some point of time.


If one angle of a triangle equals the sum of the other two angles, the triangle must be:
A. scalene
B. right angled
c. obtuse angled
D. acute angled


A body of mass 3 kg hits a wall at an
angle of \( 600 \& \) returns at the same angle. The impact time was0.2 s. Calculate the force exerted on the wall:
A. \( 150 \sqrt{3} N \)
В. \( 50 \sqrt{3} N \)
c. \( 100 \mathrm{N} \)
D. \( 75 \sqrt{3} N \)


Constructive and destructive
interference occur in:
A. cosmic rays
B. light raus
c. sound waves
D. water waves
E. All of these


One end of metal bar of area of cross
section \( 5 c m^{2} \) and \( 25 c m \) in length is in stream and other end is in contact with
ice. The amount of ice melts in one
minute is :
\( (\boldsymbol{L}=\mathbf{8 0} \mathbf{c a l} / \boldsymbol{g} \boldsymbol{m}, \boldsymbol{K}=\mathbf{0 . 8} \boldsymbol{c g} \boldsymbol{s} \boldsymbol{u n i t s}) \)
\( \mathbf{A} \cdot 16 g m \)
в. \( 12 g m \)
\( \mathrm{c} \cdot 24 g m \)
D. \( 36 g m \)


The altitude of an equilateral triangle of side lenght of \( 2 \sqrt{3} \mathrm{cm} \) is:
A \( \cdot \frac{\sqrt{3}}{2} c \)
в. \( \frac{1}{2} c m \)
c. \( \frac{\sqrt{3}}{4} c \)
D. 3 ст


Arrange the following rational number
in descending order
\( \frac{1}{5}+\frac{1}{-6},\left|-\frac{7}{6}+1\right|,\left(-\frac{1}{2}\right)^{3}, \frac{5}{8} \div \frac{-15}{4} \)
\( \stackrel{1}{5}+\frac{1}{-6},\left(-\frac{1}{2}\right)^{3}, \frac{5}{8} \div \frac{-15}{8},\left|-\frac{7}{6}+1\right| \)
\( \left(-\frac{1}{2}\right)^{3}, \frac{1}{5}+\frac{1}{-6}, \frac{5}{8} \div \frac{-15}{4},\left|-\frac{7}{6}+1\right| \)
\( \mathbf{C} \cdot\left|-\frac{7}{6}+1\right|, \frac{1}{5}+\frac{1}{-6},\left(-\frac{1}{2}\right)^{3}, \frac{5}{8} \div \frac{-15}{4} \)
\( \frac{5}{6} \div \frac{-15}{4},\left|-\frac{7}{6}+1\right|, \frac{1}{5}+\frac{1}{-6},\left(-\frac{1}{2}\right)^{3} \)


Write each amount as a fraction and
then express it as percentage. 105 children out of 200 voted in favour
of more sport at school


The endoplasmic reticulum is mainly concerned with:
A. Proteolysis
B. Fatty acid synthesis
c. cholesterol synthesis
D. Peptide bond synthesis


The word standard in standard molar
enthalpy change implies:
A. temperature \( 298 K \)
B. pressure 1 atm
C . temperature 298 K and pressure 1 atm
D. all temperatures and all pressures


Among the given compounds, the compound which is most susceptible to
a nucleophilic attack at the carbonyl
group is:
A \( \cdot C H_{3} C O C l \)
в. \( C H_{3} C H O \)
\( \mathbf{c} \cdot C H_{3} C O O C H_{3} \)
D. \( C H_{3} \) СООСОСН\( _{3} \)


Radiation is passing through a transparent medium, then:
A. the temperature of medium increases
B. the temperature of medium decreases
C. the temperature of medium does not alter
D. the temperature of medium first increases and then becomes steady


Weight:
A. is a vector quantity
B. of a body in interplanetary space is maximum
C. increases when the bodies go up
D. is none of these


The position function of a particle is
given by \( \boldsymbol{x}(t)=\boldsymbol{k} \boldsymbol{t}^{5 / 2}, \) where \( \boldsymbol{k} \) is a
constant.
If the particle starts at rest and is propelled through some distance \( d \) so
that the trajectory matches \( x(t), \) the
work done on the particle is
proportional to which power of \( t ? \)
\( \mathbf{A} \cdot t^{5} \)
B \( \cdot t^{3} \)
\( \mathbf{c} \cdot t^{5 / 2} \)
\( \mathbf{D} \cdot t^{3 / 2} \)
E. Not enough information


Viruses with two types of symmetry,
that is, icosahedral head and helical tail
are termed as
A. Picornaviruses
B. Binal viruses
c. Riboviruses
D. None of the above


The increase in energy of a metal bar of length 'L' and cross-sectional area 'A'
when compressed with a load 'M' along its length is (Y = Young's modulus of the material of metal bar)
\( ^{\mathbf{A}} \cdot \frac{F L}{2 A Y} \)
в. \( \frac{F^{2} L}{2 A Y} \)
c. \( \frac{F L}{A Y} \)
D \( \cdot \frac{F^{2} L^{2}}{2 A Y} \)


A die if thrown once. Find the probability
of getting a number less than 5


A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to \( \frac{1}{1000} \) of the original amplitude is close to :-
A . 100 s
в. \( 20 s \)
\( c .10 s \)
D. \( 50 s \)


Which of the following is/are true regarding breakdown voltage of Zener
diode?
A. If the reverse bias voltage across a p-njunction diode is increased, at a particular voltage the reverse current suddenly decreases to a large value
B. The holes in the n-side and the conduction electrons in the p-side are accelerated due to the reverse bias voltage.
C. The voltage at which the rate of creation of holeelectron pairs is increased leading to the increased current is called avalanche breakdown
D. None of the above


Two cubes have edge lengths in the ratio of 2: 3 respectively. The ratio of
their surface areas is
A \( \cdot \frac{4}{9} \)
в. \( \frac{8}{27} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{\sqrt{2}}{\sqrt{3}} \)
E \( \cdot \frac{\sqrt{3}}{\sqrt{2}} \)


The distance, once around the circle is
called
A. diameter
B. center
c. circumference
D. chord


An unknown chlorohydrocarbon as 3.55 \( \% \) of chlorine. If each molecule of the
hydrocarbon has one chlorine atom only
chlorine atoms present in \( 1 g \) of
chlorohydrocarbon are: (Atomic wt. of \( C l=35.5 u ; \) Avogadro constant \( = \)
\( 6.023 \times 10^{23} m o l^{-1} \)
A. \( 6.032 \times 10^{9} \)
В. \( 6.032 \times 10^{23} \)
c. \( 6.032 \times 10^{2} \)
D. \( 6.032 \times 10^{20} \)


A person buys 100 cups at Rs. 20 each
On the way 10 cups are broken. He sells the remaining cups at Rs. 22 each. His loss percent is :
A . 1
B. 2
\( c .3 \)
\( D \)


Give four uses of emulsions.


Aristotle wrote
A. Historia Animalium.
B. De Partibus Animalium.
C. De Generatione Animalium.
D. All the above.


The motion of a pendulum is an example of :
A. translatory motion
B. rotational motion
c. oscillatotry motion
D. curvilinear motion


Range of \( f(x)=\tan ^{-1}\left[\frac{2}{\pi}\left(2 \tan ^{-1} x-\right.\right. \)
\( \left.\left.\sin ^{-1} x+\cot ^{-1} x-\cos ^{-1} x\right)\right] \) contains
A. Only one integer
B. More than 2 integers
c. only two integers
D. No integer


Name of functional group shown.
A. Aldehyde
B. Ketone
C. Alcohol
D. Carboxylic acid


A light ray is incident on a prism in minimum deviation position and
suffers a deviation of \( 34^{\circ} \). If the shaded
half of the prism is removed off, then the same ray will suffer a deviation of :
A \( \cdot 0^{\circ} \)
B. 65
\( \mathrm{c} \cdot 17^{\circ} \)
D. 34


Which one of the following paires of elements is most likely to form an ionic
compount?
\( \mathbf{A} \cdot \mathbf{B} \) and \( C I_{2} \)
B. \( \mathrm{K} \) and \( \mathrm{O}_{2} \)
c. \( O_{2} \) and \( C I_{2} \)
D. Al and \( I_{2} \)


When chlorine water is added to a
solution of \( K B r, \) the solution
immediately turns orange red, because
A. Chlorine is reduced to chloride ion
B. of the formation of \( B r C l \)
c. Bromide ion is oxidized to bromine
D. of the formation of \( B r_{3} \)


A magnet is dropped freely towards a
loop of copper wire as shown in figure.
The acceleration of magnet will be:
A. equal to 9
B. greater than gless than \( g \)
c. less than \( g \)
D. zero


The following observations have been arranged in ascending order, if the median of data is 63
Find the value of \( x: \)
\( \mathbf{2 9}, \mathbf{3 2}, \mathbf{4 8}, \mathbf{5 0}, \boldsymbol{x}, \boldsymbol{x}+\mathbf{2}, \mathbf{7 2}, \mathbf{7 8}, \mathbf{8 4}, \mathbf{9 5} \)


When a cell is placed in pure water then?
A. Wall pressure is increased
B. Turgor pressure is increased
c. water potential of cell is increased
D. All the above


In the hydrogenation of ethylene, \( \Delta n \) is equal to:
\( \mathbf{A} \cdot \mathbf{1} \)
B. - -
\( c \cdot-1 \)
\( D \cdot 2 \)


Acetylene is a linear molecule is shown
by:
\( A \cdot \) its \( C \equiv C \) bond distance being \( 1.21 A^{0} \)
B. its \( C \) - H bond distance being \( 1.08 A^{0} \)
C . its \( \mathrm{H}-\mathrm{C} \) - \( \mathrm{C} \) bond angle being \( 180^{\circ} \)
D. All of the above


The nuclei having same number of protons but different number of
neutrons are called
A. Isobars
B. \( \alpha \) -particles
c. Isotopes
D. \( \gamma \) -particles


An element M belongs to the group 1 and period 3 of the modern periodic table. Out of the following statement, which is
the true about 'M'?
A. It forms an acidic oxide having formula \( M_{2} O_{3} \)
B. It is a non-metal
c. It is highly electro positive in nature
D. It has a valency of three


Calculate \( (\Delta S)_{\text {universe}}(\text {in cal/K }) \) when 1 kg water at \( 300 K \) is brought into
contact with a heat reservoir at \( 600 K \)
Specific heat of water is 1 cal \( / \) gm \( -^{\circ} \boldsymbol{C} \) ( \( \ln 2=0.7) \)


Which of the following represents true statement(s)?
This question has multiple correct options
A. Natural gas is an important fossil fuel as it is easy to transport through pipes.
B. Natural gas is stored under low pressure
C . CNG is used for power generation.
D. \( \mathrm{CNG} \) is used as fuel for transport vehicles.


Two points \( A \) and \( B \) on a disc have
velocities \( v_{1} \) and \( v_{2} \) at some moment.
Their directions make angles \( 60^{\circ} \) and
\( 30^{\circ} \) respectively with the line of
separation as shown in figure. The
angular velocity of disc is not given by :
A \( \cdot \frac{v_{1}}{\sqrt{3} d} \)
B. \( \frac{v_{2}}{d} \)
\( ^{\mathbf{c}} \cdot\left(\frac{\sqrt{3} v_{1}-v_{2}}{2 d}\right) \)
D. None of these


If in a birefracting crystal the magnitude
\( E_{x} \) and \( E_{y} \) are equal and phase angle
between the two is \( 60^{0} \) then the waves are
A. linearly polarised
B. plane polarised
C. circularly polarised
D. elliptically polarised


The two compounds
\( \left[\boldsymbol{C o}\left(\boldsymbol{S O}_{4}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\right] \boldsymbol{B r} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{S O}_{4}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\right] \boldsymbol{C l} \) represent
A. Linkage is isomerism
B. lonisation isomerism
c. co - ordination isomerism
D. No isomerism


A cube of sponge rubber with edge length \( 5 \mathrm{cm} \) has a force of \( 2 \mathrm{N} \) applied horizontally to the top face (parallel to an edge) while the bottom face is held fixed. If the top face is displaced horizontally through a distance of \( 1 \mathrm{mm} \) find the shear modulus for the sponge rubber.
A. \( S=7 \times 10^{4} N m^{-2} \)
B. \( S=6 \times 10^{4} N m^{-2} \)
c. \( S=4 \times 10^{4} N m^{-2} \)
D. \( S=5 \times 10^{4} N m^{-2} \)


toppr
\( Q \)
meters. Arter this the bus travels at a
constant speed for 15 seconds. Then the driver notices a red light 18 meters ahead and applies brakes with
acceleration \( a_{b} . \) Assume that the bus
decelerates at a constant rate and
comes to a stop sometime later just at the light.
1. What was the initial acceleration of
the bus?
2. What was the velocity of the bus after
5 seconds?
3. Calculate \( a_{b} \)
4. How long did does the bus brake?
b) Two athletes Usha and Shiney are playing athletic games. Usha is running at a constant velocity towards Shiney who is stationary. When Usha is 12 meters away from Shiney, Shiney starts to accelerate at a constant rate of
\( 1.5 m s^{-2} \)
1. What is the minimum velocity with which Usha needs to run in order to just catch up with Shiney?
2. How long does Usha take to catch up with Shiney?


Given diagram is showing a defect of
a human eye. Study it and answer the
following question:
Give the reason for this defects of the
eye in the human being.


The potential energy of a particle is given by formula \( U=100-5 x+ \)
\( 100 x^{2}, U \) and \( x \) are in SI units if mass of
the particle is \( 0.1 \mathrm{kg} \) then magnitude of it's acceleration.
A . At \( 0.05 \mathrm{m} \) from the origin is \( 50 \mathrm{m} / \mathrm{s}^{2} \)
B. At \( 0.05 \mathrm{m} \) from the mean position is \( 100 \mathrm{m} / \mathrm{s}^{2} \)
c. At \( 0.05 \mathrm{m} \) from the origin is \( 150 \mathrm{m} / \mathrm{s}^{2} \)
D. At 0.05 m from the mean position is 200 \( \mathrm{m} / \mathrm{s}^{2} \)


A right angles prism \( \left(45^{\circ}, 90^{\circ}, 45^{\circ}\right) \) of refractive index \( n \) has a plate of
refractive index \( \left(n_{1}<n\right) \) cemented to
its diagonal face. The assembly is in air. A ray is incident on \( \mathrm{AB} \)

If the angle of incidence at \( A B \) for which the ray strikes the diagonal face at the
critical angle is \( X \) in degrees. Find \( X ? \)


Identify the incorrect statement.
A. Key is a taxonomic aid for identification of specimens
B. Herbarium houses dried, pressed and preserved plant specimens
C. Botanical gardens have collection of living plants for reference
D. A museum has collection of photographs of plants and animals


By the graphical method, find whether
the following pair of equations are consistent or not. If consistent, solve
them.
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{3} \) and \( \mathbf{3} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{9} \)


The genes are responsible for growth and differentiation in an organism. They achieve this regulation through
A. Translocation
B. Transformation
c. Transduction and translation
D. Translation and transcription


Discuss the respiratory pathway is an amphibolic pathway.


A die is thrown once. What is the
probability of getting a number less
than \( 3 ? \)


A parallelogram has sides \( 6 \mathrm{cm} \) and
\( 4 \mathrm{cm} \) and one of its diagonals is \( 8 \mathrm{cm} \)
then its area is :-


\( \operatorname{Let}\left(1+x^{2}\right)^{2}(1+x)^{n}=\sum_{k=0}^{n+4} a_{k} x^{k} \)
\( a_{1}, a_{2} \) and \( a_{3} \) are in arithmetic
progression, find \( n \)


Mention the hypothesis of Dalton's atomic theory.
OR
Write the limitations of Dalton's atomic
theory.


A particle is dropped on Earth from
height \( \mathbf{R}(\text { radius of Earth }) \) and it
bounces back to a height \( \mathbf{R} / \mathbf{2} \)
coefficient of restitution for collision is
(ignore air resistance and rotation of Earth)
\( A \cdot \frac{2}{3} \)
B. \( \sqrt{\frac{2}{3}} \)
\( c \cdot \sqrt{\frac{1}{3}} \)
D. \( \sqrt{\frac{1}{2}} \)


Dimensions of pressure are same as
that of:
A. energy
B. force
c. energy per unit volume
D. force per unit volume


Choose the correct answer from the
alternatives given.

Which is the best definition of active
transport?
A. Movement of molecules from an area of their higher concentration to an area of their lower concentration
B. Movement of water across a semi-permeable membrane from an area of high water concentration to an area of lower water concentration
C. Movement of molecules from an area of their lower
concentration to an area of their higher concentration
D. Movement of a substance against its concentration through the release of energy from ATP


The radius of oxygen nucleus \( \left(_{8} O^{16}\right) \) is
\( 2.8 \times 10^{-15} \mathrm{m} . \) Calculate the radius of
the lead nucleus.


The rate constant for a recation is
\( 10.8 \times 10^{-5} \) mol \( L^{-1} S^{-1} . \) The reaction
obeys:
A. First order
B. Zero order
c. second order
D. All are wrong


Which is the decreasing order of
stability?
(i) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C H}_{3} \)
(ii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{O}-\boldsymbol{C H}_{3} \)
(iii) \( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\boldsymbol{C O}-\boldsymbol{C H}_{3} \)
\( A . \) (i) \( < \) (ii) < (iii)
B. (ii)>(i)> (iii)
\( c \cdot(\text { iii) }>(\text { ii) }>(i) \)
D. (ii) > (iii) > (i)


From among the elements, choose the
following:
\( \mathrm{Cl}, \mathrm{Br}, \mathrm{F}, \mathrm{O}, \mathrm{Al}, \mathrm{C}, \mathrm{Li}, \mathrm{Cs} \) and \( \mathrm{Xe} \)
The element which has the smallest
radius.


A solution of a substance 'X' is used for
white washing.

Write the reaction of the substance 'X'
named in given with water


Assertion: The addition of acid to a
solution buffered to pH 7 slightly lowest the pH.
Reason: \( \mathrm{pH} \) of any neutral solution always lowers on the addition of acids.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Which of the following according to LeChatelier's principle is correct?
A. Increase in temperature favours the endothermic reaction
B. Increase in temperature favours the exothermic reaction
c. Increase in pressure shifts the equilibrium in that side in which number of gaseous moles increases
D. All of the above are true


Classify \( N a H_{2} P O_{2} \) and \( N a H S O_{4} \)
salts as acid salt or normal salt.


Degeneracy of the genetic code denotes the existence of
A. Multiple codons for a single amino acid
B. Wobble hypothesis
c. Base triplets that do not code for amino acids
D. All of the above


In case of a man,
when the entire sole rests on the ground during walking, it is known as
A. Plantigrade
B. Digitigrade
c. Perikaryon
D. Hallux


If pressure on a gas is increased from \( \boldsymbol{P} \)
to \( 2 P, \) then its heat conductivity
A . increases
B. decreases
c. becomes zero
D. remains unchanged


A thin lens has focal length \( f \), and its
aperture has diameter \( d \). If the central
part of the aperture, of diameter \( \boldsymbol{d} / \mathbf{2} \) is blocked by an opaque paper, the focal length of the lens and the intensity of image will become:
A \( \cdot \frac{f}{2}, \frac{1}{2} \)
в. \( _{f}, \frac{I}{4} \)
c. \( \frac{3 f}{4}, \frac{I}{2} \)
D. \( _{f, \frac{3 I}{4}} \)


Which of the following is a character of
gymnospermous wood?
A. Porous
B. Ring porous
c. Diffused porous
D. Non-porous


The functional groups present in cytosine are:
A. Keto and amino
B. Keto only
c. Amino only
D. methy


SONAR is based on the principle of :
A. echo
B. resonance
c. reverberation
D. damping


If we rotate the dipole of moment \( p \)
placed in an electric field \( \boldsymbol{E} \) from an \( \boldsymbol{\theta}_{\mathbf{1}} \)
to \( \theta_{2} \), the work done by the external force is
A \( \cdot p E\left(\cos \theta_{2}-\cos \theta_{1}\right) \)
B . \( p E\left(\cos \theta_{1}-\cos \theta_{2}\right) \)
c. \( p E\left(\sin \theta_{2}-\sin \theta_{1}\right) \)
D・ \( p E\left(\sin \theta_{1}-\sin \theta_{2}\right) \)


Write the place value of 3 in the following decimal numbers.
\( \mathbf{3 . 4 6} \)


The term "Keel" is used for special type
of
A. Sepals
B. Petals
c. stamens
D. carpels


If \( \int \frac{2^{x}}{\sqrt{1-4^{x}}} d x=k \sin ^{-1} 2^{x}+c, \) then
\( \boldsymbol{k}= \)
\( A \cdot \log 2 \)
в. \( \frac{1}{\log 2} \)
c. \( \frac{1}{2 \log 2} \)
D. \( 2 \log 2 \)


The polymer used as packaging material in orthopaedic devices and for controlled drug release is:
A. Kevlar
B. PHBV
c. Glyptal
D. Bakelite


The Sl unit of amplitude of oscillation is
A \( . c m \)
в. \( m \)
\( c . k m \)
D. \( \mu \) m


Which of the following statements for the reaction, is correct?
\( N a_{2} C r O_{4}+H_{2} S O_{4} \rightarrow \)
A. It is a redox reaction in which green solution of \( \left[C r\left(H_{2} O\right)_{6}\right]^{+3} \) is produced.
B. one of the product is reaction has trigonal planar structure
c. Dimeric bridged tetrahedral metal ion is produced.
D. Dark blue color in obtained in reaction


Asexual reproduction are
A. Fission
B. Budding
C. Vegetative propagation
D. All of the above


The meristem that gets consumed is
A. Lateral meristem
B. Intercalary and reproductive
C . Apical meristem
D. All the above


What percentage of sulphur is used in the vulcanization of rubber?
A . \( 5 \% \)
B. 3\%
c. \( 30 \% \)
D. 55\%


Identify the compound \( A \) in the reaction
given below.
\( N a_{2} B_{4} O_{7}+2 H_{2} O \rightarrow 2 N a O H+A \)
A. Orthoboric acid
B. Metaboric Acid
c. Tetraboric Acid
D. Pyroboric acid


Prove \( \int \frac{d x}{\sqrt{a^{2}-x^{2}}} \)


\( 2 C_{3} H_{8}+7 O_{2} \rightarrow 2 C O_{2}+8 H_{2} O+ \)
\( 2 C O+2 C \)
Name the type of reaction.
A. Combustion
B. Incomplete combustion
c. condensation
D. None of these


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & \mathbf{2} \\ \mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{3} & \boldsymbol{a} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{A}^{-\mathbf{1}}= \)
\( \left[\begin{array}{ccc}1 / 2 & -1 / 2 & 1 / 2 \\ -4 & 3 & c \\ 5 / 2 & -3 / 2 & 1 / 2\end{array}\right] \)
then
A \( a=2, c=1 / 2 \)
2
В. \( a=1, c=-1 \)
c. \( a=-1, c=1 \)
D. \( a=1 / 2, c=1 / 2 \)


Which of the following is true about the given compound?
A. It is aromatic
3. It is non- aromatic
\( c . \) It is anti-aromatic
D. Its aromatic behaviour cannot be predicted


Which of the following is true
statement?
A. The lower aldehydes have pungent ordour, but as molecular mass increases odour becomes less pungent and more fragrant.
B. The lower aldehydes have fragrant ordour, but as molecular mass increases odour becomes less
fragrant and more pungent.
C. The lower aldehydes have pungent ordour, but as molecular mass increases odour disappears.
D. The lower aldehydes have fragrant ordour, but as molecular mass increases odour disappears.


If the angle of incidence is changed to
\( 60^{\circ} . \) State whether the angle of
deviation will be equal to, less than or
more than \( 36^{\circ} ? \)


Calculate the approximate speed of sound in oxygen from the following data The mass of 22.4 liter of oxygen at
\( \boldsymbol{S} \boldsymbol{T} \boldsymbol{P}(\boldsymbol{T}=\mathbf{2 7 3} \boldsymbol{K} \boldsymbol{a n d \boldsymbol { p }}=\mathbf{1 . 0} \times \)
\( \left.10^{5} N m^{2}\right) \) is \( 32 g \) the molar heat
capacity of oxygen at constant volume
is \( C_{V}=2.5 R \) and that at constant
pressure is \( \boldsymbol{C}_{\boldsymbol{P}}=\mathbf{3 . 5} \boldsymbol{R} \)


Boiling water is a \( ---- \) change
because
A. Physical, the gaseous water produced is chemically identical to the liquid water the process began with
B. Physical, the water was disappeared
C. Chemical, heat was required for the change
D. Chemical, the process produced a gas


ionizes in a fused
or in aqueous solution state and furnish
positive ions other than \( \boldsymbol{H}^{+} \) and
negative ions other than \( \boldsymbol{O} \boldsymbol{H}^{-} \)
A. Mineral acids
B. Bases
c. lonic salts
D. compounds


Energy hidden in a definite quantity of substance is:
A. Enthalpy
B. Internal energy
c. Free energy
D. Entropy


What type of magnetism is shown by a substance if magnetic moments of domains are arranged in same direction?


The sum of 100 terms of the series. \( 9+ \)
\( \mathbf{0 9}+.009 . \) will be?
\( ^{\mathbf{A}} \cdot_{1}-\left(\frac{1}{10}\right)^{100} \)
B. \( 1+\left(\frac{1}{10}\right)^{106} \)
\( ^{\mathrm{c}} \cdot_{1-}\left(\frac{1}{10}\right)^{106} \)
D. \( _{1+}\left(\frac{1}{10}\right)^{100} \)


A wave is represented by the equation \( \boldsymbol{y}=\boldsymbol{A} \sin (\mathbf{1 0} \boldsymbol{\pi} \boldsymbol{x}+\mathbf{1 5} \boldsymbol{\pi} \boldsymbol{t}+\boldsymbol{\pi} / \mathbf{3}) \) where \( \boldsymbol{x} \)
is in meters and \( t \) is in seconds. The
expression represents:
A. a wave travelling in the positive \( x \) -direction with a velocity \( 1.5 \mathrm{m} / \mathrm{s} \)
B. a wave travelling in the negative \( x \) -direction with a velocity \( 1.5 \mathrm{m} / \mathrm{s} \)
c. a wave travelling in the negative \( x \) -direction having a wavelength \( 0.2 m \)
D. a wave travelling in the positive \( x \) -direction having a wavelength \( 0.2 m \)


\( 250 m l \) of a sodium carbonate contains
\( 2.65 \operatorname{grams} N a_{2} C O_{3} . \) If \( 10 m l \) of that
solution is diluted to one litre, what is the concentration of the resultant
solution (mol wt. of \( \left.\boldsymbol{N a}_{2} \boldsymbol{C O}_{3}=\mathbf{1 0 6}\right) \)
\( \mathbf{A} \cdot 0.1 M \)
в. \( 0.001 M \)
c. \( 0.01 M \)
D. \( 10^{-4} M \)


Which of the following is not present in cis-platin?
A. Platinum
B. Fluorine
c. chlorine
D. Ammonia


Figure shows a capillary tube \( C \) dipped
in a liquid that wets it. The liquid rises
to a point A. If we blow air through the horizontal tube H, what will happen to
the liquid column in the capillary tube?
A . Level will rise above
B. Level will fall below A
c. Level will remain at \( A \)
D. It is difficult to predict


Which statements is/are correct?
dl or \( (\pm) \) or raccmic
(A)
This question has multiple correct options
A. Compound
(B) is meso- and (C) is racemic-1, 2dimethyl cyclohexane
B. Compound
(B) is racemic-and (C) is meso-1, 2dimethyl cyclohexane
c. compound
(D) is 1,2 -dimethyl cyclohexane
D. Octane-2,7-dione is obtained on reductive ozonolysis of compound (D)


Among the following molecules:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{3} \)
(ii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{4}(\text { iii }) \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \)
those having same number of lone pairs on Xe are:
A. (i) and (ii) only.
B. (i) and (iii) only.
c. (ii) and (iii) only.
D. (i), (ii) and (iii)


Evaluate \( \boldsymbol{I}=\int_{\boldsymbol{\pi} / \mathbf{6}}^{\boldsymbol{\pi} / \mathbf{3}} \sin \boldsymbol{x} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{1-\sqrt{3}}{2} \)
в. \( \frac{\sqrt{3}+1}{2} \)
c. \( \frac{\sqrt{3}-1}{2 \sqrt{3}} \)
D. None of these


Describe an experiment to demonstrate that copper is a better conductor of heat
than wood.


A man covers 60 m distance in one
minute on the surface of earth. The
distance he will cover on the surface of moon in one minute is \( \left(g_{m}=\frac{g_{e}}{6}\right) \)
\( A .60 m \)
в. 60 Х 6 т
c. \( \frac{60}{6} m \)
D. \( \sqrt{60} m \)


Assertion
Nucleic acid complexes alone cannot cause diseases.
Reason
Only nucleoproteins can function as infectious agents.
A. both assertion and reason are true and reason is the correct explanation of assertion.
B. both assertion and reason are true but reason is not the correct explanation of assertion
c. assertion is true but reason is false.
D. both assertion and reason are false


The blood vascular system of mammals is known as double vascular system because
A. A group of arteries carries oxygenated and other groups of veins conducts deoxygenated blood
B. Oxygenated blood runs from heart to different organs by one set of arteries while deoxygenated blood runs from heart to lung by pulmonary artery
c. The two different systems never meet
D. All of the above


A sinusoidal alternating current of peak
value \( I_{0} \) passes through a heater of
resistance \( R \). What is the mean power
output of the heater?
A \( \cdot I_{0}^{2} R \)
B. \( \frac{I_{0}^{2} R}{2} \)
\( \mathbf{c} \cdot 2 I_{0}^{2} R \)
D. \( \sqrt{2} I_{0}^{2} R \)


Most acidic hydrogen is present in :
\( A \)
B.
c. \( \left(C H_{3} C O\right)_{3} C H \)
D. \( \left(C H_{3}\right)_{3} C O H \)


If the maximum concentration of \( \boldsymbol{P b C l}_{2} \)
in water is \( 0.01 M \) at \( 298 K \), Its
maximum concentration in
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{N} \boldsymbol{a} \boldsymbol{C l} \) will be:
A \( \cdot 4 \times 10^{-3} M \)
В. \( 0.4 \times 10^{-4} M \)
\( \mathbf{c} \cdot 4 \times 10^{-2} M \)
D. \( 4 \times 10^{-4} M \)


The reaction \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} \) is
studied in a one litre vessel at \( 250^{0} C \).
The initial concentration of \( A \) was \( 3 n \)
and of \( B \) was n. After equilibrium was attained then equilibrium concentration of \( B \). What is the
concentration of \( D \) at equilibrium : -
A \( \cdot \frac{n}{2} \)
в. \( \left(3 n-\frac{n}{2}\right) \)
\( ^{c} \cdot\left(n+\frac{n}{2}\right) \)
D.


The slope of a distance-time graph of a moving body gives its
A. Speed
B. Displacement
c. velocity
D. Acceleration


Find the area of the region bounded by
the curves \( y=\log _{e} x, y=\sin ^{4} \pi x, x= \)
\( \mathbf{0} \)
A \( \cdot \frac{11}{8} \) sq.units
B. \( \frac{9}{8} \) sq.units
c. \( \frac{13}{8} \) sq.units
D. \( \frac{15}{8} \) sq.units


Yeast reproduces by the process called
as
A. Binary fission
B. Spore formation
c. Fragmentation
D. Budding


Solve: \( \sum_{n=1}^{13}\left(t^{n}-t^{n+1}\right)= \)


Two sound waves each of amplitude \( a \) and of frequencies \( 500 H z \) and \( 512 H z \)
superpose. Then the resultant of the amplitude of the resultant wave at \( t= \) \( \frac{5}{48} s \) is
A . 0
в. \( \frac{a}{\sqrt{2}} \)
\( c \cdot a \sqrt{2} \)
D. \( 2 a \)


Alkali and alkaline earth metals are
elements.
A. same
B. different
c. both A and B
D. none of these


Which of the following expressions are polynomials in one variable and which
are not? State reasons for your answer
(i) \( 4 x^{2}-3 x+7 \)
(ii) \( y^{2}+\sqrt{2} \)
(iii) \( 3 \sqrt{t}+t \sqrt{2} \)
(iv) \( \boldsymbol{y}+\frac{\mathbf{2}}{\boldsymbol{y}} \)
(v) \( x^{10}+y^{3}+t^{50} \)


Consider a uniform disc of mass \( 4 \mathrm{kg} \) performing pure rolling with velocity 5 \( \mathrm{m} / \mathrm{s} \) on a fixed rough surface
A. Kinetic energy of upper half will be 37.5 J
B. Kinetic energy of upper half will be less than 37.5
c. Kinetic energy of upper half will be more than 37.5 j
D. Kinetic energy of upper half will be more than 75


The anhydride of orthophosphoric acid is :
A. \( \mathrm{P}_{4} \mathrm{O}_{6} \)
в. \( \mathrm{P}_{2} \mathrm{O}_{4} \)
\( \mathrm{c} \cdot \mathrm{P}_{4} \mathrm{O}_{10} \)
D. \( \mathrm{H}_{2} \mathrm{P}_{2} \mathrm{O}_{6} \)


In the expansion of \( \left(x-\frac{1}{x}\right)^{6} \), the
constant term is
A . -20
B . 20
c. 30
D. -30


A body of mass \( M_{1} \) collides elastically
with another body of mass \( M_{2} \) at rest. There is maximum transfer of energy
when
A. \( M_{1}>M_{2} \)
В. \( M_{1}<M_{2} \)
\( \mathbf{c} \cdot M_{1}=M_{2} \)
D. same for all values of \( M_{1} \) and \( M_{2} \)


Match the following
\begin{tabular}{lll|l}
& List I & & List II \\
A. & \( \mathrm{PCl}_{3} \) & I. & Square planar \\
B. & \( B F_{3} \) & II. & T-shape \\
C. & \( C I F_{3} \) & II. & Trigonal-pyramidal \\
D. & \( X e F_{4} \) & IV. & See-saw \\
& & V. & Trigonal planar
\end{tabular}
D-II
A \( . \) A-IV, B-II, C-I.
B. A-III, B-V, C-II. D-IV
\( c \)
A-III B-V, C-II, D-1
D. A-II, B-IV, C-III \( D-v \)


Two substances \( A\left(t_{\frac{1}{2}}=5 \min \right) \) and \( B \) \( \left(t_{\frac{1}{2}}=15 \mathrm{min}\right) \) are taken in such a way that initially \( [\boldsymbol{A}]=\mathbf{4}[\boldsymbol{B}] . \) The time after
which both the concentrations will be
equal is:
A. 5 minutes
B. 15 minutes
c. 20 minutes
D. concentrations can never be equal


Irregular reflection laws of
reflection.
A. obeys
B. violates
c. obeys sometimes
D. violates sometimes


An electron falls through a distance of
\( 1.5 c m \) in a uniform electric field of
magnitude \( 2 \times 10^{4} N / C . \) Now the
direction of the field is reversed keeping the magnitude and unchanged and a proton falls through the same distance. Compute the time of fall in each case,
neglecting gravity.


If \( \left(x^{3 / 2}-x y^{1 / 2}+x^{1 / 2} y-y^{3 / 2}\right) \) is
divided by \( \left(x^{1 / 2}-y^{1 / 2}\right), \) the quotient is:
\( \mathbf{A} \cdot x+y \)
в. \( x-y \)
C \( \cdot x^{1 / 2}-y^{1 / 2} \)
D. \( x^{2}-y^{2} \)


Consider the following reactions
Anti-addition takes place in:
A \( .(I),(I I),(V) \)
B . \( (I I I),(I V),(V I) \)
\( \mathbf{c} \cdot(I),(I I),(I V) \)
D. \( (I I I),(I V),(V) \)


Why d-block element form complexes?
A. due to larger size and higher nuclear charge
B. due to small size and low nuclear charge
C. due to small size and higher nuclear charge
D. none of the above


If sum of \( n \) terms of a sequence is given
by \( S_{n}=2 n^{2}+3 n, \) find its \( 50^{t h} \) term.
A . 250
в. 225
\( c \cdot 201 \)
D. 205


Among the compounds:
The order of decreasing reactivity towards electrophilic substitution is :
\( \mathbf{A} \cdot\|>|>\||>\mid V \)
B. ||| >| >|| >IV
C . IV > > >|> III
D. | >|| >||| > IV


Kunal took few iron turnings and mixed them well with Sulphur powder. He could separate the iron turnings with the help of a magnet. He heated the
mixture for some time and tried to
separate the iron turnings with the magnet but he could not. Why?
A. on heating, a chemical change takes place and a new compound is formed.
B. on heating, iron becomes non-magnetic hence, it is not attracted by magnettet
c. on heating, a physical change takes place hence iron and Sulphur gets mixed up
D. on heating, iron evaporates and only sulphur is left behind


Three ammeters \( A, B \) and \( C \) of
resistances \( \boldsymbol{R}_{\boldsymbol{A}}, \boldsymbol{R}_{\boldsymbol{B}} \) and \( \boldsymbol{R}_{\boldsymbol{C}} \)
respectively are joined as shown. When
some potential difference is applied
across the terminals \( T_{1} \) and \( T_{2}, \) their
readings are \( I_{A}, I_{B} \) and \( I_{C} \) respectively
This question has multiple correct options
\( \mathbf{A} \cdot I_{A}=I_{B} \)
B \( \cdot I_{A} R_{A}+I_{B} R_{B}=I_{C} R_{C} \)
\( \mathbf{C} \cdot \frac{I_{A}}{I_{C}}=\frac{R_{C}}{R_{A}} \)
D. \( \frac{I_{B}}{I_{C}}=\frac{R_{C}}{R_{A}+R_{B}} \)


Thermite is a mixture of:
\( \mathbf{A} \cdot M g O+A l \)
в. \( F e_{2} O_{3}+A l \)
c. \( Z n+C a C O_{3} \)
D. \( Z n+P_{2} O_{5} \)


Identify Z in the given reaction. \( \mathrm{CH} \equiv \mathrm{CH} \frac{\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{HgSO}_{4}+60^{0} \mathrm{C}}{\longrightarrow} \boldsymbol{Z} \)
A \( \cdot C_{2} H_{5} I \)
в. \( C_{2} H_{5} O H \)
с. \( C H I_{3} \)
D. \( C H_{3} C H O \)


A body of mass 10 mg is moving with a
velocity of \( 100 m s^{-1} . \) The wavelength of
the de Broglie wave associated with it would be
A \( \cdot 6.63 \times 10^{-7} \mathrm{m} \)
B. \( 6.63 \times 10^{-31} m \)
\( c \cdot 6.63 \times 10^{-4} m \)
D. \( 6.63 \times 10^{-35} m \)


A body is projected with velocity \( 24 m s^{-1} \) making an angle \( 30^{\circ} \) with the horizontal. The vertical component of its
velocity after \( 2 s \) is \( \left(g=10 m s^{-2}\right) \)
A. \( 8 m s^{-1} \) upward
B. \( -8 m s^{-1} \) downward
c. \( 32 m s^{-1} \) upward
D. \( 32 m s^{-1} \) downward


Find \( A \triangle B \) and by definition:
\( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\} \) and \( \boldsymbol{B}=\{\mathbf{1}, \mathbf{3}, \mathbf{5}, \mathbf{7}\} \)


If \( S \) is the circumcenter, \( O \) is the orthocenter of \( \triangle A B C, \) then \( \overrightarrow{S A}+ \) \( \overrightarrow{\boldsymbol{S B}}+\overrightarrow{\boldsymbol{S C}}= \)
A \( \cdot 2 \overrightarrow{O S} \)
B . 2 SO
\( c \cdot \partial s \)
D. \( \overrightarrow{S O} \)


If \( \boldsymbol{S}_{\boldsymbol{n}}=\frac{\boldsymbol{3}}{\boldsymbol{4}}+\frac{\boldsymbol{5}}{\boldsymbol{3} \boldsymbol{6}}+\frac{\boldsymbol{7}}{\boldsymbol{1 4 4}}+\frac{\boldsymbol{9}}{\boldsymbol{4 0 0}}+\ldots \) to \( \boldsymbol{n} \)
terms, then find \( \frac{1}{1-S_{40}} \)


How can the resolving power of a microscope be increase?


Coke is used in the preparation of:
This question has multiple correct options
\( \mathbf{A} \cdot C O+H_{2} \)
B \( \cdot C O+N_{2} \)
C . graphite artificially
D. diamond artificially


In a Young's double-slit experiment, the fringe width is \( \beta . \) If the entire
arrangement is now placed inside a liquid of refractive index \( \mu \), the fringe width will become
\( \mathbf{A} \cdot \mu \beta \)
в. \( \frac{\beta}{\mu} \)
\( c \cdot \frac{\beta}{\mu+1} \)
D. \( \frac{\beta}{\mu-1} \)


According to Newton's Law of cooling, the rate of cooling of a body is
proportional to \( (\Delta \theta)^{n}, \) where \( \Delta \theta \) is the difference of temperature of the body
and the surrounding and \( n \) is equal to
A .2
B. 3
\( c \cdot 4 \)
D.


Define a reflexive relation.


\( R H_{2} \) (ion exchange resin) can replace
\( C a^{2+} \) in hard water:
\[
\boldsymbol{R} \boldsymbol{H}_{2}+\boldsymbol{C} \boldsymbol{a}^{2+} \rightarrow \boldsymbol{R} \boldsymbol{C} \boldsymbol{a}+\boldsymbol{2} \boldsymbol{H}^{+}
\]
\( 1 L \) of hard water after passing through
\( R H_{2} \) has \( p H=2 . \) Hence, hardness in
ppm of \( \boldsymbol{C a}^{2+} \) is :
A . 200
в. 100
c. 50
D. 125


The resultant of \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) is \( \boldsymbol{R} \) If \( \boldsymbol{Q} \) is
doubled, \( R \) is also doubled and if \( Q \) is
reversed, \( \boldsymbol{R} \) is again doubled. Then, \( \boldsymbol{P}^{2} \) :
\( Q^{2}: R^{2} \) given by
B. 3: 2: 2
c. 2: 3: 2
D. 2: 3: 1


Show that the coefficient of \( a^{m} \) and \( a^{n} \)
in the expansion of \( (1+a)^{m+n} \) are
equal.


The mean of a distribution is \( 4 . \) If its
coefficient of variation is \( 58 \% \). Then the
S.D. of the distribution is
A . 2.23
B. 3.23
c. 2.32
D. none of these


A golf ball has mass of \( 30 g \) and a speed of \( 50 \mathrm{m} / \mathrm{s} \). If the speed can be
measured within accuracy of \( 1 \% \) then uncertainty in the position is:
A. \( 2.4 \times 10^{-32} \mathrm{m} \)
В. \( 3.5 \times 10^{-33} \mathrm{m} \)
c. \( 3.5 \times 10^{-34} \mathrm{m} \)
D . 2.4 \( \times 10^{-33} \mathrm{m} \)


Which of the following is true due to intermolecular H- bonding in HF?
A. High boiling point liquidd
B. Capable of forming two series of salt
c. Dibasic
D. capable of forming acid salt


The values of \( f^{\prime}(1) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Analysis by mass of a certain compound shows that it contains \( 14 \% \) hydrogen and \( 86 \% \) carbon. On the basis of the
given data which of the following options can properly be made about the compound? This question has multiple correct options
A. It is a hydrocarbon
B. Its empirical formula is \( C H_{2} \)
c. Its molecular formula is \( C_{2} H_{4} \)
D. Its molar mass is \( 28 \mathrm{g} / \mathrm{mol} \)
E. It contains a triple bond


Consider statements a-c about
pollution.
(a) To control air pollution all Delhi buses were asked to run on unleaded
petrol by the end of 2002
(b) Electrostatic precipitator can
remove \( 99 \% \) of particulate matter from
thermal power plant exhaust.
(c) It is possible to estimate amount of organic matter in sewage water by measuring BOD. Of the statements.
\( A \cdot b \) and \( c \) correct
B. a alone correct
c. b alone correct
D. c alone correct
E. a and b correct


A particle moves in the plane xy with constant acceleration a directed along the negative y-axis. The equation of motion of the particle has the form \( y= \) \( p x-q x^{2} \) where \( p \) and \( q \) are positive
constants. Find the velocity of the
particle at the origin of co-ordinates.


A sample of protein was analysed for me metal content and analysed for metal cotent and analysis revealed that it contained magnesium and titanium in equal amount by mass. If these are the only metallic species present in the protein and contains \( 0.016 \% \) metal, the minimum possible molar mass of the protein is \( [M g=24, T i=48] \)
A .6,00,000
В. 1,50,000
c. 3,00,000
D. 12,00,000


What effect will there be on a magnetic
compass when it is brought near a current carrying solenoid?
A. The needle of the compass will rest in the direction of magnetic field due to solenoid at that point
B. The needle of the compass will rest in the direction opposite to magnetic field due to solenoid at that point
c. No effect
D. cannot say


Identify the molecule with the highest boiling point.
A \( \cdot C H_{3} C H_{2} C H_{2} C H O \)
в. \( C H_{3} \) СОСН\( _{3} \)
c. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
D. \( C H_{3} C H_{2} C H_{2} C H_{2} C H_{3} \)


During phloem transportation sugar is moved in form of sucrose in to the
companion cells and them into the
living phloem sieve tube cells by
A. Passive transport
B. Active transport
c. Facilitated diffusion
D. Osmosis


If \( \boldsymbol{R}=\left\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4} ; \boldsymbol{x}, \boldsymbol{y} \in \mathbb{Z}\right\} \)
a relation on \( \mathbb{Z} \), write the domain of \( \boldsymbol{R} \)


A current of \( 10.0 \mathrm{A} \) flows for \( 2.00 \mathrm{hrs} \) through an electrolytic cell containing a molten salt of metal \( X . \) This results in
the decomposition of 0.250 mol of metal \( X \) at the cathode. The oxidation state of \( X \) in the molten salt is: \( (F= \)
\( 96500 C) \)
\( A \cdot+1 \)
\( B \cdot+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)


Mention the exact location of the
following:
Myelin sheath.


Assuming Z-axis as molecular axis, the molecular orbitals formed by the following combination of atomic orbitals is labeled as:
\( 2 s+2 s: p i 2 s \)
\( A \)


The perimeter of a rectangular filed is \( 82 \mathrm{m} \) and its area is \( 400 \mathrm{m}^{2} \). Find the
breadth of the rectangle.


Diatoms perform which type of movement in water?
A. Swimming
B. Amoeboid
c. Floating
D. Ciliary


Transverse waves are produced in a long string by attaching its free end to a vibrating tuning fork. Figure shows the shape of a part of the string. The points in phase are
A. A and
B. B and E
\( c \cdot c \) and \( F \)
D. A and G


Dialysis comes under
A. Surgery
B. Neurology
c. Nephrology
D. Haematology


The volume of air that will remain in the
lungs after a normal expiration is called
A. Vital capacity
B. Functional residual capacity
c. Residual volume
D. Total lung capacity


The gravitational force which acts on a body of mass \( 1 \mathrm{kg} \) on the surface of the earth is
\( A \cdot 9.8 \mathrm{N} \)
B \cdot \( \frac{1}{9.8} \) N
c. \( 980 \mathrm{N} \)
D. \( \frac{1}{980} \mathrm{N} \)


Identify which one of the following can be represented by the product of the
other two?
I. Speed
Il. Wavelength
III. Frequency
\( A \)
B. I
c. ॥
D. Any one is the product of the other two
E. None of the three is the product of the other two


What is the smallest number by which
2560 must be multiplied so that the product is a perfect cube?
\( \mathbf{A} \cdot \mathbf{5} \)
B . 25
c. 10
D. 15


Arrange the following esters in increasing order of their ease of hydrolysis with suitable explanation.
(a) Phenyl acetate
(b) p-nitrophenyl acetate
(c) p-methoxyphenyl
(d) Tolyl acetate
A \( . c<d<a<b \)
B. \( b<a<d<c \)
c. \( c<d<b<a \)
D. None f these


A dip needle shows angle of dip \( \tan ^{-1}\left(\frac{2}{\sqrt{3}}\right) \) in a vertical plane which is
at an angle of \( 60^{0} \) with the magnetic meridian. The real dip at the place is
then
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{0} \)
D. \( 90^{\circ} \)


\( \int\left(e^{a \log x}+e^{x \log a}\right) d x \)


Which of the following statements is
wrong for a homologous series?
A. All members have a same general formula
B. All members have the same functional group
C. All members have the same chemical properties
D. All members have the same physical properties


The mean lives of a radioactive material
for \( \alpha \) and \( \beta \) radiations are 1620 years
and 520 years respectively. The material decays simultaneously for \( \alpha \) and \( \beta \) radiations.The time after which
one fourth of the material
remains undecayed is
A. 546 years
B. 324 years
c. 720 years
D. 840 years


Sheela's teacher said in her classroom
that we should not dispose of motor oils and medicines in the drain. Why did her teacher say this statement?
A. Motor oil and medicine allows the bacteria to grow.
B. Motor oil and medicine hamper the degradation process
c. Motor oil and medicine blocks the soil pores.
D. None of the above


Four angles of a quadrilateral are in the ratio \( 3: 5: 7: 9 . \) The greatest angle is
A . \( 125^{\circ} \)
B . \( 75^{\circ} \)
\( \mathbf{c} \cdot 135^{\circ} \)
D. \( 120^{\circ} \)


Long Answer
Give an account of the different layers of the atmosphere


Four identical solid spheres each of
mass \( M \) and radius \( R \) are fixed at four
corners of a light square frame of side length \( 4 R \) such that centres of spheres coincide with corners of square.
The moment of inertia of 4 spheres about an axis perpendicular to the plane of frame and passing through its centre is:
A \( \cdot \frac{21 M R^{2}}{5} \)
в. \( \frac{42 M R^{2}}{5} \)
c. \( \frac{84 M R^{2}}{5} \)
D. \( \frac{168 M R^{2}}{5} \)


Gymnosperms were placed between dicot and monocot by
A. De candolle
B. Bentham and Hooker
c. Engler and Pranti
D. Hutchinson


From the following the wrong statement
is:
A. Half-life of a free neutron is 10.3 minutes
B. The stability of a nucleus is only determined by the number of neutrons present in it.
c. Both fast and slow neutrons are capable of penetrating the nucleus
D. A free neutron decays into a proton, an electron and positron


What is the Enthalpy change?
A. the amount of energy as heat that is lost or made by a system
B. the total amount of energy in a system
C . a chemical reaction
D. when energy is neither created nor destroyed
E. when one or more substances are changed into one or more different substances.


Factorise the expression: \( 10 a b+4 a+ \)
\( 5 b+2 \)
A . \( (a+1)(5 b+1) \)
B . \( (2 a-1)(5 b+1) \)
c. \( (a+1)(b+10) \)
D. \( (2 a+1)(5 b+2) \)


The relative molecular masses of
hydrogen, nitrogen, oxygen and chlorine are double their relative atomic
masses.
A. True
B. False


A current i is flowing in a conductor as
shown in the figure. The magnetic
induction at point 0 will be :
A . zero
B. \( \mu_{0} i / r \)
\( c \cdot 2 \mu_{0} i / r \)
\( \mathbf{D} \cdot \mu_{0} i / 4 r \)


Choose the correct statement:
The angle of deviation for Indigo is greater than the angle of deviation of the orange colour The angle of deviation increases with
increase in the wave length of the incident light.
A. Only A is true
B. Only B is true
c. Both A and B are true
D. Both A and B are false


The derivative of \( \left[\frac{e^{x}+1}{e^{x}}\right] \) is equal to
\( A \cdot O \)
B. \( \frac{1}{e^{x}} \)
\( c \cdot-\frac{1}{e^{x}} \)
D. \( e^{x} \)


Find the \( 6^{t h} \)
term from the end of the A.P:
\( \mathbf{1 7}, \mathbf{1 4}, \mathbf{1 1}, \dots \dots-\mathbf{4 0} \)


If the sum of squares of deviations of 15
observations from their mean 20 is 240
then what is the value of coefficient of
variation \( (\mathrm{CV}) ? \)
A . 20
B . 21
c. 22.36
D. 24.70


Thermistor has a resistance of
A. 250 to 500 k ohms
B. 50 to 10 k ohms
c. 1 to 1 k onms
D. 100 to 100 k ohms


The filtration units of kidney are called
as
A . Ureter
B. Urethra
c. Neurons
D. Nephrons


Terylene is a condensation polymer of
ethylene glycol and
A. salicylic acid
B. phthalic acid
c. benzoic acid
D. terephthalic acid


A body of mass \( m \) and radius \( r \) is
released from rest along a smooth inclined plane of angle of inclination \( \boldsymbol{\theta} \) The angular momentum of the body about the instantaneous point of
contact after a time \( t \) from the instant
of release is equal to
A. mgrt cos \( \theta \)
B. \( m g r t \sin \theta \)
c. \( (3 / 2) \) mgrt sin \( \theta \)
D. None of the above


For \( k=\frac{1}{\sqrt{50}}, \) find \( a, b, c \) such that \( \boldsymbol{P P}^{T}=\boldsymbol{I} \) where, \( \boldsymbol{P}=\left[\begin{array}{ccc}\frac{2}{3} & \boldsymbol{3} \boldsymbol{k} & \boldsymbol{a} \\ -\frac{1}{3} & -\boldsymbol{4} \boldsymbol{k} & \boldsymbol{b} \\ \frac{2}{3} & -\boldsymbol{5} \boldsymbol{k} & \boldsymbol{c}\end{array}\right] \)
A \( \cdot a=\pm \frac{13}{15 \sqrt{2}}, b=\pm \frac{16}{15 \sqrt{2}}, c=\frac{1}{3 \sqrt{2}} \)
в. \( a=\pm \frac{13}{15 \sqrt{2}}, b=\pm \frac{16}{15 \sqrt{2}}, c=\pm \frac{1}{15 \sqrt{2}} \)
c. \( a=\pm \frac{13}{15 \sqrt{2}}, b=\pm \frac{16}{15 \sqrt{2}}, c=\pm \frac{1}{3 \sqrt{2}} \)
D. None of these


For a particle showing motion number
under the force \( F=-5(x-2)^{2} \), the
motion is
A. Translatory
B. Oscillatiory
c. sнm
D. All of these


The specific conductivity of \( N / 10 K C l \)
solution at \( 20^{\circ} \mathrm{C} \) is 0.0212 ohm \( ^{-1} \)
\( c m^{-1} \) and the resistance of the cell
containing this solution at \( 20^{\circ} \mathrm{C} \) is 55
ohm. The cell constant is:
A \( \cdot 3.324 \mathrm{cm}^{-1} \)
B. \( 1.166 \mathrm{cm}^{-1} \)
\( \mathbf{c} \cdot 2.372 \mathrm{cm}^{-1} \)
D. \( 3.682 \mathrm{cm}^{-1} \)


Assertion
The net magnetic force on a current loop in a uniform magnetic field is zero but torque may or may not be zero
Reason
Torque on a current carrying coil in a magnetic field is given by \( \bar{\tau}= \) \( \boldsymbol{n} \boldsymbol{I}(\overline{\boldsymbol{A}} \boldsymbol{X} \overline{\boldsymbol{B}}) \)
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


Match Column-I with Column-II


Given the standard potential of the
following at \( 25^{\circ} \mathrm{C} . M n O_{2} \rightarrow M n^{3+} \)
\( \boldsymbol{E}^{\ominus}=\mathbf{0 . 9 5} \boldsymbol{V} \)
\( M n^{3+} \rightarrow M n^{2+} ; E^{\ominus}=1.51 V \)
The standard potential of \( M n O_{2} \rightarrow \)
\( M n^{2+} \) is:
A. \( -0.56 V \)
B . \( -2.46 V \)
c. \( -1.23 V \)
D. \( 1.23 V \)


Two charges \( +20 \mu C \) and \( -20 \mu C \) are
placed \( 10 m m \) apart. The electric field at
point \( P, \) on the axis of the dipole \( 10 \mathrm{cm} \) away from its centre \( \boldsymbol{O} \) on the side of
the positive charge is
\( \mathbf{A} \cdot 8.6 \times 10^{9} N \quad C^{-1} \)
B . \( 4.1 \times 10^{6} N \quad C^{-1} \)
C \( .3 .6 \times 10^{6} N^{-1} \)
D . \( 4.6 \times 10^{5} N \quad C^{-1} \)


At room temperature chlorine gas reacts with the following:
This question has multiple correct options
A. sodium
B. carbon
c. oxygen
D. phosphorus


Fossil man expert in making cave paintings and tools was
A. Cro-Magnon Man
B. Peking Man
c. Java Man
D. Neanderthal Man


Water gas is a mixture of :
A. \( C O+H_{2} \)
в. \( C O+N_{2} \)
c. \( C O+C O_{2}+N_{2} \)
D. \( C O+C H_{4} \)


The radius of a circle is \( 17.0 \mathrm{cm} \) and the
length of perpendicular drawn from its centre to a chord is \( 8.0 \mathrm{cm} . \) Calculate
the length of the chord.


If
\( \mathbf{3}\left[\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{z} & \boldsymbol{w}\end{array}\right]=\left[\begin{array}{cc}\boldsymbol{x} & \boldsymbol{6} \\ -\mathbf{1} & \boldsymbol{2} \boldsymbol{w}\end{array}\right]+ \)
\( \left[\begin{array}{cc}\mathbf{4} & \boldsymbol{x}+\boldsymbol{y} \\ \boldsymbol{z}+\boldsymbol{w} & \mathbf{3}\end{array}\right], \) find the values of
\( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \& \boldsymbol{w} \)


A solution containing 7 g of a solute (molar mass 210 g \( m o l^{-1} \) ) in 350 g of acetone raised the boiling point of
acetone from \( 56^{\circ} \mathrm{C} \) to \( 56.3^{\circ} \mathrm{C} \). The value
of ebullioscopic constant of acetone in \( \mathrm{K} \mathrm{kg} \operatorname{mol}^{-1} \) is :
A . 2.66
B. 3.15
c. 4.12
D. 2.86


A body of mass \( m=1 k g \) falls from a
height \( h=20 m \) from the ground level
a. What is the magnitude of total change in momentum of the body before it strikes the ground?
b. What is the corresponding average
force experienced by it? \( \left(g=10 m s^{-2}\right) \)


Assertion (A) : Silver is a ductile
material, Reason (R): For a ductile material yield point and breaking point are separated by larger distance than for brittle
materials on the stress-strain curve.
A. Both assertion and reason are true and the reason is correct explanation of the assertion
B. Both assertion and reason are true, but reason is not correct explanation of the assertion
c. Assertion is true, but the reason is false
D. Assertion is false, but the reason is true


The ground state energy of hydrogen atom is \( -13.6 \mathrm{eV} \). If an electron makes
a transition from an energy level -1.51 \( \mathrm{eV} \) to \( -3.4 \mathrm{eV} \), then calculate the wavelength of the spectral line emitted and name the series of hydrogen spectrum to which it belongs.


Optimum growth occurs in
A. Blue light
B. Red light
c. white light
D. Green light


Which gas is not poisnous?
A. Nitrogen dioxide
B. Chlorine
c. oxygen
D. carbon monooxide


Find coordinates of center of mass of a
quarter ring of radius \( r \) placed in the first quadrant of a Cartesian coordinate system, with centre at origin.


Find the middle term(s) in the
expansion of :
\( \left(2 a x-\frac{b}{x^{2}}\right)^{12} \)
A \( \cdot \frac{59136 a^{6} b^{6}}{x^{6}} \)
В. \( \frac{59163 a^{5} b^{5}}{x^{5}} \)
c. \( \frac{59631 a^{7} b^{7}}{x^{7}} \)
D. None of these


IUPAC name of the first member of
alkyne is
A. ethene
B. ethyne
c. ethane
D. methane


Find the number of values of \( \boldsymbol{\theta} \)
satisfying the equation \( \sin 3 \theta= \) \( 4 \sin \theta \cdot \sin 2 \theta \cdot \sin 4 \theta \) in \( 0 \leq \theta \leq 2 \pi \)


If it is assumed that \( _{92}^{235} U \) decays only by emitting \( \alpha- \) and \( \beta \) -particles, the possible product of the decay is
A \( \cdot \frac{225}{89} \mathrm{Ac} \)
B . \( \frac{297}{A c} \)
\( \mathbf{C} \cdot_{89}^{230} A c \)
D・ \( _{89}^{23} A C \)


The soil near the surface is usually
darker than about one meter down, this
is because the top soil
A. Is richer in Ca and Mg
B. Contains more organic matter
C. Is wetter than the sub soil
D. Is drier than the sub soil


A pack of cards was found to contain
only 51 cards. If first 13 cards, which are examined, are all red, then find the probability that the missing cards is black?
A \( \cdot 2 / 3 \)
в. \( 1 / 3 \)
c. \( 2 / 9 \)
D. \( 1 / 6 \)


Two vectors \( \vec{A} \) and \( \vec{B} \) such that \( (\vec{A}+ \)
\( \vec{B}) \perp(\vec{A}-\vec{B}) . \) Then
\( \mathbf{A} \cdot \vec{A} \| \vec{B} \)
B. \( \vec{A} \perp \vec{B} \)
C \( \cdot|\vec{A}|=|\vec{B}| \)
D \( \cdot|\vec{A}| \neq|\vec{B}| \)


In the circuit diagram, the current
through the Zener diode is :
\( \mathbf{A} \cdot 10 m A \)
B. \( 3.33 m A \)
\( \mathbf{c} \cdot 6.67 m A \)
\( \mathbf{D} \cdot 0 m A \)


Find the approximate change in the volume \( V \) of a cube of side \( x \) metres
caused by increasing side by \( 1 \% \)
percent


\( K_{h} \) values for
\( \boldsymbol{A} \boldsymbol{r}(\boldsymbol{g}), \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}), \boldsymbol{H} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O}_{(\boldsymbol{g})} \) and \( \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) \)
are \( 40.39,1.67,1.83 \times 10^{-5} \) and 0.413
respectively. The order of their increasing solubility is:
A. \( H C H O<C H_{4}<C O_{2}<A r \)
в. \( H C H O<C O_{2}<C H_{4}<A r \)
c. \( A r<C O_{2}<C H_{4}<H C H O \)
D. \( A r<C H_{4}<C O_{2}<H C H O \)


In presence of which acid organic compound is heated during estimation of phosphorous using carius method?
A. Sulphuric Acid
B. Hydrochoric Acid
c. Nitric Acid
D. Acetic Acid


State True or False:
On subtracting \( -2 x^{2} y+3 x y^{2} \) from
\( 8 x^{2} y, \) the answer is \( 10 x^{2} y-3 x y^{2} \)
A. True
B. False


The temporary hardness of water due to calcium bicarbonate can be removed by
adding:
A. \( C a C O_{3} \)
в. \( C a(O H)_{2} \)
c. \( C a C l_{2} \)
D. \( H C l \)


Sunlight of intensity \( 1.3 k W m^{-2} \) is
incident normally on a thin convex lens of focal length \( 20 \mathrm{cm} \). Ignore the energy loss of light due to the lens and assume
that the lens aperture size is much smaller than its focal length. The
average intensity of light, in \( k W m^{-2}, \) at
a distance \( 22 c m \) from the lens on the
other side is


Ethylene gas
A. Is a saturated hydrocarbon.
B. Slows down the ripening of apples.
C. Retards ripening of tomatoes.
D. Speeds up maturation of fruits and early ripening of some fruits.


What percent of 85 is \( 17 ? \)


Correct the given statements:
Materials which allow electric current
to pass through them are called Insulators.


Possible value of Poisson's ratio is
\( A \)
B. 0.9
\( c \cdot 0.8 \)
D. 0.4


Which one of the following areas is an example of secondary succession if the succession takes place in/on?
A. Abandoned farm land
B. Newly cooled lava
c. Newly created pond
D. Bare rock


\( y=\frac{6}{x^{2}}+2 x, \) then find \( \frac{d y}{d x} \)


When water is heated from \( 0^{\circ} \mathrm{C} \) to \( 10^{\circ} \mathrm{C} \)
its volume:
A . increases
B. decreases
c. does not changes
D. first decreases and then increases


Assertion
(A): Oxygen exhibits
anomalous behavior.
Reason (R): Absence of d-orbitals
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Non-stoichiometric hydrides are
produced by:
A. palladium, vanadium
B. manganese, lithium
c. nitrogen, filorine
D. carbon, nockel


Electronic configuration \( \boldsymbol{O} \) is:
A \( \cdot[H e] 2 s^{2} 2 p^{4} \)
B . \( [H e] 2 s^{3} 2 p^{4} \)
\( \mathbf{c} \cdot[H e] 2 s^{2} 2 p^{5} \)
D \cdot \( [H e] 3 s^{2} 2 p^{4} \)


What will be the \( p O_{2} \) and \( p C O_{2} \) in the atmospheric air compared to those in the alveolar air?
(i) \( p O_{2} \) lesser, \( p C O_{2} \) higher
(ii) \( p O_{2} \) higher, \( p C O_{2} \) lesser
(iii) \( p O_{2} \) higher, \( p C O_{2} \) higher
(iv) \( p O_{2} \) lesser, \( p C O_{2} \) leser


Saprophytic angiosperms are also
called
A. Mycorrhizal plants
B. Mesophytic plants
C. Humus plants
D. Myrmecophilous plants


ff \( y=\tan ^{-1}\left[\frac{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}\right] \)
what would be \( \frac{d y}{d x} \)
A \( \cdot \frac{-x}{\sqrt{1-x^{4}}} \)
в. \( \frac{1}{\sqrt{1-x^{4}}} \)
c. \( \frac{x}{\sqrt{1-x^{4}}} \)
D. none of thes


Calculate the focal length of a corrective
lens having power \( +2 D \)


Which of the following polynuclear hydrocarbon is/are carcinogenic in nature?
A . 1,2-Benzanthracene
B. 3-methylcholanthrene
c. 1,2 -Benzpyrene
D. All of the above


Few reactions of industrial importance
are listed below. Which of the following catalysts is not correctly matched with
the reaction?
A. Haber's process: Finely divided \( F e+M o \) as promoter
B. Contact process: \( V_{2} O_{5} \)
c. ostwalds process: \( F e_{2} O_{3} \)
D. None of these


Which of the following chemical is released by chlorofluorocarbon that is harmful to ozone?
A. Fluorine
B. Sulphur dioxide
c. Nitrogen peroxide
D. Chlorine


In an atom two electrons move around
the nucleus in circular orbitals of radii
\( R \) and \( 4 R \). The ratio of the time taken by
them to complete one resolution is:
A . 1: 4
B. 4: 1
\( c \cdot 1: 8 \)
D. 8: 7


The naturally occurring polymer among the following is:
A. Rayon
B. Nylon - 6
c. Decron
D. Proteins


From below which are the applications of heating effect of electric current?
A. Electric immersion water heater
B. Electric Iron Box
c. Electric Fuse
D. All of the above


The biodegradable polymer is:
A. Nylon-6,6
B. Nylon-2-Nylon 6
c. Nylon-6
D. Buna-s


Match the entries of :List-A and List-B.


Choose the correct statement.
A. Arteries always carry oxygenated blood while veins always carry deoxygenated blood
B. Venous blood is returned to left auricle
C. Arteries are provided with valves while veins are devoid to valves
D. Arteries always carry blood away from the heart, while veins always carry blood towards the heart


In which of the following molecules, central atom involve expansion of octet?
A \( \cdot P C l_{3} \)
в. \( N C l_{3} \)
c. \( C l F_{3} \)
D. None of these


On decomposition of \( N H_{4} H S, \) the
following equilibrium is established:
\( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{H} \boldsymbol{S}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \) If
the total pressure is \( P \) atm, then
the equilibrium constant \( \boldsymbol{K}_{\boldsymbol{P}} \) is equal
to:
\( A \cdot P \) atm
B. \( P^{2} a t m^{2} \)
\( \mathbf{c} \cdot P^{2} / 4 a t m^{2} \)
D. 2P atm


In the following Haber synthesis of \( N H_{3} \)
the equilibrium constant for \( \boldsymbol{N} \boldsymbol{H}_{3} \) formation, on increase in temperature,
is:
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 H N_{3}(g)+ \) heat
energy
A. Decreased
B. Increased
c. First decreased and then increased
D. Not altered


The complex number z satisfies the equation \( z+|z|=2+8 i . \) Then the value of
\( |z| \) is
A . 15
B. 16
\( c \cdot 17 \)
D. 18


A stair case contains ten step each 10
\( \mathrm{cm} \) high and \( 20 \mathrm{cm} \) wide.The maximum horizontal velocity with which the ball has to be rolled off the upper most
step,so as to hit directly the edge of the lowest step is (approximately)
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. \( 4.2 m s^{-1} \)
\( \mathrm{c} \cdot 24 \mathrm{ms}^{-1} \)
D. \( 2.4 m s^{-1} \)


Compounds with identical molecular
formulae but different structures are
called


A uniformly charged non-conducting thin hemispherical shall is shown in
figure. What is correct direction of net
electric field at any point on its open
plane surface?
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


In which of the following compound, all the monosaccharide units are not
joined by only \( C_{1}-O-C_{4} \) chain?
A . Lactos
B. Maltose
c. cellulose
D. Amylopectin


Write the correct order of acidity:
A. \( P>Q>R>S \)
в. \( Q>P>R>S \)
c. \( Q>R>S>P \)
D. \( S>R>Q>P \)


Which of these should be a
characteristic of the semi permeable membrane used in ultra filtration
method?
A. The membrane should be a polymer material
B. The pore size of the membrane should be very small
c. Both A and B
D. None of the above


Sound waves are traveling along positive x-direction. Displacement of
particle at any time \( t \) is as shown in figure. Select the correct statement:
A. Particle located at E has its velocity in negative \( x \) direction
B. particle located at E has zero velocity
c. Both (a) and
(b) are correct
D. Both (a) and
(b) are wrong


The displacement of a particle of mass
\( 3 g m \) executing simple harmonic motion is given by \( y=3 \sin (0.2 t) \) in \( s \)
units. The kinetic energy of the particle at a point which is at a distance equal to \( \frac{1}{3} \) of its amplitude from its mean position is
A \( \cdot 12 \times 10^{-3} J \)
\( J \)
B . \( 25 \times 10^{-3} J \)
c. \( 0.48 \times 10^{-3} J \)
D. \( 0.24 \times 10^{-3} \mathrm{J} \)


A block of mass \( 5 \mathrm{kg} \) is placed on a
horizontal ground as shown in the figure. The magnitude of normal reaction exerted by the block on the ground is
\( A \cdot 10 N \)
в. 20 N
\( c . \) 50
D. 40 N


The tangent drawn on electric field lines
at a point gives the direction of lines of
force at that point.
A. True
B. False


What is the energy band gap of:
(i) silicon and
(ii) germanium


How many trapezoids congruent to this
one:
are there in the following diagram?
\( A \cdot 8 \)
B. 12
\( c \cdot 16 \)
D. 2


Two electrons are moving with nonrelativistic speeds perpendicular to each other. If corresponding de Broglie
wavelengths are \( \lambda_{1} \) and \( \lambda_{2}, \) their de
Broglie wavelength in the frame of
reference attached to their centre of
mass is:
\( \mathbf{A} \cdot \lambda_{C M}=\lambda_{1}=\lambda_{2} \)
\( ^{\mathrm{B}} \cdot \frac{1}{\lambda_{C M}}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}} \)
\( ^{\mathbf{C}} \lambda_{C M}=\frac{2 \lambda_{1} \lambda_{2}}{\sqrt{\lambda_{1}^{2}+\lambda_{2}^{2}}} \)
\( \lambda_{C M}=\left(\frac{\lambda_{1}+\lambda_{2}}{2}\right) \)


Elephants communicate with
A. Sonic sound
B. Infrasonic sound
c. Ultrasonic sound
D. None of these


The difference between the greatest and
least value of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \sin 2 x-x \) on \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \) is
A \( \cdot \frac{\sqrt{3}+\sqrt{2}}{2} \)
B. \( \frac{\sqrt{3}+\sqrt{2}}{2}+\frac{\pi}{6} \)
c. \( \frac{\sqrt{3}}{2}+\frac{\pi}{3} \)
D. \( \frac{\sqrt{3}+\sqrt{2}}{2}-\frac{\pi}{3} \)


Let \( \boldsymbol{y}=\boldsymbol{g}(\boldsymbol{x}) \) be the inverse of \( \mathbf{a} \)
bijective mapping \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \quad \boldsymbol{f}(\boldsymbol{x})= \)
\( 3 x^{3}+2 x . \) The area bounded by graph of
\( g(x), \) the axis and the ordinate at \( x=5 \)
is
A \( \cdot \frac{5}{4} \)
B. \( \frac{7}{4} \)
\( c \cdot \frac{9}{4} \)
D. \( \frac{13}{4} \)


Find \( g \) o \( f \) and \( f \circ g \) if \( f: R \rightarrow R \) and \( g: \)
\( R \rightarrow R \) are given by \( f(x)=\cos x \) and
\( g(x)=3 x^{2} . \) Show that \( g \circ f \neq f \circ g \)


Prove that in an equilateral triangle, three time the square of a side is equal to four time the square of its altitude.


During a \( \beta^{-} \) decay which of the following statements are correct?
A. The daughter nucleus has one proton less than the parent nucleus
B. The daughter nucleus has one proton more than the parent nucleus
c. An electron which is already present within the nucleus is rejected
D. A neutron in the nucleus decays emitting an electron


Simplify:
\( 2^{2} \times \frac{3^{2}}{2^{-2}} \times 3^{-1} \)


Vapour pressures of pure acetone and
chloroform at \( 328 K \) are 741.8 mm \( H g \)
and 632.8 mm \( H g \) respectively. Assuming that they form ideal solution over the entire range of composition,
plot \( \boldsymbol{p}_{\text {total}}, \boldsymbol{p}_{\text {chloroform}}, \) and \( \boldsymbol{p}_{\text {acetone}} \) as a
function of \( x_{\text {acetone}} . \) The experimental
data observed for different
compositions of mixture is:
100x \( x_{\text {acetone }} \) What is and
\( P_{\text {actone}} / m m H g \) 54
\( P_{\text {chloro}} \) of or \( / m m \) \( H g \) 632.8 548.1
Plot this data also on the same graph paper. Indicate whether it has positive
deviation or negative deviation from the
ideal solution.


When electrons in a material are free to
move, the material is:
A. an insulator
B. a conductor
c. a semiconductor
D. none of these


Give equations for chemical reactions to carry out following conversions.
(a) Cumene to phenol
(b) Phenol from aniline


On dividing \( 3 x^{3}+x^{2}+2 x+5 \) by a
polynomial \( g(x), \) the quotient and
remainder are \( (3 x-5) \) and \( (9 x+10) \)
respectively. Find \( g(x) \)


The charge flowing through a resistor \( \boldsymbol{R} \)
varies with time \( t \) as \( Q=3 t-6 t^{2} . \) The
heat produced in \( \boldsymbol{R} \) till the current in it becomes zero is
A \( \cdot \frac{3 R}{4} \)
в. \( \frac{3 R}{2} \)
c. \( \frac{4 R}{2} \)
D. \( \frac{9 R}{2} \)


Ammonia, \( N H_{3} \) and hydrazine,
\( N H_{2} N H_{2}, \) are two compounds of nitrogen, \( N_{2} . \) Which statement is
correct?
A. The N-N bond in \( N H_{2} N H_{2} \) is polar
B. \( N H_{3} \) and \( N H_{2} N H_{2} \) have lone pairs of electrons but \( N_{2} \) does not
C. The oxidation number of each nitrogen in \( N H_{2} N H_{2} \) is +2
D. The reaction of nitrogen with hydrogen has a highth activation energy


When a sphere rolls down an inclined plane, then identify the correct statement related to the work done by
friction force
A. The friction force does positive translational work
B. The friction force does negative rotational work
c. The net work done by friction is zero
D. All of the above


State True or False.
\( C H C l_{3} \) and acetone mixture shows
negative deviation from Raoult's law.
A. True
B. False


Consider a cylinder of mass \( M \) resting
on a rough horizontal rug that is pulled out from under it with acceleration \( a \)
perpendicular to the axis of the cylinder.
What is \( F_{f r i c t i o n} \) at point \( P ? \) It is assumed that the cylinder does not slip.
\( A \cdot \frac{M a}{3} \)
в. \( M g \)
\( c \cdot \frac{M a}{2} \)
D. \( M a \)


Each of these diagrams is supposed to show two different rays being reflected from the same point on the same mirror Which option is correct:-
A. Only i
B. only ii
c. only iii
D. All


The structures of three molecules are
shown.
Which homologous series is not
represented?
A. alcohols
B. alkanes
C. alkenes
D. carboxylic acids


Which of the following is not an electromagnetic wave?
A. Light rays
B. X-rays
c. Alpha rays
D. Gamma rays


Prove that, one and only one out of
\( \boldsymbol{n}, \boldsymbol{n}+\mathbf{2}, \) or \( \boldsymbol{n}+\mathbf{4} \) is divisible by \( \boldsymbol{3} \)
where \( n \) is any positive integer.


Assertion
Three equal charges are situated on a circle of radius r such that they form on equilateral triangle, then the electric field intensity at the centre is zero
Reason
The force on unit positive charge at the centre, due to the three equal charges are represented by the three sides of a triangle taken in the same order Therefore, electric field intensity at centre is zero
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Assertion
Statement -1: Boron does not show
univalent nature but unipositive nature
of thallium is quite stable.
Reason
Statement -2: Inert pair effect
predominates in thallium.
A. Statement -1 is true, Statement -2 is true and Statement -2 is correct explanation for Statement -
1.
B. Statement -1 is true, Statement -2 is true and Statement - 2 is not the correct explanation for Statement - 1
c. Statement - 1 is true, Statement - 2 is false.
D. Statement -1 is false, Statement -2 is true


Which blood group called as universal
donar?
A. \( A B \)
в. \( A \)
\( c . B \)
D.


Find the work requires to compress adiabatically \( 1 g \) of air initially at \( N T P \) to half its volume. Density of air at \( N T P=0.001129 g c m^{-3} \) and \( \frac{C_{p}}{C_{v}}=1.4 \)
A . \( 62.64 J \)
в. \( 32.64 J \)
c. \( -32.64 J \)
D. \( -62.64 J \)


When lemonjuice is added to milk it curdles. This is an example of:
A. coaguluation
B. sublimation
c. chemical decomposition reaction
D. photochemical change


The correct set of four quantum
numbers for the valence electron of
rubidium atom \( (Z=37) \) is
\( \mathbf{A} \cdot+5,+1,+1 / 2 \)
В. \( 6,0,0,+1 / 2 \)
c. \( 5,0,0,+1 / 2 \)
D. None of the above


Which of the following present in the soil is most helpful to the growth of plants?
A. Humus
B. Sand
c. clay
D. small porous rocks


Statement I : The physical state of halogen molecules may be solids, liquids or gases at room temperature. Statement 2 : The halogen molecules are considered as nonpolar and by increasing mass the dispersion forces
between them increases.
A. true, true, correct explanation
B. true, true, not correct explanation
c. true, false
D. false, true


If the range of \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2}+\sqrt[3]{\boldsymbol{x}},-\boldsymbol{3} \leq \)
\( \boldsymbol{x}<-1 \) is \( [\mathbf{0}, \sqrt[3]{\boldsymbol{n}}] \) where \( \boldsymbol{n} \in \boldsymbol{N} \) then \( n= \)