Find the values of \( p \) for which the
straight lines \( 8 p x+(2-3 p) y+1=0 \)
and \( p x+8 y-7=0 \) are perpendicular
to each other.
A \( . p=1,2 \)
в. \( p=2,2 \)
c. \( p=1,3 \)
D. None of these


The collecting agent in froth floatation
process is:
A. sodium ethyl xanthate
B. pine oil
c. lime
D. water


What are the conditions required for the formation of coal?
This question has multiple correct options
A. High temperature
B. High pressure
c. Low temperature
D. Low pressure


Assertion
Statement -1: If \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{c}\boldsymbol{x} \cos \boldsymbol{x} \cdot \sin \left(\frac{1}{\boldsymbol{x} \cos \boldsymbol{x}}\right), \quad \text { whenever de } \\ \mathbf{0}\end{array}\right. \)
then \( f(x) \) is continuous
Reason
Statement - \( 2: \lim _{x \rightarrow \infty} \frac{\sin x}{x}=0 \)
A. Statement -1 is True, Statement -2 is True ; Statement
-2 is a correct explanation for Statement -
B. Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-
c. Statement- -1 is True, Statement-2 is False
D. Statement- -1 is False, Statement-2 is True


A ball is projected horizontally with a velocity of \( 5 ~ m / s \) from the top of a
building \( 19.6 ~ m \) high. How long will the
ball take to hit the ground
A \( \cdot \sqrt{2} \) s
B. 2
\( c \cdot \sqrt{3} s \)
D. 3 s


The vapour pressure is a solvent decreased by \( 10 \mathrm{mm} \) of mercuity when a non velocity was added to the solvent.
The mole traction of the solve in the
solution is \( 0.2 . \) What would be the mole
traction of the solvent.if decrease in the
vaspour pressure is t be \( 20 \mathrm{mm} \) of mercurity?
A. 0.8
B. 0.6
\( c \cdot 0.4 \)
\( D \cdot 0.2 \)


Silical gel is commonly used as:
A. wetting agent
B. drying agent
c. solvent
D. catalyst


If the resistance is removed from the
circuit and the value of induction is
doubled, then the variation of current with time in the new circuit is given as \( \frac{x}{100} \cos 314 t . \) The value of \( x \) is


Simplify combining like terms:
\( 5 x^{2}-5 x^{2}+3 y x^{2}-3 y^{2}+x^{2}-y^{2}+ \)
\( 8 x y^{2}-3 y^{2} \)


If Q increases then:
\( A \cdot \Delta G \) increases and the reaction becomes more
spontaneous
B. \( \Delta \) G increases and the reaction becomes less
spontaneous
c. \( \Delta \) G decreases and the reaction becomes more
spontaneous
D. \( \Delta \) G decreases and the reaction becomes less
spontaneous


The unit vector perpendicular to both \( L_{1} \)
and \( \boldsymbol{L}_{2} \) is
\( ^{\mathbf{A}} \cdot \frac{-\hat{i}+7 \hat{j}+7 \hat{k}}{\sqrt{99}} \)
\( ^{\text {B. }} \frac{-\hat{i}-7 \hat{j}+5 \hat{k}}{5 \sqrt{3}} \)
\( \frac{-\hat{i}+7 \hat{j}+5 \hat{k} \hat{k}}{5 \sqrt{3}} \)
D. \( \frac{7 \hat{i}-7 \hat{j}-\hat{k}}{\sqrt{99}} \)


The fundamental cause of all colligative properties is:
A. higher entropy of the solution relative to that of pure solvent
B. lower entropy of the solution relative to that of pure solvent
c. higher enthalpy of the solution relative to that of pure solvent
D. lower enthalpy of the solution relative to that of pure solvent


Consider an infinite line charge having uniform linear charge density and
passing through the axis of a cylinder. What will be the effect on the flux
passing through the cylinder if the
portions of the line charge outside the
cylinder is removed.
A. decreases
B. increases
c. remains same
D. cannot say


A body travels \( 200 \mathrm{cm} \) in the first two
seconds and \( 220 \mathrm{cm} \) in the next 4
seconds with same acceleration. The velocity of the body at the end of the 7 th second is:
\( A \cdot 5 \mathrm{cm} / \mathrm{s} \)
B. \( 10 \mathrm{cm} / \mathrm{s} \)
\( c \cdot 15 \mathrm{cm} / \mathrm{s} \)
D. 20 cm/s


A cylinder is filled with non-viscous
liquid of density d to a height \( h_{0} \) and \( a \)
hole is made at a height \( h_{1} \) from the
bottom of the cylinder. The velocity of the liquid issuing out of the hole is:
в. \( \sqrt{2 g\left(h_{0}-h_{1}\right)} \)
c. \( \sqrt{d g h_{1}} \)
D. \( \sqrt{d g h_{0}} \)


The lower ether are highly volatile and flammable.
A . True
B. False


The volume of \( N H_{3} \) gas desorbed from
charcoal surface at STP is:
A . 0.526
B. 0.426 L
c. 0.326
D. 0.226 L


Consider the following molecules
\( \boldsymbol{I}: \boldsymbol{O}_{2} \)
\( \boldsymbol{I} \boldsymbol{I}: \boldsymbol{O}_{2}\left(\boldsymbol{A} \boldsymbol{s} \boldsymbol{F}_{6}\right) \)
\( \boldsymbol{I} \boldsymbol{I} \boldsymbol{I}: \boldsymbol{K} \boldsymbol{O}_{2} \)
Choose the correct answer.
A. The correct decreasing bond order is \( I>I I I>I I \)
B. The correct decreasing order of bond length is \( I I I> \) \( I>I I \)
C. The bond strength of I is less than that of \( I I I \)
D. Bond dissociation energy is highest in case of \( I I I \)


In kjeldahl's method of estimation of nitrogen, nitrogen is quantitatively converted to ammonium sulphate. It is
the treated with the standard solution
of alkali. The nitrogen which is present is estimated as:
A . \( N_{2} \) gas
B. \( N O_{2} \) gas
C. \( N H_{3} \) gas
D. \( \left(N H_{4}\right)_{2} S O_{4} \)


Emergency Hormone in Animals is the
A. Adrenaline
B. Insulin
c. Oestrone
D. Secretin


In the following figure, \( X Y \) is parallel to
\( B C, A X=9 \mathrm{cm} . X B=4.5 \mathrm{cm} \) and
\( B C=18 \mathrm{cm} . \) Find \( X Y \) in cm.


fthe matrix \( A \) is such that \( \left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right] A= \) \( \left[\begin{array}{cc}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & -\mathbf{1}\end{array}\right], \) then what is equal to \( \mathbf{A} ? \)
A. \( \left[\begin{array}{cc}1 & 4 \\ 0 & -1\end{array}\right] \)
в. \( \left[\begin{array}{ll}1 & 4 \\ 0 & 1\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-1 & 4 \\ 0 & -1\end{array}\right] \)
D. \( \left[\begin{array}{cc}1 & -4 \\ 0 & -1\end{array}\right] \)


How soil erosion is a cause of soil
pollution?
A. By decreasing area of productive land.
B. By increasing area of productive land.
C. By decreasing area of land.
D. By decreasing area of non-productive land.


Which of the following plant hormone is extracted from fungus?
A. Ethylene
B. Gibberellin
c. cytokinin
D. 2, 4-D


Write the structure of eye lens and state
the role of ciliary muscle in the human
eye


During long distance travel you would like to take drinking water in a bottle
made up of :
A . glass
c. leather
D. steel


Solve \( \left(\sec ^{2} \theta-1\right)\left(1-\operatorname{cosec}^{2} \theta\right)=-1 \)


Solve: \( \int_{0}^{\pi / 4} \tan ^{3} x \sec x d x \)


The molar conductivities at infinite
dilution of \( K C l, K N O_{3} \) and \( A g N O_{3} \) at
\( \mathbf{2 9 8} \boldsymbol{K} \) are
0.01499 mho \( m^{2} m o l^{-1}, 0.01250 m h o r \)
and 0.01334 mho \( m^{2} m o l^{-1} \)
respectively. What is the molar
conductivity of \( A g C l \) infinite dilution at
this temperature?


The rising and setting of sun appear red
because of :
A. refraction
B. reflection
c. defraction
D. scattering


Vikas and Vasu punt a ball into the air.
The equation \( \boldsymbol{h}=-\mathbf{1 6} \boldsymbol{t}^{2}+\boldsymbol{6 0} \boldsymbol{t} \)
represents the height of ball in feet, seconds after it was punted for Vikas's ball. Which of the following can be Akanksha's ball height equation if her ball goes higher?
A \( \cdot h=-16\left(t^{2}-3 t\right) \)
B . \( h=-8 t\left(2 t^{2}-9\right) \)
c. \( h=-4\left(2 t^{2}-5\right)^{2}+48 \)
D. \( h=-4\left(2 t^{2}-6\right)^{2}+52 \)


Given \( P: 25 \) is a multiple of \( 5, q: 25 \) is a multiple of 8. Write the compound statement connecting these two
statements with "and", "or" in \( 60^{t h} \)
cases. Check the validity of the
statement.


Plant in which chromosomal basis of
sex determination was discovered first
is?
A. Rumex
B. Melandrium
c. coccinia
D. Sphaerocarpus


There are two block \( A \) and \( B \) placed on
smooth surface Block A has mass 10 kg
and it is moving with velocity \( 0.8 \mathrm{m} / \mathrm{s} \) towards stationary B of unknown mass.


Equation of the ellipse whose axes are the axes of coordinates and which
passes through the point (-3,1) and has eccentricity \( \sqrt{\frac{2}{5}} \) is
A \( \cdot 5 x^{3}+3 y^{2}-48=0 \)
B . \( 3 x^{2}+5 y^{2}-15=0 \)
c. \( 5 x^{2}+3 y^{2}-32=0 \)
D. \( 3 x^{2}+5 y^{2}-32=0 \)


Which of the following statement is not
correct?
A. Phenol is neutralised by sodium carbonate
B. Phenol is used to prepare analgesic drugs
C. Solubility of phenol in water is more than that of chlorobenzene
D. Boiling point of o-nitrophenol is lower than that of \( p \) nitrophenol


The non-metal that does not exhibit
positive oxidation state is:
A. fluorine
B. oxygen
c. iodine
D. chlorine


Figure shows ray \( A B \) that has passed
through a divergent lens. Construct the
path of the ray up to the lens if the
position of its foci is known


Solve \( \int x \log x d x \)


Atul is traveling from Mumbai to Nagpur by train, in between, he felt
uneasy because
A. He used an improperly sanitized public toilet
c. He was already sick.
D. None of the above


First acidic compound formed in \( C_{4} \)
cycle is
A. OAA
B. Malic acid
c. Pyuvic acid
D. PGAA


Food Corporation of India stacks of bags containing wheat in the shape of cuboidal blocks in an open field on
wooden platform and these blocks are covered with tarpaulin. If there be 10 blocks, each having dimensions
\( 10 m \times 5 m \times 3 m, \) then find the cost of
the tarpaulin used to cover these blocks
at the rate of RS. 12.5 per \( m^{2} \). Assuming that there is negligible wastage of tarpaulin in folds.


In a transformer, number of turns in primary and secondary are 500 and 2000 respectively. If current in primary is \( 48 \mathrm{A} \), current in the secondary is :
\( A \cdot 144 A \)
B. 24 A
\( c \cdot 48 A \)
D. 12 A


During which stage of prophase I, genetic recombination of parental characters, takes place?
A. Zygotene
B. Pachytene
c. Diplotene
D. Diakinesis


If a system is displaced from its equilibrium position and released, it
moves according to the equation \( \ddot{\boldsymbol{\theta}}=-\frac{\boldsymbol{I}^{2}}{\boldsymbol{k} \boldsymbol{l}} \boldsymbol{\theta} \)
where \( I, \) k and I are constants. It will
oscillate with a frequency:
\( ^{A} \cdot \sqrt{\frac{I^{2}}{k l}} \)
в. \( 2 \pi \sqrt{\frac{k l}{I^{2}}} \)
\( ^{\mathrm{c}} \cdot \frac{1}{2 \pi} \sqrt{\frac{I^{2}}{k l}} \)
D. \( \frac{1}{2 \pi} \sqrt{\frac{k l}{I^{2}}} \)


State Brewster's law of polarisation of light. The polarising angle for a
transparent medium is \( 60^{\circ} . \) What will be the refractive index and angle of refraction of the medium?
\( \tan 60^{\circ}=\sqrt{3} \)


Who was Paul Ehrlich?
A. Bacteriologist
B. Chemist
c. Botanist
D. None of these


Study the following graph carefully and answer the question given. The total number of all the three types of
tyres manufactured was the least in which of the following years?
A . 1995
B. 1996
\( c .1992 \)
D. 1994


Which of the following cannot be used to prepare an emulsion of benzene in
water?
A \( \cdot C H_{3}-\left(C H_{2}\right)_{9}-\left(S O_{3}\right)^{-} N a^{+} \)
в. \( C H_{3}-\left(C H_{2}\right)_{9}-C O O^{-} N a^{+} \)
C \( . C H_{3}-\left(C H_{2}\right)_{9}-N H_{3}^{+} C l^{-} \)
D \cdot \( \left(C H_{3}\right)_{4} \stackrel{+}{N B r} \)


Assertion
If the order of reaction is zero, then
degree of dissociation will be independent of initial concentration.
Reason The degree of dissociation of zero order reaction is given by \( \boldsymbol{\alpha}=\frac{\boldsymbol{k} \boldsymbol{t}}{\boldsymbol{c}_{0}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Write the four properties of ionic
compounds?


An unknown resistance \( R_{1} \) is connected
in series with a resistance of 10 ohm.
This combination is connected to one
gap of a metre bridge, while other gap is
connected to another resistance \( \boldsymbol{R}_{2} \)
The balance point is at \( 50 \mathrm{cm} . \) Now, when the 10 ohm resistance is removed, the balance point shifts to \( 40 \mathrm{cm} . \) Then,
the value of \( \boldsymbol{R}_{1} \) is
A. \( 60 \Omega \)
B. 40\Omega
c. \( 20 \Omega \)
D. \( 10 \Omega \)


A system of binary stars of masses \( \boldsymbol{m}_{\boldsymbol{A}} \)
and \( m_{B} \) are moving in circular orbits of
radii \( r_{A} \) and \( r_{B}, \) respectively. If \( T_{A} \) and
\( T_{B} \) are the time periods of masses \( m_{A} \)
and \( m_{B}, \) respectively then
\( \stackrel{T_{A}}{T_{B}}=\left(\frac{r_{A}}{r_{B}}\right)^{\frac{3}{2}} \)
B \( \left.\cdot T_{A}>T_{B} \text { (if } r_{A}>r_{B}\right) \)
c. \( T_{A}>T_{B} \) (if \( m_{A}>m_{B} \) )
D. \( T_{A}=T_{B} \)


Find the measure of the alternate angle
of the angle of measure of \( 65^{0} \)
A \( \cdot 65^{\circ} \)
B . 25
\( \mathrm{c} \cdot 115^{\circ} \)
D. Depends on the orientation of lines


Metal 'M' has the electronic
configuration 2, 8, 1.
(i) What is the valency of Metal'M'?
(ii) Is it oxidizing or reducing in nature?
(iii) Give the formula of its chloride.


Select the correct I.U.P.A.C. name
for \( \mathrm{Mn}(\mathrm{CO})_{5}\left(\sigma-\mathrm{C}_{3} \mathrm{H}_{5}\right) \)
This question has multiple correct options
A. Allylpentacarbonylmanganese (I)
B. Cyclopropylpentacarbonylmanganese (I)
c. Pentacarbonylcyclopropylmanganese (।)
D. Pentacarbonyl allylmanganese (I)


The number of resonance structures for
\( N \) is:


Find the polynomials whose zeroes are
three times the zeroes of \( 2 x^{2}-3 x+1 \)


\( 0.25 g \) of an organic compound gave \( 30 \mathrm{cm}^{3} \) of moist nitrogen at \( 288 \mathrm{K} \) and 745mm pressure. Calculate the percentage of nitrogen (aqueous tension at \( 288 \mathrm{K}=12.7 \mathrm{mm} \)
A. 33.6
в. 23.6
c. 13.7
D. 24.5


To be known as a constellation, a collection of stars should form
A. a geometric form
B. a recognisable shape
c. a straight line
D. a circular form


A solid sphere roll down an inclined
plane inclined at an angle \( \theta \) with horizontal. Find its linear acceleration \( \vec{a} \)


Apoplastic movement of water in plants
occurs on the outer side of
A. Casparian strips
B. Plasma membrane
c. Plasmodesmata
D. None of the above


A proton, a neutron, an electron and an
\( \alpha \) -particle have same energy. Then their de Broglie wavelengths compare as:
\( \mathbf{A} \cdot \lambda_{p}=\lambda_{n}>\lambda_{e}>\lambda_{\alpha} \)
B . \( \lambda_{\alpha}<\lambda_{p}=\lambda_{n}<\lambda_{e} \)
\( \mathbf{c} \cdot \lambda_{e}<\lambda_{p}=\lambda_{n}>\lambda_{\alpha} \)
\( \mathbf{D} \cdot \lambda_{e}=\lambda_{p}=\lambda_{n}=\lambda_{\alpha} \)


Find the radius of a sphere whose circumference and solid content have
the same numerical value.


Find the area of the region bounded by the ellipse \( \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 \)


The structure of \( X e F_{2} \) and \( N H_{3} \)
respectively are:
A . linear, see-saw
B. bent, see-saw
c. bent, tetrahedral
D. linear, pyramidal


In fig, if \( f_{1}, f_{2} \) and \( T \) are the frictional
forces on \( 2 \mathrm{kg} \) block, \( 3 \mathrm{kg} \) block and tension in the string, respectively, the find their values. Initially before applying the forces, tension in string
was zero.


Show that the function \( f \) given by
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x}, \boldsymbol{x} \in \boldsymbol{R} \) is strictly
increasing.


Nutrients are required for proper growth of producers in aquatic environment. Excess nutrient will cause
A. Over growth of producers
B. Depletion of \( 0_{2} \)
c. Decrease in the number of nektons
D. All of the above


In the adjoining figure, find the
measure of \( \angle B C D \)


The electromagnetic waves do not
transport
A. energy
B. charge
c. momentum
D. information


Augmentation of phosphorylation of glucose in a cell is affected by which hormone?
A. Testosterone
B. Estrone
c. Insulin
D. Tri iodo Thyroxine


Which do not react with fluorine?
\( A \cdot K r \)
B. Ar
\( c \cdot x e \)
D. All


Select the characters which are not
applicable to the family Solanaceae.
(i) Epipetalous and syngenesious anthers
(ii) Bicarpellary and synchronous ovary
(iii) Superior ovary with axile placentation
(iv) Stamens six and are arranged in
two whorls
(v) Bicarpellary, synchronous and inferior ovary
A. (ii) and (iii) only
B. (i), (iv) and (v) only
c. (ii), (iv) and (v) only
D. (i) and (iii) only
E. (iii), (iv) and (v) only


Rutherford's atomic model could not
explain stability of atom as a whole.
A. True
B. False


Dimensions of equilibrium constant, \( \boldsymbol{K}_{c} \)
for the reaction \( 2 N H_{3} \rightleftharpoons N_{2}+3 H_{2} \)
are
A \( \cdot m o l L^{-2} \)
B \( \cdot m o l^{2} L^{-2} \)
\( \mathbf{c} \cdot m o l^{2} L^{-3} \)
D. \( m o l^{2} L^{-1} \)


Which of the option is correct for
photorespiration?
A. In peroxisome, glycerate forms phosphoglycolate
B. In chloroplast, glycerate forms glycine
C. In mitochondrion, glycine forms serine
D. In bundle sheath, serine forms glycine.


If \( 2=10^{m} \) and \( 3=10^{n} \) then find the
value of 0.15
A \( \cdot 10^{n-m-1} \)
B . \( 10^{n-m+1} \)
c. \( 10^{n-m-2} \)
D. \( 10^{n-m}-m \)


For detection of sulphur in an organic compound, sodium nitroprusside is added to
the lassaigne's filtrate the ppt. obtained
as:
A. purple colour
B. black colour
c. blood-Red colour
D. white colour


State whether given statement is true or false:
Given reaction is for preparing \( \boldsymbol{S} \boldsymbol{O}_{2} \)
such that the oxidation state of
sulphur is not effected.
\( \boldsymbol{S}+\boldsymbol{O}_{2} \longrightarrow \boldsymbol{S} \boldsymbol{O}_{2} \)
A. True
B. False


In an experiment of photoelectric effect,
the graph of maximum kinetic energy
\( E_{k} \) of the emitted photoelectrons versus
the frequency v of the incident light is a
straight line \( A B \) as shown in Figure
below:
(i) Threshold frequency of the metal.
(ii) Work function of the metal.
(iii) Stopping potential for the photoelectrons emitted by the light of
frequency \( \boldsymbol{v}=\mathbf{3 0 x} \times \mathbf{1 0}^{\mathbf{1 4}} \mathbf{H z} \)


When an electron makes transition from
\( (n+1) \) state, to \( n \) state the wavelength of
emitted radiations is related to \( n(n>> \)
\( >1), \) according to \( \lambda \propto n^{x} \). The value of \( x \)
is:


If the line \( h x+k y=1 \) touches \( x^{2}+ \)
\( y^{2}=a^{2}, \) then the locus of the point \( (h \)
k) is a circle of radius
\( A \cdot a \)
B.
\( c \cdot \sqrt{a} \)
D. \( \frac{1}{\sqrt{a}} \)


Which of the following are not rational?
This question has multiple correct options
A \( \cdot \frac{2}{\sqrt{3}} \)
B. \( \sqrt{16} \)
\( c . \pi \)
D. \( 2+\sqrt{25} \)


Multicostate divergent reticulate venation is seen in
leaf.
A. Zizyphus
B. Bamboo
c. castor
D. Mango


In the co-ordination compound \( \boldsymbol{N} \boldsymbol{a}_{4} \)
\( \left.[\boldsymbol{F e}) \boldsymbol{C N})_{5} \boldsymbol{N O S}\right] \) oxidation state of \( \boldsymbol{F e} \)
is:
\( A \cdot+1 \)
\( B \cdot+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)


Calculate the binding energy of an
alpha-particle. Given mass of proton \( = \) 1.0073 a.m.u., mass of neutron \( = \)
1.0087 a.m.u., mass of \( \alpha \) -particle \( = \)
4.0015a.m.u.


The gram molecular mass of sulphur in
its crown shape is:
A. 128 g
в. 64 g
c. \( 256 g \)
D. 32 g


\( f(x)=\frac{x}{x^{2}+5 x+4} \) is maximum at
\( \boldsymbol{x}= \)
\( A \cdot 2 \)
B. -
\( c \cdot 6 \)
D. - 6


Tyndall effect is applicable when:
This question has multiple correct options
A. the diameter of the dispersed particle is not much smaller than the wavelength of the light used
B. the diameter of the dispersed particles is much smaller than the wavelength of the light used
C. the refractive indices of the dispersed phase and the dispersion medium are the same
D. the refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude


Choose the correct statement among
the following. This question has multiple correct options
A. The upper surface of a stationary liquid is always horizontal.
B. Pressure of a given liquid is directly proportional to the depth of the liquid.
C. Pressure at a given depth inside a stationary liquid is different all points in the horizontal plane.
D. Pressure at a point in a fluid is inversely proportionally to the density of the fluid.


The image of an object placed in front of a concave mirror of focal length \( 12 \mathrm{cm} \) is formed at a point which is \( 10 \mathrm{cm} \) more distant from the mirror than the object. The magnification of the image is:
A . 1.5
B. 2
c. 2.5
D. 3


A sulphide of iron contains \( 46.5 \% \) of iron by weight. The empirical formula of the sulphide is:
A. Fes
в. \( F e_{2} S \)
c. \( F e S_{2} \)
D. \( F e_{2} S_{3} \)


The function \( \mathbf{f}(\mathbf{x})=\frac{\cos \mathbf{3} \boldsymbol{x}-\cos \mathbf{4} \boldsymbol{x}}{\boldsymbol{x} \sin \mathbf{2} \boldsymbol{x}} \) for
\( \neq \mathbf{0}, \mathbf{f}(\mathbf{0})=\frac{\mathbf{7}}{\mathbf{4}} \mathbf{a t} \boldsymbol{x}=\mathbf{0}, \) is
This question has multiple correct options
A. Continuous
B. discontinuous
c. left continuous
D. right continuous


If \( \cos \alpha, \cos \beta, \cos \gamma \) are the direction
\( \operatorname{cosines} \) of a vector \( \vec{a}, \) then \( \cos 2 \alpha+ \)
\( \cos 2 \beta+\cos 2 \gamma \) is equal to
A . 2
B. 3
\( c \cdot-1 \)
D. 0


Solution of \( \left(\frac{\boldsymbol{x}+\boldsymbol{y}-\boldsymbol{a}}{\boldsymbol{x}+\boldsymbol{y}-\boldsymbol{b}}\right)\left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)= \)
\( \left(\frac{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{a}}{\boldsymbol{x}+\boldsymbol{y}+\boldsymbol{b}}\right) \)
A \( \cdot \log \left[(x+y)^{2}-a b\right]=\frac{2}{b-a}[x-y]+k \)
B \( \cdot \log \left[(x+y)^{2}+a b\right]=\frac{1}{b-a}[x-y]+k \)
c. \( \left(\frac{b-a}{2}\right)\left[\log \left((x+y)^{2}-a b\right)\right]=x+c \)
D.


\( \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{5} & \mathbf{2} \\ \mathbf{7} & \mathbf{3}\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{2} & \mathbf{- 1} \\ \mathbf{- 1} & \mathbf{2}\end{array}\right) \)
verify that \( (\boldsymbol{A B})^{\boldsymbol{T}}=\boldsymbol{B}^{\boldsymbol{T}} \boldsymbol{A}^{\boldsymbol{T}} \)


A group of acidic oxide is:
A \( \cdot C r O_{3}, M n_{2} O_{7} \)
в. \( Z n O, A l_{2} O_{3} \)
c. \( C a O, Z n O \)
D. \( N a_{2} O, A l_{2} O_{3} \)


Liquids and gases never exhibit
A. diamagnetic properties
B. para magnetic properties
C . ferro magnetic properties
D. electro magnetic properties


Sulphur when warmed with nonmetal in the absence of air, forms a mixture of
nonmetallic trisulphide and pentasulphide. Identify the nonmetal and give the reaction.


In the figure given below, \( \boldsymbol{C D} \| \boldsymbol{E} \boldsymbol{F} \)
\( A B . \) If \( A B=22.5 \mathrm{cm}, E P=7.5 \mathrm{cm} \)
\( P C=15 \mathrm{cm} \) and \( D C=27 \)
m. Calculate \( \boldsymbol{E} \boldsymbol{F} \)
A. \( E F=14.5 \mathrm{cm} \)
3. \( E F=13.5 \mathrm{cm} \)
\( c . E F=12.5 \mathrm{cm} \)
Done of the above


If \( \cot ^{-1}\left[(\cos \alpha)^{1 / 2}\right]+ \)
\( \left[\tan ^{-1}(\cos \alpha)^{1 / 2}\right]=x, \) then \( \sin x \)
equals
A .
B \( \cdot \cot ^{2}\left(\frac{\alpha}{2}\right) \)
\( \mathbf{c} \cdot \tan \alpha \)
D. \( \cot \left(\frac{\alpha}{2}\right) \)


Units of plane angle is


If \( \tan \theta=\frac{1}{2} \) and \( \tan \phi=\frac{1}{3}, \) then the
value of \( \boldsymbol{\theta}+\boldsymbol{\phi} \) is
A \( \cdot \frac{\pi}{6} \)
в. \( \pi \)
c. \( \frac{\pi}{4} \)
D.


Which of the following hormone acts antagonist to aldosterone?
A. FSH
B. Testosterone
c. Progesterone
D. ANP


If one gram of \( S \) contains \( x \) atoms,
atoms is one gram \( \boldsymbol{O} \) will be:
A . \( x \)
B. \( x / 2 \)
c. \( \frac{2}{3} x \)
D. \( 2 x \)


On applying an external magnetic field, to a ferromagnetic substance domains.
A. Align in the direction of magnetic field.
B. Align in the direction opposite to magnetic field
c. Remain unaffected
D. align randomly


In an experiment to measure focal length of a concave mirror, the values of focal length in successive observations are \( 17.3 \mathrm{cm}, 17.8 \mathrm{cm}, 18.3 \mathrm{cm}, 18.2 \mathrm{cm} \)
\( 17.9 \mathrm{cm} \) and \( 18.0 \mathrm{cm} . \) Calculate mean
absolute error and percentage error Express the result in a proper way


toppr Loain Jolv Now
Q Type your question107 and a. which must
be invested
in reaction
to get it
started
a state in
which the
rate of
forward
baction is
exactly
equal to the
rate of the
reverse
reaction. a process
c.
or reaction
which
consumes
heat
a process
or reaction
that
releases
heat.
t. A
\( A \)
\( (a \rightarrow t) \)
\( (b \rightarrow q) \)
\( (c \rightarrow s) \)
\( (d \rightarrow r) \)
в. \( (a \rightarrow q) \)
\( (b \rightarrow p) \)
\( (c \rightarrow r) \)
\( (d \rightarrow s) \)
\( \mathbf{c} \cdot(a \rightarrow t) \)
\( (b \rightarrow p) \)
\( (c \rightarrow s) \)
\( (d \rightarrow r) \)
D. \( (a \rightarrow s) \)
\( (b \rightarrow r) \)
\( (c \rightarrow q) \)
\( (d \rightarrow p) \)


Explain the adsorption theory of catalysis.


Let \( s_{1}(n) \) be the sum of the first n terms
of the arithmetic progression \( 8,12,16, \)
and let \( s_{2}(n) \) be the sum of the first \( n \)
terms of arithmetic progression 17,19,21
.... If for some value of \( n, s_{1}(n)=s_{2}(n) \)
then this common sum is
A. not uniquely determinable
B. 260
\( c \cdot 216 \)
D. 200


If \( \sec \theta+\tan \theta=p \)
Find \( \csc =? \)


An oxide of nitrogen is found to contain nitrogen and oxygen combined together in the ratio 7: 16 by mass. Derive
formula of oxide and name it.


A convex lens forms a real image \( 9 \mathrm{cm} \)
long on a screen. Without altering the position of the object and the screen, the lens is displaced and we get again a real image \( 4 \mathrm{cm} \) long on the screen. Then the length of the object is
\( A \cdot 9 c m \)
в. 4 ст
\( c .6 c m \)
D. \( 36 \mathrm{cm} \)


In triangle \( P Q R L P=110^{\circ} \) and \( L R= \)
\( 60^{\circ} \) which side of the triangle is
smallest.


Identify the changes in a circuit on adding a light bulb in parallel to the actual resistance of the circuit. It will:
A. decrease the total resistance
B. increase the total resistance
c. make the voltage lost in each light bulb different
D. make the current through each light bulb the same
E. not change the total current through the circuit


A solid conducting sphere having a charge \( Q \) is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the
solid sphere and that of the outer
surface of the hollow shell be V. If the
shell is now given a charge of \( -3 Q, \) the new potential difference between the same two surface is :
A. \( V \)
B. \( 2 V \)
\( c .4 V \)
D. \( -2 V \)


An incident ray strike at a plane mirror
at an angle of \( 15^{0} \) with the mirror. The angle between the reflected ray and incident ray is:


A tiny mirror M is fixed on a piece of
cardboard placed on a table. The cardboard is illuminated by light from a bulb. The position of eye with respect to
position of bulb is shown in Fig. as \( A, B \)
\( \mathrm{C} \) and \( \mathrm{D} . \) In which of the shown figure, the light will be visible to eye?
This question has multiple correct options
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D \)


Ratio of \( C_{P} \) and \( C_{V} \) of gas ' \( X^{\prime} \) is 1.4. The
number of atoms of the gas ' \( X \) ' present
in 11.2 litres of at NTP will be:
A. \( 6.02 \times 10^{23} \)
B. \( 5.61 \times 10^{23} \)
c. \( 3.01 \times 10^{23} \)
D. \( 2.01 \times 10^{23} \)


The brakes of a car moving at \( 20 m / s \)
along a horizontal road are suddenly applied and it comes to rest after travelling some distance. If the coefficient of friction between the tyres and the road is 0.90 and it is assumed
that all four tyres behave identically, find the shortest distance the car would
travel before coming to a stop.
A. \( 2.22 m \)
В. \( 11.35 m \)
c. \( 22.2 m \)
D. \( 4.54 m \)


The IUPAC name of the compound
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)- \)
\( \boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H O} \) is:
A. 5,6 -Dimethylhept- - -en-1-al
B. 2,3-Dimethyl-4-en-7-al
c. 5,6 -Dimethylhept- - -ene-1-al
D. 5,6-Isopropylpent-3-ene-1-al


If 'Q' is the quantity of charge, 'V' the potential and 'C' the capacity of a conductor, they are related as:
A. \( C=Q V \)
в. \( Q=V C \)
c. \( V=C Q \)
D. \( C V Q= \) costant


The following is not an appropriate reaction for the preparation of tert. butyl ethyl ether \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{N} \boldsymbol{a}+\left(\boldsymbol{C} \boldsymbol{H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{C l} \rightarrow \)
\( \left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C}-\boldsymbol{O}-\boldsymbol{C}_{2} \boldsymbol{H}_{5} \)
Write a suitable reaction for the
preparation of tert., butyl ethyl ether
Justify your answer in both cases.


Two moles of helium gas are taken over
the cycle \( A B C D A, \) as show in the \( P-T \)
diagram. Assuming the gas to be ideal
the work done on the gas in taking it from state \( A \) to \( B \) is :
\( \mathbf{A} \cdot 200 R \)
B. \( 300 R \)
c. \( 400 R \)
\( \mathbf{D} \cdot 500 R \)


Assertion
Gaseous molecules are assumed to be
point masses' occupying no volume.
Reason

Gaseous molecules suffer no energy
loss due to friction.
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


Two waves of frequencies \( 1 H z \) and
\( 3 H z \) are moving in a medium with same velocity. The ratio of intensities at a point where amplitudes of two waves are equal will be
A . 1: 1
B. 1: 4
c. 1: 2
D. 1: 9


The kinetic energy acquired by a mass \( \mathrm{m} \) after travelling a fixed distance from rest under the action of constant force
is
A. directly proportional to velocity.
B. directly proportional to m.
c. independent of m.
D. inversely proportional to \( \mathrm{m} \).


Briefly explain the following terms:
(i) monohybrid cross
\( (i i) \)
Biomedical waste
(iii) Innate
immunity.
(iv) Diapedesis
(v) Hormones.


Polyhydroxy aldehydes or ketones
and their derivatives or as substances
that yield one of these compounds on hydrolysis.


Chandrasekhar limit is about:
A. 2.4 times the solar mass
B. 1.4 times the solar mass
C. 14 times the solar mass
D. 24 times the solar mass


Two sound waves, each of amplitude \( \boldsymbol{A} \)
and frequency \( \omega, \) superpose at a point with a phase difference of \( \frac{\pi}{2} \) The amplitude and the frequency of the
resultant wave are, respectively
A \( \cdot A^{2}, \omega \)
B. \( 2 A, \omega \)
c. \( A, \omega \)
D. \( \sqrt{2} A, \omega \)


Which of the following process defines the amount of turgidity of the guard
cell?
A. Photosynthesis
B. Excretion
c. secretion
D. Absorption


For what values of \( m \) will the expression \( y^{2}+2 x y+2 x+m y-3 \) be capable of
resolution into two rational factors?


The sum of the first three terms of an
A.P. is 9 and the sum of their square is
35. The sum to first \( n \) terms of the
series can be

This question has multiple correct options
A. \( n(n+1) \)
B \( \cdot n^{2} \)
c. \( n(4-n) \)
D. \( n(6-n) \)


The charge on an electron is:
A . \( 1 \mathrm{c} \)
B \( \cdot+1.6 \times 10^{-19} \mathrm{C} \)
\( \mathrm{c} \ldots 1.6 \times 10^{-19} \mathrm{C} \)
D. 6.25 \( \times 10^{18} \mathrm{C} \)


The length of conductor ab carrying
current \( I_{2} \) is \( l . \) Find the force acting on it due to a long current carrying conductor
having current \( I_{1} \) as shown in Fig. The
mid-point of wire ab is distance \( x \) apart
from conductor.


\( f\left|\begin{array}{ccc}6 i & -3 i & 1 \\ 4 & 3 i & -1 \\ 20 & 3 & i\end{array}\right|=x+i y \) then
A \( . x=3, y=1 \)
B. \( x=1, y=3 \)
c. \( x=0, y=3 \)
D. \( x=0, y=0 \)


2,4 DNP reacts with carbonyls (aldehyde/ketones) to give yellow ppt. This reaction is dehydration type
reaction as shown above.

A mixture of benzaldehyde and formaldehyde is heated with 2,4 DNP.
How many organic products will be
obtained after fractional distillation?


The general electronic configuration \( (n-1) d^{8} n s^{2} \) indicates that the
particular element belongs to
A. VIII group
B. V B group
c. IV B group
D. II B group


If \( f(x y-1)=f(-x) f(-y)+f(x)- \)
\( \boldsymbol{y}+\mathbf{1} \) and if \( \boldsymbol{f}(\mathbf{0})=\mathbf{1}, \) then \( \boldsymbol{f}(\boldsymbol{x})=? \)
\( \mathbf{A} \cdot x-1 \)
B. \( -x+1 \)
\( c \cdot-x-1 \)
D. \( x+1 \)
E \( .1-2 x \)


The order of the differential equation
whose general solution is \( y= \)
\( c, \cos 2 x+c_{2} \cos ^{2} x+c_{3} \sin ^{2} x+c_{4} \)
\( A \cdot 2 \)
B. 4
\( c .3 \)
D. None of these


In the figure shown, \( q \) is in coulomb and \( t \) in second. At time \( t=1 s \)
This question has multiple correct options
A \( \cdot V_{a}-V_{b}=4 V \)
в. \( V_{b}-V_{c}-1 V \)
C \( . V_{c}-V_{d}=16 V \)
D. \( V_{a}-V_{d}=20 V \)


Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards
Find mean variance and standard
deviation of the number of kings.


Consider the following isotopes of chlorine:
\( \mathbf{1 7} \boldsymbol{C l}^{\mathbf{3 5}}, \mathbf{1 7} \boldsymbol{C l}^{\mathbf{3 7}} \)
Atomic masses of these isotopes are different, while their chemical
properties are same. In the Mendeleev's periodic table isotopes of chlorine
was placed:
A. in the different groups
B. in the same group
c. in different periods
D. both (A) and (C) are correct


The temperature at which the reaction given below is at equilibrium is \( A g_{2} O(s) \longrightarrow 2 A g(s)+\frac{1}{2} O_{2}(g) \)
Given that \( \Delta H^{o}=30.5 k J m o l^{-1} \) and
\( \boldsymbol{\Delta} \boldsymbol{S}^{o}=\mathbf{0 . 0 6 6} \boldsymbol{k} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)
A. \( T=412.12 K \)
в. \( T=432.12 K \)
c. \( T=422.12 K \)


An object, moving with a speed \( 6.25 m s^{-1}, \) is decelerated at a rate
given by \( \frac{d v}{d t}=-2.5 \sqrt{v} \) where \( v \) is intantaneous velocity. The time taken by the object to come to rest would be:
A \( .2 s \)
B. \( 4 s \)
\( c \cdot 8 s \)
\( D \)


In the given figure, the red-brown gas
evolved is
A . oxygen
B. carbon dioxide
c. nitrogen dioxide
D. carbon monoxide


Calculate the greatest and least pressure exerted by a metal block of \( \operatorname{size} 20 c m \times 8 c m \times 5 c m \) and having
mass 5kg. Take \( \boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2} \)
A. \( 12500 P a ; 3125 P a \)
в. \( 11500 P a ; 3125 P a \)
c. \( 13500 P a ; 5125 P a \)
D. \( 12500 P a ; 5125 P a \)


Find the values of \( x, y \) and \( z \) if \( \left[\begin{array}{lll}\boldsymbol{x} & \mathbf{5} & \mathbf{4} \\ \mathbf{5} & \mathbf{9} & \mathbf{1}\end{array}\right]=\left[\begin{array}{lll}\mathbf{3} & \mathbf{5} & \boldsymbol{z} \\ \mathbf{5} & \boldsymbol{y} & \mathbf{1}\end{array}\right] \)


A uniformly charged solid sphere of
radius R has potential \( V_{0} \) (measured
with respect to \( \infty \) ) on its surface. For
this sphere the equipotential surfaces with potentials \( \frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4} \) and \( \frac{V_{0}}{4} \)
have radius \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2}, \boldsymbol{R}_{3} \) and \( \boldsymbol{R}_{4} \)
respectively. Then :
A \( . R_{1}=0 \) and \( R_{2}>\left(R_{4}-R_{3}\right) \)
B . \( R_{1} \neq 0 \) and \( \left(R_{2}-R_{1}\right)>\left(R_{4}-R_{3}\right) \)
\( \mathbf{c} \cdot 2 R<R_{4} \)
D. None of the above


Match Coumn I with Column II


The angle of dip increases as we move from
A. Poles to equator
B. Equator to poles
c. Dip is equal at all places
D. None of these


A junction transistor does not have a/an
A. emitter-base junction
B. base-collectorjunction
c. emitter-collector junciton
D. none of the above


Air pollution takes place in two different layers of the earth's atmosphere
A. troposphere and stratosphere
B. mesosphere and troposphere
c. stratosphere and hydrosphere
D. troposphere and hydrosphere


A transformer consists of 500 turn in
primary coil and 10 turns in secondary coil with the load of \( 10 \Omega \). Find out
current in the primary coil when the voltage across secondary coil is \( 50 \mathrm{V} \)
A . \( 0.3 \mathrm{A} \)
B. 0.1A
c. \( 0.5 \mathrm{A} \)
D. \( 0.7 \mathrm{A} \)


Show that \( x=1, y=3 \) satisfy the linear
equation \( 3 x-4 y+9=0 \)


Evaluate:
\( (1+\cos x) d y=(1-\cos x) d x \)


The solution of the differential equation \( \frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{\left(1+x^{2}\right)^{2}} \)
A \( \cdot y\left(1+x^{2}\right)=c+\tan ^{-1} x \)
B. \( \frac{y}{1+x^{2}}=c+\tan ^{-1} x \)
C・ \( y \log \left(1+x^{2}\right)=c+\tan ^{-1} x \)
D \( \cdot y\left(1+x^{2}\right)=c+\sin ^{-1} x \)


The prussian blue colour obtained during the test of nitrogen by Lassaigne's test is due to the formation of:
\( \mathbf{A} \cdot F e\left[F e(C N)_{6}\right]_{3} \)
B. \( F e\left[F e(C N)_{6}\right] \)
\( \mathbf{c} \cdot F e(C N)_{3} \)
D. \( N a_{4}\left[F e(C N)_{5}\right] \) NOS


Which of the following possess fluidity?
A. Alcohol
B. Rubber
c. oxygen
D. Both a and c


Two straight infinitely long and thin parallel wires are spaced \( 0.1 \mathrm{m} \) apart and carry a current of 10 ampere each. Find the magnetic field at a point distant \( 0.1 \mathrm{m} \) from both wires in the two
cases when the currents are in the :
1) Same and
2) Opposite direction.


Ways of expressing the concentration of
a solution are:
\( \frac{\text {Mass of solute}}{\text {Mass of solution}} \times 100 \)
II) \( \frac{\text { Mass of solute }}{\text {Volume of solution}} \times 100 \)
\( A \)
B. I
\( c \cdot 1,1 \)
D. none of the above


Extent of physisorption of a gas increases with:
A. increase in temperature
B. decrease in temperature
c. decrease in surface area of adsorbent
D. decrease in strength of van der Waals forces


The vitamin essential for synthesis of lipids is
A. Pantothenic acid
B. Pyridoxine
c. Retinol
D. Biotin


The characteristics which remains
same on moving down a sub-group:
A. atomic size
B. ionization potential
c. valence shell electrons
D. electronegativity


\( Z n S \rightarrow \) solubility in water \( =0.97 g K \) we
mixed 2 moles of \( Z n\left(N O_{3}\right)_{2} \) is \( 5 L \)
solution. Find new solubility of Zn?


Assertion
Glycolysis is the first step of respiration, where glucose completely
breaks into \( \mathrm{CO}_{2} \) and \( \mathrm{H}_{2} \mathrm{O} \)
Reason
In this process, there is net gain of twenty four molecules of ATP.
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


Assertion
If \( A \) and \( B \) are two \( 3 \times 3 \) matrices such
that \( A B=0, \) then \( A=0 \) or \( B=0 \)
Reason
If \( A, B \) and \( X \) are three \( 3 \times 3 \) matrices
such that \( \boldsymbol{A} \boldsymbol{X}=\boldsymbol{B},|\boldsymbol{A}| \neq \mathbf{0}, \) then \( \boldsymbol{X}= \)
\( A^{-1} B \)
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. Assertion is incorrect but Reason is correct


Which of the following molecules will form a linear polymeric structure due to hydrogen bonding?
A. \( H C l \)
в. \( H F \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( N H_{3} \)


Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be.
A . 2
B. 3
c. 5
D. 6


The figure above shows which magnetic instrument?
A. solenoid
B. power transformer
c. toroid
D. None of these


In aqueous solution, the liquid that absorbs nitric oxide to a considerable
extent is :
A. lead nitrate
B. nitric acid
c. ferrous sulphate
D. sodium hydroxide


Name the compounds which give fluidity and functional specificity to biomembranes.
A. Fluidity by proteins, functional specificity by lipids
B. Fluidity by lipids, functional specificity by proteins
C. Fluidity by sugar, functional specificity by proteins
D. Fluidity by sugar, functional specificity by lipids


Aluminium appears like gold when mixed with :
A. \( 90 \% \) Cu
B. 75 \% Ni
\( c \cdot 80 \% \) sn
D. 80 \% Co


Find the interval in which \( f(x)=x|x| \) is
differentiable.
\( A \cdot(-\infty, \infty) \)
В. \( (-\infty, 0) \cup(0, \infty) \)
\( c \cdot(0, \infty) \)
D. \( [0, \infty) \)


About phosphorous acid \( \left(\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3}\right) \)
which of the following statements is/are true?

This question has multiple correct options
A. Hybridization of P is the same as the hybridization of N in \( H N O_{3} \)
B. It is a dibasic acid
c. It is a reducer acid
D. Hybridization of P is the same as that of \( x \) e in \( X e O_{4} \)


Prove that:
\( ^{n} C_{r}+^{n} C_{r-1}=^{n+1} C_{r} \)


Tadpole of Herdmania exhibits
A. Absence of notochord
B. Retrogressive metamorphosis
c. Absence of tail
D. None of these


When a body is placed on a surface, the body exerts a force in
direction on the surface. Fill in the
blank
A. Downwards
B. Upwards
c. Both A and B
D. None


Fig shown below represents an area
\( A=0.5 m^{2} \) situated in a uniform
magnetic field \( B=2.0 w e b e r / m^{2} \) and
making an angle of \( 60^{\circ} \) with respect to
magnetic field. The value of the
magnetic flux through the area would be equal to:
A. 2.0 weber
B. \( \sqrt{3} \)weber
c. \( \sqrt{3} / 2 \) weber
D. 0.5 weber


The product of sexual reproduction
generally produces
A. Longer viability of seeds
B. Prolonged dormancy
C. New genetic combination leading to variation
D. Large biomass


Protozoans should be better termed as
A. Acellular
B. Cellular
c. Multicellular
D. coenocytic


In 16 throws of a die getting an even
number is considered a success, then
the variance of the success is
A . 4
B. 6
\( c \cdot 2 \)
D. 256


Ethylene is a
A. Gaseous hormone
B. Gaseous enzyme
c. Solid hormone
D. Liquid gas mixture


The amplitude of a particle executing
SHM about 0 is \( 10 \mathrm{cm} . \) Then:
A. when the KE is 0.64 times of its maximum KE, its displacement is 6 cm from 0
B. its speed is half the maximum speed when its displacement is half the maximum displacement
\( c . \) Both
(a) and
(b) are correct
D. Both (a) and
(b) are wrong


If a remainder of 4 is obtained when
\( x^{3}+2 x^{2}-x-k \) is divided by \( x-2 \)
find the value of \( k \)
A . 4
B. 6
c. 10
D. 12


How many equilateral triangles of side 2a with one vertex at origin and side along the \( x \) -axis is possible.


From the figure given, what is the angle
of reflection?
A \( .90-6 \)
B .26
\( c .3 \theta \)
D. 46


f \( \boldsymbol{y}=\tan (2 \boldsymbol{x}+\mathbf{3}) \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


3 Faradays of electricity was passed through an aqueous solution of iron
\( (I I) \) bromide. The weight (in \( g \) ) of iron metal (atomic weight \( =\mathbf{5 6} \) amu) deposited at the cathode is:
A . 56
B. 84
\( c \cdot 112 \)
D. 168


A solution of metal salt was electrolyzed
with a current of 0.1 A for 160 minutes.
Ni deposited at cathode was found 0.2950 g.
What is the charge on metal ion? (Atomic mass of metal is 58.71 )


Which one of the following reactions is
not correct?
\( \mathbf{A} \cdot C H_{3} C H O+\frac{1}{2} O_{2} \stackrel{M n(O A c) 2 / a i r}{\rightarrow} C H_{3} C O O H \)
B. \( C H_{3} C H_{2} O H+O_{2}^{\text {Micodermaceti}} C H_{3} C O O H+H_{2} O \)
c. \( C H_{3} M g B r \underbrace{(1) C O_{2}}_{(2) H_{2} O \oplus} C H_{3} C O O H+M g(O H) B r \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{O} \mathrm{H}+\mathrm{CO}^{\mathrm{Ca} / \Delta_{\rightarrow, \text {prssure}}} \mathrm{CH}_{3} \mathrm{COOH} \)


Assertion
STATEMENT-1: A straight line passing
through the origin intersects the branches of the hyperbola \( x y=9 \) at \( Q \) in the first and \( \mathrm{R} \) in the third quadrant. The
point P divides the segment QR internally in the ratio \( 1: 2, \) then the locus of \( P \) is ellipse
Reason
STATEMENT- 2 : \( \boldsymbol{A} \equiv\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right), \boldsymbol{B} \equiv \)
\( \left(x_{2}, y_{2}\right) \)
If \( P \) divides line joining Aand \( B \) in the ratio \( m: n, \) then \( c o \) -ordinates of \( P \) are \( \left[\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right] \)
A. Statement-1 is True, Statement -2 is True ; Statement
-2 is a correct explanation for Statement- -
B. Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


Under a given concentration in blood, dissociation of oxyhaemoglobin will increase if
A. pH of blood falls
B. pH of blood rises
c. \( C O_{2} \) concentration in blood falls.
D. Free fatty acid concentration in blood falls


A circular table with smooth horizontal
surface is rotating at an angular speed \( \omega \) about its axis. A groove is made on
the surface along a radius, and a small
particle is gently placed inside the groove at a distance I from the center.
Find the speed of the particle with respect to the table as its distance from
the center becomes \( L \)


Liquation is used to refine:
A . iron
B. tin
c. copper
D. gold


If in a triangle \( \boldsymbol{L} \boldsymbol{M} \boldsymbol{N} \)
\( \angle M=60^{\circ}, \angle N=60^{\circ}, \) find \( \angle L \)
Mention the kind of triangle also.


What type of energy is described from heated ground water?
A. Hydroelectricç
B. Nuclear
c. solar
D. Geothermal


When a resistance of 2 ohms is
connected across the terminals of a
cell,the current is 0.5 A. When the
resistance is increased to 5 ohms,the current becomes 0.25 A. The e.m.f. of the cell is :-
A . 1.0
B. 1.5
c. \( 2.0 v \)
D. 2.5


Which of these is a good electrical conductor?
A. water
B. Sweat
c. The human body
D. All of the above


Xenon hexafluoride on partial
hydrolysis produces compounds 'X' and
'Y'. Compounds 'X' and 'Y' and the oxidation state of \( \mathrm{Xe} \) are respectively
A \( \cdot X e O F_{4}(+6) \) and \( X e O_{2} F_{2}(+6) \)
в. \( \operatorname{XeOF}_{4}(+6) \) and \( X e O_{3}(+6) \)
c. \( X e O_{2} F_{2}(+6) \) and \( X e O_{2}(+4) \)
D. \( X e O_{2}(+4) \) and \( X e O_{3}(+6) \)


Find the maximum zener current for the
zener diode as shown in figure. Given,
\( \boldsymbol{V}_{Z}=\mathbf{6} \boldsymbol{V}, \boldsymbol{R}_{Z}=\mathbf{1 . 5 \Omega}, \boldsymbol{R}=\mathbf{4 0 0 \Omega} \)
A. \( 35.00 \mathrm{mA} \)
в. \( 30.87 m A \)
\( c .34 .87 m A \)
D. \( 34.87 A \)


Two fat astronauts each of mass \( 120 k g \)
are travelling in a closed spaceship
moving at a speed of \( 15 k m \) inthe outer space far removed from all other
material objects.


Pratap paid \( 20 \% \) of this salary as income tax. if he is left with \( R s 8,400 \)
after paying the tax, find his salary.
A. \( R s .11,500 \)
B. Rs. 11,000
c. \( R s .10,000 \)
D. Rs. 10, 500


Separation of the isotopes of uranium requires a physical method rather than a chemical method because:
A. it is too dangerous to mix other chemical with uranium
B. the isotopes are chemically the same element
c. the isotopes differ in number of neutrons
D. natural uranium contains only \( 0.7 \% U^{235} \)


Hydride of nitrogen is called:
A. Hydrogen sulphide
B. Water
c. Ammonia
D. Nitrous oxide


An electric motor exerts a constant
torque \( 10 \mathrm{N}-\mathrm{m} \) on a grind stone mounted on a shaft. MOI of the grind stone about
the shaft is \( 2 \mathrm{kg} m^{-2} . \) If the system
starts from rest, find the work done in
\( 8 s \)
A . \( 1600 J \)
B. \( 1200 J \)
\( c .800 J \)
D. \( 600 J \)


The angle of the prism for which there is
no emergent ray will be, if its critical
angle is \( i_{c} \)
A . greater than \( i_{c} \)
B. less than \( i_{c} \)
c. \( 2 i_{c} \)
D. greater than \( 2 i_{c} \)


Carrier concept proposed by Honert
(1937) is related with
A. Passive absorption of water
B. Active absorption of ions
c. Passive absorption of ions
D. Active absorption of water


A body of mass ' \( m^{\prime} \) starting from is
acted on by a force producing a velocity \( v=\sqrt{k \times s} \) where \( k \) is a constant and \( s \)
is displacement.The work done by the
force in the first \( ^{\prime} t^{\prime} \) seconds is:
\( \mathbf{A} \cdot m^{2} k^{2} t^{2} / 8 \)
B \( \cdot m k^{2} t^{2} / 4 \)
\( \mathbf{c} \cdot m k^{2} t^{2} / 8 \)
D. \( m^{2} k^{2} t / 4 \)


The range of \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1 0}+|\boldsymbol{x}+\mathbf{4}| \) is
A. \( (0, \infty) \)
)
B. \( [10, \infty) \)
c. \( (-\infty, 10] \)
\( D \cdot(-\infty, \infty) \)


In family Papilionaceae, 5 petals form a unique association, in which 3 different elements participate, these are vexillum, alae and carina.What is the number of these elements?
A. 1,2,2 respectively
B. 2, 1, 2 respectively
c. 1,1,3 respectively
D. 2, 2, 1 respectively


A polythene piece rubbed with wool is
found to have a negative charge of \( 3 x \) \( \mathbf{1 0}^{-\mathbf{7}} \mathbf{C} \)
(a) Estimate the number of electrons
transferred (from which to which?)
(b) Is there a transfer of mass from wool
to polythene?


Write the name of excretory organs and draw a labelled diagram of excretory system in humans.


The value of the definite integral, \( \int_{0}^{\pi / 2} \frac{\sin 5 x}{\sin x} d x \) is
A .
в.
\( c . \pi \)
D . \( 2 \pi \)


Choose the correct order of reactivity
toward nucleophilic substitution:
\( (\mathbf{I}) \)
\( (\mathbf{I I}) \)
\( (\mathbf{I I I}) \)
\( \mathbf{A} \cdot(1)<(\|)<(\| 1) \)
B. \( (1)<(111)<(11) \)
\( \mathbf{C} \cdot(\| I)<(\|)<(1) \)
D. \( (11)<(111)<(1) \)


\( \mathbf{v}-\mathrm{t} \) graph of a particle moving in a
straight line is as shown in figure. The
whole graph is made up of four straight lines \( P, Q, R \) and \( S . \) These four straight line indicate four type of motions
\( \left(M_{1} \ldots M_{4}\right) \) discussed above. State
which straight line corresponds to which type of motion.
A \( \cdot P \rightarrow M_{2} ; Q \rightarrow M_{1} ; R \rightarrow M_{4} ; S \rightarrow M_{3} \)
B \( . P \rightarrow M_{4} ; Q \rightarrow M_{3} ; R \rightarrow M_{2} ; S \rightarrow M_{1} \)
c. \( P \rightarrow M_{1} ; Q \rightarrow M_{2} ; R \rightarrow M_{4} ; S \rightarrow M_{3} \)
D. \( P \rightarrow M_{1} ; Q \rightarrow M_{2} ; R \rightarrow M_{3} ; S \rightarrow M_{4} \)


\( \frac{N}{10} \) acetic acid was titrated with \( \frac{N}{10} \) NaOH.When \( 25 \%, 50 \% \) and \( 75 \% \) of
titration is over then the pH of the
solution will be : \( \left[\mathbf{K}_{\boldsymbol{a}}=\mathbf{1 0}^{-\mathbf{5}}\right] \)
A \( .5+\log 1 / 3,5,5+\log 3 \)
B. \( 5+\log 3,4,5+\log 1 / 3 \)
c. \( 5-\log 1 / 3,5,5-\log 3 \)
D. \( 5-\log 1 / 3,4,5+\log 1 / 3 \)


Light traveling through three transparent substances follows the
path shown in Fig. Arrange the indices
of refraction in order from smallest to
largest. Note that total internal
reflection does occur on the bottom
surface of medium 2
\( \mathbf{A} \cdot n_{1}<n_{2}<n_{3} \)
B \( . n_{2}<n_{1}<n_{3} \)
\( \mathbf{c} \cdot n_{1}<n_{3}<n_{2} \)
\( \mathrm{D} \cdot n_{3}<n_{1}<n_{2} \)


Sideways pressure exerted by a liquid is called its lateral pressure.
True \( =1 ; \) False \( =0 \)


Ethyl butyrate has the flavour of which fruit?
A. Apple
B. Pineapple
c. orange
D. Banana


The shape of the cell is related to
A. the habitat of the organism
B. the body size of the organism
C. the function it performs
D. the number of cells in an organism


Given set of equations is \( \mathbf{1} . \mathbf{3} \boldsymbol{g}+\mathbf{1} . \mathbf{7} \boldsymbol{h}=\mathbf{5} \)
\( 3 h=20+13 g \)
Based on the system of equations
above, determine the value of \( h \)
\( ^{A} \cdot \frac{7}{2} \) or 3.5
B. 3
c. \( \frac{9}{2}=4.5 \)
D. 4


Find the equation of the plane through
the intersection of the planes \( 3 x- \)
\( 4 y+5 z=10 \) and \( 2 x+2 y-3 z=4 \)
and parallel to the line \( \boldsymbol{x}=\mathbf{2} \boldsymbol{y}=\mathbf{3} \boldsymbol{z} \)


A convex lens of focal length \( 0.12 \mathrm{m} \) produces a virtual n image which is thrice the size of the object. Find the distance between the object and the lens
A. \( 0.04 \mathrm{m} \)
B. \( 0.08 \mathrm{m} \)
c. \( 0.12 \mathrm{m} \)
D. 0.24 m


The pressure exerted by a women wearing shoes with pointed heels is than what an elephant with one foot can exert on ground:
A. Much lesser
B. Much greater
c. Both equal
D. None of these


Which vector, electric or magnetic, is
used to represent the polarisation of
e.m. waves? How will you show that light
waves are transverse in nature??


Match the compounds/reactions in column I with their correct number of
isomers in column II. Matching can be one or more than one.


The general electronic configuration \( (n-1) d^{3} n s^{2} \) indicates that particular
element belongs to:
A. \( V B \)
в. \( I V B \)
c. \( V I B \)
D. IIIB


The difference between \( \Delta H \) and \( \Delta E \) on
a molar basis for the combustion of \( n \)
octane at \( 25^{\circ} \mathrm{C} \) would be:
B. \( -1.14 \mathrm{kJ} \)
c. \( -11.15 \text { k }] \)
D. +11.15 k


The square of any positive odd integer for some integer \( m \) is of the form
\( A \cdot 7 m+1 \)
B. \( 8 m+1 \)
\( c \cdot 8 m+3 \)
\( D \cdot 7 m+2 \)


The \( 4^{t h} \& 7^{t h} \) of an are \( A . P \) are \( 17 \& 23 \)
respectively find o is.


A stream of electrons enters an
electrical field normal to the lines of force with a velocity of \( 3 \times 10^{7} m / s \). The
electric intensity is \( 1800 v / m \) While traveling through a distance of 10
\( c m, \) the electron beam is deflected by 2
mm. Then \( e / m \) value in coulomb per \( \mathrm{kg} \) is
A \( \cdot 2 \times 10^{10} \)
B. \( 2 \times 10^{7} \)
\( c \cdot 2 \times 10^{11} \)
D. \( 2 \times 10^{4} \)


If \( A \) and \( B \) are mutually exclusive such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3 5} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4 5} \)
find
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)


When plastic comb is rubbed against dry hair, the plastic comb becomes negative and dry hair becomes positive
A. True
B. False
c. Ambiguous
D. Data insufficient


A man of mass \( m \) walks from end \( A \) to
the other end \( B \) of a boat of mass \( M \)
and length \( l . \) The coefficient of friction
between the man and the boat is \( \mu \) and
neglect any resistive force between the
boat and the water.
This question has multiple correct options
A. If the man runs at his maximum acceleration, the acceleration of the boat is \( (m / M) g \)
B. The maximum time take by the men to reach the other end of the boat is \( \sqrt{\frac{2 M l}{(M+m) \mu g}} \)
c. If the man runs at his maximum acceleration, the acceleration of the boat is \( \frac{m}{m+M} \mu g \)
D. The minimum time take by the men to reach the other end of the boat is \( \sqrt{\frac{2 m l}{(M+m) \mu g}} \)


Evaluate : \( \left(\frac{5}{3}\right)^{x} \cdot\left(\frac{9}{25}\right)^{x^{2}+2 x-11}= \)
\( \left(\frac{5}{3}\right)^{9} \)


The magnitude of the component of the \( \operatorname{vector}(2 \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}+\hat{\mathbf{k}}) \) along \( (\mathbf{3} \hat{\mathbf{i}}+\mathbf{4} \hat{\mathbf{k}}) \) is :
\( A \cdot 1 / 2 \)
B. 14/5
\( c \cdot 3 \)
D.


Consider the following statements A \& B and identify correct choice in the
given answers
(A) When light falls on two polaroid sheets having their axes mutually perpendicular, it is completely extinguished.
(B) When polyvinyl alcohol is subjected to a large strain the molecules get
oriented parallel to the direction of
strain and material becomes
double refractive.
A . A \& B are correct
B. Both A \& B are wrong
C. A correct B wrong
D. A wrong B correct


If \( f(x+1)=3 x-9, \) then what will be
the value of \( \boldsymbol{f}\left(\boldsymbol{x}^{2}-\mathbf{1}\right) ? \)
A \( \cdot 3 x^{2}-9 \)
B. \( 3 x^{2}-15 \)
c. \( x^{2}-10 \)
D. \( 3 x^{2}-10 \)


Which of the following aqueous solutions, when added to 100 ml of
\( 0.1 M H C l(a q) \) will cause no change in its \( p H ? \) Assume volumes to be additive.
A . \( 100 \mathrm{ml} \) distilled water
B. \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{HNO}_{3} \)
\( \mathrm{c} .50 \mathrm{ml} \) of \( 0.2 \mathrm{M} \) HCl
D. \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} \mathrm{AgNO}_{3} \)


In a circuit a coil of resistance \( 2 \Omega \), then
magnetic flux charges from 2.0 \( W \) b to
10.0 \( W b \) in 0.2 sec. The charge flow in
the coil during this time is:
\( \mathbf{A} \cdot 5.0 C \)
в. \( 4.0 C \)
c. \( 1.0 C \)
D. \( 0.8 C \)


The oxidation state of chlorine in
chlorous acid is:
\( A \cdot+2 \)
\( B .+3 \)
\( c .-1 \)
\( D \cdot-2 \)


Which of the following is used in
conveyor belt? This question has multiple correct options
A. PVC
B. Polythene
c. Neoprene
D. none of these


In astronomical telescope, the final image is formed at:
A. the least distance of distinct vision
B. the focus of objective lens
c. the focus of the eye lens
D. beyond the focal length of eyepiece


The H.M. of two number is 4 and their \( A \)
\( m . \) and \( G . M . \) satisfy the relation \( 2 A+ \)
\( G^{2}=27, \) then the numbers are :


Following reactions are taking place in
a Galvanic cell, \( Z n \rightarrow Z n^{2+}+ \)
\( \mathbf{2} e^{-} ; \boldsymbol{A} \boldsymbol{g}^{+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g} \)
Which of the given representations is the correct method of depicting the
cell?
A \( \cdot Z n_{(s)}\left|Z n_{(a q)}^{2+}\right|\left|A g_{(a q)}^{+}\right| A g_{(s)} \)
B . \( Z n^{2+}|Z n \| A g| A g^{+} \)
c. \( Z n_{(a q)}\left|Z n_{(s)}^{2+}\right|\left|A g_{(s)}^{+}\right| A g_{(a q)} \)
D. \( Z n_{(s)}\left|A g_{(a q)}^{+}\right|\left|Z n_{(a q)}^{2+}\right| A g_{s s} \)


Similar to electron diffraction, neutron
diffraction microscope is also used for the determination of the structure of
molecules. If the wavelength used here
is \( 800 \mathrm{pm} \), calculate the characteristic velocity associated with the neutron.


If the heat absorbed by a heat engine is \( 600 \mathrm{kJ} \) per cycle and it releases \( 480 \mathrm{kJ} \) of heat each cycle, what is its efficiency?
A . 20\%
B. 80\%
c. \( 100 \% \)
D. 30\%


What are fossil fuels ? How were coal
and petroleum formed?


The locus of complex number z such
that \( z \) is purely real and real part is equal to -2 is
A. Negative y-axis
B. Negative x-axis
c. The point (-2,0)
D. The point ( 2, 0)


The vectors \( \vec{a}(x)=\cos x \hat{i}+\sin x \hat{j} \) and
\( \vec{b}(x)=x \hat{i}+\sin (x) \hat{j} \) are collinear for
A \cdot Unique value of \( x, 0<x<\frac{\pi}{6} \)
B. Unique value of \( x, \frac{\pi}{6}<x<\frac{\pi}{3} \)
c. No value of \( x \)
D \cdot Infinite values of \( x, 0<x<\frac{\pi}{2} \)


If \( \boldsymbol{A}=\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}\left[\begin{array}{cc}\mathbf{1} & \boldsymbol{i}+\mathbf{1} \\ \boldsymbol{i}-\mathbf{1} & \mathbf{1}\end{array}\right], \) then \( \boldsymbol{A}\left(\boldsymbol{A}^{\boldsymbol{T}}\right) \)
equals
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( I \)
\( c .-I \)
D. \( 2 I \)


If \( a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+ \)
\( c=0 \) then \( \frac{d y}{d x}= \)
A. \( -\left(\frac{a x+h y+g}{h x+b y+f}\right) \)
в. \( -\left(\frac{a x+h y+g}{b x+h y+f}\right) \)
c. \( -\left(\frac{h x+b y+f}{a x+h y+g}\right) \)
D. \( -\left(\frac{h x+b y+f}{h x+a y+g}\right) \)


Which is not correct
A. A museum has collection of photographs of plants and animals
B. Botanical gardens have collection of living plants for reference
C. Herbarium houses dried, pressed and preserved plant specimens
D. Key is taxonomic aid for identification of specimens


Show that the given differential equation is homogenous and solve them \( \boldsymbol{Y}^{\prime}=\frac{\boldsymbol{x}+\boldsymbol{y}}{\boldsymbol{x}} \)


Centre of gravity is lowered in equilibrium. Fill in the blank.
A . Stable
B. Unstable
c. Neutral
D. All of the above


A sound signal is simultaneously sent in air and water from a boat on a river.
The echo of sound striked by river bed is heard in \( 4 s, \) while echo striked by aeroplane is heard in \( 8 s \). Find the distance between aeroplane and river
bed.
[velocity of sound in air \( =350 m / s \)
velocity of sound in water \( =1500 m / s] \)
A. \( 4.4 k m \)
B. \( 6.4 k m \)
c. \( 8.8 k m \)
D. \( 13.4 k m \)


The condensation reaction between one
equivalent of acetone and two
equivalents of benzaldehyde in presence of dilute alkali leads to the
formation of:
A. Benzalacetophenone
B. Benzylideneacetone
c. Dibenzalacetone
D. Benzoic acid and acetic acid
E. Only benzoic acid


A book of mass \( 5 \mathrm{kg} \) is placed on a table and it is pressed by \( 10 \mathrm{N} \) force then normal force exerted by the table on the book is
A . 10 N
в. 70 N
\( c . \) 59 \( \mathrm{N} \)
D. 50 N


The inclination of a line is \( 30^{\circ}, \) then the
slope of the line is
A . 0
B.
\( c \cdot \sqrt{3} \)
D. \( \frac{1}{\sqrt{3}} \)


Draw the curve \( y=\sin ^{4} x \) between \( x= \)
0 and \( x=2 \pi \)


The 4 th term of a geometric progression is \( \frac{2}{3} \) and 7 th term is \( \frac{16}{81} . \) Find the
Geometric series.
A \( \cdot \frac{9}{4},-\frac{3}{2}, 1,-\frac{2}{3}, \dots \dots \)
в. \( \frac{9}{4}, \frac{3}{2}, 1, \frac{2}{3}, \ldots . . . \)
c. \( -\frac{9}{4}, \frac{3}{2}, 1, \frac{2}{3}, \ldots \ldots \)
D. None of these


Discuss the continuity of the function defined by \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{5}| \)


A gale is on a house. The force on the
roof due to the gale is:
B. zero
c. directed upward
D. information insufficient


Of the diodes shown in the following
diagrams, the reverse biased diode is
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
D.


Bertin are extensions of
A. Hilum in pelvis
B. Medulla in pelvis
c. Medulla in cortex
D. cortex in medulla


If \( A B=A \) and \( B A=B \) then \( B^{2} \) is
equal to
A. \( B \)
в. \( A \)
\( c .-B \)
D. \( B^{2} \)


If \( 4 \hat{i}+7 \widehat{j}+8 \widehat{k}, 2 \hat{i}+3 \widehat{j}+4 \widehat{k} \) and \( 2 \hat{i}+ \)
\( \mathbf{5} \widehat{\boldsymbol{j}}+\mathbf{7} \widehat{\boldsymbol{k}} \) are the position vectors of the
vertices \( A, B \) and \( C \) respectively, of
triangle \( A B C, \) then the position vector of the point where the bisector of angle
\( A \) meets \( B C \) is
A \( \cdot \frac{2}{3}(-6 \hat{i}-8 \hat{j}-6 \widehat{k}) \)
B \( \cdot \frac{2}{3}(6 \hat{i}+8 \hat{j}+6 \widehat{k}) \)
c. \( \frac{1}{3}(6 \hat{i}+13 \hat{j}+18 \widehat{k}) \)
D \( \cdot \frac{1}{3}(5 \hat{j}+12 \widehat{k}) \)


A buffer solution, \( 0.080 M \) in \( N a_{2} P O_{4} \)
and \( 0.020 M \) in \( N a_{3} P O_{4} \) is prepared. The electrolytic oxidation of 1.0 mmol of
the organic compound \( R N H O H \) is carried out in \( 100 \mathrm{m} L \) of the buffer. The
reaction is as follows:
\( \boldsymbol{R} \boldsymbol{N} \boldsymbol{H} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \boldsymbol{R} \boldsymbol{N} \boldsymbol{O}_{2}+ \)
\( 4 H^{+}+4 e \)
Calculate the approximate \( p H \) of the solution after the oxidation is complete.
A . 6.19
B. 7.81
c. 10.34
D. 12.45


Expiration is normally brought about by the relaxation of diaphragm
A. True
B. False


Write the value of \( 2 \sin ^{-1} \frac{1}{2}+ \)
\( \cos ^{1}\left(-\frac{1}{2}\right) \)


The maximum value of \( 3 \cos \theta+4 \sin \theta \)
is
A . -5
B. 5
c. 25
D. None of these


In the given figure, \( P A \) and \( P B \) are
tangents from an external point \( \boldsymbol{P} \) to a
circle with center \( O . L N \) touches the
circle at \( M . \) Prove that \( \boldsymbol{P} \boldsymbol{L}+\boldsymbol{L} \boldsymbol{M}= \)
\( \boldsymbol{P} \boldsymbol{N}+\boldsymbol{M} \boldsymbol{N} \)


In the given figure, \( \angle \theta \) is less than one-
third of a right angle, then:
A \( \cdot \phi>150^{\circ} \)
B \( \cdot \phi \geq 150^{\circ} \)
c. \( \phi \leq 150^{\circ} \)
D. \( \phi<150^{\circ} \)


For the reaction: \( \mathbf{3} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \)
mechanism is Step \( 1: \boldsymbol{A}+\boldsymbol{B} \stackrel{\boldsymbol{k}_{1}}{\longrightarrow} \boldsymbol{E} \)
Step \( 2: E+2 A \stackrel{k_{2}}{\longrightarrow} C+D \)
What is the total order of reaction
considering steady state approximation?


If \( \sqrt{2 x-1}-\sqrt{2 x+1}+4=0, \) then
\( 128 x \) is equal to
A . 120
в. 260
c. 165
D. 200


A person is walking along positive \( \boldsymbol{x} \)
axis for \( 10 m \) and then takes left turn by
angle \( 60^{\circ} \) and then moves for 8 m. The
direction of displacement of person with \( x- \) axis is:
\( ^{\mathrm{A}} \cdot_{\theta}=\tan ^{-1}\left(\frac{\sqrt{3}}{14}\right) \)
в. \( _{\theta}=\tan ^{-1}\left(\frac{\sqrt{3}}{7}\right) \)
c. \( _{\theta=\tan ^{-1}}\left(\frac{3 \sqrt{3}}{7}\right) \)
D. \( _{\theta=\tan ^{-1}}\left(\frac{2 \sqrt{3}}{7}\right) \)


A spring with spring constants K when compressed by \( 1 \mathrm{cm} \), the potential energy stored is U.If it is further
compressed by \( 3 \mathrm{cm}, \) then its final potential energy is
A . \( 16 U \)
в. \( 9 U \)
c. \( 8 U \)
D. \( 15 U \)


\( H_{2} S O_{4} \) has very corrosive action on
skin because:
A. it reacts with proteins
B. it acts as oxidising agent
c. it acts as oxidising agent and absorption of water is highly exothermic
D. none of these


dentify the type of reaction indicated by
\( D \) in the diagram.
A. Uncatalyzed exothermic
B. Catalyzed exothermic
c. Catalyzed endothermic
E. Reversible


Describe the experiment to find internal resistance of a cell by Potentiometer under the following points.
(i) Labelled electric circuit diagram.
(ii) Derivation of formula
(iii) Observation table
(iv) Two precautions.


Let \( R \) be a reflexive relation in a finite
set having \( n \) elements and let there be
\( m \) ordered pairs in \( R \). Then
A \( . m \geq n \)
в. \( m \leq n \)
c. \( m=n \)
D. None of these


When sucrose is heated with
concentrated nitric acid the product is:
A. Saccharic acid
B. Oxalic acid
c. Formic acid
D. Invert sugar


Draw a neat labelled diagram of
excretory system in human beings.


27 identical drops of mercury are charged simultaneously with the same potential of \( 10 V . \) Assuming the drop to
the spherical, if all the charged drops are made to combine to form one large
drop, then its potential will be
\( \boldsymbol{V} \)
A . 40
B. 90
\( c .160 \)
D. 10


In a parallelogram PQRS, X is the mid
point of PS and Y is the mid point of QR, then \( X Y \) divides \( Q S \) in the ratio of
A .1: 4
B. 1: 1
c. 1: 2
D. 1: 3


The number \( x \) was multiplied by 0.5 and
the product divided by \( 3 . \) The result was
squared and 1 added to it. The final result was \( 50 . \) What was the value of
number \( \boldsymbol{x} \) ?
A .42
B. 30
\( c \cdot 24 \)
D. 18


If we weigh a given substance five times, and get 5 kg each time, then your measurement is very
A. Accurate
B. Precised
c. Accurate and Precised
D. cannot be judged


The \( p H \) of pure water at \( 80^{\circ} C \) will be:
A. 7
B . >7
\( c \cdot<7 \)
D. cannot be predicted


If \( 0.6 x+0.8=0.28 x+1.16, \) then \( x= \)
A \( \cdot x=\frac{6}{7} \)
в. \( x=\frac{9}{8} \)
c. \( x=\frac{11}{2} \)
D. \( x=\frac{13}{5} \)


What is the ratio between the energies
of two radiations one with a wavelength of \( 6000 A \) and other with 2000 A?


\( \lim _{n \rightarrow \infty}(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \dots(1+ \)
\( \left.x^{2 n}\right),|x|<1, \) is equal to
A \( \cdot \frac{1}{x-1} \)
в. \( \frac{1}{1-x} \)
c. \( 1-x \)
\( D \)


Which among the following is a double displacement?
A. \( A g N O_{3}+K I \rightarrow A g I+K N O_{3} \)
в. \( P b+C u C l_{2} \rightarrow P b C l_{2}+C u \)
c. \( C+O_{2} \rightarrow C O_{2} \)
D. \( S n O_{2}+C \rightarrow S n+C O_{2} \)


Production of a human protein in
bacteria by genetic engineering is possible because
A. Bacterial cell can carry out the RNA splicing reactions.
B. The mechanism of gene regulation is identical in humans and bacteria
c. The human chromosome can replicate in bacterial cell.
D. The genetic code is universal


The first ionization energies of alkaline earth metals are higher than those of
the alkali metals. This is because:
A. there is increase in the nuclear charge of the alkaline earth metal
B. there is decrease in the nuclear charge of the alkaline earth metal
c. there is no change in the nuclear charge
D. none ofthe above


In a damped harmonic oscillator, periodic oscillations have
amplitude.
A. Gradually increasing
B. Suddenly increasing
c. suddenly decreasing
D. Gradually decreasing


What is the percentage increase in the
number of students in 2002 over 2000?
Number of students who qualified CATIXAT/CET Fxams
A . 30\%
B. 17.64\%
c. \( 117.6 \% \)
D. 85\%


Four identical metal plates are located
in air at equal distance \( d \) from one
another as shown in figure. The area of
each plate is equal to \( A \). Find the
capacitance of the system between points \( A \) and \( B \)


The work function of tungsten coated with Barium Oxide is nearly
A. 5 ev
B. 10 ev
\( c \cdot 1 e v \)
D. 0.01 ev


Assertion: Gasses obey Boyle's law at
high temperature and low pressure only. Reason: At low pressure and high temperature, gasses would behave like
ideal gases.
A. Both assertion (A) and reason
(R) are correct and gives the correct explanation
B. Both assertion (A) and reason
(R) are correct but \( R \) does give the correct explanation
c. \( A \) is true but \( R \) is false
D. A is false but R is true


Count total number of S.F. in 300.00
A. 5
B. 6
\( c \cdot 8 \)
D. 9


The maximum refractive index of a
prism which permits passage of the light through it when the refracting
angle of the prism is \( 90^{\circ}, \) is :
A. \( 1 / \sqrt{2} \)
B. \( \sqrt{2} \)
c. \( \sqrt{\frac{3}{2}} \)
D. \( \frac{3}{2} \)


Which of the following on reaction with acetylene \( (\boldsymbol{C H} \equiv \boldsymbol{C H}) \) produce
\( \operatorname{gas}(e s) ? \)
I. \( K \) in liquid \( N H_{3} \) II. \( N^{\ominus} \) IIII.CH\( _{3} \) IV.OH
A. \( (I),(I I) \) and \( (I I I) \)
B. \( (I),(I I) \) and \( (I V) \)
c. \( (I),(I I I) \) and \( (I V) \)
D. \( (I I),(I I I) \) and \( (I V) \)


What is the refractive index of a prism
whose angle \( A=60^{\circ} \) and the angle of
minimum deviation \( \boldsymbol{d}_{m}=\mathbf{3 0}^{o} \) ?
A \( \cdot \sqrt{2} \)
B. \( \frac{1}{\sqrt{2}} \)
\( c \cdot 1 \)
D. \( \frac{1}{\sqrt{3}} \)


What is the shape of \( F e(C O)_{5} \) molecule
and which of the following d-orbitals involved in hybridization?
A . Tetrahedral \( d_{x^{2}-y^{2}} \)
B. Trigonal bipyramidal, \( d_{x^{2}-y^{2}} \)
C. Trigonal bipyramidal, \( d_{z} \)
D. Square pyramidal


Two uniform rods of equal length \( \left(l_{n}\right) \) and equal mass have the coefficient of linear expansion \( \alpha \) and \( 2 \alpha \) are placed in
contact on a smooth horizontal surface
as shown in the figure. The temperature
of the system is \( \theta^{0} C . \) Now the
temperature is increased by \( \Delta \theta^{0} C \).The junction of the rods will shift its initial
position by:
A \( \cdot \frac{l_{0} \alpha \Delta \theta}{2} \)
B. \( \frac{l_{0} \alpha \Delta \theta}{3} \)
c. \( \frac{l_{0} \alpha \Delta \theta}{4} \)
D


A body is dropped from a height of \( 2 \mathrm{m} \) It penetrates into the sand on the
ground through a distance of \( 10 \mathrm{cm} \) before coming to rest. What is the retardation of the body in sand?
B. \( 196 \mathrm{ms}^{-2} \)
c. \( -196 \mathrm{ms}^{-2} \)
D. \( 9.8 \mathrm{ms}^{-2} \)


f \( z_{1}, z_{2} \) and \( z_{3} \) are complex numbers
such that \( \left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|= \)
\( \left|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}\right|=1, \) then find the value
of \( \left|z_{1}+z_{2}+z_{3}\right| \)


Lymph contains proteins than plasma.
A . Less
B. More
c. Equal
D. None of the above


Give suitable examples of the following:
(a) Rod-shaped bacteria
(b) Pigments of cyanobacteria
(c) Nitrogen fixing
monerans.


Integrate: \( \int \frac{\sec ^{2} \sqrt{x}}{\sqrt{x}} d x \)
\( \mathbf{A} \cdot I=2 \tan \sqrt{x}+c \)
B. \( I=2 \cot \sqrt{x}+c \)
\( \mathbf{c} \cdot I=3 \tan \sqrt{x}+c \)
D \( \cdot I=2^{2} \tan \sqrt{x}+c \)


The last and stable community is an area is called
A. Pioneer community
B. Climax community
c. Transitional community
D. Seral community


If \( \boldsymbol{y}(\boldsymbol{t}) \) is a solution of \( (\boldsymbol{1}+\boldsymbol{t}) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{t}}-\boldsymbol{t} \boldsymbol{y}= \)
1 and \( y(0)=-1, \) then \( y(1) \) equal to
A. \( -\frac{1}{2} \)
B. \( e+\frac{1}{2} \)
c. \( _{e-\frac{1}{2}} \)
D. \( \frac{1}{2} \)


The renal abnormality detection procedure uses the following techniques except
A. Pyelography
B. Polarography
c. cytoscope
D. x-ray photography


The difference of the degrees of the
polynomials \( 3 x^{2} y^{3}+5 x y^{7}-x^{6} \) and
\( 3 x^{5}-4 x^{3}+2 \) is
\( A \cdot 2 \)
B. 3
\( c \)
D. None


What is the difference between Land
and Sea breeze?


What is photorespiration? Explain it with diagrammatic representation.


An elevator is moving with an upward acceleration a. A coin is dropped from
rest from the roof of the elevator. After
what time the coin will strike the base
of the elevator?


Which of the following parameters does not charaterize the thermodynamic
state of matter?
A. temperature
B. pressure
c. work
D. volume


Solve the following linear programming problem by graphical method:
Maximize \( Z=3 x+2 y \)
subject to the in constraints \( \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \leq \mathbf{1 0}, \mathbf{3} \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{1 5}, \boldsymbol{x}, \boldsymbol{y} \geq \mathbf{0} \)


Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}-\boldsymbol{x}^{2} \) on \( [\mathbf{0}, \mathbf{1}] \)


\( \int \frac{\csc ^{2} x-2005}{\cos ^{2005} x} d x \) is equal to
A. \( \frac{\cot x}{(\cos x)^{2005}}+C \)
B. \( \frac{\tan x}{(\cos x)^{2005}}+C \)
c. \( \frac{-\tan x}{(\cos x)^{2005}}+C \)
D. None of these


\( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{1}\end{array}\right], \) and \( \boldsymbol{I}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) then
prove that \( \boldsymbol{A}^{n}=\boldsymbol{n} \boldsymbol{A}-(\boldsymbol{n}-\mathbf{1}) \boldsymbol{I}, \boldsymbol{n} \geq 1 \)


Measuring vessel to measure density of
liquid is


Let \( \boldsymbol{f}(\boldsymbol{x})=\log \left(1+\boldsymbol{x}^{2}\right) \) and \( \boldsymbol{A} \) be a
constant such that \( \frac{|\boldsymbol{f}(\boldsymbol{x})-\boldsymbol{f}(\boldsymbol{y})|}{|\boldsymbol{x}-\boldsymbol{y}|} \leq \boldsymbol{A} \)
for all \( x, y \) real and \( x \neq y . \) Then the least
possible value of \( \boldsymbol{A} \) is
A. Equal to 1
B. Bigger than 1 but less than 2
c. Bigger than 0 but less than 1
D. Bigger than 2


The distance between the parallel lines \( \boldsymbol{y}=\mathbf{2} \boldsymbol{x}+\mathbf{4} \) and \( \mathbf{6} \boldsymbol{x}=\mathbf{3} \boldsymbol{y}+\mathbf{5} \) is
A \( \cdot \frac{17}{\sqrt{3}} \)
B.
c. \( \frac{3}{\sqrt{5}} \)
D. \( \frac{17 \sqrt{5}}{15} \)


Mark the odd one in the series.
indica, Ficus, Mangifera, Tamarindus


The area bounded by \( y=\cos x, y= \)
\( x+1 \) and \( y=0 \) in the second quadrant
is
A \( \cdot \frac{3}{2} \) sq. units
B. 2 sq. units
c. 1 sq. unit
D. \( \frac{1}{2} \) sq, units


f \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{5}\end{array}\right] \) then \( \boldsymbol{A}+\boldsymbol{B} \)


Write the names of the orbitals of the
following quantum numbers.
\( \boldsymbol{n}=\boldsymbol{2}, \boldsymbol{l}=\mathbf{0} \)


Which of the following is aromatic?
A . Lysine
B. Proline
c. serine
D. Tyrosine


In a population of families having three children each, the percentage of population of families having both boys and girls is?
A . 10
B . 25
c. 50
D. 75


Find the number of terms in the
following \( \boldsymbol{A} . \boldsymbol{P .} \mathbf{7}, \mathbf{1 3}, \mathbf{1 9}, \dots, \mathbf{2 0 5} \)


Find the greatest and the least values of the following functions. \( f(x)=\left(2^{x}+2^{-x}\right) / I n 2 \) on the
interval [-1,2]


Two horizontal discs of different radii
are free to rotate about their central
vertical axes. One is given some angular
velocity, the other is stationary. Their rims are now brought in contact. There
is friction between the rims. Then which
of the following statement(s) is/are true
\( ? \)
This question has multiple correct options
A. The force of friction between the rims will disappear when the discs rotate with equal angular speeds.
B. The force of friction between the rims will disappear when they have equal linear velocities
C. The angular momentum of the system will be conserved.
D. The rotational kinetic energy of the system will not be conserved


Assign number 1 for least to 4 for most to indicate the relative base strength of the following.
\( \mathbf{C}_{6} \mathbf{H}_{5}^{\mathbf{I}} \mathbf{N} \mathbf{H}_{\mathbf{2}} \)
\( \mathbf{p}-\mathbf{N} \mathbf{O}_{2} \mathbf{C}_{6} \mathbf{H}_{4} \mathbf{N} \mathbf{H}_{\mathbf{2}} \)
\( \mathbf{m}-\mathbf{N} \mathbf{O}_{2} \mathbf{C}_{6} \mathbf{H}_{4} \mathbf{N} \mathbf{H}_{\mathbf{2}} \)
\( \mathbf{m}-\mathbf{C} \mathbf{H}_{3} \mathbf{O} \mathbf{O}_{6} \mathbf{H}_{\mathbf{4}} \mathbf{N} \mathbf{H}_{\mathbf{2}} \)
A. III IIIIV
3124
в. IIIIIIIV
1234
c. ।॥ III IV
2 3 4 1
D. III IIIIV
4132


The work done in the given figure is
A \( .3 \times 10^{5} J \)
B \( \cdot 2 \times 10^{5} J \)
\( \mathbf{c} \cdot 10^{5} J \)
D. zero


When a moss spore lands on an appropriate site, it germinates into the first stage of the gametophyte called as
A. Antheridium
B. Rhizoid
c. Protonema
D. Thallus


The average speed of all the molecules
in a gas at a given instant is zero,
whereas the average velocity of all the molecules is zero. Explain why?


Solve: \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\cos (\boldsymbol{x}+\boldsymbol{y}) \)


A hole is made at the bottom of a tank
filled with water (density \( \left.=10^{3} k g / m^{3}\right) \)
If the total pressure at the bottom of the \( \operatorname{tank} \) is \( 3 a t m\left(1 a t m=10^{5} N / m^{2}\right), \) then
the velocity of efflux is
\( \mathbf{A} \cdot \sqrt{400} m / s \)
B. \( \sqrt{200} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{600} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{500} \mathrm{m} / \mathrm{s} \)


Select the correct option:
During electron transport system(ETS), electron transport proceeds from carriers that have
potential to those having redox potential. This electron transport down the energy gradient leads to the formation of ATP from ADP and Pi, which
is referred to as
A. Low, high, oxidative phosphorylation
B. Low, high, oxidative decarboxylation
c. High, low, oxidative phosphorylation
D. High, low, oxidative decarboxylation


The solution of the differential equation \( \left(x+3 y^{2}\right) \frac{d y}{d x}=y, y>0 \) is
A \( \cdot \frac{x}{y}=3 y+c \)
B . \( x=2 y^{3}+3 y^{2}+c \)
c. \( y=3 x^{2}+c \)
D. \( y=3 x+c \)


Assertion
Adding inert gas to dissociation
equilibrium of \( N_{2} O_{4} \) at constant
temperature and pressure increases
the dissociation of \( N_{2} O_{4} \)
Reason
Due to the addition of inert gas molar concentration of reactants and
products decreases.
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


Lead nitrate on strong heating gives:
A. PbO, \( \mathrm{NO}_{2}, \mathrm{O}_{2} \)
в. \( \mathrm{PbO}_{2}, \mathrm{PbO}, \mathrm{NO}_{2} \)
\( \mathrm{c} \cdot \mathrm{PbO}, \mathrm{NO}, \mathrm{O}_{2} \)
D. \( \mathrm{PbO}, \mathrm{NO}, \mathrm{NO}_{2} \)


Refractive indices of 2 different media
with separating boundary at the
diagonal of rectangular glass slab are
shown. Total angle of deviation of the ray
as shown in the figure, when it emerges
in air is :
air
A \( \cdot 120^{\circ} \)
B. 90
\( c \cdot 60^{\circ} \)
D \( .45^{\circ} \)
\( E \cdot 30 \)


The period of time for which the interest is calculated is called the.
A. Market period
B. Cooling period
c. conversion period
D. None of the above


What is the effect on density if we increase atomic number in
lanthanides?
A. Increase
B. Very low
c. Decrease
D. Very high


A force of \( 400 N \) exerts a pressure of
\( 20 N / c m^{2} . \) What is the area on which
the force acts?
\( \mathbf{A} \cdot 20 m^{2} \)
B. \( 20 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 1 \mathrm{cm}^{2} \)
D. \( 10 \mathrm{cm}^{2} \)


Assertion
Electromotive force is a force which
help the electrons to flow and produce
current.
Reason
Electromotive force is independent of
the voltage across the cell
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The values of heat of combustion of
graphite and \( H_{2} \) are -395 and -269 kJ/mol respectively. If heat of formation of glucose is \( -1169 \mathrm{kJ} / \mathrm{mol} \), then the heat of combustion of glucose is:
A . -2815 kJ/mol
B. -1169 kJ/mol
c. 1169 kJ/mol
D. 2815 kJ/mol


A chemical reaction \( 2 A \rightleftharpoons 4 B+C \) in
gas phase occurs in a closed vessel. The
concentration of \( B \) is found to be
increased by \( 5 \times 10^{-3} \) mole 1: 1 in 10
second. Calculate \( C O \) the rate of
appearance of \( B \) (ii) the rate of
disappearance of \( \boldsymbol{A} \)


Williamson's synthesis is used to
prepare:
A. diethyl ether
B. PVC
c. bakelite
D. ethyl alcohol


The portion of nephron which is relatively impermeable to water is
A. Collecting tubule
B. Ascending limb of loop of henle
c. Distal tubule
D. Loop of Henle


In the given figure, the instantaneous
value of the alternating e.m.f is \( e= \)
14.14sinwt. The voltmeter reading in
volts will be:
\( \mathbf{A} \cdot 141.4 \)
B. 10
c. 200.0
D. 70.7


If the mean of 5 observations \( x, x+ \) \( 2, x+4, x+6 \) and \( x+8 \) is \( 11, \) find the
value of \( x \)


A constant pressure calorimeter consists of an insulated beaker of mass
\( 82 g \) made up of glass with heat capacity \( 0.75 J K^{-1} g^{-1} . \) The beaker
contains \( 100 \mathrm{m} L \) of \( 1 \mathrm{M} \) HCl at
\( \mathbf{2 2 . 6}^{\circ} \boldsymbol{C} \) to which \( \mathbf{1 0 0} \boldsymbol{m} \boldsymbol{L} \) of \( \mathbf{1} \boldsymbol{M} \)
NaOH at \( 23.4^{\circ} C \) is added. The final
temperature after the reaction is complete at \( 29.3^{\circ} \mathrm{C} \). What is \( \Delta H \) per mole for this neutralisation reaction?
Assume tha the heat capacities of all solutions are equal to that of same
volumes of water


The number of lobes in most of the \( d \)
orbits are:
A. 6
B. 10
\( c \cdot 8 \)
D. 4


Two charges - \( q \) and \( +q \) are located at points \( (0,0,-a) \) and \( (0,0, a) \) respectively.
(a) What is the electrostatic potential at the points \( (0,0, z) \) and \( (x, y, 0) ? \)
(b) Obtain the dependence of potential on the distance r of a point from the origin when \( r / a>>1 \)
(c) How much work is done in moving a small test charge from the point (5,0,0) to (-7,0,0) along the \( x \) -axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?


While measuring the side of an
equilateral triangle an error of \( k \% \) is marked, the percentage error in its area is
A. \( k \% \)
в. \( 2 k \% \)
\( c \cdot \frac{k}{2} \% \)
D. \( 3 k \% \)


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{\boldsymbol{m} \times \boldsymbol{n}^{\prime}} \boldsymbol{B}=\left[\boldsymbol{b}_{\boldsymbol{i} j}\right]_{\boldsymbol{m} \times \boldsymbol{n}^{\prime}} \) then the
element \( C_{23} \) of the matrix \( C=A+B \)
is:
A \( . C_{23} \)
В. \( a_{23}+b_{32} \)
\( \mathbf{c} \cdot a_{23}+b_{23} \)
D \( \cdot a_{32}+b_{23} \)


Describe the role of rods and cones in
visual perception.


In an experiment to determine the
specific heat capacity of a solid, following observations were made:
Mass of calorimeter + stirrer= \( \boldsymbol{x} \boldsymbol{k} \boldsymbol{g} \)
Mass of water= \( \boldsymbol{y} \boldsymbol{k} \boldsymbol{g} \)
Initial temperature of water \( =t_{1}^{o} C \)
Mass of solid \( =\boldsymbol{z} \boldsymbol{k} \boldsymbol{g} \)
Temperature of solid= \( t_{2}^{o} \boldsymbol{C} \)
Temperature of mixture \( =t^{o} C \) Specific heat capacity of calorimeter
and water are \( c_{1} \) and \( c_{2} \) respectively.
Express the specific heat capacity c of the solid in terms of the above data
A \( \cdot \frac{\left(x c_{1}+y c_{2}\right)\left(t-t_{1}\right)}{z\left(t_{2}-t\right)} \)
B. \( \frac{\left(x c_{1}+y c_{2}\right)\left(t-t_{2}\right)}{z\left(t_{1}-t\right)} \)
c. \( \frac{\left(x c_{1}+y c_{2}\right)\left(t+t_{2}\right)}{z\left(t_{1}+t\right)} \)
D. \( \frac{\left(x c_{1}+y c_{2}\right)\left(t+t_{1}\right)}{z\left(t_{2}+t\right)} \)


\( X \) is an element of the modern periodic table. It is surrounded by elements
having the atomic numbers 17,34,36
and \( \mathbf{5 3} \)
(i) What is the atomic number of \( X ? \)
(ii) Predict its position in the periodic table.
(iii) Which among these do not belong to the same period?


Physical independence of force is a consequence of 'X'. Identify 'X'
A. Newton's third law of motion
B. Newton's second law of motion
c. Newton's first law of motion
D. All of the above


In the long form of periodic table, elements are arranged in the increasing order of :
A. atomic mass
B. atomic number
C. mass number
D. metallic character.


Some equipotential surfaces of the
magnetic scalar potential are shown in
figure. Magnetic field at a point in the
region is:
A \( \cdot 10^{-4} \mathrm{T} \)
B . \( 0.5 \times 10^{-4} \mathrm{T} \)
c. \( 2 \times 10^{-4} \mathrm{T} \)
D. None of these


A survey of people in a given region showed that \( 20 \% \) were smokers. The
probability of death due to lung cancer, given that a person smoked, was 10 times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is \( 0.006, \) what is the probability of death due to lung cancer given that a person is a smoker?
A \( \cdot 1 / 140 \)
в. \( 1 / 70 \)
\( c \cdot 3 / 140 \)
D. \( 1 / 10 \)


Assertion
A transistor amplifier in common emitter configuration has a low input impedance.
Reason
The base to emitter region is forward
biased.
A. Assertion is true, Reason is true; Reason is a correct explanation for Assertion
B. Assertion is true, Reason is true; Reason is not a correct explanation for Assertion
c. Assertion is true, Reason is false
D. Assertion is false, Reason is true


A horizontally oriented tube \( A B \) of length
rotates with a constant angular
velocity \( \omega \) about a stationary vertica
axis \( 00^{\prime} \) passing through the end \( A \) (fig) The tube is filled with an ideal fluid. The
end \( A \) of the tube is open, the closed end
B has a very small orifice. Find the velocity of the fluid relative to the tube as a function of the column 'height' \( \boldsymbol{h} \)
A \( . v=\omega \sqrt{h(l-h)} \)
В . \( v=\omega \sqrt{h(2 l-h)} \)
c. \( v=\omega h \)
D. \( v=\omega \sqrt{2 h(l-h)} \)


\( P C l_{5} \) exists as solid in the form of
\( \left[\boldsymbol{P C l}_{4}\right]^{+}\left[\boldsymbol{P C l}_{6}\right]^{-}, \) and it is a non
conductor of electricity.
A . True
B. False
c. Ambiguous
D. None of the above


The compound used for etching of glass
is:
A. \( H \)
B. HBr
c. нс।
D. нF


If \( \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi}, \) show that \( \sin \left(\frac{\boldsymbol{A}}{\mathbf{2}}\right)+ \)
\( \sin \left(\frac{B}{2}\right)+\sin \left(\frac{C}{2}\right)=1+ \)
\( 4 \sin \frac{\pi-A}{4} \sin \frac{\pi-B}{4} \sin \frac{\pi-C}{4} \)


A mass \( m_{1} \) moves with a great velocity.
It strikes another mass \( m_{2} \) at rest in a
head on collision and comes back along
its path with a low speed after collision. Then :
\( \mathbf{A} \cdot m_{1}>m_{2} \)
В. \( m_{1}=m_{2} \)
\( \mathbf{c} \cdot m_{1}<m_{2} \)
D. there is relation between \( m_{1} \) and \( m_{2} \)


If \( \alpha \) and \( \beta \) are the zeroes of the
polynomial \( 2 y^{2}+7 y+5, \) write the
values of \( \boldsymbol{\alpha}+\boldsymbol{\beta}+\boldsymbol{\alpha} \boldsymbol{\beta} \)


A series \( L C R \) circuit is connected to a
source of alternating emf \( 50 \mathrm{V} \) and if the potential differences across inductor and capacitor are \( 90 \mathrm{V} \) and
\( 60 V \) respectively, the potential
difference across resistor is:
\( \mathbf{A} \cdot 400 V \)
в. \( 40 V \)
\( c .80 V \)
D. \( 1600 V \)


Find \( S_{10} \) if \( a=6 \) and \( d=3 \)
A . 105
B. 95
\( c .195 \)
D. None of these


Cyclohexene on ozonolysis followed by a reaction with zinc dust and water gives
compound (A). Compound (A) is:
\( A \)
B.
\( c \)
D.


Priya bent a plastic wire to form the given figure. The figure is made up of 4 squares and 4 equilateral triangles. Find the length of wire.
A. \( 110 \mathrm{cm} \)
B. \( 90 \mathrm{cm} \)
\( c .100 \mathrm{cm} \)
D. \( 80 \mathrm{cm} \)


Figure shows three spherical and
equipotential surfaces \( A, B \) and \( C \)
around a point charge \( q . \) The potential
difference \( \boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}}=\boldsymbol{V}_{\boldsymbol{B}}-\boldsymbol{V}_{\boldsymbol{C}} . \) If \( \boldsymbol{t}_{1} \)
and \( t_{2} \) be the distances between them,
then :
\( \mathbf{A} \cdot t_{1}=t_{2} \)
в. \( t_{1}>t_{2} \)
c. \( t_{1}<t_{2} \)
\( \mathbf{D} \cdot t_{1} \leq t_{2} \)


Electrons at rest are accelerated by a potential of \( V \) volt. These electrons enter the region of space having a uniform, perpendicular magnetic induction field
B. The radius of the path of the electrons inside the magnetic field is?
A \( \cdot \sqrt{(m e V) / B e} \)
B. \( \sqrt{(2 m e V) / B e} \)
\( \mathbf{c} \cdot \sqrt{(m e V) / 2 B e} \)
D. None of these


In an electrolytic cell:
This question has multiple correct options
A. anode is positively charged
B. cathode is negatively charged
C. oxidation takes place at anode
D. reduction takes place at cathode


is the electronic
configuration of the highest electronegative element.


Cortisol is a:
A . glucocorticoid
B. mineralocorticoid
c. sex hormone
D. none of these


A block mass ' \( m^{\prime} \) is released from rest
at point A. The compression in spring,
when the speed of block is maximum is:
A \( \cdot \frac{m g \sin \theta}{k} \)
B. \( \frac{2 m g \sin \theta}{k} \)
\( c \cdot \frac{m g \cos \theta}{k} \)
D. \( \frac{m g}{k} \)


The common ion effects is shown by which of the following sets of solutions:-
A \( \cdot \) Ва \( a_{2}+B a\left(N O_{3}\right)_{2} \)
в. \( N a C l+H C l \)
c. \( N H_{4} O H+N H_{4} C l \)
D. None


A circular loop of wire is in the same
place as an infinitely long wire carrying a constant current i. Four possible motion of the loop are marked by \( \mathrm{N}, \mathrm{E}, \mathrm{W} \)
and \( \mathrm{S} \) as shown.
A clockwise current is induced in the
loop when loop is pulled towards
\( A \)
B.
\( c \cdot w \)
\( D \)


The converse of the contrapositive of the
conditional \( \boldsymbol{p} \rightarrow \sim \boldsymbol{q} \) is :
A \( . p \rightarrow q \)
в. \( p \rightarrow \sim q \)
\( \mathbf{c} . \sim q \rightarrow p \)
\( \mathbf{D} \cdot \sim p \rightarrow q \)


A ray of light from air suffers partia reflection and refraction at the
boundary of water as shown in the
figure. In Fig, which of the ray is the correct refracted ray?
\( A \cdot A \)
в. \( B \)
\( c \)
\( D \)


\( \left(1+\tan ^{2} \theta\right) \cdot \sin ^{2} \theta= \)
\( \mathbf{A} \cdot \sin ^{2} \theta \)
B \( \cdot \cos ^{2} \theta \)
\( \mathbf{c} \cdot \tan ^{2} \theta \)
\( \mathbf{D} \cdot \cot ^{2} \theta \)


In a Wheatstones's bridge, three resistances \( P, Q \) and \( R \) are connected in the three arms and the fourth arm is
informed by two resistances \( S_{1} \) and \( S_{2} \) connected in parallel. The condition for the bridge to be balanced will be
\( ^{\mathrm{A}} \cdot \frac{P}{Q}=\frac{2 R}{S_{1}+S_{2}} \)
B. \( \frac{P}{Q}=\frac{R\left(S_{1}+S_{2}\right)}{S_{1} S_{2}} \)
c. \( \frac{P}{\bar{Q}}=\frac{R\left(S_{1}+S_{2}\right)}{2 S_{1} S_{2}} \)
D. \( \frac{P}{Q}=\frac{R}{S_{1}+S_{2}} \)


The arithmetic mean of \( 1+\sqrt{2} \) and \( 7+ \) \( \mathbf{5} \sqrt{\mathbf{2}} \) is \( \sqrt{\boldsymbol{a}}+\sqrt{\boldsymbol{b}} . \) Then \( \boldsymbol{a}-\boldsymbol{b}= \)
A . -
B.
\( c \cdot 2 \)
\( D \cdot-2 \)


Which of the following is the most reactive metal?
A. copper
B. Gold
c. silver
D. Francium


For \( N_{3}^{-} \) which statement is wrong.
A . Iso electronic with \( C O_{2} \)
B. \( N H_{2} O H \) and \( N_{3}^{-} \) have same O.N. on nitrogen atom
c. N-N bond length are same
D. \( H N_{3} \) have linear shape


For matrices \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{1} \\ \mathbf{3} & \mathbf{2}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right], \) write \( A+B \) and \( A-B \)


Hydrogen atoms are excited from
ground state to the state of principal quantum number 4. Then, the number of spectral lines observed will be
A . 3
B. 6
\( c .5 \)
\( D \)


The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the
string. The angular amplitude of the pendulum is?
A \( \cdot 90^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 30^{\circ} \)


\( \frac{B D}{B E}=\frac{C D}{C E} \)
A. True
B. False


If the non-zero numbers \( x, y, z \) are \( A P \)
and \( \tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z \) are also in
\( A P, \) then
A. \( x y=y z \)
B \( \cdot z^{2}=x y \)
c. \( x=y=z \)
D . \( x^{2}=y z \)


The number of distinct solutions of
\( \sin 5 \theta \cdot \cos 3 \theta=\sin 9 \theta \cdot \cos 7 \theta \) in \( \theta \in \)
\( [\mathbf{0}, \boldsymbol{\pi} / \mathbf{2}] \) is
\( A \cdot 4 \)
B. 5
\( c \cdot 8 \)
D.


Which out of following cannot produce two coherent source?
A. Lloyd's mirror
B. Fresnel biprism
c. Young's double slitt
D. Prism


Neanderthal man lived in
A. Desert
B. Deep forest
c. Mountains
D. caves


The coefficient of static friction
between the two blocks shown in figure
is \( \mu \) and the table is smooth.What
maximum horizontal force \( F \) can be
applied to the block of mass \( \mathrm{M} \) so that the blocks move together?


Find the Adjoint matrix of the matrix \( \left|\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 2 \\ 3 & 3 & 4\end{array}\right| \)


Show that \( f(x)=(x-1) e^{x}+1 \) is an
increasing function for all \( x>0 \)


Evaluate : \( \int \frac{x^{2}-1}{(x-1)^{2}(x+3)} d x \)


A bead slide freely along a curve wire lying on a horizontal surface at
constant speed as shown in Fig.
a. Draw the vectors representing the force exerted by the wire on the bead at points \( A, B \) and \( C . \)
b. Suppose the bead in fig. speeds up with constant tangential acceleration as it moves towards the right. Draw the vectors representing the force on the bead at point \( A, B, \) and \( C \)


Organic chemistry is basically focused
on:
A. oxygen-containing compounds
B. carbon-containing compounds
c. proteins and enzymes
D. carbohydrates
E. nitrogen-containing compounds


An electron is travelling along the \( x \) direction. It encounters a magnetic field in the ydirection. Its subsequent motion will be
A. straight line along the x-direction
B. a circle in the zx-plane
c. a circle in the yz-plane
D. a circle in the xy-plane


Evaluate \( \int_{0}^{4}(x-2) d x \)


Magnetic field is not associated with
A. a change in uniform motion
B. an accelerated charge.
c. a deaccelerated charge
D. a stationary charge.


\( \cos 20^{\circ} \cos 100^{\circ}+\cos 100^{\circ} \cos 140^{\circ}- \)
\( \cos 140^{\circ} \cdot \cos 200^{\circ} \) is equal to
\( A \cdot \frac{3}{4} \)
B. \( \frac{1}{4} \)
\( c \cdot-\frac{1}{4} \)
D. \( -\frac{3}{4} \)


If \( \alpha \) and \( \beta \) are different complex
numbers with \( |\boldsymbol{\alpha}|=1, \) then what is
\( \left|\frac{\boldsymbol{\alpha}-\boldsymbol{\beta}}{\mathbf{1}-\boldsymbol{\alpha} \overline{\boldsymbol{\beta}}}\right| \) equal to?
\( \mathbf{A} \cdot|\beta| \)
B. 2
\( c . \)
D.


Which of the following statements is true about red blood cells?
A. Protect the body from diseases
B. Carry oxygen to every part of the body
c. Biconcave in shape and have no nucleus
D. Both B and C


\( \int \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{x} \cos \boldsymbol{\theta}+1} \cdot \)
A. \( \frac{1}{\cos \theta} \tan ^{-1} \frac{x-\cos \theta}{\sin \theta} \)
s. \( \frac{1}{\sin \theta} \tan ^{-1} \frac{1-\cos \theta}{\sin \theta} \)
D. \( \frac{1}{\sin \theta} \tan ^{-1} \frac{x-\cos \theta}{\sin \theta} \)
\( \frac{1}{\sin \theta} \tan ^{-1} \frac{x+\cos \theta}{\sin \theta} \)


AT \( 25^{\circ} C, \) a solution containing 0.2 g of polyisobutylene in \( 100 \mathrm{mL} \) of benzene developed a rise of \( 2.4 \mathrm{mm} \) at osmotic equilibrium. The molar mass of polyisobutylene if the density of the solution is \( 0.88 \mathrm{g} / \mathrm{mL} \) is :
A \( \cdot 2.39 \times 10^{5} g m o l^{-1} \)
B . \( 7.36 \times 10^{5} \mathrm{g} \) mol \( ^{-1} \)
c. \( 5.45 \times 10^{5} g \) mol \( ^{-1} \)
D. None of these