If \( \frac{1+4 p}{4}, \frac{1-p}{4}, \frac{1-2 p}{4} \) are probabilities of three mutually exclusive and exclusive and exhaustive events, then the
possible value of \( p \) belong to the set
\( \mathbf{A} \cdot\left(0, \frac{2}{3}\right) \)
В. \( \left[0, \frac{1}{2}\right] \)
\( \mathbf{c} \cdot\left[-\frac{1}{4}, \frac{1}{2}\right] \)
D. \( \left[-\frac{2}{3}, \frac{2}{3}\right] \)


Arrange the following in the increasing strength: \( S<C l<N<O<F \)
if true enter 1 , else enter 0 .


If the complement of an angle is \( 27^{\circ} \)
then find its supplement.


Electric flux over a surface in an electric
field may be:
A. positive
B. negative
c. zero
D. positive, negative, zero


A plane polarized light is incident normally on a tourmaline plate. Its \( \overrightarrow{\boldsymbol{E}} \)
vectors make an angle of \( 60^{\circ} \) with the
optic axis of the plate. Find the percentage difference between initial and final intensities.
A . \( 25 \% \)
B . 50\%
c. \( 75 \% \)
D. 90\%


Find the image of :
(-2,3,4) in the \( y z \) -plane


If \( \mathrm{M} \) is the molarity, d is the density (in
\( g / m !), M_{B} \) is the molar mass of solute and \( m \) is the molality, then choose the correct relation?
A. \( \frac{1000 M}{1000 d+M \cdot M_{B}}=m \)
в. \( \frac{1000 M}{1000 d-m \cdot M_{B}}=M \)
c. \( \frac{1000 M}{1000 d-M \cdot M_{B}}=m \)
D. \( \frac{1000 M}{1000 d+m . M_{B}}=M \)


f \( f(x)=4-3 x, \) find \( f(-5) \) and \( f(13) \)


For a reaction, where the \( \Delta G^{o}= \)
\( -553.91 k J \) and 2 electrons are
transferred, what will be the \( E_{c e l l}^{o} \) of the reaction?
A . \( -2.87 V \)
В. \( -0.00287 V \)
c. \( 0.00287 V \)
D. \( 2.87 V \)


Find the area of the region bounded by
the curves
\( x^{2}+y^{2}=36 \) and \( y^{2}=9 x \)


n the given, \( \Delta A B C \) has sides \( A B= \) \( \mathbf{7} . \mathbf{5} \mathrm{cm}, \mathbf{A} \boldsymbol{C}=\mathbf{6 . 5} \mathbf{c m} \) and \( \mathbf{B C}=\mathbf{7} \mathrm{cm} \)
On base \( B C \) a parallelogram \( D B C E \) of
same area as that of \( \Delta A B C \) is
constructed. Find the height \( D F \) of the
parallelogram.
\( 4.7 \mathrm{cm} \)
в. 5 ст
\( c .3 \mathrm{cm} \)
\( 0.2 \mathrm{cm} \)


Braille system is categorized under:
A. non optical aids
B. optical aids
C. both \( A \) and \( B \)
D. none of these


toppr
Q Type your question_
1.
of certain molarity was added gradually. The mass of precipitate produced (in g)
were measured and it was plotted
against volume of \( A g N O_{3} \) solution
added (in ml). Its known that \( A g I \) is
precipitated first. Precipitation of \( \boldsymbol{B} \boldsymbol{r} \)
does not start until the already
precipitating \( \boldsymbol{I}^{-} \) precipitates
completely. Find out the value of \( \boldsymbol{A B} \times \)
CD where:
\( A B= \) Atomic weight of metal \( M \)
\( C D= \) Mole percent of \( N a l \) in original
mixture.
\( \mathbf{A} \cdot 4994 \)
B . 2040
c. 3202
D. 3332


Atmospheric CO2 concentrations have
increased from 280 ppmvin preindustrial times to 365 ppmv today. What is the corresponding increase in the mass of atmospheric carbon? Assume CO2 to be well mixed in the
atmosphere.


\( N a^{+}, K^{+} \) pump is found in membranes of many cells, like nerve cells. It work against electro chemical gradient and involve an integral protein ATP. For each molecule of ATP used
A. 3 ions of \( N a^{+} \) pumped out and \( 2 K^{+} \) are taken in
B. 3 ions of \( N a^{+} \) are taken in and 2 \( K^{+} \) are pumped out.
C. 2 ions of \( N a^{+} \) are thrown out and \( 3 K^{+} \) are absorbed.
D. 3 ions of \( K^{+} \) are absorbed and 3 \( N a^{+} \) are pumped out


Given below is a list of different steps (i
vi) involved in respiration.
(i) Utilisation of \( O_{2} \) by the cells for catabolic reactions
(ii) Transport of gases by the blood
(iii) Pulmonary ventilation by which
atmospheric air is drawn in and \( C O_{2} \) is released out
(iv) Release of resultant \( C O_{2} \)
(v) Diffusion of \( O_{2} \) and \( C O_{2} \) between
blood and tissues
(vi) Diffusion of gases \( \left(O_{2} \text { and } C O_{2}\right) \)
across alveolar tissues.

Select an option which has correct
sequence of all the steps.
A \( . \) (iii), (vi), (ii), \( (v) \), (i) (ii)
B. (iii), (vi), (i), (v), (ii), (iv)
\( c \cdot(i v),(i i),(v),(i i i),(i),(v i) \)
\( D \cdot(i v),(v i),(i),(v),(i),(\text { iii }) \)


A molecule \( \boldsymbol{H}-\boldsymbol{X} \) will be \( 50 \% \) ionic if
electronegativity difference of \( \boldsymbol{H} \) and \( \boldsymbol{X} \)
is:
A . 1.2 ev
B. \( 1.4 \mathrm{eV} \)
c. \( 1.5 \mathrm{ev} \)
D. 1.7 ev


\( \ln \) an \( A P, \operatorname{given} a=2, d=8, S_{n}=90 \)
find \( n \) and \( a_{n} \)


\( \int \cos x \log \left(\tan \frac{x}{2}\right) d x= \)
\( A \cdot \sin x \log |\tan x|-x+c \)
B. \( -\sin x \log \left|\tan \frac{x}{2}\right|+x+c \)
\( \mathbf{c} \cdot-\sin x \log \left|\tan \frac{x}{2}\right|-x+c \)
\( \mathbf{D} \cdot \sin x \log \left|\tan \frac{x}{2}\right|-x+c \)


The area of the region bounded by \( 3 x \pm \)
\( 4 y \pm 6=0 \) in sq.units is
\( A \cdot 3 \)
в. 1.5
c. 4.5
D. 6


Gas \( A \) (molar mass 16 ) and \( \operatorname{gas} B \)
(molar mass 4 ) are confirmed in a
vessel at partial pressure of 2 atm each at \( 27^{0} C . \) The gases are then allowed to
effuse out at \( 27^{0} C \) through a value till the pressure inside the vessel becomes 2 atm after which the value is closed
and the gases are heated to \( 127^{0} C \) and
allowed to react as \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C} ; \boldsymbol{K}_{\boldsymbol{p}}= \)
\( 0.1 a t m^{-1} . \) The partial pressure of \( C \) at
equilibrium assuming \( C \) is not formed till the effusing process is completed at \( 27^{0} C \) is \( X \) atm. \( X \) is:
A. 0.126
B. 0.177
c. 0.187
D. 0.113


Assertion
Aromatic aldehydes and formaldehyde undergo Cannizzaro reaction.
Reason
Aromatic aldehydes are almost as reactive as formaldehyde.
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


Choose the correct statement from the
following:
This question has multiple correct options
A. Soft iron is used as the core of transformer.
B. The strength of an electromagnet increases when the current in the coil is increased.
C. An electric bell works on the principle of an electromagnet.
D. The direction of a magnetic field due to current in a straight conductor is obtained using right hand grip rule.


Glycerol can be separated from spentlye in soap industry by:
A. crystallisation
B. sublimation
c. differential extraction
D. chromatography
E. distillation under reduced pressure


Air in a sealed syringe is slowly
compressed by moving the piston. The
temperature of the air stays the same. Which statement about the air is
correct?
A. The pressure of the air increases because its molecules now travel more slowly
B. The pressure of the air increases because the area of the syringe walls is now smaller.
C. The pressure of the air increases because its molecules now hit the syringe walls more frequently
D. The pressure of the air increases because its molecules now travel more quickly


Factorize :
\( (2 a+1)^{3}+(a-1)^{3} \)


Eight small droplets of mercury of equal radii are charged to the same potential \( 10 V \). If they coalesce to form one big drop, the potential on big drop is:
A . \( 10 V \)
в. \( 20 V \)
\( c .30 V \)
D. \( 40 V \)


Assertion
The Cl-ionCl-ion is formed, when 'Cl'
Cl' atom loses an electron.
Reason
Anion is form by accepting an electron.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


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


Assertion
In desert area, days get hot fastly and the nights get cold fastly.
Reason
The specific heat capacity for air and land is less than of water.
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


How many chlorine atoms are present in chloretone?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Which of the following is/are source(s) of internal radiations?
A. Solar radiations
B. Radioactive substances present inside the body
c. Beta radiations
D. Naturally occurring radioactive substances


Which of the following species has
planar geometry?
A \( \cdot C l O_{2}^{-} \)
в. \( N_{2} H_{4} \)
c. \( C H_{2}=N H \)
D. NF


A broadcasting station transmits waves
of frequency \( 71 \times 10^{4} H z \) with a speed
of \( 3 \times 10^{8} m / s . \) The wavelength of the
wave is :
A \( .418 .8 m \)
в. \( 324.6 m \)
c. \( 208.4 m \)
D. \( 422.5 \mathrm{m} \)


Find the modulus and the principal value of the argument of the number
\( 1-i \)
A \( \cdot \sqrt{2}, \pi / 4 \)
B \( \cdot \sqrt{2},-\pi / 4 \)
c. \( \sqrt{2},-\pi / 3 \)
D. \( \sqrt{2}, 3 \pi / 4 \)


\( \mathrm{DE}=\mathrm{FE} \)


Assertion
First period of periodic table is the shortest period.
Reason
K shell can accommodate a maximum
of two electrons
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.


How many sigma bonds are present in \( \boldsymbol{C H} \boldsymbol{C l}_{3} ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


If Rs. 250 amounts to Rs. 285 in 2 years
find the rate per cent per annum.


The sum of 12 terms of an A.P., whose
first term is \( 4, \) is \( 256 . \) What is the last
term?
A . 35
B. 36 6
\( c .37 \)
D. None


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is a function which is
defined by \( f(x)=\max \left\{x, x^{3}\right\} . \) The set of all points on which \( f(x) \) is not differentiable
is
A \( \cdot\{-1,1\} \)
the
B. \{-1,0\}
\( c \cdot(0,1) \)
D. \{-1,0,1\}


Which of the following polymers of glucose is stored by animals?
A. Cellulose
B. Amylose
c. Amylopectin
D. Glycogen


The length, breadth and height of a
cuboid are in the ratio \( 6: 5: 3 . \) If the
total surface area is \( 504 \mathrm{cm}^{2} \), find its
dimension. Also find the volume of the
cuboid.


The small projections present on the surface of pineapple fruit represent
A. Persistent styles
B. Persistent stamens
c. Persistent calyx
D. Persistent bracts


Planet moves in an elliptical orbit around one of the foci. The ratio of
maximum velocity \( V_{\max } \) and minimum
velocity \( V_{\min } \) ansd eccentricity e of the
ellipse is given by
A \( \cdot \frac{1-e}{1+e e} \)
В \( \cdot \frac{e-e}{e+e e} \)
c. \( \frac{1+e}{1-e-e} \)
D. \( \frac{e}{e-e} \)


A particle \( A \) moves along a circle of
radius \( R=50 \mathrm{cm} \) so that its radius
vector \( r \) relative to the point \( O \) (figure)
rotates with the constant angular
velocity \( \omega=0.40 \) rad \( / \) s. Then
magnitude of the velocity of the
particle, and the magnitude of its total acceleration will be
A \( \cdot v=0.4 \mathrm{m} / \mathrm{s}, a=0.4 \mathrm{m} / \mathrm{s}^{2} \)
B . \( v=0.32 \mathrm{m} / \mathrm{s}, a=0.32 \mathrm{m} / \mathrm{s}^{2} \)
C \( \cdot v=0.32 \mathrm{m} / \mathrm{s}, a=0.4 \mathrm{m} / \mathrm{s}^{2} \)
D. \( v=0.4 \mathrm{m} / \mathrm{s}, a=0.32 \mathrm{m} / \mathrm{s}^{2} \)


Four conductors of resistance 4,3,9
and 6 ohm are connected in \( A B, B C, C D \) and DA arms of a Wheatstone bridge. The bridge can be balanced by connecting.
A. \( 1) 6 \) ohm in series with 3 ohm conductor
B. 2) 4 ohm in parallel with 6 ohm conductor
c. 3 ) 3 ohm in series with 3 ohm conductor
D. 4 ) 5 ohm in series with 6 ohm conductor


The graph of velocity vs. time of a moving particle plotted at right. How do the acceleration and displacement of
the particle at point \( B \) compare to the acceleration and displacement of the particle at point \( \mathbf{A} \) ?
A. Acceleration is less, displacement is less
B. Acceleration is less, displacement is the same
C. Acceleration is less, displacement is greater
D. Acceleration is greater, displacement is less
E. Acceleration is greater, displacement is greater


The value of determinant \( \left|\begin{array}{lll}\mathbf{1} & \boldsymbol{x} & \boldsymbol{y}+\boldsymbol{z} \\ \mathbf{1} & \boldsymbol{y} & \boldsymbol{z}+\boldsymbol{x} \\ \mathbf{1} & \boldsymbol{z} & \boldsymbol{x}+\boldsymbol{y}\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( x+y+z \)
c. \( 1+x+y+z \)
D. \( (x-y)(y-z)(z-x) \)


In bugs and cockroaches (insects), the sex determinations takes place by
A. \( x x \) and \( x o \) chromosomes
B. \( x x \) and \( x \) y chromosomes
c. zz - zw chromosomes
D. zo - zz chromosomes


Two solutions labelled as \( 3 \mathrm{M} \) HCl and 1
M HCl are mixed in the ratio of \( x: y \) by
volume and the molarity of mixture solution becomes 1.5 M. What is the
molarity of the resulting solution if they
are mixed in the ratio of \( y: x \) by volume
\( ? \)
A. 4 м
в. 3 м
c. 2 м
D. 2.5 М


Ethanol-Water mixture(95\% by volume of ethanol) forms:
A. maximum boiling azeotrope
B. minimum boiling azeotrope
c. solution which shows negative deviation
D. ideal solutions


The radius of curvature of a convex
mirror is \( 40 \mathrm{cm} . \) Find its focal length
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. \( 40 \mathrm{cm} \)
\( \mathrm{c} \cdot 20 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Find the later surface area and total
surface area of the following right
prisms.


Which of the following statements is
true for \( \boldsymbol{I} \boldsymbol{O}_{2} \boldsymbol{F}_{2}^{-} ? \)
A. The electrons are located at the corners of a trigonal bipyramidal but one of the equatorial pairs is unshared
B. It has \( s p^{3} d \) hybridisation and is \( T \) - shaped
C . Its structure is analogous to \( S F_{4} \)
D. (A) and
(C) both


KCI can be used in salt bridge as
electrolyte in which of the following
cells?
\( \mathbf{A} \cdot Z n\left|Z n C l_{2} \| A g N O_{3}\right| A g \)
B . \( P b\left|P b\left(N O_{3}\right)_{2} \| C u\left(N O_{3}\right)_{2}\right| C u \)
c. \( C u\left|C u S O_{4} \| A u C l_{3}\right| A u \)
D. \( F e\left|F e S O_{4} \| P b\left(N O_{3}\right)_{2}\right| P b \)


If \( z_{1}=3+4 i, z_{2}=2-i \) find \( z_{2}-z_{1} \)
A . -1-5
B. 2-5
\( c \cdot 1+5 i \)
D. 1-5


\( (1+x y) \frac{d y}{d x}+y^{3}=0 y(0)=1 \) Find \( k \) if
the constant in the solution is \( \frac{k}{e} \)


If the forward voltage in a semiconductor diode is changed from \( 0.5 V \) to \( 0.7 V, \) then the forward current
changes by \( 1.0 m A . \) The forward resistance of diode junction will be
\( \mathbf{A} \cdot 100 \Omega \)
в. \( 120 \Omega \)
c. \( 200 \Omega \)
D. 240\Omega


Decarboxylation is involved in the
A. Electron transport system
B. Glycolysis
c. Krebs cycle
D. Lactic acid fermentation


Evaluate the following limits.
\[
\lim _{x \rightarrow \infty}(((x+1)(x+2)(x+3)(x+4)
\]


Assertion
Kerogen is converted into liquid and gaseous hydrocarbons via a process known as catagenesis.
Reason
Kerogen is a waxy material obtained from inorganic matter
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
Bond angle of \( \boldsymbol{H}_{2} \boldsymbol{S} \) is smaller than \( \boldsymbol{H}_{2} \boldsymbol{O} \)
Reason
As the electronegativity of the central atom increases, bond angle 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


Assertion
Gold occurs in native state.
Reason

Gold dissolves in aqua-regia.
Choose the correct option:
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


When the length of a microscope tube increases, its magnifying power:
A. decreases
B. increases
c. does not change
D. can't say


Assertion(A): \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by
\( f(x)=(x-9)(x-10)(x-11) \) is onto
but not one one
Reason \( (\mathrm{R}): \) If \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} ; \boldsymbol{x}_{1}, \boldsymbol{x}_{2} \in \boldsymbol{A} \) and
\( \boldsymbol{f}\left(\boldsymbol{x}_{1}\right) \neq \boldsymbol{f}\left(\boldsymbol{x}_{2}\right) \Rightarrow \boldsymbol{x}_{1}=\boldsymbol{x}_{2}, \) then \( \boldsymbol{f} \) is
one-one.
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not correct explanation of
c. A is true but R is false
D. A is false but R is true


For production of methane, methanogens
A. Oxidise carbon dioxide
B. Reduce carbon dioxide
c. Reduce alcohol
D. oxidise alcohol


Which set does not show correct
matching?
A \( \cdot S c^{3+}:[N e] 3 s^{2} 3 p^{6}: \) zero group
B . \( F e^{2+}:[A r] 3 d^{6} \) : VIII group
C \( \cdot C r:[A r] 3 d^{5} 4 s^{1}: \) VIB group
D. All of the above


Q Type your question
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
\( D \)


Which of the following statements is
not correct?
A. Taking in of oxygen is inhalation.
B. Taking in of carbon dioxide is inhalation
C. Breathing rate is number of inhalation and exhalation in one minute.
D. Giving out of carbon dioxide is exhalation.


A gas bulb is filled with \( N O_{2} \) gas and
immersed in an ice bath at \( 0^{\circ} \mathrm{C} \) which
becomes colourless after some time.
This colourless gas will be:
A \( \cdot N O_{2} \)
в. \( N_{2} \),
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \)
D. \( N_{2} O_{5} \)


The pH of the solution produced when an aqueous solution of strong acid pH 5 is mixed with equal volume of an aqueous solution of a strong acid of pH
3 is:
A. 3.3
B. 3.5
\( c \cdot 4.5 \)
D. 4.0


Evaluate the following integral:
\( \int \frac{e^{x}}{\sqrt{16-e^{2 x}}} d x \)


Assertion (A): The displacement time graph for a particle in SHM begins from mean position. Reason
(R): The displacement of a particle in SHM is given by \( y=A \sin \omega t \)
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of
C. A is true and R is false
D. A is false and R is true


When a body is whirled in a circle, the work done on it is
A. Positive
B. Negative
c. zero
D. Infinite


S.I. unit of momentum is :
A. \( k g . m s^{-1} \)
в. \( k g . m g^{-2} \)
\( \mathrm{c} \cdot k g, m g^{2} \)
D. \( k g, m^{-1} s^{-1} \)


A \( 10 \mu F \) condenser is charged to a potential of 100 volt. It is now connected to another uncharged condenser. The common potential reached is 40 volt. The capacitance of second condenser is
A \( .2 \mu F \)
в. \( 10 \mu F \)
c. \( 15 \mu F \)
\( \mathbf{D} \cdot 22 \mu F \)


The condition for obtaining secondary maxima in the diffraction pattern due to single slit is (symbols have their usual meaning)
\( A \cdot a \sin \theta=n \lambda \)
B. \( a \sin \theta=(2 n-1) \frac{\lambda}{2} \)
\( c \cdot a \sin \theta=(2 n-1) \lambda \)
D. \( a \sin \theta=\frac{n \lambda}{2} \)


If \( a_{1}, a_{2}, a_{3}, \dots \dots \dots \) be in \( A . P . \) such that
\( \boldsymbol{a}_{1}+\boldsymbol{a}_{5}+\boldsymbol{a}_{10}+\boldsymbol{a}_{15}+\boldsymbol{a}_{20}+\boldsymbol{a}_{24}=\mathbf{2 2 5} \)
then the sum of first 24 terms of the
A.P is


Earthing is provided in buildings to
protect it form
A . lightning
B. leakage of electric current
c. cyclone
D. thunderstorm


Explain \( e . f . \) due to a uniformly charged
plane sheet


A diver reaches a depth of 300 m. The pressure (in atm) exerted by water at
that depth is \( 2.94 \times 10^{x} . \) (in Pascal).
Take \( g=9.8 m / s^{2} . \) Find \( x \)


A negatively charged ebonite rod is brought near the glass rod which has been robbed on silk. State your
observation between them
A . Attraction
B. Repulsion
c. No change
D. cant say


The fourth term in the expansion of \( \left(p x+\frac{1}{x}\right)^{n} \) is \( \frac{5}{2} . \) Then
This question has multiple correct options
\( \mathbf{A} \cdot n=6 \)
B . \( n=7 \)
c. \( p=\frac{1}{2} \)
D. \( p=\frac{1}{4} \)


If \( \boldsymbol{f}(\boldsymbol{x})=\int_{0}^{\sin \boldsymbol{x}} \cos ^{-1} \boldsymbol{t} \boldsymbol{d} \boldsymbol{t}+ \)
\( \int_{0}^{\cos x} \sin ^{-1} t d t, 0<x<\frac{\pi}{2} \)
then \( f\left(\frac{\pi}{4}\right) \) is?
A \( \cdot \frac{\pi}{\sqrt{2}} \)
B \( \cdot 1+\frac{\pi}{2 \sqrt{2}} \)
c.
D. none of these


A point moves on the \( x-y \) plane
according to the law \( x=a \sin \omega t \) and
\( \boldsymbol{y}=\boldsymbol{a}(\mathbf{1}-\cos \boldsymbol{\omega} \boldsymbol{t}) \) where \( \boldsymbol{a} \) and \( \boldsymbol{\omega} \) are
positive constants and \( t \) is in seconds.
Find the distance covered in time \( t_{0} \)
A \( . a \omega t_{0} \)
B. \( \sqrt{2 a^{2}+2 a^{2} \cos \omega t_{0}} \)
\( ^{\mathrm{C}} 2 a \sin \frac{\omega t_{0}}{2} \)
D. \( 2 a \cos \frac{\omega t_{0}}{2} \)


For the reaction \( 2 A+3 B \rightarrow \) products,
\( A \) is taken in excess and on changing the concentration of \( \mathrm{B} \) from \( 0.1 \mathrm{M} \) to 0.4
M, the rate becomes doubled. Thus, the rate law of the reaction is:
A \( \cdot \frac{d x}{d t}=k[A]^{2}[B]^{2} \)
в. \( \frac{d x}{d t}=k[A][B] \)
\( \stackrel{d x}{d t}=k[A]^{0}[B]^{2} \)
D. \( \frac{d x}{d t}=k[B]^{1 / 2} \)


The ionization constant of ammonium
hydroxide is \( 1.77 \times 10^{-5} \) at \( 298 K \)
Hydrolysis constant of ammonium chloride is
A \( .5 .65 \times 10^{-12} \)
B . \( 5.65 \times 10^{-10} \)
c. \( 6.50 \times 10^{-12} \)
D. \( 5.65 \times 10^{-13} \)


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


Compute \( \lim _{x \rightarrow 2+}([x]+x) \) and \( \lim _{x \rightarrow 2-}([x]+ \)
\( \boldsymbol{x}) \)


A conductor \( A B \) of length \( L \) carrying a
current \( I^{\prime} \) as shown in figure. The force
on \( A B \) has magnitude
\( ^{\text {A }} \cdot \frac{\mu_{0} I^{\prime} I}{2 \pi} \log 2 \)
В. \( \frac{\mu_{0} I^{\prime} I}{2 \pi} \log 3 \)
\( ^{\text {c. }} \frac{3 \mu_{0} I^{\prime} I}{2 \pi} \log \frac{3}{2} \)
D. \( \frac{2 \mu_{0} I^{\prime} I}{3 \pi} \)


ABC is an equilaterial triangle with side
\( a . A \) point \( P \) is taken inside ABC. The sum of lengths of perpendiculars from to all the sides is
A. greater than altitude from A to BC
B. less than altitude form A to BC
c. equal to altitude from A to BC
D. can't he determined


A ray of light travelling in air is incident on the plane of a transparent medium.
The angle of incident is \( 45^{0} \) and that of
refraction is \( 30^{0} . \) The refractive index of
the medium with respect to air is:
A .2
в. \( \frac{1}{\sqrt{2}} \)
c. \( 2 \sqrt{2} \)
D. \( \sqrt{2} \)


Two thermometers are used to record
the temperature of a room. If the bulb of
one is wrapped in wet hanky:
A. The temperature recorded by both will be same.
B. The temperature recorded by the wet-bulb thermometer will be greater than that recorded by the other
C. The temperature recorded by dry-bulb thermometer will be greater than that recorded by the other
D. None of the above


What are the products of hydrolysis of
sugar?


How do nitric oxide molecules cause
ozone depletion?


Factorize:
\( 4 a^{2} b-9 b^{3} \)
\( \mathbf{A} \cdot b(2 a+3 b)(2 a+3 b) \)
B. \( b(2 a+3 b)(a-3 b) \)
\( \mathbf{c} \cdot b(a+3 b)(2 a-3 b) \)
D. \( b(2 a+3 b)(2 a-3 b) \)


\( 30 \% \) passengers from a train got down at station \( A, 70 \% \) of the remaining got
down at station \( B \). If there are still 1050
passengers in the train, how many passengers were there before stations
\( A, \) provided no one boarded the train at
station \( A \) and \( B ? \)
A . 10,000
B. 5,000
c. 2000
D. 1000


The perimeter of a parallelogram is 150
\( \mathrm{cm} \) and one of its side is greater than
the other by \( 25 \mathrm{cm} . \) Find the lengths of all the sides of that parallelogram


Which one of the following is an example of buffer system in blood?
A. Haemoglobin and oxyhaemoglobin
B. Oxygen and carbon dioxide
c. Albumin and globulin
D. Sodium bicarbonate and carbonic acid


Black sweaters are effective than
white sweaters.
A . less
B. equally
c. more
D. Can't be determined


The resin duct of a gymnosperm stem is an example of
A. Schizogenous cavity
B. Lysigenous cavity
c. Big vacuole
D. Interecellular space


A particle moving on a curve has the
position given by \( \boldsymbol{x}=\boldsymbol{f}^{\prime}(\boldsymbol{t}) \sin \boldsymbol{t}+ \)
\( f^{\prime \prime}(t) \cos t, y=f^{\prime}(t) \cos t-f^{\prime \prime}(t) \sin t \) at
time \( t \) where \( f \) is a thrice-differentiable function.Then the velocity of the particle
at time \( t \) is
\( \mathbf{A} \cdot f^{\prime \prime \prime}(t) \)
B . \( f^{\prime}(t)+f^{\prime \prime \prime}(t) \)
c. \( f^{\prime}(t)+f^{\prime \prime}(t) \)
D. \( f^{\prime}(t)-f^{\prime \prime \prime}(t) \)


A metal oxide has the formula \( M_{2} O_{3} \). It
can be reduced by \( \boldsymbol{H}_{2} \) to give free metal
and water. \( 0.15 \% \) g of \( M_{2} O_{3} \) required 6
mg of \( \boldsymbol{H}_{2} \) for complete reduction. The
atomic mass of the metal is:
A. 27.9
B. 79.8
\( c . \) 55.8
D. 159.8


Which of the following has \( s p^{2} \)
hydridization?
\( A \cdot S O_{2} \)
в. \( H_{2} \) о
c. \( N H_{3} \)
\( \mathrm{D} \cdot \mathrm{SO}_{3}^{2-} \)


Colour of Bougainvillea is due to
A. Coloured sepals
B. Coloured bracts
c. Coloured petals
D. None of the above


A fish looking up through the water sees the outside world in a circular horizon. If
the refractive index of water is \( 4 / 3 \) and
the fish is \( 12 m \) below the surface, the
radius of the circle in \( \mathrm{cm} \) is
A. \( 36 \sqrt{7} \)
в. \( \frac{36}{\sqrt{7}} \)
c. \( 36 \sqrt{5} \)
D. \( 4 \sqrt{5} \)


Let \( \boldsymbol{I}= \)
\( \int_{-a}^{a}\left(p \tan ^{3} x+q \cos ^{2} x+r \sin x\right) \)
dx, where \( p, q, r \) are arbitrary
constants.
The numerical value of \( I \) depends on?
A \( . p, q, r, a \)
B. \( q, r, a \)
\( c \cdot q, a \)
\( \mathbf{D} \cdot p, r, a \)


Which of the following is the most toxic excretory product?
A. \( C O_{2} \)
B. Ammonia
c. urea
D. Amino acids


How is methoxyethane prepared from:
(a) Methyl iodide
(b) Diazomethane


A force \( \vec{F}=4 \hat{i}+6 \hat{j}+3 \hat{k} \) acting on a particle produces a displacement of \( \vec{S}= \) \( 2 \hat{i}+3 \hat{j}+5 \hat{k} \) where \( F \) is expressed in
Newtonn and \( S \) in the metre. Find the
work done by the force.


Which of the particles would move to
the right?
A. I and II only
B. I and III only
c. II and III only
D. II only
E. I only


Find the reminder when \( x^{3}+3 x^{2}+1 \) is
divided by \( x^{3}+3 x^{2} \)
\( \mathbf{A} \cdot x+1 \)
B . \( x-\frac{1}{2} \)
c. \( x \)
D.


Transcription unit
A. starts with TATA box
B. starts-with pallendrous regions and ends with rho factor
C. starts with promoter region and ends in terminator region
D. starts with CAAT region


The position of a particle is given by \( s=t^{3}-6 t^{2}-15 t \) where \( s \) in metres, \( t \)
is in seconds. If the particle is at rest,
then time \( t=\dots . \)
A . 5
B.
\( c .5,1 \)
D.


How much percentage of fresh water is present in the world?
A . 97.
B. 2.5
\( c .30 \)
D. 40


Aqueous solutions of hydrogen sulphide and sulphur dioxide when mixed
together yield :
A. Sulphur trioxide and water.
B. Presence of \( d \) -orbital.
c. Sulphur and water.
D. Hydrogen preroxide and sulphur.


If \( (4)^{x+y}=1 \) and \( (4)^{x-y}=4 \) then the
values of \( x \) and \( y \) will be respectively
A \( \cdot \frac{1}{2} \) and \( -\frac{1}{2} \)
B \( \cdot \frac{1}{2} \) and \( \frac{1}{2} \)
c. \( -\frac{1}{2} \) and \( -\frac{1}{2} \)
D. \( -\frac{1}{2} \) and \( \frac{1}{2} \)


Assertion
An ionic solid is a good conductor of electricity.
Reason
An ionic solid is composed of positive and negative ions joined together by
electrostatic forces.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


Reduce each of the following differentia equations to the variables separable
\( i \) ) \( 1+\frac{d y}{d x}= \)
form and hence solve.
\( \operatorname{cosec}(\boldsymbol{x}+\boldsymbol{y}) \)
ii) \( (x-y)^{2} \frac{d y}{d x}=a^{2} \)


Assertion
DDT shows biological magnification.
Reason

UV radiation causes ozone depletion.
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


In the given figure, find
\( \angle M N R \)


Rainbow is not caused due to:
A. Reflection of light
B. Refraction of light
C. Dispersion
D. Scattering


The minimum value of \( f(x)=\mid 2 x+ \)
\( \mathbf{5} \mid+\mathbf{6} \) is:
A . 2
B. 3
c. 5
D. 6
E . 8


Arhenius equation is not applicable for:
A . first order reactions
B. second order reactions
c. zero order reaction
D. radioactive decay


Find the area under the curve \( \boldsymbol{y}= \)
\( \left(x^{2}+2\right)^{2}+2 x \) between the lines \( x=0 \)
\( x=2 \) and the \( X \) -axis


The sum of the values of k for which the
roots are real and equal of the following equation \( 4 x^{2}-2(k+1) x+(k+4)=0 \) is


Which one is the most abundant protein
in the animal world
A. Trypsin
B. Haemoglobin
c. collagen
D. Insulin


The wave front is a surface in which:
A. All points are in the same phase
B. There is a pair of points in opposite phase
C there is a pair of points with phase difference \( \left(\frac{\pi}{2}\right) \)
D. There is no relation between the phase


A bulb of \( 2.5 V, \) draws a current of \( 0.5 A \) If the bulb is switched on for 2 minutes,
calculate the energy released by the
bulb.
A . \( 1.25 . J \)
в. \( 260 J \)
c. \( 5 . J \)
D. \( 150 J \)


The probabilites of three events \( \boldsymbol{A}, \boldsymbol{B} \)
and \( C \) are \( P(A)=0.6, P(B)=0.4 \) and
\( \boldsymbol{P}(\boldsymbol{C})=\mathbf{0 . 5 .} \). If \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})= \)
\( \mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{C})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \boldsymbol{C})= \)
0.2 and \( P(A \cup B \cup C) \geq 0.85, \) then
A \( \cdot 0.2 \leq P(B \cap C) \leq 0.35 \)
B . \( 0.5 \leq P(B \cap C) \leq 0.85 \)
c. \( 0.1 \leq P(B \cap C) \leq 0.35 \)
D. None of these


State the condition to get interference
pattern


The efficiency of a heat engine if the temperature of source \( 227^{0} C \) and that
of \( \operatorname{sink} \) is \( 27^{0} C \) nearly
A. 0.4
B. 0.5
\( c \cdot 0.6 \)
D. 0.7


In the figure shown, a T-shaped conductor moves with constant angular
velocity \( \omega \) in a plane perpendicular, to uniform magnetic field \( \vec{B} \). The potential
difference \( V_{A}-V_{B} \) is
A. zero
в.
\[
\frac{1}{2} B \omega l^{2}
\]
c. \( 2 B \omega l^{2} \)
D. B\omega \( l^{2} \)


The device known as prolong is used in the extraction of :
\( A \cdot z n \)
B. Agg
\( c \cdot c u \)
D. Fe


Discuss with theory the method of inducing emf in a coil by changing its orientation with respect to the direction of the magnetic field.


Consider the statements about
cellulose.
I. It is the principle structural component of vegetable matter.
II. Wood has \( 40-50 \% \) cellulose.
III. Cotton has \( 90 \% \) cellulose.
IV. Cellulose is formed in the
photosynthesis process. The incorrect statements is/are:
A. only I
B. only II and III
c. only I, Il and IV
D. none of the above


A satellite of mass \( 250 k g \) is orbiting the Earth a height of \( 500 k m \) above the
surface of Earth. How much energy
must be expended to rocket the satellite out of the gravitational influence of the Earth ? Given mass of
the Earth \( =6.0 \times 10^{24} \) kgradius of the
Earth \( =6400 \mathrm{km} ; \) and \( \mathrm{G}=6.67 \mathrm{x} \)
\( 10^{-11} N m^{2} k g^{-2} \)


A uniform disc of radius \( R \) is put over
another uniform disc of radius \( 2 R \)
made of same material having same thickness. The peripheries of the two discs touches each other. Locate the
centre of mass of the system taking centre of large disc at origin.


Which of the following biologists has been dubbed as the architect of molecular biology?
A. Francis Crick
B. Frederick Sanger
c. Jacques Lucien Monod
D. James Watson


A wire loop is formed by joining two sections of radil \( r \) and \( r \) subtending an angle at o The magnetic field at 0 is \( B \)


Statements that are true of transition
and inner transition metals are :
This question has multiple correct options
A. osmium is the heaviest transition metal
B. \( C u^{+}\left(3 d^{10}\right) \) is more stable than \( C u^{2+}\left(3 d^{9}\right) \) in aqueous medium
C . actinides are generally strong reducing agents
D. \( Y, L a \) and \( A c \) exhibit variable valency


Which of the following are properties of Iyophilic sols? This question has multiple correct options
A. Cannot be prepared by direct mixing and requires special methods
B. Viscosity is more than that of solvent
c. Particles are highly solvated
D. Irreversible


adod
\( \operatorname{In} \Delta A B C, \angle A=90^{\circ} \) and \( A D \perp B C \)
Then, \( \Delta A B C \sim \Delta D A C \)
A. True
B. False


Jet plane is traveling west at the speed of \( 1800 \mathrm{km} / \mathrm{h} \). What is the voltage difference developed between the ends of the wing \( 25 \mathrm{m} \) long, if the earth's magnetic field at the location has a magnitude of \( 5 \times 10^{-4} \) and the dip
angle is 30
A. 0
B. 3.12 \( v \)
\( c \cdot 10.20 v \)
D. 50 v


Select correct statements:
Bond order of:
This question has multiple correct options
\( \mathbf{A} \cdot H e_{2} \) is zero
B. \( H e_{2}^{+} \) is 0.5
\( \mathbf{c} \cdot H e_{2}^{2+} \) is 1.0
D. \( B e_{2} \) is zero


In the Venn diagram, the universal set, \( \boldsymbol{\xi}=\boldsymbol{P} \cup \boldsymbol{Q} \cup \boldsymbol{R} \)
Which of the four regions labelled \( A, B, C \)
and D represents the sets \( \boldsymbol{P} \cap \boldsymbol{Q} \cap \boldsymbol{R} \) ?
\( A \)
B
\( c . c \)
\( D \)


8
8
8
8
8


A mixture of sand and salt can be
separated by:
A. Sublimation
B. Sieving
c. Dissolving salt and sand mixture in water and then filtration
D. Dissolving salt in water and then distillation


A block of mass \( m_{1} \) is resting on a
rough horizontal plane, coefficient of kinetic friction between block and
surface is \( \mu . \) If \( m_{1} \) is connected to
another mass \( m_{2} \) with the help of string
and pulley as shown in figure, then the common acceleration when the system
is released from rest will be:
A \( \cdot \frac{m_{2} g}{m_{1}+m_{2}} \)
B. \( \left[\frac{m_{2}-m_{1}}{m_{1}+\mu m_{2}}\right] g \)
C. \( \frac{\mu\left(m_{2}+m_{1}\right)}{m_{1}+m_{2}} g \)
\( \mathbf{D} \cdot\left[\begin{array}{l}\frac{m_{2}-\mu m_{1}}{m_{1}+m_{2}} \\ g\end{array}\right] \)


Solve \( \int_{\frac{\pi}{4}}^{\frac{\pi}{2}}(2 \sin x-\cos 5 x) d x \)


While performing the experiment to trace the path of a ray of light passing through a glass prism, four students marked the incident ray and the emergent ray in their diagrams in the manner shown below.

The correct path of the rays has been
shown by:


Fuel with highest calorific value is:
A \( \cdot C O_{2} \)
в. \( C O+H_{2} \)
c. \( C O+N_{2} \)
D. coal gas


\( h \)


A circular disc rolls on a horizontal floor
without slipping and the centre of the disc moves with a uniform velocity \( v \)
Which of the following values of the velocity at a point on the rim of the disc can have?
This question has multiple correct options
\( A \)
В. \( -v \)
\( c \cdot 2 v \)
D.


If \( 10 g \) of ice is added to \( 40 g \) of water at
\( 15^{\circ} \mathrm{C}, \) then the temperature of the
mixture is (specific heat of water= \( 4.2 \times 10^{3} J k g^{-1} K^{-1}, \) Latent heat of
fusion of ice \( =\mathbf{3 . 3 6} \times \mathbf{1 0}^{\mathbf{5}} \boldsymbol{J} \mathbf{k g}^{-\mathbf{1}} \mathbf{)} \)
A \( \cdot 15^{\circ} \mathrm{C} \)
В. \( 12^{\circ} \mathrm{C} \)
\( c \cdot 10^{\circ} C \)
D. \( 0^{\circ} \mathrm{C} \)


If \( \sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1, \) then find
the value of \( x \)
A . -1
B.
\( c \cdot \frac{1}{5} \)
D.


Two points \( (a, 3) \) and \( (5, b) \) are the opposite vertices of a rectangle. If the other two vertices lie on the line \( y= \)
\( 2 x+c \) which also passes through the
point \( (\boldsymbol{a} / \boldsymbol{c}, \boldsymbol{b} / \boldsymbol{c}) \) then what is the value
of c?
This question has multiple correct options
A \( \cdot 2 \sqrt{2}+1 \)
B. \( 2 \sqrt{2}-1 \)
c. \( 1-2 \sqrt{2} \)
D. \( -1-2 \sqrt{2} \)


What is the maximum precision with which the momentum of an electron
can be known if the uncertainty in the position of electron is \( \pm \mathbf{0 . 0 0 1} \boldsymbol{A} \) ? Will there be any problem in describing the momentum if it has a value of \( \frac{\boldsymbol{h}}{\mathbf{2} \boldsymbol{\pi} \boldsymbol{a}_{\mathbf{0}}} \)
where \( a_{0} \) is Bohr's radius of first orbit,
i.e., 0.529 A?


\( \infty \)
\( \infty \)
\( \infty \)
00


The \( v-t \) plot of a moving objects is
shown figure. the average velocity of the
objects that first 10 seconds is then
\( A \cdot 0 \)
B . \( 2.5 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 5 m s^{-1} \)
D. \( 2 m s^{-1} \)


If area of cross section of one end of
tube is \( 8 \mathrm{cm} \) and velocity of liquid flow is
\( 1.5 m s^{-1} . \) What is the speed of ejection of the liquid if the life area of cross
reaction of the other end is \( 4.0 \mathrm{cm} \)


Point \( P(6,6) \) lies on the circle with
center (2,3) and radius 5 coordinate
units. Find the co-ordinates of the
image of point \( \mathrm{P} \) after the circle is
rotated \( 90^{\circ} \) clockwise ( \( \circlearrowright \) ) about its
center.
A \( .(2,3) \)
B. (3,2)
\( c \cdot(5,-1) \)
\( D \cdot(6,0) \)
E. (7,3)


Developed photography film is due to:
A. \( A g B r \)
в. \( \left[A g\left(S_{2} O_{3}\right)_{2}\right]^{3} \)
\( c . A g \)
D. \( A g_{2} O \)


An organic substance bound to an enzyme and essential for its activity is
A. Isoenzyme
B. Coenzyme
c. Apoenzyme
D. Holoenzyme


Which have the same number of \( s \) -
electrons as the \( d \) -electrons in \( F e^{2+} ? \)
\( \mathbf{A} \cdot L i \)
в. \( N a \)
\( c \cdot N \)
D. \( P \)


For a body in S.H.M. the velocity is given by the relation \( \boldsymbol{v}=\sqrt{144-16 x^{2}} \boldsymbol{m} / \boldsymbol{s} \)
The maximum acceleration is
A \( \cdot 12 m / s^{2} \)
в. \( 16 m / s^{2} \)
\( \mathrm{c} \cdot 36 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 48 \mathrm{m} / \mathrm{s}^{2} \)


The number of moles of \( K_{2} C r_{2} O_{7} \) that
will be needed to react with one mole of
\( H_{2} S \) in acidic medium is :
A \( \cdot \frac{1}{6} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{5} \)
D. \( \frac{2}{3} \)


What is the average speed of farmer
during the walk?
Fig. 3.43


Suppose \( \boldsymbol{U}= \)
\( \{3,4,5,6,7,8,9,10,11,12,13\}, A= \)
\( \{3,4,5,6,9\}, B=\{3,7,9,5\} \) and \( C= \)
\( \{6,8,10,12,7\} . \) Write down the
following set and draw Venn diagram for
\( \boldsymbol{B}^{\prime} \)


The compound \( \boldsymbol{X} \) is:
A. o-methylchlorobenzene
B. p-methylchlorobenzene
c. m-methylchlorobenzene
D. both \( A \& B \)


The time(in seconds) taken by a group of people to walk across a pedestrian crossing is given in the table below.
Time
(in
\( \sec \)
\( \begin{array}{llll}5- & 10- & 15- & 20- \\ 10 & 15 & 20 & 25\end{array} \)
No. of people
If variation is \( 36.76, \) so calculate
standard deviation of the data.


The total surface area of a solid
hemisphere is \( 462 \mathrm{cm}^{2} . \) Find its radius.


The molecular formula of Mercury (II)
chloride is:
A. \( H g C l \)
в. \( H g_{2} C l_{2} \)
с. \( H g C l_{3} \)
D. \( H g C l_{2} \)


The quarks have fractional electronic charge e/3 and 2e/3. Then why is such a fractional electronic charge not reflected on the oil drops? This question has multiple correct options
A. Quarks cannot be gained or lost
B. Only electrons can be gained or lost
c. To lose quark, energy in MeV is required
D. single quark is unstable


A body starts from rest and moves with an uniform acceleration. The ratio of
distance covered in the \( n^{t h} \) second to
the distance covered in \( n \) seconds is :
A \( \cdot\left(\frac{2}{n}-\frac{1}{n^{2}}\right) \)
в. \( \left(\frac{1}{n^{2}}-\frac{1}{n}\right) \)
c. \( \left(\frac{2}{n^{2}}-\frac{1}{n}\right) \)
D. \( \left(\frac{2}{n}+\frac{1}{n^{2}}\right) \)


"If Deb and Sam go to the mall then it is
snowing" Which statement below is logically equivalent?
A. If Deb and Sam do not go to the mall then it is not snowing
B. If Deb and Sam do not go to the mall them it is snowing
C. If it is snowing then Deb and Sam go to the mall
D. If it is not snowing then Deb and Sam do not go to the mal


The amount of ion discharged during electrolysis is not directly proportional
to
A . resistance
B. time
c. current
D. chemical equivalent of ion


Reaction \( \boldsymbol{A}+\boldsymbol{B} \longrightarrow \boldsymbol{C}+\boldsymbol{D} \) follow's
following rate law rate \( =\boldsymbol{k}=[\boldsymbol{A}]^{\frac{1}{2}}[\boldsymbol{B}]^{\frac{1}{2}} \)
Starting with initial conc. of one mole of \( A \) and \( B \) each, what is the time taken for amount of A of become 0.25 mole. Given
\( \boldsymbol{k}=\mathbf{2 . 3 1} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{s e c}^{-\mathbf{1}} \)
A. 300 sec
B. 600 sec
c. 900 sec
D. none of these


A parallel plate capacitor with air between the plates has a capacitance of \( 8 p F\left(1 p F=10^{-12} F\right) . \) What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a
substance of dielectric constant \( 6 ? \)


Evaluate: \( \lim _{x \rightarrow 1} \frac{x^{\frac{1}{3}}-1}{x^{-\frac{2}{3}}-1} \)
A \( \cdot \frac{-1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{3}{2} \)


State true or false:
With reference to the figure, \( R \) is mid-point of \( B C \)
A. True
B. False


The number of lone pairs of electrons on
xenon atom in \( \mathrm{XeF}_{4} \) molecule is:
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D. zero


Solve \( : \boldsymbol{y}=\sin ^{-1}\left(\frac{1-\boldsymbol{x}^{2}}{1+\boldsymbol{x}^{2}}\right), \boldsymbol{0}<\boldsymbol{x}<1 \)


Purification of aluminium by electrolytic refining is called:
A. Serpeck's process
B. Hoope's process
c. Hall's process
D. Baeyer's process


A current \( I \) is flowing in a straight
conductor wire of length \( L \). The magnetic induction at a point perpendicular distance \( \frac{L}{4} \) from its centre will be:
A \( \cdot \frac{4 \mu_{0} i}{\sqrt{5} \pi L} \)
в. \( \frac{\mu_{0} i}{2 \pi L} \)
c. \( \frac{\mu_{0} i}{\sqrt{2} L} \)
D. zero


If \( A \) and \( B \) be two events associated
with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{A} \)
\( B)=0.6, \) then value of \( P\left(\frac{\bar{A}}{B}\right)+ \)
\( P\left(\frac{A}{\bar{B}}\right) \) is
\( A \)
в. \( \frac{3}{4} \)
\( c \cdot \frac{2}{5} \)
D. \( \frac{13}{12} \)
E. \( \frac{11}{12} \)


\( \ln \operatorname{an} A \cdot P . S_{3}=6, S_{6}=3, \) then it's
common difference is equal to?
\( A \cdot 3 \)
B. - 1
\( c . \)
D. None of these


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


The specific gravity of a salt solution is 1.025. If \( V \) mL of water is added to 1.0 L
of this solution to make its density
\( 1.02 g m L^{-1}, \) what is the value of \( V \) in
\( \mathrm{mL}, \) approximately?


The general values of ' \( \theta \) ' satisfying the
equation \( \sec 4 \theta-\sec 2 \theta=2 \) is


What do you mean by buffer solution?
A. Buffer solution have no \( p H \)
B. Its \( p H \) changes very little when a small amount of acid or base is added to the it
C. Its \( p H \) changes very largely when a small amount of acid or base is added to the it
D. All solutions are buffer


Blocking of arteries due to deposition of fats and calcium is called as
A. Heart syndrome
B. Atherosclerosis
c. Emphysema
D. None of the above


\( \frac{2}{2} \)


\( \int \frac{\boldsymbol{x} \boldsymbol{T} \boldsymbol{a} \boldsymbol{n}^{-1} \boldsymbol{x}}{\left(1+\boldsymbol{x}^{2}\right)^{3 / 2}} \boldsymbol{d} \boldsymbol{x}= \)
A. \( \frac{x+\operatorname{Tan}^{-1} x}{\left(1+x^{2}\right)^{3} / 2}+c \)
в. \( \frac{x-\operatorname{Tan}^{-1} x}{\sqrt{\left(1+x^{2}\right)}}+c \)
c. \( \frac{x}{\sqrt{1+x^{2}}}-\operatorname{Tan}^{-1} x+c \)
D. \( \frac{x}{1+x^{2}}+\operatorname{Tan}^{-1} x+c \)


Air pollution is not reduced by
A. Using precipitators
B. Reusing wastes
c. Cleaning air
D. All of the above


If \( f(x)=\left\{\begin{array}{l}2 x+b(x<\alpha) \\ x+d(x \geq \alpha)\end{array} \) is such \right.
that
\( \lim _{x \rightarrow \alpha} f(x)=L, \) then \( L= \)
\( \mathbf{A} \cdot 2 d-b \)
B. \( b-d \)
c. \( d+b \)
D. \( b-2 d \)


Number of terms in the expansion of \( \left(x^{1 / 3}+x^{2 / 5}\right)^{40} \) with integral power of \( x \)
is equal to


A parallel-plate air condenser of plate
area \( A \) and separation d is charged to
potential \( V \) and then the battery is
removed. Now a slab of dielectric
constant \( k \) is introduced between the
plates. If \( Q, E \) and \( W \) denote respectively the magnitude of charge on each plate, the electric field between the plates
(after introduction of dielectric slab)
and work done on the system in the process of introducing the slab, then This question has multiple correct options
A \( \cdot W=\frac{\varepsilon_{0} A V h^{2}}{2 d}(1-1 / k) \)
\( ^{\mathbf{B}} \cdot Q=\frac{\varepsilon_{0} K A V}{d} \)
\( ^{\mathbf{C}} \cdot Q=\frac{\varepsilon_{0} A V}{d} \)
D. \( \quad E=\frac{V}{k d} \)


In \( \triangle A B C, D \) is mid-point of \( A B, \) and \( E \) is
mid-point of BC. Calculate : \( D E \), if
\( \boldsymbol{A C}=\mathbf{6 . 4} \mathrm{cm} \)
A. \( 3.2 \mathrm{cm} \)
B. \( 3.3 \mathrm{cm} \)
\( c .4 .2 \mathrm{cm} \)
D. \( 2.6 \mathrm{cm} \)


Which of the following statement is NOT
true?
A. Lightning and spark from woolen clothing are essentially the same phenomena.
B. When you rub a plastic scale on your dry hair, it acquires a charge.
C. Charge acquired by a glass rod when it is rubbed with silk is negative charge.
D. Static charges are called so, because they do not move by themselves.


The figure shows a relationship
between the sets \( P \) and \( Q . \) Write this
relation in
(i) in set-builder form (ii) roster form


Assertion
Metals like Na, K, Ca and Mg are never
found in their free state in nature.
Reason
Metals are very reactive elements. So, it
combine with other non metal to
complete its octet. Metals like \( \mathrm{Na}, \mathrm{K}, \mathrm{Ca} \) and Mg are never found in their free state in nature.
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


What is the diameter of a hydrogen
atom in nm?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 10
c. \( 0 . \)
D. 0.01


If \( \{(x, 2),(4, y)\} \) represents an identity function, then \( (x, y) \) is :
\( A \cdot(2,4) \)
B. (4,2)
c. (2,2)
\( D \cdot(4,4) \)


Which of the following is/are ionization?
This question has multiple correct options
A \( \cdot N a \rightarrow N a^{+}+e^{-} \)
B. \( C l+e^{-} \rightarrow C l^{-} \)
c. \( N a C l \rightarrow N a^{+}+C l^{-} \)
D. \( M g B r_{2} \rightarrow M g^{2+}+2 B r \)


When \( \ln K \) is plotted against \( \frac{1}{T} \) using the Van't Hoff equation, a straight line is expected with a slope equal to:
A \( \cdot \Delta H^{o} / R T \)
в. \( -\Delta H^{o} / R \)
c. \( \Delta H^{o} / R \)
D. \( R / \Delta H^{\circ} \)


Compare \( S-O \) bond angle for the
following molecules.
A \( . x>y \)
B. \( y>x \)
c. \( x=y \)
D. None of these


Paramagnetic species are :
A. \( N O, N O_{2}, O_{2} \)
в. \( N_{2} O_{2}, N_{2} O_{2}, N_{2} O_{4}, O_{3} \)
c. \( N O^{+}, N O_{2}^{+}, O_{2}^{+} \)
D. \( O_{2}, C O, C O_{2} \)


If a rod has resistance 4 ohm and if rod
is turned as half circle, then the
resistance along diameter is
A. 1.56 ohm
B. 2.44 ohm
c. 4 ohm
D. 2 ohm


Passing percentage marks in an exam are \( 40 \% \). A student obtained 72 out of
200. By what percent did he fail?
\( A \cdot 8 \)
B. 5
\( c \cdot 4 \)
D. 6


lime-knots of slime moulds are
A. Swarm cells
B. Spore
c. capillitia
D. Fruit bodies


The increasing order of the atomic radii of the following elements is :
(a) \( C \)
(b) \( \boldsymbol{O} \)
\( (c) F \)
(d) \( C l \)
\( \boldsymbol{B} \boldsymbol{r} \)
A \( \cdot(b)<(c)<(d)<(a)<(e) \)
в. \( (c)<(b)<(a)<(d)<(e) \)
c. \( (d)<(c)<(b)<(a)<(e) \)
D. \( (a)<(b)<(c)<(d)<(e) \)
\( e \)


\( \boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x} \neq \mathbf{0},-\boldsymbol{4} \leq \boldsymbol{x} \leq \mathbf{4}\} \boldsymbol{f} \)
\( A \rightarrow R \) is defined as \( f(x)=\frac{|x|}{x} \) then
the range of \( \boldsymbol{f} \) is
A \( \cdot\{1,-1\} \)
B . \( \{x: 0 \leq x \leq 4\} \)
c. \{1\}
D \cdot \( \{x:-4 \leq x \leq 0\} \)


There is change in the type of
hybridisation when:
This question has multiple correct options
\( \mathbf{A} \cdot N H_{3} \) combines with \( H^{+} \)
B. \( A l H_{3} \) combines with \( H^{-} \)
\( \mathbf{C} \cdot N H_{3} \) forms \( N H_{2} \)
D. \( \operatorname{Si} F_{4} \) forms \( \operatorname{Si} F_{4}^{2-} \)


Which of the following is true? Non-competitive inhibitor differs from a competitive inhibitor in that it
A. Reduces the affinity of substrate for enzymes
B. Does not alter \( \mathrm{K}_{m} \)
c. May attach it self to the enzyme at a site other than the active site
D. Both B and C


Mothballs and camphor are examples
of:
A. sublimation
B. liquation
c. vaporisation
D. solidification


Why are root nodules useful for the
plants?


Which of the following groups includes
organs of the same organ system?
A. Trachea, Oesophagus, stomach
B. Pancreas, Lungs, Stomach
c. oesophagus, Rectum, stomach
D. Stomach, Pancreas, Heart


The moment of inertia of a thin square
plate \( A B C D \) of uniform thickness about
an axis passing through the centre 0
and perpendicular to the plane of the
plate is :
This question has multiple correct options
A \( \cdot I_{1}+I_{2} \)
B \( \cdot I_{3}+I_{4} \)
\( \mathbf{c} \cdot I_{1}+I_{3} \)
\( \mathbf{D} \cdot I_{1}+I_{2}+I_{3}+I_{4} \)


A voltaic cell converts:
A. electrical energy into chemical energy
B. chemical energy into electrical energy
C. light energy into electrical energy
D. mechanical energy into electrical energy


Blackman's law of limiting factor is applied to
A. Growth
B. Respiration
c. Transpiration
D. Photosynthesis


Zygomorphic flower with vexillary aestivation, diadelphous androecium and marginal placentation occurs in
A. Pisum
B. Aloe
c. Brinjal
D. Belladona
E. Asparagus


Acetyl chloride cannot be obtained by treating acetic acid with:
A. \( C H C l_{3} \)
в. \( P C l_{3} \)
c. \( P C l_{5} \)
D. \( S O C l \)


Identify the derived quantities among the following. This question has multiple correct options
A. Gravitational constant
B. Frequency
c. Electric charge
D. Electric current


Find the mode of given data.
\( \begin{array}{llll}\text { Marks } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}20- \\ 30\end{array}\end{array} \)
Frequency \( 20 \quad 24 \) In


Which of the following notations shows the product incorrectly?
\( \mathbf{A} \cdot_{96} C m^{242}(\alpha, 2 n)_{97} B k^{243} \)
В. \( _{5} B^{10}(\alpha, n)_{7} N^{13} \)
\( \mathbf{C} \cdot_{7} N^{14}(n, p)_{5} C^{14} \)
D. \( _{14} S i^{28}(d, n)_{15} P^{29} \)


Arm ratio in metacentric condition is
A . 1:
B. 1:
\( c \cdot 1: 3 \)
D. 2:


Q Type your question
ferromagnetic material can be ploted
as :
\( A \)
B.
\( c \)
\( D \)


The cell organelle in which aerobic respiration occurs is known as
A. Ribosomes
B. Mitochondria.
c. Lysosomes.
D. chloroplasts


Hydrogen is a non-metal having electron in the valence
shell.
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Three particles, each of mass \( m \) are
situated at the vertices of an
equilateral triangle \( A B C \) of side \( C \mathrm{cm} \)
(as shown in the figure). The moment of
inertia of the system about a line \( A x \)
perpendicular to \( A B \) and in the plane of
\( A B C, \) in \( g r a m c m^{2} \) units will be :-
\( \mathbf{A} \cdot 2 \mathrm{m} \ell^{2} \)
\( \mathbf{B} \cdot \frac{5}{4} m \ell^{2} \)
\( \mathbf{c} \cdot \frac{3}{2} m t^{2} \)
D \( \cdot \frac{3}{4} m^{2} \)


The uses of water are:
A. It is used as a universal solvent
B. It constitutes a major part of human body
C. It is used for controlling climatic conditions
D. All of the above


In given fig. of sector of circle of radius
\( 10.5 \mathrm{cm} . \) What is the perimeter of
sector?


A \( 10 k g \) ball is dropped from a height of 10 \( m \). Find (a) the initial potential
energy of the ball,
(b) the kinetic energy just before it reaches the ground, and
(c) the speed just before it reaches the ground.


Complete the table given below:
\( \begin{array}{llll}\text { Element } & \begin{array}{l}\text { Atomic } \\ \text { mass }\end{array} & \begin{array}{l}\text { Molecular } \\ \text { mass }\end{array} & \begin{array}{l}\text { Atomicit } \\ \text { number }\end{array} \\ \text { Chlorine } & 35.5 & 71 & - \\ \text { Ozone } & - & 48 & 3 \\ \text { Sulphur } & 32 & - & 8 \\ \text { Nitrogen } & 14 & - & 2\end{array} \)


Perimeter of a circle is called its
A . circumference
B. area
c. diameter
D. none of these


Mannitol is the stored food in
A. Gracillaria
B. Chara
c. Porphyra
D. Fucus


Select the correct order of boiling point:
A. diethyl ether \( >n \) -butyl alcohol \( >n \) -butaraldehyde \( >n- \) pentane
B. n-butyl alcohol > n-butaraldehyde > n-pentane> diethylether
C. n-pentane \( >n \) -butaraldehyde \( >n \) -butyl alcohol \( > \) diethylether
D. n-butyl alcohol > n-butaraldehyde > diethylether > npentane


Write the electronic configuration of the following elements
(a) Sulphur \( (\mathrm{Z}=16) \)
(b) Krypton \( (z=36) \)


A cricket ball of mass \( \mathrm{m} \) is hitted at the
angle \( 45^{\circ} \) to the horizontal with velocity
v.lts kinetic energy at the topmost point is
\( \mathbf{A} \cdot \mathbf{0} \)
B \( \cdot \frac{1}{2} m v^{2} \)
c. \( \frac{m v^{2}}{4} \)
D. \( \frac{m v^{2}}{2 \sqrt{2}} \)


In our country, large patches of forests are being cleared for cultivation of
crops. The environmental impact of such a practice will lead to
A. Soil erosion
B. Soil conservation
c. soil pollution
D. Soil fertility


The correct relationship between free energy change in a reaction and the corresponding equilibrium constant \( \boldsymbol{K} \)
is:
A \( .-\Delta G^{\circ}= \) RTin \( K \)
в. \( \Delta G= \) RT in \( K \)
c. \( -\Delta G=R T \) in \( K \)
D. \( \Delta G^{\circ}=R T \) in \( K \)


Let \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}, \boldsymbol{b} \in \boldsymbol{N} \text { and } \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b}= \)
12 \( \} . \) Find the domain and range of R.


The area bounded by the curves \( y=x^{2} \)
and line \( \boldsymbol{y}=\boldsymbol{x} \)
\( A \cdot \sin 1 \)
B. \( 1-\sin 1 \)
c. \( 1+\sin 1 \)
D. None of these


\( \boldsymbol{Z} \boldsymbol{n}_{(s)}\left|\boldsymbol{Z} \boldsymbol{n}_{(\boldsymbol{a q})}^{\boldsymbol{2}+}(\boldsymbol{1} \boldsymbol{M}) \| \boldsymbol{N} \boldsymbol{i}_{(\boldsymbol{a q})}^{2+}(\boldsymbol{1} \boldsymbol{M})\right| \boldsymbol{N} \boldsymbol{i}_{(s)} \)
Which is incorrect for the above given
cell?
A. Electrochemical cell
B. Voltaic cell
c. Galvanic cell
D. Daniel cell


Which of the following is a saprophytic angiosperm?
A. cuscuta
B. Neottia
c. Agaricus
D. Mango


Two cells \( A \) and \( B \) of emf \( 2 V \) and \( 1.5 \vee \)
respectively, are connected as shown in
figure through an external resistance
10 \( \Omega \). the internal resistance of each cell
and is \( 5 \Omega . \) The potential difference \( \boldsymbol{E}_{\boldsymbol{A}} \)
and \( E_{B} \) across the terminals of the cells
A and B respectively are:
\( \mathbf{A} \cdot E_{A}=2.0 V \cdot E_{B}=1.5 V \)
B \( . E_{A}=2.125 V, E_{B}=1.375 V \)
\( \mathbf{c} \cdot E_{A}=1.875 V, E_{B}=1.625 V \)
D \( . E_{A}=1.875 V, E_{B}=1.375 V \)


At a certain temperature, equilibrium
constant \( \left(K_{c}\right) \) is 16 for the reaction:
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g})+\boldsymbol{N} \boldsymbol{O}(\boldsymbol{g}) \)
If we take 1 mole of each of the four
gases in \( 1 L \) container, what would be
the equilibrium concentration of \( N O \)
and \( N O_{2} ? \)


Find the derivative of \( \frac{x+\cos x}{\tan x} \) with
respect to \( x \)


In our municipal drinking water purification and supply scheme chlorine is added to water because
A. Chlorine gives sweat taste to water
B. Chlorine kills harmful bacteria
c. Chlorine cools water
D. chlorinated water is now a days fashionable


Find vector equation for the line passing through the points \( 3 \bar{i}+4 \bar{j}- \) \( \mathbf{7} \bar{k}, \overline{\boldsymbol{i}}-\overline{\boldsymbol{j}}+\mathbf{6} \overline{\boldsymbol{k}} \)
A \( . \bar{r}=(3-2 \lambda) \bar{i}+(4-5 \lambda) \bar{j}+(-7+13 \lambda) \bar{k} \)
B. \( \bar{r}=(2 \lambda) \bar{i}+(4+5 \lambda) \bar{j}+(-7-13 \lambda) \bar{k} \)
c. \( \bar{r}=(3-2 \lambda) \bar{i}-(4-5 \lambda) \bar{j}+(-7+13 \lambda) \bar{k} \)
D. \( \bar{r}=(3-2 \lambda) \bar{i}+(4-5 \lambda) \bar{j}-(-7+13 \lambda) \bar{k} \)


The bond between carbon atom (1) and
carbon atom (2) in compound \( \boldsymbol{N} \equiv \)
\( C-C H=C H_{2} \) involves respectively
1
the hybrid orbitals:
A \( \cdot s p^{2} \) and \( s p^{2} \)
B. \( s p^{3} \) and \( s p \)
c. \( s p \) and \( s p^{2} \)
D. \( s p \) and \( s p \)


What is the final significant digit in the measurement of \( 16.280 g ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
c. 8
D. 6
E . 2


Suppose \( n \) conducting plates are
placed face to face, and the distance
between two successive plates is \( d \)
Each plate is half of the area of the
previous one. If area of first plate is \( A \). If
the area of the first plate is \( A \), the
equivalent capacitance of the system is \( \operatorname{given} \operatorname{as} \frac{\varepsilon_{0} A}{d\left(x^{n}-2\right)} . \) Find \( x \)


\( 7 \neq 10 . \) Choose the option that
expresses the statement using the correct connective.
A \( . \sim(7=10) \)
В. \( (7 \neq 10) \)
c. \( \sim(-7=10) \)
D. \( (-7 \neq-10) \)


Solve \( 16 a^{2}-40 a b+25 b^{2}-9 x^{2}+ \)
\( 42 x-49 \)


Carbon atoms in \( C_{2}(C N)_{4} \) are:
A. sp hybridizedd
B. \( s p^{2} \) hybridized
c. \( s p \) and \( s p^{2} \) hybridized
D. \( s p, s p^{2} \) and \( s p^{3} \) hybridized


A nichrome wire \( 1 \mathrm{m} \) long and \( 1 \mathrm{mm}^{2} \) in
crosssectional area draws 4 ampere at
2 volt. The resistivity of nichrome is
A \( \cdot 1 \times 10^{-7} n m \)
В. \( 2 \times 10^{-7} n m \)
c. \( 4 \times 10^{-7} n m \)
D. \( 5 \times 10^{-7} n m \)


Assertion
The degree of complex formation in
actinides decreases in the order
\( \boldsymbol{M}^{\mathbf{4}+}>\boldsymbol{M} \boldsymbol{O}_{\mathbf{2}}^{\mathbf{2}+}>\boldsymbol{M}^{\mathbf{3}+}>\boldsymbol{M} \boldsymbol{O}_{\mathbf{2}}^{+} \)
Reason
Actinides form complexes with \( \pi \) bonding ligands such as alkyl phosphines and thioethers.
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


Very short answer type.
Name a group of algae which contain plenty of fucoxanthin


Calculate the de Broglie wavelength for a beam of electron whose energy is \( \mathbf{1 0 0} e V: \)
\( \mathbf{A} \cdot 1 A^{0} \)
B . \( 1.23 A^{\circ} \)
c. \( 2.46 A^{\circ} \)
D. None of these


Water is broken down into its
constituent elements ............. and


A typical gymnospermous plant has 8 chromosomes in leaf cells. What will be number of chromosomes in the cells of
its gametophyte?
A . 16
B. 8
\( c \cdot 4 \)
D. 24


Equivalent resistance between \( A \) and \( B \)
in figure is
A \( \cdot 8 r / 7 \)
\( 3.7 r / 8 \)
\( c \cdot 3 r / 4 \)
\( D \)


Bipinnate leaves and spiny stipules is the characteristics of
A. Papilionatae
B. Cesalpinoideae
c. Mimosoideae
D. Malvaceae


Find the roots of the quadratics equation \( 3 x^{2}-4 \sqrt{3} x+4=0 \)


Formation of secondary xylem and phloem respectively are
A. Centrifugal and centripetal
B. Centripetal and centrifugal
c. Both centripetal
D. Both centrifugal


The total salary drawn by 3 watchmen, A, B and C is Rs. 1720. They spend 70\%, \( 60 \% \) and \( 50 \% \) respectively from their salaries. If the balance with them are
into Ratio \( 1: 2: 3, \) what is the salary of
each?
A. A Rs. 300; B Rs. 500; C- Rs. 700
B. A Rs. 200; B Rs. 300; C-Rs. 650
c. A Rs. 100; B Rs. 300; C-Rs. 600
D. A Rs. 400; B Rs. 600; C- Rs. 720


All of the following statements about
eutrophication is true except
A. It is caused by acid rain.
B. It is caused by the addition of nutrients to a water system.
C. It is most harmful when there is little flow through in the system.
D. Phosphorus is the main causal agent
E. Humans are responsible for most eutrophication.


On hybridization of one s-orbital and
one p-orbital we get:
A. mutual perpendicular orbitals
B. two orbitals at \( 180^{\circ} \) to each other
C. four orbitals directed tetraheadrally
D. three orbitals in one plane


In the circuit shown in Fig. potential
difference between \( A \) and \( B \) is:
A . \( 60 V \)
B. \( 10 V \)
\( c .30 V \)
D. \( 90 V \)


A rhombus is symmetrical across -
A. its diagonals
B. its vertices
\( \mathrm{C} \). its sides
D. its angles


A rectangular park, whose grass area is 10800 sq. \( \mathrm{m} \). and the sides are in the ratio of \( 4: 3 . \) Calculate the wire required
to cover outer boundry of the park.


What is the magnitude of a point charge due to which the electric field
\( 30 c m \) away has the magnitude
2 Newton/coulomb? \( [1 / 4 \pi \varepsilon 0=9 \times \)
\( \left.\mathbf{1 0}^{\mathbf{9}} \mathbf{N m}^{\mathbf{2}}\right] \)
A \( \cdot 2 \times 10^{-1} c \) coulomb
B. \( 3 \times 10^{11} \) coulomb
c. \( 5 \times 10^{11} \) coulomb
D. \( 9 \times 10^{11} \) coulomb


\( P \) is the centre of the square \( B_{p}=? \) Four
\( \boldsymbol{L} \) shaped wires, each carrying current \( \boldsymbol{I} \)
Find the magnetic field at point \( \boldsymbol{P} \) ?
A \( \cdot 1 w b / m^{2} \)
В. \( 0 w b / m^{2} \)
\( c \cdot 2 w b / m^{2} \)
D. none of these


Calculate the power used in the \( 2 \Omega \)
resistor in each of the following circuits:
(i) a \( 6 V \) battery in series with \( 1 \Omega \) and \( 2 \Omega \)
resistors, and (ii) a \( 4 V \) battery in parallel with \( 12 \Omega \) and \( 2 \Omega \) resistors.


If \( c \) is an arbitrary constant then \( \int \frac{\cos (x+a)}{\sin (x+b)} d x= \)
A \( \cdot \cos (a-b) \ln |\sin (x-b)|-x \sin (a-b)+c \)
B. \( \cos (a-b) \ln |\sin (x+b)|-x \sin (a-b)+c \)
\( \mathbf{c} \cdot \cos (a+b) \ln |\sin (x+b)|-x \sin (a+b)+c \)
D. \( \cos (a-b) \ln \sin |(x+b)|-x \sin (a+b)+c \)
E \( \cdot \cos (a-b) \ln |\sin (x+b)|+x \sin (a-b)+c \)


Prove using PM \( \left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right) \dots\left(1+\frac{(2 n+1)}{n^{2}}\right)= \)
\( (n+1)^{2} \)


f DE \( \| \) BC and \( A D=1.7 c m, A B= \)
\( 6.8 c m \) and \( A C=9 c m . \) Then length of
AE is
A . \( 2.25 \mathrm{cm} \)
B. \( 4.5 \mathrm{cm} \)
\( c .3 .4 \mathrm{cm} \)
D. \( 5.1 \mathrm{cm} \)


Rakesh consumes an average of 1680 calories per day.On the day of his finals, Rakesh consumes \( 12 \% \) more calories
per day than he usually does. During the last day of finals, he celebrates by consuming an additional 900 calories. Which of the following represents the total number of calories Rakesh
consumes during d days of finals?
A. \( 1.12(1680 d+900) \)
в. \( 1.12(1680 d)+900 \)
c. \( 1.12(1680+900) d \)
D. \( (180+0.12 d)+900 \)


Write names of different parts of human
digestive system and explain functions
of any three parts.


Units of the rate constant of first and
zero order reactions in terms of molarity
M unit are respectively:
A \( \cdot \sec ^{-1}, \) M sec \( ^{-1} \)
B . \( \sec ^{-1}, \) М
c. \( M s e c^{-1}, s e c^{-1} \)
D. \( M, s e c^{-1} \)


If \( x^{4}+7 x^{2} y^{2}+9 y^{4}=24 x y^{3}, \) then
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{x}{y} \)
B. \( \underline{y} \)
c. \( -\frac{x}{y} \)
D. \( -\frac{y}{x} \)


Three objects, A:(a solid sphere), B: (a thin circular disk) and \( \mathrm{C} \) : \( (\mathrm{a} \) circular
ring \( ), \) each have the same mass \( \mathrm{M} \) and radius R. They all spin with the same angular speed \( \omega \) about their own
symmetry axes. The amounts of work
(W) required to bring them to rest, would satisfy the relation.
A \( \cdot W_{B}>W_{A}>W_{C} \)
в. \( W_{C}>W_{B}>W_{A} \)
c. \( w_{A}>W_{C}>W_{B} \)
D. \( W_{A}>W_{B}>W_{C} \)


If \( p, q, r, s \) are in \( A . P \) ad if \( (x)= \)
\[
\begin{array}{rl}
\boldsymbol{p}+\sin \boldsymbol{x} & \boldsymbol{q}+\sin \boldsymbol{x}-\boldsymbol{r}+\sin \boldsymbol{x} \\
\| \boldsymbol{q}+\sin \boldsymbol{x} & \boldsymbol{r}+\sin \boldsymbol{x} \quad-\mathbf{1}+\sin \boldsymbol{x} \\
\boldsymbol{r}+\sin \boldsymbol{x} & \boldsymbol{s}+\sin \boldsymbol{x} \quad \boldsymbol{s}-\boldsymbol{q}+\boldsymbol{s} \boldsymbol{i} \boldsymbol{n} \boldsymbol{x}
\end{array}
\]
such that \( \int_{0}^{2} f(x) d x=-4 \) then the common difference of the \( A . P . \) cn
A. -1
B.
c. 1
D. none


If \( 0.1 J \) of energy is stored for the flow of current of \( 0.2 A \) in an inductor, then its
inductance value is:
A \( .5 H \)
в. \( 0.5 H \)
\( \mathrm{c} \cdot 5 m H \)
D. \( 50 H \)
E . \( 50 \mathrm{mH} \)


During leaching, gold is recovered from the solution by the addition of
A. zinç
B. zinc oxide
c. silver oxide
D. zinc sulphide


If the radius of a sphere is doubled, what will be the ratio of its surface area
and volume as to that of the first sphere
A. 7: 1,8: 1
B. 5: 1,8: 1
c. 3: 1,8: 1
D. 4: 1,8: 1


A monoprotic acid in a \( 0.1 \mathrm{M} \) solution ionises to \( 0.001 \% \). Its ionization
constant is:
\( \mathbf{A} \cdot 1 \times 10^{-11} \)
B. \( 1 \times 10^{-3} \)
C \( .1 \times 10^{-6} \)
D. \( 1 \times 10^{-8} \)


When a man stands on a moving escalator he goes up in \( 40 s \) and when
he walked up the moving escalator he goes up in 20 s. The man walk up the
stationary escalator in a time of:
\( \mathbf{A} \cdot 60 \)
B. \( 40 s \)
\( c \cdot 20 s \)
D. \( 50 s \)


Find \( |\vec{a} \times \vec{b}|, \) if \( \vec{a}=\hat{i}-7 \hat{j}+7 \hat{k} \) and \( \vec{b}= \)
\( \mathbf{3} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\mathbf{2} \hat{\boldsymbol{k}} \)


Among the following, the pair in which the two species are not isostructural is :
\( A \cdot I O_{3}^{-} \) and \( X e O_{3} \)
B \( \cdot P F_{6}^{-} \) and \( S F_{6} \)
\( \mathbf{c} \cdot B H_{4}^{-} \) and \( N H_{4}^{+} \)
D. \( C O_{3}^{2-} \) and \( N O_{2}^{-} \)


Thermococcus, Methanococcus and
Methanobacterium exemplify
A. Bacteria that contain a cytoskeleton and ribosomes
B. Archaebacteria that contain protein homologous to eukaryotic core histones
C. Archaebacteria that lack any histones resembling those found in eukaryotes but whose DNA is negatively supercoiled
D. Bacteria whose DNA is relaxed or positively supercoiled but which have a cytoskeleton as well as mitochondria


In thermodynamics, which one of the following properties is not an intensive property?
A. Pressure
B. Temperature
c. volume
D. Density


During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at
\( 40.0 \mathrm{cm} \) using a standard resistance of
\( 90 \Omega, \) as shown in the figure. The least count of the scale used in the metre
bridge is 1 mm. The unknown
resistance is
A. \( 60 \pm 0.15 \Omega \)
B. \( 135 \pm 0.56 \Omega \)
c. \( 60 \pm 0.25 \Omega \)
D. \( 135 \pm 0.23 \Omega \)


Let \( \boldsymbol{f}:(e, \infty) \rightarrow \boldsymbol{R} \) be a function
defined by \( f(x)=\log (\log (\log x)), \) the
base of the logarithm being \( e \). Then
A. \( f \) is one-one and onto
B. \( f \) is one-one but not onto
\( c . f \) is onto but not one-one
D. the range of \( f \) is equal to its domain


The tip of the root apical meristem is capped by the histogen known as
A. Periblem
B. Dermatogen
c. Plerome
D. Calyptrogen


The ingredients from a mixture of
iodine and sand can be separated by:
A. Filteration
B. Sublimation
c. crystallisation
D. Precipitation


Find \( x, \) if the given numbers are in A.P.
\( (a+b)^{2}, x,(a-b)^{2} \)


Which of the following pairs is the most acidic?
\( A \cdot N_{2} O_{5}, P_{2} O_{3} \)
B. \( \mathrm{N}_{2} \mathrm{O}_{5}, \mathrm{P}_{2} \mathrm{O}_{5} \)
\( \mathbf{c} \cdot \mathbf{H}_{3} \mathbf{P} \mathbf{O}_{4}, \mathbf{H}_{3} \mathbf{P} \mathbf{O}_{3} \)
D. None of the above


Find the ratio of the total sales of laptop
in Rajasthan state for both years to the
total sales of laptop in Gujarat state for both years?
Sales of laptop
\( A \cdot 8: 13 \)
B. 13: 8
c. 11: 8
D. 8: 11


Which one of the following books was not contributed by Linnaeus?
A. systema Naturae
c. Philosophia Botanica
D. All of the above


Fill in the blank:
1 mean solar day =
\( \mathbf{A} \cdot 43200 \)
B. 86636
c. 21600
D. 10800


An Arithmetic Series is defined as
\( \boldsymbol{f}(\boldsymbol{n})=\boldsymbol{a}+(\boldsymbol{n}-\mathbf{1}) \boldsymbol{d}, \boldsymbol{n} \in \boldsymbol{N}, \) prove
that A.M. of \( \boldsymbol{f}(\mathbf{1}) \) and \( \boldsymbol{f}(\boldsymbol{2 n}-\mathbf{1}) \) is \( \boldsymbol{f}(\boldsymbol{n}) \)


Why earthing is important?
A. To protect us from electrical shocks.
B. Transfers charge from a charged body to the Earth.
C. Both A and B.
D. Neither A nor B.


What is the significance of pores present
on the nuclear membrane?


Which is the commercially largest produced aldehyde?
A. Acetaldehyde
B. Formaldehyde
c. Benzaldehyde
D. Butyraldehyde


Which of the following is most reactive
towards aqueous \( N a O H ? \)
A \( \cdot C_{6} H_{5} C l \)
в. \( C_{6} H_{5} C H_{2} C l \)
\( \mathbf{c} \cdot C_{6} H_{5} B r \)
D. \( B r C_{6} H_{4} B r \)


For a complex number z, the minimum
value of \( |z|+|z-2| \) is
A. 1
в. 2
\( c .3 \)
D. None of these


When acetone and chloroform are
mixed together, hydrogen bonds are formed between them. Which of the
following statements is correct about the solution made by mixing acetone and chloroform ?
A. on mixing acetone and chloroform will form an ideal solution
B. On mixing acetone and chloroform positive deviation is shown since the vapour pressure increases
c. on mixing acetone and chloroform negative deviation is shown since there is decrease in vapour pressure
D. At a specific composition, acetone and chloroform will form minimum boiling azeotrope


Negate each of the following
statements:
There exists a number which is equal to
¡ts square.


\( 1 \mathrm{Nm}^{-2} \) is equal to :
A \( .1 P a \)
B. \( 0.1 P a \)
c. \( 0.01 P a \)
D. \( 10 P a \)


Why is a layer of zinc coated on iron?
A. To protect it from corrosion
B. To reduce on cost
c. To make it appear shining
D. All of the above


Which of the following is a rational number \( (s) ? \)
A \( \cdot \frac{-2}{9} \)
B. \( \frac{4}{-7} \)
\( c \cdot \frac{-3}{17} \)
D. All the three given numbers


Evaluate \( \int \frac{1}{\sqrt{9-25 x^{2}}} d x \)


A uniform chain of mass \( m \) and length \( l \) is kept on a smooth horizontal surface such that \( 1 / 4 \) th of its length is hanging
from the edge of the table. If it slides
down, the change in kinetic energy when hanging length becomes
\( 3 l \)
\( \frac{w}{4} \) will be
\( \mathbf{A} \cdot \frac{m g l}{4} \)
в. \( \frac{m g l}{2} \)
\( \mathbf{c} \cdot \frac{m g l}{32} \)
D. \( \frac{9 m g l}{32} \)


Which one of the following statements
is false?
A. The presence of albumin in urine is albuminuria.
B. The presence of glucose in urine is glycosuria.
C. The absence of ketone bodies in urine is ketonuria.
D. The presence of excess urea in blood is uremia.
E. The presence of haemoglobin in urine is haemoglobinuria.


The lower jaw consists of single bone is known as
A. Mandible
B. Alveoli
c. Pterygoid
D. Maxilla


Which structure of eye is related to focussing of light?
A. Lens
B. Cornea
c. Retina
D. Aqueous and vitreous humor


In blast furnace, haematite is reduced
to iron mainly by:
A. \( O_{2} \) gas
B . \( H_{2} \) gas
c. \( C O \) gas
D. \( C l_{2} \) gas


The process requiring the absorption of energy is:
A \( . F \rightarrow F^{-} \)
в. \( H \rightarrow H^{-} \)
c. \( C l \rightarrow C l^{-} \)
D. \( O \rightarrow O^{2-} \)


\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g)+ \) heat
For the reaction above, what is the effect
on the equilibrium position when the pressure is decreased?
A. Increased production of products
B. Increased production of reactants
c. Fluctuations in the amounts of reactants and products
D. No impact on the equilibrium
E. Cannot be determined


Minimum number of unequal vectors
which can give zero resultant are:
A . two
B. three
c. four
D. more than four


Find the value of unknown \( x \) in the
following diagram.


Match the terms to these definitions.
Anaerobe, aerobe, kiss of life, spirograph, inspiration, chloride shift, tidal volume, oxygen debt tidal air.
The drawing in of the breath


The electron configuration for \( \boldsymbol{C u} \) is
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} 3 d^{10} \)
Based on the electron configuration,
what can be said about the relative
ionization energies of the electrons in
\( \boldsymbol{n}=\mathbf{3} ? \)
A. The ionization energies gradually decrease from sto p to d subshells
B. The ionization energies gradually increase from s to \( \mathrm{p} \) to d subshells
C. The ionization energies are relatively the same from s to p to d subshells.
D. The ionization energies are unpredictable at this energy level.


Anode mud is obtained in which of the
following processes?
A. Roasting
B. zone refiningg
c. Electrolytic refining
D. Calcination


Suppose \( \vec{a} \) is a vector of magnitude 4.5 unit due north. What is the vector \( -4 \vec{a} \) ?


Out of cis-2 butene and trans-2-butene,
which one has the lowest melting point
?
A. cis-2-butene
B. Trans-2- butene
c. Both are equal
D. cannot be determined


The horizontal component of the flux density of earth's magnetic field is
\( 1.7 \times 10^{-5} T . \) The value of the horizontal
component of the intensity of earth's magnetic field will be:
A \( \cdot 24.5 A m^{-1} \)
B. \( 13.5 A m^{-1} \)
c. \( 1.53 A m^{-1} \)
D. \( 0.35 A m^{-1} \)


The \( _{--}-_{-}-_{-}- \) of a triangle is the perpendicular from a vertex to the opposite side.
A. centroid
B. altitude
c. midpoint
D. orthocenter


What is the square of \( (2+\sqrt{2}) ? \)
A. A rational number
B. An irrational number
c. A natural number
D. A whole number


Mark out the correct statement(s)
This question has multiple correct options
A. in alpha decay, the energy released is shared between alpha particle and daughter nucleus in the form of kinetic energy and share of alpha particle is more than that of the daughter nucleus
B. in beta decay, the energy released is in the form of kinetic energy of beta particles
C. in beta minus decay, the energy released is shared between electron and antineutrino
D. in gamma decay, the energy released is in the form of energy carried by photons termed as gamma rays


How many electrons will be present in
the subshells having \( m_{s} \) value of \( -1 / 2 \)
for \( \boldsymbol{n}=\mathbf{4} ? \)
A . 10
B. 12
\( c \cdot 14 \)
D. 16


The plant which reproduces by apical meristem is
A. Gymnosperm
B. Pteridophyte
c. Angiosperm
D. Algae


Total flux produced by a source of \( 1 c d \) is
A \( \cdot \frac{1}{4 \pi} \)
B. \( 8 \pi \)
c. \( 4 \pi \)
D. \( \frac{1}{8 \pi} \)


Prove \( n^{n}>1.3 .5, \dots . . .(2 n-1) \)


As a lead storage battery is charged.
A. Lead dioxide dissolves
B. Sulphuric acid is regenerated
C. Lead electrode becomes coated with lead sulphate
D. The concentration of sulphuric acid decreases


In which of the following configuration
(s) the value of 'spin only' magnetic moment is 2.84 BM for octahedral
complex:
This question has multiple correct options
A . \( d^{4} \) (in strong field ligand)
B. \( d^{2} \) (in weak field ligand)
c. \( d^{3} \) (in weak asa well as in strong field ligand)
D. \( d^{5} \) (in strong field ligan)
E \( \cdot d^{8} \) (in weak field ligand)


\( \frac{\sqrt{a^{2}-b^{2}}+a}{\sqrt{a^{2}+b^{2}}+b} \div \frac{\sqrt{a^{2}+b^{2}}-b}{a-\sqrt{a^{2}-b^{2}}} \)


An iron sphere of mass \( 20 \times 10^{-3} k g \)
falls through a viscous liquid with terminal velocity \( 0.5 m s^{-1} \). The terminal
velocity \( \left(\text { in } m s^{-1}\right) \) of another
iron sphere of mass \( 54 \times 10^{-2} k g \) is:
A . 4.5
в. 3.
c. 2.5
D. 1.5


Rex Things throws his mother's crystal vase vertically upwards with an initia velocity of \( 26.2 m / s . \) Determine the height to which the vase will rise above its initial height.
A . \( 34.0 m \)
B. \( 39.0 m \)
c. \( 35.0 m \)
D. \( 37.0 m \)


Between two rational numbers, there
exists-
A. No rational number
B. Only one rational number
c. Infinite numbers of rational numbers
D. No irrational number


Is \( C O_{2} \) is more solution in water than
\( O_{2} ? \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


These cells are absent in phloem of
gymnosperms
A. Albuminous cells
B. Companion cells
C. Phloem parenchyma
D. Phloem fibre


One end of a uniform wire of length \( \boldsymbol{L} \) and of weight \( W \) is attached rigidly to a
point in the roof and \( W_{1} \) weight is suspended from looser end. If \( A \) is area
of cross-section of the wire, the stress in the wire at a height \( \frac{L}{4} \) from the upper end is
\( \mathbf{A} \cdot \frac{W_{1}+W}{a} \)
B. \( \frac{W_{1}+3 W / 4}{a} \)
c. \( \frac{W_{1}+W / 4}{a} \)
D. \( \frac{4 W_{1}+3 W}{a} \)


Which ordered number pair represents the center of the circle \( x^{2}+y^{2}-6 x+ \)
\( 4 y-12=0 ? \)
\( A \cdot(9,4) \)
B. (3,2)
\( c \cdot(3,-2) \)
\( D \cdot(6,4) \)


Which of the following statements is/are correct about real gases?
This question has multiple correct options
A. The molecules do cause attractive forces on each
another.
B. They obey gas laws at low temperature and high pressure.
C. They show deviations from ideal behaviour.
D. The molecules have negligible mass.


In which of the following process
\( \Delta H \) and \( \Delta U \) are of same magnitude
A. evaporation of \( C C l_{4}(l) \)
B. \( C a C O_{3}(s) \longrightarrow C a O(s)+C O_{2}(g) \)
c. \( N H_{4} C l(s) \longrightarrow N H_{4} C l(g) \)
D. \( 2 H I(g) \quad \longrightarrow H_{2}(g)+I_{2}(g) \)


Hormone secreted during emergency is
A. Aldosterone
B. Calcitonin
c. Thyroxine
D. Adrenaline


In a factory which manufactures bolts, machines \( A, B \) and \( C \) manufacture \( 30 \%, 50 \% \) and \( 20 \% \) of the bolts
respectively. Of their output \( 3 \%, 4 \% \) and \( 1 \% \) respectively are defective bolts. bolt is drawn at random from the
product and is found to be defective Find the probability that this is not manufactured by machine B.


What is the correct formula for
dinitrogen monoxide?
A \( \cdot N_{2} O \)
в. \( N_{2} O_{5} \)
c. \( N_{4} O_{2} \)
D. \( N O \)
E. \( N O_{2} \)


The energy equivalent of \( 1 \mathrm{mg} \) of mass in joule is
\( A \cdot 3 \times 10^{2} \)
B. 3 \times10 \( ^{10} \)
\( c \cdot 9 \times 10^{10} \)
D. \( 9 \times 10^{2} \)


Calculate the area enclosed by a circle
of diameter \( 1.12 m \) to the correct
number of significant figures.


At what voltage and frequency is the electric power generated at the power generating station?
\( \mathbf{A} \cdot 15 k V, 50 H z \)
в. \( 11 k V, 100 H z \)
c. \( 11 k V, 50 H z \)
D. \( 11 k V, 500 H z \)


A car is moving along a straight line OP as shown in the figure. It moves from 0 to \( P \) in 18 s and returns from \( P \) to \( Q \) in 6
s. Which of the following statements is not correct regarding the motion of the
car?
A. The average speed of the car in going from 0 to \( P \) and come back to \( \mathrm{Q} \) is \( 20 \mathrm{m} s^{-1} \)
B. The average velocity of the car in going from 0 to and come back to \( \mathrm{Q} \) is \( 10 \mathrm{m} \mathrm{s}^{-1} \)
c. The average speed of the car in going from 0 to \( \mathrm{P} \) and come back to 0 is \( 20 \mathrm{m} s^{-1} \)
D. The average velocity of the car in going from 0 to and come back to 0 is \( 20 \mathrm{m} s^{-1} \)


Mohan paid tax Rs.1, 000 on purchase value and collected Rs.1, 200 tax on sale value. Find the M-VAT payable by Mohan


State true or false:
If we multiply both sides of an equation by zero, then we can create an
equivalent equation.
A. True
B. False


A plane surface is inclined at an angle
of \( 60^{0} \) with the horizontal. A body of
mass \( 10 \mathrm{kg} \) is uniformly accelerating, along the inclined plane surface. The
value of coefficient of friction \( \mu_{k} \)
between the body and the inclined
surface is \( 0.2, \) if the length of the
inclined plane is \( 10 \mathrm{m} \), then the work
done to pull it to the top is ( Take \( \boldsymbol{g}= \)
\( 10 m / s^{2} \)
A . 666 J
B. 766 J
c. 866 J
D. 966 J


If the mean deviation about the median
of the numbers \( a, 2 a, 3 a, \dots . ., 50 a \) is 50
then \( |a| \) is equal to?
A .2
B. 3
\( c \cdot 4 \)
D. 5


The metal having highest ionisation potential is :
A. lithium
B. sodium
c. potassium
D. caesium


Which one causes photochemica
smog?
\( A \cdot O_{3}, \) PAN and \( N O_{2} \)
B. \( O_{3} \), PAN and \( C O \)
c. HCN, NO and PAN
D. \( O_{2} \), PAN and \( N O_{2} \)


If the middle term of \( \left(x+\frac{1}{x} \sin ^{-1} x\right)^{8} \)
is \( \frac{35 \pi^{4}}{8}, \) then value of \( x \) can be
A \( \cdot \frac{1}{2} \)
B. \( \frac{\sqrt{3}}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D.


The correct acidic order of the following
is
I. Phenol II. 4-methylphenol
III. 4-nitrophenol
B. ॥I>1>11
c. ॥>॥ᅵ>।


The range of \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{6}-|\mathbf{2} \boldsymbol{x}+\mathbf{3}| \) is
\( A \cdot(-\infty, 6] \)
B. \( [6, \infty) \)
c. [2,6]
D. \( (0, \infty) \)


Active transport involves transport of
ions
A. Against concentration gradient and require ATP
B. Against concentration gradient and not require ATP
C. With concentration gradient and not require ATP
D. None of the above


\( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \) What is the
IUPAC name of the compound?


\( \ln \) a test an examinee either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is \( 1 / 3 \& \) the probability that he copies the answer is \( 1 / 6 . \) The probability that his answer is correct given that he copied it, is \( 1 / 8 . \) Find the probability that he knew the answer to the question given that he correctly answered it. If expressed in the form of \( a / b \) (simplest form), \( b-a=? \)


In the relation \( y=r \sin (\omega t-k x), \) the
dimensions of \( \omega / k \) are
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
B . \( \left[M^{0} L^{1} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{0} T^{1}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{1} T^{0}\right] \)


The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position, so that the water surface in the tank is at
the same level as the top of the cylinder
as shown in the figure. The density of
the water is \( \rho \)
n equilibrium, the height H of the water column in the cylinder satisfies
A \( \cdot \rho g\left(L_{0}-H\right)^{2}+P_{0}\left(L_{0}-H\right)+L_{0} P_{0}=0 \)
B \( \cdot \rho g\left(L_{0}-H\right)^{2}-P_{0}\left(L_{0}-H\right)-L_{0} P_{0}=0 \)
\( \mathbf{c} \cdot \rho g\left(L_{0}-H\right)^{2}+P_{0}\left(L_{0}-H\right)-L_{0} P_{0}=0 \)
D \( \cdot \rho g\left(L_{0}-H\right)^{2}-P_{0}\left(L_{0}-H\right)+L_{0} P_{0}=0 \)


\( (\sqrt{3}+\sqrt{2})^{4}-(\sqrt{3}-\sqrt{2})^{4}= \)
A \( .20 \sqrt{6} \)
в. \( 30 \sqrt{6} \)
c. \( 5 \sqrt{10} \)
D. \( 40 \sqrt{6} \)
E \( .10 \sqrt{6} \)


Periderm includes
A. Cork cambium (phellogen), cork (phellem) and secondary cortex (phelloderm)
B. Cork cambium and cork
c. cork
D. Cork and secondary phloem


Energy in the sun is mainly generated
by
A. Fusion of radioactive materials
B. Fission of helium nucle
c. Fusion of hydrogen nuclei
D. Chemical reaction


Solve the following inequality and show it graphically:
\( -2<x+3<5, x \in N \)
\( A \)
B.
\( c \)
D.


Deduce the condition when the De-
Broglie wavelength associated with an
electron would be equal to that
associated with a proton if a proton is 1836 times heavier than an electron


The highest concentration of chloroplast is present in
A. Stomata
B. Epidermal layer
c. Palisade mesophyll
D. Phloem
E. cuticle


Solve: \( 30 x<200 \) when \( x \) is a real
number.


A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random
from the bag. The probability that all of
them are red, is:
A \( \cdot \frac{1}{91} \)
в. \( \frac{2}{91} \)
c. \( \frac{3}{91} \)
D. \( \frac{4}{91} \)


Which one of the tissue is formed in
stems from cells cut off by the cambium on its inner side?
A. Wood fibres
B. Bast fibres
c. sieve tubes
D. Companion cells


Which of the following is not absorbed through soil?
A. carbon
B. Nitrogen
c. Potassium
D. All of the above


Arrange the given steps in CORRECT order, while constructing \( \triangle P Q R \) where \( P M \perp Q S \) and it is given that \( Q R=4.2 \)
\( \mathrm{cm}, \angle \mathrm{Q}=120^{\circ} \) and \( \mathrm{PQ}=3.5 \mathrm{cm} \)
Step 1: Now, extend RQ to S and with P
as centre and with a sufficient radius,
draw an arc, cuffing \( \mathrm{SQ} \) at \( \mathrm{A} \) and \( \mathrm{B} \). Step 2. Along QX, set off QP = 3.5 cm. Step 3. Draw a line segment \( Q R=4.2 \mathrm{cm} \)
and construct \( \angle \mathrm{RQX}=120^{\circ} \)
Step 4. Joint PR.
Step 5. Joint PC, meeting RQ product at
M. Then, PM \( \perp \) QS
Step 6. With A as centre and radius
more than half \( A B, \) draw an arc. Now
with \( \mathrm{B} \) as centre and with the same
radius draw another arc, cutting the previous arc at \( \mathbf{C} \)
A \( \cdot 1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5 \rightarrow 6 \)
B . \( 4 \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 5 \rightarrow 6 \)
\( c \cdot 2 \rightarrow 4 \rightarrow 3 \rightarrow 1 \rightarrow 5 \rightarrow 6 \)
D. \( 3 \rightarrow 2 \rightarrow 4 \rightarrow 1 \rightarrow 6 \rightarrow 5 \)


Which group of the following scientists discovered the EMP pathway or glycolysis?
A. Embden, Meyerhof and Parnas
B. Embden, Hoffman and Peterson
c. Embden, Morrison and Pitcher
D. Avery, McLeod and McCarthy


The reaction, \( \boldsymbol{A}+\boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \) Products
obeys rate law expression as:
\( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}]\left[\boldsymbol{O H}^{-}\right] \)
If initial concentrations of \( [A] \) and
\( \left[\boldsymbol{O} \boldsymbol{H}^{-}\right] \) are \( \boldsymbol{0 . 0 0 2} \boldsymbol{M} \) and \( \boldsymbol{0 . 3} \boldsymbol{M} \)
respectively and if it take 30 sec for \( 1 \% \)
\( A \) to react at \( 25^{\circ} \mathrm{C} \), calculate the rate
constant for the reaction.


Which of the following statements is
true?
A \( \cdot \) Gas (G) reacts with conc NaOH to form \( O F_{2} \)
B. Pale blue gas (E) oxidises alkaline KI to \( K I O_{3} \)
C. Pale blue gas (E) in acidic medium reacts with \( K_{2} C r_{2} O_{7} \) to form a bright blue coloured compound
\( \left(C r O_{5}\right) \)
D. (B) and
(C) both.


If the boiling points of two liquids is close to each other, they are separated
by:
A. fractional distillation
B. chromatography
c. steam Distillation
D. differential Extraction


What happens when an emulsion is
centrifuged?


When a nucleus with atomic number \( z \)
and mass number A undergoes a
radioactive decay process
A. both \( z \) and \( A \) will decrease if the process is \( \alpha \) -decay
B. Z will decrease but A will not change if the process is \( \beta^{+}- \) decay
c. z will increase but A will not change, if the process is \( \beta^{-}- \) decay
D. z and A will remain unchanged if the process is \( \gamma \) decay


Which is false regarding EMP pathways?
A. End product is \( C O_{2} \) and \( H_{2} O \)
B. Substrate level phosphorylation
c. Production of ATP
D. Expenditure of ATP


In electrical field, equipotential
surfaces must:
A. be plane surfaces
B. be tangential to the direction of field
C. be spaced such that surfaces having equal difference in potential are separated by equal distance
D. have decreasing potential in the direction of field


regarding biological museums.
(i) Biological museums are generally set up in educational institutes such as
schools and colleges.
(ii) Museums have collections of
preserved plant and animal specimens for study and reference.
(iii) Specimens are preserved in the containers or jars in preservative solutions.
(iv) Insects are preserved in insect boxes after collecting killing and
pinning.
(v) Larger animals like birds and mammals are usually stuffed and
preserved.
(vi Skeletons of mammals are not
allowed to be kept in museums. Which of the given statements is/are
not correct?
A . (ii) and (iii)
B. (i) and (vi)
\( \mathbf{C} \cdot(v) \) only
D. (vi) only


Assertion
Angle and angular displacement are dimensionless quantities.
Reason
Angle is equal to arc length divided by
radius.
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
Aryl halides undergo electrophilic substitution less readily than benzene.
Reason

Aryl halide gives only meta product w.r.t. electrophilic substitution.
A. Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
c. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect but the Reason is correct


Give both chemical equations of leaching of silver in silver metallurgy by using sodium cyanide?


Which one of the following property is high in the case of water?
A. Surface tension
B. Specific heat
c. Heat of vaporization and heat of fusion
D. All of the above


Water soluble chlorides are:
This question has multiple correct options
A. zinc chloride
B. ferric chloride
C . silver chloride
D. calcium chloride


Myopia of the common defects of vision and the type of lens used to remove it.


Calculate the mean \% error in five
observations:
80.0,80.5,81.0,81.5,82
A . \( 0.75 \% \)
в. \( 1.74 \% \)
c. \( 0.38 \% \)
D. \( 1.38 \% \)


Magnitude of vector \( \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \sqrt{2} \)
c. 1
D. 2


Suppose that \( n \) is a natural number and
\( \boldsymbol{I}, \boldsymbol{F} \) are respectively the integral part
and fractional part of \( (7+4 \sqrt{3})^{n} . \) Then
show that
i) \( I \) is an odd integer
ii) \( (\boldsymbol{I}+\boldsymbol{F})(\mathbf{1}-\boldsymbol{F})=\mathbf{1} \)


What is the gas liberated when
alkaline formaldehyde solution is reacted with hydrogen peroxide in the
presence of pyrogallol?
A \( . H_{2} \)
в. \( O_{2} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( C O_{2} \)


Equation of plane parallel to \( 3 x+4 y+ \)
\( \mathbf{5} \boldsymbol{z}-\mathbf{6}=\mathbf{0}, \mathbf{6} \boldsymbol{x}+\mathbf{8} \boldsymbol{y}+\mathbf{1 0} \boldsymbol{z}-\mathbf{1 6}=\mathbf{0} \)
and equidistant from them is
A. \( 3 x+4 y+5 z=7 \)
B. \( 3 x+4 y+5 z=10 \)
c. \( 6 x+8 y+10 z=0 \)
D. \( 6 x+8 y+10 z=3 \)


Gammexane is the name given to:
\( \mathbf{A} \cdot C_{6} H_{3} C l_{3} \)
в. \( C_{6} H_{4} C l_{2} \)
\( \mathbf{c} \cdot C_{6} H_{6} C l_{6} \)
D. Diphenyltrichloroethane


Statement 1:
In a zero order reaction, if the
concentration of the reactant is
doubled, the half-life period is also
doubled.
Statement 2:
For a zero-order reaction, the rate of the
reaction is independent of initial
concentration.
A. Statement 1 is True, statement 2 is True, statement 2 is a correct explanation of statement 1.
B. Statement 1 is True, statement 2 is True, statement 2 is not a correct explanation of statement 1
c. Statement 1 is true, Statement 2 is False
D. Statement 1 is False, Statement 2 is True.


For \( \boldsymbol{r}=\mathbf{0}, \mathbf{1}, \mathbf{2},, \dots \mathbf{1 0} \) let \( \boldsymbol{A}_{r}, \boldsymbol{B}_{r} \) and \( \boldsymbol{C}_{\boldsymbol{r}} \)
denote respectively the coefficient of \( \boldsymbol{x}^{r} \) in the expansions of \( (1+x)^{10},(1+x)^{20} \) and \( (1+x)^{30} . \) Then
\( \sum_{r=1}^{10} A_{r}\left(B_{10} B_{r}-C_{10} A_{r}\right) \) is equal to
A. \( B_{10}-C_{10} \)
B . \( A_{10}\left(B_{10}^{2}-C_{10} A_{10}\right) \)
c.
D. \( C_{10}-B_{10} \)


f \( \boldsymbol{y}=\boldsymbol{a} \cos (\log \boldsymbol{x})-\boldsymbol{b} \sin (\log \boldsymbol{x}), \) then
the value of \( x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. 3


How many statements are incorrect
regarding succession?
(a)During succession climax community is always mesophytes
(b)Future seral community productivity
(c) Increases species diversity, Biomass and humus content.
(d)Gradual replacement from long lived to short lived plant
\( A \)
B. 2
\( c \cdot 4 \)
D.


If the length of Rough inclined plane is \( 10 m \) and the value of \( g \) is \( 10 m / s^{2} \) and
the Angle of Inclination is \( 30^{\circ} \) and
coefficient of friction is \( 0.2, \) then the
Acceleration of the block is
A . 4.13
B. 3.27
c. 1.43
D. 1.34


Figure below shows pressure (P) versus volume(V) graphs for a certain mass of
a gas at two constant temperatures \( T_{1} \)
and \( T_{2} . \) Which of the inferences given
below is correct?
\( A \cdot T_{1}=T_{2} \)
в. \( T_{1}>T_{2} \)
\( c \cdot T_{1}<T_{2} \)
D. none of the above


The force experienced by a charged particle of charge \( q \) at (1,1,1) is
A. \( -5 q \)
в. \( 5 q \hat{\imath} \)
c. \( 5 q(\hat{i}+\hat{j}) \)
D. \( -5 q(\hat{i}+\hat{j}) \)


The Geometric mean of \( 4,4^{2}, 4^{3}, \cdots, 4^{n} \)
is
A. \( 2^{\frac{2}{2}} \)
\( \frac{2}{2} \)
B. \( 2^{\frac{n-1}{2}} \)
c. \( 4^{n+1} \)
D. \( 2^{n+1} \)


State True or False.
\( A^{\infty} \) of weak electrolytes can be
obtained only by Kohlrausch law.
A. True
B. False


Two particles \( A \) and \( B \) are released
from the top of incline. If \( \boldsymbol{m}_{\boldsymbol{A}}>\boldsymbol{m}_{\boldsymbol{B}} \)
then
A. Both will reach simultaneously if \( A \) released before \( B \)
B. Both will reach simultaneously if \( A \) released after \( B \)
c. Both will reach simultaneously if both are released together
D. Both will reach simultaneously if both are released together and \( A \) is given some initial velocity


If vector \( \vec{A}=\hat{i}+c \hat{j}+5 \hat{k} \) and vector
\( \vec{B}=2 \hat{i}+\hat{j}-\hat{k} \) are perpendicular,then
calculate the value of \( c \)


Element 'X' in period 3 has high electron affinity and electronegativity. It is likely to be a
A . alkali metal
B. alkaline metal
c. transition metal
D. non-metal


Represent the set of real values of \( x \) on the number line satisfying \( \frac{1}{2}(2 x- \)
1) \( \leq 2 x+\frac{1}{2} \leq 5 \frac{1}{2}+x . \) Also, find the
greatest and the smallest values of \( x \)
satisfying the inequations.
\( \mathbf{A} \cdot x \epsilon[-1,4] \)
В. \( x \in[-1,5] \)
\( \mathbf{c} \cdot x \epsilon[-2,5] \)
D. \( x \epsilon[-2,7] \)


Assertion
Suger and alcohols are soluble in water
Reason

They have \( \boldsymbol{O}-\boldsymbol{H} \) bonds which bind to
water by hydrogen bonding
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


Kjeldhahl's method is applicable to all nitrogenous organic compounds.
A. True
B. False


The volume of a cube in \( m^{3} \) is equal to
the surface area of the cube. The volume
of the cube is:
\( \mathbf{A} \cdot 64 m^{3} \)
B. 216 \( m^{3} \)
c. \( 512 \mathrm{m}^{3} \)
D. 196 \( m^{3} \)


The number of neutrons present in the deuterium isotope of hydrogen is
A .2
B. 3
\( c \cdot 5 \)
\( D \)


Fungi also grow on
A. Pickles
B. Leather
c. clothes and other articles
D. All of the above


Write the \( I U P A C \) name of the following
(i) iso-Butane
(ii) Ethyl methyl ketone.


prefix for side chain attached to the
parent chain lring is correct?
\( A \)
Prefix: Ethanoyloxy
B.
Prefix: Methoxycarbony
\( c \)
Prefix: cyano
\( D \)
Prefix: Carbamoy