Find the value of the sum \( \sum_{r=1}^{n} \) \( \sum_{s=1}^{n} \delta_{r s} 2^{r} 3^{s} \) where \( \delta_{r s} \) is zero if \( r \neq s \& \)
\( \delta_{r s} \) is one if \( r=s \)
A \( \cdot \frac{6\left(6^{n}-1\right)}{5} \)
B. \( \frac{6\left(6^{n}+1\right)}{5} \)
c. \( \frac{5\left(6^{n}+1\right)}{6} \)
D. \( \frac{n\left(6^{n}-1\right)}{6} \)


Two balls of masses in ratio 1: 2 are
dropped from the same height. Find the ratio between their velocities when they
strike the ground:
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4


A 20 Henry inductor coil is connected to
a 10 ohm resistance in series as shown
in figure. The time at which rate of
dissipation of energy (joule's heat)
\( \operatorname{across} \) resistance is equal to the rate at
which magnetic energy is stored in the
inductor is
A \( \cdot \frac{2}{\ln 2} \)
B. \( \ln 2 \)
\( \mathbf{c} \cdot 2 \ln 2 \)
D. \( \frac{1}{2} \ln 2 \)


Consider the function \( \boldsymbol{y}= \)
\( \log _{a}(x+\sqrt{x^{2}+1}), a>0, a \neq 1 . \) The
inverse of the function
A. does not exist
B \cdot is \( x=\log _{a}(y+\sqrt{y^{2}+1}) \)
\( \mathbf{c} \cdot \) is \( x=\sin (y \ln a) \)
D \( \quad \) is \( x=\cosh \left(-y \ln \frac{1}{a}\right) \)


For the gaseous reaction involving the complete combustion of isobutane:
\( \mathbf{A} \cdot \Delta H=\Delta E \)
B. \( \Delta H>\Delta E \)
c. \( \Delta H=\Delta E=0 \)
D. \( \Delta H<\Delta E \)


IUPAC name of the above compound is:
A. 3 -Chlorotoluene
B. 4-chlorotoluene
c. 4 -Methylchlorobenzene
3-Methylchlorobenzen


If (-3,0) is the vertex and \( Y \) -axis is the directrix of a parabola, then its focus is at the point
A. (0,-6)
()
в. (-6,0)
D. (0,0)
E . (3,0)


Find the initial acceleration of the rod


The number of bacteria in a certain
culture doubles every hour. If there were
30 bacteria present in the culture originally, how many bacteria will be
present at the end of \( 2^{n d} \) hour \( 4^{t h} \) hour
and \( n^{t h} \) hour?


Define injective function. Give an example of function.


Metals are usually hard. Hence metals are strong and can with stand heavy loads over them. Due to this property they are difficult to cut and can be used in the construction of heavy machines, buildings etc. On the other hand, non-
metals are usually brittle. On hammering them they break into small pieces converting themselves into the fine powder

In the following elements identify the element that is relatively brittle. This question has multiple correct options
A. sulphur
B. Diamond
c. Iron
D. Magnesium


If \( I_{1} \) and \( I_{2} \) are the magnitudes if
inclined current in the cases I and II
respectively, then.
\( \mathbf{A} \cdot I_{1}=I_{2} \)
\( \mathbf{B} \cdot I_{1}>I_{2} \)
\( \mathbf{C} \cdot I_{1}<I_{2} \)
D. Nothing can be said


A pair of straight lines drawn through the origin forms an isosceles right
triangle with the line \( 2 x+3 y=6, \) then
the lines and the area of the triangle thus formed is
\( \mathbf{A} \cdot x-5 y=0 \)
\[
\begin{array}{c}
5 x+y=0 \\
\Delta=\frac{36}{13}
\end{array}
\]
B. \( 3 x-y=0 \)
\[
x+3 y=0
\]
\[
\Delta=\frac{12}{17}
\]
c. \( 5 x-y=0 \)
\[
\begin{array}{c}
x+5 y=0 \\
\Delta=\frac{13}{5}
\end{array}
\]
D. None of these


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


One liter of solution contains \( 10^{-5} \)
moles of \( \boldsymbol{H}^{+} \) ions at \( 25^{\circ} \) C.Percentage
ionisation of water in solution is:
A \( .1 .8 \times 10^{-7} \% \)
В. \( 1.8 \times 10^{-5} \% \)
c. \( 3.6 \times 10^{-9} \% \)
D. \( 1.8 \times 10^{-11} \% \)


Two long straight cylindrical conductors
with resistivities \( \rho_{1} \) and \( \rho_{2} \) respectively
are joined together as shown in figure. If current I flows through the conductors, the magnitude of the total free charge at the interface of the two conductors is
A . zero
в. \( \frac{\left(\rho_{1}-\rho_{2}\right) I \varepsilon_{0}}{2} \)
\( \mathbf{c} \cdot \varepsilon_{0} I\left|\rho_{1}-\rho\right| \)
\( \mathbf{D} \cdot \varepsilon_{0} I\left|\rho_{1}+\rho\right| \)


Strong reducing behaviour of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) is
due to :
A. low oxidation state of phosphorus
B. presence of two - OH groups and one P-H bond
C. presence of one - OH group and two P-H bonds
D. high electron gain enthalpy of phosphorus


The gradual addition of electronic shells in the noble gases causes a decrease in their
A. ionization energy
B. atomic radius
c. boiling point
D. density


The subjective property of light related to its wavelength is .......... (colour, refractive index).


Convert \( 19200 \mathrm{kg} / \mathrm{m}^{3} \) into \( g \mathrm{cm}^{-3} \)
A \( \cdot 192 g c m^{-3} \)
В. \( 1.92 g \mathrm{cm}^{-3} \)
c. \( 19.2 g \mathrm{cm}^{-3} \)
D. \( 1920 \mathrm{g} \mathrm{cm}^{-3} \)


(a) Define the power of lens.
(b) Draw a ray diagram for formation of image of an object situated at a point in
between \( 2 f_{1} \) and \( f_{1} \) distances from the optical centre of the concave lens and write the nature of the image formed.
(c) What happens when light is falling perpendicular to an interface of two media?


A glass rod of length \( \ell \) moves with a velocity \( v \) in a uniform magnetic field \( B \)
what will be the emf induced in the rod:
A . \( B l v \)
в. \( \frac{B l}{v} \)
c. \( B l \)
D. None of these


One end of uniform wire of length \( L \) and
of weight \( W \) is attached rigidly to a
point in the roof and a weight \( W_{1} \) is
suspended from its lower end. If \( s \) is the
area of cross section of the wire, the
stress in the wire at a height \( (3 L / 4) \) from its lower end is
\( A \cdot \frac{W_{1}}{S} \)
в. \( \left[W_{1}+\frac{W}{4}\right] / S \)
\( \frac{\left[W_{1}+\frac{3 W}{4}\right]}{S} \)
D. \( \frac{W_{1}+W}{S} \)


The graph shows the behaviour of a
steel wire in the region for which the wire obeys Hooke's law.The graph is a part of a parabola. The variables x and y might represent
A. \( x= \) stress \( ; y= \) strain
B. \( x= \) strain ; \( y=\operatorname{str} e s \)
c. \( x= \) strain \( ; y= \) elastic energy
D. \( x= \) elastic energy \( ; y= \) strain


The equivalent weight of \( N a H_{2} P O_{4} \) in
the following reaction is:
\( N a O H+H_{3} P O_{4} \rightarrow N a H_{2} P O_{4}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
A . 96
B. 100
\( c \cdot 120 \)
D. 98


In the following reaction \( : \boldsymbol{C r}(\boldsymbol{O H})_{3}+ \)
\( \boldsymbol{O H}^{-}+\boldsymbol{I O}_{3}^{-} \rightarrow \boldsymbol{C r} \boldsymbol{O}_{4}^{2-}+\boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \boldsymbol{I}^{-}: \)
A \( \cdot I O_{3} \) - is oxidising agent
B. \( C r(O H)_{3} \) is oxidised
C. \( 6 e^{-} \) are being taken per iodine atom
D. all of these


The minimum value of \( \mathbf{a}^{2} \sec ^{2} \boldsymbol{\theta}+ \)
\( \mathbf{b}^{2} \cos \mathbf{e c}^{2} \boldsymbol{\theta} \) is
\( A \cdot a^{2}-b^{2} \)
B. \( 2\left(a^{2}+b^{2}\right) \)
\( c \cdot(a-b)^{2} \)
D. \( (a+b)^{2} \)


Multiple Choice Questions
Which one of the following is
mismatched?
A. Fossil fuel burning - Release of \( C O_{2} \)
B. Nuclear power - Radioactive wastes
C. Solar energy - Green house effect
D. Biomass burning - Release of \( C O_{2} \)


Write balanced redox reactions of the
following:
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \) reduces \( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-}(\boldsymbol{a} \boldsymbol{q}) \) to
green coloured \( C r^{3+}(a q) \) in acidic
medium.
A \( \cdot C r_{2} O_{7}^{2-}+3 H_{2} O_{2}+8 H^{+} \rightarrow 2 C r^{3+}+3 O_{2}+7 H_{2} O \)
B . \( C r_{2} O_{9}^{2-}+3 H_{2} O_{2}+4 H^{+} \rightarrow 2 C r^{3+}+3 O_{2}+7 H_{2} O \)
c. \( C r_{2} O_{7}^{2-}+3 H_{2} O_{2}+8 H^{+} \rightarrow 2 C r^{3+}+3 O_{2}+9 H_{2} O \)
D. None of these


The point \( P(x, y, z) \) lies in the first octant and its distance from the origin
is 12 units. If the position vector of \( P \)
make \( 45^{\circ} \) and \( 60^{\circ} \) with the \( x \) -axis and \( y \)
axis respectively, then the coordinates of \( \boldsymbol{P} \) are
A \( \cdot(3 \sqrt{3}, 6,3 \sqrt{2}) \)
B. \( (4 \sqrt{3}, 8,4 \sqrt{2}) \)
c. \( (6 \sqrt{2}, 6,6,) \)
D. \( (6,6,6 \sqrt{2}) \)
E \( .(4 \sqrt{2}, 8,4 \sqrt{3}) \)


A planet of mass \( m \) moves around the
sun of mass \( M \) in an elliptical orbit. The
maximum and minimum distances of
the planet from the sun are \( r_{1} \) and \( r_{2} \) respectively. The time period of the planet is proportional to:
\( \mathbf{A} \cdot r_{1}^{3 / 2} \)
B \( \cdot r_{2}^{3 / 2} \)
c. \( \left(\frac{r_{1}+r_{2}}{2}\right)^{3 / 2} \)
D. \( \frac{\left(r_{1}-r_{2}\right)^{3 / 2}}{2} \)


Solve:
\( \lim _{x \rightarrow-5} \frac{2 x^{2}+9 x-5}{x+5} \)


\( \int \frac{1}{7 x+6} d x \)


In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit?
A. Only resistor
B. Resistor and inductor
c. Resistor and capacitor
D. Only inductor.


A value of \( \theta \) for which \( \frac{2+3 i \sin \theta}{1-2 i \sin \theta} \) is
purely imaginary, is:
\( ^{\mathrm{A}} \cdot \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
в. \( \frac{\pi}{3} \)
\( \mathbf{c} \cdot \cos ^{-1} \sqrt{-} 1 \)
D. Noneofthese


Which of the following complexes has lowest molar conductance?
A. \( \operatorname{CoCl}_{3} .3 \mathrm{NH}_{3} \)
в. \( \operatorname{CoCl}_{3} .4 \mathrm{NH}_{3} \)
c. \( \operatorname{CoCl}_{3} .5 \mathrm{NH}_{3} \)
D. \( \operatorname{CoCl}_{3} .6 \mathrm{NH}_{3} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=[\boldsymbol{x}]^{2}+[\boldsymbol{x}+\mathbf{1}]-\boldsymbol{3}, \) where \( [\boldsymbol{x}] \)
is greatest integer less than or equal to
\( x, \) then
This question has multiple correct options
A. \( f(x) \) is a many one and into function
B. \( f(x)=0 \) for infinite number of values of \( x \)
c. \( f(x)=0 \) for only two real values
D. None of these


In the given figure \( \Delta A B C \cong \Delta A B T \)
write all the corresponding sides.


Pancreatic enzyme and bicarbonate secretion is stimulated by
A. Gastrin
B. Cholecystokin
c. Duocrinin
D. Enterogastrone


Describe briefly.
(a) Arithmetic growth
(b) Geometric growth
(c) Sigmoid growth curve
(d) Absolute and relative growth rates


Aluminium reacts with \( \boldsymbol{H} \boldsymbol{C l} \) to form \( \boldsymbol{H}_{2} \)
gas, but do not react with \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \) why?
A. \( A l \) with \( H N O_{3} \) forms \( A l_{2} O_{3} \) which is passive for further reaction
B. \( A l \) with \( H N O_{3} \) forms \( A l_{2} O_{7} \) which is passive for further reaction
c. \( A l \) with \( H N O_{3} \) forms \( A l_{2} O_{4} \) which is passive for further reaction
D. \( A l \) with \( H N O_{3} \) forms \( A l_{3} O_{2} \) which is passive for further reaction


From the top of a vertical tower, the
angles of depression of two cars, in the same straight line with the base of tower, at an instant are found to be 45 and \( 60 . \) If the cars are \( 100 \mathrm{m} \) apart and
are on the same side of the tower, find the height of the tower. [ Use \( \sqrt{3}=1.73] \)


Solve:
\( \int x^{2 / 3}\left(1+x^{5 / 3}\right)^{\frac{-13}{3}} d x \)
\( \mathbf{A} \cdot-\frac{9}{25\left(1+x^{5 / 3}\right)^{\frac{10}{3}}}+C \)
B. \( -\frac{9}{15\left(1+x^{5 / 3}\right)^{\frac{10}{3}}}+C \)
c. \( -\frac{9}{50\left(1+x^{5 / 3}\right)^{\frac{10}{3}}}+C \)
D. None of these


The diagram shows some food moving
along the alimentary canal. What is the
name of the process that pushes the
food along?
A. Absorption
B. Digestion
c. Peristalsis
D. Swallowing


Element \( X \) is a metal with a valency 2
Element \( Y \) is a non-metal with a
valency 3.
The balance equations to show how \( \boldsymbol{X} \) and \( Y \) form ions is :
A. \( X-2 e^{-} \rightarrow X^{2+} \)
B. \( Y+2 e^{-} \rightarrow Y^{2} \)
c. \( X-e^{-} \rightarrow X^{+} \)
D. None of these


The charge \( q \) on a plate of a condenser
of capacity \( C \) charged through a
resistance \( \boldsymbol{R} \) by a steady voltage \( \boldsymbol{V} \) satisfies the differential equation \( R \frac{d q}{d t}+\frac{q}{c}=V . \) If \( q=0 \) at \( t=0 \) then the
expression for the charge on the condenser is?
A \( \cdot q=C V\left(1-\cos \frac{-t}{R C}\right) \)
В \cdot \( q=C V\left(1-\sin \frac{-t}{R C}\right) \)
c. \( q=C V\left(1-e^{-t / R C}\right. \)
D・ \( q=C V\left(1-\cot \frac{-t}{R C}\right) \)


Which component is not directly involved in the process known as translation?
A. Ribosomes
B. tRNA
c. DNA
D. mRNA


Which compound is volatile on heating?
A. \( M g C l_{2} \)
в. \( \mathrm{HgCl}_{2} \)
c. \( Z n C l_{2} \)
D. none of these


The development of antenna-like structure in place of the eye in lobster is an example of
A. Compensatory hypertrophy
B. Heteromorphic regeneration
c. Morphollaxis
D. None of the above


In the adjacent figure \( \mathrm{PQ} \) and \( \mathrm{RS} \) are two
mirrors placed parallel to each other. An incident ray \( \overrightarrow{A B} \) strikes the mirror \( \mathrm{PQ} \) at
B, the reflected ray moves along the path \( \overrightarrow{B C} \) and strikes the mirror RS at \( C \)
and again reflected back along \( \overrightarrow{C D} \) Prove that AB II CD.


Time taken to completely (in hr) decompose \( 36 g \) water by passing \( 3 A \)
current is :
A. 35.8 hrs
в. \( 40 \mathrm{hr} \)
c. \( 51.8 \mathrm{hr} \)
D. 22.5 hr


If \( f(x)=\frac{\tan x}{\tan x} \) then
A \( \cdot \lim _{x \rightarrow 0} f(x) \) does not exists
B \( \cdot \lim _{x \rightarrow 0} f(x) \) exists
c. \( f(x) \) has fundamental period \( \pi \)
D. all of these


A reaction takes place in three steps.
The rate constants are \( k_{1}, k_{2} \) and \( k_{3} \)
The over all rate constant \( \boldsymbol{k}=\frac{\boldsymbol{k}_{1} \boldsymbol{k}_{3}}{\boldsymbol{k}_{2}} . \) If
(energy of activation) \( E_{1}, E_{2} \) and \( E_{3} \)
The overall energy of activation is:
A. 40
B. 30
c. 400
D. 60


Solve:-
\( \lim _{x \rightarrow 0} \frac{\sqrt{x^{2}+1}-1}{\sqrt{x^{2}+4}-2} \)


Traffic policeman in Tokyo
A. Wears gas mask
B. Requires daily oxygen treatment
C. Suffers from black lung disease
D. All the above


Choose the correct answer from the
alternative given. When an oxide of manganese (P) is fused with KOH in the presence of an
oxidizing agent and dissolved in water, it gives a dark green solution of compound (Q). Compound (Q) disproportionates in neutral or acidic solution to give purple compound (R). An alkaline solution of compound (R)
oxidizes potassium iodide solution to a compound (S) and compound (P) is also formed. Compounds \( P \) to \( S \) are:
A \( \cdot(P)-M n O_{4}^{-},(Q)-K I O_{3},(R)-M n O_{2},(S)- \)
\( K_{2} M n O_{4} \)
B . \( (P)-M n O_{2},(Q)-K_{2} M n O_{4},(R)-M n O_{4}^{-},(S)- \)
\( K I O_{3} \)
C \( \cdot(P)-M n O_{2},(Q)-M n O_{4}^{-},(R)-K 2 M n O_{4},(S) \)
\( K I O_{3} \)
D \( \cdot(P)-K_{2} M n O_{4},(Q)-M n O_{2},(R)-M n O_{4}^{-},(S)- \)
\( K I O_{3} \)


Light of intensity \( =3 W / m^{2} \) is incident
on a perfectly absorbing metal surface of area \( 1 m^{2} \) making an angle of \( 60^{\circ} \) with the normal. If the force exerted by
the photons on the surface is \( \boldsymbol{p} \times 10^{-9} \)
(in Newton), then the value of p is :
A. 5
B. 2
\( c \)
\( D .3 \)


Why water is called an universal
solvent?
A. Because plants use water for taking minerals from the soil
B. Water can dissolve a wide variety of substances
C. Water is clear and transparent
D. None of the above


Prove that \( f(x)=\sin x+\sqrt{3} \cos x \) has
maximum value at \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{6}} \)


State whether the given statement is True or False:

You find your mass to be \( 42 \mathrm{kg} \) on a weighing machine. You can say that your mass is more or less than \( 42 \mathrm{kg} \)
A. True
B. False


According to the definition of oblique collision in the paragraph, which of the following collision cannot be oblique?
A. Collision between two point masses.
B. Collision between two rings of same radius
c. collision between two rings of different radius
D. All the above


A diwali rocket moves vertically up with
a constant acceleration \( a_{1}=20 / 3 m s^{-2} \)
After sometimes, its fuel gets
exhausted and then it falls freely with
an acceleration \( a_{2}=10 m s^{-2} . \) If the
maximum height attained by the diwali rocket is \( h, \) using graphical method,
find its speed when the fuel is just exhausted. Assume \( h=50 \mathrm{m} \)


Lifting automobiles in service stations is based on the principle of


\( \mathbf{n} \)
Fig., \( \mathrm{M}, \mathrm{N} \) and \( \mathrm{P} \) are the mid-points of
\( A B, A C \) and \( B C \) respectively. If \( \mathrm{MN}=3 \mathrm{cm} \) \( \mathrm{NP}=3.5 \mathrm{cm} \) and \( \mathrm{MP}=2.5 \mathrm{cm}, \) calculate
\( \mathrm{BC}, \mathrm{AB} \) and \( \mathrm{AC} \)


How many diagonals does a regular hexagon have?
\( \mathbf{A} \cdot \mathbf{8} \)
B. 9
c. 10
D. 1


What is the value of \( \sqrt[3]{27} \times \sqrt[3]{-27} ? \)
A . -9
в. -27
c. 9
\( D \)


Which one of the following is an essential amino acid?
A. Tyrosine
B. Cysteine
c. Isoleucine
D. serine


Occurence of excess urea in blood due
to kidney failure is
A. Urochrome
B. Uraemia
c. Uricotelism
D. Ureotelism


The percentage composition of \( \boldsymbol{P b} \) in
\( \left[\boldsymbol{P b}_{3}\left(\boldsymbol{P O}_{4}\right)_{3}\right] \) is: (Given molar mass of
\( \left.\left[\boldsymbol{P b}_{3}\left(\boldsymbol{P O}_{4}\right)_{3}\right]=\mathbf{8 1 1 . 0} \boldsymbol{g} \boldsymbol{m o l}\right) \)
A. 73.4
в. 76.5
c. 80.1
D. 68.54


The charge on the colloidal particle is due to preferential adsorption of ions.
A. True
B. False


A small bulb is placed at the bottom of a tank containing water to a depth of 1 \( m \). Find the critical angle for water air
interface and also calculate the
diameter of the circular bright patch of light formed on the surface of water
[Refractive index of water \( =\mathbf{1 . 3 3}] \)


As shown in the image, a series of enzymes catalyze the conversion of Molecule A to Molecule C. Molecule C
functions as a co-repressor for the operon controlling production of
Enzyme A. Which of the following scenarios would most likely result from the introduction
of a large amount of Molecule C?
A. concentration of Enzyme A will decrease.
B. Concentration of Molecule A will decrease
c. concentration of Molecule B will increase
D. concentration of Enzyme B will increase.


\( \boldsymbol{g}(\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{1} & \boldsymbol{x} \leq-\boldsymbol{2} \\ \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{x} & -\boldsymbol{2}<\boldsymbol{x}<\mathbf{4} \text { .then } \\ \sqrt{\boldsymbol{x}} & , \boldsymbol{x} \geq \mathbf{4}\end{array}\right. \)
A. \( g \) is a continuous function
B. all the discontinuities are removable discontinuities
c. all the discontinuities are jump
D. all the discontinuities are infinitt


A particle initially starts from rest, travels a distance Y in the first two
seconds and a distance of \( X \) in next two
seconds then,
This question has multiple correct options
B. \( X+Y=4 X \)
c. \( X+Y=4 Y \)
\( . X=3 Y \)
\( Y \)


In a survey conducted among 400 students of \( X \) standard in Pune district,
187 students offered to join Science faculty after \( X \) standard and 125
students offered to join Commerce
faculty after \( X \). If a student is selected
at random from this group, find the probability that the student prefers Science or Commerce faculty.


Evaluate the integral \( \int_{1}^{\sqrt[7]{2}} \frac{1}{x\left(2 x^{7}+1\right)} d x \)
\( ^{\mathrm{A}} \cdot \log \frac{6}{5} \)
B. \( 6 \log \frac{6}{5} \)
c. \( \frac{1}{7} \log _{5}^{6} \)
D. \( \frac{1}{5} \log \frac{6}{5} \)


Calculate the area of a regular pentagon
with sides of \( 2 \mathrm{cm} \) and apothem is 12
\( \mathrm{cm} \)
\( A \cdot 60 \mathrm{cm}^{2} \)
B. \( 61 \mathrm{cm}^{2} \)
\( c \cdot 62 c m^{2} \)
\( \mathrm{D} \cdot 63 \mathrm{cm}^{2} \)


How many five letters words can be
formed using the letter \( \boldsymbol{T} \boldsymbol{I} \) MRET?


The angular momentum of a rotating
body changes from \( A_{0} \) to \( 4 A_{0} \) in 4 seconds. The torque acting on the body is :
A \( \cdot \frac{3}{4} A_{0} \)
B . \( 4 A_{0} \)
c. \( 3 A_{0} \)
D. \( \frac{3}{2} A_{0} \)


An Alcohol X pass over Cu at \( 300 \mathrm{C} \), then
produced compound decolourised
Bromine liquid, X is:
\( A \)
B.
\( c \)
\( D \)


If \( P(3,2,-4), Q(5,4,-6) \) and \( R \)
(9,8,-10) are collinear, then \( R \) divides PQ in the ratio
A. 3: 2 internally
B. 3: 2 externally
c. 2: 1 internally
D. 2: 1 externally


Which one of the following is not central tendency?
A. Mean deviation
B. Arithmetic mean
c. Median
D. Mode


A change of \( 2 x^{-7} C \) moves from the
origin to the point (4,4) with co-
ordinates measured in meters (see
figure). Calculate the work done by the
uniform electric field \( \boldsymbol{E}=(\mathbf{1} . \mathbf{0} \times \)
\( \left.10^{4}\right) \hat{i} N / C \) for each of three paths:
(a) (0,0)\( \rightarrow(4,0) \rightarrow(4,4) \)
(b) \( (0,0) \rightarrow(4,4), \) along the diagonal
\( (c)(0,0) \rightarrow(0,4) \rightarrow(4,4) \)
(d) What is the electrostatic potential
at point (4,4) relative to the origin?


Evaluate the given integral. \( \int x^{2} \cos x d x \)


Find an angle \( \theta, 0<\theta<\frac{\pi}{2}, \) which
increases twice as fast as its sine.


A diatomic gas is filled inside a conducting cylinder. Now we push the piston slowly to make volume of gas
half of initial. Pick correct statements
\begin{tabular}{|ccccc|}
\hline & & & & \\
\hline & & & & \\
\( \bullet \) & \( \bullet \) & \( \bullet \) & \( \bullet \) & & \\
& \( \bullet \) & \( \bullet \) & \( \bullet \) & & \( \bullet \) & \( \bullet \) \\
\( \bullet \) & \( \bullet \) & \( \bullet \) & \( \bullet \) & \( \bullet \) \\
\hline
\end{tabular}
This question has multiple correct options
A. Pressure of gas Increases because there is more average change in linear momentum of molecule in each collision
B. Pressure force on side wall of container increased
C. Pressure force on piston is increased
D. More molecules collide with piston per unit time


Calculate mean deviation from median
for the following:
Marks less 80
70 60 50 than
No. of
90 ol Students


Find the limits of the following \( \operatorname{expression} \frac{1-x^{2}}{2 x^{3}-1} \div \frac{1-x}{2 x^{2}},(1) \) when
(2) when \( \boldsymbol{x}=\mathbf{0} \)
\( \boldsymbol{x}=\infty \)


f \( p, q \) and \( r \) are three points with coordinates (1,4) and (4,5) and \( (m, m) \) respectively, are collinear then value of
\( 2 m \) is


Differentiate w.r.t \( \boldsymbol{x} \)
\( e^{\operatorname{cosec}^{2} x} \)


If molar heat capacity of the given process (as shown in figure) is \( \mathrm{C} \), then
A \( \cdot C<C_{v} \)
B. \( C=0 \)
c. \( C>C_{v} \)
D. \( C=C_{v} \)


What are the problems caused by the non-biodegradable wastes that we generate?


A block of mass \( \mathrm{m} \) is lying at rest at point \( P \) of a wedge having a smooth semi-circular track of radius R. What
should be the minimum value of \( a_{0} \) so
that the mass canjust reach point \( Q \)
\( A \cdot \frac{q}{2} \)
В. \( \sqrt{g} \)
\( c \cdot g \)
D. Not possible


If each orbital can hold a maximum of 3
electrons. The number of elements in
\( 2^{n d} \) period of the periodic table (long form) will be:
A . 27
B. 9
c. 18
D. 12


The \( L S A \) (lateral surface area) of a cube
of side \( 1 \mathrm{cm} \) is
\( \mathbf{A} \cdot 16 \mathrm{cm}^{2} \)
B. \( 4 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 2 c m^{2} \)
D. \( 1 \mathrm{cm}^{2} \)


True solution does not show Tyndall effect.
A . True
B. False


A bird is sitting on train A moving towards East with a velocity \( 300 \mathrm{km} / \mathrm{hr} \) Another train B of same speed is
moving in West direction on the same track. When the trains are \( 6 \mathrm{km} \) apart,
the bird starts flying with a velocity 30 km/hr with respect to ground towards B After touching \( \mathrm{B} \), it returns back to \( \mathrm{A} \) and continue repeating this process until the trains collide. In this process,
the total distance traveled by the bird
is:
A. \( 100 \mathrm{m} \)
B. 200 \( m \)
\( c . \) 300 \( m \)
\( D .6 \mathrm{km} \)


A cube of side \( x \) has a charge \( q \) at each of its vertices. The potential due to this charge array at the centre of the cube is
A \( \cdot \frac{4 q}{3 \pi \varepsilon_{0} x} \)
В. \( \frac{4 q}{\sqrt{3} \pi \varepsilon_{0} x} \)
c. \( \frac{3 q}{4 \pi \varepsilon_{0} x} \)
D. \( \frac{2 q}{\sqrt{3} \pi \varepsilon_{0} x} \)


Which of the following is/are the
characteristic(s) of a catalyst?
This question has multiple correct options
A. It changes equilibrium point.
B. It alter the rate of reaction.
C. it initiates the reaction.
D. It increases the average kinetic energy of molecules.


The plot of velocity (v) versus
displacement \( (x) \) of a particle executing
simple harmonic motion is shown in figure. The time period of oscillation of
particle is
\( \mathbf{A} \cdot \frac{\pi}{2} s \)
B. \( \pi s \)
\( c \cdot 2 \pi s \)
D. \( 3 \pi s \)


The amount of work done in lifting a
mass ' \( m \) ' from the surface of the earth
to height \( 2 R \) is
A. \( 2 m g R \)
в. \( 3 m g R \)
c. \( \frac{3}{2} m g R \)
D. \( \frac{2}{3} m g R \)


The temperature dependence of rate
constant \( (k) \) of a chemical reaction is
written in terms of Arrhenius equation,
\( \boldsymbol{k}=\boldsymbol{A} \boldsymbol{e}^{-\boldsymbol{E}_{a} / \boldsymbol{R} \boldsymbol{T}} . \) Activation energy \( \left(\boldsymbol{E}_{\boldsymbol{a}}\right) \)
of the reaction can be calculated by plotting:
\( \mathbf{A} \cdot \log k \) vs \( T \)
B. \( \log k \) vs \( \frac{1}{T} \)
c. \( k \) vs \( T \)
D. \( k \) vs \( \frac{1}{\log T} \)


A wire has resistance of 3.1 at \( 30 C \) and
resistance 4.5 at \( 100^{\circ} C . \) The
temperature coefficient of resistance of the wire is
B. \( 0.0024^{\circ} \mathrm{C}^{-1} \)
c. \( 0.0032^{\circ} \mathrm{C}^{-1} \)
D. \( 0.0064^{\circ} \mathrm{C}^{-1} \)


Which of the following are diasaccharides?
This question has multiple correct options
A. Lactose
B. Sucrose
c. cellulose
D. Maltose


If \( f(x)=\frac{2 x+1}{2 x^{3}+3 x^{2}+x} \) and
\( \{S=x: f(x)>0\} \) then \( S \)
\( A \cdot(-\infty,-3 / 2) \)
B . \( (-3 / 2,-1 / 4) \)
c. \( (-1 / 4,1 / 2) \)
D \( \cdot(-1 / 2,3) \)


In Fig. 3 , if 0 is the centre of the circle
\( \mathrm{OL}=4 \mathrm{cm}, \mathrm{AB}=6 \mathrm{cm} \) and \( \mathrm{OM}=3 \)
\( \mathrm{cm}, \) then \( \mathrm{CD}=? \)
\( A \cdot 4 c m \)
в. \( 8 \mathrm{cm} \)
\( c . \) 6cm
D. 10cm


Which of the following is not a saturated hydrocarbon?
A. Cyclohexane
B. Benzene
c. Butane
D. Pentane


Which of the following is not a aftereffect of earthquake?
A. Destruction of livelihood
B. Death and injuries
c. water waves and tsunamis
D. Rainfall


Brown heart disease is due to the
deficiency of
A. Boron.
B. Iron
c. Molybdenum.
D. Phosphorus


What is the advantage of choosing the wavelength of light as a standard of length?
A. Travels fast
B. Speed independent of location and temperature
c. No medium to travel
D. No advantage


How many significant figures should be present in the answer of the following calculations?
(i) \( \frac{\mathbf{0 . 0 2 8 5 6} \times \mathbf{2 9 8 . 1 5} \times \mathbf{0 . 1 1 2}}{\mathbf{0 . 5 7 8 5}} \)
(ii) \( 5 \times 5.364 \)
(iii) \( 0.0125+0.7864+0.0215 \)


The number of stereoisomers possible
for compound \( \boldsymbol{O} \) is:
\( A \cdot 2 \)
\( B .4 \)
\( c \cdot 6 \)
\( D \cdot 8 \)


Would you consider the bacteria and
yeast as plants? Give reason.


Which of the following is a true term regarding chemical reactions?
A. Reversible
B. Irreversible
c. Interchangeable
D. reliable


Give the schematic representation of Glycolysis


Let \( \boldsymbol{E} \) and \( \boldsymbol{F} \) be two independent events.
The probability that both \( \boldsymbol{E} \) and \( \boldsymbol{F} \)
happens is \( 1 / 6 \) and the probability that neither \( \boldsymbol{E} \) nor \( \boldsymbol{F} \) happens is \( \mathbf{1} / \mathbf{3} \). Then This question has multiple correct options
A \( \cdot P(E)=1 / 2, P(F)=1 / 3 \)
B . \( P(E)=1 / 2, P(F)=1 / 6 \)
C \( \cdot P(E)=1 / 6, P(F)=1 / 2 \)
D \cdot \( P(E)=1 / 3, P(F)=1 / 2 \)


The mathematical expression which is true for the uncertainty principle is:
A \( \cdot(\Delta x)(\Delta v) \geq \frac{h}{4 \pi} \)
в. \( (\Delta E)(\Delta x) \geq \frac{h}{4 \pi} \)
c. \( (\Delta \theta)(\Delta \phi) \geq \frac{h}{4 \pi} \)
D. \( (\Delta x)(\Delta m) \geq \frac{h}{4 \pi} \)


Find the area included between the
parabolas \( \boldsymbol{y}^{2}=\boldsymbol{x} \) and \( \boldsymbol{x}=\boldsymbol{3}-\boldsymbol{2} \boldsymbol{y}^{2} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D.


Two chambers, one containing \( m_{1} g \) of a
gas at \( P_{1} \) pressure and other containing
\( m_{2} g \) of a gas at \( P_{2} \) pressure are put in communication with each other. If
temperature remains constant, the
common pressure reached will be:


Find the inverse if \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}_{1}, \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{2 x+1}{3} \)


For a reaction, \( \boldsymbol{A}(\boldsymbol{s})+\mathbf{2} \boldsymbol{B}^{+} \rightarrow \boldsymbol{A}^{2+}+ \)
\( 2 B, K_{c} \) has been found to be \( 10^{12} \). The
\( \boldsymbol{E}_{c e l l}^{o} \) is:
A. \( 0.138 V \)
\( V \)
в. \( 0.235 \mathrm{V} \)
c. \( 0.354 V \)
D. none of these


Which of the following ions does not have the configuration of argon?
A \( \cdot C l \)
в. \( K^{+} \)
\( c \cdot C a^{2} \)
D. \( I \)


The displacement - time graph of a particle moving along a straight line is given below. Find the time at which its
velocity is equal to zero.
\( A \)
В.
\( c \)
D. None of these


What do you mean by short-
sightedness?


Protein synthesis in living cells is also called,
A. Transcription
B. Translation
c. Replication
D. Duplication


A ball is thrown upward from edge of a cliff with an initial velocity of \( 6 \mathrm{m} / \mathrm{s} \) How fast is it moving \( 1 / 2 \) s later \( ?(g=10 \) \( \left.\boldsymbol{m} / \boldsymbol{s}^{2}\right) \)


The following data give the amount of loans (in crores of rupees)disbursed by
a bank during some years:
Year \( \begin{array}{lll}1992 & 1993 & 1994\end{array} \)
Loan (in
crores of 28
33
55
rupees
With the help of the bar graph, indicate the year in which amount of loan is not
increased over that of the preceding
year.


In Figure \( 1, \) the ratio of \( A B \) to \( B C \) is 7:
5. If \( A C=1, \) calculate the distance
from \( A \) to the midpoint of \( B C \)
A \( \cdot \frac{5}{8} \)
B. \( \frac{2}{3} \)
c. \( \frac{19}{24} \)
D. \( \frac{3}{4} \)


Three observers \( A, B \) and \( C \) measure
the speed of light coming from a source
to be \( \boldsymbol{v}_{A}, \boldsymbol{v}_{B} \) and \( \boldsymbol{v}_{C} . \) The observer \( \boldsymbol{A} \)
moves towards the source and \( C \) moves
away from the source at the same
speed. The observer \( \boldsymbol{B} \) stays stationary. The surrounding space is vacuum
everywhere.
This question has multiple correct options
\( \mathbf{A} \cdot v_{A}>v_{B}>v_{C} \)
В . \( v_{A}<v_{B}<v_{C} \)
\( \mathbf{c} \cdot v_{A}=v_{B}=v_{C} \)
D. \( v_{B}=\frac{1}{2}\left(v_{A}+v_{C}\right) \)


The angle between the vectors \( \vec{a} \) and \( \vec{b} \) such that \( |\vec{a}|=|\vec{b}|=\sqrt{2} \) and \( \vec{a} \cdot \vec{b}=1 \)
is
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{\pi}{3} \)
\( c \cdot \frac{\pi}{4} \)
D.


Sex ratio refers to the number of
females per
A. 100 males
B. 1000 males
c. 10000 males
D. None of the above


A low concentration of chlorine, i.e parts per million (ppm), is used for the sterilisation of water to make it fit for
drinking purposes.
A. True
B. False


The equivalent Resistance:
This question has multiple correct options
A. increases in series
B. decreases in series
C . increases in parallel.
D. decreases in parallel.


Non metals are usually poor conductors of heat and electricity. They are nonlustrous, non-sonorous, non-malleable
and are coloured.
Non-metal which is required for combustion is
A. nitrogen
B. chlorine
c. oxygen
D. sulphur


Given that there is a relationship between the orbital radius of a planet and its period of revolution and that the
periods of revolution of Mercury, Earth, Jupiter and Neptune are nearly 0.24,1 11.8 and 165 years. It follows that the period of revolution of
A. Venus is less than 0.24 years
B. Mars is less than 12 years.
C. Uranus is more than 165 years
D. Uranus is less than 165 years but
more than 12 years. Of these the correct statement(s) is 1
are :
A. A and C
B. D only
c. c only
D. B and D


In the circuit shown in figure,
This question has multiple correct options
A \( \cdot V_{R}=80 V \)
В. \( X_{C}=50 \Omega \)
c. \( V_{L}=40 V \)
D. \( V_{0}=100 V \)


If the area (in sq. units) bounded by the parabola \( y^{2}=4 \lambda x \) and the line \( y= \) \( \lambda x, \lambda>0, \) is \( \frac{1}{9}, \) then \( \lambda \) is equal to
A .24
B . 48
\( c \cdot 4 \sqrt{3} \)
D. \( 2 \sqrt{6} \)


Photo-respiratory reactions are
operated in
A. Chloroplasts, ribosomes and peroxisomes
B. Chloroplasts, mitochondria and peroxisomes
C. Mitochondria, peroxisomes and lysosomes
D. Mitochondria, chloroplasts and ribosomes


Lichen is the pioneer vegetation on which succession?
A. Hydrosere
B. Lithosere
c. Psammosere
D. Xerosere


The resistance of the wire made of silver
at \( 27^{\circ} C \) temperature is equal to \( 2.1 \Omega \)
While at \( 100^{\circ} \mathrm{C} \) it is \( 2.7 \Omega \). Calculate the
temperature coefficient of the resistivity of the silver.Take the
reference temperature is equal to \( 20^{\circ} C \)


Complex which is formed during the estimation of hardness of water is:
\( \mathbf{A} \cdot\left[C a\left(S O_{4}\right)_{2}\right]^{2} \)
B \( \cdot\left[C a\left(H C O_{3}\right)_{6}\right]^{4-} \)
\( \mathbf{c} \cdot[C a(E D T A)]^{2} \)
D. \( N a_{2}\left[C a_{2}\left(P O_{3}\right)_{6}\right. \)


Sound can not travel in


How many electrodes are there in PNP or NPN transistor?
\( A \cdot 3 \)
B.
\( c \cdot 2 \)
\( D \)


Waves that travel in a direction
perpendicular to direction of vibration are known as
A. Transverse waves
B. Longitudinal waves
c. sound waves
D. None of above


p-Dichlorobenzene has higher m.p. than those of 0 - and \( \mathrm{m} \) -isomers. Discuss.


If \( f\left(\frac{3 x-4}{3 x+4}\right)=x+2, x \neq-\frac{4}{3}, \) and
\( \int \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}=\boldsymbol{A} \log |\mathbf{1}-\boldsymbol{x}|+\boldsymbol{B} \boldsymbol{x}+\boldsymbol{C} \)
then the ordered pair \( (A, B) \) is equal to
(where \( C \) is a constant of integration)
\( ^{A} \cdot\left(\frac{8}{3}, \frac{2}{3}\right) \)
B \( \cdot\left(-\frac{8}{3}, \frac{2}{3}\right) \)
\( ^{\mathbf{C}} \cdot\left(-\frac{8}{3},-\frac{2}{3}\right) \)
D. \( \left(\frac{8}{3},-\frac{2}{3}\right) \)


Which of the following is found in human faces, animal waste, oil, urea, pesticides, herbicides, fruits and vegetable waste, etc?
A. Inorganic impurities
B. organic impurities
C. Nutrients
D. Bacteria


A solid sphere rolls without slipping on
a rough horizontal floor, moving with a
speed \( \boldsymbol{v} . \) It makes an elastic collision
with a smooth vertical wall. After
impact,

This question has multiple correct options
A. it will move with a speed \( v \) initially.
B. its motion will be rolling without slipping
C. its motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant.
D. its motion will be rolling without slipping only after some time.


For a hypothetical \( \boldsymbol{H} \) -like atom, the
wavelength in \( A^{o} \) for the spectral lines
for radiations from \( n=p \) to \( n=1 \) are
given by \( \lambda=\frac{1500 p^{2}}{p^{2}-1} ; \) where \( p= \)
\( 2,3,4 \dots \)
The wavelengths of most energetic photon and least energetic photons (in
\( \left.A^{o}\right) \) during the transition are:
\( \mathbf{A} \cdot 1500,2000 A^{\circ} \)
B . \( 2000,1500 A^{\circ} \)
\( \mathbf{c} \cdot 1000,2000 A^{\circ} \)
D. \( 2000,1000 A^{\circ} \)


Solubility of alcohols in water is
to that of hydrocarbons of comparable molecular masses.
A. greater than
B. similar
c. lesser than
D. none of these


A point charge \( q \) is brought from infinity(slowly so that the heat developed in the shell is negligible) and is placed at the centre of a conducting
neutral spherical shell of inner radius a and outer radius \( b \), then work done by
external agent is:
\( A \cdot O \)
B. \( \frac{k q^{2}}{2 b} \)
c. \( \frac{k q^{2}}{2 b}-\frac{k q^{2}}{2 a} \)
D. \( \frac{k q^{2}}{2 a}-\frac{k q^{2}}{2 b} \)


Given that \( \vec{A} \times \vec{B}=\vec{B} \times \vec{C}=\overrightarrow{0} \) if \( \overrightarrow{A B C} \)
are not null vectors, Find the value of \( \vec{A} \times \vec{C} \)
A \( . \vec{A} \times \vec{B} \)
B. \( \overrightarrow{0} \)
c. \( \vec{c} \times \vec{B} \)
D. \( \vec{C} \times \vec{A} \)


Combustion of fuel is:
A. displacement reaction
B. double displacement reaction
C. oxidation reaction
D. isomerisation reaction


Find variance for following data:
\( \begin{array}{lllll}\text { Marks } & \mathbf{0}- & \mathbf{5}- & \mathbf{1 0}- & \mathbf{1 5}- \\ & \mathbf{4} & \mathbf{9} & \mathbf{1 4} & \mathbf{1 9}\end{array} \)
Frauency \( \quad 2 \quad 5 \quad 7 \) 3
\( A \cdot 7 \)
в. 55
c. 64
D. 78


A body is suspended from a spring balance kept in a satellite. The reading
of the balance is \( W_{1}, \) when the satellite
goes in an orbit of radius \( \boldsymbol{R} \) and is \( \boldsymbol{W}_{2} \)
when it goes in an orbit of radius \( 2 R \)
A. \( W_{1}=W_{2} \)
в. \( W_{1}<W_{2} \)
c. \( W_{1}>W_{2} \)
D. \( W_{1} \neq W_{2} \)


Prove that \( \operatorname{cosec}^{6} \theta=\cot ^{6} \theta+ \)
\( 3 \cot ^{2} \theta \cdot \operatorname{cosec}^{2} \theta+1 \)


Angular displacement is:
\( A \). a scalar
B. a vector
c. neither \( (a) \) nor \( (b) \)
D. either \( (a) \) or \( (b) \)


Which among the following species have the same number of electrons in
its outermost as well as penultimate shell ?
A. \( M g^{2+} \)
B. \( O^{2} \)
\( c \cdot F^{-} \)
D. \( C a^{2} \)


If concentration quotient, \( Q \) is greater
than \( K_{c}, \) the net reaction is taking place in backward direction
A. True
B. False
c. Can not be predicted
D. none of the above


Evaluate the following definite integral:
\( \int_{0}^{1} x+x^{2} d x \)


Which of the following combinations should be selected for better tuning of an L-C-R circuit used for
communication?
A. \( R=20 \Omega, L=1.5 \mathrm{H}, \mathrm{C}=35 \mu F \)
B. \( R=25 \Omega, L=2.5 \mathrm{H}, \mathrm{C}=40 \mu F \)
c. \( R=15 \Omega, L=3.5 \mathrm{H}, \mathrm{C}=30 \mu F \)
D. \( R=25 \Omega, L=1.5 \mathrm{H}, \mathrm{C}=45 \mu F \)


Let \( A, B, C \) be unit vectors. Suppose
\( A \cdot B=A \cdot C=0 \) and the angle between \( B \) and \( C \) is \( \frac{\pi}{6} . \) Then \( A \) equals
\( \mathbf{A} \cdot \pm 2(B \times C) \)
B . \( -2(B \times C) \)
\( \mathbf{c} \cdot 2(B \times C) \)
D. \( (B \times C) \)


Find the geometric mean of the following pairs of numbers:
\( a^{3} b \) and \( a b^{3} \)
\( \mathbf{A} \cdot a^{2} b^{2} \)
B. \( a b \)
\( c \cdot a b^{2} \)
D. \( a^{2} b \)


\( N a^{+} / K^{+} \) pump in a cell is an example
of
A. Osmosis
B. Diffusion
c. Passive transport
D. Active transport


When the electron in the discharge tube is accelerated to high speeds
A. the charge on the electron will decrease.
B. the specific charge will decrease.
c. the charge of the electron will increase.
D. the value of e/m will increase


Particular solution of differential
equation \( e^{\frac{d y}{d x}}=x ; y(1)=3 ; x>0 \) is
A \( \cdot \log y=x^{2}+4 \)
B. \( y=\ln x-x+4 \)
c. \( y^{2}=\log x+4 \)
D. \( 2 y=x^{2}+5 \)
E. \( y=x \ln x-x+4 \)


What is stomatal apparatus? Explain
the structure of stomata with a labelled
diagram.


Given that \( 13 x+7 \) is equal to \( -9-3 x \)
the value of \( x \) is
\( A \cdot 8 \)
в. \( \frac{1}{5} \)
\( c \cdot \frac{1}{8} \)
D. -


f \( \mathrm{D} \) is the mid point of \( \mathrm{CA} \) in triangle \( A B C \) and \( \Delta \) is the area of triangle, then show that \( \tan (\angle A D B)=\frac{4 \Delta}{a^{2}-c^{2}} \)


Formation of metallic copper from the
sulphide ore in the commercial
metallurgical process involves:
A \( \cdot C u_{2} S+\frac{3}{2} O_{2} \rightarrow C u_{2} O+S O_{2} ; C u_{2} O+C \rightarrow 2 C u+C O \)
B. \( C u_{2} S+\frac{3}{2} O_{2} \rightarrow C u_{2} O+S O_{2} ; 2 C u_{2} O+C u_{2} S \rightarrow 6 C u+ \)
\( S O_{2} \)
c. \( C u_{2} S+2 O_{2} \rightarrow C u S O_{4} ; C u S O_{4}+C u_{2} S \rightarrow 3 C u+ \)
\( 2 S O_{2} \)
D. \( C u_{2} S+\frac{3}{2} O_{2} \rightarrow 2 C u+S O_{2} ; C u_{2} O+C O \rightarrow 2 C u+ \)
\( C O_{2} \)


The word 'VIBGYOR' is made of the
initial letters of the seven colours of the
A. Prism
B. Red light
c. shadow
D. Rainbow


The reaction of ethyl magnesium bromide with water would give (ethane/methane/propane)?


An organic compound weighing 0.244 g on combustion with dry oxygen produces 0.616 g of \( C O_{2} \) and 0.108 g of \( H_{2} O . \) Determine the percentage
composition of the oxygen in compound
A . \( 11.16 \% \)
B . 26.23\%
c. \( 30.41 \% \)
D. 25.66\%


A cylindrical rod is reformed to half of its original length keeping volume constant. If its resistance before this
change were \( R \), then the resistance after
reformation of rod will be.
\( A \cdot R \)
в. \( R / 4 \)
c. \( 3 R / 4 \)
D. \( R / 2 \)


Kelvin scale has:
A. no fixed points
B. one fixed point.
C . two fixed points
D. none of these


Mid point \( \boldsymbol{A}(\mathbf{0}, \mathbf{0}) \) and \( \boldsymbol{B}(\mathbf{1 0 2 4}, \mathbf{2 0 4 8}) \) is
\( A_{1} \) and mid point of \( A_{1} \) and \( B \) is \( A_{2} \) and
so on. Coordinates of \( \boldsymbol{A}_{\mathbf{1 0}} \) are:
A. (1022,2044)
) (1022,2444)
B. (1025,2050)
c. (1023,2046)
D. (1,2)


Two equal point charges are fixed at \( x= \)
\( -a \) and \( x=+a \) on the \( x \) -axis. Another
point charge \( Q \) is placed at the origin. The change in the electrical potential energy of \( \mathrm{Q}, \) when it is displaced by a smal distance \( x \) along the \( x \) -axis, is approximately proportional to :
\( A \cdot x \)
B . \( x^{2} \)
c. \( x^{3} \)
D. \( 1 / x \)


The dark coloured dead wood present in the central region of old trees is
A. Spring wood
B. Heart wood
c. sap wood
D. Cambium


\( 6 \times 10^{22} \) gas molecules each of mass
\( 10^{-24} \mathrm{kg} \) are taken in a vessel of 10 litre. What is the pressure exerted by gas molecules if the root mean speed of gas molecules is \( 100 \mathrm{m} / \mathrm{s} ? \)
A. 20Pa
В. \( 2 \times 10^{4} \) Ра
c. \( 2 \times 10^{5} \) Ра
D. \( 2 \times 10^{7} \) Ра


\( K_{a} \) for acetic acid in water is \( 1.7 \times \)
\( 10^{-5} \) at \( 25^{\circ} \mathrm{C} . \) The \( \mathrm{pH} \) of a mixture of 25
\( \mathrm{ml} \) of \( 0.02 \mathrm{N} \) acetic acid and \( 2.5 \mathrm{ml} \) of
0.1N NaOH (neglecting volume change) will be \( (\log 1.7=0.23) \)
A . 2.
B. 4.8
\( c .7 .5 \)
D. 1.0.


The main reason for larger number of oxidation state exhibited by the actinides than that corresponding lanthanide, is:
A. lesser energy difference between \( 5 f \) and \( 6 d \) orbital than between \( 4 f \) and \( 5 d \) -orbital
B. larger atomic size of actinides than the lanthanides
C. more energy differenc between 5f and 6d orbitals than between 4f and 5d-orbitals
D. greater reactive nature of the actinides than the lanthanides


Simple two neuron reflex arc involves
A. Sensory neuron
B. Spinal cord
C. Effector neuron
D. All of the above


Misch metal is:
A. an alloy of lathanide and copper
B. an alloy of lanthanide and nickel
C . an alloy of lathanide,iron and carbon
D. an alloy of calcium and copper


If \( f(x)=\frac{1-x}{1+x} \) then the value of
\( (f o f)(x) \)
A \( \cdot \frac{1-x}{1+x} \)
B. \( x \)
\( c \cdot \frac{1}{x} \)
D. none of these


A fair die is thrown two times. Find the
chance that
Product of the numbers on the
uppermost face is 12.


\( \operatorname{Let} \boldsymbol{D}_{1}=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d} & \boldsymbol{c}+\boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{a}-\boldsymbol{b}\end{array}\right|, \quad \boldsymbol{D}_{2}= \)
\( \left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{d} & \boldsymbol{b}+\boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c}\end{array}\right|, \) then the value of
\( \left|\frac{\boldsymbol{D}_{1}}{\boldsymbol{D}_{2}}\right|, \) where \( \boldsymbol{b} \neq \mathbf{0} \) and \( \boldsymbol{a} \boldsymbol{d} \neq \boldsymbol{b} \boldsymbol{c}, \) is


Sand and sawdust can be separated by
A. gravity separation
B. calcination
c. magnetic separation
D. none of these


Draw products formed in each of the
following reaction and indicate
stereochemistry.
\( (a) \)
\( (b) \)
\( \frac{(\mathrm{i}) \mathrm{HC} \equiv \mathrm{C}^{-}}{(\mathrm{ii}) \mathrm{H}_{2} \mathrm{O}} \)
\( (c) \)
\( (d) \)
\( \frac{(\mathrm{i}) \mathrm{HC} \equiv \mathrm{C}^{-}}{(\mathrm{ii}) \mathrm{H}_{2} \mathrm{O}} \)


The engine of a motorcycle can produce a maximum acceleration of \( 5 m s^{-2} . \) Its
brakes can produce a maximum
retardation of \( 10 \mathrm{ms}^{-2} \). What is the
minimum time in which the motorcycle
can cover a distance of \( 1.5 \mathrm{km} \) ?


DNA-dependent RNA polymerase catalyze transcription on one strand of the DNA which is called the
A. Alpha strand
B. Antistrand
c. Template strand
D. coding strand


Solve the following linear programming problem:
\[
\begin{array}{c}
\text { Maximise: } \boldsymbol{z}=\mathbf{1 5 0} \boldsymbol{x}+\mathbf{2 5 0} \boldsymbol{y} \\
\text { Subject to: } \mathbf{4} \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{4 0} \\
\mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} \leq \mathbf{6 0} \\
\boldsymbol{x} \geq \mathbf{0} \\
\boldsymbol{y} \geq \mathbf{0}
\end{array}
\]


The name of the compound is 1,2
diethenyl cyclohexene.
f true enter 1 , else enter 0


What are permanent magnets? Give one example.


When a battery connected across a resistor of \( 15 \Omega, \) voltage across the resistor in \( 12 V . \) When the same battery
is connected across a resistor of \( 10 \Omega \)
voltage across it is \( 11 \mathrm{V} \). The internal
resistance of the battery (in ohm) is
A. \( \frac{10}{7} \)
в. \( \frac{20}{7} \)
\( c \cdot \frac{2}{7} \)
D. \( \frac{30}{7} \)


In turbulent flow, the velocity of the liquid molecules in contact with the walls of the tube.
A . is zero
B. is maximum
c. is equal to critical velocity
D. may have any value


A person is in front of a vertical
mountain fires a bullet and hears its
echo after a time 6 s. The person walks a
distance d towards mountain then fires
another bullet and hears its echo after a
time 2 s. If velocity of sound in air is 340
\( \mathrm{ms}^{-1} . \) The value of d is
A. 340 \( m \)
B. 170 \( m \)
c. \( 255 \mathrm{m} \)
D. \( 680 \mathrm{m} \)


Podocarpus, Ginkgo and Cycas share which one of the following character?
A. All show polyembryony
B. All have multiflagellated antherozooids.
c. All have coralloid roots
D. Both A and c


Evaluate the following:
\( \sin ^{-1}\left(\frac{2 \pi}{4}\right) \)
ii. \( \cos ^{-1}\left(\cos \frac{7 \pi}{6}\right) \)
iii. \( \tan ^{-1}\left(\tan \frac{2 \pi}{3}\right) \)
iv. \( \cos \left(\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)+\frac{\pi}{6}\right) \)
A \( \cdot \) i. \( -\frac{\pi}{3} \) ii. \( -\frac{5 \pi}{6} \) iii. \( \frac{\pi}{3} \) iv. 1
B . i. \( \frac{2 \pi}{3} \) ii. \( \frac{\pi}{6} \) iii. \( -\frac{2 \pi}{3} \) iv. 1
C \( \cdot \) i. \( -\frac{2 \pi}{3} \) ii. \( -\frac{\pi}{6} \) iii. \( \frac{2 \pi}{3} \) iv. -1
D \cdot i. \( \frac{\pi}{3} \) ii. \( \frac{5 \pi}{6} \) iii. \( -\frac{\pi}{3} \) iv. -1


Assertion
Crossing over leads to recombination of genetic material on the two
chromosomes.
Reason
Crossing over is the exchange of genetic material between two homologous
chromosomes.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which statement is inconsistent with
the concept of isotopes of the same element?
A. Isotopes have the same number of protons
B. Isotopes have the same atomic number
c. Isotopes differ in mass number
D. Isotopes differ in number of neutrons present
E. Isotopes differ in their nuclear charge


Assertion
At a point in space, the electric field points towards north. In the region,
surrounding this point the rate of
change of potential will be zero along
the east and west
Reason
Electric field due to a charge is in the
space around the charge
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


Find the value of 'k' so that the equation
\( \boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+(\boldsymbol{k}+\mathbf{2})=\mathbf{0} \) has one root
equal to zero.


Tertiary amines have lowest boiling points amongst isomeric amines because:
A. they have highest molecular mass
B. they do not form hydrogen bonds
c. they are more polar in nature
D. they are most basic in nature


Calculate the standard EMF of the
following cell \( \boldsymbol{C} \boldsymbol{d}\left|\boldsymbol{C} \boldsymbol{d}^{2+} \| \boldsymbol{A} \boldsymbol{g}^{+}\right| \boldsymbol{A} \boldsymbol{g} \)
Given that \( \boldsymbol{E}_{\boldsymbol{C d}^{2+} \mid \boldsymbol{C d}}^{\boldsymbol{o}}= \)
\( -\mathbf{0 . 4 0} V, E_{A g^{o} \mid A g}^{o}=\mathbf{0 . 8 V} \)


In stars, when many hydrogen nuclei in
the nuclear reaction are joined, is called
as:
A. mass defect
B. sunburn
c. fusion reaction
D. fission reaction
E. helium reaction


Assertion \( \operatorname{As} A=\left[\begin{array}{lll}2 & 1 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 2\end{array}\right] \) satisfies the
equation \( x^{3}-5 x^{2}+7 x-3=0 \)
therefore \( A \) is invertible.
Reason
If a square matrix \( A \) satisfies the
equation \( a_{0} x^{n}+a_{1} x^{n-1}+\ldots a_{n-1} x+ \)
\( a_{n}=0, \) and \( a_{n} \neq 0, \) then \( A \) is invertible.
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


Given below is an example of a certain structure and its special functional
activity:
Kidney and excretion. Fill in the blanks on a similar pattern:
Diaphragm and


Obtain the mean and standard
deviation for the following data set:
\[
x
\]
२० \( \begin{array}{lll}\text { 30 } & \text { 40 } & \text { 50 }\end{array} \) 10
\( Y \) \( \begin{array}{llll}05 & 15 & 30 & 35\end{array} \)


If \( P(1) \) be the probability of an event \( A \)
then
A. \( -1 \leq P(1) \leq 1 \)
B. \( 0 \leq P(1)<0.5 \)
c. \( 0 \leq P(1) \leq 1 \)
D. None of these


Find \( b \)
\[
\begin{array}{l}
\lim _{x \rightarrow 0}\left[\frac{\sin (x+a)+\sin (a-x)-2 \sin a}{x \sin x}\right] \\
=-b \sin a
\end{array}
\]


Hypertrophy of muscle is
A. Muscles become thin and weak due to excessive work.
B. Muscles become thick and strong due to excessive work.
C. Muscles become thin and weak due to no work.
D. Muscles become thick and strong due to no work.


Name the following:
A photosynthetic stage which may take place in the presence and absence of light.


A potentiometer wire of length \( 1 m \) has a
resistance of \( 10 \Omega \). It is connected to a
\( 6 V \) battery in series with a resistance of
5. Determine the emf of the primary cell which gives a balance point at
\( 40 \mathrm{cm} \)


A particle executes \( S . H . M . \) of
amplitude \( a \)
1- At what distance from mean position is its kinetic energy equal to its potential energy
2- At what points is its speed half the maximum speed


Complexes formed in the following
methods are:
(1) Mond's process for purification of nicke
(II)Removal of lead poisoning from the
body
(III) Cyanide process for extraction of silver
(IV) Froth floatation process for
separation of \( Z n S \) from galena are by using depressant
\( \begin{array}{llll}\text { A } \cdot \operatorname{Ni}(C O)_{4} & {[P b(E D T A)]^{2-}} & {\left[A g(C N)_{2}\right]} & {\left[Z n(C N)_{2}\right]}\end{array} \)
B. \( N i(C O)_{4} \quad[P b(E D T A)]^{2-} \quad\left[A g(C N)_{2}\right]^{-} \)
\[
\left[Z n(C N)_{4}\right]^{2}
\]
\( \begin{array}{lll}\text { C. } N i(C O)_{6} & {[P b(E D T A)]^{4-}} & {\left[A g(C N)_{2}\right]^{-}\left[Z n(C N)_{6}\right]^{4}}\end{array} \)
\( D \)
\( N i(C O)_{4} \) \( [P b(E D T A)]^{2-} \) \( \left[A g(C N)_{4}\right]^{3-} \) \( \left[Z n(C N)_{4}\right] \)


Assertion
A body is dropped form height \( h \) and
another body is thrown vertically upwards with a speed \( \sqrt{\boldsymbol{g} \boldsymbol{h}} \). They meet at height \( \frac{\boldsymbol{h}}{\mathbf{2}} \)
Reason
The time taken by both the blocks in reaching the height \( \frac{h}{2} \) is same.
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 is incorrect but Reason is correct


The substances which behave as
colloidal solutions at higher concentration are called:
A. associated colloids
B. multimolecular colloids
c. macromolecular colloids
D. protective colloids


In a dam,where water has a height of \( h \)
then centre of pressure is
A . below the height of \( \frac{h}{2} \)
B. above the height of \( \frac{h}{2} \)
c. at the height of \( \frac{h}{2} \)
D. any of the above


The area of the shaded field shown in
the given figure is:
\( \mathbf{A} \cdot(4 \pi+32) \mathrm{cm}^{2} \)
B \( \cdot(2 \pi+32) \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot(2 \pi+16) \mathrm{cm}^{2} \)
\( \mathbf{D} \cdot(4 \pi+24) \mathrm{cm}^{2} \)


If the string is burnt, find the angle
between \( A B \) and the vertical at
equilibrium position
\( A \)
B. \( \tan ^{-1}\left(\frac{1}{4}\right) \)
\( c \cdot \tan ^{-1}(3) \)
' \( \quad \tan ^{-1}\left(\frac{1}{2}\right) \)


The control rods in the reactor of a
nuclear power plant are made of
A. radium
B. strontium
c. barium
D. boron


\( D \) is a point on the side \( B C \) of a triangle \( A B C \) such that \( \angle A D C=\angle B A C \)
Show that \( C A^{2}=C B . C D \)


The power of Iens is equal to
A. Focal length
B. Reciprocal of focal length
C. Square of its focal length
D. Reciprocal of its radius of curvature


A ball is dropped from height hon the ground level. If the coefficient of
restitution is e then the height
upto which the ball will go after \( n^{t h} \)
jump will be-
\( A \cdot \frac{h}{e^{2 n}} \)
B. \( \frac{e^{2 n}}{h} \)
\( \mathbf{c} \cdot h e^{n} \)
D. \( h e^{2 n} \)


Which are the species in which central
atom undergoes \( s p^{3} \) hybridization?
This question has multiple correct options
\( \mathbf{A} \cdot S F_{4} \)
в. \( S C l_{2} \)
\( \mathbf{c} \cdot S O_{4}^{2-} \)
D. \( H_{2} O \)


A thin glass (refractive index 1.5) lens has optical power of -8 D in air Its optical power in a liquid medium with refractive index 1.6 will be :
A . 10
B. -1 D
\( c \cdot 25 D \)
D. -25 D


A spherical ball of lead \( 3 \mathrm{cm} \) in diameter is melted and recast into
three spherical balls. If the diameter of two balls be \( \frac{3}{2} \mathrm{cm} \) and \( 2 \mathrm{cm}, \) find the diameter of the third ball.


What is the wavelength of light emitted when the electron in a hydrogen atom undergoes a transition from an energy
level with \( n=4 \) to an energy level with
\( \boldsymbol{n}=\mathbf{2} ? \)
A \( .5654 A^{\circ} \)
B. \( 3852 A^{\circ} \)
\( \mathbf{c} \cdot 4920 A^{\circ} \)
D. \( 4852 A^{\circ} \)


If \( 2 p+3 q+4 r=15 \) then the
maximum value of \( p^{3} q^{5} r^{7} \) is?
A . 2180
в. \( \frac{5^{4} \cdot 3^{5}}{2^{15}} \)
c. \( \frac{5^{5} \cdot 7^{7}}{2^{17} \cdot 9} \)
D. 2285


An object is placed before a plane
mirror as shown. A student views the
image of the object in the mirror from point P. Where does she see the image?


A steering wheel of diameter \( 0.5 \mathrm{m} \) is rotated anticlockwise by applying two forces each of magnitude 5 N. Draw a diagram to show the application of
forces and calculate the moment of
couple applied.


Honey is:
A. acidic
B. neutral
C . alkaline
D. basic after some days


Among the following, the reaction that
proceeds through an electrophilic
substitution is:
\( A \)
B.
\( c \)
\( D \)


An object \( A B \) is placed parallel and
close to the optical axis between focus
\( F \) and center of curvature \( C \) of a
converging mirror of focal length \( \boldsymbol{f} \) as
shown in figure. Then
This question has multiple correct options
A. Image of \( A \) will be closer than that of \( B \) from the
mirror
B. Image of \( A B \) will be parallel to the optical axis
c. Image of \( A B \) will be a straight line inclined to the optical axis
D. Image of \( A B \) will not be a straight line


A ball dropped freely takes \( 0.2 s \) to
travel the last 6 m distance before
hitting the ground. Total time of fall is \( \left(g=10 m s^{-2}\right) \)
A . \( 2.9 s \)
в. 3.1 s
\( c .2 .7 s \)
D. 0.2


Continuous mitosis in plants is shown
by
A. Pith
B. Xylem
c. Phloem
D. cortex
E. Cambium


Ichthyophis belongs to
A. Amphibia
B. Mollusca
C. Annelida
D. Reptila


In a saturated solution the relative
amount of solute when
compared to the unsaturated solution.
A. More
B. Less
c. Equal
D. \( C, D \)


All orbitals in d subshell are degenerate under all conditions.
A. True
B. False


Using LMV Theorem, find a point on the curve \( y=(x-3)^{2} \), where the tangent is
parallel to the chord joining (3,0) and
\( (\mathbf{5}, \mathbf{4}) \)


It two parallel wires carry current in
opposite directions
A. The wires attract each other
B. The wires repel each other
C. The wires experience neither attraction nor repulsion
D. The forces of attraction or repulsion do not depend on current direction


Current flowing in the circuit


Differentiate with respect to \( x \) :
\( \sin ^{-1}\left(\frac{2^{x+1}}{1+4^{x}}\right) \)


The sum of the first \( n \) terms of the
geometric progression, whose first term
is 4 and the common ratio is \( 3, \) is 4372
Find \( n \)


Find the \( n^{t h} \) term and the \( 7^{t h} \) term of
\( \mathbf{3},-\mathbf{6},+\mathbf{1 2},-\mathbf{2 4}, \ldots \)
A . 191
в. 193
\( c \cdot 192 \)
D. 194


Cement is formed by burning of in a hot kiln.
A. limestone and clay
B. limestone and graphite
c. chalk and graphite
D. sulphur and limestone


Find the slope of a line passing through the points (-5,2) and (6,7)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 5
\( c .-5 \)
D. \( \frac{5}{11} \)
\( E \cdot-\frac{5}{11} \)


The maximum number of \( 90^{\circ} \) angles
between bond pair of electrons is
observed in:
A. \( d s p^{2} \) hybridization
B. \( s p^{3} d \) hybridization
c. \( d s p^{3} \) hybridization
D. \( s p^{3} d^{2} \) hybridization


How much \( \% \) of the atmosphere's mass is contained in the troposphere?
A . 20
B. 80
\( c .50 \)
D. 60


Prove that the points \( (a, 0),(0, b) \) and
(1,1) are collinear if \( \left(\frac{1}{a}+\frac{1}{b}=1\right) \)


Why are non-metals poor conductors of
electricity?
A. They have high melting point
B. They vibrate at high speed
C. They do not have free electrons
D. All of above


Potential energy of a bar magnet, of magnetic moment M is placed in a magnetic filed of induction B such that
it makes an angle \( \theta \) with the direction of B is?
\( \mathbf{A} \cdot M B \sin \theta \)
B. \( -M B \cos \theta \)
c. \( M B(1-\cos \theta) \)
D. \( M B(1+\cos \theta) \)


Which of the following solutions will be acidic?
(1) \( 0.1 M F e S O_{4} \)
(2) \( 0.1 M\left(N H_{4}\right)_{2} S O_{4} \)
(3) \( 0.1 M C H_{3} C O O N a \)
(4) \( 0.1 M N H_{4} O H \)
A \( \cdot 1,2 \) and 3 are correct
B. 1 and 2 are correct
\( c \cdot 2 \) and 4 are correct
D. 1 and 3 are correct


\( \boldsymbol{x}^{5} \sqrt{\boldsymbol{a}^{3}+\boldsymbol{x}^{3}} \)


The range of the data
25,18,20,22,16,6,17,12,30,32,10,19,8,11,20
is
A . 20
B . 16
c. 18
D. 26


A sparrow flies around a circular path
at a constant speed. If the radius of the
circular path is \( 15.0 \mathrm{m} \) and the sparrow takes 10 seconds to complete one lap. how fast is the sparrow flying?
\( A \cdot 15 \mathrm{m} / \mathrm{s} \)
B. 20 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 1.5 \mathrm{m} / \mathrm{s} \)
D. \( 9 \mathrm{m} / \mathrm{s} \)
\( E .5 \mathrm{m} / \mathrm{s} \)


The bond strength in \( O_{2}^{+}, O_{2}, O_{2}^{-} \) and
\( \boldsymbol{O}_{2}^{2+} \) follows the order
A \( \cdot O_{2}^{2+}>O_{2}^{-}>O_{2}>O_{2}^{+} \)
в. \( O_{2}^{+}>O_{2}>O_{2}^{-}>O_{2}^{2} \)
\( \mathrm{c} \cdot \mathrm{O}_{2}>\mathrm{O}_{2}^{-}>\mathrm{O}_{2}^{2+}>\mathrm{O}_{2}^{+} \)
D. \( O_{2}^{-}>O_{2}^{2-}>O_{2}^{+}>O_{2} \)


A proton and an \( \alpha- \) particle enter a
uniform magnetic field perpendicular with the same speed. If proton takes \( 20 \mu s \) to make 5 revolution, then the
periodic time for the \( \alpha \) -particle would
be:
\( A \cdot 5 \mu s \)
в. \( 8 \mu s \)
c. \( 10 \mu s \)
D. \( 12 \mu s \)


A solid sphere of radius r made of a soft material of bulk modulus K is
surrounded by a liquid in a cylindrical container.A massless piston of area a floats on the surface of the liquid, covering entire cross section of
cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, \( \left(\frac{d r}{r}\right), \) is?
A \( \cdot \frac{m g}{3 K a} \)
в. \( \frac{m g}{K a} \)
с. \( \frac{K a}{m g} \)
D. \( \frac{K a}{3 m g} \)


What will be the unit digit of \( (87)^{75^{63}} \)


Balance the following redox reactions by the ion-electron method in basis
medium
\( M n O_{4}^{-}(a q)+I^{-}(a q) \rightarrow M n O_{2}(s)+ \)
\( \boldsymbol{I}_{2}(\boldsymbol{s}) \)


While dusting a carpet, we give it a
suddenjerk or beat it with a stick
because:
A. the inertia of rest keeps the dust in its position and the dust is removed when the carpet moves away.
B. the inertia of motion removes dust.
C. no inertia involved in process.
D. jerk compensates for the force of adhesion between dust and carpet and dust is removed.


Find the correct graph regarding
equilibrium state:
\( A \)
B.
\( c \)
D. All of these


Which of the following statements is
correct about the given Daniell cell?
Solution containing Solution containing salt of Zinc \( \quad \) salt of Copper
A. This cell converts the electrical energy liberated during the redox reaction to chemical energy
B. This cell has an electrical potential greater than \( 1.1 \mathrm{v} \) when concentration of \( Z n^{2+} \) and \( C u^{2+} \) ions by unity (1 \( \left.\operatorname{mol} d m^{-3}\right) \)
c. In this cell, zinc is acting as anode and copper is acting as cathode
D. Redox reaction occurring in this cell is \( C u_{(s)}+ \) \( Z n_{(a q)}^{2+} \rightarrow C u_{(a q)}^{2+}+Z n_{(s)} \)


If a random variable \( \boldsymbol{X} \) has probability distribution function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{c}}{\boldsymbol{x}}, \mathbf{1}< \)
\( \boldsymbol{x}<\mathbf{3}, \boldsymbol{c}>\mathbf{0} \)
find \( c, E(X) \) and \( \operatorname{Var}(X) \)


Fill in the blanks with suitable words.
The zone that provides an efficient
means of transporting energy near the core of the sun is


How is the following compound I and II
related?
A. Geometrical isomers
B. Chain isomers
c. Position isomers
D. conformers


Assuming that the number of maximum permissible shells is 5 elements would be there in the periodic
table is:
A . 52
B. 54
\( c .55 \)
D. 51


Give any two differences between
lanthanoids and actinoids.


Real part of \( \frac{(1+i)^{2}}{3-i}= \)
A. \( -1 / 5 \)
в. \( 1 / 5 \)
c. \( 1 / 10 \)
D. \( -1 / 10 \)


Which of the following graphs closely represents the kinetic energy \( (K) \) of a
freely falling body and its height \( (h) \)
above the ground?
\( A \)
в.
c.
D.


What will be the wavelength of the \( x \) rays which give a diffraction angle \( 2 \theta \)
equal to \( 16.80^{\circ} \) for a crystal, if the inter planner distance in the crystal is 0.200 nm and only first order diffraction is
observed \( \left(\sin 8.40^{\circ}=0.146\right) \)


Which one of the following statements
is incorrect?
A. Specific conductivity decreases with dilution
B. Equivalent and molar conductivities increases with dilution
\( \mathrm{C} \cdot \Lambda_{m}^{o} \) for a weak electrolyte cannot be found by
extrapolation of \( \Lambda_{m} \) to zero concentration
D. Molar conductivity of a strong electrolyte increases with dilution because ionization increases with dilution


Solar radiation emitted by the sun resembles that emitted by a black body at a temperature of 6000 K. Maximum intensity is emitted at a wavelength of
about \( 4800 A^{\circ} \). If the sun were to cool
down from \( 6000 K \) to \( 3000 K \), then
the peak intensity would occur at a wavelength of:
A .4800 A
B. 96000 \( ^{\text {? }} \)
c. \( 2400 A^{\circ} \)
D. 19200 A


\( C_{P}-C_{V} \) for an ideal gas is R. Explain.


Arrange electron(e), proton (p) and deuteron(d) in the increasing order of their specific charge:
A \( . e>p<d \)
B. \( d<p<e \)
c. \( p>e>d \)
D. \( d>e>p \)


When a light ray moves from air to a transparent medium the angle of incidence and the angle of refraction
\( \operatorname{are} 45^{\circ} \) and \( 30^{\circ} \) respectively. Find the refractive index of this medium is
A . 1.21
B. 1.42
c. 1.88
D. 2.42


When we touch a steel rod and a paper
simultaneously, we feel that the rod is
colder because:
A. iron being a good conductor conducts more heat from our body
B. paper being a good conductor conducts more heat from our body
C. more heat flows from the iron to our body
D. more heat flows from the paper to our body


Two metallic solid sphere of radii \( \mathrm{R} \) and
\( 2 R \) are charged such that both of them
have same charge density \( \sigma \). If the
sphere are located far away from each other and connected by a thin conducting wire,the new charge density on bigger sphere is:


A cube with an edge length 4 is divided into 8 identical cubes. Calculate the
difference between the combined
surface area of the 8 smaller cubes and
the surface area of the original cube.
A . 48
B. 56
c. 96
D. 288


If \( \boldsymbol{m}\left[\begin{array}{ll}-\mathbf{3} & \mathbf{4}\end{array}\right]+\boldsymbol{n}\left[\begin{array}{ll}\mathbf{4} & -\mathbf{3}\end{array}\right]=\left[\begin{array}{ll}\mathbf{1 0} & -\mathbf{1 1}\end{array}\right] \)
then \( 3 m+7 n= \)
\( A \cdot 3 \)
B. 5
c. 10
\( D \)


Assertion
Statement-I: Wolframite impurities are separated from cassiterite by electromagnetic separation.
Reason
Statement- II : Cassiterite being magnetic is attached by the magnet and forms a separate heap.
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


If \( D, E, F \) are respectively the midpoints of the sides \( A B, B C, C A \) of \( \Delta A B C \) and the area of \( \Delta A B C \) is
\( 24 s q . c m, \) then the area of \( \Delta D E F \) is:
\( \mathbf{A} \cdot 24 \mathrm{cm}^{2} \)
B. \( 12 \mathrm{cm}^{2} \)
c. \( 8 \mathrm{cm}^{2} \)
D. \( 6 \mathrm{cm}^{2} \)


On simplification the product of given expression \( \left(x-\frac{1}{x}\right)\left(x+\frac{1}{x}\right)\left(x^{2}+\frac{1}{x^{2}}\right) \)
A \( \cdot x^{3}-\frac{1}{x^{3}} \)
в. \( x^{3}+\frac{1}{x^{3}} \)
c. \( x^{4}-\frac{1}{x^{4}} \)
D. \( x^{4}+\frac{1}{x^{4}} \)


If \( I=\int_{0}^{\pi} \frac{x^{2} \sin ^{2} x \cos ^{4} x}{x^{2}-3 \pi x+3 x^{2}} d x \) then the
value of \( \frac{32}{\pi^{2}} I+298 \) is equal


Solve: \( \frac{34}{3 x+4 y}+\frac{15}{3 x-2 y}=5 \) and
\( \frac{25}{3 x-2 y}-\frac{8.50}{3 x+4 y}=4.5 \)
A. \( x=7 ; y=2 \)
в. \( x=5 ; y=2 \)
c. \( x=1 ; y=2 \)
D. \( x=3 ; y=2 \)


The value of \( c \) for which the area of the
figure bounded by the curve \( y=8 x^{2}- \)
\( x^{5}, \) the straight lines \( x=1 \) and \( x=c \) and the \( x- \) axis is equal to \( \frac{16}{3} \) is
\( A \cdot 2 \)
B . \( \sqrt{8-\sqrt{17}} \)
\( c .3 \)
D. -


Recently, a new device is innovated which allows brain to bypass spinal cord and can directly send signal to limbs and thus can allow movement of
paralysed limbs.What kind of signals the device must be generating which controls these muscles?
A. Thermal signals
B. Electric signals
c. optical signals
D. Chemical signals


A proton moving with a velocity V is acted upon by electric field E and magnetic field B. The proton will move undeflected if
A. E is perpendicular to B
B. E is parallel to V and perpendicular to B
C. E is parallel to B and both are perpendicular to
D. E, V and B are mutually perpendicular and \( V=E / B \)


Draw a ray diagram to show the angle of deviation when a ray of light passes through a glass prism.


An inductive coil has a resistance of 100
When an AC signal of frequency \( 1000 \mathrm{Hz} \) is applied to the coil, the voltage leads
the current by \( 45^{\circ} . \) The inductance of the coil is
A \( \cdot \frac{1}{10 \pi} \)
в. \( \frac{1}{20 \pi} \)
c. \( \frac{1}{40 \pi} \)
D. \( \frac{1}{60 \pi} \)


Assertion
On cooling, the brown colour of nitrogen dioxide disappears.
Reason
On cooling, \( N O_{2} \) undergoes
dimerisation resulting in the pairing of
the odd electrons in \( N O_{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A ray of white light shows no dispersion on emerging from a glass plate (slab). Is there no dispersion inside the glass plate as well?


Describe the JJ. Thomson method for
determining the specific charge of an
electron.


Three resistors are connected in series
\( \operatorname{across} \) a 12 V battery. the first resistor has value of \( 1 \Omega, \) second has a voltage
drop of \( 4 \mathrm{V} \) and third has a power dissipation of 12 W. Then, the value of
the circuit current is
A \( \cdot 2 \) A
B. 6 A
c. either 2 A or 6 A
D. none of the above


A white light ray is incident on a glass
prism, and it create four refracted rays A, B, \( C \) and \( D \). Match the refracted rays with the colors given (1 and D are rays due to total internal reflection)


When slightly different weights are placed on the two pans of a beam balance, the beam comes to rest at an
angle with the horizontal. The beam is supported at a single point \( P \) by a pivot. Then which of the following statement(s) is/are true?
nonzero at the equilibrium position
B. The whole system does not continue to rotate about \( P \) because it has a large moment of inertia
c. The centre of mass of the system lies below P.
D. The centre of mass of the system lies above P.


Solid body with no deformation is-
A. rigid body
B. liquid body
c. both of them
D. none of them


Assertion
Alkaline earth metal oxides are quite
stable to heat.
Reason
Enthalpies of formation of alkaline
earth metal oxides are quite high.
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


\( \underset{n \rightarrow \infty}{L t}\left[\frac{n^{1 / 2}}{(n+3)^{3 / 2}}+\frac{n^{1 / 2}}{(n+6)^{3 / 2}}+\frac{n^{1 / 2}}{(n+9)}\right. \)
is equal to :
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{3} \)
D. None of these


Assertion
Areas near the equator receive rainfall throughout the year
Reason
High Temperature and high humidity cause conventional rain in most
afternoons near the equator.
A. Both A and R are true but R is the correct explanation of
B. Both A and R are true but R is not a correct explanation of A
C. A is true but \( R \) is false
D. A is false but R is true


Plants continue to grow throughout
their life.
A. True
B. False


Assertion
When sodium hydride in fused state is electroysed, hydrogen is discharged at anode
Reason
Sodium hydride is an electroovalent compound in which hydrogen is present
as cation
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


Verify Rolle's theorem for \( \boldsymbol{f}(\boldsymbol{x})= \) \( x \sqrt{a^{2}-x^{2}} \) in \( [0, a] \)


12 coplanar non collinear forces (all of equal magnitude) maintain a body in equilibrium, then the angle between any two adjacent forces is:
A . 15
в. 30
c. 45
D. \( 60^{\circ} \)


What is the molecular formula of \( 3- \)
ethyl-1-2, 3-dimethylpentanol?


The organic product of which reaction from the following is used as anaesthetic :
A \( \cdot C S_{2}+3 C l_{2} \frac{S n h . A C C_{3}}{\longrightarrow} \)
B . chloral \( +C a(O H)_{2} \longrightarrow \)
c. chorral + Cholorbenzene \( \rightarrow \)
D. \( C H C l_{3} \stackrel{H_{2} / N i}{\longrightarrow} \)


In the Boolean Algebra A.B is same.
\( A \cdot A+B \)
B. A-B
c. \( A-B \)
D. A\divs


Which of the following metals, adsorb hydrogen on their surface?
A. \( Z n \)
в. \( P d \)
\( c \cdot P t \)
D. \( K \)


The electrostatic potential energy of two point charges, \( 1 \mu C \) each, placed 1 meter apart in air is?
\( \begin{array}{l}\text { A } \cdot 9 \times 10^{3} \\ \text { j }\end{array} \times 10^{\times 10} \)
В. \( 9 \times 10^{9} \),


During inspiration, which of the following condition takes place?
A. Thoracic volume increases
B. Thoracic volume decreases
c. Thoracic volume remains same
D. None of the above


Explain why we dont store lemon pickle in an aluminum utensil.


If the \( n^{t h} \) term of geometric progression
\( 5,-\frac{5}{2}, \frac{5}{4},-\frac{5}{8}, \ldots . \) is \( \frac{5}{1024}, \) then the value
of \( n \) is
A . 11
B. 10
\( c .9 \)
\( D \)


An electric charge in uniform motion produces:
A. An electric field only
B. A magnetic field only
c. Both electric and magnetic fields
D. No such field at all


If
\( A, B \) and \( C \) are the three elements of
Dobereiner's triad, and atomic weights of \( A \) and \( B \) are 7 and \( 15, \) respectively then the atomic weight of \( C \) is :
\( A \cdot 1 \)
B. 11
\( c \cdot 23 \)
D. 25


Prove that the length of the common chord of the two circles whose
equations are \( (x-a)^{2}+(y-b)^{2}=c^{2} \)
and \( (x-b)^{2}+(y-a)^{2}=c^{2} \) is
\( \sqrt{4 c^{2}-2(a-b)^{2}} \)
Hence find the condition that the two
circles may touch.


The weight of a stand bag is 40 kg. In a hurry it was weighted as 40.9 kg. The error percentage is :
A . 1\%
B. 0.5\%
c. 1.5\%
D. 2\%


Average life span of human RBC is
A. 100 days
B. 90 days
c. 120 days
D. None of the above


Carbon brushes are not necessary in a
dynamo, if the coil remains stationary
and the magnet moves, because
A. Current is drawn from a stationary source
B. Current is drawn from a moving source
c. Direct current is produced
D. It is not necessary to reverse the direction of the current


Let \( f \) be a function defined for every \( x \)
such that \( f^{\prime \prime}=-f, f(0)=0, f^{\prime}(0)=1, \) then \( f(x) \)
is equal to
A. \( \tan x \)
B \( \cdot e^{x}-1 \)
\( c \cdot \sin x \)
\( D \cdot 2 \sin x \)


Convert speed into \( \boldsymbol{k m} / \boldsymbol{h} \) \( 15 m / s \)


Hydrocarbons are:
A. compounds of carbon and hydrogen
B. compounds of carbon and oxygen
C. compounds of carbon and halogen
D. none of the above


Let \( \boldsymbol{f} \) be differential for all \( \boldsymbol{x} \). If \( \boldsymbol{f}(\mathbf{1})= \)
-2 and \( f^{\prime}(x) \geq 2 \) for \( x \epsilon[1,6], \) then \( ? \)
A. \( f(6)=5 \)
В. \( f(6)<5 \)
C. \( f(6)<8 \)
D. \( f(6) \geq 5 \)
is \( 5(6) \geq 5 \)


What methods could be used to
distinguish between cis and trans isomer of a complex?


Magnification produced by a concave lens is always:
A. less than 1
B. more than 1
c. equal to 1
D. equal to 2


Which one of the elements with the
following outer orbital configurations may exhibit the largest number of oxidation states?
\( \mathbf{A} \cdot 3 d^{5} 4 s^{1} \)
B . \( 3 d^{5} 4 s^{2} \)
c. \( 3 d^{2} 4 s^{2} \)
D. \( 3 d^{3} 4 s^{2} \)


What is the output Y in the following circuit when all the three inputs \( A, B, C \)
are first 0 and then \( 1 ? \)
A . 1,1
в. 0,1
\( c .0,0 \)
D. 1,0


Evaluate the Given limit:
\( \lim _{x \rightarrow 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a}, a+b+c \neq 0 \)


The correct statement is/are:
A) Vitamins in high concentrations catalyse biological reactions
B) Daily dose of vitamins for an individual depend on his or her age, site and rate of metabolism
C) Youngsters need higher quantities of vitamins than elders
D) The need of vitamins for younger,
growing children and pregnant women is lower
A. \( A \) and \( B \)
B. \( A, B \) and \( C \)
c. \( A \) and \( D \)
D. \( C \) and \( D \)


What is a hemichordate?


The speed of a reaction is determined
by:
A. rate of reaction
B. temperature of reaction
c. nature of reactant
D. flow of reactants


Evaluate \( \int_{1}^{2}\left(x^{2}-1\right) d x \)


An aromatic molecule will:
This question has multiple correct options
\( \mathbf{A} \). Have \( 4 n \pi \) electrons
B. Have \( (4 n+2) \pi \) electrons
C. Be planar
D. Be cyclic


India's ranking on Mulberry Sillk
production is
A. Fourth
B. Third
c. second
D. First


Who among the following are associated with SONAR?
A. Plumber
B. Doctor
c. carpenter
D. Navigators


\( \int \frac{\sqrt{4+x^{2}}}{x^{6}} d x= \)
\( \frac{\boldsymbol{A}\left(\boldsymbol{4}+\boldsymbol{x}^{2}\right)^{\frac{3}{2}}\left(\boldsymbol{B} \boldsymbol{x}^{2}-\boldsymbol{6}\right)}{\boldsymbol{x}^{5}}+\boldsymbol{C} \)
This question has multiple correct options
A \( \cdot A=\frac{1}{120} \)
B. \( B=1 \)
c. \( A=-\frac{1}{120} \)
D. \( B=-1 \)


Which of the following was the first successful animal clone?
A. Dolly goat
B. Dolly sheep
c. Molly goat
D. Molly sheep


Evaluate : \( \int \frac{(3 x+5) d x}{\sqrt{x^{2}+4 x+3}} \)


Plot a graph showing the variation of current density (j) versus the electric field
(E) for two conductors of different
materials. What information from this
plot regarding the properties of the conducting material, can be obtained
which can be used to select suitable
materials for use in making (i) standard resistance and
(ii) connecting wires in electric circuits?

Electron drift speed is estimated to be
of the order of \( \mathrm{mm} s^{-1} \). Yet large current
of the order of few amperes can be set up in the wire. Explain briefly.


Azeotropic mixtures can be seperated by distillation of solution. If true enter 1 , else enter 0 .


The electron dot structure for \( B F_{3} \) is
\( A \)
B.
\( c \)
\( D \)


A chemical substance which cures
some disease, is safe to use, and has
negligible toxicity, is known as:
A. medicine
B. drug
c. antiseptic
D. antipyretic


Epithelial cells get nutrient material
from.
A. Neighbourig cells
B. Blood vessels
c. Lymph vessels
D. Underlying tissue


A wheel of mass \( 10 k g \) and radius \( 0.2 m \)
is rotating at an angular speed of 100rpm, when the motion is turned off Neglecting the friction at the axis, the force that must be applied tangentially to the wheel to bring it to rest in 10 rev is approximately o. \( x N \). Find \( x \). Assume
wheel to be a disc.


Let \( A \) be a \( 3 \times 3 \) matrix and \( B \) be its
adjoint matrix. If \( |\boldsymbol{B}|=\mathbf{6 4}, \) then \( |\boldsymbol{A}|= \)
\( A \cdot \pm 2 \)
B. ±4
\( c .\pm 8 \)
D. ±12


Ruptured blood cells are not trapped in
A . Liver
B. Spleen
c. Bone marrow
D. Both A and C


Using section formula. show that the points (-3,-1),(1,3) and (-1,1) are collinear.


State True or False.
In a galvanic cell, reduction occurs at
cathode.
A. True
B. False


The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) given by
\( f(x)=\cos x \) for all \( x \in R, \) is :
A. surjective bu nor injective
B. injective but nor surjective
c. neither injective nor surjective
D. injective


A closed organ pipe and an open pipe of
same length produce 4 beats when they are set into vibrations simultaneously.
If the length of each of them were twice their initial lengths, the number of beats produced will be [Assume same mode of vibration in both cases
\( A \cdot 2 \)
B. 4
\( c \)
D. 8


Which of the following is/are the raw materials used to manufacture
cement?

This question has multiple correct options
A. clay
B. Limestone
c. calcium sulphate
D. Slaked lime


a)Write a note on convent or molecular
hydrides. Give examples
b) What is water-gas shift reaction?
c)Write any three postulated of Dalton's atomic theory.
d)What is empirical formula? Give an example of a compound whose empirical formula and molecular formula are same
e)What is intensive property of a system? Pickout the intensive property from mass. internal energy density and
volume.
f) Describe the experiment to determine the internal energy change by bomb calorimeter with neat labelled diagram.


A wire is in the shape of a square of side \( 10 \mathrm{cm} . \) If the wire is rebent into a
rectangle of length \( 12 \mathrm{cm} \), find its breadth. Which figure encloses more area and by how much?


Which of the following is an example of
liquid dishwashing detergent?
A \( C H_{3}\left(C H_{2}\right)_{10}-C H_{2} O S O_{3}^{-} N a \)
\( a \)
\( B \)
\( c \)
D


On \( R-\{1\}, \) a binary operation \( * \) is
defined by \( a * b=a+b-a b . \) Prove
that \( * \) is commutative.


FAD participates in Krebs' cycle as electron acceptor during conversion of
A. succinyl CoA to succinic acid
B. \( \alpha \) -ketoglutarate to succinyl CoA
c. succinic acid to fumaric acid
D. fumaric acid to malic acid


The lock of a safe consists of five disce
each of which features the digits. \( 0,1,2, \ldots .9 . \) The safe can be opened by dialing a special combination og the digits. The number of days sufficient enough to open the safe, if the work day lasts \( 13 h \) and \( 5 s \) are needed to dial one
combination of digits is:
\( A \cdot 9 \)
B. 10
\( c \cdot 11 \)
D. 12


The correct order of solubility in water
for \( \mathrm{He}, \mathrm{Ne}, \mathrm{Ar}, \mathrm{Kr}, \) Xe is :
\( \mathbf{A} \cdot H e>N e>A r>K r>X e \)
В \( . X e>K r>A r>N e>H e \)
C \( . N e>A r>K r>H e>X e \)
D \( . A r>N e>H e>K r>X e \)


As the mass number A varies which of
the quantity related to nucleus does not change
A . mass
B. volume
c. binding energy
D. density


How many structural isomers are there
of trichloropropane, \( C_{3} H_{5} C l_{3} ? \)
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6


Is the given equation quadratic? Enter 1 for True and 0 for False.
\( \boldsymbol{n}-\mathbf{3}=\mathbf{4} \boldsymbol{n}^{2} \)


If heat of formation of \( C a C l_{2} \) and \( N a C l \)
are 191 and 97.5 kcal, the heat of
reaction for \( \boldsymbol{C a} \boldsymbol{C l}_{2}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{a} \longrightarrow \)
\( 2 N a C l+C a \) is:


If the points \( \boldsymbol{A}(-2,1), B(a, b) \) and \( C(4,-1) \) are collinear and \( a-b=1 \)
find the values of \( a \) and \( b \)
A \( . a=1, b=5 \)
В. \( a=1, b=0 \)
c. \( a=2, b=0 \)
D. None of these


Assertion
\( N H_{3} \) is a Lewis base.
Reason
Ammonia can accept a proton.
A. Both Assertion and Reason are correct and the 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 and the Reason is correct


Light of a single colour is passed through a liquid having a piece of glass suspended in it. On changing the temperature of liquid, at a particular temperature the glass piece is not seen. The glass piece is not seen when the refractive index of liquid becomes
the refractive index of the
glass.
A. greater than
B. less than
c. equal to
D. cant say


The convex surface of a thin concavo-
convex lens of the glass of refractive
index 1.5 has a radius of curvature
\( 20 \mathrm{cm} . \) The concave surface has a radius
of curvature \( 60 \mathrm{cm} . \) The convex side is
silvered and placed on a horizontal
surface.
(a) Where should a pin be placed on the optic axis such that its image is formed at the same place?
(b) If the concave part is filled with
water of refractive index \( 4 / 3, \) find the
distance through which the pin should be moved, so that the image of the pin again coincides with the pin.


Cells of the pancreas are not digested by their own enzymes because
A. Enzymes are secreted in inactive form
B. Cells are not lined by mucous membrane
C. Enzymes are released only when needed
D. None of the above


Classify the following function as injection, surjection or bijection:
\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \operatorname{given} \operatorname{by} \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} \)


If rotational inertial parameter of a body rolling down a rough inclined plane (of inclination \( \theta \) and height \( h \) ) without slipping is given by \( \beta=\frac{I_{c m}}{M R^{2}}, \) then the time taken by the body to reach the bottom of the inclined plane is given by
\( ^{\mathrm{A}} t=\frac{1}{\sin \theta} \sqrt{(1+\beta) \frac{h}{2 g}} \)
в. \( t=\frac{1}{\sin \theta} \sqrt{(1+\beta) \frac{2 h}{g}} \)
\( ^{c} t=\frac{1}{\sin \theta} \sqrt{(1-\beta) \frac{h}{2 g}} \)
D \( t=\frac{1}{\sin \theta} \sqrt{(1+\beta) \frac{h}{g}} \)


Prove that sine function is continuous
at every real number.


ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on
AB
Prove that (i) \( a r(A B C D)= \)
\( a r(A B E F) \)
(ii) \( a r(A B C D)=A B \times D G \)


The monomer of neoprene is:
\( A \cdot 1,3-B u t a d i e n e \)
B. 2-Chloro-1, 3-butadiene
C. 2 -Methyl-1, 3-butadiene
D. vinyl chloride


Convert into percentage:
i) \( \frac{12}{24} \)


The fusion of two nuclide will require a temp of order of
\( \mathbf{A} \cdot 10^{6} K \)
B . \( 10^{7} K \)
\( \mathbf{c} \cdot 10^{8} K \)
D \cdot \( 10^{9} K \)


A metallic wire has a resistance of \( 3.0 \Omega \)
at \( 0^{\circ} \mathrm{C} \) and \( 4.8 \Omega \) at \( 150^{\circ} \mathrm{C} \). Find the
temperature coefficient of resistance of
its material


Which of the following pairs have identical value of \( e / m ? \)
A. A proton and a neutron
B. A proton and deuteriumm
c. A deuterium and an \( \alpha \) -particle
D. An electron and a \( \gamma \) -ray


The first and last term of an \( A . P . \) are \( a \)
and \( l \) respectively. If \( S \) is the sum of all
the terms of the \( A . P . \) and the common
difference is \( \frac{l^{2}-a^{2}}{k-(l+a)}, \) then \( k \) is
equal to
\( A \)
B . \( 2 s \)
\( c \cdot 3 s \)
D. None of these


In Boyles experiment for a given gas at
different temperatures the graph drawn
between pressure and density are
straight lines as shown then:
A \( \cdot T_{1}>T_{2} \)
в. \( T_{2}>T_{1} \)
\( \mathrm{c} \cdot T_{1}=T_{2} \)
D. \( T_{1}^{3}=T_{2} \)


Which of the following are antidepressants? This question has multiple correct options
A . Iproniazid
B. Phenelzine
c. Equanil
D. Salvarsan


Find the relation between \( x \) and \( y \) from
the following statements. \( -\boldsymbol{x}= \)
\( \mathbf{5} ;-\mathbf{5}<\boldsymbol{y} \)
A \( . x<y \)
В. \( x=y \)
c. \( x>y \)
D. none


Saheli is?
A. An oral contraceptive for females
B. A surgical sterilization method for females
C. A diaphragm for females
D. A diaphragm used by males
E. A surgical method of sterilization in males


The incident ray, the reflected ray and
the ........... all lie on the ....... plane.
A. Normal, different
B. Normal, same
c. Emergent ray, different
D. Emergent ray, same


The differential equation \( (3 x+4 y+ \)
1) \( \boldsymbol{d} \boldsymbol{x}+(\boldsymbol{4} \boldsymbol{x}+\boldsymbol{5} \boldsymbol{y}+\mathbf{1}) \boldsymbol{d} \boldsymbol{y}=\boldsymbol{0} \) represents
a family of
A. Circles
B. Parabolas
c. Ellipses
D. Hyperbolas


AOBCA is a quadrant of a circle of
radius \( 3.5 \mathrm{cm} \) with centre \( 0 . \mathrm{P} \) is adjoint
on OB such that \( O P=2 c m \). The area of
the shaded part is
A \( \cdot 12.25 \mathrm{cm}^{2} \)
8. \( 6.125 \mathrm{cm}^{2} \)
\( c \cdot 12.5 \mathrm{cm}^{2} \)
D. None of thes


Peacock shows which of the following
genotype?
A. \( x x \)
B. XY
\( c \cdot z z \)
D. zw


A uniform magnetic field of induction \( \boldsymbol{B} \)
is confined to a cylindrical region of radius \( R \). The magnetic field is
increasing at a constant rate of \( \boldsymbol{d B} / \boldsymbol{d t T} \)
\( s^{-1} . \) An electron placed at the point \( P \) on the periphery of the field, experiences an acceleration:
\( ^{\mathbf{A}} \cdot \frac{1}{2} \frac{e R}{m} \frac{d B}{d t} \) toward left
B. \( \frac{1}{2} \frac{e R}{m} \frac{d B}{d t} \) toward right
c. \( \frac{e R}{m} \frac{d B}{d t} \) toward left
D. zero


Which of the following is true?
A. The gaseous form is the water vapour present in the air around us.
B. The liquid form is the water vapour present in the air around us.
C. The gaseous form is the water vapour present in the river.
D. The gaseous form is the water vapour present at the poles of the earth.


Which one of the following is the true in electrolytic refining?
A. Impure metal is made cathode
B. Impure metals is made anode
c. Impure metals is made cathode and pure metal as anode
D. Both electrodes must be of pure metal.


Water is flowing continuously from a \( \operatorname{tap} \) of area \( 10^{-4} m^{2} . \) The water velocity
as it leaves the top is \( 1 \boldsymbol{m} / \boldsymbol{s} \) Find out area of the water stream at a
distance \( 0.15 m \) below the top.
A \( .0 .5 \times 10^{-4} m^{2} \)
B . \( 1 \times 10^{-4} m^{2} \)
c. \( 2 \times 10^{-4} m^{2} \)
D. \( 0.25 \times 10^{-4} m^{2} \)


Lines of force
A. are not imaginary lines
B. cannot be mapped on paper
c. do not intersect each other
D. always intersect each other


\( a x+b y+c=0 \) does not represent an
equation of line if
A. \( a=c=0, b \neq 0 \)
B. \( b=c=0, a \neq 0 \)
c. \( a=b=0 \)
D. \( c=0, a \neq 0, b \neq 0 \)


Write the following decimals in the place value table.
\( \mathbf{1 4 8 . 3 2} \)


The IUPAC name of the given compound
\( \boldsymbol{C H}_{3} \boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right) \boldsymbol{C H O} \) is \( \boldsymbol{x} \)
methylpropanal. What is \( x ? \)


(a) Explain with example
(i) Saturated hydrocarbon
(ii) Hydrogenation of unsaturated hydrocarbons.
(b) Write two characteristics of carbon
atom
(c) What is substitution reaction?


A straight wire lying in a horizontal plane carries a current from magnetic north to magnetic south. What is the direction of force felt by the wire?


A pressure meter attached to a closed
water tap reads \( 1.5 \times 10^{5} \) Pa. When the
\( \operatorname{tap} \) is opened, the velocity of flow of
water is \( 10 \mathrm{ms}^{-1} \) and the reading of the
pressure meter is
A . \( 1.5 \times 10^{5} \mathrm{Pa} \)
B. \( 3 \times 10^{5} \mathrm{Pa} \)
c. \( 0.5 \times 10^{5} \mathrm{Pa} \)
D. \( 10^{5} \mathrm{Pa} \)


The area of quadrilateral constructed by lines \( |\boldsymbol{x}|+|\boldsymbol{y}|=\mathbf{1} \) is
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


If \( a+3 b+2 c=12 \), then the maximum
value of \( 6 b c(1+a)+a(3 b+2 c) \) is
A. 112
в. 115
\( c \cdot 102 \)
D. 92


If vector \( \overline{O P} \) in \( X Y \) plane whose
magnitude is \( \sqrt{3} \) makes an angle \( 60^{\circ} \) with \( Y \) -axis, the length of the component of the vector in the direction of X-axis is
A .
B. \( \sqrt{3} \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{3}{2} \)


The basic reason for the extra ordinary sparkle of a suitably out diamond is
that.
A. It is very hard
B. It has a very high refractive index
c. It has a very high transparency
D. It has well-defined cleavage planes


The correct decreasing order of dehydration of following alcohols with
conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is:
\( \mathbf{B} \)
\( \mathbf{D} \)
\( A \cdot C>A>B>D \)
B. \( D>A>C>B \)
\( \mathrm{c} \cdot \mathrm{A}>\mathrm{B}>\mathrm{C}>\mathrm{D} \)
\( D \cdot D>C>A>B \)


Which of the following essential amino
acid is present in wheat?
A. glycine
B. alanine
c. Iysine
D. serine


Three wires of same material are
connected in parallel to a source of emf. The length ratio of the wires is 1: 2: 3 and the ratio of their area of cross
section is 2: 4: 1
Table 1 Table 2 1 T
6: 6: 1
(p) (a)Resistance ratio : 6: 1
(b) \( \begin{array}{ll}\text { Current ratio } & \text { (q) } 1: 6: 6 \\ \text { Power ratio } & \text { (r) } 1: 1: 6 \\ & \text { (s) None }\end{array} \)
(c)
\( \mathbf{A} \cdot 1) \)
\( a-r, b-q, c-p \)
B. 2) a-p,b-q,c-r
c. \( 3) a-r ; b-p, c-p \)
D. 4 ) a \( -q, b-p, c-r \)


A car accelerates from rest at constant
rate of \( 2 m / s^{2} \) for some time. Then its
retards at a constant rate of \( 4 m / s^{2} \) and comes to rest. if it remains in motion for
3 seconds, then the maximum speed attained by the car is:-
A. \( 2 m / s \)
B. \( 3 m / s \)
\( \mathrm{c} \cdot 4 m / s \)
D. \( 6 m / s \)


A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a
grinding/cutting machine and a sprayer. It takes 2 hours
on grinding/cutting machine and 3
hours on the sprayer to manufacture a
pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for
at the most 20 hours and the
grinding/cutting machine for at the
most 12 hours. The profit from the sale of a lamp is \( \boldsymbol{R} \boldsymbol{s} .5 \) and that from a shade is \( R s .3 . \) Assuming that
the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?


Which of the following is not produced by human body?
A. Enzymes
B. Vitamins
c. Proteins
D. Nucleic acid


Aniline is reacted with bromine water
and the resulting product is treated with an aqueous solution of sodium nitrite in presence of dilute hydrochloric acid. The compound so formed is reacted with a tetrafluoroborate which
is subsequently heated. The final
product is:
A. \( p \) - bromoaniline
в. \( p \) - bromofluorobenzene
c. \( 1,3,5- \) tribromobenzene
D. \( 2,4,6- \) tribromofluorobenzene


\( 10 m L \) of a strong acid solution of
\( \boldsymbol{p} \boldsymbol{H}=\boldsymbol{2} \) are mixed with \( \boldsymbol{9} \boldsymbol{9} \boldsymbol{m} \boldsymbol{m} \)
another acid solution of \( \boldsymbol{p} \boldsymbol{H}=\mathbf{4} . \) The
\( \boldsymbol{p} \boldsymbol{H} \) of the following solution will be:
\( A \cdot 3 \)
в. 3.3
\( c .3 .7 \)
D. none of the above


Identify the graph of the polynomial function \( \boldsymbol{f} \)
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{\boldsymbol{4}}+\mathbf{1} \)
\begin{tabular}{|l|l|l|l|l|}
\hline 1 & & & & & \\
\hline & & & & & \\
\hline & & & & & \\
\hline & & & & & \\
\hline & & & & \( \mathrm{d} \) & & \\
\hline & & & & & & \\
\hline
\end{tabular}
A. graph a
B. graph b
C. graph c
D. graph d


What principle is violated here?
A . Laws of Motion
B. Energy conservation
c. Nothing is violated
D. Cannot be decided


If the initial concentration is reduced to
\( 1 / 4 \) th in a zero order reaction, then the time taken for half the reaction to
complete:
A. remains same
B. becomes 4 times
c. becomes one-fourth
D. doubles


Which of the following statement is
correct?
A. Motion of soldiers on march past is a periodic motion
B. Motion of a train along a curved track on hills is the example of curvilinear motion.
C. Every periodic motion is also a oscillatory motion
D. Hockey player running after a ball is a combined motion


For any two rational numbers \( x \) and \( y \) which of the following is/are correct, if \( x \)
is positive and \( y \) is negative?
(1) \( \boldsymbol{x}<\boldsymbol{y} \)
(2) \( x=y \)
(3) \( x>y \)
A. Both 1 and 2
B. Both 2 and 3
c. only 3
D. 1,2 and 3


The bark of tree commonly comprises
A. All the tissues outside the vascular cambium
B. All the tissues outside teh cork cambium
C . Only the cork
D. The cork and secondary cortex


The order and degree of \( \left(\frac{d^{2} y}{d x^{2}}\right)^{1 / 3}= \) \( \mathbf{1 0}+\mathbf{9} \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) is:
A . 2,3
B. 2,
\( c \cdot 1,3 \)
D. 1


If the resistance of conductor is \( R \), then
total heat dissipated across resistance
\( R \) is:
A \( \cdot \frac{i_{0}^{2} R t_{0}}{2} \)
B.
\( c \cdot \frac{i_{0}^{2} R t_{0}}{3} \)
D \( \cdot i_{0}^{2} R t_{0} \)


Sum of \( \frac{1}{2.7}+\frac{1}{7.12}+\frac{1}{12.17}+ \)
\( \frac{1}{17.22}+\ldots \) to \( n \) terms


What is the action of the following reagents on ethanoic acid?
\( P_{2} O_{5}, \) heat.


It is hotter over the top of a fire than at
the same distance on the sides because
of
A. convection of heat
B. conduction of heat
c. Radiation of heat
D. conduction, convection and radiation of heat


Integrate:
\( \int \sin x^{2} d x \)


How many teeth in man grows twice in life?
A . 32
B. 28
\( c \cdot 20 \)
D. 12


Rotary motion is of two types.
A. True
B. False


Assertion
The total translational kinetic energy of
all the molecules of a given mass of an ideal gas is 1.5 times the product of its
pressure and its volume.
Reason
The molecules of a gas collide with each other and the velocities of the
molecules change due to the collision.
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 and Reason is correct


If altitudes \( \mathrm{CE} \) and \( \mathrm{BD} \) of a triangle \( \mathrm{ABC} \)
are equal, then \( A B=\dots \)
A . AC
B. сE
\( c . \) ВD
D. BC


Suggest a few measures that can help in the conservation of water in daily life.