The standard oxidation potential of Zn referred to SHE is \( 0.76 \mathrm{V} \) and that of \( \mathrm{Cu} \)
is \( -0.34 V \) at \( 25^{\circ} \mathrm{C} . \) When excess of Zn
is added to \( C u S O_{4}, Z n \) displaces
\( C u^{2+} \) till equilibrium is reached. What
is the ratio of \( Z n^{2+} \) to \( C u^{2+} \) ions at
equilibrium? Express the ans in the form \( \left[Z n^{2+}\right] /\left[C u^{2+}\right]=k \times 10^{37}, \) and find \( k \)
A .1 .94
в. 2.34
c. 1.45
D. none of these


Which one of the following body functions is not performed by kidneys?
A. Excretion
B. osmoregulation
c. Regulation of blood volume
D. Destruction of dead blood corpuscles


Taking force,length and time to be the fundamental quantities.Find the direction, density,momentum and
energy


The relation between \( u, v \) and \( f \) for a
mirror is given by
A \( \cdot f=\frac{u \times v}{u-v} \)
в. \( f=\frac{2 u \times v}{u+v} \)
c. \( _{f}=\frac{u \times v}{u+v} \)
D. \( f=\frac{u-v}{u+v} \)


The value of \( \mathbf{M} \) is:
\( (\mathbf{A}) \)
\( A \cdot 2 \)
\( B .3 \)
\( c \cdot 4 \)
\( D \cdot 5 \)


In a trapezium \( A B C D, \) side \( A B \) is parallel to side \( \mathrm{DC} ; \) and the diagonals \( \mathrm{AC} \) and \( \mathrm{BD} \)
intersect each other at a point
Such that:
\( \boldsymbol{P A} \times \boldsymbol{P D}=\boldsymbol{P B} \times \boldsymbol{P C} \)
A. True
B. False


Complete the following statements with an appropriate word / term to be filled in the blank space(s).
Magnetic fields are produced by
A. Currents
B. Charges
c. capaciatnce
D. Inductance


Describe the bulk preparation of dihydrogen by electrolytic method. What
is the role of an electrolyte in this
process?


Incorrect statement in the following
A. Glomerulus is a group of fine blood capillaries
B. Loop of Henle is a part of malpighian body
C. Jatropa is the source of bio-diesel
D. Symptoms of uremia is swelling of feet


A constant torque of \( 50 \mathrm{N} \mathrm{m} \) is needed
to keep a wheel moving at a constant angular speed of 20 rads/s. The amount of work performed by this torque in 5 minutes
B. 100 KJ
c. 300 KJ
D. 30 KJ


What are hot spots?
A. Molten rock in the earths crust is pushed upward and trapped in certain regions
B. Solid rock in the earths crust is pushed upward and trapped in certain regions
C. Molten rock in the earths crust is pushed downward and trapped in certain regions
D. Solid rock in the earths crust is trapped in certain regions


Dry seeds when placed in water swell up
due to
A. Imbibition
B. Absorption
c. Diffusion
D. Adsorption


The electric field on two sides of a large charged plate is shown in Fig. The charge density on the plate in Sl units is
given by \( \left(\varepsilon_{0} \) is the permittivity of free \right. space in Sl units):
A \( .2 \varepsilon_{0} \)
в. \( 4 \varepsilon_{0} \)
c. \( 10 \varepsilon_{0} \)
D. zero


If \( \boldsymbol{A}=\{\boldsymbol{m}, \boldsymbol{a}, \boldsymbol{t}, \boldsymbol{h}, \boldsymbol{e}, \boldsymbol{m}, \boldsymbol{a}, \boldsymbol{t}, \boldsymbol{i}, \boldsymbol{c}, \boldsymbol{s}\}, \boldsymbol{B}= \)
\( \{a, m, t, h, e, i, c, s\}, \) then:
A \( . A=B \)
в. \( A \neq B \)
c. \( A \subset B \)
D. \( B \subset A \)


The valency of mercurous ion is :
A . two
B. one
\( c . \) three
D. four


A force is a result of:
A. interaction between two bodies
B. interaction of one body with itself
C. friction
D. all of the above


Statement \( 1:-273^{0} C \) is also known as
absolute zero.
Statement 2: \( ^{0} C=K+273 \)
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both the Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


In column chromatography, the moving phase is?
A. The substances which are to be separated
B. Eluent
c. Adsorbent
D. Mixture of eluent and substances to be separated


Oil is converted into fat by using as a catalyst.
A . Ni
B. Fe
\( c . \) мп
D. \( V_{2} O_{5} \)


Assertion: The standard potential of
\( \boldsymbol{C l}^{\ominus}|\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}| \boldsymbol{A} \boldsymbol{g} \) half cell is related to that
of \( \boldsymbol{A} \boldsymbol{g}^{\ominus} \mid \boldsymbol{A} \boldsymbol{g} \)
Reason:
\( \boldsymbol{E}_{\boldsymbol{A} \boldsymbol{g}^{\ominus} \mid \boldsymbol{A} \boldsymbol{g}}^{\ominus}=\boldsymbol{E}_{C l^{\ominus}|A \boldsymbol{g} C l| \boldsymbol{A} \boldsymbol{g}}^{\ominus}+\frac{\boldsymbol{R} \boldsymbol{T}}{\boldsymbol{F}} \ln \boldsymbol{K}_{s p} \)
\( (A g C \mid) \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


The magnetic field normal to the plane
of a wire of \( n \) turns and radius \( r \) which
carries a current i is measured on the
axis of the coil at a small distance \( h \)
from the centre of the coil. This is
smaller than the magnetic field at the
centre by the fraction
\( \mathbf{A} \cdot(2 / 3) r^{2} / h^{2} \)
B. \( (3 / 2) r^{2} / h^{2} \)
c. \( (2 / 3) h^{2} / r^{2} \)
D. \( (3 / 2) h^{2} / r^{2} \)


State whether the given statement is true or false:

A pair of linear equations is given by \( \boldsymbol{a}_{1} \boldsymbol{x}+\boldsymbol{b}_{1} \boldsymbol{y}+\boldsymbol{c}_{1}=\boldsymbol{0} \) and \( \boldsymbol{a}_{2} \boldsymbol{x}+\boldsymbol{b}_{2} \boldsymbol{y}+ \)
\( c_{2}=0 \) and \( \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}} \)
In this case, the pair of linear equations is consistent.
A. True
B. False


If unit vectors \( \hat{\boldsymbol{i}} \& \hat{\boldsymbol{j}} \) are at right angles to each other and \( \overrightarrow{\boldsymbol{p}}=\mathbf{3} \hat{\boldsymbol{i}}+\boldsymbol{4} \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{q}}= \)
\( \mathbf{5} \hat{\mathbf{i}}, \mathbf{4} \overrightarrow{\boldsymbol{r}}=\overrightarrow{\boldsymbol{p}}+\overrightarrow{\boldsymbol{q}} \) and \( \mathbf{2} \overrightarrow{\boldsymbol{s}}=\overrightarrow{\boldsymbol{p}}-\overrightarrow{\boldsymbol{q}} \) then
This question has multiple correct options
A \( \cdot|\vec{r}+k \vec{s}|=|\vec{r}-k \vec{s}| \) for all real \( \mathrm{k} \)
B. \( \vec{r} \) is perpendicular to \( \vec{s} \)
c. \( \vec{r}+\vec{s} \) is perpendicular to \( \vec{r}-\vec{s} \)
D・|\vec| = |\vec| = | \( \vec{p}|=| \vec{q} \)


The pH of the solution obtained on
neutralisation of \( 40 m L \) of \( 0.1 M \)
NaOH with 40 m \( L \) of \( 0.1 M \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) is:
\( A \cdot 7 \)
B. 8
\( c \cdot 4 \)
D.


Which of these metals do not corrode?
A. Lead
B. copper
C. Platinum
D. Silver


Name the gas that is produced in the following cases.

At the anode during the electrolysis of acidified water


A simple closed curve made up of only line segments is called a
A . Curve
B. Polygon
c. surface
D. concave


In which stage of meiosis, homologous chromosomes are segregated
A. Metaphase I
B. Anaphase I
c. Anaphse II
D. Metaphase II


If the roots of the equation \( x^{2}-2 a x+ \)
\( a^{2}+a-3=0 \) are real and less than 3
then
A \( . a<2 \)
в. \( 2 \leq a \leq 3 \)
c. \( 3<a \leq 4 \)
D. \( a>4 \)


The wavelength of maximum intensity
of emission of solar radiation is \( \lambda_{m}= \)
\( 4753 A^{\circ} \) and from moon it is \( 14 \mu \mathrm{mm} \)
The surface temperature of sun and
moon are \( \left(\operatorname{given} b=2.898 \times 10^{-3}\right. \)
meter-kelvin)
A. 6097 К. 207К
в. 8097 К, зот к
c. 10000 К, \( 400 \mathrm{k} \)
D. 3000 К, 100 к


Two cell of emf \( 6 V \) and \( 4 V \) having
internal resistance \( 3 \Omega \) and \( 2 \Omega \)
respectively are connected in parallel so
all to send a current through extend
resistance of \( 8 \Omega \) in the same direction.
Find the current through the cells and
the potential difference across \( 8 \Omega \)
Resistor.


Which of the following statement is
incorrect?
A. Glycogen is the carbohydrate resource in human and animals
B. Cellulose makes the cells walls of the plants
C. Sucrose is the polysaccharides known as invert sugar
D. Homopolysaccharides are made up of one type of monosaccharides


A \( 100 m H \) coil carries \( 1 A \) current.
Energy stored in its magnetic field is.
A. 0.15
J \( 5.1 .5 . \)
B. \( 0.05 J \)
\( c .0 .5 J \)
D. \( 1 . \)


What is the molality of a solution containing \( 200 m g \) of urea (molar mass
\( 60 g m o l^{-1} \) ) dissolved in \( 40 g \) of water?
A . 0.0833
B. 0.825
c. 0.498
D. 0.0013


\( \boldsymbol{A} \rightleftharpoons \mathbf{2} \boldsymbol{B}, \boldsymbol{K}_{\boldsymbol{p}} \) and \( \boldsymbol{C} \rightleftharpoons \boldsymbol{D}+\boldsymbol{E}, \boldsymbol{K}_{\boldsymbol{p}^{*}}^{\prime} \) If
degrees of dissociation of \( A \) and \( C \) are
same and \( K_{p}=2 K_{p}^{\prime}, \) then the ratio of total pressure \( \frac{\boldsymbol{p}}{\boldsymbol{p}^{\prime}} \) is:
A. \( 1 / 2 \)
B. \( 1 / 3 \)
c. \( 1 / 4 \)
D. 2


What will happen if chemical fertilizers are used for a longer time.
A. soil always stays fertile for plant growth
B. soil fertility is damaged
c. soil stops responding to fertilizers
D. soil health is maintained


Active mass of eight grams of oxygen at
STP is


In the given figure \( A B \| C D \). find the
value of \( x \) and \( y \)
A \( \cdot x=35^{\circ}, y=65^{\circ} \)
B . \( x=95^{\circ}, y=65^{\circ} \)
C . \( x=85^{\circ}, y=65^{\circ} \)
D. \( x=25^{\circ}, y=65 \)


Name the other ion formed when
ammonia dissolves in water


Measure of \( \angle A \) in \( \Delta A B C \) is
\( A \cdot 90^{\circ} \)
В. \( 99.3^{\circ} \)
\( c \cdot 100.3^{\circ} \)
\( 800.7^{\circ} \)


Point out the wrong statement about
proteins.
A. They are nitrogenous organic compounds of high molecular mass.
B. They on hydrolysis by enzymes give aminoacids.
C. Many of them are enzymes.
D. They do not contain polypeptide.


In the nuclear reaction, there is a
conservation of
A. momentum
B. mass
c. energy
D. all of these


Highly electrical conducting behaviour
is present in anhydrous \( H_{2} S O_{4} \) due to autoprotolysis.
If true enter 1 , else enter 0 .


Solve \( \int \frac{1}{\sqrt{9-25 x^{2}}} d x \)
A. \( \frac{1}{5} \sin ^{-1}\left(\frac{5 x}{3}\right)+C \)
B \( \cdot \sin ^{-1}\left(\frac{5 x}{3}\right)+C \)
c. \( \frac{1}{5} \sin ^{-1}\left(\frac{3 x}{5}\right)+C \)
D. \( \sin ^{-1}\left(\frac{3 x}{5}\right)+C \)


If \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{x}^{\boldsymbol{y}} \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{e q u a l s -} \)
A \( \frac{y x^{y-1}-1}{1-x^{y} \log x} \)
В. \( \frac{y x^{y-1}-1}{x^{y} \log x-1} \)
c. \( \frac{y x^{y-1}+1}{x^{y} \log x+1} \)
D. None of these


(iii) Which class of drugs is used in sleeping pills?
A. tranquilizers
B. Antacid
c. Disprine
D. Paracetamol


Match list 1 with list 2
List 1
A) Aspirin
p) Non-narcotic
q) Acts against gram-positive and
B) Ofloracin \( \quad \) gram-negative bacteria
C) Penicillin G antibiotic
r) Narrow spectrum
D) Ibuprofen
s) Broad spectrum antibiotic
t) Anti inflammatory drug
\( A \cdot a-p, b-s, c-r, d-t \)
B. \( a-r, b-p, c-q, d-t \)
c. \( a-s, b-s, c-r, d-p \)
D. a-p,b-s,c-t,d-r


Draw V-I characteristics of a p-n junction diode. Answer the following questions, giving reasons:
(i) Why is the current under reverse bias almost independent of the applied upto a critical voltage?
(ii) Why does the reverse current show a sudden increase at the critical voltage?
Name any semiconductor device which operates under the reverse bias in the
breakdown regions


Show that in case of one-dimensional
elastic collision of two bodies, the relative
velocity of separation after the collision
is equal to the relative velocity of approach before the collision.


For bacteria to continue growing rapidly when they are shifted from an
environment containing \( \boldsymbol{O}_{2} \) to an
anaerobic environment, they must
A. Produce more ATP per mole of glucose during glycolysis
B. Produce ATP during oxidation of glucose
c. Increase the rate of glycolysis
D. Increase the rate of TCA cycle


The spring shown in figure is
unstretched when a man starts pulling
the block. The mass of the block is \( M . \) If
the man exerts a constant force \( \boldsymbol{F} \)
The energy stored in the spring when the block passes through the
equilibrium position is
\( ^{A} \cdot \frac{2 F^{2}}{k} \)
B. \( \frac{F^{2}}{k} \)
\( ^{\mathbf{c}} \cdot \frac{F^{2}}{4 k} \)
D. \( \frac{F^{2}}{2 k} \)


An object of mass \( \mathrm{m} \) is allowed to fall from rest along a rough inclined plane. The speed of the object on reaching the bottom of the plane is proportional to?
\( \mathbf{A} \cdot m^{0} \)
B. \( m \)
\( c \cdot m^{2} \)
D. \( m^{-1} \)


Evaluate: \( \lim _{x \rightarrow 1} \frac{1-x^{\frac{-1}{3}}}{1-x^{\frac{-2}{3}}} \)


Which of the following oxides is
neutral?
A. \( C O \)
в. \( S n O_{2} \)
\( c \cdot Z n O \)
D. \( \operatorname{si} O_{2} \)


Concentrated nitric acid dissolves gold.
If true then enter 1 , if false then enter 0 .


The process "translation" means
A. DNA synthesis
B. RNA synthesis
c. Protein synthesis
D. Ribosome assembly


Which of the following names represents the foul smelling, black, thick, viscous liquid obtained from destructive distillation of coal?
A. coke
B. Coal tar
c. coal gas
D. None of these


Say true or false:
The service tax is an indirect tax.
A . True
B. False


High reactivity of white phosphorus is
due to:
A. unusual bonding that produces considerable strain
B. high solubility in water
c. oxide layer made on it
D. all of the above


For the equilibrium reaction
\( \boldsymbol{C a} \boldsymbol{C O}_{3}(\boldsymbol{s}) \rightleftharpoons \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) . \) The
addition of more \( C a C O_{3}(s) \) causes?
A. The decrease in the concentration of \( C O_{2}(g) \)
B. The increase in the concentration of \( C O_{2}(g) \)
C. No change in the concentration of \( C O_{2}(g) \)
D. Increase in the concentration of \( C a O(s) \)


A current of \( 2 A \) is flowing through a
circular coil of radius \( 10 \mathrm{cm} \) containing 100 turns. The magnetic flux density at the centre of the coil is \( \left(\operatorname{in} W b / m^{2}\right) \)
В. \( 1.26 \times 10^{-2} \)
c. \( 1.26 \times 10^{-4} \)
D. \( 1.26 \times 10^{-5} \)


In ammonia molecule
covalent bond formation takes place between nitrogen and hydrogen.


If the symmetry is such that you can find a surface on which the electric field
is constant, then evaluating the electric flux can be done by
A. dividing the value of the field by the area of the Gaussian surface.
B. multiplying the value of the field times the area of the Gaussian surface
c. multiplying the square of the value of the field times the area of the Gaussian surface.
D. dividing the square of the value of the field times the area of the Gaussian surface


Conduction is:
A. the process of transfer of heat which does not require any material medium
B. the process of transferring heat from molecule to molecule, without the actual movement of molecules
C. the process in which molecules conduct heat by moving from hotter regions to colder regions
D. the process in which heat energy moves through the medium of protons


Which of the following complexes will show optical isomerism?
A \( \cdot\left[C r\left(N H_{3}\right)_{6}\right]^{2+} \)
B . \( \left[N i\left(H_{2} O\right)_{6}\right]^{2+} \)
c. \( \left[P t\left(N H_{3}\right)_{3} B r\right] N O_{3} \)
D. \( \left[C r(e n)_{3}\right] C l_{3} \)


State with the reason whether the given
figures are optically active or not


Choose the correct answers from the
alternatives given Water and minerals that cross the
cortex through the symplast move
A. Extracellularly along the matrix of cell walls
B. From cell to cell through plasmodesmata
c. By active transport
D. By pressure flow


The type of egg in cockroach is called as
A. Microlecithal
B. Centrolecithal
c. Isolecithal
D. Telolecithal


If air is taken as a binary solution, the
solvent is:
\( A \cdot N_{2} \)
B. \( 0_{2} \)
\( c \cdot c O_{2} \)
D. Ar


A wooden piece is balanced by a brass weight in a sensitive balance. Now the
pan contained by wooden piece is covered by a bell jar and then evacuated;
A. the pan containing the wooden piece will go up
B. the pan containing the wooden piece will go down
c. the beam will remain horizontal
D. nothing can be said definitely


Find the mean deviation about the
mean for the data in
\( \begin{array}{lllll}x_{i} & 10 & 30 & 50 & 70\end{array} \) \( \mathbf{9 0} \)
\( f_{i} \quad 4 \quad 24 \quad 28 \quad 16 \)


AB is a line segment \( C \) and \( D \) are points on opposite sides of \( A B \) such that each
of them is equidistant from the point \( \mathbf{A} \)
and \( \mathrm{B} \) as in the figure. The line \( \mathrm{CD} \) is
perpendicular bisector of \( \mathrm{AB} \)
A. True
B. False


S.I unit of intensity of sound is
A \cdot joule \( s^{-1} m^{-2} \)
B. watt \( m^{-2} \)
c. joule/s/m \( ^{2} \)
D. all


A beam of protons is deflected sideways. could this deflections be caused
a.) By an electric field
b) by a magnetic field
c.) if either could be responsible how would you be able to tell which was
present


Which of the following condition even if satisfied, does not make the two
triangles congruent?
A. S.S.S ( side-side-side)
B. A.A.A (angle-angle-angle)
c. s.A.S (side-angle-side)
D. A.S.A (angle-side-angle)


Solve each of the following equations and check your answers: \( \boldsymbol{x}-\mathbf{3}=\mathbf{5} \)


Chloroethane, \( C_{2} H_{5} C l, \) does not react with methanol under mild conditions.
What reagent could be added to the reaction mixture to increase the rate of
substitution?
A. \( H C l \) (conc.)
в. \( N a O H \)
c. \( N H_{4} O H \)
D. \( A g N O_{3} \)


If \( \cos \left(65^{0}-A\right) \cos \left(25^{0}+B\right)- \)
\( \sin \left(65^{0}-A\right) \sin \left(25^{0}+B\right)=\sin (m+ \)
\( A-B) \).Find \( m \)


Solve: \( \lim _{x \rightarrow 2} \frac{\left(1-3^{x}-4^{x}+12^{x}\right)}{\sqrt{(2 \cos x+7)}-} \)


In the given figure, \( \boldsymbol{A B} \| \boldsymbol{C D}, \angle \boldsymbol{A B E}= \)
\( 120^{\circ}, \angle E C D=100^{\circ} \) and \( \angle B E C=x^{o} \)
Find the value of \( x \)


If \( ^{16} C_{r}=^{16} C_{r+1}, \) then the value of \( ^{r} P_{r-3} \)
is
\( A \cdot 31 \)
в. 120
c. 210
D. 840
E. No option is correct


A plane \( \pi \) makes intercept 3 and 4
respectively on z-axis and x-axis. If \( \pi \) is
parallel to y-axis, then its equation is
A. \( 3 x+4 z=12 \)
B. \( 3 z+4 x=12 \)
c. \( 3 y+4 z=12 \)
D. \( 3 z+4 y=12 \)


Poisson's ratio cannot exceed
A . 0.25
B. 1.0
c. 0.75
D. 0.5


The essential distinction between \( X \)
rays and \( \gamma \) -rays is that the \( \gamma \) -rays:
A. have greater ionizing power than \( x \) -rays
B. emanate from nucleus, white X-rays emanate from outer part of the atom
C. have smaller wave-length than X-rays
D. none of the above


State the working principle of potentiometer explain with the help of circuit diagram. How the emf of two primary cells are compared by using the potentiometer


The product of the digits of a two-digit number is twice as large as the sum of
its digits. If we subtract 27 from the required number, we get a number consisting of the same digits written in the reverse order. Find the number.


A plano-convex lens has thickness \( 4 \mathrm{cm} \) When placed on a horizontal table with the curved surface in contact with it,
the apparent depth of the bottom-most point of the lens is found to be \( 3 \mathrm{cm} \). If the lens is inverted such that the plane face is in contact with the table, the
apparent depth of the centre of the
plane face of the lens is found to be \( 25 / 8 \mathrm{cm} . \) Find the focal length of the lens


Check whether the following pair of statements is negation of each other. Give reasons for the answer
(i) \( x+y=y+x \) is true for every real
numbers \( \boldsymbol{x} \) and \( \boldsymbol{y} \)
(ii) There exists real number \( x \) and \( y \) for
which \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{y}+\boldsymbol{x} \)


Among \( \boldsymbol{C H}_{4}, \boldsymbol{N H}_{3} \) and \( \boldsymbol{H}_{2} \boldsymbol{O}, \) acidity of
\( H_{2} O \) is maximum because:
A. Oxygen contains two lone pairs of electrons.
B. Bond angle on \( H_{2} O \) is less than \( 109^{\circ} 28^{\prime} \) due to \( V S E P R \)
c. oxygen is more electronegative than \( C \) or \( N \).
D. \( H_{2} O \) is an associated liquid.


Shanti, a domestic helper of Mrs. Anuradha, fainted while mopping the
floor. Mrs. Anuradha immediately took her to the nearby hospital where she was diagnosed to be severely 'anaemic'. The doctor prescribed an iron rich diet and multivitamins supplement to her.
Mr.s Anuradha supported her financially to get the medicines. After a month, Shanti was diagnosed to be normal.
(i) What values are displayed by Mrs. Anuradha?
(ii) Name the vitamin whose deficiency causes 'pernicious anaemia!
(iii) Give an example of a water soluble vitamin


Find the refractive index of glass with respect to water. The refractive indices of these with respect to air are \( 3 / 2 \) and \( 4 / 3 \) respectively
A \( .2 / 1 \)
в. \( 1 / 2 \)
c. \( 9 / 8 \)
D. \( 8 / 9 \)


The dissociation constant of a
substituted benzoic acid at \( 25 \mathrm{C} \) is
\( 1.05 \times 10^{-4} . \) The pH of \( 0.01 \mathrm{M} \) solution
of its sodium salt is.
\( A \cdot 8 \)
B. 6
\( c \cdot 5 \)
D. 4


In what ratio does the plane \( 2 x+y- \)
\( z=3 \) divide line segment joining the
point \( \boldsymbol{a}=(\mathbf{2}, \mathbf{1}, \mathbf{3}), \boldsymbol{b}=(\mathbf{9},-\mathbf{2}, \mathbf{5}) \)


How many parents were involved in cloning and production of Dolly?
A .2
B.
\( c \cdot 3 \)
\( D \)


If \( \lambda_{m} \) denotes the wavelength at which the radioactive emission from a black
body at a temperature \( T K \) is maximum then:
A. \( \lambda \) is independent of \( T \)
в. \( \lambda_{m} \propto T \)
\( \mathbf{c} \cdot \lambda_{m} \propto T^{-1} \)
D. \( \lambda_{m} \propto T^{-4} \)


The organic acid present in vinegar is :
A. methanoic acid
B. ethanoic acid
c. propanoic acid
D. none of these


Let \( A \) and \( B \) be two sets such that \( A \times \)
\( B \) consists of 6 elements.lf three
elements of \( \boldsymbol{A} \times \boldsymbol{B} \) are
\( \{(1,4),(2,6),(3,6)\} . \) Find \( A \times B \) and
\( \boldsymbol{B} \times \boldsymbol{A} \)


If \( f(x)=x \sin x, \) then \( f^{\prime}\left(\frac{\pi}{2}\right) \) is equal
to:
A.
B.
c. -1
D.


Scientific name of sunn hemp is
A. Crotalaria juncea
B. Erythrina indica
c. Arachis hypogea
D. Glycine max
E. Dalbergia sisso


Define the unit of self inductance.


What will be the product of the given
reaction?


The \( V-I \) graph of a conductor at two
different temperatures is shown in Fig. The ratio of temperature \( \frac{T_{1}}{T_{2}} \) is :
A \( \cdot \tan ^{2} \theta \)
B \( \cdot \cot ^{2} \theta \)
\( \mathbf{c} \cdot \sec ^{2} \theta \)
\( \mathrm{D} \cdot \operatorname{cosec}^{2} \theta \)


Geochemistry is:
A. The study of the chemical composition and changes in organisms
B. The study of the chemical composition and changes in rocks, minerals, and atmosphere of the earth or a celestial body.
C. The study of the chemical composition and changes in plants
D. None of the above


Brown,black and gold is the color band on the resistor,find its resistance?
A \( \cdot 10 \times 10^{-2} \Omega \)
B. 1\Omega
c. \( 100 \Omega \)
D. \( 10 \times 10^{0} \Omega \)


The moon's radius is \( 1 / 4 \) times that of the earth and its mass \( 1 / 80 \) times that
of the earth. If \( g \) represents the acceleration due to gravity on the surface of the earth, then on the surface
of the moon its value is :
\( \mathbf{A} \cdot g / 4 \)
в. \( g / 5 \)
c. \( g / 6 \)
D. \( g / 8 \)


Assertion
In its rest position the clapper is held away from the bell a short distance by
its springy arm.
Reason
The spring constant of spring must be such that clapper should be able to give
reaction to the magnetic force of
attraction upto a certain extent
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
An \( n- \) type semiconductor has a large
number of electrons but still it is
electrically neutral
Reason
An \( n- \) type semicondutor is obtained
by doping an intrinsic semiconductor with a pentavalent impurity.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The number of times a person breathes in a minute is called as
A. Inhalation
B. Respiratory rate
c. Breathing
D. Breathing rate


A wheel having a diameter of 3 m starts
from rest and accelerates uniformly to an angular velocity of 210 r.p.m. in 5 seconds. Angular acceleration of the wheel is:
A. 4.4 rad \( s^{-2} \)
B. 3.3 rad \( s^{-2} \)
c. 2.2 rad \( s^{-2} \)
D. 1.1 rad \( s^{-2} \)


If \( S=\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+\ldots . ., \) then
\( ^{\mathbf{A}} \cdot T_{n}=\frac{1}{4}\left(\frac{1}{4 n-3}-\frac{1}{4 n+1}\right) \)
B. \( s_{n}=\frac{1}{4}\left[1-\frac{1}{4 n+1}\right] \)
c. \( S_{\infty}=1 \)
D. None


Elements \( A, B, C, D \) have atomic
numbers as 35,19,17,9 respectively. Choose the odd element
\( A \cdot A \)
в. \( B \)
c. \( C \)
D. \( D \)


Given the following bond dissociation
enthalpies \( \left(k J . m o l^{-1}\right) \)
\( \boldsymbol{P} \equiv \boldsymbol{P}-\mathbf{4 9 0}, \boldsymbol{P}-\boldsymbol{P}-\mathbf{2 0 9}, \boldsymbol{N} \equiv \boldsymbol{N}- \)
\( \mathbf{9 4 6}, N-N-160 \)
Compare the enthalpy changes for the
process
(i) \( 2 P_{2}(g) \longrightarrow P_{4}(g) \)
(ii) \( 2 N_{2}(g) \longrightarrow N_{4}(g) \)
Choose the correct option.
A \( \cdot P_{4} \) is feasible but \( N_{4} \) is not feasible
B. \( P_{4} \) is not feasible but \( N_{4} \) is feasible
c. Both \( P_{4} \) and \( N_{4} \) are feasible
D. Both \( P_{4} \) and \( N_{4} \) are not feasible.


Formaldehyde is used as formalin in
industries:
A. to preserve biological specimens
B. to prepare bakelite
c. both \( A \) and \( B \)
D. none of these


The complex number system, denoted
by \( C, \) is the set of all ordered pairs of
real numbers (that is, \( \boldsymbol{R} \times \boldsymbol{R} \) ) with the
operations of addition (denoted by \( +) \) which satisfy
A \( \cdot(a, b)+(c, d)=(a+d, b+c) \)
в. \( (a, b)+(c, d)=(a c-b d, b c-a d) \)
C. \( (a, b)+(c, d)=(a+c, b+d) \)
D. None of these


A wave is measured to have a frequency of \( 60 H z \). If its wavelength is \( 24 c m \) determine how fast it is moving.
\( \mathbf{A} \cdot 24 m / s \)
в. \( 10 \mathrm{m} / \mathrm{s} \)
c. \( 12 m / s \)
D. \( 14 \mathrm{m} / \mathrm{s} \)


Which of the following forms of energy
is released or absorbed in most
chemical reactions?
A. Light energy
B. Electrical energy
c. sound energy
D. Heat energy


In vapour state a metal is
atomic.


In Young's double slit experiment shows
in figure, \( S_{1} \) and \( S_{2} \) are coherent
sources and \( \mathrm{S} \) is the screen having a
hole at a point \( 1.0 \mathrm{mm} \) away from the
central line. White light \( (400 \text { to } 700 \) nm)
is sent through the slits. Which
wavelength passing through the hole
has the strongest intensity?
A. \( 400 \mathrm{nm} \)
B. 700 nm
\( c .500 \mathrm{nm} \)
D. 667 nm


A ball of mass \( 5 k g \) is suspended from a
chord of length \( l=0.5 m \) is attached to
a cart \( A \) of mass \( 2.5 k g \), which slides
freely on a frictionless horizontal track
as shown in figure. The ball given an initial horizontal velocity 1 m / \( s \) relative to the ground while the cart is at rest.
Find
(a) The velocity of the ball when string makes minimum angle with vertical
(b) The maximum vertical distance
through which the ball will rise.


The numbers 3.845 and 3.835 on
rounding off to 3 significant figures will give then
A. 3.85 and 3.84
B. 3.84 and 3.83
c. 3.85 and 3.83
D. 3.84 and 3.84


With four bases the number of possible triplet codons is
A . 24
B. 32
\( c \cdot 48 \)
\( D \cdot 64 \)


Find the derivative of \( x^{2} \) with respect to
\( \log \boldsymbol{x} \)


Consider a spherical shell of radius \( \mathrm{R} \) with a total charge + q uniformly spread on its surface(center of the chell lies at
the origin \( x=0 \) ). Two point charges, \( +q \) and \( -q \) are brought, one after the other, from far away and placed at \( x=-a / 2 \)
and \( \boldsymbol{x}=+\boldsymbol{a} / 2(\boldsymbol{a}<\boldsymbol{R}), \) respectively
Magnitude of the work done in this
process is?
A \( \cdot(Q+q)^{2} \cdot 4 \pi \varepsilon_{0} \)
\( a \)
B. Zero
\( \mathbf{c} \cdot q^{2} / 4 \pi \varepsilon_{0} \)
D \( \cdot Q q / 4 \pi \varepsilon_{0} a \)


Which of the following states of matter have two specific heats?
A. solid
B. gass
c. liquid
D. vapour


'A' represents central atom, 'B' number of bond pairs and 'E' number of lone
pairs. Then the one having \( \boldsymbol{A} \boldsymbol{B}_{\mathbf{5}} \boldsymbol{E} \)
formula is
A \( \cdot P C l_{5} \)
в. \( S F_{6} \)
c. \( B C l_{3} \)
D. \( C l F_{5} \)


The resistance of a \( \frac{N}{10} K C l \) aqueous solution is \( 245 \Omega \). If the electrodes in the
cell are \( 4 \mathrm{cm} \) apart and area having
\( 77 \mathrm{cm}^{2} \) each, the molar conductance of
the solution will be:
A . 233
B. 2.12
c. 23.32
D. 0.233


A particle moves along x-axis in such a way its coordinate (x) varies with time
(t) according to the expression \( \boldsymbol{x}=\mathbf{2}- \)
\( 5 t+6 t^{2} \). its intial velocity is
A. \( -3 m s^{-1} \)
B. \( -5 m s^{-1} \)
\( \mathbf{c} \cdot 2 m s^{-1} \)
D. \( 3 m s^{-1} \)


In which of the following work is being
done?
This question has multiple correct options
A. Man sitting on a bench
B. Person Standing with a basket of fruit on the head.
c. Climbing a tree to pluck
D. Pushing a wheelbarrow of bricks.


Explain the action cu releasing IUO and hormone releasing IUD reperatily.


Which of the following is scientific explanation of depression?
A. An increased level of sugar in the blood leads to depression
B. Low levels of noradrenaline, a neurotransmitter in the blood lead to depression
c. Release of extra gastric juice in the stomach lead to depression
D. Sleep incducing drugs lead to depression


Be on dissolving in aqueous \( N a O H \)
yields:
A. \( N a_{2} B e O_{2} \)
B \( \cdot N a_{2}\left[\operatorname{Be}(O H)_{4}\right] \)
c. \( \operatorname{Na}\left[\operatorname{Be}(O H)_{3}\right] \)
D. Both (A) and (B)


What sum invested for \( 1 \frac{1}{2} \) years compounded half-yearly at the rate \( 8 \% \) p.a. will amount to \( R s .140608 ? \)


A particle moves under the force
\( \boldsymbol{F}(\boldsymbol{x})=\left(\boldsymbol{x}^{2}-\boldsymbol{6} \boldsymbol{x}\right) \boldsymbol{N}, \) where \( \boldsymbol{x} \) is in
meters. Show that for small
displacements from the origin the force constant in the simple harmonic motion is approximately 6


From a supply of identical capacitors rated \( 8 \mu F, 250 V \) the minimum number of capacitors required to form a composite of \( 16 \mu F, 1000 V \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 16 \)
D. 32


A car is travelling on a straight road. The maximum velocity the car can
attains is \( 24 m s^{-1} . \) The maximum
acceleration and deceleration it can
attain are \( 1 m s^{-2} \) and \( 4 m s^{-2} \)
respectively. The shortest time the car
takes from rest to rest in a distance of
\( 500 \mathrm{m} \) is
A . 22.4
B. 30 s
c. \( 11.2 \mathrm{s} \)
D. 35.8 s


In a pseudo first order acid catalysed
hydrolysis of ester in water the following
results were obtained:
\( t / s \)
0.30
60
[ester]/M 0.550 .31
0.17 \( \quad 0.085 \)
Which of the following is/are correct for
the given reaction? This question has multiple correct options
A. The average rate of reaction between time interval 30 to 60 seconds is \( 4.67 \times 10^{-3} \) mol \( L^{-1} s^{-1} \)
B. Order of reaction is 2.
c. Pseudo first order rate constant for the acid catalysed hydrolysis of ester is \( 1.92 \times 10^{-2} s^{-1} \)
D. All are correct.


What is the common name of
\( \mathbf{C H}_{3} \mathbf{C O O H} ? \)


If the roots of the equation \( x^{2}-8 x+ \)
\( a^{2}-6 a=0 \) are real, then the value of \( a \)
will be
A \( .-2<a<8 \)
в. \( -2 \leq a \leq 8 \)
\( \mathbf{c} \cdot 2<a<8 \)
D. \( 2 \leq a \leq 8 \)


What should be added in vector \( 3 i+ \)
\( 4 j-2 k \) to get its resultant a unit vector
\( i \)
A . \( -2 i-4 j+2 k \)
B. \( 2 i+4 j+2 k \)
\( c .-2 i+4 j+2 k \)
D. None of these


Probability of getting 2 when we roll a
dice


Two fair dice are thrown. What is the
probability that the two scores do not
add to \( 5 ? \)
\( A \cdot \frac{7}{9} \)
в. \( \frac{5}{9} \)
\( c \cdot \frac{8}{9} \)
D. \( \frac{1}{9} \)


Diopter is the unit of :
A. Telescope
B. Microscope
c. Power of lens
D. Eye sight


If \( P \) and \( Q \) are the sum and product
respectively of all integral values of \( x \)
satisfying the equation \( |\mathbf{3}[\boldsymbol{x}]-\mathbf{4} \boldsymbol{x}|=\mathbf{4} \)
then
(where [.] denotes represents greatest integer function \( ) \) This question has multiple correct options
\( \mathbf{A} \cdot P=0 \)
B . \( P=8 \)
c. \( Q=-16 \)
D. \( Q=-9 \)


Among the most polluted cities in India,
Delhi stands at
(According to latest annual average values)
A. Second most polluted
B. Third most polluted
c. Fourth most polluted
D. Fifth most polluted
E. Sixth most polluted


\( \boldsymbol{H}_{2}(\boldsymbol{g})+\frac{1}{2} \boldsymbol{O}_{2}(\boldsymbol{g}) \longrightarrow \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}(l) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -286 k J \)
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{O}_{\mathbf{2}}(\boldsymbol{g}) \longrightarrow \)
\( 2 H_{2} O(l) \dots \dots \dots J(\pm ?) \)
A \( \cdot 2 H_{2}(g)+O_{2}(g) \longrightarrow 2 H_{2} O(l)+572 k J \)
В \( \cdot 2 H_{2}(g)+O_{2}(g) \rightarrow 2 H_{2} O(l)-572 k J \)
C. \( 2 H_{2}(g)+O_{2}(g) \longrightarrow 2 H_{2} O(l)+0 k J \)
D. None of these


A drop of water is placed on a glass plate. A double convex lens having radius of curvature of each surface 20
\( \mathrm{cm} \) is placed on it. The focal length of water lens \( \left(\mu \text { for water }=\frac{3}{4}\right), \) will be
A . -0.20
B. -0.60 \( \mathrm{m} \)
\( c .0 .30 \)
D. \( 0.40 \mathrm{m} \)


A uniform chain has a mass \( M \) and
length \( L \). It is placed on a frictionless table with length \( l_{0} \) hanging over the edge. The chain beings to slide down. Then the speed \( V \) with which the end
slides away from the edge is given by :
A \( \cdot V=\sqrt{\frac{g}{L}\left(L+l_{o}\right)} \)
B. \( V=\sqrt{\frac{g}{L}\left(L-l_{o}\right)} \)
c. \( V=\sqrt{\frac{g}{L}\left(L^{2}-l_{o}^{2}\right)} \)
D. \( V=\sqrt{2 g\left(L-l_{o}\right)} \)


The height of cylinder is \( 4 \mathrm{cm} \) The
Radius of cylinder is \( 5 \mathrm{cm} \) find its
volume


The ratio of the radius of Bohr first orbit
for the electron orbiting the hydrogen nucleus to that of the electron orbiting the deuterium nucleus (mass nearly
twice that of nucleus) is approximately:
A . 1: 1
B. 1: 2
c. 2: 1
D. 1: 4


Cartesian equation of a line is \( \frac{x-5}{3}= \) \( \frac{\boldsymbol{y}+\boldsymbol{4}}{\mathbf{7}}=\frac{\boldsymbol{z}-\boldsymbol{6}}{\boldsymbol{2}} . \) Write it in vector form


A sample of potato was ground in a ball mill to give a starch-like molecule of lower molecular weight. the product analysed \( 0.086 \% \) phosphorous if each molecule is assumed to contain one
atom of phosphorous, what is the molecule weight of material
A. 36000
B. 37000
c. 46000
D. 3600


How does temperature affect reaction
rate?
A. It usually increases it
B. It always decreases it
C . It always increases it
D. Reaction rate is independent of temperature
E. It usually decreases it


\( P_{4} \) is a stable from of phosphorus. The percentage of \( p \) -character in the orbital
forming \( (P-P) \) bonds in \( P_{4} \) is
A . 25
B. 33
\( c .50 \)
D. 75


Match Column \( I \) with Column \( I I: \)


Steroid hormones lead to the :
A. destruction of normal DNA
B. replication of hormones by the cell DNA
C. synthesis of new enzymes
D. alteration of the Krebs cycle


If \( 400 \Omega \) of resistance is made by adding four \( 100 \Omega \) resistance of tolerance \( 5 \% \)
then the tolerance of the combination
is?
A . \( 15 \% \)
B. 20\%
c. \( 5 \% \)
D. \( 10 \% \)


Find the differential coefficient of
\( \tan ^{-1} x \) w.r to \( x \)


Vascular bundles of monocot stem are
A. Conjoint, collateral and open
B. Conjoint, collateral and closed
C. Conjoint, bicollateral and open
D. Conjoint, concentric and closed


More electronegative elements have:
A. negative reduction potential
B. tendency to lose electrons
C. positive reduction potential
D. positive oxidation potential


Cod liver is an example of:
A . oil emulsion
B. oil in water emulsion
c. water in oil emulsion
D. water in water emulsion


The gravitational force between two
objects in \( 200 N \) How should the distance between these objects be changed so that force between them becomes \( 50 N ? \)


Which of the following is not found in vertebrates?
A. Bilateral symmetry
B. Gill opening
c. Body scales
D. cnidoblasts


A graph was plotted between
molar conductivity of various
electrolytes
\( \left(\begin{array}{lll}\text { NaCl, } & \text { HCl } & \text { and } & \text { NH }\left._{\mathbf{4}} \text { OH }\right) \text { and }\end{array}\right. \)
\( \sqrt{\boldsymbol{C}}\left(\text { in } \quad \boldsymbol{m o l} \boldsymbol{L}^{-1}\right) \). correct set is:
A \( \cdot I(N a C l), I I(H C l), I I I\left(N H_{4} O H\right) \)
B \cdot \( I(H C l), I I(N a C l), I I I\left(N H_{4} O H\right) \)
c. \( _{I\left(N H_{4} O H\right), I I(N a C l), I I I(H C l)} \)
D - \( _{I}\left(N H_{4} O H\right), I I(H C l), I I I(N a C l) \)


Find the projection of vector \( 2 \hat{i}+\hat{j} \) on the vector \( \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}} \)


An example of inelastic collision is:
A. scattering of \( \alpha \) particle from a nucleus
B. collision of ideal gas molecules
C. collision of two steel balls lying on a frictionless table
D. collision of a bullet with a wooden block


\( \int_{0}^{a} x^{4}\left(a^{2}-x^{2}\right)^{1 / 2} d x \) equals
\( ^{A} \cdot \frac{\pi a^{5}}{32} \)
в. \( \frac{\pi a^{6}}{32} \)
c. \( \frac{\pi a^{2}}{32} \)
D. None of these


A solenoid \( 1.5 \mathrm{m} \) long and \( 4.0 \mathrm{cm} \) in diameter possesses 10 turns/cm. current of 5 A is flowing through it. Then the magnetic induction (i) inside and
(ii) at one end on the axis of solenoid
are respectively
A \( \cdot 2 \pi \times 10^{-3} T, \pi \times 10^{-3} T \)
В . \( 3 \pi \times 10^{3} T, 1.5 \pi \times 10^{3} T \)
c. \( 0.5 \pi \times 10^{3} 10^{3} T, 4 \pi \times 10^{3} T \)
D. \( 4 \pi \times 10^{3} T, 2 \pi \times 10^{3} \)


The IUPAC name of compound is:
A. Butan-2-aldehyde
B. 2-Methyl-butanal
c. 3-Methyl-butanal
D. 2-Ethylpropanal


If
\( \lim _{x \rightarrow 0^{+}} x\left(\left[\frac{1}{x}\right]+\left[\frac{5}{x}\right]+\left[\frac{11}{x}\right]+\left[\frac{19}{x}\right]+\right. \)
430 (where [.] denotes the greatest
integer function), then \( n= \)
A . 8
B. 9
\( c .10 \)
D. 11


Find odd one out according to the presence of Methane.
A . LPG
B. LNG
c. см
D. Biogas


Product (C) obtained is:
\( A \)
\( \mathbf{C H}_{3}-\mathbf{C H}=\mathbf{C H}-\mathbf{C H}_{\mathbf{3}} \)
B.
\( c \)
D.


Which one of following statement(s)
is/are not correct in respect of Iyophilic
Sols?
A. There is a considerable interaction between the dispersed phase and dispersion medium
B. These are quite stable and are not easily coagulated
C. They need stabilizing agent
D. The particles are hydrated


A copper wire and a steel wire of the
same length and same cross section are joined end to end to form a
composite wire. The composite wire is hung from a rigid support and a load is suspended from the other end. If the increase in length of the composite wire is 2.4 mm, then the increase in lengths
of steel and copper wires are:
\( \left(Y_{c u}=10 \times 10^{10} N / m^{2}, Y_{s t e e l}=2 \times\right. \)
\( \left.10^{11} N / m^{2}\right) \)
\( \mathbf{A} \cdot 1.2 m m, 1.2 m m \)
в. \( 0.6 \mathrm{mm}, 1.8 \mathrm{mm} \)
c. \( 0.8 m m, 1.6 m m \)
D. \( 0.4 \mathrm{mm}, 2.0 \mathrm{mm} \)


The negative and positive ions are held by of attraction.
A. negative force
B. positive force
c. electrostatic force
D. none of the above


The value of \( (x- \)
\( \left(x+\frac{1}{2}-\frac{\sqrt{3}}{2} i\right)\left(x+\frac{1}{2}+\frac{\sqrt{3}}{2} i\right) \)
A. \( x^{3}+x^{2}+x 1 \)
B . \( x^{3}-1 \)
c. \( x^{3}+1 \)
D. \( x^{3}-x^{2}+x+1 \)


The type of linkage present in carbohydrates is
A. Peptide
B. Glycosidic
c. Amide
D. Phosphate bonds


In a Young's double slit experiment, the
intensity at the cetral maximum is \( l_{0-} \)
The intensity ata distance \( \beta / 4 \) from the central maximum is ( \( \beta \) is frige width)
A \( \cdot l_{0} \)
в. \( \frac{l_{0}}{2} \)
c. \( \frac{l_{0}}{\sqrt{2}} \)
D. \( \frac{l_{0}}{4} \)


Q Type your question-
\( \mathrm{CaCl}_{2}+\mathrm{U}-\mathrm{tube}=80.483 \mathrm{g} \)
After:Porcelain boat + contents =
\( \mathbf{5 4 . 8 6 9 g} \)
\( \mathrm{CaCl}_{2}+\mathrm{U}-\mathrm{tube}=89.483 \mathrm{g} \)
Reactions: \( Z n(s)+2 H C l(a q) \rightarrow \)
\( Z n C l_{2}(a q)+H_{2}(g) \) then \( H_{2}(g)+ \)
\( \boldsymbol{C u O}(\boldsymbol{s}) \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{C u}(\boldsymbol{s}) \)
What was the reason placing tube of
\( \mathrm{CaCl}_{2} \) between the generator and the
tube containing the porcelain boat?
A. To absorb evaporated HCI
B. To absorb evaporated \( H_{2} O \)
C. To slow down the gases released
D. To absorb the evaporated Zn particles
E. To remove the initial air that passes through the tube


A glycoside is the carbohydrate form of
an:
A. Ether
B. Acetal
c. Aglycone
D. Alcohol


If the product of all solution of the equation \( \frac{(2009) x}{2010}=(2009)^{\log _{x}(2010)} \) can
be expressed in the lowest form as \( \frac{m}{n} \) then the value of \( (\boldsymbol{m}+\boldsymbol{n}) \) is


Total reflecting prisms are
prism.
A . Right angled
B. Acute angled isosceles
c. Right angled isosceles
D. obtuse angled isosceles


n the given figure, If \( M L \| B C \) and
\( N L \| D C, \) then \( \frac{A M}{A B}=\frac{A N}{A D} \)
4. True
3. Falss


Is \( g=\{(1,1),(2,3),(3,5),(4,7)\} \)
function? If this is described by the formula.
\( g(x)=\alpha x+\beta, \) then what values should be assigned to \( \alpha \) and \( \beta ? \)


A sum of Rs. 10,000 is borrowed at \( 8 \% \)
per annum compounded annually. If the amount is to be paid in three equal installments,what will be the annual
installment?


\( f(x)=\frac{\left(e^{k x}-1\right)(\sin k x)}{4 x^{2}}, x \neq 0 \)
\( \boldsymbol{f}(\mathbf{0})=\mathbf{9}, \) is continuous at \( \boldsymbol{x}=\mathbf{0}, \) then \( \mathbf{k} \)
\( =? \)
\( \mathbf{A} \cdot \pm 2 \)
B. ±6
\( c .\pm 4 \)
D. None of the above


Which of the following steps of respiration is amphibolic?
A. Glycolysis
B. Oxidative decarboxylation of pyruvate
c. TCA cycle
D. Oxidative phosphorylation


Name of the compound is:
A. 3 -methyl-trans-3-octene.
B. 5-ethyl-trans-3-octene
c. 4 -ethyl-cis-2-octene
D. 5-ethyl-trans-5-octene


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


Assertion
The present position of hydrogen in the modern periodic table is completely justifiable.
Reason
Hydrogen is a metallic diatomic
element.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is/are the properties of halogen compounds?
A. Hydrogen halides are binary compounds of halogens with hydrogen
B. They are strong hydrohalic acids when dissolved in water
c. Among all the halide compounds the exceptional is \( H F \)
D. All of the above


Find the value of \( x+y \) in the given
figure (in degrees)


Electric field at point (30,30,0) due to a
point charge of \( 8 \times 10^{-3} \mu C \) placed at
origin will be (coordinates are in \( \mathrm{cm} \) )
A. \( 8000 N / C \)
в. \( 4000(\hat{i}+\hat{j}) N / C \)
c. \( 200 \sqrt{2}(\hat{i}+\hat{j}) N / C \)
D. \( 400 \sqrt{2}(\hat{i}+\hat{j}) N / C \)


A skew-symmetric matrix \( M \) satisfies
the relation \( M^{2}+I=0, \) where \( I \) is the
unit matrix. Then, \( M M^{\prime} \) is equal to
A . \( I \)
B . \( 2 I \)
\( c .-I \)
D. None of these


Isotopes have different:
A. arrangement of electrons
B. no. of p and \( e^{-} \)
c. no. of neutrons
D. no. of electrons


The van der Waals forces in halogens increase in the order:
A \( \cdot \mathrm{F}_{2}<\mathrm{Cl}_{2}<\mathrm{Br}_{2}<\mathrm{I}_{2} \)
В \( \cdot I_{2}>\mathrm{Cl}_{2}>\mathrm{Br}_{2}>\mathrm{F}_{2} \)
c. \( \mathrm{F}_{2}<\mathrm{Br}_{2}<\mathrm{I}_{2}<\mathrm{Cl} \)
D. \( \operatorname{Br}_{2}<\mathrm{F}_{2}<\mathrm{Cl}_{2}<\mathrm{I}_{2} \)


When bleaching powder reacts with
excess of dilute acids, the gas liberated is:
A \( \cdot C l_{2} \)
в. \( O_{2} \)
c. \( B \mathrm{r}_{2} \)
D. \( I_{2} \)


Which of the following statement (s) is/are true regarding the change:
\( \boldsymbol{C N}^{-} \rightarrow \boldsymbol{C N O}^{-} ? \)
This question has multiple correct options
A. Carbon is losing two electrons per atom.
B. The oxidation state of carbon change from +2 to +4
c. oxidation state of nitrogen is not changing
D. oxidation state of nitrogen changes from - 3 to -


Molecule with double bond is :
A \( . H_{2} \)
B. \( F_{2} \)
\( c \cdot C l_{2} \)
D. \( O_{2} \)


n-Butane \( \left(C_{4} H_{10}\right) \) is produced by
monobromination of \( C_{2} H_{6} \) followed by
Wurtz reaction. Calculate the volume of
ethane at STP required to produce 55 g of \( n \) -butane. The bromination takes
place with \( 90 \% \) yield and the Wurtz reaction with \( 85 \% \) yield.
A . 27.75 느
B . 55.5 느
c. 111
D. 5.55


Assertion
Sodium reacts with oxygen to form
\( N a_{2} O_{2} \) but postassium reacts with
oxygen to form \( K O_{2} \)
Reason
Potassium is more reactive metal than
sodium.
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


Tell what property allows you to compute \( \frac{1}{3} \times\left(6 \times \frac{4}{3}\right) \) as \( \left(\frac{1}{3} \times 6\right) \times \)
4
\( \overline{\mathbf{3}} \)


Which final acid obtained in contact
process?
A. conc. \( H_{2} S O_{4} \)
B. dil. \( H_{2} S O_{4} \)
c. fuming sulphuric acid.
D. None of the above


A stone thrown vertically upwards with
a speed of \( 5 m / s \) attains a height \( H_{1} \)
Another stone thrown upwards from the same point with a speed of \( 10 m / s \)
attains a height \( \boldsymbol{H}_{2} \). The correct relation
between \( H_{1} \) and \( H_{2} \) is
A \( . H_{2}=4 H_{1} \)
В. \( H_{2}=3 H_{1} \)
\( \mathbf{c} \cdot H_{1}=2 H_{2} \)
D. \( H_{1}=H_{2} \)


Select the incorrect statement(s):
This question has multiple correct options
A. Magnesium can be burnt in the atmosphere of \( C O_{2} \)
and \( S O_{2} \)
B. Magnesium reacts with alkyl halides to form Grignard's reagent
C. Out of \( M g \) and \( C a \), only \( M g \) reacts with \( N_{2} \) to form magnesium nitride
D. Calcium is less reactive than magnesium


The molecular mass of benzoic acid in
benzene as determined by depression in freezing point method corresponds to:
A. ionization of benzoic acid
B. dimerization of benzoic acid
c. trimerization of benzoic acid
D. solvation of benzoic acid


Short / Long Answer question Type :
Write short notes on Menarche


Which one is the most easily
dehydrated?
\( A \cdot(1) \)
B. (II)
\( c \)
D. All of equally dehydrated


The sublimation of iodine is due to
A. Low melting point
B. Weak \( I-I \) Bond
C. Weak van der Waals forces among \( I_{2} \) molecules
D. Lone pair - lone pair repulsion in \( I_{2} \) molecule


Find gain or loss per cent. \( \mathrm{CP}=\boldsymbol{R s} .900 \) and \( \mathrm{SP}=\boldsymbol{R} \boldsymbol{s} .1, \mathbf{0 8 0} \)


A square aluminium rod is \( 1 \mathrm{m} \) long and \( 5 \mathrm{mm} \) on edge. What must be the radius of another aluminium rod whose length
is \( 1 \mathrm{m} \) and which has the same
resistance as the previous rod?
A. \( 5.0 \mathrm{mm} \)
B. 4.2 mm
\( c .2 .8 \mathrm{mm} \)
D. \( 1.4 \mathrm{mm} \)


Passing \( \boldsymbol{H}_{2} \boldsymbol{S} \) gas into a mixture of \( M n^{2+}, N i^{2+}, C u^{2+} \) and \( H g^{2+} \) ions in
an acidified aqueous solution precipitates:
A. \( C u S \) and \( H g S \)
B. \( M n S \) and \( C u S \)
c. \( M n S \) and \( N i S \)
D. \( N i S \) and \( H g S \)


\( \sum_{k} \)


\( \ln \triangle A B C \) is \( \angle B \) is right angle. If \( a=16 \)
and \( c=12 \) then \( b= \)
A . 8
B . 18
c. 20
D . 28


Ammonia gas is not prepared by:
A. reduction of sodium nitrite or sodium nitrate by the reaction of zinc dust and sodium hydroxide.
B. hydrolysis of calcium cyanamide.
C. heating ammoniumchloridewith slaked lime.
D. heating of \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)


Food reserve in Rhodophyta is
A. Floridean starch
B. Mannitol
c. Leucosin
D. All of the above


Two triangles \( A B C \) and \( P Q R \) are \( \operatorname{similar}, \) if \( B C: C A: A B=1: 2: 3 \)
then \( \frac{Q R}{P R} \)
A \( \cdot \frac{3}{2} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \frac{2}{3} \)


Leaching method is used to concentrate
the ores of:
A. Gold
B. Silver
c. Aluminium
D. All of these


Figure shows which type of vascular
bundle?
A. Radial
B. Closed vascular bundle
c. Conjoint open
D. Conjoint closed


The D.E of the family of ellipse with centre at the origin and having co ordinate axes as axes is
A \( . x\left[y y_{2}+y_{1}^{2}\right]=y y_{1} \)
B . \( x^{2} y_{2}+y_{1}^{2}=y \)
\( \mathbf{c} \cdot x y y_{2}+y_{1}^{2}=y \)
D. \( x y y_{2}+y_{1}^{2}+y=0 \)


Passivity is exhibited by:
\( A) B e, B) M g, C) A l, D) B \)
A \( . A, B \)
в. \( B, C \)
c. \( A, C \)
D. \( B, D \)


What is the de-broglie wavelength for the electron of third class of hydrogen?
\( \mathbf{A} \cdot 9.96 \times 10^{-10} \mathrm{cm} \)
В. \( 9.96 \times 10^{-8} \mathrm{cm} \)
\( \mathbf{c} .9 .96 \times 10^{4} \mathrm{cm} \)
D. \( 9.96 \times 10^{8} \mathrm{cm} \)


One of the allotrope of oxygen is ozone. It
is a pale-blue poisonous gas with a strong odour.
A. True
B. False


State:
first law of thermodynamics


Assertion
Graphite is used as anode but not
diamond.
Reason
Graphite is good conductor of current
due to sp \( ^{2} \) hybridisation having mobile
\( \pi \) electrons. Diamond has \( s p^{3} \)
hybridisation and is insulater.
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


Figure shows a plane mirror onto which
a light ray is incident. If the incident
light ray is turned ray is turned by \( 10^{\circ} \)
and the mirror by \( 20^{\circ} \) as shown, find the
angle turned by the reflected ray.
ted ray
\( \mathbf{A} \cdot 10^{\circ} \)
B. \( 20^{\circ} \)
\( c \cdot 30^{\circ} \)
D. 40


\( \mathbf{\Psi}_{1 s}=\left[\frac{1}{\sqrt{\pi a_{o}^{3}}}\right] e^{-r / a_{0}} \)
Above relation is wave function of
hydrogen atom in ground state \( (r= \) distance of electron from nucleus and
\( \boldsymbol{a}_{0}=\mathbf{0 . 5 2 9} \times \mathbf{1 0}^{-8} \boldsymbol{c m} \) ). For \( \mathbf{1} \boldsymbol{s} \) orbital of
hydrogen, the maximum probability of finding an electron is at \( r= \)
A. \( a_{0} / 2 \)
2
в. \( a_{0} \)
\( c \cdot 2 a_{0} \)
D. \( \sqrt{a_{0}} \)


Which of the following is not a method of refining?
A. Roasting
B. Electrolysis
c. Distillation
D. Oxidation


The positive value of \( k \) for which \( \mathbf{k e}^{\mathbf{x}}- \)
\( \mathbf{x}=\mathbf{0} \) has only one root is
A . \( 1 / e \)
B. 1
\( c \)
D. \( \log _{\mathrm{e}} 2 \)


The most common form of
diagrammatic representation of a grouped frequency distribution is -
A . Ogive
B. Histogram
C. Frequency polygon
D. None of these


The statment that is true about 'Light' is
A. requires a material medium to travel from one place to another
B. does not require a material medium
c. light has mass but it is negligible
D. light waves are longitudinal wave


If \( f(x)=\log _{e}\{\log (x)\}, \) then \( f^{\prime}(x) \) at
\( \boldsymbol{x}=\boldsymbol{e} \) is :
\( A \)
B. \( -c \)
\( c \cdot e^{2} \)
D. \( e^{-1} \)


\( f\left(\begin{array}{ccc}-1 & 2 & 4 \\ 3 & 6 & -5\end{array}\right] \) then find \( 3 A \)


The domain of \( \log (x-5) \) is
\( A \cdot(5, \infty) \)
B \( \cdot R^{+}-(1) \)
\( c \cdot R-11 \)
D. None of these


According to laws of refraction(Snell's law
A. \( \angle i=\angle r \)
B. \( \sin i=\sin r \)
c. \( \frac{\sin i}{\sin r}= \) constant
D. \( \tan i=\tan r \)


Write the converse and contrapositive of
the statement "lf the two lines are
parallel then they do not intersects in the same plane".


Find the mean
\( \begin{array}{llllll}x: & 10 & 30 & 50 & 70 & 89 \\ f: & 7 & 8 & 10 & 15 & 10\end{array} \)
\( \mathbf{A} \cdot 55 \)
B. 65
\( \mathbf{c} \cdot 45 \)
D. 95


The vapour pressure of water is \( 12.3 k P a \) at \( 300 K . \) Calculate the vapour
pressure 1 molal solution of a non-
volatile solute in it
\( \mathbf{A} \cdot 12.08 k P a \)
B. 1.208 Ppa
\( \mathrm{c} .2 .4 \mathrm{kPa} \)
D. \( 0.4 k P a \)


Which statement is wrong from the following for the reflection by plane mirror?
A. The size of image is same as size of object
B. object distance and image distance is same
c. A plane mirror forms virtual and erect image
D. Image of the object in not laterally inverted


\( 200 g \) ball is tied to one end of a string of length \( 20 \mathrm{cm} . \) It is revolved in a
horizantal circle at an angular frequency of 6 rpm. Then, angular velocity \& linear velocities of the ball respectively are
rads \( ^{-1} \) and \( m s^{-1}: \)
A. 0.7284,0.1257
7
в. 0.6284,0.1257
c. 0.6284,0.1457
D. 0.7284,0.1457


The sum of the series \( 1+\frac{1}{4 \times 2 !}+ \) \( \frac{1}{16 \times 4 !}+\frac{1}{64 \times 6 !}+\ldots \infty \) is?
A \( \cdot \frac{e+1}{\sqrt{e}} \)
в. \( \frac{e-1}{\sqrt{e}} \)
c. \( \frac{e+1}{2 \sqrt{e}} \)
D. \( \frac{e-1}{2 \sqrt{e}} \)


A uniform ladder which is 5 m long has
a mass of \( 30 k g \) with its upper end against a smooth vertical wall and its
lower end is on a rough ground. The
bottom of the ladder is \( 3 m \) from the
wall. Calculate the frictional force
between the ladder and the ground.
\( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)


What is the measurement of
temperature in Celsius scale in the above figure?
\( A \cdot 25^{\circ} C \)
B. \( 30^{\circ} \) C
\( c \cdot 26^{\circ} C \)
D \( \cdot 29^{\circ} C \)


Area bounded by curve \( x\left(x^{2}+p\right)= \)
\( \boldsymbol{y}-\mathbf{1} \) with \( \boldsymbol{y}=\mathbf{1} \boldsymbol{p}<\mathbf{0} \) is
A \( \cdot \frac{p^{2}}{4} \)
в. \( \frac{p}{2} \)
c. \( \frac{p^{2}}{2} \)
D. \( \frac{p}{4} \)


\( \frac{2 x^{3}+1}{(x-1)(x+1)(x+2)}= \)
A \( \cdot 2+\frac{1}{2(x-1)}+\frac{1}{2(x+1)}-\frac{5}{x+2} \)
B \( \cdot 2-\frac{1}{2(x-1)}-\frac{1}{2(x+1)}-\frac{15}{x+2} \)
c. \( 2+\frac{1}{2(x-1)}-\frac{1}{2(x+1)}+\frac{15}{x+2} \)
D. \( \frac{1}{2(x-1)}+\frac{1}{2(x+1)}-\frac{15}{x+2} \)


Reflection can occur on
A. Transparent surfaces
B. Translucent surfaces
c. Opaque surfaces
D. \( B \) and \( c \)


Observe the following lists Let \( f(x) \) be
any function
List - I
A) \( f^{\prime}(\mathrm{a})=0 \) and
I) \( f(x) \) is increasing at \( x=a \)
\[
f^{\prime \prime}(\mathrm{a})<0 \text { then }
\]
B) \( f^{\prime}(\mathrm{a})=0 \) and
2) \( f(x) \) has maximum value
\[
f^{\prime \prime}(\mathrm{a})>0 \text { then } \quad \text { at } x=a
\]
3) \( f(x) \) has
C) \( f^{\prime}(a) \neq 0 \) then neither maximum nor minimum
D) \( f^{\prime}(a)>0 \)
4) \( f(x) \) has minimum value at \( x=a \)
5) \( f(x) \) is decreasing at \( x=a \)
\( A \cdot A-4, B-2, C-3, D-5 \)
B. A -2,B -4, C -3, D -1
C. \( A-2, B-4, C-3, D-5 \)
D. A -2,B -4, C -5, D-1


1.0 \( \mathrm{ml} \) of a solution of \( \mathrm{H} C l \) with a \( p H \) of
4.0 is added it to \( 9.0 \mathrm{ml} \) of distilled
water, the \( p H \) of the final solution will
be:
A. The pH would remain unchanged.
B. The pH would rise to 5.5
c. The pH would rise to 5.0
D. The pH would be unmeasurable due to the amount of dilution
E. The pH would rise to 7.0


Which of the following statement is
CORRECT?
A. rolling a body is easier than sliding
B. sliding a body is easier than rolling
C. rolling a body is harder than sliding
D. None of these


The number of sub-energy levels in any energy level is given by:
\( A \cdot n \)
B. \( l \)
\( c \cdot m \)
D.


If \( f(x)=x^{3}-3 x^{2}+5 \)
Find \( f(0)+f(3) \)


Meiosis occurs in
A. Embryo sac
B. Megaspore
c. Megaspore mother cell
D. Nucellus


Three vertices of a tetrahedron are
(0,0,0),(6,-5,-1) and \( (-4,1,3) . \)
the centroid of the tetrahedron be
(1,-2,5) then the fourth vertex is
A. (2,-4,18)
в. (1,-4,18)
\( ^{c} \cdot\left(\frac{3}{2}, \frac{-3}{2}, \frac{7}{4}\right) \)
D. none of these


Dinitrophenol (DNP) allows hydrogen ions to leak across a membrane which
can harm the \( H^{+} \) gradient. Select the
correct statement.
A. It would permit a greater growth rate, since the cell would no longer have to spend energy pumping \( H^{+} \) across the membrane
B. It would permit a greater growth rate, because the equalization of \( H^{+} \) on both sides of a membrane would help the cell cope with an acidic environment.
c. If the cell was a neuron, it would have no impact, because the charge difference on the surface of the neuron membrane is based on \( N a^{+} \) and \( K^{+}, \) not on
\( H^{+} \)
D. The cell would lose the bulk of its energy production because of DNP's interference with chemiosmosis
E. It would slow the growth rate slightly, but the cell would compensate by maintaining the function of proton pumps


In the Lassaigne's solution with nitrogen present in the organic compound, ferrous sulphate solution is added and then boiled. It is neutralised
with dilute \( H_{2} S O_{4} . \) A bright solution is formed.


What different criteria would you
choose to classify people that you meet often?


BOD refers to the
A. Bidding of Dermatology
B. Binding of Dirt
C. Biochemical occupied Date
D. Biochemical Oxygen demand


H \( C l \) gas can fume in moist air
A. True
B. False


Briefly explain natural methods of birth
control.


Which shows increasing the kinetic energy of a liquid?
\[
\| \underbrace{x}
\]
\( \mathbf{A} \cdot A B \)
в. \( B C \)
c. \( C D \)
D. \( D E \)
E . \( E F \)


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


Solar radiation is
A. Transverse electromagnetic wave
B. Longitudinal electromagnetic wave
C. Stationary wave
D. None of the above


A body colls from \( 70^{\circ} \mathrm{C} \) to \( 60^{\circ} \mathrm{C} \) in 10
minutes when kept in air at \( 30^{\circ} \mathrm{C} \). In the next ten minutes its temprature will fall
A . Below \( 50^{\circ} \mathrm{C} \)
В. \( \operatorname{To} 50^{\circ} \mathrm{C} \)
c. To above \( 52.5^{\circ} \mathrm{C} \)
D. To any of the above depending on its specific heat


The first term in an arithmetic
sequence is -5 and the second term is
\( -3 . \) What is the 50 th term? (Recall that
in an arithmetic sequence, the difference between successive terms is
constant)
\( A \cdot 87 \)
B . 78
\( c \cdot 74 \)
D. 93


Lake test of \( A l^{3+} \) ion is based on
adsorption of blue litmus on solid
surface of :
A . \( A l \)
B \( \cdot A l(O H)_{3} \)
c. \( A l_{2}, o_{3} \)
D. \( A l C l_{3} \)


A given resistor has the following colour scheme of the various strips on it:
Brown, black, green and silver. Its value in ohm is :
A \( \cdot 1.0 \times 10^{4} \pm 10 \% \)
В. \( 1.0 \times 10^{5} \pm 10 \% \)
C. \( 1.0 \times 10^{6} \pm 10 \% \)
D. \( 1.0 \times 10^{7} \pm 10 \% \)


A Diwali rocket is ejecting 0.05 kg of gases per second at a velocity of \( 400 m s^{-1} . \) The accelerating force on the rocket is equal to :
A. 20 dyne
B. 20 newton
c. \( 20 \mathrm{kg} \) wt
D. sufficient data not giver


\( 200 \mathrm{ml} \) of \( 1 \mathrm{M} H C l \) is mixed with \( 400 \mathrm{ml} \)
of \( 0.5 \mathrm{M} \) NaOH.The temperature rise in
the calorimeter was found to be \( 4.0^{\circ} \mathrm{C} \)
Water equivalent of calorimeter is \( 25 g \)
and the specific heat of the solution is 1 cal/mL/degree. If the theoritical heat of neutralization of a strong acid and strong base is -13.5 kcal, then the
percentage error (as nearest integer) incurred in this experiment while calculating the heat of neutralization is


Which statement is incorrect?
A. Catalytic decomposition of \( K C l O_{3} \) by \( M n O_{2} \) is an example of homogeneous catalysis.
B. Only the surface atoms in an adsorbent play an active role in adsorption.
C. The rate of adsorption is very rapid in the beginning but decreases gradually until equilibrium is attained.
D. Absorption proceeds at a steady rate.


With usual notation, the following equation, said to give the distance
covered in the \( n^{t h} \) second i.e., \( S_{n}=u+ \)
\( a \frac{(2 n-1)}{2} \) is :
A. numerically correct
B. dimensionally correct
c. both dimensionally and numerically correct
D. neither numerically nor dimensionally correct


Assertion
It is difficult to move a bike with its
breaks on
Reason
Sliding friction is greater than rolling friction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Consider the function \( f \) defined by \( f(x) \)
\( =x-x(x), \) where \( x \) is a positive
veriable,and (x) denotes the integral part of \( x \) and show that it is
discontinuous for intergral values of x,and continuous for all others. Is the function periodic? If periodic,what is its
period? Draw its graph.


The most general values of \( \theta \) for which
\( \sin \theta-\cos \theta=\min _{a \in R}\left(1, a^{2}-6 a+10\right) \)
are given by
A \( \cdot n \pi+(-1)^{n} \frac{\pi}{4}-\frac{\pi}{4} \)
B. \( n \pi+(-1)^{n} \frac{\pi}{4}+\frac{\pi}{4} \)
c. \( 2 n \pi+\frac{\pi}{4} \)
D. None of these


Find the sum of the first 25 terms of an
A.P whose \( n \) th term is given by \( a_{n}= \)
\( 2-3 n \)
\( \mathbf{A} \cdot-925 \)
B . -928
\( \mathbf{c} .-923 \)
D \( .-929 \)


0.40 g of an organic compound containing phosphorous gave 0.555 g of \( M g_{2} P_{2} O_{7} \) by usual analysis.
Calculate the percentage of the phosphorous in the organic compound.
A . \( 38.75 \% \) \%
в. \( 31.56 \% \)
c. \( 25.99 \% \)
D. 63.45\%


The most common ground tissue in plants is
A. Epidermis
B. cortex
c. Parenchyma
D. collenchyma


Write the balance equation for the reaction occurring when a solution of calcium chloride is mixed with a
solution of sodium carbonate.


Calculate the magnetic field induction B at the centre of a circular coil having \( \mathbf{5 0 0} \) turns, radius \( \pi \mathrm{cm} \) and carrying \( \mathbf{5} \mathbf{A} \) of current
\( \mathbf{A} \cdot 0.1 T \)
в. 0.005 न
c. 0.5 न
D. 0.05 न


Which of the following are APs?
This question has multiple correct options
\( \mathbf{A} \cdot 2.4,8,16, \ldots \)
B. \( 2, \frac{5}{2}, 3, \frac{7}{2}, \ldots \)
C \( .-1.2,-3.2,-5.2,-7.2, \ldots \)
D. \( -10,-6,-2,2, \ldots \)
E \( .3,3+\sqrt{2}, 3+2 \sqrt{2}, 3+3 \sqrt{2}, \ldots \)
F. \( 0.2,0.22,0.222,0.2222, \ldots . \)
G. \( 0,-4,-8,-12, \dots \)
\( \mathrm{H} \cdot-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}, \ldots \)


The sum of the squares of deviation
of 10 observations from their mean 50 is
\( 250, \) then coefficient of variation is
A . 10\%
B. 40\%
c. 50\%
D. none of these


Describe the structure of a neuron with
the help of a neat, labelled diagram.


At what temperature is the Fahrenheit scale reading equal to half of Celsius
scale?


Show that
\( \begin{array}{l}\sin 10^{\circ} \quad-\cos 10^{\circ} \\ \sin 80^{\circ} \quad \cos 80^{\circ}\end{array} \mid=1 \)


1 mole of \( H_{2}, 2 \) moles of \( I_{2} \) and 3 moles
of \( H I \) were taken in a 1 litre flask. The
equilibrium constant of the reaction \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is 50 at
\( 330^{\circ} \mathrm{C} . \) The concentration of \( \mathrm{HI} \) at
equilibrium is (moles.lit \( ^{-1} \) ):
A . 0.3
в. 1.3
c. 4.4
D. 2.


Assertion
PhBr is less reactive than \( C_{2} H_{5} B r \)
towards \( S_{N} \) reactions.
Reason
The forces of attraction between \( \boldsymbol{R} \boldsymbol{X} \)
and \( H_{2} O \) molecules are weaker than
those present between the molecules of
\( R X \) and water separately.
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 are correct


A charge \( Q \) is to be divided into two parts such the force between them is
maximum. They should be divided as
A \( \cdot \frac{Q}{4}, \frac{3 Q}{4} \)
B . \( \frac{a}{3}, \frac{20}{3} \)
c. \( \frac{a}{8}, \frac{7 Q}{8} \)
D. \( \frac{Q}{2}, \frac{a}{2} \)


Take \( C_{i c e}=0.53 c a l / g-^{\circ} C, C_{w a t e r}= \)
\( \mathbf{1 . 0 c a l} / \boldsymbol{g}-^{\circ} \boldsymbol{C},\left(\boldsymbol{L}_{f}\right)_{\text {water}}=\mathbf{8 0 c a l} / \boldsymbol{g} \)
and \( \left(\boldsymbol{L}_{v}\right)_{\text {water}}=\mathbf{5 2} \mathbf{9} \) cal \( / \mathbf{g} \). In a
container of negligible mass \( 140 g \) of ice
initially at \( -15^{\circ} \mathrm{C} \) is added to \( 200 \mathrm{g} \) of
water that has a temperature of \( 40^{\circ} \mathrm{C} \). If no heat is lost to the surroundings, what is the final temperature of system
in \( ^{\circ} \boldsymbol{C} \) ?


Which one of the following sets form the biodegradable polymer?
A \( \cdot H_{2} N-C H_{2}-C O O H \) and \( H_{2} N-\left(C H_{2}\right)_{5}-C O O H \)
в.
\( \langle\bigcirc\rangle-\mathrm{cH}=\mathrm{cH}_{2} \mathrm{and} \mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2} \)
D. \( C H_{2}=C H-C N \) and \( C H_{2}=C H-C H=C H_{2} \)


Which one is a polymer of fructose?
A. Glycogen
B. Starch
c. Inulin
D. Raffinose


In hydrogen-oxygen fuel cell the carbon rods are immersed in hot aqueous
solution of.
A . \( K C l \)
в. КОН
c. \( H_{2} S O_{4} \)
D. \( N H_{4} C l \)


A drawing pin is pushed against a wooden table with a force of \( 10 \mathrm{N} \)
Calculate the pressure exerted by the pin at a point on the table, if area of the
point is \( 0.01 \mathrm{cm}^{2} \)
\( \mathbf{A} \cdot 10^{5} P a \)
B . \( 10^{6} P a \)
\( \mathbf{c} \cdot 10^{7} P a \)
D. \( 10^{8} \mathrm{Pa} \)


Total reflecting prism is used for
A. deviating a ray of light through \( 180^{\circ} \)
B. deviating a ray of light through \( 90^{\circ} \)
c. obtaining the invented image without producing deviation in its path
D. all of these


Why skin feels dry in an air-conditioned
room?
A. Because the rate of evaporation decreases with lower humidity.
B. Because the rate of evaporation increases with lower humidity.
C. Because the rate of evaporation remains same with lower humidity.
D. Because the rate of evaporation increases with higher humidity.


Synthetic polymer among the following
is :
A. protein
B. plastic
c. starch
D. cellulose
E. nucleic acid


Write any four differences between
lyophilic sols and Iyophobic sols.


The escape velocity of a body from the
earth is \( u . \) What is the escape velocity from a planet whose mass and radius are twice those of the earth?
A \( .2 u \)
в. \( u \)
c. \( 4 u \)
D. \( 16 u \)


The wave number of the \( H_{\alpha} \) -line in
Balmer series of hydrogen spectrum is :
A . 5R / 36
в. зв
c. \( 21 \mathrm{R} / 100 \)
D. 3R / 4


\( M g(O H)_{2} \) in the form of milk of
magnesia is used to neutralize excess
stomach acid. How many moles of
stomach acid can be neutralized by 1 g
of \( M g(O H)_{2} ? \)
(Molar mass of \( \left.M g(O H)_{2}=58.33\right) \)
A . 0.017
B. 0.0343
c. 0.686
D. 1.25


State whether true or false.
Angle of incidence is always equal to the angle of reflection.
A. True
B. False


Find the equation of the tangent and the normal to the following curves at the indicated points.
\( \boldsymbol{y}=\boldsymbol{x}^{4}-\boldsymbol{6} \boldsymbol{x}^{3}+1 \mathbf{3} \boldsymbol{x}^{2}-\mathbf{1 0} \boldsymbol{x}+\mathbf{5} \) at \( \boldsymbol{x}= \)
\( \mathbf{1} \)


The total number of lone-pairs of
electrons in Melamine is:


Which of the following factors contribute towards higher stability of Iyophilic colloid?
A. Charge on their particles
B. Attractive forces between particles
c. Small size of their particles
D. High solvation due to a layer of dispersion medium


Which of the following is not a source of
carbon?
A. limestone
B. dolomite
c. calcite
D. haemetite


How many gram of \( K M n O_{4} \) is
contained in 4 litre of \( 0.05 N \) solution.
The \( K M n O_{4} \) is to used as an oxidant in
acid medium \( \left(M_{W}=158\right): \)
A. \( 1.58 g \)
B. \( 15.8 g \)
c. \( 6.32 g \)
D. \( 31.6 g \)


Consider the following data gathered from a survey of a colony:

Cricket \( \begin{array}{ll}\text { Favourate } & \text { cricket } \quad \text { Basket } \\ \text { port: }\end{array} \) sport:
1240 470 watching
Participating 620 320
Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph? Which sport is most popular?


The force of interaction (attraction or
repulsion) between two stationary point charges in vacuum is directly proportional to the product of the charges and inversely proportional to the square of distance between them.
This is called
A. Curie's Law
B. Coulomb's law
c. Faraday's Law
D. Amperr's Law


What are inner transition elements?
Decide which of the following atomic
numbers are the atomic numbers of the
inner transition elements :
\( \mathbf{2 9}, \mathbf{5 9}, \mathbf{7 4}, \mathbf{9 5}, \mathbf{1 0 2}, \mathbf{1 0 4} \)


A cell of e.m.f. \( \varepsilon \) and internal resistance
is used to send current to an external resistance R. The total resistance of
circuit,
A \( \cdot \frac{R r}{(R+r)} \)
в. \( \frac{R+r}{2} \)
\( c \cdot R r \)
D. \( R+r \)


The magnitude of the EMF in a coil depends on
A. flux density passing through it
B. density of material
c. amount of flux leakage
D. rate of change of flux linkages


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H I} \stackrel{A l C l_{3}}{\rightarrow} \boldsymbol{A} \stackrel{A q . \boldsymbol{K O H}}{\rightarrow} \)
\( B^{c o n c . H_{2} S O_{4}} C,^{\prime} C^{\prime} i s: \)
A. Ethoxy ethane
B. Ethanol
c. Ethanal
D. Acetone


Which of the following species, do not show disproportionation reaction and why?
\( \mathbf{C l O}^{-}, \mathbf{C l O}_{\mathbf{2}}^{-}, \mathbf{C l O}_{\mathbf{3}}^{-} \) and \( \mathbf{C l O}_{\mathbf{4}}^{-} \)
Also, write the reaction for each of the
species that disproportionate.


The sides of a triangle with positive area have lengths 5,7 and \( a . \) The sides of a second triangle with positive area
have lengths 5,7 and \( b \) Which of the following is NOT a possible
value of \( |\boldsymbol{a}-\boldsymbol{b}| ? \)
A . 3
B. 5
\( c \cdot 7 \)
D. 10


Differentiate \( \log \left(\cos e^{x}\right) \) w.r.t to \( x \)


An alkane which can exhibit optical activity is:
A. 3-methylhexane
B. 3-methylpentane
c. isopentane
D. neopentane


Integrate with respect to \( x \) \( \int \frac{1}{x^{6}\left(1+x^{-5}\right)^{\frac{1}{5}}} d x \)


A circular hole of radius \( \frac{x}{2} \) is cut from a
circular disc of radius \( R \). The disc lies
in the XY-plane and its centre coincides
with the origin. If the remaining mass of
the disc is \( M \) then,
(1)determine the initial mass of the
disc.
(2)determine its moment of inertia
about the z-axis.


Which one of the following is the direct ancestor of modern man?
A. Australopithecus
B. Ramapithecus
c. Homo erectus
D. Homo habilis


An electron moving with a constant velocity \( v \) along \( X \) -axis enters a uniform electric field applied along Y-axis. Then,
the electron moves
A. with uniform acceleration along Y-axis
B. without any acceleration along Y-axis
C \( . \) in a trajectory represented as \( y=a x^{2} \)
D. in a trajectory represented as \( y=a x \)
E. with uniform deceleration along \( \mathrm{x} \) -axis


How are the field lines in a uniform
magnetic field ?
A . curved
B. parallel equidistant straight lines
c. parallel but non-equispaced straight lines
D. nothing can be said.


\( \mathbf{3} N_{2} H_{4}+2 B r O_{3}-3 N_{2}+ \)
\( 2 B r^{-}+6 H_{2} O \)
The above reaction shows:
A. intermolecular redox
B. auto-redox
C. intramolecular redox
D. either of these


The most abundant constituent of dry air
in terms of volume is
A. carbon dioxide
B. nitrogen
c. oxygen
D. none of these


Solve the equations using graphical
method: \( x+y=7 \) and \( 2 x-3 y=9 \)
\( A \cdot(6,-1) \)
B. (-6, 1)
\( c \cdot(6,1) \)
D. (-6,-1)


What is the order of magnitude of the distance of a quasar from us if light takes 2.9 billion years to reach us?
A \( \cdot 2.7 \times 10^{25} \mathrm{m} \)
В. \( 10^{25} \mathrm{m} \)
\( \mathbf{c} \cdot 10^{2} 4 m \)
D. \( 3 \times 10^{25} m \)


A card is drawn at random from a pack
of 52 cards. Find the probability that the card drawn is a jack, a queen or a king.


The average energy in one time period in simple harmonic motion is.
A \( \cdot \frac{1}{2} m \omega^{2} A^{2} \)
B \( \cdot \frac{1}{4} m \omega^{2} A^{2} \)
\( \mathrm{c} \cdot m \omega^{2} A^{2} \)
D. zero


If \( f(x) \) is continuous for \( 0 \leq x<\infty \)
then the most suitable values of \( a \) and \( b \)
are
A \( . a=1, b=-1 \)
B. \( a=-1, b=1+\sqrt{2} \)
c. \( a=-1, b=1 \)
D. none of these


In how much time would the simple
interest on a certain sum be 0.3 times
the principal at \( 10 \% \) per annum?
A. 1 year
B. 2 years
c. 3 years
D. 4 years


Capitulum inflorescence is found in
A. Compositae (Asteraceae)
B. Cruciferae (Brassicaceae)
c. Solanaceae
D. Malvaceae


The present population of a town is \( 14000 . \) If it increases at the rate of \( 10 \% \)
per annum, what will be its population
after 4 years?
\( \mathbf{A} \cdot 10497 \)
B . 20497
c. 30497
D. 40497


The electron present in the 5th orbit in an excited hydrogen atom returns back to the ground state. The number of lines
which appear in Lyman series of hydrogen spectrum is:
A . 5
B. 10
\( c \cdot 4 \)
D. 6


An electron in a hydrogen atom
undergoes a transition from an orbit
with quantum number \( n_{i} \) to another
with quantum number \( n_{f} . V_{i} \) and \( V_{f} \) are respectively the initial and final potential energies of the electron. If \( \frac{V_{i}}{V_{f}}=6.25, \) then the smallest possible \( \boldsymbol{n}_{f} \) is


Verify Rolle's theorem for the function \( f(x)=\sin x+\cos x-1 \) in the interval
\( \left[0, \frac{\pi}{2}\right. \)


Possibility of occurrence of coal in an area, is determined by study of
A. Microfossils
B. Ecology
c. Economic botany
D. Mining contents


If the real-valued function \( f(x)=x^{3}+ \)
\( 3\left(a^{2}-1\right) x+1 \) be invertible then the
set of possible real values of a is
A \( \cdot(-\infty,-1) \cup(1+\infty) \)
в. (-1,1)
c. [-1,1]
D \( \cdot(-\infty,-1] \cup[1,+\infty) \)


Vector equation of line \( \frac{\mathbf{3}-\boldsymbol{x}}{\mathbf{3}}= \)
\( \frac{2 y-3}{5}=\frac{z}{2} \) is \( _{--}-------k \in R \)
A \( \cdot \bar{r}=(3,5,2)+k(3,3,0) \)
B \( \cdot \quad \bar{r}=\left(3, \frac{3}{2}, 0\right)+k(-6,5,4) \)
c. \( \bar{r}=(3,3,0)+k(3,5,2) \)
D \( \cdot_{\bar{r}}=(-6,5,4)+k\left(3, \frac{3}{2}, 0\right) \)


Assertion
Let \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x} \)
Statement I \( \boldsymbol{f} \) is not a polynomial
function
Reason
Statement II \( n \) th derivative of \( f(x), \) w.r.t.
\( x \) is not a zero function for any positive
integer \( n \)
A. Statement I is true,Statement II is also true; Statement II is the correct explanation of Statement
B. Statement I is true,Statement II is also true; Statement II is not the correct explanation of Statement
c. Statement l is true,Statement II is false
D. Statement I is false,Statement II is true


Assertion
Conversion of 1,3 -biphosphoglycerate (BPGA) to 3-phosphoglyceric acid (PGA) is an energy-yielding step.
Reason
This energy is trapped in the form of
ATP.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A second harmonic has to be generated in a string if length I stretched between two rigid supports. The points where the string has to be plucked and touched are respectively
A \( \cdot \frac{l}{4}, \frac{l}{2} \)
в. \( \frac{l}{4}, \frac{3 l}{4} \)
c. \( \frac{l}{2}, \frac{l}{2} \)
D. \( \frac{l}{2}, \frac{3 l}{4} \)


The poisson's ratio for \( O_{2} \) is \( 1.4 . \) Which
of the following are correct for \( O_{2} ? \)
This question has multiple correct options
A. \( C_{V M}=5 c a l \)
В. \( C_{V}=0.156 \mathrm{cal} \)
\( \mathbf{c} \cdot C_{P}=\frac{R \Upsilon}{\Upsilon-1} \)
D. \( C_{V}=\frac{R}{(\Upsilon-1)} \)


When a running horse suddenly stops, the rider falls
A. forwards
B. backwards
c. to his right
D. to the horse's right


The arithmetic mean of first five natural
numbers is
A . 3
B. 4
c. 5
\( D \)


If \( 25^{x+1}=\frac{125}{5^{x}}: \) then the value of \( x \) is
1
\( \bar{m} \)
Value of \( m \) is
A .2
B. 4
\( c \cdot 3 \)
D. none of the above


The ratio of phase difference and path difference is:
A \( .2 \pi \)
в. \( \frac{2 \pi}{\lambda} \)
c. \( \frac{\lambda}{2 \pi} \)
D.


An object of length \( 6 \mathrm{cm} \) is placed on
the principle axis of a concave mirror of focal length \( f \) at a distance of 4 f. The length of the image will be
A \( .2 \mathrm{cm} \)
в. \( 12 \mathrm{cm} \)
\( \mathrm{c} .4 \mathrm{cm} \)
D. \( 1.2 \mathrm{cm} \)


A balanced chemical equation is in accordance with:
A. Avogadro's Law
B. Law of constant proportion
c. Law of conservation of mass
D. Law of gaseous volumes


Who was the first to suggest, "A planet moves most quickly when it is closest to the sun, but slows down as it moves
farther away"?
A. Johannes Kepler
B. Galileo Galilei
c. Tycho Brahe
D. Edwin Hubble


The vector \( \overrightarrow{O A} \) where \( O \) is origin is \( \operatorname{given} \) by \( \overrightarrow{O A}=2 \hat{i}+2 \hat{j} . \) Now it is
rotated by \( 45^{\circ} \) anticlockwise about \( O \)
What will be the new vector?
A \( \cdot 2 \sqrt{2} \hat{j} \)
is \( \sqrt{2} \) is \( \sqrt{2} \)
в. 2 ई
\( c \cdot 2 \hat{\imath} \)
D. \( 2 \sqrt{2} \hat{\imath} \)


Assertion: Formula mass (in grams) of
magnesium chloride has \( 12.044 \times 10^{23} \)
magnesium ions. Reason: One formula
mass of an ionic compound has \( 6.022 \times 10^{23} \) ions of each type.
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
E. Both assertion and reason are incorrect


What is the molarity of \( 11.2 V \) of \( H_{2} O_{2} \)
\( ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .5 .6 \)
D. 11.2


Using Rutherford model of the atom,
derive the expression for the total energy of the electron in hydrogen atom What is the significance of total negative energy possessed by the electron?
OR
Using Bohr's postulates of the atomic model derive the expression for radius
of nth electron orbit. Hence obtain the
expression for Bohrs radius.


\( P=\frac{V^{2}}{R} \) is applied when
A. Current is constant
B. Potential difference is constant
c. Resistance is constant
D. None


Match the column in list I with list II.


Which of the following statements is/are correct?
I. The formula of cellulose is \( \left(C_{6} H_{10} O_{5}\right) \)
II. The formula of sucrose, maltose and
lactose is \( C_{12} H_{22} O_{11} \)
III.The formula of Glucose, Fructose and
Ribose is \( C_{6} H_{12} O_{6} \)
IV. The formula of Fructose of \( C_{6} H_{12} O_{6} \)
A . all
B. ।, ॥ land IV
c. ॥, ॥ा and ।
D. I, III and IV


State whether true or false.
Only a couple can produce pure rotation in a body.
A. True
B. False


Determine \( \Delta H \) for the following
reaction at \( 500 \mathrm{K} \) and constant pressure
\[
\boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g})
\]
use the following data:
\begin{tabular}{lll}
Substance & \( C_{P}(\mathrm{J} / \) \( \operatorname{mol} \mathrm{K}) \) & \( \Delta_{f} H(298 \mathrm{K})( \) \( \mathrm{kJ} / \mathrm{mol}) \) \\
\hline
\end{tabular}
-110.5 \begin{tabular}{l|l}
со & 29.12 \\
& \\
\( H_{2} O \) & 33.58 \\
& \\
\( \mathrm{CO}_{2} \) & 37.11 \\
\( \mathrm{H}_{2} \) & 29.89
\end{tabular} -241.8
-393.5 0.0
\( \mathbf{A} \cdot \Delta H=-30.3 \mathrm{k} \)
B. \( \Delta H=-50.3 \mathrm{kJ} \)
c. \( \Delta H=-40.3 \mathrm{kJ} \)
D. \( \Delta H=-20.3 \mathrm{kJ} \)


Which of the following method is not
used in the preparation of acetylene:
A. Dehydrohalogenation
B. Dehalogenation
c. Hydrolysis
D. Hydrogenation


A given unit vector is orthogonal to \( \mathbf{5} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{6} \hat{\boldsymbol{k}} \) and coplanar with \( \hat{\mathbf{i}}-\hat{\boldsymbol{j}}+ \)
\( \hat{k} \) and \( 2 \hat{i}+\hat{j}+\hat{k} \) then the vector is?
A \( \cdot \frac{3 \hat{j}-\hat{k}}{\sqrt{10}} \)
\( ^{\text {В } \cdot \frac{6 \hat{i}-5 \hat{k}}{\sqrt{61}}} \)
c. \( \frac{2 \hat{i}-5 \hat{k}}{\sqrt{29}} \)
\( \frac{2 \hat{i}+\hat{j}-2 \hat{k}}{3} \)


Figure shows position and velocities of two particles moving under mutual gravitational attraction in space at
time \( t=0 . \) The position of centre of
mass after one second is :
\( \mathbf{A} \cdot x=4 m \)
B . \( x=6 m \)
\( \mathbf{c} \cdot x=8 m \)
D. \( x=10 m \)


The sum of non-real roots of the
polynomial equation \( x^{3}+3 x^{2}+3 x+ \)
\( \mathbf{3}=\mathbf{0}: \)
A . Equal 0
B. Lies between 0 and 1
c. Lies between -1 and 0
D. Has absolute value bigger than 1


State, whether the following statement
is True or False:

Methane was named as firedamp as it
formed an explosive mixture with air.


Discovery of the nucleus of an atom was due to the experiment carried out by:
A. Bohr
B. Rutherford
c. moseley
D. Thomson


In a region, uniform electric field exists as \( \overrightarrow{\boldsymbol{E}}=[\mathbf{1 0 \hat { \boldsymbol { i } }}+\mathbf{1 0 \hat { \boldsymbol { j } }}] \boldsymbol{N} / \boldsymbol{C} . \) If the
potential of origin is 0 volts, the potential of point \( (10 m, 10 m, 10 m) \)


Why do only valence electrons involve in
bond formation? Why not electron of inner shells? Explain.


In general, the properties that decrease and increase down a group in the periodic table, respectively, are:
A. electronegativity and electron gain enthalpy.
B. electronegativity and atomic radius
c. atomic radius and electronegativity
D. electron gain enthalpy and electronegativity


For the same signal emitted by a radio antenna, Observer A measures its
intensity to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is
what fraction of the distance of
Observer B from the radio antenna?
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{16} \)
c. \( \frac{1}{64} \)
D. \( \frac{1}{256} \)


Two cells of same emf \( E \) but different
internal resistances \( r_{1} \) and \( r_{2} \) are
connected in series with an external
resistance \( R \). The potential drop across
the first cell is zero. Then \( \boldsymbol{R} \) is
A \( \cdot r_{1}+r_{2} \)
В. \( r_{1}-r_{2} \)
c. \( r_{2}-r_{1} \)
D. \( r_{1} r_{2} \)


A current-carrying wire in a magnetic field is subjected to a magnetic force. If the current in the wire is quadrupled. Find out the change in magnetic force acting on the wire?
A. It is quartered
B. It is halved
c. It is unchanged
D. It is doubled
E. It is quadrupled


If \( E_{1}^{o}, E_{2}^{o} \) and \( E_{3}^{o} \) are standard oxidation potentials for \( \boldsymbol{F e}\left|\boldsymbol{F} \boldsymbol{e}^{2+}, \boldsymbol{F} \boldsymbol{e}^{2+}\right| \boldsymbol{F} \boldsymbol{e}^{3+} \) and
\( \boldsymbol{F} e \mid \boldsymbol{F} e^{3+}, \) then \( \boldsymbol{E}_{3}^{o}=\frac{\boldsymbol{E}_{2}^{o}+\boldsymbol{2} \boldsymbol{E}_{1}^{o}}{\boldsymbol{n}} . \) The
value of \( n \) is:


Focal length of the plano-convex lens is
\( 15 \mathrm{cm} . \) A small object is placed at \( A \) as
shown in the figure. The plane surface is silvered. The image will form at
A. \( 60 \mathrm{cm} \) to the left of lens
B. \( 12 c m \) to the left of lens
\( \mathrm{c} .60 \mathrm{cm} \) to the right of lens
D. \( 30 c m \) to the left of lens


The ratio of maximum and minimum intensities in an interference pattern is
\( 36: 1 . \) The ratio of the amplitudes of the two interfering waves will be
A . 5: 7
B. 7:4
\( c \cdot 4: 7 \)
D. 7:5


The exact mathematical expression of Raoult's law is:
\( ^{\text {A }} \cdot \frac{P_{0}-P_{s}}{P_{0}}=\frac{n}{N} \)
в. \( \frac{P_{0}-P_{s}}{P_{0}}=\frac{N}{n} \)
c. \( \frac{P_{0}-P_{s}}{P_{s}}=\frac{n}{N} \)
D. \( \frac{P_{0}-P_{s}}{P_{0}}=n \times N \)


toppr \( E \)
\( Q \) тур
Note: the rate-flow vectors are not drawn
to scale. Identify the case(es) in which the
effective current through the conductor is the highest.
\( \mathbf{A} \)
\[
\begin{array}{l}
\odot 5 \mathrm{c} / \mathrm{s} \\
5 \mathrm{c} / \mathrm{s} \longleftrightarrow
\end{array}
\]
в.
\[
\Leftrightarrow 9 \mathrm{c} / \mathrm{s}
\]
\[
1 \mathrm{c} / \mathrm{s} \longleftrightarrow
\]
\( c \)
\[
\begin{array}{l}
\Leftrightarrow 7 \mathrm{c} / \mathrm{s} \\
3 \mathrm{c} / \mathrm{s} \longleftrightarrow(\oplus)
\end{array}
\]
D
\[
\Leftrightarrow 1 \mathrm{C} /
\]
\[
\text { 9 C/s } \longleftarrow
\]


Find \( k, \) so that \( (k-12) x^{2}+2(k- \)
12) \( x+2=0 \) has equal roots, where
\( k \neq 12 \)
\( \mathbf{A} \cdot k=4 \)
B. \( k=12 \)
c. \( k=14 \)
D. none of these


The compound that inhibits the growth
of tumors is:
A \( \cdot \operatorname{cis}-\left[P d(C l)_{2}\left(N H_{3}\right)_{2}\right. \)
B . \( \operatorname{cis}-\left[P t(C l)_{2}\left(N H_{3}\right)_{2}\right] \)
c. \( \operatorname{trans}-\left[P t(C l)_{2}\left(N H_{3}\right)_{2}\right] \)
D. \( \operatorname{trans}-\left[P d(C l)_{2}\left(N H_{3}\right)_{2}\right] \)


Draw a triangle \( A B C \) in which \( A B=4.5 \)
\( \mathrm{cm}, \mathrm{BC}=6 \mathrm{cm} \) and \( \angle B=80^{\circ} \)


In the above reaction, the major proauct
is:
\( A \)
B.
\( c \)
D.


Calculate the resistance between
points \( X \) and \( Y \) in the circuit shown in the figure.


The species which is not tetrahedral in
structure :
A \( \cdot I C l_{4}^{-} \)
B. \( B I_{4}^{-} \)
c. \( A l H_{4}^{-} \)
D. \( N F_{4}^{+} \)


If a is any real number, the number of
roots of \( \cot x-\tan x=a \) in the first
quardrant is
A . 2
B. 0
c. 1
D. 4


ff \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) is given by \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{3}- \)
\( \left.\boldsymbol{x}^{3}\right)^{1 / 3}, \) find \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{f}(\boldsymbol{x}) \)


\( R-C H_{2}-C H_{2} O H \) can be converted
to \( \boldsymbol{R}-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C O O H} . \) The correct
sequence of reagents is:
A \( \cdot P B r_{3}, K C N, H_{3} O^{+} \)
в. \( P B r_{3}, K C N, H_{2} \)
c. \( K C N, H^{+} \)
D. \( H C N, P B r_{3}, H^{+} \)


Why the blood that flows from the lungs
to the heart appears bright red rather
than dark red?
A. Oxygen makes it red.
B. Carbon dioxide makes it red.
c. Gastric juices produce the red color of blood.
D. The lungs add a pigment to the blood as it flows through them


A hemispherical bowl of internal radius \( 9 \mathrm{cm} \) is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius \( 1.5 \mathrm{cm} \) and height \( 4 \mathrm{cm} \)
How many bottles are needed to empty
the bowl?


A wire elongates by \( l \) mm when a load
\( W \) is hanged from it. If the wire goes over a pulley and two weights \( W \) each are hung at the two ends, the elongation of the wire will be (in \( m m \) ):
A . 1
в. 2
c. zero
D. \( l / 2 \)


Find the value \( k \). for which the point \( (-1, \)
3) lies on the graph of the equation \( 2 x- \) \( y+k=0 \)


Determine the number of sides of a
polygon whose exterior and interior angles are in the ratio 1: 5


Respiratory disease associated with excess histamine is
A. Bronchitis
B. Emphysema
c. Asthma
D. All of the above


The minimum angular momentum that can be possessed by an electron in a hydrogen atom is:
A \( \cdot 2 \times 10^{-34} \operatorname{kg} m^{2} s^{-1} \)
B. \( 1 \times 10^{-34} \mathrm{gm}^{2} \mathrm{s}^{-1} \)
C . \( 1 \times 10^{-34} \mathrm{kgm}^{2} \mathrm{s}^{-1} \)
D. none of these


If \( x^{3}+y^{3}=3 a x y, \) find \( \frac{d y}{d x} \)


The hormone ADH is released from the
A. Adenohypophysis
B. Neurohypophysis
c. Adrenal gland
D. None of the above


Show that the plane whose vector equation is \( \vec{r} .(\hat{i}+2 \hat{j}-\hat{k})=3 \) contains the line \( \vec{r}=\hat{i}+\hat{j}+\lambda(2 \hat{i}+\hat{j}+4 \hat{k}) \)


\( A \) is known to tell the truth in 5 cases
out of 6 and he states that a white ball
was drawn from a bag containing 8
black and 1 white ball. The probability that the white ball was drawn, is
A \( \cdot \frac{7}{13} \)
B. \( \frac{5}{13} \)
\( c \cdot \frac{9}{13} \)
D. None of these


There is a hole to the wall at the bottom
of a vessel filled with water to a height 10 \( c m . \) Water flows out completely in
5 sec. If the height of the water column above the hole is increased to \( 160 \mathrm{cm} \)
the total time taken for water flow is
A \( .2 .5 \mathrm{sec} \)
B. 5 sec
c. 10 sec
D. 20 sec


Fuse wire is a
A. tin-lead alloy
B. copper-lead alloy
C. tin-copper alloy
D. silver-lead alloy


Let \( A \) and \( B \) be two finite sets having \( m \)
and \( n \) elements respectively. Then the
total number of mapping from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is:
A . \( m n \)
B. \( 2^{\text {mn }} \)
\( \mathrm{c} \cdot m^{n} \)
D. \( n^{\text {m }} \)


A calorimeter of water equivalent 5 g has water of mass 55 g upto a certain level. Another identical calorimeter has
a liquid of mass 38 g up to same level. As both of them cool in the same
surroundings from \( 50^{\circ} \mathrm{C} \) to \( 46^{\circ} \mathrm{C}, \) water takes 80 s whereas the liquid takes 32 s
to cool. If the specific heat of water is 1
cal/g-o \( C \), the specific heat of the liquid in cal/g-o \( C \) is :
A . 0.8
B. 0.4
\( c \cdot 0.5 \)
D. 0.2


The acid which gives only primary phosphites and secondary phosphites is :
\( A \cdot H_{3} P O_{3} \)
в. \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
\( \mathrm{c} \cdot \mathrm{HPO}_{3} \)
D. \( \mathrm{H}_{3} \mathrm{PO}_{5} \)


One of the causes of water pollution is that the farmers use excessive:
A. manure and water
B. fertilizers and pesticides
c. fertilizers and seeds
D. pesticides and seeds


The specific conductance of a solution is \( 0.3568(o h m)^{-1} \mathrm{cm}^{-1} \mathrm{When} \) placed in a cell
the conductance is 0.0268 oh \( m^{-1} \)
The cell constant is:
A \( \cdot 1.331 \mathrm{cm}^{-1} \)
B. \( 13.31 c m^{-1} \)
\( \mathbf{c} \cdot 0665 \mathrm{cm}^{-1} \)
D. \( 6.65 \mathrm{cm}^{-1} \)


In the figure. \( A C=24 \mathrm{cm}, B C=10 \)
and \( O \) is the
centre of the circle. Find the area of
shaded region


The longest loop of Henle is found in
A. Kangaroo ratt
B. Opposum
c. Rhesus monkey
D. Porcupine


\( l=m=n=1 \) represents the direction
cosines of
A. \( x \) -axis
B. \( y \) -axis
c. \( z \) -axis
D. none of these


The figure given shows the
displacement-time curve of two
particles \( P \) and \( Q . \) Which of the following
statements is correct?
A. Both \( P \) and \( Q \) move with uniform equal speed
B. \( P \) is accelerated \( Q \) is retarded
C. Both P and Q move with uniform speeds but the speed of \( P \) is more than the speed of \( Q \)
D. Both P and Q move with uniform speeds but the speed of \( Q \) is more than the speed of \( P \)


Evaluate: \( \int \frac{\cos x-\sin x}{1+\sin 2 x} d x \)
A \( \cdot \frac{1}{\sin x+\cos x}+C \)
в. \( -\frac{1}{\sin x+\cos x}+C \)
c. \( \frac{2}{\sin 2 x+\cos x}+C \)
D. \( -\frac{2}{\sin 2 x+\cos x}+C \)


Which of the following isomerisms is are shown by the complex.
\( \left[\operatorname{CoCl}_{2}\left(O H_{2}\right)_{2}\left(N H_{3}\right)_{2}\right] B r ? \)
A. Ionization
B. Linkage
c. Geometrical
D. optical


Consider the isoelectronic species,
\( N a^{+}, M g^{2+}, F^{-} \) and \( O^{2-} . \) The correct
order of increasing length of their radii is:
A \( \cdot F^{-}<O^{2-}<M g^{2+}<N a^{+} \)
B. \( M g^{2+}<N a^{+}<F^{-}<O^{2} \)
C. \( O^{2-}<F^{-}<N a^{+}<M g^{2+} \)
D. \( O^{2-}<F^{-}<M g^{2+}<N a^{+} \)


Which of the following sequences of taxa and the animal kingdom is
correct?
A. Kingdom, Phylum, Class, Order, Family, Species and Genus
B. Kingdom, Phylum, Class, Order, Family, Genus and Species
C. Kingdom, Phylum, Class, Family, Order, Species and Genus
D. Phylum, Kingdom, Class, Family, Order, Genus and Species


As they release hydrolase that digest old and damaged cells, the term suicide bags is aptly used by cell biologists for
A. Golgi bodies
B. Lysosomes
c. Glyoxysomes
D. Peroxisomes


The correct order of dipole moments is :
A \( \cdot C H_{4}<N F_{3}<N H_{3}<H_{2} O \)
в. \( N F_{3}<C H_{4}<N H_{3}<H_{2} O \)
c. \( N H_{3}<N F_{3}<C H_{4}<H_{2} O \)
D. \( H_{2} O<N H_{3}<N F_{3}<C H_{4} \)


How many protons and neutrons are there in the nuclei of \( _{12}^{25} M g \)
A \( \cdot 12,13 \)
B. 13, 12
c. 25,12
D. 12, 25


The number of sigma bonds in Ziese's salt is:
A . 4
B. 6
\( c \cdot 8 \)
D. none of these


Two planets \( A \) and \( B \) have the same
average density. Their radii \( \boldsymbol{R}_{A} \) and \( \boldsymbol{R}_{B} \)
are such that \( \boldsymbol{R}_{\boldsymbol{A}}: \boldsymbol{R}_{\boldsymbol{R}}=\boldsymbol{3}: \boldsymbol{1} \) If \( \boldsymbol{g}_{A} \) and
\( g_{B} \) are the acceleration due to gravity at
the surfaces of the planets, the \( g_{A}: g_{B} \)
equals
A . 3: 1
B. 1: 3
c. 9: 1
D. 1: 9
E . \( \sqrt{3}: 1 \)


Consider a sphere of radius \( \mathrm{R} \) made of
glass of refractive index \( \mu . \) A small
object moves along the diameter with a constant velocity u. Find the velocity of the image as seen by an observer outside when the object passes through
center
\( A \)
B. \( \mu u \)
c. \( u / \mu \)
D.


Conversion of chlorobenzene to phenol
involves?
A. electrophilic substitution
B. nucleophilic substitution
c. free radical substitution
D. electrophilic addition


Net reaction taking place when amalgam is in contact with Al foil:
A \( \cdot 2 H_{2} O+O_{2} \rightarrow 2 H_{2} O \)
B. \( 4 A l+3 O_{2}+12 H^{\oplus} \rightarrow 4 A l^{3+}+6 H_{2} O \)
c. \( A l+O_{2}+\stackrel{\delta}{O} \rightarrow\left[A l(O H)_{4}\right]^{\ominus}+H_{2} O \)
D. \( 4 A l+3 O_{2} \rightarrow 2 A l_{2} O_{3} \)


\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{lll}\mathbf{5} & \mathbf{3} & \mathbf{8} \\ \mathbf{2} & \mathbf{0} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} & \mathbf{3}\end{array}\right|, \) write the minor of the
element \( a_{23} \)


Amongst the following statements, that
which was not proposed by Dalton was:
A. chemical reactions involve reorganizations of atoms. These are neither created nor destroyed in a chemical reaction.
B. when gases combine or reproduced in a chemical reaction they do so in a simple ratio by volume provided all gases are at the same \( T \) and \( P \)
C. All the atoms of a given element have identical properties including identical mass. Atoms of different elements differ in mass.
D. matter consists of indivisible atoms


Electrolyte \( \quad \wedge^{\infty}\left(S c m^{2} m o l^{-1}\right) \)
\( K C l \quad 149.9 \)
\( K N O_{3} \)
145.0
\( H C l \quad 426.2 \)
\( N a O A c \quad 91.0 \)
\( N a C l \quad 126.5 \)
Calculate \( \Lambda^{\infty}_{H O A c} \) using appropriate
molar conductances of the electrolytes
listed above at infinite dilution with \( H_{2} O \)
at \( 25^{\circ} \mathrm{C} ? \)
A. 217. 5 \( \operatorname{Scm}^{2} \) mol \( ^{-1} \)
В. 390.7 \( S c m^{2} \) mol \( ^{-1} \)
c. \( 552.7 \mathrm{Scm}^{2} \mathrm{mol}^{-1} \)
D. 517.2 \( S c m^{2} m o l^{-1} \)


Express the following in scientific notation:
(i) \( 0.0024, \) (ii) 600.0


Which statement about noble gases is
not correct:
\( \mathbf{A} \cdot \) Xe forms \( X e F_{6} \)
B. Ar is used in electric bulbs
C. \( K r \) is obtained during radioactive disintegration.
D. He has the lowest b.pt among all the noble
gases


The nuclide which disintegrates by
emitting a \( \beta \) - particle to form \( _{7}^{14} \) N contains:
A. 8 neutrons
B. 10 neutrons
c. 7 neutrons
D. 6 neutrons


\( ?+\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \rightarrow \boldsymbol{C} \boldsymbol{u} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O} \)
A \( \cdot \) CuSO \( _{4} \)
в. \( C u C l_{2} \)
c. \( C u \)
D. \( C u O \)


Which of the following properties of a solution of \( N a C l \) will not vary as the concentration of salt is increased?
A \( . p H \)
B. Density
c. Refractive index
D. Electrical conductivity


\( P \) is a point on the X-axis.lt is equidistant from the points (2,6) and \( (-4,0) . \) The co-ordinates of \( P \) are
A. \( P(-2,0) \)
в. \( P(2,0) \)
c. \( P(-6,0) \)
D. \( P(6,0) \)