The dimension of stopping potential \( V_{0} \) in photoelectric effect in units of Planck's constant 'h', speed of light 'c'
and Gravitational constant 'G' and
ampere \( A \) is:
A \( \cdot h^{-2 / 3} c^{-1 / 3} G^{4 / 3} A^{-1} \)
B \( \cdot h^{2} G^{3 / 2} c^{1 / 3} A^{-1} \)
c. \( h^{0} c^{5} G^{-1} A^{-1} \)
D. \( h^{1 / 3} G^{2 / 3} c^{1 / 3} A^{-1} \)


Which of these is more unstable?
Or


cis-Polyisoprene possesses elastic
property because:
A. it is soft and soluble in non-polar solvent
B. it is unsaturated and porous
\( \mathrm{C} \). it has a coiled structure and chains held together by weak van der Waals forces
D. it has a fibrous structure and reactive sites at various double bonds


Using properties of determinants, prove
\[
\operatorname{that}\left[\begin{array}{ccc}
\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{q}+\boldsymbol{r} & \boldsymbol{y}+\boldsymbol{z} \\
\boldsymbol{c}+\boldsymbol{a} & \boldsymbol{r}+\boldsymbol{p} & \boldsymbol{z}+\boldsymbol{x} \\
\boldsymbol{a}+\boldsymbol{b} & \boldsymbol{p}+\boldsymbol{q} & \boldsymbol{x}+\boldsymbol{y}
\end{array}\right]=
\]
\( \mathbf{2}\left[\begin{array}{lll}\boldsymbol{a} & \boldsymbol{p} & \boldsymbol{x} \\ \boldsymbol{b} & \boldsymbol{q} & \boldsymbol{y} \\ \boldsymbol{c} & \boldsymbol{r} & \boldsymbol{z}\end{array}\right] \)


When light passing through rotating nicol is observed, no change in intensity
is seen. What inference can be drawn?
A. The incident light is unpolarized.
B. The incident light is circularly polarized.
c. The incident light is unpolarized or circularly polarized.
D. The incident light is unpolarized or circularly polarizedd or combination of both


Find the area of the closed figure bounded by the following curves \( \boldsymbol{y}=\sqrt{\boldsymbol{x}}, \boldsymbol{y}=\sqrt{\mathbf{4}-\mathbf{3} \boldsymbol{x}}, \mathbf{y}=\mathbf{0} \)
A \( \cdot \frac{8}{9} \)
B. \( \frac{7}{9} \)
\( c \cdot \frac{5}{9} \)
D.


What is the use of needle line leaves
and sloped branches to Pinus?


The diagram shows some parts of the
periodic table with few elements.
Identify the set of two elements which
combine together to form a covalent
compound with a formula of the type
\( \boldsymbol{X} \boldsymbol{Y}_{3} \)
A \( \cdot 2 \) and 3
B. 4 and 6
\( c .5 \) and 7
D. 1 and 7


The volume occupied by \( 17.75 g o f C l_{2} \)
at S.T.P is:
A. 5.6 litre
B. 11.2 litre
c. 22.4 litre
D. 44.8 litre


An electron at rest gives rise to only
A. Magnetic field
B. Electric field
C. Both electric and magnetic field
D. Neither electric field nor magnetic field


Sap ascents in woody stems because of
A. Transpiration pull
B. Capillarity
c. Molecular adhesion
D. Photosynthesis


For a zoo to incur a profit,it needs to sell
at least 350 admission tickets each
day. Four student groups, each of which includes 48 students, have purchased
tickets for admission. If \( z \) represents
the number of additional ticket sold
today, and the zoo made its daily profit goal successful, which of the following inequalities could represent all
possible values for \( z ? \)
\( \mathbf{A} \cdot 4(48)+z \leq 350 \)
B \( \cdot 4(48)+z \geq 350 \)
\( \mathbf{c} \cdot 4(48)-z \leq 350 \)
\( \mathbf{D} \cdot 4(48)-z \geq 350 \)


\( \lim _{n \rightarrow \infty} \sum_{r=1}^{n} \frac{1}{\sqrt{n r}} \) is equal to
\( A \cdot 2 \)
B.
\( c \cdot 0 \)
D. none of these


Anomalous behaviour of oxygen,
compared to other VIA group elements is due to:
A. its high electronegativity
B. its small atomic size
c. non availability of d-orbitals
D. all


Find the area of the quadrilateral whose vertices are \( \boldsymbol{A}(\mathbf{1}, \mathbf{1}) \boldsymbol{B}(\mathbf{7},-\mathbf{3}), \boldsymbol{C}(\mathbf{1} \mathbf{2}, \mathbf{2}) \)
and \( D(7,21) \)


An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of \( \frac{4}{3} \) and \( \frac{2}{3}, \) then the ratio of the currents passing through the wire will be:
\( A \cdot 3 \)
B. \( 1 / 3 \)
\( c \cdot 8 / 9 \)
D.


Draw a ray diagram in each of the following cases to show the formation of image, when the object is placed:
(i) between optical centre and principal focus of a convex lens.
(ii) anywhere in front of a concave lens.
(iii) at \( 2 \mathrm{F} \) of a convex lens.
State the signs and values of magnifications in the above mentioned cases (i) and (ii).


A partition divides a container having insulated walls into two compartments and II. The same gas is filled in the two
compartments whose initial parameters are given in figure. The partition is a conducting wall which can move freely without friction. Which of
the following statements is/are correct with reference to teh final equilibrium position?
\begin{tabular}{|c|c|}
\hline\( P, V, T \) & \( 2 P, 2 V, T \) \\
\( I \) & \( I I \) \\
\hline
\end{tabular}
This question has multiple correct options
A. The pressure in the two compartments are equal
B. Volume of the compartment I is \( \frac{3 V}{5} \)
C. volume of the compartment II is \( \frac{12 V}{5} \)
D. Final pressure I in compartment I is \( \frac{5 P}{3} \)


4 grams of sodium hydroxide pellets were dissolved in \( 100 \mathrm{cm}^{3} \) of water. The
temperature before adding the sodium hydroxide pellets was 25 degrees \( C \), and after adding the pellets it was 35 degrees C. Calculate the enthalpy change in \( k J / \) mole of the reaction. [Specific heat capacity of water \( = \) \( \mathbf{4} . \mathbf{2} \boldsymbol{J} / \boldsymbol{k} / \boldsymbol{g}] \)
A. \( 42 k J / \) mole
в. \( 4.2 k J / \) mole
c. \( 4200 k J / \) mole
D. None


Which one of the following is a false
statement?
A. Cell fluid is an example of sol.
B. Butter is an example of gel
C. Hair cream is an example of emulsion
D. Whipped cream is an example of foam
E. Cheese is an example of emulsion


The Sl unit of \( \frac{1}{2 \pi \sqrt{L C}} \) is equivalent to
that of :
A. time period
B. frequency
c. wavelength
D. wave number


The rise of a liquid in a capillary tube is
due to :
A. Visosity
B. Osmosis
c. Diffusion
D. Surface tension


The activity of a radioactive element decreases to one-third of the origina
activity \( A_{0} \) in a period of 9 years. After \( a \) further lapse of 9years, its activity will be
\( A \cdot A_{0} \)
B. \( \frac{2}{3} A_{0} \)
c. \( \frac{A_{0}}{9} \)
D. \( \frac{A_{0}}{6} \)


What are state functions? Give the
examples.


A man of mass \( 60 \mathrm{kg} \) start falling from
building of height \( 80 m \) with a bag of \( 2 k g \) in his hand. After falling through a
distance \( 20 m \) he throw the bag horizontally with respect to him so that he fail in a pond \( 2 m \) away from the vertical lines of fail. Calculate horizontal
distance of bag from the vertical line of fall where it lands. (take \( \left.g=10 m / s^{2}\right) \)


If \( a \) and \( b \) are the roots of \( x^{2}-p x+q= \)
\( 0, \) then \( a^{2}+b^{2} \) is
A \( \cdot p^{2}+q^{2} \)
B . \( p^{2}+2 q \)
c. \( p^{2}-q^{2} \)
D. \( p^{2}-2 q \)


A particle moves in \( x \) -y plane according to the equation \( \vec{r}=(\hat{i}+\hat{j})(A \sin \omega t+B \)
\( \cos \omega t) . \) Motion of the particle is:
A. periodic
в. sнм
c. along a straight line
D. along an ellipse


Which one of the following generally acts as an antagonist to gibberellins?
A. Zeatin
B. Ethylene
c. АВА
\( D \cdot \) IAA


Which of the following represent circular motion
A. Ball sliding down an inclined plane
B. Motion of a simple pendulum
c. A freely falling body
D. A stone tied to a thread and whirled


The boiling points of alcohols decreases with increase in branching of alky chain.


Which of following the plant has reticulate venation?
A. Musa
B. Mangifera
c. oryza
D. canna


Assertion
The nucleus of gold is stable even though there is a very strong coulombic
repulsion among the protons.
Reason
The inverse square coulomb force is exactly balanced by another inverse square force which is very powerful than nuclear force.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the solubility product of \( M O H \) is
\( 1 \times 10^{-10} \) mol \( ^{2} d m^{-2} . \) Then the \( p H \) of
its aqueous solution will be:
A . 12
B. 9
\( c \cdot 6 \)
D. 3


As shown in the figure, \( P \) and \( Q \) are two coaxial conducting loops separated by
some distance. When the switch \( S \) is
closed, a clockwise current \( l_{p} \) flows in \( P \)
(as seen by \( E \) ) and an induced current
\( l_{Q 1} \) flows in \( Q . \) The switch remains
closed for a long time. When \( S \) is
opened, a current \( l_{Q 2} \) flows in \( Q \). Then
the direction \( l_{Q 1} \) and \( l_{Q 2}(\text { as seen by } E) \)
are
A. respectively clockwise and anti-clockwise
B. both clockwise
\( c . \) both anti-clockwise
D. respectively anti-clockwise and clockwise


Evaluate \( \left(x^{2}-8 x+12\right) \div(x-6) \)
A. \( x-2 \)
B. \( x+2 \)
c. \( x \)
D. None


The main constituents of cement are:
A. calcium oxide, silicon dioxide, aluminium oxide
B. calcium oxide, Iron oxide, sulphur dioxide
C. magnesium oxide, silicon dioxide, aluminium oxide
D. none of these


The site of meiosis is
A. VI
B. I and VI
c. ॥, ॥I, IV, and
D. II, \( v \), and \( v \) I
E. III and VI


3 mole of liquid \( A(V . P .=60 m m) \) and
a mole of \( B(V . P .=40 m m) \) results in a solution having V.P. of 50mm. The value of a is :


\( \vec{A} \cdot(\vec{A} \times \vec{B}) \)
\( A \cdot \vec{A} \cdot \vec{B} \)
\( \mathbf{B} \cdot \underset{A}{\longrightarrow} \times \underset{B}{\longrightarrow} \)
\( c \cdot 0 \)
D. 1


Which of the following makes the Venaparthy an area free from water
crisis?
A. Percolation tank
B. Green mufflers
c. Afforestation
D. None of the above


\( Z n\left|Z n^{2+}(a q)\right|\left|C u^{2+}(a q)\right| C u . E^{o} \) for \( C u \)
and \( Z n \) are 0.35 and -0.76
respectively:
Find EMF of cell (nearest integer) if
\( Z n^{2+} \) and \( C u^{2+} \) are 1 M each.


5 Indian \( \& 5 \) American couples meet at a party \& shake hands. If no wife
shakes hands with her own husband \&
no Indian wife shakes hands with male,
then the number of hand shakes that
takes place in the party is :
A . 95
в. 110
\( c .135 \)
D. 150


Which of the following is likely to have the largest resistance?
A. Voltmeter of range 10 v
B. Moving coil galvanometer
c. Ammeter of range 1 A
D. A copper wire of length \( 1 \mathrm{m} \) and diamete


Corpuscular theory of light was advanced by
A. Huygen
B. Newton
c. мaxwell
D. Hertz


The average velocity of the molecules in a gas in equilibrium is
A. proportional to \( \sqrt{T} \)
B. proportional to T
C. proportional to \( T^{2} \)
D. equal to zero


Thermodynamic parameter which is a state function and is also used to
measure disorder of the system is:
A. Entropy
B. Fugacity
c. viscosity
D. Periodicity


A body of mass 100 g is sliding from an inclined plane of inclination \( 30^{0} \). What is the frictional force experienced if
\( \mu=0.7 ? \)
A. \( 0.35 \times \sqrt{3} \)
B.
\( c \cdot \frac{\sqrt{3}}{2} \)
D. 0.35


During electrolytic reduction of
alumina,
\( \mathbf{A} \cdot A \mid \) is formed at cathode and oxygen is formed at anode
B. Al is formed at anode and oxygen is formed at cathode
C. \( A I \) is formed at cathode and hydrogen is formed at anode
D. Al is formed at anode and hydrogen is formed at cathode


A body moving in circular motion with constant speed has:
A. constant velocity
B. constant acceleration
c. constant kinetic energy
D. constant displacement


ff \( f(x) \) a polynomial of degree 2 in \( x \) such that \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{f}(\mathbf{1})=\mathbf{3} \boldsymbol{f}(\mathbf{2})=-\mathbf{3} \)
then \( \int \frac{\boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{x}^{3}-\mathbf{1}} \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \log \left|x^{2}+x+1\right|+\log |x+1|+c \)
B \( \cdot \log |x-1|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c \)
\( ^{\mathbf{c}} \cdot \log \left|x^{2}+x+1\right|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c \)
D \( \cdot \log \left|x^{2}+x+1\right|-\log |x-1|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c \)


Fog is a collodial solution of:
A. liquid in gas
B. gas in liquid
C . solid in gas
D. gas in gas


According to Mendeleev's periodic law, the properties of elements are a periodic function of:
A. atomic number
B. atomic weight
c. number of electrons
D. density


Which of the following cannot be in equilibrium?
A. \( 10 N, 10 N, 5 N \)
\( N \)
B. \( 5 N, 7 N, 9 N \)
c. \( 8 N, 4 N, 13 N \)
D. \( 9 N, 6 N, 5 N \)


A piece of magnesium ribbon was heated to redness in an atmosphere of nitrogen and on cooling water was added the gas evolved was:
A. ammonia
B. hydrogen
c. nitrogen
D. oxygen


The area bounded by \( y=f(x), x-a x i s \)
and the line \( y=1, \) where \( f(x)=1+ \) \( \frac{1}{x} \int_{1}^{x} f(t) d t \) is
A \( \cdot 2(e+1) \)
B \( \cdot\left(1-\frac{1}{e}\right) \)
c. \( 2(e-1) \)
D. None of these


A buffer solution is made up of acetic
acid \( \left[\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{5}\right] \) having conc. \( =\mathbf{1 . 5} \boldsymbol{M} \)
and sodium acetate having conc. \( = \)
\( 0.15 M . \) What is the number of \( O H^{-} \)
ions present in 1 litre solution?
В. \( 10^{-4} M \)
\( \mathrm{c} \cdot 10^{-3} M \)
D. \( 10^{-6} M \)


The frequency, wavelength and speed of
a sound wave are related as :
\( \boldsymbol{v}=\operatorname{velocity} \) of \( \boldsymbol{w} \boldsymbol{a v e}, \boldsymbol{u}= \)
frequency, \( \lambda= \)wavelength
This question has multiple correct options
A \( . \lambda=v T \)
В. \( \lambda=v / u \)
c. \( u=v / \lambda \)
D. \( \lambda=u v \)
\( v \)


\( \int \sqrt{e^{2 x}-1} d x \) is equal to


Assertion
Li electrode always acts as anode in
voltaic cell.
Reason
Li electrode has lowest SRP among all
the electrodes.
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.


In the relation \( \boldsymbol{F}=\boldsymbol{a} \sin \boldsymbol{k}_{1} \boldsymbol{x}+ \)
\( \boldsymbol{b} \sin \boldsymbol{k}_{2} \boldsymbol{t}, \) the units \( (\mathrm{Sl}) \) of \( \frac{\boldsymbol{k}_{1}}{\boldsymbol{k}_{2}} \) is
\( (F, x \& t \) have usual meanings)
\( \mathbf{A} \cdot s / m \)
B. sm
\( c \cdot s t \)
D. s/t


What is the order of basicity of the
following compounds?
\( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2},\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{N} \boldsymbol{H},\left(\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{N} \) (in
protic solvent)
A \( \cdot\left(C H_{3}\right)_{2} N H>C H_{3} N H_{2}>\left(C H_{3}\right)_{3} N \)
B . \( \left(C H_{3}\right)_{2} N H<C H_{3} N H_{2}<\left(C H_{3}\right)_{3} N \)
C. \( \left(C H_{3}\right)_{2} N H>\left(C H_{3}\right)_{3}>C H_{3} N H_{2} N \)
D. None of these


Write the following decimals in the place value table.
\( \mathbf{2 . 0 8} \)


The non-proteinaceous substance, which certain enzymes require for their activity are called
A. catalysts
B. inhibitors
c. co-enzymes
D. epimers


The last element in Newlands' periodic table was:
A . zinc
B. barium
c. cesium
D. thorium


From the Ellingham graph between
Gibb's energy and temperature, out of \( C \)
and \( C O \) which is a better reducing
agent for \( Z n O ? \)
A. Carbon
в. \( C O \)
c. Both of these
D. None of these


What is the temperature of water in
kelvin if the water is at \( 44^{\circ} \mathrm{C} \) ?
A . 330
в. 317
\( c \cdot 229 \)
D. 230


Find \( x \)
i)x-4=3
ii) \( 9 x=81 \)
iii)x+6=10
A \( . x=7,9,4 \)
\( c \cdot x=-1,4,5 \)
D. \( x=-3,6,7 \)


ntegrate the function \( \frac{\mathbf{5} \boldsymbol{x}+\mathbf{3}}{\sqrt{\boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+\mathbf{1 0}}} \)


toppr
Q Type your question_
have variable acceleration. The
acceleration can vary in magnitude, or
in direction or both. In such cases we
find acceleration at any instant, called
the instantaneous acceleration. It is
\( \operatorname{defined} \operatorname{as} \vec{a}=\lim _{\Delta t=0} \frac{\Delta \vec{v}}{\Delta t}=\frac{d \vec{v}}{d t} \)
That is acceleration of a particle at time
\( t \) is the limiting value of \( \frac{\Delta v}{\Delta t} \) at time \( t \) as \( \Delta t \) approaches zero. The direction of the
instantaneous acceleration \( \vec{a} \) is the
limiting direction of the vector in
velocity \( \Delta v \)

A particle travels according to the equation such that it's acceleration \( a=-k v \) where \( k \) is constant of
proportionality. Find the distance
covered when it's velocity falls from \( \boldsymbol{v}_{\mathbf{0}} \)
to \( \boldsymbol{v} \)
\( ^{\mathbf{A}} \cdot_{x}=\frac{-1}{k}\left[\frac{1}{v_{0}}-\frac{1}{v}\right] \)
в. \( _{x}=\frac{v_{0}-v}{k} \)
c. \( _{x}=k \log _{e} \frac{v_{0}}{v} \)
D. \( x=\frac{1}{k} \log _{e} \frac{v_{0}}{v} \)


Draw a circuit diagram of a full wave rectifier. Explain its working and draw input and output waveforms.


While comparing the L-C oscillations with the oscillations of spring block system, with whom the magnetic energy can be compared and why?


Two particles of masses \( 1.0 \mathrm{kg} \) and \( 2.0 \mathrm{kg} \) are placed at a separation of
\( 50 \mathrm{cm} . \) Assuming that the only forces acting on the particles are their mutual gravitation, find the initial accelerations of the two particles.


In the dichromate dianion:
A. four \( C r-O \) bonds are equivalent
B. six \( C r-O \) bonds are equivalent.
C. all \( C r-O \) bonds are equivalent.
D. all \( C r-O \) bonds are non-equivalent.


The greatest value of the function \( \mathbf{f}(\mathbf{x})=\sin \left\{\boldsymbol{x}[\boldsymbol{x}]+\mathbf{e}^{[x]}+\frac{\boldsymbol{\pi}}{2}-1\right\} \) for all
\( \boldsymbol{x} \in[\mathbf{O}, \infty) \) is
\( A \cdot-1 \)
B.
\( c \)
D.


Chromium - plated steel is a material of
popular use. During its process of manufacture, the effluent contains
chromate and cyanide ions as impurities. After these are chemically removed, carbon dioxide and salt (sodium chloride) still remain as
impurities. This salt solution is purified electrolytically by adding carbonaceous matter which acts as:
A. a microcell
B. an electrode
c. a cathode
D. a salt absorber


The null point should be obtained on the meter bridge wire to get maximum
accuracy at
A. the middle of the wire.
B. the left end of the wire
c. the right end of the wire
D. the 1/4th distance from the left end


A horizontal pipe line carries water in a streamline flow. At a point along the tube where the cross-sectional area is
\( 10^{-2} m^{2}, \) the water velocity is \( 2 m s^{-1} \)
and the pressure is 8000 Pa. The
pressure of water at another point where the cross-sectional area is \( 0.5 \times \)
\( 10^{-2} m^{2} \) is?


By selling 20 articles, a person gains \( \mathrm{CP} \) of 5 articles. Find the profit\% incurred by him.


Reduce the equation \( 9 x+7 y-3=0 \)
to intercept form.Hence find the length of the segment intercepted between the
axes.


The friction coefficient between an
athlete's shoes and the ground is 0.90
Suppose a superman wears these shoes and races for \( 50 \mathrm{m} \). There is no upper
limit on his capacity of running at high speeds. Suppose he takes exactly this
minimum time to complete the \( 50 \mathrm{m} \)
what minimum time will he take to
stop?


One oscillation completed by a vibrating body in one second is known
as:
A . 1 tesla
B. 1 Hertz
c. 1 horse power
D. none


An ecosystem is a complex interacting
system of
A . Individuals
B. Population
c. communities and their physical environment
D. Communities and their soil condition


"Brain sand"' is found in
A. Thyroid
B. Thymus
c. Pineal body
D. All of the above


The minimum magnetic dipole moment of electron in hydrogen atom is
A \( \cdot \frac{e h}{2 \pi m} \)
в. \( \frac{e h}{4 \pi m} \)
c. \( \frac{e h}{\pi m} \)
\( D \)


Which chemical substance is a
greenhouse gas that scientists link to
global climate change? This question has multiple correct options
A. Nitrogen oxides
B. Leadd
c. Carbon dioxide
D. DDT
E. Nitrates


Two mirrors M1 and M2 are placed at right angle to each others as shown. The total number of images of an object 'O'
that can be seen are
A. Two
B. Three
\( c . \) Four
D. Infinite


Most swollen segment in leg cockroach is
A. Tarus
B. Coxa
c. Trochanter
D. None of these


Gadolinium belongs to \( 4 f \) series. It's
atomic number is \( 64 . \) Which of the
following is the correct electronic configuration of gadolinium?
\( \mathbf{A} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)
B. \( [X e] 4 f^{6} 5 d^{2} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{8} 6 d^{2} \)
D \( \cdot[X e] 4 f^{9} 5 s^{1} \)


What is the IUPAC name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\left(\boldsymbol{O} \boldsymbol{H}_{2}\right) \boldsymbol{I}\right] \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. Tetraammineaquaiodocobalt(III) sulphate
B. Tetraammineaquaiodocobalt(II) sulphate
C. Tetraammineaquaiodocobaltate(III) sulphate
D. None of these


Which of the following is used as antiemetic?
A. Antihistamine
B. Antibiotic
c. calcitonine
D. None of the above


Glucose cannot be classified as:
A. hexose
B. carbohydrate
c. oligosaccharide
D. aldose


Give a reason for the following. lonisation potential increases across a period, from left to right.


Oxygen in atmosphere has been formed
by
A. Evaporation of water
B. Photosynthesis of blue green algae
c. Metabolism of microorganisms
D. Decaying organisms


The figure shows two immiscible liquids (Kerosens and water). Kerosene
has density \( \rho_{2} \) and water has density \( \rho_{1} \)
Find the velocity of water flow.


When 45 gm of a solute is added to 900 \( \mathrm{gm} \) of water, its vapour pressure decreased from \( 30 \mathrm{mm} \) to \( 24 \mathrm{mm} \). The
mole fraction of the solvent in the
solution is :
A . 0.2
B. 0.8
\( c .0 . \)
D. 0.9


The value of the determinant
\( \left|\begin{array}{ccc}b^{2}-a b & b-c & b c-a c \\ a b-a^{2} & a-b & b^{2}-a b \\ b c-a c & c-a & a b-a^{2}\end{array}\right| \)
A \( . a b c \)
B. \( a+b+c \)
\( c \)
\( \mathbf{D} \cdot a b+b c+c a \)


triangles become always similar.
A. Acute-angled
B. Equilateral
c. obtuse-angled
D. None of the above


Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{D}-\boldsymbol{A} \)


The ionic product of a saturated solution is \( _{-}-_{-}-_{-} \) the solubility product constant of its solute.
A. lesser than
B. greater than
c. equal to
D. not related to


The muzzle velocity of a certain rifle is
\( 330 m s^{-1} . \) At the end of one second, a
bullet fired straight up into the air will travel a distance of
A \( \cdot(330-4.9) m \)
B. \( 330 m \)
c. \( (330+4.9) m \)
D. \( (330-9.8) m \)


A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be
affected?
A. Moment of inertia
B. Angular momentum
c. Angular velocity
D. Rotational kinetic energy


If equal quantities of electricity are
passed through three voltmeter
containing \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{F} \boldsymbol{e}_{2}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)_{3} \) and
\( F e\left(N O_{3}\right)_{2}, \) then which of the following
is not true?
A. Amount of iron deposited in \( F e S O_{4} \) and \( F e_{2}\left(S O_{4}\right)_{3} \) is equal
B. Amount of iron deposited in \( F e\left(N O_{3}\right)_{3} \) is \( \frac{2}{3} \) of the
amount of iron deposited in \( F e S O_{4} \)
C. Amount of iron deposited in \( F e_{2}\left(S O_{4}\right)_{3} \) and \( F e\left(N O_{3}\right)_{3} \) are equal
D. Same gas will evolve in all three cases at anode


Secondary growth is not found in
A. Dracaena
B. Cucurbita
c. Bambusa
D. Both B and C


The forbidden energy band gap in
conductors


Study the following flow chart and
select the correct option for \( P, Q, R \) and
\( \mathbf{S} \)
\( A \cdot P \) - Banana, Canna
\( \mathrm{Q} \) - Fan palm
\( \mathrm{R} \) - Mango, Peepal
\( \mathrm{S}- \) Smilax, Zizyphus
B. P- Banana, Canna Q- Smilax, Zizyphus
\( \mathrm{R} \) - Mango, Peepal
\( S \) - Fan palm
C. P - Mango, Peepal
\( \mathrm{Q}- \) Banana, Canna
\( \mathrm{R} \) - Fan palm
S - Smilax, Zizyphus
D. P - Mango, Peepal
\( \mathrm{Q}- \) Fan palm
R - Smilax, Zizyphus
S-Banana, Canna


Evaluate the integral \( \int_{0}^{\pi / 2} \frac{\cos x}{1+\sin ^{2} x} d x \)
\( A \)
в. \( \pi / 3 \)
c. \( \pi / 2 \)
D. \( \pi / 4 \)


Two vessels \( A \) and \( B \) of different shapes
have the same base area and are filled
with water up to the same height h (see figure). The force exerted by water on
the base is \( F_{A} \) for vessel \( A \) and \( F_{B} \) for
vessel B. The respective weights of the
water filled in vessels are \( W_{A} \) and \( W_{B} \)
Then
\( \mathbf{A} \cdot F_{A}>F_{B} ; W_{A}>W_{B} \)
B . \( F_{A}=F_{B} ; W_{A}>W_{B} \)
C \( \cdot F_{A}=F_{B} ; W_{A}<W_{B} \)
D. \( F_{A}>F_{B} ; W_{A}=W_{B} \)


Two small loud speakers \( A \) and \( B \) are
driven by the same amplifier as shown in Fig and emit pure sinusoidal waves in phase. Speaker \( A \) is \( 1 \mathrm{m} \) away as
shown and speaker \( B \) is 2 m away from
the amplifier. The microphone is \( 4 \mathrm{m} \)
away from the amplifier in transverse direction as indicated in the Figure. For
what frequencies constructive interference will occur at \( \boldsymbol{P} \)
(microphone point)
B. 500 Нz, 1500 нz
c. 550 Нz, 1100 Н \( z_{\text {... }} \)
D. 500 нz, 1000 Нz,1500 нz


Check if the series is an A.P. Find the
common difference \( d \) and write three
more terms of the the following series. \( 2, \frac{5}{2}, 3, \frac{7}{2}, \dots \)
A \( \cdot a=2 ; d=\frac{1}{2} ; \) other terms \( 4, \frac{9}{2}, 5 \)
B. \( a=3 ; d=\frac{1}{2} ; \) other terms 6,8,10
c. \( _{a}=2 ; d=\frac{3}{2} ; \) other terms 7,8,15
D. \( a=3 ; d=\frac{3}{2} ; \) other terms 4,5,15


A right circular cone has a semi-vertical angle \( \alpha . \) Calculate the solid angle at the
apex P of the cone.
A \( \cdot d \Omega=2 \pi(1-\cos \alpha) \)
в. \( d \Omega=2 \pi(1-\sin \alpha) \)
c. \( d \Omega=2 \pi(\cos \alpha) \)
D. \( d \Omega=2 \pi(\sin \alpha) \)


Which of the following statement is
incorrect:
A. On addition of catalyst the equilibrium constant value is not affected.
B. Equilibrium constant value for negative \( \Delta H \) value decreases as the temperature increases
C. In equilibrium mixture of ice and water, kept in insulated flask mass of ice and water does not change with time
D. The intensity of red colour increases when oxalic acid is added to the solution containing iron nitrate(III) and potassium thiocynate


Which of the following is possible
A \( \cdot \sin \theta=\frac{5}{3} \)
B. \( \tan \theta=1002 \)
\( ^{\mathrm{c}} \cdot \cos \theta=\frac{1+p^{2}}{1-p^{2}},(p \neq\pm 1) \)
D. \( \sec \theta=\frac{1}{2} \)


The librarian at the public library
counted the number of books on each
shelf. The lowest number of
books contained by any of the self is
Books per shel
\( A \)
B.
\( c . \)
\( D \)


State whether true or false.
Metals as compared to non-metals are generally bad conductors of electricity.
A. True
B. False


Write the name of the point where the
two axes meet.


Two condensers each of capacitance \( 2 \mu F \) are connected in parallel and this
combination is connected in series with
a \( 12 \mu F \) capacitor. The resultant
capacity of the system will be:
A. \( 16 \mu f \)
в. \( 13 \mu f \)
c. \( 6 \mu f \)
D. \( 3 \mu f \)


Which of the following is the strongest
base?
\( \mathbf{A} \cdot S c(O H)_{3} \)
\( \mathbf{B} \cdot L a(O H)_{3} \)
c. \( L u(O H)_{3} \)
D. \( Y b(O H)_{3} \)


Write the two examples of acceptor
impurities


The circuit shown below is working as a
\( 8 V \) de regulated voltage source. When
\( 12 V \) is used as input, the power
dissipated (in \( \boldsymbol{m} \boldsymbol{W} \) ) in each diode is;
(considering both zener dioses are
identical)


A cell, an ammeter and a voltmeter are
all connected in series. The ammeter
reads a current I and the voltmeter a
potential difference V. If a torch bulb is connected across the voltmeter, then.
A. Both I and v will increase
B. Both I and V will decrease
c. I will increase but \( V \) will decrease
D. I will decrease but V will increase


Which is the greatest side in the following triangle? \( \angle \boldsymbol{A}: \angle \boldsymbol{B}: \angle \boldsymbol{C}=\mathbf{4}: \mathbf{5}: \mathbf{6} \)
\( \mathbf{A} \cdot A B \)
в. \( B C \)
\( c . A C \)
D. cannot be determined


\( \frac{x^{2}}{r^{2}-r-6}+\frac{y^{2}}{r^{2}-6 r+5}=1 \) will
represents the ellipse, if r lies in the interval:
This question has multiple correct options
B. \( (3, \infty) \)
\( c \cdot(5, \infty) \)
D. \( (1, \infty) \)


Using identity find the value of \( (4.7)^{2} \)


If \( P(n) \) is the statement \( " n(n+1) \) is
even", then what is \( \boldsymbol{P}(\boldsymbol{3}) \) ?


If \( f(x)=a-(x-3)^{89}, \) then greatest
value of \( \boldsymbol{f}(\boldsymbol{x}) \) is
\( \mathbf{A} \cdot \mathbf{3} \)
B. \( a \)
c. no maximum value
D. none of these


If the cost of \( x \) metres of wire is \( d \)
rupees, then what is the cost of \( y \)
metres of wire at the same rate?
A \( \cdot \) Rs. \( x \frac{d}{y} \)
B. Rs. \( x d \)
c. Rs. \( y \frac{d}{x} \)
D. Rs. \( y d \)


Two coherent light sources \( S_{1} \) and \( \boldsymbol{S}_{2}(\boldsymbol{\lambda}=\mathbf{6 0 0 0} \boldsymbol{A}) \) are 1 mm apart from
each other. The screen is placed at a distance of \( 25 \mathrm{cm} \) from the sources. The width of the fringes on the screen
should be
A. \( 0.015 \mathrm{cm} \)
В. \( 0.013 \mathrm{cm} \)
c. \( 0.01 \mathrm{cm} \)
D. \( 0.10 \mathrm{cm} \)


Evaluate the determinant: \( \left|\begin{array}{ccc}\mathbf{8} & \mathbf{2} & \mathbf{7} \\ \mathbf{1 2} & \mathbf{3} & \mathbf{5} \\ \mathbf{1 6} & \mathbf{4} & \mathbf{3}\end{array}\right| \)


The addition compound obtained by treating propanone with hydrogen cyanide is:
A. propene cyanohydrin
B. ethene cyanohydrin
c. propane cyanohydrin
D. ethane cyanohydrin


Find the value of \( R \) so that no deflection
is noticed in the galvanometer when the
switch \( S \) is closed or open
A . \( 4 \Omega \)
B. \( 8 \Omega \)
\( c \cdot 6 \Omega \)
D. None of these


The reactivity of 2 -bromo- 2 methylbutane \( (I), 1 \) -bromopentane \( (I I) \)
and \( 2- \) bromopentane \( (I I I) \) towards
\( \boldsymbol{S}_{N} 2 \) displacement is such that:
A \( I>I I>I I I \)
\( I \)
В. \( I>I I I>I I \)
c. \( I I>I I I>I \)
D. \( I I>I>I I I \)


Figure represents the displacement-
time graph of motion of two cars \( A \) and
B. Find the distance by which the car B was initially ahead of Car A
A. \( -40 k m \)
B. \( 40 k m \)
\( c .0 k m \)
D. \( 100 k m \)


Find the largest value of a third-order
determinant whose element are 0 or 1


\( P C l_{5} \) exists but \( N C l_{5} \) does not
because:
A. nitrogen has no vacant 2d-orbitals
B. \( N C l_{5} \) is unstable
c. nitrogen atom is much smaller than P
D. nitrogen is highly inertttrt


In an arithmetic series, \( a_{1}=7 \) and
\( a_{12}=29 . \) Find the sum of the first 12
terms.
A . 116
в. 216
\( c \cdot 316 \)
D. 416


Which is true according to the Faraday
Law of electrolysis? Here \( m \) is the mass
deposited at an electrode, \( Q \) is the
charge at the electrode and \( I \) is the
current passed.
\( A \cdot m \propto I^{2} \)
в. \( m \propto Q \)
\( \mathrm{c} \cdot m \propto Q^{2} \)
D. \( m \) does not depend on \( Q \)


The perimeter of a rectangle is \( 130 \mathrm{cm} \) If the breadth of the rectangle is \( 30 \mathrm{cm} \)
find its length. Also find the area if the
rectangle.


Rays parallel to the principle axis are refracted by the lens through the point:
A .
B. 2F
\( c \cdot F \)
D. None


A closed set with respect to some binary operation is called semi- group if
\( A \cdot * \) is associative
B. \( * \) is commutative
c. \( * \) is anti-commutative
D. identity element exists


Corrosion of metals can be prevented
when contact between metal and
is cut off.
A. nitrogen
B. hydrogen
c. oxygen
D. carbon


In a certain double slit experimental arrangement interference fringes of width 1.0 mm each are observed when
light of wavelength \( 5000 \dot{A} \) is used. Keeping the set up unaltered, if the source is replaced by another source of wavelength \( 6000 A \), the fringe width will
be
A. \( 0.5 \mathrm{mm} \)
в. \( 1.0 \mathrm{mm} \)
\( \mathrm{c} .1 .2 \mathrm{mm} \)
D. \( 1.5 \mathrm{mm} \)


If \( f(x)=x^{3}+3 x^{2}+12 x-2 \sin x \)
where \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}, \) then prove that \( \boldsymbol{f} \) is
bijective


Which combination is best explained by co-ordinate covalent bond?
\( \mathbf{A} \cdot H^{+}+H_{2} O \)
в. \( H_{2}+O_{2} \)
\( \mathbf{c} \cdot C l_{2}+H_{2} \)
D. \( C l+C l \)


What are electric lines of force? State
the properties of lines of force.


The following arrangement consists of five identical metal plates. Area of each plate is \( A \) and separation between the successive plates is d. The capacitance between \( P \) and
A. \( \frac{5 \varepsilon_{0} A}{d} \)
В. \( \frac{7}{3} \varepsilon_{0} \frac{A}{d} \)
c. \( \frac{4}{3} \frac{\varepsilon_{0} A}{d} \)
D. \( \frac{5}{3} \frac{\varepsilon_{0} A}{d} \)


Identify the reaction during electrolytic reduction of alumina at cathode.
A \( \cdot 2 H_{2} O_{2} \rightarrow O_{2}+4 H^{+}+4 e^{-} \)
B. \( 3 F^{-} \rightarrow 3 F+3 e^{-} \)
c. \( A l^{+3}+3 e^{-} \rightarrow A l \)
D. \( 2 H^{+}+2 e^{-} \rightarrow H_{2} \)


Naphthalene balls are obtained from
coal tar and are used as:
A. mosquito repellant
B. honey bee repellant
c. moth repellant
D. snake repellant


Select correct alternates(s).
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{In} N a H C O_{3}, \) the \( H C O_{3}^{-} \) ions are linked into infinite
chain
B. \( \ln K H C O_{3} \), a dimer is formed by H-bonding
C \( \cdot \ln N a H C O_{3}, \) a dimer is formed by H-bonding
D. \( \ln K H C O_{3} \), the \( H C O_{3}^{-} \) ions are linked into infinite chain


The pressure at the bottom of a tank of
water is \( 3 P \) where \( P \) is the atmospheric pressure. If the water is drawn out till
the level of water is lowered by one fifth, the pressure at the bottom of the tank will now be:
A \( .2 P \)
B. \( (13 / 5) P \)
c. \( (8 / 5) P \)
D. \( (4 / 5) P \)


If \( A \) and \( B \) are matrices given below:
\[
\begin{array}{l}
A=\left[\begin{array}{ccc}
0 & c & -b \\
-c & o & a \\
b & -a & 0
\end{array}\right] \text { and } B= \\
{\left[\begin{array}{ccc}
a^{2} & a b & a c \\
a b & b^{2} & b c \\
a c & b c & c^{2}
\end{array}\right]}
\end{array}
\]
then \( A B \) is a unit matrix. Is this
statement true?


Draw the graph of the equation \( y=3 x \)


\( A_{3 * 3} \) is a non - singular matrix \( \Rightarrow \)
\( \boldsymbol{A}^{2}(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A})= \)
\( \mathbf{A} \cdot|A| A \)
B. \( I \)
c. \( |A| \)
D・ \( |A|^{2} I \)


The value of \( \sec ^{-1}\left(\sec \frac{8 \pi}{5}\right) \) is
A \( \cdot \frac{2 \pi}{5} \)
в. \( \frac{3 \pi}{5} \)
\( c \cdot \frac{8 \pi}{5} \)
D. none of these


If \( \frac{x^{2}+n}{x^{2}+4}=1, \) then \( n= \)
A. 4
B. 3
c.
D.
E . -3


Boolean relation at the output stage- \( \boldsymbol{Y} \)
for the following circuit is:
A \( . \bar{A}+\bar{B} \)
в. \( A \cdot B \)
\( c \cdot \bar{A} \cdot \bar{B} \)
D. \( A+B \)


\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})\left|\boldsymbol{Z} \boldsymbol{n} \boldsymbol{C l}_{2}(\boldsymbol{a} \boldsymbol{q}) \| \boldsymbol{C l}^{-}(\boldsymbol{a q})\right| \boldsymbol{C l}_{2}(\boldsymbol{g}) \mid \boldsymbol{C} \)
In the electrochemical cell described by
the cell diagram above, what reaction occurs at the anode?
A. \( Z n \rightarrow Z n^{2+}+2 e^{-} \)
B. \( Z n^{2+}+2 e^{-} \rightarrow Z n \)
c. \( C l_{2}+2 e^{-} \rightarrow 2 C l \)
D. \( 2 C l^{-} \rightarrow C l_{2}+2 e^{-} \)


Bi-collateral vascular bundles are
typically seen in
A. cucurbitaceae
c. Monocot stem
D. Acorus


Separation of homologous chromosomes is called
A. Dispersion
B. Bivalent formation
c. Disjunction
D. crossing over


Evaluate \( \lim _{x \rightarrow 0} \frac{\sin x}{x} \)


On rotating a wheel of radius \( 4 m, a \)
force of \( 20 N \) is applied at an angle \( 30^{\circ} \) to the radius, at a point of application. The resulting torque on the wheel is:
\( \mathbf{A} \cdot 80 N-m \)
B. \( 60 N-m \)
c. \( 40 N-m \)
D. \( 20 N-m \)


The ozone layer forms naturally by:
A. the interaction of CFC with oxygen
B. the interaction of UV radiation with oxygen
C. the interaction of IR radiation with oxygen
D. the interaction of oxygen and water vapour


If \( f(t)=\frac{1+t}{1-t}, \) then \( f(-t) \) is
A \( \cdot \frac{1}{f(t)} \)
в. \( \frac{1}{f(-t)} \)
c. \( f_{t} \frac{1}{t} \)
D. \( f\left(-\frac{1}{t}\right) \)
E. \( 1+f(t) \)


Why teflon is used to make nonstick
cooking pans and other cookwares?


Which of the following does earth's magnetic field deflect coming from outersphere?
A. Gas atoms
B. Radioactive isotopes
c. charged particles
D. Ozone molecules


Characteristic free swimming larva of coelenterates is
A. Oncosphere
B. Rhabditiform
c. Planula
D. cysticercus


The \( p H \) of the solution cantaining
\( \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \& \mathbf{0 . 1} \boldsymbol{M} \boldsymbol{H} \boldsymbol{C O O H} \mathbf{~ i s : ~} \)
\( \left[\boldsymbol{K}_{s} \text { of } \boldsymbol{H} \boldsymbol{C O O H} \text { is } \mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{1 4}}\right] \)
A . \( 0 . \)
B.
\( c \cdot 2 \)
D. 0.2


What are Fraunhofer lines??


Let \( A \) and \( B \) be events in a sample space \( S \) such that \( P(A)=0.5, P(B)= \) 0.4 and \( P(A \cup B)=0.6 . \) Observe the
following lists:
List I List I
\( P(A \cap B) \) a 0.4
\( P(A \cap \bar{B}) \) \( b \) 0.2
iii \( P(\bar{A} \cap B) \) 0.3
\( P(\bar{A} \cap \bar{B}) \)
The correct match of List I from List II is
A . i- a, ii-b, iii-c, iv- d
B. i-c, ii-b, iii- d, iv- a
c. i-c, ii-b, iii- a, iv- d
D. i-c, ii- a, iii-b, iv-


Which of the following is not produced by E.Coli in the lactose operon?
A. \( \beta \) galactosidase
B. Galactoside transacetylase
c. Lactose dehydrogenase
D. Galactoside permease


Write two differences between emf and
potential difference (pd).


(a) Distinguish between primary, secondary and tertiary amines.
(b) Explain the structure of fructose.


In the given figure, ABCD is a
parallelogram, \( \angle \boldsymbol{A} \boldsymbol{D} \boldsymbol{E}= \)
\( \mathbf{5 0}^{\circ} \) and \( \angle \mathbf{A C E}=\angle B E D=90^{\circ} \) The
value of \( \angle \boldsymbol{E} \boldsymbol{A} \boldsymbol{C}+\angle \boldsymbol{A} \boldsymbol{B} \boldsymbol{C}-\mathbf{2} \angle \boldsymbol{D} \boldsymbol{A} \boldsymbol{C} \)
A . \( 10^{\circ} \)
В. \( 15^{\circ} \)
\( c \cdot 18^{0} \)
D. \( 23.5^{\circ} \)


These questions consist of two statement, each printed as assertion and reason. While answering these question you are required to choose any one of the following five responses.
Assertion : If a body is thrown upwards. the distance covered by it in the last second of upward motion is about \( 5 \mathrm{m} \) irrespective of its initial speed.
Reason: The distance coveted in the
last second of upward motion is equal
to that covered in the first second of
downward motion when the particle is dropped.
A. If both assertion and reason are true but the reason is the correct explanation of assertion
B. If both assertion and reason are true but the reason is not the correct explanation of assertion
c. If assertion is true but reason is false.
D. If both the assertion and reason are false
E. If reason is true but assertion is false


Which of the following is the purest form of carbon?
A. charcoal
B. coal
c. diamond
D. graphite


A particle projected from the origin \( (x=y=0) \) moves in \( x y \) plane so that
its velocity is \( v=(2 \hat{i}+4 x \hat{j}) \mathrm{m} / \mathrm{s}, \) when it is at point \( (x, y) \) m. \( (\hat{i} \text { and } \hat{j} \) are the unit vectors along \( x \) and \( y \) axis). What
is the value of \( y, \) when \( x=3 \)
A . 15
B. 10
\( c .9 \)
D. 8


For a random variable \( \boldsymbol{X} . \) If \( \boldsymbol{E}(\boldsymbol{X})=\mathbf{5} \)
and \( V(X)=6, \) then \( E\left(X^{2}\right) \) is equal to
A . 19
B. 31
c. 61
D. 11


A stationary body explodes into two
fragments of masses \( m_{1} \) and \( m_{2} . \) If
momentum of one tangent is \( p \), the
minimum energy of explosion is
A \( \cdot \frac{p^{2}}{2\left(m_{1}+m_{2}\right)} \)
B. \( \frac{p^{2}}{2 \sqrt{m_{1} m_{2}}} \)
c. \( \frac{p^{2}\left(m_{1}+m_{2}\right)}{2 m_{1} m_{2}} \)
D. \( \frac{p^{2}}{2\left(m_{1}-m_{2}\right)} \)


Calculate mean deviation about for the
following data.
\( \begin{array}{lllll}\text { Class } & \begin{array}{l}0- \\ 10\end{array} & \begin{array}{l}10 \\ 20\end{array} & \begin{array}{l}\text { 20- } \\ 30\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array}\end{array} \)
Frequence 6.7 15 16


\( \boldsymbol{K}_{\boldsymbol{a}_{1}}, \boldsymbol{K}_{\boldsymbol{a}_{2}}, \boldsymbol{K}_{\boldsymbol{a}_{3}} \) values for \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) are
\( 10^{-3}, 10^{-8}, 10^{-12} \) respectively. If
\( \boldsymbol{K}_{\boldsymbol{w}}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=\mathbf{1 0}^{-14}, \) then
(i) What is dissociation constant of \( H P O_{4}^{2-} ? \)
(ii) What is \( K_{b} \) of \( H P O_{4}^{2-} \)
(iii) What is \( K_{b} \) of \( H_{2} P O_{4}^{2-} \) ?
(iv) What order of \( \boldsymbol{K}_{\boldsymbol{b}} \) of
\( \boldsymbol{P O}_{4}^{3-}\left(\boldsymbol{K}_{b_{3}}\right), \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-}\left(\boldsymbol{K}_{b_{2}}\right) \) and
\( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{-}\left(\boldsymbol{K}_{b_{1}}\right) ? \)


When a particle moves in a circle with a
uniform speed
A. Its velocity and acceleration are both constant
B. Its velocity is constant but the acceleration changes
C. Its acceleration is constant but the velocity changes
D. Its velocity and acceleration both change


The equilibrium constant of a reaction at \( 298 K \) is \( 5 \times 10^{-3} \) and at \( 1000 K \) is
\( 2 \times 10^{-5} . \) What is the sign of \( \Delta H \) for
the reaction?
\( \mathbf{A} \cdot \Delta H \) is \( +v e \)
B. \( \Delta H \) is -ve
\( \mathbf{c} \cdot \Delta H \propto 0 \)
D. \( \Delta H \) is \( \pm v e \)


The energy required to convert all atoms
presents in \( 1.2 g \) magnesium to \( M g^{2+} \)
ions if \( I E . \) and \( I E_{2} \) of magnesium are \( 120 \mathrm{kJ} \) mol \( ^{-1} \) and \( 240 \mathrm{kJ} \) mol\( ^{-1} \)
respectively:
A. \( 18 \mathrm{kJ} \)
J
в. 36 к
c. 360 k.
D. 24 kJ


The force required just to move a body up an inclined plane is double the force required just to prevent the body sliding down. If the coefficient of friction is 0.25
the angle of inclination of the plane is
A \( \cdot 36.8^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 42.6^{\circ} \)


Find the distance \( x_{0} \) to the point on the
axis at which the value of \( B \) differs by
\( \eta=1 \% \) from that in the middle section
of the solenoid.
A \( . x_{0} \approx R \)
в. \( x_{0} \approx 7 R \)
\( \mathbf{c} \cdot x_{0} \approx 5 R \)
D. \( x_{0} \approx 3 R \)


Fixation of nitrogen means:
A. reaction of nitrogen with oxygen
B. conversion of free atmospheric nitrogen into
nitrogen compounds
C. the action of dentrifying bactria on nitrogen
compounds
D. decomposition of nitrogenous compounds to
yield free nitrogen


Ice blocks covered with rice husk as air
trapped avoids heat flow by


Explain the process of twinkling of stars
\( ? \)


Choose the correct statement:
A. A p-type semiconductor is positively charged
B. The Boolean expression \( 1 \cdot 0=0 \)
C. The majority carrier in \( N \) - type semiconductor is hole
D. A transistor cannot be used as a switch


Colour of the solution when \( K I \) reacts
with \( B r_{2} \) is:
A . pale yellow
B. reddish-brown
c. black
D. none of the above


Light, like sound, cannot pass through vacuum. State whether true or false
A. True
B. False


Find the smallest no. by which of the following no. must be multiplied to obtain a perfect cube
(i) 243
(ii) 256
(iii) 72
(iv) 675
(v) 100


Prove that the parallelogram
circumscribing a circle is a rhombus.


\( \mathbf{A} \)
\( 13 N \) weight and a \( 12 N \) weight are
connected by massless string over a
mass less friction less pulley, The \( 13 N \) weight has a downward acceleration with magnitude equal to that of a freely falling body time
A . 1
B. 1/12
c. \( 1 / 13 \)
D. \( 1 / 25 \)


The whitish part of eye mainly:
A. provides characteristic colour to the eye
B. acts as protective layer for the eye
C. regulates the amount of light entering into the eye
D. perceives the sensations


Extraction of aluminium from oxide
\( \left(A l_{2} O_{3}\right) \) is best done by:
A . Electrolytic reduction of \( A l_{2} O_{3} \)
B. Reduction of \( A l_{2} O_{3} \) with carbon
c. Reduction of \( A l_{2} O_{3} \) with sodium
D. Reduction of \( A l_{2} O_{3} \) with \( c 0 \)


The adjoining diagram shows the
spectral energy density distribution \( \boldsymbol{E}_{\lambda} \)
of a black body at two different temperatures. If the areas under the curves are in the ratio \( 16: 1, \) the value
of temperature \( \boldsymbol{T} \) is :
A . \( 32,000 K \)
в. 16,000 К
c. \( 8,000 K \)
D. 4,000 К


Propyne is produced during the hydrolysis of:
A. \( C a C_{2} \)
в. \( A l_{4} C_{3} \)
c. \( M g_{2} C_{3} \)
D. \( S i C \)


Maximum fats present in seeds of
A. Arachis hypogea
B. Oryza sativa
c. Cicer arietinum
D. Hibiscus esculentus


Part of the eye which controls the amount of light entering is called:
A. Iriss
B. Cornea
c. Lens
D. Retina


Cytochrome \( c \) is a small protein found
attached to outer surface of inner
mitochondrial membrane. It is a mobile
electron carrier that transfers electrons
between.
A. Complex II and III
B. Complex II and IV
c. Complex III and IV
D. Complex land!


The number of different signals that can be formed by using any number of flags from 4 flags of different colours is
A .24
B. 256
\( c \cdot 64 \)
D. 60


Which of the following ion has the maximum theoretical magnetic moment?
\( \mathbf{A} \cdot V^{3} \)
в. \( C r^{3} \)
\( c \cdot T i^{3} \)
D. \( C o^{3} \)


Two point charges \( +\boldsymbol{q} \) and \( -\boldsymbol{q} \) are held fixed at \( (-d, 0) \) and \( (d, 0) \) respectively of a \( (x, y) \) coordinate system, then
A. the electric field \( \vec{E} \) at all points on the \( x \) -axis has the same direction
B. \( \vec{E} \) at all points on the \( y \) -axis is along \( \hat{i} \)
C. positive work is done in bringing a test charge from infinity to the origin
D. all of the above


What is a Venturimeter? On what
principle does the Venturimeter work?


A body of mass 2 kg starts with an initial velocity \( 5 \mathrm{m} / \mathrm{s} \). If the body is acted upon by a time dependent force
(F) as shown in figure, then work done
on the body in 20 s is?


A mechanical wave needs
for propogating
energy
A. a set of photons
B. a set of electrons
c. a medium
D. water


At temperatures close to \( 0 \mathrm{K} \), the specific heat capacity c of a particular solid is given by \( c=b T^{3}, \) where \( T \) is the
temperature and b is a constant, characteristic of the solid.
The Sl unit of specific heat capacity is \( \boldsymbol{k} \boldsymbol{g}^{-1} \boldsymbol{K}^{-1} \)
What is the unit of constant b,
expressed in SI base units?
B. \( m^{2} s^{-2} K^{-4} \)
c. \( \operatorname{kgm}^{2} s^{-2} K^{-3} \)
D. \( k g m^{2} s^{-2} K^{-4} \)


If the roots of \( \frac{1}{x+a}+\frac{a}{x+b}=\frac{1}{c}, \) are equal in magnitude and opposite in sign, then the product of the roots is :
A \( \cdot-\frac{1}{2}\left(a^{2}+b^{2}\right) \)
B. \( \frac{1}{2}\left(a^{2}+b^{2}\right) \)
c. \( -\frac{3}{2}\left(a^{2}+b^{2}\right) \)
D. None


Compounds of carbon and hydrogen which form long chains or branched chains are:
A. carbo hydrides
B. hydrogen carbon
c. hydrogen carbides
D. hydro carbons


A farmer plans to mix two types of food
to make a mix of low cost feed for the
animals in his farm. A bag of food \( \boldsymbol{A} \)
\( \operatorname{costs} \$ 10 \) and contains 40 units of
proteins, 20 units of minerals and 10
units of vitamins. A bag of food \( B \) costs
\( \$ 12 \) contains 30 units of proteins, 20
units of minerals and 30 units of
vitamins. How many bags of food \( A \) and
\( B \) should the consumed by the animals
each day in order to meet the minimum
daily requirements of 150 units of
proteins, 90 units of minerals and 60 units of vitamins at a minimum cost?


A lawn roller is pulled along a horizon
surface through a distance of \( 20 \mathrm{m} \) by
with a force of \( 200 \mathrm{N} \). If the rope make
angle of \( 60^{\circ} \) with the vertical while pu
the amount of work done by the pulli
force is
\( \mathbf{A} \cdot 3464 \mathbf{J} \)
B. \( 1000 \mathrm{J} \)
D. 2000J


A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The
mass of the wire is \( 3.5 \times 10^{-2} k g \) and
its linear mass density is \( 4.0 \times \) \( 10^{-2} k g m^{-1} . \) What is
(a) the speed of a
transverse wave on the string, and
the tension in the string?


In the reaction,
\( 4 H N O_{3}+P_{4} O_{10} \rightarrow 4 H P O_{3}+X ; \) the
product \( \boldsymbol{X} \) is
A. \( N_{2} O_{5} \)
в. \( N_{2} O_{3} \)
\( c \cdot N O_{2} \)
D. \( H_{2} O \)


Which of the following is not a deuterolysis reaction
A. \( S O_{3}+D_{2} O \rightarrow D_{2} S O_{4} \)
в. \( C a C_{2}+2 D_{2} O \rightarrow C a(O D)_{2}+C_{2} D_{2} \)
c. \( M g_{3} N_{2}+6 D_{2} O \rightarrow 3 M g(O D)_{2}+2 N D_{3} \)
D. \( A l C l_{3} 3 D_{2} O \rightarrow A l(O D)_{3}+3 D C l \)


State whether the following statement is True or False?

The differential equation of a circuit
with inductance \( L \) and resistance \( R \) is
\( \operatorname{givenby} \frac{\boldsymbol{d} \boldsymbol{i}}{\boldsymbol{d} \boldsymbol{t}}+\frac{\boldsymbol{R}}{\boldsymbol{L}} \boldsymbol{i}=\frac{\boldsymbol{E}}{\boldsymbol{L}} \boldsymbol{e}^{-\boldsymbol{a t}}(\boldsymbol{i}= \)
0 at \( t=0 \). The current at time \( t \) is given
by \( i=\frac{E}{R-a L}\left(e^{-a t}\right) \)
A . True
B. False


There exist an (infinite) non-constant
arithmetical progression whose terms are all prime numbers
If true then enter 1 and if false then
enter 0


The reading shown in AC Voltmeter
when \( \mathrm{S} \) is moved to \( \mathrm{B} \) is:
A . \( 120 v \)
B. 100 \( v \)
\( c \cdot 140 v \)
D. \( 160 \mathrm{V} \)


Solve \( : \int_{0}^{\frac{\pi}{2}} x^{2} \sin x d x \)


The maximum oxidation state of
osmium is:
\( A \cdot+6 \)
B. +7
\( c \cdot+8 \)
D. +5


An electric refrigerator rated \( 600 W \)
operates 8 hours / day. What is the cost
of the energy to operate it for 30 days at Rs.4.00 per k Wh?


Let \( x=2 \) be a root of \( y=4 x^{2}-14 x+ \)
\( \boldsymbol{q}=\mathbf{0} . \) Then \( \boldsymbol{y} \) is equal to
A \( \cdot(x-2)(4 x-6) \)
В. \( (x-2)(4 x+6) \)
c. \( (x-2)(-4 x-6) \)
D. \( (x-2)(-4 x+6) \)


Increase 5 by \( 35 \% \)


The parallel rays of white light are made an incident normally on an air film of uniform thickness. 250 fringes are seen in the transmitted light between
\( 4000 A^{\circ} \) and \( 6500 A^{\circ} . \) Thickness of air
film is
A . \( 1.3 m m \)
в. \( 1.5 \mathrm{mm} \)
c. \( 0.13 m m \)
D. \( 0.11 m m \)


\( x \)


Equations \( 2 \sin ^{-1} x+3 \sin ^{-1} y=\frac{5 \pi}{2} \)
and \( y=k x-5 \) hold simultaneously
when k equals
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D. no such k exists


In the following \( \boldsymbol{A P} \), find the missing
terms in the boxes:
\( \square, 13, \square, 3 \)


A high concentration of synthetic auxin is generally used for
A. control of cell enlargement
B. Weed control
c. Prevention of the growth of lateral buds
D. Enhancing root initiation


Which of the following materials are non-biodegradable?
A. Plastic mugs
B. Egg shell
c. Leather belt
D. Both A and C


Predict major product in each of the following reactions, the structure of the
product is:


Mark correct option or options:
A. The minimum distance between a real image and the real object in concave mirror is zero
B. The minimum distance between a real object and real image in concave mirror is greater than \( 4 f \), where \( f \) is focal length of the lens
C. The focal length of concave mirror depends upon the wavelength of light incident on it
D. The focal length of mirror depends upon medium infront of the mirror


What type of molecules form micelles?
A. Non-polar molecules
B. Polar molecules
c. surfactant molecules
D. Salt of weak acid and weak base


There are 500 wrist watches in a box.
Out of these 50 wrist watches are found defective. One watch is drawn randomly from the box. Find the probability that wrist watch chosen is a defective watch.


\( \frac{5}{4} \)


The freezing point depression of 0.1 molal solution of acetic acid in benzene
is \( 0.256 \mathrm{K}, K_{f} \) for benzene is \( 5.12 K K g m o l^{-1} . \) What condition can
you draw about the molecular state of
acetic acid in benzene?
A. Acetic acid is doubly associated
B. Benzene is doubly associated
c. Both are equally associated
D. None of the above


Why athletes stop themselves before the line marked for javelin throw
A. Due to inertia of rest
B. Due to inertia of motion
c. Due to inertia of direction
D. All


Write the values(at least two) shown by
Shyam.


Write the next four terms of the
following A.P. \( \frac{1}{6}, \frac{1}{3}, \frac{1}{2} \)


Glycolysis
A. Occurs in mitochondria.
B. Has no connection with ETC.
C . Reduces 2 molecules of NAD \( ^{+} \) per glucose.
D. Produces no ATP.


At \( 373 \mathrm{K}, \) a gaseous reaction \( \boldsymbol{A} \rightarrow \)
\( 2 B+C \) is found to be of first order.
Starting with pure \( A \), the total pressure at the end of 10 min. was \( 176 \mathrm{mm} \) and
after a long time when A was completely dissociated, it was \( 270 \mathrm{mm} \). The pressure of \( A \) at the end of 10 minutes
was?
A. \( 94 \mathrm{mm} \)
B. 47mm
c. \( 43 \mathrm{mm} \)
D. 90mm


The formation of nitric oxide from
Nitrogen and Oxygen is endothermic in nature. What will be the sign of \( \Delta H ? \)
A. \( \Delta H \) is positive
B. \( \Delta H \) is negative
\( \mathrm{c} \cdot \Delta H \) is zero
D. None of these


Narcotic analgesics are called opiates.
If true enter 1 , if false enter 0 .
\( A \)


Assertion: All chemical added to food
items are called food preservatives.
Reason: All the chemicals increase the
nutritive value of the food.
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. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct


A conducting ball is given a certain charge and fixed at point \( P . \) An another
charge of mass \( 1 g m \) and charge \( 20 \mu C \)
when kept at \( Q(3 m, 9 m) \) starts moving with acceleration \( \overrightarrow{\boldsymbol{a}}=(1.08 \hat{\boldsymbol{i}}+ \)
1.44 \( \hat{\boldsymbol{j}} \) ) \( \boldsymbol{m} \boldsymbol{s}^{-2} \). The potential at \( \boldsymbol{Q} \) is \( +\mathbf{7 2 0} \)
volt. Calculate
(a) charge given to ball
(b) position of the ball
\( \mathbf{A} \cdot 6.4 \times 10^{-7} C(\mathrm{b})(-1.8 m, 4 m) \)
B . \( 6.4 \times 10^{-7} C(\text { b ) }(-2.8 m, 2 m) \)
C \( .7 .4 \times 10^{-7} C(\mathrm{b})(-1.8 m, 2 m) \)
D. \( 6.4 \times 10^{-7} C \) (b) \( (-1.8 m, 2 m) \)


Define one "Coulomb"' on the basis of
Coulomb's law.


The colour of light that travels with maximum speed in the glass is:
A. Blue
B. Green
c. Red
D. Violet


\( \int \cos ^{2} \theta d \theta=? \)


Find the area of one of the curvilinear
triangles formed by \( \boldsymbol{y}=\sin \boldsymbol{x}, \boldsymbol{y}= \)
\( \cos x \) and \( x \) axis


Two identical concentric coils \( X \) and \( Y \)
carrying currents in the ratio 1: 2 are
arranged in mutually perpendicular planes. If the magnetic field due to coil \( X \) is \( B \) the net field at their common
centre is:
A. \( B \)
в. \( 2 B \)
\( c .3 B \)
D. \( \sqrt{5} B \)


Which pair is not correct order of lattice
energy?
A. \( K C I>M g O \)
в. \( A l N>M g O \)
c. \( B e C O_{3}>M g C O_{3} \)
D. \( K C I<M g O \)


In moss, spores on germination
A. Forms degenerating protonema
B. Directly forms a leafy gametophyte
C. Form a protonema on which moss plant comes out like a bud
D. Produces antheridia and archegonia


Find the coefficient of \( x^{5} \) and \( x^{-15} \) in the
expansion of \( \left(3 x^{2}-\frac{1}{3 x^{3}}\right)^{10} ? \)


Find the set of values of \( a \) for which
\( f(x)=x+\cos x+a x+b \) is
increasing on \( \boldsymbol{R} \)


What will be the molar conductivity of
\( A l^{3+} \) ions at infinite dilution if molar
conductivity of \( A l_{2}\left(S O_{4}\right)_{3} \) is \( 858 S c m^{2} \) \( m o l^{-1} \) and ionic conductance of \( S O_{4}^{2-} \)
is 160 S \( c m^{2} \) mol \( ^{-1} \) at infinite dilution?
A \( \cdot 189 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
B. \( 698 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. \( 1018 \mathrm{s} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
D. \( 429 \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1} \)


The weights of various ions liberated by passing the same current through different electrolytes are in the ratio of their:
A. Atomic weights
B. Equivalent weights
c. Molecular weights
D. Atomic numbers


Cassiopeia appears in hemisphere.
A. northern
B. southern
c. eastern
D. western


If the lines \( \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4} \) and
\( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{1}}=\frac{\boldsymbol{y}-\boldsymbol{k}}{\mathbf{2}}=\frac{\boldsymbol{z}}{\mathbf{1}} \) intersect, then \( \boldsymbol{k}= \)
A. 0
B. 3
\( c \cdot \frac{7}{2} \)
D. -


A block of mass \( 300 k g \) is set into
motion on a frictionless horizontal
surface with the help of frictionless pulley and a rope system as shown in
the figure. What horizontal force \( \boldsymbol{F} \)
should be applied to produce in the block an acceleration of \( 1 \mathrm{m} / \mathrm{s}^{2} \) ?
A. \( 150 N \)
в. \( 100 N \)
\( c .300 N \)
D. \( 50 N \)


A sphere \( P(\text { emissivity }=1 \) ) of radius
\( 2 R \) and and another sphere \( Q \) (emissivity \( =1 / 2 \) ) of radius \( R \) are
placed in vacuum at some distance. There are no other objects. The temperature of the sphere \( Q \) is
maintained at \( 200 K \) by the means of a
heater. A fraction \( 1 / 32 \) of the power
emitted by the sphere \( Q \) falls on the sphere \( P \). If the equilibrium
temperature of the sphere \( \boldsymbol{P} \) is \( 10 \boldsymbol{T} \) (in
\( K \) ), find the value of \( T: \)


The value of \( c \) of mean value theorem
when \( f(x)=x^{3}-3 x-2 \) in [-2,3] is
A \( \cdot \sqrt{\frac{7}{3}} \)
B. \( \sqrt{\frac{3}{7}} \)
c. \( \frac{\sqrt{7}}{3} \)
D. \( \frac{\sqrt{3}}{7} \)


Which of these is correctly matched with the accompanying description?
A. Pancreas - Delta cells of islets of Langerhans secrete a hormone which stimulates glycolysis in liver
B. Thyroid - Hyperactivity in young children causes cretinism
C. Thymus - Starts undergoing atrophy after puberty
D. Parathyroid - Secretes parathormone that promotes movement of \( C a^{2+} \) ions from blood into bones during
calcification


Find the area of a square whose
perimeter is \( 160 \mathrm{m} . \) A floor \( 3.0 \mathrm{m} \) long and \( 2.0 \mathrm{m} \) wide is to be covered with
square shaped tiles of length \( 10 \mathrm{cm} . \) Find
the cost of flooring it, if the cost of tiles
is Rs.150 per 100 tiles.


Organisms called methanogens are most abundant in a
A. Hot spring
B. Sulphur rock
c. cattle yard
D. Polluted stream


For the galvanic cell, \( \boldsymbol{A} \boldsymbol{g} \mid \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}), \boldsymbol{K} \boldsymbol{C l}(\mathbf{0} . \boldsymbol{2} \boldsymbol{M}) \| \boldsymbol{K} \boldsymbol{B r}(\mathbf{0 . 0 0 1} \)
Calculate the emf generated and assign correct polarity to each electrode for the spontaneous process after taking into
account the cell reaction at \( 25^{\circ} C \).
Given, \( \boldsymbol{K}_{s p A g C l}=\mathbf{2 . 8} \times \)
\( \mathbf{1 0}^{-\mathbf{1 0}} ; \mathbf{K}_{s p A g B r}=\mathbf{3 . 3} \times \mathbf{1 0}^{-\mathbf{1 3}} \)


The speed of electrons in the second
orbit of \( B e^{3+} \) ion will be
A \( \cdot \frac{c}{137} \)
в. \( \frac{2 c}{137} \)
c. \( \frac{3 c}{137} \)
D. \( \frac{4 c}{137} \)


Predict major addition product when the following addition reaction carried out in presence of peroxide:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{3}+\boldsymbol{C C l}_{4} \rightarrow \)
A \( \cdot C_{6} H_{5}-C H\left(C C l_{3}\right)-C H(C l)-C H_{3} \)
в. \( C_{6} H_{5}-C H(C l)-C H\left(C C l_{3}\right)-C H_{3} \)
c. \( C_{6} H_{5}-C H\left(C C l_{3}\right)-C H_{2}-C H_{2} C l \)
D. \( C_{6} H_{5}-C H_{2}-C H\left(C C l_{3}\right)-C H_{2} C l \)


The ratio in which the line segment
joining the points whose position vectors are \( 2 \hat{i}-4 \hat{j}-7 \hat{k} \) and \( -3 \hat{i}+ \) \( \mathbf{5} \hat{\boldsymbol{j}}-\boldsymbol{8} \hat{\boldsymbol{k}} \) is divided by the plane whose
equation is \( \hat{r} \cdot(\hat{i}-2 \hat{j}+3 \hat{k})=13 \) is-
A. 13: 12 internally
B. 12: 25 externally
c. 13: 25 internally
D. 37: 25 internally


Prove that a line drawn through the midpoint of one side of a triangle parallel to second side bisects the third side.


The equation of a progressive wave for a
wire is:
\( \boldsymbol{Y}=\mathbf{4} \sin \left[\frac{\boldsymbol{\pi}}{\mathbf{2}}\left(\boldsymbol{8} \boldsymbol{t}-\frac{\boldsymbol{x}}{\boldsymbol{8}}\right)\right] . \) If \( \boldsymbol{x} \) and \( \boldsymbol{y} \) are
measured in cm then velocity of wave is
A. \( 64 \mathrm{cm} / \mathrm{s} \) along \( -x \) direction
B. \( 32 c m / s \) along \( -x \) direction
c. \( 32 c m / s \) along \( +x \) direction
D. \( 64 \mathrm{cm} / \mathrm{s} \) along \( +x \) direction


In an open system, system and
surroundings can exchange
A. Energy only
B. Matter only
C. Both energy and matter
D. Neither energy nor matter


For a particle executing SHM. The KE 'K' is given by \( K=K_{0} \cos ^{2} w t . \) The
maximum value of PE is
A. \( K_{0} \)
B. zero
c. \( \frac{K_{0}}{2} \)
D. \( \frac{K_{0}}{4} \)


If co-efficient of friction is \( \sqrt{3} \) then what
will be the angle between two surfaces?


A current of 2 amp when passed for 5
hour through a molten salt deposits \( 22.2 g \) of metal of atomic mass 177
Then calculate the positive oxidation state of the metal in the metal salt.


If the median of data
\( \mathbf{3 1}, \mathbf{3 3}, \mathbf{3 5}, \boldsymbol{x}, \boldsymbol{x}+\mathbf{1 0}, \mathbf{4 8}, \mathbf{4 8}, \mathbf{5 0} \) is \( \mathbf{4 0} \)
than find the value of \( x \)


Balance the following chemical
equation \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{O}_{3} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \)
Indicating the changes in oxidation numbers of oxygen, find the equivalent
weight of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) for this reaction.


Prove that \( \int \sqrt{\left(a^{2}-x^{2}\right)} d x= \)
\( \frac{x \sqrt{\left(a^{2}-x^{2}\right)}}{2}+\frac{a^{2}}{2} \sin ^{-1} \frac{x}{a} \)


An infinite line charge is at the axis of a cylinder of length \( 1 \mathrm{m} \) and radius \( 7 \mathrm{cm} \)
If electric field at any point on the
curved surface of cylinder is \( 250 N C^{-1} \) then net electric flux through the cylinder is:


Which row in the table shows the
correct percentage of oxygen in atmospheric and exhalend air?
\begin{tabular}{lll}
& Atmospheric air \( / \% \) & Exhaled air \( / \% \) \\
\( \mathrm{A} \) & 78 & 21 \\
\( \mathrm{B} \) & 21 & 16 \\
\( \mathrm{c} \) & 16 & 4 \\
\( \mathrm{D} \) & 4 & 0.04 \\
\hline
\end{tabular}


Optimum temperature of photosynthesis is
\( \mathbf{A} \cdot 10-15^{\circ} \mathrm{C} \)
В. \( 20-25^{\circ} \mathrm{C} \)
c. \( 20-35^{\circ} \mathrm{C} \)
D. \( 35-50^{\circ} \mathrm{C} \)


\( \boldsymbol{S} \boldsymbol{O}_{2} \) gas may be produced by:
A. Heating 'S' in absence of air
B. Roasting \( Z n S \)
c. Heating ferric sulphate
D. Hydrolysing \( N a_{2} S O_{4} \)


\( \left(1-x y+x^{2} y^{2}\right) d x=x^{2} d y \)
A. \( _{y}=\frac{1}{x} \tan (\ln |c y|) \)
B. \( _{x}=\frac{1}{y} \tan (\ln |c x|) \)
c. \( x=\frac{1}{y} \cot (\ln |c y|) \)
D. \( y=\frac{1}{x} \cot (\ln |c x|) \)


What concentration of \( \mathrm{CO} \) 2 be in
equilibrium with \( 0.025 \mathrm{M} \mathrm{CO} \) at \( 120^{\circ} \mathrm{C} \)
for the reaction
\( \boldsymbol{F e O}(\boldsymbol{s})+\boldsymbol{C O}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \) if
the value of \( \boldsymbol{K}_{c}=\mathbf{5 . 0 ?} \)
A. 0.125
B. 0.0125 М
c. \( 1.25 \mathrm{M} \)
D. 12.5 M


Based on above isomers answer the
following.
Which isomer on dehydration with conc.
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) undergo maximum
rearrangement?
\( A \)
B.
\( c \)
D.


Three bodies, a ring, a solid cylinder
and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies
are identical. Which of the bodies
reaches the ground with maximum
velocity?
A. The ring body
B. The solid sphere body
c. The solid cylinder body
D. can't'tind out


If an element \( X \) is placed in group \( 14, \) the formula its chloride is:
A. \( X C l \)
в. \( X C l_{2} \)
c. \( x C l_{3} \)
D. \( X C l_{4} \)


Find the quotient and remainder on dividing \( p(x) \) by \( g(x) \) in the following case, without actual division.
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{3}+\boldsymbol{4} \boldsymbol{x}^{2}-\boldsymbol{6} \boldsymbol{x}+\boldsymbol{2} ; \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}- \)
3


A burning strip of \( M g \) is introduced into
a jar containing a gas. After some time, the walls of the container are coated
with carbon. The gas in the container is :
\( A \cdot O_{2} \)
в. \( N_{2} \)
\( c \cdot C O_{2} \)
D. \( H_{2} O \)


The ion(s) that act/s as oxidizing agent in solution is/ are :
A \( \cdot T l^{+} \) and \( A l^{3} \)
B . \( B^{3+} \) and \( A l^{3+} \)
C \( \cdot T l^{3+} \) only
D. \( B^{3+} \) only


At a place, value of acceleration due to
gravity \( g \) is reduced by \( 2 \% \) of its value
on the surface of the earth (Radius of
earth \( =6400 \mathrm{km} \). The place is:-
A. \( 64 \mathrm{km} \) below the surface of the earth
B. \( 64 \mathrm{km} \) above the surface of the earth
\( \mathrm{c} .32 \mathrm{km} \) above the surface of the earth
D. \( 32 \mathrm{km} \) below the surface of the earth


The cup-shaped structure of pelvic girdle, the acetabulum in man is formed by
A . llium, ischium and pubis
B. llium, ischium and cotyloid
c. llium and ischium
D. llium and cotyloid


Calculate the following integral
\( \int_{0}^{3}\left[3^{1-x}+\left(\frac{1}{3}\right)^{2 x-1}\right] d x \)


Write:
(a) IUPAC name
(b) Central metal ion
(c) Ligand
(d) Coordination number
(e) Geometry of the complex
\( \left[\boldsymbol{C r}(\boldsymbol{e n})_{3}\right] \boldsymbol{C l}_{3} \)


A desk sells for Rs. 1000. The tax is 12\%.
What is the total cost of the desk?
A. 1120
B. 2120
\( c .3120 \)
D. 4120


Find the coefficient of range for the data
43,24,38,56,22,39,45
A . 0124
B. 0.212
c. 0.236
D. 0.436


What is true for Archaebacteria?
A. All are halophiles
B. All are photosynthetic
C. All are fossils
D. Oldest living organisms


Which of the following is not hydrolyzed?
A \( \cdot C C l_{4} \)
в. \( \operatorname{si} C l_{4} \)
\( \mathbf{c} \cdot \operatorname{Sn} C l_{4} \)
\( \mathbf{D} \cdot P b C l_{4} \)


If a cell of constant E.M.F. produces the same amount of the heat during the same time in two independent resistors
\( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}, \) when they are separately connected across the terminals of the
cell, one after the another, the internal resistance of the cell is \( \sqrt{x R_{1} R_{2}} \). Find \( x \)


The battery is an arrangement of an electrolytic cell connected in series.
A. True
B. False


Alginic acid is a product of
A. Red algae
B. Green algae
c. Blue green algae
D. Brown algae


The value of \( \mu_{o} \) is
\( \mathbf{A} \cdot 2 \pi \times 10^{-7} H m^{-1} \)
B \( \cdot 4 \pi \times 10^{-7} \mathrm{Hm}^{-1} \)
\( \mathbf{c} \cdot 8 \pi \times 10^{-7} \mathrm{Hm}^{-1} \)
D \( \cdot \pi \times 10^{-7} \mathrm{Hm}^{-1} \)


Find the slope of the inclination of the
line of the following:
\( \boldsymbol{\theta}=\mathbf{3 0}^{\circ} \)
A. \( \sqrt{3} \)
B. \( \frac{1}{\sqrt{3}} \)
c. \( \frac{2}{\sqrt{3}} \)
D. \( \frac{\sqrt{3}}{2} \)


What is the SI prefix for \( 10^{-9} ? \)
A. Nano
B. Pico
c. Micro
D. Mill


Yadaiah for his family needs borrowed
Rs. 5120 at \( 12 \frac{1}{2} \% \) per annum compounded annually. How much
amount he has to pay to clear the debt
at the end of two year nine months? Also
find total how much interest he has
paid?


A certain mass of a gas occupies a volume of \( 0.2 \mathrm{dm}^{3} \) at \( 273 \mathrm{K} \). Calculate
the volume of the gas if its absolute temperature is doubled at the same
pressure.


The study of fresh water ecosystem is called as
A. Limnology
B. Ethology
c. synecology
D. Autecology


Assertion
An object from a greater height reaches a steady terminal velocity.
Reason
The viscous forces on a body depends upon its velocity. The greater the velocity the greater is the viscous force.
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


Physical nature of ionic compounds
is
A. solid
B. liquid
c. gas
D. May exist in any state


Find the position vector of a point \( \boldsymbol{R} \)
which divides the line joining two
points \( P \) and \( Q \) whose position vectors \( \operatorname{are}(2 \vec{a}+\vec{b}) \) and \( (\vec{a}-3 \vec{b}) \) externally in
the ratio \( 1: 2 . \) Also, show that \( P \) is the
mid point of the line segment \( \boldsymbol{R} \boldsymbol{Q} \)


ATP is produced during which of the following processes?
I. Photosynthesis
Il. Aerobic respiration
III. Fermentation
A. I only
B. II only
c. I and III only
D. Il and III only
E. I, II and III


Calculate the wave length of the
longitudinal wave.
A. \( 1.5 \mathrm{m} \)
B. 3 \( m \)
c. \( 4.5 \mathrm{m} \)
D. \( 9 \mathrm{m} \)
E. 18 m


Global warming will cause.
A. Rise is level of oceans
B. Decrease in glaciers
c. Reduction in ice caps
D. All the above


Let \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{4} \boldsymbol{x}-\mathbf{3} . \) If \( \boldsymbol{f}(\boldsymbol{a})=\mathbf{9} \) and
\( f(b)=5, \) then calculate \( f(a+b) \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 7
c. 14
D. 16
E . 17


Nylon-6 is manufactured from which of
the following?
A. maleic anhydride and hexamethylene diamine.
B. caprolactum
C. adipic acid and hexamethylene diamine.
D. sebasic acid and hexamethylene diamine.


Oxides which show both acidic and
basic nature are called as
oxides.


The length of a given cylindrical wire is
increased by \( 100 \% . \) Due to the consequent decrease in the diameter,
the change in the resistance of the wire will be :-
A. \( 300 \% \)
B. 200\%
\( c \cdot 100 \% \)
D. \( 50 \% \)


S.I unit of specific heat capacity is
A. Joule per kilogram per kelvin
B. Joule per kilogram per second
C. Degree Celsius per joule per second
D. All


Fill in the boxes with the symbols '<' or
'>' to make the given statements true:
\( \frac{5}{11} \square \frac{3}{7} \)
\( \frac{8}{15} \square \frac{3}{5} \)
\( \frac{11}{14} \square \frac{29}{35} \)
\( \frac{13}{27} \square \frac{15}{48} \)


In resonance tube exp. we find \( l_{1}= \)
\( 25.0 \mathrm{cm} \) and \( l_{2}=75.0 \mathrm{cm} . \) If there is no
error in frequency, what will be maximum permissible error in speed of
sound. (Take \( \left.f_{0}=325 H z\right) \)
\( \boldsymbol{V}=\mathbf{2} \boldsymbol{f}_{0}\left(\boldsymbol{l}_{2}-\boldsymbol{l}_{1}\right) \)
A. \( v=(329 \pm 1.3) \mathrm{m} / \mathrm{s} \)
B. \( v=(326 \pm 1.3) \mathrm{m} / \mathrm{s} \)
c. \( v=(325 \pm 1.4) \mathrm{m} / \mathrm{s} \)
D. \( v=(325 \pm 1.3) \mathrm{m} / \mathrm{s} \)


Q Type your question
gas particles from both sides as shown
in the figure. The solid dots are
representing the molecules hitting from left side and the faint dots are the
molecules hitting from right side. The
mass of these gas particles is \( \boldsymbol{m}= \)
\( 10^{-26} k g \) and velocity before hitting is
\( v_{0}=5 m / s . \) Volume density of the gas
particles on both sides is \( n=10^{25} \) per
\( m^{3} . \) Each beam has an area \( A=1 m^{2} \)
and the collisions are perfectly elastic.
What is the external force \( F \) (in newton)
required to move the plate with a
constant velocity \( \boldsymbol{v}=2 \boldsymbol{m} / \boldsymbol{s} \)


Obtain the differential equation of all
circles of radius \( r \). and center at \( (\mathbf{0}, \mathbf{0}) \)


In the complex numbers, where \( i^{2}=-1 \)
what is the value of \( 5+6 i \) multiplied
by \( 3-2 i ? \)
A . 27
в. 27
c. \( 27+8 i \)
D. \( 15+8 i \)
E . \( 15-18 i \)


\( \int \frac{2^{x}}{\sqrt{1-4^{x}}} d x=K \sin ^{-1}\left(2^{x}\right)+C, \) then
the value of \( K \) is equal to
A \( . e n 2 \)
B. \( \frac{1}{2} \ell 2 \)
\( c \cdot \frac{1}{2} \)
D. \( \frac{1}{\ell n^{2}} \)


The osmotic pressure of \( 0.1 \mathrm{M} \) aqueous
solution of \( M g C l_{2} \) at \( 300 \mathrm{K} \) is \( 4.92 \mathrm{atm} \)
What will be the percentage ionization of the salt?
A . \( 49 \% \)
B. \( 29 \% \)
\( c .39 \% \)
D. \( 69 \% \)


The mass percentage composition of the elements in nitric acid are \( \boldsymbol{H}= \) \( \mathbf{1 . 5 9 \%}, \boldsymbol{N}=\mathbf{2 2 . 2 2 \%}, \boldsymbol{O}=\mathbf{7 6 . 1 9 \%} \)
respectively. \( (\boldsymbol{H}=\mathbf{1}, \boldsymbol{N}=\mathbf{1 4}, \boldsymbol{O}=\mathbf{1 6}) \)
A. True
B. False


What would be the change in
the freezing point of \( H_{2} O \) in a solution
of \( 1 m N a C l(a q) ? \)
\( \mathbf{A} \cdot-1.86^{\circ} \mathrm{C} \)
B. \( -0.52^{\circ} \mathrm{C} \)
c. \( -3.72^{\circ} \mathrm{C} \)
D. \( 1.86^{\circ} \mathrm{C} \)
E \( .3 .72^{\circ} \mathrm{C} \)


Statement-1: Micelles are formed by surfactant molecules above the critical
micellar concentration \( (\boldsymbol{C} \boldsymbol{M} \boldsymbol{C}) \)
Statement-2: The conductivity of a solution having surfactant molecules
decreases sharply at the CMC.
A. Statement-1 is True, Statement-2 is True; Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis NOT a correct explanation for Statement-1
c. Statement-1 is True, Statement-2 is False.
D. Statement- is False, Statement-2 is True


\( q_{1}, q_{2}, q_{3}, \) and \( q_{4} \) are point charges located at points as shown in the figure and \( \mathrm{S} \) is a spherical Gaussian surface
of radius R. Which of the following is
true according to the Gauss's law?
A \( \cdot \oint_{5}\left(\vec{E}_{1}+\vec{E}_{2}+\vec{E}_{3}\right) \cdot d \vec{A}=\frac{q_{1}+q_{2}+q_{3}}{2 \varepsilon_{0}} \)
B.
c. \( \oint_{5}\left(\vec{E}_{1}+\vec{E}_{2}+\vec{E}_{3}\right) \cdot d \vec{A}=\frac{\left(q_{1}+q_{2}+q_{3}+q_{4}\right)}{\varepsilon_{0}} \)
D. None of the above


Match the colum:
\( \begin{array}{ll}\text { List - A } & \text { List - B } \\ \text { (Molecule) } & \begin{array}{l}\text { (Pure and hybrid } \\ \text { orbitals involved) }\end{array} \\ \text { A) } C_{2} H_{6} & \text { 1) } 12,18 \\ \text { B) } C_{2} H_{4} & \text { 2) } 6,4 \\ \text { C) } C_{2} H_{2} & \text { 3) } 6,6 \\ \text { D) } C_{6} H_{6} & \text { 4) } 6,8\end{array} \)
\( \mathbf{A} \)
B. A-2, B-3, C-4, D-1
c. \( A-3, B-4, C-2, D-1 \)
D. A-4, B-3, C-2, D-1


If \( \boldsymbol{A} \times \boldsymbol{B}= \)
\( (2,4),(2, a),(2,5),(1,4),(1, a),(1,5) \)
find \( B \)
A \( \cdot\{4,2,5\} \)
в. \( \{4, a, 5\} \)
c. \{4,1,5\}
D. \( \{2, a, 5\} \)


A wooden piece \( 5 N \) in weight and
\( 5 c m \times 3 c m \times 2 c m \) in size lies on
\( 5 c m \times 2 c m \) face. The pressure exerted
by it in \( N \) per \( c m^{2} \) is:
A. 150
B. 50
c. 0.5
D. 15


The monomers of Buna-S rubber are:
A. vinyl chloride and sulphur
B. butadiene
C. styrene and butadiene
D. isoprene and butadiene


\( \mathrm{IF} \cos \theta=\frac{3}{5}, \) then the value of
\( \frac{\sin \theta \tan \theta+1}{2 \tan ^{2} \theta} \) is
A \( \cdot \frac{88}{160} \)
в. \( \frac{91}{160} \)
c. \( \frac{92}{160} \)
D. \( \frac{93}{160} \)


In the \( \Delta A B C, \) if \( A B=\sqrt{2} ; A C= \)
\( \sqrt{\mathbf{2 0}}, \boldsymbol{B}=(\mathbf{3}, \mathbf{2}, \mathbf{0}) \) and \( \boldsymbol{C}=(\mathbf{0}, \mathbf{1}, \mathbf{4}) \)
then the length of the median passing
through \( \boldsymbol{A} \) is
A \( \cdot \frac{3}{2} \)
B. \( \frac{9}{2} \)
c. \( \frac{3}{\sqrt{2}} \)
D. \( \frac{\sqrt{3}}{2} \)


A seven-digit number without repetition
and divisible by 9 is to be formed by using seven digits out of
\( \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}, \mathbf{6}, \mathbf{7}, \mathbf{8}, \mathbf{9} . \) The number of ways
in which this can be done is
A . 9
в. \( 2(7 !) \)
c. \( 4(7 !) \)
D. None of these


In the absence of any current a
compass needle rests in which
direction (with respect to the Earth)?
A. South-north
B. North-south
c. East-west
D. west-east


The Young's modulus of the material of
the wire of length \( L \) and radius \( r \) is
\( \boldsymbol{Y} \boldsymbol{N} / \boldsymbol{m}^{2} . \) If the length is reduced to \( \boldsymbol{L} / \mathbf{2} \)
and radius \( r / 2 \), the Young's modulus
will be:
A \( \cdot \frac{Y}{2} \)
в. \( Y \)
\( c .2 Y \)
D. \( 4 Y \)


The number of turns per unit length in a
toroid is \( 10^{3} \) and current flowing in it is
\( \frac{1}{4 \pi} \) ampere,then the magnetic induction produced in it, is :
\( \mathbf{A} \cdot 10^{-4} T \)
в. \( 10^{4} T \)
c. \( 10^{-2} T \)
D. \( 10^{2} T \)


The unit vectors orthogonal to \( -i+ \) \( 2 j+2 k \) and making equal angles with
\( x \) and \( y \) axis are
A \( \cdot \pm \frac{1}{3}(2 \bar{i}+2 \bar{j}-\bar{k}) \)
B. \( _{\pm \frac{1}{3}(\bar{i}+\bar{j}-\bar{k})} \)
c. \( \pm \frac{1}{3}(2 \bar{i}-2 \bar{j}-\bar{k}) \)
D. \( \pm \frac{1}{4}(\bar{i}+\bar{j}-\bar{k}) \)


Cochlea is located in the
A. skin
B. Eye
c. Nose
D. Ear


Explain the term with example:Covalent
bond.


Four blocks of different masses \( \left(\boldsymbol{m}_{1}=\right. \)
\( \mathbf{1} \boldsymbol{k} \boldsymbol{g}, \boldsymbol{m}_{2}=\mathbf{2} \boldsymbol{k} \boldsymbol{g}, \boldsymbol{m}_{3}=\mathbf{1} \boldsymbol{k} \boldsymbol{g} \) and \( \boldsymbol{m}_{4}= \)
\( 5 k g) \) are connected with light,
inextensible strings, as shown in figure. This system is pulled along the frictionless surface by a horizontal force of \( 36 N . \) The force pulling the block of
\( \operatorname{mass} \boldsymbol{m}_{1} \) will be
A \( .2 N \)
в. \( 4 N \)
c. \( 12 N \)
D. \( 36 N \)


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{5}, \) then \( \boldsymbol{f}(-\mathbf{4}) \) is:
A . 26
B. 21
c. 20
D. -20


Fill in the blanks
Nitrogen is a \( ------- \) gaseous
molecule.


Histones associated with the genetic material apart from maintaining its also act as
A. Modulators
B. Apozymes
c. Isozymes
D. Activators


The ratio of the deBroglie wave length for the electron and proton moving with same velocity is:
\( \left[m_{p}-\text { mass of propton, } m_{e}- \) mass of \right. electron]
\( \mathbf{A} \cdot m_{p}: m_{e} \)
в. \( m_{p}^{2}: m_{e}^{2} \)
\( \mathbf{c} \cdot m_{e}: m_{p} \)
D. \( m_{e}^{2}: m_{p}^{2} \)


Which of the following oxide is an
amphoteric oxide?
A. \( B i_{2} O_{3} \)
B. \( N_{2} O_{3} \)
\( \mathrm{c} \cdot P_{4} \mathrm{O}_{10} \)
D. \( S b_{2} O_{3} \)


Find the number of pi bonding
molecular orbital from the following set if z the internuclear axis :
\( \boldsymbol{p}_{z} \) and \( \boldsymbol{d}_{z^{2}}, \boldsymbol{p}_{\boldsymbol{x}} \) and \( \boldsymbol{d}_{\boldsymbol{x} z}, \boldsymbol{d}_{\boldsymbol{x} z} \) or \( \boldsymbol{d}_{\boldsymbol{y} z}, \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{z}} \)
and \( \boldsymbol{d}_{\boldsymbol{y} \boldsymbol{z}} \)


The essential difference between an AC
generator and a DC generator is that
A. AC generator has an electromagnet while a DC generator has permanent magnet.
B. DC generator will generate a higher voltage.
C. AC generator will generate a higher voltage
D. AC generator has slip rings while the DC generator has commutator


Construct a triangle \( A B C \) in which
\( B C=8 c m, \angle B=45^{\circ} \) and \( A B-A C= \)
\( \mathbf{3 . 5 c m} \)


Two halves of pectoral girdle fuse in
A. Lateral sides
B. Mid-dorsal sides
c. Mid-ventral line
D. Both dorsal and ventral lines


What is nutrition? Explain heterotrophic nutrition with their types.


Elements and their isotopes have different:
A. mass numbers
B. number of protons
c. number of electrons
D. chemical properties


Water contains hydrogen and oxygen in
the ratio:
A . 2:
B. 1:
\( c \cdot 1: 4 \)
D. 4:


Which of the following are polyester polymers? This question has multiple correct options
A. Bakelite
B. Dacron
c. Glyptal resins
D. Nylon - 5


What is the number when it
is increased by \( 10 \% \) becomes \( 88 ? \)


If a sentence can be judged to be true or false, but not both then it is called
A. an open sentence
B. a statement
c. a tautology.
D. a contradiction.


Transformer \( \rightarrow \) ideal \( \rightarrow \boldsymbol{E}_{\boldsymbol{P}}= \)
\( \mathbf{1 0 0 0} \boldsymbol{V}, \boldsymbol{I}_{\boldsymbol{P}}=\mathbf{5 0 A} \)
\( 220 V \rightarrow 80 \) houses
Resistance of secondary coil will be
A . \( 2 \Omega \)
B. 3\Omega
\( c .1 \Omega \)
D. \( 4 \Omega \)


Suppose gravitational force between two masses were to be given by \( \boldsymbol{F}= \) \( k \frac{\sqrt{m_{1} m_{2}}}{d^{3}} \) where \( k \) is some constant
two equal masses attract each other with a certain force when the distance
is d. If each of the masses is doubled,
than what value the distance between
them must be maintained for the force
to remain the same as earlier?
A. \( \sqrt[3]{3 d} \)
B. "3/3d
\( c \cdot \sqrt[13]{2 d} \)
D. \( \sqrt[3]{2 d} \)


For a reaction \( 2 N O(g)+C l_{2}(g) \rightarrow \)
\( 2 N O C l(g), \) when concentration of \( C l_{2} \)
is doubled the rate of reaction becomes
two-times of the original. When the concentration of \( N O \) is doubled the
rate becomes four times. What is the
order of the reaction?
A . 1
B. 2
\( c .3 \)
D. 4


The optically active molecule is:
\( A \)
B.
\( \mathbf{c} \)
D.


single \( N-N \) bond is weaker than the
single \( P-P \) bond. This is because of:
This question has multiple correct options
A. larger \( N-N \) bond length in comparison to \( P-P \)
bond length
B. high interelectronic repulsion of the non-bonding electrons, owing to the small \( N-N \) bond length in comparison to that in \( P-P \) single bond
c. higher electronegativity of \( N \) in comparison to \( P \)
D. smaller atomic size of \( N \) as compared to that of \( P \)


Consider the equation \( \boldsymbol{p}=\mathbf{5}-|\mathbf{2 q - 3}| \)
f \( p=|r|+5, \) then number of possible
ordered pair \( (r, q) \) is?


Which of the following species does not
exert a resonance effect?
A \( \cdot C_{6} H_{5} N H_{2} \)
B. \( C_{6} H_{5} N^{+} H_{3} \)
\( \mathbf{c} \cdot C_{6} H_{5} O H \)
D. \( C_{6} H_{5} C l \)


Two complementary angles are in the ratio \( 4: 5 . \) Find the angles.


Choose the correct answer from the
alternatives given In the sinuses of an open circulatory system,-blood is not segregated from:
A . urine
B. interstitial fluid
c. digestive cavity
D. cytoplasm


Which of the following is an example of
condensation?
This question has multiple correct options
A. Dew forms in the morning
B. The mirror in the bathroom during a shower getting foggy
C. Water droplets formation on cold water bottle
D. Cooling of water in refrigerator


Find the greatest and the least values of the following functions. \( y=x^{3}+3 x^{2}+3 x+2 \) on the
interval [-2, 2].


Draw number lines and locate the
points on them. \( \frac{1}{2}, \frac{1}{4}, \frac{3}{4}, \frac{4}{4} \)


Describe the method of sexual
reproduction in human beings


If \( \boldsymbol{R}=\{(1,-1),(2,-2),(3,-1)\} \) is
relation, then find the range of \( R \)


The reaction \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g), \Delta H=-X k J, \) is favoured by
high pressure and high temperature.
A. True
B. False


What ways do you know to reduce
friction?


Rays of light are entering from glass to glycerine. If refractive indexes of glass and glycerine are respectively 1.5 and 1.47, find the refractive index of
glycerine with respect to glass.
A. 0.03
B. 1.02
\( c \cdot 2.20 \)
D. 0.98


If \( \bar{A} \times \bar{B}=\bar{C} \) which of the following
statement is not correct?
A. \( \bar{C} \) T \( \bar{A} \)
в. \( \bar{C} \) Т \( \bar{B} \)
c. \( \bar{C} \) T \( \bar{A} \times \bar{B} \)
D. \( \bar{C} \top \bar{A}+\bar{B} \)


Find the value of:
\( 2 \tan 45^{\circ}+\cos 45^{\circ}-\sin 45^{\circ} \)


Number of floating ribs in human are
A. 6 pairs
B. 5 pairs
c. 3 pairs
D. 2 pairs


Calculate \( \angle B A C \)
\( A \cdot 90^{\circ} \)
B \( .50^{\circ} \)
\( c \cdot 60^{\circ} \)
\( \mathbf{D} \cdot 80 \)


Oxidation state of oxygen in hydrogen peroxide is?
A . -
B. +1
\( c \cdot 0 \)
\( D \cdot-2 \)


In a transistor
A. the emitter has the least concentration of impurity
B. the collector has the least concentration of impurity
C. the base has the least concentration of impurity
D. all the three regions have equal concentrations of impurity


Assertion
The atomic mass of potassium is 39
Reason
An atom of potassium is 39 times heavier than \( \frac{1}{12} \) th of the mass of carbon
\( \operatorname{atom}\left(\boldsymbol{C}^{12}\right) \)
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A force of \( (7 \hat{i}+6 \hat{k}) \) newtons makes a
body move on a rough plane with a velocity of \( (3 \hat{i}+4 \hat{k}) m s^{-1} \) The power in
watt is:
A . 24
B. 34
c. 21
D. 45


For what values of \( x \) is the rate of
increase of \( x^{3}-5 x^{2}+5 x+8 \) is twice
the rate of increase of \( x ? \)
A \( \cdot-3,-\frac{1}{3} \)
в. \( _{-3, \frac{1}{3}} \)
c. \( _{3,-\frac{1}{3}} \)
D. \( _{3, \frac{1}{3}} \)


Which class of drugs are used to relieve
stress?
A. Antihistamine
B. Antidepressant
c. Antacid
D. Disinfectant


Two skaters \( A \) and \( B \) of mass 50 kg and 70 kg respectively stand facing each other 6 metres apart. They then pull on a light rope stretched between them. How far has each moved when they meet?
A. Both have moved 3 metres
B. A moves 2.5 metres and B moves 3.5 metres.
C. A moves 3.5 metres and \( B \) moves 2.5 metres
D. A moves 2 metres and B moves 4 metres


Assertion
Liquefication of a gas is a continuous
process with increase in pressure below
\( \boldsymbol{T}_{\boldsymbol{c}} \)
Reason
Liquefication of a gas is a
discontinuous process with increase in
pressure below \( \boldsymbol{T}_{\boldsymbol{c}} \)
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Assertion
Polished iron nails do not rust when
kept immersed in a test tube
containing boil water covered with a
layer of oil.
Reason
Rust formation can be controlled with
coatings such as paint or varnish that isolate the iron from environment. When
only temporary protection is needed for
storage or transport a thin layer of oil, grease can be applied to an iron
surface
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


Solve: \( (\boldsymbol{x}-\boldsymbol{y} \ln \boldsymbol{y}+\boldsymbol{y} \ln \boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}+ \)
\( \boldsymbol{x}(\ln \boldsymbol{y}-\ln \boldsymbol{x}) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
A \( \cdot x \ln \left(\frac{y}{x}\right)-y+x \ln x+c y=0 \)
в. \( y \ln \left(\frac{x}{y}\right)-y+x \ln x+c x=0 \)
c. \( x \ln \left(\frac{x}{y}\right)-y+x \ln x+c y=0 \)
D. \( y \ln \left(\frac{y}{x}\right)-y+x \ln x+c x=0 \)


A train is moving forward at a velocity of \( 2.0 m / s . \) At the instant the train begins
to accelerate at \( 0.80 m / s^{2}, \) a passenger drops a coin which takes \( 0.50 s \) to fall
on the floor. Relative to a spot on the floor directly under the coin at release, the coin lands
A. \( 1.1 \mathrm{m} \) towards the rear of the train
B. \( 1.0 \mathrm{m} \) towards the rear of the train
c. \( 0.10 \mathrm{m} \) towards the rear of the train
D. \( 0.90 \mathrm{m} \) towards the front of the train


What is the position of an image, when an object is placed at a distance of 10cm in front of the concave mirror? The
image is virtual and double in size as
compared to the object


Short/Long answer type questions What are the chromosomal similarities
found in apes and man? What do such similarities indicate?


In a steady incompressible flow of a
İiquid.
A. The speed does not change if the area of cross-section changes
B. The speed increases if the area of cross-section increases
C. The speed decreases if the area of cross-section increases
D. Bubbles are produced when the area of the crosssection increases


Which of the following statements is
NOT true for friction force?
A. Friction force is produced when two objects rub against each other
B. A lighter object will experience a smaller frictional force
C. Friction produces more wear and tear
D. Friction is harmful


Why do third period elements expand
their coalence above four?


Which of the following statement is
false:
A. Sound and light wave exhibit interference
B. Sound and light wave exhibit diffraction
C. Light wave exhibits polarization while sound wave does not
D. Sound wave exhibits polarization while light wave does not


IUPAC name of the compound:
\( \boldsymbol{H}-\underset{\boldsymbol{O}}{\boldsymbol{C}}-\left(\boldsymbol{C H}_{2}\right)_{4} \boldsymbol{C O O H} \)
A. Hexanoic acid-5 - al-
B. 6-oxohexanoic acid
c. Hexanal-1-carboxylic acid
D. None of these


If the temperature of the sun is doubled
then the maximum emission
wavelength as compared to its initial value will be
A. \( 1 / 4 \) times
B. \( 1 / 2 \) times
c. double
D. 4 times


In Drosophila sex is determined by
A. \( x \) and \( Y \) chromosomes
B. Ratio of pairs of X-chromosomes to the pairs of autosomes
C. Ratio of number of X-chromosomes to the sets of
autosomes
D. Whether the egg is fertilized or develops parthengenetically


Assertion
A greenish layer appears on copper vessels, if left uncleaned.
Reason
It is due to the formation of a layer of basic copper carbonate.
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
Concentrated \( H_{2} S O_{4} \) reacts with \( K C l \)
to give \( C l_{2} \) gas
Reason
\( H C l \) cannot be oxidised by
concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
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


State the advantages and
disadvantages of a moving coil galvanometer. A moving coil galvanometer (M.C.G.) has
10 turns each of length \( 12 \mathrm{cm} \) and
breadth \( 8 \mathrm{cm} . \) The coil of M.C.G. carries a
current of \( 125 \mu A \) and is kept
perpendicular to the uniform magnetic field of induction \( 10^{-2} \) T. The twist
constant of phosphor bronze fibre is \( 12 \times 10^{-9} \mathrm{Nm} / \) degree. Calculate the
deflection produced.


Which atoms in \( H_{2} O \) and \( C l F \) are
negatively charged?
A. \( O \) in \( H_{2} O \) and \( C l \) in \( C I F \)
B. \( H \) in \( H_{2} O \) and \( F \) in \( C I F \)
\( \mathrm{c} \cdot O \) in \( H_{2} \mathrm{O} \) and \( F \) in \( C I F \)
D. None of the above is correct.


Length of a wire is increased by \( 1 \mathrm{mm} \) on the application of a given load. If same load is applied to another wire of same material but of length and radius twice that of the first then increase in its
length will be
\( \mathbf{A} \cdot 2 m m \)
в. \( \frac{1}{2} m m \)
\( \mathrm{c} .4 \mathrm{mm} \)
D. \( \frac{1}{4} m m \)


What is the value of \( k, \) if the line \( 2 x- \)
\( 3 y=k \) passes through the origin.
A .
B. 1
\( c \cdot 3 \)
D. -


Mosaic disease was first reported by
A. Adolf Mayer
B. Robley Williams
c. Louis Pasteur
D. None of the above


biased has a drop of \( 0.5 \% \) which is
assumed to be independent of current.
The current in excess of \( 10 m A \)
through the diode produces large joule
heating which damages the diode. If we
want to use a \( 1.5 ~ V \) battery to forward
bias the diode, the resistor used in
series with the diode so that the
maximum current does not exceed
\( 5 m A \) is
A \( .2 \times 10^{2} \Omega \)
B . \( 2 \times 10^{5} \Omega \)
C \( \cdot 2 \times 10^{3} \Omega \)
D . \( 2 \times 10^{4} \Omega \)


A disc of moment of inertia \( ^{\prime} I_{1}^{\prime} \) is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant
angular speed ' \( \omega_{1}^{\prime} \). Another disc of
moment of inertia \( ^{\prime} I_{2}^{\prime} \) having zero angular speed is placed coaxially on a rotating disc. Now both the discs are rotating with constant angular speed
\( \omega_{2}^{\prime} . \) The energy lost by the initial rotating disc is
\( ^{A} \cdot \frac{1}{2}\left[\frac{I_{1}+I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2} \)
в. \( \frac{1}{2}\left[\frac{I_{1} I_{2}}{I_{1}-I_{2}}\right] \omega_{1}^{2} \)
c. \( \frac{1}{2}\left[\frac{I_{1}-I_{2}}{I_{1} I_{2}}\right] \omega_{1}^{2} \)
D. \( \frac{1}{2}\left[\frac{I_{1} I_{2}}{I_{1}+I_{2}}\right] \omega_{1}^{2} \)


If \( (2+\sin x) \frac{d y}{d x}+(y+1) \cos x=0 \) and
\( y(0)=1, \) then \( y=\left(\frac{\pi}{2}\right) \) is equal to
A \( \cdot \frac{1}{3} \)
B. \( -\frac{2}{3} \)
\( c \cdot-\frac{1}{3} \)
D.


Match the columns and choose the
correct option.
II 70-75 action
potential per
minute
Ventricular
repolarisation and \begin{tabular}{c|c|c|c}
& 1 & \\
(i) & Stroke volume & (a) & II 70-75 potent minute \\
(ii) & Cardiac output & (b) & Ventric repolar \\
(iii) & SAN & (c) & 70 ml of cardiac \\
(iv) & P-wave & (d) & 5000 ml per cardi \\
(v) & T-wave & (e) & Atrial depolaris \\
& &
\end{tabular} er 70 ml of blood per
cardiac cycle and \( - \)
O ml of blood
cardiac cycle oyor an
1 depolarisation
\( A \cdot \) i-d, ii-c, iii-a, iv-b, v-e
B. i-a, ii-e, iii-c, iv-d, v-b
C. i-c, ii-d, iii-a, iv-e, v-b
D. i-c, ii-a, iii-d, iv-e, v-b
E. \( i-d, \) ii-a, ii \( -b, \) iv-e, v-


Which of the following is the other name of a cube?
A. Tetrahedron
B. Regular hexahedron
c. Square antiprism
D. cuboctanedron


Which of these is not a macromolecule?
A . Cellulose
B. DNA
c. Glycogen
D. None of the above


Calculate the wavelength of an electron
moving with a velocity of \( 2.05 \times \) \( 10^{7} m s^{-1} \)


Solid fuels among the following are
A . coal
B. coke
c. cow dung
D. All


Using properties of determinants, show that triangle \( A B C \) is isosceles, if :
\( \mid \begin{array}{ccc}\mathbf{1} & \mathbf{1} \\ \mathbf{1}+\cos \boldsymbol{A} & \mathbf{1}+\cos \boldsymbol{B} & \mathbf{1} \\ \cos ^{2} \boldsymbol{A}+\cos \boldsymbol{A} & \cos ^{2} \boldsymbol{B}+\cos \boldsymbol{B} & \mathbf{c o s}^{2}\end{array} \)
0


\( \int_{0}^{2 \pi} \cos m x \cdot \sin n x d x \) where \( m, n \) are
integers \( = \)
\( A \cdot O \)
B . \( \pi \)
\( \mathbf{c} \cdot \pi / 2 \)
D. \( 2 \pi \)


Let \( p(x) \) be the fifth degree polynomial
such that \( p(x)+1 \) is divisible by
\( (x-1) \) and \( p(x)-1 \) is divisible by
\( (x+1) . \) Then find the value of
\( \int_{-10}^{10} p(x) d x \)


Find the number of permutations which can be formed out of the letters of the
word series taken three together?
\( A \cdot 32 \)
B. 36
c. 42
D. 46


Select the correct reduction process:
This question has multiple correct options
\( \mathbf{A} \cdot 2\left[A g(C N)_{2}\right]^{-}+Z n \longrightarrow\left[Z n(C N)_{4}\right]^{2-}+2 A g \)
\( \mathbf{B} \cdot C u O+H_{2} \longrightarrow C u+H_{2} O \)
\( \mathbf{c} \cdot A l_{2} O_{3}+3 Z n \longrightarrow 2 A l+3 Z n O \)
D. \( M g O+C \frac{\text {high}}{\text {temp}} M g+C O \)


The dissolution of ozone layer cause
ozone hole in the blanket surrounding the atmosphere. What the ill effects of ozone hole?
A. Greenhouse effect
B. Global warming
c. Acid rain
D. UV rays reaching the earth.


Use Euclid's division algorithm to find
the \( H C F \) of 210 and 55


Longitudinal strain can be produced in :
A. glass
B. water
c. honey
D. hydrogen gas


Saccharin, an artificial sweetner is
manufactured from:
A . cellulose
B. toluene
c. cyclohexane
D. starch


Assertion
Phylogeny is the developmental history
of a species.
Reason
Species is the basic unit of taxonomy.
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 transformer steps up an AC supply from \( 220 \mathrm{V} \) to \( 2200 \mathrm{V} \). If the secondary coil of the transformer has 2000 turns,
the number of turns in its primary coil will be :
A . 200
B. 100
\( c .50 \)
D. 20