A circular disc \( A \) of a radius \( r \) is made
from an iron plate of a thickness \( t \) and
another circular disc \( B \) of radius \( 4 r \) is made from an iron plate of thickness \( \frac{t}{4} \) The relation between the moments of
inertia \( I_{A} \) and \( I_{B} \) is
\( A \cdot I_{A}>I_{B} \)
B \( . I_{A}=I_{B} \)
\( \mathrm{c} \cdot I_{A}<I_{B} \)
D. depends on the actual value of \( t \) and \( r \)


Benzene reacts with chlorine in sunlight
to give a final product:
A. \( C C l_{4} \)
B \( . C_{6} H_{6} C l_{6} \)
\( \mathbf{c} \cdot C_{6} C l_{6} \)
D. \( C_{6} H_{5} C l \)


Write a linear equation representing a line which is parallel to y-axis and it is at a distance of 2 units on the left side
of y-axis.


Express the following in the form of a =
ib, \( a, b \in R i=\sqrt{-1} . \) State the values of \( a \)
and b.
\( (1+i)(1-i)^{-1} \)


If \( \left|\begin{array}{lll}a & a^{3} & a^{4}-1 \\ b & b^{3} & b^{4}-1 \\ c & c^{3} & c^{4}-1\end{array}\right|=0 \) and \( a, b, c \) are all
distinct then \( a b c(a b+b c+c a) \) is equal
to
A \( . a+b+c \)
в. \( a b c \)
c. 0
D. none of these


Which metal can react with hydrogen?
A. Na and Ca
в. мв
\( c . k \)
D. All of these


If the liquid in a U-tube rises to high level in the limb placed between poles of an electromagnet, then the liquid is:
A. non-magnetic
B. diamagnetic
c. paramagnetic
D. ferromagnetic


Show that vectors \( 2 \hat{i}-\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k} \)
and \( 3 \hat{i}-4 \hat{j}-4 \hat{k} \) form the vertices of
the triangle.


In the circuit below, the potential
difference between \( A \) and \( B \) is
\( \mathbf{A} \cdot 10 V \)
\( \mathbf{B} \cdot 20 V \)
\( \mathbf{c} .30 V \)
D. \( 40 V \)


In a hydrocarbon, \( C \) is \( 3 g \) per \( g \) of
hydrogen. Hence, the hydrocarbon is :
A \( \cdot C H_{4} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{4} H_{10} \)


Show that \( \left|\begin{array}{lll}\boldsymbol{b} \boldsymbol{c} & \boldsymbol{b}+\boldsymbol{c} & \mathbf{1} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c}+\boldsymbol{a} & \mathbf{1} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b} & \mathbf{1}\end{array}\right|= \)
\( (\boldsymbol{a}-\boldsymbol{b})(\boldsymbol{b}-\boldsymbol{c})(\boldsymbol{c}-\boldsymbol{a}) \)


A very thin film in reflected white light
appears
A . coloured
B. white
c. black
D. red


Five identical plates are connected
across a battery as shown. If the charge
on plate 1 be \( +q, \) then the charges on the plates 2,3,4 and 5 are:
\( \mathbf{A} \cdot-q,+q,-q,+q \)
в. \( -2 q,+2 q,-2 q,+q \)
c. \( -q,+2 q,-2 q,+q \)
D. none of the above


Salinity of the soil is often caused due
to
A. Accumulation of soluble minerals near or in the surface in arid region
B. Excessive addition of water
C. Rapid evaporation of surface water
D. Excessive leaching


In the propagation of light waves, the angle between the plane of vibration \( \& \) plane of polarisation is:
A \( \cdot 0^{\circ} \)
B. \( 90^{\circ} \)
c. \( 45^{\circ} \)
D. \( 80^{\circ} \)


The diagram shows the cross section of six identical marbles touching each other on a horizontal surface. f the volume of a mabrle is \( \frac{9 \pi}{2} c m^{3} \) calculate the length of \( \mathrm{PQ} \), in \( \mathrm{cm} \).
\( A \)
в. 2
\( c \cdot 18 \)
0.22


When a lens of refractive index \( n_{1} \)
is placed in a liquid of refractive index
\( n_{2}, \) the lens looks to be disappeared
only, if
A \( \cdot n_{1}=n_{2} / 2 \)
в. \( n_{1}=3 n_{2} / 4 \)
c. \( n_{1}=n_{2} \)
D. \( n_{1}=5 n_{2} / 4 \)


Three blocks, each of same mass \( m \)
are connected with wire \( W_{1} \) and \( W_{2} \) of
same cross sectional area 'a' and

Young's modulus Y. Neglecting friction,
the strain developed in wire \( W_{2} \) is
A \( \frac{2 m g}{3} \frac{m g}{a Y} \)
в. \( \frac{3}{2} \frac{m g}{a Y} \)
\( c \)
\( D \)


Select the wrong statement.
A. Forest provide variety of products.
B. Forest have great plant diversity.
C. Forest does not conserve soil.
D. Forest conserves water.


Two components of ecosystem are
A. Plants and animalss
B. Trees and fungi
c. Living and non living
D. Frogs and man


In the figure, if \( \angle B O C=7 x+20^{\circ} \) and
\( \angle C O A=3 x, \) then the value of \( x \) for
which \( A O B \) becomes a straight line is:
\( 4 \cdot 16^{\circ} \)
B. 14
\( c \cdot 20 \)
D. \( 21^{\circ} \)


What is IUPAC name of
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{5} \boldsymbol{N} \boldsymbol{O}\right] ? \)


The probability of an event that cannot happen is \( _{--}-_{-} ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


By using the properties of definite integrals, evaluate the integral \( \int_{0}^{1} x(1-x)^{n} d x \)


What is the molecular formula of
Oleum?
A. \( H_{2} S O_{3} \)
в. \( H_{2} S O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
D. \( H_{2} S_{2} O_{8} \)


One of the major constituents of baking powder is sodium hydrogen carbonate, the other constituent is:
A. hydrochloric acid
B. tartaric acid
c. acetic acid
D. sulphuric acid


Give reasons for the following
Arteries have thick walls.


Solve \( \int\left(4 e^{3 x}+1\right) d x \)


If the inductance \( L \) in an oscillating \( L C \) circuit having a given maximum charge \( Q \) is increased, then
A. the current magnitude increases
B. the maximum magnetic energy increases
c. othere maximum magnetic energy decreases
D. currentt magnitude and maximum magnetic energy remain constant


A sphere is placed in an inverted hollow conical vessel of base radius \( 5 \mathrm{cm} \) and
vertical height \( 12 \mathrm{cm} . \) If the highest point of the sphere is at the level of the
base of the cone; find the radius of the
sphere. Also find the ratio of the volume
of the sphere to that of the cone.


Show that the line of intersection of the
planes
\( \bar{r} \cdot(\hat{i}+3 \hat{j}-2 \hat{k})=0 \) and
\( \bar{r} \cdot(2 \hat{i}+4 \hat{j}-3 \hat{k})=0 \) is equally incline
to \( \hat{i} \) and \( \hat{j} \). Also find the angle it make with \( \hat{k} ? \)


\( \int \frac{1}{x \sqrt{x^{2}-1}} d x \) is equal to
\( \mathbf{A} \cdot \cos ^{-1} x+C \)
B . \( \sec ^{-1} x+C \)
\( \mathbf{c} \cdot \cot ^{-1} x+C \)
D. \( \tan ^{-1} x+C \)


If a line makes angles \( 90^{0}, 135^{0}, 45^{0} \)
with \( X, Y \) and \( Z \) axes respectively, then find its direction cosines.


Common between sclerenchyma and collenchyma is
A. Material transport
B. Conduction of water and minerals
C. Providing buoyancy
D. Providing support


The mole fraction of a solute in a
solution is \( 0.1 . \) At \( 298 \mathrm{K} \), molarity of this solution is the same as its molality Density of this solution at \( 298 K \) is
\( 2.0 g \mathrm{cm}^{-3} . \) The ratio of the molecular
weights of the solute and solvent, \( \left(\frac{M W_{\text {solute}}}{M W_{\text {solvent}}}\right) \) is:


Which of the following changes at an antinode in a stationary wave?
A. Density only
B. Pressure only
C. Both pressure and density
D. Niether pressure nor density


The sum of first 20 terms of the series
\( 1,6,13,22- \) is
A . 5580
B. 5780
\( c .7789 \)
D. 1237


For protecting a sensitive equipment from external magnetic field, it should
be
A. placed inside an iron can
B. placed inside an aluminium can
c. surrounded with fine copper sheet
D. wrapped with insulation around it when passing current through it


All four charges in figure have the same magnitude. At point P,the electric field produced by these charge is directed toward the left. Charge \( q_{1} \) is negative.
What are the signs of \( \boldsymbol{q}_{2}, \boldsymbol{q}_{3}, \boldsymbol{q}_{4} ? \)


A parallel plate capacitor has a
dielectric (of dielectric constant \( k \) )
between the plates. The plates are
charged to a surface charge density \( \sigma_{0} \) What is the density of the polarized charge that appear on the surface of the dielectric.


If \( V_{0} \) be the potential at origin in an electric field \( \overrightarrow{\boldsymbol{E}}=\boldsymbol{E}_{\boldsymbol{x}} \hat{\boldsymbol{j}}+\boldsymbol{E}_{\boldsymbol{y}} \hat{\boldsymbol{j}}, \) then the
potential at point \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) is
\( \mathbf{A} \cdot V_{0}+x E_{x}+y E_{y} \)
B. \( V_{0}+x E_{x}-y E_{y} \)
C \( . V_{0}-x E_{x}-y E_{y} \)
D. \( \sqrt{\left(x^{2}+y^{2}\right)} \sqrt{E_{x}^{2}+E_{y}^{2}}-V_{0} \)


How much heat is evolved if 3.2 g of methane is burnt and if the heat of
combustion of methane is \( -880 \mathrm{kJ} \)
\( m o l^{-1} ? \)
\( A \cdot 88 \mathrm{kJ} \)
B. 264 kJ
c. 176 kJ
D. 440 kJ


Direction ratio of line given by \( \frac{x-1}{3}= \) \( \frac{6-2 y}{10}=\frac{1-z}{-7} \) are:
\( A \cdot<3,10,-7> \)
в. \( <3,-5,7> \)
c. \( <3,5,7> \)
D. \( <3,5,-7> \)


Which of the following cells can be used to experimentally determine the reduction potential of Zinc?
A \( \cdot Z n(s)\left|Z n^{2+}(a q)\right|\left|H^{+}(a q)\right| H_{2}(g), P t \)
B . \( P t, H_{2}(g)\left|H^{+}(a q)\right||Z n(s)| Z n^{2+}(a q) \)
c. \( Z n(s)\left|Z n^{2+}(a q)\right|\left|C u^{2+}(a q)\right| C u(s) \)
D. any one of these


Find the smallest number by which 128
must be divided so that the result is a
perfect cube.


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


Predict if there will be any precipitate by mixing \( 50 \mathrm{mL} \) of \( 0.01 \mathrm{M} \) NaCl and 50
mL of \( 0.01 \mathrm{M} A g N O_{3} \) solution. The
solubility product of \( A g C l \) is \( 1.5 \times \)
\( 10^{-10} \)
A. since ionic product is greater than solubility product no precipitate will be formed
B. since ionic product is lesser than solubility product. precipitation will occur
c. since ionic product is greater than solubility product. precipitation will occur.
D. since ionic product and solubility product are same, precipitation will not occur


The correct statement(s) about \( \boldsymbol{O}_{3} \)
is(are):
This question has multiple correct options
A. 0 -o bond lengths are equal
B. thermal decomposition of \( O_{3} \) is endothermic
\( \mathrm{c} \cdot O_{3} \) is diamagnetic in nature
\( \mathrm{D} \cdot O_{3} \) has a bent structure


The atomic number of non transition
element of \( 6 \mathrm{d} \) series of \( ^{\prime} d^{\prime} \) block
elements
A . 112
B. 111
\( c .110 \)
D. 80


A proton of mass \( m \) charge \( e \) is released from rest in a uniform electric field of
strength \( E . \) The time taken by it to travel a distance \( d \) in the field is :
A \( \cdot \sqrt{\frac{2 d e}{m E}} \)
в. \( \sqrt{\frac{2 d m}{E e}} \)
c. \( \sqrt{\frac{2 d E}{m e}} \)
D. \( \sqrt{\frac{2 E e}{d m}} \)


Which of the following is a true solution?
A. Copper in gold
B. Sulphur in water
c. мilk
D. water in sulphur dioxide


Phenol and benzyl alcohol are:
A. functional isomers
B. homologous
c. position isomers
D. none of these


Study given chart and select the option
which incorrectly identifies any of the
animals, \( P, Q, R \) and \( S \)
A. P is Aurelia and Q is Ascaris
B. Q is Ascaris and R is Nereis
C. \( R \) is Ascaris and \( S \) is Cockroach
D. S is Periplaneta and P is Spongilla


What is the source of energy associated with the current obtained in part when a
magnet is moved towards a coil having a galvanometer at its ends?


The focal length of a mirror is given by \( \frac{1}{v}-\frac{1}{u}=\frac{2}{f} . \) If equal errors \( (\alpha) \) are
made in measuring \( u \) and \( v \), then the
relative error in \( \boldsymbol{f} \) is
A \( \cdot \frac{2}{\alpha} \)
B \( \cdot \alpha\left(\frac{1}{u}+\frac{1}{v}\right) \)
\( ^{c} \cdot \alpha\left(\frac{1}{u}-\frac{1}{v}\right) \)
D. none of these


Phytochrome is found in
A. Fungi
B. Algae
c. Pteridophytes
D. Angiosperms


For which of the following reaction, will
\( \triangle \mathrm{H} \) be equal to \( \triangle \mathrm{E} ? \)
\( \mathbf{A} \cdot H_{2}(g)+\frac{1}{2} O_{2}(g) \rightarrow H_{2} O(l) \)
B . \( H_{2}(g)+I_{2}(g) \rightarrow 2 H I(g) \)
\( \mathbf{c} \cdot 2 N O_{2}(g) \rightarrow N_{2} O_{4}(g) \)
D \( \cdot 2 \operatorname{SO}_{3}(g) \rightarrow 2 \operatorname{SO}_{2}(g)+O_{2}(g) \)


Metals are usually hard. Hence metals are strong and can withstand heavy loads over them. Due to this property,
they are difficult to cut and can be used
in the construction of heavy machines, building etc. On the other hand, non-metals are usually brittle. On hammering them they break into small pieces converting themselves into a fine powder.
In the following elements identify the elements that is relatively brittle?
A. Sulphur
B. Diamond
c. Iron
D. Magnesium


\( S_{1}: \) In an elastic collision initial and
final K.E. of system will be same.
\( S_{2}: \) In a pure \( L-C \) Circuit average
energy stored in capacitor is zero. \( S_{3}: \ln Y D S E \) coherent sources are formed by division of wave front method
\( S_{4}: \) If a physical Quantity is quantized then it must be integral multiple of it's lowest value.
A . FFTF
в. \( T T F T \)
c. \( F T F T \)
D. \( T F T F \)


Which statement regarding significant
figures is false?
A. Zeros can be significant
B. When multiplying, the answer is determined by the number of significant figures
C. When adding, the answer is determined by the number of decimal places
D. When dividing, the answer is determined by the number of decimal places
E. The number 50,004 has five significant figures


If \( D_{p}=\left|\begin{array}{ccc}\boldsymbol{p} & \mathbf{1 5} & \mathbf{8} \\ \boldsymbol{p}^{2} & \mathbf{3 5} & \mathbf{9} \\ \boldsymbol{p}^{\mathbf{3}} & \mathbf{2 5} & \mathbf{1 0}\end{array}\right|, \) then \( \boldsymbol{D}_{1}+\boldsymbol{D}_{2}+ \)
\( D_{3}+D_{4}+D_{5} \) is equal to
A .
B. 25
c. 625
D. none of these


Assertion
Physical adsorption increases with increase in temperature.
Reason
Physical adsorption is an endothermic
process.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which part of the curve shown in fig
represents the postitive resistane?
This question has multiple correct options
\( \mathbf{A} \cdot A B \)
B. \( B C \)
\( \mathbf{c} \cdot C D \)
\( \mathbf{D} \cdot D E \)


classify the following as addition and condensation polymers:
Terylene, Bakelite, Polyvinyl chloride,Polythene


In solid state N205 exits as:
\( \mathbf{A} \cdot[N O 3]^{-}[N O 2]^{+} \)
в. \( [N O 2]^{-}[N O 3]^{+} \)
c. \( [N 2 O 4]^{+} O^{-} \)
D. \( [N O 3][N O 2] \)


A particle of mass \( M \) and charge \( Q \)
moving with velocity \( \vec{v} \) describe a
circular path of radius \( R \) when subjected to a uniform transverse
magnetic field of induction \( \boldsymbol{B} \). The work
done by the field when the particle completes one full circle is:
\( ^{\mathbf{A}} \cdot\left(\frac{M v^{2}}{R}\right)^{2 \pi R} \)
B. zero
с. \( B Q 2 \pi R \)
D. \( B Q v 2 \pi R \)


Podocytes are the cells, present in
A. Cortex of nephron
B. Inner wall of Bowman's capsule
C. Outer wall of Bowman's capsule
D. Well of glomerular capilaries


The two vectors \( \left(x^{2}-1\right) \hat{i}+(x+2) \hat{j}+ \)
\( x^{2} \hat{k} \& 2 \hat{i}-x \hat{j}+3 \hat{k} \) are orthogonal
A. For no real value of \( x \)
B. For \( x=-1 \)
\( \mathrm{c} \cdot \operatorname{For} x=\frac{1}{2} \)
D. For \( x=-\frac{1}{2} \& x=1 \)


Which nomenclature system is employed for naming plants?
A. Vernacular
B. Binomial
c. Mononomial
D. Polynimial


The molecular formula of a methyl
group is:
A \( \cdot C H_{4} \)
в. \( C H_{3} \)
c. \( C H \)
D. \( C H_{2} \)


Animals like camels walk easily in desert as broad feet exert less pressure
on sandy ground.
A. True
B. False


Which of the following cells in earthworm play a role similar to liver in vertebrates?
A. Amoebocytes
B. Mucocytes
c. chloragogen cells
D. Epidermal cells


A body of mass \( m \) slides down an incline and reaches the bottom with a
velocity \( v \). If the same mass was in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been:
\( A \)
B . \( (\sqrt{2}) v \)
c. \( \frac{v}{\sqrt{2}} \)
D. \( (\sqrt{\frac{2}{5}}) \)


q.1 A block is released from rest from a height \( h=5 \) m. After traveling through the smooth curved surface it moves on
the rough horizontal surface through
length \( I=8 \mathrm{m} \) and climb onto the other
smooth curved surface through a height
h. If \( \mu=0.5, \) find \( h \)
\( A \cdot 2 m \)
в. 3
\( c \cdot 1 m \)
D. zero


Organismal theory was proposed by
A. Van Mohl
B. sachs.
c. Virchow.
D. Haberlandt


Two roads cross at right angles at \( O \)
One person \( A \) walking along one of the
roads at \( 3 m s^{-1} \) sees another person \( B \)
walking at \( 4 m s^{-1} \) along the other road at \( O, \) when he is 10 m off. The
nearest distance between the two
persons is
A . \( 10 m \)
в. \( 9 m \)
\( c .8 m \)
D. \( 7.2 m \)


The radio active isotope of hydrogen is


Which have correct order of dipole
moment?
A. \( S O_{2}>H_{2} O \)
В. \( N F_{3}>N H_{3} \)
c. \( B F_{3}<N H_{3} \)
D. \( S O_{2}<S O_{3} \)


If \( P(A)=0, \) then the event \( A \)
A. Will never happen
B. Will always happen
c. May happen
D. May not happen


A body of mass \( 0.2 \mathrm{kg} \) falls from a height of \( 10 \mathrm{m} \) to a height of \( 6 \mathrm{m} \) above the ground. Find the loss in potential energy taking place in the body. \( [\boldsymbol{g}= \)
\( \left.10 m s^{-2}\right] \)


Consider the determinant \( \Delta= \) \( \left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3}\end{array}\right| \)
\( M_{i j}= \) Minor of the element of \( i^{t h} \) row \( \& \) \( j^{t h} \) column \( C_{i j}= \) Cofactor of element of \( i^{t h} \) row \( \& \) \( j^{t h} \) column
\( a_{2} \cdot C_{12}+b_{2} \cdot C_{22}+c_{2} \cdot C_{32} \) is equal to
A.
B. \( \Delta \)
\( c \cdot 2 \Delta \)
D. \( \Delta^{2} \)


The half-life of a certain radioactive
isotopes is \( 32 h . \) What fraction of a
sample would remain after \( 16 h ? \)
A . 0.25
в. 0.71
c. 0.29
D. 0.75


If \( z_{1} \) and \( z_{2} \) are two non zero complex
numbers such that \( \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+ \)
\( \left|z_{2}\right| \) then \( \arg z_{1}-\arg z_{2} \) is equal to
A. \( -\pi \)
в. \( \frac{\pi}{2} \)
\( c \cdot-\frac{\pi}{2} \)
D.


When a rubber cord is stretched, the change in volume is negligible compared to the change in its linear dimension. Then poisson's ratio for rubber is
A . infinite
B. zero
\( c \cdot 0.5 \)
D. -


What is the use of ATP binding site?


\( \mathrm{f}[\mathbf{2} \mathbf{1} \mathbf{3}]\left[\begin{array}{ccc}-\mathbf{1} & \mathbf{0} & \mathbf{1} \\ -\mathbf{1} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1} & \mathbf{1}\end{array}\right]\left[\begin{array}{l}\mathbf{1} \\ \mathbf{0} \\ \mathbf{1}\end{array}\right]=\boldsymbol{A}, \) then
write the order of matrix \( \boldsymbol{A} \)


The developing embryo in Hydra drops down from the body of the parent
A. soon after the formation of zygote
B. after the formation of blastula
c. after the formation of stereo gastrula
D. only after it has developed into a young Hydra


State work energy theorem. Plot spring
force \( F \) versus \( x \) and obtain the
expression for elastic potential energy of spring.


What is the shape of a current-carrying conductor whose magnetic field pattern
resembles that of a bar magnet?
A. circular loop
B. straight
c. U-shaped
D. solenoid


Explain Krichhoff's laws with examples.


\( \mid f \hat{i}+\hat{j}+\hat{k}, 2 \hat{i}+5 \hat{j}, 3 \hat{i}+2 \hat{j}-3 \hat{k} \) and
\( \hat{\mathbf{i}}-\mathbf{6} \hat{\mathbf{j}}-\hat{\boldsymbol{k}} \) are the position vectors of
points \( A, B, C \) and \( D \) respectively, then find the angle between \( \overrightarrow{A B} \) and \( \overrightarrow{C D} \)


The ratio of the angular speed of
minutes hand and hour hand of a watch
is:
A . 6: 1
B. 12: 1
c. 1: 6
D. 1: 12


The most thermodynamically stable allotropic form of phosphorus is
A . red
B. white
c. black
D. yellow


An electric bulb consumes \( 7.2 k J \) of
electrical energy in 2min. What is the power of the electric bulb?


\( E_{O_{3} \mid O_{2}}^{0} \) (acidic medium) \( =2.07 \mathrm{V} \)
\( E_{O_{3} \mid O_{2}}^{0} \) (basic medium) \( =1.24 \mathrm{V} \)
\( E_{H_{2}}^{0} o_{2} \mid H_{2} O \) (acidic medium) \( =1.78 \mathrm{V} \)
\( E_{O_{2} \mid H_{2}}^{0} O_{2}(\text { acidic medium })=0.695 \mathrm{V} \)
\( E_{O_{2} \mid H_{2}}^{0},_{\Omega_{2}} \) (basic medium) \( =0.076 \mathrm{V} \)
\( E_{H O_{2}^{-} \mid O H^{-}}^{0}(\text { basic medium })=0.878 \mathrm{V} \)
Using the above data, find which of the following is incorrect?
A. Ozone is a better oxidising agent than \( H_{2} O_{2} \) in both acidic and basic medium.
B. \( H_{2} O_{2} \) is better oxidising agent in acidic medium than in basic medium.
C. \( H_{2} O_{2} \) is better reducing agent in basic medium than in acidic medium.
D. In basic medium \( H_{2} O_{2} \) reduces all \( O_{3} \) to \( O_{2} \) completely.


The graph below shows the atomic radii
of atoms in picometers \( (\mathrm{pm}) \) as a function of atomic number.
Which letter on this graph most closely
shows the location of the transition
metals of period 5?

Atomic Radius vs. Atomic Number
A. Region E
B. Region D
c. Region \( c \)
D. Region B


Solve the following systems of
inequalities graphically: \( \boldsymbol{x}+\boldsymbol{y} \leq \)
\( \mathbf{9}, \boldsymbol{y}>\boldsymbol{x}, \boldsymbol{x} \geq \mathbf{1} \)


State which of the following are not the
probability distributions of a random
variable. Give reasons for your answer.
\( (i) \)
\begin{tabular}{|c|l|l|l|}
\hline \( \mathrm{X} \) & 0 & 1 & 2 \\
\hline \( \mathrm{P}(\mathrm{X}) \) & 0.4 & 0.4 & 0.2 \\
\hline
\end{tabular}
(ii) \begin{tabular}{|c|l|l|l|c|l|}
\hline \( \mathrm{X} \) & 0 & 1 & 2 & 3 & 4 \\
\hline \( \mathrm{P}(\mathrm{X}) \) & 0.1 & 0.5 & 0.2 & -0.1 & 0.3 \\
\hline
\end{tabular}
(iii) \begin{tabular}{|c|r|l|l|}
\hline \( \mathrm{Y} \) & -1 & 0 & 1 \\
\hline \( \mathrm{P}(\mathrm{Y}) \) & 0.6 & 0.1 & 0.2 \\
\hline
\end{tabular}
(iv) \begin{tabular}{|c|l|l|l|l|l|}
\hline \( \mathrm{Z} \) & 3 & 2 & 1 & 0 & -1 \\
\hline \( \mathrm{P}(\mathrm{Z}) \) & 0.3 & 0.2 & 0.4 & 0.1 & 0.05 \\
\hline
\end{tabular}


Three stars each of mass \( \mathrm{M} \) and radius
\( \mathrm{R} \) are initially at rest and the distance between centres of any two stars is d
and they form an equilateral triangle. They start moving towards the centroid
due to mutual force of attraction. What
are the velocities of the stars just before the collision?
Radius of each star is \( \mathrm{R} \).


The excess pressure in soap bubble
is \( 10 \mathrm{N} / \mathrm{m}^{2} \). If eight soap bubbles are combined to form a big soap bubble, then the excess pressure in big bubble is :
A. \( 5 \mathrm{N} / \mathrm{m}^{2} \)
B. \( 10 \mathrm{N} / \mathrm{m}^{2} \)
c. \( 20 \mathrm{N} / \mathrm{m}^{2} \)
D. 2.5 N / m^


A quantity which expresses a part of the whole is called a/an
A. Fraction
B. Prime number
c. Integer
D. None of these


The bacteriostatic antibiotic is:
A . tetracycline
B. aminoglycosides
C. penicillin
D. ofloxacin


Consider the following reaction. \( o^{16} \)
\( \boldsymbol{C H}_{3}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}^{18}-\boldsymbol{C}_{2} \boldsymbol{H}_{5}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}^{16} \frac{\boldsymbol{H} \boldsymbol{e} \boldsymbol{a} \boldsymbol{t}}{\boldsymbol{H}^{+}} \)
The products formed in the reaction are:
\( A \)
\( C H_{3}-\stackrel{\vartheta^{16}}{C}-O^{16} H \) and \( C_{2} H_{5} O^{18} H \)
В.
\[
C H_{3}-C^{\mid 6}-O^{18} H \text { and } C_{2} H_{5} O^{16} H
\]
\( c \)
\( C H_{3}-\stackrel{\vartheta^{16}}{C}-O^{16} H \) and \( C_{2} H_{5} O^{16} H \)
D. \( C H_{3}-\stackrel{\vartheta_{1}^{\prime 8}}{C}-O^{18} H \) and \( C_{2} H_{5} O^{18} H \)


A man standing on the edge of the terrace of a high rise building throws a stone, vertically up with a speed of 20
\( \mathrm{m} / \mathrm{s} . \) Two seconds later, an identical stone is thrown vertically downwards with the same speed of \( 20 \mathrm{m} / \mathrm{s} \). Then :
This question has multiple correct options
A. the relative velocity between the two stones remains constant till one hits the ground
B. both will have the same kinetic energy, when they hitt the ground
c. the time interval between their hitting the ground is 2 s
D. if the collision on the ground is perfectly elastic, both will rise to the same height above the ground


A mixture of \( N H_{4} C l \) and \( N a C l \) can be
separated by
A. filtration
B. Distillation
c. Sublimation
D. Decantation


In the human circulation, the Iymph
A. Transports oxygen to brain
B. Transports \( C O_{2} \) to lungs
C. Returns interstitial fluid back to heart
D. Contains RBCs, leucocyte, and more protein as compared to blood


Assertion
Under conditions of high light intensity
and limited \( C O_{2} \) supply,
photorespiration has a useful role in
protecting the plants from photooxidative damage.
Reason
If enough \( C O_{2} \) is not available to utilize
light energy for carboxylation to proceed, the excess energy may not cause damage to plants.
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


Membrane surrounding the heart is
A. Peritoneum
B. Visceral membrane
c. Pericardium
D. None of the above


Variation of resistance of the conductor
with temperature is as shown

The temperature co-efficient \( (\alpha) \) of the
conductor is
\( A \cdot \frac{R_{0}}{m} \)
В \( \cdot m R_{o} \)
\( \mathbf{c} \cdot m^{2} R_{o} \)
D. \( \frac{m}{R_{n}} \)


Which of the following metals are present in Devarda alloy?

This question has multiple correct options
A. \( C u \)
в. \( A l \)
\( c \cdot Z n \)
D. \( A g \)


The length of latus rectum of the
hyperbola \( \boldsymbol{x} \boldsymbol{y}-\mathbf{3} \boldsymbol{x}-\mathbf{3} \boldsymbol{y}+\mathbf{7}=\mathbf{0} \) is
A .4
B. 3
\( c \cdot 2 \)
D.


Which of the following is paramagnetic
A. Rhombic \( S_{8} \)
B. Rhombic \( S_{6} \)
C. vapour \( S_{2} \)
D. None of these


\( 20 g \) of ice and \( 20 g \) of hot water are
mixed, when the ice is melted the
temperature of the mixture was found
to be \( 0^{\circ} \mathrm{C} \). The temperature of hot water taken should be
\( \left(L_{i c e}=80 \mathrm{cal} / \mathrm{g}\right) \)
A \( \cdot 40^{\circ} \mathrm{C} \)
B . \( 72^{0} C \)
\( \mathbf{c} \cdot 80^{\circ} C \)
D. \( 96^{\circ} C \)


Find the slope of the line passing through the points \( A(2,3) \) and \( B(4,7) \)


The power of a lens is -5 D. Find its focal
length.


A ball is thrown vertically upwards (relative to the train) in a compartment
of a moving train. The face of the person sitting inside the compartment is towards engine of the train.
This question has multiple correct options
A. The ball will maintain the same horizontal velocity as that of the person (or the compartment) at the time of throwing.
B. If the train is accelerating then the horizontal velocity of the ball will be different from that of the train velocity, at the time of throwing.
C. If the ball appears to be moving backward to the person sitting in the compartment it means that speed of the train is increasing
D. If the ball appears to be moving ahead of the person sitting in the compartment it means the train's motion is retarding.


A chemical reaction occurs as a result
of collisions between reacting molecules. Therefore, the reaction rate
is given by:
This question has multiple correct options
A. total number of collision occuring in a unit volume per second
B. fraction of molecules which possess energy less than the threshold energy
c. total number of effective collisions
D. none of the above


Describe Bohrs model of the atom


If \( z_{1} \) and \( z_{2} \) are two complex numbers
such that \( \left|z_{1}\right|=\left|z_{2}\right| \) and \( \arg \left(z_{1}\right)+ \)
\( \operatorname{rag}\left(z_{2}\right)=\pi, \) then show that \( z_{1}=-\bar{z}_{2} \)


Derive an expression for magnetic field strength at any point on the axis of a circular current carrying loop using Biot-Savart's law.


Expand \( \sin (A+B) \)


The shape selective catalysts depend
upon pore sizes.
A. True
B. False


Let \( \boldsymbol{U} \) be the universal set and \( \boldsymbol{A} \cup \boldsymbol{B} \cup \)
\( C=U . \) Then
\( \{(\boldsymbol{A}-\boldsymbol{B}) \cup(\boldsymbol{B}-\boldsymbol{C}) \cup(\boldsymbol{C}-\boldsymbol{A})\}^{\prime} \) is
equal to
A. \( A \cup B \cup C \)
в. \( A \cup(B \cap C) \)
c. \( A \cap B \cap C \)
D. \( A \cap(B \cup C) \)


Vibrating bodies produce
A. Sound
в. Heat
c. Light
D. None of these


Which one of the following pairs of hormones are the examples of those that can easily pass through the cell membrane of the target cell and bind to a receptor inside it(mostly in nucleus)?
A. Insulin, glucagon
B. Thyroxine, insulin
c. Somatostatin, oxytocin
D. cortisol, testosterone


Which of the following compounds does not give nitrogen on heating?
A. \( N a N_{3} \)
B \( \cdot\left(N H_{4}\right)_{2} S O_{4} \)
c. \( N H_{4} N O_{2} \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)


toppr \( E \)
Q Type your question
that applies a force \( \boldsymbol{F}=-\boldsymbol{k v}, \) where \( ^{\prime} \boldsymbol{k}^{\prime} \)
is a constant, on the body? (Graphs are
schematic and not drawn to scale)
\( A \)
B.
\( c \)
\( D \)


The slope of the line, \( l_{2} \) is 5 and \( l_{1} \) and \( l_{2} \)
are parallel. Find the slope of \( l_{1} \)
A . -
B. 5
\( c \)
D. -


Yellow light is used in a single slit diffraction experiment with a slit of
width \( 0.6 m m . \) If yellow light is replaced
by \( \boldsymbol{X}- \) rays, then the observed pattern will reveal:
A. more number of fringes
B. less number of fringes
c. no diffraction pattern
D. that the central maximum is narrower


Which gas has the largest molecular
volume?
A. \( A \)
в. \( B \)
\( c . c \)
D. None


Why is the melting point of cis isomers lower?
This question has multiple correct options
A. Better packing of trans isomers
B. Poorer packing of cis isomers
c. Better packing of cis isomers
D. Poorer packing of trans isomers


Basic soil can be corrected by adding:
A. urea
B. nitric acid
c. organic manure
D. formic acid


Two thin lenses of focal lengths \( f_{1} \) and \( f_{2} \) are in contact and coaxial. The power of the combination is :
A \( \cdot \frac{f_{1}+f_{2}}{2} \)
в. \( \frac{f_{1}+f_{2}}{f_{1} f_{2}} \)
c. \( \sqrt{\frac{f_{1}}{f_{2}}} \)
D. \( \sqrt{\frac{f_{2}}{f_{1}}} \)


Find the numerically greatest term in the expansion \( (3-5 x)^{15} \) when \( x=\frac{1}{5} \)


Rakhi takes 5 round of a garden which
is hexagonal(regular) in shape. she covers a total distance of \( 1500 \mathrm{m} \). What
is the side of the hexagon?


What are ketone bodies?
A. Acetoacetic acid, acetone and beta-hydroxybutyric acid
B. Nicotinic acid, folic acid and ascorbic acid
C. Acetone, betahydroxybutyryl CoA and acetoacetic acid
D. Acetic acid, acetone and beta-hydroxybutyric acid


\( \mathbf{5 8 0 0} \boldsymbol{A} \) in nm will be?
A. 58
B. 5.8
\( c .580 \)
D. 0.58


A solid of density \( D \) is floating in a
liquid of density \( d . \) If \( v \) is the volume of
solid submerged in the liquid and \( V \) is the total volume of the solid, then \( v / V \)
equals to
A \( \cdot \frac{d}{V} \)
в. \( \frac{D}{d} \)
c. \( \frac{D}{(D+d)} \)
D. \( \frac{D+d}{D} \)


Which one of the following is mainly responsible for depletion of ozone layer?
A. Methane
B. Carbon dioxide
c. water
D. Chlorofluorocarbons


In the circuit shown in figure, the
current through
A. The \( 3 \Omega \) resistor is \( 1.00 A \)
B. The \( 3 \Omega \) resistor is 0.25 A
C. The \( 4 \Omega \) resistor is \( 0.50 A \)
D. The \( 4 \Omega \) resistor is \( 0.25 A \)


A steel wire is suspended from a fixed end, while the other end is loaded with a
weight W. This produced an extension \( x \) As the weight is increased, the extension was also increased. A plot of
extension vs load within elastic limits
will give rise to
A. a curve
B. an ellipse
c. a straight line
D. a hyperbola


Write the postulates of Bohr's atomic model. What is the relationship between
the radii of the \( n \) th and first bohr orbit
of hydrogen atom?


The solution of the D.E. \( \left(x^{3}-\right. \)
\( \left.\mathbf{3} \boldsymbol{x} \boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{x}=\left(\boldsymbol{y}^{3}-\boldsymbol{3} \boldsymbol{x}^{2} \boldsymbol{y}\right) \boldsymbol{d} \boldsymbol{y}, \) is:
A \( \cdot y^{2}-x^{2}=c\left(y^{2}+x^{2}\right)^{2} \)
B . \( y^{2}-x^{2}=\left(y^{2}+x^{2}\right)^{2} \)
C \( \cdot y^{2}+x^{2}=c\left(y^{2}-x^{2}\right)^{2} \)
D. \( c\left(y^{2}+x^{2}\right)=\left(y^{2}-x^{2}\right)^{2} \)


Prove \( : \sqrt{\frac{1+\sin A}{1-\sin A}}=\sec A+\tan A \)


An ideal gas can be expanded from an initial state to a certain volume through
two different processes
(i) \( P V^{2}= \)
constant and \( (i i) P=K V^{2} \) where \( K \) is
a positive constant. Based on the given situation, choose the correct
statements
This question has multiple correct options
A. Final temperature in
(ii) will be greater than in (i)
B. Final temperature in (ii) will be less than in (i)
c. Total heat given to the gas in case (ii) is greater than in
(i)
D. Total heat given to the gas in case (ii) is less than in (i)


If the mean of \( x, x+2, x+4, x+8 \) is
20 find \( x \)


If \( (a, 3) \) is the point lying on the graph of
the equation \( 5 x+2 y=-4, \) then find
\( \boldsymbol{a} \)
A . -2
B. 5
\( c .-3 \)
D. 9


Say true or false.
The derivative of a constant function is
always non-zero.
A. True
B. False


Check the distributive property for the stated triples of rational numbers:
\( \frac{3}{8}, 0, \frac{13}{7} \)


The electronegativity of elements below sodium in the same group will be :
A. lower
B. higher
c. same
D. none of these


The reaction, \( A B \rightarrow A+B \) is a:
This question has multiple correct options
A. Decombination reaction
B. Combination reaction
c. chemical composition
D. Decomposition reaction


The diagonals of a rhombus are \( 24 \mathrm{cm} \)
and \( 10 \mathrm{cm} . \) Calculate its area.
A \( \cdot 120 \mathrm{cm}^{2} \)
в. \( 130 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 220 \mathrm{cm}^{2} \)
D. None of these


If mean deviation about Mean of a
particular data consisting 10 observations is7, then what will be
value of mean deviation when each is
multiplied by \( 5 ? \)
A . 35
B . 45
c. 55
D. 65


is the study of chemical reactions that take place in living things. It tries to explain them in chemical terms.
A. Biochemistry
B. Geochemistry
c. organic chemistry
D. Nano chemistry


The velocity of the block at the midpoint
between \( B \) to \( C \) will be :
A. \( \frac{\sqrt{2 g h}}{2} \)
B. \( \sqrt{2 g h} \)
\( \mathbf{c} \cdot \sqrt{g h} \)
\( D \cdot \frac{\sqrt{g h}}{2} \)


Restorage of nucleocytoplasmic ratio is performed in
\( \mathbf{A} \cdot G_{1} \) phase
B. s phase
\( \mathrm{c} \cdot G_{2} \) phase
D. M phase


Amount of water in enamel is
A. \( 90-92 \% \)
B. 75 - 80\%
c. \( 40-50 \% \)
\( \mathbf{D} \cdot \approx 3 \% \)


Assuming the earth to be a homogeneous sphere, determine the
density of the earth from the following data:
\( g=9.8 \mathrm{m} / \mathrm{s}^{2}, \mathrm{G}=6.673 \times 10^{-11} \mathrm{Nm}^{2} / \mathrm{kg}^{2} \)
\( R=6400 \mathrm{km} \)


Checking re-radiation of heat reflected
by earth by \( \mathrm{CH}_{4}, \mathrm{CO}_{2}, \mathrm{O}_{3} \) and
chlorofluorocarbons is called as
A. Green house effect
B. Bohr's effect
c. Pasteur's effect
D. cosmozoic effect


What is the angle of rotation when
\( 5 M \alpha-D \) mannopyranose is taken in
of length 200mm?
A \( .52 .2^{\circ} \)
B . 29
\( c \cdot 26.1^{\circ} \)
D. 14.5


A mark on the surface of a glass sphere( \( \boldsymbol{\mu}=1.5) \) is viewed from a diametrically opposite position. It appears to be at a distance \( 10 \mathrm{cm} \) from its actual position. The radius of sphere is:
A. \( 5 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. 20 cm


Assertion
Hydrides of group-16 elements show
volatility in the order \( : \boldsymbol{H}_{2} \boldsymbol{O}>\boldsymbol{H}_{2} \boldsymbol{S}> \)
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e}>\boldsymbol{H}_{2} \boldsymbol{T} \boldsymbol{e} \)
Reason
Electronegativity of group-16 elements increases down the group from oxygen to tellurium.
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


Two particles \( A \) and \( B \) execute simple
harmonic motion of periods \( \boldsymbol{T} \) and \( \mathbf{5} \boldsymbol{T} / \boldsymbol{4} \)
They start from mean position. The phase difference between them when
the particle \( A \) completes an oscillation
will be?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
c.
D. \( \frac{2 \pi}{5} \)


Balancing of equations is based on:
A. Avogadro's number
B. Principle of conservation of momentum
C. Conditions for a chemical reaction to take place
D. Law of conservation of mass or matter


The value of the expression \( \frac{\left(x^{2}-y^{2}\right)^{3}+\left(y^{2}-z^{2}\right)^{3}+\left(z^{2}-x^{2}\right)^{3}}{(x-y)^{3}+(y-z)^{3}+(z-x)^{3}} \) is
A \( \cdot\left(x^{2}-y^{2}\right)\left(y^{2}-z^{2}\right)\left(z^{2}-x^{2}\right) \)
B. \( 3(x-y)(y-z)(z-x) \)
C. \( (x+y)(y+z)(z+x) \)
D. \( 3(z+y)(y+z)(z+x) \)


Which of the following statements is
not correct?
A. Proteins are poly amides formed from aminoacids
B. Except glycine, all other amino acids show optical activity
C. Natural proteins are made up of L isomers of amino acids
D. In amino acids \( \mathrm{NH}_{2} \) and \( \mathrm{COOH} \) groups are attached to
different carbon atoms


Ozone-layer is getting depleted because of:
A. excessive use of automobiles
B. excessive formation of industrial units
c. excessive use of man-made compounds containing both fluorine and chlorine
D. excessive deforestation


SONAR is an instrument used for
finding the heights of a mountain.
A. True
B. False


Two tangents are drawn to a circle from
an external point \( A \), touching the circle at the points \( P \) and \( Q . A \) third tangent
intersects segment \( \boldsymbol{A P} \) at \( \boldsymbol{B} \) and
segment \( A Q \) at \( C \) and touches the
circle at \( R \) If \( A Q=10 \) units, then the
perimeter of \( \Delta A B C \) is
A . 22.0
в. 20.5
\( c .20 .0 \)
D. 40.0


Duramen is present in
A. Inner region of secondary wood
B. Part of sap woodd
c. outer region of secondary wood
D. Region of pericycle


Two waves having equation \( x_{1}= \)
\( a \sin \left(\omega t+\phi_{1}\right) \) and \( x_{2}=a \sin \left(\omega t+\phi_{2}\right) \)
If in the resultant wave the frequency and amplitude remains equals to amplitude of superimposing waves.
Then phase difference between them-
A \( \cdot \frac{\pi}{6} \)
в. \( \frac{2 \pi}{3} \)
c. \( \frac{\pi}{4} \)
D. \( \frac{\pi}{8} \)


This flower produces enormous trumpet shaped flowers, which smell of rotting meat. Each flower lasts for two days. On
the first day, it is in the female phase, attracting flies by its foul smell. On the next day, the flower changes to male phase and pollen is deposited on the pollinators. Which flower is this?
A. Dead horse arum lily
B. Flypaper flower
c. waterwheel flower
D. Pelican flower


An ether is more volatile than an alcohol
having the same molecular formula. This is due to:
A. dipolar character of ethers
B. alcohols having resonance structures
c. inter-molecular hydrogen bonding in ethers
D. inter-molecular hydrogen bonding in alcohols


The concentration of pesticide required to destroy \( 50 \% \) of pest is called as
A . LD 50
B. LC 50
c. LB 50
D. LE 50


Calculate the work done by the force of
gravity to pull a \( 10 k g \) box down a \( 30^{\circ} \)
inclined plane of length \( 8.0 m ? \) Note that \( \sin 30^{0}=\cos 60^{0}=0.500 \) and
\( \cos 30^{0}=\sin 60^{0}=0.866 \)
A . \( 40 J \)
B. \( 69 J \)
c. \( 400 J \)
D. \( 690 J \)
E. \( 800 J \)


In which of the following reactions, the concentration of reactant is equal to the concentration of product at equilibrium? \( (K= \) equilibrium constant)
A. \( A \rightleftharpoons B ; K=0.01 \)
в. \( R \rightleftharpoons P ; K=1 \)
c. \( X \rightleftharpoons Y ; K=10 \)
D. \( L \rightleftharpoons J ; K=0.025 \)


The radius of gyration of a disc of mass \( 100 g \) and radius \( 5 c m \) about an axis passing through its centre of gravity and perpendicular to the plane is (in \( \mathrm{cm} \)
A . 0.5
B . 2.
\( c .3 .54 \)
D. 6.54


A little amount of fertilizer makes your
lawn grow better but a larger amount of the same kills grasses.Why?


Proteins give a red precipitate with
Millon's reagent. The reagent is :
A. mercurous and mercuric nitrate and nitrites in \( H N O_{3} \)
B. mercurous and mercuric chloride in \( H C l \)
c. mercurous and mercuric chloride in \( H N O_{3} \)
D. none of the above


Activated sludge acts as inoculum in:
A. Primary treatment
B. Secondary treatment
c. Tertiary treatment
D. More that one option


Above reaction is known as:
\[
\begin{array}{c}
\mathrm{O} \\
\mathrm{H}-\mathrm{C}-\mathrm{D}-\mathrm{H}^{28} \mathrm{O}^{-}
\end{array} \mathrm{H}-\mathrm{N}^{-18} \mathrm{O}^{-}+\mathrm{CH}_{2} \mathrm{D}-\mathrm{OH}
\]
A. Cannizaro reaction, Disproportionation reaction
B. Tischenko reaction, Disproportionation reaction
C. Cross Cannizaro reaction, Redox reaction
D. Tischenko reaction, Redox reaction


The frequency and the intensity of a
beam of light falling on the surface of a
photoelectric material are increased by
a factor of two. This will:
A. Increase the maximum kinetic energy of the photoelectrons by 2 and photoelectric current by a factor of \( 1 / 2 \)
B. Increase the maximum kinetic energy of the photoelectrons, and increase the photoelectric current by a factor of 2
C. Increase the maximum kinetic energy of the photoelectrons by a factor of 2 and will have no effect on the magnitude of the photoelectric current produced
D. Not produced any effect on the kinetic energy of the emitted electrons but will increase the photoelectric current by a factor of 2


The reaction taking place is:
\( \mathbf{A} \cdot H g_{2} C l_{2}(s)+2 A g(s) \rightarrow 2 A g C l(s)+2 H g(l) \)
B \( \cdot 2 H g_{2} C l_{2}(s)+2 A g(s) \rightarrow 4 A g C l(s)+2 H g(l) \)
\( \mathbf{c} \cdot H g_{2} C l_{2}(s)+3 A g(s) \rightarrow A g C l(s)+2 H g(l) \)
D. None of these


Which of the following is released from biomass?
A. Cow-dung
B. Methane
c. oxygen
D. Helium


Solve the following:
¡¡) \( \sqrt{99} \times \sqrt{396} \)
ii) \( \sqrt{\mathbf{0 . 0 3 2 4}} \)
\( \mathbf{A} \cdot 192 ; 0.18 \)
B. \( 192 ; 0.12 \)
c. \( 198 ; 0.18 \)
D. \( 198 ; 0.12 \)


Given the function \( f(x) \) such that \( 2 f(x)+x f\left(\frac{1}{x}\right) \)
\( 2 f\left(\left|\sqrt{2} \sin \pi\left(x+\frac{1}{4}\right)\right|\right)= \)
\( 4 \cos ^{2} \frac{\pi x}{2}+x \cos \left(\frac{\pi}{x}\right), \) then which one
of the following is correct? This question has multiple correct options
A \( \cdot f(2)+f\left(\frac{1}{2}\right)=1 \)
B. \( f(1)=-1, \) but the values of \( f(2), f\left(\frac{1}{2}\right) \) cannot be determined
c. \( f(2)+f(1)=f\left(\frac{1}{2}\right) \)
D. \( f(2)+f(1)=0 \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}, \) if \( \boldsymbol{x} \sin \boldsymbol{y}+\boldsymbol{y} \sin \boldsymbol{x}=\mathbf{0} \)


\( 40 k g \) of water flows out of a tap at
uniform speed of \( 5 m s^{-1} \). Calculate the
amount of energy possessed by water


Which of the following is a saturated
hydrocarbon?
\( \mathbf{A} \cdot C_{2} H_{2} \)
в. \( C_{2} H_{4} \)
c. \( C_{2} H_{6} \)
D. \( C_{4} H_{4} \)
E . \( C_{6} H_{10} \)


What is \( C_{v} \) values for mono atomic and
diatomic gases?


An acid having basicity of one and having only one replaceable hydrogen ion per molecule of the acid is :
This question has multiple correct options
A. carbonous acid
B. nitric acid
c. sulphuric acid
D. hydrochloric acid


The number of envelopes that can be
made out of sheet of paper \( 384 \mathrm{cm} \) by
\( 172 \mathrm{cm} \) if each envelope requires a
piece of paper of size \( 16 \mathrm{cm} \) by \( 12 \mathrm{cm} \), is
A. 340
B. 344
c. 338
D. 342


In a Young's double slit set-up, light from a laser source falls on a pair of
very narrow slits separated by 1.0 micrometer and bright fringes separated by 1.0 millmeter are observed on a distant screen. It the
frequency of the laser light is doubled, what will be the separation of the bright fringes?
A. \( 0.25 \mathrm{mm} \)
в. \( 0.5 \mathrm{mm} \)
c. \( 1.0 \mathrm{mm} \)
D. 2.0 \( m \) m


The velocity of the electron in 3rd orbit
of hydrogen atom in \( \mathrm{cm} s^{-1} \)
A \( \cdot 4.88 \times 10^{4} \)
B . \( 2.44 \times 10^{8} \)
c. \( 7.29 \times 10^{7} \)
D. \( 2.44 \times 10^{12} \)


A sum of money invested at \( 6 \% \) p.a. simple interest for a certain period of
time yields Rs. 960 as interest. If this
sum has been invested for 5 years more
it would have yielded Rs. 2160 as interest. Find the sum.


Before a race the chances of three
runners, \( A, B, C, \) were estimated to be
proportional to 5,3,\( 2 ; \) but during the race \( A \) meets with an accident which
reduces his chance to one-third. What
are now the respective chances of \( \boldsymbol{B} \)
and \( C ? \)


Aluminum is used to make electrical
wire.
A . True
B. False


A charge of \( 1 \mu C \) is given to one plate of
a capacitors and a charge of \( 2 \mu \mathrm{C} \) is
given to the other plate of a \( 0.1 \mu \mathrm{F} \) capacitor. Find the potential difference across the two plates of the capacitor:
\( \mathbf{A} \cdot 5 V \)
в. \( 10 V \)
\( \mathrm{c} \cdot 15 \mathrm{V} \)
D. 30 \( V \)


A chemist interested in the reactivity of iodine concentrates his study on the decomposition of gaseous hydrogen iodide (Reaction 1).
\( 2 H I(g) \leftrightharpoons H_{2}(g)+I_{2}(g) \)
What is the equilibrium expression for Reaction 1?
\( \mathbf{A} \cdot\left[H_{2}\right]^{2}\left[I_{2}\right] \)
B \cdot \( \left[\mathrm{H}_{2}\right] \)
\( \mathbf{c} \cdot\left[H_{2}\right]\left[I_{2}\right] /[H I]^{2} \)
D \( \cdot\left[H_{2}\right]\left[I_{2}\right]^{2} \)


The track shown in figure is frictionless.
The block B of mass \( m \) is pushed along the track with some speed. The collision
between \( A \) and \( B \) is perfectly elastic. With what velocity should the block \( A \) be
started to get the sleeping man
awakened ?


Arrange the following compounds in the increasing order of homolytic \( (\boldsymbol{C}-\boldsymbol{C}) \)
bond dissociation energy.
I. Propane
II. Ethane
III. 2,2 -Dimethyl propane
IV. 2-Methyl propane
\( A \cdot((11)<(11)<(11)<(1) \)
B. (II) <(I) <(IV) <(III)
\( c \cdot(\| I)<(\mid V)<(\mid)<(||) \)
\( D \cdot(1)<(\| 1)<(11)<(1 V) \)


Under isothermal condition, energy \( \boldsymbol{E} \) is supplied to a soap bubble of surface tension \( \sigma \) and radius \( r \) to double the
radius of the soap bubble. The value of
\( \boldsymbol{E} \) is:
A \( \cdot 16 \pi r^{2} \sigma \)
B. 24 \( \pi r^{2} \sigma \)
\( \mathbf{c} \cdot 8 \pi r^{2} \sigma \)
D. \( 12 \pi r^{2} \sigma \)


There are four large parallel conducting
plates each of Area A, placed parallel to
each other. Plates 1,2,3,4 are given
charges equal to \( \boldsymbol{q}_{1}, \boldsymbol{q}_{2}, \boldsymbol{q}_{3} \) and \( \boldsymbol{q}_{4} \)
respectively:
This question has multiple correct options
A. Charge appearing on the left hand side of plate 1 will be \( \frac{q_{1}+q_{2}+q_{3}+q_{4}}{2} \)
B. Electric field intensity at the point \( P \), towards right, will be \( \frac{q_{1}+q_{2}-q_{3}-q_{4}}{2 A \varepsilon_{0}} \)
C. Electric field intensity at the point \( Q \), towards right, will be \( \frac{q_{1}-q_{2}+q_{3}+q_{4}}{2 \varepsilon_{0}} \)
D. Electric field at P will be equal to that at Q, for any
values of \( q_{1}, q_{2}, q_{3} \) and \( q_{4} \)


Number of hydrogen ions present in 10
millionth part of \( 1.33 \mathrm{cm}^{3} \) of pure water
\( \operatorname{at} 25^{\circ} C \) is:
B. 60 million
c. 8.01 million
D. 80.23 million


Look at the picture. What is this item
made of?
A. Leather
B. Glass
c. Rubber
D. Plastic


Which of these is not a unit of pressure?
A. \( N m^{-2} \)
B. Bar
c. Ра
D. kgwtt


Edible oils shows rancidity when stored for long period.
A . True
B. False


To test the quality of a tennis ball, you
drop it onto the floor from a height of
\( 4.00 \mathrm{m} . \) It rebounds to a height of \( 2.00 \mathrm{m} \) If the ball is in contact with the floor for
\( 12.0 \mathrm{ms}, \) what is its average acceleration during that contact? Take \( \boldsymbol{g}=\mathbf{9} \mathbf{8} \boldsymbol{m} / \boldsymbol{s}^{2} \)


A \( 4 \mathrm{m} \) long ladder weighing 25 kg rests with upper end against a smooth wall and lower end of rough ground. What should be the minimum coefficient of
friction between the ground and the ladder for it to be inclined at 60 with the
horizontal without slipping? (Take \( g=10 \)
\( \left.m s^{-2}\right) \)
A . 0.19
B. 0.29
\( c \cdot 0.39 \)
D. 0.49


If \( \vec{a}=2 \hat{i}+4 \hat{j}-5 \hat{k}, \vec{b}=\hat{i}+ \)
\( \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{c}}=\hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}}, \) then the unit vectors
parallel to \( \overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}+\overrightarrow{\boldsymbol{c}} \) is
A \( \cdot \pm \frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k}) \)
в. \( (3 \hat{i}+6 \hat{j}-2 \hat{k}) \)
\( ^{\mathrm{C}} \pm \frac{1}{7}(3 \hat{i}+6 \hat{j}+2 \hat{k}) \)
D. \( (3 \hat{i}+6 \hat{j}+2 \hat{k}) \)


A fraction whose numerator is greater than its denominator is fraction.
A. an improper
B. a proper
c. a mixed
D. None of these


Which of the following is not true for
wire wound resistor?
A. It has a lower order of stability and reliability.
B. It has high power rating with a low tolerance value.
C. Easy to make wire wound resistor of value 0.01 Ohm.
D. It is not suitable for high-frequency circuits.


In a group of 400 people, 160 are
smokers and non-vegetarian, 100 are smokers and vegetarian and the remaining are non-smokers and vegetarian. The probabilities of getting a special chest disease are \( 35 \%,, 20 \% \)
and \( 10 \% \) respectively. A person is chosen from the group at random and is
found to be suffering from the disease. What is the probability that the selected person is a smoker and non-
vegetarian?


The ability of coralloid roots to fix atmospheric nitrogen is due to the
presence of
A. Blue-green algae
B. Mycorrhiza
c. Rhizobium
D. None of these


Consider the following statements:
According the Werner's theory.
(1) Ligands are connected to the metal ions by covalent bonds.
(2) Secondary valencies have directional properties
(3) Secondary valencies are non-
ionisable
A \( \cdot 1,2 \) and 3 are correct
B. 1,2 are correct
\( c \cdot 2 \) and 3 are correct
D. 1,3 are correct


In this equilibrium reaction: \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \)
\( A B+h e a t, \) in a closed container, how
could the forward reaction rate be
increased?

This question has multiple correct options
A. Increasing \( [A B] \)
B. Increasing \( [A] \)
c. Removing some of \( A B \)
D. Removing some of \( [A],[B] \)
E. All of the above


\( f:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow(\infty, \infty), f(x)=\tan x \)
is.
A. one-one and onto
B. one-one but not onto
c. onto but not one-one
D. neither one-one nor onto


Mention the isotopes of hydrogen.


Two solenoids of equal number of turns having their length and the radii in the
same ratio \( 1: 2 . \) The ratio of their self-
inductance will be
A .1: 2
B . 2: 1
c. 1: 1
D. 1: 4


The non-metallic element present in the
mineral cryolite is:
A. \( F \)
в. \( C l \)
\( c \cdot B r \)
D. \( I \)


The diameter of a piston \( P_{2} \) is \( 50 \mathrm{cm} \)
and that of a piston \( P_{1} \) is \( 10 \mathrm{cm} \). What is
the force exerted on \( P_{2} \) when a force of
\( \mathbf{1} N \) is applied on \( \boldsymbol{P}_{1} ? \)


Find the components of \( \overrightarrow{\boldsymbol{a}}=2 \hat{\boldsymbol{i}}+\boldsymbol{3} \boldsymbol{j} \)
along the directions of vectors \( \hat{i}+\hat{j} \) and
\( \hat{\mathbf{i}}-\hat{\boldsymbol{j}} \)


Match the following.
\begin{tabular}{lllll}
& List - I & & & List - II \\
& A & Sucralose & I & Antioxidant \\
B & lodine & II & Artificial sweetener \\
C & Sodium benzoate & III & Antacid \\
D & Ranitidine & IV & Antiseptic \\
\hline & V & Food preservative
\end{tabular}
B. A-II, B-IV, C-V, D-III
C. \( A-\|, B-\| I, C-V D-1 \)
D. A- II, B-I C-III D-IV


The junction diode shown in the figure
is ideal. The current in the circuit is
A \( .20 m A \)
B. \( 2 m A \)
\( c .200 m A \)
D. 200 A


A bomb of \( 12 \mathrm{kg} \) explodes into two pieces of masses 4 kg and 8 kg. The velocity of \( 8 \mathrm{kg} \) mass is \( 6 \mathrm{m} \) per second
.The kinetic energy of other mass is?
A. 48 joules
B. 32 joules
c. 24 joules
D. 288 joule


Solve for \( x \) and \( y \) \( \frac{\boldsymbol{a} \boldsymbol{x}}{\boldsymbol{b}}-\frac{\boldsymbol{b} \boldsymbol{y}}{\boldsymbol{a}}=\boldsymbol{a}+\boldsymbol{b}, \boldsymbol{a} \boldsymbol{x}-\boldsymbol{b} \boldsymbol{y}=\boldsymbol{2} \boldsymbol{a} \boldsymbol{b} \)


If \( f(x+y)=f(x y) \) and \( f(1)=5, \) then
the value of \( \sum_{k=0}^{6} f(k) \)
A . 25
B. 35
\( c .36 \)
D. 24


Write the IUPAC name for \( \left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\right. \)
\( \mathrm{CO}] C l_{3} \)
A. Carbonatopentaamminechromium (III) chloride
B. Pentaamminecarbonatochromium (III) chloride
C. Pentaaminecarbonatochromium (III) chloride
D. Pentaammoniacarbonatochromium (III) chloride


In which of the following processes the bond order has increased and
paramagnetic character has changed to diamagnetic?
\( \mathbf{A} \cdot N_{2} \rightarrow N_{2}^{+} \)
в. \( N O \rightarrow N O^{+} \)
\( \mathrm{c} \cdot \mathrm{O}_{2} \rightarrow \mathrm{O}_{2}^{2} \)
D. \( O_{2} \rightarrow O_{2}^{+} \)


Draw a circle of radius \( 3 \mathrm{cm} \) and
construct two tangents to it from an
external point \( 8 c m \) away from its
centre


Five years ago, Shikha was thrice as old as Rani. 10 years later, Shikha will be twice as old as Rani. How old are they now?
A. Rani 20 yrs, Shikha 50 yrs
B. Shikha 20 yrs, Rani 50 yrs
c. Shikha 80 yrs, Rani 30 yrs
D. Shikha 30 yrs, Rani 80 yrs


Assertion
When there is no external force on a
system, its kinetic energy must remain
constant
Reason
When there is no external force on a
system its linear momentum must
remain constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


What is the importance of moderator in
a nuclear reactor?
A. Moderator controls the flow of water inlet
B. Controls the nuclear fission by absorbing the excess neutrons
c. controls the nuclear fission by slowing down the neutrons.
D. None of these


The function \( \mathbf{f}(\boldsymbol{x})=\frac{|\boldsymbol{x}|}{\boldsymbol{x}} \) at \( \boldsymbol{x}=\mathbf{0} \) is
A. Ieft continuous
B. right continuous
c. continuous
D. Discontinuous


\( \$ \$ 0.08= \)
\( \mathbf{A} \cdot 0.80 \)
B . 0.800
c. 0.080
D. 0.8


n Fig, POQ is a line. The value of \( x \) is:
A . \( 20^{\circ} \)
B \( \cdot 25^{\circ} \)
\( c \cdot 30^{0} \)
D. 35


The coefficient of apparent volume expansion of a liquid in a copper vessel is \( C \) and in a silver vessel is \( S \). The
coefficient of volume expansion of
copper is \( \gamma_{c} . \) What is the coefficient of linear expansion of silver?
A \( \cdot \frac{\left(C+\gamma_{c}+S\right)}{3} \)
в. \( \frac{\left(C-\gamma_{c}+S\right)}{3} \)
c. \( \frac{\left(C+\gamma_{c}-S\right)}{3} \)
D. \( \frac{\left(C-\gamma_{c}-S\right)}{3} \)


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


Determine the angle which the vector \( \boldsymbol{A}=\mathbf{5} \boldsymbol{i}+\boldsymbol{6} \boldsymbol{j}+\mathbf{5} \boldsymbol{k} \) makes with \( \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z} \)
axis.


A wire is stretched and fixed at two
ends. Transverse stationary waves are formed in it. It oscillates in its third
overtone mode. The equation of stationary wave is \( Y=A \sin k x \cos \omega t \)
Choose the correct options.
This question has multiple correct options
A \( \cdot \) Amplitude of constituent waves is \( \frac{A}{2} \)
B. The wire oscillates in three loops
C ' the length of wire is \( \frac{4 \pi}{k} \)
D. speed of stationary wave is \( \frac{\omega}{k} \)


The phase relationships between the voltages across the inductor, the capacitor and the source.


Match the column
\( \begin{array}{lll} & \text { । } & \text { ॥ } \\ \text { A } & \text { Force } & \text { erg } \\ \text { B } & \text { Pressure } & \text { Kgm } / s^{2} \\ \text { C } & \text { Power } & J s^{-1} \\ \text {D } & \text { Energy } & \text { Nm }^{-2}\end{array} \)


\( -O C H_{3} \) group is
A. Stronger +R group than-OH
B. Weaker +R group than -OH
C. weaker +lgroup than - 0 H
D. Inert group


The slope of the tangent to the curve
\( \boldsymbol{y}=\boldsymbol{e}^{\boldsymbol{x}} \cos \boldsymbol{x} \) is minimum at \( \boldsymbol{x}=\boldsymbol{\alpha}, \boldsymbol{0} \leq \)
\( a \leq 2 \pi, \) then the value of \( \alpha \) is
A . 0
в. \( \pi \)
c. \( 2 \pi \)
D. \( \frac{3 \pi}{2} \)


Apparatus required to prove the laws of reflection:
A. A spherical mirror
B. A plane mirror, a laser light, a pencil, a protactor
c. A mirror with black paper
D. A ray of light


Sucrose doesn't respond to tollen's test.
But, it gives a positive result after
boiling with conc. \( H C l . \) It is due to the:
A . cleavage of glycosidic linkage
B. formation of glycosidic linkage
c. formation of a compound containing carboxylic acid group
D. isomerization to glucose units


Natural rubber is heated with an
element \( X \) to make it hard, strong and
more elastic. X is:
A . zinc
B. sulphur
c. lead
D. \( H_{2} \)


Among these ores the highest phosphorus content is in :
A. chlorapatite.
B. phosphorite
c. fluorspar.
D. equal


The radius of a hydrogen atom is \( 0.5 \dot{A} \). Find the order of magnitude of volume
of one hydrogen atom is \( 10^{-10 x} \). The
value of \( x \) is:


In the double slit experiment, the
distance between two slits is \( 0.6 m m \)
and these are illuminated with light of
wavelength \( 4800 A^{\circ} . \) The angular width of dark fringes on the screen distant
\( 120 c m \) from slits will be
A . \( 8 \times 10^{-4} \) Radian
B. \( 6 \times 10^{-4} \) Radian
c. \( 4 \times 10^{-4} \) Radian
D. \( 16 \times 10^{-4} \) Radian


If tangents are drawn from the endpoints of two radii that are inclined
at an angle of \( 165^{\circ}, \) what is the angle between the tangents?
A \( \cdot 5^{\circ} \)
B. 35
\( c \cdot 15^{\circ} \)
D. None of these


The distance of the point \( P(6,8) \) from the origin is
\( \mathbf{A} \cdot \mathbf{8} \)
B. \( 2 \sqrt{7} \)
c. 10
D. 6


At what time \( t \) will the volume of the
sphere be 27 times its volume at \( t=0 \)


Assertion
In a Meter Bridge experiment, null point for unknown resistance is measured. Now, the unknown resistance is put
inside an enclosure maintained at a
higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance. and
Reason
Resistance of a metal increases with
increase in temperature.
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


The first human fossil probably belonged to
A. Zinjanthropus
B. Australopithecus
c. Pleisanthropus
D. Pithecanthropus


Assertion
A small amount of acid or alkali is
added before electrolysis of water.
Reason
Pure water is weak electrolyte.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.


Which of the following reactions have
same heat of reaction at constant \( \boldsymbol{P} \)
and constant volume as well?
This question has multiple correct options
\( \mathbf{A} \cdot 2 N O(g) \longrightarrow N_{2}(g)+O_{2}(g) \)
B \( \cdot N_{2}(g)+3 H_{2}(g) \longrightarrow 2 N H_{3}(g) \)
\( \mathbf{c} \cdot \operatorname{Co}_{3} O_{4}(s)+4 C O(g) \longrightarrow 3 \operatorname{Co}(s)+4 C O_{2}(g) \)
D. \( H_{2}(g)+C l_{2}(g) \longrightarrow 2 H C l(g) \)


The emf of a cell corresponding to the reaction,
\( Z n+2 H^{+}(a q .) \rightarrow Z n^{2+}(0.1 M)+ \)
\( H_{2}(g) 1 a t m \)
is 0.28 volt at \( 25^{\circ} \mathrm{C} \). Write the half-cell
reactions and calculate the \( p H \) of the
solution at the hydrogen electrode.
\( \boldsymbol{E}_{\boldsymbol{Z n}^{2+} / \boldsymbol{Z n}}^{\circ}=-\mathbf{0 . 7 6} \boldsymbol{v o l t} \) and \( \boldsymbol{E}_{\boldsymbol{H}^{+} / \boldsymbol{H}_{2}}^{\circ}=\boldsymbol{0} \)


Concentrated hydrochloric acid is \( 36.5 \% \) by weight. What is the molality of the
solution?
A . 1.575 molal
B. 15.75 molall
c. 157.5 molal
D. 1575 molal


Correct to two places of decimal


\( \frac{\sin A}{\sin \left(90^{\circ}-A\right)}+\frac{\cos A}{\cos \left(90^{\circ}-A\right)}= \)


plate \( 1 ? \)
Well water and nutrient agar
Well water and nutrient agar-antibiotic (tetracycline)
A. Bacteria 2 produces an antibiotic to which bacteria 1,3, and 4 are susceptible.
B. Bacteria 2 produces an antibiotic to which bacteria 4 is susceptible.
C. Bacteria 2 produces an antibiotic to which bacteria 1 and 4 is susceptible.
D. Bacteria 4 require a protein produced by bacteria 1.
E. Bacteria 4 require a protein produced by bacteria 3.


\( \mathrm{CaCO}_{3} \) naturally exists in:
A. one crystal form
B. two crystal form
c. three crystal form
D. four crystal form


Passage of air through the respiratory tract during inspiration is
A. Nostril - Nasal cavity - Larynx - Pharynx - Bronchi Trachea - Bronchioles - Alveoli
B. Nostril - Nasal cavity - Pharynx - Larynx - Trachea Bronchi -Bronchioles - Alveoli
C. Nostril - Nasal cavity - Larynx - Pharynx - Trachea Bronchi -Bronchioles - Alveoli
D. Nostril - Nasal cavity - Bronchioles - Bronchi - Larynx Pharynx - Trachea - Alveoli


The central \( C \) - \( C \) bond in 1 , 3-butadiene
is shorter than that of n-butane.
If true enter 1 else 0
\( A \)


The process involving heating of rubber with sulphur is called
A. Galvanisation
B. Vulcanization
c. Bessemerisation
D. sulphonation


An ant moves along the sides of a square room of length 4 m starting from \( A \) and reaches the opposite corner
C by travelling from \( A \) to \( B \) and from \( B \) to
C. If the time taken is 2 s, the average
velocity of the particle is :
\( \mathbf{A} \cdot 4 m s^{-1} \)
В. \( 2 \sqrt{2} \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 2 m s^{-1} \)
D. \( 4 \sqrt{2} \mathrm{ms}^{-1} \)


What is one environmental problem
associated with the use of detergents?
A. Global warming
B. Eutrophication
c. Errosion
D. Photochemical smog


A person writes letters to six friends
and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that all of them are in wrong envelope.


Comment on electrovalent Bond
Formation


In permanent hardness of water, when washing soda is treated with water,
is precipitated out
A. sodium carbonate
B. magnesium carbonate
c. calcium carbonate
D. \( N a_{2} C O_{3} \)and \( M g C O_{3} \)


If \( f(x)=b e^{a x}+a e^{b x}, \) then \( f^{\prime \prime}(0)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 2 a \)
\( \mathbf{c} \cdot a b(a+b) \)
\( \mathbf{D} \cdot a b \)


Calculate the electrical energy
consumed in units when a 60 W bulb is used for 10 hours
A.
B. 0.6
\( c \cdot 0.3 \)
D.


The instantaneous voltage through a device of impedence \( 20 \Omega \) is \( e= \)
\( 80 \sin 100 \pi t . \) The effective value of the
current is
\( A .3 A \)
в. \( 2.828 A \)
c. \( 1.732 A \)
D. \( 4 A \)


This wonderful acid has many uses. It is used for making explosives, pigments, dyes, hydrochloric acid, in sulphonation of oils to make detergents and in lead accumulators. Can you identify it?
A. Sulphuric acid
B. Sulphonic acid
c. Nitric acid
D. Sulphamic acid


The number of non-zero terms in the
expansion of \( (\sqrt{7}+1)^{75}-(\sqrt{7}-1)^{75} \)
is
A . 36
B. 37
c. 38
D. 39


toppr
Q Type your question
\( v_{0} . \) Which of the following graph truly depicts the variation of current through the conductor with time?
3
2


The wheel of a motor, accelerated
uniformly from rest, rotates through 2.5 radian during first second, find the angle rotates during next second
A . 5 rad
B. 7.5 radd
c. 3.5 rad
D. 10 rad


The codon AUG has dual function. It is
an initiation codon and also codes for
A. Formaldehyde
B. Methionine
c. Phenylalanine
D. serine


\( \mid \begin{array}{cccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{d} \\ \boldsymbol{a} & \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c} & \boldsymbol{a}+\boldsymbol{b}+\boldsymbol{c} \\ \boldsymbol{a} & \boldsymbol{2} \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{3} \boldsymbol{a}+\boldsymbol{2} \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{4} \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b}+\boldsymbol{2} \\ \boldsymbol{a} & \boldsymbol{3} \boldsymbol{a}+\boldsymbol{b} & \boldsymbol{6} \boldsymbol{a}+\boldsymbol{3} \boldsymbol{b}+\boldsymbol{c} & \boldsymbol{1} \boldsymbol{0} \boldsymbol{a}+\boldsymbol{6} \boldsymbol{b}+\boldsymbol{3}\end{array} \)


A particle moving, eastwards with a velocity of \( 5 m / s . \) In \( 10 s, \) its velocity changes to \( 5 m / s \) northwards. The average acceleration in this time is
A. zero
B. \( \frac{1}{\sqrt{2}} m / s^{2} \) towards north-west
c. \( \frac{1}{\sqrt{2}} m / s^{2} \) towards north-east
D \( \cdot \frac{1}{2} m / s^{2} \) towards north-west


Alkali metals cannot be extracted by
reduction of their oxides and other
compounds because:
A. alkali metals are strong reducing agents
B. alkali metals have low ionisation enthalpy
C. alkali metals have high lattice enthalpy
D. alkali metals are strongly basic in nature


Draw a circle of radius \( 6 \mathrm{cm} \). Take an
external point \( \boldsymbol{P} \) at a distance of \( \mathbf{1 0} \boldsymbol{c m} \) from centre and construct tangents to
the circle from \( P . \) The sum of the
lengths of the tangent segments (in \( c m \)
is:


The value of \( ^{n} C_{0}+3 \times^{n} C_{1}+9 \times^{n} \)
\( \boldsymbol{C}_{2}+\ldots+\boldsymbol{3}^{n} \times^{n} \boldsymbol{C}_{n} \)
A \( \cdot 2^{n} \)
B. \( 3^{n} \)
\( c \cdot 4^{n} \)
D. \( 5^{n} \)


In which region is the acceleration
decreasing?
A. V to \( w \)
\( B . W \) to \( X \)
\( c \cdot x \) to \( Y \)
D. Y to z


In a \( \triangle A B C, B C=A B \) and \( \angle B=80^{0} \)
Then \( \angle A \) is equal to?
A \( \cdot 80^{\circ} \)
\( ^{0} 0 \cdot 8 \cdot 8^{00} \)
B . \( 40^{\circ} \)
\( c \cdot 50^{0} \)
D. \( 100^{\circ} \)


If \( L, M \) are the feet of the
perpendiculars from (2,4,5) to the \( x y \)
plane, \( \boldsymbol{y} \boldsymbol{z} \) -plane respectively, then the distance \( L M \) is:
A \( \cdot \sqrt{41} \)
B. \( \sqrt{20} \)
c. \( \sqrt{29} \)
D. \( 3 \sqrt{5} \)


Two bars \( A \) and \( B \) of circular section
and of the same volume and made of
the same material are subjected to tension. If the diameter of \( A \) is half that
of \( B \) and if the force supplied to both the rods is the same and is within the
elastic limit, the ratio of the extension
of \( A \) to that of \( B \) will be
A . 16
B. 8
\( c \cdot 4 \)
\( D \)


The radiation from the sun, incident normally at the surface of the earth is
\( 20 k c a l / m^{2} \) min. What would be the radiant energy incident normally on the earth if the sun had a temperature,
twice of the present one?
A. \( 80 k c a l / m^{2} \min \)
B . \( 320 k c a l / m^{2} \min \)
c. \( 160 k c a l / m^{2} \) min
D. \( 40 k c a l / m^{2} \) min


A man is climbing up a spiral type staircase. His degrees of freedom are :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. more than 3


The power consumed in \( 10 \Omega \) resistor in
the given circuit is :
A. \( 10 W \)
В. \( 8 W \)
\( c .>10 W \)
\( D \)


In exclusion chromatography sized particles are eluted first.
A . large
B. middle
c. small
D. all are eluted with same speed


State whether the statement is
true/false.

An die is tossed twice. Find the
probability of getting 4,5 or 6 on the
first toss and 1,2,3 or 4 on the second \( \operatorname{toss} \) is \( \frac{1}{3} \)
A. True
B. False


sewage ettluent on the levels of oxygen concentration, bacterial population and
algal growth in a fresh water stream.
The given graph is plotted based on his
findings.
select the correct statement regarding
the given graph.
A. There is a fall in oxygen concentration between point and \( 4 \mathrm{km} \) downstream because it is utilized by algae for respiration during day
B. There is a rise in oxygen concentration between \( 4 \mathrm{km} \) and \( 8 \mathrm{km} \) downstream because of oxygen for respiration is lower
C. Bacterial population never recovers from 8 km onwards because all the oxygen is used by algae
D. There is decrease in the level of bacteria between \( 5 \mathrm{km} \) and \( 7 \mathrm{km} \) downstream because all the oxygen and organic matter has been used up by algal population


State whether the following statements are true or false.
Semilunar valves open during the
ventricular diastole.
A. True
B. False


Draw the diagram of Permutit column used in softening hard water and label
the part:


Two mole of an ideal gas is heated at constant pressure of one atomosphere
from \( 27^{\circ} \mathrm{C} \) to \( 127^{\circ} \mathrm{C} . \) If \( C_{v, m}=20+ \)
\( 10^{-2} T J K^{-1} m o l^{-1}, \) then \( q \) and \( \Delta U \) for
the process are respectively.
A. 6362.8 J, 4700 .
B . 3037.2 J, 4700 J
c. 7062.8, 5400 J
D. 3181.4 J, 2350 J


If the compressibility of water is \( \sigma \) (sigma) per unit atmospheric pressure, then the decrease in volume V due to \( p \)
atmospheric pressure will be :
A. \( \sigma V / p \)
в. \( \sigma p V \)
\( \mathbf{c} \cdot \sigma / p V \)
D. \( \sigma p / V \)


Are metals sonorous?
A. Yes
B. No
c. мауbе
D. None of above


The difference of two numbers is 21 , the
larger number is \( x, \) then smaller number
is
A. 21+x
B. 21-x
c. \( x-21 \)
D. -x-21


Find the multiplicative inverse of each
of the complex numbers given in the
Exercises 11 to 13
\( -i \)


An object stars from rest at \( t=0 \) and
accelerates at a rate given by \( a=6 t \)
What i) its velocity and ii) its
displacement at any time \( t ? \)
A \( \cdot t^{3}, 3 t^{2} \)
B. \( 3 t^{2}, t^{3} \)
\( \mathbf{c} \cdot t^{2}, t^{3} \)
D. \( 2 t^{2}, 3 t^{3} \)


lce at \( 20 C \) is added \( t o 50 g \) of water at
\( 40 C . \) When the temperature of the
mixture reaches \( 0 C \),it is found that \( 20 g \)
of ice is still unmelted. The amount of
ice added to the water was close to
(specific heat of water \( \left.=\mathbf{4 . 2} \boldsymbol{J} / \boldsymbol{g} /^{o} \boldsymbol{C}\right) \)
Specific heat of Ice \( =\mathbf{2 . 1} \boldsymbol{J} / \boldsymbol{g} /^{o} \boldsymbol{C} \) Heat
of fusion of water at \( 0^{\circ} C=334 j / g \)
A \( .50 g \)
в. \( 40 g \)
\( c .60 g \)
D. \( 100 g \)


A polymer used in paints is:
A. nomex
B. thiokol
c. saran
D. glyptal


If the sum of all the angles of a polygon except one angle is \( 2220^{\circ}, \) then the number of sides of the polygon is
A . 12
B. 13
\( c \cdot 14 \)
D. 15


Which of the following statements is
wrong?
A. Acidified \( K M n O_{4} \) solution decolourises on the addition of sodium oxalate
B. In the reaction between \( B r_{2} \) and \( C s I, B r_{2} \) is an oxidising agent and \( C s I \) is a reducing agent
c. In the reaction \( 2 K_{2} S_{2} O_{3}+I_{2} \rightarrow 2 K I+K_{2} S_{4} O_{6} \), the
change in the oxidation number of \( S \) is 0.5
D. \( C \) has the same oxidation number in both \( C H_{4} \) and
\( C O_{2} \)


Multiply 137592 by the smallest number so that the product is a perfect cube.


Prove that the lengths of the tangents drawn from an external point to a circle
are equal.


Sneh buys \( X \) eggs to resell them at a profit of \( 10 \% \) but loses \( 10 \% \) of the eggs. By how much should she mark up the selling price in order to retain \( 10 \% \) profit
A. 30\%
в. 33.33 \%
c. 22.1 \%
D. 25 \%


The temporary hardness of water is due
to:
A \( \cdot C a\left(H C O_{3}\right)_{2} \)
B. \( N a C l \)
\( \mathbf{c} \cdot N a_{2} S O_{4} \)
D. \( C a C l_{2} \)


The fourth term of an A.P. is 11 and the
eighth term exceeds twice the fourth
term by 5. Find the A.P. and the sum of
first \( \mathbf{5 0} \) terms.
A . 3540
в. 6754
c. 4850
D. 7819


Ultraviolet radiations from sunlight cause a reaction which produces
\( A \cdot O_{3} \)
в. \( S O_{2} \)
\( c \cdot c o \)
D. \( C H_{4} \)


Find the slope of a line, which passes through the origin, and the mid-point of
the line segment joining the points \( \boldsymbol{P}(\mathbf{0},-\mathbf{4}) \) and \( \boldsymbol{B}(\mathbf{8}, \mathbf{0}) \)


Only vibrating bodies produce sound. State true or false
A . True
B. False


The brightest constellation is:
A. Great Bear
B. Cassiopeia
c. Orion
D. Canis Major


The IUPAC name of the compound is 3 Methyl pentane nitrile

State whether the following statement is true or false.


The Zeroth law of thermodynamics
leads to the concept of
A. internal energy
B. heat content
c. pressure
D. temperature


For a reaction \( \frac{\boldsymbol{d} \boldsymbol{X}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{K}\left[\boldsymbol{H}^{+}\right]^{n} . \) If \( \boldsymbol{p} \boldsymbol{H} \) of
reaction medium changes from two to one, the rate becomes 100 times of the
value at \( p H=2 . \) The order of reaction
is:
\( A \)
B. 2
\( c \cdot 0 \)
D. 3


The oxoacid of phosphorus having the strongest reducing property is:
A. \( H_{3} P O_{3} \)
в. \( H_{3} P O_{2} \)
\( \mathrm{c} . H_{3} P O_{4} \)
D. \( H_{4} P_{2} O_{7} \)


Though three fundamental particles are present in almost all elements. One element does not have :
A. neutron
B. proton
c. electron
D. nucleons


In the expansion of the expression \( (x+a)^{15}, \) if the eleventh term in the
geometric mean of the eighth and
twelfth terms, which term in the
expression is the greatest?
A. \( T_{6} \)
в. \( T_{7} \)
c. \( T_{8} \)
D. \( T_{9} \)


Which is not represented by quadratic equation?
A . Circle
B. Straight line
c. Parabola
D. Hyperbola


Draw the \( V-I \) characteristies of an
LED. state two advantages of LED lamps over conventional incandescent lamps.


Variation in the Acceleration Due to
Gravity:

Outside the earth \( : g=g_{0}\left(\frac{R_{e}}{x}\right)^{2} \)


Given that the two numbers appearing on throwing two dice are different.
Find the probability of the event 'the sum of numbers on the dice is 4


The value of \( ^{\prime} x^{\prime} \) satisfying the
determinant is \( \left|\begin{array}{ccc}1 & x & x^{2} \\ 1 & a & a^{2} \\ 1 & b & b^{2}\end{array}\right|=0, a \neq b \)
\( A \)
B. \( b \)
c. \( a \) or \( b \)
D. none of these


A string oscillates according to the
equation \( \boldsymbol{y}^{\prime}= \)
\( (0.50 c m) \sin \left[\left(\frac{\pi}{3} c m^{-1}\right) x\right] \cos \left[\left(40 \pi s^{-1}\right)\right. \)
What is the speed of the two waves(identical except for direction of travel) whose superposition gives this oscillation?


Which of the following is an implication of the zeroth law of thermodynamics?
A. Energy in the universe can neither be created nor destroyed
B. A pure crystal kept at \( -273.15^{\circ} \mathrm{C} \) has a very low entropy
C. If systems A and B are in thermal equilibrium with system C , then systems A, B,C are in thermal equilibrium with each other
D. Entropy of the universe is always increasing


Explain total internal reflection using
diagram.


The chemicals and the reaction
conditions required for the preparation
of ethanol are:
\( \mathbf{A} \cdot C_{2} H_{5} I, N a O H(a q) \)
B \( \cdot C H_{3} C l, N a, H_{2} O \)
c. \( K O O C-C H=C H-C O O K \), electrolysis
D. \( C H_{3} C O_{2} N a, N a O H, C a O, \Delta \)


A monochromatic source of light
operating at \( 200 \mathrm{W} \) emits \( 4 \times 10^{20} \)
photons/second. Then the wavelength of light used is
A. 3000 \( A^{0} \)
B . \( 5000 A^{0} \)
c. \( 4000 A^{0} \)
D. \( 6000 A^{\circ} \)


Area of circle \( A \) is 121 times the area of
circle B. The ratio of the circumference
of circle \( A \) to that of \( B \) is
A . 121:
B. 1: 11
c. 11: 1
D. Cannot be determined


It is known that the cells of a given
bacterial culture divide every 3.5 hours (on average). If there are 500 cells in a dish to begin with, how many cells will there be after 12 hours?
A . 4653
в. 9876
\( c .5383 \)
D. None of these


When the load on a wire is slowly increased from 3 to \( 5 k g w t, \) the
elongation increases from 0.61 to 1.02mm. The work done during the extension of wire is
\( \mathbf{A} \cdot 0.16 J \)
в. \( 0.016 J \)
c. 1.6 .5
D. 16.5


Which of the following pairs of compounds are tautomers?
A. Propanol and propanone
B. Ethanol and vinyl alcohol
c. Ethanol and allyl alcohol
D. vinyl alcohol and ethanal


Anushka noted down the following observations in her practical book.
i. Weight of the metal block in air \( =260 \)
\( \boldsymbol{g}-\boldsymbol{w} \boldsymbol{t} \)
i \( i . \) Weight of the metal block in water \( = \) \( 220 g-w t \)
iii. Weight of the metal block in salt
water \( =180 g-w t \)
Find the relative density of the salty
water


If \( \frac{1}{5} C_{r}+\frac{1}{6} C_{r}=\frac{1}{4 C_{r}}, \) then the value of \( r \)
equals to
A . 4
B . 2
c. 5
D. 3


The metal that is present in brass, bronze, and German silver is :
\( A \cdot \) Mg
B. zn
\( c \cdot c u \)
\( D \cdot A \)


When sugar is stirred with a spoon in a
glass of water, more sugar is dissolved
and faster. Why?
A. Spoon acts as a catalyst
B. On stirring, temperature increases
c. stirring increases the rate of interaction
D. spoon increases the attraction between the molecules of water and sugar


Suppose you push a spring with a force
\( F_{1} \) as shown in figure, the spring also
pushes up on your hand with a force \( F_{2} \)
What is the relationship between \( \boldsymbol{F}_{1} \)
and \( F_{2} ? \)
A \( \cdot F_{1}>F_{2} \)
B \( . F_{1}=2 F_{2} \)
\( \mathrm{c} \cdot F_{1}<F_{2} \)
D. \( F_{1}=F_{2} \)


What is the change in potential energy (in calories) of a \( 10 \mathrm{kg} \) mass after \( 10 \mathrm{m} \) fall?
A. 1000 call \( l \)
в. \( 0.1 \mathrm{kcal} \)
c. 238.9 cal
D. 23.89 cal


Find \( a \), if the distance between the
points \( P(11,-2) \) and \( Q(a, 1) \) is 5 units.


The magnitude of the induced emf in a coil of inductance \( 30 m H \) in which the
current changes from \( 6 A \) to \( 2 A \) in \( 2 s \)
is:
A \( .0 .06 \mathrm{V} \)
в. \( 0.6 \mathrm{V} \)
c. \( 1.06 V \)
D. \( 6 V \)


Which colour of light has a higher critical angle? Red light or Green light.


A new system of unit is evolved in which
the values of \( \mu_{0} \) and \( \varepsilon_{0} \) are 2 and 8
respectively. Then the speed of light in this system will be \( (\text { in } \mathrm{m} / \mathrm{s}) \)
A . 0.25
B. 0.5
c. 0.75
\( D \)


The ground state electronic configurations of the elements, U, \( \mathrm{V}, \mathrm{W} \) \( x \) and \( Y \) (these symbols do not have any
chemical significance) are as follows:
U \( 1 s^{2} 2 s^{2} 2 p^{3} \)
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} \)
W \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2} \)
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{5} 4 s^{2} \)
\( Y 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} \)
Determine which sequence of elements
satisfy the following statements:
(i) Element forms a carbonate which is
not decomposed by heating
(ii) Element is most likely to form coloured ionic compounds
(iii) Element has largest atomic radius
(iv) Element forms only acidic oxide
A. vw y u
в. \( \vee \times Y \) w
c. \( v \) w \( Y x \)
D. \( v \times w u \)


For both pure and doped silicon,
calculate the probability that a state at
the bottom of the silicon conduction
band is occupied?
\( A \cdot 5.20 \times 10^{-2} \)
B . \( 1.40 \times 10^{-2} \)
c. \( 10.5 \times 10^{-2} \)
D. \( 14 \times 10^{-2} \)


Select the correct statements(s)
This question has multiple correct options
A. For the same charge and the same size, a pseudo noble gas type cation with \( 18 e^{-} \) in the outermost shell is more polarizing than the cation of noble gas type with \( 8 e^{-} \) in the outermost shel
B. The degree of covalency increases in descending a group in the transition metal ions for a particular oxidation state
C. Size increases in descending a group in the transition metal ions for a particular oxidation state
D. Covalency decreases in descending a group in the transition metal ions for a particular oxidation


If the term \( 10, k,-2 \) are in A.P then the
value of \( k \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 2 \)
D.


When light falls on matter, it can produce :
A. mechanical effect
B. chemical effect
c. heating effect
D. all the above


When the current in a coil changes from
8 ampere to 2 ampere in \( 3 \times 10^{-2} \)
second, the e.m.f. induced in the coil is 2
volt. The self inductance of the coil (in
millinery) is
\( A \)
B. 5
c. 20
D. 10


State whether the following statement is True or False?

The size of the image produced by plane
mirror is the same as that of the
objects.
A. True
B. False


With respect to chlorobenzene, which of
the following statements is not correct?
A. \( C l \) is ortho-para directing
B. \( C l \) exhibits \( +M \) effect
c. \( C l \) is ring deactivating
D. \( C l \) is meta directing


2 moles of an ideal gas expands at a
constant temperature of \( 27 C \) from 10
litre to 100 litre. The work done by the gas in this process will be nearly:
A . \( 114800 J \)
в. 11486.5
c. \( 1148 J \)
D. \( 114.8 J \)


Which of the following statements is
not correct about the electron gain
enthalpy?
A. In general, the electron gain enthalpy becomes less negative in going from top to bottom in a group.
B. The electron gain enthalpy becomes less negative in a period from left to right.
C. The elements having stable configuration like noble gases have large positive electron gain enthalpies.
D. Electron gain enthalpy of O or F is less than that of succeeding element.


During secondary treatment of primary effluent, how does significant decrease
in BOD occur?


The co-ordinates of the vertices \( A, B, C \)
of a triangle are \( (\mathbf{6}, \mathbf{3}),(-\mathbf{3}, \mathbf{5}),(\mathbf{4},-\mathbf{2}) \)
respectively and \( P \) is any point \( (x, y) \)
then the ratio of areas of triangles PBC and ABC is
A \( \cdot|x-y-2|: 7 \)
B \cdot | \( x+y+2 \mid: 7 \)
c. \( |x+y-2|: 7 \)
D. None of these


Assertion
Blood coagulates in the injured blood
vessels.
Reason
Uninjured blood vessels release an
anticoagulant heparin.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following statements is
not true about \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} ? \)
\( \mathbf{A} \cdot \) It is a tribasic acid
B. One mole of it is neutralised by 0.5 mole of \( C a(O H)_{2} \)
C \( . N a H_{2} P O_{2} \) is not an acidic salt
D. It disproportionates to \( H_{3} P O_{3} \) and \( P H_{3} \) on heating


The de Broglie wavelength associated with an electron of energy 500 ev is given by (take \( \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4} \mathbf{J}} \boldsymbol{s}, \boldsymbol{m}=\mathbf{9 . 1 1} \times \)
\( \left.10^{-31} k g\right) \)
A \( \cdot 0.28 A^{0} \)
B . 1.410 \( A^{\circ} \)
\( c \cdot 0.66 A^{0} \)
D. 0.55 \( A^{\circ} \)


Which of the following options are correct regarding the degree of dissociation of a weak electrolyte:
This question has multiple correct options
A. depends on the nature of solute and solvent
B. increases with increase in dilution
c. increases with increase in temperature
D. none of the above


Find the equation of the plane passing through the points (0,0,0) and (3,-1,2) are parallel to the line \( \frac{\boldsymbol{x}-\mathbf{4}}{\mathbf{1}}=\frac{\boldsymbol{y}+\mathbf{3}}{\mathbf{- 4}}=\frac{\boldsymbol{z}+\mathbf{1}}{\mathbf{7}} \)


Plants which exhibit photorespiration
are
\( \mathbf{A} \cdot C_{4} \) plants
B. \( C_{3} \) plants
c. cam plants
D. Alpine plants


Salicylic acid is produced when phenol in alcoholic KOH is treated with
A. \( C H_{3} C l \)
в. \( C H C l_{3} \)
\( \mathbf{c} \cdot C H_{2} C l_{2} \)
D. \( C C l_{4} \)


Assertion
Cockroach undergoes periodic ecdysis during its growth.
Reason
Cockroach has compound eyes.
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


Using Rolle's theorem, the equation \( \boldsymbol{a}_{0} \boldsymbol{x}^{\boldsymbol{n}}+\boldsymbol{a}_{1} \boldsymbol{x}^{\boldsymbol{n}-1}+\ldots+\boldsymbol{a}_{\boldsymbol{n}}=\mathbf{0} \) has
atleast one root between 0 and \( 1, \) if
A \( \cdot \frac{a_{0}}{n}+\frac{a_{1}}{n-1}+\ldots .+a_{n-1}=0 \)
в. \( \frac{a_{0}}{n-1}+\frac{a_{1}}{n-2}+\ldots+a_{n-2}=0 \)
c. \( n a_{0}+(n-1) a_{1}+\ldots .+a_{n-1}=0 \)
D. \( \frac{a_{0}}{n+1}+\frac{a_{1}}{n}+\ldots .+a_{n}=0 \)


Means of two samles of sizes 50,100
respectivly are 54.1,50.3 and \( \$ D \) are 8
and \( 7 . \) The combined \( \$ D \) of two samples
is
A . 7.56
B. 7.00
c. 7.28
\( D \)


A solid cylinder has mass ' \( M \) ', radius ' \( \boldsymbol{R} \) and length 'l'. Its moment of inertia about an axis passing through its center and perpendicular to its own axis is
\( ^{\mathrm{A}} \cdot \frac{2 M R^{2}}{3}+\frac{M l^{2}}{12} \)
B. \( \frac{M R^{2}}{3}+\frac{M l^{2}}{12} \)
\( ^{\mathbf{C}} \cdot \frac{3 M R^{2}}{4}+\frac{M l^{2}}{12} \)
D. \( \frac{M R^{2}}{4}+\frac{M l^{2}}{12} \)


Write a pair of linear equations which has the unique solution \( x=-1, y=3 . \) How many such pairs can you write?
A. \( x+y=2 \& x-y=-4 ; \) infinite
B. \( 2 x+y=6 \& 2 x-3 y=6 ; 3 \)
c. \( 5 x-8 y=13 \) \& \( x+3 y=7 ; 8 \)
D. Cannot be determined


\( \boldsymbol{F} \boldsymbol{e}_{2}(\boldsymbol{C} \boldsymbol{O})_{9} \) is diamagnetic. Which of the
following reason is correct?
A. Presence one \( C O \) as bridge group
B. Presence of monodenate ligand
c. Metal-metal (Fe - Fe) bond in molecular
D. Resonance of \( C O \)


Which one of the following statements
İS wrong?
A. Direction of torque is parallel to axis of rotation
B. Direction of moment of couple is perpendicular to the plane of rotation of body
C. Torque vector is perpendicular to both position vector and force vector
D. The direction of force vector is always perpendicular to the directions of both position vector and torque vector


Calculate the equivalent resistance for
each arrangement.
Series arrangement


First discovered enzyme was
A. Isomerase
B. Transaminase
c. zymase
D. Transferase


Which of the following reactions
represent correct method?

This question has multiple correct options
\( \mathbf{A} \cdot N a C l_{(\text {molten})} \longrightarrow N a^{+}+C l^{\ominus}: \) Down cell
B. \( N i(C O)_{4} \longrightarrow N i+4 C O: \) Mond process
\( ^{\mathrm{C}} \cdot \mathrm{Ag}_{2} \mathrm{CO}_{3} \longrightarrow 2 \mathrm{Ag}+\mathrm{CO}_{2}+\frac{1}{2} \mathrm{O}_{2}: \operatorname{Van} \) Arkel methoo
D. \( Z r I_{4} \longrightarrow Z r+2 I_{2}: \) Van Arkel method


In a certain species of animals, black fur
(B) is dominant over brown fur (b).
Show the possible ratio of genotypes and phenotypes of the offspring of the pure breeding different coloured parents.


Mention the respiratory quotient(RQ)
values for carbohydrates, fats and
proteins during aerobic respiration.


Aspirin has a degree of unsaturation of:
A .4
B. 5
\( c .6 \)
D. 7


The highest oxidation state shown by element with atomic number 23 is:
\( A \cdot+5 \)
\( B \cdot+4 \)
\( c \cdot+3 \)
\( D \cdot+6 \)


At resonance, what is the relation
between impedance of a series \( L C R \) circuit and its resistance \( \boldsymbol{R} \) ?


The hypodermis present in maize stem
is
A. Parenchymatous
B. Collenchymatous
c. Sclerenchymatous
D. Meristematic


\( \operatorname{Let} f(x)=\int \frac{x^{2} d x}{\left(1+x^{2}\right)(1+\sqrt{1+x^{2}})} \)
and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} . \) Then \( \boldsymbol{f}(\mathbf{1}) \) is
A \( \cdot \log (1+\sqrt{2}) \)
B \( \cdot \log (1+\sqrt{2})-\frac{\pi}{4} \)
\( c \cdot \log (1+\sqrt{2})+\frac{\pi}{4} \)
D. none of these


If a current carrying coil is close to a magnet and both are moving with the same speed in same direction, what is
the effect on induced current?
A. Induced current increases
B. Induced current decreases
c. Induced current flows to oppose motion
D. Induced current remains equal to zero


Frictionless track as shown in figure.
The bullet remains inside the block and
the system proceeds towards the semicircular track of radius \( 0.2 \mathrm{m} \)
Where will be the block strike the
horizontal part after leaving the
semicircular track?


In the course of evolution, a heart for
pumping blood was first found in which of these?
A. Annelids
B. Roundworms
c. Arthropods
D. Flat worms


The maximum deflection of the thread
with the vertical is
\( ^{\mathbf{A}} \cdot \cos ^{-1}\left(\frac{4}{5}\right) \)
B. \( \cos ^{-1}\left(\frac{3}{5}\right) \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left(\frac{2}{3}\right) \)
D \( \cos ^{-1}\left(\frac{3}{4}\right) \)


A charged particle moves in a gravityfree space without change in velocity. Which of the following is/are possible? This question has multiple correct options
A. \( E=0, B=0 \)
0
B. \( E=0, B \neq 0 \)
c. \( E \neq 0, B=0 \)
D. \( E \neq 0, B \neq 0 \)


Explain saprozoic and parasitic nutrition.


The valence electrons of an element are
responsible for:
A. physical properties of an element
B. chemical properties of an element
c. Both A and B
D. None of the above


The acceleration of a particle is given by the \( a=X \) where \( X \) is a constant. if the
particle starts at origin from rest. its distance from origin after time t is given by.


An equilateral triangular conducting
frame is rotated with angular velocity \( \omega \)
in uniform magnetic field \( B \) as shown.
Side of triangle is \( l \). Choose the correct
options
This question has multiple correct options
A. \( V_{a}-V_{c}=0 \)
B. \( v_{a}-V_{c}=\frac{B \omega l^{2}}{2} \)
c. \( _{V_{a}-V_{b}}=\frac{B \omega l^{2}}{2} \)
D. \( V_{c}-V_{b}=-\frac{B \omega l^{2}}{2} \)


A body released from certain height
reaches the ground after \( ^{\prime} t^{\prime} \) seconds.
The time taken to reach half height is
A \( \cdot t / 2 \)
B . \( t / \sqrt{2} \)
\( c \cdot \sqrt{2} t \)
D. None


Under electron microscope, chromatin fibres appear like beads in a string. The beads are
A. Chromosomes
B. Nucleosomes
c. Solenoids
D. Chromonemas


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 generator a higher voltage
D. AC generator has slip rings while the DC generator has commutator.


Prove the following
\( 1 .\left(1-\sin ^{2} A\right) \sec ^{2} A=1 \)
\( 2 . \sec ^{4} \theta-\sec ^{2} \theta=\tan ^{4} \theta+\tan ^{2} \)
3. \( (\sec \theta-\tan \theta)^{2}=\frac{1-\sin \theta}{1+\sin \theta} \)
4. \( \frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+}=\frac{1+\sin \theta}{\cos \theta} \)


On \( 26^{\text {th }} \) January, 2001 , a major earthquake occured in district
of Gujarat.
A. Uri
B. Tangdhar
c. Bhu
D. Kachchh


Why is the potential inside a hollow spherical charged conductor, constant
and has the same value as on its
surface ?


If \( f(x)=\frac{80}{3 x^{4}+8 x^{3}-18 x^{2}+60}, \) then
the points of local maxima for the
function \( \boldsymbol{f}(\boldsymbol{x}) \) are
A . 1,3
в. -3,1
c. -1,3
D. -1,-3


The coil is rotated in a clockwise
direction in the magnetic field at a
constant rate to induce a current in the
wire. If the direction of rotation of the
coil is reversed and coil remains
rotating at the same constant rate, Identify the correct statement.
A. The current in the coil will reverse its direction
B. The current in the coil will stop flowing
c. The current in the coil will continue to flow in the same direction as before
D. The current in the coil will decrease steadily
E. The current in the coil will increase steadily


A gyroscope, a uniform disc of radius \( R=5.0 \mathrm{cm} \) at the end of a rod of length
\( l=10 \mathrm{cm} \) (figure shown above), is
mounted on the floor of an elevator car
going up with a constant acceleration
\( \boldsymbol{w}=\mathbf{2 . 0} \boldsymbol{m} / \boldsymbol{s}^{2} . \) The other end of the rod
is hinged at the point \( O . \) The gyroscope
precesses with an angular velocity \( n= \)
0.5 rps. Neglecting the friction and the
mass of the rod, the proper angular
velocity of the disc in \( r a d / s \) is \( 100 x \)
Find the value of \( x \)


Number of unpaired electrons in
\( \boldsymbol{O}_{2}\left[\boldsymbol{A} \boldsymbol{s} \boldsymbol{F}_{4}\right] \) is :


Assertion
The downward displacement of air method used for drying and collecting
ammonia gas.
Reason
Ammonia gas is lighter than air and
hence collected by the downward displacement of air. Ammonia is not
collected over water since it is highly
soluble in water.(1 vol.of water dissolves
about 702 vol.at \( 20 C \) and 1 atm
pressure). The drying agent used is
calcium oxide.
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


Sandeep has three soil samples \( X, Y \) and \( Z \), each with weight 50 g. 100 mL of water is poured drop by drop with the
help of a dropper on all the soil samples. The given graph shows weight of water
absorbed by each soil samples. Select the correct option regarding the soil samples.
A. \( x \) is a mixture of sand, silt and a good amount of clay.
B. \( Y \) is a mixture of sand, silt and appropriate amount of clay.
C. \( z \) is a sandy soil with very little clay.
D. \( z \) is a mixture of clay and slit with higher amount of sand


The anti diabetic drug which also has anorectic effect is
A . Glipizide
B. Chlorpropamide
c. Gliclazide
D. Metformin


A metallic piece gets hot when surrounded by a coil carrying high frequency alternating current. Why
\( ? \)


If \( \vec{x} \) and \( \vec{y} \) be unit vectors and \( |\vec{z}|=\frac{2}{\sqrt{7}} \)
such that \( \vec{z}+\vec{z} \times \vec{x}=\vec{y}, \) then the angle
\( \theta \) between \( \vec{x} \) and \( \vec{z} \) can be
\( A \cdot 30^{\circ} \)
B. \( 60^{\circ} \)
\( c .90^{\circ} \)
D. None of these


A sewage treatment process, in which a part of decomposer bacteria present in the wastes is recycled into the starting of the process is called a/an:
A. Cyclic treatment
B. Activated sludge treatment
c. Primary treatment
D. Tertiary treatment


Define transition temperature.


\( \ln \) a \( 0.1 M \) solution of \( H_{3} P O_{4} \) the ionic
species present are (besides \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \) and
\( \left.\boldsymbol{O} \boldsymbol{H}^{-}\right) \)
\( \mathbf{A} \cdot H_{2} P O_{4}^{-}, H P O_{4}^{2-}, P O_{3}^{3-} \)
в. \( H_{2} P O_{2}^{3-}, H_{2} P O_{4}^{-}, P O_{4}^{3-} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{PO}_{4}^{-}, \mathrm{HPO}_{3}^{2-}, \mathrm{PO}_{2}^{3-} \)
D. \( P O_{3}^{4-}, P O_{4}^{3-}, H P O_{4}^{2-}, H_{2} P O_{4} \)


What is the main source of water
pollution in India?
A. Discharge of untreated sewage
B. Bathing
c. Discharge of industrial waste
D. Both A and C


A wire of uniform cross-section has a
resistance of \( \boldsymbol{R} \) \Omega. What would be the
resistance of a similar wire, made of the
same material, but twice as long and of
twice the diameter?
A \( \cdot \frac{3}{2} R \)
в. \( \frac{5}{2} R \)
c. \( \frac{1}{2} R \)
D. \( \frac{1}{4} R \)


Define an ideal solution


Khadins, Ahars and Kattas are ancient
structures that are example of water harvesting.
A. True
B. False


The displacement y of a wave traveling in the X-direction is given by \( \boldsymbol{y}= \) \( 10^{-4} \sin \left(600 t-2 x+\frac{\pi}{3}\right) \) metres. where
\( x \) is expressed in metres and \( t \) in
seconds. The speed of the wave motion
\( \operatorname{in} m s^{-1} \) is:
A . 200
в. 300
c. 600
D. 1200


\( f\left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1, \) then find
the value of \( x \)


Stages of hydrarch are
(a) Marsh meadow stage,
(b) Reed swamp stage,
(c) Submerged plant stage,
(d) Phytoplankton stage,
(e) Submerged free floating stage. Identify the correct sequence.
\( A \cdot d, c, e, b, a \)
B. \( c, e, a, b, d \)
c. \( b, d, c, \) a, e
D. \( \mathrm{d}, \mathrm{e}, \mathrm{c}, \mathrm{b}, \mathrm{a} \)


Lowering in vapour pressure is highest for:
A. \( 0.2 \mathrm{m} \) urea
B. 0.1 m glucose
\( \mathrm{c} \cdot 0.1 \mathrm{m} \mathrm{MgSO}_{4} \)
D. \( 0.1 \mathrm{m} \) BaCl \( _{2} \)


Find the derivative of \( f(x) \) from the first
principles, where \( \boldsymbol{f}(\boldsymbol{x}) \) is
\( \sin x+\cos x \)


Construct a triangle \( A B C \) whose perimeter \( 12 \mathrm{cm} \) and who base angles
\( \operatorname{are} 50^{\circ} \) and \( 80^{\circ} \)


Calculate the gravitational field intensity and potential at the centre of the base of a solid hemisphere of mass
\( \mathrm{m}, \) radius \( \mathrm{R} \)


TWO point charges \( +2 n c \) and \( -4 n c \) are
1 \( m \) apart in air. Find the positions along the line joining the two charges at which resultant potential is zero.


Soap form lathers in hard water, but a
detergent does not
A. True
B. False