The solution which has \( p H \) less than 7
¡s:
A. solution of caustic soda in water
B. solution of common soda in water
C. solution of blue vitriol in water
D. solution of baking soda in water


Which one is not correctly matched?
A. Mucor- Autotroph
B. Orobanche-Root parasite
c. cuscuta- stem parasite
D. Drosera- Insectivore


As per 2011 census literacy rate in India
is
A . 54.16\%
в. 85.85\%
c. 74.04\%
D. 63.80\%


The specific heat of an ideal gas depends on temperature is-
A \( \cdot \frac{1}{T} \)
в. \( T \)
c. \( \sqrt{T} \)
D. Does not depend on temperature


An electric dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle \( \theta \) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \( =90^{0}, \) the torque and the
potential energy of the dipole will respectively be
A. \( p E \sin \theta, p E \cos \theta \)
B. \( p E \sin \theta,-2 p E \cos \theta \)
c. \( p E \sin \theta, 2 p E \cos \theta \)
D. \( p E \cos \theta,-p E \cos \theta \)


Fossils of Pithecanthropus have been recovered from
A. China
B. Germany
c. Java
D. Japan


Fill in the blank space by choosing the correct word.
Coal and petroleum are commonly called fuels.
A . renewable
B. biomass
c. fossil
D. tidal


Determine the number of significant figure in the following.
\( 3.64 \times 10^{45} \mathrm{kg} \)


In a particular week the average
number of people visited the museum is \( 70 . \) If we exclude the holidays then the average number is increased by 28 Further if we exclude the day which the maximum of 210 visitors visited the
museum, then the average become 40 Find the no of holidays in the week


Identify the physical change in the following:
A. Reaction of zinc metal with dilute sulphuric acid
B. Formation of solutions of soluble substances in water
c. Burning of coal
D. Photosynthesis


A car starts from rest and accelerates
as shown in the accompanying
diagram. At what time would the car be
moving with the maximum velocity?
A. 2 seconds
B. 4 seconds
c. 6 seconds
D. 8 seconds


What vector when added to \( (2 \hat{i}-2 \hat{j}+ \)
\( \hat{\boldsymbol{k}}) \) and \( (\mathbf{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{k}}) \) will give a unit vector
along negative \( y- \) axis?


The efficiency of drip irrigation is around:
A . \( 40 \% \)
B. 85\%
c. 20\%
D. 100\%


The model class for the following
frequency distribution is
\begin{tabular}{lllll}
Marks & \( 0- \) 10 & \( 10- \) 20 & \( 20- \) 40 & \( 40- \) 50 \\
Number of students & 4 & 6 & 14 & 16 \\
\hline
\end{tabular}
A. \( 20-40 \)
B . \( 40-50 \)
\( \mathbf{c} .50-60 \)
D. \( 70-90 \)


Presence of furcula is a characteristic
feature 'of
A . Frogs
B. Reptiles
c. Birds
D. Mammals


The Keto form of phenol contains:
A. \( 3 \pi, 13 \sigma, 4 \) non-bonding electrons
B. \( 4 \pi, 15 \sigma, 3 \) non-bonding electrons
C. \( 3 \pi, 14 \sigma, 4 \) non-bonding electrons
D. \( 2 \pi, 15 \sigma, 6 \) non-bonding electrons


In a closed tube when air column is 20
\( \mathrm{cm} \) it is in resonance with tuning fork \( \mathrm{A} \) When the length is increased by \( 2 \mathrm{cm} \) then the air column is in resonance with
tuning fork B. When A and B are sounded together they produce 8 beats per second. The frequencies of the tuning forks \( A \) and \( B \) are \( (\text { in } H z): \)
\( A \cdot 40,44 \)
B. 88, 80
\( c \cdot 80,88 \)
D. 44,40


Evaluate \( \lim _{x \rightarrow 0} f(x), \) where \( f(x)= \)
\( \left\{\begin{array}{ll}|x|, & x \neq 0 \\ 0, & x=0\end{array}\right. \)


How will you identify the sequence is an
infinite geometric progression?
A. An geometric sequence containing finite number of terms
B. An geometric sequence containing infinite number of terms
C. An arithmetic sequence containing infinite number of terms
D. An arithmetic sequence containing finite number of terms


\( f \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\dots \dots \dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \dots \dots \infty\right)=\frac{\pi}{2} \)
and \( 0<x<\sqrt{2} \) then \( x= \)
\( A \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
D. - -


If the bandwidth of a filter increases:
A. Q factor decreases
B. the roll-off rate increases
c. the half-power frequency decreases
D. the center frequency decreases


affect the soil profile and bring changes in soil structure.
A. Vegetation
B. Animals
c. climatic factors
D. Fertilizers


Which one of the following is a slime mould?
A. Physarum
B. Thiobacillus
c. Anabaena
D. Rhizopus


Rate of dissipation of Joules heat in resistance per unit volume is (symbols have usual meaning)
A \( . \sigma E \)
в. \( \sigma J \)
\( c . J E \)
D. None


List List - II
A) Polystyrene
\( p \)
Condensation polymer
B) Polythene Thermoplastic polymer
C) Nylon- 6,6
r) Polyamide
D) Terylene
s) Addition
polymer
A \( \cdot(a-q, s),(b-q, s),(c-p, q, r),(d-p) \)
B. \( (a-p),(b-s),(c-p, r),(d-p, q) \)
\( c \cdot(a-s),(b-q),(c-p, r),(d-q) \)
D. \( (a-q),(b-s),(c-r),(d-p, q) \)


Figure
(a) shows two plano-convex lenses in contact as shown. The
combination has focal length \( 24 \mathrm{cm} \) Figure (b) shows the same with a liquid introduced between them. If refractive
index of glass of the lenses is 1.50 and that of the liquid is \( 1.60, \) the focal length of system in Fig. (b) will be
(a)
(b)
A \( .-120 \mathrm{cm} \)
В. \( 120 \mathrm{cm} \)
\( \mathbf{c} .-24 c m \)
D. \( 24 c m \)


Three thin prisms are combined as
shown in figure. The refractive indices of the crown glass for red, yellow and
violet rays are \( \mu_{r}, \mu_{y} \) and \( \mu_{v} \)
respectively and those for the flint glass \( \operatorname{are} \mu_{r}^{\prime}, \mu_{y}^{\prime} \) and \( \mu_{v}^{\prime} \) respectively. Find the
\( \frac{A^{\prime}}{\text { for which, there is no net angular }} \)
\( \boldsymbol{A} \)
dispersion.
A \( \cdot \frac{\mu_{y}-1}{\mu_{y}^{\prime}-1} \)
в. \( \frac{2 \mu_{y}-1}{\mu_{y}^{y}-1} \)
c. \( \frac{3 \mu_{y}-1}{\mu_{y}^{y}-1} \)
D. \( \frac{4 \mu_{y}-1}{\mu_{y}^{\prime}-1} \)


A current of \( 9.65 A \) is passed for 3 hours between nickel electrodes immersed in
\( 0.5 \mathrm{dm}^{3} \) solution of concentration \( 2 \mathrm{mol} \)
\( \mathrm{dm}^{-3} \boldsymbol{N i}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \)
The molarity of the solution after electrolysis would be:
\( \mathbf{A} \cdot 0.46 M \)
B. \( 0.92 M \)
c. \( 1.25 M \)
D. \( 0.625 M \)


Unpolarised light of intensity
\( 32 W m^{-2} \) passes through three polarizers such that transmission axis of first is crossed with third. If intensity
of emerging light is \( 2 W m^{-2} \), what is the angle of transmission axis between
the first two polarisers?
\( A \cdot 30 \)
B . 45
\( c \cdot 22.5 \)
D. \( 60^{\circ} \)


The most acidic compound among the following is:
A \( \cdot P_{2} O_{3} \)
в. \( S b_{2} O_{3} \)
\( \mathrm{c} \cdot B_{2} \mathrm{O}_{3} \)
D. \( A s_{2} O_{3} \)


In the troposphere, the temperature
decreases at the rate of \( 1^{\circ} \) Celsius for
every
A. 100 meters
B. 135 meters
c. 150 meters
D. 165 meters


The hour hand and the minute hands of
a clock are \( 4 \mathrm{cm} \) and \( 6 \mathrm{cm} \) long
respectively Find the sum of distances travelled by their tips in 2 days?


Which of the following helps in protein digestion.
A. Pancreatic juice
B. Saliva
c. Bile
D. Intestinal juice


Where will he have the highest potentia
energy?
A. In water
B. On land
\( c . \) on
D. ons


If \( \vec{b} \) and \( \vec{c} \) are two non colinear vectors such that \( \vec{a} \|(\vec{b} \vec{c}) \) then prove that \( (\vec{a} \vec{b}) \cdot(\vec{a} \vec{c}) \) is equal to \( |\vec{a}|^{2}(\vec{b} \cdot \vec{c}) \)


A ball is thrown vertically upwards from the top of a tower with a velocity of 10 \( \mathrm{m} / \mathrm{sec} . \) If the ball falls on the ground after 5 seconds, the height of the tower will be
\( \left(\text { use } g=10 m / s^{2}\right) \)
\( A \cdot 25 \mathrm{m} \)
B. 50 \( m \)
\( c \cdot 75 m \)
D. 100 \( m \)


In a basket of apples, \( 12 \% \) of them are
rotten and 66 are in good condition. Find the total number of apples in the basket.
A . 75
B. 70
c. 71
D. 80


The orbital speed \( v \) of each moon, such that they maintain the triangular configuration is:
A \( \cdot \sqrt{\frac{G M}{R^{2}}+\frac{G m}{\sqrt{3} R}} \)
B. \( \sqrt{\frac{G M}{R}+\frac{G m}{\sqrt{3} R}} \)
\( ^{\mathrm{c}} \cdot \sqrt{\frac{G M^{2}}{R}+\frac{G m}{\sqrt{3} R}} \)
D. \( \sqrt{\frac{G M}{R}+\frac{G m^{2}}{3 R}} \)


Well water is an example of:
A. surface water
B. rain water
c. underground water
D. river water


If \( f(x+1)=3 x-9, \) then what will be
the value of \( f\left(x^{2}-1\right) ? \)
A \( \cdot 3 x^{2}-9 \)
B. \( 3 x^{2}-15 \)
c. \( x^{2}-10 \)
D. \( 3 x^{2}-10 \)


Particle A and B moving in co-planar circular paths centered at O.They are
rotating in the same sense.Time periods of rotation of \( A \) and \( B \) around 0
\( \operatorname{are} \boldsymbol{T}_{A} \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{T}_{B}, \) respectively, with \( \boldsymbol{T}_{B}> \)
\( T_{A} . \) Time required for \( B \) to make one
rotation around 0 relative to a is :
A \( \cdot T_{B}-T_{A} \)
в. \( T_{B}+T_{A} \)
c. \( \frac{T_{A} T_{B}}{T_{A}-T_{B}} \)
D. \( \frac{T_{B} T_{A}}{T_{B}-T_{A}} \)


Match the Column I and Column II and
pick the correct matching from the codes given below.


A metal rod having a linear coefficient
of expansion \( 2 \times 10^{-5} /^{\circ} \mathrm{C} \) has a length 1
\( \mathrm{m} \) at \( 25^{\circ} \mathrm{C}, \) the temperature at which it is shortened by \( 1 \mathrm{mm} \) is :
\( A \cdot 50^{\circ} \mathrm{C} \)
B. \( -50^{\circ} \mathrm{C} \)
c. \( -25^{\circ} \mathrm{C} \)
D. \( -12.5^{\circ} \mathrm{C} \)


Prove that the area of triangle with vertices \( (\boldsymbol{t}, \boldsymbol{t}-\mathbf{2}),(\boldsymbol{t}+\mathbf{2}, \boldsymbol{t}+\mathbf{2}),(\boldsymbol{t}+ \)
\( \mathbf{3}, \boldsymbol{t} \) ) is independent of \( \mathbf{t} \)


How many consecutive odd numbers are needed to make sum as \( 13^{3} ? \)
A. 11
B . 13
\( c .15 \)
D. 17


Prove that if \( x \) and \( y \) are odd positive
integer, then \( x^{2}+y^{2} \) is even but not
divisible by 4


The value of \( x \) in the figure given below
is
\( A \cdot 2 \mathrm{cm} \)
\( B .1 \mathrm{cm} \)
\( c .2 .5 \mathrm{cm} \)
D. 3 cm


A bicycle tyre in motion has:
A. linear motion only
B. rotatory motion only
c. linear and rotatory motion
D. vibratory motion only


n figure, line \( n \) is a transversal to lines
and \( m \). Identify the following pairs of
interior and exterior angles on the same
side of the transversal in figure.


If \( A+B=C \) and that \( C \) is
perpendicular to \( A \). What is the angle
between \( \boldsymbol{A} \) and \( \boldsymbol{B} \), if \( |\boldsymbol{A}|=|\boldsymbol{C}| \) ?
A \( \cdot \frac{\pi}{4} r a d \)
B. \( \frac{\pi}{2} r a d \)
c. \( \frac{3 \pi}{4} r a d \)
D. \( \pi r a d \)


If the primitive of \( \frac{1}{x^{6}+x^{4}} \) is \( f(x)+ \) \( \frac{1}{x}+g(x) x^{-3}+C, \) then
This question has multiple correct options
A \( \cdot f(x)=\tan ^{-1} x \)
B \( \cdot f(x)=2 \tan ^{-1} x \)
c. \( g(x) \) is a constant function
D. \( g(x)=-1 / 3 \)


If \( L \) and \( R \) denote inductance and
resistance then dimension of \( L / R \) is
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0}\right] \)
в. \( \left[M^{0} L^{0} T\right] \)
\( \mathbf{c} \cdot\left[M^{2} L^{0} T^{2}\right] \)
D \cdot \( \left[M L T^{2}\right]^{2} \)


In Kreb's cycle, OAA accepts acetyl CoA
to form
A . Citric acid
B. Oxalosuccinate
c. Fumarate
D. succinyl CoA


If \( \boldsymbol{P}(\boldsymbol{B})=\frac{\boldsymbol{3}}{\boldsymbol{4}}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \overline{\boldsymbol{C}})=\frac{1}{3} \) and
\( P(\bar{A} \cap B \cap \bar{C})=\frac{1}{3}, \) then what is
\( \boldsymbol{P}(\boldsymbol{B} \cap \boldsymbol{C}) \) equal to?
A \( \cdot \frac{1}{12} \)
B. \( \frac{3}{4} \)
c. \( \frac{1}{15} \)
D.


Perimeter of \( \triangle A B C \) is \( 14 \mathrm{cm}, \mathrm{AB}=4.5 \mathrm{cm} \)
and \( \angle A=80^{\circ} . \) Construct \( \triangle A B C \)


What is the arithmetic mean of the
progression \( 11,22,33,44,55,66,77 ? \)
A . 44
в. 208
c. 308
D. 48


Solve by using suitable identity: \( a^{4}- \)
\( b^{4}+2 b^{2}-1 \)


A body moves in a straight line along \( Y \)
axis. Its distance \( y \) (in metre) from the
origin is given by \( y=8 t-3 t^{2} \). The
average speed in the time interval from \( t=0 \) second to \( t=1 \) second is
A. \( -4 m / s \)
в. zero
\( \mathbf{c} \cdot 5 m / s \)
D. \( 6 \mathrm{m} / \mathrm{s} \)


\( f(x)=\left\{\begin{array}{c}a \sin \frac{\pi}{2}(x+1), x \leq 0 \\ \frac{\tan x-\sin x}{x^{3}}, x>0\end{array}\right. \)
continuous at \( x=0 . \) Find the value of
\( \boldsymbol{a} \)


Fertilized eggs of Periplaneta americana are encased in
A. Ootheca
B. cocoon
c. Phallomere
D. Genital chamber


What is the chief constituent of Pyrex glass?
A. \( B_{2} O_{3} \)
as
в. \( \operatorname{si} 0_{2} \)
c. \( A l_{2} O_{3} \)
D. \( N a O_{2} \)


Given reaction \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{H} \boldsymbol{O} \rightarrow \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H}+ \)
\( H C O O^{-} \) is an example of
A. intermolecular redox change
B. intramolecular redox change
c. disproportionation or auto redox
D. none of these


For what distance ray optics a good approximation when the aperture is 4
\( \mathrm{mm} \) wide and the wavelength is \( 500 n m ? \)
A . \( 32 m \)
B. \( 69 m \)
\( c .16 m \)
D. \( 8 m \)


Foul smell in the water of tanks, ponds
etc., is due to:
A. Anaerobiosis
B. Aerobiosis
c. Biological magnification
D. Psammophytes


Name three groups of plants that bear archegonia. Briefly describe the life cycle of any one of them?


The mentioned equation is in which form?
\( \mathbf{3} \boldsymbol{y}^{2}-\mathbf{7}=\sqrt{\mathbf{3}} \boldsymbol{y} \)
A. linear
B. Quadratic
c. Cubic
D. None


Two identical charged spheres suspended from a common point by two massless strings of length I are initially a distance \( d(d<<I) \) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance \( x \)
between them
A \( . v \propto x^{-1 / 2} \)
B. \( v \propto x^{-1} \)
\( \mathbf{C} \cdot v \propto x^{1 / 2} \)
D. \( v \propto x \)


Which can be used as reducing agent?
A. Coal tar
B. Coal gas
c. coke
D. All


Assertion
Langmuir adsorption isotherm is based on the concept of monolayer adsorption.
Reason At high pressure, the surface is fully occupied by adsorbate molecules and the further increase in pressure does not effect adsorption.
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 ....................is used in a clinical
thermometer.


\( \ln C_{4} \) plant \( R u B i s C O \) activate during:
A . Day
B. Night
c. Midnight
D. Remain activated all time


The foot of the perpendicular drawn from the origin to the plane is (2,5,7) Find the equation of the plane.


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)
whose element \( a_{i j} \) is \( a_{i j}=\frac{(i-j)^{2}}{2} \)


A block strikes the free end of a
horizontal spring with the other end fix, placed on a smooth surface with a
speed \( v . \) After compressing the spring by \( x, \) the speed of the block reduce to
half. Calculate the maximum
compression of the spring.


In Acheson's process 'A' is heated with silica in an electrical furnace at \( 3700 \mathrm{K} \)
to obtain an intermediate 'B' and finally
to give 'C' and 'D'.'D' goes out as vapour. Then:
A \( \cdot \) 'A' is an element and 'B's its oxide
B. 'B'is an oxide and 'C' is an element
c. 'A' and 'C' are allotropes
D. 'B' and 'C' are allotropes


A satellite is orbiting the earth. Its speed is more at point \( \mathrm{B} \) as compared to point A. Which of the following statements are true?
I. The gravitational force is greater at \( \mathrm{B} \)
than at \( \mathbf{A} \)
II. The speed is greater at \( \mathrm{B} \) than at \( \mathrm{A} \)
III. The kinetic energy is greater at \( \mathrm{B} \) than at \( A \)
IV. The angular momentum is greater at
\( B \) than at \( A \)
A. I only
B. I and II only
c. ॥ only
D. I, II and III only
E . ।, ॥।, ॥I।, IV


A particle of small mass \( m \) is joined to
a very heavy body of mass \( M \) by a light
string passing over a light pulley. Both
bodies are free to move. The total
downward force on the pulley is nearly
A . \( m g \)
в. \( 2 m g \)
c. \( 4 m g \)
D. Can not be determined


A man is standing on a boat in still water. If he walks towards the shore the
boat will
A. Move away from the shore
B. Remain stationary
c. Move towards the shore
D. sink


A common example of precession is
\( A \cdot a \) spinning top
B. a ball bearing
C. a ball rolling down an inclined plane
D. a ball sliding down an inclined plane


Algae which form motile colony is
A. Volvox
B. Nostoc
c. spirogyra
D. chlamydomonas


Two squares have sides \( x \mathrm{cm} \) and \( (x+5) \)
cm. The sum of their areas is 697 sq.cm.
Express this as an algebraic equation \( \operatorname{in} x \)


Theo bakery sells red velvet cakes and
cheese cakes in boxes of 12 at a cost of
\( \$ 15 \) per box of red velvet and \( \$ 9 \) per box
of cheese cakes. On Monday and Tuesday, the shop earned \( \$ 396 \) by selling a total of 46 boxes of these two
items. If \( r \) and \( l \) represent the number of
boxes of red velvet and cheese cakes
respectively, which of the following systems of equations could be used to
find the number of boxes of each type of item sold?
\( \mathbf{A} \cdot r+l=46 \)
\[
15 r+9 l=396
\]
B . \( r+l=12 \times 46 \)
\[
15 r+9 l=396
\]
\( \mathbf{c} \cdot r+l=46 \)
\[
15 r+9 l=\frac{396}{2}
\]
D. \( r+l=46 \times 12 \)
\( 15 r+9 l=\frac{396}{12} \)


Prove that \( \frac{\left(1+\cot ^{2} \theta\right) \tan \theta}{\sec ^{2} \theta}=\cot \theta \)


Refractive index of glass relative to
water is \( 9 / 8 . \) What is the refractive index of water relative to glass?


ABCD is a square \( P, Q \) and \( R \) are the points on \( A B, B C \) and \( C D \) respectively;
such that \( A P=B Q=C R \)
Hence, \( P B=Q C \)
If the above statement is true then
mention answer as 1 , else mention 0 if
false


Only a diamond cuts another diamond.
A. True
B. False


A cyclist riding the bicycle at a speed of \( 14 \sqrt{3} m s^{-1}, \) takes a turn around a circular of radius \( 20 \sqrt{3} m, \) without
skidding. Given \( g=9.8 m s^{-2}, \) what is
his inclination to the vertical?
A . \( 30^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


Many hundred years ago, a ship was transporting calcium carbide and calcium phosphide (stored in different container). By chance sea-water entered sea and luminous flame appeared a ghost would have come. However, a chemist travelling in it explained it based on reactions. These reactions are \( \underset{\text { Calcium }}{\boldsymbol{C a C}_{2}}+\mathbf{6 H}_{2} \boldsymbol{O} \longrightarrow \)
\( \boldsymbol{C a}(\boldsymbol{O H})_{2}+ \)
\( \underset{\text { Acetylene }}{C_{2} H_{2}} \quad_{\text {Calcium phosphide }}+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O} \longrightarrow \mathbf{3} \boldsymbol{C} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2}+\underset{\boldsymbol{P h o s p h i n e}}{\boldsymbol{2 P H}_{\boldsymbol{e}}} \)
A. True
B. False


Use Euclids division lemma to show
that the cube of any positive integer is of the form \( 9 m, 9 m+1 \) or \( 9 m+8 \)


Angle of incidence is the angle between
and the


Assertion
Coal is a fossil fuel.
Reason
It is formed due to compression of
inorganic material over millions of
years.
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
C. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect and the Reason is correct


Find the incorrectly matched pair.


Find the equation of the ellipse with
centre at the origin, one vertex at \( (\mathbf{4}, \mathbf{0}) \) and which passes through the point \( P \) \( \left(2, \frac{\sqrt{3}}{2}\right) \)


Mac Arthur process is used for the extraction of:
A . \( A u \)
в. \( P t \)
c. \( C u \)
D. \( Z n \)


Draw labelled circuit diagram of a
potentiometer to compare emfs of two
cells.

Write the working formula (Derivation not required)


Joule's experiment converts
A. work into heat
B. work into electricity
C. heat into work
D. electricity into work


The wave function for \( 1 s \) orbital of the
hydrogen atom is given by
\[
\mathbf{\Psi}_{1 s}=\frac{\boldsymbol{\pi}}{\sqrt{\mathbf{2}}} \boldsymbol{e}^{-\boldsymbol{r} / \boldsymbol{a}_{0}}
\]
where \( a_{0}= \) Radius of first Bohr orbit \( r= \) Distance from the nucleus
(Probability of finding the electron varies with respect to it)
What will be the ratio of probabilities of finding the electrons at the nucleus to
first Bohr's orbit \( a_{0} ? \)
\( A \)
B \( \cdot e^{2} \)
\( c \cdot 1 / e^{2} \)
D. zero


A \( 50 k g \) skydiver falls through the air and reaches terminal velocity after
some time. The drag force is a function of velocity given by
\[
\boldsymbol{F}_{d r a g}=-\boldsymbol{b} \boldsymbol{v}^{2}
\]
where the negative sign denotes that the drag force is opposite to the direction of the velocity. What is the terminal velocity of the
skydiver (assuming the drag constant \( b \)
is \( 0.2 k g / m \) )?
A \( \cdot 5 \frac{m}{s} \)
B.
\[
50 \frac{m}{s}
\]
\( c \)
\[
100 \frac{m}{s}
\]
D.
\[
250 \frac{m}{s}
\]
E
\[
2500 \frac{m}{s}
\]


The sum of the series \( \frac{1}{2}+\frac{1}{3}+\frac{1}{6}+ \)
to 9 terms be \( k . \) Find \( -2 k \)


Which of the following bacteria is observed as chain-like formation?
A. Escherichia coli
B. Bacillus subtilis
c. streptococcus phosphatase
D. Micrococcus flavus


Sum the series \( 1^{3}+3^{3}+5^{3}+\dots \dots \dots \)
to \( n \) terms is
A \( \cdot n^{2}\left(2 n^{2}-1\right) \)
В \( \cdot n\left(2 n^{2}-1\right) \)
c. \( n\left(2 n^{2}+1\right) \)
D \cdot \( n^{2}\left(2 n^{2}+1\right) \)


From point \( A \) located on a highway, one
has to get by a car as soon as possible to point \( B \) located in the field at a
distance \( l \) from point \( D . \) If the car
moves \( n \) times slower in the field, at
what distance \( x \) from \( D \) one must turn
off the highway.
A \( \cdot x=\frac{l}{\sqrt{n^{3}-1}} \)
B. \( x=\frac{l}{\sqrt{n^{2}-1}} \)
c. \( _{x}=\frac{l}{\sqrt{n^{3}-2}} \)
D. \( x=\frac{l}{\sqrt{n^{2}-2}} \)


If \( y=e^{\left(x^{2}+2 \sin x\right)}, \) then \( \frac{d y}{d x} i s \)
\( \mathbf{A} \cdot e^{\left(x^{2}-2 \sin x\right)} \)
\( \mathbf{B} \cdot e^{\left(x^{2}+2 \sin x\right)} \times(2 x+2 \sin x) \)
C \( \cdot e^{\left(x^{2}+2 \sin x\right)} \times(2 x+2 \cos x) \)
\( \mathbf{D} \cdot e^{x} \)


With the help of appropriate ray diagram, state the sign conventions for reflection by spherical mirror.


Which of the following gases on dissolution in water make the solution
acidic?
This question has multiple correct options
A. \( c o \)
в. \( C O_{2} \)
\( c \cdot S O_{3} \)
D. \( P H_{3} \)


In stretching a spring by \( 2 \mathrm{cm} \) energy
stored is given by \( U, \) then stretching by
\( 10 \mathrm{cm} \) energy stored will be :
A. \( U \)
B. \( 5 U \)
c. \( \frac{U}{25} \)
D. 25U


Ordinary gasoline (petrol) that is used as fuel cars, scooters and automobiles
contain many different chemicals that
are added in small quantities, each performing an important role. Some of these are mentioned here. Which of the
option is false?
A. Soaps used for removing particles of grease from petrol tanks ensure a free flow of petrol
B. Anti-icing agents are used for depressing the freezing point of particles of ice
C. Anti-rust agents are used for protecting against corrosion by water
sticking on the walls of the carbureter


If \( \boldsymbol{A} \times \boldsymbol{B}= \)
\( \{(3, a),(3,-1),(3,0),(5, a),(5,-1),(5 \)
find \( \boldsymbol{A} \)
A \( \cdot\{a, 5\} \)
в. \( \{a,-1\} \)
c. \{0,5\}
D. \{3,5\}


The electric field intensity at a point near and outside the surface of a
charged conductor of any shape is ' \( \boldsymbol{E}_{1} \) :
The electric field intensity due to uniformly charged infinite thin plane
sheet is ' \( E_{2} \) '. The relation between ' \( E_{1} \) ?
and ' \( \boldsymbol{E}_{2} \) ' is :
A \( \cdot 2 E_{1}=E_{2} \)
в. \( E_{1}=E_{2} \)
\( \mathbf{c} \cdot E_{1}=2 E_{2} \)
D. \( E_{1}=4 E_{2} \)


ff \( \boldsymbol{x}=\mathbf{1}+\boldsymbol{a}+\boldsymbol{a}^{2}+\boldsymbol{a}^{3}+\ldots \) and \( \boldsymbol{y}= \)
\( 1+b+b^{2}+b^{3}+\ldots ., \) then show that \( \mathbf{1}+\boldsymbol{a} \boldsymbol{b}+\boldsymbol{a}^{2} \boldsymbol{b}^{2}+\boldsymbol{a}^{3} \boldsymbol{b}^{3}+\ldots=\frac{\boldsymbol{x} \boldsymbol{y}}{\boldsymbol{x}+\boldsymbol{y}-\mathbf{1}} \)


f \( \boldsymbol{A}=(-\mathbf{3}, \mathbf{4}), \boldsymbol{B}=(-\mathbf{1},-\mathbf{2}), \boldsymbol{C}= \)
\( (\mathbf{5}, \mathbf{6}), \boldsymbol{D}=(\boldsymbol{x},-\mathbf{4}) \) are vertices of \( \mathbf{a} \)
quadrilateral such that \( \Delta A B D= \)
\( 2 \Delta A C D . \) Then \( x, \) is equal to:
\( \mathbf{A} \cdot \mathbf{6} \)
B. 9
\( c \cdot 69 \)
D. 96


The number of ways of arranging the letters \( \boldsymbol{A A A A A}, B B B, C C C, D, E E \& \)
\( F \) in a row if no two \( ^{\prime} C^{\prime} s \) are together:
\( ^{\mathbf{A}} \cdot_{13} C_{3} \cdot \frac{12 !}{5 ! 3 ! 2 !} \)
в. \( \frac{13 !}{5 ! 3 ! 3 ! 2 !} \)
c. \( \frac{14 !}{5 ! 3 ! 2 !} \)
D. \( 11 . \frac{13 !}{6 !} \)


A \( 30.0 \mathrm{kg} \) hammer, moving with speed speed \( 20.0 m s^{-1}, \) strikes a steel Spike
\( 2.30 \mathrm{cm} \) in diameter. The hammer
rebounds with speed \( 10.0 \mathrm{ms}^{-1} \) after
0.110 s.What is the average Strain in the Spike during the impact?


Which of the following is in correct
order?
\( \mathbf{A} \cdot S b H_{3}<N H_{3}<A s H_{3}<P H_{3}(\text { Boling point }) \)
B . \( N-H<P-H<A s-H<S b-H \) (Bond
dissociation enthalpy)
\( \mathbf{C} \cdot N H_{3}>P H_{3}>A s H_{3}>S b H_{3}>B i H_{3} \) (Thermal
stability）
\( \mathbf{D} \cdot S b_{2} O_{5}>A s_{2} O_{5}>P_{2} O_{5}>N_{2} O_{5} \) (Acidic strength)


Which of the following statement(s)
is/are true about holes?
A. They flow from positive terminal to negative terminal
B. They flow from negative terminal to positive terminal
C. They do not flow
D. None of these


Find the diffrentiation of \( x \sin x \)


Write ionic equations for the reaction of
dichromate ions with
i) hydroxyl ions
ii) \( F e^{+2} \) ions in Acidic medium
In which one of the above two reactions
will the oxidation number of chromium
remains unchanged?


Elements \( A, B \) and \( C \) belong to the same period in the long form of the periodic table. The nature of the oxides of \( A, B \)
and \( \mathrm{C} \) is amphoteric, basic and acidic respectively. The correct order of the
atomic numbers of these elements is:
A. \( C>B>A \)
в. \( C>A>B \)
c. \( A>B>C \)
D. \( B>A>C \)


Which one of the following corresponds to a photon of highest energy?
A \( . \lambda=300 n m \)
В . \( v=3 \times 10^{8} s^{-1} \)
c. \( v=30 c m^{-1} \)
D . \( \varepsilon=6.626 \times 10^{-27} J \)


Which of the following gas is formed at the electrode connected to the negative
terminal of the battery?
A. Nitrogen gas
B. Hydrogengas
c. oxygen gas
D. carbon dioxide gas


Verify LMVT :
\( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}} \) for \( \boldsymbol{x}=[\mathbf{1}, \boldsymbol{3}] \)


What is the displacement of the crosscountry team if they begin at the school
run 10 miles and finish back at the
school?


The value of \( ^{\prime} n^{\prime} \) in the reaction is:
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-}+\mathbf{1 4} \boldsymbol{H}^{+}++\boldsymbol{n} \boldsymbol{F} \boldsymbol{e}^{2+} \rightarrow \)
\( 2 C r^{3+}+n F e^{3+}+7 H_{2} O \)
\( A \cdot 2 \)
B. 3
\( c \cdot 6 \)
D.


The 4 th term of an A.P. is zero. Prove that
the 25 th term of the A.P. is three times
its 11 th term.


If two mirrors are kept at \( 60^{0} \) to each other and a body is placed in the middle, then total number of images
formed is
A. Three
B. Four
c. Five
D. six


How many 3 digit numbers can be formed using the digits
0,1,2,3,4,5,6,7,8 where digits may be repeated?
A . 900
в. 980
c. 800
D. 250


\( \lim _{x \rightarrow 0} \frac{1-\cos x \cos 2 x \cos 3 x}{\sin ^{2} 2 x} \) is equal to
\( A \cdot 7 / 2 \)
в. \( 7 / 3 \)
\( c \cdot 7 / 4 \)
D. \( 7 / 5 \)


The value of \( 1+i^{2}+i^{4}+i^{6}+i^{8}+ \)
\( +i^{20} \) is :


Two metal spheres each of radius 'r' are kept in contact with each other. If d is
the density of the material of the sphere, then the gravitational force between those spheres is propositional
to
\( \mathbf{A} \cdot d^{2} r^{6} \)
B. \( d^{2} r^{4} \)
c. \( \frac{d^{2}}{r^{4}} \)
D. \( \frac{r^{4}}{d^{2}} \)


Neglecting the mass of the thread, find the time dependence of the
instantaneous power developed by the
gravitational force :
\( ^{\mathbf{A}} \cdot P=\frac{2}{3} m g^{2} t \)
B. \( P=\frac{3}{2} m g^{2} t \)
\( ^{\mathbf{C}} P=2 \frac{2}{3} m g^{2} t \)
D. \( P=2 \frac{3}{2} m g^{2} t \)


Which of the following is primarily an
ectotherm?
A. Pigeon
B. Camel
c. Lizard
D. Rabbit


The purine base present in RNA is:
A. guanine
B. thymine
c. cytosine
D. uraci


A particle of mass \( \mathrm{m} \) is performing simple harmonic motion along line AB with amplitude 2 a with centre of oscillation as \( 0 . \) At time \( t=0 \) particle is
at point \( C(O C=a) \) and is moving towards B with velocity \( \boldsymbol{v}=\boldsymbol{a} \sqrt{\mathbf{3}} \mathrm{m} / \mathrm{s} \)
The equation of motion can be given by This question has multiple correct options
A. \( x=2 a(\sin t+\sqrt{3} \cos t) \)
B \cdot \( x=2 a \sin \left(t+\frac{\pi}{6}\right) \)
c. \( x=a(\sin t+\sqrt{3} \cos t) \)
D. \( x=a(\sqrt{3} \sin t+\cos t) \)


In alcoholic fermentation
A. Triose phosphate is the electron donor, while acetaldehyde is the electron acceptor
B. Triose phosphate is the electron donor, while pyruvic acid is the electron acceptor.
C. There is no electron donor.
D. Oxygen is the electron acceptor


In which of the following pairs both members contain peroxy linkage?
A \( \cdot H_{2} S_{2} O_{8}, H_{4} P_{2} O_{6} \)
в. \( H_{2} S O_{5}, H_{4} P_{2} O_{7} \)
c. \( H_{2} T i O_{4}, H_{4} P_{2} O_{8} \)
D. \( S_{3} O_{9}, P_{4} O_{7} \)


Which of the following statement is
correct?
This question has multiple correct options
A . oxidizing power order: \( \operatorname{SiCl}_{4}<\operatorname{SnCl}_{4}<P b C l_{4} \)
B. Ionic character order: \( C s B r>R b B r>K B r>N a B r>L i B r \)
c. The ionic character of lead(II) halides decrease with the increase in atomic no. of halogen
D. The oxidation state of \( T l \) in \( T l I_{3} \) is +3


When \( p(x)=x^{3}+a x^{2}+2 x+a \) is
divided by \( (x+a), \) the remainder is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( a \)
\( c .-a \)
D. \( 2 a \)


The work function of a metal surface is 1
eV. A light of wavelength \( 3000 A^{0} \) is incident on it. The maximum velocity of the photo-electrons is nearly
\( \mathbf{A} \cdot 10^{6} m s^{-1} \)
B . \( 10^{4} m s^{-1} \)
c. \( 10^{2} m s^{-1} \)
D. \( 10 m s^{-1} \)


A student measures the terminal
potential difference (V) of a cell (of emf
\( \varepsilon \) and internal) resistance \( r \) as a
function of the current (I) flowing
through it. The slope and intercept of
the graph between \( V \) and \( I \), then respectively equal to:
\( \mathbf{A} \cdot-\in \) and \( r \)
B. \( \in \) and \( -r \)
c. \( -r \) and \( \epsilon \)
D. \( r \) and \( -\epsilon \)


Assertion
Let \( p<0 \) and \( \alpha_{1}, \alpha_{2}, \dots, \alpha_{9} \) be the nine
roots of \( \boldsymbol{x}^{\mathbf{9}}=\boldsymbol{p}, \) then
\( \boldsymbol{\Delta}=\left|\begin{array}{lll}\boldsymbol{\alpha}_{1} & \boldsymbol{\alpha}_{2} & \boldsymbol{\alpha}_{3} \\ \boldsymbol{\alpha}_{4} & \boldsymbol{\alpha}_{5} & \boldsymbol{\alpha}_{6} \\ \boldsymbol{\alpha}_{4} & \boldsymbol{\alpha}_{8} & \boldsymbol{\alpha}_{9}\end{array}\right|=0 \)
Reason
If two rows of a determinant are
identical, then determinant equals zero
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


Successful adaptation simply means
\( A \cdot \) an increase in fitness
B. moving to a new place
C . producing offspring
D. evolving new characteristics


Fill in the blanks:
In the game of tug-of-war, both the
teams pulls each other. So
A. force is applied due to interaction.
B. force is not applied although there is interaction
c. force is applied although there is an interaction.
D. none of the above


\( A, B \) and \( c \) can do a piece of work in 12 days, 15 days and 10 days respectively In what time will they all together finish it?
A. 6 days
B. 4 days
c. 8 days
D. 2 days


Which one of the following is an amphoteric oxide?
A. \( M n O_{2} \)
в. \( Z n O \)
\( c \cdot C a O \)
D. \( C O_{2} \)


Q Type your question-
tative cu titteratur ac a mgin \( n_{1} \)
above the floor of the elevator. After
making a collision with the floor of the
elevator it bounces to height \( h_{2} \). The
coefficient of restitution for collision is
e. For this situation, mark the correct
statement(s).
A . If elevator is moving down with constant velocity \( \nu_{0} \) then \( h_{2}=e^{2} h_{1} \)
B. If elevator is moving down with constant velocity \( \nu_{0} \) then \( h_{2}=e^{2} h_{1}-\frac{\nu_{0}^{2}}{2 g} \)
c. If elevator is moving with constant acceleration of \( g / 4 \) in upward direction, then impulse imparted by floor of the elevator to the ball is \( m(\sqrt{2 g h_{2}})+\sqrt{2 g h_{1}}+2 \nu_{0} \)
D. If elevator is moving with constant acceleration of \( g / 4 \) in upward direction, then it is not possible to determine a reaction between \( h_{1} \) and \( h_{2} \) from the given information.


2p orbitals have:
A \( . n=1, l=2 \)
B. \( n=1, l=0 \)
c. \( n=2, l=1 \)
D. \( n=2, l=0 \)


The yellow colour of urine of the vertebrates is due to
A. Cholesterol
B. Urochrome
c. Uric acid
D. Melanin


When 5 is subtracted from the length and breadth of the rectangle, the
perimeter becomes 26 . What is the
mathematical form of the statement


Of a certain sum, \( \frac{1}{3} r d \) is invested at \( 3 \%, \frac{1}{6} t h \) at \( 6 \% \) and the rest at \( 8 \% \). If the
81 for 2 years from all these
investments amounts to Rs. 600. Then
the original sum was
A. Rs. 2000
B. Rs. 3000
c. Rs. 4000
D. Rs. 5000


How will you represent 49 in cube root?
A \( \cdot \sqrt[7]{49} \)
B. \( \sqrt[2]{49} \)
\( c \cdot \sqrt[4]{49} \)
D. \( \sqrt[3]{49} \)


A certain reactant \( X O_{3}^{-} \) is getting
converted to \( X_{2} O_{7} \) in solution. The rate
constant of this reaction is measured
by titrating a volume of the solution with a reducing agent which reacts only
with \( X O_{3}^{-} \) and \( X_{2} O_{7} . \) In this process of reduction both the compounds
converted to \( X^{-} . \) At \( t=0, \) the volume of
the reagent consumed is \( 30 \mathrm{mL} \) and at \( \mathrm{t} \)
\( =9.212 \mathrm{min.} \) the volume used up is 36
mL. Find the rate constant(in \( h r^{-1} \) ) of
the conversion of \( \boldsymbol{X} \boldsymbol{O}_{3}^{-} \) to \( \boldsymbol{X}_{2} \boldsymbol{O}_{7} ? \)
Assuming reaction is of 1st order. (Given that \( \ln 10=2.303, \log 2=0.30 \) ).


Spiracles found in cockroach are which helps in gaseous exchange.
A. 2 pairs in thorax and 10 pairs in abdomen
B. 2 pairs in thorax and 6 pairs in abdomen
c. 2 pairs in thorax and 8 pairs in abdomen
D. 2 pairs in thorax and 4 pairs in abdomen


If an object is placed at \( A(O A>f) \) Where \( f \) is the focal length of the convex lens the image is found to be formed at
B. A perpendicular is erected at 0 and \( C \) is chosen on it such that the angle \( \angle \) BAC is a right angle. Then the value of will be
\( A \cdot A B / O C^{2} \)
B. (AC)(BC)/OC
c. \( (\mathrm{OC})(\mathrm{AB}) / \mathrm{AC}+\mathrm{BC} \)
D. OC^/AB


Organic substances such as sugars are translocated in phloem can be demonstrated by
A. Defoliation
B. Girdling the stem
c. Grafting
D. Root pressure


Carrier ions like \( \mathrm{Na}^{+} \) facilitate the
absorption of substances like
A. Fructose and some amino acids
B. Amino acids and glucose
c. Glucose and fatty acids
D. Fatty acids and glycerol


A full-wave rectifier circuit along with
the output is shown. The contribution(s)
from the diode 1 is (are).
A.
B. A, C
\( c . B, D \)
D. \( A, B, C, D \)


What is CFC?


Though the law gives women equal status in India, many people hold unscientific views on a woman's innate
nature, capacity and intelligence, and in practice give them a secondary status and role. Demolish this view
using scientific arguments, and by quoting examples of great women in science and other spheres; and persuade yourself and others that, given equal opportunity, women are on par with men.


Find the circumference of the circle
whose radius is \( 28 \mathrm{mm} . \) Take \( \pi=\frac{22}{7} \)


A ray of light is incident on one face of
prism with refracting angle \( \boldsymbol{A}\left(<\mathbf{9 0}^{\circ}\right) \)
The incident ray is normal to the other face of the prism. If \( C \) is the critical angle for prism air interface, then the ray will emerge from this faces only if
A \( \cdot \cot C<\cot A+1 \)
B. \( \cot C>\cot A+1 \)
c. \( \cot A<\cot C+1 \)
D. \( \cot A>\cot C+1 \)


Find the coefficient of: \( x \) in the
expansion of \( \left(1-3 x+7 x^{2}\right)(1-x)^{16} \)
Enter 1 if answer is -19 otherwise enter
0


The value of the definite integral \( \int \frac{d \theta}{1+\tan \theta}=\frac{501 \pi}{K} \) where \( a_{2}=\frac{1003 \pi}{2008} \) and
\( \boldsymbol{a}_{1}=\frac{\pi}{2008} \) The value of \( \mathrm{K} \) equalls
A. 2007
B. 2006
c. 2009
D. 2008


For a reversible reaction at \( 298 \mathrm{K} \), the
equilibrium constant K is 200. What is
the value of \( \triangle G^{0} \) at \( 298 \mathrm{K} ? \)
A . -13.13 kcal
B . -0.13 kcal
c. -3.158 kcal
D. - 0.413 kcal


Which one is the descending order of atomic radius of elements of third
period? \( N a(z=11), M g(z=12), A l(z=13) \)
and \( \boldsymbol{S} \boldsymbol{i}(\boldsymbol{z}=\mathbf{1 4}) \)
A. \( S i>A l>M g>N a \)
в. \( N a>M g>A l>S i \)
c. \( N a<M g<A l>S i \)
D. \( N a>A l>M g=S i \)


The various kinds of teeth present in human beings are
A. Premolars and canines
B. Molars and incisors
c. Muscular pharynx and molars
D. Incisors, canines, premolars and molars


Other things being equal, the EMF of a Daniell cell may be increased by
A. Keeping low temperature
B. Using large copper electrodes
c. using large zinc electrodes
D. Decreasing concentration of \( C u^{2+} \) ions


Density is a physical quantity.
A. fundamental
B. derived
c. semi-derived
D. semi-fundamental


Find the magnitude of the shortage
distance between the lines \( , \frac{x-8}{3}= \)
\( \frac{y+9}{-16}=\frac{z-10}{7} ; \frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5} \)


Which of the following group belongs to actinide series?
A. Th, Pa, U
B. Ce Pr, Nd
c. Ва, La, нf
D. Pt, Au, Ag


The population of a town is 1200 in
2010. From 2010 to 2015, the
population of the town increased by \( 10 \% \) per year. Whats the population of the town in \( 2015 ? \)
A .4932 .612
B . 3932.612
c. 2932.612
D. 1932.612


The solution of \( \frac{d^{2} y}{d x^{2}}=x e^{x}+1 \) is:
A \( \cdot y=(x-1) e^{x}+\frac{1}{2} x^{2}+C_{1} x+C_{2} \)
B. \( y=(x-2) e^{x}+\frac{1}{2} x^{2}+C_{1} x+C_{2} \)
c. \( y=(x+2) e^{x}+\frac{1}{2} x^{2}+C_{1} x+C_{2} \)
D. \( y=(x+2) e^{x}+C_{1} \)


Following equlibrium is of which type?
\( N a C l(s)+H_{2} O(l) \rightleftharpoons N a C l . H_{2} O(a q) \)
A. Solid-solid equilibrium
B. Solid-liquid equilibrium
c. Liquid-liquid equilibrium
D. Liquid-gas equilibrium


Choose the correct answer from the
alternative given. Area of triangle formed by straight lines
\( \boldsymbol{x}-\boldsymbol{y}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}=\mathbf{5} \) is
A . 25
в. \( \frac{25}{2} \)
c. \( \frac{25}{4} \)
D. None of these


A particle of mass \( m \) moving with a velocity of \( (4 \hat{i}-\hat{j}) m / s \) strikes a fixed wall and finally moves with a velocity of \( (3 \hat{i}+2 \hat{j}) m / s . \) Find
(a) the impulse received by the particle
(b) the coefficient of restitution between them in the collision


Draw the circles whose equation are
\( 3 x^{2}+3 y^{2}=4 x \)


which have the same positive kinetic energy but different masses. For this
ensemble, which graph best represents
the relationship between the particle's
mass and its total energy?
\( A \)
в.
\( c \)
D.


Portion of gene, which is transcribed but not translated is?
\( A \). Exon
B. Intron
c. cistron
D. codon


Plot a graph showing variation of capacitive reactance with the change in the frequency of the \( A C \) source.


Which of the following has the dimension of \( M L^{0} T^{-2} ? \)
A. Coefficient of viscosity
B. Surface tension
c. Vapour pressure
D. Kinetic energy


Hybridization of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{4}} \) is:
\( A \cdot s p^{3} \)
В . \( d s p^{2} \)
c. \( s p^{3} d^{2} \)
D. \( s p^{3} d \)


High voltage transmission results in
lower current and hence lower heat loss.
AC is preferred over DC because
A. Voltage level transformation is easier in AC at same power levels.
B. Voltage level transformation is easier in DC at same power levels.
c. Ac voltage levels are always greater than DC voltage levels
D. None of the above


When a steady current of \( 1 A \) flows
through a copper wire, the number of electrons crossing any cross-section area of the wire in one second is
A \( \cdot 6.25 \times 10^{16} \)
B . \( 6.25 \times 10^{18} \)
\( \mathbf{c} \cdot 625 \times 10^{18} \)
D. \( 6.25 \times 10^{20} \)


Carbon cannot be used in the reduction
of \( A l_{2} O_{3} \) because:
A. It is expensive
B. The enthalpy of formation of \( C O_{2} \) is more than that of \( A l_{2} O_{3} \)
C. Pure carbon is not easily available
D. The enthalpy of formation of \( A l_{2} O_{3} \) is too high


A square plate of edge 'a' and a circular
disc of same diameter are placed
touching each other at the midpoint of an edge of the plate as shown in figure. If mass per unit area for the two plates
are same then find the distance of
centre of mass of the system from the
centre of the disc.


A door of length \( 2 m \) and breadth 1 m is fitted in a wall. The length of the wall is 4.5 and the breadth is 3.6 m. Find the
\( \operatorname{cost} \) of the wall washing the wall, if the
rate white washing the wall is \( R s .20 \) per
\( \boldsymbol{m}^{2} \)


State True or False.
The plot of \( P V \) vs \( P \) at particular temperature is called isobar.
A. True
B. False


In the reaction \( \boldsymbol{B C l}_{3}+\boldsymbol{P H}_{3} \rightarrow \)
\( \left[\boldsymbol{C l}_{3} \boldsymbol{B} \leftarrow \boldsymbol{P} \boldsymbol{H}_{3}\right] \) the Lewis base is:
\( \mathbf{A} \cdot B C l_{3} \)
в. \( P H_{3} \)
c. both
D. none of them


A cricket ball is rolled on ice with a
velocity of \( 5.6 ~ m / s \) and comes to rest
after traveling 8 m. Find the coefficient
of friction. Given \( \boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2} \)


In a unit cube, find the angle between
the diagonal of the cube and a diagonal of a skew to it?


A one kilogram roll of copper wire has a resistance of \( 2 \Omega . \) The Ratio
of resistance of \( 4 k g \) roll of copper wire of
half the thickness of the wire to the
first roll is
A . 64
B. 32
c. 16
D. 4


Find the value of \( \cos ^{-1}\left(\cos \frac{13 \pi}{6}\right) \)


Though the stone tied to a thread is moved with a constant speed of \( 10 \mathrm{m} / \mathrm{s} \) along a circular path it's motion is called an acceleration motion.


The point in a Meter bridge is at \( 35.6 \mathrm{cm} . \) If the resistances in the gaps
are interchanged,the new balance point is:
A. \( 64.4 \mathrm{cm} \)
B. \( 56 \mathrm{cm} \)
c. 41.2 ст
D. \( 56.7 \mathrm{cm} \)


Define Heredity. Give two examples.


Small amount of glucose and amino acids are absorbed by-
This question has multiple correct options
A. Simple diffusion
B. Pinocytosis
c. Facilitated diffusion
D. Active transport


Let \( f(x) \) be a function such that \( \lim _{x \rightarrow 0} \frac{f(x)}{x}=1 . \) If
\[
\lim _{x \rightarrow 0} \frac{x(1+a \cos x)-b \sin x}{\{f(x)\}^{3}}=1
\]
then \( |a+b|= \)


Find the equations corresponding to following graph:
A. \( y=-4 x-6 \)
B. \( y=4 x-6 \)
\( c \cdot y=4 x \)
D. none of these


Integrate \( \frac{(x+12)}{(x+1)^{2}(x-2)} \)


The quantity of heat needed to raise the
temperature of 'M' g of water from \( t_{1}^{o} C \) \( \operatorname{to} t_{2}^{o} C \) is \( M C\left(t_{2}-t_{1}\right) \)
A. True
B. False


The polarising angle for glass is:
A. same for different kinds of glass
B. different for different kinds of glass
C. same for lights of all colours
D. varies with time


The current that must flow through the coil of a galvanometer so as to produce a deflection of one division on its scale
is called
A. charge sensitivity of the galvanometer
B. current sensitivity of the galvanometer
c. micro-volt sensitivity
D. none of the above


Identify the open curve.
\( \mathbf{A} \cdot 1 \) only
B. 4 only
\( \mathrm{C} \cdot 1,4 \) only
D. 1,2,3 only


Which of the following is used as preservative and flavoring agent?
A. Phophoric acid
B. Sulphuric acid
c. citric acid
D. Tartaric acid


"Xenon fluorides are Lewis acids and
Lewis bases."

If the given statement is true enter 1
else enter 0


Assertion
Pascal's law is the working principle of a hydraulic lift
Reason
Pressure is thrust per unit area
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


\( 7.5 \mathrm{ml} \) of a gaseous hydrocarbon was
exploded with \( 36 \mathrm{ml} \) of \( \mathrm{O}_{2} . \) On cooling,
the volume of gases was found to be \( 28.5 \mathrm{ml}, 15 \mathrm{ml} \) of which was absorbed by KOH and the rest was absorbed in a
solution of alkaline pyrogallol. The formula of hydrocarbon is:
A. \( C_{2} H_{6} \)
в. \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{6} \)


In the expansion of \( (1+x)^{n} \) the
coefficients of \( p^{t h} \) and \( (p+1)^{t h} \) terms
are respectively \( p \) and \( q \) then \( p+q= \)
\( \mathbf{A} \cdot \boldsymbol{n} \)
B. \( n+1 \)
\( c \cdot n+2 \)
\( \mathbf{D} \cdot n+3 \)


According to Newton's second law of
motion, the force acting on a body acts in the direction of :
A. Velocity
B. Acceleration
c. Momentum
D. wind velocity


If the resistance of a conductor is \( 5 \Omega \) at
\( 50^{\circ} \mathrm{C} \& 7 \Omega \) at \( 100^{\circ} \mathrm{C}, \) then mean
temperature coefficient of resistance (of material) is
A \( \cdot 0.013 /^{\circ} \mathrm{C} \)
B. 0.004/ \( ^{\circ} \mathrm{C} \)
c. \( 0.006 /^{\circ} \mathrm{C} \)
D. \( 0.008 /^{\circ} \mathrm{C} \)


Which of the following products is
formed in good yield by the reduction of
methyl 4-oxo-hexanoate \( (M) \) with
Li \( A l H_{4} \) in ether?
A. Methyl 4-hydroxyhexanoate
B. 1,4-Hexanediol
c. 4-Hydroxyhexanal
D. 6 -Methoxy-3-hexanone


A block B of mass \( 4 \mathrm{kg} \) is placed on a
rough horizontal plane. A time dependent horizontal plane. A time
dependent horizontal force \( \boldsymbol{f}=\boldsymbol{k} \boldsymbol{t}^{2} \) acts
on the block, \( k=2 N / s^{2} . \) The frictional
force between the block and the plane at
\( \boldsymbol{t}=2 \sec \) is \( \boldsymbol{\mu}=\mathbf{0 . 2} \)
A . 4 N
B. 8N
c. 12 N
D. zero


If \( \frac{x-3}{3+i}+\frac{y-3}{3-i}=i \) where \( x, y \in R \)
then
A. \( x=2 \) \& \( y=-8 \)
B. \( x=-2 \) \& \( y=8 \)
c. \( x=-2 \& y=-6 \)
D. \( x=2 \) \& \( y=8 \)


What is Poling process?


\( " * " \) is said to be commutative in \( A \) for
all \( a, b \epsilon A \)
A \( . a+b=b+a \)
B. \( a * b=b * a \)
\( c \cdot a-b=b-a \)
\( a \)
D. \( a * b \neq b * a \)


Define uniform circular motion. A
particle is travelling in a circle of diameter \( 15 m \). Calculate the distance
covered and the displacement when it completes two rounds.


\( \ln \) a \( \Delta P Q R, \) if \( P Q=P R \) and \( \angle Q \) is
twice that of \( \angle P, \) then \( \angle Q= \)
A .72
B. 36
c. \( 144^{\circ} \)
D. \( 108^{\circ} \)


The perimeter of the table.
A \( .402 .60 \mathrm{cm} \)
B. \( 522.60 \mathrm{cm} \)
c. \( 342.60 \mathrm{cm} \)
D. None of these


Which of the following statements is
true?
A. Normal is always perpendicular to the mirror
B. Incident ray is always on the left side of the normal
C. Reflected ray is always on the right side of the normal
D. Both B and C are true


Which of the following dissolves more rapidly in blood haemoglobin than oxygen?
A. Ozone
B. Nitrous oxide
c. sulphur dioxide
D. Carbon monoxide


Function of moderator in a reactor is to
A. slow down neutrons
B. absorb neutrons
c. speed up neutrons
D. catalyse neutrons


Assertion
Ionic reactions are not instantaneous.
Reason

Oppositely charged ions exert strong
forces.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Find the volume(in \( \mathrm{cm}^{3} \) ) of a cuboid
whose length \( =15 \mathrm{cm}, \) breadth \( =10 \mathrm{cm} \) and height \( =8 \mathrm{cm} \)


In the circuit shown in figure, \( \boldsymbol{E}_{1}= \)
\( \mathbf{3} \boldsymbol{V}, \boldsymbol{E}_{2}=\mathbf{2} \boldsymbol{V}, \boldsymbol{E}_{3}=\mathbf{1} \boldsymbol{V} \) and \( \boldsymbol{r}_{\mathbf{1}}=\boldsymbol{r}_{\mathbf{2}}= \)
\( r_{3}=1 o h m \)
(a) Find the potential difference
between the points \( A \) and \( B \) and the
currents through each branch.
(b) If \( r_{2} \) is short circuited and the point
\( A \) is connected to point \( B \) through a
resistance \( R, \) find the currents through
\( \boldsymbol{E}_{1}, \boldsymbol{E}_{2}, \boldsymbol{E}_{3} \) and the resistor \( \boldsymbol{R} \)


If \( \boldsymbol{A}=\left(\begin{array}{c}-121 \\ 1 & 23\end{array}\right), B=(1) \) and \( C=(21) \)
verify \( (A B) C=A(B C) \)


Which of the following is not a major greenhouse gas?
A. Carbon dioxide
B. Methane
c. calcium carbonate
D. water vapour


Which of the following show
paramagnetism? This question has multiple correct options
A \( \cdot N O_{2} \)
B. \( N O \)
\( c \cdot K O_{2} \)
D. \( N a_{a} O \)


\( K M n O_{4} \) solution is:
A . red
B. purple
c. orange
D. green
E. blue


The minus \( \operatorname{sign} \) in \( r a t e=-\frac{d[A]}{d t} \)
indicates the
concentration of the
time. The rate of a reaction is always quantity. The rate of reaction increases with
concentration of reactants. The blanks
in the question corresponds to:
A. decrease, products, positive, increase
B. increase, reactants, negative, decrease
c. decrease, reactants, positive, increase
D. increase, products, positive, increase


How many mitotic divisions are needed
for a single cell to make 128 cells?
A. 7
B. 14
\( c \cdot 28 \)
D. 32


Gabriel phthalimide reaction is used for the preparation of :
A. Primary aromatic amines
B. Secondary amines
c. Primary aliphatic amines
D. Tertiary amines


Which of the following functions represent a simple harmonic motion?
\( \mathbf{A} \cdot \sin \omega t-\cos \omega t \)
B. \( \sin ^{2} \omega t \)
\( \mathbf{c} \cdot \sin \omega t+\sin ^{2} \omega t \)
D. \( \sin \omega t-\sin ^{2} \omega t \)


Acid rain produced when rain mixes
with gases such as sulphur dioxides. This will eventually result in:
A. lowering of pH and change of temperature in ponds
B. raising of pH in ponds, encouraging growth of microorganisms
c. lowering of pH in ponds, limiting survival of aquatic organism
D. raising of pH in ponds, limiting development of organisms


The four general methods of extracting metals are thermal, decomposition, displacement of one element by another, chemical reduction and
electrolytic reduction. how are the group
metals obtained and why are the other methods unsuitable?


Solve: \( \int \frac{\cos x}{1+\cos x} \)


\( \boldsymbol{I}-\boldsymbol{V} \) graph for a metallic wire at two
different temperatures, \( \boldsymbol{T}_{1} \) and \( \boldsymbol{T}_{2} \) is a
shown in the figure.

Which of the two temperature is lower
and why?


Give an account of the disorder of
human respiratory system


Ethylenediamine displaces \( H_{2} O \) in the
complex \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \) in three steps.
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+}+\boldsymbol{3} \boldsymbol{e n} \rightarrow\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{e n})_{3}\right]^{3+}+ \)
\( 6 H_{2} O \)
Stepwise formation constants are:
\( \log K_{1}=4.34 \)
\( \log K_{2}=3.31 \)
\( \log K_{3}=2.05 \)
Overall formation constant is \( \boldsymbol{A} \times \mathbf{1 0}^{\mathbf{2 B}} \)
\( B \) in question is:


A metal cube of side length \( 8.0 \mathrm{cm} \) has its upper surface displaced with
respect to the bottom by \( 0.10 m m \) when
a tangential force of \( 4 \times 10^{9} \mathrm{N} \) is applied
at the top with bottom surface fixed. The rigidity modulus of the material of the cube is :
A \( \cdot 4 \times 10^{9} N / m^{2} \)
B. \( 5 \times 10^{14} N / m^{2} \)
c. \( 8 \times 10^{9} N / m^{2} \)
D. \( 1 \times 10^{9} N / m^{2} \)


Cationic surfactants is/are:
A. \( C_{17} H_{35} \)COONa
в. \( C_{17} H_{35} \)СООК
c \( \cdot C_{17} H_{35} S O_{3} N a \)
D. \( C_{16} H_{33} N\left(C H_{3}\right)_{3} C l \)


Fill the columns and complete the given
table. Give explanation for your answer


The left hand derivative of \( f(x)= \)
\( [x] \sin \pi x \) at \( x=k, k \) is an integer, is
\( \mathbf{A} \cdot(-1)^{k}(k-1) \pi \)
B \cdot \( (-1)^{k-1}(k-1) \pi \)
\( \mathbf{c} \cdot(-1)^{k} k \pi \)
D. \( (-1)^{k-1} k \pi \)


If force \( F, \) work \( W \) and velocity \( v \) are
taken as fundamental quantities, then the dimensional formula of time is :


Proximal convoluted tubule of nephron
is responsible for
A. Filtration of blood
B. Maintenance of Glomerular Filtration Rate
C. Selective reabsorption of glucose, amino acid, NaCl and water
D. Reabsorption of salts only


The final product of setting of plaster of paris is
A. gypsum
B. anhydrite
c. cement
D. mortar


Which kind of isomerism is exhibited
by octahedral complex \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right. \)
\( \left.\boldsymbol{B} \boldsymbol{r}_{2}\right] \boldsymbol{C l} ? \)
A. Geometrical and ionization
B. Geometrical and optical
c. optical and ionization
D. Geometrical only


Details of some gases taken at \( 273 \mathrm{K} \)
temperature and 1 atm pressure are given in the table.
\( \begin{array}{lll}\text { Gas } & \text { Volume (L) } & \text { Number of moles } \\ \text { Hydrogen } & 224 & 10 \\ \text { Helium } & 112 & 5 \\ \text { Oxygen } & 224 & 10 \\ & & \end{array} \) Ammonia 56 2.5
(a) On the basis of which gas law, the volume and the number of moles are
given in the table?
(b) Represent this gas law in mathematical form.
(c) Among these, if the pressure of hydrogen gas is changed to 2 atm. Calculate the new volume.


\( A \) and \( B \) are two candidates seeking
admission in I.I.T. The probability that \( \boldsymbol{A} \)
is selected is 0.5 and the probability that both \( A \) and \( B \) are selected is
atmost \( 0.3 . \) Is it possible that the probability of \( \boldsymbol{B} \) getting selected is \( \mathbf{0 . 9} \) ?
If it is possible then enter 1 , else enter 0


Balloon type inflated persistent calyx is characteristic of
A. Helianthus
B. Colutea
c. Physalis
D. All of the above


A very thin metal sheet is inserted
halfway between the parallel plates of an air-gap capacitor. The sheet is thin compared to the distance between the plates, and it does not touch either plate when fully inserted. The system had capacitance, \( C \), before the plate is inserted.

What is the equivalent capacitance of the system after the sheet is fully
inserted?
\( ^{A} \cdot \frac{1}{4} C \)
в. \( \frac{1}{2} C \)
c. \( C \)
D. \( 2 C \)
E . \( 4 C \)


Length of one turn of DNA is
\( A \cdot 3.4 \AA \)
B. 34 \( \dot{A} \)
\( c \cdot 20 \dot{A} \)
D. 3.04 \( \hat{A} \)


Due to the weak Van der Waals' forces
and less distance between the layers,
graphite:
A. show lubricating property
B. has lusture
c. is hexagonal
D. is a good conductor of electricity


On a stationary sail boat, air is blown at
the sails from a fan attached to the
boat. The boat will
A. remain at rest
B. spin round
c. move in the direction in which air is blown
D. move in a direction opposite to that in which air is blown


Name the two major defects of an eye.
Explain causes of their development
and discuss methods of their
correction.


\( A B C \) is a right angled triangle and 0 is
the mid point of the side opposite to the
right angle. Explain why \( O \) is
equidistant from \( A, B \) and, \( C \)


Suppose \( \boldsymbol{f}(\boldsymbol{n})= \)
\( \log _{2}(3) \cdot \log _{3}(4) \cdot \log _{4}(5) \dots \dots \log _{n-1}(n) \)
then the sum \( \sum_{k=2}^{100} f\left(2^{k}\right)=\lambda \)
then \( \frac{\lambda}{1683} \) is equal to?


Which element has the highest valency with respect to oxygen?
A. Sodium
B. Aluminium
c. chlorine
D. Sulphur


Assertion
\( G_{1} \) phase is the interval between
mitosis and initiation of DNA
replication
Reason
The cell is metabolically inactive during
\( G_{1} \) phase.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In an experiment, 20 g of vanadium \( (V) \) oxide (molar mass \( =182 \) g/mol) was
reduced by excess of zinc dust in acidic solution to vanadium
(II) ions. If the
required number of moles of iodine to
reoxidise vanadium
(II) to \( V O^{2+} \) is
\( 22 \times 10^{-x}, \) then what is the value of \( x ? \)


The process by which the cytoplasm of a
cell divides to form two daughter cells.
A. Cytokinesis
B. Prophase
c. Metaphase
D. Anaphase
E. Telophase


When an \( \alpha \) -particle of mass ' \( m^{\prime} \) moving
with velocity \( ^{\prime} v^{\prime} \) bombards on a heavy
nucleus of charge \( ^{\prime} Z e^{\prime}, \) its distance of
closest approach from the nucleus
depends on \( m \) as:
A \( \cdot \frac{1}{m} \)
в. \( \frac{1}{\sqrt{m}} \)
c. \( \frac{1}{m^{2}} \)
D. \( m \)


A body, projected vertically up with a velocity of \( 20 m s^{-1}, \) reaches a height of \( 20 m . \) If it is projected with a velocity of
\( 40 m s^{-1}, \) then the maximum height
reached by the body is:
A . \( 20 m \)
в. 10 т
\( c .80 m \)
D. \( 40 m \)


Which of the following is a transition element?
A. Element with atomic number 2
B. Element with atomic number 7
c. Element with atomic number 19
D. Element with atomic number 35
E. Element with atomic number 74


Find the degree of the differential equation: \( \sqrt{1+x^{2}}=\frac{d y}{d x} \)
\( A \cdot 2 \)
B.
\( c \cdot 4 \)
D. None of these


\( \frac{1}{c},\left(\frac{1}{c a}\right)^{\frac{1}{2}}, \frac{1}{a} \) is in
\( A \cdot A P \)
в. GP
\( c . \) не
D. NONE


Then
Answer: DC produced bisects BC at right angle. If true then enter 1 else if False enter 0


Which of the above represents the formula for the most common
compound of \( X \) and \( Y ? \) Where \( X \) is \( C a \)
and \( Y \) is \( F \)
A. \( X_{2} Y \)
\( Y \)
в. \( X Y \)
c. \( X Y_{2} \)
D. \( X Y_{3} \)
E. \( X Y_{4} \)


The pair of molecules in which one of
the molecule has linear shape while
another one has square based pyramid
shape is:
\( \mathbf{A} \cdot\left[B r_{3}^{-}, P F_{5}\right] \)
в. \( C O_{2}, N F_{3} \)
\( \mathrm{c} \cdot \mathrm{SO}_{2}, \mathrm{CIF}_{5} \)
D \( \cdot\left[l_{3}^{-}, B r_{5}\right] \)


A battery jar contained a solution of
copper sulfate. Two electrodes. one
made of copper the other a metal object to be copper plated, were placed in the jar and connected to a source of direct current. Which of the following statements concerning this system is correct?
A. The object to be placed is the anode
B. Oxidation occurs at the anode
c. The sulfate ions migrate toward the cathode
D. The concentration of the copper sulfate solution increases as electrolysis proceeds
E. The copper electrode increases in mass


Lymph is transported through the
A. Lymph nodes
B. Lymphocytes
c. Lymph nerves
D. Lymph vessels


Which of the following elements has lowest electronegativity?
A. \( N a \)
в. \( M g \)
c. \( A l \)
D. \( S \) i


Assertion (A): Aldehydes are one of the constituents of photochemical
\( \operatorname{sinog} \)
Reason (R): Aldehydes are produced by photochemical oxidation of hydrocarbons by ozone.
A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true but R is not correct explanation of A.
c. A is true and \( \mathrm{R} \) is false
D. A is false and R is true


A Sound wave with an amplitude of \( 3 c m \)
starts moving towards right from origin
and gets reflected at a rigid wall after a
second. If the velocity of the wave is
\( 340 m s^{-1} \) and it has a wavelength of \( 2 m \)
the equations of incident and reflected
waves are
A \( \cdot y=3 \times 10^{-2} \sin \pi(340 t-x), y=-3 x \)
\( 10^{-2} \sin \pi(340 t+x) \) towards left
B . \( y=4 \times 10^{-2} \sin \pi(340 t+x), y=-4 \times \)
\( 10^{-2} \sin \pi(340 t+x) \) towards left
C . \( y=5 \times 10^{-2} \sin \pi(340 t-x), y=-5 \times \)
\( 10^{-2} \sin \pi(340 t-x) \) towards left
D . \( y=6 \times 10^{-2} \sin \pi(340 t-x), y=-6 \times \)
\[
10^{-2} \sin \pi(340 t+x) \text { towards left }
\]


The handles of cooking vessels are covered with plastic or wood because:
A. They are beautiful.
B. It is customary
c. They are good conductors of heat
D. They are bad conductors of heat


The work done by a force \( \overline{\boldsymbol{F}}= \)
\( \left(-6 x^{3} i\right) N \) in displacing particle from
\( \boldsymbol{x}=\boldsymbol{a} \boldsymbol{m} \boldsymbol{t} \boldsymbol{o} \boldsymbol{x}=-\boldsymbol{2} \boldsymbol{m} \) is


The maximum value of \( \left(\frac{\log x}{x}\right) \) is
A \( \cdot\left(\frac{1}{e}\right. \)
B. \( \frac{2}{e} \)
\( c \cdot e \)
D.


In a survey of 600 students in a school,
(i) 160 students were found to be taking
Tea 215 taking Coffee, 150 were taking both Tea and Coffee.
(ii) 150 students were found to be
taking tea and 225 taking coffee, 100 were taking both Tea and Coffee. Find how many students were taking neither tea nor coffee?


The largest sphere is carved out of a cube of a side \( 7 \mathrm{cm} . \) Find the volume of
the sphere.


In order to extract isobutyric acid from a solution of diethyl ether, one should wash the solution with:
A. one \( 30 m L \) wash of water
B. three \( 10 m L \) washes of water
c. one \( 30 m L \) wash of hexane
D. three \( 10 m L \) washes of hexane


A solid cylinder and a hollow cylinder of the same mass and radius, both
initially at rest, roll down the same inclined plane without slipping. Choose the correct options. This question has multiple correct options
A. The hollow cylinder reaches the bottom first
B. The solid cylinder reaches the bottom first
c. The two cylinder reach the bottom together
D. Their kinetic energies at the bottom are equal.


\( \tan \left(\rho \frac{\pi}{4}\right)=\cot \left(q \frac{\pi}{4}\right) \)
A \( . \rho+q=0 \)
В \( \cdot \rho+q=2 n+1 \)
c. \( \rho+q=2 n \)
D \( \cdot \rho+q=2(2 n+1) \)


Find the coordinates of those points on the line \( \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{2}}=\frac{\boldsymbol{y}+\mathbf{2}}{\mathbf{3}}=\frac{\boldsymbol{z}-\mathbf{3}}{\mathbf{6}} \) which
is at a distance of 3 units from the point
(1,-2,3)


When a ball is thrown up, the
magnitude of its momentum decreases
and then increases. Does this violate
the conservation of momentum
principle?


If the distance between the parallel lines given by \( x^{2}+2 x y+y^{2}-9 a^{2}=0 \)
is \( 90 \sqrt{2} \) then \( a \) is equal to


It is known that \( \sin \beta=\frac{4}{5} \& 0<\beta<\pi \)
then the value of
\( \frac{\sqrt{\mathbf{3}} \sin (\boldsymbol{\alpha}+\boldsymbol{\beta})-\frac{\mathbf{2}}{\mathbf{c o s}} \frac{\boldsymbol{\pi}}{\mathbf{6}} \cos (\boldsymbol{\alpha}+\boldsymbol{\beta})}{\sin \boldsymbol{\alpha}} \)
A. independent of \( \alpha \) for all \( \beta \) in \( (0, \pi) \)
В. \( \frac{5}{\sqrt{3}} \) for \( \tan \beta<0 \)
c. \( \frac{\sqrt{3}(7+24 \cot \alpha)}{15} \) for \( \tan \beta>0 \)
\( D . \) none


Which of the following element is expected to have highest electron gain enthalpy:
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{3} \)
c. \( 1 s^{2} 2 s^{2} 2 p^{4} \)
D \( \cdot 1 s^{2} 2 s^{2} 2 p^{5} \)


Two wires carry currents of \( 100 A \) and
\( 200 A \) respectively and they repel each other with a force of \( 0.4 N / m . \) The distance between them will be
A . \( 1 m \)
B. \( 1 \mathrm{cm} \)
\( c .50 \mathrm{cm} \)
D. \( 25 \mathrm{cm} \)


During bleaching action, \( \mathbf{S O}_{2} \) converts
into
\( A \cdot S O_{3} \)
в. \( \mathrm{H}_{2} \mathrm{SO}_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)


For a metallic wire, the ratio of voltage
to corresponding current is?
A. Independent of temperature
B. Increases with rise in temperature
C. Increases or decreases with rise in temperature depending upon the metal
D. Decreases with rise in temperature


2-acetoxybenzoic acid is used as:
A. antiseptic
B. antidepressant
c. antimalaria
D. antipyretic


Which of the following alkenes gives
only ketones on ozonolysis?
\( A \)
B.
c.
D. \( \mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3} \)


\( b \)
\( d \)
\( d \)
\( y \)


If \( \int \frac{d x}{(x+2)\left(x^{2}+1\right)}=a \ln \left(1+x^{2}\right)+ \)
\( b \tan ^{-1} x+\frac{1}{5} \ln |x+2|+C \) then
A. \( a=-\frac{1}{10}, b=-\frac{2}{5} \)
B. \( a=\frac{1}{10}, b=\frac{2}{5} \)
c. \( a=-\frac{1}{10}, b=\frac{2}{5} \)
D. \( a=\frac{1}{10}, b=-\frac{2}{5} \)


\( \mathbf{f} \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{2} & \mathbf{3} \\ \mathbf{4} & \mathbf{5} & \mathbf{6} \\ \mathbf{7} & \mathbf{1} & \mathbf{0}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{3} & \mathbf{0} \\ \mathbf{0} & \mathbf{4} & \mathbf{5}\end{array}\right] \)
\( , \operatorname{Tr}(\mathrm{BA})=\dots \)
A. 40
в. 45
\( c .39 \)
\( D \)


State whether true or false:
The angle of incidence is always smaller than angle of refraction when a ray travels from air to glass, at an oblique angle
A. True
B. False


In electroplating, the metal to be used for coating is made the
A. Cathode (negative electrode)
B. Anode(positive electrode)
c. cathode(positive electrode)
D. Anode(negative electrode)


The oxidation state of cobalt in the
following molecule is:
\( A \cdot 3 \)
B.
\( c \cdot 2 \)
\( D \)


The resistance of a metal increases
with the increase of temperature due to
A. Number of electrons
B. Velocity of electrons
c. Scattering of electrons with core ions
D. Thermal motion of core ions


The solubility of alcohols in water gradually increases with molecular weight
A. True
B. False


Ductility of a metal can be stated as:
A. the property to produce sound on striking
B. the property to have shiny surface
C. the property to be drawn into wires
D. the property to conduct heat and electricity.


Which of the following gates corresponds to the truth table given below?
\( A B Y \)
\[
\begin{array}{ccc}
1 & 1 & 0 \\
1 & 0 & 1 \\
0 & 1 & 1
\end{array}
\]
\( 0 \quad 0 \quad 1 \)
A. xor
в. ок
c. NAND
D. NOR


The orange solution of \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) turns
yellow on adding NaOH to it .If true enter
else 0
\( A \)


\( \operatorname{Let} \alpha(a) \) and \( \beta(a) \) be the roots of the
equation \( (\sqrt[3]{1+a}-1) x^{2}+(\sqrt{1+a}- \)
1) \( x+(\sqrt[6]{1+a}-1)=0 \) where \( a>-1 \)
Then \( \lim _{a \rightarrow 0^{+}} \alpha(a) \) and \( \lim _{a \rightarrow 0^{+}} \beta(a) \) are
A \( \cdot-\frac{5}{2} \) and 1
B. \( -\frac{1}{2} \) and -1
\( c \cdot-\frac{7}{2} \) and 2
D. \( -\frac{9}{2} \) and 3


Assign the IUPAC names for the given compounds:


\( \operatorname{Let} f(x)=\left\{\begin{aligned} a x+1, & x<1 \\ 3, & x=1 . \text { The valu } \\ b x^{2}+1, & x>1 \end{aligned}\right. \)
of \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime} \) for which \( f(x) \) is
continuous at \( x=1 \), is given by
A .2,2
в. 1,2
\( c .3,2 \)
D. \( 1, \)


A ray of light \( O P \) passes through a right
angled prism as shown in the adjacent
diagram. State the angles of incidence at the faces \( A C \) and \( B C . \) Given critical
angle is \( 42^{\circ} \)
A . Angle of incidence at the face \( A C=45^{\circ} \) and angle of
incidence at the face \( B C=90^{\circ} \)
B. Angle of incidence at the face \( A C=90^{\circ} \) and angle of
incidence at the face \( B C=45^{\circ} \)
C. Angle of incidence at the face \( A C=45^{\circ} \) and angle of
incidence at the face \( B C=0^{\circ} \)
D. Angle of incidence at the face \( A C=0^{\circ} \) and angle of
incidence at the face \( B C=45^{\circ} \)


The velocity-time graph of a particle in one-dimensional motion is shown in the
figure. Which of the following formulae
is correct for describing the motion of
the particle over the time interval \( t_{1} \) to
\( t_{2} ? \)
A \( \cdot x\left(t_{2}\right)=x\left(t_{1}\right)+v\left(t_{1}\right)\left(t_{2}-t_{1}\right)+\left(\frac{1}{2}\right) a\left(t_{2}-t_{1}\right)^{2} \)
B \( \cdot v\left(t_{2}\right)=v\left(t_{1}\right)+a\left(t_{2}-t_{1}\right) \)
C \( \cdot v_{\text {average }}=\frac{\left(x\left(t_{2}\right)-x\left(t_{1}\right)\right)}{\left(t_{2}-t_{1}\right)} \)
D. \( a_{\text {average}}=\frac{\left(v\left(t_{t}\right)+v\left(t_{1}\right)\right)}{\left(t_{2}-t_{1}\right)} \)


For the manufacture of cement various
steps are given below. Arrange the steps in a proper sequence.
(a) Clinker formation
Crushing
(c) Addition of gypsum Mixing of raw materials
(e) Grinding to fine powder Calcination in rotary kiln
\( A \cdot d b f a c e \)
B. \( b d f \) c e a
c. \( d c \) a fe \( b \)
D. a b c de f


Draw Venn diagrams to illustrate \( (\boldsymbol{A} \mid \)
\( \boldsymbol{B}) \cup(\boldsymbol{A} \backslash \boldsymbol{C}) \)


A concave lens of focal length \( \boldsymbol{f} \) produces an image \( (1 / n) \) times the size of the object. The distance of the object from the lens is
A \( \cdot(n+1) f \)
в. \( \frac{(n-1)}{n} f \)
c. \( \frac{(n+1)}{n} f \)
D. \( (n-1) f \)


Write balanced chemical equations to
show:
The dehydrating property of conc. Sulphuric acid with sugar.


A circular racket of radius \( 300 \mathrm{m} \) is
backed at an angle of \( 15^{0} \). The
coefficient of friction between the
wheels of a race car and the road is 0.2
the maximum permissible speed to avoid slipping is ( Take \( \left.\tan 15^{0}=0.27, g=10 m s^{-2}\right) \)
\( \mathbf{A} \cdot 18.6 \mathrm{ms}^{-1} \)
B. 28.6 \( m s^{-1} \)
c. \( 38.6 \mathrm{ms}^{-1} \)
D. \( 48.6 \mathrm{ms}^{-1} \)


The number of students absent in a
class were recorded for 120 days and the information is given in the following frequency table:
No. of students absent
\( x \)
No. of
\[
\operatorname{days}(f)
\]
50
Find the mean number of students
absent per day.


Enthalpy of sublimation of a substance
is equal to :
A. Enthalpy of fusion + enthalpy of vapourisation
B. Enthalpy of fusion
c. Enthalpy of vapourisation
D. Twice the enthalpy of vapourisation


The protein coat of virus is called
A. capsid
B. cosmid
c. capsomere
D. Chromophore


Metals which can be obtained by carbon reduction of their oxides are
This question has multiple correct options
A. cu
B. Fe
c. \( A l \)
D. Pb


Explain some harmful effects of agricultural practices on the environment.


For a binary liquid solution obeying Raoult's law at \( 300 K \)
\( \boldsymbol{X}_{\boldsymbol{A}}=\mathbf{0 . 7 5}, \) Given: \( \boldsymbol{P}_{\boldsymbol{A}}^{\boldsymbol{o}}= \)
\( 400 m m H g ; P_{B}^{o}=600 m m H g \)
Then select correct statement
This question has multiple correct options
A. Vapour pressure of solution will be \( 450 \mathrm{mm} \mathrm{Hg} \)
B. In distillate mol fration of \( B \) will be \( 2 / 3 \)
c. If distillate is removed \( \& \) condensed then it is redistilled, then mole fraction of \( A \) in \( I I \) distillate is \( 4 / 7 \)
D. Normal boiling point of liquid solution should be more than \( 300 K \)


Three charges \( -q,+q \) and \( -q \) are
placed at the corners of an equilateral triangle of side a. The resultant electric force on a charge \( +\boldsymbol{q} \) placed at the centroid 0 of the triangle is:
A \( \cdot \frac{3 q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
в. \( \frac{q^{2}}{4 \pi \varepsilon_{0} a^{2}} \)
c. \( \frac{q^{2}}{2 \pi \varepsilon_{0} a^{2}} \)
D. \( \frac{3 q^{2}}{2 \pi \varepsilon_{0} a^{2}} \)


Fluid friction is exerted by
A. solids and liquids
B. solids and gases
c. liquids and gases
D. all the above


What happens when \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \) is
heated?


A parallel plate capacitor having plates
of area \( \mathrm{S} \) and plate separation \( \mathrm{d}, \) has
capacitance \( C_{1} \) in air. When two
dielectrics of different relative
permittivities \( \left(\varepsilon_{1}=2 \text { and } \varepsilon_{2}=4\right) \) are
introduced between the two plates as
shown in the figure, the capacitance becomes \( C_{2} . \) The ratio \( \frac{C_{2}}{C_{1}} \) is
A . \( 6 / 5 \)
B. \( 5 / 3 \)
\( c \cdot 7 / 5 \)
\( 0.7 / 3 \)


Three types of tissue systems namely epidermal, fundamental, \& vascular,
were proposed by
A. Hanstein
B. Buvat
c. sachs
D. Nageli


f \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{4} \\ -\mathbf{1} & \mathbf{1}\end{array}\right] \) Find \( \boldsymbol{A}^{2} \)


\( \left|\begin{array}{ccc}\text { If } & \\ \cos (\boldsymbol{A}+\boldsymbol{B}) & -\sin (\boldsymbol{A}+\boldsymbol{B}) & \cos 2 \boldsymbol{B} \\ \sin \boldsymbol{\operatorname { s o s }} \boldsymbol{\operatorname { s i n }} \boldsymbol{A} & \boldsymbol{\operatorname { s i n } \boldsymbol { \operatorname { m o s } }}\end{array}\right| \)
\( =0 \) then \( B= \)
\( A \cdot(2 n+1) \frac{\pi}{2} \)
B. \( n \pi \)
\( c \cdot(2 n+1) \pi \)
D. 2 nn


Find the maximum and minimum value
of the function:
\( f(x)=2 x^{3}-21 x^{2}+36 x-20 \)


Male gametes are flagellated in
A. Ectocarpus.
B. Spirogyra.
c. Polysiphonia.
D. Anabaena.


Write down ten positive rational numbers such that the sum of the
numerator and the denominator of each
is
11. Write them in decreasing order


A block of mass \( 2 \mathrm{kg} \) is pushed against a rough vertical wall with a force of \( 40 \mathrm{N} \) coefficient of static friction being 0.5
Another horizontal force of \( 15 \mathrm{N} \), is
applied on the block in a direction
parallel to the wall. If the block will move, then its direction would be:
B. \( 53^{\circ} \) with \( 15 N \) force
C. \( 45^{\circ} \) with \( 15 N \) force
D. 75 \( ^{\circ} \) with 15N force


The coordinates of a point, which lies on \( y \) -axis and is at a distance of 4 units
above \( x \) -axis is
A \( .(0,4) \)
в. (4,4)
c. (4,0)
D. (0,-4)


Which pair in the following has maximum and minimum ionic
character respectively?
A. \( L i C l, R b C l \)
в. \( R b C l, \) Ве \( C l_{2} \)
c. \( B e C l_{2}, R b C l \)
D. \( A g C l, R b C l \)


The equilibrium constant for the reaction
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{S}(s) \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \)
is 18.5 at \( 925 K \) and 9.25 at \( 1000 K \)
respectively. Calculate the enthalpy of
the reaction.


Myopia is due to
A. Elongation of the eye ball
B. Excessive curvature of the cornea
C. Both A and B
D. None of the above


Assertion
The point \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{1}, \boldsymbol{6}) \) is the mirror image
of the point \( B(1,3,4) \) in the plane \( x- \)
\( \boldsymbol{y}+\boldsymbol{z}=\mathbf{5} \)
Reason
The plane \( x-y+z=5 \) bisects the line
segment joining \( \boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6}) \) and
\( \boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4}) \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Assertion
A ray of light is incident from outside on
a glass sphere surrounded by air. This ray may suffer total internal reflection
at second interface.
Reason
If a ray of light goes from denser to rarer
medium, it bends away from the
normal.
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


Fill in the blanks.
Dry nitrogen gas cannot be collected by the displacement of


The oxidation number of Phosphorus in
\( M g_{2} P_{2} O_{7} \) is:
\( A \cdot+3 \)
\( B .+2 \)
\( c \cdot+5 \)
\( D \cdot-3 \)


Which of the following compound is more acidic?
A. ethyne
B. propene
c. ethene
D. propane


Q Type your question-
connected to a fixed vertical wall and
the other end has a block of mass \( \mathrm{m} \)
initially at rest on a smooth horizontal
surface. The spring is initially in natural length. Now a horizontal force F acts on the block as shown. Then the maximum
extension in spring is equal to the maximum compression in the spring.
Reason

To compress and to expand an ideal unstretched spring by equal amount, same work is to be done on the spring.
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


\( \operatorname{Let} f(x)=\sin ^{-1} \sin x+ \)
\( \cos ^{-1} \cos x, \quad g(x)= \)
\( m x \quad \) and \( \quad h(x)=x \) are three
functions. Now \( g(x) \) divided area
between \( \boldsymbol{f}(\boldsymbol{x}), \boldsymbol{x}=\boldsymbol{\pi} \) and \( \boldsymbol{y}=\boldsymbol{0} \) into two
equal parts. The value of m is:
A \( \cdot \frac{1}{4} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{5}{4} \)
D. \( \frac{7}{4} \)


The velocity of a kerosene oil in a
horizontal pipe is \( 5 m / s . \) If \( g=10 m / s^{2} \)
then the velocity head of oil will be
\( \mathbf{A} \cdot 1.25 m \)
B. \( 12.5 m \)
c. \( 0.125 m \)
D. \( 125 m \)


\( \operatorname{Let} \frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}=\ln \sqrt{\frac{1+x}{1-x}}, \) then find \( x \)


A ball resting on a tray attached to a spring is made to oscillate vertically, such that the fixed end of the spring is attached to the ground. If the spring is compressed and let go, the ball will execute SHM until
A. the ball is in contact with the spring
B. the ball occasionally loses contact with the spring
c. the ball loses contact with the spring beyond the mean position
D. the ball loses contact with the spring beyond the extreme position


n \( \Delta P Q R \) are the mid points of side \( A B \)
BC and AC respectively. PQ and QR are
joined. Prove that BRQP is a
parallelogram


Assertion
Separation of isotope is possible because of the difference in electron
numbers of isotope.
Reason
Isotope of an element can be separated by using a mass spectrometer
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. Reason is correct but Assertion is incorrect


Two bodies having the same mass, \( 2 \mathrm{kg} \)
each have different surface areas \( 50 \mathrm{m}^{2} \)
and \( 100 \mathrm{m}^{2} \) in contact with a horizontal
plane. If the coefficient of friction is 0.2 the forces of friction that come into play when they are in motion will be in the ratio.
A . 1:
B. 1: 2
c. 2: 1
D. 1: 4


The points \( (-2,-1),(1,0),(4,3), \) and (1,2) are the vertices
A. Parallelogram
B. Rectangle
c. square
D. Both (1) \& (2)


In the circuit shown in the figure, ammeter and voltmeter are ideal. If
\( E=4 V \) and \( R=15 \Omega \) and \( r=1 \Omega, \) then
the reading of the ammeter is
A \( \cdot \frac{1}{3} A \)
\( B \cdot \frac{2}{3} A \)
\( c \cdot 1 A \)
D. \( \frac{1}{4} A \)


Choose the wrong statement about subspecies.
A. They do not interbreed with individual of other subspecies
B. They are new species in the making
c. Geographically isolated populations of a species
D. They show minor variations from parent population


Kiran purchase a house for \( R s 7,45,000 . \) He spent \( R s 30,000 \) on
repairs and painting. Then sold it for
Rs 9 lakhs. Find his profit in
percentage.


What is the sum of two numbers?
I. The bigger of these two numbers is 6 more than the smaller number.
II. \( 40 \% \) of the smaller number is equal to \( 30 \% \) of the bigger number.
III. The ratio between half of the bigger number and one-third of the smaller
number is 2: 1
A. Only II and III are sufficient
B. Only I and II are sufficient
c. I and either II or III is sufficient
D. All, II and III together are sufficient


A heat engine operating between 227 \( \operatorname{deg} \mathrm{C} \) and 27 deg \( \mathrm{C} \) absorbs 1 kcal of heat from the 227 deg \( C \) reservoir per cycle. Calculate
(1) the amount of heat discharged into
the low temperature reservoir.
(2) the amount of work done per cycle.
(3) the efficiency of cycle.
A. 0.4 kcal, 0.6 kcal, 40\%
B. 0.6 kcal, 0.4 kcal, 40\%
c. 0.4 kcal, 0.6 kcal, \( 60 \% \)
D. 0.7 kcal, 0.4 kcal, 40\%


Three resistances are connected to form
a \( T \) -shape as shown in the figure. Then
the current in the \( 4 \mathrm{K} \) resistor is :
A. \( 0.93 \mathrm{mA} \)
B. \( 1.42 \mathrm{mA} \)
c. \( 2.5 \mathrm{mA} \)
D. 1.57 m


In Cockroach, the common duct of salivary reservoir opens at the base of
A. Pharynx
B. Maxilla
c. Mandible
D. Hypopharynx


Total diastereomeric and enantiomeric
pairs possible from respectively are:-
\( \boldsymbol{C H}_{3}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3} \)
\( \boldsymbol{C l} \)
A . 2,2
B. 2,4
c. 2,3
D. 4,2


Write IUPAC name and chemical
formula of Acetone.


Number of unpaired electrons in inert gas is:
A. 0
B. 8
\( c \cdot 4 \)
D. 18


Analyze the mass spectrum graph.
Calculate the average atomic mass of
the unknown element:
\( A \cdot 10.2 a m \)
B. 10.5 amu
D. 11.0 amu


A line OP where \( 0=(0,0,0) \) makes
equal angles with ox, oy, oz. The point on OP, which is at a distance of 6 units
from 0 is:
A. \( \left(\frac{6}{\sqrt{3}}, \frac{6}{\sqrt{3}}, \frac{6}{\sqrt{3}}\right) \)
B . \( (2 \sqrt{3},-2 \sqrt{3}, 2 \sqrt{3}) \)
\( c \cdot-(2 \sqrt{3}, 2 \sqrt{3}, 2 \sqrt{3}) \)


A neutral atom of an element has \( 2 \mathrm{K}, 8 \mathrm{L} \)
and \( 5 \mathrm{M} \) electrons. What is the total
number of unpaired electrons?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Consider the following reactions. In which case the formation of product is favoured by decrease in pressure?
(1) \( \boldsymbol{C O}_{2}(\boldsymbol{g})+\boldsymbol{C}(\boldsymbol{s}) \rightarrow \boldsymbol{2} \boldsymbol{C O}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( +172.5 \mathrm{kJ} \)
(2) \( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
\( \Delta \boldsymbol{H}=-\mathbf{9 1 . 8} \mathbf{k} \mathbf{J} \)
(3) \( N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) ; \Delta H= \)
\( +181 k J \)
\( (4) 2 H_{2} O(g) \rightarrow 2 H_{2}(g)+ \)
\( \boldsymbol{O}_{2}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}=\mathbf{4 8 4 . 6} \mathbf{k J} \)
A . 2,3
B. 3,4
\( c \cdot 2,4 \)
D. 1.4


During galvanization of iron, which metal is used for coating iron surface?
A. copper
B. zinç
c. Nickel
D. Tin


Which of the following statement is
correct?
\( \mathbf{A} \cdot \) The \( p H \) of one litre solution containing \( 0.49 \mathrm{g} \) of \( H_{2} S O_{4} \) is 2.0
B. The conjugate base of \( H_{2} S \) is \( S^{-2} \)
\( \mathrm{C} \cdot B F_{3} \) is Lewis base
D. Phenolphthalein is colorless in basic medium


Two electric wires coming out of the
meter are connected to the
A. electric equipment
B. switch of the bulbs
c. main switch
D. switch of the electric equipments


The degree of dissociation of water at \( 25^{\circ} \mathrm{C} \) is \( 1.8 \times 10^{-7} \% \) and density is
\( 1.0 g c m^{-3} . \) The ionic constant for water
is:
A \( \cdot 1.0 \times 10^{-14} \)
В. \( 2.0 \times 10^{-16} \)
c. \( 1.0 \times 10^{-16} \)
D. \( 1.0 \times 10^{-8} \)


Length of petiole increases by the activity of
A. Apical meristem
B. Lateral meristem
c. Intercalary meristem
D. All the above


\( \int_{0}^{\pi} x f(\sin x) d x \) is equal to
\( \mathbf{A} \cdot \pi \int_{0}^{x} f(\cos x) d x \)
\( \mathbf{B} \cdot \pi \int_{0}^{x} f(\sin x) d x \)
\( ^{\mathbf{C}} \cdot \frac{\pi}{2} \int_{0}^{x / 2} f(\sin x) d x \)
D \( \cdot \pi \int_{0}^{\pi / 2} f(\cos x) d x \)


Match the items in List 1 with those in
List 2


In a free space a rifle (fixed) of mass \( M \)
shoots a bullet of mass \( m \) at a
stationary block of mass \( M \) distance \( D \) away from it. When the bullet has
moved through a distance \( d \) towards the
block the centre of mass of the bullet-
block system is at a distance of:
A \( \cdot \frac{(D-d) m}{M+m} \) from the block
B. \( \frac{m d+M D}{M+m} \) from the rifle
c. \( \frac{2 d m+D M}{M+m} \) from the rifle
D. \( (D-d) \frac{M}{M+m} \) from the bullet


Four point charges \( \boldsymbol{q}_{\boldsymbol{A}}=\boldsymbol{2 \mu C}, \boldsymbol{q}_{\boldsymbol{B}}= \)
\( -5 \mu C, q_{C}=2 \mu C, \) and \( q_{D}=-5 \mu C \)
are located at the corners of a square
\( A B C D \) of side \( 10 \mathrm{cm} . \) What is the force
on a charge of \( 1 \mu C \) placed at the centre
of the square?


By means of the given analytical results show that law of multiple proportions is true.
Mercurous chloride Mercuric chloride
Mercury = 84.92 \% \( \quad \) Mercury = 73.80\%
Chlorine \( =15.08 \) \( \% \) Chlorine = 26.20\%


Define Super Conductivity


Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of \( 20 \mathrm{cm} \) are placed
with their convex surfaces in contact at
the centre. The intervening space is filled with oil of refractive index 1.7. The
focal length of the combination is
A. -50 cm
B. 50 \( \mathrm{cm} \)
\( c .-20 \mathrm{cm} \)
D. -25 cm


The value of \( \left|\begin{array}{ccc}-a^{2} & a b & a c \\ a b & -b^{2} & b c \\ a c & b c & -c^{2}\end{array}\right| \) is
A . a perfect cube
B. zero
c. a perfect square
D. negative


topp
0
Fill in the blanks in the following passage(s) from the words given above.
The magnetic field produced around a straight current carrying conductor is in the form of with the
lying on the straight conductor. Take a copper wire AB. Pass it through a cardboard. Connect the wire to a battery through a key. Sprinkle some iron filings on the cardboard. Switch on the key and tap the cardboaro gently. You will find that the iron filings arrange themselves in the form of concentric circles. Reverse the direction
of current by changing the of the battery. You will find that this time too, the iron filings arrange themselves in concentric circle but in
direction. Hence, the magnetic field lines of force around a carrying electric current are concentric circles with the
conductor at the centre. The direction of
magnetic field changes if the direction of current is


Consider the following figure,
The correct relationship between
fahrenheit and celsius scale is:
\( \mathbf{A} \cdot^{0} F=^{0} C+273.15 \)
\( \mathbf{B} \cdot^{0} F=\frac{2}{5}^{0} C+16 \)
\( \mathbf{c} \cdot^{0} F=\frac{9}{5} C+32 \)
D. \( ^{0} F=\frac{1}{3}^{0} C+32 \)


Which of the following is responsible for the relatively low vapour pressure of water?
A. Metallic bonding
B. lonic bonding
c. Hydrogen bonding
D. Polar covalent bonding
E. Nonpolar covalent bonding


The mean and variance of 20
observations are found to be 10 and 4
respectively. On rechecking, it was found that an observation 9 was
incorrect and the correct observation
was \( 11 . \) Then the correct variabce is:
A . 3.98
в. 4.02
c. 4.01
D. 3.99


A beaker containing liquid is placed on a table, underneath a microscope which can be moved along a vertical scale. The microscope is focused through the liquid on to a mark on the table when
the reading on the scale is \( h_{1} . \) It is next
focused on the upper surface of the
liquid and the reading is \( h_{2} . \) More liquid
is added and the observations are
repeated, the corresponding readings \( \operatorname{are} h_{1}^{\prime} \) and \( h_{2}^{\prime} . \) The refractive index of the liquid is
\( \mathbf{A} \)
\[
\frac{h_{2}^{\prime}-h_{2}}{h_{2}^{\prime}-h_{1}^{\prime}-h_{2}+h_{1}}
\]
B.
\[
\frac{h_{2}^{\prime}-h_{1}^{\prime}}{h_{2}^{\prime}-h_{1}^{\prime}-h_{2}+h_{1}}
\]
\( \mathbf{c} \)
\[
\frac{h_{1}^{\prime}-h_{2}}{h_{2}^{\prime}-h_{1}^{\prime}-h_{2}+h_{1}}
\]
D. None of these


Find the value of \( \tan \left[\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right] \)


Which enzyme is concerned with transfer of electrons?
A. Desmolase
B. Hydrolase
c. Dehydrogenase
D. Transaminase


In the path of the cathode rays, a tungsten metal is placed in the way. Then the rays produced are:
A. cathode rays
B. anode rays
c. \( x \) -rays
D. UV rays


Evaluate the following integrals:
\( \int_{0}^{\pi} x d x \)


Given find \( \boldsymbol{P}(\boldsymbol{A})=\frac{1}{5}, \) find \( \boldsymbol{P}(\boldsymbol{A} \text { or } \boldsymbol{B}), \) if
\( A \) and \( B \) are mutually exclusive events.


Variance is independent of change of
A . only origin
B. only scale
c. origin and scale both
D. none of these


For an isolated system, the entropy:
A. Either increases or remains constant
B. Either decreases or remains constant
c. can never decrease
D. can never increase


Plants like sugarcane and sorghum have indigenously developed system to overcome the loss by photorespiration as they are .......... plants.
\( \mathbf{A} \cdot C_{4} \)
в. \( C_{3} \)
c. \( C_{2} \)
D. \( C_{1} \)


Names three types of rainfall.


Draw a quadrilateral that have four
lines of symmetry.


Due to balanced forces on the surface
absorbents attract molecules of gas or
liquid.
If this is true enter 1 , if false enter 0 .


A sample of \( C a C O_{3} \) has \( C a-40 \%, C= \) \( 12 \% \) and \( 0=48 \% \). If the law of constant
proportions is true, then the mass of Ca
in 5 g of \( C a C O_{3} \) from another source
will be:
A. 2.0
B. \( 0.2 \mathrm{g} \)
c. \( 0.02 g \)
D. 20.0


Which of the following has a bond
formed by overlap of \( s p^{3}- \) hybrid
orbitals?
A. \( C H_{3}-C \equiv C-C H_{3} \)
в. \( C H_{3}-C H=C H-C H_{3} \)
C \( . C H_{2}=C H-C H=C H_{2} \)
D. \( H C \equiv C H \)


A line \( 4 x+y=1 \) passes through the
point \( \boldsymbol{A}(\mathbf{2},-\mathbf{7}) \) and meets line \( \boldsymbol{B} \boldsymbol{C} \) at \( \boldsymbol{B} \)
whose equation is \( 3 x-4 y+1=0, \) the
equation of line \( A C \) such that \( A B= \) \( \boldsymbol{A C} \) is
A \( .52 x+89 y+519=0 \)
В. \( 52 x+89 y-519=0 \)
c. \( 82 x+52 y+519=0 \)
D. \( 89 x+52 y-519=0 \)


Stomata of a plant open due to
A. Influx of potassium ions
B. Efflux of potassium ions
c. Influx of hydrogen ions
D. Influx of calcium ions


Let \( p: A \) triangle is equilateral, \( q: A \) triangle is equiangular then inverse of
\( \boldsymbol{q} \rightarrow \boldsymbol{p} \) is
A. If a triangle is not equilateral then it is not equiangular
B. If a triangle is not equiangular then it is not equilateral
C. If a triangle is equiangular then it is not equilateral
D. If a triangle is equiangular then it is equilateral


The two different ways of harnessing energy from ocean are :
A. Tidal Wave, OTEC
B. Geothermal, wave energy device
C. Solar energy, point wave absorber
D. All of the above


Arrange the following in the increasing order of their basicities.
I. \( p- \) Toluidine
II. \( N, N- \) Dimethyl - \( p \) - toluidine
III. \( p- \) Nitroaniline
IV. Aniline
A. \|\|\( <\|v<1<\| \)
B. II \( <\mid V<1<11 \)
c. \( \|<\|<1<1 V \)


Which of the following is the first oxidation product of secondary alcohol?
A. Alkene
B. Aldehyde
c. Ketone
D. carboxylic acid


Pure benzene freezes at \( 5.3^{\circ} \mathrm{C} \). A
solution of 0.223 g of phenyl acetic acid \( \left(C_{6} H_{5} C H_{2} C O O H\right) \) in 4.4 g of benzene \( \left(K_{f} 5.12 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1}\right) \) freezes at \( 4.47^{\circ} \mathrm{C} \)
From the observation one can conclude
that:
A. phenyl acetic acid exists as such in benzene
B. phenyl acetic acid undergoes partial ionization in benzene
c. phenyl acetic acid undergoes complete ionization in benzene
D. phenyl acetic acid dimerizes in benzene


Find discriminant of the equation \( 5 x- \) \( 6=\frac{1}{x} \)


Find the slope of tangent of the curve
\( \boldsymbol{x}=\boldsymbol{a} \sin ^{3} \boldsymbol{t}, \boldsymbol{y}=\boldsymbol{b} \cos ^{3} \boldsymbol{t} \) at \( \boldsymbol{t}=\frac{\pi}{2} \)
A . cott
B. \( - \) tant
c. \( - \) cott
D. not defined at \( \frac{\pi}{2} \)


The acid hydroylsis of ester is:
This question has multiple correct options
A. first order reaction
B. bimolecular reaction
C . pseudo unimolecular reaction
D. none of the above


Which of the following statements is
not correct for \( \boldsymbol{S O}_{2} \) gas?
A. It acts as bleaching agent in moist conditions.
B. Its dilute solution is used as disinfectant.
C. Its molecules have linear geometry.
D. Acidified \( K M n O_{4} \) is decolourised when \( S O_{2} \) is passed through it


Prolonged liberal irrigation of agricultural fields is likely to create a problem of
A . Acidity
B. Alkalinity
c. salinity
D. Metal toxicity


If the side of a rectangle are \( 7 \mathrm{cm} \) and
\( 5 \mathrm{cm}, \) find its area.


A point is moving along the curve \( y^{3}= \) \( 27 x \). The interval in which the abscissa
changes at slower rate than ordinate, is
A \( \cdot(-3,3) \)
B \( \cdot(-\infty, \infty) \)
c. (-1,1)
D. \( (-\infty,-3) \cup(3, \infty) \)


If the radian measures of two angles of a triangle are \( \frac{5 \pi}{9}, \frac{5 \pi}{18} . \) Find the radian measure and the degree measure of the third angle.


A Planar Complex (Mabcd) gives:
A. Two optical isomer
B. Two geometrical isomer
c. Three optical isomer
D. Three geometrical isomers


Assertion
The Sl unit of weight is Newton.
Reason
Weight is the force of gravity with which
a body is attracted towards the earth.
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


If \( f(x)=x^{2}-3 x+4 \), then find the
value of \( 3\left(x_{1}+x_{2}\right) \) if \( x_{1}, x_{2} \) satisfying
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{2} \boldsymbol{x}+\mathbf{1}) \)


Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with
concentration.


The domain of \( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\mathbf{2}|-|\boldsymbol{x}-\mathbf{5}| \)
is
A. \( R-(2,5) \)
B . \( R-0 \)
\( c \cdot(0, \infty) \)
D. \( R \)


Name asexual reproductive structures in the following organism.
¡) Hydra
ii) Chlamydomonas
iii) Penicillium


Find the angle between the planes:
\( x+y-2 z=3 \) and \( 2 x-2 y+z=5 \)


Find the coefficient of variation.
A. 72.66
B. 81.24
\( c \cdot 264 \)
D. 330
E. None


For an exothermic reaction to be
spontaneous:
A. temperature must be high
B. temperature must be zero
c. temperature may have any magnitude
D. temperature must be low


The nuclear reaction is given as \( _{6} C^{11} \rightarrow_{5} B^{11}+\beta+X . \) Here, \( X \) is?
A. A proton
B. An electron
c. A neutrino
D. A neutron


Easy to shape materials like ceramics are used as
A. conductors
B. insulators
c. electrodes.
D. catalysts.


CO is absorbed by:
A. Haemoglobin
в. \( C H C l_{3} \)
c. \( C C l_{4} \)
D. pyrogallol


Which of the following species has been oxidized?
\( M g(O H)_{2(a q)}+2 N a_{(s)} \rightarrow M g_{(s)}+ \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H}_{(a q)} \)
A. \( M g^{+2} \)
в. \( N a \)
\( \mathrm{c} . M g \)
D. \( O H^{-} \)


In the propagation of electromagnetic waves, the angle between the direction of propagation and plane of polarisation
is
A \( \cdot 0^{\circ} \)
B. \( 45^{\circ} \)
c. \( 90^{\circ} \)
D. \( 180^{\circ} \)


The empirical formula of natural rubber
is:
\( \mathbf{A} \cdot\left(C_{3} H_{5}\right)_{n} \)
B \( \cdot\left(C_{5} H_{8}\right)_{n} \)
\( \mathbf{c} \cdot\left(C_{5} H_{3}\right)_{n} \)
D. \( \left(C_{8} H_{5}\right)_{n} \)


Assertion
Separation of lanthanides is very
difficult.
Reason
Lanthanides differ only with electronic
configuration in antipen ultimate shell.
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


Find the mean deviation about mean for
the data in \( \mathrm{Ex} 9 \) and 10 .
\( \begin{array}{lll}\text { Income per day } & \text { No of persons } \\ 0-100 & 4 \\ 100-200 & 8 \\ 200-300 & 9 \\ 300-400 & 10 \\ 400-500 & 7 \\ 500-600 & 5 \\ 600-700 & 4 \\ 700-800 & 3\end{array} \)


Two dimetrically opposite points of a metal ring are connected to two terminals of the left gap of metrebridge.
The resistance of \( 11 \Omega \) is connected in
right gap. If null point is obtained at a distance of \( 45 \mathrm{cm} \) from the left end, find
the resistance of metal ring.


Three waves of amplitudes \( 12 \mu m, 4 \mu m \)
and \( 9 \mu m \) but of same frequency arrive at a point in a medium with a successive phase diffeerence of \( \frac{\pi}{2} \) Then the resultant amplitude is
A .4
B. 7
\( c .5 \)
D. 25


In the Lassaignes test for nitrogen in an organic compound, the Prussian
blue colour is obtained due to the
formation of: