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


The product of frequency and
wavelength of a sound wave is equal to
its


\( X^{2} \) test is equal to
A \( \cdot \sum_{i=1}^{n} A x^{1}=A x^{1}+A x^{2}+\ldots+A x^{n} \)
B . \( V=(r-1)(e-1) \)
\( \frac{\Sigma(O-E)^{2}}{E} \)
D \( r=\frac{\Sigma_{x y}}{\sqrt{\Sigma x^{2} y^{2}}} \)


In LPG cylinder, the gas filled is in the liquefied state.
A . True
B. False


Convert \( 5^{0} F \) according to (i) Celsius scale, and (ii) Kelvin scale.
A \( \cdot\left(\text { i) }-15^{0} C\right. \)
(ii) \( 258 K \)
B. (i) \( -17^{0} C \)
(ii) \( 288 K \)
c. \( \left(\text { i) }-15^{0} C\right. \)
(ii) \( -258 K \)
D. (i) 20 \( ^{0} C \)
(ii) \( 237 K \)


A table lamp of power 60 W consumed 9 (commerical) units of electricity in the month of April. For how many hours per day, on an average, was the lamp in
use?
\( A \cdot 1 h \)
B. 3h
\( c \cdot 5 h \)
\( D \cdot 6 h \)


\( \int x \sec ^{-1} x d x= \)
\( \frac{2}{k}\left[x^{2} \sec ^{-1} x-\sqrt{x^{2}-1}\right] . \) Find the
value of \( k \)


Akhila went to a fair in her village. She
wanted to enjoy rides on the Giant
Wheel and play Hoopla (a game in which you throw a ring on the items kept in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla half the number of rides she had on the
Giant Wheel. Each ride costs \( R s .3 \), and
a game Hoopla costs \( R s .4 . \) If she spent
Rs.20 in the fair, represent this situation algebraically


topp \( L \)
Q Type your question
4
3
\( r \)
\( D \)


The current model of atomic structure
is the:
A. Quantum mechanical model
B. Quantum physiochemical model
c. Atomic mass theory
D. None of the above


Find \( \boldsymbol{R} \)


A parachutist with total weight \( 75 k g \) drops vertically onto a sandy ground with a speed of \( 2 m s^{-1} \) and comes to a
halt over a distance of 0.25 m. The
average force from the ground on her is close to
\( \mathbf{A} \cdot 600 N \)
в. \( 1200 N \)
c. \( 1350 N \)
D. \( 1950 N \)


Draw a circle and mark a point in its
interior.


The \( K_{s p} \) for \( A g C l \) is \( 2.8 \times 10^{-10} \) at a
given temperature. The solubility of \( A g C l \) in 0.01 molar \( H C l \) solution at
this temperature will be:
A. \( 2.8 \times 10^{-12} \) mol \( L^{-1} \)
-
B . \( 2.8 \times 10^{-8} \mathrm{mol} \mathrm{L}^{-1} \)
c. \( 5.6 \times 10^{-8} \) mol \( L^{-1} \)
D. 2.8 \( \times 10^{-4} \mathrm{mol} \mathrm{L}^{-1} \)


Divide the number 26244 by the
smallest number so that the quotient is a perfect cube


What is the nature of \( \boldsymbol{C} \boldsymbol{H}_{3}-\boldsymbol{C} \boldsymbol{H}_{2}-\boldsymbol{X} \)
bond towards nucleophilic substitution?
A. More reactive than halobenzene
B. Less reactive than halobenzene
c. Equal reactive as halobenzene.
D. Non-reactive towards nucleophilic substitution


The de Broglie wavelength of an electron
moving with a velocity \( 2.25 \times 10^{8} m s^{-1} \)
is equal to that of a photon. The ratio of the kinetic energy of the electron to that of the energy of photon is :
A \( \cdot \frac{3}{8} \)
B. 4
\( c \cdot \frac{1}{2} \)
D. \( 2-\sqrt{3} \)


Which of the following is not required for the Calvin cycle to occur?
A. ATP, NADPH
B. Carbon dioxide
c. Light
D. Ribulose bisphosphate


\( 1 \mu C \) charge is uniformly distributed on a spherical shell given by equation \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}+\boldsymbol{z}^{2}=\mathbf{2 5} . \) What will be
intensity of electric field at a point
(1,1,2)\( ? \)


The moisture present in mercury the barometric height of simple barometer
A . increases
B. decreases
c. doesn't change
D. can't say


Which one of the following is correct in respect of the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}(\boldsymbol{x}-\mathbf{1})(\boldsymbol{x}+\mathbf{1}) ? \)
A. The local maximum value is larger than local minimum value
B. The local maximum value is smaller than local minimum value
c. The function has no local maximum
D. The function has no local minimum


How many words can be formed with the
letters of the word 'OMEGA' when
vowels occupy only odd places?
A . 12
B . 24
c. 18
D. 36


The main factor responsible for weak acidic nature of \( B-F \) bonds in \( B F_{3} \) is:
A. large electronegativity of F
B. three centred two electron bonds in \( B F_{3} \)
c. \( p \pi-d \pi \) back bonding
D. \( p \pi-p \pi \) back bonding


When a sample of \( H I \) is warmed to a particular temperature the equilibrium below is established.
\( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
At this temperature, it is found that the partial pressure of \( \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \) is 28 times
the partial pressure of \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
What is the value of \( \boldsymbol{K}_{\boldsymbol{p}} \) at this temperature?
A \( \cdot 1.28 \times 10^{-3} \)
в. 0.035
\( c \cdot 28 \)
D. 784


Two particles of masses \( m_{1} \) and \( m_{2} \) in
projectile motion have velocities \( v_{1} \) and
\( v_{2} \) respectively at time \( t=0 . \) They
collide at time \( t_{0} . \) Their velocities
become \( v_{1}^{\prime} \) and \( v^{\prime}_{2} \) at time \( 2 t_{0} \) while
still moving in air. The value of
\( \left[\left(\boldsymbol{m}_{1} \boldsymbol{v}_{1}^{\prime}+\boldsymbol{m}_{2} \boldsymbol{v}_{2}^{\prime}\right)-\left(\boldsymbol{m}_{1} \boldsymbol{v}_{1}+\boldsymbol{m}_{2} \boldsymbol{v}_{2}\right)\right] \)
A . zero
в. \( \left(m_{1}+m_{2}\right) g t_{0} \)
c. \( 2\left(m_{1}+m_{2}\right) g t_{0} \)
D. \( \frac{1}{2}\left(m_{1}+m_{2}\right) g t_{0} \)


Evaluate \( \lim _{x \rightarrow 3}\left(4 x^{2}+3\right) \)
A . 36
B . 39
c. 40
D. None of these


At what temperature will he atom have
the same \( r m s \) speed as \( H_{2} \) molecules have at \( 27^{0} C \) ?
A \( \cdot 127^{0} C \)
в. \( 227^{\circ} \mathrm{C} \)
c. \( 327^{\circ} \mathrm{C} \)
D. \( 27^{0} C \)


At what angle should a ray of light be incident on the face of a prism of
refracting angle \( 60^{\circ} \) so that it just
suffers total internal reflection at the
other face? The refractive index of the
material of the prism is 1.524


An opaque cylindrical tank with an open
top has a diameter of \( 3.00 \mathrm{m} \) and is
completely filled with water. When the
setting sun reaches an angle of \( 37^{\circ} \) above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank in meter?


An electrical generator works on the principle of electromagnetic induction
A. True
B. False


Presence of halogen in organic compounds can be detected using:
A. Liebig's test
B. Duma's test
c. Kjeldahl test
D. Beilstein test


Which polysaccharide component of carbohydrates is commonly present in bread?


A ray of light moving along the vector \( (\hat{i}-\hat{\mathbf{2}} j) \) undergoes refraction at an interface of two media, which is \( x-z \)
plane. The refractive index for \( y>0 \) is 2 while for \( y<0 \) it is \( \frac{\sqrt{5}}{2} . \) The unit vector along the refracted ray is 2
\( ^{\mathbf{A}} \cdot \frac{-3 \hat{i}-5 \hat{j}}{\sqrt{34}} \)
\( \frac{(-4 \hat{i}-5 \hat{j})}{5} \)
\( ^{\mathbf{C}} \frac{-3 \hat{i}-4 \hat{j}}{5} \)
D. \( \frac{4 \hat{i}-3 \hat{j}}{5} \)


Microscopic examination of tissue in order to study the manifestations of disease is
A. Cytology
B. Histopathology
C. Histology
D. Dermatology


Out of the following which has the highest absolute refractive index?
A. fused quartz
B. diamond
c. crown glass
D. ruby


Which of the following compounds has
\( 2 p \pi-2 p \pi \) bond?
\( A \cdot B F_{3} \)
в. \( B C l_{3} \)
\( \mathbf{c} \cdot B B r_{3} \)
D. \( B I_{3} \)


An electron enters a chamber in which a
uniform magnetic field is present as
shown. Ignore gravity. During its motion inside the chamber
field
A. The force on the electron remains constant
B. The kinetic energy of the electron remains constantt
c. The momentum of the electron remains constant
D. The speed of the electron increases at a uniform rate


The amount of energy absorbed or
released during a chemical reaction can be expressed in terms of?
A. Degree and gram
B. Torr and mmHg
c. Gram and liter
D. Calorie and joule
E . Meter and \( c m^{3} \)


A student noticed a rainbow appearing in the sky. If he walked towards it, what will happen to the apparent height of the rainbow above the ground?
A. It increases
B. It decreases
c. It remains the same
D. It may increase or decrease


What is polygon?


A saturated solution of \( \boldsymbol{C} \boldsymbol{a}_{\boldsymbol{3}}\left(\boldsymbol{P} \boldsymbol{O}_{4}\right)_{2} \)
contains \( 2.0 \times 10^{-8} \mathrm{M} C a^{2+} \) and
\( 1.6 \times 10^{-5} \mathrm{M} P O_{4}^{3-} \) at a certain
temperature. The solubility product
\( \left(K_{s p}\right) \) of \( C a_{3}\left(P O_{4}\right)_{2} \) at that temperature is:
A . \( 2.048 \times 10^{-3} \)
В. \( 2.04 \times 10^{-33} \)
c. \( 3.20 \times 10^{-34} \)
D. \( 8 \times 10^{-34} \)


Why is sodium metal not used in the
lab preparation of hydrogen?


In cold region during winter freezes at room temperature itself and looks ice.
A. Palmitic acid
B. Linoleic acid
c. Oleic acid
D. Ethanoic acid


The powdered ore is agitated with water
or washed with running stream of water The heavy ore particles and lighter impurities are separated. This method of concentration is known as:
A. metallurgy
B. leaching
c. gravity separation
D. forth floatation process


What is the difference between the
terms hydrolysis and hydration?


Multiple bonds are not present in:
A. nitrogen
B. oxygen
c. diamond
D. carbon dioxide


An altitude and a median drawn from
the same vertex of a triangle divide the angle at that vertex into.three equal
parts. Prove that the angles of that
triangle are equal to \( 30^{\circ}, 60^{\circ}, \) and \( 90^{\circ} \)


By how much \( \% \) is 2500 greater than \( \mathbf{5 0 0} \) ?


Wool is used in making garments used
in winter because
A. Wool is a good conductor of heat
B. Wool is a bad conductor of heat
C. Air, trapped in between the wool fibres, prevents the flow of heat from our body to the cold surroundings.
D. Both B and C


The boiling point of a liquid can be raised by
A. Increasing pressure
B. Decreasing pressure
c. Increasing the heat supply
D. Increasing the quantity of the liquid


\( X, Y \subset \mathrm{R}, f: X \rightarrow Y \) is a function and
\( f(x)=x^{2} \forall x \in X \) then the condition
for it to be one-one but not onto is
A \( . X=Y=R^{+} \)
B . \( X=R, Y=R^{+} \)
c. \( X=R^{+}, Y=R \)
D. \( X=Y=R \)
\( R \)


\( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sqrt{1-\sqrt{\sin 2 x}}}{\pi-4 x}=-\frac{1}{m} . \) Find \( n \)


A proton and an \( \alpha \) -particle enter in a
uniform magnetic field perpendicular to it with same speed. The ratio of time periods of both particle \( \square \frac{T_{p}}{T_{\alpha}} \) 回 will be
\( A \cdot 1: 2 \)
B. 1:3
c. 2:
D. 3:


What current strength in amperes will be required to liberate 10 gm of iodine from potassium iodide solution in one hour? (Equivalent mass of lodine is 127 ).


How can you appreciate the effort of scientists in classifying a wide range of
organisms?


Assertion
The oxidation state of Cr in
\( A l_{2}\left(C r_{2} O_{7}\right)_{3} \) is +3
Reason
As a neutral compound, the sum of the oxidation numbers of all the atoms
must equal 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. Both assertion and reason are incorrect


Find the equation of parabola whose
focus is \( S(1,-7) \) and vertex is
\( \boldsymbol{A}(\mathbf{1},-\mathbf{2}) \)


The topmost and bottom most
velocities of a disc are \( v_{1} \) and \( v_{2} \) in the
same direction. The radius is R. What is
the angular velocity of the disc
A \( \cdot \frac{\left(v_{1}-v_{2}\right)}{R} \)
в. \( \frac{\left(v_{1}-v_{2}\right)}{2 R} \)
c. \( \frac{\left(v_{1}+v_{2}\right)}{2 R} \)
D. \( _{\text {a }} \frac{\left(v_{1}+v_{2}\right)}{R} \)


Find the value of ' \( n \) ' in the following:
\( \left(\frac{2}{3}\right)^{3} \times\left(\frac{2}{3}\right)^{5}=\left(\frac{2}{3}\right)^{n-2} \)


Which is not a mineral of aluminium?
A. Anhydrite
B. Bauxite
c. corundum
D. Diaspore
E. Answer Required...


Name the colour used in insulated
wired of electrical appliance.
A. Blue
B. Green
c. Brown
D. All of these


Assertion
It is harder to open and shut the door if
we apply force near the hinge.
Reason
Torque is maximum at hinge of the
door
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


Bryophyta like to grow in moist places because
A. Roots are absent, they has to absorb the moisture from ground
B. Male gametes require water for swimming
C. They do not have water proof coating of cutin on their aerial surface to prevent the loss of water
D. All of the above


Which one of the following statements
is wrong about adsorption?
A. It is a selective and specific process.
B. It is a reversible process.
c. An increase in the gaseous adsorbate causes an increase in adsorption. However, the adsorption becomes constant at high pressure.
D. It is an endothermic process


The focal length of the objective of an
astronomical telescope is \( 1 \mathrm{m} \) and it is
in normal adjustment.Initially the telescope is focussed to a heavenly
body. If the same telescope is to be
focussed to an object at a distance of 21 \( \mathrm{m} \) from the objective,then identify the
correct choice
A. eye piece should be displaced by \( 2 \mathrm{cm} \) away from the objective
B. eye piece should be displaced by \( 2 \mathrm{cm} \) towards the objective
C. eye piece should be displaced by \( 5 \mathrm{cm} \) towards the objective
D. eye piece should be displaced by \( 5 \mathrm{cm} \) away from the objective


How many primary amines are possible
for the formula \( \boldsymbol{C}_{4} \boldsymbol{H}_{11} \boldsymbol{N} \) ?
A. one
B. Two
c. Three
D. Four


The groups from \( 1^{s t} \) to \( 7^{t h} \) of
Mendeleev's periodic table were divided into \( _{-}-_{-}-_{-}- \) subgroups
A .2
B. 3
\( c \cdot 4 \)
D.


Evaluate \( 3 \times(9)^{5 / 2} \times(9)^{-1 / 2} \)


Integrate the function \( \sqrt{1-4 x-x^{2}} \)


A point source of light is placed at the centre of curvature of a hemispherical surface. The radius of curvature is r and
the inner surface is completely reflecting. Find the force on the hemisphere due to the light falling on it
if the source emits a power \( \mathbf{W} \)


If power (P), surface tension (S) and Planck's constant (h) are arranged so that the dimensions of time in their
dimensional formulae are in ascending order, then which of the following is correct then?
\( A \cdot P, S, h \)
B. P, h, S
\( c \cdot s, P, h \)
D. s, h, P.


If the sum of the roots of the equation
\( a x^{2}+b x+c=0 \) is equal to sum of the
squares of their reciprocals, then \( b c^{2}, c a^{2}, a b^{2} \) are in
A . \( A . P \)
в. \( G . P \)
c. \( H . P \)
D. A.G.P


Mark correct option or options.
This question has multiple correct options
A. Displacement may be equal to the distance
B. Displacement must be in the direction of the acceleration of the body
C. Displacement must not be in the direction of velocity
D. None of the above


Change of \( \boldsymbol{H} \) into \( \boldsymbol{H}^{+} \) is:
A. oxidation of hydrogen
B. acid base reaction
c. reduction of hydrogen
D. displacement reaction


Ten milliliters of a gaseous hydrocarbon
was burnt completely in \( 80 \mathrm{ml} \) of \( \mathrm{O}_{2} \) at STP. The Volume of the remaining gas is 70 ml. The volume became \( 50 \mathrm{ml} \) on
treatment with NaOH. The formula of
the hydrocarbon is :
A \( \cdot C_{2} H_{6} \)
в. \( C_{2} H_{4} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{3} H_{6} \)


The atomic number of magnesium is 12 How many protons are there in the nucleus of magnesium atom? How
many electrons and protons does an ion
of magnesium which has a charge of +2 contain.
A . 10,10
в. 10,13
c. 11,12
D. 10,12


Evaluate the following definite integral:
\( \int_{\pi / 6}^{\pi / 4} \operatorname{cosec} x d x \)


If Molar conductivity of \( C a^{2+}=119 \& \)
Molar conductivity of \( C l^{=} 71 \) then find
the molar conductivity of \( C a C l_{2} \)
A .341
в. 261
\( c \cdot 126 \)
D. 431


\( S \) and \( T \) are the foci of an ellipse and \( B \)
is an end of the minor axis, if \( \triangle \boldsymbol{S T B} \) is
equilateral, then \( e \) is equals to:
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{2} \)
D. None of these


What is the tension in string at \( A \) immediately after the string at \( \mathrm{B} \)
breaks?
A \( \cdot \frac{m g}{5} \)
в. \( \frac{2 m g}{31} \)
c. \( \frac{m g}{37} \)
D. \( \frac{5 m g}{37} \)


Explain why an astronaut in an orbiting satellite has a feeling of
weightlessness.


All the interacting organisms in an area together with the non-living constituents of the environment form
an


If the force is given by \( \boldsymbol{F}=\boldsymbol{a} \boldsymbol{t}+\boldsymbol{b} \boldsymbol{t}^{2} \) with \( \boldsymbol{t} \)
as time. The dimensions of a and b are:
\( \mathbf{A} \cdot\left[M L T^{-4}\right],\left[M L T^{-2}\right. \)
B . \( \left[M L T^{-3}\right],\left[M L T^{-4}\right] \)
C \( \cdot\left[M L^{2} T^{-3}\right],\left[M L^{2} T^{-2}\right] \)
D \cdot \( \left[M L^{2} T^{-3}\right],\left[M L^{3} T^{-4}\right] \)


The degree of unsaturation of the
compound formed by the partial hydrogenation of phenol is:
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
D.


Electrons used in an electron
microscope are accelerated by a voltage of \( 25 \mathrm{kV} \). If the voltage is increased to \( 100 \mathrm{kV} \) then the de-Broglie wavelength associated with the electrons would?
A. Increase by 2 times
B. Decrease by 2 times
c. Decrease by 4 times
D. Increase by 4 times


If \( \vec{x} \) and \( \vec{y} \) are two non-collinear vectors and \( A B C \) is a triangle with sides \( a, b, c \) satisfying \( (20 a-15 b) \vec{x}+(15 b- \)
\( 12 c) \vec{y}+(12 c-20 a)(\vec{x} \times \vec{y})=\overrightarrow{0}, \) then
the triangle \( A B C \) is
A. An acute angle triangle
B. An obtuse angle triangle
c. A right angle triangle
D. An isosceles triangle


Gametes formed by meiosis are called
as
A. coenogametes
B. Meiogametes
c. Mitogametes
D. None of the above


Find the number of ligand(s) which is/are non-classical ligand.
\( \boldsymbol{C O}, \boldsymbol{N O}, \boldsymbol{C}_{2} \boldsymbol{H}_{4}, \boldsymbol{C}_{3} \mathrm{H}_{5}^{-}, \boldsymbol{H}^{-} \)


The figure shows a square loop[ of resistance \( 1 \Omega \) side \( 1 m \) being moved
towards right at a constant speed of
1 \( m / s \). The front edge enters the \( 3 m \) wide magnetic field \( (B=1 T) \) at \( t=0 \)
draw the graph of current induced in the loop as time passes. (Take the anticlockwise direction of current as
positive)
\[
\begin{array}{l}
x \times x \times x \times \\
x \times \times \times \times \times \\
\times \times \times \times \times \times \\
\times \times \times \times \times \times \\
\times \times \times \times \times \times
\end{array}
\]


State the following statement is True or
False
The value of \( -32 \times-13=-416 \)
A . True
B. False


Two batteries of emf \( 3 V \) and \( 6 V \) with
internal resistance \( 2 \Omega \) and \( 4 \Omega \) are
connected in a circuit with resistance
of \( 10 \Omega \) as shown in figure. The current and potential difference between the
points \( P \) and \( Q \) are
A \( \cdot \frac{3}{16} A \) and \( \frac{8}{15} V \)
B \( \cdot \frac{16}{3} A \) and \( \frac{15}{8} V \)
c. \( \frac{3}{16} A \) and \( 8 V \)
D. \( \frac{3}{16} A \) and \( \frac{15}{8} V \)


Add:
\( -7 m n+5,12 m n+2,8 m n-8,-2 m n-3 \)


When \( 262 g \) of xenon (atomic mass \( = \)
131) reacted completely with 152 g of
fluorine (atomic mass \( =\mathbf{1 9} \) ), a mixture
of \( X e F_{2} \) and \( X e F_{6} \) was produced. The
molar ratio \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{2}: \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6} \) is :
A . 1: 2
B. 1: 4
c. 1: 1
D. 1: 3


The addition of 0.643 g of a compound to \( 50 \mathrm{mL} \) of benzene (density \( 0.879 g m L^{-1} \) ) lowers the freezing point
from 5.51 to \( 5.03^{\circ} \mathrm{C} . \) If \( K_{f} \) for benzene is
\( \mathbf{5 . 1 2} \boldsymbol{K} / \boldsymbol{m}, \) calculate the molecular
weight of the compound.


What are Intrinsic and Extrinsic semi-
conductors?


In Young's double slit experiment wavelength of light is 6000 A The the phase difference between the light waves reaching the third bright fringe from the central fringe will be:
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( 2 \pi \)
c. \( 4 \pi \)
D. \( 6 \pi \)


The number of molecules of the
reactants taking part in a single step of the reaction is indicative of :
A. order of a reaction
B. Molecularity of a reaction
c. Fast step of the mechanism of a reaction
D. Half-life of the reaction


A rectangular parallelopiped is formed by drawing planes through the point (-1,2,5) and (1,-1,-1) and paralle to the coordinates planes. The length of the diagonal of the parallelopiped is


If an ice cube is wrapped in a black cloth and another in an aluminium foil
and both are placed in sunlight, which will melt first?


Two tankers contain 850 litres and
680 litres of petrol respectively. Find
the maximum capacity of a container which can measure the petrol of either tanker in exact number of times.


IUPAC name of \( \boldsymbol{C}_{\mathbf{6}} \boldsymbol{H}_{\mathbf{5}}-\boldsymbol{C} \boldsymbol{H}_{\mathbf{2}}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{N H}_{2} \) is :
A. 2-phenyl ethanamide
B. 2-phenyl ethanamine
c. 2-phenyl ethylamine
D. 3-phenyl ethanamine


A moving coil galvanometer A has 200
turns and resistance \( 100 . \) Another
meter \( \mathrm{B} \) has 100 turns and resistance
\( 40 . \) All the other quantities are same in both the cases. The current sensistivity of
A. B is double as that of A
B. A is 2.5 times of B
c. A is 5 times of B
D. B is 5 times of A


Water cannot be converted into ice by
adding ice to it.
A . True
B. False


Select the incorrect statements among
the following.
(i) Bitumen is used for metalling the
roads.
(ii) Some inexhaustible natural
resources like coal, petroleum and
natural gas formed from the dead remains of living organisms are known as fossil fuels.
(iii) Many useful substances are obtained from coal (commercial
importance), so it is also called as Black gold'.
(iv) Natural gas is used as starting
material for the manufacture of a
number of chemicals and fertilizers.
A. (i) and (ii)
B. (ii) and (iii)
c. (ii),(iii) and (iv)
D. All are correct


On passing 0.01 Faraday of elctricity through a solution of aluminum chloride, the weight of Aluminium metal (at.wt. \( =\mathbf{2 7} \) ) deposited on
cathode is:
\( \mathbf{A} \cdot 0.9 g m \)
В. \( 0.09 g m \)
c. \( 2.7 g m \)
D. \( 0.27 g m \)


An amide with the formula \( C_{2} H_{5} N O \) is:


The basic chemical building block of natural rubber obtained from trees is:
A. acetylene
B. vinyl chloride
c. isoprene
D. neoprene


Which of the following compound has no existence?
A. \( \mathrm{CF}_{4} \)
B. \( \mathrm{XeF}_{4} \)
\( \mathrm{c} \cdot \mathrm{KrF}_{4} \)
D. HeF \( _{4} \)


Write \( I U P A C \) names of the following alchohols:
\( \boldsymbol{C H}-\underset{C_{2} H_{5}}{\boldsymbol{C} \boldsymbol{H}}-\underset{_{O H} \boldsymbol{I} \boldsymbol{H}-\boldsymbol{C} \boldsymbol{H}_{3}}{\boldsymbol{O H}} \)


A cubical block of wood of length 5 cm
is kept on a table top. The density of the block is \( 800 k g / m^{2} \) and \( g=9.8 m / s^{2} \)
Find the pressure exerted by the wooden block on the table top.


Largest number of chloroplasts in the leaf is in.
A. Spongy tissue
B. Palisade tissue
c. Guard cells
D. Bundle sheath


The main mineralocorticoid seen in
human is
A. Adrenaline
B. Testosterone
c. Androsterone
D. Aldosterone


\( \operatorname{Let} \boldsymbol{A}=\{1,2,3\}, B=\{4,5,6,7\} \) and
let \( \boldsymbol{f}=\{(1,4),(2,5),(3,6)\} \) be a
function from \( A \) to \( B \). State whether \( f \) is
one-one.


Find all values of \( \theta \) satisfying the equation \( \sin \theta=\sin \theta+\sin 3 \theta, \) where
\( \mathbf{0} \leq \boldsymbol{\theta} \leq \boldsymbol{\pi} \)


In oil solution of soap, the head is
towards the surface of the oil and the
tail is pointing away from the oil. If the given statement is true, enter 1
else enter 0


A heavy plank is moving with horizontal
acceleration \( a=2 m / s^{2} . \) A hollow
cylinder of mass \( \boldsymbol{m}=\mathbf{3} k \boldsymbol{g} \) and
radius \( =25 \mathrm{cm} \) is on the upper surface
of the plank and moves without slipping. Find the angular acceleration (about the axis in \( r a d / s^{2} \) ) of the hollow
cylinder?


In iron atom \( (z=26), \) the
differentiating electron enters sublevel:
A \( .4 d \)
B. \( 3 d \)
c. \( 4 p \)
D. \( 5 p \)


Find the complementary angle of \( 60^{\circ} \)


Give the unit of rate of reaction.
A. Molar
B. Second
c. Second/molar
D. Molar/second


Which of the following plants was used as a wound dressing as late as World war I
A. copper moss
B. Sphagnum
c. Hornworts
D. Red algae


Evaluate the following integral:
\( \int_{0}^{2}(3 x+2) d x \)


Let \( A(1,1,1), B(2,3,5) \) and \( C(-1,0,2) \) be three points, then equation of a plane parallel to the plane ABC which is at distance 2 units is:


Write 2760000 in scientific form.


The decomposition \( N H_{3} \) gas on a
heated tungsten surface gave the
following results:
Initial
pressure 65
105
\[
(\mathrm{mm})
\]
Half-life
\[
\begin{array}{lll}
\text { 290 } & \text { x } & \text { 670 }
\end{array}
\]
\( (\mathrm{sec}) \)
Calculate approximately the values of \( x \)
and \( y \)
A. \( x=410 \) sec, \( y=115 \) mm
B. \( x=467 \) sec, \( y=150 \mathrm{mm} \)
C \( . x=490 \) sec, \( y=120 \mathrm{mm} \)
D. \( x=430 \) sec \( , y=105 \mathrm{mm} \)


Other than lightning conductor, what are the objects which indirectly protect building from lightning / thunderstorm?
A. Metal column used during construction
B. Electrical wires in the building
c. water pipe in the building.
D. All of the above


What is difference between habitat and
ecosystem?


Would you place the two isotopes of
chlorine, \( C l-35 \) and \( C l-37 \) in
different slots because of their different
atomic masses or in the same slot
because their chemical properties are the same? Justify your answer.


The usage of dihydrogen is:
\( \mathbf{A} \cdot \) It acts a a fuel cell
B. Energy is distributed in the form of dihydrogen
C. It is economical fuel
D. All of the above


The cell has an emf of \( 2 V \) and the
internal resistance of this cell is \( 0.1 \Omega \), i is connected to a resistance of \( 3.9 \Omega \), the
voltage across the cell will be
\( \mathbf{A} \cdot 0.5 V \)
в. \( 1.9 V \)
c. \( 1.95 V \)
D. \( 72 ~ V \)


Lymph provides immunity because
A. It has lymphocytes
B. It has erythrocytes
c. It has thromobocytes
D. None of the above


If the radius of a sphere is doubled, what is the ratio of the volume of the
first sphere to that of the second sphere?
A . 1: 8
B. 1: 4
\( \mathbf{c} \cdot 1: 27 \)
D. 8: 1


The p-orbitals are directed towards \( X, Y \) \( \mathbf{Z} \) coordinates and are at right angles to
one another.
A. True
B. False


Metals which liberate hydrogen on treatment with acids must be:
A. more electronegative than hydrogen
B. less electropositive than hydrogen
c. higher compound
D. more electropositive than hydrogen


Two charges of same magnitude move
in two circles of radii \( \boldsymbol{R}_{1}=\boldsymbol{R} \) and
\( R_{2}=2 R \) in a region of constant
uniform magnetic field \( B_{0} \)

The work \( W_{1} \) and \( W_{2} \) done by the
magnetic field in the Two cases,
respectively are such that:
\( \mathbf{A} \cdot W_{1}=W_{2}=0 \)
в. \( W_{1}>W_{2} \)
\( \mathbf{c} \cdot W_{1}=W_{2} \neq 0 \)
D. \( W_{1}<W_{2} \)


Why do high rise buildings have a red light on the top of the building?
A. Red light is the least scattered by fine particles
B. Red light can be easily spotted by the pilot
c. Both A and B
D. None


If \( f(x)=\log \left[\frac{1+x}{1-x}\right] \) and \( -1_{1}, x_{2}<1, \) then \( f\left(x_{1}\right) \)
\( \mathbf{f}\left(\mathbf{x}_{2}\right) \) is equal to:
\( \mathbf{A} \cdot f\left[\left(x_{1}-x_{2}\right) / 1+x_{1} x_{2}\right] \)
B \( \cdot f\left[\left(x_{1}-x_{2}\right) / 1-x_{1} x_{2}\right] \)
\( \mathbf{c} \cdot f\left[\left(x_{1}+x_{2}\right) / 1-x_{1} x_{2}\right] \)
\( \mathbf{D} \cdot f\left[\left(x_{1}+x_{2}\right) / 1+x_{1} x_{2}\right] \)


\( a c \)
Chlorobenzene
Reaction \( \rightarrow \) Salicylaldehyde. \( X \) and \( Y \)
reactions are respectively:
A. Fries rearrangement and Kolbe-Schmidt
B. Cumene and Reimer-Tiemann
c. Dow and Reimer-Tiemann
D. Dow and Friedal-Craft


In the given figure 0 is the centre of the
circle \( 0 B=5 c m, \) Distance from 0 to
Chord \( A B \) is \( 3 c m \).Find the length of \( A B \)


Six charges are kept at the vertices of a regular hexagon as shown in the figure. f magnitude of force applied by \( +Q \) on \( +q \) charge is \( F \), then net electric force
on the \( +Q \) is \( n F \). Find the value of \( n \)


An observer \( A \) fires a gun and another observer \( B \) at a distance \( 1650 m \) away
from \( A \) hears its sound. If the speed of
sound is \( 330 m s^{-1}, \) find the time when
\( B \) will hear the sound after firing by \( A \)
\( \mathbf{A} \cdot 5 s \)
в. \( 15 s \)
\( c .50 s \)
D. None of these


List the main difference between
mitosis and meiosis.


A long straight wire along the z-axis carries a current lin the negative z direction. The magnetic vector field \( \bar{B} \) at a point having coordinates \( (x, y) \) in the z=0 plane is:
A \( \cdot \frac{\mu_{0} I(y \hat{i}-x \hat{j})}{2 \pi\left(x^{2}+y^{2}\right)} \)
B. \( \frac{\mu_{0} I(x \hat{i}-y \hat{j})}{2 \pi\left(x^{2}+y^{2}\right)} \)
c. \( \frac{\mu_{0} I(x \hat{j}-y \hat{i})}{4 \pi\left(x^{2}+y^{2}\right)} \)
D. \( \frac{\mu_{0} I(x \hat{i}-y \hat{j})}{4 \pi\left(x^{2}+y^{2}\right)} \)


The solubility of silver acetate in pure water at \( 25^{\circ} \mathrm{C} \) 8.35g.litre \( ^{-1} \) and
\( 61.8 g . l i t r e^{-1} \) in an acid solution of
\( \boldsymbol{p} \boldsymbol{H}=\mathbf{3} . \) Calculate:
(i) \( K_{s p} \) of silver acetate and
(ii) dissociation constant of acetic acid.


Identify \( A \) and \( B \) the following reactions. \( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N}_{2} \boldsymbol{C l} \frac{\boldsymbol{H O H}}{\Delta} \boldsymbol{A} \stackrel{\boldsymbol{B r}_{2}}{\boldsymbol{B}} \boldsymbol{B} \)


Which of the following quantities has its unit as newton second?
A. Energy
B. Torque
c. Momentum
D. Angular momentum


\( \boldsymbol{C u} \boldsymbol{O}+\boldsymbol{H}_{2} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C u}, \) reaction is
an example of :
A. redox reaction
B. synthesis reaction
c. neutralisation
D. analysis reaction


Which of the following is sonorous?
A. Sodium
B. Silver
c. Lead
D. All of the above


In Nelson cell, \( N a O H \) are formed at
(cathode/anode) electrode.


Tickets numbered from 1 to 30 are
mixed up and then a ticket is drawn at
random. What is the probability that the
drawn ticket has a number which is
divisible by both 2 and \( 6 ? \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{8}{15} \)
D.


The energy of an electron in the \( 1 s \)
orbital of \( \boldsymbol{H}^{-}, \boldsymbol{H} e, \boldsymbol{L} \boldsymbol{i}^{+} \) and \( \boldsymbol{B} \boldsymbol{e}^{2+} \)
follows the order.
A \( . H^{-}>H e>L i^{+}>B e^{2} \)
B . \( L i^{+}>B e^{2+}>H e>H^{-} \)
\( \mathbf{c} \cdot B e^{2+}>L i^{+}>H e>H \)
D. \( H^{-}>L i^{+}>H e>B e^{2} \)


\( \sin \cot ^{-1} \tan \cos ^{-1} x \) is equal to
A . \( x \)
B. \( \sqrt{1-x^{2}} \)
c. \( \frac{1}{x} \)
D. none of these


If \( |\boldsymbol{v}|= \) const; circular motion place
then
A \( \cdot \alpha= \) angular accl" \( = \) const
B \( \cdot a_{t}= \) const
\( \mathbf{c} \cdot a_{c}= \)const
D. All are false


At \( 227^{0} C, 60 \% \) of 2 moles of \( P C l_{5} \) gets dissociated in a two-litre. the value of
\( \boldsymbol{K}_{\boldsymbol{p}} \) will be
\( A \cdot 450 R \)
B. 400 R
\( c . \) 50
D. 100 R


In the Castner's process of extraction of sodium, the cathode is:
A. iron rod
B. nickel rod
c. copper rod
D. graphite rod


The fractional change in the volume of oil is 1 percent when a pressure of \( 2 \times 10 \)
\( 7 \mathrm{N} / \mathrm{m}^{2} \) is applied. The bulk modulus and its compressibility is :
A \( \cdot 3 \times 10^{8} \mathrm{N} / \mathrm{m}^{2}, 0.33 \times 10^{-9} \mathrm{m}^{2} / \mathrm{N} \)
B. \( 5 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}, 2 \times 10^{-10} \mathrm{m}^{2} / \mathrm{N} \)
c. \( 2 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}, 5 \times 10^{-10} \mathrm{m}^{2} / \mathrm{N} \)
D. 3 \( \times 10^{+9} \mathrm{N} / \mathrm{m}^{2}, 5 \times 10^{-9} \mathrm{m}^{2} / \mathrm{N} \)


The major binding force in diamond, silicon and quartz is :
A. electrostatic force
B. covalent bond
c. non-covalent bond
D. van der Waals force


Which of the following may show photosynthesis in moonlight
A. some thermal algae
B. some marine algae
c. some fresh water algae
D. None of the above


Four alphabets \( \mathrm{E}, \mathrm{K}, \mathrm{S} \) and \( \mathrm{V}, \) one in each, were purchased from a plastic warehouse. How many ordered pairs of alphabets, to be used as initials, can be formed from them?


The maximum force of friction when the
body is just begining to move is known
as the
A. limiting friction
B. Rolling friction
C. Kinetic friction
D. (1) and (2) both


Formula of rust:
\( \mathbf{A} \cdot F e_{2} O_{3} \cdot x H_{2} O \)
B. \( F e_{3} O_{4} \cdot x H_{2} O \)
\( \mathbf{c} \cdot F e_{6} O_{16} \cdot x H_{2} O \)
D. None of the above


Assertion
If \( \vec{a}=5 \hat{i}-\hat{j}+2 \widehat{k}, \) then a vector having magnitude of 8 units along \( \vec{a} \) is \( \frac{8}{\sqrt{30}}(5 \hat{i}-\widehat{j}+2 \widehat{k}) \)
Reason
Vector having modulus m along a given
vector \( ^{\prime} \boldsymbol{a}^{\prime} \) is given by, \( \boldsymbol{m} \times \widehat{\boldsymbol{a}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The length of a wire is 4 m. Its length is
increased by \( 2 m m \) when a force acts on
it. The strain is:
A. \( 0.5 \times 10^{-3} \)
B. \( 5 \times 10^{-3} \)
\( c \cdot 2 \times 10^{-3} \)
D. 0.05


The following characteristics of a substance are given. What is the name of this substance?
(i) It is used as an abrasive for cutting glass.
(ii) It is used as a tip of deep boring drills.
(iii) It is used for making dies for
drawing wires.
(iv) It is used in generating laser beams in electronics.
A. Diamond
B. Buckminister fullerene
c. Lampblack
D. Graphite


In the given arrangement, the loop is moved with constant velocity \( v \) in a
uniform magnetic field \( B \) in a restricted
region of width \( a \). The time for which the
emf is induced in the circuit is
A \( -\frac{2 b}{v} \)
в. \( \frac{2 a}{v} \)
c. \( \frac{(a+b)}{v} \)
D.


Total possible octet structural formula
for \( \boldsymbol{N}_{\mathbf{3}}^{-\text {is }} \)


Which of the following is required both during photosynthesis and respiration?
A. Phytochrome
B. Cytochrome
c. chlorophyll
D. Glucose


When sodium and chlorine react, energy
¡s:
A. released and ionic bond is formed.
B. released and covalent bond is formed.
C. absorbed and covalent bond is formed.
D. absorbed and ionic bond is formed.


If \( A(-2,-1), B(a, 0), C(4, b) \) and \( D(1,2) \) are
the vertices of a parallelogram, find the
values of a and b.


Rohan wants to test whether a white
object or a black object would heat up faster in the Sun. The given picture shows you his experiment. These thermometers were left out in the Sun
for 30 minutes.

Which of the following statements is
true?
A. Thermometer 1 reads the same as thermometer
B. Thermometer 2 shows a higher temperature than thermometer
c. Thermometer 3 shows a higher temperature than thermometer
D. Thermometer 1 reads the same as thermometer


Photophosphorylation is the process in
which
A \( \cdot C O_{2} \) and \( O_{2} \) unite
B. Phosphoglyceric acid is produced.
c. Aspartic acid is formed
D. Light energy is converted into chemical energy through production of ATP


Pectoral girdle, pelvic girdle and limb
bones are constituted with
A. Visceral skeleton
B. Outer skeleton
C. Axial skeleton
D. Appendicular skeleton


If \( A \subseteq B, \) then \( A \cap B \) is equal to
A. \( A \)
в. \( B \)
c. \( A^{\prime} \)
D. \( B^{\prime} \)


\( \lim _{x \rightarrow 5} \frac{\sin ^{2}(x-5) \tan (x-5)}{\left(x^{2}-25\right)(x-5)} \) is equal to
A. 1
B. \( \frac{1}{10} \)
\( c \cdot 0 \)
\( D \)


f \( n(A \times B)=36 \) then \( n(A) \) can
possibly be
\( A \cdot 7 \)
B. 8
\( c .9 \)
D. 10


The line joining the points \( A(3,0) \) and
\( B(5,2) \) is rotated about \( A \) in the
anticlockwise direction through an
angle \( 15^{\circ} \).If \( B \) goes to \( C \) in the new position now the line joining \( A \) and \( C \) is rotated about \( A \) in the anticlockwise
direction through an angle of \( 45^{\circ} \) of \( C \)
goes to \( D \) in the new position,then the
coordinates of \( D \) are
A. \( (4-\sqrt{3}, \sqrt{3}-1) \)
B. \( (4+\sqrt{3}, \sqrt{3}-1) \)
c. \( (4-\sqrt{3}, \sqrt{3}+1) \)
D. \( (4+\sqrt{3}, \sqrt{3}+1) \)


Entropy change \( (\Delta S) \) for adsorption:
A. negative
B. positive
c. zero
D. cannot be said


An example of dibasic acid is:
A. orthophosphorus acid
B. orthophosphoric acid
c. hypophosphorus acid
D. pyrophosphoric acid


Which of the following in electricity is
analogous to momentum \( m v \) in dynamics?
A. IV
B . IL
c. \( \mathrm{Q} \)
D. IQ


Identify the two tissues the combination, which enables animals to
move rapidly in response to stimuli.
A. Epithelial and muscular tissue
B. Epithelial and nervous tissue
c. connective tissue and nervous tissue
D. Muscular and nervous tissue


Value of \( \left[\frac{\sin 49^{\circ}}{\cos 41^{\circ}}+\frac{\cos 41^{\circ}}{\sin 49^{\circ}}\right]^{2} \) is
\( A \cdot 2 \)
B. 4
c. 1
D. None of these


The length and breadth of a rectangular
field are \( 110 m \) and 85 m respectively. Find the perimeter of the field. How
much will it cost to fence the field at the
rate of \( R s 25 \) per metre?


A point moves with uniform
acceleration and \( v_{1}, v_{2}, v_{3} \) denote the
average velocities in three successive
intervals of time \( t_{1}, t_{2}, t_{3} . \) Then, the
relation \( \frac{\boldsymbol{v}_{1}-\boldsymbol{v}_{2}}{\boldsymbol{v}_{2}-\boldsymbol{v}_{3}} \) is
A \( \frac{t_{1}-t_{2}}{t_{2}+t_{3}} \)
B. \( \frac{t_{1}+t_{2}}{t_{2}+t_{3}} \)
c. \( \frac{t_{1}-t_{2}}{t_{1}+t_{3}} \)
\( \mathbf{D} \cdot \frac{t_{1}-t_{2}}{t_{2}-t_{3}} \)


Which of the following species are expected to have spectrum similar to hydrogen? This question has multiple correct options
A \( . H e^{+} \)
B. \( H e^{2+} \)
\( c \cdot L i^{2} \)
\( \mathbf{D} \cdot L i^{+} \)


Arrange the following lengths in descending order of their magnitudes:
Light year, parsec end Astronomical unit


Ohm's law is valid for
A. gases only
B. liquids only
C. both liquids and gases
D. metallic conductors


The solution of the equation \( 10-3 y=1 \) is
\( y= \)
A. 0
B. 1
\( c \cdot 2 \)
D. 3


In the process of extraction of gold, the following reaction takes place:
Roasted gold ore \( +\boldsymbol{C} \boldsymbol{N}^{-}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
\( [\boldsymbol{X}]+\boldsymbol{O H}^{-} \)
\( [\boldsymbol{X}]+\boldsymbol{Z} \boldsymbol{n} \rightarrow[\boldsymbol{Y}]+\boldsymbol{A} \boldsymbol{u} \)
Identify the compounds \( [\mathrm{X}] \) and \( [\mathrm{Y}] \)
A \( \cdot[X]=\left[A u(C N)_{2}\right]^{-},[Y]=\left[Z n(C N)_{4}\right]^{2-} \)
B . \( [X]=\left[A u(C N)_{4}\right]^{3-},[Y]=\left[Z n(C N)_{4}\right]^{2-} \)
C \( \cdot[X]=\left[A u(C N)_{2}\right]^{-},[Y]=\left[Z n(C N)_{6}\right]^{4} \)
D \( \cdot[X]=\left[A u(C N)_{4}\right]^{-},[Y]=\left[Z n(C N)_{6}\right]^{2} \)


According to adsorption theory of catalysis, the reaction rate increases,
because:
A. Adsorption produces heat which increases the rate of reaction
B. In the process of adsorption, the kinetic energy of the molecules increases
C. The concentration of reactants at the active centres becomes high due to adsorption
D. The activation energy of the reaction becomes high due to adsorption


\( \frac{1+2 i}{1-(1-i)^{2}} \)
A .
в. \( \frac{(-3+4 i)}{5} \)
c. \( \frac{(+3-4 i)}{5} \)
D. -


By how many times the absolute temperature of a gas would increase
when \( u_{r m s} \) of a gas in a container of fixed volume is increased from \( 5 \times \)
\( 10^{4} \mathrm{cm} \sec ^{-1} \) to \( 10 \times 10^{4} \mathrm{cm} \mathrm{sec}^{-1} ? \)


The compound which contains both
ionic and covalent bonds is:
A. \( A l C l_{3} \)
в. \( H C l \)
c. \( N H_{4} C l \)
D. KCl


The direction cosines of \( A B \) are -2,2,1
If \( \boldsymbol{A} \equiv(\mathbf{4}, \mathbf{1}, \mathbf{5}) \) and \( l(\boldsymbol{A} \boldsymbol{B})=\mathbf{6 u n i t s} \)
find the coordinates of \( \boldsymbol{B} \)


If the mean of the following frequency
distribution is 7.2 find value of \( ^{\prime} K^{\prime} \)
\( \boldsymbol{x} \) 2 4 8 \( \mathbf{1 0} \)
7
\[
K
\]
\( f \quad 4 \) and 10 16 3.


Assertion
Through the use of catalytic converters, unburnt hydrocarbons are changed into carbon monoxide which in turn is
changed into nitrogen oxides and water.
Reason

Motor vehicles equipped with catalytic
converters should use leaded petrol to protect the catalyst from degradation.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Two isolated metallic solid spheres of
radii \( \boldsymbol{R} \) and \( 2 \boldsymbol{R} \) are charged such that
both of these have same charge density
\( \rho . \) The spheres are located far away from each other, and connected by a thin conducting wire. Then the new charge
density on the bigger sphere is:


Choose the correct answer among the alternatives given :
Classify the following compounds as primary, secondary and tertiary halides.
(i) 1-Bromobut-2-ene
(ii) \( 4- \) Bromopent.2-ene
(iii) 2-Bromo-2-methylpropane
A. (i)-secondary, (ii)-tertiary, (iii)-primary
B. (i)-secondary, (ii)-primary, (iii)-tertiary
c. (i)-primary,
(ii)-tertiary, (iii)-secondary
D. (i)-primary, (ii)-secondary, (iii)-tertiary


If \( \boldsymbol{a} \boldsymbol{x}_{1}^{2}+\boldsymbol{b} \boldsymbol{y}_{1}^{2}+\boldsymbol{c} \boldsymbol{z}_{1}^{2}=\boldsymbol{a} \boldsymbol{x}_{2}^{2}+\boldsymbol{b} \boldsymbol{y}_{2}^{2}+ \)
\( \boldsymbol{c} \boldsymbol{z}_{2}^{2}=\boldsymbol{a} \boldsymbol{x}_{3}^{2}+\boldsymbol{b} \boldsymbol{y}_{3}^{2}+\boldsymbol{c} \boldsymbol{z}_{3}^{2}=\boldsymbol{d} \) and
\( \boldsymbol{a} \boldsymbol{x}_{2} \boldsymbol{x}_{3}+\boldsymbol{b} \boldsymbol{y}_{2} \boldsymbol{y}_{3}+\boldsymbol{c} \boldsymbol{z}_{2} \boldsymbol{z}_{3}=\boldsymbol{a} \boldsymbol{x}_{3} \boldsymbol{x}_{1}+ \)
\( \boldsymbol{b} \boldsymbol{y}_{3} \boldsymbol{y}_{1}+\boldsymbol{c} \boldsymbol{z}_{3} \boldsymbol{z}_{1}=\boldsymbol{a} \boldsymbol{x}_{1} \boldsymbol{x}_{2}+\boldsymbol{b} \boldsymbol{y}_{1} \boldsymbol{y}_{2}+ \)
\( \boldsymbol{c} \boldsymbol{z}_{1} \boldsymbol{z}_{2}=\boldsymbol{f}, \) then prove that
\( \left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \boldsymbol{z}_{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \boldsymbol{z}_{2} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & \boldsymbol{z}_{3}\end{array}\right|=(\boldsymbol{d}- \)
\( f)\left[\frac{d+2 f}{a b c}\right]^{1 / 2}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \neq \mathbf{0}) \)


Parotid salivary glands are present
A. Below the tongue
B. Below the cheeks
c. In the angle between two jaws
D. Below the eye orbits


The figure shows a point \( P \) on the axis of
a circular loop carrying current I.The
correct direction of magnetic field vector at \( P \) due to \( \overrightarrow{d l} \) is represented by
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Reflection of the Sun's light from the upper layers of the Earth's atmosphere
causes.
A. day and night
B. tides
c. eclipses
D. twilight


If \( f(x)=\frac{e^{x^{2}}-\cos x}{x^{2}}, \) for \( x \neq 0, \) is
continuous at \( \boldsymbol{x}=\mathbf{0}, \) find \( \boldsymbol{f}(\mathbf{0}) \)


\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \\ \mathbf{2} \boldsymbol{x} & \mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y} & \boldsymbol{4} \boldsymbol{x}+\boldsymbol{3} \boldsymbol{y}+\boldsymbol{2} \boldsymbol{z} \\ \boldsymbol{3} \boldsymbol{x} & \boldsymbol{6} \boldsymbol{x}=\boldsymbol{3} \boldsymbol{y} & \boldsymbol{1} \boldsymbol{0} \boldsymbol{x}+\boldsymbol{6} \boldsymbol{y}+\boldsymbol{3} \boldsymbol{z}\end{array}\right|=\mathbf{6 4} \)
then the real value of \( x \) is


Taking an example of an ambidentate ligand, explain why it is called as ambidentate ligand.


80YATU in plane mirror appears as:
A. 80YATU
B. 80Yatu
c. UTAYO8
D. 8оYАТบ


The king, queen and jack of clubs are removed from a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the
remaining cards. Find the probability of getting a card of A King.


\( \boldsymbol{A}(\mathbf{1},-\mathbf{1},-\mathbf{3}), \boldsymbol{B}(\mathbf{2}, \mathbf{1},-\mathbf{2}) \)
\( \& \quad C(-5,2 \)
are the position vectors of the vertices of a triangle \( A B C \), then the length of the bisector of its internal
angle \( A \) is


If \( \vec{a}, \vec{b}, \vec{c} \) are three vectors such that \( \vec{a} \times \) \( \overrightarrow{\boldsymbol{b}}=\overrightarrow{\boldsymbol{c}}, \overrightarrow{\boldsymbol{b}} \times \overrightarrow{\boldsymbol{c}}=\overrightarrow{\boldsymbol{a}}, \overrightarrow{\boldsymbol{c}} \times \overrightarrow{\boldsymbol{a}}=\overrightarrow{\boldsymbol{b}} \) then prove
that \( |\overrightarrow{\boldsymbol{a}}|=|\overrightarrow{\boldsymbol{b}}|=|\overrightarrow{\boldsymbol{c}}| \)


Which of these steps in Krebs cycle
indicates substrate level
phosphorylation?
A. Conversion of succinic acid to \( \alpha \) -ketoglutaric acid
B. Conversion of succinic acid to malic acid
c. conversion of succinyl CoA to succinic acid
D. Conversion of malic acid to oxaloacetic acid
E. conversion of citric acid to \( \alpha \) -ketoglutaric acid


Suppose an integer from 1 through 100 is chosen at random, find the
probability that the integer is a multiple of 2 or a multiple of 9


The sum of length, breadth and height
of a cuboid is \( 38 \mathrm{cm} \) and the lengths of
its diagonal is \( 22 \mathrm{cm} . \) Find the total
surface area of the cuboid (in \( c m^{2} \) )


Which of the reaction defines molar
\( \Delta \boldsymbol{H}_{\boldsymbol{f}}^{\circ} ? \)
This question has multiple correct options
\( \mathbf{A} \cdot H^{+}(a q)+O H^{-}(a q) \rightarrow H_{2} O(\iota) \)
B \( \cdot \quad B r_{2}(\iota)+H_{2}(g) \rightarrow H B r(g) \)
\( \mathbf{C} \cdot N_{2}(g)+2 H_{2}(g)+O_{2}(g) \rightarrow N H_{4} N O_{3} \)
\( \mathbf{D} \cdot H_{2}(g)+S_{\text {monoclinic}}+2 O_{2}(g) \rightarrow H_{2} S O_{4}(\iota) \)


Two circular coils are placed adjacent
to each other. Their planes are paralle
and currents through them \( i_{1} \) and \( i_{2} \) are
in same directions. Choose the correct
options
This question has multiple correct options
A. When \( A \) is brought near \( B \), current \( i_{2} \) will decrease
B. When \( A \) is brought near \( B \), current \( i_{2} \) will increase
C. When current \( i_{1} \) is increased, current \( i_{2} \) will decrease
D. When current \( i_{1} \) is increased, current \( i_{2} \) will increase


Glycogen yield only glucose on hydrolysis?
A. True
B. False


A circular coil of wire is connected to a battery of negligible internal resistance and has magnetic induction \( B \) at its centre. If the coil is unwound and
rewound to have double the number of
turns, and is connected to the same
battery, then the magnetic induction at
the center is :
\( \mathbf{A} \cdot 2 B \)
в. \( 4 B \)
\( c . B \)
D. \( 0.5 B \)


Q Type your question
vertical position and touching a block of mass \( M \) which is a rest on a horizontal
surface. The rod is given a slight jerk
and it starts rotating about point \( \boldsymbol{O} \)
This causes the block to move forward
as shown. The rod loses contact with the
block at \( \boldsymbol{\theta}=\mathbf{3 0}^{\circ} \) All surfaces are
smooth. Now answer the following
questions. The velocity of block when
the rod loses contact with the block is
A \( \cdot \frac{3 g l}{4} \)
B. \( \frac{5 g l}{4} \)
c. \( \frac{6 g l}{4} \)
D. \( \frac{7 g l}{4} \)


Find the degree of the given algebraic expression \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}+\boldsymbol{c} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


The values of van't Hoff factors for
\( K C l, N a C l \) and \( K_{2} S O_{4} \) respectively
are:
A. 1,1,2
B. 1,1,1
c. 2,2,3
D. 2,3,2


The ionization energy for excited hydrogen atom in eV will be
A . 13.6
B. less than 13.6
c. greater than 13.6
D. 3.4 or less


The function which has neither
maximum nor minimum at \( x=0=0 \) is
A \( \cdot f(x)=x^{2} \)
B. \( f(x)=\cos x \)
\( c \cdot f(x)=x^{3}-8 \)
D. \( f(x)=\cos h x \)


Which of the law can be understood in
terms of Stefan's law
A. Wien's displacement law
B. Kirchoff's law
c. Newton's law of cooling
D. Planck's law


A rocket with a lift-off mass \( 3.5 \times 10^{4} \)
kg is blasted upwards with an initia
acceleration of \( 10 m / s^{2} . \) Then the initial
thrust of the blast is:
A \( \cdot 3.5 \times 10^{5} N \)
в. \( 7.0 \times 10^{5} N \)
c. \( 14.0 \times 10^{5} N \)
D. \( 1.75 \times 10^{5} N \)


Differentiate :
\( y^{x}=x^{y} \)


Gaussian surface obtains a measure
of the electric charge within the surface
A. depending how that internal charge is configured.
B. no matter how that internal charge is configured.
C. and may sometimes depend how that internal charge is configured
D. None of these


Dry hydrogen can oxidise copper oxide to form metal.
A. copper
B. zinç
c. carbon
D. Boron


Select the correct statement regarding
"A trace element is an element which".
\( A \cdot \) Is a radio active and can be traced by Geiger counter
B. Is required in very minute amounts.
C. Draws other element out of protoplasm.
D. Was one of the first to be discovered in protoplasm.


The probability distribution of a random variable \( X \) is given below:
\[
\begin{array}{ccccc}
\mathbf{x}: & \mathbf{0} & 1 & \mathbf{2} & \mathbf{3} \\
\mathbf{P}(\mathbf{x}): & \mathbf{k} & \frac{k}{2} & \frac{k}{4} & \frac{k}{8} \\
& & & \\
\text { Determine } \boldsymbol{P}(\boldsymbol{X} \leq \mathbf{2})+\boldsymbol{P}(\boldsymbol{X}>\mathbf{2})
\end{array}
\]


A body dropped freely from a height hon to a horizontal plane, bounces up and
down and finally comes to rest.The coefficient of restitution is e. The ratio
of velocities at the beginning and after two rebounds is
A \( \cdot 1: e \)
B. e:
\( c \cdot 1: e^{3} \)
D. \( e^{2}: 1 \)


In organic compounds, Sulphur is estimated as:
A. \( B a S O_{4} \)
в. \( B a C l_{2} \)
\( \mathbf{c} \cdot B a_{3}\left(P O_{4}\right)_{2} \)
D. \( H_{2} S O_{4} \)


A charged particle with velocity \( 2 \times \) \( 10^{3} m / s \) passes undeflected through
electric and magnetic field. Magnetic field is 1.5 tesla. The electric field
intensity would be
A \( \cdot 2 \times 10^{3} N / C \)
в. \( 1.5 \times 10^{3} N / C \)
c. \( 3 \times 10^{3} N / C \)
\( \mathbf{D} \cdot 4 / 3 \times 10^{-3} N / C \)


\( \triangle \mathrm{ABC} \) and \( \triangle \) DEF are two triangles, then to ensure that two triangles ABC and DEF are congruent, 3 conditions \( \operatorname{given} ; A B=D E, A C=D F, \angle A B C=\angle \)
DEF are
A. sufficient but not necessary
B. necessary but not sufficient
c. neither necessary nor sufficient
D. both necessary and sufficient


Around the centre of gravity vanishes. Fill in the blank.
A. Resultant acceleration due to gravity force
B. Resultant velocity due to gravity force
c. Resultant torque due to gravity force
D. None


A telephone company charges \( x \) cents for the first minute of a call and charges for any additional time at the rate of \( y \) cents per minute. If a certain call costs \( \$ 5.55 \) and lasts more than 1 minute, which of the following expressions represents the length of that call, in minutes?
\( ^{\text {A. }} \frac{555-x}{y} \)
B. \( \frac{555+x-y}{y} \)
c. \( \frac{555-x+y}{y} \)
D. \( \frac{555-x-y}{y} \)
E \( \frac{555}{x+y} \)


The difference between two positive integers is \( 75 . \) The ratio of these
integers is \( 7: 4 . \) Find the integers.


happens when a wave passes from one medium to another at an angle.
A. Refraction
B. Reflection
c. Dispersion
D. Scattering


The position of a body moving along the x-axis at time \( t \) is given by \( t^{2}-4 t+6 \)
The distance traveled by body in time interval \( t=0 \) to \( t=3 s \) is
A. \( 5 m \)
в. \( 7 m \)
c. \( 4 m \)
D. \( 3 m \)


What would be the final temperature of
the mixture when 5 g of ice at \( -10^{\circ} \mathrm{C} \) are
mixed with \( 20 g \) of water at \( 30^{\circ} \mathrm{C} \)
Specific heat of ice is 0.5 and latent
heat of water \( 80 \mathrm{cal} g^{-1} \)


Assertion
If \( \boldsymbol{\lambda}_{N a^{+}}^{\circ} \) and \( \boldsymbol{\lambda}_{C l^{-}}^{\circ} \) are molar limiting
conductivity of sodium and chloride ions respectively, then the limiting
molar conductivity for sodium chloride
is given by the equation: \( \wedge_{N a C l}^{\circ}= \) \( \boldsymbol{\lambda}_{N a^{+}}^{\circ}+\boldsymbol{\lambda}_{C l^{-}}^{\circ} \)
Reason
This is according to Kohlrausch law of independent migration of ions.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In the absence of specific data, it can only be said that (R)-2-bromopentane
is:
A. laevorotatory (-)
B. dextrorotatory ( \( + \) )
c. optically inactive
D. analogous in absolute configuration to (R)- \( 2- \) chloropentane


At \( 25^{\circ} \mathrm{C} \) the heat of formation of \( H_{2} \mathrm{O}(l) \) is
\( -285.9 \mathrm{KJ} \) mole \( ^{-1} \) and that for \( H_{2} O(g) \) is
\( -242.8 \mathrm{KJmole}^{-1} . \) The heat of vaporization
of water at the same temperature is
A \( \cdot 43.1 \mathrm{KJ} \mathrm{mole}^{-1} \)
B. 242.8 KJ mole \( ^{-1} \)
C . -43.1 KJ mole \( ^{-1} \)
D. - 242.8 KJ mole \( ^{-1} \)


Four point masses each of mass \( \mathrm{m} \) are kept at the vertices of a square. A point mass \( m \) is kept at the point of intersection of the diagonal of a square What will be the force experienced by
central mass \( m ? \)


The number of \( S \) - 0 -S bonds in cyclic
\( \boldsymbol{S} \boldsymbol{O}_{3} \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. none of the above


A coin is tossed \( (\mathbf{m}+\mathbf{n}) \) times \( (\mathbf{m}<\mathbf{n}) \) The probability for getting atleast 'n consecutive heads is
A \( \cdot \frac{m+2}{2^{n+1}} \)
в. \( \frac{n+2}{2^{m+1}} \)
c. \( \frac{m}{2^{n+1}} \)
D. \( \frac{(m+1) \times(m+2)}{2^{(m+n+1)}} \)


The chemical substances which relieve the pain either completely or partially are called agonist If this is true enter 1 , if false enter 0 .


Solve \( : \int_{0}^{1} \cot ^{-1}\left(1+x+x^{2}\right) d x \)


Atoms of eight elements \( A, B, C, D, E, F \) \( G \) and \( H \) have the same number of
electronic shells but different number
of electrons in their outermost shell. It
was found that elements \( A \) and \( G \)
combine to form an ionic compound which can also be extracted from sea
water. This compound is added in a small amount to almost all vegetable dishes during cooking. Oxides of elements A and B are basic in nature
while those of \( \mathrm{E} \) and \( \mathrm{F} \) are acidic. The
oxide of \( \mathrm{D} \) is almost neutral. Based on
the above information answer the
following question.

Which two of these elements could
definitely be metals.


A batsman hits back a ball of mass 0.15
kg straight in the direction of the bowler without changing its initial speed of 12 \( m s^{-1} . \) If the ball moves linearly, then the impulse imparted to the ball is
A . \( 1.8 \mathrm{N} \)
B. 2.8 N s
c. 3.6 N s
D. 4.2 N s


Washing powders contain detergents in the range of (by mass):
A. \( 10-15 \% \)
В. \( 15-30 \% \)
c. \( 50-60 \% \)
D. \( 40-50 \% \)


The letter 'T' in T-lymphocyte refers to
A. Thyroid
B. Thalamus
c. Tonsil
D. Thymus


A light bulb is rated at \( 100 W \) for a
\( 220 V \) supply. Find the resistance of the
bulb:
A . \( 184 \Omega \)
B. \( 284 \Omega \)
c. \( 384 \Omega \)
D. \( 484 \Omega \)


Assertion
\( \alpha- \) rays have greater ionizing power
than \( \beta- \) rays.
Reason
\( \alpha- \) particles carry two unit positive
charge while \( \beta- \) particles carry only one unit negative charge.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Hydrolysis of \( X e F_{4} \) and \( C a N C N \) gives
respectively:
A. \( X e O_{3} \) and \( C a C O_{3} \)
в. \( X e O_{2} \) and \( C a C N_{2} \)
c. \( X e O F_{3} \) and \( C a C N_{2} \)
D. \( X e O F_{2} \) and \( C a C O_{3} \)


Cyanide process is used for the concentration of

This question has multiple correct options
A . Au
B. Agg
c. \( A l \)
D. Fe


Number of variables in a simple linear equation are
A. Two
B. one
c. 0
D. None


If the mean deviation of number \( 1,1+ \)
\( \boldsymbol{d}, \mathbf{1}+\mathbf{2} \boldsymbol{d}, \dots, \mathbf{1}+\mathbf{1 0 0} \boldsymbol{d} \) from their mean
is \( 255, \) then the \( d \) is equal to:
A . \( 10 . \)
B. 20.2
c. 20
D. 10


The line \( 3 x+2 y=13 \) divides the area
enclosed by the curve \( 9 x^{2}+4 y^{2}- \)
\( 18 x-16 y-11=0 \) in two parts Find
the ratio of the larger area to the smaller area
A \( \cdot \frac{3 \pi+2}{\pi-2} \)
в. \( \frac{3 \pi-2}{\pi+2} \)
c. \( \frac{\pi+2}{\pi-2} \)
D. \( \frac{\pi-2}{\pi+2} \)


Q Type your question
and radius \( 20 \mathrm{cm} . \) A steady pull of \( 25 \mathrm{N} \)
is applied on the cord as shown in the
figure. The fly wheel is mounted on a horizontal axle with frictionless
bearings. Find the workdone by the pull when \( 2 \mathrm{m} \) of the cord is unwound.
A. 30
3. 40
c. 50
)


Identify \( (C): \)
A. \( N_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( N_{2} \) O


An algae which lives as parasite on
plants is
A. Porphyra
B. Cephaleuros
c. chromulina
D. Laminaria


Find \( x \)
\[
\frac{\mathbf{5} \boldsymbol{x}-\mathbf{4}}{\mathbf{6}}=\mathbf{4} \boldsymbol{x}+\mathbf{1}-\frac{\mathbf{3} \boldsymbol{x}+\mathbf{1 0}}{\mathbf{2}}
\]


Assertion
In case of a projectile, the angle
between velocity and acceleration changes from point to point.
Reason
Because its horizontal component of
velocity remains constant, while vertical component of velocity changes from point to point due to gravitational acceleration.
A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. Both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.
c. Assertion is true, but the Reason is false
D. Assertion is false, but the Reason is true.


Which one of these statement is true for
fibrous proteins?
A. They are soluble in water
B. Polypeptide chains are held together by hydrogen and disulphide bonds
c. polypeptides coil together to give spherical shape
D. hydrogen bond is not present


Answer the following questions:
1. Explain the mechanism of aldol addition reaction.
2. Mention two uses of carboxylic acids.


If a sitar string is plucked at about \( \frac{1}{4} \) th of its length, then the most prominent harmonic would be
A. second
B. third
c. fourth
D. eight


Given graph represents the response of organisms to various abiotic factors. On
this basis, select the correct option for
(i), (ii) and (iii)
A. Conformers Regulators Partial regulators
B. Regulators Partial regulators Conformers
c. Partial regulators Regulators Conformers
D. Regulators Conformers Partial regulators


Which of the following travels to different part of body through blood stream and provides oxygen?
A. Haemoglobin
B. Oxyhaemoglobin
c. carboxyhaemoglobin
D. none of these


An inorganic salt (A) is decomposed at about \( 523 \mathrm{K} \) to give products \( (\mathrm{B}) \) and
(C). compound (C) is a liquid at room temperature and is neutral to litmus paper while oxide (B) on burning with white phosphorous, given a dehydrating agent (D). compounds (A),
(B), (C) and (D) will be identified as:
A. \( N H_{4} N O_{3}, N_{2} O, H_{2} O, P_{2} O_{5} \)
в. \( N H_{4} N O_{2}, N_{2} O, H_{2} O, P_{2} O_{5} \)
c. \( C a C O_{3}, C a O, H_{2} O, C a C l_{2} \)
D. \( \operatorname{CaCO}_{3}, \) Са С \( , \) На\( _{2} \) О, СаОН\( _{2} \),


f \( \sin ^{-1}\left(\tan \frac{17 \pi}{4}\right)-\sin ^{-1}(\sqrt{\frac{3}{x}}) \)
\( \left(\frac{\pi}{6}\right)=0, \) then \( x \) is a root of the
equation
A \( \cdot x^{2}-x-6=0 \)
B . \( x^{2}+x-6=0 \)
c. \( x^{2}-x-12=0 \)
D. \( x^{2}+x-12=0 \)


Find the equations of the lines for which \( \tan \theta=\frac{1}{\sqrt{2}}, \) where \( \theta \) is the angle of
inclination of the line and \( x- \) intercept
is 3


\( \sin \frac{7 \pi}{4}=\frac{1}{\sqrt{2}} \)
A. True
B. False


Rate of disappearance of the reactant \( \boldsymbol{A} \)
at two different temperature is given by
\( \boldsymbol{A} \rightleftharpoons \boldsymbol{B} \)
\( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d t}}=\left(\boldsymbol{2} \times \mathbf{1 0}^{-2} \boldsymbol{S}^{-1}\right)[\boldsymbol{A}]-\boldsymbol{4} \times \)
\( \mathbf{1 0}^{-3} \boldsymbol{S}^{-\mathbf{1}}[\boldsymbol{B}], \boldsymbol{T}=\mathbf{3 0 0} \boldsymbol{K} \)
\( \frac{-\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d t}}=\left(\boldsymbol{4} \times \mathbf{1 0}^{-2} \boldsymbol{S}^{-1}\right)[\boldsymbol{A}]-\mathbf{1 6} \times \)
\( \mathbf{1 0}^{-\mathbf{4}}[\boldsymbol{B}], \boldsymbol{T}=\mathbf{4 0 0} \boldsymbol{K} \)
Calculate heat of reaction in the given temperature range, when equilibrium is
\( \operatorname{set} \) up.
A. \( 16.06 k J \)
в. \( 23.04 k J \)
c. \( 26.78 k J \)
D. \( 29.34 k J \)


Which of the following is non biodegradable?
A. Plastic
B. cotton
c. Paper
D. Left over food stuff


An element has its electronic
configuration as \( 2,8,2 . \) Now answer the following question:

To which period does does this element belong?


Subtract -26 from +32
A. - -
B. +6
\( c .-58 \)
\( D \cdot+58 \)


Why is bithional added to soap?


Complete and balance the following
compound \( \boldsymbol{A l} \boldsymbol{B} \boldsymbol{r}_{3}+\boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7}+ \)
\[
\boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \rightarrow \boldsymbol{K}_{3} \boldsymbol{P} \boldsymbol{O}_{4}+\boldsymbol{A} \boldsymbol{l} \boldsymbol{P} \boldsymbol{O}_{4}+
\]


Find the squares of the following numbers without actual multiplication:
49
52
\( \mathbf{A} \cdot 2441 ; 2704 \)
B. 2401; 2784
c. \( 2401 ; 2704 \)
D. \( 2441 ; 2784 \)


Show that the triangle whose vertices \( \operatorname{are}(8,-4),(9,5) \) and (0,4) is an
isosceles triangle.


Which of the following is known as glacial phosphoric acid?
A. \( H P O_{3} \)
в. \( H_{3} P O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{PO}_{2} \)
D. \( H_{3} P O_{4} \)


Who unified electricity and magnetism?


The octet rule is not followed by:
A. \( F_{2} \)
в. NaF
c. \( C a F_{2} \)
D. \( B F_{3} \)


Recall that two circles are congruent if they have the same radii. Prove that
equal chords of congruent circles subtend equal angles at their centres.


The expression for the magnification of a spherical mirror in the terms of focal length (f) and the distance of the object from mirror (u) is
A. \( \frac{-f}{u-f} \)
B. \( \frac{f}{u+f} \)
c. \( \frac{-f}{u+f} \)
D. \( \frac{f}{u-f} \)


In the circuit of given figure (1) and (2) are ammeters. Just after key \( \boldsymbol{K} \) is pressed to complete the circuit, the reading is
A. maximum in both 1 and 2
B. zero in both 1 and 2
c. zero in 1 , minimum in 2
D. maximum in 1, zero in 2


If \( V=100 \sin 100 t \) volt, and \( I= \)
\( 100 \sin \left(100 t+\frac{\pi}{6}\right) A . \) then find the watt
less power in watt?
A \( \cdot 10^{\text {। }} \cdot 100 \)
в. \( 10^{3} \)
\( c \cdot 10^{2} \)
D. \( 2.5 \times 10^{3} \sqrt{3} \)


Which of these is not an endocrine
gland?
A. Liver
B. Pancreas
c. Testes
D. Thymus


Secondary structure of protein refers to
\( ? \)
A. sequence of amino acids in polypeptide chain
B. bonds between alternate polypeptide chains
C . folding patterns of polypeptide chain
D. bonding between \( N H_{3}^{+} \) and \( C O O^{-} \) of two peptides


For the first order reaction, \( \boldsymbol{A}(\boldsymbol{g}) \rightarrow \)
\( 2 B(g)+C(g), \) the initial pressure is
\( \boldsymbol{P}_{\boldsymbol{A}}=\mathbf{9 0} \) mm Hg. Then pressure after 10
minutes is found to be 180 mm Hg. The
half-life period of the reaction is:
A \( \cdot 1.15 \times 10^{-3} \mathrm{sec}^{-1} \)
в. 600 sec
c. \( 3.45 \times 10^{-3} s e c^{-1} \)
D. 200 sec


Four particles of masses \( \mathrm{m}, 2 \mathrm{m}, 3 \mathrm{m} \) and \( 4 \mathrm{m} \) are arranged at the corners of the parallelogram with each side equal to a
and one of the angle between two
adjacent sides is \( 60^{\circ} \).The parallelogram
lies in the \( x \) -y plane with mass \( m \) at the origin and \( 4 \mathrm{m} \) on the \( \mathrm{X} \) -axis.The center
of mass of the arrangement will be
located at
A \( \cdot\left(\frac{\sqrt{3}}{2} a, 0.95 a\right) \)
в. \( \quad\left(0.95 a, \frac{\sqrt{3}}{4} a\right) \)
c. \( M R^{2}=2 I \)
D. \( \left(\frac{a}{2}, \frac{3 a}{4}\right) \)


Convert the given measurement into the bigger unit. Then, multiply by the second number and find the products.
\( 43 g 732 m g \) and 18


If \( y=\frac{\sqrt{x}(2 x+3)^{2}}{\sqrt{x+1}}, \) then \( \frac{d y}{d x} \) is equal to
A \( \cdot y\left[\frac{1}{2 x}+\frac{4}{2 x+3}-\frac{1}{2(x+1)}\right] \)
в. \( y\left[\frac{1}{3 x}+\frac{4}{2 x+3}+\frac{1}{2(x+1)}\right] \)
c. \( y\left[\frac{1}{3 x}+\frac{4}{2 x+3}+\frac{1}{x+1}\right. \)
D. None of these


Zone refining is based on the principle
that
A. impurities of low boiling metals can be separated by distillation
B. impurities are more soluble in molten metal than in solid metal
C. different component of a mixture are differently adsorbed on an adsorbent
D. vapours of volatile compound can be decomposed in pure metal


Plutonium has atomic mass 210 and a
decay constant equal to \( 5.8 \times 10^{-8} s^{-1} \)
The number of \( \alpha- \) particles emitted
per second by 1 mg plutonium is
(Avogadro's constant \( \left.=\mathbf{6 . 0} \times \mathbf{1 0}^{\mathbf{2 3}}\right) \)
A \( \cdot 1.7 \times 10^{9} \)
B . \( 1.7 \times 10^{11} \)
c. \( 2.9 \times 10^{11} \)
D. \( 3.4 \times 10^{9} \)


A spherical mirror with its outer bulging surface as the reflecting surface is a :
A. convex mirror
B. concave mirror
c. plane mirror
D. none of these


The average human ear can not distinguish the variation of intensity
A. if the variation is more than 100 times
B. if the variation is more than 16 times
c. if the variation is less than 16 times
D. if the variation is zero


Which of the following are not electromagnetic waves?
A. cosmic rays
B. gamma rays
c. \( \beta \) -rays
D. x-rays


Ecosystem may be defined as
A. A species along with environment
B. Plants found in water
C. Plants found on land
D. All plants and animal species along with environment


\( \int \frac{\sqrt{1-x^{2}}+\sqrt{1+x^{2}}}{\sqrt{1-x^{4}}} d x= \)
A \( \cdot \cosh ^{-1} x+\sin ^{-1} x+c \)
B. \( \cosh ^{-1} x+\cos ^{-1} x+c \)
\( c \cdot \sinh ^{-1} x+\sin ^{-1} x+c \)
D. \( \sinh ^{-1} x+\cos ^{-1} x+c \)


Suppose a particle \( a \) of charge \( 2 e \) and
\( \operatorname{mass} 2 m_{e}\left(m_{e} \) being mass of electron) \right.
revolves around the proton in nearest allowed circular orbit of radius r. If the
radius of first Bohr orbit for the electron
is \( A_{0}, \) then the relation between \( r \) and
\( a_{0} \) is
A. \( a_{0}=4 r \)
\( r \)
B . \( a_{0}=8 r \)
c. \( a_{0}=2 r \)
D. \( a_{0}=\frac{r}{4} \)


A construction company used to cut 10
trees every month and planted 10 new saplings every month as replacement. Do you think they are successful in maintaining the number of trees in a
forest. Justify.


The centre of gravity of the floating ship.
A. Coincides with the metacentre
B. Lies below the metacentre
C. Lies above the metacentre
D. None of the above


Write short note on adipose tissue


Dilute sulphuric acid produces white precipitate when added to the solution of:
A. copper nitrate
B. zinc nitrate
c. lead nitrate
D. sodium nitrate


\( P b^{4+} \) salts are better oxidizing agent agents, while \( G e^{2+} \) salts are better
reducing agents. Explain.


Consider a solenoid carrying current supplied by a DC source with a constant emf containing iron core inside it. When the core is pulled out of the solenoid, the change in current will
A. Remain same
B. Decrease
c. Increase
D. Modulate


Assertion
Nuclear fusion are made at very high
temperature, \( \boldsymbol{i} \boldsymbol{e}_{\bullet}, \boldsymbol{1} \boldsymbol{0}^{\boldsymbol{7}} \boldsymbol{K} \)
Reason
Nuclear fusion reactions are exoergic.
\( \mathbf{A} \cdot S \) is correct but \( E \) is wrong
B. \( S \) is wrong but \( E \) is correct
C. Both \( S \) and \( E \) are correct and \( E \) is correct explanation
of \( S \)
D. Both \( S \) and \( E \) are correct but \( E \) is not correct
explanation of \( S \)


Give balanced equations for the
following reactions:
Concentrated hydrochloric acid and Potassium permanganate solution.


An image formed by a plane mirror is:
A. erect and smaller than the object
B. erect and of same size as the object
C. inverted and larger than the object
D. inverted and smaller than the object


The total number of flags with three horizontal strips in order, which can be
formed using 2 identical red, 2 identical green and 2 identical white strips is equal to
A. \( 4 ! \)
в. \( 3 \times(4 !) \)
c. \( 2 \times(4 !) \)
D. None of these


How are microwaves produced? Why is it necessary in microwave ovens to select the frequency of microwaves to match the resonant frequency of water molecules?


Particle 1 with mass \( M \) has \( x \) position
defined by the function \( x_{1}(t)= \)
\( 2 t(t+3) \) where units are in meters
time is in seconds, and are abbreviated
in the function. Particle 2 has mass \( 2 M \)
and \( x \) position defined by \( x(t)= \)
\( (t-1)(t-2) / 2 \)
Considering the system of these two particles, what is the velocity of the
center of mass of the system at \( t=2 ? \)
A. \( 5 m / s \)
в. \( 9 m / s \)
c. \( 10 m / s \)
D. \( 10.5 m / s \)
E \( .16 \mathrm{m} / \mathrm{s} \)


Rahul Sharma, an intelligent student of class 12 follows the lesson taught in class easily, has friendship with Amit
and Krishan who do not follow the
lessons easily. Rahul helps Amit and Krishan to understand the concepts and in turn, they are thankful to him. Their friendship is long lasting because both are happy. Rahul feels sense of achievement.
a) Should intelligent students make friends with weak students?Give
reason
b) If you compare this kind of friendship to atoms what kind of bond will be
formed
c) Comment on the strength of such bonding. Name the force that keeps them bonded.
d) Discuss any one property in which these atoms are different from each
other.


Write the total number of one-one
functions from set \( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}\} \) to
\( \operatorname{set} B=\{a, b, c\} \)


Which of the following are magnetic?
A. Eraser
B. Plastic ruler
c. safety pins
D. Paper


Two inclined planes intersect in a horizontal plane. their inclinations to
the horizontal being \( \alpha \) and \( \beta . \) If a particle is projected with velocity u at right angle to the former from a point on
it, find the time after which the velocity
vector will become perpendicular to the other inclined plane.
\( t_{t}=\frac{u \sin (\alpha+\beta)}{g \sin \beta} \)
B. \( t=\frac{u \cos (\alpha+\beta)}{g \cos \beta} \)
c. \( _{t}=\frac{u \cos (\alpha+\beta)}{g \sin \beta} \)
D. \( t=\frac{u \sin (\alpha+\beta)}{g \cos \beta} \)


When body tissues are injured resulting in the loss of blood, the process of blood clott begins and the blood platelets
release
A. Prothrombin
B. Thrombin
c. Fibrinogen
D. Thromboplastin


An odd cube number will have a/an
cube root.
A . odd
B. even
C. fraction
D. none of these


Focal point of a lens is a point where
A . light spreads
B. light rays meet
c. light rays spread to meet
D. lens can magnify the most


Find the area of the triangle whose vertices are (-5,7),(4,5) and (-4,-5)


When an atom reacts chemically and gains one or more electrons, it is said to have been?
A. Catalyzed
B. Oxidized
c. Reduced
D. Decomposed


A disc of mass \( m \), radius \( r \) wrapped
over by a light and inextensible string is
pulled by force \( \boldsymbol{F} \) at the free end of the string. If it moves on a smooth
horizontal surface, find linear and
angular acceleration of the disc.


Theory of heterogamesis for sex determination was proposed by.
A. Morgan
B. Darwin
c. correns
D. Bridges


What is meant by complex compound?
Describe the main points of Werner's
theory.


A sample of 0.50 gm of an organic compound was treated according to Kjeldahl's method. The ammonia evolved was absorbed in \( 50 \mathrm{ml} \) of \( 0.5 \mathrm{M} \)
\( H_{2} S O_{4} . \) The residual acid required 60 \( \mathrm{ml} \) of \( 0.5 \mathrm{M} \) solution of \( \mathrm{NaOH} \) for
neutralization. Find the percentage composition of nitrogen(X) in the compound.


A circular loop of radius \( 0.3 \mathrm{cm} \) lies
parallel to a much bigger circular loop of radius \( 20 \mathrm{cm} . \) The centre of the small
loop is on the axis of the bigger loop. The distance between their centres is \( 15 \mathrm{cm} \)
If a current of \( 2.0 A \) flows through the smaller loop, then flux liked with bigger loop is:
A \( \cdot 6 \times 10^{-11} \) weber
В. \( 3.3 \times 10^{-11} \) weber
c. \( 6.6 \times 10^{-9} \) weber
D. \( 9.1 \times 10^{-11} \) weber


Find the slope of a line which is parallel to the line \( 8 x+9 y=3 \)
A. -8
в. \( -\frac{8}{9} \)
\( c \cdot \frac{8}{3} \)
D. 3
E . 8


In a 20 litre vessel initially 1,1,1 mole
of \( C O, H_{2} O, C O_{2} \) are present, then for
the equilibrium of \( \boldsymbol{C O}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \)
\( C O_{2}+H_{2} . \) Which of the following is
true?
A. \( H_{2} \) more then 1 mole
B. \( C O, H_{2} O, H_{2} \) less then 1 mole
c. \( C O_{2} \) and \( H_{2} O \) both more than 1 mole
D. All of these


If the point \( (x, y) \) is equidistant from the points \( (a+b, b-a) \) and \( (a- \)
\( b, a+b), \) then \( b x=a y \)
A. True
B. False


Choose the correct option regarding change in oxidation number of the underlined atom in the following
conversion.
\( \boldsymbol{H}_{2} \underline{\boldsymbol{S}} \boldsymbol{O}_{5}+\boldsymbol{2} \boldsymbol{K} \boldsymbol{I} \rightarrow \boldsymbol{K}_{2} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{I}_{2} \)
\( A \cdot 2 \)
B. 3
\( c \)
D. No Change


The formula of the calcium ion is \( C a^{2+} \)
and that of the acetate ion is
\( C H_{3} C O O^{-} . \) What is the formula of
calcium acetate?
\( \mathbf{A} \cdot C a\left(C H_{3} C O O\right)_{2} \)
в. \( C a C H_{3} C O O \)
\( \mathrm{c} \cdot \mathrm{Ca}_{2}\left(\mathrm{CH}_{2} \mathrm{COO}\right)_{2} \)
D. \( C a_{2} C H_{3} \) COO


\( \int x \sin \left(-x^{2}\right) d x= \)
A \( \cdot \frac{1}{2} \sin \left(x^{2}\right)+c \)
B \( \cdot \frac{1}{2} \cos \left(x^{2}\right)+c \)
c. \( \frac{1}{8} \cos \left(x^{2}\right)+c \)
D. \( \frac{1}{2} x \sin x^{2}+c \)


used to plot the magnetic field around a
bar magnetic field around a bar magnet
with poles marked \( N \) (North) and \( S \) (South). Which of the following diagrams correctly shows the expected
field pattern?
\( A \)
B.
\( c \)
\( \theta \)
D.


State an expression for \( \boldsymbol{K} . \boldsymbol{E} \) (kinetic energy) and \( P . E \) (potential energy) at
displacement ' \( x^{\prime} \) for a particle
performing linear \( \boldsymbol{S} . \boldsymbol{H} . \boldsymbol{M} . \) Represent
them graphically. Find the displacement at which \( K . E \) is equal to \( \boldsymbol{P} . \boldsymbol{E} \)


The word ecosystem was coined by..........


In the following diagram, the potentials
is \( P \) and \( Q \) are
A \( .40 V,-60 V \)
в. \( 60 V,-40 V \)
\( \mathbf{c} \cdot 40 V, 60 V \)
D. \( 60 V, 40 V \)


The Young's modulus of the material of a wire is \( 6 \times 10^{12} N / m^{2} \) and there is no
transverse in it, then its modulus of rigidity will be
A \( \cdot 3 \times 10^{12} N / m^{2} \)
В . \( 2 \times 10^{12} N / m^{2} \)
C \( \cdot 10^{12} N / m^{2} \)
D. None of the above


A bag contains 3 white and 2 black balls
and another bag contains 2 white and 4 black balls. One bag is chosen at
random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.


Degree of unsaturation in the
empirical formula \( C_{4} H_{8} O \) is:


A, \( B, \) and \( C \) are three elements with
atomic number \( 6,11, \) and 17
respectively. Which of these cannot form covalent bond and why?


\( \int \frac{4 \sec ^{2} x \tan x}{\sec ^{2} x+\tan ^{2} x} d x= \)
A \( \cdot 2 \log \left(\sec ^{2} x+\tan ^{2} x\right)+c \)
B \( \cdot \log \left(2 x+\tan ^{2} x\right)+c \)
c. \( 2 \tan ^{2} x+c \)
\( \mathbf{D} \cdot \log \left(\sec ^{2} x+\tan ^{2} x\right)+c \)


Which of the following is not an example of muscular force?
A. An animal pulling a cart.
B. A man pushing a stationary car.
c. An apple falling from a tree.
D. Two girls pushing each other.


For the next three (03) items that follow
The number of telephone calls received
in 245 successive one minute intervals
at an exchange is given below in the following frequency distribution.
Number of calls 0 2
Frequency
\( \begin{array}{llll}\text { 21 } & \text { 25 } & \text { 43 } & \text { 35 } & \text { 43 }\end{array} \)
What is the median of the distribution
\( ? \)
A . 3.5
B. 4
c. 4.5
D. 5


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{2}}, \boldsymbol{x} \in \boldsymbol{R} \).Find \( \boldsymbol{f}(\boldsymbol{4}) \)


Hydrogen bonding can exist between two molecules or within a single molecule.
A. True
B. False


Assertion
SnO is more reactive towards acid than
\( \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2} \)
Reason
Both SnO and \( S n O_{2} \) are amphoteric
oxides
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


Four students, \( W, X, Y \) and \( Z, \) made
the following statements about alkanes and alkenes.
\( W \) Bromine reacts with alkanes by
electrophilic substitution. \( X \) Bromine reacts with alkenes by a
free-radical addition mechanism.
\( Y \) Alkenes can be oxidised by acidified
manganate(VII) ions.
\( Z \) Alkenes are formed from alkanes by
cracking. Which two students are correct?
A. \( W \) and \( X \)
B. \( W \) and \( Z \)
c. \( X \) and \( Y \)
D. \( Y \) and \( Z \)


If \( \boldsymbol{A}(-2,1), B(a, b), C(4,6) \) and \( D(1,2) \)
are the vertices of parallelogram. Find
\( a+b \)


Assertion
Pent-1-ene and 2-methylbut-1-ene are position isomers.
Reason
Position isomers have the same
molecular formula but differ in the
position of functional group.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason are correct


If \( f(x)=|\cos x| \) then \( f^{\prime}\left(\frac{3 \pi}{4}\right) \) is equal to
\( ^{\mathbf{A}} \cdot-\frac{1}{\sqrt{2}} \)
в. \( \frac{1}{\sqrt{2}} \)
c. 1
D. None of these


A ray of light incident parallel to the base PQ of an isosceles right-angled
triangular prism PQR suffers two
successive total internal reflections at
the faces \( \mathrm{PQ} \) and \( \mathrm{QR} \) before reversed in
direction as shown. If the
refractive index of the material of the
prism is \( \mu, \) then find the value of \( \mu \)


The equivalent capacitance between \( \mathrm{P} \)
and \( Q \) is
\( A \cdot \frac{C}{3} \)
в. \( 3 C \)
\( c .2 C \)
D.


A 0.5 M solution of weak electrolyte Nax at 285 K temperature is \( 10 \% \) dissociated. What will be the osmotic
pressure? \( (\boldsymbol{R}=\mathbf{0 . 0 8 2} \mathrm{L} \text { atm/mol / K }) \)
A. 5.2 atm
B. 9.7 atm
c. 12.9 atm
D. 17.8 atm


Photorespiration occurs in
A. Ribosomes
B. Mitochondria
c. Peroxisomes
D. Both B and C


In the first two or three lumbar
vertebrae there is a small median
process below the centrum, called as
A. Pre-zygapophysis
B. Post-zygapophysis
C. Hypapophysis
D. Neural spine


lce at \( -20^{\circ} \mathrm{C} \) is dropped into \( 0.25 \mathrm{kg} \) of
the water at \( 20^{\circ} \mathrm{C} \). The final
temperature of the system is \( 0^{\circ} C \)
when all the ice is melted. Find
approximate mass of ice in the water in kg. (Specificheat of ice = \( \mathbf{2 0 0 0} \boldsymbol{J} \boldsymbol{k g}^{-1} \boldsymbol{K}^{-1}, \boldsymbol{L}=\mathbf{3 3 . 4} \times \mathbf{4} \boldsymbol{J} \boldsymbol{k g}^{-1} \)
A . 0.06
B. 6
\( c \cdot 60 \)
D.


For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in \( 100 g \) of water, the elevation in boiling point at 1 atm pressure is 2 ?. Assuming
that the concentration of solute is much
lower than the concentration of solvent,
the vapour pressure (in \( \mathrm{mm} \) of \( \mathrm{Hg} \) ) of the
solution is:
[Take \( : K_{b}=0.76 K k g \) mol \( ^{-1} \) ]


To prepare a buffer of pH 8.26 amount of
\( \left(N H_{4}\right)_{2} S O_{4} \) to be added to \( 500 \mathrm{mL} \) of
\( 0.01 \mathrm{M} N H_{4} O H \) solution is :
\( \left[\boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}}\left(\boldsymbol{N} \boldsymbol{H}_{4}^{+}\right)=\mathbf{9 . 2 6}\right] \)
A. 0.05 mole
B. 0.025 mole
c. 0.10 mole
D. 0.005 mole


Describe the formation of sea breeze in
coastal region


Particles having half integral spin are :
This question has multiple correct options
A . Electron
B. Photon
c. Proton
D. Neutron


In the urinogenital organs of rabbit, which one of following part is present in male but not in female?
A. Urethra
B. Fallopian tube
c. vagina
D. Vas deferens


Let \( S \) be the sample space of all \( 3 \times 3 \)
matrices with entries from the set
\( \{0,1\} . \) Let the events \( E_{1}= \)
\( \{A \in S: \operatorname{det} A=0\} \) and \( E_{2}= \)
\( \{A \in S: S u m \text { of entries of } A \text { is } 7\} \)
If a matrix is chosen at random from \( \boldsymbol{S} \)
then the conditional probability
\( \boldsymbol{P}\left(\boldsymbol{E}_{1} \mid \boldsymbol{E}_{2}\right) \) equals.


Nuisance growth of aquatic plants and bloom forming algae in natural waters is generally due to high concentrations
of
A. Carbon
B. Sulphur
c. calcium
D. Phosphorus


In the given figure you find two
triangles. Indicate whether the triangles
are similar. Give reasons in support of
your answer.


All the angles between and which
satisfy \( 90^{\circ} \) the \( 0^{\circ} \) equation \( \sec ^{2} \theta \cdot \cos e c^{2} \theta+2 \cos e c^{2} \theta=8 \)


Which of the following do not show the properties of the constituents?
A. water
B. Air
c. sugar solution
D. None of these


Find the number of sesquioxide(s) from the following:
\( \boldsymbol{A l}_{2} \boldsymbol{O}_{3}, \quad \boldsymbol{C}_{3} \boldsymbol{O}_{2}, \quad \boldsymbol{C O}_{2}, \quad \boldsymbol{P b}_{2} \boldsymbol{O}_{3} \)


\( X e F_{6} \) reacts with quartz forming \( X e O_{3} \)
\[
\mathbf{2} \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\mathbf{6}}+\boldsymbol{x} \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2} \longrightarrow
\]
What is value of \( x ? \)


Consider the following statements regarding the major pigments and stored food in the different groups of algae and select the correct options
given.
A. In chlorophyceae, the stored food
material is starch and the major pigments are chlorophyll a and d.
B. In phaeophyceae, laminaria is the
stored food and major pigments are
chlorophyll a and b.
C. In rhodophyceae, floridean starch is the stored food and the major pigments are chlorophyll a, d and phycoerythrin
A. A is correct, but B and C are wrong.
B. A and B are correct, but C is wrong.
C. A and C are correct, but B is wrong.
D. B is correct, but A and C are wrong.
E. \( C \) is correct, but \( A \) and \( B \) are wrong


Which are extensive properties?
A. \( V \) and \( E \)
B. \( V \) and \( T \)
c. \( V \) and \( C p \)
D. \( P \) and \( T \)


In which of the following reactions,
\( H_{2} O_{2} \) acts as a reducing reagent?
A \( \cdot \) HOCl \( +H_{2} O_{2} \stackrel{H^{+}}{\rightarrow} H_{3} O^{+}+C l^{-}+O_{2} \)
B - \( M n^{2+}+H_{2} O_{2} \stackrel{\text { OH }}{\rightarrow} M n^{4+}+2 O H^{-} \)
\( \mathbf{c} \cdot 2 F e^{2+}+H_{2} O_{2} \stackrel{O H}{\rightarrow} 2 F e^{3+}+2 O H^{-} \)
D \( \cdot P b S(s)+4 H_{2} O_{2}(a q) \stackrel{H^{+}}{\rightarrow} P b S O_{4}(s)+4 H_{2} O(l) \)


Fill in the blanks with suitable words
The Sl unit of electromotive force is


A river is flowing with velocity \( 5 k m / h r \)
as shown in the figure. A boat starts
from \( A \) and reaches the other bank by
covering shortest possible distance.
Velocity of boat in still water is \( 3 k m / h r \)
The distance boat covers is :
\( \mathbf{A} \cdot 500 m \)
B. \( 400 \sqrt{2} \)
c. \( 300 \sqrt{2} \)
D. \( 600 m \)


Carbon and hydrogen are estimated in organic compounds by:
A. Kjeldahl's method
B. Duma's method
c. Liebig's method
D. Carius method


When Abhishek looked at a lighted torch through an object he could see a faint glow, but not the torch. The object
is
A. Transparent
в. ораяче
c. Translucent
D. None of these


If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) is a skew-symmetric matrix then write a value of \( \sum_{i} \sum_{j} a_{i j} \)


Statement 1: When a man is standing on a stationary horizontal surface, the normal force exerted by the ground on him is equal and opposite to his weight.
Statement 2: According to Newton's 3 \( ^{r d} \)
law , every action has an equal and
opposite reaction.
A. Statement 1 - is true, statement- 2 is true and statement-2 is correct explanation for statement-
B. Statement 1 - is true, statement- 2 is true and statement-2 is NOT the correct explanation for statement-
c. Statement 1 - is true, statement- 2 is false
D. Statement 1 - is false, statement- - 2 is true


Assertion
Nitrogen turns moist red litmus paper
blue.
Reason
Ammonia is a basic gas.
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 \( y=\tan ^{-1}\left(\frac{2^{x}}{1+2^{2 x+1}}\right), \) then \( \frac{d y}{d x} \) at
\( \boldsymbol{x}=\mathbf{0} \) is?
A \( \cdot \frac{1}{10} \log 2 \)
B. \( \frac{1}{5} \log 2 \)
c. \( -\frac{1}{10} \log 2 \)
D. \( \log 2 \)


In the reaction, \( 4 M+8 C N^{-}+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \mathbf{4}\left[\boldsymbol{M}(\boldsymbol{C} \boldsymbol{N})_{2}\right]+\mathbf{4} \boldsymbol{O} \boldsymbol{H}^{-} \)
identify the metal \( \mathrm{M} \) as:
A. copper
B. Iron
c. silver
D. zinc


Bohr's model could not explain the of multi electron
species.
A. spectra
B. nucleus
c. spin
D. orbital


If \( A \) and \( B \) are subsets of a set \( X, \) then
what is \( (\boldsymbol{A} \cap(\boldsymbol{X}-\boldsymbol{B})) \cup \boldsymbol{B} \) equal to
\( \mathbf{A} \cdot A \cup B \)
в. \( A \cap B \)
\( c . A \)
D. \( B \)


\( \ln \Delta A B C, A D \) is drawn such that
\( \Delta A B D \) and \( \Delta A C D \) are equal in area
then, the AD is
A. any segment drawn from A to BC
B. the bisector of \( \angle B A G \)
c. A median of \( \Delta A B C \)
D. None of these


in a meter bridge, the balance point is found to be \( 40 \mathrm{cm} \) from one end (say end
A). if a resistance of \( 10 \Omega \) is connected
in series with \( R, \) a balance point is
obtained \( 60 \mathrm{cm} \) from end
A. What are
the values of \( R \) and \( S(S \) is other resistance in series with \( \boldsymbol{R} \) )?


The correct set of four quantum numbers for the outermost electrons of
rubidium \( (z=37) \) is:
A. \( _{5,0,0,+\frac{1}{2}} \)
в. \( _{5,1,0,+\frac{1}{2}} \)
c. \( _{5,1,1,+\frac{1}{2}} \)
D. \( _{6,0,0,+\frac{1}{2}} \)


If the equation of the locus of a point
equidistant from the point \( \left(a_{1}, b_{1}\right) \) and
\( \left(a_{2}, b_{2}\right) \) is \( \left(a_{1}-a_{2}\right) x+\left(b_{1}-b_{2}\right) y+ \)
\( c+0, \) then the value of \( c \) is
A \( \cdot a_{1}^{2}-a_{2}^{2}+b_{1}^{2}-b_{2}^{2} \)
в. \( \sqrt{a_{1}^{2}+b_{1}^{2}-a_{2}^{2}-b_{2}^{2}} \)
c. \( \frac{1}{2}\left(a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2}\right. \)
D \( \cdot \frac{1}{2}\left(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2}\right. \)


Why does your body get more rest when you're lying down than it does when
you're sitting?
A. Body exerts less pressure while lying down
B. Body exerts more pressure while lying down
c. Body exerts zero pressure while lying down
D. none of these


State whether \( P_{1}>P_{2} \) or \( P_{2}>P_{1} \) for
given mass of a gas?


Two blocks of masses \( \boldsymbol{m}_{1}=\mathbf{5} k \boldsymbol{g} \) and
\( m_{2}=6 k g \) are connected by a light
string passing over a light frictionless
pulley as shown. The mass \( m_{1} \) is at rest
on the inclined plane and mass \( m_{2} \)
hangs vertically. If the angle of incline
\( \boldsymbol{\theta}=\mathbf{3 0}^{\mathbf{0}} \) what is magnitude and
direction of force of friction on the \( 5 \mathrm{kg} \)
block
\( \left(g=10 m s^{-2}\right) \)
A. 35 N up the plane
B. 35 N down the plane
c. 85 N up the plane
D QEN down the plane


Analogue of mass in rotational motion
is
A. Moment of inertia
B. Angular momentum
c. Gyration
D. None of these


Present atmospheric \( \boldsymbol{C O}_{2} \)
concentration is not limiting factor for
\( C_{4} \) plants as \( C_{4} \) plants
A. Posses PEPcase as primary carboxylase enzyme
B. Primary carboxylation reaction product is a four carbon acid
C. No oxygenation of RUBP due to kranz anatomy
D. Primary carboxylation reaction occurs in mesophyll cells


If in the experiment of Wheatstone's bridge, the positions of cells and galvanometer are interchanged, then balance point will
A. change
B. remain unchanged
c. depend on the internal resistance of cell and resistance of galvanometer
D. none of these


The factor that can reduce the enzyme
activity is
I. Increasing pH level
II. Decreasing temperature
III. Placing enzyme in a nonpolar liquid
A. I only
B. II only
c. ॥ only
D. I and II
E. I, II, and III


Find the image of the point (5,7,3) in the line \( \frac{x-15}{3}=\frac{y-29}{8}=\frac{5-z}{5} \)
A \( \cdot(9,13,15) \)
В. (13,19,27)
c. (18,37,0)
D. (0,-11,30)


Which one of the following cannot be the probability of an event
A \( \cdot \frac{2}{3} \)
в. -1.5
c. \( 15 \% \)
D. 0.7


Consider the statements
(i)Two plus three is five.
(ii) Every square is a rectangle.
(iii) Sun rises in the east.
(iv) The earth is not a star.
Which of the above statements have
truth value (T) ?
A. (i) and (ii)
B. (ii) and (iii)
c. (iii) and (iv)
D. All of these


The area of cross-section of a large tank
is \( 0.5 m^{2} \) It has an opeoing near the
bottom having area ofcross-section
\( 1 c m^{2}, A \) load of \( 20 \mathrm{kg} \) is applied on the water at the top. Find the velocity of the
water coming out of the opening at the time when the height of water level is
\( 50 \mathrm{cm} \) above the bottom. (Takeg=
\( \left.10 m / s^{2}\right) \)


When light moving in one medium falls at the surface of another medium,
light returns back to the
same medium.
\( A \). all of
B. a part of
\( c \cdot \) no
D. either all or no


Which of the following is not a merit of
Mendeleev's periodic table?
A. It helped in correcting the atomic masses of some of the elements
B. He predicted the properties of some undiscovered elements and left gaps for them
C. He framed the periodic table with vertical and horizontal columns and gave shape to it
D. He gave separate places to isotopes in his periodic table


Calculate the effective capacitance
\( \operatorname{across} X Y \)
\( A \cdot \frac{5}{2} C \)
\( B \cdot \frac{3}{E} C \)
\( c \cdot \frac{5}{2} c \)
D. \( C \)


Find \( x, y, z \)


For a polymerization reaction:
\( 6 H C H O \rightleftharpoons C_{6} H_{12} O_{6} \) degree of
association was found to be 0.96
Calculate mean mass of mixture at
equilibrium. Report value of mean
molar mass of mixture dividing by 50


Which of the following metals loses its meniscus after reacting with ozone?
\( A \cdot P b \)
в. \( \mathrm{Hg} \)
\( c \cdot c u \)
D. zn


The resistors of resistances \( 2 \Omega, 4 \Omega, 5 \Omega \) are connected in parallel. The total resistance of the combination will be :
A \( \cdot \frac{29}{10} \Omega \)
в. \( \frac{19}{20} \Omega \)
c. \( \frac{10}{20} \Omega \)
D. \( \frac{20}{19} \Omega \)


The synthesis and storage of ATP molecules required for cell division takes place in
A. Prophase
B. G_phase
c. Anaphase
D. \( G_{2} \) phase


State two uses of : Irregular reflection


If \( \vec{A}=2 \hat{i}+3 \hat{j}+8 \hat{k} \) is perpendicular to \( \vec{B}=4 \hat{j}-4 \hat{i}+\alpha \hat{k}, \) then the value of ' \( \alpha^{\prime} \)
is
A .
B.
c. -1
D. \( \frac{1}{-2} \)


Hydrogen is not a metal-but it has been assigned a place in the reactivity series of metals. Give the reason for it.


When a piece of sodium metal is dropped in water, hydrogen gas evolved because:
A. sodium is reduced and acts as an oxidising agent
B. water is oxidised and acts as a reducing agent
c. sodium loses electrons and is oxidised while water in reduced
D. water loses electrons and is oxidised to hydrogen


\( 2 \mathrm{kg} \) of ice at \( -20^{\circ} \mathrm{C} \) is mixed with \( 5 \mathrm{kg} \)
of water at \( 20^{\circ} C \) in an insulating vessel having a negligible heat capacity

Calculate the final mass of water in the
vessel. It is given that the specific heats of water and ice are \( 1 k c a l k g^{-1} o C^{-1} \) and \( 0.5 k \) calk \( g^{-1} o C^{-1} \) respectively and the latent heat of fusion of ice is 80
kcal/kg.
\( A \cdot 5 \mathrm{kg} \)
B. \( 6 \mathrm{kg} \)
\( c \cdot 7 k g \)
D. 8 kg


As a builder lifts a \( 3.0 \mathrm{kg} \) brick at a steady speed from the ground to a platform 2.0 meters high. How much work is done on the brick by the builder and by the earth while it is being lifted, and what is the net work done on the
brick by all forces while it is being lifted?
A. \( 60 \mathrm{N},-60 \mathrm{N}, \mathrm{O} \)
в. - -60 N, 60 N, 0
c. \( 60 \mathrm{N}, 60 \mathrm{N}, 0 \)
D. - -60 N,-60 N, 0
E. 60 N, 60 N, -60 N


If \( A \) is a square of order 3 , then
\( \left|\boldsymbol{A} \boldsymbol{d} \boldsymbol{j}\left(\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}^{2}\right)\right|= \)
\( \mathbf{A} \cdot|A|^{2} \)
B . \( |A|^{4} \)
c. \( |A|^{8} \)
D・ \( |A|^{1} \)


If \( \Delta H_{f}^{\circ} \) of \( H_{2} S_{(g)} \) and \( H_{2} S_{(a q)} \) are -4.5 and -9.5 kcal. The amount of heat
required for the change is
\[
\boldsymbol{H}_{2} \boldsymbol{S}_{(a q)} \longrightarrow \boldsymbol{H}_{2} \boldsymbol{S}_{(g)}
\]


f the energy loss during collision is \( \frac{y m g l}{16}, \) find the value of \( y \)


\( f \frac{1}{x\left(x^{2}+a^{2}\right)}=\frac{A}{x}+\frac{B x+C}{x^{2}+a^{2}}, \) then
\( \tan ^{-1}\left(\frac{A}{B}\right)= \)
A \( \cdot \frac{3 \pi}{4} \)
в.
\( c \cdot-\frac{\pi}{4} \)
D.


Find the A.P. whose first term is 4 and
common difference is - 3


The area of triangle whose vertices are (1,2,3),(2,5,-1) and (-1,1,2) is
A . 150 sq.units
B. 145 sq.units
c. \( \sqrt{155} / 2 \) sq.units
D. \( 155 / 2 \) sq.units


When stearic acid \( \left(C_{18} H_{36} O_{2}\right) \) is added to water, its molecules collect at the
surface and form a monolayer. The cross-sectional area of each stearic
acid molecule is \( 0.21 n m^{2} . \) If \( 1.4 \times \)
\( 10^{-4} g \) of stearic acid is needed to form
a monolayer over water in a dish of diameter \( 20 \mathrm{cm} \). (The area of the circle
of radius \( r \) is \( \left(\pi r^{2}\right), \) then the value of
Avogadro's number is
A \( \cdot 3 \times 10^{23} \)
B. \( 6 \times 10^{23} \)
c. \( 4 \times 10^{23} \)
D. \( 1 \times 10^{23} \)


\( \operatorname{In} \) an acute triangle \( A B C, \angle A B C= \) \( \mathbf{4 5}^{\circ}, \boldsymbol{A B}=\mathbf{3} \) and \( \boldsymbol{A C}=\sqrt{\mathbf{6}} . \) The angle
\( \angle B A C, \) is
A \( .60^{\circ} \)
B. 65
\( c \cdot 75 \)
D. \( 15^{\circ} \) or \( 75^{\circ} \)


The box of a pinhole camera of length \( L \) has a hole of radius a. It is assumed that when the hole is illuminated by a
parallel beam of light of wavelength \( \lambda \) the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size say
\( \boldsymbol{b}_{m i n} \) when:
\( ^{\mathrm{A}} \cdot_{a}=\frac{\lambda^{2}}{L} \) and \( b_{\min }=\frac{2 \lambda^{2}}{L} \)
B. \( a=\sqrt{\lambda L} \) and \( b_{\min }=\frac{2 \lambda^{2}}{L} \)
C \( . a=\sqrt{\lambda L} \) and \( b_{\min }=\sqrt{4 \lambda L} \)
D. \( a=\frac{\lambda^{2}}{L} \) and \( b_{m i n}=\sqrt{4 \lambda L} \)


The bond dissociation energy of \( \boldsymbol{C}-\boldsymbol{H} \)
in \( C H_{4} \) from the equation
\( \boldsymbol{C}(\boldsymbol{g})+\boldsymbol{4} \boldsymbol{H}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{4}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -397.8 k c a l \) is:
\( \mathbf{A} \cdot+99.45 k c a l \)
B . - 99.45 k cal
c. \( +397.8 k c a l \)
D. \( +198.9 k c a l \)