Assertion
The bar magnet falling vertically along the axis of the horizontal coil will be
having acceleration less than \( \mathfrak{g} \)
Reason
Clockwise current induced in the coil.
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


Solution of \( \boldsymbol{y}^{2} \boldsymbol{x}+\boldsymbol{y}-\boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\mathbf{0} \) is
A \( \cdot \frac{y^{2}}{5}+\frac{y^{2}}{4 x^{2}}=c \)
в. \( \frac{x^{2}}{2}+\frac{x}{y}=C^{\prime} \)
c. \( \frac{y^{2}}{4}+\frac{y^{5}}{5 x^{4}}=c \)
D. \( \frac{x^{2}}{5}+\frac{x^{4}}{4 y^{4}}=c \)


What is the equivalent resistance of the system about \( A \) and \( C ? \)
\( A \)
\( B . r \)
2
\( c \cdot 3 r \)
2
D. \( 2 r \)


Find the value of \( x .\left(\tan ^{-1} x\right)^{2}+ \)
\( \left(\cot ^{-1} x\right)^{2}=\frac{5 \pi^{2}}{8} \)


Construct the graphs of the following
functions.
\( \boldsymbol{y}=(|\mathbf{1}-\boldsymbol{x}|+\mathbf{2})(\boldsymbol{x}+\mathbf{1}) \)


If reactivity for chlorination with \( 1^{\circ} \boldsymbol{H} \)
\( 2^{\circ} H \) and \( 3^{\circ} H \) is 1: 3.8: 4.5
respectively, what is the percentage of
\( (P 2) \) formed:
(closest to the nearest integer of \( \left.\frac{(P 2)}{10}\right) \)


If \( \vec{A} \cdot \vec{B}=0, \) the angle between the
vectors \( A \) and \( B \) will be:
A \( \cdot 0^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
\( D \cdot 180^{\circ} \)


The amount of heat required to change \( 1 \mathrm{gm} \) of a substance at its melting point into liquid state without any rise in temperature is called:
A. Latent heat of fusion
B. Latent heat of vaporisation
c. Steam
D. Melting point


Two identical rods \( A \) and \( B \) are of equal
Iengths and at the same temperature.
The rod \( A \) is placed at smooth surface
but \( \boldsymbol{B} \) is placed at rough surface. If the
temperature of both are raised by the
same amount, then :
A. final length of \( A \) is greater than that of \( B \)
B. final length of both are same
c. final length of \( A \) is lesser than that of \( B \)
D. none of the above


Le Chatelier's principle is applicable to what equilibrium.
A. Physical equilibrium.
B. Chemical equilibrium.
c. Both equilibrium.
D. None of these


The eccentricity of the conic
represented by the equation \( x^{2}+ \)
\( 2 y^{2}-2 x+3 y+2=0 \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{2} \)
c. \( \frac{1}{\sqrt{2}} \)
D. \( \sqrt{2} \)


Which one does not belong to Monera?
A. Archaebacteria
B. Slime mould
c. Eubacteria
D. Mycoplasma


The acceleration due to gravity on the planet \( A \) is 9 times the acceleration due to gravity on the planet B. A manjumps to a height of \( 2 \mathrm{m} \) on the surface \( \mathrm{A} \). What is the height of jump by the same person on the plane B?
\( A \cdot 6 m \)
B. 2/9 m
\( c \cdot 2 / 3 m \)
D. 18 m


Based on the following reaction identify alkene \( \boldsymbol{A} \)
\[
A \frac{o_{3} / H_{2} O / Z n}{2 H C H O+}
\]
A \( \cdot C H_{2}=C H-C H=C H_{2} \)
в. \( C H_{3}-C H=C H-C H_{3} \)
\( \mathbf{c} \cdot C H_{2}=C H-C H_{2}-C H_{3} \)
D. None of these


Choose the chemical properties of metals and non-metals with reference
to electrochemical nature.
A. Both are reducing agent
B. Both are oxidising agent
C. Metal acts as reducing agent while non metals acts as oxidising agent
D. Non-metal acts as reducing agent while metals acts as oxidising agent


Chlorophyll, the green colouring matter of plants, contains \( 2.68 \% \) of magnesium by mass. Calculate the number of magnesium atoms in 3.00 g of chlorophyll. [Atomic mass of magnesium \( =24.3 \mathrm{g}] \)


A spherical conducting shell of inner
radius \( r_{1} \) and outer radius \( r_{2} \) has a
charge \( Q \)
(a) A charge q is placed at the centre of the shell. What is the surface charge
density on the inner and outer surfaces of the shell?
(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.


Let the perpendiculars from any point on the line \( 2 x+11 y=5 \) upon the lines
\( 24 x+7 y-20=0 \) and \( 4 x-3 y-2= \)
0 have the lengths \( p_{1} \) and \( p_{2} \)
respectively. Then,
A \( \cdot 2 p_{1}=p_{2} \)
B . \( p_{1}=p_{2} \)
\( \mathbf{c} \cdot p_{1}=2 p_{2} \)
D. None of these


Lucky started working 2 years ago. Her starting salary was half of Karthik's salary at that time. Each year since then Lucky and Karthik have received a rise of \( 10 \% \) in their respective salary. What percentage (to the nearest percent) of Karthik's current salary is Lucky's
current salary?


Explain the formation of a chemical
bond.


The \( C a(O H)_{2} \) is \( 4.42 \times 10^{-5} \) at \( 25^{\circ} C \)
with \( 500 m L \) of saturated solution of
\( C a(O H)_{2} \) is mixed with equal volume
of \( 0.4 M \) NaOH. How much \( C a(O H)_{2} \)
in \( m g \) is precipitated?


A ball of mass \( 0.20 \mathrm{kg} \) falls freely from a certain height and rebounds elastically
with a speed of \( 40 \mathrm{ms}^{-1} . \) The change in momentum of the ball is:
A \( \cdot 4 k g m s^{-1} \)
B. \( 8 \mathrm{kg} \mathrm{ms}^{-1} \)
c. \( 16 k g m s^{-1} \)
D. \( 40 \mathrm{kg} \mathrm{ms}^{-1} \)


The density of a mixture of \( N_{2} \) and \( O_{2} \) at
NTP is \( 1.3 g L^{-1} \). Calculate partial
pressure of \( \boldsymbol{O}_{2} \)


Which one of the following is used as a disinfectant in water treatment?
A. Alum
B. Charcoal
c. Kieselguhr
D. Potassium permanganate


A concave mirror produces a real image of half the size of an object placed at 60 \( \mathrm{cm} \) infront of it. Where should the object
be placed to obtain a virtual image of double the size of the object?


If the interior angle of a regular polygon
exceeds the exterior angle by \( 132^{\circ}, \) then the number of sides of the polygon is :
A . 15
B. 14
c. 13
D. 12


A circular coil of radius \( 10 \mathrm{cm} \) having
100 turns carries a current of 3.2 A. The magnetic field at the centre of the coil
is:
A . 2.01 \( \times 10^{-3} T \)
B. 5.64 \( \times 10^{-3} T \)
c. \( 2.64 \times 10^{-4} T \)
D. 5.64 \( \times 10^{-4} T \)


Presbyopia can be corrected with the help of
A. Bifocal lens
B. Diverging lens
c. convex lens
D. All of the above


Write the relation for the speed of
electromagnetic waves in terms of the
amplitudes of electric and magnetic fields.


The molar conductivities \( \wedge^{0}_{N a} O A c \) and
\( \wedge^{0}_{H C l} \) at infinite dilution in water at \( 25^{0} \)
\( \mathrm{C} \) are 91.0 and \( 426.2 \mathrm{Scm}^{2} / \mathrm{mol} \)
respectively. To calculate \( \wedge^{0}_{H O A c} \), the additional
value required is :
\( \mathbf{A} \cdot \wedge^{0} H_{2} O \)
B . \( \wedge^{0} \)кСl
c. \( \wedge_{N a O H}^{0} \)
D. \( \wedge^{0} \)Nacl


Mark the statement which is true for
diffused reflection:
A. Diffused reflection is due to failure of laws of reflection
B. It is caused due to irregularities in the reflecting surface
c. When the incident light is diffused in nature it causes diffused reflection
D. All are true


Give two uses of sulphur dioxide.


Balance the following redox reactions:
\[
\boldsymbol{I}_{2}(\boldsymbol{s})+\boldsymbol{O} \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q}) \longrightarrow \boldsymbol{I} \boldsymbol{O}_{3}^{-}(\boldsymbol{a} \boldsymbol{q})+
\]
\( \boldsymbol{C l}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
\( \mathbf{A} \cdot I_{2}(s)+5 O C l^{-}(a q)+H_{2} O(l) \longrightarrow 2 I O_{3}^{-}(a q)+ \)
\[
5 C l^{-}(a q)+2 H^{+}(a q)
\]
B \( \cdot I_{2}(s)+5 O C l^{-}(a q)+2 H_{2} O(l) \longrightarrow I O_{3}^{-}(a q)+ \)
\[
4 C l^{-}(a q)+2 H^{+}(a q)
\]
\( \mathbf{c} \cdot I_{2}(s)+3 O C l^{-}(a q)+4 H_{2} O(l) \longrightarrow I O_{3}^{-}(a q)+ \)
\( 4 C l^{-}(a q)+2 H^{+}(a q) \)
\( \mathbf{D} \cdot I_{2}(s)+5 O C l^{-}(a q)+7 H_{2} O(l) \longrightarrow I O_{3}^{-}(a q)+ \)
\( 5 C l^{-}(a q)+2 H^{+}(a q) \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by
\( f(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} \) then
A. \( f \) is a bijection
B. \( f \) is an injection only
c. \( f \) is a surjection
D. \( f \) is neither an injection nor a surjection


The number of line symmetries that the
given figure have- -
\( A \)
B. 3
\( c \cdot 2 \)
D.


The given figure shows a network of
currents. The current \( i \) is
A . 23 A
B. 22 A
\( c \cdot 20 A \)
D. 25 A


State True or False.
A rational number can always be written in what as a fraction \( \frac{a}{b}, \) where a
and b are not integers \( (\boldsymbol{b} \neq \mathbf{0}) \)
A. True
B. False


What is the structural formula of
fumaric acid?
\( A \)
\[
\text { HOOC }-\mathbf{C}-\mathbf{C H}_{3}
\]
B.
\[
\mathbf{H}_{3} \mathbf{C}-\mathbf{C}-\mathbf{C O O H}
\]
\( c \)
D.
HOOC \( -\mathbf{C}-\mathbf{H} \)


A particle moves along the \( x \) -axis
according to the equation \( \boldsymbol{x}= \)
10 \( \sin 3(t) \). The amplitudes and
frequencies of component SHMs are
A \( \cdot \) amplitude \( \frac{30}{4}, \frac{10}{4} ; \) frequencies \( \frac{3}{2}, \frac{1}{2} \)
B. amplitude \( \frac{30}{4}, \frac{10}{4} ; \) frequencies \( \frac{1}{2}, \frac{3}{2} \)
C. amplitude 10,\( 10 ; \) frequencies \( \frac{1}{2}, \frac{1}{2} \)
D. amplitude \( \frac{30}{4}, 10 ; \) frequencies \( \frac{3}{2}, 2 \)


For electrolytes, Ohm's Law may be written as:
A \( \cdot \frac{V}{I}=R \)
B. \( \frac{V+V_{b a c k}}{I}=R \)
c. \( \frac{V-V_{b a c k}}{I}=R \)
D. \( \frac{V_{b a c k-V}}{I}=R \)


Write down four differences between
interference and diffraction:


In \( _{88} R a^{226} \) nucleus there are
A. 226 protons and 88 electrons
B. 138 protons and 88 neutrons
c. 226 neutrons and 138 electrons
D. 138 neutrons and 88 protons


What is the speed of the proton when it is \( 8 A \) away from the nucleus?
A \( \cdot 1.85 \times 10^{5} \mathrm{ms}^{-1} \)
В. \( 1.85 \times 10^{4} m s^{-1} \)
c. \( 1.85 \times 10^{3} m s^{-1} \)
D. \( 1.85 \times 10^{2} \mathrm{ms}^{-1} \)


Short / long answer type questions. Oxygenation of blood promotes the
release of \( C O_{2} \) from the blood in lungs. Explain


A person is moving on a rough horizontal surface towards east. Then
the direction of friction force is towards
A. west
B. east
c. north
D. cant say depends on the situation


The IUPAC name of above compound is:
A. 2 -chlorocarbonylethylbenzoate
B. 2-carboxyethylbenzoylchloride
C. Ethyl-2-(chlorocarbonyl)benzoate
D. ethyl-1-(chlorocarbonyl)benzoate


\( Q \) Type your ques
same material, A is solla but b is
hollow. These are connected by an idea
spring and this system is kept over a
smooth plank such that center of mass of two balls coincide with mid point of
the plank. Initially the spring is
compressed by a certain amount and
the plank is in horizontal position. Now
we release the system then,
A. Plank will rotate clock wise
B. Plank will rotate anti clock wise
C. Plank will not rotate
It will depend upon st


In meiosis, centromere divides during
A. Prophase
B. Metaphase
c. Anaphase
D. Anaphase II


In the hydrolytic equilibrium;
\( \boldsymbol{B}^{+}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{B} \boldsymbol{O} \boldsymbol{H}+\boldsymbol{H}^{+} \)
\( K_{b}=1 \times 10^{-5} . \) The hydrolysis constant
is:
A \( \cdot 10^{-5} \)
\( ^{5} \)
B . \( 10^{-19} \)
c. \( 10^{-10} \)
D. \( 10^{-9} \)


Yasmeen wrote few series of
hydrocarbon and left blanks in between.
Look at the chemical formula in the
series of hydrocarbon carefully. Answer
the following questions accordingly.
\( \begin{array}{cccc}1 & \mathrm{II} & \mathrm{III} \\ C H_{4} & C_{2} H_{4} & \mathrm{X} \\ C_{2} H_{6} & C_{3} H_{6} & C_{3} H_{4} \\ \mathrm{Y} & C_{4} H_{8} & C_{4} H_{6} \\ C_{4} H_{10} & \mathrm{z} & C_{5} H_{8}\end{array} \)
X and Y respectively are:
\( \mathbf{A} \cdot C_{2} H_{2} \) and \( C_{3} H_{8} \)
B. \( C_{2} H_{2} \) and \( C_{4} H_{10} \)
\( \mathbf{c} \cdot C_{2} H_{2} \) and \( C_{3} H_{6} \)
\( \mathbf{D} \cdot C_{2} H_{4} \) and \( C_{3} H_{8} \)


How the man's
respiration will be affected if he ascends
a height of 25000 feet
A. No effect on respiration
B. Respiratory rate will be decreased
C. Respiratory rate will be increased
D. Anything can happen


Select the correct option regarding
features present in
Butterfly Haemoç
(4)


The lymph is ....... in nature.
A. Solid
B. Liquid
c. Semi-solid
D. Gas


At what approximate temperature, zinc
and carbon have equal affinity for
oxygen?
A \( \cdot 1000^{\circ} \mathrm{C} \)
В. \( 1500^{\circ} \mathrm{C} \)
\( c \cdot 500^{\circ} C \)
D. \( 1200^{\circ} \mathrm{C} \)


Plutonium decays with a half life of 24,000 years. If plutonium is stored for 72,000 years, the fraction that remains is:
A. \( 1 / 2 \)
в. 1/4
c. \( 1 / 6 \)
D. \( 1 / 8 \)


In the given reaction, alkaline \( \mathrm{KMnO}_{4} \) behaves as :
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{O H} \stackrel{\text {Alkaline } \boldsymbol{K M n O}_{4}+\boldsymbol{H e a t}}{\boldsymbol{N}} \boldsymbol{C H}_{3}- \)
COOH
A. reducing agent
B. oxidising agent
c. catalyst
D. dehydrating agent


Write a short note on N type
semiconductor


Evaluate the following:
\( ^{35} \boldsymbol{C}_{35} \)


The radius of an atom is of the order of:
A \( \cdot 10^{-10} \mathrm{cm} \)
B . \( 10^{-13} \mathrm{cm} \)
\( c \cdot 10^{-15} \mathrm{cm} \)
\( D \cdot 10^{-8} \mathrm{cm} \)


Equilibrium constant for the following
reaction is \( 1 \times 10^{-9} \)
\( \boldsymbol{C}_{5} \boldsymbol{H}_{5} \boldsymbol{N}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \rightleftharpoons \)
\( \boldsymbol{C}_{5} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q} \cdot)+\boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q} \cdot) \)
Determine the mole of pyridinium
chloride \( \left(C_{5} H_{5} N . H C I\right) \) that should be
added to \( 500 \mathrm{mL} \) solution of \( 0.4 \mathrm{M} \)
pyridine \( \left(C_{5} H_{5} N\right) \) to obtain a buffer
solution of \( \mathrm{pH}=5 \)
A. 0.1 mole
B. 0.2 mole
c. 0.3 mole
D. 0.4 mole


Chloramine-T is used as:
A . antipyretic
B. analgestic
c. antiseptic
D. disinfectant


The domain of the function \( f(x)= \) \( \frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}} \) is
A . [2,3]
в. [1,2]
c. [1,2]
D. [2,3)


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{B r}_{2} \stackrel{N a C l}{\longrightarrow} \quad \boldsymbol{P r o d u c t s} \)
Which of the following product is not formed in the above reaction?
\( \mathbf{A} \cdot B r C H_{2} C H_{2} B r \)
в. \( C l C H_{2} C H_{2} C l \)
c. \( B r C H_{2} C H_{2} C l \)
D. All are formed


Obtain the sum of the first 56 terms of
an A.P whose \( 25^{t h} \) and \( 32^{n d} \) terms are 52
and 148 respectively.


\( X Y_{2} \) dissociates as:
\( \boldsymbol{X} \boldsymbol{Y}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{X} \boldsymbol{Y}(\boldsymbol{g})+\boldsymbol{Y}(\boldsymbol{g}) \)
When the initial pressure of \( X Y_{2} \) is 600 \( \mathrm{mm} H g, \) the total equilibrium pressure is \( 800 \mathrm{mm} \) Hg. Calculate \( K \) for the reaction assuming that the volume of the system remains unchanged.
A. 50
в. 100
c. 166.6
D. 400.0


Integrate with respect to \( x \).
\( e^{x} \sin x \)


A current of 2 A passing through conductor produces 80 J of heat in 10 seconds. The resistance of the
conductor is -
A . \( 0.5 \Omega \)
B. 2\Omega
\( c .4 \Omega \)
D. 20\Omega


Two oxides of a metal contain \( 50 \% \) and
\( 40 \% \) of the metal respectively. The formula of the first oxide is \( M O \). The
formula of the second oxide is :
A. \( M O_{2} \)
B. \( M_{2} O_{3} \)
c. \( M_{2} O \)
D. \( M_{2} O_{5} \)


Numbers of geometric isomers of
\( P B r_{2} C l_{3} \) molecule which have non-zero
dipole moment are:


Find the direction cosines of the vector
\( \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}} \)


What function is performed by
Condenser in a refrigerator?
A. To deliver the heat to the heat pump
B. To deliver the heat to the evaporator
C. To deliver the heat to the refrigerator
D. To deliver the heat to the atmosphere


The points moving downwards is/are
\( A \)
\( B \)
\( c \cdot d \)
D


The probability of an event \( A+ \) Probability of the event 'not \( A^{\prime}= \)


Product formed by the activity of malic dehydrogenase in the TCA cycle is
A. Fumaric acid
B. Malic acid
c. Oxaloacetic acid.
D. succinic acid


Which of the following is not a criterion for congruence of triangles?
A. SAS
B. ASA
\( c \cdot \operatorname{ssa} \)
D. sss


Emf of hydrogen electrode in term of \( p H \)
is (at 1 atm pressure).
\( ^{\mathbf{A}} \cdot_{E_{H_{2}}}=\frac{R T}{F} \times p H \)
В. \( \quad E_{H_{2}}=\frac{R T}{F} \frac{1}{p H} \)
c. \( \quad E_{H_{2}}=\frac{2.303 R T}{F} p H \)
D. \( E_{H_{2}}=-0.0591 p H \)


What are 3 main parts of cell?


At point \( x=1, \) the function \( f(x)= \) \( \left\{\begin{array}{ll}x^{3}-1 ; & 1<x<\infty \\ x-1 ; & -\infty<x \leq 1\end{array}\right. \)
A. continuous and differentiable
B. continuous but not differentiable
c. discontinuous and differentiable
D. discontinuous and not differentiable


Copper metal is a:
A. good conductor of electricity
B. bad conductor of electricity
C . magnetic substance
D. bad conductor of heat
E. none of these


Which of the following compounds is optically active?
A. \( 1- \) Bromobutane
B. 2- Bromobutane
c. 1 -Bromo-2-methylpropane
D. 2-Bromo-2-methylpropane


\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{- 1} & \mathbf{1} \\ \mathbf{2} & \mathbf{1} & -\mathbf{3} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right] \) If \( B \) is the adjoint of \( A \)
then \( \alpha \) equals
A .2
в.
\( c \cdot-2 \)
D.


Find the volume of a hemisphere whose radius is \( \left.7 \mathrm{cm} . \text { (use } \pi=\frac{22}{7}\right) \)
A \( \cdot 112.66 \mathrm{cm}^{3} \)
в. \( 718.66 \mathrm{cm}^{3} \)
c. \( 12.66 \mathrm{cm}^{3} \)
D. \( 132.66 \mathrm{cm}^{3} \)


\( \int_{0}^{\infty} \frac{x \tan ^{-1} x}{\left(1+x^{2}\right) x^{2}} d x \)
A \( \cdot \frac{\pi}{2} \log 2 \)
B.
c.
D.


If \( \boldsymbol{y}=\tan \boldsymbol{x}+\cot \boldsymbol{x} \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


Which of the following is non-vascular?
A. Nervous tissue
B. Connective tissue
c. Epithelial tissue
D. Muscular tissue


Four equal electric charges are arranged at the four corners of a square of side \( a . \) Out of these four charges, two
charges are positive and placed at the ends of one diagonal. The other two charges are positive and placed at the ends of the other diagonal. The energy of
the system is:
This question has multiple correct options
A. Negative
B. Positive
\( ^{\mathrm{C}} \). \( _{\text {Less than }} \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{2 q^{2}}{a}\right) \)
Deater than \( \frac{1}{4 \pi \varepsilon_{0}}\left(\frac{2 q^{2}}{a}\right) \)


When brakes are applied to a bus, the
retardation produced is \( 25 \mathrm{cm} \mathrm{s}^{-2} \) and
the bus takes \( 20 s \) to stop. Calculate the initial velocity of the bus.
\( \mathbf{A} \cdot 5 m s^{-1} \)
B. \( 10 m s^{-1} \)
\( \mathbf{c} \cdot 15 m s^{-1} \)
D. \( 20 m s^{-1} \)


A wire of length L and three identical cells of negligible internal resistance are connected in series. Due to the
current, the temperature of the wire is raised by \( \triangle T \) in time t. N identical cells
are now connected in series with a wire
of length \( 2 L \) of same material and across-section. The temperature is raised by same amount \( \triangle \boldsymbol{T} \) in same
time t. The value of N is
A. 6
B. 4
\( c \cdot 8 \)
\( D \)


Solve for \( \boldsymbol{x}: \boldsymbol{3} \boldsymbol{x}=\frac{\boldsymbol{2} \mathbf{0}}{\mathbf{7}}-\boldsymbol{x} \)
A \( \cdot \frac{2}{7} \)
B.
\( c \cdot \frac{4}{7} \)
D.


Ferromagnetic materials have their
properties due to
A. vacant inner subshells
B. partially filled inner subshells
C. filled inner subshells
D. completely filled outer shells


Van't Hoff factor, when benzoic acid is
dissolved in benzene, will be:
A . 2
B.
\( c .0 .5 \)
D. 1.5


Ecological succession in a hydrosere
includes
A. Increase in species diversity
B. Increase in structural complexity
c. Increase in organic matter
D. All of the above


A company makes a metallic block having square bases with volume 640
\( c m^{3}, \) and height \( 10 \mathrm{cm} . \) If Robin wants to paint the block with the paints at the
rate of Rs 15 per \( c m^{2} \), then find the cost
of painting Robin has to pay.
A . Rs 5680
B. Rs 6595
c. Rs 6720
D. Rs 6690


Which of the following is not physically
change? Magnetizing of a piece of iron.


If \( \boldsymbol{A}=\left(\begin{array}{cc}1 & -2 \\ -\mathbf{3} & 4\end{array}\right) \) and \( \boldsymbol{A}+\boldsymbol{B}=\boldsymbol{O}, \) then \( \mathbf{B} \) is
A \( \cdot\left(\begin{array}{cc}1 & -2 \\ -3 & 4\end{array}\right) \)
B. \( \left(\begin{array}{c}-1 \\ 3\end{array}\right) \)
c. \( \left(\begin{array}{cc}-1 & -2 \\ -3-4\end{array}\right) \)
D. \( \left(\begin{array}{c}1 \\ 0 \\ 0\end{array}\right) \)


The number of oxygen atoms in 1 mol of the tetrahydrocannabinol is where, \( N_{A}=6.023 \times 10^{23} \)
A \( .2 N_{A} \)
в. \( N_{A} \)
\( c \cdot 3 N_{A} \)
D. \( 4 N_{A} \)


Convert the following into percentage:
\( \frac{5}{12} \)


The structure of diborane \( \left(B_{2} H_{6}\right) \)
contains:
A. Four \( 2 C-2 e \) bonds and two \( 3 C 2 e \) bonds
B. Two \( 2 C-2 e \) bonds and two \( 3 C 2 e \) bonds
c. Two \( 2 C-2 e \) bonds and four \( 3 C 2 e \) bonds
D. Four \( 2 C-2 e \) bonds and four \( 3 C 2 e \) bonds


Why is sulphur dioxide considered as
an air pollutant?
A. It increases the temperature of the atmosphere.
B. It is used as insecticide which causes air pollution.
C. It causes acid rain due to formation of sulphuric acid on combining with \( O_{2} \) and \( H_{2} O \)
D. It is a strong oxidising agent hence oxidises the other components of air.


What is the equation of the plane containing the parallel lines
\( \boldsymbol{r}=\boldsymbol{a}+\boldsymbol{t c}, \boldsymbol{r}=\boldsymbol{b}+\boldsymbol{p} \boldsymbol{c} \)
\( \mathbf{A} \cdot r \cdot(b-a) \times c=[a b c] \)
B \cdot \( r \cdot(a-b) \times c=[a b c] \)
C \( \cdot r \cdot(b-a) \times c=-[a b c] \)
D \( \cdot r c \times(b-a) \times c=[a b c] \)


Which of the following is the shortest phase of meiosis?
A. Prophase
B. Metaphase I
c. Anaphase I
D. Prophase II
E. Metaphase II


The structures develops into the seed once fertilization has occurred is
A. Integument
B. cotyledon
c. Ovule
D. Ovary
E. Endosperm


Give reason
Metals are regarded as electropositive elements.


Find the common difference of an \( A P \)
whose first term is 100 and the sum of
whose first six terms is five times the
sum of the next six terms.
A . 15
B. -10
c. -20
D. 30


Explain ground wave propagation.


The electric charge for electrode deposition of 1 g equivalent of a substance is:
A. 1 ampere per second
B. 96500 Coulombs per second
c. 1 ampere for one hour
D. The charge on one mole of electrons


Which of the following molecules is/are dimagnetic?
This question has multiple correct options
A \( \cdot L i_{2} \)
в. \( B_{2} \)
c. \( C_{2} \)
D. \( N_{2} \)


Calculate the scalar product of the following vectors
Given two vectors \( \boldsymbol{a}= \)
\{-1,1,1\} and \( b=\{2,0,1\} . \) Find the
vector \( x \) if it is known that it is coplanar with the plane of the vectors a and b, is perpendicular to the vector
\( b, \) and \( a x=7 \)


A body of mass \( 60 k g \) has the
momentum \( 3000 k g m s^{-1} . \) Calculate the
speed of the body.
\( \mathbf{A} \cdot 5 m s^{-1} \)
B . \( 0.05 m s^{-1} \)
\( \mathrm{c} \cdot 50 \mathrm{ms}^{-1} \)
D. \( 500 m s^{-1} \)


Lateral root arises from
A. Pericycle
B. Cortex
c. Pith
D. Endodermis


By using the elementary
transformation, find the inverse of the \( \operatorname{matrix} \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & -\mathbf{2} \\ \mathbf{2} & \mathbf{1}\end{array}\right] \)


Remedy for a bee sting is baking soda whereas wasp sting is cured with vinegar.Why?
A. Vinegar is better than baking soda
B. Baking soda has side effects
c. Bee sting is acidic while wasp sting is slightly basic
D. Vinegar has more remedial properties


A car drives along straight level frictionless road by an engine delivering constant power. Then velocity is directly proportional to?
\( A \cdot t \)
B. \( \frac{1}{\sqrt{t}} \)
\( c \cdot \sqrt{t} \)
D. None of these


The \( D . E \) of the family of circles
touching \( X- \) axis at (0,0) is
The \( D . E \) of the family of circle passing through the origin and having their centre on \( \boldsymbol{Y}-\boldsymbol{a} \boldsymbol{x} \boldsymbol{i} \boldsymbol{s} \) is
A \( \cdot \frac{d y}{d x}=\frac{2 x y}{x^{2}-y^{2}} \)
в. \( \frac{d y}{d x}=\frac{x^{2}-y^{2}}{2 x y} \)
c. \( \frac{d y}{d x}=x^{2}-y^{2} \)
D. \( \frac{d y}{d x}+\frac{x}{y}=0 \)


Which apparatus are used to measure
Y of a wire and shear modulus of the
wire?
This question has multiple correct options
A. Searle's Apparatus, Ewing extensometer
B. Searle's Apparatus, Maxwell needle method
c. Searle's Apparatus, Torsion pendulum
D. Kundt's Apparatus, Searle's Apparatus


\( \ln C u S O_{4} .5 H_{2} O \) how many molecules
of water are indirectly connected to Cu?
\( \mathbf{A} \cdot \mathbf{5} \)
B. 4
\( c \cdot 2 \)
D.


A neutron star has a density equal to that of the nuclear matter. Assuming the star to be spherical, find the radius of a neutron star whose mass is \( 4.0 \times \)
\( 10^{30} k g( \) twice the mass of the sun)


Illuminating the surface of a certain metal alternately with light of
wavelength \( \lambda_{2}=0.54 \mu m \) and \( \lambda_{2}= \)
\( 0.54 \mu m, \) it was found that the
corresponding maximum velocities of photo electrons have a ratio \( \eta=2, \) Find the work function of that metal.
A \( .6 .99 e V \)
B. \( 1.9 e V \)
c. \( 7.53 e V \)
D. \( 1.88 e V \)


Are senses reliable for accurate
measurement?
A . True
B. False


If \( I=\int(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}) d x, \) then
equals
\( \mathbf{A} \cdot 2 \sin ^{-1}\left(\frac{x}{a}\right)+C \)
B. \( 2 a \sin ^{-1}\left(\frac{x}{a}\right)+C \)
\( c \cdot 2 \cos ^{-1}\left(\frac{x}{a}\right)+C \)
D \( \cdot 2 a \cos ^{-1}\left(\frac{x}{a}\right)+C \)


In Rutherford experiment, number of
particles scattered at \( 90^{0} \) angle are \( x \)
per second.number of particles
scattered oper second at angle \( 0^{0} \) is
\( A \)
B. \( 4 x \)
\( c \cdot 8 x \)
D. \( 16 x \)


solve
\( \mathbf{3} \boldsymbol{x}=\mathbf{3} \mathbf{3} \mathbf{6}+\mathbf{2} \mathbf{4} \mathbf{3} \)


What are outside raw materials used by
an organism?
A. Food by heterotrophic organisms
B. Carbon dioxide, minerals and water by autotrophic organisms
C. Oxygen by all aerobic organisms
D. All of the above


What happens to the rate of evaporation when there is more exposed surface area of liquid?
A. It decreases gradually
B. It increases
c. Remains same
D. It decreases rapidly


Give a mathematical relation between
Heat Capacity and Specific Heat Capacity.


Acceleration due to gravity as a
function of \( r \) is given by
A \( \cdot \frac{4}{3} \pi G r(A-B R) \)
B . \( 4 \pi G r(A-B R) \)
c. \( \frac{4}{3} \pi G r\left(A-\frac{3}{4} B R\right) \)
D \( \cdot \frac{4}{3} \pi G r\left(A-\frac{4}{3} B R\right) \)


The points with the co-ordinates
\( (2 a, 3 a),(3 b, 2 b) \&(c, c) \) are collinear.


The stress-strain curve shows a
straight line along the third quadrant
What does it depict
A. Elongation in the negative \( x \) - direction
B. compression
c. Negative Youngs modulus
D. Decreasing stress


Decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) can be
prevented by addition of
A . Acetanilide
B. Benzene
c. Alkali metal oxide
D. \( M n O_{2} \)


Which of the following has tendency to \( \operatorname{act} \) as an oxidising agent?
\( A \cdot C e^{4} \)
B. \( \mathrm{Sm}^{2+} \)
\( c \cdot L u^{3} \)
D. \( \operatorname{Gd}^{3} \)


50 g limestone is heated. The quantity of quicklime produced is:
A. \( 56 g \)
в. 28 \( g \)
\( c \cdot 14 g \)
D. 108


A material 'B' has twice the specific resistance of 'A'. A circular wire made of
B' has twice the diameter of wire made
of 'A' then for the two wires to have the same resistance, the ratio, \( \frac{\boldsymbol{I}_{B}}{\boldsymbol{I}_{A}} \) of their
respective length must be
\( A \)
B. 1/2
\( c \cdot 1 / 4 \)
D. 2


Aqueous humour is a
and vitreous humour is
\( a \)
A. transparent jelly, viscousfluid
B. transparent jelly, watery fluid
c. viscous fluid, viscous fluid
D. viscous fluid, transparent jelly


Write two differences between ideal
solutions and non-ideal solutions.


If the square of \( (a+i b) \) is real, then
\( \boldsymbol{a} \boldsymbol{b}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. -1
D. 2


Cortical portions projecting between the medullary pyramids in the human kidney


Which of the following is an example of simple fuel cell?
A. Lead storage battery
B. Leclanche cell
c. \( H_{2} O_{2} \)
D. All of the above


The only liquid which is a good conductor of heat is-
A. water
B. turpentine
c. alcohol
D. mercury


Which of the following phenomena will occur when two atoms of the elements
having same spin of electron approach for bonding?
A. Orbital overlap will not occur
B. Bonding will not occur
c. Both \( A \) and \( B \) are correct
D. None of the above


The branched sclereids present in hydrophytes are
A. Osteosclereids
B. Trichosclereids
c. Macrosclereids
D. Astrosclereids


State whether given statement is True or False

Light waves require no medium for their propagation.
A. True
B. False


If five \( G . M .^{\prime} s \) are inserted between 486
and \( \frac{2}{3} \) then fourth \( G . M \) will be
\( A \cdot 4 \)
B. 6
c. 12
D. - 6


A elevator car whose floor to distance is
\( 2.7 \mathrm{m} \) starts ascending with a constant
acceleration of \( 1.2 m / s^{2}, 2 s \) after a bolt is begin to fall from the ceiling of the car. The free fall time of the bolt is \( (g= \)
\( \left.9.8 m / s^{e}\right) ? \)
A \( \cdot \sqrt{\frac{2.7}{9.8}} s \)
в. \( \sqrt{\frac{5.4}{9.8}} s \)
c. \( \sqrt{\frac{5.4}{8.6}} s \)
D. \( \sqrt{\frac{5.4}{11}} \)


Give the next decimal numbers the
sequence:
\( (a) 1.32,1.42,1.52, \dots \dots . . \)
(b) \( 1.14,1.25,1.36, \dots \dots . . . \)


A maths exam is marked out of 120
Passing mark percentage is \( 40 \% \).What are marks required for passing?
\( \mathbf{A} \cdot 48 \)
в. 110
c. 54
D. 72


The most important features of
superconductor is that
A. once current is set up in a superconductor ring, it will continue indefinitely even if the battery is off
B. it has high efficiency compared to other conductors
C. it can pass maximum no of electrons when current is passed through it.
D. none of the above


The minimum possible angular momenturn of an election present in an orbital is \( \ldots \ldots . . . . . . \) if the magnetic quanthem number associated with this
orbinal are -1,0,+1
A \( \cdot \frac{5 h}{2 \pi} \)
в. \( \frac{3 h}{2 \pi} \)
\( c \cdot \frac{h}{2 \pi} \)
D. \( \frac{h}{\pi} \)


The distance between a north pole of
strength \( 6 \times 10^{-3} A m \) and south pole of
strength \( 8 \times 10^{-3} \mathrm{Am} \) is \( 10 \mathrm{cm} . \) The poles
are separated in air. The force between
them:
A \( \cdot 4.8 \times 10^{-11} N \)
В. \( 24 \times 10^{-11} N \)
\( \mathbf{c} \cdot 48 \times 10^{-11} N \)
D. \( 24 \times 10^{-12} N \)


Medicines are more effective in their
colloidal form.


I ne IIgure snows lour palrs ol unılormıy
charged spheres. The red spheres are positively charged while the blue spheres are negatively charged. Each sphere has the same amount of charge. Assume each pair is isolated. For which pair there is a point between
them on the dotted line where the
magnitude of electric field is zero as well as the electric potential is also
zero?
A.
B. 2
\( c \cdot 3 \)
D. 4
E. None of the pairs has points that meet these conditions


In this circuit, when certain current
flows, the heat produced in \( 5 \Omega \) is \( 4.05 J \)
in a time \( t . \) The heat produced in \( 2 \Omega \) coil
in the same time interval is
A . 5.76
в. 1.44
\( c .2 .88 \)
D. 2.02


Prove that \( : \cos ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{4}{5}\right)= \)
\( \frac{\pi}{2} \)


In which of the following reaction, the
value of \( \boldsymbol{K}_{\boldsymbol{P}} \) will be equal to \( \boldsymbol{K}_{\boldsymbol{C}}- \)
A \( \cdot N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \)
в. \( P C l_{5}(g) \rightleftharpoons P C l_{3}(g)+C l_{2}(g) \)
C. \( 2 N H_{3}(g) \rightleftharpoons N_{2}(g)+3 H_{2}(g) \)
\( \mathbf{D} \cdot 2 S O_{2}(g)+O_{2} \rightleftharpoons 2 S O_{3}(g) \)


Find the gases which is the densest at standard temperature and pressure.
A. Helium
B. Argon
c. carbon dioxide
D. xenon
E. Nitrogen


Consider a square of side length 1 unit.
What is its area?


Natural rubber is a
\( A \). trans isomer
B. cis isomer
C. racemic mixture
D. equal amount of cis and trans


Which of the following are used as nuclear fuel?
\( \mathbf{A} \cdot_{82} P b^{208} \)
В \( \cdot 92 U^{235} \)
\( \mathbf{c} \cdot_{92} U^{238} \)
D. Both (B) and (C)


Choose the correct answer from the
alternatives given :
Given \( 1+2+34++10=55 \) then the \( \operatorname{sum} 6+12+18+24++60 \) is equal to
A . 300
B. 655
\( c .330 \)
D. 455


Construct \( \triangle M N O \) such that \( N O= \)
\( \mathbf{6 . 2} \mathrm{cm}, \angle \boldsymbol{N}=\mathbf{5 0}^{\circ} \) and \( \boldsymbol{M} \boldsymbol{O}-\boldsymbol{M} \boldsymbol{N}= \)
\( 2.4 \mathrm{cm} \)


How many grams of ammonium chloride should be dissolved in \( 500 \mathrm{mL} \)
of water to have a solution of pH \( 4.5 ? \)
\( \left[K_{b} \text { for ammonium hydroxide is } 1.8 \times\right. \)
\( \left.10^{-5}\right] \)
A . 25.22
B. 48.15
c. 53.5
D. 90


\( f(x)=\lim _{n \rightarrow \infty} \frac{\tan ^{2 n} x \cdot \sin x}{x} \) then
\( \lim _{x \rightarrow 0} f(x)=1 \)
If true enter 1 , else enter 0 .


An inductance of \( 2 H \) carries a current
of \( 2 A . \) To prevent sparking when the circuit is broken a capacitor of \( 4 \mu F \) is connected across the inductance. The
voltage rating of the capacitor is of the order of :
B. \( 10 V \)
\( \mathbf{c} \cdot 10^{5} V \)
D. \( 10^{6} V \)


Factorize by the grouping method:
\( 16(a+b)^{2}-4 a-4 b \)
A \( .4(a-3 b)(4 a+4 b-1) \)
B . \( 4(2 a+b)(a+4 b-3) \)
c. \( 4(a-b)(4 a-4 b-1) \)
D. \( 4(a+b)(4 a+4 b-1) \)


Evaluate: \( \int_{0}^{1} e^{x} d x+\int_{1}^{e} \ln x d x \)


Which of the statements are false?
A. The units of physical quantity represented by volume is \( c m^{3} \)
B. The unit of physical quantity represented by mass is \( \operatorname{ton} \)
C the work done is represented by \( \frac{k g}{m} \)
D. The unit of physical quantity represented by weight is Newton


If \( f(x)=x+3, \) then find the value of
the function \( \boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(-\boldsymbol{x}) \)


In the figure if \( D E \| B C \) and \( A D= \)
\( \mathbf{3} \boldsymbol{x}-\mathbf{2}, \boldsymbol{A} \boldsymbol{E}=\mathbf{5} \boldsymbol{x}-\mathbf{4}, \boldsymbol{B} \boldsymbol{D}=\mathbf{7} \boldsymbol{X}-\mathbf{4} \)
\( B D-7 x-5 \) AND \( C E=5 x-3 . \) Find
\( \mathbf{x} \)


If one of the diagonals of a square is along the line \( x=2 y \) and one of its
verices is \( (3,0), \) then its side through this vertex nearer to the origin is given by the equation.
A. \( y-3 x+9=0 \)
В. \( 3 y+x-3=0 \)
c. \( x-3 y-3=0 \)
D. \( 3 x+y-9=0 \)


Name two \( \alpha \) -amino acids, which form a dipeptide, which is 100 times more
sweet than cane sugar?
This question has multiple correct options
A. Aspartic acid
B. Alanine
c. serine
D. Phenylalanine
E. Tryptophan


Which of the following is incorrect regarding ZW-ZZ type of sex determination?
A. It occurs in birds and some reptiles.
B. Females are homogametic and males are heterogametic.
c. sex ratio is produced in the offsprings.
D. All of the above


A bullet moving at \( 250 \mathrm{m} / \mathrm{s} \) penetrates \( 5 \mathrm{cm} \) into a tree limb before coming to
rest. Assuming that the force exerted by the tree limb is uniform, find its magnitude. Mass of the bullet is \( 10 g \).
A . \( 625 N \)
В. \( 6250 N \)
\( c \cdot 62.50 N \)
D. \( 6.250 N \)


Which of the following compounds exhibits stereoisomerism?
A. 2-Methylbutene
B. 3-Methylbutane
c. 3-Methylbutanoic acid
D. 2-Methylbutanoic acid


Find the values of the following
determinants
\( \left|\begin{array}{cc}\mathbf{2} \boldsymbol{i} & -\mathbf{3} i \\ \boldsymbol{i}^{3} & -\mathbf{2} \boldsymbol{i}^{5}\end{array}\right| \) where \( \boldsymbol{i}=\sqrt{-\mathbf{1}} \)


If the focal length of a convex mirror is
\( 16 \mathrm{cm}, \) what is its radius of curvature?
\( A \cdot 8 \mathrm{cm} \)
B. \( 16 \mathrm{cm} \)
c. \( 32 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


A rectangular \( A 4 \) size paper is kept on cartesian plane coinciding the points \( (3,0),(-1,0),(0,-2) . \) Find the area of the paper in sq. units.
A . 12
B. 8
c. 16
D. 10


A gold leaf electroscope is given a positive charge so that its leaves diverge. How is the divergence of leaves affected, when a negatively charged rod is brought near its disc?
A. divergence increases
B. divergence decreases
c. divergence remains same
D. can't say


How many moles of electrons are
needed in the balanced equation for the oxidation of ethanol (1 mol) to acetic
\( \operatorname{acid} ?\left(C_{2} H_{5} O H \rightarrow C H_{3} C O O H\right) \)
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4


An electric heater operating at \( 220 V \) boils \( 5 l \) of water in 5 min. If it is used
on \( 110 V, \) it will boil the same amount of water in:
A . 10 min
B. 20 min
\( c .15 \) min
D. 25 min


Prove that no matter what the real
number \( a \) and \( b \) are, the sequence with
the \( n t h \) term \( (a+n b) \) is always an \( A P \)
Also find the sum of first 20 terms.


What value does chipko movement
invoke?


For the following reaction at \( 250^{\circ} \mathrm{C} \), the
value of \( K_{c} \) is \( 26, \) then the value of \( K_{p} \) at the same temperature will be:
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \)
A . 0.57
B. 0.61
c. 0.83
D. 0.91


When is a transistor said to be in active
state? Draw a circuit diagram of a p-np transistor and explain how it works as
a transistor amplifier. Write clearly, why in the case of a transistor
(i) the base is
thin and lightly doped and (ii) the emitter is heavily doped.


Bioluminescence was first recorded in
A. Gonyaulax
B. Peridinium
C. Noctiluca
D. Pyrodinium


Aerobic respiratory pathway is appropriately termed
A. Catabolic.
B. Parabolic.
c. Amphibolic.
D. Anabolic.


In three test tubes \( A, B \) and \( C, \) three
different liquids namely, distilled water, underground water and distilled water in which a pinch of calcium sulphate is dissolved, respectively are taken. An equal amount of soap solution is added
to each test tube and the contents are
shaken. In which test tube will the
ength of the foam (lather) be longest?
Justify your answer.


Find the smallest number which should
be multiplied to 10584 to get a perfect
cube.


Fire can be extinguished by spraying:
A. carbon dioxide
B. carbon tetrachloride
c. water
D. all of the above


To construct a triangle similar to given \( \Delta A B C \) with its sides \( \frac{4}{5} \) of that of
\( \Delta A B C, \) locate points \( X_{1}, X_{2}, X_{3}, \dots . . \)
on ray \( B X \) at equal distances such that
\( \angle A B X \) is acute. The points to be joined
in the next step are:
A. \( X_{4}, C \)
в. \( X_{5}, C \)
c. \( x_{4}, A \)
D. \( X_{5}, A \)


Diarrhoea:: Constipation :: Enteritis::
A . Diarrhoea
B. Typhoid
c. Tetanus
D. Malaria


Give examples androgens and
estrogens.


Peptization is a characteristic property
of sols.
A . True
B. False


What will be the volume of the air that
will be expelled from a vessel of
\( 300 \mathrm{cm}^{3} \) when it is heated from \( 27^{\circ} \mathrm{C} \) to
\( 37^{\circ} \mathrm{C} \) at the constant pressure will be :
A \( \cdot 310 \mathrm{cm}^{3} \)
В. \( 290 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 10 \mathrm{cm}^{3} \)
D. \( 37 \mathrm{cm}^{3} \)


The amplitudes of two interfering waves are \( 4 \mathrm{cm} \) and \( 3 \mathrm{cm} \) respectively. If the
resultant amplitude is \( 1 \mathrm{cm} \) then the
interference becomes
A. constructive
B. Destructive
c. Both constructive and destructive
D. given data is insufficient


Write hybridization and geometry of
\( a) \dot{C} l O_{3} \)
b) \( \dot{C} F_{3} \)


A small uniform tube is hent into a
circle of radius r whose plane is vertical. Equal volumes of two fluids whose
densities are \( p \) and \( \sigma(\rho>\sigma) \) fill
half the circle. Find the angle that the
radius passing through the interface
makes with the vertical


The initial concept about the origin of universe was given by
A. Bondi
B. Hawllacks
c. Narlikar
D. Hubble


The heat energy obtainable from hot
rocks present inside the earth crust is
termed as
A. Nuclear energy
B. Tidal energy
c. Geothermal energy
D. None of these


(a) Why does a paramagnetic sample display greater magnetisation (for the same magnetising field) when cooled?
(b) Why is diamagnetism, in contrast, almost independent of temperature?
(c) If a toroid uses bismuth for its core,
will the field in the core be (slightly) greater or (slightly) less than when the core is empty?
(d) Is the permeability of a ferromagnetic material independent
of the magnetic field? If not, is it more for lower or higher fields?
(e) Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?
(f) Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation of a ferromagnet?


\( H_{2} O_{2} \) has the higher boiling point than water due to stronger hydrogen bonding
A. True
B. False


Point out the correct statement
amongst the following.
\( \mathbf{A} \)
\( \left[C u\left(C N_{4}\right)\right]^{3-} \) has tetrahedral geometry and \( d s p^{2} \)
hybridization
B. \( \left[N i\left(C N_{6}\right)\right]^{4-} \) is octahedral and \( \mathrm{Ni} \) had \( d^{2} s p^{3} \)
hybridization
\( ^{\mathbf{C}} \cdot\left[Z n B r_{4}\right]^{2-} \) is tetrahedral and diamagnetic
D. \( \left[C r\left(N H_{3}\right)_{6}\right]^{3+} \) has octahedral geometry and \( s p^{3} d^{2} \)
hybridization


A primary suffix are:
A . -ane
B. -ene
\( c . \) -yne
D. all of these


Show that \( \sin ^{-1}(2 x \sqrt{1-x^{2}})=2 \sin ^{-1} x \)


Polythene is which type of waste?
A. Domestic
B. Industrial
c. Chemical
D. None of these


Total order of reaction \( \boldsymbol{X}+\boldsymbol{Y} \rightarrow \boldsymbol{X} \boldsymbol{Y} \) is
3
The order of reaction with respect to \( X \) is
2.
State the differential rate equation for
the reaction.
\( ^{\mathbf{A}} \cdot-\frac{d[X]}{d t}=k[X]^{0}[Y]^{3} \)
в. \( -\frac{d[X]}{d t}=k[X]^{3}[Y]^{0} \)
\( ^{\mathrm{c}} \cdot \frac{d[X]}{d t}=k[X]^{2}[Y] \)
D. \( -\frac{d[X]}{d t}=k[X][Y]^{2} \)


2,4 -dichlorophenoxyacetic acid is used
as:
A. fungicide
B. insecticide
C. herbicide
D. moth repellant


When \( \mathrm{NH}_{4} \mathrm{NO}_{3} \) is heated the gas formed
is :
\( A \cdot N_{2} O \)
в. NO
\( c \cdot N O_{2} \)
D. NH


For an elementary reaction, \( \boldsymbol{X}(\boldsymbol{g}) \rightarrow \) \( \boldsymbol{Y}(\boldsymbol{g})+\boldsymbol{Z}(\boldsymbol{g}) \)
the half life period is 10 min. In what period of time would concentration of \( \boldsymbol{X} \)
be reduced to \( 10 \% \) of original concentration?
A . 20 min
B. 33 Min
c. 15 min
D. 25 Min


An ideal choke takes a current of \( 8 A \)
when connected to an a.c source of 100
volt and 50 Hz. A pure resistance under
the same conditions takes a current of
10A. If two are connected in series to an
a.c. Supply of \( 150 \mathrm{V} \) and \( 40 \mathrm{Hz} \), then the current in the series combination of
above resistor and conductor is:


Fill in the blanks


Action of soap is due to emulsification and micelle formation. Comment.


The value of \( \int_{0}^{\pi / 4} \log (1+\tan x) d x \) is
equal to
A \( \cdot \frac{\pi}{8} \log _{e} 2 \)
в. \( \frac{\pi}{4} \log _{e} 2 \)
c.
D. none of these


The formation of the oxide ion \( O^{2-}(g) \)
requires first an exothermic and then an endothermic step as shown below.
\( \boldsymbol{O}(\boldsymbol{g})+\boldsymbol{e}^{-} \rightarrow \boldsymbol{O}^{-}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{0}= \)
\( -142 k J m o l^{-1} \)
\( \boldsymbol{O}^{-}(\boldsymbol{g})+\boldsymbol{e}^{-} \rightarrow \boldsymbol{O}^{2-}(\boldsymbol{g}) ; \boldsymbol{\Delta} \boldsymbol{H}^{0}= \)
\( 844 k J m o l^{-1} \)
The correct statement is?
A. Oxygen is more electronegative
B. \( O^{-} \) ion has comparatively larger size than oxygen atom
\( \mathrm{c} \cdot O^{-} \) ion will tend to resist the addition of another
electron
D. Oxygen has high electron affinity


How many lone pairs are associated with xenon in xenon difluoride?
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


Write the differences between:
Open and closed systems of circulation


Base of the rectangular prism is in the
form of a
A. Square
B. Rectangle
c. circle
D. Triangle


Florigen is synthesized in
\( A \cdot \) Stem
B. Leaves
\( c . \) Root
D. Fruits


Force \( \times \) time \( = \) . Fill in the
blank
A. Acceleration
B. Impulse
c. Velocity
D. Momentum


PAHs generally have a low degree of acute toxicity to humans.
A . True
B. False


Assertion: Receptors are crucial to body's communication process
Reason : Receptors are proteins
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is NOT the correct explanation for Assertion
C. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct
\( F . \) None of these


Which of the following is/are incorrect
about solubility trend in group I and II ?
This question has multiple correct options
A. The solubility of the alkali metal fluorides increases on moving down the group.
B. The solubility of the alkali metal hydroxides decreases on moving down the group.
C. The solubility of hydroxides, fluorides and oxalates decreases from calcium to barium
D. The solubility of carbonates, sulphates and chromates decreases on moving down the group.


1 kg of cold water at \( 5^{\circ} \mathrm{C} \) is mixed with
\( 5 k g \) of hot water at \( 65^{\circ} \mathrm{C} \). Calculate the
final temperature of the water when it arrives at thermal equilibrium?
A \( \cdot 10^{\circ} \mathrm{C} \)
В. \( 15^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 35^{\circ} C \)
D. \( 55^{\circ} \mathrm{C} \)
E \( \cdot 60^{\circ} \mathrm{C} \)


paracetamolis:
\( \mathbf{A} \)
\( B \)
\( \mathbf{c} \)
D.


The blood vessel which brings oxygenated blood from lungs towards
the heart of frog is
A. Pre-caval
B. Post-caval
c. Pulmonary vein
D. Pulmonary artery


Evaluate: \( \int_{-1}^{2}\left|x^{3}-x\right| d x \)


Write the different types of Hydrogen Spectral series. The Lyman series of Hydrogen spectrum lies in the ultraviolet region. Why?


A solution containing \( 30 g \) of a nonvolatile solute in exactly \( 90 g \) water has a vapour pressure of 21.85 mm \( H g \) at
\( 25^{\circ} \mathrm{C} . \) Further 18 gm of water is then added to the solution. The resulting solution has a vapour pressure of 22.18 \( \mathrm{mmHg} \) at \( 25^{\circ} \mathrm{C} \). Calculate
(a) molar mass of the solute, and (b) vapour
pressure of water at \( 25^{\circ} \mathrm{C} \)
В. \( (a) 61.21 g \) тод\( ^{-1} \),
(b) 23.99 \( \mathrm{mm} \) Н \( g \)
\( (b) 28.87 \mathrm{mm} \mathrm{Hg} \)
D. \( (a) 84.87 g \) mol \( ^{-1} \),


Which of the following ions is NOT isoelectronic to a noble gas?
A \( . A l^{3} \)
в. \( K^{+} \)
\( c \cdot B r^{-} \)
D. \( C o^{2} \)


In the following reaction:
\( \boldsymbol{K}_{2} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}+\boldsymbol{C l}_{2} \longrightarrow 2 \boldsymbol{K} \boldsymbol{C l}+ \)
\( 2 K M n O_{4} \)
2 moles \( C l_{2} \) and 2 moles \( K_{2} M n O_{4} \)
form \( \ldots \ldots . . . . . . \) moles \( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \)
Fill in the above blank.


When the turns ratio of a step-up transformer is 20 and the primary ac voltage is \( 12 V \), the secondary voltage is
A . \( 12 V \)
B. \( 120 V \)
c. \( 240 V \)
D. 2, 400V


Assertion
Metaphase II begins with splitting of centromere of each chromosomes into
two
Reason
In Anaphase II chromosomes align at
the equator.
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


For waht value of \( \lambda \), the three numbers
\( 2 \lambda-1, \frac{1}{4}, \lambda-\frac{1}{2} \) can be the direction
cosines of a straight line?
A \( \cdot \frac{1}{2} \pm \frac{\sqrt{3}}{4} \)
B. \( \frac{3}{4} \)
\( c \cdot \pm \frac{3}{4} \)
D. \( \frac{\sqrt{3}}{2} \pm \frac{1}{4} \)


A thermodynamic equilibrium
represents the state when all the three equilibrium (i.e., chemical, thermal and mechanical equilibrium) are attained at a time.
If true enter 1 , else enter 0 .


Which term of the G.P.: \( \frac{1}{3}, \frac{1}{9}, \frac{1}{27} \dots \) is \( \frac{1}{19683} ? \)


A pan containing a layer of uniform thickness of ice is placed on a circular turn- table with its centre coinciding with the centre of the turn-table.
The turn-table is now rotated at a
constant angular velocity about a vertical axis passing through its centre and the driving torque is withdrawn. There is no friction between the table
and the pivot. The pan rotates with the
table. As the ice melts,
This question has multiple correct options
A. the angular velocity of the system decreases
B. the angular velocity of the system increases
c. the angular velocity of the system remains unchanged
D. the moment of inertia of the system increases


Prove that \( x^{2}-y^{2}=c\left(x^{2}+y^{2}\right)^{2} \) is the
general solution of differential equation
\( \left(x^{3}-3 x y^{2}\right) d x=\left(y^{3}-3 x^{2} y\right) d y \)
where \( c \) is a parameter


Molarity of a substance decreases with increase in temperature.
A. True
B. False


Entamoeba gingivalis lives in the
A. Intestine
B. Colon
c. Pus pockets of pyorrhoea
D. Intestine and colon


Write the IUPAC name of the following compound:
\( \boldsymbol{C H}_{2}=\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)-\boldsymbol{C}(\boldsymbol{H})\left(\boldsymbol{C H}_{3}\right)(\boldsymbol{B r}) \)
A. 3-Bromo-2-methylbut-1-ene
B. 2-Bromo-2-methylbut-1-ene
c. 1 -Bromo-2-methylbut-1-ene
D. none of these


Citrus fruits are rich in vitamin:
\( A \cdot A \)
B.
\( c . \) в
D.


The velocity \( (v)- \) time \( (t) \) graph of a
body is as shown in the figure. What is
the displacement in \( 5 s ? \)
\( A \cdot 2 m \)
B. 3 m
\( c .4 m \)
D. 5 m


a) Explain bragg's spectrometer method.
b) Write about the preparation of colloids by chemical methods.


Identify \( A \)
A. \( H C H O \)
\( \mathbf{B} \cdot C H_{3} C H O \)
\( \mathbf{C} \cdot C_{6} H_{5} C H O \)
\( \mathrm{D} \cdot \mathrm{CH}_{3} \mathrm{COCH}_{3} \)


The colour of caustic soda turns pink when phenolphthalein is added.
A. True
B. False


Which of the following is true regarding derivation of the name of californium?
A. The name of californium was derived from the name of the place.
B. The name of californium was derived from its color.
c. The name of californium was derived from the name of the scientist who discovered it
D. The name of californium was derived from mythological character name.


The least reactive element among the following is
A \( , x^{1} \)
?
В . \( _{18} Y^{16} \)
c. \( _{11} X^{23} \)
D. \( _{12} Y^{24} \)


Which compound requires use of the Bronsted-Lowry theory to be identified as a base?
A. \( N H_{3} \)
в. \( H_{2} \).
c. \( L i O H \)
D. \( N a C l \)


Who am I? I depend on plants for food.


A coil of area \( A_{0} \) is lying in such a magnetic field whose value changes
from \( B_{0} \) to \( 4 B_{0} \)
in \( t \) seconds. The induced emf in the coil
will be :
A \( \cdot \frac{4 B_{0}}{A_{0} t} \)
в. \( \frac{4 B_{0} A_{0}}{t} \)
c. \( \frac{3 B_{0} A_{0}}{t} \)
D. \( \frac{3 B_{0}}{A_{0} t} \)


A disk of mass \( M, \) radius \( R \) and
thickness \( \frac{R}{6} \) has a moment of intertia \( I \) about an axis passing through the centre and perpendicular to the disk. The disk is recasted to form a sphere.
Obtain the moment of inertia of the
sphere about its diameter.


Find the integrals of the functions.
i) \( \sin ^{2}(2 x+5) \)
ii) \( \sin 3 x \cos 4 x \)
iii) \( \cos 2 x \cos 4 x \cos 6 x \)
iv) \( \sin ^{3}(2 x+1) \)


The atom \( A, B, C \) have the configuration \( A \rightarrow[Z(90)+n(146)], B \rightarrow[Z(92)+ \)
\( \mathrm{n}(146)], \mathrm{C} \rightarrow[\mathrm{Z}(90)+\mathrm{n}(148)] \) So that
(a) \( A \) and \( C- \) Isotones
(b) A and C -
Isotopes
(c) \( A \) and \( B \) - Isobars
(d) \( B \) and \( c- \)
Isobars
(e) \( \mathrm{B} \) and \( \mathrm{C} \) - Isotones
The wrong statements are:
A. a, bonly
B. c, d, e only
c. a \( , c, d \) only
D. a, d, e only


Show that the following points are collinear.
(3,-2),(-2,8) and (0,4)


Plots of \( E_{\text {cell}} \) with \( \log _{10} Q \) for the reaction, \( Z n(s)+C u^{2+}(a q .) \rightleftharpoons \)
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{Z} \boldsymbol{n}^{2+}(\boldsymbol{a q} .) \) gives a straight
line with an intercept \( 1.10 . \) If \( \boldsymbol{E}_{c e l l}= \) \( 1.1591 V \), then value of \( Q \), i.e. \( \frac{\left[Z n^{2+}\right]}{\left[C u^{2+}\right]} \) is:
A . 0.01
B. \( 0 . \)
c. 100
D. 10


If \( \cos B \cos C+\sin B \sin C \sin ^{2} A=1 \)
then triangle \( A B C \) is
A. isosceles and right angled
B. equilateral
C. isosceles whose equal angles are greater than \( \pi / 4 \)
D. none


With age 'Near point' and 'Far point' recedes due to
A. Weakening of ciliary muscles
B. decreasing ability to change the focal length
A . A is correct
B. B is correct
c. Both A and B are correct
D. Neither A nor B is correct


The number of positive integral
solutions of the equation \( \tan ^{-1} x+ \) \( \cot ^{-1} y=\tan ^{-1} 3 \) is :
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


The self inductance of the motor of an
electric fan is \( 10 \mathrm{H} \). In order to impart
maximum powr of \( 50 \mathrm{Hz} \), it should be
connected to a capacitance of
\( A \cdot 8 \mu F \)
в. \( 4 \mu F \)
\( c \cdot 2 \mu F \)
D. \( 1 \mu F \)


The temperature of 5 mol of a gas which was held at constant volume was
changed from \( 100^{\circ} \mathrm{C} \) to \( 120^{\circ} \mathrm{C} \). The
change in internal energy was found to
be 80 . \( J \). The total heat capacity of the
gas at constant volume will be equal to
\( \mathbf{A} \cdot 8 J K^{-1} \)
B . \( 0.8 \mathrm{JK}^{-1} \)
\( \mathbf{c} \cdot 4 J K^{-1} \)
D. \( 0.4 \mathrm{JK}^{-1} \)


A particle of mass m moving with a velocity v makes a head on elastic
collision with another particle of the same mass initially at rest. The velocity of the first particle after collision is
\( A \)
B. \( v / 2 \)
c. \( 2 v \)
D.


Very fine particles mainly scatter light.


By splitting into prime factors, find the
square root of 11025
A. 1005
в. 105
c. 100
D. 115


What is smog? How is classical smog different from photo chemical smog?


Find \( m \) if the following equation holds true \( 1.3+2.4+3.5+\ldots+n(n+2)= \)
\( \frac{1}{m} n(n+1)(2 n+7) \)


According to the Bohr model of the atom, which electron transition will emit the lowest energy photon?
A \( n=2 \) to \( n=5 \)
5
B . \( n=3 \) to \( n=2 \)
c. \( n=3 \) to \( n=4 \)
D. \( n=6 \) to \( n=2 \)
2


Find the fraction equivalent to 0.5436 and \( 0 . \overline{5436} \)


Fill in the blanks.
is the fastest mode
of transfer of heat.


Write a rational function \( f \) that has
vertical asymptote at \( x=4, \) a
horizontal asymptote at \( y=5 \) and \( a \)
zero at \( x=-7 \)
A \( \quad f(x)=\frac{5(x-7)}{(x-4)} \)
B. \( f(x)=\frac{5(x+7)}{(x-4)} \)
c. \( f(x)=\frac{5(x-7)}{(x+4)} \)
D. \( f(x)=\frac{(x+7)}{(x+4)} \)


Which of the following is the most widely accepted method of contraception in India at present?
A. Cervical caps
B. Tubectomy
c. Diaphragms
D. IUDs (Intra uterine devices)


Describe the working of AC electric generator with diagram:


If \( f(x)=\left|\begin{array}{cc}x & \lambda \\ 2 \lambda & x\end{array}\right|, \) then \( f(\lambda x)-f(x) \) is
equal to:
A \( \cdot x\left(\lambda^{2}-1\right) \)
B \( \cdot 2 \lambda\left(x^{2}-1\right) \)
C \( \cdot \lambda^{2}\left(x^{2}-1\right) \)
D. \( \lambda\left(x^{2}-1\right) \)
E \( \cdot x^{2}\left(\lambda^{2}-1\right) \)


The value of \( (\operatorname{adj} A) \) is equal to
A . \( 2 A \)
в. \( 4 A \)
\( c .8 A \)
D. \( 16 A \)


The masses of \( \alpha \) -particle, proton and neutron are 4.00150 amu, 1.00728 amu
and 1.00867 amu respectively. Binding Energy per nucleon of \( \alpha \) -particle is :
\begin{tabular}{l}
A .2835 \\
\hline
\end{tabular}
в. 931.5 Ме \( V \)
c. \( 28.3 \mathrm{MeV} \)
D. \( 7.08 \mathrm{MeV} \)


One \( g m \) metal \( M^{3+} \) was discharged by
the passage of \( 1.81 \times 10^{23} \) electrons.
What is the atomic mass of metal?
\( \mathbf{A} \cdot 8 g / m o l \)
в. \( 9 g / m o l \)
c. \( 10 g / \) mol
D. None of these


What should be the angle between corresponding radii such that the tangents don't intersect?
A . \( 0^{\circ} \)
B. \( 90^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 45^{\circ} \)


Magnesium is used in fireworks.
A. True
B. False


In the figure, \( \triangle A B C \) is right angled at
\( B . D \) is any point on \( A B \)
\( \operatorname{seg} D E \perp \operatorname{sid} e A C . \) If \( A D= \)
\( 6 \mathrm{cm}, A B=12 \mathrm{cm} A C=18 \mathrm{cm} . \) Find
\( A E \)
\( A \cdot 5 c m \)
в. 3 ст
\( c .4 c m \)
\( 0.6 \mathrm{cm} \)


Two identical spherical masses are kept at some distance. Potential energy when a mass \( m \) is taken from the
surface of one sphere to the other
A. increases continuously
B. decreases continuously
c. first increases, then decreases
D. first decreases, then increases


The difference between birth rate and
death rate is termed as
A. life rate
B. survival rate
c. birth ratio
D. none of the above


What must be added to \( 7 z^{3}-11 z^{2}- \)
129 to \( \operatorname{get} 5 z^{2}+7 z-92 ? \)
A \( \cdot 7 z^{3}+16 z^{2}+7 z+37 \)
B . \( -7 z^{3}+16 z^{2}+7 z+37 \)
D. \( -7 z^{3}-7 z^{2}+7 z-37 \)


In case a solute associates in solution,
the van't Hoff factor is :
A \( . i>1 \)
в. \( i=1 \)
\( c \cdot i<1 \)
D. None of these


\( \ln P_{4} O_{10}, \) find the number of oxygen
atoms bonded to each phosphorous
atom


Through a fixed point \( (h, k) \) secants are
drawn to the circle \( x^{2}+y^{2}=r^{2} \) Then
the locus of the midpoints of the chords
intercepted by the circle is
A \( \cdot x^{2}+y^{2}=h x+k y \)
B . \( x^{2}-y^{2}=h x+k y \)
C. \( x^{2}+y^{2}=h x-k y \)
D. \( x^{2}-y^{2}=h x-k y \)


The S.I unit of wavelength is
A \( . c m \)
в. \( d m \)
\( c \cdot m \)
D. \( k m \)


\( 40 \% \) of \( P C l_{s} \) is not dissociated at
\( 300^{0} C . \) The reaction is carried out in a
flask of 1 litre capacity. The value of \( \boldsymbol{K}_{\boldsymbol{c}} \)
would be:
A. 3.2
B. 1.6
\( c .2 .8 \)
D. 0.9


Solve the following equation. \( 2 x-\frac{1}{3}=\frac{1}{5}-x \)


toppr
Q Type your question
\( A \)
\( B \)
\( c \)
\( D \)


Cell wall of both bacteria and
cyanobacteria contains
A. Lipid
B. Pectin
c. Protein
D. Muramic acid


A certain force acting on a body of mass 2kg increase its velocity from 6m/s to \( 15 \mathrm{m} / \mathrm{s} \) in \( 2 \mathrm{s} \). The work done by the force during this interval is?
A. 27
B. 3J
c. \( 94.5 \mathrm{J} \)
D. 1890


\( \alpha \) -particle consists of :
A. 2 protons and 2 neutrons only
B. 2 electrons, 2 protons and 2 neutrons
C \( . \) 2 electrons and 4 protons only
D. 2 protons only


Which one of the following statements
is false for hydrophilic colloids?
A. They do not require electrolytes for stabillity
B. Their coagulation is reversible
C. Their viscosity is of the order of that of water
D. Their surface tension is usually lower than that of dispersion medium


If \( A=1 \) and \( B=0, \) than \( A . A+B \) in the
Boolean expression is equal to
A. \( B \)
в.
c. \( A . B \)
D. B.B


For the reaction, \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+ \)
\( \boldsymbol{C l}_{2}(\boldsymbol{g}) \)
The forward reaction at constant
temperature is favored by:
A. introducing an inert gas at constant volume
B. introducing chlorine gas at constant volume
c. introducing an inert gas at constant pressure
D. none of the above


A charge \( +q \) is placed at the origin 0 of \( x-y \) axes as shown in the figure. The work done in taking a charge \( Q \) from \( A \) to B along the straight line \( A B \) is:
A \( \cdot \frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{a-b}{a b}\right) \)
в. \( \frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{b-a}{a b}\right) \)
c. \( \frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{b}{a^{2}}-\frac{1}{b}\right) \)
D. \( \frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{a}{b^{2}}-\frac{1}{b}\right) \)


Answer the following questions:
(i) Obtain the expression for the cyclotron frequency.
(ii) A deuteron and a proton are accelerated by the cyclotron. Can both be accelerated with the same oscillator
frequency? Given reason to justify your
answer


Choose the correct on from the given four
options:
Consider equation:
\[
\mathrm{P}_{4} \mathrm{O}_{10}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4}
\]
Number of moles of \( \mathrm{H}_{3} \mathrm{PO}_{4} \) produced by
reaction are 1 mole of \( P_{4} O_{10} \)
is
2
4
6
8


What are the advantages of sexual
reproduction?


A car and a lorry are moving with same momentum. If same brake force is
applied then,
A. car comes to rest in shorter distance
B. lorry comes to rest in shorter distance
c. both travels the same distance before coming to rest
D. Insufficient data


A force can change:
A. shape of a body
B. size of a body
c. direction of motion
D. all the above


The dimensional formula \( M^{-1} L^{3} T^{-2} \)
refers to:
A . Force
B. Power
c. Gravitational constant
D. Energy


Two current carrying loops of same area but of different materials have same
current flowing in them in anticlockwise direction. if a magnetic field is applied in upward direction then potential energy of loop 1 and loop 2 will
always be:
A. Different
B. Equal
c. can be different or equal depend upon material
D. Can't say


are a class of chemical
compounds used for the treatment of
stress, and mild or even severe mental diseases.
A. Tranquilizers
B. Antiseptics
c. Analgesics
D. None of above


Glycolysis occurs
A. In cytoplasm
B. In aerobic respiration
C. In anaerobic respiration
D. All of the above


How much would a W kg man weigh on the moon in terms of gravitational
units?
A \( \cdot \frac{W}{6} \) kg wt
B. 6 W kg wt
c. w kg wt
D. zero


The odd one amongst following is
A. Nitrococcus, Nitrobacter, Nitrosomonas
B. Rhizobium, Bacillus Polymyxa, Pseudomonas
c. clostridium, Rhizobium, Nostoc
D. Anabaena, Nostoc, Azotobacter, Clostridium


In human, teeth are
A. Homodont and polyphydont
B. Heterodont and polyphyodont
C. Homodant anddiphyodont
D. Heterodont and diphyodont


Match the following


Divide the polynomial \( p(x) \) by the polynomial \( g(x) \) and find the quotient and remainder.
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}^{2}+\mathbf{5} \boldsymbol{x}-\boldsymbol{3} \)
\( g(x)=x^{2}-2 \)
\( \mathbf{A} \cdot q(x)=x-3, r(x)=7 x+9 \)
в. \( q(x)=x+3, r(x)=-7 x-9 \)
C \( . q(x)=x+3, r(x)=7 x-9 \)
D. \( q(x)=x-3, r(x)=7 x-9 \)


The radius of a sphere is changing at the rate of \( 0.1 \mathrm{cm} / \) sec. The rate of
change of its surface area when the radius is \( 200 \mathrm{cm}, \) is.
A \( \cdot 8 \pi c m^{2} / \) sec
В. \( 12 \pi c m^{2} / \)sec
c. \( 160 \pi c m^{2} / \) sec
D. \( 200 \pi c m^{2} / \) sec


Heart of rabbit does not have
A. Right auricle
B. sinus venosus
c. Conus arterious
D. Both B and C


The partial pressure of \( N_{2}, O_{2} \) and \( C O_{2} \)
in a vessel are \( 38 \mathrm{cm} \) of \( \mathrm{Hg}, 190 \) torr and
0.5 atm, respectively. The total pressure
of the mixture at the same temperature is?
A. 0.96 atm
B . 1.02 atm
c. 1.64 atm
D. 1.25 atm


Which of these are correct?
(a) If any two rows or columns of a determinant are identical, then the
value of the determinant is zero.
(b) If the corresponding rows and columns of a determinant are
interchanged, then the value of the determinant does not change.
(c) If any two rows (or column) of a determinant are interchanged, then the value of the determinant changes in
\( \operatorname{sign} \)
A \( \cdot(a) \) and \( (b) \)
B. \( (b) \) and \( (c) \)
c. \( (a) \) and \( (c) \)
D. \( (a),(b) \) and \( (c) \)


If the \( p^{t h}, q^{t h} \) and \( r^{t h} \) term of an
arithmetic sequence are \( a, b \) and \( c \)
respectively, then the value of \( [\boldsymbol{a}(\boldsymbol{q} \boldsymbol{r})+\boldsymbol{b}(\boldsymbol{r} \boldsymbol{p})+\boldsymbol{c}(\boldsymbol{p} \boldsymbol{q})]= \)
\( A \)
B. -
\( c \cdot c \)
D. \( 1 / 2 \)


Experts are worried about Taj mahal
because:
A. pollutants in air are discolouring its white marble
B. it is not only living organisms that get affected by polluted air
C. non-living things like buildings, monuments and statues also get affected
D. all of the above


Express in Degrees:
\( (a)\left(\frac{2 \pi}{15}\right)^{c} \)
\( (b)(-2)^{c} \)
A \( \cdot(a) 14^{\circ} \)
\( (b) 244^{\circ} 32^{\prime} 44^{\prime \prime} \)
B . \( (a) 74^{\circ} \)
\( (b)-114^{\circ} 32^{\prime} 44^{\prime \prime} \)
c. \( (a) 14^{\circ} \)
\( (b)-120^{\circ} 32^{\prime} 44^{\prime \prime} \)
D \cdot \( (a) 24^{\circ} \)
\( (b)-114^{\circ} 32^{\prime} 44^{\prime \prime} \)


When a body is placed on a surface, the
body exert a force equal to its weight on the surface, but the body does not move (or fall) because the
surface exerts equal and opposite forces.
A. Upwards
B. Downwards
c. Both
D. None


Name the kinds of cells found in the
following places:
This question has multiple correct options
A. Surface of the human skin
B. Salivery gland
c. Brain
D. Inner lining of the wind pipe


Quadrilateral JUMP
\( J U=3.5 \mathrm{cm} \)
\( \mathrm{UM}=4 \mathrm{cm} \)
\( \mathrm{MP}=5 \mathrm{cm} \)
\( P J=4.5 \mathrm{cm} \)
\( P U=6.5 \mathrm{cm} \)


Alkyl isocyanides \( \left(R N \oplus \equiv C^{\ominus}\right) \) are
reduced to \( 2^{\circ} \) amines \( \left(R-N H-C H_{3}\right. \)
with:
\( \mathbf{A} \cdot L A H \)
в. \( N a B H_{4} \)
c. \( H I+P \)
D. \( H_{2} / P t \)


State following are True or False
If \( m=n=p \) and the groups have identical qualitative characterstic then the number of groups \( =\frac{(3 n) !}{n ! n ! n ! 3 !} \)
Note : If 3n different things are to be
distributed equally three people then the number of ways \( =\frac{(3 n) !}{(n !)^{3}} \)
A . True
B. False


Mode of the following frequency
distribution
\( \begin{array}{lccccc}\mathrm{x}: & 4 & 5 & 6 & 7 & 8 \\ \mathrm{f}: & 6 & 7 & 10 & 8 & 3\end{array} \)
A. 5
B. 6
\( c \cdot 8 \)
D. 19


The number of atoms present in 100 grams of sodium is:
B . \( 0.6182 \times 10^{24} \)
c. \( 2.6182 \times 10^{24} \)
D. 2.6182 \( \times 10^{20} \)


\( \operatorname{cis}\left[\operatorname{Co}(e n)_{2} C l_{2}\right]^{+} \) can have \( d \) and \( l \)
optical isomers
A. True
B. False


If \( \frac{2 x+A}{(x-3)(x+2)}=\frac{9}{5(x-3)}+ \)
\( \frac{B}{(x+2)}, \) then
This question has multiple correct options
\( \mathbf{A} \cdot A=3 \)
B. \( B=5 \)
c. \( _{A}=\frac{1}{3} \)
D. \( B=\frac{1}{5} \)


The figure shows an assembly
consisting of a number of pendulums of
varying lengths. The driver pendulum is pulled aside and released so that it
oscillates in a plane perpendicular to
that of the diagram.
It will be observed that :
A. all pendulums oscillate with the frequency of the driver pendulum and have the same amplitude.
B. pendulums oscillate with different frequencies but equal amplitude, the shortest pendulum oscillating with the highest frequency,
c. all pendulums oscillate with the frequency of the driver pendulum; the pendulum with length equal to that of the driver has the greatest amplitude
D. pendulums oscillate with different frequencies and rent amplitudes


If \( 0<x<1, \) then \( \tan ^{-1}\left(\frac{\sqrt{1-x^{2}}}{1+x}\right) \) is
equal to
\( ^{\mathbf{A} \cdot} \frac{1}{2} \cos ^{-1} x \)
B. \( \cos ^{-1} \frac{\sqrt{1+x}}{2} \)
c. \( \sin ^{-1} \sqrt{\frac{1-x}{2}} \)
D. \( \frac{1}{2} \sqrt{\frac{1+x}{1-x}} \)


Caustic soda is the common name for:
\( \mathbf{A} \cdot M g(O H)_{2} \)
в. КОН
\( \mathbf{c} \cdot C a(O H)_{2} \)
D. \( N a O H \)


In gamma ray emission from a nucleus
A. both the neutron number and the proton number change
B. there is no change in the proton number and the neutron number
C . only the neutron number changes
D. only the proton number changes


If \( : n(A)=m, \) then number of relations
in \( A \) are
\( \mathbf{A} \cdot 2^{m} \)
B. \( 2^{m}-2 \)
\( \mathbf{c} \cdot 2^{m^{2}} \)
D. None of these


Speed \( v \) of a particle moving along a
straight line, when it is at a distance \( x \)
from a fixed point on the line is given by \( v^{2}=108-9 x^{2} \) (assuming mean
position to have zero phase constant)
(all quantities in are in \( c g s \) unit):
A. The motion is uniformly accelerated along the straight line
B. The magnitude of the acceleration at a distance \( 3 \mathrm{cm} \) from the fixed point is \( 27 \mathrm{cm} / \mathrm{s}^{2} \)
C. The motion is simple harmonic about \( x=\sqrt{12} \mathrm{m} \)
D. The maximum displacement from the fixed point is \( 4 \mathrm{cm} \)


State True or False :
Human body is a good conductor of electricity.
A. True
B. False


Which the following interaction form nonbonding molecular orbital when zaxis is the bonding axis?
\( \mathbf{A} \cdot d_{y z}+d_{z^{2}} \)
\( \mathbf{B} \cdot d_{y z}+d_{x y} \)
C \( \cdot d_{x^{2}-y^{2}}+d_{x y} \)
D. All form N.B.M.O.


\( 3 V \) potentiometer used for the
determination of internal resistance of
a \( 2.4 \mathrm{V} \) cell. The balance point of the cell is open circuit is \( 75.8 \mathrm{cm} \). When a
resistor of \( 10.2 \Omega \) is used in the external
circuit of the cell the balance point
shifts to \( 68.3 \mathrm{cm} \) length of the potentiometer wire. The internal
resistance of the cell is?
A . \( 2.5 \Omega \)
B . \( 2.25 \Omega \)
c. \( 1.12 \Omega \)
D. 3.2\Omega


An element (X) forms compounds of the
formula \( \boldsymbol{X} \boldsymbol{C l}_{3}, \boldsymbol{X}_{2} \boldsymbol{O}_{5} \) and \( \boldsymbol{C} \boldsymbol{a}_{3} \boldsymbol{X}_{2}, \) but
does not form \( X C l_{5} . \) Which of the following is the element?
\( A \cdot B \)
B. Al
c.
D.


If \( a m \neq b l, \) then the system of
equations \( a x+b y=c \) and \( l x+m y= \)
\( n \) has:
A. A unique solution
B. No solution
c. Infinitely many solutions
D. May or may not have a solution


Polynuclear hydrocarbons are non toxic.
A. True
B. False


Calculate the Standard Deviation and
coefficient of variation for the given
frequency table:
\( \begin{array}{ll}\text { Class-interval } & \text { Frequency } \\ 1-5 & 1 \\ 6-10 & 2 \\ 11-15 & 3 \\ 16-20 & 4\end{array} \)


How did a citizen group called Friends of Arcata Marsh, Arcata, California, USA, help to improve water quality of the marshland using Integrated Waste Water Treatment? Explain in four steps.


A gas will approach ideal behavior at:
A. low temperature and low pressure
B. low temperature and high pressure
c. high temperature and low pressure
D. high temperature and high pressure


The path along which light travels is called a
\( A \cdot \operatorname{ray} \)
B. line
c. line segment
D. none


\( \int \sec x \cdot \log (\sec x+\tan x) d x= \)
\( A \cdot[\log (\sec x+\tan x)]^{2}+c \)
B. \( \frac{[\log (\sec x+\tan x)]^{2}}{2}+c \)
c. \( -\log (\sec x+\tan x)+c \)
D. \( \log (\sec x+\tan x)+c \)


Evaluate the following limits. \( \lim _{x \rightarrow 5} \frac{x^{3}-125}{x^{2}-7 x+10} \)


Assertion
De Broglie equation has significance for any microscopic or submicroscopic particles.
Reason
De Broglie wavelength is inversely proportional to the mass of the object.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A boy throws balls into air at regular
interval of 2 second. The next ball is
thrown when the velocity of first ball is zero. How high do the ball rise above his
hand? [Take \( \left.\boldsymbol{g}=\mathbf{9 . 8} \boldsymbol{m} / \boldsymbol{s}^{2}\right] \)
A . \( 4.9 \mathrm{m} \)
B. \( 9.8 m \)
c. \( 19.6 m \)
D. 29.4 \( m \)


Which of the following is/are responsible for the higher boiling points of aldehydes and ketones compared to
ethers and hydrocarbons of comparable molecular mass?
A. Intermolecular dipole-dipole interactions between opposite ends of \( C=O \) dipoles
B. Intermolecular hydrogen bonds
c. Dipole induced dipole interactions.
D. All of these


In a photo-electric cell, a retarding
potential of \( 0.5 V \) is required to block
the movement of electrons from the
cathode when monochromatic light of wavelength \( 400 n m \) is incident on its surface. Find the work function of the
material of the cathode.


The time taken by an \( A C \) of frequency
\( \mathbf{5 0} \boldsymbol{H} z \) to complete one cycle will be
A. 2 second
B. 0.2 second
c. 0.02 second
D. 0.002 second


Simplify:
\( -45 p^{3} \div 9 p^{2} \)


Some liquid is filled in a cylindrical
vessel of radius \( R \) Let \( F_{1} \) be the force
applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square
cross-section of side \( \boldsymbol{R} \). Let \( \boldsymbol{F}_{2} \) be the
force applied by the liquid on the bottom of this new vessel. (Neglect atmosphere pressure). Then
\( \mathbf{A} \cdot F_{1}=\pi F_{2} \)
B. \( F_{1}=\frac{F_{2}}{\pi} \)
\( \mathbf{C} \cdot F_{1}=\sqrt{\pi F_{2}} \)
\( \mathbf{D} \cdot F_{1}=F_{2} \)


Two numbers are given as i) 20.96 and
ii) \( 0.0003125 . \) Rounding off above numbers to 3 significant figures will lead to :
A \( . \) i) \( 21.0, \) ii) 312
B . i) 21.0, ii) 3.12 \( \times 10^{-4} \)
\( c \cdot \) i) \( 2.10, \) ii) \( 3.12 \times 10^{-4} \)
4
4


Water flows at the rate of 10 m/minute
through a cylindrical pipe \( 5 m m \) in diameter. How long would it take to fill a
conical vessel whose diameter at the
base is \( 40 \mathrm{cm} \) and depth \( 24 \mathrm{cm} \) ?


Nuclear charge with
decrease in atomic number.
A. increases
B. decreases
c. remains same
D. increases then decreases


Assertion
When charges are shared between any
two bodies no charge is really lost some
loss of energy does occurs.
Reason
Some energy disappears in the form of heat, sparking etc.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The reading of voltmeter and ammeter
in the following figure will respectively
be :
\( A \cdot O \) and \( 2 A \)
B. 2A and OV
c. \( 2 v \) and \( 2 A \)
D. ov and on


The product of two consecutive even
numbers is \( 120 . \) Can you express this information in the form of a Quadratic
Equation? If yes, what would be the resulting Quadratic Equation?


Sulphide ores of metals are usually concentrated by froth floatation process. Which one of the following sulphide ores offers an exception and is concentrated by chemical leaching?
A. Argentite
B. Galena
c. copper pyrite
D. sphalerite


Among the following, the branched chain polymer is:
A. PVC
B. polyester
c. low density polyethylene
D. nylon - 6,6


Three six-faced fair dice are thrown
together let \( P(k) \) denote the probability
that the sum of the numbers appearing
on the dice is \( k(9 \leq k \leq 4) \). Find 54 s where \( \boldsymbol{S}=\sum_{\boldsymbol{k}=\mathbf{9}}^{\mathbf{1 4}} \boldsymbol{P}(\boldsymbol{k}) \)


The electric field in a region of space is given by \( \mathrm{E}=5 \mathrm{i}+2 \mathrm{j} \) N/C. The electric flux
due to this field through an area \( 2 m^{2} \)
lying in the YZ plane, in S.l unit, is
A . 10
B. 20
c. \( 10 \sqrt{2} \)
D. \( 2 \sqrt{29} \)


A car is moving on a circular road of curvature \( 300 \mathrm{m} . \) If the coefficient of
friction is 0.3 and acceleration due to
gravity is \( 10 \mathrm{m} / \mathrm{s}^{2} \), the maximum speed the car can have is:
\( A \cdot 30 \mathrm{km} / \mathrm{hr} \)
B. 81 km/hr
c. \( 108 \mathrm{km} / \mathrm{hr} \)
D. \( 162 \mathrm{km} / \mathrm{hr} \)


When a bacterium is provided with flagella arising from two opposite ends, it is called
A. Monotrichous
B. Lophotrichous
c. Amphitrichous
D. Polytrichous


At \( 0^{\circ} \mathrm{C} \) and a pressure of \( 1000 \mathrm{mm}, \) a given weight of nitrogen occupies a
volume of \( 1.0 l . A t-100^{\circ} C, \) the same
weight of gas under the same pressure occupies a volume of \( 0.61 . \) What is the value of absolute zero in degree Celsius?
A . \( -250^{\circ} \mathrm{C} \)
B. \( 250^{\circ} \mathrm{C} \)
c. \( -273^{\circ} \mathrm{C} \)
D. \( 273^{\circ} \mathrm{C} \)


In a series resonant circuit, the AC voltage across resistance \( R, \) inductor and capacitor \( C \) are \( 5 \vee, 10 \vee \) and \( 10 ~ V \) respectively. The AC voltage applied to the circuit will be
A . \( 10 v \)
B. 25
\( c \cdot 5 v \)
D. 20


What is observed when an emulsion is
centrifuged?


The velocity of a body moving in a straight line is increased by applying a constant force \( F \) for some distance in
the direction of the motion. The increase
in the kinetic energy of the body is equal to
A. the potential energy of the body.
B. the work done by the force on the body.
c. the momentum of the body.
D. the torque on the body.


The formula of tetrachloro methane is:
A \( . C C l H_{3} \)
в. \( C C l_{2} \)
c. \( C H C l_{3} \)
D. \( C C l \)


Monoclinic sulphur is an example of
monoclinic crystal system. What are the
characteristics of the crystal system?
\( \mathbf{A} \cdot \mathbf{a} \neq b \neq c, \alpha=\beta=\gamma=90^{\circ} \)
B \( \cdot a \neq b \neq c, \alpha \neq \beta \neq \gamma \neq 90^{\circ} \)
\( \mathbf{C} \cdot a=b \neq c, \alpha=\beta=\gamma=90^{\circ} \)
D \( \cdot a \neq b \neq c, \alpha=\gamma=90^{\circ}, \beta \neq 90^{\circ} \)


Galvanized iron sheets are coated with:
A. \( C \)
в. \( C u \)
\( c \cdot Z n \)
D. \( N i \)


A ketone has molar mass \( 86 . \) Which of
the following cannot be IUPAC name of this ketone?
A. 2 -pentanone
B. 2-methyl butanone
c. 3 -methyl butanone
D. 3 -pentanone


Write the value of \( x \) for which \( 2 x, x+10 \)
and \( 3 x+2 \) are in \( A . P \)


The shape of \( X e O_{2} F_{2} \) molecule is :
A. tetrahedron
B. pyramid
c. see-saw
D. square planar


lce has lower density than water because :
A. hydrogen bonding
B. hydrogen bonding and cage like structure of ice
c. bent structure of water
D. diamond structure of water


Which of the following produces
colorless gas with dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
This question has multiple correct options
A \( \cdot N a_{2} S_{2} O_{3} \)
в. \( \operatorname{NaH} \mathrm{CO}_{3} \)
c. \( C H_{3} C O_{2} N H_{4} \)
D. All


Mention a cause and symptom of each
of the following
(i) Emphysema
(ii) Renal calculi
(iii) Diarrhoea


Assertion
Dielectric material (dielectric for short)
is an electrical insulator that can be
polarized by an applied electric field.
Reason

Electric field attracts the polarised or
even non polarised atoms in a element
and those atoms get collected on the
Surface
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Fossils are generally found in
A. Sedimentary rocks
B. Igneous rocks
c. Metamorphic rocks
D. Any type of rock


To increase the angular magnification of a simple microscope, one should increase
A. the focal length of the lens
B. the power of the lens
c. the aperture of the lens
D. the object size


Find the surface area of a sphere of
diameter:
\( \mathbf{3 . 5} \mathrm{cm} \)


A solenoid is \( 1.5 m \) long and its inner
diameter is \( 4.0 \mathrm{cm} . \) It has 3 layers of
winding's of 1000 turns each and
carries a current of 2.0 amperes. The magnetic flux for a cross-section of the solenoid is nearly.
A . \( 4.1 \times 10^{-5} \) weber
B. \( 5.2 \times 10^{-5} \) weber
c. \( 6.31 \times 10^{-3} \) weber
D. \( 2.5 \times 10^{-7} \) weber


Assertion
\( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{4} & \mathbf{0} & \mathbf{4} \\ \mathbf{2} & \mathbf{3} & \mathbf{2} \\ \mathbf{1} & \mathbf{2} & \mathbf{1}\end{array}\right], \mathbf{B}^{-\mathbf{1}}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{3} & \mathbf{3} \\ \mathbf{1} & \mathbf{4} & \mathbf{3} \\ \mathbf{1} & \mathbf{3} & \mathbf{4}\end{array}\right] \)
Then \( (A B)^{-1} \) does not exist.
Reason
since \( |\boldsymbol{A}|=\mathbf{0},(\boldsymbol{A B})^{-1}=\boldsymbol{B}^{-1} \boldsymbol{A}^{-1} \) is
meaningless.
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


How are \( g \) and \( G \) related?
A \( \cdot g=\frac{G M}{R^{3}} \)
в. \( g=\frac{M}{G R^{2}} \)
c. \( _{g}=\frac{G M}{R^{2}} \)
D. \( g=\frac{G M}{R} \)


Pick out the wrong statement about
retardation.
A. Retardation is negative acceleration
B. Retardation is rate of decrease of velocity with time
C \( . \) Sl unit of retardation is \( m s^{-2} \)
D. Retardation is a scalar quantity


What is the name for substances that
cannot be broken down into simpler types of matter?
A . Electrons
B. Molecules
c. Nuclei
D. Elements


If \( f \) and \( g \) two function defined on \( N \)
such that \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}2 n-1 i f n \text { isven } \\ 2 n+2 i f \text { is odd }\end{array} \text { and } g(n)=f(n)+\right. \)
Then range of \( g \) is
A \( \cdot\{m \epsilon N: m=\text { multiple of } 4\} \)
B. setofevennaturalnumber
C \( \cdot\{m \epsilon N: m=4 k+3, k i s \text { a natural number }\} \)
D. \( m \epsilon N: m= \) multiple of 3 or multiple of 4


The electronic configuration of
actinides is:
A \( \cdot[\operatorname{Rn}] 5 f^{0-14} 6 d^{0-2} 7 s^{1} \)
B . \( [R n] 5 f^{0-14} 6 d^{0} 7 s^{0} \)
C \( \cdot[R n] 5 f^{0-14} 6 d^{0-2} 7 s^{2} \)
D \cdot \( [R n] 5 f^{0-14} 6 d^{0-2} 7 s^{0} \)


Water as ice has a cooling effect, whereas water as steam may cause
severe burns. Explain these observations:


Q Type your question
\( A \)
\( (a) \)
B.
\( (b) \)
\( \mathbf{C} \)
\( (c) \)
\( D \)
\( (d) \)


Divide
\( 17 \mathrm{km} 250 \mathrm{m} \) by \( 6 \mathrm{m} \)


At an election meeting 10 speakers are to address the meeting. The only protocol to be observed is that whenever they speak P.M. will speak before M.P. and M.P. will speak before M.L.A. In how
many ways can the meeting be addressed?


Where are reflex arcs formed?
\( A \). Brain
B. Spinal chord
c. Muscle
D. skin


A mouse moving along a straight line moves forward \( 8 \mathrm{cm} \) and then backward
\( \mathbf{5} \mathrm{cm} . \) What are the magnitudes of the displacement and distance of the mouse's motion?
A. Displacement : \( 13 \mathrm{cm} ; \) Distance : \( 3 \mathrm{cm} \)
B. Displacement : 3 \( \mathrm{cm} ; \) Distance : \( 13 \mathrm{cm} \)
c. Displacement\( : 13 \mathrm{cm} ; \) Distance \( : 13 \mathrm{cm} \)
D. Displacement : 3 \( c m ; \) Distance : 3 \( c m \)


In the year 2009 , during rainy season of 90 days, it was observed that it rain to
20 days only. Find the probability that it did not rain.


A double convex lens has radii of
curvature of \( 1 \mathrm{m} \) and \( 2 \mathrm{m} \), What should
be the refractive index of the material
such that the focal length of the lens is \( 50 \mathrm{cm} ? \)
A \( \cdot 3 \frac{1}{3} \)
B. \( 2 \frac{1}{3} \)
\( c \cdot_{4} \frac{1}{3} \)
D. 1.13


Write the name of following compounds:
\( (\mathrm{A}) C_{6} H_{5} N_{2}^{\oplus} H S O_{4}^{\ominus} \)
(B) Ref. image
\[
\langle 0\rangle-\mathrm{N}=\mathrm{N}-\sqrt{\bigcirc}\rangle-\mathrm{o} \mathrm{H}
\]


The diagram above represents the energy states for a particular atom.Photons having which of the
following energies could be absorbed by
atoms of this kind in the ground state?
Assume that the absorbed electrons do
not ionize the atom.
\( \mathbf{A} \cdot 7 e V \)
B. 6 eV
\( \mathbf{c} .5 \mathrm{eV} \)
D. \( 4 e V \)
\( \mathrm{E} \cdot 3 \mathrm{eV} \)


The oxidation state of iron in the
coordination sphere of prussian blue is:
\( A \cdot+2 \)
B. 0
\( c \cdot+1 \)
D. +3


Laminarin and mannitol, the reserve
food of brown algae, are
A. lipids
B. complex carbohydrates
C. proteins
D. lipoproteins


What is the length of an arc of a circle with a radius of 5 if it subtends an
angle of \( 60^{\circ} \) at the center?
A . 3.14
B. 5.24
c. 10.48
D . 2.62


When two thin lenses of focal lengths \( f_{1} \)
and \( f_{2} \) are kept coaxially and in contact, prove that their combined focal length "f' is given by \( \frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}} \)


The dimensional formula for plank's
constant and angular momentum are
\( \mathbf{A} \cdot\left[M L^{2} T^{-2}\right] \) and \( \left[M L T^{-1}\right] \)
B \( \cdot\left[M L^{2} T^{-1}\right] \) and \( \left[M L^{2} T^{-1}\right] \)
\( \mathbf{c} \cdot\left[M L^{3} T^{1}\right] \) and \( \left[M L^{2} T^{-2}\right] \)
D・ \( \left[M L^{2} T^{-1}\right] \) and \( \left[M L^{2} T^{-2}\right] \)


A capacitor has a capacitance of 27.0 microfarads
If we triple the area of the plates of the capacitance and cut the distance between the plates to \( 1 / 3 \) of its original value, what is the new capacitance of the capacitor?
A. 243 microfarads
B. 9.0 microfarads
c. 3.0 microfarads
D. 81.0 microfarads
E. 27.0 microfarads


What will be the velocity of the electron when it just reaches the positive plate?
A \( \cdot \sqrt{\frac{2 V e d}{m}} \)
в. \( \sqrt{\frac{2 V e}{m}} \)
c. \( \sqrt{\frac{2 V e}{m d}} \)
D. \( \sqrt{\frac{V e d}{m}} \)


The mean and median of 100 items are
50 and 52 respectively. The value of largest item is \( 100 . \) If was later found that it it 110 and not \( 100 . \) The true mean
and median are:
A. 50.10,51.5
B . 50.10,52
\( c .50,51.5 \)
D. none of these


CFC are not recommended to be used
in refrigerators because they
A. Increase temperature
B. Deplete ozone
c. Affect environment
D. Affect human body


Find the points of maxima, minima and the intervals of monotonicity of the following function:
\( \boldsymbol{y}=\boldsymbol{x}^{4}+\boldsymbol{4} \boldsymbol{x}^{3}-\boldsymbol{8} \boldsymbol{x}^{2}+\boldsymbol{3} \)


At what speed will the velocity head of
stream of water be equal to \( 40 \mathrm{cm} ? \)
\( A \cdot 280 \mathrm{ms}^{-1} \)
в. \( 2.80 \mathrm{cm} / \mathrm{s} \)
c. \( 280 \mathrm{cms}^{-1} \)
D. \( 0.280 \mathrm{m} / \mathrm{s} \)


If the position of the electron is measured within an accuracy of \( \pm \) \( 0.002 \mathrm{nm}, \) calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is \( \frac{h}{4 \pi m} \times 0.05 n m, \) is there any problem in defining this value?


Which of the following substances are crystalline allotrope of carbon?
(i) Diamond (ii) Charcoal (iii) Graphite
(iv) Lamp black (v) Coke (vi) Fullerene
A. (i) to (vi) all
B. (i), (ii) \& (iv)
\( c . \) (i), (iii) \& (vi)
D. (iv), (ii), (v)


A petite young woman of \( 50 k g \) distributes her weight equally over her high-heeled shoes. Each heel has an area of \( 0.75 \mathrm{cm}^{2} . \) Find the pressure
exerted by each heel? Take \( g=10 m / s^{2} \)
A \( .6 .66 \times 10^{6} P a \)
B . \( 3.33 \times 10^{6} P a \)
c. \( 1.67 \times 10^{6} P a \)
D. \( 4.44 \times 10^{6} \mathrm{Pa} \)


The figure showing Fleming's left hand
rule is given. Which figure or thumb
shows the direction of flow of electric
current?
A. First finger
B. Second finger
c. Thumb
D. Small finger


If \( X \) is a \( 2 \times 3 \) matrix such that
\( \left|\boldsymbol{X}^{\boldsymbol{T}} \boldsymbol{X}\right| \neq \mathbf{0} \) and \( \boldsymbol{A}=\boldsymbol{I}_{2}- \)
\( X\left(X^{T} X\right)^{-1} X^{T} \) then \( A^{2} \) is equal to:
\( \left(X^{T} \text { denotes transpose of matrix } X\right) \)
A. \( A \)
B. \( I \)
\( c \cdot A^{-1} \)
D. \( A X \)


An air bubble rises from bottom to top of
a liquid of density \( 1.5 \mathrm{g} / \mathrm{cm}^{3} . \) If its volume is doubled, the depth of liquids is
A. \( 689 \mathrm{cm} \)
B. 398 \( \mathrm{cm} \)
\( c .760 \mathrm{cm} \)
D. 152 \( \mathrm{cm} \)


Which of the following is not a tautology?
A. \( p \rightarrow(p \vee q) \)
в. \( (p \wedge q) \rightarrow p \)
c. \( (p \vee q) \rightarrow(p \wedge(\sim q)) \)
D. \( (p \vee \sim p) \)


What happens to glucose which enters
the nephron along with filterate during excretion in human beings? State two vital functions of kidney.


The sum \( \frac{3}{1.2}, \frac{3}{1.2}, \frac{1}{2}, \frac{4}{2.3}\left(\frac{1}{2}\right)^{2}+\frac{5}{3.4}\left(\frac{1}{2}\right)^{2} \)
A \( \cdot 1-\frac{1}{(n+1) 2^{n}} \)
B. \( 1-\frac{1}{n .2^{n-1}} \)
\( \mathbf{C} \cdot 1=\frac{1}{(n+1) 2^{n}} \)
D. \( \frac{1}{(n-1) 2^{n-1}} \)


LED is better than bulb to use in a tester
as:
A. it glows even when weak current passes through it.
B. it emits more light
c. it is cheaper.
D. all of the above


Number of isomers of hexane.


Which of the following is responsible for the earth's magnetic field?
A. Convective currents in earth's core
B. Diversive current in earth's core
c. Rotationa motion of earth.
D. Translational motion of earth


\( A B C D \) is a rectangle and \( \angle B O C= \)
\( 66^{\circ} . \) The value of \( x \) is
A \( \cdot 104^{\circ} \)
B. \( 114^{\circ} \)
\( c \cdot 60^{\circ} \)
\( D \cdot 33^{\circ} \)


Which of the following statement is
correct:
A. Sodium hydroxide turns blue litmus red.
B. Nitric acid turns red litmus blue.
C. Sodium hydroxide turns red litmus blue
D. tooth decay is caused by the presence of a base


Find the area of the circular park of
Janakpuri whose circumference is
\( 77 m 77 m \)
A \( .671 .87 m^{2} \)
B. \( 331.62 m^{2} \)
\( \mathbf{c} \cdot 471.62 m^{2} \)
D \( .401 .62 m^{2} \)


Nucleic acids are polymers of:
A. Nucleotides
B. Nucleosides
c. Nuclei of heavy metals
D. Proteins


A charge \( q \) is located at the centre of a cube. The electric flux through any face is :
A \( \cdot \frac{\pi q}{6\left(4 \pi \varepsilon_{0}\right)} \)
в. \( \frac{q}{6\left(4 \pi \varepsilon_{0}\right)} \)
c. \( \frac{4 \pi q}{6\left(4 \pi \varepsilon_{0}\right)} \)
D. \( \frac{4 \pi q}{\frac{1}{6}\left(4 \pi \varepsilon_{0}\right)} \)


If the rate of \( V A T \) increases by \( 2 \% \) then selling price of an article goes up by
Rs. 140. Find the marked price of the article
A. \( R s .1000 \)
в. \( R s .7000 \)
c. \( R s .7500 \)
D. \( R s .9000 \)


Water rises in the stem due to
A. Cohesion and transpiration pull
B. Turgor pressure
c. osmotic pressure
D. None of the above


In right triangle \( E D F \) is figure, the
length of \( \overline{D F} \) is \( 2 \mathrm{cm}, \) and the length of EF is \( 7 \mathrm{cm} \). Calculate the measure of
\( \angle E F D, \) to the nearest hundredth of a
degree. (Use \( \left.\sin 73.4^{0}=0.9583\right) \)
\( \mathbf{A} \cdot 15.95^{\circ} \)
в. \( 16.6^{\circ} \)
\( c \cdot 73.40^{\circ} \)
D. \( 90^{\circ} \)
E . 99.9


For the function \( f(x)=x^{2}+2 x+2 \)
the point \( x=-1 \) is a:
A. Point of Inflection
B. Maxima
c. Minima
D. None of these


What is the Sl unit of electric charge?
A . coulombs
B. amperes
c. volts
D. watts


On a dry day, sound travels a certain distance in 10 seconds. What is the time
required for sound to travel the same distance on a humid day. The densities
of dry air and humid air are in the ratio 3: 2:
A. 8.165 sec
B. 7.165 sec
c. 5.165 sec
D. 4.165 sec


An emf can be induced between the two
ends of straight copper wire when it is moved through a uniform magnetic field.
A. True
B. False


Divide \( \left(36 x^{2}-4\right) \) by \( (6 x-2) \)
A. \( 3 x-1 \)
B. \( 3 x+1 \)
c. \( 6 x-2 \)
D. \( 6 x+2 \)


In ethane \( C_{2} H_{6}, \) C-C forms:
A. sigma bond
B. pibond
c. covalent bond
D. electrovalent bond


The level formed due to impurity atom, in the forbidden energy gap, very near to the valence band in a P-type semiconductor is called
A. an acceptor level
B. a donor level
c. a conduction level
D. none of these


Mercury is a good conductor of heat.State true or false.
A . True
B. False


The shortest distance travelled by a
particle performing SHM from its mean position in \( \operatorname{secs} \text { is } 1 / \sqrt{(} 2) \) of its amplitude. Find its time period:
\( A \cdot 8 \)
B. 16
\( c \cdot 4 \)
D.


Birds glide effortlessly in the air with the help of
A. Conduction of heat in the air
B. Radiation of light through the atmosphere
c. convection currents of air
D. More sugar


The potential barrier of a silicon junction diode is \( 0.7 V . \) If the thickness
of the depletion layer in it is \( 10^{-4} \mathrm{cm} \) Then the intensity of electric field across the junction is
A \( \cdot 7 \times 10^{3} V / m \)
в. \( 7 \times 10^{5} V / m \)
C \( .7 \times 10^{-5} V / m \)
D. \( 7 \times 10^{-4} V / m \)


If the points (2,0),(0,1),(4,5) and \( (0, c) \) are concyclic, then the value of \( c \) is This question has multiple correct options
A . -1
B.
c. \( \frac{14}{3} \)
D. \( -\frac{14}{3} \)


Electron density studies have revealed that \( X \) and \( Y \) have an equal number of
electrons.What are \( X \) and \( Y ? \)
\( \mathbf{A} \cdot C a^{+} \) and \( \mathbf{K} \)
B. \( H^{+} \) and \( \mathrm{He} \)
c. \( \mathrm{cl} \) and \( \mathrm{F} \)
D. \( O^{-} \) and \( S^{+} \)
E. None of the above


For a binomial distribution if \( \boldsymbol{P}=\frac{\mathbf{2}}{\mathbf{3}} \)
and \( n=10 \) the probability of mode is
\( ^{\mathbf{A}} \cdot_{^{10}} C_{4}\left(\frac{1}{3}\right)^{7}\left(\frac{2}{3}\right)^{3} \)
\( ^{\mathrm{B}} \cdot_{^{10}} C_{7}\left(\frac{2}{3}\right)^{7}\left(\frac{1}{3}\right)^{3} \)
\( ^{c}\left(\frac{2}{3}\right)^{7}\left(\frac{1}{3}\right)^{3} \)
\( ^{\text {D }}\left(\frac{1}{3}\right)^{7}\left(\frac{2}{3}\right)^{3} \)


Epigynous and unisexual flowers are found in members of family
A. Caryophyllaceae
B. Campanulaceae
c. Myrtaceae
D. Cucurbitaceae


Find the partial fraction \( \frac{2 x+1}{(3 x+2)\left(4 x^{2}+5 x+6\right)} \)


Four similar particles of mass \( \mathrm{m} \) are orbiting in a circle of radius \( r \) in the
same angular direction because of their
mutual gravitational attractive force.
Velocity of a particle is given by
\( A \)
B. \( \sqrt{\frac{G m}{r}} \)
c. \( \sqrt{\frac{G m}{2}(1+2 \sqrt{2})} \)
\( \frac{1}{2}\left[\frac{G m}{r}\left(\frac{1+2 \sqrt{2}}{2}\right)\right]^{\frac{1}{2}} \)


Consider the following liquid-vapour equilibrium
Liquid \rightleftharpoons्<__ACCGRAVE__>ेvapour Which of the following relations is
correct?
\( \mathbf{A} \cdot \frac{d}{d T} \underbrace{I n}_{P}=\frac{-\Delta H_{v}}{R T} \)
в. \( \frac{d n \quad P}{d T^{2}}=\frac{-\triangle H_{v}}{T^{2}} \)
\( ^{\mathrm{c}} \cdot \frac{d \operatorname{In} P}{d T}=\frac{\Delta H_{v}}{R T^{2}} \)
D. \( \frac{d \text { In } G}{d T^{2}}=\frac{\Delta H_{v}}{R T^{2}} \)


Q Type your question
1.5 has a radius of curvature \( 20 \mathrm{cm} . \) The
concave surface has a radius of
curvature \( 60 \mathrm{cm} . \) The convex side is
silvered and placed on a horizontal
surface.
If the concave part is filled with water of
refractive index \( 4 / 3, \) find the distance
through which the pin should be moved
so that the image of the pin again
coincides with the pin?
A. \( \Delta x=1.15 c m, u p \)
B. \( \Delta x=3.15 \mathrm{cm}, \) down
c. \( \Delta x=0.05 c m, u p \)
\( \Delta x=1.15 c m, d o w n \)


Write IUPAC name of the following
compound.
A. 3 -Hydroxy-2-methylpentanoic acid
B. 4 -Methyl-3-hydroxypentanoic acid
c. 3 -hydroxy-4-methylpentanoic acid
D. 2-Methyl-2-hydroxypentanoic acid


Associate law of vector addition is
A. The sum of vectors remains same irrespective of their order or grouping in which they are arranged.
B. The sum of vectors is different irrespective of their order or grouping in which they are arranged.
C. The sum of vectors changes with the change of their order or grouping in which they are arranged
D. None of the above


Among the following, the incorrect
statement is:
A. Cellulose and amylose has 1,4 -glycosidic linkage
B. Maltose and lactose has 1,4-glycosidic linkage
C. Lactose contains \( \beta \) - D-galactose and \( \beta \) -D-glocose
D. Sucrose and amylose has 1,2-glycosidic linkages


A truck and a car are moving with same kinetic energy. They are brought to rest by the application of brakes which provide equal force.
A. both will cover equal distance
B. the truck will cover a greater distance
c. the car will cover a greater distance
D. none of the above


What are inter-halogen compounds?


When common salt is added to a
saturated solution of soap, soap is precipitated. This is based on the principle of
A. Common ion effect
B. Principle of solubility product
c. Adsorption from solution
D. Peptisation


A hollow metallic sphere of radius
\( 10 \mathrm{cm} \) is given a charge of \( 3.2 \times 10^{-9} \mathrm{C} \)
The electric intensity at a point \( 4 \mathrm{cm} \)
from the centre is
A \( \cdot 9 \times 10^{-9} N C^{-1} \)
В. \( 288 N C^{-1} \)
c. \( 2.88 N C^{-1} \)
D. zero


At \( 25^{\circ} C, \) the vapour pressure of methyl alcohol is 96.0 torr. The mole fraction of
\( C H_{3} O H \) in solution in which the
(partial) vapor pressure of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O H} \) is 23.0 torr at \( 25^{\circ} C \) is \( \frac{x}{y} . \) Find \( y-x \)


Electric flux is a
A. scalar
B. vector
c. constant
D. independent


Differentiate with respect to \( x \) :
\( e^{x} \log \sin 2 x \)