The pressure exerted by a liquid column of height h is given by (the symbols have their usual meanings).
\( ^{\mathrm{A}} \cdot \frac{h}{\rho g} \)
в. \( h \rho g \)
\( c \cdot \frac{h}{\rho} \)
D. \( h g \)


An element has 12 neutrons in its
nucleus. To which group of the periodic table it will belong?
\( A \)
B. 2
\( c \cdot 6 \)
D. Impossible to predict


\( \sin ^{-1}(\sin (4))=? \)


A car is traveling is blanked curved road
\( \operatorname{at} \theta=37^{\circ} \) of radius \( 125 \mathrm{m} \). If the
coefficient of friction between the tyres
and road is \( \mu=0.5 \) and \( g=10 m / s^{2} \)
The maximum speed to avoid skidding
is.
A. \( 50 \mathrm{m} / \mathrm{s} \)
B. 25 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 20 m / s \)
D. \( 10 \mathrm{m} / \mathrm{s} \)


The common name, "cream of tartar"
refers to:
\( \mathbf{A} \cdot K H C_{4} H_{4} O_{6} \)
\( \mathbf{B} \cdot K(S b O) C_{4} H_{4} O_{6} \)
\( \mathbf{c} \cdot K N a C_{4} H_{4} O_{6} \)
D. \( M g_{2}(O H)_{2}\left(C_{4} H_{4} O_{6}\right) H_{2} O \)


Show that the points \( A(1,2,7), B(2,6,3) \) and \( C(3,10,-1) \)
are collinear.


If \( f(x)=\int_{-1}^{x}|t| d t, x \geq-1, \) then
A. \( f \) and \( f^{\prime} \) are continuous for \( x+1>0 \)
B. \( f \) is continuous but \( f^{\prime} \) is not continuous for \( x+1>0 \)
\( \mathrm{c} \cdot f \) and \( f^{\prime} \) are not continuous at \( x=0 \)
D. \( f \) is continuous at \( x=0 \) but \( f^{\prime} \) is not so


Which row shows a quantity and an
incorrect unit?
\( \begin{array}{ll}\text { quantity } & \text { unit } \\ \text { A. efficiency } & \text { no unit } \\ \text { B. moment of force } & N m^{-1} \\ \text {C. momentum } & \text { Ns } \\ \text { D. work done } & \text { J }\end{array} \)


Given that \( -6 x=64-2(-x) \)
calculate the value of \( x \)
A . -8
B. -4
\( c \cdot 6 \)
D. 16


Solve the following inequality and show
it graphically:
\( \frac{\boldsymbol{x}+\mathbf{4}}{\boldsymbol{x}-\mathbf{3}}>\mathbf{0}, \boldsymbol{x} \in \boldsymbol{W} \)
\( ^{A} \cdot \underbrace{0}_{-3-2-1} \cdot 1,0 \)
в.
\( c_{1}+ \)\begin{tabular}{ccccccc}
\hline-5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4
\end{tabular}


The H. C. F. of 252,324 and 594 is
A . 36
B. 18
c. 12
D. 6


\( R-X \) bond polarity order is:
A. \( C-F>C-C l>C-B r>C-I \)
в. \( C-C l>C-F>C-B r>C-I \)
c. \( C-B r>C-F>C-I>C-C l \)
D. \( C-I>C-C l>C-B r>C-F \)


In effective resistance between \( C \) and \( B \)
is
A . \( 2 \Omega \)
B. 3\Omega
c. \( 1 \Omega \)
D.


Which are acidic salts?
\( \mathbf{A} \cdot N a H_{2} P O_{2}, N a_{2} H P O_{3} \)
B \( \cdot N a_{2} H P O_{3}, N a_{2} H P O_{4} \)
\( \mathbf{c} \cdot N a H C O_{3}, N a H_{2} P O_{4} \)
D. all of these


Gravitational potential energy of interaction of a system of two particles
of masses \( m_{1} \) and \( m_{2} \) separated by a
distance \( r \)
\( U=-\frac{G m_{1} m_{2}}{r} \)


Among \( \boldsymbol{C a} \boldsymbol{C l}_{2}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \boldsymbol{C a O}, \) which
compound can be used for the drying of ammonia gas? Why?


Write minors and cofactors of the
elements of following determinants
(i) \( \left|\begin{array}{cc}2 & -4 \\ 0 & 3\end{array}\right| \)
(ii) \( \left|\begin{array}{ll}\boldsymbol{a} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{d}\end{array}\right| \)


Consider the reaction: \( N_{2}+3 H_{2} \rightarrow \)
\( 2 N H_{3} . \) It is carried out at constant
temperature and pressure. If \( \Delta H \) and
\( \Delta U \) are the enthalpy and internal energy changes for the reaction respectively, then which of the following expression is true?
\( \mathbf{A} \cdot \Delta H>\Delta U \)
в. \( \Delta H<\Delta U \)
c. \( \Delta H=\Delta U \)
\( \mathbf{D} \cdot \Delta H=0 \)


A ray of light is incident on a plane
mirror and the angle of incidence is \( 25^{\circ} \)
What is the angle of reflection?
A. 0
B. \( 50^{\circ} \)
\( c .90^{\circ} \)
D. \( 25^{\circ} \)


Arrange the following in the increasing order of their basic character:
\( N H_{3}, P H_{3}, A S H_{3}, S b H_{3}, B i H_{3} \)


The question has a paragraph followed by two statements, Statement-1 and
Statement-2. Of the given four alternatives after the statements,
choose the one that describes the
statements.
A thin air film is formed by putting the convex surface of a piano-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

Statement 1: When light reflects from
the air-glass plate interface, the reflected wave suffers a phase change
of \( \pi \)
Statement 2: The centre of the
interference pattern is dark.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1
c. Statement 1 is true but statement 2 is false
D. Both statements 1 and 2 are false


If a specialised cell no longer divides, it is generally locked in which stage of the cell cycle?
A.
B.
\( \mathrm{c} \cdot G_{2} \)
D. \( G_{1} \)


Epithelial tissue with thin flat cells
appearing like packed tiles occur on
A. Inner lining of cheek
B. Inner lining of stomach
c. Inner lining of fallopian tubes
D. Outer surface of ovary


A 5 m potentiometer wire having \( 3 \Omega \) resistance per meter is connected to a storage cell of steady emf \( 2 V \) and internal resistance \( 1 \Omega . \) A primary cell is balanced against \( 3.5 m \) of it. When a resistance of \( \frac{32}{n} \Omega \) is put in series with the storage cell, the null point shifts to
the center of the last wire, i.e., 4.5 m.
What is 'n'?


Rekha borrowed Rs. 40,000 for 3 years
at \( 10 \% \) per annum compound interest. Calculate the interest earned in the
second year.


Two wires of diameter 0.25 cm. one
made of steel and the other made of
brass are loaded as shown in Fig. 9.13
The unloaded length of steel wire is
\( 1.5 m \) and that of load wire is \( 1.0 m \)
Compute the elongation of the steel and
the brass wires.


The range of \( \left|\tan ^{-1} x\right| \) is
\( \mathbf{A} \cdot\left[0, \frac{\pi}{2}\right] \)
В. \( \left[0, \frac{\pi}{2}\right) \)
c. \( \left(0, \frac{\pi}{2}\right) \)
D. \( \left(\frac{-\pi}{2}, \frac{\pi}{2}\right) \)


Internal energy of an ideal gas depends
on:
A. pressure
B. temperature
c. volume
D. none of these


A body of mass \( \mathrm{m} \) is kept on an inclined
plane of inclination \( 30^{0} \) to the
horizontal. If the angle of repose is \( 45^{0} \) static friction on the body is
A \( \cdot \frac{m g}{\sqrt{2}} \)
B. \( \frac{m g}{2} \)
\( \mathrm{c} \cdot \mathrm{mg} \)
D. \( \sqrt{2} m g \)


toppr
Q Type your question.
obtain expressions for impedance of the circuit and phase angle between voltage and current. Find the condition
when current will be in phase with the voltage. What is the circuit in this
condition called?
(ii) In a series LR circuit \( \boldsymbol{X}_{L}=\boldsymbol{R} \) and
power factor of the circuit is \( P_{1} \). When
capacitor with capacitance C such that
\( X_{L}=X_{C} \) is put in series, the power
factor becomes \( P_{2} \). Calculate \( P_{1} / P_{2} \)
OR
(i) Write the function of transformer.
state its principle of working with the help of a diagram. Mention various energy losses in this device.
(ii) The primary coil of an ideal step up transformer has 100 turns and
transformation ratio is also \( 100 . \) The
input voltage and power are respectively \( 220 \mathrm{V} \) and \( 1100 \mathrm{W} \). Calculate
(a) number of turns in secondary
(b) voltage across secondary
(c) current in primary
(d) current in secondary
(e) power in secondary


The wrong statement about colloids is:
A. colloids are heterogeneous mixture.
B. colloids show tyndall effect
C. colloids show Brownian movement
D. particle size in colloids is less than \( 1 \mathrm{nm} \).


Differentiate \( \boldsymbol{f}(\boldsymbol{x}) \) with respect to \( \boldsymbol{g}(\boldsymbol{x}) \)
for the following.
\( \boldsymbol{f}(\boldsymbol{x})=\log _{e} \boldsymbol{x}, \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}} \)


Two bodies at different temperatures are kept in contact. If the body at higher temperature gets hotter than it violates which law of thermodynamics?
A. zeroth law of thermodynamics
B. First law of thermodynamics
c. second law of thermodynamics
D. Third law of thermodynamics


Which is called as Warburg's effect on photosynthesis?
A . Low rate of the process due to \( O_{2} \) supply
B. Low rate of the process due to \( C O_{2} \) supply
c. Both A and B
D. None of the above


What do all acids and bases have in
common?


Find the expansion \( \left(3 x^{2}-2 a x+3 a^{2}\right)^{3} \)
using binomial theorem.


Find the missing terms such that the given polynomial become a perfect square trinomial:
\[
-12 x+9
\]


What is the role of adsorption in froth floatation process used especially for
concentration of sulphide ores?
A. Shape selective catalysts
B. Adsorption of pine oil on sulphide ore particles
c. Adsorption of pine oil on impurities
D. Production of heat in the process of exothermic reaction


The number of value of \( x \) in \( [0,2 \pi] \)
satisfying the equation
\( |\cos x-\sin x| \geq \sqrt{2}, \) is


A cube has a side of length \( 1.2 \times \)
\( 10^{-2} \) m. Calculate its volume?
A \( \cdot 1.7 \times 10^{-6} \mathrm{m}^{3} \)
В. \( 1.73 \times 10^{-6} \mathrm{m}^{3} \)
c. \( 1.70 \times 10^{-6} \mathrm{m}^{3} \)
D. \( 1.732 \times 10^{-6} \mathrm{m}^{3} \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}+\boldsymbol{d} \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x}-\boldsymbol{2} \)
If \( \lim _{x \rightarrow 1} \frac{f(x)}{g(x)}=1 \) and \( \lim _{x \rightarrow 2} \frac{f(x)}{g(x)}=4, \) then
find the value of \( \frac{c^{2}+d^{2}}{a^{2}+b^{2}} \)


\( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \frac{\boldsymbol{x}\left(\boldsymbol{x}^{4}+\mathbf{1}\right)(\boldsymbol{x}+\mathbf{1})+\boldsymbol{x}^{4}+\mathbf{2}}{\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}}, \operatorname{then} \boldsymbol{f}(\boldsymbol{x}) \) is
A. one-one ito
B. many-one onto
c. one-one onto
D. many-one into


Three large plates are arranged as shown. How much charge will flow
through the key k if is closed?
A. \( \frac{5 Q}{6} \)
в. \( \frac{4 Q}{3} \)
\( c \cdot \frac{3 Q}{2} \)
D. None


litre of a sample of \( H_{2} \) is at \( 0^{\circ} C \) and 1
atm pressure.1 litre of another sample
of hydrogen is at \( 0^{\circ} \mathrm{C} \) and 2 atm
pressure. Kinetic energies of the gases are in the ratio of:
A \( \cdot 1: 2 \)
B. 2:1
c. 3:
D. 1:


The long stalk in the stamen is called
A. Pollen tube
B. Anther
c. style
D. Filament


Which of the following is considered as pioneer community in xerarch?
A. Annual herb
B. Perennial herb
c. Scrub stage
D. Lichen


To find the inverse of the matrix \( \boldsymbol{A}= \)
\( [121 ; 011 ; 311] \) by elementary
transformation method


Consider the sequence
\( 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, \dots \) and
so on. Then 1025 th terms will be
A \( \cdot 2^{9} \)
B . \( 2^{11} \)
\( c \cdot 2^{10} \)
D. \( 2^{12} \)


The diameter of an objective of a telescope, which can just resolve two stars situated at an angular
displacement of \( 10^{-4} \) degree, should be
\( \left(\lambda=5000 A^{0}\right) \)
A. 35 mm
B. 35 cm
\( c \cdot 35 m \)
D. None of the above


The displacement of a body is given to be proportional to the cube of time elapsed. If the accerlation is \( x k t \) (where
\( k \text { is proportionality constant }) . \) Find \( x ? \)


The uncertainty in position of an electron \( \left(\boldsymbol{m}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{2 8}} \mathbf{g m}\right) \) moving
with a velocity \( 3 \times 10^{4} \mathrm{cm} / \mathrm{s} \) accurate
upto \( 0.001 \% \) will be:
\( A . \quad 3.84 \mathrm{cm} \)
B. 1.92 \( \mathrm{cm} \)
c. \( 7.68 \mathrm{cm} \)
D. 5.76 cm


The muscular energy required by our body is given to us by:
A. Air
B. water
c. oxygen
D. Food


\( \mathbf{1} \mathbf{0}^{\mathbf{1} \mathbf{0}^{\log _{\mathbf{1 0}} \csc (\mathbf{1 0 x})} \text { differentiate w.r.t. } \boldsymbol{x}} \)


Which of the following elements behaves as a typical non metal?
A.
B. Se
c. \( \mathrm{T} \)
D. Po


Atoms of different elements combine in
A. unequal ratios.
B. prime number ratios.
C. equal ratios.
D. whole number ratios


Buckminsterfullerene is an allotropic
form of:
A. phosphorus
B. sulphur
c. carbon
D. tin


Use analytical geometry to prove that the mid-point of the hypotenuse of a right-angled triangle is equidistant from its vertices.


Which of the following is the greatest user of ground water?
A. Chemical purposes
B. Rural water supply
c. Agriculture
D. None of the above


The density \( \left(\operatorname{in} g m l^{-1}\right) \) of a 3.60 M
sulphuric acid solution that is \( 29 \% \)
\( H_{2} S O_{4}\left(\text { Molar mass }=98 \mathrm{g} \mathrm{mol}^{-1}\right) \mathrm{by} \)
mass will be:
A .1 .64
B. 1.88
c. 1.22
D. 1.45


Bleaching powder is needed in the manufacture of chloroform.
A. True
B. False


The correct IUPAC name is:
\[
\mathrm{CH}_{3} \mathrm{CH}=\mathrm{C}(\mathrm{COOH}) \mathrm{CH}_{2} \mathrm{CH}_{3}
\]
A. 3 -carboxy- 2 -pentene
B. 2 -ethilidene butanoic acid
C. 2 -ethyl-2-butenoic acid
D. 3 -ethyl-2-buten-4-oic acid


From the artg of the periodic table given, answer the following questions
\[
\begin{array}{l}
1 \\
\text { litium }
\end{array}
\]
\( 13 \quad \) carbon
\( \mathbf{1 5} \)
\[
X
\]
\( Y \)
\( Z \)
Name the family of \( L, Q, R, T \).


\( N H_{4} C I(s) \) is heated in a test tube,
vapours are brought in contact with red litmus paper, which changes to blue
and then to red. it is because of :
A . formation of \( N H_{4} O H \) and \( H C I \)
B. formation of \( N H_{3} \) and \( H C I \)
c. greater diffusion of \( N H_{3} \) than \( H C I \)
D. grater diffusion of \( H C I \) than \( N H_{3} \)


Solve \( \lim _{x \rightarrow \infty} \frac{\sqrt{x^{2}+1}-\sqrt[3]{x^{2}+1}}{\sqrt[4]{x^{4}+1}-\sqrt[5]{x^{4}+1}} \)


Two coins are tossed simultaneously.
Write the sample space \( S \) and the
number of sample point \( n(S) . A \) is the
event of getting at least one head. Write
the event \( A \) in set notation and find
\( \boldsymbol{n}(\boldsymbol{A}) \)


Identify the reagent \( A \)
A. Conc.Sulphuric acid
B. Alcoholic KOH
c. Triethyl amine
D. t-Buok


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \sqrt{\mathbf{4} \boldsymbol{a} \boldsymbol{x}-\boldsymbol{x}^{2}},(\boldsymbol{a}>\mathbf{0}) . \) Then
\( f(x) \) has range in
A. \( (0,3 a) \)
В. \( (a, 4 a) \)
c. \( (0,4 a) \)
D. None of the above


Which of the following is an experiment?
A. Tossing a coin
B. Rolling a single 6 - sided dice
c. choosing a marble from a jar
D. All of the above


In active transport, ATP energy is used by carrier proteins to transport materials
A. Against concentration gradient across cell membrane
B. Against concentration gradient across cell wall
c. Along concentration gradient across cell wall
D. Along concentration gradient across cell membrane


Let \( X \) be a random variable which
assumes values \( x_{1}, x_{2}, x_{3}, x_{4} \) such that
\( \mathbf{2} \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_{1}\right)=\mathbf{3} \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_{2}\right)=\boldsymbol{P}(\boldsymbol{X}= \)
\( \left.\boldsymbol{x}_{3}\right)=\mathbf{5} \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_{4}\right) \)
Find the probability distribution of \( \boldsymbol{X} \)


Evaluate the given definite integrals as
limit of sums:
\( \int_{-1}^{1} e^{x} d x \)


Identify the position of the elements having outer electronic configuration
\( n s^{2} n p^{5} \) for \( n=3 \)
A. 17 th group, 3rd period
B. 8th group, sth period
c. 7th group, 5th period
D. 8th group, 4th period


A particle is moving in a circle of radius \( R \) in such a way that at any instant the normal and tangential components of its acceleration are
equal. If its speed at \( t=0 \) is \( v_{o} \) the time
taken to complete the first revolution is
A \( \cdot R / v_{o} \)
в. \( v_{o} / R \)
C \( \cdot\left(R / v_{o}\right) \times\left(1-e^{-2 \pi}\right) \)
D. \( \left(R / v_{o}\right) \times\left(e^{-2 \pi}\right) \)


Which of the following statement(s)
regarding nitrogen sesquioxide is/are
not correct?
A. Dinitrogen sesquioxide is stable only in the liquid state. It dissociates in the vapour phase.
B. Dinitrogen sesquioxide is a neutral oxide
C. Dinitrogen sesquioxide contains a weak \( N-N \) bond.
D. Dinitrogen sesquioxide exists in two different crystalline forms.


The evidence for aquatic origin of Bryophyte is This question has multiple correct options
A. Ciliated sperms
B. Green colour
c. Protonema thread
D. Some are still aquatic


If the mean of the data:
\( 7,8,9,7,8,7, \lambda, 8 \) is \( 8, \) then the variance
of this data is?


Among the following, which plant is completely devoid of roots?
A. ceratophyllum
B. Hydrilla
c. vallisneria
D. Azolla


Find the unknown using an inverse operation:
\( \frac{n}{-4}=-2 \)


There is a -ve charge - \( q \) as shown in the
figure. Take the potential to be zero at
infinity. If \( A \) and \( B \) are two points in the
charge's vicinity, then the potential at-
\( \mathbf{A} \)
\( \mathbf{B} \)
\( -\mathbf{q} \)
This question has multiple correct options
\( \mathbf{A} \cdot A \) is less than at \( B \)
B. \( A \) is more than that at \( B \)
C. \( A \) is greater in magnitude than at \( B \)
D. \( A \) is smaller in magnitude than at \( B \)


Bag I contains 1 white, 2 black and 3 red
balls; Bag II contains 2 white, 1 black and 1 red balls; Bag III contains 4 white,
3 black and 2 red balls. A bag is chosen
at random and two balls are drawn from
it with replacement. They happen to be one white and one red. What is the
probability that they came from Bag III.


ff \( y=\sin \left(\cos ^{-1} x\right) \) and \( x=99, \) then
\( 1 / y^{2} \) is equal to


Assertion: Myelinated nerve fibre are enveloped with Schwann cells, which form a myelin sheath around the axon Reason: Unmyelinated nerve fibre is not enclosed by a Shwann cell and hence does not form a myelin sheath around the axon
A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
c. If assertion is true but reason is false
D. If both assertion and reason are false


The resistance of a conductivity cell
containing \( 0.001 \mathrm{M} \) KCl solution at \( 298 \mathrm{K} \) is \( 1500 \Omega . \) What is the cell constant if
conductivity of \( 0.001 \mathrm{M} \) KCl solution at \( 298 K \) is 0.146 times \( 10^{-3} S c m^{-1} ? \)


The ore copper pyrites has two different metal atoms.
A . True
B. False


toppr \( t \)
Q Type your question
emf induced with time
\( s \)


What should be the projection velocity for a body to reach the same height on the Moon as compared to that on the Earth?
A. Higher velocity on the moon
B. Lower velocity on the moon
c. Same velocity on the moon and earth
D. It depends on the mass of the body


Two materials of dielectric constants
\( k_{1} \) and \( k_{2} \) are introduced to fill the
space between the two parallel plates of
a capacitor as shown in the figure. The
capacitance of the capacitor is :
A \( \cdot \frac{A \in_{0}\left(k_{1}+k_{2}\right)}{2 d} \)
в. \( \frac{2 A \in_{0}}{d}\left(\frac{k_{1} k_{2}}{k_{1}+k_{2}}\right) \)
c. \( \frac{A \in_{0}}{d}\left(\frac{k_{1} k_{2}}{k_{1}+k_{2}}\right) \)
\( \frac{A \epsilon_{0}\left(k_{1}+k_{2}\right)}{2 d k_{2} k} \)


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}(\boldsymbol{O H})- \)
\( \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \stackrel{[\boldsymbol{O}]}{\rightarrow} \boldsymbol{A} \frac{\boldsymbol{C H}_{3} M \boldsymbol{g}-\boldsymbol{I}}{\boldsymbol{H}_{2} \boldsymbol{O} / \boldsymbol{H}^{+}} \boldsymbol{B} \)
What is \( A \) in the given reaction sequence?
A. \( C H_{3}-C H_{2}-C H_{2}-C O-C H_{3} \)
B. \( C H_{3}-C H_{2}-C O-C H_{2}-C H_{3} \)
c. \( C H_{3}-C H_{2}-O-C H_{2}-C H_{2} C H_{3} \)
D. \( C H_{3}-C H_{2}-C H_{2}-C H_{2}-C H O \)


A \( 14.5 \mathrm{kg} \) mass, fastened to the end of a steel wire of unstretched length \( 1.0 \mathrm{m} \) is whirled in a vertical circle with an
angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of
the wire is \( 0.065 \mathrm{cm}^{2} \). Calculate the
elongation of the wire when the mass is at the lowest point of its path.


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


A student is allowed to select at most \( n \)
books from a collection of \( (2 n+1) \)
books. If the total number of ways in
which he can select one book is 63
then the value of \( n \) is
A .2
B. 3
\( c \cdot 4 \)
D. None of these


Which of the following substances are para-magnetic? \( \boldsymbol{B} \boldsymbol{i}, \boldsymbol{A l}, \boldsymbol{C u}, \boldsymbol{C a}, \boldsymbol{P b}, \boldsymbol{N i} \)


A block of mass \( \mathrm{m} \) is in contact with the
cart as shown in figure
The coefficient of static friction
between the block and the cart is. The
acceleration of the cart that will prevent
the block from falling satisfies
A \( \cdot \alpha>\frac{m g}{\mu} \)
B . \( \alpha>\frac{g}{\mu m} \)
c. \( \alpha \geq \frac{g}{\mu} \)
D. \( \alpha<\frac{g}{\mu} \)


Which one of the following is a phenolic resin similar to Bakelite?
A. catalin
B. Melamine
c. celluloid
D. crystalate


\( 500 m L \) of \( 0.2 M \) aqueous solution of
acetic acid is mixed with \( 500 m L \) of
\( 0.2 M H C l \) at \( 25^{\circ} C \)
(a) Calculate the degree of dissociation of acetic acid in the resulting solution and pH of the solution.
(b) If \( 6 g \) of \( N a O H \) is added to the above solution, determine final pH. Assume there is no change in volume on mixing. \( K_{a} \) for acetic acid is \( 1.75 \times 10^{-5} M L^{-1} \)


Which is (are) correct out of the
following:

This question has multiple correct options
A \( \cdot C H_{2}=C H_{2}<H-C \equiv C-H \)
(rate of electrophilic addition)
B.
gena
\( \mathbf{c} \)
substitution reaction)
D.


Two spheres each of mass \( 10^{5} k g \) and
radius \( 10 m \) are kept in contact. Find the force of gravitation acting between them.
A \( \cdot 5.67 \times 10^{-3} N \)
N \( .5 .67 \times 10^{-3} .6 \times 10^{-3} \)
в. \( 6.67 \times 10^{-3} N \)
c. \( 3.67 \times 10^{-3} N \)
D. 2.67 \( \times 10^{-3} N \)


The Sl unit of 'g' is same as that of
A. velocity
B. acceleration
c. force
D. pressure


Nature and properties of soil depends
upon
A. climate
B. weathering process
c. development of soil
D. all of these


What percentage of \( C O_{2} \) flows in blood
in form of bicarbonates?
A . 7\%
B. 23\%
c. 50\%
D. 70\%


In an isosceles triangle \( A B C \) with \( A B= \)
\( A C, B D \) is perpendicular from \( B \) to the side AC. Prove that \( B D^{2}-C D^{2}= \)
\( 2 C D . A D \)


\( \boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
The given reaction is a first order gas reaction with \( k=2.2 \times 10^{-5} s e c^{-1} \) at
\( 320^{\circ} \mathrm{C} . \) What \( \% \) of \( S O_{2} C l_{2} \) is
decomposed on heating this gas for 90
\( \min ? \)
\( \mathbf{A} \cdot 11.2 \% \)
B . 12.3\%
c. \( 13.4 \% \)
D. 14.5\%


Starch and cellulose are the compounds
made up of many units of
A. simple sugar
B. Fatty acid
c. Glycerol
D. Amino acid


Construct a \( 3 \times 2 \) matrix whose
elements are given by \( a_{i j}=2 i-j \)


The minimum value of \( \mathbf{f}(\mathbf{x})= \)
\( 4 \sec ^{2} x+9 \operatorname{cosec}^{2} x \) is
A . 5
B . 25
c. 13
\( D \cdot 13^{2} \)


In an LCR circuit the capacitance is made \( \frac{1}{4} \) then what should be the change in inductance that the circuit remains in resonance again?
\( A \cdot 8 \) times
B. \( \frac{1}{4} \) times
\( c \cdot 2 \) times
D. 4 times


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


If \( l^{2}+m^{2}+n^{2}=5, \) then \( (l m+m n+ \)
\( (n) \) is
\( \mathbf{A} \cdot \geq(-5 / 2) \)
B \( \cdot \geq(-1) \)
\( c \cdot \leq 5 \)
\( D . \leq 3 \)


Two gases \( A \) and \( B \) having same pressure
P, volume \( V \) and temperature \( T \) are mixed. if the mixture has volume and
temperature as \( \mathrm{V} \) and \( \mathrm{T} \) respectively the pressure of mixture is
\( A \cdot 2 P \)
B.
\( c \cdot P / 2 \)
D. \( 4 P \)


A wheel with 8 metallic spokes each 50
\( \mathrm{cm} \) long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place is \( 0.4 \mathrm{G} \) and the angle
of \( 60^{\circ} \).Calculate the emf induced
between the axle and the rim of the
wheel.How will the value of emf be
affected if the number of spokes were increased?


Ascorbic acid resemble the structure of
\( A \). Vitamin A
B. Glucose
c. cellulose
D. Vitamin D


The median of 230 observations of the
following frequency distribution is 46
Find \( a \) and \( b: \)
\( \begin{array}{lllll}\text { Class } & \begin{array}{l}10- \\ 20\end{array} & \begin{array}{l}20- \\ 30\end{array} & \begin{array}{l}\text { 30- } \\ 40\end{array} & \begin{array}{l}\text { 40- } \\ \text { 50 }\end{array}\end{array} \)
12 \( \quad \) 30 Frequency a


Three charges of \( +5 \mu C \) are located at
the comes of an equilateral triangle whose sides are \( 6 \mathrm{cm} \) long. Find the potential at the midpoint of the base of the of the triangle.


The output of NOT gate when its input is
\( \mathbf{0} \)
\( A \). is 1
B. is 0
c. can be 0 or 1
D. is 0 and 1


Two astronauts, each of mass \( 75 k g \), are
floating next to each other in space, outside the space shuttle. They push each other through a distance of an arm's length \( =1 m \) each with a force of
\( 300 N \).If the final relative velocity of the
two, w.r.t each other is \( V_{0} m / s, \) find the value of \( \frac{\left(V_{0}\right)^{2}}{4}( \) Note that both astronauts are displaced by \( 1 \boldsymbol{m} \)


Write two differences between
autotrophic and heterotrophic nutrition.


A solid sphere, a hollow sphere and a solid cylinder, all having equal mass and radius, are placed at the top of an
incline and released. The friction
coefficients between the objects and the incline are equal and but not sufficient to allow pure rolling. Greastest time will be taken in reaching the bottom by
A. The solid sphere
B. The hollow sphere
c. The solid cylinder
D. All will take same time


If \( I=\int_{0}^{2 \pi} e^{x / 2} \sin \left(\frac{x}{2}+\frac{\pi}{4}\right) d x, \) then \( I \)
equals
\( A \)
B.
\( \mathbf{c} \cdot-\pi / 2 \)
D. \( 2 \pi \)


How many electronic charges form 1
coulomb?
A. \( 9.1 \times 10^{-31} \)
B . \( 1.6 \times 10^{18} \)
c. \( 62.5 \times 10^{17} \)
D. \( 1.76 \times 10^{11} \)


Which of the following is used as fuel in an electric generator?
A . Petrol
B. Diesel
c. Kerosene
D. cNG


A farmer has enough food to feed 28 animals in his cattle for 9 days. How long would the food last if there were 8
more animals in his cattle ?
A . 5
B. 7
c. 10
D. None of these


Which of the following cell organelles is associated with photorespiration?
A. Mitochondria
B. Peroxysome
c. chloroplast
D. All of the above


If the volume of a cuboid is \( 3 x^{2}-27 \)
then its possible dimensions are
A. \( 3, x^{2},-27 x \)
в. \( 3, x-3, x+3 \)
c. \( 3, x^{2}, 27 x \)
D. 3,3,3


State True or False.
Batteries are voltaic cells.
A. True
B. False


A solution with negative deviation among the following is:
A. ethanol- acetone
B. chlorobenzene-bromobenzene
c. chloroform-acetone
D. benzene-toluene


Total number of possible shells in
uranium atom is:
(atomic no. \( z=92) \)
A. 7
B.
\( c \cdot 6 \)
D. none of these


Evaluate \( : \lim _{x \rightarrow 1}\left(\frac{1}{1-x}-\frac{3}{1-x^{3}}\right) \)


The hormones used by athletes to increase the mass and strength of muscles is/are
A. estrogens
B. gestogens
c. androgens and testosterone
D. both estrogens and androgens


The angle between two vectors \( \vec{P}= \) \( \mathbf{3} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{Q}}=\mathbf{2} \hat{\mathbf{i}}-\hat{\mathbf{j}}+\mathbf{3} \hat{\boldsymbol{k}} \) is:
A \( \cdot \cos ^{-1}\left[\frac{5}{\sqrt{77}}\right. \)
B. \( \cos ^{-1}\left[\frac{\sqrt{77}}{6.5}\right. \)
\( ^{\mathbf{C}} \cdot \cos ^{-1}\left[\frac{6.5}{\sqrt{77}}\right. \)
D. \( \sin ^{-1}\left[\frac{\sqrt{77}}{6.5}\right. \)


The solubility of a substance is defined as the amount of solute in grams:
A. present in 100 g of the solvent
B. present in 100 g of the solution
c. present in \( 100 \mathrm{mL} \) of the solution
D. present in 1 litre of the solution


A mixture from which some of the
solute particles will settle on standing:
A. Miscible
B. Suspension
c. colloid
D. Saturated
E. Supersaturated


A body is moving on a rough horizontal plate in a circular path being tide to a nail (at the centre) by a string, while the body is in motion the friction force of the body
A. changes direction
B. changes magnitude
c. changes both magnitude and direction
D. none of he above


Reversible processes are always
A. spontaneous
B. Quasi-static
c. Both a and \( b \)
D. None of these


How many primary amines can be
formulated by \( C_{3} H_{9} N \) and how many
\( 1^{\circ} \) hydrogen are associated with carbon
atoms of each compound?
A. Two primary amines [3,6]
B. One primary amine [3]
c. Three primary amines [3,6,6
D. Two primary amines [5,6


Statement (1) : Composition and molecular structure of the reactants
can be changed by having a chemica
change
BECAUSE
Statement (2): It is said to be a
chemical reaction when new
substances and new bonds are formed
and old bonds are broken.
\( A \cdot(1) \) is true
(2) is true, (2) is the correct explanation of
(1)
B. (1) is false, (2) is true
c. (1) is true,
(2) is true
D. (1) is false,
(2) is false
\( E .(1) \) is true,
(2) is false


Points \( A \& B \) are in the first
quadrant:Point 'o' isthe origin. If the slope of \( \mathrm{OA} \) is \( 1, \) slope of \( \mathrm{OB} \) is 7 and OA=OB, then the slope of AB is-
A. \( -1 / 5 \)
B . \( -1 / 4 \)
c. \( -1 / 3 \)
D. \( -1 / 2 \)


Parallel plate condenser having a plate separation d is charged to a potential \( V \) It is then isolated. The intensity of the separation of the plates is then doubled The new electric field intensity is :
A . 2 E
B. E
\( c \cdot E / 4 \)
D. E/2


According to the property of probability, the probability of an event cannot be
A. greater than zero
B. equal to zero
c. less than zero
D. equal to one


\( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{S}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{N} \longrightarrow \boldsymbol{A} \)
\( \boldsymbol{A}+\boldsymbol{Z} \boldsymbol{n} \longrightarrow \boldsymbol{B} \)
\( B \) is a metal. Hence \( A \) and \( B \) is:
A \( \cdot \operatorname{Na}_{2}\left[\operatorname{Zn}(C N)_{4}\right], Z n \)
в. \( \operatorname{Na}\left[\operatorname{Ag}(C N)_{2}\right], \) А \( g \)
c. \( \operatorname{Na}\left[A g(C N)_{4}\right], A g \)
D. \( \operatorname{Na}_{3}\left[\operatorname{Ag}(C N)_{4}\right], A g \)


At what value of \( \eta \) will the velocity of the
disc after the collision reverse its
direction?
A. \( \eta<4 \)
в. \( \eta>4 \)
\( \mathbf{c} \cdot \eta=4 \)
D. \( \eta=0 \)


Write the relationship between angle of incidence 'i', angle of prism 'A' and angle of minimum deviations \( \Delta m \) for a
triangular prism.


Number of structural isomers which
can be obtained theoretically on monochlorination of 2-methylbutane is:
A . 1
B . 2
\( c .3 \)
D. 4


Zwitter ion contains:
A. -ve charge
B. +ve charge
C. both +ve and -ve charge
D. none of the above


Which statement best represents the
principle of conservation of energy?
A. Energy cannot be used faster than it is created.
B. The supply of energy is limited, so energy must be conserved
C. The total energy in a closed system is constant
D. The total energy input to a system is equal to the useful energy output


A running man has half the kinetic
energy of a running boy of half his mass. The man speeds up by \( 1 m / s \) and then
has \( K . E . \) as that of the boy. What were
the original speeds of man and the boy?
A \( \cdot \sqrt{2} m / s ;(2 \sqrt{2}-1) m / s \)
B . \( (\sqrt{2}-1) m / s ; 2(\sqrt{2}-1) m / s \)
c. \( (\sqrt{2}+1) m / s ; 2(\sqrt{2}+1) m / s \)
D. \( (\sqrt{2}+1) m / s ; \sqrt{2} m / s \)


In the expression \( x y^{2}, \) the values of \( x \)
and \( y \) are each decreased \( 25 \% \); the
value of the expression is
A . Decreased 50\%
B. Decreased 75\%
c. Decreased \( 37 / 64 \) of its value
D. Decreased \( 77 / 64 \) of its value
E. None of these


The horizontal distance travelled by a projectile is called its :
A. range
B. trajectory
c. amplitude
D. none of these


Two complex numbers are represented
by ordered pairs \( z_{1}:(a, b) \& z_{2}:(c, d) \)
when these two complex numbers are
equal?
A. If and only if \( a=-c, b=-d \)
B. If and only if \( a=d, b=c \)
c. If and only if \( a=c, b=d \)
D. None of these


A ball is thrown at an angle of incidence
\( \boldsymbol{\theta}^{\prime} \) on a horizontal plane such that the incident direction and the reflected
direction are at right angles to each other if the coefficient of restitution is
'e' then' \( \theta \) 'is equal to
A \( \cdot \tan ^{-1}(e) \)
B \( \cdot \tan ^{-1}(2 e) \)
c. \( \tan ^{-1}(\sqrt{2} e) \)
D. \( \tan ^{-1}(\sqrt{e}) \)


Short / Long type answer type questions. Why does the lymph contain much less proteins than the plasma?


In which of the following groups, the majority of plant orders contain the vascular tissue wherein the vessels and
companion cells are absent in the xylem and phloem?
A. Angiosperms
B. Thallophytes
c. Bryophytes
D. Gymnosperms


Which of the following is not a synthetic polymer?
A. Polyisoprene
B. Polybutadiene
c. Polyethylene terephathalate
D. Polyethylene


Which of the following functions
represent a wave
A \( \cdot(x-v t)^{2} \)
B. \( \log (x+v t) \)
c. \( e^{-(x-v t)^{2}} \)
D. \( \frac{1}{x+v t} \)


If a \( 5 \mathrm{cm} \) long capillary tube with \( 0.1 \mathrm{mm} \)
internal diameter, open at both ends,
is slightly dipped in water having surface tension 75 dyne \( / \mathrm{cm}, \) state whether:
water will overflow out of the upper end
of capillary. Explain your answer


What is the \( p H \) of a solution containing
the following zwitter ion species?


Which of the following is an example of indirect proportion?
A. Number of mangoes in a bag and weight of the bag.
B. Earning and hours worked.
c. More the speed, lesser the time taken
D. None of these.


From figure,which of the curve is
considered as the reversible process?
A. Curve A
B. Curve B
\( c \cdot \) Curve \( C \) and \( D \)
D. None of these


An azeotropic mixture of two liquids
boils at a lower temperature than either of them when :
A . it is saturated
B. it does not deviate from Raoult's law
c. it shows negative deviation from Raoult's law
D. it shows positive deviation from Raoult's law


If we place our hand below a lighted electric bulb. We feel warmer because of
A. convection
B. radiation
c. conduction
D. both A and B


What is the function of the evaporator
in a refrigerator?
A. The evaporator supplies the heat to the substance, which is to be cooled
B. The evaporator absorbs the heat from the atmosphere
c. The evaporator absorbs the heat from the substance which is to be cooled.
D. Both a and


A mixture of ordinary hydrogen and its isotope, tritium (whose nucleus is approximately three times massive than ordinary hydrogen) is excited and its spectrum is studied. Calculate the
shift in wavelength for the \( H_{\alpha} \) lines in
Balmer series. \( \boldsymbol{R}_{\infty}=\mathbf{1 0 9 7 3 7 0 0 m}^{-1} \)
mass of the proton \( M_{H}=1.67 \times \)
\( 10^{-27} k g, \) mass of electron, \( m=9.1 \times \)
\( 10^{-31} k g \)
A \( \cdot \frac{6}{36} R_{H} \)
в. \( \frac{5}{36} R_{H} \)
c. \( \frac{7}{36} R_{H} \)
D. \( \frac{8}{36} R_{H} \)


\( A \subset B \) then show that \( A \cap B \) and \( A \backslash \)
\( B \) (use Venn diagram)


Which option is an example of interest on interest?
A. simple interest
B. compound interest
c. complex interest
D. annual interest


A thin uniform rod of length \( L \) is bent at its mid point as shown in figure. The distance of the centre of mass from the
point \( \boldsymbol{L} \) is
A \( \cdot \frac{L}{4} \)
в. \( \frac{L}{4} \sin (\theta / 2) \)
c. \( \frac{L}{4} \cos (\theta / 2) \)
D. \( \frac{L}{2} \cos (\theta / 2) \)


Which of the following statements is
correct for \( \boldsymbol{C} \boldsymbol{s} \boldsymbol{B} \boldsymbol{r}_{3} \)
A. It is covalent compound
B. It contains \( C s^{3+} \) and \( B r \)
c. It contains \( C s^{+} \) and \( B r_{3}^{-} \)
D. It contains \( C s^{+} \) and \( B r^{-} \) and lattice \( B r_{2} \) molecule


Protozoans thrive successfully in diverse conditions owing to their
A. Motility
B. Rapid reproduction
c. Ability to manufacture food
D. Specialised organelles


What is qualitative analysis?
A. Identification of unknown substance by direct observation
B. Identification of unknown substance by chemical tests
C. Both A \& B
D. None of the above


At a frequency \( \omega_{0} \) the reactance of a certain capacitor equals that of a certain inductor. If frequency is
changed to \( 2 \omega_{0} . \) The ratio of reactance
of the inductor to that of the capacitor is
\( A \cdot 4: 1 \)
B. \( \sqrt{2}: 1 \)
c. \( 1: 2 \sqrt{2} \)
D. 1: 2


If uncertainty in momentum of electron is three times the uncertainty in position, then uncertainty in velocity of electron would be:
A \( \cdot \frac{1}{4 m} \sqrt{\frac{h}{3 \pi}} \)
в. \( \frac{1}{3 m} \sqrt{\frac{h}{\pi}} \)
c. \( \frac{1}{3 m} \sqrt{\frac{4 \pi}{h}} \)
D. \( \frac{1}{2 m} \sqrt{\frac{3 h}{\pi}} \)


The probabilities of three events \( A, B \& \) \( C \operatorname{are} P(A)=0.6, P(B)=0.4 \) and \( P(C)=0.5 \)
If \( P(A \cup B)=0.8, P(A \cap C)=0.3, P(A \cap \)
\( B \cap C)=0.2 \& P(A \cup B \cup C) \geq 0.85 \)
Find the range of \( \mathrm{P}(B \cap C) \)
B . [0.25,0.35]
c. [0.2,0.3]
D. [0.2,0.4]


The surroundings become warm when
water in lakes start freezing in cold
countries. Why?


Fill in the blanks so as to make the
statement true:

Two rational numbers are said to be
equal, if they have the same form.


A boy on a cycle pedals a circle of 20
metres radius at a speed of 20 metre/sec. The combined mass of the
boy and the cycle is 90 kg. The angle that the cycle makes with the vertical so that it may not fall is
\( \left(\boldsymbol{g}=\mathbf{9} . \boldsymbol{8 m} / \mathbf{s e c}^{2}\right) \)
\( \mathbf{A} \cdot 60.25 \)
B . 63.90
c. \( 26.12^{\circ} \)
D. \( 30.00^{\circ} \)


Who conducted in vitro synthesis of
DNA ?


A double convex lens of focal \( 30 \mathrm{cm} \) is made of glass of refractive index 1.6 When it is immersed in a liquid, the focal length becomes \( 126 \mathrm{cm} \). The refractive index of the liquid is :
A . 1.4
B. 1.5
\( c \cdot 1.33 \)
D. 1.6


Most of the plants contain a green colouring pigment which is responsible for photosynthesis. This pigment was named chlorophyll by
A. Melvin Calvin
B. Jean Senebier
c. Julius Robert Mayer
D. Pelletier and Caventou


A square-shaped wire loop of mass \( m \)
resistance \( \boldsymbol{R} \) and side a moving with
speed \( v_{0}, \) parallel to the \( x \) -axis, enters a
region of uniform magnetic field \( B \) which is perpendicular to the plane of the loop. The speed of the loop changes with distance \( x(x<a) \) in the field, as
A \( \cdot v_{0}-\frac{B^{2} a^{2}}{R m} x \)
B. \( _{v_{0}-\frac{B^{2} a^{2}}{2 R m} x} \)
c. \( _{v_{0}+} \frac{B^{2} a}{R m} x \)
D. \( v \)


A ray of light is incident on the plane mirror at rest. The mirror starts turning
at a uniform acceleration of \( \pi r a d / s^{2} \) about an axis in plane of mirror. The reflected ray, at the end of \( \frac{1}{4} s \) must have turned through
A \( .90^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 22.5^{\circ} \)
D. \( 11.25^{\circ} \)


Which one of the following substance possesses the highest elasticity?
A . rubber
B. glass
c. steel
D. copper


How Lewis dot structure helps in understanding bond formation between
atoms?


A cylinder containing an ideal gas is in a vertical position and has a piston of
mass \( M \) that is able to move up or
down without friction. If the
temperature is increased, then :
A. Both \( P \) and \( V \) of the gas will change
B. Only \( P \) will increase according to Charles's law
c. \( V \) will change but not \( P \)
D. \( P \) will change but not \( V \)


The equation \( \boldsymbol{y}=\boldsymbol{4}+\boldsymbol{2} \sin (\boldsymbol{6} \boldsymbol{t}-\boldsymbol{3} \boldsymbol{x}) \)
represents a wave motion with
This question has multiple correct options
A. amplitude 6 units
B. amplitude 2 units
c. wave speed 2 units
D. wave speed \( 1 / 2 \) units


One situation where mean would be
appropriate representative value


A point \( P \) is outside a circle at a
distance of \( 13 \mathrm{cm} \) from its centre.
secant from \( P \) cuts the circle in \( Q \) and
\( R \) such that \( Q R=7 \mathrm{cm} \) and the
segment \( P Q \) of the secant, exterior to
the circle is \( 9 \mathrm{cm} . \) Therefore, the radius
of circle is
A. 3 cm
в. 4 ст
\( c .5 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


Petroleum, Coal and natural gas are fossil fuels.
A . True
B. False


A drug becomes ineffective after \( 30 \% \) decomposition. The original concentration of a sample was \( 5 \mathrm{mg} / \mathrm{ml} \) which becomes \( 4.2 \mathrm{mg} / \mathrm{ml} \) in 20 months. The expiry time of the drug in months assuming the first order decomposition is:
A. 41 months
B. 79 months
c. 20 months
D. 60 months


In an LED, the longer lead is always
connected to the terminal
of the battery and the shorter lead is
connected to the
terminal of the cell (or battery)
A. positive, negative
B. negative, positive
c. positive, neutral
D. neutral, positive


A flywheel making 120 r.p.m is acted upon by a retarding torque producing
angular retardation of \( \pi \) rad/ \( s^{2} \). Time taken by it to come to rest is:
A . 1 s
B. 2 s
c. 3 s
D. 4 s


The total number of species in the
order Welwitchiales is
\( A \cdot 3 \)
B. 5
\( c \)
\( D \)


An object has a mass \( m \) kg on earth.
What will be its mass on the moon?
A. \( m \) kg
в. \( 6 m \) кg
c. \( \frac{m}{6} \) kg
D. zero


The magnetic field at the centre of
circular loop in the circuit carrying
current \( I \) shown in the figure is :
A \( \cdot \frac{\mu_{0}}{4 \pi} \frac{2 I}{r}(1+\pi) \)
в. \( \frac{\mu_{0}}{4 \pi} \frac{2 I}{r}(\pi-1) \)
c. \( \frac{\mu_{0}}{4 \pi} \frac{2 I}{r} \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{I}{r}(\pi+1 \)


The point in the \( x y- \) plane which is
equidistant from (2,0,3),(0,3,2) and (0,0,1) is
A \( .(1,2,3) \)
В. (-3,2,0)
c. (3,-2.0)
D. (3,2,0)
E \( .(3,2,1) \)


Find the gain or loss percent if \( \boldsymbol{C P}= \) Rs. \( \mathbf{7 0 0} \) and \( \boldsymbol{S . P}=\boldsymbol{R s . 6 3 0} \)


Inertia means resistance to the change
of state.
A . True
B. False


Urine is always fluid except in
A. Birds
B. Humans
c. Amphibians
D. Mammals


State Lenz's law.


\( \int \frac{1}{\left(x^{2}-1\right)\left(x^{2}+2\right)} d x= \)
A. \( \frac{1}{3}\left[\frac{1}{2} \log \left|\frac{x+1}{x-1}\right|-\frac{1}{\sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}\right]+c \)
B \( \cdot \frac{1}{3}\left[\frac{1}{2} \log \left|\frac{x-1}{x+1}\right|+\frac{1}{\sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}\right]+c \)
c. \( \frac{1}{3}\left[\frac{1}{2} \log \left|\frac{x-1}{x+1}\right|-\frac{1}{\sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}\right]+c \)
D. \( \frac{1}{3}\left[\frac{1}{3} \log \left|\frac{x-1}{x+1}\right|-\frac{1}{2 \sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}\right]+c \)


A close cylindrical tank of diameter
\( 14 m \) and height \( 5 m \) is made from a
sheet of metal. How much sheet of
metal will be required.


At an examination in which maximum
marks are \( 500 . \) P got \( 10 \% \) less than \( Q, Q \)
\( \operatorname{got} 25 \% \) more than \( \mathrm{R} \) and \( \mathrm{R} \) got \( 20 \% \) less
than S. If P got 360 marks what
percentage of marks was obtained by
?


The points at which the tangents to the curve \( y=x^{3}-12 x+18 \) are parallel to
x-axis are?
A \( \cdot(2,-2),(-2,-34) \)
в. (2,34),(-2,0)
c. (0,34),(-2,0)
D. (2,2),(-2,34)


In how many ways can 21 English and 19 Hindi books be placed in a row so that
no two Hindi are together?
A \( \cdot 1540 \)
B. 1450
\( c \cdot 1504 \)
D. 1405


When the number of turns in a coll is
doubled without any change in the length of the coll, its self-inductance
becomes
A. four times
B. Double
c. Halved
D. Not change


Orthophosphoric acid is commonly known as pyro phosphoric acid.
A. True
B. False


Boron is diagonally related to:
A. boron
B. aluminium
c. magnesium
D. silicon


Hexokinase (Glucose + ATP 一
Glucose \( 6-P+A D P \) ) belongs to the
category
A. Transferases
B. Lysases
c. oxidoreductases
D. Isomerases


Assertion
Number of waves in an orbit of atom is
equal to number of that orbit,
Reason
Number of waves in an orbit is derived by \( \frac{2 \pi r_{n}}{\lambda} \)
Read the above assertion and reason
and choose the correct option regarding
¡t
A. Statement is correct but Explanation is wrong.
B. Statement is wrong but Explanation is correct.
c. Both Statement and Explanation are correct and Explanation is the correct explanation for Statement
D. Both Statement and Explanation are correct but Explanation is not the correct explanation for Statement


A parallel plate capacitor of capacitance \( C \) is connected to a battery and is charge to a potential difference
\( V . \) Another capacitor of capacitor \( 2 C \) is similarly charged to a potential
difference \( 2 V . \) The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is:
A . zero
B \( \cdot(3 / 2) C V^{2} \)
\( \mathbf{c} \cdot 25 / 6 C V^{2} \)
\( \mathbf{D} \cdot(9 / 2) C V^{2} \)


A uniform cylinder of mass \( M \) and
radius \( R \) has a string wrapped around
it. The string is held fixed and the
cylinder falls vertically, as in figure. Show that the acceleration of the
cylinder is downward with magnitude \( \boldsymbol{a}=\frac{\mathbf{2} \boldsymbol{g}}{\mathbf{3}} \)


Light is
A. An electromagnetic radiation
B. A transverse wave
c. Massless
D. All of the above


Two radioactive substances \( X \) and \( Y \)
initially contain equal number of atoms
Their half-lives are 1 hour and 2 hours
respectively. Then the ratio of their rates of disintegration after four hours is:
A . 1: 1
B . 2: 1
c. 1: 2
D. 2: 3


Organisms attached to substratum
generally possess
A. Asymmetrical body
B. Radial symmetry
c. one single opening of digestive canal
D. cilia on the surface to create water current


The diagram given shows a piston fitted
in a cylinder. The most suitable
inference that can be drawn from it is
that
A. the piston is smooth
B. the particles can be compressed or brought closer by applying pressure
c. the handle of piston is long
D. None of the above


gravity \( g \) with distance \( d \) trom centre of
the earth is best represented by \( (\boldsymbol{R}= \)
Earths radius):
\( A \)
\( B \)
\( c \)
\( D \)


The function of adding cryolite in the electrolyte reduction of alumina by HallHeroult process is to:
This question has multiple correct options
A. dissolve alumina
B. lower melting point of alumina
c. lower the fuel bill
D. increase the electrical conductivity of alumina


Assertion
Assertion : The elastic spring force arises due to the net attraction or
repulsion between the neighbouring atoms of the spring when it is elongated or compressed.
Reason
Reason: The laws of derived forces such
as spring force, friction force are
independent of the laws of fundamental
forces in nature.
A. both assertion and reason are true and reason is the correct explanation of assertion.
B. both assertion and reason are true and reason is not the correct explanation of assertion.
c. assertion is true but reason is false
D. both assertion and reason are false.


The diagram above shows a positively charged particle moving toward the right and about to enter a magnetic
field whose direction is shown by the
blue arrows.
What is the direction of the force on the
positively charged particle (from our point of view at the instant it enters the
magnetic field?
A. Right
B. Left
c. up
D. Toward us
E. Away from us


is a list of numbers in which
each term is obtained by adding a fixed number to the preceding term except
the first term.
A . Geometric value
B. Geometric series
c. Arithmetic progression
D. Arithmetic mean


An organic compound \( (A) \) of molecular
formula \( C_{2} H_{5} N O \) reacts with
\( B r_{2} / N a O H \) to give compound \( (B) \) of molecular formula \( \boldsymbol{C} \boldsymbol{H}_{5} \boldsymbol{N} .(\boldsymbol{A}) \) is
reduced by \( L i A l H_{4} \) to give cmpound
\( (C) \) of formula \( C_{2} H_{7} N . \) Identify \( (A),(B) \) and \( (C) \)


\( \boldsymbol{X} \boldsymbol{C l}_{2}(\boldsymbol{e} \boldsymbol{x} \boldsymbol{c e s s})+\boldsymbol{Y} \boldsymbol{C l}_{2} \longrightarrow \boldsymbol{X} \boldsymbol{C l}_{4}+ \)
\( \boldsymbol{Y} \downarrow \)
\( \boldsymbol{Y} \boldsymbol{O} \frac{\boldsymbol{\Delta}}{>400} \frac{1}{2} \boldsymbol{O}_{2}+\boldsymbol{Y} \)
Ore of \( Y \) would be:
A. Siderite
B. Malachite
c. Hornsilver
D. cinnabar


Say true or false:
The zeros of the polynomial \( x^{2}-14 x+ \)
49 are equal to 7
A. True
B. False


8 drops of equal radius coleasec to form
a bigger drop. The ratio of surface energy of bigger drop to smaller one is?
A . 1: 2
B . 2: 1
c. 1: 4
D. 4: 1


\( \lim _{x \rightarrow 0} \frac{x-\sin x}{x+\cos ^{2} x}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D.


The volume of a cube is increasing at
the rate of \( 8 c m^{3} / s . \) How fast is
the surface area increasing when the
length of an edge is \( 12 \mathrm{cm} ? \)


What happens when both of the orbitals in a molecule are in phase, either both
positive or both negative and the electrons in the bonds are at their
lowest energy level?
A. Bonding takes place.
B. The chemicals don't react.
c. The atoms don't bond
D. Bonding doesn't take place.
E. The electrons in the atoms don't share orbitals


The clinical thermometer is designed to
measure the temperature of
A. Human body
B. Bodies kept in refrigerators
c. Room temperature
D. boiling water


Lysigenous cavity and 'Y'-shaped xylem
occurs in
A. Dicot stem
B. Monocot root
c. Monocot stem
D. Dicot root


Temperature is considered as the most ecologically relevant environmental factor because it affects of
organisms
A. physiology
B. morphology
c. geographical distribution
D. all of these


Give the IUPAC names of the following compounds:
Oxalic acid


In which of the following process, the bond order increases and magnetic behaviour changes?
\( \mathbf{A} \cdot N_{2} \longrightarrow N_{2}^{+} \)
B . \( C_{2} \longrightarrow C_{2}^{+} \)
c. \( N O \rightarrow N O^{+} \)
D. \( O_{2} \rightarrow O_{2}^{+} \)


In Albugo, the food reserve is mostly
A. Glycogen
B. Volutin granules
C. Protien granules
D. Fat


Draw a diagram of AC generator and describe it. Derive an expression for instantaneous value of induced emf


Draw the tangents to the circle from the
point \( L \) with radius \( 2.9 \mathrm{cm} . \) Point \( ^{\prime} L^{\prime} \) is
at a distance \( 7.5 \mathrm{cm} \) from the centre
\( \boldsymbol{M}^{\prime} \)


Write the full form of G-6-PD


A particle is travelling in a circular path of radius 4 m. At certain instant the
particle is moving at \( 20 \mathrm{m} / \mathrm{s} \) and its
acceleration is at an angle of \( 37^{\circ} \) from the direction to the centre of the circle
as seen from the particle.
(i) At what rate is the speed of the particle increasing?
(ii) What is the magnitude of the acceleration?


Assertion
A rate of reaction of most of the
reactions doubles, when temperature
increased from \( 298 K \) to \( 308 K \)
Reason

The activation energy of reaction
decreases with increase in
temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


How many obligate categories constitute hierarchy of categories?


What is the oxidation state of coloured
ion in \( \boldsymbol{C r} \boldsymbol{O}_{4}^{2-} \) ?


Explain the following:
Concentrated nitric acid appears yellow when it is left standing in a glass bottle.


2.5 molar sulphuric acid contains:
This question has multiple correct options
A. \( 29.5 \mathrm{g} \) of sulphuric acid per litre of solution.
B. \( 245.0 \mathrm{g} \) of sulphuric acid per \( 1000 \mathrm{ml} \) of solution.
C. \( 24.5 \mathrm{g} \) of sulphuric acid per \( 100 \mathrm{ml} \) of solution.
D. 59.0 g of sulphuric acid per litre of solution.


Can we get hydrogen and oxygen by setting up an arrangement for passing current through distilled water? Why?


When the angle of incidence on a
material is \( 60^{\circ} \), the reflected light is
completely polarised. The velocity of the refracted ray inside the material is
A . \( 3 \times 10^{8} \)
B. \( \frac{3}{\sqrt{2}} \times 10^{8} \)
c. \( \sqrt{3} \times 10^{8} \)
D. \( 0.5 \times 10^{8} \)


When the coil and magnet both are stationary
A. voltage increased
B. current is induced
c. voltage is induced
\( D . \) none


The period of a simple pendulum inside a satellite orbiting earth is
A . zero
B. \( \infty \)
c. can be any integer
D. cant say


The common chord of the circles \( x^{2}+ \)
\( \boldsymbol{y}^{2}-\mathbf{4} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{y}^{2}=\mathbf{3} \mathbf{2} \)
subtends at the origin an angle equal to
A \( \cdot \frac{\pi}{3} \)
B.
c.
D.


The graph between applied force and change in the length of wire within elastic limit is a
A. Straight line with positive slope
B. Straight line with negative slope
c. curve with positive slope
D. curve with negative slope


A kite is flying with the string inclined
at \( 75^{\circ} \) to the horizon. If the length of the
string is \( 25 m \), then height of the kite is :
A \( \cdot\left(\frac{25}{2}\right)(\sqrt{3}-1)^{2} \)
B. \( \left(\frac{25}{2}\right)\left(\frac{\sqrt{3}+1}{\sqrt{2}}\right) \)
c. \( \left(\frac{25}{2}\right)(\sqrt{3}+1)^{2} \)
D. \( \left(\frac{25}{2}\right)(\sqrt{6}+\sqrt{2}) \)


What do you mean by the following:
i. Sewage
ii. Eutrophication
iii. Recycling


If copper is kept open in air, it slowly loses its shining brown surface and gains a green coating. It is due to the formation of:
A \( \cdot C u S O_{4} \)
в. \( C u C O_{3} \)
\( \mathbf{c} \cdot C u\left(N O_{3}\right)_{2} \)
D. \( C u O \)


The D.E whose solution is \( y=\left(c_{1} x+\right. \)
\( \left.c_{2}\right) e^{5 x}: \)
A \( \cdot y_{2}+10 y_{1}+24 y=0 \)
B \( \cdot y_{2}-10 y_{1}+25 y=0 \)
c. \( y_{2}-5 y_{1}+25 y=0 \)
D. \( y_{2}-5 y_{1}+10 y=0 \)


The area bounded by \( |y|=1-x^{2} \) is
\( A \cdot 8 / 3 \)
в. \( 4 / 3 \)
\( \mathrm{c} \cdot 16 / 3 \)
D. None of these


For a sequence if \( S_{n}=\frac{4^{n}-3^{n}}{3^{n}} \) find the
nth term hence show that if it is a G.P


If a vector \( A \) is given as \( A=4 \hat{i}+3 \hat{j}+ \) \( 12 \hat{k}, \) then the angle subtended with the
x-axis is :
\( ^{\mathbf{A}} \cdot \sin ^{-1}\left[\frac{4}{13}\right] \)
B. \( \sin ^{-1}\left[\frac{3}{13}\right] \)
\( ^{\mathbf{c}} \cdot \cos ^{-1}\left[\frac{3}{13}\right] \)
D. \( \cos ^{-1}\left[\frac{4}{13}\right] \)


Explain, with the help of potential energy diagram, effect of temperature
on the rate of reaction.


In the reaction,
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g)-180.7 k J \)
on increasing the temperature, the production of \( \boldsymbol{N} \boldsymbol{O} \)
A. increases
B. decreases
c. remains same
D. cannot be predicted


In an experiment electrons are accelerated,from rest, by applying a
voltage of \( 500 V . \) Calculate the radius of
the path if a magnetic field \( 100 m T \) is then applied.[Charge of the electron = \( 1.6 \times 10^{-19} C \) Mass of the electron \( = \)
\( 9.1 \times 10^{-31} k g \)
A. \( 7.5 \times 10^{-4} m \)
В. \( 7.5 \times 10^{-3} m \)
\( c .7 .5 m \)
D. \( 7.5 \times 10^{-2} \mathrm{m} \)


If an object is placed symmetrically between two plane mirrors inclined at
an angle of \( 72^{\circ}, \) then the total number of
images formed is:
A . 5
B. 4
\( c \cdot 2 \)
D. Infinite


The shape of a polypeptide chain in a protein comes under:
A. primary structure of proteins
B. secondary structure of proteins
c. tertiary structure of proteins
D. none of these


Light travel in straight lines.
A. True
B. False


The process of burning a substance in the presence of air with the evolution of heat is called as
A. distillation
B. carbonisation
c. combustion
D. refining


When a rod of length I is rotated with angular velocity of \( \omega \) in a perpendicular field of induction \( \mathrm{B} \), about one end, the
emf across its ends is
\( \mathbf{A} \cdot B l^{2} \omega \)
в. \( \frac{B l^{2} \omega}{2} \)
\( c . B l \omega \)
D. \( \frac{B l \omega}{2} \)


The weight of gold formed when 1 faraday of electricity is passed through water solution of gold (III) chloride is :
A. One gram atom of Au
B. 2 gram atom of Au
c. 3 gram atom of Au
D. \( 1 / 3 \) gram atom of Au


A body is executing \( \mathrm{SHM} \), At a displacement \( x, \) its potential energy is
\( E_{1} \) and at a displacement \( y, \) its
potential energy is \( E_{2} \). Find its potential energy \( \mathrm{E} \) at displacement \( (\mathrm{x}+\mathrm{y}) \)
B . \( \sqrt{E}=\sqrt{E}_{1}+\sqrt{E}_{2} \)
c. none of these
D. all of these


f \( P(x, y) \) is such that \( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \mathbf{1} \\ \boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \boldsymbol{1}\end{array}\right|+\left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{y} & \mathbf{1} \\ \boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \boldsymbol{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & 1\end{array}\right|=\mathbf{0} \) then the
line through \( A \) and \( P \) is
A. median of \( \Delta A B C \)
B. bisector of \( \angle A \)
c. altitude through vertex \( A \)
D. perpendicular bisector of the side \( B C \)


An object \( A \) is placed on the principal
axis of a convex mirror at a distance of
\( 60 \mathrm{cm} \) in front of it. A plane mirror is
inserted between the object and the
convex mirror at a distance of \( 40 \mathrm{cm} \)
from the object with the reflecting
surface of the plane mirror facing the
object. If the images formed by the two
mirrors coincide, find the focal length of
the convex mirror.
A. \( 15 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)


For all \( n \in N, n^{4} \) is less than
A \( \cdot 10^{n} \)
B . \( 4^{n} \)
\( c \cdot 10^{10} \)
D. None of these


Find the height of a cuboid whose base
area is \( 180 \mathrm{cm}^{2} \) and volume is \( 900 \mathrm{cm}^{3} \) ?


Where are the transition metals in the
periodic table?
A. In group o
B. In group 1
c. In group 2
D. In a central block from 3-12 group number


Which process is important for the production of gametes in living organism performing sexual production
in context with chromosomes?
A. Unequal fission
B. Meiosis
c. Mitosis
D. Multiple fission


A ball after having fallen from rest under the influence of gravity for \( 6 s \) crashes through a horizontal glass plate, thereby losing two-third of its velocity. Then it reaches the ground in
\( 2 s, \) height of the plate above the ground
is
\( \mathbf{A} \cdot 19.6 m \)
B. \( 39.2 m \)
c. \( 58.8 m \)
D. \( 78.4 m \)


In Wheatstone's bridge, three resistors
\( P, Q, R \) are connected in three arms in
order and \( 4^{t h} \) arm \( \mathrm{S} \) is formed by two
resistors \( s_{1} \) and \( s_{2} \) connected in
parallel. The condition for bridge to be balanced is: \( \frac{P}{Q}= \)
A \( \cdot \frac{R\left(s_{1}+s_{2}\right)}{s_{1} s_{2}} \)
В. \( \frac{s_{1} s_{2}}{R\left(s_{1}+s_{2}\right)} \)
c. \( \frac{R s_{1} s_{2}}{\left(s_{1}+s_{2}\right)} \)
D. \( \frac{\left(s_{1}+s_{2}\right)}{R s_{1} s_{2}} \)


Find the smallest number by which 12748 be multiplied so that the product is a perfect square.
A. 3187
в. 7814
c. 4577
D. 1842


Give the scientific term used for insect
pollinated plants and one example.


During the charging of lead accumulator battery voltage varies from:
\( \mathbf{A} \cdot 2 \cdot 15 \vee \) to \( 1.88 \mathrm{v} \)
в. 1.88 V to 2.0 v
c. \( 1.88 \vee \) to 2.15 v
D. does not change


\( \int \frac{1}{x \log x[\log (\log x)]} d x= \)
\( \mathbf{A} \cdot \log |\log (\log x)|+c \)
\( \mathbf{B} \cdot \log |\log x|+c \)
\( \mathbf{c} \cdot-\log |\log x|+c \)
\( \mathbf{D} \cdot-\log |\log (\log x)|+c \)


Elliptical model of atoms is proposed by:
A. Sommer Field
B. Ruther Ford
c. Both (a) and (b) above
D. None of these


In a nuclear reactor, what is the
function of a moderator?


Of the given compounds, which one is
not an isomer of others?
\( \mathbf{A} \)
B. II
c. ॥
D. IV


If the electric field in some region of
space is zero,
A. it implies that there is no electric charge in that region.
B. it implies that there is electric charge in that region.
C. it does not imply anything concrete about the charges in the region.
D. it means there is discharging in the region


Given \( \overrightarrow{\boldsymbol{F}}=(4 \hat{\boldsymbol{i}}-10 \hat{\boldsymbol{j}}) \) and \( \overrightarrow{\boldsymbol{r}}=(-5 \hat{\boldsymbol{i}}- \)
\( 3 \hat{j}), \) then compute torque.
\( \mathbf{A} \cdot-62 \hat{j} \) unit
B. \( 62 \hat{k} \) unit
c. \( 48 \hat{i} \) unit
D. \( -48 \hat{k} \) unit


What is the measures of central
tendency for the data set \( \mathbf{5}, \mathbf{5}, \mathbf{1 0}, \mathbf{1 0}, \mathbf{5}, \mathbf{2 0}, \mathbf{2 5} ? \)


The columns of the periodic table are called groups.
A . True
B. False


For the chemical
reaction, equilibrium was established by taking 4 moles of \( A \) and 6 moles of \( B \) initially. If at equilibrium total pressure is 10 atm and equilibrium constant of the reaction is \( \frac{10^{39}}{6} \) at \( m^{4} \), then value of
\( \left[\frac{P_{C}+P_{D}}{2}\right] \) at equilibrium is:
\[
2 A(g)+3 B(g) \rightleftharpoons 4 C(g)+5 D(g)
\]


Two identical ladders, each of mass \( \mathrm{M} \)
and length I are resting on a rough
horizontal surface as shown in Fig.
block of mass \( \mathrm{m} \) hangs from P. If the
system is in equilibrium, find the
magnitude and the direction of
frictional force at \( A \) and \( B \)


The value of
\( \lim _{x \rightarrow a} \frac{\sqrt{x-b}-\sqrt{a-b}}{x^{2}-a^{2}}(a>b) \) is
A \( \cdot \frac{1}{4 a} \)
B. \( \frac{1}{a \sqrt{a-b}} \)
c. \( \frac{1}{2 a \sqrt{a-b}} \)
D. \( \frac{1}{4 a \sqrt{a-b}} \)


Which area on the Earth receives
maximum sunlight ?
A. Polar region
B. Equatorial region
c. Along the latitude of Tropic of Cancer
D. Along the latitude of Tropic of Capricorn


Find \( x \) so that the point (6,5,-3) is at a distance of 13 from the point \( (x,-7,0) \)


An element X has low ionization energy
and another element Y has high electron affinity. The bond formed
between them could be:
A . ionic
B. polar covalent
c. co-ordinate covalent
D. non polar covalent


Find the number of rectangles formed on a chessboard:
A . 1296
B. 1452
\( c \cdot 1528 \)
D. 1614


The factors of \( 1-p^{3} \) are
A \( \cdot(1-p)\left(1+p+p^{2}\right) \)
B \( \cdot(1+p)\left(1-p-p^{2}\right) \)
C . \( (1+p)\left(1+p^{2}\right) \)
D. \( (1+p)\left(1-p^{2}\right) \)


Identify the logic gate whose truth table is given below and draw its symbol:
\( \begin{array}{ccc}\boldsymbol{A} & \boldsymbol{B} & \boldsymbol{Y} \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array} \)


If the arithmetic mean of \( a \) and \( b \) is
double of their geometric mean, with \( a>b>0, \) then a possible value for the ratio \( \frac{a}{b}, \) to the nearest integer, is
A. 5
B. 8
\( c \cdot 11 \)
D. 14


0.15 mole of pyridium chloride has been
added into \( 500 c m^{3} \) of \( 0.2 M \) pyridine
solution. Calculate pH and hydroxyl ion concentration in the resulting solution assuming no change in volume. \( \left(K_{b} \text { for pyridine }=1.5 \times 10^{-9} M\right) \)


A steel ball of mass 'm' falls in a viscous
liquid with a terminal velocity \( 4 m s^{-1} .1 \)
another steel ball of mass \( 8 \mathrm{m} \) falls
through the same liquid then its terminal velocity is
\( \mathbf{A} \cdot 4 m s^{-1} \)
B. \( 8 m s^{-1} \)
\( \mathrm{c} \cdot 16 \mathrm{ms}^{-1} \)
D. \( 2 m s^{-1} \)


Find the area of the triangle whose
vertices are:
\( (\mathrm{i})(2,3),(-1,0),(2,-4) \)
\( (i i)(-5,-1),(3,-5),(5,2) \)
This question has multiple correct options
A. (i) 32 sq. units
B. (ii) 32 sq. units
c. (ii) 10.5 sq. units
D. (i) 10.5 sq. units


In which of the following phenomena, the heat waves travel along straight lines with the speed of light?
A. Thermal conduction
B. Forced convection
c. Natural convection
D. Thermal radiation


Name the isotope of hydrogen which is radio active.


Draw a line segment of length \( 6.3 \mathrm{cm} \) \&
divide it in the ratio \( 3: 4 . \) Measure the
two parts.


\( \sin ^{-1} 0 \) is equal to:
\( \mathbf{A} \cdot \mathbf{0} \)
в.
c. \( \frac{\pi}{2} \)
D. \( \frac{\pi}{3} \)


An example of the odd number of terms in an arithmetic progression written in a symmetrical format is?
A \( . a-d, a, a+d \)
в. \( a, a+d, a+2 d \).
c. \( a-2 d, a-d, a \)
D. \( a-d, a+d, a+3 d \)


If the probability of winning a game is
\( 0.07, \) what is the probability of losing it
\( ? \)


How many point charges of same magnitude are required to constitute an electric dipole?


The following distribution gives the mass of 48 objects measured to the nearest gram. Draw a histogram to illustrate the data.
\( \begin{array}{llll}\text { Mass } & \mathbf{1 0}- & \mathbf{2 0}- & \mathbf{2 5}- \\ \text { in } & \mathbf{1 9} & \mathbf{2 4} & \mathbf{3 4}\end{array} \)
\( (g m s) \)
No. o objects


Some properties of sulphuric acid are listed below. Choose the role played by
sulphuric acid as \( A, B, C \) or \( D \) which is
responsible for the reaction
(i) to (v).
Some role/s may be repeated:
\( M g O+H_{2} S O_{4} \rightarrow M g S O_{4}+H_{2} O \)
A . Dilute acid
B. Dehydrating agent
c. Non-volatile acid
D. oxidising agent


The shape of a garden is rectangular in the middle and semi-circular at the
ends as shown in the diagram. Find the
area and the perimeter of this garden. [Length of the rectangle is \( 20-(3.5+ \)
3.5 ) metres \( ] \)
A \( \cdot 129.5 \mathrm{m}^{2} ; 48 \mathrm{m} \)
B . \( 179.5 \mathrm{m}^{2} ; 48 \mathrm{m} \)
c. \( 129.5 \mathrm{cm}^{2} ; 48 \mathrm{m} \)
D. \( 129.5 \mathrm{m}^{2} ; 88 \mathrm{cm} \)


The smallest distance between the
planes and the time when this occurs are: (nearly)
\( \left(\operatorname{given} \tan ^{-1}\left(\frac{128}{252}\right)=\tan ^{-1}\left(26.9^{0}\right)\right) \)
A. \( 54 \mathrm{km}, 98 \mathrm{s} \)
B. \( 98 \mathrm{km}, 54 \mathrm{s} \)
\( c .27 \mathrm{km}, 189 \mathrm{s} \)
D. \( 189 \mathrm{km}, 54 \mathrm{s} \)


Solid crystalline \( P C I_{5} \) has structure
which of the following?
A. Bi-pyramidal
B. Octahedral and tetrahedral ions
c. Square-pyramidal
D. Pentagonal


When do the oogenesis and the spermatogenesis initiate in human females and males respectively?


Very Short Answer Types:
In which phase, the synthesis of new DNA molecules takes place?


A body starting from rest with uniform acceleration travels distance \( s_{1} \) in the
first \( t \) second and travels a distance \( s_{2} \)
with uniform velocity in the next \( 2 t \) second. Then:
A \( \cdot s_{2}=4 s_{1} \)
В. \( s_{2}=2 s_{1} \)
\( \mathbf{c} \cdot s_{1}=4 s_{1} \)
D. \( s_{1}=2 s_{2} \)


An optician while testing the eyes finds the vision of a patient to be \( 6 / 12 . \) By this he means that:
A. The person can read the letters of 6 inches from a distance of 12 \( \mathrm{m} \)
B. The person can read the letters of 12 inches from 6 \( \mathrm{m} \).
C. The person can read the letters from 6 \( \mathrm{m} \) which the normal eye can read from 12 \( \mathrm{m} \)
D. The focal length of eye lens has become half that of the normal eye


Find the 10 th term of a geometric
sequence if \( a_{1}=45 \) and the common
ratio \( r=\mathbf{0 . 2} \)


State whether the following statement
is true or false.
All squares are congruent.
A. True
B. False


General electronic configuration of
lanthanides are:
\( \mathbf{A} \cdot(n-2) f^{1-14}(n-1) s^{2} p^{6} d^{0-1} n s^{2} \)
B \( \cdot(n-2) f^{10-14}(n-1) d^{0-1} n s^{2} \)
C \( \cdot(n-2) f^{0-14}(n-1) d^{10} n s^{2} \)
D. \( (n-2) f^{0-1}(n-1) f^{1-14} n s^{2} \)


The coagulating effect is maximum
when the charge of the ion is +1
If true enter 1 else enter 0 .


Unpolarized light of intensity \( \boldsymbol{I}_{\mathbf{0}} \) is
incident on a set of 3 polaroids as shown. The pass axis of each polaroid is perpendicular to direction of
propagation. One of the polaroid is
rotated about the common direction of
propagation of light.
A. If A is rotated, the final intensity remain unchanged.
B. If B is rotated, the final intensity will change.
C. If \( B \) is rotated, the final intensity remains unchanged
D. If \( C \) is rotated, the final intensity remains unchanged


Root pressure is a
A. Pulling force
B. Pushing force
C. Both A and B
D. None of these


Find the mean weight from the following table
weight \( \mathbf{2 9} \)
\( \mathbf{3 0} \quad \mathbf{3 1} \)
\( (k g) \)
No.of
\( 01 \quad 04 \quad 03 \)
children 20


Match the following columns.
\( \begin{array}{ll}\text { Column I } & \text { Column II } \\ \text { A. Pinocytosis } & \text { 1. Euglena gracilis } \\ \text { B. Holozoic } & \text { 2. Paramecium } \\ \text { C. Parasitic } & \text { 3. Amoeba proteus } \\ \text { D. Mixotrophic } & \text { 4. Monocystis }\end{array} \)
\( A \)
3,2,4,1
B. 2,3,4,1
c. 4,3,1,2
D. 1,4,2,3


1) Drive the formula for the ionization
constant \( \left(K_{b}\right) \) for weak bases.
2) Drive the relation \( \boldsymbol{p} \boldsymbol{H}+\boldsymbol{p} \boldsymbol{O} \boldsymbol{H}= \)
\( \boldsymbol{p} \boldsymbol{K} \boldsymbol{w} \)


Explain the structure of sulphur
dioxide


Why whitewashing walls gives a shiny finish to the walls?
A. Because of the formation of \( M g C O_{3} \)
B. Because of the formation of \( C a C O_{3} \)
c. Because of the formation of \( C a(O H) \)
D. None of these


The angle between velocity and acceleration of a particle describing uniform circular motion is
\( \mathbf{A} \cdot 180^{\circ} \)
B . \( 45^{\circ} \)
\( \mathrm{c} \cdot 90^{\circ} \)
D. \( 60^{\circ} \)


Write the names of energy bands present in solids.


The dimension of \( \left(\frac{1}{2}\right) \varepsilon_{0} \boldsymbol{E}^{2} \) is \( \left(\varepsilon_{0}\right. \)
permittivity of free space, Electric field)
A . \( M L T^{-} \)
В. \( M L^{2} T^{-2} \)
c. \( M L^{-1} T^{-2} \)
D. \( M L^{2} T^{-1} \)


Which of the following country in the world is most prone to earthquake?
A. India
B. America
c. china
D. Japan


What do silk fibres consist of?
A. Vitamins
B. Carbohydrates
C. Proteins
D. Fats


Give reason why half filled or fully filled orbitals provide more stability to the molecules?


What should be the characteristic of
fuse wire?
A. High melting point, high specific resistance
B. Low melting point, low specific resistance
C. High melting point, low specific resistance
D. Low melting point, high specific resistance


Name the physical quantity which
remains same for microwaves \( 1 \mathrm{mm} \)
and UV radiation of \( 6000_{A}^{\circ} \) in a vacuum


\( 29.5 \mathrm{mg} \) of an organic compound containing nitrogen was digested according to Kjeldahl's method and the evolved ammonia was absorbed in 20
\( \mathrm{ml} \) of \( 0.1 \mathrm{M} \) HCl solution. The excess of
acid required \( 15 \mathrm{ml} \) of \( 0.1 \mathrm{M} \) NaOH solution for complete neutralisation. The percentage of nitrogen in the compound is:
A . 29.5
B. 59.0
c. 23.
D. 47.4


The correct IUPAC name of given
compound is :
A . 2 -formylclclopentaneoic acid
B. 2 -clclopentyl-1-carboxilic acid
C . 2 -formylclclopentane-1-carboxilic acid
D. none of these


If
A, \( \mathrm{B}, \mathrm{C} \) be the angles of a triangle, then
prove that \( \left|\begin{array}{ccc}-1 & \cos C & \cos B \\ \cos C & -1 & \cos A \\ \cos B & \cos A & -1\end{array}\right|=0 \)


The number of atoms in 0.1 mol of a
triatomic gas is:
A. \( 6.026 \times 10^{22} \)
2
B . \( 1.806 \times 10^{23} \)
c. \( 3.600 \times 10^{23} \)
D. \( 1.800 \times 10^{2} \)


A 15 liter of a mixture contains \( 20 \% \)
alcohol and rest water. if 3 liter of water
is added in it, find the \( \% \) of alcohol in
the new mixture.
A . \( 16.66 \% \)
B. 26.66\%
c. \( 15 \% \)
D. \( 20 \% \)


State whether true or false.
We can see objects only in the presence of light.
A. True
B. False


\( N i^{2+} \) ion \( (Z=28) \) contains
unpaired electrons
\( A \)
B. 2
\( c \cdot 3 \)
D. 5


Find the \( 13^{t h} \) term in the expansion of \( \left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18} \)


The distance of closest approach of an alpha-particle fired towards a nucleus with momentum p is r. If the
momentum of the alpha-particle is \( 2 p \) the corresponding distance of closest approach is :
\( \mathbf{A} \cdot 4 r \)
B . \( 2 r \)
\( c \cdot \frac{2}{r} \)
D.


If the price of an article is increased by per cent \( p, \) then the decrease in per cent
of sales must not exceed \( d \) in order to
yield the same income. The value of \( d \) is
A \( \cdot \frac{1}{1+p} \)
в. \( \frac{1}{1-p} \)
c. \( \frac{p}{1+p} \)
D. \( \frac{p}{p-1} \)
E \( \cdot \frac{1-p}{1+p} \)


Show that the equation \( 2 x^{2}-x y- \)
\( 3 y^{2}-6 x+19 y-20=0 \) represent a
pair of intersecting lines. Show that the
angle between them is \( \tan ^{-1}(5) \)


The displacement \( x \) of a particle moving in one dimension, under the action of a
constant force is related to time \( t \) by the equation \( t=\sqrt{x}+3 \) where \( x \) is in metre and \( t \) in second. Calculate the
work done by the force in the first \( 6 s \) in Joule
A . 10
B.
\( c .5 \)
D. 2


Vapour pressure of a pure liquid \( X \) is 2 \( \operatorname{atm} \) at \( 300 \mathrm{K} \). It is lowered to 1 atm on
dissolving 1 g of \( Y \) in \( 20 g \) of liquid \( X \). If
molar mass of \( X \) is 200 , what is the
molar mass of \( Y ? \)
A . 20
B. 10
c. 100
D. 30


Best moderator for neutron is
A. berillium oxide
B. pure water
c. heavy water
D. graphite


In the Ostwald process \( 4 N H_{3}+ \)
\( 4 O_{2} \rightleftharpoons 4 N O+6 H_{2} O \) platinum is used
as a catalyst. If the amount of catalyst is increased when the system has reached equilibrium, which of the
following will occur
A. More \( N O \) and \( H_{2} O \) will form
B. More \( N H_{3} \) and \( O_{2} \) will form
c. Reaction rate will be increased
D. No change will be evident


Note the following statements.
a. It forms the lining of the cavities of alveoli of the lungs.
b. It forms the lining of wet surfaces like
buccal cavity and oesophagus.
c. It occurs in the ducts of sweat glands.
d. It forms the lining of salivary glands and sweat glands.
e. It is a loose connective tissue.
Which of the above are associated with
simple epithelial tissue?
A. a and d
B. b and c
c. \( c \) and a
D. \( d \) and e


In an auditorium or a cinema hall, the
roof and walls are covered with
draperies or compressed fibreboard. Why?


Order of differential equation of \( y= \)
\( \boldsymbol{m} \boldsymbol{x}+\boldsymbol{c} \)


The value of \( \frac{1^{2}}{1.3}+\frac{2^{2}}{3.5}+\cdots+ \)
\( \frac{n^{2}}{(2 n-1)(2 n+1)} \) is
A \( \cdot \frac{n(n+1)}{2(2 n+1)} \)
B. \( \frac{n(n-1)}{2(2 n-1)} \)
c. \( \frac{n^{2}(n-1)^{2}}{2(2 n+1)} \)
D. none of these


An air bubble of volume \( v_{0} \) is released by
a fish at a depth h in a lake. The bubble rises to the surface. Assume constant
temperature and standard atmospheric pressure \( P \) above the lake. The volume of
the bubble just before reaching the surface is (d is the density of water)
\( \mathbf{A} \cdot v_{0}+\frac{h g d}{P} \)
B. \( \frac{v_{0}(P+h g d)}{P} \)
c. \( \frac{v_{0}}{P}+h g d \)
D. \( \left(v_{0}+v_{0} d g\right) \)


Formalin is:
A. \( 60 \% \) solution of formaldehyde
B. \( 40 \% \) solution of formaldehyde
C. \( 30 \% \) solution of formaldehyde
D. \( 50 \% \) solution of formaldehyde


Let the \( x \) -z plane be the boundary between two transparent media. Medium 1 in \( z \geq 0 \) has a refractive index of \( \sqrt{2} \) and medium 2 with \( z<0 \) has refractive index of \( \sqrt{3} . \) A ray of light in medium 1 given by the vector \( \vec{A}= \) \( 6 \sqrt{3} \hat{i}+8 \sqrt{3} \hat{j}-10 \hat{k} \) is incident on the
plane of separation. The angle of refraction in medium 2 is:
A \( \cdot 45^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 75^{\circ} \)
D. \( 30^{\circ} \)


Assertion
In humans, the gamete contributed by the male determines whether the child
produced will be male or female.
Reason
Sex in humans in a polygenic trait
depending upon a cumulative effect of
some genes on \( X \) chromosome and
some on Y chromosome.
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.


Write down the number of \( 3 d \) electrons
in each of the following ions:
\( \boldsymbol{T} \boldsymbol{i}^{2+}, \boldsymbol{V}^{2+}, \boldsymbol{C} \boldsymbol{r}^{3+}, \boldsymbol{M} \boldsymbol{n}^{2+}, \boldsymbol{F} \boldsymbol{e}^{2+}, \boldsymbol{F} \boldsymbol{e}^{3+}, \boldsymbol{C} \boldsymbol{o} \)
and \( C u^{2+} . \) Indicate how would you
expect the five \( 3 d \) orbitals to be
occupied for these hydrated ions (octahedral).


The Supreme Court ordered:
A. industries to switch to cleaner fuels like CNG (Compressed Natural Gas) and LPG (Liquefied Petroleum Gas)
B. the automobiles should switch over to unleaded petrol in the Taj zone
C. both \( A \) and \( B \)
D. none of these


Identify the mismatch of the following.
A. Photo diode - optical signal
B. LED - spontaneous emission
C. Diode laser - stimulated emission
D. Solar cell - electrical energy into light
E. Photo conducting cell - photo detector


The branch of chemistry which deals with the study of chemical reaction rate
is known as:
A. thermochemistry
B. electrochemistry
c. chemical kinetics
D. none of these


If (4,3) and (-4,3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
A \( \cdot(0,-3-4 \sqrt{3}) \)
В. \( (0,3+4 \sqrt{3}) \)
c. \( (0,3-4 \sqrt{3}) \)
D. \( (0,-3+4 \sqrt{3}) \)


In which of the following compounds iron
has the lowest oxidation state?
\( \mathbf{A} \cdot F e(C O)_{5} \)
\( \mathbf{B} \cdot F e_{2} O \)
\( \mathbf{c} \cdot K_{4}\left[F e(C N)_{6}\right] \)
D \( \cdot F e S O_{4} \cdot\left(N H_{4}\right) S O_{4} \cdot 6 H_{2} O \)


\( \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{S}+\boldsymbol{X} \longrightarrow \boldsymbol{N} \boldsymbol{a}_{2}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{5}\right. \)
purple colc
The reason of color of \( X \) is :
A. d-d transition
B. charge transfer
c. colorless compound
D. None


Stack of thylakoids is known as:
A. Granum
B. Grana
c. Intergranum membrane
D. cristae


A plank with a body of mass \( m \) placed
on it starts moving straight up
according to the law \( y=a(1-\cos \omega t) \)
where \( y \) is the displacement from the
initial position, \( \omega=11 \) rad/s. What is
the force that the body exerts on the
plank?


The equation of a progressive wave is \( \boldsymbol{y}=\mathbf{0 . 0 5} \sin \left(\mathbf{2 0 0} \boldsymbol{t}-\frac{\boldsymbol{x}}{\mathbf{2}}\right) \) where \( \boldsymbol{x}, \boldsymbol{y} \) are
in metres and \( t \) in seconds, then
a ) velocity of wave is \( 100 m s^{-1} \)
b) maximum velocity of particle in the wave is \( 10 m s^{-1} \)
c) wavelength of wave is \( 4 \pi m \)
A. only a and c are true
B. only b and c are true
c. only a and b are true
D. a,b,c are true


Chlorine, bromine and iodine are
elements in Group VII of the Periodic Table.
Describe the trend in colour and
physcial state at room temperature and pressure as the atomic number
increases.


For reducing one mole of \( C r_{2} O_{7}^{2-} \) to
\( C r^{3+}, \) the charge required is:
A. \( 3 \times 96500 \) coulomb
В. \( 6 \times 96500 \) coulomb
c. 0.3 Faradays
D. 0.6 Faradays


Which compound in the above pair
undergoes faster \( \boldsymbol{S}_{N} \) 1 reaction?


Which one of the following is related to glucaric acid?
A. saccharin acid
B. saccharic acid
c. both A\&B
D. None of these


In the given figure the diameter of the biggest semi circle is \( 56 \mathrm{cm} \) and the
radius of the smallest circle is \( 7 \mathrm{cms} \)
The area of the shaded portion is
A \( \cdot 482 \mathrm{cm}^{2} \)
B. \( 462 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 654 \mathrm{cm}^{2} \)
D. \( 804 \mathrm{cm}^{2} \)


Two non-ideal batteries are connected
in series. Consider the following
statements:
(A) The equivalent emf is larger than either of the two emfs.
(B) The equivalent internal resistance is
smaller than either of the two internal
resistances
A. Each of A and B is correct
B. A is correct but B is wrong
C. B is correct but A is wrong
D. Each of A and B is wrong


Which of the following is a condensation homopolymer?
A. Nylon - 6
B. Nylon - 6, 6
c. Nylon - 6,10
D. Dacron


Study the following.List-I List-I
a) \( \vec{P} . \vec{Q} \quad \) I)pseudo vector
b) \( \vec{P} \times \vec{Q} \)
II) undefined
c) \( \overrightarrow{\mathbf{P}} \cdot(\overrightarrow{\mathbf{Q}} \cdot \overrightarrow{\boldsymbol{R}}) \)
III) A Scalar
d) \( \vec{P} \times(\vec{Q} \times \vec{R}) \)
IV) A vector
The correct match is:
A . A-IV B-III C-I D-II
B. A-II B-I C-III D-IV
c. A-III B-IV C-II D-I
D. A-I B-II C-IV D-III


Which of the statements about
Denaturation' given below are correct? Statements:
(i) Denaturation of proteins causes loss of secondary and tertiary structures of the protein.
(ii) Denaturation leads to the conversion of double strand of DNA into
single strand.
(iii) Denaturation affects primary
structure which gets destroyed.
A. (ii) and (iii)
B. (i) and (iii)
c. (i) and (ii)
D. (i), (ii) and (iii)


A metal rod has the length of \( 50 \mathrm{cm} \) at
\( 20^{\circ} \mathrm{C} . \) When it is heated to \( 95^{\circ} \mathrm{C} \), its
length becomes \( 50.06 \mathrm{cm} . \) Find the
length of the rod at \( 0^{\circ} \mathrm{C} \)


A brass disc and a carbon disc of same
radius are assembled alternatively to make a cylindrical conductor. The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass disc to
that of the carbon disc is \( \alpha \) is
temperature coefficient of resistance \( \& \)
Neglect linear expansion
A \( \cdot \frac{\alpha_{C} \rho_{C}}{\alpha_{B} \rho_{B}} \)
в. \( \frac{\alpha_{C} \rho_{B}}{\alpha_{B} \rho_{C}} \)
c. \( \frac{\alpha_{B} \rho_{C}}{\alpha_{C} \rho_{B}} \)
D. \( \frac{\alpha_{B} \rho_{B}}{\alpha_{C} \rho_{C}} \)


The distance between two places is 25
km. Write the magnitude of the measurement.
\( A \cdot k m \)
B. distance
\( c \cdot 25 \)
D. two


Frictional force is nearly negligible on:
A. Rough surfaces
B. Semi-smooth surfaces
c. Smooth surfaces
D. None of these


In the mathematical relation of
Freundlich adsorption isotherm, the value of \( \frac{1}{n} \) is \( 0 \leq \frac{1}{n} \leq 1 \)
A. True
B. False


Rich in lather, mixed with oil, blackbrown water that goes down the drains from \( _{\text {一一一一一一一一 }} \) is dirty. It is called
waste water.
A. sinks
B. toilets, showers
c. laundries
D. all of the above


State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.


What is the IUPAC symbol for Mendelevium?
A. Md
в. мп
c. ме
D. Mv


The point (s) moving upward is/are:
4
B
\( c \)
D


How many light years Alpha Centauri away from the Earth?
A . 1.29
B. 2.29
c. 3.29
D. 4.29


The minimum energy required to
launch a \( m \) kg satellite from earth's surface in a circular orbit at an altitude
of \( 2 R \) where \( R \) is the radius of earth, will
be:
\( \mathbf{A} \cdot 3 m g R \)
в. \( \frac{5}{6} \) mg \( R \)
c. \( 2 m g R \)
D. \( \frac{1}{5} m g R \)


Heat of neutralization is least when
A. \( \mathrm{NaOH} \) is neutralised by \( \mathrm{CH}_{3} \mathrm{COOH} \)
B. NaOH is neutralised by HCI
C. \( \mathrm{NH}_{4} \mathrm{OH} \) is neutralised by \( \mathrm{CH}_{3} \mathrm{COOH} \)
D. \( \mathrm{NH}_{4} \mathrm{OH} \) is neutralised by \( \mathrm{HNO}_{3} \)


Positive deviation from ideal behaviour
takes place because of :
A . molecular interaction between atoms and \( \frac{P V}{n R T}>1 \)
B. molecular interaction between atoms and \( \frac{P V}{n R T}<1 \)
C ' finite size of atoms and \( \frac{P V}{n R T}>1 \)
D tinite size of atoms and \( \frac{P V}{n R T}<1 \)


An element \( \boldsymbol{X} \) decays first by positron emission and then \( 2 \alpha \)
particles are emitted in succession. If the product nucleus has mass number 229 and atomic number 89
then the mass number and atomic
number of element \( \boldsymbol{X} \) are
A .237,93
в. 237,94
c. 238,93
D. 237,92


Write the correct IUPAC name of the
following compound.
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)


If \( p \) and \( q \) are non-collinear unit vectors
and \( |\boldsymbol{p}+\boldsymbol{q}|=\sqrt{\mathbf{3}}, \) then \( (\mathbf{2} \boldsymbol{p}-\boldsymbol{3} \boldsymbol{q}) \)
\( (3 p+q) \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{3} \)
\( c \cdot-\frac{1}{3} \)
D. \( \frac{1}{2} \)
\( E \cdot-\frac{1}{2} \)


How does a solenoid behave like a
magnet? Can you determine the north
and south poles of a current-carrying
solenoid with the help of a bar magnet?? Explain.


Is 184 a term of the sequence \( 3,7,11, \ldots \)
\( ? \)


A piece of wood of mass 0.03 kg is
dropped from the top of a 100 m height
building. At the same time, a bullet of
mass \( 0.02 \mathrm{kg} \) is fired vertically upward,
with a velocity \( 100 m s^{-1}, \) from the
ground. The bullet gets embedded in the wood. Then the maximum height to
which the combined system reaches above the top of the building before
falling below is : \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} \boldsymbol{s}^{-2}\right) \)
A. \( 30 m \)
B. \( 10 m \)
c. \( 40 m \)
D. \( 20 m \)


In the adjoining figure, identify the pair of corresponding angles


The ratio of specific charges of an electron to that of a hydrogen ion is?
A .2: 1
B. 1: 1
c. 1: 1840
D. 1840: 1


State whether given statement is True or False
Two thin blankets are more warmer
than one thick blanket
A. True
B. False


The major product obtained on
interaction of phenol with sodium hydroxide and carbon dioxide is :
A. Benzoic acid
B. Salicylaldehyde
c. Salicylic acid
D. Phthalic acid


\( \infty \)


Enzyme catalysed reaction of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is a disproportionation redox process. If true enter 1 , else enter 0 .
\( A \)


Pure water is neutral to litmus.
A. True
B. False


Light described at a place by the equation \( \boldsymbol{E}=(\mathbf{1 0 0} \boldsymbol{V} / \boldsymbol{M}) \times[\sin (\mathbf{5} \times \)
\( \left.\mathbf{1 0}^{\mathbf{1 5}} \boldsymbol{s}^{-\mathbf{1}}\right) \boldsymbol{t}+\boldsymbol{\operatorname { s i n }}\left(\boldsymbol{8} \times \mathbf{1 0}^{\mathbf{1 5}} \boldsymbol{s}^{-\mathbf{1}}\right) \boldsymbol{t} \)
Falls on a metal surface having work function 2.0 e.V Calculate the maximum
kinetic energy of the photoelectrons
A . 3.27 ev
B. 5 ev
c. 1.27 ev
D. 2.5 ev


\( \mathrm{ff} \mathrm{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{0} \\ \mathbf{4} & \mathbf{1}\end{array}\right] \) and \( \mathrm{B}=\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{2} & \mathbf{1} \\ \mathbf{2} & \mathbf{3} & \mathbf{1}\end{array}\right] \) find
BA. Can we find AB also?


toppr
Q Type your question
the following graphs violates the law of
conservation of energy?
3
\( c \)
\( D \)


If \( P \) represents radiation pressure,
represents speed of light and \( \mathrm{Q} \) represents radiation energy striking a
unit area per second, then non-zero
integers \( x, y \) and \( z, \) such that \( P^{x} Q^{y} c^{z} \) is dimensionless, may be
A. \( x=1, y=1, z=1 \)
B. \( x=1, y=-1, z=1 \)
c. \( x=-1, y=1, z=1 \)
D. \( x=0, y=0, z=0 \)


Time required to produce 1 kg of \( C l_{2} \) in
hrs is \( (40+x) . \) Find value of \( x \) (nearest
integer value).


If \( \vec{E}=E_{0} \cos (k z) \cos (\omega t) \hat{i} \) then \( \vec{B} \) for
electromagnetic wave is:
A \( \cdot \vec{B}=\frac{E_{0}}{C} \hat{k} \)
B・ \( \vec{B}=\frac{E_{0}}{C} \sin (k z) \sin (\omega t) \hat{\imath} \)
\( \mathbf{c} \cdot \vec{B}=\frac{E_{0}}{C} \sin (k z) \cos (\omega t) \hat{\jmath} \)
D・ \( \vec{B}=\frac{E_{0}}{C} \cos (k z) \sin (\omega t) \hat{\jmath} \)


In the given figure below, \( A D \) is a
diameter. \( O \) is the centre of the circle.
\( A D \) is parallel to \( B C \) and \( \angle C B D=32^{\circ} \)
Find \( \angle B E D\left(\text { in }^{\circ}\right) \)


Say true or false. The A.M. between \( (a-b)^{2} \) and \( (a+b)^{2} \)
is \( a^{2}+b^{2} \)
A. True
B. False


Atoms of two elements \( P \) and \( Q \) have 5
electrons in \( 2^{n d} \) shell and \( 3^{r d} \) shell
respectively. What will be the atomic
numbers of these elements?
A . 4: 15
B. 5: 15
\( c \cdot 7: 13 \)
D. 7: 15


Which of the following is a correct
statement:

This question has multiple correct options
A. Calamine is the ore of zinc
B. Pyrolusite is the ore of manganese
c. cassiterite is the ore of tin
D. Calcite is the ore of calcium


Blood and lymph are types of
A. Muscular tissue
B. Epithelial tissue
c. connective tissue
D. Permanent tissue


\( \boldsymbol{A}-(\boldsymbol{B} \cup \boldsymbol{C}) \)
\( \mathbf{A} \cdot\{1,6,7,8\} \)
в. \{3,4,5\}
\( c \cdot\{2\} \)
\( D . \) none


Sum of the series, \( x^{3}, x^{5}, x^{7}, \ldots \quad n \quad \) terms
\( (i f \quad x \neq \)
土1)。


Sodium forms an oxide containing one oxygen atom for every two atoms of sodium. What is the coefficient of
sodium in the balanced equation for the
reaction of sodium with oxygen to form this oxide?
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. 3
\( E .4 \)


Number of oxygen atoms required for complete oxidation of pyruvic acid is
A. 6
B. 12
\( c \cdot 3 \)
\( D \)


Three points charges are placed at the
corners of an equilateral triangle of side
\( L \) shown in the figure.
This question has multiple correct options
A. The potential at the centroid of the triangle is zero
B. The electric field at the centroid of the triangle is zero
C. The dipole moment of the system is \( \sqrt{2} q L \)
D. The dipole moment of the system is \( \sqrt{3} q L \)


If any one term of an arithmetic
progression along with the position of the term in the A.P. and the common
difference are known, then which of the
following can be found out
A. The first term
B. The term before the known term.
c. The term after the known term
D. All of the above


A man is pushing a car but it is not moving. Which of the following is correct about the situation?
A. Force is applied.
B. Force is not appliedd
c. Force may or may not be applied.
D. None of these.


The qualitative sketches I, II and III
given below show the variation of surface tension with molar
concentration of three different
aqueous solutions of \( \boldsymbol{K} \boldsymbol{C l}, \boldsymbol{C H}_{3} \boldsymbol{O H} \)
and \( \$ \$ \mathrm{CH}_{-}\{3\} \)
\( \left(\mathrm{CH}_{-}\{2\}\right)_{-}\{11\} 0 \mathrm{SO} \)
\{3\}\( \wedge\{-\} \mathrm{Na} \wedge\{+\} \$ \$ \) at
room temperature The correct assignment of the sketches
is
A \( \cdot I: K C l ; I I: C H_{3} O H ; I I I: C H_{3}\left(C H_{2}\right)_{11} O S O_{3}^{-} N a^{+} \)
B . \( I: C H_{3}\left(C H_{2}\right)_{11} O S O_{3}^{-} N a^{+} I I: C H_{3} O H ; I I I: K C l \)
C. \( I: K C l ; I I: C H_{3}\left(C H_{2}\right)_{11} O S O_{3}^{-} N a^{+} ; I I I: C H_{3} O H \)
D. \( I: C H_{3} O H ; I I: K C l ; I I I: C H_{3}\left(C H_{2}\right)_{11} O S O_{3}^{-} N a^{+} \)


\( 480 m l \) of \( 1.5 M \) non-electrolyte solution is mixed with 520 ml of \( 1.2 ~ M \)
non-electrolyte solution. What is the molarity of the final mixture?
A . \( 2.70 M \)
в. 1.344 М
c. \( 1.50 M \)
D. \( 1.20 M \)


Which phosphorus is used as a rat
poison?
A. White
B. Violet
c. Red
D. Black


A particle is moving in a circle of radius \( 4 \mathrm{cm} \) with constant speed of \( 1 \mathrm{cm} / \mathrm{s} \)
Find
(a) time period of the particle
(b) average speed, average velocity and average acceleration in a time interval from \( t=0 \) to \( t=T / 4 \). here \( T \) is the time
period of the particle. Give only their magnitudes


The largest possible square is inscribed
in a circle of circumference \( 2 \pi \) units.
The area of the square in square units
is
\( \mathbf{A} \cdot 4 \pi \sqrt{2} \)
В. \( 2 \pi \sqrt{2} \)
\( c \cdot \sqrt{2} \)
\( D \)


The number of ways in which four letters can be selected from the word
DEGREE' is
\( A \cdot 7 \)
B. 6
c. \( \frac{6 !}{3 !} \)
D. None of these


Chordates are distinguished form non
chordates by the presence of
A. Brain
B. Dorsal tubular hollow nerve cord
c. Ventral nerve cord
D. Dorsal nerve cord


The principle source of oxygen in
industry today is:
A. thermal dissociation of dinitrogen tetraoxide
B. electrolysis of nitric acid
C. reduction of nitrous oxide
D. fractional distillation of liquid air


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


\( \mathbf{I f A}=(\mathbf{1}, \mathbf{2}, \mathbf{3}), \mathbf{B}=(\mathbf{2}, \mathbf{3}, \mathbf{4}) \) and \( \mathbf{C} \) is a
point of trisection of AB such that \( \mathbf{C}_{\mathbf{x}}+ \) \( \mathbf{C}_{\mathbf{y}}=\frac{\mathbf{1 3}}{\mathbf{3}} \) then \( \mathbf{C}_{\mathbf{z}}= \)
A \( \cdot \frac{10}{3} \)
B. \( \frac{11}{3} \)
c. \( \frac{11}{2} \)
D. 11


Hypertension occurs due to
A. Smoking
B. obesity
c. Stress
D. All of the above


Can rusting of iron nail occur in distilled water? Justify you answer.


\( \Delta A M T \sim \Delta A H E \cdot \ln \Delta A M T, M A= \)
\( 6.3 c m, \angle M A T=120^{\circ}, A T=4.9 \mathrm{cm} \)
\( \frac{M A}{H A}=\frac{7}{5} \) Construct \( \Delta A H E \)


Assertion
Use of ball bearings between two moving parts of a machine is a common
practice.
Reason
Ball bearings reduce vibrations and
provide good stability.
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


State whether true or false:
When light rays are incident on the eye, maximum deviation takes place at the
cornea.
A. True
B. False


An example of solid in non-aqueous solvent is :
A. sugar in Ethanol
B. blood
c. starch
D. sugar sol


\( \begin{array}{c}\text { If } \boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}=\boldsymbol{\pi}, \text { then } \\ \left|\begin{array}{ccc}\sin (\boldsymbol{A}+\boldsymbol{B}+\boldsymbol{C}) & \sin \boldsymbol{B} & \cos C \\ -\sin \boldsymbol{0} & \boldsymbol{\operatorname { t a n }} \boldsymbol{A}\end{array}\right|= \\ \cos (\boldsymbol{A}+\boldsymbol{B}) \quad-\boldsymbol{\operatorname { t a n } \boldsymbol { A }} & \boldsymbol{0}\end{array} \mid \)


If \( 0 \leq x, y \leq 180^{\circ} \) and \( \sin (x-y)= \)
\( \cos (x+y)=\frac{1}{2}, \) then the values of \( x \)
and \( y \) are given by This question has multiple correct options
A. \( x=45^{\circ}, y=15^{\circ} \)
В. \( x=45^{\circ}, y=135^{\circ} \)
c. \( x=165^{\circ}, y=15^{\circ} \)
D. \( x=165^{\circ}, y=135^{\circ} \)


The P.M.F of a r.v. \( \boldsymbol{X} \) is \( \boldsymbol{P}(\boldsymbol{x})=\frac{1}{5} \) for \( \boldsymbol{x}= \)
\( 1,2,3, \dots 14,15 ; P(x)=0 \) otherwise
Find (i) \( \boldsymbol{E}(\boldsymbol{X})(\text { ii) } \boldsymbol{V} \boldsymbol{a} \boldsymbol{r}(\boldsymbol{X}) \)


State Gauss theorem and uses it to
derive the Coulomb's inverse square
law.


To purify impure sample of benzoic acid by the process of crystallization:


The structure in earthworm which
serves as a wedge to force open cracks in the soil is
A. Peristomium
B. Setae
c. Typhlosole
D. Prostomium


A car goes around uniform circular track of radius \( R \) at a uniform speed \( v \)
once in every \( T \) seconds. The
magnitude of the centripetal
acceleration is \( a_{C} \). If the car now goes uniformly around a larger circular track
of radius \( 2 R \) and experiences a
centripetal acceleration of magnitude
\( 8 a_{c}, \) then its time period is
A . \( 2 T \)
в. \( 3 T \)
c. \( T / 2 \)
D. 3 / 27


Which has the lowest anion to cation
size ratio?
A . \( L i F \)
В. \( N a F \)
c. \( C s I \)
D. \( C s F \)


From the following data, calculate, bond
energy of the \( F_{2}^{-} \) ion
\( \boldsymbol{F e}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{F}(\boldsymbol{g}) ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( \mathbf{1 5 6 . 9} \boldsymbol{k J} \)
II. \( \boldsymbol{F}^{-}(\boldsymbol{g}) \rightarrow \boldsymbol{F}_{2}(\boldsymbol{g}) \boldsymbol{e}^{-} ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( \mathbf{3 3 3} \boldsymbol{k J} \)
III. \( \boldsymbol{F}_{2}^{-}(\boldsymbol{g}) \rightarrow \boldsymbol{F}_{2}(\boldsymbol{g}) \boldsymbol{e}^{-} ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( \mathbf{2 9 0} \boldsymbol{k J} \)
A . \( 446.9 k J \)
в. \( 113.9 k J \)
c. \( 779.9 k J \)
D. \( 623.0 k J \)


The Fraunhoffer 'diffraction' pattern of a single slit is formed in the focal plane of a lens of focal length 1 m. The width of
slit is 0.3 mm. If third minimum is
formed at a distance of \( 5 m m \) from
central maximum, then wavelength of
light will be
\( \mathbf{A} \cdot 5000 \stackrel{\circ}{A} \)
B . 2500 , \( ^{\text {o }} \) A
\( \mathbf{c} \cdot 7500 \hat{A} \)
D. 8500 a