If \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) then \( \boldsymbol{A}^{-\mathbf{1}}= \)
A \( \cdot \frac{-1}{2}\left[\begin{array}{cc}4 & -2 \\ -3 & 1\end{array}\right] \)
в. \( \frac{1}{2}\left[\begin{array}{cc}4 & -2 \\ -3 & 1\end{array}\right] \)
c. \( \left[\begin{array}{cc}-2 & 4 \\ 1 & 3\end{array}\right] \)
D. \( \left[\begin{array}{ll}2 & 4 \\ 1 & 3\end{array}\right] \)


State whether true or false.
The maximum number of tickets sold is
three times the minimum number of
tickets sold.
lotteries sold by an agent on a day
\( 4 . \) True
B. False


is a substance which
neutralizes stomach acidity, which in turn relieves heartburn, indigestion or
stomach upset
A. Antibiotic
B. Antacid
c. Disinfectant
D. Anti-fertility drug


Presence of 3 bond pairs corresponds to hybridisation.
\( A \cdot s p^{3} \)
B \( \cdot s p^{3} d \)
\( c \cdot s p^{2} \)
D. sp


The angle between the lines whose
direction cosines satisfy the equations \( l+m+n=0 \) and \( l^{2}+m^{2}+n^{2} \) is
A \( \cdot \frac{\pi}{2} \)
в.
c.
D. \( \frac{\pi}{6} \)


The boiling point of n-alkyl halide
increases regularly with the:
A. the increase in the number of carbon atom
B. the decrease in number of carbon atom
C. boiling point is not related to the number of carbon atoms, but related to odd and even number of carbon present in the compound
D. none of these


If Amoeba is kept in distilled water, its contractile vacuole
A. Works slowly
B. Works faster
c. Remains unaffected
D. Disappears


A particle
(A) is dropped from a height and another particle(B) is thrown in horizontal direction with speed of 5 m/sec from the same height. The
correct statement is?
A. Both particles will reach at ground simultaneously
B. Both particles will reach at ground with same speed
c. Particle (A) will reach at ground first with respect is particle (B)
D. Particle (B) will reach at ground first with respect to particle (A)


In the manufacture of \( A l, A l_{2} O_{3} \) is
dissolved in \( N a_{3} A l F_{6} \) at \( 300 K \) and
electrolysed between \( A l \) and carbon electrodes following the net reaction,
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3}(\boldsymbol{s} \boldsymbol{o l u t i o n})+\boldsymbol{3} \boldsymbol{C} \rightarrow \boldsymbol{4} \boldsymbol{A l}(l)+ \)
\( \mathbf{3} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
The minimum voltage required between the electrodes if the Gibbs energy
change for the above reaction is -1370 \( k J m o l^{-1} \) is \( _{-1} \) (write nearest
integer)


\( T i^{4+} \) ion is colourless. Give reason


Two resistances of \( 400 \Omega \) and \( 800 \Omega \) are
connected in series with a 6 volt battery of negligible internal resistance. A
voltmeter of resistance \( 10,000 \Omega \) is used to measure the potential difference across \( 400 \Omega \). The error in the
measurement of the potential difference in volts approximately is :
A . 0.01
B. 0.02
\( c .0 .03 \)
D. 0.05


Platinised asbestos is used as a
catalyst in, the manufacture of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
It is an example of:
A. homogeneous catalyst
B. heterogeneous catalyst
c. autocatalyst
D. induced catalyst


Find the value of \( x, \) if \( \left|\begin{array}{cc}\boldsymbol{x}+\mathbf{2} & \boldsymbol{x} \\ \boldsymbol{x}-\boldsymbol{4} & \boldsymbol{x}+\mathbf{3}\end{array}\right|=\left|\begin{array}{cc}\boldsymbol{4} & \boldsymbol{2} \\ -\boldsymbol{2} & \boldsymbol{5}\end{array}\right| \)


The pteridophyte, popularly known as 'quillwort' is
A. Lycopodium
B. Selaginella
c. Isoetes
D. Marselia


If the speed of light is \( 3.0 \times 10^{8} \mathrm{m} s^{-1} \)
calculate the distance covered by light
in 2.00 ns.
\( A \cdot 0.6 m \)
B. 0. 3 \( m \)
c. \( 0.9 \mathrm{m} \)
D. 1.2 \( m \)


For any integer \( \mathbf{a}, \boldsymbol{a} \times \mathbf{1}=\mathbf{1} \times \boldsymbol{a}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot a \)
D. can not be calculated


The domain of \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \sqrt{x-2-2 \sqrt{x-3}}- \)
\( \sqrt{x-2+2 \sqrt{x-3}} \)


Describe the threat to the beauty of the
Taj Mahal


The dimensions of volume strain is:
\( \mathbf{A} \cdot m^{3} \)
B . \( 1 / m^{3} \)
c. no dimensions
D. \( m^{-} \)


If \( A \) and \( B \) are two events then
This question has multiple correct options
\( \mathbf{A} \cdot P(A \cap B) \geq P(A)+P(B)-1 \)
B \( . P(A \cap B) \geq P(A)+P(B) \)
\( \mathbf{c} \cdot P(A \cap B)=P(A)+P(B)-P(A \cup B) \)
\( \mathbf{D} \cdot P(A \cap B)=P(A) \cdot P(B) \)


Find the projection of \( \vec{b}+\vec{c} \) on \( \vec{a}, \) where \( \vec{a}=2 \hat{i}-2 \hat{j}+\hat{k}, \vec{b}=\hat{i}+2 \hat{j}-2 \hat{k} \) and
\( \vec{c}=2 \hat{i}-\hat{j}+4 \hat{k} \)


Find the slope of the line having its
inclination \( 60^{\circ} \)


Three particles, each having a charge of \( 10 \mu C \) are placed at the corners of an
equilateral triangle of side \( 10 \mathrm{cm} \). The electronic potential energy of the system is: \( \left(\text { Given } \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} N-\right. \)
\( \left.m^{2} / C^{2}\right) \)
A. Zero
B. Infinite
c. 27
D. \( 100 J \)


Compare \( x \) and \( y \) bond length in above molecules? \( \boldsymbol{y}=\mathbf{2 . 6 4 4} \dot{\boldsymbol{A}} \quad \boldsymbol{x}=\mathbf{2 . 2 1} \dot{\boldsymbol{A}} \)
\( A \cdot x>y \)
B. y > x
\( c \cdot x=y \)
D. None of these


The graph represents a current-voltage
behaviour of a water-voltmeter. Spot the
correct explanation:
A . Dissociation takes place till \( E_{1} \) and it obeys Ohm's law thereafter
B. Ohm's law is not valid for low voltage
c. Ohm's law is obeyed but only for potential difference larger than back emf
D. Electrolytes do not obey ohm's law


Water and oil are poured into the two limbs of a U-tube containing mercury. The interfaces of the mercury and the liquids are at the same height in both
limbs.
Determine the height of the water
column \( h_{1} \) if that of the oil \( h_{2}=20 c m \)
The density of the oil is 0.9


Uniform speed of \( 2 c m \) diameter ball is \( 20 \mathrm{cm} / \mathrm{s} \) in a viscous liquid. Then, the
speed of \( 1 \mathrm{cm} \) diameter ball in the same liquid is:
A \( .5 \mathrm{cms}^{-1} \)
B. \( 10 \mathrm{cms}^{-1} \)
c. \( 40 \mathrm{cms}^{-1} \)
D. \( 80 \mathrm{cms}^{-1} \)


A cylinder containing an ideal gas
\( \left(0.1 \text { mol of } 1.0 d m^{3}\right) \) is in thermal
equilibrium with a large volume of 0.5 molal aqueous solution of ethylene glycol at its freezing point. If the
stoppers \( S_{1} \) and \( S_{2} \) ( as shown in the
figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be
(Given, \( \boldsymbol{K}_{\boldsymbol{f}}(\boldsymbol{w} \boldsymbol{a} \boldsymbol{t e r})= \)
\( 2.0 K k g m o l^{-1}, R= \)
\( 0.08 d m^{3} \) at \( m \quad K^{-1} m o l^{-1} \)


If \( f(x)=\log _{e} \sec x \) and \( \phi(x)= \)
\( \log _{e} \tan x \) then prove that \( e^{2 f(x)}- \)
\( e^{2 \phi(x)}=1 \)


Draw the electronic dot structure of
ethane molecule \( \left(C_{2} H_{6}\right) \)


Assertion
A particle is under SHM along the \( x \) axis. Its mean position is \( x=2 \) amplitude is \( A=2 \) and angular frequency
\( \omega . A t t=0, \) particle is at origin, then \( x-c 0 \)
ordinate versus time equation of the
particle will be \( x=-2 \cos \omega t+2 \)
Reason
At \( t=0 \) particle is at rest.
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


\( x \) if the potential to which the outer
sphere is raised is \( x \times 10^{3} V \)


Give any one difference between each of
the following:
(a) Protozoa and Metazoa
(b) Vertebrate and Invertebrate
(c) Insecta and Arachnida
(d) Flatworm and Roundworm


The oxides of \( 15^{t h} \) group elements of the
type \( M_{2} O_{3} \) which will exhibit
amphoteric or basic properties but no acidic properties are
A \( \cdot N_{2} O_{3}, P_{2} O_{3} \)
в. \( A s_{2} O_{3}, S b_{2} O_{3} \)
\( \mathrm{c} \cdot S b_{2} O_{3}, B i_{2} O_{3} \)
D. \( P_{2} O_{3}, B i_{2} O_{3} \)


Efficiency of gasoline is measured in terms of:
A. butane number
B. octane number
c. hexane number
D. none of these


Treatment of calcium carbide with
water gives:
A. ethene
B. ethyne
c. ethane
D. benzene


Find the smallest number which should
be multiplied to 392 to make it a
perfect cube.
A . 3
B. 4
\( c .5 \)
D.


Trisilylamine \( \left[\ddot{\boldsymbol{N}}\left(\boldsymbol{S} \boldsymbol{i} \boldsymbol{H}_{3}\right)_{3}\right] \) has \( \mathbf{a} \)
A. planer geometry
B. tetrahedral geometry
c. pyramidal geometry
D. none of these


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{y}\end{array}\right] \) for \( \boldsymbol{x} \neq \)
\( \mathbf{0}, \boldsymbol{y} \neq \mathbf{0}, \) then \( \boldsymbol{D} \) is:
A. divisible by neither \( x \) nor \( y \)
B. divisible by both \( x \) nor \( y \)
c. divisible by \( x \) but not \( y \)
D. divisible by \( y \) but not \( x \)


A conducting rod of length \( l \) is moving in a transverse magnetic field of strength \( B \) with velocity \( v \). The resistance of the rod is \( R \). The current in
the rod is
A \( \cdot \frac{B l v}{R} \)
в. \( B l v \)
c. \( Z e r o \)
D. \( \frac{B^{2} v^{2} l^{2}}{R} \)


If both absorption and adsorption occur simultaneously it is called sorption If this is true enter 1 , if false enter 0 .


The enzyme recombinase is required at which stage of meiosis?
A. Pachytene
B. Zygotene
c. Diplotene
D. Diakinesis


The amount of charge stored in a capacitor is directly proportional to the voltage applied across the capacitor.
A. True
B. False


In electron transport system, the last electron acceptor of
photophosphorylation is
\( \mathbf{A} \cdot N A D P H \)
B. \( N A D P^{+} \)
c. Atomic oxygen
D. chlorophyll a


A force of \( 4 N \) acts on an object of mass
\( 2 k g \) in \( X- \) direction and another force
of \( 3 N \) acts on it in \( Y- \) direction. Hence
the magnitude of the acceleration of the object will be
A \( .1 .5 \mathrm{ms}^{-2} \)
B . \( 2.0 m s^{-2} \)
c. \( 2.5 \mathrm{ms}^{-2} \)
D. \( 3.5 \mathrm{ms}^{-2} \)


Choose the correct answer from the
alternatives given.
Which of the following plant hormones
was studied in the 1880 s by Charles and Francis Darwin in experiments on
phototropism?
A. Abscisic acid
B. Auxin
c. cytokinin
D. Ethylene


Detergent action of synthetic detergents is due to their:
A. interfacial area
B. high molecular weight
c. lonisation
D. emulsifying properties


Coal can be drawn into thin wire.
A. True
B. False


Determine the empirical formula of an oxide of iron which has \( 69.9 \% \) iron and
\( 30.1 \% \) oxygen. \( (F e=55.85 a m u ; O= \)
16.00 \( a m u \)
\( \mathbf{A} \cdot F e_{2} O_{3} \)
в. \( F e_{4} O_{6} \)
\( \mathrm{c} \cdot F e_{8} O_{12} \)
D. 'None of the above


If \( f(x)=\sin x+a^{2} x+b \) is an
increasing function for all values of \( x \)
then
A \( . a \epsilon(-\infty,-1) \)
B. \( a \in R \)
\( \mathbf{c} \cdot a \epsilon(-1,1) \)
D. none of these


\( \int\left(x^{2}-5 x+7\right) d x \)


For a first order reaction, the ratio of the
time taken for \( 7 / 8^{t h} \) of the reaction to
complete to that of half of the reaction to complete is :
A . 3: 1
B. 1: 3
c. 2: 3
D. 3: 2


Use the digits 11,9,7 to form the smallest and the largest mixed number. Then find their sum giving your answer as a mixed number.
A \( \cdot 18 \frac{8}{9} \)
в. \( 20 \frac{8}{77} \)
c. \( _{18} \frac{42}{99} \)
D. \( _{19} \frac{52}{77} \)


The number of free electrons in 1 c.c. of
Copper is
A. \( 8.4 \times 10^{22} \)
B. \( 5.8 \times 10^{22} \)
\( \mathbf{c} \cdot 10^{15} \)
D. \( 10^{20} \)


Detergents are prepared by the action of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \) followed by neutralization, by
starting with:
A. cholesterol
B. Iauryl alcohol
c. cyclohexanol
D. p-nitrophenol


Find three consecutive even number
whose sum is 234


If a magnet is suspended at an angle
\( 30^{\circ} \) to the magnetic meridian, the dip
needle makes an angle of \( 45^{\circ} \) with the horizontal. The real dip is:
A \( \cdot \tan ^{-1}(\sqrt{3 / 2}) \)
B. \( \tan ^{-1} \sqrt{3} \)
\( ^{\mathrm{c}} \tan ^{-1}(\sqrt{\frac{2}{3}}) \)
D \( \cdot \tan ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)


State the conditions to get constructive and destructive interference of light.


A stone dropped from the roof of a building takes 4 s to reach the ground. The height of the building is.
\( A \cdot 9.8 m \)
B. 19.6m
c. \( 39.2 \mathrm{m} \)
D. 78.4m


Two \( n \times n \) square matrices \( A \) and \( B \) are
said to be similar if there exists a non-
singular matrix \( \boldsymbol{P} \) such that
\( \boldsymbol{P}^{-1} \boldsymbol{A} \boldsymbol{P}=\boldsymbol{B} \)
If \( A \) and \( B \) are two non-singular
matrices, then
\( \mathbf{A} \cdot A \) is similar to \( B \)
B. \( A B \) is similar to \( B A \)
C. \( A B \) is similarto \( A^{-1} B \)
D. none of these


\( A, B \) and \( C \) are three tuning forks. Frequency of \( A \) is 350 Hz. Beats produced by A and B are 5/s and by B and \( C \) are \( 4 / \) s. When a wax is put on \( A \)
beat frequency between \( A \) and \( B \) is \( 2 \mathrm{Hz} \) and between \( A \) and \( C \) is 6 Hz. Then
frequency of \( \mathrm{B} \) and \( \mathrm{C} \) respectively are
\( A \cdot 355 \) НZ, 349 Нz
B. 345 Нz, 341 Нz
c. 355 Нz, 341 Нz
D. 345 Hz, 349 Нz


Potentiometer measures potential more accurately because
A. it measures potential in open circuitt
B. it uses sensitive galvanometer for null deflection
c. it uses high resistance potentiometer wire.
D. it measures potential in closed circuit


A very long, solid insulating cylinder
with radius \( R \) has a cylindrical hole
with radius \( a \) bored along its entire
length. The axis of the hole is a distance
\( b \) from the axis of the cylinder, where
\( a<b<R \) (as shown in figure). The
solid material of the cylinder has a uniform has a uniform volume charge
density \( \rho . \) Find the magnitude and
direction of the electric field inside the
hole, and show that this is uniform over
the entire hole.


Stressis a \( -\ldots--- \) quantity.
A. scalar
B. vector
c. tensor
D. dimensionless


In which of the following numbers, all zeros are significant?
A. 0.00004
B. 0.0060
c. 20.000
D. 0.800


In a Circus, a motor-cyclist having mass
of \( 50 k g \) moves in a spherical cage of
radius \( 3 m . \) Calculate the least velocity
with which he must pass the highest point without losing contact. Also calculate his angular speed at the highest point.


The complete balanced equation is:
\( M n O_{2}+H_{2} O_{2} \rightarrow M n O_{4}^{-}+H_{2} O \)
(Basic medium)
A \( \cdot 3 \mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{MnO}_{2}+2 \mathrm{OH}^{-} \rightarrow 2 \mathrm{MnO}_{4}^{-}+4 \mathrm{H}_{2} \mathrm{O} \)
B. \( 3 H_{2} O_{2}+M n O_{2}+3 O H^{-} \rightarrow 2 M n O_{4}^{-}+5 H_{2} O \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{MnO}_{2}+\mathrm{OH}^{-} \rightarrow 2 \mathrm{MnO}_{4}^{-}+4 \mathrm{H}_{2} \mathrm{O} \)
D. none of these


State true or false
If square of a number ends with \( 5, \) then
its cube ends with 25
A. True
B. False
c. Ambiguous
D. Data insufficient


of the 1000 persons of a town, \( 60 \% \) are males of whom , \( 20 \% \) are literate. If of
all the person \( 25 \% \) are literate then what percentage of the female of the town are
literate?
A . 32.5\%
B. 22.5\%
c. \( 45 \% \)
D. 13\%


In which one of the following equilibria,
\( \boldsymbol{K}_{\boldsymbol{p}} \neq \boldsymbol{K}_{c} ? \)
A \( \cdot N O_{2}(g)+S O_{2}(g) \rightleftharpoons N O(g)+S O_{3}(g) \)
B . \( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
c. \( 2 N O(g) \rightleftharpoons N_{2}(g)+O_{2}(g) \)
D \( \cdot 2 C(s)+O_{2}(g) \rightleftharpoons 2 C O(g) \)


Which of the following does not contain fluorine?
A. Fluorspar
B. cryolite
c. Flouorospatite
D. Chile saltpeter


Spores of true slime moulds are
produced in structures called
A. Sporocytes
B. Plasmodia
c. sporangia
D. Pseudoplasmodia


A heavy ball is suspended as shown. A quick jerk on the lower string will break
that string but a slow pull on the lower
string will break the upper string. The first result occurs because:
A. the force is too small to move the ball
B. action and reaction is operating
c. the ball has inertia
D. air friction holds the ball back


Which of the following will produce more energy in a short time?
A. nuclear fission
B. nuclear fusion
c. both will produce the same amount of energy
D. none of these


As oxygen is soluble in water.
Air dissolved in water contains a higher percentage of oxygen \( (30-35 \%) \) than ordinary air \( (21 \%) \)
A . less
B. more
\( c \cdot \) not
D. none of these


Mean life of a radioactive sample is 100
s. Find its half life in minutes
A. 0.693
B.
\( c \cdot 10^{-4} \)
D. 1.155


If force \( \overrightarrow{\boldsymbol{F}}=4 \hat{\hat{\boldsymbol{i}}}+5 \hat{\boldsymbol{j}} \) and displacement
\( \vec{S}=3 \hat{i}+6 \hat{j} \) then the work done is
A \( .4 \times 3 J \)
B. \( 5 \times 6 \)
\( c \cdot 6 \times 3 \)
D. \( 4 \times 6 \)


What is value of gravitational acceleration at the center of the earth?
\( \mathbf{A} \cdot 9.8 m s^{2} \)
B. zero
c. infinite
D. \( 6.67 \times 10^{-11} \mathrm{ms}^{-2} \)


Enzymes involved used in the fermentation of cane sugar to alcohol?
A. Diastase, invertase
B. Invertase, zymase
c. Diastase, zymase
D. Maltase, zymase


Which one is the correct option for
labels \( A, B \) and \( C \) in the given diagram?
A. A- Liver, B- Mucosa, C- Peritoneum
B. A- Liver, B- Circular muscle layer, C- - serosa
D. A- Pancreas, B- Submucosa, C- - Serosa


Root pressure can be demonstrated by means of
A. Wilting
B. Guttation
c. Transpiration
D. Exudation/bleeding


When strong base \( (N a O H) \) is added to the weak acid (acetic acid,
\( \left.C H_{3} C O O H\right), \) then dissociation of
acetic acid increases; this effect is
known as:
A. Common ion effect
B. Reverse ion effect
c. Saltation effect
D. Solubility effect


ff \( \boldsymbol{y}=\sec ^{2} \boldsymbol{\Theta}+\cos ^{2} \boldsymbol{\Theta}, \boldsymbol{0} \neq \boldsymbol{0}, \) then
A. \( y=0 \)
B. \( y \leq 0 \)
\( \mathbf{c} \cdot y>2 \)
D. \( y \neq 2 \)


Find the ratio in which y-axis divides the line segment joining the points \( A(5,-6) \) and \( B(-1,-4) \)


The catalyst used in the manufacturing of sulphuric acid by contact process is:
A. \( A l_{2} O_{3} \)
в. \( C r_{2} O_{3} \)
c. \( V_{2} O_{5} \)
D. \( M n_{3} O_{4} \)


\( \lim _{x \rightarrow a}\left(\frac{x+1}{2 x+1}\right)^{x^{2}}= \)


A system consists of \( \mathrm{N} \) particles, which have independent K relations among one another. The number of degrees of freedom of the system is given by :
\( A \cdot 3 N K \)
B. N/3K
\( c .3 \mathrm{N} / \mathrm{K} \)
D. 3N - K


For any positive integer \( a \), what is \( (-1) \times a \) equal to?


Red phosphorus can be obtained from
white phosphorus by:
This question has multiple correct options
A. heating it with a catalyst in an inert atmosphere
B. distilling it in an inert atmosphere
C. dissolving it ins \( C S_{2} \) and crystallizing
D. melting it and pouring liquid into water


Using the method of successive subtraction of numbers
\( \mathbf{1}, \mathbf{7}, \mathbf{1 9}, \mathbf{3 7}, \mathbf{6 1}, \mathbf{9 1}, \mathbf{1 2 7}, \mathbf{1 6 9}, \mathbf{2 1 7}, \mathbf{2 7 1}, \mathbf{3 3} \)
Examine if the following number is a perfect cube or not 792


Locate the COM of following system of
particle
A . 45.5 a
B. 49.5a
\( c \cdot 50 a \)
D. None of these


The nature of the graph of pressure 'P' against reciprocal of volume 'V' of an ideal gas at constant temperature is
A. a straight line not passing through origin
B. a parabola
c. a straight line passing through origin
D. a rectangular hyperbola


If \( 0<x \leq \frac{\pi}{2}, \) then \( \sin x+\operatorname{cosec} x \geq \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Which one does not occur in xylem
A. Medullary rays
B. Vascular rays
c. vessels
D. Tracheids


The magnetism is minimum . in
a bar magnet.
A. near the ends
B. near the middle
c. at the ends
D. at the middle


When white light passed through glass prism, why dispersion occurs?
A. Colours of white light travels at different speeds through prism
B. Colours of white light travels at same speeds through prism
c. colours of white light travels at different acceleration through prism
D. Colours of white light travels at same acceleration through prism


Formula of ruby copper is :
\( \mathbf{A} \cdot C u_{2} O \)
в. \( C u_{2} S \)
c. \( C u C O_{3} \cdot C u(O H)_{2} \)
D. \( C u F e S_{2} \)


Q Type your question
constant angular velocity \( \boldsymbol{\omega}=\frac{1}{\sqrt{L C}} \)
with the help of an external agent. A
uniform magnetic field B exists in
space and is directed into the plane of
the figure. (circuit part remains at rest
(left part is at rest) ). Then,
This question has multiple correct options
A the rms value of current in the circuit is \( \frac{\pi B a^{2}}{R \sqrt{2 L C}} \)
B. the rms value of current in the circuit is \( \frac{\pi B a^{2}}{2 R \sqrt{L C}} \)
c. the maximum energy stored in the capacitor is \( \frac{\pi^{2} B^{2} a^{4}}{8 R^{2} C} \)
D. the maximum power delivered by the external agent is \( \frac{\pi^{2} B^{2} a^{4}}{4 L C R} \)


If \( y=e^{m \sin ^{-1} x},-1 \leq x \leq 1 \), show that
\( \left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-a^{2} y=0 \)


If the sequence \( a_{1}, a_{2}, a_{3}, \dots \) is in A.P.
then the sequence \( a_{5}, a_{10}, a_{15}, \dots \) is
\( A \). A G.P.
B. An A.P.
c. Neither A.P. nor G.P.
D. A constant sequence


If we assume that \( N_{o}=1.2 \times 10^{23} \)
\( m o l^{-1}, \) then molar mass of \( O_{2} \) will be taken as:
A \( \cdot \frac{32}{5} g m o l^{-1} \)
в. \( \frac{32}{6} g m o l^{-1} \)
c. \( 32 \times 10^{23} \mathrm{g} \) mol \( ^{-1} \)
D. \( \frac{1 \times 10^{23}}{32} g \) mol \( ^{-1} \)


A second lens is now placed adjacent to
the first in contact with it. The new lens
is concave, with a focal length \( \boldsymbol{f}=-\mathbf{3} \boldsymbol{f} \)
In which region does the focus of the
two lens system lie? Treat the lenses as
thin.
\( A \)
B.
\( c \cdot c \)
\( D \)


If \( a=b^{6}, \) then \( a^{3}= \)
A \( \cdot b^{12} \)
2
B. \( b^{16} \)
\( c \cdot b^{18} \)
D. \( b^{216} \)


\( \sum_{i=1}^{\frac{-1}{2}} \)


Using the reals \( a_{n} ;(n=1,2, \dots, 5), \) if \( l, m, n \in\{1,2,3,4,5\} m<n \)
A \( \cdot\left(\sum a_{n}\right)^{2}=\sum\left(a_{l}^{2}\right)+2\left(\sum a_{m} a_{n}\right) \)
B . \( 0=\sum\left(a_{l}^{2}\right)-\sum\left(a_{m} a_{n}\right) \)
C \( \cdot\left(\sum a_{n}\right)^{2}=\sum\left(a_{l}^{2}\right)-2\left(\sum a_{m} a_{n}\right) \)
D. \( \left(\sum a_{n}\right)^{2}=\sum\left(a_{l}^{2}\right)+\sum\left(a_{m} a_{n}\right) \)


What remains constant in uniform
circular motion?
A. Velocity
B. Speedd
c. Displacement
D. Direction


Find the absolute maximum and the
absolute minimum values of the
following function in the given intervals. \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\mathbf{2}) \sqrt{\boldsymbol{x}-\mathbf{1}} \) in \( [\mathbf{1}, \boldsymbol{9}] \)


Elephant drinks water through
A. Probosics
B. Mouth
c. First sucks water in probosics and then pours the same in mouth
D. Elephant does not drink water


Fishes in eutrophic lake is died due to
A. Oxygen
B. Nutrient enrichment
\( c \cdot C O_{2} \)
D. None


Match following


The herbicidal property is shown by
A . IAA
B. 2,4-D
c. NAA
D. GA3


Which of the following is true regarding monosaccharides?
A. Always have six carbon atoms
B. Always have five carbon atoms
c. Always have four carbon atoms
D. May contain 3 to 7 carbon atoms


Calculate the area of a segment of a
circle with a central angle of 165 degrees and a radius of \( 4 . \) Express answer to nearest integer.
A . 10
B . 20
c. 30
D. 40


Match the atomic number of the
transuranium element (in List I) with
their IUPAC representation in (List II).


A long copper wire is wound in the form
of a coil of radius \( r . \) A current of \( 2 A \) is
passed through this coil and the magnetic induction at the centre of this coil is noted. The same wire is now
folded end to end and coil of the same
radius \( r \) is prepared and the same current is passed through it. The magnetic induction at the centre
A. Will be doubled
B. Will be halved
c. will remain same
D. Will drop to zero


The waves used by artificial satellites for communication is the
A. microwaves
B. infrared waves
c. radio waves
D. x-rays


In man, kidney is
A. Pronephros
B. Mesonephros
C . Metanephros
D. None of the above


The heart of a crocodile consists of
A. A single auricle and two ventricles
B. Two auricles and a single ventricle
c. Two auricles and two ventricles
D. A single auricle and a single ventricle


The integral \( \int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{d x}{1+\cos x} \)
A .2
B. 4
\( c \cdot-1 \)
D. -


All gases have the same number of moles in the same volume at constant \( T \)
and \( P \) is stated by :
A. Boyle's law
B. Charle's law
c. Avogardro's law
D. ideal gas law
E. Dalton's law


The ends \( Q \) and \( R \) of two thin wires, \( P Q \) and \( R S, \) are soldered (joined) together Initially each of the wires has a length of
\( 1 \mathrm{m} \) at \( 10^{\circ} \mathrm{C} \). Now the end \( \mathrm{P} \) is
maintained at \( 10^{\circ} \mathrm{C} \), while the end \( \mathrm{S} \) is
heated and maintained at \( 400^{\circ} \mathrm{C} \). The
system is thermally insulated from its surroundings. If the thermal conductivity of wire \( \mathrm{PQ} \) is twice that of
the wire \( \mathrm{RS} \) and the coefficient of linear
thermal expansion of PQ is \( 1.2 \times \)
\( 10^{-5} K^{-1}, \) the change in length of the
wire PQ is?
\( \mathbf{A} \cdot 0.78 \mathrm{mm} \)
в. \( 0.90 \mathrm{mm} \)
c. \( 1.56 \mathrm{mm} \)
D. \( 2.34 \mathrm{mm} \)


The presence of which of the following gases in air checks the ultraviolet from sun light?
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
c. \( N O \)
D. \( O_{3} \)


Calculate the PH of a buffer solution
prepared by dissolving 30 g of \( N a 2 C O 3 \) in \( 500 \mathrm{ml} \) of an aqueous solution containing \( 150 \mathrm{ml} \) of \( 1 \mathrm{m} \) HC \( L \). ka for
\( H C O^{-3}=5.63 \times 10-11 \)
\( \mathbf{A} \cdot 8.197 \)
B. 9.197
c. 10.437
D. 11.197


Dissolving salt in water-is a/an:
A. endothermic change
B. exothermic change
c. both \( A \& B \)
D. chemical combination


Q Type your question.
negligible resistance (Fig 3.126). The
rails are connected to each other at the
bottom by a resistanceless rail paralle
to the wire so that the wire and the rails
form a closed rectangular conducting
loop. The plane of the rails makes an
angle \( \theta \) with the horizontal and a
uniform vertical magnetic field of
induction B exist throughout the region.
Find the steady-state velocity of the
wire.
A. \( m g=\sin \theta \)
B. \( \frac{m g}{R} \frac{\sin ^{2} \theta}{B^{2} l^{2} \cos ^{2} \theta} \)
c. \( \frac{m g R \sin \theta}{B^{2} l^{2} \cos ^{2} \theta} \)
D. \( \operatorname{mgr} \frac{\sin ^{2} \theta}{B^{2} / 2 \cos \theta} \)


A uniform wire of length \( l \) is bent into
the shape of \( V \) as shown. The distance
of its centre of mass from the vertex \( \boldsymbol{A} \)
is
A \( . l / 2 \)
B. \( \frac{1 \sqrt{3}}{1} \)
\( \frac{1 \sqrt{3}}{8} \)
D. None of these


Four bulbs marked \( 40 W, 250 V \) are
connected in series with \( 250 V \) mains,
the total power consumed is
A. \( 10 W \)
в. \( 40 W \)
c. \( 320 W \)
D. \( 160 W \)


In a hydrogen atom, electron is in the
\( n^{t h} \) excited state. It comes down to the
first excited state by emitting 10 different wavelengths. The value of \( n^{t h} \) is
A. 6
B. 7
c. 8
D.


The continuity of protoplasm from cell to cell is maintained through
A. Stomata
B. Tracheids
c. vessels
D. Plasmodesmata


Electrical resistivity of a given metallic
wire depends upon:
A. its length
B. its thickness
c. its shape
D. nature of the material


The vapour pressure of a solvent decreased by \( 10 \mathrm{mm} \) of mercury when a non-volatile solute was added to the
solvent. The mole fraction of the solute
in the solution is 0.2. What should be the mole fraction of the solvent if the
decrease in the vapour pressure is to be \( 20 \mathrm{mm} \) of mercury?
A. 0.4
B. 0.6
\( c \cdot 0.8 \)
\( D \cdot 0.2 \)


Find the value of \( x \) which satisfy equation \( : \sin ^{-1} x+\sin ^{-1} 2 x=\frac{\pi}{3} \)
A \( \cdot x=\frac{1}{2} \sqrt{\frac{3}{7}} \)
B・ \( x=\frac{1}{3} \sqrt{\frac{4}{7}} \)
c. \( x=\frac{1}{3} \sqrt{\frac{3}{7}} \)
D. \( x=\frac{1}{2} \sqrt{\frac{4}{7}} \)


An old man and a boy are walking
towards
each other and a bird is flying over them as shown in the figure. Find the
velocity of bird as seen by the boy.
A \( .12 \hat{j} \)
B. \( 16 \hat{j} \)
\( c .-12 \hat{j} \)
D. \( -16 \hat{j} \)


If \( \log _{1 / 3} \frac{3 x-1}{x+2} \) is less than unity then \( x \)
must lie in the interval
\( ^{\mathbf{A}} \cdot(-\infty,-2) \cup\left(\frac{5}{8}, \infty\right) \)
B \( \cdot\left(-2, \frac{5}{8}\right) \)
\( ^{\mathrm{c}} \cdot(-\infty,-2) \cup\left(\frac{1}{3}, \frac{5}{8}\right) \)
D. \( \left(-2, \frac{1}{3}\right) \)


Compute:
\( \left(\frac{56}{28}\right)^{0} \div\left(\frac{2}{5}\right)^{3} \times \frac{16}{25} \)


There are several methods for refining metals. Explain a method for refining Zirconium.


\( \lim _{x \rightarrow \pi / 2} \frac{\cot x-\cos x}{(\pi-2 x)^{3}} \) equals
A. \( \frac{1}{16} \)
в.
\( c \cdot \frac{1}{4} \)
D.


Find the remainder when \( p(x)=2 x^{2}- \)
\( 5 x-1 \) is divided by \( x-3 \)
A .
B.
\( c \cdot 2 \)
D. 3


Metamerically segmented body exhibits
A. Repeated segments
B. Linear repetition of body parts
c. Repetition of nephridia
D. Repetition of reproductive organs


A full wave rectifier along with the
output is shown in the given figure. The
contributions from the diode \( \left(D_{2}\right) \) are
\( A \cdot C \)
B. A, C
\( c \cdot B, D \)
D. \( A, B, C, D \)


If y denotes the displacement and t denote the time and the displacement is given by \( y=a \sin t, \) the velocity of the particle is-


A resistance of \( 2 \Omega \) is connected across
one gap of a metre-bridge (the length of the wire is \( 100 \mathrm{cm} \) ) and an unknown
resistance, greater than \( 2 \Omega \), is connected across the other gap. When these resistance are interchanged, the balance point shifts by \( 20 \mathrm{cm} \) Neglecting any corrections, the unknown resistance is
A. \( 3 \Omega \)
в. \( 4 \Omega \)
\( c \cdot 5 \Omega \)
D. \( 6 \Omega \)


The terminal arm is in II quadrant, what
are the measures of possible angles?
A . In between \( 90^{\circ} \) and \( 180^{\circ} \) or \( -270^{\circ} \) and \( -180^{\circ} \)
B. In between \( 180^{\circ} \) and \( 270^{\circ} \) or \( -90^{\circ} \) and \( -180^{\circ} \)
C. In between \( -90^{\circ} \) and \( 0^{\circ} \) or \( 270^{\circ} \) and \( 360^{\circ} \)
D. None of these


Where would an object be placed in a
medium of refractive index \( \mu_{1}, \) so that
its real image is formed at equidistant from sphere (of radius \( \mathrm{R} \) and refractive
index \( \mu_{2} \) ) which is also placed in the
medium of refractive index \( \mu_{1} \) as shown
in figure?
A \( \cdot\left(\frac{\mu_{2}-\mu_{1}}{\mu_{2}+\mu_{1}}\right) R \)
B \( \cdot\left(\frac{\mu_{2}}{\mu_{2}-\mu_{1}}\right) R \)
c. \( \left(\frac{\mu_{1}}{\mu_{2}-\mu_{1}}\right) R \)
D. \( \left(\frac{\mu_{2}+\mu_{1}}{\mu_{2}-\mu_{1}}\right) R \)


Oxidation of which of the following
reagent with manganese dioxide
\( \left(M n O_{2}\right) \) gives chlorine?
A. conc. \( H C l \)
B . Dil. \( H C l \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. \( H N O_{3} \)


A transverse wave is described by the
equation \( \boldsymbol{Y}=\boldsymbol{Y}_{0} \sin 2 \boldsymbol{\pi}(\boldsymbol{f} \boldsymbol{t}-\boldsymbol{x} / \boldsymbol{\lambda}) . \) The
maximum particle velocity is equal to four times the wave velocity if?
A \( \cdot \lambda=\pi Y_{0} / 4 \)
B . \( \lambda=\pi Y_{0} / 2 \)
\( \mathbf{c} \cdot \lambda=\pi Y_{0} \)
D \( . \lambda=2 \pi Y_{0} \)


Compare hydration energy of \( B e^{2+} \) and
\( \boldsymbol{A} \boldsymbol{l}^{3+} \)


In which pair, 1st compound having more heat of combustion as compared
to 2nd compound
\( A \)
\( = \)
в.
\( c \)
D.


An example of rolling friction is:
A. using oil to lubricate
B. skateboard moving on wheels
C. dragging your sister across floor on a blanket
D. a fish swimming through ocean


Which of the following pair has electron deficient compounds?
A. \( B_{2} H_{6}, \) AlCla
в. \( C_{2} H_{6}, \) Аl\( _{2} C l_{6} \)
c. \( S F_{2}, C l_{2} O \)
D. \( N a B H_{4}, I C l \)


The general body plan and the body symmetry are similar in
A. Frog and locust
B. Sea horse and starfish
C. Annelids and sponge
D. Pigeon and liver fluke


If an antiderivative of \( f(x) \) is \( e^{x} \) and
that of \( g(x) \) is \( \cos x, \) then \( \int f(x) \cos x d x+\int g(x) e^{x} d x= \)
\( \mathbf{A} \cdot f(x) g(x)+c \)
в. \( f(x)+g(x)+c \)
c. \( e^{x} \cos x+c \)
D. \( -e^{x} \cos x+c \)


Find \( \boldsymbol{x} \)
\( \frac{3}{x-2}<1 \)


Which term of the
\( A . P ., 12,7,2,-3, \dots \dots . \) is \( -98 ? \)


4 buses runs between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are
A . 12
B. 16
\( c \cdot 4 \)
D. 8


The danger signals installed at the top of tall buildings are red in colour. These can be easily seen from a distance
because among all other colours, the red light:
A. is scattered the most by smoke or fog.
B. is scattered the least by smoke or fog
c. is absorbed the most by smoke or fog.
D. moves fastest in air


f 0.2 mol of the following substances are required how many grams of those
substances should be taken?
a. Sodium chloride
b. Magnesium oxide
c. Calcium carbonate


Pick up a set with non-essential
amino acids:
A. Lysine, Valine, Leucine
B. Serine, Tyrosine, Cysteine
C. Tryptophan, Phenylalanine, Isoleucine
D. Threonine, Methionine, Lysine


\( 1 \times 10^{-3} \) mole of \( H C l \) is added to a
buffer solution made up of \( 0.01 M \)
acetic acid and \( 0.10 M \) sodium acetate.
The final pH of the buffer will be: (given
\( \boldsymbol{p} \boldsymbol{K}_{a} \) of acetic acid is \( \boldsymbol{4} . \boldsymbol{7} \boldsymbol{5} \) at \( \boldsymbol{2} \boldsymbol{5}^{\boldsymbol{o}} \boldsymbol{C} \boldsymbol{)} \)
A . 4.60
B. 4.66
c. 4.75
D. 4.8


For paraxial rays, show that the focal length of a spherical mirror is one-half
of its radius of curvature.


Evaluate \( \cos ^{-1} x+ \)
\( \cos ^{-1}\left\{\frac{x}{2}+\frac{1}{2} \sqrt{3-3 x^{2}}\right\}, x \epsilon\left[\frac{1}{2}, 1\right] \)
A \( \cdot-\frac{\pi}{6} \)
B. \( +\frac{\pi}{6} \)
\( c \cdot-\frac{\pi}{3} \)
D. \( +\frac{\pi}{3} \)


In nature, metal \( A \) is found in a free
state while metal \( B \) is found in the form
of its compounds. \( B \) of these two will be
nearer to the top of the activity series of metals.
A. True
B. False


\( f \) is a linear function. Values of \( x \) and
\( f(x) \) are given in the table; complete the table
\begin{tabular}{cc}
\( \boldsymbol{x} \) & \( \boldsymbol{f}(\boldsymbol{x}) \) \\
-3 & 17 \\
0 & \( - \) \\
\( - \) & 1 \\
4 & -18 \\
\hline \\
\( - \) & -30
\end{tabular}


Consider the time interval \( t=0 \) to \( t= \)
\( \mathbf{2 . 0 s} \)
The magnetic field is perpendicular to
the plane of the loop.


Which is of the following is the correct
order in evolutionary history of man?
A. Peking man \( \rightarrow \) Habilus man \( \rightarrow \) Neanderthal man \( \rightarrow \) Cro-Magnon man
B. Peking man \( \rightarrow \) Heidelberg man \( \rightarrow \) Neanderthal man \( \rightarrow \) Cro-Magnon man
C. Peking man \( \rightarrow \) Neanderthal \( \operatorname{man} \rightarrow \) Homo sapiens \( \rightarrow \) Heidelberg man
D. Peking man \( \rightarrow \) Homo sapeins \( \rightarrow \) Neanderthal \( \operatorname{man} \rightarrow \) Cro-Magnon mann


Consider two conducting spheres of
radii \( R_{1} \) and \( R_{2} \) with \( R_{1}>R_{2} \). If the two
are at the same potential, and the larger sphere has more charge than the smaller sphere, then
A. the charge density of smaller sphere is less than that of larger sphere
B. the charge density of smaller sphere is more than that of larger sphere.
c. both spheres may have same charge density
D. None of these.


The ionisation constant of acetic acid is
\( 1.8 \times 10^{-5} \).The concentration at which
it will be dissociated to \( 2 \% \) is:
\( \mathbf{A} \cdot 1 M \)
В. \( 0.045 M \)
\( c .0 .018 M \)
D. \( 0.45 M \)


Using properties of determinants, prove
\[
\text { the following: }\left|\begin{array}{ccc}
\mathbf{1} & \mathbf{1} & \mathbf{1} \\
\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\
\boldsymbol{a}^{\mathbf{3}} & \boldsymbol{b}^{\mathbf{3}} & \boldsymbol{c}^{3}
\end{array}\right|=(\boldsymbol{a}-
\]
\( b)(b-c)(c-a)(a+b+c) \)


Assertion: Hard water consumes more
soap. Reason: The ion responsible for cleansing action is precipitated out by
\( C a^{2+} \) or \( M g^{2+} \) ion.
A. Assertion is correct but Reason is wrong.
B. Assertion is correct but Reason is right
c. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
D. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.


The oxidation state of the underlined
element in the given compound is:
\( \boldsymbol{N} \boldsymbol{a}_{2}\left[\underline{\boldsymbol{F}} e(\boldsymbol{C} \boldsymbol{N})_{5} \boldsymbol{N} \boldsymbol{O}\right] \)
\( A \cdot-2 \)
\( B .+2 \)
\( c \cdot+3 \)
D. none of these


An atom has two main regions.Which are those?
A. Planetary electrons and energy levelss
B. Nucleus and kernel
c. Principal energy levels and energy sublevels
D. Nucleus and energy levels


If \( \boldsymbol{\alpha} \boldsymbol{\epsilon}\left(\boldsymbol{0}, \frac{\boldsymbol{\pi}}{2}\right), \) then the expression
\( \sqrt{x^{2}+x}+\frac{\tan ^{2} x}{\sqrt{x^{2}+x}} \) is always greater
than or equal to
\( A \cdot 2 \tan \alpha \)
B. 2
\( c . \)
\( D \cdot \sec ^{2} \alpha \)


Biotic factors are
A. Chemical factors of soil which affect life
B. Physical factors of soil which affect life
C. All living organisms which influence other organisms
D. Factors of atmosphere which affect life


If \( \boldsymbol{A}=\{\boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}\} \) and \( \boldsymbol{B}=\{\boldsymbol{x}, \boldsymbol{y}\} . \) Find
which of the following are elements of
\( \boldsymbol{A} \times \boldsymbol{A} \)
A \( \cdot\{b, b\} \)
в. \( \{b, c\} \)
c. \( \{b, d\} \)
D. All of the above


Compared to the case with zero magnetic field, does it take the loop a longer or shorter time to rotate through
\( 90^{\circ} ? \) Explain.


A car is moving in a straight line with speed \( 18 k m h^{-1} . \) It is stopped in \( 5 s \) by applying the brakes. Find : (i) the speed
of car in \( m s^{-1} . \) (ii) the retardation and
(iii) the speed of car after \( 2 s \) of applying
the brakes.
A \( .5 \mathrm{ms}^{-1} \)
B. \( 1 m s^{-1} \)
\( \mathbf{c} \cdot 3 m s^{-1} \)
D. none on these


The absolute maximum of \( \boldsymbol{y}=\boldsymbol{x}^{3}- \)
\( 3 x+2 \) in \( 0 \leq x \leq 2 \) is:
A . 4
B. 6
\( c \cdot 3 \)
D.


Why are lithium salts commonly
hydrated and those of the other alkali ions usually anhydrous?


Which of the following element is found in its native state?
A . Silver
B. Gold
c. sodium
D. Both (A) and (B)


A sphere of maximum volume is cut out from a solid hemisphere of radius r.The ratio of the volume of the hemisphere to that of the cut out sphere is:


sum of the series is \( 1+3+6+10+ \)
\( 15+\ldots \) to \( n \) terms \( \frac{n(n+m)(n+p)}{k} \) Find \( \boldsymbol{k}-\boldsymbol{m}-\boldsymbol{p} ? \)


Find the scalar components and magnitude of the vector joining the
points \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}, \boldsymbol{z}_{1}\right) \) and \( \boldsymbol{Q}\left(\boldsymbol{x}_{2}, \boldsymbol{y}_{2}, \boldsymbol{z}_{2}\right) \)


A body of mass 'M' collides against a wall with a velocity 'v' and retraces its path with the same velocity, the change in momentum is
A . zero
в. \( 2 M v \)
c. \( M v \)
D. \( -M v \)


The name of the compound is 3 -bromo-
5-methyl cylopentanone
If true enter 1 , else enter 0 .


There is a current of 1.344 amp in a
copper wire whose area of cross-section
normal to the length of the wire is
\( 1 m m^{2} . \) If the number of free electrons
per \( c m^{3} i s 8.4 \times 10^{2} 2, \) then the drift
velocity would be
A . \( 1.0 \mathrm{mm} / \mathrm{sec} \)
B. 1.0 \( \mathrm{m} / \mathrm{sec} \)
c. \( 0.1 \mathrm{mm} / \mathrm{sec} \)
D. 0.01 \( \mathrm{mm} / \mathrm{sec} \)


The units digit of a two-digit number is greater than its tens digit by 2 and the product of that number by the sum of its digits is \( 144 . \) Find the number.


State whether true or false:
The Sl unit of force is newton.
A. True
B. False


Bicarbonate ion is an example of :
A . an acid
B. an acidic salt
c. a basic salt
D. an amphoteric substance


When zinc is treated with conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
an oxide of nitrogen is formed. The change in oxidation state of nitrogen during this reaction is:
A . +5 to 0
B. +5 to +2
\( c .+5 t o+4 \)
\( \mathbf{D} \cdot+5 \) to +1


Which element has electrons in \( f \)
orbitals?
\( A \cdot A r \)
B.
\( c \cdot s \)
D. Ti
E.


Evolution of man was possible because our ape-like ancestors
A. Showed bipedal movement on open land
B. Used fire
c. Had difficulty in gaining nutrition
D. Developed community hunting


The velocity of a sound wave in \( v \) and
the wave energy density is \( E, \) then the
amount of energy transferred per unit area per second by the wave in a direction normal to the wave
propagation is
A. \( E \)
в. \( E v \)
\( \mathrm{c} \cdot E^{2} v^{2} \)
D. \( \sqrt{E v} \)


State whether True or False:
\( (2 \sqrt{3}+3 \sqrt{2})^{2}=12+18+12 \sqrt{6}= \)
\( 30+\sqrt{6} \)


Find the natural frequency of oscillation
of the system as shown in figure. Pulleys are massless and frictionless.
Spring and string are also massless.
A \( \cdot \frac{\pi}{2} \)
B. \( \sqrt{\pi} \)
\( c \cdot \sqrt{\frac{1}{\pi}} \)
\( D \)


A 78.0 g sample of an unknown compound contains \( 12.4 \mathrm{g} \) of hydrogen. What is the percent by mass of hydrogen in the compound?
A . 25\%
B. 35\%
c. \( 16 \% \)
D. 50\%


Find the image of point (1,6,3) in the \( \operatorname{line} \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \)


From the given diagram, find the
elements of:
\( A-(B \cap C) \) and \( (A-B) \cup(A-C) \) and enter
1 or 0 respectively if the given relation
holds True or False: \( A-(B \cap C)=(A-B) \cup \)
\( (A-C) \)


Interstitial fluid is called as tissue fluid
A. True
B. False


Factorize:
\( \boldsymbol{p q} \boldsymbol{r}-\boldsymbol{p}^{2} \boldsymbol{q}+\boldsymbol{p} \boldsymbol{q}^{2} \boldsymbol{r} \)


A ball is thrown vertically upward from ground with speed \( 40 m / s . \) It collides with ground after returning. Find the total distance traveled and time taken
during its bouncing. \( (e=0.5)(g= \)
\( 10 m / s^{2} \)


Dielectric constant of a metal is
A. zero
B. Infinite
c. Finite
D. Unpredictable


Find the number of metal oxides which
are decomposed on normal heating from the given oxides:
\( \left(N a_{2} O, A l_{2} O_{3}, P b O, A g_{2} O, H g O\right) \)


Given :
Oxidation:
\( H_{2} O_{2} \rightarrow O_{2}+2 H^{\oplus}+2 e^{-} \)
\( E^{\ominus}=-0.69 V \)
\( 2 F^{\ominus} \rightarrow F_{2}+2 e^{-} \)
\( E^{\ominus}=-2.87 V \)
Reduction:
\( H_{2} O_{2}+2 H^{\oplus}+2 e^{-} \rightarrow 2 H_{2} O \)
\( E^{\ominus}=-1.77 V \)
\( 2 I^{\ominus} \rightarrow I_{2}+2 e^{-} E^{\ominus}=-0.54 V \)
Which of the following statements is/are
correct?
This question has multiple correct options
A \( \cdot H_{2} O_{2} \) behaves as an oxidant for \( I^{\ominus} \)
B. \( H_{2} O_{2} \) behaves as a reductant for \( I_{2} \)
C. \( H_{2} O_{2} \) behaves as an oxidant for \( F^{\ominus} \)
D. \( H_{2} O_{2} \) behaves as a reductant for \( F_{2} \).


The measure of an angle in degrees, grades and radians be \( \mathrm{D}, \mathrm{G} \) and \( \mathrm{C} \)
respectively, then relation between them \( \frac{\boldsymbol{D}}{\mathbf{9 0}}=\frac{\boldsymbol{G}}{\mathbf{1 0 0}}=\frac{\boldsymbol{2 C}}{\boldsymbol{\pi}} \) but \( \mathbf{1}^{\circ}= \)
\( \left(\frac{180}{\pi}\right)^{0} \simeq 57^{\circ}, 17^{\prime}, 44.8^{\prime \prime} \) and sum of
interior angles of a \( n \) -sided regular polygon is \( (2 n-4) \frac{\pi}{2} . \) On the basis of above information, answer the following questions :The number of sides of two
regular polygon are as 5: 4 and the difference between their angles is \( \frac{\pi}{20} \)
then the number of sides in the
polygons respectively are -
A. 25, 20
B. 20, 16
c. 15,12
D. 10,8


Upon inserting a parallel-sided slab of
glass between the lens and the screen,
it was found necessary to move the screen a distance d away from the lens
in order for the image to be again sharply focussed. If the refractive index
of glass relative to air is \( \mu \) then the thickness of the slab is:
\( \mathbf{A} \cdot \frac{d}{\mu} \)
в. \( \frac{\mu}{d} \)
c. \( \frac{\mu d}{(\mu-1)} \)
D. \( \frac{(\mu-1) d}{\mu} \)


Carbon has six protons and six neutrons in its nucleus. What is the
atomic mass of carbon?
\( A \cdot 4 \)
B. 12
\( c \cdot 8 \)
D. 6


Which one of the following is an optically active compound?
A. \( C H_{3} C H_{2} \) COOH
в. \( C H_{3} C H(O H) C O O H \)
с. НООС СН\( _{2} \).СООН
D. \( C H_{3} \) СО СООН


Which of the following is true regarding
periodicity of elements?
A. Elements of same group are characterized by same valence shell electronic configuration.
B. The most electropositive elements are positioned on right hand side of the Modern periodic Table
C. On going from Li of F there would be decrease in ionization energy
D. reducing property of elements increases from Na to Cl in 3 rd period elements.


SONAR is frequently used by :
A. Austronauts
B. Doctors
c. Engineers
D. Navigators


A spring mass system is in simple harmonic motion. Immediately after the upward extreme end point, which of the following increase?
A. Kinetic energy, gravitational potential energy, elastic potential energy
B. Kinetic energy and gravitational potential energy
c. Kinetic energy only
D. Gravitational potential energy and elastic potential energy
E. Elastic potential energy only


The is the difference
between the greatest and the least
value of the variate.
A . Range
B. Data
c. Average
D. Variance


Find the area bounded by the curves \( \boldsymbol{x}=\boldsymbol{a} \cos \boldsymbol{t}, \boldsymbol{y}=\boldsymbol{b} \sin t \) in the first
quadrant
A \( \cdot \frac{\pi a b}{4} \)
B. \( \frac{\pi a^{2} b}{4} \)
c. None of these
D. \( \frac{\pi a b^{2}}{4} \)


Velocity of sound is maximum in-
A. water
B. oil
c. Air
D. Iron


Out of white phosphorus and red phosphorus, which one is more reactive and why?


\( K O_{2} \) is used to bleach silk, wool, ivory
and hair. If this is true enter 1 , if false enter 0 .


Factorise:
\( (i) 25-4 x^{2}-12 x y-9 y^{2} \)
\( (i i) x^{2}-a^{2}+10 a b-25 b^{2} \)
\( (i i i) 6 x y+x^{2}+9 y^{2}-4 a^{2} \)
\( (i v) 9 x^{2}+4+12 x-a^{2}+2 a b-b^{2} \)


A solution of known concentration is
known as:
A. molar solution
B. normal solution
C. mole solution
D. standard solution


\( 1 \mathrm{kg} \) of water is supplied \( 630 \mathrm{kJ} \) of energy. Specific heat of water is 4200
J/kg \( ^{\circ} \) C.So calculate the rise in temperature of 1 kg water
A \( \cdot 40^{\circ} \mathrm{C} \)
B . \( 60^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 80^{\circ} \mathrm{C} \)
D. \( 150^{\circ} \mathrm{C} \)


In case \( A, \) when an 80 kg skydiver falls with arms and legs fully extended to maximize his surface area, his terminal velocity is \( 60 \mathrm{m} / \mathrm{s} \). In Case \( B \), when the
same skydiver falls with arms and legs pulled in and body angled downward to minimize his surface area, his terminal velocity increases to \( 80 \mathrm{m} / \mathrm{s} \). In going from Case A to Case B, which of the
following statements most accurately describes what the skydiver experiences?
A \( \cdot F_{\text {air ressitanne }} \) increases and pressure \( P \) increases
B. \( F \) aireesisance increases and pressure \( P \) decreases
c. \( F_{\text {ir resistance decreases and pressure } P \text { increases }} \)
D. \( F_{\text {air easitance remains the same and pressure }} P \) increases


Which of the following statements is
true?
A. A stationary charge will experience a force in both a magnetic and electric field
B. A charge moving parallel to field lines will experience a force in both magnetic and electric fields.
C. A charge moving perpendicular to field lines will experience a force in both magnetic and electric fields.
D. It is impossible for a charge to move with constant velocity through an area that has both electric and magnetic fields


The adjoining diagram shows the view
through the eyepiece of a prism
spectrometer with its slit illuminated
by the source of light emitting three wavelengths corresponding to yellow
(Y), Green (G) and unknown colour (X).
The colour at \( X \) may be:
\( \mathbf{A} \cdot \operatorname{Red} \)
B. Orange
c. Pink
D. Blue


Equilibrium constants for four different
reactions are given as:
\( \boldsymbol{K}_{\mathbf{1}}=\mathbf{1 0}^{\mathbf{6}}, \boldsymbol{K}_{\mathbf{2}}=\mathbf{1 0}^{-\mathbf{4}}, \boldsymbol{K}_{\mathbf{3}}=\mathbf{1 0}, \boldsymbol{K}_{\mathbf{4}}= \)
1. Which reaction will take maximum
time to attain equilibrium?
A \( \cdot K_{1}=10^{6} \)
B \( \cdot K_{2}=10^{-4} \)
\( \mathbf{c} \cdot K_{3}=10 \)
D. can't predict


A vessel of volume \( 0.2 m^{3} \) contains
hydrogen gas at temperature \( 300 K \) and pressure 1 bar. Find the heat required to raise the temperature to \( 400 K . \) The molar heat capacity of hydrogen at constant volume is
\( \mathbf{5} \) cal / molK.
A \( \cdot(\Delta Q)_{v}=2.1 k c a l \)
B . \( (\Delta Q)_{v}=4.2 \mathrm{kcal} \)
C \( \cdot(\Delta Q)_{v}=2 k c a l \)
D. \( (\Delta Q)_{v}=4 k c a l \)


Briefly describe the modes of
reproduction in bacteria


Nucleic acids control heredity at:
A. atomic Level
B. ionic level
c. complex level
D. molecular level


Which one has the highest coagulation
power?
A. \( K^{+}+ \)
B. \( C a^{+}+ \)
c. \( A l^{+++} \)
\( D \cdot S n^{4} \)


Let tangent at a point \( \mathrm{P} \) on the curve \( x^{2 m} y^{\frac{n}{2}}=a^{\frac{4 m+n}{2}} \) meets the x-axis
and y-axis at A and B respectively if AP:
\( \mathrm{PB} \) is \( \frac{n}{\lambda m} \) where \( \mathrm{P} \) lies between \( \mathrm{A} \) and \( \mathrm{B} \)
then find the value of \( \lambda \)


Consider following statements. Choose
the correct ones:
This question has multiple correct options
A. \( \mathrm{CM} \) of a uniform semicircular disc of radius \( \mathrm{R} \) is \( 2 R \pi \)
from the centre.
B. \( \mathrm{CM} \) of a uniform semicircular ring of radius \( 2 R / 3 \) is \( 4 R / 3 \pi \) from the centre.
C. \( \mathrm{CM} \) of a solid hemisphere of radius \( \mathrm{R} \) is \( 4 R / 3 \pi \) from the centre.
D. \( \mathrm{CM} \) of a solid hemisphere shell of radius \( \mathrm{R} \) is \( R / 2 \) from the centre.


If true enter 1 , else enter 0 .
The bond strength increases as the number of lone pairs on neighbouring atoms increases.
A. 0
B.
c. none
D. both


The value of \( \int\left(x e^{\ell n \sin x}-\cos x\right) d x \) is
equal to:
\( \mathbf{A} \cdot x \cos x+C \)
B. \( \sin x-x \cos +C \)
c. \( -e^{e n x} \cos x+C \)
\( \mathbf{D} \cdot \sin x+x \cos x+C \)


Hooke's law holds good up to
A. Plastic point
B. Limit of proportionality
c. Breaking point
D. None of these


A metal obtained by auto reduction or self reduction
A . Na a
B. zn
c. \( \mathrm{Fe} \)
D. cu


The interval(s) of decrease of of the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2} \log 2 \mathbf{7}- \)
\( 6 x \log 27+ \)
\( \left(3 x^{2}-18 x+24\right) \log \left(x^{2}-6 x+8\right) \) is
This question has multiple correct options
A \( \cdot(3-\sqrt{1+1 / 3 e}, 2) \)
B. \( (4,3+\sqrt{1+1 / 3 e}) \)
c. \( (3,4+\sqrt{1+1 / 3 e}) \)
D. none of these


The corresponding altitudes of two
similar triangles are \( 6 \mathrm{cm} \) and \( 9 \mathrm{cm} \)
respectively. Find the ratio of their
areas.


In a complete circular motion, first half circle is covered with 6.The other half circle is covered in two equal times
intervals at speed 4 and 2 respectively.The average speed during the circular motion is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


By splitting into prime factors, find the square root of 729
A . 27
B. 21
c. 17
D. 87


The end product \( (Z) \) of the given
reaction is:
A. a cyanide
B. a carboxylic acid
c. an amine
D. an arene


The bond order in \( N O \) is 2.5 while that
in \( N O^{+} \) is \( 3 . \) Which statement is true
for these two species?
A. Bond length is unpredictable
B. Bond length in \( N O \) is greater than in \( N O^{+} \)
C. Bond length in \( N O^{+} \) is equal to that in \( N O \)
D. Bond length in \( N O^{+} \) is greater than in \( N O \)


The spontaneity of a reaction is
indicated by:
A. enthalpy change
B. entropy change
c. gibbs free energy change
D. activation energy
E. specific heat capacity


Which one of these is not damaged due to excess lead in drinking water?
A. Kidney
B. Liver
C. Reproductive system
D. Teeth


Iron exhibits +2 and +3 oxidation states
Which of the following statements about iron is incorrect?
A. Ferrous oxide is more basic in nature than the ferric oxide
B. Ferous compounds are relatively more ionic than the corresponding ferric compounds
c. Ferrous compounds are less volatile than the corresponding ferric compounds
D. Ferrous compounds are more easily hydrolysed than the corresponding ferric compounds


State true or false.
\( \sqrt{3}+\sqrt{4} \) is an rational number.
A. True
B. False


The incident intensity on a horizontal surface at sea level from the sun is
about \( 1 k W m^{-2} \). Find the ratio of this
pressure to atmospheric pressure \( \boldsymbol{p}_{0} \)
(about \( \left.1 \times 10^{5} P a\right) \) at sea level.
[Assuming that \( 50 \% \% \) of this intensity is reflected and \( 50 \% \% \text { is absorbed }] \)
A \( .5 \times 10^{-11} \)
B. \( 4 \times 10^{-8} \)
c. \( 6 \times 10^{-12} \)
D. \( 8 \times 10^{-11} \)


A strong base can abstract an \( \alpha \)
hydrogen from :
A . amine
B. alkene
c. alkane
D. ketone


The dihybrid ratio of 9: 3: 3: 1 proves the law of


\( \int\left\{\frac{(\log x-1)}{\left(1+(\log x)^{2}\right.}\right\}^{2} d x \) is equal to
A \( \frac{\log x}{(\log x)^{2}+1}+c \)
B. \( \frac{x}{x^{2}+1}+c \)
c. \( \frac{x e^{x}}{1+x^{2}}+c \)
D. \( \frac{x}{(\log x)^{2}+1}+c \)


How can you say circular motion of an object is said to be an accelerated
motion.


Three moles of an ideal gas being
initially at a temperature \( \boldsymbol{T}_{\boldsymbol{i}}=\mathbf{2 7 3} \mathbf{K} \)
were isothermally expanded 5 times its initial volume and then isochorically heated so that the pressure in the final
state become equal to that in the initial state. The total heat supplied in the process is \( 80 \mathrm{kJ} \). If \( \gamma=\frac{C_{p}}{C_{v}} \) of the gas is \( \frac{x}{10}, \) find \( x \)


Explain conservation of charge giving two examples


If both the rectangles are similar, find \( x \)
\( A \)
B.
\( c \)
D. none of the above


The common immediate source of
energy in cellular activity is
A. ADP
B. ATP
c. FAD
D. NAD


Which one of the following represents the correct ratio of the energy, of electron in ground state of H atom to
that of the electron in the first excited
state of \( \boldsymbol{L} \boldsymbol{i}^{+} ? \)
A .4: 9
B. 9: 4
\( c \cdot 1: 4 \)
\( D \cdot 4: 1 \)


The formula relating youngs modulus
(Y), rigidity modulus (n) and Poisson's ratio \( (\sigma) \) is
\( \mathbf{A} \cdot Y=2 n(1-\sigma) \)
В . \( Y=2 n(1+\sigma) \)
c. \( Y=n(1-2 \sigma) \)
D. \( Y=n(1+2 \sigma) \)


Current \( i \) as shown in the circuit will be
\( \mathbf{A} \cdot 10 A \)
B. \( \frac{10}{3} A \)
\( \mathbf{c} \). zero
D. infinite


A body of mass \( \mathrm{m} \) is projected from
ground with speed \( u \) at an angle \( \theta \) with
horizontal the power delivered by
gravity to it at half of maximum heigh from ground is


\( \int x^{9} d x \)


Using the cross-section image of an
iodine solid, which of the following
explains why it cannot conduct
electricity in the solid or molten states?
A. The molecular lattice points are too far away to conduct electricity
B. Only metallic solids conduct electricity
C. The electrons are tightly bound within the covalent bond of the \( I_{2} \) molecules.
D. The electrons are too polarizable to conduct electricity.


ff \( a_{1}, a_{2}, a_{3}, b_{1}, b_{2}, b_{3} \in R \) and are such
\( \operatorname{that} a_{i} b_{j} \neq 1 \) for \( 1 \leq i, j \leq 3, \) then
\( \begin{array}{|lll|}\frac{1-a_{1}^{3} b_{1}^{3}}{1-a_{1} b_{1}} & \frac{1-a_{1}^{3} b_{2}^{3}}{1-a_{1} b_{2}} & \frac{1-a_{1}^{3} b_{3}^{3}}{1-a_{1} b_{3}} \\ \frac{1-a_{2}^{3} b_{1}^{3}}{1-a_{2} b_{1}} & \frac{1-a_{2}^{3} b_{2}^{3}}{1-a_{2} b_{2}} & \frac{1-a_{2}^{3} b_{3}^{3}}{1-a_{2} b_{3}} \\ \frac{1-a_{3}^{3} b_{1}^{3}}{1-a_{3} b_{1}} & \frac{1-a_{3}^{3} b_{2}^{3}}{1-a_{3} b_{2}} & \frac{1-a_{3}^{3} b_{3}^{3}}{1-a_{3} b_{3}}\end{array} \)
either \( a_{1}<a_{2}<a_{3} \) and \( b_{1}<b_{2}<b_{3}, \) or
\( a_{1}>a_{2} a_{3} \) and
\( \boldsymbol{b}_{1}>\boldsymbol{b}_{2}>\boldsymbol{b}_{3} \)
then show \( \left(a_{1}-a_{2}\right)\left(a_{2}-a_{3}\right)\left(a_{3}-\right. \)
\( \left.\boldsymbol{a}_{1}\right)\left(\boldsymbol{b}_{1}-\boldsymbol{b}_{2}\right)\left(\boldsymbol{b}_{2}-\boldsymbol{b}_{3}\right)\left(\boldsymbol{b}_{3}-\boldsymbol{b}_{1}\right)<\mathbf{0} \)


A uniform electric field and a uniform
magnetic field are produced pointing in the same direction. An electron is
projected with its velocity pointed in the
same direction.Then:
A. the electron will turn to its right
B. the electron will turn to its left
c. the electron velocity will increase in magnitude
D. the electron velocity will decrease in magnitude


The standard reduction potentials \( \boldsymbol{E}^{\mathbf{C}} \)
for the half reactions are follows:
\( \boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{Z} \boldsymbol{n}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} ; \quad \boldsymbol{E}^{\ominus}= \)
\( +0.76 V \)
\( \boldsymbol{F e} \rightarrow \boldsymbol{F} \boldsymbol{e}^{2+}+\boldsymbol{2} \boldsymbol{e}^{-} ; \quad \boldsymbol{E}^{\ominus}=\mathbf{0 . 4 1} \boldsymbol{V} \)
The EMF for the cell reaction
\( \boldsymbol{F} \boldsymbol{e}^{2+} \boldsymbol{Z} \boldsymbol{n} \rightarrow \boldsymbol{Z} \boldsymbol{n}^{2+}+\boldsymbol{F} \boldsymbol{e} \) is:
A . \( -0.35 V \)
в. \( +0.35 V \)
c. \( +1.17 v \)
D. -1.17V


International broadcasting requires.
A. Medium frequency radio waves
B. High frequency radio waves
c. Low frequency radio waves
D. Longitudinal waves


Compare and contrast fossil fuels and the Sun as direct sources of energy.


The probability for a randomly chosen month to have its \( 10^{t h} \) day as Sunday,
is.
A \( \cdot \frac{1}{84} \)
в. \( \frac{10}{12} \)
c. \( \frac{10}{84} \)
D.


When the flux linked with a coil
changes:
A. current is always induced
B. an emf and a current are always induced
c. an emf is induced but a current is never induced
D. an emf is always induced and a current is induced when the coil is a closed one


An inductor \( 10 \Omega / 60^{\circ} \) is connected to a
\( 5 \Omega \) resistance in series. Find net
impedance.
A . \( 15 \Omega \)
B. \( 12 \Omega \)
c. \( 13.2 \Omega \)
D. \( 18 \Omega \)


Bond angle is largest in:
A \( \cdot \mathrm{xeF}_{2} \)
в. \( \mathrm{xeF}_{4} \)
c. \( \mathrm{xeF}_{6} \)
D. \( \mathrm{xeO}_{4} \)


An object becomes charged when the atoms in the object gain or lose.
A. Protons
B. Neutrons
c. Electrons
D. All of these


Let \( ^{*} \) be a binary operation on the set \( \boldsymbol{Q} \)
of rational numbers as follows:
\( \boldsymbol{a} * \boldsymbol{b}=\frac{\boldsymbol{a} \boldsymbol{b}}{\boldsymbol{4}} \)
Find which of the binary operations are commutative and which are
associative.


Relation between current in a conductor
and time is shown in Figure. If the
resistance of the conductor is \( R \), then
the total heat dissipated across
resistance \( \boldsymbol{R} \) is :
A \( \cdot \frac{i_{0}^{2} R t_{0}}{2} \)
B. \( \frac{i_{0}^{2} R t_{0}}{4} \)
c. \( \frac{i_{0}^{2} R t_{0}}{3} \)
D \( \cdot i^{2}_{0} R t_{0} \)


List any two significance of meiosis?


pH signifies
A. Power of hydrogen
B \( .-\log \left[H^{+}\right] \)
c. \( 14- \) pOH
D. All of the above


The sounds having frequency less than
\( 20 H z \) are called ultrasonics. True or
False?


A force \( -F \widehat{k} \) acts on \( 0, \) the origin of the
coordinate system.The torque about the point (1,-1) is
A \( . F(\hat{i}-\hat{j}) \)
B . \( -F(\hat{i}+\widehat{j}) \)
C \( . F(\hat{i}+\widehat{j}) \)
D . \( -F(\hat{i}-\widehat{j}) \)


w."15 ivsiv
circuit is
\( A \)
B.
\[
\left|\begin{array}{lll}
A & B & Y \\
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 1
\end{array}\right|
\]
\( c \)
\( D \)


When two progressive waves \( \boldsymbol{y}_{1}= \)
\( 4 \sin (2 x-6 t) \) and \( y_{2}=3 \sin (2 x- \)
\( \left.6 t-\frac{\pi}{2}\right) \) are superimposed, the
amplitude of the resultant wave is


An example of Agnatha (jawless vertebrate)/cyclostomata is
A . Labeo rohita
B. Scoliodon
c. Rana tigrina
D. Petromyzon


Evaluate the given integral.
\( \int \frac{1}{x\left(x^{4}+1\right)} d x \)


Find the differential equation of the family of lines passing through the origin.


The electric potential at a point on the equatorial line of an electric dipole is
A. directly proportional to distance
B. inversely proportional to distance
c. inversely proportional to square of the distance
D. none of the above


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be defined as \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{5} \)
show that it is a bijective function.


Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities are
A. Impulse, pressure and area
B. Impulse and area
c. Area and gravitational potential
D. Impulse and pressure


Which of the following is the natural cause of deforestation?
A. Urbanization
B. Forest fires
c. Agricultural activities
D. All of the above


The heavenly body which revolves around a planet is called a
A . comet
B. star
c. satellite
D. nebulae


A ball is dropped from a height of \( 10 \mathrm{m} \) If the energy of the ball reduces by \( 40 \% \) after striking the ground, how high can
the ball bounce back? \( \left(g=10 m s^{-2}\right) \)
\( A \cdot 6 m \)
B. 10 \( m \)
\( c \cdot 3 m \)
D. 12


Which of the following is a catfish?
A. Labeo rohita
B. Catla catla
c. cirrhina mrigala
D. wallago attu


\( \int_{-\pi / 2}^{\pi / 2} \tan x^{3} d x=? \)
A . 1
B.
\( c \cdot 2 \)
D.


The number of triplets \( (x, y, z) \) satisfies
the equation \( \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z})=\sin ^{-1} \boldsymbol{x}+ \)
\( \sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2} \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
c. 0
D. Infinite


The additive inverse of \( \frac{2}{7} \) is
A \( \cdot \frac{2}{7} \)
B. \( \frac{-2}{7} \)
c. \( \frac{7}{2} \)
D. \( \frac{-7}{2} \)


Using definite integration, find area of the triangle with vertices at \( A(1,1), B(3,3) A(1,1), B(3,3) \)


The bluish colour of water in deep sea is
due to:
A. the presence of algae and other plants found in water.
B. reflection of sky in water
c. scattering of light.
D. absorption of light by the sea


Assertion
Sound waves do not travels through
vacuum.
Reason
The speed of sound is too small when
compared to speed of light.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The vapour density of undecomposed
\( N_{2} O_{4} \) is \( 46 . \) When heated, vapour density decreases to 24.5 due to its
dissociation to \( N O_{2} . \) The percentage
dissociation of \( N_{2} O_{4} \) at the final
temperature is:
\( \mathbf{A} \cdot 88 \)
B. 60
c. 40
D. 70


The \( P . E . \) and \( K . E . \) of a helicopter flying horizontally at a height \( 400 m \) are in the
ratio \( 5: 2 . \) The velocity of helicopter is:
A. \( 56 \mathrm{m} / \mathrm{s} \)
в. \( 28 \mathrm{m} / \mathrm{s} \)
c. \( 14 \mathrm{m} / \mathrm{s} \)
D. \( 42 \mathrm{m} / \mathrm{s} \)


If a vector \( \vec{A} \) makes an angles \( \alpha, \beta \) and
\( Y \) respectively with the \( x, y \) and \( z \) axes
respectively. Then \( \sin ^{2} \alpha+\sin ^{2} \beta \)
\( +\sin ^{2} \gamma \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. 2
D. 3


Aluminum displaces hydrogen in dil. HCl whereas silver does not. The e.m.f of
a cell prepared by combination \( A l / A l^{3+} \) and \( A g / A g^{+} \) is 2.46 V. The
reduction potential reduction potential of aluminum electrodes is:
A \( .+1.66 v \)
B. - -3.26 V
\( c .+3.26 v \)
D. -1.66 V


Write the degree of the differentia
equation:
\( \left(\frac{d y}{d x}\right)^{4}+3 x \frac{d^{2} y}{d x^{2}}=0 \)


Explain \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right]^{3+} \) is an inner
orbital complex whereas \( \left[N i\left(N H_{3}\right)_{6}\right]^{2+} \) is an outer orbital complex.


How many \( F_{2} \) plants having two dominant alleles typically dihybrid cross?
A . \( 6 / 16 \)
B. \( 10 / 16 \)
c. \( 9 / 16 \)
D. 1/16


Obtain the differential equation of the family of circles touching the y-axis at the origin.


Match the following


Two flasks \( A \) and \( B \) is 500 m \( L \) each are
respectively filled with \( O_{2} \) and \( S O_{2} \) at
\( 300 K \) and 1 atm pressure. The flasks
contain :
A. The same number of atoms
B. The same number of molecules
c. More number of moles in flask \( A \) as compared to flask \( B \)
D. The same amount of gases


A frame \( C D E F \) is laced in a region
where a magnetic field \( \vec{B} \) is present. \( \mathbf{A} \)
rod of length one metre moves with
constant velocity \( 20 m / s \) and strength
of magnitude field is one tesia. The
power spent in the process is (take
\( R=0.2 \Omega \) and all other wires and rod
have zero resistance)
\( \mathbf{A} \cdot 1 k W \)
\( \mathbf{B} \cdot 2 k W \)
\( \mathbf{c} .3 k W \)
\( \mathbf{D} \cdot 4 k W \)


Calculate the work done by electric field
when a point charge q is moved from
point \( \mathrm{B} \) to \( \mathrm{A} \) along the curved path. Given that electric field is created by the
stationary charge \( \mathrm{Q} \) and \( V_{A}= \)
\( 200 V, V_{B}=100 V, q=0.05 C, \) length of line
segment \( A B=10 \mathrm{cm}, \) length of curved
path \( =20 \mathrm{cm} \)
A . O
B. 5
c. 10
D. 15 J
E. 20


To warn ships for underwater rocks, a lighthouse spreads a red coloured light
over a sector of angle \( 80^{\circ} \) to a distance
of \( 16.5 k m . \) Find the area of the sea over
which the ships are warned. (Use \( \pi= \)
3.14)


Convert into factorials:
\( \mathbf{3} \times \mathbf{6} \times \mathbf{9} \times \mathbf{1 2} \times \mathbf{1 5} \times \mathbf{1 8} \)


For a normal eye, in case of an adult, the
least distance of distinct vision is:
A. 5 to \( 8 \mathrm{cm} \)
B. 10 to \( 15 \mathrm{cm} \)
c. 20 to \( 25 \mathrm{cm} \)
D. 30 to \( 35 \mathrm{cm} \)


Negative feed back
A . increases stability
B. decreases stability
c. produces oscillation
D. stops current in the tube


In the given network, the current flowing
through \( 15 \Omega \) resistance is
\( \mathbf{A} \cdot 0.8 A \)
B. \( 1.0 A \)
\( c .1 .2 A \)
D. \( 1.4 A \)


A refrigerator converts \( 100 g \) of water at
\( 20^{\circ} \mathrm{C} \) to ice at \( -10^{\circ} \mathrm{C} \) in 35 minutes
Calculate the average rate of heat extraction in terms of watts.
Given:
Specific heat capacity of ice \( = \) \( 2.1 J g^{-1 o} C^{-1} \)
Specific heat capacity of water \( = \) \( 4.2 J g^{-1 o} C^{-1} \)
Specific Latent heat of fusion of ice
\( 336 J g^{-1} \)


In a division sum a student took 63 as
divisor instead of \( 36 . \) His answer was
24. What is the correct answer?
A .42
B . 24
\( c .36 \)
D. 63


\( \frac{1+\sin 2 \theta}{1-\sin 2 \theta}=\left(\frac{1+\tan \theta}{1-\tan \theta}\right)^{b} \)
Find \( b \)


A body of mass \( m \) has heat capacity
equal to \( C . \) If mass is doubled to \( 2 m \)
what is the new heat capacity?
A \( \cdot \frac{C}{2} \)
в. \( C \)
c. \( 2 C \)
D. \( \frac{3 C}{2} \)


A leaky capacitor \( 10 \Omega / 60^{\circ} \) is
connected in series with a \( 10 \Omega \)
resistance. Find the overall impedance.
Fig. 26.42
A. \( 10 \Omega \)
B. \( 10 \sqrt{2} \) ?
\( \mathrm{c} \cdot 15 \Omega \)
D. \( 10 \sqrt{3} \Omega \)


What is the correct IUPAC name of
HOOC \( -\boldsymbol{C H}_{2}- \) COOH


In which of the following doped semiconductors majority of charge carriers are holes?
A. Antimony doped with germanium
B. Boron doped with silicon
c. Arsenic doped with silicon
D. Phosphorus doped with germanium


Show that \( f(x)=x^{3}-15 x^{2}+75 x- \)
50 is an increasing function for all \( x \in \)
\( \boldsymbol{R} \)


(a) Calculate \( \Delta_{r} G^{0} \) for the reaction
\( M g(s)+C u^{2+}(a q) \rightarrow M g^{2+}(a q)+ \)
\( \boldsymbol{C u}(\boldsymbol{s}) \)
Given: \( \boldsymbol{E}_{c e l l}^{0}=\mathbf{2 . 7 1} \boldsymbol{V}, \mathbf{1} \boldsymbol{F}= \)
\( 96500 C m o l^{-1} \)
(b) Name the type of cell that was used in Apollo space program for providing electrical power.


The geometric mean of 2,6,8,24 is
A \( \cdot \sqrt{48}=4 \sqrt{3} \)
3
B. 16
c. 24
D. 36 6


A flat square sheet of charge (side 50 \( \mathrm{cm} \) carries a uniform surface charge density. An electron 0.5 cm from a point near the center of the sheet experiences a force of \( 1.8 \times 10^{-12} N \) directed away
from the sheet. Determine the total
charge on the sheet


A sample of \( O_{2} \) gas and a sample of
hydrogen gas both have the same no. of moles, the same volume and same
pressure. Assuming them to be perfect gases, the ratio of temperature of oxygen
gas to the temperature of hydrogen gas is :
A . 1:
B. 1:
c. 2:
D. 1:


Using section formula, show that the
points \( \boldsymbol{A}(\mathbf{2},-\mathbf{3}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1}, \mathbf{2}, \mathbf{1}) \) and
\( C\left(0, \frac{1}{3}, 2\right) \) are collinear.


Write balanced chemical equations for each of the following:
(i) The action of warm water on AIN.
(ii) The action of hot and concentrated
nitric acid on copper.
(iii) The action of hydrochloric acid on sodium bicarbonate.
(iv) The action of dilute sulphuric acid on sodium sulphite.
(v) Preparation of ethanol from ethyl chloride.


Q Type your question-
11a a poriviacu cauruuc anu containing air at very low pressure of
about \( 0.001 \mathrm{mm} \) of mercury, a faint red glow is observed behind the cathode.
What were the conclusions of this
experiment?
. Anode rays are positively charged.
ii. since these rays are formed at the
anode, they are known as anode rays.
iii. The experiment led to the discovery
of electrons
¡v. The experiment led to the discovery of protons.
tube
\( A \). i, ii and iii
B. ii, iii and iv
c. i, ii and iv
D. i, iii and


A bag contain 4 white and 2 black balls.
Two balls are drawn at random. The
probability that they are of the same colour is
A \( \cdot \frac{5}{7} \)
B.
c. \( \frac{7}{15} \)
D. \( \frac{1}{15} \)


\( A \) and \( B \) each throw a die. The probability that \( A^{\prime} \) 's throw is not greater than B's is
A \( \cdot \frac{21}{36} \)
в. \( \frac{12}{35} \)
c. \( \frac{7}{12} \)
D. \( \frac{5}{12} \)


The lines \( (a+b) x+(a-b) y-2 a b= \)
\( \mathbf{0},(\boldsymbol{a}-\boldsymbol{b}) \boldsymbol{x}+(\boldsymbol{a}+\boldsymbol{b}) \boldsymbol{y}-\boldsymbol{2} \boldsymbol{a} \boldsymbol{b}=\boldsymbol{0} \) and
\( x+y=0 \) forms an isosceles triangle
whose vertical angle is
A \( \cdot \frac{\pi}{2} \)
B. \( \mid \tan ^{-1}\left(\frac{2 a b}{a^{2}-b^{2}}\right) \)
c. \( \mid \tan ^{-1}\left(\frac{a}{b}\right) \)
D・ \( 2 \mid \tan ^{-1}\left(\frac{\mathrm{a}}{b}\right) \)


If \( z_{1} \) and \( z_{2} \) are \( z \) co-ordinates of the
points of trisection of the segment joining the points \( \boldsymbol{A}(\mathbf{2}, \mathbf{1}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1}, \mathbf{3}, \mathbf{6}) \)
then \( z_{1}+z_{2}= \)
A . 1
B. 4
\( c .5 \)
D. 10


For a process to be spontaneous at
constant \( \boldsymbol{T} \) and \( \boldsymbol{P}: \)
\( \mathbf{A} \cdot \$ \$(1 \text { Delta } G)_{-}\{\text {system }\} \) must be negative
B. \( \$ \$ \) (IDelta G) \( _{-}\{\text {system }\} \) must be positive
\( \mathbf{C} . \$ \$(1 \mathrm{Delta} \)
S) \( _{-}\{\text {system }\} \) must be positive
D. \( \$ \$ \) ( ( Delta S) \( _{-} \) (system) must be negative


The Sl units of mass and weight are
A. \( \mathrm{kg} \) and \( \mathrm{kg} \)
B. N and kg
c. kg and \( \mathrm{N} \)
D. N and N


For the following equilibrium, \( N_{2} O_{4} \rightleftharpoons \)
\( 2 N O_{2} \) in gaseous phase, \( N O_{2} \) is \( 50 \% \) of
the total volume when equilibrium is
set up. Hence, percent of dissociation of
\( N_{2} O_{4} \) is:
A . 50\%
B. 25\%
c. \( 66.66 \% \)
D. 33.33\%


Very strong acids, such as \( H N O_{3} \) and
\( H C l, \) appear to be equally strong in
water. This "leveling effect" of water is because
A \( \cdot O H^{-} \) is a stronger base than the conjugate bases of
\( H N O_{3} \) and \( H C l \)
B. \( H_{3} O^{+} \) is a stronger acid than \( H N O_{3} \) and \( H C l \)
c. \( H_{2} O \) is a stronger base than the conjugate bases of \( H N O_{3} \) and \( H C l \)
D. \( H_{2} O \) is a weaker base than the conjugate bases of \( H N O_{3} \) and \( H C l \)


below?
The shape is uniformly dense.
All answers are stated with respect to
the origin, which is at the center of the
large sphere.
\( ^{\mathbf{A}} \cdot\left(0, \frac{R}{2}\right) \)
B. \( \left(0, \frac{R}{4}\right) \)
c. \( \left(0,-\frac{R}{4}\right) \)
D. \( \left(0,-\frac{R}{6}\right) \)
\( E \cdot\left(0,-\frac{R}{3}\right) \)


If the time period of revolution of earth is 365 days, then, the frequency of revolution of earth is
A \( \cdot 3.17 \times 10^{-6} \mathrm{Hz} \)
В. \( 3.17 \times 10^{-8} \mathrm{Hz} \)
c. \( 3.17 \times 10^{-4} \mathrm{Hz} \)
D. \( 3.17 \times 10^{-7} \mathrm{Hz} \)


Solve:
\( \frac{\cos ^{2} y}{x} d y+\frac{\cos ^{2} x d x}{y}=0 \)


Briefly explain any three types of taxonomical aids.


Orion is a name of a:
A . star planet
B. planet
c. galaxy
D. constellation


equal and opposite tensile forces \( F \) at
its ends. Consider a plane through the
bar making an angle \( \theta \) with a plane at
right angles to the bar. Then shearing
stress will be maximum if \( \boldsymbol{\theta} \)
\( \mathbf{A} \cdot 0^{\circ} \)
B \( .30^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. \( 60^{\circ} \)
E .90


The unique feature of longitudinal
division of diatom cells in successive
generations is
A. Progressive reduction in the size of daughter cells
B. Formation of daughter cells larger than the parent cell
c. Formation of daughter cells of equal size
D. None of these


A block performs simple harmonic
motion with equilibrium point \( \boldsymbol{x}=\mathbf{0} \)
Graph of acceleration of the block as a
function of time is shown. Which of the
following statement is correct about the
block?
A. Displacement from equilibrium is maximum at \( t=4 s \)
B. Speed is maximum at \( t=4 s \)
C. Speed is maximum at \( t=2 s \)
D. Speed is maximum at \( t=3 s \)


"Concentrated \( H N O_{3} \) converts
graphite into metallic acid
\( \boldsymbol{C}_{6}(\boldsymbol{C O O H})_{6} \)
Answer whether the above statement is
true or false.
If true enter 1 , else 0


A rod is placed in a beaker of full of water. It appears to be bent inside the water. Which of the following property of light is responsible for the rod appearing to be bent?
A. refraction
B. reflection
c. diffraction
D. interference
E. polarization


Calculate the vapour pressure of solution having 3.42 g of canesugar in 180 g water at \( 40^{\circ} C \) and \( 100^{\circ} \) C. Given that, the boiling point of water is \( 100^{\circ} \mathrm{C} \) and heat of vaporisation is 10 kcal
\( m o l^{-1} \) in the given temperature range. Also, calculate the lowering in vapour pressure of 0.2 molal cane-sugar at
\( 40^{\circ} C: \)
\( \mathbf{A} .58 \mathrm{mm} \)
B. \( 13 \mathrm{mm} \)
c. \( 78 \mathrm{mm} \)
D. none of these


Cushing's syndrome and myxoedema are associated with which of the
following glands respectively?
A. Thyroid and adrenal
B. Adrenal and thyroid
c. Parathyroid and thyroid
D. Adrenal and pituitary


Which compound polymerises to
neoprene?
A. \( C H_{2}=C H C l \)
В. \( C H_{2}=C C l-C H=C H_{2} \)
c. \( C l_{2} C=C C l_{2} \)
D. \( F_{2} C=C F_{2} \)


State True or False.
The properties of elements are periodic function of their atomic number
A. True
B. False


If \( 0 \leq x \leq 2 \pi, \) then the number of
solutions of the equation \( \sin ^{6} x+ \)
\( \cos ^{6} x=1 \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5
E . 8


If \( a=\frac{9}{3-b}, b=\frac{9}{3-c} \) then the value of
\( c \) in terms of \( a \) is
A \( \frac{8}{3-a} \)
в. \( \frac{9}{3-a} \)
c. \( \frac{7}{3-a} \)
D. \( \frac{6}{3-a} \)


f a unit charge is taken from one point to another over an equipotential surface, then work done on the charge is
A. Positive
B. Negative
c. zero
D. constant


In YDSE, find the missing wavelength in front of one of the slits.
\( ^{A} \cdot \frac{d^{2}}{2 D} \)
B. \( \frac{2 d^{2}}{D} \)
c. \( \frac{d^{2}}{3 D} \)
D. \( \frac{d^{2}}{4 D} \)


Find the degree of following polynomial \( -\frac{3}{2} \)
A .
B. 2
c. 0
D. Cannot be determined


3
8
8
3


Identify the state functions from the following:
A. heat
B. work
c. enthalpy
D. none of the above


\( F e C r_{2} O_{4}(\text { Chromite }) \) is a good source
of chromium and its compound like
\( N a_{2} C r O_{4} \) and \( N a_{2} C r_{2} O_{7} \)
I. \( \boldsymbol{F e} \boldsymbol{C r}_{2} \boldsymbol{O}_{4}+\boldsymbol{N a O H}+\boldsymbol{a i r} \longrightarrow \)
\( (\boldsymbol{A})+\boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3} \)
II. \( (\boldsymbol{A})+(\boldsymbol{B}) \longrightarrow \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \)
\( \mathrm{III} . N a_{2} C r_{2} O_{7}+X \stackrel{\triangle}{\longrightarrow} C r_{2} O_{3} \)
IV. \( \boldsymbol{C r}_{2} \boldsymbol{O}_{3}+\boldsymbol{Y} \stackrel{\Delta}{\longrightarrow} \boldsymbol{C r} \)
Compounds \( (A) \) and \( (B) \) are:
A \( \cdot N a_{2} C r O_{4}, H_{2} S O_{4} \)
в. \( N a_{2} C r_{2} O_{7}, H C l \)
c. \( N a_{2} C r O_{6}, H_{2} S O_{4} \)
D. \( N a_{4}\left[F e(O H)_{6}\right], H_{2} S O_{4} \)


If moving with equal speeds, the longest wavelength of the following matter waves is that for a (an):
A. electron
B. \( \alpha \) -particle
c. proton
D. neutron


Express the relation among cell constant, resistance of the solution in
the cell and conductivity of the solution. How is molar conductivity of a solution related to its conductivity?


The permeases are
A. Structural membrane proteins
B. Enzymatic membrane proteins
C. Carrier membrane proteins
D. None of the above


Write a note on the factors affecting enzyme activity.


State whether the following sets are
finite or infinite
(i) \( A=\{x: x \text { is a multiple of } 5, x \in \mathbb{N}\} \)
(ii) \( B=\{x: x \) is an even prime
number
(iii) The set of all positive integers
greater than 50


\( \boldsymbol{R}= \)
\( \{(a, b): a, b \epsilon N, a \neq b \text { and } a \text { divided } b\} \)
is \( R \) reflexive. Give reason


\( \mathbf{f} A=\left\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{1} ; \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R}\right\} \)
and \( B=\left\{(x, y): x^{2}+y^{2} \geq 4 ; x, y \epsilon R\right\} \)
then
\( \mathbf{A} \cdot A-B=\phi \)
в. \( B-A=\phi \)
c. \( A \cap B \neq \phi \)
D. \( A \cap B=\phi \)


A company has two plants to manufacture televisions. The plant
manufacture \( 70 \% \) of televisions and
plant II manufacture \( 30 \% . \) At plant 1,80 \( \% \) of the televisions are rated as of
standard quality and at plant II, \( 90 \% \) of
the televisions are rated as of standard
quality. A television is chosen at random and is found to be of standard
quality. The probability that it has come from plant II is


Oxygen occurs in nature as a mixture of isotopes \( ^{1} 60,17 O \) and \( ^{1} 8 O \) having
atomic masses of 15.995 u, 16.999 u and
\( 17.999 \mathrm{u} \) and relative abundance of
\( 99.763 \%, 0.037 \%, \) and \( 0.200 \% \)
respectively. What is the average atomic mass of oxygen?
A . 15.999 u
B . 16.999 u
c. 17.999 u
D. 18.999 u


What is the bond angle for the \( \boldsymbol{H}- \)
\( C_{2}-H \) atom?
A . \( 90^{\circ} \)
B . \( 107.5^{\circ} \)
\( c \cdot 109.5^{\circ} \)
D. 120


\( \mathbf{A} \)
\( 3 k g \) object has initial velocity \( (6 \hat{i}- \) \( \mathbf{2} \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} . \) The total work done on the
object if its velocity changes to \( (8 \hat{i}+ \) \( 4 \hat{j}) m / s \) is :
A .2165
J 52665.53
в. \( 44 J \)
c. \( 60 J \)
D. \( 120 J \)


A horse is tied to a vertex of a field
having the shape of an equilatera triangle with a rope, the length of which is half of the length of a side of the triangle. The percentage of the total area of the field over which the horse can graze is approximately
A . 20 to 22\%
B. 25 to 27\%
c. 30 to 32\%
D. 48 to 50\%


Pyrolusite is a/an:
A. oxide ore
B. sulphide ore
c. carbide ore
D. not an ore


The members of algae found in littora
zone is
A. Volvox
B. Spirogyra
c. Ectocarpus
D. Ulothrix


Which of the following is not characteristic of chemisorption?
A. It is irreversible
B. It is specific
c. It is multilayer phenomenon
D. Heat of adsorption of about \( 400 K J \)


The diagram shows the principal
regions of the electromagnetic
spectrum, with some details labelled.
The diagram is not to scale. What is a typical order of magnitude of the wavelength of the radiation in
region Q?
\( A \cdot 10^{-7} m \)
B. \( 10^{-5} \) m
\( c \cdot 10^{-2} m \)
\( D \cdot 10^{0} m \)


A thick metallic cubical container of inner dimensions \( 1 \mathrm{m} 1 \mathrm{m} \) 1m and outer
dimensions \( 1.2 \mathrm{m} 1.2 \mathrm{m} 1.2 \mathrm{m} \) at \( 27^{0} \mathrm{C} \) is
used to store gas of volume \( 1 m^{3} \). The linear thermal expansion coefficient of the metal is positive. If the container is
heated upto \( 100^{0} C \), then volume of gas
it can contain at \( 100^{0} C \) is :
A. more than \( 1 m^{3} \)
B. less than1 \( m^{3} \)
c. same a \( 1 m^{3} \)
D. zero


Identify in which of the following medium, a sound wave would travel with fastest speed.
A. solid
B. liquid
c. gas
D. vacuum
E. plasma


A catalyst:
A. stops the reaction
B. initiates the reaction
C. always increases the rate of reaction
D. either increases or decreases the rate of reaction


Fill in the blanks:
A point where three surface of a solid
meet is called a


A physical quantity \( x \) is calculated from
the relation \( \boldsymbol{x}=\boldsymbol{a}^{3} \boldsymbol{b}^{2} / \sqrt{\boldsymbol{c} \boldsymbol{d}} \). Calculate
percentage error in \( x, \) if \( a, b, c \) and \( d \) are measured respectively with an error of \( 1 \%, 3 \%, 4 \% \) and \( 2 \% \)
A. \( 12 \% \)
в. \( 22 \% \)
c. \( 2 \% \)
D. \( 0.2 \% \)


The image formed by a plane mirror is always ........ inverted.
A. laterally
B. virtually
c. really
D. none


Which term is the most specific group
to which \( C_{2} H_{6} \) belongs?
A. alkynes
B. hydrocarbons
c. allkenes
D. alkanes
E. functional groups


The relation between the volume \( V \) and
the mass \( M \) of a nucleus is:
A. \( V \propto M^{3} \)
B \( \cdot V \propto M^{1 / 3} \)
c. \( V \propto M \)
D. \( V \propto 1 / M \)


Give the major product of reaction between \( \left(C H_{3}\right)_{3} C O N a /\left(C H_{3}\right)_{3} C O H \)
and 4 -bromo 2 -hexene:
\( A \)
в.
c. No reaction
D.


If Ohm's law is presumed to be valid,
then drift velocity \( V_{d} \) and electric field \( E \)
are related as
A \( \cdot v_{d} \propto E^{2} \)
B \( \cdot v_{d} \propto \sqrt{E} \)
c. \( v_{d} \propto E \)
D. \( v_{d} \propto E_{0} \)


Which of the following frequencies of sound elephants produce?
A. ultrasonic
B. infrasonic
\( c \cdot \) both \( A \& B \)
D. cant say


Assertion
\( P_{4} \) exists but \( N_{4} \) does not; \( N_{2} \) exists
but \( P_{2} \) does not
Reason
white phosphorus : \( \boldsymbol{P}_{4} \boldsymbol{N} \equiv \)
\( N 946 k J m o l^{-1}, P \equiv \)
\( \boldsymbol{P} \mathbf{4 8 1} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1}, \boldsymbol{N}- \)
\( N 160 k J m o l^{-1}, P-P 215 k J m o l^{-1} \)
Greater the B.E., greater the stability [compare BE of \( N \equiv N \) and \( N-N \) (in
\( \left.\left.N_{4}\right) \text { and } P-P\left(\text { in } P_{4}\right)\right] \)
Read the above assertion and reason
and choose the correct option regarding
¡t.
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


A swimming pool is \( 40 \mathrm{m} \) long and \( 15 \mathrm{m} \)
wide. Its shallow and deep ends are 1.5
\( m \) and \( 3 m \) deep respectively. If the
bottom of the pool slopes uniformly, find
the amount of water in litres required to
fill the pool.
A .42,33,000 litres
B. 13,50,000 litres
c. 22,17,000 litres
D. 41,12,000 litres


The valence configuration of a transition element is \( (n-1) d^{1 \rightarrow 10} n s^{1 \rightarrow 2} \)
The impossible values of \( n \) are:
\( A \cdot 4,5 \) and 6
B. 1 and 2
c. 2,4 and 6
D. 1,2 and 3


The change in focal length of an eye lens is caused by the action of
A. pupil
B. retina
c. ciliary muscles
D. iris


Rajdhani Express stops at six intermediate stations between Kota
and Mumbai.Five passengers board at Kota. Each passengers can get down at any station till Mumbai. The probability that all five passengers will get down at different stations, is
\( ^{A} \cdot \frac{^{6} P_{5}}{6^{5}} \)
в. \( \frac{^{6} C_{5}}{6^{5}} \)
c. \( \frac{7}{7^{5}} \)
D. \( \frac{7}{7^{5}} \)


Sunlight can undergo internal reflection if it enters from:
A. glass to air
B. air to glass
c. air to water
D. water to glass


Oxygen belongs to which group in the periodic table?


State four most common electrical
appliances based on heating effect of electric current. Why do we use finely heated platinum wire in surgery?


Clouds get electrically charged when:
A. The UV rays of sun falls on them
B. Air molecules rub against water molecules
C. Cold currents of air rub against hot currents of air
D. Both B and C


Which of the following is not correct reason for the substantially lower rate of reaction than the collision frequency?
A. All the collisions do not attain threshold energy level
B. The activated complex formed is short lived
c. All the collisions do not have proper orientation
D. Effective collision are lesser in number than all collisions


Express the following angle in terms of first-quadrant reference angle:
\( \tan 336^{\circ} \)
A . \( \tan 45 \)
B . \( -\tan 36 \)
c. \( -\tan 24 \)
D. \( \tan 24 \)


Which one of the following combinations is false?
A . Colloidal solution \( 10^{-5} \) to \( 10^{-7} \mathrm{cm} \)
B. True solution \( 10^{-7} \) to \( 10^{-8} \mathrm{cm} \)
C. Suspension \( 10^{-9} \) to \( 10^{-12} \) cm
D. All are correct combinations


\( A g_{3} P O_{4} \) would be least soluble at \( 25^{\circ} \mathrm{C} \)
in
в. 0.1 М \( H N O_{3} \)
c. pure water
D. 0.1 М \( N a_{3} P O_{4} \)
E. solubility in (a), (b), (c) or (d) is not different


Complementary cells of lenticels are
A. Compact and suberised
B. Loose and suberised
c. compact and lignified
D. Loose and lignified


Use figure given below that shows our
Solar system to answer the given
questions. The objects \( C \) and \( E \) are
collectively called :
A. Jovian planets
B. Inferior planets
c. Superior planets
D. Gas giants


A complex number \( z \) is said to be
unimodular if \( |z|=1 . \) Suppose \( z_{1} \) and
\( z_{2} \) are complex numbers such that \( \frac{z_{1}-2 z_{2}}{2-z_{1} \bar{z}_{2}} \) is unimodular and \( z_{2} \) is not
unimodular. Then the point \( z_{1} \) lies on a
A. straight line parallel to x-axis
B. straight line parallel to y-axis
c. circle of radius 2
D. circle of radius \( \sqrt{2} \)


Which one of the following is correct in respect of the equations \( \frac{x-1}{2}=\frac{y-2}{3} \)
and \( 2 x+3 y=5 ? \)
A. They represent two lines which are parallel
B. They represent two lines which are perpendicular
C. They represent two lines which are neither parallel nor perpendicular
D. The first equation does not represent a line


We have seen how we can draw a series
of right triangles as in the picture.
What are the lengths of the sides the
tenth triangle?


Thoracic chamber is formed dorsally by
the \( _{--}(\mathrm{i})_{--}- \) ventrally by the
(ii) \( _{--\rightarrow} \), laterally by the
(iii) \( _{---} \) and on lower side by the dome shaped (iv)
Select the correct option to complete
the above paragraph.
A. (i)vertebral column (ii)sternum (iii)ribs (iv)diaphragm
B. (i)sternum (ii)vertebral column (iii)diaphragm (iv)ribs
c. (i)diaphragm (ii)ribs (iii)vertebral column (iv)sternum
D. (i)ribs (ii)diaphragm (iii)vertebral column (iv)sternum


The effects are produced at a given point in space by two waves described
by the equations \( y_{1}=y_{m} \sin \omega t \) and
\( \boldsymbol{y}_{2}=\boldsymbol{y}_{m} \sin (\omega t+\phi) \) where \( \boldsymbol{y}_{m} \) is the
same for both the waves and \( \phi \) is a
phase angle. Tick the correct statement
among the following
A. the maximum intensity that can be achieved at a point is twice the intensity of either wave and occurs if \( \phi=0 \)
B. the maximum intensity that can be achieved at a point is four times the intensity of either wave and occurs if \( \phi=0 \)
c. the maximum amplitude that can be achieved at the point its twice the amplitude of either wave and occurs at \( \phi=0 \)
D. When the intensity is zero the net amplitude is zero and at this point \( \phi=\pi / 4 \)


Deflection in the galvanometer
A. Towards right
B. Left
c. No defection
D. None of these


Is it possible to have a polygon, whose sum of interior angles is \( 870^{\circ} \)
Answer: No
State true or false:
A. True
B. False


\( L \) is circular loop carrying a current. \( \boldsymbol{P} \)
is a point on its axis \( O X . d l \) is an
element of length on the loop at a point
\( A \) on it. The magnetic field at \( P: \)
This question has multiple correct options
A. due to \( L \) is directed along \( O X \)
B. due to dl is directed along \( O X \)
c. due to dl is perpendicular to \( O X \)
D. due to dl is perpendicular to \( A P \)


Solve \( \left(4 x^{4}-5 x^{3}-7 x+1\right) \div(4 x-1) \)


General molecular formula of a
compound which cal show ring chain isomerism is:
\( \mathbf{A} \cdot C_{n} H_{2 n} \)
B. \( C_{n} H_{2 n+2} \)
c. \( C_{n} H_{2 n-2} \)
D. none of these


Find the greatest and the least values of
the moduli of complex numbers \( z \)
satisfying the equation \( |z-4 / z|=2 \)


Find the coefficient of \( x^{17} \) in \( (x+y)^{20} ? \)


Chalcacite is a type of:
A. Oxide
B. Sulphide
c. Chloride
D. Floride


What is pure culture?


\( f\left(\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right], \) then find \( A^{2} \)


fone mole of an ideal gas \( \left(\gamma=\frac{4}{3}\right) \) is expanded reversibly and adiabatically from \( 800 \mathrm{K} \) to \( 200 \mathrm{K}, \) which of the following statement's are correct? This question has multiple correct options
A. ratio of final volume to initial volume is 64
B. ratio of final pressure to initial pressure is \( \frac{1}{256} \)
c. ratio of final volume to initial volume is 32
D. ratio of final pressure to initial pressure is \( \frac{1}{16} \)


Which of the following are correct?
This question has multiple correct options
A. The shear modulus of a liquid is infinite.
B. Bulk modulus of a perfectly rigid body is infinity.
C. According to Hookes law, the ratio of the stress and strain remains constant.
D. None of the above.


Function of optic nerve in human eye:
A. Image is modified by the optic nerves
B. Electric signals are generated on the retina are carried by the optic nerve to the brain
C. Image brightness is reduced by the optic nerve
D. All the above


During lightning which of the following is not a safe place?
A. In car
B. Bus stop
c. Inside a house
D. open field


Mass differs from weight in which ways:
A. weight is a force where as mass is not a force.
B. the mass of an object is always more than its weight.
C. mass can be expressed only in the metric system.
D. there is no difference


Assertion
Magnetic field interacts with a moving charge and not with a stationary charge.
Reason

A moving charge produces a magnetic field.
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


An aqueous solution containing \( \boldsymbol{V}^{\boldsymbol{x}} \) ion has magnetic moment equal to \( \sqrt{15} B M . \) Therefore, the \( x \) is:
\( A \cdot 5 \)
B. 2
\( c .3 \)
D. 4


\( \gamma \) is the ratio of molar specific heat
capacity of the given gas at to
its specific heat capacity at
A. Constant temperature, constant volume
B. Constant volume, Constant pressure
c. constant pressure, Constant temperature
D. constant pressure, constant volume


The axis of the parabola \( x^{2}-4 x-y+ \)
\( \mathbf{1}=\mathbf{0} \) is
A \( \cdot y=-3 \)
B. x=-3
c. \( x=2 \)
D. none of these


Check the validity of the following
statement:
\( \boldsymbol{p}: 125 \) is a multiple of 5 and 7
A. True
B. False


Binomial nomenclature means
indication of the name of an organism's
A. Order and family
B. Family and genus
c. Genus and species
D. species and variety


Identify and explain about the diode
whose characteristics curve is:


Which of the following limits vanishes?
A \( \cdot \lim _{x \rightarrow \infty} x^{\frac{1}{4}} \sin \frac{1}{\sqrt{x}} \)
B. \( \lim _{x \rightarrow \pi^{2}}(1-\sin x) \cdot \tan x \)
C \( \lim _{x \rightarrow \infty} \frac{2 x^{2}+3}{x^{2}+x-5} \cdot \) sgn
D. \( \lim _{x \rightarrow 3^{\circ}} \frac{[x]^{2}-9}{x^{2}-9} \) where [] denotes greatest integer function


Derive an expression for kinetic energy,
when a rigid body is rolling on a horizontal surface without slipping.
Hence find kinetic energy for a solid sphere


What is the value of \( \frac{d P}{P} \) for adiabatic expansion of the gas?
A \( \cdot \gamma \frac{d V}{V} \)
B. \( -\frac{d V}{V} \)
c. \( \frac{d V}{V} \)
D. \( -\gamma \frac{d V}{V} \)


Consider a new system of units in which \( c( \) speed of light in vacuum), h(Planck's constant) and G (gravitational constant) are taken as fundamental
units. Which of the following would correctly represent mass in this new
system?
\( ^{\mathrm{A}} \cdot \sqrt{\frac{h c}{G}} \)
B. \( \sqrt{\frac{G c}{h}} \)
c. \( \sqrt{\frac{h G}{c}} \)
D. \( \sqrt{h G c} \)


Most hazardous metal pollutant of automobile exhaust is:
A. mercury
B. tin
c. cadmium
D. leadd


In photosynthesis, for the fixation of one mole of glucose, the number of ATP and
NADPH \( _{2} \) required is
\( A \cdot 12 \) and 18
B. 18 and 12 .
c. 6 and 12 .
D. 18 and 18 .


\( \boldsymbol{p} \boldsymbol{K}_{a} \) and \( \boldsymbol{K}_{a} \) of an acid are connected
by the relation - -
A \( \cdot p k_{a}=\log k_{a} \)
B \( \cdot p k_{a}=-p H \)
c. \( p k_{a}=-\log k_{a} \)
D・ \( p k_{a}=- \) logk \( _{b} \)


One of the acid listed below is formed
only from \( P_{2} O_{3} \), the rest are formed
from \( P_{2} O_{5} . \) Acid formed from \( P_{2} O_{3} \) is :
A. \( H P O_{3} \)
в. \( H_{2} P_{2} O_{7} \)
c. \( H_{2} P O_{4} \)
D. \( H_{3} P O_{3} \)


The differential equation satisfied by all
the straight lines \( x y \) - plane (not parallel to \( y \) -axis ) is:
A \( \cdot \frac{d y}{d x}=a \) constant
в. \( \frac{d^{2} y}{d x^{2}}=0 \)
c. \( _{y+\frac{d y}{d x}}=0 \)
D. \( \frac{d^{2} y}{d x^{2}}+y=0 \)


Two samples \( A \) and \( B \) of same radioactive nuclide are prepared Sample A has twice the initial activity of sample B. For this situation, mark out the correct statement(s):
This question has multiple correct options
A. The half-lives of both the samples would be same
B. The half-lives of the samples are different
C. After each has passed through 5 half-lives, the ratio of activity of A to B is 2:
D. After each has passed through 5 half-lives, ratio of activities of A to B is 64:


If a note \( x \) of unknown frequency
produces 8 beats/sec, with a source of \( 250 \mathrm{Hz} \) and 12 beats/sec with a source
of \( 270 \mathrm{Hz} \), the frequency of unknown source will be:
A . 258 \( \mathrm{Hz} \)
в. 242 на
c. 262 н
D. 282 нz


As the beam enters the medium, it will
A . diverge
B. converge
c. diverge near the axis and converge near the periphery
D. travel as a cylindrical beam


In the given graph.
The slope of line \( A B \) gives the information of the:
A value of \( \frac{E_{a}}{2.303} \)
B. value of \( \frac{2.30}{E_{0}} \)
c. value of \( -\frac{E_{a}}{2.303 R} \)
'D value of \( -\frac{E_{a}}{2303 R T} \)


The value of shear stress which is
induced in the shaft due to applied
couple varies
A. from maximum at the centre to the zero at the circumference
B. from zero at the centre to the maximum at the circumference
c. from maximum at the centre to the minimum at the circumference
D. from minimum at the centre to the maximum at the circumference


Form the different equations of all concentric circles at the origin.


A first order reaction takes 23.1 min.
for \( 50 \% \) completion. Calculate the time required for \( 75 \% \) completion of this
reaction.
\( [\text {Given }: \log 2=\mathbf{0 . 3 0 1}, \log \mathbf{3}=\mathbf{0 . 4 4 7 7 1} \)


Which type of polynomial is \( 45 y^{2} ? \)
A. Linear Polynomial
B. Bi-quadratic polynomial
c. Cubic Polynomial
D. Quadratic Polynomial


The mixed anhydride of nitrogen is:
A. \( N_{2} O_{2}(2 N O) \)
в. \( N_{2} O_{4}\left(2 N O_{2}\right) \)
c. \( N_{2} O_{5} \)
D. \( N_{2} O_{3} \)


Given are the examples of some acidic
substances. Select the option which
easily furnishes \( \boldsymbol{H}^{+} \) ions.
\( \mathbf{A} \cdot B F_{3} \)
в. \( C O_{2} \)
\( c \cdot s O_{2} \)
D. HCl