If the function \( \boldsymbol{f}(\boldsymbol{x})=\log \left(\frac{1+\boldsymbol{x}}{1-\boldsymbol{x}}\right) \)
then the value of \( f\left(\frac{2 x}{1+x^{2}}\right) \) is equal to
A \( . f(x) \)
B. \( 2 f(x) \)
c. \( 3 f(x) \)
D. \( 4 f(x) \)


Heat evolved in the reaction \( \boldsymbol{H}_{2}+ \)
\( C l_{2} \rightarrow 2 H C l \) is \( 182 k J \)
(Bond energies \( \boldsymbol{H}-\boldsymbol{H}= \)
\( 430 k J / m o l e, C l-C l-242 k J / m o l e) \)
The \( H-C l \) bond energy is:
A. \( 763 k J / \) mole
в. \( 427 k J / \) mole
c. \( 336 k J / \) mole
D. \( 154 k J / \) mole


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


What should be lengths of steel and copper rod, so that the length of steel rod is \( 5 \mathrm{cm} \) longer than the copper rod
at all temperature? ( \( \alpha \) for copper \( = \) \( 1.7 \times 10^{-5} \circ C^{-1} \) and \( \alpha \) for steel \( = \)
\( \left.1.1 \times 10^{-5}^{\circ} C^{-1}\right) \)


The magnitude of scalar product of two
vectors is 8 and of vector product is \( 8 \sqrt{3} . \) The angle between them is This question has multiple correct options
A. 30
B. \( 60^{\circ} \)
\( c .120 \)
D. 150


How does the proper inflation of tyre
save fuel?
A. Normal reaction decreases.
B. Normal reaction increases
c. Sliding contact with the road decreases.
D. Sliding contact with the road increases


The snakes are included under
A. Saprophytes
B. Primary consumers
c. Second trophic level
D. None of the above


The oxidation number of sulphur in the
sulphur molecule \( \left(S_{8}\right) \) is :


A person climbs up a stopped escalator
in \( 60 s . \) If standing on the same escalator but escalator running with constant velocity, he takes 40 s. How much time is taken by the person to walk up in the moving escalator?
A. \( 37 s \)
в. 27 s
\( c \cdot 24 s \)
D. \( 45 s \)


An organic compound undergoes firstorder decomposition. The time taken for its decomposition to \( 1 / 8 \) and \( 1 / 10 \) of its
initial concentration are \( t_{1 / 8} \) and \( t_{1 / 10} \) respectively. The value of \( \frac{\left[t_{1 / 8]}\right.}{\left[t_{1 / 10}\right]} \times 10 \) is \( ? \)
\( \left(\operatorname{take} \log _{10} 2=0.3\right) \)


The thickness of cathode increases in :
A . electrorefining of copper
B. electroplating of copper
c. anodizing of copper
D. none of the above


Construct the bisector of an angle \( 75^{\circ} \)


What type of isomerism is exhibited by? \( \boldsymbol{O} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O}-\boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3} \)


Which of the following is steam volatile?
A. Phenol
B. o-Nitrophenol
c. m-Nitrophenol
D. p-Nitrophenol


Which one of the following is the best material for making connecting wires?
A. Nichrome
B. Constantan
c. copper
D. Tungsten


One gram of radium is reduced by \( 2 m g \)
in 5 years by \( \alpha \) - decay. The half life of radium is:
\( \left(\log _{10} 998=2.9991\right) \)
A. 1520.4 years
B. 1671.7 years
c. 1617.5 years
D. 1732.86 years


The \( p H \) of \( 0.001 M C H_{3} C O O H \) is:
\( A \cdot 3 \)
B. 1
c. \( 3-7 \)
D.


The mass of a spaceship is 1000 kg. It is to be launched from the earths
surface out into free space. The value of \( g \) and \( R(\text { radius of earth) are } 10 m / s \)
and \( 6400 \mathrm{km} \) respectively. The required energy for this work will be:
A \( \cdot 6.4 \times 10^{11} J \)
\( J \)
В. \( 6.4 \times 10^{8} J \)
c. \( 6.4 \times 10^{9} J \)
D. \( 6.4 \times 10^{10} J \)


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


Find the \( 10^{t h} \) term from end for the A.P.
\( \mathbf{3 . 6 . 9 . 1 2} \ldots \ldots .300 \)


In a dsDNA number of phosphodiester
bonds are 3250 , then find the number of
base pairs.
A. 1625
B. 1626
c. 3252
D. 3250


Let \( E_{1}(r), E_{2}(r) \) and \( E_{3}(r) \) be the
respective electric fields at a distance from a point charge \( Q, \) an infinitely long wire with constant linear charge density \( \lambda, \) and an infinite plane with uniform
surface charge density \( \sigma . \) If \( \mathrm{E}_{1}\left(r_{0}\right)= \)
\( E_{2}\left(r_{0}\right)=E_{3}\left(r_{0}\right) \) at a given distance \( r_{0} \)
then :
A \( \cdot Q=4 \sigma \pi r_{0}^{2} \)
B . \( r_{0}=\frac{\lambda}{2 \pi \sigma} \)
c. \( E_{1}\left(r_{0} / 2\right)=2 E_{2}\left(r_{0} / 2\right) \)
D. \( E_{2}\left(r_{0} / 2\right)=4 E_{3}\left(r_{0} / 2\right) \)


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\boldsymbol{4} & \boldsymbol{1} & \boldsymbol{0} \\ \boldsymbol{1} & \boldsymbol{-} \boldsymbol{2} & \boldsymbol{2}\end{array}\right], \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}\boldsymbol{2} & \boldsymbol{0} & -\boldsymbol{1} \\ \boldsymbol{3} & \boldsymbol{1} & \boldsymbol{4}\end{array}\right], \boldsymbol{C}=\left[\begin{array}{c}\boldsymbol{1} \\ \boldsymbol{2} \\ -\mathbf{1}\end{array}\right] \) and \( \left(\boldsymbol{3} \boldsymbol{B}-\boldsymbol{t}_{\boldsymbol{}}\right) \)
\( \boldsymbol{2} \boldsymbol{A}) \boldsymbol{C}+\boldsymbol{2} \boldsymbol{X}=\boldsymbol{0} \operatorname{then} \boldsymbol{X}= \)
A \( \cdot \frac{1}{2}\left[\begin{array}{c}3 \\ 13\end{array}\right] \)
B \( \cdot \frac{1}{2}\left[\begin{array}{c}3 \\ -13\end{array}\right] \)
c. \( \frac{1}{2}\left[\begin{array}{c}-3 \\ 13\end{array}\right] \)
D. \( \left[\begin{array}{c}3 \\ -13\end{array}\right] \)


Find the bolt's free fall time.
A . \( 1.4 s \)
в. \( 0.6 s \)
c. \( 0.9 s \)
D. \( 0.7 s \)


The maximum value of the function
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-\boldsymbol{4}| \) exists at
\( \mathbf{A} \cdot x=0 \)
B. \( x=2 \)
c. \( x=4 \)
D. \( x=-4 \)


\( \ln C u S O_{4} \cdot 5 H_{2} O \) all \( C u-O \) bond length
are not equal. Find the total number of
shorter Cu-O bonds.


The number of permutations of letters of the word "PARALLAL" atken four at a
time must be,
A .216
в. 244
c. 286
D. 1680


Find the area of a quadrilateral one of
whose diagonals is \( 30 \mathrm{cm} \) long and the perpendiculars from the two other
vertices on this diagonal are \( 19 \mathrm{cm} \) and
\( 11 \mathrm{cm} \) respectively.
A \( \cdot 450 \mathrm{cm}^{2} \)
В. \( 540 \mathrm{cm}^{2} \)
D. \( 350 \mathrm{cm}^{2} \)


Among the following compounds, which one is not responsible for the depletion of ozone layer?
A \( . C H_{4} \) н 2 СО
в. \( C F C l_{3} \)
c. \( N O \)
D. \( C l_{2} \)


The prediction of the existence of black holes came from which theory or law?
A. Newton's law of universal gravitation
B. Faraday's law of electromagnetic induction
c. quantum theory.
D. Einstein's theory of general relativity
E. Snell's law.


Answer the following by appropriately matching the lists based on the
information given in the paragraph.
If the process on one mole of
monatomic ideal gas is as shown in the TV-diagram with \( P_{0} V_{0}=\frac{1}{3} R T_{0} \), the
correct match is,
A. \( I \rightarrow P, I I \rightarrow R, I I I \rightarrow T, I V \rightarrow S \)
в. \( I \rightarrow P, I I \rightarrow T, I I I \rightarrow Q, I V \rightarrow T \)
c \( . I \rightarrow S, I I \rightarrow T, I I I \rightarrow Q, I V \rightarrow U \)
D. \( I \rightarrow P, I I \rightarrow R, I I I \rightarrow T, I V \rightarrow P \)


One gram of ice at \( 0^{\circ} \mathrm{C} \) is added to 5
yarn of water at \( 10^{\circ} \mathrm{C} \). If the latent heat
of ice be 80 cal /g, then the final temperature of the mixture is
A \( .5^{\circ} \mathrm{C} \)
B. \( 0^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot-5^{\circ} \mathrm{C} \)
D. None of the above


The vapour pressure of the solution of
two liquids \( A\left(P^{\circ}=80 m m\right) \) and
\( B\left(p^{\circ}=120 m m\right) \) is found to be
\( 100 m m \) when \( x_{A}=0.4 . \) The result
shows that:
A. Solution exhibits ideal behaviour
B. Solution shows positive deviations
c. Solution shows negative deviations
D. Solution will show positive deviations for lower concentration and negative deviations for higher concentrations


The mean and standard deviation of a
group of 100 observations were found to
be 20 and 3 respectively. Later on it was
found that three observations were
incorrect which were recorded as 21,21
and \( 18 . \) Find the mean and standard
deviation if the incorrect observation
are omitted


The water moving upward forms a column, which is maintained up to a certain height due to
A. Osmosis
B. Transpiration pull
c. Translocational pool
D. Diffusion


A particle of mass \( M \) is moving in a horizontal circle of radius \( R \) with a
uniform speed \( v . \) When it moves from
one point to a diametrically opposite point, its This question has multiple correct options
A. Momentum does not change
B. Momentum changes by 2 \( M v \)
c. Kinetic energy does not change
D. Kinetic energy changes by \( M v^{2} \)


Trivial name of methanol is
A. wood spirit
B. methyl alcohol
c. wood alcohol
D. all of the above


An oxidation process involves:
A. increase in oxidation number
B. Decrease in oxidation number
c. Addition of electrons
D. Removal of electronegative element


Which is the part of the nephron that exists in outer zone of kidney?
A. Loop of the henle
B. PCT
c. DCT
D. Bowman's capsule


A circuit consists of a battery, a resistor
\( \mathrm{R} \) and two light bulbs \( \mathrm{A} \) and \( \mathrm{B} \) as shown.
If the filaments in light A burns out,
then the following is true for light bulb
A. It is turned off
B. Its brightness does not change
c. It gets dimmer
D. It gets brighter


Which of the following sets of elements follows Newland's octave rule?
A. \( B e, M g, C a \)
в. \( N a, K, R b \)
c. \( F, C l, B r \)
D. \( B, A l, G a \)


Explain actinoid contraction.


The following flow chart represents the
extraction of
Froth flotation
\( t \)
Roasting
\( t \)
Smelting
\( t \)
Bessemerization
\( t \)
Electrolytic refining
A. Copper
B. zinç
c. Iron
D. Aluminium


The maximum number of fish belong to
A. Elasmobranchii
B. Dipnoi
c. Actinopterygii
D. crossopterygii


If a polar covalent bond shows \( 50 \% \) ionic character, then the electronegativity difference of the atoms that form the
bond is :
A. more than 1.7
B. equal to 1.7
c. less than 1.7
D. much greater than 1.7


A light ray traveling from one medium
into another:
A. always bends towards the normal
B. always bends away from the normal
C. bends towards or away from the normal depending on the densities of the two media
D. never suffers a refraction


Current density is a:
A. Vector expressed in \( A m^{-1} \)
B. Scalar expressed in \( A m^{-2} \)
C . Vector expressed in \( A m^{-2} \)
D. Scalar expressed in \( A m^{-1} \)


A train is moving towards east and a car is along north, both with same speed. The observed direction of car to
the passenger in the train is
A. East-north direction
B. West-north direction
c. south-east direction
D. None of the above


What is the radius of a circle of area
\( 616 \mathrm{cm}^{2} ? \)
\( \mathbf{A} \cdot 16 \mathrm{cm} \)
B. \( 12 \mathrm{cm} \)
\( c \cdot 14 c m \)
D. None of these


A single electron orbit around a stationary nucleus of charge +Ze where \( \mathrm{Z} \) is the atomic number and 'e' is the
magnitude of the electric charge. The hydrogen-like species required \( 47.2 e v \) to excite the electron from the second
Bohr orbit to the third Bohr orbit. The
value of \( Z \) is:
A. 5
B. 3
\( c \cdot 2 \)
\( D \)


Which of the following is formed from phosphorylation?
A. Fructose 1,6-bisphosphate
B. Phosphoglyceric acid
c. PEP
D. Pyruvic acid


When an alkali metal is reacted with
hydrogen then metallic hydride is formed. In this reaction:
A. hydrogen is oxidized
B. hydrogen is reduced
c. hydrogen is neither oxidised nor reduced
D. hydrogen is oxidized as well as reduced


The entire positive charge of the atom is located in the nucleus while the
electrons are distributed in the vacant
space around it. This statement was
given by Thomson.
A. True
B. False


Upto which element, the law of octaves
was applicable?
A. oxygen
B. Calcium
c. cobalt
D. Potassium


Which of the following is used as a preservative to protect processed food?
A. Sodium sulphate
B. Saccharin
c. sucralose
D. Sodium metabisulphite


The potential difference between points \( A \) and \( B \) in the circuit shown in figure
is \( 16 \mathrm{V} \). Then,
This question has multiple correct options
A. the current through the \( 2 \Omega \) resistance is 3.5 A
B. the current through the \( 4 \Omega \) resistance is 2.5 A
c. the current through the \( 3 \Omega \) resistance is 1.5 A
D. the potential difference between the terminals of the V battery is 7 V


What type(s) of intermolecular forces exist between the following pair?
\( C l_{2} \) and \( C B r_{4} \)
A. Dispersion forces
B. Hydrogen bonding
C. Dipole-Dipole interactions
D. None of the above


The rusting of iron takes place as follows:
\( \mathbf{2} \boldsymbol{H}^{\oplus}+\mathbf{2} e^{-}+\frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{O}_{2} \rightarrow \)
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) ; \boldsymbol{E}^{\ominus}=+\mathbf{1} \cdot \boldsymbol{2} \boldsymbol{3} \boldsymbol{V} \)
\( \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e}(s) ; \boldsymbol{E}^{\ominus}= \)
\( -0.44 V \)
Calculate \( \Delta G^{\ominus} \) for the net process.
B. \( -152 k J \) mol\( ^{-1} \)
c. \( -76 k J \) mol \( ^{-1} \)
D. - \( 161 k J \) mol \( ^{-1} \)


Find the angle between two vectors \( a \) and \( b \) if \( |a+b|=|a-b| \)


toppr
Q Type your question
corresponding thermodynamic co-
ordinates are given. Here, the \( P \) and \( V \)
scales are so chosen that these cycles
on \( P-V \) diagram appear to be
circular.
Analyse these cycles on \( P-V \) diagram
and answer the following questions
about these processes.
What is the net work done in the given
process?
Cycle on System
\( \mathbf{A} \cdot \frac{\pi P_{0} V_{0}}{4} \)
\( \mathbf{B} \cdot-\frac{\pi P_{0} V_{0}}{4} \)
\( c \)
D.


If \( \mathbf{0} \leq[\boldsymbol{x}]<\mathbf{2},-\mathbf{1} \leq[\boldsymbol{y}]<\mathbf{1} \) and \( \mathbf{1} \leq \)
\( [z]<3([.] \) denotes the greatest integer
function) then the maximum value of
determinant
\( \boldsymbol{\Delta}=\left|\begin{array}{ccc}{[\boldsymbol{x}]+\mathbf{1}} & {[\boldsymbol{y}]} & {[\boldsymbol{z}]} \\ {[\boldsymbol{x}]} & {[\boldsymbol{y}]+\mathbf{1}} & {[\boldsymbol{z}]} \\ {[\boldsymbol{x}]} & {[\boldsymbol{y}]} & {[\boldsymbol{z}]+\mathbf{1}}\end{array}\right| \)
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


Which of the following acid has the same molecular weight and equivalent weight ?
A \( . H_{3} P O_{2} \)
в. \( H_{3} P O_{3} \)
\( \mathrm{c} \cdot H_{3} P O_{4} \)
D. \( H_{2} S O_{4} \)


Numbers greater than 1000 but not greater than 4000 which can be formed
with the digits 0,1,2,3,4 (repetiion of digits is allowed) are
A . 350
в. 374
c. 450
D. 575


\( \boldsymbol{C a C O}_{3} \rightarrow \boldsymbol{C a O}+\boldsymbol{C O}_{2} \)
\( \boldsymbol{E}+\boldsymbol{C O}_{2} \rightarrow \boldsymbol{F} \)
\( N a C l+F \rightarrow A+N a H C O_{3} \)
The other compound formed with sodium bicarbonate is:
A. \( C a C l_{2} \)
в. \( N H_{4} C l \)
c. \( N H_{4} O H \)
D. none of these


Two coils \( X \) and \( Y \) are placed in a
circuit such that a current changes by
\( 3 A \) in coil \( X \) and magnetic flux changes of \( 1.2 ~ W b \) occurs in \( Y \). The
value of mutual inductance of the coils
is :
\( \mathbf{A} \cdot 0.2 H \)
в. \( 0.4 \mathrm{H} \)
c. \( 0.6 H \)
D. \( 3.6 H \)


The following reaction is balanced if \( \boldsymbol{X}+\boldsymbol{Y} \) is
\( \mathbf{5} \boldsymbol{H}_{2} \boldsymbol{O}_{2}+\boldsymbol{X} \boldsymbol{C l} \boldsymbol{O}_{2}+\mathbf{2} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \)
\( \boldsymbol{X} \boldsymbol{C l}^{-}+\boldsymbol{Y} \boldsymbol{O}_{2}+\boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} \)


If \( H \) is harmonic mean between \( P \) and
\( Q . \) Then the value of \( \frac{\boldsymbol{H}}{\boldsymbol{P}}+\frac{\boldsymbol{H}}{\boldsymbol{Q}} \) is
\( A \cdot 2 \)
в. \( \frac{P Q}{P+Q} \)
c. \( \frac{P+Q}{P Q} \)
D. None of these


A step-down transformer has primary voltage \( 1100 V . \) The ratio of turns of
primary to secondary coil is \( 5: 1 . \) If the
primary current is \( 10 A \) then what is the secondary voltage and secondary current assuming the transformer to be an ideal transformer?
\( \mathbf{A} \cdot 220 V, 50 A \)
в. \( 220 V, 5 A \)
c. \( 22 V, 50 A \)
D. \( 22 V, 5 A \)


The current flowing in the primary circuit of potentiometer is \( 2 A \) and the resistance of its wire is \( 0.2 \Omega / m . \) If a one ohm standard coil gets balanced at \( 250 \mathrm{cm} \) length of the wire, then the
current flowing in the coil will be
A . \( 0.1 \mathrm{A} \)
B. 1A
c. \( 1.5 \mathrm{A} \)
D. 0.05A


The given image depicts which of the following phenomena in amoeba?
A. Digestion
B. Egestion
c. Growth
D. Development


If \( \boldsymbol{P}=\left[\begin{array}{ccc}1 & 2 & -3 \\ 3 & -1 & 2 \\ -2 & 1 & 3\end{array}\right], Q= \)
\( \left[\begin{array}{lll}2 & 3 & 1 \\ 3 & 1 & 2 \\ 1 & 2 & 3\end{array}\right], \) then find matrix \( R \) such
that \( \boldsymbol{P}+\boldsymbol{Q}+\boldsymbol{R} \) is a zero matrix


The three resistance of equal value are
arranged in the different combinations
shown below.
Arrange them in increasing order of power dissipation.
A. \( \||<\|<| V<1 \)
B. \( \|<\|<\mid V<1 \)
c. \( |<| V<\|\mid<\| \)
D. \( |<\|\mid<\|<1 V \)


The length of the segment of the straight line passing through (3,3) and (7,6) cut off by the coordinate axes is?
A
в.
\( c \cdot \frac{7}{4} \)
D. \( \frac{4}{7} \)


\( \boldsymbol{A}=(\mathbf{1},-\mathbf{2}, \mathbf{3}), \boldsymbol{B}=(2,1,3), \boldsymbol{C}=(4,2, \)
1) and \( G=(-1,3,5) \) is the centroid of
the tetrahedron \( A B C D . \) Then the fourth
coordinate is
A. (11,11,13)
В. (-11,11,45)
c. (-11,11,13)
D. (11,13,11)


If \( \mathbf{A}, \mathbf{B} \) and \( \mathbf{C} \) are three sets such that \( \mathbf{A} \cap \mathbf{B}=\mathbf{A} \cap \mathbf{C} \) and \( \mathbf{A} \cup \mathbf{B}=\mathbf{A} \cup \mathbf{C} \)
then
A \( . A=B \)
B. \( A=C \)
c. \( \mathrm{B}=\mathrm{C} \)
\( \mathbf{D} \cdot A \cap \mathbf{B}=\phi \)


\( \frac{2}{3} r d \) of a number when multiplied by \( \frac{3}{4} \) th of the same number make 338 .The
number is
\( \mathbf{A} \cdot \pm 18 \)
B. ±24
\( c .\pm 36 \)
D. ±26


A transformer has 200 turns in primary and 400 turns in secondary. When a battery of \( 6 \mathrm{V} \) and negligible internal resistance is connected to the primary a current of \( 2 \mathrm{A} \) is produced in it. The secondary voltage and current are
\( A \cdot 12 v, 1 A \)
B. 12 V, zero
c. zero, 1A
D. zero, zero


What is the mass of one curie of \( U^{234} ? \)
A . \( 3.7 \times 10^{10} g \)
B. \( 3.7 \times 10^{-10} g \)
c. \( 6.25 \times 10^{-34} g \)
D. \( 1.438 \times 10^{-11} g \)


\( \vec{A}, \vec{B} \) and \( \vec{C} \) satisfy the relations, \( \vec{A} \cdot \vec{B}=0 \) and \( \vec{A} \cdot \vec{C}=0, \) then \( \vec{A} \) is
parallel to
A . \( \vec{B} \)
в. \( \vec{c} \)
c. \( \vec{B} \times \vec{C} \)
D. 高广


The presence of electric charge
on colloidal particles is indicated by the property, called:
A. dialysiss
B. solubility
c. eletrophoresis
D. osmosis


\( A \) block \( X \) kept on an inclined surface
just begins to slide, if the inclination is
\( \boldsymbol{\theta}_{1} . \) The block is replaced by another block \( Y \) and it is found that it just
begins to slide, if the inclination \( \theta_{2} \) if
\( \boldsymbol{\theta}_{2}>\boldsymbol{\theta}_{1} \) ). Then
A. Mass of \( x= \) mass of \( Y \)
B. Mass of \( x< \) mass of \( Y \)
c. Mass of \( x> \) mass of \( Y \)
D. All the above three options are possible


Viruses multiply in
A. Bacteria only
B. All living cells
C . Specific living cells
D. Rotten food


A stone is dropped in a well of depth 500
\( \mathrm{m} \) and a sound is heard after \( 80 / 7 \)
seconds. Then speed of sound is: \( [\boldsymbol{g}= \)
\( \left.\mathbf{1 0 m} / \boldsymbol{s}^{\mathbf{2}}\right] \)
A. \( 300 \mathrm{m} / \mathrm{s} \)
B. \( 350 \mathrm{m} / \mathrm{s} \)
c. \( 400 \mathrm{m} / \mathrm{s} \)
D. \( 330 \mathrm{m} / \mathrm{s} \)


Refractive index of a transparent medium, so that it is invisible in
vacuum is
\( A \)
B. \( < \)
\( c \cdot>1.33 \)
D. 1.33


Which of the following statement is incorrect for a stationary wave?
A. Every particle has fixed amplitude which is different from the amplitude of its nearest particle
B. All the particles cross their mean position at the same time
C. All the particles are oscillating with same amplitude.
D. There is no net transfer of energy across any plane


The molar conductance of a \( 0.01 M \)
solution of acetic acid was found to be
\( 16.30 \times 10^{-4} S m^{2} m o l^{-1} \) at \( 25^{\circ} C . \) The
molar ionic conductance of \( \boldsymbol{H}^{+} \) and
\( C H_{3} C O O^{-} \) ions at infinite dilution are
\( 349.8 \times 10^{-4} \) and \( 40.9 \times \)
\( 10^{-4} S m^{2} m o l^{-1}, \) respectively, at the
same temperature. What percentage of acetic acid is dissociated at this
concentration?


The nearest star to our solar system is
4.29 light years away. How much is this distance in terms of parsecs? How
much parallax would this star (named Alpha Centauri) show when viewed from
two locations of the Earth six months
a part in its orbit around the Sun?


A ship sends a sonar wave to the sea bed which is flat and measured several
times over a large area. One day the reflected sound wave takes longer time than in previous measurements. The possible reason is :
A. the frequency of the sonar wave, generated by the equipment is lower than previous measurements
B. there is a solid object of large size in the path of sonar wave
c. there is a huge air bubble in the path of sonar wave
D. the loudness of the sonar wave, generated by the equipment is lower than previous measurement


Two metal spheres \( A \) and \( B \) of exactly same mass are given equal positive and negative charges respectively. Their masses after charging:
A. Remains unaffected
B. Mass of \( A> \) mass of B
c. Mass of \( A< \) mass of \( B \)
D. Nothing can be said


Transverse waves on a string have wave speed \( 12.0 \mathrm{m} / \mathrm{s}, \) amplitude \( 0.05 \mathrm{m} \) and wavelength 0.4 m. The waves travel in
the \( +x \) direction and at \( t=0, \) the \( x=0 \)
end of the string has zero displacement and is moving upwards. Find the transverse displacement of a point at \( x \) \( =0.25 \mathrm{m} \) at time \( t=0.15 \mathrm{s} \)
A. \( -4.54 \mathrm{cm} \)
B. \( -5.54 \mathrm{cm} \)
c. \( -3.54 \mathrm{cm} \)
D. \( -9.54 \mathrm{cm} \)


A particle is vibrating in simple harmonic motion with amplitude of \( 4 \mathrm{cm} . \) At what displacement from the equilibrium position is its energy half potential and half kinetic?
A. \( 1 ~ c m \)
B. \( \sqrt{2} \mathrm{cm} \)
\( c \cdot 2 c m \)
D. \( 2 \sqrt{2} \) cm


Which part of mammalian brain
controls the muscular co-ordination?
A. Cerebrum
B. Cerebellum
c. Corpus callosum
D. Medulla oblongata


Which of the following electrolytes will not be most effective in the coagulation of gold sol? This question has multiple correct options
A. \( N a N O_{3} \)
в. \( K_{4}\left[\operatorname{Fe}(C N)_{6}\right] \)
c. \( N a_{3} P O_{4} \)
D. \( M g C l_{2} \)


Copy and complete the following table relating to important industrial
process:
Name O
process
Haber's
process


In the given v-t graph the distance
travelled by the body in 5 seconds will
be
A . \( 100 \mathrm{m} \)
B. 80 m
\( c \cdot 40 m \)
D. 20 \( m \)


A mixture of helium and argon contains
3 moles of \( H e \) for every 2 moles of \( A r \) The partial pressure of argon in the mixture is
A. two thirds the total pressure
B. one third the total pressure
c. three fifths the total pressure
D. two fifths the total pressure


Can you use soaps and synthetic
detergents to check the hardness
of water?


Which among the following are biological methods that are being used
to control population growth?
A. Condoms
B. oral contraceptives
\( c \cdot c u-T \)
D. All of the above


Solve the differential equation \( \cos \left(\frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}\right)=\boldsymbol{a},(\boldsymbol{a} \in \boldsymbol{R}) \)


A stage in cell division is shown in the
figure. Identify the stage of cell division
with its characteristics.
A. Late anaphase - Chromosomes move away from equatorial plate, golgi complex not present
B. Cytokinesis - Cell plate formed mitochondria distributed between two daughter cells
C. Telophase - Endoplasmic reticulum and nucleolus not reformed yet
D. Telophase - Nuclear envelope reforms, golgi complex reforms


Vectors \( \vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=2 \hat{i}-\hat{j}+\hat{k} \)
and \( \vec{c}=3 \hat{i}+\hat{j}+4 \hat{k} \) are so placed that
the end point of one vector is the starting point of the next vector, then
the vectors are
A. Not coplanar
B. Coplanar but cannot form a triangle
c. coplanar and form a triangle
D. coplanar and can form a right-angled triangle


Which of the following conclusions
could not be derived from Rutherford's
\( \alpha \) -particles scattering experiment?
A. Most of the spaces in the atom is empty.
B. The radius of the atom is about \( 10^{-10} \mathrm{m} \) while that of
nucleus is \( 10^{-15} \mathrm{m} \)
C. Electrons move in a circular path of fixed energy called orbits
D. Electrons and the nucleus are held together by electrostatic force of attraction


One of the following statements is
correct. Pick out the one.
A. Diffraction can not take place without interference
B. Sustained interference will not take place without diffraction for non-coherent sources
C. Interference and diffraction are the result of
polarization
D. The fringe width in Young's double slit experiment does not depends on the wave length.


A white solid \( X \) on heating gives a white solid Y and an acidic gas Z. Gas Z is
also given out when \( X \) reacts with an acid. The compound Y is also formed if caustic soda is left open in the atmosphere. \( X, Y \) and \( Z \) are :
A \( \cdot X-N a H C O_{3}, Y-N a_{2} C O_{3}, Z-C O_{2} \)
в. \( X-N a_{2} C O_{3}, Y-N a O H, Z-C O_{2} \)
c. \( X-N a H C O_{3}, Y-N a H C O_{3}, Z-C O_{2} \)
D. \( X-N a O H, Y-N a H C O_{3}, Z-C O_{2} \)


What will be the ratio of molar
capacities for monoatomic gas \( \left(C_{v}=3\right. \)
)?
A . 1.66
B . 2.
\( c .6 . \)
D. 1.5


Short / Long type answer type questions. Why does the left ventricle possess a thicker wall than the right ventricle?


Find the common ratio in the following
G.P. \( -5,1, \frac{-1}{5}, \dots \)


Which of the following is not a proper fraction?
A \( \cdot \frac{2}{3} \)
B. \( \frac{3}{4} \)
\( c \cdot \frac{5}{7} \)
D. \( \frac{6}{5} \)


\( 20 m L \) of \( 0.1 N \) acetic acid is mixed
with \( 10 m L \) of \( 0.1 N \) solution of \( N a O H \)
The \( p H \) of the resulting solution is :
\( \left[\text { Given }: p K_{a} \text { of acetic acid is } 4.74\right] \)
A . 3.74
в. 4.74
\( c .5 .74 \)
D. 6.74


A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube
is then rotated in a horizontal plane about one of its ends with a uniform
angular velocity \( \omega . \) The force exerted by the liquid at the other ends is:-
A \( \cdot \frac{M L \omega^{2}}{2} \)
B. \( \frac{M L^{2} \omega}{2} \)
c. \( M L \omega^{2} \)
D. \( \frac{M L^{2} \omega^{2}}{2} \)


The bond order of individual carbon-
carbon bonds in benzene is:
A. one
B. two
c. between one and two
D. one and two alternately


Observe the bins and waste material
heaps and suggest what materials can be used for preparing handicrafts materials.


Give four rational numbers equivalent \( \frac{4}{9} \)


\( f(a+b+c=0, \) then one root of \( \left|\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{x} & \boldsymbol{c} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{b}-\boldsymbol{x} & \boldsymbol{a} \\ \boldsymbol{b} & \boldsymbol{a} & \boldsymbol{c}-\boldsymbol{x}\end{array}\right|=0 \) is
\( A \cdot a+b \)
B.
\( c \cdot b+c \)
D. atca


An average emf of \( 20 \mathrm{V} \) is induced in an
inductor when the current in it is
changed from \( 2.5 A \) in one direction to the same value in the opposite direction in 0.1 s. The self-inuctance of
the inductor is
A . zero
в. \( 0.2 H \)
\( c .0 .4 H \)
D. \( 1 H \)


Find a vector in thedirection of \( 5 \hat{i}-\widehat{j}+ \)
\( 2 \widehat{k} \) which has magnitude 8 units.
A \( \cdot \frac{8}{\sqrt{30}} \hat{i}-\frac{40}{\sqrt{30}} \hat{j}+\frac{16}{\sqrt{30}} \widehat{k} \)
B. \( \frac{16}{\sqrt{30}} \hat{i}+\frac{8}{\sqrt{30}} \hat{j}-\frac{40}{\sqrt{30}} \widehat{k} \)
c. \( \frac{40}{\sqrt{30}} \hat{i}-\frac{8}{\sqrt{30}} \hat{j}+\frac{16}{\sqrt{30}} \widehat{k} \)
D. None


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\mathbf{2} \boldsymbol{x}^{2}+\mathbf{2}^{2} \boldsymbol{x}^{\boldsymbol{4}}+\ldots \ldots+ \)
\( 2^{10} x^{20} . \) Then \( f(x) \) has
A. more than one minimum
B. exactly one minimum
c. at least one maximum
D. none of these


The traits which are acquired by an organism during its lifetime are called
as
A. Acquired traits
B. Inherited traits
c. skilled traits
D. None of the above


Which element has the most metallic
character?
A. Boron
B. Aluminium
c. Indium
D. Thallium


Evaluate: \( \int \frac{\left(x^{2}+1\right)}{\left(x^{4}+1\right)} d x \)


Find the magnetic field intensity due to
a thin wire carrying current \( I \) in the
figure :
A \( \cdot \frac{\mu_{0} i}{2 \pi R}(\pi-a+\tan a) \)
в. \( \frac{\mu_{0} i}{2 \pi R}(\pi-a) \)
c. \( \frac{\mu_{0} i}{2 \pi R}(\pi+a) \)
D. \( \frac{\mu_{0}}{2 \pi R}(\pi+a-\text { tana }) \)


The ground state magnetic property of
\( B_{2} \) and \( C_{2} \) molecules will be:
A . \( B_{2} \) paramagnetic and \( C_{2} \) diamagnetic
B. \( B_{2} \) diamagnetic and \( C_{2} \) paramagnetic
c. both are diamagnetic
D. both are paramagnetic


The oxidation state of \( A, B, \) and \( C \) in a
compound are +2,+5 and -2 respectively. The compound is :
\( \mathbf{A} \cdot A_{2}(B C)_{2} \)
B \( \cdot A_{2}(B C)_{3} \)
\( \mathbf{c} \cdot A_{3}\left(B C_{4}\right)_{2} \)
D. \( A_{2}\left(B C_{4}\right)_{3} \)


For a given material Young's modulus is
2.4 times that of its rigidity modulus. Its Poisson's ratio is
A . 2.4
B. 1.2
\( c .0 .4 \)
D. 0.2


\( f(x)=\frac{1-\cos (1-\cos x)}{x^{4}} \) is continuous at
\( x=0, \) then \( f(0)= \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{6} \)
D.


The formula of phosgene is \( C O C l_{2} \) If true enter 1 , else 0


A tank, which is open at the top,
contains a liquid up to a height \( \boldsymbol{H} . \mathbf{A} \)
small hole is made in the side of a tank
at a distance y below the liquid surface.
The liquid emerging from the hole lands at a distance \( x \) from the tank.
his question has multiple correct options
A. If \( y \) is increased from zero to \( H, x \) will first increase and then decrease
B. x is maximum for \( y=H / 2 \).
c. The maximum value of \( x \) is \( H \)
D. The maximum value of \( x \) will depend on the density of the density of the liquid.


Any device or drug which prevents pregnancy in women is called


Using truth tables, examine whether
the statement pattern \( (\boldsymbol{p} \wedge \boldsymbol{q}) \vee(\boldsymbol{p} \wedge \boldsymbol{r}) \)
is a tautology, contradiction or contingency


Soil erosion is more where
A. Rainfall is high
B. No rainfall
C. Low rainfall
D. None of the above


A wall is made up of square bricks of unit length. Then its area is
A. 1 sq unit
B. 3 sq units
c. 20 sq units
D. 24 sq units


Write the relation between standard
deviation of a set of scores and
its variance


What is the product of the following
reaction?


\( D L \) and \( B M \) are the height on sides
\( A B \) and \( A D \) respectively of parallelogram \( A B C D \) figure. If the area
of the parallelogram is \( 1470 \mathrm{cm}^{2} \) \( A B=35 \mathrm{cm} \) and \( A D=49 \mathrm{cm}, \) find the
ength of \( B M \) and \( D L \)


The ratio of \( d- \) Broglie wavelength of molecular of hydrogen and oxygen kept in two vessels separately at \( 27^{\circ} C \) and
\( 127^{\circ} \mathrm{C} \) respectively is:
A. \( \sqrt{\frac{4}{3}} \)
B. \( \sqrt{\frac{3}{32}} \)
c. \( \frac{8}{\sqrt{3}} \)
D.


In the figure, PR and QS are two
diameters of the circle.
If \( P R=28 c m \) and \( P S=14 \sqrt{3} \mathrm{cm} \)
then find the total area of two shaded
segments. \( (\sqrt{3}=1.73) \)
A \( \cdot 249,12 \mathrm{cm}^{2} \)
B . \( 240.76 \mathrm{cm}^{2} \)
c. \( 251.12 \mathrm{cm}^{2} \)
D. None of these


The unit of Planck's constant is
equivalent to that of :
A. energy
B. angular momentum
c. velocity
D. force


A cutted diamond sparkles because of its:
A. high refractive index
B. hardness
c. emission of light by the diamond
D. absorption of light by the diamond


Choose correct option which suitably
represents value of \( \boldsymbol{x} \)
\( \boldsymbol{x}<\mathbf{5}, \boldsymbol{x} \in \boldsymbol{N} \)
A \( \cdot\{0,1,2,3,4\} \)
в. \{1,2,3,4\}
c. \{1,2,3,4,5\}
D. \{0,1,2,3,4,5\}


Find the angles between the lines,
whose direction cosines are give by the equation \( l^{2}-m^{2}+n^{2}=0, l+m+ \)
\( \boldsymbol{n}=\mathbf{0} \)
A. 0
в. \( \frac{\pi}{6} \)
\( c \cdot \frac{\pi}{4} \)
D.


The electron density of intrinsic semiconductor at room temperature is \( 10^{16} m^{-3} . \) When doped with a trivalent impurity, the electron density is decreased to \( 10^{14} m^{-3} \) at the same
temperature. The majority carrier density is:
A \( \cdot 10^{16} m^{-3} \)
В. \( 10^{18} m^{-3} \)
\( \mathbf{c} \cdot 10^{21} m^{-3} \)
D. \( 10^{20} \mathrm{m}^{-3} \)
E \( .10^{19} m^{3} \)


Which one of the following pairs of substances on the reaction will not
evolve \( \boldsymbol{H}_{2} \) gas?
A . Iron and \( H_{2} S O_{4}(a q) \)
B. copper and \( H C l(g) \)
c. Na and \( C_{2} H_{5} O H \)
D. Iron and steam


If \( O \) is the centre of a circle, \( P Q \) is a
chord and the tangent \( P R \) at \( P \) makes
an angle of \( 50^{0} \) with \( P Q \), then find the
Angle \( (P O Q) \)


The equation of the circle passing through (2,0) and (0,4) and having the minimum radius is
A \( \cdot x^{2}+y^{2}=20 \)
B . \( x^{2}+y^{2}-2 x-4 y=0 \)
c. \( x^{2}+y^{2}=4 \)
D. \( x^{2}+y^{2}=16 \)


A kind of filtration method, where the suspended solids/ solutes are
separated from the colloidal solution because of their concentration gradient by passing the solution through a semipermeable membrane is known as
A. Ultra filtration
B. Ultra centrifugation
c. Dialysis
D. Electrodialysis


A particle of mass \( \boldsymbol{m}=12 \boldsymbol{k} \boldsymbol{g} \) falling
freely from rest under gravity and air resistance force \( (\boldsymbol{F}) \). The velocity of the particle when reaches ground is \( 6 m / s \)
Then total external work done on the
particle is
\( \mathbf{A} \cdot 216 J \)
в. \( (120-F) J \)
\( \mathbf{c} .6 F J \)
D. Data insufficient


A ball of mass \( m \) is dropped onto a floor
from a certain height. The collision is
perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval.


The ease of esterification of following alcohols with HCOOH will be highest for \( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O H} \quad\left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H O H} \)
\( \left(\begin{array}{c}\left.\boldsymbol{C H}_{3}\right)_{3} \boldsymbol{C O H} \\ \mathbf{3}\end{array}\right. \)


The length of a rectangle is 10 m more than its breadth. if the perimeter of rectangle is 80 m. find the dimensions
and area of the rectangle.


A taut string for which \( \mu=5.00 \times \)
\( 10^{-2} k g / m \) is under a tension of \( 80.0 \mathrm{N} \)
How much power must be supplied to the string to generate sinusoidal waves at a frequency of \( 60.0 \mathrm{Hz} \) and an
amplitude of \( 6.00 \mathrm{cm} ? \)


If \( f(x)=3 x+1, g(x)=x^{3}+2, \) then
\( \frac{\boldsymbol{f}+\boldsymbol{g}}{\boldsymbol{f} \boldsymbol{g}}(\mathbf{0})= \)
A . \( x \)
B. 1
\( c \cdot 3 \)
\( D \cdot \frac{3}{2} \)


Which of the following is not a basic physical quantity?
A. Length
B. Time
c. Density
D. Amount of substance


The area of a triangle is 5 and its two vertices are \( \boldsymbol{A}(\mathbf{2}, \mathbf{1}) \) and \( \boldsymbol{B}(\mathbf{3},-\mathbf{2}) . \) The
third vertex lies on \( y=x+3 . \) Then third
vertex is
This question has multiple correct options
A \( \cdot\left(\frac{7}{2}, \frac{13}{2}\right) \)
в. \( \left(\frac{5}{2}, \frac{5}{2}\right) \)
\( ^{c} \cdot\left(-\frac{3}{2}, \frac{3}{2}\right) \)
D. (0,0)


The acceleration-time graph of a body being a straight line parallel to the time axis implies (Assume graph in first quadrant)
A. that the velocity of the body increases uniformly with time
B. that the velocity of the body decreases uniformly with time
c. that the velocity of the body is constant
D. that the body is at rest


State, whether the following statements are true or false.
If \( a<b \) and \( c>0, \) then \( a-c<b-c \)
where \( a, b, c \) are real numbers and \( c \neq 0 \)
A. True
B. False


Why nuclei invariably have mass less
than the sum of the masses of the
individual nucleons in them?


Consider the situation shown if figure
Initially the string is unstretched when
the system is released from rest

Assuming no friction in the pulley, what is the maximum elongation of the
spring?


Fuels are present in which of the following forms?
A. Solids
B. Liquids
c. Gases
D. All of these


Three magnets of the same length but
moments \( \mathrm{M}, 2 \mathrm{M} \) and \( 3 \mathrm{M} \) are arranged in the forms of an equilateral triangle with opposite pole nearer, the resultant
magnetic moment of the arrangement is?
A. 6 м
B. zero
c. \( \sqrt{3} \) м
D. \( \frac{\sqrt{3}}{2} \) M


\( \lim _{x \rightarrow x_{1}} \frac{x}{x-x_{1}} \int_{x_{1}}^{x} f(t) d t \) is equal to
В \( \cdot x_{1} f\left(x_{1}\right) \)
\( \mathbf{c} \cdot f\left(x_{1}\right) \)
D. Does not exist


The bulk modulus for an
incompressible liquid is?
\( A \cdot \infty \)
B. 0
c. 1
\( D \)


An alternating voltage \( \boldsymbol{V}=\boldsymbol{V}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}) \)
is applied across a circuit. As a result, a
current \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{\pi} / 2) \) flows in it
The power consumed per cycle is
A . zero
в. \( 0.5 V_{0} I_{0} \)
c. \( 0.707 V_{0} I_{0} \)
D. \( 1.414 \mathrm{V}_{0} \mathrm{I}_{0} \)


Two identical condensers M and N are
connected in series with a battery. The space between the plates of M is
completely filled with a dielectric medium of dielectric constant 8 and a
copper plate of thickness \( \frac{d}{2} \) is introduced between the plates of \( \mathrm{N}(d \) is
the distance between the plates). Then
potential differences across \( \mathrm{M} \) and \( \mathrm{N} \) are, respectively, in the ratio:
\( \mathbf{A} \cdot 1: 4 \)
B . 4: 1
\( \mathbf{c} \cdot 3: 8 \)
D. 1: 6


Differentiate the following w.r.t. \( x \)
\( \sin ^{2} \sqrt{x} \)
A \( \cdot \frac{1}{2 \sqrt{x}} \sin (3 \sqrt{x}) \)
B. \( \frac{1}{\sqrt{x}} \sin (2 \sqrt{x}) \)
c. \( \frac{1}{2 \sqrt{x}} \sin (2 \sqrt{x}) \)
D. \( \frac{1}{2 \sqrt{x}} \sin (4 \sqrt{x}) \)


The dimension of angular momentum is
\( \mathbf{A} \cdot\left[M^{0} L^{1} T^{-1}\right] \)
B . \( \left[M^{1} L^{2} T^{-2}\right] \)
C \( \cdot\left[M^{1} L^{2} T^{-1}\right] \)
D \cdot \( \left[M^{2} L^{1} T^{-2}\right] \)


In peritrichous bacteria, flagella occur
A. At one end
B. At both ends
c. All over the body
D. Absent


The uncertainty (in meters) in the position of an insect weighing \( 0.68 g \) and traveling at a velocity of \( 0.85 \mathrm{m} / \mathrm{s} \) (the uncertainty in the velocity is 0.1 \( m / s), \) is:
A. \( 8 \times 10^{-21} \mathrm{m} \)
В. \( 4 \times 10^{-25} \mathrm{m} \)
c. \( 8 \times 10^{-31} m \)
D. \( 8 \times 10^{-34} m \)


Find the area of parallelogram (in square \( m \) ) whose base and altitude are
given base \( =15 \mathrm{dm}, \) altitude \( =4.5 \mathrm{dm} \)


Rename the following percents as decimals.
\( \mathbf{0 . 0 0 2 \%} \)
A. 0.02
B. 0.002
c. 0.0002
D. 0.00002


For capacitors in the series combination, the total capacitance \( C \) is
given by
\( ^{\mathbf{A}} \cdot_{C}=\left(\frac{1}{C_{1}}+\frac{1}{C_{2}}+\ldots \ldots\right) \)
в. \( C=C_{1}+C_{2}+\ldots \)
\( ^{\mathbf{c}} \cdot \frac{1}{\bar{C}}=\left(\frac{1}{C_{1}}+\frac{1}{C_{2}}+\ldots . .\right) \)
\( \stackrel{\mathrm{D}}{\mathrm{C}}=C_{1}+C_{2}+\ldots \)


In a hydrogen atom, the electron moves
in an orbit of radius \( 0.5 A^{\circ} \) making \( 10^{16} \) revolution per second. The magnetic moment associated with the orbital
motion of the electron is \( A m^{2} \)
A. \( 1.602 \times 10^{-19} \)
?
В. \( 1.256 \times 10^{-22} \)
c. \( 1.67 \times 10^{-2} \)
D. \( 1.256 \times 10^{-23} \)


\( \mathbf{f}(x)=\cos x-\cos ^{2} x . \) Find range


Fill up the gaps (shown by-) in the
following A.P. \( 34,-,-,-,-, 48 \)


Find the interval in which \( \boldsymbol{f}(\boldsymbol{x})=\int_{-1}^{x}\left(\boldsymbol{e}^{t}-\mathbf{1}\right)(\mathbf{2}-\boldsymbol{t}) \boldsymbol{d t},(\boldsymbol{x}>\mathbf{1}) \)
is
increasing
\( A \cdot[3,5] \)
B . [1,3]
\( \mathbf{c} \cdot[0,3] \)
D. [0,2]


If the resistivity of an alloy is \( \rho^{\prime} \) and that
of constituent metal is \( \rho \) then :
A \( \cdot \rho^{\prime}>\rho \)
B . \( \rho^{\prime}<\rho \)
C \( \cdot \rho^{\prime}=\rho \)
D. there is no simple reaction between \( \rho^{\prime} \& \rho \)


Which of the following elements is used for vulcanizing rubber?
A. sulphue
B. chlorine
c. bromine
D. phosphorus


The molecule of aspartame
Nutrasweet ), depicted below, has
stereogenic centers.
\( A \)
B. 3
\( c \cdot 4 \)
\( D \)


The mean distance between the atoms
of iron is \( 3 \times 10^{-10} m \) and interatomic
force constant for iron is \( \mathbf{7} N \boldsymbol{m}^{-1} \). The
Young's modulus of electricity for iron
is
A \( .2 .33 \times 10^{5} \mathrm{Nm}^{-2} \)
в. \( 23.3 \times 10^{10} \mathrm{Nm}^{-2} \)
c. \( 2.33 \times 10^{9} \mathrm{Nm}^{-2} \)
D. \( 2.33 \times 10^{10} \mathrm{Nm}^{-2} \)


Determine the values of \( p \) for which
the quadratic equation \( 2 x^{2}+p x+8= \)
0 has real roots.
A. \( p<-8 \) or \( p>8, p \in R \)
в. \( p \geq-8 \) and \( p \leq 8, p \in R \)
c. \( p \leq-8 \) or \( p \geq 8, p \in R \)
D. \( p>-8 \) and \( p<8, p \in R \)


Find the relation between drift velocity
and relaxation time of charge carriers in a conductor. A conductor of length \( \boldsymbol{L} \)
is connected to a d.c. The source of emf
\( E^{\prime} . \) If the length of the conductor is
tripled by stretching it, keeping \( ^{\prime} \boldsymbol{E}^{\prime} \) constant, explain how its drift velocity would be affected.


The term biocoenosis was coined by
A. Darwin
B. Haeckel
c. Odum
D. Mobius


A single slit Fraunhoffer diffraction pattern is formed with white light. For what wavelength of light the third secondary maximum in the diffraction pattern coincides with the second
secondary maximum in the pattern for red light of wavelength 6500 A?
B . \( 4642 A^{\circ} \)
c. \( 4100 A^{\circ} \)
D. \( 4400 A^{\circ} \)


A uniform sphere of radius \( \boldsymbol{R} \) is placed on a smooth horizontal surface and a
horizontal force \( \boldsymbol{F} \) is applied on it at a
distance \( h \) above the centre. The
acceleration of the centre of mass of the
sphere is
A. maximum when \( h=0 \)
B. maximum when \( h= \) R
c. maximum when \( h=R / 2 \)
D. independent of \( h \)


Find the coordinates of \( C \)
A. (97,248)
в. (87,238)
c. (87,258)
D. (97,268)


\( \mathbf{2} \boldsymbol{s} \stackrel{I}{\rightarrow} \mathbf{2} \boldsymbol{p} \stackrel{I I}{\rightarrow} \mathbf{3} \boldsymbol{d} \stackrel{I I}{\rightarrow} \mathbf{3} \boldsymbol{p} \stackrel{I V}{\rightarrow} \mathbf{4} \boldsymbol{s} \stackrel{\boldsymbol{V}}{\rightarrow} \mathbf{2} \boldsymbol{p} \)
The electronic transitions show above
are observed when lithium atoms are
sprayed into a hot flame. The various
transitions are numbered for
identification. Which of these
transitions would result in emission of
electromagnetic radiation (light)?
A. I and II only
B. I and III only
c. I and v only
D. III and IV only
E. III and v only


Endocrine glands are also called as glands.
A. Exocrine
B. Ductless
c. Ducted
D. None of the above


Two particles are simultaneously projected in the horizontal direction
from a point \( \boldsymbol{P} \) at a certain height. The
initial velocities of the particles are
oppositely directed to each other and
have magnitude v each. The separation between the particles at a time when their position vectors (drawn from the point \( P \) ) are mutually perpendicular, is
\( ^{\mathrm{A}} \cdot \frac{v^{2}}{2 g g} \)
В. \( \frac{v^{2}}{g} \)
c. \( \frac{4 v^{2}}{g} \)
D. \( \frac{2 v^{2}}{g} \)


Silicon nitride has band gap energy of
\( e v \)


Convert the following into fraction.
\( 44 \% \)
A \( \cdot \frac{11}{44} \)
в. \( \frac{44}{1000} \)
c. \( \frac{44}{11} \)
D. \( \frac{11}{25} \)


A body is standing on a merry-go-round which is rotating uniformly in a horizontal plane. His frame of reference
is
A. an inertial frame
B. a non-inertial frame
c. either inertial or non-inertial
D. neither inertial nor non- inertial


The decomposition of \( N H_{3} \) on
platinum surface is zero order. What are
the rate of production of \( N_{2} \) and \( H_{2} \) in mole.lit\( ^{-1} \cdot \sec ^{-1} \) if \( K=2.5 \times \)
\( 10^{-4} \) mole.lit \( ^{-1} . \) sec \( ^{-1} ? \)
\( \begin{array}{ll}\text { A } \cdot 3.75 \times 10^{-4}, & 1.25 \times 10^{-4}\end{array} \)
B. \( 1.25 \times 10^{-4}, \quad 3.75 \times 10^{-4} \)
C . \( 2.5 \times 10^{-4}, \quad 7.5 \times 10^{-4} \)
D. \( 1.25 \times 10^{4}, \quad 3.75 \times 10^{-4} \)


\( \infty \)
\( \infty \)
\( \infty \)
\( \infty \)


The values of and \( y \) satisfying the two
equations \( 32 x+33 y=31,33 x+ \)
\( 32 y=34 \) respectively will be
A. -1,2
в. 2,-1
c. 0,0
D. 2,3


Find the derivative of \( \sin \left(2 \sin ^{-1} x\right) \)
A \( \cdot \frac{2 \cos \left(2 \sin ^{-1} x\right)}{\sqrt{1-x^{2}}} \)
B. \( \frac{\cos \left(2 \sin ^{-1} x\right)}{\sqrt{1-x^{2}}} \)
c. \( \frac{2 \cos \left(2 \cos ^{-1} x\right)}{\sqrt{1-x^{2}}} \)
D. \( -\frac{\cos \left(2 \cos ^{-1} x\right)}{\sqrt{1-x^{2}}} \)


\( K M n O_{4} \) on treatment with conc.
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) forms a compound \( (X) \) which
decomposes explosively on heating forming (Y). The (X) and (Y) are respectively:
A. \( M n_{2} O_{7}, M n O_{2} \)
В. \( M n_{2} O, M n_{2} O_{3} \)
c. \( M n S O_{4}, M n_{2} O_{3} \)
D. \( M n_{2} O_{3}, M n O_{2} \)


Match the element with its associated
functions/roles and choose the correct
option given among below.


Which layer of atmosphere contains
ozone in it?
A. Hydrosphere
B. Lithosphere
c. Stratosphere
D. None of these


Fuse wire should be placed in the path
of wire
A. Neutral
B. Phase
c. Earth
D. None of these


Identify closed curve.
\( \mathbf{A} \cdot 1 \) only
B. 2 only
C. 3 only
D. 1 and 2 only


Derive the relationship between relative lowering of vapour pressure and molar mass of non-volatile solute.


Assertion
Loss in friction due to a decelarating metallic block on the ground,is the loss which is reversible.
Reason
At every point of motion of the block there is a net force acting on it which is decelarating its motion.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


\( t=0 \) to \( t=2 s \)


Two spherical rain drops with radiii in the ratio 1: 2 fall from a great height through the atmosphere. The ratio of
their momenta after they have attained terminal velocity is
A .1: 8
B. 2:
\( c \cdot 1: 32 \)
D. 1: 2
E . 1: 16


The correct IU \( P A C \) name of the
following compound \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{C} \equiv \)
\( \boldsymbol{C H} \)
A. Butadiene
B. Butyne
c. Butenynw
D. Butynene


\( \boldsymbol{x}(\boldsymbol{x}-1) \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-(\boldsymbol{x}-\boldsymbol{2}) \boldsymbol{y}=\boldsymbol{x}^{3}(\boldsymbol{2} \boldsymbol{x}- \)
1). The solution to the above given differential equation is \( \boldsymbol{y}(\boldsymbol{x}+\boldsymbol{k})= \)
\( \boldsymbol{x}^{m}\left(\boldsymbol{x}^{n}-\boldsymbol{x}+\boldsymbol{c}\right) . \) Find \( \boldsymbol{k}+\boldsymbol{m}+\boldsymbol{n} ? \)


In which of the following cases does the electromagnetic induction occur?
This question has multiple correct options
A. A current is started in a wire held near a loop of wire.
B. The current is stopped in a wire held near a loop of wire
C. A magnet is moved through a loop of wire.
D. A loop of wire is held near a magnet


Velocity-time graph \( A B \) (Fig. 2.1 ) shows
that the body has:
A. a uniform acceleration
B. a non-uniform retardation
c. uniform speed
D. initial velocity OA and is moving with uniform retardation


A diagram of T.S. of dicot root is given.
Select the option which correctly labels
\( A, B, C, D \) and \( E \)
A. A-Protoxylem, B-Metaxylem, C-Phloem, D-Pericycle, EEndodermis
B. A-Metaxylem, B-Protoxylem, C-Phloem, D-Percyicle, EEndodermis
C. A-Protoxylem, B-Metaxylem, C-Phloem, D-Endodermis E-Pericycle
D. A-Metaxylem, B-Protoxylem, C-Phloem, DEndodermis, E-Pericycle


From 2 mg calcium \( 1.2 \times 10^{19} \) atoms
are removed. The number of \( g \) - atoms of calcium left is \( (\boldsymbol{C} \boldsymbol{a}=\mathbf{4 0}) \)
A \( .5 \times 10^{-5} \)
В. \( 2 \times 10^{-5} \)
c. \( 3 \times 10^{-5} \)
D. \( 5 \times 10^{-6} \)


Oxidation state of iodine in iodic acid
is:
\( A \cdot+1 \)
B. +3
\( c .+5 \)
D. +7


A resistor and a capacitor are in series \( \operatorname{across} \) a \( 20 V \) ac source. Circuit
impedance is \( 4.33 k \Omega . \) Current flow in the circuit is
\( \mathbf{A} \cdot 9.2 m A \)
в. \( 92 m A \)
c. \( 4.6 m A \)
D. \( 460 m A \)


If \( A=\left|\begin{array}{l}1 \\ 3\end{array}\right| B=\left|\begin{array}{c}-1 \\ 4\end{array}\right| \) then \( 2 A+B= \)
\( A \cdot \mid 10 \)
9
B. \( \mid 10 \) 1
\( c \cdot\left|\begin{array}{l}1 \\ 10\end{array}\right| \)
D. \( \mid 1 \) 9


Find the stationary point of \( \boldsymbol{y}=\boldsymbol{x}^{2}+ \)
\( 5 x-6 \)


Write IUPAC name of the following coordinate compounds:
(i) \( \boldsymbol{K}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \)
(ii) \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
(iii) \( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right] \boldsymbol{C l} \)
\( (\text { iv })\left[\boldsymbol{C r}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)


Which one of the following is true for the
given triangle?
\( \mathbf{A} \cdot \angle 3=\angle 1+\angle 2 \)
B . \( \angle 1=\angle 3+\angle 2 \)
c. \( \angle 2=\angle 1+\angle 3 \)
D. Both (A) and (B)


An element \( A \) combines with oxygen to
form an oxide \( A O . \) Find the group to
which the element \( \boldsymbol{A} \) belongs.
A . \( I A \)
в. \( I I A \)
c . III \( A \)
D. IVA


The conduction of urine from kidney to the urinary bladder takes place by
A. Ureter
B. Urethra
c. Ovary
D. None of the above


If the derivative of the functions \( f(x)= \) \( \left\{\begin{array}{cc}b x^{2}+a x+4 ; & x \geq-1 \\ a x^{2}+b ; & x<-1\end{array}\right\} \) is
everywhere continuous then
A \( . a=2, b=3 \)
В. \( a=3, b=2 \)
C \( . a=-2, b=-3 \)
D. \( a=-3, b=-2 \)


f \( a \neq b \neq c, \) prove that the points
\( \left(a, a^{2}\right),\left(b, b^{2}\right),\left(c, c^{2}\right) \) can never be
collinear.


Fungi shows mode of nutrition.
A. Saprophytic
B. Phagocytic
C. Pinocytic
D. None of these


Prove that:
\( \tan ^{-1} \frac{1}{4}+\tan ^{-1} \frac{2}{9}=\frac{1}{2} \cos ^{-1} \frac{3}{5} \)


The domain of the function \( \mathbf{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\boldsymbol{x}^{\log \boldsymbol{x}}} \)
is
A.
B. \( (0, \infty) \)
c. \( R-\{1\} \)
D. R - \{9


Which gas is emitted by the combustion of fossil fuels?
A. \( C O_{2} \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot H_{2} \)
D. \( N O_{2} \)


toppr ócin
Q Type your question
conductor as shown. Now as the point
charge \( Q \) is pushed away from
conductor, the potential difference
\( \left(V_{A}-V_{B}\right) \) between two points \( A \) and
\( B \) within the cavity of sphere remains
constant
Reason
The electric field due to charge on outer
surface of conductor and outside the
conductor is zero at all points inside the
conductor
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


From the given cells:
Lead storage cell, Mercury cell, Fuel cell and Dry cell Answer the following:
(i) Which cell is used in hearing aids?
(ii) Which cell was used in Apollo Space
Programme?
(iii) Which cell is used in automobiles
and inverters?
(iv) Which cell does not have long life?


Air filled in dead space is
A . 150 ç
B. 350 сс
c. 500 cc
D. 1500 cc


The product formed when horn silver ore (chlorargyrite) is leached with aqueous \( N a C N \) solution is:
A. silver metal
B. silver chloride
c. silver cyanide
D. sodium argentocyanide


A fraction with denominator \( 3, \) which is
less than 1 is
\( A \cdot \frac{4}{3} \)
B.
\( c \cdot 1 \frac{2}{3} \)
D. None


Give \( I U P A C \) name


Convert \( 1 g / c m^{3} \) to \( k g / m^{3} \)
A. 1000
B. 100
c. \( 0 . \)
D. 10


De-Broglie wavelength depends on
A. Mass of the particle
B. Size of the particle
C. Material of the particle
D. Shape of the particle


Assertion
\( F e^{3+} \) can be used for coagulation of
\( A s_{2} S_{3} \) sol.
Reason
\( F e^{3+} \) reacts with \( A s_{2} S_{3} \) to give \( F e_{2} S_{3} \)
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


Extinct human ancestor who ate only
fruits and hunted with stone weapons
was
A. Australopithecus
B. Dryopithecus
c. Ramapithecus
D. Homo erectus


Describe the extraction of magnesium and bromine from sea water


When transistors are used in digital circuits they usually operate in
A. active region
B. breakdown region
c. linear region
D. saturation and cutoff regions


Calculate the current through a lamp of \( 25 w \) operating at \( 220 v \)
\( A \cdot 2 A \)
B. 25A
c. 0.114 A
D. \( 6 A \)


Two resistors are connected in series
\( \operatorname{across} \) a \( 5 ~ V \) rms source of alternating potential. The potential difference \( \operatorname{across} 6 \Omega \) resistor is \( 3 V . \) If \( R \) is
replaced by a pure inductor \( L \) of such
magnitude that current remains same, then the same potential difference \( \operatorname{across} L \) is:
\( \mathbf{A} \cdot 1 V \)
B. \( 2 V \)
c. \( 3 V \)
D. \( 4 V \)


Which of the following materials conducts electricity?
A. crystalline potassium chloride
B. Fused sulphur
c. Molten sodium chloride
D. Diamond


For the same value of angle of incidence, the angles of refraction in
three media \( A, B \) and \( C \) are \( 15^{\circ}, 25^{\circ} \)
and \( 35^{\circ} \) respectively. In which medium
would the velocity of light be minimum?


The force applied on a body on a rough
surface of coefficient of friction \( \mu \)
produces an acceleration \( a \). If
coefficient of friction between the body
and the surface is reduced to \( \mu / 3, \) the
acceleration increases by 2 units. The
value of \( \mu \) is:
\( \mathbf{A} \cdot \frac{2}{3} g \)
B. \( \frac{3}{2} g \)
\( c \cdot \frac{3}{g} \)
D. \( \frac{1}{g} \)


Cathode rays gain kinetic energy when accelerated by an electric field. If they are subjected to a uniform magnetic field, then their
A. energy increases
B. momentum increases
c. energy and momentum decrease
D. energy and momentum remain unaffected


A vector \( \vec{A} \) points vertically downward(south)and \( \vec{B} \) points towards east, then the vector product \( \vec{A} \times \vec{B} \) is:
A . Along west
B. Along east
c. zero
D. Outwards or inwards


If \( a, b, c \) are the lengths of sides of a triangle, then the minimum value of \( \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \)
\( A \)
B. 2
\( c \cdot 5 \)
D.


A.M. of \( 1,2, x, 3 \) is \( 0, \) then \( x= \)


Which of the following is a nonnarcotic analgesic?
A. Morphine
B. Codeine
c. Heroin
D. Aspirin


The vectors \( 3 i+j-5 k \) and \( a i+b j- \)
\( 15 k \) are collinear, if
A \( . a=3, b=1 \)
в. \( a=9, b=1 \)
c. \( a=3, b=3 \)
D. \( a=9, b=3 \)


In an uniform electric field \( \boldsymbol{E}=\mathbf{1 0} \boldsymbol{N} / \boldsymbol{C} \)
as shown in figure, find \( V_{B}-V_{C}: \)
\( \mathbf{A} \cdot 10 V \)
B. \( -10 V \)
\( \mathbf{c} \cdot 20 V \)
D \( .-20 V \)


\( A(2,6) \) and \( B(1,7) \) are two vertices of a triangle \( A B C \) and the centroid is (5,7) The coordinates of \( C \) are
A. (8,12)
B. (12,8)
c. (-8,12)
D. (10,8)


is calculated by deducting tax credit from tax collected during the payment period.
A. vat
B. profit
c. sales tax
D. discount


Which will have move inertia?
A. A plastic eraser
B. Pencil
\( c \). A book
D. A table


Out of benzene, m dinitrobenzene and
toluene which will undergo nitration most easily and why?


If \( a, b, c \) are three positive numbers,then the minimum value of the expression \( \frac{\boldsymbol{a b}(\boldsymbol{a}+\boldsymbol{b})+\boldsymbol{b} \boldsymbol{c}(\boldsymbol{b}+\boldsymbol{c})+\boldsymbol{c} \boldsymbol{a}(\boldsymbol{c}+\boldsymbol{a})}{\boldsymbol{b} \boldsymbol{c} \boldsymbol{a}} \)
A . 3
B. 4
\( c .6 \)
\( D \)


The trend in metallic characters of
elements in a period :
A. decreases
B. increases
c. constant
D. none of these


Suppose \( X \) has a binomial distribution with \( n=6 \) and \( p=\frac{1}{2} . \) Show that \( X=3 \)
is the most likely outcome.


Of the following quatities, which one
has dimensions different from the
remaining three?
A. Energy per unit volume
B. Force per unit area
c. Product of voltage and charge per unit volume
D. Angular momentum


Prove \( \frac{\cos 20^{\circ}+\sin 20^{\circ}}{\cos 20^{\circ}-\sin 20^{\circ}}=\tan 65^{\circ} \)


Which is not the characteristic of \( \pi- \)
bond?
A. \( \pi \) bond is formed when a sigma bond already exists
B. \( \pi \) bonds are formed from hybrid orbitals
C. \( \pi \) bond may be formed by the overlapping of p orbitals
D. \( \pi \) bond results from lateral overlap of atomic orbitals


The position \( x \) of a particle varies with
time \( t \) as \( a t^{2}-b t^{2} . \) The acceleration of
the particle be 0 at time \( t \) equals to
\( A \cdot \frac{a}{b} \)
B・彎
\( c \cdot \frac{a}{3} \)
D. zero


The nuclear reaction,
\( _{29}^{63} C u+_{2}^{4} H e \longrightarrow_{17}^{37} C l+14_{1}^{1} H+16_{0}^{1} n \)
is referred to as:
A. spallation reaction
B. fusion reaction
c. fission reaction
D. chain reaction


A metal wire of linear mass density of
\( 9.8 g m \) is stretched with a tension of
10 kg \( -w t \) betweentwo rigid supports 1
metre apart. The wire passes at its middle point between the poles of aper magnet and it vibrates in resonance when carrying an alternating current of frequency \( n \).The frequency nof the alternating source is
\( \mathbf{A} \cdot 50 H z \)
в. \( 100 H z \)
c. \( 200 H z \)
D. \( 25 H z \)


Solve the following equation: \( 10 p+ \)
\( \mathbf{1 0}=\mathbf{1 0 0} \)


Show that "Law of conservation of mass
is fullyjustified in a balanced chemical equation"


A uniform semicircular ring of radius \( \boldsymbol{R} \)
,and mass \( M \) is rotating about a vertical axis (passing through its circumference mid point) with angular
velocity \( \omega \) then its angular momentum is given as \( \frac{8 M R^{2}}{11 k} \omega \) then the value of \( k \) is


Assertion: The reaction; \( _{1} \boldsymbol{H}^{2}+_{0} \boldsymbol{n}^{1} \rightarrow \)
\( _{2} H e^{4}+_{0} n^{1} \) will not happen
Reason: The equation given is not balanced.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


What is the maximum number of
orbitals that can be identified with the
following quantum numbers?
\( n=3, l=1, m_{l}=0 \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


The following one represents logic addition is
A. \( 1+1=2 \)
B. \( 1+1=10 \)
c. \( 1+1=1 \)
D. \( 1+1=11 \)


If the temperature of a gas is increased
by \( 1 \mathrm{K} \) at constant pressure, its volume increases by 0.0035 of the initial volume.
The temperature of the gas is:
\( A \cdot 100 K \)
B. 150 K
c. \( 300 k \)
D. 285.7 K


A material that lets electricity to pass through it is called a/an-
A. Electrical appliances
B. Electrical conductor
c. Electrical insulator
D. None of these


The value of acceleration due to gravity as we move from equator to
pole
A . increases
B. decreases
c. remains same
D. becomes zero


Assertion
Velocity time graph of two particles undergoing head-on collsion is shown in the figure. If collision is inelastic then
value of y must be less than \( x \)
Reason

Coefficient of restitution(e) \( = \) velocity of |velocity of
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


Solids which break or rupture above the elastic limit are classified as:
A . brittle
B. elastic
c. ductile
D. malleable


The safety fuse should have
A. high resistance and high melting point
B. high resistance and low melting point
C. low resistance and high melting point
D. low resistance and low melting point


The following equation represents a method of purification of nickel by:
\( N i+4 C O(\text {impure}) \stackrel{320 K}{\rightarrow} N i(C O)_{4} \stackrel{420 L}{\longrightarrow} \)
A. Cupellation
B. Mond's process
c. van Arkel method
D. zone refining


A reaction mixture containing \( \boldsymbol{H}_{2}, \boldsymbol{N}_{2} \)
and \( N H_{3} \) has partial pressure 2 atm, latm and 3 atm respectively at 725 K. If
the value of \( K \) for the reaction. \( N_{2}+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3} \) is \( \mathbf{4 . 2 8} \times \mathbf{1 0}^{-\mathbf{5}} \)
\( \operatorname{atm}^{-2} \) at \( 725 \mathrm{K}, \) in which direction the net reaction will go:
A. forwarddard
B. backward
c. no net reaction
D. direction of reaction cannot be predicted


Corrosion can be prevented by :
A. painting the metal surface
B. alloying the metal with more anodic metal
C. to prevent the contact of the metal surface with good electrical conducting media
D. all


Two balls are rolling on a flat smooth
table. One ball has velocity components \( \sqrt{3} \hat{j} \) and \( \hat{i} \) while the other has components \( 2 \hat{i} \) and \( 2 \hat{j} \). If both start moving simultaneously from the same point, the angle between their paths is:
A . 15
в. 30
c. 45
D. \( 60^{\circ} \)


Aquaregia is part conc. HCl and
part conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \)
A. one,three
B. one,one
c. three,three
D. three,one


Calculate the mean deviation about the
mean of the set of first \( n \) natural
numbers when \( n \) is an even number


For position of real object at \( x_{1} \) and
\( x_{2}\left(x_{2}>x_{1}\right) \) magnification is equal to 2
Find out \( \frac{x_{1}}{x_{2}} . \) if focal length of converging
lens \( \boldsymbol{f}=\mathbf{2 0} \boldsymbol{c m} \)
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{4} \)
\( c \cdot 2 \)
D.


The volume change of a solid copper
cube \( 10 c m \) on an edge, when subjected
to a pressure of \( 7 M P a \) is then (Bulk modulus of copper \( =140 G P a) \)
A \( .5 \times 10^{-2} \mathrm{cm}^{3} \)
В. \( 10 \times 10^{-2} \mathrm{cm}^{3} \)
\( \mathbf{c} \cdot 15 \times 10^{-2} c m^{3} \)
D. \( 20 \times 10^{-2} \mathrm{cm}^{3} \)


A cylinder of capacity \( 20 L \) is filled with
\( \boldsymbol{H}_{2} \) gas. The total average kinetic energy
of translatory motion of its molecules is
\( 1.5 \times 10^{5} J . \) The pressure of hydrogen in
the cylinder is
A \( .2 \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \)
в. \( 3 \times 10^{6} \mathrm{N} / \mathrm{m}^{2} \)
c. \( 4 \times 10^{6} N / m^{2} \)
D. \( 5 \times 10^{6} N / m^{2} \)


Comets revolve around the Sun:
A. in a highly elliptical orbit
B. along a circular orbit
C. in an elliptical orbit
D. varying orbit depending on the comet


238
92 \( \mathrm{U} \) atom disintegrates to \( ^{214} 84 P \mathrm{o} \)
with a half life of \( 4.5 \times 10^{9+} \) years by
emitting six alpha particle and \( n \) electrons. Here n is
\( A \cdot 6 \)
B. 4
\( c \cdot 10 \)
D.


Find the median of the following data.
\[
\begin{array}{lllll}
\text { Maths } & \mathbf{6 0}- & \mathbf{6 5}- & \mathbf{7 0 -} & \mathbf{7} \\
\text { marks } & \mathbf{6 5} & \mathbf{7 0} & \mathbf{7 5} & \mathbf{8} \\
\begin{array}{l}
\text { No. of } \\
\text { students }
\end{array} & 8 & 12 & 14 & 8
\end{array}
\]
A. 73.05
B. 72.54
c. 63.54
D. 91.09


What is global warming?


The acute angle between two lines such
that the direction cosines \( I, m, n \) of each
of them satisfy the equations \( l+m+ \)
\( \boldsymbol{n}=\mathbf{0} \) and \( l^{2}+\boldsymbol{m}^{2}-\boldsymbol{n}^{2}=\mathbf{0} \) is :
A . 30
B . 45
c. 60
D. 15


Dispersed phase and dispersion medium in butter are respectively:
A. solid and liquid
B. liquid and liquid
c. liquid and solid
D. solid and solid


Match the columns.
\( \mathbf{A} \)
\( a-2, b-3, c-1, d-4 \)
B. \( a-1, b-4, c-2, d-3 \)
c. \( a-3, b-1, c-4, d-2 \)
D. \( a-2, b-4, c-1, d-3 \)


On the opposite sides of a wide vertical vessel filled with water two identical
holes are opened, each having the cross-sectional area \( S=0.50 \mathrm{cm}^{2} . \) The
height difference between them is
equal to \( \Delta h=51 \mathrm{cm} . \) If the resultant
force of reaction of the water flowing out
of the vessel is \( x N, \) find the value of \( 4 x \)


The coeff. of \( 8^{t h} \) term in the expansion of
\( (1+x)^{10} \) is
A. 120
B. 7
c. \( ^{10} C_{8} \)
D. 210


The solubility in water of a sparingly soluble salt \( A B_{2} \) is \( 1.0 \times 10^{-5} \) mol \( L^{-1} \)
Its solubility product will be:
A \( \cdot 4 \times 10^{-15} \)
В. \( 4 \times 10^{-10} \)
c. \( 1 \times 10^{-15} \)
D. \( 1 \times 10^{-10} \)


Which of the following carries glucose from digestive tract to liver?
A. Pulmonary vein
B. Hepatic portal vein
c. Hepatic artery
D. Data insufficient


Describe anomalous behaviour of
fluorine with the other elements of
group 17 with reference to:
Hydrogen bonding.


Select the correct statement:
This question has multiple correct options
A. High density polythene is a linear polymer
B. Low densiy polythene is a branched chain polymer
C. Chain growth polymers are also known as addition polymer
D. Step growth polymer is also known condensation polymer


A quantity of \( 5 g \) of a crystalline salt when rendered anhydrous lost \( 1.8 g \) of water. The formula mass of the
anhydrous salt is \( 160 . \) The number of molecules of water of crystallization in the salt is
A . 3
B. 5
\( c \cdot 2 \)
\( D \)


A dihaloalkane \( ^{\prime} X^{\prime} \), having formula
\( C_{3} H_{6} C l_{2}, \) on hydrolysis gives a
compound, that can reduce Tollen's
reagent. The compound' \( X^{\prime} \) is
A. 1,2 -dichloropropane
B. 1,1-dichloropropane
c. 1,3 -dichloropropane
D. 2, 2-dichloropropane


\( 2850 \div ?=75 \)
A . 31
B. 34
\( c \cdot 38 \)
D. 39


The given bar graph shows the number
of matches played by different teams.
Read the bar graph and answer the
questions
How many matches did both India and
Bangladesh play?
\( A \cdot 34 \)
B . 22
\( c .38 \)
D. 40


Which of the following is the correct description of calcium oxide?
A. Very stable
B. Prepared by the process of calcination
c. Low affinity for water
D. Less efficient desiccant than silica gel


In which of the following reaction, Boron does not act as reducing agent?
A. \( B+C O_{2} \rightarrow \)
в. \( B+M g \rightarrow \)
c. \( B+S i O_{2} \rightarrow \)
D. \( B+H N O_{3} \rightarrow \)


If \( X \) follows a binomial distribution with
parameters \( n=100 \) and \( P=\frac{1}{3}, \) then
\( P(X=r) \) is maximum when \( r= \)
A . 33
B. 50
c. 25
D. none of these


The ratio of \( F e_{2} O_{3} \) and \( A l \) by weight, in thermite is about:
A . 1: 3
B. 1: 2
c. 3: 1
D. none of the above


A rigid body is made of three identical uniform thin rods each of length \( \boldsymbol{L} \)
fastened together in the form of letter
H. The body is free to rotate about a
fixed horizontal axis \( A B \) that passes
through one of the legs of the \( \boldsymbol{H} \). The
body is allowed to fall from rest from a
position in which the plane of \( \boldsymbol{H} \) is
horizontal. What is the angular speed of
the body, when the plane of \( \boldsymbol{H} \) is
vertical.


In the set \( Q^{+} \) of all positive rational
numbers, the operation \( * \) is defined by the formula \( a * b=\frac{a b}{6} . \) Then, the
inverse of 9 with respect to \( * \) is
A . 4
B. 3
\( c \cdot \frac{1}{9} \)
D.


If vector \( \vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k} \) then, find
unit vector.


Short / Long answer type questions. What are (a) methanogens, (b) halophiles, and
(c) themoacidophiles?


Given below are some points, with their
co-ordinates.
\( \boldsymbol{P}(\mathbf{4}, \boldsymbol{3}), \boldsymbol{Q}(-\boldsymbol{3}, \boldsymbol{2}), \boldsymbol{R}(\mathbf{5}, \mathbf{1}), \boldsymbol{S}(\mathbf{0},-\boldsymbol{4}) \)
What is the \( y- \) coordinate of point \( R ? \)


If the inductance and capacitance are both doubled in L-C-R circuit, the resonant frequency of the circuit will:
A. Decrease to one-half of the original value
B. Decrease to one-fourth of the original value
c. Increase to twice the original value
D. Decrease to twice the original value


Two stones, having masses in the ratio of \( 3: 2, \) are dropped from the heights in the ratio of \( 4: 9 . \) The ratio of magnitudes of their linear momenta just before reaching the ground is (neglect air resistance)
A . 4:
B. 2:3
\( c \cdot 3: 2 \)
D. 1:


Which of the following represents the example of a homopolymer? This question has multiple correct options
B. Bakelite
c. Nylon - 6,6
D. Neoprene


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


Let \( \vec{a}, \vec{b} \) and \( \vec{c} \) be non-coplanar unit vectors equally inclined to one another at an acute angle \( \theta \) then \( [\vec{a} \vec{b} \vec{c}] \) in terms of \( \theta \) is equal to :
A \( \cdot(1+\cos \theta) \sqrt{\cos 2 \theta} \)
B . \( (1+\cos \theta) \sqrt{1-2 \cos 2 \theta} \)
C \( \cdot(1-\cos \theta) \sqrt{1+2 \cos \theta} \)
D \cdot \( (1-\sin \theta) \sqrt{1+2 \cos 2 \theta} \)


The purest form of silica is:
A. quartz
B. flint
c. sand stone
D. jaspar


In the nuclear reaction
\( \boldsymbol{n}+_{\mathbf{9 2}}^{235} \boldsymbol{U} \rightarrow_{\mathbf{5 4}}^{\boldsymbol{a}} \boldsymbol{X} \boldsymbol{e}+_{\boldsymbol{b}}^{\mathbf{9 4}} \boldsymbol{S r}+\mathbf{2 n} \)
determine the values of a and \( b \)


\( \int \frac{d x}{\sqrt{2 a x^{3}}} \)


A complex number is represented by an ordered pair \( (a, b), \) which of the following is true for \( a \) and \( b ? \)
A. \( a \) and \( b \) both are imaginary numbers
B. \( a \) and \( b \) both are real numbers
c. \( a \) is real and \( b \) is an imaginary number.
D. None of these


The magnitude of a physical quantity consists of
A. a number and a unit
B. a number
c. a unit
D. a unit and its symbol


Voice of which of the following creatures is likely to have maximum frequency?
A. Man
B. cow
c. Bird
\( D \cdot \operatorname{Dog} \)


The diagram of a logic circuit is given below, the output of the circuit is
represented by
\( A \cdot W+(X+Y) \)
B. \( w+(x . y) \)
\( c . w .(x+y) \)
D. w. (x.y)


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


The points \( A \) and \( B \) have co-ordinate (1,2,4) and (-1,3,5) respectively. Find \( A B \) and its magnitude.


\( f\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4} \)
then find the value of \( x \)


A cylinder of mass \( 10 \mathrm{kg} \) and radius 15 \( \mathrm{cm} \) is rolling perfectly on a plane of
inclination \( 30^{\circ} . \) The coefficient of static
friction \( \mu_{s}=0.25 \)
(a) How much is the force of friction
acting on the cylinder?
(b) What is the work done against friction during rolling?
(c) If the inclination \( \theta \) of the plane is
increased, at what value of \( \theta \) does the
cylinder begin to skid, and not roll
perfectly?


How many number of aluminium ions
are present in 0.051 g of aluminium oxide?
A. \( 6.023 \times 10^{20} \) ions
B. 3 ions
c. \( 6.023 \times 10^{23} \) ions
D. 9 ions


The volume of gas is reduced to half from its original volume. The specific heat will:
A. get reduced to half
B. get doubled
c. remains constant
D. get increased by four times


An electric dipole is placed in a non-
uniform electric field, then
A. The resultant force acting on the dipole is always zero
B. Torque acting on it may be zero
C. The resultant force acting on the dipole may be zero
D. Torque acting on it is always zero


\( H_{2} \) reacts much faster with \( C l_{2} \) then \( D_{2} \)
because:
A. rate of diffusion of \( H_{2} \) is greater than \( D_{2} \)
B. \( H_{2} \) has lower energy of activation than \( D_{2} \)
C. both (A) and (B) are correct
D. none of the above is correct


Gram molar volume for a gas is always considered at conditions.
A . NTP
B. STP
c. variable temperature
D. none of these


\( \int_{0}^{\frac{2}{3}} \frac{d x}{4+9 x^{2}}= \)


Which of the following does not represent a disaccharide?
A. Maltose
B. Sucrose
c. Lactose
D. Dextrose


Which of the following is most soluble in water?
A. n-butyl alcohol
B. Iso-butyl alcohol
c. Tertiary butyl alcohol
D. None of the above


A sulphate of a metal (A) on heating evolves two gases \( (\mathrm{B}) \) and \( (\mathrm{C}) \) and an
oxide (D). Gas (B) turns \( K_{2} C r_{2} O_{7} \) paper
green while gas (C) forms a trimer in which there is no \( S-S \) bond.

Compound (D) with \( H C l \), forms a lewis
acid (E) which exists as a dimer.

Compounds \( (A),(B),(C),(D) \) and \( (E) \) are
respectively:
A \( \cdot \) FeSO\( _{4}, S O_{2}, S O_{3}, F e_{2} O_{3}, F e C l_{3} \)
в. \( A l_{2}\left(S O_{4}\right)_{3}, S O_{2}, S O_{3}, A l_{2} O_{3}, F e C l_{3} \)
c. FeS\( , S O_{2}, S O_{3}, \) FeSO\( _{4}, \) FeCl\( _{1} \)
D. FeS, \( S O_{2}, S O_{3}, F e_{2}\left(P O_{4}\right)_{3}, F e C l_{2} \)


Which of the following part is excluded from the study of T.S. of gut.
A. Pharynx
B. Esophagus
c. colon
D. Rectum


If \( \bar{a}=\hat{i}-\hat{j}+\hat{k} \) and \( \bar{b}=2 \hat{i}-\hat{j}+3 \hat{k} \)
then the unit vector along \( \bar{a}+\bar{b} \) is
A \( \cdot \frac{3 \hat{i}+4 \hat{k}}{5} \)
B. \( \frac{-3 \hat{i}+4 \hat{k}}{5} \)
c. \( \frac{-3 \hat{i}-4 \hat{k}}{5} \)
D. none of these


Which of the following statement
regarding free radical halogenation of
alkane is not true?
A. Hydrogen abstraction by halogen radical in the propagation step is exothermic in both chlorination and bromination
B. Hydrogen abstraction by halogen radical in the propagation step is exothermic in cholorination but endothermic in bromination
C. A single halogen radical may bring about halogenation to thousands of alkane molecule
D. Continuous source of energy is required to continue the halogenation reaction


A sample of \( \mathbf{C} \mathrm{O}_{2} \) contains \( 2 \mathrm{N}_{\mathrm{A}} \) atoms
of
C. From this \( \frac{1}{10} \) moles of \( C O_{2} \) are removed what will will be remaining mass of carbon dioxide in the sample?


Which of the following does not react with oxygen directly?
\( A \cdot z n \)
в. \( T \)
\( c \cdot P t \)
D. Fe


A body is suspended from a spring balance kept in a satellite The reading
of the balance is \( W_{1} \) when the satellite
goes in an orbit of radius \( R \) and is \( W_{2} \)
when it goes in an orbit of radius \( 2 R \) Then
A. \( W_{1}=W_{2} \)
B. \( W_{1}<W_{2} \)
\( \mathbf{c} \cdot W_{1}>W_{2} \)
D. \( W_{1} \neq W_{2} \)


Two atoms of the same element are
found to have different number of
neutrons in their nuclei. These two
atoms are :
\( \mathbf{A} \cdot \) Isomers
B. Isotopes
c. Isobars
D. Allotropes


Which of the following statement is/ are correct?
I. A person suffering from myopia can see distant obhects clearly.
II.. The bluish color of water in deep sea is only due to reflection of sky in water.
III. In vacuum, all the colored of the light
move with the same speed.
IV. At noon, the sun appears white as light is least scattered
A. I only
B. Il only
c. I and II only
D. III and IV only


The equation of the image of the circle \( x^{2}+y^{2}+16 x-24 y+183=0 \) by the
line mirror \( 4 x+7 y+13=0 \) is:
A \( \cdot x^{2}+y^{2}+32 x-4 y+235=0 \)
B. \( x^{2}+y^{2}+32 x+4 y-235=0 \)
C. \( x^{2}+y^{2}+32 x-4 y-235=0 \)
D. \( x^{2}+y^{2}+32 x+4 y+235=0 \)


From the following which are the factors affecting the rate of evaporation?
A. Temperature
B. Humidity
c. Exposed Surface Area
D. All of the above


In insecta heart is
circulatory system is
A. Ventral, closed
B. Ventral, open
c. Dorsal, open
D. Dorsal, closed


How many \( P=O \) bonds and \( P-O H \)
bonds (respectively) are present in orthophosphoric acid?
A .2,1
в. 3,3
\( \mathrm{c} .1,3 \)
D. 4,3


Which form of energy is a measure of
the electron stability when it is in bound state with nucleus?
A. Potential energy
B. Kinetic energy
c. vibrational energy
D. lonization energy


\( 1.2375 \mathrm{g} \) of cupric oxide on being heated in a current of hydrogen gave 0.9322 g of the metal In another experiment \( 0.9369 \mathrm{g} \) of pure copper was dissolved in nitric acid Excess of acid evaporated and the residue has ignited The weight of the cupric oxide left was 1.2469 g. Which law of chemical combination is
shown by the above results?
A. Law of constant proportions
B. Law of multiple proportions
c. Law of conservation of mass
D. Law of constant volumes


Assertion
CuT, Cu7 and multiload 375 are the
hormone releasing IUDs.
Reason
Cu ions released by some UDS affect the ability of uterine wall to support embryo thus cause contraception.
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 driving mirror on a car is never
concave because:
\( \mathbf{A} \). its field of view is too small.
B. the image would be inverted.
C. the image would be virtual and therefore useless for the driver.
D. only a plane mirror forms true images.


A block of mass \( m \) moving with speed \( v \)
collides with another block of mass \( 2 m \)
at rest. The lighter block comes to rest after collision. What is the value of
coefficient of restitution?
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{3}{4} \)
D. \( \frac{1}{4} \)


Find derivative of \( \sin ^{-1}\left(x^{2}\right) \) using first
principle.
A \( \cdot \frac{2 x}{\sqrt{1-x^{2}}} \)
в. \( \frac{2 x}{\sqrt{1-x}} \)
c. \( \frac{2 x}{\sqrt{1-x^{4}}} \)
D. \( \frac{x}{\sqrt{1-x^{4}}} \)


Reaction of Chlorobenzene with \( \boldsymbol{C H}_{3} \boldsymbol{C l} \)
in presence of \( A l C l_{3} \) gives:
A. Toulene
B. m-chloro toulene
c. only o-chloro toulene
D. Mixture of o- and p-chlorotoulene


The reaction which gives Borazole as a
major product is ?
\( \mathbf{A} \cdot L i H+B_{2} H_{6}^{2 m o l e s L i H_{\rightarrow} 1 m o l e B_{2} H_{6}} \)
\( \mathbf{B} \cdot B_{2} H_{6}+N H_{3} \frac{2 m o l e s B_{2} H_{6} 1 m o l e N H_{3}}{l o w t e m p} \)
\( \mathbf{c} \cdot B_{2} H_{6}+N H_{3} \frac{1 m o B_{2} H_{6} .2 m o l e s N H_{3}}{l o w t e m p} \)
D. \( B_{2} H_{6}+N H_{3} \frac{1 m o B_{2} H_{6} .2 \text { moles } N H_{3}}{\text {hightemp}} \)


Prove that: \( 2\left|\begin{array}{cc}8 & -5 \\ -2 & 6\end{array}\right|=\left|\begin{array}{cc}14 & -2 \\ -4 & 6\end{array}\right| \)


Differentiate between dendrites and
axon.


The angle of a triangle are in the ratio 2 :
1: 3. then, the triangle is right angled triangle.
A. True
B. False


Which of the following gas when taken in the discharge tube produces maximum specific charge of positive
rays?
A. oxygen
B. Nitrogen
c. Helium
D. Hydrogen


Fill in the spaces \( a, b, c \) and \( d \) in the
following table of contraceptive devices
and the methods of contraception.
\begin{tabular}{|c|c|}
\hline Multiload 375 \( b \) \( c \) & \( a \) Non-medicated IUD Barier (mcthod) used by f fmales \( d \) \\
\hline Progestasert & \\
\hline
\end{tabular}


If the \( 7^{t h} \) and \( 13^{t h} \) term an Arithmetic
progression are 34 and 64 respectively. then the common difference is,
\( A \cdot 5 \)
B. 10
c. 17
D. 32


Assertion
Essential oils are volatile and are
insoluble in \( \boldsymbol{H}_{2} \boldsymbol{O} \)
Reason
Essential oils are purified by steam distillation
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 capacitor of \( 10 \mu F \) capacitance is charged by a \( 12 V \) battery. Now the space
between the plates of capacitors is filled with a dielectric of dielectric constant
\( K=3 \) and again it is charged. The
magnitude of the charge is :
A. \( 120 \mu C \)
в. \( 240 \mu C \)
c. \( 360 \mu C \)
D. \( 480 \mu C \)


For a reversible reaction, if the
concentrations of the reactants are
doubled, then the equilibrium constant value
A. gets doubled
B. gets halved
c. remains the same
D. increases four times


Statement: Combustion can take place
at all temperatures less than an ignition temperature.
State whether the given statement is
true or false.
A. True
B. False


In glomerulus of rabbit
A. Afferent glomerular capillary is wider than efferent glomerular capillary
B. Afferrent glomerular capillary is narrower than efferent glomerular capillary
C. Afferent glomerular arteriole is narrower than the efferent glomerular arteriole
D. Afferent glomerular arteriole is wider than the efferent glomerular arteriole


Conducting part of xylem is also known
as
A. Leptom
B. Bast
c. Rhytidome
D. Hadrom


If \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x} \boldsymbol{y}}{\boldsymbol{x}^{2}+\boldsymbol{y}^{2}} ; \boldsymbol{y}(1)=1 ; \) then a value
of \( \boldsymbol{x} \) satisfying \( \boldsymbol{y}(\boldsymbol{x})=\boldsymbol{e} \) is
A \( \cdot \sqrt{3} e \)
B. \( \frac{e}{\sqrt{2}} \)
\( c \cdot \sqrt{2} e \)
D. \( \frac{1}{2} \sqrt{3} \epsilon \)


When \( S O_{2} \) gas is passed through solution of colemanite solution in
boiling water, which product is formed?
A. Borax
B. Boric acid
c. Meta boric acid
D. None of these


The smelting of iron in a blast furnace involves the following processes:
This question has multiple correct options
A. combustion
B. reduction
c. slag foramtoin
D. sublimation


The latest space ship launched by ISRO the "MANGALYAN" was targeted to reach which planet?
A. Mars
B. Saturn
c. sun
D. Mercury


n given fig. sides \( A B \) and \( A C \) of
\( \Delta A B C \) are produced to \( E \) and \( D \)
respectively. If angle bisectors \( B O \) and
\( C O \) of \( \angle C B E \) and \( \angle B C D \) meet each
other at point \( O, \) then prove that:
\( \angle B O C=90^{\circ}-\frac{\angle x}{2} \)


Study of external structure of a plant is
called
A. Histology
B. Morphology
c. taxonomy
D. Phyllotaxy


In the figure above, find the value of \( a \)
given that \( \boldsymbol{x} \| \boldsymbol{y} \)
\( \mathbf{A} \cdot b+c \)
B. \( 2 b-c \)
c. \( 180-b+c \)
D. \( 180-b-c \)


If \( A \) and \( B \) are square matrices such that \( A B=I \) and \( B A=I, \) then \( B \) is
A. Unit matrix
B. Null matrix
c. Multiplicative inverse matrix of \( A \)
D. \( -A \)


Hari bought two fans for \( R s .2,400 \) each.
He sold one at a loss of \( 10 \% \) and the
other at a profit of \( 15 \% \). Find the selling price of each fan and also the total
profit or loss.


Explain the formation of stationary waves by analytical method. Show that nodes and antinodes are equally spaced in stationary waves.


Why asexual reproduction is
sometimes disadvantageous?
A. It allows animals that do not move around to produce offspring without finding mates
B. It allows an animal to produce many offspring quickly
C. It saves the time and energy of gamete production
D. It produces genetically uniform populations


The ages of Vivek and Sumit are in the
ratio of \( 2: 3 . \) After 12 years, their ages
will be in the ratio of \( 11: 15 . \) The age
of Sumit is
A. 32 years.
B. 42 years
c. 48 years
D. 56 years


What do you understand by the term
nuclear fusion?


Vein loading of sucrose into companion
cell is
A. Diffusion
B. Active process
c. Passive transport
D. Turgor


What are the values of the elements?


Goldfish are sold at Rs.15 each. The
rectangular coordinate graph showing the cost of 1 to 12 goldfish is:
A. a straight line segment
B. a set of horizontal parallel line segments
c. a set of vertical parallel line segments
D. a finite set of distinct points
E a straight line


When an object is moved along the
principal axis of a thin converging lens of focal length \( 12 \mathrm{cm} \), two images, three times the size of the object are obtained
when the object is at \( x_{1} \) and \( x_{2} \) distance from the lens. Which one of the following
could be the value of the ratio \( \frac{x_{1}}{x_{2}} ? \)
\( A \cdot 3 \)
B. 6
\( c \cdot 4 \)
D. 2


What are extrinsic semiconductors?
Write two differences between the two
types of extrinsic semiconductors.


Which of the following absorbs largest volume of hydrogen?
A. Colloidal palladium
B. Finely divided nickel
c. colloidal ferric hydroxide
D. Finely divided platinum


Wilkinsons catalyst is:
\( \mathbf{A} \cdot\left[\left(P P h_{3}\right)_{3} R h\right] C l \)
B. used in hydrogenation of alkenes and alkynes
C. homogeneous catalyst
D. all of these


box and covered it with a black paper
from all sides. They fixed a source of light (a torch) at one end of the box by making a hole in it and made another
hole on the other side to view the light.
They placed a milk sample contained in a beaker/tumbler in the box as shown
in the Fig.2.4. They were amazed to see
that milk taken in the tumbler was
illuminated. They tried the same
activity by taking a salt solution but
found that light simply passed through
it?
Can you suggest two more solutions
which would show the same effect as
shown by the milk solution?


Chlorine reacts with nitric oxide to
form?
A. \( N O C l_{2} \)
в. \( N O C l \)
\( \mathbf{c} \cdot N O_{2} C l_{2} \)
D. \( N O_{2} C l \)


The hybridization of \( I C l_{2}^{-} \) and \( C l O_{4}^{-} \) respectively are:
\( \mathbf{A} \cdot s p^{3} d^{2}, s p^{3} \)
B. \( s p^{2}, s p^{3} d \)
c. \( s p^{3} d, s p^{3} \)
D. None of these


No part of india is situated on the
equator .Is it possible to have a
geostationary satellite which always
remains over New Delhi?


In an adiabatic change, the pressure and temperature of a monoatomic gas
are related as \( \boldsymbol{P} \propto \boldsymbol{T}^{C}, \) where \( \boldsymbol{C} \) equals
A
в. \( \frac{5}{2} \)
\( c \cdot \frac{3}{5} \)
D.


The sum of all the coefficient of those
terms in the expansion of \( (a+b+c+d)^{8} \) which contains \( b \) but
not \( \boldsymbol{c} \) is
\( \mathbf{A} \cdot 6305 \)
B \( \cdot 4^{8}-3^{8} \)
C. Number of ways of forming 8 digit numbers using digits 1,2,3 each number as atleast one 3
D. Number of ways of forming 4 digit numbers using digits 1,2,3 each number as atleast one 3


Use the figure below to answer the question that follows. Which molecule or molecules has/have the same empirical formula as one of the others?
\[
\begin{array}{ll}
O=\mathbf{O} & \quad 0=\text { lone pair } \\
D=\mathbf{N} & 0=\text { partially filled } \\
\text { orbital }
\end{array}
\]
\[
0=\mathbf{H}
\]
II
A. II only.
B. III and IV
c. IV only
D. I and III, and III and IV


Find the measure of the complementary
angle of \( 90^{\circ} \)
A \( \cdot 0^{\circ} \)
B . 45
\( c .90 \)
D. 60


By inserting an iron core in a coil carrying current,the strength of its magnetic field will:
A. Increase
B. Decrease
c. Remain same
D. Become zero


Metallic sodium reacts with methanol
and ethanol to give \( O_{2} \) gas.
A. True
B. False


In Mendeleev's periodic table few elements that are chemically similar are placed in the same groups.
A. True
B. False


Which one of the following is not a chemical change?
A. Sublimation
B. Combustion
c. Electrolysis
D. Rusting


Iron filling and water were placed in a 5
litre vessel and sealed. The tank was
heated to \( 1000^{\circ} \mathrm{C} \). Upon analysis the tank was found to contain \( 1.1 \mathrm{g} \) of hydrogen and 42.5 g of water vapour. If the reaction in the tank is represented
by \( 3 \mathrm{Fe}(\mathrm{s})+4 \boldsymbol{H}_{2} \boldsymbol{O}_{(g)} \rightleftharpoons \boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}(\boldsymbol{s})+ \)
\( \mathbf{4} \boldsymbol{H}_{2}(\boldsymbol{g}) \)
The value of equilibrium constant, \( \boldsymbol{K}_{c} \)
is:
A . 30
B. 0.03
\( c \cdot 3 \)
D. 0.003


The distance between an object and the
screen is \( 100 \mathrm{cm} . \) A lens produces an
image on the screen when placed at
either positions \( 40 \mathrm{cm} \) apart. The power
of the lens is :
\( A \cdot 3 D \)
B. 5D
\( c .70 \)
D. 90


A circular grass lawn of \( 35 m \) in radius
has a path \( 7 m \) wide running around it
on the outside. The area ofthe path is?
A \( \cdot 1,496 m^{2} \)
B . \( 1,450 m^{2} \)
c. \( 1,576 m^{2} \)
D. \( 1,694 m^{2} \)


A and B are two solid spheres of equal masses. A rolls down an inclined plane
without slipping from a height \( \boldsymbol{H} . \) B falls vertically from the same height. Then on reaching the ground. This question has multiple correct options
A. both can do equal work
B. A can do more work than B
c. B can do more work than A
D. both A and B will have different linear speeds


The substance added to increase the
stability of a lyophobic sol are called:
A. promoters
B. stabilizers
c. inhibitors
D. poison


Maximum number of electrons that can
be filled in the third orbit of an atom is :
A . 18
B. 8
c. 10
D. 32


If \( \boldsymbol{R} \) is a symmetric relation on a set
\( A=\{1,2,3\}, \) then write the relation
between \( R \) and \( R^{-1} \)


Q Type your question
oe
4
3
\( c \)
\( D \)


If there is no greenhouse effect, then the average temperature at surface of earth would have been
A . 15
B. -18
\( c .-6 \)
D. 10


Mixing of non-reacting ideal gases at constant pressure is generally accompanied by:
A. decrease in entropy
B. increase in entropy
c. change in enthalpy
D. increase in free energy


State whether the given statement is true
or false:
Elements with an odd number of
protons usually have only one or two stable isotopes.
A. True
B. False


A group of worms lacking digestive system harbour these bacteria in their
tissues and use them as a source of
organic molecules. In this unique ecosystem, these specific groups of bacteria are playing the role of?
A. Decomposer only
B. Producer only
c. Primary consumer only
D. Secondary consumers only


The current in resistance \( \boldsymbol{R} \) at
resonance is
\( A \cdot \) zero
B. minimum but finite
c. maximum but finite
D. infinite


Expansion of series: \( \sum_{n=0}^{4} 2 n \)
A. \( 0+2+4+8+16 \)
B. \( 0+2+4+6+8 \)
c. \( 2+4+6+8+10 \)
D. None of the above


The clear sky appears blue because:
A. blue light gets absorbed in the atmosphere.
B. ultraviolet radiations are absorbed in the atmosphere.
C. violet and blue lights get scattered more than lights of all other colours by the atmosphere.
D. light of all other colours is scattered more than the violet and blue colour lights by the atmosphere.


What would be new resistance if length of conductor is doubled and thickness
is halved?


A charged particle q of mass m is in
equilibrium at a height h from a horizontal infinite line charge with
uniform linear charge density \( \lambda \). The
charge lies in the vertical plane containing the line charge. If the particle is displaced slightly (vertically), prove that the motion of the charged particle will be simple harmonic. Also find its time period


Arrange \( A g F, A g C l, A g B r \) and \( A g l \) in the increasing order of solubility in water.
A \( . A g B r<A g I<A g C l<A g F \)
в. \( A g I<A g B r<A g C l<A g F \)
c. \( A g I<A g C l<A g B r<A g F \)
D. None of the above


Which of the following is not primary pollutant?
\( A \cdot S O_{2} \)
в. \( H_{2} S \)
c. \( C O \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


If the frequency of a sound wave is doubled then the velocity of sound will be
A. zero
B. half
c. double
D. unchanged


Electromagnetic waves are:
A. Transverse
B. Longitudinal
C. May be longitudinal or transverse
D. Neither longitudinal nor transverse


If the function \( f(x)=\frac{K \sin x+2 \cos x}{\sin x+\cos x} \)
is strictly increasing for all values of \( x \)
then
\( \mathbf{A} \cdot K<1 \)
в. \( K>1 \)
c. \( K<2 \)
D. \( K>2 \)


A thermodynamic system goes from
states (i) \( P_{1}, V \) to \( 2 P_{1}, V \) (ii) \( P_{1}, V_{1} \) to
\( P_{1}, 2 V_{1} . \) Then work done in the two
cases is respectively
A .0,0
в. \( 0, P_{1} V_{1} \)
c. \( P_{1} V_{1}, 0 \)
D. \( P_{1} V_{1}, P_{1} V_{1} \)


Find the eccentricity, foci and the length
of the latus-rectum of the ellipse \( x^{2}+ \)
\( 4 y^{2}+8 y-2 x+1=0 \)


A parallelopiped has edges described by the \( \hat{i}+2 \hat{j}, 4 \hat{j} \) and \( \hat{j}+3 \hat{k} . \) Then the
volume is:
A . 1
B. 12
\( c \cdot 15 \)
D. 28


The energy of an electron in second Bohr
orbit of hydrogen atom is:
A. \( -5.44 \times 10^{-19} \) ev
B . - 5.44 \( \times 10^{-19} \) cal
c. \( -5.44 \times 10^{-19} \mathrm{kJ} \)
D. - \( -5.44 \times 10^{-19} \) 」


Rate of physisorption increases with:
A. decrease in temperature
B. increase in temperature
c. decrease in pressure
D. decrease in surface area


The fields due to a bar magnet at equal distance on its axial and equatorial lines are
A. Equal to each other
B. The field on the axial line is double that on the equatorial line
c. The field on the equatorial line is double that on the axial line
D. There is no relationship between the two fields


maximum current that will flow in the
circuit


Following elements do not show the properties characteristic of d-block
elements:
A. \( C u, A g, A u \)
в. \( Z n, H g, C d \)
c. \( S c, T i, V \)
D. Fe, Co, Ni


The negative effect of excessive heat on
enzyme function is that
A. It alters the three-dimensional shape of the enzyme
B. It alters the amino acid sequence of the enzyme
C. It alters the composition of the active site of the
enzyme
D. It alters the shape of the substrate molecule
E. It alters the chemical identity of the substrate


Find the \( 1.4 .7+2.5 .8+3.6 .9+ \)
\( \ldots \ldots . n^{t h} \) terms


For the parabola \( \boldsymbol{y}^{2}+\mathbf{8} \boldsymbol{x}-\mathbf{1 2} \boldsymbol{y}+\mathbf{2 0}= \)
\( \mathbf{0} \)
This question has multiple correct options
A. vertex is (2,6)
B. Focus is (0.6)
c. Latusrectum 4
D. Axis \( y=6 \)


An alternating current of \( 1.5 m A \) and
angular frequency 300 rad/sec flows
through a \( 10 K \Omega \) resistor and a \( 0.50 \mu F \) capacitor in series. find the rms voltage across the capacitor and impedance of the circuit?
A \( \cdot 1.2 \times 10^{4} \Omega ; 10 V \)
B . \( 10^{4} \Omega ; 10^{4} V \)
c. \( 1.0 \times 1.0^{4} \Omega ; 50 V \)
D. \( 10 \Omega ; 10 v \)


Eight drops of water, each of radius 2 \( \mathrm{mm} \) are falling through air at a terminal
velocity of \( 8 c m s^{-1} . \) If they coalesce to form a single drop, then the terminal velocity of combined drop will be:
A \( .32 \mathrm{cms}^{-1} \)
B. \( 30 \mathrm{cms}^{-1} \)
c. \( 28 \mathrm{cms}^{-1} \)
D. \( 24 \mathrm{cms}^{-1} \)


A ray of light travelling in water is
incident on its surface open to air. The
angle of incidence \( \theta \), which is less than
the critical angle. Then there will be:
A. only a reflected ray and no refracted ray
B. only a refracted ray and no reflected ray
C . a reflected ray and a refracted ray and the angle between them would be less than \( 180^{\circ}-2 \theta \)
D. a reflected ray and a refracted ray and the angle between them would be greater than \( 180^{\circ}-2 \theta \)


Using the SONAR, sound pulses are emitted at the surface of water. These
pulses after being reflected from the bottom are detected. If the time internal
from the emission to the detection of
sound pulses is \( 8 s \), find the depth of
water:
(net of sound in water \( =\mathbf{1 4 9 8 m} / \boldsymbol{s} \) )
\( \mathbf{A} \cdot 1498 m \)
B. \( 5992 m \)
c. \( 374.5 m \)
D. \( 18182 m \)


What characteristics do you except
from an electron-deficient hydride with respect to its structure and chemical
reactions?


A spaceship is launched into a circular orbit close to earth's surface. The
additional velocity that should be imparted to the spaceship in the orbit to overcome the gravitational pull is:
(Radius of earth \( =6400 k m \) and \( g= \)
\( \mathbf{9 . 8 m} \quad \boldsymbol{s}^{-1} \mathbf{)} \)
\( \begin{array}{lll}\text { A } \cdot & 11.2 k m & s^{-1}\end{array} \)
\( \mathbf{B} \cdot 8 k m \quad s^{-1} \)
\( \begin{array}{ll}\text { c. } 3.2 k m & s^{-1}\end{array} \)
D. \( 1.5 k m \quad s^{-} \)