In figure a certain mass of gas traces
three path 1,2,3 from state \( A \) to the state
B.If work done by the gas along the three
paths are \( W_{1}, W_{2}, W_{3} \) respectively,then:
A \( . W_{1} \)
в. \( W_{1}=W_{2}=W_{3} \)
c. \( W_{1}>W_{2}>W_{3} \)
D. cannot say


Which of following statements is/are
INCORRECT?
I. If \( f(x) \) and \( g(x) \) are one-one, then \( f(x)+g(x) \) is also one-one.
II. If \( f(x) \) and \( g(x) \) are one-one, then \( f(x) \cdot g(x) \) is also one-one.
III. If \( \boldsymbol{f}(\boldsymbol{x}) \) is odd, then it is necessarily
one to one.
A. I and II only
B. II and III only
c. III and I only
D. I, II and III


How many different signals can be given by using any number of flags from six flags of different colors?


Assertion
Purine bases present in DNA are adenine and guanine.
Reason
The base thymine is present in RNA while base uracil is present in DNA.
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


Beneath the surface of the ocean, there
is no air available for burning fuel. Which of the following chemicals is
used with oil as an underwater fuel?
A. Sulphuric acid
B. Hydrogen peroxide
c. Hydrogen
D. Magnesium


f \( x, y \in\{1,2,3,4\} \) then check whether
\( \boldsymbol{f}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}+\boldsymbol{y}=\mathbf{5}\} \) is a function?


The set of angles between \( 0 \& 2 \pi \)
satisfying the equation \( 4 \cos ^{2} \theta \) \( 2 \sqrt{2} \cos \theta-1=0 \) is -
A \( \cdot\left\{\frac{\pi}{12}, \frac{5 \pi}{12}, \frac{19 \pi}{12}, \frac{23 \pi}{12}\right\} \)
В \( \cdot\left\{\frac{\pi}{12}, \frac{7 \pi}{12}, \frac{17 \pi}{12}, \frac{23 \pi}{12}\right\} \)
c. \( \left\{\frac{5 \pi}{12}, \frac{13 \pi}{12}, \frac{19 \pi}{12}\right\} \)
D. \( \left\{\frac{\pi}{12}, \frac{7 \pi}{12}, \frac{19 \pi}{12}, \frac{23 \pi}{12}\right\} \)


\( a-t \) graph for a particle moving in a
straight line is as shown in
figure.Change in velocity of the particle
from \( t=0 \) to \( t=6 s \) is \( :(\text { in } m / s) \)
A . 5
B. 4
\( c .6 \)
D. 3


Write the IUPAC name of
\( \left[\boldsymbol{A} \boldsymbol{g}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2}\right]\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \) coordination
compound.


At \( 27^{0} C \) if temperature of 1 mol of gas
is increased by \( 50^{0} C \) the \( \% \) change in
kinetic energy of system is:
A . 16.67
B. 18.57
c. 85.18
D. 7.66


Waste products are stored as resins and gums in the
A. old xylem
B. Young xylem
c. old phloem
D. Young phloem


The gas which is added to air by photosynthesis is:
A. nitrogen
B. carbon dioxide
c. oxygen
D. argon


Which resonance form in each of the
following sets is the major contributor to the real structure?


Find the length of a chord which is at a
distance of \( 15 \mathrm{cm} \) from the centre of a
circle of radius \( 25 \mathrm{cm} \)


Which of the following classification is
not correct.
1. Pen - Non-living thing
2. Lion- Animal
3. Rose - Mammal
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. nonw of these


Very short answer type.
Name major forms in which \( C O_{2} \) is
transported by blood.


Acid rain occurs due to atmospheric pollution of:
\( A \cdot S O_{2} \)
в. \( N H_{3} \)
\( c \cdot C O_{2} \)
D. \( N_{2} O \)


Calculate the velocity of an electron
having wavelength of \( 0.15 n m . \) Mass of an electron is: \( 9.109 \times 10^{-28} g \)
\( \left(h=6.626 \times 10^{-27} e r g-s\right) \)
A \( \cdot 2.062 \times 10^{-8} \mathrm{cms}^{-1} \)
B. \( 2.062 \times 10^{15} \mathrm{cms}^{-1} \)
c. \( 2.062 \times 10^{10} \mathrm{cms}^{-1} \)
D. \( 4.84 \times 10^{8} \mathrm{cms}^{-1} \)


Gas that strikes in thundering of light
is :
A. \( C O \)
в. \( N O \)
\( c \cdot C O_{2} \)
D. \( H_{2} \)


A particle having a charge \( 10 \mathrm{mC} \) is held fixed on a horizontal surface. A block of
mass 80 g and having charge stays in equilibrium on the surface at a distance of \( 3 \mathrm{cm} \) from the first charge. The coefficient of friction between the
surface and the block is \( \mu=0.5 . \) Find
the range within which the charge on the block may lie
A. \( -4 \times 10^{-12} \mathrm{C} \) to \( 4 \times 10^{-12} \mathrm{C} \)
B. \( -2 C \) to \( 2 \times 10^{2} C \)
\( \mathbf{c} .-4 \times 10^{-19} \mathrm{C} \) to \( 4 \times 10^{-19} \mathrm{C} \)
D. \( -2 \times 10^{-19} \mathrm{C} \) to \( 2 \times 10^{-19} \mathrm{C} \)


A person's eye is at point \( P \) and she is looking into the mirror as shown in the figure. Which of the numbered card(s)
can she see reflected in the mirror?
A. Cards with number 1 and number 2
B. Cards with number 2 and number 3
c. Cards with number 1 , number 2 , number 3
D. Only the card with number 2


The 3 rd and 6 th term of an arithmetic
progression are 13 and -5 respectively. What is the 1 1th term?
A . -29
в. -41
c. -47
D. -35


A cell converts:
A. electrical energy into chemical energy
B. chemical energy into electrical energy
C . magnetic energy into electrical energy
D. electrical energy into mechanical energy


Which of the following are chiral (optically active)?
A. Benzoic acid
B. Pent-2,3-diene \( \left(C H_{3}-C H=C=C H-C H_{3}\right) \)
c. Hex- 2,3,4 -triene \( \left(C H_{3}-C H=C=C=C H-C H_{3}\right) \)
D. 1,1,3,3 - tetrachloroprop- 1,2 -diene \( \left(C C I_{2}=C=C I_{2}\right) \)
E. 2-(2-Carboxy-6-Nitrobenzyl)-3-Nitrobenzoicacid


Which statements about mercury are
correct?
This question has multiple correct options
A. \( \mathrm{Hg} \) is a liquid metal
B. Hg forms two series of salts
C. Hg forms no amalgam with iron and platinum
D. Anhydrous Hg does not show variable valency


Prepare Dipeptide from Alanine.


What is the did
charge \( q \) is projected towards an
infinitely long line of a charge (having linear density of charge \( +\lambda \) ) from a
distance \( t_{0} . \) The direction of initial
velocity \( v_{0} \) makes an angle \( 30^{\circ} \) with the
normal to the line of charge as shown in
figure. The minimum distance of
approach of the charge particle with the line of charge will be (neglect gravity). \( \operatorname{take} \lambda=\frac{\pi \varepsilon_{0} m v_{0}^{2}}{4 q} \)
\( A \cdot \frac{r_{0}}{e} \)
B. \( \frac{r_{0}}{e^{2}} \)
c. \( \frac{r_{0}}{e^{3}} \)
D. \( \frac{r_{0}}{2} \)


In Sedum, the R.Q at night is
A. Unity
B. More than unity
c. Less than unity
D. zero


A wire of length \( L \) has a linear mass
density \( \mu \) and area of cross-section \( \boldsymbol{A} \)
and Young's modulus \( Y \) is suspended vertically from a rigid support. If the
mass \( M \) is hung at the free end of the
wire, then the extension produced in the
wire is:
\( ^{\mathbf{A}} \cdot \frac{\mu g L^{2}+M g L}{2 Y A} \)
\( ^{\mathbf{B}} \cdot \frac{2 \mu g L^{2}+M g L}{2 Y A} \)
c. \( \frac{\mu g L^{2}+2 M g L}{2 Y A} \)
\( \frac{\mu g L^{2}+M g L}{Y A} \)


Coelom is the
A. Internal body cavity between visceral organs and body wall
B. Internal body cavity between visceral organs and cellular wall
C. External body cavity between visceral organs and cellular wall
D. Internal body cavity between lateral organs and cellular wall


Two moles of \( N_{2} \) and two moles of \( H_{2} \)
are taken in a closed vessel of \( 5 L \)
capacity and suitable conditions are provided. When the equilibrium is reached, it is found that 0.6 mole of \( N_{2} \)
is used up. The equilibrium
concentration of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is
A . 0.4
B. 0.08
\( c .0 .8 \)
D. 0.24


Find the mean of the following frequency distribution:
\( \begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 30- \\ \text { interval: } & 10 & 20 & 30 & 40\end{array} \) 10 Frequency: \( \quad 9 \quad 12 \quad 15 \)


Compared to blood our lymph has
A. More RBCs and less WBCs
B. No plasma
c. Plasma without protiens
D. More WBCs and no RBCs


Which of the following processes takes place in the presence of ATP?
I. Diffusion
Il. Active transport
III. Facilitated diffusion
A. I only
B. II only
c. ॥ only
D. I and III
E. Il and III


A wheel with 10 metallic spokes each
\( 0.5 m \) long is rotated with a speed of
120rev/min in a plane normal to the horizontal component of earth's
magnetic field \( \boldsymbol{H}_{\boldsymbol{E}} \) at a place.lf \( \boldsymbol{H}_{\boldsymbol{E}}= \)
\( 0.4 G \) at the place, what is the induced
emf between the axle and the rim of the
wheel? Note that \( 1 G=10^{-4} \)


Which type of polymer is the Buna-Srubber?
A. Homo polymer
B. Condensation polymer
c. copolymer
D. None of the above


In a primary rainbow what is the order
of colours observed from earth?
A. Violet innermost, Red outermost
B. Red innermost, Violet outermost
c. Random
D. White and dark alternatively


Solve the equation \( \sin \theta+\sin 3 \theta+\sin 5 \theta=0 \)


Express in degree form \( \left(\frac{5 \pi}{12}\right)^{c} \)
A \( .60^{\circ} \)
B . 45
\( c \cdot 180 \)
D. \( 90^{\circ} \)


Which one of the following is a measure of dispersion?
A. Mean
B. Median
c. mode
D. standard deviation


Five cells of emf \( 1.5 \mathrm{V} \) and internal
resistance 0.2 ohm are connected in
series. The maximum current that can
be delivered is
A . 7.5A
B. 1.5A
\( c \cdot 4 A \)
D. 2A


In which one of the following pairs, is the specific characteristic of a soil not
correctly matched?
A. Chernozems - Richest soil in the world.
B. Black soil-Rich in calcium carbonate and iron
c. Laterite - contains aluminium compound.
D. Terra rossa - Most suitable for roses


Find the potential energy to a system of four particles placed at the vertices of a square of side \( l \). Also obtain the
potential at the centre of the square


A small electric dipole is placed at origin with its axis being directed along the positive x-axis. The direction of
electric field due to the dipole at a point \( (1 \mathrm{m}, \sqrt{2} \mathrm{m}, 0) \) is along the:
A . z-axis
B. y-axis
c. x-axis
D. line \( y=x \)


\( \begin{array}{ll}\text { Table } 1 & \text { Table } 2 \\ \begin{array}{l}\text { (a) If current is } \\ \text { increased }\end{array} & \begin{array}{l}\text { (p) Induced current in } \\ \text { loop is clockwise }\end{array} \\ \begin{array}{l}\text { (b) If current is } \\ \text { decreased }\end{array} & \begin{array}{l}\text { (q) Induced current in } \\ \text { loop is anticlockwise }\end{array} \\ \begin{array}{l}\text { (c) If loop is moved } \\ \text { away from the wire }\end{array} & \begin{array}{l}\text { (r) Wire will attract the } \\ \text { loop }\end{array} \\ \begin{array}{l}\text { (d) If loop is moved } \\ \text { towards the wire }\end{array} & \begin{array}{l}\text { (s) wire will repel the } \\ \text { loop }\end{array}\end{array} \)
A square loop is placed near a long straight current carrying wire as shown, match the following table
1
\( A \cdot a-q, s ; b-p, r ; c-q, s ; d-p, r \)
B. \( a-p, r ; b-q, s ; c-p, r ; d-q, s \)
c. \( a-q, s ; b-p, r ; c-q, r ; d-p, q \)
D. \( a-q, s ; b-p, r ; c-p, r ; d-q, s \)


Number of acidic hydrogen atoms in 1 Butyne is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


An insect crawls up a hemispherical surface. The coefficient of friction
between the insect and the surface is
1/3. If the line joining the centre of the hemispherical surface to the insect
makes an angle \( \alpha \) with the vertical, the
maximum possible value of \( \alpha \) is given
by
A. \( \cot \alpha=3 \)
B. \( \tan \alpha=3 \)
c. \( \sec \alpha=3 \)
D. \( \operatorname{cosc} \alpha=3 \)


If \( 1 \frac{2}{3}+1 \frac{2}{8}=\frac{35}{a} \) then, find the value of
\( a \)


The IUPAC name of
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}\right)_{\boldsymbol{4}} \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \boldsymbol{C l} \) is
A. Tetraamminechloridonitrito-N-cobalt(III) chloride
B. Tetraamminechloridonitrocobalt(II) chloride
C. Tetraamminechloridonitrocobalt(I) chloride
D. Tetraamminechloridodinitrocobalt(III) chloride


There is \( 25 \% \) chance that it rains on any
particular day. What is the probability that there is at least one rainy day within a period of 7 days?
\( ^{A} \cdot_{1-}\left(\frac{1}{4}\right)^{7} \)
B. \( \left(\frac{1}{4}\right)^{7} \)
\( ^{c}\left(\frac{3}{4}\right)^{7} \)
D. \( _{1-}\left(\frac{3}{4}\right)^{7} \)


Two resistors, \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2}, \) are identical
but the potential difference across \( \boldsymbol{R}_{1} \)
is half the potential difference across
\( R_{2} . \) What is the ratio of the current in
\( R_{1} \) to the current in \( R_{2} ? \)
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
c.
D. 2
E . 4


Very short answer type.
Name the protein found in A-band and I-
band of a myofibril.


Which of the following chemical is used in making metal polishes:
A . oxalic acid
B. methanoic acid
c. both A and B
D. none of these


A pair of fair coins is tossed yielding the equiprobable space \( \mathrm{S}=\{\mathrm{HH}, \mathrm{HT}, \mathrm{TH}, \mathrm{TT}\} \)
Consider the events:
\( A=\{\text { head on first } \operatorname{coin}\}=\{\mathrm{HH}, \mathrm{HT}\} \)
\( \mathrm{B}=\{\text { head on second coin }\}=\{\mathrm{HH}, \mathrm{TH}\} \)
\( \mathrm{C}=\{\text { head on exactly one coin }\}=\{\mathrm{HT}, \mathrm{TH}\} \)
Then check whether \( A, B, C \) are
independent or not.


The centre of the earth is a core, mainly containing:
A. silicon that forms clay
B. copper that gives radiation
c. iron that creates a magnetic field
D. magnesium that colours volcanic flames


\( \int \frac{\boldsymbol{a}}{\boldsymbol{b}+\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x} \)
A \( \cdot \frac{a}{b}\left[x-\log \left(b+c e^{x}\right)\right] \)
B \( \cdot \frac{a}{b}\left[x+\log \left(b+c e^{x}\right)\right] \)
c. \( \frac{a}{b}\left[x-\log \left(c e^{x}\right)\right] \)
D. \( \frac{a}{c}\left[x+\log \left(b+c e^{x}\right)\right] \)


If \( \int \frac{x^{4}+1}{x^{6}+1} d x=\tan ^{-1}(f(x)) \)
\( \frac{2}{3} \tan ^{-1}(g(x))+C, \) then
A. Both \( f(x) \& g(x) \) are odd functions
B. \( g(x) \) is monotonic function
c. none of these
D. None


Which one of the following processes does not involve coagulation?
A. Peptization
B. Formation of delta
c. Purification of drinking water using alum
D. tanning of leather using tannin


The chordates without jaw are placed in
A. Agnathostomes
B. Gnathosomes
c. vertebrates
D. Euchordates


Evaluate:-
\( \lim _{t \rightarrow-3} \frac{6+4 t}{t^{2}+1} \)


Free \( ^{238} \boldsymbol{U} \) nuclei kept in a train emit
alpha particles.When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particles
and the recoiling nucleus becomes \( x, \) in
\( t \) time after the decay. If a decay takes
places, when the train is moving at a
uniform speed \( v, \) the distance between the alpha particle and the recoiling nucleus at a time \( t \) after the decay, as
measured by the passenger will be
A \( . x+v t \)
B. \( x-v t \)
\( c \)
D. depends on the directions of the train


What is the name of the group \( \boldsymbol{C H}_{3}- \)
\( \boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}_{2}-? \)
A. viny
B. Ally
c. crotyl
D. Isopropeny!


A gas of monoatomic hydrogen is bombarded with a stream of electrons
that have been accelerated from rest
through a potential difference of
\( 12.75 V . \) In the emission spectrum one
cannot observe any line of
A. Lyman series
B. Balmer series
c. Paschen series
D. Pfund series


The energy per unit area associated
with a progressive sound wave will be doubled if:
A. The amplitude of the wave is doubled
B. The amplitude of the wave is increased by \( 50 \% \)
C. The amplitude of the wave is increased by \( 41 \% \)
D. The frequency of the wave is increased by 50\%


The following data gives the information on the observed lifetimes (in hours) of
225 electrical components:
Lifetimes
\( 0- \)
\( \begin{array}{lll}\text { 20- } & \text { 40- } & \text { 60- }\end{array} \)
\[
\text { in } \quad 20 \quad 40 \quad 60
\]
hours)
Frequency 10
\[
35
\]
52
Determine the modal lifetimes of the
components.
A. 69.268 hours
B. 65.625 hours
c. 62.126 hours
D. 58.267 hours


Cadmium amalgam is prepared by
electrolysis of a solution of \( C d C l_{2} \) using a mercury cathode. Find how long a current of 5 ampere should be passed in order to prepare \( 12 \% C d-H g \)
amalgam on a cathode of \( 2 g \) mercury.
At. mass of \( C d=112.40 \)


\( A l_{2} O_{3} \) can be converted to anhydrous
\( A l C l_{3} \) by heating:
A . Hydrated \( A l_{2} O_{3} \) with \( C l_{2} \) gas
в. \( A l_{2} O_{3} \) with aqueous \( H C l \)
c. \( A l_{2} O_{3} \) with \( N a C l \) in solid state
D. A mixture of \( A l_{2} O_{3} \) and carbon in dry \( C l_{2} \) gas


Calculate the number of neutrons in
\( 18 m L \) of water. (Density of water \( =1 \) ).


Which is wrongly matched?
A. Rhizobium - Free living nitrogen fixer
B. Humus - Abiotic component
C. Phosphorous cycle - Sedimentary
D. Cedrus deodara - Coniferous forest
E. Shorea robusta - Tropical deciduous forest


Choose the correct statement for proton.
\( \mathbf{A} \cdot \) It is a nucleus of deuterium
B. It is an ionized hydrogen atom
C. It is an ionized hydrogen molecule
D. It is an \( \alpha \) - particle


Which of the following are macromolecular colloids?
This question has multiple correct options
A. starch
B. Soap
c. Detergent
D. Cellulose


A metal wire is stretched by a load. The force-extension graph is shown. What is represented by the area under
the whole graph?
A. The change in gravitational potential energy of the wirt
B. The energy that would be released from the wire if the final load was removed
c. The energy transferred into heat energy in the wire
D. The work done in stretching the wire


State True or False.
The order of energy of orbitals is \( s< \)
\( \boldsymbol{p}<\boldsymbol{d}<\boldsymbol{f} \)
A . True
B. False


Rationalise the denominator of
\( \frac{\mathbf{5}}{\sqrt{\mathbf{3}}-\sqrt{\mathbf{5}}} \)


lonic reactions are instantaneous.
If true enter 1 , if false enter 0 .


prove that \( C_{0}^{2 n} C_{n}-^{2 n-2} C_{n}+ \)
\( ^{2 n-4} C_{n}=2^{n} \)where\( C_{r}=^{n} C_{r} \)


\( 0.216 g \) of an organic compound gives
\( 28.8 c m^{3} \) of moist nitrogen measured at 288K and 732.7mm pressure.
The percentage of nitrogen in the substance is approximately:
tension at \( 288 \mathrm{K}=12.7 \mathrm{mm} \)
A . 15
B. 20
c. 25
D. 30


A black, metal foll is warmed by radiation from a small sphere at temperature 'T' and at a distance 'd'. It is found that the power received by the foils is P. If both the temperature and
distance are doubled, the power received by the foil will be
A . 16 P
B. 4 P
\( c \cdot 2 P \)
D.


How many electrons are involved for the formation of 1 mole of glucose and \( 60_{2} \)
molecules?
\( A \cdot 6 \)
B. 12
\( c \cdot 18 \)
D. 24


Find the coordinates of the point which
divides the line segment joining the points (-2,3,5) and (1,-4,6) in the ratio
(i) 2: 3 internally
(ii) 2: 3 externally


Two conducting rings of radii r and 2 r move in opposite directions with
velocities \( 2 v \) and \( v \) respectively on a
conducting surface \( S \). There is a
uniform magnetic field of magnitude \( B \) perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is
A . zero
в. \( 2 r v B \)
\( \mathbf{c} \cdot 4 r v B \)
D. \( 8 r v B \)


Explain some cases of Normal reaction
on a block of mass \( \mathrm{m} \) placed on
acceleration lift


In the anaerobic process of glycolysis, energy is released from ATP is used to
A. phosphorylate glucose
B. Phosphorylate ADP
c. Move glucose into the Calvin cycle.
D. Carry ATP to the electron transport chain


The circular motion of a particle with
constant speed is
A. periodic and simple harmonic
B. simple harmonic but not periodic.
c. neither periodic nor simple harmonic.
D. periodic but not simple harmonic.


Elements with eight electrons in their
outermost energy shell are called:
A. noble gases
B. halogens
c. alkalis
D. oxides


Among the following what should not be done while or before using a clinical thermometer?
A. Ensure that before use the mercury level is below \( 35^{\circ} \mathrm{C} \)
B. Wash the thermometer with hot water.
c. Handle the thermometer with care, as you handle any glass articles.
D. Don't hold the thermometer by the bulb while reading it


Write the general term in the expansion of \( \left(x^{2}-y^{2}\right)^{6} \)


Natural coke is also called as:
A. carbonite coke
B. bakelite
C . petroleum fuel
D. none of above


Which atom would require the shortest
wavelength photon to remove a single
electron?
A. \( M g \)
B. \( S \) i
\( c . P \)
D.
E . \( C l \)


Oxygen reacts with an element to form:
A . a salt
B. oxidation
c. an oxalate
D. an oxide


The area of the parallelogram with
diagonals \( 5 c m, 6 c m \) respectivelu
\( \mathbf{A} \cdot 18 \mathrm{cm}^{2} \)
B. \( 27 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 15 c m^{2} \)
D. None of these


ff \( f(x) \) be a polynomial function
satisfying \( f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right) \) and
\( \boldsymbol{f}(\mathbf{4})=\mathbf{6 5} . \) Then, find \( \boldsymbol{f}(\boldsymbol{6}) \)


Dimensional methods provide three major advantages in verification, derivation and changing the system of units. Any empirical formula that is derived based on this method has to be
verified and proportionality constants found by experimental means. The presence or absence of certain factors -
non dimensional constants or variables
cannot be identified by this method. So every dimensionally correct relation cannot be taken as perfectly correct.
The time period of oscillation of a drop
depends on surface tenson \( \sigma, \) density of
the liquid \( \rho, \) and radius \( r . \) The relation is
B. \( \sqrt{\frac{r^{2}}{\rho \sigma}} \)
c. \( \sqrt{\frac{r^{3} \rho}{\sigma}} \)
D. \( \sqrt{\frac{\rho \sigma}{r^{3}}} \)


Integrate the function \( \sqrt{x^{2}+4 x+6} \)


If \( S_{n} \) denotes the sum of \( n \) terms of \( g . p \)
whose common ratio is \( r, \) then
\( (r-1) \frac{d S_{n}}{d r} \) is equal to
A \( \cdot(n-1) S_{n}+n S_{n-1} \)
B . \( (n-1) S_{n}-n S_{n-1} \)
\( \mathbf{c} \cdot(n-1) S_{n} \)
D. None of these


The energy barrier to rotation about the
\( C-C \) bond in ethane, is about 12.55
KJ/mol at room temperature \( (\mathbf{2 9 8 k}) \) assuming the contribution of entropy negligible. The ratio of staggered to eclipsed conformation is about:
A . 150
в. 159
c. 165
D. 175


When a rod is heated from \( 25^{\circ} \mathrm{C} \) to
\( \mathbf{7 5}^{\circ} \boldsymbol{C}, \) it expands by \( \mathbf{1} \boldsymbol{m} \boldsymbol{m} . \) When a rod
of same material but with 4 times the
length is heated from \( 25^{\circ} C \) to \( 50^{\circ} C \) The increase in length is :
\( \mathbf{A} \cdot 1 m m \)
в. \( 1.5 \mathrm{mm} \)
\( \mathrm{c} .1 .6 \mathrm{mm} \)
D. \( 2 m m \)


\( \boldsymbol{H}-\boldsymbol{F} \) form stronger bond than
\( \boldsymbol{H}_{2} \boldsymbol{O}[\because \boldsymbol{E} \boldsymbol{N} \boldsymbol{o} \boldsymbol{f} \boldsymbol{F}>\boldsymbol{O} \& \boldsymbol{H} \text { bond } \boldsymbol{\alpha} \)
\( \boldsymbol{E} \boldsymbol{N}] \) still heat of vapourisation of \( \boldsymbol{H} \boldsymbol{F} \)
is lower than that of pure water. Why?


The value of \( \int e^{x} \frac{1+n x^{n-1}-x^{2 n}}{\left(1-x^{n}\right) \sqrt{1-x^{2 n}}} d x \)
is equal to
A \( \cdot e^{x}(\sqrt{1-x^{2}})+c \)
B. \( e^{x} \frac{\sqrt{1+x^{2 n}}}{1+x^{2 n}}+c \)
C \( \frac{e^{x} \sqrt{1-x^{n}}}{1-x^{2 n}}+c \)
D. \( \frac{e^{x} \sqrt{1-x^{2 n}}}{1-x^{n}}+c \)


Nitro chloroform is prepared by the
action of \( \boldsymbol{C H C l}_{3} \) and
A. hot aq. \( K N O_{3} \)
B. hot aq. solution of \( N a N O_{2} \)
c. hot conc. \( H N O_{3} \)
D. hot dil. \( H C l+a q . N a N O_{2} \) solution


Soaps are and \( _{-1}- \) salts
of certain acids.
A. potassium and calcium
B. sodium and calcium
c. sodium and potassium
D. calcium and magnesium


The spectrum, in which the colours are separated using a narrow source of light, is called:
A. pure spectrum
B. rainbow
c. impure spectrum
D. none of these


Which of the following statement(s) is/are true?
"Internal energy of an ideal gas
A. Decreases in an isobaric process
B. Remains constant in an isothermal process
c. Increases in an isobaric process
D. Decreases in an isobaric expansion


Which of the following statement is
incorrect according to Thomson's model
of an atom?
A. The electrons, in a sphere of positive charge, were like currants (dry fruits) in a spherical Christmas pudding.
B. The positive charge in the atom is spread all over like the red edible part of the watermelon.
C. The electrons are studded in the positively charged sphere, like the seeds in the watermelon.
D. The protons are studded in the positively charged sphere, like the seeds in the watermelon.


The radius of the circular base of an ear
of corn is \( 6.6 \mathrm{cm} \) and its length is
\( 11.2 \mathrm{cm} . \) If on an average 1 sqcm area
contains 2 corn kernels, find the total
number of kernels on an ear of corn.


An electron having energy \( 10 e V \) is circulating in a path of radius \( 0.1 m \)
having a magnetic field of \( 10^{-4} \) T. The
speed of the electron will be :
A \( .2 .0 \times\left(10^{6}\right) m s^{-1} \)
B . \( 4.8 \times\left(10^{6}\right) m s^{-1} \)
c. \( 2.0 \times\left(10^{12}\right) m s^{-1} \)
D. \( 4.8 \times\left(10^{12}\right) m s^{-1} \)


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


Larva of Jelly Fish (Aurelia) is
A. Planula
B. Medusa
c. Polyp
D. Blastula


Consider the following statements A and \( \mathrm{B} \) and identify the correct answer. Statement(A):A Zener diode is always
connected in reverse bias to use it as
voltage Statement(B):The potential barrier of a p-njunction lies between 0.1 to \( 0.3 V \)
approximately.
A. A and B are correct
B. A and B are wrong
c. A is correct but B is wrong.
D. A is wrong but B is correct.


Epiphysis cerebri and hypophysis are found attached with
A. Forebrain
B. Midbrain
c. Hindbrain
D. None of the above


Consider a disc rolling without slipping
on a horizontal surface at a linear speed
Vas shown in figure:
This question has multiple correct options
A. the speed of the particle A is \( 2 v \)
B. the speed of B, C and D are all equal to v.
C. the speed of \( C \) is zero
D. the speed of 0 is less than the speed of \( B \)


The amount of DNA per cell remains the same during
A. \( s, \) G2 and metaphase
B. G2, M phase
c. Anaphase, Telophase, Gı phase
\( D \cdot(A) \) and \( (c) \)


State True or False:
n-p-n transistors exhibit higher transconductance and speed than \( \mathrm{p}-\mathrm{n}-\mathrm{p} \)
transistors.
A. True
B. False


A solid cylinder at rest at the top of an
inclined plane of height \( 2.7 m \) rolls down without slipping. If the same cylinder has to slide down a frictionless inclined
plane and acquire the same velocity as that acquired by the center of mass of
the rolling cylinder at the bottom of the
inclined plane, the height of the inclined plane in meters should be: \( (\boldsymbol{g}= \)
\( \left(0 m / s^{2}\right) \)
A \( .2 .2 m \)
в. \( 1.2 m \)
c. \( 1.6 m \)
D. \( 1.8 m \)


Which of the following is true:
A. Acetylene is more reactive than ethylene to an electrophilic attack
B. Acetylene is less reactive than ethylene to an electrophilic attack
C. Acetylene may show more reactivity or less reactivity towards electrophilic reagent.
D. Acetylene and ethylene show indentical reactivities towards an electrophilic attack


The poisonous gas emitted by motor vehicles is
A. \( C O_{2} \)
в. \( C O \)
\( c \cdot S O_{2} \)
D. \( N O_{2} \)


A bullet of mass \( m=50 \) gm strikes a bag of mass \( \mathrm{M}=5 \mathrm{kg} \) hanging from a fixed point, with a horizontal velocity \( \bar{V}_{p} . \) If bullet sticks to the sand bag then just after collision the ratio of final
\( \& \) initial kinetic energy of the bullet is approximately:
A \( \cdot 10^{-2} \)
- \( ^{-2} \)
B. \( 10^{-3} \)
\( \mathbf{c} \cdot 10^{-6} \)
D. \( 10^{-4} \)


A sonar device on a submarine sends
out a signal and receives an echo 5 s
later. Calculate the speed of sound in water if the distance of the object from the submarine is \( 3625 \mathrm{m} \)


Assertion
In an atom, the velocity of electron in
the higher orbits keeps on decreasing.
Reason
Velocity of electrons is inversely proportional to the radius of the orbit.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion,
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The volume occupied by half a mole of a gas at STP is:
A. 5.6
B. \( 11.2 \mathrm{L} \)
c. 22.4
D. 44.8 L


In a hydraulic lift, the small piston has
an area of \( 2 \mathrm{cm}^{2} \) and the large piston
has an area of \( 80 \mathrm{cm}^{2} \). What is the
mechanical advantage of the hydraulic
lift?
A . 40
B. 42
c. 10
\( D .4 \)


Two perpendicular lines are intersecting at \( (4,3) . \) One meeting coordinate axis at \( (4,0), \) find the distance between origin and the point of intersection of other line with the
cordinate axes.
A . 4
B. 7
\( c .3 \)
D. 5


Which of the following is steam volatile?
A. O-nitrophenol
B. P-nitrophenol
c. Both of them
D. Neither of them


What is the action of the following reagent on ethanoic acid?
\( \boldsymbol{L} \boldsymbol{i} \boldsymbol{A l} \boldsymbol{H}_{4} / \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)


Let \( f \) be a decreasing function in \( (a, b] \)
then which of the following must be true?
A. \( f \) is continuous at \( b \)
B \( \cdot f^{\prime}(b)<0 \)
c. \( \lim _{x \rightarrow b} f(x) \leq f(b) \)
D. \( \lim _{x \rightarrow b} f(x) \geq f(b) \)


A glass rod rubbed with silk is brought
near the fur rubbed with an ebonite rod.
What will be your observation between
them?
A . Attraction
B. Repulsion
c. No change
D. cant say


Starch molecules are polymer with
repeating glucose units. Select the
correct statement
A. Glucose units are joined through \( \beta \) -glycosidic linkage
B. The branches of amylopectin are linked to the chain with \( \alpha \) -1,4'-glycosidic linkages
c. The linear linkages of amylopectin are formed by \( \alpha \)
-1,4'-glycosidic bond
D. Amylose has an unbranched skeleton of glucose molecules with \( \alpha \) -1,6-glycosidic linkages


Assertion
First law of thermodynamics can be applied for ideal gases only.
Reason
First law is simply, law of conservation of energy.
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


Which is an important raw material in the chemical industry to produce polyethyelene?
A. acetylene
B. ethyne
c. both a and
D. none of the above


Explain the following:
Boron trichloride has triangular planar geometry whereas aluminium
trichloride has tetrahedral
dimeric structure.
\( A \)


Q Type your question-
\( (\boldsymbol{C}) \stackrel{\bullet}{\longrightarrow}(\boldsymbol{A})+(\boldsymbol{D}) \)
conc. solution of \( (C) \frac{\operatorname{conc.H}_{2} S O_{4}}{(E)} \)
(weak acid)
\( (D)+ \) cobalt oxide \( \stackrel{\Delta}{\longrightarrow}(F) \) (coloured
bead)
\( (\boldsymbol{E})+\boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{O} \boldsymbol{H} \stackrel{\boldsymbol{\Delta}}{\longrightarrow} \) green edged flame
\( (G) \)
\( A \) to \( G \) based on the following reactions
are:
\( \mathbf{A}: \boldsymbol{N} \boldsymbol{a} \boldsymbol{B} \boldsymbol{O}_{2} \)
\( \mathbf{B}: \boldsymbol{C O}_{\mathbf{2}} \)
\( \mathbf{C}: \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{B}_{4} \boldsymbol{O}_{7} \)
\( \mathrm{D}: B_{2} O_{3} \)
E: \( \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3} \)
\( \mathrm{F}: \boldsymbol{C o}\left(\boldsymbol{B O}_{2}\right)_{2} \)
\( \mathrm{G}:\left(C_{2} H_{5} O\right)_{3} B \)
If the statement is true enter 1 , else
enter 0


Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{2}+\mathbf{2}}{[\boldsymbol{x}]}, \mathbf{1} \leq \boldsymbol{x} \leq \mathbf{3}, \) where [
represents greatest integer function,
then
A \( . f(x) \) is increasing in [1,3]
B. Least value of \( f(x) \) is 3
c. Greatest value of \( f(x) \) is \( \frac{11}{2} \)
D. \( f(x) \) has no greatest value


The term -dx/dt in the rate expression
refers to:
A. The concentration of the reactants
B. Increase in the concentration of the reactants
c. The instantaneous rate of the reaction
D. The average rate of the reaction


Which of the following is not a
statement?
A. Every set is a finite set.
B. Every square is a rectangle.
c. The sun is a star.
D. Shut the window.


A particle of mass \( 0.5 k g \) travels in a straight line with velocity \( \boldsymbol{v}=\boldsymbol{a} \boldsymbol{x}^{3 / 2} \)
where \( a=5 m^{-1 / 2} s^{-1} . \) What is the work
done by the net force during its displacement from \( \boldsymbol{x}=\mathbf{0} \) to \( \boldsymbol{x}=\mathbf{2 m} ? \)


Cathodic standard reduction potential
minus anodic standard reduction
potential is equal to:
A. Faraday
B. Coulomb
c. cell potential
D. Ampere


An object is kept at \( x=0, \) force on the
object is F(constant) from \( t=0 . \) Friction
coefficient varies as \( \mu=c x \). Find the
ratio of the maximum value of friction
force and magnitude of static friction just after the block stopped.


Percentage composition of fibroin and
sericin in silk is
A .50: 40
B. 80: 20
c. 30: 70
D. 40: 60


The system of linear equations:
\( \boldsymbol{\lambda} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y}+\boldsymbol{2} \boldsymbol{z}=\mathbf{5} \)
\( 2 \lambda x+3 y+5 z= \)
\( 4 x+\lambda y+6 z=10 \) has
A. no solution when \( \lambda=2 \)
B. a unique solution when \( \lambda=-8 \)
c. infinitely many solutions when \( \lambda=2 \)
D. no solution when \( \lambda=8 \)


If the radius of a circle is increased by
\( 10 \%, \) then the corresponding area of the new circle will be \( \ldots(\pi=3.14) \)
A. \( 121 \pi r^{2} \)
2
В. \( 12.1 \pi r^{2} \)
c. \( 1.21 \pi^{2} \)
D. None of the given three


Give the electron configuration of the given metal (atom/ions)
\( M n O_{2} \)
A \( \cdot[A r] 3 s^{2} 3 p^{1} \)
B \( \cdot[A r] 3 d^{1} 4 s^{2} \)
c. \( [A r] 3 d^{3} \)
D. None of these


Assertion
Cathode rays are deflected towards positive plate in an electric field.
Reason
These consist of negatively charged
particles.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The structure given above can be
written as:
\( A \)
в.
\( c \)
D.
\[
H_{3} C-C H_{2}-C H=C H-C H_{3}
\]


Which of the following describe a
frictional force?

This question has multiple correct options
A. Frictional force always opposes the state of motion of an object.
B. Frictional force is parallel to the surface in contact.
C. Frictional force always produces heat
D. Frictional force can be increased or reduced


Carbon footprint is the amount of
carbon dioxide released into the
atmosphere because of human activities. By which of the following ways we can reduce the carbon footprint?
A. By keeping an electrical device on standby mode when not in use
B. Print on single side of paper instead of writing
c. Use of CFLs in daytime and bulbs in night to study
D. Use of public transport or carpool wherever and whenever we can


What are the substances which mimic
the chemical messengers?
A. Antibiotics
B. Antagonists
c. Agonists
D. Receptors


Ammonium nitrate crystals on heating at \( 250-260^{0} \mathrm{C} \) gives :
A \( . \mathrm{N}_{2} \)
в. \( \mathrm{NO}_{2} \)
\( c \cdot \mathrm{N}_{2} \mathrm{O} \)
D. NO


Heavy water is used in nuclear reactors
as:
A. source of \( \alpha- \) particles
B. slowing down the speed of high energy neutrons
C. transporting heat of the reactor
D. heating purpose


\( \left|\begin{array}{ccc}\cos C & \tan A & 0 \\ \sin B & 0 & -\tan A \\ 0 & \sin B & \cos C\end{array}\right| \) has the value
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \sin A \sin B \cos B \)
D. none of these


A light ray is incident a glass sphere at
an angle of incidence of \( 45^{\circ} \) as shown in figure. Find the total deviation suffered by ray of two successive reflection.
A \( \cdot 45^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 120^{\circ} \)


Allyl chloride can be produced by many different methods. The most common
method is chlorination of propene which proceeds via a free-radical substitution mechanism.
The initiation step in this reaction is
the formation of chlorine radicals \( \left(C l^{\circ}\right) \)
from \( C l_{2} \) molecules.

State the conditions required to initiate this reaction.


A vector of magnitude 100 units is
inclined at \( 30^{0} \) to another vector of
magnitude 80 units. Then vector
product is:
A. 4000
B. \( 4000 \sqrt{3} \)
c. 8000
D. \( 8000 \sqrt{3} \)


Equation of a stationary wave is given by
A. \( y=A \sin (k x-\omega t) \)
B. \( \mathrm{y}=2 \mathrm{A} \sin k x . \cos \omega t) \)
c. \( \mathrm{y}=\mathrm{A} \cos 2 \pi(\mathrm{kx}-\mathrm{t} / \mathrm{T}) \)
D. \( y=A \cos (2 \pi t / I) \)


Cholrine gas is produced from HCl by the addition of:
A. \( K_{2} S O_{4} \)
в. КСl
c. \( K N O_{3} \)
D. \( K M n O_{4} \)


How far into the classroom did the
student move?
Distance \( / m \) \( \mathbf{1} \) \( \mathbf{0} \) \( \mathbf{3} \)
0 Time \( / s \) \( 1 \quad 2 \quad 3 \)


Mesitylene was synthesized by passing a mixture of acetylene and propyne \( (1: 3) \) through red hot tube.
A. True
B. False


Which reaction shows that amine is
base?


Which of the following parameters does not characterize the thermodynamic
state of matter?
A. temperature
B. pressure
c. work
D. volume


Select the incorrect statement for
developing of an exposed camera film involving the reaction.
A. Hydroquinol acts as reductant.
B. \( A g^{+} \) acts as oxidant.
C. Hydroquinol and AgBr undergoes redox change
D. It involves intramolecular change.


STRUCTURED/APPLICATION/SKILL TYPE
The volume of air in the lungs and the rate at which it is exchanged
during inspiration and expiration was measured.

The following diagram shows a group of lung volumes and capacities. Study the diagram carefully and explain briefly the following:
Vital capacity


Explain electroplating with suitable example.


A vessel of volume of \( 0.2 m^{3} \) contains
hydrogen gas at temperature \( 300 K \) and
pressure 1 bar. Find the heat required
to raise the temperature to \( 400 K . \) The
molar heat capacity of hydrogen at constant volume is 5 cal \( / \) mol \( K \)
\( \mathbf{A} \cdot 4 k c a l \)
B. 5 kcall
c. \( 6 k c a l \)
D. \( 2 k c a l \)


The best source of vitamin A is:
A. oranges
B. beans
c. carrots
D. wheat


toppr \( x \)
Q Type your question
question.
The auxin was dissolved in a gelatin
block; gelatin does not affect the
biological activity of the auxin. Several
plant seedlings were prepared in a
gelatin block; gelatin does not affect the biological, activity of the auxin. Several
plant seedlings were prepared as described above and growth was
measured every 5 days.
Based on the results of the experiment,
one can conclude that the tip of the plant contains
What proves that auxin is necessary for
plant growth?
rem applied
A. Plant 1 grew faster than plants 2 or 3
B. Plant 4 grew faster than plants 2 or 3
C. Plant 5 grew faster than plant 1
D. Plant 3 grew faster than plant 2
E. Plant 4 grew faster than plant 5


Common bread mold is
A. Rhizopus oryzae
B. Rhizobium species
C . Rhizopus nedosus
D. Rhizopus stolonifer


Draw V-T curve


Assertion
For a reaction, \( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}) \longrightarrow \boldsymbol{N}_{\mathbf{2}}(\boldsymbol{g})+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \)
\( \triangle \boldsymbol{H}>\triangle \boldsymbol{E} \)
Reason
Enthalpy change is always greater than
internal energy change.
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


What is a regular polygon?


If the length of the largest chord of a circle is \( 17 \mathrm{cm}, \) find the radius of a circle.
\( A \cdot 34 \mathrm{cm} \)
B. \( 8.5 \mathrm{cm} \)
c. \( \sqrt{17} \mathrm{cm} \)
D. \( \sqrt{34} \mathrm{cm} \)


What is the Si unit of magnetic flux, is it vector or scalar quantity?


Find the derivative of \( f(x)=3 x \) at \( x= \)
2


How many cuboids of size \( 4 c m \times \)
\( 3 c m \times 1 c m 4 c m \times 3 c m \times 2 c m \) can be
inscribed on cube of size \( 12 \mathrm{cm} \times \)
\( 12 c m \times 12 c m ? \)


Examine the figures \( A, B, C \) and \( D . \) In
which one of the four options all the
items \( A, B, C \) and \( D \) are correct?
A. \( A \) - Selaginella, \( B \) - Equisetum, \( C \) - Salvinia, D - Ginkgo
B. A - Equisetum, B - Ginkgo, C - Selaginella, D Lycopodium
C. A - Chara, B - Marchantia, C - Fucus, D - Pinus
D. A - Funaria,B - Adiantum,
C - Salvinia
D - Riccia


\( H_{2} O_{2} \) is a:
A. monobasic acid
B. dibasic acid
C. neutral compound
D. weak alkali


Assertion
Enzymes becomes inactive below
minimum temperature.
Reason
The inactivity of the enzyme is due to
denaturation.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The equation of the latus rectum of the ellipse \( 9 x^{2}+4 y^{2}-18 x-8 y-23=0 \)
are
A \( . y=\pm \sqrt{5} \)
B \( \cdot y=-\sqrt{5} \)
c. \( y=1 \pm \sqrt{5} \)
D. \( y=-1 \pm \sqrt{5} \)


How many valence electrons are present in the Lewis structure of nitrogen?
A. 7
B. 5
\( c \cdot 3 \)
\( D \)


How does dihydrogen reacts with
halogens like
(i) Chlorine and (ii)
Fluorine?


Pressure \( \boldsymbol{P}_{\boldsymbol{r}}=\frac{\boldsymbol{3} \boldsymbol{F} \boldsymbol{v}^{2}}{\boldsymbol{\pi}^{2} \boldsymbol{t}^{2} \boldsymbol{x}}\left(\text { where } \boldsymbol{P}_{\boldsymbol{r}}=\right. \)
Pressure \( F= \) force, \( v= \) velocity, \( t=\operatorname{time}, x \) \( = \) distance
State whether true or false: the above
equation is dimentionally correct
A. True
B. False


Assertion: Addition of \( N H_{4} O H \) to
an aqueous solution of \( B a C l_{2} \) in the
presence of excess \( N H_{4} C l \) precipitates
\( \boldsymbol{B} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \)

Reason: \( \boldsymbol{B a}(\boldsymbol{O H})_{2} \) is soluble in water.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both Assertion and Reason are not correct


\( N_{2(g)}+3 H_{2(g)} \leftrightarrow 2 N H_{3(g)} \) If some \( H C l \)
gas is passed into the reaction mixture at the equilibrium of this reaction,then:
A. Equilibrium position shifts towards left
B. Equilibrium position shifts towards right
c. concentration of \( H_{2} \) increases
D. The equilibrium position is not affected


The two years between which the rate of
change of cellular phones is minimum
are?
A . 1997 and 1998
B. 1999 and 2000
c. Both option (A) and (B)
D. 2001 and 2002


Narrow thin-walled cells with a large
nucleus and lying on the side of sieve tube are absent in
A. Angiosperms
B. Pteriodophytes
c. Gymnosperms
D. Both B and C


A hollow metal sphere of radius \( R \) is
charged with a charge \( Q . \) The electric potential and intensity inside the sphere are respectively:
A \( \cdot \frac{Q}{4 \pi \epsilon_{0} R^{2}} \) and \( \frac{Q}{4 \pi \epsilon_{0} R} \)
B. \( \frac{Q}{4 \pi \epsilon_{0} R} \) and zero
c. zero and sero
D. \( \frac{4 \pi \epsilon_{0} Q}{R} \) and \( \frac{Q}{4 \pi \epsilon_{0} R^{2}} \)


The value of acceleration due to gravity on earth is.
\( \mathbf{A} \cdot 9.8 \mathrm{ms}^{-2} \)
B. 15376
c. 227004
D. 127008


A sample of \( 2 \mathrm{kg} \) of monoatomic Helium(assume ideal) is taken through
the process \( A B C \) and another sample of
\( 2 \mathrm{kg} \) of the same gas is taken through the process ADC. Given, relative molecular mass of Helium \( =4 \)
What is the temperature of Helium in
each of the states \( A, B, C \) and \( D ? \)
A \( \cdot T_{A}=220.33 K ; T_{B}=T_{D}=2 T_{A} ; T_{C}=5 T_{A} \)
B. \( T_{A}=320.33 K ; T_{B}=T_{D}=3 T_{A} ; T_{C}=4 T_{A} \)
\( \mathbf{c} \cdot T_{A}=120.33 K ; T_{B}=T_{D}=2 T_{A} ; T_{C}=4 T_{A} \)
D. \( T_{A}=520.33 K ; T_{B}=T_{D}=2 T_{A} ; T_{C}=4 T_{A} \)


If
100 joule of work must be done to move electric charge equal to \( 4 C \) from
a place, where potential is -10 volt to another place, where potential is \( V \) volt, find the value of \( V \)


When molten sulphur is quenched, then which of the following is formed?
A. Monoclinic sulphur
B. Rhombic sulphur
c. crystex (plastic)
D. Gamma sulphur


(A) The kinetic energy of the photoelectron ejected increases with increase in the intensity of incident radiation.
(R) Increase in intensity of incident light increases the rate of emission.
A. Both (R) and (A) are true and reason is the. correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
c. Assertion (A) is true but reason
(R) is false
D. Assertion
(A) and reason
(R) both are false
E. Assertion (A) is false but reason (R) is true


Fast neutrons can easily be slowed down by
A. the use of lead shielding
B. passing them through water
c. elastic collision with heavy nuclei
D. applying a strong electric field


Assertion
Let \( A \) be a \( 2 \times 2 \) matrix with real
entries. Let \( I \) be the \( 2 \times 2 \) identity
matrix. Denote by \( t r(A), \) the sum of
diagonal entries of \( A \). Assume that
\( \boldsymbol{A}^{2}=\boldsymbol{I} \)
If \( \boldsymbol{A} \neq \boldsymbol{I} \) and \( \boldsymbol{A} \neq-\boldsymbol{I}, \) then \( \operatorname{det}(\boldsymbol{A})=-\mathbf{1} \)
Reason
If \( \boldsymbol{A} \neq \boldsymbol{I} \) and \( \boldsymbol{A} \neq-\boldsymbol{I}, \) then \( \boldsymbol{t r}(\boldsymbol{A}) \neq \mathbf{0} \)
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


Find the fourth vertex of the rhombus
formed by (-1,-1),(6,1) and (8,8)


\( \frac{k}{k} \)


The electronic potential \( V \) at a point on the circumference of a thin non-
conducting disk of radius r and uniform charge density \( \sigma \) is given by equation \( \boldsymbol{V}=\mathbf{4} \boldsymbol{\sigma} \boldsymbol{r} . \) Which of the following
expression correctly represents
electrostatic energy store in the electric
field of a similar charge disk of radius
R?


Of the students in a college, it is known that \( 60 \% \) reside in hostel and \( 40 \% \) are
day scholars (not residing in hostel) Previous year results report that \( 30 \% \) of all students who reside in hostel attain
\( A \) grade and \( 20 \% \) of day scholars attain
\( A \) grade in their annual examination. At
the end of the year, one student is chosen at random from the college and
he has an \( A \) grade, what is the probability that the student is a hosteller?


The value of \( \lim _{x \rightarrow 0} \frac{(\tan (\{x\}-1)) \sin \{x\}}{\{x\}(\{x\}-1)} \)
is given by :
where \( \{x\} \) denotes the fractional part
function
\( A \cdot 1 \)
B. \( \tan 1 \)
\( c \cdot \sin 1 \)
D. Does not exist


Two non-conducting solid spheres of radii R and 2R, having uniform volume
charge densities \( \rho_{1} \) and \( \rho_{2} \) respectively, touch each other. The net electric field
at a distance \( 2 \mathrm{R} \) from the centre of the
smaller sphere, along the line joining the centre of the spheres is zero. The
ratio \( \rho_{1} / \rho_{2} \) can be:
This question has multiple correct options
\( A \cdot-4 \)
B. \( -\frac{32}{25} \)
c. \( \frac{32}{25} \)
D. 4


If \( A \) and \( B \) are independent events such that \( \mathbf{0}<\boldsymbol{P}(\boldsymbol{A})<\mathbf{1}, \mathbf{0}<\boldsymbol{P}(\boldsymbol{B})<\mathbf{1}, \) then
This question has multiple correct options
A. A, B are mutually exclusive
B. A and \( \bar{B} \) are independent
c. \( \bar{A} \) and \( \bar{B} \) are independent
D. \( P(A / B)+P(\bar{A} / B)=1 \)


The linear equation \( (2 x+5 y=7) \) has
A. a unique solution.
B. two solutions.
c. infinitely many solutions
D. no solution


The oxidation state of \( N \) in \( N a N O_{3} \) is
\( +x . \) Here, \( x \) is :


Which of the following statements are
incorrect?
A. \( N b \) is stable in +4 oxidation state
B. \( B k \) in +4 oxidation state is strongly oxidising but more stable than \( C m \) and \( A m \) in +4 oxidation state
C. Uranium can form oxygenated ion such as \( U O_{2}^{2+} \)
D. \( P u \) shows oxidation state up to +7


State True or False.
\( K O_{2} \) is paramagnetic.
A. True
B. False


Very short answer type.
Name three enzymes of small intestine, which catalyze the hydrolysis of carbohydrates


An appliance / machine which does not
use an electric motor is
A. Washing machine
B. Refrigerator
c. Electric iron
D. Hair dryer


The activity of catalyst increases in finely divided state or colloidal state.
A. True
B. False


The angular displacement of an object
having uniform circular motion is \( \frac{\pi}{4} \) rad in every 3 s.Find the frequency of revolution.


What is the domain of the function
\( f(x)=\frac{1}{\sqrt{|x|-x}} ? \)
A \( \cdot(-\infty, 0) \)
B. \( (0, \infty) \)
c. \( 0<x<1 \)
D. \( x>1 \)


The length of a wire under stress changes by \( 0.01 \% . \) The strain produced is
\( \mathbf{A} \cdot 1 \times 10^{-4} \)
B. 0.01
\( c \)
D. \( 10^{4} \)


Carbon: non-metal:: Germanium:
A . Metal
B. Non-metal
c. Metalloid
D. Liquid non-metal


State whether true or false:
The quantity of heat required by one gram of a substance to raise its
temperature by \( 1 \mathrm{K} \) is called its specific heat(s).
A. True
B. False


is measured in terms of the
number of persons per square kilometer.
A. Size of population
B. Sex-Ratio
c. Density of population
D. Life - Expectancy at Birth


\( H_{2} S \) is bubbled into a \( 0.2 \mathrm{M} \) NaCN solution which is, \( 0.02 \mathrm{M} \) each in
\( A g(C N)_{2}^{\ominus} \) and \( \left(C d(C N)_{4}\right)^{2-} . \) If \( K_{s p} \) of
\( A g_{2} S \) and \( C d S \) are \( 10^{-50} \) and \( 7.1 \times \)
\( 10^{-28} \) and \( K \) instability for \( \left[A g(C N)_{2}^{\ominus}\right] \)
and \( \left[\boldsymbol{C d}(\boldsymbol{C N})_{4}^{2-}\right] \) are \( 1.0 \times 10^{-20} \) and
\( \mathbf{7} .8 \times 10^{-18}, \) which sulphide will
precipitate first?
A. \( C d S \)
в. \( A g_{2} S \)
c. \( N a_{2} S \)
D. Either \( A g_{2} S \) or \( N a_{2} S \) depending on acidity of solution


Reduce it into fraction:
\( 6.25 \% \)


Which one is the most suitable soil for
the growth of plants?
A. Sandy soil
B. Loamy Soil
c. silty soil
D. Clayey soil


Which of the following helps in formation of alveoli of the mammary
glands?
A. Estrogen
B. Prolactin
c. Progesterone
D. All of the above


toppr
Q Type your question
from point \( P \) to \( Q \) as shown in figure. The velocities at \( P \) and \( Q \) are respectively, \( \boldsymbol{v} \overrightarrow{\boldsymbol{i}} \) and \( -2 v \vec{j} . \) Then which of the following
statements \( (A, B, C, D) \) are the correct?
(Trajectory shown in schematic and not
to scale)
\( (\mathbf{A}) \boldsymbol{E}=\frac{\mathbf{3}}{\mathbf{4}}\left(\frac{\boldsymbol{m} \boldsymbol{v}^{2}}{\boldsymbol{q} \boldsymbol{a}}\right) \)
(B) Rate of work done by the electric field at \( P \) is \( \frac{3}{4}\left(\frac{m v^{3}}{a}\right) \)
(C) Rate of work done by both the fields
at Qis zero
(D) The difference between the
magnitude of angular momentum of
the particle at \( P \) and \( Q \) is 2 mav.
\( A \cdot(A),(B),(C),(D) \)
B. \( (A),(C),(D) \)
\( c \cdot(B),(C),(D) \)
D. \( (A),(B),(C) \)


Let \( \bar{a}, \bar{b}, \bar{c} \) be three non-zero vectors, no two of which are collinear. If the vector
\( \bar{a}+2 \bar{b} \) is collinear with \( \bar{c} \) and \( \bar{b}+3 \bar{c} \) is
collinear with \( \bar{a}, \) then \( \bar{a}+\bar{b}+3 \bar{c}= \)
\( \mathbf{A} \cdot \lambda \bar{a} \bar{a} \)
в. \( \lambda \bar{b} \)
\( c \cdot \lambda \bar{c} \)
D.


Match the following:
List - List - II
1) Molality
A) unity
2) Relative
B) dilute solutions vapour lowering
3) Raoult's law
C) independent of temperature
4) \( X_{\text {solute}} X_{\text {solvent}} \)
D) Mole fraction of solute
\( \mathbf{A} \cdot 1-C, 2-D, 3-B, 4-A \)
B . \( 1-A, 2-C, 3-D, 4-B \)
C \( .1-C, 2-B, 3-A, 4-D \)
D . \( 1-D, 2-A, 3-B, 4-C \)


A block of mass m slides with velocity
of \( 10 m / s \) on a rough horizontal surface It comes to rest after converting a distance of 50 meters. If \( g \) is \( 10 m / s e c^{2} \) then the coefficient of dynamic friction between the block and the surface is
A . \( 0 . \)
B. 1
c. 10
D. 5


State true or false:
If two parallel lines are intersected by a transversal, then the interior angles on
the same side of the transversal are
supplementary
A. True
B. False


If principle of moments for any object holds, then object is in state of
A . inertia
B. equilibrium
c. suspension
D. motion


The lightest metal among the following is:
A . cs
B. Be
c. Na
D. Li


In the chemical reaction, the
compounds \( A \) and \( B \) respectively are:
A. Benzene diazonium chloride and benzonitrile
B. Nitrobenzene and chlorobenzene
C. Phenol and bromobenzene
D. Flurobenzene and phenol


Law of conservation of energy states
that:
A. energy cannot be destroyed but can be created and transformed from one form to another
B. energy exists in only one form
C. energy exists in many forms but it cannot be transformed
D. energy can neither be created nor be destroyed but can be transformed from one form to another


A beam of electrons moving with a uniform speed of \( 4 \times 10^{7} m s^{-1} \) is
projected normal to the uniform magnetic field where \( \boldsymbol{B}=\mathbf{1 0}^{-3} \boldsymbol{W} \boldsymbol{b} / \boldsymbol{m}^{2} \)
What is path of the beam in magnetic field?


The trigonometric equation \( \sin ^{-1} x= \)
\( 2 \sin ^{-1} 2 a \) has a real solution, if
A \( \cdot|a|>\frac{1}{\sqrt{2}} \)
в. \( \frac{1}{2 \sqrt{2}}<|a|<\frac{1}{\sqrt{2}} \)
c. \( |a|>\frac{1}{2 \sqrt{2}} \)
D \( \cdot|a| \leq \frac{1}{2 \sqrt{2}} \)


A photon of light from which of the following electromagnetic radiations carries the greater amount of energy?
A. Blue
B. Green
c. orange
D. Red
E. Yellow


The force on a particle of mass 10 g is \( (10 \hat{i}+5 \hat{j}) N . \) if it starts from rest, what would be its position at time \( t=5 s ? \)
A . \( 12500 \hat{i}+6250 \hat{j} \mathrm{m} \)
B. 6250\hat \( +12500 \hat{j} \mathrm{m} \)
c. \( 12500 \hat{i}+12500 \hat{j} \mathrm{m} \)
D. 6250\hat + 6250\hat m


Find the value of \( \sqrt{49} \)


A bus is moving with a speed of \( 10 m s^{-1} \) on a straight road. A scooter wishes to
overtake the bus in 100 s. If the bus is at
a distance of \( 1 k m \) from the scooterist, with what speed should the scooterist chase the bus?


A ball is dropped onto a floor from a height of \( 10 \mathrm{m} \). If \( 20 \% \) of its initial energy is lost, then the height of bounce is-
\( A \cdot 2 m \)
B. \( 4 \mathrm{m} \)
\( c \cdot 8 m \)
D. \( 6.4 \mathrm{m} \)


on a rough horizontal surface and has
inner radius \( r \) and outer radius \( \mathrm{R} \). The
angle \( \theta \) between the applied force and
the horizontal can be varied. The critical
angle \( (\theta) \) for which the spool does not
roll and remains stationary is given by :
\( ^{\mathbf{A}} \cdot_{\theta}=\cos ^{-1}\left(\frac{r}{R}\right) \)
B. \( \theta=\cos ^{-1}\left(\frac{2 r}{R}\right) \)
\( ^{\mathrm{C}} \theta=\cos ^{-1} \sqrt{\frac{r}{R}} \)
" \( \quad \theta=\sin ^{-1}\left(\frac{r}{R}\right) \)


If \( \boldsymbol{y}=\frac{\log \boldsymbol{x}}{\boldsymbol{x}}, \) then prove by
mathematical induction
\( \boldsymbol{y}_{n}= \)
\( \frac{(-1)^{n}(n !)}{x^{n+1}}\left[\log x-1-\frac{1}{2}-\dots-\frac{1}{n}\right] \)


Which is the coloured ion?
\( \mathbf{A} \cdot\left[C u(C N)_{4}\right]^{3} \)
B . \( \left[S c\left(H_{2} O\right)_{6}\right]^{3+} \)
\( \mathbf{c} \cdot\left[M n\left(H_{2} O\right)_{6}\right]^{3+} \)
D. All of these


is a process of converting waste materials to reusable material.
A. Recycling
B. Reuse
c. Reduce
D. All of the above.


The price of petrol decreased from Rs.77.50 by 4.8\%. What is the reduced price of petrol?


Factors of \( 4 x^{4}-25 x^{2}+36 \) are:
A. \( (x+2)(x-2)(2 x+3)(2 x-3) \)
B. \( (x+1)(x-1)(x+3)(x-3) \)
c. \( (x+3)(x-3)(4 x+3)(4 x-3) \)
D. None of these


Cadmium rods are used in a nuclear
reactor
A. To produce neutrons
B. To speed up neutrons
c. To absorb neutrons
D. None of these


Construct a quadrilateral PQRS such
that \( \boldsymbol{P Q}=\mathbf{3 . 5} \boldsymbol{c m}, \boldsymbol{Q} \boldsymbol{R}= \)
\( 4.5 c m, R S=4 c m, \angle Q=110^{\circ} \) and
\( \angle R=80^{\circ} \)


What are vitamins? Write various kinds
of vitamins?


A well preserved and most complete homonid fossil named Lucy belongs to
genus
A. Dryopithecus
B. Oreopithecus
c. Pithecanthropus
D. Australopithecus


If \( \mathbf{y}=\mathbf{b} \cos \log \left(\frac{\boldsymbol{x}}{\boldsymbol{n}}\right)^{\boldsymbol{n}}, \boldsymbol{t h e n} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot \frac{-n b \sin \log (x)^{n}}{x} \)
B. \( n b \sin \log \left(\frac{x}{n}\right)^{n} \)
c. \( _{-n b \sin \log }\left(\frac{x}{n}\right)^{n} \)
D. None of these


Assertion: The upper surface of the wings of an aeroplane is made convex
Reason: The air current at the top will
have greater velocity and thus pressure at the bottom will be greater than at the
top
A. Both assertion and reason are true and reason is 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. Both assertion and reason are false


A mass \( \mathrm{M} \) is lowered with the help of a string by a distancex at a constant
acceleration \( \frac{\mathrm{g}}{2} . \) The magnitude of work doneby the string will be:
\( ^{\mathbf{A}} \cdot \frac{M g}{2} k \)
B - \( \frac{1}{2} M g x^{2} \)
\( \mathbf{c} \cdot \frac{1}{2} M g x \)
D. \( M g x^{2} \)


Coal is a renewable source of energy.
A. True
B. False
c. Ambiguous
D. Data insufficient


Current in a circuit falls from \( 5.0 A \) to
\( 0.0 A \) in \( 0.1 s . \) If an average emf of \( 200 V \)
induced, find an estimate of the selfinductance of the circuit.


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{A}=\left\{\boldsymbol{y}: \boldsymbol{0} \leq \boldsymbol{y}<\frac{\boldsymbol{\pi}}{2}\right\} \) be a
function such that \( f(x)=\tan ^{-1}\left(x^{2}+\right. \)
\( \boldsymbol{x}+\boldsymbol{k}), \) where \( \boldsymbol{k} \) is a constant. The value
of \( k \) for which \( f \) is an onto function is
A . 1
B.
c. \( \frac{1}{4} \)
D. none of these


Which of the following has the most negative heat of hydrogenation?
\( A \)
B.
\( c \)
\( D \)


If \( \vec{a}=x \hat{i}+(x-1) \hat{j}+\hat{k} \) and \( \vec{b}= \)
\( (x+1) \hat{i}+\hat{j}+a \hat{k} \) always make an
acute angle with each other for every
value of \( x \in R, \) then
A \( . a \in(-\infty, 2) \)
B . \( a \in(2, \infty) \)
c. \( a \in(-\infty, 1) \)
D. \( a \in(1, \infty) \)


Find the L.S.A of a cuboid whose
dimensions are given by \( 3 m \times 5 m \times \)
\( 4 m \)


The door of an almirah is \( 6 \mathrm{ft} \) high, 1.5 wide \( 8 \mathrm{kg} \). The door is supported by two hings situated at a distance of 1 ft from the ends. If the magnitude of the forces exerted by the hinges on the door are equal, find this magnitude.


Answer in 200 to 250 words:
Write a brief account of functioning of 'Electrostatic Precipitator' with diagram.


\( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H} \boldsymbol{N H}_{2} \) is a primary amine.
If true enter 1 else 0
\( A \)


In a class of 60 students, 30 opted for
NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these
students is selected at random, find the
probability that
(i) The student opted for NCC or NSS
(ii) The student has opted neither NCC
nor NSS
(iii) The student has opted NSS but not
\( \mathrm{NCC} \)


An atom has \( 2 \mathrm{K}, 8 \mathrm{L}, 5 \mathrm{M} \) electrons. Which
of the following is its correct electronic configuration?
A \( .1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3} \)
C. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4} \)
D. None of these


Maximum absorption of water in mammals is in
A. Lung
B. skin
c. Kidney
D. Small intestine


We should wash our eyes with:
A. water at room temperature
B. chilled water
C. warm water
D. boiling water


The pressure energy per unit mass of liquid of density \( \rho \) at a pressure P is
A \( \cdot \frac{P}{\rho} \)
в. \( \rho \times P \)
\( c \cdot \frac{\rho}{P} \)
D. \( \sqrt{\frac{P}{\rho} \frac{P}{\rho} \frac{P}{\rho}} \)


Which of the following statements is true about IIA group elements?
A. All form nitrides in air.
B. \( B e \) is amphoteric
c. \( M H_{2} \) is ionic salt-like hydride.
D. All are correct.


f \( a=2 \) and \( b=3, \) find the value of
(i) \( 2 a-3 b \)
(ii) \( 5 a^{2}-2 a b \)
(iii) \( a^{3}-b^{3} \)


The continuous cycling of water among
its three forms keeps:
A. the total amount of water on the earth constant
B. the total amount of water on the earth decreasing continuously
C. water fresh
D. none of these


ass an in is
at the bottom of a fixed circular,
vertical task,which has a radius of R.
The contact surface between the mass
and loop is frictionless. A bullet of mass
\( m \) strikes the block horizontally with
initial speed \( v_{0} \) and remain embedded
in the block as the block and the bullet
circle the loop. Determine each of the
following in terms of \( \mathrm{m}, v_{0}, \mathrm{R} \) and \( \mathrm{g} \)
a)The speed of the masses immediately
after the impact.
b)The minimum initial speed of the
bullet if the block and bullet are to
successfully execute a complete ride on
the loop.


A lamp is connected in series with a
capacitor and an AC source. What
happens if the capacity of the capacitor
is reduced?
A. The lamp shines more brightly
B. The lamp shines less brigthly
C. There is no change in the brightness of the lamp
D. Brightness may increase or decrease depending on the frequency of the \( A C \)


Which is correct about the bile of
rabbit?
A. It is synthesized by gall bladder and also stored there.
B. It is an enzyme which emulsify the fats.
C. It contain bile salts and bile pigments.
D. Bilirubin present in it decomposes fats.


Identify the graph of the polynomial
function \( \boldsymbol{f} \)
\( f(x)=x^{3}-2 x^{2}-x+2 \)
A. graph a
B. graph b
c. graph c
D. graph d


Write the relation between mean,
median and mode.


When the temperature is increased, surface tension of water:
A. increases
B. decreases
c. remains constant
D. shows irregular behaviour


Inverse circular functions,Principal
values of \( \sin ^{-1} x, \cos ^{-1} x, \tan ^{-1} x \)
\[
\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y}
\]
\( \boldsymbol{x} \boldsymbol{y}<\mathbf{1} \)
\[
\boldsymbol{\pi}+\tan ^{-1} \frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{1}-\boldsymbol{x} \boldsymbol{y}}, \quad \boldsymbol{x} \boldsymbol{y}>1
\]
(a) \( \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}=\frac{\pi}{4} \)
\( (b) \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{8}=\frac{\pi}{4} \)
\( (c) \tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{3}{5}-\tan ^{-1} \frac{8}{19}=\frac{\pi}{4} \)


Explain Hall-Heroult method of obtained pure aluminium from alumina with
figure.


What is the impulse of force shown in the following fingre?
A. 205 Ns
B. 450 Ns
\( c .800 \mathrm{Ns} \)
D. 1000 Ns


For given vectors, \( \vec{a}=2 \hat{i}-\widehat{j}+2 \widehat{k} \) and \( \vec{b}=-\hat{i}+\widehat{j}-\widehat{k}, \) find a unit vector in
the direction of the vector \( \vec{a}+\vec{b} \)


Solve the following pair of equations by
method of substitution
\( x+y=3 \) and \( 2 x+5 y=12 \)


Which of the following is the set of products formed when propanol
\( C_{2} H_{2} O H, \) undergoes a combustion
reaction?
A \( \cdot C O_{2(g)} \) and \( H_{2} O_{(l)} \)
B. \( C O_{2(g)} \) and \( H_{2} O_{(g)} \)
\( \mathbf{c} \cdot C_{(a)}, O_{2(g)} \) and \( H_{2} O_{(g)} \)
D. \( C_{(a)}, H_{2(g)} \) and \( H_{2} O_{(g)} \)
E \( \cdot C O_{2(g)}, H_{2} O_{(g)} \) and \( O_{2(g)} \)


Consider the following reaction:
ethanol \( \frac{P B r_{3}}{\longrightarrow} X \frac{a l c . K O H}{\longrightarrow} \)
\( \boldsymbol{Y} \stackrel{(i) \boldsymbol{H}_{2} S \boldsymbol{O}_{4}, \text {room temp}(i \boldsymbol{i}) \boldsymbol{H}_{2} \boldsymbol{O} / \text {heat}}{\boldsymbol{X}} \boldsymbol{Z} \)
The product \( Z \) is:
A. \( C H_{3} C H_{2}-O-C H_{2}-C H_{3} \)
B. \( C H_{3}-C H_{2}-O-S O_{3} H \)
c. \( C H_{3} C H_{2} O H \)
D. \( C H_{2}=C H_{2} \)


For \( \Delta A B C, \) find the measure of \( \angle A C D \)


Assertion
A beam of protons is moving towards east in vertically upward magnetic field.Then,this beam will deflect
towards south.
Reason
A constant magnetic force will act on the proton beam.
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


Liquid ammonia is a fuel for:
A. motorcar
B. aeroplane
c. monorial
D. rocket


General formula of aldehyde is:
A. \( C_{n} H_{2 n} O_{2} \)
в. \( C_{n} H_{2 n} O \)
c. \( C_{n} H_{2 n+1} O \)
D. \( C_{n} H_{2 n+2} O \)


A protractor has - symmetry.
A .
B. 2
\( c .3 \)
\( D \)


A cell has four chromosomes, which
are represented in the original cell
drawing. At the end of meiosis I, the possible outcome is represented by
A. I only
B. II only
c. III only
D. IV only
E. None of the above


\( \operatorname{tet} f(\theta)=\left|\begin{array}{ccc}\cos \frac{\theta}{2} & 1 & 1 \\ 1 & \cos \frac{\theta}{2} & -\cos \frac{\theta}{2} \\ -\cos \frac{\theta}{2} & 1 & -1\end{array}\right| \)
\( f(\pi)+f(-\pi) \) is equal to
A. The maximum value of \( f(\theta) \)
B. The minimum value of \( f(\theta) \)
c. Average value of the range of \( f(\theta) \)
D. None of these


Nickel metal is purified by the vapour phase refining process. This process is based on the fact that:
A. nickel metal sublimes at high temperature
B. nickel reacts with carbon monoxide to form nickel carbonyl which decomposes at high temperature to form nickel
c. nickel reacts with chlorine to form nickel chloride which is volatile and decomposes easily to nickel
D. nickel can be vapourized under vacuum leaving behind impurities


Energy of the electron in H-atom is 1.50
tionss as much as energy as the minimum required for its escape (13.6
ev) from the atom. The energy difference between two energy livels is?
A . 13.6 ev
B. 20.4 ev
c. 6.8 ev
D. 9.07 ev


The voltmeter shown in figure, reads 18
V across the \( 50 \Omega \) resistor. Find the
resistance of the voltmeter


For the following sequential reaction \( \boldsymbol{E}^{\boldsymbol{o}} \) values in volts at \( 298 \mathrm{K} \) are given:
\( M n O_{4}^{-0.564}^{V} M n O_{4}^{-2}^{2.26 V} \)
\( M n O_{2} \stackrel{0.95}{\rightarrow} M n^{+3} \stackrel{1.51 V}{\rightarrow} M n^{+2} \)
Calculate \( \boldsymbol{E}^{o} \) for \( \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{\boldsymbol{4}}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{+2} \)
A. -1.81 volt
B. -1.18 volt
c. 1.51 volt
D. 1.18 volt


Electron has nearly the equal mass as
that of a/an:
A. proton
B. neutron
C. positron
D. \( \alpha \) -particle


If a particle of mass m moving with
velocity \( v_{1} \) is subject to an impulse \( I \)
which produces a final velocity \( v_{2}, \) then
\( \boldsymbol{I} \) is given by :
B. \( m\left(v_{1}+v_{2}\right) \)
c. \( m\left(v_{2}-v_{1}\right) \)
D. \( \frac{m\left(v_{2}^{2}-v_{1}^{2}\right)}{2} \)


A frog can be levitated in magnetic field produced by a current in a vertical solenoid placed below the frog. This is possible because the body of the frog behaves as
A. Paramagnetic
c. Ferromagnetic


Consider the following equilibrium in a closed container \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
At a fixed temperature, the volume of the reaction container is halved. For this
change, which of the following statements held true regarding the
equilibrium constant \( \left(\boldsymbol{K}_{\boldsymbol{p}}\right) \) and degree
of dissociation \( (\alpha): \)
A. Neither \( K_{p} \) nor \( \alpha \) changes
B. Both \( K_{p} \) and \( \alpha \) -changes
C. \( K_{p} \) changes, but \( \alpha \) does not change
D. \( K_{p} \) does not change, but \( \alpha \) -changes


toppr
Q Type your question
pressure in atmospheres. For example if
a substance at a particular temperature and pressure lies in gas area, the substance exists only as a
gas.

However, if the temperature-pressure
pairing is on the line segment between gas and liquid, the substance exists as
both a gas and a liquid.. If \( \boldsymbol{T}>\mathbf{0} \) and
\( P>0, \) which of the following systems of
inequalities would describe the
temperature and pressure ranges in which this substance exists only as a liquid?
\( ^{\text {A }} P<\frac{17}{2} T-1,860 ; P>\frac{5}{18} T-\frac{460}{9} \)
В \( \cdot P>\frac{17}{2} T-1,860 ; P<\frac{5}{18} T-\frac{460}{9} \)
c. \( \quad P<\frac{17}{2} T-1,860 ; P>\frac{11}{200} T-\frac{460}{9} \)
\( P \geq \frac{17}{2} T-1,860 ; P \leq \frac{11}{200} T-\frac{460}{9} \)


Hypotheca of parent diatom forms in daughter
A. Hypotheca
B. Epitheca
c. Is shed
D. Forms the whole frustule


The IUPAC name of crotonaldehyde is:
A. prop-2-en-1-al
B. propenal
c. But-2-en-1-al
D. butenal


Two chords \( A B \) and \( A C \) of a circle with
centre \( O \) are on the opposite sides of
\( \boldsymbol{O} \boldsymbol{A} . \) Then:
A. \( \angle O A B=\angle O A C \).
в. \( \angle O A B \neq \angle O A C \).
c. Cannot be determined
D. None of the above


If \( \boldsymbol{y}=|\cos \boldsymbol{x}|+|\sin \boldsymbol{x}|, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}= \)
\( \frac{2 \pi}{3} \) is
A \( \cdot \frac{1-\sqrt{3}}{2} \)
в. 0
c. \( \frac{\sqrt{3}-1}{2} \)
D. \( \frac{\sqrt{3}+1}{2} \)


An equilateral triangle is inscribed in a circle of radius \( 6 \mathrm{cm} . \) Find its side.


The greatest value of the function
\( f(x)=\sin ^{2} x-20 \cos x+1 \) is
A . 20
B. 1
c. 21
D.


A block of mass \( M \) is at rest on a rough horizontal surface. The coefficient of
friction between the block and the
surface is \( \mu . \) A force \( \boldsymbol{F}=\boldsymbol{M} \boldsymbol{g} \) acting at
an angle \( \theta \) with the vertical side of the block pulls it. In which of the following cases, the block can be pulled along the surface?
\( \mathbf{A} \cdot \tan \theta \geq \mu \)
B. \( \cot \theta \geq \mu \)
\( \mathbf{c} \cdot \tan \theta / 2 \geq \mu \)
D. \( \cot \theta / 2 \geq \mu \)


What are fossils?


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left\{\cos \boldsymbol{x}^{0}\right\}=? \)


1 volt is equal to
A .1 Joule
B. \( \frac{1 \text { Joule}}{1 \text { Coulomb }} \)
c. \( \frac{1 \text { Joule}}{1 \text { meter }} \)
D. \( \frac{1 \text { Newton }}{1 \text { Coulomb }} \)


Average osmotic pressure of human
blood is 7.4 at \( m \) at \( 27^{\circ} C, \) then total
concentration of various solutes is:
\( \mathbf{A} \cdot 0.1 \mathrm{molL}^{-1} \)
B. 0.2 molL\( ^{-1} \)
c. 0.3 molL \( ^{-1} \)
D. 0.4 molL\( ^{-1} \)


Solve \( \int \tan ^{-1} \sqrt{x} d x= \)


A hole is made at the bottom of the tank
filled with water (density \( 1000 k g / m^{3} \) ), If the total pressure at the bottom ofthe tankis 3 atmosphere
\( \left(1 \text { atmosphere }=10^{5} N / m^{2}\right), \) then the velocity of efflux is :
A \( . \sqrt{200} \mathrm{m} / \mathrm{s} \)
B. \( \sqrt{400} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{500} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{800} \mathrm{m} / \mathrm{s} \)


Write the function in simplest form:
\( \tan ^{-1}\left(\frac{x}{\sqrt{a^{2}-x^{2}}}\right) w h e r e,|x|<a \)


Select correct statement for \( \boldsymbol{B} \boldsymbol{r} \boldsymbol{F}_{5} \)
A. All fluorine atoms are in same plane
B. Four fluorine atoms and \( B r \) atom is in same plane
C. Four fluorine atoms are in same plane
D. It has all \( F-B r-F \) bond angles at \( 90^{\circ} \)


fin \( (A)=120, N(B)=250 \) and \( n(A-B)= \)
52, then find \( n(A \cup B) \)
A . 302
B. 250
\( c .368 \)
D. None of the above


Two small blocks of charges \( 5 \mu C \) and
\( 3 \mu C \) are kept on a rough surface \( (\mu= \)
0.5) at a separation of 0.1 m. Find the
separation between the blocks when
they come to rest.
A . \( 0.27 \mathrm{m} \)
в. 0.6 т
c. \( 0.72 m \)
D. 1.27 m


Calculate the amount of \( C a C l_{2} \) (van't
Hoff factor \( i=2.47 \) ) dissolved in \( 2.5 L \)
solution so that its osmotic pressure at
\( 300 K \) is 0.75 atmosphere
Given: Molar mass of \( C a C l_{2} \) is
\( 111 g \cdot m o l^{-1} \)
\( \boldsymbol{R}=\mathbf{0 . 0 8 2} \boldsymbol{L} . \boldsymbol{a t m} . \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1} \)


In forest, trees basically function as


What is necessary for the production and transmission of sound?
A. Medium
B. Acceleration
c. Reciever
D. None of the above


What are pelvic bones?


Which of the following are pseudo
unimolecular reactions?
This question has multiple correct options
\( \mathbf{A} \cdot C H_{3} C O O C_{2} H_{5}+H O H \stackrel{H^{+}}{\longrightarrow} C H_{3} C O O H+ \)
\( C_{2} H_{5} O H \)
B \( \cdot C H_{3} C O O C_{2} H_{5}+H O H \stackrel{O H^{-}}{\longrightarrow} C H_{3} C O O H+ \)
\( C_{2} H_{5} O H \)
\( ^{\mathbf{C}} \cdot C_{12} H_{22} O_{11}+H O H \frac{H^{+}}{\rightarrow} \begin{aligned} C_{6} H_{12} O_{6}_{+} C_{6} H_{12} O_{6} & \\ & g l u c o s e \quad \text { fructose } \end{aligned} \)
D \( \cdot S O_{2} C l_{2}(g) \longrightarrow S O_{2}(g)+C l_{2}(g) \)


Myasthenia gravis is a/an
A. Autoimmune disease caused due to non-secretion of acetylcholine at neuromusclar junction.
B. Muscle related disease, caused by hormonal disorder.
C. Autoimmune disease, caused due to non-section of
\( \mathrm{CSF} \)
D. Autommune disease, caused due to non-conduction of impulses at neural junction.


The principal value of \( \cos ^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\} \) is
A. \( -\frac{3 \pi}{20} \)
В. \( -\frac{7 \pi}{20} \)
c. \( -\frac{7 \pi}{10} \)
D. none of these


Which of the following shows radial
symmetry?
A. Porifera and coelenterata
B. Coelenterata and echinodermata
C . Coelenterata and platyhelminthes
D. Arthropoda and mollusca


The dimension of magnetic field in \( M, L, T \) and \( C \) (Coulomb) is given as:
A. \( M L T^{-1} C^{-1} \)
B. \( M T^{2} C^{-2} \)
c. \( M T^{-1} C^{-1} \)
D. \( M L T^{-2} C^{-1} \)


CP and \( \mathrm{CQ} \) are tangents to a circle with
centre \( 0 . A R B \) is another tangent
touching the circle at \( \mathrm{R} . \) If \( C P= \)
\( 11 c m, B C=7 c m, \) then the length BR is
\( A \cdot 11 c m \)
B. \( 7 \mathrm{cm} \)
\( c .3 c m \)
\( \mathrm{D} \cdot 4 \mathrm{cm} \)


State the law of radioactive decay
Hence derive the expression \( N= \)
\( N_{0} e^{-\lambda t} \) where symbols have their usual
meanings.


The fragrance of the flower is due to the presence of some steam volatile
organic compounds called essential oils. These are generally insoluble in water at room temperature but are miscible with water vapour in the vapour phase. A suitable method for the extraction of these oil from the flower is:
A. distillation
B. crystallisation
c. distillation with reduced pressure
D. steam distillation


In the reaction of hydrogen bromide with an alkene ( in the absence of
peroxides \( ), \) the first step of the reaction is the \( \quad \) to the alkene.
A. Fast addtion of an electrophilic
B. Slow addition of a electrophile
c. fast additon of a nucleophilic
D. slow addition of a nucleophile


An object lies on the principal axis of a
concave mirror with radius of curvature
160cm. Its vertical image appears at a
distance \( 70 \mathrm{cm} \) from it. Determine the
position of the object and also the magnification.


Use Euclid's division algorithm to find
the HCF of :
\( \mathbf{1 9 6} \) and \( \mathbf{3 8 2 2 0} \)
A. 169
в. 196
c. 206
D. 192


Which of the following statement is incorrect for the composition of water?
A. For water, the gravimetric or mass ratio of hydrogen to oxygen is 1: 8
B. In water, the ratio of hydrogen and oxygen is 2: 1 by
volume
C. The ratio in which hydrogen and oxygen combine gives the composition of water.
D. None of the above


A 0.5 m solution could be prepared by dissolving 20 g NaOH in:
A . 0.5 L water
B. 0.5 kg water
c. 1 L water
D. 1 kg water
E. 2 L water


The primary winding of a transformer has 100 turns and its secondary winding has 200turns. The primary is connected to an A.C supply of \( 120 \mathrm{V} \) and the current flowing in it is 10 A. The voltage and the current in the secondary
are
A. \( 240 V, 5 A \)
в. \( 240 V, 10 A \)
c. \( 60 V, 20 A \)
D. \( 120 V, 20 A \)


The e.m.f. of the cell
\( \boldsymbol{A} \boldsymbol{g}|\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \| \boldsymbol{K} \boldsymbol{C l}(\boldsymbol{a q} .)| \boldsymbol{H}_{2} \boldsymbol{C l}_{2} \mid \boldsymbol{H} \boldsymbol{g} \) is
\( 0.0455 \mathrm{K} \) at \( 298 \mathrm{K} \) and the temperature
coefficient is \( 3.38 \times 10^{-4} V K^{-1} . \) The
reaction is taking place is:
A. \( H g_{2} C l_{2}(s)+2 A g(s) \rightarrow 2 A g C l(s)+2 H g(l) \)
B. \( H g_{2} C l_{2}(s)+3 A g(s) \rightarrow 3 A g C l(s)+4 H g(l) \)
C. \( H g_{2} C l_{2}(s)+A g(s) \rightarrow 2 A g C l(s)+4 H g(l) \)
D. none of these


Grinding and chewing teeth are called
as
A. Premolars
B. Canines
c. Incisors
D. Molars


If \( f(x) \) is an even function, and \( n \in N \) then \( \int_{-\pi}^{\pi} \boldsymbol{f}(\boldsymbol{x}) \sin \boldsymbol{n} \boldsymbol{x} \boldsymbol{d} \boldsymbol{x}= \)
A .
B \( \cdot 2 \int_{0}^{\pi} f(x) \sin n x d x \)
c. \( 4 \int_{0}^{\frac{\pi}{2}} f(x) \sin n x d x \)
D. \( \int_{0}^{\pi} f(x) \sin x d x \)


In 1909 discovered
nucleus in his famous gold foil experiment.
A. Rutherford
B. Goldstein
c. J.J.Thompson
D. None of the above


Light which is incident on a flat surface
makes an angle of \( 15^{\circ} \) with the surface.
i) What is the angle of incidence?
ii) What is the angle of reflection?
iii) Find the angle of deviation


In a golf tournament, if we designate
the hole as the origin, and the putter
(like a bat) is at \( -5.0 \mathrm{m} \) at time \( 0 \mathrm{s} \), the
velocity-time graph for the golf ball will
be
A. a straight line inclined to the time axis
B. a straight line parallel to the time axis
c. a concave curve
D. a convex curve


Solve: \( \int_{0}^{\infty}\left(a^{-x}-b^{-x}\right) d x \)


Lentic ecosystem occurs in
A. Rain water
B. Running water
c. standing water
D. Gravitational water


The coefficient of the middle term in the
binomial expansion in power of \( x \) of
\( (1+\alpha x)^{4} \) and of \( (1-\alpha x)^{6} \) is the same
if \( \alpha \) equals-
A \( \cdot-\frac{5}{3} \)
в. \( \frac{10}{3} \)
\( c \cdot \frac{-3}{10} \)
D.


Find the value of \( \lambda \) so that the vector
\( \bar{A}=2 \hat{i}+\lambda \hat{j}-\hat{k} \quad, \bar{B}=4 \hat{i}-2 \hat{j}-2 \hat{k} \)
are perpendicular to each other


The critical temperature for
superconductors is the temperature at which the electrical resistivity of a
metal
A. drops to zero
B. increase to maximum limit
c. decrease to a certain limit
D. none of the above


Sunlight is reflected from a calm lake. The reflected light is \( 100 \% \) polarized at a certain instant. The angle between the sun light and the surface of lake is \( (\mu \) of
water is \( \frac{4}{3} \) ) \( \left(\tan ^{-1}\left(\frac{4}{3}\right)=53^{\circ} 4^{\prime}\right) \)
A .90
В. \( 53^{\circ} 4^{\prime} \)
\( \mathbf{c} \cdot 36^{\circ} 56^{\prime} \)
D. 45


Evaluate: \( \lim _{x \rightarrow \infty} \frac{\sin ^{4} x-\sin ^{2} x+1}{\cos ^{4} x-\cos ^{2} x+1} \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. \( \frac{1}{2} \)
D.


Two glass jars \( A \) and \( B \) are filled with carbon dioxide and oxygen gases,
respectively. In each jar a lighted candle is placed simultaneously. In which jar will the candle remain lighted for a longer time and why?


A steamer is going downstream
overcome a raft point \( A .2 h r \) later it
turned back and after some time
passed the raft at a distance \( 4 \mathrm{km} \) from point \( A . \) The speed of the river is
A. \( 1 \mathrm{km} / \mathrm{h} \)
B. \( 2 \mathrm{km} / \mathrm{h} \)
\( \mathrm{c} .3 \mathrm{km} / \mathrm{h} \)
D. \( 4 \mathrm{km} / \mathrm{h} \)


The line joining two points \( A(2,0), B(3,1) \) is rotated about \( A \) in anti-clockwise direction through an
angle of \( 15^{\circ} . \) The equation of the line in the now position, is
A \( \cdot \sqrt{3} x-y-2 \sqrt{3}=0 \)
B. \( x-3 \sqrt{y}-2=0 \)
c. \( \sqrt{3} x+y-2 \sqrt{3}=0 \)
D. \( x+\sqrt{3} y-2=0 \)


To convert \( ^{o} \mathrm{F} \) to \( ^{\circ} \mathrm{C} \) formula we use, is
A \( \cdot(F-32) \times \frac{5}{12} \)
B \( \cdot\left(F \times \frac{5}{9}\right)-32 \)
c. \( (F-32) \times \frac{9}{5} \)
D. \( (F-32) \times \frac{5}{9} \)


\( f\left|\begin{array}{ll}\boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{4} & \boldsymbol{2}\end{array}\right|=\mathbf{7} \) and \( \left|\begin{array}{ll}\boldsymbol{2} & \boldsymbol{3} \\ \boldsymbol{y} & \boldsymbol{x}\end{array}\right|=\boldsymbol{4} \) then
A \( \cdot x=-3, y=-\frac{5}{2} \)
B. \( x=-\frac{5}{2}, y=-3 \)
c. \( _{x}=-3, y=\frac{5}{2} \)
D. \( x=-\frac{5}{2}, y=3 \)


These questions consist of two
statements each, printed as assertion
and reason. While answering these questions you are required to choose anyone of the following five responses.
Assertion: Molecular nitrogen is less
reactive than molecular oxygen.
Reason: The bond length of \( N_{2}, \) is
shorter than that of oxygen.
A. If both assertion and reason are true and the reason is a correct explanation of the assertion
B. If both assertion and reason are true but reason is not correct explanation of the assertion
c. If the assertion is true but reason is false
D. If both the assertion and reason are false
E. If the assertion is false but the reason is true


In plant cell cytokinesis is marked by
the appearance of the cell plate. Cell plate resembles
A. Plasma membrane
B. Primary cell wall
c. secondary cell wall
D. middle lemella


Three planets of same density have
radii \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2} \) and \( \boldsymbol{R}_{3} \) such that \( \boldsymbol{R}_{1}= \)
\( 2 R_{2}=3 R_{3} \) The gravitational field at
their respective surfaces are \( g_{1}, g_{2} \) and
\( g_{3} \) and escape velocities from their
surfaces are \( \boldsymbol{v}_{1}, \boldsymbol{v}_{2} \) and \( \boldsymbol{v}_{3} \) then
This question has multiple correct options
A. \( g_{1} / g_{2}=2 \)
В \( \cdot g_{1} / g_{3}=3 \)
c. \( v_{1} / v_{2}=1 / 4 \)
D. \( v_{1} / v_{3}=3 \)


Find the sum of the first 1000 positive integers.


Three particles, each of mass \( m \), are
placed at the corner of right angle triangle as shown in the figure. if \( \mathrm{OA}=\mathrm{a} \)
and \( \mathrm{OB}=\mathrm{b}, \) the position vector of the
centre of mass is :
(here \( \hat{i} \) and \( \hat{j} \) are unit vector along \( \times \) and \( y \) axes, respectively
A \( \cdot \frac{1}{3}(a \hat{i}+b \hat{j}) \)
B \( \cdot \frac{1}{3}(a \hat{i}-b \hat{j}) \)
c \( \cdot \frac{2}{3}(a \hat{i}+b \hat{j}) \)
\( D \)


A \( 1.2 c m \) long pin is placed
perpendicular to the principal axis of a convex mirror of focal length \( 12 \mathrm{cm}, \) at a
distance of \( 8 c m \) from it. Is the image erect or inverted?


The electric field associated with an
e.m. wave in vacuum is given by \( \overrightarrow{\boldsymbol{E}}= \) \( 40 \cos \left(k z-6 \times 10^{8} t\right) \hat{i}, \) where \( E, z \) and \( t \)
in volt\( / \boldsymbol{m}, \) meter and seconds
respectively. The value of wave vector \( k \)
is
\( A \cdot 6 m^{-1} \)
B. \( 3 m^{-1} \)
\( \mathbf{c} \cdot 2 m^{-1} \)
D. \( 0.5 m^{-1} \)


The position time graphs above
represent the motions of cars 1 to 5. How
do they rank according to their speeds (greatest first)?
A. 1,2,3,4,5
B. 1,2,3 and 5 tie, 4
c. 1,2,4,3 and 5 tie
D. 3 and 5 tie, 4,2,1
\( E .5,4,3,2,1 \)


Find \( A \triangle B \) and draw Venn diagram
when:
\( \boldsymbol{A}=\{\mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\} \) and \( \boldsymbol{B}=\{\mathbf{2}, \mathbf{4}\} \)


Sewage water is purified for recycling by the action of:
A . fish
B. micro-organisms
c. fuels
D. non-biodegradable chemicals


Quick silver is now known as:
A. lead
B. mercury
\( c . \) tin
D. brass


If \( f(x)=\left(x^{2}-x+2\right)\left(x^{2}-4\right) \) then the
\( \operatorname{set}\{x \mid f(x)>0, x \in R\} \) is equal to
\( \mathbf{A} \cdot(-\infty,-2) \)
в. \( (2,+\infty) \)
c. (-2,2)
D \( \cdot(-\infty,-2) \cup(2,+\infty) \)


List the uses of detergents.


Q Type your question
\( \operatorname{speea} v_{0}=1.00 \times 10^{-} \mathrm{ms}^{-} \) into tne
uniform field between the parallel
plates as shown in figure. Assume that the field between the plates is uniform and directed vertically downward, and
that the field outside the plates is zero. The electron enters the field at a point
midway between the plates. Mass of
electron is \( 9.1 \times 10^{-31} k g . \) For the
condition that electronjust misses the
upper plate, the magnitude of electric field is :
\( \mathbf{A} \cdot 124 N C^{-1} \)
B . \( 364 N C^{-1} \)
C \( .224 \mathrm{NC}^{-1} \)
D. \( 520 N C^{-1} \)


A particle has an initial velocity of \( 9 m / s \) due east and a constant
acceleration of \( 2 m / s^{2} \) due west. The distance covered by the particle in the fifth second of its motion is : ( in
metres)
A . 0.5
B. 1
\( c \cdot 2 \)
D. 3


A buffer of \( \mathrm{pH} 8.50 \) is prepared from
0.02 mole of \( K C N . \) The desired volume
of buffer solution is to be 1 litre. How
will you make this buffer using \( \boldsymbol{H} \boldsymbol{C l} \) ? What is the change after addition of \( 0.5 \times 10^{-4} \) mole \( H C l \) to \( 100 c m^{3} \) and
same amount of \( N a O H \) in \( 100 c m^{3} \) of
buffer?
\( \left(\boldsymbol{K}_{\boldsymbol{a}} \boldsymbol{H} \boldsymbol{C} \boldsymbol{N}=\boldsymbol{6} . \boldsymbol{2} \times \mathbf{1 0}^{-10}\right) \)


Form the differential equation of the
family of curves represented by \( y^{2}= \)
\( (x-c)^{3} \)


The electron configuration for the noble gas with the highest first ionization
energy is:
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{3} 3 p^{6} \)
B . \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)
c. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} \)
D. \( 1 s^{2} \)
E \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 p^{1} \)


When a body moves in a circular motion
A. its direction constantly changes
B. its direction remains constant
C. its velocity vector is always perpendicular to the direction
D. all of the above


The reverse breakdown voltage of a
Zener diode is \( 5.6 \mathrm{V} \) in the given circuit
The current \( I_{Z} \) through the Zener is
\( \mathbf{A} \cdot 7 m A \)
В. 17 тА
\( c .10 m A \)
D. \( 15 \mathrm{mA} \)


Find the inverse of \( \boldsymbol{A}=\left[\begin{array}{lll}\mathbf{1} & \mathbf{3} & \mathbf{3} \\ \mathbf{1} & \mathbf{4} & \mathbf{3} \\ \mathbf{1} & \mathbf{3} & \mathbf{4}\end{array}\right] \)
column transformation.


Which of the following is responsible for groundwater shortage?
A. Heavy rainfalı
B. Aforestation
c. Increasing population
D. None of the above


Give any three differences between \( n \)
type and \( p \) -type semiconductors


Assertion
\( H C l \) diffuses faster than ammonia.
Reason

Rate of diffusion of a gas is inversely proportional to the square root of its
density
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


Select correct statement(s).
A. Equivalent of \( X e O_{3} \) in \( I \) and \( I I \) is in the ratio 1: 1
B . Equivalent mass of \( I_{2}=\frac{\text { molar mass }}{9} \)
c. Equivalent mass of \( F e^{2+}=\frac{\text { molar mass }}{6} \)
D. All the above are correct statements


is the major source of fresh
water and this water is neither used by animals and nor exposed to evaportion.


If the eccentricity of the ellipse \( a x^{2}+ \)
\( 4 y^{2}=4 a,(a<4) \) is \( \frac{1}{\sqrt{2}}, \) then its semi minor axis is equal to
A .2
B. \( \sqrt{2} \)
c. 1
D. \( \sqrt{3} \)
E . 3


Which of the following type of forces are present in natural rubber?
A. Weakest intermolecular forces
B. Hydrogen bonding
c. Three dimensional network of bonds
D. Metallic bonding


A car is parked among \( N \) cars standing
in a row, but not at either end. On his
return, the owner finds that exactly \( r \) of
the \( N \) places are still occupied. What is
the probability that both the places neighboring his car are empty?
A \( . \) Required probability \( =\frac{(N-r)(N-r-2)}{(N-1)(N-2)} \)
B. Required probability \( =\frac{(N-r)(N-r-1)}{(N-1)(N-2)} \)
c. Required probability \( =\frac{(N-r-2)(N-r-1)}{(N-1)(N-2)} \)
D. none of these


The alkyne which gives above ketone as the only product after hydration with
\( H_{2} O, H_{2} S O_{4} \) and \( H g S O_{4} \) is \( x \)
cyclohexylethyne. What is x?


Which of the following primary and
secondary valencies are not correctly
marked against the compound?
\( \mathbf{A} \cdot\left[C r\left(N H_{3}\right)_{6}\right] C l_{3}, p=3, s=6 \)
В \( \cdot K_{2}\left[P t C l_{4}\right], p=2, s=4 \)
\( \mathbf{C} \cdot\left[P t\left(N H_{3}\right)_{2} C l_{2}\right], p=0, s=4 \)
\( \mathbf{D} \cdot\left[C u\left(N H_{3}\right)_{4}\right] S O_{4}, p=4, s=4 \)


If \( \boldsymbol{P}=\mathbf{3} \boldsymbol{x}-\mathbf{4} \boldsymbol{y}-\mathbf{8} \boldsymbol{z}, \boldsymbol{Q}=-\mathbf{1 0} \boldsymbol{y}+ \)
\( 7 x+11 z \) and \( R=19 z-6 y+4 x, \) then
\( \boldsymbol{P}-\boldsymbol{Q}+\boldsymbol{R} \) is equal to
A \( .13 x-20 y+16 z \)
B. 0
c. \( x+y+z \)
D. \( 2 x-b y+3 z \)


What do you mean by green chemistry?
How will it help decrease environmental pollution?


Solve \( 4 \cos \theta-3 \sec \theta=\tan \theta \)
A \( \cdot \theta=n \pi+(-1)^{n} \alpha, \theta=n \pi+(-1)^{n} \beta \)
B \( \cdot \theta=n \pi+(-1)^{n} \alpha, \theta=n \pi+(-1)^{n} 2 \beta \)
c. \( _{\theta=n \pi+(-1)^{n}} \alpha, \theta=n \pi+(-1)^{n} 3 \beta \)
D. \( \theta=n \pi+(-1)^{n} \alpha, \theta=n \pi+(-1)^{n} 4 \beta \)


Which of these is the major air pollutant in cities like Delhi and
Kolkata?
A. Carbon monoxide
B. Hydrocarbons
c. suspended particulate matter
D. Oxides of nitrogen


Prepare a brief speech on global warming, you have to deliver the speech in your class.


A coil of radius \( R \) carries current \( I \).
Another concentric coil of radius \( r(r< \) \( <R) \) carries current \( i . \) Planes of two
coils are mutually perpendicular and both the coil are free to rotate about
common diameter. Find the maximum
kinetic energy of the smaller coil when both the coils are released. Masses of
coils are \( M \) and \( m, \) respectively.


Describe the bonding in \( \boldsymbol{H}_{2} ? \)
A. s-s bonds
B. s-p bonds
c. p-p bonds
D. \( s p^{3}-p \) bonds
E \( \cdot s p^{2}-s p^{2} \) bonds


An ordinary pack of 52 cards is well shuffled. The top card is then turned
over. What is the probability that the top card is a king card.


Which of the following has the highest electronegativity?
A . Na a
B. cl
\( c \cdot k \)
\( D \)


Cell reaction is spontaneous, when:
A \( \cdot E_{r e d}^{o} \) is negative
B \( \cdot E_{r e d}^{o} \) is positive
c. \( \Delta G \) is negative
D. \( \Delta G^{o} \) is positive


\( \int_{0}^{\pi / 2} \log \cot x d x= \)
A .
в. \( \pi \)
c. 0
D. \( \frac{\pi}{2} \)


The shapes and hybridisation of
\( B F_{3} \) and \( B H_{4} \) respectively are:
\( \mathbf{A} \cdot B F_{3}- \) Trigonal, \( s p^{2} \) hybridisation
\( B H_{4}^{-}- \) Square planar, \( s p^{3} \) hybridisation
B. \( B F_{3} \) - Triangular, \( s p^{3} \) d hybridisation
\( B H_{4}^{-}- \) Hexagonal, \( s p^{3} \mathrm{d} \) hybridisation
\( \mathbf{C} \cdot B F_{3}- \) Trigonal, \( s p^{2} \) hybridisation
\( B H_{4}^{-}- \) Tetrahedral, \( s p^{3} \) hybridisation
D. \( B F_{3} \) - Tetrahedral, \( s p^{3} \) hybridisation;
\( B H_{4}^{-}- \) Tetrahedral, \( s p^{3} \) hybridisation.


A pond \( 100 m \) in diameter is
surrounded by a circular grass walk
\( 2 m \) wide. How many square meters of grass is there on the walk?
\( \mathbf{A} \cdot 98 \pi \)
в. \( 100 \pi \)
\( c .204 \pi \)
D. 202\pi


Which force is strongest of all fundamental forces?
A. Weak nuclear force
B. Strong nuclear force
c. Electromagnetic force
D. Gravitational force


Pick out the statement which is not
relevant in the discussion of colloids:
A. sodium aluminium silicate is used in the softening of hard water
B. potash alum is used in shaving rounds and as a styptic in medicine
C. artificial rain is caused by throwing electrified sand on the clouds from an aeroplane
D. deltas are formed at a place when the river pours its water into the sea


Iron nails rust fast when used for fixing plates or strips of aluminium on a building. Similarly, a water pipe made of iron corrodes faster when connected
to a pipe of copper. This happens because of the?
A. Greater wetting of iron
B. Easier flow of electrons to iron
c. Higher rusting power of iron
D. Chemical reduction of iron


Solve \( \int(2 t-4)^{-4} d t \)


Among the following which is least acidic?
A. Phenol
B . o-cresol
c. p-nitrophenol
D. p-chlorophenol


Which of the following statement is true on a scattering of atom according to Rutherfords experiments on the alpha particle ?
A. Atoms are roughly spherical with a radius of about \( 10^{-10} m \)
B. The electrons occupy quantized energy levels absorbing or emitting energy only when they make a quantum jump between these levels
c. The density of positive charge within an atom is not uniform throughout the atoms volume
D. Allowed electron orbits must have a circumference equal to a whole number times the electrons de Broglie wavelength
E. Alpha particles are positively charged


What was the major
contribution/discoveries of
Archimedes?
A. Principle of buoyancy; Principle of the lever
B. Wave theory of light
C. Laws of electromagnetic induction
D. Generation of electromagnetic waves


Given that \( a(a+b)=36 \) and \( b(a+ \)
\( b)=64, \) where \( a \) and \( b \) are positive,
\( (a-b) \) equals:
A . 2.8
B. 3.2
\( c .-2.8 \)
D. - 2.5


Assertion
The regulation of RBC production is
accompanied by the kidneys.
Reason
Erythropoietin hormone criculates to
the
red bone marrow., Where it increase
stem
cell mitosis and speeds up the
development
of RBCS.
A. If both the assertion and the reson are true and the
reason
is correct explanation of the assertion.
B. If both the assertion and the reson are true but the
reason
is not correct explanation of the assertion.
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Assertion
Newton's third law of motion is
applicable only when bodies are in
motion.
Reason
Newton's third law applies to all types of
forces. e.g. gravitational, electric or
magnetic force etc.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Assertion
A balloon filled with hydrogen will fall with acceleration \( \frac{\boldsymbol{g}}{\boldsymbol{6}} \) on the moon.
Reason
Moon has no atmosphere.
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


Given that she is successful, the chance
she studied for 4 hours, is
A \( \cdot \frac{6}{12} \)
в. \( \frac{7}{12} \)
c. \( \frac{8}{12} \)
D. \( \frac{9}{12} \)


Line \( 3 x-4 y=k \) will cut the circle
\( x^{2}+y^{2}-2 x+4 y-11=0 \) at distinct
points, if
A \( \cdot k>\frac{25}{7} \)
в. \( 15<k<30 \)
c. \( -9<k<31 \)
D. None of these


I. Rutherford's gold foil experiment
directed a beam of alpha particles at a thin sheet of gold foil and helped to prove the existence of positively charged particles.
II. Most of the positively charged alpha
particles were able to pass directly through the gold foil.
A. Statement \( I \) is true, Statement \( I I \) is true
B. Statement I is true, Statement II is false
c. Statement \( I \) is false, statement \( I I \) is true
D. Statement I is false, Statement \( I I \) is false


Isobaric bulk modules of elasticity is
\( A \cdot \infty \)
B. 0
\( c . P \)
D. \( \frac{C_{p}}{C_{v}} \)


Velocity-time graph \( A B \) (Fig. 1.2 ) shows
that the body has
A. uniform acceleration
B. uniform retardation
C. uniform velocity throughout its motion and has zer initial velocity
D. none of these


A body rests on a rough horizontal plane. A force is applied to the body directed towards the plane at an angle \( \emptyset \) with the vertical. The body can be moved along the plane
A. Only \( \emptyset \) is more than the angle of friction
B. Only \( \emptyset \) is less than the angle of friction
c. only \( \emptyset \) is equal to the angle of friction
D. For all values of


If \( f(x)=\left\{\begin{array}{cl}x-1, & x \geq 1 \\ 2 x^{2}-2, & x<1\end{array}, g(x)=\right. \)
\( \left\{\begin{array}{cl}\boldsymbol{x}+\mathbf{1}, & \boldsymbol{x}>\mathbf{0} \\ -\boldsymbol{x}^{2}+\mathbf{1}, & \boldsymbol{x} \leq \mathbf{0}\end{array}, \text { and } \boldsymbol{h}(\boldsymbol{x})=|\boldsymbol{x}| \), then \right.
\( \lim _{x \rightarrow 0} f(g(h(x))) \) is
A.
B.
\( c \cdot 2 \)
\( D \)


Molecules possess more energy than the total energy of their combining atoms.
A. True
B. False