The leaves are modified into tendrils,
hooks, pitcher and bladder in the following plants respectively.
A. Sweet pea, cat's nail, Nepenthes, Utricularia
B. Sweet pea, cat's nail, Utricularia, Nepenthes
c. Nepenthes, cat's nail, sweet pea, Utricularia
D. Nepenthes, sweet pea, cat's nail, Utricularia
E. Utricularia, Nepenthes, cat's nail, sweet pea


What is meant by Thermochemical
Equation?


Find out the only wrong statement in
the following:
A. Light travels with a speed greater than that of sound
B. Light cannot travel through vacuum
C. Light travels in a straight line
D. Light has no weight


A lift moves upward with an acceleration of \( 1.2 m s^{-2} . \) Two seconds
after the lift starts, a nail falls from the ceiling of the lift \( 3 m \) above the floor of the lift. Distance of its fall with
reference to the shaft of the lift is
A . \( 0.75 \mathrm{m} \)
B. \( 0.5 \mathrm{m} \)
\( c .1 m \)
D. \( 1.5 m \)


Will the current be time dependent?


Volume of a hollow sphere is \( \frac{11352}{7} \mathrm{cm}^{3} \) If the outer radius is \( 8 \mathrm{cm} \), find the inner
radius of the sphere. (Take \( \pi=\frac{22}{7} \) )


Consider the reactions.
a) \( C H_{3}-C H=C H_{2} \frac{(i) B H_{3} / T H F}{(i i) H_{2} O / O H} \)
\( \frac{P C C}{\left(i n C H_{2} C l_{2}\right)} B \)
b) \( C H_{3}-C H=C H_{2} \frac{(i) H g(O A c)_{2}}{(i i) N a B H_{4} \bar{O} H} \)
\( \boldsymbol{C} \frac{\boldsymbol{P C C}}{\left(\boldsymbol{i n} C \boldsymbol{H}_{2} C l_{2}\right)} \boldsymbol{D} \)
Product B and D are:
A. Functional isomers
B. Positional isomeress
c. chain isomeres
D. Metamers


Two planets, \( A \) and \( B \), orbit a star. Planet A moves in an elliptical orbit whose semi major axis has length a. Planet B moves in an elliptical orbit whose semi major axis has a length of 9a. If planet \( A \) orbits with a period \( T, \) what is the period
of planet Bs orbit?
A. 7297
в. 27 T
\( c \cdot 3 T \)
D. \( T / 3 \)
E. т/27


Shobos mothers present age is six times Shobos present age. Shobos age five years from now will be one third of
his mothers present age. What are their resent ages?
A. Shobos age: 5 years; Shobos mothers age: 30 years
B. Shobos age: 4 years; Shobos mothers age: 24 years
c. Shobos age: 10 years; shobos mothers age: 60 years
D. Shobos age: 1 years; shobos mothers age: 6 years


A very small hole in an electrical
furnace used for treating metal acts nearly as black body. If the hole has an
area \( 100 m m^{2} \) and it is desired to
maintain the metal at \( 727^{\circ} C \), then how
much power travels through the hole?
A. zero
B. 5.7 \( w \)
c. \( 57 \mathrm{w} \)
D. 57 kw


Correct order of stability of group IIA
metal carbonates is :
\( \mathbf{A} \cdot M g C O_{3}>C a C O_{3}>S r C O_{3}>B a C O_{3} \)
B. \( B a C O_{3}>S r C O_{3}>C a C O_{3}>M g C O_{3} \)
\( \mathbf{c} \cdot \operatorname{Sr} C O_{3}>B a C O_{3}>C a C O_{3}>M g C O_{3} \)
\( \mathrm{D} \cdot \mathrm{CaCO}_{3}>\mathrm{MgCO}_{3}>\mathrm{BaCO}_{3}>\mathrm{SrCO}_{3} \)


Which compound is matched up with
its correct name?
This question has multiple correct options
A. CO - monocarbon oxide
B. \( C a F_{2} \) - calcium fluoride
C \( \cdot C C l_{4} \) - carbon tetrachloride
D. \( P C l_{3} \) - potassium trichloride
E . \( T i F_{4}-\operatorname{tin}(I V) \) fluoride


If the energy of an electron in Hydrogen atom is given by expression, \( -1312 / n^{2} k J m o l^{-1}, \) then the energy required to excite the electron from ground state to second orbit is
A \( \cdot 328 k J m o l^{-1} \)
B. \( 656 k J \) mol \( ^{-1} \)
\( \mathbf{c} \cdot 984 k J m o l^{-1} \)
D. \( 1312 k J m o l^{-1} \)


Evaluate the following using suitable
identities
\( (999)^{3} \)


Which of the following quantities are always zero in SHM? This question has multiple correct options
A \( \cdot \vec{F} \times \vec{a} \)
В. \( \vec{v} \times \vec{r} \)
c \( . \vec{a} \times \vec{r} \)
D. \( \vec{F} \times \vec{r} \)


The oscillators that can be described in
terms of sine or cosine functions are
called
A. simple harmonic
B. natural
c. sympathetic
D. free


Identity the correct statements from the
following:
This question has multiple correct options
A. When hot water is poured into a thickly walled glass tumbler suddenly it develops cracks because of unequal expansions of the surfaces.
B. For the use of hot liquids, thin-walled glass containers are preferred
C. A steel disc is fixed tightly in a hole in a brass plate. The disc can be separated by cooling.
D. Bimetallic strip works on the principle of unequal expansions.


If a water particle of mass \( 10 \mathrm{mg} \) and having a charge of \( 1.5 \times 10^{-6} C \) stays
suspended in a room, then the
magnitude and direction of electric field in the room is
A. \( 15 N / C \), vertically upwards
B. 15 N/C, vertically downwards
c. \( 65.3 \mathrm{N} / \mathrm{C} \), vertically upwards
D. \( 65.3 \mathrm{N} / \mathrm{C} \), vertically downwards


In the case of hypermetropia:
A. the image of a near object is formed behind the retina
B. the image of a distant object is formed in front of the retina
C. a concave lens should be used for correction
D. a bifocal lens should be used for correction


Assertion
If the series represented by function
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x}^{4}+\boldsymbol{x}^{\boldsymbol{6}}+\boldsymbol{x}^{\boldsymbol{8}}+\ldots \)
converges, then function \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}] \)
(where [.] denotes the greatest integer function) is continuous at one fixed
point of \( \boldsymbol{f}(\boldsymbol{x}) \)
Reason
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \Rightarrow \boldsymbol{x}^{2}+\boldsymbol{x}-\mathbf{1}=\mathbf{0} \) which
gives two fixed points.
A. If both assertion and reason are correct and reason is the correct explanation of the assertion
B. If both assertion and reason are correct but reason is not correct explanation of the assertion
c. If assertion is correct, but reason is incorrect
D. If assertion is incorrect, but reason is correct


Basic principle of hydrogen economy is:
A. transportation of energy in the form of liquid or gaseous dihydrogen
B. storage of energy in the form of liquid or gaseous dihydrogen
\( c \cdot \operatorname{both} A \) and \( B \)
D. none of the above


Which of the following activity causes water depletion?
A. Increasing population
B. Increasing industries
c. Agricultural activities
D. All of the above


Which of the following compounds is reasonable for the transmission of hereditary characters?
A. RNA
B. DNA
c. Glucose
D. Haemoglobin


In which of the following form is the food stored in animal body?
A. Glucose
B. Glycogen
c. Cellulose
D. ATP


A root of the equation \( (x-1)(x- \)
2) \( =\frac{30}{49} \) is
A \( -\frac{17}{7} \)
B. \( \frac{15}{7} \)
c. \( \frac{13}{7} \)
D. \( \frac{11}{7} \)


After reflection from a concave mirror, a plane wavefront becomes
A. Cylindrical
B. Spherical
c. Remains planar
D. None of the above


A simple harmonic oscillation has an amplitude \( A \) and time period \( T . \) The time required to travel from \( \boldsymbol{x}=\boldsymbol{A} \) to
\( \boldsymbol{x}=\frac{\boldsymbol{A}}{2} \) is :
A \( \cdot \frac{T}{6} \)
в. \( \frac{T}{4} \)
c. \( \frac{T}{3} \)
D. \( \frac{T}{12} \)


Sn denotes the sum of first \( n \) terms of
the A.P.1 \( , 2,3,4, \dots . ., \) then \( S_{2 n}=3 S n \)
\( \frac{\boldsymbol{S}_{\boldsymbol{3 n}}}{\boldsymbol{S} \boldsymbol{n}}=? \)


Which mixture of the solution will lead
to the formation of negatively charged
colloidal \( [\boldsymbol{A} \boldsymbol{g} \boldsymbol{I}] \boldsymbol{I}^{-} \) sol?
A. \( 50 m L \) of \( 1 M A g N O_{3}+50 m L \) of \( 1.5 M K I \)
B. \( 50 m L \) of \( 1 M A g N O_{3}+50 m L \) of \( 2 M K I \)
C. \( 50 m L \) of \( 2 M A g N O_{3}+50 m L \) of \( 1.5 K I \)
D. \( 50 m L \) of \( 0.1 M A g N o_{3}+50 m L \) of \( 0.1 M K I \)


The principal nitrogenous excretory compound in humans is synthesized
\( \mathbf{A} \cdot \) In the liver, but eliminated mostly through kidneys.
B. In kidneys, but eliminated mostly through liver.
C. In kidneys as well as eliminated by kidneys.
D. In liver and also eliminated by the same through bile.


Solve: \( 6 x-1=2 x+9 \)
A \( \cdot 1 \frac{1}{2} \)
в. \( -2 \frac{1}{2} \)
c. \( \frac{4}{10} \)
D. \( _{2} \frac{1}{2} \)


Find the measure of \( \angle P, \) if \( \overline{S P} \| \overline{R Q} \) in
the given figure.


If 4 men or 6 women earn Rs 360 in one
day, then find how much less does a woman earn in one day than men.
A. Rs 20
B. Rs 30
c. Rs 40
D. Rs 35


Assuming that water vapour is an ideal
gas, the internal energy change \( (\Delta U) \) when 1 mol of water is vaporised at 1
bar pressure and \( 100^{\circ} \mathrm{C} \) will be:
(Given: Molar enthalpy of vapourisation of water at 1 bar and \( 373 K= \)
\( 41 k J . m o l^{-1} \) and \( R=8.3 J m o l^{-1} K^{-1} \)
A \( \cdot 4.100 k J \) mol \( ^{-1} \)
В. 3.7904 k J \( \mathrm{mol}^{-1} \)
c. \( 37.904 k J \) mol \( ^{-1} \)
D. \( 41.00 \mathrm{kJ} \mathrm{mol}^{-1} \)


The difference between \( \Delta H \) and \( \Delta E \)
(on a molar basis) for the combustion of n-octane (I) at 25C would be :
A. \( -13.6 \mathrm{kJ} \)
The \( -13.6 \mathrm{c} \).
B . - 1.14 k
c. - 11.15 k
D. \( +11.15 \mathrm{kJ} \)


The number of solutions of the
equation, \( 2\{x\}^{2}+5\{x\}-3=0 \) is
A. No solution
B.
\( c \cdot 2 \)
D. Infinite


The quantity of heat which can rise the
temperature of \( x \) gm of a substance
through \( t_{1}^{o} C \) can rise the temperature of
y gm of water through \( t_{2}^{o} C \) is same. The ratio of specific heats of the substances
is:
A \( \cdot y t_{1} / x t_{2} \)
B. \( x t_{2} / y t_{1} \)
c. \( y t_{2} / x t_{1} \)
D. \( x t_{1} / y t_{2} \)


The general solution of differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\frac{\boldsymbol{x}+\boldsymbol{y}}{\boldsymbol{x}-\boldsymbol{y}} \) is


Which of these is obtained by electrolytic reduction of its compound?
A. \( C u \)
в. \( A u \)
\( \mathrm{c} \cdot M g \)
D. \( B i \)


What are the uses of sodium
bicarbonate? (Any three)


Calculate the number of nitrogen bases in E.coli, if the length of E.coli DNA is 1.36
\( \mathrm{mm} \)
A \( \cdot 4 \times 10^{6} \)
B. \( 8 \times 10^{6} \)
\( c \cdot 2 \times 10^{6} \)
D. \( 16 \times 10^{6} \)


A rigid diatomic ideal gas undergoes an adiabatic process at room temperature,. The relation between
temperature and volume of this process
is \( \boldsymbol{T} \boldsymbol{V}^{\boldsymbol{x}}= \) constant, then \( \boldsymbol{x} \) is :
A \( \cdot \frac{5}{3} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{3}{5} \)


Number of aromatic rings in ferrocene
is


The depression in freezing point is 0.24 K obtained by dissolving 1 gram kel in 200 gram water, calculate Van't Hoff
factor. The molal depression constant is \( 1.86 \mathrm{K} \mathrm{kg} \) mole\( ^{-1} \)


Which of the following is not peroxide?
A. \( N a H O_{2} \)
в. \( B a O_{2} \)
с. \( N a_{2} O_{2} \)
D. \( P b O_{2} \)


Define Friction:


How many significant figures are present in \( 7 \times 2.232 ? \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. 3
\( c \cdot 4 \)
D.


What does a neutron decays to?
\( \mathbf{A} \cdot \) one \( p, \) one \( v \) one \( \beta^{+} \)
B. one \( \beta+, \) one \( \beta- \) and \( v \)
C . one \( p \), one \( \beta^{-} \) and one \( \bar{v} \)
D. all the above


Three fuse wires \( A, B \) and \( C \) tinned
copper having identical cross section and length \( 8 \mathrm{cm}, 12 \mathrm{cm} \) and \( 16 \mathrm{cm} \) are
used as fuses. For the same value of
current
A. fuse A will melt first
B. fuse B will melt first
c. fuse C will melt first
D. all fuse will melt for same current


State whether the given statement is
True or False :

A block of mass \( M \) is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force \( \boldsymbol{F} \). The kinetic
energy of the block increases by \( 40 \mathrm{J} \) in
1 \( s . \) The tension in the string is \( F \)
A . True
B. False


The hybrid orbitals with \( 33.33 \% \) Scharacter are involved in the bonding of one of the crystalline allotropes of carbon. The allotrope is :
A. carbon black
B. Graphite
c. Diamond
D. Gas carbon


Q Type your question
following apparatus was set up. Which
among the following statement(s)
is(are) correct?
(i) Bulb will not glow because electrolyte is not acidic.
(ii) Bulb will glow because NaOH is a strong base and furnishes ions for
conduction.
(iii) Bulb will not glow because circuit
is incomplete.
(iv) Bulb will not glow because it
depends upon the type of electrolytic
solution.
\( A \cdot \) (i) and (iii)
B. (ii) and (iv)
c. (ii) only
D. (iv) only


The Sl unit of pressure gradient is
A. \( N m^{-2} \)
в. \( N m \)
\( \mathbf{c} \cdot N m^{-1} \)
D. \( N m^{-3} \)


Two soaps bubbles (surface tension \( \boldsymbol{T} \) )
coalesce to form a big bubble under isothermal condition. If in this process the change in volume be \( V \) and the
surface area be \( S, \) then the correct
relation is \( (P \) is atmospheric pressure):
A. \( P V+T S=0 \)
в. \( 3 P V+4 T S=0 \)
c. \( 3 P V+T S=0 \)
D. \( 4 P V+3 T S=0 \)


In gymnosperms, pollen drop is the
A. Red drop
B. Pollens dropped by wind
c. Secretion of nucellus
D. water drops


Thomson proposed the model of an
atom similar to :
A. christmas tree
B. christmas pudding
c. chocolate
D. none of the above


Consider the equation:
\( \boldsymbol{y}+\mathbf{7} \boldsymbol{x}=\mathbf{3} \boldsymbol{x}-\mathbf{2} \boldsymbol{y}+\mathbf{2 8} \)
f \( \boldsymbol{y}=\mathbf{2}, \) what is the value of \( \boldsymbol{x} \) ?
\( \mathbf{A} \cdot \mathbf{5} \)
B. 5.5
\( c \cdot 6 \)
D. 6.5


A sphere \( ^{\prime} \boldsymbol{P}^{\prime} \) of mass \( ^{\prime} \boldsymbol{m}^{\prime} \) moving with
velocity \( ^{\prime} u^{\prime} \) collides head-on with
another sphere \( ^{\prime} Q^{\prime} \) of mass \( ^{\prime} m^{\prime} \) which is at rest. The ratio of final velocity of \( ^{\prime} Q^{\prime} \)
to initial velocity of \( ^{\prime} \boldsymbol{P}^{\prime} \) is
\( (e=\operatorname{coefficient} \) of restitution)
A \( \cdot \frac{e-1}{2} \)
B. \( \left[\frac{e+1}{2}\right]^{1 / 2} \)
c. \( \frac{e+1}{2} \)
D. \( \left[\frac{e+1}{2}\right]^{2} \)


A eukaryotic gene contains two kinds of base sequences.Which of these plays an important role in protein synthesis?
A. Introns
B. Exons
c. Both A and B
D. None of the above


A \( 500 \mu F \) capacitor is charged at a
steady rate of \( 100 \mu C / \) sec. The potential difference across the capacitor will be
\( 10 V \) after an interval of
\( \mathbf{A} \cdot 5 \) sec
B. 20 sec
c. 25 sec
D. 50 sec


Energy released in the nuclear fusion
reaction is :
\( _{1} \mathbf{H}^{2}+_{1} \mathbf{H}^{3} \rightarrow_{2} \mathbf{H} \mathbf{e}^{4}+_{0} \mathbf{n}^{1} \)
Atomic mass of some species are given
below.
\( _{1} \mathbf{H}^{2}=\mathbf{2 . 0 1 4},_{1} \mathbf{H}^{3}=\mathbf{3 . 0 1 6} \)
\( _{2} \mathbf{H e}^{4}=\mathbf{4 . 0 0 3},_{0} \mathbf{n}^{1}=\mathbf{1 . 0 0 9} \mathbf{a m u} \)
A . \( 8.30 \mathrm{eV} \)
B. \( 16.758 \mathrm{MeV} \)
c. \( 500 \mathrm{J} \)
D. \( 4 \times 10^{6} \) kcal


If \( x+3 \) is the geometric mean between \( x \) +1 and \( x+6 \) then find \( x \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D.


Which energy state of a doubly ionized
lithium \( \left(L i^{++}\right) \) has the same energy as
that of the ground state of hydrogen \( z=3, \) for lithium):
\( \mathbf{A} \cdot n=1 \)
B. \( n=2 \)
\( \mathbf{c} \cdot n=3 \)
D. \( n=4 \)


Examine the functions for continuity:
\( f x=\left\{\begin{array}{ll}\frac{\sin 2 x}{\sin 3 x}, & \text { when } x \neq 0 \\ 2, & \text { when } x=0\end{array} \text { at } x=0\right. \)


Find the common difference of the A.P.
and write the next two terms.
\( \mathbf{5 1}, \mathbf{5 9}, \mathbf{6 7}, \mathbf{7 5}, \dots \dots \)


A particle starts moving from point \( (2, \)
10,1)\( . \) Displacement for the particle is 8 \( \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\boldsymbol{k}} . \) The final coordinates of the
particle is
A. (10,8,2)
)
в. (8,10,2)
\( c \cdot(2,10,8) \)
D. (8,2,10)


The order and degree of the differentia equation \( y=\frac{d y}{d x} x+\sqrt{a^{2}\left(\frac{d y}{d x}\right)^{2}+b^{2}} \)
is
\( A \cdot 3,1 \)
в. 1,3
\( c .2,1 \)
D. 1,2


Give the composition and functions of
CSF.


If the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{1-\cos 4 x}{x^{2}} & \text { if } x<0 \\ a & \text { if } x=0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}-4}} & \text { if } x>0\end{array}\right. \)
is continuous at \( x=0 \) then \( a= \)
\( \mathbf{A} \cdot \mathbf{8} \)
B.
\( c .-8 \)
\( D \)


Differentiate \( \frac{x^{2}-1}{x} \) w.r.t \( x \)


The existence of isotopes violated which one of the postulates of Dalton's atomic theory?
A. All matter is made of very tiny particles called atoms
B. Atoms of a given element are identical in mass and chemical properties
c. Atoms are indivisible particles and cannot be created nor destroyed
D. Atoms of same elements are alike in all respects


If the lines \( y=m_{1} x+c \) and \( y= \)
\( \boldsymbol{m}_{2} \boldsymbol{x}+\boldsymbol{c}_{2} \) are parallel, then
A. \( m_{1}=m_{2} \)
в. \( m_{1} m_{2}=1 \)
c. \( m_{1} m_{2}=-1 \)
D. \( m_{1}=m_{2}=0 \)


Electrolytic refining is used to purify which of the following metals?
A. Cu and zn
B. Ge and si
c. zrand Ti
D. zn and \( \mathrm{Hg} \)


Constructive interference is the method
of superimposing waves which has a phase difference of \( \pi / 2 \) rads.
A. True
B. False


Two identical uniform discs roll without
slipping on two different surfaces \( A B \) and \( C D \) starting at \( A \) and \( C \) with linear
speed \( v_{1} \) and \( v_{2}, \) respectively, and always remain in contact with the
surfaces. If they reach \( \mathrm{B} \) and \( \mathrm{D} \) with the
same linear speed and \( \boldsymbol{v}_{1}=\mathbf{3} \boldsymbol{m} / \boldsymbol{s} \) then
\( v_{2} \) in \( m / s \) is \( \left(g=10 m / s^{2}\right) \)


Find the area between the region of
parabola \( \boldsymbol{y}^{2}=\mathbf{2} \boldsymbol{x} \) and circle \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}= \)
8


A sample of \( C a C O_{3}(s) \) is introduced
into a sealed container of volume 0.821
litre \( \& \) heated to \( 1000 \mathrm{K} \) until
equilibrium is reached. The equilibrium constant for the reaction \( C a C O_{3}(s) \rightleftharpoons \)
\( \boldsymbol{C a O}(\boldsymbol{s})+\boldsymbol{C O}_{2}(\boldsymbol{g}) \) is \( \boldsymbol{4} \times 10^{-2} \) atm at
this temperature. Calculate the mass of
CaO present at equilibrium.


Gas D that is colourless and can be
used as a bleaching agent. identify the
gas.


Atomic number of an element \( X \) is 16
its group number will be :
A . 14
B . 15
c. 16
D. 17


A uniform triangle of side length \( l \),and
mass \( M \) is rotating about an axis (passing through its one of side) with angular velocity \( \omega \) then its angular momentum is given as \( \frac{M l^{2}}{k} \omega \) then the value of k is


Dyne - second is the unit of:
A. Force
B. Momentum
c. Energy
D. Power


If \( S_{n} \) denotes the sum of \( n \) terms of a
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


An aeroplane flying in the sky
possesses:
A. Kinetic but not Potential Energy
B. Potential but not Kinetic Energy
C. Both Kinetic and Potential energy
D. Neither Kinetic nor potential energy


The phenomenon of radioactivity is associated with:
A. decay of nucleus
B. fussion of nucleus
c. emission of electrons or protons
D. rearrangement in the extra nuclear electron


What is ecosystem? Who coined the
term?


The element having no neutron in the nucleus of its atom is:
A. hydrogen
B. nitrogen
c. helium
D. boron


In the absence of oxygen, plants will
break down sugars into carbon dioxide
and alcohols or acids. This pathway likely arose
A. To get the most out phosphorylation per molecule of pyruvate without the ability to utilize respiration
B. As an alternative process to compete with respiration
c. To regenerate depleted NAD \( ^{+} \)
D. Because of human cultivation


on wow
\( F \)


If \( A^{T}=\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right], \) then find \( A^{T}-B^{T} \)


\( X \) has three children in his family. The
probability of one girl and two boys is......
A \( \cdot \frac{1}{8} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{3}{8} \)


Find a
\( \lim _{\boldsymbol{\theta} \rightarrow \boldsymbol{\pi}} \frac{\sqrt{(\mathbf{2}-\cos \boldsymbol{\theta})}-\mathbf{1}}{(\boldsymbol{\pi}-\boldsymbol{\theta})^{2}} \) is \( =\frac{\mathbf{1}}{\boldsymbol{a}} \)


For \( \boldsymbol{a}<\mathbf{0}, \) arg \( \boldsymbol{a}= \)
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{-\pi}{2} \)
\( c . \pi \)
D. - \( \pi \)


Draw the structural formula of Ethanoic
acid.


In an electrical circuit, which of the
following quantities is analogous to
temperature?
A. Potential
B. Resistance
c. current
D. charge


Which is a monosaccharide among the following?
A. sucrose
B. Cellulose
c. Maltose
D. Glucose


If \( \boldsymbol{y}=\boldsymbol{a} \sin \boldsymbol{x}+\boldsymbol{b} \cos \boldsymbol{x}, \) then \( \boldsymbol{y}^{2}+ \)
\( \left(\frac{d y}{d x}\right)^{2} \)
A. function of \( x \)
B. function of \( y \)
c. function of \( x \) and \( y \)
D. constant


In a thermodynamic system, working substance is ideal gas, its internal energy is in the form of
A. Kinetic energy
B. Kinetic and potential energy
c. Potential energy
D. None of the above


The area of the region bounded by the
parabola \( \boldsymbol{y}=\boldsymbol{x}^{2}-\mathbf{4} \boldsymbol{x}+\mathbf{5} \) and the
straight line \( \boldsymbol{y}=\boldsymbol{x}+\mathbf{1} \) is
A \( \cdot \frac{1}{2} \)
B. 2
\( c \cdot 3 \)
D. \( \frac{9}{2} \)


Which statement is true for
a liquid/gas mixture at equilibrium?
A. The equilibrium constant is dependent on temperature
B. The amount of the gas present at equilibrium is independent of pressure
C. All interchange between the liquid and gas phases has ceased
D. All of the above
E. None of the above


If the wavelength of particle of momentum \( P \) is equal to \( \lambda \), then what
will be its wavelength for momentum
\( \mathbf{1 . 5 P ?} \)
A \( \cdot \frac{2}{3} \lambda \)
в. \( \frac{4}{3} \lambda \)
c. \( \frac{3}{2} \)
D. \( \lambda \)


Find the magnetic moment of the spiral
with a given current.
A \( \cdot p=25 m A \cdot m^{2} \)
B . \( p=15 \mathrm{mA} \cdot \mathrm{m}^{2} \)
C \( \cdot p=30 \mathrm{mA} \cdot \mathrm{m}^{2} \)
D. \( p=50 \mathrm{mA} \cdot \mathrm{m}^{2} \)


Solve:
\( \int \frac{1}{x-x^{3}} d x \)


If velocity of a particle is 3 times of that of electron and ratio of de brogile wavelength of particle to that of
electron is \( 1.814 \times 10^{-4} . \) The particle
will be:-
A. Neutron
B. Deutron
c. Alpha
D. Tritium


A straight steel wire of length \( l \) has
magnetic moment \( m \). If the wire is bent
in the form of a semicircle, the new
value of the magnetic dipole moment is
A . \( m \)
в. \( \frac{m}{2} \)
\( c \cdot \frac{m}{\pi} \)
D. \( \frac{2 m}{\pi} \)


If \( f(x)=\frac{a x+b}{c x+d} \) and \( (f o f)(x)=x \)
then
This question has multiple correct options
A \( \cdot a^{2}+b c=1 \)
B . \( d^{2}+b c=1 \)
\( \mathbf{c} \cdot a+d=0 \)
D. none of these


The circumference of a circle exceeds
its diameter by \( 16.8 \mathrm{cm} . \) Find the radius of the circle.


The sum of magnitudes of two forces
acting at a point is 16 N. If their resultant is normal to the
smaller force and has a magnitude of 8
N, the forces are:
A. \( 6 N, 10 N \)
в. \( 8 N, 8 N \)
c. \( 4 N, 12 N \)
D. \( 2 N, 14 N \)


Polywool is made by blending polyester
and :
A. acrylic
B. rayon
c. cotton
D. wool


\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l} \rightarrow \mathbf{2} \boldsymbol{A l} \boldsymbol{C l}_{3}+\mathbf{3} \boldsymbol{H}_{2}, \) in the
given reaction oxidation state of \( A l C l_{3} \)
is?
\( A \cdot+2 \)
\( B \cdot+3 \)
\( c \cdot+4 \)
D. +5


topp
Q Type your question
A.
3
\( c \)
\( D \)


Fill in the blank.
Concentration of 1 ppm means that 1 solution contains ................ mg solute.


Each carbon atom in the diamond
crystal is strongly linked with:
A. 2 other carbon atoms
B. 3 other carbon atoms
c. 5 other carbon atoms
D. 4 other carbon atoms


OA.OB are the radii of a circle with \( O \)
as centre, the angle \( A O B=120^{\circ} \)

Tangents at \( A \) and \( B \) are drawn to meet
in the point \( C . \) If \( O C \) intersects the circle in the point \( D \), then \( D \) divides
\( O C \) in the ratio
A . 1: 2
B. 1: 3
c. 1: 1
D. 2: 3


The number of amino acids found in
proteins that a human body can
synthesize is:
A \( \cdot 12 \)
B. 10
\( c \cdot 5 \)
D. 14


In a triangle \( A B C, \) the angle bisectors of
angle \( A B C \) and \( A C B \) meet at point \( 0 . \) If \( \angle \)
\( \mathrm{BAC}=32^{\circ}, \) find \( \angle \mathrm{BOC} \)


In the dispersion of white light from a prism, the violet light is deviated more
than the red light because:
A. Velocity of violet rays of light is more
B. Wavelength of violet rays of light is more
c. The frequency of violet rays of light is more
D. The refractive index of prism for violet rays of light is more


Which of the following are the essential things required for rusting?
A. oxygen
B. water
c. both
D. none of the above


Factorise \( a-b-a^{2}+b^{2} \)


Assertion
In the extraction of aluminium by
electrolysis it is necessary to renew the anode periodically.
Reason
Oxygen gas is formed and at high temperature of the electrolysis cell it burns and oxidises away the carbon
electrodes to form toxic carbon
monoxide or carbon dioxide
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


Hydrogen atoms are almost terminal
atoms in Lewis formula.
If true enter 1 , else enter 0 .
\( A \)
B.
\( c \cdot \) both
D. none


Heat exchangers work in the principle of
A. Convection
B. conduction
c. mixed convection
D. Both A and E


Which of the following animals have a lophophore?
A. Waldheimia
B. Wallago
c. wall-lizard
D. Heart-urchin


If \( \mathrm{S} \) is the sample space for the event \( \mathrm{A} \)
then find the correct alternative from
the following:
A \( .0 \geq P(A) \geq 1 \)
B. \( 0 \leq P(A)<1 \)
c. \( 0<P(A) \leq 1 \)
D. \( 0 \leq P(A) \leq 1 \)


What is the name given to a parallelogram whose all sides are equal
\( ? \)


\( \mathbf{4} D_{2} \boldsymbol{O}+\mathbf{3} \boldsymbol{F} \boldsymbol{e} \stackrel{\boldsymbol{R e d} \text {hot}}{\boldsymbol{*}} \boldsymbol{F} \boldsymbol{e}_{3} \boldsymbol{O}_{4}+\boldsymbol{g} \boldsymbol{a} \boldsymbol{s} . \) The
gas produced in the above reaction is:
\( A \cdot O_{2} \)
в. \( H_{2} \)
c. \( D_{2} \)
D. \( T_{2} \)


mark the appropriate choice?
olum \( c \) Sr.No. Column I Column I Cold
II
\( (A) \)
\( C H_{4}(g)+ \)
\( 2 O_{2}(g) \rightarrow \)
\( C O_{2}(g)+ \)
(i) \( \Delta_{s o l} H^{0} \) A \( C U_{2}(g)+ \)
\( H_{2} O \)
(B) (ii) \( \Delta_{\text {lattice}} H^{0} \)
\( (C) \)
\( H_{2} O \)
\( H_{2(g)} \rightarrow \)
\( 2 H_{(g)} \)
\( N a C I_{(s)} \rightarrow \)
\( N a_{(g)}^{+}+ \)
\( C I_{(g)}^{-} \)
\( N a C l_{(g)} \rightarrow \)
\( N a_{(a q)}^{+}+ \)
\( C l_{(a q)}^{-} \) (iii) \( \quad \Delta_{C} H^{0} \)
\( (D) \)
\( r_{i j} \)
\( \mathbf{A} \cdot(A) \rightarrow(i v),(B) \rightarrow(i i i),(C) \rightarrow(i),(D) \rightarrow(i i) \)
B. \( (A) \rightarrow(\text { ii) },(B) \rightarrow(i),(C) \rightarrow(i v),(D) \rightarrow( \text { iii) } \)
\( \mathbf{C} \cdot(A) \rightarrow(i),(B) \rightarrow(i i),(C) \rightarrow(i i i),(D) \rightarrow(i v) \)
\( \mathbf{D} \cdot(A) \rightarrow(\text { iii }),(B) \rightarrow(i v),(C) \rightarrow(i i),(D) \rightarrow(i) \)


\( \frac{\boldsymbol{x}+\mathbf{1}}{(\mathbf{2} \boldsymbol{x}-\mathbf{1})(\mathbf{3} \boldsymbol{x}+\mathbf{1})}=\frac{\boldsymbol{A}}{\mathbf{2} \boldsymbol{x}-\mathbf{1}}+ \)
\( \frac{B}{3 x+1} \Rightarrow 16 A+9 B= \)
\( A \)
B. 5
\( c \cdot 6 \)
\( D \)


An element has atomic number \( 30 . \) Its
cation has 2 units positive charge. How many protons and electrons are present in the cation?


Which of the following belongs to the halogen family?
A. Francium
B. Polonium
c. Radium
D. Astatine


Rickettsiae is a group of
A. Viruses
B. Microorganisms
C. Bacteria
D. PPLO


If one side of a rhombus has end points
(4,5) and (1,1) then find the maximum area of rhombus.


Identify the pairs of ions possessing eq ual spin only magnetic moments:
A. \( C o^{-2}, N i^{+2} \)
B. \( C o^{+2}, C r^{+3} \)
c. \( F e^{+2}, F e^{+3} \)
D. \( F e^{+2}, C r^{+3} \)


Write briefly about the preparation of colloids by chemical methods.


Add the following expressions:
\( \boldsymbol{a}+\boldsymbol{b}-\mathbf{3}, \boldsymbol{b}-\boldsymbol{a}+\mathbf{3}, \boldsymbol{a}-\boldsymbol{b}+\mathbf{3} \)


Which of the following orders is correct regarding the basicity of aliphatic amines?
A \( \cdot C H_{3} N H_{2}>\left(C H_{3}\right)_{2} N H>\left(C H_{3}\right)_{3} N \)
B . \( C H_{3} N H_{2}<\left(C H_{3}\right)_{2} N H<\left(C H_{3}\right)_{3} N \)
c. \( C H_{3} N H_{2}>\left(C H_{3}\right)_{2} N H<\left(C H_{3}\right)_{3} N \)
D. \( C H_{3} N H_{2}<\left(C H_{3}\right)_{2} N H>\left(C H_{3}\right)_{3} N \)


Oxygen can show positive oxidation state in its compounds with:
A. Fluorine
B. Nitrogen
c. Hydrogen
D. Sulphur


The \( (n+1)^{t h} \) term from the end in
\( \left(x-\frac{1}{x}\right)^{3 n} \) is
A. \( 3 n_{n} . . x^{-n} \)
B . \( (-1)^{n} .^{3 n} C_{n} . x^{-n} \)
\( \mathrm{c} \cdot^{3 n} C_{n} \cdot x^{n} \)
D. \( (-1)^{n} .^{3 n} C_{n} . x^{n} \)


A man was infested with germs and
was taken to the hospital. On
pathological tests, it was found that he
had
a. A low number of RBC
b. A high number of WBC and a low
number of RBC
c. A low number of WBC
d. \( A \) high number of platelets Which of the following alternative is
correct?
A. bonly
B. a and d
c. conly
D. donly


A thin circular disk is in the \( x y \) plane as
shown in the figure. The ratio of its
moment of inertia about \( z \) and \( z^{\prime} \) axes
will be
A . 1: 2
B. 1: 4
c. 1: 3
D. 1: 5


An electromagnetic waves can be produced, when charge is
A. Moving with constant velocity
B. Moving in a circular orbit
c. Falling in an electric field
\( D . \) both \( (b) \) and \( (c) \)


Which of the following reagents converts both acetaldehyde and acetone
to alkanes?
A \( . N i / H_{2} \)
в. LiАlH\( _{4} \)
\( \mathbf{c} \cdot I_{2} / N a O H \)
D. zn-Hg/conc. HCI


The dimensions of two wires \( A \) and \( B \)
are the same. But their materials are
different, Their load- extension
graphs are shown. If \( Y_{A} \) and \( Y_{B} \) are the
values of Young's modulus of elasticity
of \( A \) and \( B \) respectively then :
A. \( Y_{A}>Y_{B} \)
В. \( Y_{A}<Y_{B} \)
\( \mathbf{c} \cdot Y_{A}=Y_{B} \)
\( \mathbf{D} \cdot Y_{B}=2 Y_{A} \)


What is the pressure on a swimmer 10 m below the surface of a lake?


The reaction of white phosphorus with
aqueous \( N a O H \) gives phosphine along with another phosphorus containing compound. The reaction type, the oxidation states of phosphorus in phosphine and the other product are, respectively:
A. redox reaction; -3 and -5
B. redox reaction; +3 and +5
c. disproportionation reaction; -3 and +1
D. disproportionation reaction; -3 and +3


Inner bark is composed of
A. Secondary xylem
B. Secondary phloem
\( c . \) cork
D. Phellogen


If \( \sin A=\frac{3}{5} \) and \( A \) is not in the first quadrant then find \( \frac{\cos A+\sin 2 A}{\tan A+\sec A} \)
A \( \cdot \frac{16}{25} \)
в. \( \frac{17}{25} \)
c. \( \frac{22}{25} \)
D. \( \frac{19}{25} \)


\( \left[\begin{array}{ll}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{ll}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right] \)
\( =\left[\begin{array}{ll}a & -b \\ -b & a\end{array}\right] \) then
\( A \cdot a=1 \)
B \( \cdot a=\sec ^{2} \theta, b=0 \)
c. \( a=0, b=\sin ^{2} \theta \)
\( \mathbf{D} \cdot \mathbf{a}=\sin 2 \theta, \mathbf{b}=\cos 2 \theta \)


The figures given show the types of coelom. Identify them and select the correct group of organisms which
possess them.
A. A - Annelids, B - Aschelminthes, C - Platyhelminthes
B. A - Molluscs, B - Arthropods, C - Platyhelminthes
c. A - Echinoderms, B - Aschelminthes, C - Annelids
D. A - Echinoderms, B - Arthropods, C - Platyhelminthes


Transpiration occurs through
A. Leaves
B. Stem
c. Roots
D. None of the above


If the activation energies of the forward and backward reactions of a reversible
reaction are \( \boldsymbol{E}_{\boldsymbol{a}}(\boldsymbol{f}) \) and \( \boldsymbol{E}_{\boldsymbol{a}}(\boldsymbol{b}) \)
respectively. The \( \Delta E \) of the reaction is
A \( \cdot E_{a}(F)-E_{a}(b) \)
B . \( E_{a}(F)+E_{a}(b) \)
\( \mathbf{c} \cdot E_{a}(F)=E_{a}(b) \)
D. \( -E_{a}(F)+E_{a}(b) \)


The elements of one period are given below in order from left to right
\( \boldsymbol{L} \boldsymbol{i}, \boldsymbol{B} \boldsymbol{e}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{O}, \boldsymbol{F}, \boldsymbol{N} \boldsymbol{e} \)
Which is the missing element?
A . Na a
B.
c. \( c 1 \)
\( D \)


Kidneys are not only organs of excretion. Their work is supplemented
by
A . Liver
B. Heart
c. Large intestine
D. skin


Name the polymer which is used for making non-stick utensils.


Product of two integers with unlike
signs is -
A. 0
B. Positive
c. Negative
D. None of these


\( \beta \) -pleated sheet structure of
polypeptide contains:
A. intermolecular hydrogen bonds
B. intramolecular hydrogen bonds
\( c . \) both \( A \) and \( B \)
D. none of these


Conversion of \( S O_{2} \) to \( S O_{3} \) requires \( P t \)
or \( V_{2} O_{5} \) as catalyst
A. True
B. False


A transverse sine wave of amplitude 10cm and wavelength 200cm travels from left to right along a long horizontal stretched string with a speed of 100cm / s. Take the origin at left end of the string. At time \( t=0 \), the left end of
the string is at the origin and is moving downward. Then the equation of the wave will be (in C.G.S. system)
A. \( 10 \sin (0.01 \pi x-\pi t) \)
В. \( 10 \sin (0.02 \pi x-\pi t) \)


State whether the following sequence is an Arithmetic Progression or not. \( \mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{2 4}, \dots \dots \)


For the arrangement shown in fig., the
force at the bottom
of the vessel is
A. 200 N
B. 100 N
c. \( 20 \mathrm{N} \)
D. 2


\( \operatorname{Let} \boldsymbol{y}=\log \sin \left(\boldsymbol{x}^{2}\right), \boldsymbol{0}<\boldsymbol{x} \leq \frac{\boldsymbol{\pi}}{2} . \) The
value of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) at \( \boldsymbol{x}=\frac{\sqrt{\boldsymbol{\pi}}}{\boldsymbol{2}} \) is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. 1
c. \( \frac{\pi}{-4} \)
D. \( \sqrt{\pi} \)


Evaluate:
\( \int \sqrt{x^{2}+4 x+5} d x \)


Sl unit of Magnetic flux is weber and its CGS unit is maxwell. Then \( 1 \mathrm{Wb}= \)
A \( \cdot 10^{6} \) maxwel
B . \( 10^{7} \) maxwell
c. \( 10^{8} \) maxwell
D. \( 10^{9} \) maxwell


Assertion
Combining equal volumes of \( 0.2 M \)
\( A g N O_{3}, \) and \( 0.2 M H C l \) does not
produce a precipitate of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
Reason
The silver ion is rapidly reduced to silver metal, producing chlorine gas.
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


Solve: \( 2 A-B=-2 C \) and
\( \boldsymbol{A}-\boldsymbol{B}=-\boldsymbol{C} \)
Find \( A \) and \( B \).


Five charges of magnitudes
\( 24 \mu C,-25 \mu C, 3 \mu C,-7 \mu C \) and \( 28 \mu C \)
are situated along the circumference of
a circle of radius \( 3 \mathrm{cm} \). Then the
potential at the centre of the circle is
A \( .54 \times 10^{7} V \)
В. \( 45 \times 10^{6} V \)
\( \mathbf{c} \cdot 72 \times 10^{6} V \)
\( \mathbf{D} \cdot 69 \times 10^{5} V \)


Write the common name and IUPAC
name of the following.
(a) \( C H_{3} C H_{2} C H O \)
(b) \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \)
\( (c) C H_{3}-\underset{\mid O H}{C} H-C H_{3} \)
(d) \( C H_{3} C O O H \)
(e) \( H C H O \)


When the road is dry and coefficient of friction is \( \mu, \) the maximum speed of a
car in a circular path is \( 10 \mathrm{ms}^{-1} \). If the road becomes wet and coefficient of friction become \( \frac{\mu}{2}, \) what is the maximum speed permitted?


Which forms maximum compounds with Xenon?
A.
B. Cl
\( c \cdot B r \)
\( D \)


Stomata in grass leaf are
A. Rectangular
B. Kidney shaped
c. Dumb-bell shaped
D. Barre shaped


At certain temperature, \( 50 \% \) of \( H I \) is
dissociated into \( H_{2} \) and \( I_{2} \). Then the
equilibrium constant is:
A . 1.0
B. 3.0
\( c \cdot 0.5 \)
D. 0.25


Express each of the following without using decimals:
\( 8.354 k g \)


Hilswer untulury quesuuris Na>tu
on the following.
\( C_{1} \) and \( C_{2} \) are two circles and points
\( \boldsymbol{P}_{1}, \boldsymbol{P}_{2}, \boldsymbol{P}_{3}, \boldsymbol{P}_{4}, \boldsymbol{P}_{5} \) are noted. From which
point tangent is possible to \( C_{2} \) but not
\( C_{1} \)
\( A \cdot P_{2} \)
в. \( P_{3} \)
\( c \cdot P_{4} \)
D. \( P_{5} \)


Can an object possess translatory and rotatory motion at the same time? Give
an example.


Complete the following sentence:
The kinetic energy of a body is the energy by virtue of its
A . force
B. motion
c. roughness
D. all the above


Isobars have same mass numbers
becausetheir nuclei contain
equalnumber of
A. protons
B. electrons
c. neutrons
D. nucleons


The outlets in your home provide.
A. Direct current
B. Alternating current
C. Electric discharge
D. Static Electricity


Which of the following are done to
increase friction?
A. Greasing the machines
B. Treading the tyres
c. sprinkling powder on the carom board
D. All of the above


\( \ln H_{3} P O_{3}, \) hybridisation of \( P \) atom is :
\( A \cdot s p \)
B. \( s p^{2} \)
\( c \cdot s p^{3} \)
D. \( s p^{3} d \)


State True or False.
Hydraulic press is used in the extraction of oil from oil seeds.
A. True
B. False


The number of ways in which 10
candidates \( A_{1}, A_{2}, \dots, A_{10} \) can be
ranked so that \( A_{1} \) is always above \( A_{2} \)
is:-
A \( \cdot \frac{10 !}{2} \)
B . \( 2^{7} 3^{4} 5^{2} 7^{1} \)
\( \mathbf{c} \cdot 2^{8} 5^{2} \)
D. \( 3^{4} 5^{2} 7 \)


If \( A \) and \( B \) are events such that \( P(A)= \) \( \frac{1}{2}, P(B)=\frac{1}{3} \) and \( P(A \cap B)=\frac{1}{4}, \) then
find \( \boldsymbol{P}(\boldsymbol{A} / \boldsymbol{B}) \)


What will happen if the reverberation time in a big hall is too long?
A. sound persists for some time in the hall.
B. the reflection may become an echo.
C. multiple reflection occurs
D. all


\( \int_{0}^{1} \frac{\sin x+\cos x}{\sqrt{1+\sin 2 x}} d x \)


If force, acceleration and time are taken
as fundamental quantities, then the dimensions of length will be
A. \( F T^{2} \)
B . \( F^{-1} A^{2} T^{-1} \)
c. \( F A^{2} T \)
D. \( A T^{2} \)


A short bar magnet placed with its axis at \( 30^{0} \) with a uniform external magnetic
field of \( 0.35 T \) experiences a torque of magnitude equal to \( 4.5 \times 10^{-2} \mathrm{N} \) m. The
magnitude of magnetic moment of the given magnet is
A \( \cdot 26 J T^{-1} \)
B . \( 2.6 J T^{-1} \)
c. \( 0.26 J T^{-1} \)
D. \( 0.026 J T^{-1} \)


Which of the following statements is
not correct from the view point of
molecular orbital theory?
\( \mathbf{A} \cdot B e_{2} \) is not a stable molecule.
B. \( H e_{2} \) is not stable but \( H e_{2}^{+} \) is expected to exist.
C. Bond strength of \( N_{2} \) is maximum amongst the homonuclear diatomic molecules belonging to the second period.
D. The order of energies of molecular orbitals in \( N_{2} \) molecule is \( \sigma 2 s<\sigma * 2 s<\sigma 2 p_{z}<\left(\pi 2 p_{x}=\pi 2 p_{y}\right)< \)
\( \left(\pi * 2 p_{x}=\pi 2 p_{y}\right)<\sigma * 2 p_{z} \)


Radioactivity of an isotope falls to \( 1 / 8 \) of its original value in 48 days. What is its half-life period (in days)?
A . 48
B . 16
\( c \cdot 12 \)
D.


Assertion
\( (A): \) Let \( n \in N \)
\( \boldsymbol{p}(\boldsymbol{n})=\boldsymbol{n}(\boldsymbol{n}+1) \) is an even number
Reason
(R): Product of two consecutive natural
numbers is even.
A. Both (A) \& (R) are individually true \&
(R) is correct explanation of (A),
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A)is true but (R) is false
D. (A)is false but (R) is true


A coating of zinc is deposited on iron to protect it from
A . rain
B. corrosion
c. sun
D. none of these


Fill in the blanks using the appropriate words given below:
(Sulphur dioxide, Nitrogen dioxide, Nitric oxide, Sulphuric acid)
(i) Cold, dilute nitric acid reacts with
copper to give
(ii) Hot, concentrated nitric acid reacts
with sulphur to form


Assume that a molecule is moving with the root mean square speed at temperature \( 300 \mathrm{K} \). The de Broglie wavelength of nitrogen molecule is (Atomic mass of nitrogen \( =14.0076 \mathrm{u}, \mathrm{h} \) \( =\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{J} \boldsymbol{s}, \boldsymbol{k}_{\boldsymbol{B}}=\mathbf{1 . 3 8} \times \)
\( \mathbf{1 0}^{-\mathbf{2 3}} \boldsymbol{J} \boldsymbol{K}^{-\mathbf{1}}, \mathbf{1} \boldsymbol{u}=\mathbf{1 . 6 6} \cdot \times \mathbf{1 0}^{-\mathbf{2 7}} \boldsymbol{k} \boldsymbol{g} \)
\( \mathbf{A} \cdot 2.75 \times 10^{-11} m \)
В. \( 2.75 \times 10^{-12} m \)
c. \( 3.24 \times 10^{-11} \mathrm{m} \)
D. \( 3.24 \times 10^{-12} \mathrm{m} \)


The water can be made to boil even at 0
if the pressure of surrounding is:
\( A .56 \mathrm{cm} \) of \( \mathrm{Hg} \)
B. \( 5 \mathrm{cm} \) of \( \mathrm{Hg} \)
c. \( 0.1 \mathrm{cm} \) of \( \mathrm{Hg} \)
D. \( 4.6 \mathrm{mm} \) of \( \mathrm{Hg} \)


Rate of heart beat in frog is
A. 72 times per minute
B. 75 times per minute
c. 50 times per minute
D. 64 times per minute


The displacement \( x \) of a particle at time t is given by \( \boldsymbol{x}=\boldsymbol{A} \boldsymbol{t}^{2}+\boldsymbol{B} \boldsymbol{t}+\boldsymbol{C} \) where \( \boldsymbol{A} \)
B, \( C \) are constants and \( v \) is velocity of a particle, then the value of \( 4 A x-v^{2} \) is:
\( \mathbf{A} \cdot 4 A C+B^{2} \)
В. \( 4 A C-B^{2} \)
c. \( 2 A C-B^{2} \)
D. \( 2 A C+B^{2} \)


The ratio of molecular mass of two
radioactive substances is \( 3 / 2 \) and the ratio of their decay constant is \( 4 / 3 \) Then, the ratio of their initial activity per mole will be
A . 2
в. \( \frac{8}{9} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{9}{8} \)


Match the physical property (in List I) with unit (in List II) :
\( \begin{array}{ll}\text { List-I } & \text { List-II } \\ \text { a) Viscosity } & \text { i) } \mathrm{Jm}^{-2} \\ \text {b) Surface tension } & \text { ii) } \mathrm{Nm}^{-1} \\ \text {c) Surface energy } & \text { iii) } \mathrm{Kg} \mathrm{m}^{-1} \mathrm{s}^{-1} \\ \text {d) Vapour pressure } & \text { iv) atm }\end{array} \)
A. a - iii, b-ii, c-i, d-iv
B. a-iv, b-ii, c-i, d-iii
c. a-i, b-iv, c-iii, d-ii
D. a-ii, b-iv, c-i, d-iii


The capacity of a parallel plate capacitor with no dielectric substance
but with a separation of \( 0.4 \mathrm{cm} \) is \( 2 \mu F \)
If the separation is reduced to half and it is filled with a dielectric substance of
value \( 2.8, \) then the final capacity of the
capacitor is
A \( .11 .2 \mu F \)
в. \( 15.6 \mu F \)
c. \( 19.2 \mu F \)
D. 22.4 \( \mu F \)


The area of the circle whose centre is
(1,2) and which passes through the point (4,6) is
A \( .25 \pi \)
в. \( 100 \pi \)
c. \( 92 \pi \)
D. None of these


If \( \boldsymbol{x}^{m}+\boldsymbol{y}^{m}=\mathbf{1} \) such that \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=-\frac{\boldsymbol{x}}{\boldsymbol{y}} \)
then what should be the value of \( m ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. None of the above


The portion of heart which doesn't
receive proper blood supply becomes
A. Strong
B. Dead
c. weak
D. Diseased


In half-wave rectification, what is the
output frequency if the input frequency
is \( 50 H z \)

What is the output frequency of a fullwave rectifier for the same input
frequency.


The equation of the line which is parallel to \( 3 \cos \theta+4 \sin \theta+\frac{5}{r}=0 \)
\( \cos \theta+4 \sin \theta+\frac{10}{r}=0 \) and
equidistant from these lines is
\( ^{\mathbf{A}} \cdot_{3 \cos \theta}+4 \sin \theta-\frac{5}{r}=0 \)
B. \( 3 \cos \theta+4 \sin \theta+\frac{15}{r}=0 \)
c. \( 6 \cos \theta+8 \sin \theta+\frac{15}{r}=0 \)
D. \( 6 \cos \theta+8 \sin \theta-\frac{15}{r}=0 \)


Find the speed of two objects if, when they move uniformly towards each other they get 4 m closer in every sec and when they move uniformly in the same direction with their original speeds,
they get \( 4 \mathrm{m} \) closer every \( 10 \mathrm{s} \)
A. \( 1.8 \mathrm{m} / \mathrm{s}, 1.6 \mathrm{m} / \mathrm{s} \)
B. 2 \( \mathrm{m} / \mathrm{s}, 1.8 \mathrm{m} / \mathrm{s} \)
c. \( 2.2 \mathrm{m} / \mathrm{s}, 1.8 \mathrm{m} / \mathrm{s} \)
D. \( 1.6 \mathrm{m} / \mathrm{s}, 1.4 \mathrm{m} / \mathrm{s} \)


In the estimation of nitrogen, the kjeldahlised liquid is heated with:
A \( . \) conc.H \( \mathrm{NO}_{3} \)
в. сопс. \( H_{2} S O_{4} \)
c. conc. \( H C l \)
D. conc. NaOH


How many organisms in the list given below are autotrophs? Lactobacillus, Nostoc, Chara, Nitrosomonas Nitrobacter, Streptomyces, Sacharomyces Trypanosoma, Porphyra, Wolfia
A . Five
B. Six
c. Three
D. Four


The vapour pressure of pure water at 25
\( ^{o} \mathrm{C} \) is 23.76 torr. The vapour pressure of a solution containing 5.40 g of a nonvolatile substance in 90.0 g water in 23.32 torr. Compute the molecular weight of the solute
A. 58.82 g/mol
B. \( 58.20 \mathrm{g} / \mathrm{mol} \)
c. 59.25 g/mol
D. \( 60.24 \mathrm{g} / \mathrm{mol} \)


Give reasons for the following:
Iron is rendered passive with fuming nitric acid.


Which of the following is true for pupil?
a. It regulates and controls the amount of light entering the eye.
b. It opens completely when the iris is relaxed.
c. Iris controls the expansion and contraction of the pupil.
d. Bright light causes the pupils to contract and dim light causes it to relax.
A. a and
B. b and c
\( c . \) a and \( c \)
D. all of the above


Find the moment of inertia of a solid
cylinder of mass \( M \) and radius \( R \) about a line parallel to the axis of the cylinder
and on the surface of the cylinder.


For transistor action, state which statements are true:
(1) Base, emitter and collector regions should have similar size and doping concentrations.
(2) The base region must be very thin and lightly doped.
(3) The emitter-base junction is forward
biased and base-collector junction is reverse biased
(4) Both the emitter-base junction as well as the base-collectorjunction are
forward biased
\( A \cdot(4) \) and (1)
B. (1) and (2)
c. (2) and (3)
\( D \cdot(3) \) and (4)


Solve \( \int_{\pi / 2}^{3 \pi / 2}[2 \sin x] d x \)


The number of unpaired electrons in a paramagnetic diatomic molecule of an element with atomic number 16 is:
A . 1
B . 2
\( c .3 \)
D. 4


Choose the correct answers from the
alternatives given:
Select the true statement
A. glycolysis produces equal numbers of ATP molecules regardless of the presence or absence of oxygen
B. more ATP molecules are produced per molecule of glucose when glycolysis occurs in aerobic conditions
C. more ATP molecules are produced per molecule of glucose wvhen glycolysis occurs in anaerobic conditions
D. none of the above are true


Escape velocity at surface of earth is
11.2Km/s. Escape valocity from a planet whose mass is the same as that of earth and radius \( 1 / 4 \) that of earth, is?
A \( .2 .8 \mathrm{km} / \mathrm{s} \)
B. \( 15.6 \mathrm{km} / \mathrm{s} \)
c. \( 22.4 \mathrm{km} / \mathrm{s} \)
D. \( 44.8 \mathrm{km} / \mathrm{s} \)


The capacitive time constant of the RC
circuit shown in the figure is:
A. zero
B. infinity
\( c \cdot 2 s \)
D. 2 \( \mu \) s


Let \( \boldsymbol{A}=\boldsymbol{R}_{0} \times \boldsymbol{R}, \) where \( \boldsymbol{R}_{0} \) denote the
set of all non-zero real numbers. A
binary operation ' \( O^{\prime} \) is defined on \( A \) as follows: \( (a, b) O(c, d)=(a c, b c+d) \) for
all \( (a, b)(c, d) \in R_{0} \times R \)
Find the identity element in \( \boldsymbol{A} \)


Formaldehyde is a liquid at room
temperature.
A. True
B. False


Write the units digit of the cube for
\( \mathbf{5 9 2 2} \)
A . 8
B. 4
\( c .6 \)
D. none of these


One drop of methyl orange solution
when added to the solution obtained
after electrolysis of a concentrated solution of NaCl with Pt electrodes, the
colour of the solution will turn:
A . orange
B. pink
c. yellow
D. colourless


Which of the following helps in the release of water vapour in the plant?
A. Stomata
B. Lenticels
c. Epidermis
D. None of the above


What is the role of graphite rod in the electrometallurgy of aluminium?


Assertion
Old ladies are prone to osteoporosis.
Reason
Oestrogen at menopause also maintains calcium balance in the
bones and blood.
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


Which of the following factors may be
regarded as the main cause of
lanthanide contraction?
A. Greater shielding of 5 d-electron by 4 f-electrons
B. Poor shielding of 5 d-electron by 4 f-electrons
c. Effective shielding of one 4 f-electrons by another in the subshel
D. Poor shielding of one of 4-electrons by another in the subshell


Who is the founder of the law of triads?


Which of the following quantities changes during the process of scattering?
A. speed.
B. Wavelength.
c. Direction of propagation.
D. None of the above


A block has been placed on an inclined plane with the slope angle \( \theta \), block slide down the plane at constant speed. The coefficient of kinetic friction is equal to:
A \( . \sin \theta \)
B. \( \cos \theta \)
\( c \cdot \sec \theta \)
D. \( \tan \theta \)


For a first-order reaction, \( \boldsymbol{A} \rightarrow \) Product
the initial concentration of \( A \) is \( 0.1 \mathrm{M} \) and
after 40 minutes it becomes 0.025 M.
Calculate the rate of reaction at
reactant concentration of \( 0.01 \mathrm{M} \)
A \( \cdot 3.47 \times 10^{-4} \mathrm{M} \cdot \min ^{-1} \)
В. \( 3.47 \times 10^{-5} \mathrm{M} \cdot \min ^{-1} \)
c. \( 1.735 \times 10^{-6} \) M. \( \min ^{-1} \)
D. \( 1.735 \times 10^{-4} \mathrm{M} . \min ^{-1} \)


The correct order of increasing ionic character is:
A. \( B e C l_{2}<M g C l_{2}<C a C l_{2}<B a C l_{2} \)
в. \( B e C l_{2}<C a C l_{2}<M g C l_{2}<B a C l_{2} \)
c. \( B a C l_{2}<C a C l_{2}<M g C l_{2}<B e C l_{2} \)
D. \( M g C l_{2}<C a C l_{2}<B e C l_{2}<B a C l_{2} \)


In accordance with Newton's third law of
motion
A. Action and reaction never balance each other
B. For appearance of action and reaction, physical contact is not necessary
c. This law is applicable whether the bodies are at rest or they are in motion
D. All of these


The sum of rms potential difference across each of the three elements is
A . 50 volt
B. \( 50 \sqrt{2} \) volt
c. \( \frac{50}{\sqrt{2}} \) volt
D. None of these


All the values of 'a' for which the
quadratic expression \( a x^{2}+(a- \)
2) \( x-2 \) is negative for exactly two
integral values of \( x \) may lie in
A. \( (1,3 / 2) \)
B. \( (3,2 / 2) \)
c. (1,2)
(i) 5
D. (-1,2)


The major product obtained
when benzene reacts with
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C I} \) in presence of
anhydrous \( A l C l_{3} \) is
\( A \)
B.
\( c \)
D. None of these


Which of the following is a good nuclear fuel?
A. uranium_236
B. neptunium_239
c. thorium_236
D. plutonium-239


Assertion
In case of burning, air and moisture are
necessary.
Reason
Oxygen is a combustible gas.
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


Column-
Column-II
(Atomic number of elements)
(IUPAC name)
(A) 105
(P) Uun
(В) 107
(Q) Uns
(C) 109
(R) Unp
(D) 110
(h)
(S) Une
The correct match for \( A, B, C, D \) are
respectively:
A \( . \) R, P, s,
в. Р, R, s,
c. R, Q, s, p
D. Q, R, s,


State the types of compounds formed by the transfer of valence electrons from
one atom to another


Which of the following is an example of appendicular skeleton?
A. Bones of skull
B. Bones of vertebral column
c. Ribs
D. Bones of fore and hind limb


During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of \( \frac{C_{p}}{C_{v}} \) for the gas is
A \( \cdot \frac{4}{3} \)
B. 2
\( c \cdot \frac{5}{3} \)
D. \( \frac{3}{2} \)


The highest magnetic moment is shown
by the transition metal ion with outer electronic configuration:
A \( \cdot d^{9} \)
B . \( d^{7} \)
\( c \cdot d^{5} \)
\( \mathbf{D} \cdot d^{3} \)


Calculate the ratio of atomic masses of
Sulphur \( \& \) Oxygen.
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Mark the correct statment:
A. An electron and a proton when released from rest in a uniform electric field experience the same force and the same acceleration
B. Two equipotential surfaces may intersect.
C. A solid conducting sphere holds more charge than a hollow conducting sphere of the same radius.
D. No work is done in taking a positive charge from one point to another inside a negatively charged metallic sphere.


Filtrate \( A \) contains:
\( \mathbf{A} \cdot N H_{4} C l \)
\( \mathrm{B} \cdot \mathrm{Na}_{2} \mathrm{CO}_{3} \)
\( \mathbf{c} \cdot N a H C O_{3} \)
\( \mathbf{D} \cdot C a C O_{3} \)


Nature of \( C-X \) bond is:
A. ionic
B. covalent
c. co-ordinate
D. none of these


Construct a triangle \( A B C \) whose
perimeter is \( 12.5 \mathrm{cm} \) and whose base
angles are \( 60^{\circ} \) and \( 75^{\circ} \)


A dietician wishes to mix two types of
foods in such away that the vitamin contents of the mixture contains at
least 8 units of vitamin \( A \) and 10 units
of vitamin C. Food I contains 2 units/kg of vitamin \( A \) and 1 unit/kg of vitamin \( C \) while Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin 1 unit/kg of vitamin C. It costs \( R s .5 \) per
kg to purchase food I and \( R s .7 \) per kg to purchase Food II. Determine the maximum cost of such a mixture.
Formulate the above as a LPP and solve
t graphically.


How many points are there on the \( x- \) axis whose distance from the point
(2,3) is less than 3 units?


Considering the element \( B, A l, M g \) and
\( K, \) write the correct order of their
metallic character.


Let \( \boldsymbol{\alpha}=\boldsymbol{\pi} / \mathbf{5} \) and
\[
\begin{array}{c}
\boldsymbol{A}=\left[\begin{array}{cc}
\cos \boldsymbol{\alpha} & \sin \boldsymbol{\alpha} \\
-\sin \boldsymbol{\alpha} & \cos \boldsymbol{\alpha}
\end{array}\right] \text { and } \boldsymbol{B}=\boldsymbol{A}+ \\
\boldsymbol{A}^{2}+\boldsymbol{A}^{3}+\boldsymbol{A}^{4}, \text { then }
\end{array}
\]
This question has multiple correct options
A. singular
B. non-singular
c. skew-symmetric
D. \( |B|=1 \)


In an ideal adiabatic gas expansion,
This question has multiple correct options
A. entropy change in the gas itself is \( 0 . \)
B. entropy change of the surrounding amosphere is zero.
C. entropy change of the surrounding amosphere \( + \) entropy change in the gas itself \( >0 \)
D. all of the above


Two moles of a monoatomic gas at 300 Kis kept in a non-conducting container
enclosed by a piston. Gas is now compressed to increase the temperature from \( 300 \mathrm{K} \) to \( 400 \mathrm{K} \). Find work done by the gas \( (\boldsymbol{R}= \) \( \left.\frac{\mathbf{2 5}}{\mathbf{3}} \boldsymbol{J} / \boldsymbol{m o l} \boldsymbol{K}\right) \)


A person took spoiled food. This would happen in him.
A. Vomiting sensation
B. Belching
c. Burning in chest and throat
D. All above


Find he equation of the line passing through (1,2,3) and perpendicular to the two lines \( \frac{x}{1}=\frac{y}{2}=\frac{z}{-1} \) and \( \frac{x-1}{3}=\frac{y}{2}=\frac{z}{6} \)


If a line has the direction ratios
4,-12,18 then find its direction
cosines.
A \( \cdot-\frac{2}{11},-\frac{6}{11},-\frac{9}{11} \)
B. \( -\frac{2}{11}, \frac{6}{11},-\frac{9}{11} \)
c. \( \frac{2}{11},-\frac{6}{11}, \frac{9}{11} \)
D. \( \frac{2}{11}, \frac{6}{11}, \frac{9}{11} \)


The ratio in which the plane \( \vec{r} \cdot(\vec{i}- \) \( \mathbf{2} \overrightarrow{\boldsymbol{j}}+\boldsymbol{3} \overrightarrow{\boldsymbol{k}})=17 \) divides the line joining
the points \( -2 \vec{i}+4 \vec{j}+7 \vec{k} \) and \( 3 \vec{i}- \) \( \mathbf{5 j}+\mathbf{8 k} \) is
A .1: 5
B. 1: 10
\( c .3: 5 \)
D. 3: 10


Using mass(M), length (L), time(T), and electric current(A) as fundamental
quantities, the dimensions of permittivity will be
\( \mathbf{A} \cdot\left[M L T^{-1} A^{-1}\right] \)
в. \( \left[M L T^{-2} A^{-2}\right] \)
\( \mathbf{C} \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)
D・ \( \left[M^{2} L^{-2} T^{-2} A\right. \)


A body is brought near to a negatively charged gold leaf electroscope. If the divergence of leaves increases. What is the nature of charge on the body?
A. Positive
B. Negative
c. No charge
D. cant say


A cylinder fitted with a movable piston contains liquid water in equilibrium with water vapour at \( 25 . \) Which operation result in a decrease in the equilibrium vapour pressure?
A. Moving the piston downward a short distance
B. Removing a small mass of vapour
c. Removing a small mass of the liquid water
D. Dissolving salt in the water


Assertion(A): If centroid and
circumcentre of a triangle are known its orthocentre can be found.

Reason (R) : Centriod, orthocentre and
circumcentre of a triangle are collinear
A. Both A and R are individually true and R is the correct explanation of
B. Both A and R individually true but R is not the correct explanation of \( A \)
c. \( A \) is true but \( R \) is false
D. A is false but R is true


Which of the following statements are
correct?
This question has multiple correct options
A. A reaction in which different stereisomers produce different products or act at different rates is called stereospecific reaction
B. A reaction in which a given substrate produces diastereoisomeric products in different amounts and where one diastereomer predominates very much over the other is called stereoselective reaction
C. If the replacement of one group at an a chiral centre by a new substituent generates a chiral centre, the original molecule is said to be enantiopic
D. The E and Z system of naming geometrical isomers is based on the CIP sequence rule


\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \) in the interval [-1,1] Is Rolle's
Theorem applicable?


Rate expression of a chemical change is \( -\frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}]^{2}[\boldsymbol{B}]^{1}[\boldsymbol{C}]^{0} . \) The order of
reaction is:
\( A \cdot 3 \)
B . 2
c. 1
D.


The diagram shows stress v/s strain
curve for the materials \( A \) and \( B \). From
the curve we infer that
A. A is brittle but B is ductile
B. A is ductile but B is brittle
c. Both A and B are ductile
D. Both A and B are britlle


Write the reaction to prepare
acetaldehyde from hydrogen gas and an acid chloride?


What type of motion do the following objects have?
(a) A galloping of a horse.
(b) The needle of a sewing machine.
(c) A flying mosquito.
(d) The blades of an electric fan.
(e) The wheels of moving car.


\( \begin{array}{cc} & C H_{3} \\ C H_{3}-C H-C H_{2}- & C \\ _{I} H_{3} & C H_{3}\end{array}-C H_{3} \)
How many primary, secondary, tertiary and quaternary carbon atoms are present in the following compound?
A. One primary, two secondary and one tertiary
B. Five primary, three secondary
C. Five primary, one secondary, one tertiary, and one Quaterrnary
D. Four primary, two secondary and two quaternary


In an electromagnetic wave
A. Power is equally transferred along electric and magnetic fields
B. Power is transmitted in a direction perpendicular to both the field
C. Power is transmitted along electric field
D. Power is transmitted along magnetic field


In bridge game of playing cards, 4 players are distributed one card each
by turn so that each player gets 13 cards. Find out the probability of a
specified player getting a black ace and
a king.
This question has multiple correct options
A \( \cdot p=\frac{82251}{978775} \)
В. \( \quad p=\frac{164502}{978775} \)
C \( \quad p=\frac{329004}{978775} \)
D. \( _{p}=\frac{82251}{1957550} \)


In which of the following numbers, all zeros are significant?
A . 5.0005
B. 0.0030
c. 30.000
D. 0.5200


A rod of length \( L \) rotates in the form of a
conical pendulum with an angular velocity \( \omega \) about its axis as shown in
figure. The rod makes an angle \( \boldsymbol{\theta} \) with the axis. The magnitude of the motional emf developed across the two ends of
the rod is
\( A \)
в.
\( ^{\mathrm{c}} \cdot \frac{1}{2}^{B \omega L^{2} \cos ^{2} \theta} \)
D.
E. answer required


Which one of the following is not a part of a renal pyramid?
A. Loops of Henle
B. Peritubular capiliaries
c. convoluted tubules
D. collecting ducts


Wind energy is an \( _{-}-_{-}- \) -energy
resource
A. Inexhaustible
B. Exhaustible
c. Both A and B
D. None of the above


If, \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left[\begin{array}{cc}\boldsymbol{x} \tan ^{-1} \boldsymbol{x}+\sec ^{-1} \frac{1}{x} & , \boldsymbol{x} \boldsymbol{\epsilon}(-1,1)-\mathbf{0} \\ \frac{\boldsymbol{\pi}}{2} & \boldsymbol{i} \boldsymbol{f} \boldsymbol{x}=\mathbf{0}\end{array}\right] \)
then \( \boldsymbol{f}^{\prime}(\mathbf{0}) \) is
A. equal to -
B. equal to 0
c. equal to 1
D. non existent


The hormone which promotes flowering in long day conditions and controls sex expression is
A . Auxin
B. Cytokinins
c. Gibberellins
D. Ethylene


List five rational numbers between:
\( \frac{1}{2} \) and \( \frac{2}{3} \)


A piece of cork is floating on water in a
small tank. The cork oscillates up and
down vertically when small ripples pass
over the surface of water. The velocity of
the ripples being \( 0.21 m s^{-1}, \) wave
length \( 15 \mathrm{mm} \) and amplitude \( 5 \mathrm{mm} \), the
maximum velocity of the piece of cork is \( \left(\boldsymbol{\pi}=\frac{\mathbf{2 2}}{\mathbf{7}}\right) \)
A. \( 0.44 \mathrm{ms}^{-1} \)
B. \( 0.24 \mathrm{ms}^{-1} \)
c. \( 2.4 \mathrm{ms}^{-1} \)
D. \( 4.4 \mathrm{ms}^{-1} \)


The element with atomic number 35
belongs to :
A. s -block
B. p-block
c. d.-block
D. f-block


Name the following:
Hormone secreted by pituitary gland that helps in child birth


The process of electric discharge cannot occur between clouds and the
earth.Enter 0 for false and 1 for true
statement


The chemical formula of diaspore, an ore of aluminium, is:
A. \( A l_{2} O_{3} .3 H_{2} O \)
в. \( A l_{2} O_{3} .2 H_{2} O \)
c. \( A l_{2} O_{3} . H_{2} O \)
D. \( A l_{2} O_{3} \)


A closed container of volume \( V \) contains
an ideal gas at pressure \( P \) and Kelvin
Temperature T. The temperature of the gas is changed to 4 T due to passing heat to the container. Choose correct
pairs of pressure and volume after
change of the temperature.
A . P and \( V \)
B \( \cdot \operatorname{Pand}_{2}^{1} V \)
c. 4 Pand \( 4 V \)
D. \( 4 P \) and \( V \)
E \( \cdot \frac{1}{4} P \) and \( V \)


Prove that
\( \cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right)= \)
\( \frac{x}{2} ; x \in\left(0, \frac{\pi}{4}\right) \)


Among the following outermost configuration of metals which shows the highest oxidation state?
A \( \cdot 3 d^{3} 3 s^{2} \)
B . \( 3 d^{5} 4 s^{1} \)
\( \mathbf{c} \cdot 3 d^{5} \mathbf{4} s^{2} \)
D. \( 3 d^{4} 4 s^{2} \)


Gravity is :
A. Down wardly directed force
B. Upwardly directed force
C. Leftward directed force
D. Rightward directed force


Find
\( \frac{d y}{d x}, \) If \( x=4 t \) and \( y=\frac{4}{t} \)


A sulphate salt of group 2 element of the periodic table is a white, soft substance, which can be moulded into
different shapes by making its dough.
When this compound is left in open for some time, it becomes a solid mass and cannot be used for
moulding purposes. Identify the sulphate salt.
A. White paris
B. Plaster of paris
c. Calcium hydroxide
D. Calcium carbonate


Ramrao bought a cupboard for Rs. 4500 and sold it for Rs.4950. Shamrao bought a sewing machine for Rs. 3500 and sold
it for Rs. \( 3920 . \) Whose transaction was
more profitable?


If the rate of reaction increases by 27
times, when temperature is increased by \( 30 \mathrm{K}, \) then temperature coefficient of the reaction is:
\( A \cdot 3 \)
B. 2
\( c \)
D. 2.5


What is the nature of the intersection of
the set of planes \( \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y}+(\boldsymbol{b}+\boldsymbol{c}) \boldsymbol{z}+ \)
\( \boldsymbol{d}=\mathbf{0}, \boldsymbol{x}+\boldsymbol{b} \boldsymbol{y}+(\boldsymbol{c}+\boldsymbol{a}) \boldsymbol{z}+\boldsymbol{d}=\mathbf{0} \) and
\( \boldsymbol{x}+\boldsymbol{c} \boldsymbol{y}+(\boldsymbol{a}+\boldsymbol{b}) \boldsymbol{z}+\boldsymbol{d}=\mathbf{0} ? \)
A. They meet at a point.
B. They form a triangular prism.
c. They pass through a line.
D. They are at equal distance from the origin


Line spectrum contains information about the :
A. Atoms of the prism
B. Atoms of the source
c. Molecules of the source
D. Atoms as well as molecules of the source


The plates or the fragments of the Earth's crust is also known as:
A. crust plates
B. surface plates
c. tectonic plates
D. none of the above


The apparent weight of a body, weighing
M kg, during free fall is:
A. less than M kg wt
B. more than M kg wt
c. equal to M kg wt
D. zero


Give an example of a metal which can be easily cut with a knife.


A convex glass lens \( \left(\mu_{g}=1.5\right) \) has a
focal length of \( 8 \mathrm{cm} \) when placed in air. What is the focal length lens when it is immersed in water? \( \left(\mu_{\omega}=\frac{4}{3}\right) \)
\( \mathbf{A} \cdot 32 \mathrm{cm} \)
B. \( 60 \mathrm{cm} \)
c. \( 16 \mathrm{cm} \)
D. \( 30 \mathrm{cm} \)


A sample of coconut oil weighing
\( 1.573 g \) is mixed with \( 25 m L \) of
\( 0.4210 M K O H \) is used in
saponification of coconut oil. After the
saponification is complete, \( 8.46 m L \) of
\( 0.2732 M H_{2} S O_{4} \) is required to
neutralize excess \( K O H . \) The
saponification number of peanut oil is:
A . 209.6
B. 98.9
c. 108.9
D. 218.9


Evaluate the integral \( \int_{2}^{3}\left(x^{2}+2 x+\right. \)
5) \( d x \)


Particle A moves along X-axis with a
uniform velocity of magnitude \( 10 \mathrm{m} / \mathrm{s} \) Particle B moves with uniform velocity \( 20 \mathrm{m} / \mathrm{s} \) along a direction making an
angle of \( 60^{\circ} \) with the positive direction of X-axis as shown in the figure. The
relative velocity of B with respect to that
of \( A \) is.
\( A \cdot 10 \mathrm{m} / \mathrm{s} \) along \( \mathrm{x} \) -axis
B. \( 10 \sqrt{3} \mathrm{m} / \mathrm{s} \) along Y-axis (perpendicular to \( \mathrm{X} \) -axis)
long the bisection of the velocities of A and B
D /s along negative X-axi


Fill in the blanks.
Device that converts mechanical energy into electrical energy
is


If a particle \( A \) is moving along a straight line with velocity \( 3 m / s \) and another particle \( B \) has a velocity \( 5 m / s \)
at an angle of \( 60^{\circ} \) to the path of \( A, \) then
the velocity \( B \) relative to \( A \) is
A \( \cdot \sqrt{39} \mathrm{m} / \mathrm{s} \)
B . \( \sqrt{19} \mathrm{m} / \mathrm{s} \)
c. \( 19 m / s \)
D. None of these


The diagram below a ray of light
incident on a glass prism. Calculate the
refractive index of the glass prism.


Which of the following is/are true regarding the following linear equation:
\( y=\frac{3}{2} x+\frac{2}{3} \)
A \( \cdot \) It passes through \( \left(0, \frac{2}{3}\right) \) and \( m=\frac{3}{2} \)
B. It passes through \( \left(0, \frac{3}{2}\right) \) and \( m=\frac{2}{3} \)
\( ^{\mathbf{c}} \cdot \) it passes through \( \left(0,-\frac{2}{3}\right) \) and \( m=-\frac{3}{2} \)
D. It passes through \( \left(0,-\frac{3}{2}\right) \) and \( m=-\frac{2}{3} \)


There are 4 boys and 4 girls. In how
many ways they can sit in row Not all girls sit together.


Where Bicarbonate is converted into
carbonic acid
A. In the RBC of capillaries around the lungs
B. In the body fluid
c. in the arcolar cavity of lungs
D. In the RBC of blood capillaries around body tissue


Monkey's puzzle is common name for
A . Araucaria araucana
B. Cycas revoluta
c. Gnetum genon
D. Pinus gerardiana


In comparison to \( C-C l \) bond in ethyl
chloride, the \( C-C l \) bond in vinyl
chloride is:
A. longer and weaker
B. shorter and weaker
c. longer and stronger
D. shorter and stronger


Which of the following oxides can act as a reducing agent?
A. \( C O \)
в. \( C O_{2} \)
\( \mathrm{c} \cdot \operatorname{sn} \mathrm{O}_{2} \)
D. \( P b O_{2} \)


How the value of \( g \) varies with height.


A moving body with a mass \( m_{1} \) and velocity u strikes a stationary body of
\( \operatorname{mass} \boldsymbol{m}_{2} . \) The masses \( \boldsymbol{m}_{1} \) and \( \boldsymbol{m}_{2} \)
should be in the ratio \( m_{1} / m_{2} \) so as to decrease the velocity of the first body to
\( 2 u / 3 \) and \( \operatorname{giving} \) a velocity of \( v \) to \( m_{2} \) assuming a perfectly elastic impact.
Then the ratio \( m_{1} / m_{2} \) is :
A. 5
B. 1/5
\( c \cdot 1 / 25 \)
D. 25


Assuming that the period of vibration of a tuning fork depends upon the length \( l \)
of its prongs density \( \rho \) of its material and the elastic constant \( \boldsymbol{E} \) of its
material what would be the formula for
the period of its vibration
A \( \cdot \frac{k}{l} \sqrt{\frac{y}{d}} \)
B. \( \frac{2 k}{l} \sqrt{\frac{y}{d}} \)
c. \( \frac{k}{2 l} \sqrt{\frac{2 y}{d}} \)
D. \( \frac{3 k}{l} \sqrt{\frac{y}{2 d}} \)


A spherical iron ball \( 10 \mathrm{cm} \) in radius is
coated with a layer of ice of uniform
thickness that melts at a rate of \( 50 \mathrm{cm}^{3} \)
/min. When the thickness of ice is \( 5 \mathrm{cm} \)
then the rate at which the thickness of
ice decreases, is
\( ^{A} \cdot \frac{1}{18 \pi} \mathrm{cm} / \mathrm{min} \)
B. \( \frac{1}{36 \pi} \mathrm{cm} / \mathrm{min} \)
c. \( \frac{5}{6 \pi} \mathrm{cm} / \mathrm{min} \)
D. \( \frac{1}{54 \pi} \mathrm{cm} / \mathrm{min} \)


Name the functional group present in
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{C H O} \)


The metal showing resemblance with lithium is
\( A . B e \)
в. \( M g \)
c. \( A l \)
D. \( C a \)


An event \( X \) can take place in
conjunction with any one of the mutually exclusive and exhaustive events \( A, B \) and \( C . \) If \( A, B, C \) are equiprobable and the probability of \( X \) is \( 5 / 12 \) and the probability of \( X \) taking place when A has happened is 3/8 while it is \( 1 / 4 \) when \( \mathrm{B} \) has taken place, then
the probability of \( X \) taking place on conjunction with \( \mathrm{C} \) is
A . \( 5 / 8 \)
в. \( 3 / 8 \)
\( c \cdot 5 / 24 \)
D. none of these


Solve
\( \lim _{x \rightarrow 0} \frac{\cos 3 x-\cos x}{x^{2}} \)


Describe the following:
Carius method for the estimation of
sulphur in an organic compound.


If \( \boldsymbol{x} \epsilon \boldsymbol{R}, \) the numbers \( \boldsymbol{2}^{1+\boldsymbol{x}}+ \)
\( 2^{1-x}, \frac{b}{2}, 36^{x}+36^{-x} \) form an A.P., then
must lie in the interval
\( \mathbf{A} \cdot[12, \infty) \)
B. \( [6, \infty) \)
\( c \cdot(-\infty, 6] \)
\( \mathbf{D} \cdot[6,12] \)


Solution of differential equation \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}- \)
\( 2 x y=x \) is
A \( \cdot y=C e^{x^{2}}-\frac{1}{2} \)
B. \( y=C e^{x^{2}}+\frac{1}{2} \)
c. \( y=C x^{2}-\frac{1}{2} \)
D. None


A thermodynamical system is changed
from state \( \left(P_{1}, V_{1}\right) \) to \( \left(P_{2}, V_{2}\right) \) by two
different processes, the quantity which
will remain same will be
A. \( \Delta Q \)
в. \( \Delta W \)
c. \( \Delta Q+\Delta W \)
D. \( \Delta Q-\Delta W \)


\( \int_{-1}^{1} x(1-x)(1+x) d x \) is equal to
\( A \cdot \frac{1}{3} \)
B. \( \frac{2}{3} \)
c. 1
D. -
E .


\( 160^{\circ} \) in radian measure is
A \( \cdot \frac{2 \pi^{c}}{5} \)
в. \( \frac{3 \pi^{c}}{5} \)
c. \( \frac{8 \pi^{c}}{9} \)
D. \( \pi c \)


Account for the acidity of L-ascorbic
\( \operatorname{acid}\left(p K_{a}=4.21\right) . \) Which of the
following is most acidic \( H ? \) (Marked in
the structures as \( H^{a}, H^{b}, H^{c} \) and \( H^{d} \) )
A \( . H^{a} \)
В \( \cdot H^{b} \)
\( \mathbf{c} \cdot H^{c} \)
\( \mathbf{D} \cdot H^{d} \)


Draw the diagram of human brain Explain its functions.


Complete the table choosing the right
term from the list given in brackets: \( \left(10^{9}\right. \)
micro, \( \left.\mathbf{d}, \mathbf{1 0}^{-\mathbf{9}}, \mathbf{m i} \| \mathbf{i}, \mathbf{m}, \mathbf{M}\right) \)
\begin{tabular}{lll}
Factor & Prefix & Symbol \\
\( 10^{-1} \) & deci & \\
\( 10^{-6} \) & & \( \mu \) \\
& giga & G \\
\( 10^{6} \) & mega & \\
\hline
\end{tabular}


How many significant digits does the
measurement 124.04g possess?
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c .3 \)
D. 4
E . 5


In a bolt factory, machines \( A, B \) and \( C \)
manufacture \( 25 \%, 35 \% \) and \( 40 \% \)
respectively of the total number of bolts.
The percentage of defective bolts
among the manufactured bolts is \( 5 \% \)
for \( A, 4 \% \) for \( B \) and \( 2 \% \) for \( C . \) A bolt is
drawn randomly from the manufactured
products and is found to be defective then
This question has multiple correct options
A. the probability that the selected bolt is defective \( = \) 0.0345
B. the probability that the defective bolt was manufactured by machine \( A=\frac{25}{69} \)
C. the probability that the defective bolt was manufactured by machine \( B=\frac{28}{69} \)
D. the probability that the defective bolt was manufactured by machine \( C=\frac{16}{69} \)


Which one of the following process occurs inside the nucleus during protein synthesis in a eukaryotic cells?
A. Processing of hnRNA
B. Activation of amino acids
c. Translation
D. Formation of polypeptide chain


A point source of light is kept in front of a convex mirror of radius of curvature
40cm. The image is formed at \( 10 \mathrm{cm} \)
behind the mirror. Calculate the object distance
A . 30
B. 20
\( c .50 \)
D. 40


Explain the phenomenon of total internal reflection of light with an
example. Draw necessary ray of diagram.


In earthworm, pharyngeal nephridia occur in segments
A. 4,5 and 6
B. \( 5,6, \) and 7
\( c \cdot 6,7 \) and 8
D. 3,4 and 5


A square loop of side \( b \) is rotated in a
constant magnetic field \( B \) at angular
frequency \( \omega \) as shown in figure. What is
the emf induced in it?
\( \mathbf{A} \cdot b^{2} B \omega \sin \omega t \)
\( \mathbf{B} \cdot b B \omega \sin ^{2} \omega t \)
\( \mathbf{C} \cdot b B^{2} \omega \cos \omega t \)
D. \( b^{2} B \omega \)


Figure shows position and velocities of
two particles moving under mutual gravitational attraction in space at
time \( t=0 \)
The position of centre of mass after one
second is
A \( . x=4 m \)
в. \( x=6 m \)
c. \( x=8 m \)
D. \( x=10 m \)


Find the edge of the cube whose volume
is \( 216 m^{3} \)


A unit radial vector \( \hat{r} \) makes angles of
\( \boldsymbol{\alpha}=\mathbf{3 0}^{o} \) relative to the \( \boldsymbol{x} \) -axis, \( \boldsymbol{\beta}=\mathbf{6 0}^{\circ} \)
relative to the \( y \) -axis, and \( \gamma=90^{\circ} \)
relative to the \( z- \) axis. The vector \( \hat{r} \) can
be written as:
A \( \cdot \frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2} \hat{j} \)
B. \( \frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j} \)
c. \( \frac{\sqrt{2}}{3} \hat{i}+\frac{1}{\sqrt{3}} \hat{j} \)
D. none of these


A chemical reaction, \( A \rightleftharpoons B \),is said to
be in equilibrium when:
A. Rate of forward reaction is equal to rate of backward reaction
B. Conversion of \( A \) to \( B \) is only \( 50 \% \) complete
C . Complete conversion of \( A \) to \( B \) has taken place
D. Only \( 25 \% \) conversion of \( A \) to \( B \) has taken place


In a wind tunnel experiment, the
pressures on the upper and lower
surfaces of the wings are \( 0.90 \times 10^{5} \) Pa
and \( 0.91 \times 10^{5} \) Pa respectively. If the area
of the wing is \( 40 \mathrm{m}^{2} \) the net lifting force
on the wing is
A \( \cdot 2 \times 10^{4} \mathrm{N} \)
B. \( 4 \times 10^{4} \mathrm{N} \)
c. \( 6 \times 10^{4} \mathrm{N} \)
D. \( 8 \times 10^{4} \mathrm{N} \)


A balanced diet should contain \( 12 \% \) of
proteins, \( 25 \% \) of fats and \( 63 \% \) of
carbohydrates If a child needs 2600 calories in his food daily, find in calories the amount of carbohydrates in his daily food intake.


The number of geometrical isomer(s)
possible for \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{C l}_{2}\right] \)
(octahedral) is/are:
\( A \cdot 3 \)
B. 2
\( c \cdot 4 \)
D. none


Ammonia gas can be collected by the displacement of:
A. conc. \( H_{2} S O_{4} \)
B. Brine
c. water
D. Mercury


When electric current is passed
through water, hydrogen is deposited
over:
A. positive pole
B. negative pole
c. no dissociation
D. both the poles


The oil used in the froth floatation
method for the purification of ore is
A. coconut oil
B. olive oil
c. Pine oil
D. castor oil


State radioactive decay law. Derive \( N=N_{o} e^{-\lambda t} \) for a radioactive element.


An object of \( 10 \mathrm{cm} \) is placed at a
distance of \( 20 \mathrm{cm} \) from a lens of focal
length \( 25 \mathrm{cm} . \) The object is placed erect
on the principal axis of the lens yet a crooked image was formed. Explain why.


The filament of a bulb takes a current
\( 0.1 \mathrm{A} \) when potential difference across it is \( 0.2 \mathrm{V} \). When the potential difference across it becomes \( 1.0 \mathrm{V} \), the current
becomes 0.4 A. The resistance of
filament in each case will be
A. \( 2.0 \Omega, 2.5 \Omega \)
B. \( 2.5 \Omega, 2 \Omega \)
c. \( 1.0 \Omega, 2.5 \Omega \)
D. \( 2.0 \Omega, 2 \Omega \)


In general, when the temperature of a conductor increases, its resistance
A. increases
B. decreases
c. remains the same with rise
D. first increases then decreases


In the given figure, which line is
perpendicular to AB?
A. CD
B. EF
\( c \cdot G H \)
\( D \cdot \mid J \)


A small ball is suspended from a fixed
point \( \boldsymbol{O} \) by means of a light and inextensible string of length \( l \). The bal is first taken aside such that string becomes horizontal and then released
from rest. At the bottom it collides with
a fixed obstacle. The coefficient of
restitution is \( e . \) Find the maximum
angular deflection of the string after \( n \) th collision


If a street light of mass \( \mathrm{M} \) is suspended from the end of a uniform rod of length
in different possible patterns as shown in figure, then
\( (a) \)
\( (b) \)
A. Pattern A is more sturdy
B. Pattern B is more sturdy
c. Pattern C is more sturdy
D. All will have same sturdiness


Bipinnate leaves and spiny stipules are the characteristics of family
A. Papilionaceae
B. Cesalpinoideae
c. Mimosoideae
D. Malvaceae


The number of \( g \) -atom of oxygen in \( 6.02 \times 10^{24} \mathrm{CO} \) molecule is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0.5
\( c .5 \)
D. 10


If \( x^{y}+y^{x}=a^{b} \) then show that \( \frac{d y}{d x}= \) \( -\left[\frac{\boldsymbol{y} \boldsymbol{x}^{\boldsymbol{y}-\mathbf{1}}+\boldsymbol{y}^{\boldsymbol{x}} \log \boldsymbol{y}}{\boldsymbol{x}^{\boldsymbol{y}} \log \boldsymbol{x}+\boldsymbol{x} \boldsymbol{y}^{\boldsymbol{x}-1}}\right] \)


Which one is the general formula of
monohydric alcohols?
A. \( C_{n} H_{2 n-2} O H \)
в. \( C_{n+1} H_{2 n} O H \)
c. \( C_{2 n} H_{2 n+2} 2 O H \)
D. \( C_{n} H_{2 n} O H \)


Which of the following is not matter?
A. Oxygen
B. Microwaves
c. water
D. All of above


In which of the following the inert pair effect is most prominent?
A. \( C \)
B. \( S \) i
c. \( G e \)
D. \( P b \)


Two adjacent sides of a parallelogram are \( 10 \mathrm{cm} \) and \( 12 \mathrm{cm} . \) If one diagonal of
it is \( 16 \mathrm{cm} \) long; find area of the
parallelogram. Also, find distance between its shorter sides.
A \( \cdot 119.8 \mathrm{cm}^{2} ; 11.98 \mathrm{cm} \)
B . \( 119.9 \mathrm{cm}^{2} ; 11.20 \mathrm{cm} \)
\( \mathrm{c} \cdot 117.6 \mathrm{cm}^{2} ; 10.28 \mathrm{cm} \)
D. \( 120.8 \mathrm{cm}^{2} ; 15.98 \mathrm{cm} \)


A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black
balls. One of the two bags is selected at random and a ball is drawn from the
bag which is found to be red. Find the probability that the ball is drawn from the first bag.


Force acting on a block is \( \boldsymbol{F}=(-4 x+ \)
8). Here \( F \) is in Newton and \( x \) the position of block on \( x \) -axis in meters
A. motion of the block is periodic but not simple harmonic
B. motion of the block is not periodic
c. motion of the block is simple harmonic about origin, \( x=0 \)
D. motion of the block is simple harmonic about \( x=2 m \).


A \( 100 \Omega \) resistor is connected to a
\( 220 V, 50 H z \) AC supply. Find rms value
of current in the circuit and the net
power consumed for a complete cycle.
A. \( 2.20 A, 484 W \)
в. \( 3.20 A, 564 W \)
c. \( 1.60 A, 278 W \)
D. \( 5.80 A, 646 W \)


Calculate the momentum of a bullet of
\( 25 g \) when it is fired from a gun with a velocity of \( 100 m / s \)
A. 20 kg \( m / s \)
в. \( 2500 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. \( 2.5 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. None


In an experiment, mature leaves on the plant were enclosed for a fixed amount
of time in a transparent bag that had
radioactive \( C O_{2} . \) In which part of the plant will maximum radioactivity be found after some time?
A. Actively growing leaves
B. Guard cells of all the leaves
c. In mature leaves
D. Senescing leaves and roots


Which is/are correct?
\( \mathbf{A} \cdot 2.303 \log K=-\Delta H^{o} / R T+\Delta S^{o} / R \)
B \( \cdot \Delta G^{o}=-2.303 \log K \)
\( \mathbf{c} \cdot-2.303 \log K=-\Delta H^{o} / R T^{2}+\Delta S^{o} / R \)
D. \( 2.303 \log K=(1 / R T)\left(\Delta H^{o}+\Delta S^{o}\right) \)


The atoms of different elements having
the same number of neutrons are
known as:
A. isobars
B. isomers
c. isotones
D. isotopes


Show that the logarithmic function \( \boldsymbol{f} \)
\( R_{0}^{+} \rightarrow R \) given by \( f(x)=\log _{a} x, a>0 \)
is a bijection.


While forming crystals, it is important
to:
A. evaporate to dryness to get purest possible crystals
B. attach gas syringes to collect fumes
C . not evaporate water of crystallization
D. use high flames


On increasing the salary of a man by \( 12 \%, \) his salary becomes how much if the initial salary was Rs. \( 12,000 ? \)


What is a de-icing agent? How does it
work?


Which of the following is a limitation of Thomson's model of an atom?
A. Arrangement of fundamental particles in an atom
B. closeness of positive and negative charge
c. Both a and b
D. None of above


Which of the following is not a naturally occurring plant hormone?
A. \( 2,4- \) D
B. GAz
c. Gibberellin
D. IAA


Answer the following question:
a. What is the basicity of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and
why?
b. Why does fluorine not play the role of a central atom in interhalogen compound?
c. Why do noble gases have very low boiling points?


The element which has the maximum
number of valence electrons
is
A. \( N a \)
в. \( M g \)
\( c \cdot s \)
D. \( A l \)


A company deposits \( \$ 200 \) in bank with an interest rate of \( 5 \% \). After how many
years will the amount increase by \( \$ 50 \) with the same interest rate?
A . 5
B. 10
c. 15
D. 25


The \( K_{s p} \) of salt \( A g C l \) at \( 25^{\circ} C \) is \( 2.56 \times \)
\( 10^{-10} . \) The how much volume of \( H_{2} O \) is
required to dissolve 0.01 mole of salt.
\( \mathbf{A} \cdot 800 L \)
B. \( 400 L \)
c. \( 625 L \)
D. \( 50 L \)


Which of the following gas that is slightly soluble in water and gives a weakly acid solution?
A \( . H_{2} \)
в. \( S O_{2} \)
c. \( C O \)
D. \( H C l \)
E \( . O_{3} \)


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


If \( \sin \theta=\frac{7}{25} \) and \( 90^{0}<\theta<180^{0}, \) then
find the value of \( \sec \theta+\tan \theta \)


The inequality. \( \min f(x)>-7 / 18[-\pi, \pi] \) holds for
the function \( f(x)=(\cos x)^{2}(\sin x) \)
A. True
B. False


In YDSE ratio of width of slit is 4: 1
then ratio of maximum to minimum
intensity
\( \mathbf{A} \cdot \mathbf{9} \)
B . 27
\( c .3 \)
D. 81


For a reaction \( A+2 B \longrightarrow C, \) rate is
\( \operatorname{given} \mathrm{by}+\frac{\boldsymbol{d}[\boldsymbol{C}]}{\boldsymbol{d} \boldsymbol{t}}=\boldsymbol{k}[\boldsymbol{A}][\boldsymbol{B}], \) hence the
order of the reaction is:
A . 3
B. 2
c. 1
\( D \)


Which of the following undergoes two step hydrolysis :
A \( \cdot \mathrm{NCl}_{3} \)
в. PCI
\( c \cdot \mathrm{PCl}_{3} \)
D. SF \( _{6} \)


Evaluate: \( \int \sqrt{x^{2}} \mathrm{d} x \)


For the same cross-section area and for
a given load, the ratio of depression for the beam of a square cross-section and circular cross-section is
A . \( 3: \pi \)
в. \( \pi: 3 \)
\( c \cdot 1: \pi \)
D. \( \pi: 1 \)


A rod bent in right angle along its centre
line, is placed on a rough horizontal
fixed cylinder of radius \( R \) as shown in
fig. Mass of rod is \( 2 m \) and rod is in
equilibrium. Assume that friction force
on rod at \( A \) and \( B \) are equal in
magnitude

This question has multiple correct options
A. Normal force applied by cylinder on rod at \( A \) is \( 3 m g / 2 \)
B. Normal force applied by cylinder on rod at \( B \) must be zero
C. Friction force acting on rod at \( B \) is upward
D. Normal force applied by cylinder on rod at \( A \) is \( \mathrm{mg} \)


Let \( Z \) be the set of integers. Show that
the relation \( \boldsymbol{R}= \)
\( \{(a, b): a, b \in Z \text { and } a+b \text { is even }\} \) is
an equivalence relation on \( Z \)


If the line \( x=\alpha \) divides the area of the
region \( \boldsymbol{R}= \)
\( \left\{(x, y) \in \mathbb{R}^{2}: x^{3} \leq y \leq x, 0 \leq x \leq 1\right\} \)
into two equal parts, then
A \( \cdot 0<\alpha \leq \frac{1}{2} \)
в. \( \frac{1}{2}<\alpha<1 \)
c. \( 2 \alpha^{4}-4 \alpha^{2}+1=0 \)
D. \( \alpha^{4}+4 \alpha^{2}-1=0 \)


\( 4 C l O_{3(a q)}^{-} \rightarrow 3 C l O_{4(a q)}^{-}+C l_{(a q)}^{-} \) is an
example of
A. Oxidation reaction
B. Reduction reaction
c. Decomposition reaction
D. Disproportionation reaction


If "All odd numbers are primes and the
sum of three angles in a triangle is \( 190^{\circ} \)
", then "All odd numbers are primes or the sum of the angles in a triangle is
\( 190^{\circ \prime \prime} \) is a
A. tautology
B. contradiction
c. contingency
D. not a statement


An example of natural biopolymer is:
A. Teflon
B. Nylon - 6, 6
c. Rubber
D. DNA


Thermosetting plastics can be remoulded on gentle heating.
A. True
B. False


Find the product \( :(x-3)(x+3)\left(x^{2}+\right. \)
\( \mathbf{9} \)


Bohr's theory is not applicable to:
This question has multiple correct options
A. He
B . \( L i^{2} \)
\( \mathrm{c} \cdot \mathrm{He}^{2} \)
D. the H-atom


How can the brightness of the pattern on the screen or cathode ray tube be changed?
A. By changing the negative potential on grid
B. By changing the positive potential on grid
c. we can't increase the brightness
D. None of the above


Suppose a girl throws a die. If she gets a
5 or \( 6, \) she tosses a coin three times and
notes the number of heads. If she gets
1,2,3 or \( 4, \) she tosses a coin once and
notes whether a head or tail is obtained.
If she obtained exactly one head, what
is the probability that she threw 1,2,3 or 4 with the die?


A speaker emits a sound wave of
frequency \( f_{0} . \) When it moves towards a stationary observer with speed \( u \). The
observer measures a frequency \( f_{1} \). If the
speaker is stationary, and the observer
moves towards it with speed \( u, \) the
measured frequency is \( f_{2} \). Then
A \( \cdot f_{1}=f_{2}<f_{0} \)
в. \( f_{1}>f_{2} \)
c. \( f_{1}<f_{2} \)
D. \( f_{1}=f_{2}>f_{0} \)


If \( \boldsymbol{f}(\boldsymbol{x})=(\mathbf{1}+\boldsymbol{x})^{15}=\boldsymbol{C}_{0}+\boldsymbol{C}_{1} \boldsymbol{x}+ \)
\( C_{2} x^{2}+\ldots+C_{15} x^{15}, \) then \( f(2)= \)
\( \mathbf{A} \cdot 1^{15} \)
B. \( 3^{15} \)
\( c \cdot 2^{15} \)
D. None of these


If \( C \) is skew-symmetric matrix of order \( n \)
and \( X \) in \( n \times 1 \) column matrix, then \( X^{T} \)
\( \mathrm{CX} \) is
This question has multiple correct options
A. singular
B. non-singular
c. invertible
D. non-invertible


Fill in the blanks with \( >,< \) or \( =\operatorname{sign} \) \( \$ \$(-21)-(-10) \)
\( ? \)


Find the equations of the lines for which \( \tan \theta=\sqrt{2}, \) where \( \theta \) is the angle of
inclination of the line and \( y- \) intercept
is -1


In a semiconductor at room
temperature
A. the valence band is partially empty and the conduction band is partially filled.
B. the valence band is completely empty and the conduction band is partially filled.
C. the valence band is completely filled.
D. the conduction band is completely empty.


Choose the correct answer from the
allternatives given. What are the respiratory organs in cockroach ?
A. Lung
B. Trachea
c. skin
D. None of these


Which of the following are responsible
for causing acid-rain?
A. Oxides of sulphur and carbon dioxide.
B. Oxides of nitrogen and carbon monoxide.
C. Hydrogen sulphide and carbon dioxide.
D. Oxides of sulphur and nitrogen.


Astronomers study about:
A . celestial bodies
B. microorganisms
C. nuclear reactions
D. electricity


Hydrogen bonding is seen in \( \boldsymbol{H}_{2} \boldsymbol{O} \) and
not in \( \boldsymbol{H}_{2} \boldsymbol{S} . \) Why?


\( 4 D_{2} O+3 F e \stackrel{r e d-h o t}{\longrightarrow} F e_{3} O_{4}+g a s . \) The gas
produced in the above reaction is:
\( A \cdot O_{2} \)
в. \( H_{2} \)
c. \( D_{2} \)
D. none


\( 380 \mathrm{mL} \) of a gas at \( 27^{0} \mathrm{C}, 800 \mathrm{mm} \) of \( \mathrm{Hg} \)
weight
\( 0.455 \mathrm{g} . \) the mol.wt.of gas is:
A .27
B . 28
c. 29
D. 30


Solve:
\( \lim _{x \rightarrow 0} \frac{x}{3-\sqrt{x+9}} \)


One mole of helium gas is heated in a vessel with variable volume so that the
pressure is fixed at 1 atmosphere. When the temperature increased from \( 273 \mathrm{K} \) to \( 274 \mathrm{K}, \) it was found that \( 21 J \) of heat energy was absorbed. The value of \( \Delta U, \) and \( \Delta H, \) respectively, are:
A. 4.4 Jand \( 12.7 \mathrm{J} \)
B. 12.7Jand21J
c. 21 Jand \( 29.3 \mathrm{J} \)
D. 29.3Jand21J


A satellite of mass \( m \) revolves around
the earth of radius \( R \) at a height \( x \) from its surface. If \( g \) is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is
A . \( \sqrt{g x} \)
в. \( \sqrt{\frac{g R}{R-x}} \)
\( ^{\mathrm{c}} \cdot \sqrt{\frac{g R^{2}}{R-x}} \)
D. \( \sqrt{\frac{g R^{2}}{R+x}} \)


Which of the following noble gas is the least polarizable?
A. Radon
B. Krypton
c. xenon
D. Helium


Carotid artery supplies
A. Oxygenated blood to lungs
B. Oxygenated blood to intestine
C. Oxygenated blood to brain
D. None of these


The addition of oxygen to a substance is called
A. oxidation
B. reduction
c. synthesis
D. none of these


Find the electric field at a distance \( x \)
from the centre inside the shell.
\( \mathbf{A} \cdot E=0 \)
в. \( \quad E=\frac{Q}{4 \pi \epsilon_{0} a^{2}} \)
c. \( _{E}=\frac{Q}{4 \pi \epsilon_{0} x^{2}} \)
D. \( _{E}=\frac{Q}{4 \pi \epsilon_{0}(a-x)^{2}} \)


If \( y=\tan ^{-1}(\cot x)+\cot ^{-1}(\tan x) \)
then \( \frac{d y}{d x} \) is equal to-
\( A \cdot 1 \)
B. 0
c. -1
D. - 2


In the figure shown, if the area of the
shaded region is 3 times the area of the
smaller circular region, then the
circumference of the larger circle is how many times the circumference of the
smaller circle?
A .4
B. 3
\( c \cdot 2 \)
\( D \cdot \sqrt{3} \)
\( E \cdot \sqrt{2} \)


A normal human eye can see an object
making an angle of \( 1.8^{\circ} \) at the eye. What is the approximately height of
object which can be seen by an eye
placed at a distance of \( 1 \mathrm{m} \) from the object.


At \( 25 C \) molar conductance of 0.1 molar
aqueous solution of ammonium hydroxide is 9.54 ohm \( ^{1} c m^{2} \) mol \( ^{1} \) and at
infinite dilution its molar conductance
is 238 ohm \( ^{1} \mathrm{cm}^{2} \) mol \( ^{1} \). The degree of
ionisation of ammonium hydroxide at the same concentration and
temperature is:
A. \( 2.080 \% \)
B. 20.800 \%
c. 4.008 \%
D. \( 40.800 \% \)


A solid conducting sphere having a charge \( Q \) is surrounded by an uncharged concentric conducting hollow spherical
shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be
\( V . \) If the shell is now given a charge of \( 3 Q \)
the new potential difference between the same two surfaces is :
A. \( V \)
B. 2 \( V \)
\( c \cdot 4 v \)
D. \( -2 V \)


Which of the following statements
about the behaviour of light is not
correct?
A. Interference patterns are evident for light behaving as rays.
B. Ray properties of light are useful for understanding how images are formed by optical devices such as eyes.
C. Wave properties are important for observing the behaviour of light at a fine scale.
D. Both wave and particle theories of light can be related to the colour sensations produced by light.


Which element do not have valency equals to its group number?
A. Sodium
B. Magnesium
c. oxygen
D. Potassium


What are synthetic detergents?


ff \( P(x)=2 x^{3}-3 x^{2}+4 x-2, \) then \( P(-1) \)
is:
\( A \cdot-2 \)
B. -11
\( c \cdot 0 \)
D.


After implantation interdigitation of material and foetal tissues takes takes
place.Identify the tissues involved and justify their role.


Newton's law of motion were published
in the year 1699
A . True
B. False


Which is a coordination compund?
A. Ferrous ammonium sulphate
B. Carnallite
C . Potassium ferrocyanide
D. Gypsum


respectively, constitute an electric
dipole. Distance \( A B=2 a, 0 \) is the mid point of the dipole and OP is
perpendicular to AB. A charge Q is placed at \( P \) where \( O P=y \) and \( y>>2 a . \) The charge \( Q \) experiences and electrostatic
force F. If \( Q \) is now moved along the
equatorial line to \( P^{\prime} \) such that \( O P^{\prime}= \) \( \left(\frac{y}{3}\right) \) the force on \( Q \) will be close to \( L \) \( \left(\frac{y}{3}>>2 a\right) \)
\( A \cdot \frac{F}{3} \)
в. зF
\( c . \) 9F
D. 27


It is hotter at some distance over the
flames than in front of it because:
A. air conducts heat upwards only
B. heat is radiated upwards only
c. convection of heat occurs upwards only
D. heat is radiated downwards only


Evaluate the following:
\( \sum_{n=1}^{11}\left(2+3^{n}\right) \)


Which of the following will have the largest value of solubility product, or is most soluble in water?
A \( \cdot \operatorname{Be}(O H)_{2} \)
в. \( B a(O H)_{2} \)
c. \( \operatorname{Ca}(O H)_{2} \)
D. \( M g(O H)_{2} \)


If \( 2 x+y=23 \) and \( 4 x-y=19, \) find
the values of \( 5 y-2 x \) and \( \frac{y}{x}-2 \)
A \( \cdot 36,-\frac{1}{3} \)
в. \( _{31,-\frac{5}{7}} \)
c. \( _{38, \frac{6}{7}} \)
D. None of these


\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\cos \boldsymbol{x}+\sin \boldsymbol{x} \)


The arithmetic mean and mode of a
data are 24 and 12 respectively, Then the median of the data is
A . 20
B . 18
\( c \cdot 21 \)
D. 22


If a zero of \( p(x)=x^{2}+3 x+g \) is \( 2, \) then
value of \( g \) is
A . -10
B. 10
\( c .5 \)
D. -5


How does the electron mobility vary with
(i) temperature and
(ii) potential difference?


A particle moves in a circle of diameter \( 1.0 \mathrm{cm} \) under the action of a magnetic field of \( 0.40 \mathrm{T} . \) An electric field of
\( 200 V m^{-1} \) makes the path straight.
Find the charge / mass ratio of the particle.


Why is it easier to pull a lawn roller than
to push it?
A. Pulling involves sliding friction
B. Pulling involves dry friction.
c. Pulling increases the effective weight.
D. Pulling decreases normal reaction


(I) \( \quad \mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{O}_{3} \rightarrow \mathrm{H}_{2} \mathrm{O}+2 \mathrm{O}_{2} \)
(II) \( \mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Ag}_{2} \mathrm{O} \rightarrow 2 \mathrm{Ag}+\mathrm{H}_{2} \mathrm{O}+\mathrm{O} \)
Role of hydrogen peroxide in the above reactions is:
A. oxidizing agent in (I) and reducing agent in (II)
B. reducing agent in (I) and oxidizing agent in (II)
c. reducing agent in both (I) and (II)
D. oxidizing agent in both (I) and (II)


On the addition of a solution containing \( C r O_{4}^{2-} \) ions to the solution of \( B a^{2+}, S r^{2+}, C a^{2+} \) ions, the precipitate
obtained first will be of:
A. \( C a C r O_{4} \)
B \( . \) SrCrO \( _{4} \)
\( \mathrm{c} \cdot B a C r O_{4} \)
D. A mixture of all the three


Write the role of
Dilute \( N a C N \) in the extraction of Gold


The management committee of a residential colony decided to award some of its members (say \( x \) ) for
honesty, some (say \( y \) ) for helping others
and some others (say \( z \) ) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is 12
Three times the sum of awardees for
cooperation and supervision added to two times the number of awardees for
honesty is \( 33 . \) If the sum of the number of awardees for honesty and supervision
is twice the number of awardees for
helping others using matrix category. Apart from these values namely, honesty, cooperation and supervision,
suggest one more value which the
management of the colony must include for awards.


In the integral type of power brake, the diaphragm acts directly on the hydraulic piston in the
A. Master cylinder
B. Wheel cylinder
c. Adjacent cylinder
D. Multiplier unit


For synthesis of one gram of hexose, the
land plant consumes
A. Only \( 1 / 3 \) rd of the \( C O_{2} \) of air
B. Only \( 1 / 4 \) th of the \( C O_{2} \) of air
C. only \( 2 / 3 \) rd of the \( C O_{2} \) of air
D. None of the above


Mosses and ferns are found in moist
and shady places because both
A. Require presence of water for fertilization
B. Do not need sunlight for photosynthesis
c. Depend for their nutrition on micro- organisms which can survive only at low temperature.
D. Cannot compete with sun-loving plants