(a) A DNA segment has a total of 1,500 nucleotides, out of which 410 are
guanine containing nucleotides. How many pyrimidine bases this segment possesses?
(b) Draw a diagrammatic sketch of a
portion of DNA segment to support your
answer


Fill in the blanks:
\( \frac{-9}{14}+\ldots . .=-1 . \) Hence find the sum of the numerator and denominator so
obtained.


ATP-ase needed for muscle contraction
is present over
A. Aetinin
B. Troponin
c. Myosin
D. Actin


The analogous term to voltage.
A. True
B. False


The contrapositive of \( (\boldsymbol{p} \vee \boldsymbol{q}) \Rightarrow \boldsymbol{r} \) is
A \( \cdot r \Rightarrow(p \vee q) \)
в. \( r \Rightarrow(p \vee q) \)
c. \( r \Rightarrow(\sim p \wedge \sim q) \)
D. \( p \Rightarrow(q \vee r) \)


The average path difference between
two waves coming from third and fifth
Fresnel zones of a wave front at the
centre of the screen is :
\( A \cdot \frac{\lambda}{2} \)
B. \( 2 \lambda \)
\( c \cdot \lambda \)
D. \( 4 \lambda \)


IUPAC name of the following compound:
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\underset{\boldsymbol{C H}_{2} C \boldsymbol{H}_{3}}{\boldsymbol{C} \boldsymbol{H}-\boldsymbol{C H}_{2}}-\underset{\boldsymbol{C H}_{3}}{\boldsymbol{C H}}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
A. 3-Ethyl-5-methylheptane
B. 5-Ethyl-3-methylheptane
c. 1,1-Diethyl-3-methylpentane
D. 3-Methyl-5,5-diethylpentane


Assertion \( (A): H P O_{3} \) is monobasic acid
Reason(R) : The salts of \( H P O_{3} \) are called meta-phosphates The correct answer is:
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of (A)
c. (A) is true and (R) is false
D. (A) is false but (R) is true


Avogadro's law shows the relationship
between which two variables?
A. Volume and number of moles
B. Pressure and number of moles
C. Volume and pressure
D. Temperature and pressure
E. Temperature and number of moles


A body starts rolling down an inclined plane of length \( L \) and height \( h \) This body reaches the bottom of the plane in time \( t . \) The relation between \( L \)
and \( t \) is
\( \mathbf{A} \cdot t \propto L \)
в. \( t \propto \frac{1}{L} \)
c. \( L \propto t^{2} \)
D \( \cdot t \propto \frac{1}{L^{2}} \)


Which of the following are conditions necessary for observing rainbow?
A. The Sun should be behind us
B. It should have rained and the sun should be present.
c. None of A and B
D. Both A and B


List
List II
A) Constant
I) At highest point speed and varying \( \quad \) of body velocity \( \quad \) projected vertically up
B) Zero
II) Uniform displacement and \( \quad \) circular motion finite distance
III) At any
C) Zero velocity \( \quad \) intermediate point of and finite acceleration \( \quad \) freely falling body
D) Non-zero
IV) Body on reaching point of velocity and nonzero acceleration
The correct match is:
\( A \cdot A-|V, B-| I, C-|I|, D-1 \)
B. \( A-11, B-1 V, C-1, D-11 \)
\( \mathbf{C} \cdot A-\|I, B-I, C-I V, D-\| \)
D. \( A-1, B-111, C-11, D-1 V \)


The bulk of histone proteins are synthesized in
A \( \cdot G_{1} \) phase
B. \( G_{2} \) phase
c. s phase
D. \( G_{0} \) phase


Which of the following is the correct chemical formula of sodium
phosphate?
A \( . \) NaPO \( _{4} \)
в. \( N a_{3}\left(P O_{4}\right)_{2} \)
c. \( N a_{2}\left(P O_{4}\right)_{2} \)
D. \( N a_{3} P O_{4} \)


Which of the following is a physical change?
A. Rusting of Iron.
B. The burning of coal
c. cooking food
D. Converting ice in the water


How many hydrogen atoms are present in a molecule of hexane?
A . 12
B. 14
c. 16
D. 10
E . 18


The lattice energies of
\( N a C l, N a F, K C l \) and \( R b C l \) follow the
order:
A. \( K C l<R b C l<N a C l<N a F \)
в. \( N a F<N a C l<K C l<R b C l \)
c. \( R b C l<K C l<N a C l<N a F \)
D. \( N a C l<R b C l<N a F<K C l \)


32 gram of oxygen gas at temperature
\( 27^{\circ} \mathrm{C} \) is compressed adiabatically to
\( 1 / 3 \) of its change in internal energy. \( \gamma=1.5 \text { of oxygen }) \)


Let \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{a}),(\boldsymbol{b}, \boldsymbol{c}),(\boldsymbol{a}, \boldsymbol{b})\} \) be a
relation on a set \( A=\{a, b, c\} . \) Then the
minimum number of ordered pairs
which when added to R make it an
equivalence relation are


lonization energy of noble gas is very high. Why?


Which of the following will not give a
white ppt. When \( A g N O_{3} \) is added to the solution?
A. \( C C l_{4} \)
B. NaCl
c. \( M g C l \)
D. KCI


An object attached to one end of a spring makes 20 vibrations in 10 s. Its frequency is
A. \( 2 \mathrm{Hz} \)
B. 10 s
c. \( 0.05 \mathrm{Hz} \)
D. 2s


Solve the following. It is known that 5 microgram of an enzyme convert 10 million molecules of
substrate to end products per second. To calculate the enzyme's turnover what else must be known?
A. Molecular weight of the enzyme.
B. Molecular weight of the enzyme and substrate both.
c. The molecular weight of substrate only.
D. Molecular weight of end product only


Assertion : Earthworms excrete both
ammonia and urea

Reason : Excretion in earthworm
depends on the
environment.
A. If both the assertion and the reason are true and the reason
is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is
not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false
E. If the assertion is false but reason is true


The domain for, \( \boldsymbol{f}(\boldsymbol{x})=\cos ^{-1}[\boldsymbol{x}] \) is
A. \( x \in[-1,2) \)
B . \( x \in[-1,1] \)
c. \( x \in(-1,2) \)
D. \( x \in(-1,1) \)


Assertion
Latent heat of fusion of ice is
\( \mathbf{3 3 6 0 0 0} \boldsymbol{J} \boldsymbol{k g}^{-\mathbf{1}} \)
Reason
Latent heat refers to heat required to
change of state without any change in temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A circular disc is rotated in clockwise
direction in horizontal plane. The
direction of torque is
A. Horizontally right side
B. horizontally left side
c. Vertically upwards
D. Vertically downwards


In which of the following situations, the sequence formed will form an A.P?
1) Number of students left in the school
auditorium from the total strength of
1000 students when they leave the
auditorium in batches of 25
2) The amount of money in the account every year when Rs 100 are deposited annually to accumulate at compound
interest at \( 4 \% \) per annum.


Two uniform thin rods each of Length \( L \)
and mass \( m \) are joined as shown in the figure. Find the distance of center of mass the system from point 0


What is the capacity of a conductor?
Explain the principle of a capacitor


Among the following organic acids, the acid present in rancid butter is:
A . pyruvic acid
B. lactic acid
c. butyric acid
D. acetic acid


The sun's angular diameter is
measured to be \( 1920^{\prime \prime} . \) The distance of
the sun from the earth is \( 1.496 \times \)
\( 10^{11} \) m. What is the diameter of the sun?
A \( \cdot 1 \times 10^{9} m \)
В. \( 1.39 \times 10^{9} m \)
c. \( 13.9 \times 10^{9} \mathrm{m} \)
D. \( 139 \times 10^{9} m \)


If \( \boldsymbol{a}(\boldsymbol{p}+\boldsymbol{q})^{2}+2 \boldsymbol{b} \boldsymbol{p} \boldsymbol{q}+\boldsymbol{c}=\boldsymbol{0} \) and \( \boldsymbol{a}(\boldsymbol{p}+ \)
\( r)^{2}+2 p b r+c=0(a \neq 0), \) then
A \( \cdot q r=p^{2} \)
B \( \cdot q r=p^{2}+\frac{c}{a} \)
c. \( q r=-p^{2} \)
D. None of the above


Sequence of energy conversion in a thermal power plant is:
P) Heat energy Q) Electrical energy R Mechanical energy
A \( . P \rightarrow Q \rightarrow R \)
в. \( P \rightarrow R \rightarrow Q \)
c. \( R \rightarrow Q \rightarrow P \)
D. \( Q \rightarrow R \rightarrow P \)


A block of mass \( m \) slides in an inclined
right angled trough as shown in figure. If coefficient of kinetic friction between
block and material composing the
trough is \( \mu_{k}, \) find the acceleration of the
block.


The heat capacity for aluminium, iron,
and for zinc are \( 0.89 \mathrm{J} . \mathrm{g}^{-10} \mathrm{C}^{-1}, 0.45 \mathrm{J} \)
\( \boldsymbol{g}^{-10} \boldsymbol{C}^{-1}, 0.39 \mathrm{J} . \boldsymbol{g}^{-10} \boldsymbol{C}^{-1} \) respectively. If
\( 100 \mathrm{J} \) of heat energy was added to \( 10.0 \mathrm{g} \) sample of each of the metals, which of the following would be true?
A. \( A l \) would have the largest temperature increase
B. Fe would have the largest temperature increase
c. \( Z n \) would have the largest temperature increase
D. \( F e \) and \( Z n \) would have the same temperature increase
E. All three metals would have the same temperature increase.


Let \( p \geq 3 \) be an integer and \( \alpha, \beta \) be the
roots of \( x^{2}-(p+1) x+1=0 . \) Using mathematical induction show that
\( \boldsymbol{\alpha}^{n}+\boldsymbol{\beta}^{n} \)
is an integer


1.008 grams of hydrogen combines with \( 35.453 \mathrm{g} \) of chlorine to form \( 36.463 \mathrm{g} \) of a pure compound (hydrogen chloride) Dalton's explanation for this experimental fact might be:
A. One atom of hydrogen combines with 35.453 atoms of chlorine in this reaction
B. Hydrogen and chlorine atoms always combine in a 1:35 ratio
C. Chlorine accepts hydrogen's electron to form polar covalent hydrogen chloride
D. Hydrogen and chlorine atoms aren't created or destroyed in the process so the reactant mass is the same as the product mass.


Assertion
Solubility product of \( B a F_{2} \) will increase
on dilution.
Reason
Solubility of \( B a F_{2} \) will not change in
changing temperature
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The significance of leaching in the extraction of aluminium is:
A . it helps to remove the impurities like \( \operatorname{Si} \mathrm{O}_{2}, \mathrm{Fe}_{2} \mathrm{O}_{3} \), etco from the bauxite ore
B. it converts the ore into oxide
c. it reduces melting point of the ore
D. it eliminates water from bauxite


\( \ln \frac{2}{3} p-2 \frac{1}{2}=3 \frac{1}{2}, \) the value of \( p \) is
A . - 9
B. +6
\( c \cdot+9 \)
D.


The relationship between acceleration due to gravity \( (g) \) and universal
gravitational constant( \( G \) ) may be
represented as:
\( (M \text { and } R \) are the mass and radius of
the earth respectively
A. \( G=\frac{g M}{R^{2}} \)
В. \( g=\frac{G M}{R^{2}} \)
c. \( g=\frac{G}{R^{2}} \)
D. None of these


Name two hormones secreted by
pancreas.Write one function of each.


\( \int e^{x / 2} \sin \left(\frac{\pi}{4}+\frac{x}{2}\right) d x= \)
A \( \cdot \sqrt{2} e^{x / 2} \sin \frac{x}{2}+c \)
B . \( \sqrt{2} e^{x / 2} \cos \frac{x}{2}+c \)
C \( \cdot-\sqrt{2} e^{x / 2} \sin \frac{x}{2}+c \)
D. \( -\sqrt{2} e^{x / 2} \cos \frac{x}{2}+c \)


\( \cos ^{2} 10^{\circ}+\cos ^{2} 50^{\circ}-\cos 10^{\circ} \cos 50^{\circ} \) is
equal to?
A \( \cdot \frac{3}{2} \)
B. \( \frac{3}{4} \)
c. \( \frac{3}{2}\left(\cos 20^{\circ}+1\right) \)
D. \( \frac{3}{4}\left(\cos 20^{\circ}+1\right) \)


Which instrument is used to measure
depth of ocean?
A. Galvanometer
B. Fluxmeter
c. Endoscope
D. Fathometer


Twice the number is 24 greater than its half. Find the number.


A rectangle of sides \( 5 \mathrm{cm} \) and \( 7 \mathrm{cm} \) are
rotated along the side \( 7 \mathrm{cm} \) Find the
volume of solid so obtained.


If tangent and normal to the curve \( y= \)
\( 2 \sin x+\sin 2 x \) are drawn at
\( \boldsymbol{P}\left(\boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{3}}\right) \)
then area of the quadrilateral formed by tangent, the normal at \( p \) and coordinate
axes is
A \( \frac{\pi}{3} \)
в. \( 3 \pi \)
c. \( \frac{\pi \sqrt{3}}{2} \)
D.


Dimensional analysis of the equation
\( (V e l o c i t y)^{x}= \)
\( (\text {Pressuredifference})^{\frac{3}{2}} \cdot(\text { density })^{\frac{-3}{2}} \)
gives the value of \( x \) as:
\( A \)
B. 2
\( c \cdot 3 \)
\( D \cdot-3 \)


Hlgher is the bond order, greater is:
A. bond dissociation energy
B. covalent charcter
c. bond length
D. paramagnetism


How many carbon-hydrogen bond orbitals are available for overlap with the vacant p-orbital in ethyl carbonation
\( ? \)
A. 0
B. 3
\( c .5 \)
D.


Instantaneous rate of reaction for the
reaction \( 3 A+2 B \rightarrow 5 C \) is
A \( \cdot+\frac{1}{3} \frac{d[A]}{d t}=-\frac{1}{2} \frac{d[B]}{d t}=+\frac{1}{5} \frac{d[C]}{d t} \)
B. \( -\frac{1}{3} \frac{d[A]}{d t}=-\frac{1}{2} \frac{d[B]}{d t}=+\frac{1}{5} \frac{d[C]}{d t} \)
C \( \cdot-\frac{1}{3} \frac{d[A]}{d t}=+\frac{1}{2} \frac{d[B]}{d t}=-\frac{1}{5} \frac{d[C]}{d t} \)
D. \( +\frac{1}{3} \frac{d[A]}{d t}=-\frac{1}{2} \frac{d[B]}{d t}=-\frac{1}{5} \frac{d[C]}{d t} \)


Which is the smallest side in the
following triangle? \( \angle P: \angle Q: \angle R=1: 2: 3 \)
A. \( P Q \)
в. \( Q R \)
c. \( P R \)
D. cannot be determined


If \( f(x) \) is differentiable in \( [a, b] \) such that \( f(a)=2, f(b)=6, \) then there
exists at least one \( c, a<c<b, \) such
\( \operatorname{that}\left(b^{3}-a^{3}\right) f^{\prime}(c)= \)
A \( \cdot c^{2} \)
B . \( 2 c^{2} \)
\( c .-3 c^{2} \)
D. \( 12 c^{2} \)


For the gas phase exothermic reaction,
\( A_{2}+B_{2} \rightleftharpoons C_{2}, \) carried out in a closed
vessel, the equilibrium moles of \( A_{2}, \) can be increased by:
A. increasing the temperature
B. decreasing the pressure
c. adding inert gas at constant pressure
D. removing some \( C_{2} \)


A particle's velocity \( v \) at time \( t \) is given by \( v=2 e^{2 t} \cos \frac{\pi t}{3} . \) The least value of \( t \) at
which the acceleration becomes zero is
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{3}{2} \)
\( ^{\mathrm{c}} \cdot \frac{3}{\pi} \tan ^{-1}\left(\frac{6}{\pi}\right) \)
D. \( \frac{3}{\pi} \cot ^{-1}\left(\frac{6}{\pi}\right) \)


Give one point of dissimilarity between lanthanides and actinides.


Discuss the applicability of Rolle's theorem for the following function on the indicated interval:
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{3}[\boldsymbol{x}] \) for \( -\mathbf{1} \leq \boldsymbol{x} \leq \mathbf{1}, \) where \( [\boldsymbol{x}] \)
denotes the greatest integer not
exceeding \( \boldsymbol{x} \)


By heating pig iron in furnace it is converted to
A. wrought iron
B. impure iron
c. carbon iron
D. none of the above


The pressure exerted on the fluid contents of the cortical cells of root by turgidity, which forces the water into
xylem vessels and upward into stem for a certain height is
A. Imbibition
B. Root pressure
c. capillarity
D. None of the above


The correct statements with respect to Ellingham's diagram among the following are
(I) Magnesium reduces aluminium oxide below \( 1700 \mathrm{K} \)
(II) Aluminium reduces magnesium
oxide above \( 1700 \mathrm{K} \)
(III) Aluminium reduces magnesium oxide below \( 1700 \mathrm{K} \)
(IV) Magnesium reduces aluminium oxide above \( 1700 \mathrm{K} \)
\( A \cdot|\&| \mid \)
B. ॥ \& ॥ I
c. III \& IV
D. II, III \& IV


In the Kjeldahl's process, the nitrogen present in the organic compound is changed into by heating the compound with concentrated
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)


If the point \( (2 K-3, K+2) \) lies on the
\( \operatorname{graph} \) of equation \( 2 x+3 x+15=0 \)
find the value of \( x \)


If 100 calorie of heat are added to the
system and a work of 50 calorie is done
on the system, calculate the energy change of the system.


If value of acceleration due to gravity changes from one place to another, which of the following force will undergo a change?
A. Viscous force
B. Buoyant force
c. Magnetic force
D. All of the above


Verify the following:
\( \left|z_{1}-z_{2}\right|^{2}=\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}-2 \operatorname{Re}\left(z_{1} \overline{z_{2}}\right) \)


A body weighs \( 160 N \) on the earth. Find
its weight on another planet whose mass is \( \frac{5}{2} \) times mass of earth and radius \( \frac{4}{5} \) times that of earth.
A . \( 125 N \)
B. \( 625 N \)
c. \( 225 N \)
D. 25 N


One Volt is equal to -
A. 1 Joule
B. 1 Newton/Coulomb
c. 1 Joule/Coulomb
D. 1 Coulomb/Newton


In which of the following medium speed of the sound is maximum?
A. steel
B. wood
c. water
D. Air
E. Helium


Read the following statements and answer whether the given statement is true or false.

The magnitude of induced current can be decreased by increasing the area of cross section of coil
A. True
B. False


Two drops of same radius are falling through air with steady speed \( 2^{\frac{1}{3}} m / s . \) If the two drops coalesce, what would be
the terminal speed in \( m / s ? \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 4
\( c \cdot 2 \)
D.


The centre of a circle touching two intersecting lines lies on the angle bisector of the lines.
A. True
B. False


List three ways how humans have
affected the water cycle.
Prepare slogans on green house effect to announce in assembly.


All are natural fibres except
A . silk
B. cotton
c. Nylon
D. wool


\( \ln \) a series, \( \boldsymbol{T}_{\boldsymbol{n}}=\boldsymbol{2} \boldsymbol{n}+\boldsymbol{5}, \) find \( \boldsymbol{S}_{\boldsymbol{4}} \)
A .40
B. 30
c. 20
D. 10


Which of the following best describes image formation by a plane mirror?
A. A real image is formed in front of the mirror
B. A real image is formed behind the mirror
c. A virtual image is formed in front of the mirror
D. A virtual image is formed behind the mirror


The resistance of carbon \( \ldots \ldots . . . . . . . . . \) with
rise in the temperature
A. increases
B. decreases
c. remains the same
D. first increases then decreases


The minimum energy required to overcome the attractive forces between
an electron and the surface of \( A g \) metal
is \( 552 \times 10^{-19} J . \) What will be the
maximum kinetic energy of electrons ejected out from \( A g \) which is being exposed to \( U V \) light of \( \lambda=360 \), i?


Solve the inequalities for real \( x \) \( \frac{(2 x-1)}{3} \geq \frac{(3 x-1)}{4}-\frac{(2-x)}{5} \)


The number of ways of arranging \( \boldsymbol{m} \)
positive and \( n(<m+1) \) negative
signs in a row so that no two negative signs are together is
A \( .^{m+1} P_{n} \)
B. \( n+1 P_{m} \)
\( \mathrm{c} \cdot^{m+1} C_{n} \)
D. \( n+1 C_{m} \)


\( \int \frac{\cos x+\sin x}{\cos x-\sin x} d x \)
\( \mathbf{A} \cdot \log \sin (\pi / 4+x) \)
\( \mathbf{B} \cdot \log \sec (\pi / 4+x) \)
\( \mathbf{C} \cdot \log \cos (\pi / 4+x) \)
D \( \cdot \log \sec (\pi / 4-x) \)


A point \( R \) with \( x \) -coordinate 4 lies on the line segment joining the points
\( P(2,-3,4) \) and \( Q(8,0,10) . \) Find the
coordinates of the point \( \boldsymbol{R} \)


A conductor of length 2 m carrying
current \( 2 \mathrm{A} \) is held parallel to an infinitely long conductor carrying current of \( 12 \mathrm{A} \) at a distance of \( 100 \mathrm{mm} \)
the force j on a small conductor is:
A \( \cdot 8.6 \times 10^{-5} N \)
B. \( 6.6 \times 10^{-5} N \)
c. \( 7.6 \times 10^{-5} N \)
D. 9.6 \( \times 10^{-5} N \)


Newton postulated his corpuscular theory of light on the basis of
A. newton's rings
B. rectilinear propagation of light
c. colour through thin films
D. dispersion of white light into colours


For the reaction:
\( 4 A l(s)+3 O_{2}(g)+6 H_{2} O+ \)
\( \boldsymbol{4} \stackrel{\theta}{\boldsymbol{O}} \boldsymbol{H} \rightarrow \boldsymbol{4}\left[\boldsymbol{A l}(\boldsymbol{O} \boldsymbol{H})_{4}\right]^{\oplus} \)
\( \boldsymbol{E}_{c e l l}^{\ominus}=\mathbf{2 . 7 3} \boldsymbol{V} \)
If \( \boldsymbol{\Delta}_{f} \boldsymbol{G}^{\ominus}[\stackrel{\oplus}{\boldsymbol{O}} \boldsymbol{H}]=-\mathbf{1 5 7} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
\( \boldsymbol{\Delta}_{f} \boldsymbol{G}^{\ominus}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=-\mathbf{2} \mathbf{3} \mathbf{7} . \mathbf{2} \boldsymbol{k} \boldsymbol{J} \boldsymbol{m o l}^{-1} \)
The value of \( \Delta_{f} G^{\ominus}\left[A l(O H)_{4}\right]^{\ominus} \) is:
[free energy of formation of \( \left(A l(O H)_{4}^{\ominus}\right] \)
A \( \cdot \Delta_{f} G^{\ominus}\left[A l(O H)_{4}\right]^{\ominus}=+3.50 \times 10^{3} k J m o l^{-} \)
в. \( \Delta_{f} G^{\ominus}\left[A l(O H)_{4}\right]^{\ominus}=+2.40 \times 10^{3} k J \) тог\( ^{-} \)
c. \( \Delta_{f} G^{\ominus}\left[A l(O H)_{4}\right]^{\ominus}=-1.30 \times 10^{3} k J m o l^{-1} \)
D. None of these


Which of the following provide maximum mechanical strength to a
tree trunk ?
A. Heart wood
B. Sap wood
\( c . \) cork
D. Late wood


What is the coordination number of
\( C s^{+} \) and \( C l^{-} \) in \( C s C l \) structure?


As the temperature of a transistor increases, the collector current will
A. increase
B. decrease
c. remain constant
D. depends on the situation


If Kabir pays back Rohan Rs.6232.50 for the loan of Rs 4500 that he had tajen at \( 28 \% \) interest p.a., how many months did Kabir take to pay back Rohan's money?


A particle of charge \( \boldsymbol{q}=\mathbf{1 6} \times \mathbf{1 0}^{-18} \mathbf{C} \)
moving with \( 10 m s^{-1} \) along \( x- \) axis
enter a magnetic field of induction \( \boldsymbol{B} \) along the \( y- \) axis and an electric field \( 10^{4} \mathrm{Vm}^{-1} \) along negative \( z- \) direction. If
the particle continues to move along \( x- \) axis then the strength of magnetic field is
\( \mathbf{A} \cdot 10^{5} \mathrm{Wbm}^{-2} \)
B. \( 10^{16} \mathrm{wbm}^{-2} \)
c. \( 10^{-3} \mathrm{wbm}^{-2} \)
D. \( 10^{3} \mathrm{wbm}^{-2} \)


Chemiosmosis is a universal
mechanism by which organisms
harvest and store energy.
Which of the following best describes
the process?
A. It is the process of whereby a proton gradient drives an energy-requiring reaction.
B. It is the process used to move protons up a concentration gradient for subsequent production of ATP
C. It is the process that uses pumps to drive chemicals across the membrane
D. It is the movement of specific chemicals against its gradient coupled to the flow of protons down its concentration gradient.


If the price of potatoes is reduced by \( 25 \%, \) one can buy \( 6.25 \mathrm{kg} \) more for Rs.
100. The reduced price of potatoes is
A. Rs. 3 per kg
B. Rs. 3.50 per kg
c. Rs. 4 per \( \mathrm{kg} \)
D. Rs. 4.50 per kg


If the work done by a body on
application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking
the constant force as 5 units. Also read
from the graph the work done when the distance travelled by the body is
(i) 2 units
(ii) 0 unit.


A real image is always .......(inverted,
magnified)


Podocytes occur in
A. Large intenstine
B. Bowman's capsule
c. wall of capillaries
D. Neck region


Which of the following is an example of biodegradable waste?
A . Glass
B. Metal
c. Plastic
D. Fruits


Which of the following metals form just one kind of oxide?
This question has multiple correct options
A. Sodium
B. Rubidium
c. caesium
D. Potassium


Equal volumes of \( 0.1 M A g N O_{3} \) and
\( 0.2 M N a C l \) are mixed. The
concentration of \( N O_{3}^{-} \) ions in the mixture will be:
\( \mathbf{A} \cdot 0.1 M \)
B. \( 0.05 M \)
\( c \cdot 0.2 M \)
D. \( 0.15 M \)


\( \frac{x^{4}}{(x-a)(x-b)(x-c)}=p(x)+ \)
\( \frac{\boldsymbol{A}}{\boldsymbol{x}-\boldsymbol{a}}+\frac{\boldsymbol{B}}{\boldsymbol{x}-\boldsymbol{b}}+\frac{\boldsymbol{C}}{\boldsymbol{x}-\boldsymbol{c}} \Rightarrow \boldsymbol{p}(\boldsymbol{x})= \)
\( A \)
B. x+a
c. \( x+a+b \)
D. \( x+a+b+c \)


IUPAC name of \( \boldsymbol{N} \boldsymbol{a}_{3}\left[\boldsymbol{C o}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})_{6}\right] \) is:
A. Sodium cobaltinitrite
B. Sodium hexanitritocobaltate (III)
c. Sodium hexanitrocobalt (III)
D. Sodium hexanitritocobaltate (II)


A heat engine is supplied with \( 250 \mathrm{kJ} / \mathrm{s} \) of heat at a constant fixed temperature of \( 227^{0} C ; \) the heat is rejected at \( 27^{0} C \)
the cycle is reversible, then what amount of heat is rejected?
A . 24kJ/s
B. 223kJ/s
c. \( 150 k J / \)
D. none of the above


Corrosion of statues and monuments
occurs due to
A. Photochemical smog
B. Carbon monoxide
c. Acid rain
D. Methane


\( \boldsymbol{I}=\int_{0}^{1} x^{2} e^{-x} d x \)
A \( \cdot_{I=1-\frac{1}{e}} \)
B \( \cdot \quad I=2-\frac{1}{e} \)
C \( \cdot \quad I=2-\frac{1}{2 e} \)
D \( \quad I=2-\frac{1}{e^{2}} \)


If \( m \) and \( n \) are order and degree of the equation \( \left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \cdot \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{3} y}{d x^{3}}\right)}+ \)
\( \left(\frac{\boldsymbol{d}^{3} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{3}}\right)=\boldsymbol{x}^{2}-\mathbf{1}, \) then
A \( . m=3, n=3 \)
в. \( m=3, n=2 \)
c. \( m=3, n=5 \)
D. \( m=3, n=1 \)


The complete graph of the function \( \boldsymbol{f} \) is
shown in the \( x y \) -plane above. For what
value of \( x \) is the value of \( f(x) \) at its
minimum?
A. -5
B. - 3
\( c .-2 \)
\( D \)


Match the terms in List 1 with those of
List 2


Find the value of \( \frac{i^{4 n+1}-i^{4 n-1}}{2} \)
A . -1
B.
\( c .-i \)
\( D \)


ff \( f(x)=a x+b \) and \( g(x)=c x+d \)
\( \operatorname{then} f(g(x))=g(f(x)) \) implies
\( \mathbf{A} \cdot f(a)=g(c) \)
B. \( f(b)=g(b) \)
c. \( f(d)=g(b) \)
D. \( f(c)=g(a) \)


If in a polygon the number of diagonals
is 54 then the number of sides of this
polygon is?


The inverse of statement" If a
quadrilateral is a rectangle,then it has two pairs of parallel sides."
A. If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides.
B. If a quadrilateral is a rectangle, then it has two pairs of parallel sides.
C. If a quadrilateral does not have two pairs of parallel sides, then it is not a rectangle.
D. None of these


What does coulomb's law of attraction
and repulsion states?
\( \mathbf{A} \cdot F \) is directly proportional to \( q_{1} q_{2} \) and inversely proportional to \( \left(r_{12}\right)^{2} \)
B. F is directly proportional to \( q_{1} q_{2} \) and inversely proportional to \( \left(r_{12}\right) \)
C. \( F \) is indirectly proportional to \( q_{1} q_{2} \) and directly proportional to \( \left(r_{12}\right)^{2} \)
D. None


\( \int(2+\log x)(e x)^{x} d x=\dots .+C ; x>1 \)
\( \mathbf{A} \cdot(e x)^{x} \)
B . \( x^{x} \)
c. \( (e x)^{-x} \)
D. \( e^{x^{x}} \)


Urea is formed in
A. Liver
B. spleen
c. Kidney
D. Lungs


If two supplementary angles have equal measure, what is the measure of each
angle?


A conductor has resistance of \( 15 \Omega \) at
\( 10^{\circ} C \) and \( 18 \Omega \) at \( 400^{\circ} C . \) Find
temperature coefficient of resistance of the material.


\( f\left(1, \frac{\pi}{6}\right),\left(2, \frac{\pi}{3}\right) \) and \( \left(3, \frac{\pi}{2}\right) \) be the
angular points of a triangle.Then the
area of the triangle is
\( \left(\frac{13-3 \sqrt{3}}{4}\right) \) sq.unit
\( ^{\mathbf{B}} \cdot\left(\frac{11-3 \sqrt{3}}{4}\right) \) sq.unit
\( ^{c} \cdot\left(\frac{10-3 \sqrt{3}}{4}\right) \) sq.unit
\( D \)


If \( \bar{u}, \bar{v}, \bar{w} \) are non-coplanar vectors and p, \( q \) are real numbers, then the equality \( [\mathbf{3} \overline{\boldsymbol{u}} \boldsymbol{p} \overline{\boldsymbol{v}} \boldsymbol{p} \overline{\boldsymbol{w}}]-[\boldsymbol{p} \overline{\boldsymbol{v}} \overline{\boldsymbol{w}} \boldsymbol{q} \overline{\boldsymbol{u}}]-[\mathbf{2} \overline{\boldsymbol{w}} \boldsymbol{q} \overline{\boldsymbol{v}} \boldsymbol{q} \overline{\boldsymbol{u}}]= \)
0 hold for
A. Exactly one value of \( (p, q) \)
B. Exactly two value of \( (p, q) \)
c. More than two but not all values of \( (p, q) \)
D. All value of \( (p, q) \)


Write the expression for the generalized form of Ampere's circuital law. Discuss its significance and describe briefly how the concept of displacement current is explained through charging/discharging of a capacitor in an electric circuit


In a mass spectrometer used for
measuring the masses of ions, the ions are initially accelerated by an electric potential \( V \) and then made to follow
semicircular paths of radius \( R \) using a
magnetic field \( B . \) If \( V \) and \( B \) are kept
constant, the ratio \( \left(\frac{\operatorname{charg} \text { on the ion }}{\text { mass of the ion }}\right) \) will be proportional to
A \( \cdot \frac{1}{R} \)
в. \( \frac{1}{R^{2}} \)
c. \( R^{2} \)
D. \( R \)


Calculate I for the given circuit
diagram.
\( A \cdot 10 A \)
\( B .5 A \)
\( c \cdot 2.5 A \)
D. 20 A


In the arrangement shown in fig, 0 is the object. An observer is to the left of
convex lens and looking towards lens. The observer will see an image
A. behind the mirror
B. between lens and mirror
c. to the left of lens
D. no image will be seen


The drain cleaner, Drainex contains
small bits of aluminium which react
with caustic soda to produce
dihydrogen. What volume of dihydrogen
at \( 20 C \) and one bar will be released
when \( 0.15 g \) of aluminium reacts?


An unbiased die is thrown again and again until three sixes are obtained. The
probability of obtaining \( 3 \mathrm{rd} \) six in the sixth throw of the die is \( \frac{1250}{x^{x}} \)


Find the number of numbers of 5 digits that can be formed with the digits
0,1,2,3,4 if the digits can be repeated
in the same number.


Fill in the blanks:
Rainbows are caused by the dispersion of white light in
A. raindrops
B. prism
c. glass slab
D. air


\( \operatorname{Let} \overrightarrow{\boldsymbol{A}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{7} \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{B}}=\hat{\boldsymbol{i}}+\mathbf{2} \hat{\boldsymbol{j}}+ \)
\( \mathbf{4} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{C}}=\frac{\mathbf{9} \hat{\mathbf{i}}+\mathbf{3 0} \hat{\mathbf{j}}+\mathbf{4} \hat{\boldsymbol{k}}}{\mathbf{5}} \)
The ratio in which \( \vec{C} \) divides \( \overrightarrow{A B} \)
internally is?
A . 1: 4
B . 2: 3
c. 3: 2
D. 5: 1


A long string having a cross-sectional
area \( 0.80 m m^{2} \) mm2and density,
\( 12.5 g / c c \) is subjected to a tension of
\( 64 N \) along the positive \( x \) -axis. One end of this string is attached to a vibrator at \( x=0 \) moving in transverse direction at
a frequency of \( 20 H z . A t t=0, \) the source is at a maximum displacement
\( \boldsymbol{y}=1.0 \mathrm{cm} . \) What is the displacement of
the particle of the string at \( x=50 c m \) at
time \( t=0.05 s ? \)
A \( .0 .71 \mathrm{cm} \)
B. \( 0.91 \mathrm{cm} \)
c. \( 0.58 \mathrm{cm} \)
D. \( 0.31 \mathrm{cm} \)


Statement-1: The core of the transformer
is laminated to avoid loss of energy. Statement-2: A laminated metal sheet
placed in a changing magnetic field has
lower eddy current.
A. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
B. Statement-! is true, statement-2 is false
c. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement- -
D. Statement-1 is false, statement-2 is true


Assertion: When number of turns in a
coil is doubled, coefficient of self inductance of the coil becomes 4 times.
Reason: This is because \( \boldsymbol{L} \propto \boldsymbol{N}^{2} \)
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Two dice are thrown simultaneously. If \( X \) denotes the number of sixes, find the
expectation of \( \boldsymbol{X} \)


State whether the given statement is
True or False.

In a telescope the focal length of eye lens is greater than objective lens.


Which of the following statements is
wrong about hydroboration oxidation?
A. The reaction proceeds through cyclic intermediate transition state and syn addition takes place
B. Reagent diborane in ether (THF) exists as borane- THF complex
C . Diborane in polar solvent \( \left(H_{2} O\right) \) exists as
\( \left[B H_{2}\right]^{\oplus}\left[B H_{4}\right]^{\ominus} \)
D. The reaction proceed through ionic intermediate and syn addition takes place.


The maximum covalency of nitrogen is
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6


Nucleic acids were discovered by
A. Watson and Crick
B. Khorana
c. wilkins
D. Miescher


An organic compound contains sulphur which is oxidised to sulphuric acid and then an excess amount of barium
chloride solution is added to it. Identify the precipitate.
A. \( B a_{2} O \)
в. \( H_{2} S O_{4} \)
\( c \cdot B a S O_{4} \)
D. None of these


An isotone of \( _{32}^{76} \) Ge is :
\( A \cdot_{34}^{78} S e \)
\( \mathrm{c} \cdot \frac{78}{33} \mathrm{Se} \)
D. \( \frac{77}{32} \) Ge


Three identical blocks, each of mass
10 kg , are pulled as shown on the
horizontal frictionless surface. If the
tension (F) in the rope is \( 30 N . \) What is the acceleration of each block? And
what are the tensions in the other
ropes? (Neglect the masses of the ropes)


Given diagram represents the
process of reproduction.
A. Fragmentation
B. Binary fission
c. Budding
D. Sexual


What is the emergency hormone?


If we plot \( \left|Z_{1}\right|=2 \) and \( \left|Z_{2}-6-8 i\right|=4 \)
on the argand plane, the locus of \( Z_{1} \)
and \( Z_{2} \) are
A. two circle touching each other
B. two circles neither touching nor intersecting
c. two circles intersecting
D. none of these


A lens produces an image of an object on a screen. If a slab of refractive index
n is placed in between lens and screen,
the screen has to be moved by distance
d behind. The thickness of slab is
A \( . n d \)
в. \( \frac{n-1}{n d} \)
c. \( \frac{(n-1) d}{n} \)
D. \( \frac{n d}{n-1} \)


In a young sporophyte of fern, nourishment from prothallus is drawn
through
A. Root
B. Rhizoids
c. Haustoria
D. Foot


Select pair of compounds in which both have different hybridization but have same molecular geometry.
A. \( B F_{3}, B r F_{3} \)
B . \( I C I_{2}^{\ominus}, B e C l_{2} \)
c. \( B e C l_{3}, P C l_{3} \)
D. \( P C l_{3}, N C l_{3} \)


Zinc sulphate contains \( 22.65 \% Z n \) and
\( 43.9 \% H_{2} O . \) If the law of constant
proportions is true, then the mass of
zinc required to give \( 40 g \) crystal will be:
A. \( 9.06 g \)
в. \( 90.6 g \)
c. \( 0.906 g \)
D. \( 906 g \)


A potentiometer wire of length 10 m and resistance \( 30 \Omega \) is connected in
series with a battery of emf \( 2.5 V \) internal resistance \( 5 \Omega \), and an external
resistance \( \boldsymbol{R} \). If the fall of potential
along the potentiometer wire is \( \mathbf{5 0} \mu V \boldsymbol{m} \boldsymbol{m}^{-1}, \) then the value of \( \boldsymbol{R} \) is
found to be \( 23 n \Omega \). What is \( n ? \)


An electric iron is connected to the 230
V mains supply. A current of 8 A flows through the iron. How much energy is transferred to the heater each second?
A . \( 1640 J \)
B. 1840J
c. \( 1750 J \)
D. 980J


What happens to the following after
fertilization?
Stamens


Which of the following exists as a liquid
at room temperature due to the formation of associated molecules
only?
A. Benzene
B. Ammonia
c. Bromine
D. carbon disulphide


Q Type your question
spherical shell that has radius \( R_{2} \) and
charge \( Q \)
Which of the following changes will
increase the capacitance of the
system?
: Increase the magnitude of the charge,
\( Q \)
II: Increase \( \boldsymbol{R}_{2} \) while leaving \( \boldsymbol{R}_{1} \) fixed.
III: Increase \( \boldsymbol{R}_{1} \) while leaving \( \boldsymbol{R}_{2} \) fixed.
IV: Increase both R1 and R2 while leaving
the difference in radii, \( \boldsymbol{R}_{2}-\boldsymbol{R}_{1}, \) fixed
A. I only
B. Il only
c. III only
D. III and IV only


Fill in the blank.
In a Ruby laser, the colour of laser light is due to
A. Oxygen
B. Aluminium
c. xenon
D. Chromium


What is the speed of Light \( c \) ?
A \( \cdot c=3 \times 10^{-8} \mathrm{ms}^{-1} \)
B . \( c=3 \times 10^{8} k m s^{-1} \)
c. \( c=3 \times 10^{8} \mathrm{mms}^{-1} \)
D. \( c=3 \times 10^{8} \mathrm{ms}^{-1} \)


Tungsten filament is:
A. non-polar covalent substance
B. polar covalent substance
C. ionic substance
D. metallic substance
E. noble gas


what emf \( E \) of the source must be
applied to maintain the required current? Consider the total resistance
of the circuit to be constant and equal
to
\( R . \) Disregard the inductance of the circuit.


The order of decreasing \( \boldsymbol{S}_{N} \mathbf{1} \) reactivities of the halides:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C l} \quad \boldsymbol{C H}_{2}= \)
\( \boldsymbol{C H} \boldsymbol{C H} \boldsymbol{C l C H}_{3} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H C l C} \)
\( \boldsymbol{I} \)
\( \boldsymbol{I} \)
A. \( I>I I>I I I \)
в. \( I I>I>I I I \)
c. \( I I>I I I>I \)
D. \( I I I>I I>I \)


Calculate the steady current through
the \( 2 \Omega \) resistor in the circuit shown in
the figure.


A particle has an initial velocity of \( 3 \hat{i}+ \) \( 4 \hat{j} \) and an acceleration of \( 0.4 \hat{i}+0.3 \hat{j} . \) Its
speed after \( 10 s \) is?


Two important groups of detritivores
are
A. Animals and plants
B. Prokaryotes and algae
c. Prokaryotes and fungi
D. Plantae and prokaryotes


In the periodic table, the element with atomic number 6 will be in:
A. second period
B. third period
c. fourth period
D. fifth period


In a meter bridge experiment, the ratio of the left gap resistance to right gap resistance is \( 2: 3, \) the balance point
from left is?
\( \mathbf{A} \cdot 60 \mathrm{cm} \)
B. \( 50 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


Which of the following is not the
configuration of Lanthanoid?
\( \mathbf{A} \cdot[X e] 4 f^{10} 6 s^{2} \)
B \( \cdot[X e] 4 f^{1} 5 d^{1} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{14} 5 d^{10} 6 s^{2} \)
\( \mathbf{D} \cdot[X e] 4 f^{7} 5 d^{1} 6 s^{2} \)


Total volume of gases evolved at STP
when \( 36 g \) of \( H_{2} O \) are completely
electrolyzed between platinum electrodes:
A. 22.4 litt
B. 44.8 litt
c. 33.6 litt
D. 67.2 lit


Let the complex number \( z_{1}, z_{2}, z_{3} \) be the
vertices of an equilxeral triangle. let \( z z_{0} \) be the circumcentre of the triangle,
then \( z_{1}^{2}+z_{2}^{2}+z_{3}^{2}- \)
A. \( z_{0}^{2} \)
an \( ^{2} \cdot \frac{z^{2}}{2}_{2}^{2} \)
B. \( -z_{0}^{2} \)
\( c \cdot 3 z_{0}^{2} \)
D. \( -3 z_{0}^{2} \)


One second is defined to be equal to:
A. 1650763.73 periods of krypton clock
B. 652189.63 periods of krypton clock
C. 1650755.73 periods of cesium clock
D. 9,19,26,31,770 periods of cesium clock


Evaluate \( : \int_{10}^{2}\left(x^{2}+x+2\right) d x \)


\( 10 \% \) of all aliens are capable of intelligent thought and have more than 3 arms, and \( 75 \% \) of aliens with 3 arms or less are capable of intelligent thought. If \( 40 \% \) of all aliens are capable of intelligent thought, what percent of aliens have more than 3 arms?
\( \mathbf{A} \cdot 60 \)
B. 70
c. 40
D. 45


A geometric sequence can be written as
A \( \cdot a r, a r^{2}, a r^{4}, a r^{6} \dots a r^{n} \)
B . \( a, a r^{2}, a r^{3}, a r^{4} \ldots a r^{n} \)
C. \( a, a r, a r^{1}, a r^{3}, a r^{4} \dots a r^{n} \)
D. \( a, a r, a r^{2}, a r^{3}, a r^{4} \dots a r^{n} \)


In a circle diameter, \( 40 \mathrm{cm} \), the length of a chord is \( 20 \mathrm{cm} . \) Find the length of
minor arc of the chord.


Find the odd one out
A. Transcription
B. Transduction
c. Translocation
D. Mutation


The diagram given is that of a structure present in a human kidney. Study the same and answer the question that follow.
a. What is the fluid that comes to part 2 called?
b. Name the main nitrogenous waste in
¡t.


A ray stands on a line, then the sum of
the two adjacent angles so formed is
A \( .180^{\circ} \)
B. \( 90^{\circ} \)
\( c .360^{\circ} \)
D. \( 270^{\circ} \)


Which of the following reactions taking place in the blast furnace during extraction of iron is endothermic?
A \( \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( 2 C+O_{2} \rightarrow 2 C O \)
c. \( C+O_{2} \rightarrow C O_{2} \)
D. \( F e_{2} O_{3}+3 C O \rightarrow 2 F e+3 C O_{2} \)


The interval in which \( y=x^{2} e^{-x} \) is
increasing is:
\( A \cdot(-\infty, \infty) \)
в. (-2,0)
c. \( (2, \infty) \)
D. (0,2)


A polysaccharide that is used to determine the glomerular filtration rate is inulin, is extracted from roots of
A. Dahlia
B. Gladiolus
c. chrysanthemum
D. Sunflower


Which one of the following ores is best concentrated by froth floatation method?
A. Siderite
B. Galena
c. Malachite
D. Magnetite


Molal elevation constant and molal
depression constant of water
respectively \( \left(\text { in } \quad K m^{-1}\right) \) are:
A. 0.52,1.86
В. 1.86,0.52
c. 1.52,0.86
D. 0.86,1.52


The inter nuclear distance in \( H_{2} \) and
\( C l_{2} \) molecules are 74 and 198 pm.
respectively. What will be the bond
length of \( H C l ? \)


The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius \( 3 \mathrm{cm} \) and height 7 \( \mathrm{cm} \) is
\( \mathbf{A} \cdot 108 \pi c m^{3} \)
в. \( 36 \pi c m^{3} \)
c. \( 12 \pi c m^{3} \)
D. \( \frac{4}{3} \pi c m^{3} \)


In a certain electronic transition in the
hydrogen atoms from an initial state (1) to a final state (2), the difference in the
orbital radius \( \left(r_{1}-r_{2}\right) \) is 24 times the
first Bohr radius.
Identify the transition.
\( A \cdot 5 \rightarrow 1 \)
B. 25 \( \rightarrow 1 \)
\( c \cdot 8 \rightarrow 3 \)
\( D \cdot 6 \rightarrow 5 \)


Molecular formula of sodium hydride is
A. \( \mathrm{NaH}_{3} \)
в. \( \mathrm{Na}_{2} \mathrm{H}_{2} \)
c. ман
D. \( \mathrm{Na}_{2} \mathrm{H} \)


A solution is to be kept between \( 68^{\circ} \) F
and \( 77^{\circ} \) F. What is the range in temperature in degree Celsius
(C) if the
Celcius / Fahrenheit (F) conversion
formula is given by \( \mathbf{F}=\frac{9}{5} \mathbf{C}+\mathbf{3 2} ? \)


The conjugate base of a weak acid has \( \boldsymbol{K}_{\boldsymbol{b}}=\mathbf{1 0}^{-\mathbf{9}} . \) The equilibrium constant
for the reaction of an acid with a strong
base is \( 10^{x} \) then \( x \) is:


A heating element has a resistance of
\( 100 \Omega \) at room temperature. When it is
connected to a supply of \( 220 V, a \) steady current of \( 2 A \) passes in it and
temperature is \( 500^{\circ} \mathrm{C} \) more than room
temperature. What is the temperature
coefficient of resistance of the heating element?
A. \( 1 \times 10^{-4} \cdot C^{-1} \)
-
B. \( 5 \times 10^{-4} \circ C^{-1} \)
D. \( 0.5 \times 10^{-4} \cdot C^{-1} \)


Which of the following is an improper fraction?
A \( \cdot \frac{15}{1} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D. none of the above


Partial pressure of a solution
component is directly proportional to its mole fraction. This is known as:
A. Henry's law
B. Raoult's law
c. Distribution law
D. ostwald's dilution law


Which of the following negative radical is present in bleaching powder?
A. Hypochlorite
B. Chlorate
c. Chloride
D. Both \( (A) \) and \( (C) \)


If both the mass of a body and the force acting on it are doubled, the acceleration:
A. is doubled
B. is halved
c. becomes zero
D. remains the same


Aspirin should not be taken in empty stomach, why?


The reaction \( \boldsymbol{A}(\boldsymbol{g})+\boldsymbol{B}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{C}(\boldsymbol{g})+ \)
\( D(g) \) is elementry \( 2^{n d} \) order reaction.
When started with equimolar amounts of \( A \) and \( B, \) at equilibrium, it is found that the concentration of \( A \) is twice that
of C. Specific rate for forward reaction is \( 2 \times 10^{-3} \) mol \( ^{-1} \) Lsec \( ^{-1} \). The specific
rate constant for backward reaction is:
B. \( 8 \times 10^{-3} M^{-1} \)sec\( ^{-1} \)
c. \( 1.5 \times 10^{2} M^{-1} \sec ^{-1} \)
D. None of these


If \( \boldsymbol{y}=\log _{10} \boldsymbol{x}+\log _{x} \mathbf{1 0}+\log _{x} \boldsymbol{x}+ \)
\( \log _{10} 10, \) then \( \frac{d y}{d x}= \)
A \( \cdot \frac{1}{x \log _{e} 10}-\frac{\log _{e} 10}{x\left(\log _{e} x\right)^{2}} \)
B. \( \frac{1}{\log _{e} 10}-\frac{\log _{e} 10}{x\left(\log _{e} x\right)^{2}} \)
c. \( \frac{1}{x \log _{e} 10}-\frac{\log _{e} 10}{x^{2}\left(\log _{e} x\right)^{2}} \)
D. None of these


The resistance of a decinormal solution
of an electrolyte in a conductivity cell was found to be 245 ohms Calculate the
equivalent conductivity of the solutions.


The non-metallic cation is present in:
A. \( C r O_{2} C l_{2} \)
в. \( V O C l \)
c. \( N H_{4} C l \)
D. \( P C l_{3} \)


Zero is a rational number.
if true then enter 1 and if false then
enter 0


Let \( E^{c} \) denote the complement of an
event Let \( E, F, G \) be pairwise
independent events with \( P(G)>0 \) and
\( \boldsymbol{P}(\boldsymbol{E} \cap \boldsymbol{F} \cap \boldsymbol{G})=\mathbf{0} \operatorname{then} \boldsymbol{P}\left(\boldsymbol{E}^{c} \cap \boldsymbol{F}^{c} \mid \boldsymbol{G}\right) \)
equals
\( \mathbf{A} \cdot P\left(E^{c}\right)+P\left(F^{c}\right) \)
B . \( P\left(E^{c}\right)-P\left(F^{c}\right) \)
\( \mathbf{c} \cdot P\left(E^{c}\right)-P(F) \)
D. \( P(E)-P\left(F^{c}\right) \)


The given figure represents a material
which is
A. Paramagnetic
B. Diamagnetic
c. Ferromagnetic
D. Ferrimagnetic


The amount of \( _{6}^{14} C \) isotope in a piece of wood is found to be one-fifth of that
present in a fresh piece of wood.

Calculate the age of wood. (Half life of \( ^{14} C=5577 \) years


Factorise
\( 63 a^{2}-112 b^{2} \)


Let \( \boldsymbol{A}=\{\mathbf{3}, \mathbf{6}, \mathbf{1 2}, \mathbf{1 5}, \mathbf{1 8}, \mathbf{2 1}\}, \boldsymbol{B}= \)
\( \{\mathbf{4}, \mathbf{8}, \mathbf{1 2}, \mathbf{1 6}, \mathbf{2 0}\}, \boldsymbol{C}= \)
\( \{\mathbf{2}, \mathbf{4}, \mathbf{6}, \mathbf{8}, \mathbf{1 0}, \mathbf{1 2}, \mathbf{1 4}, \mathbf{1 6}\} \) and \( \boldsymbol{D}= \)
\( \{\mathbf{5}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{2 0}\} . \) Find \( \boldsymbol{A}-\boldsymbol{C} \)


A man walks \( 30 m \) towards north, then
\( 20 m, \) towards east and in the last
\( 30 \sqrt{2} m, \) towards south-west. The
displacement from origin is:
A. \( 10 m \) towards west
B. \( 10 m \) towards east
c. \( 60 \sqrt{2} \mathrm{m} \) towards northwest
D. \( 60 \sqrt{2} m \) towards east north


Two identical ladders are arranged as
shown in the figure. Mass of each ladder
is \( M \) and length \( L \). The system is in
equilibrium. Find direction and
magnitude of friction force acting at \( \mathbf{A} \)
or B.
A \( \cdot f=\left(\frac{M+m}{2}\right) g \tan \theta \) horizontally outwards
B. \( f=\left(\frac{M+m}{2}\right) g \cot \theta \) horizontally inwards
\( ^{\mathrm{C}} \cdot f=\left(\frac{M+m}{2}\right) g \cos \theta \) horizontally outwards
D. None of these


What is electroplating? Explain the process. Give two uses of electroplating


A ball tied at the end of a string and swinging back and forth, at what point in the swing would the ball have the highest potential energy?
A. At the bottom of the swing
B. Mid way between the bottom and the top of the swing
c. At the top of the swing
D. just past the bottom of the swing on the way up
E. Just past the top of the swing on the way back down


\( z_{1} \) and \( z_{2} \) are two distinct points in an
Argand plane. If \( a\left|z_{1}\right|=b\left|z_{2}\right| \) (where \( a, b \)
\( \epsilon \mathrm{R} \) ), then the point \( \left(a z_{1} / b z_{2}\right)+ \)
\( \left(b z_{2} / a z_{1}\right) \) is a point on the
A. Line segment [-2, 2] of the real axis
B. Line segment [-2, 2] of the imaginary axis
c. Unit circle \( |z|=1 \)
D. The line with arg \( z=\tan ^{-1} 2 \)


Hydrolysis of \( \mathbf{N C l}_{3} \) gives \( \mathbf{N H}_{3} \) and \( \mathbf{X} \) Which of the following is \( X ? \)
\( A \cdot H C l O_{4} \)
в. \( \mathrm{HClO}_{3} \)
c. HOCl
D. \( \mathrm{HClO}_{2} \)


A body was supplied 1000 kilocalories
of heat. Express this heat in mega joules.


Who was the first pre-Socratic philosopher to suggest that matter could neither be created nor destroyed?
A. kepler
B. Newton
c. parmenides
D. None of these


When 100 g of ethylene polymerizes to polyethylene according to the above given equation. The weight of polyethylene produced will be :
\[
\left.n\left(\mathrm{CH}_{2}=\mathrm{CH}_{2}\right) \rightarrow+\mathrm{CH}_{2}-\mathrm{CH}_{2}-\right)_{\pi}
\]
\( A \)
\[
\frac{n}{2} g
\]
в. \( 100 \mathrm{g} \)
\( c \)
\[
\frac{100}{n} \mathrm{g}
\]
D. \( 100 \mathrm{mg} \)


Find odd one out
A. copper
B. Mercury
c. Gold
D. wood


The orbital diagram which violates the aufbau principle' is:
\( A \)
\( 2 s \) \( \boldsymbol{2 p} \) \( \uparrow \downarrow \) \( \uparrow \downarrow \quad \uparrow \)
в. \( 2 s \) 一 2 \( \uparrow \) \( \uparrow \downarrow \quad \uparrow \quad \uparrow \)
\( c \)
\( 2 s \) \( 2 p \) \( \uparrow \downarrow \) \( \uparrow \quad \uparrow \quad \uparrow \)
D. \( 2 s \)
\( \prec 2 p \) Why \( \uparrow \downarrow \) \( \uparrow \downarrow|\uparrow \downarrow| \uparrow \)


The stomach pain impulses are received by receptors known as
A. Proprioreceptors
B. Exteroreceptors
c. visceral receptors
D. chemoreceptors


Which of the following oxo-acids of sulphur has more than one oxidation state of sulphur?
A \( \cdot H_{2} S_{2} O_{3} \)
в. \( H_{2} S_{2} O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{6} \)
D. \( H_{2} S_{2} O_{8} \)


\( 1 \mathrm{cc} \) of water is taken from the surface
to the bottom of a lake having depth 100m. If bulk modulus of water is \( 2.2 \times \)
\( 10^{9} N / m^{2} \) then decrease in the volume
of the water will be
A \( .4 .5 \times 10^{-4} c c \)
B. \( 8.8 \times 10^{-4} c c \)
c. \( 2.2 \times 10^{-4} c c \)
D. \( 1.1 \times 10^{-4} c c \)


Assertion
The temperature coefficient of resistance is always positive
Reason
On increasing the temperature the resistance of metals and alloys
increase
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


\( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{5} & \mathbf{5} \boldsymbol{a} & \boldsymbol{a} \\ \mathbf{0} & \boldsymbol{a} & \mathbf{5} \boldsymbol{a} \\ \mathbf{0} & \mathbf{0} & \mathbf{5}\end{array}\right] \) If \( \left|\boldsymbol{A}^{2}\right|=\mathbf{2 5} \) then
\( |\boldsymbol{a}|= \)
\( A \cdot 5 \)
В. \( 5^{2} \)
\( c \)
\( D \)


What is the non linear \( V-I \) relation in
a pn Junction in forward bias?
A. \( I=I_{s} e^{V / V_{T}} \)
В . \( I=I_{s}\left(e^{V / V_{T}}-1\right) \)
C \( . I=I_{s}\left(1-e^{V / V_{T}}\right) \)
\( D \)


toppr
Q Type your question
decay products of the neutron.
Therefore, considering the decay of a
neutron as a two-body decay process, it
was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic
energy has a continuous spectrum. Considering a three-body decay
process, i.e. \( \boldsymbol{n} \rightarrow \boldsymbol{p}+\boldsymbol{e}^{-}+\overline{\boldsymbol{v}}_{e}, \) around
1930, Pauli explained the observed
electron energy spectrum. Assuming
the anti-neutrino \( \left(\bar{v}_{e}\right) \) to be massless
and possessing negligible energy, and
the neutron to be at rest, momentum
and energy conservation principles are
applied. From this calculation, the maximum kinetic energy of the electron
is \( 0.8 \times 10^{6} e V . \) The kinetic energy
carried by the proton is only the recoil
energy. What is the maximum energy of the
anti-neutrino?
A. Zero
B. Much less than \( 0.8 \times 10^{6} e V \).
C . Nearly \( 0.8 \times 10^{6} \mathrm{eV} \)
D. Much larger than \( 0.8 \times 10^{6} e V \)


Gymnosperms differ from angiosperms in
A. Absence of seed
B. Presence of seed coat
c. Absence of polymbryony
D. Presence of bordered pits


Let L be the set of all lines in XY-plane and \( \mathrm{R} \) be the relation in L defined as
\( \boldsymbol{R}=\left\{\left(\boldsymbol{L}_{1}, \boldsymbol{L}_{2}\right): \boldsymbol{L}_{1} \text { is parallel to } \boldsymbol{L}_{2}\right\} \)
Show that \( R \) is an equivalence relation. Find the set of all lines related to the
line \( y=2 x \)


Pick up the correct statement for Gibberellins.
1) Abnormal growth of plants is due to
\( \mathrm{G} \mathrm{A} \)
II) GA is more in concentration in tall
varieties than dwarf
III) Gibberellins have the ability to
induce flowering.
IV) GA generally inhibits flowering.
A. I and II are correct.
B. II and III are correct
c. I and III are correct
D. III and IV are correct


Assertion: In the calomel half-cell, the
reduction reaction to be considered is
\( \mathrm{Hg}_{2} \mathrm{Cl}_{2}(\mathrm{s})+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{Hg}(\mathrm{I})+2 \mathrm{Cl}^{-}(\mathrm{aq}) \)
Reason: The Saturated calomel
electrode (SCE) is a reference electrode
based on the reaction between
elemental mercury and mercury(l) chloride
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Examples of non-narcotic analgesics
are:
This question has multiple correct options
A . galactose
B. codeine
c. aspirin
D. ibuprofen


Given \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{6}, \mathbf{7}\} \) and \( \boldsymbol{B}=\{\mathbf{3}, \mathbf{4}\} \)
Form all possible ordered pairs and write the total number of
ordered pairs formed so that both the
components are from B.


By what number should \( (2)^{-7} \) be
multiplied so that the product is 1


Which type of Linkage is present in amylopectin?
A \( \cdot \alpha-D- \) Glucose \( , C_{1}-C_{4} \& C_{2}-C_{6} \)
B . \( \alpha-D- \) Glucose, \( C_{1}-C_{4} \) \& \( C_{1}-C_{6} \)
c. \( \beta-D- \) Glucose \( , C_{1}-C_{4} \) \& \( C_{2}-C_{6} \)
D. \( \beta-D- \)Glucose\( , C_{1}-C_{4} \& C_{1}-C_{6} \)


Two blocks of masses \( 10 k g \) and \( 4 k g \) are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulsive force
gives a velocity of \( 14 m s^{-1} \) to the
heavier block in the direction of the
lighter block. The velocity of centre of mass of the system at that moment is
A \( .30 m s^{-1} \)
B. \( 20 m s^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
\( \mathbf{D} \cdot 5 m s^{-1} \)


Name the unit in which work function of
a metal is generally expressed.
A. Newton
B. Kilojoule
\( c \cdot e v \)
\( D \)


The smallest and the largest values of \( \tan ^{-1}\left(\frac{1-x}{1+x}\right), 0 \leq x \leq 1 \) are
A \( .0, \pi \)
в. \( 0, \frac{\pi}{4} \)
\( c \cdot-\frac{\pi}{4}, \frac{\pi}{4} \)
D. \( \frac{\pi}{4}, \frac{\pi}{2} \)


Name the two important non-metallic oxides which causes acid rain.


A convex lens forms a real image \( 4 \mathrm{cm} \)
long on a screen.When the lens is
shifted to a new position without disturbing the object or the screen, again real image is formed on the screen which is \( 16 \mathrm{cm} \) long. The length of the object is :
A. \( 8 \mathrm{cm} \)
B. 10 \( \mathrm{cm} \)
c. \( 12 \mathrm{cm} \)
D. \( 6 \mathrm{cm} \)


The number of rational terms in the
expansion of \( \left(x^{\frac{1}{5}}+y^{\frac{1}{10}}\right)^{45} \) is
A. 5
B. 6
\( c \cdot 4 \)
D.


Mayr's biological concept of species is mainly based on
A. Morphological traits
B. Reproductive isolation
c. Modes of reproduction
D. Morphology and reproduction


What is the contribution of W.C. pei?
A. He discovered Cro-Magnon man
B. He discovered Peking man.
c. He discovered Java man
D. None of the above.


\( \int \frac{1}{1-\cos ^{4} x} d x=-\frac{1}{2 \tan x}+ \)
\( \frac{k}{\sqrt{2}} \tan ^{-1}\left(\frac{\tan x}{\sqrt{2}}\right)+C, \) where \( k= \)
A \( \frac{1}{2} \)
B. \( -\frac{1}{2} \)
\( c \cdot-1 \)
D.


Fill in the blanks by choosing the appropriate word/words from those given in the brackets:
(increases, decreases, positive, efficient, \( 68, \) non-efficient, no \( \alpha \)
hydrogen, \( \alpha \) -hydrogen, negative, Rosenmund's, greater, Cannizzaro, 74 common-ion effect, lesser, buffer action, diamagnetic, paramagnetic) The more is standard reduction
potential of a metal, the is its
ability to displace hydrogen from acids.


Acceleration due to gravity - - depth from the surface of the earth.
A. Decreases
B. Increases
c. Remains constant
D. Data insufficient


Who among the following anticipated Newton by declaring that all things gravitate to the earth?
A. Buddhagupta
B. Varahamihira
c. Aeyabhatta
D. Brahmagupta


A schematic representation of the blood
circulation is given. Which circulatory parts are incorrectly placed in it?
A. Right atrium and right ventricle
B. Left atrium and left ventricle
c. Pulmonary artery and pulmonary veins
D. Aorta and vena cava


\( \int_{0}^{1} \frac{x e^{x}}{(1+x)^{2}} d x \)


Loss of calcium due to lack of
reabsorption causes
A. Arthritis
B. osteoporosis
c. Myasthenia graviss
D. Muscular dystrophy


What is conductive hearing loss?
A. When outer or middle ear leads to problem and inefficient transfer of sound
B. When inner ear leads to problem and inefficient transfer of sound
C. When only middle ear leads to problem and inefficient transfer of sound
D. When inner and middle ear leads to problem and inefficient transfer of sound


Dominant generation in bryophyte is
A. Capsule
B. Sporophyte
c. Gametophyte
D. seta


Dilute \( 20.8 \mathrm{mL} \) of \( 6.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} \) to a
volume of 1 L. The concentration of the
resultant \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) solution is \( \boldsymbol{2 5} \boldsymbol{y} \times \)
\( 10^{-3} M, \) then \( y \) is


Water in a canal, \( 30 d m \) wide and
\( 12 d m \) deep, is flowing with a speed of
10 \( k m / \) hour. How much area will it irrigate in 30 minutes, if 8 cm of
standing water is required for irrigation
A \( \cdot 220500 m^{2} \)
B . \( 22500 m^{2} \)
c. \( 220000 m^{2} \)
D. 225000 \( m^{2} \)


The de-Broglie wavelength of a bus moving with speed 'v' is ' \( \lambda^{\prime} \). Some
passengers left the bus at a stoppage. Now when the bus moves with twice its initial speed, its kinetic energy is found to be twice its initial value. The de-
Broglie wavelength now is
\( A \cdot \lambda \)
B. \( 2 \lambda \)
c. \( \lambda / 2 \)
D. \( \lambda / 4 \)


A shell is fired from point 0 on the level ground with velocity \( 50 m / s \) at angle
\( 53^{\circ} . A \) hill of uniform slope \( 37^{\circ} \) starts
from point \( A \) that is \( 100 m \) away from the point 0 as shown in the figure. Calculate the time of flight (in seconds)


Geotropic response of roots is due to
A. Inhibition of stem growth
B. More growth on lower side
C. More growth on upper side
D. Uniform growth


The two tangents to the curve \( a x^{2}+ \)
\( 2 h x y+b y^{2}=1, a>0 \) at the points
where it crosses the X-axis, are
A. parallel
B. perpendicular
C . inclined at an angle \( \frac{\pi}{4} \)
D. None of these


Find the principal value of the following
\( \cos ^{-1}\left(\cos \frac{7 \pi}{6}\right) \)


An acellular slime mould is
A. Dictyostelium
B. Fuligo
c. Polysphondylium
D. All of the above


ESR (erythrocyte sedimentation rate) is meant for knowing
A. Degree of disease
B. Erythrocyte count.
c. Plasma volume.
D. Percentage of hemoglobin.


When Rani was buying her flat she had to put down a deposit of \( \frac{1}{10} \) of the value of the flat. What percentage was this?
A . \( 10 \% \)
B. 20\%
c. \( 30 \% \)
D. 1\%


The nucleus \( ^{23} N e \) decays by \( \beta- \) emission into the nucleus \( ^{23} N a \). Write
down the \( \beta- \) decay equation and determine the maximum kinetic energy of the electrons emitted. Given,
\( \boldsymbol{m}\left(_{\mathbf{1 0}}^{23} \boldsymbol{N} \boldsymbol{e}\right)=\mathbf{2 2 . 9 9 4 4 6 6 a m u} \) and
\( \boldsymbol{m}\left(_{11}^{23} \boldsymbol{N a}\right)=22.989770 a m u . \) Ignore the
mass of antineutrino \( (\overline{\boldsymbol{v}}): \)


In the figure six lines of emission spectrum are shown. Which of them will
be absent in the absorbtion spectrum.
A \( \cdot 1,2,3 \)
в. 1,4,6
\( c \cdot 4,5,6 \)
D. 1,2,3,4,5,6


A \( 40 k g \) boy whose leg bones are \( 4 c m^{2} \) in
area and \( 50 \mathrm{cm} \) long falls through a
height of \( 50 c m \) without breaking his leg bones. If the bones can stand a stress of
\( 0.9 \times 10^{8} N / m^{2} . \) Calculate Young's
Modulus for the material of the bone


The state of an ideal gas was changed
isobarically. The graph depicts three
such isobaric lines. Which of the
following is true about the pressures of
the gas????????
\( A \cdot P_{1}=P_{2}=P_{3} \)
в. \( P_{1}>P_{2}>P_{3} \)
\( c \cdot P_{1}<P_{2}<P_{3} \)
- \( P_{1} / P_{2}=P_{3} / P \)
\( P \)


Which of the following is a non-metal?
A . Ge
B. As
c. \( T \) e
D. se


Ether is formed when alkyl halide is treated with sodium alkoxide. This
method is known as:
A. Hoffmann reaction
B. Williamson synthesis
c. Wurtz synthesis
D. Kolbe's reaction


The expansion of a solid body depends
on:
A. Mass of the solid only
B. Nature of the solid only
c. Temperature of the solid only
D. Nature and temperature of the solid


In the given electric circuit, the current
flowing through 3 ohm resistor is 1
ampere. Find the voltage of the battery
and the current drawn from it.


If \( \boldsymbol{A}^{\prime}\left[\begin{array}{cc}-\mathbf{2} & \mathbf{3} \\ \mathbf{1} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}-\mathbf{1} & \mathbf{0} \\ \mathbf{1} & \mathbf{2}\end{array}\right] \) Find
\( [\boldsymbol{A}+\mathbf{2} \boldsymbol{B}] \)


Find the intervals in which the function
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{4} \boldsymbol{x}+\boldsymbol{6} \) is strictly
decreasing.


Q Type your question
\( A \)
COOH
B
\( c \)
coof
\( D \)


The ratio of the area of a square to that
of the square drawn on its diagonal is?
A . 1:
B. 2:
c. 1: 2
D. 1: 4


Write two principles that are used in
rocket propulsion.


Solve the following:
\( \frac{3 x}{4}-\frac{1}{4}(x-20)=\frac{x}{4}+32 \)
A .112
в. 126
\( c .108 \)
D. 102


A metal wire length \( L \), cross sectional
area \( A \) and Young's modulus \( Y \) is
stretched by a variable force \( \boldsymbol{F} . \boldsymbol{F} \) is
varying in such a way that \( \boldsymbol{F} \) is always
slightly greater than the elastic forces or resistance in the wire. When the
elongation in the wire is \( l \), up to this
instant
This question has multiple correct options
A \( \cdot \) The work done by \( F \) is \( \frac{Y A l^{2}}{2 L} \)
B. The work done by \( F \) is \( \frac{Y A l^{2}}{L} \)
C the elastic potential energy stored in wire is \( \frac{Y A l^{2}}{2 L} \)
D. No energy is lost during elongation


How many number of electrons are involved in the formation of a nitrogen
molecule?
A. Three
B. Four
c. Eight
D. six


DDT concentration recorded in human
body has been
в. \( 1.3-3.1 \) ppm
c. \( 13-31 \) ppm
D. \( 30-70 \) ppm


(a) Show, giving via suitable diagram, how unpolarized light can be polarised by reflection.
(b) Two polaroids \( P_{1} \) and \( P_{2} \) are placed with their pass axes perpendicular to
each other. Unpolarised light of
intensity \( I_{0} \) is incident on \( P_{1} . \) A third
Polaroid \( P_{3} \) is kept in between \( P_{1} \) and \( P_{2} \)
such that its pass axis makes an angle
of \( 60^{\circ} \) with that of \( P_{1} \). Determine the
intensity of light transmitted through
\( P_{1}, P_{2} \) and \( P_{3} \)


Select the correct I.U.P.A.C. name for \( \left[\left(\mathrm{C}_{6}\right.\right. \)
\( \left.\left.\mathrm{H}_{5}\right)_{3} \mathrm{P} C l \operatorname{Pd} \mathrm{Cl}_{2} \operatorname{Pd} C l\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3} \mathrm{P}\right] \)
This question has multiple correct options
A. Chloridotriphenylphosphinepalladiun (II) \( \mu \) -dich
oridochloridotriphenylphosphinepalladiun (II)
B. \( \mu \) -Dichloridodichloridobis(triphenylphosphinc)
dipalladium (II)
C . \( \mu \) -Dihloridobis( chloridotriphenylphosphinepallad
iun) (II)
D. Bis ( \( \mu \) -chloridochloridotriphenylphosphinepallad
iun) (II)


A potentiometer wire is \( 100 \mathrm{cm} \) long and a constant potential difference is maintained across it. Two cells are
connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 \( \mathrm{cm} \) and \( 10 \mathrm{cm} \) from the positive end of the wire in the two cases. The ratio of
emf's is:
A . 5: 1
в. 5: 4
\( c .3: 4 \)
D. 3: 2


The equation of a curve is \( y=\frac{e^{2 x}}{4 x+1} \)
and the point \( P \) on the curve has \( y \)
coordinate 10.

Find the gradient of the curve at \( P \)


S.I. unit of electric current is:
A. ampere
B. volt
c. farad
D. coulomb


For rusting of iron to take place, are required.
\( A \cdot H_{2} O \) and \( O_{2} \)
\( B \cdot C O_{2} \) and \( O_{2} \)
\( \mathbf{C} \cdot \mathrm{H}_{2} \) and \( \mathrm{H}_{2} \mathrm{O} \)
D. \( \mathrm{N}_{2} \) and \( \mathrm{H}_{2} \mathrm{O} \)


Multiple spathes around a spadix are
found in
A. Plantain
B. Maize
c. Lily
D. Ginger


A charge \( +q \) is fixed at each of the
points \( \boldsymbol{x}=\boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{3} \boldsymbol{x}_{0}, \boldsymbol{x}=\mathbf{5} \boldsymbol{x}_{0} \dots \dots \) up
to infinity on \( x \) axis and a charge \( (-q) \) is
fixed on each of points of \( \boldsymbol{x}=\mathbf{2} \boldsymbol{x}_{0}, \boldsymbol{x}= \)
\( \mathbf{4} \boldsymbol{x}_{0}, \boldsymbol{x}=\boldsymbol{6} \boldsymbol{x}_{0} \ldots \ldots . . \) up to infinity, here \( \boldsymbol{x}_{\mathbf{0}} \)
is a positive constant. Take the potential at a point due to a charge \( Q \) at a distance \( r \) from it \( \frac{Q}{4 \pi \varepsilon_{0} r}, \) then the potential at the origin due to above
system of charges will be :
A . 0
B. \( \infty \)
c. \( \frac{q \log _{e} 2}{4 \pi \varepsilon_{a}} \)
D. \( \frac{q}{8 \pi \varepsilon_{0} x_{0} \log _{e} 2} \)


A metal sphere of diameter \( 7 \mathrm{cm} \) falls
through a liquid of coefficient of viscosity \( 0.8 P a . s . \) When its velocity is
\( 20 c m \cdot s^{-1} \) the viscous force acting on
it is nearly \( -\cdots-N \)
A . 0.11
B. 0.22
\( c .0 .3 \)
D. 0.01


In Rosenmund reactions, presence of
\( B a S O_{4} \) acts as for Pd.
A. promoter
B. moderator
c. inhibitor
D. poison


The correct relation between
equilibrium constant \( (K), \) standard
free energy \( \left(\Delta G^{o}\right) \) and temperature
\( (T) \) is:
\( \mathbf{A} \cdot \Delta G^{o}=R T \ln K \)
B . \( K=e^{\Delta G^{G} / 2.303 R T} \)
c. \( \Delta G^{o}=-R T \log K \)
D. \( K=10^{-\Delta G^{\circ} / 2.303 R T} \)


The degree of hydrolysis of a salt of weak acid and weak base in its \( 40.1 M \)
solution is found to be \( 50 / \% \). If the molarity of the solution is \( 0.2 M, \) the percentage hydrolysis of the salt should
be
A . \( 100 \% \)
B . 50\%
c. \( 25 \% \)
D. none of the above


The receptors are found to be located in
the
A. Stomach
B. Brain
c. spinal cord
D. sense organs


Calculate Mean deviation from Median
for the given data.
Wages(Rs) \( \quad 20 \) 18 \( \mathbf{1 6} \) 14
Frequency \( \quad 2 \quad 4 \quad 9 \)
A .6 .84
в. 4.44
c. 2.24
D. 3.21


Explain the term "SYNGAS".


\( \int_{-2}^{1} \frac{|x|}{2} d x=? \)
A . 3
в. 2.
c. 1.5
D. None of these


A ball is thrown vertically up. If the ball reached at maximum height in \( 3 s \) Assume air resistance is negligible. The initial velocity of the ball is most nearly
A. \( 10 \mathrm{m} / \mathrm{s} \)
в. \( 15 \mathrm{m} / \mathrm{s} \)
c. \( 30 m / s \)
D. \( 45 \mathrm{m} / \mathrm{s} \)
E . \( 60 \mathrm{m} / \mathrm{s} \)


Solve for 'u' and 'v', 2 \( (3 u-v)=5 u v \)
and \( 2(u+3 v)=5 u v \)


For the reaction \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B}^{+} \rightleftharpoons \boldsymbol{A}^{2+}+ \)
\( 2 B ; K_{c} \) has been found to be \( 10^{12} \). The
\( \boldsymbol{E}_{c e l l}^{o} \) is:
A . 0.354
в. 0.708
c. \( 0.0098 \mathrm{v} \)
D. 1.36 \( v \)


Which oxoacid of sulphur contain \( S-S \) bond in its structure?
A. Disulphurous acid
B. Disulphuric acid
c. Perdisulphuric acid
D. Hydrosulphurous acid


Write the chemical formulae of four oxy
acids of sulphur.


A certain radioactive isotope decay has \( \alpha \) -emission, \( A_{1} X \longrightarrow A_{1}-4 \)
\( Z_{1} \)
half life of \( \boldsymbol{X} \) is 10 days. If 1 mol of \( \boldsymbol{X} \) is taken initially in a sealed container, then what volume of helium will be
collected at STP after 20 days?
A \( .22 .4 L \)
B. \( 11.2 L \)
c. \( 16.8 L \)
D. \( 33.6 L \)


Two vessels each of volume \( V \) have air at
pressure \( \boldsymbol{P}_{1} \) and temperature \( \boldsymbol{T}_{1} \). They are connected through a narrow tube and in one of the vessel the temperature
changes from \( T_{1} \) to \( T_{2} \) keeping the
other at \( T_{1} \). Find the pressure of the gas.Assume the volume of gas is negligible.
A \( \cdot \frac{2 P_{1} T_{1}}{T_{1}+T_{2}} \)
в. \( \frac{2 P_{1}}{T_{1}+T_{2}} \)
c. \( \frac{2 P_{1} T_{2}}{T_{1}+T_{2}} \)
D. None of these


Match following.
1.Kidneys
(a) Air
2.Heart
(b) Food
3.Lungs
(c) Blood
4.Stomach
(d) Wastes
A \( \cdot 1-a, 2-c, 3-d, 4-d \)
B. \( 1-d, 2-c, 3-a, 4-b \)
\( c \cdot 1-c, 2-d, 3-b, 4-a \)
D. \( 1-d, 2-c, 3-b, 4-a \)


What product is formed when
cyclohexanone is oxidised?
A. НООС\( \cdot\left(C H_{2}\right)_{4} \cdot \)СООН
в. \( C H_{3} C H_{2} C O O H \)
c. \( C H_{3}\left(C H_{2}\right)_{4} \cdot C O O H \)
D. None of the above


ff \( y=x^{2} \cos x \) then \( y_{8}(0) \) is
A . 72
B . 56
\( c \cdot 0 \)
D. - 56


The measures of the angles of a triangle are in the ratio \( 4: 5: 9 . \) The triangle is:
A. An acute angled triangle
B. A right angled triangle
c. An obtuse angled triangle
D. None of the above


For the general reaction,
If \( K_{f} \) and \( K_{b} \) are the equilibrium constant for the forward and backward
reactions, then, which of the following relationships hold good?
\[
A+B \frac{K_{f}}{F_{B_{b}}} C+D
\]
This question has multiple correct options
\( \mathbf{A} \cdot K_{f}=\frac{1}{K_{b}} \)
\( \mathbf{B} \cdot K_{f} \times K_{b}=1 \)
\( \mathbf{c} \cdot K_{f}-1=K_{b} \)
\( \mathbf{D} \cdot K_{b}+1=K_{f} \)


\( \lim _{x \rightarrow 2}\left[\frac{x^{5}-32}{x^{3}-8}\right] \)


Find the sum of the series \( 1+(1+ \)
\( \boldsymbol{x})+\left(\mathbf{1}+\boldsymbol{x}+\boldsymbol{x}^{2}\right)+\ldots \) to \( n \) terms, \( \boldsymbol{x} \neq \mathbf{1} \)


Which of the following conditions are favourable for cyclic
photophosphorylation?
A. Anaerobic condition
B. Aerobic and optimum light
c. Aerobic and low light intensity
D. Anaerobic and low light intensity


A car is travelling with linear velocity \( \mathbf{v} \) on a circular road of radius R. If its
speed is increasing at the rate of a
\( m / s^{2}, \) then the net acceleration will be
\( ^{\text {A }} \cdot \frac{v^{2}}{R}+a \)
в. \( \frac{v^{2}}{R}-a \)


\( \boldsymbol{X Y}=? \)
4.26
3.12
\( c \cdot 14 \)
\( D \)


A boy rotates his arm in clockwise
direction in front of mirror. His mirror
image rotates its arm in:
A. anticlockwise direction
B. clockwise direction
c. oscillatory motion
D. insufficient info


Thermometer construction is based on
the principle of
A. zeroth Law of Thermodynamics
B. First Law of Thermodynamics
c. Second Law of Thermodynamics
D. Third Law of Thermodynamics


At noon, the sun and the earth pull the objects on the earth's surface in opposite directions. At midnight, the \( \mathrm{gm} \) and the earth pull these objects in the same direction. Is the weight of an object, as measured by a string balance on the earth's surface, more at midnight
as compared to its weight at noon?


Complete the following equations:
(a) \( 2 N a O H+C l_{2} \rightarrow N a C l+ \)
\( +H_{2} O \)
(b) \( N a_{2} S O_{3}+2 H C l \rightarrow 2 N a C l+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( (c) C l_{2}+3 F_{2} \frac{573 K}{ } \)


Typical vertebra of human is
A. Amphiplatyan
B. Procoelous
c. Amphicoelous
D. None of the above


In fungi, mycelium breaks into fragments of hyphae and each broken fragment give rise to a new mycelium. Which of the following explains this process?
A. Fragmentation
B. Budding
c. Fermentation
D. Sedimentation


How many litres of oxygen are required for complete combustion of 39 grams of liquid benzene at STP?
\( A \cdot 84 \)
B. 22.4
\( c \cdot 42 \)
D. 11.2


A gun fires a bullet. the barrel of the gun
is inclined at an angle of \( 45^{\circ} \) with horizontal. when the bullet leaves the
barrel it will be travelling at an angle greater than \( 45^{\circ} \) with horizontal.
A. True
B. False


In the figure, 0 is the centre of the circle
Find the length of \( \mathrm{CD} \), if \( \mathrm{AB}=5 \mathrm{cm} \)


This is non biodegradable pollutant
A. Sulphur dioxide
B. Oxides of nitrogen
c. Lead vapour
D. sewage


For the coil shown in the figure what
must be done to induce a clockwise
current?
A. Either move the north pole of a magnet down into the coil, or move the south pole of the magnet up out of the coil
B. Either move the south pole of a magnet down into the coil, or move the north pole of the magnet up out of the coil
C. Move either pole of the magnet down into the coil
D. Move either pole of the magnet up into the coil


The principle of LASER action involves:
A. Amplification of particular frequency emitted by the system
B. Population inversion
c. Stimulated emission
D. All of the above


Find the Odd one among : 2,5,11,22,32
47
A . 23
B. 36
c. 27
D. 51


The probability of getting at least a
single \( ^{\prime} 1^{\prime} \) when two dice are rolled is
A \( \cdot \frac{11}{36} \)
в. \( \frac{25}{36} \)
\( c \cdot \frac{1}{6} \)
D. \( \frac{1}{8} \)


Write the stoichiometric coefficient for
the following reaction:
\( \boldsymbol{x} \boldsymbol{I}_{2}+\boldsymbol{y} \boldsymbol{O} \boldsymbol{H}^{-} \rightarrow \boldsymbol{I} \boldsymbol{O}_{3}^{-}+\boldsymbol{z} \boldsymbol{I}^{-}+\boldsymbol{3} \boldsymbol{H}_{2} \boldsymbol{O} \)
B. \( x-(3), y-(2), z-(3) \)
\( c \cdot x-(3), y-(6), z-(5) \)
\( D \cdot x-(3), y-(3), z-(3) \)


The critical temperature of a gas is the
temperature:
A. above which it can no longer remain in the gaseous state
B. above which it cannot be liquefied by pressure
C. at which it solidifies
D. at which the volume of the gas becomes zero


The ratio between the sum of \( n \) terms of
two A.P.'s is \( 3 n+8: 7 n+15 \).Find the
ratio between their 12 th terms.
A \( \cdot \frac{7}{12} \)
в. \( \frac{7}{16} \)
c. \( \frac{7}{20} \)
D. \( \frac{7}{18} \)


Fill in the blanks with appropriate
words.
Cell organelle rich in acid phosphatase and other hydrolytic enzymes is


Match The following:
\begin{tabular}{ll|l|l}
& Column-1 & & Column-2 \\
\hline \( \mathrm{A} \) & Audible range & \( \mathrm{p} \) & Faster transmission of sound \\
\hline \( \mathrm{B} \) & Infrasonic range & \( \mathrm{q} \) & Slower transmission of sound \\
\hline \( \mathrm{C} \) & Ultrasonic range & \( \mathrm{r} \) & Less than \( 20 \mathrm{Hz} \) \\
\( \mathrm{E} \) & Denser medium & \( \mathrm{s} \) & \( 20 \mathrm{Hz}-20 \mathrm{kHz} \) \\
& & & \\
Rarer medium & \( \mathrm{t} \) & More than \( 20 \mathrm{kHz} \)
\end{tabular}


Oxidation state of 'S' in sodium
tetrathionate is :
\( \mathbf{A} \cdot+5,0,0,+5 \)
в. +6,+6,0
\( \mathbf{c} \cdot+4,+2,+5 \)
D. +2,0,+2,+3


Which is wrong with respect to our responsibility as a human being to protect our environment?
A. Avoiding the use of floodlighted facilities.
B. Restricting the use of vehicles
c. Using plastic bags
D. setting up compost tin in gardens


How many \( \sigma \) and \( \pi \) bonds are present in tetracyanoethylene?
A. nine \( \sigma \) and nine \( \pi \)
B. five \( \sigma \) and nine \( \pi \)
c. nine \( \sigma \) and seven \( \pi \)
D. eight \( \sigma \) and eight \( \pi \)


Let \( A=(x \mid x \) is a prime number and
\( x<300> \) the number of different
rational numbers, whose numerator and denominator belong to \( \boldsymbol{A} \) is:
\( A \cdot 91 \)
B. 84
\( c \cdot 106 \)
D. None of these


Goldstein's work with anode rays of \( \boldsymbol{H}^{+} \) was apparently the first observation of
the :
A. protons
B. electrons
c. neutrons
D. atoms


The function \( 3 .(2)^{n-1} \) will follow which
sequences?
\( \mathbf{A} \cdot 2,6,12,24 \)
в. \( 2,4,12,24 . \)
c. 0,6,12,24
D. 3,6,12,24


The process by which the vegetable ghee can be made from the cooking oil is called as:
A. hydrogenation
B. distillation
c. crystallization
D. oxidation


The table below gives the distribution of villages under different heights from sea level in a certain region. Compute the mean height of the region:
Height in \( \begin{array}{lll}\text { 200 } & \text { 600 } & \text { 1000 }\end{array} \) meters:

No. of \( \quad 142 \quad \) 265 \( \quad 560 \) village:


If \( P(x, y) \) is any point on the line joining the points \( (a, 0) \) and \( (0, b) \) then the value of \( \frac{x}{a}+\frac{y}{b} \)
\( A \)
B. 2
\( c \cdot 3 \)
D.


Find the name of the triangle.
A. acute isosceles triangle
B. acute scalene triangle
C . acute obtuse triangle
D. acute equilateral triangle


Largest group of insecticide of plant origin are
A. Organochlorines
B. Triazines
c. Pyrethroids
D. Carbamates


The average kinetic energy \( E \) of a gas
molecule is given by the equation \( \boldsymbol{E}= \)
\( \frac{3}{2} k T \)
where \( T \) is the absolute (kelvin
temperature)

What are the SI base units if \( k \) ?
A \( \cdot k g^{-1} m^{-1} s^{2} K \)
B. \( k g^{-1} m^{-2} s^{2} K \)
c. \( k g m s^{-2} K^{-1} \)
D. \( \operatorname{kgm}^{2} s^{-2} K^{-1} \)


During electrification by friction
A. Proton are transferred from one body to another body
B. Neutrons are transferred from one body to another body
C. Electrons are transferred from one body to another body
D. None


a. What are the features of an ideal
contraceptive?
b. Mention the natural methods of
contraception.


Two drops of equal radii are falling through air with a terminal velocity of
\( 5 \mathrm{cm} s^{-1} . \) If they coalesce into one drop,
what will be the terminal velocity of the
new drop?


Which one of the following statements
concerning the ring strain in
cyclopropene is correct?
A. \( C-C=C \) angle is reduced by 30 degree compared to its normal value in propene
B. \( C-C=C \) angle is reduced by 40 degree compared to ¡ts normal value in propene
C. \( C-C=C \) angle is reduced by 50 degree compared to its normal value in propene
D. \( C-C=C \) angle is reduced by 60 degree compared to its normal value in propene


Two capacitors of capacitance \( C \) are
connected in series. If one of them is
filled with a substance of dielectric
constant \( K, \) what is the effective
capacitance?
\( ^{A} \cdot \frac{K C}{(1+k)} \)
в. \( C(K+1) \)
c. \( \frac{2 K C}{(1+k)} \)
D. None of these


The emf of a cell is \( \varepsilon \) and its internal
resistance is \( r . \) Its terminals are
connected to a resistance \( R \) The
potential difference between the
terminals is \( 1.6 V \) for \( R=4 \Omega, \) and \( 1.8 \mathrm{V} \)
for \( \boldsymbol{R}=\mathbf{9} \boldsymbol{\Omega} . \) Then
\( \mathbf{A} \cdot \varepsilon=1 V, r=1 \Omega \)
B. \( \varepsilon=2 V, r=1 \Omega \)
\( \mathbf{c} \cdot \varepsilon=2 V, r=2 \Omega \)
D. \( \varepsilon=2.5 V, r=0.5 \Omega \)


If \( \log _{\sqrt{3}} \frac{\left|z^{2}\right|-|z|+1}{2+|z|}<2, \) then locus of
\( z \) is
A \( .|z|<1 \)
В. \( 0<|z|<5 \)
c. \( |z|>1 \)
D. \( |z|>5 \)


The periodic time of a vibrating body is 0.01 sec. Its frequency will be
A. 1.0 cycles \( / s \)
B. 10.0 cycles / s
c. 100.0 cycles \( / \) s
D. 1000.0 cycles \( / s \)


\( \operatorname{Let} f(x)=7 \tan ^{8} x+7 \tan ^{6} x- \)
\( 3 \tan ^{4} x-3 \tan ^{2} x \) for all \( x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)
then the correct expression(s) is (are) This question has multiple correct options
\( \int_{0}^{\frac{\pi}{4}} x f(x) d x=\frac{1}{12} \)
B. \( \int_{0}^{\frac{\pi}{4}} f(x) d x=0 \)
c. \( \int_{0}^{\frac{\pi}{4}} x f(x) d x=\frac{1}{6} \)
D \( \int_{0}^{\frac{\pi}{4}} x f(x) d x=1 \)


Which of the following is used in the management of psychoses and
neuroses?
A. Tranquilizers
B. Opiates
c. Hallucinogens
D. cocaine


The flux of the electric field due to
charges distributed in a sphere of
radius \( 5 \mathrm{cm} \) is \( 10 \mathrm{Vm} \). What will be the
electric flux, through a concentric
sphere of radius \( 10 \mathrm{cm} ? \)
\( \mathbf{A} \cdot 20 \mathrm{Vm} \)
B. \( 30 \mathrm{Vm} \)
\( \mathbf{c} .5 \mathrm{Vm} \)
D. \( 10 \mathrm{Vm} \)


If \( A \) and \( B \) are two event such that
\( P(A)=\frac{3}{4} \) and \( P(B)=\frac{5}{8}, \) then
\( ^{\mathbf{A}} \cdot P(A \cup B) \geq \frac{3}{4} \)
В. \( P(\bar{A} \cap B) \leq \frac{1}{4} \)
c. \( \frac{3}{8} \leq P(A \cap B) \leq \frac{5}{8} \)
D. All of these


Which of the following is a soft material
in the tooth?
A. Root
B. Dentine
c. Pulp
D. crown


In a first order reaction the
concentration of reactant decreases
from \( 800 m o l / d m^{3} \) to \( 50 m o l / d m^{3} \) in
\( 2 \times 10^{2} s . \) The rate constant of reaction
\( \operatorname{in} s^{-1} \) is:
\( A \cdot 2 \times 10^{4} \)
B . \( 3.45 \times 10^{-5} \)
c. \( 1.386 \times 10^{-2} \)
D. \( 2 \times 10^{-4} \)


Energy band gap between valence band and conduction band for insulator is:
A. Zero
B. greater than 9 eV
c. less than conductors
D. approximately \( 1 e V \)


Kidneys are organs of excretion in
A. All chordates
B. Mammals only
C. Mammals, reptiles and amphibians only
D. Mammals and amphibians


Which of the following is not lewis
base?
A \( . C H_{4} \)
в. \( C_{2} H_{5} O H \)
c. Acetone
D. Secondary Amine


A step down transformer having efficiency of \( 75 \% \) supplies 3
ampere current at 120 volt. Calculate
the current in its primary coil, if it is operated at 440 volt.
\( A \cdot 2 \)
B.
\( c \cdot 3 \)
D. 4


Select the liquid which has the specific heat capacity of \( 4180 J K g^{-1} K^{-1} \) from the following.(mercury, kerosene, water, coconut oil)


A copper voltameter is connected in
series with a coil of resistance \( 10 \Omega \)
When a steady current is passed through the circuit, \( 0.297 g \) of copper is found to be deposited at the cathode in 15 \( \min \). The electrochemical equivalent
of copper is \( 3.3 \times 10^{-7} k g C^{-} . \) Heat
liberated in the coil is:
A. \( 900 J \)
в. \( 90 J \)
c. \( 9 J \)
D. \( 9 k J \)


Entropy change in \( \mathrm{JK}^{-1} \)
is
(Give answer to the nearest integer)


A carnot refrigeration cycle absorbs heat at270 Kand rejects heat at \( 300 K \)
If the cycle is absorbing \( 1260 K J / \) min at \( 270 K \), then work required per second
is :
A \( .2 .33 \mathrm{KJ} / \mathrm{sec.} \)
в. \( 4.66 K J / \)sec.
c. \( 1 K J / \) sec.
D. \( 4 K J / \)sec.


An object is placed \( 10 \mathrm{cm} \) away from a
glass piece \( (\mu=1.5) \) of length \( 20 \mathrm{cm} \)
bound by spherical surfaces of radii of
curvature \( 10 \mathrm{cm} . \) Find the position of
final image formed after refractions.


Compare the fractions. \( \frac{1}{3} \square \frac{7}{8} \)


When we say a nephron is the structural and functional unit of the kidneys, we mean that
(P) The kidney is made up of many nephrons.
(Q) The filtration of blood that occurs in the kidneys is because of what the nephrons do.
(R) Urea formation occurs in the
nephrons.
A. Only P and Q
B. Only Q and R
c. only \( \mathrm{P} \) and \( \mathrm{R} \)
D. P, Q and R


Conversion of glucose to glucose- 6 phosphate can be termed as
A. Anabolic reaction
B. Catabolic reaction
c. Both A and B
D. None of the above


The electronic configuration of gadolinium (At. no.64) is:
A \( \cdot[X e] 4 f^{8}, 5 d^{0}, 6 s^{2} \)
B . \( [X e] 4 f^{7}, 5 d^{1}, 6 s^{2} \)
C . \( [X e] 4 f^{3}, 5 d^{5}, 6 s^{2} \)
D . \( [X e] 4 f^{6}, 5 d^{2}, 6 s^{2} \)


Choose the correct statement about
displacement d:
A. It is inversely proportional to the length a
B. It is directly proportional to the kinetic energy of incident particle \( \left(\frac{1}{2} m v_{0}^{2}\right) \)
c. It is directly proportional to the electric field E
D. For lesser \( \frac{q}{m} \) (charge to mass ratio), it is higher


There are two spheres of same material and radius. One is solid and the other is
hollow. If they are heated to the same temperature the expansion of:
A. Solid sphere is more.
B. Hollow sphere is more
c. Solid and hollow spheres are equal.
D. Solid is outwards while that of hollow inwards


Assertion
On heating a substance to its melting
point, inter-particle space increases.
Reason
When a substance is heated, the kinetic
energy of the particles(molecules/atoms) increases,
due to which they push each other farther than their mean position.
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.


Draw a schematics representation of transport and exchange of oxygen and carbon dioxide in human body


Which of the following mixtures in aqueous solution acts as a buffer?
A. \( H N O_{3}+K N O_{3} \)
в. \( H_{2} S O_{4}+K_{2} S O_{4} \)
c. \( N H_{4} O H+N H_{4} C l \)
D. \( C H_{3} \) СООН \( + \) NaCl


A source of sound gives five beats per second, when sounded with another
source of frequency \( 100 s^{-1} \). The second
harmonic of the source together with a source of frequency \( 205 s^{-1} \) gives
5 beats/sec. The frequency of the first source is
A \( \cdot 105 s^{-1} \)
B. \( 205 s^{-1} \)
c. \( 95 s^{-1} \)
D. \( 100 s^{-1} \)


Subtract the sum of -340 and 170 from
-45


In a set of \( 2 n \) observations, half of them
are equal to ' \( \alpha \) ' and the remaining half
are equal to ' - \( \boldsymbol{\alpha} \) '. If the standard
deviation of all the observations is 2 then the value of \( |\boldsymbol{\alpha}| \) is equal to
A .2
B. \( \sqrt{2} \)
\( c \cdot 2 \sqrt{2} \)
D. 4


Consider \( \mathbf{f}(\mathbf{x})=\left\{\begin{array}{l}\frac{x^{2}}{|x|}, \mathbf{x} \neq 0 \\ \mathbf{0}, \mathbf{x}=0\end{array}\right. \)
Then find the continuity of the function
\( f(x) \)
\( \mathbf{A} \cdot f(\mathrm{x}) \) is discontinuous every where
B. \( f(x) \) is continuous only at \( x=0 \)
C \( . f(x) \) is discontinuous everywhere except at \( x=0 \)
D. \( f(x) \) is continuous everywhere


Let \( \lim _{x \rightarrow a} f(x) \) exists but it is not equal to \( f(a) \). Then \( f(x) \) is discontinuous
at \( x=a \) and a is called a removable
discontinuity. If \( \lim _{x \rightarrow a^{-}} f(x)= \)
\( l \) and \( \lim _{x \rightarrow a^{+}} f(x)=m \) exist but \( l \neq \)
\( m . \) Then a is called a jump
discontinuity. If one of the limits (left hand limit or right hand limit ) does not exist, then a is called an infinite discontinuity.
\( \operatorname{Let} f(x)\left\{\begin{array}{cc}2|x|, & x \leq-1 \\ 2 x, & -1 \leq x \leq 0 \\ x+1, & 0<x \leq 1 \\ 2 & x>1\end{array} \) Then \right.
\( f(x) \) at
This question has multiple correct options
A. \( x=-1 \) is a removable discontinuity
B. \( x=0 \) is a jump discontinuity
c. \( x=1 \) is a removable discontinuity
D. \( x=-1 \) is a jump discontinuity


particular coastal location in Japan
seem mostly to resemble the legendary face of a Samurai. Given below are two
explanations of this observed fact. Which of these strikes you as a
scientific explanation?
(a) A tragic sea accident several centuries ago drowned a young Samurai. As a tribute to his bravery,
nature through its inscrutable ways immortalised his face by imprinting it
on the crab shells in that area.
(b) After the sea tragedy, fishermen in
that area, in a gesture of honour to their dead hero, let free any crab shell caught by them which accidentally had a shape resembling the face of a Samurai. Consequently, the particular shape of the crab shell survived longer and therefore in course of time the
shape was genetically propagated. This is an example of evolution by artificial selection.


An electrolytic cell is taken with two graphite rods inserted in it and connected to opposite terminals of a battery. An electric bulb is also
introduced on the circuit. Different
substances are taken in the cell and the
conductivity is tested. Identify the case
where the bulb glows most brilliantly.
A. Molten lead bromide
B. Molten wax
c. Kerosene oil
D. Barium sulphate in water


\( \sum_{k=1}^{2 n+1}(-1)^{k-1} k^{2}= \)
\( \mathbf{A} \cdot(n+1)(2 n+1) \)
B. \( (n+1)(2 n-1) \)
\( \mathbf{c} \cdot(n-1)(2 n-1) \)
D. \( (n-1)(2 n+1) \)


Amoeba is
A. Ammonotelic
B. Ureotelic
c. Uricotelic
D. None of the above


Hertz is the unit of
A. wavelength
B. amplitude
c. frequency
D. None of these


Find the derivative of the following functions (it is to be understood that
\( a, b, c, d, p, r \) and \( s \) are fixed non-zero constants and \( m \) and \( n \) are integers) \( \frac{\boldsymbol{a}}{\boldsymbol{x}^{4}}-\frac{\boldsymbol{b}}{\boldsymbol{x}^{2}}+\cos \boldsymbol{x} \)


Symplastic movement of water takes place through
A. cell wall
B. plasmodesmata
c. endodermis
D. casparian strip


In the given situation it is known that
when released the blocks slide. Find the
time(in second) when the small block
will fall off from the larger block. (The
size of \( m \) is very -very small then \( M, \) see
figure). If \( \boldsymbol{m}=\mathbf{1} \mathbf{k g}, \boldsymbol{M}=\mathbf{4 k g}, \boldsymbol{l}=\mathbf{4 m} \)
\( \boldsymbol{\theta}=\mathbf{3 7}^{o}, \boldsymbol{\mu}=\mathbf{0 . 4} \)


Two masses \( m_{1} \) and \( m_{2} \) are connected
to a spring of spring constant \( K \) at two
ends. The spring is compressed by \( y \) and released. The distance moved by
\( m_{1} \) before it comes to a stop for the first time is
A. \( \frac{m_{1} y}{m_{1}+m_{2}} \)
в. \( \frac{m_{2} y}{m_{1}+m_{2}} \)
c. \( \frac{2 m_{1} y}{m_{1}+m_{2}} \)
D. \( \frac{2 m_{2} y}{m_{1}+m_{2}} \)


Draw a diagram of show how NAND gates can be combined to obtain an OR gate.(Truth table is not required).


A charge \( q \) is placed at 0 in the cavity in a spherical uncharged conductor, Point S is outside the conductor. If q is
displaced from 0 towards \( S \) (still
remaining within the cavity)
A . electric field at S will increase
B. electric field at S will decrease
c. electric field at \( S \) will first increase and then decreas
D. electric field at S will not change


The \( u_{r m s} \) of gas at \( 327^{\circ} C \) is :
A \( \cdot 611.66 \frac{m}{s e c} \)
В . \( 19342.44 \frac{\mathrm{m}}{\mathrm{sec}} \)
с. \( 1223.22 \frac{m}{s e c} \)
D. \( 96.71 \frac{m}{s e c} \)


Which of the following is zerone?
A \( \cdot C H_{3} C H O \)
в. \( C H_{3} O H \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( C_{2} H_{5} O H \)


Which of the following is not a cause of acid rain?
A. Burning of fossil fuels
B. Bacterial decomposition of organic matter
c. Internal combustion engines
D. None of the above


Calculate the mass of a body in tonnes
whose volume is \( 2 \mathrm{m}^{3} \) and \( \mathrm{R.D} \) is 5.2


Find the inclination of the line whose
slope is 0


A curved road of \( 50 m \) in radius is
banked to correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should
be changed to
A. 200 \( \mathrm{m} \)
B. 100 \( m \)
\( c \cdot 50 m \)
D. None of the above


Explain the mechanism of alkaline
hydrolysis of tert-butyl bromide with energy profile diagram.
Define carbolic acid
How carbolic acid is prepared from benzene sulphonic acid?


In the given Fig
f \( \boldsymbol{A B} \| \boldsymbol{C D}, \boldsymbol{E F} \perp \boldsymbol{C D} \boldsymbol{a n d} \angle \boldsymbol{G} \boldsymbol{E D}= \)
\( 126^{\circ}, \) Find \( \angle A G E, \angle G E F, \angle F G E \)


A first order reaction is \( 75 \% \) completed
in 100 minutes. How long time will it take for it's \( 87.5 \% \) completion?
A. 125 min
B. 150 min
c. 175 min
D. 200 min


Platinum forms two different
compounds with chlorine. One contains
\( 26.7 \% C l \) by mass, and the other contains 42.1 per \( C l \) by mass \( (P t= \)
195). The empirical formulae of the two
compounds are \( \boldsymbol{P t C l}_{2} \) and \( \boldsymbol{P t C l}_{4} \) respectively. If true enter 1 , else enter 0 .


Botanical gardens are living herbaria?
Comment.


Tyndall effect is applicable when:
This question has multiple correct options
A. the diameter of the dispersed particles is not much smaller than the wavelength of the light used
B. the diameter of the dispersed particles is much smaller than the wavelength of the light used
C. the refactive indices of the dispersed phase and the dispersion medium must be same
D. the refractive indices of the dispersed phase and the dispersion medium must differ greatly in magnitude


If the angle between the lines joining the end points of minor axis of an ellipse with its foci is \( \frac{\pi}{2}, \) then the eccentricity of the ellipse is
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{\sqrt{2}} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{1}{2 \sqrt{2}} \)


Which of the following metal reacts with steam to liberate hydrogen?
A. Magnesium
B. Aluminium
c. zinc
D. All of the above


Two dice are thrown together. Find the
probability of getting a sum equal to 8


One angle of a seven-sided polygon is
\( 114 . \) and each of the other six angles is \( x \)
\( 0^{0} \) The value of \( x \) is
A \( .114^{\circ} \)
B . \( 121^{\circ} \)
\( c \cdot 131^{0} \)
D. \( 151^{\circ} \)


If \( A \) is a \( 3 \times 3 \) invertible matrix, then
what will be the value of \( k \) if
\( \operatorname{det}\left(A^{-1}\right)=(\operatorname{det} A)^{k} \)


Which one is as incorrect match?
A. Myopia - Biconvex lens
B. Olfactory - Smell
C. Algerireceptor - Pain
D. Organ of corti cells - Sensory and supporting


Number of heart chambers present in human is 3
A . True
B. False


Which of the following is not related to
baking soda?
A. The molecular formula is \( N a H C O_{3} \)
B. It is used in soda -acid fire extinguishers
C. It is alkaline in nature
D. It is acidic in nature


\( \int \sqrt{1-\sin x} d x= \)
A. \( 2 \sqrt{1+\sin x}+C \)
B . \( 2 \sqrt{1-\sin x}+C \)
c. \( 2 \sqrt{1-2 \sin x}+C \)
D. \( 2 \sqrt{1-\sin 2 x}+C \)


Differentiate with respect to \( x \) :
\( \left(\sin ^{-1} x^{4}\right)^{4} \)


If \( G \) and \( G^{\prime} \) be the centroids of the
triangles \( A B C \) and \( A^{\prime} B^{\prime} C^{\prime} \) respectively, then \( \overrightarrow{\boldsymbol{A A}^{\prime}}+\overrightarrow{\boldsymbol{B B}^{\prime}}+\overrightarrow{\boldsymbol{C C}^{\prime}}= \)
A \( \cdot \frac{2}{3} \overrightarrow{G G^{\prime}} \)
в. \( \overrightarrow{G G^{\prime}} \)
\( \mathbf{c} \cdot 2 \overrightarrow{G G^{\prime}} \)
\( \mathbf{D} \cdot 3 \overrightarrow{G G^{\prime}} \)


Resistance of a electric heater is \( 20 \Omega \)
and it draws a current of 2A. Calculate
its power.
A. 0 (zero) \( w \)
B. 20w
c. \( 40 \mathrm{w} \)
D. 80w


Best stage to observe shape, size and number of chromosomes is
A. Interphase
B. Metaphase
c. Prophase
D. Telophase


Aldehydes and ketones are
differentiated by using:
\( \mathbf{A} \cdot N a O H / I_{2} \)
B. \( N a H S O_{3} \)
\( \mathbf{c} \cdot A g N O_{3} / N H_{4} O H \)
D. \( N H_{2}-N H_{2} \)


Find the factor which will rationalise:
\( 2+\sqrt[4]{7} \)


An organic compound gave 0.4655 g of
\( C O_{2} \) on complete combustion. If the
mass of the compound taken was 0.2115
g. what is the percentage of \( C \) in it?
A . 13.30\%
в. 26.67\%
c. 60.03\%
D. 28.80\%


An ungraduated thermometer of
uniform bore is attached to a
centimeter scale and is found to read
\( 10 \mathrm{cm} \) in melting ice, \( 30 \mathrm{cm} \) in boiling
water and \( 16 \mathrm{cm} \) in a liquid. Find
temperature of the liquid.


What is the shortest wavelength present in the Paschen series of
spectral lines?


Number of segments present in earthworm is
A. \( 85-400 \)
B. 100-200
c. 20-95
D. 115-120


\( \mathrm{n} P O_{4}^{-3} \) ion, the formal charge on the oxygen atom of \( \boldsymbol{P}-\boldsymbol{O} \) bond is :
\( A \cdot+1 \)
B. - 1
c. -0.75
D. +0.75


Peroxisomes are related in
A. Photosynthesis
B. Photorespiration
C . Respiration
D. None of the above


The quadratic polynomial whose sum of
zeroes is 3 and product of zeroes is -2 is:
A \( \cdot x^{2}+3 x-2=0 \)
B . \( x^{2}-2 x+3=0 \)
c. \( x^{2}-3 x+2=0 \)
D. \( x^{2}-3 x-2=0 \)


Heating of sugar solution is a chemical change
A . True
B. False


find the value of the following:
\( (i) \sin ^{-1}\left(\frac{-1}{2}\right) \)
\( (i i) \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
\( (i i i) \operatorname{cosec}^{-1}(2) \)
\( (i v) \tan ^{-1}(-\sqrt{3}) \)
\( (v) \cos ^{-1}\left(\frac{-1}{2}\right) \)
\( (v i) \tan ^{-1}(-1) \)


Mitochondria is the site of
A. \( C O_{2} \) uptake in photosynthesis
B. \( O_{2} \) uptake during respiration
C. The release of energy during respiration
D. Cell division


A p-type semiconductor is
A. positively charged
B. negatively charged
C . uncharged
D. uncharged at OK but charged at higher temperatures


A particle execute S.H.M from the mean position. its amplitude is \( A \), its time period is "T.' At what displacement,its speed is half of its maximum speed.
A \( \cdot \frac{\sqrt{3} A}{2} \)
в. \( \frac{\sqrt{2}}{3} A \)
c. \( \frac{2 A}{\sqrt{3}} \)
D. \( \frac{3 A}{\sqrt{A}} \)


Tautomerism is shown by:
\( \mathbf{A} \cdot H C N \)
\( c \)
D. \( C C l_{3} C H O \)


Increasing entropy in the universe
means that
A. Organisms can use the energy released to break down food products.
B. There is increasing amounts of heat energy and small particles of matter becoming disordered
C. Reactions cannot occur spontaneously
D. The entropy in a system also must increase.


In potassium bromide solution, chlorine displace:
A. bromide
B. iodide
c. chloride
D. fluoride


According to MOT (Molecular Orbital Theory), the molecular orbitals are
formed by mixing of atomic orbitals through LCAO (linear combination of
atomic orbitals). The correct statement
(s) about molecular orbitals is/are
Statement (a): bonding molecular orbitals are formed by addition of wavefunctions of atomic orbitals of same
phase Statement (b) : anti-bonding molecular orbitals do not take part in
bond formation because they belong to inner shells Statement (d) : anti-
bonding molecular orbitals provide stability to molecules while bonding molecular orbitals make the molecules
unstable.
A. statement a, d
B. Statement a, b, c
c. Statement \( a, b, d \)
D. Statement a


In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.17 sec. The frequency of the wave is :
A . \( 1.47 \mathrm{Hz} \)
в. 0.36 н \( z \)
c. о.73 н н
D. 2.94 нz


Let \( [x] \) denote the greatest integer less
than or equal to \( x \). If \( f(x)=[x \sin \pi x] \)
\( \operatorname{then} f(x) \) is :
This question has multiple correct options
A. continuous at \( x=0 \)
B. continuous in (-1,0)
c. differentiable at \( x=1 \)
D. differentiable in (-1,1)