Heat produced in a wire of resistance \( \boldsymbol{R} \)
due to current flowing at constant potential difference is proportional to
A \( \cdot \frac{1}{R^{2}} \)
в. \( \frac{1}{R} \)
\( c . R \)
D. \( R^{2} \)


The frequency of oscillation of the
electric field vector of a certain e.m.
wave is \( 5 \times 10^{4} \) Hz.What is the
frequency of oscillation of the corresponding magnetic field vector and to which part of the
electromagnetic spectrum does it belong?


A man walks \( 8 \mathrm{m} \) towards East and then \( 6 \mathrm{m} \) towards North. His magnitude of displacement is
A . \( 10 \mathrm{m} \)
B. 14 \( \mathrm{m} \)
\( c \cdot 2 m \)
D. zero


What is the percentage of free carbon in bituminous coal?
A . 30
B. 50
c. 70
D. 90


Identify the correct sequence of increasing number of \( \pi \) - bonds in the
structures of the following molecules:
I) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{6} \)
II) \( \boldsymbol{H}_{2} \boldsymbol{S O}_{3} \)
III) \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{5} \)
A. \( I<I I<I I \)
в. \( I I<I I I<I \)
c. \( I I I<I I<I \)
D. II \( <I<I I I \)


If an electron and positron annihilate, then the energy released is
A . \( 3.2 \times 10^{-13} \mathrm{J} \)
В. \( 1.6 \times 10^{-13} \mathrm{J} \)
c. \( 4.8 \times 10^{-13} \mathrm{J} \)
D. \( 6.4 \times 10^{-13} \mathrm{J} \)


Evaluate:
\( \int \sqrt{\frac{\boldsymbol{a}+\boldsymbol{x}}{\boldsymbol{a}-\boldsymbol{x}}} \boldsymbol{d} \boldsymbol{x} \)


Assertion
A cloth covers a table. Some dishes are
kept on it. The cloth can be pulled out without dislodging the dishes from
the table.
Reason
For every action there is an equal and opposite reaction.
A. Statement- - - is True, Statement-2 is True; Statement is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement- is NOT a correct explanation for Statement-1
c. Statement- - 1 is True, Statement- 2 is False
D. Statement- -1 is False, Statement-2 is True


Use prime factorisation to find the square root of 1225
A . 122
в. 225
c. 35
D. 50


The D on of family of circles with radius \( =5 \& \) and center on \( y=2 \) is


The non-renewable source of energy
amongst the following is :
A. wind energy
B. hydel energy
c. solar energy
D. fossil fuels


Mineral essential for the coagulation of blood is
A. Potassium
B. Magnesium
c. Calcium
D. Sodium


Let a steel bar of length \( ' l \) ', breadth 'b' and depth 'd' be loaded at the centre by a load 'W'. Then the sag of bending of beam is (Y = Young's modulus of material of steel)
A \( \frac{W l^{3}}{2 b d^{3} Y} \)
в. \( \frac{W l^{3}}{4 b d^{3} Y} \)
c. \( \frac{W l^{2}}{2 b d^{3} Y} \)
D. \( \frac{W l^{3}}{4 b d^{2} Y} \)


Which of the following statements
regarding the E1 mechanism is not
correct?
A. the rate-determining step in \( E 1 \) reactions is unimolecular
B. \( E 1 \) reaction is normally of first order
C. \( E 1 \) reaction mechanism usually occur in one step
D. \( E 1 \) reaction mechanism is a multistep process


The hormone that increases the blood
calcium level and decreases its
excretion by kidney is
A. Parathormone
B. Calcitonin
c. Thyroxine
D. Insulin


Which of the following are fossils?
A. Pollen grains buried in the bottom of a peat bog.
B. The petrified cast of a clam's burrow.
C. The impression a clam shell made in mud, preserved in mudstone.
D. All of the above.


then velocity in circular orbits is given \( \operatorname{as} \sqrt{\frac{\boldsymbol{x} \boldsymbol{G} \boldsymbol{M}}{\boldsymbol{r}}} . \) Find \( \boldsymbol{x} \)


Using differentials, find the sum of digits approximate value of the
following up to 3 places of decimal. \( (0.999)^{\frac{1}{3}} \)


A current \( i \) ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any
point inside the tube is
\( A \cdot \infty \)
в. zero
c. \( \frac{\mu_{0}}{4 \pi} \cdot \frac{2 i}{r} \) tesla
D. \( \frac{2 i}{r} \) tesla


Jacob and Monad studied lactose
metabolism in E. Coli ad proposed
operon concept. Operon concept is applicable for?
A. All prokaryotes
B. All prokaryotes and some eukaryotes
c. All prokaryotes and all eukaryotes
D. All prokaryotes and some protozoans


For the square planar complex [Mabcd] where \( \mathrm{M} \) is the central atom and \( \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} \) are monodentate ligands, the number of possible geometrical isomers are:
A. one
B. two
\( c . \) three
D. four


If the \( \Delta G \) of a cell reaction, \( A g C l+ \)
\( e^{-} \rightarrow A g+C l^{-} \) is \( -21.20 \mathrm{kJ}, \) the
standard emf of cell is
A . \( 0.239 \mathrm{v} \)
B. \( 0.220 v \)
c. \( -0.320 v \)
D. - 0.110v


The number of points \( (p, q) \) such that
\( \boldsymbol{p}, \boldsymbol{q} \in\{1,2,3,4\} \) and the equation
\( p x^{2}+q x+1=0 \) has real roots is
\( A \cdot 7 \)
B. 8
c. 9
D. none of these


\( H_{2} O_{2} \) forms prismatic crystals at:
\( \mathbf{A} \cdot 0^{\circ} C \)
B . \( 2^{\circ} \mathrm{C} \)
\( c .2 K \)
D. \( -1.7^{\circ} \mathrm{C} \)


State for 'T' true and 'F' for false.
(i) Number 0 has both rotational and
line of Symmetry.
(ii) A regular polygon of \( n \) sides has \( 2 n \) lines of symmetry.
(iii) A square has four lines of
symmetry and rotational symmetry of
order 2
(iv) A circle has finite number of lines of
symmetry.
(i) (ii) (iii) (iv)
\( A \cdot T F F F \)
B. T F T F
c. F T F \( T \)
D. F T T T


The angle between the two refracting surface of a prism is called angle of :
A. incidence
B. base
c. dispersion
D. prism


In nitroalkanes \( -N O_{2} \) group is
converted to \( -N H_{2} \) group by using the
reagent:
A. \( S n / H C l \)
B. \( Z n \) dust
c. \( Z n / N H_{4} C l \)
D. \( Z n / N a O H \)


Which one of the following undergoes nucleophilic substitution exclusively by
\( \boldsymbol{S}_{N} 1 \) mechanism?
A. Benzyl chloride
B. Ethyl chloride
c. chlorobenzene
D. Isopropyl chloride


\( \boldsymbol{S O}_{2} \) bleaches by
A. reduction
B. oxidation
C. ionisation
D. hydration


A steel wire \( 1.5 m \) long and of radius
1 \( m m \) is attached with a load \( 3 k g \) at one
end the other end of the wire is fixed it
is whirled in a vertical circle with a
frequency \( 2 H z . \) Find the elongation of
the wire when the weight is at the
lowest position:
\( \left(Y=2 \times 10^{11} N / m^{2} \text { and } g=10 m / s^{2}\right) \)
A \( .1 .77 \times 10^{-3} m \)
В. \( 7.17 \times 10^{-3} m \)
c. \( 3.17 \times 10^{-7} m \)
D . \( 1.37 \times 10^{-7} m \)


The sum of a series of terms in A.P. is
128. If the first term is 2 and the term
ids \( 14, \) find the common difference.


The voltage can be increased, but
electric breakdown will occur if the
electric field inside the capacitor becomes too large. The capacity can be increased by
A. expanding the electrode areas
B. reducing the gap between the electrodes
c. expanding the gap between the electrodes
D. Both A and B


Find the area of the following
rhombuses


Strength of hydrogen bond is intermediate between:
A. van der Waal's forces and covalent bond
B. ionic bond and covalent bond
c. ionic bond and metallic bonding
D. none of the above


Which one of the following is correct?
A. Reproduction is linked to stability of population of a species.
B. Reproduction is linked to instability of a population.
C. Reproduction is linked to instability of a species.
D. None of the above.


If \( E_{P} \) and \( E_{k} \) represent potential energy and kinetic energy respectively, of an orbital electron, then according to
Bohr's theory:
A \( . E_{k}=-E_{p} / 2 \)
B. \( E_{k}=-E_{p} \)
c. \( E_{k}=-2 E_{p} \)
D. \( E_{k}=2 E_{p} \)


If one penetrates a uniformly charged spherical cloud, electric field strength
A. Decreases directly as the distance from the centre
B. Increases directly as the distance from the centre
c. Remains constant
D. None of the above


The \( (x, y) \) co-ordinates of the corners of
a square plate are \( (\mathbf{0}, \mathbf{0})(\boldsymbol{L}, \mathbf{0})(\boldsymbol{L}, \boldsymbol{L}) \& \)
\( (0, L) . \) The edges of the plate are clamped \& transverse standing waves are set up in it. If \( u(x, y) \) denotes the displacement of the plate at the point \( (x, y) \) at some instant of time, the possible expression(s) for \( u \) is/are : \( (a= \) positive constant) This question has multiple correct options
A \( \cdot a \cos \left(\frac{\pi x}{2 L}\right) \cos \left(\frac{\pi y}{2 L}\right) \)
B. \( a \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{\pi y}{L}\right) \)
\( ^{\mathbf{c}} \cdot a \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{2 \pi y}{L}\right) \)
D. \( a \cos \left(\frac{2 \pi x}{L}\right) \sin \left(\frac{\pi y}{L}\right) \)


\( 2.4+4.7+6.10+\ldots(n-1) \) terms
A \( \cdot 2 n^{3}-2 n^{2} \)
B. \( \frac{n^{3}+3 n^{2}+1}{6} \)
c. \( 2 n^{3}+2 n \)
D. \( 2 n^{3}-n^{2} \)


Proteins are:
A. polysaccharides
B. polynucleotides
C . polypeptides
D. triglycerides


Show that all the chords of the curve
\( 3 x^{2}-y^{2}-2 x+4 y=0 \) which subtend
a right angle at the origin?


What is the solution of the differential
equation \( \boldsymbol{x} \boldsymbol{d} \boldsymbol{y}+\boldsymbol{y} \boldsymbol{d} \boldsymbol{x}=\mathbf{0} \)
A \( . x y=c \)
в. \( y=c x \)
c. \( x+y=c \)
D. \( x-y=c \)


What are the essential things required
for rust?
A. Strong acid, oxygen, an electrical current
B. Sunlight, air, salt
c. water, oxygen, a metal
D. An anode, a cathode, salt


Consider the following reaction, taking
place in a container fitted with a movable piston.
\( 2 S O_{2}(g)+O_{2}(g) \rightarrow 2 S O_{3}(g) \)
Suppose we place two moles each of
\( \boldsymbol{S O}_{2} \) and \( \boldsymbol{O}_{2} \) in the reaction vessel at
\( 25^{\circ} \mathrm{C}, \) and adjust the volume to give a
total pressure of 1.0 atm. The reaction
is ignited by a spark, and goes to completion. The temperature is
returned to \( 25^{\circ} \mathrm{C} \)
Which of the following best describes this system after reaction is complete?
\( A \cdot S O_{2} \) is limiting. The volume of the system remains the same
B. Neither reactant is limiting. The volume of the system decreases
C. \( S O_{2} \) is limiting. The volume of the system decreases.
D. \( O_{2} \) is limiting. The volume of the system remains the same


The fixation of nitrogen can be brought artificially also.
A . True
B. False


The chemical equations to represent the most probable outcome in the following is :
\( H g O \stackrel{\Delta}{\rightarrow} ? \)
A \( \cdot 4 \mathrm{HgO} \triangleq 3 \mathrm{Hg}+\mathrm{HgO}_{2}+\mathrm{O}_{2} \)
в. \( 2 \mathrm{HgO} \stackrel{\Delta}{\rightarrow} 2 \mathrm{Hg}+\mathrm{O}_{2} \)
c. No reaction
D. None of these


Which of the following statements
about photochemical smog is not
correct?
A. It occurs in warm, dry and sunny climate.
B. Chemically, it is a reducing mixture and is called reducing smog.
C. It is formed as a result of action of sunlight on unsaturated hydrocarbons and nitrogen oxides.
D. It has high concentration of oxidising agents and is also called oxidising smog.


At thermal equilibrium:
A \( . \Delta P=0 \)
в. \( \Delta T=0 \)
c. \( \Delta V=0 \)
D. \( \Delta n=0 \)


Which of the following does not represent a cluster of stars?
A. Rigel
B. Aquarius
c. capricorn
D. Aries


What is diagonal relationship? Give two examples to illustrate the concept?


In the relation, \( \boldsymbol{p}=\frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \boldsymbol{e}^{-} \frac{\boldsymbol{\alpha} \boldsymbol{Z}}{\boldsymbol{k} \boldsymbol{\theta}} \)
\( P \) is pressure, \( Z \) is distance, \( k \) is
Boltzmann's constant and \( \theta \) is the
temperature. The dimensional formula
of \( \boldsymbol{\alpha} \) will be:
\( \mathbf{A} \cdot\left[M L T^{-2}\right] \)
B \( \cdot\left[M L^{2} T\right] \)
\( \mathbf{c} \cdot\left[M L^{0} T^{-1}\right] \)
D \cdot \( \left[M^{0} L^{2} T^{-1}\right] \)


What is 'boiling point'? Derive a relation between \( \triangle H \) and \( \triangle U \)
for a chemical reaction Draw neat
labelled diagram of calomel electrode Resistance and conductivity of a cell
containing \( 0.001 M K C l \) solution at
\( 298 K \) are \( 1500 \Omega \) and \( 1.46 \times \)
\( 10^{-4} \)S.cm\( ^{-1} \) respectively. What is the
cell constant?


Express \( \overrightarrow{A B} \) in terms of unit vectors \( \hat{i} \) and \( \hat{j}, \) when the points are:
\( A(4,-1), B(1,3) \)
Find \( |\overrightarrow{A B}| \) in each case.
A \( \cdot \overrightarrow{A B}=-3 \hat{i}-4 \hat{j},|\overrightarrow{A B}|=5 \)
B・方 \( =+3 \hat{i}+4 \hat{j},|A \vec{B}|=5 \)
c. \( \overrightarrow{A B}=-3 \hat{i}+4 \hat{j},|\overrightarrow{A B}|=5 \)
D. none of these


Evaluate: \( \int \frac{d x}{1-\tan x} \)


Relation \( R \) in the set \( A \) of human beings
in a town at a particular time given by
\[
\boldsymbol{R}=
\]
\( \{(x, y): x \text { and } y \) work at the same plac
enter 1 -reflexive and transitive but not
symmetric 2-reflexive only 3-Transitive only
4-Equivalence 5-None


Nylon-66 is a
A. natural polymer
B. synthetic polymer
C . mixed polymer
D. polyester


What percentage is equivalent to \( \frac{3}{8} \)
\( \mathbf{A} \cdot 37.5 \% \)
B. \( 37 \% \)
c. \( 34.5 \% \)
D. \( 25 \% \)


An arc lamp requires a direct current of \( 10 A \) at \( 80 \mathrm{V} \) to function. If it is connected to a \( 220 \mathrm{V}(\mathrm{rms}), 50 \mathrm{Hz} \) AC supply, the series inductor needed for it to work is
close to:
A . 80H
B. 0.08H
c. 0.0444
D. 0.065H


When a stationary wave is formed, then its frequency is
A. Same as that of the individual waves
B. Twice that of the individual waves
c. Half that of the individual waves
D. That of the individual waves


State whether the following statements
are true or false with reasons.

Elastic forces are always conservative.
A. True
B. False


The coefficient of linear expansion of a crystalline substance in one direction is
\( 2 \times 10^{-4} /^{0} \mathrm{C} \) and in every direction
perpendicular to it is \( 3 \times 10^{-4} /^{0} \mathrm{C} \). The coefficient of cubical expansion of crystal is equal to
A. \( 5 \times 10^{-4} /^{0} \mathrm{C} \)
B. \( 4 \times 10^{-4} /^{0} \mathrm{C} \)
c. \( 8 \times 10^{-4} /^{0} \mathrm{C} \)
D. \( 7 \times 10^{-4} /^{0} \mathrm{C} \)


Energy barrier between staggered and eclipsed ethane is :
A. \( 6.0 \mathrm{kcal} / \mathrm{mole} \)
B. 3.0 kcal/mole
c. \( 2.0 \mathrm{kcal} / \mathrm{mol} \)
D. \( 4.0 \mathrm{cal} / \mathrm{mole} \)


Which one of the following statement is
true?
A. The greater the BOD of waste water, more is its polluting potential
B. The greater the BOD of waste water, , less is its polluting potential
c. The lesser the BOD of waste water, more is its polluting potential.
D. None of the above


The atomic number of an element 'y' is
20. The electronic configuration of the ion having inert gas configuration is:
A .2,8,10
B. 2,18
c. 2,10,8
D. 2, 8, 8


Prove the following:
\( \left|\begin{array}{ccc}\boldsymbol{b} \boldsymbol{c} & \boldsymbol{b} \boldsymbol{c}^{\prime}+\boldsymbol{b}^{\prime} \boldsymbol{c} & \boldsymbol{b}^{\prime} \boldsymbol{c}^{\prime} \\ \boldsymbol{c} \boldsymbol{a} & \boldsymbol{c} \boldsymbol{a}^{\prime}+\boldsymbol{c}^{\prime} \boldsymbol{a} & \boldsymbol{c}^{\prime} \boldsymbol{a}^{\prime} \\ \boldsymbol{a b} & \boldsymbol{a b}^{\prime}+\boldsymbol{d}^{\prime} \boldsymbol{b} & \boldsymbol{d}^{\prime} \boldsymbol{b}^{\prime}\end{array}\right|= \)
\[
\left(b c^{\prime}-b^{\prime} c\right)\left(c a^{\prime}-c^{\prime} a\right)\left(a b^{\prime}-d b\right)
\]


Write the formula for the refraction of
light on a spherical surface. Establish lens formula \( \frac{1}{\boldsymbol{f}}=(\boldsymbol{n}-1)\left(\frac{\mathbf{1}}{\boldsymbol{R}_{1}}-\frac{\mathbf{1}}{\boldsymbol{R}_{2}}\right) \)
with its help. Symbols used their usual meanings.


What is the conjugate acid of ammonia?
A. \( N H_{2} \)
B. \( O H^{-} \)
c. \( N H_{4}^{+} \)
D. \( H_{3} O^{+} \)


An electric generator converts mechanical energy into
energy.


\( (2 x+3 y)^{2}-16 z^{2} \)


Solve the equations simultaneously to find the value of \( h \)
\( 3 h-j=7 \) and \( 2 h+3 j=1 \)
\( A \cdot 2 \)
B.
\( c \cdot 4 \)
D. 3


Which of the following statements is/are incorrect for diamond?
(a) The refractive index of diamond is
highest among solids.
(b) Diamond is hard because all the
valence electrons of each carbon atom
are involved in bond formation.
(c) Diamond is thermodynamically more stable than graphite.
(d) One carat of diamond represents
its weight.
A. All are correct
B. a, b and c
c. a and b
D. conly


In photoelectric effect, the photoelectric current is independent of
A. intensity of incident light
B. potential difference applied between the two electrodes
c. the nature of emitter material
D. frequency of incident light


The sum of infinite series \( \frac{1.3}{2}+\frac{3.5}{2^{2}}+ \)
\( \frac{5.7}{2^{3}}+\frac{7.9}{2^{4}}+\ldots \infty \)
A . 21
B . 22
\( c \cdot 23 \)
D. None


How many nuclear power plants does India have in \( 2018 ? \)
\( A \cdot 2 \)
B. 3
c. 7
D. None of these


The price of an article rises by \( 25 \% \) every odd year and falls by \( 20 \% \) next year. Which of the following statement is correct about the price exactly after
10 years?
A. Price would have risen by \( 50 \% \)
B. The price would have fallen by \( 20 \% \)
c. The price would remain as it is
D. The price would have risen by \( 25 \% \)


Which of the following is not a protonic acid?
\( \mathbf{A} \cdot P O(O H)_{3} \)
\( \mathbf{B} \cdot B(O H)_{3} \)
\( \mathrm{c} \cdot S O(O H)_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2}(\mathrm{OH})_{2} \)


A reaction that absorbs heat is:
A. Endothermic
B. An equilibrium process
c. spontaneous
D. Non-spontaneous
E. Exothermic


The equation \( \sec ^{2} \theta=\frac{4 x y}{(x+y)^{2}} \) is only
possible, when
\( \mathbf{A} \cdot x=y \)
в. \( x<y \)
c. \( x>y \)
D. None of these


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


If the degree of ionization of water be \( 1.8 \times 10^{-9} \) at \( 298 K . \) What will be its
ionization constant?


Assertion
The force between two electric charges
in a dielectric medium is less than it
would be in a vacuum.
Reason
Quantity of energy stored in an electric field per unit volume of a dielectric medium is greater than that of vaccum
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


Two identical coils carry equal currents have a common centre and their planes
are at right angles to each other. The ratio of the magnitude of the resultant magnetic field at the centre and the field due to one coil is :
A . 2: 1
B. 1: 2
\( \mathbf{c} \cdot \sqrt{2}: 1 \)
D. \( 1: \sqrt{2} \)


If \( f \) and \( g \) are differentiable functions in
\( [\mathbf{0}, \mathbf{1}] \) satisfying \( \boldsymbol{f}(\mathbf{0})=\mathbf{2}= \)
\( g(1), g(0)=0 \) and \( f(1)=6, \) then for
some \( \boldsymbol{c} \in[\mathbf{0}, \mathbf{1}] \)
A \( \cdot 2 f^{\prime}(c)=g^{\prime}(c) \)
B \( \cdot 2 f^{\prime}(c)=3 g^{\prime}(c) \)
c. \( f^{\prime}(c)=g^{\prime}(c) \)
D. \( f^{\prime}(c)=2 g^{\prime}(c) \)


State True or False.
Calcium bicarbonate is known in solid
state.
A. True
B. False


Three charged particles, \( A, B, \) and \( C \)
are kept apart by distance d from each
other as shown in figure. If particle \( B \) is
attracted to particle \( A, \) what can we
predict about the charge, \( \boldsymbol{q}_{A}, \) of particle
\( A ? \)
A \( \cdot q_{A}<-q \)
в. \( -q<q_{A}<0 \)
\( \mathbf{c} \cdot q_{A}=0 \)
D. \( 0<q_{A}<+q \)
. \( q_{A}>+q \)


Verify Lagrange's mean value theorem for the following function on the indicated interval. In each case find a
point \( ^{\prime} c^{\prime} \) in the indicated interval as
stated by the Lagrange's mean value theorem:
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2} \) on [-1,2]


Find the centre and radius of the circle
\( x^{2}+y^{2}-4 x-8 y-45=0 \)
\( \mathbf{A} \cdot(2,6), \sqrt{63} \)
B . \( (2,4), \sqrt{65} \)
c. \( (2,-4), \sqrt{66} \)
D. None


If \( a, b, c \) are the percentage errors in the
measurement of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) then
percentage error in \( \boldsymbol{A B C} \) would be
A \( . a b c \)
B . \( a+b+c \)
c. \( a b+b c+c a \)
D. \( a-b-c \)


The magnetic field \( B=2 t^{2}+4 t^{2} \)
(where \( t= \) time ) is applied perpendicular to the plane of a circular wire of radius \( r \) and resistance \( R \). If all
the units are in SI the electric charge that flows through the circular wire during \( t=0 s \) to \( t=2 s \) is
A \( \cdot \frac{6 \pi r^{2}}{R} \)
в. \( \frac{24 \pi r^{2}}{R} \)
c. \( \frac{32 \pi r^{2}}{R} \)
D. \( \frac{48 \pi r^{2}}{R} \)


Which isomer of \( C_{6} H_{14} \) has two
isopropyl groups?
A. 2-Methylpentane
B. 3-Methylpentane
c. 2,3 -Dimethylbutane
D. 2,2-Dimethylbutane


The sum of the focal lengths of the objective and an eyepiece, In case of an astronomical telescope is equal to :
final image is at \( \infty) \)
A. The length of the telescope
B. Half the length of the telescope
c. Double the length of the telescope
D. None of these


If force and displacement of the particle (in direction of force) are doubled. Work
should be :
A. Doubled
B. 4 times
c. Halved
D. \( \frac{1}{4} \) times


If \( 3 \cos \theta=1, \) find the value of
\( \frac{6 \sin ^{2} \theta+\tan ^{2} \theta}{4 \cos \theta} \)


Which of the following orbitals are in the increasing order of energy.
\( \mathbf{A} \cdot 1 s, 2 s, 2 p, 3 s \)
В. \( 4 s, 3 s, 3 p, 4 d \)
c. \( 5 p, 4 d, 5 d, 4 f, 6 s \)
D. \( 4 p, 2 s, 3 s, 2 p \)


Arrange the following in the increasing order of solubility in water:
¡) \( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{2}} \)
ii) \( \left(C_{2} H_{5}\right)_{2} N H \)
iii) \( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \)
A. is iis iii
B. iisisiii
\( c . \) iiisisi
D. iii <iisi


If the ionization energy of hydrogen is
\( 313.8 K c a l / \) mol, then the energy of
electron in \( 2^{n d} \) excited state will be:
A . \$\$-113.2K |cal/mole\$\$
B. \$\$-78.45Klcal/mole\$\$
c. \( \$ \$-313.8 \) lcal/moless
D. none of these


If a plant cell is covered with the cell
wall, but the plasma membrane is absent, will it affect the cell? Explain how and why?


Which hormone affects physical
appearance?
A. male and female
B. steroid
c. growth
D. gonadotropin-releasing hormone


A particle is released from rest from a
tower of height 3 h.The ratio of times to
fall equal height h,i.e., \( t_{1}: t_{2}: t_{3} \) is
\( \mathbf{A} \cdot \sqrt{3}: \sqrt{2}: 1 \)
B. 3: 2: 1
\( \mathbf{C} \cdot 9: 4: 1 \)
D. \( 1:(\sqrt{2}-1):(\sqrt{3}-\sqrt{2}-1) \)


Angular velocity of minute hand of a clock is
A \( \cdot \frac{\pi}{30} r a d / s \)
в. \( 8 \pi r a d / s \)
c. \( \frac{2 \pi}{1800} \) rad/s
D. \( \frac{\pi}{1800} \) rad \( / s \)


Molecular weight of cellulose is:
A. \( 50000-500000 \)
B. 2000 - 10000
\( c .5000-45000 \)
D. 5000 - 25000


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


An excited hydrogen atom emits a photon of wavelength \( \lambda \) in returning to
the ground state. If \( R \) is the Rydberg
constant, then the quantum number \( n \)
of the excited state will be:
\( A \cdot \sqrt{\lambda R} \)
B. \( \sqrt{\lambda R-1} \)
c. \( \sqrt{\frac{\lambda R}{\lambda R-1}} \)
D. \( \sqrt{\lambda R(\lambda R-1)} \)


Identify the geometric series.
A. \( 1+3+5+7+\dots \)
B. \( 2+12+72+432 \)
c. \( 2+3+4+5+\dots \)
D. \( 11+22+33+44+\ldots \)


n figure if \( x=y \) and \( a=b, \) then prove
that \( r \| n \)


The number of ways in which one or more letters be selected from the letters
\( A A A A B B C C C D E F \) is
A . 476
в. 487
c. 435
D. 47


Tyndall effect in colloidal solution is due
to:
A. absorption of light
B. scattering of light
C. reflection of light
D. presence of electrically charged particles


A charged particle is projected in a plane perpendicular to uniform magnetic field. The areal velocity (area swept per unit time) of the particle is :
This question has multiple correct options
A. directly proportional to kinetic energy of particle
B. directly proportional to momentum of the particle
c. inversely proportional to magnetic field strength
D. inversely proportional to charge on particle


A current \( i_{0} \) is flowing through an \( L-R \)
circuit of time constant \( t_{0} . \) The source
of the current is switched off at time
\( \boldsymbol{t}=\mathbf{0} . \) Let \( \boldsymbol{r} \) be the value of \( (-\boldsymbol{d i} / \boldsymbol{d} \boldsymbol{t}) \) at
time \( t=0 . \) Assuming this rate to be
constant, the current will reduce to zero
in a time interval of:
A \( \cdot t_{0} \)
B . \( e t_{0} \)
\( c \cdot t_{0} / e \)
D. \( \left(1-\frac{1}{e}\right) t_{0} \)


The equation of the tangent to the curve \( y=\sqrt{9-2 x^{2}} \) at the point where the
ordinate and abscises are equal is?
A. \( 2 x+y-3 \sqrt{3}=0 \)
В. \( 2 x+y+3 \sqrt{3}=0 \)
c. \( 2 x-y-3 \sqrt{3}=0 \)
D. \( 2 x-y+3 \sqrt{3}=0 \)


In which direction from \( \beta \) Saptarish (or
Ursa Major or Great Bear) shown in the
figure, do we search for Pole star?
\( A \cdot \alpha \) to \( \beta \)
B. \( \gamma \) to \( \delta \)
\( c \cdot \beta \) to \( \alpha \)
D. \( \delta \) to \( \gamma \)


How much is the profit at \( 8 \% \) on \( R s 500 \)
\( ? \)


If \( \boldsymbol{A}=\{\mathbf{5}, \mathbf{7}\}, \boldsymbol{B}=\{\mathbf{7}, \mathbf{9}\} \) and \( \boldsymbol{C}= \)
\( \{7,9,11\}, \) find \( (A \times B) \cup(A \times C) \)
B . \{(5,7),(5,9),(5,11),(7,7),(7,9),(7,11)\}
c. \{(5,5),(5,9),(5,11),(7,7),(7,9),(7,11)\}
D. none of these


Explain magnetic separation process of
ores with the help of a neat, labelled
diagram.


Which of the following is the best example of law of conservation of
mass?
In and \( m \) are the masses of reactants
and \( p \) and \( q \) are the masses of products formed.]
A \( . n-m=p-q \)
в. \( n+m=p+q \)
c. \( n=m \)
D. \( p=q \)


Solve for \( x: \cos ^{-1} x+\sin ^{-1}\left(\frac{x}{2}\right)=\frac{\pi}{6} \)


HCOOH\( \frac{\operatorname{conc} \boldsymbol{H}_{2} \boldsymbol{S O}_{4}}{\mathbf{3 7 3 K}} \boldsymbol{A}+\boldsymbol{B}, \) then
identify the incorrect statement
regarding \( B ? \)
A. It act as a \( \pi \) -acceptor ligand in coordinates compounds
B. It acts as a reducing agent
\( \mathrm{C} \). It is almost water insoluble gas
D. It is failed to reduce an aqueous \( P d C I_{2} \) solution to metallic \( P d \)


Which of the following is a compound?
A. Baking soda
B. Octane
c. Hydrogen peroxide
D. All of above


Heat energy produces a sensation of
A. warmth
B. coldness
c. both warmth and coldness
D. none of these


Nayan tosses a coin thrice. Find the
probability of getting a) exactly 2 heads
and
b) at most 2 tails


Let \( n \) and \( r \) be two positive integers such that \( n \geq r+2 . \) Suppose \( \Delta(n, r)= \)
\( \left|\begin{array}{ccc}n & C_{r} & ^{n} C_{r+1} & ^{n} C_{r+2} \\ ^{n+1} C_{r} & ^{n+1} C_{r+1} & ^{n+1} C_{r+2} \\ ^{n+2} C_{r} & ^{n+2} C_{r+1} & ^{n+2} C_{r+2}\end{array}\right| \) Show that
\( \Delta(n, r)=\frac{n+2}{n+2} C_{3} \Delta(n-2, r-1) \) Hence
or otherwise,
A \( \cdot \frac{\left(^{n+2} C_{3}\right)\left(^{n+1} C_{3}\right) \ldots . .\left(^{n-r+3} C_{3}\right)}{\left.\left(r+2 C_{3}\right)\left(r+1 C_{3}\right) \ldots . .^{3} C_{3}\right)} \)
B. \( -\frac{\left(^{n+2} C_{3}\right)\left(^{n+1} C_{3}\right) \ldots . .\left(^{n-r+3} C_{3}\right)}{\left(r+2 C_{3}\right)\left(^{r+1} C_{3}\right) \ldots\left(^{3} C_{3}\right)} \)
c. \( \frac{(n+3}{(r+3)}(\sqrt[n+2]{(r+2)}) \ldots . .\left(^{n-r+3} C_{3}\right) \)
D. \( -\frac{\left.\left(^{n+3} C_{3}\right)(n+2)_{3}\right) \ldots . .\left(^{n-r+3} C_{3}\right)}{\left(r+3 C_{3}\right)\left(r+2 C_{3}\right) \ldots\left(^{3} C_{3}\right)} \)


Match the followings and mark the
correct option.
Column I n Il
A. Sternum
(i) Synovial fluid ne
B. Glenoid d cavity
(ii) Vertebrae
(iii) Pectoral girdle
C. Freely movable joint
D. Cartilaginous joint
(iv) Flat bones \( t \) (i
\( A \cdot A-(i i), B-(i), C-(i i i), D-(i v) \)
B. \( A-(\text { iv }), B-(\text { iii) }, C-(i), D-(i i) \)
C \( \cdot A-(\text { ii) }, B-(i), C-(i v), D-(i i i) \)
D. \( A-(\text { iii) }, B-(i), C-(i i), D-(i v) \)


Classify the following measure as
scalar and vector:
10 meters south-east
A. a vector with magnitude 5
B. a vector with magnitude 10
c. a scalar with magnitude 10
D. none of the above


A buffer solution contain
\( \mathbf{0 . 8} \boldsymbol{M} \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{O} \boldsymbol{H} \boldsymbol{\&} \)
\( \mathbf{0 . 2 M} N \boldsymbol{H}_{4} \boldsymbol{C l}, \boldsymbol{K} \boldsymbol{a}\left(\boldsymbol{N} \boldsymbol{H}_{4}^{+}\right)=\mathbf{5} \times \mathbf{1 0}^{-10} \)
Find \( p H \) of the solution \( (\log 2=0.3) \&(\log 3=0.48) \)
A . 9.9
B. 8.7
\( c .9 .6 \)
D. 4.


A solenoid has a core of a material with
relative permeability \( 400 . \) The windings of the solenoid are insulated from the
core and carry a current of \( 2 A \).f the
number of turns is 1000 per meter, calculate (a) \( \boldsymbol{H} \)
(b) \( B \) and
\( (c) \) the
magnetising current \( \boldsymbol{I}_{m} \)


Function \( f(x)=a^{x} \) is increasing on \( R \)
if
\( \mathbf{A} \cdot a>0 \)
B. \( a<0 \)
c. \( 0<a<1 \)
\( \mathbf{D} \cdot a>1 \)


The standard quantity used for comparison is called
A. Scale
B. Unit
c. Magnitude
D. All


The correct structure of
tribromooctaoxide is:
\( A \)
B.
\( c \)
D.


the mass of carbon anode consumed
(giving only carbon dioxide) in the production of \( 270 K g \) of aluminium metal from bauxite by the Hall's process is:
\( \mathbf{2} \boldsymbol{A} \boldsymbol{l}_{2} \boldsymbol{O}_{3}+\mathbf{3} \boldsymbol{C} \rightarrow \mathbf{4} \boldsymbol{A} \boldsymbol{l}+\mathbf{3} \boldsymbol{C} \boldsymbol{O}_{2} \)
A. \( 180 \mathrm{Kg} \)
в. \( 270 K g \)
c. \( 240 K g \)
D. \( 90 K g \)


Given \( \left|\overrightarrow{\boldsymbol{A}}_{1}\right|=2,\left|\overrightarrow{\boldsymbol{A}}_{2}\right|=\overrightarrow{\mathbf{3}} \) and
\( \left|\vec{A}_{1}+\vec{A}_{2}\right|=3 . \) Find the value of \( \left(\overrightarrow{\boldsymbol{A}}_{1}+\mathbf{2} \overrightarrow{\boldsymbol{A}}_{2}\right) \cdot\left(\boldsymbol{3} \overrightarrow{\boldsymbol{A}}_{1}-\boldsymbol{4} \boldsymbol{\vec { A }}_{2}\right) \)
A . -64
B. 60
c. -60
D. 64


The compound, which give a positive ninhydrin test and a negative Benedict's solution test, is:
A. a monosaccharide
B. a disaccharide
c. a lipid
D. a protein


\( P(4,3) \) and \( Q \) lies on the same straight line which is parallel to the \( x \) -axis. If \( Q \) is 3 units from the \( x \) -axis, the possible
coordinates of Q are:
A \( .(4,0) \)
в. (2,4)
c. (-4,3)
D. (8,4)


A brass rod has a length of \( 0.2 m, \) area of
cross section \( 1.0 \mathrm{cm}^{2} \) and young's
modulus \( 10^{11} \mathrm{Nm}^{-2} . \) If it is compressed
by \( 5 k g \) weight along its length, then the change in its energy will be :
A. an increase of \( 2.4 \times 10^{-5} \) j
B. a decrease of \( 2.4 \times 10^{-5} \mathrm{J} \)
c. an increase of \( 2.4 \times 10^{7} \) J
D. a decrease of \( 2.4 \times 10^{7} \) j


What does the given diagram represent
with respect to the various
photosynthetic processes?
A \( \cdot C_{2} \) cycle
B. Cyclic photophosphorylation
c. Non-cyclic photophosphorylation
D. z-scheme of photophosphorylation


\( 40 \% \) by weight solution will contain how much mass of the solute in 1 L solution?
Density of the solution is \( 1.2 \mathrm{g} / \mathrm{mL} \)
A. \( 480 g \)
B. \( 48 g \)
\( c \cdot 38 g \)
D. \( 380 g \)


Hydrophobic is another name for a substance which:
A. bonds weakly to oil
B. bonds weakly to water
c. repels oil
D. attracts water


Shooting star is another name for
A . comet
B. meteor
c. solar flare
D. nebulae


In the reaction,
\( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{3}(\boldsymbol{g}) \) the
amounts of \( \boldsymbol{P C l}_{5}, \boldsymbol{P C l}_{3} \) and \( \boldsymbol{C l}_{2} \) are \( \boldsymbol{2} \)
mole each at equilibrium and the total
pressure is 3 atmospheres. The
equilibrium constant, \( \boldsymbol{K}_{\boldsymbol{p}} \) is:
\( A \cdot 1 \) atm
B. 2 atm
\( c .3 \) atm
D. 1.5 atm


Peptization is a process of :
A. precipitating colloidal particles.
B. purifying colloidal particles.
C. dispersing the precipitate into colloidal state.
D. none of the above.


State whether the " Or" used in the
following statements is "exclusive "or" inclusive Give reasons for your answer
(i) Sun rises or Moon sets
(ii) To apply for a driving licence you should have a ration card or a passport
(iii) All integers are positive or negative


The number of stomata present per \( c m^{2} \)
of leaf is
A. Less than 100
B. 1000 to 60000
c. one million
D. None of the above


If \( \boldsymbol{A} \) is matrix of order \( \boldsymbol{3}, \) then \( \boldsymbol{d} \boldsymbol{e} \boldsymbol{t}(\boldsymbol{k} \boldsymbol{A}) \)
is:
A \( \cdot k^{3} d e t(A) \)
B . \( k^{2} d e t(A) \)
c. \( k d e t(A) \)
D. \( \operatorname{det}(A) \)


Shear modulus is zero for
A. Solids
B. Liquids
c. Gases
D. Liquids and gases


Mercury has low boiling point. Therefore it can be purified by the process of:
A. liquation
B. polling
c. oxidation
D. distillation


If \( A B C \) is a triangle, then the vectors
\( (-1, \cos C, \cos B),(\cos C,-1, \cos A) \)
and \( (\cos B, \cos C,-1) \) are
A. linearly independent for all triangles
B. linearly dependent for all triangles
c. linearly independent for all isosceles triangles
D. none of these


The oxidation state of \( N \) in \( H N O_{3} \) is:
\( A \cdot+7 \)
B. +10
\( c .+5 \)
D. +3


Choose the correct answers from the
alternatives given
Pancreatic juice contains
A. hydrogen carbonate
B. hydrochloric acid
c. sulphuric acid
D. deoxyribonucleic acid


Which of the following statement is incorrect about the reaction?
A. The degree of decomposition is \( N_{2} O_{5}, \alpha=1-e^{-K_{1} \cdot t} \)
B. The forward reaction is endothermic
C. The forward reaction is exothermic
D. The half-life of reaction is \( \frac{l n 2}{K_{1}} \)


Find the angle of intersection of the
following curve:
\( x^{2}+y^{2}=2 x \) and \( y^{2}=x \)


How are proteins classified on the basis of molecular shapes?


Write three differences between \( C_{3} \) and
\( C_{4} \) cycles.


How many atoms of hydrogen are
present in \( 7.8 g \) of \( A l(O H)_{3} ? \)
A. \( 6.0 \times 10^{22} \)
В. \( 1.8 \times 10^{23} \)
c. \( 1.7 \times 10^{23} \)
D. \( 5.1 \times 10^{22} \)


Express the following expression in the
form of \( \boldsymbol{a}+\boldsymbol{i} \boldsymbol{b} \)
\( \frac{(3+i \sqrt{5})(3-i \sqrt{5})}{(\sqrt{3}+\sqrt{2} i)-(\sqrt{3}-i \sqrt{2})} \)


An electric iron draws a current of \( 15 \mathrm{A} \)
from a \( 220 \mathrm{V} \) supply. What is the cost of using iron for 30 min everyday for 15 days if the cost of unit (1 unit \( =1 \mathrm{k} \) W hr)
is 2 rupees?
A. Rs. 49.5
B. Rs. 60
c. Rs. 40
D. Rs. 10


Is the sequence \( \sqrt{\mathbf{3}}, \sqrt{\mathbf{6}}, \sqrt{\mathbf{9}}, \sqrt{\mathbf{1 2}}, \ldots \ldots \)
from an Arithmetic Progression?Give
reason.


Which of the following is true for an electrolytic cell?
A. An electric current causes an otherwise nonspontanteous chemical reaction to occur
B. Reduction occurs at the anode.
C. A spontaneous electrochemical reaction produces an electric current
D. The electrode to which electrons flow is where oxidation occurs
E. None of the above


Which compound is used as an explosive?
A. \( X e F_{2} \)
в. \( X e O_{3} \)
c. \( X e F_{6} \)
D. \( X e O_{4} \)


If planes \( \boldsymbol{x}-\boldsymbol{c} \boldsymbol{y}-\boldsymbol{b} \boldsymbol{z}=\boldsymbol{0}, \boldsymbol{c} \boldsymbol{x}-\boldsymbol{y}+ \)
\( \boldsymbol{a} \boldsymbol{z}=\mathbf{0} \) and \( \boldsymbol{b} \boldsymbol{x}+\boldsymbol{a} \boldsymbol{y}-\boldsymbol{z}=\mathbf{0} \) pass
through a straight line then \( a^{2}+b^{2}+ \)
\( \boldsymbol{c}^{2}= \)
A. \( 1-a b c \)
B . \( a b c-1 \)
c. \( 1-2 a b c \)
D. \( 2 a b c-1 \)


Find the point on the curve \( 4 x^{2}+ \) \( a^{2} y^{2}=4 a^{2}, 4<a^{2}<8 \) that is farthest
from the point \( (\mathbf{0},-\mathbf{2}) \)
A \( .(0,0) \)
в. (0,1)
\( c \cdot(0,2) \)
D. (0,3)


A freshly prepared sample of a radioisotope of half-life \( 1386 s \) has activity \( 10^{3} \) dps.Given that \( l n 2=0.693, \) the fraction of the initial number of nuclei
(expressed in nearest integer percentage) that will decay in the first \( 80 s \) after preparation of the sample is


The velocity time graph of particle moving along a straight line is shown in the figure in the time interval from \( t=0 \) t=8second answer the following three questions.


Let \( R= \) the set of real numbers, \( Z= \)
the set of integers, \( N= \) the set of
natural numbers. If \( S \) be the solution
set of the equation \( (x)^{2}+[x]^{2}=(x- \)
\( \mathbf{1})^{2}+[\boldsymbol{x}+\mathbf{1}]^{2}, \) where \( (\boldsymbol{x})= \) the least
integer greater than or equal to \( x \) and \( [x]= \) the greatest integer less than or
equal to \( x, \) then
A \( . S=R \)
в. \( S=R-Z \)
c. \( S=R-N \)
D. \( S=\phi \)


Reproduction is needed
A. To produce offsprings
B. To ensure the continuation of similar kinds of
individuals
C. For metabolism
D. Both A and B


Neglecting the density of air, the terminal velocity obtained by a raindrop of radius 0.3 mm falling through air of viscosity \( 1.8 \times 10^{-5} N s m^{-2} \) will be:
\( \mathbf{A} \cdot 10.9 \mathrm{ms}^{-1} \)
B. \( 7.48 \mathrm{ms}^{-1} \)
c. \( 3.7 \mathrm{ms}^{-1} \)
D. \( 12.8 \mathrm{ms}^{-1} \)


Find the value of \( x, \) if \( \tan 3 x= \)
\( \sin 45^{\circ} \cos 45^{\circ}+\sin 30^{\circ} \)
A . \( 15^{\circ} \)
B . 10
c. \( 45^{\circ} \)
D. \( 25^{\circ} \)


An object is kept at \( 15 \mathrm{cm} \) from a convex mirror of focal length \( 25 \mathrm{cm} . \) What is the magnification?
A \( \cdot 4 / 9 \)
B. 5/8
\( c \cdot 9 / 4 \)
D. 8/5


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


An inductance coil of \( 1 H \) and \( a \)
condenser of capacity \( 1 p F \) produce
resonance. The resonant frequency will be
\( ^{\text {A }} \cdot \frac{10^{6}}{\pi} H z \)
в. \( 27 \pi \times 10^{6} \mathrm{Hz} \)
c. \( \frac{2 \pi}{10^{6}} H z \)
D. \( \frac{10^{6}}{2 \pi} H z \)


Two reactions, \( A \rightarrow \) Products and \( B \rightarrow \)
Products, have rate constants \( k_{A} \) and
\( k_{B} \) at temperature \( T \) and activation
energies \( \boldsymbol{E}_{\boldsymbol{A}} \) and \( \boldsymbol{E}_{\boldsymbol{B}} \) respectively. If
\( k_{A}>k_{B} \) and \( E_{A}<E_{B} \) and assuming
that collision frequency for both the
reactions is same, then:
This question has multiple correct options
A. At higher temperature \( k_{A} \) will be greater than \( k_{B} \)
B. At lower temperature \( k_{A} \) and \( k_{B} \) will be close to each other in magnitude
C . As temperature rises, \( k_{A} \) and \( k_{B} \) will be close to each other in magnitude
D. At lower temperature \( k_{A}>k_{B} \)


On what does the quality of voice
depend?
A. Thickness of vocal chords
B. Length of local chords
c. stiffness of vocal chords
D. All of these


The chief advantage of encystment to an Amoeba is
A. The chance to get rid of accumulated waste products
B. The ability to survive during adverse physical conditions
c. The ability to live for some time without ingesting food
D. Protection from parasites and predators


The emission of beta particles is from:
A. the valence shell of an atom
B. the inner shell of an atom
C. the nucleus due to the nuclear conversion proton \( \rightarrow \) neutron + electron
D. the nucleus due to the nuclear conversion neutron \( \rightarrow \) proton + electron


Which is incorrect
A. Novestrol - Antifertility
B. Serotonine - Tranquilizer
c. zentac - antacid
D. none of these


Prove that the general equation \( \boldsymbol{a} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{h} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{b} \boldsymbol{y}^{2}+\boldsymbol{2} \boldsymbol{g} \boldsymbol{x}+\boldsymbol{2} \boldsymbol{f} \boldsymbol{y}+\boldsymbol{c}= \)
0
represents two parallel straight lines if \( h^{2}=a b \) and \( b g^{2}=a f^{2} \)
Prove also that the distance between
them is
\( \frac{2 \sqrt{g^{2}-a c}}{a(a+b)} \)


The general solution of the differential equation, \( \sin 2 x\left(\frac{d y}{d x}-\sqrt{\tan x}\right)-y= \)
\( 0, \) is
\( \mathbf{A} \cdot y \sqrt{\tan x}=x+c \)
B. \( y \sqrt{\cot x}=\tan x+c \)
c. \( y \sqrt{\tan x}=\cot x+c \)
D. \( y \sqrt{\cot x}=x+c \)


Why can't we hear the scream of bat?
A. Because its scream consists of infrasonic sound
B. Because its scream consists of ultrasonic sound
C. Because its scream consists of subsonic sound
D. None of these


Find the range and the coefficient of
range of 43,24,38,56,22,39,45


Which of the following statements(s)
is(are) correct?
This question has multiple correct options
\( \mathbf{A} \cdot \) The \( \mathrm{pH} \) of \( 1.0 \times 10^{-8} \mathrm{M} \) solution of \( \mathrm{HCl} \) is 8
B. The conjugate base of \( H_{2} P O_{4}^{\ominus} \) is \( H P O_{4}^{2-} \)
C. Autoprotolysis constant of water increases with temperature
D. When a solution of weak monoprotic acid is titrated against a strong base, at half-neutralisation, point \( p H=(1 / 2) p K_{a} \)


The minimum \& maximum value of \( f(x)=\sin (\cos x)+\cos (\sin x) \forall-\frac{\pi}{2} \leq \)
\( x \leq \frac{\pi}{2} \) are respective
A. \( \cos 1 \) and \( 1+\sin 1 \)
1
B. \( \sin 1 \) and \( 1+\cos 1 \)
c. \( \cos 1 \) and \( \cos \left(\frac{1}{\sqrt{2}}\right)+\sin \left(\frac{1}{\sqrt{2}}\right) \)
D. None of these


Lanthanoid contraction is caused due
to:
A. imperfect shielding of outer electrons by \( 4 f \) - electrons from the nuclear charge.
B. appreciable shielding on outer electrons by \( 4 f \) electrons from the nuclear charge.
C . appreciable shielding on outer electrons by \( 5 d \) electrons from nuclear charge.
D. the same effective nuclear charge from Ce to Lu.


An atom of an element has 3 electrons
in \( 4 p \) subshell. The atomic number of
the element is :
A . 31
B. 33
c. 35
D. 34


A convex lens has focal length \( 20 \mathrm{cm} \)
Calculate at what distance from the
lens should the object be placed so that it forms an image at \( 40 \mathrm{cm} \) on the other
side of the lens. State the nature of the
image formed.


Which of the following is coloured compound?
A. \( C u F_{2} \)
в. \( C u I \)
c. \( N a C l \)
D. \( M g C l_{2} \)


We separate mixtures to:
A. remove unwanted components
B. to get pure substances
C. Both of the above
D. None of the above


How will you quantize the relative permeability of a paramagnetic
substance ?
A. Much more than one
B. Slightly more than one
c. Less than one but greater than zero
D. zero


The antiseptic action of dettol is due to:
A. Chloro benzene
B. Chloroxylenol
c. chloroquine
D. chloramphenicol


For the reaction \( 5 B r^{-1}(a q)+ \)
\( 6 H^{+}(a q)+B r O_{3}^{-}(a q) \rightarrow 3 B r_{2}(a q)+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
\( \mathrm{f},-\frac{\Delta\left[B r O_{3}^{-}\right]}{\Delta t}= \)
\( 0.01 m o l L^{-1} m i n^{-1}, \frac{\Delta\left[B r_{2}\right]}{\Delta t} \) in
\( \operatorname{mol} L^{-1} \min ^{-1} \) is :
A. 0.0
B. 0.3
c. 0.03
D. 0.005


Which one of the following is the ratio of the lowering of vapour pressure of \( 0.1 M \) aqueous solution of
\( B a C l_{2}, N a C l \) and \( A l_{2}\left(S O_{4}\right)_{3} \)
respectively?
A .3: 2: 5
B. 5: 2: 3
\( \mathrm{c} .5: 3: 2 \)
D. 2: 3: 5


The second law of thermodynamics
implies:
A. whole of heat can be converted into mechanical
energy
B. no heat engine can be \( 100 \% \) efficient
C. every heat engine has an efficiency of \( 100 \% \)
D. a refrigerator can reduce the temperature to absolute
zero


From among the elements, choose the
following:
\( \mathrm{Cl}, \mathrm{Br}, \mathrm{F}, \mathrm{O}, \mathrm{Al}, \mathrm{C}, \mathrm{Li}, \mathrm{Cs} \) and \( \mathrm{Xe} \)
The element whose oxide is amphoteric.


What is meant by osmoregulation? How is it maintained in human body?


Which of the following is not a typical property of an ionic compound?
A. They have a high melting point
B. They conducts electricity in the molten and in the aq. solution state
C. They are insoluble in water
D. They exist as oppositely charged ions even in the solid state


Find the median of the following frequency distribution
\( \begin{array}{llll}\text { Class } & \begin{array}{l}4- \\ 8\end{array} & \begin{array}{l}\text { 8- } \\ 12\end{array} & \begin{array}{l}\text { 1 } \\ \text { 1 }\end{array}\end{array} \) \( 12- \)
16 20
Frequency 9
16
1


The degree of the equation, given by \( (x+2)(x-1)=(x+1)(x+3), \) is
\( A \cdot 2 \)
B. 3
\( c . \)
D.


In an experiment, 17 g of ice is used to
bring down the temperature of \( 40 g \) of
water at \( 34^{\circ} \mathrm{C} \) to its freezing
temperature. The specific heat capacity of water is \( 4.2 J g^{-1} K^{-1} \) Calculate the specific latent heat of ice. State one important assumption made
in the above calculation
A \( .33600 J g^{-1} \)
В. \( 3.36 J g^{-1} \)
c. \( 168 J g^{-1} \)
D. \( 336 . J g^{-1} \)


A gas turns moist blue litmus red but
bleaches the colour of litmus is:
A. sodium oxide
B. sulfur dioxide
c. magnesium oxide
D. copper dioxide


\( \mathbf{2} C_{51} \boldsymbol{H}_{98} \boldsymbol{O}_{6}+\mathbf{1 4 6} \boldsymbol{O}_{2} \rightarrow \mathbf{1 0 2} \boldsymbol{C O}_{2}+\mathbf{9 8} \boldsymbol{H} \)
the R.Q for the above reaction is
A. 0.7
в.
c. \( 1-45 \)
D. 1-62


A uniform disc of mass \( m \) and radius \( R \)
rolls without slipping up a rough
inclined plane at an angle of \( 30^{\circ} \) with the horizontal. If the coefficient of static
and kinetic friction are each equal to \( \mu \)
and the forces acting on the disc are gravity and contact force, then find the direction and magnitude of the friction force acting on it.


The space-charge region on either side
of the junction together is known as depletion region because
A. neither electrons nor holes exist in this region
B. the electrons and holes taking part in the initial movement across the junction freed the region of its free charges.
c. the electrons and holes in this region are immobile
D. None of these


Consider the following statements with regard to chemical equilibria:
(1) Equilibrium constant is independent
of initial concentrations of reactants
and products.
(2) Equilibrium constant for the reverse reaction is equal to the inverse of the equilibrium constant for the forward
reaction.
(3) Equilibrium constant is independent of temperature. Which of the above statements are
correct?
A. 1 and 2 only
B. 2 and 3 only y
c. 1 and 3 only
D. 1,2 and 3


Draw a simplified labelled diagram of a hot cathode ray tube.


For the given figure Find \( \sin ^{2} C+ \)
\( \cos ^{2} C \)
\( A \)
B. 0
\( c \)
\( D \)


Pure silicon doped with phosphorus is :
A. Metallic conductor
B. Insulator
c. n-type semiconductor
D. p-type semi conductor


The magnitude of electric force on \( 2 \mu c \)
change placed at the centre \( O \) of two
equilateral triangle each of side \( 10 \mathrm{cm} \)
as shown in figure is \( P \). If charge
\( A, B, C, D, E \& F \) are
\( 2 \mu c, 2 \mu c, 2 \mu c,-2 \mu c,-2 \mu c,-2 \mu c \)
respectively, then \( \boldsymbol{P} \) is:
A . \( 21.6 N \)
B. \( 64.8 N \)
\( c \)
D. \( 43.2 N \)


If \( y=\sqrt{\frac{1+\tan x}{1-\tan x}} \) then \( \frac{d y}{d x} \) is equal to
A \( \cdot \frac{1}{2} \sqrt{\frac{1-\tan x}{1+\tan x}} \sec ^{2}\left(\frac{\pi}{4}+x\right) \)
в. \( \sqrt{\frac{1-\tan x}{1+\tan x}} \sec ^{2}\left(\frac{\pi}{4}+x\right) \)
c. \( \frac{1}{2} \sqrt{\frac{1-\tan x}{1+\tan x}} \sec \left(\frac{\pi}{4}+x\right) \)
D. None of these


\( f(x)=x^{2}\left(1-\cos \left(\frac{2}{x}\right)\right) \) for \( x \neq 0 \)
and \( f(0)=k . \) If \( f(x) \) is continuos at
\( x=0 \) then find \( k \)


The sum of the interior angles of a
pentagon is...


The dependence of the critical
temperature for superconductivity
upon
A. isotopic mass
B. isotonic mass
c. isobaric mass
D. Both A and B


When does overloading occur?
A. When live wire and neutral wire come into direct
contact
B. When live wire and neutral wire come into indirect
contact
C. When two live wires come into direct contact.
D. When two neutral wire come into direct contact.


In mammals, which of these causes the
production of toxic products and foul smelling gases during digestion?
A. Bacteria in large intestine
B. Digestive juices
c. Digestive enzymes
D. All of the above


Calculate the amount of ammonium
chloride required to dissolve in \( 500 m L \)
water to have \( \boldsymbol{p} \boldsymbol{H}=\mathbf{4 . 5}\left(\boldsymbol{K}_{\boldsymbol{b}} \) for \right.
\( \left.N H_{4} O H \text { is } 1.8 \times 10^{-5}\right) \)


Vinodh purchased musical instrument for \( 12,000 . \) If the rate of sales tax is \( 8 \% \)
find the sales tax and the total amount
paid by him.


Column II gives method to separate phases mentioned in column I. Match
them and select the correct answer
from the codes given below.
Column Column I
(a) Miscible liquids
(p) Distillation
\( (q) \)
(b) Immiscible liquids \( \quad \) Crystallization
(c) Pure copper sulphate from
\( (r) \)
an impure sample Sublimation
(s) Separating
(d) Salt and ammonium chloride funnel
\( A \cdot(a)-(q),(b)-(s),(c)-(p),(d)-(r) \)
B. \( (a)-(p),(b)-(s),(c)-(q),(d)-(r) \)
\( c \cdot(a)-(r),(b)-(s),(c)-(p),(d)-(q) \)
D. (a) - (r), (b) - (s), (c) - (q), (d) - (p)


If \( p \) is added to \( -5, \) the result is \( 7 . \) Hence
\( \mathbf{3} \boldsymbol{p}= \)
\( A \cdot 6 \)
B . 18
\( c .36 \)
D. 4


Rs. 69 were divided among 115 students
so that each girl gets 50 paise less than
a boy. Thus each boy received twice the
paise as each girl received. The no. of girls in the class is


if \( a, b, c \) are unequal what is the condition that the value of following determinat is zero \( \delta=\left|\begin{array}{lll}a & a^{2} & a^{3}+1 \\ b & b^{2} & b^{3}+1 \\ c & c^{2} & c^{3}+1\end{array}\right| \)
A \( .1+a b c=0 \)
B. \( a+b+c+1=0 \)
c. \( (a-b)(b-c)(c-a)=0 \)
D. None of these


Let \( A \) and \( B \) be two finite sets having \( m \)
and \( n \) elements respectively. Then the
total number of mapping from \( \boldsymbol{A} \) to \( \boldsymbol{B} \) is
\( A \cdot m n \)
B. \( 2^{m} \)
\( c \cdot m^{n} \)
D. \( n^{\text {m }} \)


A wheel rolling on a horizontal surface
is an example of
A. Stable equilibrium
B. Unstable equilibrium
c. Neutral equilibriumm
D. All of the above


Let two mirrors \( A \) and \( B \) be separated by a distance of \( 10 \mathrm{m} \). Let object 0 be
placed at midpoint of the mirrors. Let \( \boldsymbol{I}_{1} \) be the first image in mirror \( A \) and \( I_{2} \) be the second image in mirror B. What is
the distance between \( I_{1} \) and \( I_{2} ? \)
A . \( 10 m \)
B. \( 20 m \)
\( c .30 m \)
D. \( 40 m \)


The next homologue of \( C_{3} H_{7} O H \) is :
A. butanol
B. propanol
c. pentanol
D. ethanol


Spacecraft like the satellites that circle
the earth and are used in television
transmission have electric batteries
that supply power for various purposes These batteries contain ion-exchange resins instead of a liquid electrolyte
solution because:
A. of extreme cold conditions
B. of lack of oxygen
c. a high electric voltage is required
D. of zero gravity


Select the true statement about
benzene amongst the following
A. Because of unsaturation benzene easily undergoes addition
B. There are two types of C-C bonds in benzene molecule
C. There is cyclic delocalisation in pi bonds in benzene
D. Mono substitution of benzene gives 3 isomeric products.


When an object is kept within the focus of a concave mirror, an enlarged image is formed behind the mirror. The nature
of the image is:
A . Real
B. Inverted
c. Virtual and inverted
D. Virtual and erect


A manufactures purchases a second
hand machine for \( R s .60000 \) and
spends some amount towards repairs
then its value goes up to \( R s .90000 . \) If depreciation is \( 10 \% \) per annum, what will be the value of the machine after
two years?
(a) \( R s .48600 \)
(b) \( R s .81000 \)


Assertion
Cannizaro reaction converts HCHO into
HCOONa and \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H} \)
Reason
It is a proton-hydride transfer reaction.
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


Asexual reproduction produces
offspring that are
A. Genetically identical to their parents
B. Genetically identical to their siblings
C. Both A and B
D. None of the above


In the reaction of \( Z n+F e S O_{4} \rightarrow \)
\( Z n S O_{4}+F e \)
A. zn gets oxidized
B. Fe gets oxidized
c. zn is oxidizing agent
D. zn and Fe both get oxidized


f \( z_{1}=1+2 i, z_{2}=2+3 i, z_{3}=3+4 i \)
\( \operatorname{then} z_{1}, z_{2} \) and \( z_{3} \) are collinear.
A . True
B. False


\( \boldsymbol{y}=\sin ^{1}\left[\frac{\boldsymbol{2} \boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}^{2}}\right], \boldsymbol{t h e n} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


State Heisenberg's uncertainty principle. Give its mathematical expression.


A wire of length 5 m is twisted through
\( 30^{\circ} \) at the free end. If the radius of wire
is 1 m \( m \), the shearing strain in the wire
is:
\( A \cdot 30 \)
B . \( 0.36^{\prime} \)
\( c \cdot 1^{c} \)
D. 0.18


An electric dipole will experience a net force when it is placed in :
A. Uniform electric field
B. A non-uniform electric field
c. Both the above cases
D. None of these


\( \operatorname{Let} \boldsymbol{S}(\boldsymbol{k})=\mathbf{1}+\boldsymbol{3}+\mathbf{5}+\ldots+(\mathbf{2} \boldsymbol{k}- \)
1) \( =3+k^{2} . \) Then which of the following
is true?
A. Principle of mathematical induction can be used to prove the formula
в. \( S(k) \Rightarrow S(k+1) \)
c. \( S(k) \neq S(k+1) \)
D. \( S(1) \) is correct


Sea weeds are important source of
A. Chlorine
B. Fluorine
c. lodine
D. Bromine


The bisector of the angle \( A \) of a triangle ABC meets BC in D, and BC is produced
up to E. Such that:
\( \angle A B C+\angle A C E=2 \angle A D C \)
A. True
B. False


The heat of formation for \( C O_{2} \) is given
as \( \triangle \mathrm{H}=-94.2 \mathrm{kcal} / \mathrm{mole} . \) The negative
value of \( \triangle \mathrm{H} \) indicates that:
A. \( C O_{2} \) is formed form its elements by an endothermic reaction
B. The reaction of carbon with oxygen occurs rapidly at \( 25^{\circ} \mathrm{C} \)
C. The enthalpy of the product \( C O_{2} \) is less than that of the reactants, \( O_{2} \) and \( c \)
D. No heat is liberated when carbon is oxidized
E. \( 94.2 \mathrm{kcal} \) must be added to oxidize one mole of carbon


A boy of height \( 1.5 \mathrm{m} \) with his eye level at \( 1.4 \mathrm{m} \) stands before a plane mirror of length \( 0.75 \mathrm{m} \) fixed on the wall. The
height of the lower edge of the mirror above the floor is \( 0.8 \mathrm{m} \). Then :
A. the boy will see his full image
B. the boy can't see his hair
c. the boy can't see his feet
D. the boy can see neither his hair nor his feet


If \( \boldsymbol{y}=\sqrt{\boldsymbol{x}+\sqrt{\boldsymbol{y}+\sqrt{\boldsymbol{x}+\sqrt{\boldsymbol{y}+\ldots \ldots \infty}}}} \)
then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) is equal to?
A \( \cdot \frac{y+x}{y^{2}-2 x} \)
В. \( \frac{y^{3}-x}{2 y^{2}-2 x y-1} \)
c. \( \frac{y^{3}+x}{2 y^{2}-x} \)
D. None of these


An elastic metal rod will change its
length when it
This question has multiple correct options
A. falls vertically under its weight
B. is pulled along its length by a force acting at one end
c. rotates about an axis at one end
D. slides on a rough surface


If the line \( p x-q y=r \) intersects the co
ordinate axes at \( (a, 0) \) and \( (0, b), \) then
value of atb is equal to
A \( \cdot_{r}\left(\frac{q+p}{q p}\right) \)
В \( \cdot_{r}\left(\frac{q-p}{p q}\right) \)
c. \( _{r}\left(\frac{p-q}{p q}\right) \)
D. \( r\left(\frac{p+q}{p-q}\right) \)
E \( \cdot r\left(\frac{p-q}{p+q}\right) \)


Two particles \( X \) and \( Y \) having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field
and describe circular paths or radii \( \boldsymbol{R}_{1} \)
and \( R_{2} \) respectively. The ratio of mass
of \( X \) to that of \( Y \) is equal to:
\( ^{\mathbf{A}} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{2} \)
B. \( \left(\frac{R_{1}}{R_{2}}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{R_{1}}{R_{2}}\right)^{1 / 2} \)
D. \( \frac{R_{2}}{R_{1}} \)


Assertion
Red phosphorus is less reactive than
yellow phosphorus.
Reason
Red phosphorus is insoluble in \( C S_{2} \) whereas white phosphorus is soluble.
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


If \( A \) and \( B \) mutually exclusive events associated with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \)
then find \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \boldsymbol{B}) \)


Which is correct statement about \( \sigma- \)
and \( \pi- \) molecular orbitals? Statements
are
(i) \( \pi- \) bonding orbitals are ungerade
(ii) \( \pi- \) antibonding orbitals are
ungerade
(iii) \( \sigma- \) antibonding orbitals are gerade
\( A \cdot( \) i) only
B. (ii) and (iii) only
c. (iii) only
D. (ii) only


The relative permeability is represented
by \( \mu_{r} \) and the susceptibility by \( \chi \) for a magnetic substance. Then, for a paramagnetic substance. Then, for a paramagnetic substance
A \( \cdot \mu_{r}>1, \chi>0 \)
в. \( \mu_{r}>1, \chi<0 \)
c. \( \mu_{r}>1, \chi>0 \)
D. \( \mu_{r}<1, \chi<0 \)


Fossil \( X \) is older than fossil \( Y \). Most
evident answer is:
A. Fossil Y has got some of the vestigial organs which are functional in \( x \).
B. Fossil Y has got homologous and analogous organs of fossil X.
C. Fossil \( X \) is found in deeper sedimentation than \( Y \)
D. Fossil \( Y \) was found in better state than that of \( x \).


An air bubbles starts rising from the bottom of a lake. Its diameter is \( 3.6 \mathrm{mm} \)
at the bottom and \( 4 \mathrm{mm} \) at the surface.
The depth of the lake is \( 2.5 \mathrm{m} \) and the temperature at the surface is \( 40^{\circ} \mathrm{C} \) then
temperature at the bottom is :
A \( \cdot 25^{\circ} \mathrm{C} \)
в. 20 \( ^{\circ} \) С
\( c \cdot 15^{0} c \)
D. \( 12^{0} \mathrm{C} \)


Assertion
\( \int_{0}^{\pi / 2} x \cot x d x=\frac{\pi}{2} \log 2 \)
Reason
\( \int_{0}^{\pi / 2} \log \sin x d x=-\frac{\pi}{2} \log 2 \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the , correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Which of the following changes in the respective bond order values are caused by removal of an electron from
\( N_{2} \) and \( F_{2} \) molecules?
A. Decrease by 0.5 In both
B. Increase by 0.5 In both
c. Increase by 0.5 in the former and decrease by 0.5 in the latter
D. Decrease by 0.5 In the former and Increase by. 0.5 in the latter
E. No change in both


At \( p H=2, E_{\text {Quinhydrone will be: }} \)
Given: \( E_{\text {Quinhydrone }}^{o}=1.30 V \)
\( \mathbf{A} \cdot 1.36 V \)
B . \( 1.30 V \)
c. \( 1.42 V \)
D . \( 1.20 V \)


In the circuit shown the resistance \( R \)
has a value that depends on the current.
Specifically, R is 20 ohms when I is zero and the increase in resistance in ohms
is numerically equal to one half of the
current in amperes. What is the value of current I in circuit?
A. 8.33 amp
B. 10 amp
c. 12.5 amp
D. 18.5 amp


Which of the following gives the maximum number of isomers?
\( \mathbf{A} \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{4} C l_{2}\right] \)
B . \( \left[N i(e n)\left(N H_{3}\right)_{4}\right]^{2+} \)
\( \mathbf{c} \cdot\left[N i\left(C_{2} O_{4}\right)(e n)_{2}\right] \)
D. \( \left[C r(S C N)_{2}\left(N H_{3}\right)_{4}\right]^{+} \)


If dissolved oxygen is not present, the
aquatic life would die.
A. True
B. False


Lindane can be obtained by the reaction
of benzene with:
\( \mathbf{A} \cdot C H_{3} C l / \) anhy. \( A l C l_{3} \)
B. \( C l_{2} \) /sunlight
c. \( C_{2} H_{5} \) Ilanhy. \( A l C l_{3} \)
D. \( C H_{3} C O C l / A l C l_{3} \)


Magnetic flux linked with a stationary loop resistance \( \boldsymbol{R} \) varies with respect to
time during the time period \( T \) as
follows:
\( \phi=a t(T-t) \)
The amount of heat generated in the loop during that time (inductance of the coil is negligible) is
A \( \cdot \frac{\alpha T}{3 R} \)
В. \( \frac{a^{2} T^{2}}{3 R} \)
\( ^{\mathbf{C}} \cdot \frac{a^{2} T^{2}}{R} \)
D. \( \frac{a^{2} T^{3}}{3 R} \)


A weak acid \( H A \) is found to be \( 10 \% \)
ionized in \( 0.01 M \) aqueous solution. Calculate the pH of a solution which is
\( 0.1 M \) in \( H A \) and \( 0.05 M \) in \( N a A \)
\( \mathbf{A} \cdot 5.365 \)
B. 6.355
c. 3.653
D. 6.593


Which one of the following sequences shows the correct hierarchy of
classification, going from the most inclusive to the least inclusive?
A. Kingdom, Domain, Phylum, Order, Class, Family Genus, Species
B. Domain, Kingdom, Phylum, Class, order, Family Genus, Species
c. Genus, species, Kingdom, Phylum, order, Class, Family
D. species, Genus, Family, Class, order, Phylum, Kingdon
E. Domain, Phylum, Kingdom, Genus, Species, Family, Order, Class


Among the following groups the group that deactivates the benzene ring for
further electrophilic substitution is:
A. Methyl
B. Amino
c. Hydroxyl
D. Chloro


Sound waves from a tuning fork A reach a point \( P \) by two separate paths ABP and ACP.When ACP is greater than ABP by \( 11.5 \mathrm{cm}, \) there is silence at P. When the difference is \( 23 \mathrm{cm} \) the sound becomes
loudest at \( P \) and when \( 34.5 \mathrm{cm} \) there is
silence again and so on. Calculate the minimum frequency (in Hz) of the fork if the velocity of sound is taken to be 331.2 \( \mathrm{m} / \mathrm{s} \)


Why should electric field lines never
cross each other?
A. Electric field due to a charge at any point is always singular in magnitude.
B. Electric field due to a charge at any point is always singular in direction.
C. Electric field due to a charge at any point cannot be multi-directional.
D. All of the above


An organic compound was used with sodium metal and extracted with
distilled water. On adding freshly
prepared \( F e S O_{4} \) solution followed by
the addition of \( F e C l_{3} \) and dil. \( H C l \) used
greenish-blue solution. 0.30 g of the organic compound after kjeldahlisation evolved a gas \( (\mathrm{X}), \) which
was passed on \( 100 \mathrm{ml} \) of \( 0.1 \mathrm{M} H_{2} S O_{4} \)
The excess of acid required \( 20 \mathrm{ml} \) of 0.5 M NaOH for neutralisation. The amount
of acid left after neutralisation
with base is:
\( \mathbf{A} \cdot 10 \mathrm{ml} \)
B. \( 90 \mathrm{ml} \)
c. \( 50 \mathrm{ml} \)
D. \( 80 \mathrm{ml} \)


The final electron acceptor of mitochondria is
A. Pyruvate.
B. NADP.
\( c \cdot 0_{2} \)
D. OAA (oxalo acetic acid)


The reaction,
\( 3 C l O^{-}(a q) \rightarrow C l O_{3}^{-}(a q)+2 C l^{-} \)
A. Oxidation reaction
B. Reduction reaction
c. Disproportionation reaction
D. neutralisation reaction


Let \( f \) be a function defined on \( R \) (the set
of all real numbers) such that \( \mathbf{f}^{\prime}(\mathbf{x})= \) \( 2010(x-2009)(x-2010)^{2}(x- \)
2011)\( ^{3}(x-2012)^{4}, \) for all \( x \in R \). If \( g \) is a
function defined on \( \mathbf{R} \) with values in the
interval \( (0, \infty) \) such that \( f(x)= \) \( \ln (\mathrm{g}(\mathrm{x})), \) for all \( \mathrm{x} \in \mathrm{R}, \) then the number
of points in \( \mathbf{R} \) at which \( \mathbf{g} \) has a local maximum is
A .
B.
\( c \cdot 2 \)
D. 3


A body produces sound only if it
is
A. made of steel
B. made of glass
c. plucked
D. vibrating


For any square matrix \( \boldsymbol{A}, \boldsymbol{A}+\boldsymbol{A}^{T} \) is
A. unit matrix
B. symmetric matrix
c. skew symmetric matrix
D. zero matrix


A person meets with an accident and
great loss of blood has occurred. There is no time to analyse his blood group. It is safe to transfer blood of group
A. AB.Rht
B. AB,Rh-
\( c \cdot O, R h- \)
D. O,Rht


How is diethyl ether prepared by continuous etherification process?


Write the equation of a line which is parallel to \( x- \) axis at a distance of 5
units from it, and another line parallel
to \( y- \) axis at a distance of 7 units from
it. Draw the graphs and write the coordinates of point of intersection.


When ozone reacts with unsaturated
hydrocarbons, the products formed are called:
A . ozonites
B. ozonides
c. carbazone
D. unsaturated ozone


Can there be mitosis without DNA
replication in 'S' phase?


Which of the following is nucleophilic
addition reaction?
A. Hydrolysis of ethyl chloride by \( N a O H \)
B. Purification of acetaldehyde by \( \mathrm{NaH} \mathrm{SO}_{3} \)
C. Alkylation of anisol
D. Decarboxlation of acetic acid


If \( \bar{X} \) is the mean of \( x_{1}, x_{2}, x_{3}, \dots, x_{n} \)
Then, the algebraic sum of the deviations about mean \( \bar{X} \) is
A. 0
в. \( \frac{\bar{X}}{n} \)
\( c \cdot n \bar{X} \)
D. none of these


On applying brakes the angular velocity of a flywheel reduces from 900
cycles/min to 720 cycles/min in 6 seconds. Its angular retardation in rad
\( / s^{2} \) will be?
A . \( \pi / 3 \)
в. \( \pi \)
c. \( 2 \pi / 3 \)
D. \( 2 \pi \)


simultaneously from point A. P moves
along a smooth horizontal wire \( A B . Q \)
moves along a curved smooth track. \( Q \)
has sufficient velocity at \( A \) to reach \( B \) always remaining in contact with the curved track. At A, the horizontal
component of velocity of \( Q \) is same as
the velocity of \( \mathrm{P} \) along the wire. The
plane of motion is vertical. If \( t_{1}, t_{2}, \) are
times taken by \( P \& Q \) respectively to
reach B then (Assume velocity of P is
constant)
\( \mathbf{A} \cdot t_{1}=t_{2} \)
\( \mathbf{B} \cdot t_{1}>t_{2} \)
\( \mathbf{c} \cdot t_{1}<t_{2} \)
D. none of these


Find the coordinates of the point on the \( x \) -axis that is equidistant from
\( \boldsymbol{P}(\mathbf{4}, \mathbf{3}, \mathbf{1}) \) and \( \boldsymbol{Q}(-\mathbf{2},-\mathbf{6},-\mathbf{2}) \)
A \( \cdot\left(\frac{3}{2}, 0,0\right) \)
B \( \cdot\left(-\frac{3}{2}, 0,0\right) \)
c. \( \left(0,-\frac{3}{2}, 0\right) \)
D. \( \left(0, \frac{3}{2}, 0\right) \)


Which of the following statements is
true?

Heat produced in a current carrying conductor depends upon:
This question has multiple correct options
A. The time for which the current flows in the conductor
B. The resistance of the conductor
C. The strength of the current
D. The nature of current (ac or dc)


A particle moves in a circular path with
a uniform speed. Its motion is:
A. Periodic
B. Oscillatory
c. simple harmonic
D. Angular simple harmonic


A spehere of mass \( 0.2 \mathrm{kg} \) is attached to an inextensible string of length \( 0.5 m \)
whose upper end is fixed to the cielling. The sphere is made to describe a
horizontal circle of radius \( 0.3 m \) The
speed of the sphere will be


A plank with a uniform sphere placed on it rests on a smooth horizontal plane.
The plank is pulled to the right by a constant force \( F \). If the sphere does not
slip over the plank, then This question has multiple correct options
A. both have the same acceleration
B. acceleration of the centre of sphere is less than that of the plank
c. work done by friction acting on the sphere is equal to its total kinetic energy
D. total kinetic energy of the system is equal to work done by the force \( F \)


The area of the region bounded by \( y^{2}= \) \( x \) and \( x=36 \) is divided in the ratio 1: 7 by
the line \( x=a \). then a equals-
A. 7
B. 8
\( c \cdot 9 \)
D.


Find a quadratic polynomial each with the give numbers as the sum and
product of its zeros respectively.
4,1


f \( p \lambda^{4}+p \lambda^{3}+p \lambda^{2}+s \lambda+t= \)
\( \left|\begin{array}{ccc}\lambda^{2}+3 \lambda & \lambda+1 & \lambda+3 \\ \lambda+1 & 2-\lambda & \lambda-4 \\ \lambda-3 & \lambda+4 & 3 \lambda\end{array}\right|, \) then value
of t is
A . 16
B . 18
\( c .17 \)
D. 19


Define critical angle. Prove that the refractive index of the denser medium
is reciprocal of the sine of the critical angle.


A cricket ball of mass \( 500 \mathrm{g} \) is moving with a speed of \( 36 \mathrm{km} h^{-1} . \) It is reflected
with the same speed. What is the impulse applied on it?
A. 20 kg m \( s^{-1} \)
B. \( 5 \mathrm{kg} \mathrm{m} s^{-1} \)
C. \( 25 \mathrm{kg} \mathrm{m} s^{-1} \)
D. \( 10 \mathrm{kg} \mathrm{m} s^{-1} \)


State whether the following statements
are true or false.
Humans often disrupt natural succession to produce agricultural fields and managed forests.
A. True
B. False


Simplify the following:
\( \frac{3}{1+i}-\frac{2}{2-i}+\frac{2}{1-i} \)


What is the volume occupied by 17.75 g of \( C l_{2} \) at STP?
A . \( 5.6 l \)
в. 22.4
c. \( 11.2 l \)
D. 2.8l


The largest number which divides
30,78 and 102 to leave the same
remainder in each case is ?


The mole fraction of water in a
sulphuric acid solution is 0.85 Calculate the molality of the solution:


Number of mole cules present in 4.2 g \( N_{2} \) is \( x x \times 10^{22} . \) What is the value of
\( x(\text { round off to } 1 \) digit)?


The 'Indian Botanical Garden' is
situated near
A. New Delhi
B. Kolkatata
c. Mumbai
D. Lucknow


The Moon orbits the Earth once in 27.3
days in an almost circular orbit Calculate the centripetal acceleration experienced by the Earth? (Radius of the Earth is \( 6.4 \times 10^{6} \mathrm{m} \) )


Pyrolusite is \( M n O_{2} \) used to prepare
\( K M n O_{4} . \) Steps are:
\( M n O_{2} \stackrel{I}{\longrightarrow} M n O_{2}^{2-} \stackrel{I I}{\longrightarrow} M n O_{4}^{-} \)
Steps \( I \) and \( I I \) are respectively:
This question has multiple correct options
A. fuse with \( K O H / \) air, electrolyte oxidation
B. fuse with \( K O H / K N O_{3} \), electrolyte oxidation.
c. fuse with concentrated \( H N O_{3} \) /air, electrolytic reduction
D. dissolve in \( H_{2} O \) oxidation


Which of the following compounds has lowest boiling point?
A. n-butyl alcohol
B. Isobutyl alcohol
c. Tert-butyl alcohol
D. Sec-butyl alcohol


Enzyme required to oxidise
acetaldehyde is
A. Ethanol oxidase
B. Acetaldehyde dehydrogenase
C. Alcohol hydrogenase
D. Glyceraldehyde dehyadrogenase


IUPAC name of \( \left[P t\left(N H_{3}\right)_{3} B r\left(N O_{2}\right) C l\right] C l \)
is:
A. Triamminechlorobromonitroplatinum (IV) chloride
B. Triamminebromonitrochloroplatinum (IV) chloride
C. Triamminebromochloronitroplatinum (IV) chloride
D. Triamminenitrochlorobromoplatinum
(III) chloride


In Searle's experiment to find Young's modulus the diameter of wire is
measured as \( \boldsymbol{d}=\mathbf{0 . 0 5 c m}, \) length of
wire is \( l=125 c m \) and when a weight,
\( \boldsymbol{m}=\mathbf{2 0 . 0 k g} \) is put, extension in wire
was found to be \( 0.100 \mathrm{cm} \). Find the
maximum permissible error in Young's modulus \( (Y) . \) Use: \( Y=\frac{m g l}{(\pi / 4) d^{2} x} \)
A . \( 6.3 \% \)
в. \( 5.3 \% \)
\( c .2 .3 \% \)
D. 1\%


The value of \( \int_{-8}^{8}\left(\sin ^{93} x+x^{295}\right) d x \)
A .
B. -
c. 0
D.


In which event, the experiment is impossible?
A. Tossing a coin for head or tail
B. 5 in case of throwing a dice.
c. Rolling a dice for 7
D. Tossing a coin to get a tail.


What are biodegradable polymers? Give chemical equation for the preparation of any one biodegradable polymer.


If the solution of these equations. \( x-12=2 \frac{2}{5} \)


What are the substances which mimic
the natural chemical messengers?
A. Antibiotics
B. Antagonist
c. Agonists
D. Recepter


When a sound wave travels from one
medium to another, the quantity that remains unchanged is
A. Speed
B. Amplitude
c. Frequency
D. wavelength


If in an unpolarised light \( \mathrm{E}=2 \vec{i}+3 \vec{j} \) and \( \vec{H}=3 \vec{i}-2 \vec{j}, \) then the direction of
propagation is given by
A \( -13 \vec{k} \)
the \( -13 \vec{k} \).
B . \( -13 \vec{j} \)
\( \mathbf{c} \cdot-6 \vec{i}+6 \vec{k} \)
D. \( 5 \vec{i}-4 \vec{k} \)


\( A \) and \( B \) are two concentric spherical
shells, If \( A \) is given a charge \( +q \) while \( B \) is earthed as show in the figure, then :
A. Charge on the outer surface of shell B is zero
B. The charge on B is equal and opposite to that of \( A \)
C. The field inside \( A \) and outside \( B \) is zero
D. All of the above


Semiconductors are materials having
an electrical conductivity :
A. Less than insulators
B. between \( 10^{-8} S / \) cm to \( 10^{3} \) S/cm
c. Equal to zero
D. Greater than \( 10^{3} \mathrm{S} / \mathrm{cm} \)


In mammalian kidney, Henle's loop is
present in
A. cortex
B. Caput epididymis
c. Medulla
D. Ureter


In Kjeldahl's method,organic compound containing nitrogen after reacting with concentrated sulphuric acid forms:
A . nitrite salt
B. nitrate salt
c. ammonium salt
D. azide salt


Law of limiting factor was proposed by
\( A \). Robot Hill
B. Kolvin
c. Blackmann
D. Arnon


Chlorine water on standing loses its colour and forms:
A. \( H O C l \) and \( H O C l_{2} \)
B. HCl only
c. \( H C l \) and \( H C l O_{2} \)
D. \( H C l \) and \( H O C l \)


Value of \( x \) for which \( \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)= \)
\( 2 \tan ^{-1} x \) satisfied is \( x \epsilon[a, \infty) \)
Find the value of \( a \)
A \( . a=-\infty \)
B . \( a=-1 \)
\( \mathbf{c} \cdot a=0 \)
D. \( a=1 \)


Recently, the phenomenon of superconductivity has been observed at
\( 95 K . \) This temperature is nearly equal
to.
\( \mathbf{A} \cdot-288^{\circ} F \)
B . \( -146^{\circ} F \)
c. \( -368^{\circ} F \)
\( \mathrm{D} \cdot+178^{\circ} \mathrm{C} \)


\( \boldsymbol{S} \boldsymbol{O}_{2} \) turns lime water milky due to formation of
A. calcium sulphite
B. calcium carbonate
c. calcium sulphide
D. carbon dioxide


Which of the following is an example of thermosetting polymer?
A. Sealing wax
B. Nylon - 6, 6
c. PVC
D. Bakelite


The molar heat capacities of lodine vapour and solid are 7.8 and 14 cal/mol respective enthalpy of
sublimation of iodine is 6096 cal \( / \) mol
\( \operatorname{at} 200^{\circ} C, \) then what is \( \Delta H \) the value at
\( 250^{\circ} \mathrm{C} \) in cal/mol.
A . 5360
в. 4740
\( c .6406 \)
D. none of these


A man is slipping on a fritionless inclined plane \( \& \) a bag falls down from the same height. Then the final speed of both is related as:-
A. \( V_{B}>V_{m} \)
B. \( V_{B}<V_{m} \)
c. \( V_{B}=V_{m} \)
D. \( V_{B} \) and \( V_{m} \) can't related


The package's velocity at the instant the parachute opens is (approximately nearest whole number)
A. \( 84 \mathrm{m} / \mathrm{s} \)
B. \( 82 \mathrm{m} / \mathrm{s} \)
\( c \cdot 89 \mathrm{m} / \mathrm{s} \)
D. \( 92 \mathrm{m} / \mathrm{s} \)


If L and R denote inductance and
resistance, respectively, then the dimensions of L/R are
A \( \cdot M^{1} L^{0} T^{0} Q^{-1} \)
В. \( M^{0} L^{0} T Q^{0} \)
c. \( M^{0} L^{1} T^{-1} Q^{0} \)
D. \( M^{-1} L T^{0} Q^{-1} \)


Heat of solution is always positive.
\( A \)


In general alkyl haldies are insolube in
water. The main reason is:
A. they are slightly polar
B. they do not form hydrogen bonds with \( H_{2} \) O
c. the halogen end is repelled by water
D. they are unreactive compounds


A circle has two equal chords \( \$ \$ P Q \$ \$ \) and \( \$ \$ P R \$ \$ \)
diameter \( \$ \$ P D \$ \$ \) cuts \( \$ \$ Q R \$ \$ \) in \( \$ \$ E \)
\( \$ \$ . \) If \( P R=12 c m \) and \( P E=8 c m, \) then
the length of \( \$ \$ \) PD \( \$ \$ \) is \( ? \)
\( \mathbf{A} \cdot 25 \mathrm{cm} \)
B . \( 22 \mathrm{cm} \)
c. \( 20 \mathrm{cm} \)
D. \( 18 \mathrm{cm} \)


\( 10=0 \)
\( \alpha \)
\( \alpha \)
\( \alpha \)


What is the major product of the
reaction?
A. I and III
B. I and IV
C. II and III
D. II and IV


The mineral carnallite contains
(i) \( _{--} \) and
(ii) metals.
(iii) \( _{---}- \) is purified by cupellation and (iv) purified by distillation.
A . (i) -calcium,
(ii)- zinc, (iii)- mercury, (iv)- - tin
B. (i)- calcium, (ii)- magnesium, (iii)- zinc, (iv)- - lead
c. (i)- potassium, (ii)- calcium, (iii)- copper, (iv)- mercury
D. (i)- magnesium, (ii)-potassium, (iii)- - silver, (iv) mercury


Explain the role of each of the following.
(i) NaCN in the extraction of silver
(ii) \( S i O_{2} \) in the extraction of copper


The tropical rainforests has a large population of animals. Explain why it is
so.


Aryl halides are less reactive towards nucleophilic substitution reaction as
compared to alkyl halides due to:
This question has multiple correct options
A. the formation of less stable carbonium ion
B. resonance stabilisation
C . longer carbon-halogen bond
D. the inductive effect
\( \mathrm{E} \cdot s p^{2}- \) hybridised carbon attached to the halogen


Find the ratio by mass of the combining
elements in the \( C a C O_{3} \)
A . 1: 3: 2
B. 10: 3: 12
c. 1: 13: 12
D. none of these


The equation of sound wave is \( y= \) \( 0.0015 \sin (62.4 x+316 t) . \) Find the
wavelength of this wave
A. 0.2 unit
B. 0.1 unit
c. 0.3 unit
D. None of these


An angiosperm differs from a
gymnosperm by possessing
A . Ovule
B. Xylem vessels
c. xylem tracheids
D. seed


There are 3 boxes each having two drawers The first box contains a gold coin in each drawer. The second, a gold coin in one drawer and a silver coin in
the other. The third box contains a silver
coin in each drawer. A box is chosen at
random and a drawer is opened. If a gold coin is found in that drawer, then the probability that the other drawer also contains a gold coin is
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{2}{3} \)
\( D .3 \)
5


Evaluate the following determinant:
\[
\left|\begin{array}{ccc}
102 & 18 & 36 \\
1 & 3 & 4 \\
17 & 3 & 6
\end{array}\right|
\]


An infinite number of equal charges \( (q \) each) are placed at distance \( x= \)
\( 1,2,4,8, \dots \dots \). \( 0 . \) Then the electric potential at the origin \( (x=0) \) will be :
A. zero
B. infinite
c. \( \frac{q}{4 \pi \varepsilon_{0}} \)
D. \( \frac{2 q}{4 \pi \varepsilon_{0}} \)


\( \boldsymbol{K} \boldsymbol{B r}+\boldsymbol{M n O}_{2}+\boldsymbol{H}_{2} \boldsymbol{S O}_{4}(\text {conc.}) \longrightarrow \)
\( \boldsymbol{K} \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{\mathfrak{S}}+\boldsymbol{M} \boldsymbol{n} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{H}_{2} \boldsymbol{O}+[\boldsymbol{X}] \)
(unbalanced equation). Which statement is/are correct?
This question has multiple correct options
A. \( X \) turns starch paper orange red
B. \( X \) with \( A g N O_{3} \) solution gives a pale yellow ppt. which 's completely soluble in excess ammonium hydroxide
c. \( X \) produces violet colour in organic layer in \( K I \) solution
D. \( X \) is liberated when a mixture of \( K B r, K_{2} C r_{2} O_{7} \) and
conc. \( H_{2} S O_{4} \) is heated


\( A B, \) if \( D C=20 \mathrm{cm} \) and \( M N=27 \mathrm{cm} \)
\( 4.43 \mathrm{cm} \)
3. 31 ст
\( c \cdot 34 c m \)
\( 30 \mathrm{cm} \)


What type of reflection will take place from a polished surface?


In the given figure, if \( A B C D \) is a
parallelogram and \( E \) is the mid-point of
\( B C, \) then area \( (\triangle D E C)=k \) area
\( (A B C D) . \) Find \( k \)


Which of the following is non-
permissible?
A. \( n=4, l=3, m=0 \)
B. \( n=4, l=2, m=1 \)
c. \( n=4, l=4, m=1 \)
D. \( n=4, l=0, m=0 \)


solve the limit
\( \lim _{x \rightarrow 3} \frac{2}{x-3} \)
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. Does not exist


Form the differential equation of all family of lines \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x}+\frac{\boldsymbol{4}}{\boldsymbol{m}} \) by
eliminating the arbitrary constant ' \( m^{\prime} \)
is
A \( \cdot \frac{d^{2} y}{d x^{2}}=0 \)
в. \( \quad x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}+4=0 \)
\( ^{\mathrm{c}} x\left(\frac{d y}{d x}\right)^{2}+y \frac{d y}{d x}+4=0 \)
D. \( \frac{d y}{d x}=0 \)


Ice is an example of the following crystal:
A . covalent
B. ionic
c. van der Waal
D. hydrogen bonding


Which of the following reactions of potassium superoxide supply oxygen gas in the breathing equipments used in space and submarines?
(A) Reaction of superoxide with nitrogen in the exhaled air.
(B) Reaction of superoxide with moisture in the exhaled air.
(C) Reaction of superoxide with carbondioxide in the exhaled air.
\( A \cdot(A),(B) \) and \( (C) \)
B. (B) and (C) only
\( c \cdot(B) \) only
D. (A) and (B) only


Centromere is required for which of the following?
A. Movement of chromosomes towards poles
B. Cytoplasmic cleavage
c. crossing over
D. Transcription process


Vascular cryptogams or seed less vascular plants belongs to
A. Bryophyta
c. Thallophyta
D. spermatopoyta


Binomial of vilvam is
A. Acalypha indica
B. Aegle marmelos
c. cissus quadrangularis
D. Mimosa pudica


For \( \boldsymbol{x} \in \boldsymbol{R}, \) let \( [\boldsymbol{x}] \) denotes the greatest integer \( \leq x \), then the value of \( \left[-\frac{1}{3}\right]+ \) \( \left[-\frac{1}{3}-\frac{2}{100}\right]+\ldots+\left[-\frac{1}{3}-\frac{99}{100}\right] \) is
A. -100
B. -123
c. -135
D. -153


Glucose reacts with \( C H_{3} O H, \) in
presence of dry \( \boldsymbol{H} \boldsymbol{C l} \) gas, to form:
A . \( \alpha \) -methyl glucoside
B. \( \beta \) -methyl glucoside
c. both A and B
D. none of these


Electroscope is an instrument used to
find the quantity of charge on different bodies.
A. True
B. False


A parallel line is drawn from point \( P(5,3) \) to \( y \) -axis, what is the distance
between the line and \( y \) -axis.


Avogadro's number is the number of
molecules present in:
A. \( 1 \mathrm{g} \) of molecule
B. 1 atom of molecule
c. 1 mole
D. 1 litre of molecule


If \( 2 \vec{a}+3 \vec{b}-5 \vec{c}=\overrightarrow{0}, \) then ratio in which
\( \vec{c} \) divides \( \overrightarrow{A B} \) is
A. 3: 2 internally
B. 3: 2 externally
c. 2: 3 internally
D. 2: 3 externally


The equation for the reflected wave is \( \operatorname{given} \operatorname{as} y_{2}=\pm \frac{s}{10} A \cos (a x-b t) \) Find
\( \mathcal{S} \)


The diagram shows identical lamps \( x \) and connected in series with a battery.
The lamps light with normal
brightness.If a third lamp \( z \) is connected in parallel with lamp \( X \), then
what will happens to the brightness of
the lamp Y?
A. Brighter than normal
B. Normal
c. Dimmer than normal
D. very dim (cannot be seen)


Solve for \( x \) and \( y, \) if \( x+y=7 \) and \( 2 x+ \)
\( 3 y=18 \)
A \( . x=3, y=4 \)
в. \( x=2, y=5 \)
c. \( x=1, y=6 \)
D. \( x=4, y=3 \)


Sodium chloride is added to the
solution after saponification to cause
the :
A. hydrolysis of soap
B. precipitation of soap
c. sedimentation of soap
D. none of these


The growth regulator that retards ageing of plant organ is
A . Auxin
B. Gibberellin
c. cytokinin
D. Abscisic acid


If \( p, q \) are the perpendicular distances from the origin to the lines \( x \sec \alpha+ \)
\( y \operatorname{cosec} \alpha=a \) and \( x \cos \alpha-y \sin \alpha= \)
\( a \cos 2 \alpha, \) then \( 4 p^{2}+q^{2}= \)
A \( \cdot a^{2} \)
B. \( 4 a^{2} \)
\( c \cdot 2 a^{2} \)
\( D \cdot 6 a^{2} \)


Most abundant water pollutant is
A . Detergents
B. Industrial wastes
c. Pesticides
D. Oil spills


The diagonals of a parallelogram
\( P Q R S \) are along the lines \( x+3 y=4 \)
and \( 6 x-2 y=7, \) then \( P Q R S \) must be
\( a \)
A. rectangle
B. square
c. cyclic quadrilateral
D. rhombus


Choose the incorrect statement among
the following.
A. Many useful substances are obtained from petroleum and natural gas. These are termed as 'petrochemicals'
B. Hydrogen gas obtained from natural gas is used in the production of fertilizers
C. Due to the great commercial importance of petroleum, it is also called 'black gold
D. Natural gas is stored under low pressure as compressed natural gas (CNG)


Which of the following oxide is
amphoteric?

This question has multiple correct options
A. \( S n O_{2} \)
в. \( C a O O \)
\( \mathrm{c} \cdot \operatorname{si} O_{2} \)
D. \( C O_{2} \)


The ionic radius of \( _{57} L a^{3+} \) is \( 1.06 \mathrm{A} \) Which one of the following given values will be closest to the ionic radius of
\( \mathbf{7}_{1} \boldsymbol{L} \boldsymbol{u}^{\mathbf{3}+} ? \)
A . 1.06 A
B. 1.56 A
c. \( 0.85 \mathrm{A} \)
D. 1.35 A


The vertices of \( \triangle A B C \) are
\( \boldsymbol{A}(\mathbf{1}, \mathbf{8}), \boldsymbol{B}(-\mathbf{2}, \mathbf{4}), \boldsymbol{C}(\mathbf{8},-\mathbf{5}) . \) If \( \boldsymbol{M} \) and \( \boldsymbol{N} \)
are the midpoints of \( A B \) and \( A C \)
respectively, find the slope of \( M N \) and
hence verify that \( M N \) is parallel to \( B C \).
A \( \cdot-\frac{9}{10} \)
в. \( \frac{9}{10} \)
\( c \cdot-\frac{9}{5} \)
D. None of these


Find \( ^{\prime} x^{\prime} \) for the given figure below


In lungs, gaseous exchange occurs in
A. Bronchioles
B. Trachea
c. oesophagus
D. Alveol


Vasopressin released from the
neurohypophysis is mainly responsible
for
A. Facultative reabsorption of water through Henle's loop
B. Obligatory reabsorption of water through Bowman's capsule
C. Facultative reabsorption of water through DCT
D. Obligatory reabsorption of water through PCT


The focal length of a concave mirror is \( 50 \mathrm{cm} \) where an object is to be placed so that its image is two times magnified, real and inverted:
A. \( 75 \mathrm{cm} \)
B. 72 cm
\( c \cdot 63 \mathrm{cm} \)
D. 50 cm


Which term of the A.P. \( 3,10,17, \ldots \ldots . \) wil
be 84 more than its 13 th term?


Innermost zone is the
A. hottest part
B. moderately hot part
c. least hot part
D. cold part


To make an electromagnet, the best material which should be used is
A . Silver
B. Nickel
c. stainless steel
D. Soft iron


Show that the relation R defined on the
\( \operatorname{set} A=\{1,2,3,4,5\}, \) given by \( R= \)
\( \{(a, b):|a-b| \text { is even }\} \) is an
equivalence relation


A hollow half cylinder surface of radius R and length I is placed in a uniform electric field \( \vec{E} \). Electric field is acting
perpendicular on the ABCD. If the flux through the curved surface of the hollow
cylindrical surface is \( \boldsymbol{E} \times \boldsymbol{X} \boldsymbol{R} \boldsymbol{l} \). Find \( \mathbf{X} \) ?


Find the inverse of the following matrix by using elementary row transformation:
\( \left[\begin{array}{ll}5 & 2 \\ 2 & 1\end{array}\right] \)


If PQRS is a convex quadrilateral with 3 4,5 and 6 points marked on side \( P Q, Q R \) RS and PS respectively. Then, the
number of triangles with vertices on different sides is
A .220
в. 270
\( c \cdot 282 \)
D. 342


What is coordination number of oxygen
in \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) ? \)


Assertion: Solution of \( A l C l_{3} \) in water is
neutral
Reason: \( \left[A l\left(H_{2} O\right)_{6}\right]^{3+} \) is formed
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
E. Both Assertion and Reason are incorrect


Find the principal value of:
\( \cot ^{-1}(\sqrt{3}) \)


Which of the following will be readily soluble in water?
\( A \)
B.
\( c \)
D.


It is not possible to construct a triangle when its sides are:
A. \( 8.3 \mathrm{cm}, 3.4 \mathrm{cm}, 6.1 \mathrm{cm} \)
B. \( 5.4 \mathrm{cm}, 2.3 \mathrm{cm}, 3.1 \mathrm{cm} \)
c. \( 6 \mathrm{cm}, 7 \mathrm{cm}, 10 \mathrm{cm} \)
D. 3 cm, 5 cm, 5 cm


In a meter bridge, a standard resistor of \( \mathrm{R} \) ohm is connected in the left gap and two wires \( A \) and \( B \) are connected one
after the other in the right gap. The balancing length measured from the left is \( 50 \mathrm{cm} \) for either of them. If the two wires are connected is series and put in
the right gap, the balancing length measured from the left would be (in cm)
A . 25
в. 33.3
\( c .66 .7 \)
D. 75


Antinodal curves correspond to
interference.
A. constructive
B. destructive
C. where intensity is less than maximum but not completely zero
D. none of these


Among the following compounds which has the highest boiling point?
A. 2-Bromopentane
B. 3-Bromopentane
c. 1-Bromopentane
D. All have same boiling point


The alcohol which gives the most
stable carbonium ion on dehydration is:
A \( \cdot\left(C H_{3}\right)_{2} C H C H_{2} O H \)
В . \( \left(C H_{3}\right)_{3} C-O H \)
c. \( C H_{3} C H_{2} C H_{2} C H_{2} O H \)
D. \( C H_{3}-C H-C H_{2} C H_{3} \)


The emissivity of tungsten is \( 0.4 . \) A tungsten sphere with a radius of \( 4.0 \mathrm{cm} \) is suspended within a large evacuated
enclosures whose walls are 300 K. What
power input is required to maintain the
sphere at a temperature is \( 3000 \mathrm{K} \) if heat conduction along supports is neglected ? Take \( \sigma=5.6 \times \) \( \mathbf{1 0}^{-6} \boldsymbol{W} / \boldsymbol{m}^{2}-\boldsymbol{K}^{4} \)
\( \mathbf{A} \cdot 3.7 \times 10^{4} W \)
в. \( 3.7 \times 10^{5} W \)
c. \( 3.7 \times 10^{6} W \)
D. \( 3.7 \times 10^{7} W \)


The part of a trasistor which is heavily doped to produce large number of majority carriers is :
A . emitter
B. base
c. collector
D. can be any of the above three


A compound \( (80 \mathrm{g}) \) on analysis gave \( \boldsymbol{C}=\mathbf{2 4} \) g, \( \boldsymbol{H}=\mathbf{4} \) g, \( \boldsymbol{O}=\mathbf{3 2} \) g. Its
empirical formula is :
A \( \cdot C_{2} H_{2} O_{2} \)
в. \( C_{2} H_{2} O \)
c. \( C H_{2} O_{2} \)
D. \( C H_{2} O \)


A copper coil has a resistance of \( 2.43 \Omega \)
at \( 50^{\circ} \mathrm{C} \). Find its resistance at \( 60^{\circ} \mathrm{C} \)
The resistance temperature coefficient
of copper is 0.0043 per \( ^{\circ} C \) at \( 0^{\circ} C \)


Fusion reaction takes place at high temperature because:
A. atoms are ionised at high temperature
B. molecules break up at high temperature
c. nuclei break up at high temperature
D. kinetic energy is high enough to overcome repulsion between nucle


A ball is moving with speed \( 20 \mathrm{m} / \mathrm{s} \) collides with a smooth surface as
shown in figure. The magnitude of change in velocity of the ball will be
(Smooth horizontal surface)
\( \mathbf{A} \cdot 10 \sqrt{3} \mathrm{m} / \mathrm{s} \)
B. \( 20 \sqrt{3} \mathrm{m} / \mathrm{s} \)
\( c \cdot \frac{40}{\sqrt{3}} m / s \)
D. \( 40 \mathrm{m} / \mathrm{s} \)


The magnetic flux linked with a coil at
any instant \( t \) is given by the equation
\( \phi=5 t^{3}-100 t+300 . \) The magnitude
of emf induced in the coil after \( 3 s \) is
A . \( 10 V \)
в. \( 20 V \)
\( c .35 V \)
D. \( 70 V \)


carried \( 1000 \mathrm{kg} \) of watermelon in
summer by train. In the beginning, the water content was \( 99 \% . \) By the time I
reached the destination, the water
content had dropped to \( 95 \% . \) The reduction in the weight of the
watermelon was
A. \( 300 \mathrm{kg} \)
в. 200 kg
c. \( 800 \mathrm{kg} \)
D. 700 kg


Bathing soap are usually hard and free from the unused alkali, while washing soap are usually soft and also contains some residual alkali.
If true enter 1 , if false enter 0 .
\( A \)


By taking one example of a local plant and animal, how would you help these parents to overcome such inhibitions
about reproduction and reproduction?


The diagram given here is the standard
ECG of a normal person. The P-wave
represents the
A . Initiation of the ventricular contraction
B. Beginning of the systole
c. End of systole
D. Contraction of both the atria


Find the centre and radius of the circle
\( x^{2}+y^{2}-4 x-8 y-45=0 \)


\( \int_{0}^{\infty}\left(\cot ^{-1} x\right)^{2} d x=\frac{\pi}{k} \log 2 . \) Find the
value of \( k \)


Addition Theorem of Probability states
that for any two events \( A \) and \( B \)
\( \mathbf{A} \cdot P(A \cup B)=P(A)+P(B) \)
B \( \cdot P(A \cup B)=P(A)+P(B)+P(A \cap B) \)
\( \mathbf{c} \cdot P(A \cup B)=P(A)+P(B)-P(A \cap B) \)
D \( . P(A \cup B)=P(A) \times P(B) \)


Let \( \quad A=\{x:-1 \leq x \leq 1\} \) and \( f \)
\( \boldsymbol{A} \rightarrow \boldsymbol{A} \) such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}|\boldsymbol{x}| \), then \( \boldsymbol{f} \) is
A. a bijection
B. injective but not surjective
c. surjective but not injective
D. neither injective nor surjective


Find \( \frac{d y}{d x} \) when \( y=e^{\sqrt{x}+\sin x} \)


A body at rest cannot have
and


The number of sigma and pi bonds in benzene are:
\( \mathbf{A} \cdot 6 \sigma \) and \( 3 \pi \)
B. \( 12 \sigma \) and \( 3 \pi \)
\( \mathbf{c} \cdot 9 \sigma \) and \( 3 \pi \)
D. \( 6 \sigma \) and \( 6 \pi \)


The principal emulsifying agent for w/o emulsion is:
A. proteins
B. gum
c. lamp black
D. synthetic soaps


Given \( \boldsymbol{A}=\mathbf{2}, \mathbf{3}, \boldsymbol{B}=\mathbf{4}, \mathbf{5}, \boldsymbol{C}=\mathbf{5}, \mathbf{6}, \) find
(i) \( \boldsymbol{A} \times(\boldsymbol{B} \cap \boldsymbol{C})=\ldots \ldots \)
(ii) \( (\boldsymbol{A} \times \boldsymbol{B}) \cup(\boldsymbol{B} \times \boldsymbol{C})=\ldots \ldots \)


Which of the following has the time period two seconds specifically:
A. Wrist watch
B. Linear expansion of iron rodd
C. Frequency of ripples on the surface of water
D. Seconds pendulum


Construct a quadrilateral \( \boldsymbol{A B C D} \), with \( \boldsymbol{B C}=\mathbf{5} \mathrm{cm}, \boldsymbol{C D}=\mathbf{9} \mathrm{cm}, \boldsymbol{D} \boldsymbol{A}=\mathbf{6} \mathrm{cm} \)
\( \angle C=60^{\circ}, \angle D=75^{\circ} \)


Assertion
Displacement \( (S) \) -time
(t) graph of a
particle moving in a straight line is
shown in figure. Work done by all the
forces is equal to change in kinetic
energy.
Reason
Work done by all the forces between
time interval \( t_{1} \) and \( t_{2} \) is definitely zero.
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.


Two trains, each \( 50 m \) long, are travelling in opposite directions with velocity \( 10 m / s \) and \( 15 m / s . \) The time of crossing is-
\( \mathbf{A} \cdot 2 s \)
B . \( 4 s \)
c. \( 2 \sqrt{3} s \)
D. \( 4 \sqrt{3} s \)


Assertion
Copper is used to make hot water tanks
and not steel (an alloy of iron)
Reason
Copper does not react with cold water, hot water or steam. However, iron reacts
with steam. If the hot water tanks are
made of steel (an alloy of iron), then iron would react vigorously with the steam formed from hot water.
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


If the area enclosed by \( y^{2}=4 a x \) and line \( y=a x \) is \( \frac{1}{3} . \) sq.unit, then the area enclosed by \( y=4 x \) with same parabola is \( \frac{4}{3} \) squnit
A. True
B. False


'Snake' and 'wolves' are examples of
A. Secondary Consumers
B. Primary consumers
c. Tertiary Consumers
D. consumers


If \( \boldsymbol{m}, \boldsymbol{n} \in \boldsymbol{N}, \) then the value of
\( \lim _{x \rightarrow 0} \frac{\sin x^{n}}{(\sin x)^{m}} \) is
This question has multiple correct options
\( \mathbf{A} \cdot 1, \) if \( n=m \)
B. \( 0, \) if \( n>m \)
\( c \cdot \infty, \) if \( n<m \)
D. \( n / m, \) if \( n<m \)


Triangle \( A B C \) is inscribed in the
parabola described by the equation \( y^{2}-6 x-4 y+10=0 \) so that \( A \) is the
vertex of the parabola and \( B \) and \( C \) are
the end points of the latus rectum of the
parabola. The area of triangle \( A B C \) is
A . 18
B. 9
\( c .4 .5 \)
D. 2.25


A parallel plate capacitor is charged and
the charging battery is then
disconnected. If the plates of the
capacitor are moved further apart by means of insulating handles, then:
A. the charge in the capacitor becomes zero
B. the capacitance becomes infinite
C. the charge in the capacitor increases
D. the voltage across the plates increases


The method of rainwater harvesting which can be adopted by individual house owners is:
A. construction of recharge trenches
B. on channel storage of water
c. creation of new water bodies
D. roof-top rainwater harvesting


Solve: \( \int \frac{d x}{\sqrt{x^{2}+2 x+5}} \)
A \( \cdot \ln |\sqrt{x^{2}+2 x+5}-x+1|+C \)
B \( \cdot \ln |\sqrt{x^{2}+2 x+5}+x+1|+C \)
c. \( \ln |\sqrt{x^{2}+2 x+5}-x|+C \)
D. None of these


Two thin uniform circular rings each of
radius \( 10 \mathrm{cm} \) and mass \( 0.1 \mathrm{Kg} \) are
arranged such that they have common centre and their planes are perpendicular to each other. The moment of inertia of this system about an axis passing through their common centre and perpendicular to the plane of one of the rings in \( k g m^{2} \) is:
A \( \cdot 15 \times 10^{-3} \)
В . \( 5 \times 10^{-3} \)
c. \( 15 \times 10^{-4} \)
D. \( 18 \times 10^{-4} \)


The probability of a man hitting the \( \operatorname{target} \) is \( \frac{1}{4} . \) If he fires 7 times, the probability of hitting the target exactly six times is
\( ^{\mathrm{A}} \cdot_{^{7}} C_{5}\left(\frac{1}{4}\right)^{6}\left(\frac{3}{4}\right) \)
\( ^{\mathrm{B} \cdot}^{7} C_{6}\left(\frac{3}{4}\right)^{6}\left(\frac{1}{4}\right) \)
\( ^{\mathbf{c}} \cdot_{7} C_{6}\left(\frac{1}{4}\right)^{6}\left(\frac{3}{4}\right) \)
\( ^{\mathrm{D} \cdot}^{7} C_{6}\left(\frac{1}{2}\right)^{6}\left(\frac{1}{2}\right) \)


Which among the following is an example of polar molecule?
\( A \cdot O_{2} \)
в. \( H_{2} \)
c. \( N_{2} \)
D. нс


Statement \( 1: \frac{13}{6} C \) and \( _{6}^{14} C \) are isotopes of the element carbon.
Statement 2: Isotopes of an element
have the same number of protons in the nucleus but have a different number of
neutrons.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct but Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


Column II gives type of reaction mention in column I, match them correctly