What coefficients are required to balance the following equation?
\( \boldsymbol{F} \boldsymbol{e}+\boldsymbol{O}_{2} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{O} \)
\( \mathbf{A} \cdot 2,1,2 \)
B. 1,1,1
c. 4,2,4
D. 2,1,1


Solve \( \int_{0}^{\pi / 2}(2 \log \sin x-\log \sin 2 x) d x \)
A \( \cdot \frac{\pi}{2} \log 2 \)
B. \( -\frac{\pi}{2} \log 2 \)
c. \( \frac{\pi}{4} \log 2 \)
D. None


Which one of the following is the most likely root cause, why menstruation is not taking place in a human female, having regular menstrual cycle?
A. Fertilization of the ovum
B. Maintenance of the hypertrophic endometrial lining
c. Maintenance of high concentration of sex-hormones in the blood stream


How does the angle of minimum deviation produced by a prism change with increase in the wavelength of incident light
A. increases
B. decreases
C. remains same
D. cant say


Match and find the correct option.
A. a-ii-s, b-iii-p, c-i-q, d-iv-r
\( B \)
\( a-i i-p \) \( b-i-r, c-i v-q, d-i i i-s \)
C \( \cdot a-i-s, b-i i \) i-q, c-iv-p, d-ii-r
D. a-iv-r, b-ii-s, c-iii-p, d-i-q


In which pairs first compound is weak acid than the second?
This question has multiple correct options
A. Adipic acid, succinic acid
B. Fumaric acid, maleic acid
c. Phthalic acid, terepthalic acid
D. Salicylic acid, o - toluic acid


The ratio e/m i.e., specific charge for a cathode ray:
A. has the smallest value when the discharge tube is
filled with \( H_{2} \)
B. is constant
C. varies with the atom number of gas in the discharge tube
D. varies with the atomic number of an element forming the cathode


\( \boldsymbol{H} \) -atoms in ground state \( (\mathbf{1 3 . 6 e V}) \) are excited by monochromatic radiations of
photon of energy \( 12.1 e V \). The number of spectral lines emitted in \( \boldsymbol{H} \) -atom will
be:
A . 1
B. 2
\( c .3 \)
D. 6


Electrons in a colour T.V. are accelerated
through a potential difference of \( 25 \mathrm{KV} \) If the current produced is \( 0.25 \mathrm{mA} \), what is the power dissipated in the T.V. screen by the electrons?


Find the range of \( f(x)= \) \( \frac{1}{1-3 \sqrt{1-\sin ^{2} x}} \)


Per day expenses of 25 families of the frequency distribution of a Dhani of a village is given as follows.
Per day 25
\( \begin{array}{lll}\text { 35- } & \text { 45- } & \text { 55 }\end{array} \) expense \( \quad 35 \quad 45 \quad 55 \quad 65 \)
(In Rs.)
Number
of
families
Find the mean expense of families by Direct Method.


The greater reactivity of \( F_{2} \) is due to
A. lower electron affinity of \( F \)
B. lower bond energy of \( F-F \) bond.
c. higher electronegativity of F.
D. gaseous state of \( F_{2} \)


Write the ionic equation showing the oxidation of \( F e(I I) \) salt by acidified dichromate solution.


Which one can represent a probability
of an event
A \( \cdot \frac{7}{4} \)
B. - 1
c. \( -\frac{2}{3} \)
D. \( \frac{2}{3} \)


Select the correct option related to
stability of following structure.
\( A \)
B.
\( c \)
\( D \)


Assertion
The escape speed does not depend on the direction in which the projectile is
fired.
Reason
Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.
A. STATEMENT-1 is True, STATEMENT-2 is True:
STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True STATEMENT-2 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


Find a particular solution of the differential equation \( \frac{d y}{d x}+y \cot x= \) \( 4 x \operatorname{cosec} x(x \neq 0), \) given that \( y=0 \)
when \( \boldsymbol{x}=\frac{\boldsymbol{\pi}}{\boldsymbol{2}} \)


The simplest type of AC voltage or
current is the one which
A. Varies exponentially
B. Varies sinusoidally
C . Varies linearly
D. Does not vary uniformly


DNA found in the nucleus is wrapped
around a simple protein which is basic in nature. This protein is also thought to regulate DNA functioning find some way. Name this protein.
A. Collagen
B. Renin
c. Pepsin
D. Histones


First product of photorespiration is
A. Phosphoglycolate
B. Glycolate
c. Glycine
D. None of the above


A rocket is moving in a gravity free space with a constant acceleration of
\( 2 m s^{-2} \) along \( +x \) direction (see figure). The length of a chamber inside the
rocket is \( 4 \mathrm{m} \). A ball is thrown from the
left end of the chamber in \( +x \) direction
with a speed of \( 0.3 m s^{-1} \) relative to the rocket. At the same time, another ball is thrown in \( -x \) direction with a speed of
\( 0.2 m s^{-1} \) from its right end relative to the rocket. The time in seconds when the two balls hit each other is


Darwin was most influenced by :
A. Lamarck's theory of acquired characters
B. Weisman's theory of origin of species
C. Wallace's theory of origin of species
D. Essay on Population by Malthus


How much time does it take the
automobile to overtake the truck?


A long string under tension of \( 100 N \)
has one end at \( x=0 . \) A sinusoidal
wave is generated at \( x=0 \) whose
equation is given by
\( \boldsymbol{y}= \)
\( (0.01 c m) \sin \left[\left(\frac{\pi x}{10} m\right)-50 \pi t(s e c)\right] \)
Find the average power transmitted by
the wave.


Iron, hydrogen peroxide and carbon dioxide are given. When the same amount of heat is
supplied to these three substances, which expands most?
A. Hydrogen peroxide
B. Carbon dioxide
c. Iron
D. All of these


A plane mirror gives a real image when the incident beam is:
A. Wide
B. Narrow
c. convergent
D. Divergent


A square frame of side carries i produces a field \( B \) at its centre. The
same current is passed through a circular coil having the same perimeter as the square. The field at the centre of circular coil is \( \mathrm{B} \) '. Find the ratio of \( \left(\mathrm{B}^{\prime} / \mathrm{B}\right) \).
A. \( \frac{\pi^{2}}{3 \sqrt{2}} \)
В. \( \frac{\pi^{2}}{5 \sqrt{2}} \)
c. \( \frac{\pi^{2}}{7 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{8 \sqrt{2}} \)


The cartesian product \( \boldsymbol{A} \times \boldsymbol{A} \) has \( \mathbf{9} \)
elements among which are found (-1,0) and \( (0,1) . \) Find the set \( A \) and
the remaining elements of \( \boldsymbol{A} \times \boldsymbol{A} \)


Resistance of a metal wire of length 1 m
is \( 26 \Omega \) at \( 20^{\circ} \mathrm{C} \). If the diameter of the
wire is 0.3 mm, what will be the
resistivity of the metal at that temperature? Using Table 12.2. predict the material of the wire.


Assertion
It is difficult to distinguish the strengths of the strong acids such as
\( \boldsymbol{H} \boldsymbol{C l}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \boldsymbol{H} \boldsymbol{B} \boldsymbol{r}, \boldsymbol{H} \boldsymbol{I} \) or
\( \boldsymbol{H} \boldsymbol{C l O}_{4} \) in dilute aqueous solutions.
Reason

In dilute aqueous solution all strong acids donate a proton to water and are
essentially \( 100 \% \) ionised to produce a
solution containing \( H_{3} O^{+} \) ions plus the anions of strong acid.
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


List the hormones secreted by the Testis.


The principal argument of \( \frac{i-3}{i-1} \) is
A \( \cdot \tan ^{-1} \frac{1}{2} \)
в. \( \tan ^{-1} \frac{3}{2} \)
c. \( \tan ^{-1} \frac{5}{2} \)
D. \( \tan ^{-1} \frac{7}{2} \)


Draw the structure of butanone
molecule.


A red LED emits light at0.1 watt uniformly around it. The amplitude of the electric field of the light at a
distance of \( 1 \mathrm{m} \) from the diode is :
\( \mathbf{A} \cdot 6 V / m \)
в. \( 2.45 V / m \)
c. \( 5.48 V / m \)
D. \( 1.73 V / m \)


\( x= \)
\( x \)
\( x \)


Assertion
When a pulse on string reflects from free end, the resultant pulse is formed
in such a way that slope of string at free end is zero.
Reason
Zero resultant slope ensures that there
is no force component perpendicular to string.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Find the sum of the following vectors:
\( \overrightarrow{\boldsymbol{a}}=\hat{\boldsymbol{i}}-\mathbf{2} \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{b}}=\mathbf{2} \hat{\boldsymbol{i}}-\boldsymbol{3} \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{c}}=\mathbf{2} \hat{\boldsymbol{i}}+\boldsymbol{3} \hat{\boldsymbol{k}} \)


At what \( \frac{\left[\boldsymbol{B r}^{+}\right]}{\sqrt{\left[\boldsymbol{C O}_{3}^{2-}\right]}} \) does the following
cell have its reaction at equilibrium? \( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s})\left|\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C} \boldsymbol{O}_{3}(\boldsymbol{s})\right| \boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3}(\boldsymbol{a} \boldsymbol{q}) \| \boldsymbol{K} \boldsymbol{B} \boldsymbol{r} \)
\( \boldsymbol{K}_{s p}=\mathbf{8} \times \mathbf{1 0}^{-12} \) for \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C} \boldsymbol{O}_{2} \) and
\( \boldsymbol{K}_{s p}=\mathbf{4} \times \mathbf{1 0}^{-13} \) for AgBr.
A. \( \sqrt{1} \times 10^{-7} \)
B . \( \sqrt{2} \times 10^{-7} \)
c. \( \sqrt{3} \times 10^{-7} \)
D. \( \sqrt{4} \times 10^{-7} \)


If a star is \( 5.2 \times 10^{16} \) m away. What is
the parallax angle in degrees?
A \( \cdot 1.67 \times 10^{-4} \) degrees
B . \( 1.67 \times 10^{-5} \) degrees
c. \( 0.67 \times 10^{-4} \) degrees
D. \( 2.3 \times 10^{-4} \) degrees


Differentiate the following function with
respect to \( x \) \( \left(1+x^{2}\right) \cos x \)


Proof resilience is related to
A. PE stored in an elastic body
B. stiffness of a beam
C . elastic fatigue
D. elastic relaxation


In \( \Delta A B C, \angle A=90^{\circ} \) and \( A D \perp B C \)
Then, \( \boldsymbol{A} \boldsymbol{D}^{3}=\boldsymbol{B} \boldsymbol{D} \times \boldsymbol{D} \boldsymbol{C} \)
A. True
B. False


If \( \Delta A B C \cong \Delta F E D \) under the
correspondence \( \boldsymbol{A B C} \leftrightarrow \boldsymbol{F E D}, \) write
all the corresponding congruent parts of the triangles.


In the circuit shown the current through
the \( 4 \Omega \) resistor is 1 amp when the
points \( P \) and \( M \) are connected to a d.c voltage source. The potential difference
between the points \( M \) and \( N \) is:
A. 0.5 volt
B. 3.2 volt
c. 1.5 volt
D. 1.0 volt


An object starts moving with a velocity \( 6 m / s \) and acceleration \( 105 m / s^{2} \) after. What time will it acquire the velocity \( 15 m / s ? \) Find the distance traveled by the object in this time.


This year, a salesman sells a total of
\( \$ 60,000 \) worth of steak knives by going door-to-door. This represents a \( 20 \% \)
increase from the year before. What was the value of his sales last year?
A. \( \$ 45,000 \)
в. \( \$ 48,000 \)
\( c . \$ 50,000 \)
D. \( \$ 52,000 \)
E. \( \$ 56,000 \)


Fill in the blanks with approriate words. Volume of air inspired and expired in a breath in normal respiration by man is called


The stage during which separation of the paired homologous chromosomes begins is
A. Diakinesis
B. Pachytene
c. zygotene
D. Diplotene


\( \boldsymbol{m}: \boldsymbol{n} \)


A pendulum oscillates 40 times in 4 seconds. Find its time period and frequency.


In each of the following cases, state whether the function is one-one, onto or
bijective. Justify your answer.
(i) \( f: R \rightarrow R \) defined by \( f(x)=3-4 x \)
(ii) \( f: R \rightarrow R \) defined by \( f(x)=1+x^{2} \)


\( A \) earns \( 800 R s . \) more than \( B . \) They
both save together \( 3,200 R s . \) which is
one-fourth of \( \boldsymbol{A}^{\prime} \) s salary plus one-sixth
of \( B^{\prime} \) s salary. Find out their total monthly expenditure.
A. Rs. 12,000
B. Rs. 15,000
c. Rs. 10,000
D. Rs. 17,000


lime is added to the soil, when it is too
A. Sandy
B. Salty
c. Alkaline
D. Acidic


In Young's double slit experiment, interference pattern will not be seen if
one uses
A. a LASER as the source of light
B. two LASER sources in front of two slits
c. two sodium light lamps in front of two slits
D. in both (b) and (c) above


If \( \alpha \) and \( \beta \) are the zeroes of a polynomial
\( x^{2}-4 \sqrt{3} x+3, \) then find the value of
\( \boldsymbol{\alpha}+\boldsymbol{\beta}-\boldsymbol{\alpha} \boldsymbol{\beta} \)


When limestone is heated in a lime-kiln
we get:
A. milk of lime
B. slaked lime and carbon dioxide
c. quicklime and carbon dioxide
D. calcium hydroxide and carbon dioxide


The equation of the displacement of two particles making SHM are represented by
\( \boldsymbol{y}_{1}=a \sin (\omega t+\phi) \& \boldsymbol{y}_{2}=a \cos (\boldsymbol{\omega} \boldsymbol{t}) \)
The phase difference of the velocities of the two particles is :
\( \mathbf{A} \cdot \frac{\pi}{2}+\phi \)
B. \( -\phi \)
c. \( \phi \)
D. \( \phi-\frac{\pi}{2} \)


The volume occupied by the molecules of an ideal gas is:


What is the technique for in vitro sex determination?


Elements of group 14:
This question has multiple correct options
A. exhibit oxidation state of +4 only
B. exhibit oxidation state of +2 and +4
C. form \( M^{2} \) and \( M^{4+} \) ions
D. form \( M^{2+} \) and \( M^{4+} \) ions


What are the assumption on which the
Bohr the theory of the structure of the hydrogen atom is based?


If \( \boldsymbol{A} \) satisfies the equation \( \boldsymbol{x}^{3}-\mathbf{5} \boldsymbol{x}^{2}+ \)
\( 4 x+k I=0, \) then \( A^{-1} \) exists if
A. \( k \neq-1 \)
в. \( k \neq 0 \)
c. \( k \neq 1 \)
D. none of these


The \( \ldots \ldots . . . \) capture the energy present in sunlight and convert it into chemical
energy.


The speed of electromagnetic wave is
same for
A. odd frequencies
B. even frequencies
c. all frequencies
D. all intensities


Which of the following is added to make the copper sulphate solution more conducting?
A. Hydrochloric acid
B. Sulphuric acid
c. Nitric acid
D. Carbonic acid


Viscosity of a liquid is increases by :
A. increase in temperature
B. decrease in molecular size
c. increase in molecular size
D. none of the above


Thallous chloride is more stable than
thallic chloride because of:
A. More ionic character
B. Larger size of \( T l^{+} \) ion
C. High hydration energy of \( T l^{+} \) ion
D. Inert pair effect.


What is the truth value of the statement
'Two is an odd number iff 2 is a root of
\( \boldsymbol{x}^{2}+\mathbf{2}=\mathbf{0}^{\prime} ? \)
A. \( T \)
B. F
C. Neither T nor F
D. cannot be determined


Solve \( \int \frac{\sqrt{1-x^{2}}+\sqrt{1+x^{2}}}{\sqrt{1-x^{4}}} d x \)
\( \mathbf{A} \cdot I=\log |x-\sqrt{1+x^{2}}|+\sin ^{-1} x+c \)
B . \( I=\log |x+\sqrt{1+x^{2}}|+\sin ^{-1} x+c \)
\( \mathbf{C} \cdot I=\log |x+\sqrt{1+x^{2}}|-\sin ^{-1} x+c \)
D. None of these


On what basis the New Systematics
differs from classical systematics? Mention about the various approaches
which are adopted for classification
under New Systematics.


Gravitational constant is
experimentally measured using a
A. physical balance
B. torsional balance
c. beam balance
D. gyrometer


The general formula \( C_{n} H_{2 n} O_{2} \) could be
for open chain:
A. diketones
B. carboxylic acids
\( c \cdot \) diols
D. dialdehydes


When equal volumes of two liquids are mixed,the specific gravity of mixture is
\( \frac{7}{2} . \) When equal masses of the same two liquids are mixed, the specific gravity is \( \frac{12}{7} . \) The specific gravities of two liquids
are:
A. 1 and 6
B. 2 and 6
\( c \cdot 2 \) and 4
D. 3 and 6


The Sl unit of weight is
\( \mathbf{A} \cdot \) кgf
B. Gf
\( c \cdot N \)
D. None of these


A uniform of rod of length \( l \) is placed
symmetrically on two walls as shown in the figure. The rod is in equilibrium. If
\( N_{1} \) and \( N_{2} \) are the normal forces
exerted by the walls on the rod, then :
A. \( N_{1}>N_{2} \)
B. \( N_{1}<N_{2} \)
\( \mathbf{c} \cdot N_{1}=N_{2} \)
D. \( N_{1} \) and \( N_{2} \) would be in the vertical directions \( N_{1} N_{2} \)


What is the mole fraction of glucose in
\( 10 \% \) w/w glucose solution?
A . 0.01
B. 0.02
c. 0.03
D. 0.04


The potential of a single electrode
depends upon:
A. the nature of the electrode
B. Temperature
C. concentration of the ion with respect to which it is reversible
D. all the above


How are the following conversions carried out?
\( 2- \) methylbutan \( -1-01 \) into \( 2- \)
methylbutanoic acid.


State whether the following statement
is True or False
The Sl unit of charge is coulomb.


A quantity of air \( (\gamma=1.4) \) at \( 27^{\circ} \mathrm{C} \) is
compressed suddenly, the temperature of the air system will
A . fall
B. rise
c. remain unchanged
D. first rise and then fall


The gills of mushroom
A. Bear spores which help in reproduction
B. Help in nutrition
C. Help in respiration
D. Help in enhancing buoyancy


An electron is moving in an orbit of a hydrogen atom from which there can be
a maximum of six transitions. An
electron is moving in an orbit of another
hydrogen atom from which there can be
a maximum of three transitions. The
ratio of the velocity of the electron in these two orbits is
\( \mathbf{A} \cdot \frac{1}{2} \)
B. \( \frac{2}{1} \)
\( \mathbf{c} \cdot \underline{5} \)
D. \( \frac{3}{4} \)


A solution of weak acid \( H A \) was
titrated with base NaOH. The
equivalence point was reached when
\( 36.12 m L \) of \( 0.1 M \) NaOH has been
added. Now \( 18.06 m L \) of \( 0.1 M H C l \)
were added to titrated solution, the \( p H \)
was found to be \( 4.92 . \) What will be the
\( \boldsymbol{p} \boldsymbol{H} \) of the solution obtained by mixing \( 10 m L \) of \( 0.2 M N a O H \) and \( 10 m L \) of
\( 0.2 M H A ? \)
\( \mathbf{A} \cdot p H=3 \)
В. \( p H=4 \)
\( \mathbf{c} \cdot p H=9 \)
D. \( p H=11 \)


What is a triplet codon?
\( A \). Fixed
B. Degenerate
c. Ambiguous
D. Non-wobbly


Find the value of \( x \)
\( \mathbf{A} \cdot x=10 \)
B. \( x=8 \)
\( \mathbf{c} \cdot x=6 \)
D. \( x=3 \)


Solve the equation : \( \sqrt{\frac{x}{x-1}}+ \) \( \sqrt{\frac{x-1}{x}}=\frac{13}{6}, x \neq 0,1 \)


The compound which reacts with ozone
to liberate oxygen is:
A . \( N O \)
в. \( C O_{2} \)
\( c \cdot N O_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


What is the number of degrees of
freedom of an oscillating simple pendulum?
A. more than three
B. 3
\( c \cdot 2 \)
D.


Which one of the following statements
İs incorrect?
A. Direct and indirect methods are used for the
measurement of physical quantities.
B. Scientific notation and the prefixes are used to simplify numerical computation.
C. A dimensionally correct equation need not be a correct equation.
D. The Sl units is based on six base units.


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


f \( 2 y-x=8, \) and \( 3 x-y=1, \) what is
the value of \( x ? \)
A
B. 2
\( c \cdot 3 \)
D. -


The value of \( k \) for which the system of
equations
\( 2 x+3 y=5 \)
\( 4 x+k y=10 \)
has an infinite number of solutions, is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c \cdot 6 \)
D. 0


Elements \( S e, C l \) and \( S \) have been
arranged in the order of increasing ionisation energies. Identify the correct order.
A. \( S<S e<C l \)
в. \( S e<S<C l \)
c. \( C l<S<S e \)
D. \( S e=S<C l \)


The two femurs each of the cross-
sectional area \( 10 \mathrm{cm}^{2} \) support the upper
part of a human body of mass \( 40 \mathrm{kg} \) The average pressure sustained by the femurs is then (Takes \( g=10 \mathrm{m} \mathrm{s}^{-2} \) )
A \( \cdot 2 \times 10^{3} \mathrm{N} \mathrm{m}^{-2} \)
B. 2 \( \times 10^{4} \mathrm{N} \mathrm{m}^{-2} \)
c. \( 2 \times 10^{5} \mathrm{N} \mathrm{m}^{-2} \)
D. 2 \( \times 10^{6} \mathrm{N} \mathrm{m}^{-2} \)


In solid state \( N_{2} O_{5} \) exists as:
\( \mathbf{A} \cdot\left[N O_{3}\right]^{-}\left[N O_{2}\right]^{+} \)
в. \( \left.\left[N O_{2}\right]^{-} N O_{3}\right]^{+} \)
c. \( \left.N_{2} O_{4}\right]^{2+} O^{2-} \)
D. \( \left[N O_{3}\right]\left[N O_{2}\right] \)


The food stocks in a hostel are
sufficient for 1200 students for 20 days.
If 400 more students joined the hostel, the stocks just for ... days.


The coefficient of \( x^{5} \) in the expansion of
\( (x+3)^{8} \) is
A . 1542
в. 1512
\( c .2512 \)
D. 12
E . 4


If an electron and a proton have the
same kinetic energy, the ratio of the de Broglie wavelengths of proton and electron would approximately be :
A . 1: 1837
в. 43: 1
\( c \cdot 1837: 1 \)
D. 1: 43


Which of the following molecules can act as an oxidizing as well as a
reducing agent?
A \( \cdot H_{2} S \)
в. \( S O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \)
D. \( F_{2} \)


One end of a cylindrical glass rod \( (\mu= \)
1.5) is in the shape of a concave refracting surface of radius \( 10 \mathrm{cm} . \) An
air bubble is situated in the glass rod at a point on its axis such that it appears to be at distance \( 10 \mathrm{cm} \) from the
surface and inside the glass when seen from the other medium. The actual
location of air bubble is
A. \( 15 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
c. \( 30 \mathrm{cm} \)
D. 25 cm


\( \left|\begin{array}{ccc}\left(a^{x}+a^{-x}\right)^{2} & \left(a^{x}-a^{-x}\right)^{2} & 1 \\ \left(b^{x}+b^{-x}\right)^{2} & \left(b^{x}-b^{-x}\right)^{2} & 1 \\ \left(c^{x}+c^{-x}\right)^{2} & \left(c^{x}-c^{-x}\right)^{2} & 1\end{array}\right| \) is equa
to
\( A \)
B. \( 2 a b c \)
\( \mathbf{c} \cdot a^{2} b^{2} c^{2} \)
D. None of these


How many moles of Grignard reagent
will be required by one mole of given
compound?
4
\( B \)
\( c \)
\( D \)


What should be the kinetic energy of electron in the first orbit of hydrogen
atom?


Detergents are made usually from products obtained by cracking of petroleum, like:
A. the sulphide of hydrogen
B. the sulphur compounds of benzene
c. the chloroalkanes
D. propylene derivatives


Find the angle between the plares
\( r \cdot(2 i-3 j+4 k) \) and \( r \cdot(-i+j)=4 \)


On a large tray of mass \( \mathrm{M} \), an ice cube of mass \( \mathrm{m} \), edge \( \mathrm{L} \) is kept. If the ice melts completely, the center of mass of the
system comes down by:
\( ^{\mathbf{A}} \cdot \frac{m L}{2(M+m)} \)
в. \( \frac{(M-m) L}{2(M+m)} \)
c. \( \frac{(M+2 m) L}{2(M+m)} \)
D \( \cdot \frac{2 M L}{2(M+m)} \)


An observer is moving away from a
sound source of frequency \( 100 H_{z} \). If the observer is moving with a velocity of \( 49 m / s e c \) and the speed of the speed of the sound in air is \( 330 m / \)sec , then the
apparent frequency is:
A. \( 91 H_{z} \)
в. \( 100 H_{z} \)
\( \mathbf{c} \cdot 85 H_{z} \)
D . \( 149 \mathrm{H}_{2} \)


Give expressions in the following cases.
\( \boldsymbol{y} \) is multiplied by 5 and results is subtracted from 16.


If Rolles theorem holds for the function
\( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{3}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{c} \boldsymbol{x}, \boldsymbol{x} \in[-1,1] \) at
the point \( x=\frac{1}{2} \) then \( 2 b+c \) equals
\( A \)
B.
\( c \cdot 2 \)
\( D \cdot-3 \)


Rayon is different from synthetic fibres because:
A. it has a silk appearance
B. it is obtained from wood pulp
c. it can also be woven like those of natural fibres
D. it is natural


Assertion
Assertion: The basic laws of
electromagnetism govern all electric and magnetic phenomena.
Reason
Reason: The attempts to unify
fundamental forces of nature reflect the
quest for unification.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false


Find the \( p H \) of the resulting solution and then mark the option in which \( p H \) exists between color transition range of an indicator.
\( 100 \mathrm{ml} \) of \( 0.8 \mathrm{M} \mathrm{HCO}_{3}^{-}+100 \mathrm{ml} \) of \( 0.4 \mathrm{M} \)
\( \boldsymbol{C O}_{3}^{2-} \)
[For \( \boldsymbol{H}_{2} \boldsymbol{C O}_{3}: \boldsymbol{K}_{\boldsymbol{a}_{1}}=\boldsymbol{4} \times \mathbf{1 0}^{-\boldsymbol{7}} \boldsymbol{\&} \boldsymbol{K}_{\boldsymbol{a}_{2}}= \)
\( \left.4 \times 10^{-11}\right] \)
A. phenol red \( (6.8 \text { to } 8.4) \)
B. propyl red \( (4.6 \text { to } 6.4) \)
c. phenolphthalein \( (8.3 \text { to } 10.1) \)
D. Malachite green (11.4 to 13)


Combustion of a piece of paper to form
ash, water vapour and carbon dioxide follows law of conservation of mass.
A. True
B. False


Express \( 45^{\circ} \mathrm{C} \) in kelvin.


Protonation of 1,2 -butadiene gives
carbocation \( (\mathrm{A}) \) and protonation of \( 3^{-} \)
methyl-1, 2-butadiene gives carbocation \( (\mathrm{B}) . \) In both case the most
stable carbocation possible is produced
but no carbocation rearrangements
take place. Which of the two carbocation is more stable and why?
A. A is more stable because it is a terminal carbocation, according to Markownikoff's rule
B. A is more stable because it is stabilized by resonance and hyperconjugation
C. A is more stable because cationic carbon is \( s p \) hybridized
D. B is more stable because it has two methyl groups that can provide extra stabilization by hyperconjugation and inductive effect


The inability among the elderly to see nearby objects clearly because of the weaking of the ciliary muscles is called
A. far-sightedness
B. near-sightedness
c. presbyopia
D. astigmatism


Substrate level phosphorylation is seen which of these phases?
A. Glycolysis \& ETS
B. ETS \& TCA cycle
c. HSK pathway \& Krebs cycle
D. TCA cycle


With excess of water, both \( P_{2} O_{5} \) and
\( \boldsymbol{P C l}_{5} \) give:
A \( . H_{3} P O_{3} \)
в. \( H_{3} P O_{2} \)
c. \( H_{3} P O_{4} \)
D. \( H_{4} P_{2} O_{7} \)


The order of increasing relative molecular mass of the following gases
is, hydrogen, oxygen, carbondioxide, sulphurdioxide, chlorine. Given 8 gram of each gas at STP, which will contain the least number of molecules and
which the most?


Cyathium and hypanthodium types of inflorescence are similar in having.
A. Nectarglands
B. Apical pore
c. Petaloid bracts
D. Unisexual flowers


A plano-concave lens is placed on a
paper on which a flower is drawn. How
far above its actual position does the
flower appear to be?
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( c .50 \mathrm{cm} \)
D. None of these


Benzene when heated in air burns with
and produces \( C O_{2} \) and
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
A. sooty flame
B. non-sooty flame
c. light color flame
D. none of these


Which of the following is the most electronegative element?
A. \( H e \)
B. \( I \)
c. \( N \)
D.
E. \( C \)


In the arrangement, 11 wires each of
resistance \( 5 \Omega \) are used as sides of
cube. A potential difference of \( 70 \mathrm{V} \) is
maintained between corners \( A \) and \( B \) of
cube. Current flowing in wire \( \boldsymbol{E} \boldsymbol{F} \) is :
\( \mathbf{A} \cdot 4 A \)
3. \( 2 A \)
\( c \cdot 5 A \)
D. \( 10 A \)


The structure of sodium atom is shown
in the figure given above. Identify the
correct statement.
An atomic sodium
\( A . \) is a non-metal
B. reacts vigorously with wate
\( c . \) is stored in oil to avoid contact with moisture
D. all of the above


Evaluate the following determinant : \( = \) \( \begin{array}{|lll|}\mathbf{6 7} & \mathbf{1 9} & \mathbf{2 1} \\ \mathbf{3 9} & \mathbf{1 3} & \mathbf{1 4} \\ \mathbf{8 1} & \mathbf{2 4} & \mathbf{2 6}\end{array} \)


Consider the equation \( 2+\mid x^{2}+4 x+ \)
\( \mathbf{2} \mid=\boldsymbol{m}, \boldsymbol{m} \epsilon \boldsymbol{R} \) so that the given
equation has three solutions is:
\( A \cdot\{4\} \)
B \( \cdot\{2\} \)
\( c \cdot\{1\} \)
\( D \cdot\{0\} \)


Extra nuclear DNA in E. coli is termed as
\( \mathbf{A} \cdot F^{-} \) factor
B. Sex factor
c. Episome
D. All of above


By selling a transistor for Rs \( 572, \) a shopkeeper earns a profit equivalent to
\( 30 \% \) of the cost price of the transistor. What is the cost price of the transistor?
A . Rs 340
B. Rs 390
c. Rs 440
D. Rs 490


Consider three planes \( 2 x+p y+6 z= \)
\( \mathbf{8}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y}+\boldsymbol{q} \boldsymbol{z}=\mathbf{5} \) and \( \boldsymbol{x}+\boldsymbol{y}+\mathbf{3} \boldsymbol{z}=\mathbf{4} \)
These planes do not have any common point of intersection if-
A. \( p=2, q \neq 3 \)
B . \( p \neq 2, q \neq 3 \)
c. \( p \neq 2, q=3 \)
D. \( p=2, q=3 \)


Human RBC has
A. A nucleus
B. No nucleus
c. More than one nucleus
D. None of the above


In an experiment of Wheatstone bridge,
if the positions of cells and
galvanometer are interchanged, then the balance points will
A. change
B. remain unchanged
c. depend on the internal resistance of the cell and resistance of the galvanometer
D. none of these


Select correct statement(s):
\( \mathbf{A} \cdot O_{3} \) molecule is resonance stabilised.
B. There is 3 -centre, 4 -electron \( \pi \) -bond system in \( O_{3} \)
C. Ozone layer is being depleted by fluorocarbons.
D. All the above are correct statements.


Find \( \frac{d y}{d x}, i f x^{y}=e^{x-y} \)


The electric field on two sides of a thin
sheet of charge is shown in the figure. The charge density on the sheet is :
A \( \cdot 2 \varepsilon_{0} \)
B . \( 4 \varepsilon_{0} \)
\( c \cdot 10 \varepsilon_{0} \)
D. zer


State whether the given statement is True or False.

Most of the heat transfer that is taking
place on the earth is by Radiation.
A. True
B. False


Susceptibility of ferromagnetic substance is
\( A \cdot>1 \)
в. \( <1 \)
c. zero
D.


Find the areas of the triangles the coordinates of whose angular points \( \operatorname{are}\left(1,30^{\circ}\right),\left(2,60^{\circ}\right) \) and \( \left(3,90^{\circ}\right) \)


State whether the following statements are true or false with reasons.
When a wire is loaded beyond the elastic limit and then deloaded. the
work done disappears completely as
heat
A. True
B. False


\( B a C l_{2} \) dissociates in water to give one
\( B a^{2+} \) ion and two \( C l^{-} \) ions. If
concentrated \( H C l \) is added to this
solution:
A \( \cdot\left[B a^{2+}\right] \) increases
B・ \( \left[B a^{2+}\right] \) remains constant
c. \( \left[O H^{-}\right] \) increases
D. The number of moles of undissociated \( B a C l_{2} \) increases
E \( \cdot\left[H^{+}\right] \) decreases


When steam in passed over red hot iron,
water gas is formed.
If this is true enter 1 , if false enter 0 .


The diameter of a wheel of a cycle is 21
cm How far will it go in 28 complete revolutions?
\( A \cdot 3696 \mathrm{cm} \)
B. 3669 cm
c. \( 3966 \mathrm{cm} \)
D. None of these


The inverse of the statement "lf a
number is divisible by 4 then it is also divisible by \( 2^{\prime \prime} \) is -
A. If a number is divisible by 4 , then it is always divisible by 2
B. If a number is not divisible by 4 , then it is divisible by
2.
c. If a number is not divisible by \( 4, \) then it is not divisible by 2.
D. None of the above


A body of mass \( 6 \mathrm{kg} \) is under a force whic causes displacement in it which is given by \( s=\frac{t^{2}}{4} \mathrm{m}, \) where \( t \) is time. The work done
by the force in 2 s is
A . \( 12 J \)
в. \( 9 J \)
c. 6.5
D. 3


0
00
0
0


Assertion
Low frequency waves are transmitted
via ground waves.
Reason
When a wave has high wavelength, it undergoes more diffraction.
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 and Reason is correct


\( H_{2} O_{2} \) can be manufactured by the
electrolysis of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) solution
A. True
B. False


Which of the following is/are true about acceleration
A. Acceleration is defined as the rate of change of velocity with respect to time
B . Its SI unit is \( m / s^{2} \)
c. Negative acceleration is called retardation
D. All the above


Assertion
The molecular weight of acetic acid determined by depression in freezing point method in benzene and water was found to be different.
Reason
Water is polar and benzene is non-polar.
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


Ampicillin and amoxicillin are
semisynthetic modifications of penicillin used for penicillin-sensitive patients.


Without any stoppage a person travels a certain distance at an average speed of \( 42 \mathrm{km} / \mathrm{hr} \), and with stoppages he covers the same distance at an average speed of \( 28 \mathrm{km} / \mathrm{hr} \). How many minutes per hour does he stop?
A. 14 minutes
B. 15 minutes
c. 28 minutes
D. 20 minutes


An electric dipple has dipple moment
\( 4 \times 10^{-11} \) and the two charges have
magnitudes 4 nC each. Calculate the electric field due to the dipole
i) At a point on the axis at a distance \( 0.01 \mathrm{m} \) from one of the charges and
ii) At a point on the perpendicular bisector at a distance \( 0.02 \mathrm{m} \) from the
middle point.


In the Boolean algebra, the following one
is wrong
A \( .1+0=1 \)
B. \( 0+1=1 \)
c. \( 1+1=1 \)
D. \( 0+0=1 \)


Match the statements/expressions in
List 1 with the values given in List 2


Find the curve for which the sum of the
lengths of the tangent and subtangent at any of its point is proportional to the product of the coordinates of the point of tangency, the proportionality factor is equal to k.
A \( \cdot y=\frac{1}{k} \ln \left|c\left(k^{2} x^{2}-1\right)\right| \)
B. \( y=\frac{1}{k} \ln \mid c\left(k x^{2}-1\right) \)
c. \( y=\frac{1}{k} \ln \mid c\left(k x^{2}+1\right) \)
D. \( y=\frac{1}{k} \ln \mid c\left(k^{2} x^{2}+1\right) \)


A tunnel is dug along a diameter of earth. The force on a particle of mass \( \boldsymbol{m} \)
and distance \( x \) from the centre in this
tunnel will be :
A \( \cdot \frac{G M_{e} m}{R^{3} x} \)
в. \( \frac{G M_{e} m R^{3}}{x} \)
c. \( \frac{G M_{e} m x}{R^{2}} \)
D. \( \frac{G M_{e} m x}{R^{3}} \)


Consider the reaction, \( 2 N_{2} O_{5} \rightarrow \)
\( 4 N O_{2}+O_{2} \)
In the reaction \( N O_{2} \) is being formed at
the rate of 0.0125 mol \( L^{-1} s^{-1} . \) What is
the rate of reaction at this time?
A \( \cdot 0.0018 \) mol \( L^{-1} s^{-1} \)
B. 0.0031 mol \( L^{-1} s^{-1} \)
c. 0.0041 mol \( L^{-1} s^{-1} \)
D. 0.050 mol \( L^{-1} s^{-1} \)


What is Raoult's Law?
Derive Raoult's Law for solution which
contain non-volatile solute.


In the above question, during loading and unloading the force exerted by the
material is conservative upto?
A. \( O A \) only
B. \( O B \) only
c. \( O C \) only
D. \( O D \) only


Hydrocarbon which gives oxyacetylene
flame is:
A. ethane
B. ethene
c. ethyne
D. ethanal


Volume of the box of outer dimensions
\( 22 \mathrm{cm} \times 12 \mathrm{cm} \times 9 \mathrm{cm} \)
A \( \cdot 2276 \mathrm{cm}^{3} \)
B. 2500 \( c m^{3} \)
c. \( 2600 \mathrm{cm}^{3} \)
D. 2376 \( c m^{3} \)


What is Richmond Lang effect?


A town's population increased by 1200 people, and then this new population decreased \( 11 \% \). The town now had 32
less people than it did before the 1200 increase. Find the original population.
A . 10000
B. 11000
c. 12000
D. 13000


State whether given statement is True or False.
Linear momentum is always in the direction of velocity
A. True
B. False


A short linear object of length \( \boldsymbol{I} \) lies
along the axis mirror of focal length \( \boldsymbol{F} \)
at a distance u form the of the mirror.
The size of the image is approximately equal to:
\( ^{\mathbf{A}} \cdot\left(\frac{u-f}{f}\right)^{1 / 2} \)
\( ^{\mathrm{B}} \cdot_{I}\left(\frac{u-f}{f}\right)^{2} \)
\( ^{\mathrm{c}} \cdot\left(\frac{f}{u-f}\right)^{1 / 2} \)
D. \( _{I}\left(\frac{f}{u-f}\right) \)


Widely distributed hydrocarbon in the atmosphere of earth is :
A. Butane
B. Methane
c. \( \operatorname{smog} \)
D. PAN


Statement 1: The drift speed of electrons
in metals is small (in the order of a few
\( m m / s) \) and the charge of an electron is also very small \( \left(1.6 \times 10^{-19} C\right), \) yet we
can obtain a large current in a metal.
Statement 2: At room temperature, the thermal speed of electrons is very high
(about \( 10^{7} \) times the drift speed)
A. Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1
B. Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for statement
c. Statement 1 is True; Statement 2 is False
D. Statement 1 is False; Statement 2 is True


The following diagram represents the atomic structure of which element?
A. Fluorine
B. Chlorine
c. carbon
D. oxygen


The probability of picking a nondefective item from a sample is \( \frac{7}{12} \)
Find the probability of picking a defective item


If the sum of three consecutive terms of
an increasing A.P. is 51 and the product of the first and third of these terms is
\( 273, \) then the third term is
A . 13
B. 9
\( c \cdot 21 \)
D. 17


\( 1 / 2 \) mole of Helium gas is contained at
S.T.P. The heat energy needed in cal to double the pressure of the gas, keeping the volume constant
A . \( 3276 J \)
B. \( 1638 J \)
\( c .819 J \)
D. \( 409.5 J \)


The value that present between right atrium and right ventricle can be name
as


In the reaction, \( \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}, \) if \( \mathbf{2} \)
moles of \( A, 3.0 \) moles of \( B \) and 2.0 moles of \( C \) are placed in a \( 2 L \) flask and the
equilibrium concentration of \( \mathrm{C} \) is 0.5 mol \( / L . \) The equilibrium constant
\( \left(K_{c}\right) \) for the reaction is:
\( \mathbf{A} \cdot 0.073 \)
B. 0.1470
c. 0.0500
D. 0.0080


Balance the following redox reactions:
\( \boldsymbol{S}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{I}_{2}(\boldsymbol{s}) \longrightarrow \boldsymbol{S} \boldsymbol{O}_{4}^{2-}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
A \( \cdot S^{2-}(a q)+4 I_{2}(s)+4 H_{2} O(l) \rightarrow 8 I^{-}(a q)+S O_{4}^{2-}(a q)+ \)
\( 8 H^{+}(a q) \)
B . \( S^{2-}(a q)+6 I_{2}(s)+4 H_{2} O(l) \longrightarrow 8 I^{-}(a q)+4 S O_{4}^{2-}(a q)+ \)
\( 8 H^{+}(a q) \)
\( \mathbf{c} \cdot 3 S^{2-}(a q)+4 I_{2}(s)+4 H_{2} O(l) \longrightarrow \)
\( 8 I^{-}(a q)+5 S O_{4}^{2-}(a q)+8 H^{+}(a q) \)
D \( \cdot 2 S^{2-}(a q)+4 I_{2}(s)+H_{2} O(l) \rightarrow 8 I^{-}(a q)+S O_{4}^{2-}(a q)+ \)
\( 8 H^{+}(a q) \)


A block of mass \( 1 \mathrm{kg} \) is pressed against
a wall by applying a horizontal force of 10N on the block. If the coefficient of
friction between the block and the wall
is \( 0.5, \) magnitude of the frictional force
acting on the block is
\( \mathbf{A} \cdot 9.8 N \)
B. \( 0.98 N \)
c. \( 1.96 N \)
\( D .5 N \)


Suppose that the reliability of a HIV test is specified as follows:Of people having HIV, \( 90 \% \) of the test detect the disease
but \( 10 \% \) go undetected. Of people free of \( \mathrm{HIV}, 99 \% \) of the test are judged HIV-ive but \( 1 \% \) are diagnosed as showing HIV+ive. From a large population of which only \( 0.1 \% \) have \( \mathrm{HIV} \), one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV+ive. What is the probability that the
person actually has HIV?


A cyclist is moving on a circular track of
radius \( 80 m \) with a velocity of
\( 72 k m / h r . \) He has to lean from he vertical approximately through an angle-
\( \mathbf{A} \cdot \tan ^{-1}(1 / 4) \)
B \cdot \( \tan ^{-1}(1) \)
c. \( \tan ^{-1}(1 / 2) \)
\( D \cdot \tan ^{-1}(2) \)


The diameter of a wire as measured by
screw gauge was found to be
2.620,2.625,2.628 and \( 2.626 \mathrm{cm} \)
Calculate percentage error.


A uniform chain of length \( 2 m \) is kept on
a table such that a length of \( 50 \mathrm{cm} \)
hangs freely from the edge of the table. The total mass of the chain is \( 5 k g . \) What
is the work done in pulling the entire chain on the table. (in J)
A . 7.2
B. 3
c. 4.6
D. 12


Leaf fall occurs when the amount of
A. Auxin increases
B. Auxin decreases
c. Abscisic acid decreases
D. Gibberellic acid decreases


Ratio of WBC to RBC in human blood is
A .1: 100
B. 1: 200
c. 500:
D. 1: 600


Assertion
Red phosphorus is less volatile than
white phosphorus
Reason
Red phosphorus has a discrete tetrahedral structure
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The value of \( \lim _{x \rightarrow 1^{+}}(x)^{\frac{1}{x}}, \) is : (where
denotes the fractional part function)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. None of these


Which of the following methods is used in purification of mercury?
A. Liquation
B. Distillation
c. Electrolytic refining
D. Chemical reduction


The value of determinant \( \left|\begin{array}{lll}1 / a & b c & a^{3} \\ 1 / b & c a & b^{3} \\ 1 / c & a b & c^{3}\end{array}\right| \)
A \( \cdot a^{2} b^{2} c^{2}(a-b)(b-c)(c-a) \)
B. 0
c \( \cdot(a-b)(b-c)(c-a) \)
D. None of the above


In the Sun, about 4billion kg of matter is converted into energy each second. The power output of Sun in watt is
A. \( 3.6 \times 10^{26} \)
B. \( 0.36 \times 10^{26} \)
c. \( 36 \times 10^{26} \)
D. 0.036 \( \times 10^{26} \)


If \( a \sin ^{-1} x-b \cos ^{-1} x=c, \) then the
value of \( a \sin ^{-1} x+b c o s^{-1} x \) (whenever
exists) is equal to
A . 0
B. \( \frac{\pi a b+c(b-a)}{a+b} \)
\( c \cdot \frac{\pi}{2} \)
D. \( \frac{\pi a b+c(a-b)}{a+b} \)


The empirical formula of the solid product is:
A \( \cdot U F_{2} O_{2} \)
в. \( U F O_{2} \)
\( \mathbf{c} \cdot U F_{2} O \)
D. UFO


Choose the correct answer from the
alternatives given:

Identify the labels \( A, B, C \) and Din the
given structure of tRNA and select the
correct option.
A. A - Anticodon loop, B T \( \Psi \mathrm{C} \) loop, \( \mathrm{C} \) - AA binding site, D DHU loop
B. A - AA binding site, B - T\PsiC loop, C - Anticodon loop, D DHU loop
C. \( A-M \) binding site, \( B \) - DHU loop, \( C \) - Anticodon loop, \( D \) T \( \Psi \) C loop
D. A - M binding site, B - DHU loop, C - T\PsiC loop, D Anticodon loop


Protruded part of meristem flank bearing leaf primordium is called
A. Leaf base
B. Leaf buttress
c. Node
D. Plastochron


Which of the following constellation contains the Pole Star?
A. Ursa Major
B. Ursa Minor
c. Pleides
D. Orion


Which of the following factors affect pressure? This question has multiple correct options
A. Area
B. Acceleration
c. Force
D. None


\( 2 p_{x} \) atomic orbital undergoes linear combination with:
A \( \cdot 2 p_{y} \) orbital
B . \( 2 p_{x} \) orbital
C. Both \( 2 p_{y} \) and \( 2 p_{x} \) orbitals
D \( \cdot 2 p_{z} \) orbital


Bond order is associated with the
strength of bond and bond length. The higher the bond order, the smaller will
be the bond length and stronger will be the bond.

Arrange \( O_{2}, O_{2}^{+}, O_{2}^{-} \) and \( O_{2}^{2-} \) in order of increasing bond order.
A \( \cdot O_{2}<O_{2}^{-}<O_{2}^{2-}<O_{2}^{+} \)
в. \( O_{2}^{2-}<O_{2}^{-}<O_{2}<O_{2}^{+} \)
c. \( O_{2}^{-}<O_{2}^{2-}<O_{2}^{+}<O_{2} \)
D. \( O_{2}^{2+}<O_{2}^{+}<O_{2}^{-}<O_{2} \)


Who invented the first true battery?
A. Faraday
B. onm
c. volta
D. Alva Edison


A shell fired from a gun at an angle to the horizontal explodes in mid air. Then
the centre of mass of the shell
fragments will move
A. vertically down
B. horizontally
c. along the same parabolic path along which the 'intact shell was moving
D. along the tangent to the parabolic path of the 'intact shell, at the point of explosion.


The factors that promote electro
chemical corrosion are
A. the nature of the impurity metal with which the metal under consideration is associated.
B. the concentration of \( O_{2} \) in contact with the surface of
the metal.
C. highly conducting solutions.
D. all the above.


Match List I and List II.


The motion of a particle is given by \( \boldsymbol{x}= \)
\( a \sin \omega t+b \cos \omega t . \) The motion of the
particle is:
A. Not simple harmonic
B. Simple harmonic with amplitude \( (A-B) / 2 \)
C. Simple harmonic with amplitude \( (A+B) / 2 \)
D. Simple harmonic with amplitude \( \sqrt{A^{2}+B^{2}} \)


\( \frac{1}{1} \)
\( \frac{1}{2} \)
\( \frac{1}{2} \)


If coefficient of range is 0.092 and the largest value is 71 , the range is?
A . 12
B. 13
c. 14
D. 16


A cylindrical bar magnet is lying along the axis of a circular coil. If the magnet
is rotated about the axis of the coil then
A. emf will be induced in the coil
B. only induced current will be generate in the coil
c. no current will be induced in the coil
D. both emf and current will be induced in the coil


Specimen used for original publication by the author is
A. Holotype
B. Isotype
c. syntype
D. Lactotype


The area of the region bounded by the curves \( \boldsymbol{f}(\boldsymbol{x})=\operatorname{maximum}\left\{|\boldsymbol{x}|, \boldsymbol{x}^{2}, \sqrt{\boldsymbol{x}}\right\} \)
where \( \boldsymbol{x}>\mathbf{0}, \boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{x}| \forall \boldsymbol{x} \leq \mathbf{0} \) and
\( h(x)=4 \) is-
\( A \cdot \frac{7}{3} \)
B. 9
c. 13
D. \( \frac{40}{3} \)


High energetic radiations among the following:
A \( . \lambda=0.01 A \)
B . \( \lambda=0.10 A \)
c. \( \lambda=1.00 A \)
\( \mathbf{D} \cdot \lambda=40.0 A \)


When glycerol is reacted with \( P X_{3} \) one
of the byproduct is \( X_{2} . \) The \( P X_{3} \) must
be:
A. \( P I_{3} \)
в. \( P B r_{3} \)
c. \( P C l_{3} \)
D. \( P F_{3} \)


A \( 5 \% \) by mass of an aqueous solution of \( A \) of molar mass \( 342 \mathrm{g} \mathrm{mol}^{-1} \) is isotonic with \( 0.878 \% \) by mass of an aqueous solution of another substance
B. The molar mass of \( B \) in \( g \) mol \( ^{-1} \) is:
A . 120
B. 180
\( c \cdot 60 \)
D. 90


How is \( \boldsymbol{P C l}_{3} \) produced industrially?
A. Reacting chlorine with white phosphorus
B. Reacting chlorine with phosphorus acid
c. Reacting chlorine with black phophorous
D. All of the above


Two thin lenses of focal lengths \( 20 \mathrm{cm} \)
and \( 25 c m \) are placed in contact. The effective power of the combination is
A \( \cdot(1 / 9) D \)
в. \( (1 / 45) D \)
\( c .45 D \)
D. \( 9 D \)


Write the chemical reaction to prepare
novolac polymer.


For the reaction
\( 2 N H_{3} \rightarrow N_{2}+3 H_{2} \)
a curve is plotted between \( \left[N H_{3}\right] \) is
time as shown
Calculate the
(A) Rate of disappearance between 5
and 10 sec
(B) Rate of disappearance between 10
and 20 sec


Carbonic acid, \( \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{O}_{3}, \) is a diprotic
acid for which \( \boldsymbol{K}_{\mathbf{1}}=\mathbf{4 . 2} \times \mathbf{1 0}^{-\mathbf{7}} \) and
\( \boldsymbol{K}_{2}=\mathbf{4 . 7} \times \mathbf{1 0}^{-11} . \) Which solution will
produce a \( p H \) closest to \( 9 ? \)
A \( .0 .1 M H_{2} C O_{3} \)
в. \( 0.1 M \) Na\( _{2} \) С \( O_{3} \),
c. \( 0.1 M \) NaHCO\( _{3} \)


Three bodies \( A, B \) and \( C \) of masses \( 1 k g \)
\( 2 k g \) and \( 3 k g \) are at rest on a horizontal
surface of coefficient of friction \( 0.5 . \) If
they are pulled with forces \( 20 N, 30 N \)
and \( 25 N \) respectively
their accelerations \( a_{A}, a_{B} \) and \( a_{C} \) will be in ascending order as follows:
A \( \cdot a_{A}, a_{B}, a_{C} \)
в. \( a_{C}, a_{B}, a_{A} \)
\( \mathbf{c} \cdot a_{B}, a_{A}, a_{C} \)
D. \( a_{B}, a_{C}, a_{A} \)


A copper rod \( A B \) of length \( l \) is rotated about end A with a constant angular
velocity \( \omega . \) Find electric field at a
distance \( x \) from the axis of rotation:
A \( \cdot \frac{m \omega^{2} x}{e} \)
B. \( \frac{m \omega x}{e l} \)
c. \( \frac{m x}{\omega^{2} l} \)
D. \( \frac{m e}{\omega^{2} x} \)


Two point masses \( m \) and \( M \) are
separated by a distance \( L \). The distance
of the center of mass of the system from
\( \boldsymbol{m} \) is :
\( \mathbf{A} \cdot L(m / M) \)
в. \( L(M / m) \)
c. \( _{L\left(\frac{M}{m+M}\right)} \)
D. \( L\left(\frac{m}{m+M}\right) \)


Calculate the wavelength (in nanometer) associated with a proton moving at \( 1.0 \times 10^{3} m s^{-1} \)
(Mass of proton= \( 1.67 \times 10^{-27} k g \) and
\( \boldsymbol{h}=\mathbf{6 . 6 3} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J} \boldsymbol{s} \)
A. \( 0.40 n m \)
в. \( 2.5 n m \)
\( \mathrm{c} .14 .0 \mathrm{nm} \)
D. \( 0.32 n m \)


The degree to which numerical data tend to spread about value is called
A. mean
B. variation
c. median
D. mode


If the kinetic energy of an electron is increased four times, then what would
be the wavelength of the de-Broglie wave associated with it.


Which of the following reactions does not take place during leaching for concentration of bauxite?
A \( \cdot A l_{2} O_{3}+2 N a O H+3 H_{2} O \rightarrow 2 N a\left[A l(O H)_{4}\right. \)
B . \( 2 \mathrm{Na}\left[\mathrm{Al}(\mathrm{OH})_{4}\right]+\mathrm{CO}_{2} \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3} . \mathrm{xH}_{2} \mathrm{O}+2 \mathrm{NaHCO}_{3} \)
c. \( A l_{2} O_{3} .2 H_{2} O \stackrel{\Delta}{\longrightarrow} A l_{2} O_{3}+2 H_{2} O \)
D. \( A l_{2} O_{3} \cdot x H_{2} O \stackrel{\Delta}{\longrightarrow} A l_{2} O_{3}+x H_{2} O \)


The Sl unit of pressure is
\( A \cdot \) atm
B. dyne/cm \( ^{2} \)
c. pascal
D. mm of Hg


In abscissa of a point \( P \) is negative and ordiante of \( P \) is positive, then \( P \) lies in :
A. I Quadrant
B. II Quadrant
c. III Quadrant
D. IV Quadrant


Potassium permanganate \( \rightarrow \)
potassium manganate \( +A+ \) oxygen
What is \( A \) in the given reaction?
A. Manganese
B. Manganese dioxide
c. Manganese trioxide
D. Manganese tetraoxide


Which equation has the solution shown
on the number line?
\( \mathbf{A} \cdot 4>x \geq 1 \)
B. \( x<1 \)
c. \( x \neq 1 \)
D. \( x<0 \)


Find the value of friction forces between
the blocks \( A \) and \( B \) and between \( B \) and
ground (Take \( \left.g=10 m s^{-2}\right) \)
\( A \cdot 90 N, 5 N \)
B. 5 N, 90 \( N \)
\( c \cdot 5 N, 75 N \)
D. O N, 80 N


Identify whether the following sequence is a geometric sequence or not \( \mathbf{1}, \mathbf{4}, \mathbf{9}, \mathbf{1 6} \)


Behaviour of hydrogen gas towards litmus paper is :
A. neutral behaviour
B. turns red litmus to blue
c. turns blue litmus to red
D. litmus paper starts burning


The strength of acid is highest in:
A \( \cdot p K_{a}=6 \)
в. \( p K_{a}=5 \)
c. \( p K_{a}=10 \)
D \( \cdot p K_{a}=1 \)


Can the coefficient of the friction be
grater than one?


The direction of the force acting on a current carrying conductor when placed in a magnetic field can be obtained by
A. Fleming left hand rule
B. Fleming right hand rule
c. Both
D. None


Salt is added to preserve meat, pickles, etc. because salting kills bacteria by the process of
A. Dissolution
B. Distillation
c. Plasmolysis
D. Imbibition


Crus cerebri is located in
A. Forebrain
B. Hindbrain
c. Midbrain
D. None of the above


Provide the proper IUPAC name for the
compound below.
A. oct-4-ene-1-carbonyl chloride
B. oct-3-en-1-oyl chloride
c. oct-5-ene-1-oyl chloride
D. oct-3-en-8-oyl chloride


Let \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{4} \\ \mathbf{3} & \mathbf{2}\end{array}\right], \boldsymbol{B}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ -\mathbf{2} & \mathbf{5}\end{array}\right] \) and
\( \boldsymbol{C}=\left[\begin{array}{cc}\mathbf{- 2} & \mathbf{5} \\ \mathbf{3} & \mathbf{4}\end{array}\right] . \) Find:
\( \boldsymbol{B}-\mathbf{4} \boldsymbol{C} \)


Assertion
\( \lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \frac{\sqrt{1-\cos 2 x}}{\boldsymbol{x}} \) does not exist.
Reason \( |\sin x|=\left\{\begin{array}{cc}\sin x ; & 0<x<\frac{\pi}{2} \\ -\sin x ; & -\frac{\pi}{2}<x<0\end{array}\right. \)
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


Two atoms of similar electronegativity would be expected to form a covalent compound if true enter 1 else 0


A point charge q is kept on the vertex of the cone of base radius \( r \) and height \( r \)
The electric flux through the curved surface will be
\( ^{A} \cdot \frac{q}{2 \varepsilon_{0}}\left(1-\frac{1}{\sqrt{2}}\right) \)
В \( \cdot \frac{q}{\varepsilon_{0}}\left(\frac{1}{2 \sqrt{2}}\right) \)
\( c . \) zer
D. \( \frac{q}{\varepsilon_{0} \sqrt{2}} \)


Which of the following do not contain polyester fabric?
A. Terrywool
B. Terrycot
c. Terylene
D. Orlon


\( \int x^{x} \ln (x) d x= \)
A \( \cdot \frac{x^{x}}{\ln x}+c \)
B . \( x^{x}+c \)
c. \( \frac{x^{x+1}}{x+1}+c \)
D. none of these


A body moves for a total of nine second starting from rest with uniform acceleration and then with uniform
retardation, which is twice the value of
acceleration and then stops. The
duration of uniform acceleration
A . 3 s
в. 4.5 s
\( c .5 s \)
D. \( 6 s \)


Which metal sol can not be prepared by
Bredig's arc method?
\( \mathbf{A} \cdot K \)
в. \( C u \)
c. \( A u \)
D. \( P t \)


Solve \( x^{2}-6 x+2=0 \)


A car is moving with the speed 20 \( \mathrm{m} / \mathrm{sec} \) for first half distance of total
distance and in next half distance it
travels with the speed \( 40 \mathrm{m} / \mathrm{sec} \) find out average speed


Digestion and absorption of nutrients
take place in
A. Small intestine
B. Large intestine
c. Stomach
D. Esophagus
E. Mouth


are the smallest unit of
matter that can take part in a chemical
reaction.
A . Molecules
B. Compounds
c. Atoms
D. Electrons


A \( 500 g \) tooth paste sample has \( 0.02 g m \) fluoride concentration. What is the
concentration of fluorine in terms of
ppm levels?
A .250
B. 40
c. 400
D. 1000


Chemical name and formula of washing soda is hydrated sodium carbonate and
\( N a_{2} C O_{3} .10 H_{2} O \) respectively
A. True
B. False


\( A \) and \( B \) are two independent events such that \( \boldsymbol{P}\left(\boldsymbol{A}^{\prime} \cap \boldsymbol{B}^{\prime}\right)=\frac{1}{6} \) and
\( P\left(A^{\prime}\right)=\frac{5}{24} . \) Then \( P(B) \) is equal to
\( A \cdot \frac{4}{5} \)
B.
\( c \cdot \frac{1}{5} \)
D.


Two charges of equal magnitude ' \( q \) ' are
placed in air at a distance \( ^{\prime} 2 a^{\prime} \) apart
and third charge \( -2 q^{\prime} \) is placed at midpoint. The potential energy of the system is \( \left(\epsilon_{0}= \) permittivity of free \right. space) :
\( ^{\mathrm{A}} \cdot-\frac{q^{2}}{8 \pi \epsilon_{0} a} \)
в. \( -\frac{3 q^{2}}{8 \pi \epsilon_{6} a} \)
c. \( -\frac{5 q^{2}}{8 \pi \epsilon_{0} a} \)
D. \( -\frac{7 q^{2}}{8 \pi \epsilon_{6} a} \)


Determine the order and degree(if defined) of the following differentia
equation. \( \left(\frac{\boldsymbol{d} \boldsymbol{s}}{\boldsymbol{d} \boldsymbol{t}}\right)^{\boldsymbol{4}}+\boldsymbol{3} \boldsymbol{s} \frac{\boldsymbol{d}^{2} \boldsymbol{s}}{\boldsymbol{d} \boldsymbol{t}^{2}}=\mathbf{0} \)


The mass of \( 3.01 \times 10^{23} \) molecules of a
gas iss \( 32.0 g . \) What volume does 8.00 g of the gas occupy at STP?
A \( .2 .80 L \)
B. \( 8.00 L \)
c. \( 11.2 L \)
D. 22.4 L
E . \( 64.0 L \)


Find the sum of the following series. \( 1+(1+a)+r+\left(1+a+a^{2}\right) r^{2}+\dots \)
to \( \infty(|\boldsymbol{r}|<\mathbf{1}) \)


Two pipes running together can fill a cistern in \( 3 \frac{1}{13} \) minutes. If one pipe takes 3 minutes more than the other to
fill the cistern, find the time in which each pipe would fill the cistern.


'Carbon forms backbone of biology of life on earth'. Justify


Find GM between 4 and 36


In a triangle \( A B C, \) right angled at the
vertex \( A, \) if the position vectors \( A, B \) and \( C \) are respectively \( 3 \tilde{i}+\tilde{j}-\tilde{k},-\tilde{i}+ \) \( \mathbf{3} \tilde{j}+p \tilde{k} \) and \( 5 \tilde{i}+q \tilde{j}-4 \tilde{k}, \) then the
point \( (p, q) \) lies on a line
A. makeing an obtuse angle with the positive direction of \( x- \) axis
B. Parallel to \( x- \) axis
c. Parallel to \( y- \) axis
D. making an acute angle with the positive direction of \( x-a x i s \)


A charged particle \( X \) moves directly towards another charged particle Y. For
the \( X \) plus \( Y \) system, the total
momentum is \( \mathrm{p} \) and the total energy is
E.
This question has multiple correct options
\( A \cdot p \) and \( E \) are conserved if both \( X \) and \( Y \) are free to move.
B. (a) is true only if \( X \) and \( Y \) have similar charges.
C. If \( Y \) is fixed, \( E \) is conserved but not \( P \)
D. If \( Y \) is fixed, neither \( E \) nor \( P \) is conserved


An element \( z M^{A} \) emits one \( \alpha \) (alpha) particle followed by two \( \beta \) (beta)
particles. Among the following, the daughter element is :
A \( \cdot z-2 M^{A-4} \)
B . \( _{z-2} M^{A} \)
\( \mathbf{c} \cdot_{z} M^{A-4} \)
D. \( _{z+2} M^{A-4} \)


Find the area of the region.
\( \left\{(x, y): x^{2}+y^{2} \leq 8, x^{2} \leq 2 y\right\} \)


Choose the correct answer among the alternatives given :
The correct order of reactivity is:
A. \( A>B>C \)
в. \( B>C>A \)
c. \( B>A>C \)
D. \( C>B>A \)


Which of the following set contains species having same angle around the
central atom?
A. \( S F_{4}, C H_{4}, N H_{3} \)
B. \( N F_{3}, B C l_{3}, N H_{3} \)
c. \( B F_{3}, N F_{3}, A l C l_{3} \)
D. \( B F_{3}, B C l_{3}, B B r_{3} \)


Match the column I with column II and
select the correct option from the gives
codes
\( \begin{array}{llll} & \text { Column } & & \text { Column II } \\ & \text { I } & & \\ \text { A. } & \text { Pedicel } & \text { (i) } & \text { Reduces leaf } \\ \text { B. } & \text { peduncle } & \text { (ii) } & \begin{array}{l}\text { Stalk of the } \\ \text { flower }\end{array} \\ \text { C. } & \text { Bract } & \text { (iii) } & \text { Stalk of the leaf } \\ \text { D. } & \text { Petiole } & \text { (iv) } & \begin{array}{l}\text { Inflorescence } \\ \text { axis }\end{array}\end{array} \)
\( \mathbf{A} \)
B. \( A-(\text { iii) }, B-(i v), C-(i), D-(i i) \)
C. A-(iii), B-(ii), C-(i), D-(iv)
D. A-(ii), B-(iii), C-(i), D-(iv)


Compared to other acids like \( \boldsymbol{H} \boldsymbol{C l} \)
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is highly syrupy and
viscous in nature. Identify the correct
reason
A \( \cdot H_{2} S O_{4} \) is highly concentrated
B. \( H_{2} S O_{4} \) is a stronger acid than \( H C l, H N O_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{SO}_{4} \) is associated by more number of hydrogen bonds
D. Both \( A \) and \( B \).


Choose the correct answer from the four
options given below. Chromosomes get aligned at the centre of the cell during
A. Metaphase
B. Anaphase
c. Prophase
D. Telophase


Write the mechanism of the reaction of
\( H I \) with methoxymethane.


Integrate \( \int x \log 2 x d x \)


What is the maximum number of
electrons that can be present in \( 2 d \) orbitals is \( X, \) then \( X \) is :


The potential energy function for
a particle executing linear simple harmonic motion is given by
\( V(x)=k x^{2} / 2, \) where \( k \) is the force
constant of the oscillator.
For \( \boldsymbol{k}=\mathbf{0 . 5} \boldsymbol{N} \boldsymbol{m}^{-1}, \) the \( \operatorname{graph} \) of \( \mathbf{V}(\mathbf{x}) \)
versus \( x \) is shown in Fig. Show that \( a \)
particle of total energy 1 J moving under this potential must turn back when
it reaches \( \boldsymbol{x}=\pm \mathbf{2 m} \)


Three resistors of values \( 2 \Omega, 4 \Omega, 6 \Omega \) are connected is series. The equivalent
resistance of combination of resistors
is


Add the following rational numbers:
\( \frac{7}{-18} \) and \( \frac{8}{27} \)


If we take some water at \( 0^{\circ} \mathrm{C} \) and start
heating it,we find that in the
temperature range \( 0^{\circ} \mathrm{C} \) to \( 4^{\circ} \mathrm{C} \)
A. It expands on heating
B. It contracts on heating
c. Both
D. None


The surface charge density on a copper
sphere is \( \sigma . \) So the intensity of electric field on its surface will be:
A. \( \sigma \)
B. \( \frac{\sigma}{2} \)
c. \( \frac{\sigma}{2 \varepsilon o} \)
D. \( \frac{\sigma}{\varepsilon o} \)


Evaluate: \( \int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x \)


Two resistors, with resistances \( R_{1} \) and
\( R_{2}, \) are connected in parallel
The resistance \( R_{1} \) is greater than the
resistance \( \boldsymbol{R}_{2} \)

What is the resistance of the parallel
combination?
A. Less than either \( R_{1} \) or \( R_{2} \)
B. Equal to \( R_{1} \)
c. Equal to \( R_{2} \)
D. The average of \( R_{1} \) and \( R_{2} \)


Two coils \( P \) and \( Q \) are kept near each other. When no current flows through coil \( P \) and current increases in coil \( Q \) at
the rate \( 10 A / s \), the e.m.f. in coil \( P \) is
\( 15 m V . \) When coil \( Q \) carries no current
and current of \( 1.8 A \) flows through coil
\( P, \) the magnetic flux linked with the coil
\( Q \) is
A. \( 1.4 \mathrm{m} \mathrm{Wb} \)
B . \( 2.2 \mathrm{m} \mathrm{Wb} \)
\( \mathbf{c} .2 .7 \mathrm{m} \mathrm{Wb} \)
D. \( 2.9 \mathrm{m} \mathrm{Wb} \)


Consider following reaction in equilibrium with equilibrium concentration \( 0.01 \mathrm{M} \) of every species
(।) \( \boldsymbol{P} \boldsymbol{C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
(II) \( 2 H I(g) \rightleftharpoons H_{2}(g)+I_{2}(g) \)
(III) \( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
Extend of the reaction taking place is:
A. \( I>I I>I I I \)
в. \( I<I I<I I I \)
c. \( I I<I I I<I \)
D. III \( <I<I I \)


Give one significant difference between
puberty and menarche.


What is the density of lead under a pressure of \( 2.0 \times 10^{8} N / m^{2}, \) if the bulk
modulus of lead is \( 8.0 \times 10^{9} N / m^{2} \)
Also, the initial density of lead is \( 11.4 g / c m^{3} \)
A \( \cdot 12.89 g / c m^{3} \)
в. \( 14 g / \mathrm{cm}^{3} \)
c. \( 11.69 g / c m^{3} \)
D. Zero


All dilute acids react with bleaching powder, liberating
A. oxygen gas
B. chlorine gas
c. sulphur dioxide gas
D. hydrogen gas


The greatest acceleration or deceleration that a train may have is \( a \). The minimum
time in which the train can get from one station to the next at a distance \( s \) is:
A \( \cdot \sqrt{\frac{s}{a}} \)
B. \( \sqrt{\frac{2 s}{a}} \)
\( ^{c} \cdot 2 \sqrt{\frac{s}{a}} \)
D. \( \frac{1}{2} \sqrt{\frac{s}{a}} \)


Number of points where \( \boldsymbol{f}(\boldsymbol{x})=(1- \)
\( x)\left|x-x^{2}\right|+x \) is not differentiable is
A .
B.
\( c \cdot 2 \)
D.


In which of the following decays the element reduced does not change?
A. \( \alpha \) -decay
B. \( \beta^{+} \) -decay
c. \( \beta^{-} \) -decay
D. \( \gamma \) -decay


A particle is projected up along a rough
plane inclined at an angle of \( 45^{\circ} \) with the horizontal, if the coefficient of friction is \( \frac{1}{2}, \) then the retardation is:
A \( \cdot \frac{g}{\sqrt{2}} \)
в. \( \frac{g}{2} \)
c. \( \frac{g}{\sqrt{2}}\left(1+\frac{1}{2}\right) \)
D. \( \frac{g}{\sqrt{2}}\left(1-\frac{1}{2}\right) \)


A particle of mass \( m \) is allowed to
oscillate on a smooth parabola: \( \boldsymbol{x}^{2}= \)
\( 4 a y, a>1 \) as shown in the figure. The
angular frequency \( (\omega) \) of small
oscillations is
A \( \cdot \omega=\sqrt{\frac{g}{4 a}} \)
B. \( \omega=\sqrt{\frac{g}{2 a}} \)
c. \( \omega=\sqrt{\frac{2 g}{a}} \)
\( \omega=\sqrt{\frac{g}{a}} \)


A car travelling at \( 72 \mathrm{km} / \mathrm{h} \) decelerates
uniformly at \( 2 m / s^{2} . \) Calculate
(a) the
distance it goes before it stops, (b) the time it takes to stop, and (c) the distance it travels during the first and third seconds.


From which graph, the class interval is proportional to the width of the bars?
A. histogram
B. bar
c. line
D. pie


In the manufacture of sulphuric acid by
contact process, Tyndall box is used to:
A. filter dust particles
B. remove impurities
C . convert \( S O_{2} \) to \( S O_{3} \)
D. test the presence of dust particles


Evaluate \( \mid \begin{array}{ccc}\cos \left(x+x^{2}\right) & \sin \left(x+x^{2}\right) & -\cos (x+1) \\ \sin \left(x-x^{2}\right) & \cos \left(x-x^{2}\right) & \sin (x-x) \\ \sin 2 x & 0 & \sin 2 x^{2}\end{array} \)
A \( \cdot \sin \left(2 x+2 x^{2}\right) \)
B. \( -\sin \left(2 x+2 x^{2}\right) \)
\( c \cdot \cos \left(2 x+2 x^{2}\right) \)
D. \( -\cos \left(2 x+2 x^{2}\right) \)


Total reflecting prisms are:
A. right angled prism
B. acute angled isosceles prism
C . right angled isosceles prism
D. obtuse angled isosceles prism


Find the square root of the following number by the prime factorisation method
\( \mathbf{1 9 3 6} \)


The charge on \( \alpha \) -particle is the charge on proton.
A . twice
B. thrice
c. half
D. same as


A piece of wood collected from Cro Magnon caves gave 4 dpm. A freshly cut wood of the same weight gives \( 16 d p m \)
The cro magnon man lived about
years ago
(Half life of \( C^{14} \) is 5760 years. Assume
the activity is due to \( C^{14} \) only
A .5700
в. 2900
c. 11520
D. 1400


Statement I: The equation
\( \left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}-a \pi^{3}=0 \) has
solution for all \( a \geqslant \frac{1}{32} \)
Statement II : For any \( \boldsymbol{x} \boldsymbol{\epsilon} \boldsymbol{R}, \boldsymbol{s} \boldsymbol{i n}^{-1} \boldsymbol{x}+ \)
\( \cos ^{-1} x=\frac{\pi}{2} \) and \( 0 \leq\left(\sin ^{-1} x-\frac{\pi}{4}\right)^{2} \leq \)
\( \frac{9 \pi^{2}}{16} \)
A. Both statements I and II are true.
B. Both statements I and II are true but I is not an explanation of I
c. statement l is true and statement II is false
D. Statement I is false and statement II is true.


can be moved from \( a \) to \( b, \) connecting
either inductance \( L \) or capacitance \( C \)
to a resistor \( R \) when the key is pressed
the switch \( S \) will be at either \( a \) or \( b \). In
column \( I, \) the variation of physical
quantities charge,current,voltage etc.in
time are given in terms of constants
\( C^{\prime} s \) and \( K^{\prime} s \) the values of which
depends on emf \( V, R, L \) and \( C . \ln \)
column \( \boldsymbol{I} \boldsymbol{I}, \) the physical quantities
under different switch positions are
given. the variation in column \( \boldsymbol{I} \) may
correspond to one or more quantities of
Column \( \boldsymbol{I} \boldsymbol{I} \)


Two people push a car for 3 sec, with a combined net force of 200 N.The
impulse provided to the car....
A . \( 400 \mathrm{N} \) -sec
B. 500 N-sec.
c. 600 N-sec.
D. 300 N-sec.


A particle started moving from \( \boldsymbol{P} \)
towards \( S \) with uniform acceleration
along a straight line. The average velocity of the particle from \( P \) to
intermediate point \( Q \) is \( 8 m / s \) and that
\( Q \) to \( S \) is \( 12 m / s . \) If \( Q S=P Q, \) then the
average velocity from \( \boldsymbol{P} \) to \( \boldsymbol{S} \) is:
A. \( 9.6 \mathrm{m} / \mathrm{s} \)
B. \( 12.87 \mathrm{m} / \mathrm{s} \)
\( c .64 m / s \)
D. \( 327 \mathrm{m} / \mathrm{s} \)


A climax community is recognized by
A. Grass,herbs and shrubs
B. Trees
c. High biomass
D. Uniform composition


Alkali metals dissolve in ammonia to
give a blue solution which is conducting in nature due to:
A. ammoniated electrons
B. loss of electrons
c. ammoniated cations
D. both \( A \) and \( C \)


Wave no. of a spectral line for a given
transition is \( x \mathrm{cm}^{-1} \) for \( H e^{+} \) then its
value for \( B e^{3+} \) for the same transition
is:
A. \( 4 x \mathrm{cm}^{-1} \)
B. \( x \mathrm{cm}^{-1} \)
c. \( \frac{x}{4} c m^{-1} \)
D. \( 2 x \mathrm{cm}^{-1} \)


The normal boiling point of a liquid' \( \boldsymbol{X}^{\prime} \) is \( 400 K . \) Which of the following statement(s) is/are true about the
process \( X(l) \longrightarrow X(g) ? \)
This question has multiple correct options
A. at \( 400 K \) and 1 atm pressure \( \Delta G=0 \)
B. at \( 400 K \) and 2 atm pressure \( \Delta G=+v e \)
C. at \( 400 K \) and 0.1 atm pressure \( \Delta G=-v e \)
D. at \( 410 K \) and 1 atm pressure \( \Delta G=+v e \)


Out of \( \boldsymbol{F} \boldsymbol{e}^{2+}, \boldsymbol{F} \boldsymbol{e}^{3+}, \boldsymbol{M} \boldsymbol{n}^{2+} \) and \( \boldsymbol{T} \boldsymbol{i}^{2+}, \) the
least size is of:
\( \mathbf{A} \cdot M n^{2+} \)
B. \( T i^{2} \)
\( \mathrm{c} \cdot F e^{2} \)
D. \( F e^{3} \)


toppr
Q Type your question
insulated from each other. The entire
loop lies in the plane (of the paper). A
uniform magnetic field \( B \) point into the
plane of the paper. At \( t=0, \) the loop
starts rotating about the common
diameter as axis with a constant
angular velocity \( \omega \) in the magnetic field Which of the following options is/are
correct?
This question has multiple correct options
A. The amplitude of the maximum net \( e m f \) induced due to both the loops is equal to the amplitude of maximum \( e m f \) induced in the smaller loop alone
B. The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the paper
c. The \( e m f \) induced in the loop is proportional to the surn of the areas of the two loops
D. The net \( e m f \) induced due to both the loops is proportional to cos \( \omega t \)


An accumulator battery (storage cell)
of emf \( \mathrm{E} \) and internal resistance \( \mathrm{r} \) is
being charged from a DC supply whose
terminals are \( T_{1} \) and \( T_{2} \)
This question has multiple correct options
A. potential difference between \( T_{1} \) and \( T_{2} \) must be \( >E \)
B. \( T_{1} \) must be positive with respect to \( T_{2} \)
\( \mathrm{c} \). in the battery, current flows from the positive to the negative terminal
D. all the above options are incorrect


A ball released from a height falls \( 5 m \) in
one second. In 4 seconds it falls through
(Take \( \left.g=10 m s^{-2}\right) \)
A \( .20 m \)
B. \( 1.25 m \)
\( c .40 m \)
D. \( 80 m \)


\( (\boldsymbol{A}) \boldsymbol{C}_{4} \boldsymbol{H}_{6} \frac{\boldsymbol{H}_{2} / \boldsymbol{P t}}{\longrightarrow}(\boldsymbol{B}) \boldsymbol{C}_{4} \boldsymbol{H}_{8} \frac{\boldsymbol{O}_{3} / \boldsymbol{H}_{2} \boldsymbol{O}}{_{\boldsymbol{}}} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
Hence \( A \) and \( B \) are :
A. \( C H_{3} C \equiv C C H_{3}, C H_{3} C H=C H C H_{3} \)
в. \( C H_{2}=C H C H_{3}=C H_{2}, C H_{3} C H=C H C H_{3} \)
\( ^{c} \cdot \mid, \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{3} \)
D. None of these


condition is not considered for
the similarity of triangle.
A. \( S A S \)
в. \( S S S \)
c. \( A A A \)
D. \( A S A \)


three events \( A, B \) and \( C \) which are
mutually exclusive but not exhaustive.


On adding 0.04 g solid \( N a O H \) to a 100 \( \mathrm{ml} \frac{M}{200} B a(O H)_{2} \) solution, determine change in \( p H \)
\( A \cdot O \)
\( B .+0.3 \)
\( c \cdot-0.3 \)
\( D \ldots+0.7 \)


\( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{1} \\ \mathbf{0} & \mathbf{0}\end{array}\right], \) show that \( (\boldsymbol{a} \boldsymbol{I}+\boldsymbol{b} \boldsymbol{A})^{n}= \)
\( a^{n} I+n a^{n-1} b A, \) where \( I \) is the identity
matrix of order 2 and \( n \in N \)


In a leaf with reticulate venation
A. Veins forms a network on the leaf
B. Veins run parallel to the midrib
C. Veins run horizontal to the midrib
D. Veins criss-cross each other in an irregular pattern


Identify \( A \) and \( B \) in the following reaction \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{3} \longleftarrow \boldsymbol{B} \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \stackrel{\boldsymbol{A}}{\longrightarrow} \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O H} \)
A. \( H I+r e d P, L i A l H_{4} \)
B. \( N V / \Delta, \) LiAIH \( _{4} \)
c. \( \operatorname{LiAlH}_{4}, H I+r e d P \)
D. \( P d-B a S O_{4}, Z n+H C l \)


Exception of octet rule is:
\( \mathbf{A} \cdot K \)
в. \( C a \)
\( c . N \)
D. \( H e \)


Find the free-fall acceleration of an
object on the surface of the moon, if the radius of the moon and its mass are
\( 1740 \mathrm{km} \) and \( 7.4 \times 10^{22} \mathrm{kg} \) respectively.
Compare this value with free fall acceleration of a body on the surface of
the earth.


A girl weighing 50 kgf wears sandals of pencil heel of area of cross section 1 \( c m^{2}, \) stands on a floor. An elephant weighing 2000 kgf stands on foot each of area of cross section \( 25 \mathrm{cm}^{2}, \) on the
floor. Compare the pressure exerted by them.


Forty persons were examined for their Haemoglobin \% in blood (in mg per 100
\( \mathrm{ml} \) ) and the results were grouped as
below:
Determine modal value of Haemoglobin \( \% \) in blood of persons.
Haemoglobins 5
\[
\%(\mathrm{mg} /
\]
13. -14 100mI)
No. of Persons
A. \( 3.71 \mathrm{mg} / 100 \mathrm{ml} \)
B. \( 14.71 \mathrm{mg} / 100 \mathrm{ml} \)
c. \( 15.71 \mathrm{mg} / 100 \mathrm{ml} \)
D. \( 16.71 \mathrm{mg} / 100 \mathrm{ml} \)


The length of the chord of the circle \( (x-3)^{2}+(y-5)^{2}=80 \) cut off by the
line \( 3 x-4 y-9=0 \) is
A . 16
B. 8
\( c \cdot \sqrt{96} \)
\( \mathbf{D} \cdot 2 \sqrt{96} \)


If \( x>0, \) then the minimum value of \( \boldsymbol{x}^{1000}+\boldsymbol{x}^{900}+\boldsymbol{x}^{90}+\boldsymbol{x}^{6}+\frac{\mathbf{1 9 9 6}}{\boldsymbol{x}} \) is
A . 1000
B. 2000
\( c \cdot \) 1996
D. 3000


Which of the following statements is
true?
A. Chemical changes are reversible
B. Only very few chemical reactions are reversible
C. Growth of a tree is periodic change
D. Rusting of iron is a fast change


The correct order of magnitude of bond
angles among the compounds \( \boldsymbol{C H}_{4} \)
\( N H_{3} \) and \( H_{2} O \) is:
A. \( C H_{4}>H_{2} O<N H_{3} \)
B. \( H_{2} O<N H_{3}<C H_{4} \)
c. \( N H_{3}<C H_{4}<H_{2} O \)
D. \( N H_{3}<H_{2} O<C H_{4} \)


The equilibrium constant for \( \boldsymbol{A}(\boldsymbol{g})+ \)
\( B_{2}(g) \rightleftharpoons A B_{2}(g) \) is \( k_{p}=100 a t 522 K \)
Structure of \( A B_{2} \) is like \( H_{2} O . \) If bond
energy of \( A-B \) bond is \( 200 \mathrm{kJ} / \mathrm{mol} \) and
that of \( B-B \) bond is \( 100 \mathrm{kJ} / \mathrm{mol} \), then
\( \Delta S^{o} \) of the above reaction is:
A . -0.53 J/mol-K
B . - -536 J/mol-K
c. - -550 J/mol-K
D. - -5.36 J/mol-K


\( \lim _{x \rightarrow \infty} x \sin \left(\frac{2}{x}\right) \) is equal to
A \( \cdot \infty \)
B.
\( c \cdot 2 \)
D. \( \frac{1}{2} \)


The area bounded by \( y=x e^{|x|} \) and lines
\( |\boldsymbol{x}|=\mathbf{1}, \boldsymbol{y}=\mathbf{0} \) is
A. 4 sq units
B. 6 sq units
c. 1 sq units
D. 2 sq units


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


True or False.
Baking soda is a compound.
A. True
B. False


In the cube of side ' \( a^{\prime} \) shown in the
figure, the vector from the central point
of the face \( A B O D \) to the central point
of the face \( B E F O \) will be
A \( \cdot \frac{1}{2} a(\hat{i}-\hat{k}) \)
B \( \cdot \frac{1}{2} a(\hat{j}-\hat{i}) \)
c. \( \frac{1}{2} a(\hat{k}-\hat{i}) \)
D. \( \frac{1}{2} a(\hat{j}-\hat{k}) \)


Which one of the following is paramagnetic in nature?
A . \( N O \)
в. \( N_{2} \),
c. \( N_{2} O_{5} \)
D. All of the above


Calculate the heat absorbed by the
system in going through the process
shown in the given figure
A \( .31 .4 J \)
B . \( 3.14 J \)
c. \( 3.14 \times 10^{4} J \)
\( D \cdot \) none


Consider the functions defined
implicitly by the equation \( y^{3}-3 y+ \)
\( x=0 \) on various intervals in the real
line. If \( \boldsymbol{x} \epsilon(-\infty,-2) \cup(2, \infty), \) the
equation implicitly defines a unique real valued differentiable function \( y= \)
\( f(x) . \) If \( x \epsilon(-2,-2) \) the equation
implicitly defines a unique real valued
differentiable function \( \boldsymbol{y}=\boldsymbol{g}(\boldsymbol{x}) \)
satisfying \( \boldsymbol{g}=\boldsymbol{g}(\mathbf{0})=\mathbf{0} \)
If \( f(-10 \sqrt{2})=2 \sqrt{2} \) then
\( f^{\prime \prime}(-10 \sqrt{2})= \)
A \( \cdot \frac{4 \sqrt{2}}{7^{3} \cdot 3^{2}} \)
B. \( -\frac{4 \sqrt{2}}{7^{3} \cdot 3^{2}} \)
c. \( \frac{4 \sqrt{2}}{7^{3} \cdot 3^{3}} \)
D. \( \frac{4 \sqrt{2}}{7 \cdot 3} \)


Which of the following is a chemical messenger that produced in the body region but affect a different body region?
A. Hormones
B. Enzyes
c. Endocrines
D. Nucleic acids


A beam of electrons emitted from the
electron gun G is accelerated by an
electric field E. The area of cross section
of the beam remains constant. As the
beam moves away from G
This question has multiple correct options
A. the speed of the electrons increases
B. the current constituted by the beam increases
c. the number of electrons per unit volume in the beam increases
D. the number of electrons per unit volume in the beam decreases


What is the charge per unit area in
\( C / m^{2}, \) of an infinite plane sheet of
charge if the electric field produced by the sheet of charge has magnitude 3.0 N/C?


Show that the equation \( 10 x^{3}-17 x^{2}+ \)
\( x+6=0 \) has a root between 0 and -1


Show that the vector \( \overrightarrow{\boldsymbol{a}}=(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}) \) is
equally inclined to the coordinate axes.


The solution of \( \frac{d y}{d x}=x \log x \)
A \( \cdot 2 y=x^{2}\left[\log x+\frac{1}{2}\right]+c \)
B. \( 2 y=x^{2}\left[\log x-\frac{1}{2}\right]+c \)
c. \( _{y}=\frac{x^{2}}{2}(\log 2-x)+c \)
D. \( y^{2}=x^{2} \log x+x+c \)


When a junction diode is reverse biased, the current called drift current
is due to
A. majority charge carriers of both \( n \) - and p-side.
B. minority charge carriers of both \( n \) - and p-side.
c. holes of both \( n \) - and p-side.
D. conduction band electrons of n-side only


Acid rain corrodes the marble of the
monument. The phenomenon is also called:
A. destruction
B. marble cancer
c. corrosion
D. rusting


Assertion
The young stern of Funaria is
photosynthetic
Reason
It contain hydroids
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Elaters are present in sporogonium of
A . Riccia
B. Marchantia
c. selaginella
D. Sphagnum


The number of molecules in 89.6 litre of
a gas at NTP are:
A \( \cdot 6.02 \times 10^{23} \)
В. \( 2 \times 6.02 \times 10^{23} \)
c. \( 4 \times 6.02 \times 10^{23} \)
D. \( 3 \times 6.02 \times 10^{23} \)


If the diameter of circle is \( 10 \mathrm{cm}, \) then find the radius of circle.


Non metals are usually poor conductors of heat and electricity. They are nonlustrous, non-sonorous, non-malleable
and are coloured.
Non-metal other than carbon, which
shows allotropy is:
A. sulphur
B. phosphorus
c. nitrogen
D. both A and B


Find the minimum allowed values of
energy of the neutron.
B. 0.32 eV
\( c .0 .25 \mathrm{eV} \)
D. 0.43 eV


The standard reduction potentials of
\( A g, C u, C o \) and \( Z n \) is 0.799,0.337
\( -0.277,-0.762 \mathrm{V} \) respectively. Which of the following cells will have maximum cell e.m.f.?
A \( \cdot Z n\left|Z n^{2+}(1 M) \| C u^{2+}(1 M)\right| C u \)
в. \( Z n\left|Z n^{2+}(1 M) \| A g^{+}(1 M)\right| A g \)
C . \( C u\left|C u^{2+}(1 M)\right|\left|A g^{+}(1 M)\right| A g \)
D. \( Z n\left|Z n^{2+}(1 M) \| C o^{2+}(1 M)\right| C o \)


A bar magnet has a coercivity of \( 4 \times \) \( 10^{3} A m^{-1} . \) It is placed inside a solenoid
of length \( 12 \mathrm{cm} \) having 60 turns in order
to demagnetize it, the amount of current that should be passed through the solenoid is:
A. \( 16 A \)
в. \( 8 A \)
c. \( 4 A \)
D. \( 2 A \)


What is the hybridization of Phosphorus
Trichloride?
\( A \cdot s p^{3} \)
B \( \cdot s p^{2} \)
\( c \cdot s p \)
D. None of these


A cord is wound round the
circumference of a solid cylinder of
radius \( R \) and mass \( M . \) The axis of the
cylinder is horizontal. A weight \( m g \) is
attached to the end of the cord and falls
from rest. After falling through a
distance \( h \)
The angular velocity of the cylinder will
be :
A \( \cdot \frac{2 m g}{M+2 m} \)
в. \( \sqrt{\frac{2 g h}{R^{2}}} \)
c. \( \sqrt{\frac{4 m g h}{(M+2 m) R^{2}}} \)


A rope thrown over a pulley has a ladder
with a man A no one of its ends and a
counterbalancing mass \( \mathrm{M} \) on its other end. The man whose mass is \( \mathrm{m} \), climbs upwards by \( \vec{\Delta} r \) relative to the ladder
and then stops. Ignoring the masses of the pulley and the rope, as well as the friction in the pulley axis, find the displacement of the centre of mass of
this system


Make a labelled diagram of a candle flame.


The equilibrium constant for the reaction:
\( N_{2}(g)+O_{2}(g) \rightleftharpoons 2 N O(g) \) at \( 2000 \mathrm{K} \) is
\( 4 \times 10^{4} \)
In presence of catalyst the equilibrium is established ten times faster at the
same temperature
What is the value of equilibrium constant in presence of catalyst?
A \( \cdot 40 \times 10^{-4} \)
B . \( 4 \times 10^{-4} \)
c. \( 4 \times 10^{4} \)
D. None


Which of the following oxoacids of nitrogen has most acidic character?
I. \( N_{2} O_{3} \)
\( \boldsymbol{I} \boldsymbol{I} \cdot \boldsymbol{N} \boldsymbol{O}_{2} \)
III. \( N_{2} O_{5} \)
\( I V . N O \)
\( \mathbf{A} \cdot I I \)
в. \( I I I \)
\( c . I V \)
\( D \)


\( \int(e x)^{x}(2+\log x) d x=\ldots .+c, x \in \)
\( \boldsymbol{R}^{+}-\{\mathbf{1}\} \)
\( \mathbf{A} \cdot x^{x} \)
B. \( (e x)^{x} \)
\( \mathbf{c} \cdot e^{x} \)
D \( \cdot(1+\log x)(e x)^{x} \)


Choose the correct answer from the
alternatives given
Phytochrome is:
A. photoreceptor
B. present as Pfr during the day
c. activates regulatory proteins
D. all of the above


Which one of the following is not a characteristic feature of the sub
phylum vertebrate?
A. Dorsal tubular nerve cord
B. Ventral muscular heart
c. Presence of notochord in the adult
D. Presence of kidneys
E. Two pairs of lateral appendages, fins or limbs


Two waves are represented by the equations \( \boldsymbol{y}_{1}=\boldsymbol{a} \sin (\boldsymbol{\omega}+\boldsymbol{k} \boldsymbol{x}+\mathbf{0 . 5 7}) \boldsymbol{m} \) and
\( \boldsymbol{y}_{2}=\boldsymbol{a} \cos (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{k} \boldsymbol{x}) \boldsymbol{m} \)
where \( x \) is in meter and \( t \) in sec. The phase difference between them is
A. 0.57 radian
B. 1.0 radian
c. 1,25 radian
D. 1.57 radian


A six coordinate complex of formula
\( \boldsymbol{C r} \boldsymbol{C l}_{3} \cdot \boldsymbol{6} \boldsymbol{H}_{2} \boldsymbol{O} \) has green colour. A \( \boldsymbol{0 . 1} \boldsymbol{M} \)
solution of the complex when treated
with excess of \( A g N O_{3} \) gave \( 28.7 g \) of white precipitate. The formula of the complex would be
\( \mathbf{A} \cdot\left[C r\left(H_{2} O\right)_{6}\right] C l_{3} \)
B . \( \left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} . \mathrm{H}_{2} \mathrm{O} \)
c. \( \left[C r\left(H_{2} O\right)_{4} C l\right] C l_{2} .2 H_{2} O \)
D. \( \left[C r\left(H_{2} O\right)_{3} C l_{3}\right] .3 H_{2} O \)


The area bounded by \( \boldsymbol{x}=\boldsymbol{a} \cos ^{3} \boldsymbol{\theta}, \boldsymbol{y}= \)
\( a \sin ^{3} \theta \) is:
A \( \cdot \frac{3 \pi a^{2}}{16} \)
в. \( \frac{3 \pi^{2}}{8} \)
c. \( \frac{3 \pi a^{2}}{32} \)
D. \( 3 \pi a^{2} \)


Evaluate the following integral:
\( \int_{0}^{2}\left(x^{2}+3\right) d x \)


\( (\Delta H-\Delta U) \) for the formation of
carbon monoxide \( (C O) \) from its
element at \( 298 K \) is:
\( \left(\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right) \)
A \( .-1238.78 \mathrm{Jmol}^{-1} \)
B . \( 1238.78 \mathrm{Jmol}^{-1} \)
c. \( -2477.57 \mathrm{Jmol}^{-1} \)
D. \( 2477.57 \mathrm{Jmol}^{-1} \)


If \( D_{P}=\left|\begin{array}{ccc}\boldsymbol{P} & \mathbf{1 5} & \mathbf{8} \\ \boldsymbol{P}^{2} & \mathbf{3 5} & \mathbf{9} \\ \boldsymbol{P}^{3} & \mathbf{2 5} & \mathbf{1 0}\end{array}\right|, \) then \( \boldsymbol{D}_{1}+ \)
\( D_{2}+D_{3}+D_{4}+D_{5} \) is equal to
A. -29000
в. -25000
c. 25000
D. none of these


Use differential to approximate \( \sqrt{\mathbf{1 0 1}} \)
A .10 .00
B. 10.05
\( c \cdot 11.00 \)
D. Non of these


Predict all the alkenes that would be
formed by dehydrohalogenation of the following halides with sodium ethoxide
in ethanol and identify the major alkene:
(i) \( 1- \) Bromo-1-methylcyclohexane
(ii) 2 -Chloro-2-methylbutane
(iii) 2,2,3 -Trimethyl-3-bromopentane.


A \( 10 \mathrm{m} \) long copper wire while remaining in the east-west horizontal direction is
falling down with a constant speed of \( 5.0 \mathrm{m} / \mathrm{s} . \) If the horizontal component of
the earth's magnetic field \( 0.30 \times \)
\( 10^{-4} W \) erber \( / m^{2} \)
What is the instantaneous value of the
e.m.f induced in water?
A. 0.15 volts
B. 1.5 volts
c. 0.15 mili volts
D. 1.5 mili volts


In the thermal decomposition of potassium chlorate given as
\( 2 K C l O_{3} \rightarrow 2 K C l+3 O_{2}, \) law of mass
action
A. Cannot be applied
B. Can be applied
c. can be applied at low temperature
D. can be applied at high temp. and pressure


Assertion
Specific heat does not depend upon the mass of the substance.
Reason
Thermal capacity depends on the mass of the substance.
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 volume of a wire remains constant
when subjected to tensile stress, the value of Poisson's ratio of the material
of the wire is:
A . \( 0 . \)
B. 0.2
\( c .0 .4 \)
D. 0.5


Let \( \boldsymbol{f}\left(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{c}_{1}\right)=\mathbf{0} \) and \( \boldsymbol{f}\left(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{c}_{2}\right)=\mathbf{0} \)
define two integral curves of a homogeneous first order differential
equation. If \( P_{1} \) and \( P_{2} \) are respectively the points of intersection of these
curves with an arbitrary line, \( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x} \)
then prove that the slopes of these two
curves at \( P_{1} \) and \( P_{2} \) are equal


Using the fact that \( \sin (\boldsymbol{A}+\boldsymbol{B})= \)
\( \sin A \cos B+\cos A \sin B \) and the
differentiation, obtain the sum formula
for cosines.


In the parallelogram ABCD the angles \( A \) and \( C \) are obtuse Points \( X \) and \( Y \) are
taken on the diagonal BD such that the angles \( \mathrm{XAD} \) and \( \mathrm{YCB} \) are right angles. And hence, \( \boldsymbol{X} \boldsymbol{A}=\boldsymbol{Y} \boldsymbol{C} \)
If the above statement is true then
mention answer as 1 , else mention 0 if
false


Each of the six ideal batteries of emf
\( 20 V \) is connected to an external
resistance of \( 4 \Omega \) as shown in the figure.
The current through the resistance is
\( \mathbf{A} \cdot 6 A \)
в. \( 3 A \)
\( c .4 A \)
D. \( 15 A \)


The molar heat capacity in a process of diatomic gas if it does a work of \( \frac{Q}{4} \) when a heat of \( Q \) is supplied to it is
A \( \cdot \frac{2}{5}^{R} \)
в. \( \frac{5}{4} \) R
c. \( \frac{10}{3} \) R
D. \( \frac{6}{4} \) R


The function of gizzard seen in grasshopper and cockroach digestive system is
A. Removal of excretary products
B. Storage of food materials
c. Grinding of food materials
D. secretion of digestive enzymes


In periodic table, which period have most electronegative elements?
A .
B. 2
\( c \cdot 3 \)
D. 4
E. 5


The movement of Earth's plates causes
A. Lightening
B. Cyclons
c. Earthquake
D. Thunderstorms


Define the following term:
Emulsifying agents


Find the component statements of the
following compound statements and check whether they are true or false
(i) Number 3 is prime or it is odd
(ii) All integers are positive or negative
(iii)100 is divisible by 3,11 and 5


In which of the following reactions, the product obtained is chiral?
A. \( C H_{3} C O C H_{3} \stackrel{N a B H_{4}}{\longrightarrow} \)
B. \( C H_{3} \) COCl Rosenmund's reduction
c. \( C H_{3} C H_{2} C O_{2} C H_{2} C H_{3} \stackrel{S n, H C l}{\longrightarrow} \)
D. \( C H_{3} C H_{2} C O C H_{3} \stackrel{L i A H H_{4}}{\longrightarrow} \)


Find the sum: \( \frac{1}{2}+\frac{1}{4}+\dots \dots \dots+\frac{1}{2^{10}} \)


In antarctica, ozone depletion is due to the formation of which of the following compounds?
A. Acrolein
B. PAN
c. PCBs
D. Chlorine nitrate


In the following compound, groups
designated as \( A, B, C \) will be numbered
as:
\( A .3,2,1 \)
3. 6,1,2
\( c .3,1,2 \)
D. 1,2,3


Write the dimensions of \( \boldsymbol{E} / \boldsymbol{B} \). Here \( , \boldsymbol{E} \) is
the electric field and \( B \) is the magnetic field.


Draw the diagram showing froth floatation method and label its parts


If \( \sin ^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}+\dots \dots \dots \dots \infty\right)+ \)
\( \cos ^{-1}\left(x^{2}-\frac{x^{4}}{2}+\frac{x^{6}}{4}-\dots \dots \dots \infty\right)=\frac{\pi}{2} \)
and \( 0<x<\sqrt{2} \) then \( x= \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-\frac{1}{2} \)
D. -


Define isotopes.


\( \int \frac{4 e^{x}+6 e^{-x}}{9 e^{x}-4 e^{-x}} d x=A x+B \log _{e}\left(9 e^{2 x}-4\right) \)
\( A=_{----}, B=_{----}, C= \)


Assertion
Displacement reactions of chlorine, bromine and iodine using fluorine are not generally carried out in aqueous Solution.
Reason
Fluorine being highly reactive attacks
water and displaces the oxygen of
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


In the figure, pulleys are smooth and
strings are massless \( m_{1}=1 k g \) and
\( m_{2}=\frac{1}{3} k g . \) To keep \( m_{3} \) at rest, \( m_{3} \)
should be
A. \( 1 k g \)
в. \( \frac{1}{2} k g \)
c. \( \frac{4}{3} k g \)
D. \( 2 k \)


The displacement of a particle varies
with time according to the relation \( y= \)
asin\omegat \( + \)bcos\omegat.
A. The motion is oscillatory but not SHM.
B. The motion is SHM with amplitude a + b.
c. The motion is SHM with amplitude \( a^{2}+b^{2} \)
D. The motion is SHM with amplitude \( \sqrt{a^{2}+b^{2}} \)


Which is the principal cation in the plasma of the blood
A. Calcium
B. Sodium
c. Potassium
D. Magnesium


What is true about telophase stage of
mitosis?
A. Chromosomes lose their identity as discrete elements.
B. Chromosomes cluster at opposite spindle poles.
C . Nuclear envelope, nucleolus, Golgi complex and ER reform.
D. All of these


If the distance between the place of a parallel plate capacity \( 10 \mu F \) is doubled, then new capacity will be:
A \( .5 \mu F \)
в. \( 20 \mu F \)
c. \( 10 \mu F \)
D. \( 15 \mu F \)


Which of the following method is used
for extracting metals from ores?
A. Reduction
B. Melting
c. Electrolysis
D. Both \( A \) and \( C \)


It is hotter at the same distance over
the top of a fire than it is on the side of
it mainly because
A. Heat is radiated upwards
B. Air conducts heat upwards
c. convection takes more heat upwards
D. conduction, convection and radiation all contribute significantly in transferring heat upwards


The smallest natural number by which 1296 be divided to get a perfect cube is
A . 16
B. 6
\( c \cdot 60 \)
D. none of these


Between two similar or dissimilar
atoms, only one sigma bond is possible whereas two pi bonds can be formed
between them. Explain.


Positive charge in an atom is :
A. Scattered all over the atom
B. Concentrated in the nucleus
c. Revolving around the nucleus
D. None of these


Hormone inducing fruit ripening is
A. Cytokinin
B. Ethylene
c. Abscissic acid
D. Gibberellic acid


Snow on the mountain top does not melt
as a consequence of
A. high specific latent heat capacity of ice
B. low specific latent heat capacity of ice
C. high specific heat capacity of water
D. low specific heat capacity of water


Which of the following is not the measure of dispersion.
A. Quartile Deviation
B. Range
c. Mean Deviation
D. None of these


The non-zero vectors \( \vec{a}, \vec{b} \) and \( \vec{c} \) are related by \( \vec{a}=8 \vec{b} \) and \( \vec{c}=-7 \vec{b}, \) then the
angle between \( \vec{a} \) and \( \vec{c} \) is
A \( \cdot \frac{\pi}{2} \)
в. \( \pi \)
\( c \cdot 0 \)
D.


A copper wire with a cross-section area
of \( 2 \times 10^{-6} m^{2} \) has a free electon
density equal to \( 5 \times 10^{22} / c m^{2} . \) If this
wire carries a current of \( 16 A \), the drift
velocity of the electron is?
\( \mathbf{A} \cdot 1 m / s \)
в. \( 0.1 m / s \)
c. \( 0.01 m / s \)
D. \( 0.001 m / s \)
E. \( 0.00001 \mathrm{m} / \mathrm{s} \)


Solve the following differential equation \( \frac{d y}{d x}=\sec ^{2} x \)


Total number of inner transition
elements are :


The following diagram shows a protein coding DNA and specifies the positions of its translational start and stop
signals
\( 5^{\prime} . . . . . . . . \mathrm{G} \mathrm{AT} \ldots . . . . . . . \)
Which of the following statements with
regard to template strand for the RNA
polymerase and the C-terminus of the
resulting protein is true?
A. Upper is template strand, carboxy terminus of protein to right.
B. Upper is template strand, carboxy terminus of protein to left
C. Lower is temperate stand, carboxy terminus of protein to right.
D. Lower is template strand, carboxy terminus of protein to left.
E. Either strand could be a template on basis of this information


The protein \( \alpha-1 \) antitrypsin is used to
treat which of the following disease?
A. Cancer
B. Rhematoid arthritiss
c. Emphysema
D. ADA deficiency disease in children


Which polymer is used in non-stick
cooking vessels?
A. Polythene
B. Isoprene
c. Teflon
D. Neoprene


Identify \( F: \)
\( \mathbf{A} \cdot H F \)
в. \( N H_{3} \)
c. \( H N_{3} \)
D. None ofthese


What is the dimensional formula of
Inductance?
\( \mathbf{A} \cdot\left[M L^{2} T^{-2} A^{-2}\right] \)
B . \( \left[M L^{2} T A^{-2}\right] \)
\( \mathbf{c} \cdot\left[M L^{2} T^{-1} A^{-2}\right. \)
D \( \cdot\left[M L^{2} T^{-2} A^{-1}\right] \)


Unit of latent heat of fusion is :
\( A \cdot K \)
B. J/Kgg
\( c \cdot J / K \)
D. J/Kg-K


Tricuspid valve is present between
A. Right atria and right ventricle
B. Both atria
C. Both ventricles
D. Left atria and left ventricle


Among the nitrogenous base involved in DNA and RNA formation, which is the
double ring base?
A. Uracil
B. Guanine
c. Thymine
D. Cytosine


Which of the following order regarding the size of hybrid orbital of carbon is
correct?
\( \mathbf{A} \cdot s p>s p^{2}>s p^{3} \)
B . \( s p<s p^{2}<s p^{3} \)
C \( . s p>s p^{2}<s p^{3} \)
D \( \cdot s p<s p^{2}>s p^{3} \)


\( \boldsymbol{C H}_{2}=\boldsymbol{C H}-\boldsymbol{C} \equiv \boldsymbol{N} \)
Hybridisation state of \( N \) atom is:
\( A \cdot s p^{3} \)
B . \( s p \)
\( c \cdot s p^{2} \)
D. none of the above


The strength of gravity on Mars is only \( 40 \% \) of that on earth. If a child has a
mass of \( 60 \mathrm{kg} \) on earth, what would the
child's weight be on Mars?
A . 24
в. 60 N
c. \( 240 N \)
D. \( 600 N \)
E. None of the above is correct within \( 10 \% \)


Find the value of \( x \) in \( \left[\begin{array}{cc}2 x-y & 5 \\ 3 & y\end{array}\right]= \)
\( \left[\begin{array}{cc}\mathbf{6} & \mathbf{5} \\ \mathbf{3} & -\mathbf{2}\end{array}\right] \)


Which has larger lattice energy among \( Z n O \) and \( N a C l ? \)
A \( . Z n O>N a C l \)
в. \( Z n O<N a C l \)
c. \( Z n O=N a C l \)
D. None of these


In a projectile motion from a point of horizontal surface to another point on
the same surface (Take \( \overrightarrow{\boldsymbol{a}}= \)
acceleration and \( \vec{v}= \) instantaneous
velocity) This question has multiple correct options
A. \( \vec{a} \cdot \vec{v}=0 \) at maximum height
B . \( \vec{a} \cdot \vec{v}=0 \) only if angle of projection is \( 90^{\circ} \)
c. \( \vec{a} \times \vec{v}= \) constant every where in air
D. None of these


Choose the correct statements from the
following?
A. Rhombic sulphur is blue in colour.
B. Rhombic sulphur is soluble in water but insoluble in organic solvents
C. Rhombic and monoclinic sulphur have \( S_{6} \) molecules.
D. In Cyclo- \( S_{6} \) molecule, the ring adopts chair form.


The major product in the following reaction is:
\( \mathbf{A} \)
B.
c.
D.


Atoms combine through the:
A. interaction of protons
B. presence of catalyst
C. interaction of electrons
D. rise in temperature


Cell division is initiated by
A. Cytokinin
B. Auxin
c. Gibberellin
D. ABA


Explain with a suitable diagram and
appropriate examples why some nonideal solutions show positive deviation from ideal behaviour.


The sum of 100 terms of the
progression \( 5,5,5, \dots \dots \)


\( \boldsymbol{M B} \)
\( \mathbf{A} \cdot \overrightarrow{M B}=\frac{1}{2}(\bar{a}-2 \bar{b}) \)
B \( \cdot \overrightarrow{M B}=\frac{1}{2}(2 \bar{a}-\bar{b}) \)
C \( \cdot \overrightarrow{M B}=\frac{1}{2}(\bar{a}+2 \bar{b}) \)
D \( \cdot \overrightarrow{M B}=\frac{1}{2}(2 \bar{a}+\bar{b}) \)


Which of the following dihalobenzene is solid at room temperature?
A. Ortho
B. Meta
c. Para
D. None of these


State whether true or false.
The beating of the heart of a healthy person at rest is a non-periodic motion.
A. True
B. False


When an object is placed at a distance of \( 60 \mathrm{cm} \) from a convex mirror, the magnification produced is 1/2. Where should the object be placed to obtain a magnification of 1/3?


A body weight \( 72 N \) on the surface of
the earth. What is the gravitational force acting on it due to the earth at a height equal to half the radius of the earth from the surface?
A. \( 16 N \)
в. 32 N
c. \( 8 N \)
D. \( 48 N \)


Study the following graph carefully and
answer the question given What was the difference between the
number of B type tyres manufactured in
\( \mathbf{1 9 9 4} \) and \( \mathbf{1 9 9 5} ? \)
A .1,00,000
B. 20,00,000
c. 10,00,000
D. 12,50,000


A disc of mass \( m \) and radius \( r \) is free to
rotate about its center as shown in the
figure. A string is wrapped over its rim
and a block of mass \( m \) is attached to
the free end of the string. The system is released from rest. The speed of the
block as it descends through a height \( h \)
is?


In which form does the Light
propagates?
A. Electric waves
B. Magnetic waves
c. Electromagnetic waves
D. sound wave


A wheel of radius \( 1 \mathrm{m} \) rolls forward half
a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is
A \( .2 \pi m \)
В. \( \sqrt{2} \pi m \)
\( \mathbf{c} \cdot \sqrt{\pi^{2}+4 m} \)
D. \( \pi m \)