IUPAC name of \( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\right] \) is:
A. platinum diaminechloronitrite
B. chloronitrito-N-ammineplatinum (II)
c. diamminechloridonitrito-N-platinum (II)
D. diamminechloronitrito-N-platinate (II)


Show that the height of the cylinder of maximum volume that can be inscribed
\( \boldsymbol{h} \)
in a cone of height his


A body is projected horizontally from the top of a hill with a velocity of \( 9.8 m / s \) What time elapses before the vertical velocity is twice the horizontal velocity?
A . 0.5 sec
B. 1 sec
\( c .2 s e c \)
D. 1.5 sec


What are the coordinate of the centre of
mass of the three particles system
shown in figure?


The partial pressure of \( \boldsymbol{O}_{2} \) in air is 0.21 at \( m \) at sea level. If aquatic life
requires a concentration of \( \boldsymbol{O}_{2} \) at least
4.16 \( m g / \) litre, will the aquatic life
sustain in sea level lake. \( \boldsymbol{K}_{\boldsymbol{H}} \) for \( \boldsymbol{O}_{2} \) is \( 1.3 \times 10^{-3} \) mol / litre - atm.
A. 0.82 mg/litre
в. \( 0.87 \mathrm{mg} / \) litre
c. 0.95 mg/litre
D. \( 0.9 \mathrm{mg} / \) litre


are important decomposers that cause decay and decomposition of dead bodies of plants and animals.
A. Saprophytic bacteria
B. Saprotrophic fung
C. Plants like Sarracenia
D. Both (a) and (b)


Q Type your question
coll ana aırectea ınto the paper Is varying according to the relation \( \phi= \)
\( 6 t^{2}+7 t+1, \) where \( \phi \) is in milliweber
and \( t \) is in second. The magnitude of the
emf induced in the loop at \( t=2 s \) and
the direction of induce current through
\( \boldsymbol{R} \) are
8
A. 39 mV; right to left
B. 39 mV; left to right
c. \( 31 \mathrm{mV} ; \) right to left
D. 31 mV; left to right


What may be the stable oxidation state of the transition element with the
following delectron configurations in the ground state of their atoms:
\( 3 d^{3}, 3 d^{5}, 3 d^{8} \) and \( 3 d^{4} ? \)


x-y curve at an instant for a wave
travelling along \( x \) axis on a string is shown. Slope at the point \( A \) on the curve,
as shown, is \( 53^{\circ} \)
This question has multiple correct options
A. Transverse velocity of the particle at point A is positive if the wave is travelling along the positive x axis.
B. Transverse velocity of the particle at point A is positive if the wave is travelling along the negative x axis of the particle at point \( A \)
C. The magnitude of transverse velocity of the particle at point A is greater than the wave speed.
D. The magnitude of the transverse velocity of the particle at point A is lesser than wave speed


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


The angle between the normal and the
reflected ray is \( 40^{\circ} . \) Then the angle of incidence will be
A \( .50^{\circ} \)
B. \( 20^{\circ} \)
\( c \cdot 40^{\circ} \)
D. Can't be predicted


What is Henry's constant for neon
dissolved in water given \( C_{N e}= \) \( 23.5 m L / L \) solution and STP volume
\( 22,414 \mathrm{mL} / \text { mole gas }) \) and pressure \( \operatorname{atm}) ? \)
A. 0.00105
5
В. 0.11004
\begin{tabular}{l}
\( c .0 .00115 \) \\
\hline
\end{tabular}
D. 0.00015


The power of accommodation is achieved by by changing:
A. curvature of eye lens
B. focal length of eye lens
c. both A and B
D. neither A nor B


Determine uncertainty in the position of an electron moving with a velocity 300
\( \mathrm{m} \cdot \mathrm{sec}^{-1} \) accurate up to \( 0.001 \% \)
\( \left[h=6.63 \times 10^{-34} \mathrm{J} . \mathrm{s} \) and mass of \right.
electron \( =9.1 \times 10^{-31} \mathrm{kg} \)
A \( \cdot 1.92 \times 10^{-2} \mathrm{m} \)
в. \( 1.5 \times 10^{-2} \mathrm{m} \)
C. \( 2.5 \times 10^{-2} m \)
D. \( 2.5 \times 10^{-3} \mathrm{m} \)


The mean of a finite set \( X \) of numbers is
14, the median of this set of numbers is
\( 12, \) and the standard deviation is \( 1.8 . A \) new set Y is formed by multiplying each
member of the set \( \$ \) by \( 3 . \) Determine the correct statements w.r.t. set \( Y: \)
I. The mean of the numbers is set Y is 42
II. The median of the numbers in set Y is
\( \mathbf{3 6} \)
III. The standard deviation of the
numbers is set Y is 5.4
A. I only
B. II only
c. I and II only
D. I and III only
E. ।, ॥।, and ॥|


The energy of an electron in the first
Bohr orbit of H-atom is -13.6 eV. The
possible energy value(s) of the excited state(s) for electrons in Bohr orbits of
hydrogen is:
A. \( -3.4 e V \)
в. \( -4.2 e V \)
c. \( -6.8 e V \)
D. \( +6.8 e V \)


Assertion
A reaction which is spontaneous and accompanied by decrease of
randomness must be exothermic.
Reason
All exothermic reactions are
accompanied by decrease of
randomness.
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


Above conversion can be achieved by :
A \( \cdot \) Li \( A l H_{4} \)
в. \( N a B H_{4} \)
c. \( H_{2} / N i \)
\( \mathrm{D} \cdot \mathrm{CrO}_{3} \)


\( 33 \% \) marks are required to pass an examination. A candidate who gets 210
marks fails by 21 marks. What are the total marks for the examination.
A . 700
в. 650
c. 600
D. 550


Number of chiral isomers are:
\( A \)
B. 3
\( c \)
D. none of these


The value of \( \lim _{x \rightarrow 0} \frac{(1+x)^{1 / 4}-(1-x)^{1 / 4}}{x} \)
is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-1 \)
D. \( -\frac{1}{2} \)


Name the body structure concerned
with the given functional activity. Provides actual diffusion of respiratory gases in lungs.


Select the correct statement about
elements of group \( 15^{t h} \)
A. the order of stability of oxidation state of +3 is \( B i^{3+}> \) \( S b^{3+}>A s^{3+} \) and for +5 is \( B i^{5+}<S b^{5+}<A s^{5+} \)
B. in case of nitrogen, all oxidation states from +1 to +4 tend to disproportionate in acid solution
C. there is a considerable increase in covalent radius
from \( \mathrm{N} \) to \( \mathrm{P} \) but from As to Bi only a small increase in covalent radius is observed
D. all of the above


The radius and density of two
artificial satellites are \( \boldsymbol{R}_{1}, \boldsymbol{R}_{2} \) and \( \boldsymbol{\rho}_{1} \)
\( \rho_{2} \) respectively. The ratio of
accelerations due to gravity on them will be:
\( \mathbf{A} \cdot \frac{R_{2} \rho_{2}}{R_{1} \rho_{1}} \)
в. \( \frac{R_{1} \rho_{2}}{R_{2} \rho_{1}} \)
c. \( \frac{R_{1} \rho_{1}}{R_{2} \rho_{2}} \)
D. \( \frac{R_{2} \rho_{1}}{R_{1} \rho_{2}} \)


Choose the correct statement
A. Brewster's angle is independent of the wavelength of light.
B. Brewster's angle is independent of nature of reflecting the surface.
C. Brewster's angle is different for different wavelengths.
D. Brewster's angle depends on the wavelength but not on the nature of reflecting the surface.


If a leap year is selected at random,
what is the chance that it will contain
53 tuesdays?


Fill in the blank:
When the angle of incidence increases, glancing angle of reflection
A. increases
B. remains same
c. decreases
D. becomes infinite


Placentation in Brassicaceae is
A. Parietal
B. Marginal
c. Axile
D. Basal


Which of the following is most soluble?
A \( \cdot B i_{2} S_{3}\left(K_{s p}=1 \times 10^{-17}\right) \)
B . \( \operatorname{MnS}\left(K_{s p}=7 \times 10^{-16}\right) \)
c. \( C u S\left(K_{s p}=8 \times 10^{-37}\right) \)
D. \( A g_{2} S\left(K_{s p}=6 \times 10^{-51}\right) \)


Movement of dispersion medium under the influence of electric field is known
as:
A. electrodialysis
B. electrophoresis
c. electroosmosis
D. cataphoresis


An unknown compound has molecular
formula \( C_{7} H_{12} \)
The unknown reacts with \( H_{2} \) in
presence of Pt at high temperature to
give \( C_{6} H_{16} . \) What information does this
provide about the structure of unknown?
A.


A quadratic equation \( a x^{2}+b x+c=0 \)
with distinct coefficients is formed. It a
b, c are chosen from the numbers 2,3,5 then the probability that the equation has real roots is
A \( \cdot \frac{1}{3} \)
B. \( \frac{2}{5} \)
\( c \cdot \frac{1}{4} \)
D.
E \( \cdot \frac{2}{3} \)


Find the measure of the supplementary
angle of \( 132^{\circ} \)
A \( \cdot 48^{\circ} \)
B. \( 32^{\circ} \)
\( c \cdot 42^{\circ} \)
\( D \cdot 38^{\circ} \)


During summer sault, a swimmer bends his body to
A. Increase moment of Inertia
B. Decrease moment of Inertia
c. Decrease the angular momentum
D. Reduce the angular velocity


Which is not true for glycolysis?
A. End product is \( C O_{2} \) and \( H_{2} O \)
B. Substrate level phosphorylation
c. Production of ATP
D. Expenditure of ATP


The slope of the tangent to the curve \( \boldsymbol{x}=\mathbf{3} \boldsymbol{t}^{2}+\mathbf{1}, \boldsymbol{y}=\boldsymbol{t}^{3}-\mathbf{1} \) at \( \boldsymbol{x}=\mathbf{1} \) is
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot-2 \)
\( D \cdot \infty \)


In the process of electromagnetic induction, the magnitude of the induced emf does not depend on
A. The number of turns of the coil
B. The magnetic flux linked with the coil
c. The rate of change of magnetic flux linked with the coil
D. Area of the coil


How does exchange of respiratory gases take place in the alveoli or lungs?


Give Reason:
A histogram is not a diagram.


Which of the following would not react
with benzene sulphonyl chloride in aq.
NaOH ?
A. Aniline
B. Methylamine
c. \( N, N \) -dimethyl aniline
D. \( N \) -methyl aniline


In a galvanic cell, the salt bridge:
A. does not participate chemically in the cell reaction
B. stops the diffusion of ions from one electrode to another
C. is necessary for the occurrence of the cell reaction
D. ensures mixing of the two electrolytic solutions


After you have dinner tonight wash your own plate with soap / detergent.
(a) What colour change is observed when soap / detergent is applied?
(b) Name the type of reaction and explain it.


Find \( g o f \) and \( f o g, \) if \( (i) f(x)=|x| \) and
\( g(x)=|5 x-2| \)
ii) \( f(x)=8 x^{3} \) and \( g(x)=x^{\frac{1}{3}} \)


A particle of mass \( m \) is made to move
with uniform speed \( v_{0} \) along the
perimeter of a regular hexagon, inscribed in a circle of radius \( \boldsymbol{R} \). The
magnitude of impulse applied at each corner of the hexagon is:
\( \mathbf{A} \cdot 2 m v_{0} \sin \pi / 6 \)
в. \( m v_{0} \sin \pi / 6 \)
c. \( m v_{0} \sin \pi / 3 \)
D. \( 2 m v_{0} \sin \pi / 3 \)


Above \( (\boldsymbol{C}-\boldsymbol{N}) \) coupling reaction take
place at:
A . low \( p H \)
B. nearly nutral \( p H \)
\( c . \) high \( p H \)
D. any \( p H \)


Differentiate \( \boldsymbol{y}=\cos (2 x-5) \) with
respect to \( x \)


Which endocrine gland produces the
growth hormone?


Aluminium does not react with:
A . NaOH
в. нс
c. \( N_{2} \)
D. \( H N O_{3} \)


The carbonate and silicate ore of zinc is
called as
A. Calamine, pyrite
B. Calamine, hemimorphite
c. Hemimorphite, cryolite
D. cryolite, calamine


Solve the following pair of simultaneous equations:
\( \frac{\mathbf{3}}{\mathbf{a}}+\frac{\mathbf{4}}{\mathbf{b}}=\mathbf{2} ; \frac{\mathbf{9}}{\mathbf{a}}-\frac{\mathbf{4}}{\mathbf{b}}=\mathbf{2} \)
A \( . a=3, b=4 \)
в. \( a=1, b=-2 \)
c. \( a=5, b=-3 \)
D. \( a=0, b=6 \)
6


Find the differential equation of the family of all the circles.
(A) touching X-axis at the origin.
(B) touching Y-axis at the origin.


The diagram alongside shows the refraction of a ray of light from air to a liquid. The refractive index of liquid
with respect to air is :
\( 4 \sqrt{\frac{1}{2}} \)
B. \( \sqrt{\frac{2}{3}} \)
\( c \cdot \sqrt{\frac{3}{2}} \)
D. \( \sqrt{3} \)


At \( 400^{\circ} \mathrm{C}, \) the vapour pressure of water
is 55.3 mm \( H g \). Calculate the vapour
pressure at the same temperature over
\( 10 \% \) aqueous solution of urea
\( \left[\boldsymbol{C O}\left(\boldsymbol{N} \boldsymbol{H}_{2}\right)_{2}\right] ? \)


Which portion of the basilar membrane vibrates most vigorously in response to high-pitch sounds?


What is ozone depletion?


Give the correct IUPAC names of the
following:
2-Vinyl propane


Assertion
An electric field \( \vec{E} \) is induced in a
closed loop where magnetic flux is varied.The induced \( \overrightarrow{\boldsymbol{E}} \) is not a
conservative field
Reason The line integral \( \vec{E} . \overrightarrow{d l} \) around the closed loop is nonzero
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


When \( A g N O_{3} \) is added to a solution of
\( \boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{C l}_{3}, \) the precipitate of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l} \)
shows two ionized chloride ions. This
means:
This question has multiple correct options
A. only two chlorine atoms satisfy primary valency and one secondary valency
B. one chlorine atom satisfies primary as well as secondary valency
c. two chlorine atoms satisfy primary valency
D. three chlorine atoms satisfy secondary valency


In Figure \( 5, \) rectangle \( A B C D \) is
inscribed in a circle. If the radius of the
circle is 2 and \( \overline{C D}=2, \) find the area of
the shaded region.
A. 0.36
3. 0.47
7
\( c .0 .57 \)
D. 0.707
\( =0.86 \)


Solve: \( 3 x+4 y=10,2 x-2 y=2 \) by the
method of elimination.


When a particle moves in a circle with a
uniform speed
A. its velocity and acceleration are both constant
B. its velocity is constant but the acceleration changes
C. its acceleration is constant but the velocity changes
D. its velocity and acceleration both change


Circles with centres \( A, B \) and \( C \) touch
each other externally. If \( \boldsymbol{A B}= \)
\( \mathbf{3} c \boldsymbol{m}, \boldsymbol{B} \boldsymbol{C}=\mathbf{3} \boldsymbol{c m}, \boldsymbol{C} \boldsymbol{A}=\mathbf{4} \boldsymbol{c m}, \) then
find the radii of each circle


Given below are the half-cell reactions:
\( M n^{2+}+2 e^{-} \rightarrow M n ; E^{o}=-1.18 V \)
\( \mathbf{2}\left(\boldsymbol{M} \boldsymbol{n}^{+\mathbf{3}}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+}\right) ; \boldsymbol{E}^{\boldsymbol{o}}= \)
\( +1.51 V \)
The \( \boldsymbol{E}^{o} \) for \( \boldsymbol{3} \boldsymbol{M} \boldsymbol{n}^{2+} \rightarrow \boldsymbol{M} \boldsymbol{n}+\boldsymbol{2} \boldsymbol{M} \boldsymbol{n}^{3+} \)
will be:
A. \( +0.33 V ; \) the reaction will occur
B. \( -2.69 V \); the reaction will not occur
c. \( +2.69 V ; \) the reaction will occur
D. \( -0.33 V \); the reaction will not occur


In order to find the density of a solid we have to first know its :
\( A . \) mass and area
B. weight and area
c. shape and volume
D. mass and volume


The value of \( \left|\begin{array}{ccc}\boldsymbol{a}+\boldsymbol{p} \boldsymbol{d} & \boldsymbol{a}+\boldsymbol{q} \boldsymbol{d} \boldsymbol{a}+\boldsymbol{r} \boldsymbol{d} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} \\ \boldsymbol{d} & \boldsymbol{f} & \boldsymbol{d}\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
\( c \cdot 1 \)
D. \( p+q+r \)


Epipetalous stamen, obliquely placed placenta and fruit berry or capsule are diagnostic feature of family
A . Cruciferae
B. Solanceae
c. Malvaceae
D. Labiatae


Soil erosion is common in areas devoid
of vegetation cover.Why?


A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation
\( \boldsymbol{y}(\boldsymbol{x}, \boldsymbol{t})= \)
\( 0.01 m \sin \left[\left(62.8 m^{-1}\right) x\right] \cos \left[\left(628 s^{-1}\right) t\right] \)
Assuming \( \pi=3.14, \) the correct statement(s) is/are

This question has multiple correct options
A. The number of nodes is 5
B. the length of the string is 0.25 m
c. The maximum displacement of the midpoint of the string, fom its equilibrium position is \( 0.01 m \).
D. The fundamental frequency is \( 100 H z \)


400 g of vegetable oil of specific heat capacity \( 1.98 J g^{-1} o C^{-1} \) is cooled from
\( \mathbf{1 0 0}^{\circ} \boldsymbol{C} \). Find the final temperature, if the heat energy given out by oil is \( 47376 \mathrm{J} \)
A \( .30 .2^{\circ} \mathrm{C} \)
в. \( 40.2^{\circ} \mathrm{C} \)
c. \( 50.2^{\circ} \mathrm{C} \)
D. \( 43.2^{\circ} \mathrm{C} \)


A circular coil a carrying current
produces a magnetic field \( B_{0} \) at its
centre. This coil is made itself to 10
turns and the same current is set up in
it. The magnetic field \( B \) at its centre
would be
A. \( B=B_{0} \)
В. \( B=10 B_{0} \)
c. \( B=50 B_{0} \)
D. \( B=100 B_{0} \)


Write balanced equations for:
(i) \( \boldsymbol{B} \boldsymbol{F}_{3}+\boldsymbol{L} \boldsymbol{i} \boldsymbol{H} \rightarrow \)
(ii) \( B_{2} H_{6}+H_{2} O \rightarrow \)
(iii) \( N a H+B_{2} H_{6} \rightarrow \)
(iv) \( H_{3} B O_{3} \stackrel{\leftrightarrow}{\rightarrow} \)
(v) \( A l+N a O H \rightarrow \)
(vi) \( B_{2} H_{6}+N H_{3} \rightarrow \)


Measure of \( \angle B \) and \( \angle C \) are
\( \mathbf{A} \cdot 75^{\circ}, 85 \)
B \( \cdot 75^{\circ}, 75 \)
\( \mathbf{c} \cdot 55^{\circ}, 55^{\circ} \)
D. \( 65^{\circ}, 65^{\circ} \)


\( f\left(x_{A}=2 V \) calculate current flowing \right.
through the circuit and calculate \( V_{B} \)
and \( V_{C} ? \)


Nitrogen is restricted to a maximum
covalency of 4 since only four (one s and three \( p \) ) orbitals are available for
bonding. The heavier elements have vacant d orbitals in the outermost shell
which can be used for bonding (covalency) and hence, expand their
covalence as in \( \boldsymbol{P} \boldsymbol{F}_{\mathbf{6}}^{-} \)


If the radius of the earth is reduced by \( 1 \% \) keeping the mass constant. The escape velocity will :
A. increase by \( 0.5 \% \)
B. decrease by \( 0.5 \% \)
c. decrease by \( 11 \% \)
D. remain same


The value of \( \int_{1}^{3} x^{2} d x \) is:
A \( \cdot \frac{26}{3} \)
в. \( \frac{28}{3} \)
c. \( \frac{25}{3} \)
D. None of these


Which of the following process does not
occur during the formation of \( \boldsymbol{C H C l}_{3} \)
from \( C_{2} H_{5} O H \) and \( C a O C l_{2} ? \)
A. Hydrolysis
B. Oxidation
c. Reduction
D. chlorination


If \( a_{k}, b_{k}, c_{k} \epsilon R \) for \( k=1,2,3 \) and
\( \left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \boldsymbol{c}_{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \boldsymbol{c}_{2} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & \boldsymbol{c}_{3}\end{array}\right| \)
then sum of the roots of the equation \( \left|\begin{array}{lll}a_{1}+i b_{1} x & i a_{1} x+b_{1} & c_{1} \\ a_{2}+i b_{2} x & i a_{2} x+b_{2} & c_{2} \\ a_{3}+i b_{3} x & i a_{3} x+b_{3} & c_{3}\end{array}\right| \)
is
\( \mathbf{A} \cdot a_{1}+a_{2}+a_{3} \)
B. \( b_{1}+b_{2}+b_{3} \)
\( \mathbf{c} \cdot a_{1} b_{1}+a_{2} b_{2}+a_{3} b_{3} \)
D. none of these


When the rubber band is stretched, it
heats up and it cools down if it is suddenly released. This is depicted using
A. the area under the hysteresis curve
B. the x intercept of the hysteresis curve
c. the y intercept of the hysteresis curve
D. the saturation point of the hysteresis curve


Tropical cyclones that originate in the Chine sea are?
A. Hurricanes
B. Typhoons
c. Tornadoes
D. Cyclones


If the magnitude of the cross product of two vector is \( \sqrt{3} \) times to the
magnitude of their scalar product the angle between two vector will be :
\( A \)
B.
c.
D.


Evaluate \( \lim _{x \rightarrow \infty} \sqrt{x^{2}+x+}-\sqrt{x^{2}+1} \)


When a small quantity of \( \boldsymbol{F e C l} \) la solution is added to the fresh
precipitate of \( \boldsymbol{F e}(\boldsymbol{O H})_{3}, \) a colloidal sol is obtained. The process through which this sol is formed is known as:
A. exchange of solvent
B. chemical double decomposition
c. peptization
D. electrophoresis


The following acids have been arranged in the order of decreasing acid strength. Identify the correct orderCIOH(I) \( \quad \) BrOH(II) \( \quad \mid O H(\| I) \)
B. ॥>1>111
\( c \cdot\|\mid>\|>1 \)


\( \bar{\sigma} \)
\( d \)
\( \alpha \)


Differentiate: \( \log \left(\cos e^{x}\right) \)


Fluorine shows only +1,-1 oxidation state while other halogen element
shows +3,+5 and +7 oxidation states
in addition to \( +1,-1, \) why?


Which of the following is not a property of covalent compounds?
A. Low boiling points
B. Solids are brittle and variously colored
c. Poor conductors of heat and electricity
D. Superior malleability


Identify the name of the following reaction. \( \boldsymbol{C H}_{3} \boldsymbol{B r}+\boldsymbol{N a I} \stackrel{\text {dryacetone}}{\longrightarrow} \boldsymbol{C H}_{3} \boldsymbol{I}+ \)
\( N a B r \)
A. Finkelstein reaction
B. Gattermann reaction
c. sandmeyer reaction
D. Wurtz reaction


How can you demonstrate the process of atmospheric pressure experimentally?


Which of the following polymers can be made by free radical addition polymerisation mechanism? This question has multiple correct options
A . PE
B. HDPE
c. LDPE
D. Telfon


Prove that the points \( \boldsymbol{A}(\mathbf{1}, \mathbf{7}), \boldsymbol{B}(\mathbf{4}, \mathbf{2}), \boldsymbol{C}(-\mathbf{1},-\mathbf{1}) \) and
\( D(-4,4) \) are the vertices of a square.


Given \( \boldsymbol{A}=\{\mathbf{2}, \mathbf{3}, \mathbf{5}\} \) and \( \boldsymbol{B}= \)
\{6,10,14,18\}\( ; \) find the number of elements in relation \( R \) such that \( R= \)
\( \left\{(x, y) \in A \times B, x<y \text { and } \frac{y}{x} \epsilon N\right\} \)


Find the sum of \( 7+10 \frac{1}{2}+14+\ldots+84 \)
A \( \cdot \frac{2093}{2} \)
в. \( \frac{1093}{2} \)
c. \( \frac{2193}{2} \)
D. \( \frac{3093}{2} \)


A vessel contains oil (density =
\( 0.8 g / c m^{3} \) ) over mercury (density \( = \) \( \left.13.6 g / c m^{3}\right) . \) A uniform sphere floats with half its volume immersed in
mercury and the other half in oil. The
density of the material of sphere in \( \boldsymbol{g} / \boldsymbol{c m}^{3} \) is
A . 3.3
B. 6.4
c. 7.2
D. 12.8


Which of the following transformations
is not correct?
\( \mathbf{A} \cdot_{33}^{75} A s+_{2}^{4} H e \longrightarrow_{35}^{78} B r+_{0}^{1} n \)
B . \( _{3}^{7} L i+_{1}^{1} H \longrightarrow_{4}^{7} B e+_{0}^{1} n \)
C. \( 45 \mathrm{Sc}+_{0}^{1} n \longrightarrow_{20}^{45} \mathrm{Ca}+_{0}^{1} n \)
\( n \)
D. \( _{83}^{099} \mathrm{Bi}+_{1}^{2} \mathrm{H} \longrightarrow_{84}^{210} \mathrm{Po}+_{0}^{1} n \)


Give the formula of each of the following
coordination entities:
(i) \( C o^{3+} \) ion is bound to one \( C l^{-} \), one
\( N H_{3} \) molecule and two bidentate
ethylene diamine (en) molecule.
(ii) \( N i^{2+} \) ion is bound to two water
molecules and two oxalate ions.
Write the name and magnetic behavior of each of the above coordination entities. (At. no.: \( \mathrm{Co}=27, \mathrm{Ni}=28 \) )


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


Give the functional group of the following.
\( -\mathrm{CHO} \)
A. Aldehydic group
B. Alcoholic group
c. Ketonic group
D. Carboxylic group


The degree of constant polynomial is
A .
B. 2
c. 0
\( D \)


Particles \( P \) and \( Q \) of masses \( 20 g \) of \( 40 g \) respectively are projected from the
positions \( A \) and \( B \) on the ground. The
initial velocities of \( \boldsymbol{P} \) and \( \boldsymbol{Q} \) make
angles of \( 45^{\circ} \) and \( 135^{\circ} \) respectively with
the horizontal as shown in the figure. Each particle has an initial speed of \( 49 m / s . \) The separation \( A B \) is \( 245 m \)
Both particles travel in the same vertical plane and undergo a collision After the collision \( P \) retraces its path.
What is the distance of \( Q \) (w.r.t its
initial position) where it hits the ground?


Draw the graph of \( 2 x+y=6 \) and \( 2 x- \)
\( \boldsymbol{y}+\mathbf{2}=\mathbf{0} . \) Shade the region bounded by
these lines and \( x-y . \) Find the area of
the shaded region.


Which of the following reactions occur
at the cathode during the charging of
lead storage battery?
\( \mathbf{A} \cdot P b^{2+}+2 e^{-} \rightarrow P b \)
B \( \cdot P b^{2+}+S O_{4}^{2-} \rightarrow P b S O_{4} \)
\( \mathbf{c} \cdot P b \rightarrow P b^{2+}+2 e^{-} \)
D \( \cdot P b S O_{4}+2 H_{2} O \rightarrow P b O_{2}+4 H^{+}+S O_{4}^{2-}+2 e^{-} \)


If \( \rho \) is the density, \( m \) is the mass of 1
molecule and \( K \) is the Boltzman constant
for a gas then the pressure of the gas is:
A \( \cdot P=\frac{\rho K T}{m} \)
B. \( P=\frac{m K T}{\rho} \)
c. \( _{P}=\frac{\rho m T}{K} \)
D. \( P=\rho K m T \)


At \( 298 K, \) the equilibrium constant for the reaction
\( Z n^{2+}+4 N H_{3} \rightleftharpoons\left[Z n\left(N H_{3}\right)_{4}\right]^{2} \) is \( 10^{\circ} \)
If \( \boldsymbol{E}_{\left[Z n\left(N H_{3}\right)^{4}\right]^{2} /\left[Z n, 4 N H_{3}\right]}=-1.03 V \) then
the value of \( E_{Z n / Z n^{2+}}^{o} \) will be:
A. \( -0.7654 V \)
в. \( -1.1 V \)
c. \( +1.1 V \)
D. none of these


An equilateral triangle is constructed between two parallel line \( \sqrt{\mathbf{3}} x+\boldsymbol{y}- \)
\( 6=0 \) and \( \sqrt{3} x+y+9=0 \) with base
on one and vertex on the other. Then the
area of triangle is ?


\( C H_{3} C H_{2} O H \) on reaction with
bleaching powder forms:
A \( . C H C l_{3} \)
в. \( C C l C H O \)
c. \( C H_{2} \) ClCHO
D. \( C C l_{4} \)


When an \( \alpha \) -particle is
emitted
A. element moves 2 places to the right in the periodic table
B. element moves one place to the left
C. element moves 2 places to the left in the periodic table
D. elements maintains its position


\( \cos \left[2 \cos ^{-1} \frac{1}{5}+\sin ^{-1} \frac{1}{5}\right]= \)


Correct pathway of water movement in
plant roots is
A. Soil water \( \longrightarrow \) Root hair cell \( \longrightarrow \) Passage cells \( \longrightarrow \) Cortical cells \( \longrightarrow \) Xylem \( \longrightarrow \) Pericycle
B. Soil water \( \longrightarrow \) Root hair cell \( \longrightarrow \) Pericycle \( \longrightarrow \) Cortical cells \( \longrightarrow \) Passage cells \( \longrightarrow \) Xylem
C. Soil water \( \longrightarrow \) Root hair cell \( \longrightarrow \) Cortical cells \( \longrightarrow \) Passage cells \( \longrightarrow \) Pericycle \( \longrightarrow \) Xylem
D. Soil water \( \longrightarrow \) Root hair cell \( \longrightarrow \) Cortical cells \( \longrightarrow \)
Pericycle \( \longrightarrow \) Passage cells \( \longrightarrow \) Xylem


\( P b O_{2} \) is :
This question has multiple correct options
A. acidic.
B. basic.
C . reducing agent.
D. oxidizing agent.


Fill in the blanks
\( (-8)+(-3)= \)


In rabbit and humans, the kidney is
A. Metanephric
B. Mesonephric
c. Pronephric
D. Opisthonephric


\( \lim _{x \rightarrow \frac{\pi}{2}} \frac{\left[1-\tan \left(\frac{x}{2}\right)\right][1-\sin x]}{1+\tan \left(\frac{x}{2}\right)[\pi-2 x]^{3}} \) is
A \( \cdot \infty \)
B.
c. 0
D. \( \frac{1}{32} \)


Ecological factors, which prevent a species from producing at its maximum rate is termed as
A. Survival curve
B. Ecological drift
c. Environmental resistance
D. None of the above


Which complex is more stable between
\( \left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]^{4-} \) and \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{6}\right]^{3-} ? \)


The complex ion \( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5}(\boldsymbol{O} \boldsymbol{N} \boldsymbol{O})\right]^{2+} \)
and \( \left[\boldsymbol{C o}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5} \boldsymbol{N} \boldsymbol{O}_{2}\right]^{2+} \) are called
A. linkage isomer
B. ionization isomer
c. co-ordination isomer
D. geometrical isomer


Which of the following is not a synthetic polymer?
A. Polyethylene
B. PVC
c. Nylon
D. Cellophane


A terahedron has vertices \( \boldsymbol{P}(\mathbf{1}, \mathbf{2}, \mathbf{1}) \)
\( Q(2,1,3), R(-1,1,2) \) and \( O(0,0,0) \)
The angle between the faces OPQ and PQR is :
A \( \cdot \cos ^{-1}\left(\frac{9}{35}\right) \)
B. \( \cos ^{-1}\left(\frac{19}{35}\right) \)
c. \( \cos ^{-1}\left(\frac{17}{31}\right) \)
D. \( \cos ^{-1}\left(\frac{7}{31}\right) \)


The heat produced by one gram of charcoal is:
A . 20
в. 29.6 k
c. 39.2 k
D. 50 J


Differentiate between conductors and
insulators (any two points).


If \( \overline{O A}=3 \bar{i}+\bar{j}-\bar{k},|\overline{A B}|=2 \sqrt{6} \) and \( A B \)
has the direction ratios 1,-1,2 then
\( |\boldsymbol{O} \boldsymbol{B}|= \)
A . \( \sqrt{35} \)
B. \( \sqrt{41} \)
c. \( \sqrt{26} \)
D. \( \sqrt{55} \)


The reaction used to prepare \( N a O H \)
from \( C a(O H)_{2} \) in earlier days is:
\( N a_{2} C O_{3}+C a(O H)_{2} \rightarrow 2 N a O H+ \)
\( \boldsymbol{C a C O}_{3} \downarrow \)
If true enter 1 , else enter 0 .


Application of adsorption
chromatography is/are
A. separation of relatively non polar, water insoluble compounds
B. seperation of isomers
C . purification of antibody fragments
D. all of the above


Q Type your question-
is pulled by means of a string attached
at \( \mathrm{D} \) and inclined at an angle of \( 30^{0} \) with
the horizontal, as shown in the figure. The force \( P \) which should be applied to
the string to just lift the block off the roller is approximately \( \left(\frac{M g}{n}\right) . \) Find the
value of \( n .\left(\text { Given } \sin 75^{0}=0.9660\right) \)
\( A \)
B. 2
\( c \cdot 4 \)
\( D \)


\( -675-(25)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. 100
\( c .700 \)
D. - 700


The ratio of two adjacent sides of a parallelogram is 2: 3 and its perimeter
is \( 50 \mathrm{cm} . \) Find its area if altitude
corresponding to large side is \( 10 \mathrm{cm} \)


A ladder makes an angle \( 30^{\circ} \) with the
floor and its lower end is 12 m away
from the wall. Find the length of the ladder


Given that \( \vec{P}+\vec{Q}=\vec{P}-\vec{Q} \). This can
be true when :-
A \( \cdot \vec{P}=\vec{Q} \)
B . \( \vec{Q} \) is a null vector
C. Niether \( \vec{P} \) and \( \vec{Q} \) is a null vector
D. \( \vec{P} \) is perpendicular to \( \vec{Q} \)


\( A \) line cuts the \( x \) -axis at \( A(7,0) \) and the y-axis at \( B(0,-5), \) A variable line \( P Q \) is
drawn perpendicular to \( A B \) cutting the
x-axis at \( \boldsymbol{P} \) and the \( y \) -axis at in \( \boldsymbol{Q} \)

If \( A Q \) and \( B P \) intersect at \( R, \) the locus
of \( \boldsymbol{R} \) is
A \( \cdot x^{2}+y^{2}+7 x-5 y=0 \)
B . \( x^{2}+y^{2}-7 x+5 y=0 \)
c. \( 5 x-7 y=35 \)
D. None of these


\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{O}_{2} \) reacts with
This question has multiple correct options
A. \( N a_{2} C O_{3} \)
в. \( C O_{2} \)
\( c . H F \)
D. HCl


A particle has an initial velocity of \( 9 m / s \) due east and a constant acceleration of \( 2 m / s^{2} \) due west. The distance covered by the particle in the fifth second of its motion is:
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( 0.5 \mathrm{m} \)
\( c .2 m \)
D. \( 0.25 m \)


Two numbers are selected at random
from integers 1 through \( 9 . \) If the sum is even, find the probability that both the
numbers are odd.


What is the curve which passes through the point (1,1) and whose slope is \( \frac{2 y}{x} ? \)
A . Circle
B. Parabola
c. Ellipse
D. Hyperbola


Any salt \( M C l_{2} \) is soluble in water. If the hydration energy should exceed the
lattice energy of \( M C l_{2} \)
A. True
B. False


f \( \boldsymbol{y}=\left[\begin{array}{cc}1 & 2 \\ -1 & 5\end{array}\right], \) find a matrix \( X \) such
that \( 2 \boldsymbol{X}+\boldsymbol{Y}=\left[\begin{array}{cc}\mathbf{5} & \mathbf{0} \\ -\mathbf{3} & \mathbf{3}\end{array}\right] \)


A wire made of the material of Young's modulus \( Y \) has an stress \( S \) applied to
it. If Poisson's ratio of the wire is \( \sigma \), the
lateral strain is:
\( ^{\text {A }} \cdot \frac{S}{Y} \)
в. \( \sigma \frac{Y}{S} \)
c. \( \sigma Y \times S \)
D. \( \frac{s}{\sigma Y} \)


Nitrogen is inert because:
A. it supports combustion
B. of low boiling point
C . of high electronegativity
D. dissociation energy of its molecule is fairly high


A car (open at the top) of mass \( 9.75 \mathrm{kg} \) is coasting along a level track at 1.36 \( \mathrm{m} / \mathrm{s}, \) when it begins to rain hard. The raindrops fall vertically with respect to the ground. When it has collected 0.5 kg of rain, the speed of the car is
A. \( 0.68 \mathrm{m} / \mathrm{s} \)
B. 1.29 \( \mathrm{m} / \mathrm{s} \)
c. \( 2.48 \mathrm{m} / \mathrm{s} \)
D. \( 9.8 \mathrm{m} / \mathrm{s} \)


Assertion
At high temperatures the sodium sulphate or potasium sulphate formed, forms a crust and sticks to the glass
apparatus.
Reason
The non volatile residue of the metal
sulphate remains in the vessel. The
dissolved nitrogen oxides are removed at reduced pressure to give fuming nitric 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. Both Assertion and Reason are incorrect


Ordered pairs \( (x, y) \) and (-1,-1) are
equal if \( \boldsymbol{y}=-\mathbf{1} \) and \( \boldsymbol{x}= \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
c. 0
D. 2


How much \( O_{2} \) gas will be collected at
the anode at \( 300 K \) temperature and 1
bas pressure if 2.5 ampere electric
current is passed for one hour in electrolysis of aqueous solution of \( N a_{2} S O_{4} .(F=96500 \text { Coulomb) }[1\text { mole } \)
gas volume is 22.4 litre at STP].


The incident ray, reflected ray and the normal, to the interface of any two given mediums; all lie in the same plane this is
called laws of refraction of light.Type 1 for true and 0 for flase


A capacitor of capacitance \( C \) has initial
charge \( Q_{0} \) and connected to an inductor
of inductance \( L \) as shown. At \( t=0 \) switch
S is closed. The current through the inductor when energy in the capacitor is three times the energy of inductor is
A \( \cdot \frac{Q_{0}}{2 \sqrt{L C}} \)
в. \( \frac{Q_{0}}{\sqrt{L C}} \)
c. \( \frac{2 Q_{0}}{\sqrt{L C}} \)
D. \( \frac{4 Q_{0}}{\sqrt{L C}} \)


Radius of nucleus may be given as \( \boldsymbol{R}_{N}=\boldsymbol{R}_{0} \boldsymbol{A}^{1 / 3}, \) where \( \boldsymbol{A}= \) mass
number and \( R_{0}= \) constant. Calculate
the density of nucleus of an atom if \( \boldsymbol{R}_{0}=\mathbf{1 . 2} \times \mathbf{1 0}^{-\mathbf{1 5}} \)


\( \mathbf{f}|\boldsymbol{z}-\mathbf{1}+\boldsymbol{i}|+|\boldsymbol{z}+\boldsymbol{i}|=\mathbf{1} \) then find
range of principle argument of z.


What is the correct order of covalent
size of the following?
Ca
A. \( C a=S c \)
в. \( C a<S c \)
\( \mathbf{c} \cdot C a>S c \)
D. Noneofthese


What is the total pressure of the dry gas collected if the vapor pressure due to
water at \( 25^{\circ} C \) is 24 mm Hg\( ? \)
A. \( 24 \mathrm{mm} \mathrm{Hg} \)
в. \( 240 \mathrm{mm} \mathrm{Hg} \)
\( \mathbf{c} .736 \mathrm{mm} \mathrm{Hg} \)
D. \( 760 \mathrm{mm} \mathrm{Hg} \)


Which of the following will have highest
value of \( p K a ? \)
A. \( F C H_{2} C H_{2} \) СООН
в. \( C H_{3} C H(F)- \) СООН
c. \( C H_{3} C H(B r)-C O O H \)
D. \( C H_{3} C H_{2} C O O H \)


Solid \( N_{2} O_{5} \) is :
A. lonic
B. Covalent
c. coordinate
D. None


Write any two chemical different
between DNA and RNA.


In haemoglobin, which of the following amino acids acts as a blood
buffer?
A. Histidine
B. Glutamine
c. Aspartic acid
D. Lysine


Calculate the weight of \( N a O H \) present
in \( 500 m l \) of \( 0.2 M N a O H \) solution


A system absorbs \( 600 \mathrm{J} \) of energy and does work equivalent to \( 400 \mathrm{J} \) of energy. The internal energy change is
A . 1000
B. 200 J
c. \( 600 \mathrm{J} \)
D. 300 J


Simplify the following:\( (-441) \div(21)=? \)
A . 21
B. -21
\( c \cdot 20 \)
D. - 20


Discuss motion of a car along a banked
road with figure and show that \( v_{\max }= \) \( \left(R g \frac{\mu_{s}+\tan \theta}{1-\mu, \tan \theta}\right)^{\frac{1}{2}} \)


2, 7, 24, 77, 238, ....
A . 721
B. 722
\( c \cdot 723 \)
D. 733


Find the coordinates of the point equidistant from three given points \( A(5,1), B(-3,-7) \) and \( C(7,-1) \)
A \( \cdot(-2,-4) \)
в. (2,-4)
c. (2,4)
(年. \( (2,4)) \)
D. (-2,4)


Beer is prepared from
A. Maize
B. Barley
c. sugarcane
D. Grape


Tell if the following statement is true or false. In case give a valid reason for saying so
\( \boldsymbol{p}: \) Each radius of a circle is a chord of the circle.
A. True
B. False


Two identical conductors of copper and
aluminium are placed in an identical electric field. The magnitude of induced charge in the aluminium will be :
A. zero
B. Greater than in copper
c. less than in copper
D. Equal to that of copper


Which of the following processes is not a step involved in the water-cycle operating in nature?
A. Evaporation
B. Transpiration
c. Precipitation
D. Photosynthesis


Describe Malpighian body. Explain its role in urine formation.


The value of \( \left|\begin{array}{cc}\boldsymbol{x} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}+\mathbf{1} & \boldsymbol{x}\end{array}\right| \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( x \)
\( \mathbf{c} \cdot x^{2} \)
D.


Bohr, model postulated that electrons move along fixed circular paths which was contradicted by Heisenberg's uncertainty principle and deBroglie concept of dual nature of electron.
If true enter 1 , if false enter 0 .


If three vectors along coordinate axis represents the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be
\( \mathbf{A} \cdot \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{2}} \)
B. \( \frac{i+3+\hat{k}}{\sqrt{36}} \)
\( \mathbf{c} \cdot \hat{i}+\hat{j}+\hat{k} \)
D. \( \frac{i+\vec{j}+\hat{k}}{\sqrt{3}} \)


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 \( 4 m . \) 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


The curve represented by \( \boldsymbol{R} \boldsymbol{s}\left(\frac{1}{z}\right)=\boldsymbol{C} \)
is (where \( C \) is a constant and \( \neq 0 \) )
A. Ellipse
B. Parabola
c. circle
D. Straight line


\( 19 g \) of water at 30 and \( 5 g \) of ice at
\( -20 C \) are mixed together in a
calorimeter. What is the final
temperature of the mixture? (Given specific heat of ice \( =\mathbf{0 . 5} \)calg\( ^{-1}()^{-1} \)
and latent heat of fusion of ice \( = \)
\( 80 c a l g^{-1} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. -5
\( c .5 \)
D. 10


An infinitely large thin plane sheet has
a uniform surface charge density \( +\sigma \) Obtain the expression for the amount of work done in bringing a point charge \( q \) from infinity to a point, distant \( r, \) in front of the charged plane sheet.


Diwali rocket is ejecting 50 g of gases/s at a velocity of \( 400 \mathrm{m} / \mathrm{s} \). The accelerating force on the rocket will be?
A. 22 dynes
B. 20N
c. 20 dynes
D. 100N


Q Type your question
Determine the time it would take to
plate \( 10.0 g A g \) with a current of \( 0.452 A \)
A \( .2 .5 h r \)
B. \( 3.5 h r \)
c. \( 4.5 h r \)
\( 0.5 .5 h \)


What kind of image is obtained always for concave lens?
A. Virtual, Erect and Diminished
B. Real, Erect and Large
c. Real, Erect and Diminished
D. All of these


The correct floral formula of chilli is
\( A \)
\[
\oplus \bigoplus_{2+2} C_{4} A_{2+4} C_{(2)}
\]
B. \( B r . \%, K_{4} C_{4} \) Аа \( G_{1} \)
\( c \)
\[
\bigoplus \bigoplus_{(5)} A_{(5)} G_{(2)}
\]
\( D \)
\[
\bigoplus \bigoplus_{3+3} A_{3+3} G_{(3)}
\]


\( \mathrm{Cl}_{2} \) cannot form addition compound
with :
A. NO
в. \( \mathrm{co} \)
\( c \cdot \mathrm{sO}_{2} \)
D. \( \mathrm{H}_{2} \) S


lonic compounds have high melting point and boiling point. Explain.


Write about dispersion of human
population and factors influencing it.


A container contains three gases, \( \boldsymbol{A}, \boldsymbol{B} \) and \( C \) in equilibrium, \( A \rightleftharpoons 2 B+C \)
At equilibrium the concentration of \( \boldsymbol{A} \)
was \( 3 M \) and of \( B \) was \( 4 M . \) On doubling
the volume of container, the new
equilibrium concentration of \( \boldsymbol{B} \) was
\( 3 M . \) Calculate \( K_{C} \) of the reaction:
A . 28.8
B. 5.9
c. 0.14
D. 0.55


A radioactive substance has density \( \rho \)
volume \( V \) and decay constant \( \lambda \). If the molecular weight of the substance is
\( M, \) and Avogadro's number is \( N_{a}, \) then the radioactivity of the substance after
time \( ^{\prime} \boldsymbol{t}^{\prime} \) is:
\( ^{\mathbf{A}} \cdot\left(\frac{\lambda V \rho N_{a}}{M}\right)\left(1-e^{\lambda t}\right) \)
B. \( \left(\frac{t N_{a} V}{\rho M}\right) e^{\lambda t / 2} \)
c. \( \frac{\lambda N_{a}}{V \rho M} e^{-\lambda t} \)
D. \( \frac{\lambda V \rho N_{a} e^{-\lambda t}}{M} \)


Which one of the following reaction conditions are used for preparing diethyl ether from ethyl alcohol?
A. \( H I / 200^{\circ} C \)
в. Сопс.Н\( _{2} S O_{4} / 140^{\circ} C \)
c. \( N a O H / 70^{\circ} C \)
D. \( N a O C_{2} H_{5} / 27^{\circ} C \)


A plane wavelength \( \left(\boldsymbol{\lambda}=\mathbf{6} \times \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{m}\right) \)
falls on a slit \( 0.4 m m \) wide. A convex
lens of focal length \( 0.8 m \) placed behind the slit focusses the length on a screen What is the linear diameter of second
maximum
A. \( 0.16 \mathrm{mm} \)
B. \( 12 \mathrm{mm} \)
\( c .3 m m \)
\( \mathbf{D} \cdot 9 m m \)


The domain of \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{|\boldsymbol{x}|+\boldsymbol{x}} \) is
\( A \cdot(-\infty, 0) \)
B. \( (0, \infty) \)
\( c \cdot(-\infty, 1) \)
D. (-2,-1)


In a first order reaction, the
concentration of the reactant,
decreases from \( 0.8 \mathrm{M} \) to \( 0.4 \mathrm{Min} 15 \)
minutes. The time taken for the
concentration to change from \( 0.1 \mathrm{M} \) to \( 0.025 \mathrm{M} \) is:
A. 30 min
B. 15 min
\( c .7 .5 \mathrm{min} \)
D. 60 min


An infintely long straight wire carrying current of \( 10 \mathrm{A} \) is passing through the centre of the above circuit vertically with the direction of the current being into the plane of the circuit.What is the
force acting on the wire at the centre due to the current in the circuit?What is
the force acting on the arc \( A C \) and the straight segment CD due to the current at the centre?


The foci of a hyperbola coincide with the foci of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 . \) Then
the equation hyperbola with eccentricity 2 is
A \( \frac{x^{2}}{12}-\frac{y^{2}}{4}=1 \)
B. \( \frac{x^{2}}{4}-\frac{y^{2}}{12}=1 \)
c. \( 3 x^{2}-y^{2}+12=0 \)
D. \( 9 x^{2}-25 y^{2}-225=0 \)


Arrange the following elements in increasing order of their atomic radii \( \boldsymbol{L} \boldsymbol{i}, \boldsymbol{B} \boldsymbol{e}, \boldsymbol{F}, \boldsymbol{N} \)
A. \( N<F<B e<L i \)
B. \( F<N<L i<B e \)
c. \( F<B e<N<L i \)
D. \( F<N<B e<L i \)


Action of bleaching powder on ethyl alcohol gives?
A. Chloroform
B. Dichlore methane
c. Trichloro ethenb
D. Ethylene chloride


The least count of a stop watch is \( \frac{1}{5} s \)
The time of 20 oscillations of a
pendulum is measured to be \( 25 s \). What is the maximum percentage error in this measurement?
\( A \cdot 8 \% \)
B. 1\%
\( c .0 .8 \% \)
D. \( 16 \% \)


An otherwise infinite, straight wire has
two concentric loops of radii \( a \) and \( b \)
carrying equal currents in opposite directions as shown in figure. The
magnetic field at the common center is
zero for:
\( ^{\mathrm{A}} \cdot \frac{a}{b}=\frac{\pi-1}{\pi} \)
B. \( \frac{a}{b}=\frac{\pi}{\pi+1} \)
c. \( \frac{a}{b}=\frac{\pi-1}{\pi+1} \)
D. \( \frac{a}{b}=\frac{\pi+1}{\pi-1} \)


The image of the point (1,6,3) in the \( \operatorname{line} \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} \) is
A. (1,0,7)
в. (1,3,5)
c. (2,4,6)
D. (-1,-6,-3)


In case of formation of ionic
compounds, the electronegativity difference between them is less than 1.7
A. True
B. False


The ionization energy of hydrogen atom
is \( 13.6 \mathrm{eV} \). The energy required to excite the electron in a hydrogen atom from the ground state to the first excited state is:
A \( \cdot 1.69 \times 10^{-18} \mathrm{J} \)
В. \( 1.69 \times 10^{-23} \) 」
c. \( 1.69 \times 10^{23} \) 」
D. \( 1.69 \times 10^{25} \mathrm{J} \)


Assertion
In the Contact process, the catalyst mass is heated electrically only initially
Reason
To conserve energy the mixture is heated by exhaust gases from the catalytic converter by heat exchangers.
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


According to Ampere's swimming rule, if a man swims along a direction opposite to the direction of the current, south pole of the needle deflects
towards his


Which of the following ions has a magnetic moment of 5.93 BM?
\( [A t . N o .: V=23, C r=24, M n=25, F e=26] \)
\( \mathbf{A} \cdot M n^{2}+ \)
B. \( F e^{2} \)
\( c \cdot C r^{2} \)
\( D \cdot V^{3} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \boldsymbol{y}=\cos ^{-1}\left(\frac{\boldsymbol{2} \boldsymbol{x}}{\boldsymbol{1}+\boldsymbol{x}^{2}}\right),-\boldsymbol{1}< \)
\( \boldsymbol{x}<\mathbf{1} \)


In a group of 50 persons, 14 drink tea
but not coffee and 30 drink tea, then
find how many drink tea and coffee both?


The tiocyanate ion has a formula of
\( S C N^{-} . \) When asked to draw the Lewis
Structure for thiocyanate, you came up with the following three drawings:
Which of the three drawings is/are correct?
\( : \ddot{\mathrm{s}}=\mathrm{c}=\ddot{\mathrm{n}}: \quad \ddot{\mathrm{s}} \equiv \mathrm{c}-\ddot{\mathrm{N}}: \)
\( : \ddot{\mathrm{S}} \)
This question has multiple correct options
A. The picture on the left is valid
B. The picture on the middle is valid
c. The picture on the right is valid
D. All three pictures are equally valid.


Which is most ionic?
\( A \cdot P_{2} O_{5} \)
B. \( M n O \)
\( \mathrm{c} \cdot \mathrm{CrO}_{3} \)
D. \( M n_{2} O_{7} \)


Which of the following quantity does not have any unit?
A. Velocity of light
B. Light year
c. Magnification
D. Power of a lens


Find the mean and variance for the
following frequency distribution
\( \begin{array}{lllll}\text { Classes } & \begin{array}{l}0- \\ 30\end{array} & \begin{array}{l}\text { 30- } \\ 60\end{array} & \begin{array}{l}\text { 60- } \\ \text { 90 }\end{array} & \begin{array}{l}\text { 9 } \\ \text { 1 }\end{array}\end{array} \) 120
Frequencies 2 3


Solve: \( 8 x-7=6 \)


Energy equivalent to \( 10.00 \mathrm{cm}^{-1} \) is:
A \( .2 .0 \times 10^{-22} \) J per atom
B . 28.6 \( \times 10^{-3} \) kcal.mol \( ^{-1} \) photon
c. \( 12.0 \times 10^{-2} k J . m o l^{-1} \) photon
D. All of the above


A particle starts moving such that position with respect to origin 0 varies with time \( t \) as \( x\{t\}=2 t \) m. Find
(a) average velocity between (i) \( t=0 \& t \) \( =1 s(i i) t=0 \& t=2 s \)
(iii) \( t=1 s \& t=2 s \)
(b) instantaneous velocity at general
time t.


f \( 2^{x+1}=3^{1-x} \) then find the value of \( x \)


Statement 1: An emf \( \in=€_{0} \)
\( \sin \left(\omega t+\frac{\pi}{6}\right) \) is applied in a circuit and a current of \( i=i_{0} \sin \left(\omega t-\frac{\pi}{3}\right) \) flows
Then the average power delivered by the source is zero.

Statement 2: If the average value of \( \in \)
and \( i \) is separately zero, then the power
consumed will be zero.
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-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True.


Four students showed the following
traces of the path of a ray of light
passing through a rectangular glass
slab

The trace most likely to be correct is
that of student
\( A \)
B. II
c. III
D. IV


The empty space between two Saturn rings is called
A. the inter-planetary space
B. zones
c. belts
D. cassini division


Which one of the following ores is concentrated by chemical leaching method?
A. Galena
B. Copper pyritee
c. cinnabur
D. Argentite


The boiling point of 0.1molal
\( \boldsymbol{K}_{4}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \) solution will be :
\( \left(\text {Given } \boldsymbol{K}_{\boldsymbol{b}} \text {for water}=\mathbf{0 . 5 2 K k g} \mathbf{m o l}\right. \)
A \( \cdot 100.52^{0} C \)
В. \( 100.104^{0} C \)
c. \( 100.26^{\circ} \mathrm{C} \)
D. \( 102.6^{\circ} \mathrm{C} \)


Which of the following products are not correctly matched in the given
reactions?
A \( \cdot C_{2} H_{5} O C H_{3}+H B r \frac{373 K}{\longrightarrow} C_{2} H_{5} O H+C H_{3} B r \)
B . \( C_{2} H_{5} O C_{2} H_{5}+2 H I \rightarrow C_{2} H 5 I+C_{2} H_{5} O H \)
C \( \cdot C_{2} H_{5} O C_{2} H_{5}+H C C l \stackrel{\text {Exess}}{\text {Cold}}\left[\left(C_{2} H_{5}\right)_{2} O^{+} H\right] C l \)
D. \( \left(C H_{3}\right)_{3} C O C_{2} H_{5} \stackrel{H I}{\longrightarrow}\left(C H_{3}\right)_{3} C I+C_{2} H_{5} O H \)


The velocity of the image when the
object crosses the mean position and
goes towards \( Q \) is
\( A . A \omega \)
B. \( -A \omega \)
\( \mathbf{c} \cdot A \omega / 2 \)
D. none of these


Solve:
\( \frac{x \sin x}{1+\cos x} \)


If \( \int \frac{\sin x}{\sin (x-\alpha)} d x=A x+ \)
\( B \log \sin (x-\alpha)+c \) then find the value
of \( (\boldsymbol{A}, \boldsymbol{B}) \)


A man of mass \( 50 k g \) climbs up a ladder
of height \( 10 m \). Calculate the increase in
his potential energy. \( \left(\boldsymbol{g}=\mathbf{9 . 8 m} \boldsymbol{s}^{-2}\right) \)
A . \( 490 J \)
B . \( 2450 J \)
c. \( 4900 J \)
D. \( 0 . \)


How is the retention factor or \( \boldsymbol{R}_{\boldsymbol{f}} \) of \( \mathbf{a} \)
particular compound measured in a Thin layer of Chromatography (TLC)
experiment?
A. Distance traveled by the compound on the TLC plate divided by the total distance traveled by the mobile phase
B. Distance traveled by the compound on the TLC plate multiplied by the total distance traveled by the mobile phase
C. The total distance traveled by the mobile phase divided by distance traveled by the compound on the TLC plate
D. The total distance traveled by the mobile phase multiplied by distance traveled by the compound on the TLC plate


Two particle \( A \) and \( B \) having initial position (0,0) \( \mathrm{m} \) and \( \left(\frac{48}{5}, \frac{36}{5}\right) m . \) Their initial velocity is \( (4 \hat{i}+3 \hat{j}) \mathrm{m} / \mathrm{s} \) and \( (-4 \hat{i}-3 \hat{j}) \mathrm{m} / \mathrm{s} \) respectively. Both have same acceleration \( \vec{a}=-9 \hat{j} \mathrm{m} / \mathrm{s}^{2} . \) Then
two particles will collide after time
A . \( 1.2 \mathrm{s} \)
B. 12 s
\( c \cdot 2.4 \mathrm{s} \)
D. They will not collide


If \( A \) and \( B \) are mutually exclusive events
with \( \boldsymbol{P}(\boldsymbol{B}) \neq 1, \) then \( \boldsymbol{P}(\boldsymbol{A} \mid \overline{\boldsymbol{B}})= \)
\( ^{A} \cdot \frac{1}{P(B)} \)
В. \( \frac{1}{1-P(B)} \)
c. \( \frac{P(A)}{P(B)} \)
D. \( \frac{P(A)}{1-P(B)} \)


Electromagnetic waves obey law of
A. refraction only.
B. reflection and refraction both
c. reflection only.
D. momentum


What are food preservatives? Give an example.


Which of the following is not an element of first transition series?
\( A \cdot F e \)
B. co
c. \( \mathrm{Ni} \)
D. Agg


A thin convex lens of focal length \( 20 \mathrm{cm} \)
is kept in contact with a plane mirror. The focal length of the combination will
be :
A . \( 5 \mathrm{cm} \)
B. \( -10 \mathrm{cm} \)
\( \mathrm{c} .-20 \mathrm{cm} \)
D. Infinite


Multiple Choice Questions
BOD is a measure of
A. Industrial wastes passed into water bodies
B. amount of carbon monoxide combined with
haemogloblin
C. extent of pollution with organic matter
D. amount of oxygen required by plants during night.


The perimeter of a trapezium is \( 52 \mathrm{cm} \) Its non-parallel sides are \( 10 \mathrm{cm} \) each and the distance between two parallel sides is \( 8 \mathrm{cm} . \) Find the area of the
trapezium.


If we want to maximise the magnitude
of the magnetic force acting on a charged particle moving in a magnetic field. By which of the following statements we can maximise it.
I. Maximize the strength of the
magnetic field
Il. Minimize the velocity of particle.
III. Ensure that the particle is moving in the same direction as the magnetic field lines
A. I only
B. I and II only
c. I and III only
D. II and III only
E . ।, II, and III


A gas can never be liquefied at?
A. \( T=T_{C} \) and \( P=P_{C} \)
в. \( T<T_{C} \) and \( P=P_{C} \)
c. \( T<T_{C} \) and \( P<P_{C} \)
D. \( T>T_{C} \) and \( P>>P_{C} \)


Scientist previously thought an atom looked like plum pudding. In this model, it was assumed that protons and electrons were distributed throughout the atom almost randomly. Which of the following contributions DISPROVED the Plum Pudding model?
A. Rutherford's Gold Foil Experiment.
B. J.J. Thomson's Cathode Ray Experiment.
c. Millikan's Oil Drop Experiment
D. Bohr's Model of the Atom.


An object of mass \( \mathrm{m} \) is tied to a string of length I and a variable force \( \mathrm{F} \) is applied on it which brings the string
gradually at angle \( \theta \) with the vertical Find the work done by the force \( F \)


Which of the following have the chances to get eliminated from urine if there is
too much increase of sugar during
fever?
A. Glucose
B. Uric acid
c. Phosphates
D. Fructose


The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months
and standard deviation of 2 months.
Find the probability that an instrument produced by this machine will last less than 7 months.
A . 0.2316
B. 0.0062
c. 0.0072
D. 0.2136


Subtract the second expression from
the first:
\( 5 x^{2}+4 y^{2}-6 y+8 \) and \( x^{2}-5 y^{2}+ \)
\( 2 x y+3 y-10 \)
A \( \cdot 4 x y^{2}+9 x y^{2}+9 y-2 y+12 \)
В. \( 4 x^{y}+9 y^{3}+9 y+2 x y+18 \)
c. \( 4 x^{2}+9 y^{2}-9 y-2 x y+18 \)
D. \( x^{2}+9 y^{2}-9 y-2 x y+12 \)


Which phenomenon is exhibited by the
figure above?
Funnal
wate
A. A- Hydroponic
B. A- Hydrostatic
c. A- Just a plant in a tub
D. A- None of the above


An inductor coil stores \( U \) energy when \( i \)
current is passed through it and
dissipates energy at the rate of \( P . \) The time constant of the circuit, when this
coil is connected across a battery of
zero internal resistance is :
A \( \cdot \frac{4 U}{P} \)
в. \( \frac{U}{P} \)
c. \( \frac{2 U}{P} \)
D. \( \frac{2 P}{U} \)


An inductor may store energy in
A. its electric field
B. its coils
c. its magnetic field
D. both in electric and magnetic fields


The relation between density of air \( (D a) \) and water vapour \( (D c o) \) is:
\( \mathbf{A} \cdot D a=D c o \)
B. \( D a>D c o \)
c. \( D a<D c o \)
D. \( D a \leq D c o \)


Galapagos finches are associated with
A. Linnaeus
B. Darwin
c. Hugo de Vries
D. Muller


Two identical buggies each of mass \( M \) moves one after due to inertia (without
friction) with the some velocity. A man
of mass \( m \) rides the rear buggy. At a certain moment, the manjumps into the front buggy with velocity relative to this buggy. Knowing that the mass of each buggy is equal to \( M \). Find the velocity with which the buggies will
move after that.


A force of \( - \) Fk acts on \( \mathrm{O} \), the origin of the coordinate system. The torque about the point (1,-1) is :
\( \mathbf{A} \cdot-\mathrm{F}(\hat{\mathrm{i}}-\hat{\mathrm{j}}) \)
B. \( \mathrm{F}(\hat{\mathrm{i}}-\hat{\mathrm{j}}) \)
\( \mathbf{c} .-\mathrm{F}(\hat{\mathbf{i}}+\hat{\mathbf{j}}) \)
D. F(í+j)


An aeroplane flies along a straight line from \( A \) to \( B \) with air speed \( V \) and back
again with the same air speed.ff the distance between \( A \) and \( B \) is \( l \) and \( a \)
steady wind blows perpendicular to AB with speed \( u \), the total time taken for
the round trip is
A. \( \frac{2 l}{\sqrt{V^{2}-u^{2}}} \)
в. \( \frac{2 l}{\sqrt{V^{2}+u^{2}}} \)
c. \( \frac{l}{\sqrt{V^{2}-u^{2}}} \)
D. \( \frac{3 l}{\sqrt{V^{2}-u^{2}}} \)


Two lenses with power +12 D and \( -2 D \) are kept in close contact with each
other. Find the power of the combination


Let \( \boldsymbol{f}(\boldsymbol{x})=\frac{2}{\pi} \operatorname{cosec}^{-1} \frac{x+1}{2} \) Then
\( \mathbf{A} \cdot \lim _{x \rightarrow 1^{+}} f(x)=0 \)
\( \mathbf{B} \cdot \lim _{x \rightarrow 1} f(x)=\frac{\pi}{2} \)
\( \mathbf{C} \cdot \lim _{x \rightarrow-3^{-}} f(x)=-1 \)
\( \mathbf{D} \cdot \lim _{x \rightarrow-3} f(x)=1 \)
E \( \cdot \lim _{x \rightarrow-3} f(x)=-\frac{\pi}{2} \)


Based on cross-multiplication method,
solve the following pairs of equations by cross multiplication rule. \( \frac{x}{2}-\frac{y}{3}+4=0, \frac{x}{2}-\frac{5 y}{3}+12=0 \)
Then \( x+y \) is equal to


In lead chamber process, which one of the following oxides is used as a catalyst?
A . \( N O \)
в. \( N O_{2} \)
c. \( N_{2} O_{3} \)
D. \( N_{2} O_{5} \)


Which important property did Mendeleev use to classify the element
in his periodic table and did he stick to
that?


Given the following sequence, determine whether it is arithmetic
progression or not. If it is an Arithmetic Progression, its general term. \( -5,2,9,16,23,30, \dots \dots \dots \)
A \( .7 n-12 \)
в. \( 6 n-12 \)
\( c \cdot 5 n-12 \)
D. \( 4 n-12 \)


Which of the following are causes of industrial pollution?
A. Asbestos
B. Oils
c. Nitrates \& Phosphates
D. All of above


In which of the following reactions,
\( H_{2} O_{2} \) acts as oxidizing agent?
A \( \cdot A g_{2} O+H_{2} O_{2} \rightarrow 2 A g+H_{2} O+O_{2} \) moist
в. \( 2 \mathrm{NaOH}+\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{Na}_{2} \mathrm{O}_{2}+2 \mathrm{H}_{2} \mathrm{O} \)
c. \( K N O_{2}+H_{2} O_{2} \rightarrow K N O_{3}+H_{2} O \)
D. \( C l_{2}+H_{2} O_{2} \rightarrow 2 H C l+O_{2} \)


For a chemical reaction \( \boldsymbol{A} \rightarrow \) products
the rate of disappearance of \( \boldsymbol{A} \) is given
by:
\( \frac{-d C_{A}}{d t}=\frac{K_{1} C_{A}}{1+K_{2} C_{A}} \) at low \( C_{A} \) the
reaction is of the .......order with rate
constant. (Assume \( K_{1}, K_{2} \) are lesser
than \( 1) \)


If the \( 1^{s t} \) terms of a series is 7 and \( 13^{t h} \)
terms is 35 . Find the sum of 13 terms of
the sequence.


A girl having mass of 35 kg sits on a trolley of mass 5 kg. The trolley is
given an initial velocity of \( 4 m s^{-1} \) by applying a force. The trolley comes to rest after traversing a distance of \( 16 \mathrm{m} \) How much work is done on the
trolley?
A. ०
B. 320 J
c. \( 120 \mathrm{J} \)
D. 250 J


Which of the following compounds does not contain a multiple bond?
A. Ethane
B. Ethene
c. Ethyne
D. Benzene


Two liquids \( A \) and \( B \) form an ideal
solution at temperature \( T . \) When the
total vapour pressure above the
solution if 600 torr, the amount
fraction of \( A \) in the vapour phase is 0.40
and in the liquid phase is \( 0.6 . \) What are the vapour pressure of pure \( A \) and \( B \) at
temperature \( T ? \)


Which one of them satisfy octet rule?
A. 2 electrons in valence shell
B. 8 electrons in valence shell
c. 18 electrons in valence shell
D. All of these


Distinguish between \( C_{6} H_{5} N H_{2} \) and
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H} \boldsymbol{C} \boldsymbol{H}_{3} \)


What does Bohr's atomic theory explain?
A. About quantum numbers
B. About the shape of sub-levels
c. About nucleus
D. About stationary states


Express each of the following ratios as a
per cent.
\( \mathbf{2}: \mathbf{3} \)


The electric flux emerging through the
closed surface \( S_{1} \) shown in figure which
intersects the spherical conductor \( \boldsymbol{S} \)
due to the presence of a positive charge
very near to conductor is:
A. Positive
B. Negative
c. zero
D. None of the above


For any vector \( \vec{a}, \) the value of \( (\vec{a} \times \hat{i})^{2}+ \)
\( (\vec{a} \times \hat{j})^{2}+(\vec{a} \times \hat{k})^{2} \) is equal to
A \( \cdot 3 \vec{a}^{2} \)
в. \( \vec{a}^{2} \)
c. \( 2 \vec{a}^{2} \)
D. \( 4 \vec{a}^{2} \)


The \( 31 s t \) term of the \( A P \) whose first two
terms are respectively -2 and -7 is
\( \mathbf{A} \cdot-152 \)
в. 150
c. 148
D. -148


During burning of candle, different zones of combustion in the flame are listed below:
a) Outermost zone
b) Innermost zone
c) Middle zone
The correct order of temperature of zones is :
\( \mathbf{A} \cdot A>B>C \)
в. \( C>B>A \)
c. \( B>C>A \)
D. \( A>C>B \)


The solubility product of \( M g F_{2} \) is \( 7.4 x \)
\( 10^{-11} . \) Calculate the solubility of \( M g F_{2} \) in \( 0.1 \mathrm{M} \) NaF solution.
A \( .7 .4 \times 10^{-9} \)
В. \( 3.7 \times 10^{-9} \)
c. \( 3.7 \times 10^{-11} \)
D. \( 7.4 \times 10^{-11} \)


The weight of the column of the mercury in the tube above the surface of the
mercury in the cup is balanced by
A. The weight of air column
B. Friction Force
c. viscous force
D. Buoyant force


The initial quantum no. of electron in the atom is :
A .2
B. 3
\( c \cdot 4 \)
D.


A balloon contains \( 14.0 L \) of air at
760 torr.. What will be the volume of
the balloon when it is taken to a depth
of \( 10 f t \) in a swimming pool? Assume that the temperature of the air and water are equal (density: \( \boldsymbol{H} \boldsymbol{g}= \) \( \mathbf{1 3 . 6} \boldsymbol{g} / \boldsymbol{m} \boldsymbol{L} \)
A . 11.0
в. 11.3
c. 10
D. 10.8


A body of mass \( 1 \mathrm{kg} \) has a kinetic energy
of motion 8 J. Its linear momentum is
equal to:
A \( \cdot 2 k g m s^{-1} \)
B. \( 4 k g m s^{-1} \)
c. \( 6 k g m s^{-1} \)
D. \( 8 k g m s^{-1} \)


In monocot stem, the pericycle is?
A. Indistinguishable
B. One layeredd
c. Two layeredd
D. Multi layered


\( A \) is singing a note and at the same
time \( B \) is also singing a note with
1 / 8 the frequency of \( A \). The energies of the two sounds are equal. The disparagement amplitude of the note if
\( \boldsymbol{B} \) is:
A. same as that of \( A \)
B. Twice that of \( A \)
c. four times that of \( A \)
D. eigth times that of \( A \)


When \( N_{2}^{+} \) is formed from \( N_{2}, \) bond
order is \( _{--}-_{-}- \) and when \( O_{2}^{+} \) is formed
from \( O_{2}, \) bond-order is
A. increases
B. decreases
c. increases, decreases
D. decreases, increases


The rate constant of a reaction is
\( 0.0693 \mathrm{min}^{-1} . \) Starting with \( 10 \mathrm{mol} \), the
rate of the reaction after 10 min is:
A. 0.0693 mol \( \min ^{-1} \)
B. \( 0.0693 \times 2 \) mol \( \min ^{-1} \)
c. \( 0.0693 \times 5 \) mol \( \min ^{-1} \)
D. 0.0693 \( \times 5^{2} \) mol \( \min ^{-1} \)


The colloidal solution of \( X \) in gelatin is applied in glass plates to form sensitive plates in photography. Identify \( \boldsymbol{X} \)
A. Silver chloride
B. Silver bromide
c. sodium chloride
D. Sodium bromide


State whether true or false:
Elastic waves need material medium
for their propagation.
A. True
B. False


The \( x \) -coordinate of a point \( P \) is twice
its y-coordinate. If \( \boldsymbol{P} \) is equidistant from
\( Q(2,-5) \) and \( R(-3,6), \) then find the
coordinates of \( \boldsymbol{P} \)


If an error of \( k \% \) is made in measuring
the radius of a sphere, then percentage error in its volume is
A. \( k \% \)
B. \( 3 k \% \)
c. \( 2 k \% \)
D. \( \frac{2}{3} k \% \)


is the basic unit of ecological hierarchy.
A. Gene
B. Species
c. Individual
D. Animals


Differentiate
\( \mathbf{3} \boldsymbol{x}^{\mathbf{1} / \mathbf{3}}+\frac{\mathbf{6}}{\mathbf{7}} \boldsymbol{x}^{\mathbf{7} / \mathbf{6}}+\mathbf{3} \boldsymbol{x}^{\mathbf{2} / \mathbf{3}}+\boldsymbol{C} \)


The process of addition of sulphur to rubber is called
A. oxidation
B. vulcanization
c. adulteration
D. dilution


Assertion: In Joules bulb apparatus, as
reservoir is moved up, the mercury level
raises into the bulb.

Reason: The pressure on the enclosed gas increases.
A. Both assertion (A) and reason (R) are correct and R gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
C. A is true but R is false
D. A is false but R is true


Define nucleus.


A car is travelling round the curve of \( 300 m \) radius. A pendulum hanging to the ceiling of the car makes an angle of
\( 30^{\circ} \) with the vertical. Then the speed of
the car is \( (\text { in } k m / h) \)
A . 140
в. 150
c. 160
D. 120


If ammonia is added to pure water, the concentration of a chemical species
already present will decrease. The
species is:
A \( \cdot O_{2}^{\circ} \)
в. \( \stackrel{\circ}{O}_{H} \)
c. \( H_{3} O^{\oplus} \)
D. \( H_{2} O \)


The process involved in the formation of
product in the following reaction is called as:
A. hydrolysis
B. dehydration
c. decomposition
D. none


The Jupiter's period of revolution around
the Sun is 12 times that of the

Earth. Assuming the planetary orbits to be circular, find the acceleration of Jupiter in the heliocentric reference frame.
A \( \cdot 2 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
B. \( 4.2 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
C \( .2 .2 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)
D. \( 4 \times 10^{-4} \mathrm{m} / \mathrm{s}^{2} \)


The parts of two concentric circular arcs joined by two radial lines and carries current \( i . \) The arcs subtend an
angle \( \theta \) at the center of the circle. The magnetic field at the centre 0 , is
A \( \cdot \frac{\mu_{0} i(b-a) \theta}{4 \pi a b} \)
В. \( \frac{\mu_{0} i(b-a)}{\pi-\theta} \)
c. \( \frac{\mu_{0} i(b-a) \theta}{\pi a b} \)
D. \( \frac{\mu_{0} i(a-b)}{2 \pi a b} \)


If the sum of first n term is
A. 123
B . 118
\( c \cdot 109 \)
D. 107


A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time \( t \) is given by \( s=t^{2}+a t-b+17, \) where
\( a \) and \( b \) are real numbers. If the particle
comes to rest after \( 5 s \) at a distance of
\( s=25 \) units from the fixed point, then
value of \( a \) and \( b \) are respectively.
A .10,-33
B. -10,-33
c. -8,33
D. -10,33


When a ray of light passes from an optically more dense medium to a less dense medium, it:
A. goes undeviated
B. bends towards the normal
c. bends away from the normal
D. none of these


The particle comes to rest in a time
A \( \cdot \frac{2 u^{2} / 2}{3 k} \)
в. \( \frac{\sqrt{u}}{k} \)
c. \( 2 k \sqrt{u} \)
D. \( k \sqrt{u} \)


A mixture of hydrogen and iodine in the mole ratio 1.5: 1 is maintained at
\( 450^{\circ} \mathrm{C} \) After the attainment of
equilibrium, \( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}), \) it is found
on analysis that the mole ratio of \( I_{2} \) to \( H I \) is \( 1: 18 . \) The equilibrium constant
is :
A . 54
B. 46
\( c \cdot 64 \)
D. 76


When a lead storage battery is charge:
\( \mathbf{A} \cdot P b O_{2} \) dissolves
B. the lead electrode becomes coated with lead sulphate
C . sulphuric acid is regenerated
D. the amount of acid decreases


Identify the correct balanced chemical equation from the following:
\( \mathbf{A} \cdot S O_{3}+H_{2} O \longrightarrow H_{2} S O_{4} \)
B . \( 6 N a O H+12 S \longrightarrow N a_{2} S_{5}+ \)
\( N a_{2} S_{2} O_{3}+3 H_{2} O \)
\( \begin{array}{llll}\text { c. } C u & + & 2 S & \rightarrow & C u S_{2}\end{array} \)
D. \( S+4 H N O_{3} \longrightarrow H_{2} S O_{4}+4 N O_{2}+ \)
\( 2 H_{2} O \)


A disc of mass \( M \) is attached to a
horizontal massless spring of force
constant \( K \) so that it can roll without
slipping along a horizontal surface. If the disc is pushed a little towards right and then released, its center of
mass executes SHM with a period of
A \( \cdot 2 \pi \sqrt{\frac{M}{K}} \)
В. \( 2 \pi \sqrt{\frac{3 M}{K}} \)
с. \( _{2 \pi} \sqrt{\frac{M}{2 K}} \)
D. \( 2 \pi \sqrt{\frac{3 M}{2 K}} \)


Which statement is true for second law
of thermodynamics?
A. Heat can flow spontaneously from a cold object to a hot object.
B. You can not create a heat engine which extracts heat and converts it all to useful work
c. According to Plank-Kelvin's law under some circumstances a perfect heat engine is possible.
D. None of these.


Anodic product in the electrolytic
reduction of alumina is:
A. \( C O_{2}, \quad O_{2} \)
в. \( O_{2} \)
\( c \cdot F_{2} \)
D. \( O_{2}, \quad 4 F_{2} \)


Ozone reacts with which of the following reagents?
A. \( K_{2} M n O_{4} \)
B. Moist lodine
c. Potassium ferrocyanide
D. All of the above


Explain an experiment to detect the presence of argemone oil in edible oil


State the following statement true or false:
Arteries have openings
A. True
B. False


Lightning rod can be most effective if it draws charge from lowest cloud by method of contact. This statement is
True/ False?
A. True
B. False


A vector of magnitude 10 has its rectangular components as 8 and 6 along \( x \) and \( y \) axes. Find the angle it make with these axes.


Which of the following is an anionic detergent?
A. Sodium lauryl sulphate
B. Cetyltrimethyl ammonium bromide
c. Glyceryl oleate
D. Sodium stearate


When a nitrogenous organic compound is fused with sodium, the nitrogen present in the compound is converted into
\( A \). sodium nitrate
B. sodium nitrite
c. sodamide
D. sodium cyanide


Which of the following is a protein by
nature?
A. Polyethylene
B. Silk and wool
c. Cellulose
D. Terylene


A volume of \( 6 L H_{2} O \) is placed in a
closed evacuated room of volume \( 827 L \)
at the temperature \( 300 \mathrm{K} \). The density of liquid water at \( 300 \mathrm{K} \) is \( 1.0 \mathrm{g} / \mathrm{ml} \). The
vapour pressure of water at \( 300 \mathrm{K} \) is
\( 22.8 \mathrm{mm} \) Hg. Neglect the change in volume of liquid water by vaporization.


Mark the correct alternative of the
following.
The measure of an angle which is its own complement is?
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c .90^{\circ} \)
D. \( 45^{\circ} \)


A plane wave front falls on a convex lens
The emergent wave front is :
A. plane
B. cylindrical
c. spherical diverging
D. spherical converging


A machine has fourteen identical
components that function
independently. It will stop working if three or more components fail. If the probability that a component fails is equal to \( 0.1, \) find the probability that the machine will be working.


If \( \frac{1}{2} \leq \log _{0.1} x \leq 2, \) then:
A \( \cdot \) maximum value of \( x \) is \( \frac{1}{\sqrt{10}} \)
B. \( x \) lies between \( \frac{1}{100} \) and \( \frac{1}{\sqrt{10}} \)
C. minimum value of \( x \) is \( \frac{1}{10} \)
D. minimum value of \( x \) is \( \frac{1}{100} \)
E . maximum value of \( x \) is \( \frac{1}{100} \)


Male gamete of Cycas, largest in plant kingdom, is
A. Non-motile
B. Biflagellate
c. Multiciliate
D. Uniflagellate


Intramolecular \( \boldsymbol{H}- \) bonding is present
in:
A . o-nitrophenol
B. salicylaldehyde
c. m-nitrophenol
D. both \( (A) \) and \( (B) \)


The variation of PE of a simple harmonic
oscillator is as shown. Then force
constant of the system is (PE 'U' is in
joules, displacement \( ^{\prime} x^{\prime} \) is in \( \mathrm{mm} \) )
A. \( 100 \mathrm{N} / \mathrm{m} \)
B. \( 150 \mathrm{N} / \mathrm{m} \)
c. \( \frac{200}{3} \mathrm{N} / \mathrm{m} \)
D. \( 300 \mathrm{N} / \mathrm{m} \)


A particle with charge \( q \) having
momentum \( p \) enters a uniform
magnetic field normally. The magnetic filed has magnitude \( B \) and is confined to a region of width \( d, \) where \( d<\frac{p}{B q} \)
The particle is deflected by an angle \( \theta \) in
crossing the field.
\( A \)
\[
\sin \theta=\frac{p d}{B q}
\]
B.
\[
\sin \theta=\frac{B q}{q d}
\]
\( c \)
\[
\sin \theta=\frac{p}{B d q}
\]
D.
\[
\sin \theta=\frac{B q d}{p}
\]


\( \frac{4}{7}+\frac{2}{5}+\frac{-4}{5}+\frac{1}{7}+\frac{-5}{7}=\frac{-2}{m} . \) Find
\( \boldsymbol{m} \)


A sum of Rs. 1550 was lent partly at \( 5 \% \) and partly at \( 8 \% \) p.a. simple interest. The total interest received after 3 years
was Rs. 300. The ratio of the money lent
at \( 5 \% \) to that of lent at \( 8 \% \) is
A . 5: 8
B. 8: 5
c. 16: 15
D. 31: 6


A car is moving with a velocity of \( 10 \mathrm{m} / \mathrm{s} \) The driver sees a wall ahead of him and
applied brakes. The car stops after
covering \( 10 m \) distance. If the car was
moving with a speed pf \( 20 m s^{-1}, \) it
would have stopped in \( 30 m \) distance. The reaction of the driver is
A . \( 0.5 s \)
B. \( 0.6 s \)
\( c .0 .7 s \)
D. \( 1 s \)


Which point on y-axis is equidistant from (2,3) and (-4,1)\( ? \)


Assertion
Magnetic field due to current carrying solenoid is independent of its length
and cross-sectional area.
Reason
The magnetic field inside the solenoid is uniform.
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 \( \sum_{x=1}^{10} \sum_{r=0}^{r=x-1}\left(2^{x}-2^{r}\right) \) is
A .16392
B . 16398
\( \mathbf{C} .15462 \)
D. 15468


\( X Y_{2} \) dissociates as: \( X Y_{2}(g) \rightleftharpoons \)
\( \boldsymbol{X} \boldsymbol{Y}(\boldsymbol{g})+\boldsymbol{Y}(\boldsymbol{g}) \)
Initial pressure of \( \boldsymbol{X} \boldsymbol{Y}_{2} \) is \( \boldsymbol{6} \boldsymbol{0} \boldsymbol{0} \boldsymbol{m} \boldsymbol{m} \boldsymbol{H} \boldsymbol{g} \)
The total pressure at equilibrium is \( 800 m m H g . \) Assuming volume of system to remain constant, the value of
\( \boldsymbol{K}_{p} \) is:
A . 50
в. 100
c. 200
D. 400


Assertion
limiting line in the Balmer series has a
wavelength of \( 364.4 m m \)
Reason
limiting line is obtained for a jump of electron from \( n=\infty \)
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


Four chargers \( q_{1}=-0.02 \mu C, q_{2}= \)
\( +0.04 \mu C, q_{3}=+0.02 \mu C, \) and \( q_{4}= \)
\( -0.04 \mu C \) are at the four corners of a
square of side \( 9 \mathrm{cm} \). Then the potential at
the centre of the square is :
A . \( 9 V \)
в. \( 3 V \)
\( \mathrm{c} .1 .2 \mathrm{V} \)
D. Zero


Which RNA carries information from
DNA in protein synthesis?
A. snRNA
B. tRNA
c. rRNA
D. mRNA


A complex is represented as \( C o C l_{3} \)
\( X N H_{3} . \) Its 0.1 molal solution in water
shows \( \Delta T_{f}=0.558^{\circ} C . K_{f} \) of \( H_{2} O \) is
\( 1.86 \mathrm{K} / \mathrm{m} . \) Assuming \( 100 \% \) ionisation,
the number of \( N H_{3} \) molecules
associated with Co is:


An electric field of \( 1500 V / m \) and \( a \)
magnetic field of \( 0.04 W b / m^{2} \) act on a moving electron. The minimum uniform speed along a straight line the electron could have is.
A \( \cdot 1.6 \times 10^{15} \mathrm{m} / \mathrm{s} \)
в. \( 6 \times 10^{-16} \mathrm{m} / \mathrm{s} \)
C \( .3 .75 \times 10^{4} \mathrm{m} / \mathrm{s} \)
D. \( 3.75 \times 10^{2} \mathrm{m} / \mathrm{s} \)


The pollutants released by jet aeroplanes in the atmosphere as fluorocarbons are:
A. photochemical oxidants
B. photochemical reductants
c. aerosols
D. physical pollutants


The S.I. unit of velocity is
\( \mathbf{A} \cdot k m h^{-1} \)
B. \( m \) min \( ^{-1} \)
c. \( k m \) min \( ^{-1} \)
\( \mathbf{D} \cdot m s^{-1} \)


For the reaction, \( \boldsymbol{C}_{3} \boldsymbol{H}_{8}(\boldsymbol{g})+ \)
\( \mathbf{5} O_{2}(\boldsymbol{g}) \longrightarrow \mathbf{3} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{4} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \) at
constant temperature, \( \Delta \boldsymbol{H}-\Delta \boldsymbol{E} \) is:
\( \mathbf{A} \cdot+3 R T \)
B . \( -R T \)
\( \mathbf{c} \cdot+R T \)
D. \( -3 R T \)


\( \int_{0}^{\pi / 4} \frac{\tan ^{3} x}{1+\cos 2 x} d x \)


Q Type your question
the dids ul divig sultilulu dis shuwn III
fig. The ring has a narrow gap of width \( d \)
in its circumference. The solenoid has
cross sectional area \( A \) and a uniform
internal field of magnitude \( B_{0} . \) Now
beginning at \( t=0, \) the solenoid current
is steadily increased so that the field
magnitude at any time \( t \) is given by
\( \boldsymbol{B}(\boldsymbol{t})=\boldsymbol{B}_{0}+\boldsymbol{\alpha} \) where \( \boldsymbol{\alpha}>0 . \) Assuming
that no change can flow across the gap,
the end of ring which has excess of positive charge and the magnitude of induced e.m.f in the ring are
respectively
A. \( X, A \alpha \)
В. \( X, \pi R^{2} \alpha \)
c. \( Y, \pi A^{2} \alpha \)
D. \( Y, \pi R^{2} \alpha \)


A sphere of aluminium of mass 0.047 kg placed for sufficient time in a vessel containing boiling water, so that the
sphere is at \( 100^{\circ} \mathrm{C} \).It is then immediately transferred to \( 0.14 \mathrm{kg} \) copper calorimeter containing \( 0.25 \mathrm{kg} \) of water at \( 20^{\circ} \mathrm{C} \). The temperature of water rises and attains a steady state
at \( 23^{\circ} C \). Calculate the specific \( h \) capacity of aluminium. Given :specific heat capacity of water is 4186 \( J k g^{-1} K^{-1} \) specific heat capacity of copper calorimeter is 385 Jkg\( ^{-1} \boldsymbol{K}^{-1} \)


Which part of electromagnetic
spectrum has largest penetrating
power?


Dilute nitric acid is generally
considered a typical acid except for its reaction with metals. In what way is
dilute nitric acid different from other
acids when it reacts with metals.
A. It acts as an reducing agent so hydrogen gas is liberated
B. It acts as an oxidising agent so hydrogen gas is liberated
c. It acts as an oxidising agent so NO gas and water are formed
D. It acts as an reducing agent so NO gas and water are formed


A transformer of efficiency \( 90 \% \) has
turns ratio \( 1: 10 . \) If the voltage across
the primary is \( 220 V \) and current in the
primary is \( 0.5 A \), then the current in
secondary is
\( \mathbf{A} \cdot 5.5 A \)
B. \( 5 A \)
\( c \cdot 4 A \)
D. \( 4.5 ~ A \)


If chloroform is left open in air in the presence of sun rays, which of the following changes takes place?
A. Explosion takes place.
B. Poisonous gas phosgene is formed.
c. Polymerization takes place.
D. No reaction takes place


Write the negation of the statement " \( \sqrt{7} \) is irrational"


The agricultural field that produces maximum methane gas
into atmosphere is:
A. wheat field
B. paddy field
c. cotton field
D. groundnut field


If \( y=6 x-x^{3} \) and \( x \) increases at the
rate of 5 units per second, the rate of
change of slope when \( x=3 \) is
A. -90 units/sec
B. 90 units/ sec
c. 180 units/sec
D. -180 units/sec


Aliphatic cyclic compounds are known
as:
A. alicyclic compounds
B. polycyclic compounds
c. aromatic compounds
D. hetero cyclic compounds


The amplitude of a particle executing
SHM about O is 10 cm. Then:
This question has multiple correct options
A. When the K.E. is 0.64 of its max. K.E. its displacement is \( 6 \mathrm{cm} \) from 0 .
B. When the displacement is 5 cm from 0 its K.E. is 0.75 of its max.P.E.
C. Its total energy at any point is equal to its maximum
K.E.
D. Its velocity is half the maximum velocity when its displacement is half the maximum displacement.


Chipko movement in the year 1974 in
Garhwal Himalayas involved
A. Protecting tigers
B. Preventing soil erosion by planting trees
C. Preventing pollution by closing down industries
D. Hugging trees to prevent the contractors from felling them


Integrate:
\( \int \frac{x^{4}}{x^{2}+1} d x= \)
A \( \cdot \frac{x^{3}}{3}-x+\tan ^{-1} x+c \)
B. \( \frac{x^{5}}{5}+\tan ^{-1} x+c \)
C \( \cdot 4 x^{3}+\tan ^{-1} x+c \)
D \( \frac{x^{4}}{4}-x+\tan ^{-1} x+c \)


Prove that
\( \left|z_{1}\right|+\left|z_{2}\right|=\left|\frac{1}{2}\left(z_{1}+z_{2}\right)+\sqrt{z_{1} z_{2}}\right|+ \)
\( \left|\frac{1}{2}\left(z_{1}+z_{2}\right)-\sqrt{z_{1} z_{2}}\right| \)


Which of the following is an antacid?
A. Sodium bicarbonate
B. Magnesium hydroxide
c. Magnesium carbonate
D. All of the above


If the ratio of diameters, lengths and
Young's modulus of steel and copper wires shown in the figure are \( p, q \) and \( s \) respectively, then the corresponding ratio of increase in their lengths would
be


Law of multiple proportions can be illustrated by taking the example of
A. \( N a O H \) and \( K O H \)
B. \( N a C l \) and \( N a B r \)
\( c \cdot S O_{2} \) and \( S O_{3} \)
D. \( H_{2} C O_{3} \) and \( C O_{2} \)


A plane electromagnetic wave travels in free space along X-direction. If the value of \( \vec{B} \) (in tesla) at a particular point in space and time is \( 1.2 \times 10^{-8} \hat{k}, \) the value of \( \vec{E}\left(\operatorname{in} \vee \boldsymbol{m}^{-1}\right) \) at that point is,
A. \( 1.2 \hat{j} \)
B. \( 3.6 \hat{k} \)
c. \( 1.2 \hat{k} \)
D. 3.6


Which region is described by the shade
in the graph given above?
This question has multiple correct options
A \( .2 x+3 y=3 \)
B . \( 2 x+3 y<3 \)
c. \( 2 x+3 y>3 \)
D. \( -2 x+3 y<3 \)


A container with rigid walls is covered with perfectly insulating material. The container is divided into two parts by a partition. One part contains a gas while the other is fully evacuated (vacuum). The partition is suddenly removed. The gas rushes to fill the entire volume and
comes to equilibrium after a little time. If the gas is not ideal. Choose the
correct option:
A. The initial internal energy of the gas equals its final internal energy
B. The initial temperature of the gas equals its final temperature.
C. The initial pressure of the gas equals its final pressure
D. The initial entropy of the gas equals its final entropy


A particle of mass \( m \) is moving along the X-axis under the potential \( U(x)= \) \( \frac{k x^{2}}{2}+\lambda \) where \( k \) and \( \lambda \) are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency
\( (\omega) \) given by
A \( \cdot_{3} \frac{k}{m} \)
в. \( 3 \frac{m}{k} \)
c. \( \sqrt{\frac{k}{m}} \)
D. \( \sqrt{3 \frac{m}{k}} \)
E \( \cdot \sqrt{3 \frac{k}{m}} \)


In which of the following preparation, orthophosphoric acid is used?
A. Metaphosphoric acid
B. Phosphorus acid
c. sulphurous acid
D. Pyrophosphoric acid


The IUPAC name of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C H C H}_{3} \) is:
A. 2-methylpropane
B. 2, 2-dimethylethane
c. trimethylmethane
D. none of these


If \( \alpha \) represent linear expansion, \( \beta \)
represent superficial expansion and \( \gamma \) represent cubical expansion, then choose the correct statement:
B. \( \alpha: \beta: \gamma::: 2: 3: 1 \)
c. \( \alpha: \beta: \gamma:: 3: 1: 1 \)
D. \( \alpha: \beta: \gamma:: 1: 2: 3 \)


Given below (Fig. 23.11) is the bar graph
indicating the marks obtained out of 50
in mathematics paper by 100 students.
Read the bar and answer the following
questions:
Every student belonging to the highest mark group is entitled to get prize of Rs
10. How much amount of money is
required for distributing the prize
money?


Vascular cambium forms one of the
following on its inner side.
A. Bast fibres
B. Sieve tubes
c. wood fibres
D. Companion cells


A pendulum suspended from the ceiling of a train has a time period T when the train is at rest. When the train is
accelerating with a uniform acceleration, the time period will
\( A \). increase
B. decrease
c. become infinite
D. remain unaffected


The energy equivalent of 1 g of matter is
A \( \cdot 9 \times 10^{13} \) joule
B. \( 9 \times 10^{13} \) erg
c. \( 3 \times 10^{5} \) joule
D. \( 3 \times 10^{5} \) erg


Leucaena a fast growing tree has been
selected as a fuel yielding tree under the social forestry program in the rural area of our country. What is the common name of this tree?
A . Babul
B. Subabul
c. Jojoba
D. None of the above


is regarded as father of genetics?


\( \mathbf{S} \) and \( \mathbf{S}^{\prime} \) are the foci of the ellipse
\( 25 x^{2}+16 y^{2}=1600, \) then the sum of
the distances from \( \mathrm{S} \) and \( \mathrm{S}^{\prime} \) to the point
\( (4 \sqrt{3}, 5) \) is:
A . 20
B. 15
c. 40
D. 30


Which of the following is an anhydride
of \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A \( . H_{2} S \)
в. \( H_{2} S_{2} \)
\( c \cdot S O_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{3} \)


a) How is chlorine prepared in Deacon's process? How does it react with the
following?
¡) Cold and dilute NaOH
ii) Hot and concentrated NaOH
b) Give chemical equations to
manufacture of Sulphuric Acid by
contact process.


\( 50 \mathrm{ml} \) of a certain sample of \( \mathrm{H}_{2} \mathrm{O}_{2} \) gives
\( 1200 \mathrm{ml} \) of \( O_{2} \) at STP. The volume
strength of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is:
A . 22.4
B. 20
c. 24 v
D. 11.2 V


Benzyl amine may be alkylated as shown in the following equation:
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C H}_{\mathbf{2}} \boldsymbol{N} \boldsymbol{H}_{\boldsymbol{2}}+\boldsymbol{R}-\boldsymbol{X} \rightarrow \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{N} \boldsymbol{H} \boldsymbol{R} \)
Which of the following alkyl halides is best suited for this reaction through
\( \boldsymbol{S}_{N} 1 \) mechanism?
A \( \cdot C H_{3} B r \)
в. \( C_{6} H_{5} B r \)
c. \( C_{6} H_{5} C H_{2} B r \)
\( \mathbf{D} \cdot C_{2} H_{5} B r \)


The maximum number of possible oxidation states of actinoides are
shown by:
A. Berkelium \( (B k) \) and califormium \( (C f) \)
B. Nobelium (No) and lawrencium (Lr)
c. Actinium \( (A c) \) and throium \( (T h) \)
D. Neptunium (Np) and plutonium (Pu)


A gas is filed in a rigid container at pressureP \( ^{0} \). If the mass of each molecule
is halved

Keeping the total number of molecules same and their r.m.s
speed is doubled then find the new
pressure.


Which is/are the correct method-metal
matching for refining of crude metals? This question has multiple correct options
A. Distillation: zinc and mercury
B. Liquation: tin
c. Van Arkel :zirconium
D. Mond process: lead


Find the value of the following
determinant:
\( \left|\begin{array}{cc}\mathbf{3} \sqrt{\mathbf{6}} & -\mathbf{4} \sqrt{\mathbf{2}} \\ \mathbf{5} \sqrt{\mathbf{3}} & \mathbf{2}\end{array}\right| \)
A. \( 20 \sqrt{6} \)
B. \( 16 \sqrt{6} \)
c. \( 26 \sqrt{6} \)
D. \( 10 \sqrt{6} \)


What do you understand by the term 'auto-protolysis' of water? What is its significance?


Two identical loops \( A \) and \( B \) lying in the
same plane carry equal currents. Four points \( P, Q, R \) and \( S \) are in the plane of
the loops. Choose the correct statement
A. The field at P must be out of the plane of the paper
B. The field at \( Q \) must be into the plane of the paper
c. the field at \( R \) must be out of the plane of the paper
D. The field at \( s \) must be out of the plane of the paper


The graphs below the position versus
time for three differences cars 1,2 and 3
Rank these cars according the
magnitudes of their velocities at the
time "t" indicated on the graph,
greatest first
A .1,2,3
B. 1,3,2
c. 2,1,3
D. 3, 2,
E. 3,1,2


The homogeneous catalysts is shown
by:
A \( . \) Haber's process, \( N_{2}+3 H_{2} \stackrel{F e}{\longrightarrow} 2 \mathrm{NH}_{3} \)
B. Ostwald process, \( 4 N H_{3}+5 O_{2} \stackrel{P t}{\longrightarrow} 4 N O+6 H_{2} O \)
C. Contact process, \( 2 S O_{2}+O_{2} \frac{V_{2} O_{5}}{\longrightarrow} 2 S O_{3} \)
\( \mathbf{D} \cdot 2 C_{2} H_{5} O H \frac{H_{2} S O_{4}}{\longrightarrow} C_{2} H_{5}-O-C_{2} H_{5}+H_{2} O \)


Using the given indicators, construct RNA nucleotide and any one DNA nucleotide.
\( G \)
hosphat


If the cell voltage is 1.23 V for the \( H_{2}-O_{2} \)
fuel cell and for the
half cell :
\( O_{2}+2 H_{2} O+4 e^{-} \rightleftharpoons 4^{\ominus} H \)
\( \boldsymbol{E}^{\ominus}=\mathbf{0 . 4 0} \boldsymbol{V}, \) then \( \boldsymbol{E}^{\ominus} \) for \( \boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O}+ \)
\( \mathbf{2} e^{-} \rightleftharpoons \boldsymbol{H}_{2}+\mathbf{2} \stackrel{\ominus}{O} \boldsymbol{H} \) will be:
\( \mathbf{A} \cdot 0.56 V \)
в. \( 0.73 V \)
c. \( 0.41 V \)
D. \( 0.83 V \)


The order of the differential equation
whose solution is
\( \boldsymbol{y}=\boldsymbol{c}_{1} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{c}_{2} \sin \boldsymbol{x}+\boldsymbol{c}_{3} \cos \boldsymbol{x} \) is
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
\( D \)


Which of the following molecule has a planar structure?
\( A \cdot O_{2} S F_{2} \)
в. \( O S F_{2} \)
c. \( X e F_{4} \)
\( \mathbf{D} \cdot C l O_{4}^{-} \)


The volume of a cube is 64 cubic inches.
What is its surface area?
A. 84 square inches
B. 94 square inches
c. 96 square inches
D. 98 square inches


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


Which cells do not form any layer but remain structurally separate?
A. Nerve cells
B. Gland cells
c. Muscle cells
D. Epithelial cells


A definite amount of gaseous
hydrocarbon was burnt with just
sufficient amount of \( O_{2} \). The volume of all reactants was \( 600 \mathrm{ml} \), after the explosion the volume of products
\( \left[\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) \text { and } \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g})\right] \) was found to be
700 ml under the similar conditions.
The molecular formula of the compound
is :
A. \( C_{3} H_{8} \)
в. \( C_{3} H_{6} \)
c. \( c_{3} H_{4} \)
D. \( C_{4} H_{10} \)


A: Coloured spectrum is seen when we look through a cloth
R: Diffraction of light takes place when light is travelling through the pores of cloth
A. Both A and R are true, and R is not correct explanation of A
B. Both A and R are true, and R is correct explanation of A
C. A is true but R is false
D. A is false but R is true


First transgenic sheep were carrying
A. genes for \( \beta \) - lactoglobulin
B. Genes for Antihemophilic IX
C. Genes for Thyroxine
D. More than one correct answer


A solution is prepared by dissolving \( 5.64 \mathrm{g} \) of glucose in \( 60 \mathrm{g} \) of water. Calculate the mole fraction of
each of glucose and water respectively.
B. 0.009, 0.991
c. 1.12,0.08
D. 0.789, 0.211


Consider a hypothetical annihilation of a stationary electron with a stationary positron. What is the wavelength of the resulting radiation?
A \( \cdot \lambda=\frac{h}{2 m_{c} c} \)
B. \( \lambda=\frac{2 h}{m_{c} c^{2}} \)
c. \( \lambda=\frac{h}{2 m_{c} c^{2}} \)
D. None of these


The \( \$ \$ \) IUPAC \( \$ \$ \) name of
\( \left[N i\left(N H_{3}\right)_{4}\right]\left[N i C l_{4}\right] \) is:
A. Tetrachloronickel (II)-tetraamminenickel(II)
B. Tetraamminenickel(II)-tetrachloronickel(II)
C. Tetraamminenickel(II)-tetrachloronickelate(II)
D. Tetrachloronickel (II)-tetraamminenickelate(O)


The mass of a solid rectangle block of
iron is \( 23.6 g \) and its dimensions are
\( 2.1 \mathrm{cm} \times 1.2 \mathrm{cm} \times 1.1 \mathrm{cm} . \) Calculate the
density of iron.


An elliptical cavity is carved out in a
perfect conductor. A positive charge q is placed at the centre of the cavity. The points \( A \) and \( B \) are shown in figure. Then
This question has multiple correct options
A. electric field near A in the cavity = electric field near in the cavity
B. charge density at \( A= \) charge density at \( B \)
C. potential at \( A= \) potential at \( B \)
D. total electric field flux through the surface of the cavity \( =\frac{q}{\varepsilon_{0}} \)


A wire elongates by 1 m \( m \) when a load Wis hanged from it. If the wire goes over a pulley and two weights Weach are hung at the two ends, the elongation of the wire will be (in \( \mathrm{mm} \) ):
A . \( 1 / 2 \)
B. 1
\( c \cdot 2 \)
D. zero


For a rigid diatomic molecule, universal
gas constant \( \boldsymbol{R}=\boldsymbol{n} \boldsymbol{C} \boldsymbol{p} \) where \( ^{\prime} \boldsymbol{C} \boldsymbol{p}^{\prime} \) is
the molar specific heat at constant
pressure and ' \( n^{\prime} \) is a number. Hence \( n \)
is equal to
A . 0.2257
B. 0.4
c. 0.2857
D. 0.3557


The average kinetic energy of the particles of a gas is most closely associated with which of the following quantity?
A. heat capacity.
B. temperature
c. specific heat
D. absolute zero.
E. potential enemy.


Bichromatic light is used in YDSE
having wavelengths \( \lambda_{1}=400 n m \) and
\( \lambda_{2}=700 n m . \) Find the minimum order
of \( \lambda_{1} \) which overlaps with \( \lambda_{2} \)


The locus of a point \( P \) which moves such
that \( P A^{2}-P B^{2}=2 k^{2} \) where \( A \) and \( B \)
\( \operatorname{are}(3,4,5) \) and (-1,3,-7) respectively
is
A. \( 8 x+2 y+24 z-9+2 k^{2}=0 \)
B. \( 8 x+2 y+24 z-2 k^{2}=0 \)
c. \( 8 x+2 y+24 z+9+2 k^{2}=0 \)
D. \( 8 x-2 y+24 z-2 k^{2}=0 \)


\( z \) is a complex number. If \( a=|x|+|y| \)
and \( b=\sqrt{2}|x+i y| \)


\( \left(14 x^{2} y z-28 x^{2} y^{2} z^{3}+32 y^{2} z^{2}\right) \div \)
\( (-4 x y) \) is equal to
A \( \cdot \frac{7}{2} y z+7 x y z^{2}+8 x y z \)
B. \( -\frac{7}{2} x z+7 x y z^{3}-\frac{8 y z^{2}}{x} \)
\( ^{\mathbf{C}}-\frac{7}{2} x z-7 x y z^{3}+\frac{8 y z^{2}}{x} \)
D \( -\frac{7}{2} x z-7 x y z^{2}-\frac{8 y z^{2}}{x} \)


Find out the side view of the diagram.
\( \mathbf{A} \)
B.
\( c \)
D.


What is molecular state of Sulphur as reactant in the reaction?
Sulphur \( +12 O H^{-} \longrightarrow 4 S^{2-}+ \)
\( 2 S_{2} O_{3}^{2-}+3 H_{2} O \)
A \( \cdot S_{8}^{2} \)
B \( \cdot 2 S_{4}^{2} \)
\( c \cdot S_{8} \)
D. \( S_{8}^{-} \)


Which of the following statements is
wrong regarding amino acids?
A. The living systems in plants can synthesise essential amino acids
B. The living systems in animals can synthesise only essential amino acids
C. The living systems in animals can synthesise only non essential amino acids.
D. The living systems in plants can synthesise non essential amino acids


Solubility of a gas in a liquid increases
on:
A. increasing temperature.
B. decreasing pressure.
C. increasing pressure.
D. increasing temperature and pressure


The process of adsorption of hydrogen over palladium surface is called:
A. sorption
B. occlusion
c. desorption
D. None of these


Fossils of CroMagnon Man were discovered in
A . 1924
B. 1891
\( c \cdot 1868 \)
D. 1856


Number of stereoisomers are:
\( A \cdot 21 \)
В. 56
\( c .64 \)
D. none of these


When we drink liquid with a straw, the air pressure inside the straw
A. Increases
B. Decreases
\( c \cdot \) Both
D. Remains equal to the air pressure


Write the catalyst used in the
decomposition of potassium chlorate to get potassium chloride and oxygen.


The number of values of \( x \) for which
\[
\begin{array}{l}
\sin ^{-1}\left(x^{2}-\frac{x^{4}}{3}+\frac{x^{6}}{9} \dots\right)+ \\
\cos ^{-1}\left(x^{4}-\frac{x^{8}}{3}+\frac{x^{12}}{9} \dots\right)=\frac{\pi}{2}, \text { where } \\
0 \leq|x|<\sqrt{3}, \text { is }
\end{array}
\]


In a hydrogen atom, the binding energy
of the electron in the nth state is \( \boldsymbol{E}_{\boldsymbol{n}} \)
, then the frequency of revolution of the electron in the nth orbit is:
A \( \cdot 2 E_{n} / n h \)
в. \( 2 E_{n} n / h \)
c. \( E_{n} / n h \)
D. \( E_{n} n / h \)


Hydrogen from \( H C l \) can be prepared by
A . \( M g \)
в. \( C u \)
\( c . P \)
D. \( P t \)


The secondary structure of a protein
refers to?
A. Hydrophobic interactions
B. Sequence of \( \alpha \) -amino acids
C. Fixed configuration of the polypeptide backbone
D. \( \alpha \) -helical backbone


Translocation of photosynthetic end products in sieve tubes is
\( A \cdot 3-5 m m / \) hour
B. 3 - 5 cm / hour
c. \( 1-15 \mathrm{cm} / \) hour
D. \( 50-100 \mathrm{cm} / \) hour


When Li, Na, and K are placed in decreasing order of their ionisation
energy, the order is :
A . Li, к, Na
B. \( \mathrm{K}, \mathrm{Na}, \mathrm{Li} \)
c. Na, Li, K
D. Li, Na, K


Write the modern definition of acid and
base. Explain it by giving one example
of each?


The geometry of \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{\boldsymbol{6}} \) is:
A. planar hexagon
B. regular octahedron
c. distorted octahedron
D. square bipyramid


The acid showing salt-like character in aqueous solution is:
A . acetic acid
B. benzoic acid
c. formic acid
D. \( \alpha \) -amino acetic acid


In the half wave rectifier circuit
operating from \( 50 H z \) mains frequency, the fundamental frequency in the ripple would be
\( \mathbf{A} \cdot 25 H z \)
B. \( 50 \mathrm{Hz} \)
c. \( 70.7 H z \)
D. \( 100 H z \)


Assertion
lonization takes place in polar covalent
compounds
Reason
It involves transfer of electron from less
electronegative to more electronegative element to form charged species
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


Equal torsional torques act on two rods X and Y having equal length but the
diameter of \( Y \) is twice that wire \( X . \) If \( \theta_{x} \)
and \( \theta_{y} \) are angles of twist,
A \( \cdot \theta_{x}=\frac{1}{2} \theta_{y} \)
в. \( \quad \theta_{x}=\frac{1}{4} \theta_{y} \)
\( \mathbf{c} \cdot_{\theta_{y}}=\frac{\theta_{x}}{8} \)
D. \( _{\theta_{y}}=\frac{1}{16} \theta_{x} \)


The rate of reaction does not depend
upon
A. Temperature
B. Concentration
c. catalyst
D. None of these


A body of weight \( 72 \mathrm{N} \) moves from the surfaceof earth at a height half of the radius of theearth, then gravitational force exerted on it will be :
A. 36 N
в. 32 N
c. 144 N
D. 50 N


Gymnosperms are naked seeded plants, because
A. There is no ovule.
B. There is no fruit.
c. There is no ovary and fruit.
D. There is no fertilization


What is breathing? Explain the mechanism of breathing.


Assertion
Alkali metals are strong reducing agents, while halogens [non-metals], are strong oxidising agents.
Reason
Metals have 1,2 or 3 valence electrons so
they always ionize by losing electrons while non metals have 4,5,6 or 7 valence electrons so they ionize by gaining electrons.
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