A particle moves along y-axis according to the equation \( y(\text { in } c m)= \)
\( 3 \sin 100 \pi t+8 \sin ^{2} 50 \pi t-6 \)
This question has multiple correct options
A. the particle performs SHM
B. the amplitude of the particle's oscillation is 5 cm
c. the mean position of the particle is at \( y=-2 \mathrm{cm} \)
D. the particle does not perform SHM


Find \( y^{2}+\frac{1}{y^{2}} \) and \( y^{4}+\frac{1}{y^{4}} \) if \( y+\frac{1}{y}=9 \)


Represent \( -\frac{7}{5} \) on no line


Which of the following statement is
incorrect about \( \boldsymbol{I F}_{\mathbf{7}} ? \)
A. The total number of \( 90^{\circ} F-I-F \) bond angles is 10
and the total number of \( 72^{\circ} F-I-F \) bond angles is
5
B. The axial \( F-I \) bond lengths are not longer than
equatorial \( F-I \) bond lengths
C. The molecular geometry is pentagonal bipyramidal
D. The hybridisation of central atom is \( s p^{3} d^{3} \)


Among \( N H_{3}, H_{2} O \) and \( H F, \) which
would you expect to have highest magnitude of hydrogen bonding and why?


Morphines are:
A. tranquilizers
B. analgesics
C . narcotic analgesics
D. none of these


Find the slope of the line passing through the points (3,-2)\( \&(7,-2) \)


Liquid \( S O_{2} \) is aprotic solvent. If true
write 1 , else write 0 .


The function \( f(x)=|x| \) at \( x=0 \) is:
A. continuous but non-differentiable
B. discontinuous and differentiable
c. discontinuous and non-differentiable
D. continuous and differentiable


The vapour pressure of a mixture of two
volatile liquids is expressed as \( \boldsymbol{P}_{\boldsymbol{m}}= \)
\( 6.0+1.5 X_{B}, \) where, \( X_{B} \) is mole
fraction of \( \boldsymbol{B} \) is a mixture. The vapour
pressure of \( \boldsymbol{A} \) at the same temperature is:


To determine the position of a point like object precisely light should
be used.
A. polarized
B. short wavelength
c. long wavelength
D. intense


Iso-propyl amine is a:
A. primary amine
B. secondary amine
C . teritary amine
D. quaternary amine


If \( A \) is a square matrix of order 3 such
that \( A^{2}+A+4 I=0, \) where 0 is the
zero matrix and \( I \) is the unit matrix of
order \( 3, \) then
A. \( A \) is singular and \( A+I \) is non-singular
B. A is non-singular and \( A+I \) is non-singular
c. \( A \) is non-singular and \( A+I \) is singular
D. \( A \) is singular and \( A+I \) is singular
E. \( A \) is non-singular and \( A-I \) is singular


Find the common solution:
\( 2 x+y=8 \)
\( \boldsymbol{x}-\boldsymbol{y}=\mathbf{1} \)


Solve and graph the inequality. Give
answer in interval notation.
\( -6 x+12>-7 x+17 \)
\( A \cdot(5, \infty) \)
В \( \cdot(-\infty, 5) \)
\( c \cdot(29, \infty) \)
\( \mathbf{D} \cdot(-\infty, 29) \)


\( \operatorname{does} f(x)=x \) is equivalence function?


Electrolysis of water to form hydrogen
and oxygen gases is :
A. precipitation
B. oxidation-reduction
c. distillation
D. hydration
E. condensation


\( \int \frac{5 x-2}{1+2 x+x^{2}} d x \)


A solid metal cone with radius of base
\( 12 \mathrm{cm} \) and height \( 24 \mathrm{cm}, \) is melted to form spherical solid balls of diameter 6 \( \mathrm{cm} \) each. Find the number of balls thus
formed.
A . 30
B. 31
\( c \cdot 32 \)
D. 34


Factorise: \( 7 y^{3}+12 z^{3} \)


For an ideal liquid solution, which of the
following is unity?
A. Activity coefficient
B. Fugacity coefficient
c. Fugacity
D. Activity


The moment of inertia of a hollow
cubical box of mass \( M \) and side a
about an axis passing through the centres of two opposite faces is equal to
A \( \cdot \frac{5 M a^{2}}{3} \)
в. \( \frac{5 M a^{2}}{6} \)
c. \( \frac{5 M a^{2}}{12} \)
D. \( \frac{5 M a^{2}}{18} \)


Evaluate:
\( 8\left(x^{3} y^{2} z^{2}+x^{2} y^{3} z^{2}+x^{2} y^{2} z^{3}+x^{2} y^{2} z^{2}\right) \)
\( 4 x^{2} y^{2} z^{2} \)


In what respect do you consider
bacteria as simple organisms?


Magnetic flux has the dimension
\( \mathbf{A} \cdot M L^{2} A^{-2} \)
B \( \cdot M L^{2} T^{-2} A^{-1} \)
\( \mathbf{C} \cdot M T^{-2} A^{-1} \)
D. \( M L^{2} T^{-2} A^{-2} \)


A thin copper wire length L increases its length by \( 1 \% \) heated from
temperature \( T_{1} \) and \( T_{2} \) What is the
percentage change in area when a thin copper plate having dimension \( 2 \mathrm{Lx} \) Lis
heated from \( \boldsymbol{T}_{1} \) to \( \boldsymbol{T}_{2} \)
A. \( 0.5 \% \)
B . 1 \%
c. \( 2 \% \)
D. 4 \%


Magnetic lines of force
A. are mere directions
B. have no physical reality
C. can be used to indicate the direction of the magnetic field at point
D. all the above are correct


Find the area of a trapezoid with bases of 21 and \( 17 \mathrm{mm}, \) and a height of \( 10 \mathrm{mm} \)
A \( .190 m^{2} \)
в. \( 190 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 190 m m^{3} \)
D. \( 190 \mathrm{mm}^{2} \)


An ice cube floats on water in a beaker with \( \frac{9}{10} \) th of its volume submerged under water. What fraction of its volume
will be submerged if the beaker of water is taken to the moon where the gravity is \( 1 / 6^{t h} \) that on the earth?
\( A \cdot \frac{9}{10} \)
в. \( \frac{27}{50} \)
\( c \cdot \frac{2}{3} \)
D. zero


Greatest ratio of roots of \( 4 x^{2}-2\left(a^{2}+\right. \)
\( \left.b^{2}\right) x+a^{2} b^{2}=0 \) if \( a=2 b \)


Osmotic pressure of a solution is:
This question has multiple correct options
A. directly proportional to the molar concentration of the solution
B. inversely proportional to the molecular weight of the solute
C. inversely proportional to the temperature
D. directly proportional to the volume of the solution


Find the \( Q \) -value and the kinetic energy
of the emitted \( \alpha \) - Particle in the \( \alpha \) -decay of \( (a)_{86}^{220} R n \) and
(b) 226
88 Ra.
Given:
\( \boldsymbol{m}\left(_{\mathbf{8 8}}^{226} \boldsymbol{R} \boldsymbol{a}\right)=\mathbf{2 2 6 . 0 2 5 4 0} \boldsymbol{u} \)
\( \boldsymbol{m}\left(_{86}^{222} \boldsymbol{R} \boldsymbol{n}\right)=\mathbf{2 2 2 . 0 1 7 5 0} \boldsymbol{u} \)
\( \boldsymbol{m}\left(_{84}^{216} \boldsymbol{P o}\right)=\mathbf{2 1 6 . 0 0 1 8 9} \boldsymbol{u} \)


Which of the following is unipolar transistor?
A . p-n-p transistor
B. n-p-n transistor
C. Field effect transistor
D. Point contact transistor


The use of zener diode is as


Which one of the following types of medicines is for treating indigestion?
A. Antibiotic
B. Analgesic
c. Antacid
D. Antiseptic


The process of reproduction which involves only a single parent to form an individual is called as
A. Sexual reproduction
B. Asexual reproduction
c. Isogamy
D. None of the above


The area of the region bounded by \( y= \)
\( \boldsymbol{x}-\mathbf{1} \mid \) and \( \boldsymbol{y}=\mathbf{1} \) is
A .
B. 2
\( c \cdot \frac{1}{2} \)
D. None of these


A car moving with speed v on a straight
road can be stopped with in distance
on applying brakes.id same car is
moving with speed 3 v and brakes provide half retardation, then car will stop after travelling distance.


A unit vector vectors perpendicular to each of the vectors \( 2 \hat{i}-\hat{j}+\hat{k} \) and \( 3 \hat{i}- \) \( 4 \hat{j}-\hat{k} \) is


If the velocity of a particle is \( \left(10+2 r^{2}\right) \)
\( \mathrm{m} / \mathrm{s} \) then the average acceleration of the particle between 2 s and 5 s is
A \( \cdot 2 m / s^{2} \)
B . \( 4 m / s^{2} \)
c. \( 12 m / s^{2} \)
D. \( 14 m / s^{2} \)


Figure shows a Wheatstone bridge
circuit. Which of the following correctly
shows the currents \( I_{1}, I_{2} \) and \( I_{3} \) in the
decreasing order of magnitude?
\( A \cdot I_{1}, I_{2}, I_{3} \)
В \( \cdot I_{2}, I_{3}, I_{1} \)
\( \mathrm{c} \cdot I_{2}, I_{1}, I_{3} \)
D \( \cdot I_{3}, I_{2}, I_{1} \)


Refer the given figure and select the
correct option regarding it.
A. P are dead sclerenchyma fibers that provide mechanical strength
B. Q helps in maintaining pressure gradient
C. \( R \) is the main conducting part of the phloem formed of cylindrical cells
D. S is living parenchyma cell that stores food


A car is traveling with linear velocity
on a circular road of radius \( r \). If it is
increasing its speed at the rate of 'a'
\( m s^{-2}, \) then the resultant acceleration
will be
A \( \cdot \sqrt{\frac{v^{4}}{r^{2}}+a^{2}} \)
B. \( \sqrt{\frac{v^{4}}{r^{2}}-a^{2}} \)
c. \( \sqrt{\frac{v^{2}}{r^{2}}+a^{2}} \)
D. \( \sqrt{\frac{v^{2}}{r^{2}}-a^{2}} \)


An electrovalent compound does not exhibit space isomerism due to:
A. presence of ions
B. high melting point
c. strong electrostatic forces between the constituent inss
D. non-directional nature of electrovalent bond


If \( \boldsymbol{y}=\log (\sec x+\tan x), \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A. \( \sec x-\tan x \)
B. \( \tan x \)
\( c \cdot \sec x \)
D. \( \cos x \)


State whether the following statements
are true or false.
All of the molecules available for
biosynthesis constitute the metabolic pool
A. True
B. False


A charge particle of mass 'm' \& charge q is released from rest from a given position \( Q \) inside a fixed vertical
semicircular trough. For the presence and the absence of magnetic field
normal reaction acting on the change at
Pare \( N_{1} \) and \( N_{2} \) respectively. Neglecting friction and assuming
gravity presence. The value of \( N_{1}-N_{2} \)
is:
A \( .2 B q \sqrt{2 g R} \)
в. \( \frac{B q \sqrt{2 g R}}{2} \)
с. \( B q \sqrt{2 g R} \)
D. \( \frac{B q \sqrt{2 g R}}{4} \)


Unpolarized light of intensity \( 32 W m^{-2} \) passes through three polarizes such that the transmission axis of the last
polarizers is crossed with that of the first. The intensity of final emerging light is \( 3 W m^{-2} \). The intensity of light transmitted by the first polarizered will be
\( \mathbf{A} \cdot 32 W m^{-2} \)
B. \( 16 \mathrm{Wm}^{-2} \)
\( \mathrm{c} \cdot 8 \mathrm{Wm}^{-2} \)
D. \( 4 \mathrm{Wm}^{-2} \)


The equilibrium constant for the
following reaction is \( 64 . H_{2} O(l)+ \)
\( \boldsymbol{C O}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g}) . \) If the rate
constant for the forward reaction is 160
the rate constant for the backward
reaction is:
A . 0.4
B . 2.
c. 6.2
D. 10.24


The point where the waves originate is called the \( _{-}--_{-}- \) of the earthquake
A. centre
B. epicenter
c. focus
D. origin


Electric field due to an infinite sheet of
charge having surface density \( \sigma \) is \( E \) Electric field due to an infinite
conducting sheet of same surface density of charge is
A. \( E / 2 \)
в. \( E \)
\( c .2 E \)
D. \( 4 E \)


\( \int \frac{2 d x}{x^{2}-1} \) equals:
\( \mathbf{A} \cdot \frac{1}{2} \log \left(\frac{x+1}{x-1}\right)+C \)
B \( \cdot \frac{1}{2} \log \left(\frac{x-1}{x+1}\right)+C \)
\( \mathbf{c} \cdot \log \left(\frac{x+1}{x-1}\right)+C \)
D \( \log \left(\frac{x-1}{x+1}\right)+C \)


If \( f(n+1)=f(n) \) for all \( n \in \)
\( N, f(7)=5 \) then \( f(35)= \)
A . 25
B . 49
\( c .35 \)
D. 5


Which of the following ions can easily cause coagulation of proteins?
A. \( A g^{+} \)
в. \( N a^{\text {t }} \)
c. \( M g^{2+} \)
D. \( C a^{2} \)


The best reducing agent of the following
is :
A \( . H_{2} S \)
B. \( C l^{-} \)
\( \mathbf{c} \cdot S O_{4}^{2-} \)
D. \( O_{3} \)


If we want to see our full image then the minim um size of the plane mirror
A. Should be twice of our height
B. Should be of our height
c. should be half of our height
D. Depends upon our distance from mirror


A ring of mass \( m \) sliding on a smooth
surface with velocity \( v_{0} \) enters rough surface with coefficient of kinetic
energy \( \mu_{k}, \) then
A. The linear distance moved by centre of mass before the riong starts pure rolling is \( \frac{3 v_{0}^{2}}{8 \mu_{k} g g_{0}^{2}} \)
B. The gain in kinetic energy is \( \frac{m v_{0}^{2}}{8} \)
C. The loss in kinetic energy is \( \frac{m v_{0}^{2}}{4} \)
D. The work done by friction force is \( -\frac{3 m v_{0}^{2}}{8} \)


Define echo.


\( \int \sqrt{\boldsymbol{x}} \cdot \log \boldsymbol{x} \boldsymbol{d} \boldsymbol{x}= \)
A. \( \frac{2}{3} x^{3 / 2} \cdot \log x-\frac{4}{9} x^{3 / 2}+c \)
B \( \cdot \frac{2}{3} x^{3 / 2} \cdot \log x+x^{3 / 2}+c \)
c. \( \quad x^{3 / 2} \cdot\left(\log x-\frac{2}{3}\right)+c \)
D \( \cdot \frac{2}{5} x^{3 / 2}(\log x+1)+c \)


Two masses \( m_{1} \) and \( m_{2} \) are suspended
together by a massless spring of spring
constant \( k \) as shown in the figure. When
the masses are in equilibrium, \( m_{1} \) is
removed without disturbing the system.
Find the angular frequency and
amplitude of oscillation of \( \boldsymbol{m}_{2} \)
A \( \cdot \sqrt{\frac{k}{3 m_{2}}} \)
B. \( \sqrt{\frac{k}{m_{2}}} \)
c. \( \sqrt{\frac{k}{2 m_{2}}} \)
D. \( \sqrt{\frac{k}{4} m_{2}} \)


\( \int \frac{\ln (1+x)}{1+x} d x \) equals
A \( \cdot \frac{(\ln (1+x))^{2}}{2} \)
B . \( -\pi \ln (1+x) \)
c. \( \frac{\pi}{2} \ln (1+x) \)
D. \( -\frac{\pi}{2} \ln (1+x) \)


Sound is a form of:
A . heat
B. vibration
c. energy
D. frequency


Differentiate with respect to \( x \)
\( \boldsymbol{y}=\log (1+\sin \boldsymbol{x}) \)


The IUPAC name of the compound
\( \boldsymbol{C}_{3} \boldsymbol{H}_{5}-\boldsymbol{C H}_{2}-\boldsymbol{C} \equiv \boldsymbol{C H} \) is 3
cyclopropyl-1-propyne.
A. True
B. False


Illustrate with example, the difference between a double salt and coordination
compound.


For which reaction will \( \Delta \boldsymbol{H}=\Delta \boldsymbol{U} ? \)
Assume each reaction is carried out in
an open container.
\( \mathbf{A} \cdot H_{2}(g)+B r_{2}(g) \longrightarrow 2 H B r(g) \)
B \( \cdot C(s)+2 H_{2} O(g) \longrightarrow 2 H_{2}(g)+C O_{2}(g) \)
\( \mathbf{c} \cdot 4 C O(g)+2 O_{2}(g) \longrightarrow 4 C O_{2}(g) \)
D. \( 2 P C l_{5}(g) \longrightarrow 2 P C l_{3}(g)+2 C l_{2}(g) \)


Which of the following process does not occur through convection:
A. Boiling of water
B. Land breeze and Sea breeze
c. circulation of air around furnace
D. Heating of glass bulb through filament


A shell of mass \( 0.020 k g \) is fired by a
gun of mass \( 100 k g . \) If the muzzle speed
of the shell is \( 80 m s^{-1} . \) What is the
recoil speed of the gun?
\( \mathbf{A} \cdot 1.6 \mathrm{cm} s^{-1} \)
B. \( 0.5 \mathrm{cms}^{-1} \)
\( \mathrm{c} \cdot 2 \mathrm{cms}^{-1} \)
D. \( 3 c m s^{-1} \)


The figure shows the graphical
variation of the reactance of a capacitor
with frequency of ac source.
An ideal inductor has the same
reactance at \( 100 H z \) frequency as the
capacitor has at the same frequency.
Find the value of inductance of the
inductor.


Find the domain of the following real
functions :
(i) \( f(x)=\sqrt{16-x^{2}} \)


Integrate \( \int \frac{3 x-1}{(x-1)(x-2)(x-3)} d x \)


f \( \alpha, \beta, \gamma \) are the angles which a directed line makes with the positive directions
of the coordinate axes, then \( \sin ^{2} \alpha+ \)
\( \sin ^{2} \beta+\sin ^{2} \gamma \) is equal to
A . 1
B. 4
\( c .3 \)
D. 2


Which one of the following electrolytes has the same value of van't Hoff's factor
(i) as that of \( A l_{2}\left(S O_{4}\right)_{3} \) (if all are \( 100 \% \) ionised)?
\( \mathbf{A} \cdot A l\left(N O_{3}\right)_{3} \)
B . \( K_{4}\left[F e(C N)_{6}\right] \)
\( \mathrm{c} \cdot \mathrm{K}_{2} \mathrm{SO}_{4} \)
D. \( K_{3}\left[F e(C N)_{6}\right] \)


\( X \times 100 \mathrm{mL} \) water must be added to
\( 300 \mathrm{mL} \) of \( 0.2 M \) solution of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) for the degree of
dissociation of the acid to double?
The value of \( X \) is
\( \left[\boldsymbol{K}_{a} \text { for acetic acid }=\mathbf{1 . 8} \times \mathbf{1 0}^{-\mathbf{5}}\right] \)


A smooth steel ball strikes a fixed
smooth steel plate at an angle \( \theta \) with the vertical. If 'e' is the coefficient of
restitution, the angle at which the rebounce will take place with the vertical is
A \( \cdot \alpha=\tan ^{-1}\left(\frac{\tan \theta}{e}\right) \)
B. \( \alpha=\tan ^{-1}\left(\frac{\cot \theta}{e}\right) \)
c. \( _{\alpha=\tan ^{-1}\left(\frac{\sin \theta}{e}\right)} \)
D・ \( \alpha=\tan ^{-1}\left(\frac{e}{\tan \theta}\right) \)


If 10 grams of ice and 1 gram of steams are allowed to attain thermal
equilibrium, what will be the resultant temperature.


Ethylidene chloride and ethylene dichloride are:
A. chain isomers
B. position isomers
c. functional isomers
D. metamers


A solid sphere starts rolling down on an inclined plane from a vertical height
\( 3.5 m . \) The velocity of centre of mass of sphere on reaching the bottom of inclined plane is :
A \( .2 .45 \mathrm{ms}^{-1} \)
в. \( 4.9 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 7 m s^{-1} \)
D. \( 9.8 m s^{-1} \)


A circle touches the hypotenuse of a right-angled triangle at its middle point and passes through the mid-point of the shorter side. If \( a \) and \( b(a<b) \) be the
length of the sides, then prove that the radius is \( \frac{b}{4 a} \sqrt{a^{2}+b^{2}} \)


Tyndall effect is shown by:
A . precipitate
B. sol
c. plasma
D. solution


Which electrons are easy to create as
free electrons?
A. Electrons in the first shell
B. Electrons in the outermost valence shell
C. Electrons present beyond the valence shell
D. All of the above


Find \( \mathrm{BC} \), if \( \mathrm{AB}=7.2 \mathrm{cm} \)
A. \( 7.2 \mathrm{cm} \)
B. \( 7.1 \mathrm{cm} \)
\( c \cdot 0.72 \mathrm{cm} \)
D. \( 72 \mathrm{cm} \)


Label the given diagram showing lead
storage battery
\( \mathbf{A} \cdot p-P b, q-P b O_{2}, r-5 M H_{2} S O_{4} \)
B. p- \( P b O_{2}, q-P b, \) r- conc. \( H_{2} S O_{4} \)
c. \( p-P b_{3} O_{4}, q-P b O_{2}, r-50 \% H_{2} S O_{4} \)
D. \( p-P b O_{2}, q-P b, r- \) dil. \( 38 \% H_{2} S O_{4} \)


Assertion
Medicines in the colloidal state are
more effective.
Reason
In the colloidal state, the medicines are
easily assimilated by the body.
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 incorrect but Reason is correct
D. Both Assertion and Reason are correct


The number of subsets \( \boldsymbol{R} \) of \( \boldsymbol{P}= \)
\( (1,2,3, \dots, 9) \) which satisfies the
property "There exit integers \( \mathbf{a} \in \mathbf{R}, \mathbf{b} \in \) \( \mathbf{R}, \mathbf{c} \in \mathbf{R}^{\prime \prime} \) is
A .512
в. 466
c. 467
D. None of these


The rain drops falling from the sky neither injure us nor make holes on the ground because they move with:
A. constant acceleration
B. variable acceleration
c. variable speed
D. constant terminal velocity


Prove that \( 2.7^{n}+3.5^{n}-5 \) is divisible
by 24 for all \( n \in N \)


Which of the following have identical bond order?
(I) \( \boldsymbol{C} \boldsymbol{N}^{-} \)
(II) \( \boldsymbol{O}_{\mathbf{2}}^{-} \)
\( (\|\|) N O^{+} \)
\( (\mid V) C N^{+} \)
A . ।, ॥
B. ॥, IV
c. ।, ॥।, ॥।
D. I, IV


Find a point on the \( x \) -axis which is
equidistant from the points (7,6) and
(3,4)


How many molecules are present in \( 10 g \)
of \( \boldsymbol{H}_{2} \boldsymbol{O} ? \)


Which of the following structures helps in the absorption of water from the soil?
A. Root hair
B. Root tip
c. Stomata
D. None of the above


If \( \triangle(r)=\left|\begin{array}{cc}r & r^{3} \\ 1 & n(n+1)\end{array}\right|, \) then \( \sum_{r=1}^{n} \triangle(r) \)
is equal to
\( ^{A} \cdot \sum_{i=1}^{n} r \)
B. \( \sum_{n=1}^{n} r \)
\( c \cdot \sum^{n} \)
D. \( \sum_{n=1}^{n} r^{4} \)


State whether the triangles are
congruent or not \( ? \) Give reasons for your
answer?


The ratio of the energy required to raise a satellite the upto a height h above the earth of radius \( R \) to that the kinetic
energy of the satellite into that orbit is:
A . R: h
B. h: R
\( c \cdot R: 2 h \)
D. 2h: R


\( \lim _{x \rightarrow 0} \frac{\sin m x}{\sin n x}[m / n] \)


The energy of an electron in the ground
state of \( \boldsymbol{H} \) atom is \( -\mathbf{1 3 . 6 e V} \)
The negative sign indicates that:
A. electrons are negatively charged
B. \( H \) atom is more stable than a free electron
c. energy of the electron in the H atom is lower than that of a free electron
D. work must be done to make a \( H \) atom from a free electron and proton


If a line intersects a circle in two
distinct points then it is known as a
A. chord
B. secant
c. tangent
D. segment


Two 220 volt, 100 watt bulbs are connected first in series and then in
parallel. Each time the combination is connected to a 220 volt a.c.supply line. The power drawn by the combination in each case respectively will be
A. 50 watt, 100 watt
B. 100 watt, 50 watt
c. 200 watt, \( , 150 \) watt
D. 50 watt, 200 watt


Three equal charges, each having a
magnitude of \( 2.0 \times 10^{-6} C \) are placed
at the three corners of a right angled triangle of sides \( 3 \mathrm{cm}, 4 \mathrm{cm} \) and \( 5 \mathrm{cm} \) The force (in magnitude) on the charge
at the right angled corner is :
\( A .50 N \)
B . \( 26 N \)
\( \mathbf{c} \cdot 29 N \)
D. 45.9 N


Two drops of the same radius are falling are falling through air with a steady velocity of \( 5 \mathrm{cm} / \mathrm{s} \). If the two drops coalesce, the terminal velocity would be
A \( .10 \mathrm{cm} / \mathrm{s} \)
B. \( 2.5 \mathrm{cm} / \mathrm{s} \)
c. \( 5(4)^{1 / 3} c m / s \)
D. \( 5(3)^{1 / 3} \mathrm{cm} / \mathrm{s} \)


Succession on secondary bare area is
A. Primosere
B. Xerosere
c. subsere
D. None of the above


The chemical digestion of food starts in the
A. Mouth
B. Stomach
c. Esophagus
D. Small intestine
E. Large intestine


The solution of \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\left(\boldsymbol{1}+\boldsymbol{y}^{2}\right)(\boldsymbol{1}+ \)
\( \left.x^{2}\right)^{-1} \) is?
A. \( y-x=c(1+x y) \)
в. \( y+x=c(1+x y) \)
c. \( y=(1+2 x) c \)
D. \( x y=x^{2}+x+x \)


Find product in the following reaction is
Y. What is Y?
A. benzamide
B. benzophenone
\( c . \) benzoic acid
D. benzaldehyde


A 1000 Wheater has more resistance
than a 100 W bulb.


The link between parents and offspring
is
A. Gonads
B. Gametes
c. zooids
D. Hybrids


Which of the following are necessary for photosynthesis?
A. Light and suitable temperature
B. Chlorophyll and water
c. Carbon dioxide
D. All of the above


An element has nine positive charges in its nucleus. Its common oxidation state
is:
\( A \cdot+7 \)
B. +5
\( c \cdot-1 \)
D. +1


If the longitudinal strain in a cubical body is three times the lateral strain then the bulk modulus \( K, \) Young's modulus \( Y \) and rigidity \( \eta \) are related by
This question has multiple correct options
A. \( K=Y \)
в. \( \eta=\frac{3 Y}{8} \)
c. \( Y=\frac{3 \eta}{8} \)
D. \( Y=\eta \)


Stream line motion becomes turbulent
motion when the velocity of the liquid is:
A. beyond critical velocity
B. critical velocity
c. below critical velocity
D. variable velocity


Which of the following element has the
least metallic character?
A. \( C \)
B. \( S \) i
c. \( G e \)
D. \( S n \)


The following reaction is known to occur in the human body:
\( \boldsymbol{C O}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \rightleftharpoons \boldsymbol{H}_{2} \boldsymbol{C O}_{3} \rightleftharpoons \boldsymbol{H}^{+}+ \)
\( \boldsymbol{H} \boldsymbol{C O}_{\mathbf{3}}^{-} \)
If \( C O_{2} \) escapes from the system
A . pH will decrease
B. \( H^{+} \) ion concentration will decrease
c. \( H_{2} C O_{3} \) concentration will be unaltered
D. The forward reaction will be promoted


The period of oscillation of a simple pendulum of length lis given by \( \boldsymbol{T}= \) \( 2 \pi \sqrt{l / g} . \) The length lis about \( 10 \mathrm{cm} \) and
is known to \( 1 \mathrm{mm} \) accuracy. The period of oscillation is about 0.5 s. The time of 100 oscillations has been measured
with a stop watch of 1 s resolution. Find
the percentage error in the determination of \( \mathfrak{g} \)


A fraction becomes \( \frac{4}{5}, \) if 1 is added to
both numerator and denominator. If
however, 5 is subtracted from both
numerator and denominator, the fraction becomes \( \frac{1}{2} . \) What is the fraction?


How many lines of symmetry are there in a triangle which has all the angles equal?
A . 1
B . 2
\( c .3 \)
D. 4


The least value of \( \boldsymbol{f}(\boldsymbol{x})=\left(\boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{e}^{-\boldsymbol{x}}\right) \) is
A . -2
B.
\( c \cdot 2 \)
D. none of these


Calvin cycle is
A. Dependent on light
B. Not dependent on light
C. All of the above
D. None of the above


The name of the figure formed by the points (0,0,0),(1,0,1) and (0,1,1) is
A . a straight line
B. an isosceles triangle
c. an equilateral triangle
D. a scalene triangle


Find the centre and radius of the circle
\( x^{2}+y^{2}=36 \)


Write the IUPAC name of the following amine.
\( \boldsymbol{H}_{2} \boldsymbol{N}-\left(\boldsymbol{C} \boldsymbol{H}_{2}\right)_{6}-\boldsymbol{N} \boldsymbol{H}_{2} \)


A metal 'X' is found in form of filing which burns vigorously when sprinkled on flame when these filings are heated
with sulphur, a black coloured compound 'Y' is formed which is not
attracted by magnet 'X' reacts with di HCl to hydrogen gas 'X' reacts with steam to form 'Z' along with hydrogen
gas. Identify 'X', 'Y' and 'Z' and write the
chemical reactions involved?


Identify the non-Green House Gas (GHG) from the following
A. Methane
B. Nitrous oxide
c. sulphur hexafluoride
D. Carbon monoxide


\( \ln 20 \) minutes of \( 80 \% \) of \( N_{2} O_{5} \) is
decomposed. Rate constant is:
\[
\begin{array}{l}
\mathrm{N}_{2} \mathrm{O}_{5} \stackrel{\mathrm{Keq}}{\longleftarrow} \mathrm{NO}_{2}+\mathrm{NO}_{3}(\text { fast equilibrium }) \\
\mathrm{NO}_{2}+\mathrm{NO}_{3} \frac{\mathrm{k}_{1}}{ } \mathrm{NO}_{2}+\mathrm{NO}+\mathrm{O}_{2}(\text { slow }) \\
\mathrm{NO}+\mathrm{NO}_{3} \frac{\mathrm{k}_{2}}{\longrightarrow} 2 \mathrm{NO}_{2}(\text { fast })
\end{array}
\]
A . 0.08
B. 0.05
c. 0.12
D. 0.2


Assertion
A spectral line will be observed for
\( 2 P_{z}-2 P_{y} \) transition
Reason
The energy of \( 2 P_{x} \) and \( 2 P_{y} \) orbitals is
the same
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


In the expansion of \( \left(7^{1 / 3}+11^{1 / 9}\right)^{6561} \)
prove that three will be only 730 term which are free from radicals


A metallic carbide on treatment with
water gives a colourless gas which burns readily in air and gives a precipitate with ammonical silver nitrate solution. The gas evolved is :
A \( . C H_{4} \)
в. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{2} H_{4} \)
D. \( C_{2} H_{2} \)


Let \( A=Q \times Q \) and let \( ^{\star} \) be a binary
operation on \( A \) defined by \( (a, b) * \)
\( (c, d)=(a c, b+a d) \) for \( (a, b),(c, d) \in \)
A. Determine, whether \( ^{*} \) is
commutative and associative. Then
with respect to \( ^{*} \) on \( A \).Find the identity
element of \( \boldsymbol{A} \)


Evaluate \( \int_{0}^{1} e^{2-3 x} d x \) as a limit of a sum.


An example of chemical change is:
A. water condensing on the outside of your cold beverage
B. bending a wire
C . slicing bread
D. freezing water
E. burning a candle


The domain of \( f(x)=\tan 2 x \) is
\( A \cdot(-\infty, \infty) \)
B . \( R-\left\{(2 n+1) \frac{\pi}{4}, n \in Z\right\} \)
c. \( R-\left\{(n+1) \frac{\pi}{4}, n \in Z\right\} \)
D. \( R-\{n \pi, n \in Z\} \)


For a moving particle doing round trip which of the following options may be
correct? Here, \( V_{a v} \) is average velocity
and \( u_{a v} \) the average speed.
A \( \cdot\left|V_{a v}\right|<u_{a v} \)
В . \( \left|V_{a v}\right|>u_{a v} \)
C \( \cdot V_{a v}=0 \) but \( u_{a v} \neq 0 \)
D. \( V_{v v} \neq 0 \) but \( u_{a v}=0 \)


Let \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}+\cos \boldsymbol{x}+\tan \boldsymbol{x}+ \)
\( \arcsin x+\arccos x+\arctan x . \) If \( \mathrm{M} \) and
\( \mathrm{m} \) are maximum and minimum values
of \( f(x) \) then their arithmetic mean is
equal to
A \( \cdot \frac{\pi}{2}+\cos 1 \)
B . \( \frac{\pi}{2}+\sin 1 \)
C \( \cdot \frac{\pi}{4}+\tan 1+\cos 1 \)
D. \( \frac{\pi}{4}+\tan 1+\sin 1 \)


A force of 50 dynes is acted on a body of mass \( 5 g \) which is at rest for an interval
of 3 seconds, then impulse is \( (\text { in } N s) \)
A. \( 1.5 \times 10^{-3} \)
B. \( 1.5 \times 10^{-2} \)
c. \( 2.5 \times 10^{-} 3 \)
D. \( 1.5 \times 10^{3} \)


Burial of dead with due rites is
considered to be important step in human evolution. Which human was
first to perform these ceremonies?


Study the graph which shows results of
three different experiments \( P, Q \) and \( R \)
Concentrate on graphs \( \mathrm{P} \) and \( \mathrm{Q} \) and
answer the following questions?
What is the difference between the
Curves?
A. The temperature has increased at
B. The rate of photosynthesis increased faster in \( Q \) and in \( P \)
C. The rate of photosynthesis lowered in \( Q \) and
D. The temperature has lowered at \( Q \)


A compound of vanadium has a
magnetic moment of \( 1.73 B M . \) The
electronic configuration of vanadium ion in the compound is:
A \( \cdot[A r] 3 d^{2} \)
B \cdot \( [A r] 3 d^{1} 4 s^{0} \)
c. \( [A r] 3 d^{3} \)
\( \mathbf{D} \cdot[A r] 3 d^{0} 4 s^{1} \)


Gold ore is concentrated by leaching
with
A. sodium cyanide in presence of air.
B. sodium cyanide in absence of air
c. sodium hydroxide in presence of air
D. sodium hydroxide in absence of air


Match the physical quantities given in Column I with suitable dimensions
expressed in Column II.
II Column I \( \quad \) Column
a) Angular momentum
1) \( M^{-1} L^{3} T^{-2} \)
b) Torque
2) \( M L T^{-2} \)
c) Gravitational constant
3) \( M L^{2} T^{-2} \)
d) Tension
4) \( M L^{2} T^{-1} \)
A. a-1, b-3, c-4, d-2
B. a-1, b-4, c-3 d-2
c. \( a-4, b-3, c-1, d-2 \)
D. a-1, b-2, c-4, d-3


Assertion
Energy is a scalar quantity
Reason
All conserved quantities are scalars
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 displacement of particle from \( t=0 \)
to \( t=2 \) seconds is
\( \mathbf{A} \cdot 1 m \)
B. \( 2 m \)
\( c .3 m \)
D. \( 4 m \)


The radius of the circular conducting
loop shown in figure is \( \boldsymbol{R} \). Magnetic field
is decreasing at a constant rate \( \alpha \) Resistance per unit length of the loop is
\( \rho . \) Then, the current in wire \( A B \) is \( (A B \)
is one of the diameters)
\( ^{\mathbf{A}} \cdot \frac{R \alpha}{2 \rho} \) from \( A \) to \( B \)
в. \( \frac{R \alpha}{2 \rho} \) from \( B \) to \( A \)
\( ^{c} \cdot \frac{R \alpha}{\rho} \) from \( B \) to \( A \)
D.
E . answer required


\( \cot A \) is the product of \( \cot \) and \( A \)
A. True
B. False


\( \int(\tan x-\cot x)^{2} d x= \)
A \( \cdot \tan x+x+c \)
B. \( \tan x-x+c \)
c. \( \tan x-\cot x+c \)
D. \( \tan x-\cot x-4 x+c c \)


n the figure of \( \Delta A B C, D E \| A B \)
\( f A D=2 x, D C=x+3, B E=2 x-1 \) and
\( C E=x, \) then find the value of \( x \)


Differentiate w.r.t. \( \boldsymbol{x} \)
\( \frac{\boldsymbol{x}}{\boldsymbol{y}^{3}}=\mathbf{1} \)


What is the difference between
distillation, distillation under reduced
pressure and steam distillation?


Most reactive nobel gas is :
A . \( A r \)
в. \( X e \)
\( \mathrm{c} . \) Не
D. Ne


The odds that a book will be reviewed
favourably by three independent critics are 5 to 2,4 to 3 and 3 to 4 respectively; what is the probability that of three reviews a majority will be favourable?
A \( \cdot p=\frac{149}{343} \)
В. \( p=\frac{209}{343} \)
c. \( _{p}=\frac{129}{3 \frac{13}{33}} \)
D. \( _{p}=\frac{185}{343} \)


If \( \frac{\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{1}}=\boldsymbol{A}+\frac{\boldsymbol{B}}{\boldsymbol{x}+\mathbf{1}}+ \)
\( \frac{C}{(x+1)^{2}} \) then \( A-B= \)
A . \( 4 C \)
B. \( 4 C+1 \)
\( c .3 C \)
D. \( 2 C \)


Which of the following does not give oxygen on heating?
A. \( K C l O_{3} \)
B. \( Z n\left(C l O_{3}\right)_{2} \)
c. \( K_{2} C r_{2} O_{7} \)
D. \( \left(N H_{4}\right)_{2} C r_{2} O_{7} \)


Which one of the following compound is most reactive for E1 reaction?
A \( \ldots_{H_{3}-C H_{2}-C_{I B}^{r}}-C H_{3} \)
в. \( \quad C H_{3}-C H_{2}-\stackrel{P}{C}_{\}^{Y}-C_{6} H_{5} \)
\( ^{\mathrm{c}} \mathrm{CH}_{3}-C H_{2}-\stackrel{^{B r}}{_{\mathrm{I}}^{\mathrm{C}}}-C_{2} H_{5} \)
D. \( \quad \) Br CH \( _{3}-C H_{2}- \) CH \( -C H_{3} \),


\( \int_{2-\ell n 3}^{3+\ell n 3} \frac{\ln (4+x)}{\ell n(4+x)+\ell n(9-x)} d x \) is
equal to:
A. cannot be evaluated
B. is equal to \( \frac{5}{2} \)
c. is equal to \( 1+2 \ell n 3 \)
D. is equal to \( \frac{1}{2}+\ell n \) 3


In a vessel containing \( S O_{3}, S O_{2} \) and \( O_{2} \)
at equilibrium, some helium gas is introduced so that total pressure
increases while temperature and volume remain the same. According to Le Chatelier's principle, the dissociation
of \( \boldsymbol{S O}_{3} \)
A. increases
B. decreases
c. remains unalered
D. changes unpredictably


A living continuum of cells connected by plasmodesmata is
A. Dermal tissue
B. Ground complex
c. Donnan free space
D. symplast


A particle of mass \( 5 g \) is moving in a
circle of radius \( 0.5 m \) with an angular
velocity of 6 rad\( / \)s. Find
(i) the change
in linear momentum in half a revolution
(ii) the magnitude of the acceleration of the particle.


ff \( (x)=3 e^{x^{2}}, \) then \( f^{\prime}(x)-2 x f(x)+ \)
\( \frac{1}{3} f(0)-f^{\prime}(0) \) is equal to
A.
B.
\( \mathrm{c} \cdot \frac{7}{3} \mathrm{e}^{x} \)
D. ex \( ^{x^{2}} \)


\( 2 A+3 B \rightarrow 4 C \) if the rate of
decomposition of \( A \) is \( 2.5 \times 10^{-4} \) then
Calculate the rate of decomposition of B and rate of formation of 'C'.


Write the structure of Oelum \( \left(\boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{7}\right) \)


What is the procedure followed for testing the starch?


The co-ordination number of sodium in
sodium chloride is:
\( \mathbf{A} \cdot \mathbf{6} \)
B. 4
c. 8
\( D \)


The shape of methane molecule is:
A . pentahedral
B. hexahedral
c. octahedral
D. tetrahedral


Draw all of the isomers of an octahedral
complex which has three identical bidentate ligands.


Prove that:
\( \sin \left(\frac{\pi}{2}+\theta\right)= \)


The magnification produced by a mirror is \( -1.5 . \) What does it signify about the image formed?


We do not feel the pressure of the atmosphere around us, because the pressure in our bodies is roughly the same as the atmospheric pressure outside. Therefore, both the forces
acting on our bodies cancel out and we
do not feel uncomfortable. Type 1 for true and 0 for false


Calculate the acceleration of the athlete
during the first \( 3.0 s \) of the race


Solve the following equation using systematic method:
\( \boldsymbol{x}+\mathbf{7}=\mathbf{1 8} \)


Eka - silicon is a :
A. metal
B. non-metal
c. metalloid
D. none of the above


Two regular polygons are such that the
ratio between their number of sides is
1: 2 and the ratio of measures of their
interior angles is \( 3: 4 . \) Find the number of sides of each polygon.


Which one of the following hormones is released by posterior lobe of pituitary gland?
A. FSH
B. ADH
c. АСТН
D. MSH


A wire of radius \( r, \) Youngs modulus \( Y \) and length \( l \) is hung from a fixed point and supports a heavy metal cylinder of volume \( V \) at its lower end. The change
in length of wire when cylinder is immersed in a liquid of density \( \rho \) is in fact
A \( \cdot \) decreases by \( \frac{V l \rho g}{Y \pi r^{2}} \)
B. increases by \( \frac{V r \rho g}{Y \pi l^{2}} \)
c. decreases by \( \frac{V \rho g}{Y \pi r} \)
D. increases by \( \frac{V \rho g}{\pi r l} \)


Which of the following properties is not true for ozone?
A. It oxidises lead sulphide
B. It oxidises potassium iodide
c. It oxidises mercury
D. It cannot act as a bleaching agent


An astronaut can not hear his
compansion's sound at the surface of
moon because:
A. produced frequencies are above the audio frequency
B. sound wave does not propagate through vaccummmen
c. temperature is too low during night and high during day
D. none of the above


Explain Tranquilizers?


Solve
\( \left(3 x^{2}+4 y\right) \times(2 x+3 y) \)


Draw the structure of a nephron and label the following ; Glomerulus Bowman capsule, renal artery, collecting duct,
b) What happen to glucose that enters the nephron along with the filtrate


Obtain an expression for the magnetic field due to a short bar magnet, at a point on its axis at a distance x from its centre considering it as an equivalent of a solenoid.


Vapour pressure of a solvent containing nonvolatile solute is
A. more than the vapour pressure of a solvent
B. less than the vapour pressure of solvent
C. equal to the vapour pressure of solvent
D. none


If a curve passes through the point \( \left(2, \frac{7}{2}\right) \) and has slope \( \left(1-\frac{1}{x^{2}}\right) \) at any
point \( (x, y) \) on it, then the abscissa of the point on the curve whose ordinate is
\( \frac{-3}{2} \) is
\( A \cdot 2 \)
B. -2
c. 1
D. -


State whether the following statements
are true or false.
The term taxon is used to refer to the
concrete biological objects included in
a category
A. True
B. False


The numerical value of tan \( \left(2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right) \) is


A spherical body P has a positive charge on it. It attracts an another sphere \( \mathrm{Q} \)
placed near it. The sphere \( Q \) is
A. negatively charge
B. positively charge
c. neutral
D. may be negative or neutral


Calcium cyanamide on treatment with steam produces:
A. \( N H_{3}+C a O \)
в. \( N H_{3}+ \) СаНСО
c. \( N H_{3}+C a C O_{3} \)
D. \( N H_{3}+C a(O H)_{2} \)


Weight of a body of mass m decreases
by \( 1 \% \) when it is raised to height \( h \) above the Earth's surface. If the body is taken to a depth h in a mine, then its weight will:
A. Decreases by \( 0.5 \% \)
B. Decreases by \( 2 \% \)
c. Increases by \( 0.5 \% \)
D. Increase by \( 1 \% \)


Which of the following sulphates has the highest solubility in water?
A \( . . M g S O_{4} \)
в. \( B a S O_{4} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \)
D. \( B e S O_{4} \)


The points (2,-3),(4,3) and \( (5, k / 2) \) are on the same straight line. The value(s) of k is (are):
A . 12
B. -12
\( c .\pm 12 \)
D. 12 or 6


Two moles of gas \( A_{2} \) are mixed with two
moles of gas \( B_{2} \) in a flask of volume 1 lit.
If at equilibrium 0.5 moles of \( A_{2} \) is obtained. Then find out Kp for reaction
\( \boldsymbol{A}_{2}(\boldsymbol{g})+\boldsymbol{B}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{2} \boldsymbol{A} \boldsymbol{B}(\boldsymbol{g}) \)
\( A \cdot 12 \)
B. 9
\( c \cdot 4 \)
D. 36


\( 9 \mathrm{gm} \) of \( A l \) (at. \( \mathrm{Wt} \). = 27 ) will react
completely with an acid to give :
A. one mole of \( H_{2} \)
B. one half mole of \( H_{2} \)
c. one-third mole of \( H_{2} \)
D. none of these


Perimeter of triangle whose vertices are (0,4,0),(3,4,0) and \( (0,4,4), \) is
A . 10
B. 12
c. 25
D. 15


A conducting shell \( S_{1} \) having a charge \( Q \)
is surrounded by an uncharged concentric conducting spherical shell \( S_{2} \). Let the potential difference between
\( S_{1} \) and that \( S_{2} \) be \( V \). If the shell \( S_{2} \) is now
given a charge \( -3 Q, \) the new potential difference between the same two shells
is :
\( A \cdot 1 v \)
B. 2
\( c \cdot 4 v \)
D. -2 v


The graph of which inequality is shown
below:
A. \( y-x \leq 0 \)
B . \( x-y \leq 0 \)
c. \( y+x \leq 0 \)
D. None of the above


\( \lim _{x \rightarrow a^{+}} \frac{\{x\} \sin (x-a)}{(x-a)^{2}}= \) where \( \{x\} \)
denotes fractional part of \( x \) and \( a \epsilon N \)
A . 0
B. 1
\( c \cdot a \)
D. 5


In the adjacent triangle \( A B C \), find the
value of \( x \) and calculate the measure of
all the angles of the triangle.


A particle of mass \( m \) is in a uni-
directional potential field where the potential energy of a particle depends
on the \( x \) -coordinate given by \( \phi_{x}= \)
\( \phi_{0}(1-\cos a x) \&^{\prime} \phi_{0}^{\prime} \) and \( ^{\prime} a^{\prime} \) are
constants. Find the physical
dimensions of \( ^{\prime} \boldsymbol{a}^{\prime} \& \boldsymbol{\phi}_{0} \)
A \( \cdot L^{-1}, M^{1} L^{2} T^{-2} \)
B . \( L^{-2}, M^{1} L^{3} T^{-2} \)
C \( \cdot L^{-1}, M^{0} L^{2} T^{-1} \)
D. None of these


The angle between the internal and the
external bisectors of an angle of a triangle is
A \( .90^{\circ} \)
B. \( 180^{\circ} \)
\( c \cdot 270^{\circ} \)
D. \( 30^{\circ} \)


State the differential equation of linear simple harmonic motion. Hence obtain
the expression for acceleration, velocity and displacement of a particle performing linear simple harmonic motion.

A body cools from \( 80^{\circ} \mathrm{C} \) to \( 70^{\circ} \mathrm{C} \) in 5
minutes and to \( 62^{\circ} C \) in the next 5
minutes. Calculate the temperature of the surroundings.


\( \operatorname{lf} \lim _{x \rightarrow 0} \frac{\sin 2 x+\cos 2 x}{x^{3}+5}=k \) then \( k= \)
\( A \cdot 2 \)
B . - -
\( c \cdot 1 / 5 \)
D.


The vertices of triangle \( A B C \) are \( \boldsymbol{A}(\mathbf{1},-\mathbf{2}), \boldsymbol{B}(-\mathbf{7}, \mathbf{6}) \) and \( \boldsymbol{C}(\mathbf{1 1} / \mathbf{5}, \mathbf{2} / \mathbf{5}) \)


If \( a=\cos 2 \alpha+i \sin 2 \alpha, b=\cos 2 \beta+ \)
\( i \sin 2 \beta \operatorname{then} \sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}}= \)
A. \( 2 i \sin (\alpha-\beta) \)
B. \( 2 i \sin (\alpha+\beta) \)
\( c \cdot 2 \cos (\alpha+\beta) \)
D. \( 2 \cos (\alpha-\beta) \)


Choose the correct statement for
chemical adsorption:

This question has multiple correct options
A. Value of adsorption enthalpy is above \( -20 k J m o l^{-1} \)
B. Van der Waals forces exist between adsorbent and
adsorbate
C. Usually monomolecular layer is formed on adsorbent
D. Multimolecular layer may be formed on adsorbent


Show that the function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \cot ^{-1}(\sin x+\cos x) \) is decreasing on
\( \left(0, \frac{\pi}{4}\right) \) and increasing on \( \left(\frac{\pi}{4}, \frac{\pi}{2}\right) \)


When a beam of light from an object meets actually at a point after reflection from a mirror then the image formed is known as
A. Real and virtual image both
B. Real image
c. virtual image
D. No image


Fibres are likely to be absent in:
A. Secondary phloem
B. Secondary xylem
C. Primary phloem
D. Leaves


State Gauss's theorem and state its any
'two' applications.


Plants with inferior ovary belongs to
A. Malvaceae
B. Poaceae
c. Solanaceae
D. Rubiaceae


What is displacement current? Why was this concept introduced? Explain.
Also obtain the
Ampere-Maxwell equation.


electrification is due to the
excess of electrons.
A. Positive
B. Negative
c. Nuetral
D. None of the above


Two blocks of masses \( M_{1} \) and \( M_{2} \) are
connected by spring of constant \( \boldsymbol{K} \). The spring is initially compressed and the system is released from rest at \( t=0 \)
second. The work done by spring on the blocks \( M_{1} \) and \( M_{2} \) be \( W_{1} \) and \( W_{2} \) respectively by time t. The speeds of both the blocks at time t are non zero.
Then the value of \( \frac{W_{1}}{W_{2}} \) equals to
A \( \cdot \frac{M_{1}}{M_{2}} \)
в. \( \frac{M_{2}}{M_{1}} \)
\( ^{\mathrm{c}}\left(\frac{M_{1}}{M_{2}}\right)^{2} \)
\( ^{\mathrm{D}}\left(\frac{M_{2}}{M_{1}}\right)^{2} \)


In figure \( -1, \) which of the following
statement is true?
\( \mathbf{A} \cdot \angle B=\angle C \)
B. \( \angle B \) is the greatest angle in triangle
\( \mathrm{c} . \angle B \) is the smallest angle in triangle
D. \( \angle A \) is the smallest angle in triangle


The separation of Lanthanoids by ion exchange method is based on
A. basicity of the hydroxides
B. size of the ions
c. the solubility of their nitrates
D. oxidation state of the ion


The following data gives the amount of manure (in thousand tonnes)
manufactured by a company during
some years:
Year \( \begin{array}{ll}\text { 1992 } & \text { 1993 } \quad 1994 \\ \end{array} \)
Manure
in thousand tonnes
Indicate with the help of the bar graph
the year in which the amount of manure manufactured by the company was maximum.


Determine for what values of \( x, \) the
function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}+\frac{\mathbf{1}}{\boldsymbol{x}^{3}}(\boldsymbol{x} \neq \mathbf{0}) \) is
strictly increasing or strictly decreasing.


A 10 kg satellite completes one revolution around the earth at a height of \( 100 \mathrm{km} \) in 108 minutes. The work
done by the gravitational force of earth will be?
A . \( 108 \times 100 \times 10 \) J
в. \( \frac{108 \times 10}{100} \)
c. 0 J
D. \( \frac{100 \times 10}{108} \)


An electron makes \( 3 \times 10^{5} \) revolutions
per second in a circle of radius 0.5
angstrom. Find the magnetic field \( B \) at
the centre of the circle.


Find the sum of \( n \) terms of the series
\( 3+8+22+72+266+1036+\dots \)
A \( \cdot \frac{3 n}{4}+n(n+1)+\frac{1}{12}(4 n-1) \)
B . \( \frac{3 n}{4}+n(n+1)+\frac{1}{12}\left(4^{n-1}\right) \)
c. \( \frac{3 n}{4}+n(n+1)+\frac{1}{12}(4 n-2) \)
D. \( \frac{3 n}{4}+n(n+1)+\frac{1}{12}\left(4^{n-2}\right) \)


Write the importance of forest.


What will be the emf of a cell of two
hydrogen electrodes, if a negative
electrode is in contact with \( 10^{-8} M H^{+} \)
ion positive electrode is in contact with
\( \mathbf{0 . 0 2 5 M} \boldsymbol{H}^{+} \mathbf{?} \)
A. \( -0.18 V \)
в. \( -0.28 V \)
c. \( -0.38 V \)
D. - \( 0.48 V \)


\( 0.16 \mathrm{g} \) of methane was subjected to combustion at \( 27^{\circ} \mathrm{C} \) in a bomb
calorimeter. The temperature of the calorimeter system (including water)
was found to rise by \( 0.5^{\circ} \mathrm{C} \). If the heat of
combustion of methane at constant
volume and constant pressure is \( \boldsymbol{x} \) kJ.
The thermal capacity of the calorimeter
system is \( 17.7 k J K^{-1} \)
Then \( -x \) (nearest integer value) is:
\( \left[\boldsymbol{R}=\mathbf{8 . 3 1 4} \boldsymbol{J} \boldsymbol{K}^{-1} \boldsymbol{m o l}^{-1}\right] \)


(a) Which physical quantity has its \( \mathrm{S} \) I unit \( (1) \mathrm{Cm}(2) \mathrm{N} / \mathrm{C} \)
(b) Two point charges \( q \) and \( -q \) is placed at a distance \( 2 a \) apart. Calculate the
electric field at a point \( P \) is situated at a distance r along the perpendicular bisector of the line joining the charges. What is the electric field when \( r>> \) a?
Also, give the direction of electric field
w.r.t. electric dipole moment?


The product of \( n \) positive integers is 1
then their sum is a positive integer,
that is
A. equal to 1
B. equal to \( n+n^{2} \)
c. divisible by \( n \)
D. never less than \( n \)


Which of the following statements
about molecular and empirical formulas is lare false?
I. \( A \) given compound can have the same, molecular and empirical formula.
II. The molecular formula is a whole
number multiple of the empirical
formula.
III. \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) represents the empirical formula of hydrogen peroxide.
A. III only
B. I and II only
c. Il and III only
D. I, II an III
E. I only


When light travels from one medium to the other of which the refractive index is
different, then which of the following will change
A. Frequency, wavelength and velocity
B. Frequency and wavelength
c. Frequency and velocity
D. Wavelength and velocity


\( \int_{0}^{\frac{\pi}{4}} \sin 3 x \sin 2 x d x \)


Succession in a 6 metre deep pond
exhibits a sequence of
A. Submerged Plants - Reeds - Herbs - Floating Plants Shrubs - Trees
B. Floating Plants - Submerged Plants - Reeds - Herbs Shrub - Trees
C. Shrubs - Trees - Submerged Plants - Floating Plants Reeds - Herbs
D. Submerged Plants - Floating Plants - Reeds - Herbs Shrubs - Trees


If \( \boldsymbol{\theta} \in\left(\mathbf{0}, \frac{\boldsymbol{\pi}}{\mathbf{2}}\right), \) then the value of
\( \cos \left(\theta-\frac{\pi}{4}\right) \) lies in the interval
\( ^{\mathbf{A}} \cdot\left(\frac{1}{2}, 1\right) \)
B \( \cdot\left(\frac{1}{\sqrt{2}}, 1\right) \)
\( ^{\mathbf{c}} \cdot\left(-\frac{1}{\sqrt{2}}, 1\right) \)
D. (0,1)


\( (x+1)^{2}=x^{2}+2 x+1 \) is an identity in
\( \boldsymbol{x} \)
A. True
B. False


If \( P(x, y, z) \) is a point on the line
segment joining \( Q(2,2,4) \) and
\( \boldsymbol{R}(\boldsymbol{3}, \boldsymbol{5}, \boldsymbol{6}) \) such that the projection of
\( O P \) on the axes are \( \frac{13}{5}, \frac{19}{5}, \frac{26}{5} \)
respectively, then \( P \) divides \( Q R \) in the ratio
A .1: 2
B. 3: 2
\( c \cdot 2: 3 \)
D. 1: 3


Acceleration due to gravity of a body
during free fall does not depend upon
the:
A. mass of earth
B. mass of body
c. universal gravitational constant
D. radius of earth


A rectangular loop, carrying current \( i, \) is
lying near a long straight conductor PQ as shown in the figure in such way that
the wire is parallel to one of the sides of the loop and is in the plane of the loop. If
constant current \( I \) is passed in the wire
then the loop will
A. move towards the wire
B. move away from the wire
c. remain stationary
D. rotate about an axis parallel to the wircre


\( \int \frac{d x}{1+x^{3}} \)


The \( t_{1 / 2} \) of a radioactive substance is
100sec. Its decay constant is:
A \( \cdot 6.93 \times 10^{-3} \mathrm{sec}^{-1} \)
B. \( 6.93 \times 10^{-2} \) sec \( ^{-1} \)
D. \( 6.93 \times 10^{-4} s e c^{-1} \)


The special feature of bile juice is that
it
A. Has no enzyme
B. Has amylase
c. contains lipase
D. contains \( \mathrm{H}_{2} \) 0


The line \( b x+a y=3 a b \) cuts the
coordinate axes at \( A \) and \( B \), then
centroid of \( \triangle O A B \) is -
\( \mathbf{A} \cdot(b, a) \)
B \( \cdot(a, b) \)
c. \( \left(\frac{a}{3}, \frac{b}{3}\right) \)
D \cdot \( (3 a, 3 b) \)


The blood groups of 36 students of \( 1 x \)
class are recorded as follows.
\( \begin{array}{llll}\boldsymbol{A} & \boldsymbol{O} & \boldsymbol{A} & \boldsymbol{O}\end{array} \) \( \boldsymbol{B} \) \( A \)
В \( o \) \( o \)
\( \Omega \)
Represent the data in the form of a frequency distribution table. Which is the most common and which is the rarest blood group among these
students?


Which one of the following is an example of coordination isomerism?
A \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} B r\right] S O_{4} \) and \( \left[C o\left(N H_{3}\right)_{5} S O_{4}\right] B r \)
B . \( \left[\operatorname{Co}\left(N H_{3}\right)_{5} N O_{2}\right] C l_{2} \) and \( \left[C o\left(N H_{3}\right)_{5} O N O\right] C l_{2} \)
C \( \cdot\left[C r\left(H_{2} O\right)_{6}\right] C l_{3} \) and \( \left[C r\left(H_{2} O\right)_{5} C l\right] C l_{2} \cdot H_{2} O \)
D. \( \left[C r\left(N H_{3}\right)_{6}\right]\left[C o(C N)_{6}\right] \) and \( \left[C o\left(N H_{3}\right)_{6}\right]\left[C r(C N)_{6}\right] \)


An object will not undergo rotational
motion when:
A. the forces are acting on it at different positions
B. every forces is creating different turning effects
C. every moment has the same amplitude
D. all the forces are acting at its centre of gravity


If \( y=\log \left(\frac{1-x^{2}}{1+x^{2}}\right), \) then \( \frac{d y}{d x} \) is equal
to
A \( \cdot \frac{-4 x}{1-x^{4}} \)
в. \( \frac{4 x^{3}}{1-x^{4}} \)
c. \( \frac{1}{4-x^{4}} \)
D. \( \frac{-4 x^{3}}{1-x^{4}} \)


Find \( k \) if \( k, 12,24, \dots \) are in GP
\( A \cdot 6 \)
B. 3
\( c \cdot 9 \)
D. none of these


A carpet of mass \( M \) made of inextensible material is along its length
in the form of a cylinder of radius \( R \) and
is kept on a rough floor. The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. If the horizontal velocity of the axis of the cylindrical part of the
carpet when its radius reduces to \( \boldsymbol{R} / \mathbf{2} \) is \( \sqrt{\frac{x}{3} g R}, \) find the value of \( x \)


Which of the following is true for a line \( l \) lying in the same plane and
intersecting \( \triangle A B C \) but not perpendicular to \( \overline{B C} ? \)
A. \( l \) intersects \( \overline{A B} \) or \( \overline{A C} \)
B. \( l \) intersects \( \overline{A C} \)
c. \( l \) does not intersects \( \overline{A B} \) or \( \overline{A C} \)
D. \( l \) intersects \( \overline{A B} \)


Assertion
In angiosperms, the conduction of water is more efficient because their xylem
has vessel.
Reason
Conduction of water by vessel elements
is an active process with energy
supplied by xylem parenchyma rich in mitochondria.
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 correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


Which of the following is an emulsifying
agent?
A. Milk
B. Butter
c. Gum
D. Lamp black


If the radius of the earth were to shrink
by \( 1 \% \) its mass remaining the same, the acceleration due to gravity on the earths surface would
A. decrease by \( 2 \% \)
B. remain unchanged
c. increase by \( 2 \% \)
D. will increase by \( 9.8 \% \)


The parallel sides of a trapezium are 20 \( \mathrm{m} \) and \( 30 \mathrm{m} \) and its non parallel sides are \( 6 \mathrm{m} \) and \( 8 \mathrm{m} \). Find the area of the trapezium.
A \( \cdot 96 m^{2} \)
в. \( 82 m^{2} \)
c. \( 100 \mathrm{m}^{2} \)
D. \( 120 m^{2} \)


A TV was bought at a price of Rs. 21000
After 1 year the value of the TV was depreciated by \( 5 \% \). (Depreciation means reduction of the value due to use
and age of the item). Find the value of
the TV after 1 year.


Find out \( C \) in the given flowchart:
\( A \)
\( A \cdot C O_{2} \)
B. \( S O_{2} \)
\( c \cdot S O \)
D. \( N O_{2} \)


Solve the following equations:
\( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{2} \boldsymbol{3} \)
\( \boldsymbol{x} \boldsymbol{z}+\boldsymbol{x}+\boldsymbol{z}=\boldsymbol{4} \mathbf{1} \)
\( \boldsymbol{y} \boldsymbol{z}+\boldsymbol{y}+\boldsymbol{z}=\mathbf{2 7} \)
A. \( x=4,-2 ; y=2 ; 6 ; z=6,-5 \)
в. \( x=2,-4 ; y=2,4 ; z=2,-6 \)
c. \( x=5,-7 ; y=3,-5 ; z=6,-8 \)
D. \( x=3,4 ; y=2,-5 ; z=2,-7 \)


Chloramine-T is a:
A. antihistamine
B. antiseptic
c. analgesic
D. antipyretics


If the Plane mirror is rotated by an angle
\( \theta, \) keeping the incident ray fixed, the reflected ray is rotated by an angle:
\( \mathbf{A} \cdot 3 \theta \)
B. \( \theta \)
\( c \cdot 2 \theta \)
D. \( 4 \theta \)


Identify the correct statement with
reference to transport of respiratory
gases by blood.
A. Haemoglobin is necessary for transport of carbon dioxide and carbonic anhydrase for transport of oxygen.
B. Haemoglobin is necessary for transport of oxygen and carbonic anhydrase for transport of carbon dioxide.
C. Only oxygen is transported by blood.
D. Only carbon dioxide is transported by blood.


A number of elements are available in
earth's crust but most abundant
elements are
\( \mathbf{A} \cdot A l \) and \( F e \)
B. Fe and \( C u \)
c. \( C u \) and \( A g \)
D. none of these


If is the angular momentum is \( L \) and \( I \) is the moment of inertia of a rotating body, then \( \frac{L^{2}}{2 I} \) represents its
A. rotational PE
B. total energy
c. rotational KE
D. translation KE


The probability of occurrence of \( \boldsymbol{p}_{\boldsymbol{z}} \) orbital along \( x \) -axis and \( y \) -axis is:
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 0.5 \)
D. 0.7


The degree and order of the differential equation of the family of all parabolas whose axis is \( x \) -axis are respectively:
A . 2,1
в. 1,2
\( c .3,2 \)
D. 2,3


The time period of a geo-stationary satellite in its orbit is
A . 12 hrs
B. 24 hrs
c. 365 days
D. none of these


\( \boldsymbol{K}_{\boldsymbol{w}} \) of pure water is \( \mathbf{1 0}^{-12} \) at \( \mathbf{6 0}^{\circ} \boldsymbol{C} \). The
\( p H \) of pure water at \( 60^{\circ} \mathrm{C} \) is:


Hydrogen finds a place in VII A group of
periodic table because
A. it is a light element
B. \( H- \) atom has only one electron in its valence shell
C. it forms hydride of the type \( N a H \)
D. it has 7 isotopes


A thin uniform disc of mass \( M \) and
radius \( R \) is rotating in a horizontal
plane about an axis passing through its centre and perpendicular to it with angular velocity \( \omega . \) Another disc of the same radius but of mass \( \frac{M}{4} \) is placed gently on the first disc coaxially. The angular velocity of the system will now finally change to:
A \( \cdot \frac{2 \omega}{\sqrt{5}} \)
в. \( \frac{2 \omega}{5} \)
c. \( \frac{3 \omega}{5} \)
D. \( \frac{4 \omega}{5} \)


The angular momentum of particle of mass \( 0.01 K g \) and position vector \( \vec{r}= \) \( (10 \hat{i}+6 \hat{j}) \) meter and moving with a velocity 5 ìmetre/ sec about the origin
will be :
A. \( -0.3 \hat{k} \) Joulesec
B. \( 3 \hat{k} \) joulesec
c. \( 1 / 3 \) joulesec
D. \( 0.03 \hat{k} \) Joulesec


Copper becomes green when exposed to moist air for a long period of time due to
the
A. formation of a layer of cupric oxide on the surface of copper.
B. formation of a layer of basic carbonate of copper on the surface of copper
c. formation of a layer of cupric hydroxide on the surface of copper.
D. none of the above


Which of the following is a fully flourinated polymer?
A. Thiokol
B. Teflon
c. Neoprene
D. PVC


A value of a machine depreciates every year at the rate of \( 12 \% . \) The present value of a machine is Rs. 5500. What
was the value of the machine 2 years
before?


Solid \( N a C l \) is a \( _{---} \) of electricity
A. good conductor
B. bad conductor
c. insulator
D. none


Q Type your question-
object can affect the shadow formed on
the screen. when she placed the object
at position \( Y \) shadow 1 was formed on
the screen as shown.

When the object was placed at position \( X, \) which of the following would be
observed about the shadow on the
screen?
1. The shadow would be upright.
2. The shadow would be inverted.
3. The shadow would be bigger than
shadow 1.
4. The shadow would be smaller than
shadow 1.
A . 1 and 3 only
B. 2 and 3 only
c. 1 and 4 only
D. 3 and 4 only


A charge 10 esu is placed at a distance of \( 2 \mathrm{cm} \) from a charge 40 esu and \( 4 \mathrm{cm} \)
from another charge of 20 esu. The potential energy 10 esu in ergs is
A. 87.5
в. 112.5
\( c \cdot 150 \)
D. 250


Legume is the characteristic fruit of
family.


Write the following in decimal form and say what kind of decimal expansion
each has:
(i) \( \frac{\mathbf{3 6}}{\mathbf{1 0 0}} \)
(ii) \( \frac{\mathbf{1}}{\mathbf{1 1}} \)
(iii) \( 4 \frac{1}{8} \)
(iv) \( \frac{\mathbf{3}}{\mathbf{1 3}} \)
\( \mathbf{2} \)
(vi) \( \frac{329}{400} \)
\( \overline{\mathbf{1 1}} \)


Prove that
\( \mathbf{2 5}_{\mathbf{4}}^{C}+\sum_{r=\mathbf{0}}^{4}(\mathbf{2 9}-\boldsymbol{r})_{\mathbf{3}}^{\boldsymbol{C}}=\mathbf{3 0}_{\mathbf{4}}^{\boldsymbol{C}} \)


The enthalpy of formation of ammonia
is \( -46.0 K J \) mol \( ^{-1} . \) The enthalpy
change for the reaction \( 2 N H_{3}(g) \rightarrow \)
\( N_{2}(g)+3 H_{2}(g) \) is:
A \( .46 .0 K J \) mol\( ^{-1} \)
B. \( 92.0 K J \) mol\( ^{-1} \)
c. \( -23.0 \mathrm{KJ} \mathrm{mol}^{-1} \)
D. \( -92.0 K J \) mol\( ^{-1} \)


In experiment of convection heat
transfer, water inside the pipe can be convectively heated with higher rate by
A. Increasing thermal conductivity of container
B. increasing heat intensity
c. Using external force to increase the circulation speed
D. all of the above


Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene
glycol which should be added to 4 kg of water to prevent it from freezing at
\( -6^{o} C \) will be :
\( \left(K_{f} \text { for water }=1.86 \mathrm{K} \mathrm{kg} / \mathrm{mol} \) and molar \right. mass of ethylene glycol \( =62 \) g mol \( ^{-1} \) )
A . \( 304.6 \mathrm{g} \)
в. \( 800 \mathrm{g} \)
c. 204.3 g
D. \( 400.00 \mathrm{g} \)


Anisole on reaction with chloromethane
in presence of anhydrous \( A l C l_{3} \) gives
A. o-methyl anisole and p-methoxy anisole
B. p-methyl anisole and p-methoxy anisole
c. o-methyl anisole and p-methyl anisole
D. o-methoxy acetphenone and p-methoxy acetophenone


Evaluate the following (using identities):
\( (11)^{3} \)


Evaluate the following limits. \( \lim _{x \rightarrow 2} \frac{\sqrt{1+4 x}-\sqrt{5+2 x}}{x-2} \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot \frac{1}{4} \)
D.


Find the mean deviation from the mean
of the following data:
\[
\boldsymbol{x}_{1}
\]
\[
\begin{array}{ccccccccc}
2 & 5 & 6 & 8 & 10 & 12 \\
\hline & f_{1} & 2 & 8 & 10 & 7 & 8
\end{array}
\]


Use figure given below that shows our
Solar system to answer the given questions. The region H represents :
A. Meteor belt
B. Kuiper belt
c. Asteroid bel
Dort Cloud


Correctly arrange the parts of the
alimentary canal in descending order.
A. Mouth, oesophagus, stomach, intestine
B. Oesophagus, mouth, stomach, intestine
C. Intestine, mouth, stomach, oesophagus
D. Stomach, Intestine, mouth, oesophagus


Cane sugar underoges the inversion as
follow:
\( \boldsymbol{C}_{12} \boldsymbol{H}_{22} \boldsymbol{O}_{11}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6}+ \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\mathbf{1 2}} \boldsymbol{O}_{\boldsymbol{6}} \)
If solution of 0.025 moles of sugar in \( 200 \mathrm{gm} \) of water show depression in
freezing point \( 0.372^{\circ} \mathrm{C}, \) then what \( \% \)
sucrose has inverted. \( \left(\boldsymbol{K}_{f}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)=\right. \)
1.86 \( \left.K k g m o l^{1}\right) \)


Draw the experimental set-up to verify
that \( \frac{V}{I} \) is constant for a Conductor


The electronic configuration of an
element x is :
\( k \)
\( \mathbf{L} \)
2
8
6
a) What is the group no. element x in the periodic table?
b) What is the period no. of element x is the period table ?
c) What is the number of valence
electrons in an atom of \( \times ? \)
d) What is the valency of \( x ? \)
e) Is the element \( x, \) a metal or a non-
metal?


In primary succession on rocks, the pioneer species are usually
A. Algae
B. Fungi
c. Lichens
D. Bryophytes


Which process is applied on a circuit for the working of an electric bell?
A. Magnetization
B. Make and break
c. Both A and B
D. None of the above


Compute the area of one of the curvilinear triangles bounded by the \( x \)
axis and the curves \( y=\sin x \) and \( y= \)
\( \cos x \)


f \( \vec{a} \times \vec{b}=\vec{b} \times \vec{c} \neq \overrightarrow{0} \) with \( \vec{a} \neq-\vec{c} \) then
show that \( \vec{a}+\vec{c}=k \vec{b}, \) where \( k \) is scalar.


Which of the following is the main
product in the photorespiration of \( \boldsymbol{C}_{3} \)
plants?
A. Phosphoglycerate
B. Phosphoglycolate
c. Glycerate
D. Glycolate


Assertion
Nitrogen turns red litmus paper blue.
Reason
Ammonia is a basic gas.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The magnetic force between the infinite
wire and the square loop is
A \( \frac{\mu_{0} i^{2}}{4 \pi}, \) repulsiv
B. \( \frac{\mu_{0} i^{2}}{2 \pi}, \) repulsive
C \( \frac{\mu_{0} i^{2}}{4 \pi}, \) attractive
D. \( \frac{\mu_{0} i^{2}}{2 \pi}, \) attractive


If the heights of 5 persons are \( 144 \mathrm{cm} \) \( 152 \mathrm{cm}, 151 \mathrm{cm}, 158 \mathrm{cm}, \) and \( 155 \mathrm{cm} \)
respectively. Find the mean height.


Find the area of the trapezium.
\( \mathbf{A} \cdot 144 \sqrt{3} \mathrm{cm}^{2} \)
B. \( 154 \sqrt{3} \mathrm{cm}^{2} \)
\( \mathbf{C} \cdot 162 \sqrt{3} \mathrm{cm}^{2} \)
D. None of these


Number of Sugden's singlet bonds in
\( \boldsymbol{P C l}_{5} \) is :


The number of rational terms in the
expansion of \( \left(\mathbf{9}^{1 / 4}+\mathbf{8}^{1 / 6}\right)^{1000} \) is:
A . 500
в. 400
\( c .501 \)
D. none of the above


A particle executes SHM about a point
other than \( x=0 \) as shown in the graph
Choose a CORRECT option(s)
This question has multiple correct options
A. Amplitude is equal to \( 4 m \)
B. Equilibrium position is at \( x=0 \)
C. Equilibrium position is at \( x=2 m \)
Angular frequency \( \frac{2 \pi}{3} \)


What is meant by term Quantization of of charge?


A redox reaction is shown in the
diagrams. Identify the reaction.
\( \left.\mathbf{A} \cdot Z n(s)+C u_{(a q)}^{2+} \rightarrow Z n_{(a q)}^{2+}+C u_{(} s\right) \)
B. \( \left.C u(s)+2 A g_{a q}^{+} \rightarrow C u_{(a q)}^{2+}+2 A g_{(} s\right) \)
C \( \cdot 2 A g(s)+C u_{(a q)}^{2+} \rightarrow 2 A g_{(a q)}^{+}+C u(s) \)
\( \left.\mathbf{D} \cdot C u_{(} s\right)+Z n_{(a q)}^{2+} \rightarrow C u_{(a q)}^{2+}+Z n(s) \)


In an annual examination, Hardik got
\( \mathbf{5 0 0} \) marks out of \( \mathbf{7 2 5} \). What is his
approximate per cent in the examination?


If length of a solenoid is increased then
what change should be made on no. of turns to keep self inductance constant-
\( A \). increase
B. remain same
c. decrease
D. none of these


Which of the following reagent reacts with ethanoic acid to liberate hydrogen
gas?
A . Na a
B. zn
c. Both A and B
D. ç


Two parallel straight conductors carrying currents 5A each repel other
with a force of \( 25 \times 10^{-5} N m^{-1} . \) The
distance between the conductors is
A. \( 4 \mathrm{cm} \)
B. \( 0.4 \mathrm{cm} \)
\( c \cdot 2 \mathrm{cm} \)
D. \( 0.2 \mathrm{cm} \)


(a) Deduce the expression for the
potential energy of a system of two
charges \( q_{1} \) and \( q_{2} \) located \( \overrightarrow{r_{1}} \) and \( \overrightarrow{r_{2}} \)
respectively, in an external electric
field.
(b) Three point charges, \( +Q+2 Q \) and
\( 3 Q \) are placed at the vertices of an equilateral triangle ABC of side I. If these charges are displaced to the mid-
point \( A_{1}, B_{1} \) and \( C_{1}, \) respectively, find
the amount of the work done in shifting
the charges to the new locations.


Area of \( \triangle A B C=68.2 s q m . \) Find the
area of shaded region


Assertion
The order of reaction is equal to
molecularity of simple reactions:
Reason
Molecularity of the reaction can not be
fractional:
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


List out the effects of global warming
and efforts to control global warming.


Assertion
Falling raindrops acquire a terminal
velocity.
Reason
A constant force in the direction of
motion and a velocity dependent force
opposite to the direction of motion,
never results in the acquisition of
terminal velocity.
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


Write two methods of preventing the rusting of iron


Solve: \( x^{2}+y^{2}-4 x-4 y+8=0 \)


Find the values of \( K \) if Area of the
triangle is 4 sq. units and vertices are \( (k 0)(40)(02) \) using determinants.


\( I_{2} \) has less solubility in water, but its
solubility increases on adding \( K I \) in
the solution. When \( K I \) and \( I_{2} \) react,
then a species \( X \) is formed and
solubility of \( I_{2} \) solution increases.
The geometry of the anionic part of \( \boldsymbol{X} \)
is:
A. Linear
B. T-shape
c. Pyramidal
D. See-saw


Plant growth hormones extracted from a
fungus and a fish are respectively
A. Gibberellins and zeatin
B. Ethylene and cytokinin
c. Auxin and \( 2,4-0 \)
D. Gibberellin and kinetin


Conjugate acid of \( N H_{2}^{-} \) is
A \( . N H_{3} \)
B. \( N H_{4}^{+} \)
\( c \cdot N \)
D. \( N H_{2}^{+} \)


The IUPAC name of this compound is:
\( \boldsymbol{C H}_{3} \quad \boldsymbol{O} \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2} \boldsymbol{O H} \)
A. 1 -Hydroxy- 4 -methyl-3-pentanone
B. 2-Methyl-5-hydroxy-3-pentanone
c. 4-Methyl-3-oxo-1-pentanol
D. Hexan-1-one-3-o


How do we differentiate between \( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+} \)
and \( C r^{3+} \) in group III?
A . By taking excess of \( N H_{4} O H \)
B. By increasing \( N H_{4}^{+} \) ion cocentration
C. By decreasing \( O H^{-} \) ion concentration
D. Both (b) and (c)


If the first term of G.P. is \( 7, \) its \( n^{t h} \) term
is 448 and sum of first \( n \) terms is 889
then find the fifth term of G.P.


In a study of two groups, the following results were obtained
Group
Sample size 20
Sample mean 22
Sample standard deviation 10
Which of the following statements is
correct?
A. Group A is less variable than Group B because Group A's standard deviation is smaller.
B. Group A is less variable than Group B because Group A's sample size is smaller.
C. Group \( A \) is less variable than Group \( B \) because Group A's sample mean is smaller
D. Group A is less variable than Group B because Group A's coefficient of variation is smaller.


A particle is projected vertically
upwards with velocity \( 40 m s^{-1} \). Find the displacement and distance travelled by
the particle in 6 s. \( \left[\text { take } g=10 m / s^{2}\right] \)
A. \( 60 m, 100 m \)
B. \( 60 m, 120 m \)
c. \( 40 m, 100 m \)
D. \( 40 m, 80 m \)


At \( 500 K \), the half-life period of a gaseous reaction at an initial pressure of \( 80 k P a \) is 350 sec. When the pressure
is \( 40 k P a, \) the half life period is 175 sec;
the order of the reaction is:
A. zero
B. One
c. Two
D. Three


The electrical conductivity of a semiconductor increases when
electromagnetic radiation of wavelength shorter than 248 nm is
incident on it. The forbidden band
energy for the semiconductor in \( e V \) is


A point moves along a circle having a radius \( 20 c m \) with a constant tangential
acceleration \( 5 \mathrm{cm} s^{-2} . \) How much time
is needed after motion begins for the normal acceleration of the point to be
equal to tangential acceleration?
A . \( 1 \mathrm{s} \)
B. 2
\( c \cdot 3 s \)
D. 4 s


Calculate the weight of \( \left(N H_{4}\right)_{2} S O_{4} \) which must be added to \( 500 \mathrm{mL} \) of \( 0.2 \mathrm{M} \)
\( N H_{3} \) to yield a solution of \( \mathrm{pH}=9.35, K_{b} \)
for \( \boldsymbol{N} \boldsymbol{H}_{3}=\mathbf{1 . 7 8} \times \mathbf{1 0}^{-\mathbf{5}} \) (in \( \mathrm{gm} \) )(Write
answer upto 3 decimal places)


The cell, \( \boldsymbol{P b} \mid \boldsymbol{H}_{2}(\mathbf{1} \boldsymbol{a t m}) \| \boldsymbol{H}^{+}(\boldsymbol{p} \boldsymbol{H}=\boldsymbol{x}) \)
normal calomel electrode, has an emf of
0.67 volt as \( 25^{\circ} \mathrm{C} \). Calculate the \( p H \) of
the solution. The oxidation potential of calomel electrode on the hydrogen scale is :-0.28 volt.
A. \( p H=7.61 \)
в. \( p H=8.61 \)
c. \( p H=6.61 \)
D. none of these


Periodic abstinence is a method used to
avoid which of the following situations?
A. Fertilization of sperm and ovum after coitus
B. Unwanted pregnancy
c. Release of the ovum in a female body
D. None of these


Find the derivative of the following functions (it is to be understood that
\( a, b, c, d, p, q, r \) and \( s \) are fixed non-zero constants and \( m \) and \( n \) are integers) \( \sin (x+a) \)


In the given figure current from \( A \) to \( B \) in
the straight wire is decreasing.

The direction of induced current in the
loop is
A . clockwise
B. anticlockwise
c. changing
D. nothing can be said


What is \( \tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{3}\right) \) equa
to?
A \( \cdot \frac{\pi}{2} \)
в. \( \frac{\pi}{3} \)
c. \( \frac{\pi}{4} \)
D.


If \( \boldsymbol{f}(\boldsymbol{x})=\cos (\boldsymbol{\pi} / \boldsymbol{x}), \) then find the
intervals in which the function
decreasing.
A \( . \pi<\theta<2 \pi \)
в. \( \pi / 2<\theta<\pi \)
c. \( \pi / 4<\theta<\pi / 2 \)
D. \( 0<\theta<2 \pi \)


\( \left|\begin{array}{cc}\boldsymbol{x} & \mathbf{2} \\ \mathbf{1 8} & \boldsymbol{x}\end{array}\right|=\left|\begin{array}{cc}\mathbf{6} & \mathbf{2} \\ \mathbf{3} \boldsymbol{x} & \mathbf{6}\end{array}\right|, \) then \( \boldsymbol{x} \) is equal to
\( A \cdot 6 \)
B. ±6
\( c .-6 \)
\( D \)


Convection of heat takes place in:
A. Metals only
B. Liquids only
c. Gases only
D. Liquids and gases


Which of the following statements are
correct for action and reaction forces?
This question has multiple correct options
A. These act on two different bodies
B. These are equal in magnitude but opposite in direction.
C. These act on a single body.
D. These are necessary to explain reaction in third law.


The smallest number by which 8,788 must be divided so that the quotient is
perfect cube is:
\( A \cdot 4 \)
B. 12
\( c \cdot 16 \)
D. 32


What will be the condition of image
when you stand in front of a plane flat mirror and look at yourself and you raise your right hand?
A. Erect and enlarged
B. Erect and reduced
c. Erect and reversed
D. Inverted and reversed
E. Inverted and reduced


In the figure \( A B \) is a wire of length 100
\( \mathrm{cm} \) whose resistance is \( 5 \Omega \). If
galvanometer reads zero, the current
flowing in the wire AB is
A . \( 0.1 \mathrm{A} \)
B. 0.5
\( c \cdot 1 A \)
D. \( 1.4 A \)


Common salt obtained from Clifton
beach contained \( 60.75 \% \) chlorine while
\( 6.40 \mathrm{g} \) of a sample of common salt from Khewra mine contained 3.888 g of chlorine. State the law illustrated by these chemical combinations.
A. Law of reciprocal proportion
B. Law of multiple proportion
c. Law of constant composition
D. None of the above


At what height above the surface of
earth acceleration due to gravity reduces by \( 1 \% ? \)


If the vector \( -\hat{\mathbf{i}}+\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}} \) bisects the
angles between the vector \( \hat{c} \) and the vector \( 3 \hat{i}+4 \hat{j}, \) then the unit vector in
the direction of \( \hat{\boldsymbol{c}} \)
\( \mathbf{A} \cdot 11 \hat{i}+10 \hat{j}+2 \hat{k} \)
B . \( -(11 \hat{i}+10 \hat{j}+2 \hat{k}) \)
c. \( -\frac{1}{15}(11 \hat{i}+10 \hat{j}+2 \hat{k}) \)
D. \( \frac{1}{15}(11 \hat{i}+10 \hat{j}+2 \hat{k}) \)


For which of the following hybridisation, the bond angle is maximum?
\( A \cdot s p^{2} \)
B. \( s p \)
\( c \cdot s p^{3} \)
D. \( d s p^{2} \)


If \( P(A)=\frac{1}{8} \) and \( P(B)=\frac{5}{8} . \) Which of
the following statements is not correct? This question has multiple correct options
\( ^{\mathbf{A}} \cdot P(A \cup B) \leq \frac{3}{4} \)
в. \( P(A \cap B) \leq \frac{1}{8} \)
\( ^{\mathrm{c}} \cdot_{P(\bar{A} \cap B)} \leq \frac{5}{8} \)
D. None of the above


Which of the following statement are
true regarding the log K vs.1/T plot
shown in the given diagram?
This question has multiple correct options
A. Plot P shows that the energy of activation is independent of temperature
B. Plot Q describes the behaviour of temperature dependence of energy of activation
c. Arrhenius behaviour is described by


Photorespiration involves oxidation of
A. Chlorophyll a
B. PGAA
c. RuBP
D. Both B and C


Which nature of matter is shown when
salt dissolves in water completely?
A. wave
B. Particle
c. Both A and B
D. None of the above


For which of these would you use a
histogram to show the data.
The number of letters for different areas
in a postman's bag.


Two vehicles, each moving with speed \( \mathbf{u} \)
on the same horizontal straight road,
are approaching each other. Wind blows
along the road with velocity w. One of these vehicles blows a whistle of
frequency \( \mathbf{f}_{1} . \) An observer in the other
vehicle hears the frequency of the
whistle to be \( f_{2} . \) The speed of sound in
still air is \( \mathrm{V} \). The correct statement(s) is
\( (\operatorname{are}) \)
This question has multiple correct options
A. If the wind blows from the observer to the source, \( f_{2}> \)
\( f_{1} \)
B. If the wind blows from the source to the observer, \( f_{2}> \)
\( f_{1} \)
C. If the wind blows from observer to the source, \( f_{2}<f_{1} \)
D. If the wind blows from the source to the observer \( f_{2}< \)
\( f_{1} \)


What are the principal components of an artificial kidney?


An alpha particle \( \left(^{4} H e\right) \) has a mass
4.00300 amu. A proton has a mass
\( \mathbf{1 . 0 0 7 8 3} \) amu and a neutron has a mass
\( \mathbf{1 . 0 0 8 6 7} \) amu respectively. The binding
energy of alpha estimated from these data is closest to:
\( \mathbf{A} \cdot 27.9 \mathrm{MeV} \)
в. \( 22.3 \mathrm{MeV} \)
c. \( 35.0 \mathrm{MeV} \)
D. 20.4 MeV


In the following figure, in
\( \triangle A B C, B C=1, A C=2, \angle B=90^{\circ} \)
Find the value of \( \sin \theta \)


If \( \phi \) represents an impossible event then \( \boldsymbol{P}(\phi)=? \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot \phi \)
D. -


Find the differential equation representing the family of curves \( \boldsymbol{y}= \)
\( a e^{b x+5}, \) where a and \( b \) are arbitrary
constants.


State True or False :
The n-type collector moves very little while p-type moves appreciably.
A. True
B. False


Which of the following polymer is used in paints?
A. Gutta percha
B. Melamine
c. Buna- -
D. Novolac


The wavefront of a light beam is given
by the equation \( x+2 y+3 z=c \) (where
\( c \) is arbitrary constant of light). What is the angle made by the light with the \( y- \) axis is
\( ^{A} \cdot \cos ^{-1} \frac{1}{\sqrt{14}} \)
B. \( \sin ^{-1} \frac{2}{\sqrt{14}} \)
\( ^{\mathrm{c}} \cdot \cos ^{-1} \frac{2}{\sqrt{14}} \)
D. \( \sin ^{-1} \frac{3}{\sqrt{14}} \)


Which plastic is used for replacing materials like glass for making bottles and jars?
A. PET (polyethylene terephthalate)
B. PVC (Polyvinyl chloride)
c. Bakelite
D. Teflon


Which of the following statement is
incorrect for \( C O \) molecule?
A. Intramolecular Lewis acid - base interaction is present
B. Charge separation is present
C. \( \sigma \) - bond, \( \pi \) - bond and back - bond all are present together
D. Direction of dipole moment is from \( C \) to \( O \)


A circular disc has a hole of diameter \( d_{1} \)
and an external diameter \( d_{2} \), where
\( d_{2}=3 d_{1} . \) On heating \( d_{2} \) increases by
\( 0.3 \% . \) Find \( d_{1} \)


State true or false.
If \( \left(1+\sin ^{2} \theta\right)=3 \sin \theta \cos \theta \) then
\( \tan \theta=-1 o r \frac{1}{2} \)
A . True
B. False


If the sum of the \( 3^{r d} \) and the \( 8^{t h} \) terms of
an AP is 7 and the sum of the \( 7^{t h} \) and the
\( 14^{t h} \) term is \( -3, \) find the \( 10^{t h} \) term.


Which is more easily reduced: Ca or O?
\( \mathbf{A} \cdot \mathbf{C a} \)
\( B . O \)
C . Both are equally reduced
D. None of the above


Find the terminal voltage across \( \boldsymbol{E}_{1} \) and
\( \boldsymbol{E}_{2} \) in fig :
A. \( 3.6 V, 7.8 V \)
B. \( 2.4 V, 7.8 V \)
c. \( 3.6 V, 10 V \)
D. \( 2.4 V, 10.2 V \)


Energy is required for
A. Active transport
B. Facilitated transport
C. Diffusion
D. All of these


In the first half of a trivia game, Mark
scored 200 points. Then, during the second half, he scored -100 points.
What was his final score?
A . 100
в. 300
c. -100
D. -200


If position vector of a point varies with time " \( \boldsymbol{t}^{\prime \prime} \) as \( \overrightarrow{\boldsymbol{r}}=\left(\boldsymbol{t}+\boldsymbol{t}^{2}\right)(\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}) \) meter
then velocity at time \( t=4 s \) will be
A \( \cdot(6 \hat{i}+6 \hat{j}) m / s \)
B . \( (6 \hat{i}+9 \hat{j}) m / s \)
c. \( (9 \hat{i}+6 \hat{j}) m / s \)
D. \( (9 \hat{i}+9 \hat{j}) m / s \)


\( C O_{2} \) is isostructural with
A \( \cdot N_{2}^{+} \)
в. \( \operatorname{SnCI}_{2} \)
c. \( C_{2} H_{2} \)
D. \( N O_{2} \)


Six particles are situated at the corners
of a regular hexagon of side \( a \), they
move at a constant speed \( v \). Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet
each other:
A \( \cdot 2 \) a/v
B. 3 a/v
\( c \cdot 5 a / v \)
D. 6 a/v


You have learnt in the text how Huygens principle leads to the laws of reflection and refraction. Use the same principle to deduce directly that a point object placed in front of a plane mirror produces a virtual image whose distance from the mirror is equal to the object distance from the mirror.


A beaker contains a saturated solution
of copper(l) chloride. Copper(l) chloride is slightly soluble salt with a solubility product of \( 1.2 \times 10^{-6} \)
Which of the following salts when added to the solution would precipitate
copper(l) chloride?
A. Sodium chloride
B. Potassium bromide
c. Silver(I) nitrate
D. Lead(II) acetate
E. Magnesium iodide


A galvanometer of resistance \( 50 \Omega \) is
connected to a battery of \( 3 V \) along with a resistance of \( 2950 \Omega \) in series shown,
full-scale deflection of 30 divisions. The
additional series resistance required to reduce the deflection to 20 divisions is
A . \( 4440 \Omega \)
B. 1500\Omega
c. \( 7400 \Omega \)
D. \( 2950 \Omega \)


How many mole of helium gas occupy
\( 22.4 L \) at \( 0^{\circ} C \) at 1 atm pressure?
\( \mathbf{A} \cdot 0.11 \) atm
B. 0.90 atm
c. 1.0 atm
D. 1.11 atm


Bromine monochloride, Br \( C l \)
decomposes into bromine and chlorine and reaches the equilibrium:
\( \begin{array}{lllll}2 B r C l & (g) & \rightleftharpoons & B r_{2} & (g)\end{array}+ \)
\( \boldsymbol{C l}_{2} \quad(\boldsymbol{g}) \)
for which \( K=32 \) at \( 500 K . \) If initially
pure \( B r C l \) is present at a concentration
of \( 3.3 \times 10^{-3} \) mol \( L^{-1}, \) what is its molar
concentration in the mixture at
equilibrium?
A \( \cdot 3 \times 10^{-4} \)
В. \( 1 \times 10^{-4} \)
c. \( 1.5 \times 10^{-4} \)
D. \( 6 \times 10^{-4} \)


Find the value of \( k \) for which the given
system of equations has infinite number of solutions.
\( \mathbf{5} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{2} \boldsymbol{k} \) and \( \mathbf{2}(\boldsymbol{k}+\mathbf{1}) \boldsymbol{x}+\boldsymbol{k} \boldsymbol{y}= \)
\( (3 k+4) \)
A . 4
B. 7
\( c \cdot 3 \)
D. 6


A body crosses the topmost point of a vertical circle with critical speed. What
will be its centripetal acceleration when the string is horizontal:
\( \mathbf{A} \cdot g \)
B. \( 2 g \)
c. \( 3 g \)
D. \( 6 g \)


Which symbols represent atoms that are isotopes?
A. C-14 and N-14
B. 0-16 and 0-18
c. \( c-16 \) and \( N-14 \)
D. Rn-222 and Ra-222


What kind of energy transformation takes place at the thermal power
station?


The equation of the straight line passing through the point (4,3) and making intercepts on the cordinate axes whose sum is \( -1, \) is :
A \( \cdot \frac{x}{2}+\frac{y}{3}=-1 \) and \( \frac{x}{-2}+\frac{y}{1}=-1 \)
B. \( \frac{x}{2}-\frac{y}{3}=-1 \) and \( \frac{x}{-2}+\frac{y}{1}=-1 \)
c. \( \frac{x}{2}+\frac{y}{3}=-1 \) and \( \frac{x}{-2}+\frac{y}{1}=1 \)
D. \( \frac{x}{2}-\frac{y}{3}=1 \) and \( \frac{x}{-2}+\frac{y}{1}=1 \)


What is the standard deviation of
\( 7,9,11,13,15 ? \)
A . 2.4
B . 2.
c. 2.7
D. 2.8


Who was the first scientist which
proposed that "Matter is made up of indivisible particles called atoms"?
A. Lavoiser
B. Dalton
c. Thomson
D. Faraday


Evaluate the following expressions:
\( \operatorname{cosec}^{2} 30^{\circ} \sin ^{2} 45^{\circ}-\sec ^{2} 60^{\circ} \)


Splitting a compound using electricity is called:
A. electrolysis
B. electrolyte
c. electrokinesis
D. none of the above


The displacement ( in \( \mathrm{m} \) ) of a particle of mass 100 g from its equilibrium position is given by the equation:
\[
\boldsymbol{y}=\mathbf{0 . 0 5} \sin 3 \boldsymbol{\pi}(\mathbf{5} \boldsymbol{t}+\mathbf{0 . 4})
\]
A. the time period of motion is \( 1 / 30 \) sec
B. the time period of motion is \( 1 / 705 \) sec
c. the maximum acceleration of the particle is
\[
11.25 \pi^{2} m / s^{2}
\]
D. the force acting on the particle is zero when the displacement is 0.05 \( \mathrm{m} \).


What is meant by radioactivity?


Evaluate \( \left(\frac{1+\cos \frac{\pi}{8}-i \sin \frac{\pi}{8}}{1+\cos \frac{\pi}{8}+i \sin \frac{8}{8}}\right)^{8}= \)
A .
B. - -
\( c \cdot 2 \)
D.


\( \boldsymbol{K}_{C}=\mathbf{9} \) for the reaction, \( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \)
\( C+D . \) If \( A \) and \( B \) are taken in equal
amounts. Then what is the amount of \( C \)
in equilibrium?
A. 0.75
в. 0.98
\( c \cdot 1.23 \)
D. 2.45


Actual flame temperature is always lower than the adiabatic flame
temperature, because there is
A. no possibility of obtaining complete combustion at high temperature
B. always loss of heat from the flame
c. both (a) and (b).
D. neither (a) nor (b)


Two conducting rings of radii r and \( 2 r \)
move in opposite directions with velocities \( 2 v \) and \( v \) respectively on a conducting surfaces S. There is a
uniform magnetic field of magnitude B
perpendicular to the plane of the rings. The potential difference between the
highest points of the two rings is?
\( A \cdot \) zero
B. 2rvB
c. 4 rv \( B \)
D. 8rvB


Match the items given in Column I with
those in Column II and select the correct
options given below:
Column I
Fibrinogen osmotic balance
Globulin 2 Blood clotting
Defence Albumin \( \quad 3 \quad \) mechanism
A. \( A-1, B-3, C-2 \)
B. \( A-3, B-2, C-1 \)
c. \( A-2, B-3, C-1 \)
D. \( A-1, B-2, C-3 \)


Give the type of isomerism exhibited by each of the following pairs 1,1 Dibromoethane and 1,2
dibromoethane?
A . Positional
B. Functional
c. Ring chain
D. Metamerism


Which letter corresponds to the
activation energy in this reaction
without the addition of a catalyst?
\( A \cdot A \)
B. B
\( c . c \)
\( D . \) D
\( E . E \)


End product of glycolysis is
A . Citric acid
B. Glyceraldehyde
c. Phosphoglyceraldehyde
D. Pyruvic acid


How many grams of \( C O_{2} \) gas is
dissolved in a 1 It bottle of carbonated
water if the manufacturer uses a
pressure of 2.4 atmosphere in the bottling process at \( 25^{\circ} \mathrm{C} \) ? \( \left(K_{H} \text { of } C O_{2}\right. \)
water \( \left.=29.76 a t m / m o l e / l \text { at } 25^{\circ} C\right) \)
A . 3.52
в. 4.2
\( c .3 .1 \)
D. 2.5


What processes would be considered essential for maintaining life?
A. Nutrition and metabolism
B. Respiration and exchange of materials
c. Transportation and excretion
D. All of the above


Which term of the sequence
\( -1,3,7,11, \dots \) is \( 95 ? \)


If \( \bar{v}, v_{r m s} \) and \( v_{p} \) represent the mean
speed, root mean square and most probable speed of the molecules in an ideal monoatomic gas at temperature
\( T \) and if \( m \) is mass of the molecule,
then
A \( \cdot v_{p}<\bar{v}<v_{r m} \)
B. No molecule can have a speed greater than \( \sqrt{2 v_{r m s}} \)
C. No molecule can have a speed less than \( v_{p} / \sqrt{2} \)
D. None of the above


Evaluate: \( \cos \left[2 \tan ^{-1}\left[\frac{1}{7}\right]\right] \)
\( A \cdot \sin \left(4 \cot ^{-1} 3\right) \)
B. \( \sin \left(3 \cot ^{-1} 4\right) \)
\( c \cdot \cos \left(3 \cot ^{-1} 4\right) \)
D. \( \cos \left(4 \cot ^{-1} 4\right) \)


Find the domain of \( \cos ^{-1}[X] \) where \( [X] \)
is the greatest integer functions.


The van 't Hoff factor of a weak
electrolyte \( A B \) in a solution is \( 1.1 . \) Its degree of dissociation would be 0.1 . If
true enter 1 else 0


A sphere rolls down on an inclined plane of inclination \( \theta . \) What is the
acceleration as the sphere reaches bottom?
A \( \cdot \frac{5}{7} g \sin \theta \)
в. \( \frac{3}{5} g \sin \theta \)
c. \( \frac{2}{7} g \sin \theta \)
D. \( \frac{2}{5} g \sin \theta \)


Which of the following produces virtual image?
A. simple microscope
B. Ordinary camera
c. Projector
D. cinemascope


Name the physical principle on which the working of optical fibres is based.


When 2 g of gas \( A \) is introduced into an evacuated flask kept at \( 25^{\circ} \mathrm{C} \), the pressure was found to be 1 atm. If 3 g of another gas B is then added to the same flask containing A, the pressure
becomes 1.5 atm. Assuming ideal behaviour, the ratio of molecular
weights \( \left(M_{A}: M_{B}\right) \) is :
A . 1: 3
B. 3:
\( c \cdot 2: 3 \)
D. 3:


Reducing nature in increases
with increase in atomic number in
alkali metals.
A. period
B. group
c. both \( A \) and \( B \)
D. none of these


The dihedral angle between the
hydrogen atoms of two methyl groups in staggered of ethane is :
\( A \cdot 120^{\circ} \)
B . \( 180^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 60^{\circ} \)


Assertion : 20 gm of argon (atomic mass of \( A r=40) \) occupies volume of
\( 22400 c m^{3} \) at STP.
Reason : 20 gm of Neon (atomic mass of
\( N e=20) \) occupies a volume of
\( 22400 c m^{3} \) at STP.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.
E. Both assertion and reason are incorrect.


In the reaction,
\( \left(N H_{4}\right)_{2} C r_{2} O_{7} \stackrel{\Delta}{\longrightarrow} N_{2}+H_{2} O+ \)
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{3} \)
The coefficient of \( \boldsymbol{H}_{2} \boldsymbol{O} \) is :
\( \mathbf{A} \cdot \mathbf{1} \)
B . 2
\( c \cdot 3 \)
D.


Co. \( C l_{3} .5 N H_{3} H_{2} O \) is a pink solid, the solution of this salt is also pink and
formed 3 mol of \( A g C l \) with silver nitrate
solution. On heating pink solid, it loses one water molecule and forms purple
solid having same ratio of \( \boldsymbol{C} \boldsymbol{o}: \boldsymbol{N} \boldsymbol{H}_{3} \)
\( C l \) as that of pink solid. The purple solid
when dissolved in water and treated
with silver nitrate forms 1 mol of \( A g C l \)
Draw the structures and name of the
pink and purple solids.


Which of the following should be added to \( 9 x^{3}+6 x^{2}+x+2 \) so that the sum is
divisible by \( (3 x+1) ? \)
A . -4
B. -
\( c \cdot-2 \)
D. -


The wavelength of a wave is \( \lambda=6000 A \)
then wave number will be
A \( \cdot 1.66 \times 10^{7} \mathrm{m}^{-1} \)
В . \( 1.66 \times 10^{6} \mathrm{m}^{-1} \)
c. \( 16.6 \times 10^{-1} \mathrm{m}^{-1} \)
D . 166 \( \times 10^{3} \mathrm{m}^{-1} \)


Polynomial classification has recently begun to replace the binomial system
A. True
B. False


Assertion
\( \mathbf{A} \)
\( 60 W \) bulb is connected in parallel with a room heater and this combination is connected across the
mains. If the \( 60 W \) bulb is replaced by a
\( 100 W \) bulb, the heat produced by the
heater will be more.BECAUSE
Reason
When resistances are connected in parallel across the mains, the heat produced is inversely proportional to the resistance
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


Energy levels \( A, B \) and \( C \) of a certain
atoms correspond to increasing values
of every level i.e., \( \boldsymbol{E}_{\boldsymbol{A}}<\boldsymbol{E}_{\boldsymbol{B}}<\boldsymbol{E}_{\boldsymbol{C}} \). If
\( \lambda_{1}, \lambda_{2} \) and \( \lambda_{3} \) are the wavelengths of radiations corresponding to the transitions \( C \) to \( B, B \) to \( A \) and \( C \) to
A respectively, then which of the following statements is correct?
B. \( \lambda_{3}=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}} \)
c. \( \lambda_{1}+\lambda_{2}+\lambda_{3}=0 \)
D. \( \lambda_{3}^{2}=\lambda_{1}^{2}+\lambda_{2}^{2} \)


A hammer weighing \( 3 \mathrm{kg}, \) moving with a velocity of \( 10 \mathrm{m} / \mathrm{s} \), strikes against the head of a spike and drives it into a block of wood. If the hammer comes to rest in
\( 0.025 s, \) the average (retarding) force acting on the spike will be
A . 600 N
B. -600 N
c. \( 1200 \mathrm{N} \)
D. -1200 N


The third supralabial is the largest touching the nasal shield and eye is found in
A. Krait
B. Cobra
c. viper
D. Anaconda


Consider a uniform electric field \( \boldsymbol{E}= \)
\( 3 \times 10^{3} \hat{i} N C^{-1} \)
(a) What is the flux of
this field through a square of \( 10 \mathrm{cm} \) on a side whose plane is parallel to the yz plane?
(b) What is the flux through the same square if the normal to its plane
makes a \( 60^{\circ} \) angle with the \( x \) -axis?


\( \mathbf{0 . 1 6} \boldsymbol{g} \boldsymbol{N}_{\mathbf{2}} \boldsymbol{H}_{4}\left(\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{4} \times \mathbf{1 0}^{-\mathbf{6}}\right) \) are
dissolved in water and the total volume
made up to 500 m \( L \). Calculate the
percentage of \( N_{2} H_{4} \) that has reacted to water in this solution.


Consider the following statements
(a) The \( p H \) of a mixture containing
\( 400 m L \) of \( 0.1 M H_{2} S O_{4} \) and \( 400 m L \) of
\( 0.1 M N a O H \) will be approximately 1.3
(b) lonic product of water is temperature dependent
(c) A monobasic acid with \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1 0}^{-5} \)
has a \( p H=5 . \) The degree of
dissociation of this acid is \( 50 \% \)
(d) The Le Chatelier's principle is not applicable to common-ion effect.
The correct statement are :
A \( \cdot(a),(b) \) and \( (d) \)
B. (a), (b) and (c)
c. (a) and (b)
D. (b) and (c)


Which of the following assertions are
correct?
This question has multiple correct options
A. A neutron can decay to a proton only inside a nucleus
B. A proton can change to a neutron only inside nucleus
C. An isolated neutron can change into a proton
D. An isolated proton can change int a neutron


Two cards are drawn from a well
shuffled pack of 52 cards. Find the
probability distribution of the number of aces.


In a school, \( \frac{5}{8} \) of the total students are girls. If the number of girls is 120 more than that of the boys. What is the strength of the school? how many boys are there?
A .160
в. 120
c. 100
D. 180


Physical properties of any compound depend largely on:
A. its mass
B. the type of intermolecular and intramolecular forces of attraction
c. both mass and type of intermolecular and intramolecular forces of attraction
D. none of the above


How do you condemn the use of alcohol
as a social practice.


In an experiment 0.2430 gm of magnesium on burning with oxygen yielded 0.4030 gm of magnesium oxide. In another experiment 0.1820 gm of magnesium on burning with oxygen yielded 0.3020 gm of magnesium oxide. Show that the data explain the law of definite proportions.


Which is not anomalous pair of elements in the Mendeleev's periodic
table?
\( \mathbf{A} \cdot A r \) and \( K \)
B. \( C o \) and \( N i \)
c. \( T e \) and \( I \)
D. \( A l \) and \( S i \)


\( \vec{A} \) and \( \vec{B} \) are two vectors \( \operatorname{given} \vec{A}= \) \( 2 \hat{i}+3 \hat{j} \) and \( \vec{B}=\hat{i}+\hat{j} . \) The magnitude of the component \( \vec{A} \) along \( \vec{B} \) is


Which compounds is related to Haber's
process:
A. \( C O_{2} \)
в. \( H_{2} \)
\( c \cdot N O_{2} \)
D. \( N H_{3} \)


Highest DDT deposition shall occur in
A. Phytoplankton
B. Sea Gull/Birds
\( c \cdot \) crab
D. Eel


Answer the following questions for Zn
atom:

How many electrons have \( n+m=3 ? \)


The increasing order of the first ionisation enthalpies of the elements \( B, P, S \) and \( F \) is:
\( \mathbf{A} \cdot B<S<P<F \)
B. \( F<S<P<B \)
c. \( P<S<B<F \)
D. \( B<P<S<F \)


Calculate the no of moles present in \( 2.044 \times 10^{23} \) number of Helium gas?


There is a hole in the bottom of tank
having water. If total pressure at bottom
is 3 atm \( \left(1 \text { at } m=10^{5} N / m^{2}\right) \) then the velocity of water flowing from hole is:
\( \mathbf{A} \cdot \sqrt{400} m / s \)
B. \( \sqrt{600} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{60} m / s \)
D. None of these


In a circuit for finding the resistance of a galvanometer by half deflection
method, a \( 6 V \) battery and a high resistance of \( 11 k \Omega \) are used. The figure
of merit of the galvanometer \( 60 \mu A / \) division. In the absence of shunt
resistance, the galvanometer produces a deflection of \( \theta=9 \) divisions when
current flows in the circuit. The value of
the shunt resistance that can cause the
deflection of \( \boldsymbol{\theta} / 2, \) is closest to
A . \( 55 \Omega \)
B. \( 110 \Omega \)
c. \( 220 \Omega \)
D. \( 550 \Omega \)


If Planck's constant \( (h), \) surface tension
\( (s) \) and moment of inertia \( (I) \) are taken as fundamental quantities, then dimensions of linear momentum \( (p) \) will be given as:
\( \mathbf{A} \cdot h s^{2} I^{1 / 2} \)
B . \( h^{1 / 2} s^{1 / 2} I \)
c. \( h^{0} s^{1 / 2} I^{1 / 2} \)
D. None of these


Find the velocity of an electron having
an energy of 1280 electron volt. \( \boldsymbol{m}= \)
\( 9.1 \times 10^{-31} k g \)


Find the area of the region
\( \left\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}^{2}+\boldsymbol{y}^{2} \leq \mathbf{4}, \boldsymbol{x}+\boldsymbol{y} \geq \mathbf{2}\right\} \)


Evaluate \( \int x \cdot e^{-x^{2}} d x \)


The distance at which an object should be placed in front of a convex lens of
focal length \( 10 \mathrm{cm} \) to obtain a real
image double the size of object will be:
\( A .30 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
\( c \cdot 5 \mathrm{cm} \)
D. \( 10 \mathrm{cm} \)


Read the following statements
(a) \( x^{2}-5 x+\sqrt{2} \) is a polynomial in \( x \)
(b) \( 4 x^{2}-3 \sqrt{x}+7 \) is not a polynomial
in \( x \)
(c) \( \frac{x^{2}+2 x+5}{x+3}(x \neq-3) \) is a rational
expression.
(d) \( \frac{x^{3}-5 \sqrt{x}-1}{x^{2}+x+4} \) is not a rational expression.
Correct options is -
A . acd
B. abc
\( c \cdot a b d \)
D. abcd


In Dow's process, the starting raw material is:
A. phenol
B. chlorobenzene
c. aniline
D. diazobenzene


Piston cylinder device initially contains
\( 0.5 m^{3} \) of nitrogen gas at \( 400 k P a \) and
\( 27^{\circ} \mathrm{C} . \) An electric heater within the
device is turned on and is allowed to
pass a current of \( 2 A \) for 5 min from a
\( 120 V \) source. Nitrogen expands at
constant pressure and a heat loss of
\( 2800 J \) occurs during the process. \( \boldsymbol{R}= \) \( \frac{25}{3} k J / k m o l K . \) The final temperature of nitrogen is
\( \mathbf{A} \cdot 2.6^{\circ} \mathrm{C} \)
в. \( 56.6^{\circ} \mathrm{C} \)
c. \( 29.6^{\circ} \mathrm{C} \)
D. \( 5.67^{\circ} \mathrm{C} \)


Oxygen we breathe is obtained from
A. Respiration
B. Guttation
c. Photosynthesis
D. All of the above


Gases deviate from the ideal gas
behaviour because their molecules:
A. possess negligible volume
B. have forces of attraction between them
c. are polyatomic
D. are not attracted to one other


A deficiency of pulmonary surfactant would
A. Decrease surface tension
B. Decrease the work of breathing
c. Both of the above
D. None of the above


Classify the following function \( \boldsymbol{f}(\boldsymbol{x}) \)
defined in \( R \rightarrow R \) as injective,
surjective, both or none:
\( \boldsymbol{f}(\boldsymbol{x})=\left(\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{5}\right)\left(\boldsymbol{x}^{2}+\boldsymbol{x}-\boldsymbol{3}\right) \)
A. only injective
B. Only surjective
c. Neither injective not surjective
D. Both injective and surjective.


Name the method of concentration of
haematite ore and explain the method.


Taxonomically, the most controversial group is
A. Dinoflagellates
B. Diatoms
c. Euglenoids
D. Prokaryotes


Represents these number on number
line
\( \frac{-5}{6} \)