Read the given statements and mark
the correct option
Statement 1: If an earth satellite is on a
lower orbit, the speed of satellite increases
Statement 2: The speed of satelite is a constant quantity for all orbits of earth
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. both statements 1 and 2 are true but statement 2 is not correct explanation of statement
c. statement 1 is true but statement 2 is false
D. Both statements 1 and 2 are false


Determine the relationship between the
torque \( N \) and the torsion angle \( \varphi \) for the solid rod of circular cross-section. Their
length \( l, \) radius \( r, \) and shear modulus \( G \)
are supposed to be known.
\( ^{\mathbf{A}} \cdot_{N}=5 \frac{\pi r^{4} G \varphi}{3 l} \)
B. \( N=\frac{\pi r^{4} G \varphi}{2 l} \)
c. \( _{N}=3 \frac{\pi r^{4} G \varphi}{2 l} \)
D. None of these


Solve
\( \int \frac{v}{1-v} d v \)


In figure, lines \( X Y \) and \( M N \) intersect at 0
If \( \angle P O Y=90^{\circ} \) and \( a: b=2: 3, \) find \( c \)
\( 4 \cdot 106 \)
B. \( 156^{\circ} \)
\( c \cdot 126^{\circ} \)
D. 136


At what temperature would the volume of a given mass of a gas at constant
pressure be twice its volume at \( 0^{\circ} \mathrm{C} \) ?
\( \mathbf{A} \cdot 546^{\circ} C \)
B. \( 100^{\circ} \mathrm{C} \)
c. \( 273^{\circ} \mathrm{C} \)
D. \( 373^{\circ} \mathrm{C} \)


Which of the following constitutes an edible fungi?
A . Agaricus
B. Morchella
c. Lycoperdon
D. Both A and B


A stick of length \( L \) and mass \( M \) lies on
a frictionless horizontal surface on
which it is free to move in any way, \( A \)
ball of mass is \( m \) and speed \( v \) as shown
in fig. What must be the mass of the ball so that it remains at rest
immediately after the collision?


Isotopes has different:
This question has multiple correct options
A. physical properties
B. chemical properties
C. atomic number
D. mass number


A capacitor acquires a potential
difference of \( 200 \mathrm{V} \) when \( 10^{12} \) electrons
are taken from one plate and placed
on the other plate. Its capacitance is:
A \( \cdot 2 \times 10^{-10} F \)
В. \( 4 \times 10^{-10} F \)
c. \( 8 \times 10^{-10} F \)
D. \( 12 \times 10^{-10} F \)


Given ordered pairs :(5,4),(5,5),(5,6) \( (6,4),(6,5),(6,6),(6,7),(8,4),(8,5),(8, \)
6), (8,8)
Use these ordered pairs to find the following relation:
\( R_{2}= \) "is equal to"


For two ionic solids \( C a O \) and \( K I \) which
of the following statement(s) is false?
A. Lattice enthalpy of \( C a O \) is much higher than that of \( K I \)
B. \( C a O \) has high melting point
c. \( K I \) has low melting point
D. \( C a O \) is not soluble in benzene


The probabilities that three men hit a target are \( 1 / 6,1 / 4 \) and \( 1 / 3 . \) Each man
shoots once at the target. What is the probability that exactly one of them hits the target?
A \( \cdot 11 / 72 \)
B. 21/72
c. \( 31 / 72 \)
D. 3/4


An electron in the hydrogen atom is
excited from the first orbit to the fifth
orbit. Find the change in energy of the electron in eV.
A \( .+(13.6 \times 24) / 25 \)
в. \( -(13.6 \times 4) / 5 \)
C . \( -(0.529 \times 4) / 5 \)
D. \( -(13.6 \times 4) / 9 \)


Stability of ions of \( G e, S n \) and \( P d \) will be in the order:
This question has multiple correct options
A. \( G e^{2+}<S n^{2+}<P b^{2+} \)
B. \( G e^{4+}>S n^{4+}>P b^{4+} \)
\( \mathrm{c} \cdot S n^{4+}>S n^{2} \)
\( D \cdot P b^{2+}>P b^{4} \)


which harmone controls carbohydrate metabolism?


Integrate the function \( x \log x \)


A projectile is fired with a velocity \( u \) at
angle \( \theta \) with the ground surface. During
the motion at any time it is making an
angle \( \alpha \) with the ground surface. The speed of particle at this time will be
A . ucos\theta\( \theta \)seca
B. ucos\theta.tana
c. \( u^{2} \cos ^{2} \alpha \sin ^{2} \alpha \)
D. usin\theta.sina


element has one
electron in the outermost shell and
attains duplet configuration after one more electron and attains stability.


ff \( y=4 x-5 \) is a tangent to the curve
\( \boldsymbol{y}^{2}=\boldsymbol{p} \boldsymbol{x}^{3}+\boldsymbol{q} \) at \( (\boldsymbol{2}, \boldsymbol{3}), \) then \( (\boldsymbol{p}+\boldsymbol{q}) \) is
equal to
A . -5
B. 5
\( c .-9 \)
D.
E .


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{2} \boldsymbol{C H}(\boldsymbol{F})-\boldsymbol{C H}_{3} \) is a
alkyl flouride.
A. primary
B. secondary
c. tertiary
D. None of these


If the straight line draw through the point \( P(\sqrt{3}, 2) \) and inclined at an angle \( \frac{\pi}{6} \) with the \( x \) -axis,meets the line \( \sqrt{3} x- \) \( 4 y+8=0 \) at Q.Find the length \( P Q ? \)


There are 30 tickets numbered from 1 to
30 in a box. A ticket is drawn at random.
If \( A \) is the event that the number on the
ticket is a prime number less than 15 write the sample space \( S, n(S) \) the event \( \boldsymbol{A} \) and \( \boldsymbol{n}(\boldsymbol{A}) \)


Calculate the value of \( h, \) when \( S=198 \)
and \( \left.r=3.5 \text { (Take } \pi \text { to be } \frac{22}{7}\right) \)
A . 2.5
B. 5.5
\( c .7 .2 \)
D. 9


If momentum of a body remains
constant, then mass-speed graph of body is:
A . a circle
B. a straight line
c. a rectangular hyperbola
D. a parabola


Atomic number of \( S c^{3+}(18 e) \)
is


A satellite of mass \( m \) is orbiting around the earth at a height \( h \) above the
surface of the earth. Mass of the earth is
\( M \) and its radius is \( R \). The angular
momentum of the satellite is
independent of :
A .
в. \( M \)
\( c \cdot h \)
D. None of these


Match column i with column-ii and
select the correct answer.
\( \begin{array}{lll} & \text { Coloumn-1 } & \text { Column-2 } \\ \mathrm{A} & \text { Spring wood } & \text { Duramen } \\ \mathrm{B} & \text { Autumn wood } & \text { Alburnum } \\ \mathrm{c} & \text { Heartwood } & \text { Late wood } \\ \mathrm{d} & \text { Sap wood } & \text { Early wood }\end{array} \)
\( A \)
\( A-(i v), B-(i i i), C-(i), D-(i i) \)
B. \( A-(\text { iii) }, B-(i v), C-(i i), D-(i i) \)
\( c \)
\( A-(\text { iii) }, B-(i v), C-(i), D-(i i) \)
D. A-(iii), B - (iv), (ii), D-(i)


Which of the following is true during electroplating?
A. The metal gets transferred from one electrode to another
B. The metal gets deposited from positive terminal of a battery to negative terminal of the battery.
c. An equal amount of metal gets dissolved in the solution of the electrolyte
D. All of the above


ohm and 2 ohm are connected in
series across the left gap of a metre-
bridge. The balancing length is \( 60 \mathrm{cm} \). If the resistors were connected in parallel instead of in series, the balancing length would be (in cm)
A . 25
B. 20
\( c \cdot 40 \)
D. 75


A fruit appears to be bigger in a glass of
water due to


Divide the first expression by the second. Write the quotient and the remainder.
\( x^{2}-\frac{1}{4 x^{2}} ; x-\frac{1}{2 x} \)
A \( \cdot \) Quotient \( =x+\frac{2}{2 x}, \) Remainder \( =1 \)
B. Quotient \( =2 x+\frac{1}{2 x} \), Remainder = 0
c. quotient \( =x-\frac{1}{2 x}, \) Remainder \( = \)
D. Quotient \( =x+\frac{1}{2 x}, \) Remainder \( =0 \)


\( \mathbf{f} \mathbf{P}=\left\{\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right\} \mathbf{A}=\left\{\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right\} \)
and \( \mathbf{Q}=\mathbf{P} \mathbf{A} \mathbf{P}^{\mathbf{T}} \) and \( \mathbf{x}=\mathbf{P}^{\mathbf{T}} \mathbf{Q}^{2005} \mathbf{P} \)
then \( x \) is equal to
A. \( \left\{\begin{array}{ll}1 & 2005 \\ 0 & 1\end{array}\right\} \)
в. \( \left\{\begin{array}{ll}4+2005 \sqrt{3} & 6015 \\ 2005 & 4-2005 \sqrt{3}\end{array}\right\} \)
c. \( _{\frac{1}{4}}\left[\begin{array}{cc}2+\sqrt{3} & 1 \\ -1 & 2-\sqrt{3}\end{array}\right] \)
D. \( \frac{1}{4}\left\{\begin{array}{ll}2005 & 2-\sqrt{3} \\ 2+\sqrt{3} & 2005\end{array}\right\} \)


Which of the following sodium compound(s) are formed when an
organic compound containing both nitrogen and sulphur is fused with sodium?
A. Cyanide and sulphide
B. Thiocyanate
c. Sulphite and cyanide
D. Nitrate and sulphide


A body having 1680 J of energy is supplied to 1000 g of water. If the entire amount of energy is converted into heat, the rise in temperature of water (sp.
heat of water \( \left.=4200 J k g^{-1 o} C^{-1}\right) \)
\( \mathbf{A} \cdot 0.4^{\circ} C \)
В . \( 40^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 4^{\circ} C \)
D. \( 44^{\circ} \mathrm{C} \)


The sum of two numbers is \( \frac{-4}{3} . \) If one of
the numbers is \( -5, \) find the other


Select the correct option:
Match column I with column II and
select the correct option from the codes given below.
Column I Column I I I I nnn
(A) Vermicomposting
(i) Ectonephric
(B) Phayngeal nephridia
(ii) Locomotion
(C) Integumentary
(iii) Earthworm nephridia
(D) Setae
(iv) Enteronephric
(v) Store
(E) Spermathecae \( \quad \) spermatozoa
A \( \cdot A-(\text { iii) } ; B-(i v) ; C-(i) ; D-(\text { ii }) ; E-(v) \)
B. \( A-(v) ; B-(i) ; C-(i v) ; D-(\text { ii }) ; E-(\text { iii }) \)
c. \( A- \) (iii); \( B- \) (ii); \( C-(\text { iv } v) ; D-(i) ; E-(v) \)
D. A- (iii); B- (v); C- (i); D- (iv): E- (ii)


An airplane is flying at a height of
\( \mathbf{1 9 6 0} \mathbf{m} \) in the horizontal direction with
a velocity of \( 360 \mathrm{km} / \mathrm{hr} \). It drops a bomb. The bomb strikes a point on the ground, then the time took \( t \) by the bomb to reach the ground is:
A. \( 20 \sqrt{2} \) sec
B. 20 sec
c. \( 10 \sqrt{2} \mathrm{sec} \)
D. 10 sec


An electric dipole moment \( \vec{P}=(2.0 \hat{i}+3.0 \hat{j}) \mu C . . m \) is placed in a
uniform electric field \( \vec{E}=(3.0 \hat{\mathrm{i}}+2.0 \widehat{k}) \times 10^{5} \)
A \( \cdot \) The torque that \( \overrightarrow{\mathrm{E}} \) exert on \( \overrightarrow{\mathrm{P}} \) is \( (0.6 \hat{\mathrm{f}}+0.4 \hat{\mathrm{j}}-0.9 \widehat{\mathrm{k}}) \mathrm{Nm} \)
B. The potential energy of the dipole is -0.6
c. The potential energy of the dipole is 0.6 .
D. None of these


Which of the following is/are main
component present in LPG?
A. methane
B. propane
c. butane
D. both B and C


Match the maxima of the functions \( f(x) \)
on L.H.S


n Fig., the side \( Q R \) of \( \triangle P Q R \) is produced
to a point \( S \) If the bisectors of \( \angle P Q R \) and \( \angle P R S \)
meet at point \( T, \) then prove that \( \angle \mathrm{QTR}=\frac{1}{2} \angle \mathrm{QPR} \)


The potential at a point \( (x, 0,0) \) is given by \( V=\left(\frac{1000}{x}+\frac{1500}{x^{2}}+\frac{500}{x^{3}}\right) . \) The
intensity of the electric field at \( x=1 \)
will be
A. \( 550 V / m \)
B. \( 55 V / m \)
\( \mathbf{c} .55000 V / m \)
D. \( 5500 V / m \)


What kind of bonding is responsible for the secondary structure of proteins?
A. Covalent bonding
B. Hydrogen bonding
c. lonic bonding
D. Van der Waal's forces


Arterial blood pressure in human beings
A. 120 and \( 80 \mathrm{mm} \) Hg
B. 150 and 100 \( \mathrm{mm} \) Н
c. 50 and \( 100 \mathrm{mm} \) Hg
D. None of the above


In a 0.2 molal aqueous solution of a weak acid HX, the degree of ionization
is \( 0.3 . \) taking \( K_{f} \) for water as \( 1.85, \) the freezing point of the solution will be
nearest to:
A. -0.360
B. -0.260
c. +0.480
D. -0.481


The slope and y-intercept of the following line are respectively
\( 5 x-2 y=3 \)
A \( \cdot \) slope \( =m=-\frac{5}{2} \quad \) and \( \quad y- \) intercept \( =-\frac{3}{2} \)
B \( \cdot \) slope \( =m=\frac{5}{2} \quad \) and \( \quad y- \) intercept \( =\frac{3}{2} \)
C \( \cdot \) slope \( =m=\frac{5}{2} \quad \) and \( \quad y- \) intercept \( =-\frac{3}{2} \)
D. slope \( =m=-\frac{5}{2} \quad \) and \( \quad y- \) intercept \( =\frac{3}{2} \)


Lung diseases are four times more in
urban areas than in rural areas. This is
due to the presence of:
\( A \cdot S O_{2} \)
в. \( C O_{2} \)
c. \( N_{2} \)
D. water vapour


Humans fall into which kingdom Animalia category?
A. Hemichordata
B. Mollusca
c. chordata
D. None of the above


The correct order of melting points is:
A. ethane < propane \( < \) butane
B. butane < propane < ethane
C. propane < ethane < butane
D. none of the above


The position vectors of \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are \( \overline{\boldsymbol{i}}+ \)
\( \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}}, \boldsymbol{4} \overline{\boldsymbol{i}}+\overline{\boldsymbol{j}}+\overline{\boldsymbol{k}}, \boldsymbol{4} \overline{\boldsymbol{i}}+\mathbf{5} \overline{\boldsymbol{j}}+\overline{\boldsymbol{k}} . \) Then
the position vector of the circumcentre
of the triangle \( A B C \) is
\( \mathbf{A} \cdot 3 \hat{i}+2 \hat{j}+\hat{k} \)
B. \( \frac{1}{2}(6 \hat{i}+\hat{j}+\hat{k}) \)
c \( \cdot \frac{1}{2}(5 \hat{i}+6 \hat{j}+2 \hat{k}) \)
D. \( \frac{1}{2}(9 \bar{i}+7 \bar{j}+3 \bar{k}) \)


The energy of photon of visible light with maximum wavelength in \( e V \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
в. 1.6
\( c .3 .2 \)
D.


A device for producing electric current
is
A. Ammeter
B. Voltmeter
c. Generator
D. Galvanometer


Which of the following represents the
expression for \( \frac{3}{4} \) th life of first order reaction?
\( ^{\mathrm{A}} \cdot \frac{2.303}{k} \log 4 / 3 \)
в. \( \frac{2.303}{k} \log 3 / 4 \)
c. \( \frac{2.303}{k} \log 4 \)
D. \( \frac{2.303}{k} \log 3 \)


If \( x=\frac{1-t^{2}}{1+t^{2}} \) and \( y=\frac{2 t}{1+t^{2}} \) at then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
A \( \cdot \frac{-1}{x^{3}} \)
в. \( \frac{y}{x} \)
c. \( \frac{-x}{y} \)
D. \( \frac{x}{y} \)


Give examples of hypercalcemic
hormone.


The electrical resistance of pure
platinum increases linearly with increasing temperature over a small range of temperature. This property is used in a Platinum resistance
thermometer. The relation between \( \boldsymbol{R}_{\boldsymbol{\theta}} \)
(Resistance at \( \theta \) K) and \( R_{0} \) (Resistance
\( \left.\operatorname{at} \theta_{0} K\right) \) is given by \( R_{\theta}=R_{0}[1+\alpha(\theta- \)
\( \left.\left.\boldsymbol{\theta}_{0}\right)\right], \) where \( \boldsymbol{\alpha}= \) temperature coefficient
of resistance. Now, if a Platinum
resistance thermometer reads \( 0^{\circ} \mathrm{C} \)
when its resistance is \( 80 \Omega \) and \( 100^{\circ} \mathrm{C} \)
when its resistance is \( 90 \Omega \), find the
temperature at which its resistance is
\( 86 \Omega \)


In a cubical vessel \( 1 m \times 1 m \times 1 m \) the gas
molecules of diameter \( 1.7 \times 10^{-8} \mathrm{cm} \) are
at a temperature \( 300 \mathrm{K} \) and a pressure of
\( 10^{-4} \mathrm{mm} \) mercury. The mean free path of
the gas molecule is
A. 1 meter
B. 4 meter
c. 2.42 meter
D. \( 1 \mathrm{cm} \)


A material has poisson's ratio of \( 0.5 . \) If a uniform rod suffers a longitudinal strain of \( 2 \times 10^{-3} \) the percentage
increase in its volume is :
A . २\%
в. 0.5\%
c. \( 4 \% \)
D. 0\%


Which is true about the difference
between cortical and juxtamedullary nephrons?
A. Most nephrons are juxtamedullary.
B. The efferent arteriole's of cortical nephrons give rise to most of the vasa recta
c. The aaferent arterioles of the juxtamedullary nephrons give rise to most of the vasa recta
D. Juxtamedullary nephrons generate a hyperosmotic medullary interstitium


Give any two advantages of hydrogen as
a fuel.


\( \ln H_{2} O_{2} \) molecule the 0 - 0 bond length
is:
A \( .1 .34 \AA \)
В. 1.48 月
c. \( 1.54 \dot{A} \)
D. 1.20 à


\( 15 g \) ice at \( 0^{\circ} C \) is mixed with \( 10 g \) water and ice in the mixture. final
temperature will be in \( ^{\circ} \boldsymbol{C} \) ?


What is the IUPAC symbol of Rutherfordium?
A . Rt
B. Ru
c. Rf
D. Rd


Potassium and sodium are not used for
reaction with dilute hydrochloric acid or dilute sulphuric acid in laboratory preparation of hydrogen. Explain why?


In carbon cycle of fusion, 4 protons combine to yield one alpha particle and
A. one positron
B. two positrons
c. ten positrons
D. three positrons


\( 2.32 \mathrm{gm} \) mixture of \( \mathrm{FeO} \) and \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3} \)
when burnt in atmosphere of oxygen, 56
\( \mathrm{ml} \) of \( \mathrm{O}_{2} \) is required at STP for complete oxidation. Find mole percentage of
\( F e_{2} O_{3} \) in the given mixture.
A . 50\%
B. 40\%
c. \( 45 \% \)
D. 60\%


The range of wavelength of visible light is:
A \( .10 \AA \) to \( 100 \AA \)
в. 4000 月 to 7000 音
c. \( 8000 \dot{A} \) to \( 10,000 \dot{A} \)
D. \( 10,000 \dot{A} \) to \( 15,000 \dot{A} \)


Dimension of \( \epsilon_{0} \) are
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{0} A^{0}\right] \)
в. \( \left[M^{0} L^{-3} T^{3} A^{3}\right. \)
\( \mathbf{c} \cdot\left[M^{-1} L^{-3} T^{3} A^{1}\right] \)
\( \mathbf{D} \cdot\left[M^{-1} L^{-3} T^{4} A^{2}\right] \)


The length of chord of circle with radius 10cm drawn at a distance of 8cm
\( A \cdot 12 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( c \cdot 14 c m \)
D. 30cm


To which logic gate does the truth table given below correspond?
\( \begin{array}{ccc}\mathbf{A} & \mathbf{B} & \mathbf{Y} \\ 0 & 0 & 1 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0\end{array} \)
A. OR gate
B. AND gate
c. NAND gate
D. NOR gate


A fixed container is filled with a liquid of
density \( \rho \) up to a height \( 4 m . \) A horizontal
slit of small width but of area \( =0.5 \mathrm{m}^{2} \) is
made a height of \( 2 m \) from bottom. The
speed of top surface of the water level is Area of top surface of container is \( 4 m^{2} \)
and \( g=10 m / s^{2} \) ).
A \( \cdot \sqrt{\frac{20}{63}} \mathrm{m} / \mathrm{sec} \)
в. \( \sqrt{\frac{40}{63}} \) m/sec
c. \( \sqrt{\frac{80}{63}} \mathrm{m} / \mathrm{sec} \)
D. None of these


Which of the following is not a characteristic of an irreversible
process?
A. Spontaneity
B. Energy loss
C. Slow change in system variables
D. All of the above


Which of the following is not an interstitial compound?
A . \( T i C \)
в. \( M o C \)
\( \mathrm{c} \cdot F e_{0.82} \mathrm{O} \)
\( \mathrm{D} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)


Which of the following while in motion cannot be deflected by a magnetic field?
A. Protons
B. Cathode rays
c. Alpha particles
D. Neutrons


Find the coordinates that was of the
equation \( \boldsymbol{x}^{3}-\boldsymbol{p} \boldsymbol{x}^{2}+\boldsymbol{q} \boldsymbol{x}-\boldsymbol{r}=\mathbf{0}, \) may
be in A.P. and hence solve the equation \( x^{3}-12 x^{2}+34 x-28=0 \)


The equation of the curve obtained by connecting all those points where the vapors of above mixture (all mixtures of
different composition are taken) just start forming will be
A \( \cdot P=P_{C}^{o}+\left(P_{B}^{o}-P_{C}^{o}\right) X_{B}^{l} \)
B . \( P=P_{B}^{o}+\left(P_{B}^{o}-P_{C}^{o}\right) X_{B}^{l} \)
\( ^{\mathrm{c}} \cdot p=\frac{P_{B}^{o} P_{C}^{o}}{X_{B}^{o}\left(P_{C}^{o}-P_{B}^{o}\right)+P_{B}^{o}} \)
D. \( P=\frac{P_{B}^{o} P_{C}^{o}}{X_{B}^{l}\left(P_{C}^{o}-P_{B}^{o}\right)+P_{B}^{o}} \)


The period of oscillation \( \boldsymbol{T} \) of a
pendulum of length \( l \) at a place of acceleration due to gravity \( g \) is given by \( \boldsymbol{T}=2 \pi \sqrt{\frac{l}{g}} . \) If the calculated length is 0.992 times the actual length and if the value assumed for \( g \) is 1.002 times its actual value, the relative error in the computed value of \( \boldsymbol{T} \) is
A. 0.005
в. -0.005
c. 0.003
D. -0.003


The arithmetic mean of following data
is
17. find the value of \( P \)
\( 10 \quad 15 \quad 20 \) Term(x) 25
Frequency(f) \( \quad \) 7 \( \quad 10 \quad \) P


Which one of the following is not a tranquiliser?
A. Equanil
B. veronal
c. Salvarsan
D. Serotonin


Cell membranes consist mainly of a
A. Carbohydrate bilayer and proteins
B. Protein bilayer and phospholipids
C. Lipid bilayer and proteins
D. None of these


Non-degradable and fat-soluble
pollutant, such as DDT enters the food
chain, the pollutant:
A. magnifies in concentration at each trophic level
B. degrades at first trophic level
C . accumulates in the body fat of organism at the first trophic level and does not pass to second trophic level
D. decreases in concentration at each trophic level


Which one has higher frequency?
A. Infrasonic sound
B. Ultrasonic sound
C. Audible sound
D. All of the above have same frequency


A biconvex lens of focal length \( f \) forms a
circular image of sun of radius \( r \) in focal plane. Then,
A \( \cdot \pi r^{2} \propto f \)
В \( \cdot \pi r^{2} \propto f^{2} \)
c. if lower half part is covered by black sheet, then area of the image is equal to \( \pi r^{r} / 2 \)
D. if \( f \) is doubled intensity will increase


A solution containing 10 g per \( \mathrm{dm}^{3} \) of urea (m.w. = 60) is isotonic with a 5\%
solution of a non-volatile solute. The
molecular mass of this non-volatile
solute is:
A . \( 250 \mathrm{g} \mathrm{mol}^{-1} \)
B . 300 g mol-
c. \( 350 \mathrm{g} \) mol \( ^{-1} \)
D. \( 200 \mathrm{g} \mathrm{mol}^{-1} \)


If \( \bar{a}, \bar{b} \) are the position vectors of \( A \) and
\( B \) then one of the following points lie on
\( A B \)
A \( \cdot \frac{2(\bar{a}+\bar{b})}{3} \)
в. \( \frac{(\bar{a}-\bar{b})}{3} \)
c. \( \frac{(\bar{a}+\bar{b})}{3} \)
\( ^{\mathrm{D}} \cdot \frac{2 \bar{a}+2 \bar{b}}{3} \)
E. None of these


In the circuit shown, the readings of
ammeter and voltmeter are \( 4 A \) and
\( 20 V \) respectively. The meters are non
ideal, then \( \boldsymbol{R} \) is:
\( A \cdot 5 \Omega \)
B. greater than \( 5 \Omega \)
C. Less than \( 5 \Omega \)
D. between \( 4 \Omega \) and \( 5 \Omega \)


Which of the following snakes has vestiges of hind limbs?
A. Hydrophis
B. Python
c. Eryx
D. Viper


\( \int \frac{x^{2}}{(x \sin x+\cos x)^{2}} d x \)
A. \( \cot x+\frac{x \csc x}{x \cos x-\sin x}+c \)
в. \( \frac{\sin x-x \cos x}{x \sin x+\cos x}+c \)
c. \( -\cot x+\frac{x \csc x}{x \cos x-\sin x}+c \)
D. \( \cot x-\frac{x \csc x}{x \cos x-\sin x}+c \)


The figure is a circle with center \( O \) and
diameter \( 10 \mathrm{cm}, P Q=1 \mathrm{cm} . \) Find the
length of \( \boldsymbol{R} \boldsymbol{S} \)
\( \mathbf{A} \cdot 6 \mathrm{cm} \)
B. \( 4 \mathrm{cm} \)
\( \mathbf{c} .5 \mathrm{cm} \)
D. \( 3 \mathrm{cm} \)


Which of the following forms the floor of
the chest cavity?
A. Lungs
B. Membrane
c. Diaphragm
D. Pleura


n an isosceles, trapezium \( A B C D, \angle C \)
is equal to:
45
155 5
3. \( 65^{\circ} \)
\( c \cdot 105 \)
0.75


The radius of a right circular cylinder increases at a constant rate. Its altitude
is a linear function of the radius and
increases three times as fast as radius.
When the radius is \( 1 \mathrm{cm} \) the altitude is
\( 6 \mathrm{cm} . \) When the radius is \( 6 \mathrm{cm} \), then
volume is increasing at the rate of \( 1 \mathrm{Cu} \) \( c m / \)sec. When the radius is \( 36 \mathrm{cm}, \) the
volume is increasing at a rate of \( n \) cu.
\( \mathrm{cm} / \) sec. The value of ' \( n^{\prime} \) is equal to:
A .12
в. 22
\( c .30 \)
D. 33


Among Valine, Leucine, Isoleucine, Lysine and Phenyl alanine, odd member
is:
A. Leucine, since others are acidic
B. Valine, since others are basic
c. Isoleucine, since others are optically active
D. Leucine, since others are neutral


In an ice rink a skator is moving at \( 3 m s \)
-1 and encounters a rough patch that
reduces her speed by \( 45 \% \) due to a friction force that is \( 25 \% \) of her weight. Find the length of the rough patch
A . \( 1.56 m \)
B. \( 1.46 m \)
c. \( 1.36 m \)
D. \( 1.26 m \)


Find out the correct statement.
A. Endocrine glands regulate neural activity but not vice
versa.
B. Neurons regulate endocrine activity but not vice versa.
C. Endocrine glands regulate neural activity and nervous system regulates endocrine glands.
D. Neither hormones control neural activity nor the neurons control endocrine activity.


Find the real and imaginary parts of the complex number \( \frac{a+i b}{a-i b} \)


In electrolytic refining, is
used as anode and is used
as cathode.
A. pure metal, impure metal
B. impure metal, pure metal
c. pure metal, pure metal
D. impure metal, \( C u C l_{2} \)


The three important oxidation state of
\( \boldsymbol{P} \) are:
A. -3,+3,+5
в. -3,+3,-5
c. -3,+4,-4
D. -3,+3,+4


Give uses of heavy water.


When ferrous oxalte is titrated against
\( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) m eq. of \( \boldsymbol{F} \boldsymbol{e}^{2+}, \boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-} \) and
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{7}^{2-} \) in the redox reaction are \( \boldsymbol{X}, \boldsymbol{Y} \)
and \( Z \) respectively, then:-
A \( . X=Y \)
в. \( X+Y=Z \)
c. \( X+2 Y=Z \)
D. \( 2 X+6 Y+6 Z \)


\( K_{c} \) for the synthesis of \( \mathrm{Hl}(\mathrm{g}) \) from \( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
and \( I_{2}(g) \) is \( 50 . \) The degree of dissociation of HI is:
A . 0.10
B. 0.14
c. 0.18
D. 0.22


Two wave of wavelength \( 1.00 \mathrm{m} \) and 1.01
\( \mathrm{m} \) produce 10 beats in \( 3 \mathrm{s} \) in a gas. The speed of sound in the gas will be
A \( .316 .6 m s^{-1} \)
B. \( 336.6 m s^{-1} \)
\( \mathbf{c} \cdot 356.6 m s^{-1} \)
D. \( 396.6 m s^{-1} \)


Given the numbers: \( 161 \mathrm{cm} ; 0.161 \mathrm{cm} \)
\( 0.0161 \mathrm{cm} . \) The number of significant figure for three numbers is:
\( \mathbf{A} \cdot 3,4,5 \)
в. 3,3,3
c. 3,3,4
D. 3,4,4


Isotopes of an element have:
A. same physical properties
B. different chemical properties
C. different no. of neutrons
D. different atomic number


Calculate the work done in moving the
object from \( x=2 \) to \( x=3 \mathrm{m} \) from the
given graph.


The characteristic not related to alkali
metals is :
A. their ions are isoelectronic with noble gases.
B. metallic character
c. low electronegativity.
D. high ionization energy.


The solubility product of ferric
hydroxide in aqueous solution is \( 6 \times \)
\( 10^{-38} \) at \( 298 K . \) The solubility of \( F e^{3+} \)
ion will increase when the:
\( \mathbf{A} \cdot p H \) is increased
B. \( p H \) is 7.0
c. \( p H \) is decreased
D. saturated solution is exposed to the atmosphere


If \( f(x)=\left|\begin{array}{ccc}a & -1 & 0 \\ a x & a & -1 \\ a x^{2} & a x & a\end{array}\right|, \) using
properties of determinets find the value
of \( f(2 x)-f(x) ? \)


Electric current flows through:
A. a conductor
B. an insulator
c. free space
D. none of these


An electric pole of dipole moment \( \underset{\boldsymbol{p}}{\rightarrow} \) is lying along uniform electric field \( \overrightarrow{\boldsymbol{E}} . \) The work done in rotating the dipole by \( 90^{\circ} \) is:-
A \( \cdot \sqrt{2} \) pE
B. \( \frac{p}{2} \)
c. 2 p
D. pE


Impulse 0.45 is applied to a 200 g model rocket at rest what will be its
final speed? (neglect gravity)
\( A \cdot 2.25 \mathrm{m} / \mathrm{s} \)
B. 22.5 \( \mathrm{m} / \mathrm{s} \)
c. \( 2250 \mathrm{m} / \mathrm{s} \)
D. \( 4500 \mathrm{m} / \mathrm{s} \)


Give a detailed account of the collision
theory of reaction mils of Bimolecular gaseous reactions.


toppr
Q Type your question
smaller sphere with a large amount of
negative charge.

The differences in color for the larger
sphere demonstrate that the smaller,
negatively charged sphere has influenced the larger sphere so that some electrons have moved left,
causing the left side to become
negative and the right side to become
positive, although the large sphere
remains neutral, as a whole.

Which of the following tables best
describes the electric field and electric
potential inside the large sphere, while the small, negative sphere is near it?
Large Negative Charge
A. Electric Field Inside Large Sphere - Electric Potential Inside Large Sphere, zero - same everywhere
B. Electric Field Inside Large Sphere - Electric Potential Inside Large Sphere, non-zero pointing left - higher on right
C. Electric Field Inside Large Sphere - Electric Potential Inside Large Sphere, non-zero pointing right - higher on left
D. Electric Field Inside Large Sphere - Electric Potential Inside Large Sphere, non-zero pointing left - same everywhere
E. Electric Field Inside Large Sphere - Electric Potential Inside Large Sphere, non-zero pointing right - same everywhere


carrying a current \( \boldsymbol{I} \) A. Three
circular Amperian loops 1,2 and 3 are
shown by dashed lines. Point \( P \) is an
interior point. Point \( Q \) is an exterior
point. What is the magnetic field due to
the toroid at points \( P \) and \( Q \)
respectively?
A . 0,0
В \( \cdot 0, \mu_{o}, n \)
C \( \cdot \mu_{o} n I, \mu_{o} n I \)
\( \mathbf{D} \cdot \mu_{o} n I, 0 \)


A car takes 2 hours to reach a
destination by travelling at the speed of \( 60 \mathrm{km} / \mathrm{h} \). when the car travels at the speed of \( 80 \mathrm{km} / \mathrm{h} \) it takes
A. one and half hour
B. one hour
c. two hour
D. None


Find the modulus and argument of the complex number \( \frac{1+2 i}{1-3 i} \)


The de-Broglie wavelength of an electron traveling with speed equal to \( 1 \% \) of the speed of light:
\( A \cdot 400 \mathrm{pm} \)
в. 120 pm
\( c .242 \mathrm{pm} \)
D. 375 pm


Which of the following statements is
incorrect?
A. The bulk modulus for solids is much larger than for liquids
B. Gases are least compressible
C. For a system in equilibrium, the value of bulk modulus is always positive
D. The SI unit of bulk modulus is same that of pressure


Give the geometric representations of
\( 2 x+9=0 \) as an equation
(i) in one variable
(ii) in two variable


At the surface of a certain planet,
acceleration due to gravity is one quarter of that on earth. A brass ball is
transported to this planet, then find the percentage change in its weight.
A . \( 50 \% \)
B . 25\%
c. \( 75 \% \) \%
D. 100\%


Red blood cells are also known as
A. Erythrocytes
B. Leukocytes
c. Neurocytes
D. Oxycytes


A device for measuring temperatures at a distance is:
A. gas thermometer
B. mercury thermometer
c. radiation pyrometer
D. maximum-minimum thermometer


Find the total surface area of a closed
cylindrical petrol storage tank whose diameter \( 4.2 \mathrm{m} \) and height \( 4.5 \mathrm{m} \)


How are lanthanides extracted from
monazite sand?


If 36 grams of carbon and 32 grams of oxygen gas are allowed to react to form carbon dioxide, which one is the
limiting reagent?


From a lot of 15 bulbs which include 5
defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of
the distribution.


Find the \( 10^{t h} \) term of A.P whose sum of \( n \)
terms is given by \( 2 n^{2}+3 n . \) Also find
the \( n^{t h} \) term.


Enzyme amylase belongs to class
A. Transferases
B. Hydrolases
c. Isomerases
D. Oxidoreductases


If \( \boldsymbol{y}=\boldsymbol{e}^{\sin ^{2} \boldsymbol{x}+\sin ^{4} \boldsymbol{x}+\sin ^{6} \boldsymbol{x}+\ldots \infty}, \) then \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}= \)
A \( \cdot e^{\tan ^{2} x} \)
B. \( e^{\tan ^{2} x} \sec ^{2} x \)
C \( \cdot 2 e^{\tan ^{2} x} \tan x \cdot \sec ^{2} x \)
D. 1


suspended from a point \( A \) by an inextensible string of length L. Ball is
drawn to a side and held at same level
as \( A \) but at a distance \( \frac{\sqrt{3}}{2} L \) from \( A \) as
shown. Now the ball is released. Then:
(assume string applies only that much jerk which is required so that velocity
along string becomes zero).
This question has multiple correct options
A. speed of ball just before experiencing jerk is \( \sqrt{g L} \)
B. speed of ball just after experiencing jerk is \( \frac{\sqrt{3 g L}}{2} \)
C. Impulse applied by string \( \frac{\sqrt{g L}}{10} \)
D. ball will experience jerk after reaching to point B


What is binomial nomenclature?
Explain it with a suitable example. Give
its advantages.


Fifteen years from now Ravi's age will be four times his present age. What is Ravi's present age?
A .4
B. 8
c. 5
D. 3


Which of the following shows sublimation at room
temperature?
A. water
B. oil
c. Ammonium chloride
D. sodium carbonate


An experiment succeeds twice as often as it fails. Find the chance that in the
next six trials, there shall be at least
four successes.
A \( \cdot \frac{233}{729} \)
в. \( \frac{64}{729} \)
c. \( \frac{496}{729} \)
D. \( \frac{432}{729} \)


\( \mathbf{1} P a=1 N m^{-2} \)
If mass of air at sea level is 1034 g
\( c m^{-2}, \) calculate the pressure in pascal
A \( \cdot 101 \times 10^{5} P a \)
C. \( 1.0133 \times 10^{5} P a \)
D. \( 10133 \times 10^{5} P a \)


Reflex action is
A. Stimulus - -> sensory neuron - -> spinal cord - -> motor neuron - -> response
B. Stimulus - -> motor neuron - -> sensory neuron - ->
response
C. Reception - -> motor neuron - -> sensory neuron - ->
response
D. Sensory neuron - -> stimulus - -> motor neuron - -> response


Fill in the blanks.
\( \boldsymbol{C}_{6} \boldsymbol{H}_{12} \boldsymbol{O}_{6} \rightarrow \ldots \ldots \ldots+2 \boldsymbol{C} \boldsymbol{O}_{2}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{T} \boldsymbol{P} \)


Obtain an expression for the e.m.f. induced in a coil rotating in uniform magnetic field.


A point on the curve \( \boldsymbol{f}(\boldsymbol{x})=\sqrt{\boldsymbol{x}^{2}-\boldsymbol{4}} \)
defined in [2,4] where the tangent is
parallel to the chord joining two points
on the curve
A \( \cdot(\sqrt{2}, \sqrt{6}) \)
B . \( (\sqrt{6}, \sqrt{2}) \)
C \( \cdot(2,6) \)
D \( \cdot(6,2) \)


The ratio of the amounts of energy
released as a result of the fusion of \( 1 k g \)
hydrogen \( \left(E_{1}\right) \) and fission of \( 1 k g \) of
\( \mathbf{9 2} \boldsymbol{U}^{\mathbf{2 3 6}}\left(\boldsymbol{E}_{\mathbf{2}}\right) \) will be:
A . 1.28
B. 3.28
c. 5.28
D. 7.28


Phloem parenchyma is absent
in
A. Dicot leaf
B. Monocot stem
c. Dicot stem
D. Dicot root


The line represented by \( x=7 \) is parallel
to the \( x \) -axis. Justify whether the statement is true or not.
A . True
B. False


15th term of the series \( 243,81,27, \ldots \) is This question has multiple correct options
\( ^{\mathbf{A}} \cdot\left(\frac{1}{3}\right)^{9} \)
\( ^{\text {B }}\left(\frac{1}{3}\right)^{10} \)
\( ^{\text {c. }}\left(\frac{1}{3}\right)^{10}\left(\frac{1}{3}\right)^{-1} \)
\( ^{\mathrm{D} \cdot}\left(\frac{1}{3}\right)^{10}\left(\frac{1}{3}\right) \)


Find the value of the determinant:
\[
\left|\begin{array}{cc}
\mathbf{5} & -\mathbf{2} \\
-\mathbf{3} & \mathbf{1}
\end{array}\right|
\]


Assertion
Some farmers feel that lightning helps produce better crop.
Reason
Lighting forms No which is converted to
\( N O_{2}, H N O_{2} \) and \( H N O_{3} \) under
atomospheric condition. Thus, \( N O_{3}^{-} \) is a source of nutrients (fertilisers) to the
plant. Thus there are chances of better crops when lightning occurs.
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


Define the following term:
Zeta potential


Evaluate \( \left(\frac{2 x}{7}-\frac{7 y}{4}\right)^{2} \)
A \( \cdot \frac{x^{2}}{49}+\frac{17 y^{2}}{16}-x y \)
B. \( \frac{4 x^{2}}{49}+\frac{49 y^{2}}{16}-x y \)
C \( \cdot \frac{4 x^{2}}{9}+\frac{49 y^{2}}{4}-x y \)
D. \( \frac{x^{2}}{13}+\frac{49 y^{2}}{13}-x y \)


For the circuit shown, what is the
current (in \( \mathrm{mA} \) ) in the ideal inductor
when the current in the battery is \( 0.50 A \)
in the direction shown


Two moles of an ideal mono-atomic gas
is taken through a cyclic process as
shown in the \( P-T \) diagram. In the
process \( B C, P T^{2}= \) constant. Then the
ratio of heat absorbed and heat
released by the gas during the process
\( A B \) and process \( B C \) respectively is:-
\( A \cdot 2 \)
B. 3
\( c .5: 6 \)
\( D . \)


thermometers include
two different metals that are bonded
together and expand at different rates as they warm up.
A. Liquid in glass
B. Gas
c. Bimetallic strip
D. Resistance


If the dielectric constant and dielectric
strength be denoted by \( K \) and \( X \) respectively, then a material, suitable for use as a dielectric in a capacitors,
must have :
A. high \( K \) and high \( X \)
B. high \( K \) and low \( X \)
c. low \( K \) and high \( X \)
D. low \( K \) and low \( X \)


A conductor (shown in the figure) carrying constant current I is kept in
the \( x \) -y plane in a uniform magnetic field \( \vec{B} \). If \( F \) is the magnitude of the total
magnetic force acting on the conductor, then the correct statement(s) is (are)
This question has multiple correct options
\( \mathbf{A} \cdot \) if \( \vec{B} \) is along \( \hat{z}, F \propto(L+R) \)
B. if \( \vec{B} \) is along \( \widehat{x}, F=0 \)
C. if \( \vec{B} \) is along \( \hat{y}, F \propto(L+R) \)
D. if \( \vec{B} \) is along \( \hat{z}, F=0 \)


One of the twelve-mega biodiversity countries of the world is
A. India
B. The USA.
c. The United Kingdom.
D. Africa


\( \operatorname{Let} \boldsymbol{A}=\left(\begin{array}{cc}\mathbf{3} & \mathbf{2} \\ \mathbf{5} & \mathbf{1}\end{array}\right) \) and \( \boldsymbol{B}=\left(\begin{array}{cc}\mathbf{8} & -\mathbf{1} \\ \mathbf{4} & \mathbf{3}\end{array}\right) \)
Find the matrix \( C, \) if \( C=2 A+B \)


The phenomenon of scattering of light by colloidal particle is called Tyndal effect
If true enter 1 , else enter 0 .
\( A \)


Soap bubble appears coloured due to
the phenomenon of:
A. Total internal feflection
B. Interference by division of amplitude
c. Interference by division of wavefront
D. Diffraction of light


Let \( f(n) \) equals to the sum of the cubes
of three consecutive natural numbers.
\( f(n) \) leaves the remainder zero when
divided by
A . 11
B. 9
c. 99
D. none of these


The gases carbon-monoxide \( (C O) \) and nitrogen at the same temperature have
kinetic energies \( \boldsymbol{E}_{1} \) and \( \boldsymbol{E}_{2} \) respectively Then
A. \( E_{1}=E_{2} \)
в. \( E_{1}>E_{2} \)
c. \( E_{1}<E_{2} \)
D. \( E_{1} \) and \( E_{2} \) cannot be compared


Verify \( a-(-b)=a+b \) for the following values of a and b.
(i) \( a=21, b=18 \)
(ii) \( a=118, b=125 \)


The charge on a body is +1 C. Find the number of electrons in excess or deficit
on the body.
A \( \cdot 6.25 \times 10^{1} \) coulomb
B. \( 6.25 \times 10^{-18} \) coulomb
c. \( 6.25 \times 10^{-1} \) coulomb
D. \( 6.25 \times 10^{18} \) coulomb


Oxidizing property is highest of:
\( \mathbf{A} \cdot I_{2} \)
в. \( B r_{2} \)
\( c \cdot F_{2} \)
D. \( C l_{2} \)


Chlorobenzene can be prepared by reacting benzene diazonium chloride
with:
A. \( H C l \)
в. \( C u_{2} C l_{2} \)
c. \( C l_{2} / A l C l_{3} \)
D. \( H N O_{2} \)


If \( \sin \theta=\frac{12}{13}, \) find the value of \( \frac{\sin ^{2} \theta-\cos ^{2} \theta}{2 \sin \theta \cos \theta} \times \frac{1}{\tan ^{2} \theta} \)


Write short notes on Hemodialysis


The speed of sound in hydrogen at \( N T P \)
is \( 1270 m s^{-1} . \) Then the speed in a
mixture of hydrogen and oxygen in the ratio 4: 1 by volume will be
\( \mathbf{A} \cdot 317 m s^{-1} \)
B . \( 635 \mathrm{ms}^{-1} \)
c. \( 830 m s^{-1} \)
D. \( 950 \mathrm{ms}^{-1} \)


Explain with a neat circuit diagram how will you determine unknown resistance X' by using meter bridge.


Mark the correct alternative of the
following.
In figure, if \( A O B \) and \( C O D \) are straight
lines. Then, \( \boldsymbol{x}+\boldsymbol{y}=? \)
A .120
B. 140
\( c .100 \)
D. 160


Prove that polynomial \( \boldsymbol{x}^{\boldsymbol{4} \boldsymbol{p}}+\boldsymbol{x}^{\boldsymbol{4} \boldsymbol{q}+1}+ \)
\( x^{4 r+2}+x^{4 s+3} \) can be divided by \( x^{3}+ \)
\( \boldsymbol{x}^{2}+\boldsymbol{x}+1, \) where \( \boldsymbol{p}, \boldsymbol{q}, \boldsymbol{r}, \boldsymbol{s} \in \boldsymbol{N} \)


Is it possible to have a regular polygon
whose each interior angle is \( 170^{\circ} \)
State true or false:
A. True
B. False


An ultrasonic source emits sound of
frequency \( 220 k H z \) in air. If this sound
meets a water surface, what is the
wavelength of
(a) the reflected sound,
(b) the transmitted sound? (At the
atmospheric temperature, speed of
sound in air \( =352 m s^{-1} \) and in water
\( =1496 m s^{-1} \)


The conjugate acid of \( N H_{2}^{-} \) is:
\( \mathbf{A} \cdot N H_{4}^{+} \)
в. \( N H_{3} \)
\( \mathbf{c} \cdot N H_{2} O H \)
D. \( N H^{-} \)


When the two ecosystems overlap each other, the area is called as
A. Habitat.
B. Niche
c. Ecotone.
D. Ecotype.


Two glass bulbs of internal volume 0.5 and \( 0.2 L \) respectively are connected by a narrow tube of negligible volume. The
pressure of air in the vessel is \( 75 \mathrm{cm} \) at
\( 17^{\circ} \mathrm{C} . \) The smaller bulb is immersed in
melting ice and the larger bulb in boiling water. Calculate final pressure in the bulbs neglecting the expansion of glass.


Which of the following process is not associated with steel making?
A. Bessemer process
B. Open-Hearth process
c. Kaldo process
D. Auto-oxidation


In which of the following changes bond
order decreases?
This question has multiple correct options
A \( \cdot C O \) to \( C O^{+} \)
B. \( N_{2} \) to \( N_{2}^{+} \)
\( \mathbf{c} \cdot H_{2} \) to \( H_{2}^{+} \)
D. \( H_{2} \) to \( H_{2}^{-} \)


Hydrogen does not resemble alkali
metals in which one of the following
properties?
A. Tendency to form cation
B. Nature of oxide
c. combination with halogens
D. Reducing character


A capillary tube of radius \( r \) is immersed in water and water rises in it to a height
h. Mass of water in the capillary tube is
m. If the radius of the tube is doubled,
mass of water that will rise in the
capillary tube will now be
A .
B. \( 2 m \)
\( c \cdot \frac{m}{2} \)
D. \( 4 m \)


Solids which break above the elastic
limit are called the
A . brittle
B. ductile
c. malleable
D. elastic


\( \int_{2}^{5} \sqrt{\frac{5-x}{x-2}} d_{X}= \)
\( A \)
B . \( \pi / 2 \)
\( \mathrm{c} .3 \pi / 2 \)
D. \( \pi / \)


To initiate cell plasmolysis, the soution outside the cell must be
A. Isotonic
B. Hypotonic
c. Hypertonic
D. Atonic


What are the conditions for a species to
act as a donor and an acceptor during dative bond formation?


Molecule mass of HCl is :
A. \( 22.8 \mathrm{g} \)
B. \( 36.5 \mathrm{g} \)
\( c \cdot 28 g \)
D. \( 51 g \)


If a source is transmitting an electromagnetic wave of frequency \( 8.2 \times 10^{6} H z, \) then the wavelength of
the electromagnetic waves transmitted from the source will be:
A . \( 36.6 m \)
в. \( 40.5 \mathrm{m} \)
c. 42.3 m
D. \( 50.9 m \)


Benzenediazonium chloride on
treatment with water gives:
A. Benzene
B. o-chlorophenol
c. Anisole
D. Pheno


Which of the following is not correctly matched?
A. Hard soaps-sodium salts of fatty acids
B. Soft soaps-potassium salts of fatty acids
c. Hydrophilic-water insoluble
D. None of these


\( "\left[B e\left(H_{2} O\right)_{4}\right]^{2+} \) is an acid."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


State Kirchoff's law for an electrical
network. Using these laws deduce the condition for balance in a wheatstone
bridge. Three resistors \( 2 \Omega, 4 \Omega \) and \( 5 \Omega \) are combined in parallel. What is the total resistance of the combination?


Which of the following oxides of nitrogen is a coloured gas?
A \( \cdot N_{2} O \)
B. NO
\( \mathrm{c} \cdot \mathrm{N}_{2} \mathrm{O}_{4} \)
D. \( N O_{2} \)


The diameter of a sphere is \( 6 \mathrm{cm} \). It is
melted and drawn into a wire of water in
the rise by \( 21 \mathrm{cm} ? \)


A neutral atom (Ar) is converted to
\( \left(A r^{+3}\right) \) by the following process;
\( \boldsymbol{A r} \frac{\boldsymbol{E}_{1}}{-\boldsymbol{e}} \boldsymbol{A r}^{+} \frac{\boldsymbol{E}_{2}}{-\boldsymbol{e}} \boldsymbol{A r}^{+2} \frac{\boldsymbol{E}_{3}}{-\boldsymbol{e}} \boldsymbol{A r}^{+3} \)
The correct order of \( E_{1}, E_{2}, E_{3} \) energies
is:
A. \( E_{1}<E_{2}<E_{3} \)
в. \( E_{1}>E_{2}>E_{3} \)
c. \( E_{1}=E_{2}=E_{3} \)
D. \( E_{1}>E_{2}<E_{3} \)


If \( \boldsymbol{\alpha}=\boldsymbol{2} \boldsymbol{s} \boldsymbol{i} \boldsymbol{n}^{-1}(\boldsymbol{2} / \boldsymbol{3}) \) and \( \boldsymbol{\beta}=\boldsymbol{2} \boldsymbol{t} \boldsymbol{a} \boldsymbol{n}^{-1} \boldsymbol{9} \)
then \( 80 \operatorname{cosec}^{2} \alpha+81 \operatorname{cosec}^{2} \beta \) is equal
to


When four hydrogen nuclei combine to
form a helium nucleus in the interior of
sun, the loss in mass in 0.0625 amu.
How much energy is released?


STATEMENT-1: If a and b are positive and \( [x] \) denotes the greatest integer
less than or equal to \( x, \) then \( \lim _{x \rightarrow 0^{+}} \frac{x}{a}\left[\frac{b}{x}\right]=\frac{b}{a} \)
STATEMENT-2: \( \lim _{x \rightarrow \infty} \frac{\{x\}}{x} \rightarrow 0, \) where \( \{x\} \)
denotes the fractional part of \( x \)
A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-
B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True


Solubility product of \( C a C O_{3} \) is
\( 5 \times 10^{-9} . \) Find its solubility.


Hydrogen peroxide is obtained by the electrolysis of:
A. water
B. sulphuric acid
C. hydrochloric acid
D. fused sodium peroxide


An example of fossil fuel is?
This question has multiple correct options
A. Coal gas
B. Coke
C. Natural gas
D. Producer gas


Draw the circuit and the graph of Ohm's
Law.


What is plastic?


components comprising physical factors like temperature, rainfall, wind, soil and minerals


Latent heat of vapourisation of water or
latent heat of steam \( = \)


From a well shuffled pack of 52 playing cards, four are drawn at random. The
probability that all are spades, but one is a king is:
\( ^{\mathrm{A}} \cdot \frac{39}{^{52} C_{4}} C_{4} \)
в. \( \frac{12}{52} C_{3} \)
\( ^{\mathrm{C}}-\frac{^{39} C_{4}}{^{52} C_{4}} \)
D. \( \frac{12}{52} C_{4} \)


Two blocks of masses \( m \) and \( M=2 m \)
are connected by means of a metal wire of cross sectional area \( A \), passing over a frictionless fixed pulley as shown in figure. The system is then released. The stress produced in the wire is :
\( A \cdot \frac{m g}{A} \)
в. \( \frac{2 m g}{3 A} \)
\( c \)


A colloidal sol can be prepared by:
A. breaking the bulky substance into fine particles of colloidal dimensions
B. increasing the size of molecular particles to form larger aggregates.
C. mixing a substance directly with a dispersion medium
D. all of the above


Although \( C u^{+} \) disproportionates in
aqueous solution as \( 2 C u^{+}(a q) \rightarrow \)
\( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{C u}^{2+}(\boldsymbol{a q}) . \) Write down a
reaction in which disproportionation is reversed.
A \( \cdot C u(s)+C u^{2+}(a q)+2 C l^{-} \rightarrow C u C l(s) \)
в. \( C u(l)+C u^{2+}(a q)+2 C l^{-} \rightarrow C u C l(l) \)
c. \( C u(s)+C u^{+}(a q)+C l^{-} \rightarrow C u C l(s) \)
D. None of these


The unit
\( m o l L^{-1} s^{-1} \) is meant for the rate
constant of the reaction having the
order:
A. 0
B. 2
\( c \cdot 1 \)
D.


\( A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right], U_{1}, U_{2} \) and \( U_{3} \) are
columns matrices satisfying \( \boldsymbol{A} \boldsymbol{U}_{1}= \) \( \left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], A U_{2}=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], A U_{3}=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right] \) and \( U \) is
\( 3 \times 3 \) matrix whose columns are
\( U_{1}, U_{2}, U_{3} \) then answer the following question The value of \( \left[\begin{array}{lll}\mathbf{3} & \mathbf{2} & \mathbf{0}\end{array}\right] \boldsymbol{U}\left[\begin{array}{l}\mathbf{3} \\ \mathbf{2} \\ \mathbf{0}\end{array}\right] \) is
\( A \cdot[5] \)
в. \( \left[\frac{5}{2}\right] \)
\( c \cdot[4] \)
D. \( \left[\frac{3}{2}\right. \)


In 15 throws of a die 4 or 5 is considered
to be a success. The mean number of
success is
A . 3
B. 4
\( c .5 \)
D. 6


\( n^{\prime} \) cells, each of emf \( ^{\prime} e^{\prime} \) and internal
resistance ' \( r^{\prime} \) are joined in series to
form a row.' \( m^{\prime} \) such rows are
connected in parallel to form a battery of \( \boldsymbol{N}=\boldsymbol{m} \boldsymbol{n} \) cells. This battery is
connected to an external resistance \( ^{\prime} \boldsymbol{R}^{\prime} \)
What is the emf of this battery and how much is its internal resistance?


State True or False.
Collision frequency depends upon mean free path
A. True
B. False


The focal lengths of the objective and eye-piece of a compound microscope are \( 1 \mathrm{cm} \) and \( 5 \mathrm{cm} \) respectively. An
object is placed at a distance of \( 1.1 \mathrm{cm} \) from the objective has its final image formed at least distance of distinct
vision, then the magnifying power is
A . 20
B. 30
c. 50
D. 60


The population of a certain country is known to increase at a rate proportional to the number of people presently living
in the country. If after two years the population has doubled, and after three years the population is 20000 , estimate the number of people initially living in
the country.
A .607
в. 707
c. 7061
D. 6077


Which option is inconsistent for
Raoult's Jaw?
A. The change in heat of dilution for solution \( =0 \)
B. Volume of liquid solvent + volume of liquid solute = volume of solution
C. Solute does not undergo association in solution
D. Solute undergoes dissociation in solution


The magnitude of the magnetic field at the centre of the tightly wound 150 turn coil of radius \( 12 \mathrm{cm} \) carrying a current of
\( 2 \mathrm{A} \) is:
A . 18 G
B. 19.7 G
c. \( 15.7 \mathrm{G} \)
D. 17.7 G


A non-zero external force acts on a
system of particles. The velocity and acceleration of the centre of mass are
found to be \( v_{0} \) and \( a_{C} \) respectively at
any instant \( t . \) It is possible that
(i) \( \boldsymbol{v}_{\mathbf{0}}=\mathbf{0}, \boldsymbol{a}_{\boldsymbol{C}}=\mathbf{0} \)
(ii) \( \boldsymbol{v}_{0} \neq \mathbf{0}, \boldsymbol{a}_{C}=\mathbf{0} \)
(iii) \( \boldsymbol{v}_{0}=\mathbf{0}, \boldsymbol{a}_{C} \neq \mathbf{0} ;(\text { iv }) \boldsymbol{v}_{\mathbf{0}} \neq \mathbf{0}, \boldsymbol{a}_{C} \neq \mathbf{0} \)
Then
A. (iii) and (iv) are true
B. (i) and (ii) are true
\( c . \) (i) and (iii) are true
D. (i), (iii) and (iv) are true


A cone, a hemisphere and a cylinder stand on equal bases and have the
same height What is the ratio of their
respective volumes?


An explosive compound (A) reacts with
water to produce \( N H_{4} O H \) and HOCl
Then, the compound (A), is:
A. TNGG
в. \( N C l_{3} \)
c. \( P C l_{3} \)
D. \( H N O_{3} \)


I wo very long stralght parallel wires
having current \( I \) and \( 2 I \) as shown in the
figure. A point charge \( q \) is at a point
equidistant from the two wires in the plane of the wires. Its instantaneous
velocity \( \bar{v} \) is parallel to currents in the plane. The magnitude of force due to the magnetic field acting on the charge at
this instant is:
A \( \cdot \frac{q v \mu_{0} l}{2 \pi d} \)
B. \( \frac{2 q v \mu_{0} l}{3 \pi d} \)
C. \( \frac{6 q v \mu_{0} l}{2 \pi d} \)
D. \( \frac{q v \mu_{0} l}{\pi d} \)


The blood leaving the tissues becomes richer in
A. Carbon dioxide
B. water
c. Heamoglobin
D. oxygen


Using the periodic table, predict the formulas of compounds which might be formed by the following pairs of elements:
(a) silicon and bromine
(b) aluminium and suplhur.


Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,
A. negative and distributed uniformly over the surface of the sphere
B. negative and appears only at the point on the sphere closest to the point charge
c. negative and distributed non-uniformly over the entire surface of the sphere
D. zero


At critical angle, the angle of refraction
is


Unburnt carbon particles are present in
the:
A. Blue zone
B. Dark inner zone
c. Luminous zone
D. Non-luminous zone


An ideal refrigerator is working between temperature 27 and \( 127 . \) If it expels 120
calorie of heat in one second then
calculate its wattage.


After fertilization, ovule grows into
A. Seed
B. Fruit
c. Placenta
D. None of the above


The diagram shows the displacement-
time graph for a vibrating body. Why is the amplitude of the wave gradually
decreasing?


While we catch a cricket ball, we catch
it at the front and make the hands move
with the ball backwards. Why is that?
A. to increase the impulse on the hand
B. to increase the time of contact, there by increase the force experienced by the hand
C. to increase the time of contact, there by decrease the force experienced by the hand
D. None of the above


Statement 1: Lanthanides have much
less tendency to form complexes than
actinides.

Statement 2: Compared to actinides, the lanthanides have relatively larger size of atoms and less nuclear charge.
A. Statement 1 is True, statement 2 is True, statement 2 is a correct explanation of statement 1.
B. Statement 1 is True, statement 2 is True, statement 2 is not a correct explanation of statement 1
c. Statement 1 is true, Statement 2 is False
D. Statement 1 is False, Statement 2 is True


In an electrochemical cell, cathode is:
A. always neutral
B. always positive
C. the electrode at which reduction takes place
D. always negative


If it is safe to jump from a height of \( 2 m \) on to the earth, what would be the safe height on a planet where the value of 'g'
is \( 1.96 m s^{-2} ? \)
A . \( 2 m \)
в. \( 4 m \)
\( c .6 m \)
D. \( 10 m \)


A secondary cell can provide
current.
A . Low
B. Highh
c. Both
D. None


A steel ball is dropped from a height \( h_{0} \) The collision of the ball with the floor is
inelastic with coefficient of restitution
e. Then, the height up to which the ball will rise after second collision is :
\( \mathbf{A} \cdot e^{4} h_{0} \)
B. 2eh
\( c \cdot e^{2} h_{0} \)
D. \( e^{-2} h_{0} \)


A sound wave whose frequency is 220
\( \mathrm{Hz} \) has a speed of \( 440 \mathrm{ms}^{-1} \) in a given
medium. Find the wavelength of the
sound.


The function \( f(x) \) is defined on the interval \( [0,1] . \) Find the domain of the function:
\( \boldsymbol{f}(\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}) \)
\( ^{A} \cdot-\frac{3}{2} \leq x \leq-1 \)
в. \( -\frac{3}{2} \leq x \leq \frac{3}{2} \)
\( ^{\mathrm{c}}-1 \leq x \leq \frac{3}{2} \)
D. \( -1 \leq x \leq 1 \)


When an atom accepts 2 electrons in its outermost shell, its valency is +2
A. True
B. False


20 is written as the product of primes
as:
\( \mathbf{A} \cdot 2 \times 5 \)
в. \( 2 \times 2 \times 3 \times 5 \)
c. \( 2 \times 2 \times 5 \)
D. \( 2 \times 2 \times 3 \)


Express the following in terms of trigonometric ratios of angles lying
between 0 and \( 45^{\circ} \)
\( \sec 76^{\circ}+\operatorname{cosec} 52^{\circ} \)


Two protons are brought nearer; what will be the effect on potential energy of
system?


Light falls from glass to air. Find the angle of incidence for which the angle of
deviation is \( 90^{\circ} . \) If refractive index of
glass is \( \sqrt{2} \)


An infinite large plate has a net positive charge. When referring to the electric
field just as it is coming out of the
plate:
A. Some of the electric field is perpendicular to the plate
B. All of the electric field is perpendicular to the plate
C. None of the electric field is perpendicular to the plate
D. There is no electric field coming out of the plate


A man who is \( 1.40 \mathrm{m} \) tall stands in front
of a mirror and can just see himself from head to top. Assuming that his eyes are \( 0.14 \mathrm{m} \) below the top of his head, the minimum height of the mirror is:
\( A \cdot 1.4 \mathrm{m} \)
B. \( 1.26 \mathrm{m} \)
c. \( 0.70 \mathrm{m} \)
D. 0.63 \( m \)


Find the mean deviation about the
median for the following data:
4,6,9,3,10,13,2


Hydrogen is mainly found in the combined state like in water and not
the free state.
A. True
B. False


If the circumference of the inner edge of a hemispherical bowl is \( \frac{132}{7} c m, \) then what is its capacity?
\( \mathbf{A} \cdot 12 \pi c m^{3} \)
В. \( 18 \pi c m^{3} \)
\( \mathbf{c} \cdot 24 \pi c m^{3} \)
\( \mathrm{D} \cdot 36 \pi c m^{3} \)


What are the advantages of sexual over asexual reproduction?


The domain of \( \boldsymbol{f}(\boldsymbol{x})=\cot \frac{\boldsymbol{x}}{\mathbf{3}} \) is
\( A \cdot(-\infty, \infty) \)
B . \( R-\{n \pi: n \in Z\} \)
c. \( R-\{3 n \pi: n \in Z\} \)
D. \( (0, \infty) \)


\( P \) and \( Q \) are two points with position vectors \( 3 \vec{a}-2 \vec{b} \) and \( \vec{a}+\vec{b} \)
respectively. Write the position vector of a point R which divides the line
segment \( \boldsymbol{P Q} \) in the ratio \( \mathbf{2}: \mathbf{1} \) externally


The conductivity \( \left(\operatorname{in} \Omega^{-1} m^{-1}\right) \) of
\( K_{2} S O_{4} \) solution is: \( ( \) write your answer to nearest integer)


Which of the following reacts with ethanol to form chloroform?
A. \( \operatorname{SOCl}_{2} \)
в. \( P C l_{5} \)
c. \( H C l \)
D. \( \mathrm{CaOCl}_{2}+\mathrm{H}_{2} \mathrm{O} \)


Collect the information about lenses
used by Galileo in his telescope


In the modern periodic table, how does the atomic size of the elements vary
along the period and down the group? Explain.


Acceleration due to gravity on moon is
0.166 times than that on the earth. \( A \)
man weighing 60kg on earth would weigh \( _{\text {十一一一一一一一一一 }} \) on moon
A. \( 60 \mathrm{kg} \)
в. 30kg
c. \( 16.6 \mathrm{kg} \)
D. \( 10 \mathrm{kg} \)


The standard enthalpy of combustion of sucrose is-5645 kJ mol \( ^{-1} \).What is the
advantage (in kJ \( m o l^{-1} \) of energy released as heat) of complete aerobic oxidation compared to anaerobic hydrolysis of sucrose to lactic acid? \( \triangle H_{\int}^{\circ} \) for lactic acid,CO_ \{2\} and \( H_{2} O \) is
-694,-395 and -286.0 respectively
A . advantage=4356 k..mol \( ^{-1} \)
B. advantage=5396 k..mol-
c. advantage=4756 kJ.mol-
D. advantage=5657 kJ.mol-


Calculate the equilibrium constants for the reactions with water of
\( H_{2} P O_{4}^{\ominus}, H P O_{4}^{2-} \) and \( P O_{4}^{3-} \) as base
Comparing the relative values of two equilibrium constants of \( \boldsymbol{H}_{2} \boldsymbol{P} \boldsymbol{O}_{4}^{\ominus} \) with
water, deduce whether solutions of this
ion in water are acidic or bases. Deduce
whether solutions of \( \boldsymbol{H} \boldsymbol{P} \boldsymbol{O}_{4}^{2-} \) are acidic
or bases. Given \( K_{1}, K_{2} \) and \( K_{3} \) for
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) are \( \mathbf{7 . 1} \times \mathbf{1 0}^{-\mathbf{3}}, \mathbf{6 . 3} \times \mathbf{1 0}^{-\mathbf{8}} \) and
\( 4.5 \times 10^{-13} \) respectively
A \( .1 .4 \times 10^{-12}, 1.6 \times 10^{-7}, 2.2 \times 10^{-2}, H_{2} P O_{4}^{\circ} \) is acidic
and \( H P O_{4}^{2-} \) is basic
B . \( 2.2 \times 10^{-12}, 1.6 \times 10^{-7}, 1.4 \times 10^{-2}, H_{2} P O_{4}^{\ominus} \) is basic and
\( H P O_{4}^{2-} \) is basic
C \( .2 .2 \times 10^{-12}, 1.6 \times 10^{-7}, 1.4 \times 10^{-2}, H_{2} P O_{4}^{\circ} \) is acidic
and \( H P O_{4}^{2-} \) is basic
D. \( 1.4 \times 10^{-12}, 1.6 \times 10^{-7}, 2.2 \times 10^{-2}, H_{2} P O_{4}^{\circ} \) is basic
and \( H P O_{4}^{2-} \) is acidic


The part of the electromagnetic spectrum which is produced by bombarding a metal target with high energy electrons is :
A . Ultraviolet
B. x-Rays
c. Infrared
D. Gamma Rays


Let \( A \) be a \( 2 \times 2 \) matrix with non-zero
entries and let \( \mathbf{A}^{2}=\boldsymbol{I}, \) where I is \( \mathbf{2} \times \mathbf{2} \)
identity matrix. Define \( \operatorname{Tr}(\mathbf{A})=\operatorname{sum} \) of diagonal elements of \( A \) and \( |\mathbf{A}|= \) determinant of matrix A.

Statement-1 \( \operatorname{Tr}(\mathrm{A})=0 \) Statement-2:
\( |\mathbf{A}|=\mathbf{1} \)
A. Statement-1 is true, Statement-2 is true; Statement- is not the correct explanation for statement-
B. Statement-1 is true, Statement-2 is false
c. Statement- 1 is false, statement- 2 is true
D. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-


Inverse of the matrix \( \left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right] \)
is.
\( \mathbf{A} \cdot\left[\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right] \)
B. \( \left[\begin{array}{cc}\cos 2 \theta & \sin 2 \theta \\ \sin 2 \theta & -\cos 2 \theta\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}\cos 2 \theta & \sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right] \)
D. \( \left[\begin{array}{cc}\cos 2 \theta & \sin 2 \theta \\ -\sin 2 \theta & \cos 2 \theta\end{array}\right] \)


How would you synthesize an alcohol from appropriate alkenes?


Plants with woody trunks and branches
are called as
A. Trees
B. Creepers
c. Lianas
D. Mesophytes


The value of the integral \( \int_{0}^{\pi / 2} \log [\sin (x)] d x \) is
\( A \cdot \log 2 \)
B. \( -\log 2 \)
c. \( \frac{\pi}{2} \log 2 \)
D. \( -\frac{\pi}{2} \log 2 \)


Milk of magnesia is an:
This question has multiple correct options
A . acid
B. antacid
c. alkali
D. rock salt


Write structures of compounds \( A \) and \( B \)
in each of the following reactions:


Assertion
Statement-1: In water, orthoboric acid
behaves as a weak monobasic Lewis
acid.
Reason
Statement-2: In water, orthoboric acid
acts as a proton donor.
A. Statement-1 is True, Statement-2 is True; Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statementis NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement- 1 is False, Statement-2 is True


A physical parameter a can be determined by measuring the parameters b, \( c, d \) and e using the relation \( a=b^{\alpha} c^{\beta} d^{\gamma} e^{\delta} . \) If the maximum
errors in the measurement of \( b, c, d \) and
e are \( b_{1} \%, c_{1} \%, d_{1} \% \) and \( e_{1} \%, \) then find
the maximum error in the value of a
determined by the experiment.


The points \( \boldsymbol{O}, \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \) are the vertices of
a pyramid and \( P, Q, R, S \) are the mid-
points of \( \boldsymbol{O} \boldsymbol{A}, \boldsymbol{O} \boldsymbol{B}, \boldsymbol{B} \boldsymbol{C}, \boldsymbol{A} \boldsymbol{C} \)
respectively. If \( \overrightarrow{\boldsymbol{O A}}=\boldsymbol{a}, \overrightarrow{\boldsymbol{O B}}=\boldsymbol{b}, \overrightarrow{\boldsymbol{O C}}= \)
\( c, \) express in terms of \( a, b, c \) the vectors \( \boldsymbol{O P}, \overrightarrow{\boldsymbol{O Q}}, \overrightarrow{\boldsymbol{O R}} \) and \( \overrightarrow{\boldsymbol{O S}} \)
A \( \cdot \overrightarrow{O P}=\frac{1}{2} a, \overrightarrow{O Q}=\frac{1}{2} b, \overrightarrow{O R}=\frac{1}{2}(b+c), \overrightarrow{O S}=\frac{1}{2}(a+c) \)
B \( \cdot \overrightarrow{O P}=\frac{1}{2} c, \overrightarrow{O Q}=b, \overrightarrow{O R}=\frac{1}{2}(b+c), \overrightarrow{O S}=\frac{1}{2}(a+c) \)
c・ \( \overrightarrow{O P}=\frac{1}{2} c, \overrightarrow{O Q}=b, \overrightarrow{O R}=\frac{1}{2}(a+c), \overrightarrow{O S}=\frac{1}{2}(b+c) \)
D・ \( \overrightarrow{O P}=\frac{1}{2} a, \overrightarrow{O Q}=b, \overrightarrow{O R}=\frac{1}{2}(a+c), \overrightarrow{O S}=\frac{1}{2}(b+c) \)


Which forms the smallest of the +1 ions?
A. Lithium
B. Sodium
c. Potassium
D. Rubidium
E. cesium


Which one will have highest boiling
point, if 1 mole of each of the following substances was discovered in 1,000
grams of water?
A. Nacı
в. кс।
c. \( C a C l_{2} \)
D. \( C_{6} H_{10} O_{5} \)
E \( \cdot C_{12} H_{22} O_{11} \)


3 years ago, the average age of a family of 5 members was 17 years. \( A \) baby having been born, the average age of the family is same today. The present age of the baby is
A. 3 years
B. 2 years
c. \( 1 \frac{1}{2} \) years
D. 1 years


The equation of the curve through the point (3,2) and whose slope is \( \frac{x^{2}}{y+1}, \) is
\( ^{\mathrm{A}} \cdot \frac{y^{2}}{2}+y=\frac{x^{3}}{3}+5 \)
B . \( y+y^{2}=x^{3}-21 \)
c. \( y^{2}+2 y=\frac{2 x^{3}}{3}-10 \)
D. \( \frac{y^{2}}{2}+y=\frac{x^{3}}{3}-5 \)


Find the equation of the line
perpendicular to \( \boldsymbol{x}-\mathbf{7} \boldsymbol{y}+\mathbf{5}=\mathbf{0} \) and
having \( \boldsymbol{x} \) -intercept 3


If the beads are released from rest, such
that the bead \( A \) is at the highest
position of ring at time \( t=0, \) the
magnitude of acceleration of the bead
\( B \) in the vertical direction at the same
instant is
\( A \). Zero
B. \( \frac{g}{4} \)
c. \( \frac{g}{2} \)
\( D \)


\( S_{1}, S_{2} \) are two coherent sources of
sound located along x-axis separated
by \( 4 \lambda \) where \( \lambda \) is wavelength of sound
emitted by them. Number of maxima
located on the elliptical boundary
around it will be :
\( A \cdot 16 \)
B. 12
\( c \)
\( D \)


A shopkeeper sold a T.V set for Rs17,940
with a discount of \( 12.5 \% \) and Gained \( 5 \% \)
If no discount is allowed then what will
be his gain percent?


The atomic number of the element next
to bromine (atomic no 35 ) in the same
group is:
A . 43
B. 50
\( c .56 \)
D. 53


A charged particle of radius \( 5 \times 10^{-7} \mathrm{m} \)
is loacted in a horizontal electric field of
intensity \( 6.28 \times 10^{5} V m^{-1} . \) The
surrounding medium has the
coefficient of viscosity \( \boldsymbol{\eta}=\mathbf{1 . 6} \times \)
\( 10^{5} N s m^{-2} . \) The particle starts moving
under the effect of electric field and
finally attains a uniform horizontal speed of \( 0.02 m s^{-1} . \) Find the number of
electrons on it :
(Assume gravity free space)
A . \( 3 \times 10^{11} \)
в. \( 6 \times 10^{1} \)
\( \mathbf{c} \cdot 9 \times 10^{11} \)
D. \( 1 \times 10^{11} \)


Allelopathy is caused by release of
A. Poison
B. Toxin
c. Pheromone
D. Chemicals


\( A \) thin rod of length \( \frac{f}{3} \) is placed along the optic axis of a concave mirror of focal length f such that its image which is real and elongated just touches the rod. The magnification is:
A \( \cdot \frac{3}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{3}{2} \)
D. None of the above


Which of the following is not a covalent nitride?
\( A \cdot B N \)
в. Аl N
\( \mathrm{c} \cdot \mathrm{Ge}_{3} N_{4} \)
D. \( S c N \)


Let \( f(x) \) be a real valued function not identically zero, such that
\( \boldsymbol{f}\left(\boldsymbol{x}+\boldsymbol{y}^{n}\right)=\boldsymbol{f}(\boldsymbol{x})+(\boldsymbol{f}(\boldsymbol{y}))^{n} \quad \forall \boldsymbol{x}, \boldsymbol{y} \in \)
\( \boldsymbol{R} \)
where \( n \in N(n \neq 1) \) and \( f^{\prime}(0) \geq 0 . \) We
may get an explicit form of the function \( \boldsymbol{f}(\boldsymbol{x}) \)
\( \int_{0}^{1} f(x) d x \) is equal to
A \( \cdot \frac{1}{2 n} \)
B. \( 2 n \)
\( c \cdot \frac{1}{2} \)
D. 2


State True or False.
Electron was discovered by Goldstein.
A. True
B. False


Transverse waves on a string have wave speed \( 12.0 \mathrm{m} / \mathrm{s}, \) amplitude \( 0.05 \mathrm{m} \) and
wavelength 0.4 m. The waves travel in
the \( +x \) direction and at \( t=0, \) the \( x=0 \)
end of the string has zero displacement and is moving upwards. Write a wave function describing the wave.


VA group hydrides are:
A. ionic compounds
B. covalent compounds
C . oxidizing agents
D. Bleaching agents


The Sl unit of magnetic field induction
is
A. Tesla
B. weber
c. weber/m
D. weber. m


A certain particle carries \( 2.5 \times 10^{-16} C \)
of static electric charge. Calculate the
number of electrons present in it.


What is the angular momentum of an electron in Bohr's hydrogen atom whose energy is \( -3.4 e V ? \)
\( ^{\mathbf{A}} \cdot_{L}=\frac{h}{\pi} \)
B. \( L=\frac{4 h}{\pi} \)
\( c \cdot_{L}=\frac{3 h}{\pi} \)
D. \( L=\frac{5 h}{\pi} \)


Light shows:
A. Curvilinear propagation
B. Rectilinear propagation
C. Random propagation
D. None of the above


The velocity-time graph of a body is shown in Fig.The displacement of the
body in 8 s is
\( 4.9 \mathrm{m} \)
\( 3.12 \mathrm{m} \)
\( c \cdot 10 m \)
D. 28 n


The moment of inertia of a fly-wheel is \( 4 k g m^{2} . \) A torque of 10 Newton-meter is
applied on it. The angular acceleration produced will be :
A .25 radians \( / \mathrm{sec}^{2} \)
B. 0.25 radians \( / \) sec \( ^{2} \)
c. 2.5 radians \( / \) sec \( ^{2} \)
D. Zero


Find the areas of the triangles the coordinates of whose angular points
\( \operatorname{are}\left(-3,-30^{\circ}\right),\left(5,150^{\circ}\right) \) and \( \left(7,210^{\circ}\right) \)


A piece of ice of mass \( 40 g \) is dropped
into \( 200 g \) of water at \( 50^{\circ} \mathrm{C} \). Calculate the final temperature of the water after all the ice has melted. Specific heat
capacity of water \( =4200 J k g^{-1} K^{-1} \)
Specific latent heat of fusion of ice \( = \)
\( 336 \times 10^{3} J k g^{-1} \)


Calculate the wavelength for the emission transition if it starts from the
orbit having radius \( 1.3225 \mathrm{nm} \) and ends at \( 211.6 \mathrm{pm} . \) Name the series to which this transition belongs and the region of
the spectrum.


Which of the following has maximum
bond energy?
A \( . C=C \)
B. \( C=O \)
c. \( O=O \)
D. \( N=O \)


Two persons entered a Railway compartment in which 7 seats were
vacant.The number of ways in which
they can be seated is
A . 30
B. 42
\( c \cdot 720 \)
D. 360


A mass \( M \) is broken in two parts : \( m \)
and (M- m). What would be the relation
between \( m \) and \( M \) so that the force of
gravitation between the two parts is maximum?
A. \( m M=2 \)
в. \( m=\frac{M}{2} \)
\( \mathbf{c} \cdot M=m^{2} \)
D. none of these


A current of 1.5 ampere is passed through a solution of a salt of a bivalent
metal for 30 minutes. Increase in mass
of cathode is \( 0.8898 g . \) Find the atomic
mass of the metal.
\( A \cdot 63 g \)
B. 63.6 g
c. \( 73.6 g \)
D. 70g


Assertion
Presence of photorespiration is considered as a wasteful and energy
consuming process in crop plants, ultimately leads to reduction in yield.
Reason

During \( C_{3} \) synthesis upto \( 50 \% C O_{2} \) fixed may have to pass through photosynthesis process to form carbohydrate such as sucrose.
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.


Which molecule contains both polar
and non-polar covalent bond?
\( \mathbf{A} \cdot N H_{4}^{+} \)
в. НС l
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( H_{2} O_{2} \)


For the network shown in the figure the
value of the current is :
A \( \cdot \frac{18 V}{5} \)
в. \( \frac{5 V}{9} \)
c. \( \frac{9 V}{35} \)
D. \( \frac{5 V}{18} \)


How does CuT act as an effective
contraceptive for human females?


State whether true or false.
The S.I. unit of frequency is Hertz (Hz).
A. True
B. False


The speed of a homogenous solid sphere after rolling down an inclined plane of vertical height \( h \) from rest
without sliding is
A \( \cdot \sqrt{\left(\frac{g}{5}\right) g h} \)
в. \( \sqrt{g h} \)
c. \( \sqrt{\left(\frac{4}{3}\right) g h} \)
D. \( \sqrt{\left(\frac{10}{7}\right) g h} \)


The Poisson's ratio of a material is \( 0.5 . \) If
a force is applied to a wire of this material, there is a decrease in the
cross-sectional area by \( 4 \% \). The percentage increase in the length is:
A . \( 1 \% \)
B. 2\%
\( c .2 .5 \% \)
D. \( 4 \% \)


Back emf of a cell is due to
A. Electrolytic polarization
B. Peltier effect
c. Magnetic effect of current
D. Internal resistance


What is peptide linkage? How is dipeptide formed?


Assertion
If the magnitude of displacement is zero, then it is not a vector quantity.
Reason

A vector have both magnitude and direction.
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 Iymph serves to
A. Return the interstitial fluid to the blood
B. Return the \( \mathrm{WBCs} \) and RBCs to the lymph nodes
C. Transport \( C O_{2} \) to the lungs
D. Transport \( O_{2} \) to the brain


Cartesian product of sets \( A \) and \( B \) is
denoted by
A \( . A \times B \)
в. \( B \times A \)
c. \( A \times A \)
D. \( B \times B \)


The eccentricity of the conic \( 9 x^{2}+ \)
\( 5 y^{2}-54 x-40 y+116=0 \) is:
A \( -\frac{1}{3} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{4}{9} \)
D. \( \frac{2}{\sqrt{5}} \)


One angle of a pentagon is \( 140^{\circ} . \) If the
remaining angles are in the ratio 1: 2:
\( 3: 4 . \) What is the size of the largest
angle?


Solve the following differential equation \( \cos x \frac{d y}{d x}-\cos 2 x=\cos 3 x \)


How many took 'soup'


State the position of the object in front of a converging lens if it is used as a magnifying lens.


The given figure is made up of identical
squares. Find the area of the shaded
region.
\( A \cdot 50 \mathrm{cm}^{2} \)
B. \( 54 \mathrm{cm}^{2} \)
\( \mathrm{c} \cdot 58 \mathrm{cm}^{2} \)
D. \( 52 \mathrm{cm}^{2} \)


The concentration of \( \left[\boldsymbol{H}^{+}\right] \) in a sample
soft drink is \( 3 \times 10^{-3} M . \) What is its
\( \boldsymbol{p} \boldsymbol{H} \cdot(\log 3=\mathbf{0 . 4 8}) \)


If instantaneous current in a circuit is
given byl \( =(3+4 \sin \omega t) A \) os then the
maximum value of current in the
circuit is
\( A \cdot 4 A \)
B. 5 A
\( c \cdot 7 A \)
\( D .3 \mathrm{A} \)


Fill in the blanks:
The equation of mirror formula is


A cell is the \( \ldots \ldots . . . \) and functional unit of
an organism.
A. Longest structural
B. Smallest structural
c. Biggest structural
D. Strongest structural


Four chambered heart is present in
\( A \cdot F \operatorname{rog} \)
B. Crocodile
c. shark
D. Lizard


Which Oxide of Nitrogen is most stable?
A \( \cdot 2 N O_{2(g)} \rightleftharpoons N_{2(g)}+2 O_{2(g)} \)
\[
K=6.7 \times 10^{16} \mathrm{mol} L^{-1}
\]
B. \( 2 N O_{(g)} \rightleftharpoons N_{2(g)}+O_{2(g)} \)
\[
K=2.2 \times 10^{30}
\]
\( \mathbf{c} \cdot 2 N_{2} O_{5(g)} \rightleftharpoons 2 N_{2(g)}+5 O_{2(g)} \)
\[
K=1.2 \times 10^{34} \mathrm{mol}^{5} \mathrm{L}^{-5}
\]
D. \( 2 N_{2} O_{(g)} \rightleftharpoons 2 N_{2(g)}+O_{2(g)} \)
\[
K=3.5 \times 10^{33} \mathrm{mol} L^{-1}
\]


The bony labyrinth is filled with
A. Endolymph
B. Synovial fluid
c. Perilymph
D. Humour


The oxide that gives \( H_{2} O_{2} \) on treatment
with dilute \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) is:
\( \mathbf{A} \cdot P b O_{2} \)
в. \( B a O_{2} .8 H_{2} O \)
c. \( M n O_{2} \)
D. \( T i O_{2} \)


A number \( A \) exceeds \( B \) by \( 25 \% \). By what percentage is \( A \) more than \( B ? \)
A . \( 20 \% \)
B. 25\%
c. \( 30 \% \)
D. \( 15 \% \)


Match List 1 with List 2


Out of the following redox reactions \( \boldsymbol{I} \cdot \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{O}_{3} \stackrel{\Delta}{\rightarrow} \boldsymbol{N}_{2} \boldsymbol{O}+\boldsymbol{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
III.N \( \boldsymbol{H}_{4} \boldsymbol{N} \boldsymbol{O}_{2} \stackrel{\Delta}{\rightarrow} \boldsymbol{N}_{2}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O} \)
IIII.PCl\( _{5} \stackrel{\Delta}{\rightarrow} P C l_{3}+C l_{2} \)
disproportionation is not shown in:
A . I and II
B. II and III
c. I and III
D. I, II and III


Let \( y=\log (\log (x)) \) then find \( \frac{d y}{d x} \)


Choose the correct answer from the
alternatives given.

Which of the following represents the pulmonary circulation as the blood flows from
the right ventricle?
A. Pulmonary trunk \( \rightarrow \) pulmonary veins \( \rightarrow \) pulmonary capillaries \( \rightarrow \) pulmonary arteries
B. Pulmonary arteries \( \rightarrow \) pulmonary capillaries \( \rightarrow \) pulmonary trunk \( \rightarrow \) pulmonary veins
c. Pulmonary capillaries \( \rightarrow \) pulmonary trunk \( \rightarrow \) pulmonary arteries \( \rightarrow \) pulmonary veins
D. Pulmonary trunk \( \rightarrow \) pulmonary arteries \( \rightarrow \) pulmonary capillaries \( \rightarrow \) pulmonary veins


In case of substituted aniline the group
which decreases the basic strength is :
A. \( -O C H_{3} \)
в. \( -C H_{3} \)
\( \mathrm{c} \cdot-N H_{2} \)
D. \( -C_{6} H_{5} \)


What is \( p H \) of a solution whose \( H^{+} \) ion
concentration is \( 2 \times 10^{-5} \) ions/litre?
A . 4.7
B. 6.7
\( c .9 .3 \)
D. None of these


Underground soil in cities is likely to be polluted by:
A. floods
B. decomposed and partially decomposed materials of sanitary wastes
c. fertilisers
D. landslides


\( C_{40} H_{56} O_{2} \) is the chemical formula of a
A. xanthophyll
B. Carotene
c. Anthocyanin
D. chlorophylı.


At DO below \( 4 \mathrm{mg} / l, \) water at normal temperature is considered as
A. Heavily polluted
B. Moderately polluted
c. Little polluted
D. Nearly pure


A source of wave produces 3 crests and
3 troughs in \( 2 m s, \) the frequency of the
wave is
A. \( 1250 H z \)
в. \( 1500 H z \)
с. \( 1000 H z \)
D. \( 750 H z \)


The atomic masses of two elements \( P \)
and \( Q \) are 20 and 40 , respectively. If
\( a^{\prime} g \) of \( P \) contains \( ^{\prime} b^{\prime} \) atoms, how many
atoms are present in \( ^{\prime} 2 a^{\prime} g \) of \( Q ? \)
\( A \)
B. \( b \)
c. \( 2 a \)
D. \( 2 b \)


Calculate the resonant frequency and \( Q \)
factor (Quality factor) of a series L-C-R circuit containing a pure inductor of inductance \( 4 \mathrm{H} \), capacitor of
capacitance \( 27 \mu F \) and resistor of resistance \( 8 \cdot 4 \Omega \)


During inspiration muscles of diaphragm
A. Contracts
B. Expands
c. No effect
D. Coiled like string


What is the projection of \( \vec{P} \) on \( \vec{Q} ? \)
A \( . \vec{Q} . \vec{P} \)
в. \( \hat{P} . \hat{Q} \)
c. \( \vec{P} . \vec{Q} \)
D. \( \vec{P} . \hat{Q} \)


The atomic masses of \( H e \) and \( N e \) are 4
and 20 amu, respectively. The value of
the de Broglie wavelength of \( H e \) gas at
\( -73^{0} C \) is \( " M^{\prime \prime} \) times that of the de
Broglie wavelength of \( N e \) at \( 727^{0} C . M \)
is:
\( \mathbf{A} \cdot \mathbf{5} \)
B. 0.2
\( c \cdot 2 \)
D. 0.5


A heavier body moving with certain velocity collides head on elastically with
a lighter body at rest. Then
A. smaller body continues to be in the same state of rest
B. smaller body starts to move in the same direction with same velocity as that of bigger body
c. the smaller body starts to move with twice the velocity of the bigger body in the same direction
D. the bigger body comes to rest


Aromatic amines are insoluble in water
because:
A. Due to the larger hydrocarbon part which tends to retard the formation of H-bonds.
B. Due to the larger hydrocarbon part which tends to retard the formation of H-Nbonds.
C. Due to the larger hydrocarbon part which tends to retard the formation of H-Cbonds.
D. none of these


Identify which of the following
statements is FALSE?
A. The vapor pressure of a liquid decreases with increasing atmospheric pressure.
B. The value of an equilibrium constant is dependent on temperature
C. The rate of a spontaneous reaction cannot be determined solely by its Gibbs free energy.
D. During a phase transition, the temperature of a substance must be constant.
E. The addition of a catalyst to a reaction at equilibrium has no net effect on the system.


The colour of \( _{62} S m^{3+} \) is yellow. What is
the colour of \( _{66} D y^{3+} ? \)
A. Colourless
B. Yellow
c. Red
D. Blue


Write the electronic configuration of the
\( C a^{2+} \) in absence of Aufbau Principle.
A \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} \)
B \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{3} 3 p^{3} 4 d^{3} \)
c. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{5} 4 d^{1} \)
D. none of these


Curie-Weiss law is obeyed by iron:
A. at Curie temperature only.
B. at all temperatures.
C . below Curie temperature.
D. above Curie temperature.


The stability of cation in dihalides of
Si, Ge, Sn and Pb increases in the
sequence is:
A \( \cdot G e X_{2}<\operatorname{Si} X_{2}<S n X_{2}<P b X_{2} \)
B. \( \operatorname{SiX}_{2}<\operatorname{GeX}_{2}<\operatorname{Pb} X_{2}<\operatorname{SnX}_{2} \)
c. \( \operatorname{six}_{2}<\operatorname{Ge} X_{2}<\operatorname{Sn} X_{2}<\operatorname{Pb} X_{2} \)
D. \( P b X_{2}<\operatorname{Sn} X_{2}<G e X_{2}<\operatorname{Si} X_{2} \)


Which type of reproduction is found in Hydra?
A. Polyembryony
B. Sexual and Asexual both
c. Parthenogenesis
D. None of the above


The side of a square sheet is increasing at the rate of \( 4 \mathrm{cm} \) per minute. The rate by which the area increasing when the side is \( 8 \mathrm{cm} \) long is-
A \( \cdot 60 \mathrm{cm}^{2} / \mathrm{sec} \)
B. \( 66 \mathrm{cm}^{2} / \mathrm{sec} \)
\( \mathrm{c} \cdot 62 \mathrm{cm}^{2} / \mathrm{sec} \)
D. \( 64 \mathrm{cm}^{2} / \mathrm{sec} \)


Due to hectic and busy schedule, Mr. Angad made his life full of tensions
and anxiety. He started taking sleeping pills to overcome the depression without consulting the doctor. Mr. Deepak, a close friend of Mr. Angad advised him to stop taking sleeping pills and suggested to change his life lifestyle by doing yoga, meditation and some physical exercise. Mr. Angad followed his friends advice and after few
days he started feeling better. After reading the above passage, answer the following.
(i) What are the values (at least two)
displayed by Mr. Deepak?
(ii) Why is it not advisable to take
sleeping pills without consulting doctor?
(iii) What are tranquilisers? Give two examples.


\( \mathbf{P}(-1,-1,-1) \) and \( Q(\lambda, \lambda, \lambda) \) are two
points in the space such that \( \boldsymbol{P} \boldsymbol{Q}= \) \( \sqrt{48}, \) then value(s) of \( \lambda \) can be
This question has multiple correct options
A . 3
B. - 5
\( c \cdot 4 \)
D.


A group of 50 house owners contributes money towards children's education of their street. The amount of money collected is shown in the table below:
(use direct method).
A . Rs. 27
B. Rs. 17
c. Rs. 10
D. Rs. 23


Which of the following will be an advantage of inter-linking the rivers in
India?
A. Lot of people will be displaced
B. Floods will take place uniformly throughout the country
c. Surplus water will be distributed uniformly
D. The cost of implementain will be very high


Shape of Staphylococcus bacteria is
A. Circular
B. oval
c. Elongated
D. cubical


A particle executing simple harmonic motion completes
1200 oscillations per minute and
passes through the mean position with a velocity of 3.14 ms\( ^{-1} \). Determine the
maximum displacement of the particle
from its mean position. Also obtain the
displacement equation of the particle if it particle if its displacement be zero at the instant \( \boldsymbol{t}=\mathbf{0} \)


Which of the following enzyme is allosteric?
A. Hexokinase
B. Glucokinase
c. Glucose-6-phosphatase
D. Lipase


Two capacitors of capacity \( C_{1} \) and \( C_{2} \)
are connected in parallel, then the
equivalent capacity is:
A \( \cdot C_{1}+C_{2} \)
в. \( C_{1} C_{2} /\left(C_{1}+C_{2}\right) \)
c. \( C_{1} / C_{2} \)
D. \( C_{2} / C_{1} \)


The radius of a circular plate is
increased at \( 0.01 \mathrm{cm} / \) sec. If the area is
increased at the rate of \( \frac{\pi}{10} . \) Then its radius is
\( A \cdot 5 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
c. \( 15 \mathrm{cm} \)
D. \( 20 \mathrm{cm} \)


Frequent use of sprays, oils and antiseptics in the nose during a bad cold may result in :
A. the spreading of the infection to the sinuses
B. damage to the olfactory nerve
c. destruction of white blood cells
D. congestion of the mucous membrane in the nose


A plane mirror:
(i) can form real image of a real object
(ii) neither converges not diverges the
rays
(iii) cannot form real image of a real object

Choose the correct option or options.
A. (i) is correct
B. (i) and (ii) are correct
c. (ii) and (iii) are correct
D. None of the above


Find the values of \( a \) and \( b \) so that the
points \( (\boldsymbol{a}, \boldsymbol{b}, \mathbf{3}),(\mathbf{2}, \mathbf{0},-\mathbf{1}) \) and
(1,-1,-3) are collinear. This question has multiple correct options
A \( . a=4, b=2 \)
В. \( a=0, b=2 \)
c. \( a=4, b=-2 \)
\begin{tabular}{l}
D. \( a=-4, b=-2 \) \\
\hline
\end{tabular}


Formal charge on sulphur in \( S O_{2} \) is:


The streaks of bright light seen during lightning is essentially the path followed by:
A. UV rays from Sun
B. cosmic rays
c. accumulated electric charges
D. none of the above


Protein synthesis in an animal cell
occurs
A. Only on the ribosomes present in cytosol
B. On ribosomes present in cytoplasm as well as in mitochondria
C. Only on ribosomes attached to the nuclear envelope and smooth endoplasmic reticulum
D. On ribosomes present in the nucleolus as well as in cytoplasm


A bob is suspended by a string of length
I. The minimum horizontal velocity imparted to the ball for reaching it to the height of suspension is
\( \mathbf{A} \cdot \sqrt{l / g} \)
B . \( \sqrt{2 g l} \)
c. \( \sqrt{g / l} \)
D. \( 2 \sqrt{g l} \)


Which of the following pairs of elements form oxides of polyanions and polycations respectively:
A. \( S i \) and \( A l \)
B. \( C u \) and \( S i \)
c. \( A l \) and \( B \)
D. \( T i \) and \( A s \)


A series is:
A. A number of events, objects, or people of a similar or related kind coming one after another.
B. Combination of terms following a particular pattern.
C. Both A and B
D. Non of the above


f \( A \) and \( B \) are two events associated
with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 5}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 3} \) and \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( \boldsymbol{B})=\mathbf{0 . 2}, \) find \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)


In a college of 300 students, every
student reads 5 newspapers and every
newspaper is read by 60 students. The number of newspapers is
A. at least 30
B. at most 20
c. exactly 25
D. none of these


The current in a coil of inductance \( 2 \mathrm{H} \) is
changing according to varying current \( \boldsymbol{I}=\sin (2 t) . \) The amount of magnetic
energy in the inductor during \( t=0 \) to \( \boldsymbol{t}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \boldsymbol{s} \) is:
A . 4
B . 3J
c. 1 J
D. 2


In biprism experiment the fringes are observed in the focal plane of the eyepiece at a distance of \( 1.2 \mathrm{m} \) from slit.
The distance between the
central bright band and the \( 20^{t h} \) bright
band is \( 0.4 \mathrm{cm} . \) When convex lens is
interposed between the biprism and eyepiece, at a distance of \( 90 \mathrm{cm} \) from the eyepiece, the distance between two magnified virtual images is found to be \( 0.9 \mathrm{cm} . \) Find the wavelength of light used.


Which of the following has zero average value in a plane electromagnetic wave?
A. Kinetic energy
B. Magnetic field
c. Electric field
D. Both (b) and (c)


The magnetic field inside a solenoid is:
A . infinite
B. zero
c. uniform
D. non-uniform


A pole \( 5 \mathrm{m} \) high is situated on a horizontal surface. Sun rays are
incident at an angle \( 30^{\circ} \) with the
vertical. What will be the size of shadow
on horizontal surface


Consider two children riding on the merry-go-round Child 1 sits near the edge, child 2 sits closer to the centre.
Let \( v_{1} \) and \( v_{2} \) denote the linear speed of
child 1 and child \( 2, \) respectively. Which of the following is true?
\( A \cdot v_{1}>v_{2} \)
В . \( v_{1}=v_{2} \)
\( \mathrm{c} \cdot v_{1}<v_{2} \)
D. (4) we cannot determine which is true, without mo nformatio


Indicate the point of the complex plane
\( z \) which satisfy the following equation \( \boldsymbol{\operatorname { R e }} \boldsymbol{z}^{2}=\mathbf{0} \)


The energy difference (in \( k c a l \) mol \( ^{-1} \) ) between the staggered and eclipsed conformations of ethane is:
A . 2.9
в. 2.0
c. 3.6
D. 1.5


A disc of radius \( 10 \mathrm{cm} \) is rotating about
its axis at an angular speed of 20 rad/s. Find the linear speed of point of the rim.


Assertion
The dialysis a technique for purification of sol is used to remove the soluble and
insoluble impurities present in sol.
Reason
The dialysis is based on different rate of diffusion of true solution and collodial
solution particles.
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 value of the current \( \boldsymbol{I}_{1}, \boldsymbol{I}_{2} \) and \( \boldsymbol{I}_{3} \)
flowing through the circuit given below
is?
A \( \cdot I_{1}=-3 A, I_{2}=2 A, I_{3}=-1 A \)
B . \( I_{1}=2 A, I_{2}=-3 A, I_{3}=-1 A \)
C \( . I_{1}=3 A, I_{2}=-1 A, I_{3}=-2 A \)
D \( \cdot I_{1}=1 A, I_{2}=-3 A, I_{3}=-2 A \)
E \( \cdot I_{1}=2 A, I_{2}=-1 A, I_{3}=-3 A \)


If the equilibrium constant for \( \boldsymbol{A}_{2}+ \)
\( B_{2} \rightleftharpoons 2 A B \) is \( K, \) then equilibrium
constant for \( \frac{1}{2} A_{2}+\frac{1}{2} B_{2} \rightleftharpoons A B \) is \( \sqrt{K} \)
If true enter \( 1, \) if false enter 0


A heavy uniform chain lies on a
horizontal table top. If the coefficient of friction between the chain and the table
surface is \( 0.25, \) then find the maximum
\( \% \) of the length of the chain that can hang over one edge of the table.
A . \( 20 \% \)
B. 25\%
\( c .35 \% \)
D. \( 15 \% \)


Match the items of List 1 with those in
List 2


NaOH is not produced in:
A. Nelson Cell method
B. Downs process
c. castner kellners method
D. Causticising process


The sign of the quadratic polynomial
\( a x^{2}+b x+c \) is always positive, if?
\( \mathbf{A} \cdot \) a is positive and \( b^{2}-4 a c \leq 0 \)
B. a is positive and \( b^{2}-4 a \geq 0 \)
\( \mathrm{C} \cdot \) a can be any real number and \( b^{2}-4 a c \leq 0 \)
D. a can be any real number and \( b^{2}-4 a c \geq 0 \)


Which of the following functions represents a simple harmonic oscillation?
A. sinwt - coswt
B. \( \sin ^{2} \omega t \)
c. sinwt \( +\sin 2 \omega t \)
D. \( \sin \omega t-\sin 2 \omega t \)


is used for making carpets and blankets.


Evaluate the following integral \( \int \frac{x \sin ^{-1} x^{2}}{\sqrt{1-x^{4}}} d x \)


Find the area enclosed by the curves \( \boldsymbol{y}=\bmod (\boldsymbol{x}-\mathbf{1}) \) and \( \boldsymbol{y}=\boldsymbol{\operatorname { m o d }}(\boldsymbol{x}- \)
1) +1


A solution of \( N a_{2} S O_{4} \) in water is
electrolysed using inert electrodes. The
products at the cathode and anode respectively, are:
A. \( O_{2}, H_{2} \)
в. \( O_{2}, \) Na
c. \( H_{2}, O_{2} \)
D. \( O_{2}, S O_{2} \)


The oxidation numbers of phosphorus in \( B a\left(H_{2} P O_{2}\right)_{2} \) and xenon in
\( N a_{4} X e O_{6} \) respectively are:
\( A \cdot+3 \) and +4
B. +2 and +6
\( c \cdot+1 \) and +8
D. -1 and -6


Which forms \( p \pi-p \pi \) multiple bonds
with itself and with \( \mathrm{C} \) and \( 0 ? \)
\( A \cdot P, A S \)
B. N,As
c. \( \mathrm{N}, \mathrm{P} \)
D.


The co-efficient of restitution for a
perfectly elastic collision is:
A .
B. 0
c. lies in between 0 and 1
D. infinity


Position of double bond in alkenes can
be identified by:
A. bromine water
B. ammoniacal silver nitrate solution
c. ozonolysis
D. Baeyer's test


The cost of a vehicle is Rs. \( 1,75,000 . \) If its value depreciates at the rate of \( 20 \% \) per annum, then the total depreciation
after 3 years was
A. Rs. 86,400
B. Rs. 82,500
c. Rs. 84,500
D. Rs. 85,400


The equilibrium:
\( \boldsymbol{P}_{4}(\boldsymbol{g})+\boldsymbol{6} \boldsymbol{C l}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{4} \boldsymbol{P} \boldsymbol{C l}_{3}(\boldsymbol{g}) \)
is attained by mixing equal moles of \( \boldsymbol{P}_{4} \)
and \( C l_{2} \) in an evacuated vessel. Then at
equilibrium:
\( \mathbf{A} \cdot\left[C l_{2}\right]>\left[P C l_{3}\right] \)
в \( \cdot\left[C l_{2}\right]>\left[P_{4}\right] \)
\( \mathbf{c} \cdot\left[P_{4}\right]>\left[C l_{2}\right] \)
D・ \( \left[P C l_{3}\right]>\left[P_{4}\right] \)


The product of each positive integer with -1 is always
A. Positive
B. Negative
\( c \cdot 0 \)
D. None of these


A bullet of mass \( \mathrm{m} \) and velocity v is fired into a large block of wood of mass \( \mathrm{M} \)
The final velocity of the system is :
A. \( v+m+M \)
в. \( (m+M) v \)
c. \( V=\frac{m}{m+M} v \)
D. \( V=\frac{m+M}{m-M} v \)


\( \lim _{x \rightarrow a} \frac{x^{m}-a^{m}}{x^{n}-a^{n}} \) is equal to.
A \( . m n a^{m-n} \)
в. \( \frac{m}{n} a^{m-n} \)
c. \( \frac{n}{m} a^{m-n} \)
D. \( m n a^{m+n} \)


If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be:
A. only inside the pipe
B. only outside the pipe
c. both inside and outside the pipe
D. neither inside not outside the pipe


The last stage of cellular respiration which yields ATP by the oxidation of organic molecules, derived from glucose is
A. Chemiosmosis
B. Citric acid cycle.
c. Electron transport chain
D. Glycolysis.
E. Oxidation phosphorylation.


Explain binding energy curve.Write its importance.What is gamma decay? Explain with example.


Calculate Vant Hoff factor for \( 0.2 m \)
aqueous solution of KCl which freezes
at \( -\mathbf{0 . 6 8 0}^{\circ} \mathbf{C} .\left(\boldsymbol{K}_{\boldsymbol{f}}=\mathbf{1 . 8 6} \mathbf{K} \mathbf{k g} \boldsymbol{m o l}^{-\mathbf{1}} \mathbf{)}\right. \)
A . 3.72
в. 1.83
\( c .6 .8 \)
D. 1.86


The line spectrum is noticed during the transition of an electron from higher
excited state to lower one in \( \boldsymbol{H} \) -atom
only when an electron falls from:
A . \( 2 s \) -orbital to \( 1 s \) -orbital
B. 2p-orbital to 1s-orbital
c. \( 3 s \) -orbital to \( 2 p \) -orbital
D. \( 4 p \) -orbital to \( 2 p \) -orbital


The mass of carbon anode consumed
(giving the only carbon dioxide) in the production of \( 270 k g \) of aluminium metal from bauxite by the Hall process is:
[atomic mass \( \boldsymbol{A l}=\mathbf{2 7}] \)
A. \( 180 \mathrm{kg} \)
в. \( 270 \mathrm{kg} \)
c. \( 540 \mathrm{kg} \)
D. \( 90 \mathrm{kg} \)


If you touch the outside surface of the
metal container, your hand will become
warmer directly by which of the above choices?
A. I only
B. I and II only
c. I and III only
D. Il only
E . III only


Differentiate: \( y=\frac{x+2}{3 x+5} \) w.r.t \( x \)


An open box with a square base is to be
made out of a given quantity of cardboard of area \( c^{2} \) square units. Show
that the maximum volume of the box is
\( \frac{c^{3}}{6 \sqrt{3}} \) cubic units.


A conducting rod \( A B \) moves parallel to the x-axis in a uniform magnetic field
pointing in the positive z direction. The
end \( A \) of the rod gets positively charged. explain.


Expand using suitable identities
\( (-2 a+5 b-3 c)^{2} \)


Differentiate \( \sin \boldsymbol{h}^{-1}\left(\frac{\boldsymbol{x}}{\mathbf{3}}\right) \) with respect
to
\( x \). Find out the solution of the
integration \( \int \frac{1}{\left(x^{2}+9\right)} d x \) Further find
out the value of the integral
\( \int \frac{1}{\left(x^{2}+49\right)} d x ? \)


In an ac circuit the instantaneous
values of current and applied voltage are respectively \( i= \)
\( 2(A m p) \sin \left(250 \pi s^{-1}\right) t \) and \( \epsilon= \)
\( (10 V) \sin \left[\left(250 \pi s^{-1}\right) t+\frac{\pi}{3}\right] . \) Find the
instantaneous power drawn from the source at \( t=\frac{2}{3} m s \) and its average
value.


A sample of gas occupies \( 1.50 \mathrm{L} \) at \( 25^{\circ} \)
C. If the temperature is raised to \( 60^{\circ} \mathrm{C} \) what is the new volume of the gas if pressure remains constant?
A . 1.2
B . 1.68
\( c .2 .9 L \)
D. 0.86


Show that the products of the corresponding terms of the sequences ,ar \( , a r^{2}, a r^{n-1}, \) and \( A \)
from a G.P. and find the common ratio.


f \( \mathrm{E} \) and \( \mathrm{F} \) are independent events then:
This question has multiple correct options
A. E \& F mutually exclusive
B. E \& \( \bar{F} \) (complement of the event \( F \) ) are independent
C \( . \bar{E} \& \bar{F} \) are independent
D \( . P(E / F)+P(\bar{E} / F)=1 \)


Á is equal to:
\( \mathbf{A} \cdot 0.1 \mathrm{nm} \)
B . \( 10^{-10} \mathrm{cm} \)
\( \mathbf{C} \cdot 10^{-8} m \)
\( \mathbf{D} \cdot 10^{-4} \mu \)


The hours in a clock are marked by points. When it is put in front of a mirror and seen in the mirror, then time noted
is 8.20 The correct time is
A . 4: 40
B. 8: 20
\( c \cdot 2: 40 \)
D. 3:40


Name three undefined terms.
A. Point
B. Line
c. Plane
D. All of the above


Epipetalous stamens are seen in
A. Thespesia
B. Datura
c. Male flower of ricinus
D. Ravenala


Based on lattice energy and other considerations which one of the
following alkali metal chloride has the
highest melting point?
A. \( K C l \)
B. \( R h C l \)
c. LiCl
D. \( N a C l \)


A long-jumper runs before jumping to
A. Cover greater distance
B. Maintain momentum conservation
C. Gain energy by running
D. Gain momentum


A ray of light is incident on a plane
mirror at an angle of incidence of \( 30^{\circ} \) The deviation produced by the mirror is:
A \( .30^{\circ} \)
В \( \cdot 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 120^{\circ} \)


If \( \boldsymbol{A}=\left[\begin{array}{cc}1 & 2 \\ 3 & 4 \\ 5 & 6\end{array}\right] \) and \( B=\left[\begin{array}{cc}-3 & -2 \\ 1 & -5 \\ 4 & 3\end{array}\right] \)
then find \( D=\left[\begin{array}{ll}\boldsymbol{p} & \boldsymbol{q} \\ \boldsymbol{r} & \boldsymbol{s} \\ \boldsymbol{t} & \boldsymbol{u}\end{array}\right] \) such that \( \boldsymbol{A}+ \)
\( \boldsymbol{B}-\boldsymbol{D}=\boldsymbol{O} \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}-1 & 0 \\ 4 & -1 \\ 9 & 9\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{cc}-3 & 0 \\ 4 & -1 \\ 9 & 9\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}-2 & 0 \\ 4 & -1 \\ 9 & 9\end{array}\right] \)
D. \( \left[\begin{array}{cc}-2 & 0 \\ 4 & -5 \\ 9 & 9\end{array}\right] \)


In terms of energy 1 u is equal to?
\begin{tabular}{l}
A. \( 100 J \) \\
\hline
\end{tabular}
B. \( 931.1 k c a l \)
c. \( 931.1 \mathrm{MeV} \)
D. \( 10^{7} \) erg


In given figure \( A B C D \) is a rhombus. If
\( \angle B A C=38^{\circ}, \) find:
\( \angle A D C \)


A galvanometer coil \( 5 \mathrm{cm} \times 2 \mathrm{cm} \) with 200 turns is suspended vertically in a field of \( 5 \times 10^{-2} \) T.The suspension fibre
needs a torque of \( 0.125 \times 10^{-7} N-m \)
to twist it through one radian. If \( i \) is the
strength of the current required to be maintained in the coil when we require
a deflection of \( 6^{\circ} \) then find \( x \) such that
\( \boldsymbol{x}=\boldsymbol{i} \times \mathbf{1 0}^{8} \)


A galvanometer is shunted by \( \frac{1}{r} \) of its
resistance. Find the fraction of total
current passing through the galvanometer.


Compare the structures of \( H_{2} O \) and
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)


The inertia of an object tends to cause
the object:
A. to increase its speed
B. to decrease its speed
C . to resist any change in its state of motion
D. to decelerate due to friction