A ray light travelling in the direction \( \frac{1}{2}(\hat{i}+\sqrt{3} \hat{j}) \) is incident on a plane mirror. After reflection, it travels along
the direction \( \frac{1}{2}(\hat{i}-\sqrt{3} \hat{j}) . \) What is the angle of incidence?
A . \( 30^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 75^{\circ} \)


The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Literacy
\( 55-\quad 6 \)
\[
75
\]
rate (in \( 45- \)
55
\( 65 \quad 75 \quad 85 \)
\( \% \)
vumbe
of cities


An element \( X \) has IE and EA respectively 275 and \( 1450 k J \) mole \( ^{-1} \). The
electronegativity of element according to Mullikan scale is ?
A . 2.4
в. 2.8
\( c .3 .20 \)
\( D \cdot 4.0 \)


Some word/ words are missing in the following statements. You are required
to rewrite the statements in the correct
form using the appropriate word/ words:
Magnesium nitride reacts with water to liberate ammonia.


A particle executes SHM given by the equation \( x=5 \sin (3.14 t), x \) is measured in mms. The time period and the amplitude of the oscillations are
A. The amplitude is \( 5 \mathrm{cms} \) and time period is 1 sec
B. The amplitude is 5 \( \mathrm{mms} \) and time period is \( 1 \mathrm{sec} \)
c. The amplitude is \( 5 \mathrm{mms} \) and time period is 3.142 seo
D. The amplitude is \( 5 \mathrm{cms} \) and time period is 3.142 sec


As we move from left to right, the electronegativity increases. An atom which is highly electronegative has:
A. large size
B. low electron affinity
c. high ionisation enthalpy
D. low chemical reactivity


Match the plants with their respective
rate of growth. Choose the answer which gives the correct combination of
alphabets of two columns.
Plants \( \quad \) Rate of growth plants
\( A \) cycas 40 centimeters
\( p \quad \) per day
в Gaint
bamboo 10 feet in
q \( \quad \) hundred years
Cucumber
tendril 6 centimeters per hour
A \( \cdot A-r, B-p, C-q \)
B. A-p, B-r, C-q
c. A-q, B-p, C-r
D. A-p, B-q, C- -


If the ratio of the height of tower and the length of its shadow is \( 1: \sqrt{3} \), then the
angle of elevation of the sum has
measure
A . \( 60^{\circ} \)
B . \( 45^{\circ} \)
\( c \cdot 30^{\circ} \)
D. \( 75^{\circ} \)


An ideal gas initially at \( 30 K \) undergoes
an isobaric expansion at 2.50 kPa. If
the volume increases from \( 1.00 m^{3} \) to
\( 3.00 m^{3} \) and \( 12.5 k J \) is transferred to
the gas by heat, What is the change in its internal energy?
\begin{tabular}{l}
A \( .7500 \mathrm{J} \) \\
\hline
\end{tabular}
в. \( 7000 J \)
c. \( 700 J \)
D. \( 750 J \)


Evaluate the following limits. \( \lim _{x \rightarrow 1} \frac{\sqrt{5 x-4}-\sqrt{x}}{x-1} \)


The chemistry of lithium is very similar to that of magnesium even though they are placed in different groups. Its reason is that:
A. both are found together in nature
B. both have nearly the same size
c. both have similar electronic configurations
D. the ratio of their charge to size is nearly the same


The standard electrode potential of Cu/Cu
\( ^{+2} \) electrode is \( 0.336 . \) It corresponds to
the reaction:
A. \( C u \rightarrow C u^{+2}+2 e^{-} \)
В \( \cdot \frac{1}{2} C u^{+2}+e^{-} \rightarrow \frac{1}{2} C u \)
\( \mathrm{c} \cdot \mathrm{Cu}^{+2}+2 e^{-} \rightarrow \mathrm{Cu} \)
D. \( 2 C u^{+} \rightarrow C u+2 e^{-} \)


Which of the polymer has weakest
intermolecular force of attraction?
A. nylon
B. poly(vinyl chloride)
c. cellulose
D. natural rubber


The coefficient of friction between the
tryes and the road is 0.25 . the maximum speed with which a car can
be driven round a curve of radius \( 40 \mathrm{m} \)
without skidding is (assume \( g=10 m s^{-2} \)
A. \( 40 \mathrm{ms}^{-1} \)
B . \( 20 m s^{-1} \)
\( \mathbf{c} \cdot 15 m s^{-1} \)
D. \( 10 \mathrm{ms}^{-1} \)


What is difference between \( \mathrm{Nm} \) \& mN?


Commercial common salts become
slightly damp on keeping. This is due to
the fact that:
A. common salt is hygroscopic
B. common salt contains some impurities which are hygroscopic
c. common salt is efflorescent
D. common salt is crystalline


State differences between the blood
vessels-artery, vein and capillary


The separation of the atria and ventricle helps to
A. Prevent mixing of the blood
B. Pump blood only to lower parts of the body
c. Pump blood only to upper parts of the body
D. Both A and C


Two metal spheres (radii \( r_{1}, r_{2} \) with
\( \left.r_{1}<r_{2}\right) \) are very far apart but are
connected by a thin wire. If their combined charge is \( Q \), then what
is their common potential?
A \( \cdot k Q /\left(r_{1}+r_{2}\right) \)
B . \( k Q /\left(r_{1}-r_{2}\right) \)
\( \mathbf{c} \cdot-k Q /\left(r_{1}+r_{2}\right) \)
D. \( -k Q / r_{1} r_{2} \)


Why diazonium salts do not show
positive Lassaigne's test for nitrogen?


Which of the following is not correct?
A. Milk is naturally occurring emulsion
B. Gold sol is Iyophilic sol
C. Physical adsorption decreases with rise in temperature
D. Chemical adsorption is unilayered


Three identical balls each of mass \( \boldsymbol{m}= \)
\( 0.5 \mathrm{kg} \) are connected with each other as shown in Figure and rest over a smooth
horizontal table. At moment \( t=0, \) ball \( B \)
is imparted a horizontal velocity \( \boldsymbol{v}_{0}= \) \( 9 m s^{-1} . \) Calculate velocity of A just
before it collides with ball \( C \).


The contrapositive of "if in a triangle
\( A B C, A B=A C, \) then \( \angle B=\angle C^{\prime \prime}, \) is
\( \mathbf{A} \cdot \) If in a triangle \( A B C, \angle B=\angle C, \) then \( A B=A C \)
B. If in a triangle \( A B C, A B \neq A C \), then \( \angle B \neq \angle C \).
C. If in a triangle \( A B C, \angle B \neq \angle C, \) then \( A B \neq A C \).
D. If in a triangle \( A B C, \angle B \neq \angle C, \) then \( A B=A C \).


\( \left\{29 \cos \theta=20, \text { find } \sec ^{2} \theta-\tan ^{2} \theta\right. \)


Explain the construction and working of electric bell with figure.


In which part of the body blood gets purified (becomes oxygenated)?
A. Atrium
B. Lungs
c. Heart
D. Ventricle


Which expression gives the correct
value for the standard potential for a
gold-rhodium voltaic cell?
Half-reaction \( \mathbb{E}^{\circ}(\mathbf{V}) \)
\( R h_{(q q)}^{+3}+3 e^{-} \rightarrow R h_{(s)} \)
\( A u_{(q q)}^{+}+e^{-} \rightarrow A u_{(s)} \)
A . \( 1.69 V+0.76 V \)
B . \( 1.69 V-0.76 V \)
c. \( 3(1.69) V+0.76 V \)
D. \( 3(1.69) V-0.76 V \)


The sides of a right angled triangle are in A.P. The ratio of sides is
A .1: 2: 3
B. 2:3:4
\( c \cdot 3: 4: 5 \)
\( D \cdot 5: 8: 3 \)


Locomotion is possible due to skeleton.
A. Appendicular
B. Axial
c. skull
D. None of these


The measures of a rectangular field are
\( 20 \mathrm{m} \) by \( 16 \mathrm{m} . \) A cubical ditch of edge 4 \( \mathrm{m} \) is dug at each of the four corners of the field and earth removed is spread uniformly over the remaining field. by what height does the field get raised?


Light from the Sun travels in straight
lines. Yet, the light reaches our rooms
and brightens it. Name the phenomenon of light that causes this.


What is the degree of the following polynomial expression:
\( \boldsymbol{u}^{\frac{-1}{2}}+\boldsymbol{3} \boldsymbol{u}+\boldsymbol{2} \)
\( \mathbf{A} \cdot \mathbf{1} \)
B. 0
\( c \cdot \frac{-1}{2} \)
D. Not Defined


Which of the following chemical
reaction correctly shows Aqua-regia dissolving in gold?
\( \mathbf{A} \cdot A u+2[C l] \longrightarrow A u C l_{2} \stackrel{H C l}{\longrightarrow} H_{2}\left[A u C l_{4}\right] \)
B \( \cdot A g+3[C l] \longrightarrow A g C l_{3} \stackrel{H C l}{\longrightarrow} H\left[A g C l_{4}\right] \)
c. \( A u+3[C l] \longrightarrow A u C l_{3} \stackrel{H C l}{\longrightarrow} H\left[A u C l_{4}\right] \)
D \( \cdot A g+2[C l] \longrightarrow A g C l_{2} \stackrel{H C l}{\longrightarrow} H_{2}\left[A g C l_{4}\right] \)


In a reaction, \( \Delta H \) and \( \Delta S \) both are
more than zero. In which of the following cases, the reaction would not be
spontaneous? This question has multiple correct options
\( \mathbf{A} \cdot \Delta H>T \Delta S \)
в. \( T \Delta S>\Delta H \)
c. \( \Delta H=T \Delta S \)
D. \( \Delta G<0 \)


A wire of lenth L suppleid heat to raise its temperature by T.if y is the coefficient of volume expansion of the wire and Young's modulus of the wire
then the energy density stored in the wire is.


Fifty millilitre of a mixture of \( \mathrm{CO} \) and
\( C H_{4} \) was exploded with \( 85 \mathrm{ml} \) of \( O_{2} \). The
volume of \( C O_{2} \) produced was 50
ml.Calculate the percentage composition of the gaseous mixture.
A . 20\%
B. 40\%
c. 60\%
D. 80\%


Two plane mirror are inclined to one
another at an angle of \( 60 . \) A ray is
incident on mirror M1 at an angle i. The
reflected ray from mirror \( M_{1} \) is shown
in figure. The angle of incidence lis
A \( .20^{\circ} \)
B. \( 10^{\circ} \)
\( c \cdot 30^{\circ} \)
D. 40


A pyramid has a square base of side \( a \) and four faces which are equilateral triangles. A charge \( Q \) is placed on the centre of the base of the pyramid. What is the net flux of electric field emerging from one of the triangular faces of the
pyramid?
A. 0
в. \( \frac{Q}{8 \epsilon_{0}} \)
c. \( \frac{Q a^{2}}{8 \epsilon_{0}} \)
D. \( \frac{Q}{2 \epsilon_{0}} \)


Out of \( N a^{+}, M g^{+2}, O^{-2} \) and \( N^{-3}, \) the pair of species having the minimum and the maximum IP would be?
A \( . N a^{+}, M g^{+2} \)
B . \( M g^{+2}, N^{-3} \)
C . \( N^{-3}, M g^{+2} \)
D. \( O^{-2}, N^{-3} \)


Methyl vinyl ketone on reaction with
LiCu Me gives a major product,
whose structure is:
\( A \)
B.
\( c \)
\( D \)


If \( A \) and \( B \) are two independent events such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{1} / 2 \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{1} / \mathbf{5} \)
then
This question has multiple correct options
A \( \cdot P(A \cup B)=\frac{3}{5} \)
B. \( P(A \mid B)=\frac{1}{2} \)
\( ^{\mathbf{c}} \cdot P(A \mid A \cup B)=\frac{5}{6} \)
D . \( P\left[(A \cup B) \mid\left(A^{\prime} \cup B^{\prime}\right)\right]=0 \)


Rutherford's alpha particle scattering experiment established that:
A. protons are not evenly distributed throughout an atom
B. electrons have a negative charge
c. electrons have a positive charge
D. atoms are made of protons, neutrons, and electrons


The sugar moiety present in \( \boldsymbol{R} \boldsymbol{N} \boldsymbol{A} \)
molecule is:
A. \( \beta-D-2 \) - deoxyribose
B. \( \beta-D- \) galactose
c. \( \beta-D \) - fructofuranose
D. \( \beta-D- \) ribose
E. \( \beta-D-3- \) ribose


If the value of \( x \) is 6
A \( \cdot \frac{2}{3} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{5}{6} \)
D.


associated with electromagnetic radiations in different contexts in
physics. State the part of the electromagnetic spectrum to which
each belongs.
(a) \( 21 \mathrm{cm} \) (wavelength emitted by atomic hydrogen in interstellar space).
(b) 1057 MHz (frequency of radiation
arising from two close energy levels in hydrogen; known as Lamb shift).
(c) \( 2.7 \mathrm{K} \) [temperature associated with the isotropic radiation filling all space thought to be a relic of the big-bang origin of the universe].
\( (d) 5890 A-5896 \dot{A}[ \) double lines of
sodium]
(e) 14.4 ke \( V \) [energy of a particular transition in \( ^{57} \) Fe nucleus associated
with a famous high resolution spectroscopic method Mössbauer spectroscopy)].


Convection occurs in
A. solids only
B. liquids only
C. gases only
D. fluids


First row of the matrix \( \boldsymbol{A} \) is \( \left[\begin{array}{lll}\mathbf{1} & \mathbf{3} & \mathbf{2}\end{array}\right] . \)
\[
\begin{array}{l}
\boldsymbol{a d j}(\boldsymbol{A})= \\
{\left[\begin{array}{ccc}
-\mathbf{2} & \mathbf{4} & \boldsymbol{a} \\
-\mathbf{1} & \mathbf{2} & \mathbf{1} \\
\mathbf{3} \boldsymbol{a} & \mathbf{- 5} & \mathbf{- 2}
\end{array}\right]}
\end{array}
\]
then a possible value of \( \operatorname{det}(\boldsymbol{A}) \) is
A . 1
B . 2
\( c \cdot-1 \)
D. -2


In which phase does the spindle fiber disappear
A. Prophase
B. Metaphase
c. Anaphase
D. Telophase


Assertion
(A): When hot water is poured in athick glass tumbler then the tumbler breaks.
Reason (R): Glass is a bad conductor of
heat
A. A and R are correct and R is correct explanation for
B. A and R are correct and R is not correct explanation for \( A \)
C. A is true and R is false
D. A is wrong and R is true


What was the average speed of the cyclist for the past hour when he travels at a constant \( 25 k m / h r \) for 30 minutes,
coasts for 15 minutes at a constant
\( 20 \mathrm{km} / \mathrm{hr} \) and then pedals at a
constant \( 40 \mathrm{km} / \mathrm{hr} \) for another 15
minutes?
A. \( 27.5 \mathrm{km} / \mathrm{hr} \)
B. \( 25 \mathrm{km} / \mathrm{hr} \)
c. \( 22.5 \mathrm{km} / \mathrm{hr} \)
D. \( 30 \mathrm{km} / \mathrm{hr} \)
E . \( 32.5 \mathrm{km} / \mathrm{hr} \)


A particle of mass \( 2 \times 10^{-5} k g \) moves
horizontally between two horizontal plates of a charged parallel plate capacitor between which there is an electric field of \( 200 N C^{-1} \) acting upward. A magnetic induction of \( 2.0 T \) is applied at right angles to the electric field in a direction normal to both \( \vec{B} \) and
\( \vec{v} \). If \( g \) is \( 9.8 m s^{-2} \) and the charge on the
particle is \( 10^{-6} C, \) then find the velocity of charge particle so that it continues to move horizontally
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. 20 \( m s^{-1} \)
c. \( 0.2 m s^{-1} \)
D. \( 100 \mathrm{ms}^{-1} \)


Friction is a type of:
A. resistance force
B. non contact force
c. contact force
D. motion


The strongest attractive forces are
A. electrostatic
B. gravitational
c. nuclear
D. nothing can be decided


Consider the Arrhenius equation given
below and mark the correct option \( : k= \)
\( \boldsymbol{A} \boldsymbol{e}^{-\boldsymbol{E}_{a} / \boldsymbol{R} \boldsymbol{T}} \)
A. Rate constant increases exponentially with increasing activation energy and decreasing temperature
B. Rate constant decreases exponentially with increasing activation energy and decreasing temperature
C. Rate constant increases exponentially with decreasing activation energy and decreasing temperature
D. Rate constant increases exponentially with decreasing activation energy and increasing temperature


The vector \( \hat{B}=4 \hat{i}+2 \hat{j}-S \hat{k} \) is
perpendicular to the vector \( \overrightarrow{\boldsymbol{A}}=\mathbf{3} \hat{\mathbf{i}}+ \)
\( \hat{\boldsymbol{j}}+\boldsymbol{2} \hat{\boldsymbol{k}} \) if \( \boldsymbol{S}= \)
\( A \)
B. 7
\( c \cdot 6 \)
D. 8


Water occurs in frozen state over the
land is
A . 0.75\%
B . 1.97\%
c. 2.1\%
D. 2.5\%


The \( p H \) of \( 10^{-4} M K O H \) solution will
be:
\( A \cdot 4 \)
B. 1
\( c \cdot 10.5 \)
D. 10


(a). Name the forces acting on a plastic bucket containing water held above ground level in your hand.
(b). Discuss why the force acting on the bucket do not bring change its state of
motion?
(c). Why do porters place a round of cloth on their heads when they have to
carry heavy loads?


Which of the following statements is
true?
\( \mathbf{A} \cdot 6 x+3 x=9 x^{2} \)
B . \( 4(x+5)=4 x+5 \)
c. \( 4(x+5)=4 x+20 \)
D \( \cdot x(4 x+5)=4 x^{2}+5 \)


A circle and a parabola intersect at four points \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \) and
\( \left(x_{4}, y_{4}\right) . \) Then \( y_{1}+y_{2}+y_{3}+y_{4} \) is equal
to
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3/2
\( c \cdot 2 \)
D.


image of an object approching a convex mirror of radius of curvature \( 20 \mathrm{m} \) along its optical axis so is observed to move from \( \frac{25}{3} m \) to \( \frac{50}{7} m \) into 30 s. what is the speed of the object in \( K m / h ? \)
A . 3
B. 4
\( c .5 \)
D. 6


A stream of electrons enters an electric
field normal to the lines of force with a
velocity of \( 3 \times 10^{7} m / s . \) The electric
intensity is \( 1800 \mathrm{V} / \mathrm{m} \). While traveling through a distance of \( 10 \mathrm{cm}, \) the electron beam is deflected by \( 2 \mathrm{mm} \) Then e/m in coulomb per kg will be
A \( \cdot 2 \times 10^{-11} \)
в. \( 2 \times 10^{7} \)
\( c \cdot 2 \times 10^{11} \)
D. \( 2 \times 10^{14} \)


If \( F \) is the force between two bodies of
masses \( m_{1} \) and \( m_{2} \) at certain
separation. Find the force between \( \sqrt{2} m_{1} \) and \( \sqrt{3} m_{2} \) at same separation.


A battery of emf \( 10 \mathrm{V} \) and internal resistance \( 3 \mathrm{W} \) is connected to a
resistor. If the current in the circuit is
\( 0.5 \mathrm{A}, \) what is the resistance of the
resistor? What is the terminal voltage of
the battery when the circuit is closed?


The reaction
\( \mathbf{1} / \mathbf{2} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g})+\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s}) \rightarrow \boldsymbol{H}^{\oplus}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \boldsymbol{C l}^{\ominus}(\boldsymbol{a q})+\boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \) occurs in the
galvanic cell:
A \( \cdot A g|A g C l(s)| K C l(s o l)\left|A g N O_{3}\right| A g \)
B . \( P t\left|H_{2}(g)\right| H C l(s o l)\left|A g N O_{3}(s o l)\right| A g \)
c. \( P t\left|H_{2}(g)\right| H C l(s o l)|A g C l(s)| A g \)
D. \( P t\left|H_{2}(g)\right| K C l(s o l)|A g C l(s)| A g \)


It has been found that if \( A \) and \( B \) play a game 12 times, \( A \) wins 6 times, \( B \) wins 4
times and they draw twice. A and B take
part in a series of 3 games. The probability that they win alternately, is :
A \( \cdot \frac{5}{12} \)
в. \( \frac{5}{36} \)
c. \( \frac{19}{27} \)
D. \( \frac{5}{27} \)


Convert the given functional numbers to
per cents.
\( \frac{3}{40} \)


What is membrane biogenesis? Which cell organelle is responsible for it?


A green light is incident from the water
to the air - water interface at the critical
angle ( \( \theta \) ). Select the correct statement.
A. The spectrum of visible light whose frequency is more than that of green light will come out to the air medium
B. The entire spectrum of visible light will come out of the water at various angles to the normal
C. The entire spectrum of visible light will come out of the water at an angle of \( 90^{\circ} \) to the normal.
D. The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.


Two vessels \( A \) and \( B \) of cross-sections
as shown in figure contain a liquid up
to the same height. As the temperature
rises, the liquid pressure at the bottom
(neglecting expansion of the vessels)
will:
\( \mathbf{A} \). increase in \( A \), decrease in \( B \)
B. increase in \( B \), decrease in \( A \)
C. increase in both \( A \) and \( B \)
D. decrease in both \( A \) and \( B \)


Predict the order of reactivity of the
following compounds in \( S_{N} 1 \) and \( S_{N} 2 \)
reactions:
The four isomeric bromobutanes
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C H}_{2} \boldsymbol{B r}, \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C H}\left(\boldsymbol{C}_{6} \boldsymbol{H}_{5}\right) \boldsymbol{B r}, \boldsymbol{C}_{6} \)


An organisation sent out 420 invitations for a fund-raiser function. Of
the people invited, 315 attended. What percent of the people invited attended the fund-raiser?
A . \( 33 \% \)
B. 25\%
c. \( 43 \% \)
D. \( 75 \% \)


Which of the following metal is purified by Mond carbonyl method?
\( \mathbf{A} \cdot T i \)
в. \( G e \)
\( c \cdot Z r \)
D. \( N i \)


Consider the following statements-
(a) Alluvial soil are formed by sediments deposited by rivers.
(b) Black soil is found in the dry and Semi-dry areas of Rajasthan and
Gujarat.
(c) Red soil cannnot retain much
moisture.
(d) Laterite soil is found over lava
deposits in the Deccan.

Which of the above statements are
correct?
B. (a) and (c)
c. (b) and (d)
D. None of them


If \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{t}-\sin t) \) and \( \boldsymbol{y}=\boldsymbol{a}(\boldsymbol{1}+\cos \boldsymbol{t}) \)
then the value of \( y_{2} \) at \( t=\frac{\pi}{2} \) is
\( A \)
B . a \( ^{2} \)
\( c \cdot \frac{1}{a} \)
D. \( \frac{1}{a^{2}} \)


Which of the following substance exists as a gas at room temperature?
A. Formaldehyde
B. Para formaldehyde
c. Trioxane
D. All of the above.


Why lime has been used in mortar (a
lime, sand and water paste) in building houses, etc. for several thousand years?


Differentiate between aerobic and
anaerobic respiration.


A solution having hydrogen ion concentration is \( 0.0005 g \) eqvt/litre, its
\( p O H \) is
A . 8.2798
в. 10.6990
c. 12.7854
D. 13.3344


\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{4}(\boldsymbol{C} \boldsymbol{N})_{2}\right] \) is the empirical
formula of a compound which has a
magnetic moment corresponding to \( 2 \frac{2}{3} \) unpaired electrons per iron. The best possible formula of the compound is
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right] 2\left[F e(C N)_{6}\right. \)
B . \( \left[F e\left(H_{2} O_{6}\right)\right]\left[F e\left(H_{2} O\right)_{2}(C N)_{4}\right] \)
C \( \cdot\left[F e\left(H_{2} O\right)_{4}(C N)_{2}\right]_{2}\left[F e\left(H_{2} O\right)_{4}(C N)_{2}\right. \)
D. None of these


If \( A=\left[\begin{array}{l}45 \\ 21\end{array}\right], \) then show that \( A^{-1}= \)
\( \frac{1}{6}(A-5 I) \)


Most balloons, tyres and footballs are made-of rubber. This is because rubber
is:
A. naturally available
B. cheap
c. an electrical insulator
D. soft and flexible


A class has 15 students whose ages are 14,17,15,14,21,17,19,20,16,18,20,17,16
19 and 20 years. One student is selected
in such a manner that each has the
same chance of being chosen and the
age \( X \) of the selected student is
recorded. What is the probability distribution of the random variable \( \boldsymbol{X} \) ?
Find mean, variance and standard
deviation of \( \boldsymbol{X} \)


states the possibility of the prime factorization of any natural number is unique. The numbers can be
multiplied in any order
A. Pythagora's theorem
B. Remainder theorem
c. Fundamental theorem of arithmetic
D. none of the above


The magnitude of electric field as a
function of the distance r inside the
sphere is given by :
\( ^{\mathbf{A}} \cdot_{E}=\frac{\rho_{0}}{\varepsilon}\left[\frac{r}{3}-\frac{r^{2}}{4 R}\right] \)
B. \( \quad E=\frac{\rho_{0}}{\varepsilon}\left[\frac{r}{4}-\frac{r^{2}}{3 R}\right] \)
\( ^{\mathrm{C}}=\frac{\rho_{0}}{\varepsilon}\left[\frac{r}{3}+\frac{r^{2}}{4 R}\right] \)
D. \( \quad E=\frac{\rho_{0}}{\varepsilon}\left[\frac{r}{4}+\frac{r^{2}}{3 R}\right. \)


When we realize a specific implementation of a pancake algorithm, every move when we find the greatest of the sized array and flipping can be modeled through
A. Combinations
B. Exponential functions
c. Logarithmic functions
D. Permutations


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


Oil spills reduce \( _{\text {一一一一一一一一- }} \) supplies within the water environment.
A. carbon dioxide
B. oxygen
c. nitrogen
D. none of these


The following acids have been arranged in order of decreasing acid strength. Identify the correct order. \( \boldsymbol{C l O H}(\boldsymbol{I}), \boldsymbol{B r O H}(\boldsymbol{I I}), \boldsymbol{I O H}(\boldsymbol{I I I}) \)
A \( . I>I I>I I I \)
\( I \)
В. \( I I>I>I I I \)
c. \( I I I>I I>I \)
I II \( I>I I I>I I \)
\( I \)


If a fully charged capacitor \( C \) with
initial charge \( q_{0} \) is connected to a coil of
self inductance \( L \) at \( t=0 . \) The time at
which the energy is stored equally between the electric field and magnetic
field is :
A \( . \pi \sqrt{L C} \)
в. \( \frac{\pi}{4} \sqrt{L C} \)
c. \( \frac{\pi}{2} \sqrt{L C} \)
D. \( \frac{\pi}{6} \sqrt{L C} \)


Assertion
Annelids are ureotelic
Reason
Only excretory product of annelids is
uric acid.
A. If both the assertion and the reason are true and the
reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the
reason is not a correct explanation of the assertion
C. If the assertion is true but the reason is false
D. If both the assertion and reason are false


In sulphur detection of an organic compound, sodium nitropruside solution is added to sodium extract.
Formation of violet colour is due to the
formation of:
A \( \cdot \operatorname{Na}_{3} \) Fe \( (C N)_{6} \)
B . \( \operatorname{Na}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS} \mathrm{Na}\right] \)
c. \( \operatorname{Na}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NS}\right] \)
D. \( F e(C N S)_{3} \)


Chronic obstructive pulmonary disease (COPD) is due to
A. Damage to the lungs
B. Damage to the kidneys
c. Damage to the stomach
D. None of the above


Find the length of the shadow on the
ground of a pole of height \( 6 m \) when
the angle of elevation \( \theta \) of the Sun is such that \( \tan \theta=\frac{3}{4} \)


A crystalline hydrated salt on being rendered anhydrous, loses \( 45.6 \% \) of its weight. The percentage composition of anhydrous salt is : \( A I=10.5 \%, K=15.1 \%, S \) \( =24.8 \% \) and \( I=49.6 \% . \) Find the
empirical formula of the salt.
A . \( K A l S_{2} I \)
в. \( K_{2} \) А \( l S_{2} I \)
c. \( K A l S_{2} I .12 H_{2} O \)
D. \( K_{2} A l S_{2} I .12 H_{2} O \)


In Bentham and Hookers classification,
the sub class Polypetalae and Gamopetalae have the cohorts in the ratio of
A . 1:
B. 2:1
\( c \cdot 2: 3 \)
D. 3:2


\( A, B \) and \( C \) can finish a job working alone in 72,24 and 36 days respectively In how many days they can finish the job if they worked together?
A . 12
B. 9
c. 15
D. 18


Why does p-dichlorobenzene have a
higher m.p than its o- and m- isomers?


The half life of \( S r \) is 28 years. The
fraction of the specimen that remains
undecayed after 40 years will be
A . \( 21 \% \)
в. 37\%
c. \( 45 \% \) \%
D. 63 \%


Which of the following statements is
related to biological magnification?
A. There is a progressive increase in biological activities through trophic levels
B. There is a progressive increase in the level of harmful substances through trophic levels.
C. There is a progressive increase in the body weight through trophic levels.
D. There is a progressive increase in the number of organisms through trophic levels.


A strong electrolyte in aqueous solution exhibit:
This question has multiple correct options
A. almost completely dissociated
B. hydration
c. partial dissociation
D. none of the above


On the real number line below, numbers increase in value from left to right. If \( B>0, \) then the value of \( A \) must be:
A. Negative
B. Positive
c. Less than \( B \)
D. Greater than \( B \)
E. Between 0 and \( B \)


Find the inclination of a line whose
slope is
(i) 1
(ii) -1
(iii) \( \sqrt{3} \)
\( (i v)-\sqrt{3} \)
\( (v) \frac{1}{\sqrt{3}} \)


Match the following with reference to
adaptations.
The correct match is
A \( . \) A- II, B- \( 1 \mathrm{V}, \mathrm{C}-1 \mathrm{II}, \mathrm{D}-1 \)
B. A-III, B -II, C-I, D -V
C. \( A-11, B-111, C-1 V, D-1 \)
D. \( A-\| I, B-I V, C-1, D-V \)


Diamond is a allotrope of
A. carbon
B. Ieadd
c. antimony
D. germanium


The mass of \( N a_{2} C O_{3} \) of \( 95 \% \) purity
that would be required to neutralise \( 45.5 \mathrm{mL} \) of \( 0.235 \mathrm{N} \) acid is:
(write in multiples of 10 (only the nearest single digit)）


In secondary rainbow what is the order of colours observed from earth?
A. Violet innermost, Red outermost
B. Red innermost, Violet outermost
c. Random
D. White and dark alternatively


The most appropriate method of
making egg-albumin sol is:
A. Break an egg carefully and transfer the transparent part of the content to \( 100 \mathrm{mL} \) of \( 5 \% \mathrm{w} / \mathrm{V} \) saline solution and stir well.
B. Keep the egg in boiling water for 10 minutes. After removing the shell, transfer the white part of the content to \( 100 \mathrm{mL} \) of \( 5 \% \mathrm{w} / \mathrm{V} \) saline solution and homogenize with a mechanical shaker.
C. Keep the egg in boiling water for 10 minutes. After removing the shell, transfer the yellow part of the content to \( 100 \mathrm{mL} \) of \( 5 \% \mathrm{w} / \mathrm{V} \) saline solution and homogenize with a mechanical shaker
D. Break an egg carefully and transfer only the yellow part of the content to \( 100 \mathrm{mL} \) of \( 5 \% \mathrm{w} / \mathrm{V} \) saline solution and stir well.


Find the mode for the following data:
22 26 Term 30 Frequency \( \quad 3 \quad 5 \quad \) 10 \( \quad 2 \)
A . 22
B . 30
\( c \cdot 34 \)
D. None of these


(i) The acidic character of hydrides of
group 15 increases from \( H_{2} O \) to \( H_{2} \) Te.
Why?
(il) Dioxygen is a gas while sulphur \( \left(\boldsymbol{S}_{8}\right) \)
is a solid. Why?


Reflection is
A. Bending of ray of light.
B. Bouncing back of ray of light.
C. Light travelling in a straight line.
D. None of these.


If \( x \& y \) are in inverse proportion then
find proportionality constant at \( \boldsymbol{x}= \)
\( \mathbf{3}, \boldsymbol{y}=\mathbf{2} \)
A . 4
B. 5
\( c .6 \)
D.


n the Fig. \( 8.12 \angle R \) is the right angle of
\( \Delta P Q R \) write the following ratios.
(i) \( \sin P \)
(ii) \( \cos Q \)
(iii) \( \tan \mathrm{P} \)
(iv) \( \tan \mathrm{Q} \)


Air pollution can be
A. Gasesous
B. Particulate type
C. Both A and B
D. None of these


The value of ionization potential for inert gases is
A. zero
B. Low
c. Highh
D. Negative


The glycosidic linkage involved in linking the glucose units in amylose part of starch is:
A \( \cdot C_{1}-C_{4} \beta- \) linkage
в. \( C_{1}-C_{6} \alpha- \) linkage
c. \( C_{1}-C_{6} \beta- \) linkage
D. \( C_{1}-C_{4} \alpha- \) linkage


Most gymnosperms have
A. Both archegonia and antheridia
B. Antheridia but no archegonia
C. Archegonia but no antheridia
D. Neither antheridia nor archegonia


The list of numbers \( 10,6,2,-2, \cdots \) is
A . an A.P. with \( d=16 \)
B. an A.P. with \( d=-4 \)
c. an \( A . P . \) with \( d=4 \)
D. not an \( A . P \).


Select the correct I.U.P.A.C. name for
\( \left[\boldsymbol{C r}\left(\boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\mathbf{6}}\right)_{2}\right] \)
\( \mathbf{A} \cdot \) bis \( \left(\eta^{5} \text { -benzene }\right) \) chromium (0)
B. bis( \( \eta^{6} \) -benzene) chromate (O)
C. bis \( \left(\eta^{5} \text { -benzene }\right) \) chromate (O)
D. bis( \( \eta^{6} \) -benzene) chromium (0)


If \( i^{2}=-1, \) then \( (5+6 i)^{2}= \)
A . -11
B . \( -11+11 i \)
c. \( -11+30 i \)
D. \( -11+60 i \)
E . 61


Define event


The muscles of a normal eye are least
strained when the eye is focused on an object :
A. far away from the eye
B. very close to the eye
c. at about \( 25 \mathrm{cm} \) from the eye
D. at about \( 1 \mathrm{m} \) from the eye


Two sound waves travelling in the same
direction are represented by equations \( \boldsymbol{Y}_{1}=\boldsymbol{A}_{1} \operatorname{Sin} \mathbf{5 0 4} \boldsymbol{\pi} \boldsymbol{t} ; \boldsymbol{Y}_{2}= \)
\( A_{2} \) Sin \( 512 \pi t . \) These two sound waves
superpose to produce beats. The intensity of sound changes from minimum to maximum in a time of
A \( .1 / 2 s \)
B. 1/4s
c. \( 1 / 8 \) s
D. \( 1 / 16 \) s


The total deviation of the incident ray
when it emerges out of the prism is.
\( \mathbf{A} \cdot 30^{\circ} \)
B \( .60^{\circ} \)
\( \mathrm{c} \cdot 90^{\circ} \)
D. \( 45^{\circ} \)


Find the common ratio and the general
term of the following geometric
sequences. \( \mathbf{0 . 0 2}, \mathbf{0 . 0 0 6 , 0 . 0 0 1 8}, \ldots . \)


When light is incident on a polished surface reflection
takes place
A. regular
B. irregular
\( c . \) both (a) and (b)
D. None of these


The dissociation constant of acetic acid
and aniline are \( 1.8 \times 10^{-5} \) and \( 4.2 \times \)
\( 10^{-10} \) respectively. What is the pH of the
solution?
A .4 .684
B. 46.84
\( c \cdot 0.4684 \)
D. 684.2


Cyanohydrin of which of the following compound on hydrolysis gives optically active products?
A. \( H C H O \)
в. \( C H_{3} C H O \)
c. \( C H_{3} \) COCH\( _{3} \)
D. all of the above


Write Faraday's laws of electromagnetic
induction and obtain an expression of induced e.m.f.


A trader purchases \( 70 \mathrm{kg} \) of tea at Rs. 15 per kg and \( 30 \mathrm{kg} \) of tea at Rs. 18.50
per kg. If the packing charges are 2 percent, then at what price he must sell the mixture of two to gain \( 15 \% ? \)
A. Rs. 18.80 per kg
B. Rs. 18 per kg
c. Rs. 18.50 per \( \mathrm{kg} \)
D. Rs. 17.80 per kg


If we use a powerful electromagnet in place of permanent magnet in a
generator, then:
A. voltage produced by the generator increases
B. current produced by the generator increases.
c. Both A and B are true
D. No effect on current or voltage occurs.


f \( m \) and \( n \) are the order and degree of
the differential equation \( \left(\frac{d^{2} y}{d x^{2}}\right)^{5}+4 \frac{\left(\frac{d^{2} y}{d x^{2}}\right)^{3}}{\left(\frac{d^{2} y}{d x^{2}}\right)}+\frac{d^{2} y}{d x^{2}}=x^{2}-1 \)
then
A \( . m=3, n=3 \)
B. \( m=2, n=6 \)
\( \mathrm{c} \cdot m=3, n=5 \)


In Millikan's oil drop experiment, the
charge of three oil drops \( X, Y \) and \( Z \) have been found to be 2,0.04 and 0.8 respectively. What could be the number
of electrons attached to oil drop \( X ? \)
A . 1
B . 20
c. 40
D. 50


A thin prism of angle \( 5^{\circ} \) is placed at a
distance of \( 10 \mathrm{cm} \) from object. What is the distance of the image from object?
(Given \( \mu \) of prism \( =1.5 \) )
A \( \cdot \frac{\pi}{8} c m \)
в. \( \frac{\pi}{12} \mathrm{cm} \)
c. \( \frac{5 \pi}{36} c m \)
D. \( \frac{\pi}{7} c m \)


Name the enzyme which possibly acts as an ion carrier.


Innominate is a
A. A nerve
B. An artery
C. A vein
D. Part of skeleton and an artery


Differentiate between Distance and
Displacement.


A billiard ball, initially at rest, is given a
sharp impulse by cue. The cue is held
horizontally at a distance \( h \) above the
central line as shown in the figure. The
ball leaves the cue with a speed \( \boldsymbol{v}_{\mathbf{0}} . \) It
rolls and slides while moving forward
and eventually acquires a final speed
\( (9 / 7) v_{0} . \) If \( R \) is the radius of the ball,
then \( h \) is
\( A \cdot \frac{2 R}{5} \)
B. \( \frac{3 R}{5} \)
c. \( \frac{4 R}{5} \)
D. \( \frac{R}{5} \)


For zero order reaction, the integrated rate equation is:
A
B. \( k t=[A]-[A]_{o} \)
C \( \cdot[A]=-k t+[A]_{0} \)
\( \mathbf{D} \cdot[A]=k t-[A]_{o} \)


In the figure given below, if DE \( \| \mathrm{BC} \)
then the value of \( x \) equals to:
\( A \cdot 3 \mathrm{cm} \)
B. \( 2 \mathrm{cm} \)
\( c \cdot 4 \mathrm{cm} \)
D. \( 6.7 \mathrm{cm} \)


Which of the following are iso-electronic
species?
A. \( C O_{2}, N O_{2} \)
B. \( N O_{2}^{-}, C O_{2} \)
c. \( C N^{-}, C O \)
D. \( S O_{2}, C O_{2} \)


Pis a point inside \( \Delta A B C . \) If \( \angle P B A= \)
\( \mathbf{2 0}^{\circ}, \angle \boldsymbol{B} \boldsymbol{A} \boldsymbol{C}=\mathbf{5 0}^{\circ}, \) and \( \angle \boldsymbol{P C A}=\mathbf{3 5}^{\circ} \)
then the measure of \( \angle B P C \) is
\( 4 \cdot 65^{\circ} \)
B. \( 75^{\circ} \)
\( c \cdot 90 \)
D. 105


If
\( A D \) and \( \overline{B C} \) are parallel, then
calculate the value of \( x \)
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 70^{\circ} \)
\( c \cdot 80^{\circ} \)
D. 110


Blue green algae belongs to the kingdom Protista.
A . True
B. False


Due to deficiency of phosphorus.
A. The rate of protein synthesis is increased
B. The rate of protein synthesis is decreased
C. There is no effect on the rate of protein synthesis
D. The rate of protein synthesis initially declines but increases later on


A few drops of concentrated ammonia
solution added to a calcium
bicarbonate solution causes a white
precipitate. The precipitate formed is:
A \( \cdot C a C O_{3} \)
в. \( M g C O_{3} \)
\( \mathrm{c} \cdot K_{2} \mathrm{CO}_{3} \)
D. \( M g S O_{4} \)


\( \int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} d x \)


Fill in the blanks.
Nitrogen gas is used in high temperature


If two soap bubbles of different
radii are connected by a tube:
A. air flows from bigger bubble to the smaller bubble till sizes become equal
B. air flows from bigger bubble to the smaller bubble till sizes are interchanged
C . air flows from smaller bubble to bigger
D. there is no flow of air


A sphere of radius \( \boldsymbol{R} \) and mass \( \boldsymbol{M} \)
collides elastically with a cubical block
of mass \( M \) and side \( 2 R \). The entire
system is on a smooth horizontal
ground. Given that the sphere was rolling without slipping with an angular velocity \( \omega \) at the time of collision. The
velocities of the sphere and the block
after the collision are :
\( \mathbf{A} \cdot \omega_{\text {sphere}}=0, v_{\text {sphere}}=0, v_{\text {block}}=v \)
B. \( \omega_{\text {sphere}}=\omega, v_{\text {sphere}}=0, v_{\text {block}}=v \)
C. \( \omega_{\text {sphere}}=0, v_{\text {sphere}}=0, v_{\text {block}}=0 \)
D. \( \omega_{\text {sphere}}=\frac{\omega}{2}, v_{\text {sphere}}=\frac{v}{2}, v_{\text {block}}=\frac{v}{2} \)


Factorize the following \( 2 x^{2}-15 x+27 \)


Group 15 of the periodic table consists
of the elements \( N, P, A s, S b \) and \( B i \) On passing from \( \mathbf{N} \) to \( \mathrm{Bi} \), the oxides of the
elements of general formula \( \mathbf{M}_{2} \mathbf{O}_{3} \) becomes:
A. strong reducing agents
B. more ionic
c. more basic
D. more volatil


Which of the following halogens doesn't exhibit positive oxidation state in its compounds?
A \( . C l \)
в. \( B r \)
c. \( I \)
D. \( F \)


A sphere of radius \( 100 \mathrm{mm} \) shrinks to radius \( 98 \mathrm{mm} \), then the approximate decrease in its volume is
A. \( 12000 \pi m m^{3} \)
В. \( 800 \pi m m^{3} \)
c. \( 80000 \pi m m^{3} \)
D. \( 120 \pi m m^{3} \)


\( A-(A-B) \) is equivalent to which
expression
A. \( B \)
в. \( A \cup B \)
c. \( A \cap B \)
D. \( B-A \)


How many isosceles triangles are there
with \( 40^{\circ} \) as one of the three angles?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


A heater coil connected to a \( 220 \mathrm{V} \) has a
resistance of 150 oh \( m \). How long will it
take for this coil to heat \( 1 k g \) of water
from \( 20^{0} C \) to \( 60^{0} C \), assuming that all
heat is taken up by water.
A . 210 sec
B. 420 sec
\( c .520 \mathrm{sec} \)
D. None of these


Nessler's reagent on reaction with
ammonia gives ppt. having
number of mercury
atoms


Lines \( P Q \) and \( R S \) intersect at \( O \). If
\( \angle P O S=2 \angle S O Q \) then the four angles
at \( \boldsymbol{O} \) are
В. \( 60^{\circ}, 60^{\circ}, 120^{\circ}, 120^{\circ} \)
c. \( 60^{\circ}, 90^{\circ}, 90^{\circ}, 120^{\circ} \)
D. \( 30^{\circ}, 60^{\circ}, 90^{\circ}, 180^{\circ} \)


To prevent excess use of water from taps and tanks, we can collect water
from :
A . rain
B. streams
c. rivers
D. sea


What do you face when we make an \( \frac{3}{4} \)
revolution anti-clockwise from west?


With the help of a suitable example and
an equation, explain the term pair production


Equipotential surfaces associated with an electric field which is increasing in magnitude along the x-direction are:
A. Planes parallel to yz-plane
B. Planes parallel to xy-plane
c. Planes parallel to xz-plane
D. coaxial cylinders of increasing radii around
the x-axis


Find the least values of \( x \) and \( y \) which
satisfy the equations:
\( 77 y-30 x=295 \)
A . \( x=32, y=27 \)
в. \( x=21, y=34 \)
c. \( x=47, y=35 \)
D. \( x=46, y=32 \)


If \( \sqrt{1-x^{2}}+\sqrt{1-y^{2}}=a(x-y) \)
prove that \( \frac{d y}{d x}=\sqrt{\frac{1-y^{2}}{1-x^{2}}} \)


The second's hand of a watch has length
6cm. Speed of end point and magnitude
of difference of velocities at two
perpendicular positions will be:
A \( .2 \pi \& 0 \mathrm{mm} / \mathrm{s} \)
B. \( 2 \sqrt{2} \pi \& 44 \mathrm{mm} / \mathrm{s} \)
\( \mathbf{c} \cdot 2 \sqrt{2} \pi \& 2 \pi \mathrm{mm} / \)
D. \( 2 \pi \& 2 \sqrt{2} \pi \mathrm{mm} / \mathrm{s} \)


Solve: \( 1 \frac{1}{5} \times\left[\left(6 \frac{1}{3}-3 \frac{2}{5}\right) \div 4 \frac{2}{4}\right] \)


\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) is triprotic. Justify with
equations.


Which of the following is not the unit of time?
A. Leap year
B. Lunar month
c. Solar day
D. Parallactic second


Find the mean deviation about mean
and median for the following data.
\begin{tabular}{ccccc}
\multirow{2}{*} {\( \boldsymbol{C I} \)} & \( \mathbf{1}- \) & \( \mathbf{6}- \) & \( \mathbf{1 1}- \) & \( \mathbf{1 6}- \) \\
& \( \mathbf{5} \) & \( \mathbf{1 0} \) & \( \mathbf{1 5} \) & \( \mathbf{2 0} \)
\end{tabular}
\[
\begin{array}{l}
2 \\
2
\end{array}
\]


Draw the structure of xenon
hexafluoride \( \left(X e F_{6}\right) \) molecule and
state the hybridisation of the central
atom.


Arrange \( -\frac{5}{9}, \frac{7}{12},-\frac{2}{3} \) and \( \frac{11}{18} \) in
ascending order of their magnitudes, the difference between the
largest and the smallest of these
fractions is:


A simple harmonic oscillator of angular
frequency 2 rad \( s^{-1} \) is acted upon by an
external force \( F=\sin t N . \) If the
oscillator is at rest in its equilibrium position at \( t=0, \) its position at later times is proportional to
A \( \cdot \sin t+\frac{1}{2} \cos 2 t \)
B \cdot \( \operatorname{cost}-\frac{1}{2} \sin 2 t \)
\( \mathrm{c} \cdot \operatorname{sint}-\frac{1}{2} \sin 2 t \)
D. \( \sin t+\frac{1}{2} \sin 2 t \)


What are the main steps in aerobic
respiration? Where do they take place?


If in a nucleic acid there are more than
8000 nucleotides it is most likely
A. RNA
B. DNA
c. Both A and B
D. None of the above


Assertion
Secondary succession takes place in
recently denuded area.
Reason
It is caused due to baring of an area.
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.


An ideal monoatomic gas at \( 27^{\circ} \mathrm{C} \) is
compressed adiabatically to \( 8 / 27 \) times of its present volume. The increase in temperature of the gas is:
A \( .375^{\circ} \mathrm{C} \)
B . \( 402^{\circ} \mathrm{C} \)
c. \( 175^{\circ} \mathrm{C} \)
D. \( 475^{\circ} \mathrm{C} \)


When the tension in a metal wire is \( T_{1} \)
its length is \( l_{1}, \) when the tension is \( T_{2} \)
its length is \( l_{2} \). The natural length of
wire is :
A. \( T_{1} l_{1}+T_{2} l_{2} \)
в. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
\( \overbrace{\frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}+T_{1}}}^{\text {in }} \)
D. \( \frac{T_{2}}{T_{1}}\left(l_{1}+l_{2}\right) \)


A hemispherical bowl has inner
diameter \( 11.2 \mathrm{cm} . \) Find the volume of
milk it can hold.


Determine the domain and range of the following relation \( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a} \in \boldsymbol{N}, \boldsymbol{a}<\mathbf{5}, \boldsymbol{b}=\boldsymbol{4}\} \)


The Gibbs energy for the decomposition
of \( A l_{2} O_{3} \) at \( 500^{\circ} C \) is as follows:
\( \frac{2}{3} A l_{2} O_{3} \rightarrow \frac{4}{3} A l+O_{2} ; \triangle_{r} G= \)
\( +966 k J m o l^{-1} \)
The potential difference needed for the
electrolytic reduction of \( A l_{2} O_{3} \) at \( 500^{\circ} \)
is at least.
\( \mathbf{A} \cdot 2.5 V \)
в. \( 5.0 \mathrm{V} \)
c. \( 4.5 V \)
D. 3.0 \( V \)


The periodic vibrations of a body of decreasing amplitude in the presence of resistive force on it are called
A. Forced vibrations
B. Free vibration
c. Damped vibrations
D. All


Ephedrine is obtained by
A. Ephedra
c. Pinus
D. cycas


The time period of a seconds pendulum
\( (2 s) \) is measured repeatedly for three
times by two stop watches \( A \) and \( B \). If
the readings are as follows, then
\( \begin{array}{lll}\text { Sr. No. } & \text { A } & \text { B } \\ \text { 1. } & \text { 2.01sec } & \text { 2.56sec } \\ \text { 2. } & \text { 2.10sec } & \text { 2.55sec } \\ \text { 3. } & \text { 1.98sec } & \text { 2.57sec }\end{array} \)
A. A is more accurate but B is more precise.
B. B is more accurate but A is more precise.
C. A and B are equally precise.
D. A and B are equally accurate.


Find the number of ways of arranging six persons (having \( A, B, C \) and \( D \) among them) in a row so that \( A, B, C, \) and \( D \) are
always in order ABCD (not necessarily together)


Bag I contains 3 red and 4 black balls
and Bag II contains 4 red and 5 black
balls. Two balls are transferred at
random from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find
the probability that the transferred balls were both black


Jute fibres are
A. Sieve fibres
B. Xylem fibres
C. Phloem fibres
D. Mesocarp fibres of Coconut


The latent heat of vaporisation of a
substance is always:
A. greater than its latent heat of fusion
B. greater than its latent heat of sublimation
c. equal to its latent heat of sublimation
D. less than its latent heat of fusion


In graphite adjacent layers are separated by a distance of :
A . 3.35
B. 1.54
\( c \cdot 1.42 \)
D. 2.45


If \( |\vec{a}|=5, \mid \vec{b}=13 \) and \( |\vec{a} \times \vec{b}|=25 \), find
\( \vec{a} \cdot \vec{b} \)


Find the degree of the following polynomial
\( \boldsymbol{x}^{9}-\boldsymbol{x}^{4}+\boldsymbol{x}^{12}+\boldsymbol{x}-\boldsymbol{2} \)
A \( \cdot 12 \)
B.
\( c \cdot 4 \)
D.


Explain each of the following observations:
(i) water bottles are kept under water during summer.
(ii) a bottle of liquid ammonia is cooled
before opening the seal.
(iii) the size of weather balloon
becomes larger and larger as it ascends into higher altitudes.
(iv) tyres of automobiles are inflated to lesser pressure in summer than in winter.


If he has to continue breaking with the same constant retardation, how much
longer would it take for him to stop and
how much additional distance he
would cover?


The maximum value of \( \mathbf{V}_{0} \) for which the
disk will roll without slipping is
\( ^{4} \cdot \mu g \sqrt{\frac{M}{k}} \)
\( ^{3} \cdot \mu \mathrm{g} \sqrt{\frac{\mathrm{M}}{2 \mathrm{k}}} \)
\( ^{c} \cdot \operatorname{ag} \sqrt{\frac{3 M}{k}} \)
\( \mu_{g} \sqrt{\frac{5 \mathrm{M}}{2 \mathrm{k}}} \)


Following are four statements. Find out the correct combination.
. Glucose has high threshold value.
2. Urine is concentrated in Henles loop.
3. Haemodialyser removes urea, uric acid, glucose and proteins.
4. In glomerulus, urea, uric acid, water, glucose and plasma proteins are filtered out
\( \mathbf{A} \cdot 1,3,4 \)
в. 2,3,4
\( c .1,2 \)
D. 1,3


In an auto engine with no pollution
controls, about \( 5 \% \) of the fuel \( \left(C_{8} H_{18}\right) \)
is unburned. Molar ratio of \( C O \) and
\( \left(C_{8} H_{18}\right), \) emitted in the exhaust gas is:
A . 100
B. 152
\( c .50 \)
D. 5


Newton's law of gravitation holds good
for
A. only small bodies
B. only terrestrial bodies
c. only big bodies
D. all types of bodies


n which transition is a Balmer series
photon absorbed?
\( A \cdot I \)
3. II
\( c_{1} \)
D \( V \)


f \( ,(x-1, y+2)=(7,5) \) then values of
\( x \) and \( y \) are
A . 5,8
в. 8,3
c. -1,5
D. 7,1


In the presence of concentrated
sulphuric acid \( \left(\boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}\right), \) acetic acid
reacts with ethyl alcohol to produce :
A. aldehyde
B. alcohol
\( c . \) ester
D. carboxylic acid


Catalysts which increase rate of a reaction are called
catalyst.


Which of the following is paramagnetic as well as coloured ion?
A \( \cdot C u^{+} \)
в. \( C u^{2} \)
\( c \cdot S c^{3} \)
D. \( T i^{4} \)


A capacitor is formed by two square
metal-plates of edge \( \alpha_{1} \) separated by a
distance \( d \). Dielectrics of dielectric
constants \( K_{1} \) and \( K_{2} \) are filled in the
gap as shown figure. Find the
capacitance.


On heating,ammonium nitrate decomposes into:
A. \( N H_{3} \) and \( H N O_{3} \)
B. Nitrous oxide and water
c. \( N, H \) and \( O_{3} \)
D. Nitric oxide, \( N O_{2} \) and \( H_{2} \)


The number of elements of an identity
function defined on a set containing
four elements is
A \( \cdot 2^{2} \)
B. \( 2^{4} \)
\( c \cdot 2^{8} \)
D. \( 2^{16} \)


Nitrogen reacts with a metal \( M \) to
produce a compound \( X . \) This compound
\( X, \) when dissolved in water forms
pungent gas \( Y \) which can be identified
easily by the formation of white fumes in the presence of \( \boldsymbol{H} \boldsymbol{C l} \)
Identify \( \boldsymbol{Y} \)
A. Nitrogen dioxide
B. Ammonia
c. Nitrous oxide
D. Nitric oxide


An equilibrium mixture of \( \boldsymbol{P C l}_{5}, \boldsymbol{P C l}_{3} \)
and \( C l_{2} \) at a certain temperature
contains \( 0.5 \times 10^{-3} M P C L_{5} 1.5 \times \)
\( \mathbf{1 0}^{-2} \boldsymbol{M} \boldsymbol{P C L}_{3} \) and \( \boldsymbol{3} \times \mathbf{1 0}^{-\mathbf{2}} \boldsymbol{M} \boldsymbol{C l}_{2} \)
Calculate the equilibrium constant \( \boldsymbol{K}_{c} \)
for the reaction \( \boldsymbol{P} \boldsymbol{C} \boldsymbol{L}_{5}(\boldsymbol{g}) \rightleftharpoons \)
\( \boldsymbol{P C l}_{3}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)


Draw \( 1^{\circ} \) alcohol with the empirical
formula \( C_{4} H_{8} O \) is/are:


The young's duble slit experiment is performed with blue and green light of wavelength \( 4360 \AA \) and \( 5460 \dot{A} \)
respectively. if \( x \) is the distance of \( 4 t h \) maxima from central one, then
A. \( x(b l u e)=x(g \text { reen }) \)
в. \( x(b l u e)>x(\text { green }) \)
c. \( x(b l u e)<x(\text { gree } n) \)
D. \( \frac{x(b l u e)}{x(g r e e n)}=\frac{5460}{4360} \)


Two identical particles of mass \( m \) carry
charge \( Q \) each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large
distance with speed \( v \). The closest
distance of approach will be
A \( \cdot \frac{1}{4 \pi \varepsilon_{0}} \frac{Q^{2}}{m v} \)
B. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{4 Q^{2}}{m v} \)
\( ^{\mathbf{C}} \frac{1}{4 \pi \varepsilon_{0}} \frac{4 Q^{2}}{m v^{2}} \)
\( ^{\mathrm{D}} \frac{1}{4 \pi \varepsilon_{0}} \frac{2 Q^{2}}{m v^{2}} \)


(a) Define potential gradient.
(b) Write Kirchhoff's junction rule.
In the given diagram write the value of
current \( \boldsymbol{I} \)


In the shown figure, there are four point
charges each with a charge of \( +\mathrm{Q} \) and
situated at the four corners of a square
with a side of length \( \mathrm{D} \) What is the electric potential at the
center of the square? (k is the coulomb constant)
A \( \cdot \frac{4 k Q}{D} \)
B.
c.
D.
\( E \)


If the radii of two bubbles are \( \boldsymbol{R}_{1} \) and \( \boldsymbol{R}_{2} \)
then the ratio of respective masses of
air in them will be:
A \( \cdot \frac{R_{1}}{R_{2}} \)
в. \( \frac{R_{2}}{R_{1}} \)
\( ^{\mathbf{c}} \cdot \frac{P_{o}+\frac{4 T}{R_{1}}}{P_{o}+\frac{4 T}{R_{2}}} \)
\( ^{\mathrm{D}} \cdot \frac{P_{o}+\frac{4 T}{R_{1}}}{P_{o}+\frac{4 T}{R_{2}}}\left(\frac{R_{1}}{R_{2}}\right)^{3} \)


The number of structural isomers for
\( C_{6} H_{14} \) is :
\( A \cdot 4 \)
B. 5
\( c \cdot 6 \)
D.


A particle is projected vertically upwards from a point \( A \) on the ground. It \( \operatorname{takes} t_{1} \) time to reach a point \( B \) but it still continues to move up. If it takes
further \( t_{2} \) time to reach the ground from point B then height of point B from the
ground is
A \( \cdot \frac{1}{2} g\left(t_{1}+t_{2}\right)^{2} \)
B. \( g t_{1} t_{2} \)
c. \( \frac{1}{8} g\left(t_{1}+t_{2}\right)^{2} \)
D. \( \frac{1}{2} g t_{1} t_{2} \)


Describe the role of liver, lungs and skin in excretion.


Fill in the blank.
In the given distance-time graph, speed
from \( C \) to \( D \)
A . increases
B. decreases
C. remains same
D. can't predict


if \( z_{1}=3+7 i \) then \( \left|z_{1}\right| \) is
A \( \cdot \sqrt{28} \)
B. \( \sqrt{58} \)
\( c \cdot \sqrt{68} \)
D. none of these


Chromium and manganese oxides are reduced to metals by using:
A. aluminium
B. iron
c. silver
D. chromium


The base of a cylindrical vessel
measures \( 300 \mathrm{cm}^{2} \), water is poured into
it up to a depth of \( 6 \mathrm{cm} \). Calculate the pressure of water on the base of the
vessel. \( \left(\mathrm{g}=10 \mathrm{m} / \mathrm{s}^{2} ; \text { density of water }=\right. \)
\( 1000 k g / m^{3} \)


Read the following table and answer the
following questions.
sı. Structure Location
No.
1
Tricuspid Right auriculoriculo-
lar aperture valve
2
Guard cells \( \quad \) Epidermis of leaves
3. Glomerulus Nephron
4. Alveoli
5
Acrosome Above the head of a
sperm
Name the part performing Excretion.


What is the importance of resonance with respect to the \( C O_{3}^{2-} \) ion?


Dissolution of ammonium chloride in
water is an endothermic reaction, yet it is a spontaneous process. This is due to the fact that:
A. \( \Delta H \) is \( +v e, \Delta s \) is -ve
B. \( \Delta H \) is -ve, \( \Delta \) s is tve
c. \( \Delta \) H is \( + \) ve, \( \Delta \) s is \( + \) ve and \( \Delta \) H \( < \) T \( \Delta \) s
D. \( \Delta \) H is \( + \) ve and \( \Delta \) H \( > \) T \( \Delta \) ss


In a laminar flow at a given point the magnitude and direction of the velocity of the fluid:
A. both are constant
B. magnitude is only constant
c. direction is only constant
D. both are not constant


Ethyl alcohol containing \( 9.5 \% \) methyl alcohol land \( 0.5 \% \) pyridine is called :
B. denaturated spirit
c. rectified spirit
D. absolute alcohol


Find the value of \( : \cot ^{2} C-\frac{1}{\sin ^{2} C} \)
\( A \ldots \)
B
\( r \)


Pentane with molecular formula \( C_{5} H_{12} \)
contains:
A. 5 covalent bonds
B. 12 covalent bonds
c. 16 covalent bonds
D. 17 covalent bonds


For what value of \( k \) will the quadratic
equation: \( k x^{2}+4 x+1=0 \) have real
and equal roots?
A .2
B. 3
\( c \cdot 4 \)
\( D \)


A mixture of oxygen and ethyne is burnt for welding. Why a mixture of ethyne and air is not used?
A. ethene can not burn in air
B. incomplete combustion takes place
c. ethene burn in air with explosion
D. none of these


The ratio of the number of trucks along a highway, on which a petrol pump is located, to the number of cars running along the same highway is 3: 2 . It is known that an average of one truck in thirty trucks and two cars in fifty cars
stop at the petrol pump to be filled up with the fuel. If a vehicle stops at the petrol pump to be filled up with the fuel, find the probability that it is a car
\( A \cdot \frac{4}{9} \)
в. \( \frac{9}{250} \)
\( c \cdot \frac{3}{5} \)
D. \( \frac{1}{30} \)


Following are the thermochemical
reactions:
\( \boldsymbol{H}_{2}+\frac{1}{2} \boldsymbol{O}_{2} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O} ; \boldsymbol{\Delta} \boldsymbol{H}=-\boldsymbol{6} \boldsymbol{8} . \boldsymbol{3} \boldsymbol{9} \)
kcal/mol
\( \boldsymbol{K}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{q})+ \)
\( \frac{1}{2} H_{2} ; \Delta H=-48.0 \mathrm{kcal} / \mathrm{mol} \)
\( K O H+H_{2} O \rightarrow K O H(a q) ; \Delta H= \)
\( -14.0 \mathrm{kcal} / \mathrm{mol} \)
The heat of formation (in kcal/mol) of
KOH is:
A. \( -68.39+48-14.0 \)
B. \( -68.39-48.0+14.0 \)
c. \( +68.39-48.0+14 . \)
D. \( +68.39+48.0-14.0 \)


A vessel contains a gas under a pressure of \( 5 \times 10^{5} \) pa. If \( \frac{3}{5} \) of the mass of the gas is
flown out,What will be the gas pressure if
the temperature being maintained constant.
A. 50 MPa
B. 2MPa
c. о.२мРа
D. 0.5MPa


f \( 2 \tan ^{-1} x=\cos ^{-1}(3 / \sqrt{13}) \) then the
value of \( 60 x^{4}-540 x^{2}+360 x+9261 \)
is equal to


The refractive index of a certain flint
glass is \( 1.65 . \) Incident angle is the light reflected from the surface of the glass
completely polarized if the glass is immersed in (a) air and (b) water is
\( \left(\tan 58.8^{\circ}=1.65\right)\left(\tan 51.1^{\circ}=1.24\right) \)
A. \( 60^{\circ}, 50^{\circ} \)
B. 58.8', 51.1 \( ^{\circ} \)
\( c \cdot 65^{\circ}, 52^{\circ} \)
D. \( 61^{\circ}, 54^{\circ} \)


Identify the waves with the largest
wavelengths.
A. Radio
B. Gamma Rays
c. x-Rays
D. Visible Light
E. Infrared Radiation


An electric dipole consists of two
oppositecharges of magnitude \( 1 \mu \mathrm{C} \)
separated by a distanceof 2cm. The dipole is placed in an electric filed
\( 10^{-5} \mathrm{Vm}^{-1} . \) The maximum torque does
the field exerton the dipole is
\( \mathbf{A} \cdot 10^{-3} \mathrm{Nm} \)
В. \( 2 \times 10^{-13} \mathrm{Nm} \)
c. \( 3 \times 10^{-13} \mathrm{Nm} \)
D. \( 4 \times 10^{-13} \mathrm{Nm} \)


A convex mirror of focal length \( f \) forms
an image which is \( \frac{1}{n} \) times the object. The distance of the object from the mirror is :
\( ^{\mathbf{A}} \cdot\left(\frac{n-1}{n}\right) f \)
\( ^{\mathbf{B}} \cdot\left(\frac{n+1}{n}\right) f \)
\( \mathbf{c} \cdot(n+1) f \)
D. \( (n-1) f \)


If \( \boldsymbol{x} \geq \mathbf{0} \)
\( 3 y-2 x \geq-12 \)
\( 2 x+5 y \leq 20 \)
The area of the triangle formed in the \( x y \) plane by the system of inequalities above is:
\( \mathbf{A} \cdot 60 \)
B . 30
c. 40
D. 50


Show that \( \sin ^{-1}(2 x \sqrt{1-x^{2}})=2 \sin ^{-1} x \)
for \( \frac{-1}{\sqrt{2}} \leq x \leq \frac{1}{\sqrt{2}} \)


If \( 3- \) hexanone is reacted with
\( N a B H_{4} \) followed by hydrolysis with
\( D_{2} O, \) the product will be :
\( \mathbf{A} \cdot C H_{3} C H_{2} C H(O H) C H_{2} C H_{2} C H_{3} \)
B. \( C H_{3} C H_{2} C D(O H) C H_{2} C H_{2} C H_{3} \)
c. \( C H_{3} C H_{2} C H(O D) C H_{2} C H_{2} C H_{3} \)
D. \( C H_{3} C H_{2} C D(O D) C H_{2} C H_{2} C H_{3} \)


A student measures the level of
radiation emitted by a radioactive
sample.

The table shows the readings she
records on the counter over a short
period of time.
Counter
reading/
\( \mathbf{9 6} \)
98
counts per minute
The sample is removed and the counter
then shows a background radiation
reading of 4 counts per minute.
What is the best estimate for the
average count rate due to the
radioactive sample?
A. 96 counts per minute
B. 98 counts per minute
C . 100 counts per minute
D. 104 counts per minute


\( 1+\cos 56^{\circ}+\cos 58^{\circ}-\cos 66^{\circ}= \)
\( m \cos 28^{\circ} \cos 29^{\circ} \sin 33^{\circ} . \) Find \( m \)


Point out the wrong statement about the magnetic properties of soft iron and
steel
A. Retentivity of soft iron is more than retentivity of stee
B. Coercivity of soft iron is less than coercivity of steel
c. Area of B-H loop in soft iron is smaller than the area of B-H loop for steel
D. Area of B-H loop in soft iron is greater than the area of B-H loop for steel


Which set contains no ionic species?
A. \( N H_{4} C l, O F_{2}, H_{2} S \)
в. \( C O_{2}, C C l_{4}, C l_{2} \)
c. \( B F_{3}, A l F_{3}, T l F_{3} \)
D. \( I_{2}, C a O, C H_{3} C l \)


For making standard resistance, wire of following material is used
A. Nichrome
B. Copper
c. silver
D. Manganin


As the decimal of \( \frac{1}{3} \) repeats, \( \frac{1}{3} \) is a
decimal.
A. exact
B. negative
c. terminating
D. non-terminating


Assertion
A solution of sucrose in water is
dextrorotatory but on hydrolysis in the presence of \( \boldsymbol{H} \oplus \),it becomes
leavorotatory.
Reason
Inversion of sugar follows first order
kinetics.
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


Greatest possible difference between two of the roots if \( \boldsymbol{\theta} \boldsymbol{\epsilon}[\mathbf{0}, \boldsymbol{2} \boldsymbol{\pi}] \) is
A . 2
B.
\( c \cdot \sqrt{2} \)
D. \( 2 \sqrt{2} \)


Compression and rarefaction are seen
in
A. Transverse waves
B. Non mechanical waves
c. Longitudinal waves
D. None


There is a stream of neutrons with a
kinetic energy of \( 0.0327 e V \). If the halflife of neutron is \( 700 s, \) if \( \frac{x}{1000} \) fraction of neutrons will decay before they travel a distance 3 of \( 10 k m . \) Find \( x \)


Name an animal that stays in water like
fish but has no gills to breathe in water.
It gives birth to babies like the tiger does, but does not live in the forest.


The ease of adsorption of the hydrated alkali metal ions on an ion-exchange resins fallows the order:
\( \begin{array}{llllll}\mathbf{c} \cdot L i^{+} & < & K^{+} & + & N a^{+} & < & R b^{+}\end{array} \)


A bag contains 10 white, 5 black, 3
green and 2 red balls. One ball is drawn
at random. Find the probability that the ball drawn is white or black or green


In the given figure a block of weight
\( 10 N \) is resting on a horizontal surface.
The coefficient of static friction
between the block and the surface is
\( \mu_{s}=0.4 . \) A force of \( 3.5 N \) will keep the
block in uniform motion, once it has
been set in motion. A horizontal force of
\( \mathbf{3} N \) is applied to the block, then the
block will
A. move over the surface with constant velocity
B. move having accelerated motion over the surface.
c. will not move.
D. first it will move with a constant velocity for some time and then it will have an accelerated motion


The sum of two numbers is \( 2 \frac{1}{6} . \) An even number of arithmetic means are being inserted between them and their sum
exceeds their number by 1. Find the number of means inserted.


In a triangle \( A B C, D \) divides BC in the ratio 3: 2 and \( E \) divides \( C A \) in the ratio 1:
3. The lines \( A D \) and \( B E \) meet at \( H \) and \( C H \)
meets \( A B \) in \( F \). Find the ratio in which \( F \)
divides AB.
A. \( A F: F B=2: 1 \)
B. \( A F: F B=1: 2 \)
c. \( A F: F B=2: 3 \)
D. \( A F: F B=3: 2 \)


Find the truth value of 14 is a
composite number or 15 is a prime no.


Factorize:
\( x^{2}+14 x+33 \)


State the two Kirchhoff's laws. Explain briefly, how these rules are justified?


\( A \stackrel{K_{1}}{\longrightarrow} B \stackrel{K_{2}}{\longrightarrow} C, \) if all reaction are 1st
order and \( \frac{\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d}[\boldsymbol{t}]}=\mathbf{0 .} \) Determine \( [\boldsymbol{B}] \)
A \( \cdot\left(K_{1}+K_{2}\right)[A] \)
B . \( \left(K_{1}-K_{2}\right)[A] \)
c. \( \left(K_{1} \times K_{2}\right)[A \)
\( ^{\mathrm{D}} \cdot \frac{K_{1}}{K_{2}} \times[A] \)


Two identical billiard balls are throum
against a rigid ball and are reflected
back with the same speed. The \( 1^{s t} \) ball
is thown normal to the wall, whereas the
second ball is thrown at an angle of \( 30^{\circ} \)
to the wall. Find the ratio of the impulse of the 2 balls.


\( \boldsymbol{p} \boldsymbol{H} \) of \( \boldsymbol{B} \boldsymbol{a}(\boldsymbol{O} \boldsymbol{H})_{2} \) solution is \( 12 . \) Its
solubility product is:
A \( \cdot 10^{-6} \)
В. \( 4 \times 10^{-6} \)
c \( .5 \times 10^{-7} \)
D. \( 5 \times 10^{-6} \)


One horse power is equal to
A . \( 1000 \mathrm{W} \)
B. \( 500 W \)
c. \( 764 W \)
D. \( 746 W \)


How is sex determined in human
beings?


Let \( a_{n} \) be an A.P. for which \( d=8 \) and
\( a_{2}=12 . \) Find \( a_{1} \)
A . 1
B. 4
\( c .3 \)
D. 2


According to Maxwell, most of the optical properties of light depend on
A. Magnetic vector
B. Electric vector
c. Both Electric and Magnetic vectors
D. can not be decided


In an unbiased \( p-n \) junction
A. Potential at \( p \) is more than that at \( n \)
B. Potential at \( p \) is less than that at \( n \)
C. Potential at \( p \) is equal to that at \( n \)
D. Potential at \( p \) is +ve and that at \( n \) is -ve


When n number identical cell of emf \( \mathrm{E} \)
and internal resistance is connected in
series, the net internal resistance of the system will be
A \( \cdot \frac{n E r}{1+E} \)
B \( \cdot n^{2} r \)
\( c \cdot n r \)
D. \( n / r \)


Which of the following names of the
organic compounds is not correctly
written?
\( \mathbf{A} \)
B.
\( c \)
ethana
D.


When we take acetone in a test tube it
feels cold. Which reaction occurs in the
process?
A. endothermic reaction
B. exothermic reaction
c. reversible process
D. adiabatic process


Find the solution of the inequality
\( 3(1-x)<2(x+4) \) and draw on the
number line.


Two identical capacitors are connected in series with a source of potential V. If \( \mathrm{Q} \) is the charge on one of the capacitors, the capacitance of each capacitor is:
A \( \cdot \) Q/2
B. 2Q/V
c. \( \mathrm{Q} / \mathrm{v} \)
D. None of these


A solid cylinder is rolling down on an inclined plane of angle \( \theta . \) The coefficient of static friction between the plane and
the cylinder is \( \mu_{s} \). The condition for the
cylinder not to slip is
A \( \cdot \tan \theta \geq 3 \mu_{s} \)
B \( \cdot \tan \theta>3 \mu_{s} \)
c. \( \tan \theta \leq 3 \mu_{s} \)
\( \mathbf{D} \cdot \tan \theta<3 \mu_{s} \)


\( P \) and \( Q \) are two unlike magnetic poles
Induction due to \( P \) at the location of \( Q \) is
B, and induction due to \( Q \) at the location
of \( \mathrm{P} \) is \( \frac{B}{2} \). The ratio of pole strengths of \( \mathrm{P} \) and \( Q \) is
A . 1:
B. 1: 2
c. 2: 1
D. \( 1: \sqrt{2} \)


Write the names of isotopes of hydrogen.What is the mass ratio of these isotopes?


Expansion of \( (\boldsymbol{y}+\boldsymbol{x})^{n} \) is


In the living tissues 'energy broker' or intermediary source of energy compound formed during glucose oxidation is
A. NAD
B. DNA
c. RNA
D. ATP


A motorcycle originally cost Rs. 40,000 Its cost has decreased by \( 22 \% . \) What is its cost now.


If \( f(x)=x^{2}+9 \) and \( g(x)=24+4 x \)
what is the value of \( \frac{f(4)}{g(-1)} ? \)
A . 0.75
B. 0.8
c. 1.2
D. 1.25
E . 1.75


Spectroscopy is:
A. the study of heat changes in a chemical reaction.
B. the use of the absorption, emission, or scattering of electromagnetic radiation by matter to study the matter or the chemical processes it undergoes.
C. the mathematical description of the motion and interaction of subatomic particles. It incorporates quantization of energy, wave-particle duality, the uncertainty principle, and their relationship to chemical processes.
D. none of the above


Which of the following is not a chloride mineral?
A. Rock salt
B. sylvine
c. carnallite
D. None of the above


Why \( H C l \) gas forms a mist of droplets
of \( H C l \) acid in moist air?
A. \( H C l \) gas is less reactive and it is highly soluble in water to form hydrochloric acid
B. HCl gas is very reactive and it is highly soluble in water to form hydrochloric acid
c. \( H C l \) gas is very reactive and it is less soluble in water to form hydrochloric acid
D. \( H C l \) gas is less reactive and it is less soluble in water to form hydrochloric acid


The mean free path of a molecule of He
gas is a its mean free path along any arbitary coordinate axis will be.


The following are some statements about oxyac-ids of \( \mathbf{V} \) Ag roup elements
i) The salt of Nitric acid contains \( \mathbf{N O}_{3^{-}} \)
ion
ii) The salt of phosphoric acid contains \( \mathbf{P} \mathrm{O}_{4}^{3-} \) ion
iii) Salts of meta phosphoric acid contains \( \mathbf{H}_{\mathbf{2}} \mathbf{P} \mathbf{O}_{\mathbf{3}-} \mathbf{8} \mathbf{H} \mathbf{P} \mathbf{O}_{\mathbf{3}}^{\mathbf{2 -}} \) ions
The correct combination is :
A. i and ii are correct
B. ii and iii are correct
c. all are correct
D. only ii is correct


Identify the contour lines along which the dip measured at the Earth's surface
is equal in magnitude.
A. Aclinic lines
B. Isoclinic lines
c. Isogonic lines
D. Agonic lines


The chelating ligand used to remove excess of copper and iron in chelate therapy is:
A. D-penicill amine
B. oxalate ion
c. EDTA
D. ethylenediamine
E. dimanyl glyoxime


Three iron pieces \( A, B, C \) are taken. \( B \) is coated with zinc and the coating is
worn away partially. \( C \) is coated with tin
and the coating is worn away partially. Explain the rate at which \( \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{C} \)
undergo rusting on exposure to air. Give
reason.


The function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a} \boldsymbol{x}+\boldsymbol{b} \) is strictly
increasing for all real \( \boldsymbol{x} \), if
\( \mathbf{A} \cdot a>0 \)
B. \( a<0 \)
\( \mathbf{c} \cdot a=0 \)
D. \( a \leq 0 \)


Artificial satellites revolve around:
A. Moon
B. Sun
c. Earth
D. stars


The molecular formula of \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{2} \)
represents which oxoacid among the following?
A. Hydrosulphurous acid
B. Thiosulphurous acid
c. sulphuric acid
D. Pyrosolphurous acid


Q Type your question
\( A \)
\( B \)
\( c \)
ect presenta


Two wires, one of copper and other of
steel of equal length are suspended by the given load. The area of cross section of copper is twice that of steel. What will
be the ratio of the stress in copper to steel wires
\( A \cdot 2 \)
B. 4
\( c .0 .25 \)
D. 0.5


Chloramphenicol is:
A. Broad spectrum antibiotic
B. Narrow spectrum antibiotic
C . limited spectrum antibiotic
D. It is a antiseptic


A block of mass 10 kg placed on rough horizontal surface having coefficient of friction \( =0.5, \) if a
horizontal force of \( 100 \mathrm{N} \) acting on it then acceleration of the block will be :
\( A \cdot 10 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 5 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathrm{c} \cdot 15 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 0.5 \mathrm{m} / \mathrm{s}^{2} \)


A point charge \( q \) is kept at a distance of 2R from centre of an uncharged spherical shell of radius R. The potential at centre of the shell due to charges induced on shell is
A \( \cdot \frac{q}{4 \pi E_{0} R} \)
В \( \cdot \frac{q}{4 \pi E_{0} 2 R} \)
c. \( \frac{-q}{4 \pi E_{0} R} \)
D. zero


Differentiate the following function with
respect to \( x \)
\( \left(2 x^{2}-3\right) \sin x \)
A \( \cdot 4 x \sin x-\left(2 x^{2}-3\right) \cos x \)
B. \( 4 x \sin x+\left(2 x^{2}+3\right) \cos x \)
c. \( 4 x \sin x+\left(2 x^{2}-3\right) \cos x \)
D. None of the above


The actual frequency is
A. \( 5.645 \mathrm{Hz} \)
B. 7.685 Hz
c. \( 2.965 \mathrm{Hz} \)
D. 3.785 Нz


An Ap consists of 50 terms of which 3 rd
term is 12 and the last term is \( 106 . \) Find
the 29 th term.


In xerophytes, the presence of thick cuticle, scales and few sunken stomata
on the leaf is to
A. Stop transpiration
B. Protect from light
c. Facilitate transpiration
D. Reduce transpiration


Which reaction occurs in blast furnace
at \( 1270 K \) temperature?
\( A \cdot 3 F e_{2} O_{3}+C O \rightarrow \)
в. \( F e_{3} O_{4}+C O \)
c. \( F e_{2} O_{3}+C O \rightarrow \)
D. \( F e O+C O \rightarrow \)


Write the Rutherford - Soddi law of ratio
active decay and draw decay curve.


Among the following which one shows
that the total pressure of a mixture of gases is equal to the sum of the partial pressure of the component gases.
A. \( \vee / T=k \)
B. Р/T=k
c. \( P V=k \)
D. \( P_{T}=P_{1}+P_{2}+P_{3} \)
E . PT=k


By dissolving 13.6 g of a substance in 20 \( g \) of water, the freezing point decreased
by \( 3.7^{\circ} \mathrm{C} \). Calculate the molecular mass
of the substance.
(Molal depression constant for water = \( 1.863 \mathrm{K} \mathrm{kg} \mathrm{mol}^{-1} \) )


The element californium belongs to a
family of :
A. actinide series
B. alkali metal family
c. alkaline earth family
D. lanthanide series


When Amrita was asked to pick up a few articles from a collection, she picked up the following:
A wooden scale, a glass test tube, and a paper basket. Which article is she most likely to pick
up next?
A. Steel cup
B. Iron chain
c. Rubber gloves
D. copper wire


The number of ATP molecules formed
during aerobic respiration in the break down of one glucose molecule via the malate-aspartate shuttle is
A. 38
B. 18
\( c \cdot 28 \)
\( D \cdot 4 \)


The electromagnetic waves travel with a velocity
A. equal to velocity of sound.
B. equal to velocity of light
c. less than velocity of light
D. None of the above


The northern blot technique is used for the detection of
A. Protein
B. DNA
c. RNA
D. All of the above


Classify the following as linear, quadratic and cubic polynomials:
\( \boldsymbol{x}^{\boldsymbol{3}}-\boldsymbol{4} \)
A. Cubic
B. Linear
c. Quadratic
D. None of the above


A point object is placed at a distance of
\( 25 \mathrm{cm} \) from a convex lens of focal length
\( 20 \mathrm{cm} . \) If a glass slab of thickness \( t \) and
refractive index 1.5 is inserted between
the lens and the object, the image is formed at infinity. The thickness \( t \) is
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
в. \( 5 \mathrm{cm} \)
\( \mathbf{c} \cdot 20 c m \)
D. \( 15 \mathrm{cm} \)


A beam of light has three \( \lambda \) \( 4144 A, 4972 A \) and \( 6216 A \) with a total intensity of \( 3.6 \times 10^{-3} W m^{-2} \) equally
distributed amongst the three \( \lambda \). The
beam falls normally on an area \( 1.0 \mathrm{cm}^{2} \) of a clean metallic surface of work
function \( 2.3 e V . \) Assume that there is
no loss of light by reflection etc. Calculate the no. of photoelectrons emitted in 2 sec.


Solve the following equation
\( 7 y=77 \)


Write any two uses of \( 40 \% \) solution of
formaldehyde.


From the following substances, which carbohydrates has the maximum
sweetness?
A. sucrolose
B. Saccharin
c. Aspartme
D. Alitame


Match the column


Two similar p-njunctions can be connected in three different ways as
shown in the figures. The two connections across which the potential
difference is same are
\( a) \)
\( b) \)
\( c \)
A. circuits a and b
B. circuits b and c
C. circuits a and c
D. all the circuits


Find the age of an object that has been excavated and found to have \( 90 \% \) of its
original amount of radioactive Carbon
14
A. 378 years old
B. 248 years old
c. 878 years old
D. None of these


The components of a vector along the \( x \) and \( y \) -directions are \( (n+1) \) and 1
respectively. If the coordinate system is
rotated by an angle \( \theta=60^{\circ} \), then the
components change to \( n \) and \( 3 . \) The
value of \( n \) is
A .2
B. \( 1+\sqrt{3} \)
\( c \cdot 1-\sqrt{3} \)
D. \( 1 \pm \sqrt{3} \)


The gravitational potential energy of a body is \( _{-}--_{-}-_{-}- \) to its height above
the surface of the Earth.
A. directly proportional
B. indirectly proportional
c. independent
D. none


Divide and write the quotient and
remainder:
\( \left(4 x^{4}-5 x^{3}+0 x^{2}-7 x+1\right) \div(4 x-1) \)


Which of the following equation is a linear differential equation of order 3 ?
[Note: The original question asks for linear equation, but it should be linear differential equation]
A \( \cdot \frac{d^{3} y}{d x^{3}}+\frac{d^{2} y}{d x^{2}} \frac{d y}{d x}+y=x \)
B. \( \frac{d^{3} y}{d x^{3}}+\frac{d^{2} y}{d x^{2}}+y^{2}=x^{2} \)
c. \( \quad x \frac{d^{3} y}{d x^{3}}+\frac{d^{2} y}{d x^{2}}=e^{x} \)
D. \( \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=\log x \)


For the propagation of electromagnetic
waves
A. Medium is required
B. no medium is required
c. \( E \) and \( B \) are in mutually opposite phase
D. E and b do not contriute


The mode of nutrition in green plants is called
A. Heterotrophic
B. Holozoic
c. Autotrophic
D. Saprophytic


For the equation given below, find the the slope and the y-intercept \( : 3 y=7 \)
A \( \cdot 0 \) and \( \frac{7}{3} \)
B. \( _{0} \) and \( -\frac{7}{3} \)
c. \( -\frac{7}{3} \) and 0
D. \( \frac{7}{3} \) and 0


The total Kinetic energy of 1 mole of \( N_{2} \)
at \( 27^{\circ} C \) will be approximately :-
A . \( 1500 J \)
B . 15633 cal
c. \( 1500 \mathrm{kcal} \)
D. 1500 erg


There are two balls in an urn whose
colours are not known (each ball can be
either white or black). A white ball is put
into the urn. A ball is drawn from the
urn. The probability that it is white is
A . \( 1 / 4 \)
в. \( 1 / 3 \)
\( c \cdot 2 / 3 \)
D. \( 1 / 6 \)


Why is an air-conditioner normally
installed at the height in a room?


In \( 1938, \) Max Perutz a political refugee at Cambridge University published Xray photograph crystal data for \( \ldots \ldots . . . . \) and proteins.
A. Haemoglobin and pepsin
B. Pepsin and papain
c. Myoglobin and haemoglobin
D. Immunoglobulin and haemoglobin


\( \ln a \Delta A B C, \) prove that
\( (a) \cos (A+B)+\cos C=0 \)
(b) \( \tan \frac{(A+B)}{2}=\cot \frac{C}{2} \)


Activation energy of a chemical reaction can be determined by
temperature
B. determining the rate constants at two temperatures
c. determining probability of collision
D. using catalyst


Give reasons:
The sun appears reddish early in the morning.


Calculate the energy required for the
process:
\( \boldsymbol{H} \boldsymbol{e}^{+}(\boldsymbol{g}) \rightarrow \boldsymbol{H} \boldsymbol{e}^{2+}(\boldsymbol{g})+\boldsymbol{e}^{-} \)
If the ionisation energy for the H atom in the ground state is \( 2.18 \times 10^{-18} \)
J/atom.


The area of the parallelogram with vertices (0,0),(2,3),(-2,3) and (-4,0) is
A . 10
B. 12
\( c \cdot 13 \)
\( D \cdot 16 \)


What is the molarity of pure water?


Two regular polygons are such that the ratio between their number of sides is
1: 2 and the ratio of measure of their
interior angles is \( 3: 4 . \) The number of
sides of each polygon is
A . 5,10
B. 6, 12
c. 4,8
D. 2,3


Find the midpoint of the segment joining the points (4,-2) and (-8,6)
A \( \cdot(6,4) \)
в. (-6,-4)
D. (-2,2)


I: A straight line is such that the algebraic sum of the distance from any no. of fixed points is zero. Then that line always passes through a fixed point
II: The base of the triangle lie along the line \( x=a \) and is of length \( a \).If the area
of the triangle is \( a^{2} \) then the third vertex
lies on \( x=-a \) or \( x=3 a \)
Then which of the following is true.
A. only I
B. only II
c. both 18 ॥
D. neither I nor II


A tennis ball and an iron ball is thrown
towards us with the same velocity. Then, the tennis ball is easy to catch as compared to an iron ball.
A. True
B. False


If the equations \( 4 x+7 y=10 \) and
\( 10 x+k y=25 \) represent coincident
lines, then the value of \( k \) is
A . 5
в. \( \frac{17}{2} \)
c. \( \frac{27}{2} \)
D. \( \frac{35}{2} \)


In the following reaction \( ; x A \rightarrow y B \) \( \log _{10}\left[-\frac{\boldsymbol{d}[\boldsymbol{A}]}{\boldsymbol{d} \boldsymbol{t}}\right]=\log _{10}\left[\frac{\boldsymbol{d}[\boldsymbol{B}]}{\boldsymbol{d} \boldsymbol{t}}\right]+\mathbf{0 . 3 0 1 0} \)
'A' and 'B' respectively can be:
A. n-Butane and Iso-butane
B. \( C_{2} H_{4} \) and \( C_{4} H_{8} \)
c. \( N_{2} O_{4} \) and \( N O_{2} \)
D. \( C_{2} H_{2} \) and \( C_{6} H_{6} \)


If \( \mathbf{y}=\mathbf{c e}^{x /(x-a)}, \) then \( \frac{\mathbf{d y}}{\mathbf{d x}} \) equals
\( A \cdot a(x-a) \)
B. \( -\frac{\text { ay }}{(x-a)^{2}} \)
\( c \cdot a^{2}(x-a)^{2} \)
D.


The following table given the daily wages of workers in a factory. Compute the standard deviation and the
coefficient of variation of the wages of
the workers.
\[
\begin{array}{llll}
\text { Wages } & 125- & 175- & 225- \\
\text { (Rs) } & 175 & 225 & 275
\end{array}
\]
Number of workers


A hoop and a solid cylinder have the
same mass and radius. They both roll,
without slipping, on a horizontal
surface. If their kinetic energies are
equal, then:
A. the hoop has a greater translational speed than the cylinder
B. the cylinder has a greater translational speed than the hoop.
C. the hoop and the cylinder have the same translational speed.
D. the hoop has a greater rotational speed than the cylinder


Ammonia is basic in nature hence it
turns:
A . red litmus to blue
B. blue litmus to red
c. white litmus to red
D. white litmus to blue


\( \sigma^{m}=\sigma^{*} \)
\( \Phi \)
\( \dot{\phi}^{*} \)


Solutions for air pollution is/are:
A. use public mode of transportation
B. conserve energy
c. concept of reduce, reuse and recycle
D. all of the above


\( \mathbf{f} \boldsymbol{x}=\sum_{n=0}^{\infty} \boldsymbol{a}^{n}, \boldsymbol{y}=\sum_{n=0}^{\infty} \boldsymbol{b}^{n}, \boldsymbol{z}=\sum_{n=0}^{\infty}(\boldsymbol{a} \boldsymbol{b})^{n} \)
where \( a, b<1 \) then prove that \( x z+ \)
\( \boldsymbol{y} \boldsymbol{z}=\boldsymbol{x} \boldsymbol{y}+\boldsymbol{z} \)
Another form:
For \( \mathbf{0}<\boldsymbol{\theta}, \boldsymbol{\phi}-\frac{\boldsymbol{\pi}}{\mathbf{2}} \) if \( \boldsymbol{x}=\sum_{n=0}^{\infty} \cos ^{2 n} \boldsymbol{\theta} \)
\( \boldsymbol{y}=\sum_{n=0}^{\infty} \sin ^{2 n} \phi, z=\sum_{n=0}^{\infty} \cos ^{2 n} \theta \sin ^{2 n} \phi \)
then prove that \( \boldsymbol{x} \boldsymbol{z}+\boldsymbol{y} \boldsymbol{z}-\boldsymbol{z}=\boldsymbol{x} \boldsymbol{y} \)


toppr
Q Type your question
removed. They are termed as elastic.
Those of which not regaining are called
plastic. There may be delay in the regaining in some materials. They are said to have got elastic aftereffect, since they have gone beyond the elastic limit. Repeated application and removal of force break at any point time and so are avoided.
The stress strain graph for two materials \( A \) and \( B \) is shown in the
following figure:
The strength of the material \( A \) and \( B \) is
\( \boldsymbol{S}_{A} \) and \( \boldsymbol{S}_{B}, \) respectively, while the longevity of plastic behaviour is \( L_{A} \) and
\( \boldsymbol{L}_{\boldsymbol{B}} \cdot \) Then
A. \( S_{A}>S_{B}, L_{A}<L_{B} \)
B. \( S_{A}=S_{B}, L_{A}=L_{B} \)
c. \( S_{A}>S_{B}, L_{A}>L_{B} \)
D. \( S_{A}<S_{B}, L_{A}<L_{B} \)


If \( |\boldsymbol{x}|<\mathbf{1} \) then the coefficient of \( \boldsymbol{x}^{\mathbf{5}} \) in
the expansion of \( \frac{3 x}{(x-2)(x+1)} \) is
A \( \cdot \frac{33}{32} \)
B. \( -\frac{33}{32} \)
\( c \cdot \frac{31}{32} \)
D. \( -\frac{3}{32} \)


The deviation produced by an equilateral prism, when a ray of light is incident on it, does not depend on:
A. angle of incidence
B. colour of light
c. material of prism
D. size of prism


Sexual reproduction involves formation of the male and female gametes by?
A. Same individuals
B. Different individuals of the opposite sex
c. Different individual of the same sex
D. Either A or B


If the points \( (-3,6),(-9, a) \) and (0,15) are collinear, then find a


If \( a^{2}+b^{2}, a b+b c \) and \( b^{2}+c^{2} \) are in G.P.
\( a, b, c \) are in :
A . A.P.
B. G.P.
c. н.P.
D. cannot be determined


The fractions which have one as
the numerator are called
fractions.
A . like
B. unlike
c. unit
D. none


The equation ||\( x-1|+a|=4 \) can have
real solutions for \( x \) if \( a \) belongs to the
interval
This question has multiple correct options
\( A \cdot(-\infty, 4] \)
В. \( (-\infty,-4] \)
\( c \cdot(4,+\infty) \)
D. [-4,4]


Find the \( x- \) coordinate of the particle at
the moment of time \( t=20 s \)
A. \( -4.0 m \)
в. \( -3.0 m \)
c. \( 4.0 m \)
D. \( -2.0 m \)


In lead-acid battery electrolyte used is:
A. sulphuric acid
B. aqueous solution of \( P b S O_{4} \)
c. nitric acid
D. aqueous solution of \( \mathrm{FeSO}_{4} \)


Solve: \( \int \frac{1}{x\left(x^{4}-1\right)} d x \)
A. \( -\frac{1}{4} \ln \left|\frac{x^{4}-1}{x^{4}}\right|+c \)
B \( \cdot \frac{1}{4} \ln \left|\frac{x^{4}-1}{x^{4}}\right|+c \)
c. \( -\frac{1}{4} \ln \left|\frac{x^{2}-1}{x^{2}}\right|+c \)
D. \( \frac{1}{4} \ln \left|\frac{x^{2}-1}{x^{2}}\right|+c \)


The upper part of sea water mainly contains
A. Planktons only
B. Nektons only
c. Both nektons and planktons
D. None of the above


The derivative of \( \sin ^{-1} x \) with respect to
\( \cos ^{-1} \sqrt{1-x^{2}} \) is?
A \( \cdot \frac{1}{\sqrt{1-x^{2}}} \)
B. \( \cos ^{-1} x \)
c. 1
D. 0


In the formation of \( N_{2}^{+} \) from \( N_{2} \), the electron is lost from:
\( \mathbf{A} \cdot \) a \( \sigma \) -orbital
B . a \( \pi \) -orbital
c. a \( \sigma^{*} \) -orbital
D. a \( \pi^{*} \) -orbital


Maximize: \( \boldsymbol{z}=\mathbf{3} \boldsymbol{x}+\mathbf{5} \boldsymbol{y} \)
Subject to: \( \boldsymbol{x}+\boldsymbol{4} \boldsymbol{y} \leq \mathbf{2 4} \)
\( \mathbf{z} \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{2 1} \)
\( \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{9} \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


A small pin fixed on a table top is
viewed from above from a distance of
\( 50 \mathrm{cm} . \) By what distance would the pin
appear to be raised if it is viewed from
the same point through a \( 15 \mathrm{cm} \) thick glass slab held parallel to the table?
Refractive index of glass \( =1.5 . \) Does the answer depend on the location of the
slab?


A sphere of mass \( M \) and radius \( r \) slips
on a rough horizontal plane. At some
instant it has translation velocity \( \boldsymbol{v}_{0} \) and rotational velocity about the centre
\( v_{0} / 2 r . \) The translation velocity after the
sphere starts pure rolling
A \( \cdot 6 v_{0} / 7 \) in forward direction
B. \( 6 v_{0} / 7 \) in backward direction
\( c \cdot 7 v_{0} / 6 \) in forward direction
D. \( 7 v_{0} / 6 \) in backward direction


State whether true or false:
The number of cones in the human eye are more than the number of rods.
A. True
B. False


The refracting angle of a prism is 2radians. Refractive indices of its
material for violet and red are
respectively 1.62 and \( 1.5 . \) Dispersion produced by it is
A . 0.24
B. 0.06
c. 1.66
D. 1.12


Let \( Z \) be the set of integers and \( a R b \) where \( a, b \in Z \) if an only if \( (a-b) \) is
divisible by 5 Consider the following statements:
1. The relation \( \boldsymbol{R} \) partitions \( \boldsymbol{Z} \) into five
equivalent classes.
2. Any two equivalent classes are either equal or disjoint. Which of the above statements is/are
correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


Give the ratio of the strengths of the four fundamental forces in nature.


Which equation represents the line that
passes through the point (5,-3) and is parallel to the \( y \) -axis?
A. \( x=-3 \)
В. \( y=-3 \)
c. \( x=5 \)
D. \( y=5 \)


In the figure of the human eye, the
cornea is represented by the letter:
\( A \cdot A \)
B. B
\( c \cdot c \)
\( D . \) D


Which kind of sound is produced in an earthquake before the main shock wave begins?
A. Ultrasound
B. Infra sound
c. Audible sound
D. One of the above


Most conspicuous alternation of generation occurs in
A. Thallophyta
B. Bryophyta
c. Pteridophyta
D. spermatophyta


If \( \boldsymbol{x}=\mathbf{5} \) and \( \boldsymbol{y}=-\mathbf{2}, \) then \( \boldsymbol{x}-\mathbf{2} \boldsymbol{y}=\mathbf{9} \)
The contrapositive of this statement is/are
A. If \( x-2 y \neq 9 \), then \( x \neq 5 \) or \( y \neq 2 \)
B. If \( x-2 y \neq 9 \), then \( x \neq 5 \) and \( y \neq-2 \)
c. If \( x-2 y=9 \), then \( x=5 \) and \( y=-2 \)
D. none of these.


After tracing the path of a ray of light
passing through a rectangular glass slab for four different values of the
angle of incidence, a student reported his observations in tabular form as
given below:
\( <\mathrm{e} \) s.No \( \begin{array}{lccc}\text { । } & 30^{0} & 19^{0} & 29^{0} \\ \text { ॥ } & 40^{0} & 28^{0} & 40^{0} \\ \text { ॥। } & 50^{0} & 36^{0} & 50^{0} \\ \text { । } & 60^{0} & 40^{0} & 59^{0}\end{array} \)
The best observation is :
\( A \)
B. II
\( c \)
D. IV


\( \sin ^{3} x-\sin ^{3}\left(240^{0}-x\right)+\sin ^{3}\left(240^{0}+\right. \)
\( \boldsymbol{x}) \in \)
\( [-\boldsymbol{k}, \boldsymbol{k}]=\rangle \boldsymbol{k}= \)
\( A \)
B. \( 1 / 4 \)
\( c \cdot 3 / 4 \)
\( D \cdot 5 / 4 \)


Branch of study involving rearrangement of atoms and making nano-materials is known as?
A. Mechanical engg.
B. Chemical engg.
c. Electrical engg.
D. Nanotechnology


If the ratio of de-Broglle wavelength of a proton and an \( \alpha- \) particle is 1: 3
then


Which one of the following will show optical isomerism?
\( \begin{array}{cc}\text { в. } & H \\ & \mid \\ & C H_{3}- & C \\ & \mid \\ & O H\end{array}-C O_{2} H \)
c. \( \quad C H_{3} \) \( \left.\right|_{C H_{3}-} ^{\mid}_{C}-C O_{2} H \)
\( _{H} \)
D. \( \quad C H_{3} \) \( \begin{array}{ccc}c_{H_{3}-} & _{C} & _{-C O_{2} H} \\ & \mid & \\ & C l & \end{array} \)


A persons sees clearly at a distance of
100cm, then power of lens used to see
object at \( 40 \mathrm{cm} \) is
\( A .3 D \)
в. \( -3 D \)
c. \( -1.5 D \)
D. \( +1.5 D \)


Assertion
Two successive ionisation energies of Argon are \( 56.8 e V \) and \( 36.8 e V \)
respectively.
Reason
\( Z_{e f f} \) of \( \operatorname{Ar}\left(3 s^{2} 3 p^{6}\right) \) is greater than
\( A r^{+}\left(3 s^{2} 3 p^{5}\right) \)
Read the above assertion and reason
and choose the correct option regarding
¡t.
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


Assertion
Mass, volume and pressure are
extensive properties.
Reason
Extensive properties depend upon the
amount of the substance.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The distance travelled by the car, if a car travels \( 4 k m \) towards north at an
angle of \( 45^{\circ} \) to the east and then travels
a distance of \( 2 k m \) towards north at an
angle of \( 135^{\circ} \) to the east, is
\( \mathbf{A} \cdot 6 k m \)
в. \( 8 k m \)
\( c .5 k m \)
D. \( 2 \mathrm{km} \)


What happens if \( P b O_{2} \) is used instead
of \( N a B i O_{3} ? \)
A \( \cdot P b O_{2}+M n^{2+}+H^{+} \rightarrow M n O_{4}^{-}+P b^{2+}+H_{2} O \)
B . \( 5 P b O_{2}+2 M n^{2+}+14 H^{+} \rightarrow 2 M n O_{4}^{-}+5 P b^{2+}+2 H O \)
C. \( 5 P b O_{2}+2 M n^{2+}+14 H^{+} \rightarrow 2 M n O_{4}^{-}+5 P b^{2+}+2 H_{2} O \)
D. None of these


Find the middle term in the expansion
of
\( \left(\frac{2}{3} x-\frac{3}{2 x}\right)^{20} \)
A \( .^{20} C_{10} x^{10} y^{10} \)
B. \( ^{20} C_{11} x^{11} y^{11} \)
C. \( ^{20} C_{9} x^{11} y^{10} \)
D. None of these


Which of the following does not has fundamental unit?
A. Mass
B. Time
c. Force
D. Electric current


A gas occupies a volume of \( 250 \mathrm{ml} \) at
\( 745 \mathrm{mm} \mathrm{Hg} \) and \( 25^{\circ} \mathrm{C} . \) What additional pressure is required to reduce the gas volume to \( 200 \mathrm{ml} \) at the same time?
\( \mathbf{A} \cdot 180.25 \mathrm{mm} \)
B. \( 200.9 \mathrm{mm} \)
c. \( 186.25 \mathrm{mm} \)
D. \( 189.4 \mathrm{mm} \)


A particle starts from rest, moves with
constant acceleration for \( 15 s \). If it
covers \( s_{1} \) distance in first \( 5 s \) their
distance \( s_{2} \) in next \( 10 s, \) then find the
relation between \( s_{1} \) and \( s_{2} \)


Let \( z=x+ \) iy and \( v=\frac{1-i z}{z-i}, \) show
that if \( |\boldsymbol{v}|=1, \) then \( \boldsymbol{z} \) is purely real


Which of the following has/have zero average value in a plane electromagnetic wave?
A. Both magnetic and electric field
B. Electric field only
c. Magnetic energy
D. Electric energy


Bromine can be liberated from
potassium bromide solution by:
A. iodine solution
B. chlorine water
c. sodium chloride
D. potassium iodide


Given is a representation of a type of pollution. Study the picture and answer the question. State one gaseous compound that leads to the depletion of the ozone layer
and creates 'Ozone holes'.


Which of the following are characteristics of deuterostomes?
A. Spiral cleavage, blastopore becoming mouth
B. Radial cleavage, blastopore becoming anus
C. Spiral cleavage, blastopore becoming anus
D. Radial cleavage, blastopore becoming mouth


Write Copper, Steel, Glass and Rubber in order of increasing coefficient of elasticity
A. Steel, Rubber, Copper, Glass
B. Rubber. Copper, Glass, Steel
c. Rubber. Glass, steel, Copper
D. Rubber. Glass, copper, Steel


The nitrogeneous base present only in
RNA is?
A. Guanine
B. Adenine
c. cytosine
D. Uracil
E. Thymine


The probability that a person will get an electric contract is \( \frac{2}{5} \) and the probability that he will not get plumbing contract is \( \frac{4}{7} . \) If the probability of getting at least one contract is \( \frac{2}{3}, \) what is the probability that he will get both?


Solve the following limit \( \lim _{h \rightarrow 0} \frac{\sqrt{h}}{\sqrt{16+\sqrt{h}-4}} \)


Assertion
Ethanol is a weaker acid than phenol
Reason

Sodium ethoxide may be prepared by the reaction of ethanol with aqueous
NaOH
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


(i) What is the pH of \( 10^{-8} N H C l ? \)
(ii) Calculate pH of the basic solutions
having \( \left[\boldsymbol{O} \boldsymbol{H}^{-}\right] \) as \( - \)
(a) \( \left[\boldsymbol{O H}^{-}\right]=\mathbf{0 . 0 5} \boldsymbol{M} \)
(b) \( \left[\boldsymbol{O} \boldsymbol{H}^{-}\right]=\boldsymbol{4} \times \mathbf{1 0}^{-\boldsymbol{6}} \boldsymbol{M} \)


The three dimensional region in space around nucleus, where there is the
existence of probability spots of electrons is called:
A . orbit
B. orbital
c. probable space
D. both \( B \) and \( C \)


Identify the products.


For what value of \( x \) the matrix \( A \) is
singular? \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1}+\boldsymbol{x} & \mathbf{7} \\ \mathbf{3}-\boldsymbol{x} & \mathbf{8}\end{array}\right] \)
A \( \cdot \frac{12}{15} \)
в. \( \frac{13}{15} \)
c. \( \frac{14}{15} \)
D. none of these


If the elastic limit of copper is \( 1.5 \times \) \( 10^{8} N / m^{8}, \) the minimum diameter a
copper wire can have under a load of 10.0 \( k g \), if its elastic limit is not to be exceeded, is \( \frac{x}{10} \) mm. Find \( x \)


What happen when \( N a O H \) reacts
with?
\( N H_{4} C l \)
\( N H_{4} N O_{3} \)
\( \left(N H_{4}\right)_{2} S O_{2} \)
Urea


Let \( \bar{a}, \bar{b}, \bar{c} \) be vectors of length 3,4,5 respectively. Let \( \bar{a} \) be perpendicular to \( \bar{b}+\bar{c}, \bar{b} t o \bar{c}+\bar{a} \) and \( \bar{c} \) to \( \bar{a}+ \)
b. \( \operatorname{Then}|\bar{a}+\bar{b}+\bar{c}| \) is equals to:
A \( \cdot 2 \sqrt{5} \)
B. \( 2 \sqrt{2} \)
с. \( 10 \sqrt{5} \)
।
D. \( 5 \sqrt{2} \)


Steepness of the travelling waves is attenuated by
A. resistance of the line
B. inductance of the line
c. capacitance of the line
D. all of the above


Solve:
\( x+\frac{1}{x}=25 \frac{1}{25} \)


Lightning occurs because of :
A . rain
B. electric discharge
\( c . \) wind
D. shaking of earth


In diamond, the bonding between carbon atoms is :
A. co-ordinate
B. ionic
c. electrostatic
D. covalent


Pathogens are:
A. one which kills bacteria present in our body
B. one which live on other micro-organisms
C. disease causing agents
D. good for our health


Write all the capital letters of the English alphabets which have two lines of symmetry.
\( A \cdot H, \operatorname{land} x \)
B. A,C and B
c. \( P, Q \) and \( R \)
D. s,Y and z


The ampere, metre and second are \( \mathrm{S} \)
base units.
State two other SI base units.


The distinct linear functions which
maps from [-1,1] onto [0,2] are
A. \( x+1,-x+1 \)
в. \( x-1, x+1 \)
c. \( -x+1 \)
D. \( -x+2 \)


If \( C \) and \( L \) denote the capacitance and
inductance, the dimensions of \( L C \) are
\( \mathbf{A} \cdot\left[M^{0} L^{0} T^{-1}\right] \)
B . \( \left[M^{0} L^{-1} T^{0}\right] \)
\( \mathbf{c} \cdot\left[M^{-1} L^{-1} T^{0}\right] \)
\( \mathbf{D} \cdot\left[M^{0} L^{0} T^{2}\right] \)


The positive charge on sol particles of
\( A g I \) sol is due to preferential
adsorption of ions.
\( \mathbf{1} . \boldsymbol{I}^{-} \)
2. \( \boldsymbol{A} \boldsymbol{g}^{+} \)
3. both 1 and 2
4. none of the above


An old cycle frame was left in open for a few days. A brown layer got slowly deposited on its surface and could not
be removed when rubbed with sand
paper. What happened actually?


22.4 litres of a gas at STP weighs 16 g. Identify the gas.
A. Methane
B. Carbon monoxide
c. Ethane
D. oxygen


Scooter charges consist of fixed charges and remaining depend kilometers. If a person travels \( 12 \mathrm{km}, \) he
pays Rs.45 and for tra Express the above
statements in the from of simultaneous
equation and find charges of rate per \( \mathbf{k m} \)


In a Young's double slit experiment, the path different, at a certain point on the screen, between two interfering waves is \( \frac{1}{8} t h \) of wavelength. The ratio of the intensity at this point to that at the centre of a brigth fringe is close to :
A .0 .94
в. 0.74
c. 0.85
D. 0.80


What is meant by demineralised water and how can it be obtained?


Write the IUPAC names of the given compounds:


For the \( 6^{t h} \) to \( 8^{t h} \) second, what was the
student's movement?
Distance \( / m \)
\[
\mathbf{2}
\]
\[
\text {Time/s} \quad 0 \quad 1 \quad 2
\]


State whether the following statement
is true or false.
Enter 1 for true and 0 for false If \( \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a} & \boldsymbol{b} \\ \boldsymbol{c} & \boldsymbol{d}\end{array}\right] \) then the value of \( \mathrm{f} \) and \( \mathrm{g} \)
satisfying the matrix equation \( A^{2}+ \)
\( \boldsymbol{f} \boldsymbol{A}+\boldsymbol{g} \boldsymbol{I}=\boldsymbol{O} \) are equal to \( -\boldsymbol{t}_{\boldsymbol{r}}(\boldsymbol{A}) \) and
determinant of A respectively. Given a b, \( c, d \) are non zero reals and \( I= \) \( \left[\begin{array}{ll}\mathbf{1} & \mathbf{0} \\ \mathbf{0} & \mathbf{1}\end{array}\right] ; \boldsymbol{O}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{0}\end{array}\right] \)


The normal to the curve \( \sqrt{x}+\sqrt{y}=\sqrt{a} \) is perpendicular to \( x \) axis at the point
в. \( (a, 0) \)
c. \( \left(\frac{a}{4}, \frac{a}{4}\right) \)
D. No where


Write two difference between D.N.A. and
R.N.A:


In a survey of 100 persons it was found that 28 read magazine \( A, 30 \) read magazine B, 42 read magazine \( C, 8 \) read magazines \( A \) and \( B, 10 \) read magazines A and \( \mathrm{C}, 5 \) read magazines \( \mathrm{B} \) and \( \mathrm{C} \) and 3 read all the three magazines. Find how many read none of three magazines?


A liquid \( X \) has the maximum specific heat capacity and is used as a coolant in Car radiators. Name the liquid \( X \)


Find the number of ways in which a lady
can invite 6 guests selected from 10
friends so that two of the friends will not
attend the party together ?.


Find four rational numbers between \( \frac{-2}{5} \) and \( \frac{-3}{4} \)


ADH helps in water elimination, making the urine hypotonic.
A. True
B. False


The product obtained by heating diethyl ether with \( \boldsymbol{H} \boldsymbol{I} \) is:
A. \( C_{2} H_{5} I \)
В \( \cdot C_{2} H_{5} O H \)
\( \mathbf{c} \cdot C_{2} H_{5} O H+C_{2} H_{5} \)
D. \( C_{2} H_{5}-C_{2} H_{5} \)


Which of the following quantifies has the least number of significant digits?
A. 0.80760
в. 0.08765
c. \( 5.7423 \times 10^{2} \)
D. 80.760


A line making angles \( 45^{\circ} \) and \( 60^{\circ} \) with the positive direction of \( x- \) axis and
\( y- \) axis respectively. Then the angle made by the line with positive direction
of \( z- \) axis is
A \( .60^{\circ} \)
B. \( 120^{\circ} \)
\( \mathbf{c} \cdot 60^{\circ} \) or \( 120^{\circ} \)
D. None of these


A divalent metal with atomic number
12 reacts with an acid liberating a gas
\( X . X \) on treatment with a non metal \( Y \)
\( \operatorname{gives} Z, \) which on dissolution in water
produces the same acid. Identify \( \boldsymbol{X}, \boldsymbol{Y} \)
and \( Z \)
A \( \cdot C l_{2}, H_{2}, H C l \)
в. \( H_{2}, H C l, C l_{2} \)
c. \( H C l, H_{2}, C l_{2} \)
D. \( H_{2}, C l_{2}, H C l \)