The blood does not clot inside the body because of
A. Oxygenation of blood
B. Movement of blood
c. Heparin in blood
D. Absence of fibrinogen in blood


The adsorption of a gas, on a solid surface, varies with pressure of the gas in which of the following manner?
A. Slow fast independent of the pressure
B. Fast slow independent of the pressure
c. Independent of the pressure slow fast
D. Independent of the pressure fast slow


Three numbers are chosen at random
withput replacement from \( \{1,2, \ldots, 15\} \)
Let \( E_{1} \) be the event that minimum of
the chosen numbers is 5 and \( E_{2} \) their
maximum is 10 then
This question has multiple correct options
\( ^{\mathbf{A}} \cdot P\left(E_{1}\right)=\frac{9}{91} \)
\( ^{\mathrm{B}} \cdot P\left(E_{2}\right)=\frac{36}{455} \)
\( ^{\mathbf{C}} \cdot P\left(E_{1} \cap E_{2}\right)=\frac{4}{455} \)
\( P\left(E_{1} \mid E_{2}\right)=\frac{1}{9} \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be a function defined by
\( f(x)=\frac{e^{|x|}-e^{-x}}{e^{x}+e^{-x}}, \) then
A. \( f \) is a bijection
B. \( f \) is an injection only
c. \( f \) is surjection on only
D. \( f \) is neither injection nor a surjection


Which comound undergoes 1,4 -addition
with \( B r_{2} ? \)
\( \mathbf{A} \)
B.
\( c \)
\( D \)


If the number of bivalent are 8 in
metaphase - I, what shall be the number
of chromosomes in daughter cells after meiosis - I and meiosis - II respectively.
A. 8 and 4
B. 4 and 4
\( c \cdot 8 \) and 8
D. 16 and 8


If a metallic sphere gets cooled from
\( 62^{\circ} \mathrm{C} \) to \( 50^{\circ} \mathrm{C} \) in \( 10 \mathrm{min} \) and in the next
10 min gets cooled to \( 42^{\circ} \mathrm{C} \), then the temperature of the surroundings is
A \( \cdot 30^{\circ} \mathrm{C} \)
B . \( 36^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 26^{\circ} C \)
D. \( 20^{\circ} \mathrm{C} \)


The heat change associated with
reactions at constant volume is due to
the difference in which property of the reactants and the products?
A. internal energy
B. enthalpy
c. heat capacity
D. free energy


How much time will it take for a
uniform current of \( 6.00 \mathrm{A} \) to deposit \( 78 \mathrm{g} \)
of gold from a solution of \( A u C l_{4}^{-} ? \) What mass of chlorine gas will be
formed simultaneously at the anode of the cell?
(Atomic mass of \( A u=197 \) )
A \( \cdot t=3010 \sec , w=35.50 g \)
B. \( t=20306 \sec , w=45.54 g \)
c. \( t=19500 \) sec \( , w=54.5 g \)
D. \( t=19139.16 \sec , w=42.24 g \)


Which of the following has the maximum number of unpaired \( d \)
electrons?
A \( \cdot Z n^{2} \)
B. \( F e^{2+} \)
\( c \cdot N i^{3} \)
D. \( C u^{+} \)


Explain the effect on the characteristics
of a river when urban sewage is
discharged into it.


Find the potential at the centre of arrangement having 6 charged particles of \( Q=5 \mu C \) each arranged in
the form of a hexagon of side length 0.1
\( \mathrm{m} \)


Check whether Lagrange's mean value
theorem is applicable on \( f(x)=\sin x+ \) \( \cos x \) interval \( \left[0, \frac{\pi}{2}\right] \)


Which of the following are skeletal disorders?
A. osteoporosis
B. Arthritis
c. Diabetes
D. Both (B) and (A)


Which of the following carboxylic acids is highly insoluble in water?
A. Propanoic acid
B. Butanoic acid
c. Pentanoic acid
D. Decanoic acid


Define linkage and ionisation
isomerism?


Order of basic strength:
\( \mathbf{A} \cdot A>B>C>D \)
В \( . B>A>C>D \)
\( \mathbf{c} \cdot C>B>A>D \)
\( \mathbf{D} \cdot C>B>D>A \)


A racing motorboat speeds up in a straight line in a take, from rest.
Referring to the acceleration-
displacement graph for the speeding boat, find its speed when it passes a
raft at a distance of \( 40 \mathrm{m} \) from the
starting point.


Differentiate: \( \boldsymbol{x}^{\mathbf{1 0 0}}+\sin \boldsymbol{x}-\mathbf{1} \)
A \( \cdot 100 x^{99}-\cos x \)
\( x \)
B. \( 100 x^{99}+\cos x \)
c. \( x^{99}+\cos x \)
D. \( 100 x^{99}+\sin x \)


The following graph represents the
organismic response to certain environmental condition (e.g. temperature):
(i) Which one of these, 'a' or 'b', depicts
conformers?
(ii) What does the other line graph
depict?
(iii) How do these organisms differ from
each other with refernce to homeostasis
\( ? \)


Green chemistry means such reactions
which:
A. produce colour during reactions
B. reduce the use and production of hazardous chemicals
C. are related to the depletion of ozone layer
D. study the reactions in plant


Write any two important difference between short day plants and long day plants.


A loop of area \( 4 m^{2} \) is placed flat in the
x-y plane.There is a constant magnetic field \( 4 \hat{j} \) in the region. Find the flux through the loop
A . 2 units
B. 4 units
c. 6 units
D. 0 units


Find the intersection of \( A \) and \( B \) by
representing using by Venn diagram:
\( \boldsymbol{A}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\}, \boldsymbol{B}=\{1,2, \boldsymbol{9}\} \)
\( A \cdot \phi \)
в. \( a, b, c, 1,2,9 \)
c. \( a, c, 1,9 \)
D. None of these


Which of the following is a ductless gland?
A. Exocrine gland
B. Endocrine gland
c. Thyroid gland
D. Pituitary gland


A person travels along a straight road for the first half length with a velocity
\( V_{1} \) and the second half length with a
velocity \( V_{2} . \) Then the mean velocity v is given by
A \( \cdot v=\frac{v_{1}+v_{2}}{2} \)
B. \( v=\sqrt{v_{1} v_{2}} \)
c. \( v=\sqrt{\frac{v_{1}}{v_{2}}} \)
D. \( \frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}} \)


Show that the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{ll}3 x-2 & \text { if } 0<x \leq 1 \\ 2 x^{2}-x & \text { if } 1<x \leq 2 \\ 5 x-4 & \text { if } x>2\end{array}\right. \)
is continuous at \( x=2 \)


What causes an increase in effective
collisions without increasing average energy?
A. An increase in the reactant concentration
B. An increase in the temperature
c. A decrease in pressure
D. catalysts


If position vectors of four vertices of a square are \( \boldsymbol{A}=\mathbf{3} \boldsymbol{i}-\boldsymbol{\lambda} \boldsymbol{j}, \boldsymbol{B}=\mathbf{9} \boldsymbol{i}-\boldsymbol{6} \boldsymbol{k} \)
\( \boldsymbol{C}=\mathbf{6} \boldsymbol{j}-\mathbf{5} \boldsymbol{k} \) and \( \boldsymbol{D}=\boldsymbol{\alpha} \boldsymbol{i}-\boldsymbol{3} \boldsymbol{j}+\boldsymbol{4} \boldsymbol{k} \)
then value of \( \lambda-\alpha \) is :
A . 10
B. 15
c. 25
D. None of these


The wavelength associated with a golf
weighing \( 200 g \) and moving at a speed of
\( 5 m / h \) is of the order:
B . \( 10^{-20} m \)
\( \mathbf{c} \cdot 10^{-30} m \)
D. \( 10^{-40} m \)


A series of reactions starting from allyl
chloride is shown.
In reaction \( 2, \) the organic product of reaction 1 is mixed with concentrated
\( H_{2} S O_{4} \) and an organic acid, and then
heated under reflux.
State the role of the concentrated
\( H_{2} S O_{4} \). Identify the organic acid used.
role of the concentrated \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
identity of the organic acid


In passing \( 3 \mathrm{F} \) of electricity through three electrolytic cells connected in
series containing \( \boldsymbol{A} \boldsymbol{g}^{\oplus}, \boldsymbol{C} \boldsymbol{a}^{2+}, \boldsymbol{a} \boldsymbol{n} \boldsymbol{d} \boldsymbol{A} \boldsymbol{l}^{3} \)
ions, respectively. The molar ratio in
which the three metal ions are liberated
at the electrode is:
A. 1: 2: 3
B . 2: 3: 1
c. 6: 3: 2
D. 3: 4: 2


The difference of the squares of two consecutive even integers is divisible by which of the following integers?
\( A \cdot 3 \)
B. 4
\( c .6 \)
D. 7


\( P \rightarrow(q \rightarrow r) \) is logically equivalent to
A \( \cdot(q \vee q) \rightarrow \sim r \)
в. \( (p \wedge q) \rightarrow \sim r \)
c. \( (p \vee q) \rightarrow r \)
D. \( (p \wedge q) \rightarrow r \)


The free end of a thread wound on a
bobbin is passed round a nail \( \boldsymbol{A} \)
hammered into the wall. The thread is
pulled at a constant velocity. Assuming
pure rolling of bobbin, find the velocity
\( v_{0} \) of a center of theybobbin at heh
center at he instant when the thread
forms an angle \( \alpha \) with the vertical.
A \( \cdot \frac{v R}{R \sin \alpha-r} \)
в. \( \frac{v R}{\text { R } \sin \alpha+r} \)
c. \( \frac{2 v R}{\text { Rsind }+r} \)
D. \( \frac{v}{\text { Rsin } \alpha+r} \)


The fastest acting enzyme in the biological kingdom is
A. Lipase
B. Amylase
c. carboxypeptidase
D. Carbonic anhydrase


The value of \( \int \frac{d x}{\sin x \cdot \sin (x+\alpha)} \) is equal
to


Find the position of the centre of mass
of the \( T \) -shaped plate from \( O \) in figure.


Assertion
The Daniell cell becomes dead after
some time.
Reason
Oxidation potential of zinc anode decreases and that of copper increases.
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


Positive charge q is given to each plate of a parallel plate air capacitor having area of each plate \( A \) and separation between them, d. Then find Energy stored between the plates:
\( ^{A} \cdot \frac{1}{2} \cdot \frac{q^{2}}{C} \)
в. \( \frac{1}{3} \frac{q^{2}}{c} \)
c. \( \frac{1}{2} \cdot \frac{q}{C} \)
D. \( \frac{1}{2} \cdot \frac{q^{3}}{C} \)
E \( \cdot \frac{1}{2} \cdot \frac{q^{4}}{C} \)


Fill in the blanks with approriate words. Each haemoglobin molecule can carry molecules of oxygen, one in each


An die is tossed twice. Find the
probability of getting 4,5 or 6 on the toss and 1,2,3 or 4 on the second toss.


When ferrous sulphide reacts with a sulphuric acid, the product obtained has a characteristic odour of:
A. urine
B. fishy
c. rotten egg
D. pleasant


Two waves of amplitudes \( A \) and \( 3 A \) are superposed and they have a phase difference of \( 2 \pi . \) What kind of
interference is possible
A. constructive interference
B. Destructive interference
c. Interference depends on wavelength difference
D. Interference depends on frequency difference


\( \boldsymbol{E}^{0}\left(\boldsymbol{N} \boldsymbol{i}^{2+} / \boldsymbol{N} \boldsymbol{i}\right)= \)
\( -0.25 v o l t, E^{0}\left(A u^{3+} / A u\right)=1.50 v o l t \)
The standard emf of the voltaic cell.
\( \boldsymbol{N} \boldsymbol{i}_{(s)}\left|\boldsymbol{N} \boldsymbol{i}_{(a q)}^{2+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{u}_{(a q)}^{3+}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M})\right| \boldsymbol{A} \boldsymbol{u}_{(s)} \)
is:
A. 1.25 volt
B . - 1.75 volt
c. 1.75 volt
D. 4.0 volt


For four particles \( A, B, C \& D, \) the velocities of one with respect to other are given as \( \bar{V}_{D C} \) is \( 20 \mathrm{m} / \mathrm{s} \) towards north, \( \bar{V}_{B C} \) is \( 20 \mathrm{m} / \mathrm{s} \) towards east and
\( \bar{V}_{B A} \) is \( 20 \mathrm{m} / \mathrm{s} \) towards south. Then \( \overline{\boldsymbol{V}}_{D A} \) is:
A. \( 20 \mathrm{m} / \mathrm{s} \) towards north
B. 20 \( \mathrm{m} / \mathrm{s} \) towards south
c. \( 20 \mathrm{m} / \mathrm{s} \) towards east
D. 20 \( \mathrm{m} / \mathrm{s} \) towards west.


State true or false.
\( \mathbf{1 9 9 . 1}+\mathbf{1 9 7} . \mathbf{3}+\mathbf{1 9 5 . 5}+\ldots . \mathbf{3 . 1 9 7}+ \)
\( 1.397=666700 \)
A. True
B. False


Statement 1: The variance of first n even
natural numbers is \( \frac{\mathbf{n}^{2}-\mathbf{1}}{\mathbf{4}} \)
Statement 2: The sum of first n natural
numbers is \( \frac{\mathbf{n}(\mathbf{n}+\mathbf{1})}{\mathbf{2}} \) and the sum of
squares of first n natural numbers is \( \frac{\mathbf{n}(\mathbf{n}+\mathbf{1})(\mathbf{2 n}+\mathbf{1})}{\mathbf{6}} \)
A. Statement 1 is true, Statement2 is true,Statement 2 is a correct explanation for Statement 1
B. Statement 1 is true, Statement2 is true;Statement2 is not a correct explanation for statement 1
c. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true


A rifle bullet loses \( 1 / 20 \) th of its velocity
in passing through a plank. Assuming constant resistive force, the least
number of such planks required just to stop the bullet is:
A . 15
B. 10
\( c \cdot 11 \)
D. 20


Acidity of diprotic acids in aqueous
solutions increases in the order
A. \( H_{2} S<H_{2} S e<H_{2} T e \)
в. \( H_{2} S e<H_{2} S<H_{2} T e \)
c. \( H_{2} T e<H_{2} S<H_{2} S e \)
D. \( H_{2} S e<H_{2} T e<H_{2} S \)


A unit vector in the direction of vector \( \overrightarrow{P Q}, \) where \( P \) and \( Q \) are the points
(1,2,3) and (4,5,6) respectively is
A \( \cdot \frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \hat{j}+\frac{1}{\sqrt{3}} \bar{k} \)
B. \( \frac{1}{\sqrt{3}} \hat{i}+\frac{1}{\sqrt{3}} \hat{j}-\frac{1}{\sqrt{3}} \hat{k} \)
c. \( 2 \hat{i}-\hat{j}+\bar{k} \)
D. None


The set with the correct order of acidity
¡s:
\( \mathbf{A} \cdot \mathrm{HClO}<\mathrm{HClO}_{2}<\mathrm{HClO}_{3}<\mathrm{HClO}_{4} \)
B. \( \mathrm{HClO}_{4}<\mathrm{HClO}_{3}<\mathrm{HClO}_{2}<\mathrm{HClO} \)
C \( . \mathrm{HClO}<\mathrm{HClO}_{4}<\mathrm{HClO}_{3}<\mathrm{HClO}_{2} \)
D. \( \mathrm{HClO}_{4}<\mathrm{HClO}_{2}<\mathrm{HClO}_{3}<\mathrm{HClO} \)


A cell is destined to complete cell cycle
A. When it enters post-mitiotic phase
B. When it crosses restriction point
C. Only when it crosses \( G_{0} \) check point
D. When all check points are successfully crossed


Approximate \( K_{c} \) for the reaction at
\( 25^{\circ} C \) will be:
\( \boldsymbol{Z} \boldsymbol{n}(\boldsymbol{s})+\boldsymbol{C u}^{2+}(\boldsymbol{a q})=\boldsymbol{Z} \boldsymbol{n}^{3+}(\boldsymbol{a q})+ \)
\( \boldsymbol{C u}(\boldsymbol{s}) \)
\( \boldsymbol{E}_{Z n^{2+} / Z n}^{o}=-\mathbf{0 . 7 6} \boldsymbol{V} \boldsymbol{E}_{C u / C u^{2+}}^{o}= \)
\( -\mathbf{0 . 3 4} V \)
\( \mathbf{A} \cdot 10^{11} \)
B. \( 10^{3} \)
\( \mathbf{c} \cdot 10^{18} \)
D. \( 10^{14} \)


Force acting on a particle moving in a straight line varies with the velocities of
the particle as \( \boldsymbol{F}=\boldsymbol{K} . \boldsymbol{V} . \) Where \( \boldsymbol{K} \) is
constant. The work done by this force in time \( t \) is
A . \( K V t \)
B. \( K^{2} V^{2} t^{2} \)
c. \( K^{2} V t \)
D. \( K V^{2} t \)


The accuracy of measurement also lies in the way the result is expressed. The number of digits to which a value is to be expressed is one digit more than number of sure numbers. Rules do exist
to deal with number of digits after an operation is carried out on the given values. The error can be minimised by
many trials and using the correct methods and instruments.
The number of significant figures can reduces in
A. Addition
B. Subtraction
C. Multiplication
D. Division


The direction of the induced e.m.f. is
determined by :
A. Fleming's left hand rule
B. Fleming's right hand rule
c. Maxwell's right hand screw rule
D. Ampere's rule of swimming


A horizontal metal wire is carrying an electric current from the north to the
south. Using a uniform magnetic field, it is to be prevented from falling under gravity. The direction of this magnetic field should be towards the
A . east
B. west
c. north
D. south


The focal length of a normal eye-lens is
about:
\( \mathbf{A} \cdot 1 m m \)
B. 2 cm
c. \( 25 \mathrm{cm} \)
D. \( 1 m \)


What is PHBV? How is it useful to man?


Some non-metals are used in water
purification.
A. True
B. False


Arrange the alkyl in decreasing order of
their mass.
A \( \cdot C H_{3} C l>H_{2} O>C H_{3} B r \)
в. \( C H_{3} C l>C H_{3} B r>H_{2} O \)
\( \mathrm{c} \cdot C H_{3} B r>C H_{3} C l>H_{2} O \)
D. \( H_{2} O>C H_{3} C l>C H_{3} B r \)


Solve using factorization method:
\( \mathbf{7} \boldsymbol{m}^{2}-\mathbf{8} \mathbf{4}=\mathbf{0} \)


There are two colourless solutions \( (A) \)
and (B), both give white ppt with
\( A g N O_{3} \) which dissolves in \( a q N H_{3} \) Also (A) on reaction with \( H_{2} O \) gives orange turbidity while
(B) gives white turbidity. Identify (A) and (B).
\( \mathbf{A} \cdot(A) S b C I_{3} \)
(В) \( B i C I_{3} \)
B . (A) \( B i C I_{3} \);
(В) \( S b C I_{3} \)
C \( . \) (A) \( S e C I_{3} \);
(В) \( B i C I_{3} \)
D. (A) \( B i C I_{3} \);
(В) \( S e C I_{3} \)


(a) Complete the following chemical reaction equations
(i) \( P_{4}+S O_{2} C l_{2} \rightarrow \)
(ii) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \)
(b) Predict the shape and the asked angle \( \left(90^{\circ} \) or more or less) in each of \right.
the following cases:
(i) \( S O_{3}^{2-} \) and the angle \( O-S-O \)
(ii) \( C l F_{3} \) and the angle \( F-C l-F \)
(iii) \( X e F_{2} \) and the angle \( F-X e-F \)


The solution of the differential equation \( x d y-y d x=\sqrt{x^{2}-y^{2}} d x \) is


A steroid hormone which regulates
glucose metabolism is
A. 11-deoxycorticosterone
B. Cortisone
c. cortisol
D. corticosterone


The length of a chord of a circle of
radius \( 10 \mathrm{cm} \) is \( 12 \mathrm{cm} \). Find the
distance of the chord from the centre of
the circle
A. \( 6 \mathrm{cm} \)
B. \( 5 \mathrm{cm} \)
\( c .8 \mathrm{cm} \)
D. \( 7 \mathrm{cm} \)


Integrate:
\( \int e^{x} \sin x \cdot d x \)


Co-ordinate bond is found in
A \( . H_{2} \)
в. \( C l_{2} \)
c. \( N H_{4} C l \)
D. \( N a C l \)


Due to which property of colours they appear differently though the sunlight is passed through only one medium?
A. Due to different refractive index with respect to medium
B. Due to different frequencies with respect to medium
c. Due to different amplitudes with respect to medium
D. Due to different colour with respect to medium


Total elongation of the wire.


\( 23 g \) of sodium will react with methyl
alcohol to give:
A. one mole of oxygen
B . 22.4dm \( ^{3} \) of hydrogen gas at NTP
c. 1 mole of \( H_{2} \)
D. \( 11.2 L \) of hydrogen gas at NTP


If water of temperature \( 80^{\circ} \mathrm{C} \) and \( 60^{\circ} \mathrm{C} \)
is cooled in two different vessels, which
water gets cooled faster? Justify your
answer


A right angled triangle has a base of \( 40 \mathrm{cm}, \) height of \( 30 \mathrm{cm} \) and hypotenuse of \( 50 \mathrm{cm} . \) The triangle is rotated so that the hypotenuse forms the base. Find the altitude now.


Melting of ice is favoured by:
A. high pressure low temperature
B. high temperature high pressure
C . low pressure high temperature
D. low temperature low pressure


Ozonization of water is carried to
remove:
A. bacterial impurities
B. bad taste
c. excess of chlorine present
D. calcium and magnesium salts present in it


Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) displaces hydrogen chloride from chlorides because:
A . it is stronger acid
B. sulphates are less soluble than chlorides
c. sulphates are more soluble than chloride
D. \( H C l \) is a gas while \( H_{2} S O_{4} \) is a liauid


Which one of the followings is wrong for meiosis?
A. It leads to formation of sister chromatids
B. It occurs in diploid cell
c. It occurs in haploid cell
D. It occurs by splitting of centromeres and separation of sister chromatids


Taste buds for bitter taste are found on
tongue at
A. Tip
B. On basal surface
c. Posterior part
D. Lateral sides


Find the equation of a circle with centre
(2,2) and passes through the point (4,5)


Using grignard reagent \( \boldsymbol{C}=\boldsymbol{O}+\boldsymbol{R}-\boldsymbol{M} \boldsymbol{g} \boldsymbol{X} \rightarrow \)


At what depth in an ocean will a bubble of air have one fifth the volume it will
have on reaching the surface?
(Atmosphere pressure \( -\mathbf{7 6} \) cm of \( \mathrm{Hg} \) and density of \( \boldsymbol{H} \boldsymbol{g}=\mathbf{1 3 . 6} \boldsymbol{g} \boldsymbol{c m}^{-\mathbf{3}} \mathbf{)} \)


Assertion
As temperature increases, heat of
reaction also increase for exothermic as
well as endothermic reactions.
Reason
\( \Delta H_{\text {reaction}} \) varies according to the
relation:
\( \frac{\Delta \boldsymbol{H}_{2}-\boldsymbol{\Delta} \boldsymbol{H}_{1}}{\boldsymbol{T}_{2}-\boldsymbol{T}_{1}}=\boldsymbol{\Delta} \boldsymbol{C}_{\boldsymbol{P}} \)
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 electronic configuration of an element is
\( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2}, 3 p^{6}, 3 d^{3}, 4 s^{1} . \) This
represents its
A. Excited state
B. Ground state
c. cationic form
D. Anionic form


A body was supplied 1000 kilocalories of heat. Express this heat in mega
joules.
A. 2.2 mega joules
B. 3.2 mega joules
c. 4.2 mega joules
D. 5.2 mega joules


Name the radiations absorbed by ozone layer.What would happen to living ones on earth of ozone layer around us disappears?


The instrument which works on the
principle of mutual inductance is
A. Galvanometer
B. Ammeter
c. Potentiometer
D. Transformer


The probability that exactly one of the
independent events \( A \) and \( B \) occurs is
equal to
This question has multiple correct options
\( \mathbf{A} \cdot \mathbf{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-2 P(\mathrm{A} \cap B) \)
B \( . P(A)+P(B)-P(A \cap B) \)
\( \mathbf{c} \cdot P(\bar{A})+P(\bar{B})-2 P(\bar{A} \cap \bar{B}) \)
D \( . P(\bar{A})+P(\bar{B})-P(\bar{A} \cap \bar{B}) \)


Assertion
Extraction of metals from their ores by
chemical methods requires the use of reducing agent.
Reason
Reducing agent helps to convert the metal oxide from its ore to the metal
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which one is wrong if electrolysis of \( C H_{3} C O O N a(a q) \) is made using \( P t \)
electrodes?
A. \( p H \) of solution increases
B. Molar ratio of gases at anode and cathode is 3: 1
\( \mathrm{c} \cdot\left[C H_{3} C O O^{\ominus}\right] \) in solution decreases
D. The molar ration of gases at anode and cathode is 2 :
1


A certain radioactive material is known
to decay at a rate proportional to the amount present. If after one hour it is
observed that 10 percent of the material has decayed, find the half-life (period of time it takes for the amount of material
to decrease by half) of the material (in hrs.)
A . 6.58
B. 8.58
c. 10.58
D . 12.58


A machine gun is mounted on an armored car moving with a speed of \( 20 \mathrm{ms}^{-1} . \) The gun can point aqainst
the direction of motion of car.

The muzzle speed of bullet is equal to
speed of sound in air i.e., \( 340 \mathrm{ms}^{-1} \). The
time difference between bullet actually reaching and sound of firing reaching at a target \( 544 \mathrm{m} \) away from car at the instant of firing is:
A . \( 1.2 \mathrm{s} \)
B. \( 0.1 \mathrm{s} \)
\( c \cdot 1 s \)
D. 10 s


Which of the following methods would most likely help with recalling and writing multiple chemistry formulas down for the SAT chemistry test?
A. Writing mnemonic Devices
B. Visualizing the problem
c. using flash cards
D. categorizing information


Which of the following reactions is called slaking of lime?
A \( \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
в. \( C a O+2 H C l \rightarrow C a C l_{2}+H_{2} O \)
c. \( C a O+H_{2} O \rightarrow C a(O H)_{2}+ \) heat
D. \( C a C O_{3}+N a C l \rightarrow N a_{2} C O_{3}+C a C l_{2} \)


Define asexual reproduction. Give name
of two methods of asexual reproduction.


When phosphorus reacts with caustic
soda, the products are \( P H_{3} \) and
\( N a H_{2} P O_{2} . \) This reaction is an example
of
A. Oxidation
B. Reduction
c. Oxidation and reduction (Redox)
D. Neutralization


Boiling point of water on the Celsius scale is
A \( \cdot 0^{\circ} \mathrm{C} \)
B. 212^{ } \( \mathrm{C} \)
c. \( 32^{\circ} \mathrm{C} \)
D. \( 100^{\circ} \mathrm{C} \)


Define pH? Calculate the pH of
1. \( 10^{-3} \mathrm{M} \mathrm{HCl} \)
2. \( 10^{-3} \mathrm{M} \mathrm{HCl} \)
3. \( 0.001 M \) NaOH
4. \( 0.0008 M B a(O H)_{2} \)


DNA and RNA have similar basic
structures.
A . True
B. False


A nucleus \( X^{235} \) splits into two nuclei having the mass numbers in the ratio
\( 2: 1 . \) The ratio of the radii of those two
nuclei is:
A .2: 1
B. 1: 2
c. \( 2^{1 / 3}: 1 \)
D. \( 1: 2^{1 / 3} \)


A neutral atom of certain elements has
15 electrons. How many unpaired electrons does it have?
\( A \)
B. 3
\( c \cdot 5 \)
D.


Assertion
\( \left(C_{2} H_{5}\right)_{3} N \) is less basic than
trimethylaine \( \left(\boldsymbol{C H}_{\mathbf{3}}\right)_{\mathbf{3}} \boldsymbol{N} \)
Reason
Due to hyperconjugation of \( C_{2} H_{5} \) is
less than methyl.
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


For decolourisation of 1 mole of acidified
\( K M n O_{4} \) the moles of \( H_{2} O_{2} \) required
are:
A \( \cdot 1 / 2 \)
B. 3/2
\( c \cdot 5 / 2 \)
D. 7/2


The differential equation of the family of
curves
\( \frac{\boldsymbol{x}^{2}}{\boldsymbol{a}^{2}}+\frac{\boldsymbol{y}^{2}}{\boldsymbol{a}^{2}+\boldsymbol{\lambda}^{2}}=1 \) is \( (\boldsymbol{\lambda} \) is orbitary
constant)
A \( \cdot\left(x^{2}-a^{2}\right) y_{1}=x y \)
B . \( \left(x^{2}-a^{2}\right) y_{2}-x y=0 \)
C \( . x^{2} y_{2}-a^{2} y=0 \)
D. \( \left(x^{2}-a^{2}\right) y_{1}+x y=0 \)


A car travelling at a speed of \( 30 \mathrm{km} / \mathrm{h} \) is brought to a halt in \( 8 \mathrm{m} \) by applying brakes. If the same car is travelling at
\( 60 \mathrm{km} / \mathrm{h}, \) it can be brought to a halt with the same braking force in:
\( \mathbf{A} \cdot 8 m \)
в. 16 т
\( c \cdot 24 m \)
D. 32


A block of mass \( 20 \mathrm{kg} \) is acted upon by
a force \( \boldsymbol{F}=\mathbf{3 0} \boldsymbol{N} \) at an angle \( \mathbf{5 3}^{\mathbf{0}} \) with
the horizontal in downward direction as
shown. The coefficient of friction
between the block and the horizontal
surface is \( 0.2 . \) The friction force acting
on the block by the ground is \( (g= \) \( \left.10 m / s^{2}\right) \)
A . 40.0
B. 30.0 N
c. \( 18.0 \mathrm{N} \)
D. 44.8 N


Figure shows three systems in which a
block of mass m can execute S.H.M.
What is ratio of frequency of
oscillation?
\( A \cdot 2: 1: 4 \)
B. 1: 2: 4
c. 4: 2: 1
D. 3: 2:


Doppler's effect in sound in addition to
the relative velocity between source and
observer also depends on whether source and observer also depend on whether source or observer or both are
moving. Doppler effect in light depends only on the relative velocity of source and observer, the reason for this is:
A. Einstein's mass-energy relation.
B. Photoelectric effect.
c. the velocity of the observer with respect to the light velocity is negligible.
D. none of these


Lightning conductors are used to save the building from earthquakes.
A. True
B. False


Select incorrect statement(s):
A. Surface active agent like soaps and synthetic detergents are micelles.
B. Soaps are emulsifying agents.
C \( . C_{17} H_{35} \) (hydrocarbon part) and \( \mathrm{COO} \) (carboxylate part) of stearate ion \( \left(C_{17} H_{35} C O O^{-}\right) \) are both hydrophobic
D. The hydrophobic part accumulates inside of the micelle when soap is mixed in water.


Number of irrational terms in the
expansion of \( \left(5^{\frac{1}{6}}+2^{\frac{1}{8}}\right)^{100} \)
A . 96
B. 97
c. 98
D. 99


Assertion
The formation of \( N H_{3} \rightarrow B F_{3} \) is
neutralization according to Lewis acid base theory.
Reason
Formation of Co-ordinate covalent bond
is neutralization.
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


A wheel with 10 spokes each of length ' \( L \)
\( \mathrm{m} \) is rotated with a uniform angular velocity ' \( \omega \) ' in a plane normal to the
magnetic field ' \( B \) '. The emf induced between the axle and the rim of the
wheel.
A \( \cdot \frac{1}{2} N \omega B L^{2} \)
B. \( \frac{1}{2} \omega B L^{2} \)
\( \mathrm{c} \cdot \omega b L^{2} \)
D. \( N \omega B L^{2} \)


Which of the following instruments is used for detecting and measuring smal electric currents?
A. Galvanometer
B. Fluxmeter
C. Ammeter
D. Voltmeter


Which of the following does not belong to the same homologous series?
A \( . C H_{4} \)
B. \( C_{2} H_{6} \)
\( \mathbf{c} \cdot C_{3} H_{8} \)
D. \( C_{4} H_{8} \)


Three particles with masses 10,20 and 40 g are moving with velocities \( 10 \hat{i}, 10 \hat{j} \) and \( 10 \hat{k} m / \) sec respectively. If due to some interaction the first particle comes to rest and the velocity of second becomes \( (3 \hat{i}+4 \hat{j} m / s e c) . \) Then
the velocity of third particle after their interaction is:
\( \mathbf{A} \cdot \hat{i}+\hat{j}+5 \hat{k} \)
в. \( \hat{j}+10 \hat{k} \)
c. \( \hat{i}+\hat{j}+10 \hat{k} \)
D. \( \hat{i}+3 \hat{j}+10 \hat{k} \)


Why carboxylic acid does not give reaction of carbonyl group?


Name few devices which an
electromagnet is used


A bag contains 3 white and 2 black balls
and another bag contains 2 white and 4 black balls. One bag is chosen at
random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{0} & \mathbf{5} \\ \mathbf{0} & \mathbf{0}\end{array}\right] \) and \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1}+\boldsymbol{x}+ \)
\( \boldsymbol{x}^{2}+\ldots \ldots+\boldsymbol{x}^{6}, \operatorname{then} \boldsymbol{f}(\boldsymbol{A})= \)
A . 0
в. \( \left[\begin{array}{ll}1 & 5 \\ 0 & 1\end{array}\right] \)
c. \( \left[\begin{array}{ll}1 & 5 \\ 0 & 0\end{array}\right] \)
D. \( \left[\begin{array}{ll}0 & 5 \\ 1 & 1\end{array}\right] \)


Degenerated DNA after heating can be studied by comparing
A. A: T ratio
B. G: C ratio
c. sugar: phosphate
D. Number of nucleotides


The focal length of a lens is \( 0.12 \mathrm{m} \) and the Refractive Index (R.I.) is \( 1.5 . \) The focal
length of the same lens for blue colour is \( 0.1 \mathrm{m} \). The R.I. of the lens for blue
colour is
A . 1.5
B. 1.25
c. 1.45
D. 1.6


Formula unit mass is used for :
A . molecules
B. ionic compound
c. uncharged compounds
D. all of above


The area of a trapezium is 450 sq.cm and the lengths of the parallel sides are \( 37 \mathrm{cm} \) and \( 23 \mathrm{cm} . \) Find the distance
between them.


Is the term clone applicable to the offspring formed by vegetative reproduction?


\[
\mathrm{f}_{\mathrm{f}} \prod_{r=4}^{8} \cos \left(\frac{\theta}{2^{r}}\right)=\frac{\sin \left(\frac{\theta}{2^{n_{1}}}\right)}{(2)^{n_{2}} \sin \left(\frac{\theta}{2^{n_{3}}}\right)}
\]
then the value of \( n_{1}+n_{3}-n_{2} \) is


In Drosophila female has a pair of chromosomes
A. zz
B. xxx
c. \( Y Y \)
D. zw


Identify the given below diagram and
choose correct option.
A. Monochasial cyme
B. Dichasial cyme
c. cyathium inflorescence
D. Polychasial cyme


The equation of electromotive force in
terms of current \( i \) for an electrical
circuit having resistance \( \boldsymbol{R} \) and condenser \( C \) in series is \( \boldsymbol{E}=\boldsymbol{R} \boldsymbol{i}+ \)
\( \int \frac{i}{c} d t . \) The current at any time \( t, \) when
\( \boldsymbol{E}=\boldsymbol{E}_{0} \sin \omega \boldsymbol{t} \) is?
A \( \cdot i=\frac{E_{0} \omega c}{\sqrt{1+R^{2} c^{2} \omega^{2}}} \sin (\omega t-\phi)+k e^{-t / R c} \)
B. \( i=\frac{E_{0} \omega c}{\sqrt{1+R^{2} c^{2} \omega^{2}}} \cos (\omega t-\phi)+k e^{-t / R c} \)
c. \( _{i}=\frac{E_{0} \omega c}{\sqrt{1+R^{2} c^{2} \omega^{2}}} \cosh (\omega t-\phi)+k e^{-t / R c} \)
D. \( i=\frac{E_{0} \omega c}{\sqrt{1+R^{2} c^{2} \omega^{2}}} \sinh (\omega t-\phi)+k e^{-t / R c} \)


The sum of the digits in the unit place of all the numbers formed with the help
of 3,4,5,6 taken all at a time, is
A . 432
в. 108
\( c .36 \)
D. 18


Sewage water is purified for recycling by the action of
A. Light
B. Micro-organisms
c. Aquatic plants
D. Fishes


Construct \( \triangle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \) in which \( \angle \boldsymbol{Y}= \)
\( \mathbf{3 0}^{o}, \angle Z=\mathbf{6 0}^{\circ} \) and \( \boldsymbol{X} \boldsymbol{Y}+\boldsymbol{Y} \boldsymbol{Z}+\boldsymbol{Z} \boldsymbol{X}= \)
\( \mathbf{1 0} c \boldsymbol{m} \)


If \( \vec{a}=\hat{i}+2 \hat{j}+2 \hat{k} \) and \( \vec{b}=3 \hat{i}+6 \hat{j}+ \)
\( 2 \hat{k}, \) then a vector in the direction of \( \vec{a} \)
and having magnitude as \( |\vec{b}| \) is
A \( \cdot 7(\hat{i}+\hat{j}+\hat{k}) \)
B \( \cdot \frac{7}{3}(\hat{i}+2 \hat{j}+2 \hat{k}) \)
c. \( \frac{7}{9}(\hat{i}+2 \hat{j}+2 \hat{k}) \)
D. none of these


The radius of \( L a^{3+} \) (Atomic number of
\( \boldsymbol{L} \boldsymbol{a}=\mathbf{5} \mathbf{7}) \) is \( \mathbf{1 . 0 6} \boldsymbol{A} \) Which one of the
following given values will be closest to the radius of \( L u^{3+} \) (Atomic number of
\( \boldsymbol{L} \boldsymbol{u}=\mathbf{7} 1) ? \)
A \( .40 A \)
в. \( 1.06 A \)
c. 0.85
D. \( 1.60 A \)


The domain of the function \( y= \)
\( -2 x^{2}+6 x+5 \) is
\( \mathbf{A} \cdot x \in R \)
в. \( x \in(-2,0] \)
c. \( x \in[1,3) \)
D. \( x \in(1,3] \)


Write notes on
(a) Compensation point
(b) The blackman's principle of limiting factors
(c) Rubisco
(d) Photorespiration and aerobic respiration
(e) Light reaction and dark reaction
(f) \( C_{3} \) and \( C_{4} \) plants


Who proposed the term ecosystem?
A. Odum
B. Gardner
c. Warming
D. Tansley


A wire suspended vertically is stretched by a \( 20 \mathrm{kg} f \). Applied to its free end. The increase in length of the wire is 2 mm. The energy stored in the wire is \( \left(g=10 m s^{-2}\right) \)
B. \( 0.2 J \)
c. \( 0.4 J \)
D. \( 5 J \)


ntegrate the function \( \frac{1}{\sqrt{8+3 x-x^{2}}} \)


Which of the following has the minimum bond length?
\( A \cdot O_{2}^{+} \)
B. \( O_{2} \)
\( c \cdot o_{2}^{2} \)
D. \( O_{2} \)


Assertion
The aqueous solution of \( F e C l_{3} \) is basic
in nature.
Reason
FeCl \( _{3} \) hydrolyses in water.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Reason is correct but Assertion is incorrect
D. Both Assertion and Reason are incorrect


By applying \( S A S \) congruence rule, you
want to establish that \( \triangle \boldsymbol{P} \boldsymbol{Q} \boldsymbol{R} \equiv \)
\( \triangle F E D . \) It is given that \( P Q=F E \) and
\( R P=D E . \) What additional information
is needed to establish the congruence?


(1) \( N_{2}+2 O_{2} \leftrightarrow 2 N O_{2} ; K_{e}=2 \times 10^{-31} \)
(2) \( 2 N O^{+} \leftrightarrow N_{2}+O_{2} ; K_{e}=2.2 \times \)
\( \mathbf{1 0}^{-\mathbf{3 1}} \)
(3) \( 2 N_{2} O_{5} \leftrightarrow 2 N_{2}+5 O_{2} ; K_{e}=3.8 \times \)
\( 10^{-32} \)
(4) \( 2 N_{2}+O_{2} \leftrightarrow 2 N_{2} O ; K_{e}=4 \times \)
\( 10^{-32} \)
From the above data, the most stable
oxide is:
A. \( N O_{2} \)
B. \( N O \)
\( \mathbf{c} \cdot N_{2} O_{5} \)
D. \( N_{2} O \)


An object may appear moving to one person and at rest to another person at the same time Justify giving an example.


The change in the nucleus to form a new nuclide from a parent nucleus is called :
A. binding energy
B. transmutation
c. stability
D. generation
E. synthesis


Anxiety and eating spicy food together in an otherwise normal human may lead to
A. Indigestion
B. Jaundice
c. Diarrhea
D. Vomiting


The total energy of the electron in the hydrogen atom in the ground state is \( -13.6 \mathrm{eV} . \) Which of the following is its kinetic energy in the first excited state?
A . 13.6 ev
B. 6.8 ev
c. 3.4 ev
D. \( 1.825 \mathrm{eV} \)


Which of the following statement is
correct?
\( \mathbf{A} \cdot p K_{w}=14 \) at all temperature
B \( \cdot p K_{w}=0 \) at \( 0^{0} C \)
C \( \cdot p K_{w} \) decreases with increase temperature
D. \( p K_{w} \) increases with increase in temperature


Construct a quadrilateral \( A B C D \) in
which \( \boldsymbol{A B}=\mathbf{4 c m}, \boldsymbol{B C}= \)
\( \mathbf{3 . 1 c m}, \boldsymbol{C D}=\mathbf{3} c \boldsymbol{m} . \boldsymbol{A D}=\mathbf{4 . 2 c m} \) and
\( A C=5 c m ? \) measure the diagonal \( B D \)
\( ? \)


Find vertex and focus for the equation
\( \boldsymbol{y}^{2}-\mathbf{8} \boldsymbol{y}-\boldsymbol{x}+\mathbf{1} \boldsymbol{9}=\mathbf{0} \)


A dielectric of thickness \( 5 \mathrm{cm} \) and a
dielectric constant 10 is introduced
between the plates of a parallel plate capacitor having plate area 500 sq. \( \mathrm{cm} \) and separation between the plates \( 10 \mathrm{cm} \)
The capacitance of the capacitor with the dielectric slab is \( \varepsilon_{0}=8.8 \times 10^{-12} C^{2} / N- \)
\( m^{2} \)
A \( .4 .4 p F \)
B. \( 6.2 p F \)
c. \( 8 p F \)
D. \( 10 p F \)


In the figure given below, \( E \) is a point on
the side \( A D \) produced of a
parallelogram \( A B C D \) and \( B E \)
intersects \( C D \) at \( F \). Show that
\( \triangle A B E \sim \triangle C F B \)


Maximum prescribed limit of \( M n \) in
drinking water is:
A. 0.005 ppm
B. 0.05 ppm
c. 0.0005 ppm
D. 5 ppm


n figure, \( A B C E F G A \) is a square
conducting frame of side \( 2 m \) and
resistance \( 1 \Omega m^{-1} \). A uniform
magnetic field \( B \) is applied
perpendicular to the plane and pointing inward. It increases with time at a
constant rate of \( 10 T s^{-1} \). Find the rate
at which heat is produced in the circuit, \( A B=B C=C D=B H \)


Decomposers converts
A. Organic material into inorganic material
B. Organic matter into carbon dioxide and nutrients
C. Kill the soil microbes
D. All


Evaluate: \( 1.2+2.3+3.4+\ldots+ \)
\( n(n+1)=\frac{n}{3}(n+1)(n+2) \)


Find the probability distribution of the
number of successes in two tosses of a
die, where a success is defined as
(i) number greater than 4
(ii) six appears on at least one die


Pteridophyte called as stag's horn fern
is
A . Azolla
B. Platycerium
c. Botryopteris
D. Salvinia


Which of the following are the best
methods for the preparation of n-propy
benzene \( (\boldsymbol{A}) ? \)
This question has multiple correct options
\( \mathbf{A} \)
\[
\bigcirc+\mathrm{Me}^{\mathrm{Cl}}+\mathrm{AlCl}_{3} \longrightarrow(\mathrm{A})
\]
\( B \)
\[
\square+\mathrm{Me} \overbrace{\mathrm{BF}_{3}}^{\mathrm{OH}} \rightarrow(\mathrm{A})
\]
\( c \)
\[
\bigcirc+\mathrm{Me} \overbrace{\|}_{\mathrm{O}}^{\mathrm{Cl}}+\mathrm{AlCl}_{3} \longrightarrow
\]
D.
\[
\bigcirc+\mathrm{Me} \overbrace{\|}_{\mathrm{O}}^{\mathrm{Br}}+\mathrm{AlBr}_{3} \longrightarrow
\]
\[
\mathrm{NH}_{2} \mathrm{NH}_{2}+\stackrel{\oplus}{\mathrm{OH}}
\]


Cellulose is a:
A. protein
B. carbohydrate
C. simple sugar
D. all the above


Acetone on addition to methyl magnesium bromide forms a complex, which on decomposition with acid gives
\( X \) and \( M g(O H) B r . \) Which one of the
following is \( \boldsymbol{X} \) ?
\( \mathbf{A} \cdot C H_{3} O H \)
в. \( \left(C H_{3}\right)_{3} C O H \)
\( \mathrm{c} \cdot\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHOH} \)
D. \( C H_{3} C H_{2} \) OH


Explain the formation of a double bond
in oxygen molecule


Electrical welding works on principle of:
A. continuity equation of electric current
B. heating effect of electric current
C. heating effect of exothermic reactions
D. none of the above


The internal energy of air in a room of
volume \( 50 \mathrm{m}^{3} \) at atmospheric pressure
will be
A \( \cdot 2.5 \times 10^{7} \) erg
B . 2.5 \( \times 10^{7} \) Joule
c. \( 5.255 \times 10^{7} \) Joule
D. \( 1.25 \times 10^{7} \) Joule


The electron present in excited state of
\( H e^{\oplus \text { ion shows separation on collision }} \)
with an electron having 2.5 eV energy. What will be the minimum value of \( n \) for
this electrons of \( H e^{\oplus} \) ion?
A .4
B. 5
\( c \cdot 6 \)
D. 3


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{2} & \mathbf{3} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \boldsymbol{B}=\left[\begin{array}{ll}\mathbf{3} & \mathbf{4} \\ \mathbf{1} & \mathbf{1}\end{array}\right] . \) Prove that
\( (A B)^{\prime}=B^{\prime} A^{\prime} \)


The radius in kilometers to which the
present radius of the earth \( (\boldsymbol{R}= \)
\( 6400 k m) \) is to be compressed so that
the escape velocity is increased to 10 times is :
A. 6.4
B. 64
\( c \cdot 640 \)
D. 4800


\( 2- \)
Chlorobutane 15 percent aq. solution of ethyl
\( \boldsymbol{P} \)
In this reaction \( 70 \% \) racemization takes
place. \% of the inverted product would
be:
A . 30
B. 70
c. 35
D. 65


A car is travelling with linear velocity \( \mathbf{v} \) on a circular road of radius R. If its
speed is increasing at the rate of a
\( \boldsymbol{m} / \boldsymbol{s}^{2}, \) then the net acceleration will be :
\( ^{\text {A }} \cdot \frac{v^{2}}{R}+a \)
в. \( \frac{v^{2}}{R}-a \)


\( \boldsymbol{H O O C}-\boldsymbol{C H}_{2}-\underset{1}{\boldsymbol{C} \boldsymbol{H}}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C O O H} \)
COOH
What is the IUPAC name of the given
compound?
A. Propane-1,2,3-tricarboxylic acid
B. Propane -1,2,3 - trioic acid
c. 1,2,3 - tricarboxylic propane
D. Propanedioic carboxylic acid


Simplify \( 2(3 b-5 a)-7[9- \)
\( 62-5(a-6)] \)


Which of the following is known as
Freon?
A \( \cdot C C l_{2} F_{2} \)
в. \( C H C l_{3} \)
c. \( C H_{2} F_{2} \)
D. \( C F_{4} \)


Mass numbers of two isotopes of an element differ by 2 units \( (A \text { and } A+2) \)
Average atomic mass is 0.5 more than
the lower mass number. What could be
the ratio of the percentage abundance two isotopes respectively?


What are biodegradable substance. Give two examples.


Which of the following is referred to as the world's most problematic aquatic weed?
A. Abelmoschus esculentus
B. Eichhornia crassipes
c. Parthenium hysterophorus
D. Planktonic algae


The portion of the spectrum beyond the red end is called
B. Infrard spectrum
c. Microwave
D. All


What is the molar mass of diacidic
organic Lewis base, if 12 g of chloroplatinate salt on ignition produced 5 g residue?
A .52
B. 58
c. 88
D. None of the above


Sieves are used at construction sites to
separate pebbles and stones from sand.
A. True
B. False


The mass of the moon is about \( 1.2 \% \) of
the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the
moon exerts on earth
A. Is the same
B. Is smaller
c. Is greater
D. Varies with its phase


If \( \frac{\tan 2 \theta+\tan \theta}{1-\tan \theta \tan 2 \theta}=0, \) then the
general value of \( \boldsymbol{\theta} \) is
A \( , n \pi ; \in I \)
\( I \)
B. \( \frac{n \pi}{3} ; \in I \)
c. \( \frac{n \pi}{4} ; \in I \)
D. \( \frac{n \pi}{6} ; \in I \)


Earthworm has no skeleton. During burrowing anterior end becomes turgid and acts as hydraulic skeleton. It is due
to
A. Gut peristalsis
B. Setae
c. Coelomic fluid
D. Blood


Calculate the mass loss in the
following:
\( _{1}^{2} \boldsymbol{H}+_{1}^{3} \boldsymbol{H} \longrightarrow_{2}^{4} \boldsymbol{H} \boldsymbol{e}+_{0}^{1} \boldsymbol{n} \)
Given the masses: \( _{1}^{2} H=2.014 \) amu, \( _{1}^{3} \boldsymbol{H}=\mathbf{3 . 0 1 6} \boldsymbol{a m u} ;_{2}^{4} \boldsymbol{H e}=\mathbf{4 . 0 0 4} \boldsymbol{a m u} \)
\( \mathbf{0}_{\mathbf{n}}=\mathbf{1 . 0 0 8} \) amu.
\( \mathbf{A} \cdot 0.018 a m u \)
B. 0.18 amu
c. 0.0018 amu
D. 1.8 amu
E . 18 amu


Which of the following statement is
true?
A \( \cdot \frac{3}{-8}>\frac{-12}{32} \)
B. \( \frac{3}{-8}=\frac{-12}{32} \)
c. \( \frac{3}{-8}<\frac{-12}{32} \)
D. \( \frac{3}{5}>\frac{4}{3} \)


If the pressure within a discharge tube is reduced from \( 10^{-3} \) mm to \( 10^{-4} \) mm
mercury then the rays which are produced perpendicular to the cathode surface are known as
A. Anode rays
B. Cathode rays
c. x-rays
D. canal rays


Which of the following does not show water shortage?
A. Taps running dry
B. Long queues for getting water
c. A family getting 3 buckets of water per person per day
D. None of these


Choosing a marble from a jar and landing on heads after tossing a coin is
an act of
A. experiment
B. space
c. sample
D. event


A hydrocarbon \( Y \) decolourizes bromine water. The saturated compound resulted in this reaction, on treatment
with \( Z n \) dust gives back hydrocarbon \( Y \)
\( Y \) when passed through a solution of
\( A g N O_{3} \) dissolved in \( N H_{4} O H \) gives a white precipitate. The next higher homologue of \( Y \) that is \( X \) gives ketone
\( A \) as the product upon addition of water Identify \( X, Y, A \) and give equations.


\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{\sqrt{1+\boldsymbol{p} \boldsymbol{x}}-\sqrt{\mathbf{1}-\boldsymbol{p} \boldsymbol{x}}}{\boldsymbol{x}} \\ \frac{\mathbf{2} \boldsymbol{x}+\mathbf{1}}{\boldsymbol{x}-\mathbf{2}}, \quad \mathbf{0} \leq \boldsymbol{x} \leq \mathbf{1}\end{array} \quad, \quad-\mathbf{1} \leq \boldsymbol{x}<\right. \)
0 is continuous in the interval [-1,1]
then \( p \) equals-
A . -1
B. \( -\frac{1}{2} \)
\( c \cdot \frac{1}{2} \)
\( D \)


A real image is formed when two or
more
This question has multiple correct options
A. reflected rays meet
B. refracted rays meet
C . reflected rays appear to meet
D. rays actually meet


Solar cells are made of :
A. silicon
B. germaniuminmmmmm
c. silver
D. aluminium


In silkworm, silk is the product of
A. Salivary gland of the larva
B. Salivary gland of the adult
c. Cuticle of the larva
D. Cuticle of the adult


don't conduct electricity indicating that they do not form ions
A. Alcohol
B. Glucose
c. Both a and \( b \)
D. None of these


Find the roots of the equation \( a(b- \)
\( c) x^{2}+b(c-a) x+c(a-b)=0 \)


The inner circumference of a circular
track is \( 24 \pi \mathrm{m} \). The track is \( 2 \mathrm{m} \) wide
from everywhere. The quantity of wire required to surround the path completely is
A. \( 80 \mathrm{m} \)
B. \( 81 \mathrm{m} \)
c. \( 82 \mathrm{m} \)
D. 88m


The law of equipartition of energy is applicable to the system whose
constituents are :
A. in random motion
B. in orderly motion
c. at rest
D. moving with constant speedd


\( \angle A B D>\angle C \)
f the above statement is true then
mention answer as 1 , else mention 0 if
false


Electrical conductivity of a semiconductor increases when em
radiation of \( \lambda<2480 n m \) is incident on
it. The band gap in (ev) for the semiconductor is
\( \mathbf{A} \cdot 1.1 e V \)
B . \( 2.5 e V \)
c. \( 0.7 e V \)
\( \mathbf{D} \cdot 0.5 e V \)


Differentiate:
\( \boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}=\tan \boldsymbol{x}+\boldsymbol{y} ? \)


LPG burns more cleanly than higher molecular weight hydrocarbon:
A. because it releases volatile pollutants
B. because it releases less pollutants
c. because it releases pollutants which are toxic
D. because it releases more pollutants


The substance used to harden the
rubber for tyre manufacture is:
\( A \cdot \) wax
B. 1,3-butadiene
c. calcium carbide
D. carbon black


Express \( r^{\rightarrow}=9 i+2 j-7 k \) as a linear
combination of \( a^{\rightarrow}=i-2 j+k \) and \( b^{\rightarrow}= \)
\( i+2 j-3 k \)


A rectangular coil of 300 turns has an
average area of \( 25 \mathrm{cm} \times 10 \mathrm{cm} . \) The coil
rotates with a speed of 50 cps in uniform magnetic field of strength \( 4 \times \) \( 10^{-2} T \) about an axis perpendicular to
the field. The peak value of the induced emf is \( (\text { in } v o l t) \)
A. \( 300 \pi \)
B. 3000 \( \pi \)
\( c .3 \pi \)
D. \( 30 \pi \)


Quinine is a bitter medicine used for
treatment of malaria.
A. True
B. False


In absorbtion method, the polluted air containing gaseous pollutants is passed through:
A. porous material with very small holes
B. flame combuster
c. scrubber containing a suitable liquid absorbent
D. strainer


The correct shape of a water drop
enclosed between two glass plates in
gravity free space will be:
\( A \)
в.
\( c \)
D.


Echocardiogram (ECG) is a measure of
A. Rate of heart beat
B. Difference in electric potential
c. volume of blood pumped
D. Ventricular contraction


A series LCR circuit consists of an
inductor L a capacitor \( C \) and a resistor \( R \)
connected across a source of emf \( \varepsilon= \)
\( \varepsilon_{0} \sin \omega t . \) When \( \omega L=\frac{1}{\omega C} \) the current in
the circuit is \( l_{0} \) and if angular frequency
of the source is changed to \( \omega \) ', the
current in the circuit becomes \( \frac{l_{0}}{2}, \) then
the value of \( \left|\boldsymbol{\omega}^{\prime} \boldsymbol{L}-\frac{\mathbf{1}}{\omega^{\prime} \boldsymbol{C}}\right| \) is
\( A \)
B. \( \sqrt{3} \) R
\( c \cdot \sqrt{15} \)


The function \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}x^{2} / a, & 0 \leq x<1 \\ a, & 1 \leq x<\sqrt{2} \\ \frac{2 b^{2}-4 b}{x^{2}}, & \sqrt{2} \leq x<\infty\end{array}\right. \)
continuous for \( 0 \leq x<\infty, \) then the
most suitable values of \( a \) and \( b \) are
B. \( a=-1, b=1+\sqrt{2} \)
c. \( a=-1, b=1 \)
D. None of these


Name a metal refined by Van Arkel
method.


'Be \( _{2} C \) and \( A l_{4} C_{3} \) are called ethanides
because they react with \( H_{2} O \) yielding
ethane."

Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Any salt \( M C l_{2} \) is soluble in water, if
it's hydration energy exceeds the lattice
energy of \( M C l_{2} \)
A. True
B. False


A conductor of resistance \( 3 \Omega \) is
stretched uniformly till its length is doubled. The wire now is bent in the
form of an equilateral triangle. The effective resistance between the ends of
any side of the triangle in ohms is :
A \( \cdot \frac{9}{2} \)
B. \( \frac{8}{3} \)
\( c \cdot 2 \)
D.


\( \boldsymbol{x} * \boldsymbol{y}=\sqrt{\frac{(\boldsymbol{x}+\boldsymbol{y})\left(\boldsymbol{y}^{2}-\mathbf{1 2} \boldsymbol{x}\right)}{(\boldsymbol{x}-\mathbf{2})(\boldsymbol{y}-\mathbf{7})}} \) then what
will be the value of \( 5 * 9 ? \)
\( A \cdot 7 \)
B. 8
c. 10
D.


Chipko movement was launched for the protection of
A. Livestock
B. Wetlands
c. Grasslands
D. Forests


Subtract -24 from +38
\( A \cdot+14 \)
B. +62
\( c .-14 \)
D. -62


The magnitude of resultant of three vectors of magnitude 1,2 and 3 whose direction are those of the sides of an
equilateral triangle taken in order is:
\( A \cdot 0 \)
B. \( 2 \sqrt{2} \) units
c. \( 4 \sqrt{3} \) units
D. \( \sqrt{3} \) units


Due to lanthanide contraction:
A. \( F e, C o, N i \) have equal size
B. \( Z r \) and \( H f \) have equal size
C. all \( f- \) block ions have equal size
D. all isoelectronic ions have equal size


Undamped oscillations are practically impossible because
A. there is always loss of energy.
B. there is no force opposing friction.
C. energy is not conserved in such oscillations
D. None of these.


An amplifier has a voltage gain \( \boldsymbol{A}_{\boldsymbol{v}}= \)
1000. The voltage gain in dB is:
\( \mathbf{A} \cdot 30 d B \)
В. \( 60 d B \)
c. \( 3 d B \)
\( \mathbf{D} \cdot 20 d B \)


Two times the interior angle of a regular polygon is equal to seven times is exterior angle. Find the interior angle of
the polygon and the number of sides in ¡t.
A. \( 130^{\circ} \) and \( n=9 \)
B. \( 140^{\circ} \) and \( n=9 \)
c. \( 160^{\circ} \) and \( n=9 \)
D. \( 170^{\circ} \) and \( n=9 \)


Antacids are
A. drugs or other compounds that inhibits the physiological effects of histamine, used especially in the treatment of allergies.
B. (of a drug) used to relieve pain.
C . medicinal drugs taken to reduce tension or anxiety.
D. (chiefly of a medicine) used to prevent or correct acidity, especially in the stomach.


A boat crossing a river moves with a velocity v relative to still water. The river
is flowing with a velocity v/2 with
respect to the bank. The angle with respectively the slow direction with which the boat should move to
minimize the drift is
A \( .30^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 180^{\circ} \)
D. \( 120^{\circ} \)


When current flows through a
conductor, then the order of drift
velocity of electrons will be:-
\( \mathbf{A} \cdot 10^{10} \mathrm{cms}^{-1} \)
B. \( 10^{-2} \mathrm{cms}^{-1} \)
\( \mathbf{c} \cdot 10^{4} c m s^{-1} \)
D. \( 10^{-1} \mathrm{cms}^{-1} \)


A charged ball B hangs from a silk
thread \( S \) which makes an angle \( \theta \) with a
arge charged conducting sheet \( \mathrm{P} \) as shown in the given figure. The surface charge density \( \sigma \) of the sheet is
proportional to :
\( A \cdot \cos \theta \)
B \( \cdot \cot \theta \)
\( c \cdot \sin \theta \)
D. \( \tan \theta \)


In the commercial electrochemical
process for aluminium extraction, the
electrolyte used is:
A \( \cdot A l(O H)_{3} \) in \( N a O H \) solution
B. An aqueous solution of \( A l_{2}\left(S O_{4}\right)_{3} \)
c. A molten mixture of \( A l_{2} O_{3}, N a_{3} A l F_{6} \& C a F_{2} \)
D. A molten mixture of \( A l O(O H) \) and \( A l(O H) \)


In n type semiconductor, electrons are
majority charge carriers but it does not show any negative charge. The reason is
A. Electrons are stationary
B. Electrons neutralize with holes
c. Mobility of electrons is extremely small
D. Atom is electrically neutral


By inserting a soft iron piece into a solenoid, strength of the magnetic field
A. increases
B. decreases
c. first increases then decreases
D. remains unchanged


Assertion
Atom with large atomic radii and low
ionisation potential are more metallic
in nature.
Reason
Atom with large atomic radii and low
ionisation potential have tendency to
loose electron
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The value of acceleration due to gravity
near the earth's surface is
A \( \cdot 8.9 m / s^{2} \)
в. \( 7.9 m / s^{2} \)
\( \mathrm{c} \cdot 9.8 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 19.8 m / s^{2} \)


Oil floats on water. The most accurate
reason for this is:
A. oil is less dense than water
B. oil is immiscible (does not dissolve) in water
C. oil is both less dense and immiscible with water
D. water is heavier than oil


Which of the following is true about
given compound?
\( A \), It is aromatic
3. It is non aromatic
c. It is anti aromatic.
Denatic behavior cannot be predicted


Photorespiration takes place in
A. Chloroplast, mitochondria
B. Mitochondria, peroxisome
C. Chloroplasts, peroxisome, mitochondria
D. Chloroplasts, cytoplasm, mitochondria


A flexible chain of weight \( 10 N \) hangs
between two fixed points \( A \) and \( B \)
which are at the same horizontal level.
The inclination of the chain with the
horizontal at both the points of support
is \( 45^{\circ} . \) Find the tension (in \( N \) ) of the
chain at the mid point.


Is the acceleration uniform?
A. Yes
B. No
c. мау be
D. Can't be determined from the given data


Through the point (3,4) are drawn two
straight lines each inclined at 45 to the
straight line \( \boldsymbol{x}-\boldsymbol{y}=\mathbf{2} \)
Find their equations and also find the area of triangle bounded by the three lines.


Integrate \( \int\left(x^{3}-1\right)^{\frac{1}{3}} x^{5} d x \)
\( \frac{1}{3}\left(\frac{3}{7}\left(x^{3}-1\right)^{\frac{7}{3}}+\frac{3}{4}\left(x^{3}-1\right)^{\frac{4}{3}}\right) \)
\( \frac{1}{3}\left(\frac{3}{7}\left(x^{3}-1\right)^{\frac{5}{3}}+\frac{3}{4}\left(x^{3}-1\right)^{\frac{4}{3}}\right) \)
\( \frac{1}{3}\left(\frac{3}{7}\left(x^{3}-1\right)^{\frac{7}{3}}-\frac{3}{4}\left(x^{3}-1\right)^{\frac{4}{3}}\right) \)
D. None of these


A diatomic gas is heated at constant
pressure. The fraction of the heat energy used to increase the internal energy is
A \( \cdot \frac{3}{5} \)
B. \( \frac{3}{7} \)
\( c \cdot \frac{5}{7} \)
D. \( \frac{7}{9} \)


Assertion
Granulocytes are white blood cells.
Reason
They contain lobed nuclei and
tiny granules.
A. If both the assertion and the reason are true and the
reason is correct explanation of the assertion.
B. If both the assertion and the reason are true but the
reason is not 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


Calculate the velocity of the bob of a
simple pendulum at its mean position if it is able to rise to a vertical height of \( 10 \mathrm{cm} . \) Given: \( g=980 \mathrm{cms}^{-2} \)


A reaction in which heat is absorbed is
called an endothermic reaction.If true
enter 1 else 0
\( A \)


Alcoholic fermentation takes place in
the presence of
A. Maltase.
B. Zymase.
c. Amylase.
D. Invertase.


Find the number of acid(s) which can
form its meta derivative from the
following:
\( \boldsymbol{H}_{3} \boldsymbol{B} \boldsymbol{O}_{3}, \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4}, \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3} \)


Negation of \( \boldsymbol{q} \vee \sim(\boldsymbol{p} \wedge \boldsymbol{r}) \) is
A \( \cdot \sim q \wedge \sim(p \wedge r) \)
В . \( q \wedge(p \wedge r) \)
\( \mathbf{c} \cdot \sim q \vee(p \wedge r) \)
D. None of these


Assertion
Bond angle in \( P F_{3} \) greater than the
bond angle in \( \boldsymbol{P H}_{3} \)
Reason
Electrons in \( P F_{3} \) are displaced towards
more electro-negative \( \boldsymbol{F}, \) in \( \boldsymbol{P}-\boldsymbol{F} \) bond
A. Statement 1 is True, statement 2 is True; statement 2 is a correct explanation for statement 1.
B. Statement 1 is True, statement 2 is True; statement 2 is not a correct explanation for statement 1
c. statement 1 is True, statement 2 is False
D. Statement 1 is False, statement 2 is True


Statement I: Water is a polar molecule.
Statement II: Water has polar covalent
bonds.
A. Statement 1 is correct
B. Statement 2 is correct
c. statement 1 is correct but Statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are correct


Two cars \( X \) and \( Y \) start off to a race on a
straight path with initial velocities of 8 \( \mathrm{m} / \mathrm{s} \) and \( 5 \mathrm{m} / \mathrm{s} \) respectively. Car \( \mathrm{X} \)
moves with uniform acceleration of \( 1 m / s^{2} \) and car \( Y \) moves with uniform acceleration of \( 1.1 \mathrm{m} / \mathrm{s}^{2} . \) If both the cars reach the winning post together find the length of the track.
A. \( 1000 \mathrm{m} \)
B. 2000
c. 2500
D. 2280


A \( 10 \Omega \) resistance, \( 5 \mathrm{mH} \) coil and \( 10 \mu \mathrm{F} \)
capacitor are joined in series. When a suitable frequency alternating current source is joined to the combination, the circuit resonates. If the resistance is
halved the resonance frequency is
A. halved
B. doubled
c. remains same
D. quadrupled


The distance of the point (1,2) from the line \( x+y+5=0 \) measured along the
line parallel to \( 3 x-y=7 \) is equal to
A \( \cdot \frac{4}{\sqrt{10}} \)
B. 40
c. \( \sqrt{40} \)
D. \( 10 \sqrt{2} \)


\( \triangle A B C \) is an isosceles \( \triangle \) with \( A B= \)
\( A C \) side \( B A \) is produced to \( D \) such that
\( A B=A D \) prove \( \angle B C D \) is a right
angle.


Which of the following present in the soil is most helpful to the growth of plants?
A . Gravel
B. Humus
c. sand
D. silt


Find the values of the unknown \( x \) and \( y \)
in the following diagram.


The diagram represents an atom 'X!
Answer the following.
How many electrons will 'X' lose or gain
to become \( \boldsymbol{X}^{+1} \) ?
4
B. 2
\( c \)
\( D \)


For the reaction, \( \boldsymbol{N} \boldsymbol{H}_{3}+\boldsymbol{O C l}^{-} \rightarrow \)
\( N_{2} H_{4}+C l^{-} \) occurring in basic
medium, the coefficient of \( N_{2} H_{4} \) in the
balanced equation will be :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 4


Chromium compound widely used in the
tanning of leather is:
\( \mathbf{A} \cdot C r_{2} O_{7} \)
B. \( C r_{2} O_{2} C l_{2} \)
\( \mathrm{c} \cdot \mathrm{Cr}_{2} \mathrm{O}_{3} \)
D. \( K_{2} S O_{4} C r_{2}\left(S O_{4}\right)_{3} 24 H_{2} O \)


STATEMENT-1: Heat of neutralization of
\( \mathrm{HCl} \) and \( \mathrm{NaOH} \) is same as that of
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) with \( \mathrm{NaOH} \)
STATEMENT-2: HCI, \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) and \( \mathrm{NaOH} \)
are all strong electrolyte.
A. Statement-1 is True, Statement-2 is True; Statementis a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


Which of the following reactions are
examples of chemisorption?
This question has multiple correct options
A. Haber Process
B. Activated charcoal to decolorize sugar
C . Cross coupling reactions
D. Hydrogenation of Vanaspati ghee


The direction of the electric field in
Millikan's oil drop experiments acts.
A. Downwards
B. Upwards
c. First upwards then downwards
D. First downwards, then upwards


If radius of long solenoid is doubled, then its self inductance will be :
A. same
B. doubled
c. trippled
D. quadrupled


Evaluate using expansion of \( (a+b)^{2} \) or
\( (a-b)^{2}: \)
\( (45)^{2} \)


When two similar species live in the same area, they may evolve to become more different in order to
A. drive the other species to extinction
B. reduce competition
c. use up the other species resources
D. reduce genetic variation


Kepler's laws of planetary motion provides information about:
A. areal velocity of a planet
B. nature of motion of a planet
C. ratio of time periods of two planets
D. all the above


Find the solution of \( (x+y-1) d y= \)
\( (\boldsymbol{x}+\boldsymbol{y}) \boldsymbol{d} \boldsymbol{x} \)
\( \mathbf{A} \cdot 2(y-x)-\log (2 x-2 y-1)=k \)
B \( \cdot 2(y+x)-\log (2 x+2 y-1)=k \)
\( \mathbf{c} \cdot 2(y-x)-\log (x+2 y-1)=k \)
D \( \cdot 2(y-x)-\log (2 x+2 y-1)=k \)


\( S O_{2} \) and \( C l_{2} \) both are used as bleaching agent. Factors that cause bleaching are respectively:
A. \( H \) (that causes reduction), \( O \) (that causes oxidation)
B. \( O \) (that causes reduction), \( H \) (that causes oxidation)
c. \( H \) (that causes oxidation), \( O \) (that causes reduction)
D. \( O \) (that causes oxidation), \( H \) (that causes reduction)


If we divide a two-digit number by the
sum of its digits, we get 6 as a
quotient and 2 as a remainder. Now if
we divide it by the product of its digits,
we get 5 as a quotient and 2 as a remainder. Find the number.


Which one of the following are used to express the intensity of magnetic field in vacuum?
A . oersted
B. tesla
c. gauss
D. none of these


: The function \( f(x)=2 x^{3}-3 x^{2}- \)
\( 12 x+8 \) attains minimum value at \( x= \)
2
II: The function of \( f(x)=x^{4}-6 x^{2}+ \)
\( 8 x+11 \) attains minimum value at \( x= \)
2 which of the above statements are
true
A. onlyı
B. only II
c. both I and II
D. neither I nor II


The area of the triangle formed by the points \( (a, b+c),(b, c+a) \) and \( (c, a+b) \) is
\( A \)
B. \( a+b+c \)
\( c \cdot a b c \)
D.


If \( \alpha=\beta+\frac{2 \pi}{3} . \) then \( A_{\theta} \) is maximum
when \( \gamma \) equals
A. \( \alpha+\pi / 3 \)
в. \( \alpha-\pi / 3 \)
c. \( \alpha+2 \pi / 3 \)
D. none of these


For minima to take place between two monochromatic light waves of
wavelength \( \lambda \), the path difference
should be
A \( . n \lambda \)
B. \( (2 n-1) \frac{\lambda}{4} \)
c. \( (2 n-1) \frac{\lambda}{2} \)
D. \( (2 n-1) \lambda \)


What is a rectifier? With the help of a neat circuit diagram explain the working of a full wave rectifier.


A wire of resistance \( 20 \Omega \) is covered with
ice and a voltage of \( 210 \mathrm{V} \) is applied across the wire, then rate of melting the ice is
A. \( 0.85 \mathrm{g} / \mathrm{s} \)
B. 1.92 \( g / \) s
c. \( 6.56 \mathrm{g} / \mathrm{s} \)
D. All of these


Find the magnitude of force acting on
the conductor carrying current \( \boldsymbol{I} \) as
shown in the diagram. The magnitude of
magnetic field is \( B \) and direction is into
the plane of paper:
\( \mathbf{A} \cdot I(2 L+\mu R) B \)
\( \mathbf{B} \cdot I(2 L+R) B \)
\( \mathbf{c} \cdot I(2 L+2 R) B \)
D. none of these


Given that the \( 4^{t h} \) term in the expansion of \( \left(2+\frac{3 x}{8}\right)^{10} \) has the maximum numerical value, then \( x \) can lie in the
interval(s)
This question has multiple correct options
\( \mathbf{A} \cdot\left(2, \frac{64}{21}\right) \)
B \( \cdot\left(-\frac{60}{23},-2\right) \)
\( \mathbf{C} \cdot\left(-\frac{64}{21},-2\right) \)
D \( \cdot\left(2,-\frac{60}{23}\right) \)


Glucagon hormone is secreted by
A. Pituitary
B. Adrenal
C . Beta cells of islets of Langerhans
D. Alpha cells of islets of Langerhans


Which of the following is the correct representation of electron dot structure of nitrogen?
\( A \)
\( \therefore \ddot{N}: \dot{N} \)
в. \( \therefore \dot{\mathbf{N}}: \dot{\mathbf{N}} \)
\( \therefore \dot{\mathbf{N}}: \dot{\mathbf{N}} \)
D. \( \therefore \) N:


If \( \tan 6 \theta=\frac{p}{q}, \) find the value of \( \frac{1}{2}(p \operatorname{cosec} 2 \theta-q \sec 2 \theta) \) in terms of \( p \)
and \( \boldsymbol{q} \)
\( \mathbf{A} \cdot 2 \sqrt{p^{2}+q^{2}} \)
B \( \cdot \sqrt{p^{2}+q^{2}} \)
c. \( \frac{\sqrt{p^{2}+q^{2}}}{q} \)
D. \( \frac{\sqrt{p^{2}+q^{2}}}{p} \)


Ba is
A. more electronegative
B. more electropostive
C . less electropositive
D. none of the above


Assertion: If a block is in SHM, and a
new constant force acts in the direction
of change, the mean position may change. Reason :In SHM only variable forces
should act on the body, for example spring force.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion
c. Assertion is correct and Reason is incorrect
D. Assertion is incorrect and Reason is correct


Solve \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\mathbf{1}=\boldsymbol{e}^{\boldsymbol{x}+\boldsymbol{y}} \)
\( \mathbf{A} \cdot-1=(x+c) e^{x+y} \)
B \( \cdot 1=(x) e^{x+y}+c \)
\( \mathbf{c} \cdot 1=(x+c) e^{x-y} \)
\( \mathbf{D} \cdot-1=(x) e^{x-y}+c \)


The internal resistance of a primary cell
is 4 ohm. It generates a current of 0.2 ampere in an external resistance of 2
ohm. The rate at which chemical energy
is consumed in providing the current is
A \( .0 .42 \mathrm{J} / \mathrm{s} \)
B. 0.24 J/
\( c \cdot 5 J / s \)
\( D \cdot 1 J / s \)


The function of erepsin in the process of digestion is to convert
A. Fats into amino acids
B. Proteins in amino acids
c. Polysaccharides into saccharides
D. Disaccarides into monosaccharides


Solve \( 16^{\sin ^{2} x}+16^{\cos ^{2} x}=10 \)


Explain how you can take care of your
eyes.


The energy released when a positron is annihilated is :
A. \( 0.52 \mathrm{MeV} \)
B. 5.3Mev
c. 185 Mev
D. 200MeV


Write names and chemical formulae of
monomers used in preparing Buna-S.


Which of the following statements are
correct as per IUPAC sign convention?
This question has multiple correct options
A. The work done by the system on the surrounding is negative
B. The work done by the surrounding on the system is positive
C. The heat absorbed by the system from the surrounding is positive
D. The heat absorbed by the surrounding from the system is positive


In the above circuit, \( C=\frac{\sqrt{3}}{2} \mu F, R_{2}= \) \( 20 \Omega, L=\frac{\sqrt{3}}{10} H \) and \( R_{1}=10 \Omega . \) Current
\( \operatorname{in} L-R_{1} \) path is \( I_{1} \) and in \( C-R_{2} \) path
it is \( I_{2} \). The voltage of \( A . C \) source is \( \operatorname{given} \operatorname{by} V=200 \sqrt{2} \sin (100 t) \) volts.
The phase difference between \( I_{1} \) and \( I_{2} \)
is
A \( \cdot 30 \)
B . \( 0^{\circ} \)
\( c \cdot 150 \)
D. 60


Three vectors of magnitudes \( a, 2 a, 3 a \) meeting a point and three directions are along the diagonals of three adjacent faces of a cube. The magnitude of their resultant is
\( \mathbf{A} \cdot 3 a \)
B. \( 5 a \)
\( c \cdot 2 a \)
D. \( 4 a \)


The rate of cooling at \( 600 K \), if surrounding temperature is \( 300 K \) is \( \mathrm{H} \) The rate of cooling at \( 900 K \) is:
A \( \cdot \frac{16}{3} H \)
в. \( 2 H \)
\( c .3 H \)
D. \( \frac{2}{3} H \)


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{a}_{5} \boldsymbol{x}^{5}+\boldsymbol{a}_{4} \boldsymbol{x}^{4}+\boldsymbol{a}_{3} \boldsymbol{x}^{3}+ \)
\( a_{2} x^{2}+a_{1} x, \) where \( a_{i}^{\prime} s \) are real and
\( f(x)=0 \) has a positive root \( \alpha_{0} . \) Then
This question has multiple correct options
A \( \cdot f^{\prime}(x)=0 \) has a root \( \alpha_{1} \) such that \( 0<\alpha_{1}<\alpha_{0} \)
B . \( f^{\prime}(x)=0 \) has at least one real root
C \( \cdot f^{\prime \prime}(x)=0 \) has at least one real root
D. All of the above


toppr LoGIN vow 5
Q Type your question
acid or base is added to it. Buffer
solutions have wide applications.
\( 20.0 m L \) of \( 0.10 M \) of 1 -aminopropane is
titrated with \( 0.10 M \) of \( H C l . \) The \( p H \) at
the equivalence point is \( p \simeq 6 \) and the appropriate acid-base indicator. is
Methyl red. (4.2-6.2) wright the right
answer
Table 1.
Table 1: List of acid/base indicators
Common name \( \quad \) Transition
range, \( p \boldsymbol{H} \quad \) color
change ser red-
orange Methyl orange
Methyl red \( 4.2^{-6.2} \) red-
yellow
Phenol red \( 6.8-8.2 \) yellow-
red \( y \)
\( r \)
Phenolphthalein \( \quad 8.0-9.8 \quad \) colorlessThymolphthalein \( \quad 9.3-10.5 \quad \begin{array}{l}\text { colorless- } \\ \text { blue }\end{array} \)


The number of lines of symmetry for a rectangle is/are
A . 1
B. 2
\( c .3 \)
\( D \)


Look at the following reactions carried
out in closed vessels:
(i) \( \boldsymbol{P C I}_{5} \rightarrow \boldsymbol{P C I}_{3}+\boldsymbol{C I}_{2} \)
\( (\text { ii }) N_{2}+O_{2} \rightarrow 2 N O \)
(iii) \( 2 K C I O_{3} \rightarrow 2 K C I+3 O_{2} \)
\( (\text { iv }) \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{S} \boldsymbol{C} \boldsymbol{N}_{-} \rightarrow \boldsymbol{F} \boldsymbol{e}(\boldsymbol{S} \boldsymbol{C} \boldsymbol{N})^{2+} \)
Which one of them is irreversible?
sc
A . \( (i) \)
B. (ii)
c. \( (i i i) \)
D. (iv)


What is the equilibrium concentration of each at the substances in
equilibrium. When the initial
concentration at ICl was \( 0.70 ? \)
\( \boldsymbol{I}_{C l} \rightarrow \boldsymbol{I}_{2}+\boldsymbol{C l}_{2} \)
\( \mathrm{Kc}=0.14 \)


The \( 5^{t h} \) and \( 8^{t h} \) terms of a GP are 1458
and \( 54, \) respectively. The common ratio
of the GP is
A \( \cdot \frac{1}{3} \)
B. 3
\( c \cdot 9 \)
D. \( \frac{1}{9} \)
E


Which of the following statement is
wrong about the reaction?
A. At lower temperature, the reaction is kinetically controlled and o/p directive effects of the \( (M e) \) group operate
B. At a higher temperature, the reaction is thermodynamically controlled, and longer reaction times are employed for equilibrium to be reached. The most stable form of m-toulene sulphonic acid is obtained
C. \( (M e-) \) group is activated by +1 effect, and \( o-, p- \) directing
D. \( (M e-) \) group is deactivating by hyperconjugation and is \( m- \) directing


A glass ball collides with a smooth horizontal surface with a velocity \( a \hat{i}- \)
b \( \hat{j} \). If the coefficient of restitution of
collision be \( e, \) find the velocity of the ball just after the collision.


For an electron in the second orbit of
hydrogen, the angular momentum as per Bohr's model is :
A. \( \frac{h}{\pi} \)
в. \( \frac{2 h}{\pi} \)
c. \( \frac{h}{2 \pi} \)
D. \( 2 \pi h \)


State whether the given statement is
True or False :

Nuclear power plants as compared to other plants can generate huge amount of electricity.
A. True
B. False


\( A \) thin prism \( P_{1} \) with angle \( 6^{\circ} \) and made from glass of refractive index 1.54 is
combined with another thin prism \( P_{2} \) of
refractive index 1.72 to produce dispersion without deviation. The
angle of prism \( P_{2} \) will be.
A . \( 4^{\circ} 30^{\circ} \)
B. \( 8.5^{\circ} \)
c. \( 6.5^{\circ} \)
D. None of these


Fill in the blanks
Hypermetropia can be corrected by using lens.


The hormone ANP is produced by the
A. Adrenal glands
B. Capillary walls
c. Kidneys
D. Atria


Assertion
The time period of a simple pendulum is independent of its length.
Reason
The length of a pendulum is the distance between point of suspension
and centre of the bob
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Two pendulums differ in lengths by
\( 22 \mathrm{cm} . \) They oscillate at the same place
so that one of them makes 30
oscillations and the other makes 36
oscillations during the same time. The lengths (in \( \mathrm{cm} \) ) of the pendulums are
\( \mathbf{A} \cdot 72 \) and 50
B. 60 and 38
c. 50 and 28
D. 80 and 58


The addition of dilute \( H C l \) to unknown
metal produced a transparent gas. What is the likely identity of this gas?
A \( \cdot C l_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( C O_{2} \)
E. \( N O_{2} \)


A first order reaction is \( 60 \% \) complete in 20 min. How long will the reaction take to be \( 84 \% \) complete?
A. 60 min
B. 40 min
c. 76 min
D. 54 min


Read the given statements and select
the correct option.

Statement 1: About 70\% of \( C O_{2} \) that
enters RBCs changes into. \( \boldsymbol{H} \boldsymbol{C O}_{3} \) for transport in plasma to the lungs where
it reconverts into \( C O_{2} \) for elimination.
Statement 2: About \( 40 \% \) of \( C O_{2} \) that
enters RBCs changes into carbaminohaemoglobin which releases
\( O_{2} \) in the lungs.
A. Both statements 1 and 2 are correct.
B. Statement 1 is correct but statement 2 is incorrect
c. Statement 1 is incorrect but statement 2 is correct
D. Both statements1 and 2 are incorrect.


The compounds used as refrigerant are:
This question has multiple correct options
A. \( N H_{3} \)
в. \( C C l_{4} \)
c. \( C F_{4} \)
D. \( C F_{2} C l_{2} \)
E. \( C H_{2} F_{2} \)


The solubility product of \( A g_{2} C r O_{4} \) is
\( 1.9 X 10^{-12} . \) The volume of water in \( \mathrm{mL} \)
that can dissolve \( 4 \mathrm{mg} \) of \( A g_{2} C r O_{4} \) is
about:
A . \( 150 \mathrm{mL} \)
B. 1000 mL
\( c . \) 250 \( \mathrm{mL} \)
D. 500 mL


Evaluate the following definite integral \( \int_{0}^{\pi / 2} \frac{\cos ^{2} x}{1+3 \sin ^{2} x} d x \)


The value of susceptibility for super
conductor is
\( A \cdot O \)
\( B . \infty \)
\( \mathbf{C} \cdot+1 \)
D. - -


In vorticella, the total number of micronuclei formed at the end of prezygotic nuclear division in female
gamete is
A .4
B. 6
\( c \cdot 8 \)
D.


What is the equation for the graph
shown above?
\( \mathbf{A} \cdot y=2 \)
B. \( y=-4 \)
c. \( x=2 \)
D. \( x=-4 \)


The correct order for acid strength is:
\( \mathbf{A} \cdot A l_{2} O_{3}<S i O_{2}<P_{2} O_{3}<S O_{2} \)
B. \( S i O_{2}<S O_{2}<A l_{2} O_{3}<P_{2} O_{3} \)
\( \mathbf{c} \cdot A l_{2} O_{3}<S i O_{2}<S O_{2}<P_{2} O_{3} \)
D. \( S O_{2}<P_{2} O_{3}<S i O_{2}<A l_{2} O_{3} \)


Smoke is a form of wet deposition of acid rain. True or false?
A. True
B. False


A missile fired from ground level rises \( x \)
metres vertically upward in \( t \) second and \( \boldsymbol{x}=\mathbf{1 0 0 t}-\frac{\mathbf{2 5}}{\mathbf{2}} \boldsymbol{t}^{\mathbf{2}} \)
Find
(i) the initial velocity of the missile.
(ii) the time when the height of the
missile is a maximum
(iii) the maximum height reached and
(iv) the velocity with which the missile
strikes the ground.


Three resistors \( (2,5 \text { and } 7 \text { ohm }) \) are
wires as shown in the diagram
below. The equivalent resistance of this
combination (in ohm) is:
A \( \cdot \frac{59}{70} \)
B. \( \frac{70}{59} \)
\( c \cdot \frac{1}{14} \)
D. 14
E. Cannot be determined without additional information


Periscope works on the principle of:
A. refraction of light
B. reflection of light
c. diffraction of light
D. scattering of light


\( \infty,-0 \)
\( 01-0 \)
0,-0
\( 01-0 \)


8
8
8


The inflorescence found in coconut
plant is
A. Compound spadix
B. Hypanthodium
c. Cyathium
D. Vesti cillaster


Find the value of \( (-1+\sqrt{-3})^{2}+ \) \( (-1-\sqrt{-3})^{2} \)


A positively charged particle, having charge \( q, \) is accelerated by a potential difference V. This particle moving along the \( x \) -axis enters a region where an electric field \( \mathrm{E} \) exists. The direction of
the electric field is along positive y-axis. The electric field exists in the region
bounded by the line \( x=0 \) and \( x=a \)
Beyond the line \( x=a \) (i.e., in the region
\( x>a \) ), there exists a magnetic field of
strength B, directed along the positive y-axis. Find the pitch of the helix formed
after the particle enters the region \( x \geq \)
a. (Mass of the particle is \( m \) )


The IUPAC name of \( \boldsymbol{C H}_{3} \boldsymbol{N} \boldsymbol{H}_{2} \) is :
A. methylamine
B. amino ethane
c. methanamine
D. ethylamine


XX-XO sex chromosome complement
occurs in
A. cockroach
B. Honey Bee
c. Human beings
D. Chimpanzee


Prove that the line segment joining the mid point of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides?


In Drosophila the XXY constitution determines
A. Maleness
B. Femaleness
c. Intersex
D. Both A and C


Consider P-V diagram for an ideal gas
shown in figure. Out of the following diagrams, which
represents the T-P diagram?
A . (iv)
B. (ii)
c. (iii)
D. (i)


Sodium is not used to form hydrogen
gas. why?
A. Sodium does not react with HC
B. Sodium gives exothermic reaction with HC
c. Sodium reacts violently with HCI
D. Both B and C


\( \ln \) an \( A C \) circuit \( , \) the current is given by \( 1=4 \sin (100 \pi+300) \) ampere. The
current becomes maximum first time
(after \( t=0 \) ) at \( t \) equal to
A \( \cdot(1 / 200) \) sec
B. 300sec
c. \( (1 / 50) \) sec
D. \( (1 / 300) \) sec


The function given by \( y=\| x|-1| \) is
differentiable for all real numbers
except the points.
B. ±1
\( c \cdot 1 \)
D. -


The dissociation of water at \( 25^{\circ} \mathrm{C} \) is
\( 1.9 \times 10^{-7} \% \) and the density of water is
1.0 g/cc. The ionisation constant of water is :
A. \( 3.42 \times 10^{-6} \)
В. \( 3.42 \times 10^{-8} \)
c. \( 1.00 \times 10^{-14} \)
D. \( 2.00 \times 10^{-16} \)


A current passing through a circle coil of two turns produces a magnetic field \( B \) as its centre. The coil is then rewound
so as to have four turns and the same
current is passed through it. The magnetic field at its centre now is
A \( .2 B \)
B. \( B / 2 \)
\( c \cdot B / 4 \)
D. \( 4 B \)


Enthalpy of polymerisation of ethylene, as represented by the reaction, \( \boldsymbol{n} \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \rightarrow\left(-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\right) \boldsymbol{n} \)
is \( -100 \mathrm{kJ} \) per mole of ethylene. Given bond enthalpy of \( C=C \) bond is \( 600 \mathrm{kJ} \)
mol \( ^{-1} \), Determine enthalpy of \( C \) C bond (in \( \mathrm{kJ} \text { mol }) \)
A . 350
в. з23
c. 565
D. 453


The cost of 5 tables and 6 chairs is
Rs. \( 2884 . \) What is the cost of 15 tables
and 18 chairs?
A. \( R s .3300 \)
в. \( R s .7332 \)
c. \( R s .5600 \)
D. \( R s .8652 \)


\( \frac{8}{8} \)


A particle starts from the origin at \( t=0 \)
and moves in the \( x \) -y plane which constant acceleration 'a' in the \( y \)
direction. An equation of motion is \( y= \)
\( b x^{2} . \) The \( x \) -components of its velocity is?
A. Variable
B. \( \sqrt{\frac{2 a}{b}} \)
c. \( \frac{a}{2 b} \)
D. \( \sqrt{\frac{a}{2 b}} \)


If the radius of first Bohr orbit is \( x, \) then
de Broglie wavelength of an electron in
\( 4^{t h} \) orbit is nearly:
\( \mathbf{A} \cdot 6 \pi x \)
в. \( 16 \pi x \)
\( c .8 \pi x \)
D. None of these


The point (0,6) lies on:
A. X-axis
B. Y-axis
c. origin
D. None


At a certain location in Africa, compass
points \( 12^{\circ} \) west of geographic north. The north tip of magnetic needle of a dip circle placed in the plane of magnetic
meridian points \( 60^{\circ} \) above the horizontal. The horizontal component of earth's field is measured to be \( 0.16 \mathrm{G} \)
The magnitude of earth's field at the
location is?
A. 0.32 G
B. 0.42 G
c. \( 4.2 \mathrm{G} \)
D. 3.2G


Assertion
The order of the differential equation, of
which \( \boldsymbol{x} \boldsymbol{y}=\boldsymbol{c} \boldsymbol{e}^{\boldsymbol{x}}+\boldsymbol{b} \boldsymbol{e}^{-\boldsymbol{x}}+\boldsymbol{x}^{\boldsymbol{2}} \) is a
solution, is 2
Reason
The differential equation is \( x \frac{d^{2} y}{d x^{2}}+ \) \( 2 \frac{d y}{d x}-x y+x^{2}-2=0 \)
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


A real valued function \( f(x) \) satisfies the functional equation \( \boldsymbol{f}(\boldsymbol{x}-\boldsymbol{y})= \)
\( \boldsymbol{f}(\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{y})-\boldsymbol{f}(\boldsymbol{a}-\boldsymbol{x}) \boldsymbol{f}(\boldsymbol{a}+\boldsymbol{y}), \) where \( \boldsymbol{a} \)
is a given constant and \( f(0)=1, \) then
A. \( f(2 a-x)=f(x), f(x) \) is symmetric about \( x=a \)
B. \( f(2 a-x)=0=f(x), f(x) \) is symmetric about \( x=a \)
c. \( f(2 a-x)+f(x)=0, f(x) \) is not symmetric about \( x= \)
D. \( f(x)=0, f(x) \) is symmetric about \( x=a \)


\( \operatorname{Let} \boldsymbol{A}+\mathbf{2} \boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{0} \\ \mathbf{6} & -\mathbf{3} & \mathbf{3} \\ -\mathbf{5} & \mathbf{3} & \mathbf{1}\end{array}\right] \) and
\( \mathbf{2} \boldsymbol{A}-\boldsymbol{B}=\left[\begin{array}{ccc}\mathbf{2} & \mathbf{- 1} & \mathbf{5} \\ \mathbf{2} & -\mathbf{1} & \mathbf{6} \\ \mathbf{0} & \mathbf{1} & \mathbf{2}\end{array}\right], \) then \( \boldsymbol{t} \boldsymbol{r}(\boldsymbol{A}) \)
\( t r(B) \) has the value equal to
\( A \)
B.
\( c \cdot 2 \)
D. none of these


If the photo-diode is biased with a voltage larger than the specified maximum reverse bias, then:
A. the device may suffer breakdown
B. the device's efficiency will increase
c. the device will become forward biased
D. none of the above


A toy is purchased for Rs. 591.36 which includes \( 12 \% \) rebate on the printed price and \( 12 \% \) Sales Tax on the sale price of
the toy. Find the printed price of the toy.
A. Rs. 300
B. Rs. 450
c. Rs. 550
D. Rs. 600


A tomato plant with genotype (AABB) its length is \( 130 \mathrm{cm} \) is closed with another tomato plant with genotype (aabb) its length is \( 100 \mathrm{cm} . \) What is the ratio of tomato plants on the basis of length in the given cross?


Atomic numbers of few elements are
given below. Which of the pairs belongs
to s-block?
A . 7,14
B. 3,20
c. 8,15
D. 9,17


A uniform length of wire \( 1.2 \mathrm{m} \) has a resistance of \( 16 \Omega . \) It is stretched such
that its resistance is \( 36 \Omega \). The new
length is
A. \( 1.8 m \)
в. \( 2.4 m \)
\( c .2 .7 m \)
D. \( 3 m \)


\( f\left(m^{2} \cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{14 \pi}{15}=n^{2}\right. \)
then find the value of \( \frac{m^{2}-n^{2}}{n^{2}} \)


(D) \( \frac{(i) N H_{2} N H_{2}}{(i i) C_{2} H_{5} O N a} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3} \)
\( D \) in the given reaction is:
A. Iso-propyl alcohol
B. Butanaldehyde
c. Acetone
D. None of these


Figure (i) and (ii) below show the displacement-time graphs of two particles moving along the x-axis. We
can say that
A. Both the particles are having a uniformly accelerated motion
B. Both the particles are having a uniformly retarded motion
C. Particle (i) is having a uniformly accelerated motion while particle (ii) is having a uniformly retarded motion
D. Particle (i) is having a uniformly retarded motion while particle (ii) is having a uniformly accelerated motion


Apical dominance is caused by
A. Auxin
B. Gibberellin
c. Kinetin
D. ABA


The total number of isomers shown by
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)_{2}\right]\left(\boldsymbol{N} \boldsymbol{O}_{3}\right) \) complex is:
A . 10
B. 6
\( c \cdot 4 \)
D. 12


Two measurements of a cylinder are varying in such a way that the volume is kept constant. If the rates of change of the radius \( (r) \) and height \( (h) \) are equal in magnitude but opposite in sign, then
A \( . r=2 h \)
B . \( h=2 r \)
c. \( h=r \)
D. \( h=4 r \)


A primary monochromatic coherent
source is used in \( Y D S E \) and half of the
space between the primary source and the slits is filled with a transparent
liquid of refractive index \( \mu \) with respect
to air, such that path of the wave \( S S_{2} \) is
through this liquid. Everywhere else there is air and slits are sealed with equal glass plates. Find the ocation of central maximum.


According to Darwin, evolution is
A. A sudden but discontinuous process
B. A slow, gradual and continuous process
C. A slow, sudden and discontinuous process
D. A slow and discontinuous process


If the \( C O_{2} \) content of the atmosphere is
as high as 300 ppm
A. All plants would be killed.
B. The plants would not grow properly.
C. Plants after growing for sometime gets killed.
D. Plants would thrive well


Assertion
Many plants are propagated vegetatively even though they bear
seeds.
Reason
Potatoes multiply by tubers and apple by grafting etc.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( b_{i}=1-a_{i}, n a=\sum_{i=1}^{n} a_{i}, n b= \)
\( \sum_{i=1}^{n} b_{i} \quad, \) then \( \sum_{i=1}^{n} a_{i} b_{i}+ \)
\( \sum_{i=1}^{n}\left(\boldsymbol{a}_{i}-\boldsymbol{a}\right)^{2}= \)
\( \mathbf{A} \cdot a b \)
B. \( -n a b \)
c. \( n a b \)
D. \( (n+1) a b \)


f \( \omega \) is a cube root of unity, then \( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{\omega} & \boldsymbol{\omega}^{2} \\ \boldsymbol{\omega} & \boldsymbol{\omega}^{2} & \boldsymbol{1} \\ \boldsymbol{\omega}^{2} & \boldsymbol{1} & \boldsymbol{\omega}\end{array}\right| \) is equal to
A .
B. \( \omega \)
\( c \cdot \omega^{2} \)
D.


\( \lim _{x \rightarrow 0} \frac{(27+x)^{1 / 3}-3}{9-(27+x)^{2 / 3}} \) equals:
A . \( -1 / 6 \)
в. \( 1 / 6 \)
\( c \cdot 1 / 3 \)
D. \( -1 / 3 \)


The conclusions of Rutherford's
scattering experiment are:
A. nucleus is very small in size
B. nucleus is very heavy and carries positive charge
C. most of the space in the atom is empty
D. All of the above


f \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{8}\} \) is a
relation on \( N, \) then write the range of \( R \)


Find the value of \( x \) if \( \sin ^{-1}\left(\frac{2}{3}\right)+ \) \( \sin ^{-1}\left(\frac{2}{3}\right)=\sin ^{-1} x \)


I. \( 2 M n^{2+}(a q)+4 O H^{-}(a q)+ \)
\( O_{2}(g) \rightarrow 2 M n O_{2}(s)+2 H_{2} O(l) \)
II. \( M n O_{2}(s)+2 I^{-}(a q)+ \)
\( 4 H^{+}(a q) \rightarrow M n^{2+}(a q)+I_{2}(a q)+ \)
\( 2 H_{2} O(l) \)
III. \( 2 S_{2} O_{3}^{2-}(a q)+I_{2}(a q) \rightarrow \)
\( \boldsymbol{S}_{4} \boldsymbol{O}_{\mathbf{6}}^{2-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{2} \boldsymbol{I}^{-}(\boldsymbol{a} \boldsymbol{q}) \)
Dissolved oxygen in water is determined by using the given redox reactions.When \( 3 \times 10^{3} \) moles \( O_{2} \) is
dissolved per litre of water, then
what will be the molarity of \( I^{-} \) produced
in the given reaction?
A \( \cdot 3 \times 10^{-3} \) М
В. \( 4 \times 3 \times 10^{-3} \mathrm{M} \)
c. \( 2 \times 3 \times 10^{-3} \) М
D. \( \frac{1}{2} \times 3 \times 10^{-3} \mathrm{M} \)


\( (X)+K_{2} C O_{3}+A i r \stackrel{h e a t}{\longrightarrow}(Y) \)
\( (Y)+C l_{2} \longrightarrow(Z) \) Purple
Which of the following is correct?
\( \mathbf{A} \cdot X= \)black\( , M n O_{2} ; Y=b l u e, K_{2} C r O_{4} ; Z=K M n O_{4} \)
B. \( X= \) green, \( C r_{2} O_{3} ; Y= \) yellow, \( K_{2} C r O_{4} ; Z= \)
\( K_{2} C r_{2} O_{7} \)
c. \( X= \) black, \( M n O_{2} ; Y= \) green, \( K_{2} M n O_{4} ; Z= \)
\( K M n O_{4} \)
D. \( X= \)black\( , \quad B i_{2} O_{3} ; Y= \)colourless\( , K B i O_{2} ; Z= \)
\( K B i O_{3} \)


Simplify :
¡) \( \frac{-14 x^{8} y^{5}+21 x^{10} y-28 x^{7} y^{6}}{7 x^{7} y^{8}} \)
ii) \( \frac{15 a^{4} x^{8}-30 a^{7} x^{5}-45 a^{6} x^{6}}{20 a^{14} x^{5}} \)
iii) \( \frac{-60 x^{4} a^{5}-75 x^{3} a^{6}+8 x^{5} a^{4}}{-20 x^{8} a^{4}} \)


A solution is prepared by urea and
water. If mole fraction of water is 0.8 in
the solution. Find the ratio of mass of
water and urea.
A \( \cdot \frac{5}{6} \)
B. \( \frac{6}{5} \)
\( c \cdot \frac{1}{4} \)
D. \( \frac{4}{1} \)


What happens when a ray of light is
made to fall on a mirror along the
normal?
A. The ray that comes after reflection makes \( 60^{\circ} \) with the mirror
B. The ray that comes after reflection will be parallel to the mirror
c. The ray after reflection retraces its path.
D. After reflection, the ray does not come back


Number of \( \sigma \) and \( \pi \) -bonds in
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C O O H} \) is:
A \( .13 \sigma, 4 \pi \)
В. \( 14 \sigma, 4 \pi \)
\( \mathrm{c} \cdot 15 \sigma, 4 \pi \)
D. \( 16 \sigma, 4 \pi \)


Why sodium has a higher density than
lithium but potassium has a lower density than sodium?


In superficial expansion of solids
A. Increase in thickness is negligible as compared to increase in length and breadth
B. Increase in length and breadth is negligible as compared to increase in thickness
c. Both
D. None


Which one of the following is not true about monocotyledons?
A. Embryo has single cotyledon
B. Leaves show parallel venation
c. Flowers are generally trimerous
D. vascular bundle are conjoint, collateral and open


A chemist has synthesized a greenish yellow gaseous compound of chlorine and oxygen and finds that its density is
\( 7.71 g / L \) at \( 36^{0} C \) and 2.88 atm. Then molecular formula of the compound will
be:
A \( \cdot C l O_{3} \)
в. \( C l O_{2} \)
c. \( C l O \)
D. \( C l_{2} O_{2} \)


Phylum Coelenterata has remained at which level of body organisation?
A. Cellular level
B. Cell-tissue grade
c. Tissue organ level
D. Tissue organ and system level


The type of radiation absorbed by \( \boldsymbol{C O}_{2} \) molecule in atmosphere is
A. \( X \) -rays
B. Gamma rays
c. Infra-red rays
D. \( U V \) - rays


The sum of the intercepts on the coordinate axes of the plane passing through the point (-2,-2,2) and containing the line joining the points (1,-1,2) and (1,1,1) is?
A . 12
B. -8
\( c .-4 \)
D. 4


\( \mathbf{1} \)
- X product of diagonals is
2
A. Formula of perimeter of square
B. Formula of area of rhombus
C. Formula of perimeter of rectangle
D. Formula of area of the rectangle


If \( y=e^{\sqrt{x}}+e^{-\sqrt{x}}, \) then \( \frac{d y}{d x} \) is equal
to
This question has multiple correct options
\( \overbrace{\frac{e^{\sqrt{x}}-e^{-\sqrt{x}}}{2 \sqrt{x}}} \)
\( ^{\text {В } \cdot} \frac{e^{\sqrt{x}}-e^{-\sqrt{x}}}{2 x} \)
c. \( \frac{1}{2 \sqrt{x}} \sqrt{y^{2}-4} \)
D. \( \frac{1}{2 \sqrt{x}} \sqrt{y^{2}+4} \)


If \( 4 y^{2}+4 y+1=0, \) then \( y=0 \)
A. Yes
B. No
c. Ambiguous
D. Data insufficient


Given the fact that histone binds DNA, it
should be rich in.
A. Arginine, lysine
B. Cysteine, methionine
c. Glutamate, aspartate
D. Isoleucine, leucine


What is the result when you add the \( \operatorname{matrix}\left[\begin{array}{ll}\mathbf{4} & \mathbf{5}\end{array}\right] \) to the matrix \( \left[\begin{array}{ll}\mathbf{7} & -\mathbf{3}\end{array}\right] \)
and multiply the result by \( 2 ? \)
\( \mathbf{A} \cdot\left[\begin{array}{ll}2 & 6\end{array}\right] \)
в. \( \left[\begin{array}{ll}11 & 2\end{array}\right] \)
c. \( \left[\begin{array}{ll}22 & 4\end{array}\right] \)
D. \( [28 \quad-15] \)
E . \( \left[\begin{array}{ll}54 & -30\end{array}\right] \)


A rocket of mass \( 5700 \mathrm{kg} \) ejects mass at a constant rate of \( 15 \mathrm{kg} / \mathrm{s} \) with
constant speed of \( 12 \mathrm{km} / \mathrm{s} \). The
acceleration of the rocket 1 minute
after the blast is \( \left(\boldsymbol{g}=\mathbf{1 0} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A. \( 34.9 \mathrm{m} / \mathrm{s}^{2} \)
В. \( 27.5 \mathrm{m} / \mathrm{s}^{2} \)
\( \mathbf{c} \cdot 3.50 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 13.5 \mathrm{m} / \mathrm{s}^{2} \)


Function of nucleolus is to form
A. Lysosome
B. Specialized chromosome
c. Ribosome
D. spherosome


Fill in the blanks:
Component Inspired air Expired air Oxygen
\( a \)
Nitrogen \( 79 \% \)
\( A \cdot a=5.6 \%, b=21.6 \% \)
B. \( a=20.96 \%, b=79.6 \% \)
c. \( a=28.8, b=98 \% \)
D. \( a=1 \%, b=2 \% \)


A metallic block has no potential difference applied across it, then the mean velocity of free electrons at absolute temperature T is
A. Proportional to \( T \)
B. Proportional to \( \sqrt{T} \)
c. zero
D. Finite but independent of \( T \)


Which of the following is an epidermal
cell?
A. Guard cell
B. Root hair
c. Trichome
D. All of the above


What is vulcanization of rubber?


The formula \( \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)= \)
\( 2 \tan ^{-1} x \) holds only for
\( \mathbf{A} \cdot x \in R \)
B . | \( x \mid \leq 1 \)
c. \( x \in(-1,1) \)
D・ \( x \in(0, \infty) \)


The uncertainty in the momentum of an
electron is \( 1.0 \times 10^{-5} \mathrm{kg} \mathrm{m} \mathrm{s}^{-1} . \) The
uncertainty of its position will be:
\( \left[h=6.626 \times 10^{-34} \mathrm{kg} \mathrm{m}^{2} \mathrm{s}^{-1}\right] \)
A \( \cdot 1.05 \times 10^{-28} \mathrm{m} \)
B . \( 1.05 \times 10^{-26} \mathrm{m} \)
c. \( 5.27 \times 10^{-30} \mathrm{m} \)
D. \( 5.25 \times 10^{-28} \mathrm{m} \)


When particle revolves with uniform speed on a circular path
A. no force acts on it
B. no acceleration acts on it it
c. no work is done by it
D. its velocity is constant


The growth rate is highest in
A. Red light
B. White light
c. Green light
D. None of the above


\( \sqrt{\boldsymbol{i}}+\sqrt{-\boldsymbol{i}}=? \)
A. \( \sqrt{2} \)
B. \( -\sqrt{2} \)
\( c . \pm \sqrt{2} \)
D. \( \pm \sqrt{2}, \pm \sqrt{2} i \)


In autogenic succession
A. Community itself modifies its own environment, thus causing its own replacement by new commuity
B. Early dominance of heterotrophs
C. Replacement of existing communites due to external conditions
D. Early and continued dominance of autotrophic organisms


State any two methods by which ordinary light can be polarised.


Assertion
Molten potassium chloride is a good electrical conductor.
Reason
the melting process frees the ions in potassium chloride from their fixed positions in the crystal lattice.
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


Uranium 236 is extremely unstable
what reactions do take place in it at the time of nuclear fission?


What is the three 'R mantra'? Write its
significance.


In a potentiometer experiment, the balancing length of a cell is \( 560 \mathrm{cm} \) When an external resistance of \( 10 \Omega \) is
connected in parallel to the cell, the balancing length changes by \( 60 \mathrm{cm} . \) The internal resistance of a cell is
A . \( 1.4 \Omega \)
в. \( 1.6 \Omega \)
c. \( 0.12 \Omega \)
D. \( 1.2 \Omega \)


Two blocks of steel \( A \) and \( B \) of the same
shape and size, A being two times
heavier than \( \mathrm{B} \), are at \( 40^{\circ} \mathrm{C} \). The ratio of
heat content of \( A \) to \( B \) is
A . 1
B. 4
\( c \cdot 2 \)
D.


The expression for the velocity when a body dropped from a height reaches the
ground is
A \( \cdot V^{2}=2 s \)
В. \( V^{2}=2 g s \)
c. \( V=2 g s \)
\( \mathbf{D} \cdot V^{2}=\frac{g s}{2} \)


\( A \) and \( B \) are two independent events. The probability that both \( A \) and \( B \) occur is \( \frac{1}{6} \) and the probability that neither of them occur is \( \frac{1}{3} \). Then \( P(A) \) is equal to
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{5}{6} \)
D. \( \frac{1}{2} \) or \( \frac{1}{3} \)


Which of the following reproduces by fragmentation?
A. Spirogyra
B. Chlamydomonas
c. Bryophyllum
D. All of these


The region between two concentric
spheres of radii a and \( b(>a) \)
contains volume charge density \( \rho(r)= \)
\( C \)
\( \boldsymbol{r} \)
where \( C \) is a constant and \( r \) is the
radial distance, as shown in figure. A
point charge \( q \) is placed at the origin, \( r= \)
O.Find the value of \( C \) for which the
electric field in the region between
the spheres is constant (i.e., r
independent)


Metal (s) M in the following equation is/are
\( M+N \rightarrow M e t a l n i t r i d e: \)
This question has multiple correct options
A . Na a
B. Li
\( c \cdot c s \)
D. Mg


Assertion
In both radio activity and photoelectric effect electrons may be ejected.
Reason
In photoelectric effect and radio activity emission occurs only of unstable elements.
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


Solve \( \frac{\sin 30^{\circ}+\tan 45^{\circ}-\cos e s 60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cos 45^{\circ}} \)


Nitrogen is relatively inactive element
because:
A. its atoms has a stable electronic configuration
B. it has low atomic radius
C . its electronegativity is fairly high
D. dissociation energy of its molecule is fairly high


Volume of oxygen at NTP, required to
completely burn 1 kg of coal (100\% arbon) is
A . 22.4 \( L \)
В. \( 1.86 \times 10^{3} \mathrm{L} \)
c. \( 22.4 \times 10^{3} \mathrm{L} \)
D. 1000 L


A compound which does not give a positive result in the Lassaigne's test for nitrogen is:
A. urea
B. hydroxyl amine
c. glycine
D. phenylhydrazine


Which of the following alkali metal ions has lowest ionic mobility in aqueous
solution?
\( \mathbf{A} \cdot R b^{+} \)
в. \( C a^{+} \)
c. \( N a^{+} \)
\( \mathbf{D} \cdot L i^{+} \)


Write Faraday's laws of electrolysis.


How are the modes of reproduction
different in unicellular and
multicellular organisms?
A. Unicellular organisms reproduce mainly by asexual method, multicellular organisms reproduce by sexual and asexual methods.
B. Unicellular organisms reproduce mainly by sexual method, multicellular organisms reproduce mainly by asexual methods
C. Unicellular organisms reproduce mainly by propagation, multicellular organisms reproduce mainly by asexual methods.
D. None of these