The perimeter of the incircle is \( 30 \mathrm{m} \) and its radius \( 10 \mathrm{m} . \) What is the area of
the triangle?
A. 150 sq. \( \mathrm{m} \)
В. 140 sq. \( \mathrm{m} \)
c. 130 sq. \( \mathrm{m} \)
D. 120 sq. \( m \)


A substances A reacts with another
substances B to produce the product \( C \) and a gas D. If a mixture of the gas \( D \) and ammonia is passed through an aqueous solution of \( \mathrm{C} \), baking soda is formed. The substances \( A \) and \( B \) are:
A . \( H C l \) and \( N a O H \)
B. \( H C l \) and \( N a_{2} C O_{3} \)
c. \( N a \) and \( H C l \)
D. \( N a_{2} C O_{3} \) and \( H_{2} O \)


Study the figures given and identify the type of interaction between \( \boldsymbol{X} \boldsymbol{Y}-\boldsymbol{X} \boldsymbol{Y} \)
molecules.
(ii)
A. Dipole - -Induced dipole
B. Dipole - Dipole
c. Dispersion forces
D. Induced dipole - - Induced dipole


Division of nucleus is indirect in
A. Mitosis
B. Binary fission
c. Budding
D. Fragmentation


If \( \vec{a} \) and \( \vec{b} \) are non - zero vectors
which are linearly dependent such that \( \frac{|\vec{a}+\vec{b}|}{|\vec{a}-\vec{b}|}=2,|\vec{b}|>|\vec{a}| \) then
\( \begin{array}{l}\text { A. } \vec{b}=3 \vec{a} \\ \vec{a}\end{array}=3=3 \vec{a} \)
В . \( \vec{b}=-3 \vec{a} \)
c. \( \vec{b}=2 \vec{a} \)
D. \( \vec{b}=-2 \vec{a} \)


Differentiate between :
Klinefelters syndrome and Turners syndrome


Which of the following statement is true
for the complex, \( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4} \boldsymbol{B r}_{2}\right] \boldsymbol{N} \boldsymbol{O}_{2} ? \)
A. It shows ionisation, linkages and geometrical isomerism
B. It does not show optical isomerism because its cis and trans forms each have at least one plane of symmetry.
c. Its ionisation isomers cannot be differentiated by silver nitrate solution
D. (A) and
(B) both


During an experiment an ideal gas is found to obey an additional gas law VT =constant. The gas is initially at temperature \( T \) and pressure P. When it is heated to the temperature 2 T, the resulting pressure is
A . 2P
B. P/2
\( c \cdot 4 P \)
D. P/4


The strength of magnetic field inside a long current carrying straight solenoid is:
A. more at the ends than at the centre
B. minimum in the middle
c. same at all points
D. found to increase from one end to the other


A force has magnitude 20 N. Its one
rectangular component is \( 12 \mathrm{N} \), the other rectangular component must be:
\( A \cdot 8 N \)
B. 14 N
\( c \cdot 16 N \)
D. 32 N


Construct a quadrilateral \( M O R E \)
where \( M O=6 c m, O R= \)
\( 4.5 \mathrm{cm}, \angle M=60^{\circ}, \angle O=105^{\circ} \) and
\( \angle R=105^{\circ} \)


Select the correct option:
Four different steps that occur during meiosis are given in the following list.
(i) Complete separation of chromatids
(ii) Pairing of homologous chromosomes
(iii) Lining up of paired chromosomes on equator
(iv) Crossing over between chromatids Select the correct sequential arrangement of the steps.
A \( . \) (ii), (iii), (iv), (i)
B. (iii), (ii), (iv), (i)
\( c \cdot(\text { ii) }, \) (iv), (iii), (i)
D. (iii), (i), (ii), (iv)


Match the following substances with types of inter molecular forces:
List-I List-II
a) \( C H_{4} \)
i) London, dipole-dipole
\( b \)
ii) London
\[
C H C l_{3}
\]
\( c \)
iii) London, dipole-dipole, hydrogen
\[
C_{4} H_{9} O H \quad \text { bonding. }
\]
A . a-ii, b-i, c-iii
B. a-i, b-ii, c-iii
c. a-iii, b-i, c-ii
D. a-iii, b-ii, c-


Which of the following is correct about
starch?
A. It is a white cyrstalline powder
B. Coloured amorphous powder
c. It is white-amorphous powder
D. coloured crystalline compound


Assertion
A normal is drawn at a point \( \boldsymbol{P}(\boldsymbol{x}, \boldsymbol{y}) \) of \( \mathbf{a} \) curve. It meets the \( x \) -axis and the \( y \) -axis in point \( A \) and \( B \), respectively, such that \( \frac{1}{O A}+\frac{1}{O B}=1, \) where \( O \) is the
origin. The equation of such a curve passing through \( (\mathbf{5}, \mathbf{4}) \) is \( (x-1)^{2}+ \)
\( (y-1)^{2}=25 \)
Reason \( \boldsymbol{O A}=\boldsymbol{x}+\boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) and \( \boldsymbol{O} \boldsymbol{B}=\frac{\boldsymbol{x}+\boldsymbol{y} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}}{\frac{d \boldsymbol{y}}{d \boldsymbol{x}}} \)
A. Both Assertion and Reason are correct and Reason 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


Find the roots of the equation \( 2 x^{2}+ \)
\( x-6=0 \) by factorisation.


Part not belonging to uriniferous tubule
is
A . Glomerulus
B. Henle's loop
c. Distal convoluted tubule
D. connecting tubule


Why are traits acquired during the lifetime of an individual not inherited?


Find the equation of the circle with centre (1,1) and radius \( \sqrt{2} \)


In which case reaction is spontaneous?
\( \mathbf{A} \cdot \Delta H:-v e, \Delta S:+v e \)
B. \( \Delta H:+v e, \Delta S:-v e \)
c. Both (a) and (b)
D. None of these


In gymnosperms, the pollen chamber
represents
A. A cell in the pollen grain in which the sperms are formed
B. A cavity in the ovule in which pollen grains are stored after pollination
C. An opening in the megagametophyte through which the pollen tube approaches the egg
D. The microsporangium in which pollen grains develop


Copper does not react with HCl to give
\( H_{2} \) gas.why?
A. The reduction potential of copper is higher than hydrogen
B. The oxidation potential of copper is less than hydrogen.
c. copper is highly reactive metal
D. None of these.


The word Argon represents the
term
A. sun
B. Hidden
c. Lazy
D. Stranger


The correct order of \( +I \) effect is
A \( \cdot-C O O^{-}>-\bar{O}>-\bar{N} H>-\bar{C} H_{2} \)
В. \( -\bar{C} H_{2}>-\bar{O}>-C O O^{-}>-C\left(C H_{3}\right)_{3} \)
\( \mathbf{c} \cdot-C\left(C H_{3}\right)_{3}>-\bar{O}>-C O O^{-}>-\bar{N} H \)
D \( -\bar{O}>-\operatorname{COO}^{-}>-C\left(C H_{3}\right)_{3}>-\bar{N} H \)


Which of the following statements are
possible; \( a, b, m \) and \( n \) being non-zero
real numbers?
A \( \cdot 4 \sin ^{2} \theta=5 \)
B \( \cdot\left(a^{2}+b^{2}\right) \cos \theta=2 a \)
C. \( \left(m^{2}+n^{2}\right) \csc \theta=m^{2}-n^{2} \)
D. \( \sin \theta=2.375 \)


Which one of the following precedes reformation of the nuclear envelope during M-phase of the cell cycle?
A. Decondensation from chromosome and reassembly of the nuclear lamina
B. Transcription from chromosome and reassembly of the nuclear lamina
c. Formation of the contractile ring and formation of the phragmoplast
D. Formation of the contractile ring and transcription from chromosomes


Which of the following is/are correct?
This question has multiple correct options
A. Acid hydrolysis of an ester follows pseudo first order kinetics
B. Inversion of cane sugar follows pseudo first order kinetics
C. Decomposition of varous gases on the surface of metallic catalysts, such as decomposition of \( H I \) on gold surface also exhibits zero roder kinetics
D. Radioactivity follows first order kinetics


A die is thrown, a man \( C \) gets a prize of
Rs. 5 if the die turns up 1 and gets a prize of Rs. 3 if the die turns up \( 2, \) else
he gets nothing, A man \( A \) whose probability of speaking the truth is \( \frac{1}{2} \)
tells \( C \) that the die has turned up 1 and another man \( B \) whose probability of speaking the truth is \( \frac{2}{3} \) tells \( C \) that the
die has turned up 2. Find the
expectation value of \( \boldsymbol{C} \)


When transport proteins
simultaneously move two molecules across a membrane in the same
direction, the process is called
A. Uniport
B. Antiport
c. symport
D. Diffusive port


A conducting rod \( P Q \) of length \( 5 \mathrm{m} \)
oriented as shown in figure is moving with velocity (2 \( \mathrm{m} / \mathrm{s} \) ) in rotation in a uniform magnetic field \( (3 \hat{j}+4 \hat{k}) \) Tesla.
The emf induced in the rod is
A. 32 volts
B. 40 volts
c. 50 volts
D. none


Equation of the curve whose polar sub \( \operatorname{tangent} r^{2} \frac{d \theta}{d r} \) is constant
A. \( r(\theta+c)+k=0 \)
B \( \cdot r^{2}(\theta+c)=2 k \)
c. \( r(\theta-c)=k^{2} \)
D. \( r \theta=c \)


Assertion
Amalgam of mercury with sodium is an
example of solid solutions
Reason
Mercury is solvent and sodium is solute
in the solution
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 number \( N_{X} \) of nuclei of \( X \) at time
\( \boldsymbol{t}=\boldsymbol{T}_{1 / 2} \) is
A \( \cdot \frac{K+\lambda N_{0}}{2 \lambda} \)
в. \( \left(2 \lambda N_{0} K\right) \frac{1}{\lambda} \)
\( ^{\mathbf{c}} \cdot\left[\lambda N_{0}+\frac{K}{2}\right] \frac{1}{\lambda} \)
D. Data insufficient


Two long conductors, separated by a
distance \( \boldsymbol{d} \) carry currents \( \boldsymbol{I}_{1} \) and \( \boldsymbol{I}_{2} \) in
the same direction. They exert a force \( \boldsymbol{F} \)
on each other. Now the current in one of
them is increased to two times and its
direction is reversed. The distance is
also increases to \( 3 d \). The new value of
the force between them is:
A . \( -2 F \)
в. \( F / 3 \)
\( \mathrm{c} \cdot-2 F / 3 \)
D. \( -F / 3 \)


In the Earth's crust, Carbon is found in
the form of
A. carbonates
B. hydrogen carbonates
c. petroleum
D. All of the above


If the vertices of a triangle are \( (1,2),(4,-6), \) and \( (3,5), \) then its area is
\( ^{\mathbf{A}} \cdot \frac{23}{2} s q u n i t \)
B \( \cdot \frac{25}{2} \) squnit
c. 12 sq unit
D. none of these


Assertion
The frequency of a sound wave changes
as it travels from one medium to
another medium.
Reason
The velocity of the wave changes as well
as the wavelength if the medium
changes.
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 area included between the
parabolas \( y=\frac{x^{2}}{4 a} \) and \( y=\frac{8 a^{3}}{x^{2}+4 a^{2}} \) is
A \( a^{2}\left(2 \pi+\frac{2}{3}\right) \)
в. \( a^{2}\left(2 \pi-\frac{8}{3}\right) \)
c. \( _{a^{2}}\left(\pi+\frac{4}{3}\right) \)
D. \( a^{2}\left(\pi-\frac{4}{3}\right) \)


Which of the following substances has highest value of Young's modulus.?
A. Aluminium
B. Iron
c. copper
D. stee


The decreasing order of boiling points of the following alcohols is?
A. 3-methylbutan-2-ol > 2-methylbutan-2-ol> pentan-1 ol
B. pentan-1-ol > 3-methylbutan-2-ol > 2-methylbutan-2ol
c. 2-methylbutan-2-ol > 3-methylbutan-2-ol> pentan-1ol
D. 2-methylbutan-2-ol > pentan-1-ol >3-methylbutan-2-0


Choose the correct answer from the
alternatives given A physiological response to the duration of light and darkness is a:
A. daily phase cycle
B. circadian rhythm
c. biological clock
D. photoperiodism


An aqueous solution of hydrochloric
acid
A. obeys Raoult's law
B. shows negative deviation from Raoult's law
C. shows positive deviation from Raoult's law
D. obeys Henry's law at all compositions


A wire of initial length \( L \) and radius \( r \) is
stretched by a length \( l \). Another wire of same material but with initial length \( 2 L \) and radius \( 2 r \) is stretched by a
length \( 2 l \). The ratio of stored elastic
energy per unit volume in the first and
second wire is:
A .1: 4
B. 1: 2
c. 2: 1
D. 1: 1


Which of the following is true for vitreous humour?
a. It is a clear gel like fluid.
b. It is present between the lens and the
cornea.
c. It maintains the shape of the retina.
d. It provides nutrition to the eye.
A \( . \) a and \( b \)
B. c and d
c. a and \( c \)
D. all of the above


What per cent is the least rational
number of the greatest rational number if \( \frac{1}{2}, \frac{2}{5}, \frac{1}{3} \) and \( \frac{5}{9} \) are arranged in ascending order?
A . 60\%
B . 10\%
c. 20\%
D. 30\%


Every 20 minutes, one bacterium divides into two. How many bacteria will
be produced after two hours, if one starts with 10 bacteria?
A \( \cdot 2^{5} \times 10 \)
B . \( 2^{5} \times 10^{5} \)
c. \( 2^{6} \times 10 \)
D. \( 2^{6} \times 10^{6} \)


\( \mathbf{f} \mathbf{A}=\left\{\begin{array}{ll}\mathbf{0} & \mathbf{2} \\ \mathbf{3} & -\mathbf{4}\end{array}\right\}, \mathbf{k} \mathbf{A}=\left\{\begin{array}{ll}\mathbf{0} & \mathbf{3} \mathbf{a} \\ \mathbf{2} \mathbf{b} & \mathbf{2 4}\end{array}\right\} \)
then arrange the values of \( k, a, b, \) in
ascending order
\( \mathbf{A} \cdot k, a, b \)
в. \( b, a, k \)
\( \mathbf{c} \cdot a, k, b \)
\( \mathbf{D} \cdot b, k, a \)


Assertion
According to Mendeleev, periodic properties of elements are periodic
function of their atomic number
Reason
Atomic number is equal to the number of protons.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of assertion.
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If \( 1^{0}=\alpha \) radians then the approximate
value of \( \cos 60^{0} 1^{\prime} \) is
A \( \cdot \frac{1}{2}+\frac{\alpha \sqrt{3}}{120} \)
в. \( \frac{1}{2}-\frac{\alpha}{120} \)
\( ^{\mathrm{C}} \cdot \frac{1}{2}-\frac{\alpha \sqrt{3}}{120} \)
D. none of these


There are exactly two tangents to a circle passing through a point lying the circle.
A . inside
B. outside
c. on the circle
D. none of the above


The colour of hydrogen is:
A . yellow
B. orange
\( c \cdot \) red
D. None of the above


The focal length of a concave lens is 2
\( \mathrm{m}, \) calculate the power of the lens.
A . \( -0.5 D \)
в. \( -1.0 D \)
c. \( +0.5 D \)
D. \( +1.0 D \)


The graph below represents the motion
of a remote control car back and forth
along a straight line path.

What is the average velocity of the car
during the first 25 seconds of its
motion?
\( \mathbf{A} \cdot 8.0 m / s \)
B. \( 7.0 \mathrm{m} / \mathrm{s} \)
c. \( 5.0 m / s \)
D. \( 4.0 \mathrm{m} / \mathrm{s} \)
E . \( 3.0 \mathrm{m} / \mathrm{s} \)


The product formed when \( H_{2} O_{2} \) reacts
with acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) is:
A \( \cdot K_{2} C r_{2} O_{4} \)
в. \( C r O_{3} \)
\( \mathbf{c} \cdot \operatorname{Cr}(O H)_{3} \)
D. \( C r O_{5} \)


\( \triangle A B C \) is iscoeles in which \( A B=A C \)
\( \operatorname{seg} B D \) and \( \operatorname{seg} C E \) are medians show \( \operatorname{that} B D=C E \)


A circular coil of 100 turns has an
effective radius of \( 0.05 m \) and carries a
current of \( 0.1 A \). How much work is
required to turn it in an external
magnetic field of \( 1.5 W b / m^{2} \) through
\( 180^{\circ} \) about its axis perpendicular to the magnetic field? The plane of the coil is initially perpendicular to the magnetic field :
A . 0.456 .5
в. \( 2.65 J \)
c. \( 0.2355 J \)
D. 3.95J


The total number of alcohols (including stetroisomers ) possible with the
molecular formula \( C_{5} H_{1} 2 O \) is:


If the value of \( \left|\begin{array}{ccc}\mathbf{1} & \mathbf{2} & \mathbf{4} \\ -\mathbf{1} & \mathbf{3} & \mathbf{0} \\ \mathbf{4} & \mathbf{1} & \mathbf{0}\end{array}\right| \) is \( k, \) then find
\( \frac{-\boldsymbol{k}}{\mathbf{1 3}} \)


Unsymmetrical \( P C l_{5}(s) \) splits into
\( \boldsymbol{P C l}_{4}^{+} \) and \( \boldsymbol{P C l}_{6}^{-} \)
A. True
B. False
c. Ambiguous
D. None of these


What is the maximum value of the force
F such that the block shown in the
arrangement, does not move?
A. 20N
B. 10N
\( c \cdot \) 12N
D. 15N


How is detergent industrially
manufactured?


Which element is a metal with valency
2?


Number of moles of \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) reduced
by one mole of iodide ions is :
A . 3
B. \( \frac{1}{3} \)
\( c .6 \)
D.


Blister copper is
the purest form of copper having a
blister like surface due to the release of
gas during cooling. If true enter 1 , else enter 0 .


Which one of the following statements
is correct?
A. Neither hormones control neural activity nor neurons control endocrine activity.
B. Endocrine glands regulate neural activity, but not vice versa.
C. Neurons regulate endocrine activity, but not vice versa.
D. Endocrine glands regulate neural activity, and nervous system regulates endocrine glands.


Choose the correct answers from the
alternatives given.
For an adaptive radiation to be
Successful
A. Transitional form must be provided physical access to the new environment
B. Transitional form must face high levels of competition in order to refine the adaptations that allowed it to enter the new environment
C. Invader organisms must have a design appropriate for the new environment
D. Both
(b) and (c)


Which hormone promotes growth of tendril around a support?


topp
товою
\( \mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}^{\prime} \mathrm{CH}-\mathrm{CH}_{2}- \)
\( \mathrm{CH}_{3}-\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}- \)
\( \mathrm{CH}_{3} \)
\( \mathrm{CH}_{3}-\mathrm{C}- \)
\( \mathrm{CH}_{3} \)


Q Type your question.
mechanics. However, it turns out that
the treatment of spin angular momentum is closely analogous to the treatment of orbital
angular momentum.
Spin angular momentum \( = \) \( \sqrt{s(s+1)} h \)
Orbital angular momentum \( = \) \( \sqrt{l(l+1)} h \)
Total spin of an atom or ion is a multiple of \( \frac{1}{2} . \) Spin multiplicity isa factor to confirm the electronic configuration of
an atom or ion.Spin multiplicity \( = \)
\( \left(2 \sum s+1\right) \)
The orbital angular momentum for a \( 2 p \)
electron is:
A \( \cdot \sqrt{3} h \)
в. \( \sqrt{6} h \)
c. zero
D. \( \sqrt{2} \frac{h}{2 \pi} \)


Assertion
Anaerobic respiration sometimes occurs in our skeletal muscles during strenous exercise.
Reason
Pyruvic acid is reduced to lactic acid by lactate dehydrogenase in the absence of oxygen.
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


uniformly distributed charge \( Q \). The rod
has been bent in a \( 120^{\circ} \) circular arc of
radius \( r . \) In terms of \( Q \) and \( r, \) what is
the electric field \( \vec{E} \) due to the rod at
point \( \boldsymbol{P} ? \)
A \( \quad \vec{E}=\frac{3 \sqrt{3} \lambda}{8 \pi^{2} \epsilon_{0} r^{2}} \hat{i} \) where \( \lambda=\frac{2 Q}{3 \pi r} \)
B \( \quad \vec{E}=\frac{3 \sqrt{3} \lambda}{8 \pi^{2} \epsilon_{0} r^{2}} \hat{i} \) where \( \lambda=\frac{3 Q}{2 \pi r} \)
C \( \quad \vec{E}=\frac{3 \sqrt{3} \lambda}{8 \pi^{2} \epsilon_{0} r^{2}} \hat{j} \) where \( \lambda=\frac{2 Q}{3 \pi r} \)
D \( \quad \vec{E}=\frac{3 \sqrt{3} \lambda}{8 \pi^{2} \epsilon_{0} r^{2}} \hat{j} \) where \( \lambda=\frac{3 Q}{2 \pi r} \)


A simple pendulum has a length \( l \)
mass of bob \( m \). The bob is given a
charge \( q . \) The pendulum is suspended
between the vertical plates of the
charged parallel plate capacitor. If \( \boldsymbol{E} \) is
the field strength between the plates,
then time period \( \boldsymbol{T} \) equal to:
\( ^{\mathbf{A}} \cdot_{2 \pi} \sqrt{\frac{l}{g}} \)
\( ^{\mathbf{B}} \cdot_{2 \pi} \sqrt{\frac{l}{g+\frac{q E}{m}}} \)
\( ^{c} \cdot_{2 \pi} \sqrt{\frac{l}{g-\frac{q E}{m}}} \)
D.


A cube of Ice is floating in water. The fraction of its length lie outside the
water is (sp. Gravity of Ice \( =\mathbf{0 . 9 6} \) )
A . 0.04
в. 0.4
c. 0.96
D. None of these


is continuous but not derivable at \( x=0 \)
A. \( m \in[0,3] \)
B . \( m \in(0,2) \)
c. \( m \in(0,1] \)
D. \( m=0,1 \)


\( \lim _{x \rightarrow 0} \frac{e^{x}-e^{\sin x}}{2(x-\sin x)}= \)
A. \( -\frac{1}{2} \)
в. \( \frac{1}{2} \)
c. 1
D.


In the given figure. The maximum " \( F \) "
which will not cause motion of any of
the blocks is:
\( \mathbf{A} \cdot 10 N \)
B. \( 15 N \)
C. data is insufficient
D. None of the above


Hydrogen bonding is maximum in
A. Ethanol
B. Diethylether
c. Ethyl chloride
D. Triethylamine


Assertion
Salt dissolved in water lowers the
freezing point.
Reason
The change in freezing point is given by:
\( \Delta \boldsymbol{T}_{\boldsymbol{f}}=\boldsymbol{i} \boldsymbol{K}_{\boldsymbol{f}} \boldsymbol{m} \)
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


Draw parallelogram \( A B C D \) with the following measurements and calculate
its area
\( A B=6 c m, B D=8 \mathrm{cm} \) and \( A D= \)
\( 5 \mathrm{cm} \)


Which of the following at \( 100^{\circ} \mathrm{C} \)
produces most severe burns?
A. hot air
B. water
c. steam
D. oil


A box contains \( b \) blue balls and \( r \) red
balls. A ball is drawn randomly from the box and is returned to the box with
another ball of the same colour. The
probability that the second ball drawn from the box is blue is
A \( \cdot \frac{b}{r+b} \)
в. \( \frac{b^{2}}{(r+b)^{2}} \)
c. \( \frac{b+1}{r+b+1} \)
D. \( \frac{b(b+1)}{(r+b)(r+b+1)} \)


The given bar graph shows the demand and production of colour T.Vs of five companies. What is the difference between average
demand and average production of the
five companies taken together?
A. 1400
в. 400
\( c \cdot 280 \)
D. 138


Identify the statement in which mode of heat transfer is convection?
A. The heat of the sun warming our planet
B. The heat from an electric stove warming a frying pan
c. Ice cubes cooling a drink
D. A microwave oven cooking a meal
E. An overhead fan cooling a room


A plane electromagnetic wave is incident on a material surface. If the
wave delivers momentum \( p \) and energy
\( \boldsymbol{E}, \) then:
A \( , p=0, E=0 \)
0
В. \( p \neq 0, E \neq 0 \)
c. \( p \neq 0, E=0 \)
D. \( p=0, E \neq 0 \)


The perimeter of triangle with vertices at (1,0,0),(0,1,0) and (0,0,1) is :
\( \mathbf{A} \cdot \mathbf{3} \)
B . 2
\( c \cdot 2 \sqrt{2} \)
D. \( 3 \sqrt{2} \)


When a certain amount of ethylene was
combusted, \( 6226 \mathrm{kJ} \) heat was evolved. If
heat of combustion of ethyleneis \( 1411 \mathrm{kJ} \)
Determinethe volume of \( O_{2}(\text { at } \mathrm{NTP}) \)
that entered into the reaction
A . 996.3 L
B. 234 L
c. \( 296 L \)
D. 435 L


toppr 5
Q Type your question
\( A \)
\( B \)
\( c \)
\( D \)


Which of the following groups of organisms are ecologically similiar?
A. Producer protists and consumer protists
B. Monerans and producer protists
c. consumer protists and fungi
D. Monerans and fungi


Degree of ionisation does not depend
on:
A. nature of the solvent
B. nature of the electrolyte
c. dilution
D. molecular mass of the electrolyte


A wagon of mass 10 tons moving at a
speed of 12 kmph collides with another
wagon of mass 8 tons moving on the same track in the same direction at a
speed of \( 10 \mathrm{kmph} \). If the speed of the first wagon decreases to 8 kmph. Find the speed of the other after collision
A. \( 18 \mathrm{kmph} \)
B. 25 kmph
c. \( 5 \mathrm{kmph} \)
D. \( 15 \mathrm{kmph} \)


\( 100 m L \) of a saturated solution of
\( A g_{2} S O_{4} \) is added to \( 250 m L \) of a
saturated solution of \( P b C r O_{4} . \) Will any
precipitate form and if so what?
Given that \( : \boldsymbol{K}_{s p} \) for
\( A g_{2} S O_{4}, A g_{2} C r O_{4}, P b C r O_{4} \) and
\( P b S O_{4} \) are \( 1.4 \times 10^{-5}, 2.4 \times 10^{-12} \)
\( 2.8 \times 10^{-13} \) and \( 1.6 \times 10^{-8} \)
respectively.
\( \mathbf{A} \cdot A g_{2} C r O_{4} \)
B \( \cdot P b C r O_{4} \)
\( \mathbf{c} \cdot A g_{2} S O_{4} \)
\( \mathrm{D} \cdot \mathrm{PbSO}_{4} \)


The modern periodic table is most \( _{\text {一一一一一一一一一 }} \) form of periodic
table.
A . insignificant
B. Significant
c. Both A and B
D. None of these


Which molecule listed below is a
product of fermentation of glucose by
yeast?
A. \( C_{6} H_{10} O_{5} \)
в. \( C_{2} H_{5} O H \)
c. \( C_{6} H_{12} O_{6} \)
D. \( C H_{3} O H \)


State the following statement is True or
False

If Susan does not like spinach then the truth value of the statement "Susan
likes ice cream and she like spinach" is
True
A. True
B. False


Sonal has dropped her golden ring in
\( \mathrm{CuSO}_{4}, \) solution. Does she need to
worry? \( E_{A u^{3+} \mid A u}^{o}=1.50 V, E_{C u^{2+} \mid C u} V \)


How many significant figures are there
in \( 0.30100 ? \)


Solve \( 1+2 \operatorname{cosec} x=-\frac{\sec ^{2}(x / 2)}{2} \)


f \( \boldsymbol{E}=\mathbf{1 2} \) volts, \( \boldsymbol{X}=\mathbf{9} \Omega, \) then distance
of balance point \( P \) from end \( A \) is
A. 20 cm
B. 50 \( \mathrm{cm} \)
c. \( 70 \mathrm{cm} \)
D. Data insufficient


Gold is also extracted by cyanide
process as in case of silver.
Write the reactions.
\( \mathbf{A} \cdot 2\left[A u(C N)_{2}\right]^{-}+Z n \rightarrow\left[Z n(C N)_{4}\right]^{2-}+2 A u \downarrow \)
\( \mathbf{B} \cdot 4\left[A u(C N)_{2}\right]^{-}+Z n \rightarrow\left[Z n(C N)_{4}\right]^{2-}+4 A u \downarrow \)
\( \mathbf{c} \cdot\left[A u(C N)_{2}\right]^{-}+Z n \rightarrow\left[Z n(C N)_{4}\right]^{2-}+A u \downarrow \)
D. None of these


Simplify : \( \frac{\left(2^{4}\right)^{2} \times 7^{3}}{8^{2} \times 7} \)


A jet airplane is travelling at a speed of \( 500 \mathrm{km} / \mathrm{h} \) ejects its products of combustion with a speed of \( 1500 \mathrm{km} / \mathrm{h} \) relative to the jet plane. The speed of the latter with respect to an observer on the
ground is:
\( \mathbf{A} .1500 \mathrm{km} / \mathrm{h} \)
B. 2000 km/h
\( c \cdot 1000 \mathrm{km} / \mathrm{h} \)
D. \( 500 \mathrm{km} / \mathrm{h} \)


Find the temperature at which the fundamental frequency of an organ pipe is independent of small variation in
temperature in terms of the coefficient of linear expansion \( (\alpha) \) of the material of the tube
A . \( 1 / 3 \alpha \)
B. \( 1 / 2 \alpha \)
c. \( 1 / 4 \alpha \)
D. \( 1 / 5 \alpha \)


Issue of PUC certificate can control
A. Noise pollution
B. Water pollution
c. Sound pollution
D. Air pollution


Which combination of atoms can form a
polar covalent bond?
A. Hand
B. Hand
c. \( \mathrm{N} \) and \( \mathrm{N} \)
D. Na and F


Choose the correct answer from the
alternatives given

Maxwell in his famouse questions
of eletromagnetism introduce the
concept of:
A . ac current
B. displacement current
c. impedance
D. reatance


Rearrange the following based on the
relationship between different
primates. Chimpanzee - Gorilla - Gibbon -
Orangutan


A body is released at a distance far away from the surface of the earth.
Calculate its speed when it is near the
surface of earth. Given \( \boldsymbol{g}=\mathbf{9 . 8 m s}^{-2} \)
radius of earth \( \boldsymbol{R}=\mathbf{6 . 3 7} \times \mathbf{1 0}^{\mathbf{6}} \mathbf{m} \)
A \( \cdot 22 \times 10^{3} m s^{-1} \)
В. \( 11.2 \times 10^{3} m s^{-1} \)
\( \mathbf{c} \cdot 23 \times 10^{3} m s^{-1} \)
D. \( 10 \times 10^{3} \mathrm{ms}^{-1} \)


The price of petrol goes up by \( 20 \% . \) By how much per cent must Ajay reduce his consumption of petrol so that the expenditure on petrol remains the same?


An isotropic point source emits light. screen is situated at a given distance. If the distance between sources and
screen is decreased by \( 2 \% \), illuminance will increase by:
A . \( 1 \% \)
B. 2\%
\( c .3 \% \)
D. \( 4 \% \)


Choose the proper food from following, to keep our eyes healthy:
A. Green leafy vegetables
B. Fish
c. orange
D. All of these


If \( s \) represents the side, then the formula of surface area of cube is
A \( \cdot 6(s)^{2} \)
2) \( ^{6}\left(a^{\prime}\right)^{6} \)
B. \( 3(s)^{2} \)
\( c \cdot 5(s)^{2} \)
D・ \( 16(s)^{2} \)


Assertion
Statement 1 Range of \( \boldsymbol{f}(\boldsymbol{x})=\tan ^{-1} \boldsymbol{x}+ \)
\( \sin ^{-1} x+\cos ^{-1} x \) is \( (0, \pi) \)
Reason
Statement \( 2 f(x)=\tan ^{-1} x+ \)
\( \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}+\tan ^{-1} x \) for
\( \boldsymbol{x} \boldsymbol{\epsilon}(-\mathbf{1}, \mathbf{1}] \)
A. Both the statements are TRUE and STATEMENT 2 is the
correct explanation of STATEMENT 1
B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT
C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE


\( \sqrt{x^{2}+1} \)


RNA is more reactive than DNA. Why?


The mobility of electrons in a semiconductor is defined as the ratio of
their drift velocity to the applied electric
field. If, for an n-type semiconductor, the
density of electrons is \( 10^{19} m^{-3} \) and
their mobility is \( 1.6 m^{2} /(V . s) \) then the resistivity of the semiconductor (since it is an \( n \) -type semiconductor contribution of holes is ignored) is close to:
\( A \cdot 2 \Omega m \)
в. \( 0.4 \Omega m \)
\( c .4 \Omega m \)
D. \( 0.2 \Omega m \)


Cochineal insects have proved very useful for the control of
A . Eicchornia
B. cactus
c. weeds
D. Parathenium


A uniform circular disc of radius \( R \) lies
in the \( X Y \) plane with the centre coinciding with the origin. The moment of inertia about an axis
passing through a point on the \( X \) axis at a distance \( x=2 R \) and perpendicular
to the \( X Y \) plane is equal to its moment
of inertia about an axis
passing through a point on the \( Y \) axis at a distance \( y=d \) and parallel to the
\( X \) axis in the \( X \) -Y plane. The value of \( d \) is:
A \( \cdot \frac{4 R}{3} \)
В \( \cdot \sqrt{17}\left(\frac{R}{2}\right) \)
c. \( \sqrt{15}\left(\frac{R}{2}\right) \)
D \( \cdot \sqrt{13}\left(\frac{R}{2}\right) \)


Which of the following equations is a
balanced one?
\( \mathbf{A} \cdot 5 B i O_{3}^{-}+22 H^{+}+M n^{2+} \rightarrow 5 B i^{3+}+7 H_{2} O+M n O_{4}^{-} \)
B. \( 5 B i O_{3}^{-}+14 H^{+}+2 M n^{2+} \rightarrow 5 B i^{3+}+7 H_{2} O+2 M n O_{4}^{-} \)
\( \mathbf{c} \cdot 2 B i O_{3}+4 H^{+}+M n^{2+} \rightarrow 2 B i^{3+}+2 H_{2} O+M n O_{4}^{-} \)
D. \( 6 B i O_{3}^{-}+12 H^{+}+3 M n^{2+} \rightarrow 6 B i^{3+}+6 H_{2} O+3 M n O_{4}^{-} \)


A \( 10 \mathrm{kw} \) drilling machine is used to dril a bore in a small aluminium block of
mass \( 8.0 \mathrm{kg} . \) How much is the rise in temperature of the block in 2.5 minutes,
assuming \( 50 \% \) of power is used up in heating the machine itself or lost to the
surroundings. Specific heat of
aluminium \( =\mathbf{0 . 9 1} \boldsymbol{J} \boldsymbol{g}^{-1} \boldsymbol{K}^{-1} \)


Let a function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) satisfy the
equation \( \boldsymbol{f}(\boldsymbol{x}+\boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y}) \) for
all \( x, y . \) If the function \( f(x) \) is
continuous at \( x=0, \) then
A. \( f(x)=0 \) continuous for all \( x \)
B. \( f(x) \) is continuous for all positive real \( x \)
c. \( f(x) \) is continuous for all \( x \)
D. None of these


\( N a O H+D_{2} O \rightarrow N a O D+H D O \), is
\( a: \)
A. exchange reaction
B. deuterolysis reaction.
c. hydrolysis reaction
D. softening reaction


A particle of mass \( m \) strikes a wall with
a velocity \( v \) making an angle \( \theta \) with the
wall and rebounds.The change in
momentum of the particle will be :
\( \mathbf{A} \cdot-2 m \bar{v} \cos \theta \)
B. 0
\( \mathrm{c} \cdot 2 m \bar{v} \)
D. \( -2 m \bar{v} \sin \theta \)


The eccentricity of the ellipse \( 9 x^{2}+ \)
\( 25 y^{2}-18 x-100 y-116=0, \) is
A \( .25 / 16 \)
в. \( 4 / 5 \)
c. \( 16 / 25 \)
D. \( 5 / 4 \)


Three capacitors of capacitance 1.0,2.0
and \( 5.0 \mu F \) are connected in series to a
\( 10 V \) source. The potential difference
across the \( 2.0 \mu F \) capacitor is
A \( \cdot \frac{100}{17} \)
в. \( \frac{20}{17} v \)
c. \( \frac{50}{17} v \)
D. \( 10 V \)


Define magnetic declination.


If \( A \& B \) are independent events such \( \operatorname{that} P(B)=\frac{2}{7}, P(A \cup \bar{B})=0.8, \) then
\( P(A) \) is equal to
A . \( 0 . \)
B. 0.2
\( c .0 .3 \)
D. 0.4


Which among the following is a bi-
dentate ligand?
written as bipy
\( \mathbf{A} \cdot C H_{3} C O O^{-} \)
\( \mathbf{B} \cdot: O C N^{-} \)
\( \mathbf{c} \cdot: N C O^{-} \)
\( \begin{array}{cc}\mathbf{D} \cdot C H_{3}-C_{\|}-C H=C & -C H_{3} \\ : O & : O:\end{array} \)


\begin{tabular}{l}
\( \infty \) \\
\hline 00 \\
\hline 0 \\
\hline\( \infty \)
\end{tabular}


A closed container of volume \( 0.02 \mathrm{m}^{3} \)
contains a mixture of neon and argon gases at a temperature of \( 27^{0} \mathrm{C} \) and at a
pressure of \( 1 \times 10^{5} N / m^{2} . \) The total mass
of the mixture is 28 g. If the gram molecular weights of neon and
argon are 20 and 40 respectively, the masses of the individual gases in the
container are
respectively(assuming them to be ideal) \( [\mathrm{R}=8.314 \mathrm{J} / \mathrm{mol} \mathrm{K}] \)
\( \mathbf{A} \cdot 16 \mathrm{gm}, 12 \mathrm{gm} \)
B. \( 4 \mathrm{gm}, 24 \mathrm{gm} \)
\( \mathbf{c} \cdot 6 \mathrm{gm}, 22 \mathrm{gm} \)
D. \( 12 \mathrm{gm}, 16 \mathrm{gm} \)


The sum of intercepts of the tangent to the curve \( \sqrt{x}+\sqrt{y}=\sqrt{a} \) upon the coordinates axes is
\( \mathbf{A} \cdot 2 a \)
в.
c. \( 2 \sqrt{2} a \)
D. None of these


The value of \( \sqrt{\left(\frac{1+\cos \theta}{1-\cos \theta}\right)}-\csc \theta \)
\( \cot \theta= \)


A particle performing SHM takes time equal to T (time period of SHM) in
consecutive appearances at a
particular point. This point is
A. An extreme position
B. The mean position
C. Between positive extreme and mean position
D. Between negative extreme and mean position


In which of the following alcohols \( C-O \)
bond breaks (heterolytically) with the
greatest ease is:
\( \mathbf{A} \cdot C H_{3} C H_{2} C H_{2} O H \)
в. \( _{C H_{3}}^{\prime} \)
\( C H_{3}-C H-O H \)
c.
\[
C H_{3}-C_{\}^{C H_{3}}
\]
\( _{C H_{3}} \)
D. \( \quad C_{3} \)
\[
C H_{3}-C_{-} C H_{2}-O H
\]


The IUPAC name of the Wilkinson's
catalyst \( \left[R h C l\left(P P h_{3}\right)_{3}\right] \) is :
A. chlorotris (triphenylphosphine) rhodium (I)
B. Chlorotris (triphenylphosphine) rhodium (IV)
c. chlorotris (triphenylphosphine) rhodium (0)
D. chlorotris (triphenylphosphine) rhodium (VI)


In projectile motion, power of the gravitational force This question has multiple correct options
A. is constant throughout
B. is negative for first half, zero at topmost point and positive for rest half
c. varies linearly with time
D. is positive for complete path


In India coniferous forests are found in
A. Madhya Pradesh
B. Himalayan region
c. Satpura hills
D. Rajasthan


Function \( \boldsymbol{x}=\boldsymbol{A} \sin ^{2} \boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{B} \cos ^{2} \boldsymbol{\omega} \boldsymbol{t}+ \)
\( C \sin \omega t \cos \omega t \) represents SHM
A. For any value of \( A, B \) and \( C \) (except \( C=0 \) )
B. \( A=-B, C=2 B, \) amplitude \( =\mid B \sqrt{2} \)
c. \( A=B ; C=0 \)
D. \( A=B ; C=2 B, \) amplitude \( =|B| \)


Match the following lists


cosine of the angle of intersection of curves \( y=3^{x-1} \ln x \) and \( y=x^{x}-1 \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B. \( 1 / 2 \)
\( c \cdot 0 \)
D. \( 1 / 3 \)


velocity-time graph of a particle of mass 2 kg moving in a straight line is
as shown in Fig. \( 6.19 . \) Find the work done by all the forces acting on the particle.
A . -200
B. -400
c. -600
D . -700 J


If \( i^{2}=-1, \) calculate the value of \( 3 i^{2}+ \)
\( \boldsymbol{i}^{3}-\boldsymbol{i}^{4} \)
A \( .-4-i \)
B. \( -2-i \)
\( c \cdot 2+i \)
D. \( 4+i \)
E \( .6+2 i \)


Which of the following theory is not related to the chemical kinetics?
A. Collision theory
B. Absolute theory
c. Absolute reaction rate
D. vSEPR theory


When two compounds have the same
chemical formula, (that is, they have the same number and variety of atoms) but have different linkages between atoms and hence different properties, they are called:
\( A \). isomers
B. isomorphs
c. allotropes
D. isotopes


Name the type of solution formed in the following cases:
i) \( 20 g \) of \( N a C l \) in \( 100 g \) of water.
ii) \( 36 g \) of \( N a C l \) in \( 100 g \) of water.
iii) \( 45 g \) of \( N a C l \) in \( 100 g \) of water at
\( 80^{\circ} \mathrm{C} \)
iv) Sulphur dissolved in \( C S_{2} \)
v) Nitrogen in soil


Mendal carried out his investigations on which plant?
A. Peanuts
B. Pigeon Pea
c. Garden Pea
D. Gram


The length of the fence of a rectangled shaped field \( A B C D \) is \( 130 \mathrm{m} \) and side \( A B \) is \( 60 \mathrm{m}, \) find the area of the field.


If \( P \) is a point inside the scalene
triangle \( A B C \) such that \( \Delta A P B \)
\( \Delta B P C \) and \( \Delta C P A \) have the same
area, then \( P \) must be:
A. In centre of \( \Delta A B C \)
B. Circum centre of \( \Delta A B C \)
c. Centroid of \( \Delta A B C \)
D. Ortho centre of \( \Delta A B C \)


Which lanthanide compound is used as a pigment?
A. \( C e O_{2} \)
B. \( \operatorname{Ce}(O H) \)
c. \( L u(O H)_{3} \$ \)
D. \( \operatorname{Tb}(O H)_{3} \)


Find correcct option regarding physical property of cis/trans isomer
A. trans isomer has the higher M.P.
B. cis isomer has higher B.P.
c. both A and B
D. none of these


The magnitude of vector product of two vectors \( \overline{\mathbf{P}} \times \overline{\mathbf{Q}} \) may be:
A. equal to PQ
B. less than PQ
c. equal to zero
D. all the above


A body of mass \( 5 k g \) undergoes a change in speed from 20 to \( 0.20 m / s . \) The momentum of the body would
A. Increase by \( 99 k g m / s \)
B. Decrease by \( 99 \mathrm{kgm} / \mathrm{s} \)
c. Increase by \( 101 \mathrm{kgm} / \mathrm{s} \)
D. Decrease by \( 101 \mathrm{kgm} / \mathrm{s} \)


In the following, Table of some substances are given in Column I. In
column II some uses are given. Match the items in column I with those in
Column II.


Inside a uniformly charged spherical
conductor, the electric:
This question has multiple correct options
A. Potential is zero everywhere
B. Potential is non-zero and same everywhere
C. Field is zero everywhere
D. Field has the same magnitude everywhere but it is not
zero


A chord \( A B \) of circle of radius \( 14 c m \)
makes an angle of \( 60^{\circ} \) at the centre of
the circle .The area of the minor
segment of the circle is \( \left(\text { Use } \pi=\frac{22}{7}\right) \)
A \( \cdot \frac{308}{3} c m^{2} \)
в. \( \frac{208}{3} \mathrm{cm}^{2} \)
c. \( \frac{108}{3} \mathrm{cm}^{2} \)
D. \( \frac{408}{3} \mathrm{cm}^{2} \)


A parallel plate capacitor, at a capacity \( 100 \mu F \), is charged by a battery at \( 50 \mathrm{V} \)
The battery remains connected and if the plates of the capacitor are separated so that the distance between them is
reduced to half of the original distance, the additional energy given by the battery to the capacitor in \( J \) is:
A \( \cdot 125 \times 10^{-3} \)
В. \( 12.5 \times 10^{-3} \)
с. \( 1.25 \times 10^{-3} \)
.
D. \( 0.125 \times 10^{-3} \)


Mode of feeding in free living protozoans is
A. Holozoic
B. Saprozoic
C. Both (a) and (b)
D. None of these


Assertion
Plastic is non-biodegradable.
Reason
It takes many years to decompose.
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 \( \boldsymbol{x} \neq-\mathbf{5}, \) then the expression \( \frac{\mathbf{3} \boldsymbol{x}}{\boldsymbol{x}+\mathbf{5}} \div \)
\( \frac{6}{4 x+20} \) can be simplified to
A \( .2 x \)
в. \( \frac{x}{2} \)
c. \( \frac{9 x}{2} \)
D. \( 2 x+4 \)


Cement is a mixture of:
A . calcium silicates
B. calcium aluminates
c. calcium silicates and aluminates
D. none of these


If \( z_{1} \) and \( z_{2} \) are complex numbers, prove
that \( \left|z_{1}+z_{2}\right|^{2}=\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2} \) if and only
is \( z_{1} \bar{z}_{2} \) is pure imaginary.


Photorespiration is also called
A. \( C_{2} \) cycle
B. \( C_{3} \) cycle
c. \( C_{4} \) cycle
D. \( C_{5} \) cycle


The ratio of two adjacent sides of a
parallelogram is 3: 4 Its perimeter is
\( 105 \mathrm{cm} \) Find its area if altitude
corresponding to the larger is \( 15 \mathrm{cm} \)
в. \( 600 \mathrm{cm}^{2} \)
\( c \cdot 300 c m^{2} \)
D. \( 450 \mathrm{cm}^{2} \)


toppr
Q Type your question.
\( \left.\right|^{x \in L}\left|: \sin \left(\log _{e} \mid \overline{x-1}\right)\right|^{\operatorname{ls} a} \)
(Here, the inverse trigonometric
function \( \sin ^{-1} x \) assumes values in \( \left.\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\right) \)
Let \( \boldsymbol{f}: \boldsymbol{E}_{1} \rightarrow \mathbb{R} \) be the function define by \( f(x)=\log _{e}\left(\frac{x}{x-1}\right) \) and \( g: E_{2} \rightarrow \mathbb{R} \)
be the function defined by \( g(x)= \) \( \sin ^{-1}\left(\log _{e}\left(\frac{x}{x-1}\right)\right) \)
LIST-1
1. \( \left(-\infty, \frac{1}{1-e}\right] \)
The range of \( f \) is \( \quad\left[\frac{e}{e-1}, \infty\right) \)
Q. The range of \( g \)
contins
R. The domain of \( f \)
contains
\[
\begin{array}{ll}
\text { S. The domain of } g \text { is } & 4 .(-\infty, 0) \cup(0, \infty) \\
& 5 .\left(-\infty, \frac{e}{e-1}\right] \\
& \text { 6. }(-\infty, 0) \cup\left(\frac{1}{2}, \frac{e}{e-1}\right]
\end{array}
\]
The correct option is
A. \( P \rightarrow 4 ; Q \rightarrow 2 ; R \rightarrow 1 ; S \rightarrow 1 \)
в. \( P \rightarrow 3 ; Q \rightarrow 3 ; R \rightarrow 6 ; S \rightarrow 5 \)
c. \( P \rightarrow 4 ; Q \rightarrow 2 ; R \rightarrow 1 ; S \rightarrow 6 \)
D. \( P \rightarrow 4 ; Q \rightarrow 3 ; R \rightarrow 6 ; S \rightarrow 5 \)


In an electron microscope the accelerating voltage is increased from \( 20 \mathrm{kV} \) to \( 80 \mathrm{kV} \), the resolving power ofthe microscope will become.
\( A \cdot 2 R \)
B. \( \frac{2}{R} \)
\( c \cdot 4 R \)
D. 3R


Which of the following drugs gives relief from anxiety and stress?
A. Ofloxacin
B. Asprin
c. Luminal
D. Mestranol


A secretion which aids in digestion of
major foodstuffs is
A . Bile
B. Gastric
c. Pancreatic
D. Saliva


Match the compounds given in column I with oxidation states of carbon given in column II and mark the apropriate
choice.
\( (A) \)
(B) The the \( \begin{array}{llll}\text { Column I } & & \text { Column II } \\ & & \\ C_{6} H_{12} O_{6} & \text { (i) } & +3 \\ & C H C l_{3} & \text { (ii) } & -3 \\ & C H_{3} C H_{3} & \text { (iii) } & +2 \\ & (C O O H)_{2} & \text { (iv) } & 0\end{array} \)
(c)
(D)
\( A \)
\( (A) \rightarrow(\text { iv }),(B) \rightarrow(\text { iii }),(C) \rightarrow(\text { ii }),(D) \rightarrow(i) \)
B. \( (A) \rightarrow(\text { i }),(B) \rightarrow(\text { ii }),(C) \rightarrow(\text { iii }),(D) \rightarrow(\text { iv }) \)
C. \( (A) \rightarrow(\text { ii }),(B) \rightarrow(\text { iii }),(C) \rightarrow(\text { iv }),(D) \rightarrow(i) \)
\( D \cdot(A) \rightarrow(\text { iii }),(B) \rightarrow(\text { ii }),(C) \rightarrow(i),(D) \rightarrow(\text { iv }) \)


\( A \) and \( B \) are two square matrices of
same order. If \( A B=B^{-1}, \) then \( A^{-1}= \)
A. \( B A \)
B . \( A^{2} \)
\( c \cdot B^{2} \)
D. \( B \)


Out of the five isomeric hexanes, The isomer that can give two
monochlorinated compounds is:
A. 2,3-Dimenthyl butane
B. 2,2-Dimenthyl butane
c. 2-Dimenthyl pentane
D. n-Hexane


Show that \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}+\cot ^{-1} \boldsymbol{x}+ \)
\( \log (\sqrt{1+x^{2}}-x) \) is increasing in \( R \)


Myasthenia gravis is caused due to
A. Interferon
B. Autoantibody
c. Antigen
D. Toxins


Elements of a matrix \( A \) of order \( 10 \times 10 \)
are defined as \( a_{i j}=w^{i+j} \) (where \( w \) is
cube root of unity), then trace \( (A) \) of the
matrix is
\( A \cdot \omega \)
B.
\( c \cdot \omega^{2} \)
D.


Of more than 114 elements known so far,
are metals:
A . 74
B. 64
\( c \cdot 94 \)
\( D \cdot 84 \)


An electrical appliance is rated at 1000
KVA, 220V. If the appliance is operated for 2 hours, calculate the energy consumed by the appliance in:
(i) kWh.
(ii) joule.


A solid cylinder of mass \( 50 \mathrm{kg} \) and radius \( 0.5 \mathrm{m} \) is free to rotate about horizontal axis. A massless string
is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2
revolutions \( s^{-2} \) is :
A. 25
B. 50 N
c. 78.5 N
D. 157 N


The reactance of coil when used in an
A.C. power supply ( 220volts, 50 cycles/sec) is 50ohms. The inductance of the coil is nearly
A . 0.16 Н
B. 0.22
c. \( 2.2 \mathrm{H} \)
D. 1.6


Which one of the following statements
best describes the nature of the field
lines due to a bar magnet?
A. Field lines start from the north pole and end on the south pole. Any number of field lines can pass through a point
B. Field lines start from the north pole and end on the south pole. Only one field line passes through a point
C. Field lines are continuous lines passing inside and outside the magnet. Only one field line passes through a point
D. Field lines are continuous lines passing inside and outside the magnet. Any number of field lines can pass through a point


Isoprene is the repeating unit in:
\( A \cdot \) vitamin \( A \)
B. terpenes
c. natural rubber
D. All of the above


Find the coordinates of focus, the
equation of the directrix and length of the latus rectum of the conic
represented by the equation \( 3 x^{2}=-y \)


If \( A \) and \( B \) mutually exclusive events associated with a random experiment such that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 4} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 5} \)
then find \( \boldsymbol{P}(\overline{\boldsymbol{A}} \cap \overline{\boldsymbol{B}}) \)


Prove that \( \tan ^{-1}\left(\frac{\sin x}{1+\cos x}\right),-\pi<x<\pi \)


An emulsifier is an agent which :
A. accelerates the dispersion
B. homogenises an emulsion
c. stabilizes an emulsion
D. aids the flocculation of an emulsion


Explain why in some substances like KCl, formula mass is used instead of
molecular mass?


Examples of sublimate does not
include:
A. ammonium salts
B. nitrates
c. iodine
D. naphthalene


Explain the role of villi in absorption


A mixture of three parts of concentrated
hydrogen chloride with one part of concentrated nitric acid is known as:
A . quick lime
B. aqua regia
c. hydrazine
D. none of these


Silk moth feed on:
A. eucalyptus leaf
B. grapes Leaves
c. mulberry Leaves
D. neem leaves


Assertion
Cesium is useful as electrodes in
photoelectric cells.
Reason
Light energy absorbed by cesium is sufficient to make an atom of cesium to
lose an 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. Assertion is incorrect but Reason is correct


From the electronic configurations, one
can predict that the geometric configuration for which of the following
molecules is not correct?
\( \mathbf{A} \cdot P F_{3}, \) trigonal planar
B. \( C F_{4} \), tetrahedral
\( \mathbf{C} \cdot C H C l_{3}, \) irregular tetrahedron
D. \( O F_{2} \), bent (v-shaped)
E . \( H F \), linear


The cell
\( \boldsymbol{P t}\left(\boldsymbol{H}_{2}\right)(\boldsymbol{1} \boldsymbol{a} \boldsymbol{t m}) \mid \boldsymbol{H}^{+}(\boldsymbol{p} \boldsymbol{H}=?), \boldsymbol{I}^{-}(\boldsymbol{a}= \)
0. The electrode potential for the
reaction \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{l}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{A} \boldsymbol{g}+\boldsymbol{I}^{\ominus} \boldsymbol{i} \boldsymbol{s}- \)
0.151 volt. Calculate the \( p H \) value :-
A . 3.37
B. 5.26
\( c .2 .56 \)
D. 4.62


Discuss the applicability of Lagrange's
mean value theorem for the function
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \) on [-1,1]


Let \( \boldsymbol{v}_{\boldsymbol{K}_{\alpha}}, \boldsymbol{v}_{\boldsymbol{K}_{\beta}}, \) and \( \boldsymbol{v}_{\boldsymbol{L}_{\alpha}} \) are the
frequencies of \( \boldsymbol{K}_{\boldsymbol{\alpha}}, \boldsymbol{K}_{\boldsymbol{\beta}} \) and \( \boldsymbol{L}_{\boldsymbol{\alpha}} . \mathbf{X} \)
raylines of a material, then
\( \mathbf{A} \cdot v_{K_{\alpha}}+v_{K_{\beta}}=v_{L_{\alpha}} \)
В . \( v_{K_{a}}-v_{K_{\beta}}=v_{l_{d}} \)
\( \mathbf{c} \cdot v_{L_{\alpha}}+v_{K_{\alpha}}=v_{K_{\beta}} \)
D. \( v_{K_{\alpha}}-v_{L_{\alpha}}=v_{K_{\beta}} \)


\( X \) -rays:
A. are deflected in a magnetic field.
B. are deflected in an electric field.
C. remain undeflected by both electric and magnetic fields.
D. are deflected in both electric and magnetic fields.


Number of alary muscles in Cockroach
is
A. Twelve pairs
B. Twelve
c. Thirteen
D. Thirteen pairs


From Bohr's model, radius of the orbit
and energy of the hydrogen atom are
calculated as:
This question has multiple correct options
A. the radius of the \( 1^{s t} \) orbit is \( 0.529 A^{\circ} \)
B. the energy of the \( 1^{s t} \) orbit is \( -13.6 e V \)
C. the energy of the \( 1^{s t} \) orbit is \( -21.72 \times 10^{-19} J \)
D. the radius of the \( 1^{s t} \) orbit is \( 1.06 A^{\circ} \)


A capacitor has capacitance \( 0.5 n F . A \)
choke of \( 5 \mu H \) is connected in series. An
electromagnetic wave of wavelength \( \lambda \) is found to resonate with it. Find \( \lambda \) (in
meter)
\( \mathbf{A} \cdot 10 \pi \)
в. \( 20 \pi \)
c. \( 30 \pi \)
D. \( 5 \pi \)


In a certain city two newspapers \( A \) and
\( B \) are published. It is known that \( 25 \% \) of
the city population reads \( A \) and \( 20 \% \) of
the population reads \( B .8 \% \) of the
population reads both \( A \) and \( B \). It is
known that \( 30 \% \) of those who read \( A \) but
not \( B \) look into advertisements and \( 40 \% \)
of those who read \( B \) but not \( A \) look
advertisements while \( 50 \% \) of those who
read both \( A \) and \( B \) look into
advertisements. What is the
percentage of the population who reads an advertisement?
A \( \cdot \frac{139}{500} \)
в. \( \frac{361}{500} \)
c. \( \frac{139}{1000} \)
D. \( \frac{861}{1000} \)


(a) Write the \( \beta- \) decay of tritium in
symbolic from.
(b) Why is it experimentally found difficult to detect neutrinos in this
process?


Which of the following is a \( 3^{\circ} \) amine?
A. 1-Methylcyclohexylamine
B. Triethylamine
c. tert-butylamine
D. N-Methylaniline


In an experiment to determine e/m using Thomson's method, electrons from the cathode accelerate through a
potential difference of \( 1.5 \mathrm{kV} \). The beam
coming out of the anode enters crossed
electric and magnetic field of strengths
\( 2 \times 10^{4} V / m \) and \( 8.6 \times 10^{-4} T \)
respectively, The value of e/m.of
electron will be
A \( \cdot 1.6 \times 10^{11} \mathrm{C} / \mathrm{kg} \)
B . \( 1.7 \times 10^{11} \mathrm{C} / \mathrm{kg} \)
C \( .1 .8 \times 10^{11} \mathrm{C} / \mathrm{kg} \)
D. \( 1.9 \times 10^{11} \mathrm{C} / \mathrm{kg} \)


What is the medicinal use of narcotic
drugs?


Simplify the following:
\( \left(\frac{1}{4}\right)^{-2}-3(8)^{2 / 3}(4)^{0}+\left(\frac{9}{16}\right)^{\frac{-1}{2}} \)


A glass of water upto a height \( 10 \mathrm{cm} \) has bottom area \( 5 c m^{2} \) and top area \( 10 c m^{2} \)
The downward force exerted by water on
the bottom is? (Take \( g=10 m / s^{2}, \rho_{w}= \)
\( \mathbf{1 0}^{3} \mathbf{k g} / \boldsymbol{m}^{3}, \boldsymbol{P}_{\boldsymbol{a}}=\mathbf{1 . 0 1} \times \mathbf{1 0}^{\mathbf{5}} \mathbf{N m}^{-\mathbf{2}} \mathbf{)} \)
A. \( 102 \mathrm{N} \)
в. 120N
c. \( 22 \mathrm{N} \)
D. \( 51 \mathrm{N} \)


The energy of an electron in H atom is
\( -3.4 e V . \) If the angular momentum of
the electron is \( x \times 10^{-34} J \sec ^{-1}, \) then \( x \)
is:
A . 2.3
B. 2.1
c. 3.
D. 3.3


\( \ln \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3}, \) the number of
covalent bonds and coordinate bonds
are, respectively:
\( A \cdot 3,6 \)
B. 6,6
\( c \cdot 8,9 \)
D. 18,6


Copy and complete the following table which refers to two practical applications of electrolysis.
Anode Electrolyte
silver

Solution of plating a potassium spoo argentocya
Purificati of copper


Which hormone causes dilation of
blood vessels, increased oxygen consumption an glucogenesis?
A . ACTH
B. Insulin
c. Adrenaline
D. Glucagon


If \( \boldsymbol{a}=\sin \boldsymbol{\theta}, \boldsymbol{b}=\sin (\boldsymbol{\theta}+\boldsymbol{2} \boldsymbol{\pi} / \mathbf{3}), \boldsymbol{c}= \)
\( \sin (\theta+4 \pi / 3), x=\cos \theta, y= \)
\( \cos (\theta+2 \pi / 3), z=\cos (\theta+4 \pi / 3) \)
then value of
\( \boldsymbol{\Delta}=\left|\begin{array}{ccc}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ \boldsymbol{b} \boldsymbol{c} & \boldsymbol{c} \boldsymbol{a} & \boldsymbol{a} \boldsymbol{b}\end{array}\right| \)
is
A . 1 \( \overline{8} \)
B. \( \frac{3 \sqrt{3}}{4} \)
\( c \cdot \frac{3 \sqrt{3}}{8} \)
D. \( \frac{\sqrt{3}}{4} \)


\( \operatorname{Let} A(a \cos \theta, 0), B(0, a \sin \theta) \) be any
two points then the distance between two points is
A. \( |a| \) units
B . \( a^{2} \) units
c. \( \sqrt{a} \) units
D. \( \sqrt{2} a \) units


The unit of frequency is:-
A. Hertz
B. Joule
\( c . \) onm
D. Kilo Calorie


\( \int \cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) d x \)


A student obtains a blurred image of an
object on a screen by using a concave
mirror. In order to obtain a sharp image
on the screen, he will have to shift the
mirror:
A. towards screen.
B. away from the screen.
C. either towards or away from the screen depending upon the position of the object.
D. to a position very far away from the screen.


The number of \( \sigma \) and \( \pi \) bond in \( X e O_{3} \)
molecule are:
\( \mathbf{A} \cdot 1 \sigma, 2 \pi \)
в. \( 3 \sigma, 3 \pi \)
\( \mathbf{c} \cdot 3 \sigma, 0 \pi \)
D. \( 2 \sigma, 1 \pi \)


How many lone pairs are present in \( C l I_{3} \)
\( ? \)
A . 1
B. 8
\( c \cdot 5 \)
D. 4


Trumpet hyphae in certain brown algae resemble
A. Trachea
B. Sieve tubes
c. Sclerenchymatous fibres
D. Tracheids


A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the
other end. Show that whatever force the
monkey exerts on the rope,the monkey and the block


Which of the following is not related to
Watson and Crick model of DNA?
A. X-ray crystallography
B. The Meselson-Stahl experiment
C. Chargaff's rules
D. The different sizes of purines and pyrimidines
E. The transforming principle of Avery et al


When vanilla extract added to
it still retains the sweet
pleasant smell
A. dil . нс
B. conc. HCI
c. dil. NaOH
D. conc. NaOH


A diverging meniscus lens has a focal length of \( -20 \mathrm{cm} . \) If the lens is held 10 \( \mathrm{cm} \) from the object, the magnification is :
A . -0.667
B. +0.667
\( c \cdot-2 \)
\( D \cdot+2 \)


Graphite is used as a solid:
A. coolent
B. Iubricant
C. both (a) and (b) above
D. none of these


The end products of protein digestion
are
A. monosaccharides
B. steroids
c. amino acids
D. fatty acids


Specify the hybridization of central atom in the following species respectively.
\( N_{3}^{-}, N O C l, N_{2} O \)
\( \mathbf{A} \cdot s p, s p^{2}, s p \)
B. \( s p, s p, s p^{3} \)
\( \mathbf{c} \cdot s p^{2}, s p, s p \)
D \( \cdot s p^{2}, s p^{2}, s p \)


The angle turned by a body undergoing circular motion depends on time as
\( \boldsymbol{\theta}=\boldsymbol{\theta}_{0}+\boldsymbol{\theta}_{1} \boldsymbol{t}+\boldsymbol{\theta}_{2} \boldsymbol{t}^{2} . \) Then the angular
acceleration of the body is
\( A \cdot \theta_{1} \)
в. \( \theta_{2} \)
\( c \cdot 2 \theta_{1} \)
D. \( 2 \theta_{2} \)


Two stretched strings have lengths and 21 while tension are T and 4T
respectively. If they are made of same material the ratio of their frequency is:
A. 2:
B. 1: 2
\( c \cdot 1: 1 \)
\( D \cdot 1: 4 \)


Which of the following pair of angles is
equal if \( \boldsymbol{m} \| \boldsymbol{n} ? \)
A. \( \angle 1 \) and \( \angle 4 \)
B. \( \angle 3 \) and \( \angle 4 \)
\( c . \angle 4 \) and \( \angle 8 \)
D. \( \angle 6 \) and \( \angle 8 \)


The reaction having higher value of equilibrium constant is faster than the reaction having lower value of equilibrium constant.
A. True
B. False


Adolescence is
A. The time for growth spurts and puberty changes.
B. The time of puberty.
C. The time of reproductive cycle.
D. None of the above.


In Wurtz reaction the reagent used is:
A . \( N a \)
в. \( N a / \) liq. \( N H_{3} \)
c. \( N a / \) dry ether
D. \( N a / \) dry ethanol


What are acid anhydrides?


Prove that \( \cos ^{2} A+\cos ^{2}(A+120)+ \)
\( \cos ^{2}(A-120)=\frac{3}{2} \)


Weight of a body is a scalar quantity. True or false.
A . True
B. False


An electromagnetic wave has a frequency of \( 500 M H z \) and a wavelength of \( 60 \mathrm{cm} \). Name the medium
through which it is traveling.
A . air
B. water
c. salt
D. cardboard


In a polluted environment, maximum pollution will occur in.
A. Primary producers
B. Tertiary consumers
c. secondary consumers
D. Primary consumers


0.6 ml of glacial acetic acid with density \( 1.06 g / m l \) is dissolved in \( 1 k g \) water and the solution froze at
\( -0.0205^{\circ} \mathrm{C} . \) Calculate van't Hoff factor:
\( \boldsymbol{K}_{f} \) for water is \( 1.86 \boldsymbol{K} \boldsymbol{k g} \boldsymbol{m o l}^{-1} \)


A rational number \( \frac{-2}{3} \)
A. Lies to the left side of 0 on the number line
B. Lies to the right side of 0 on the number line
C. It is not possible to represent on the number line
D. Cannot be determined on which side the number lies


The empirical formula weight of a compound containing carbon and hydrogen is \( 13 . \) The molecule of the compound is 39 times heavier than a molecule of hydrogen. The molecular formula of the compound is:
A \( . C H \)
B. \( C_{3} H_{3} \)
c. \( C_{13} H_{13} \)
D. \( C_{6} H_{6} \)


State zeroth law of thermo dynamics?


Catenation property is maximum in:
A. phosphorus
B. carbon
c. sulphur
D. none


The unit of specific heat is
A . cal
B . Cal/g/'c
c. cal/g
D. none of these


A bar of cross-sectional area \( \boldsymbol{A} \) is
subjected two equal and opposite tensile forces at its ends as shown in
figure. Consider a plane BB' making an
angle \( \theta \) with the length.
The ratio of tensile stress to the
shearing stress on the plane BB' is:
\( A \cdot \tan \theta \)
B. \( \sec \theta \)
\( c \cdot \cot \theta \)
\( D \cdot \cos \theta \)


Energy required for the ionisation reactions are shown:
\( \boldsymbol{N a}(\boldsymbol{g}) \stackrel{+E_{1}}{\rightarrow} \boldsymbol{N} \boldsymbol{a}^{+}(\boldsymbol{g}) \)
\( M g(g) \stackrel{+E_{2}}{\rightarrow} M g^{+}(g) \) and
\( \boldsymbol{N} \boldsymbol{a}^{+}(\boldsymbol{g}) \stackrel{+\boldsymbol{E}_{3}}{\rightarrow} \boldsymbol{N} \boldsymbol{a}^{2+}(\boldsymbol{g}) \)
Then the correct order of absorbed
energy is :
A. \( E_{1}>E_{2}>E_{3} \)
в. \( E_{3}>E_{1}>E_{2} \)
c. \( E_{2}>E_{3}>E_{1} \)
D. \( E_{3}>E_{2}>E_{1} \)


Let \( b=a+c \). Then the equation \( a x^{2}+ \)
\( b x+c=0 \) has equal roots, if
\( \mathbf{A} \cdot a=c \)
B . \( a=-c \)
c. \( a=2 c \)
D. \( a=-2 c \)


Show that \( \tan ^{2} \theta-\frac{1}{\cos ^{2} \theta}=-1 \)


A die is thrown twice and the sum of the
numbers appearing is observed to be 6 What is the conditional probability that
the number 4 has appeared at least once?


A curved road is \( 7.5 ~ m \) wide and its
outer edge is raised by 1.5 m over the inner edge. The radius of curvature is
\( 50 m . \) For what speed of the car is this
road suited? \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)
A. \( 5 \mathrm{m} / \mathrm{s} \)
в. \( 10 \mathrm{m} / \mathrm{s} \)
c. \( 15 \mathrm{m} / \mathrm{s} \)
D. 20 \( m / s \)


A man spends \( 80 \% \) of his income in
expenditure, with the increase in the cost of living his expenditure increases by \( 37 \frac{1}{2} \) and his income increases by \( 16 \frac{2}{3}, \) then the present percent saving is
A \( \cdot 1 \frac{2}{3} \)
B. \( 7 \frac{6}{5} \)
\( \mathrm{c} \cdot_{5} \frac{5}{7} \)
D. \( 9 \frac{3}{11} \)


\( \boldsymbol{p}(\boldsymbol{x})=\mathbf{7} \boldsymbol{x}^{2}-\boldsymbol{9} \) is a
polynomial
A. quadratic
B. linear
c. constant
D. cubic


In a transformer, coefficient of mutual
inductance between primary and secondary coil is \( 0.2 \mathrm{H} \). When current changes by 5 Na in the primary, then:
the induced era in the secondary will be
A. \( 0.5 \mathrm{v} \)
B. 1
\( c \cdot 1.5 v \)
D. 2.0


The change in internal energy of a system
depends on
\( A . \) initial and final states of the system
B. the path if reversible
C. the path if irreversible
D. initial, final states and also on the path


From a mixture of
\( \boldsymbol{C H}_{3} \boldsymbol{C l}, \boldsymbol{C H}_{2} \boldsymbol{C l}_{2}, \boldsymbol{C H} \boldsymbol{C l}_{3} \boldsymbol{a n d} \boldsymbol{C C l}_{4} \)
chloroform can be seperated by:
A. distillation
B. fractional distillation
c. distillation under reduced pressure
D. steam distillation


Select the correct pair
A. Adaptive radiation - Darwin's Finches
B. Connecting Link - Sewall Wright effect
C . Genetic. Drift - Peppered Moth
D. Industrial melanism - Archaeopteryx


Sometimes, the remains of a dead
animal escape destruction and become buried in sediment of ash or survives
under heating, crushing or folding. The sediment or rock becomes elevated as a
part of the land, escapes destructive erosion by water or wind and the object becomes exposed or dug out and comes to the attention of a zoologist. Such a phenomenon leads to the formation of:
A. A new species
B. A new animal
c. A new fossil
D. No, this is not possible


\( " M g_{2} C_{3} \) on reaction with water forms
propane." Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


The internal resistance of a \( 2.1 \mathrm{V} \) cell
which gives a current of \( 0.2 \mathrm{A} \) through a resistance of \( 10 \Omega \) is
\( \mathbf{A} \cdot 0.2 \Omega \)
B. \( 0.5 \Omega \)
c. \( 0.8 \Omega \)
D. \( 1.0 \Omega \)


revolution is equivalent to :
A. \( \pi \) radians
B. \( 2 \pi \) radians
c. \( 3 \pi \) radians
D. \( 4 \pi \) radians


Statement
(I): If
\( \sin \alpha=\frac{12}{13},\left(0<\alpha<\frac{\pi}{2}\right) \) and
\( \cos \beta=-\frac{3}{5},\left(\pi<\beta<\frac{3 \pi}{2}\right) \) then
\( \sin (\alpha+\beta)=\frac{56}{65} \)
Statement (II): If
\( \theta \) and \( \phi \) are angles in the first quardrant such that \( \tan \theta=\frac{1}{7} \) and \( \sin \phi=\frac{1}{\sqrt{10}} \operatorname{then} \theta+2 \phi=45^{\circ} \)
Which of the above statements is
correct?
A. only
B. only ॥
c. Both I\&॥
D. Neither I nor I


Identify the compound which is obtained in following reactions:
An alcohol from ethyl bromide:


What is meant by the term 'moment of force'?


Find the sum of average oxidation
number of \( S \) in \( H_{2} S O_{5} \) (peroxy
monosulphuric acid) and \( N a_{2} S_{2} O_{3} \)
(sodium thiosulphate)


Snake's venom is
A. Alkaline in reaction
B. Acidic in reaction
C. Alkaline and rich fatty acids
D. Acidic and rich fatty acids


Magnification for erect and inverted
image is
A. Positive and negative respectively
B. Negative and positive respectively
c. Positive
D. Negative


Which of the following is wrong about silica?
A. Purest form of silica is know as quartz.
B. Quartz is also know as rock crystal.
c. Quartz contain hexagonal prisms.
D. U.V. light cannot pass through quartz


Which of the following can lose two electrons to attain the configuration of
argon?
A . Mg
B. Br
\( c \cdot s \)
D. ca


A block of wood weights \( 12 \mathrm{kg} \) and has a relative density \( 0.6 . \) It is to be of its volume immersed. What weight of a metal is needed if the metal is on the
top of wood? [Relative density of metal =
14].
\( A \cdot 2 \mathrm{kg} \)
B. \( 4 \mathrm{kg} \)
\( c \cdot 6 \mathrm{kg} \)
\( D \cdot 8 \mathrm{kg} \)


a. Write one example each for fossil fuels in solid and liquid state.
b. Which fossil fuel produces ammonia when distilled in the absence of air?


Solve
\( (3 a+4 b) \times(4 a+3 b) \)


Which of the following is not part of the
Atomic Theory?
A. Compounds are made up of combinations of atoms
B. All atoms of a given element are alike
C. All matter is composed of atoms
D. A chemical reaction involves the rearrangement of atoms
E. The atom is mainly empty space


Which one of the following pentafluorides cannot be formed?
A. \( P F_{5} \)
B. \( A s F_{5} \)
\( \mathrm{c} . S b F_{5} \)
D. \( B i F_{5} \)


What is the relation between leaf
venation and the type of roots?


Fill in the blank.
The pressure exerted on a surface by an object increases as the weight of the object or the surface area of
contact
A. decreases, increases
B. increases, increases
c. increases, decreases
D. decrases, decreases


The piston is taken completely out of the cylinder. The hole at the top is
sealed. A water tank is brought below the cylinder and put in a position, so that the water surface in the tank is at
the same level as the top of the cylinder as shown in the figure. The density of
the water is \( \rho \)
n equilibrium, then height \( H \) of the
water column in the cylinder satisfies
A \( \cdot \rho g\left(L_{0}-H\right)^{2}+P_{0}\left(L_{0}-H\right)+L_{0} P_{0}=0 \)
B . \( \rho g\left(L_{0}-H\right)^{2}-P_{0}\left(L_{0}-H\right)-L_{0} P_{0}=0 \)
C \( \cdot \rho g\left(L_{0}+H\right)^{2}+P_{0}\left(L_{0}-H\right)-L_{0} P_{0}=0 \)
D \( \cdot \rho g\left(L_{0}-H\right)^{2}-P_{0}\left(L_{0}-H\right)+L_{0} P_{0}=0 \)


Which of the following algae is being used in space research?
A. Chlorella
B. cladophora
c. Hydrodictyon
D. chlamydomonas


Which one of the following order is
correct for the bond energies?
\( \mathbf{A} \cdot I_{2}>\mathrm{Cl}_{2}>\mathrm{Br}_{2} \)
B. \( \mathrm{Br}_{2}>\mathrm{Cl}_{2}>\mathrm{I}_{2} \)
\( \mathbf{C} \cdot I_{2}>\mathrm{Br}_{2}>\mathrm{Cl}_{2} \)
\( \mathbf{D} \cdot \mathrm{Cl}_{2}>\mathrm{Br}_{2}>\mathrm{I}_{2} \)


If the diagonal of a rectangle is twice one of the sides, then the ratio of the
sides of the rectangle is
A. \( \sqrt{2}: 1 \)
в. \( \sqrt{3}: 1 \)
\( c \cdot 2 \sqrt{2}: 1 \)
D. \( 2 \sqrt{3}: 1 \)


Factorize \( (5 x-3 y)^{3}+(3 y-8 z)^{3}+ \)
\( (8 z-5 x)^{3} \)


If \( A=\left[\begin{array}{ll}\alpha & 0 \\ 1 & 1\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 5 & 1\end{array}\right] \) whenever
\( \boldsymbol{A}^{2}=\boldsymbol{B} \)
then values of \( \boldsymbol{\alpha} \) is
A .
B. -
\( c \cdot 4 \)
D. no real value of \( \alpha \)


Find the equation of the plane which
passes through the point (3,2,0) and contains the line \( \frac{\boldsymbol{x}-\mathbf{3}}{\mathbf{1}}=\frac{\boldsymbol{y}-\mathbf{6}}{\mathbf{5}}= \)
\( \frac{z-4}{4} ? \)


Solve and verify the result:
\( 4 x+7=15 \)


Square planar complex of the type \( M A X B L(\text { where } A, B, X \text { and } L \) are
unidentate ligands) shows following set of isomers.
A. Two cis and one trans
B. Two trans and one cis
c. Two cis and two trans
D. Three cis and one trans


Reduction reaction is:
A. addition of electron
B. decrease in oxidation state of element
C . addition of hydrogen
D. all of these


Dehydrating agent and dehydrohalogenating agents among the following are respectively:
A. conc. \( H_{2} S O_{4}, A l_{2} O_{3} \)
B. \( A l_{2} O_{3}, \) сопс. \( H_{2} S O_{4} \)
c. conc. \( H_{2} S O_{4}, \) Alc. \( K O H \)
D. Alc. KOH, conc. \( H_{2} S O_{4} \)


Which one of the following animal is protostomes?
A. Acorn worm
B. Spiny skinned animal
c. Earthworm
D. Echidna


Complete the blanks by identifying \( \boldsymbol{X} \)
and \( Y \)
A. Ethanal. ethen
3. Ethanol, ethene
c. Ethanal, ethyne
D. Ethanol, ethyne


Two wires are made of the same
material and have the same volume.
However wire 1 has cross-sectional area
\( A \) and wire 2 has cross-sectional area
\( 3 A . \) If the length of wire 1 increases by \( \Delta x \) on applying force \( F \), how much force
is needed to stretch wire 2 by the same
amount?
A \( .4 F \)
в. \( 6 F \)
\( \mathrm{c} .9 \mathrm{F} \)
D. \( F \)


An ion \( M^{3+} \) has electronic
configuration \( [\boldsymbol{A} \boldsymbol{r}] \boldsymbol{3} \boldsymbol{d}^{10} \boldsymbol{4} \boldsymbol{s}^{2} . \) Element \( \mathbf{M} \)
belongs to
A. s- block
B. p - block
c. \( d \) - block
D. f- bblock


Represent following complex numbers \( z_{1}=1+2 i \) and \( z_{2}=5-7 i \) by points in
Argand's diagram and determine their amplitudes approximately.


Chemical A is used for softening of water to remove temporary hardness. reacts with sodium carbonate to
produce caustic soda, when \( C O_{2} \) is
bubbled through 'A', it turns cloudy. Chemically 'A' is:
A. \( C a O \)
в. \( C a C O_{3} \)
c. \( \operatorname{Ca}\left(H C O_{3}\right)_{2} \)
D. \( C a(O H)_{2} \)


For all positive integers \( n, P(n) \) is true
and \( 2^{n-2}>3 n \), then which of the
following is true?
\( \mathbf{A} \cdot P(3) \) is true
\( \mathbf{B} \cdot P(5) \) is true
C. If \( P(m) \) is true then \( P(m+1) \) is also true.
D. If \( P(m) \) is true then \( P(m+1) \) is not true.


8
the magnetic field changes at the rate
of \( d B / d t . A B=B C . \) Calculate the
induced emf between the ends of length
\( A B, \) if \( A C \) and \( B C \) were removed from
the circuit.
\( ^{\mathbf{A}} \cdot R^{2}\left(\frac{d B}{d t}\right) \)
\( ^{\mathbf{B}} \cdot 4 R^{2}\left(\frac{d B}{d t}\right) \)
\( ^{\mathbf{C}} \cdot \frac{1}{2} R^{2}\left(\frac{d B}{d t}\right) \)
\( ^{\mathrm{D}} 2 R^{2}\left(\frac{d B}{d t}\right) \)
E. None of the above


For a radioactive element, \( \boldsymbol{\tau}= \)
\( -\tau_{1 / 2} \)
\( \mathbf{A} \cdot 0.693 \)
в. 693
\( c \cdot 144 \)
D. 1.44


The chemical reaction, \( 2 A g C l_{(s)}+ \)
\( \boldsymbol{H}_{2(g)} \rightarrow 2 \boldsymbol{H} \boldsymbol{C l}_{(a q)}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{(s)} \) taking
place in a galvanic cell is represented by the notation:
A \( \cdot P t_{(s)} \mid H_{2(g)}, 1 \) bar \( \left|1 M K C l_{(a)}\right| A g C l_{(s)} \mid A g_{(s)} \)
B . \( P t_{(s)} \mid H_{2(g)}, 1 \) bar \( \mid 1 \) M \( H C l_{(a q)}\left|1 M A g_{(a q)}^{+}\right| A g_{(s)} \)
C. \( P t_{(s)} \mid H_{2(g)}, 1 \) bar \( \mid 1 \) M \( H C l_{\left(a_{9}\right)}\left|A g C l_{(s)}\right| A g_{(s)} \)
D. \( P t_{s} \mid H_{2(g)}, 1 \) bar \( \left|1 M H C l_{(a q)}\right| A g_{(s)} \mid A g C l_{s} \)


Hydrogen combines with oxygen in a 1: 8 weight ratio to form water. If every molecule of water contains two atoms
of hydrogen and one atom of oxygen, an atom of oxygen must weigh:
A. 8 times the mass of a hydrogen atom
B. 16 times the mass of a hydrogen atom
c. \( 1 / 16 \) times the mass of a hydrogen atom
D. \( 1 / 8 \) times the mass of a hydrogen atom


A particle moving with velocity of magnitude V changes its direction of motion by angle \( \theta \) without change in
speed. Find the
(a) Magnitude of change of velocity. (b)Change in magnitude of velocity.


Let \( f \) and \( g \) be two functions defined on
an interval I such that \( f(x) \geq 0 \) and
\( g(x) \leq 0 \) for all \( x \epsilon I \) and \( f \) is strictly decreasing on \( I \) while \( g \) is strictly
increasing on \( I \) then

This question has multiple correct options
A. The product function \( f g \) is strictly increasing on \( I \)
B. The product function \( f g \) is strictly decreasing on \( I \)
c. \( \operatorname{Fog}(x) \) is monotonically increasing on \( I \)
D. \( \operatorname{Fog}(x) \) is monotonically decreasing on \( I \)


Among the following reactions, the impossible one is :
A \( \cdot^{2} H e_{4}+^{4} B e_{9} \longrightarrow^{0} n_{1}+^{6} C_{12} \)
B. \( ^{2} \mathrm{He}_{4}+^{7} \mathrm{N}_{14} \longrightarrow^{1} \mathrm{H}_{1}+^{8} \mathrm{O}_{17} \)
\( \mathbf{c} \cdot 4\left(^{1} H_{1}\right) \rightarrow^{2} H e_{4}+^{2}\left(^{-1} e_{0}\right) \)
D. \( ^{3} L i_{7}+^{1} H_{1} \longrightarrow^{4} B e_{8} \)


The earthen pots prepared by using clay only are generally
A. Porous
B. Non-porous
c. conductors of electricity
D. Transparent


Which of the following is maximum
stable?
A . Conjugated alkadiene \( \left(C H_{2}=C H-C H=C H_{2}\right) \)
B. Isolated alkadiene \( \left(C H_{2}=C H-C H_{2}-C H=C H_{2}\right) \)
c. cumulated alkadiene \( \left(C H_{2}=C=C H_{2}\right) \)
D. All are equal


In lateral inversion.
A. Right side of the object will be right side of the image
B. Left side of the object will be left side of the image
C. Upside of the object will be down side of the object
D. Right side of the object will be left side of the image


Which metal ion has highest stability in the Irving-Williams order of stability of metal ions?
\( \mathbf{A} \cdot M n^{2+} \)
в. \( Z n^{2} \)
\( \mathrm{c} \cdot F e^{2} \)
D. \( C u^{2} \)


An element has atomic number \( 16 . \) It
will belong to which period of the periodic table?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Which of the following group/linkage is absent in adenine but present in
guanine?
A \( . C-N \)
в. \( -N H_{2} \)
c. \( C=O \)
D. \( -C O N H_{2} \)


A lawn is the form of a square of side
\( 30 m . A \) cow is tied with a rope of \( 10 m \) to
a pole standing at one of its corners. The maximum area of the lawn grazed by this cow is
\( \mathbf{A} \cdot 300 m^{2} \)
B. \( 150 m^{2} \)
c. \( 78.5 m^{2} \)
D. \( 450 m^{2} \)


Hydraulic washing is based on the differences in:
A. special gravities of the ore and gangue particles
B. special density of the ore and gangue particles
c. special viscosity of the ore and gangue particles
D. both \( A \) and \( B \)


Force which is required to maintain the
velocity of the rod at that instant.


Assertion
It is not possible to use \( ^{35} C l \) as the fuel
for fusion energy.
Reason
The binding energy of \( 35 C l \) is too small.
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


One poise is equivalent to:
A. 0.001 pascal second
B. 0.0001 pascal second
c. 0.01 pascal second
D. 0.1 pascal second


If \( F e^{3+}+y^{4-} \rightleftharpoons F e Y^{\ominus} ; K_{f}=1.3 \times \)
\( 10^{25} \)
\( F e^{3+}+Y^{4-} \rightleftharpoons F e Y^{2-} ; K_{f}=2.1 \times 10^{14} \)
And \( F e^{3+}+e^{-} \rightleftharpoons F e^{2+} ; E^{\ominus}=+0.77 V \)
\( \boldsymbol{E}^{\ominus} \) for \( \boldsymbol{F} \boldsymbol{e} \boldsymbol{Y}^{\ominus}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{F} \boldsymbol{e} \boldsymbol{Y}^{2-} \)
A . 0.13 v
B. \( 0.26 \mathrm{v} \)
c. \( 1.2 v \)
D. 1.6


The segment of earthworm in which mouth is situated is called
A. Prosoma
B. Prostomium
c. Peristomium
D. Prosegment


Distance of the point (2,5) from the line
\( \mathbf{3} \boldsymbol{x}+\boldsymbol{y}+\mathbf{4}=\mathbf{0} \) measured parallel to
the line \( 3 x-4 y+8=0 \) is
A \( \cdot \frac{15}{2} \)
B. \( \frac{9}{2} \)
c. 5
D. None of the above


Water drops fall at regular intervals from a tap \( 5 \mathrm{m} \) above ground. The \( 3 \mathrm{rd} \) drop is leaving tap when first drop reaches ground. The distance of 2 nd drop at the instant is
A . \( 2.5 \mathrm{m} \)
B. 3.75 m
\( c \cdot 4 m \)
D. 1.25 \( m \)


Three charges each of magnitude q are placed at the corners of an equilateral triangle, the electrostatic force on the
charge placed at the center is(each side of triangle is \( L \) )
A. Zero
\( ^{\mathrm{B}} \frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{L^{2}} \)
c. \( \frac{1}{4 \pi \varepsilon_{0}} \frac{3 q^{2}}{L^{2}} \)
\( D \)


A wire suspended vertically from one of its ends is stretched by attaching a weight of \( 200 \mathrm{N} \) to the lower end. The weight stretches the wire by \( 1 \mathrm{mm} \). Then the elastic energy stored in the wire is:
A . 0.1
B. 0.2
c. 10
D. 20


The compound interest on Rs. 24,480 at \( 6 \frac{1}{4} \% \) per annum for 2 years 73 days, is:
A . Rs. 2,929
B. Rs. 3, 000
c. Rs. 3,131
D. Rs. 3, 636


Organism which can respire in absence
of \( \boldsymbol{O}_{2} \) is
A. Chlorella
B. Solanum
c. Saccharum
D. saccharomyces


When 2 -chlorobutane is heated with
sodium metal in THF, what would be formed (including by-products)? This question has multiple correct options
A. 3,4 - dimethyl hexane
B. butane
c. 1-butene
D. 2-butene


\( H_{2} O_{2} \) oxidises \( H_{2} S \) to :
A . \( S \)
в. \( H_{2} S O_{4} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O}_{2} \mathrm{O}_{8} \)
D. \( H_{2} S O_{5} \)


When \( 2 g \) of \( A \) gas is introduced into an
evacuated flask kept at \( 25^{\circ} C, \) the pressure is found to be 1 atm. If \( 3 g \) of another gas \( B \) is then added to the
same flask, the total pressure becomes
1.5 atm. The ratio of molecular weights
is:
A . 1: 1
B. 1: 2
\( c \cdot 2: 3 \)
D. none of these


A dynamo does not consist of
A. a bar magnet
B. two carbon brushes
c. the external circuit
D. all of these


In a right triangle the two acute angles are in the ratio \( 7: 11 . \) Find the measure
of acute angles.


The solution of \( e^{y}\left(1+x^{2}\right) \frac{d y}{d x}=2 x(1+ \)
\( \left.e^{y}\right) \) is:
A \( \cdot \frac{1+e^{y}}{1+x^{2}}=c \)
B \( \cdot e^{y}\left(1+x^{2}\right)=c \)
C \( \cdot\left(1+e^{y}\right)+\left(1+x^{2}\right)=c \)
D. \( \left(e^{y}+1\right) x^{2}=c \)


Justify that the following reactions are
redox reactions.
\( \mathbf{A} \cdot C u O(s)+H_{2}(g) \rightarrow C u(s)+H_{2} O(g) \)
B \( \cdot F e_{2} O_{3}(s)+3 C O(g) \rightarrow 2 F e(s)+3 C O_{2}(g) \)
\( \mathbf{c} \cdot 4 B C l_{3}(g)+3 L i A l H_{4}(s) \rightarrow 2 B_{2} H_{6}(s)+3 L i C l(s)+ \)
\( 3 A l C l_{3}(s) \)
D \( \cdot 2 K(s)+F_{2}(g) \rightarrow 2 K^{+} F^{-}(s) \)


The magnetic field due to a circular
wire at its center is:
A. in the plane of wire
B. \( 30^{\circ} \) to the plane of wire
C. Perpendicular to the plane of wire
D. none of the above


State any one advantage of using a reflecting telescope in place of a refracting telescope.


There are two wires of the same
material. There radii and lengths are
both in the ratio \( 1: 2 . \) If the extensions
produce dare equal, what is the ratio of the loads?
A .1: 2
B . 2: 1
c. 1: 4
D. 4: 1


Which element forms hydride?
A \( . C r \)
в. \( M o \)
c. \( W \)
D. \( S g \)


(a) Draw and label the diagram given :
(i) Incident ray
(ii) Refracted ray
(iii) Emergent ray
(iv) Angle of reflection
(v) Angle of deviation
(v) Angle of emergence
(b) The refractive index of diamond is
2.42. What is the meaning of this statement in relation to speed of light?


In a double-slit experiment, at a certain point on the screen the path difference
between the two interfering waves is \( \frac{1}{8} t h \) of a wavelength. The ratio of the
intensity of light at that point to that at the centre of a bright fringe is:
\( \mathbf{A} \cdot 0.672 \)
B. 0.853
c. 0.760
D. 0.568


In an experiment of photoelectric effect the number of photoelectrons has to be increased without changing their frequency. The suitable step to be taken about the incident radiation for this is
A. increasing intensity without changing frequency
B. increase both frequency and intensity
C. increase frequency without increasing intensity
D. increasing only frequency


Classification of matter helps us to:
A. study things systematically
B. share information with others
c. know the properties of all the members of a group if we know about one
D. All of the above


The molecular formula of Magnesium
(II) acetate is:
\( \mathbf{A} \cdot M g\left(C H_{3} C O O\right) \)
в. \( M g_{2}\left(C H_{3} C O O\right)_{3} \)
c. \( M g\left(C H_{3} C O O\right)_{2} \)
D. \( M g\left(C H_{3} C O O\right)_{3} \)


Which of the following amine gives diazonium salt on reaction with
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2} ? \)
A \( \cdot\left(C H_{3}\right)_{2} N H \)
в. \( \left(C H_{3}\right)_{3} N \)
c. \( C_{6} H_{5} N H_{2} \)
D. \( C H_{3} N H_{2} \)


Write the reactions involved in
the Diazotisation.


Balance the following equation:
\( C l O^{-}+I^{-} \rightarrow C l^{-}+I_{2} \)


Two oxides of a certain metal were
separately heated in hydrogen till water was produced. It was observed that 1 \( \mathrm{gm} \) of each oxide gave \( 0.125 \mathrm{gm} \) and \( 0.2263 \mathrm{gm} \) of water respectively. This illustrates the law of:
A. definite proportions
B. multiple proportions
c. reciprocal proportions
D. conservation of mass


The decomposition of hydrocarbon follows the equation, \( k=(4.5 x \)
\( \left.\mathbf{1 0}^{11} \boldsymbol{s}^{-1}\right) e^{-\mathbf{2 8 0 0 0 K} / \boldsymbol{T}} \)
Calculate \( \boldsymbol{E}_{\boldsymbol{a}} \)


The radius of a sphere is \( 2 r, \) then its volume will be:
A \( \cdot \frac{4}{3} \pi r^{3} \)
В. \( 4 \pi r^{3} \)
c. \( \frac{8 \pi r^{3}}{3} \)
D. \( \frac{32}{3} \pi r^{3} \)


A road network as shown in the figure
connect four cities. In how many
ways can you start from any city (say A) and come back to it without
travelling on the same road more than
once ?
\( A \)
B. 12
\( c \)
0.16


Find the distance between the points \( A(2,3,1), B(-1,2,3), \) using vector method


the velocity of the CM of the rod.
A \( \cdot \frac{5}{7} v_{0} \) at \( \tan ^{-1} \frac{4}{3} \) below horizontal
B. \( \frac{5}{7} v_{0} \) at \( \tan ^{-1} \frac{3}{4} \) below horizontal
C. \( \frac{5}{6} v_{0} \) at \( \tan ^{-1} \frac{3}{4} \) below horizontal
D. \( \frac{5}{6} v_{0} \) at \( \tan ^{-1} \frac{4}{3} \) below horizontal


The following general structure is
representative of sulphonamides.
Which of the following statements is
true for active sulphonamides?
\( A \cdot R^{1} \) can be Hor an alkyl group
B. \( R^{2} \) must be hydrogen
C. The aromatic ring is essential
D. The sulphonamide functional group can be replaced with an ester


The weight of an object at the centre of
the earth of radius \( R \) is
A. Zero
B. Infinite
C . \( R \) times the weight at the surface of the earth.
D. \( 1 / R^{2} \) times the weight at surface of the earth.


\( \int_{-1}^{1} \frac{e^{x}+1}{e^{x}-1} d x \) equals
\( \mathbf{A} \cdot \ln \left(e^{x}+1\right) \)
B \( \cdot \ln \left(e^{x}-1\right) \)
\( c \cdot 1 \)
D.


When the blood urea and blood
creatinine level are significantly high then the treatment of choice is
A. Given suitable antibiotics
B. Haemodialysis
c. Kidney transplantation
D. Steroids therapy


Prove \( \sec ^{4} x-\sec ^{2} x=\tan ^{4} x+\tan ^{2} x \)


If \( |\bar{a}+\bar{b}|<|\bar{a}+\bar{b}| \) then the angle
between the vectors \( \bar{a}, \bar{b} \) is
A. Acute angle
B. obtuse angle
c. Right angle
D. \( 45^{\circ} \)


The shown circuit of a post office box
while using it for measuring the
unknown resistance. All the keys except
the two 100 ohms in the first row and
both 2 ohm along with the 5 ohm are not
used while measuring the resistance of
the unknown wire. Find the resistance of
unknown wire in ohm.


The incorrect statement is :
A. Calamine and siderite are carbonates
B. Argentite and cuprite are oxides
C. zinc blende and iron pyrites are sulphides
D. Malachite and azurite are ores of copper


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}, \) then find
\( \frac{\boldsymbol{f}(\boldsymbol{x}+\boldsymbol{h})-\boldsymbol{f}(\boldsymbol{x}-\boldsymbol{h})}{\boldsymbol{h}}, \boldsymbol{h} \neq \mathbf{0} \)


Two thin uniform circular rings each of
radius \( 10 m \) and mass \( 0.1 k g \) are arranged such that they have Common centre and their planes are perpendicular to each other. The M.I. of the system about an axis passing through their common centre and perpendicular to the plane of either of the ring in \( k g m^{-2} \) is:
A. 1.5
в. 4.5
c. 15
D. 18


Sucrose content in sugarcane
decreases
A. If there is fluctuation in temperature during the period of growth of the plant
B. If frost occurs during the period of ripening
C. If high rainfall occurs during the period of growth of the plant
D. If there is high temperature during the time of ripening


Explain why plastic containers are favored for storing food.


Percentage of total water found as fresh
water is
A . 46\%
B. 32\%
c. \( 16 \% \)
D. 2.5\%


If the weight of 5.6 litres of a gas at NTP
is 11 gram. The gas may be:
A \( . P H_{3} \)
в. \( C O C l_{2} \)
c. \( N O \)
D. \( N_{2} \) O


Assertion
The placement of isotopes in Mendeleev's periodic table overcome in the modern periodic table.
Reason
In modern periodic table, the elements have been allotted places based on their atomic numbers
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


In the given isosceles triangle, side \( B C=14 c m \) and side \( A B=1 \frac{1}{2} l(B C) \)
Find the perimeter of the given triangle


Birth control pills as antifertility drugs, essentially contain a mixture of synthetic estrogen and
hormones.
A. protonsil
B. progesterone derivative
c. chloroxylenol
D. quaternary ammonium salt


Escape velocity from earth is 11.2km/sec. Another planet of same mass has radius \( \frac{1}{4} \) times that of earth. What is the escape velocity from this
planet?
A. \( 11.2 k m / \)sec
в. \( 44.8 k m / \)sec
c. \( 22.4 k m / \)sec
D. \( 5.6 k m / \)sec


Charge 1 attracts Charge \( 2, \) Charge 2 repels Charge \( 3, \) and Charge 3 attracts Charge 4. Which of the following option must hold good for the given condition of four point charges?
A. Charge 1 attracts Charge 4
B. Charge 2 attracts Charge 3
c. charge 1 repels Charge 3
D. charge 2 repels Charge 4
E. charge 1 repels charge 4


Find the present worth of Rs. 930 due 3 years hence at \( \% \) per annum. Also find
the discount.


The correct statement of the following:
A) Water can be boiled inside the
artificial satellite by convection
B) Heavy liquid can be boiled in artificial satellite by convection Mark correct option/s
A. Both statements are correct
B. Both statements are wrong
c. A is correct but B is wrong
D. B is correct but A is wrong


Adsorption is the phenomenon in which a substance:
A. accumulates on the surface of the other substance
B. remains close to the other substance
c. substance particles bind with each other
D. oxidises or reduces the other substance


\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{2} \)
The above electronic configuration is represented for which atoms among the following?
A. An excited state \( C a \) atom
B. A ground state \( C a \) atom
c. An excited state \( S c \) atom
D. An excited state \( K \) atom
E. None of the above


The displacement of an object attached to a spring and executing simple harmonic motion is given by \( \boldsymbol{x}=\mathbf{2} \times \)
\( 10^{-2} \) cos \( \pi t \) meters. The time at which
the maximum speed first occurs is :
A . \( 0.5 \mathrm{s} \)
B. 0.75 s
c. 0.125 s
D. \( 0.25 \mathrm{s} \)


Assertion
The two cotyledons in seed are
embryonic leaves.
Reason
The embryo contains radicle and
plumule.
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 process of zinc-plating on iron sheet is known as:
A. annealing
B. roasting
c. galvanisation
D. smelting


Lenz's law is a consequence of the law of conservation of
A. charge
B. mass
c. energy
D. momentum


\[
\begin{array}{c}
\boldsymbol{C H} \equiv \boldsymbol{C}-\boldsymbol{C H}_{3} \\
\boldsymbol{C H}
\end{array}
\]
\( \mid \)
\( C H_{3} \)
Write the IUPAC name of the compound


Heaviest vertebra in man is
A. Atlas
B. Axis
c. Lumbar
D. Thoracic


For a first order reaction, the half life is
independent of:
This question has multiple correct options
A . initial concentration
B. cube root of initial concentration
c. first power of final concentration
D. square root of final concentration


Sum the following series \( \frac{1}{1.4 .7}+\frac{1}{4.7 .10}+\frac{1}{7.10 .13}+\ldots . \) to
terms


An electric alpole consists or small
charged objects \( A \) and \( B \) of charges \( -q \)
and \( +q \) and masses \( m \) and \( 4 m \)
respectively. They are connected by a light non -conducting rod of length \( L \) This system is hinged at \( A \) so that it
can rotate in vertical plane. A uniform
electric field of intensity \( \boldsymbol{E} \) is applied vertically downward. The rod is released
from horizontal position as shown in figure. The angular velocity of the rod
when the rod becomes vertical is.
A \( \cdot \sqrt{\frac{4 m g+q E}{2 m l}} \)
B. \( \sqrt{\frac{6 m g+q E}{2 m l}} \)
c. \( \sqrt{\frac{8 m g+q E}{6 m l}} \)
D. \( \sqrt{\frac{2 m g+q E}{2 m l}} \)


A small coil of N turns has an area A
and a current i flows through it. The magnetic dipole moment of the coil will
be
\( A \cdot \) i \( N A \)
B . \( i^{2} \mathrm{NA} \)
\( c \cdot i N^{2} A \)
D. iN/A


\( \tan 3 A-\tan 2 A-\tan A= \)
\( \tan 3 \) Atan 2 Atan \( A \)


Which statement is true about the
figure formed by joining the midpoints
of the adjacent sides of a rectangle with
\( \operatorname{sides} 8 c m \) and \( 6 c m ? \)
A . It is a rectangle of area \( 24 \mathrm{cm}^{2} \)
B. It is a square of area \( 24 \mathrm{cm}^{2} \)
C. It is a trapezium of area \( 24 \mathrm{cm}^{2} \)
P. It is a rhombus of area \( 24 \mathrm{cm}^{2} \)


A flag-staff stands on a tower which is on level ground. The total height of the flag-staff and tower taken together is
300 metres. The flag-staff subtends an angle of \( \tan ^{-1}\left(\frac{1}{5}\right) \) at a point \( P \) on the level ground at a distance 300 metres from the foot of the tower. The height of the tower is:
A. 100 metres
B. 200 metres
c. 250 metres
D. 300 metres


If the coefficient of linear expansion is
A, the coefficient of superficial expansion is \( \mathrm{B} \) and the coefficient of cubic expansion is \( \mathrm{C} \), which of the following is false?
A. \( C=3 A \)
В. \( A=B / 2 \)
c. \( B=3 / 2 C \)
\( \mathbf{D} \cdot A=C / 3 \)


When a body is projected from a level
ground, the ratio of it's speed in the
vertical and horizontal direction is 4: 3
If the velocity of projection is \( u, \) the time
after which the ratio of the velocities
in the vertical and horizontal directions
is reversed is
A. \( \frac{7 u}{20 g} \)
B. \( \frac{35 u}{10 g} \)
c. \( \frac{9 u}{g} \)
D. \( \frac{10 u}{g} \)


Draw the structure of the following molecules:
(i) \( \boldsymbol{X} \boldsymbol{e} \boldsymbol{O} \boldsymbol{F}_{\mathbf{4}} \)
(ii) \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \)


Bernoulli's principle is based on the law of conservation of :
A. Mass
B. Momentum
c. Energy
D. None of these


Which has the highest \( p K_{b} \) value?
A \( \cdot R_{3} N \)
в. \( R_{2} N H \)
c. \( R N H_{2} \)
D. \( N H_{3} \)


A body of mass \( 5 k g \) is moving with
velocity \( 2 m s^{-1} . \) Calculate its linear
momentum
A \( .2 .5 \mathrm{kg} \mathrm{ms}^{-1} \)
B. \( 10 \mathrm{kg} \mathrm{ms}^{-1} \)
c. 5 kg \( m s^{-1} \)
D. \( 20 \mathrm{kg} \mathrm{ms}^{-1} \)


Draw the truth table of a NOR gate.


Absolute refractive index of a
substance is
A. Speed of light in vacuum/Speed of light in medium
B. Speed of light in water/Speed of light in medium
C. Speed of light in medium/speed of light in air
D. Speed of light in medium/speed of light in water


\( \boldsymbol{M}+\mathbf{8} \boldsymbol{C} \boldsymbol{N}^{-}+\mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{O}_{2} \rightarrow \)
\( \mathbf{4}\left[\boldsymbol{M}(\boldsymbol{C} \boldsymbol{N})_{2}\right]^{-}+\mathbf{4} \boldsymbol{O} \boldsymbol{H}^{-} \)
metal M is:
A. cu
в. \( \mathrm{Hg} \)
c. \( A g \)
D. Au


Write half-reactions using electrons.
\( \boldsymbol{C r}_{2} \boldsymbol{O}_{2}^{\boldsymbol{7}-}+\boldsymbol{6} \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{2}+}+\mathbf{1 4} \boldsymbol{H}^{+} \longrightarrow \)
\( 2 C r^{3+}+6 F e^{3+}+7 H_{2} O \)
A. Oxidation : \( F e^{2+} \longrightarrow F e^{3+}+e^{-} \); Reduction:
\[
C r_{2} O_{2}^{7-}+14 H^{+}+6 e^{-} \longrightarrow 2 C r^{2+}+7 H_{2} O
\]
B. Oxidation: \( 3 F e^{2+} \longrightarrow 3 F e^{3+}+e^{-} \); Reduction:
\( \mathrm{Cr}_{2} \mathrm{O}_{2}^{7-}+14 \mathrm{H}^{+}+6 e^{-} \longrightarrow 2 \mathrm{Cr}^{2+}+7 \mathrm{H}_{2} \mathrm{O} \)
C. Oxidation : \( 2 F e^{2+} \longrightarrow 2 F e^{3+}+e^{-} \); Reduction:
\( \mathrm{Cr}_{2} \mathrm{O}_{2}^{7-}+14 \mathrm{H}^{+}+6 e^{-} \longrightarrow 2 \mathrm{Cr}^{2+}+7 \mathrm{H}_{2} \mathrm{O} \)
D. Oxidation: \( 3 F e^{2+} \longrightarrow F e^{3+}+3 e^{-} ; \) Reduction :
\( C r_{2} O_{2}^{7-}+14 H^{+}+3 e^{-} \longrightarrow 2 C r^{2+}+7 H_{2} O \)


Name the gate, which represents the Boolean expression \( \boldsymbol{Y}=\boldsymbol{A} \cdot \boldsymbol{B} \)
A. NAND
B. AND
c. Not
D. NOR


A particle moves such that its acceleration is given by \( \boldsymbol{a}=-\boldsymbol{\beta}(\boldsymbol{x}-\boldsymbol{2}) \)
Here \( \beta \) is a positive constant and \( x \) is
the position from origin. Time period of oscillations is
A. \( 2 \pi \sqrt{\beta} \)
в. \( 2 \pi \sqrt{\frac{1}{\beta}} \)
\( \mathbf{c} \cdot 2 \pi \sqrt{\beta}+2 \)
D. \( 2 \pi \sqrt{\frac{1}{\beta+2}} \)


The equation of the base of an equilateral triangle with vertex at (2,-1) is \( x+y-2=0 . \) Then find its
length of sides.


In the given figure, \( A B C D \) is a piece of
cardboard in the shape of the trapezium
in which \( A B \| D C, \angle A B C=90^{\circ} \)
From this piece, quarter circle \( B E F C \)
is removed. Given \( D C=B C=4.2 \mathrm{cm} \)
and \( A E=2 \mathrm{cm} . \) Calculate the area of
the remaining piece of the cardboard.
\( \mathbf{A} \cdot 7.98 \mathrm{cm}^{2} \)
\( \mathbf{B} \cdot 8 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 9.08 \mathrm{cm}^{2} \)
D. \( 10.08 \mathrm{cm}^{2} \)


A given resistor has the following colour code of the various strips on it : Brown,
black, green and silver. The value of its
resistance in ohm is
A \( \cdot 1.0 \times 10^{4} \pm 10 \% \)
B . \( 1.0 \times 10^{7} \pm 5 \% \)
C. \( 1.0 \times 10^{6} \pm 10 \% \)
D. \( 1.0 \times 10^{5} \pm 5 \% \)
E . \( 1.0 \times 10^{3} \pm 10 \% \)


Sabnam has 2 school bags, 3 tiffin
boxes and 2 water bottles.show in how
many ways can she carry these item


Rutherford's scattering formula fails for very small scattering angles because:
This question has multiple correct options
A. the gold foil is very thin
B. the kinetic energy of \( \alpha \) -particles is very high
C. the full nuclear charge of the target atom is partially screened by its electron
D. there is strong repulsive force between the \( \alpha \) -particles and nucleus of the target


The phenomenon in which the amplitude of oscillation of a pendulum decreases gradually is called
A. decay period of oscillation
B. damping
c. building up of oscillation
D. maintained oscillation


If the area of a triangle with base \( x \) is
equal to area of a square of side \( x, \) then the altitude of the triangle is
A \( \cdot \frac{x}{2} \)
B. \( x \)
\( c \cdot \sqrt{2} x \)
D. \( 2 x \)


Two identical masses each of mass \( m \)
are connected by a spring and placed on a smooth surface. A third identical
mass moving with speed \( v_{0} \) collides with one of the two masses perfectly inelastically. Choose the correct option.
A. Centre of mass of the given blocks moves with a constant speed \( \frac{v_{0}}{3} \) after collision
B. Maximum elongation in spring is \( \sqrt{\frac{m v_{0}^{2}}{6 k}} \)
c. Maximum compression in spring is \( \sqrt{\frac{m v_{0}^{2}}{2 k}} \)
D. Maximum compression in spring is \( \sqrt{\frac{m v_{0}^{2}}{6 k}} \)


Dextrin is a
A. Polymer of glucose
B. Plasma expander
C. Use in dehydration condition
D. Both A and C


List five products we get from forests.


STATEMENT - 1: If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar.

STATEMENT - 2 : If in two triangles,
corresponding angles are equal, then their corresponding sides are in the
same ratio and hence the two triangles
are similar.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement -
B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement -
c. Statement - 1 is True, Statement - 2 is False
D. Statement - 1 is False, Statement - 2 is True


What is the escape velocity from the
surface of the earth of radius \( R \) and
density \( \rho ? \)
\( ^{\text {A }} \cdot 2 R \sqrt{\frac{2 \pi \rho G}{3}} \)
в. \( 2 \sqrt{\frac{2 \pi \rho G}{3}} \)
c. \( 2 \pi \sqrt{\frac{R}{g}} \)
D. \( \sqrt{\frac{2 \pi G \rho}{R^{2}}} \)


A long wire carries a current \( i . \) A rod of
length \( l \) is moved with a velocity \( v \) in a
direction parallel to the wire as shown in figure (a). Find the motional emf induced in the rod:
A \( \cdot \frac{\mu_{0} i}{2 \pi x} l v \)
В \( \cdot \frac{\mu_{0} i}{2 \pi} v \log _{e} \frac{x+l / 2}{x-l / 2} \)
C \( \frac{\mu_{0} i}{2 \pi} v \log _{e} \frac{x-l / 2}{x+l / 2} \)
D. \( \frac{\mu_{0} i v}{2 \pi} \log _{e} \frac{l+x}{x} \)


In the given figure, \( \boldsymbol{A} \boldsymbol{E} \| \boldsymbol{D} \boldsymbol{B}, \boldsymbol{B C}= \)
\( \mathbf{7} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{D}=\mathbf{5} \boldsymbol{c m}, \boldsymbol{D} \boldsymbol{C}=\mathbf{4} \boldsymbol{c m} . \) If \( \boldsymbol{C} \boldsymbol{E}= \)
\( 12 c m, \) find \( A E \) and \( A C \)


A transistor has \( \alpha=0.95 . \) If the emitter
current is \( 10 m A \), then the collector
current will be
A . \( 9.5 \mathrm{mA} \)
в. \( 10 \mathrm{mA} \)
c. \( 0.95 \mathrm{mA} \)
D. \( 95 \mathrm{mA} \)


Amplifier may be
A. multi stage
B. single stage
\( c . \) both (a) \& (b)
D. None of these


Linnaeus is credited with
A. Binomial nomenclature
B. Theory of biogenesis
c. Discovery of microscope
D. Discovery of blood circulation


Four points \( A(6,3), B(-3,5), C(4,-2) \) and \( D(x, 3 x) \) are given in such a way that \( \frac{A r e a(\Delta D B C)}{A r e a(\Delta A B C)}=\frac{1}{2} \) find \( x \)
This question has multiple correct options
A \( \cdot \frac{11}{8} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{9}{8} \)
D. None of these


By increasing the temperature, the specific resistance of a conductor and a
semiconductor
A. decreases for both
B. increases for both
c. increases, decreases
D. decreases, increases


What are the conditions for a species to
\( \operatorname{act} \operatorname{as} a \operatorname{donor} \) and an acceptor during
dative bond formation?
A. donor: Must possess higher ionization potential, big size and less charge on cations.
B. acceptor: Possess more electron affinity, less size and less negative charge on anions.
\( \mathbf{C} . \) Both \( A \) and \( \mathbf{B} \)
D. donor: Must possess less ionization potential, big size and less charge on cations. acceptor: Possess more electron affinity, less size and less negative charge on anions.