If \( A \) and \( B \) are two events. The probability
that at most one of \( A, B \) occurs is
A \( .1-P(A \cap B) \)
в. \( P(\bar{A})+P(\bar{B})-P(\bar{A} \cap B) \)
c. \( P(\bar{A})+P(\bar{B})+P(\bar{A} \cap \bar{B}) \)
D. All of the above


If tree \( =A, \) large Birds \( =B, \) Insects \( =C \) and small birds = D, then in a single tree ecosystem, the pyramid of number stays correct in all of the following
except
\( A \cdot C>D>A \)
B. \( D>A>B \)
\( c \cdot c>B>A \)
D. \( D>B>C \)


Evaluate the following definite integral:
\( \int_{-\pi / 4}^{\pi / 4} \log (\cos x+\sin x) d x \)
A . \( \pi \log 2 \)
B. - \pi log2
C \( \cdot-\frac{\pi}{4} \log 2 \)
D. \( \pi^{2} \log 2 \)


A horizontal parallel beam of light
passes through a vertical convex lens of
focal length \( 20 \mathrm{cm} \) and is then reflected by a titled plane mirror so that it coverages to a point I. The distance Pl is \( 10 \mathrm{cm} \)
M is a point at which the axis of the lens
intersects the mirror. The distance PM
is \( 10 \mathrm{cm} . \) The angle which the mirror makes with the horizontal is
\( \mathbf{A} \cdot 15^{\circ} \)
B. \( 30^{\circ} \)
\( \mathbf{c} \cdot 45^{\circ} \)
D. \( 60^{\circ} \)


During the month of July, the number of units, \( y \), of a certain product sold per
day can be modeled by the function
\( y=-3.65 x+915, \) where \( x \) is the
average daily temperature in degrees Fahrenheit. Find the statement which
directly follows from the above
equation.
A. As the temperature increases, the number of units sold decreases.
B. As the temperature increases, the number of units sold remains constant
C. As the temperature increases, the number of units sold increases
D. There is no linear relationship between temperature and the number of units sold


A body is moving along a straight line.
Its distance \( X_{t} \) from a point on its path
at a time \( t \) after passing that point is
given by \( X_{t}=8 t^{2}-3 t^{3}, \) where \( X_{t} \) is in
meter and \( t \) is in second. The correct
statement(s) is/are:
This question has multiple correct options
A. Average speed during the interval \( t=0 \) s to \( t=4 s \) is \( 20.21 \mathrm{ms}^{-1} \)
B. Average velocity during the interval \( t=0 \) s to \( t=4 s \) is
\( -16 m s^{-1} \)
C. The body starts from rest and at \( t=\frac{16}{9} s \) it reverses its
direction of motion at \( x_{t}=8.43 \mathrm{m} \) from the start
D. It has an acceleration of \( -56 \mathrm{ms}^{-2} \) at \( t=4 \mathrm{s} \)


\( C r O_{2}^{2+} \) is the cation from:
A. \( C r O \)
в. \( C r_{2} O_{3} \)
c. \( C r O_{5} \)
D. \( \operatorname{Cr} \mathrm{O}_{3} \)


Which of the following statements is
true?
A. Electrolysis is one of the applications of chemical effects of current
B. A metal wire shows chemical effect when a current is passed through it
c. Like charges attract each other
D. Charge flows only through negative charge carriers


f \( x_{1}, x_{2}, x_{3} \) and \( y_{1}, y_{2}, y_{3} \) are in GP with
same common ratio, then
\( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \)
A. lie on an ellipse
B. lie on a circle
c. are vertices of triangle
D. lie on a straight line


\( \begin{array}{ll}\text { List - I } & \text { List - II } \\ \text { A) Velocity of light } & \text { 1) Energy }\end{array} \) A) Velocity of light
B) Plank's constant Energy particle
2) Energy packet
c) Wavenumber
D)
The correct match is:
\( A \cdot A-2, B-3, C-4, D-5 \)
B. A-1, B-2, C-3. D-4
C. \( A-2, B-4, C-5, D-1 \)
D. A-3, B-4, C-5, D-1,2


The equiconvex lens has focal length 'f. If it is cut perpendicular to the principal axis passing through optical centre,
then focal length of each half is :
A \( \cdot \frac{f}{2} \)
B. \( f \)
\( c \cdot \frac{3 f}{2} \)
D. \( 2 f \)


Protists obtain food as
A. Photosynthesizers and symbionts
B. Photosynthesizers
C. Chemosynthesizers
D. Holotrophs


Young's modulis of brass and steel are
\( \mathbf{1 0} \times \mathbf{1 0}^{\mathbf{1 0}} \mathbf{N} / \boldsymbol{m} \) and \( \mathbf{2} \times \mathbf{1 0}^{\mathbf{1 1}} \mathbf{N} / \boldsymbol{m}^{\mathbf{2}} \)
respectively. A brass wire and a steel wire of the same length are extended by
1 mm under the same force. The radii of
the brass and steel wires are \( \boldsymbol{R}_{\boldsymbol{B}} \) \$and
\( \mathrm{R}_{-}\{\mathrm{S}\} \$ \$, \) respectively. Then
A. \( R_{S}=\sqrt{2} R_{B} \)
в. \( R_{S}=\frac{R_{B}}{\sqrt{2}} \)
c. \( R_{s}=4 R_{B} \)
D. \( R_{S}=\frac{R_{B}}{4} \)


A reduction of \( 20 \% \) in the price of sugar enables a purchaser to obtain \( 2 \frac{1}{2} \mathrm{kg} \) more for Rs. 160. Find the original price per kg of sugar.


\( 3.4 \mathrm{g} \) of \( H_{2} O_{2} \) decomposes, the weight of oxygen liberated from it is:
A \( .1 .6 g \)
B . 2.24 g
c. \( 1.16 \mathrm{g} \)
D. \( 3.2 \mathrm{g} \)


Whirling whips are protists which
possess two flagella that beat
A. Slightly towards one side so as to cause rotation of the organism while moving forward
B. Forward, backward and sideways depending upon the requirement
c. At right angles to each other due to being present in different grooves
D. Along with numerous cilia.


The number of elements known in
Mendeleev's presented periodic table is:
\( \mathbf{A} \cdot 50 \)
B. 90
c. 63
D. 102


If atomic eq. \( 40 \% \) of \( P C l_{5} \) dissociated
Calculate equivalent molar mass.


Consider three vectors \( \vec{P}=\hat{i}+\widehat{j}+ \) \( \widehat{k} ; \overrightarrow{\boldsymbol{q}}=2 \widehat{\hat{\boldsymbol{i}}}+4 \widehat{\boldsymbol{j}}-\widehat{\boldsymbol{k}} \) and \( \overrightarrow{\boldsymbol{r}}=\boldsymbol{2} \hat{\boldsymbol{i}}+\boldsymbol{4} \widehat{\boldsymbol{j}}+ \)
3 \( \widehat{k} \). If \( \vec{p}, \vec{q} \) and \( \vec{r} \) denotes the position vector of three non-collinear points, then the equation of the plane containing these points is
A. \( 2 x-3 y+1=0 \)
B. \( x-3 y+2 z=0 \)
c. \( 3 x-y+z-3=0 \)
D. \( 3 x-y-2=0 \)


Surface are of \( _{13} A l^{27} \) is \( S_{0}, \) then surface
area of \( Z n^{64} \) is then
A \( \cdot \frac{16}{9} S_{0} \)
в. \( \frac{4}{3} S_{0} \)
c. \( \frac{64}{27} S_{0} \)
D. \( \frac{3}{2} S_{0} \)


A glass marble dropped from a certain height above the horizontal surface reaches the surface in time \( t \) and then
continues to bounce up and down. The time in which the marble finally comes to rest is:
\( \mathbf{A} \cdot e^{n} t \)
B . \( e^{2} t \)
\( ^{\mathbf{c}} \cdot t\left[\frac{1+e}{1-e}\right] \)
D. \( t\left[\frac{1-e}{1+e}\right] \)


A student focussed the image of a
candle flame on a white screen using a convex lens. He noted down the position of the candle screen and the lens as
under:
Position of candle \( =12.0 \mathrm{cm} \)
Position of convex lens \( =\mathbf{5 0 . 0} \mathrm{cm} \)
Position of the screen \( =88.0 \mathrm{cm} \)
What will be the nature of the image formed if he further shifts the candle
towards the lens?
A. Virtual and erect
B. Real and inverted
C. Real and diminishedd
D. None of the above


The molar conductivities of \( \boldsymbol{K} \boldsymbol{C} \boldsymbol{I} \)
\( N a C l \) and \( K N O_{3} \) are 152,128 and
\( 111 S c m^{2} m o l^{-1} \) respectively. What is
the molar conductivity of \( N a N O_{3} ? \)
A \( \cdot 101 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
B. \( 87 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
c. \( -101 S \mathrm{cm}^{2} \mathrm{mol}^{-1} \)
D. \( -391 S \mathrm{cm}^{2} \mathrm{mol}^{-} \)


Find the value of \( x \) and \( y \) using cross multiplication method:
\( \boldsymbol{x}+\boldsymbol{y}=\mathbf{0} \) and \( \boldsymbol{x}-\boldsymbol{y}=\mathbf{2} \)
\( A \cdot(1,1) \)
B . (-1,1)
\( c \cdot(1,-1) \)
D. (-1,-1)


Solve: \( \left(5 p^{2}-25 p+20\right) \div(p-1) \)


Assertion
Helium shows only positive deviation from ideal behaviour at room
temperature.
Reason
Helium is an inert gas.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


toppr
Q Type your question
ring of radius \( r(<<R) \) and coaxial
with the larger ring is moving along the
axis with constant velocity then the
variation of electrical flux \( (\phi) \) passing
through the smaller ring with position will be best represented by:-
\( A \)
B.
\( c \)
\( D \)


The image of an object is formed at the least distance of distinct vision from
the lens of a simple microscope of focal length \( 2.5 \mathrm{cm} . \) Its magnifying power is:
A . 2.5
B. 5
c. 10
D. 11


Which among the following is/are
correct about the orientation of atomic
orbitals in space?
This question has multiple correct options
A. \( s \) -orbitals has single orientation
B. \( d \) -subshell orbitals have three orientations along \( x, y \) and \( z \) directions
C . \( f \) -subshell have seven orientations in their orbitals
D. None of the above


The molar solubility of \( P b B r_{2} \) is \( 2.17 \times \)
\( 10^{-3} \mathrm{M} \) at a certain temperature
Calculate \( \boldsymbol{K}_{\boldsymbol{s p}} \) for \( \boldsymbol{P b B r}_{2} \)
A \( .6 .2 \times 10^{-6} \)
B . \( 6.4 \times 10^{-7} \)
c. \( 4.1 \times 10^{-8} \)
D. \( 3.4 \times 10^{-6} \)
E . \( 1.4 \times 10^{-5} \)


If the lens is slivered at one side what
will be the new focal length (Given
refractive index of lens \( =n \) and focal
length \( =\boldsymbol{f} \) )?
A \( \cdot f^{\prime}=\frac{f}{2} \)
B. \( f^{\prime}=\frac{f(n)}{4} \)
\( ^{\mathbf{C}} f^{\prime}=\frac{f(n-1)}{2 n-1} \)
D. \( f^{\prime}=\frac{f(n+1)}{(2 n-1)} \)


An equation of sphere with centre at
origin and radius \( r \) can be represented
as
A \( \cdot x^{2}+y^{2}+z^{2}=r \)
B . \( x^{2}+y^{2}+z^{2}=r^{2} \)
c. \( x^{2}+y^{2}+z^{2}=2 r^{2} \)
D. None of the above


Sound waves of wavelength \( \lambda \) travelling
with velocity \( v \) in a medium enter into
another medium in which their velocity
is \( 4 v . \) The wavelength in \( 2^{n d} \) medium is :
A \( .4 \lambda \)
B. \( \lambda \)
\( c \cdot \lambda / 4 \)
D. \( 16 \lambda \)


Give the IUPAC names of the given compounds:
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}=\boldsymbol{C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)


Match the terms to these definitions.
Fermentation, glycolysis, Krebs cycle, chemiosmosis, acetyl Co A electron transport system, ATP cellular respiration, oxidative phosphorylation, photophosphorylation, combustion. Anaerobic breakdown of glucose that results in a gain of two ATP and end products such as alcohol and lactate.


Compare the bond energy (B.E) of \( \boldsymbol{O}- \)
\( H \) in water and \( O-D \) in heavy water:
A. B.E of \( O-H> \) B.E of \( O-D \)
B. B.E of \( O-H< \) B.E of \( O-D \)
c. B.E of \( O-H= \) B.E of \( O-D \)
D. B.E of \( O-H=2 \) times B.E of \( O-D \)


Intermolecular interactions that is
dependent on the inverse cube of distance between the new molecules is
A. lon lon interactions
B. Ion-dipole interaction
c. London forces
D. Hydrogen bond


Two circular coils are made of two
identical wires of the same length. If the number of turns of the two coils are 4
and \( 2, \) then the ratio of magnetic inductions at the centres will be:
\( A \cdot 4: 1 \)
B. 2:
\( c \cdot 1: 2 \)
D. 1:


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \tan ^{-1}\left(\frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}\right)= \)
A \( \cdot \frac{-1}{1+x^{2}} \)
B \( \cdot \frac{1}{1+x^{2}} \)
c. \( \frac{1+x}{1-x} \)
D. \( \frac{2}{1+x^{2}} \)


Write the expressions for \( \boldsymbol{K}_{c} \) and \( \boldsymbol{K}_{\boldsymbol{p}} \) and the relationship between them for
the equilibrium reaction


Solve for \( x \) and \( y \) by using method of
substitution:
\( \mathbf{0 . 2 x + 0 . 3 y}=\mathbf{1 . 3 ; 0 . 4 x + 0 . 5 y}=\mathbf{2 . 3} \)
A. -2,-3
B. 2,-3
c. 2,3
D . -2,3


Factorise: \( \boldsymbol{x}^{\mathbf{4}}+\boldsymbol{x}^{\mathbf{2}}+\mathbf{1} \)


Which of the following crude oil will produce the best quality of energy-rich fuels?
A. Heavy crude oil
B. Medium crude oil
c. Light crude oil
D. All will produce the same quality


Select the correct statements amount
the following:
1. Complexes \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]^{2+},\left[\boldsymbol{M} \boldsymbol{n} \boldsymbol{C l}_{4}\right]^{2+},\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{6}\right] \)
are all paramagnetic
2. Complexes \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3} \boldsymbol{4}\right)\right]^{2+},\left[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{C} \boldsymbol{N})_{4}\right]^{2-},[\boldsymbol{N} \boldsymbol{i}(\boldsymbol{D} \boldsymbol{M} \)
are all square planner
3. The correct stability order of the complexes will be \( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{3}\right]^{3+}< \)
\( \left[\boldsymbol{F e}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{3}\right)\right]^{3-}<\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{3}\right]^{3-} \)
4. \( \left[\boldsymbol{C r}(\boldsymbol{e n})_{3}\right]^{3+} \) exist in the three isometric forms
A. Only 1 is correct
B. 1,3 and are correct
c. 2 and 4 are correct
D. 1,2 and 3 are correct


Evaluate the dot product of the given two vectors \( (3 \vec{a}-5 \vec{b}) \cdot(2 \vec{a}-7 \vec{b}) \)


Identify the mismatched pair from the following
A. zener diode : voltage regulator
B. germanium doped with phosphorous : n-type semiconductor
C. semiconductor: band gap > 3 eV
D. p-n junction diode : rectifier
E. silicon doped with aluminium : p-type semiconductor


Assertion
The radial probability distribution curves of \( 1 s, 2 p, 3 d- \) orbitals are identical in shape.
Reason
The number of nodal planes present in
these orbitals are different.
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 and Reason are correct


What is the value of \( x \) in the given
figure?
\( \mathbf{A} \cdot 71^{\circ} \)
B \( .90^{\circ} \)
\( c \cdot 19^{c} \)
\( D \cdot 24^{c} \)


Solve:
\( \csc ^{2} \theta \cdot \tan ^{2} \theta-1=\tan ^{2} \theta \)


Which of the following process is for purification of metals?
A. Froath floatation
B. Leaching
c. Liquidation
D. washing


What is the direction of the electric field directly to the east of an isolated
negative point charge?
A. North
B. South
\( c . \) East
D. west
E. Up


Formation of mRNA from DNA is called
as
A. Translation
B. Transcription
c. Transformation
D. Transduction


Antipyretics are medicinal compounds which :
A. lowers body temperature
B. relieves pain
c. controls malaria
D. can kill other organisms


It is easier to roll a stone up a sloping
road than to lift it vertical upwards
because
A. work done in rolling is more than in lifting
B. work done in lifting the stone is equal to rolling it
C. work done in both is same but the rate of doing work is less in rolling
D. work done in rolling a stone is less than in lifting it


A china dish weighs 25 g when empty. When a saturated solution of
potassium chloride is poured into it at \( 40^{\circ} \mathrm{C}, \) the weight of the dish is 63 g. When the solution is totally evaporated, the chine dish along with the crystals weighs 40 g. Find the solubility of potassium chloride at \( 40^{0} \mathrm{C} \)
A . 35
B. 65.2
c. 39.5
D. 7.5


If \( (x)=x^{2}-2 x+4 \) then the set of
values of \( x \) satisfying \( f(x-1)= \)
\( \boldsymbol{f}(\boldsymbol{x}+\mathbf{1}) \) is
\( \mathbf{A} \cdot\{-1\} \)
B . \{-1,1\}
\( c \cdot\{1\} \)
D \( \cdot\{1,2\} \)


Henry's law constant for the solubility of
\( N_{2} \) gas in water at \( 298 \mathrm{K} \) is \( 1.0 \times 10^{5} \)
atm. The mole fraction of \( N_{2} \) in air is 0.6
The number of moles of \( N_{2} \) from air
dissolved in 10 moles of water at \( 298 \mathrm{K} \)
and 5 atm pressure is:
A \( .3 .0 \times 10^{-4} \)
В. \( 4.0 \times 10^{-4} \)
c. \( 5.0 \times 10^{-4} \)
D. \( 4.0 \times 10^{-5} \)


\( \boldsymbol{A}=\left(\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0\end{array}\right) \Rightarrow A^{2}-2 A= \)
\( A \cdot A^{-1} \)
B \( .-A^{-1} \)
\( c \)
D. -1


In a Young's double slit experiment, the
intensity at the central maximum is \( l_{0} \)
The intensity at a distance \( \frac{\beta}{2} \) above the
central maximum is (where \( \beta= \) fringe width)


A platinum wire has a resistance of
\( 10 \Omega \) at \( 0^{\circ} C \) and \( 20 \Omega \) at \( 273^{\circ} C . \) The
value of temperature coefficient of platinum is given as \( \frac{1}{x} C^{-1} . \) Find \( x \)


Anti Diuretic Hormone(ADH) acts on the
A. collecting tubule of kidney
B. Loop of Henle
c. collecting ducts of testes
D. None of the above


Two bodies are in thermal equilibrium if they have same
A. temperature
B. amount of heat
c. specific heat
D. thermal capacity


Assertion: The equivalent resistance between the points \( X \) and \( Y \) in the figure
is 10
Reason: According to Wheatstone bridge, points \( A \) and \( C \) have the same
potential.
A. Both (A) and (R) are true and (R) is the correct explanation of
B. Both (A) and (R) are true but (R) is not the correct explanation of
C. (A) is true but (R) is false
D. (A) is false but (R) is true


Assertion
Specific heat of any substance remains constant at all temperatures.
Reason
It is given by \( \boldsymbol{S}=\frac{\mathbf{1}}{\boldsymbol{m}} \cdot \frac{\boldsymbol{d} \boldsymbol{Q}}{\boldsymbol{d T}} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


\( E \)


A long straight wire of circular crosssection is made of a non-magnetic material. The wire is of radius a.The
wire carries a current \( I \) which is
uniformly distributed over its cross-
section. The energy stored per unit length in the magnetic field contained within the wire is
\( \mathbf{A} \cdot u=\frac{\mu_{0} I^{2}}{8 \pi} \)
B. \( U=\frac{\mu_{0} I^{2}}{16 \pi} \)
\( ^{\mathbf{C}} \cdot U=\frac{\mu_{0} I^{2}}{4 \pi} \)
D. \( U=\frac{\mu_{0} I^{2}}{2 \pi} \)


Animals make use of \( ----- \)
\( ----- \) to carry out their physical
activities and other tasks.
A. contact force
B. non-contact force
c. force of friction
D. muscular force


Assertion
The two Fe atoms in \( F e_{3} O_{4} \) have
different oxidation numbers.
Reason
\( F e^{2+} \) ions decolourise \( K M n O_{4} \)
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


Write four differences between
molecularity and order of reaction.


Distance between \( \boldsymbol{A}(\mathbf{4}, \mathbf{5}, \mathbf{6}) \) from origin
\( \boldsymbol{O} \) is
A \( \cdot 25 \sqrt{3} \)
B. \( \sqrt{77} \)
c. \( 3 \sqrt{5} \)
D. Data Insufficient


The source of electricity in a flash torch
is its bulb.
A . True
B. False


Consider the following statements.
(I) Rutherford's name was associated
with the development of periodic table.
(II) A metal M having electronic configuration \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{1} \)
is d-block element.
(III) Diamond is an element.
(IV) The electronic configuration of the most electronegative element is \( 1 s^{2} 2 s^{2} 2 p^{5} \)
The correct statements are:
A. ।, ॥।, IV
B. ।, ॥, ॥ा, IV
c. ॥, IV
D. I, III, IV


Assertion
A rocket work on the principle of linear
momentum.
Reason
Whenever there is the change in
momentum of one body, the same change occur in the momentum of the
second body of the same system but in
the opposite direction.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


For Balmer series in the spectrum of
hydrogen, the wave number of each line is given by \( \overline{\boldsymbol{v}}=\boldsymbol{R}_{\boldsymbol{H}}\left[\frac{\mathbf{1}}{\boldsymbol{n}_{\mathbf{1}}^{2}}-\frac{\mathbf{1}}{\boldsymbol{n}_{2}^{2}}\right] \) where \( \boldsymbol{R}_{\boldsymbol{H}} \) is
constant and \( n_{1}, n_{2} \) are integers, which of the following statements is (are)
correct?
1. As wavelength decreases, the lines in the series converge.
2. The integer \( n_{1} \) is equal to 2
3. The ionization energy of hydrogen can be calculated from the wave number of
these lines.
4. The lines of longest wavelength
corresponds to \( n_{2}=3 \)
\( A \cdot 1,2 \) and 3
B. 2, 3 and 4
\( \mathbf{c} \cdot 1,2 \) and 4
D. 2 and 4
E. 2 only


Name a phenomenon or an experiment
which proves:
(i) Particle nature of electro magnetic
radiatons.
(ii) Wave nature of particles. (Description of the phenomenon experiment is not required)


The expansion of \( (2 x-3 y)^{2} \) is:
A \( \cdot 2 x^{2}+3 y^{2}+6 x y \)
B. \( 4 x^{2}+9 y^{2}-12 x y \)
c. \( 2 x^{2}+3 y^{2}-6 x y \)
D. \( 4 x^{2}+9 y^{2}+12 x y \)


What is the first and foremost step to do when you have any problems with
your eyes?
A . Go to Eye Specialist
B. Expose to bright light
c. should rub eyes
D. wash eyes with chlorine water


State law of definite proportions.


Describe the uses of biodiversity.


Give the composition of the following alloys:
(a) German silver
(b) Brass


At Critical Micell Concentration (CMC),
the surfactant molecules:
A. dissociate
B. associate
c. become completely soluble
D. decompose


\( A \) and \( B \) are two events where \( P(A)= \) 0.25 and \( P(B)=0.5 . \) The probability of
both happening together is 0.14 . The
probability of both \( A \) and \( B \) not happening is
A . 0.39
B. 0.25
c. 0.11
D. none of these


The cost of notebook is twice the cost of
a pen. Write a linear equation in two variable to represent this statement


\( 10 \mathrm{L} \) of hard water required \( 0.56 \mathrm{g} \) of lime \( (C a O) \) for removing hardness.
Hence, temporary hardness in ppm of \( \boldsymbol{C a C O}_{3} \) is :
A . 100
в. 200
c. 10
D. 20


A bomb at rest explodes into three fragments. Two fragments fly off at right angles to each other.These two
A \( .14 \mathrm{m} / \mathrm{s} \)
B. \( 15 \mathrm{m} / \mathrm{s} \)
\( c \cdot 18 m / s \)
D. \( 16 \mathrm{m} / \mathrm{s} \)


Bond order of \( \boldsymbol{B e}_{2} \) is:
A . 1
B. 2
\( c \cdot 3 \)
D.


The Tyndall effect associated with
colloidal particles is due to the:
A. presence of electrical charges
B. scattering of light
c. absorption of light
D. reflection of light


In a plano convex lens the radius of
curvature of the convex lens is \( 10 \mathrm{cm} \). If
the plane side is polished, then the focal length will be (Refractive index \( =1.5) \)
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( \mathbf{c} \cdot 15 c m \)
D. \( 5 \mathrm{cm} \)


The term used to determine the age of tree by counting the annual ring is called as
A. Dendrochronology
B. Ageing and development
c. chronology
D. None of the above


Match list land list II.
List I
A. \( \boldsymbol{N} \boldsymbol{F}_{3} \)
1. No hydrolysis
B. \( \boldsymbol{P F}_{3} \)
2. Hydrolysed by hydrogen bonding
c. \( \boldsymbol{N} \boldsymbol{C l}_{3} \)
3. Hydrolysed by
nucleophilic attack
D. \( \boldsymbol{A} \boldsymbol{s} \boldsymbol{C l}_{3} \)
4. Lewis base
5. Lewis acid
B. A - 1; B - 1,4; C - 2,5; D - 3
c. \( A-2,4 ; B-1,5 ; C-2 ; D-4 \)
D. \( A-4 ; B-3 ; C-1,2 ; D-5 \)


\( \frac{1+\tan ^{2} x}{1-\tan ^{2} x} d x \) is equal to
A \( \cdot \log \frac{1-\tan x}{1+\tan x}+c \)
B. \( \log \frac{1+\tan x}{1-\tan x}+c \)
c. \( \frac{1}{2} \log \frac{1-\tan x}{1+\tan x}+c \)
D. \( \frac{1}{2} \log \frac{1+\tan x}{1-\tan x}+c \)


If the sum of the infinity of the series \( 3+5 r+7 r^{2}+\dots \) is \( \frac{44}{9}, \) then find the
value of \( r \)


State whether True or False:
Vector Quantities obey law of ordinary algebra.
A. True
B. False


\( \int e^{x}\left[\log \cos x+\sec ^{2} x\right] d x= \)
A \( \cdot e^{x}\left[\log \cos x+\sec ^{2} x\right]+c \)
B . \( e^{x}[\log \cos x+\tan x]+c \)
c. \( e^{x}(\cos x)+c \)
D \( \cdot e^{x}[\log (\tan x)]+c \)


The given diagram illustrate
Blackman's law of limiting factor. Which of the factor can be considered
as a limiting factor in the above
diagram?
Fig. 11.24
Ilustrate Blackman's law of limiting factors
A. carbon dioxid
B. Temperature
c. Intensity of light
D. All of the above


A child observed a permanent slide fixed under a microscope. He concluded
that the the slide shows binary fission
in amoeba. Draw the four stages.


Which of the following is a naphthaquinone derivative?
A. Vitamin K
B. Vitamin D
c. Vitamin A
D. Vitamin B
5


A ball Of \( 0.1 k g \) strikes a wall at right
angle with a speed of \( 6 m / s \) and rebounds along its original path at
\( 4 m / s . \) The change in momentum in Newton - sec is-
A \( \cdot 10^{3} \)
B. \( 10^{2} \)
c. 10
D.


What is general representation of
ordered pair for two variables \( a \) and \( b \) ?
A \( . a, b \)
в. \( (a, b) \)
c. \( (a), b \)
is
D. \( a,(b) \)


A fossilised bone is found to contain
\( 0.1 \% \) of its original C14. Find the age of the fossil.
A. 57100 years
B. 43100 years
c. 27860 years
D. None of these


At pressure \( P \) and absolute temperature T a mass \( \mathrm{M} \) of an ideal gas fills a closed container of volume \( V \). An additional
mass \( 2 \mathrm{M} \) of the same gas is added into the container and the volume is then reduced to \( \frac{v}{3} \) and the temperature to \( \frac{T}{3} \)
The pressure of the gas will now be:
A \( \cdot \frac{P}{3} \)
в. \( P \)
\( c .3 P \)
D. \( 9 P \)


Some reasons are given regarding the
limited use of \( \boldsymbol{H}_{2} \) as fuel:
I) Its calorific value is low.
Il) Its availability in free state is less.
III) It is difficult to store.
IV) It is easy to transport.
The correct statements are:
\( A \cdot \) ।, ॥ । and \( \| 1 \)
B. II, III and IV
c. ॥ and III
D. I and III


In a glass prism, spectrum is produced
due to :
A. refraction
B. dispersion
c. scattering
D. diffraction


The natural plant hormone isolated
from corn kernels and coconut milk is
A. Florigen
\( B \cdot G A_{3} \)
C. Free auxins
D. Zeatin
E. Indole acetic acid


The magnetic moment of a circular coil of radius \( (r), \) carrying a current \( (I) \) and number of turns \( (n) \) varies as
A \( \cdot \frac{1}{r^{2}} \)
B. \( \frac{1}{r} \)
c. \( r \)
D. \( r^{2} \)


\( \cot \theta+\tan \theta=x \) and \( \sec \theta-\cos \theta= \)
\( y \) then \( \left(x^{2} y\right)^{2 / 3}-\left(x y^{2}\right)^{2 / 3} \)


The measure of \( \angle P O Q \) in the following
figure is:
\( A \cdot 90 \)
3.70
\( c \cdot 20 \)
) 110


State Hooke's law, with graphical representation?


In a \( \Delta A B C, D, E \) and \( F \) are respectively, the mid-points of BC, and
AB. If the lengths of side \( A B, B C \) and \( C A \) \( \operatorname{are} 7 \mathrm{cm}, 8 \mathrm{cm}, \) and \( 9 \mathrm{cm}, \) respectively
find the perimeter of \( \Delta D E F \)


Two identical billiard balls strike a rigid
wall with the same speed by at different
angles, and get reflected without any change in speed, as shown in Fig. What
is
(i) the direction of the force on the wall
due to each ball?
(ii) the ratio of the magnitudes of
impulses imparted to the balls by the
wall?
\( \mathbf{a} \)


Give reasons for this sentence:
A mature erythrocyte lacks nucleus and mitochondria


A car moving at \( 2.5 m s^{-1} \) doubles its velocity with an acceleration of
\( 0.5 m s^{-2} \) in some time. If the same car
travels at \( 1.5 m s^{-1}, \) what will be its final
velocity if same acceleration acts on it for same time?
\( \mathbf{A} \cdot 2 m s^{-1} \)
B. \( 3 m s^{-1} \)
\( \mathbf{c} \cdot 4 m s^{-1} \)
\( \mathrm{D} \cdot 5 \mathrm{ms}^{-1} \)


Two identical coaxial coils \( P \) and \( Q \)
carrying equal amount of current in the same direction are brought nearer. The
current in
A. \( P \) increases while in \( Q \) decreases
B. \( Q \) increases while in \( P \) decreases
c. Both \( P \) and \( Q \) increases
D. Both \( P \) and \( Q \) decreases
E. Both \( P \) and \( Q \) remains constant


What is an electrochemical series? How
is it useful in predicting whether a metal can liberate hydrogen from acid or not?


The tangents drawn from the origin to the circle \( x^{2}+y^{2}+2 g x+2 f y+f^{2}= \)
0 are perpendicular, if
A. \( g=f \)
в. \( g=2 f \)
c. \( 2 g=f \)
D. \( 3 g=f \)


A degenerate gas is :
A . не
в. \( \mathrm{O}_{2} \)
c. \( \mathrm{He}(\text { II }) \)
D. He \( _{2} \)


Which one of the following is not true at room temperature and pressure?
A. \( P_{4} O_{10} \) is a white solid
B. \( S O_{2} \) is a colourless gas
\( \mathrm{c} \cdot \mathrm{SO}_{3} \) is a colourless gas
D. \( N O_{2} \) is brown gas


Describe an activity to show that sound requires a material medium for its
propagation.


Photosynthesis requires:
A. water
B. sunlight
c. chlorophyll
D. all of the above


The difference between S.I. and C.I. at
\( 12 \% \) per annum for 6 years on a certain sum is \( 500 . \) Find the sum.
A . 1976.28
в. 2976.28
c. 3976.28
D. 4976.28


Consider a uniform rod of mass \( \boldsymbol{M}= \)
\( 4 m \) and length \( l \) pivoted about its
centre. A mass \( m \) moving with velocity \( \boldsymbol{v} \) making angle \( \boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{\boldsymbol{4}} \) to the rod's long
axis collides with one of the rod and
sticks to it. The angular speed of the rod-mass system just after the collision
is:
A \( \frac{3}{7 \sqrt{2}} \frac{v}{l} \)
B. \( \frac{3 \sqrt{2}}{7} \frac{v}{l} \)
c. \( \frac{4}{7} \frac{v}{l} \)
D. \( \frac{3}{7} \frac{v}{l} \)


A heavy steel ball of mass greater than \( 1 \mathrm{kg} \) moving with a speed of \( 2 \mathrm{m} / \mathrm{s} \) collides head on with a stationary ping pong ball of mass less than 0.1 g. The collision is elastic. After the collision
the ping pong ball moves approximately
with a speed
A. \( 2 m / s \)
в. \( 4 m / s \)
c. \( 2 \times 10^{4} m / s \)
D. \( 2 \times 10^{3} \mathrm{m} / \mathrm{s} \)


Find the oxidation and reduction
process for the following reaction:
\( \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2}+\boldsymbol{H}_{2} \rightarrow \boldsymbol{C H}_{3}-\boldsymbol{C H}_{3} \)


If
\( 11 A M . s \) are inserated between 28
and \( 10, \) then the middle term in the
series is
A . 15
B. 19
\( c \cdot 21 \)
D. None of these


\( \underset{(\text {Sulphide ore})}{\boldsymbol{A}}+\boldsymbol{N a C} \boldsymbol{N} \stackrel{\boldsymbol{a i r}}{=} \underset{(c o m p l e x)}{\boldsymbol{B}}+ \)
\( N a_{2} S \stackrel{O_{2}}{\longrightarrow} N a_{2} S O_{4} \)
Then \( B \) is :
A. Ferromagnetic
B. Paramagnetic
C. Linear complex
D. coordination number of central atom is 4


A concave lens of refractive index \( \mu_{1} \) is placed in a medium of refractive index
\( \mu_{2} . \) A parallel beam of light strikes the surface of the lens on one side. Draw the
ray diagram for the refracted rays if
¡) \( \mu_{1}>\mu_{2} \)
ii) \( \mu_{1}<\mu_{2} \)
iii) \( \mu_{1}=\mu_{2} \)


Let \( t_{r}=\frac{r}{1+r^{2}+r^{4}} \) then, \( \lim _{n \rightarrow \infty} \sum_{r=1}^{n} t_{r} \)
equals
\( A \cdot \frac{1}{4} \)
B. 1
\( c \cdot \frac{1}{2} \)
D. None of these


Find differential equation
corresponding to \( y=c(x-c)^{2}, \) where \( c \)
is arbitrary constant.
A \( \cdot y^{\prime 3}=4 y\left(x y^{\prime}-2 y\right) \)
В \( \cdot y^{\prime 3}=4 y\left(x y^{\prime}+2 y\right) \)
c. \( y^{\prime 3}=-8 y\left(x y^{\prime}-2 y\right) \)
D \( \cdot y^{\prime 2}=-12 y\left(x y^{\prime}-2 y\right) \)


Find the curved surface area of a
cylinder given above:
A \( \cdot 1507.2 m^{2} \)
в. \( 1527.6 m^{2} \)
\( c \cdot 1517.8 m^{2} \)
D . \( 1588.1 m^{3} \)


A circular coil of radius \( 4 \mathrm{cm} \) and of 20
turns carries a current of 3 amperes. It is placed in a magnetic field of intensity
of 0.5 weber \( / m^{2} . \) The magnetic dipole moment of the coil is
A. 0.15 ampere \( -m^{2} \)
B. 0.3 ampere \( -m^{2} \)
c. 0.45 ampere \( -m^{2} \)
D. 0.6 ampere \( -m^{2} \)


A current carrying circular loop of radius R is placed in the \( x \) -y plane with centre at the origin. Half of the loop with \( x>0 \) is now bent so that it now lies in
the \( y-z \) plane.
A. The magnitude of magnetic moment now diminishes
B. The magnetic moment does not change.
C. The magnitude of \( \bar{B} \) at \( (0,0, z), z>>R \) increases
D. The magnitude of \( \bar{B} \) at \( (0,0, z), z>>R \) is unchanged.


Find symbols have standard meanings.
(a) electric field \( \mathrm{E} \)
(B) magnetic field B and
(c) magnetic permeability \( \eta_{0} \) The relevant equation are


Dental formula of human is


If the distance between points \( (p,-5),(2,7) \) is 13 units, then \( p \) is
A. -3 or 7
B. - 7 or 3
c. -3 or -7
D. 3 or 7


Perforated card boards are used in
halls, for
A. reflection of sound
B. absorption of sound
c. refraction of sound
D. as a decorative materia


Which of the following statements is
correct?
A. Diffraction is because of interference of light from same sources whereas interference is due to light form two isolated sources.
B. Diffraction is due to interaction of light from same wave fronts whereas interference is due to interaction
of two waves derived from the same source.
C. Diffraction is due to interference of waves derived from the same source whereas interference is bending of light from the same source
D. Diffraction is due to reflected waves whereas interference is due to transmitted waves from a
source.


Steam at \( 100^{\circ} \mathrm{C} \) is passed into \( 1.1 \mathrm{kg} \) of water contained in a calorimeter of
water equivalent \( 0.02 \mathrm{kg} \) at \( 15^{\circ} \mathrm{C} \) till the temperature of the calorimeter and
its contents rises to \( 80^{\circ} \mathrm{C} \).The mass of
the steam condensed in kg is
A. 0.130
B. 0.065
c. 0.260
D. 0.135


The displacement current was first populated by
A. Maxwell
B. Marconi
c. Ampere
D. Hertz


If \( \tan ^{-1} \frac{a+x}{a}+\tan ^{-1} \frac{a-x}{a}=\frac{\pi}{6} \)
then \( x^{2}=? \)
A \( \cdot 2 \sqrt{3} a \)
an
B. \( \sqrt{3} a \)
\( c \cdot 2 \sqrt{3} a^{2} \)
\( ^{2} \)
D. None of these


If \( \boldsymbol{y}=\tan ^{-1} \sqrt{\frac{1-\sin x}{1+\sin x}}, \) then the value
of \( \frac{d y}{d x} \) at \( x=\frac{\pi}{6} \) is
A. \( -\frac{1}{2} \)
B.
c. 1
D. -


How many substances have underlined
atoms of different nature?
\( N a_{2} S_{4} O_{6}, N a_{2} S_{2} O_{3}, C a O C l_{2}, N_{2} H_{4} O_{3} \)
A. 7
B. 5
\( c \cdot 4 \)
D. 8


A plane mirror forms image \( I \) of an object 0 kept \( 10 \mathrm{cm} \) from the mirror. It is
found that when a Plano concave thin
lens is placed in front of and in contact with the mirror (plane surface of lens in contact with mirror), the position of
image formed by plane mirror does not change. Then the refractive index of lens and radius of curvature of its curved
surface are respectively:
A. \( 1.5,10 \mathrm{cm} \)
B. \( 2.5,10 \mathrm{cm} \)
c. \( \sqrt{2}, 10 \mathrm{cm} \)
D. All of these are possible


Suppose z and \( \omega \) are two complex numbers such that \( |z| \leq 1,|\omega| \leq 1, \) and
\( |z+i \omega|=|z-i \omega|=2 \)
Which of the following is true for z and \( \omega \)
\( ? \)
\( \mathbf{A} \cdot \operatorname{Re}(z)=\operatorname{Re}(\omega) \)
B . \( \operatorname{Im}(z)=\operatorname{Im}(\omega) \)
\( \mathbf{c} \cdot \operatorname{Re}(z)=\operatorname{Im}(\omega) \)
D. \( \operatorname{Im}(z)=\operatorname{Re}(\omega) \)


Three points \( A, B \) and \( C \) on a steady flow of a non viscous and
incompressible fluid are observed. The
pressure, velocity and height of the points \( A, B \) and \( C \) are \( (2,3,1) .(1,2,2) \)
and (4,1,2) respectively. Density of the
fluid is \( 1 k g m^{-3} \) and all otner
parameters are given in Sl units. Then
which of the following is correct? \( (\boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A. points \( A \) and \( B \) lie on the same stream line
B. point B and C lie on same stream line
c. point \( C \) and \( A \) lie on same stream line
D. None of the above


If \( 9 g \) of \( H_{2} O \) is electrolyzed completely with \( 50 \% \) current efficiency:
A. \( 1 F \) of electricity will be needed
B. \( 3 F \) of electricity is needed
c. 5.6 L of \( O_{2} \) at \( S T P \) will be formed
D. \( 11.2 L \) of \( O_{2} \) at \( S T P \) will be formed


A gas bubble from an explosion under water oscillation with a period proportional to \( P^{a}, d^{b}, E^{c} \) where \( P \) is the
static pressure, \( d \) is the density of water
and \( \boldsymbol{E} \) is the energy of explosion. Then
\( a, b \) and \( c \) respectively are
A \( \cdot \quad-\frac{5}{6}, \frac{1}{2}, \frac{1}{3} \)
в. \( \frac{1}{2}, \frac{-5}{6}, \frac{1}{3} \)
c. \( \frac{1}{3}, \frac{1}{2}, \frac{-5}{6} \)
D. 1,1,1


A potentiometer wire has a length \( 2 \mathrm{m} \) and resistance of \( 10 \Omega \). It is connected in
series with a Resistance of \( 990 \Omega \) and a
cell of e.m.f. 2V. The potential gradient along the wire is
A. \( 0.01 \mathrm{v} / \mathrm{m} \)
B. \( 0.02 \mathrm{V} / \mathrm{m} \)
c. \( 0.03 \mathrm{V} / \mathrm{m} \)
D. \( 0.025 \mathrm{V} / \mathrm{m} \)


Suggest a test to find the hardness of
water and explain its procedure


is
A. An ester
B. An anhydride
C. Acetal
D. Hemiacetal


a) Define "Esterification"
b) Write any three uses of ethanol


The electric field at \( r=R \) is:
A. independent of a
B. directly proportional to a
C. directly proportional to \( a^{2} \)
D. inversely proportional to


Ordinary rubber is an insulator. But the special rubber tyres of aircrafts are made slightly conducting. Why is this
necessary?
A. The charged developed due to atmospheric electricity finds its way to the earth
B. The charged developed due to friction finds its way to the earth
c. The charged developed due to induction finds its way to the earth
D. The charged developed due to the aircraft engine finds its way to the earth


Sameer took sulphur powder on a spatula and heated it. He collected the gas evolved by inverting a test tube over
it. What will be the action of gas evolved on dry litmus paper?


A mercury drop of radius \( 1 \mathrm{cm} \) is
sprayed into \( 10^{6} \) drops of equal size. The
energy expended in joule is (surface tension of mercury is \( 460 x 10^{-3} \mathrm{N} / \mathrm{m} \) ):
A. 0.057
B. 5.7
c. \( 5.7 \times 10^{-4} \)
D. \( 5.7 \times 10^{-6} \)


What is old age far sigtedness?


There are two charges \( +2 \mu C \) and \( - \)
\( 3 \mu C . \) The ratio of forces acting on them
will be
A .2: 3
B. 1: 1
c. 3: 2
D. 4: 9


At the critical micelle concentration, the surfactant molecules:
A. decompose
B. dissociate
c. associate
D. become completely soluble


Why it is necessary to separate
oxygenated and deoxygenated blood in mammals and birds?
A. To stop mixing of oxygenated and deoxygenated blood
B. To maintain body temperature
c. To suffice higher energy need
D. All of the above


Evaluate the following integral:
\( \int_{0}^{2}\left(x^{2}+2 x+1\right) d x \)


Which of these metals would be most
reactive?
\( \mathbf{A} \cdot K \)
в. \( C a \)
c. \( T i \)
D. \( M n \)
ह. \( C u \)


Find relation between \( x \) and \( y \) such that
the point \( (x, y) \) is equidistance them the point (7,1) and (3,5)


If a stretching force \( F 1 \) is applied on a
vertical metal wire then its length is \( L 1 \)
and if force \( F 2 \) is applied on it then its
length becomes 1.2. The real length of
wire is?


A ball is bouncing down a flight of stairs. The coefficient of restitution is \( e \)
The height of each step is \( d \) and the ball descends one step each bounce. After each bounce it rebounds to a height \( h \)
above the next lower step. The height is large compared with the width of step so that the impacts are effectively head-on. Find the relationship between
\( \boldsymbol{h} \) and \( \boldsymbol{d} \)
A \( \cdot h=\frac{d}{1-e^{2}} \)
в. \( h=\frac{d}{1+e^{2}} \)
c. \( h=\frac{d}{1+e} \)
D. \( h=\sqrt{\frac{d}{1-e^{2}}} \)


Which of the following has maximum ionization energy?
A \( \cdot B a \rightarrow B a^{+}+e^{-} \)
B. \( B e \rightarrow B e^{+}+e^{-} \)
c. \( C a \rightarrow C a^{2+}+2 e^{-} \)
D. \( M g \rightarrow M g^{2+}+2 e^{-} \)


Find the sum to indicated number of
terms in the geometric progression given:
\( \mathbf{0 . 1 5}, \mathbf{0 . 0 1 5}, \mathbf{0 . 0 0 1 5}, \ldots . . \mathbf{2 0} \) terms


A faulty thermometer has its fixed
points marked 5 and 95 If the temperature of a body as shown on the celcius scale is 40 then its temperature shown on this faulty thermometer is.


In a test an examinee either guesses or copies or knows the answer to a
multiple choice question with four choices. The probability that he make, a guess is \( \frac{1}{3} \) and the probability that he copies the answer is \( \frac{1}{6} . \) The probability that his answer is correct given that he copied it is \( \frac{1}{8} . \) Find the probability that he knew the answer to the question,
given that he correctly answered it.


The true statement regarding coral is
A. They form branched colonies.
B. They are solitary or colonial polypoid.
C. They grow as massive bodies.
D. All of the above.


Trace the following central conics. \( \boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2}+\boldsymbol{x}+\boldsymbol{y}+\mathbf{1}=\mathbf{0} \)


Which character of pteridophytes is not similar to bryophytes?
A. Water requirement for fertilization
B. Dependence of sporophyte on gametophytee
c. Heterospory
D. None of these


\( \int \frac{\sec ^{2} x}{\sqrt{\operatorname{asec}^{2} x-\operatorname{btan}^{2} x}} d x \) is (where \( c \)
is integration constant
This question has multiple correct options
A \( \cdot \frac{1}{\sqrt{b-a}} \sin ^{-1}(\tan x \sqrt{\frac{b-a}{a}})+c \) if \( b>a>0 \)
B. \( \frac{1}{\sqrt{b-a}} \log _{2}(\tan x \sqrt{b-a}+\sqrt{\operatorname{asec}^{2} x-b \tan ^{2} x})+c \) if
\( b>a>0 \)
c. \( \frac{1}{\sqrt{a-b}} \sin ^{-1}(\tan x \sqrt{\frac{a-b}{a}})+c \) if \( a>b>0 \)
D. \( \frac{1}{\sqrt{a-b}} \log _{e}(\tan x \sqrt{a-b}+\sqrt{\operatorname{asec}^{2} x-b \tan ^{2} x})+c \) if
\( a>b>0 \)


Van't Hoff factor is:
A. more than one in case of association
B. less than one in case of dissociation
C. \( \frac{\text { normal molecular mass }}{\text { observed molecular mass }} \)
D. \( \frac{\text { observed molecular mass }}{\text { normal molecular mass }} \)


Distinguish between asexual and sexual reproduction. Why is vegetative reproduction also considered as a type of asexual reproduction?


One mole of magnesium nitride on reaction with an excess of water gives:
A. one mole of ammonia
B. one mole of nitric acid
c. two moles of ammonia
D. two moles of nitric acid


Oranges are to be transferred from larger boxes to smaller boxes. When a larger box is emptied, the oranges from it fill 3 smaller boxes and still 7 oranges
are left. If the number of oranges in a
small box are taken to be \( x \), then what
is the number of oranges in the larger
box


Identify \( B, X \) and \( R \) respectively in the following sequence of reactions:
\( C_{2} H_{5} M g B r \frac{C H_{3} C N}{\longrightarrow} A \frac{H_{3} O^{+}}{\longrightarrow} B \)
\( \boldsymbol{C H}_{3} \boldsymbol{C O C H}_{3} \frac{N a O \boldsymbol{H}}{\boldsymbol{I}_{2}} \boldsymbol{X} \stackrel{\boldsymbol{A} \boldsymbol{g}}{\longrightarrow} \boldsymbol{Y} \)
\( \boldsymbol{C}_{\boldsymbol{6}} \boldsymbol{H}_{\boldsymbol{5}} \boldsymbol{N} \boldsymbol{H}_{2} \frac{N a N \boldsymbol{O}_{2}}{\boldsymbol{H} C l} \boldsymbol{P} \stackrel{\boldsymbol{C u} \boldsymbol{C N}}{\longrightarrow} \boldsymbol{Q} \stackrel{\boldsymbol{+ 4 H}}{\longrightarrow} \)
\( \boldsymbol{R} \)
A \( \cdot C_{2} H_{5} C O O H, C H I_{3}, C_{6} H_{5} C H_{2} N H_{2} \)
в. \( C_{2} H_{5} C O O H, C H_{3} I, C_{6} H_{5} \) СООН
c. \( C_{2} H_{5} C H_{2} N H_{2}, C H_{3} I, C_{6} H_{5} C O O H \)
D. \( C_{2} H_{5} C O O H, C_{2} H_{5} I, C_{6} H_{5} C O N H_{2} \)


How many molecules of methane are
present in a sample that contains \( 1.0 \times 10^{10} \) moles of methane?
A. \( 6.0 \times 10^{23} \)
В. \( 1.0 \times 10^{33} \)
c. \( 6.0 \times 10^{33} \)
D. \( 6.0 \times 10^{24} \)


Which of the following is used to detect
the current?
A . Tester
B. LED
c. compass needle
D. All of the above


According to the recent reports, the country contributed maximum to hole
formation in ozone layer is
A. U.S.A.
B. Russia
c. Germany
D. Japan


In which of the following reaction, the
value of \( \boldsymbol{K}_{\boldsymbol{p}} \) will be equal to \( \boldsymbol{K}_{c} \) ?
A \( \cdot H_{2}+I_{2} \rightleftharpoons 2 H I \)
в. \( P C l_{5} \rightleftharpoons P C l_{3}+C l_{2} \)
\( \mathrm{c} \cdot 2 N H_{3} \rightleftharpoons N_{2}+3 H_{2} \)
D. \( 2 S O_{2}+O_{2} \rightleftharpoons 2 S O_{3} \)


Amount of \( C O_{2} \) delivered by every 100 \( \mathrm{ml} \) of deoxygenated blood is
A. \( 7 \mathrm{m} \)
B. \( 5 \mathrm{ml} \)
\( c \cdot 4 m \)
D. 27 m1


If the ionization potential in the ground state for hydrogen is \( 13.6 e . V . \) then find
the excitation potential of the third
orbit.


Follwing operation are carried out on a sample of ideal gas initially at pressure \( \mathrm{P} \) volume \( V \) and kelvin temperature \( T \)
a) At constant volume, the pressure is increased fourfold.
b) At constant pressure, the volume is
doubled
c) The volume is doubled and pressure
halved.
d) If heated in a vessel open to
atmosphere, one-fourth of the gas escapes from the vessel.

Arrange the above operations in the increasing order of final temperature.
A. \( a, b, c, d \)
B. \( c, b, a, d \)
\( c \cdot b, a, d, c \)
D. \( \mathrm{c}, \mathrm{d}, \mathrm{b} \),


The above process is:
\[
\begin{array}{c}
\boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \stackrel{\boldsymbol{O}_{2}}{\longrightarrow} \boldsymbol{H} \boldsymbol{g} \boldsymbol{S} \cdot \boldsymbol{H} \boldsymbol{g} \boldsymbol{O} \\
& \downarrow \boldsymbol{\Delta} \\
\boldsymbol{H} \boldsymbol{g}
\end{array}
\]
A. auto oxidation
B. self reduction
c. thermal reduction
D. none of the above


When 2 molecules of pyruvic acid forms 2 molecules of lactic acid by anaerobic respiration then
A. One ATP is lost.
B. Three ATP is lost
C. Six ATP is lost.
D. None of the above


The Torque \( \vec{\tau} \) on a body about a given point is found to be equal to \( \overrightarrow{\boldsymbol{A}} \times \overrightarrow{\boldsymbol{L}} \)
where \( \vec{A} \) is the constant vector and \( \overrightarrow{\boldsymbol{L}} \) is
the force on the body about that point. From this it follows that:
This question has multiple correct options
A \( \cdot \frac{d \vec{L}}{d t} \) is perpendicular to \( \vec{L} \) at all instants of time
B. the component of \( \vec{L} \) in the direction of \( \vec{A} \) does not change with time
c. the magnitude of \( \bar{L} \) does not change with time
D. \( \vec{L} \) does not change with time


Describe how ozone layer is formed?


The equivalent capacitance between
points \( X \) and \( Y \) in figure shown is :
\( A \)
В. \( 4 \mu F \)
c. \( \frac{18}{5} \mu F \)
D. none of these


Compound \( (D) \) is:
\( (\mathbf{D})\left(\mathbf{C}_{4} \mathbf{H}_{9} \mathbf{N} \mathbf{O}_{2} \mathbf{C l}_{2}\right) \)
\( A \)
B.
\( c \)
D. none of the above


\( A, B, C \) are three points on the axes of
\( x, y \) and \( z \) respectively at distance \( a, b, c \)
from the origin \( O ; \) then the co ordinates of the point which is
equidistant from \( A, B, C \) and \( O \) is
A \( \cdot(a, b, c) \)
B. \( \left(\frac{a}{2}, \frac{b}{2}, \frac{c}{2}\right) \)
\( ^{\mathbf{C}} \cdot\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right) \)
D. None of these


The energy of activation and specific rate constant for a first order reaction
at \( 25^{\circ} \mathrm{C} \) are \( 100 \mathrm{kJ} / \mathrm{mole} \) and \( 3.46 \times \)
\( 10^{-5} \sec ^{-1} \) respectively. Determine the
temperature at which half-life of the reaction is 2 hours:
\( A \cdot 306 k \)
B. 310 k
\( c \cdot 234 k \)
D. 280 k


Chloroprene is used in making
A. synthetic rubber
B. plasticç
c. petrol
D. All of the above


Find the speed of \( C \) after collision of \( B \)
and \( C \) for first time.
A \( \cdot \frac{V}{4} \)
в. \( \frac{2 V}{4} \)
c. \( \frac{3 V}{4} \)
\( D \)


Half life period of a first order reaction, \( A \rightarrow \) product is 6.93 hour. What is the value of rate constant?
A \( \cdot 1.596 h^{-1} \)
B. \( 0.1 h^{-1} \)
c. \( 4.802 h^{-1} \)
D. \( 10 h^{-1} \)


The IUPAC name of the above shown
compound is:
A. but-2-ene-2,3-diol
B. Pent-2-ene-2,3-diol
C. 2-methylbut-2-ene-2,3-diol
D. hex-2-ene-2,3-diol


A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent The force that acts on the player is
A. Frictional force along westward
B. Muscle force along southward
c. Frictional force along south-west
D. Muscle force along south-west


Identify the endothermic and exothermic reaction.
This question has multiple correct options
A. \( H C l+N a O H \rightarrow N a C l+H_{2} O+ \) heat
в. \( 2 K C l O_{3}(s) \triangleq 2 K C l(s)+3 O_{2} \uparrow \)
\( \mathrm{c} \cdot \mathrm{CaO}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}+ \) heat
D. \( \operatorname{CaCO}_{3}(s) \triangleq \operatorname{CaO}(s)+\mathrm{CO}_{2} \uparrow \)


A girl walks \( 4 k m \) towards west, then
she walk \( 3 k m \) in a direction \( 30^{\circ} \) east of
north and stops. Determine the girl's displacement from her initial point of
departure.


"Chlorination of calcium hydroxide produces bleaching powder". If true enter \( 1, \) if false enter 0


A composition string is made up by joining two strings of different masses
per unit length \( \longrightarrow \mu \) and \( 4 \mu . \) The
composite string is under the same tension. A transverse wave pulse : \( \boldsymbol{Y}= \) \( (6 m m) \sin (5 t+40 x), \) where \( t^{\prime} \) is in
seconds and ' \( x \) ' in meters, is sent along
the lighter string towards the joint. The joint is at \( x=0 . \) The equation of the
wave pulse reflected from the joint is
\( \mathbf{A} \cdot(2 m m) \sin (5 t-40 x) \)
B. \( (4 m m) \sin (40 x-5 t) \)
C. \( -(2 m m) \sin (5 t-40 x) \)
D. \( (2 m m) \sin (5 t-10 x) \)


Reactions which can be called as double
displacement reactions is/are:
A. precipitation reactions
B. neutralization reactions
c. both A and B
D. none of the above


Assertion
If trace of the matrix
\( \left[\begin{array}{cccc}\boldsymbol{x}-\mathbf{5} & \boldsymbol{0} & \boldsymbol{2} & \boldsymbol{4} \\ \boldsymbol{3} & \boldsymbol{x}^{\boldsymbol{2}}-\boldsymbol{1 0} & \boldsymbol{6} & \boldsymbol{1} \\ -\boldsymbol{2} & \boldsymbol{3} & \boldsymbol{x}-\boldsymbol{7} & \boldsymbol{1} \\ \boldsymbol{1} & \boldsymbol{2} & \boldsymbol{0} & \boldsymbol{-} \boldsymbol{2}\end{array}\right] \)
zero,then value of \( x \) is -6 or 4
Reason
Distinct roots of a quadratic equation
\( a x^{2}+b x+c=0 \) are possible if
discriminant of the equation is positive
i.e, \( b^{2}-4 a c>0 \)
A. Both (A) \& (R) are individually true \& (R) is correct explanation of \( (A) \)
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of \( (A) \)
C. (A)is true but (R) is false,
D. (A)is false but (R) is true.


Describe the working of sound signals
reaching the brain with the help of a figure of human ear


What is a projectile? Give example.


All gases have the same number of
moles in the same volume at constant
temperature and pressure.
A. Boyle's Law
B. Charles's Law
c. Avogadro's Principle
D. Ideal Gas Law


If one angle of a \( \Delta \) is equal to the sum of
the other two, the triangle is
A. isosceles
B. equilateral
c. right angled
D. ordinary


n the figure, \( C \) is the centre of the
circle. \( X \) and \( Y \) axes are tangents to the
circle at the points \( A \) and \( B \)
respectively. If the coordinates of \( A \) are
\( (4,0), \) find the coordinates of \( B \) and \( C \)


The possible beneficial affect of grazing animals is the
A. Removal of wild animals
B. Eradication of weeds
C. Removal of wild plants
D. Addition of their excrete to the soil


The solution of the differential equation \( y \frac{d y}{d x}=x\left[\frac{y^{2}}{x^{2}}+\frac{\phi\left(\frac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\frac{y^{2}}{x^{2}}\right)}\right] \) is (where, \( c \)
is a constant)
\( ^{\mathrm{A}} \cdot \phi\left(\frac{y^{2}}{x^{2}}\right)=c x \)
в. \( _{x \phi}\left(\frac{y^{2}}{x^{2}}\right)=c \)
\( ^{\mathrm{c}} \cdot \phi\left(\frac{y^{2}}{x^{2}}\right)=c x^{2} \)
D. \( x^{2} \phi\left(\frac{y^{2}}{x^{2}}\right)=c \)


Refer to the flow chart diagram below and give balanced equations with conditions, if any, for the following conversions \( A \) to \( D: \)


Arrange the following in order of
decreasing basic strength.
\( \mathbf{I} \)
II
III
\( \mathbf{I V} \)
A. \( |V>|>||>|| \mid \)
\( \mathbf{B} \cdot|V>|>|||>| \)
\( \mathbf{C} \cdot|V>||>|>|| \mid \)
D. \( |>||>|||>\mid V \)


The M.P. and B.P. are very low for?
A. Ne
в. не
c. \( \mathrm{kr} \)
D. A


A particle of mass \( M, \) moving with a
velocity \( u \) makes a head on collision
with a particle of \( m \) initially at rest so that the final velocities are along the
same line. If the collision is elastic and \( \frac{M}{m}=k, \) then the final velocity of the second particle of mass \( \boldsymbol{m} \) is :
A \( \frac{2 u}{1+k} \)
В \( \frac{2 k u}{1+k} \)
c. \( \frac{2 u}{1-k} \)
D. \( \frac{k M u^{2}}{2(1-k)} \)


If the eccentricity of the hyperbola \( x^{2}- \) \( y^{2} \sec ^{2} \alpha=5 \) is \( \sqrt{3} \) times the
eccentricity of the ellipse \( \boldsymbol{x}^{2} \mathbf{s e c}^{2} \boldsymbol{\alpha}+ \)
\( \boldsymbol{y}^{2}=25, \) then the value of \( \boldsymbol{\alpha} \) is
\( \mathbf{A} \cdot \pi / 6 \)
в. \( \pi / 4 \)
c. \( \pi / 3 \)
D. \( \pi / 2 \)


The drift current in a p-njunction is
A. from the n-side to the p-side
B. from the p-side to the n-side
C. from the n-side to the p-side if the junction is forwardbiased and in the opposite direction if it is reverse biased
D. from the p-side to the n-side if the junction is forwardbiased and in the opposite direction if it is reversebiased


Laxmi bought 7 books for a total of Rs.
56. How much would she pay for just 3 books?


Which of the following elements are isotopes
This question has multiple correct options
A \( \cdot c^{12} \)
в. \( c^{13} \)
\( c \cdot c^{1} \)
D. \( N^{14} \)


Which of the following is an alternative copolymer?
A. Styrene
B. Neoprene
c. Nylon - 2 - nylon - 6
D. Nylon - 6


Heat capacity is
A \( \cdot \frac{d Q}{d T} \)
B . \( d Q \times d T \)
\( ^{\mathbf{C}} \sum Q \cdot \frac{1}{d T} \)
D . \( d Q-d T \)


A code word is to consist of two English alphabets followed by two distinct numbers between 1 and \( 9 . \) For example, \( C A 23 \) is a code word. How many such
code words are there?


\( P \) is a point on the common chord \( R S \) produced by two intersecting circles.
\( A B \) and \( C D \) are the chords of the
circles,they meet at \( P \) produced.Prove that \( \boldsymbol{P A} \times \boldsymbol{P B}=\boldsymbol{P C} \times \boldsymbol{P D} \)


A rectangular loop carrying a current
is situated near a long straight wire
such that the wire is parallel to one of
the sides of the loop and is in the plane of the loop. If a steady current lis established in the wire as shown in the
figure, the loop will:
A. rotate about an axis parallel to the wire
B. move away from the wire
C. remain stationary
D. move towards the wire


The current in a metallic conductor is
plotted against voltage at two different
temperatures \( T_{1} \) and \( T_{2} . \) Which is
correct
\( A \cdot T_{1}>T_{2} \)
В \( \cdot T_{1}<T_{2} \)
\( c \cdot T_{1}=T_{2} \)
D. None


The best alternative to fossil fuels will
be
A. coal
B. Animal fat
c. Hydrogen
D. Gasoline


The following equilibrium is established when hydrogen chloride is dissolved in acetic acid.
\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a q})+\boldsymbol{C H}_{3} \boldsymbol{C O O H}(\boldsymbol{a q}) \rightleftharpoons \)
\( \boldsymbol{C l}^{-}(\boldsymbol{a q})+\boldsymbol{C H}_{3} \boldsymbol{C O O H}_{2}(\boldsymbol{a q}) \)
The set that characterizes the
conjugate acid-base pairs is
A \( \cdot\left(H C l, C H_{3} C O O H\right) \) and \( \left(C H_{3} C O O H_{2}, C l^{-}\right) \)
в. \( \left(H C l, C H_{3} C O O H_{2}\right) \) and \( \left(C H_{3} C O O H, C l^{-}\right) \)
c. \( \left(C H_{2} C O O H_{2}, H C l\right) \) and \( \left(C l^{-}, C H_{3} C O O H\right) \)
D. \( \left(H C l, C l^{-}\right) \) and \( \left(C H_{3} C O O^{-}, C H_{3} C O O H\right) \)


Evaluate the Given limit:
\( \lim _{x \rightarrow 0} \frac{\sin a x}{\sin b x}, a, b \neq 0 \)


State whether given statement is True or False

In humans, sound is produced because of the vibration of the larynx.
A. True
B. False


Assertion
\( \left[\boldsymbol{F e}(\boldsymbol{E} \boldsymbol{D} \boldsymbol{T} \boldsymbol{A})^{-} \) complex is octahedral in \right.
shape.
Reason
EDTA (Ethylenediaminetetraacetic acid) is a hexadentate ligand and
undergoing \( s p^{3} d^{2} \) hybridisation.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Two systems of rectangular axes have
the same origin. If a plane cuts them at
distance \( a, b, c \) and \( d, b^{\prime}, c^{\prime} \) from the
origin, then
A \( \cdot \frac{1}{a^{2}}-\frac{1}{b^{2}}-\frac{1}{c^{2}}-\frac{1}{a^{2}}-\frac{1}{b^{2}}-\frac{1}{c^{2}}=0 \)
B \( \cdot \frac{1}{a^{2}}-\frac{1}{b^{2}}-\frac{1}{c^{2}}-\frac{1}{a^{2}}-\frac{1}{b^{2}}+\frac{1}{c^{2}}=0 \)
c. \( \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}-\frac{1}{a^{2}}-\frac{1}{b^{2}}-\frac{1}{c^{2}}=0 \)
D \( \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}+\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}=0 \)


Find the equation of a circle of radius 5 whose centre lies on \( x- \) axis and
passes through the point (2,3)


A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is \( 30 \mathrm{cm} \) long, \( 25 \mathrm{cm} \) wide and
\( 25 \mathrm{cm} \) high.
(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges?


Two identical carts constrained to move
on a straight line, on which sit two twins of same mass, are moving with equal
velocity. At some time snow begins to
drop uniformly. Ram, sitting on one of
the carts, picks the snow from cart and
throws off the falling snow sideways and in the second cart Shyam is asleep:
A. cart carrying Ram will have more speed finally than that carrying Shyam.
B. cart carrying Ram will have less speed finally than that carrying Shyam.
C. cart carrying Ram will have same speed finally than that carrying Shyam.
D. The velocity of cart depends on the amount of snow thrown


Which of the following is/are true statement(s)?
A. A given substance may simultaneously exist in all three states.
B. Water exists in all three phases simultaneously.
C. The temperature at which all the three phases of the same substance exist simultaneously is called triple point
D. All of the above.


If \( a-b=4 \) and \( a+b=6, \) find \( a^{2}+b^{2} \)
A . 26
B . 13
c. 53
D. 40


The catalyst in photosynthesis is:
A. sunlight
B. water
c. chlorophyll
D. \( C O_{2} \)


If \( P(n) \) is the statement " \( n^{2} \) is even",
then what is \( \boldsymbol{P}(\boldsymbol{3}) \) ?


Rutherford's model explains:
This question has multiple correct options
A. Atom is a planetary model
B. Electrons never loose nor gain energy.
C. Electron revolves around the nucleus with high velocities to counterbalance the forces of electrostatic
forces of attraction between protons and electrons.
D. Electrons do not move at all.


Column I: Compounds Column II: Isomers


The two adjacent sides of a
parallelogram are \( 25 \mathrm{cm} \) and \( 40 \mathrm{cm} \) respectively. The altitude drawn on the Ionger side is \( 18 \mathrm{cm}, \) then the area of the parallelogram is
A \( \cdot 450 \mathrm{cm}^{2} \)
B \( .720 \mathrm{cm}^{2} \)
\( c \cdot 500 \mathrm{cm}^{2} \)
D. none of these


\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\left(\boldsymbol{S} \boldsymbol{O}_{4}\right)\right] \boldsymbol{B} \boldsymbol{r} \) and
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5} \boldsymbol{B r}\right] \boldsymbol{S} \boldsymbol{O}_{4} \) are linkage
isomers.
A. True
B. False


n figure, \( l, m \) and \( n \) are parallel lines
intersected by transversal \( \boldsymbol{p} \) at \( \boldsymbol{X}, \boldsymbol{Y} \)
and \( Z \) respectively. Find \( \angle 1, \angle 2 \) and \( \angle 3 \)


Structure of Guanine is
\( A \)
B.
\( c \)
D. None


How many pairs of autosomes and pairs
of sex chromosomes are present in a human being?


Mean deviation from the mean for the
observation -1,0,4 is
A. \( \sqrt{\frac{14}{3}} \)
B. \( \frac{2}{3} \)
\( c \cdot 2 \)
D. none of these


What are the postulates of Dalton's atomic theory


N' molecules each of mass 'm', of gas A
and '2N' molecules, each of mass '2m',
of gas \( \mathrm{B} \) are contained in the same vessel. Which is maintained at a
temperature T. The mean square of the velocity of molecules of B type is
denoted by \( V^{2} \) and the mean square of the \( X \) component of the velocity of \( A \) type is denoted by \( \omega^{2}, \frac{\omega^{2}}{V^{2}}= \)
\( A \cdot 2 \)
B.
\( c \cdot 1 / 3 \)
\( D \cdot 2 / 3 \)


The increase in temperature on the earth disturbs the water cycle and
reduces rainfall. The situation may lead
to:
A. floods
B. droughts
c. increased level of \( C O_{2} \)
D. all of the above


When load is applied to a wire, the extension is 3 mm. The extension in the
wire of same material and length but
half the radius extended by the same load is :
A. \( 0.75 \mathrm{mm} \)
B. \( 6 m m \)
\( c .1 .5 m m \)
D. \( 12.0 m m \)


Prove that \( \frac{2 \tan x}{1+\tan ^{2} x}=\sin 2 x \)


On increasing the reverse bias to a
large value in p-njunction diode then value of current
A. remain fixed
B. increases slowly
c. decreases slowly
D. suddenly increases


The presence of checkpoint during
mitosis ensures the attachment of all
chromosomal kinetochore proteins to
the spindle fibres. The absence of
attachment of kinetochore proteins produces a signal preventing mitosis to
proceed to next stage. The occurrence of
this check point is responsible for transition from
A. Anaphase to telophase
B. Prophase to metaphase
C. Metaphase to telophase
D. Prophase to anaphase
E. Metaphase to anaphase


Inertia means resistance to the change
of state.
A . True
B. False


The wave length of a spectral line for an electronic transition is inversely
proportional to :
A. number of electrons under going transition
B. the nuclear charge of the atommmen
c. the velocity of anelectron undergoing transition
D. the difference in the energy involved in the transition


Q Type your question-
\( 65 k m h^{-1} . \) When they reach the crossroad, one of the cars turns towards
town \( Q \) whereas the other continues
forward towards town \( R \). Both continue
to move with the same speed of
\( 65 k m h^{-1} \)
Which of the following options is correct for given statements?
(i) Both cars have the same velocities
even if the car turns towards town \( Q \)
(ii) Two bodies have same velocities if
they are moving with same speed in different directions.
A. Both (i) and (ii) are correct and (ii) is the correct explanation of (i)
B. Both (I) and (ii) are correct but (ii) is not the correct explanation of (i
c. only (i) is correct
D. Neither (i) nor (ii) is correct


Which one of the following processes depends on gravity?
A. Conduction
B. Convection
c. Radiation
D. None of these


A neutral rubber rod and a neutral piece
of fur have equal amounts of negative and positive charge. When the fur is rubbed against the rod, a transfer of electrons occurs. The transfer of
electrons and mass
transfer respectively takes place from
A. fur to rubber rod; rubber rod to fur
B. fur to rubber rod; fur to rubber rod
c. rubber rod to fur; rubber rod to fur
D. rubber rod to fur; fur to rubber rod


Work done on body equals to change in its kinetic energy is known as
A. work done principle.
B. work-energy principle.
c. work-velocity principle.
D. speed-displacement principle


In a laser tube, all the photons
A. have same wavelength
B. have same energy
c. move in same direction
D. move with same speed


Which one of the following statement is
false?
A. work is a state function
B. temperature is a state function
C. change in the state is completely defined when the initial and final states are specified
D. work appears at the boundary of the system


f the \( m \) th term of an AP is \( a \) and its \( n \) th
term is \( b \), show that the sum of its
\( (m+n) \) terms is \( \frac{(m+n)}{2}\left\{a+b+\frac{(a-b)}{(m-n)}\right\} \)


Two tangent galvanometers, which are identical except in their number of turns, are connected in parallel. The ratio of their resistances of the coils is
1 : 3. If the reflection in the two tangents
galvanometers are \( 30^{\circ} \) and \( 60^{\circ} \)
respectively, then the ratio of their number of turns is:
A .2: 3
в. 3: 1
c. 1: 2
D. 1: 6


Lymph helps is the absorption of
A. carbohydrate
B. Proteins
c. Fats
D. All of the above


The angle of prism is 60 and its refractive index for green light is \( 1.5 . \) If a green ray passes through it, the deviation will be:


If the diameter of a sphere is \( 14 \mathrm{cm} \)
then what is the surface area \( \left(\text { in } c m^{2}\right) \)
of the sphere?
A . 616
в. 308
c. 462
D. 636


The unit of latent heat is
A \( \cdot \) cal-g
B . cal/\%
c. cal/g
D. none of these


You are living very near to sea-coast
What types of minerals can be present in direct supply of tap water?
\( \mathbf{A} \cdot N a B r \)
в. \( N a I \)
c. \( M g C l_{2} \)
D. All the above


The precipitation of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}\left(\boldsymbol{K}_{s p}=\mathbf{1 . 8} \times\right. \)
\( \mathbf{1 0}^{-10} \) ) will occur when which of the
following two solutions are mixed?
A \( \cdot 10^{-4} M\left(A g^{+}\right) \) and \( 10^{-4} M\left(C l^{-}\right. \)
B . \( 10^{-5} M\left(A g^{+}\right) \) and \( 10^{-5} M\left(C l^{-}\right) \)
C. \( 10^{-5} M\left(A g^{+}\right) \) and \( 10^{-6} M\left(C l^{-}\right) \)
D. \( 10^{-10} M\left(A g^{+}\right) \) and \( 10^{-10} M\left(C l^{-}\right) \)


Which of the following letter shaped
pipe is most effective to build a Periscope?
\( A \cdot A \)
B.
\( c \cdot z \)
D.


The given table shows properties of four
cells systems \( A, B, C \) and \( D . \) The maximum rate of inward diffusion of
water will be observed in which of these
systems?
\begin{tabular}{lll}
System & Intracellular concentration of water & Extracellular concentration of water \\
\hline \( \mathrm{A} \) & \( 0.09 \mathrm{M} \) & \( 0.11 \mathrm{M} \) \\
\( \mathrm{B} \) & \( 0.2 \mathrm{M} \) & \( 0.5 \mathrm{M} \) \\
\( \mathrm{C} \) & \( 0.05 \mathrm{M} \) & \( 0.6 \mathrm{M} \) \\
\( \mathrm{D} \) & \( 0.03 \mathrm{M} \) & \( 0.7 \mathrm{M} \)
\end{tabular}
A. System A
B. System B
c. system
D. System D


What will happen if the striker of a doorbell is kept in a magnetic field in a direction perpendicular to motion of striker
A. Striker Hits Harder
B. Striker rebounds harder
c. More current is drawn
D. No effect


A concave mirror produces 2 times magnified real image of an object
placed at \( 5 \mathrm{cm} \) in front of it. Where is
image located?
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( -5 c m \)
c. \( -10 c m \)
D. \( 2.5 \mathrm{cm} \)


If \( \boldsymbol{f} \) satisfies \( |\boldsymbol{f}(\boldsymbol{u})-\boldsymbol{f}(\boldsymbol{\nu})| \leq|\boldsymbol{u}-\boldsymbol{\nu}| \) for
\( \boldsymbol{u}, \boldsymbol{\nu} \in[\boldsymbol{a}, \boldsymbol{b}] \)
then the maximum value of \( \left|\int_{a}^{b} f(x) d x-(b-a) f(a)\right| \) is?
A \( \cdot \frac{b-a}{2} \)
в. \( \frac{(b-a)^{2}}{2} \)
c. \( (b-a)^{2} \)
D. None of these


The structure formula of
hypophosphorous acid is:
\( A \)
в.
\( c \)
D.


Which of the following are the characteristics of Ethane but not of
Ethene?
This question has multiple correct options
A. Carbon is \( s p^{3} \) hybridised
B. Carbon is \( s p^{2} \) hybridised
c. Allowed rotation through \( C-C \) bond axis perpendicular to it
D. Forbidden rotation through \( C-C \) bond and axis perpendicular to it


Use of pesticides which do not contaminate soil help in control of
A. air pollution
B. soil pollution
c. industrial pollution
D. none of above


When a beam of light from an object meets actually at a point after reflection from a mirror then the image formed is known as:
A. either real or virtual image
B. real image
c. virtual image
D. neither real nor virtual image


Rearrangement of carbon skeleton of substrate is possible in which of the following reactions?
\( \boldsymbol{S}_{N} \mathbf{1}, \boldsymbol{S}_{N} \mathbf{2}, \boldsymbol{E} \mathbf{1}, \boldsymbol{E} \mathbf{2}, \boldsymbol{E} \mathbf{1} \mathbf{c} \mathbf{B}, \boldsymbol{S}_{N} \mathbf{2} \operatorname{Th}, \boldsymbol{S}_{N} \mathbf{2} \)
Ar, EAS(Electrophilic aromatic substitution), electrophilic addition on alkenes, free radical substitution of
alkanes.


Boron exists in two isotopic form \( B^{10} \)
and \( B^{11} . \) If average atomic weight of \( B \)
is \( 10.70 u \), select the correct statement.
A. \% abundance of \( B^{10}=\% \) abundance of \( B^{11} \)
B. \% abundance of \( B^{10}>\% \) abundance of \( B^{11} \)
c. \( \% \) abundance of \( B^{10}<\% \) abundance of \( B^{11} \)
De abundance of \( B^{10}=\frac{\% \text { abundance of } B^{11}}{2} \)


Four metallic plates each with a surface
area of one side \( A, \) are placed at a
distance \( d \) from each other. The two
outer plates are connected to one point
\( A \) and the two other inner plates to
another point \( B \) as shown in the figure.
Then the capacitance of the system is :
\( A \cdot \frac{\epsilon_{0} A}{d} \)
в. \( \frac{2 \epsilon_{0} A}{d} \)
c. \( \frac{3 \epsilon_{0} A}{d} \)
D. \( \frac{4 \epsilon_{6} A}{d} \)


How many X chromosomes are present in a female?
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


A proton is accelerating in a cyclotron where the applied magnetic field is \( 2 T \)
If the potential gap effectively \( 100 k V \) then how much revolutions the proton has to make between the "dees" to
acquire a kinetic energy of 20 MeV?
A . 100
в. 150
c. 200
D. 300


The equation of normal to the curve \( \boldsymbol{y}=\tan \boldsymbol{x} \) at the point \( (\boldsymbol{0}, \boldsymbol{0}) \) is
A. \( x+y=0 \)
В. \( x-y=0 \)
c. \( x+2 y=0 \)
D. None of these


Drug azidothymidine was isolated from plant and then synthesised in laboratory for treatment of which
disease?
A. AlDS
B. Parkinsons
c. cancer
D. Heart attack


How many of the following statements
are correct?
(i) Axillary buds are present in axil of leaflets
(ii) In Salvia filaments of stamens are
same length.
(iii) Apocarpous condition can be seen in lotus and rose.
(iv)Endospermous seeds can be seen in solanaceae.
(v) Sterile stamens are called
staminodes.
A. Three
B. Four
c. Two
D. one


A body is projected vertically upwards with a velocity u. After 1 and 7 s, it
crosses a reference point at a height \( h \) What is the value of u?
A \( .40 \mathrm{m} / \mathrm{s} \)
B. \( 50 \mathrm{m} / \mathrm{s} \)
c. \( 30 \mathrm{m} / \mathrm{s} \)
D. \( 20 \mathrm{m} / \mathrm{s} \)


The graph of \( f(x) \) is given below. Based
on this graph determine where the
function is discontinuous.


White phosphorus when boiled with strong solution of caustic soda
produces:
A. sodium phosphide
B. sodium phosphate
c. sodium hypophosphite
D. red phosphourus


correctly represents the ray of light
passing through the optical centre?
\( A \)
B.
\( c \)
D.


Genetic code consists of
A. 4 codons, each with two nucleotides
B. 16 codons, each with four nucleotides
C. 64 codons, each with two nucleotides
D. 64 codons, each with three nucleotides


The population \( p(t) \) a time \( t \) of a certain mouse species satisfies the differential equation \( \frac{\boldsymbol{d} \boldsymbol{p}(\boldsymbol{t})}{\boldsymbol{d} \boldsymbol{t}}=\frac{1}{2} \boldsymbol{p}(\boldsymbol{t})-\boldsymbol{4 5 0} \)
\( \boldsymbol{p}(\boldsymbol{0})=\mathbf{8 5 0}, \) then the time at which the
population becomes zero is:
A \( .2 ~ \ln 18 \)
B. \( \ln 9 \)
c. \( \frac{1}{2} \ln 18 \)
D. \( \ln 18 \)


Evaluate \( \int_{0}^{1} x^{4} d x \)


\begin{tabular}{lccccc}
Size & \( \boldsymbol{6} \) & \( \boldsymbol{7} \) & \( \boldsymbol{8} \) & \( \boldsymbol{9} \) & \( \boldsymbol{1 0} \) \\
No. of Shoes & 4 & 5 & 1 & 2 & 1 \\
\hline
\end{tabular} Find the mode
\( \mathbf{A} \cdot \mathbf{7} \)
\( B . \quad 8 \)
\( \mathbf{C} \cdot \mathbf{6} \)
D. 10


\( \ln L-C-R \operatorname{series} \) circuit, the
capacitor is changed from \( C \) to \( 4 C \). For
the same resonant frequency, the inductance should be changed from
\( \boldsymbol{L} \) to
A \( .2 L \)
в. \( \frac{L}{2} \)
c. \( \frac{L}{4} \)
D. \( 4 L \)


The range of \( \tan ^{-1} x \)
A \( \cdot(-\pi, \pi) \)
B.
D. \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \)


Propene and propyne can be distinguished by
A. \( B r_{2} / C C l_{4} \)
в. Bayer's Reagent
c. \( A g N O_{3}+N H_{4} O H \)
D. \( O_{3} \)


The mean deviation of a frequency dist. is equal to
A. \( \frac{\Sigma d_{i}}{\Sigma f_{i}} \)
в. \( \frac{\Sigma\left|d_{i}\right|}{\Sigma f_{i}} \)
c. \( \frac{\Sigma f_{i} d_{i}}{\Sigma f_{i}} \)
D. \( \frac{\Sigma f_{i} \mid d_{i}}{\Sigma f_{i}} \)


Assertion
Slime moulds are excellent material for
the study of protoplasm.
Reason

They lack cell organelles.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


Which of the following is not an
advantage of hydro energy?
A. Flowing water is found everywhere. So hydro energy can be obtained easily.
B. It is a renewable source of energy.
C. It do not cause any pollution.
D. All of the above.


If \( \frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\ldots . . \) upto \( \infty=\frac{\pi^{2}}{6} \)
then \( \frac{1}{1^{2}}+\frac{1}{3^{2}}+\frac{1}{5^{2}}+\ldots= \)
A \( \cdot \frac{\pi^{2}}{12} \)
в. \( \frac{\pi^{2}}{24} \)
c. \( \frac{\pi^{2}}{8} \)
D. \( \frac{\pi^{2}}{4} \)


Construct a triangle \( P Q R \) in which
\( \angle Q=30^{\circ}, \angle R=90^{\circ} \) and \( P Q+Q R+ \)
\( \boldsymbol{P R}=11 \mathrm{cm} \)


If \( f(x)=27 x^{3}+\frac{1}{x^{3}} \) and \( \alpha, \beta \) are the roots of \( \mathbf{3} \boldsymbol{x}+\frac{\mathbf{1}}{\boldsymbol{x}}=\mathbf{2} \) is
This question has multiple correct options
A \( . f(\alpha)=f(\beta) \)
В. \( f(\alpha)=10 \)
c. \( f(\beta)=-10 \)
D. none of these


Answer the following
The first term of an AP is -7 and the
common difference \( 5, \) Find its \( 18^{t h} \) term


Two spherical soap bubbles collapses. If \( V \) is the consequent change in volume of the contained air and \( S \) is the change
in the total surface area and \( T \) is the
surface tension of the soap solution,
then if relation between \( P_{0}, V, S \) and \( T \)
\( \operatorname{are} \lambda P_{0} V+4 S T=0, \) then find \( \lambda ?\left(\text { If } P_{0}\right. \)
is atmospheric pressure): Assume temperature of the air remain same in
all the bubbles.


n figure, OA and OB are opposite rays if
\( x=25^{\circ}, \) what is the value of \( y ? \)


Electric potential on the surface of a
hollow conducting sphere is V. The electric potential is \( \frac{V}{2} \) at a distance
A \( \cdot \frac{R}{2} \) inside the sphere
B. \( \frac{R}{2} \) from the surface of the sphere and outside it
C. \( 2 \mathrm{R} \) from the centre of the sphere
D. \( 2 \mathrm{R} \) from the surface of the sphere and outside it


Magnetic field due to a toroid inside its
turns is given by ( \( n \) is thenumber of
turns per unit length of the toroid and \( \boldsymbol{I} \) is the current in the loop)
\( \mathbf{A} \cdot B=\mu_{o} n I \)
В. \( B=\epsilon_{o} n I \)
\( \mathbf{c} \cdot B=\frac{\mu_{o}}{4 \pi} n I \)
D. None of these


Tyndall effect is observed when sunlight passes through canopy of a dense forest because:
A. in the forest, mist contains tiny droplets of water which act as particles of colloid dispersed in air
B. in the forest, smog, fog is present which contains droplets of water which act as particles of colloid dispersed in air
c. in the forest, trees leaves contains chloroplast which contains guard cells, which act as particles of colloid dispersed in air
D. all of the above


Why is not any one parameter good enough to demonstrate growth throughout the life of a flowering plant?


Living things interact with
constantly.
A. Organisms
B. Environment
c. Non-living things
D. None of the above


How is a Zener diode fabricated? What
causes the setting up of high electric field even for small reverse bias voltage
across the diode?
Describe, with the help of a circuit diagram, the working of Zener diode as
a voltage regulator.


The man-made objects which orbit the
Earth are:
A. Moon
B. U.F.O
c. Artificial satellites
D. Asteroids


Identify the reaction condition of \( \boldsymbol{P C l}_{3} \)
with water.
A. Reacts exothermically with water.
B. Reacts neutrally with water.
c. Reacts endothermically with water
D. None of these.


The value of determinant
\( \left|\begin{array}{ccc}\boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y} \\ \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y} & \boldsymbol{x} & \boldsymbol{x}+\boldsymbol{y} \\ \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{x}+\boldsymbol{2} \boldsymbol{y} & \boldsymbol{x}\end{array}\right| \) is:
A \( \cdot 9 x^{2}(x+y) \)
В \( \cdot 9 y^{2}(x+y) \)
c. \( 3 y^{2}(x+y) \)
D. \( 7 x^{2}(x+y) \)


Define absolute and relative growth
rates.


:For the reaction
\( C_{2} H_{4}(g)+3 O_{2}(g) \rightarrow 2 C O_{2}(g)+2 H_{2} O(l) \)
\( \Delta E=-1415 k J . \) The \( \Delta \mathrm{H} \) at \( 27^{0} \mathrm{C} \) is
\( \mathbf{A} \cdot-1410 k J \)
в. \( -1420 k J \)
\( \mathbf{c} .+1420 k J \)
D. \( +1410 k J \)


A particle of charge \( +q \) is at distance \( r \)
away from a charged flat surface and experiences a force of magnitude \( \boldsymbol{F} \) pulling it toward the surface. Find out the magnitude of the force exerted on the same particle if it is at a distance
\( 2 r \) from the surface?
A. \( (1 / 8) F \)
в. \( (1 / 4) F \)
c \( \cdot(1 / 2) F \)
D. \( F \)
E . \( 2 F \)


Differentiate between adolescence and
puberty


The value of \( \sin \left(2 \tan ^{-1}(1 / 3)\right)+ \)
\( \cos \left(\tan ^{-1} 2 \sqrt{2}\right) \) is
\( A \cdot 12 / 13 \)
B. \( 13 / 14 \)
c. \( 14 / 15 \)
D. none of these


Assertion
In tetrahedral hybridization ie. in \( s p^{3} \)
hybridization all p-orbitals are involved
and no p-orbital is left for forming \( \pi \) -
bonds.
Reason
Central atom can not form double bonds
in the molecules or species having \( s p^{3} \) hybridization.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.
c. Assertion is correct, but Reason is incorrect
D. Assertion is incorrect, but Reason is correct.


The value of \( \cos \left[\frac{1}{2} \cos ^{-1}\left(\cos \left(\frac{-14 \pi}{5}\right)\right)\right] \) is/are:
\( ^{\mathbf{A}} \cdot \cos \left(\frac{-7 \pi}{5}\right) \)
B・ \( \sin \left(\frac{\pi}{10}\right) \)
c. \( \cos \left(\frac{2 \pi}{5}\right) \)
D. \( -\cos \left(\frac{3 \pi}{5}\right) \)


Which process is related with
photosynthesis?
A. Phosphorylation
B. Translation
c. Transcription
D. None of the above


In class A amplifiers, current through
load flows for
A. full cycle of the signal
B. half cycle of the signal
c. \( \frac{1}{4} \) cycle of the signal
D. None of these


How as a scimilicic un raurus
\( a, \) is rotating about an axis \( P Q \) with a
constant angular velocity \( \omega=1 / \sqrt{L C} \)
with the help of an external agent. \( \mathbf{A} \)
uniform magnetic field \( B \) exists in
space and is directed into the plane of the figure. (circuit part remains at rest)
(left part is at rest)
This question has multiple correct options
A the rms value of current in the circuit is \( \frac{\pi B a^{2}}{R \sqrt{2 L C}} \)
B. The rms value of current in the circuit is \( \frac{\pi B a^{2}}{2 R \sqrt{2 L C}} \)
C. The maximum energy stored in the capacitor is \( \frac{\pi^{2} B^{2} a^{4}}{8 R^{2} C} \)
D. The maximum power delivered by the external agent is \( \frac{\pi^{2} B^{2} a^{4}}{4 L C R} \)


Which of the following is an electrophilic reagent?
A \( \cdot H_{2} O \)
в. \( O H^{-} \)
\( c \cdot N O_{2}^{+} \)
D. None


toppr
Q Type your question
the focal length away. Which of the following diagrams best
shows two correctly drawn light rays
originating from the top of the object that will enable us to locate the image? The light rays are solid blue. The dashed
blue lines help show direction
\( A \)
B.
\( c \)
\( D \)
\( E \)


Which one is a reptile?
A. Toadd
B. Salamander
c. Newt
D. Turtle


If \( \vec{u}, \vec{v} \) and \( \vec{w} \) are three non-coplanar vectors, then \( (\overrightarrow{\boldsymbol{u}}+\overrightarrow{\boldsymbol{v}}-\overrightarrow{\boldsymbol{w}}) \cdot(\overrightarrow{\boldsymbol{u}}-\overrightarrow{\boldsymbol{v}}) \times \)
\( (\vec{v}-\vec{w}) \) equals
A \( . \vec{u} .(\vec{v} \times \vec{w}) \)
B.
c. \( 2 \vec{u} \cdot(\vec{v} \times \vec{w}) \)
D. \( \vec{u} .(\vec{w} \times \vec{v}) \)


A box contains 6 red balls and 2 black
balls. Two balls are drawn at random
from it without replacement. if \( x \) denotes the number of red balls drawn, then find \( \boldsymbol{E}(\boldsymbol{x}) \)


Which of the following options is
INCORRECT?
\( \mathbf{A} \cdot \angle 1=\angle 3 \)
B . \( \angle 1+\angle 4+\angle 5=180^{\circ} \)
\( \mathbf{c} \cdot \angle 8=\angle 6 \)
D. \( \angle 1+\angle 3=180^{\circ} \)


The electric field in a region is given by \( \overrightarrow{\boldsymbol{E}}=\frac{\mathbf{3}}{\mathbf{5}} \boldsymbol{E}_{\boldsymbol{o}} \hat{\boldsymbol{i}}+\frac{\boldsymbol{4}}{\mathbf{5}} \boldsymbol{E}_{\boldsymbol{o}} \widehat{\boldsymbol{j}} \) with \( \boldsymbol{E}_{\boldsymbol{o}}=\boldsymbol{2} \boldsymbol{0} \times \mathbf{1 0}^{\boldsymbol{3}} \)
N/C. Find the flux of this field (in
\( \left.N m^{2} C^{-1}\right) \) through a rectangular
surface of area \( 0.2 \mathrm{m}^{2} \) parallel to the \( \mathrm{Y}-\mathrm{Z} \)
plane.


Statement 1: While balancing equations, same number of atoms are
there on reactant side and the product
side.

Statement 2: For all regular chemical
equations, the conservation of matter holds good.
A. Both the statements 1 and 2 are correct and statement 2 is not correct explanation of statement 1
B. Both the statements 1 and 2 are correct and statement 2 is correct explanation of statement 1
c. Statement 1 is correct but statement 2 is not correct.
D. Statement 1 is not correct but statement 2 is correct.
E. Both the statements 1 and 2 are not correct.


The process of giving a coating of to copper or brass is called tinning.
A. zinç
B. copper
\( c . \) tin
D. iron


The essential difference between AC
and DC generator is:
A. AC generator has an electromagnet while DC generator has permanent magnet.
B. DC generator will generate high voltage.
C. AC generator will generate high voltage.
D. AC generator has slip rings while DC generator has a commutator


Which of the following substances has the lowest pH-value?
A. Tomato
B. Vinegar
c. washing soda
D. Human blood


Evaluate the following \( \begin{array}{|ccc|}15 & 11 & 7 \\ 11 & 17 & 14 \\ 10 & 16 & 13\end{array} \)


Arrange the following decimal numbers in ascending order.
5.5,0.55,0.055,0.005
A. 5.5,0.055,0.005,0.55
В. 0.55,0.005,0.055,5.5
c. 5.5,0.55,0.055,0.005
D. 0.005,0.055,0.55,5.5


\( k_{p} \) for a reaction at \( 25^{0} C \) in 10 atm. Then
\( K_{c} \) for the reaction at \( 40^{0} C \) will be:
(Given \( : \Delta H=-8 k J \) and antilog
\( (0.067)=0.1167) \)
A \( \cdot 4.33 \times 10^{-1} M \)
В. \( 3.33 \times 10^{-2} M \)
\( \mathrm{c} \cdot 3.33 \times 10^{-1} \mathrm{M} \)
D. None of these


Oxidation number of \( S \) in \( \left(C H_{3}\right)_{2} S \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B. +1
\( c .-2 \)
D. +3


If the geometric mean of three
observations 40,50 and \( x \) is \( 10, \) then
the value of \( x \) is
A \( \cdot \frac{1}{2} \)
B. 4
\( c .6 \)
D.


A missile of mass \( M \) moving with velocity \( v=200 m / s \) explodes in midair
breaking into two parts of mass \( M / 4 \) and \( 3 M / 4 . \) If the smaller piece flies off
at an angle of \( 60^{\circ} \) with respect to the original direction of motion with an initial speed of \( 400 \mathrm{m} / \mathrm{s} \), what is the magnitude and direction of the initia
velocity of the other piece.


The area of the triangle formed by the
\( \operatorname{lines} y=a x, x+y-a=0 \) and the
\( y-a x i s \) is equal to
A \( \cdot \frac{1}{2|1+a|} \)
в. \( \frac{a^{2}}{|1+a|} \)
c. \( \frac{1}{2} \mid \frac{a}{1+a} \)
D. \( \frac{a^{2}}{2|1+a|} \)


Which gas is evolved when \( P b O_{2} \) is
treated with conc \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} ? \)
A \( . N O_{2} \)
в. \( O_{2} \)
c. \( N_{2} \)
D. \( N_{2} \) O


The solution of the equation \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}= \)
\( e^{x}+e^{-x} \) is -
Note : (where c \( \& \) d are arbitrary constants in the given options)
A \( \cdot y=e^{x}-e^{-x}+c x+d \)
B . \( y=e^{x}+e^{-x}+c x+d \)
c. \( y=-e^{x}+e^{-x}+c x+d \)
D. None of these


For given vectors, \( \vec{a}=2 \hat{i}-\hat{j}+2 \hat{k} \) and \( \vec{b}=-\hat{i}+\hat{j}-\hat{k}, \) find the unit vector in the direction of the vector \( \vec{a}+\vec{b} \)


In a circuit the coil of a choke:
A. Decreases the current
B. Increases the current
C. Has high resistance to D. C. circuit
D. No effect with the current


If \( f(x)=(x-a)^{2 n}(x-b)^{2 m+1} \)
where \( m \cdot n \in N, \) then
A. \( x=a \) is a point of minimum
B. \( x=a \) is a point of maximum
c. \( x=a \) is not a point of maximum or minimum
D. No value of k satisfies the requirement


Noble gas molecules are diatomic
A. True
B. False


Calcium hydroxide, \( C a(O H)_{2} \) has a
lower solubility in water than some of
the other Group II hydroxides \( \left(\boldsymbol{K}_{s p}=\right. \) \( 4.0 \times 10^{-6} \) at \( 25^{\circ} \mathrm{C} \) ). At this
temperature in a saturated solution of calcium hydroxide, determine the concentration of calcium ions?
A \( \cdot 2.0 \times 10^{-6} \)
B . \( 2.0 \times 10^{-3} \)
c. \( 1.0 \times 10^{-2} \)
D. \( 1.3 \times 10^{-2} \)
E \( .1 .6 \times 10^{-2} \)


State one function of the following. Intercostal muscles.


Identify which of the following best describe diffraction. Diffraction occurs
when they:
A. travel around an object or through an opening.
B. transition from one medium to another
c. bounce off the surface of an object
D. resonate with the molecules in a medium.
E. pass through a medium unchanged


Evaluate \( \int \frac{10 n^{9}+10^{n} \ln 10}{\sqrt{n^{10}+10^{n}+10^{10}}} d n \)


Which of the following is a correct name according to IUPAC conventions of the
given compound? This question has multiple correct options
A. 1,4 -dimethylcyclohex- - ene
B. 2, 3-dimethylcyclohexene
c. 1,5 -dimethylcyclohex- - -ene
D. 1, 6-dimethylcyclohex-1-ene


Scales are found in
A. Fishes
B. Reptiles
C. Both of A and B
D. None of the above


A sum of money invested at C.I. amounts to Rs. 800 in 3 years and to Rs.
840 in 4 years. The rate of interest per
annum is
A \( \cdot_{2} \frac{1}{2} \% \)
B . 4\%
c. \( 5 \% \)
D. \( 6 \frac{2}{3} \% \)


A sphere has the same volume as a cylinder whose height is equal to the diameter of its cross section then the
ratio of their radiii is
A \( \cdot \sqrt{\frac{2}{3}} \)
в. \( \sqrt{\frac{3}{2}} \)
D. \( \sqrt[3]{\frac{3}{2}} \)


Two balls are thrown simultaneously in air. The acceleration of the centre of
mass of the two balls while in air.
A. depends on the direction of the motion of the balls
B. depends on the masses of the two balls
c. depends on the speeds of the two balls
D. is equal to


A \( 5 \% \) solution (w/W) of cane sugar
(molar mass \( =342 g \) mol \( ^{-1} \) ) has
freezing point \( 271 K . \) What will be the freezing point of \( 5 \% \) glucose (molar mass \( =18 g \) mol \( ^{-1} \) ) in water if freezing
point of pure water is \( 273.15 K ? \)
\( \mathbf{A} \cdot 273.07 K \)
в. \( 269.07 K \)
c. \( 273.15 K \)
D. \( 260.09 K \)


Which of the following xenon compound has the same number of lone pairs on
central atom as in \( \boldsymbol{I}_{\mathbf{3}}^{-} \) ?
\( \mathbf{A} \cdot X e O_{4} \)
в. \( X e F_{4} \)
c. \( X e F_{2} \)
D. \( X e O_{3} \)


The following electrochemical cell has been set-up:
\( \boldsymbol{P t}(1) \mid \boldsymbol{F} e^{3+}, \boldsymbol{F} \boldsymbol{e}^{2+}(\boldsymbol{a}= \)
\( \mathbf{1})\left|\boldsymbol{C} \boldsymbol{e}^{\boldsymbol{4}+}, \boldsymbol{C} \boldsymbol{e}^{\boldsymbol{3}+}(\boldsymbol{a}=\mathbf{1})\right| \boldsymbol{P} \boldsymbol{t}(\boldsymbol{2}) \)
\( E^{0}\left(F e^{2+}, F e^{2+}\right)=0.77 \mathrm{V} \)
and \( \boldsymbol{E}^{0}\left(\boldsymbol{C} \boldsymbol{e}^{\boldsymbol{4}+}, \boldsymbol{C} \boldsymbol{e}^{\boldsymbol{3}+}\right)=1.61 \mathrm{V} \)
If an ammeter is connected between the
two platinum electrodes, predict the
direction of flow of current, will the
current increases or decreases with
time?


The scalar quantity among the following
is
A. weight of body
B. temperature gradient
c. elementary area
D. magnetic field strength


Verify \( \boldsymbol{a}-(-\boldsymbol{b})=\boldsymbol{a}+\boldsymbol{b} \) for \( \boldsymbol{a}= \)
\( \mathbf{1 3 1}, \boldsymbol{b}=\mathbf{1 5} \)


Chloroform is used:
A. As a general anesthetic.
B. As a solvent for fats and oils.
C. As a preservative for biological specimens.
D. All are correct.


IUPAC name is:
\[
\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{Cl}
\]
A. Allyl chloride
B. 1-Chloro-3-propene
c. 3 -chloro- - propene
D. vinyl chloride


A solid sphere is placed on a smooth
horizontal plane. A horizontal impluse \( I \) is applied at a distance \( h \) above the
central line as shown in the figure. Soon
after giving the impulse the sphere starts rolling.
The ratio \( h / R \) would be
A . 1 2
B. 2 5
\( c \cdot \frac{1}{4} \)
D. 1


Which of the following equations
represents reducing property of \( S O_{2} ? \)
A. \( 2 H_{2} S+S O_{2} \rightarrow 3 S+2 H_{2} O \)
B. 3 Fe \( +S O_{2} \rightarrow 2 F e O+F e S \)
c. \( K_{2} C r_{2} O_{7}+S O_{2}+H_{2} S O_{4} \rightarrow K_{2} S O_{4}+C r_{2}\left(S O_{4}\right)_{3}+ \)
\( H_{2} O \)
D. All of the above


In the expansion of \( \left(\sqrt[3]{4}+\frac{1}{\sqrt[4]{6}}\right)^{20} \)
This question has multiple correct options
A. the number of rational terms \( =4 \)
B. the number of irrational terms \( =19 \)
C. the middle term is irrational
D. the number of irrational terms \( =17 \)


Mass of an object on moon will be
A. One sixth of its value on earth
B. Ten times it's value on earth
c. six times it's value on earth
D. Same as on earth


\( \operatorname{Let} 2 y=\left(\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right)^{2} \)
then \( \frac{\boldsymbol{a} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) is equal to
A \( \cdot x-\frac{\pi}{6} \)
B. \( x+\frac{\pi}{6} \)
c. \( 2 x-\frac{\pi}{6} \)
D. \( 2 x-\frac{\pi}{3} \)


Two fixed charges \( -2 Q \) and \( Q \) are located at the points with coordinates \( (-3 a, 0) \) and \( (+3 a, 0), \) respectively, in the xy plane.
a. Show that all points in the xy plane
where the electric potential due to the
two charges is zero lie on a circle.Find its
radius and the location of its center.
b. Give the expression \( V(x) \) at a general point on the \( x \) -axis and sketch the
function \( V(x) \) on the whole \( x \) -axis.
c. If a particle of charge +q starts from rest at the center of the circle, show by a
short quantitative argument that the
particle eventually crosses the circle. Find its speed when it does so.


Th circular arc (in \( x-y \) plane) shown in
figure rotates (about \( z- \) axis ) with a
constant angular velocity \( \omega . \) Time in a
cycle for which there will be induced
emf in the loop is:
A \( \cdot \frac{\pi}{2 \omega} \)
B. \( \frac{\pi}{\omega} \)
c. \( \frac{2 \pi}{3 \omega} \)
D. \( \frac{3 \pi}{2 \omega} \)


Find general solution of the following equations:
\( \sin \theta=\frac{1}{2} ? \)


If \( x+y=4 \) and \( \frac{1}{x}+\frac{1}{y}=4, \) then the
value of \( x^{3}+y^{3} \) is
\( \mathbf{A} \cdot 52 \)
B. 64
\( c \cdot 4 \)
D. 25


A long rod of radius \( 1 \mathrm{cm} \) and length \( 2 \mathrm{m} \) which is fixed at one end is given a twist of 0.8 radian. The shear strain
developed will be :
A. 0.001 radians
B. 0.004 radians
c. 0.002 radians
D. 0.04 radians


What is common among amylase,
rennin and trypsin?
A. These are produced in stomach
B. These act at a pH lower than 7
C. These all are proteins
D. These all are proteolytic enzymes


A turn of radius \( 600 \mathrm{m} \) is banked for a vehicle of mass 200 kg going with a speed of 1800 kmh\( ^{-1} \). Determine the
banking angle of its path.


Two identical coherent sources of
wavelength \( \lambda \) are placed at \( (100 \lambda, 0) \) and \( (-50 \lambda, 0) \) respectively. A detector moves slowly from the origin to \( (50 \lambda, 0) \) along x-axis. The number of maxima and minima detected are, respectively [include origin and \( (50 \lambda, 0)] \)
A. 51 and 50
B. 101 and 100
c. 49 and 50
D. 50 and 49


Divide as directed.
\( 26 x y(x+5)(y-4) \div 13 x(y-4) \)


A body is allowed to fall on the ground
from a height \( h_{1} . \) If it is rebound to a
height \( h_{2} \) then the coefficient of
restitution is:
\( \mathbf{A} \cdot \frac{\mathrm{h}_{2}}{\mathrm{h}_{1}} \)
B. \( \sqrt{\frac{h_{2}}{h_{1}}} \)
\( \mathbf{c} \cdot \frac{h_{1}}{h_{2}} \)
D. \( \sqrt{\frac{\mathrm{h}_{1}}{\mathrm{h}_{2}}} \)


An astronaut,inside an earth's satellite
experiences weightlessness because
A. he is falling freely
c. no reaction is exerted by the floor of the satellite
D. he is far away from the earth's surface


Write the dispersed phase and dispersion medium of milk.


Hydrolysis of sucrose with dilute aqueous sulphuric acid yields:
\( \mathbf{A} \cdot 1: 1 \) of \( D-(+)- \) glucose \( ; D-(-)- \) fructose
B. 1: 2 of \( D-(+)- \) glucose; \( D-(-)- \) fructose
\( \mathbf{c} \cdot 1: 1 \) of \( D-(-)- \) glucose \( ; L-(+)- \) fructose
D. 1: 2 of \( D-(-)- \) glucose; \( D-(+)- \) fructose


An undifferentiated mesophyll is found
in
A. Isobilateral leaves
B. Dorsiventral mesophytic leaves
c. Dorsiventral xerophytic leaves
D. Vertical leaves


Show that \( f(x)=x^{9}+4 x^{7}+11 \) is an
increasing function for all \( \boldsymbol{x} \in \boldsymbol{R} \)


If we throw a dice, then the sample
space, \( S=1,2,3,4,5,6 . \) Now the event
of 3 appearing on the dice is simple and given by
A. \( E=2,3 \)
В. \( E=1,2,3 \)
c. \( E=3 \)
D. \( E=1,3 \)


A vehicle of mass \( m \) is driven along an un-banked curved path of radius of
curvature \( r \) with a speed \( v \). If \( \mu \) is necessary minimum coefficient of
friction between tyres of vehicle and road so that the vehicle does not skid,
then:
This question has multiple correct options
A \( \cdot \mu \propto v^{2} \)
B \( \cdot \mu \propto \frac{1}{v^{2}} \)
c. \( \mu \propto r \)
D. \( \mu \propto \frac{1}{r} \)


The chemicals used for
preparing acetophenone
are
A) \( C_{6} H_{6} \) B) \( C H_{3} C O O C H_{3} \)
3
C) \( C H_{3} C O C l \)
D) Anhydrous \( A l C l_{3} \)
\( A \cdot A, B, C \)
B. B,C,D
\( c \cdot A, C, D \)
D. A,B,D


The product of molar concentrations of hydrogen ions and hydroxide ions in a \( 0.01 M \) aqueous solution of sodium
chloride is known as
A. Hydrolysis constant of salt
B. Dissociation constant of acid
c. Dissociation constant of base
D. lonic product of water


In acetylene, there are
(two/four) \( \pi \) - bonding electrons
between carbon atoms.


Nickel shows ferromagnetic property at room temperature. If the temperature is increased beyond Curie temperature
then it will show
A. diamagnetism
B. paramagnetism
c. anti ferromagnetism
D. no magnetic property


Q Type your question-
She placed a lighted candle on one end
of a laboratory table, a screen on its other end and the lens in between the
two as shown in the figure. She
adjusted the positions of the three to
obtain a sharp image of the candle
flame on the screen.
Shoe now removes the candle flame and
obtains the image of a distant lamp on
an electric pole. She would be able to
get a sharp image of the lamp on the
screen by moving
A. the screen towards of the lens or the lens towards the screen
B. the screen towards of the lens or the lens away from the screen
c. the screen away from the lens or the lens towards the screen
D. neither the screen


How many terms of an arithmetic
progression must be taken for their
sum to be equal to \( 91, \) if its third term
is 9 and the difference between the
seventh and the second term is \( 20 ? \)


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{N} \boldsymbol{H}_{2} \) is soluble in:
This question has multiple correct options
A. dilute \( H C l \)
B. \( C u S O_{4} \) solution
\( \mathrm{c} . A g N O_{3} \)
D. none of these


Two liquids \( A \) and \( B \) form an ideal solution. At \( 300 \mathrm{K} \), the vapour pressure of a solution containing 1 mole of A and 3 mole of \( \mathrm{B} \) is \( 550 \mathrm{mm} \) of Hg. At the
same temperature, if one more mole of \( \mathrm{B} \) is added to this solution, the vapour pressure of the solution increases by 10 \( \mathrm{mm} \) of Hg. Determine the vapour pressure of \( A \) and \( B \) in their pure states.


A gas bubble of \( 2 \mathrm{cm} \) diameter rises
through a liquid of density \( 1.75 \mathrm{gm} \mathrm{cm}^{-3} \) with a fixed speed of \( 0.35 \mathrm{cm} s^{-1} \)
Neglect the density of the gas. The coefficient of viscosity of the liquid is:
A. 870 poise
B. 1120 poise
c. 982 poise
D. 1089 poise


Water flows out of a pipe and hits a wall. When the jet of water hits the wall, it has horizontal velocity v and crosssectional area A. The density of the water is \( \rho . \) The water does not rebound
from the wall. What is the force exerted
on the ball by the water?
A. \( \frac{\rho v}{A} \)
в. \( \frac{p v^{2}}{A} \)
\( c \cdot \rho A v \)
D \( \cdot \rho A v^{2} \)


For the fast chain reaction, the size of
\( U^{235} \) block, as compared to its critical size, must be
A. greater
B. smaller
c. same
D. anything


Carnivorous animals use these teeth to
tear flesh.
A. Incisors
B. Canines
c. Premolars
D. Molars