A block of mass \( 15 \mathrm{kg} \) is resting on a rough inclined plane as shown in figure The block is tied up by a horizontal string
which has a tension of 50N. Calculate the
coefficient of friction between the block
and inclined plane.


Find the arguments of each of the complex numbers.
1. \( \boldsymbol{z}=-\mathbf{1}-\boldsymbol{i} \sqrt{\mathbf{3}} \)
2. \( z=-\sqrt{3}+i \)
3. \( \boldsymbol{z}=\mathbf{1}+\boldsymbol{i} \sqrt{\mathbf{3}} \)


Anaphase differs from metaphase in
having
A. Same number of chromosomes and half number of chromatids
B. Half number of chromosomes and half number of
chromatids
C. Half number of chromosomes and same number of
chromatids
D. Same number of chromosomes and same number of
chromatids


A charged oil drop is moving downward
with a velocity \( V_{1} . \) As it acquires an
additional charge it moves up with the velocity \( V_{2} \) in the same electric field. It
fall freely with a velocity \( V \) in the absence of electric field. The ratio of the
charges before and after acquiring additional charge is
A. \( \frac{V_{1}+V}{V_{2}-V_{1}} \)
B. \( \frac{V_{1}+V_{2}}{2 V} \)
c. \( \frac{V-V_{1}}{V+V_{2}} \)
D. \( \frac{V_{2}-2 V_{1}}{2 V_{1}+V} \)


The soap molecule has a:
A. hydrophilic head and a hydrophobic tail
B. hydrophobic head and a hydrophilic tail
C. hydrophobic head and hydrophobic tail
D. hydrophilic head and a hydrophilic tail


(a) Explain the following.
(i) Roasting
(ii) Calcination.
(b) What are amphoteric oxides? Write the name of such one oxide.
(c) By which two metals is brass alloy formed?


Which of the following processes keeps the plant cool?
A. Photosynthesis
B. Transpiration
c. Respiration
D. Translocation


How is it that ionic compounds in the solid state do not conduct electricity and they do so when in molten state?


\( \int x \cos ^{2} 2 x d x \)


Which of the following has lowest boiling point?
A \( \cdot \mathrm{H}_{2} \mathrm{O} \)
в. \( \mathrm{H}_{2} \mathrm{s} \)
c. \( \mathrm{H}_{2} \mathrm{Se} \)
D. \( \mathrm{H}_{2} \mathrm{Te} \)


Which is correct with respect to 'p' orbitals?
A. They are spherical
B. They have a strong directional character
c. They are five fold degenerate
D. They have no directional character


The neutral temperature of a
thermocouple is \( 275^{\circ} \mathrm{C} \) and the
temperature of inversion is \( 600^{\circ} \mathrm{C} \). The
temperature of the cold junction is
\( A \cdot 50^{\circ} C \)
B . \( 25^{\circ} \mathrm{C} \)
\( c \cdot-25^{\circ} C \)
D. \( -50^{\circ} \mathrm{C} \)


Condensed structural formula of
propane is:
A. \( C H_{3}-C H_{2}-C H_{3} \)
в. \( C H_{2}-C H_{3}-C H_{3} \)
c. \( C H_{2}-C H_{4}-C H_{2} \)
D. none of the above


The principal argument of
\( \sqrt{2}\left[\cos \frac{5 \pi}{3}+i \sin \frac{5 \pi}{3}\right] \) is
A \( \cdot \frac{5 \pi}{3} \)
B. \( \frac{\pi}{3} \)
\( c \cdot-\frac{\pi}{3} \)
D. \( -\frac{\pi}{2} \)


If \( u, v, w \) are non-coplanar vector and
\( \boldsymbol{p}, \boldsymbol{q} \) are real numbers, then the equality \( [\mathbf{3 u} \boldsymbol{p v} \boldsymbol{p w}]-[\boldsymbol{p v} \boldsymbol{w} \boldsymbol{q} \boldsymbol{w}]-[\mathbf{2 w} \boldsymbol{q} \boldsymbol{v} \boldsymbol{q} \boldsymbol{u}]= \)
\( \mathbf{0} \) holds for
A. Exactly two values of \( (p, q) \)
B. More than but not all values of \( (p, q) \)
c. All values of \( (p, q) \)
D. Exactly one values of \( (p, q) \)


The mass of an atom resides in :
A. nucleus
B. protons
c. electrons
D. all of the above


Integrate the rational function \( \frac{2 x}{\left(x^{2}+1\right)\left(x^{2}+3\right)} \)


In a harbor, wind is blowing at the speed of \( 72 \mathrm{km} / \mathrm{h} \) and the flag on the mast of a boat anchored in the harbor flutters
along the N-E direction. If the boat starts moving at as speed of \( 51 \mathrm{km} / \mathrm{h} \) to the north, what is the direction of the
flag on the mast of the boat?


Members of hominidae are
A. Man, Lemur, Ape
B. Man, Chimpanzee, Gorilla
C. Monkey, Ape, Lemur
D. Chimpanzee, Lemur, Ape


Assertion
Acraniata is a group of organisms which do not have distinct cranium.
Reason
It includes small marine forms without
head
A. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
B. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
c. If the assertion is true but the reason is false
D. If both the assertion and reason are false


Choose incorrect statement about
photosynthesis.
A. It is a physico- chemical process
B. Oxygen is evolved as a by product in all photosynthetic organisms
C. Occurs in unicellular and multicellular
photoautotrophs
D. Anabolic and reductive process


If \( A \) and \( B \) are two perpendicular vectors given by \( \bar{A}=5 \bar{i}+7 \bar{j}+3 \bar{k}, \) and \( 4 \bar{B}= \)
\( 2 \bar{i}+2 \bar{j}+c \bar{k}, \) then the value of \( c \) is:
\( A \cdot-2 \)
B. 8
\( c .-7 \)
\( D \cdot-8 \)


The \( \left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right]^{3-} \) complex ion:
A. exhibits planar geometry
B. is diamagnetic
c. should be very stable
D. has 2 unpaired electrons


Assertion
Projectile motion is called a two dimensional motion, although it takes
place in space.
Reason
In space it takes place in a plane.
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 is incorrect but Reason is correct.


If the length and area of cross-section of a conductor are doubled, then its
resistance will be
A. unchanged
B. halvedd
c. doubled
D. quadrupled


\( 24 \mathrm{J} \) of heat are added to a gas in a container, and then the gas does 6 J of work on the walls of the container. What
is the change in internal energy for the gas?
A . - 30
B . - 18 J
c. 4 J
D. 18 J
E. 30


A postage stamp is \( 12 \mathrm{mm} \) in breadth and \( 20 \mathrm{mm} \) in length. Find the area of
\( \operatorname{stamp} \operatorname{in} c m^{2} \)
A . 0.24
в. 240
c. 24
D. 2.4


If two resistors of resistance \( 30 \Omega \) and
\( 40 \Omega \) are connected in parallel across a battery. The ratio of the potential difference across them is
A . 1: 1
B . 2: 1
\( c .3: 4 \)
D. 4: 3


The arm PQ can revolve with uniform
speed continuously about P round the
circular uniform potentiometer track
XYZ. The voltage between RS will vary
with respect to time:
A. sinusoidally
B. Linearly
c. Rectangularly
D. Like saw tooth


A concave lens of focal length \( 5 \mathrm{cm} \) is used as a simple microscope. The image is formed at the least distance of
distinct vision. Calculated the angular magnification.
\( A \cdot 6 \)
B. 5
\( c \cdot 0.5 \)
D. 4


Find the integral value of \( x, \) if \( \left|\begin{array}{ccc}\boldsymbol{x}^{2} & \boldsymbol{x} & \mathbf{1} \\ \mathbf{0} & \boldsymbol{2} & \mathbf{1} \\ \boldsymbol{3} & \boldsymbol{1} & \boldsymbol{4}\end{array}\right|=\mathbf{2} \mathbf{8} \)


Four forces act on a point object. The
object will be in equilibrium, if:
A. all of them are in the same plane
B. they are opposite to each other in pairs
C. the sum of \( x, y \) and \( z \) - components of forces zero separately
D. they form a closed figure of 4 sides when added as Polygon law


Dinoflagellates are called as fire algae due to which character?
A. They appear like fire due to pigments
B. They produce fire due to friction
c. They occur on burnt places
D. They show bioluminiscence


Which of the following \( x \& y \) are in
inverse proportion?
A \( \cdot \frac{x}{y}=K \)
в. \( x+y=K \)
c. \( x-y=K \)
D. \( x y=K \)


Equal masses of hydrogen gas and oxygen gas are placed in a closed
container at a pressure of \( 3.4 a t m . \) The
contribution of hydrogen gas to the total
pressure is:
A . \( 1.7 a t m \)
B. \( 0.2 a t m \)
c. \( 3.2 a t m \)
D. 3.02atm


The arrow with a pointed tip can move faster in air than that of with a blunt tip.
A. True
B. False
c. Ambiguous
D. Data insufficient


What is the boiling point of \( \boldsymbol{P C l}_{3} \) ?
\( \mathbf{A} \cdot-93.6^{\circ} \mathrm{C} \)
B . \( 169^{\circ} \mathrm{C} \)
c. \( 100^{\circ} \mathrm{C} \)
D. \( 76.1^{\circ} \mathrm{C} \)


The tension in the upper portion of the
chain is equal to:
\( \mathbf{A} \cdot 100 N \)
B. 120
c. 160
D. 240


Find the time dependence of the velocity
\( \overrightarrow{\boldsymbol{v}} \) vector.
A \( . \vec{v}=2 a \vec{i}-b t \vec{j} \)
B . \( \vec{v}=-2 a \vec{i}-2 b t \vec{j} \)
C \( . \vec{v}=-2 a \vec{i}-b t \vec{j} \)
D. \( \vec{v}=a \vec{i}-2 b t \vec{j} \)


Which of the following is not a category?
A. species
B. Class
c. Phylum
D. Glumaceae


The principle of conservation of linear momentum can be strictly applied during a collision between two particles provided the time of impact is
A. Extremely small
B. Moderately small
C. Extremely large
D. Depends on a particular case


Isotopes of cobalt \( \ldots \) used in the
treatment of cancer
A. \( C o-59 \)
в. \( C o-60 \)
c. \( C o-61 \)
D. \( C o-62 \)


Boron can not form more than 4 bonds
because:
This question has multiple correct options
A. of unavailability of d-orbitals
B. of unavailabilty of empty p-orbitals
C. Boron is so smaller
D. it does not have more valence electrons


Two metallic spheres of radii \( 1 \mathrm{cm} \) and
\( 3 c m \) are given charges of \( -1 \times 10^{-2} C \)
and \( 5 \times 10^{-2} C, \) respectively. If these are
connected by a conducting wire, the final charge on the bigger sphere is-
A \( \cdot 3 \times 10^{-2} \mathrm{C} \)
B. \( 4 \times 10^{-2} \mathrm{C} \)
c. \( 1 \times 10^{-2} C \)
D. \( 2 \times 10^{-2} C \)


Which of the following is not formed during anaerobic respiration?
A. Pyruvate
B. Ethyl alcohol
\( c \cdot c O_{2} \)
D. Acetyl CoA


Short / Long answer type questions. Why is osmotic potential given a negative sign?


Write balanced net ionic equation for the following reactions in acidic solution:
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \boldsymbol{N} \boldsymbol{O}_{3}^{-}+\boldsymbol{N} \boldsymbol{O}(\boldsymbol{g}) \)
A \( \cdot H N O_{2}(a q) \rightarrow H N O_{3}^{-}+2 N O(g)+H_{2} O \)
B \( \cdot 2 H N O_{2}(a q) \rightarrow 2 H N O_{3}^{-}+2 N O(g)+2 H_{2} O \)
\( \mathrm{c} \cdot 3 \mathrm{HNO}_{2}(a q) \rightarrow \mathrm{NO}_{3}^{-}+2 \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}+\mathrm{H}^{+} \)
D. None of the above


Evaluate the integral \( \int_{0}^{1} x^{2} e^{x} d x \)
\( \mathbf{A} \cdot e-2 \)
B. \( e+2 \)
\( c \)
D. \( e+3 \)


The effective atomic number of Mn,in
\( M n_{2}(C O)_{10} \) is
A . 36
B. 38
\( c \cdot 32 \)
D. 34


Which of the following statements are
incorrect about receptor proteins?
This question has multiple correct options
A. Majority of receptor proteins are embedded in the cell membranes
B. The active site of receptor proteins opens on the inside region of the cell
C. Chemical messengers are received at the binding sites of receptor proteins
D. Shape of receptor doesn't change during attachment of massenger


An alkali is titrated against an acid
with methyl orange as indicator, which of the following is a correct combination
\( ? \)
A. Base - Weak, Acid - Strong, End point- Yellow to pinkish red
B. Base - Strong, Acid - Strong, End point - Pink to colourless
c. Base - weak, Acid - Strong, End point- - Colourless to pink
D. Base - strong, Acid- Strong, End point - Pinkish red to yellow


Which of the following is a correct statement about probability?
A. It must have a value between -1 and 1
B. It is the collection of multiple experiments
c. Result can be in the form of decimal or negative
D. The probability of an event will not be less than 0


Copper has one conduction electron per atom. Its density is \( 8.89 g / m^{3} \) and its
atomic mass is \( 63.54 \mathrm{g} / \mathrm{mol} \). If a copper wire of diameter \( 1.0 \mathrm{mm} \) carries a current
of 2.0 A. What is the drift speed of the electrons in the wire?
A \( \cdot 1.9 \times 10^{-4} \)
В. \( 2.9 \times 10^{-4} \)
\( \mathbf{c} \cdot 1.9 \times 10^{4} \)
D. \( 2.9 \times 10^{4} \)


The alkali metals dissolve in liquid
\( N H_{3}, \) it is found that:
A. the dilute solution is blue but the color changes to bronze with increasing concentration
B. the blue color is due to presence of solvated electrons
c. the blue solutions are paramagnetic but the bronze colored solutions are diamagnetic
D. all the facts given above are found


In the Newton's rings set up, when a drop of water is introduced between the
glass plate and planoconvex lens the observed ring system
A. Contracts
B. Expands
c. Remains the same
D. Expands and then contracts


How do you account for the reducing
behaviour of \( H_{3} P O_{2} \) on the basis of its
structure ?


Atomic masses of isotopes of carbon
\( 6 C^{12} \) ) having neutrons 7 and 8 respectively are :
A. 14,15
B. 15,16
c. 16,17
D. 13,14


Which of the following belongs to the class of inferior planets?
A. Mercury
B. Venus
c. Pluto
D. Saturn


\( \boldsymbol{x}=\mathbf{0 . 5 0 0 m}, \boldsymbol{y}=\mathbf{0}, \boldsymbol{z}=\mathbf{0} \)


Choline is present in


ff \( f(x)=x^{2}+2 x-1, \) find \( f(2) \)
\( A \cdot 3 \)
B. 5
\( c \cdot 7 \)
D.


The order of Gymnosperm represented by a single living genera is
A. Gnetales
B. Coniferales
c. cycadales
D. Ginkgoales


\( N-O \) bond length in \( N_{2} O_{4} \) is greater
than expected due to charge repulsion.
A. True
B. False


Assertion
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{6}\right]^{3+} \) is strongly paramagnetic
whereas \( \left[\boldsymbol{F e}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{3-} \) is weakly
paramagnetic.
Reason
\( \boldsymbol{H}_{2} \boldsymbol{O} \) is a week field ligand and \( \boldsymbol{C} \boldsymbol{N}^{-} \) is
a strong field ligand.
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


Find \( S_{n}, \) the sum of the first \( n \) terms, for
the following geometric series. \( a_{1}= \)
\( \mathbf{1 2 0}, \boldsymbol{a}_{5}=\mathbf{1}, \boldsymbol{r}=-\mathbf{2} \)
A .20 .66
B. 40.66
c. 80.66
D. 100.66


Solve \( 4 x+\frac{6}{y}=15 \) and \( 6 x-\frac{8}{y}=14 \)
and hence find 'p', if \( \boldsymbol{y}=\boldsymbol{p} \boldsymbol{x}-\boldsymbol{2} \)


Which of the following is employed in
flash tubes in photography? This question has multiple correct options
A . \( A r \)
в. \( N e \)
\( c . K r \)
D. \( x e \)


What is the ratio of the areas of two
similar triangles whose corresponding sides are in the ratio \( 15: 19 ? \)
A. \( \sqrt{15}: \sqrt{19} \)
B. 15: 19
c. 225: 361
D. 125: 144


Match column I with column II.


Which of the following is the path difference for destructive interference?
A. \( n(\lambda+1) \)
B. \( (2 n+1) \frac{\lambda}{2} \)
c. \( n \lambda \)
D. \( (n+1) \frac{\lambda}{2} \)


Atomic weight of which set of elements were corrected by Mendeleev?
A. \( L i, N a, K \)
в. \( U, \)Ве \( , \) In
c. \( T c, S c, A l \)
D. None of the these


\( \operatorname{Gas}(\boldsymbol{A})+\boldsymbol{N a O H} \rightarrow \boldsymbol{B} \stackrel{\boldsymbol{A}^{+}}{\rightarrow} \boldsymbol{C} \stackrel{\boldsymbol{H}^{+}}{\rightarrow} \boldsymbol{D} \)
\( C \) and \( D \) decolorises acidified \( K M n O_{4} \) Identify \( C \) and \( D \)
A \( \cdot N a_{2} C O_{3}, N a O H \)
в. \( (C O O H)_{2},(C O O N a)_{2} \)
c. \( (C O O N a)_{2},(C O O H)_{2} \)
D. None of the above


A ball of mass \( 1 \mathrm{kg} \) is dropped from a height of \( 5 \mathrm{m} \) find
(i) K.E. of the ball as it is \( \frac{1}{2} \) way to the
ground.
(ii) Find P.E. at this instant.


Water is being pumped out through a circular pipe whose internal diameter \( 7 \mathrm{cm} . \) If the flow of water is \( 72 \mathrm{cm} \) per
second, how many liters of water are being pumped out in one hour?


The following configuration of gates is equivalent to
A. xon
B. NAND
\( c . \) ок
D. None of these


The force between two parallel
conductors, each of length \( 50 m \) and
distant \( 20 \mathrm{cm} \) apart, is \( 1 \mathrm{N} \). If the
current in one conductor is double than
that in another one, then their values
will respectively be:
\( \mathbf{A} \cdot 100 A \) and \( 200 A \)
B. \( 50 A \) and \( 400 A \)
c. \( 10 A \) and \( 30 A \)
D. \( 5 A \) and \( 25 A \)


We cannot see the oxygen that we breathe. It is freely available in the air, from which it is obtained for industrial
purposes by liquifying it. Liquid oxygen:
A. is blue in colour
B. looks like water
c. is invisible, like oxygen in the air
D. is opaque


Assertion
\( P b C l_{2} \) is more stable than \( P b C l_{4} \)
Reason
Pb \( C l_{4} \) is a powerful oxidising agent
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 reactions \( \boldsymbol{P C l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P C l}_{3}(\boldsymbol{g})+ \)
\( C l_{2}(g) \) and \( C O C l_{2}(g) \rightleftharpoons C O(g)+ \)
\( C l_{2}(g) \) are simultaneously in
equilibrium in an equilibrium box at constant volume. A few moles of \( C O(g) \) are later introduced into the vessel.
After some time, the new equilibrium concentration of
A. \( P C l_{5} \) will remain unchanged
B. \( C l_{2} \) will be greater
c. \( P C l_{5} \) will become less
D. \( P C l_{5} \) will become greater


Write the chemical reactions of
\( C_{2} H_{5} O H \) with \( P C l_{3} \) and \( P C l_{5} \)
separately


If the extremities of the base of an
isosceles triangle are the points \( (2 a, 0) \) and \( (0, a), \) and the equation of one of the sides is \( x=2 a \), then the area of the
triangle is
A. \( 5 a^{2} \) squnits
в. \( \frac{5 a^{2}}{2} \) sq.units
c. \( \frac{25 a^{2}}{2} \) sq.units
D. None of these


\( \left|\begin{array}{ccc}1+\sin ^{2} \theta & \sin ^{2} \theta & \sin ^{2} \theta \\ \cos ^{2} \theta & 1+\cos ^{2} \theta & \cos ^{2} \theta \\ 4 \sin 4 \theta & 4 \sin 4 \theta & 1+4 \sin 4 \theta\end{array}\right|= \)
\( 0, \) then \( \sin 4 \theta \) equals to
A. \( 1 / 2 \)
B.
\( c \cdot-1 / 2 \)
D. -1


n a coil of resistance \( 100 \Omega \), a current
is induced by changing the magnetic flux through it as shown in the figure.
The magnitude of change in flux through the coil is:
A \( .275 \mathrm{Wb} \)
В. \( 200 \mathrm{Wb} \)
\( c .225 W b \)
D. \( 250 \mathrm{Wb} \)


Generally pi bond is formed from the lateral overlap of:
A. \( s-s \) orbitals
B. \( p-p \) orbital
c. \( d-d \) orbitals
D. both \( B \) and \( C \)


Sitting in her parlour one night, Chitra sees the reflection of her cat in the
living room window. If the image of her
cat makes an angle of \( 40^{\circ} \) with the
normal, at what angle does Chitra see the reflected image of the cat?


A body of mass \( 2 k g \) is sliding with a
constant velocity of \( 4 m / s \) on a
frictionless horizontal table. The net
force required to keep the body moving with the same velocity is
A. \( 8 N \)
в. \( 0 N \)
c. \( 4 N \)
D. \( \frac{1}{2} N \)


Prove that \( \frac{1}{\sin 10^{\circ}}-\frac{\sqrt{3}}{\cos 10^{\circ}}=4 \)


A light ray Incidents normally on the
face of \( A B \) of a right angled prism \( A B C \). Prism is made of a material having
refractive index of \( \mu=1.5 \) as shown in
the figure. What is the largest angle \( \theta \)
for which light is totally reflected at the
surface AC?
A \( \cdot \sin ^{-1}\left(\frac{2}{3}\right) \)
B. \( \cos ^{-1}\left(\frac{2}{3}\right) \)
c. \( \sin ^{-1}\left(\frac{3}{4}\right) \)
D \( \cos ^{-1}\left(\frac{3}{4}\right) \)


Why does the school bags have broad shoulder straps?
A. To increase pressure
B. To decrease pressure
c. As a fashion trend
D. None of the above


\[
f(x)=\left\{\begin{array}{ll}
\frac{1-\sin ^{2} x}{3 \cos ^{2} x}, & x<\frac{\pi}{2} \\
a, & x=\frac{\pi}{2} \\
\frac{b(1-\sin x)}{(\pi-2 x)^{2}} & x>\frac{\pi}{2}
\end{array}\right.
\]
then \( f(x) \) is continuous at \( x=\frac{\pi}{2} \)


An isotone of \( _{32}^{76} \) Ge is:
A \( \cdot \frac{77}{32} \mathrm{Ge} \)
B. 家
\( A s \)
\( \mathrm{c} \cdot \frac{77}{34} \mathrm{Se} \)


Three copper wires of lengths and cross sectional areas are \( (l, A)\left(2 l, \frac{A}{2}\right) \) and \( \left(\frac{l}{2}, 2 A\right) . \) Resistance is minimum in
A \( \cdot \) wire of cross-sectional area \( \frac{A}{2} \)
B. wire of cross-sectional area \( A \)
c. wire of cross-sectional area \( 2 A \)
D. same in all the three cases


The image of the point \( \boldsymbol{P}(\boldsymbol{\alpha}, \boldsymbol{\beta}, \gamma) \) by
the plane \( l x+m y+n z=0 \) is the point \( \boldsymbol{Q}\left(\boldsymbol{\alpha}^{\prime}, \boldsymbol{\beta}^{\prime}, \boldsymbol{\gamma}^{\prime}\right) . \) Then
A \( \cdot \alpha^{2}+\beta^{2}+\gamma^{2}=l^{2}+m^{2}+n^{2} \)
B . \( \alpha^{2}+\beta^{2}+\gamma^{2}=\alpha^{2}+\beta^{2}+\gamma^{2} \)
\( \mathbf{c} \cdot \alpha \alpha^{\prime}+\beta \beta^{\prime}+\gamma \gamma^{\prime}=0 \)
D \( \cdot l\left(\alpha-\alpha^{\prime}\right)+m\left(\beta-\beta^{\prime}\right)+n\left(\gamma-\gamma^{\prime}\right)=0 \)


One diagonal of a square is along the
line \( 8 x-15 y=0 \) and one of its
vertices is \( (1,2) . \) Then the equations of the sides of the square passing through this vertex are
A \( .23 x+7 y=9,7 x+23 y=53 \)
в. \( 23 x-7 y+9=0,7 x+23 y+53=0 \)
c. \( 23 x-7 y-9=0,7 x+23 y-53=0 \)
D. None of these


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


If \( z_{1}, z_{2}, z_{3} \) be three unimodular complex
numbers then \( \boldsymbol{E}=\left|\boldsymbol{z}_{1}-\boldsymbol{z}_{2}\right|^{2}+ \)
\( \left|z_{2}-z_{3}\right|^{2}+\left|z_{3}-z_{1}\right|^{2} \) then cannot
exceed
\( A \cdot 6 \)
B.
\( c \cdot 12 \)
D. none


Let \( \boldsymbol{d} \in \boldsymbol{R}, \) and \( \boldsymbol{A}= \)
\( \left[\begin{array}{ccc}-2 & 4+d & (\sin \theta)-2 \\ 1 & (\sin \theta)+2 & d \\ 5 & (2 \sin \theta)-d & (-\sin \theta)+2+2 d\end{array}\right. \)
\( \boldsymbol{\theta} \in[\mathbf{0}, \mathbf{2} \boldsymbol{\pi}] . \) If the minimum value of
\( \operatorname{det}(A) \) is \( 8, \) then a value of d is?
A . -7
B. \( 2(\sqrt{2}+2) \)
\( c .-5 \)
D. \( 2(\sqrt{2}+1) \)


A ball rebounds after colliding with the
floor, then in case of inelastic collision:
A. The momentum of the ball before and after collision is
same
B. The mechanical of the ball before and after collision is
same
c. The total momentum of the earth-ball system is conserved
D. The total kinetic energy of earth and ball is conserved


Two identical metal spheres \( A \) and \( B \)
placed in contact are supported on insulating stand. What kind of charge will \( A \) and \( B \) develop when a negatively
charged ebonite rod is brought near \( A \) ?


A fixed volume of iron is drawn into a wire of length \( 1 . \) The extension produced in this wire by a constant force F is proportional to then:-
A \( \cdot \frac{1}{l^{2}} \)
B. \( \frac{1}{l} \)
\( c \cdot l^{2} \)
\( D \)


limiting factor for growth of aquatic organisms is
\( A \cdot C O_{2} \)
в. \( O_{2} \)
c. Mineral elements
D. All of the above


A solenoid having an iron core has its
terminals connected across an ideal DC
source and it is in steady state. If the
iron core is removed, the current flowing
through the solenoid just after removal
of rod.
A . increases
B. decreases
c. remains unchanged
D. nothing can be said


The pH of a \( 10^{-8} M \) solution of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) would be:
A . 4.00
B. 6.96
c. 8.54
D. 12.70


The general equation of plane which is
parallel to x-axis is
\( \mathbf{A} \cdot a x+b y+c z+d=0, a \neq 0, b \neq 0, c \neq 0 \)
B. \( b y+a x+d=0, a \neq 0, b \neq 0 \)
c. \( a x+c z+d=0, a \neq 0 . c \neq 0 \)
D. \( b y+c z+d=0, b \neq 0, c \neq 0 \)


Which of the points \( A, B, C \) and \( D \) below has the coordinates of the origin?
\( A \cdot A(-3,1) \)
B. B(0, 0)
c. \( c(1,2) \)
D. D(9, o)


Ketones show
A. metamerism
B. position isomerism
C. structural isomerism
D. functional group isomerism


Detergents are sodium salts of a long chain:
A. benzene sulphonic acids
B. alkyl hydrogen sulphate
c. both \( A \) and \( B \)
D. none of the above


The condition for the points \( (x, y),(-2,2) \) and (3,1) to be collinear is
A. \( x+5 y=8 \)
B. x+5y=6
c. \( 5 x+y=8 \)
D. 5x+y=6


\( F e S O_{4} \) is a very good absorber for \( N O \)
the new compound formed by this process is found to contain unpaired electrons.
\( A \cdot 4 \)
B. 5
\( c \cdot 3 \)
\( D \)


Find the distance between \( \boldsymbol{P}\left(\boldsymbol{x}_{1}, \boldsymbol{y}_{1}\right) \)
and \( Q\left(x_{2}, y_{2}\right) \) when PQ is parallel to the
y-axis.


A chord of length \( 16 \mathrm{cm} \) is drawn in a
circle of radius \( 10 \mathrm{cm} . \) The distance of
the chord from the centre of the circle is
\( A \cdot 8 \mathrm{cm} \)
B. \( 12 \mathrm{cm} \)
\( c \cdot 6 c m \)
D. \( 10 \mathrm{cm} \)


State the speed of sound in air.
A \( \cdot 330 k m s^{-1} \)
B. \( 330 \mathrm{cms}^{-1} \)
c. \( 330 m s^{-1} \)
D. \( 330 \mathrm{mms}^{-1} \)


A ball is dropped from a balloon going up at a speed of \( 7 \mathrm{m} / \mathrm{s} \). If the balloon was
at a height of \( 60 \mathrm{m} \) at the time of dropping the ball, how long will the ball take in reaching the ground?


When \( M g_{3} N_{2} \) react with \( H_{2} O, \) then how many type of gaseous product(s) is/are formed ?


The human eye can focus objects at different distances by adjusting the focal length of the eye.
This is due to:
A. Presbyopia
B. Accommodation
c. Near-sightedness
D. Far-sightedness


Total surface area of a cube is \( 54 \mathrm{cm}^{2} \)
Then its side is
\( \mathbf{A} \cdot \mathbf{6} \)
B. 9
c. 12
D. 3


A light body moving at some speed collides with a heavier body. Which of
the following statements is true?
I. Heavier body applies a greater impulse on the lighter body.
II. The lighter body experiences a greater change of momentum.
III. Acceleration of the lighter body will
be more than the acceleration of the
heavier body.
A. I and II only
B. II only
C. III only
D. II and III only
E . ।, II, and III


Position -time(x-t) grapg of a particle
moving along \( x \) -axis is as shown in the figure.The average speed of particle in
time interval \( t=0 \) to \( t=10 s \) is
\( \mathbf{A} \cdot 2 m s^{-1} \)
в. \( \frac{4}{5}^{m s^{-1}} \)
\( \mathbf{c} \cdot 1 m s^{-1} \)
D. \( \frac{5}{4} m s^{-} \)


Assertion
In the Contact process, sulphur trioxide vapours are absorbed in concentrated
sulphuric add and not in water to obtain sulphuric acid.
Reason Directly dissolving sulphur trioxide in water is not possible due to highly exothermic nature of the reaction.
Acidic vapors are formed. Oleum is reacted with water to form conc.
sulphuric ac
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The production of pH gradient during oxidative metabolism of glucose takes place during
A. Glycolysis
B. Anaerobic respiration
c. Krebs cycle
D. Electron transport chain
E. None of the above


Assertion:
\( \mathbf{P}_{4} \) is more reactive than \( \mathbf{N}_{2} \)
Reason:
\( \mathbf{P}-\mathbf{P} \) bonds are relatively weaker than
\( \mathbf{N}-\mathbf{N} \)
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 planets is coldest in the solar system?
A. Mercury
B. Venus
c. Neptune
D. Earth


An electron and a proton travel with equal speeds and in the same direction,
at \( 90^{\circ} \) to a uniform magnetic field. They experience forces which are initially
A. in opposite direction and differ by a factor of about 1840
B. in the same direction and differ by a factor of about 1840
c. equal in magnitude but in opposite directions
D. identical


Atomic radius is measured by:
A. Rutherfords \( \alpha \) -ray scattering experiment
B. X-ray diffraction technique
C. Millikan's oil drop method
D. Thomsons water-melon model


The process of leaching, alumina using sodium carbonate is called
A. bayer's process
B. decomposition
c. cyanide process
D. hall's process


Kelvin is the standard temperature
scale.


Find the measures of the third angle in
degrees
\( 92^{\circ}, 27^{\circ},---- \)


The locus of a point, which is
equidistant from the points (1,1) and \( (3,3), \) is
A \( . y=x+4 \)
в. \( x+y=4 \)
c. \( x=2 \)
D. \( y=2 \)
E \( . y=-x \)


A sanitary worker uses a white chemical having strong smell of chlorine gas to disinfect the water tank
¡) Identify the chemical compound.
ii) Write its chemical formula
iii) Write chemical equation for preparing it


Which of the following
can produced emission spectrum?
A. electrons in an excited gas jump up to a higher energy level and release photons.
B. electrons in an excited gas jump down to a lower energy level and release photons.
c. electrons are released from the outer orbitals of an
excited gas.
D. an unstable nucleus releases energy.
E. light is shined on a metal surface and electrons are released.


Focal length of a spherical mirror is \( 200 \mathrm{cm} . \) What will be its radius of
curvature?
A . \( 100 \mathrm{cm} \)
B. \( 25 \mathrm{cm} \)
\( c .50 c m \)
D. \( 400 \mathrm{cm} \)


Which one of the following has the lowest m.p?
\( A \cdot B \)
в. А।
\( c \cdot \) Ga
D. T


Rainbow is caused due to:
This question has multiple correct options
A. reflection of sunlight by air molecules
B. dispersion of sunlight from water drops
C. refraction of sunlight from water drops
D. refraction of sun rays by air molecules


Magnetic field lines:
A. starts from north pole
B. starts from south pole
c. starts from current-carrying wires
D. are closed loops


Which of the following metals cannot be used in electrolysis?
A. Sodium
B. Potassium
c. Magnesium
D. zinç


If \( h \) is Plancks constant, the
momentum of a photon of wavelength
\( 0.01 A^{\circ} \) is
\( \mathbf{A} \cdot 10^{-2} h \)
B. \( h \)
\( c \cdot 10^{2} \)
D. \( 10^{12} h \)


The pathogen Microsporum responsible for ringworm disease in humans belongs to the same Kingdom of organisms as that of
A. Rhizopus, a mould
B. Ascaris, a round worm
c. Taenia, a tapeworm
D. Wuchereria, a filarial worm


The formula of cryolite is :
A. \( A l_{2} O_{3} .2 H_{2} O \)
в. \( A l O_{2} .2 H_{2} O \)
c. \( N a_{3} A l F_{6} \)
D. \( K A l S i_{3} O_{8} \)


Explain the different steps involved during primary treatment phase of
sewage.


A prism of refractive index \( \sqrt{2} \) has a
reflecting angle of \( 60^{\circ} . \) At what angle
must a ray be incident on it so that it suffers minimum deviation?
A \( \cdot i=45^{\circ} \)
B . \( i=60^{\circ} \)
c. \( i=30^{\circ} \)
D . \( i=90^{\circ} \)


A storage battery contains a solution of
\( H_{2} S O_{4} 38 \% \) by weight. What will be the
Van't Hoff factor if the
\( \boldsymbol{\Delta} \boldsymbol{T}_{f \text {experiment}} \) is \( \mathbf{2 9 . 0 8} .\left[\text { Given } \boldsymbol{K}_{f}=\mathbf{1}\right. \)
B . \( i=2.5 \)
c. \( i=3 \)
D. \( i=3.5 \)


A block of mass \( 5 k g \) is at rest on a smooth horizontal surface. Water
coming out of a pipe horizontally at the
rate of \( 2 k g s^{-1}, \) hits the block with a
velocity of \( 6 m s^{-1} \). The initial
acceleration of the block is:
A. Zero
B. \( 1.2 \mathrm{ms}^{2} \)
c. \( 2.4 m s^{2} \)
D. \( 0.6 \mathrm{ms}^{2} \)


Find the derivative of \( f(x)=3 x \) at \( x= \)
2


A rheostat is used in an electrical
circuit
A. to change the resistance of the circuit.
B. to change the potential difference.
c. to change the emf
D. to change the current through a particular instrument


Complete the following statements with an appropriate word / term to be filled in the blank space(s).

Magnetic field lines emerge from the pole of a solenoid or a
permanent magnet
A. north
B. south
c. north-east
D. none of these


Which of the following is false about
fuse?
This question has multiple correct options
A. A fuse controls the current that flows to the appliance.
B. A fuse increases the resistance in the circuit to
minimize the current flow.
C. A fuse allows high current to flow through the circuit without damaging the appliance.
D. A fuse protects the wiring and the appliance in the circuit from overheating


which has the maximum conductivity
in thier \( 0.1 \mathrm{M} \) solution?
\( A \)
A) \( \left[\operatorname{Co}\left(N H_{3}\right)_{3} C l_{3}\right]_{3} \)
B.
B) \( \left[\operatorname{Co}\left(N H_{3}\right)_{4} C l\right] C l_{2} \)
c. \( \mathrm{c} \) ) \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} \)
\( D \)
D) \( \left[\operatorname{Co}\left(N H_{3}\right)_{6}\right] C l_{3} \)


Find the frequency of light that
corresponds to photons of energy \( 5.0 \times \) \( 10^{-5} \) erg.
\( \mathbf{A} \cdot 7.5 \times 10^{-21} \sec ^{-1} \)
В. \( 7.5 \times 10^{-21} \) sec
c. \( 7.5 \times 10^{21} \) sec \( ^{-1} \)
D. \( 7.5 \times 10^{2} \) sec


Construct a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right] \)


Assertion
Muscles fibres of SA node possess the lowest rhythmicity among all cardiac
muscles.
Reason
Due to this fact, it can initiate excitory waves at the highest rate
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


Out of the following reduction process-
\( \boldsymbol{A}: \boldsymbol{F} \boldsymbol{e}_{2} \boldsymbol{O}_{3}+\boldsymbol{C} \longrightarrow \boldsymbol{F} \boldsymbol{e}+\boldsymbol{C} \boldsymbol{O}_{2} \)
\( \boldsymbol{B}: \boldsymbol{Z} \boldsymbol{n} \boldsymbol{O}+\boldsymbol{C} \longrightarrow \boldsymbol{Z} \boldsymbol{n}+\boldsymbol{C} \boldsymbol{O}_{2} \)
\( \boldsymbol{C}: \boldsymbol{S} \boldsymbol{n} \boldsymbol{O}_{2}+\boldsymbol{C} \longrightarrow \boldsymbol{S} \boldsymbol{n}+\boldsymbol{C} \boldsymbol{O}_{2} \)
\( \boldsymbol{D}: \boldsymbol{P b O}+\boldsymbol{C} \longrightarrow \boldsymbol{P b}+\boldsymbol{C O}_{2} \)
Correct processes are:
в. \( A, B, D \)
c. \( A, B, C \)
D. \( B, D \)


Very short answer type. Give one example each of fibrous joint
and cartilaginous joint.


A man with normal near point \( (25 \mathrm{cm}) \) reads a book with small print using a magnifying glass: a thin convex lens of focal length \( 5 \mathrm{cm} \)
(a) What is the closest and the farthest
distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?
(b) What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?


Determine the change in oxidation
number of sulphur in \( H_{2} S \) and \( S O_{2} \) respectively in the following reaction.
\( 2 H_{2} S+S O_{2} \rightarrow 2 H_{2} O+3 S \)
A .0,+2
в. +2,-4
c. -2,+2
\( \mathbf{D} \cdot+4,0 \)


A unit vector perpendicular to the lines
\( \frac{\boldsymbol{x}+\mathbf{1}}{\mathbf{3}}=\frac{\boldsymbol{y}+\mathbf{2}}{\mathbf{1}}=\frac{\boldsymbol{z}+\mathbf{1}}{\mathbf{2}} \) and \( \frac{\boldsymbol{x}-\mathbf{2}}{\mathbf{1}}= \)
\( \frac{\boldsymbol{y}+\boldsymbol{2}}{\boldsymbol{2}}=\frac{\boldsymbol{z}-\boldsymbol{3}}{\boldsymbol{3}} \) is
\( ^{\mathbf{A}} \cdot \frac{-\hat{i}+7 \hat{j}+7 \hat{k}}{\sqrt{99}} \)
\( ^{\text {B. }} \frac{-\hat{i}-7 \hat{j}+5 \hat{k}}{5 \sqrt{3}} \)
\( \frac{-\hat{i}+7 \hat{j}+5 \hat{k}}{5 \sqrt{3}} \)
D. \( \frac{7 \hat{i}-7 \hat{j}-\hat{k}}{\sqrt{99}} \)


Which of the following statements is true when \( \Delta A B C \cong \Delta D E F \)
\( \mathbf{A} \cdot \angle A=\angle D \)
B . \( \angle A=\angle E \)
c. \( \angle A=\angle F \)
D. none of these


The species containing a \( \pi \) bond is:
A. \( B e F_{2} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{CH}_{4} \)
D. \( C H_{2} C H_{2} \)
E \( \cdot C C l_{4} \)


Consider a mass \( \mathrm{m} \) attached to a string of length I performing vertical circle.find an expression for velocity at any point and tension at any point.


A violin string emits sound of frequency \( 510 H z . \) How far will the sound waves
reach when string complete 250 vibrations? The velocity of sound is \( 340 m / s \)
A. \( 166.7 \mathrm{m} \)
B . 366.7 m.
c. \( 266.7 \mathrm{m} \)
D. \( 566.7 m \)


The differential equation representing the SHM of a particule is \( \frac{\mathbf{9} d^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{t}^{2}}+\boldsymbol{4} \boldsymbol{Y}= \)
0.The time period of the particle is fiven
by
A \( \frac{\pi}{3} \sec \)
в. \( \pi \) sec
\( ^{\mathrm{c}} \cdot \frac{2 \pi}{3} s e c \)
D. \( 3 \pi s e c \)


Most of the transition metals exhibit:
(i) paramagnetic behaviour
(ii) diamagnetic behaviour
(iii) variable oxidation states
(iv) formation of coloured ions
A. (ii), (iii) and (iv)
B. (i), (iii) and (iv)
c. (i), (ii) and (iii)
D. (i), (ii) and (iv)


A current is passed through 500 mLof
an aqueous solution of \( \boldsymbol{C a} \boldsymbol{I}_{2} \). After
sometime, it is observed that 50
millimoles of \( I_{2} \) have been formed.
Which of the following statements is(are) correct?
This question has multiple correct options
A. The number of faradays of charge passed through the solution is \( 0.10 F \)
B. The volume of dry \( H_{2} \) at \( S T P \) that has been formed during electrolysis is \( 1120 \mathrm{mL} \).
c. The \( p H \) of the solution is nearly 0.7
D. The mass of calcium produced is \( 2.0 g \).


Which of the following statements is
not correct?
A. The complexes \( \left[N i C l_{4}\right]^{2-} \) and \( \left[N i(C N)_{4}\right]^{2-} \) differ in th
B. The complexes \( \left[N i C l_{4}\right]^{2-} \) and \( \left[N i(C N)_{4}\right]^{2-} \) differ in th
C. The complexes \( \left[N i C l_{4}\right]^{2-} \) and \( \left[N i(C N)_{4}\right]^{2-} \) differ in \( g e \)
D. The complexes \( \left[N i C l_{4}\right]^{2-} \) and \( \left[N i(C N)_{4}\right]^{2-} \) differ in \( p r \)


An object has moved through a
distance. Can it have zero
displacement? If yes, support your answer with an example.


The total number of ways of formation of
five letter words from the letters of the
word \( I N D E P E N D E N T, \) is
A . 4200
в. 3320
c. 3840
D. None of these


Chloroform belong to which of the following type of alkyl halide?
A. Primary alkyl halide
B. Secondary alkyl halide
c. Tertiary alkyl halide
D. Tetra alkyl halide


A ball is moving over a horizontal smooth surface with a constant
velocity. Sum of external forces is:
A. zero
B. positive
c. negative
D. unity


Define the following terms:
(a) Triploblastic
(b) Coelomate
(c) Notochord
(d) Bilateral
symmetry


The solubility of \( P b S O_{4} \) water is 0.0608
g/L. Calculate the solubility product constant of \( P b S O_{4} . \) Molar mass \( P b S O_{4} \)
\( =304 \mathrm{g} / \mathrm{mole} \)


The value of \( \lim _{n \rightarrow \infty} \Sigma_{i=1}^{n-1} \sqrt{4+\frac{5 i}{n}} \) is equal
to?
A \( \cdot 15 / 38 \)
B. \( 38 / 15 \)
c. \( 21 / 15 \)
D . \( 22 / 15 \)


Presence of RBC in urine is known as
A. Hematuria
B. Urolithiasis
c. Nephritis
D. Proteinuria


Assertion
\( (A): \frac{\tan 3 x-\tan 2 x}{1+\tan 3 x \tan 2 x}=1 \Rightarrow x= \)
\( n \pi+\frac{\pi}{4}, n \in l \)
Reason
\( (R): \tan x \) is not defined at \( x=n \pi+ \)
\( \frac{\pi}{2}, n \in l \)
A. Both (A) and (R) are individually true and (R) is the correct explanation of (A)
B. Both (A) and (R) are individually true but (R) is not the correct explanation of \( (A) \)
C. (A) is true but (R) is false
D. (A) is false but (R) is true


The differential equation of all circles passing through the origin and having their centers on the x-axis is:
A \( \cdot y^{2}=x^{2}+2 x y \frac{d y}{d x} \)
B. \( y^{2}=x^{2}-2 x y \frac{d y}{d x} \)
c. \( x^{2}=y^{2}+2 x y \frac{d y}{d x} \)
D. None of these


Why distilled water does not conduct
electricity?


Which of the following is/ are correct?
This question has multiple correct options
A. A line segment with its endpoints lying on a circle is called a chord of the circle.
B. A line that intersects a circle at exactly one point is called a tangent to the circle.
C. Angle in a semi-circle is a right angle.
D. Lengths of the two tangents to a circle from an external point are equal


What is tooth enamel chemically? Show the condition when its start corroding.
what happens when food particles left in the mouth after eating degrade.


What is called as 'black gold'?
A. Hydrocarbons
в. coal
c. Petroleum
D. Ether


\( \tan ^{-1}\left(\frac{x+1}{x-1}\right)+\tan ^{-1}\left(\frac{x+1}{x}\right)= \)
\( \tan ^{-1}(2)+\pi \)


Consider the following statements in respect of histogram:
1. Histogram is an equivalent graphical
representation of the frequency
distribution.
2. Histogram is suitable for continuous random variables, where the total
frequency of an interval is evenly distributed over the interval.
Which of the statements given above is/are correct?
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


The dimensions of ratio of magnetic
flux \( (\phi) \) and permeability \( (u) \) are:
\( \mathbf{A} \cdot\left[M^{0} L^{1} A^{1} T^{0}\right. \)
B . \( \left[M^{0} L^{-3} T^{0} A^{1}\right] \)
\( \mathbf{c} \cdot\left[M^{0} L^{-1} T^{1} A^{-1}\right] \)
D・ \( \left[M^{0} L^{2} T^{0} A^{1}\right] \)


If \( f(x)=x+\int_{0}^{1}\left[x y^{2}+s^{2} y\right] f(y) d y \)
where \( x \) and \( y \) are independent varibles. Find \( f(x) \)
A \( \quad f(x)=x+\frac{61}{119} x+\frac{80}{119} x^{2} \)
в. \( f(x)=\frac{80 x^{2}+180 x}{119} \)
c. \( f(x)=\frac{80 x+180 x}{119} \)
D. \( f(x)=\frac{80 x^{2}+180 x}{19} \)


Is it possible to have an accelerated motion with a constant speed? Explain


Double helical structure of DNA was
proposed by
A. Kornberg
B. Nirenberg
c. watson and crick
D. Wilkins and Franklin


Assertion
The magnetic field at the ends of a very long current carrying solenoid is half of that at the centre.
Reason
If the solenoid is sufficiently long, the field within it is uniform.
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


What is the percentage of free carbon in lignite?
A . 20
B. 40
\( c \cdot 60 \)
D. 80


If \( \boldsymbol{X}=\left\{\mathbf{8}^{n}-\mathbf{7} \boldsymbol{n}-\mathbf{1}, \boldsymbol{n} \in \boldsymbol{N}\right\} \) and \( \boldsymbol{Y}= \)
\( \mathbf{4} 9(n-1), n \in N, \) then \( (\operatorname{given} n>1) \)
A. \( X \subset Y \)
в. \( Y \subset X \)
c. \( X=Y \)
D. \( X \nsubseteq Y \)


The following are some statements about oxides of VA group elements,
i) \( N O \) readily reacts with \( O_{2} \) to form
reddish-brown gas.
ii) The formula of Brown ring is
\( \left[\boldsymbol{F e}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5} \boldsymbol{N} \boldsymbol{O}\right] \boldsymbol{S} \boldsymbol{O}_{4} \)
iii) \( N_{2} O_{3} \) is called laughing gas.
The correct combination is:
A. All are correct.
B. I \& III are correct
c. I \& ॥ are correct
D. II \& III are correct


If \( \boldsymbol{A}=\left[\begin{array}{cc}\cos \boldsymbol{\theta} & -\sin \boldsymbol{\theta} \\ \sin \boldsymbol{\theta} & \cos \boldsymbol{\theta}\end{array}\right], \) then \( \boldsymbol{A}^{\boldsymbol{T}}+ \)
\( \boldsymbol{A}=\boldsymbol{I}_{2}, \) if
B \( \cdot \theta=(2 n+1) \frac{\pi}{2}, n \in Z \)
c. \( \theta=2 n \pi+\frac{\pi}{3}, n \in Z \)
D. none of these


Boiling water and steam both have the
same temperature \( \left(\mathbf{1 0 0}^{0} \boldsymbol{C}\right), \) but steam causes many severe burns than boiling water. Explain


Write Einstein's photo electric equation.


A drop of liquid of density \( \rho \) is floating
half-immersed in a liquid of density \( d \). If
\( \rho \) is the surface tension the diameter of
the drop of the liquid is
A \( \cdot \sqrt{\frac{\sigma}{g(2 \rho-d)}} \)
в. \( \sqrt{\frac{3 \sigma}{g(2 \rho-d)}} \)
c. \( \sqrt{\frac{6 \sigma}{g(2 \rho-d)}} \)
D. \( \sqrt{\frac{12 \sigma}{g(2 \rho-d)}} \)


What is the action of conc. nitric acid
on
a) Zinc metal
b) P4 - molecule
c) \( \mathbf{S} 8- \) molecule?


A hydrocarbon with formula \( \mathrm{C}_{8} \mathrm{H}_{18} \) gives
one mono chloro derivative. The
hydrocarbon can be :
A. n- Octane
B. 2-Methyl hepatane
c. 2,2,4 -Trimethyl butane
D. 2,2,3,3,- - Tetramethyl butane


Answer the following questions in about 30 words.
What is biodiversity? Why is biodiversity important for human lives?


Find the equation of the tangent to the curve \( y=\frac{x-y}{(x-2)(x-3)} \) at the point
where it cuts the \( x \) -axis.


In a battery five dry cells each of 1.5 volt
have internal resistance of
0.2,0.3,0.4,0.5 and \( 0.6 \Omega \) are present in
series. The battery is connected to a \( 1 \Omega \) resistance. Identify the correct statement \( (s) \)
A. Current in the circuit will be \( 2.5 A \)
B. Current in the circuit will be \( 1.5 A \)
c. on short circuiting the battery 3.75 d current will flow
D. Both \( (A) \) and \( (C) \)


A capacitor of capacitance \( 9 n F \) having
dielectric slab of \( \varepsilon_{r}=2.4 \) dielectric
strength \( 20 \mathrm{MV} / \mathrm{m} \) and \( \boldsymbol{P . D .}=20 \mathrm{V} \)
Calculate area of plates.
В . \( 4.2 \times 10^{-4} \mathrm{m}^{2} \)
c. \( 1.4 \times 10^{-4} m^{2} \)
D. 2.4 \( \times 10^{-4} m^{2} \)


ff \( y=\log _{\sin x}(\tan x), \) then \( \left(\frac{d y}{d x}\right)_{\pi / 4} \) is
equal to
A \( \cdot \frac{4}{\log 2} \)
B. \( -4 \log 2 \)
c. \( \frac{-4}{\log 2} \)
D. None of these


Identify and write the like terms in each
of the following groups.
(i) \( a^{2}, b^{2},-2 a^{2}, c^{2}, 4 a \)
A \( \cdot\left(a^{6}, 2 a^{2}\right)^{2} \)
В \( \cdot\left(a^{2},-2 a^{2}\right) \)
\( \mathbf{C} \cdot\left(a^{3}, 2 a^{2}\right) \)
D. \( \left(a^{2}, 2 a^{3}\right) \)


Four solutions \( A, B, C \) and \( D \) when
tested with universal indicator showed
\( \boldsymbol{p} \boldsymbol{H} \) as \( \mathbf{4}, \mathbf{1 1}, \mathbf{7} \) and \( \mathbf{9} \) respectively. Which
solution is weakly alkaline?
A . \( A \)
в. \( B \)
\( c . c \)
D. \( D \)


The time taken from the fixation of \( C O_{2} \)
to the formation of one glucose molecule is about
seconds.
A . 20
B. 40
c. 60
D. 90


Enzymes that catalyse inter-conversion of optical, geometrical or positional isomers are
A . Ligases
B. Lyases
c. Hydrolases
D. Isomerases


The total number of subsets of \{1,2,6,7\}
are?
A . 16
B. 8
c. 64
D. 32


The power of a lens being +4 dioptres suggests that it is a
A. Convex lens
B. Plano-concave lens
c. concave lens
D. convexo-concave lens


A bomb blasts on moon. Its sound will
be heard on earth after
A. 3.7 minutes
B. 10 minutes
c. 138 minutes
D. sound will never be heard


For a plane convex lens \( (\mu=1.5) \) having radius of curvature \( 10 \mathrm{cm} . \) It is silvered on its plane surface. Find focal length after silvering:
\( A \cdot 10 \mathrm{cm} \)
B. 20 cm
c. \( 15 \mathrm{cm} \)
D. 25 cm


The distance between two atoms in a
molecule is measured in order of
Angstrom
A. True
B. False


Identify \( M \) and \( N \) in the following
reaction.
Copper glance controlledheating in presence
\( \boldsymbol{M}+\boldsymbol{S O}_{2} \uparrow \)
\( \boldsymbol{M} \stackrel{N}{\longrightarrow} \boldsymbol{C} \boldsymbol{u}+\boldsymbol{S} \boldsymbol{O}_{2} \uparrow \)
\( \boldsymbol{M} \stackrel{N}{\longrightarrow} \boldsymbol{C} \boldsymbol{u}+\boldsymbol{S} \boldsymbol{O}_{2} \uparrow \)
A . \( M=C u_{2} O ; N= \) self reduction
B. \( M=C u_{2} O+C u_{2} S ; N= \) self reduction
c. \( M=C u_{2} O ; N= \) carbon reduction
D. \( M=C u_{2} O ; N= \) electrolytic reduction


\( (X),(Y),(Z) \) are elements in the third period. Oxide of \( (X) \) is ionic, that of \( (Y) \) is amphoteric, and of \( (Z) \) a giant molecule.
\( (X),(Y) \) and \( (Z) \) will have atomic
numbers in the order:
\( A \cdot(x)<(y)<(z) \)
\( B \cdot(z)<(Y)<(X) \)
\( c \cdot(x)<(z)<(y) \)
\( D \cdot(Y)<(X)<(Z) \)


Pure and dry chlorine gas is collected by the upward displacement of air.
A. True
B. False


Discuss Haber's process for industrial
manufacture of ammonia.


f \( \sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2} \)
then the value if \( x \) is
A . 5
B. 4
c. 12
D. 11


Leydig cells are meant for
A. Formation of sperm
B. Production of progesterone
C. Production of testosterone
D. Nutrition of sperm


Find the equation of plane with intercepts 2,3 and 4 on the \( x, y \) and \( z \) axis respectively.


Secondary cortex is also known as
A. Phellem
B. Phelloderm
c. Phellogen
D. Bark


\( \mathrm{U}=\{1,2,3,4,5,6,7,8,9,10\} \)
\( \mathrm{A}=\{2,4,6,8,10\}, B=\{1,3,5,7,8,10\} \)
Find \( (A \cup B) \)


If \( K \) denotes coefficient of thermal
conductivity, \( d \) the density and \( C \) the
specific heat, the unit of \( \boldsymbol{X}, \) where \( \boldsymbol{X}= \) \( \boldsymbol{K} / \boldsymbol{d} \boldsymbol{c}, \) will be
A . \( \mathrm{cm} \) sec
B. \( c m^{2} \sec ^{-2} \)
\( \mathrm{c} \cdot_{\mathrm{cm}} \sec ^{2} \)
\( \mathbf{D} \cdot c m^{2} \sec ^{-1} \)


Deplaction of the water table is due to which of the following resion?
A. insufficient rain fall
B. industrial activities
c. excess of tube wells
D. all of them


Read the statements and mark the
correct one(s)
i. Braille cells are read from left to right. ii Each Braille character is made up of
six dots.
iii Braille can only be produced manually.
A. i and i i
B. ii and iii
c. i and iii
D. All are true


An Indian rubber cord \( L \) metre long and
area of cross-section \( A \) meter \( ^{2} \) is
suspended vertically. Density of rubber is \( \rho k g / \) meter \( ^{3} \) and Young's modulus of
rubber is \( Y \) Newton/metre \( ^{2} \). If the cord
extends by \( l \) metre under its own
weight, then extension \( l \) is:
\( \mathbf{A} \cdot \frac{L^{2} \rho g}{Y} \)
B. \( \frac{L^{2} \rho g}{2 Y} \)
\( ^{\mathbf{C}} \cdot \frac{L^{2} \rho g}{4 Y} \)
D. \( \frac{Y}{L^{2} \rho g} \)


The relation between time \( t \) and
distance of \( x \) s is \( t=a x^{2}+b x \) where \( a \)
and \( b \) are constant. The acceleration is
A. \( -2 a b v^{2} \)
B . \( 2 b v^{3} \)
c. \( -2 a v^{3} \)
D. \( 2 a v^{2} \)


Term used to describe non-dominant
species that dictates community structure is
A. Pioneer species
B. Keystone species
c. Transitional species
D. Exohenous species


In rabbit, the opening of coronary sinus into the left precaval vein is bound by a fold called
A. Valve of Thebesius
B. Mitral valve
c. Tricuspid valve
D. Valve of eustachian


A proton of charge \( e \) and mass \( m_{p} \)
moves in a circular path of radius \( r \) in a
uniform magnetic field \( \boldsymbol{B} \)
The momentum of the proton can be
described by the expression:
\( \mathbf{A} \cdot e B r \)
B. \( 2 e B r \)
\( c \cdot e B r^{2} \)
D. \( e B r m_{p} \)
E \( \cdot 2 e B r m_{p} \)


If the balanced reaction is as given below, find the value of \( x, y \) and \( z \)
\( \boldsymbol{T} \boldsymbol{i}_{2} \boldsymbol{O}_{3}(\boldsymbol{s})+\boldsymbol{x} \boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( 2 T i O H(s)+y N_{2}(g)+z H_{2} O \)
A. \( x=4, y=2, z=5 \)
в. \( x=3, y=2, z=5 \)
c. \( x=4, y=2, z=4 \)
D. None of the above


What are the values of \( x \) that satisfy the
equation \( \left|\begin{array}{ccc}\boldsymbol{x} & \mathbf{0} & \mathbf{2} \\ \mathbf{2} \boldsymbol{x} & \mathbf{2} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right|+\left|\begin{array}{ccc}\mathbf{3} \boldsymbol{x} & \mathbf{0} & \mathbf{2} \\ \boldsymbol{x}^{\mathbf{2}} & \boldsymbol{2} & \mathbf{1} \\ \mathbf{0} & \boldsymbol{1} & \mathbf{1}\end{array}\right|=\mathbf{0} ? \)
B. \( -1 \pm \sqrt{3} \)
c. \( -1 \pm \sqrt{6} \)
\( \mathbf{D} \cdot-2 \pm \sqrt{6} \)


In rabbit, oxygenated blood flows from
A. Left auricle to left ventricle during auricular systole
B. Right auricle to right ventricle during ventricular systole
C. Right ventricle to aorta during ventricular systole
D. Pulmonary vein to left auricle during auricular systole


In case of unimolecular reaction, the
time required for \( 99.9 \% \) of the reaction
to take place is \( x \) times that required for half of the reaction. The value of \( x \)
is


Arrange the eccentricities of the following ellipses in particular order.
A- Ellipse whose Latus rectum is half of its major axis.
B- Ellipse whose distance between the foci is equal to the distance between a focus and one end of minor axis
C- Ellipse whose major axis is double the minor axis.
D- Ellipse whose distance between the foci is 6 and the length of minor axis is
8
\( A \)
\[
(A)=(C)>(D)>(B)
\]
B. \( (A)=(C)<(D)<(B) \)
\( c \)
\[
(A)>(C)>(D)>(B)
\]
D. none of these


Find \( \int \sqrt{\boldsymbol{x}}\left(\boldsymbol{3} \boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}+\boldsymbol{3}\right) \boldsymbol{d} \boldsymbol{x} \)


Find the 9 th term and the general term
of the progression: \( \frac{1}{4},-\frac{1}{2}, 1,-2, \dots \dots \)


Q Type your question
custom-built capacitor. The magnitude
of charge on each plate for each separate voltage is recorded. The graph shows charge in micro-coulombs
plotted against potential difference. Use the graph to answer the following two questions. What is the approximate capacitance,
\( C, \) of this capacitor?
And what is the electric potential operating range during which this device properly acts like a capacitor?
A. \( C=60 \) micro-farads; Operating Range: \( 0-100 v \)
B. \( C=60 \) micro-farads; Operating Range: \( 0-40 v \)
c. \( C=2700 \) micro-farads; operating Range: \( 60-100 v \)
D. \( C=40 \) micro-farads; Operating Range: \( 0-40 v \)
E. \( C=0.017 \) micro-farads; operating Range: \( 0-40 \)


The largest number of the three
consecutive number is \( x+1 \) then the
smallest number is
\( \mathbf{A} \cdot x+2 \)
B. \( x+1 \)
\( c \)
D. \( x-1 \)


When an air bubble of radius \( r \) rises
from the bottom to the surface of a lake, the radius becomes \( \frac{5 r}{4} . \) Taking the
atmospheric pressure to be equal to 10 \( m \) height of water column, the depth
of the lake would approximately be (ignore the surface tension and the effect of temperature):
A . \( 11.2 m \)
B. \( 8.7 m \)
\( \mathbf{c} .9 .5 m \)
D. \( 10.5 \mathrm{m} \)


Find the total surface area of a cuboid
its length, breadth and height are \( 7 \mathrm{cm} \) \( 5 \mathrm{cm}, \) and \( 10 \mathrm{cm} \) respectively.


Glyptal or alkyl resin is a polymer of:
A. ethylene glycol and phthalic acid
B. ethylene and phthalic acid
c. phthalic acid and acetylene


A black bear that eats berries and fish
would be classified as
A. A producer
B. An omnivore
c. A carnivore
D. An herbivore
E. An autotroph


Calculate the potential at a point due to a charge of \( 3 \times 10^{-9} C \) located \( 9 \times \)
\( 10^{-2} m \) away from it.


When you heat a bowl of water, we can observe that water starts circulating. This demonstrates:
A. conduction
B. convection
c. radiation
D. none


Among the following which is used to control the rate of reaction in nuclear
fission reactions?
A. water
B. Heavy water
c. Cadmium
D. Graphite


One mole of an ideal gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant
volume to raise the temperature by the same \( 10 \mathrm{K} \), the heat required is
A . \( 198.7 J \)
B. \( 29 J \)
c. \( 215.3 J \)
D. 124J


Darwins finches are an excellent
example of
A. Adaptive radiation
B. Seasonal migration
c. Brood parasitism
D. connecting links


Blue colour of wter in sea is due to
A. refraction of blue light by impurities
B. refraction blue sky by water
C. scattering of light by water
D. None of the above


Figure below shows a portion of an electric circuit with the currents in
ampere and their directions. The
magnitude and direction of the current
in the portion \( \boldsymbol{P} \boldsymbol{Q} \) is:
\( A \cdot 0 A \)
B. \( 3 A \) from \( P \) to \( Q \)
\( c .4 A \) from \( Q \) to \( P \)
D. \( 6 A \) from \( Q \) to \( P \)


State the use of aluminum


Bioenergy is obtained from energy stored in biomass.
A. chemical
B. heat
c. nuclear
D. thermal


The molecular weight of \( O_{2} \) and \( N_{2} \) are
32 and 28 respectively. At \( 15^{0} C \), the
pressure of \( 1 \mathrm{gm} \mathrm{O}_{2} \) will be the same as
that of \( 1 \mathrm{gm} N_{2} \) in the same bottle at the temperature?
A . \( -21^{0} C \)
B. \( -13^{0} C \)
\( \mathbf{c} \cdot 15^{0} C \)
D. \( 56.4^{0} V \)


The growth of which group of bacteria will be slow in comparison to the others?
A. Obligate aerobes
B. obligate anaerobes
c. Facultative aerobes
D. Facultative anaerobes


Solve the differential equation \( \boldsymbol{x}+ \)
\( y \frac{d y}{d x}=2 y \)


Find the electric flux crossing the wire frame \( A B C D \) of length \( I, \) width \( b, \) and
center at a distance \( 0 P=d \) from an
infinite line of charge with linear charge
density \( \lambda \). Consider that the plane of the
frame is perpendicular to the line OP
Fig.
A \( \cdot \frac{2 N}{\pi \varepsilon_{0}} \tan ^{-1}\left(\frac{b}{2 d}\right) \)
B. \( \frac{N}{\pi \varepsilon_{0}} \tan ^{-1}\left(\frac{b}{2 d}\right) \)
c. \( \frac{3 N}{\pi \varepsilon_{0}} \tan ^{-1}\left(\frac{7 b}{2 d}\right) \)
D. \( \frac{N}{2 \pi \varepsilon_{0}} \tan ^{-1}\left(\frac{b}{2 d}\right) \)


In which of the following solution, \( A g C l \)
has minimum solubility:
A. \( 0.05 M A g N O_{3} \)
в. \( 0.01 M \) Са \( C l_{2} \)
c. \( 0.01 M \) NaCl
D. \( 0.01 M N H_{4} O H \)


The gravitational potential at height \( h \) above the earth's surface is \( -5.12 \times \)
\( 10^{7} \mathrm{J} / \mathrm{kg} \) and acceleration due to gravity
at this point is \( 6.4 m s^{-2} . \) If radius of the
earth is \( 6400 \mathrm{km} \), the value of h is :
A. \( 1200 \mathrm{km} \)
B. 1600 km
c. \( 1800 \mathrm{km} \)
D. 2400 km


Two lenses shown are illuminated by a
beam of parallel light from the left. Lens
\( B \) is then moved slowly toward lens \( A \)
The beam emerging from lens \( B \) is
A. Always diverging
B. Initially parallel and then diverginggg
c. Always paralle!
D. Initially converging and then parallel


n fig sides QP and RQ of \( \Delta \) PQR are produced to the points \( \mathrm{S} \) and \( \mathrm{T} \)
respectively. If \( \angle S P R=105^{\circ} \angle P Q T= \)
\( 110^{\circ} \) then find \( \angle P R Q \)
\( A \cdot 35 \)
B. \( 70^{\circ} \)
\( c .105 \)
0.140


Complete the equations given below.
\( N a_{2} O+H_{2} O \rightarrow \)


A telephone cable at a place has four long straight horizontal wires carrying a current of \( 1.0 \mathrm{A} \) in the same direction
east to west. The earth's magnetic field at the place is \( 0.39 \mathrm{G}, \) and the angle of dip is 35 ?35 ? . The magnetic declination is nearly zero. What are the resultant magnetic fields at points \( 4.0 \mathrm{cm} \) below the cable?


Some medicines are more effective in
the colloidal form because of:
A. the charged colloidal particles present in it
B. the large surface area and easy assimilation
C . precipitation of medicine in the blood
D. the stabilisation of medicine in colloidal form


Consider quadratic equation \( a x^{2}+ \) \( (2-a) x-2=0, \) where \( a \in R \)
If exactly one root is negative, then the
range of \( a^{2}+2 a+5 \) is
\( A \cdot[4, \infty) \)
B \( \cdot[-2, \infty) \)
c. \( (-\infty, 4] \)
\( D \cdot(5, \infty) \)


A wave has wavelength \( 50 A^{\circ} . \) State the
speed of wave in vacuum.
A. \( 3 \times 10^{8} \mathrm{ms}^{-1} \)
В \( \ldots 3 \times 10^{8} m s^{-1} \)
\( \mathbf{c} \cdot\left\langle 3 \times 10^{8} m s^{-1}\right. \)
D. Insufficient information


\( (a) C H_{3} C O N H_{2}+K O H \longrightarrow \)
\( (b) C H_{3} C O O H+s o d a l i m e \longrightarrow \)
\( (c) C H_{3} C O O A g+B r_{2} \longrightarrow \)
All the three reactions show similarity
in:
A. Descending of carbon atoms
B. Ascending of carbon atoms
c. Both the above
D. None of above


\( 56 g \) of nitrogen and \( 8 g \) of hydrogen gas are heated in a closed vessel. At
equilibrium \( 34 g \) of ammonia is present. The equilibrium number of moles of nitrogen, hydrogen and ammonia are respectively:
\( \mathbf{A} \cdot 1,2,2 \)
в. 2,2,1
c. 1,1,2
D. 2,1,2


In which of the following pair, both the substances are chemically same?
A. Milk of lime and lime water
B. Dead burnt plaster and gypsumm
C. Alumina and gypsum
D. Gypsum and Plaster of Paris


The function \( \boldsymbol{f}:[\mathbf{2}, \infty) \rightarrow \boldsymbol{Y} \) defined by
\( f(x)=x^{2}-4 x+5 \) is both one-one \( \& \)
onto if:
A \( . Y=R \)
В. \( Y=[1, \infty) \)
c. \( Y=[4, \infty) \)
D. \( Y=[5, \infty) \)


Which of the following sources gives best monochromic light?
A. A candle
B. A bulb
c. A mercury tube
D. A laser


Fuel formed under the earths surface by the decomposition of organic matter is:
A. organic fuel
B. bio-gas
c. fossil fuel
D. underground fuel


If the points \( (k, 2 k),(3 k, 3 k) \) and (3,1) are collinear then the value of \( k \) is
A \( \cdot \frac{7}{9} \)
B. \( \frac{2}{3} \)
c. \( \frac{-2}{3} \)
D. \( \frac{-1}{3} \)


The concentration of the reactant \( R \) at
different times are given below. Find the average rate during different time intervals.
\( t(\sec ) \quad[R](\operatorname{mol} / L) \) )
0.150
10
\[
0.100
\]
20 0.050
A \( . . .005 \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1}, .005 \mathrm{mol} \mathrm{L}^{-1} \mathrm{s}^{-1} \)
B . .005molL" \( s^{-1}, .0025 \) molL\( ^{-1} s^{-1} \)
c. \( .0025 \mathrm{molL}^{-1} \mathrm{s}^{-1} . .005 \mathrm{molL}^{-1} \mathrm{s}^{-1} \)
D. None of these


Decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is retarded
by
A . Acetanilide
в. \( M n O_{2} \)
c. zinc
D. finely divided metal


A light and a heavy body have equal kinetic energies. The light body has greater momentum.
A. True
B. False


II
sodium bicarbonate solution?
This question has multiple correct options
\( A \)
B.
\( c \)
\( D \)


A particle is thrown upwards with velocity \( 2 \mathrm{m} / \mathrm{s}, \) the velocity of particle after 2 s is :
A. \( 17.6 m / s \)
B. \( -17.6 \mathrm{m} / \mathrm{s} \)
c. \( 19.6 m / s \)
D. \( -19.6 m / s \)


What will be the correct gene expression
pathway?
A. Gene-mRNA- transcription-translation-protein
B. Transcription-Gene-translation-mRNA-protein
C. Gene-transcription-mRNA-translation-protein
D. Gene-translation-mRNA-transcription-protein


A charged body is brought near a positively charged gold leaf electroscope. The divergence of its leaves increases. If the same body is brought near a negatively charged gold leaf electroscope, what will be the effect
on divergence of its leaves?


Fore-brain is centre of intelligence, control of movements, hearing, smell and sight.
A. True
B. False


35
has a non-terminating decimal
\( \overline{\mathbf{5 0}} \)
expansion
A. True
B. False


Explain the formation of root nodules in legumes.


The active mass of \( 7.0 \mathrm{g} \) of nitrogen in a
\( 2.0 L \) container would be:
A . 0.25
B. 0.125
\( c .0 .5 \)
D. 14.0


The Sl unit of radioactivity is :
A . Becquerrel
B. Curie
c. Rutherford
D. None of these


Chief anatomical feature of
Cucurbitaceae family is
A. Bicollateral vascular bundles
B. Conjoint vascular bundle
c. radial vascular bundle
D. None of the above


How is the angle of emergence \( i_{2} \)
related to the angle of incidence \( i_{1} ? \)
в. \( i_{2}<i_{1} \)
\( \mathbf{c} \cdot i_{2}>i_{1} \)
D. can't say


Within a spherical charge distribution of charge density \( \rho(r), \) N equipotential
surfaces of potential \( V_{0}, V_{0}+ \)
\( \boldsymbol{\Delta} \boldsymbol{V}, \boldsymbol{V}_{0}+\boldsymbol{2} \boldsymbol{\Delta} \boldsymbol{V}, \ldots . ., \boldsymbol{V}_{0}+ \)
\( N \Delta V(\Delta V>0), \) are drawn and have
increasing radii \( r_{0}, r_{1}, r_{2}, \dots . . r_{N} \)
respectively. If the difference in the radii of the surfaces is constant for all values
of \( V_{0} \) and \( \Delta V \) then :
A \( \cdot \rho(r)= \) constant
B. \( \rho(r) \propto \frac{1}{r^{2}} \)
c. \( \rho(r) \propto \frac{1}{r} \)
D. \( \rho(r) \propto 1 \)


In steady horizontal flow:
A. the pressure is greatest where the speed is leas
B. the pressure is independent of speed
C. the pressure is least where the speed is least
D. (a) and
(c) are correct


We move our hands while walking for
A. Fast movement
B. Balancing
c. Increasing blood circulation
D. Relieving tension


Which of the following is strongest conjugate base
в. \( \mathrm{HCO}_{3} \)
\( c . P \)
D. HSO


Evaluate \( \int_{1}^{3}(2 x+3) d x \)


A flat plate is moving normal to its plane through a gas under the action of a constant force \( \boldsymbol{F} \). The gas is kept at a
very low pressure. The speed of the plate
\( v \) is much less than the average speed
\( u \) of the gas molecules. Which of the
following options is/are true? This question has multiple correct options
A. The resistive force experienced by the plate is proportional to \( v \)
B. At a later time the external force \( F \) balances the resistive force
C. The plate will continue to move with constant non-zero acceleration, at all times
D. The pressure difference between the leading and trailing faces of the plate is proportional to \( u v \)


Name the family to which each of the following belongs
(i) Pisum
(ii) Onion
(iii) Potato.


Which of the following is paramagnetic
in nature?
\( A \cdot N_{2} O_{4} \)
B. \( \mathrm{N}_{2} \)
c. No
D. \( \mathrm{N}_{2} \mathrm{O}_{3} \)


Which of the following is the most stable oxidation state of aluminium?
A . -1
B. +1
\( c \cdot+2 \)
D. +3


The volume of air that can be inhaled
following a maximal exhalation includes IRV, TV and ERV is known as
the
A. Functional capacity
B. Lung capacity
c. vital capacity
D. Respiratory capacity


What is the square root of 506.25 using long division method?
A . 22.
B. 21.4
c. 23.4
D. 25.3


What is the formula of calamine?


The angular velocity of the earth with
which it has to rotate so that the
acceleration due to gravity on \( 60^{\circ} \)
latitude becomes zero is
A . \( 2.5 \times 10^{-3} r a d / s \)
В. \( 1.5 \times 10^{-3} r a d / s \)
C \( .4 .5 \times 10^{-3} \mathrm{rad} / \mathrm{s} \)
D. \( 0.5 \times 10^{-3} \mathrm{rad} / \mathrm{s} \)


A shopkeeper buys 15 identical articles
for Rs. 840 and pays sales-tax at the rate of \( 8 \% . \) He sells 6 of these articles at
Rs. 65 each and charges sales-tax at the same rate. Calculate the VAT paid by the
shopkeeper against the sale of these six articles.
A. Rs. 2.5 5
B. Rs.4.32
c. Rs. 7.52
D. Rs. 9.55


Appliances based on heating effect of current work on
A. only A.c.
B. only D.C.
c. both A.c. and D.c.
D. none of these


An earthquake is caused by
A. shaking of the earth
B. strain building up in the tectonic plates
C . plates slipping along the fault lines
D. all of the above


In Young's double slit experiment, the intensity at the center of screen is:
A. equal to the intensity of each source
B. equal to twice the intensity of each source
c. half the intensity of each source
D. four times the intensity of each source


Which of the following mixtures can act as a buffer?
This question has multiple correct options
\( \mathbf{A} \cdot N a O H+H C O O N a \)
B. Borax + boric acid
c. \( N a H_{2} P O_{4}+N a_{2} P O_{4} \)
D. \( N H_{4} C l+N H_{4} O H \)


A 220 volt input is supplied to a transformer. The output circuit of
2.0 ampere at 440 volts. If the efficiency of the transformer is \( 80 \% \), the current drawn by the primary windings of the transformer is


An equilibrium mixture in a vessel of capacity 100 litre contain
1 mol \( N_{2}, 2 \) mol \( O_{2} \) and
3 mol NO.No. of moles of \( 0_{2} \) to be
added so that at new equilibrium the conc. of NO is found to be 0.04 mol/lit :
A \( .(101 / 18) \)
B. (101/9)
c. (202/9)
D. None of these


Mass-flow hypothesis is also known as
A. Pressure flow hypothesis
B. Accelerated diffusion theory
c. conventional flow hypothesis
D. None of the above


The dimension of \( 1 / 2 \varepsilon_{o} E^{2}\left(\varepsilon_{o}\right. \)
permittivity of free space; E: electric field) is?
A . \( M L T^{-} \)
В. \( M L^{2} T^{-2} \)
c. \( M L^{-1} T^{-2} \)
D. \( M L^{2} T^{-1} \)


Without expanding, show that the value
of the following determinant is zero:
\( \left|\begin{array}{ccc}a & b & c \\ a+2 x & b+2 y & c+2 z \\ x & y & z\end{array}\right| \)


In which one of the following pairs the radius of the second species is greater than that of the first?
A. \( N a, M g \)
B. \( O^{2-}, N^{3-} \)
c. \( L i^{+}, B e^{2+} \)
D. \( B a^{2+}, S r^{2+} \)


Root pressure is measured by
A. Potometer
B. Barometer
c. Manometer
D. Auxanometer


What are the conditions for a chemical
change?
A. Combining particles are in close contact.
B. Energy is suppliedd
c. Both A and B
D. None of these.


The volumes of the two spheres are in
the ratio \( 64: 27 . \) Find the ratio of their
surface areas.
\( \mathbf{A} \cdot 16: 9 \)
B. 9: 16
c. 4: 3
D. 3: 4


As the distance of the planet from the sun increases, the period of revolution decreases.
A. True
B. False


Write the mechanism of hydration of ethene to yield ethanol


The most efficient engine is?
A . Petrol
B. Electric
c. Steam
D. Diesel


In which ratio the plane \( Y Z \) divides the
lines joining the points (2,1,2) and (-6,3,4)


Out of (ref. image), which one is more reactive towards nucleophilic substitution reaction and why?
and


If \( x^{y}=e^{x-y}, \) show that \( \frac{d y}{d x}= \) \( \frac{\boldsymbol{y} \log \boldsymbol{x}}{\boldsymbol{x}(\log \boldsymbol{x}+\mathbf{1})} \)


Oxygen molecule is paramagnetic in nature. What is the paramagnetic
content in terms of the magnetic
moment in \( O_{2}^{-} ? \)
A . 1.732
B. 3
c. 1.5
D. 2.5


Dimension of temperature coefficient \( \alpha \)
is


Prove that the points \( \boldsymbol{A}(\boldsymbol{a}, \boldsymbol{b}+ \)
\( c), B(b, c+a) \) and \( C(c, a+b) \) are
collinear (By determinant)


The chemical reactions involved in
the extraction of metallic silver from
argentite is -
\( \mathbf{2} N \boldsymbol{a}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]+\boldsymbol{Z} \boldsymbol{n} \rightarrow \)
\( \boldsymbol{N} \boldsymbol{a}_{2}\left[\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{C} \boldsymbol{N})_{4}\right]+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g} \downarrow \)
If the statement is true enter 1 else 0 .


If, in the reaction \( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g) \)
\( x \) is the part of \( N_{2} O_{4} \) which dissociates,
then the number of molecules at
equilibrium will be:
A
B. 3
\( c \cdot(1+x) \)
D. \( (1+x)^{2} \)


The equation of image of the line
\( \frac{x-1}{9}=\frac{y-2}{-1}=\frac{z+3}{-3} \) in the plane
\( 3 x-3 y+10 z=26 \) is
\( ^{\text {A } \cdot} \frac{x-4}{9}=\frac{y+1}{-1}=\frac{z-7}{3} \)
B. \( \frac{x-4}{9}=\frac{y+1}{-1}=\frac{z-7}{-3} \)
c. \( \frac{x+4}{9}=\frac{y+1}{-1}=\frac{z-7}{-3} \)
\( \frac{x-4}{9}=\frac{y-1}{1}=\frac{z-7}{-3} \)


Which of the following contain \( \boldsymbol{P}-\boldsymbol{P} \)
bond?
A \( \cdot P_{2} O_{7}^{4} \)
B. \( P_{2} O_{6}^{2-} \)
\( \mathrm{c} \cdot P_{3} O_{9}^{3-} \)
D. \( P_{2} O_{6}^{4-} \)


Which of the following is true regarding how increasing population helps in depletion of water table?
A. Increasing population creates demand for construction of houses, shops, offices, roads and pavements
B. This decreases the open areas like parks, and playgrounds.
c. This, in turn, decreases the seepage of rainwater into the ground
D. All of the above


\( f\left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & 1\end{array}\right|=\left|\begin{array}{lll}\boldsymbol{a}_{1} & \boldsymbol{b}_{1} & \mathbf{1} \\ \boldsymbol{a}_{2} & \boldsymbol{b}_{2} & \mathbf{1} \\ \boldsymbol{a}_{3} & \boldsymbol{b}_{3} & 1\end{array}\right| \), then the
two triangles with vertices \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right) \) and \( \left(a_{1}, b_{1}\right) \)
\( \left(a_{2}, b_{2}\right),\left(a_{3}, b_{3}\right) \) must be congruent
A. True
B. False


State Ampere's circuital law and arrive
at the expression for the magnetic field
near a straight infinite current carrying wire.


What will be the enthalpy of combustion of carbon to produce carbon monoxide on the basis of data given below?
\( \boldsymbol{C}_{(s)}+\boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2(\boldsymbol{g})} \quad \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -393.4 k J \)
\( \boldsymbol{C O}_{(\boldsymbol{g})}+\frac{1}{2} \boldsymbol{O}_{2(\boldsymbol{g})} \rightarrow \boldsymbol{C} \boldsymbol{O}_{2(\boldsymbol{g})} \quad \boldsymbol{\Delta} \boldsymbol{H}= \)
\( -283.0 k J \)
A \( .+676.4 \mathrm{kJ} \)
B . - 676.4 kJ
c. -110.4 k
D. \( +110.4 \mathrm{kJ} \)


Two identical particles of mass \( 1 \mathrm{kg} \) experience a gravitational force of 10N between them . The distance between
them is r. If the same setup is put in water (refractive index \( =1.5 \) ), how will
their gravitational force change
A. The gravitational force will reduce to 1 N
B. The gravitational force remains constant
c. The gravitational force becomes \( 20 / 3 \mathrm{N} \)
D. The gravitational force becomes 15 N


A rectangular loop PQRS, is being pulled
with constant speed into a uniform
transverse magnetic fieldby a force (as shown). E.m.f. induced in side PS
and potential difference between points
Pand S respectively are (Resistance of the \( \operatorname{loop}=r) \)
A \( \cdot \) zero, \( \frac{F r}{B \ell} \)
B. Zero, zero
c. zero, \( \frac{F r}{6 B \ell} \)
D. \( \frac{F r}{6 B \ell}, \frac{F r}{6 B \ell} \)


Displacement of a body is given by \( x= \)
\( \mathbf{5}+\mathbf{3} t+\mathbf{2} t^{2} . \) The value instantaneous
acceleration is:
A . 4 units
B. 6 units
c. 5 units
D. 2 units


Unlike phenol, 2,4-dinitrophenol is
soluble in sodium carbonate solution in
water because?
A. presence of two - \( N O_{2} \) groups in the ring makes 2,4 dinitrophenol a stronger acid than phenol.
B. presence of two - \( N O_{2} \) groups in the ring makes 2,4 dinitrophenol a weaker acid than phenol.
C. presence of two \( -N O_{2} \) groups make the hydrogen bonding easier, making 2, 4-dinitrophenol soluble
D. nitro group reacts with \( N a_{2} C O_{3} \) while \( -O H \) group does not


Predict the products formed when cyclohexanecarbaldehyde reacts with the following reagents.
(i) PhMgBr and then \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)
(ii) Tollens reagent
(iii) Semicarbazide and weak acid
(iv) Excess ethanol and acid
(v) Zinc amalgam and dilute
hydrochloric acid


What is represented by the following
sequence?
Cyanobacteria, Crustose lichens, Foliose lichens, Mosses, Shrub, Dicotyledenous plants.
A. Genetic drift
B. Eltonian pyramid
c. Ecological succesion
D. Phylogenetic relationship


If vectors \( (x-2) \vec{a}+\vec{b} \) and
\( (2 x+1) \vec{a}-\vec{b} \) are parallel then \( x \)
A \( \cdot 1 / 3 \)
B. 3
\( c \cdot-3 \)
D. \( -1 / 3 \)


The differential equation of the family of straight lines whose slope is equal to \( y \) intercept.
A \( \cdot(x+1) \frac{d y}{d x}-y=0 \)
B. \( \left(x+1 \frac{d y}{d x}+y=0\right. \)
c. \( \frac{d y}{d x}=\frac{x-1}{y-1} \)
D. \( \frac{d y}{d x}=\frac{x+1}{y+1} \)


\( \sqrt[*]{\frac{x}{1+x^{4}}} d x \)
\( \mathbf{A} \cdot \tan ^{-1} x^{2} \)
B. \( 2 \tan ^{-1} x^{2} \)
c. \( \frac{1}{2} \tan ^{-1} x^{2} \)
D. \( \frac{1}{2} \tan ^{-1} x \)


The following graph represents:
\( \mathbf{A} \cdot \cot ^{-1}(x+1) \)
\( B \cdot \sin ^{-1}\left(x^{4}+1\right) \)
\( \mathbf{c} \cdot \tan ^{-1}\left(x^{3}+1\right) \)
\( D \cdot \cos ^{-1}\left(x^{2}+1\right) \)


\( 2 \mu F \) capacitance has P.D across its two terminals of \( 200 \mathrm{V} . \) It is disconnected
from the battery and when another uncharged capacitance is connected in parallel to it, P.D becomes 20 V. The capacity of another capacitance will be:
A \( .2 \mu F \)
в. \( 4 \mu F \)
c. \( 10 \mu F \)
\( \mathbf{D} \cdot 16 \mu F \)


Two non-reactive gases A and B are present in a container with partial pressures 200 and \( 180 \mathrm{mm} \) of Hg. When
a third non - reactive gas \( C \) is added then total pressure becomes 1 atm then mole fraction of \( \mathrm{C} \) will be:
A . 0.225
B. 0.75
\( c \cdot 0.5 \)
D. none of these


An optically active halide when allowed
to react with \( C N^{\ominus} \) gives a racemic mixture, the halide is most likely:
A. primary halide
B. sec. halide
c. tert. halide
D. none of these


If \( \triangle A B C \) is right angled at \( B \) and
\( B C=7 c m, A C-A B=1 \mathrm{cm}, \) then
find the value of \( \cos A+\sin A \)


Range of vision of a normal human eye
is from:
\( A \cdot 100 \mathrm{m} \) to \( 25 \mathrm{cm} \)
B. \( 1 \mathrm{km} \) to \( 25 \mathrm{cm} \)
c. Infinity to 25 m
D. Infinity to 25 cm


In the situation shown in figure, what
should be the relation between \( Q \) and \( q \)
so that electric potential at centre of the
square is zero:
A. \( Q=q \)
в. \( Q=3 q \)
c. \( Q=2 q \)
D. \( Q=-3 q \)


A wire of resistance \( 20 \Omega \) is bent to form
a closed square. What is the resistance
across a diagonal of the square.


and mass m. A particle also of mass \( \mathrm{m} \) is fixed at a point \( A \) on the wedge of the disc as in fig. The disc can rotate freely
about a fixed horizontal chord PQ that is
at a distance \( \mathrm{R} / 4 \) from the centre \( \mathrm{C} \) of
the disc. The line AC is perpendicular to
PQ. Initially the disc is held vertical with
the point \( A \) at its highest position. It is
then allowed to fall so that it starts
rotating about PQ.
If the linear speed of the particle as it
reaches its lowest position is \( \boldsymbol{v}= \)
\( \sqrt{x g R} \) Find \( x \)


State the given statement is true or false.

Statement: Mercuric oxide is reduced
by thermal decomposition.
A. True
B. False


Assertion
Capital formation in India has been low
due to population explosion.
Reason Rising population has led to increased spending on consumption, while very little part of the national income is available for savings and investments
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 general formula of Grignard
reagent.


If \( \cos (\alpha+\beta)=\frac{4}{5} \) and \( \sin (\alpha-\beta)=\frac{5}{13} \)
where \( \alpha, \beta \) lie between \( 0^{\circ} \) and \( 45^{\circ}, \) then
the value of \( \tan 2 \alpha \) is
A \( \cdot \frac{56}{33} \)
в. \( \frac{46}{33} \)
c. \( \frac{14}{33} \)
D. \( \frac{16}{33} \)


Fill in the blank.
It becomes \( _{-}-_{-}-_{-}-_{-} \) to cut vegetable with a sharp edged knife because the pressure is
A. easy, more
B. difficult, more
c. easy, less
D. difficult, less


The Young's double slit experiment is
done in a medium of refractive index
4/3. A light of 600 nm wavelength is falling on the slits have \( 0.45 \mathrm{mm} \)
separation. The lower slit \( S_{2} \) is covered
by a thin glass sheet of thickness 10.4
mm and refractive index 1.5. The
interference pattern is observed on a
screen placed at \( 1.5 \mathrm{m} \) from the slits as
shown in the fig.
(All wavelength in this problem are for
the given medium of refractive index
4/3. Ignore dispersion.) Find the location
of central maxima (bring fringe with
zero path difference ) on the y-axis.


Find the sin angle between the vectors \( A=3 i-4 j+5 k \) and \( B=i-j+k ? \)


In a meter bridge, the balance point is obtained at \( 40 \mathrm{cm} . \) If a resistance equal
to that in the left gap is shunted across
itself, the new balance point is:
\( \mathbf{A} \cdot 40 \mathrm{cm} \)
B. \( 15 \mathrm{cm} \)
c. \( 25 \mathrm{cm} \)
D. \( 32 \mathrm{cm} \)


Number of primary carbon atoms in the given compound is:
\( \boldsymbol{C}-\underbrace{\boldsymbol{C}}_{\boldsymbol{C}}-\boldsymbol{C}-\dot{\boldsymbol{C}}-\boldsymbol{C} \)
\( A \cdot 2 \)
B. 5
\( c \cdot 4 \)
\( D \)


The number of molecules present in 2
grams of helium at \( 273^{\circ} \mathrm{C} \) and 1520
mm Hg pressure are:
\( \left[N_{A}=6.02 \times 10^{23}\right] \)
A. \( 3.01 \times 10^{23} \)
B. \( 6.02 \times 10^{23} \)
c. \( 3.01 \times 10^{22} \)
D. \( 6.02 \times 10^{22} \)


Two stones are thrown up
simultaneously from the edge of a cliff
\( 200 \mathrm{m} \) high with initial speeds of \( 15 \mathrm{m} \)
\( s^{-1} \) and \( 30 \mathrm{m} s^{-1} \) respectively. The time
variation of the relative position of the
second stone with respect to the first as
shown in the figure. The equation of the
liner part is
\( \mathbf{A} \cdot x_{2}-x_{1}=50 \mathrm{t} \)
B \( \cdot x_{2}-x_{1}=10 t \)
\( \mathbf{c} \cdot x_{2}-x_{1}=15 t \)
D. \( x_{2}-x_{1}=20 t \)


The total number of amino acids in a
molecule of the Hypoglycemic hormone is:
A . 30
B . 21
\( c \cdot 5 \)
D. 27


Electrovalent bond or ionic bond is
formed by:-
A. Sharing of electrons
B. Donation of electrons
c. Transfer of electrons
D. None of these


Which of the following statement is not
correct about Ellingham diagram?
A. \( \Delta G \) increases with an increase in temperature
B. It consists of plots of \( \Delta_{f} G^{\circ} \) vs \( T \) for formation of oxides
C. A coupling reaction can be well expressed by this diagram
D. It express the kinetics of the reduction process


If the eccentricity of an ellipse is \( \frac{5}{8} \) and the distance between its foci is \( 10, \) then
its latus rectum is
A \( \cdot \frac{39}{4} \)
B. 12
c. 15
D. \( \frac{37}{2} \)


The production of saleable steel in some of the steel plants of our country during 1999 is given below:

Plant \( \quad \) Bhilai Durgapur \( \quad \) Rourke
Production
In thousand tonnes
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big division = 20 thousand
tonnes.


Phytotron is
A. A controlled condition chamber for plants
B. Leaf culture process
C . Special culture of seeds
D. Root culture process


Magnification produced by spherical
lens is \( +2.5 . \) What is the nature of
image?
A. Virtual, erect
B. Real, invented
c. Real, erect
D. None


For the fuel cell reaction, \( 2 H_{2}+O_{2} \rightarrow \)
\( 2 H_{2} O, \Delta G=-475 k J \)
The value of \( \boldsymbol{E}^{o} \) cell is:
A . \( 1.23 \mathrm{v} \)
B. 2.46
c. \( 0.615 \mathrm{v} \)
D. 0.31


Find the vector equation of the line joining (1,2,3) and (-3,4,3) and show pependicular to the z-axis


What is the oxidation number of \( C l \) in
the \( C l O_{3}^{-} \) ion?
\( A \cdot-1 \)
B. +5
\( c \cdot-5 \)
\( D \cdot+7 \)


The number of \( s p^{2} \) hybridized carbon
atoms in the given compound is:
\[
\mathbf{H C} \equiv \mathbf{C}-\mathbf{C H}_{2}-\mathbf{U}-\mathbf{C H}_{2}-\mathbf{C H}=\mathbf{C H}_{2}
\]
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
\( D \)


\( \int \frac{t^{2}+t}{t} d t \)


The notation for an isotope of sodium
\( _{11}^{23} N a . \) Which row gives the composition
of a neutral atom of this isotope of
sodium?
\( \begin{array}{lll}\text { number } & \text { number } & \text { number } \\ \text { of } & \text { of } & \text { of } \\ \text { protons } & \text { neutrons } & \text { electrons } \\ \text { A } & 11 & 12 & 11 \\ \text { B } & 11 & 12 & 12 \\ \text { C } & 11 & 23 & 11 \\ \text { D } & 12 & 11 & 12\end{array} \)
\( A \)
B. B
\( c \cdot c \)
\( D . \)


Which type of wave is produce in a
resonance tube?
A. longitudinal
B. transverse
c. transverse stationary
D. longitudinal stationary


Calculate the de Brogile wavelength of a photon whose linear momentum has a magnitude of \( 3.3 \times 10^{-23} k g m / s \)
A. 0.0002 nm
B. \( 0.002 \mathrm{nm} \)
c. \( 0.02 \mathrm{nm} \)
D. \( 0.2 \mathrm{nm} \)
\( E \cdot 2 \mathrm{nm} \)


Among \( N_{2} O, S O_{2}, I_{3}^{+} \) and \( I_{3}^{-}, \) the linear
species are \( N_{2} O \) and \( I_{3}^{-} \)
A . True
B. False


Plants, but not animals, can convert fatty acids to sugars by a series of reactions called
A. photosynthesis
B. Krebs cycle
c. glycolysis
D. glyoxylate cycle


The number of lines which pass through point (2,-3) and are at a distance 8 from point (-1,2) is
\( A \cdot \infty \)
B. 4
\( c \cdot 2 \)
D.


For the reaction \( \mathbf{H}_{2}(\mathbf{g})+\mathbf{I}_{2}(\mathbf{g}) \rightleftharpoons \)
\( 2 H I(g) \)
\( \mathbf{K}_{\mathbf{c}}=\mathbf{6 6 . 9} \) at \( \mathbf{3 5 0}^{\circ} \mathbf{C} \) and \( \mathbf{K}_{\mathbf{c}}=\mathbf{5 0 . 0} \mathbf{a t} \)
\( 448^{\circ} \mathrm{C} . \) The reaction has:
\( \mathbf{A} \cdot \Delta H=+v e \)
B. \( \Delta H=-v e \)
c. \( \Delta H=Z \) ero
D. \( \Delta H= \) Not found the signs


The degree of dissociation of
\( \boldsymbol{C a}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2} \) in a dilute aqueous solution
containing 7 g of salt per 100 g of water at \( 100^{\circ} \mathrm{C} \) is \( 75 \% \). The vapour pressure of solution in \( \mathrm{mm} \) is \( x, \) then find the
value of \( x / 150 \) to the nearest integer.


According to the Arrhenius concept
formation of \( \boldsymbol{O} \boldsymbol{H}^{-}(\boldsymbol{a} \boldsymbol{q}) \) ions in solution
is responsible for
A. basic substance.
B. acidic substance
c. neutral substance
D. slightly acidic substance


Very short answer type. Name the monomer(s) of the following dimers/polymers proteins


Let \( n \) be an odd integer greater than 1
and let \( c_{1}, c_{2}, \cdots, c_{n} \) be integers. For
each permutation \( \boldsymbol{a}=\left(\boldsymbol{a}_{1}, \boldsymbol{a}_{2}, \cdots, \boldsymbol{a}_{n}\right) \)
of \( (1,2, \cdots, n) \) define \( S(a)=\sum_{i=1}^{n} c_{i} a_{i} \)
Prove that there exist permutations
\( a \neq b \) of \( \{1,2, \cdots, n\} \) such that \( n ! \) is a
divisor of \( \mathrm{S}(\mathrm{a})-\mathrm{S}(\mathrm{b}) \)
A \( \cdot \frac{1}{2} n !(n !-1) \equiv \frac{1}{2}(n+1) ! \sum_{i=1}^{n} c_{i}(\bmod n !) . \) Because \( n>1 \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction
B \( \cdot \frac{1}{2} n !(n !+1) \equiv \frac{1}{2}(n+1) ! \sum_{i=1}^{n} c_{0}(\text { modn! }) . \) Because \( n>1 \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction.
c. \( \frac{1}{2} n !(n !-1) \equiv \frac{1}{2}(n-1) ! \sum_{i=1}^{n} c_{0}(\text { modn! }) . \) Because \( n> \)
is odd, the right-hand side is congruent to 0 mod \( n ! \) while the lefthand side is not, a contradiction.
D. None of the above


\( A \) and \( B \) are events with \( P(A)= \) \( \mathbf{0 . 6}, \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 7} \) then compute \( \boldsymbol{P}(\boldsymbol{A} \cap \)
\( B) \)


Aerosols, decrease primary productivity by
A. Decreasing \( O_{2} \) concentration
B. Preventing \( N_{2} \) fixation
c. Reducing photosynthesis
D. None of the above


A monochromatic beam of light falls on Young's double slit experiment
apparatus as shown in figure. A thin
sheet of glass is inserted .in front of
lower slit \( S_{2} \)
The central bright fringe can be
obtained:
\( A \cdot A t O \)
B. Above \( O \)
c. Below \( O \)
D. Anywhere depending on angle \( \theta \), thickness of plate \( t \), and refractive index of glass \( \mu \)


Find \( \frac{d y}{d x}, \) when \( y=\frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}} \)


The odds against a certain event are 5 to 2 and the odds in a fvour of another
event independent to the former are 6 to
5. Find the probability that none of the events will occur.


Find the equation of parabola with vertex (0,0)\( \& \) focus at (0,2)


Equations relating to acidic properties of an aq. solution of HCl gas is/are:
A \( \cdot H C l(g)+H_{2} O \rightleftharpoons H_{3} O^{+}+C l \)
в. \( Z n(O H)_{2}+2 H C l \rightarrow Z n C l_{2}+2 H_{2} O \)
c. \( M n O_{2}+4 H C l \rightarrow M n C l_{2}+C l_{2}+2 H_{2} O \)
D. all of the above


Study involving both electricity and magnetism is called
A. electromagnetism
B. magnetoelectricism
c. electricmagnetism
D. magneticelectromerism


The frequency of generator \( (\mathrm{AC}) \) is measured using:
A. multimeter
B. AVO meter
c. tachometer
D. speedometer


Ergocalciferol is name of vitamin:
A. \( A \)
в. \( B \)
c. \( C \)
\( D \cdot D_{2} \)


Which is the correct sequence of the
components of a reflex arc?
A. Receptors - Muscle - Sensory neuron - Motor neuron Spinal cord
B. Receptors - Motor neuron - Spinal cord - Sensory neuron - Muscle
C. Receptors - Spinal cord - Sensory neuron - Motor neuron- Muscle
D. Receptors - Sensory neuron - Spinal cord - Motor neuron - Muscle


Find the integrals of the functions.
i) \( \sin ^{3} x \cos ^{3} x \)
ii) \( \sin x \sin 2 x \sin 3 x \)
iii) \( \sin 4 x \sin 8 x \)
iv \( \frac{1-\cos x}{1+\cos x} \)
v) \( \frac{\cos x}{1+\cos x} \)


A gas \( X \) bleaches the colour of flowers
by reduction while the other gas \( Y \) bleaches by oxidation. These two gases
\( X \) and \( Y \) are respectively:
A. \( C O \) and \( C O_{2} \)
B. \( N H_{3} \) and \( S O_{3} \)
\( \mathrm{c} \cdot \mathrm{CO}_{2} \) and \( \mathrm{Br}_{2} \)
D. \( S O_{2} \) and \( C l_{2} \)


Considre the sequence \( \left(a_{n}\right) n \geq 0 \) given
by the following relation: \( a_{0}=4, a_{1}= \)
\( 22, \) and for all \( n \geq 2, a_{n}=6 a_{n-1}- \)
\( a_{n-2} . \) Prove that there exist sequences
of positive integers \( \left(x_{n}\right) n \geq \)
\( \mathbf{0},\left(\boldsymbol{y}_{n}\right) \boldsymbol{n} \geq \mathbf{0} \) such that \( \boldsymbol{a}_{\boldsymbol{n}}=\frac{\boldsymbol{y}_{\boldsymbol{n}}^{\boldsymbol{2}}+\boldsymbol{7}}{\boldsymbol{x}_{\boldsymbol{n}}-\boldsymbol{y}_{\boldsymbol{n}}} \)
for all \( n \geq 0 \)


Which of the following doesn't show that
air has pressure?
A. Ball falling to the ground
B. Flying a kite
c. Riding a bicycle against the wind
D. none of these


At \( 380^{\circ} C, \) the half life period for the first
order decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is \( \boldsymbol{3} \boldsymbol{6} \boldsymbol{0} \)
min. The energy of activation of the
reaction is \( 200 k J \) mol \( ^{-1} \). Calculate the
time required for \( 75 \% \) decomposition at
\( 450^{\circ} \mathrm{C} \)


If the source is now changed to green light of wavelength \( 10^{-7} m \) and a new glass plate is placed in place of the previous glass plate, the central fringe shifts to a position initially occupied by the sixth bright fringe due to red light without the glass plate. What is refractive index of new glass plate?
A \( .2 .6 \mu m \)
в. \( 1.6 \mu m \)
c. \( 1.2 \mu m \)
D. \( 2.2 \mu m \)


For the function \( \boldsymbol{f}(\boldsymbol{x})=\left|\boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\boldsymbol{6}\right| \)
the right hand derivative \( f^{\prime}(2+) \) is
equal to.


Is this device feasible?
A. Yes
B. no
C. depends on the availability of material
D. maybe or may not be


For constant non zero mass, momentum
versus velocity graph is a:
A. straight line parallel to \( x \) - axis
B. straight line parallel to y- axis
C. straight line passing through origin
D. straight line passing through y- axis with an intercept


The value of
\( \lim _{x \rightarrow \infty} \frac{\cot ^{-1}\left(x^{-a} \log _{a} x\right)}{\sec ^{-1}\left(a^{x} \log _{x} a\right)},(a>1) \) is equal
to
A . 1
B.
c. \( \pi / 2 \)
D. does not exist


Which of the following is NOT soluble in
water?
A. Salt
B. Sugar
c. oxygen
D. sand


Assertion
\( \boldsymbol{S} \boldsymbol{c}(\boldsymbol{Z}=\mathbf{2 1}) \) is placed in d-block
elements.
Reason
Last filling electron goes into \( 3 d- \) suborbit.
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


According to 1st law of Thermodynamics,
A. Energy can be created but not destroyed
B. Energy cannot be created but can be destroyed
C. Energy can be created and destroyed
D. Energy can not be created nor destroyed


Select the correct statement.
This question has multiple correct options
A. At radioactive equilibrium, the number of atoms of \( A \) and \( B \) are in the inverse ratio of their average life.
B. In beta decay, all the emitted electrons have altogether different energy.
C. If \( n / p \) is lower than required for the belt of stability, either positron emission or \( \mathrm{K} \) -electron capture must be shown.
D. Like electrons energy level in atoms, nuclear energy level also exist.


If this enzyme were to be absent in our small intestine, digestion of proteins in our body would be severely affected.
A. Pancreatic amylase
B. Maltase
c. Lipase
D. Enterokinase


Match the List I with the List II.


If \( y=e^{m \sin ^{-1} x}, \) then show that \( (1- \)
\( \left.x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-m^{2} y=0 \)


Which element is considered
radioactive among the options given below?
A. Sodium
B. Gold
c. Thorium
D. Neon


Find the domain of the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\sqrt{|\boldsymbol{x}|-\boldsymbol{x}}} \)
A. \( [0, \infty) \)
(n)
в. \( (-\infty, 0) \)
\( c \cdot[1, \infty) \)
D. \( (-\infty, 0 \)


Which of the following is wrong
statement?
A \( \cdot D=\frac{1}{f} \) where \( f \) is focal length and \( D \) is optical power of lens.
B. Power is in diopter when \( f \) is in meters.
C. Power is in diopter and does not depend upon the system of unit used to measure \( f \)
D. \( D \) is positive for convergent lens and \( D \) is negative for divergent lens.


According to periodic law elements with similar properties fall in the vertical column called a
A. same, group
B. same, period
c. different, group.
D. none of these


If the sum to \( n \) terms of an AP is
\( \frac{4 n^{2}-3 n}{4} \) then the \( n^{t h} \) term of the AP is equal to
A \( \cdot \frac{5 n-1}{4} \)
в. \( \frac{8 n-7}{4} \)
c. \( \frac{3 n^{2}-2}{4} \)
D. \( \frac{7 n-8}{4} \)


Equation of two equal sides of a triangle are the lines \( 7 x-y+3=0 \) and \( x+ \)
\( y-3=0 \) and the third side passes
through the point \( (1,-10), \) then the equation of the third side can be
This question has multiple correct options
A . \( x-3 y=31 \)
B. \( 3 x+y+7=0 \)
c. \( x+3=0 \)
\( \mathbf{D} \cdot y=3 \)


The value of \( c \) in Lagranges mean value
theorem for \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{l} \boldsymbol{x}^{2}+\boldsymbol{m} \boldsymbol{x}+ \)
\( \boldsymbol{n},(\boldsymbol{l} \neq \mathbf{0}) \) on \( [\boldsymbol{a}, \boldsymbol{b}] \) is
A \( \cdot \frac{a}{2} \)
B. \( \frac{b}{2} \)
c. \( \frac{(a-b)}{2} \)
D. \( \frac{(a+b)}{2} \)


An electron in the ground state of
hydrogen has an angular momentum \( L_{1} \)
and an electron in the first excited state
of lithium has an angular momentum
\( \boldsymbol{L}_{2} . \) Then
A \( \cdot L_{1}=L_{2} \)
В. \( L_{1}=4 L_{2} \)
\( \mathbf{c} \cdot L_{2}=2 L_{1} \)
D. \( L_{1}=2 L_{2} \)


Which of the following is a restatement of first law of thermodynamics:
A. Guy-Lassac's Law
B. The principle of entropy
C. The principle of enthalpy
D. conservation of energy
E. Avogadro's hypothesis


Given: Parallelogram \( A B C D \) in which
diagonal \( A C \) and \( B D \) intersect at \( M \)
Prove \( M \) is the mid-point of \( L N \)


Diazomethane was photolysed to
generate singlet carbine which was
treated with cis-2-butene. The main
product(s) of the reaction is/are:
A. cis-1, 2-dimethylcyclopropane
B. trans-1, 2-dimethylcyclopropane
c. mixture of \( (A) \) and \( (B) \)
D. Ethylcyclopropane


Pressure exerted by a body on a surface
is
A. force \( \times \) area
B. force \div area
c. area \( \div \) force
D. force \div volume


What is the magnitude of the total force
on a driver by the racing car he operates, as it accelerates horizontally along a straight line from rest to \( 60 m / s \) in \( 8.0 s \text { (mass of the driver }=80 k g) \)


Which of the following statements
about ozone is true?
A. Ozone layer is benifical to us because ozone cuts the ultraviolet radiationof the sun
B. The conversion of ozone to oxygen is an endothermic reaction
C. Ozone is triatomic linear molecule
D. Ozone layer is harmul as it cuts out radiation useful for photosynthesis


\( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{N} \boldsymbol{H}_{2} \frac{N a N O_{2}+\boldsymbol{H} C l, \mathbf{0}^{o} \boldsymbol{C}}{\longrightarrow} \)
\( \boldsymbol{X} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{w} \boldsymbol{a} \boldsymbol{r} \boldsymbol{m}}{\boldsymbol{Y}} \boldsymbol{Y} \)
In the above reaction, \( \boldsymbol{Y} \) is:
\( \mathbf{A} \cdot C_{6} H_{5} C l \)
в. \( C_{6} H_{6} \)
c. \( C_{6} H_{5} O H \)
D. \( C_{6} H_{5} C H O \)


mRNA part that codes for the amino acid serine, is:
A. AMP
B. ADP
c. uca
D. d ATP


The distance of the point (1,-5,9) from the planer. \( (\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\boldsymbol{k}})=\mathbf{5} \)
measured long the line \( r=\hat{i}+\hat{j}+\hat{k} \) is
A \( 3 \sqrt{5} \)
5
B. \( 10 \sqrt{3} \)
\( c \cdot 5 \sqrt{3} \)
D. \( 3 \sqrt{10} \)


Match the column I with Column II and
select the correct option from the codes
given below.
(a) \begin{tabular}{l|l|l}
column I & & Column II \\
& \\
Hottest zone of candle flame & (i) & Zone of unburunt wax vapours. \\
Yellow zone of candle flame & (ii) & Nonluminous zone \\
Black innermost zone of the candle flame & (iii) & Incomplete combustion zone/ \\
\hline
\end{tabular}
(b)
\( (c) \)
\( A \)
(a) - (i), (b) - (ii), (c) - (iii)
B. (a) - (ii), (b) - (i), (c) - (iii)
c. (a) - (i), (b) - (iii), (c) - (ii)
D. (a) - (ii), (b) - (iii), (c) - (i)


If the Vant Hoff factor for \( \mathbf{0 . 1} \mathbf{M} \)
\( B a\left(N O_{3}\right)_{2} \) solution is 2.74 , the degree of dissociation is:
A . 0.87
в. 0.74
c. 0.91
D. 87


\( = \)
\( u \)
\( \delta \)


An atom 'X' has a mass number of 12
and contains 6 electrons. State the
atomic number of 'X' and the number of
neutrons it contains.
\( A \cdot 6,6 \)
B. 6, 12
\( c \cdot 12,6 \)
D. 12, 12


Define self inductance of a coil. Derive
the expression for magnetic energy stored in the inductor of inductance \( L \)
carrying current \( \boldsymbol{I} \)


Very Short Answer Type Question. How is atmosphere important for us?


Solve \( \lim _{x \rightarrow 0} \frac{\sin x}{\sqrt{x^{2}}} \)
\( \mathbf{A} \cdot 1 \)
B . -1
\( \mathbf{c} \cdot 0 \)
D. doesn't exist


What will be the radius of curvature of a
concave mirror whose focal length is 25
\( \mathrm{cm} ? \)