When the vapours of alcohol are passed
over copper or zinc oxide, then the following compound has no chances to be formed?
A. Alkanal
B. Alkyne
c. Alkene
D. Alkanone


Solve:
\( \frac{5 p+2}{8-2 p}=\frac{7}{6} \)


\( \mathbf{1 0} \) cells each of emf \( 1.5 V \) are
connected in
(a) series
(b) parallel What is the equivalent emf produced in each case?


Pressure is an intensive property.
A. True
B. False


The respective number of significant
figures for the numbers 23.023,0.0003
and \( 2.1 \times 10^{-3} \) are
A. 5,1,2
B. 5,1,5
\( c \cdot 5,5,2 \)
D. 4,4,2


If functions \( f, g: R \rightarrow R \) are defined as
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\mathbf{1}, \boldsymbol{g}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}-\mathbf{3}, \) then find
\( f o g(x), g o f(x) \) and \( g o g(3) \)


Very short answer type.
What is the volume of blood in the
human body?


If an AP, the sum of first ten term is -150 and the sum of its next ten terms is
-550. Find first term of AP.


If the area of two similar triangles are equal, then prove that they are
congruent.


Which of the following is not correct?
A. \( A \) sigma bond is weaker than pi bond.
B. A sigma bond is stronger than pi bond.
C. A double bond is stronger than a single bond.
D. A double bond between two atoms is shorter than a single bond between the same atoms.


A long spring is stretched by \( 2 \mathrm{cm} \) and
its potential energy is \( U . \) If the spring is stretched by \( 10 \mathrm{cm} ; \) its potential energy will be (in terms of \( U \) )
A. \( U / 5 \)
в. \( U / 25 \)
\( c .5 U \)
D. 25U


If there is no \( C O_{2} \) in the atmosphere
what would happen to the earth's temperature?
A. It would, be less than the present.
B. It would,be the same as present.
c. It would be higher than the present
D. It depends on the \( 0_{2} \) content of air.


A decoration, of mass \( M, \) is suspended by a string from the ceiling inside an elevator. The elevator is traveling
upward at a constant speed. The tension in the string is
A. Equal to \( M g \)
B. Less than \( M g \)
c. Greater than \( M g \)
D. Impossible to tell without knowing the speed


The correct order of increasing basic nature of the following bases is:
A. \( 2<5<1<3<4 \)
В. \( 5<2<1<3<4 \)
c. \( 2<5<1<4<3 \)
D. \( 5<2<1<4<3 \)


The moment of inertia of a sphere of
mass \( M \) and radius \( R \) about an axis passing through its centre is \( \frac{2}{5} M R^{2} \) The radius of gyration of the
sphere about a parallel axis tangent to
the sphere is:
A \( \cdot \frac{7}{5} R \)
B. \( \frac{3}{5} R \)
\( ^{C} \cdot \frac{\sqrt{7}}{\sqrt{5}} R \)
D. \( \frac{\sqrt{3}}{\sqrt{5}} R \)


Whose IUPAC name ends with -amine?
A. \( R-O H \)
в. \( R-O-R \)
c. \( R-N H_{2} \)
D. \( R-C O O-R \)
E . \( R-C O-R \)


A car is moving with a speed of 40
km/hr. If the car engine generated 7 kilowatt power, then the resistive force in the path of the car will be:-
A. 360 Netwon
B. 630 Newton
c. zero
D. 280 Newton


When an amino acid solution which is
slightly alkaline is subjected to electrolysis, the resulting component migrates towards
A. Cathode due to zwitter ion formation.
B. Anode due to the conversion of zwitter ion to negative ion
c. Migrate to cathode due to the conversion to negative ion
D. One component towards cathode and the other towards anode due to the zwitter ion formation


A parallel beam of white light is
incident on a thin film of air of uniform
thickness. Wavelengths \( 7200 \dot{A} \) and \( \mathbf{5 4 0 0} \dot{\boldsymbol{A}} \) are observed to be missing from the spectrum of reflected light viewed normally. The other wavelength in the visible region missing in the reflected spectrum is
В. 4320 А
c. \( 5500 \dot{h} \)


\( Y \) molal solution of a compound in benzene has mole fraction of solute
equal to \( 0.2 . \) The value of \( ? \)
A . 14
B. 3.
c. 1.4
D. 2


Electricity and magnetism are mutually
A. complementary
B. Opposite
c. Equal and opposite
D. Strongest forces


Show that the function is continuous at
\[
\begin{array}{l}
x=0, \text { if } f(x)=\frac{\sin 3 x}{\tan 2 x}, x<0 \\
=\frac{\log (1+3 x)}{e^{2 x}-1}, x>0 \\
=\frac{3}{2}, x=0
\end{array}
\]


Calculate the energy required to excite two litre of hydrogen gas at 1 atom and \( 298 \mathrm{k} \) to the first excited state of atomic
hydrogen. The energy for the
disassociation of \( \mathrm{H}_{2} \) bond is \( 436 \mathrm{kJ} \) mol
\( -1 . \) Also calculate the minimum
frequency of photon to break this bond.
A. \( 8.523 \times 10^{15} \mathrm{Hz} \)
В . \( 1.096 \times 10^{15} \) Н \( z \)
c. \( 1.633 \times 10^{15} \mathrm{Hz} \)
.
D. 2.806 \( \times 10^{15} \mathrm{Hz} \)


The unit vector perpendicular to the plane determined by \( \boldsymbol{P}(\mathbf{1},-\mathbf{1}, \mathbf{2}) \)
\( Q(2,0,-1), R(0,2,1) \) is
A \( \cdot \frac{i+2 j+k}{\sqrt{6}} \)
в. \( \frac{i-2 j+2 k}{\sqrt{6}} \)
c. \( \frac{2 i+j+k}{\sqrt{6}} \)
D. none of these


ff \( f(x+1)=3 x-9 \) then find the value
of \( \boldsymbol{f}\left(\boldsymbol{x}^{2}-\mathbf{1}\right) \)


A source emits sound waves of
frequency \( 1000 H z . \) The source moves
to the right with a speed of \( 32 m / s \) relative to ground. On the right, a
reflecting surface moves towards left
with a speed of \( 64 m / s \) relative to
ground. The speed of sound in air is
\( 332 m / s . \) Then
This question has multiple correct options
A. wavelength of reflected waves is nearly \( 0.3 \mathrm{m} \)
B. number of waves arriving per second which meets the reflected surface is 1320
C. speed of reflected wave is \( 268 \mathrm{m} / \mathrm{s} \)
D. wavelength of reflected waves is nearly \( 0.2 \mathrm{m} \)


When was Braille system first published?
A . 191
в. 1852
c. 1821
D. 1963


Find the number of integer solutions of
\( \boldsymbol{x}_{1}+\boldsymbol{x}_{2}+\boldsymbol{x}_{3}+\boldsymbol{x}_{4}=\mathbf{2 0} \) where \( \boldsymbol{x}_{1} \geq \)
\( -5, x_{2} \geq 3, x_{3} \geq 0, x_{4} \geq 1 \)


A dipole of dipole moment \( P \) is placed at
a distance r form a point change \( Q \) (as
shown in figure).Choose the incorrect
statement.
A. Torque acting on the dipole is zero
B. Force acting on the dipole due to the electrie field produce by \( \mathrm{Q} \) is zero
C. potential energy of the dipole due to the point charge \( Q \) is \( \frac{Q p}{4 \frac{Q_{0}}{r^{2}}} \)
D. Force acting on the dipole due to the point charge \( \mathrm{Q} \) is \( \frac{Q p}{4 \pi \varepsilon_{0} r^{3}} \)


Which of the following action or activity may causes undesirable effect to our
environment?
i) Catching and keeping animals such as bird and cats at home.
ii) Feeding birds such as pigeon and crows in our neighbourhood.
iii) Burning unwanted plastic product in our neighbourhood o reduce non biodegradable rubbish.
iv) Dumping biodegradable refuse such as fruit skins and bones in our sewage
to make the water nutrients rich for
healthy growth of flowering plants.
A. iii and iv only
B. ii and iv only
c. ii, iii and daily
D. i, ii, iii and D


If \( P(x), q(x) \) and \( r(x) \) are three polynomials of degree 2 , then prove that
\[
\left|\begin{array}{lll}
\boldsymbol{p}(\boldsymbol{x}) & \boldsymbol{q}(\boldsymbol{x}) & \boldsymbol{r}(\boldsymbol{x}) \\
\boldsymbol{p}^{\prime}(\boldsymbol{x}) & \boldsymbol{q}^{\prime}(\boldsymbol{x}) & \boldsymbol{r}^{\prime}(\boldsymbol{x}) \\
\boldsymbol{p}^{\prime \prime}(\boldsymbol{x}) & \boldsymbol{q}^{\prime \prime}(\boldsymbol{x}) & \boldsymbol{r}^{\prime \prime}(\boldsymbol{x})
\end{array}\right| \text { is independent }
\]
of \( X \)


ABCD is a parallelogram, E and F are the mid-points of \( A B \) and \( C D \) respectively. \( \mathrm{GH} \) is any line intersecting \( \mathrm{AD}, \mathrm{EF} \) and BC at G,P and H respectively. Prove that \( \boldsymbol{G} \boldsymbol{P}=\boldsymbol{P} \boldsymbol{H} \)


Four equal circles describe the four corners of a square such that each touches two of the others. If each side of
the square is \( 14 \mathrm{cm} \), then the area
enclosed between the circumferences of
the circle is:
A. 24 sq cm
B. 42 sq \( \mathrm{cm} \)
c. 154 sq \( \mathrm{cm} \)
D. 196 sq \( \mathrm{cm} \)


Iso-propyl bromide on Wurtz reaction
gives:
A. Hexane
B. Propane
c. 2,3 -dirnethylbutane
D. Neo-hexarte


Use Euclid's Division Lemma to show
that the cube of any positive integer is of the form \( 9 m, 9 m+1 \) or \( 9 m+8, \) for
some integer \( \boldsymbol{m} \)


Which of the following is/are true regarding the following linear equation:
\( \boldsymbol{x}+\mathbf{5} \boldsymbol{y}+\mathbf{2}=\mathbf{0} \)
A. It passes through (0,-0.4) and \( m=-0.2 \)
B. It passes through (0,0.4) and \( m=0.2 \)
C. It passes through (0,-0.2) and \( m=-0.4 \)
D. It passes through (0,0.2) and \( m=0.4 \)


The ratio of charge densities on the surface of two conducting spheres is 3:
2. lithe radii of t: the spheres are \( 4 \mathrm{cm} \) and \( 8 \mathrm{cm} \) the ratio of the electric potential on the surfaces of the sphere 2
is
\( A \cdot 3: 4 \)
B. 3:1
\( c \cdot 1: 3 \)
D. 4: 9


How many chiral carbons are present in gulcose molecule \( \mathrm{CHO}(\mathrm{CHOH})_{4} \mathrm{CH}_{2} \mathrm{OH} ? \)
\( A \cdot 4 \)
B. 3
\( c \cdot 2 \)
D.


Hydrogen behaves as a metal:
A. at low temperature
B. at low pressure
c. at high temperature
D. at high pressure


If \( 1+a+a^{2}+a^{3}+\dots \dots+a^{n}=(1+ \)
\( a)\left(1+a^{2}\right)\left(1+a^{4}\right) \) then \( n \) is given by
\( \mathbf{A} \cdot \mathbf{3} \)
B. 5
\( c \cdot 7 \)
D.


\( O H \)
\( C H_{3}-C H-C O O H \stackrel{\perp}{C H}-C O \)
How many optically active (Lactide) product(s) are formed in given reaction?
A . 3
B. 4
c. 2
D.


Which one of the following is a condensation polymer?
A. PVC
B. Teflon
c. Dacron
D. Polystyrene


Which acid on mixing with lead nitrate solution produces a white precipitate which is insoluble even on heating?


If \( \boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{4} & \mathbf{7} \\ \mathbf{2} & \mathbf{6} & \mathbf{5} \\ \mathbf{3} & \mathbf{- 1} & \mathbf{2}\end{array}\right] \) and \( \mathbf{B}=\operatorname{diag}(12 \)
5), then
trace of matrix \( \boldsymbol{A B}^{\mathbf{2}} \) is
A . 74
B. 75
c. 529
D. 23


The number of unpaired electrons in a
chromic ion \( \left.C r^{3+} \text { (atomic number } 24\right) \)
is:
\( A \cdot 6 \)
B. 4
\( c .3 \)
D.


Which of the following is not true
for Universal law of gravitation?
A. It is the gravitational force between the sun and the earth, which makes the earth move around the sun.
B. The tides formed in sea are because of gravitational pull exerted by the sun and the moon on the surface of water.
C. It is the gravitational pull of the earth which keeps us and other bodies firmly on the ground.
D. The gravitational force exerted by sun on earth is larger than that exerted by earth on sun.


If \( f(x)=a x^{2}+b x+c \) and \( f(0)=1 \)
and \( \boldsymbol{f}(-1)=\mathbf{3},(\boldsymbol{a}-\boldsymbol{b})= \)
\( \mathbf{A} \cdot \mathbf{3} \)
B. 1
\( c \cdot 2 \)
D.
E . -1


Depletion of ozone layer is noticed on
A. America
B. Asia
C. Australia
D. All over the earth


Give any three postulates of Bohr's theory of atomic model.


In what ratio does the \( x \) -axis divide the
line segment joining the points (-4,-6) and (-1,7) ? Find the coordinates of the point of division.


Three numbers form an increasing G.P. If the middle number is doubled, then
the new numbers are in A.P. The
common ratio of G.P. is-
A \( .2-\sqrt{3} \)
B. \( 2+\sqrt{3} \)
c. \( \sqrt{3}-2 \)
D. 2


At the same temperature and pressure,
ratio of RMS velocities of \( C H_{4} \) and \( S O_{2} \)
is:
A . 4: 1
B. 1: 4
\( c \cdot 1: 2 \)
D. 2: 1


A silvery-white metal \( X \) reacts with
water at room temperature to produce a
water-soluble compound \( Y \) and a
colourless gas \( Z \). The reactions are
highly exothermic and the \( Z \) catches
fire immediately during the reaction. The solution of \( Y \) in the water on
reacting with a stoichiometric amount of dilute solution of hydrochloric acid gives a solution of \( \mathrm{pH}=7.0 . \) The
compounds \( X, Y \) and \( Z \) respectively
are:
A \( . A l, A l(O H)_{3} \) and \( H_{2} \)
B. \( A g, A g O H \) and \( H_{2} \)
c. \( K, K C l \) and \( H_{2} \)
D. \( N a, N a O H \) and \( H_{2} \)


Guess who I am?
i) I am a cheap metal but highly reactive. Therefore, I sacrifice myself to save the objects made of iron.
ii) I am a solid solution. Dentists use me to fill cavities.
iii) 1 am a constituent of blood pigment. When I am less in quantity, the person is anaemic.
iv) I am formed when matrix and flux
react.


Find range of \( f(x)=\frac{x^{2}+2 x+3}{x}, \) the
range is \( R-(a, b), \) find ab?(If the
answer is \( \mathrm{m} \). Find \( -\mathrm{m} \) )


Find the pairs of consecutive even positive integers, both of which are
larger than 5 such that their sum is less
than 23


Assertion
White phosphorus is more reactive than
red phosphorus.
Reason
Red phosphorus contains tetrahedral units linked to one another to form
linear chains.
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


Incisor present in which bone of human jaw?
A. Premaxilla
B. Maxilla
c. Palatine
D. None


A ball falls from a height of \( 5 m \) and strikes the floor of the lift,which is
moving upwards with a velocity of
1 \( m / s \) what is the velocity of rebound of the ball? Assume the collision to be
elastic.
\( \mathbf{A} \cdot 12 m / s \)
в. \( 9 m / s \)
\( \mathrm{c} \cdot 6 \mathrm{m} / \mathrm{s} \)
D. \( 3 m / s \)


\( a, b, c, d, e \) are in \( A . P . \) Prove the
following results \( \boldsymbol{a}-\boldsymbol{b}+\boldsymbol{c}-\boldsymbol{d}=\mathbf{0} \)


Which one of the following is correct in
respect of the function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{2}}{|\boldsymbol{x}|} \) for
\( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} ? \)
A. \( f(x) \) is discontinuous everywhere
B. \( f(x) \) is continuous everywhere
c. \( f(x) \) is continues at \( x=0 \) only
D. \( f(x) \) is discontinuous at \( x=0 \) only


A telegraph has 5 arms and each arm is
capable of 4 distinct positions, including the position of rest. Find the total number of signals that can be
made.


Assertion: A is very dilute acidic
solution of \( C d^{2+} \) and \( N i^{2+} \) gives a
yellow precipitate of CdS on passing hydrogen sulphide. Reason: Solubility product of CdS is more than that of NiS.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
E. Both Assertion and Reason are incorrect


The brown ring test for \( N O_{2}^{-} \) and \( N O_{3}^{-} \) is due to the formation of complex ion
with formula:
\( \mathbf{A} \cdot\left[F e\left(H_{2} O\right)_{6}\right]^{2+} \)
B. \( \left[F e(N O)(C N)_{5}\right]^{2} \)
c. \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{NO}\right]^{2} \)
D. \( \left[F e\left(H_{2} O\right)(N O)_{5}\right]^{2+} \)


A man wearing a wingsuit glides through the air with a constant velocity
of \( 47 m s^{-1} \) at an angle of \( 24^{\circ} \) to the horizontal. The path of the man is shown n Fig.
The total mass of the man and the
wingsuit is 85 kg. The man takes a time
of 2.8 minutes to glide from point \( A \) to
point \( \boldsymbol{B} \)

Show that the difference in height \( h \)
between points \( A \) and \( B \) is \( 3200 m \)


Give the structural formulae for the
following:
An isomer of n-butane.


Assertion
Nitrous oxide is also known as laughing
gas
Reason
It is a colourless gas having a faint
sweet odour
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


Let \( \boldsymbol{P}(\boldsymbol{n}) \) be the statement \( " \boldsymbol{3}^{\boldsymbol{n}}>\boldsymbol{n}^{\prime \prime} . \) If
\( P(n) \) is true, \( P(n+1) \) is true.
A. True
B. False


A nuclear fission is given below \( A^{240} \rightarrow B^{100}+C^{140}+Q(\text {energy}) \)
Let binding energy per nucleon \( A, B \) and \( \mathrm{C} \) is \( 7.6 \mathrm{MeV}, 8.1 \mathrm{MeV} \) and \( 8.1 \mathrm{MeV} \)
respectively. Value of \( Q \) is :
A. 20 Mev
B. 220 MeV
c. 120 Mev
D. 240 Mev


Assertion
Froth-flotation process is used to concentrate sulphide ores.
Reason
There is difference in the wettability of
different minerals.
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


Which of the following will have a terminating decimal expansion?
A \( \cdot \frac{77}{210} \)
в. \( \frac{23}{30} \)
c. \( \frac{125}{441} \)
D. \( \frac{23}{8} \)


Find the points at which the function \( \boldsymbol{f} \) \( \operatorname{given} \operatorname{by} f(x)=(x-2)^{4}(x+1)^{3} \)
has local maxima


Assertion
If \( a, b, c \) are three positive numbers in
G.P., then \( \left(\frac{a+b+c}{3}\right) \cdot\left(\frac{c+b}{a b+b c+c a}\right)= \)
\( (\sqrt[3]{a b c})^{2} \)
Reason
(A.M.) (H.M.) \( =(G . M .)^{2} \) is true for any
set of positive numbers.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which one of the following statements
is true regarding digestion and absorption of food in humans?
A. Fructose and amino acids are absorbed through intestinal mucosa with the help of carrier ions like \( N a^{+} \)
B. Chylomicrons are small lipoprotein particles that are transported from intestine into blood capillaries
C. About \( 60 \% \) of starch is hydrolysed by salivary amylase in our mouth
D. Oxyntic cells in our stomach secrete the proenzyme pepsinogen


An object have a velocity \( \overrightarrow{\boldsymbol{v}}=(\hat{\boldsymbol{i}}+ \)
\( \hat{\boldsymbol{j}}) \boldsymbol{m} / \boldsymbol{s} \) at time \( \boldsymbol{t}=\mathbf{0} . \) It undergoes a
constant acceleration \( \boldsymbol{a}=(\hat{\boldsymbol{i}}- \)
\( 2 \hat{j}) m s^{-2} \) for 4 second. The magnitude of
velocity at the end of \( 4 s \) is:
\( \mathbf{A} \cdot \sqrt{74} m / s \)
B. \( \sqrt{80} \mathrm{m} / \mathrm{s} \)
c. \( \sqrt{97} \mathrm{m} / \mathrm{s} \)
D. \( \sqrt{47} \mathrm{m} / \mathrm{s} \)


What is dimensional formula for
magnetic flux densities?


Names of some compounds are given.
Which one is not correct in IUPAC
system?
\( \mathbf{A} \)
\[
\begin{array}{c}
C H_{3}-C H-C H-C H_{3} \\
\mid \begin{array}{cc}
_{1} & \mid \\
O H & C H_{3}
\end{array}
\end{array}
\]
3-Methyl-2-butanol
B. \( C H_{3}-C H_{2} \equiv C-C H\left(C H_{3}\right)_{2} \)
\( \mathbf{c} \)
\[
\begin{array}{c}
C H_{3}-C H_{2}-C-C H-C H_{3} \\
\|_{C H_{2}} \stackrel{1}{C H_{3}}
\end{array}
\]
2-Ethyl-3-methyl-but-1-ene
D.
\[
C H_{3}-C H_{2}-C H_{2}-C_{\mid} C H_{3}^{C H_{3}}
\]
3-Methyl-4-ethyl heptane


Which of the following statement(s) is/are correct
This question has multiple correct options
A. If the band gap becomes much more higher for a semiconductor then electrons from lower energy state can't move to higher energy state
B. Lesser the band gap lesser is the conduction
C. Lesser the band gap higher is the conduction
D. none of the above


The number of solutions of the equation \( |\cot x|=\cot x+\frac{1}{\sin x}(0 \leq x \leq 2 \pi) \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
\( D \)


The least count of burette used
normally is \( x \) (in \( \mathrm{mL} \) ). The value of \( 10 x \)
is:
\( A \)
B. 1.5
c. 0.10
D. none of these


Diarrhea through food can be avoided by
A. Eating raw food
B. Refrigerating the food
c. Thawing of food again and again
D. None of the above


A car accelerates from rest at a
constant rate \( \alpha \) for some time after
which it decelerates at a constant rate
\( \beta \) to come to rest. If the total time
elapsed is \( t, \) the maximum velocity
acquired by the car is given by
\( ^{\mathrm{A}} \cdot\left(\frac{\alpha^{2}+\beta^{2}}{\alpha \beta}\right) t \)
\( ^{\text {В }} \cdot\left(\frac{\alpha^{2}-\beta^{2}}{\alpha \beta}\right) \)
\( ^{c \cdot}\left(\frac{\alpha+\beta}{\alpha \beta}\right) t \)
\( ^{D \cdot}\left(\frac{\alpha \beta}{\alpha+\beta}\right) t \)


Propylsulphinic acid is prepared by the reaction of the following, followed by hydrolysis:
A \( \cdot C_{3} H_{7} M g B r+S O_{2} \)
B. \( C_{2} H_{5} M g B r+S O_{2} \)
c. \( C_{3} H_{7} M g B r+S O_{3} \)
D. \( C_{2} H_{5} M g B r+S O \)


The energy barrier to free rotation about carbon carbon bond of ethane is about:
A. \( 30 k J \) mol \( ^{-1} \)
B. 3 kJ mol \( ^{-1} \)
c. 3 kcal mol \( ^{-1} \)
D. \( 40 \mathrm{kJ} \mathrm{mol}^{-1} \)


Dynamo converts:
A. electric energy into magnetic energy
B. magnetic energy into potential energy
C. mechanical energy into electrical energy
D. no energy


A block moving in air breaks into two
parts and the parts separate:
This question has multiple correct options
A. the total momentum must be conserved
B. the total kinetic energy must be conserved
C. the total momentum must change
D. the total kinetic energy must change


If a random variable \( X \) follows binomial
distribution with mean 3 and variance \( \frac{3}{2}, \) and \( P(X \leq 5)=\frac{63}{2^{x}}, \) then the value
of \( ^{\prime} x^{\prime} \) is


A fair die is thrown 3 times. The chance
that sum of three numbers appearing on the die is less than 11 , is equal to -
A \( \cdot \frac{1}{2} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{1}{6} \)
D. \( \frac{5}{8} \)


\( \operatorname{Let} a, b, c, \epsilon R \) If \( f(x)=a x^{2}+b x+c \) is
such that \( a+b+c=3 \) and \( f(x+ \)
\( \boldsymbol{y})=\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})+\boldsymbol{x} \boldsymbol{y}, \forall \boldsymbol{x}, \boldsymbol{y} \boldsymbol{\epsilon} \boldsymbol{R}, \) the
\( \sum_{n=1}^{10} f(n) \) is equal to
A . 330
в. 165
c. 190
D. 255 55


Westron has the formula:
A. \( C F_{2} C l_{2} \)
в. \( C H C l_{3} \)
\( \mathbf{c} \cdot C_{2} H_{2} C l_{4} \)
D. \( C H F_{3} \)


The sum of \( 6^{t h} \) term in the geometric
\( \operatorname{series} 4,12,36 \dots \) is
A . 1456
в. 2456
\( c .3456 \)
D. 4456


The natural numbers are written in the
form of a triangle as shown below:
The sum of numbers in all the n rows.
nth


How many grams of \( 70 \% \) concentrated nitric acid solution should be used to
prepare \( 250 \mathrm{mL} \) of \( 2.0 \mathrm{M} ? \)
A \( \cdot 45.0 \mathrm{g} \) conc. \( \mathrm{H} \mathrm{NO}_{3} \)
B. 90.0 g conc. H \( \mathrm{NO}_{3} \)
c. 70.0 conc. \( H N O_{3} \)
D. 54.0 g conc. H NO


Cobalt chloride acts as catalyst in the decomposition of bleaching powder.
A. True
B. False


The distance between the object and its
image formed by a plane mirror appears to be \( 24 \mathrm{cm} . \) What is the distance
between the mirror and the object?
A. \( 24 \mathrm{cm} \)
B. 12 \( \mathrm{cm} \)
\( c \cdot 48 \mathrm{cm} \)
D. 36 cm


Find the arithmetic mean of the
progression 2,4,6,8,10
A . 10
B . 20
c. 30
\( D \)


Write the two processes that take place
in the formation of a \( \boldsymbol{p}-\boldsymbol{n} \) junction.
Explain with the help of a diagram, the formation of the depletion region and barrier potential in a \( p-n \) junction.


The triangle, quadrilateral, pentagon are all examples of
A. diagonal
B. open curve
c. polygon
D. circles


The number of octants in which \( Z \)
coordinate is positive is
A . 2
B. 3
\( c \cdot 4 \)
D. 1


Which of the following is not vector quantity?
A. Retardation
B. Acceleration due to gravity
c. Average speed
D. Displacement


Which of the following has the strongest bleaching property?
A. Chlorine
B. Fluorine
c. Bromine
D. lodine


\( A 3^{\circ} \) alcohol as shown can be obtained
by the reaction of ketone (diisopropyl
ketone) and
A. isopropyl magnesium bromide
B. isopropyl lithium
c. diisopropyl cadmium
D. diisopropyl zinc


Find correct order of polarising power
between \( A l^{+2} \) and \( B e^{+2} \) (both shows
digonal relationship):
A \( \cdot B e^{+2}>A l^{+2} \)
B. \( B e^{+2}<A l^{+2} \)
\( \mathbf{c} \cdot B e^{+2}>>A l^{+2} \)
D. \( B e^{+2}=A l^{+2} \)


Let \( A \) be an invertible matrix. Which of
the following is not true?
A \( \cdot A^{-1}=|A|^{-1} \)
B. \( \left(A^{2}\right)^{-1}=\left(A^{-1}\right)^{2} \)
c. \( \left(A^{T}\right)^{-1}=\left(A^{-1}\right)^{T} \)
D. None of these


Two bodies of mass \( 10 k g \) and \( 2 k g \) are
moving with velocities \( 2 i-7 j+3 k \) and
\( -10 i+35 j-3 k m / s \) respectively. The
velocity of their \( \mathrm{CM} \) is
A \( .2 i \mathrm{m} / \mathrm{s} \)
B. \( 2 k \) m/s
\( c \cdot(2 i+2 k) m / s \)
D. \( (2 i+2 j+2 k) \mathrm{m} / \mathrm{s} \)


Let \( f(x) \) be a real valued function not identically zero, such that
\( \boldsymbol{f}\left(\boldsymbol{x}+\boldsymbol{y}^{n}\right)=\boldsymbol{f}(\boldsymbol{x})+(\boldsymbol{f}(\boldsymbol{y}))^{n} \quad \forall \boldsymbol{x}, \boldsymbol{y} \in \)
\( \boldsymbol{R} \)
where \( n \in N(n \neq 1) \) and \( f^{\prime}(0) \geq 0 . \) We
may get an explicit form of the function
\( \boldsymbol{f}(\boldsymbol{x}) \)
The value of \( f(5) \) is :
A . 6
B. 3
\( c \cdot 5 n \)
D. 5


\begin{tabular}{l}
5 \\
\hline
\end{tabular}


Three numbers are chosen at random
without replacement from \( \{1,2, \ldots, 8 .\} \)
The probability that their minimum is 3 given that their maximum is 6 is
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{8} \)
\( c \cdot \frac{1}{5} \)
D.


What are pseudounimolecular reactions? Explain the help of suitable
example.


A car of mass 2000 kg changes its
speed from \( 18 \mathrm{km} / \mathrm{h} \) to \( 90 \mathrm{km} / \mathrm{hr} \). Find
the work done by the engine.


By IUPAC norms the formulae for Tetrahydroxozincate(ll) ion is:
\( \mathbf{A} \cdot\left[Z n(O H)_{3}\right]^{2} \)
B . \( \left[Z n(O H)_{4}\right]^{3} \)
\( \mathbf{c} \cdot\left[Z n(O H)_{4}\right]^{2} \)
D. None of the above


Most of the plants cultivated in
agriculture are actually belonging to the succession level
A . Early \( 1^{\circ} \) succession
B. Late 1 \( ^{\circ} \) succession
c. Early \( 2^{\circ} \) succession
D. Late \( 2^{\circ} \) succession


Four equal circles, each of radius \( a \) touch each other. Show that the area between then is \( \frac{6}{7} a^{2} \) (Take \( \left.\pi=\frac{22}{7}\right) \)


For a heater rated at \( 4 k W ; 220 V \)
Calculate the resistance of the heater
element.
A . \( 20 \Omega \)
B . \( 21.6 \Omega \)
c. \( 200 \Omega \)
D. \( 12.2 \Omega \)


Determine the osmotic pressure of a solution a solution prepared by
dissolving \( 2.5 \times 10^{-2} g \) of \( K_{2} S O_{4} \) in \( 2 L \)
of water at \( 25^{0} C \), assuming that it is completely dissociated \( \left(R=0.0821 L \text { at } m K^{-1} m o l^{-1}, \) Molar \right.
mass of \( K_{2} S O_{4}=174 g m o l^{-1} \)


In the figure, the potentiometer wire \( \boldsymbol{A} \boldsymbol{B} \)
of length \( L \) and resistnace \( 9 r \) is joined
to the cell \( D \) of e.m.f and internal
resistance \( r . \) The cell \( C^{\prime} \) s emf is \( \varepsilon / 2 \) and
its internal resistance is \( 2 r \)
The galvanometer \( G \) will show no
deflection when the length \( A J \) is
A. \( 4 L / 9 \)
B. \( 5 L / 9 \)
c. \( 7 L / 18 \)
D. \( 11 L / 18 \)


\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \) is added to \( \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}, \) which of
the following colour is observed?
A. Pale Pink
B. Brown
c. Black
D. Green


What is the number of mole of benzene
\( \left(P_{B}^{0}=150 \text { torrs }\right) \) per mole of toluene
\( \left(P_{T}^{0}=50 \text { tor } r s\right) \) in vapour phase if the
given solution has a vapour pressure of 120 torrs in equilibrium with its vapour?
\( A \cdot 7 \)
B. 8
c. 9
D. 10


Earliest jawed vertebrates were
A. Ostracoderms
B. Placoderms
c. crossopterygians
D. Elasmobranchs


Q Type your question
makes an angle of \( 45^{\circ} \) with the
horizontal; the wall AB is normal to the
base BC. The lengths AB and CD are much smaller than the height h of water (figure not to scale)
Let \( P_{1}, P_{2} \$ 4 a n d P_{-} 3 \$ \$ \) be the
pressures excreted by the water on the
wall \( A B, \) base \( B C \) and the wall \( C D \)
respectively. Density of water is p and \( g \) is acceleration due to gravity. Then,
approximately
A \( . P_{1}=P_{2}=P_{3} \)
B . \( P_{1}=0 P_{3}=\frac{1}{\sqrt{2}} P_{2} \)
C \( \cdot P_{1}=P_{3}=\frac{1}{\sqrt{2}} P_{2} \)
D. \( P_{1}=P_{3}=0, P_{2}=h p g \)


The solution of differential equation \( \frac{d y}{d x}+y \tan x=2 x+x^{2} \tan x \) is?
A \( \cdot y=x^{2}+c \cos x \)
B . \( y=2 x^{2}-c \cos x \)
C \( \cdot y+x^{2}=c \cos x \)
D. \( y+2 x^{2}=c \cos x \)


A sound is moving towards stationery with \( \frac{1}{10} \) the sound. The ratio of apparent to real frequency is
A \( \cdot \frac{10}{9} \)
в. \( \left(\frac{10}{9}\right)^{2} \)
c. \( \left(\frac{11}{10}\right)^{2} \)
D. \( \frac{11}{10} \)


A shell of mass \( 0.020 \mathrm{kg} \) is fired by a
gun of mass \( 100 \mathrm{kg} \). If the muzzle speed of the shell is \( 80 m / s, \) what is the recoil
speed of the gun?


How many employees get to work in
more than 100 minutes?
A . 20
B. 15
\( c \cdot 4 \)
D. 58


\( \dot{U} \)


Which substance has a higher solubility in cold water and a lower
solubility in hot water?
A. Licl
\( \mathbf{B} \cdot C a(O H)_{2} \)
\( c \cdot C O_{2} \)
D. \( C_{6} H_{12} O_{6} \)


In the given figure 0 is the centre of
circle of radius \( 28 \mathrm{cm} . \) Find the area of
the minor segment ASB


If \( M \) and \( N \) are any two events, the
probability that the exactly one of them
occurs is
This question has multiple correct options
A \( \cdot P(M)+P(N)-2 P(M \cap N) \)
B . \( P(M)+P(N)-P(M \cap N)^{c} \)
\( \mathbf{c} \cdot P\left(M^{c}\right)+P\left(N^{c}\right)-2 P\left(M^{c} \cap N^{c}\right) \)
D \( P\left(M \cap N^{c}\right)+P\left(M^{c} \cap N\right) \)


\( F e_{2} O_{3}(s) \) may be converted be Fe by the
reaction, \( \boldsymbol{F e}_{2} \boldsymbol{O}_{3}+\boldsymbol{3} \boldsymbol{H}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{F} \boldsymbol{e}(\boldsymbol{s})+ \)
\( \mathbf{3} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) ; \) for which \( \boldsymbol{K}_{\boldsymbol{p}}=\mathbf{8} \) at
temperature \( 720^{0} C . \) What \( \% \) of \( H_{2} \)
remains unreacted after the reaction
has come to equilibrium:
\( \mathbf{A} \cdot \approx 22 \% \)
в. \( \approx 34 \% \) о
\( \mathbf{c} \cdot \approx 66 \% \)
\( \mathrm{D} \cdot \approx 78 \% \)


White phosphorus can be separated from red phosphorus by This question has multiple correct options
A. sublimation
B. dissolving in \( C S_{2} \)
c. distillation
D. heating with alkali solution


Root development is promoted by
A. Abscisic acid
B. Auxin
c. Ethylene
D. Gibberellin


Class
\( 0- \)
\( \begin{array}{llll}0- & 20- & 40- & 60 \\ 20 & 40 & 60 & 80\end{array} \)
Frequency
\( f_{1} \)
32
\( f_{2} \)
Mean of the above frequency table is
given as \( 50 . \) Find \( f_{1} \) and \( f_{2} \)
A. 28 and 22
B. 25 and 25
c. 24 and 26
D. 20 and 30


The major threat to Taj Mahal is:
\( \mathbf{A} \). acid rain.
B. hydrogen peroxide.
\( c . \) Both a and b.
D. None of the above


Which branch of chemistry deals with substances consisting of living organism?
A. Physical chemistry
B. Biochemistry
c. organic chemistry
D. Analytical chemistry


Effective nuclear charge \( \left(Z_{e f f}\right) \) for \( a \) nucleus of an atom is defined as:
A. Shielding of the outermost shell electrons from the nucleus by the innermost shell electrons
B. The net positive charge experienced by electron from the nucleus
c. The attractive force experienced by the nucleus from electron
D. Screening of positive charge on nucleus by innermost shell electrons


If focii of \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) coincide with the focii of \( \frac{x^{2}}{25}+\frac{y^{2}}{9}=1 \) and eccentricity of
the hyperbola is \( 2, \) then
A \( \cdot a^{2}+b^{2}=14 \)
B. There is a director circle of the hyperbola
c. centre of the director circle is (0,0)
D. Length of latus rectum of the hyperbola is 12


Calculate the quantity of sodium carbonate (anhydrous) required to
prepare \( 250 \mathrm{ml} \) solution.
A . 2.65 gram
B. 4.95 gram
c. 6.25 gram
D. None of these


A capacitor is charged and battery is disconnected.Now the distance
between the plates is increased slightly
A. Forces between the plates will decrease
B. The potential energy of the capacitor will decrease
c. Potential differences between the plates will decrease
D. Potential differences between the plates will increase


A straight conductor of uniform cross section carries a time varying current, which varies at the rate \( \boldsymbol{d} \boldsymbol{I} / \boldsymbol{d} \boldsymbol{t}=\boldsymbol{I} \). If \( s \)
is the specific charge that is carried by each charge carrier of the conductor
and \( \ell \) is the length of the conductor, then the total force experienced by all the charge carriers per unit length of
the conductor due to their drift
velocities only is
A. \( F= \) Is
\( ^{\mathrm{B}} F=\frac{\dot{I}}{2 \sqrt{I_{S}}} \)
\( ^{\mathrm{c}} \cdot_{F}=\frac{\dot{I}}{s} \)
D. \( _{F}=\frac{2 I \dot{I}}{s} \)


Eden deposited Rs. 10000 for 4 year at a rate of \( 6 \% \) p.a. Find the interest he got.
A . 2000
B. 2400
\( c .2800 \)
D. 3200


A microscope consisting of two convex lenses of focal lengths \( 2 \mathrm{cm} \) and \( 5 \mathrm{cm} \) placed \( 20 \mathrm{cm} \) apart where must the object be placed so that the final image (virtual) is at distance of \( 25 \mathrm{cm} \) from
eye?


Among the following processes, how many are employed for the extraction of lead from ore galena?
(i) Self reduction
(ii) Carbon reduction
(iii) Metal displacement method, (iv) electrolytic reduction
, (v) Carbon
monoxide reduction,
(vi) Hydrogen reduction


A gun fires two bullets at \( 60^{\circ} \) and \( 30^{\circ} \)
with the horizontal the bullets strike att
same horizontal distance. The
maximum heights for the two bullets are in the ratio
A .2: 1
B. 3: 1
c. 4: 1
D. 1: 1


Synthesis of cell wall material take
place in
A. Dictyosome
B. Mitochondria
c. Lysosome
D. E.R


How can you determine the change of
the sol particles?


The term mass refers to the same
physical concept as:
A. weight
B. inertia
c. force
D. acceleration


Find the second order derivatives of
\( \tan ^{-1} x \)


The only, most stable nucleus formed by bombarding either \( _{13}^{27} A l \) by neutrons or \( _{11}^{23} N a \) by deutrons is:
B . \( \frac{30}{14} \) Si
\( \mathbf{c} \cdot_{12}^{24} M g \)


In nuclear fission, \( 0.1 \% \) mass is
converted into energy. The energy released in the fission of \( 1 \mathrm{Kg} \) mass in
KWH is
A \( .2 .5 \times 10^{5} \)
B . \( 2.5 \times 10^{7} \)
c. \( 2.5 \times 10^{9} \)
D. \( 2.5 \times 10^{-7} \)


Select correct statement about stability
of cations.
\( \mathbf{A} \cdot G e^{4+}>S n^{4+}>P b^{4} \)
B. \( G e^{2+}<S n^{2+}<P b^{2+} \)
c. \( P b^{2+}>P b^{4+}, S n^{4+}>S n^{2+} \)
D. All the above are correct statements


Which of the following enzymes is not produced by yeast?
A. Alcohol Dehydrogenase
B. Lactate Dehydrogenase
c. zymase
D. Invertase


How does gaseous exchange occur in plants across
(a) Leaves
(b) Roots?


When \( \alpha \) -quartz is heated to \( 575^{\circ} \mathrm{C}, \) it
changes to:
\( A \cdot \) onyx
B. \( \beta \) -quartz
c. tridymite
D. crystobalite


If \( A \) and \( B \) are mutually exclusive such
that \( \boldsymbol{P}(\boldsymbol{A})=\mathbf{0 . 3 5} \) and \( \boldsymbol{P}(\boldsymbol{B})=\mathbf{0 . 4 5} \)
find
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \)


In \( \Delta A B C \) and \( \Delta P Q R, \angle A=\angle Q \) and
\( \angle B=\angle R \) which side of \( \Delta P Q R \) should
be equal to the side \( A B \) of \( \Delta A B C, \) so two triangles become congruent. Give
reason to your answer.


Let there are 4 red, 3 yellow and 2 green
balls, then the total number of
arrangements in a row
A. 5
B. \( 4 ! \)
\( c \cdot 9 \)
D. none of these


Why is a normal eye not able to see
clearly the objects placed closer than 25
\( \mathrm{cm} ? \)


Bone ash mainly contains:
A. \( \mathrm{CaO} \)
в. \( \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} \)
\( \mathrm{c} \cdot \mathrm{CaCl}_{2} \)
D. \( \mathrm{NH}_{2} \mathrm{NH}_{2} \)


Evaluate the limit
\( \lim _{x \rightarrow \frac{\pi}{6}} \frac{\cot ^{2} x-3}{\cos e c x-2} \)


Find the probability of drawing a white ball from a box containing 3 white and 5 black balls


Is the reaction, \( 2 A l+3 F e^{2+} \rightleftharpoons \)
\( 2 A l^{3+}+2 F e \) possible?
A. No, because standard oxidation potential of \( A l<F e \)
B. Yes, because standard oxidation potential of \( A l>F e \)
c. cannot be predicted
D. Yes, because aluminium is a strong oxidising agent


If electric intensity \( \vec{E} \) is along the \( X \)
axis, then the equipotential surfaces are parallel to
A. xor plane
B. x0Z plane
c. YOZ plane
D. None of these


The separation of two chromatids of
each chromosome at early anaphase is initiated by
A. The interaction of centromere with the chromosomal fibres
B. The elongation of metaphasic spindle
C. The force of repulsion between the dividend kinetochores
D. All of the above


Which of the above given curves is
wrongly presented?
3. \( P b \rightarrow P b O \)
\( c \cdot Z r \rightarrow Z r O \)
\( . . M g \rightarrow M g O \)


The quantity which is not zero for an element in its standard state at \( 298 \mathrm{K} \) is
A . \( S^{0} \)
в. \( H^{0} \)
\( c \cdot G^{0} \)
D. Both \( H^{0} \) and \( S^{0} \)


In the reaction given below, identify the specie undergoing oxidation and reduction
\( \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g})+\boldsymbol{C l}_{2} \rightarrow \boldsymbol{2} \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{g})+\boldsymbol{S}(\boldsymbol{s}) \)


If \( E_{a} \) be the electric field intensity due to a short dipole at a point on the axis
and \( E_{r} \) be that on the right bisector at the same distance from the dipole, then
A \( \cdot E_{a}=E_{r} \)
В. \( E_{a}=2 E_{r} \)
\( \mathbf{c} \cdot E_{r}=2 E_{a} \)
D. \( E_{a}=\sqrt{2} E_{r} \)


State and explain the law of inertia (or Newton's first law of motion).


A wire has a mass \( 0.3 \pm 0.003 \mathrm{g} \), radius
\( \mathbf{0 . 5} \pm \mathbf{0 . 0 0 5} \boldsymbol{m m} \) and length \( \boldsymbol{6} \pm \)
\( 0.06 \mathrm{cm} . \) The maximum percentage
error in the measurment of its density is
A . 1
B. 2
\( c .3 \)
D. 4


ATP molecules combine with carrier
molecules and allow passage of
substances.
A. Along concentration gradient
B. Against concentration gradient
c. Both A and B
D. ATP is not required


The queen king,jack of diamonds are removed from a deck of 52 playing cards. One card is drawn. Find the
probability of getting a card of
(i) a diamond
(ii) a jack


Write the element \( a_{21} \) of the matrix
\( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{2 \times 2} \) whose elements \( \boldsymbol{a}_{i j} \) are
\( \operatorname{given} \) by \( a_{a j}=e^{2 i x} \cos j x \)


Show that \( (-1+\sqrt{3} i)^{3} \) is a real
number.


Which of the following will form a reversible sol?
A. Gold sol
B. Sulphur sol
c. Rubber sol
D. Arsenous sulphide so


Prove that,
\( \cos 20^{\circ} \cos 40^{\circ} \cos 60^{\circ} \cos 80^{\circ}=\frac{1}{16} \)


\( \left[\boldsymbol{F} e(\boldsymbol{O H})_{3}\right], \boldsymbol{F} e^{3+} \) can be coagulated
easily by
A \( \cdot C l^{-} \)
B \( . S O_{4}^{2-} \)
\( \mathbf{c} \cdot P O_{4}^{3-} \)
D. \( \left[F e(C N)_{6}\right]^{4} \)


Mass defect for the helium nucleus is
0.0303 amu. Binding energy per
nucleon for this (in \( M e V \) ) will
be
\( \mathbf{A} \cdot 28 \)
B. 7
\( c \cdot 4 \)
\( D \)


If the focal length of a magnifying glass is \( 2.5 \mathrm{cm}, \) it can magnify an object
A. 15 times
B. 11 times
c. 2.5 times
D. none of these


Give reasons for the following: Lunar
eclipse is a more frequent phonomenon than solar eclipse


Let \( \vec{a}, \vec{b}, \vec{c} \) be the vectors of length 3,4 5 respectively. Let \( \vec{a} \) be perpendicular to \( \vec{b}+\vec{c}, \vec{b} \) to \( \vec{c}+\vec{a} \) and \( \vec{c} \) to \( \vec{a}+\vec{b} \)
Then \( |\vec{a}+\vec{b}+\vec{c}| \) is equal to
A \( \cdot 2 \sqrt{5} \)
B. \( 2 \sqrt{2} \)
с. \( 10 \sqrt{5} \)
।
D. \( 5 \sqrt{2} \)


When carbon is heated in presence of oxygen, carbon monoxide and
carbondioxide are produced depending on the supply of oxygen. This illustrates:
A. conservation of mass
B. constant composition
c. multiple proportion
D. constant volume


Find the number of nonbonding molecular orbital(s) from the following (lf \( x \) is inter nuclear axis):
\( \boldsymbol{s}+\boldsymbol{p}_{\boldsymbol{y}}, \boldsymbol{p}_{\boldsymbol{y}}+\boldsymbol{p}_{\boldsymbol{y}}, \boldsymbol{p}_{\boldsymbol{x}}+\boldsymbol{p} \boldsymbol{x}, \boldsymbol{d}_{\boldsymbol{x} \boldsymbol{y}}+ \)
\( \boldsymbol{s}, \boldsymbol{d} \boldsymbol{x} \boldsymbol{y}+\boldsymbol{p}_{\boldsymbol{x}}, \boldsymbol{p}_{\boldsymbol{y}}+\boldsymbol{p}_{\boldsymbol{x}} \)


The value of \( 45^{\circ} \) in centesimal system
is
A \( \cdot 25^{9} \)
B. \( 50^{\text {9 }} \)
\( \mathrm{c} \cdot 75^{9} \)
D. \( 100^{9} \)


The phosphodiester linkage is present
in


Formation of a solution from two
components can be considered as:
(i) Pure solvent \( \rightarrow \) separated solvent
molecules, \( \Delta \boldsymbol{H}_{\mathbf{1}} \)
(ii) Pure solvent \( \rightarrow \) separated solute
molecules, \( \Delta \boldsymbol{H}_{2} \)
(ii) Separated solvent and solute
molecules \( \rightarrow \) solution, \( \Delta \boldsymbol{H}_{3} \)

Solution so formed will be ideal if
\( \mathbf{A} \cdot \Delta H_{s o l n .}=\Delta H_{1}+\Delta H_{2}+\Delta H_{3} \)
B. \( \Delta H_{\text {soln.}}=\Delta H_{1}+\Delta H_{2}-\Delta H_{3} \)
C \( . \Delta H_{\text {soln.}}=\Delta H_{1}-\Delta H_{2}-\Delta H_{3} \)
D. \( \Delta H_{\text {soln.}}=\Delta H_{3}-\Delta H_{1}-\Delta H_{2} \)


Kjeldahls method cannot be used for
the estimation of nitrogen in:
A \( \cdot C_{6} H_{5}-N=N-C_{6} H_{5} \)
B.
\( c \)
D. all of these


The heat required to change the state of
a substance at constant temperature is called latent heat.
A. True
B. False


\( (n-1) d^{10} n s^{2} \) is the general electronic
configuration of:
A. \( F e, C o, N i \)
в. \( C u, A g, A u \)
c. \( Z n, \) Cd \( , H g \)
D. \( S e, Y, L a \)


Assertion
Critical angle of light passing from glass to air is minimum for violet color.
Reason

The wavelength of blue light is greatest to the light of other colors.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A student measure the thickness of an
object by three different instruments and gets the result as \( 0.5 \mathrm{cm}, 0.50 \mathrm{cm} \) \( 0.500 \mathrm{cm} . \) State the one which is more
accurate.
A . \( 0.5 \mathrm{cm} \)
B. \( 0.50 \mathrm{cm} \)
c. \( 0.500 \mathrm{cm} \)
D. All the measurements are equally accurate.


When an equilateral glass prism is in minimum deviation position,
(A) the refracted ray is parallel to the base of the prism
(B) the angle of incidence is equal to the
angle of emergence. Choose the correct option.
A. Only A is true
B. Only B is true
c. Both A and B are true
D. Both A and B are false


Bond \( X \) is made by the overlap of which type of hybridized orbitals?
A. sp and \( s p^{3} \)
B. \( s p \) and \( s p^{2} \)
\( \mathbf{c} \cdot s p^{2} \) and \( s p^{3} \)
D. none of these


J.C. Bose proposed this theory to explain the process of ascent of sap
A. Relay-pump theory
B. Transpiration pull theory
c. Pulsatory theory
D. Capillary force theory


The process of seeping out water into the ground is called:
A. evaporation
B. infiltration
c. transpiration
D. None of these


A thin fixed ring of radius \( 1 \mathrm{m} \) has a positive charge \( 1 \times 10^{-5} \mathrm{C} \) uniformly
distributed over it. A particle of mass \( 0.9 \mathrm{g} \) and having a negative charge of
\( 1 \times 10^{-6} \mathrm{C} \) is placed on the axis at a
distance of \( 1 \mathrm{cm} \) from the centre of the ring. Calculate the time period of oscillations.
A . 0.5 secs
B. 9.28 secs
c. 0.628 secs
D. 0.1 secs


toppr
Q Type your question
that we receive from the sun is
transferred to us by a process which,
unlike conduction or convection, does
not require the help of a medium in the intervening space which is almost free of particles. Radiant energy travels in space as electromagnetic spectrum.
Thermal radiations travel through
vacuum with the speed of light. Thermal
radiations obey the same laws of
reflection and refraction as light does.
They exhibit the phenomena of interference, diffraction and
polarization as light does.
The emission of radiation from a hot
body is expressed in terms of that emitted from a reference body (called
the black body at the same
temperature. A black body absorbs and
hence emits radiations of all
wavelengths. The total energy E emitted
by a unit area of a black body per
second is given by \( \boldsymbol{E}=\boldsymbol{\sigma} \boldsymbol{T}^{4} \) where \( \boldsymbol{T} \) is
the absolute temperature of the body
and \( \sigma \) is a constant known as Stefan's
constant. If the body is not a perfect
black body, then \( E=\varepsilon \sigma T^{4} \) where \( \varepsilon \) is
the emissivity of the body.

The rate at which energy is radiated by
a body depends upon:
This question has multiple correct options
A. the surface area of the body
B. the temperature of the body
C. the nature of the surface of the body
D. the emissivity of the surface of the body


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


Pascal's law is used for the working of:
A. Hydraulic brakes
B. Hydraulic jack
c. Hydraulic press
D. All


Number of ozone depleters identified by Viena convention for Protection of Ozone
Layer (1992) is
A . 19
B . 17
c. 15
D. 13


Mass of water at \( 10^{\circ} \mathrm{C} \) increases when
heated to \( 30^{\circ} \mathrm{C} \). True or false.
A. True
B. False


The image formed by the eye lens on the retina is.
A. Real, upright and enlarged
B. Real, upright and diminished
c. Real, inverted and diminished
D. virtual, inverted and diminished


Let the solubility of an aqueous solution
of \( M g(O H)_{2} \) be \( x \) then its \( K_{s p} \) is
\( \mathbf{A} \cdot 4 x^{3} \)
B . \( x^{3} \)
\( c \cdot 27 x^{4} \)
D. \( 9 x \)


The object under thermodynamical study
is called
A. system
B. Universe
c. surrounding
D. Boundary


How do you verify experimentally that
the focal length of a convex lens is increased when it is kept in water?


Which of the following compounds are the common product/s obtained in the
hydrolysis of \( X e F_{6} \) and \( X e F_{4} \)
A. \( X e O_{2} F_{2} \)
в. \( H F \)
\( \mathbf{c} \cdot X e O_{3} \)
D. Both (B) and (C)


The kinetic energy of 1 g molecule of a gas, at normal temperature and
pressure, is?
B . \( 2.7 \times 10^{2} \) J
D . 3.4 \( \times 10^{3} \) J


Define the law of conservation of mass.


\( \left[A u(C N)_{2}\right]^{\ominus} \) is a very stable
complex under certain conditions. The concentration of cyande ion which is required to keep 99 mol\% of the gold in
the form of the cyanide complex is: [Given \( \left.K_{f}\left[A u(C N)_{2}\right]^{\ominus}=4 \times 10^{28}\right] \)
A \( .2 \times 10^{-28} M \)
в. \( 3 \times 10^{-14} M \)
c. \( 5 \times 10^{-28} M \)
D. \( 5 \times 10^{-14} M \)


If \( A \) and \( B \) are square matrices of same order and \( A A^{T}=I \) then \( \left(A^{T} B A\right)^{10} \) is
equal to
A. \( A B^{10} A^{T} \)
B . \( A^{T} B^{10} A \)
c. \( A^{10} B^{10}\left(A^{T}\right)^{10} \)
D. \( 10 A^{T} B A \)


Assertion
The first living organisms were heterotrophs.
Reason
They were surrounded by performed organic molecules which they used as
food.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In Albugo, sexual reproduction results
in the formation of :
A. zygospore
B. Teliospore
c. oospore
D. Basidiospore


A magnetic field due to a long straight wire carrying a current I is proportional
to
\( A \)
B . \( I^{2} \)
c. \( I^{3} \)
D. \( \sqrt{I} \)


What determines the intensity of light in the photon picture of light?


An f-shell containing 6 unpaired electrons can exchange:
A. 6 electrons
B. 9 electrons
c. 12 electrons
D. 15 electrons


A \( 10-k g \) block is pulled in the vertical
plane along a frictionless surface in the
form of an arc of a circle of radius \( 10 \mathrm{m} \)
The applied force is \( 200 N \) as shown in
the figure.If the block started from rest
at \( A, \) the velocity at \( B \) would be
A . \( 1.732 \mathrm{m} / \mathrm{s} \)
B. \( 17.32 \mathrm{m} / \mathrm{s} \)
c. \( 173.2 \mathrm{m} / \mathrm{s} \)
D. none of these


Evaluate:
\( (x-2)+(x-3)+(x-9)=0 \)


The set of points where \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\mathbf{1}+|\boldsymbol{x}|} \)
is differentiable, is
\( \mathbf{A} \cdot(-\infty, 0) \cup(0, \infty) \)
B \( \cdot(-\infty,-1) \cup(-1, \infty) \)
\( c \cdot(-\infty, \infty) \)
D・ \( (0, \infty) \)


Number of odd numbers of five distinct
digits can be formed by the digits \( \mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \) is
A .24
в. 120
c. 48
D. 36 6


toppr
Q Type your question
the block \( A \) is placed is taken to be
smooth. A horizontal force \( F, \) increasing linearly with time, begins to act on B.
The accelerations \( a_{A} \) and \( a_{B} \) of
blocks A and B respectively are plotted
against t. The correctly plotted graph is:
4
B.
\( c \)
D. none of the above


Mass is a measure of:
A . weight
B. inertia
c. friction
D. matter


The magnetic field at a distance x on the axis of a circular coil of radius \( \mathrm{R} \) is
\( \frac{1}{8} \) th of that at the centre.The value of \( x \)
is
A \( \cdot \frac{R}{\sqrt{3}} \)
в. \( \frac{2 R}{\sqrt{3}} \)
c. \( R \sqrt{3} \)
D. \( R \sqrt{2} \)


Find the coordinates of a point
equidistant from four points \( \boldsymbol{O}(\mathbf{0}, \mathbf{0}, \mathbf{0}), \boldsymbol{A}(\ell, \mathbf{0}, \mathbf{0}), \boldsymbol{B}(\mathbf{0}, \boldsymbol{m}, \boldsymbol{0}) \) and
\( \boldsymbol{C}(\mathbf{0}, \mathbf{0}, \boldsymbol{n}) \)


The repeated factor of the determinant \( \left|\begin{array}{lll}\boldsymbol{y}+\boldsymbol{z} & \boldsymbol{x} & \boldsymbol{y} \\ \boldsymbol{z}+\boldsymbol{x} & \boldsymbol{z} & \boldsymbol{x} \\ \boldsymbol{x}+\boldsymbol{y} & \boldsymbol{y} & \boldsymbol{z}\end{array}\right| \)
A. \( z-x \)
в. \( x-y \)
\( \mathbf{c} \cdot y-z \)
D. none of these


If \( f(x)=\sqrt{2} x+\frac{4}{\sqrt{2 x^{\prime}}} \) then \( f^{\prime}(2) \) is
equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. -
c. 1
D. 2


\( \mathrm{f} \frac{d y}{d x}+\sqrt{\frac{1-y^{2}}{1-x^{2}}}=0 . \) Prove that,
\( \boldsymbol{x} \sqrt{1-\boldsymbol{y}^{2}}+\boldsymbol{y} \sqrt{1-\boldsymbol{x}^{2}}=\boldsymbol{A} \) where \( \mathbf{A} \) is
constant.


The missing value in \( \ldots \ldots \ldots+\frac{2}{7}=\frac{2}{7}+ \)
\( \frac{-11}{13} \) is
A \( \cdot \frac{2}{7} \)
в. \( \frac{-11}{13} \)
c. \( \frac{-2}{7} \)
D. \( \frac{11}{13} \)


Let \( R \) be a relation in \( N \) defined as \( R= \)
\( \{(x, y) \in N \times N: x+2 y=39\} \) Find
the domain, co-domain and range of \( \boldsymbol{R} \)
Also write \( R^{-1} \) in roster form.


The co-ordinates of the vertices of a
rectangle are (0,0),(4,0),(4,3) and \( (0,3) . \) The length of its diagonal is
\( \mathbf{A} \cdot \mathbf{4} \)
B. 5
\( c \cdot 7 \)
D. 3


\( \mathbf{f} \boldsymbol{I}=\int \boldsymbol{x} \sin ^{-1}\left\{\frac{\mathbf{1}}{\mathbf{2}} \sqrt{\frac{\mathbf{2} \boldsymbol{a}-\boldsymbol{x}}{\boldsymbol{a}}}\right\} \boldsymbol{d} \boldsymbol{x}= \)
\( \frac{\boldsymbol{A}}{\mathbf{2 4 8}}\left(\boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{a}^{2}\right) \cos ^{-1} \frac{\boldsymbol{x}}{\boldsymbol{2} \boldsymbol{a}}- \)
\( \frac{1}{8} x \sqrt{4 a^{2}-x^{2}}+C \) then \( A \) is equal to


A thin metallic spherical shell contains
a charge \( Q \) on its surface. A point
charge \( q_{1} \) is placed at the center of the
shell, and another charge \( q_{2} \) is placed
outside the shell. All the three charges
are positive. Then the force on charge \( \boldsymbol{q}_{1} \)
is :
A. toward right
B. toward left
c. zero
of these


The enzyme trypsinogen is secreted from
A. Duodenum
B. Pancreas
c. Liver
D. Stomach


(a) Distinguish with the help of a suitable diagram, the difference in the
behaviour of a conductor and a
dielectric placed in an external electric field. How does polarised dielectric modify the original external field?
(b) A capacitor of capacitance \( C \) is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?
(i) Charge stored by the capacitor.
(ii) Field strength between the plates.
(iii) Energy stored by the capacitor. Justify your answer in each case.


The reaction involved in reduction of
\( N A D^{+} \) is
A. Glucose- -> Glucose 6- -
B. Fructose 1, 6- diphosphate>PGAL+DiBAP
c. Glucose 6-P - ->Fructose 6 - -


The period of revolution of an electron in
the ground state of hydrogen atom is \( T \) The period of revolution of the electron in the first excited state is?
A . 2 न
в. 4 न
\( c .6 \) न
D. 8 T


State whether true or false:
The highest occupied energy band is called the valence band and the lowest
unoccupied energy band is called the conduction band.
A. True
B. False


In an household electrical circuit:
a) Where is the MCB ( Miniature Circuit
Breaker ) connected?
b) What is the function of ELCB ( Earth
Leakage Circuit Breaker )?


A wedge of mass \( 10 \mathrm{kg} \) is moving
rightwards. A block of mass \( 10 k g \) is
placed on it. Friction coefficient
between wedge and block is \( 0.8 . \) Then
\( \left[\text {take } g=10 m / s^{2}\right] \)
This question has multiple correct options
A. If wedge is moving with constant velocity then friction acting on block is 64N
B. If wedge is moving with constant velocity then acceleration of block is zero
C. If wedge is moving with \( a=2 \hat{i} m / s^{2} \) then friction
acting on block is \( 44 \mathrm{N} \)
D. If wedge is moving with \( a=10 \hat{i} m / s^{2} \) then friction is
zero


The unit of calorific value is :
\( A \cdot k J / k g \)
B. kg/kJ
c. kB/kJ
D. g/ks


\( P \) and \( Q \) are any two points lying on the
sides \( D C \) and \( A D \) respectively of a
parallelogram \( A B C D . \) Show that \( \boldsymbol{a r}(\boldsymbol{A P B})=\boldsymbol{a r}(\boldsymbol{B Q C}) \)


The accuracy in the measurement of
the diameter of hydrogen atom as
\( 1.06 \times 10^{-10} m \) is
A . 0.11
B . \( 106 \times 10^{10} \)
\( c \cdot \frac{1}{1 \frac{1}{166}} \)
D. \( 0.01 \times 10 \)


The distance between the sun and the
earth is
A . 150 million kilometers
B. 100 million kilometers
c. 2 billion kilometers
D. 1.2 light years


Total income of Ramesh, Suresh and
preeti is 8,07,000 rupess. The
percentages of their expenses are \( 75 \% \) \( 80 \% \) and \( 90 \% \) respectively. if the ratio of their savings is \( 16: 17: 12, \) then
find the annual saving of each of them.


Evaluate
\( \int \frac{1}{x}\left\{\log e^{e x} \cdot \log e^{e^{2} x} \cdot \log e^{e^{3} x}\right\} d x \)


Adding sodium chloride to water is a:
A . physical change
B. chemical change
c. chemical reaction
D. none of these


The magnetic flux through a circuit of resistance 'R' changes by an amount
\( \Delta \Phi \) at a time \( \Delta t . \) Then the total
quantity of electric charge \( Q \) that passes any point in the circuit during the time \( \Delta t \) is represented by
\( ^{\mathbf{A}} \cdot Q=\frac{\Delta \Phi}{R} \)
в. \( Q=\frac{\Delta \Phi}{\Delta t} \)
c. \( Q=R \cdot \frac{\Delta \Phi}{\Delta t} \)
D. \( Q=1 R \cdot \frac{\Delta \Phi}{\Delta t} \)


If \( -\frac{\pi}{2}<\theta<\frac{\pi}{2} \), then the minimum value
of \( \cos ^{3} \theta+\sec ^{3} \theta \) is
\( A \)
B. 2
\( c \cdot 0 \)
D. none of these


Carbon-10 has a half-life of about 19
seconds. How many half-lives does it undergo in 2 minutes and 32 seconds?
A. 8 half-lives
B. 7 half-lives
c. 6 half-lives
D. 5 half-lives
E. 4 half-lives


Consider the following reactions:
\( \boldsymbol{I} \cdot \boldsymbol{C}_{2} \boldsymbol{H}_{5}-\boldsymbol{I}+\boldsymbol{N} \boldsymbol{H}_{3} \longrightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{N} \stackrel{\oplus}{\boldsymbol{H}_{3}}+\boldsymbol{I}^{\ominus} \)
\( \boldsymbol{I I} \cdot \boldsymbol{C}_{2} \boldsymbol{H}_{5}-\boldsymbol{I}+\ddot{\boldsymbol{P}} \boldsymbol{H}_{3} \longrightarrow \)
\( \boldsymbol{C}_{2} \boldsymbol{H}_{5} \boldsymbol{P} \stackrel{\oplus}{\boldsymbol{H}_{3}}+\boldsymbol{I}^{\ominus} \)
\( I I I \cdot C_{2} H_{5}-I+E t O^{\ominus} \longrightarrow C_{2} H_{5}- \)
\( \boldsymbol{O} \boldsymbol{E} \boldsymbol{t}+\boldsymbol{I}^{\ominus} \)
\( \boldsymbol{I} \boldsymbol{V} \cdot \boldsymbol{M} \boldsymbol{e}-\stackrel{\oplus}{\boldsymbol{S}}-\boldsymbol{M} \boldsymbol{e}_{2}+\stackrel{\ominus}{\boldsymbol{O}} \boldsymbol{H} \longrightarrow \boldsymbol{M} \boldsymbol{e}- \)
\( \boldsymbol{O} \boldsymbol{H}+\boldsymbol{M} \boldsymbol{e}_{2} \boldsymbol{S} \)
In which of the above reactions does the
rate of \( S_{N} 2 \) reaction increase in solvent
polarity?
This question has multiple correct options
A . (I)
в. \( (I I) \)
c. \( (I I I) \)
D. \( (I V) \)


At one end \( A \) of a diameter \( A B \) of a circle
of radius \( 5 \mathrm{cm}, \) tangent \( \mathrm{XAY} \) is drawn to the circle. Find the length of the chord
CD parallel to XY and at a distance \( 8 \mathrm{cm} \) from A.


What is the difference between
breathing and respiration?


IUPAC name of given compound is :
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\underset{\mathrm{CHO}}{\mathrm{C}} \mathrm{H}-\stackrel{\mathrm{CH}_{3}}{\mathrm{C}} \mathrm{H}-\mathrm{CH}_{2}-\mathrm{CH}_{3}
\]
A. 4-Methylhexanal-3
B. 3-Ethyl-2-methylpentanal
c. 2-Ethyl-3-methylpentanal
D. 4-Methylheptanal


Calcium bicarbonate causes hardness
in water but not calcium carbonate.
Why?


Figure shows a three arm tube in which
a liquid is filled upto levels of height I. It
is now rotated at an angular frequency
\( \omega \) about an axis passing through arm B.
The angular frequency \( \omega \) at which level
of liquid in arm B becomes zero.
\( \mathbf{A} \cdot \sqrt{\frac{2 g}{3 l}} \)
B. \( \sqrt{\frac{g}{l}} \)
c. \( \sqrt{\frac{3 g}{l}} \)
D. \( \sqrt{\frac{3 g}{2 l}} \)


If \( \frac{1+3 p}{3}, \frac{1-p}{4} \) and \( \frac{1-2 p}{2} \) are mutually exclusive events. Then, range
of \( p \) is
A \( \cdot \frac{1}{3} \leq p \leq \frac{1}{2} \)
в. \( \frac{1}{2} \leq p \leq \frac{1}{2} \)
c. \( \frac{1}{3} \leq p \leq \frac{2}{3} \)
D. \( \frac{1}{3} \leq p \leq \frac{2}{5} \)


The reaction of toluene with chlorine in
the presence of ferric chloride gives predominantly:
A. Benzoyl chloride
B. \( m- \) chlorotoluene
c. Benzyl chloride
D. \( o \) - and \( p- \) chlorotoluene


\( \boldsymbol{H}_{2} \boldsymbol{S} \) a toxic gas with rottenegg like smell is used for the qualetative
analysis, if the solubility of \( H_{2} S \) in
water,at STP is 0.195mole.kg \( ^{-1} \), the Henry's law constant is:
A. 282 bar
B. 324.8 bar
c. 462.9 bar
D. 534.8 bar


What do we need in order to see a
shadow?


A dishonest dealer sells his goods at
cost price but uses \( 20 \% \) less weight.
What is his profit or loss \( \% ? \)
\( \mathbf{A} \cdot 22.5 \% \)
B . \( 12.5 \% \)
c. \( 25 \% \)
D. 50\%


What is the IUPAC name for the
following compound?
A. 3-methylpentanoic acid
B. isohexanoic acid
c. \( \beta \) -methylvaleric acid
D. 2-methylpentanoic acid


Magnetic permeability of paramagnetic substances is?
\( \mathbf{A} \cdot \mathbf{0} \)
B \( .>1 \)
\( c \cdot<1 \)
D.


If the refractive index of water and glass with respect to air are, respectively, \( \frac{4}{3} \) and \( \frac{3}{2} \) then what will be the refractive index of glass with respect to water?
A \( \cdot \frac{9}{8} \)
в. \( \frac{8}{9} \)
\( c \cdot \frac{4}{3} \)
D. \( \frac{3}{2} \)


The refractive index of the material of a
prism is \( \sqrt{2} \) and the angle of the prism
is \( 30^{\circ} . \) One of the two refracting surface of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is?
A . \( 30^{\circ} \)
B . \( 60^{\circ} \)
c. zero
D. \( 45^{\circ} \)


Assertion
Potential difference across, resistor,
capacitor and inductor each is \( 10 V \) Then, voltage function and current functions should be in phase.
Reason
At this condition current in the circuit
should be maximum.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Draw a neat diagram of AC dynamo and represent the current in it in the
external circuit by a graph.


\( C-H \) bond energy in ethane, ethene
and ethyne is?
A. Equal in all the three compounds
B. Maximum in ethane
C. Maximum in ethene
D. Maximum in ethyne


Which of the following substance requires castle's intrinsic factor
secreted by stomach for absorbtion in the small intestine?
A. Aminoacids
B. Water
c. Vitamin \( C \)
D. Vitamin \( B_{12} \)


Cruciferae belongs to
A. Parietales
B. Bicarpellatae
C. Gamopetalae
D. Calyciflorae


1) On the Pauling's electronegativity
scale,which element is next to \( F \)
2) Why \( C a^{2+} \) has smaller ionic radius
\( \operatorname{than} \boldsymbol{K}^{+} ? \)


Cu0 can be reduced to Cu conveniently
by using \( \mathrm{C} \) or \( \mathrm{CO} \) at any temperature :
A. approximately equal to room temperature
B. above room temperature
C. below room temperature
D. at all temperature


Name the phenomenon which is responsible for bending of light around sharp corners of an obstacle. Under what conditions does this phenomenon take place?


Methanogens can be found
A. In swamps
B. In a cow's stomach
c. In marshes
D. All of the above
E. None of the above


Dot patterns in Braille system are also known as:
A. features
B. characters
c. points
D. none of these


Ethyl alcohol is manufactured from ethylene by:
A. permanganate
B. catalytic oxidation
C. absorption into Conc. \( H_{2} S O_{4} \) followed by hydrolysis
D. reduction


The distance from \( (\mathbf{9}, \mathbf{0}) \) to \( (\mathbf{3}, \mathbf{4}) \)


reactions.
\[
\begin{array}{l}
\mathrm{CH}_{3}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}+\mathrm{D}_{2} \mathrm{O} \frac{\mathrm{Hg}^{2+}, \mathrm{H}_{2} \mathrm{SO}_{4}}{ }=[\mathrm{P}] \\
\qquad \mathrm{CH}=\mathrm{CH}_{2}+\mathrm{D}_{2} \mathrm{O} \frac{\mathrm{H}_{2} \mathrm{SO}_{4}}{ }=[\mathrm{Q}]
\end{array}
\]
\( A \)
\[
\mathrm{CH}_{3}-\underset{\mathrm{O}}{\|}-\mathrm{CHD}_{2} \text { and }
\]
\( B \)
\( c \)
\( D \)
\[
\mathrm{cH}_{3}-_{\mathrm{O}}^{\mathrm{C}-\mathrm{CH}_{3}}
\]


\( 4 \mathrm{g} \mathrm{H}_{2} \) and \( 127 \mathrm{g} \mathrm{I}_{2} \) are mixed and
heated in 10 lit closed vessel until
equilibrium is reached. If the equilibrium concentration of HI is 0.05 M, the total number of moles presents
at equilibrium is
A . 3.25
в. 1.75
c. 2.25
D. 2.5


A toy company manufactures two types
of dolls, \( A \) and \( B \). Market tests and
available resources have indicated that
the combined production level should
not exceed 1200 dolls per week and the
demand for dolls of type \( B \) is at most
half of that for dolls of type \( A \). Further,
the production level of dolls of type \( \boldsymbol{A} \) can exceed three times the production
of dolls of other types by at most 600 units. If the company makes a profit of
Rs.12 and Rs.16 per doll respectively
on dolls \( A \) and \( B \), how many of each
should be produced weekly in order to maximize the profit?


If \( \boldsymbol{y}=[\log (\boldsymbol{x}+\sqrt{\boldsymbol{x}^{2}+\mathbf{1}})]^{2} \)
Prove that \( \left(\mathbf{1}+\boldsymbol{x}^{2}\right) \frac{d^{2} \boldsymbol{y}}{d x^{2}}+\boldsymbol{x} \frac{d \boldsymbol{y}}{d \boldsymbol{x}}=\mathbf{2} \)


An alpha particle after passing through a potential difference of \( 2 \times 10^{6} \) volt
falls on a silver foil. The atomic number
of silver is \( 47 . \) The \( K . E . \) of the \( \alpha \) -particle
at the time of falling on the foil is:
A \( .6 .4 \times 10^{-13} \mathrm{J} \)
В . \( 4.5 \times 10^{-13} \mathrm{J} \)
c. \( 6.8 \times 10^{-13} \mathrm{J} \)
D. \( 5.8 \times 10^{-13} \mathrm{J} \)


A matrix A of order \( 3 \times 3 \) has
determinant 6. What is the value of \( |\mathbf{3} \boldsymbol{A}| \)
\( ? \)


One litre of a sample of hard water
contains \( 55.5 \mathrm{mg} \) of \( \mathrm{CaCl}_{2} \) and \( 4.75 \mathrm{mg} \)
of \( M g C l_{2} . \) The total hardness in terms
of ppm of \( C a C O_{3} \) is :
A. 5 ppm
в. \( 10 \mathrm{ppm} \)
c. 20 ppm
D. none of the above


Write down the cleansing action of
soap?


Show that the relation \( R \) on the set \( Z \) of
integers, given by \( \boldsymbol{R}= \)
\( \{(a, b): 2 \text { divides } a-b\} \) is an
equivalence relation.


Assertion
Ether can extract LiCl from the aqueous
solution of a mixture of LiCl, NaCl and
KCI.
Reason
Hydration of \( L i^{+} \) ion is greater than that
of \( N a^{+} \) and \( K^{+} \) ions.
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 IUPAC name of the compound is :
A . 1,2,3 -triformyl propane
B. 3-formyl-1, 5-pentane dial
c. propane-1, 2, 3-trial
D. Propane-1, 2, 3-tricarbaldehyde


An automobile engine develops \( 100 k W \)
when rotating at a speed of \( \mathbf{1 8 0 0} \) rev/min. The torque it delivers is
A . \( 3.33 N-m \)
B . \( 200 N-m \)
c. \( 530.5 N-m \)
D. \( 2487 N-m \)


Does the particle's vertical velocity reach a minimum after \( t=3.00 s ? \)
A. True
B. False


A sphere has volume \( 36 \pi c m^{3} \), find the
radius of the sphere
A \( .4 \mathrm{cm} \)
B. 3 cm
\( c .6 c m \)
D. 8 ст


The \( K_{a} \) value of ammonium ion
\( \left(N H_{4}+\right) \) is \( 5.6 \times 10^{-10}, \) the \( K_{b} \) value of
\( \operatorname{ammonia} N H_{3}=1.8 \times 10^{-5}, \) then
A. Ammonia is more strongly basic than ammonium is acidic
B. Ammonia is weaker basic than ammonium is acidic
c. Both a and \( b \)
D. Data insufficient


Structural isomerism and
stereoisomerism should be considered
when answering this question.
How many isomers with the formula
\( C_{4} H_{8} \) have structures that contain a \( \pi \)
bond?
\( A \)
B. 2
\( c \cdot 3 \)
\( D \)


The number of valence electrons for
carbon are :
A . 2
B. 4
\( c .6 \)
\( D \)


The oxide which is strongest acid is:
A. \( T l_{2} O_{3} \)
в. \( P b O_{2} \)
\( c \cdot C O_{2} \)
D. \( \operatorname{sn} O_{2} \)


A solenoid of length \( 1.5 m \) and \( 4 c m \) in
diameter possesses 10 turns per metre. A current of \( 5 A \) is flowing
through it. The magnetic induction at a point inside the solenoid along the axis
is \( _{-}------\left(\mu_{0}=4 \pi \times\right. \)
\( \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{W b} / \mathbf{A . m} \)
A \( \cdot \pi \times 10^{-5} T \)
В. \( 2 \pi \times 10^{-5} T \)
c. \( 3 \pi \times 10^{-5} T \)
D . \( 4 \pi \times 10^{-5} T \)


Choose the correct answers from the
alternatives given :
Which of the following factors is least likely to affect the type of organism colonizing a pond
A. Acidity of water
B. Age of pond
c. Amount of rainfall
D. Amount of sunlight falling on the pond


Froth flotation is a process of
A . oxidation
B. reduction
C. refining
D. concentration


The self inductance of the motor of an
electric fan is \( 10 \mathrm{H} \). In order to impart
maximum power at \( 50 H z \), it should be
connected to a capacitance of
A \( .4 \mu F \)
в. \( 8 \mu F \)
\( \mathrm{c} \cdot 1 \mu F \)
D. \( 2 \mu F \)


Tension is a type of force. Fill
in the blank.
A. Contact
B. Non-contact
c. Gravitational
D. All of the above


Find the point \( (0, y) \) that is equidistant
from (4,-9) and (0,-2)
A \( \cdot\left(0,-\frac{93}{14}\right) \)
в. \( \left(\frac{93}{14}, 0\right) \)
\( ^{c} \cdot\left(0,-\frac{14}{93}\right) \)
D. \( \left(\frac{14}{93}, 0\right) \)


The value of \( c \) in lagrange's theorem for
the function \( f(x)=\log \sin x \) in the interval \( \left[\frac{\pi}{6}, \frac{5 \pi}{6}\right] \) is
A \( \cdot \frac{\pi}{4} \)
в.
c. \( \frac{2 \pi}{3} \)
D. None of these


On the surface of the earth, force of gravitational attraction between two masses kept at distance dapart is 6
Newtons. If these two masses are taken
to the surface of the moon and kept at
the same distance d, the force between
them will be
A . \( 1 \mathrm{N} \)
B. 36N
\( c \cdot \frac{1}{6} N \)
D. 6N


For an ideal gas \( V \) -T curves at
constant pressures \( P_{1} \& P_{2} \) are shown in
figure, from the figure
A \( \cdot P_{1}>P_{2} \)
в. \( P_{1}<P_{2} \)
\( c \cdot P_{1}=P_{2} \)
D. \( P_{1} \leq P_{2} \)


In a right angled \( \triangle \mathrm{ABC}, \mathrm{AC} \perp \) the
hypotenuse BC then \( A D^{2} \) is
\( \mathbf{A} \cdot A C \times C D \)
B. \( A C \times B A \)
c. \( D C \times B D \)
D. None of these


Which of the following has the similarities with the lymph?
A. Red blood cells
B. Blood plasma
c. White blood cells
D. Nutrients


Solve
\( 4 u^{2}+8 u=0 \)


Using elementary tansormations, find
the inverse of each of the matrices, if it
exists in \( \left[\begin{array}{ll}1 & 3 \\ 2 & 7\end{array}\right] \)


In the hydraulic braking system, the piston in the master cylinder is connected by mechanical linkage to the
A. Wheel cylinders
B. Brake shoes
c. Brake pedal
D. wheel pedal


The stem is modified to store the food in
A. Potato
B. Carrot
c. Turnip
D. Dahlia


Find the derivative of following functions using first principle with
respect to \( x \)
\( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x} \sin \boldsymbol{x} \)


A wooden box with lid is made of \( 2.5 \mathrm{cm} \)
thick. Inner length, breadth and height
of box are 1 m.65 \( c m \) and 55 cm. Find
the total expenditure of colouring its out surface area at the rate of \( R s .15 \) per
square meter.


In SHM match the following
Column I
a) Maximum velocity
e) \( 1 / 2 \mathrm{M} \)
\( \omega^{2} A^{2} \)
b) Maximum acceleration
f) \( 1 / 4 \mathrm{M} \)
\( \omega^{2} A^{2} \)
c) Maximum Force
g) \( A \omega \)
d) Maximum total energy
h) \( \omega^{2} A \)
¡) \( \boldsymbol{m} \boldsymbol{\omega}^{2} \boldsymbol{A} \)
A. a-g, b-h, c-i, d-e
B. a-h, b-g, c-i, d-e
c. \( a-g, b-h, c-f, d-e \)
D. a-g, b-i, c-h, d-f


Which of the following pairs has almost
same colour?
\( \mathbf{A} \cdot_{60} N d^{3+} \cdot_{69} T m^{3+} \)
\( \mathbf{B} \cdot_{70} Y b^{3+},_{59} P r^{3+} \)
\( \mathbf{C} \cdot_{63} E u^{2+},_{65} T b^{3+} \)
\( \mathbf{D} \cdot_{64} G d^{3+},_{67} H o^{3+} \)


The minimum amount of energy
required to emit an electron from a
metal surface is called
A. Force function
B. Power function
c. work function
D. None of the above


Name the reagent used in oxidation of a
primary alcohol to aldehyde.


Which one of the following diagrams correctly represents the energy levels in the p-type semiconductor?
\( A \)
в.
Band
gap
\( c \)
band
D.
Conduction band


rume is the thupuric vi vectur \( \cup \boldsymbol{r} \)
and point \( Q \) is the endpoint of vector
OQ as shown in the above figure. When
the vectors \( \overline{O P} \) and \( \overline{O Q} \) are added,
calculate the length of the resultant
vector.
A . 1.41
B. 2.24
c. 2.65
D. 3.00
E . 8.6


On what principle \( A C \) generator works?


In which pair of species, both species do have the similar geometry?
A. \( C O_{2}, S O_{2} \)
в. \( N H_{3}, B H_{3} \)
c. \( C O_{3}^{2-}, S O_{3}^{2} \)
D. \( S O_{4}^{2-}, C l O_{4}^{-} \)


From which part of the human heart does the largest artery arise?
A. Left ventricle
B. Right ventricle
c. Left atrium
D. Right atrium


Argyrodite, briartite contain appreciable amounts of \( -? \)
A . lead
B. germanium
c. zinc
D. copper


Pleurisy is
A. Air in pleural cavity
B. Blood in pleural cavity
C. Both A and B
D. Inflammation of pleural membrane


What is the electric potential at the
centre of square of side 1 m? The
charges \( 1 \times 10^{-8} C,-2 \times 10^{-8} C, 3 \times \)
\( 10^{-8} C \) and \( 2 \times 10^{-8} C \) are placed at the
corners of the square.
\( \mathbf{A} \cdot 205 V \)
B. \( 308 V \)
\( c .509 V \)
D. \( 110 V \)


Snow and ice can from compound.
A. True
B. False


\( \mathrm{f}=\cos ^{-1}\left(\frac{3 x+4 \sqrt{1-x^{2}}}{5}\right), \) find \( \frac{d_{2}}{d} \)


Assertion
A current of 96.5 amperes is passes
into aquesous \( A g N O_{3} \) solution for 100
seconds.

The weight of silver deposited is \( 10.8 g \) (At.wt. of \( A g=108 \) ).
Reason
The mass of a substance deposited during the electorlysis of an electrolyte is inversely propotional to the quantity of elctricity passing through the electrolyute.
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


Assertion - The sound emitted by the
source travels in all directions.

Reason - The relative velocity of sound with respect to the observer is the sum
of velocity of sound and velocity of
observer.
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


Evaluate: \( \sqrt[3]{\frac{216}{2197}} \)
\( A \cdot \frac{6}{13} \)
в. \( \frac{7}{13} \)
\( c \cdot \frac{8}{13} \)
D. \( \frac{4}{13} \)


The order of the differential equation
whose general solution is given by
\( \boldsymbol{y}=\left(\boldsymbol{C}_{1}+\boldsymbol{C}_{2}\right) \sin \left(\boldsymbol{x}+\boldsymbol{C}_{3}\right)-\boldsymbol{C}_{4} \boldsymbol{e}^{\boldsymbol{x}+\boldsymbol{C}_{5}} \)
is
A . 5
B. 4
\( c \cdot 2 \)
D. 3


Name of \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{H} \boldsymbol{C}-\boldsymbol{O}-\boldsymbol{C} \boldsymbol{H}_{2}- \)
\( \boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \) is:
A. isopropyl propyl ether
B. dipropyl ether
c. di-isopropyl ether
D. isopropyl propyl keton


In the following pairs, contains lignin as common structural component?
A. Tracheid and collenchyma
B. Sclerenchyma and sieve tube
c. sclerenchyma and tracheid
D. Parenchyma and endodermis


Assertion
Consider \( \boldsymbol{E}_{\boldsymbol{i}}, \boldsymbol{i}=\mathbf{1}, \boldsymbol{2}, \ldots \ldots, \boldsymbol{n} \) as \( \boldsymbol{n} \)
mutually exclusive events of an
experiment.
\( \boldsymbol{P}\left(\boldsymbol{E}_{1}\right)+\boldsymbol{P}\left(\boldsymbol{E}_{2}\right)+\ldots+\boldsymbol{P}\left(\boldsymbol{E}_{n}\right) \leq 1 \)
Reason
\( \boldsymbol{P}\left(\boldsymbol{E}_{1} \cup \boldsymbol{E}_{2} \cup \ldots . . \cup \boldsymbol{E}_{n}\right)=\boldsymbol{P}\left(\boldsymbol{E}_{1}\right)+ \)
\( \boldsymbol{P}\left(\boldsymbol{E}_{2}\right)+\ldots \ldots+\boldsymbol{P}\left(\boldsymbol{E}_{n}\right) \)
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


Assertion
MeMgBr should be prepared under
perfectly anhydrous conditions.
Reason
Grignard reagent reacts with water
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason are correct


Consider the differential equation \( \frac{d y}{d x}= \) \( \cos x \) Then we observe that
A \( \cdot y=\sin x \)
B. \( y=\sin x+2 \)
c. \( y=\sin x-\frac{1}{2} \)
D. \( y=\sin x+c \)


Four point charges, each of \( +q, \) are rigidly fixed at the four corners of a square planar soap film of side \( a \). The
surface tension of the soap film is \( \gamma \) The system of charges and planar film are in equilibrium, and \( \boldsymbol{a}=\boldsymbol{k}\left[\frac{\boldsymbol{q}^{2}}{\gamma}\right]^{1 / N}, \) where
\( k^{\prime} \) is a constant. Then \( N \) is:
\( A \cdot 3 \)
B. 2
\( c \cdot 4 \)
\( D \)


Evaluate the following limits. If \( \lim _{x \rightarrow a} \frac{x^{5}-a^{5}}{x-a}=405, \) find all possible
values of a.
A \( \cdot a=3,-3 \)
B. \( a=2,-2 \)
\( \mathbf{c} \cdot a=5,-5 \)
D. None of these


The motion of a block sliding down a frictionless ramp can be described as motion with
A. A constant speed, independent of the slope of the ramp
B. A constant speed that depends on the slope of the ramp
c. An acceleration which increases as the block slides
D. A constant acceleration less than \( 10 \mathrm{m} / \mathrm{s}^{2} \)
E. A constant acceleration greater than \( 10 \mathrm{m} / \mathrm{s}^{2} \)


Show that \( f(x)=\log _{a} x, 0<a<1 \) is a
decreasing function for all \( \boldsymbol{x}>\mathbf{0} \)


Substances burn more readily in \( N_{2} O \)
than in air because \( N_{2} O: \)
A. is reactive at high temperature
B. dissociates to give \( O_{2} \) that supports combustion.
c. the activation energy is increased on increasing temperature.
D. acts as a catalyst


When an electrolyte is dissociated in
solution, the van't Hoff's factor ( \( i \) ) is :
\( A \cdot>1 \)
B. \( <1 \)
\( \mathrm{c} \cdot=0 \)
\( \mathrm{D} \cdot=1 \)


A velocity-time graph for a moving object is shown below. What would be
the total displacement during time \( t= \)
\( \mathbf{0} \) to \( \boldsymbol{t}=\mathbf{6} \boldsymbol{s} ? \)
A. \( 10 \mathrm{m} \)
B. 20 m
\( c .15 \mathrm{m} \)
D. \( 0.0 \mathrm{m} \)


Which of the following substances, if introduced into the bloodstream, would cause coagulation of blood at the site of
its introduction?
A. Fibrinogen
B. Prothrombin
c. Heparin
D. Thromboplastin


Which of the following is more nonmetallic element from the elements 'X'
and 'Y' having electronic configurations 2,8,5 and 2,8,6 respectively?
A. \( x \)
B. Y
c. Both have same non-metallic character
D. None of the above


A particle is executing SHM with amplitude A and has maximum
velocity \( V_{0} . \) Its speed at displacement A/2 will be


If \( \frac{1}{2} \sin ^{-1}\left[\frac{3 \sin 2 \theta}{5+4 \cos 2 \theta}\right]=\tan ^{-1} x \)
then \( \boldsymbol{x}= \)
\( \mathbf{A} \cdot \tan 3 \theta \)
B. \( 3 \tan \theta \)
c. \( (1 / 3) \tan \theta \)
D. \( 3 \cot \theta \)


The total number of orbitals in the fifth
energy level is:
A . 5
B. 10
c. 18
D. 25


Two large thin metal plates are parallel and close to each other. On their inner
faces, the plates have surface charge
densities of opposite signs and
magnitude \( 27 \times 10^{-22} C \quad m^{-2} . \) The
electric field \( \overrightarrow{\boldsymbol{E}} \) in region II in between the plates is
\( \begin{array}{ll}\text { A } \cdot 4.25 \times 10^{-8} N & C^{-1}\end{array} \)
в. \( 6.28 \times 10^{-10} N \quad C^{-1} \)
\( \begin{array}{lll}\text { с. } 3.05 \times 10^{-10} N & C^{-1}\end{array} \)
\( \begin{array}{lll}\text { D } \cdot & 5.03 \times 10^{-10} N & C^{-1}\end{array} \)


If radius of the \( _{13}^{27} A l \) nucleus is
estimated to be 3.6 fermi, then the
radius of \( \frac{125}{52} \) Te nucleus be nearly.
A. 6 fermi
B. 8 fermi
c. 4 fermi
D. 5 fermi


Divide \( 3 x^{4}-5 x^{3} y+6 x^{2} y^{2}-3 x y^{3}+ \)
\( \boldsymbol{y}^{4} \) by \( \boldsymbol{x}^{2}-\boldsymbol{x} \boldsymbol{y}+\boldsymbol{y}^{2} \)
What should be subtracted from the
quotient to make it a perfect square?
A \( \cdot 2 x^{2} \)
В. \( x^{2} \)
\( c \cdot y^{2} \)
D. -xy


If Republic Day falls on Friday this year and Shyam was born on 4 days before 12th January, then he celebrates his birthday on
A. Tuesday
B. Sunday
c. Monday
D. wednesday


Which of the following orders is true
regarding the acidic nature of \( C \) OOH?
A. Formic acid \( > \) Acetic acid \( > \) Propanoic acid
B. Formic acid \( > \) Acetic acid \( < \) Propanoic acid
C. Formic acid < Acetic acid < propanoic acid
D. Formic acid < Acetic acid >Propanoic acid


Q Type your question-
at a height \( \boldsymbol{H} \) on the roof a building, tries to catch it. He misses the catch,
the ball overshoots and simultaneously
the person starts a stop-watch. The ball
reaches its highest point and he
manages to catch it upon its return. By this time, a time interval \( T \) has elapsed
as recorded by the stop watch. If \( g \) is the
acceleration due to gravity at this place, the speed with which the ball was
thrown from point \( \boldsymbol{A} \) will be
\( \mathbf{A} \cdot \sqrt{g H+g T} \)
\( \frac{(\sqrt{g^{2} T^{2}+4 g H})}{2} \)
\( \frac{(\sqrt{g^{2} T^{2}+8 g H})}{2} \)
D. \( (\sqrt{g^{2} T^{2}+2 g H}) \)


Choose the correct statement among
the following.
A. Atrioventricular node is the pacemaker that generates action potential and initiates the atrial systole
B. During each cardiac cycle the lub sound is due to closure of semilunar valves
C. Stroke volume in each cardiac cycle is approximately 170 ml of blood.
D. QRS complex in an ECG indicates depolarisation of ventricles
E. The opening between right atrium and right ventricle is guarded by bicuspid valve.


Using graphical method Find the corner points for \( 2 x+5 y \leq 25 \)
\( 6 x+5 y \leq 45 \)
\( \boldsymbol{x} \geq \mathbf{0}, \boldsymbol{y} \geq \mathbf{0} \)


A ....... eye cannot distinctly see the
objects that are too near.
A. Myopic
B. Presbyopic
c. Hypermetropic
D. Heterophoria


Suppose a liquid in a container is heated at the top rather than at the bottom. What is the main process by
which the rest of the liquid becomes hot
\( ? \)
A. Conduction
B. Evaporation
c. Sublimation
D. None of these


The period of osillation of a freely suspended bar magnet is 4 second. If it
is cut into two equal parts in length, then the time period of each part will be
A. 4 sec
B. 2sec
c. \( 0.5 s e c \)
D. 0.25 sec


A chord of a circle of radius \( 7 \mathrm{cm} \)
subtends an angle of \( 90^{\circ} \) at its centre. The ratio of areas of smaller and larger
segment is
A .2: 7
B. 1: 10
c. 1: 11
D. none of these


\( \operatorname{Let} f(x)=\left\{\begin{array}{ll}x, & \text { if } x \text { is irrational } \\ 0, & \text { if is rational }\end{array}\right. \)
then fis
A. Continuous everywhere
B. Discontinuous everywhere
c. continuous only at \( x=0 \)
D. continuous at all rational numbers


\( C l_{2} \) gas is passed aqueous \( \mathrm{NaOH} \)
solution under given conditions
(a) \( C l_{2}+ \) NaOH (cold) \( \rightarrow \)
(b) \( C l_{2}+ \) NaOH (hot) \( \rightarrow \)
Equivalent mass of \( C l_{2} \) in \( (a) \) and \( (b) \) is
A. Equivalent mass of \( C l_{2} \) in (a) is \( 71.0 \mathrm{g} \) equivalent \( ^{-1} \)
Equivalent mass of \( C l_{2} \) in (b) is \( 42.6 \mathrm{g} \) equivalent \( ^{-1} \)
B. Equivalent mass of \( C l_{2} \) in (a) is \( 142.0 \mathrm{g} \) equivalent \( ^{-1} \)
Equivalent mass of \( C l_{2} \) in (b) is \( 85.2 \mathrm{g} \) equivalent \( ^{-1} \)
C. Equivalent mass of \( C l_{2} \) in (a) is \( 142.0 \mathrm{g} \) equivalent \( ^{-1} \)
Equivalent mass of \( C l_{2} \) in (b) is \( 42.6 \mathrm{g} \) equivalent \( ^{-1} \)
D. Equivalent mass of \( C l_{2} \) in (a) is 71.0 g equivalent \( ^{-1} \)
Equivalent mass of \( C l_{2} \) in (b) is 85.2 g equivalent \( ^{-1} \)
E. None of the above


Which is not correct about heartwood?
A. It is formed of living cells.
B. It contains resins, tannin and other organic contents
c. It is of dark colour
D. It lies in the centre region


Which one correctly describe
homologous structures?
A. Organs with anatomical similarities but, performing different functions
B. Organs with anatomical dissimilarities but performing same function
C. Organs that have no function now but had an important function in ancestors
D. Organs appearing only in embrycnic stage and disappearing later in the adult


Calculate the molarity of a solution containing 20.7 g of potassium carbonate dissolved in \( 500 \mathrm{mL} \) of
solution (assume density of solution = 1
\( \left.g m L^{-1}\right) \)
в. 0.213 м
c. 0.300 М
D. 0.413 м


The formal changes on the oxygen atoms in an ozone molecule, from left to
right, are \( _{\text {一一一一一一一一一 }} \) respecting
A. +1,0,-1
B. 0,+1,-1
c. -1,0,+1
D. 0,-1,+1


Form the differential equation of the family of circles in the first quadrant, which touches the coordinate axes.


A student carries out an experiment
and plots the \( V \) -I graph of three samples
of nichrome wire
with resistances \( \mathrm{R} 1, \) R2 and \( \mathrm{R} 3 \)
respectively (Figure.12.5). Which of the
following is true?
\( \mathbf{A} \cdot R_{1}=R_{2}=R_{3} \)
B \( \cdot R_{1}>R_{2}>R_{3} \)
\( \mathbf{c} \cdot R_{3}>R_{2}>R_{1} \)
\( \mathbf{D} \cdot R_{2}>R_{3}>R_{1} \)


A tube containing two or more plane mirrors, inclined at certain angles to each other, is called a Fill
in the blanks.
A . Microscope
B. Telescope
c. Kaleidoscope
D. Periscope


Sodium hydroxide is manufacture by the electrolysis of brine solution. The
reaction by-products are:
A. \( C l_{2} \) and \( H_{2} \)
B. \( C l_{2} \) and \( \mathrm{Na}-\mathrm{Hg} \)
c. \( C l_{2} \) and \( \mathrm{NaC} \)
D. \( C l_{2} \) and \( O_{2} \)


In a chemical reaction, \( 100 g \) baking
soda mixture containing sodium bicarbonate and vinegar on heating
gives \( 43 g \) of carbon dioxide gas.What mass of solid residue is left in food?
A \( .54 g \)
B. 55
c. \( 56 g \)
D. \( 57 g \)


The diagram given alongside represents the human heart in one phase of its activity. Study the same and then
answer the questions that follow:
(a)Name the phase.
(b)Which part of the heart is
contracting in this phase? Give a reason
to support your answer
(c)Name the parts numbered 1 to 6.
(d)What type of blood flows through the parts marked 1 and 2 respectively?
(e)How many valves are closed in this
phase?


The roots of the equation \( x^{2}-2 \sqrt{2} x+ \)
\( \mathbf{1}=\mathbf{0} \) are-
A. Real and distinct
B. Imaginary and different
c. Real and equal
D. Rational and different


derivative of phenol?
\( A \)
\( B \)
\( c \)
\( D \)


Which of the following configuration
can form a diatomic molecule?
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4} \)
\( \mathbf{C} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} \)
E \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)


Which of the following compounds is
amphoteric?
\( \mathbf{A} \cdot \operatorname{Cr}(O H)_{2} \)
B. \( F e(O H)_{2} \)
\( \mathbf{c} \cdot \operatorname{Cr}(O H)_{3} \)
D. \( \mathrm{Fe}(\mathrm{OH})_{3} \)


On which carbon can a group be placed
that is both axial and cis to the hydroxyl
group?
A. First
B. Second
c. Third
D. Fourth


What is the product of oxygenase acitivity of Rubisco?
A. Phosphoglycerate
B. Phosphoglycolate
c. Both A and B
D. Phosphoglyceraldehyde


Which of the following is not the contribution of Sir Issac Newton?
A. Universal Law of Gravitation
B. Laws of Motion
c. Ultra short Radio Waves
D. Reflecting Telescope


Pure conc. \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) makes iron passive,
as the layer of is formed on
the surface.
\( \mathbf{A} \cdot F e_{2} O_{3} \)
в. \( F e O \)
\( \mathbf{c} \cdot F e_{3} O_{4} \)
D. \( \operatorname{Fe}\left(\mathrm{NO}_{3}\right)_{3} \)


Chemiosmotic mechanism of ATP
synthesis was proposed by
A. Warburg
B. Dickens
c. Krebs
D. P. Mitchell


The inequality \( n !>2^{n-1} \) is true
\( \mathbf{A} \cdot \) for all \( n>1 \)
B. for all \( n>2 \)
c. for all \( n \epsilon N \)
D. none of these


The outermost electrons are
and are called
conduction electrons:
A. not free to move in the atom
B. bound to the protons
c. static
D. able to go to nearby atoms


Youngest layer of secondary xylem in wood of dicot stem is located just
A. Outside the cambium
B. Inside the cambium
c. outside the pith
D. Inside the cortex


If the 5 th term of an A.P is eight times the first and 8 th term exceeds twice the
4 th term by 3 , then the common difference is
\( A \cdot 7 \)
B. 5
\( c .6 \)
\( D \)


Solve the following inequation and represent the solution set on a number
line
\( -8 \frac{1}{2}<-\frac{1}{2}-4 x \leq 7 \frac{1}{2}, x \in 1 \)


The sum of the digits of a two digit
number is 14. When we interchange the digits, it is found that the resulting new number is smaller than the original number by \( 18 . \) What is the original two digit number?
\( \mathbf{A} \cdot 86 \)
B. 68
c. 84
D. 48


Construct a quadrilateral \( A B C D \) with
\( \boldsymbol{A B}=\mathbf{5} \mathrm{cm}, \boldsymbol{B C}=\mathbf{9} \mathrm{cm}, \angle \boldsymbol{A}= \)
\( \mathbf{3 0}^{\circ}, \angle \boldsymbol{B}=\mathbf{9 0}^{\circ}, \angle \boldsymbol{C}=\mathbf{1 5}^{\circ} \)


Rate constant for a particular reaction is \( 3 \times 10^{-6} \) mole \( \left.^{-2}\right|^{2} s^{-1} . \) The rate of
reaction for only single reactant is found to be \( 2.4 \times 10^{2} \) mole \( I^{-1} s^{-1} . \) The
equilibrium concentration of the
reactant could be:
A \( \cdot 0.8 \times 10^{4} \)
B . \( 2 \times 10^{2} \)
c. \( 0.8 \times 10^{2} \)
D. \( 2 \times 10^{\text { }} \)


Find the tangents and normal to the
curve \( \boldsymbol{y}(\boldsymbol{x}-\mathbf{2})(\boldsymbol{x}-\mathbf{3})-\boldsymbol{x}+\mathbf{7}=\mathbf{0}, \mathbf{a t} \)
point (7,0) are
A. \( x-20 y-7=0,20 x+y-140=0 \)
в. \( x+20 y-7=0,20 x-y-140=0 \)
D. \( 7 x+20 y-1=0,20 x-7 y-100=0 \)


Second stage of hydrosere is occupied by plants like
A. salix
B. Vallisneria
c. Azolla
D. Typha


\( \operatorname{Given} \overrightarrow{\boldsymbol{F}}=(4 \hat{\boldsymbol{i}}-10 \hat{\boldsymbol{j}}) \) and \( \overrightarrow{\boldsymbol{r}}= \)
\( (5 \hat{i}-3 \hat{j}) . \) Then torque \( \vec{\tau} \) is
\( \mathbf{A} \cdot-62 \hat{j} \)
в. \( 62 \hat{k} \)
\( c .38 \hat{i} \)
D. \( -38 \hat{k} \)


\( \int \frac{x^{2}+\cos ^{2} x}{1+x^{2}} \csc ^{2} x d x \) is equal to:
This question has multiple correct options
\( \mathbf{A} \cdot \cot x-\cot ^{-1} x+c \)
B \( \cdot c-\cot x+\cot ^{-1} x \)
\( ^{\mathbf{C}}-\tan ^{-1} x-\frac{\csc x}{\sec x}+c \)
D. \( e^{\ln \tan ^{2} x}+\cos x+c \)


An ideal transformer has 400 turns in
the primary and 200 turns in the secondary. If the primary is connected to a \( 12 \mathrm{V} \) battery, then the secondary voltage is
\( A \cdot 6 v \)
B. 24
\( c \cdot 3 v \)
D. zero


The simplified form of \( i^{n}+i^{n+1}+ \)
\( \boldsymbol{i}^{\boldsymbol{n}+\boldsymbol{2}}+\boldsymbol{i}^{\boldsymbol{n}+\boldsymbol{3}} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot-1 \)
D.


Find the \( 4^{t h} \) term in the expansion of
\( (x-2 y)^{12} \)


Clove is a/an
A. Flower budd
B. Axillary bud
c. Thalamus
D. Ovule


What are the factors affecting the rate of diffusion?


A binary operation \( * \) defined \( Q-\{1\} \) is
given by \( a * b=a+b-a b \). Find the
identity element.


The area of a rhombus is \( 90 \mathrm{cm}^{2} \). If one
of the diagonal is \( 14 \mathrm{cm}, \) what is the length of the other diagonal?


The total number of possible isomer for
the complex comp.:
\( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right]\left[\boldsymbol{P t} \boldsymbol{C} \boldsymbol{I}_{4}\right] \)
A. 3
B. 6
\( c \cdot 5 \)
D.


\( \lim _{x \rightarrow 3} 2 x^{2}-3 x-5= \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
\( c .-4 \)
D. -3


The radius of an atom is of the order of:
A \( \cdot 10^{-12} \mathrm{cm} \)
B . \( 10^{-14} \mathrm{cm} \)
\( c \cdot 10^{-10} \mathrm{cm} \)
\( D \cdot 10^{-8} \mathrm{cm} \)


\( S(s)+O_{2}(g) \rightarrow S O_{2}(g) ; \quad \Delta H=-296.1 k J \)
\( 2 S O_{3}(g) \rightarrow 2 S O_{2}(g)+O_{2}(g) ; \quad \Delta H= \)
\( 198.2 k J \)
How to find the \( \Delta H \) for \( 2 S(s)+3 O_{2}(g) \rightarrow \)
\( 2 S O_{3}(g) ? \)
\( \mathbf{A} \cdot-395.8 k J \)
B. \( 395.8 k J \)
c. \( 295.8 k J \)
D. \( -790.4 k J \)


The product of 2 consecutive integers is 20 find them


The probability of an event which is sure to occur at every performance of an experiment is called a
A. simple event
B. compound event
c. complementary event
D. certain event


Chemically calgon is:
A. sodium aluminosilicate
B. sodium sulphate
c. sodium hexa meta phosphate
D. alkyl sulphonic acid


Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{g}^{\prime}(1)+\boldsymbol{g}^{\prime \prime}(2) \) and
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{x} \boldsymbol{f}^{\prime}(\boldsymbol{2})+\boldsymbol{f}^{\prime \prime}(\boldsymbol{3}) . \) Then
A \( \cdot f^{\prime}(1)=4+f^{\prime}(2) \)
B \( \cdot g^{\prime}(2)=8+g^{\prime}(1) \)
C \( \cdot g^{\prime \prime}(2)+f^{\prime \prime}(3)=4 \)
D. all of these


The process on an ideal gas, shown in
figure is :
A. isothermal
B. isobaric
C. isochoric
D. none of the above


Consider two nuclei of same radioactive
nuclide. One of the nuclei was created
in a supernova explosion 5 billion years ago. The other was created in a nuclear reaction 5 minutes ago. The probability of decay during next time is
A. different of each nuclei
B. nuclei created in explosion decays first
c. nuclei created in the reactor decays first
D. independent of time of creation


According to the law of reflection:
A \( . i r= \) constant
B. \( \sin i / \sin r= \) constant
c. \( i+r= \) constant
D. \( i=r \)


A circular metal plate of radius \( \boldsymbol{R} \) is rotating with a uniform angular velocity \( \omega \) with its plane perpendicular to a uniform magnetic field \( B \). Then the emf developed between the centre and the
rim of the plate is
A \( \cdot \pi \omega B R^{2} \)
B. \( \omega B R^{2} \)
\( \mathbf{c} \cdot \pi \omega B R^{2} / 2 \)
D. \( \omega B R^{2} / 2 \)


Loading of phloem is related to
A. Increase of sugar concentration in phloem.
B. Elongation of phloem cell.
C. Separation of phloem parenchyma.
D. Strengthening of phloem fiber.


If \( \sec \theta+\tan \theta=k, \cos \theta= \)
A. \( \frac{k^{2}+1}{2 k} \)
в. \( \frac{2 k}{k^{2}+1} \)
c. \( \frac{k}{k^{2}+1} \)
D. \( \frac{k}{k^{2}-1} \)


1 mole of \( C H_{3} C O O H \) and 1 mole of
\( C H_{3} C O O N a \) are dissolved in water to
form 1 litre aqueous solution. The pH of the resulting solution will be:
A . 9.2553
в. 4.7447
c. 14
D.


Which of the following alkyl halides will
undergo \( S_{N} 1 \) reaction most readily?
A \( \cdot\left(C H_{3}\right)_{3} C-F \)
В \( \cdot\left(C H_{3}\right)_{3} C-C l \)
C \( \cdot\left(C H_{3}\right)_{3} C-B r \)
D \( \cdot\left(C H_{3}\right)_{3} C-I \)


Explain the construction of plane wavefront using Huygen's principle.


Let \( C \) be the capacitance of a capacitor discharging through a resistor \( \mathrm{R} \).
Suppose \( t_{1} \) is the time taken for the energy stored in the capacitor to
reduced to half its initial value and \( t_{2} \) is the time taken for the charge to reduce to one-fourth its initial value. Then the
ratio \( t_{1} / t_{2} \) will be
\( A \cdot 2 \)
B.
\( c \cdot 1 / 2 \)
D. 1/4


The area of the pentagon whose vertices \( \operatorname{are}(4,1),(3,6),(-5,1),(-3,-3) \) and
(-3,0) is
A . 30 sq. units
B. 60 sq. units
c. 120 sq units
D. none of these


Short / Long answer type questions. Growth of long bones is bidirectional Comment upon the statement.


Uncertainty Principle was given by:
A. Heisenberg
B. Thomson
C. Rutherford
D. Bohr


Which of the following statements
related to VA group hydrides are true?
I. Reducing property increases from \( \mathrm{NH}_{3} \)
to BiH \( _{3} \)
II. Tendency to donate lone pair
decreases from \( \mathrm{NH}_{3} \) to \( \mathrm{BiH}_{3} \)
III. Ease of replacing H with Cl decreases
from \( \mathrm{NH}_{3} \) to \( \mathrm{BiH}_{3} \)
IV. Ease of formation of hydrides
decreases from \( \mathrm{NH}_{3} \) to \( \mathrm{BiH}_{3} \)
A. I, \( , \) I, II and 1 V
B. I, III and IV
c. I, II and IV
D. I and IV


When tall buildings are constructed on earth, the duration of day night
A. slightly increases
B. slightly decreases
c. has no change
D. none of these


Self linking property of carbon, due to which it can form number of compounds is called
A. Catenation
B. Hyperconjugation
C. Isomerisation
D. None of these


Assertion
Peptidyl transfer site is contributed by larger sub-unit of ribosome
Reason
The enzyme peptidyl transferase is contributed by both \( 23 S \) and 16 S ribosomal sub-units
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


State True or False.
Liquid \( N H_{3} \) does not contain Hydrogen bond.
A. True
B. False


All collision conserves
A. Kinetic energy
B. Potential energy
c. Momentum
D. All of the above


All members of Group IA have similar
reactivity because:
A. they have the same number of protons
B. they have the same number of electrons
C. they have similar outer shell electron configurations
D. they have valence electrons with the same quantum numbers
E. they have the same number of neutrons


A plane meets the co-ordinate axes in A,B,C such that the centroid of the
triangle \( A B C \) is the point \( (p, q, r) . \) The
equation of the plane is
A \( \cdot \frac{x}{p}+\frac{y}{q}+\frac{z}{r}=0 \)
В \( \cdot \frac{x}{p}+\frac{y}{q}+\frac{z}{r}=1 \)
c. \( \frac{x}{p}+\frac{y}{q}+\frac{z}{r}=2 \)
D. none of these


Balanced chemical equations imply which of the following?
I. Numbers of molecules are conserved
in chemical change
II. Numbers of atoms are conserved in
chemical change.
III. Mass is conserved in chemical
change.
A. I only
B. II only
c. \( I \) and \( I I I \)
D. II and III


Evaluate: \( \int \sqrt{\tan x} d x,\left(0<x<\frac{\pi}{2}\right) \)