Statement 1: Nylon fibres are stronger than terylene fibres. Statement 2: Intermolecular forces of
attraction in terylene are H-bonding.
A. Statement 1 is true; statement 2 is true; statement 2 is the correct explanation of statement
B. Statement 1 is true; statement 2 is true; statement 2 is not the correct explanation of statement
c. Statement 1 is true; statement 2 is false
D. Statement 1 is false; statement 2 is true


Determine the ratio of the volume of a
cube to that of a sphere which will exactly fit inside the cube.


The value of \( \int \cos (\log x) d x \) is
A \( \cdot \frac{1}{2}[\sin (\log x)+\cos (\log x)]+C \)
B. \( \frac{x}{2}[\sin (\log x)+\cos (\log x)]+C \)
c. \( \frac{x}{2}[\sin (\log x)-\cos (\log x)]+C \)
D \( \cdot \frac{1}{2}[\sin (\log x)-\cos (\log x)]+C \)


Name the transcriptionally active region of chromatin in a nucleus.


Let \( \boldsymbol{\alpha}, \boldsymbol{\beta} \in \boldsymbol{R} \) be such that
\( \lim _{x \rightarrow 0} \frac{x^{2} \sin (\beta x)}{a x-\sin x}=1 . \) Then \( 6(\alpha+\beta) \)
equals
A . 5
B. 7
\( c \cdot 8 \)
\( D \)


Which portion of the heating curve for
water shown would there be ONLY liquid
water present?
\( \mathbf{A} \cdot A-B \)
\( \mathbf{B}, \quad B-C \)
\( \mathbf{c} \cdot C-D \)
\( \mathbf{D}, \quad D-E \)


A circular coil expands radially in a
region of magnetic field and no electromotive force is produced in the coil. This is because
A. the magnetic field is constant
B. the magnetic field is in the same plane as the circular coil and it may or may not vary
c. the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably
\( D . \) both \( (b) \) and \( (c) \)


A particle moves along the side \( A B, B C \)
CD of a square of side 25 m with a
velocity of 15 m/s. Its average velocity
is
A \( .15 \mathrm{m} / \mathrm{s} \)
в. \( 10 \mathrm{m} / \mathrm{s} \)
\( \mathrm{c} .7 .5 \mathrm{m} / \mathrm{s} \)
D. \( 5 \mathrm{m} / \mathrm{s} \)


Floral formula of Cesalpinoideae is
\( A \)
\( \% \bigoplus_{\leftarrow} \mathrm{K}_{(5)} \mathrm{C}_{(5)} \mathrm{A}_{1+(9)} \mathrm{G} \)
в. \( \% G \mathbf{K}_{(5)} \mathbf{C}_{(5)} \mathbf{A}_{5} \underline{\mathbf{G}}_{\mathbf{1}} \)
c. \( \% \oint_{\mathrm{H}_{5}} \mathrm{C}_{(5)} \mathrm{A}_{\mathrm{l} 0} \mathrm{G}_{\mathrm{l}} \)
\( \% G \mathbf{K}_{5} \mathrm{C}_{5} \mathbf{A}_{7+3} \mathbf{G}_{\mathbf{1}} \)


\( \boldsymbol{x}=\boldsymbol{3} \cos \boldsymbol{\Theta}, \boldsymbol{y}=\boldsymbol{3} \sin \boldsymbol{\Theta}, \boldsymbol{t h e n} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=? \)
\( A \cdot-\cot \theta \)
B. \( -\sin \theta \)
\( c \cdot \sin \Theta \)
D. \( \tan \theta \)


Choose the correct answer from the
alternatives given What are the tiny clusters of chambers for diffusion of gases in lungs?
A. Pleura
B. Alveolar sacs
c. Bronchioles
D. Lobes


For gaseous reaction what is the unit of
rate of reaction?


A rational number whose product with a
given rational number is equal to a rational number
A. True
B. False


\( \underbrace{ } \)


A converging beam of rays is incident on a diverging thin lens. Having passed through the lens the ray intersect at a point \( 15 \mathrm{cm} \) from the lens. If lens is removed the point where the rays meet will move \( 5 \mathrm{cm} \) closer towards the
mounting that holds the lens. The focal length of lens is
A. \( f=10 \mathrm{cm} \)
B. \( f=15 \mathrm{cm} \)
c. \( f=30 c m \)
D. \( f=40 c m \)


In van Arkel method, if \( I_{2} \) is introduced
over impure metal at \( 1700 \mathrm{K} \), which of the following will occur?
A. lodide of the metal is formed
B. No reaction takes place
c. Impurities react with iodine
D. Metal doesn't react


What volume of \( 0.18 N-K M n O_{4} \)
solution would be needed for complete
reaction with \( 25 \mathrm{ml} \) of \( 0.21 N-K N O_{2} \)
in acidic medium ?
A \( .57 .29 \mathrm{ml} \)
в. \( 11.67 m l \)
c. \( 29.17 m \)
D. \( 22.92 m l \)


If the values of \( L, C \) and \( R \) in a series
\( \boldsymbol{L}-\boldsymbol{C}-\boldsymbol{R} \) circuit are \( 10 \mathrm{mH}, 100 \mu \boldsymbol{F} \)
and \( 100 \Omega \) respectively then the value of resonant frequency will be
\( ^{\mathbf{A}} \cdot \frac{10^{3}}{2 \pi} H z \)
в. \( 2 \times 10^{3} H z \)
c. \( _{2 \times \frac{10^{3}}{p i}} H z \)
D. \( 10^{3} H z \)


In the given structure of benzene if
single bond is represented by \( y \) and
double bond is represented by \( x \) the
\( C-C \) bond length is:
A \( . X>Y \)
В. \( X<Y \)
c. \( X=Y \)
D. none of these


Splitting up of the water molecule by an electric current is an example of electrolysis.
A. True
B. False


The line joining the points (-6,8) and
(8,-6) is divided into four equal parts;
find the coordinates of the points of
section


In the circuit of given figure (1) and (2) are ammeters. Just after key \( \boldsymbol{K} \) is pressed to complete the circuit, the reading is
A. maximum in both 1 and 2
B. zero in both 1 and 2
c. zero in 1 , minimum in 2
D. maximum in 1, zero in 2


Construct a quadrilateral \( \boldsymbol{V} \boldsymbol{A} \boldsymbol{B} \boldsymbol{N} \)
where \( \boldsymbol{V} \boldsymbol{A}=\mathbf{7} \boldsymbol{c m}, \boldsymbol{A B}=\mathbf{8} \boldsymbol{c m}, \boldsymbol{B} \boldsymbol{N}= \)
\( \mathbf{1 0} c \boldsymbol{m}, \boldsymbol{A} \boldsymbol{N}=\mathbf{1 2} \boldsymbol{c m} \) and \( \boldsymbol{V} \boldsymbol{B}=\mathbf{1 1} \boldsymbol{c m} \)
The measure of \( \angle B O N \), where \( O \) is the
intersection point of \( \boldsymbol{A} \boldsymbol{N} \) and \( \boldsymbol{B} \boldsymbol{V} \), is
A \( \cdot 100^{\circ} \)
B . \( 106^{\circ} \)
\( \mathrm{c} \cdot 96^{\circ} \)
D. \( 110^{\circ} \)


Consider the following statements \( (X \) and \( Y \) stand for two different elements)
(I) \( _{32} X^{65} \) and \( _{33} Y^{65} \) are isotopes.
(II) \( _{42} X^{86} \) and \( _{42} Y^{85} \) are isotopes.
(III) \( 85^{174} \) and \( _{88} Y^{177} \) have the same number of neutrons.
\( (\mid V)_{92} X^{235} \) and \( _{94} Y^{235} \) are isobars The correct statements are
A. Il and IV only
B. I, II and IV only
c. ॥, III and IV only
D. I, II, III and IV


Which of the following are correct?
This question has multiple correct options
\( A \)
B.
\( c \)
D.


The Bohr radius for the hydrogen atom
\( \boldsymbol{n}=\mathbf{1}) \) is approx \( \mathbf{0 . 5 3} \boldsymbol{A}^{o} . \) The radius for
the first excited state \( (n=2 \) orbit) is
\( \left(\operatorname{in} A^{o}\right) \)
A . 0.13
B. 1.06
c. 4.77
D. 2.12


An un-publicized beam of intensity \( 2 a^{2} \)
passes through a thin Polaroid. Assuming zero absorption in the Polaroid the intensity of emergent planes polarized light is
\( \mathbf{A} \cdot 2 a^{2} \)
в. \( a^{2} \)
c. \( \sqrt{2} a^{2} \)
D. \( \frac{a^{2}}{2} \)


Suppose that we change \( U_{R M S} \) of gas in
a closed container from \( 5 \times 10^{2} \mathrm{cm} / \mathrm{sec} \)
to \( 10 \times 10^{2} \mathrm{cm} / \mathrm{sec}, \) which one of the
following might correctly explain how this change was accomplished?
A. By heating the gas w double the temperature
B. By removing 75\% of the gas at constant volume we decrease the pressure to one quarter of its origina value
c. By heating the gas we quadruple the pressure
D. By pumping in more gas at constant temperature we quadruple the pressure


A motor cyclist rides around the well with a round vertical wall and does not
fall down while riding because:
A. the force of gravity disappears
B. he loses weight some how
c. he is kept in this path due to the force exerted by surrounding air
D. the frictional force of the wall balances his weight


A thin sheet of glass \( (\mu=1.5) \) of thickness 6 micron introduced in the
path of one of the interfering beams in a double slit experiment shifts the central fringe to a position previously occupied by fifth bright fringe. The the wavelength of light used is
A \( \cdot 6000 \stackrel{\circ}{A} \)
в. 3000 ,
\( c \cdot 4500 \stackrel{\circ}{A} \)
D・7500 \( \stackrel{\circ}{A} \)


A wire has a resistance of 10 ohm. Its
resistance if it is stretched by one-tenth of its original length is:
A . \( 12.1 \Omega \)
B. \( 7.9 \Omega \)
\( c \cdot 11 \Omega \)
D. \( 9 \Omega \)


Tautomerism is exhibited by:
This question has multiple correct options
\( \mathbf{A} \cdot\left(M e_{3} C C O\right)_{3} C H \)
B.
\( c \)
D.


Why are alkali metals normally kept under kerosene?


If \( f(x)=\frac{x^{2}-b x+25}{x^{2}-7 x+10} \) for \( x \neq 5 \) is
continuous at \( x=5, \) then the value of
\( \boldsymbol{f}(\mathbf{5}) \) is
A . 0
B.
\( c \cdot 2 \)
D. 3


Match the names of the scientists given
in column - I with contributions towards
the understanding of the atomic structure as given in column-II and choose the correct option from the
codes given below:


The function \( f(x)=\sin ^{-1}(\cos x) \) is?
This question has multiple correct options
A. Discontinuous at \( x=0 \)
B. Continuous at \( x=0 \)
C. Differentiable at \( x=0 \)
D. None of these


A bullet of mass \( 20 g \) is moving with a
speed of \( 150 \mathrm{ms}^{-1} . \) It strikes a target and is brought to rest after piercing 10 \( c m \) into it. Calculate the average force
of resistance offered by the target.
A \( .2500 \mathrm{N} \)
в. 2000 J
c. \( 2250 N \)
D. 2100 J


What percent is equivalent to \( \frac{\mathbf{3}}{8} \) ?


The probability that Raju arrives on
time at school is 0.72
Write down the probability that he will
not arrive on time.


Nitrogen can combine with:
A . only metals
B. only non-metals
C. both metals and non-metals
D. neither metals nor non-metals


The potential in the depletion layer is
due to:
A. electrons
B. holes
\( c . \) ions
D. forbidden band


A solution consists of 1 mole each of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \) and \( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} . \) The
p \( K a \) of acetic acid is \( 4.8 . \) What is the
\( \boldsymbol{p} \boldsymbol{H} \) of the solution, when 0.1 mole of
NaOH is added?
A . 4.8
B. Slightly greater than 4.8
c. Slightly less than 4.8
D.


The \( A s F_{5} \) molecule is trigonal bipyramidal.The atomic orbitals used
by the \( A s \) atoms for bonding are:
A \( \cdot d_{x^{2}-y^{2}}, d_{z}^{2}, s, p_{x}, p_{y} \)
В. \( s, p_{x}, p_{y}, p_{z} \)
c. \( s, p_{x}, p_{y}, p_{z}, d_{z^{2}} \)
D \( \cdot d_{x^{2}-y^{2}}, s, p_{x}, p_{y} \)


\( \lim _{n \rightarrow \infty} \frac{1^{2}+2^{2}+\ldots . .+n^{2}}{n^{3}} \) is equal to
A. \( \infty \)
B.
\( c \cdot \frac{1}{2} \)
D.


Which one of the following pairs is obtained on heating ammonium dichromate?
A. \( N_{2} \) and \( H_{2} \) O
B. \( H_{2} \) O and \( H_{2} \) 0
c. \( N O_{2} \) and \( H_{2} \) O
D. NO and \( N O_{2} \)


Express \( \frac{9}{100} \) as percentage


Mass per unit area of a disc of inner radius 'a' and outer radius 'b' is given by \( \left(\frac{\sigma_{0}}{r}\right), r \) distance from center. Its radius of gyration w.r.t. axis of rotation passing through center and perpendicular to plane is
A. \( \sqrt{\frac{b^{4}-a^{4}}{3\left(b^{2}-a^{2}\right.}} \)
B. \( \sqrt{\frac{b^{3}-a^{3}}{3(b-a)}} \)
c. \( \sqrt{\frac{b^{3}-a^{3}}{5(b-a)}} \)
D. \( \sqrt{\frac{b^{4}-a^{4}}{5\left(b^{2}-a^{2}\right.}} \)


At a certain temperature, \( \boldsymbol{K}_{\boldsymbol{C}} \) for
\( \boldsymbol{S O}_{2}(\boldsymbol{g})+\boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{S} \boldsymbol{O}_{3}(\boldsymbol{g})+\boldsymbol{N} \boldsymbol{O}(\boldsymbol{g}) \)
is \( 16 . \) If we take one mole of each of all
the four gases in one litre container, what would be the equilibrium
concentration of \( N O \) and \( N O_{2} ? \)
\( N O_{2}=10 M \)
B. \( N O=2 M \)
\( N O_{2}=2.4 M \)
\( N O_{2}=1.2 M \)
D. \( N O=1.6 M \)
\( N O_{2}=0.4 M \)


What is Autotrophic nutrition? Give one example.


Which of the following is true for universal law of gravitation?
(1) It acts on all the objects irrespective of their nature, shape and size
(2) \( \boldsymbol{F} \propto \boldsymbol{M} \times \boldsymbol{m} \)
(3) It acts along the line joining the centers of the two objects.
(4) \( \boldsymbol{F} \propto \frac{1}{d^{2}} \)
A . a and c
B. b and d
\( c \cdot a, b \) and \( d \)
D. All of the above


A charge \( +\mathrm{Q} \) is located in space at point \( (x=1 m, y=10 m, z=5 m) . \) What is
the total electric flux that passes
through the \( y-z \) plane?
A \( \cdot \frac{Q}{\varepsilon_{0}} \)
в. \( \frac{Q}{3 \varepsilon_{0}} \)
c. \( \frac{Q}{6 \varepsilon_{0}} \)
D. \( \frac{Q}{2 \varepsilon_{0}} \)


X-rays emitted from a copper target and
a molybdenum target are found to
contain a line of wavelength \( 22.85 \mathrm{nm} \) attribute to the \( K_{\alpha} \) lines of an impure
element. The \( K_{\alpha} \) lines of copper \( (\mathrm{Z}=29 \)
and molybdenum \( (\mathrm{Z}=42) \) have a
wavelength 15.42 nm and 7.12 nm respectively. Using Moseley's law, \( v^{1 / 2}=a(Z-b), \) calculate the atomic
number of the impure element:
A .24
B . 28
c. 30
D. 32


\( 4 H N O_{3}+P_{4} O_{10} \longrightarrow 4 H P O_{3}+X \)
In this above reaction the product \( X \) is :
A \( . N O_{2} \)
в. \( N_{2} O_{3} \)
c. \( N_{2} O_{4} \)
D. \( N_{2} O_{5} \)


Why do gases always tend to be less
soluble in liquids as the temperature is raised?


The major constituent of freshly obtained molasses is:
A. sucrose
B. fructose
c. glucose
D. methanol


In making an Ohm's law circuit, which of the following connection is correct?
A. Voltmeter is series and ammeter in parallel
B. Voltmeter in parallel and ammeter in series
c. voltmeter and ammeter both are in parallel
D. Voltmeter and ammeter both are in series


If \( \boldsymbol{A}=\left[\begin{array}{ll}2 & 5 \\ 2 & 1\end{array}\right] \) and \( B=\left[\begin{array}{cc}4 & -3 \\ 2 & 5\end{array}\right], \) verify
that \( |\boldsymbol{A B}|=|\boldsymbol{A}||\boldsymbol{B}| \)


The set of natural numbers is divided
into arrays of rows and columns in the
form of matrices as \( \boldsymbol{A}_{1}=(1), \boldsymbol{A}_{2}=\left(\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right), \boldsymbol{A}_{3}= \)
\( \left(\begin{array}{ccc}\mathbf{6} & \mathbf{7} & \mathbf{8} \\ \mathbf{9} & \mathbf{1 0} & \mathbf{1 1} \\ \mathbf{1 2} & \mathbf{1 3} & \mathbf{1 4}\end{array}\right) \ldots \mathbf{s o} \) on
Find the value of \( \boldsymbol{T}_{\boldsymbol{r}}\left(\boldsymbol{A}_{\mathbf{1 0}}\right) \)
\( \left[\mathrm{Note}: T_{r}(A) \) denotes sum of diagonal \right.
elements of \( \boldsymbol{A} . \)
A . 3355
в. 3434
\( c .5533 \)
D. None of these


A tank full of water has a small hole at
its bottom. Let \( t_{1} \) be the time taken to
empty first one thbird of the tank and \( t_{2} \) be the time taken to empty second one
third of the tank and \( t_{3} \) be the time
taken to empty rest of the tank then
\( \mathbf{A} \cdot t_{1}=t_{2}=t_{3} \)
В \( \cdot t_{1}>t_{2}>t_{3} \)
\( \mathbf{c} \cdot t_{1}<t_{2}<t_{3} \)
D. \( t_{1}>t_{2}<t_{3} \)


Assertion
\( \boldsymbol{S O}_{2} \) turns acidified \( \boldsymbol{K}_{2} \boldsymbol{C r}_{2} \boldsymbol{O}_{7} \) green
Reason
\( K_{2} C r_{2} O_{7} \) is reduced to \( C r^{3+}(\text { green }) \)
salt by \( S O_{2} \)
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.


Figure shows three vectors \( \vec{a}, \vec{b} \) and \( \vec{c} \) where \( R \) is the midpoint of \( P Q \). Then
which of the following relations is
correct?
A. \( \vec{a}+\vec{b}=2 \vec{c} \)
в. \( \vec{a}+\vec{b}=\vec{c} \)
c. \( \vec{a}-\vec{b}=2 \vec{c} \)
D. \( \vec{a}-\vec{b}=\vec{c} \)


The number of people having flu after 20 days is
A. 1400
B. 1540
\( c .1498 \)
D. 1492


In the diagram given above some of algae have been labelled as \( A \),' \( B \) ', 'C' D', and 'E'. These algae are respectively identified as
A. Dictyota, Polysiphonia, Porphyra, Fucus and Laminaria
B. Porphyra, Dictyota, Laminaria, Fucus and Polysiphonia
c. Dictyota, Polysiphonia, Porphyra, Laminaria and Fucus
D. Fucus, Porphyra, Dictyota, Polysiphonia and Laminaria


A fan of moment of inertia \( I \) is set into
rotation at time \( t=0 \) with constant
power \( P . \) Then
A. The angular speed of the fan is proportional to \( t \)
B. The angular acceleration of the fan remains constant
c. The magnitude of the angular displacement is proportional to \( t^{2} \)
D. The magnitude of the torque is proportional to \( t^{-1 / 2} / 2 \) -


Find the differential equation
representing the family of curves \( \boldsymbol{v}= \) \( \frac{\boldsymbol{A}}{\boldsymbol{r}}+\boldsymbol{B}, \) where \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are arbitary
constants.


The variance of the random variable \( x \)
whose probability distribution is given
by
\( \boldsymbol{X}=\boldsymbol{x}: \quad \mathbf{0} \quad \mathbf{1} \quad \mathbf{2} \quad \mathbf{3} \)
\( \boldsymbol{p}(\boldsymbol{X}=\boldsymbol{x}): \quad \frac{1}{3} \frac{1}{2} \boldsymbol{0} \frac{1}{\boldsymbol{6}} \)
A . 0.5
B. 1
\( c .1 .5 \)
D. 2.0


Although the hydrogen bonding in hydrogen fluoride is much stronger
than in water, yet water has a much higher boiling point than hydrogen fluoride. Explain.


Define the following and state their numerical value in SI system:
(a) Specific latent heat of fusion of ice
(b) Specific latent heat of vaporisation of system


The mid-points of the side of a triangle \( \operatorname{are} D(6,1), E(3,5) \) and \( F(-1,-2) \) then
the vertex opposite to D is
A. (-4,2)
в. (-4,5)
c. (2,5)
(年. (2,5)
D. (10,8)


An aqueous solution of sodium hydroxide reacts with white
phosphorous to form phosphine \( \left(\boldsymbol{P} \boldsymbol{H}_{3}\right) \)
and :
A. \( N a H_{2} P O_{2} \)
в. \( P_{2} O_{5} \)
c. \( \operatorname{Na}\left(P O_{3}\right)_{6} \)
D. \( P_{2} O_{3} \)


A light beam travelling in the \( x \)
direction is described by the electric
field \( \boldsymbol{E}_{\boldsymbol{y}}=\mathbf{3 0 0 v} / \boldsymbol{m} \sin \left(\boldsymbol{t}-\frac{\boldsymbol{x}}{c}\right) \cdot \mathbf{A} \mathbf{n} \)
electron is constrained to move along
the y-direction with a speed of \( 2.0 \times \) \( 10^{7} m / s . \) Find the maximum magnetic
force on the electron.
\( \mathbf{A} \cdot 2 \times 10^{-18} \)
B . \( 2.5 \times 10^{-18} \)
C \( .3 \times 10^{-18} \)
D. \( 3.2 \times 10^{-18} \)


Differentiate between.
Diploblastic and triploblastic animals


Which of the following is not correct?
A. Robert Brown discovered the cell.
B. Schleiden and Schwann formulated the cell theory.
C. Virchow explained that the cells are formed from preexisting cells.
D. A unicellular organism carries out its activities within a single cell


toppr
Q Type your question
\( \boldsymbol{H}_{2} \boldsymbol{O}_{2(l)} \rightarrow \boldsymbol{H}_{2} \boldsymbol{O}_{(l)}+\frac{1}{2} \boldsymbol{O}_{2(g)}: \boldsymbol{\Delta}_{r} \boldsymbol{G}^{o}= \)
\( -122.6 k J / m o l \)
As the reaction from left to right is accompanied by a decrease in free energy, it is a spontaneous process. However, its decomposition at \( 25^{\circ} \mathrm{C} \) in
the absence of catalysts is slow. The catalysts which accelerate decomposition are \( \mathrm{Pt}, \mathrm{Ag}, \) cobalt, iron, copper, manganese dioxide and light.
Concentrated \( H_{2} O_{2} \) solution can result
into uncontrolled decompositions
leading to explosion. \( H_{2} O_{2} \) thus stored in colored wax-lined bottles (as rough glass surfaces) also causes its decomposition. A few stabilizers such as acids acetanilide, pyrophosphates, and stannates are added to slow down
the decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
Here \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is a:
A. diamagnetic
c. non-polar
D. all are incorrect


An athlete completes one round of a circular track of diameter \( 200 \mathrm{m} \) in 40
s. What will be the distance covered and
also the displacement at the end of 2 \( \min 20 s ? \)


Who discovered genetic code?
A. Nirenberg
B. Khorana
c. Ochoa
D. Crick


Identify the acid which gives \( C O \) and
\( C O_{2} \) on reaction with \( H_{2} S O_{4} \)
A. Oxalic acid
B. Formic acid
c. Nitric acid
D. Hydrochloric acid


Which of the following compounds shows maximum hydrogen bonding?
\( \mathbf{A} \cdot H F \)
в. \( H_{2} O \)
c. \( N H_{3} \)
D. \( C H_{3} O H \)


According to Henry's law, the solubility of a gas in a given volume of liquid increases with increase in :
A. temperature
B. pressure
c. both A and B
D. none of the above


Amphoteric oxide is:
A. \( A l_{2} O_{3} \)
в. \( \operatorname{si} 0_{2} \)
\( \mathrm{c} \cdot P_{4} O_{10} \)
D. \( C l O_{7} \)


Choose the correct answer from the
alternatives given
What are the products of photosynthesis
A. Water and carbon dioxide
B. Water and oxygen
c. Oxygen and carbohydrate
D. Carbohydrate and water


In a galvanic cell, electrons flow through connecting wires from:
A. anode to cathode
B. cathode to anode
c. top to bottom
D. anode


When an ideal gas undergoes
expansion through a porous plug, the
gas is expected to exhibit no cooling because
A. there exist no molecular forces of attraction
B. the molecules collide with each other, without any loss of energy
C. the volume occupied by molecules is negligible in comparision to the volume of the gas
D. none of the above


\( (\sin \theta+\csc \theta)^{2}+(\cos \theta+\sec \theta)^{2} \) is
\( A \cdot \geq 9 \)
B . \( \leq 9 \)
\( \mathrm{c} \cdot=9 \)
D. None of these


Consider a cycle followed by an engine as shown in figure to 2 is isothermal
2 to 3 is adiabatic
3 to 1 is adiabatic
Such a process does not exist because
A. heat is completely converted to mechanical energy in such a process, which is not possible.
B. mechanical energy is completely converted to heat in this process, which is not possible
c. curves representing two adiabatic processes can ef
D. curves representing an adiabatic process and an isothermal process dont intersect


The most stable nucleus should have:
A. even number of proton and odd number of neutrons
B. odd number of neutrons and odd number of protons
C. even number of protons and even number of neutrons
D. even number of neutrons and odd number of protons


Find a side of a cube whose total
surface area is \( 486 \mathrm{cm}^{2} \)


If you look at this object from the top,
what will you see?
\( A \)
\( B \)
\( c \)
D.


The energy required to remove a body of mass \( m \) from earth's surface is/are
equal to:
A. \( \frac{-G M m}{R} \)
в. \( m g R \)
c. \( -m g R \)
D. none of these


A Bohr hydrogen atom undergoes a transition \( n=5 \) to \( n=4 \) and emits a
photon of frequency \( f \). Frequency of
circular motion of electron in \( \boldsymbol{n}=\boldsymbol{4} \)
orbit is \( f_{4} . \) The ratio \( f / f_{4} \) is found to be 18/5m. State the value of \( m \)


The value of the sum \( \sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right) \)
where \( \boldsymbol{i}=\sqrt{-\mathbf{1}} \) is:
\( \mathbf{A} \cdot i \)
B. \( -i \)
\( c \cdot 0 \)
D. \( i-1 \)


State True or False.
Latent heat depends on the mass of the
substance.


A \( 3000 \mathrm{Kg} \) meteorite has a speed of \( 300 m s^{-1} \) just before colliding head on
with the energy that is the recoil speed of the earth? Mass of the earth \( =6 \times \)
\( 10^{24} K g \)


Explain hybridization of central atom in
\( : P C l_{3} \)


Which of the following statement is
wrong regarding Lanthanoids?
A. The ionic size of \( L n(\| I) \) ions decreases with increasing atomic number
B. \( \ln ( \) III ) hydroxides are mainly basic in nature
C. \( \operatorname{Ln}(\text { III }) \) compounds are predominantly ionic in character
D. \( \operatorname{Ln}(\text { III }) \) compounds are generally colourless


An electric dipole of length \( 20 \mathrm{cm} \) having \( \pm 3 \times 10^{-3} C \) charge placed at \( 60^{\circ} \) with
respect to a uniform electric field
experiences a torque of magnitude \( 6 N m . \) The potential energy of the dipole
is
A. \( -2 \sqrt{3} J \)
\( J \)
B. \( 5 \sqrt{3} J \)
c. \( -2 \sqrt{2} J \)
D. \( 3 \sqrt{5} \)


In the figure \( m_{1} \) and \( m_{2}\left(m_{1}<m_{2}\right) \) are
joined together by a pulley. When the mass \( m_{1} \) is released from the height \( h \)
above the floor, it strikes the floor with
speed (Given: Acceleration due to gravity \( =g \) )
A \( \cdot \sqrt{2 g h\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right)} \)
в. \( \sqrt{2 g h} \)
c. \( \sqrt{\frac{2 m_{2} g h}{m_{1}+m_{2}}} \)
D. \( \sqrt{\frac{2 m_{1} g h}{m_{1}+m_{2}}} \)


Write the formulae of the compounds
with given oxidation number of the
given elements
\( \begin{array}{lllll} & \text { Element } & \text { O.N } & \text { Compounds } \\ \text { (a) } & \text { 0 } & \text { +2 } & \text { OF }_{2} \\ \text { (b) } & \text { 0 } & -1 & H_{2} O_{2} \\ \text { (c) } & \text { 0 } & -0.5 & K O_{2} \\ \text { (d) } & \text { S } & -2 & H_{2} S \\ \text { (f) } & \text { S } & +6 & S O_{3}\end{array} \)
\( A \cdot(a) \&(c) \) are incorrect
\( B \cdot(b) \&(f) \) are incorrect
\( c \cdot(d) \&(e) \) are incorrect
of these


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) if \( \boldsymbol{y}=\tan ^{-1}\left(\frac{\mathbf{5} \boldsymbol{x}+\mathbf{1}}{\mathbf{3}-\boldsymbol{x}-\mathbf{6} \boldsymbol{x}^{2}}\right) \)


Which of the following sets of bases are present both in both DNA and RNA?
A. Adenine, Uracil, Thymine
B. Adenine, Guanine, Cytosine
c. Adenine, Guanine, Uraci
D. Adenine, Guanine, Thymine


you are aware of the natural reasons for
the occurrence of earthquakes. mention the man-made reasons
\( (s) \) of
earthquake


A stone tied to the end of a string which is \( 80 \mathrm{cm} \) long is whirled in a horizontal
circle with a constant speed. If the stone makes 14 revolutions in \( 25 s \), what is
the magnitude of
centripetal acceleration? \( \left(\operatorname{in} \boldsymbol{m} / \boldsymbol{s}^{2}\right) \)
A . 9.91
B . 2.36
c. 10.36
D. 12.69


The equation of the stationary wave is \( y=2 A \sin \left(\frac{2 \pi c t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \)
Which of the following statements is wrong?
A. The unit of ct is same as that of \( \lambda \)
B. The unit of \( x \). is same as that of \( \lambda \)
c. The unit of ct is same as that of \( x \)
D. The unit of ct, \lambda and \( x \) are same


If \( z_{1} \) and \( z_{2} \) are two complex number
such that \( \operatorname{lm}\left(z_{1}=z_{2}\right)=0=\operatorname{lm}\left(z_{1} z_{2}\right) \)
then
B. \( z_{1}=\bar{z}_{2} \)
\( \mathbf{c} \cdot z_{1}=-z_{2} \)
D. \( z_{1}=-\bar{z}_{2} \)


Which have a giant covalent structure?
This question has multiple correct options
A. Diamond
в. \( \operatorname{si} O_{2} \)
c. \( \operatorname{sicl}_{4} \)
\( D \cdot C O_{2} \)


A man takes a step forward with
probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step
away from the starting point.
A .0 .368
B. 0.147
c. 0.22
D. 0.073


The value of \( \lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}} \) is


The number of real solutions of the
equation
\[
\begin{array}{l}
\sin ^{-1}\left(\sum_{i=1}^{\infty} x^{i+1}-x \sum_{i=1}^{\infty}\left(\frac{x}{2}\right)^{i}\right)=\frac{\pi}{2}- \\
\cos ^{-1}\left(\sum_{i=1}^{\infty}\left(-\frac{x}{2}\right)^{i}-\sum_{i=1}^{\infty}(-x)^{i}\right) \text { lying in }
\end{array}
\]
the interval \( \left(-\frac{1}{2}, \frac{1}{2}\right) \) is


Pumice stone is gas in solid type colloid in which dispersion phase is gas and dispersion medium is solid.
If true enter 1 else enter 0


Velamen, the spongy tissue found in
A. Breathing roots of halophytes
B. Parasitic plants
C. All aerial roots
D. Aerial roots of epiphytic orchids


Find the adjoint of matrix \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]= \)
\( \left[\begin{array}{ccc}1 & 1 & 1 \\ 2 & 1 & -3 \\ -1 & 2 & 3\end{array}\right] \) and evaluate the answer


Which of the following hydrocarbons has the lowest dipole moment?
A. \( C H_{3} H C=C H C H_{3} \)
B. \( C H_{3} C \equiv C C H_{3} \)
c. \( C H_{3} C H_{2} C \equiv C H \)
D. \( C H_{2}=C H-C \equiv C H \)


Find the variance of the following distribution
\( \begin{array}{llll}\text { Class } & \mathbf{3 . 5}- & \mathbf{4 . 5}- & \mathbf{5 . 5 -} \\ \text { interval } & \mathbf{4 . 5} & \mathbf{5 . 5} & \mathbf{6 . 5}\end{array} \)
Frequency
14


The electrical conductivity of a semiconductor increases when
radiation of the wavelength shorter than \( 2480 n m \) is incident on it.The bandgap (in eV) for the semiconductor is
A . 0.5
B. 0.9
\( c .0 .7 \)
D. 1.


Assertion
\( S O_{2} \) gas is easily liquefied while \( H_{2} \) is
not.
Reason
\( \boldsymbol{S} \boldsymbol{O}_{2} \) has low critical temperature while
\( \boldsymbol{H}_{2} \) has high critical temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A compound which liberates reddish brown gas around the anode during electrolysis in its molten state is
A. Sodium chloride
B. Copper (II) oxide
c. copper (II) sulphate
D. Lead (II) bromide


Two dissimilar bulbs are connected
in series, which bulb will be brighter?
A. low resistance bulb
B. more resistance bulb
c. high current pass bulb.
D. low current pass bulb


zoaluate \( \left|\begin{array}{ccc}\log _{x} x y z & \log _{x} y & \log _{x} z \\ \log _{y} x y z & 1 & \log _{y} z \\ \log _{z} x y z & \log _{z} y & 1\end{array}\right| \)


For an ideal gas undergoing isothermal irreversible expansion:
This question has multiple correct options
\( \mathbf{A} \cdot \Delta U=0 \)
B. \( \Delta H=0 \)
c. \( \Delta S=0 \)
D. \( w=0 \)


When we study the full assortment of organisms in an area as well as the abiotic environment that affects them,
we are studying the
A. populations
B. niche
c. ecosystem
D. community


Find the smallest numbers by which each of the following numbers must be divided to obtain a perfect cube:
A . 1536
B. 10985
c. 28672
D. 13718


The chemical formula of plaster of paris
is:
A \( \cdot C a S O_{4} \cdot 2 H_{2} O \)
в. \( \operatorname{CaSO}_{4} \)
\( \mathrm{c} \cdot \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \)
\( ^{\mathrm{D}} \cdot_{C a S O_{4}} \cdot \frac{1}{2} H_{2} O \)


Lenses of powers \( 3 D \) and \( -5 D \) are
combined to from a composite lens. An object is placed at a distance of \( 50 \mathrm{cm} \)
from this lens. Calculate the position of its image.
A. \( -10 \mathrm{cm} \)
B. \( +10 \mathrm{cm} \)
c. -25 ст
D. \( +25 ~ c m \)


What is transcription? What are the different parts of a DNA transcription
unit? What is their role in the process of transcription?


When a Dobernier triad is considered,
the sum of the atomic weights of the terminal elements 'X' and 'Z' is 162.5.
The atomic weight of 'Z' is 50 units less than 5 times that of \( X \). Calculate the
atomic weights of \( X, Y, \) and \( Z . \) Identify their positions in the present periodic table.


In a uniform magnetic field of induction
\( B, \) a wire in the form of semicircle of
radius \( r \) rotates about the diameter of
the circle with angular velocity \( \omega . \) If the total resistance of the circuit is \( \boldsymbol{R} \)
the mean power generated per period of rotation is :
A. \( \frac{B \pi r^{2} \omega}{2 R} \)
B. \( \frac{\left(B \pi r^{2} \omega\right)^{2}}{8 R} \)
C. \( \frac{(B \pi r \omega)^{2}}{2 R} \)
D. \( \frac{\left(B \pi r \omega^{2}\right)^{2}}{8 R} \)


The amount of work done by the gas system in increasing the volume of 10 mols of an ideal gas from one litre to 20
litres at \( 0^{0} \) C will be
A . zero
B. 3.49 Joule
c. \( 3.49 \times 10^{4} \)
D. 6.79 \( \times 10^{4} \) Joule


Oxygen is absorbed by an alkaline solution of:
A. sodium hydroxide
B. potassium hydroxide
c. pyrogallol
D. ammonium hydroxide


The coefficient of viscosity of a liquid does not depend upon
A. the density of liquid.
B. temperature of liquid.
c. pressure of liquid.
D. nature of liquid.


If \( f(x)=a \log |x|+b x^{2}+x \) has its
extremum values at \( x=-1 \) and \( x=2 \)
then
A \( . a=2, b=-1 \)
в. \( a=2, b=-\frac{1}{2} \)
c. \( a=-2, b=\frac{1}{2} \)
D. None of the above


An element \( X \) belongs to \( 3^{r d} \) period and
group 16 of the Modern Periodic Table.
Write the Molecular formula of the
compound when 'X' reacts with
hydrogen and write its electron dot structure?


A star behaves like a perfectly black body emitting radiant energy. The ratio of radiant energy emitted per second by this star to that emitted by another star having 8 times the radius of former, but
having temperature one-fourth of that of the former in kelvin is :
\( A \cdot 1: 4 \)
B . 1: 16
\( c \cdot 4: 1 \)
D. 16:1


\( N O_{2} \) is involved in the production of
one of the most unpleasant of all chemicals present in photochemical smog. It is known as:
A. methane
B. acrylonitrile
c. peroxyacetyl nitrate
D. none of these


The coach of a cricket team buys 7 bats
and 6 balls for Rs. 3800 . Later, she buys
3 bats and 5 balls for Rs. 1750 . Find the
\( \operatorname{cost} \) of each bat and each ball


Match the following
List -I \( \quad \) List -II
(Products) (Reactants-Reaction)
(1) Sabatier - Senderens reaction of
A) Methane propylene
B) Ethane
(2) Wurtz reaction of methyl iodide
(3) Decarboxylation of sodium
C) Propane \( \quad \) acetate
(4) Sodium butanoate by Kolbes
D) Butane \( \quad \) electrolysis
(5) Sodium propanoate by Kolbes electrolysis
The correct match is :
\( A \cdot A-2 B-3 C-1 D-5 \)
B. \( A-4 B-2 C-1 D-5 \)
C \( \cdot A-3 B-2 C-1 D-5 \)
D. \( A-2 B-3 C-1 D-4 \)


Figure shows the position-time graph of an object in SHM. The correct equation
representing this motion is :
A \( \cdot \sin \left(\frac{2 \pi}{5} t+\frac{\pi}{6}\right) \)
B. \( 4 \sin \left(\frac{\pi}{5} t+\frac{\pi}{6}\right) \)
c. \( \operatorname{tain}\left(\frac{2 \pi}{6} t+\frac{\pi}{3}\right. \)
D. \( 4 \sin \left(\frac{2 \pi}{6} t+\frac{\pi}{6}\right) \)


In the figure, the vertical sections of the
string are long. \( A \) is released from rest
from the position shown. Then
A. The system will remain in equilibrium
B. The central block will move down continously
C. The central block will undergo simple harmonic motion
D. The central block will undergo periodic motion but not simple harmonic motion.


Eight dipoles of charges of magnitude \( q \) are placed inside a cube. Then, the total electric flux coming out of the cube will be
A \( \cdot \frac{8 q}{\epsilon} \)
в. \( \frac{16 q}{\epsilon} \)
c. \( \underline{q} \)
D.


If one penetrates a uniformly charged spherical cloud, electric field strength
A. decreases directly as the distance from the centre
B. increases directly as the distance from the centre
c. remains constant
D. None of these


A long straight wire of radius \( a \) carries a
steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field \( \operatorname{ata} / 2 \) and \( 2 a \) is:
A . \( 1 / 2 \)
в. \( 1 / 4 \)
\( c \cdot 4 \)
D.


The space launching centres in India are located at:
This question has multiple correct options
A. Sriharikota
B. Bengaluru
c. Delhi
D. Thumba


can be obtained from
bauxite by
A. Aluminium, Electrolysis
B. Copper, Electroplating
c. Aluminium, Electroplating
D. Copper, Electrolysis


The surface tension of water at \( 0^{0} C \) is
75.5 \( d y n e / c m . \) Find surface tension of
water at \( 25^{0} C \)
(a for water \( =\mathbf{0 . 0 0 2 1} / \mathbf{K} \) )


Of the following hydrides, which has the lowest boiling point?
A \( . N H_{3} \)
в. \( P H_{3} \)
\( \mathrm{c} \cdot \operatorname{SbH}_{3} \)
D. \( A s H_{3} \)


A wheel rotating at 12 rev/s is brought
to rest in \( 6 s . \) The average angular
deceleration in \( r a d / s^{2} \) of the wheel during this process is?
A . \( 4 \pi \)
в. 4
\( c \cdot 72 \)
D. \( \frac{1}{\pi} \)
\( E . \pi \)


What is the the actual reducing agent of haematite in blast furnace


Relation between relative permitivity
\( \left(\mu_{r}\right) \) and magnetic susceptibility \( \left(X_{m}\right) \)


Symbol of palladium is:
A. \( P \)
в. \( P o \)
c. \( P d \)
D. \( P h \)


If \( m_{1} \| m_{2} \) and the slope of \( m_{1} \) is \( 3 / 4 \)
then the slope of \( m_{2} \) is
\( A \cdot 3 / 4 \)
B. - -3/4
\( c \cdot 4 / 3 \)
D. -4/3


Find the equation of the plane passing through the points \( A=(2.3,-1), B=(4,5, \)
2), \( C=(3,6,5) \)


In the radioactive transformation
\[
\underset{Z}{A} \boldsymbol{X} \rightarrow_{Z+1}^{A} \boldsymbol{X}_{1} \rightarrow_{Z-1}^{A-4} \boldsymbol{X}_{2} \rightarrow_{Z}^{A-4} \boldsymbol{X}_{3}
\]
Which are the successively emitted radiactive radiation?
\( \mathbf{A} \cdot \beta^{-}, \alpha, \beta^{-} \)
B. \( \beta^{-}, \beta^{-}, \alpha \)
c. \( \alpha, \beta^{-}, \beta^{-} \)
D. \( \alpha, \alpha, \beta^{-} \)


If ionic radius of \( C s^{+} \) and \( C s^{-} \) are \( 1.69 \AA \)
and \( 1.89 \AA \) respectively, the edge length of unit cell is :
A \( \cdot 4.04 A^{\circ} \)
B . \( 3.54 A^{\circ} \)
c. \( 7.00 A^{\circ} \)
D. \( 1.04 A^{\circ} \)


Nitric oxide is formed by the reaction of:
A \( \cdot C+N_{2} O \)
в. \( C u+H N O_{3} \)
c. \( C u+N_{2} O \)
D. \( C u+N O_{2} \)


The volume of a sphere is \( 300.5 \mathrm{cm}^{3} \)
Find its surface area.
A . \( 21.3146 \mathrm{cm} \)
в. \( 216.3146 \mathrm{cm}^{2} \)
\( \mathbf{c} \cdot 216.3146 \mathrm{mm}^{2} \)
D. \( 216.3146 \mathrm{m}^{2} \)


Complete the following statements with an appropriate word /term be filled in
the blank space(s).
The force of attraction or repulsion
between two charges is given by
A. Gauss's law
B. Kepler's law
c. Coulomb's law
D. Gravitational law


The denominator of a fraction is greater
than its numerator by \( 12, \) if numerator
is decreased by 2 and the denominator is increased by \( 7, \) the new fraction is equivalent with \( \frac{1}{2} . \) Find the fractions.


A solid spherical ball is prepared by melting a cone and cylinder having the same height and same base radius
equal to \( r . \) Find the radius of the sphere.


A particle is projected upwards from the roof of a tower \( 60 m \) high with velocity
\( 20 m / s . \) Find the average speed.


\( 1^{\circ}=------(\text { approximately }) \)
A \( .0 .0175^{\circ} \)
B. 57
\( c \cdot 45^{c} \)
D. \( 1.75^{\circ} \)


There are two coins, one unbiased with probability \( \frac{1}{2} \) of getting heads and the other one is biased with probability \( \frac{3}{4} \) of getting heads. A coin is selected at random and tossed. It shows heads up.
Then the probability that the
unbiasedcoin was selected is
A \( \cdot \frac{2}{3} \)
в. \( \frac{3}{5} \)
c. \( \frac{1}{2} \)
D. \( \frac{2}{5} \)


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


Which of the following will qualify as Lewis base?
A. \( B C l_{3} \)
в. \( C H_{4} \)
\( c \cdot C l_{2} \)
D. \( N H_{3} \)


In a \( \triangle A B C \) BD and \( \mathrm{CE} \) are the altitudes
Prove that \( \triangle A D B \) and \( \triangle A E C \) are
similar. Check whether
\( \triangle C D B \) and \( \triangle B E C \) are similar


The eye lens is a :
A. transparent double-convex lens
B. transparent double-concave lens
C . transparent concavo-convex lens
D. transparent convex mirror


Which of the following statement is correct about \( A \) and \( B \) ?
A. A and B are mixture of diastereomers
B. A and B are mixture of enantiomers
C. A and B are optically active
D. B is racemic mixture


Find the area of a regular hexagon with side of \( 15 \mathrm{m} \) and apothem is \( 20 \mathrm{m} \)
A \( .910 m^{2} \)
B. \( 920 m^{2} \)
c. \( 900 m^{2} \)
D. \( 901 \mathrm{m}^{2} \)


Select the correct statement.
A. If the critical micelle concentration (CMC) of a soap is \( 10^{-3} \mathrm{mol} / \mathrm{L} \) the \( 10^{-4} \mathrm{M} \) solution of soap is a colloidal
solution.
B. Charge of dispersed phase and dispersion medium in a colloidal solution can be identified by electrodialysis process.
C. Peptization is defined as the process of converting colloidal sol into precipitate by shaking it with dispersion medium in the small amount of electrolyte
D. The emulsion is water in oil (W/O) when some oil soluble dye is added to it and background becomes coloured.


Select the right one from the given
options.
A. Christian Huygens, a Contemporary of Newton established the Wave theory of light by assuming that light waves are transverse.
B. Maxwell provided the compelling theoretical evidence that light is transverse in nature.
C. Thomas Young experimentally proved the wave behavior of light and Huygens assumption.
D. All the statements given above are correct


The diamagnetic species is:
A . NO
в. \( N O_{2} \)
\( c \cdot O_{2} \)
D. \( C O_{2} \)


Ammonia is highly soluble in
water. Other gases showing similar solubility is/are :
A. hydrochloric gas
B. sulphur dioxide gas
c. chlorine
D. both A and B


Oxygen forms liquid hydride which is (acidic/neutral/basic) in
nature during litmus paper test.


The composition (by atoms) of compound \( A \) is \( 40 \% X \) and \( 60 \% \) Y. The composition (by atoms) of compound B is \( 25 \% \mathrm{X} \) and \( 75 \% \) Y. According to the law of multiple proportions, the ratio of the weight of element \( Y \) in compounds \( A \) and B is:
A . 1: 2
B . 2: 1
\( c \cdot 2: 3 \)
D. 3: 4


Construct a quadrilateral ABCD, when \( A B=4 \mathrm{cm}, B C=5 \mathrm{cm}, C D=6.5 \mathrm{cm} \)
\( \angle A B C=105^{\circ} \) and \( \angle D C B=80^{\circ} . \) The
length of AD is
\( \mathbf{A} \cdot 2 \cdot 9 \mathrm{cm} \)
B. \( 3.5 \mathrm{cm} \)
c. \( 5.5 \mathrm{cm} \)
D. \( 4.5 \mathrm{cm} \)


0.5 mol of \( H_{2} \) and 0.5 mole of \( I_{2} \) react
in 10 litre flask \( a t 448^{\circ} C \). the
equilibrium constant \( \boldsymbol{K}_{c} \) is \( \mathbf{5 0} \) for
\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
What is the value of \( \boldsymbol{K}_{\boldsymbol{p}} \) ?


Choose the correct statement about
electric charges:
A. Two charges exert only electrical force on each other
B. Two charges exert only magnetic forces on each other.
C. Two charges interact electromagnetically.
D. Two charges interact either electrically or magnetically.


Which of the following is the dimension of compressibility?
\( \mathbf{A} \cdot\left[M^{-1} L^{1} T^{2}\right] \)
B . \( \left[M^{1} L^{-1} T^{-2}\right] \)
c. \( \left[M^{-1} L^{-1} T^{-2}\right. \)
D・ \( \left[M^{-1} L^{-1} T^{2}\right] \)


Write the function of Female
Reproductive system


Express the given complex number \( \mathbf{3}(\mathbf{7}+\mathbf{i 7})+\mathbf{i}(\mathbf{7}+\mathbf{i 7}) \) in the form \( \boldsymbol{a}+\boldsymbol{i b} \)


pressure indicates sinking air where clouds cannot form.
pressure indicates rising air, which allows clouds to form, bringing rain or snow. Fill in the blank.
A. High, high
B. High, low
c. Low, low
D. Low, high


Match the columns:
¡)visual aids \( \quad \) a)used for minor eye
defect or partial blindness.
ii)electronic aids \( \quad \) b) includes
cassettes,tape recorders,talking books.
iii)auditory aids c)used for people having little vision iv)optical aids
d)available for
performing computational tasks.
\( A \). i-b,ii-diii-a,iv-c
B. i-d,ii-a,iii-c,iv-b
c. i-c,ii-d,iii-b,iv-a
D. i-a,ii-c,iii-d,iv-b


Assertion
A heavy object always falls faster than a light object when dropped from a height
Reason

Gravitational force is proportional to the
mass of an object.
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 incorrect but Reason is correct
D. Both Assertion and Reason are incorrect


\( a, b, c \) are three adjacent angles at a
point \( O \) on a line \( A B \) such that their
degree measures are three consecutive
numbers. Find values of \( a, b, c \)


Which of the following possesses the highest bond energy?
\( \mathbf{A} \cdot F_{2} \)
B. \( C l_{2} \)
c. \( B r_{2} \)
D. \( I_{2} \)


Assertion
The product of magnetic susceptibility and absolute temperature for a paramagnetic substance is constant
Reason

Susceptibility is positive but very small
for paramagnetic substance.
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


Discuss the nature of bonding in metal carbonyls.


Calculate the potential of hydrogen
electrode in contact with a solution
whose \( p H \) is 10


The \( 4 f \) level is successively filled up in:
A. alkali metalss
B. rare gases
c. lanthanides
D. actinides


If the sum of mean and variance of \( B . D \)
for 5 trials is \( 1.8, \) the binomial
distribution is
A \( \cdot(0.8+0.2)^{5} \)
B. \( (0.2+1.8)^{5} \)
c. \( (0.8+0.2)^{10} \)
D. \( (0.2+1.8)^{10} \)


A body of mass \( m \) is released from a
height equal to the radius \( R \) of the Earth. The velocity with which it will
strike the Earth's surface is
A \( \cdot \sqrt{2 g R} \)
в. \( \sqrt{g R} \)
\( \mathbf{c} \cdot \sqrt{2 m g R} \)
D. \( \sqrt{m g R} \)
E \( . m \sqrt{g R} \)


Match column I with column II.


If the gas particles in a rigid container slow down, what will happen to the pressure inside the container?
A. Pressure will increase
B. Pressure will decrease
c. Pressure will oscillate
D. Pressure will not change


Which among the following are the symptoms of diarrhoea?
A. Sunken eyes
B. Dehydration due to loose motions
c. Dry mouth and lips
D. All of the above


Find the range of \( c \) for which the line
\( \boldsymbol{y}=\boldsymbol{m} \boldsymbol{x}+\boldsymbol{c} \) touches the parabola \( \boldsymbol{y}^{2}= \)
\( 8(x+2) \)


Column I lists the endocrine structure
and column II corresponding hormones. Match the two columns.


Two balls \( A \) and \( B \) having masses \( 1 k g \)
and \( 2 k g \) moving with speeds \( 21 m / s \)
and \( 4 m / s \) respectively in opposite direction, collide head on. After collision
\( A \) moves with a speed of 1 m/ \( s \) in the same direction, then the coefficient of
restitution is :
A . 0.1
B. 0.2
c. 0.4
D. None


Gila Monster Heloderma occurs in
A . Africa
B. America
c. Central Asia
D. china


Integrate \( \int \frac{x^{3}-x^{2}+x-1}{x-1} d x \)


Two parallel wires in free space are \( 10 \mathrm{cm} \) apart and each carries a current
of \( 10 A \) in the same direction. The force
exerted by one wire on other per metre of length of the wire is
A \( \cdot 2 \times 10^{-6} N \)
B . \( 2 \times 10^{-4} N \)
c. \( 2 \times 10^{-3} N \)
D \( \cdot 2 \times 10^{-2} N \)


A particle executing simple harmonic
motion with an amplitude \( 5 \mathrm{cm} \) and a
time period 0.2 s. The velocity and acceleration of the particle when the displacement is \( 5 \mathrm{cm} \) is
A \( .0 .5 \pi m s^{-1}, 0 m s^{-2} \)
B. \( 0.5 m s^{-1},-5 \pi^{2} m s^{-2} \)
C. \( 0 m s^{-1},-5 \pi^{2} m s^{-2} \)
D. \( 0.5 \pi m s^{-1},-0.5 \pi^{2} m s^{-2} \)


A car is moving at \( 100 \mathrm{km} / \mathrm{h} \). If the mass of the car is \( 950 k g \), its kinetic energy is:
в. \( 0.367 M J \)
c. \( 3.67 M J \)
D. 3.67J


A small block oscillates back and forth
on a smooth concave surface of radius
\( \boldsymbol{R} \). The time period of small oscillation
of the block is :
\( ^{\mathbf{A}} \cdot T=2 \pi \sqrt{\frac{R}{g}} \)
В \( \cdot T=2 \pi \sqrt{\frac{2 R}{g}} \)
c. \( T=2 \pi \sqrt{\frac{R}{2 g}} \)
D. none of these


A spherical ball falls through viscous medium with terminal velocity \( v \). If this ball is replaced by another ball of the same mass but half the radius, then the terminal velocity will be (neglect the effect of buoyancy)
\( A \)
B . \( 2 v \)
c. \( 4 v \)
D. \( 8 v \)


A refrigerator is a device which works on the principle that evaporation of a liquid gives a cooling effect.
A. True
B. False


By which smallest number must the
following numbers be divided so that the quotient is a perfect cube?
\( \mathbf{7 8 0 3} \)


Formula unit mass of \( Z n O \) is :
A . 85
B. 90
\( c \cdot 81 \)
D. 89


\( \boldsymbol{B} \boldsymbol{a} \boldsymbol{S} \boldsymbol{O}_{4}+\boldsymbol{4} \boldsymbol{C} \rightarrow \boldsymbol{B} \boldsymbol{a} \boldsymbol{S}+\boldsymbol{4} \boldsymbol{C} \boldsymbol{O} \)
In above reaction, write for each
reactant that undergoes oxidation or reduction and identify the type of
reaction.


A direct current of \( 2 A \) and an
alternating current having a maximum
value of \( 2 A \) flow through two identical resistances. The ratio of heat produced in the two resistances in the same time
interval will be
A . 1: 1
B. 1: 2
c. 2: 1
D. 4: 1


Factorise:
\( 9 x^{2} y^{2}-16 \)


Friction between two surfaces can be
by polishing the surfaces.fill in the blank.
\( A \). increased
B. decreased
c. the same
D. cant say


Assertion
Avogadro's law hold's good only under similar conditions of temperature and
pressure.
Reason
Change in temperature or pressure brings about change in volume.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the radius (in \( \mathrm{cm} \) ) of a circle,
whose circumference is \( 22 \mathrm{m} \)


If tangents are drawn from the end
points of 2 radii that are inclined at an
angle \( 125^{\circ}, \) what is the angle between
the tangents?
A . 55
B. \( 110^{\circ} \)
c. \( 125^{\circ} \)
D. \( 90^{\circ} \)


If \( \sin ^{-1}\left(\frac{1}{3}\right)+\sin ^{-1}\left(\frac{2}{3}\right)=\sin ^{-1} x, \) then
\( x \) is equal to
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{\sqrt{5}+4 \sqrt{2}}{9} \)
c. \( \frac{5 \sqrt{2}-4 \sqrt{5}}{9} \)
D.


Which of the following is not correct?
A. Ammonia is used as refrigerant
B. A mixture of \( C a(C N)_{2} \) and \( C \) is known as nitrolim
C . ammonium hydroxide is used as domestic the cleaning agent in its dilute form
D. in production of liquid fertilizer solution


Buna \( -N, \) a synthetic rubber is
copolymer of:
\( \mathbf{A} \cdot H_{2} C=C H-C H=C H_{2} \) and \( H_{5} C_{6}-C H=C H_{2} \)
B \( \cdot H_{2} C=C H-C N \) and \( H_{2} C=C H-C H=C H_{2} \)
\( \mathbf{C} \)
\( H_{2} C=C H-C=C H_{2} \) and \( H_{2} C=C H-C H=C H_{2} \)
D. \( H_{2} C=C N-C N \) and \( H_{2} C=C H-C=C H_{2} \)


In the following figure, find \( \angle A D C \)
A \( .27 .5^{\circ} \)
B . \( 36^{\circ} \)
\( c \cdot 47.5^{\circ} \)
D. \( 37.5^{\circ} \)


Find the value of \( c \) in Rolle's theorem for
the function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x} \) in \( [-\sqrt{\mathbf{3}}, \boldsymbol{0}] \)


Which of the following configurations corresponds to element of highest ionisation energy?
A \( \cdot 1 s^{2}, 2 s^{1} \)
B . \( 1 s^{2}, 2 s^{2}, 2 p^{3} \)
C. \( 1 s^{2}, 2 s^{2}, 2 p^{2} \)
D. \( 1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{1} \)


The function \( \boldsymbol{f}:(-\infty,-1) \rightarrow\left(\mathbf{0}, e^{5}\right] \)
defined by \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{\boldsymbol{x}^{3}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2}} \) is
A. many-one and onto
B. many-one and into
c. one-one and onto
D. one-one and into


The following factors indicate improved
reproductive health of the society.
1. Better detection and cure of disease
2. Better post-natal care
3. Medically assisted deliveries
4. Increased MMR
Select the code for the correct answer
from the options given below
A. 2,3 and 4 only
B. 1,2 and 3 only
C. 1,3 and 4 only
D. 1,2 and 4 only


All gymnosperms are
A. Heterosporous
B. Arborescent
C . Seed plants
D. All of the above


Assertion
If \( A \& B \) are two events such that \( P(A)=\frac{2}{5}, P(B)=\frac{3}{4} \) then \( \frac{1}{20} \leq \)
\( P(A \cap B) \leq \frac{2}{5} \)
Reason
\( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B}) \leq \max \{\boldsymbol{P}(\boldsymbol{A}), \boldsymbol{P}(B)\} \& \)
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B}) \geq \min \{\boldsymbol{P}(\boldsymbol{A}), \boldsymbol{P}(\boldsymbol{B})\} \)
A. Both Assertion \& Reason are individually true \& Reason is correct explanation of Assertion
B. Both Assertion \& Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Isotonic solutions have:
A. same boiling point
B. same vapour pressure
c. same melting point
D. same osmotic pressure


The most ionic compound will be formed between:
A. I and IV
B. I and
c. III and IV
D. III and v


A scooter weighing \( 150 \mathrm{kg} \) together with its rider moving at \( 36 k m / h r \) is to take
a turn of radius \( 30 \mathrm{m} \). What force on the
scooter towards the center is needed to
make the turn possible? Who or what provides this?


The length of the longest interval in
which the function \( 3 \sin x-4 \sin ^{3} x \) is
increasing is
A.
в.
c. \( \frac{3 \pi}{2} \)
D.


When carbon monoxide is passed over
solid caustic soda heated to \( 200^{\circ} \mathrm{C} \), it
forms:
A. \( N a_{2} C O_{3} \)
в. \( \mathrm{NaHCO}_{3} \)
c. \( H C O O N a \)
D. \( C H_{3} \) COONa


In an induction coil, the coefficient of
mutual induction is 4 henry. If a current of 5 ampere in 1 the primary coil is cut
off in \( \frac{1}{1500} \) s, the e.m.f at the terminals of
the secondary coil will be:
A . \( 15 \mathrm{kv} \)
B. 60 kV
\( c \cdot 10 k v \)
D. 30 kV


\( N a O H \) form hydrated salts.
A. True
B. False


A ray of light enters at grazing angle of incidence into an assembly of three isosceles right-angled prisms having refractive indices \( \mu_{1}=\sqrt{2}, \mu_{2}=\sqrt{x} \)
and \( \mu_{3}=\sqrt{3} . \) If finally emergent light
ray also emerges at grazing angle then
calculate \( x \)
\( A \)
B.
\( c \)
D


The LCM of 5490 and a third number is
1890 and their HCF is 18 The third
number is
A . 36
B. 180
\( c \cdot 126 \)
D. 108


Which of the following characteristics is not shared by birds and mammals?
A. A backbone and internal skeleton
B. Respiration through lungs
c. Viviparity
D. Warm-blooded condition


The equational division is the term
used for
A. Amitosis
B. Meiosis II
c. Meiosis
D. Both B and C


Two coherent waves are represented by
\( \boldsymbol{Y}_{1}=\boldsymbol{A}_{1} \cos \omega t . \boldsymbol{Y}_{2}=\boldsymbol{A}_{2} \sin \omega \boldsymbol{t} \)
The resultant intensity due to
interference is proportional to
A \( \cdot\left(A_{1}+A_{2}\right) \)
В \( \cdot\left(A_{1}-A_{2}\right) \)
\( \mathbf{c} \cdot\left(A_{1}^{2}+A_{2}^{2}\right) \)
D \( \cdot\left(A_{1}^{2}-A_{2}^{2}\right) \)


The retroperitoneal kidney is
A. Kidney of fish
B. Kidney covered by peritoneum on ventral side
C. Kidney covered by peritoneum on dorsal side
D. Kidney uncovered by peritoneum on ventral side


An electrovalent bond or ionic bond is
formed between:-
A. Two electronegative atoms
B. Two metals
c. Electropositive and electronegatve atoms
D. Two alectropositive atoms


The wire is found to vibrate in the third
harmonic.The time when the emf
becomes maximum for the first time is
A \( \cdot \frac{2 \pi}{\omega} \)
B. \( \frac{\pi}{\omega} \)
c. \( \frac{\pi}{2 \omega} \)
\( D \cdot 2 \pi \)
1


Choose the correct answers from the
alternatives given.
The villi present on the wall of the small
intestine
A. secrete digestive enzymes
B. increase the surface area for absorption
c. hold mucus, so ulcers do not form
D. hold products of digestion, so they do not enter the large intestine


Choose the correct combination among thefollowing
A) A mixture of weak acid and its salt of strong base acts as acidic buffer.
B) As number of moles of acid or base required to change the \( p^{H} \) of the buffer
by one unit increases, the quality of buffer increases.
C) Buffer action is maximum at \( \boldsymbol{p}^{\boldsymbol{H}}= \)
\( P^{K a} \) in case of acidic buffer.
A. All are correct
B. A only correct
c. B only correct
D. A only false


Which one is correct for stability order of given diatomic molecules?
A. \( H_{2}>B_{2}>L i_{2} \)
В. \( H_{2}>L i_{2}>B_{2} \)
\( \mathbf{c} \cdot B_{2}>L i_{2}>H_{2} \)
D. \( L i_{2}>B_{2}>H_{2} \)


\( 99 \% \) of a first order reaction was
completed in 32 min. When will \( 99.9 \% \) of the reaction complete?
A. 24 min
B. 8 min
c. 4 min
D. 48 min


Matrices \( A \) and \( B \) will be inverse of
each other only if
\( \mathbf{A} \cdot A B=B A \)
в. \( A B=0, B A=I \)
c. \( A B=B A=0 \)
D. \( A B=B A=I \)


Three six-faced dice are thrown
together. The probability that the sum of the numbers appearing on the dice is
\( k(9 \leq k \leq 14) \) is
\( ^{\text {A } \cdot} \frac{21 k-k^{2}-83}{216} \)
B. \( \frac{k^{2}-3 k+2}{432} \)
c. \( \frac{21 k-k^{2}-83}{432} \)
D. None of these


If one angle of a triangle equals the sum of the other two angles, the triangle must be
A. scalene
B. right angled
c. obtuse angled
D. acute angled


An aircraft is flying at a height of
\( 2800 m \) above the ground. The angle
subtended by it in \( 10 s \) is \( 30^{\circ} . \) Find the
speed of the aircraft.
A \( \cdot 150 m s^{-1} \)
B. \( 100 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 140 \mathrm{ms}^{-1} \)
D. \( 125 \mathrm{ms}^{-1} \)


For the given circuit shown in figure, the
potential of the battery is varied from
\( 10 V \) to \( 16 V . \) If by zener diode
breakdown voltage is \( 6 V \), find
maximum current through zener diode.
A. \( 1.5 \mathrm{mA} \)
в. 3.5 тА
\( c .5 m A \)
D. 6.5 m


If \( a+b+c=2 s, \) then the value of \( (s- \)
\( a)^{2}+(s-b)^{2}+(s-c)^{2} \) will be
A \( \cdot s^{2}+a^{2}+b^{2}+c^{2} \)
B. \( a^{2}+b^{2}+c^{2}-s^{2} \)
c. \( s^{2}-a^{2}-b^{2}-c^{2} \)
D. \( 4 s^{2}-a^{2}-b^{2}-c^{2} \)


A ray of light travels from an optically
denser to rarer medium. The critical
angle of the two media is ' \( c \) '. What is
the maximum possible deviation of the
ray?


Find the slope of the tangent and the
normal to the curve \( x^{2}-2 y-y^{2}=1 \) at
(-1,-2)


A rectangular loop of sides \( 10 \mathrm{cm} \) and 5
cm carrying a current I and 12 A is placed in different orientations as
shown in the figures above. If there is a uniform magnetic field of \( 0.3 \mathrm{T} \) in the positive z direction, in which
orientations the loop would be in (i)
stable equilibrium and (ii) unstable equilibrium?
\( A \cdot(A) \) and
(B), respectively
B. (A) and
(C), respectively
\( c \cdot(B) \) and
(D), respectively
D. (B) and
(C), respectively


A body initially at rest, starts moving along \( x \) -axis in such a way so that its
acceleration vs displacement plot is as
shown in figure. The maximum velocity
of particle is
A . \( 1 \mathrm{m} / \mathrm{s} \)
B. \( 6 m / s \)
c. \( 2 m / s \)
D. None of the above


The reading of \( V_{2} \) is :
\( ^{\mathbf{A}} \cdot \frac{-\pi a^{2} B_{0} R_{1}}{R_{1}+R_{2}} \)
\( ^{\mathbf{B}} \cdot \frac{-\pi a^{2} B_{0} R_{2}}{R_{1}+R_{2}} \)
с. \( \frac{\pi a^{2} B_{0} R_{1}}{R_{1}+R_{2}} \)
D. None of these


The number of d-electrons in \( F e^{2+}(Z= \)
26) is not equal to the number of
electrons in which one of the following?
A. d- electrons in Fe \( (z=26) \)
B. p - electrons in Ne ( \( Z=10 \) )
c. s - electrons in \( \mathrm{Mg}(\mathrm{Z}=12) \)
D. p-electrons in Cl ( \( z=17 \) )


A ball of mass \( 0.1 k g \) marks an elastic
head on collision with a ball of unknown
mass initially at rest. If \( 0.1 k g \) bal
rebounds at one third of its original speed, what is mass of the other ball?


A \( 50 H z \) a.c. source of \( 20 V \) is
connected across \( \mathrm{R} \) and \( \mathrm{C} \) as shown in
figure below. The voltage across \( \mathrm{R} \) is
\( 12 \mathrm{V} \). The voltage across \( \mathrm{C} \) is:
\( \mathbf{A} \cdot 8 V \)
B. \( 16 V \)
\( c \cdot 10 V \)
D. not possible to determine unless values of \( \mathrm{R} \) and \( \mathrm{C} \) are given


\( \int\left(e^{\sin ^{-1} x}+\frac{1}{\sqrt{1-x^{2}}}\right) d x \)
\( ^{\mathbf{A}} \cdot e^{\sin ^{-1} x}\left(\frac{\sqrt{1-x^{2}}+x}{2}\right)+\sin ^{-1} x+c \)
B . \( e^{x}\left(1+\tan ^{2} x\right)+c \)
\( \mathbf{c} \cdot e^{x} \tan 2 x+c \)
D. \( e^{x}(1+\tan x)+c \)


A moving-coil galvanometer has its coil of 24 turns and \( 12 \Omega \) resistance. By how much the number of turns should be
increased so that the current sensitivity of the galvanometer increases by \( 25 \% ? \)
If, in doing so, the resistance of the coil
increases to \( 20 \Omega \), what will be the effect on the voltage-sensitivity of the galvanometer?


The change in velocity when electron jumps from the first orbit to the second
orbit is
A. half its original velocity
B. twice its original velocity
c. one fourth is original velocity
D. equal to its original velocity


Where does the center of gravity of the
atmosphere of the lie?


When a body undergoes a linear tensile strain if experience a lateral contraction also. The ratio of lateral
contraction to longitudinal strain is known as
A. Young's modulus
B. Bulk modulus
c. Poisson's law
D. Hooke's law


Formation of glycogen from glucose is an example of
A. Catabolism
B. Polymerisation
c. Dehydration synthesis
D. Anabolism


In Rutherford's alpha scattering
experiment:

This question has multiple correct options
A. distance of closest approach is of the order of \( 10^{-14} \mathrm{m} \)
B. at the distance of closest approach, the kinetic energy of the \( \alpha- \) particle is transformed into electrostatic
potential
C. the \( \alpha- \) particles moving towards the nucleus will stop
moving and then start retracing its path
D. maximum number of \( \alpha- \) particles went straight
through the metal foil


Synthetic polymer which resembles natural rubber is:
A. Neoprene
B. Chloroprene
c. Glyptal
D. Nylon


The ions associated with salt bridge are
A. sodium
B. potassium
c. calsium
D. magnesium


What is the oxidation number for As in
the chemical formula for arsenic acid,
\( \boldsymbol{H}_{3} \boldsymbol{A} \boldsymbol{s} \boldsymbol{O}_{4} ? \)
\( A \cdot+1 \)
\( B .+2 \)
\( c \cdot+3 \)
\( D \cdot+4 \)
\( E \cdot+5 \)


A particle starts from rest with constant acceleration for 20 sec. If it travels a
distance \( y_{1} \) in the first 10 sec and a
distance \( y_{2} \) in the next 10 sec then?
A \( \cdot y_{2}=2 y_{1} \)
в. \( y_{2}=3 y_{1} \)
\( \mathbf{c} \cdot y_{2}=4 y_{1} \)
D. \( y_{2}=5 y_{1} \)


Units of rate of reaction are mole \( l^{-1} s^{-1} \)
A . True
B. False


The properties of aldehydes and ketones
are:
This question has multiple correct options
A. they can form hydrogen bonds in water
B. they can form hydrogen bonds with themselves
C. they are polar in nature
D. generally boiling point decrease with the increase in molecular weight


The function \( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) defined by
\( \boldsymbol{f}(\boldsymbol{x})=-\boldsymbol{x}^{2}+\boldsymbol{6} \boldsymbol{x}-\boldsymbol{8} \) is a bijection, if
A \( . A=(-\infty, 3] \) and \( B=(-\infty, 1] \)
B. \( A=[3, \infty) \) and \( B=R \)
C. \( A=(-\infty, 3] \) and \( B=[1, \infty) \)
D. \( A=[3, \infty) \) and \( B=[1, \infty) \)


The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If
the relative errors in measuring the mass and length are respectively \( 1.5 \% \) and \( 1 \% \), the maximum error in
determining the density is?
A . \( 2.5 \% \)
в. \( 3.5 \% \)
c. \( 4.5 \% \)
D. \( 6 \% \)


The positive integerjust greater than
\( (1+0.0001)^{10000} \) is
\( A \cdot 4 \)
B. 5
\( c \cdot 2 \)
D.


The difference between the electrostatic
potential of the positive end the negative end of an electric cell is the of
the cell.


With the help of the given clues, unscramble the letters to make a
meaningful word. NASRO (A device used in the ship to locate unseen underwater objects)


Identify the correct option among the following. A volatile solid soluble in benzene would
probably:
A. have electrovalent bonding
B. have covalent bonding
c. be a good conductor of electricity
D. be a salt


What is the difference in the
construction of an astronomical
telescope and a compound microscope
? The focal lengths of the objective and eyepiece of a compound microscope are \( 1.25 \mathrm{cm} \) and \( 5.0 \mathrm{cm}, \) respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 when the final image is formed at the near point.


In the direct current
A. The direction of current is always positive
B. The direction of current is always negative
C. The direction of current changes constantly
D. The direction of current is always in the same direction.


According to classification of elements
most of non-metals are placed in
block
A. \( s \) -block
B. \( p \) - block
c. \( d \) - block
D. \( f \) - block


A cricket ball of mass 250 g collides with a bat with velocity \( 10 \mathrm{m} / \mathrm{s} \) and returns with the same velocity within
0.01 second. The force acted on bat is:
A. 25
B. 50 N
c. 250 N
D. 500 N


\( \boldsymbol{I}=\int \frac{x+2}{(x+1)^{2}} \boldsymbol{d} \boldsymbol{x} ; \) then I is equal to
\( \mathbf{A} \cdot \log (x+1)+\frac{1}{x+1}+c \)
B. \( \log (x+2)-\frac{1}{x+1}+c \)
c. \( \log (1+x)-\frac{1}{x+1}+c \)
D. \( \log (x+2)+\frac{1}{x+1}+c \)


The best evidence that electrons are
arranged in definite orbits or energy levels is based on the observation that:
A. atomic spectra consist of discrete lines and not continuous bands
B. electrons in the beta ray have high kinetic energy
c. the penetrating power of cathode ray electrons depends upon the voltage used to produce them
D. electrons revolve around the nucleus


A metal wire of mass \( m \) slides without
friction on two rails at distance \( d \) apart.
The track is in a vertical uniform field of
induction \( \vec{B} \). A constant current \( \vec{i} \) flows
along one rail across the wire and back down the other rail the velocity of the wire as a function of time, assuming it to be at rest initially.
A \( \cdot \frac{B i d}{m} \)
в. \( \frac{B i d t}{m} \)
c. \( \frac{m}{\text { Bidt }} \)
D. None of the above


A cubic meter of copper weighing \( 9000 k g \) is rolled into a square bar \( 9 m \)
long. an exact cube is cut off from the bar. How much does it weight?
A. \( 333.3 \mathrm{kg} \)
в. \( 320.5 \mathrm{kg} \)
\( \mathrm{c} .349 .1 \mathrm{kg} \)
D. \( 312.9 \mathrm{kg} \)


Two flasks \( A \) and \( B \) of an equal volume
containing 1 mole and 2 moles of \( 0_{3} \)
respectively are heated to the same
temperature. When the reaction \( 2 O_{3} \rightleftharpoons \)
\( 30_{2} \) practically stops, then both the
flasks shall have
A \( . \) the same ratio: \( \left[O_{2}\right] /\left[O_{3}\right] \)
B. the same ratio: \( \left[O_{2}\right]^{3 / 2} /\left[O_{3}\right] \)
c. only \( O_{2} \)
D. the same time to reach equilibrium


How many ATP is utilized in the preparatory phase of glycolysis?
A. 7
B. 4
\( c \cdot 2 \)
D.


Evaluate \( (4 a+3 b)^{2}-(4 a-3 b)^{2}+ \)
\( 48 a b \)
A . \( 76 a b \)
B. \( 96 a b \)
\( c .46 a b \)
D. \( 106 a b \)


\( X \frac{H_{2} \text { along with boiling xylene}}{P d / B a S O_{4}} C H_{3} C H O \)
In the above reaction \( \boldsymbol{X} \) is:
A \( \cdot C H_{3} C O O H \)
в. \( C H_{3} \) СОС\( l \)
c. \( C H_{3} C O C H_{3} \)
D. \( C H_{3} C H_{2} \) ОН


The radii of the press plunger and the pump plunger are in the ratio \( 30: 4 . \) If an effort of 32 kgf acts on the pump plunger. Find the maximum effort the press plunger can overcome.
A. \( 1600 \mathrm{kgf} \)
B. 1700 kgf
c. \( 1800 \mathrm{kgf} \)
D. 1900 kgf


What is a sol?
A. A solid dispersed in a liquid
B. A liquid dispersed in a gas
C. A gas dispersed in a liquid
D. A gas dispersed in a solid


\( \% \) ionisation of weak acid can be
calculated as:
\( \mathbf{A} \cdot \sqrt[1]{\frac{K_{a}}{c}} \)
B. \( \frac{100}{1+10^{\left(p K_{a}-p H\right)}} \)
C. Both are correct
D. None is correct


The quantum number corresponding to orbit of diameter \( 0.0001 \mathrm{mm} \) in
hydrogen atom will be nearly (Given that
the radius of orbit with \( n=1 \) is \( 0.51 \times \)
\( \left.\mathbf{1 0}^{-\mathbf{1 0}}\right): \)
A . 39
B. 31
\( c \cdot 9 \)
D. 49


Three monkeys \( A, B \) and \( C \) with masses of \( 10,15 \& 8 k g \) respectively
are climbing up \( \& \) down the rope suspended from \( D \). At the instant
represented, \( A \) is descending the rope
with an acceleration of \( 2 m / s^{2} \& C \) is pulling himself up with acceleration of
\( 1.5 m / s^{2} . \) Monkey \( B \) is climbing up with a constant speed of \( 0.8 m / s . \) Calculate
the tension \( T \) in the rope at \( D .(g= \)
\( \left.10 m / s^{-2}\right) \)


\( (4 x-5 y)-(2 x-3 y) \)


What is the common name of \( \boldsymbol{C} \boldsymbol{H}_{2}= \)
CHCOOH?
A. Anthranilic acid
B. Citric acid
c. Acrylic acid
D. Propenoic acid


\( 2 \% \) of adult globin in humans is made of
\( B \cdot \zeta_{2}, \gamma_{2} \)
c. \( \alpha_{2}, \delta_{2} \)
D. \( \alpha_{2}, \gamma_{2} \)


A cell of emf \( 2 \mathrm{V} \) delivers current equal to
\( 20 \% \) of the maximum current, which it
can produce through a resistance \( 4 \Omega \) Its internal resistance is
A . \( 0.1 \Omega \)
B. 19
\( c \cdot 0.5 \Omega \)
D. 1.5.


If \( v_{e} \) is the escape velocity for earth when a projectile is fired from the surface of earth. Then the escape velocity if the same projectile is fired from its centre is
A \( \cdot \sqrt{\frac{3}{2}} v_{e} \)
в. \( \frac{3}{2} v_{e} \)
c. \( \sqrt{\frac{2}{3}} v_{e} \)
D. \( \frac{2}{3} v_{e} \)


A film of water is formed between two
straight parallel wires each \( 10 \mathrm{cm} \) long and at separation 0.5cm. Calculate the work required to increase \( 1 \mathrm{mm} \) distance between the wires. Surface
tension of water \( =\mathbf{7 2} \times \mathbf{1 0}^{-\mathbf{3}} \mathbf{N} / \mathbf{m} \)
A \( \cdot 1.44 \times 10^{-3} \)
В. \( 1.44 \times 10^{-7} \)
c. \( 1.44 \times 10^{-5} \)
D. \( 1.44 \times 10^{-4} \)


A plate in the form of a semicircle of
radius \( R \) has a mass per unit area of \( k r \)
where \( k \) is a constant and \( r \) is the
distance form the centre of a straight
edge. By dividing plate into
semicircular rings find the centre of
mass of the plate from the centre of its straight edge.
A \( \cdot \frac{4 R}{3 \pi} \)
B. \( \frac{2 R}{\pi} \)
c. \( \frac{3 R}{2 \pi} \)
D. \( \frac{3 R}{4 \pi} \)


A boy is sitting on a horizontal platform in the shape of a disc at a distance of
\( 5 m \) from its center. The boy begins to
slip when the speed of wheel exceeds 10rpm. The coefficient of friction
between the boy and platform is \( (g= \)
\( \left.10 m s^{-2}\right) \)
A \( \cdot \pi^{2} / 6 \)
в. \( \pi^{2} / 18 \)
c. \( \pi / 6 \)
D. \( \pi / 2 \)


Calcium carbonate is a chemical
compound with the formula
\( \boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2} \)
\( A \cdot O \)


The \( C l-C-C l \) angle in \( 1,1,2,2- \)
tetrachloroethene and
tetrachloromethane will be about.
A \( \cdot 90^{\circ} \) and \( 109.5^{\circ} \)
B . \( 109.5^{\circ} \) and \( 90^{\circ} \)
C. \( 109.5^{\circ} \) and \( 120^{\circ} \)
D. \( 120^{\circ} \) and \( 109.5^{\circ} \)


The maximum value of the expression \( \frac{1}{\sin ^{2} \theta+3 \sin \theta \cos \theta+5 \cos ^{2} \theta} \)
\( A \cdot 2 \)
B. 3
\( c \cdot \frac{1}{2} \)
D.


\( \sqrt{3} \sin \theta=\cos \theta, \) find the value of
\( \frac{3 \cos \theta+2 \sin \theta}{2 \cos ^{2} \theta-2} \)


What is not true of equipotential
surface?
A. The PD between any two points on the surface is zero
B. The electric field is always perpendicular to the surface
C. Equipotential surfaces are always spherical
D. No work is done in moving a charge along the surface


Short / Long answer type questions. What is feedback control? IIlustrate
feedback mechanism of homeostasis
by an example of hormones.


What is a free electron?
A. Any electron that is not attached to an ion, atom, or molecule and is free to move under the influence of an applied electric or magnetic field
B. Any electron that is attached to an ion, atom, or molecule and is free to move under the influence of an applied electric or magnetic field
C. Any neutron that is not attached to an ion, atom, or molecule and is free to move under the influence of an applied electric or magnetic field
D. None


To get maximum current in a resistance
of \( 3 \Omega, \) one can use n rows of m cells
(connected in series) connected in
parallel. If the total number of cells is 24 and the internal resistance of a cell is
\( 0.5 \Omega, \) then
A \( . m=12, n=2 \)
в. \( n=3, m=8 \)
c. \( m=2, n=12 \)
D. \( m=6, n=4 \)


Organometallic chemistry is the study of chemical compounds containing at least one bond between a carbon atom
of an organic compound and a metal. If true enter 1 , else enter 0 .


covert it into an upper triangular matrix Convert \( \left[\begin{array}{l}1-1 \\ 23\end{array}\right] \) into an identity matrix by suitable row transformations.


The reaction, \( 2 A(g)+B(g) \rightleftharpoons \)
\( \mathbf{3} C(\boldsymbol{g})+\boldsymbol{D}(\boldsymbol{g}), \) is begun with
concentration of \( A \) and \( B \) both at initial
value of \( 1 M . \) When equilibrium is
reached, the concentration of \( D \) is
measured and found to be \( 0.25 M . \) The
value for the equilibrium constant for this reaction is given by the expression:
\( \mathbf{A} \cdot\left[(0.75)^{3}(0.25)\right] \div\left[(1.00)^{2}(1.00)\right] \)
B \( \cdot\left[(0.75)^{3}(0.25)\right] \div\left[(0.50)^{2}(0.75)\right. \)
\( ^{\mathbf{C}} \cdot\left[(0.75)^{3}(0.25)\right] \div\left[(0.50)^{2}(0.25)\right] \)
D \( \cdot\left[(0.75)^{3}(0.25)\right] \div\left[(0.75)^{2}(0.25)\right] \)


Ribose sugar is present in
A. RNA polymerase, RNA and ATP
B. RNA only
c. RNA polymerase and ATP
D. RNA and ATP


A car goes on a horizontal circular road
of radius \( R, \) the speed increasing at a
constant rate \( \frac{\boldsymbol{d v}}{\boldsymbol{d t}}=\boldsymbol{a} . \) The friction coefficient between the road and the
tyre is \( \mu \). Find the maximum value of
speed at which the car is safe to drive.


Assertion
Ranitidine is used to treat hyperacidity and brompheniramine is used to treat hypersensitivity.
Reason
Both of these drugs are antihistamines.
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 \( \int_{2}^{3} x^{2}+2 x+5 d x \)


An alpha particle of energy 5 MeV is scattered through \( 180^{\circ} \) by a fixed uranium nucleus. The distance of the
closest approach is of the order of
A \( \cdot 10^{-15} \mathrm{cm} \)
B . \( 10^{-13} \mathrm{cm} \)
\( \mathbf{c} \cdot 10^{-12} \mathrm{cm} \)
D. \( 10^{-19} \mathrm{cm} \)


The surface of the metal is illuminated
with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be \( 1.68 \mathrm{eV} \), the work function of metal is :
A . \( 1.51 \mathrm{eV} \)
B. 1.42 ev
c. 3.0 ev
D. 1.68 ev


Which statement is wrong from the following for the reflection by plane mirror?
A. The size of image is same as the size of the object.
B. object distance and image distance is same.
c. A plane mirror forms virtual and erect image
D. Image of the object is not laterally inverted


Fill in the blanks:
An aged person suffering from caused by the weak accommodation power of the eye lens associated with old age, should wear
lenses.
A. Myopia, concave
B. Hypermetropia, convex
c. Presbypoia, bifocal
D. Astigmastism, cylindrical


The law that gives a qualitative definition of force is :
A. Newton's second law of motion
B. Law of inertia
c. Newton's third law of motion
D. Law of gravitation


A well stoppered thermos flask containing some ice cubes is an example of a/an:
A. closed system
B. open systemmmmmmm
c. isolated system
D. none of these


Gauri want to the stationers and bought things worth Rs 25 out of which 30
paise went on sale tax on taxable purchases If the tax rate was \( 6 \% \) then what was the cost of the tax free item?
\( \mathbf{A} \cdot \) Rs 15
B. Rs 15.70
c. Rs 19.70
D. Rs 20


Assertion
Aqueous solution of the compound
\( \mathrm{CoCl}_{3} \cdot 4 N \mathrm{H}_{3} \) when treated with excess
of \( A g N O_{3}, 1 \) mole of \( A g C l \) is
precipitated.
Reason
The compound \( C o C l_{3} .4 N H_{3} \) has six
primary valencies and one secondary valency.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If the error in measurements of mass
and velocity is \( 1 \% \) each then error in measurement of kinetic energy is:


The rating of a zener diode is \( 1 W, 15 V \) Find the zener maximum current.
\( \mathbf{A} \cdot 66.7 A \)
в. \( 1 A \)
\( c .15 A \)
D. \( 66.7 m A \)


Assertion
Phylogeny is the developmental history
of a species.
Reason
Species is the basic unit of taxonomy.
A. Both Assertion and Reason are true and the Reason is a correct explanation of the assertion
B. Both Assertion and Reason are true but the Reason is
not a correct explanation of the Assertion.
C. Assertion is true but the Reason is false.
D. Both the Assertion and Reason are false.


Which of the following statements are true (T) and which are false (F)?
In a parallelogram, the diagonals are equal.
A. True
B. False


For a particle moving along \( x \) -axis,
acceleration is given as \( a=v \). Find the
position as a function of time? Given that \( \operatorname{at} t=0, x=0, v=1 \)
A \( \cdot e-1 \)
B \( \cdot e^{2}-1 \)
c. \( \frac{e}{2} \)
D. \( e+1 \)


Function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}}{\mathbf{1}+|\boldsymbol{x}|} \) is
A. increasing function
B. decreasing function
C. neither increasing nor decreasing
D. not differentiable at \( x=0 \)


On ozonolysis, ethylene gives:
A. aldehyde
B. ketone
c. carboxylic acid
D. ether


The graph of \( x^{2}-4 x+y^{2}+6 y=0 \) in
the xy-plane is a circle. What is the
radius of the circle?


Crystallisation is an example of
A. physical change
B. biological change
c. chemical change
D. fundamental change


Rag pickers remove reusable or recyclable articles.
A . True
B. False
c. Either
D. Neither


What is the total number of valence
electrons in the peroxydisulphate, \( S_{2} O_{8}^{2-}, \) ion \( ? \)
A . 58
B. 60
\( c \cdot 62 \)
D. 64


A fair coin is tossed four times and a
person win Re 1 for each head and lose
Rs. 1.50 for each tail that turns up. Let \( p \) be the probability of person losing Rs 3.50 after 4 tosses.Find \( 4 p ? \)


Which of the following species is linear?
\( \mathbf{A} \cdot X e F_{4} \)
B . \( I_{3}^{-} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C l O_{2}^{-} \)


Why are transmission losses so crucial
that electrical power systems are
designed to work on Alternating
currents?
A. Electrical power systems are not very efficient for transmission of power
B. It is a practice to use AC over DC
C. AC networks are easier to handle than DC Networks and constructional setup cost is really high in DC
D. since, power stations are very far away from destinations, transmission has to be done over long distances and losses add up over the distance


Assertion
In dialyzer, the plasma proteins of the blood cannot be filtered, but molecules
like urea, uric acid, creatinine and ions
can be filtered.
Reason
The cellophane membrane, used in the dialyzer is permeable to micromolecules, but impermeable to macromolecules.
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


An equlimolar quantities of ethanol and
propanol are heated with conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
The products formed is/ are :
A. \( C_{2} H_{5} O C_{2} H_{5} \)
в. \( C_{3} H_{7} O C_{3} H_{7} \)
c. \( C_{2} H_{5} O C_{3} H_{7} \)
D. all of these


During the vinyl polymerisation, the chain transfer agent is:
A. \( C C l_{4} \)
в. \( C_{6} H_{5} O H \)
c. t-butyl peroxide
D. diphenylamine


Which of the following statements is
incorrect?
\( \mathbf{A} \cdot \operatorname{In} K_{3}\left[F e(C N)_{6}\right], \) the ligand has satisfied only the secondary valency of ferric ion
B. \( \ln K_{3}\left[F e(C N)_{6}\right] \), the ligand has satisfied both primary and secondary valencies of ferric ion
C \( \cdot \ln K_{4}\left[F e(C N)_{6}\right] \) the ligand has satisfied both primary and secondary valencies of ferrous ion
D. \( \ln \left[C u\left(N H_{3}\right)_{4}\right] S O_{4} \) the ligand has satisfied only the secondary valency of copper


For how long should a force of \( 100 N \) act
on a body of \( 20 k g \) so that is acquires a
velocity of \( 100 m s^{-1} \)


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) for the following
i) \( y=\tan ^{-1}\left(\frac{3 x-x^{3}}{1-3 x^{2}}\right),-\frac{1}{\sqrt{3}}<x< \)
\( \frac{1}{\sqrt{3}} \)
ii) \( y=\sin ^{-1}\left(\frac{1-x}{1+x}\right), 0<x<1 \)


The two compounds shown above are:
A. different but not isomeriç
B. constitutional isomers
c. enantiomers
D. identical


Which is the correct sequence in the following properties? For the correct order mark(T) and for the incorrect
order mark (F):
(a) Lewis acidity order: \( \boldsymbol{S} \boldsymbol{i} \boldsymbol{F}_{4}< \)
\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4}<\boldsymbol{S} \boldsymbol{i} \boldsymbol{B} \boldsymbol{r}_{4}<\boldsymbol{S} \boldsymbol{i} \boldsymbol{I}_{4} \)
(b) Melting point: \( N H_{3}>S b H_{3}> \)
\( \boldsymbol{A} \boldsymbol{s} \boldsymbol{H}_{3}>\boldsymbol{P} \boldsymbol{H}_{3} \)
(c) Boiling point \( : N H_{3}>S b H_{3}> \)
\( \boldsymbol{A} \boldsymbol{s} \boldsymbol{H}_{3}>\boldsymbol{P} \boldsymbol{H}_{3} \)
(d) Dipole moment order : \( N H_{3}> \)
\( \boldsymbol{S b H}_{3}>\boldsymbol{A s H}_{3}>\boldsymbol{P H}_{3} \)
A. FTFT
в. TFTF
c. FFTT
D. FFTF


Simplify \( \sqrt{2+\sqrt{2+2 \cos \left(\pi+60^{0}\right)}} \)


At Absolute Zero Temperature,:
A. Molecular Energy is Zero
B. Molecular Energy is maximum
C. Molecular Energy is minimum
D. None of these


An allotropic form of carbon used for cutting and drilling is which of the following?
A. charcoal
B. bone charcoal
c. graphite
D. diamond


ACTH controls the secretion of :
A. epinephrine
B. cortisol
c. testosterone
D. aldosterone


Suppose \( f(x) \) is a function satisfying the following conditions.
\( (a) f(0)=2, f(1)=1 \)
(b) \( f(x) \) has a maximum at \( x=5 / 2, \) and
(c) for all \( x \in R \)
\( \boldsymbol{f}^{\prime}(\boldsymbol{x})= \)
\( \mid \begin{array}{ccc}2 a x & 2 a x-1 & 2 a x+b+ \\ b & b+1 & -1 \\ 2(a x+b) & 2 a x+2 b+1 & 2 a x+b\end{array} \)
where \( a, b \) are constants, then


State whether the statement is true or
false

Carbon tetrachloride burns in the air
when lighted to give phosgene.
A. The statement is true
B. The statement is false
c. Neither
D. Carbon tetrachloride rarely burns in the air when lighted to give phosgene


Assertion - the basic pf Laplace correction was that, exchange of heat between the region of compression and rarefraction in air is not possible. reason - Air is a bad conductor of heat
and velocity of sound in air is large.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the inverse of the following matrice by elementary transformation:
\( \left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5\end{array}\right] \)


The co-ordinates of the vertices of
ロPQRS are
\( P(-1,2), Q(-4,-2), R(-4,-3) \) and
\( \boldsymbol{S}(-1,-\mathbf{5}) \) respectively. Draw \( \square \boldsymbol{P} Q \boldsymbol{R} \boldsymbol{S} \)
and state it is which type of
quadrilateral.


Which of the following is able to form ionic compounds?
A. \( N \)
в. \( A s \)
\( c . B i \)
D. \( P \)


Plot of \( \log \left(\frac{x}{m}\right) \) against \( \log P \) is a
straight line inclined at an angle of \( 45^{\circ} \)
When the pressure is 0.5 atm and
Freundlich parameter, \( k \) is \( 10, \) the
amount of solute adsorbed per gram of adsorbent will be:
\( [\log 5=0.6990] \)
A . \( 1 g \)
B. \( 2 g \)
\( c .3 g \)
D. \( 5 g \)


At the initial moment three points \( A, B \) and \( \mathrm{C} \) are on a horizontal straight line at equal distances from one another. Point A beings to move vertically upward with a constant velocity v and point \( C \) vertically downward without any initial velocity but with a constant acceleration a. How should point B move
vertically for all the three points to be constantly on one straight line. The points begin to move simultaneously.
A . B moves up with initial velocity \( \frac{v}{2} \) and downward
acceleration \( -\frac{a}{2} \)
B . B moves down with initial velocity \( \frac{v}{2} \) and downward acceleration \( -\frac{a}{2} \frac{a}{2} \)
C . B moves up with initial velocity \( \frac{v}{2} \) and upward
acceleration \( -\frac{a}{2} \)
D. B moves down with initial velocity \( \frac{v}{2} \) and upward
acceleration \( -\frac{a}{2} \)


State the type of Bonding in the following molecules:
Water.


A particle carrying a charge equal to 100 times the charge on an electron is
rotating one rotation per second in a circular path of radius \( 0.8 \mathrm{m} \). The value of the magnetic field produced at the centre will be:
\( \left(\mu_{0}=\text { permeability for vacuum }\right) \)
\( ^{A} \cdot \frac{10^{-7}}{\mu_{0}} \)
B . \( 10^{-17} \mu_{0} \)
\( \mathbf{c} \cdot 10^{-6} \mu_{0} \)
D. \( 10^{-7} \mu_{0} \)


Identify from the reaction the reactants that undergo oxidation and reduction \( F e+S \rightarrow F e S \)


In contrast to Annelids the
Platyhelminths show
A. Absence of body cavity
B. Presence of pseudocoel
c. Radial symmetry
D. Bilateral symmetry


\( \frac{\sqrt{6}}{\frac{4}{5}} \)


A unit vector parallel to the intersection of the planes \( \vec{r} \cdot(\hat{i}-\hat{j}+\hat{k})=5 \) and \( \vec{r} \)
\( (2 \hat{i}+\hat{j}-3 \hat{k})=4 \) can be
This question has multiple correct options
\( \frac{2 \hat{i}+5 \hat{j}+3 \hat{k}}{\sqrt{38}} \)
B. \( \frac{2 \hat{i}-5 \hat{j}+3 \hat{k}}{\sqrt{38}} \)
c. \( \frac{-2 \hat{i}-5 \hat{j}-3 \hat{k}}{\sqrt{38}} \)
D. \( \frac{-2 \hat{i}+5 \hat{j}-3 \hat{k}}{\sqrt{38}} \)


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


Consider the following statements A and \( \mathrm{B} \) and identify the correct answer
A: Thermistors can have only -ve temperature coefficient of resistors.
B : Thermistors with -ve temperature coefficients of resistance are used as
resistance thermometers to measure
low temperature of the order of \( 10 \mathrm{K} \)
A. 1 both \( A \) and \( B \) are true
B. 2) both A and B are false
c. 3 ) A is true and \( B \) is false
D. 4 ) A is false, but \( B \) is true


In a reaction, the concentration of a
reactant
\( (A) \) changes from 0.200 mol
litre \( ^{-1} \) to 0.150 mol litre \( ^{-1} \) in 10
minutes. What is the average rate of reaction during this interval?


When \( F e S O_{4} \) is added in the sodium
extract the compound formed is?
A . only \( N a_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \)
B. only \( \mathrm{Fe}(\mathrm{OH})_{2} \)
c. only \( N a_{2} S O_{4} \)
D. Mixture of these three


In how many ways can \( n \) things be given
to \( \boldsymbol{p} \) persons, when there is no
restriction as to the number of things
each may receive?


Differentiate
\( 2 x^{3 / 2}+2 x^{5 / 2}+C \)
A \( \cdot \frac{d y}{d x}=\sqrt{x}(3+5 x) \)
B. \( \frac{d y}{d x}=\sqrt{x}(3-5 x) \)
c. \( \frac{d y}{d x}=-\sqrt{x}(3+5 x) \)
D. None of these


For \( M^{2+} / M \) and \( M^{3+} / M^{2+} \) systems the \( E^{\ominus} \) values for some metals are as follows:
\( C r^{3} / C r^{2+} \)
\( \boldsymbol{C r}^{2+} / \boldsymbol{C r} \quad_{\boldsymbol{\$}}^{-\boldsymbol{0 . 9} \boldsymbol{V}} \)
\( / M n \quad-1.2 V \) \( M n^{3+} \) \( M n^{2+} \) \( / M n^{2+} \)
\( -0.4 V \)
\( F e^{3+} / F e^{2+} \)
Use this data to comment upon:
(i) the stability of \( F e^{3+} \) in acid solution
as compared to that of \( C r^{3+} \) or \( M n^{3+} \)
and
(ii) the ease with which iron can be
oxidised as compared to a similar process for either chromium or
manganese metal


Which is not correct relationship
between \( \Delta G^{\ominus} \) and equilibrium
constant \( \boldsymbol{K}_{\boldsymbol{P}} \)
This question has multiple correct options
\( \mathbf{A} \cdot K_{P}=-R T \log \Delta G^{\ominus} \)
В \( . K_{P}=[e / R T]^{\Delta G^{\ominus}} \)
\( \mathbf{C} \cdot K_{P}=-\frac{\Delta G^{\circ}}{R T} \)
\( \mathbf{D} \cdot K_{P}=e^{-\Delta G^{\ominus} / R T} \)


Evaluate \( \int_{0}^{2}\left(3 x^{2}-2\right) d x \)


A person walks up a stationary
escalation in \( t_{1} \) second. If he remains
stationary on the escalator, then it can
take him up in \( t_{2} \) second. If the length of
the escalator is \( L \), then
a. Determine the speed of man with
respect to the escalator.
b. Determine the speed of the escalator.
c. How much time would it take him to
walk up the moving escalator?


In some observations, value of 'g' are
coming as 9.81,9.80,9.82,9.79,9.78
9.84,9.79,9.78,9.79 and \( 9.80 m / s^{2} \)
Calculate absolute errors and
percentage error in \( \mathfrak{g} \)
A \( \cdot \quad \) 'g' \( =(9.80 \pm 0.014) \mathrm{m} / \mathrm{s}^{2} \)
B. 'g'= (9.8 ±0.14 ) \( m / s^{2} \)
c. \( \operatorname{tg}^{\prime}=(9.8 \pm 0.0014) m / s^{2} \)
D. 'g'= (9.8000 \( \pm 0.00014) \mathrm{m} / \mathrm{s}^{2} \)


Based on the given figure, which of the
following statements is true?
A. \( \angle 5 \) and \( \angle 7 \) are supplementary angles.
B \( . \angle 7=55^{\circ} \)
C. \( \angle 8 \) and \( \angle 1 \) are corresponding angles.
D. \( \angle 4 \) and \( \angle 5 \) are alternate angles.


Write an essay on different events that
occur during development of human


Keystone species should be protected
as they
A. Are capable of certain minerals in the soil.
B. Indicate presence of certain minerals in the soil.
C. Have become rare due to over-exploitation.
D. Play an important role in supporting other species.


Check if \( \left(\frac{1}{2}, 2\right) \) is a solution of \( 2 x-5 y= \)
10


Identify the major product \( X \) obtained in
the following reaction.
\( \mathbf{2}, \mathbf{3}- \) dimethyl butan \( -\mathbf{2}- \)
\( \boldsymbol{o l} \stackrel{\boldsymbol{C o n c . H}_{2} \boldsymbol{S O}_{4}}{\longrightarrow} \boldsymbol{X} \)
\( \mathbf{A} \)
B.
\( c \)
D.


If a fair die is rolled 4 times, then what is
the probability that there are at least 2
sixes?
A \( \cdot \frac{19}{144} \)
в. \( \frac{25}{216} \)
c. \( \frac{125}{216} \)
D. \( \frac{175}{216} \)


Differentiate between nucleoside and
nucleotide.


The teacher distributes 6 pencils per student. Can you find how many pencils are needed for the given number of
students(use ' \( z^{\prime} \) for the number of
students).


If the molar conductivities (in \( \mathrm{S} \mathrm{cm}^{2} \)
\( \mathrm{mol}^{-1} \) ) of \( \mathrm{NaCl} \), \( \mathrm{KCl} \) and \( \mathrm{NaOH} \) at infinite
dilution are 126,150 and 250
respectively, the molar conductivity of KOH is:
\( \left[\operatorname{in} \mathrm{S} \mathrm{cm}^{2} \mathrm{mol}^{-1}\right] \)
A .526
в. 226
c. 26
D. 274


Explain the followings:
Chord


Choose the correct statement:
A. The wave velocity is less than phase velocity of the wave
B. The particle velocity is the same as phase velocity of the wave
C. The particle velocity is the same as group velocity of the wave
D. The wave velocity is the same as group velocity of the wave


Write the first term \( a \) and the common
difference \( d \) of the \( A P:-5,-1,3,7 \dots . . . \)
A \( . a=-5, d=4 \)
В. \( a=-5, d=-6 \)
c. \( a=-5, d=-4 \)
D. \( a=5, d=-4 \)
4


Determine the \( p H \) of a \( 0.05 M \) aqueous
solution of ammonium sulphate, \( k_{b} \) of
ammonia is \( 2 \times 10^{-5} ? \)
A . 4.30
B. 5.15
\( c .7 .0 \)
D. 8.75


The value of \( \lim _{x \rightarrow 3^{+}} \frac{|x-3|}{x-3} \) equals
A . 1
B. - 1
\( c .0 \)
D. Does not exist


A potential barrier of \( 0.3 \mathrm{V} \) exists across
a p-njunction. An electron with speed
\( 5 \times 10^{5} m / s e c \) approaches this p-n
junction from n-side, what will be its speed on entering the p-side?
A \( .4 .8 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
В. \( 3.8 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
c. \( 5.8 \times 10^{5} \mathrm{m} / \mathrm{sec} \)
D. \( 6.8 \times 10^{5} \mathrm{m} / \mathrm{sec} \)


ChoosChoose the correct answers from
the alternatives given A fern differs from a moss in having:
A. ciliated antherozoids
B. an independent sporophyte
c. a dependent gametophyte
D. heteromorphic alternation of generations


A and B are mutually exclusive events,
then
\( \mathbf{A} \cdot P(A) \leq P(\bar{B}) \)
B \( . P(\mathrm{A})>P(\bar{B}) \)
\( \mathbf{c} \cdot \mathrm{P}(\mathrm{A})<\mathrm{P}(\mathrm{B}) \)
D. \( P(A)=P(B) \)


There are two \( \pi \) -bonds in a nitrogen molecules.
If true enter 1 , else enter 0 .


For a \( 2 \times 2 \) matrix \( A=\left[a_{i j}\right], \) whose element is \( a_{i j}=\frac{i}{j}, \) find the value of \( a_{12} \)


If \( A \) is the coefficient of the middle term
in the expansion of \( (1+x)^{2 n} \) and \( B \) and
\( \mathrm{C} \) are the coefficients of two middle
terms in the expansion of \( (1+x)^{2 n-1} \)
then
A. \( A+B=C \)
в. \( B+C=A \)
c. \( C+A=B \)
D. \( A+B+C=0 \)


What does \( \left|\frac{\boldsymbol{d} \vec{v}}{\boldsymbol{d t}}\right| \) and \( \frac{\boldsymbol{d}|\overrightarrow{\boldsymbol{v}}|}{\boldsymbol{d} t} \) represent?


In which subject he scored minimum
marks?
A . Hindi
B. English
C. Science
D. Social studies


Which of the following is true/false regarding transport of substances in plants?
(i) Mass flow is the movement of
substance in bulk as a result of
pressure difference.
(ii) Bulk flow is achieved only through a positive hydrostatic pressure gradient.
(iii) The apoplast system is the system of interconnected protoplasts.
(iv) Most of the water flow in the roots
occurs via the apoplast since the cortical cells are loosely packed, and offer no resistance to water movement.
A . (i) and (iv) are true; (ii) and (iii) are false
B. (i) and (ii) are true; (iii) and (iv) are false
\( c . \) (ii) and
(iii) are true; (i) and (iv) are false
D. (i), (ii) and (iv) are true; (iii) is false


The half-life of carbon-14 \( \left(^{14} C\right) \) is 5715
yr. What is its decay constant?


The \( 2^{n d}, 31^{s t}, \) and last terms of an A.P. \( \operatorname{are} 7 \frac{3}{4}, \frac{1}{2} \) and \( -6 \frac{1}{2} \) respectively; find
the first term and the number of terms.


According to corpuscular theory, the velocity of light in the denser medium is
greater than that in rarer medium.
A. True
B. False


The absolute temperature of a body \( A \) is
four times that of another body \( B \). For two bodies, the difference in wave
lengths at which energy radiated is maximum is \( 3.0 \mu \) m. Then
the wavelength at which the body \( B \) radiates maximum energy in micrometre is :
A .2
B . 2.
c. 4.0
D. 4.5


Evaluate :
\( \frac{\mathbf{5 0 x y z}(\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{y}+\boldsymbol{z})(\boldsymbol{z}+\boldsymbol{x})}{\mathbf{1 0 0 x y}(\boldsymbol{x}+\boldsymbol{y})(\boldsymbol{y}+\boldsymbol{z})} \)
A \( \cdot \frac{1}{2} \)
В. \( \frac{z(z+x)}{2} \)
c. \( \frac{z+x}{2} \)
D \( \cdot z(z+x) \)


A current-carrying wire in a magnetic field is subject to a magnetic force. If the current in the wire is doubled, what
happens to the magnetic force acting on the wire?
A. It is quartered
B. It is halved
c. It is unchange
D. It is doubled
E. It is quadrupled


In the following elements identify the element that is relatively strong?
A. Hydrogen
B. Oxygen
c. Manganese
D. Chlorine


Ethanoic acid is a member of
homologous series with general
formula \( C_{n} H_{2 n+1} C O O H \)
i) Name the series and give its
functional group.
ii) Give the molecular formula and the
common name of ethanoic acid.
iii) If this compound is mixed with
ethanol in the presence of Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) a sweet smelling compound is formed. Give the equation and name the compound.
iv) Ethanoic acid reacts with
carbonates. Which gas is liberated
during this reaction?
v) Write the balanced equation for the
reaction of ethanoic acid with
carbonate.
vi) Your grandmother has prepared mango pickle. What has she added to preserve it for a long time?


Derive expression for the self
inductance of a solenoid. What factors
affect it?


The reaction \( \boldsymbol{C}_{\mathbf{6}} \boldsymbol{H}_{\mathbf{5}} \boldsymbol{I}+\mathbf{2} \boldsymbol{N} \boldsymbol{a}+ \)
\( \boldsymbol{C H}_{3} \boldsymbol{I} \rightarrow \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C H}_{3}+\mathbf{2} \boldsymbol{N} \boldsymbol{a} \boldsymbol{I} \) is called:
A. Wurtz reaction
B. Fittig reaction
c. Wurtz - Fittig reaction
D. Sandmeyer reaction


Which rule is violated in the electronic
configuration \( 1 s^{0} 2 s^{2} 2 p^{4} ? \)


How are electric vector \( (\boldsymbol{E}), \) magnetic vector \( (\vec{B}) \) velocity vector
(c) oriented in an electromagnetic wave?


Plot the following points and check whether they are collinear or not
(2,3),(3,2),(1,-5)


A non conducting sphere of radius R is filled with uniform volume charge
density - \( \rho . \) The center of this sphere is displaced from the origin by \( \vec{d} \). The electric field \( \vec{E} \) at any point \( P \) having position vector inside the sphere is :
\( A \)
B \( \cdot \frac{\rho}{3 \varepsilon_{0}}(\vec{r}-\vec{d}) \)
c. \( \frac{\rho}{3 \varepsilon_{0}}(\vec{d}-\vec{r}) \)
D. \( \frac{\rho}{3 \varepsilon_{0}}(\vec{r}) \)


How may times total internal reflection
occurs in the drop for formation of primary and secondary rainbows?


If the elevation in boiling point of a solution of 10 g of solute (mol.wt. \( =100 \) ) in 100 g of water is \( \triangle \boldsymbol{T}_{\boldsymbol{b}}, \) the ebullioscopic constant of water is :
A . 10
в. \( 100 T_{b} \)
c. \( \triangle T_{b} \)
D. \( \frac{\Delta T_{b}}{10} \)


The inheritance of sex chromosomes in
human can be described by the fact that:
A. The gametes from each parent have either an \( x \) or a \( Y \) chromosome.
B. The gamete from the mother has either an \( x \) or \( Y \) chromosomes
c. The gamete from the father has either an \( x \) or a chromosome.
D. The gamete from the father only has an \( x \) chromosome.
E. The gamete from the mother has only a \( Y \) chromosome