Non-metals do not show ductility due to
absence of:
A. metallic bonds which allow one electron to slip over another
B. covalent bonds which gives strength
C. ionic bonds which gives makes it hard
D. co-ordinate bonds which which gives extra stability


Assertion: The motion of the earth
around the sun is periodic but not
oscillatory. Reason : Oscillatory motion is necessarily periodic but periodic motion is not necessarily oscillatory.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false


The following diagram in figure shows a
fixed coil of several turns connected to a
centre zero galvanometer \( G \) and \( a \)
magnet NS which can move in the
direction shown in the
diagram. Describe the observation in
the galvanometer if the magnet is moved rapidly towards the coil.


Which of the following seeds develops a greater imbibition pressure?
A. Wheat seed
B. Gram seed
c. Rice seed
D. Mustard oil seed


Which of the following reactions defines
\( \Delta H_{f}^{o} ? \)
A. \( C_{\text {diamond}}+O_{2}(g) \rightarrow C O_{2}(g) \)
B \( \cdot \frac{1}{2} H_{2}(g)+\frac{1}{2} F_{2}(g) \rightarrow H F(g) \)
C. \( N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
\( ^{\mathrm{D}} \cdot_{C O(g)}+\frac{1}{2} O_{2}(g) \rightarrow C O_{2}(g) \)


A spool of mass \( M \) and radius \( 2 R \) lies on an inclined plane as shown in figure. A light thread is wound around the connecting tube of the spool and its free
end carries a weight of mass \( m \). The
value of \( m \) so that system is in equilibrium is
\( A \cdot 2 M \sin \alpha \)
B. \( M \sin \alpha \)
\( c .2 M \tan \alpha \)
D. \( M \tan \alpha \)


Assertion
When ideal gas expand from \( \boldsymbol{P}_{1}, \boldsymbol{V}_{1}, \boldsymbol{T}_{1} \)
to \( P_{2}, V_{2}, T_{2} \) in two steps, and work done
is high in
which number of steps are high
Reason
Work is path function
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 angle of inclination(in degrees) of the line passing through the points (1,2) and (2,3)


Calculate mole fraction of solute if
molarity of solution is \( 20 \%\left(\frac{W \%}{W}\right) \) aqueous solution of NaOH.
A. 0.2
B. 0.15
c. \( 0 . \)
D. none of these


Evaluate \( \lim _{x \rightarrow 3}\left(\frac{x^{4}-81}{2 x^{2}-5 x-3}\right) \)


Hydrogen \( \left(_{1}^{1} \boldsymbol{H}\right), \) deuterium \( \left(_{1}^{2} \boldsymbol{H}\right), \) singly
ionised helium \( \left(_{2}^{4} H e^{+}\right) \) and doubly
ionised lithium \( \left(_{3}^{6} L i^{2+}\right) \) all have one electron around the nucleus. Consider
an electron transition from \( n=2 \) to
\( \boldsymbol{n}=1 . \) If the wavelength of emitted
radiation are \( \lambda_{1}, \lambda_{2}, \lambda_{3} \) and \( \lambda_{4} \)
respectively. Then approximately which one of the following is correct?
A \( \cdot \lambda_{1}=\lambda_{2}=4 \lambda_{3}=9 \lambda_{4} \)
B . \( \lambda_{1}=2 \lambda_{2}=3 \lambda_{3}=4 \lambda_{4} \)
C \( \cdot 4 \lambda_{1}=2 \lambda_{2}=2 \lambda_{3}=\lambda_{4} \)
D. \( \lambda_{1}=2 \lambda_{2}=2 \lambda_{3}=\lambda_{4} \)


Which functional group is present in a
molecule of \( C H_{3} \) COOH ?
\( A \). Ether
B. Aldehyde
c. carboxyl
D. Ester
E. Amine


A straw is placed on the corner of a
table of length 3cm3cm.


The heat rejected by the gas in the path
CA and heat absorbed in the path \( A B \)


Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) reacts with carbon and
forms:
This question has multiple correct options
A \( \cdot C O_{2} \)
в. \( S O_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{CO}_{3} \)
D. \( H_{2} S O_{3} \)


Voltage across each elements of a
series LCR circuit are given by \( V_{L}= \)
\( \mathbf{6 0} \boldsymbol{V}, \boldsymbol{V}_{\boldsymbol{C}}=\mathbf{2 0} \boldsymbol{V}, \boldsymbol{V}_{\boldsymbol{R}}=\mathbf{3 0} \boldsymbol{V} \) Find out
source voltage
A . \( 50 v \)
B. 100v
\( c \cdot 150 v \)
D. 200v


Myrosin in plant parts is characteristic
of
A. Cruciferae
B. Malvaceae
c. Solanaceae
D. Lilaceae


State clearly how an unpolarised light gets linearly polarised when passed through a polaroid.
(i) Unpolarised light of intensity \( I_{0} \) is
incident on a polaroid \( P_{1} \) which is kept
near another polaroid \( P_{2} \) whose pass
axis is parallel to that of \( \boldsymbol{P}_{1} \). How will the
intensities of light, \( \boldsymbol{I}_{1} \) and \( \boldsymbol{I}_{2} \)
transmitted by the polaroids \( P_{1} \) and \( P_{2} \)
respectively, change on rotating \( \boldsymbol{P}_{1} \)
without disturbing \( P_{2} ? \)
(ii) Write the relation between the
intensities \( I_{2} \) and \( I_{1} \)


Arrange the following in the increasing order of their reactivity towards nucleophilic addition reaction:
\[
\mathrm{cH}_{3} \mathrm{CocH}_{3}, \mathrm{HCHO}, \mathrm{cH}_{3} \mathrm{CHO},\langle/ \sqrt{ }\rangle-\mathrm{cocH}_{3}
\]


The elements of one period are given below in order from left to right
\( \boldsymbol{L} \boldsymbol{i}, \boldsymbol{B} \boldsymbol{e}, \boldsymbol{B}, \boldsymbol{C}, \boldsymbol{O}, \boldsymbol{F}, \boldsymbol{N} \boldsymbol{e} \)
Which one of the above elements
belongs to the halogen series?
\( \mathbf{A} \cdot L i \)
B. \( O \)
\( c . F \)
D. Ne


The diagram below shows the set up for
the laboratory preparation of a pungent alkaline gas.
The balanced equation for the above
preparation is :
A \( \cdot 2 C a O+2 N H_{4} C l \rightarrow 2 C a C l_{2}+H_{2} O+2 N H_{3} \)
в. \( C a O+N H_{4} C l \rightarrow C a C l_{2}+H_{2} O+N H \)
\( \mathrm{c} \cdot \mathrm{CaO}+2 \mathrm{NH}_{4} \mathrm{Cl} \rightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O}+2 \mathrm{NH} \)
D. 2 CaO \( +N H_{4} C l \rightarrow 2 C a C l_{2}+H_{2} O+2 N H \)


Consider an equiconvex lens of radius
of curvature \( \boldsymbol{R} \) and focal length \( \boldsymbol{f} \). If \( \boldsymbol{f}> \)
\( R, \) the refractive index \( \mu \) of the material
of the lens.
A. Is greater than zero but less than 1.5
B. Is greater than 1.5 but less than 2.0
c. Is greater than 1.0 but less than 1.5
D. None of these


A man \( 1.8 \mathrm{m} \) tall wishes to see full-
length image in a plane mirror. The length of the shortest mirror in which he
can see his entire image is:
(Assume that the mirror is hanged vertically on a wall in front of the man).
A. \( 0.6 m \)
в. \( 0.9 m \)
\( c .1 .2 m \)
D. \( 1.5 \mathrm{m} \)


In the given Wedge-Dash Notation as
shown, how many atoms/groups (other than \( H \text { atoms }) \) are above the plane of the paper?
4. one
3. Two
c. Three
Pour


State the kind of charge on a negative ion:
A. positive
B. negative
c. zero
D. cant say


Four particles, each having charge \( \boldsymbol{q} \)
are placed at four verticals of a regular
pentagon. The distance of each corner
from the center is \( a \). The electric field at
the center \( O \) of the pentagon is:
A \( \cdot \frac{q}{4 \pi \epsilon_{0} a^{4}} \) along \( E O \)
B. \( \frac{q}{2 \pi \epsilon_{0} a^{2}} \) along \( E O \)
c. \( \frac{q}{\pi \epsilon_{0} a^{2}} \) along \( E O \)
D. \( \frac{q}{4 \pi \epsilon_{0} a^{2}} \) along \( E O \)


Find the order of the following matrices.
(i) \( \left.\begin{array}{ccc}1 & -1 & 5 \\ -2 & 3 & 4\end{array}\right) \)
(ii)
(iii) \( \begin{array}{rl}3 & -26 \\ 6 & -11 \\ 2 & 4\end{array} \)
(iv) (345)
\( (v)\left[\begin{array}{cc}1 & 2 \\ -2 & 3 \\ 9 & 7 \\ 6 & 4\end{array}\right] \)


If the diameter of the base and height of a cylinder are \( 6 \mathrm{cm} \) and \( 14 \mathrm{cm} \) respectively. Then find its volume.


Give balanced chemical equations for the following conversations: Ethanoic acid to ethly ethanoate.


In public urinals, the urine on standing
gives a pungent smell due to
A. Conversion of both urea and uric acid into ammonia
B. Conversion of uric acid into ammonia by ornithine cycle
c. conversion of urea into ammonia by bacteria
D. None of the above


The length of the common chord of two intersecting circles is \( 30 \mathrm{cm} \). If the radii
of the two circles are \( 25 \mathrm{cm} \) and \( 17 \mathrm{cm} \)
find the distance (in cm) between their
centres.


Noble gases do not react because they have electrons in their
valence shell.
\( A \cdot 3 \)
B. 6
\( c \)
D. 8


If non parallel sides of a trapezium are equal, prove that it is cyclic.


Which one of the following will remain unchanged when a sound wave travels in air or in water?
A. Amplitude
B. Frequency
c. wavelength
D. speedd


topp
\( \mathrm{ClCH}_{2} \mathrm{CH}^{14} \mathrm{C} \mathrm{H}_{2} \mathrm{OC}_{2} \mathrm{H}_{5} \)
14
\( \mathrm{ClCH}_{2} \mathrm{CHCH}_{2} \mathrm{ONa} \)
\( \mathrm{OC}_{2} \mathrm{H}_{5} \)
\( \underbrace{14}_{\mathrm{CH}_{2}-\mathrm{CHCH}_{2} \mathrm{OC}_{2} \mathrm{H}_{5}} \)
\( \mathrm{C}_{\mathrm{O}}^{\mathrm{H}_{2}-} \mathrm{CHCH}_{2} \mathrm{OC}_{2} \mathrm{H}_{5} \)


For a thermodynamics process to be reversible, the temperature difference between hot body and the working substance should be
A . zero
B. minimunm
c. maximum
D. infinity


A rod AB moves with a uniform velocity
\( v \) in a uniform magnetic field as shown in figure.
\( \begin{array}{llllll}\mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{A} & \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{n} & \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{n} & \mathbf{X} & \mathbf{X} & \mathbf{X} \\ \mathbf{X} & \mathbf{X} & \mathbf{X} & \mathbf{B} & \mathbf{X} & \mathbf{X} & \mathbf{X}\end{array} \)
A. The rod becomes electrically charged
B. The end A becomes positively charged
c. The end B become positively charged


Given below are the half-cell reactions:
\( M n^{2+}+2 e^{-} \rightarrow M n ; E^{o}=-1.18 V \)
\( \mathbf{2}\left(\boldsymbol{M} \boldsymbol{n}^{3+}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{M} \boldsymbol{n}^{2+}\right) ; \boldsymbol{E}^{o}= \)
\( +1.51 V \)
The \( \boldsymbol{E}^{o} \) for \( \boldsymbol{3} \boldsymbol{M} \boldsymbol{n}^{2+} \rightarrow \boldsymbol{M} \boldsymbol{n}+\boldsymbol{2} \boldsymbol{M} \boldsymbol{n}^{3+} \)
will be:
A. \( -0.33 V ; \) the reaction will not occur
B. \( -0.33 V ; \) the reaction will occur
c. \( -2.69 V \); the reaction will not occur
D. \( -2.69 V \); the reaction will occur


To dissolve argentite ore which of the following is used?
A \( \cdot \operatorname{Na}\left[\operatorname{Ag}(C N)_{2}\right] \)
в. \( N a C N \)
c. \( N a C l \)
D. HCl


Elements having atomic number higher
than \( ^{\prime} \mathbf{9} 2^{\prime} \) in the periodic table are
known as:
A. transuranic elements
B. rare earth elements
c. transitional elements
D. alkaline earth metals


A magnet is dropped free towards a loop of copper wire as shown in figure.
The acceleration of magnet will be :
A. Equal to g
B. Greater than \( g \)
c. Less than g
D. zero


The value of gravitational constant \( \boldsymbol{G} \) in Meter-Kilogram-Second system is \( 6.67 \times 10^{-11} N-m^{2} k g^{-2} . \) What will be
its value in centimetre gram
second system.
A. \( 6.67 \times 10^{-5} \)
В. \( 6.67 \times 10^{-9} \)
\( \mathbf{c} \cdot 6.67 \times 10^{-8} \)
D. \( 6.67 \times 10^{-13} \)


A box contain \( N \) coins, \( m \) of which are
fair and rest are biased. The probability of getting a head when a fair coin is tossed is \( \frac{1}{2}, \) while it is \( \frac{2}{3} . \) when a biased coin is tossed. A coin is drawn from the
box at random and is tossed twice. The
first time it shows head and the second
time it shows tail. The probability that the coin drawn is fair is
A \( \cdot \frac{8 \mathrm{m}}{8 \mathrm{N}+\mathrm{m}} \)
B. \( \frac{\mathrm{m}}{8 \mathrm{N}+\mathrm{m}} \)
c. \( \frac{9 \mathrm{m}}{8 \mathrm{N}+\mathrm{m}} \)
D. \( \frac{9 \mathrm{N}}{8 \mathrm{N}+\mathrm{m}} \)


10 g of ice at \( -20^{\circ} C \) is dropped into a calorimeter containing 10 g of water at \( 10^{\circ} \mathrm{C} ; \) the specific heat of water is twice that of ice. When equilibrium is reached, the calorimeter will contain:
A. \( 20 \mathrm{g} \) of water
B. 20 g of ice
c. \( 10 \mathrm{g} \) ice and \( 10 \mathrm{g} \) water
D. 5 g ice and 15 g water


Choose the strongest oxidizing pair
from the following:
\( \mathbf{A} \cdot N O, N_{2} O_{5} \)
\( \mathbf{B} \cdot H N O_{3}, H N O_{2} \)
\( \mathbf{c} \cdot H_{3} P O_{4}, H N O_{3} \)
D. \( H P O_{3}, H_{3} P O_{3} \)


If \( A \) is a square matrix of order \( n \), then \( |\boldsymbol{k} \boldsymbol{A}|= \)
A \( . k|A| \)
в. \( k^{n}|A| \)
c. \( k^{-n}|A| \)
D. | \( A \mid \)


The tangent to the curve \( \boldsymbol{x}=\boldsymbol{a}(\boldsymbol{\theta}- \)
\( \sin \theta) ; y=a(1+\cos \theta) \) at the points
\( \boldsymbol{\theta}=(\mathbf{2 k + 1}) \boldsymbol{\pi}, \boldsymbol{k} \in \boldsymbol{Z} \) are parallel to
\( \mathbf{A} \cdot y=x \)
в. \( y=-x \)
\( \mathbf{c} \cdot y=0 \)
D. \( x=0 \)


\( \int_{0}^{1} \frac{1}{1+x} d x= \)
\( A \cdot \log 2 \)
B. \( \frac{1}{2} \log 2 \)
\( c \cdot 2 \)
D. \( \log 3 \)


Specific volume of cylindrical virus particles is \( 6.02 \quad \times 10^{-2} \) cc/gm whose radius and length are \( 7, \dot{A} \) and \( 10 A \) respectively. If \( N_{A}=6.02 \times 10^{23} \) find
molecular weight of virus.
A. \( 15.4 \mathrm{kg} / \mathrm{mol} \)
B . \( 1.54 \times 10^{4} \mathrm{kg} / \mathrm{mol} \)
\( \begin{array}{lll}\text { C. } 3.08 & \times 10^{4} \mathrm{kg} / \mathrm{mol}\end{array} \)
D. \( 1.54 \times 10^{3} \mathrm{kg} / \mathrm{mol} \)


If \( \boldsymbol{A}=\left[\begin{array}{ccc}1 & -2 & 4 \\ 2 & 3 & 2 \\ 3 & 1 & 5\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}\mathbf{0} & -\mathbf{2} & \mathbf{4} \\ \mathbf{1} & \mathbf{3} & \mathbf{2} \\ \mathbf{- 1} & \mathbf{1} & \mathbf{5}\end{array}\right], \) then \( \boldsymbol{A}+\boldsymbol{B} \) is
\( ^{A} \cdot\left[\begin{array}{ccc}1 & -2 & 4 \\ 3 & 3 & 2 \\ 2 & 1 & 5\end{array}\right] \)
B. \( \left[\begin{array}{lll}1 & -2 & 8 \\ 3 & 3 & 4 \\ 2 & 1 & 10\end{array}\right] \)
C \( \cdot\left[\begin{array}{lll}1 & -4 & 8 \\ 3 & 6 & 4 \\ 2 & 2 & 10\end{array}\right] \)
D. none of these


The magnetic induction due to short bar magnet on its axial line at a
distance ' \( d \) ' is ' \( B \) '. What is the magnetic
induction due to the same bar magnet
on the same line at a distance
(a) \( d / 4 ? \)
(b) \( 4 d / 5 ? \)
(b) \( 125 / 64 B \)
в. (а) \( 64 B \)
(b) \( 125 / 64 B \)
c. (a) \( 32 B \)
(b) \( 125 / 32 B \)
D. (a) \( 64 B \)
(b) \( 125 / 32 B \)


\( \operatorname{Let} A=\left[\begin{array}{c}3 x^{2} \\ 1 \\ 6 x\end{array}\right], B=[a b c], \) and \( C= \)
\( \left[\begin{array}{ccc}(x+2)^{2} & 5 x^{2} & 2 x \\ 5 x^{2} & 2 x & (x+2)^{2} \\ 2 x & (x+2)^{2} & 5 x^{2}\end{array}\right] \)
three given matrices, where \( a, b, c \) and \( x \) \( \in \mathrm{R} . \) Given that \( \boldsymbol{t r}(\boldsymbol{A B})=\boldsymbol{t r}(\boldsymbol{C}) \boldsymbol{x} \in \boldsymbol{R} \)
where \( \operatorname{tr}(\mathrm{A}) \) denotes trace of \( \mathrm{A} \). If \( f(x)= \) \( a x^{2}+b x+c, \) then the value of \( f(1) \) is


An object is moving in the \( x-y \) plane
with the position as a function of time \( \operatorname{given} \operatorname{by} \vec{r}=x(t) \hat{i}+y(t) \hat{j} . \) Point \( O \) is at
\( \boldsymbol{x}=\mathbf{0}, \boldsymbol{y}=\mathbf{0 .} \) The object definitely
moving towards 0 when
A \( \cdot v_{x}>0, v_{y}>0 \)
0
B \( \cdot v_{x}<0, v_{y}<0 \)
\( \mathbf{c} \cdot x v_{x}+y v_{y}<0 \)
\( \mathbf{D} \cdot x v_{x}+y v_{y}>0 \)


Which of the following is not a fossil fuel?
A. Biomass
B. coal
c. Natural gas
D. Petroleum


Vascular bundles occur in a ring in
A. Monocot stem
B. Leaf
\( c . \) Root
D. Dicot stem


For tghis coupling reaction,which of the following conditions is most suitable?
A. strongy acidic
B. strongy alkaline
c. Slightly alkaine
D. neutral


One a.m.u is defined as mass of :
A \( \cdot \frac{1^{t h}}{16} \) the mass of one oxygen atom
B. \( \frac{1}{14}^{t h} \) the mass of one atom of nitrogen
C. \( \frac{1}{12}^{\text {th }} \) the mass of one carbon-12
D. None of above


Calculate the missing term in the geometric series \( \frac{1}{4}+x+\frac{1}{36}+\frac{1}{108}+ \)
A
в.
c. \( \frac{1}{12} \)
D. \( \frac{1}{16} \)
E \( \frac{1}{18} \)


A block of metal weighing \( 2 k g \) is resting
on a frictionless plane. It is struck by a jet releasing water at a rate of \( 1 k g / s \)
and at a speed of \( 5 m / s \).The initia acceleration of the block will be
A \( .2 .5 m / s^{2} \)
B. \( 0.5 m / s^{2} \)
c. \( 10 m / s^{2} \)
D. \( 20 m / s^{2} \)


Which of the following statements
is/are correct?
This question has multiple correct options
\( \mathbf{A} \cdot N H_{2}^{+} \) shows \( s p^{2}- \) hybridisation whereas \( N H_{2} \) shows \( s p^{3}- \) hybridisation
B. \( A l(O H)_{4}^{-} \) has a regular tetrahedral geometry
\( \mathrm{C} \cdot s p^{2}- \) hybridized orbitals have equal \( s- \) and \( p- \) character
D. Usually hybridized orbitals form \( \sigma \) bonds


A large truck and a car, both moving with a velocity of magnitude \( v \), have a head-on collision. If the collision lasts
for \( 1 s \) which vehicle experiences greater force of impact?
\( \mathbf{A} \cdot \) Truck
B. Car
c. Both experience equal and opposite force
D. Data insufficient


Two blocks \( A \) and \( B \) of masses \( 5 \mathrm{kg} \) and
\( 3 \mathrm{kg} \) respectively rest on a smooth horizontal surface with \( B \) over \( A \). The
coefficient of friction between \( A \) and \( B \)
is \( 0.5 . \) The maximum horizontal force
(in kg wt.) that can be applied to \( A, \) so that there will be motion of \( A \) and \( B \)
without relative slipping, is?
A . 1.5
B . 2.
\( c \cdot 4 \)
D.


If \( f(x)=3 x+10, g(x)=x^{2}-1, \) then
\( (f o g)^{-1} \) is equal to
\( ^{\mathbf{A}}\left(\frac{x-7}{3}\right)^{\frac{1}{2}} \)
B. \( \quad\left(\frac{x+7}{3}\right)^{\frac{1}{2}} \)
\( \left(\frac{x-3}{7}\right)^{\frac{1}{2}} \)
D. \( \quad\left(\frac{x+3}{7}\right)^{\frac{1}{2}} \)


Draw the two tangents from a point
which is \( 9 \mathrm{cm} \) away from the centre of a
circle of radius \( 3 \mathrm{cm} \). Also, measure the
lengths of the tangents.


The sex of an infant is not a case of
inheritance of characteristics.
A. True
B. False


Fill in the blank.
Vibrations inside the ear are amplified by the three bones namely the in
the middle ear
A. Hammer, anvil and stirrup
B. Hammer, Anvil and pinna
c. Hammer, cochlea and stirrup
D. Auditory bone, anvil and stirrup


An air conditioner is rated
\( 240 V, 1.5 k W . \) The air conditioner is
switched on for 8 hours each day. How much electrical energy is consumed in
30 days?
\( \mathbf{A} \cdot 360 k W h \)
B. \( 8.64 \mathrm{kW} \) h
\( \mathbf{c} \cdot 120 k W h \)
D. \( 240 \mathrm{kW} \) h


A tangent \( \mathrm{PQ} \) at a point \( \mathrm{P} \) of a circle of radius \( 5 \mathrm{cm} \) meets a line through the centre 0 at a point \( Q, \) so that \( O Q=12 \)
cm. Length of PQ is :
A. \( \sqrt{112} \mathrm{cm} \)
B . \( \sqrt{113} \mathrm{cm} \)
c. \( \sqrt{85} \mathrm{cm} \)
D. \( \sqrt{119} \mathrm{cm} \)


What is the effect of humidity on quality of sounds propagation? Is there any difference in propagation of sound in air during the summer and winter seasons? Discuss


There are two jars \( A \) and \( B \) containing food materials food in far A is pickied with acetic acid while \( B \) is not food of
which jar will stale first?


Which of the following species of silkworm are found in India?
A. Bombyx mori
B. Antheraea paphia
c. Keria
D. All of the above


When we express the velocity of light,
\( \mathbf{3 0}, \mathbf{0 0}, \mathbf{0 0}, \mathbf{0 0 0} / \mathbf{m s}^{-1}, \) in standard form
up to three significant figures, it's value
is:
A \( \cdot 3 \times 10^{8} \mathrm{ms}^{-1} \)
B . \( 3.00 \times 10^{8} \mathrm{ms}^{-1} \)
c. \( 3 \times 10^{10} \mathrm{cms}^{-1} \)
D. \( 3 \times 10^{6} \mathrm{ms}^{-1} \)


A complex cation is formed by Pt(in some oxidation state) with ligands (in
proper number so that coordination
number of Pt becomes six)
Which of the following can be its correct IUPAC name:
A. Diammineethylenediaminedithiocyanato-s platinum(II)
B. Diammineethylenediaminedithiocyanato-Splatinate(IV) ion
c. Diammineethylenediaminedithiocyanato-Splatinum(IV) ion
D. Diamminebis (ethylenediamine) dithiocyanato-Splatinum(IV) ion


A molecule of gas in a container hits one wall (1) normally and rebounds back. It suffers no collision and hits the
opposite wall (2) which is at an angle of
\( 30^{\circ} \) with wall 1
Assuming the collisions to be elastic
and the small collision time to be the
same for both the walls, the magnitude
of average force by wall 2. \( \left(F_{2}\right) \) provided the molecule during collision satisfy
\( \mathbf{A} \cdot F_{1}>F_{2} \)
B. \( F_{1}<F_{2} \)
C \( \cdot F_{1}=F_{2}, \) both non-zero
D. \( F_{1}=F_{2}=0 \)


Work done in the cyclic process shown
in figure is :
\( A \cdot 4 P_{0} V_{0} \)
\( \mathbf{B} \cdot-4 P_{0} V_{0} \)
\( ^{\mathbf{C}}-\frac{22}{7} P_{0} V_{0} \)
\( \mathbf{D} \cdot-13 P_{0} V_{0} \)


The refractive index \( (\mu) \) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate absolute error is each
measurement
A \( \cdot \Delta n_{5}=1.51-1.48=+0.03 \)
B . \( \Delta n_{4}=1.51-1.54=-0.03 \)
C \( . \Delta n_{3}=1.51-1.52=-0.01 \)
D. All of these


The rupture of air medium occurs at
\( \boldsymbol{E}=\mathbf{3} \times \mathbf{1 0}^{\mathbf{6}} \boldsymbol{V} / \boldsymbol{m} . \) The maximum
charge that can be given to a sphere of diameter 5 m will be (in coulomb):
A \( .2 \times 10^{-2} \)
B . \( 2 \times 10^{-3} \)
c. \( 2 \times 10^{-4} \)
D. \( 2 \times 10^{-5} \)


The lateral conduction in gymnosperm leaf is by
A. Veins
B. xylem parenchyma
c. Transfusion tissue
D. Medullary rays


The sum of \( n \) terms of the series \( 1^{2}+ \)
\( \mathbf{2} . \mathbf{2}^{\mathbf{2}}+\mathbf{3}^{\mathbf{2}}+\mathbf{2 . 4}^{\mathbf{2}}+\mathbf{5}^{\mathbf{2}}+\mathbf{2 . 6}^{\mathbf{2}}+\ldots . \) is
\( \frac{n(n+1)^{2}}{2}, \) where \( n \) is even. Find the
sum, where \( n \) is odd


Heating effect of current is due to
A. flow of voltage through the conductor.
B. flow of current through a conductor
c. both \( A \) and \( B \).
D. neither A nor B.


Show that the point whose distance from \( y-a x i s \) is thrice its distance
from (1,2,-1) satisfies the equation
\( 8 x^{2}+9 y^{2}+8 z^{2}-18 x-36 y+18 z+ \)
\( \mathbf{5 4}=\mathbf{0} \)


Find the cubic polynomial with three different variables.
A \( \cdot x^{3}+y^{3}+2^{3}-5^{3} \)
B \( \cdot a^{3}+b^{3}-c^{2}+1 \)
c. \( x^{3}+x^{2}+x \)
D. \( x y^{2}+x y^{3}-x y+6^{3} \)


Differentiate the following function w.r.t. \( x: \sqrt{\log \left\{\sin \left(\frac{x^{2}}{3}-1\right)\right\}} \)


Find all possible lengths of the third side, if sides of a triangle have 3 and 9
\( \mathbf{A} \cdot 6<x<12 \)
B . \( 5<x<12 \)
c. \( 6<x<10 \)


Assertion
The laws of chemical combination
ultimately led to the idea of 'atoms' being the "smallest unit of" matter.
Reason

The laws of chemical combination
played a significant role in the development of Dalton's atomic theory of matter.
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 particle moving with uniform acceleration has average velocities \( \boldsymbol{v}_{1} \)
\( v_{2} \) and \( v_{3} \) over the successive intervals
of time \( t_{1}, t_{2} \) adn \( t_{3} \) respectively. teh value of \( \frac{\left(v_{1}-v_{2}\right)}{\left(v_{2}-v_{3}\right)} \) will be
A \( \cdot \frac{\left(t_{1}-t_{2}\right)}{\left(t_{2}-t_{3}\right)} \)
B . \( \frac{\left(\frac{\left(t_{1}-t_{2}\right)}{\left(t_{2}+t_{3}\right)}\right.}{)} \)
D. \( \frac{\left(\frac{\left(t_{1}+t_{2}\right)}{\left(t_{t}+3_{3}\right)}\right.}{)_{2}} \)


What are dimensional quantities?


Convert the given mixed fractions into improper \( 2 \frac{1}{5} \)


The effectiveness of an enzyme is
affected least by
A. Temperature
B. Concentration of the substrate
c. original activation energy of the system
D. Concentration of the enzyme


What is the next term of the series \( 1+ \)
\( 3+5+7+---? \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 11
c. 10
D. 8


A device which is used to find the depth
of sea is called:
A. RADAR
B. SONAR
c. ЕСно
D. None of these


If lightning strikes you, why would you
fell electric shock?
A. Because charges are in motion
B. Because motion of charges constitutes to electric current
C. Because of magnetic effect
D. Both a \& b


Which of the following is an example of fossil fuel?
A. Coal gas
B. Coke
c. Natural gas
D. Producer gas


Find out the correct labeling
A. a - Nephron, b - Cortex, c- Medulla, d- Pelvis, e - Ureter
B. a - Cortex, b - Nephron, c- Pelvis, d- Medulla, e- - Ureter
C. a - Cortex, b - Medulla, c- Nephron, d- Pelvis, e- Ureter
D. a - Nephron, b - cortex, c- Medulla, d- Ureter, e - Pelvis


\( 10 \mathrm{mL} \) of a solution of \( K C l \) containing
\( N a C l \) on evaporation gave 0.93 g of the mixed salt, which gave 1.865 g of \( A g C l \)
by the reaction with \( A g N O_{3} \). The
quantity of \( N a C l \) in 10 mL of the
solution is (write it in multiples of 100 )


Finely divided iron combines with \( \mathrm{CO} \) to give :
\( \mathbf{A} \cdot F e(C O)_{5} \)
в. \( F e_{2}(C O)_{9} \)
\( \mathbf{c} \cdot F e_{3}(C O)_{12} \)
D. \( F e(C O)_{6} \)


Verify Rolle's theorem for the following function: \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}-\boldsymbol{4} \boldsymbol{x}+\mathbf{1 0} \) on \( [\mathbf{0}, \boldsymbol{4}] \)


The image of the line \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{3}}=\frac{\boldsymbol{y}-\mathbf{3}}{\mathbf{1}}= \)
\( \frac{z-4}{-5} \) in the plane \( 2 x-y+z+3=0 \)
is the line?
A. \( \frac{x-3}{3}=\frac{y+5}{1}=\frac{z-2}{-5} \)
в. \( \frac{x-3}{-3}=\frac{y+5}{-1}=\frac{z-2}{5} \)
c. \( \frac{x+3}{3}=\frac{y-5}{1}=\frac{z-2}{-5} \)
D. \( \frac{x+3}{-3}=\frac{y-5}{-1}=\frac{z+2}{5} \)


State whether \( f(x)=\tan x-x \) is
increasing or decreasing in its domain.


If density of earth increases 4 times and its radius becomes half of what it is, our
weight will:
A. be 4 times its present value
B. be doubled
c. remain same
D. be halved


If \( \boldsymbol{P}\left(\boldsymbol{E}_{k}\right)=\boldsymbol{C} \) for \( \mathbf{0} \leq \boldsymbol{k} \leq \boldsymbol{n}, \) then the
probability that \( X \) is the only student to pass the examination is
A \( .3 / 4 n \)
B. \( 2 /(n+1) \)
c. \( 2 / n(n+1) \)
D. \( 3 / n(n+1) \)


What is the common difference of an
A.P. in which \( a_{21}-a_{7}=84 ? \)


Define the following in photoelectric effect phenomenon:
(a) (i) Work function
(ii) Stopping potential (cut-off potential)
(b) Calculate energy of photon of wavelength \( 3.31 A \)


At random all the letters of the word
"ARTICLE" are arranged in all possible ways. The probability that the arrangement begins with vowel and ends with a consonant is
A . \( 1 / 7 \)
в. \( 2 / 7 \)
c. \( 3 / 7 \)
D. \( 4 / 7 \)


Which one of the following components of urine in a healthy human does not differ much in concentration from
that of blood plasma?
\( \mathbf{A} \cdot N H_{4}^{+} \)
в. \( K^{+} \)
c. \( N a^{\text {t }} \)
\( \mathrm{D} \cdot S O_{4}^{2} \)


For the type of interactions : (I) covalent bond, (II) van der Waals' forces, and (III)
hydrogen bonding, which represents the correct order of increasing stability?
A. \( (I)<(I I I)<(I I) \)
B. \( (I I)<(I I I)<(I) \)
C. \( (I I I)<(I I)<(I) \)
D. \( (I I)<(I)<(I I I) \)


Vitamin D is called:
A. Ascorbic acid.
B. Calciferol or ergocalciferol.
C . Thiamine.
D. Riboflavin.


If \( y=\frac{(a-x) \sqrt{a-x}-(b-x) \sqrt{x-b}}{\sqrt{a-x}+\sqrt{x-b}} \)
then find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \) wherever defined
A \( \frac{2 x-(a+b)}{2 \sqrt{(a-x)(x-b)}} \)
в. \( \frac{x}{2 \sqrt{(a-x)(x-b)}} \)
c. \( \frac{2 x-(a+b)}{4 \sqrt{(a-x)(x-b)}} \)
D. \( \frac{2 x+(a+b)}{2 \sqrt{(a-x)(x-b)}} \)


State two ways by which the magnetic field of a solenoid can be made stronger


A lightning conductor installed in a
building:
A. Does not allow the lightning to fall on the building
B. Repels the lightning
C. Forces the lightning to fall in an area where there are no buildings
D. Conducts electric charge to the ground when lightning strikes the building


A random variable \( \boldsymbol{X} \) is binomially
distributed with mean 12 and variance
8. The parameters of the distribution
are \( \ldots . . \& \ldots . \)
A \( \cdot_{36, \frac{2}{3}} \)
в. \( _{36, \frac{1}{3}} \)
c. \( _{24, \frac{1}{3}} \)
D. \( 24, \frac{2}{3} \)


Two parallel wires carrying currents in
the same direction attract each other
because of
A. potential difference between them
B. mutual inductance between them
c. electric forces between them
D. magnetic forces between them


If \( G \) is centroid and \( A D, B E, C F \) are three
medians of ABC with area \( 72 \mathrm{cm}^{2} \), then
the area of BDG is
A \( \cdot 12 ~ c m^{2} \)
B. \( 16 \mathrm{cm}^{2} \)
c. \( 24 \mathrm{cm}^{2} \)
D. \( 8 \mathrm{cm}^{2} \)


Bioamplification is due to:
A. increase in the concentration of pesticides in water
B. gradual accumulation of pesticides from lower animals to higher animals
C . gradual decrease in concentration of pesticides in \( \mathrm{H}_{2} \mathrm{O} \)
D. increase in space of biosphere


Chlorine turns moist starch iodide
paper blue black.Why?


By opening the door of a refrigerator which is inside a room, the temperature of room
A. first decreases then increases
B. remains unchanged
c. increases
D. decreases


If \( a=\frac{1}{3-2 \sqrt{2}}, b=\frac{1}{3+2 \sqrt{2}} \) then the value
of \( \boldsymbol{a}^{\mathbf{3}}+\boldsymbol{b}^{\mathbf{3}} \) is:
A \( \cdot 194 \)
B. 200
c. 198
D. 196


If \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=\boldsymbol{y}(\log \boldsymbol{y}-\log \boldsymbol{x}+1), \) then the
solution of the equation is?


Choose the correct answers from the
alternatives given. Binomial system of nomenclature means that every organism has
A. two names, one scientific and one popular
B. one name given by two scientists
C. one scientific name consisting of a generic and a specific epithet
D. two names, one denoting the .latinised name of the place and the other of the person, who determined it


If a largest sphere is inscribed in a cube of side \( 7 \mathrm{cm} \) then find the volume of the
sphere


Find the value of \( \tan ^{2}\left(\frac{1}{2} \sin ^{-1} \frac{2}{3}\right) \)


What are the differences between the
mass of an object and its weight?


Find \( \boldsymbol{n}\left(\boldsymbol{A} \cap \boldsymbol{C}^{c}\right) \)


Which of the following will be most easily corroded in moist air?
A. \( Z n \)
в. \( F e \)
c. \( N i \)
D. \( S n \)


The IUPAC name of \( \boldsymbol{C H}_{3} \boldsymbol{C O C H}\left(\boldsymbol{C H}_{3}\right)_{2} \)
is:
A. 4-methylisopropyl ketone
B. 3-Methyl-2-butanone
c. Isopropylmethyl ketone
D. 2-methyl-3-butanone


The total islets of Langerhans in human
pancreas are
A. 1 million
B. 2 million
\( c .5000 \)
D. 1000


Which of the following is a possible dimensionless quantity?
A. Velocity gradient
B. Pressure gradient
c. Displacement gradient
D. Force gradient


Gay Lussac's Law of combining volumes is applicable for combustion of carbon.
A. True
B. False


If \( \boldsymbol{y}=\sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}}, \) then \( \left(\frac{d y}{d x}\right)_{x=0}= \)
This question has multiple correct options
A \( \cdot \frac{1}{2} \)
B.
c. -2
D.


Explain the working and application of a
sonar


Choose the correct answers from the
alternatives given
Which one of the following is not true of organisms included in the kingdom
Monera?
A. They reproduce by mitosis
B. They originated at least 3.5 billion years ago
c. They have prokaryotic cellular organisation
D. Most have cell walls


Refining and extraction of metals from impure samples is called:
A. electroplating
B. cathodization
c. electrorefining
D. anionization


Assertion
An inductor coil normally produces
more current with \( D C \) source
compared to an \( A C \) source of same
value of rms voltage.
Reason
In \( D C \) source applied voltage remains
constant with time.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is true about alpha amino acids?
A. If the amino group at the chiral carbon lies on the left hand side as in L-(-)-glyceride, the amino acid belongs to L-series
B. If it is towards right as in D-(+)-glyceraldehyde, it is said to belong to D-series.
c. Both of the above
D. None of the above


Two liquids \( H N O_{3}(A) \) and water \( (B) \)
form a maximum boiling azeotrope
when mixed in the ratio of \( 68 \% \) and \( 32 \% \)
respectively. It means:
A. A-B interactions are stronger than \( A \) -A and B-B interactions
B. A-B interactions are weaker than A-A and B-B interactions
c. vapour pressure of solution is more than the pure components
D. vapour pressure of solution is less since only one component vaporises


When \( L \) is heated with iron metal, it
forms a compound \( F e L . \) What chemical term would you use to describe the change undergone by \( L ? \)


Find the shortest distance between the
skew lines \( r=(6 i+2 j+2 k)+t(i- \)
\( 2 j+2 k) \) and \( F=(-4 i-k)+s(3 i- \)
\( 2 j-2 k) \) where s,t are scalars.


Draw the circuit symbol of \( \boldsymbol{n}-\boldsymbol{p}-\boldsymbol{n} \)
transistor.


Four cards are drawn at a time from a
pack of 52 playing cards. Find the probability of getting all the 4 cards of the same suit.
A \( \cdot \frac{44}{4165} \)
В. \( \frac{11}{4165} \)
c. \( \frac{22}{4165} \)
D. none of these


The electronic configuration of chloride
ion is:
\( \mathbf{A} \cdot 2,8,7 \)
в. 2,8,6
c. 2,8,8
D. 2,


Match the columns and choose the
correct option from the following.
Hair like
cells in roots
of Monstera A Macrosclereids
\begin{tabular}{llc|l}
B & Osteosclereids & 2 & Bone like cells xerophytes \\
C & Astrosclereids & 3 & Star shaped cells in hygrophytes \\
D & Trichosclereids & 4 & Stone like cells in seed coat of Fabaceae \\
\hline
\end{tabular} 1.
\( A \cdot A-4, B-2, C-3, D-1 \)
B. A- \( 4, B-3, C-2, D-1 \)
c. \( A-4, B-2, C-1, D-3 \)
D. \( A-2, B-4, C-3, D-1 \)


Q Type your question. \( \sqrt{0} \) " \( y \)
\( \mathbf{A} \)
\( B \cdot 2 \)
\( c \cdot 3 \)
\( D \cdot 4 \)
E. None of the above


The IUPAC name of :
A. 3-methoxy-5-nitro benzaldehyde
B. 4-nitro anisaldehyde
c. 3-methoxy-4-formyl nitro benzene
D. 2-formyl-4-nitro anisole


Q Type your question-
than Segment \( 2, \) but both segments are
centered on point \( P \)

The segments are connected by straight
wires as shown, and an unseen source
of EMF creates a constant
counterclockwise current in the wire.
Which wire segment creates a stronger
magnetic field at point P?
A. segment 1 creates stronger magnetic field because Segment 1 is longer
B. Segment 2 creates stronger magnetic field becaus Segment 2 is closer
C. Both segments create the same strength magnetic field because both segments have the same angle
D. Both segments create the same strength magnetic field because both segments have the


If \( A \) is an \( n \times n \) non-singular matrix,
then \( |\boldsymbol{A} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}| \) is:
\( \mathbf{A} \cdot|A|^{n} \)
B \( \cdot|A|^{n+1} \)
c. \( |A|^{n-1} \)
D. \( |A|^{n-2} \)


Choose the correct option
A. rubber rod becomes positive and fur becomes negative
B. both rod becomes positive
C. rubber rod becomes negative and fur becomes positive
D. both becomes neutral


Use Euclid's division algorithm to find the HCF of :
\( \mathbf{8 6 7} \) and \( \mathbf{2 5 5} \)
A . 50
B. 51
c. 41
D. 52


State True or False :
Magnetic force attracts all kinds of metals.
A. True
B. False


Which of the following statements
is/are incorrect for a meter bridge,
which is used to compare two
resistances?
A. If its wire is replaced by another wire having same length, made of same material but having twice the cross sectional area, the accuracy increases.
B. If its wire is replaced by another wire of different material, having same cross sectional area but of twice the length, accuracy increases.
C. If its wire is replaced by another wire of same material, having half the cross sectional radius and half the length, accuracy decreases but sensitivity increases
D. Metre bridge works on the principle of Wheat-stone bridge


The value of \( : \tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{7}+ \)
\( \tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{8}-\frac{\pi}{4} \)


Prove by induction:
\( 2+2^{2}+2^{3}+\ldots \ldots .+2^{n}=2\left(2^{n}-1\right) \)


What is a regular polygon? State the name of a regular polygon of
(i) 3 sides
(ii) 4 sides
(iii) 6 sides


Leaves are modified into hygroscopic appendages in
A. Tamarix
B. Tamarindus
c. Albizzia
D. Butea


If suddenly the gravitational force of attraction between earth and satellite
revolving around it becomes zero, then the satellite will
A. continue to move in its orbit with same velocity
B. Move tangential to the original orbit with the same velocity
c. Becomes sationary in its orbit
D. Move towards the earth


A car is travelling along a circular curve that has a radius of \( 50 m \). If its speed is \( 16 m / s \) and is increasing uniformly at
\( 8 m / s^{2} . \) Determine the magnitude of its
acceleration at this instant.
A \( .5 .5 \mathrm{m} / \mathrm{s}^{2} \)
B. \( 7.5 \mathrm{m} / \mathrm{s}^{2} \)
c. \( 9.5 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 12.5 \mathrm{m} / \mathrm{s}^{2} \)


Two towns \( A \) and \( B \) are connected by a regular bus service with a bus leaving in either direction every T minutes with same speed. A man cycling with speed of \( 20 \mathrm{km} / \mathrm{h} \) in the direction \( \mathrm{A} \) to \( \mathrm{B} \)
notices that a bus goes past him every
\( t_{1}=18 \) minutes in the direction of motion,
and every \( t_{2}=6 \) minutes in the opposite
direction. What is the period T of the bus service? Assume that velocity of cyclist is less than velocity of bus.
A. 4.5 minutes
B. 24 minutes
c. 9 minutes
D. 12 minutes


If three events \( A, B, C \) are mutually
exclusive, then which one of the
following is correct?
A \( \cdot P(A \cup B \cup C)=0 \)
B . \( P(A \cup B \cup C)=1 \)
c. \( P(A \cap B \cap C)=0 \)
D \cdot \( P(A \cap B \cap C)=1 \)


Draw the structural formula for each of
the following:
1. 2,3 - dimethyl butane
2. Diethyl ether
3. Propanoic acid.


How many gem dihalides with different formulas are possible for \( C_{3} H_{6} C l_{2} ? \)
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


In an endothermic process, solubility increases with
temperature.
\( A \). increase
B. decrease
c. remains same
D. none of the above


A solution \( X \) is prepared by dissolving three moles of glucose in one litre of water and a solution Y is prepared by dissolving 1.5 moles of sodium chloride in one litre of water. Will the osmotic
pressure of \( \mathrm{X} \) be higher, lower or equal to that of Y? Give a reason for your
answer


Assume at \( x=x_{2}, u(x) \) is constant
Slope \( \frac{-\boldsymbol{d} \boldsymbol{u}}{\boldsymbol{d} \boldsymbol{x}}=\mathbf{0} . \) The particle is
displaced slightly from \( x=x_{2} \). Then:
A. particle will return back to \( x_{2} \) after oscillating.
B. particle will move further away from \( x_{2} \)
c. particle will stay at \( x_{2} \).
D. particle will come to a point where \( \frac{-d u}{d x} \) is maximum
or minimum


Write the observations of the
experiment which proved that respiration take place in plants


The number of complex numbers \( z \)
satisfies \( \boldsymbol{R e}\left(\boldsymbol{z}^{2}\right)=\mathbf{0},|\boldsymbol{z}|=\sqrt{\mathbf{3}} \)


The angle that is three times as large as its complement is:
\( \mathbf{A} \cdot 135 \)
в. 67.5
\( c \cdot 50.5 \)
D. 45


Prove that \( \int_{0}^{\pi / 2} \frac{d x}{1+\tan x}=\frac{\pi}{4} \)


Evaluate \( \lim _{x \rightarrow I}\left(\tan \frac{\pi x}{4}\right)^{\tan \frac{\pi x}{2}} \)


Lattice energy of alkali metal chlorides is in order:
\( \boldsymbol{L i C l}>\boldsymbol{N a C l}>\boldsymbol{K C l}>\boldsymbol{R b C l}> \)
\( \boldsymbol{C} \boldsymbol{s} \boldsymbol{C l} \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


The solid \( P C l_{5} \) exists as :
A \( \cdot P C l_{3} \)
B \( \cdot P C l_{4}^{+} \)
c. \( P C l_{6}^{-} \)
D. \( P C l_{4}^{+} \) and \( P C l_{6}^{-} \)


\( \ln \operatorname{an} A P t_{1}+t_{7}=18, t_{4}+t_{10}=54 \) find
twenty value of 520


State, for each of the following physical quantities, if it is a scalar or a vector:
volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.


Three persons entered a railway
compartment in which 5 seats were vacant. Find the number of ways in
which they can be seated
A . 30
B. 45
\( c \cdot 120 \)
D. 60


When the height of the image is less than the height of the object, then magnification will be
A. Less than 1
B. Greater than 1
c. Equal to 1
D. zero


The size of corpuscles are for different colours.
A. same
B. different
c. either (a) or (b)
D. None of these


Mean deviation of
\( \mathbf{7}, \mathbf{1 0}, \mathbf{1 0}, \mathbf{1 5}, \mathbf{1 0}, \mathbf{8}, \mathbf{8}, \mathbf{7}, \mathbf{3}, \mathbf{2}, \mathbf{1 0} \) through
mean is
A . 3.14
B. 8
\( c \cdot \frac{4}{5} \)
D. None of these


In the given LCR series circuit. Choose the correct option/options (resistance
is nonzero).
A. Reading of Voltmeter \( V_{2} \) may be greater than source
voltage
B. Reading of voltmeter \( V_{4} \) may be equal to \( V_{1} \)
C. Reading of \( V_{4} \) may be equal to source voltage \( v \)
D. None of these


What is the correct name of \( C l O_{2} ? \)
A. Chlorine dioxide
B. Chlorine (II) oxide
c. Chlorine oxide
D. Monochlorine dioxide
E. Chlorine dioxygen


Two plano convex lenses of focal lengths
\( f_{1} \) and \( f_{2} \) set for minimising spherical aberration are kept apart by \( 2 \mathrm{cm} \). If the equivalent focal length of combination
is \( 10 \mathrm{cm}, \) the values of \( f_{1} \) and \( f_{2} \) are :
A. \( 18 \mathrm{cm}, 16 \mathrm{cm} \)
в. \( 18 \mathrm{cm}, 20 \mathrm{cm} \)
c. \( 20 c m, 22 c m \)
D. \( 14 \mathrm{cm}, 20 \mathrm{cm} \)


Mean of 100 observations is 50 and
standard deviation is \( 10 . \) If 5 is added to
each observations, then what will be the
new mean and new standard deviation
respectively?
\( \mathbf{A} \cdot 50,10 \)
B. 50,15
\( \mathbf{c} .55,10 \)
D. 55,15


What is the percentage increase in the
production of Company Y from 1996 to
\( 1999 ? \)
\( A \cdot 30 \% \)
B. \( 45 \% \)
\( c \cdot 50 \% \)
D. 60\%


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \int_{\boldsymbol{f}(\boldsymbol{x})}^{\boldsymbol{g}(\boldsymbol{x})} \boldsymbol{h}(\boldsymbol{t}) \boldsymbol{d} \boldsymbol{t}= \)
A \( \cdot g^{\prime}(x) h(g(x)) \)
B. \( h(g(x))-h(f(x)) \)
c. \( h(g(x)) . g^{\prime}(x)-h(f(x)) . f^{\prime}(x) \)
D. none of these


A piece of blue glass heated to a high temperature and a piece of red glass at room temperature are taken inside a
dimly-lit room. Then
A. The blue piece will look blue and the red piece will look red as usual
B. The red piece will look brighter red and the blue piece will look ordinary blue
c. The blue will look brighter as compared to the red piece
D. Both the pieces will look equal red


Which chloride is not appreciably hydrolysed by water?
A \( \cdot \mathrm{NCl}_{3} \)
B. PCla
c. \( \mathrm{AsCl}_{3} \)
D. \( \operatorname{sb} \mathrm{Cl}_{3} \)


What is the multiplication of the numbers \( 1 \frac{1}{3} \times 3 \frac{1}{4} \times \frac{7}{8} ? \)
A \( \cdot 3 \frac{18}{24} \)
B \( \cdot_{2} \frac{19}{24} \)
c. \( _{3} \frac{19}{24} \)
D. \( _{2} \frac{18}{24} \)


No of \( \pi \) electrons in cyclobutadienyl \( \operatorname{anion}\left(C_{4} H_{4}\right)^{-2} \) is
\( A \cdot 2 \)
B. 4
\( c \cdot 6 \)
D.


When chlorine gas and hydrogen gas react to form hydrogen chloride, what will be the change of enthalpy of the reaction? (bond energies are at the end of this test)
A . \( +245 k J / m o l \)
в. +185 k \( J / \) mol
c. \( -185 k J / m o l \)
D. \( -1105 k J / m o l \)
E . \( +1105 ~ k J / m o l \)


A rope, under a tension of \( 200 N \) and
fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by \( : \boldsymbol{y}=\mathbf{0 . 1} \sin \left(\frac{\pi x}{2}\right) \sin 12 \pi t \)
Where \( x=0 \) at one end of the rope, \( x \) is in meters and \( t \) is in seconds. The length
of the rope is


Assertion
\( \mathbf{\Psi} \) indicates the amplitude of electron -
wave
Reason
\( \mathbf{\Psi}^{2} \) denotes the probability of finding an
electron in the space around the
nucleus.
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


If \( I_{1}=\int_{1}^{2} x(\sqrt{x}+\sqrt{3-x}) d x \) and
\( \boldsymbol{I}_{2}=\int_{1}^{2}(\sqrt{\boldsymbol{x}}+\sqrt{\mathbf{3 - x}}) d \boldsymbol{x}, \) then \( \frac{\boldsymbol{I}_{1}}{\boldsymbol{I}_{2}}= \)
\( A \)
\( \overline{2} \)
B. \( \frac{3}{2} \)
\( c \cdot 2 \)
\( D \)


Which of the following is correct?
A. Cells of all living organisms have a nucleus.
B. Both animal and plant cells have a well defined cell wall.
C. In prokaryotes there are no membrane bound organelles.
D. Cells are formed de novo from abiotic materials.


In Wedge-Dash Notation for three-
Dimensional Representation of an
organic molecule, the dashed bond
represents -
\( A \cdot \) a bond below the plane of the paper
B. a bond above the plane of the paper
C. a bond in the plane of the paper
D. a bond either above or below the plane of the paper


The impression of an image on the brain for one sixteenth of a second is
called


The process of mitosis can be studied
in
A. Onion root tip
B. Garlic root tip
c. Tendril tip
D. All of the above


In the purification of zirconium by Van Arkel process which halogen is used?
A. Flourine
B. Chlorine
c. Bromine
D. lodine


There is a pattern observed in the number of sum spots appearing every year called as
A. solar cycle
B. sun spot cycle
c. solar period
D. solar spot cycle


Henry cavendish discovered
A. nitrogen
B. hydrogen
c. oxygen
D. none of these


The stress required to double the length of wire (or) to produce \( 100 \% \) Iongitudinal strain is:
A. \( Y \)
в. \( \frac{Y}{2} \)
\( c .2 Y \)
D. \( 3 Y \)


\( P u^{239} \) and \( U^{238} \) are respectively:
A . fertile material, artificial fissile material
B. artificial fissile material, fertile material
c. both artificial fissile materials
D. both fertile materials


The IUPAC name of the given structure
is:


\( f \frac{\sqrt{1+\sin \frac{39 \pi}{8}}}{\sqrt{1+\sin \frac{57 \pi}{8}}}=\tan \left(\frac{k \pi}{16}\right) \) then
least positive value of \( k \) is
A . 1
B. 3
\( c .5 \)
D.


Select correct statement(s):
This question has multiple correct options
A. borax is used as a buffer
B. \( 1 \mathrm{M} \) borax solution reacts with equal volumes of \( 2 \mathrm{M} \) HCI solution
C. Titration of borax can be made using methyl orange as the indicator
D. coloured bead obtained in borax-bead test contains metaborate


Which of the following cell
representations is/are correct?
This question has multiple correct options
\( \left.\mathbf{A} \cdot P l, H_{2}(1 b a r)|H C I(a q)| C l_{2}(1 b a r)\right) P t \)
B . \( H g\left|H g_{2} C l_{2}(S)\right| H C l(a q) \mid H_{2}(1 b a r), P t \)
\( \mathbf{c} \cdot A t|A g C l(s)| K C I(a q)\left|H g_{2}(s)\right| H g \)
D \( \cdot P t_{3} H_{2}(1 b a r)|H l| A u l(s) \mid A \mu \)


Assertion
A nucleus having enrgy \( E_{1} \) decays by \( \beta \) emission to daughter nucleus having
energy \( E_{2} \) but the \( \beta \) -rays are emitted with a continuous energy spectrum
having end point energy \( \boldsymbol{E}_{\mathbf{1}}-\boldsymbol{E}_{\mathbf{2}} \)
Reason
To conserve energy and moment in \( \boldsymbol{\beta} \)
decays at least three particles must
take part in the transformation.
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


Liquation method is used for the purification of which of the following metals?
A. Tin
B. Leadd
c. Bismuth
D. All of these


A precipitate of calcium oxalate will
not dissolve in:
A. \( H C l \)
в. \( H N O_{3} \)
c. aqua regia
D. \( C H_{3} \) СООН


Catalytic poisoning is due to:
A. increasing activation energy
B. adsorption of poisoner on the reactants surface
C. adsorption of poisoners on the catalyst surface
D. increase in heat of reaction


Give reasons for the \( S O_{4} \) is easily
hydrolysed whereas \( S O_{2} \) is not easily
hydrolysed.


Chemically bleaching powder is called:
A. Calcium oxychloride
B. Calcium chlorohypochlorite
c. calcium monooxygen chloride
D. Calcium oxygen dichloride


Calculate the work done in lifting water of \( 200 \mathrm{kg} \) through a vertical distance of
\( 6 \mathrm{m} .\left(g=10 m s^{-2}\right) \)
в. 2000 J
c. \( 6000 J \)
D. \( 12000 J \)


A gas for which \( \gamma=1.5 \) is suddenly compressed to \( \frac{1}{4} \) th of its initial value then the ratio of the final to initia
pressure is
A . 1: 16
B. 1:8
\( c \cdot 1: 4 \)
D. 8:


Sequencing of genomic DNA is included under
A. Structural genomics
B. Functional genomics
c. Proteomics
D. Transgenesis


Consider the situation shown in fig. The wall is smooth but the surface of \( A \) and
B in contact are rough The friction on B
due to A in equilibrium-
A. is upward
c. is zero
D. the system cannot remain in equilibrium


In land plants, the guard cells differ from other epidermal cells in having
A. Chloroplasts
B. cytoskeleton
c. Mitochondria
D. Endoplasmic reticulum


A body weighs \( 160 \mathrm{N} \) on the earth. Find
its weight on the other planet whose:
(a) mass is \( \frac{1}{4} \) times the mass of earth and radius \( \frac{1}{3} \) times that of the earth.
(b) mass is \( \frac{5}{2} \) times the mass of earth and radius \( \frac{4}{5} \) times that of the earth.


Form an arithmetic progression with its
first term as 14 and common difference
as -3


Find total number of stereoisomers for
each compound given below.
\( A \cdot 16 \)
B. 2
\( c .3 \)
D. none


Identify \( (A) \) and \( (B) \) based on following
results:

Colourless salt \( (A)+ \) dil. \( H C l \rightarrow \) White \( \operatorname{ppt}(B) \) soluble in hot water
In the reaction, vinegar smell is also observed.
A \( \cdot\left(\text { A) } P b\left(C H_{3} C O O\right)_{3} ; \text { (B) } P b C l_{2}\right. \)
B . (A) \( P b\left(C H_{3} C O O\right)_{2} ; \) (В) \( P b C l_{3} \)
c. (A) \( P b\left(C H_{3} C O O\right)_{2} ; \) (В) \( P b C l_{2} \)
D \( \cdot\left(\text { A) } P b\left(C H_{3} C O O\right)_{3}\right. \)
, (В) \( P b C l_{3} \)


In Maxwell's velocity distribution curve
area under the graph
A. Increases when temperature is increased
B. Deccreases when temperature is increased
C. Remains same at all temperature
D. Depends on the pressure of the gas


Find the adjoint of the matrix \( A= \) \( \left[\begin{array}{lll}1 & 4 & 3 \\ 4 & 2 & 1 \\ 3 & 2 & 2\end{array}\right] \)


Molecules/ions and their magnetic
properties are given below
Molecule/lon Magnetic property
(i) \( C_{6} H_{6} \)
(1) Antiferromagnetic
(ii) \( C r O_{2} \)
(2) Ferrimagnetic
(iii) \( M n O \)
(3) Ferromagnetic
(iv) \( F e_{3} O_{4} \)
(4) Paramagnetic
(v) \( F e^{3+} \)
(5) Diamagnetic
The correctly matched pairs in the above is:
A. \( i-5 i i-3 \) iii -2 iv \( -1 v-4 \)
B. \( i-3 \) ii -5 iii -1 iv \( -4 v-2 \)
c. \( i-5 \) ii -3 iii -1 iv \( -2 v-4 \)
D. \( i-5 \) ii -3 iii -1 iv \( -4 v-2 \)
E . \( i-4 i i-5 \) iii -1 iv \( -2 v-3 \)


Two identical charges of magnitude \( +\mathrm{Q} \) are fixed as shown.A third charge - \( Q \)
is placed mid way between them at point P. Then small displacements of - Q are made in the directions indicated by
arrows. The -Q is stable with respect to displacement .
\( \odot \) (out of the What is and
A . I and III
B. I and
c. ॥ and \( I V \)
D. III and \( v \)
E. stable for any small displacement


A bag contains 3 white and 2 black balls
and another bag contains 2 white and 4 black balls. One bag is chosen at
random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.


If the root hair cell is surrounded by a
dilute solution of mineral ions. The
mineral ions will move
A. Against the concentration gradient by diffusion or osmosis
B. Against the concentration gradient by active transport
C. Along the concentration gradient by diffusion or osmosis
D. Along the concentration gradient by active transport


Out of the following,identify the metal present in the green plant:
A . zinc
B. aluminium
c. magnesium
D. tin


When a piece of magnesium ribbon is placed in a beaker of copper sulfate solution, which one of the following is most likely to happen?
A. A vigorous reaction immediately takes place, with the release of a lot of heat
B. The blue colour of the copper sulfate solution gets darker
c. The blue colour of the copper sulfate solution gets lighter.
D. The magnesium catches fire


At \( t=0, \) when the magnetic field is
switched on, the conducting rod is
moved to the left at a constant speed of
\( 5 \mathrm{cm} s^{-1} \) by some external means. The
rod moves perpendicular to the rail. At
\( t=2 s, \) induced emf has magnitude
A . \( 0.12 V \)
B. \( 0.08 V \)
c. \( 0.04 V \)
D. \( 0.02 V \)


If \( f(x)=\frac{\log (1+a x)-\log (1-b x)}{x} \) for
\( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\boldsymbol{k} \) and \( \boldsymbol{f}(\boldsymbol{x}) \) is
continuous at \( x=0, \) then \( k \) is equal to:
A \( \cdot a+b \)
в. \( a-b \)
\( c \)
D.


Electrical power can be calculated by
A. Current \( \times \) resistance
B. Current x potential difference
c. Resistance \( \times \) voltage
D. Resistance x charge


If a bar magnet is dropped vertically into a, long copper tube then its final acceleration will be
\( A \cdot a=g \)
B. a>g
\( c \cdot a \)
December 26, 2019
Dipesh Bhutada
(B) \( \square \)
Share Save


\( K_{p} \) is how many times equal to \( K_{c} \) for the given reaction?
\( N_{2}(g)+3 H_{2}(g) \rightleftharpoons 2 N H_{3}(g) \)
A \( \cdot \frac{1}{R^{2} T^{2}} \)
В \( \cdot R^{2} T^{2} \)
c. \( \frac{R}{T} \)
D. \( R T \)


The spectrum of helium is expected to be similar to that of :
\( \mathbf{A} \cdot H \)
в. \( B e \)
\( \mathbf{c} \cdot L i^{+} \)
D. Ne


In how many different ways can four
books \( A, B, C \) and \( D \) be arranged one above another in a vertical order such
that the books \( A \) and \( B \) are never in
continuous position?
\( A \cdot 9 \)
B. 12
c. 14
D. 79


\( \mathrm{NH}_{4} \mathrm{NO}_{3} \) on heating to \( 250^{\circ}-260^{\circ} \mathrm{C} \)
gives the gas:
A \( . N_{2} \) O
в. \( N_{2} \)
\( c \cdot N O_{2} \)
D. \( N O \)


The value of \( a \) in order that \( f(x)= \) \( \sqrt{3} \sin x-\cos x-2 a x+b \) decreases
for all real values of \( x, \) is given by
\( \mathbf{A} \cdot a<1 \)
в. \( a \geq 1 \)
\( c \cdot a \geq \sqrt{2} \)
D. \( a<\sqrt{2} \)


On the basis of Thomson's model of an
atom, explain how the atom is neutral as a whole?


A force produces an acceleration of \( 4 m / s^{2} \) in a body of mass \( m_{1} \) and the
same force produces an acceleration of
\( 6 m s^{-2} \) in another body of mass \( m_{2} . \) If
the same force is applied to \( \left(\boldsymbol{m}_{1}+\boldsymbol{m}_{2}\right. \)
, then the acceleration will be :
A \( \cdot 10 m / s^{2} \)
B \( \cdot 2 m / s^{2} \)
c. \( 2.4 m / s^{2} \)
D. \( 5.4 \mathrm{m} / \mathrm{s}^{2} \)


Burning of fossil fuels is the main
source of which of the following pollutant?
A. Nitrogen oxide
B. Nitric oxide
c. Nitrous oxide
D. Sulphur dioxide


A sonar device on a submarine send out
a signal and receives an echo 5 seconds later. Calculate the speed of sound in water, if the distance of the object from the submarine is \( 3625 \mathrm{m} \)
A. \( 1440 \mathrm{ms}^{1} \)
B. \( 1460 \mathrm{ms}^{1} \)
c. \( 1450 m s^{1} \)
D. \( 1470 \mathrm{ms}^{1} \)


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R}: \boldsymbol{f}(\boldsymbol{x})=\left(\boldsymbol{x}^{2}-\boldsymbol{3} \boldsymbol{x}+\boldsymbol{2}\right) \)
Find \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{f}(\boldsymbol{x}) \)


\( \sqrt{x^{2}+2 x+5} d x \) is equal to
\( \mathbf{A} \cdot(x+1) \sqrt{x^{2}+2 x+5}+\frac{1}{2} \log |x+1+\sqrt{x^{2}+2 x+5}|+C \)
В . \( (x+1) \sqrt{x^{2}+2 x+5}+2 \log |x+1+\sqrt{x^{2}+2 x+5}|+C \)
c. \( (x+1) \sqrt{x^{2}+2 x+5-2} \log |x+1+\sqrt{x^{2}+2 x+5}|+C \)
D \( \cdot \frac{1}{2}(x+1) \sqrt{x^{2}+2 x+5}+2 \log |x+1+\sqrt{x^{2}+2 x+5}|+ \)


Certain plane wavefronts are shown in
figure. The refractive index of medium
is
4
B.
\( c \cdot 1.5 \)
D. cannot be determined


\( \mathbf{A} \)
42 molal solution of sodium chloride
in water causes an elevation in the
boiling point of water by \( 1.88 \mathrm{K} \). What is
the value of Van't Hoff factor? What does
it signify? \( \left[\boldsymbol{K}_{\boldsymbol{b}}=\mathbf{0 . 5 2} \boldsymbol{K} \mathbf{k g} \boldsymbol{m o l}^{-\mathbf{1}}\right] \)


\( N_{2} O_{2}(g) \rightarrow 2 N O \) is a first-order
reaction interms of the concentration of
\( N_{2} O_{2}(g) . \) Which of the following is
valid, \( \left[N_{2} O_{2}\right] \) being constant?
A \( \cdot[N O]=\left[N_{2} O_{2}\right]_{0} e^{-k t} \)
B . \( [N O]=\left[N_{2} O_{2}\right]_{0}\left(1-e^{k t}\right) \)
C \( \cdot[N O]=\left[N_{2} O_{2}\right]_{0}\left(e^{-k t}-1\right) \)
D \( \cdot[N O]=\left[N_{2} O_{2}\right]_{0}\left(1-e^{-k t}\right) \)


A police van moving on a highway with a speed of \( 30 \mathrm{km} / \mathrm{hr} \) fires a bullet at a
thief's car speeding away in the same
direction with a speed of \( 192 k m / h r \) If the muzzle speed of the bullet is \( 150 m / s, \) with what speed does the bullet hit the thief's car? (Note:Obtain
that speed which is relevant for
damaging the thief's car)


The number of neutrons present in the
nucleus of an element \( X \), which is represented as \( _{15}^{31} X \) is:
A . 13
B. 18
\( c \cdot 16 \)
D. 19


Let \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) be given by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( x^{2}+3 . \) Find \( (\text { a })\{x: f(x)=28\} \)
the pre-images of 39 and 2 under


Two skaters \( A \) and \( B \) of mass 50 kg and 70 kg respectively stand facing each other 6 metres apart. They then pull on a light rope stretched between them. How far has each moved when they meet?
A. Both have moved 3 metres
B. A moves 2.5 metres and B moves 3.5 metres.
C. A moves 3.5 metres and \( B \) moves 2.5 metres
D. A moves 2 metres and B moves 4 metres


If \( y=\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}, \) prove that \( (1- \)
\( \left.x^{2}\right) \frac{d y}{d x}=(x y+1) \)


A box contains 2 silver coins and 4 gold coins and the second box contains 4
silver coins and 3 gold coins. If a coin is
selected from one of the box, what is the
probability that it is a silver coin.
A . 0.3
B. 0.4
c. 0.5
D. 0.6


There are two balls in an urn whose
colors are not known ( ball can be either
white or black). A white ball is put into
the urn. A ball is then drawn from the
urn. The probability that it is white is
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{2}{3} \)
D.


A system has two charges \( \boldsymbol{q}_{\boldsymbol{A}}=\boldsymbol{2 . 5} \times \)
\( \mathbf{1 0}^{-7} \boldsymbol{C} \) and \( \boldsymbol{q}_{B}=-\mathbf{2 . 5} \times \mathbf{1 0}^{-\mathbf{7}} \boldsymbol{C} \) located
at points \( \boldsymbol{A}:(\mathbf{0}, \mathbf{0}, \mathbf{1 5} \mathbf{c m}) \) and \( \boldsymbol{B} \)
\( (0,0,+15 c m), \) respectively. What are
the total charge and electric dipole
moment of the system?


A sample consisting of 1mol of a
monoatomic perfect gas \( \left(C_{v}=\frac{3}{2} R\right) \) is
taken through the cycle as shown:
Temperature at points (1),(2) and (3)
respectively is :
A \( .273 K, 546 K, 273 K \)
B . \( 546 K, 273 K, 273 K \)
C . \( 273 K, 273 K, 273 K \)
D. \( 546 K, 546 K, 273 K \)


The correct way to represent an unit amount of force is :
A. 1 newton
B. 1 Newton
c. 1 NEWTON
D. None of these


State the number of significant figures
in each of the following:
453


Induction of cell division and delay in
senescence are due to
A . Gibberellin
B. Auxin
c. cytokinin
D. Ethylene


The standard potential of the following
cells is \( 0.23 \mathrm{V} \) at \( 15^{\circ} \mathrm{C} \) and \( 0.21 \mathrm{V} \) at \( 35^{\circ} \mathrm{C} \)
\( \boldsymbol{P t}\left|\boldsymbol{H}_{2}(\boldsymbol{g})\right| \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a q})|\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l}(\boldsymbol{s})| \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \)
Calculate \( -\Delta H^{o} \) (in \( \mathrm{kJ} \) ) for the cell
reaction by assuming that these quantities remain unchanged in the range \( 15^{\circ} \mathrm{C} \) to \( 35^{\circ} \mathrm{C}( \) to the nearest integer)


A student is rotating on a stool at an
angular velocity \( ^{\prime} \omega^{\prime} \) with their arms outstretched while holding a pair of
masses. The frictional effects of the
stool are negligible. Which of the following actions would
result in a change in angular momentum for the student?
A. A clockwise torque of \( 50 \mathrm{Nm} \) and a counterclockwise torque of \( 25 \mathrm{Nm} \) are both applied to the students arms by fellow students
B. The student brings the masses closer to their body
c. The student stretches the masses further away from their body
D. A second student steps onto the stool with the first student
E. A clockwise torque of \( 50 \mathrm{Nm} \) and a counterclockwis torque of \( 50 \mathrm{Nm} \) are both applied to the students arms
by fellow students


The work done by a weightless piston in
causing an expansion \( \Delta V \) (at constant temperature), when the opposing pressure \( \boldsymbol{P} \) is variable. What will be the
final expression of the work?


When the speed at which a conductor is moved through a magnetic field is increased, the induced voltage
A . increases
B. decreases
c. remains constant
D. reaches zero


Let \( A \) be a \( 3 \times 3 \) matrix such that \( A^{2}- \)
\( \mathbf{5 A}+\mathbf{7 I}=\mathbf{O} \)
Statement I: \( \boldsymbol{A}^{-1}=\frac{\mathbf{1}}{\mathbf{7}}(\mathbf{5} \boldsymbol{I}-\boldsymbol{A}) \)
Statement II: The polynomial \( \boldsymbol{A}^{\mathbf{3}}- \)
\( 2 A^{2}-3 A+I \) can be reduced to \( 5(A- \)
\( 4 I) \) Then:
A. Both the statements are true
B. Both the statements are false
c. Statement - - lis true, but Statement - -I is false
D. Statement-lis false, but Statement- -II is true


Give reason:
Nitrogen exists as a diatomic molecule.


The ion \( A^{n+} \) is oxidised to \( A O_{3}^{-} \) by
\( M n O_{4}^{-} \) changing to \( M n^{2+} \) in acid
solution. Given that \( 2.68 \times 10^{-3} \) mol of
\( A^{n+} \) requires \( 1.61 \times 10^{-3} \) mol of
\( M n O_{4}^{-} \)
What is the weight of one gram
equivalent of \( A C l_{n} \) for the above
reaction if the atomic mass of \( A \) is \( 97 ? \)


Which of the following arylamines will not form a diazonium salt on reaction
with sodium nitrite in hydrochloric acid?
A. m-Ethylaniline
B. p-Aminoacetophenone
c. 4 -chloro-2-nitroaniline
D. N-Ethyl-2-methyaniline


Mass can neither be created nor
destroyed. This is in agreement with which law of chemical combination?
A. Law of definite proportion
B. Law of multiple proportion
c. Law of conservation of mass
D. Law of conservation of momentum


Which of the following statements is or are not true?
1. Cork cambium is otherwise called as
phellogen.
2. Cork is otherwise called as phellem.
3. Secondary cortex is otherwise called
as periderm.
4. Cork cambium, cork and secondarycortex are collectively called as phelloderm
\( A \cdot 3 \) and 4 only
B . 1 and 2 only
c. 2 and 3 only
D. 2 and 4 only


The bisector of any two adjacent angles of a square form an isosceles-rightangled triangle. If the above statement is true then
mention answer as 1 , else mention 0 if
false


A ligand is:
A. lewis acid
B. bronsted acid
C. either a lewis acid or a lewis base
D. lewis base


(i) In a cathode ray tube what is the function of anode?
(ii) State the energy conversion taking place in a cathode ray tube.
(iii) Write one use of cathode ray tube.


Water in oil(w/o), what is added as
emulsifying agent.
A. Soap
B. Heavy metal
c. Gold
D. None


Vinylite resins are copolymers of vinyl acetate and vinyl chloride. They are resistant to wear and tear to chemicals.
One of their well-known uses is in:
A. floor coverings
B. ropes
c. tyres
D. electrical insulators


Find the value of \( (4+2 i)(4-2 i) \)
given that \( i^{2}=-1 \)
\( \mathbf{A} \cdot 12 \)
B . 20
\( c \cdot 16-4 i \)
D. \( 4+16 i \)
E . \( 12-16 i \)


The sides of a triangle are \( \mathbf{5 0} \mathrm{cm}, \mathbf{7 8} \mathrm{cm} \) and \( 112 \mathrm{cm} . \) The smallest
altitude is...
\( \mathbf{A} \cdot 20 \mathrm{cm} \)
B. \( 30 \mathrm{cm} \)
c. \( 40 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)
E. None of these


A bag \( A \) contains 10 white and 3 black
balls. Another bag \( B \) contains 3 white
and 5 black balls. Two balls are
transferred from bag \( A \) and put in the bag \( B \) and a ball is drawn from bag \( B \)
Find the probability that the ball drawn is white ball.


\( \mathrm{NH}_{3}+\mathrm{HCl} \rightarrow \)


Mirror equations for convex mirror and
concave mirror are:
A. same
B. different
C. different depending on object position
D. same for only a few image positions


392 is a perfect cube
A. True
B. False
c. Ambiguous
D. Insufficient information


What are the essential conditions for
rusting to take place? This question has multiple correct options
A. Presence of pure water
B. Presence of oxygen
c. Presence of impure water
D. Presence of oxygen alone is enough


If \( z=-3+2 i, \) then \( \frac{1}{z} \) is equal to
A \( \cdot \frac{1}{13}(3+2 i) \)
B. \( -\frac{1}{13}(3+2 i) \)
c. \( \frac{1}{\sqrt{13}}(3+2 i) \)
D. \( -\frac{1}{\sqrt{13}}(3+2 i) \)


2-methyl-1,3-cyclohexanedione is more acidic than cyclohexanone
A. True
B. False


Assertion
The molecularity of the reaction, \( \boldsymbol{H}_{2}+ \)
\( B r_{2} \longrightarrow 2 H B r \) is 2
Reason
The order of this reaction is \( 3 / 2 \)
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. Assertion is incorrect, but Reason is correct


A bottle of liquor ammonia should be cooled before opening. Explain.


Which of the following has more number of water of crystallisation?
A. Corundum
B. Gibsite
c. Bauxite
D. Diaspore


The electronic configuration is given as:
\( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{10} 5 s^{2} \)
is for:
A. \( f \) -block element
B. \( d \) -block element
c. \( p \) -block element
D. \( s \) -block element


Phenol is acidic, because:
A. it contains \( O H \) group
B. it has a cyclic structure
c. it conjugate base is stabilized by resonance
D. all the above


Find three numbers in G.P. whose sum
is \( 13 \& \) sum of those squares is \( 91 ? \)


Two parallel rails with negligible
resistance are \( 10.0 \mathrm{cm} \) apart and are
connected by a \( 5.00 \Omega \) resistor. The
circuit also contains two metal rods
having resistance of \( 10.0 \Omega \) and \( 15.0 \Omega \)
sliding along the rails. The rods are
pulled away from the resistor at a
constant speeds \( 8.00 m / s \) and \( 4.00 m / s \) respectively. A uniform magnetic field
\( 0.010 T \) is applied perpendicular to the
plane of the rails. Determine the current
in the \( 5.00 \Omega \) resistor.


Given \( \boldsymbol{R}_{1}=\mathbf{5 . 0} \pm \mathbf{0 . 2} \mathbf{\Omega} \) and \( \boldsymbol{R}_{2}= \)
\( 10.0 \pm 0.1 \Omega . \) What is the total
resistance in parallel with possible \( \% \)
error?


Strong reducing behaviour of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2} \) is
due to:
A. high oxidation state of phosphorus
B. presence of two -OH groups and one P- H bond
C. presence of one - OH group and two P - H bonds
D. high electron gain enthalpy of phosphorus


Temperature of a monoatomic gas is
increased from \( T_{0} \) to \( 2 T_{0} \) in three
different processes: isochoric, isobaric and adiabatic. Heat given to the gas in
these processes are \( Q_{1}, Q_{2} \) and \( Q_{3} \) respectively. Then choose the correct
option. This question has multiple correct options
A \( \cdot Q_{1}>Q_{3} \)
в. \( Q_{2}>Q_{1} \)
\( \mathbf{c} \cdot Q_{2}>Q_{3} \)
D. \( Q_{3}=0 \)


The Tyndall's effect associated with colloidal particles is due to:
A. absorption of light
B. reflection of light
c. scattering of light
D. presence of charge


In each fission of \( _{92}^{235} \mathrm{U}, 200 \mathrm{MeV} \) energy is released. How many fissions must occur per second to produce power of \( \mathbf{1} k W ? \)
A \( \cdot 1.25 \times 10^{18} \)
В. \( 3.125 \times 10^{13} \)
C \( .3 .2 \times 10^{18} \)
D. \( 1.25 \times 10^{13} \)


The three phases of water (Solid, Liquid, Gas) are:
A . ice, water, steam
B. water, ice, steam
c. steam, ice, water
D. steam, water, ice


If heat radiated from Earth's surface is
retained, outcome will be:
A. formation of smog
B. green house effect
c. van der Waals forces of attraction among smoke particles
D. all of these


Fill up the blanks:
a) light sensitive screen of human
eye.................
b) near sightedness is corrected
by
c) hypermetropia is corrected by.....
d) range of vision for a normal eye.............
\( A \cdot \) a. retina
b. concave lens
c. convex lens
d. \( 25 \mathrm{cm} \) -infinity
B. a. cornea
b. convex lens
c. concave lens
d. \( 0-25 \mathrm{cm} \)
c. a. iris
b. converging lens
c. diverging lens
d. 0 -infinity
D. a. sclera
b. diverging lens c convex lens
d. infinity


High purity copper metal is obtained by:
A. carbon reduction
B. hydrogen reduction
c. electrolytic reduction
D. thermite reduction


Hypersecretion of parathyroid hormone
results in
A. Stronger bones due to increased incorporation of calcium in them
B. Deposition of calcium in various skeletal structure
C. No effect on the constitution of bones
D. Weaker bones due to increased removal of calcium from them


Metals generally have number
of electron(s) in their valence shell.
A. \( 1,2, \) or 3
B. 7, 8 or 9
c. \( 10,11, \) or 12
D. 20, 30, or 40


The potential differnce \( \left(\boldsymbol{V}_{\boldsymbol{A}}-\boldsymbol{V}_{\boldsymbol{B}}\right) \)
between the points \( A \) and \( B \) in the given
figure is
A \( .9 V \)
B. \( 6 V \)
\( c .3 V \)
D. \( 4 V \)


Find the quotient the and remainder of the following division:
\( \left(5 x^{3}-8 x^{2}+5 x-7\right) \div(x-1) \)


A cylinder piston arrangement has molecules at an absolute temperature
T. If the number of molecules in the
arrangement is doubled, the total kinetic energy of all the molecules remains the same as before. The ratio of
the temperature of the arrangement before and now.


Air resistance is proportional to
This question has multiple correct options
A \( . v \)
B \( \cdot v^{2} \)
\( c \cdot v^{-2} \)
\( \mathbf{D} \cdot v^{3} \)


Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
\( x+x^{2}-4 \)


Find the product of the following:
\( (1+x)\left(1-x+x^{2}\right) \)


If \( p(x)=x^{2}-4, q(x)=x^{3}-8, r(x)= \)
\( (x+2) \) and \( s(x)=\left(x^{2}+2 x+4\right) \) then
choose the correct options -
A \( \cdot p(x) \cdot s(x)=q(x) \cdot r(x) \)
B . \( p(x) . s(x) \neq q(x) . r(x) \)
c. \( p(x) . q(x)=s(x) . r(x) \)
D. None of these


Three identical charges, each having a
value \( 1.0 \times 10^{-3} \mathrm{C} \) are placed at the
corners of an equilateral triangle of side \( 20 \mathrm{cm} \) Find the potential at the center of the triangle
\( \mathbf{A} \cdot 2.3 \times 10^{6} \mathbf{V} \)
В. \( 2.3 \times 10^{5} \mathrm{V} \)
c. \( 2.3 \times 10^{4} \mathrm{V} \)
D. \( 2.3 \times 10^{3} \mathrm{V} \)


A gas cylinder contains \( 14.2 \mathrm{Kg} \) butane
gas. it is consumption of energy in a family is \( 10000 \mathrm{KJ} \) for cooking purposes how long this cylinder will be sufficient to supply. If the enthalpy of combustion of butane is \( 2658 \mathrm{KJ} \) mol


Factorize:
\( 4 a^{2}-12 a+9-49 b^{2} \)
A \( \cdot(2 a+7 b-3)(8 a-7 b-3) \)
в. \( (2 a-7 b-3)(8 a-7 b+3) \)
c. \( (2 a-7 b-3)(2 a-7 b+3) \)
D. \( (2 a+7 b-3)(2 a-7 b-3) \)


Find the derivative of \( \boldsymbol{y}= \)
\( n \sqrt{\frac{1-\sin x}{1+\sin x}} \)


The uniform magnetic field perpendicular to the plane of a conducting ring of radius a changes at
the rate of \( \alpha, \) then
This question has multiple correct options
A. all the points on the ring are at the same potential
B. the emf induced in the ring is \( \pi a^{2} \alpha \)
C. electric field intensity \( E \) at any point on the ring is zero
\( \mathbf{D} \cdot E=(a \alpha) / 2 \)
E . answer required


Neutron stars, having masses more than 5 times the solar mass, end their
lives as:
A. white dwarfs
B. red giants
c. black dwarfs
D. black holes


In a magnetic field of \( 0.05 T \) area of coil
changes from \( 101 \mathrm{cm}^{2} \) to \( 100 \mathrm{cm}^{2} \)
without changing the resistance which
is \( 2 \Omega . \) The amount of charge that flow during this period is
A \( .2 .5 \times 10^{-6} \mathrm{C} \)
В. \( 2 \times 10^{-6} C \)
\( \mathbf{c} \cdot 10^{-6} C \)
D. \( 8 \times 10^{-6} C \)


Find the median if total students are 40
Weight \( \quad \mathbf{4 5} \quad \mathbf{4 6} \quad \mathbf{4 7} \) and 48
3 Median \( \quad 6 \quad 2 \) 4


When electromagnetic radiation at wavelength 300 nm falls on the surface of sodium, electrons are emitted with a kinetic energy of \( 1.68 \times 10^{5} \mathrm{Jmol}^{-1} \)
What Is the minimum energy needed to remove an electron from sodium?


A transverse progressive wave on a stretched string has a velocity of
\( 10 m s^{-1} \) and frequency of \( 100 H z . \) The phase difference between two particles
of the string which nbare \( 2.5 \mathrm{cm} \) apart will be :
A \( \cdot \frac{\pi}{8} \)
в.
c. \( \frac{3 \pi}{8} \)
D. \( \frac{\pi}{2} \)


Variations of acceleration a of a particle executing SHM with displacement x is:


Define chemotheropy?


A vector \( n \) of magnitude 8 units is
inclined to \( x \) -axis at \( 45^{0}, y \) -axis at \( 60^{\circ} \)
and at an acute angle with \( z \) -axis. If a
plane passes through a point \( (\sqrt{2},-1,1) \) and is normal to \( \vec{n}, \) find its
equation in vector form
A \( \cdot r .(\sqrt{2} i+j+k)=2 \)
B . r. \( (\sqrt{2} i+j+k)=4 \)
c. \( r .(\sqrt{2} i-j+k)=2 \)
D \cdot r. \( (\sqrt{2} i-j+k)=4 \)


Matter is made up of
A. wood
B. blocks
c. particles
D. None of the above


Name the products formed when
chlorine is mixed with
a) a little ammonia
b) excess
ammonia


\( (k, k),(2,3) \) and (4,-1) are collimear
So find the value of \( k \)


Spherical balls of radius \( \boldsymbol{R} \) are failing
in a viscous fluid of viscosity \( \eta \) with a
velocity \( v . \) The retarding viscous force
acting on the spherical ball is
A. directly proportional to \( R \) but inversely proportional to
\( v \)
B. directly proportional to both radius \( R \) and velocity \( v \).
c. inversely proportional to both radius \( R \) and velocity \( v \)
D. inversely proportional to \( R \) but inversely proportional to \( v \)


Consider the speed-time graph of a
vehicle given here.What type of motion is represented by PQ?
A. Uniform acceleration
B. Uniform deceleration
C. Constant speed
D. Vehicle at rest


If \( A^{-1}=\left[\begin{array}{ccc}3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2\end{array}\right] \) and \( B= \)
\( \left[\begin{array}{ccc}1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1\end{array}\right] \), find \( (A B)^{-1} \)


Equation \( (2+\lambda) x^{2}-2 \lambda x y+(\lambda- \)
1) \( y^{2}-4 x-2=0 \) represents a
hyperbola if
A \( . \lambda=4 \)
B . \( \lambda=1 \)
\( c \cdot \lambda=\frac{4}{3} \)
\( D \cdot \lambda=3 \)


As \( \theta \) increases from \( \frac{\pi}{4} \) to \( \frac{5 \pi}{4}, \) the value
of \( 4 \cos \frac{1}{2} \theta \)
A. increases, then decreases
B. decreases, and then increases
C. decreases throughout
D. increases throughout
E. decreases, increases, and then decreases again


If \( \boldsymbol{A}(\boldsymbol{x})=\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \mathbf{2} \boldsymbol{x}+\mathbf{1} & \mathbf{3} \boldsymbol{x}+\mathbf{1} \\ \mathbf{2} \boldsymbol{x}+\mathbf{1} & \mathbf{3} \boldsymbol{x}+\mathbf{1} & \boldsymbol{x}+\mathbf{1} \\ \boldsymbol{3} \boldsymbol{x}+\mathbf{1} & \boldsymbol{x}+\mathbf{1} & \boldsymbol{2} \boldsymbol{x}+\mathbf{1}\end{array}\right| \)
\( \operatorname{then} \int_{0}^{1} \boldsymbol{A}(\boldsymbol{x}) \boldsymbol{d} \boldsymbol{x}= \)
A . -15
\( B \cdot \frac{-1}{2} \)
\( c .-30 \)
\( D \)


The domain of function satisfying \( f(x)+f\left(x^{-1}\right)=\frac{x^{3}+1}{x}, \) is
A. an empty set
B. a singleton
c. a finite set
D. an infinite set


Nature of aqueous solution with pH
equal to zero is:
A . acidic
B. alkaline
c. neutral
D. amphoteric


A bullet hits and gets embedded in a
solid block resting on a frictionless surface. In this process which one of the following is correct?
A. Only momentum is conserved
B. Only kinetic energy is conserved
c. Neither momentum nor kinetic energy is conserved
D. Both momentum and kinetic energy are conserveç


An insect trapped in a circular groove of radius \( 12 \mathrm{cm} \) moves along the groove steadily and complete 8 revoluation in 100s,then angular velocity of insect is equal to
A. \( 0.44 \mathrm{rad} / \mathrm{s} \)
B. 0.50 rad/s
c. \( 0.66 \mathrm{rad} / \mathrm{s} \)
D. \( 0.77 \mathrm{rad} / \mathrm{s} \)


A condenser of capacity \( C \) is charged to a potential difference of \( V_{1} . \) The plates
of the condenser are then connected to
an ideal inductor of inductance L. The
current through the inductor when the potential difference across the
condenser reduces to \( V_{2} \) is:
A \( \cdot \frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L} \)
B. \( \frac{C\left(V_{1}^{2}+V_{2}^{2}\right)}{L} \)
c. \( \sqrt{\frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L}} \)
D. \( \sqrt{\frac{C\left(V_{1}-V_{2}\right)^{2}}{L}} \)


Which of the following properties of white phosphorus are shared by red phosphorus?
A. It exhibits phosphorescence in air
B. It reacts with hot aqueous \( N a O H \) to give phosphine
c. It dissolves in carbon disulphide
D. It burns when heated in air


A body at \( 50^{\circ} \mathrm{C} \) cools in a surroundings
maintained at \( 30^{\circ} \mathrm{C} \). The temperature
at which the rate of cooling is half that of the begining is :


Assertion
For the planets orbiting around the sun, angular speed, linear speed and K.E. changes with time, but angular
momentum remains constant.
Reason
No torque is acting on the rotating planet. So its angular momentum is
constant.
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


t is desired to orbit an erect image of an object, using concave mirror of a
focal length of \( 12 \mathrm{cm} \)
1. What should be the range of distance
\( p \) an object placed in front of the mirror?
2. Will the image be smaller or large then the object? Draw the ray diagram to show the formation of an image in this case?
3. Will the image be smaller or large then the object? Draw the ray diagram to show the formation of the image in this case?
4. Where will the image of the object be, fit is placed \( 24 c m \) in front of the
mirror?
Draw ray diagram for this situation also justify your answer


A resistance of \( 10 \Omega \) and an inductance
of \( 100 m H \) are connected in series with
an AC source of voltage \( \boldsymbol{V}= \) \( 100 \cos (100 t) \) volt. The phase difference
between the voltage applied and the current flowing in the circuit will be
A . zero
в. \( \frac{\pi}{2} \)
c.
D. \( \pi \)


Nitrogen combines with metals to form:
A . nitrites
B. nitrates
c. nitrosyl chloride
D. nitrides


One way of defining or identifying carbohydrates is to say that they can be described by the general formula,
\( C_{m}\left(H_{2} O\right)_{n}, \) where \( m \) and \( n \) may or may not be the same integer. Of the four structures displayed in the figure above, which one does NOT fit this definition of a carbohydrate?
The four figures, I-IV, below, are all composed of carbon(C)
\[
O=C \quad \text { oxygen }(O), \text { and hydrogen }(\mathbf{H})
\]
\( 0=0 \quad \) as indicated by the legendat left \( \circ=\mathbf{H} \quad \) You will be asked to use these figures to answer a series of questions.
0
\( \mathbf{I} \)
\( A \)
в. ॥
\( c \)
D. IV


What is the, difference between
the compound interests on Rs. 5,000 for \( 1 \frac{1}{2} \) years at \( 4 \% \) per annum compounded yearly and half-yearly?
A. Rs. 2.04
B. Rs. 3.06
c. Rs. 4.80
D. Rs. 8.30


angular frequency \( (\omega) \)
\( A \)
\( B \)
\( c \)
\( D \)


Find the arithmetic mean of the sales
per day in a fair price shop in a week. Rs.10000, Rs.10250, Rs.10790, Rs.986


What is the tangential acceleration?
A . \( 3 \alpha \)
B. \( 2 \alpha \)
\( c \)
D. \( 4 a \)


Which one is not true about \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} ? \)
A. It is composed of \( 2 \mathrm{H}, 1 \mathrm{S} \) and 40 atoms.
B. Its molar mass is 98 g/mol.
C. It is composed of one molecules \( H_{2} \), one atom S and two molecules \( O_{2} \)
D. Its relative molecular mass is 98


Which of the following statements is true for lymph?
A. WBCs + serum
B. Blood - RBCs and some proteins
c. RBCs+WBCs+plasma
D. RBCs+ proteins + platelets


Which of the following enhances lathering property of soap?
A. Sodium carbonate
B. Sodium rosinate
c. sodium stearate
D. Trisodium phosphate


Find the diameter of a circle whose
circumference is equal to the sum of the circumference of the two circles of
diameters \( 36 \mathrm{m} \) and \( 20 \mathrm{m} \)


A particle of mass \( m \) initially moving
with speed \( v . A \) force acts on the particle \( \boldsymbol{f}=\boldsymbol{k} \boldsymbol{x} \) where \( \boldsymbol{x} \) is the distance travelled
by the particle and \( k \) is constant. Find the speed of the particle when the work done by the force equals \( W \)
A \( \cdot \sqrt{\frac{k}{m}+v^{2}} \)
B. \( \sqrt{\frac{2 W}{m}+v^{2}} \)
c. \( \sqrt{\frac{2 W}{k}+v^{2}} \)
D. \( \sqrt{\frac{W}{2 m}+v^{2}} \)


Price elasticity of demand of \( G o o d-X \)
is -2 and of \( G \) ood \( -Y \) is \( -3 . \) Which of
the two goods is more price elastic and
why?


In a rectangle \( A B C D, P, Q, R \) and \( S \)
are the midpoints of the sides \( A B, B C \)
\( C D \) and \( D A \) respectively. Find the area
of \( P Q R S \) in terms of area of \( A B C D \)


Find four numbers in an \( A P \) whose sum
is 20 and sum of whose square is 120
A .2,4,6,8
В. 2,-4,6,8
c. 2,4,7,8
D. 0,4,6,8


In the following which of the two are paramagnetic
\( (a) N_{2} \)
\( (b) C O \)
\( (c) B_{2} \)
\( (d) N O_{2} \)
Correct answer is:
A. a and c
B. b and c
\( c \cdot c \) and \( d \)
D. b and d


Electrolysis is the passage of electricity through a liquid or a solution accompanied by a chemical change.
A. True
B. False


A wooden block of mass \( 10 g \) is dropped from the top of a tower 100 m high. Simultaneously, a bullet of mass \( 10 g \) is fired from the foot of the tower
vertically upwards with a velocity of \( 100 m s^{-1} . \) If the bullet is embedded in
it, how high will it rise above the tower before it starts falling?(Consider \( \boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
\( A \cdot 80 m \)
B. 85
\( c \cdot 75 m \)
D. 10


Why is it not possible to cool the liquid at absolute OK?


Find the inverse of the matrix
\( \left[\begin{array}{ccc}1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & 1\end{array}\right] \)


If you subtract \( \frac{1}{2} \) from a number and multiply the result by \( \frac{1}{2}, \) you get \( \frac{1}{8} \) What is the number?
A \( \cdot \frac{3}{4} \)
B. \( \frac{1}{6} \)
\( c \cdot \frac{7}{4} \)
D. \( \frac{3}{5} \)


A \( 2 m \) wide truck is moving with a
uniform speed \( v_{0}=8 m / s \) along a
straight horizontal road. A pedestrain
starts to cross the road with a uniform
speed \( \boldsymbol{v} \) when the truck is \( 4 \boldsymbol{m} \) away
from him. The minimum value of \( \boldsymbol{v} \) so
that he can cross the road safely is
\( \mathbf{A} \cdot 2.62 m / s \)
B. \( 4.6 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} .3 .57 \mathrm{m} / \mathrm{s} \)
D. \( 1.414 \mathrm{m} / \mathrm{s} \)


The brownish-white deposit on kettles, heating elements and utensils formed
by boiling water is due to:
A. moisture in the air
B. temporary hardness of water
c. permanent hardness of water
D. reaction of sulphur dioxide in the air with hot water


The number of waves in the third orbit
of H atom is
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 4 \)
\( D \)


\( C-X \) bond is strongest in:
A \( \cdot C H_{3} C l \)
в. \( C H_{3} B r \)
c. \( C H_{3} F \)
D. \( C H_{3} I \)


The half year period for a zero order reaction is equal to:
\( \mathbf{A} \cdot 2 K /[A] o \)
в. \( \frac{[A]_{0}}{2 k} \)
c. \( \frac{0.693}{k} \)
D. \( \frac{0.693}{k[A]_{o}} \)


are the outer layers of a
star that are lost when the star changes from a red giant to white dwarf
A. planetary nebula
B. dark nebula
c. reflection nebula
D. emission nebula


For an ellipse, \( A \) and \( B \) are the ends of major axis and minor axis respectively. Area of \( \Delta O A B \) is 16 sq.units and \( e= \) \( \frac{\sqrt{3}}{2}, \) then equation of the ellipse is:
\( \stackrel{\text { A }}{-} \frac{x^{2}}{32}+\frac{y^{2}}{8}=1 \)
в. \( \frac{x^{2}}{16}+\frac{y^{2}}{64}=1 \)
c. \( \frac{x^{2}}{64}+\frac{y^{2}}{8}=1 \)
D. \( \frac{x^{2}}{64}+\frac{y^{2}}{16}=1 \)


If \( y=\sin ^{-1} x \) then \( \frac{d y}{d x} \) is equal to
A . sec \( y \)
B. \( \cos x \)
\( c \cdot \tan x \)
D.


If the following quadratic equation has two equal and real roots then find the
value of \( \mathrm{k}: \)
\( 4 x^{2}-5 x+k=0 \)


Importance of fossils in deciding evolutionary relationships is
A. Fossils are just for visual beauty
B. Fossils provide missing links between two different groups and indicate their evolutionary relationship
c. All fossils are useless
D. None of these


Assertion: The absolute value of
standard electrode potential can be determined experimentally. Reason: Standard electrode potentials are measured using a hydrogen halfcell reference electrode whose potential is known.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Compare boiling point of isomeric alkyl amines.
A \( \cdot 1^{\circ}>2^{\circ}>3^{\circ} \)
B . \( 1^{\circ}>2^{\circ}<3^{\circ} \)
c. \( 1^{\circ}<2^{\circ}<3^{\circ} \)
D. \( 1^{\circ}<2^{\circ}>3^{\circ} \)


Nissl granules are found in cyton of nerve cells. These have affinity for basic dyes. The granules are made up of
A. Mitochondria
B. Cell metabolites
c. Fat granules
D. Ribosomes


A ray of light is incident at an angle \( i \) on
a glass slab of refractive index \( \mu \). The
angle between reflected and refracted
light is \( 90^{\circ} . \) Then, the relationship
between i and \( \mu \) is :
A \( \cdot i=\tan ^{-1}\left(\frac{1}{\mu}\right) \)
В. \( \tan i=\mu \)
\( \mathrm{c} \cdot \sin i=\mu \)
D. \( \cos i=\mu \)


Assertion
Fuse wire must have high resistance
and low melting point.
Reason
Fuse is used for small current flow only.
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


Methanol can be prepared when:
A. iodomethane is heated with moist silver oxide
B. iodomethane react with sodium in the presence of ether
C. both \( A \) and \( B \)
D. none of these


Arrange the following in order of increasing acid strength.
\( \boldsymbol{C H}_{3} \boldsymbol{C H} 2 \boldsymbol{C H B r C O O H} ; \boldsymbol{C H}_{3} \boldsymbol{C H B r C} \)


\( A B C D \) is a quadrilateral
\( \mathbf{s} \boldsymbol{A B}+\boldsymbol{B C}+\boldsymbol{C D}+\boldsymbol{D A}>\boldsymbol{A C}+\boldsymbol{B D} \)
A. True
3. Falss


Obtain the maximum kinetic energy of
\( \boldsymbol{\beta} \) -particles, and the
radiation frequencies of \( \gamma \) decays in the
decay scheme shown
You are given that
\( \boldsymbol{m}\left(^{198} \boldsymbol{A u}\right)=\mathbf{1 9 7 . 9 6 8 2 3 3} \boldsymbol{u} \)
\( m\left(^{198} H g\right)=197.966760 u \)


Identify the system of equations: \( 2 x- \)
\( 2 y=2 \) and \( x-y=1 \)
A. inconsistent
B. consistent
c. dependent
D. non-linear


A proton, a deuteron and an a-particle are moving with same momentum in a
uniform magnetic field. The ratio of magnetic forces acting on them will be
A. 1: 1: 2
B. 1: 2: 3
\( c \cdot 2: 1: 1 \)
D. 1: 1: 1


DNA duplication occurs in
A. Mitosis only
B. Meiosis only
C. Meiosis I and mitosis
D. Meiosis II and mitosis


The area of the region bounded by the curve \( y=2 x-x^{2} \) and the line \( y=x \) is
square units.
A \( \cdot \frac{1}{6} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
D. \( \frac{7}{6} \)


While subtracting 24.24 from 25.7630 the correct answer to be expressed in significant numbers will be :
A . 1.52
B. 1.523
c. 1.5230
D. 1.5


The fossils of Homo habilis was
discovered by Leaky et al. (1964) in
A. Germany
B. Europe
c. Australia
D. Africa


Starting from an origin, a body oscillates simple harmonically with a period of \( 2 s . \) After what time will its
kinetic energy be \( 75 \% \) of the total
energy?
A . \( 1 / 6 s \)
B. \( 1 / 12 s \)
\( \mathrm{c} \cdot 1 / 3 s \)
D. \( 1 / 4 s \)


What is the mass of an object whose weight is \( 98 \mathrm{N} ? \)
A. \( 98 \mathrm{kg} \)
B. \( 9.8 \mathrm{kg} \)
\( c \cdot 10 \mathrm{kg} \)
D. none of these


Determine the factors of \( 216 u^{3}+1 \)
A \( \cdot(6 u-1)\left(36 u^{2}-6 u+1\right) \)
B . \( (6 u+1)\left(36 u^{2}-6 u+1\right) \)
c. \( (6 u+1)\left(6 u^{2}-6 u+1\right) \)
D. \( (u+1)\left(6 u^{2}-6 u+1\right) \)


Removal of the soil by the action of wind and water is known as
A. Errosion
B. Fossilization
c. Leaching
D. Calcification


The work done in holding 15 kg suitcase while waiting for a bus for 45 minutes is :
\( A \cdot 675 J \)
B. 40500
c. 4500
D. zero


Purification of \( N a C l \) by the passage of \( H C l \) through brine solution is based on
which of the following?
A. Distribution coefficient
B. Le Chatelier's principle
c. Displacement Law
D. common ion effect


Which of the following material is likely to have least friction?
A. woodd
B. Plasticç
c. Glass
D. Paper


According to Charles's law:
This question has multiple correct options
\( \mathbf{A} \cdot(d V / d T)_{P}=K \)
\( \mathbf{B} \cdot(d V / d T)_{P}=-K \)
\( \mathbf{C} \cdot(d V / d T)_{P}=-K / T \)
D. \( V \propto T \)


State whether given statement is True or False
A lower Q produces a narrower bandwidth.
A. True
B. False


Which of the following statements
is/are correct?
This question has multiple correct options
A. Nitroprusside ion is \( \left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NO}\right]^{2-} \)
B. Nitroprusside ion is \( \left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right]^{2-} \)
C. Prussian blue and Tumbull's blue, respectively, are \( F e_{4}\left[F e(C N)_{6}\right]_{3} \) and \( F e_{3}\left[F e(C N)_{6}\right]_{2} \)
D. Prussian blue and Thmbull's blue, respectively, are \( F e_{3}\left[F e(C N)_{6}\right]_{2} \) and \( F e_{4}\left[F e(C N)_{6}\right]_{3} \)


Find image of point (1,3,4) in the plane \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}+\mathbf{3}=\mathbf{0} \)


Write uses of baking powder
\( \left(N a H C O_{3}\right) \)


You are given an arrangement of three point charges \( q, 2 q \) and \( x q \) separated by equal finite distances so that electric potential energy of the system is zero. then the values of \( x \) is:
\( A \cdot-2 / 3 \)
B. -1/3
\( c \cdot 2 / 3 \)
D. 3/2


Find the speed of sound in a mixture of
mole of \( H e \) and 2 mole of \( O_{2} \) at \( 27^{\circ} C \)
A \( \cdot 480 m s^{-1} \)
B. \( 621 m s^{-1} \)
c. \( 401 \mathrm{ms}^{-1} \)
D. \( 601 m s^{-1} \)


If \( f(x)=\frac{1}{x-1}, \) then determine the
number of points of discontinuity of
\( \boldsymbol{f}[\boldsymbol{f}\{\boldsymbol{f}(\boldsymbol{x})\}] \)


An unbiased die bearing the integers
-2 to 3 is thrown once
find the probability that the number drawn is,
A perfect square


If two angles in a triangle are \( 75^{\circ} \) and 95
then the third angle is \( _{--} \)
A. 30
B. 20
\( c \cdot 10^{\circ} \)
D. \( 40^{\circ} \)


Assertion
The percentage weight of a compound \( A \) in a solution is given by
\( \% \boldsymbol{o} \boldsymbol{f} \boldsymbol{A}= \)
\[
\frac{\text {Mass } \boldsymbol{A}}{\text {Total mass of solution}} \times \mathbf{1 0 0}
\]
Because
Reason
The mole fraction of a component \( A \) is given by, Mole fraction of \( \boldsymbol{A}= \)
Numberof moles of \( \boldsymbol{A} \) Total number of moles of all compo
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


Segregation or Mendelian factors (no linkage, no crossing over) occurs during
A. Anaphase!
B. Anaphase II
c. Diplotene
D. Metaphase I


There is a complex number \( z \) with
imaginary part 164 and a positive integer \( n \) such that \( \frac{z}{z+n}=4 i . \) The value of \( n \) is


Soaking of water by a sponge is an example of :
A. simple adsorption
B. physical adsorption
c. chemisorption
D. absorption


Assertion
Frictional force is independent of the
velocity of the body
Reason
Friction is due to surface irregularities.
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


Geometrical isomerism can be shown
by:
A \( \cdot\left[A g(C N)\left(N H_{3}\right)\right. \)
в. \( _{N a_{2}}\left[C d\left(N O_{2}\right)_{4}\right] \)
\( \mathbf{c} \cdot\left[P t C l_{4} I_{2}\right] \)
D. \( \left[P t C l\left(N H_{3}\right)_{3}\right]\left[A u(C N)_{4}\right] \)


Express the following in the form \( A+i B \)
\( \frac{1}{1-\cos \theta+2 i \sin \theta} \)


For what value of \( \alpha, \) the system of
equations \( \boldsymbol{\alpha} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\boldsymbol{\alpha}-\boldsymbol{3} \)
\( 12 x+\alpha y=\alpha \)
will have no solution
\( \mathbf{A} \cdot \alpha=5 \)
B . \( \alpha=-6 \)
c. \( \alpha=-4 \)
D. \( \alpha=2 \)


Coordinates of a point at unit distance from the lines \( 3 x-4 y+1=0 \) and
\( 8 x+6 y+1=0 \) are
This question has multiple correct options
\( ^{A} \cdot\left(\frac{6}{5},-\frac{1}{10}\right) \)
в. \( \left(-\frac{2}{5},-\frac{13}{10}\right) \)
c. \( \left(0, \frac{3}{2}\right) \)
D. \( \left(-\frac{8}{5}, \frac{3}{10}\right) \)


Which of the following will react with
AcOAg?
This question has multiple correct options
A \( . R-N H_{2} \)
в. \( R-O T s \)
c. \( R-N_{3} \)
\( \mathbf{D} . \quad R-B r \)


In order to shift a body of mass \( \mathrm{m} \) from a circular orbit of radius \( 3 R \) to a higher orbit of radius \( 5 R \) around the earth, the
work done is?
\( ^{A} \cdot \frac{3 G M m}{5 R} \)
в. \( \frac{G M m}{2 R} \)
c. \( \frac{2}{15} \frac{G M m}{R} \)
D. \( \frac{G M m}{5 R} \)


sky appears blue because of
A. Total Internal
B. Scattering
c. Refraction
D. Total internal reflection


Assertion
The inverse of the matrix \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right]_{n \times n} \)
where \( a_{i j}=0, i \geq j \) is \( B=\left[a_{i j}^{-1}\right]_{n \times n} \)
Reason
The inverse of singular matrix does not exist.
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 toy car of mass \( 500 g \) travels with a uniform velocity of \( 25 \mathrm{cm} s^{-1} \) for \( 5 s . \) The
brakes are then applied and the car is uniformly retarded and comes to rest in
further \( 10 s . \) Calculate the distance
which the car travels after the brakes
are applied.
A . \( 1.25 \mathrm{cm} \)
B. \( 125 \mathrm{m} \)
c. \( 1.25 m \)
D. \( 25 m \)


Vegetative organs of plants are:
A. leaves, stem, roots
B. flower, stem, leaves
c. flower, fruit, seeds
D. root, fruit, flower


Subtract -30 from -10
\( A \cdot+20 \)
B . 40
\( c \cdot-20 \)
D. -40


The sea breeze is caused due to the low
pressure generated over
A. Land
в. Sea
c. Air
D. Both A and B


Which of the following would happen if
the supply of \( O_{2} \) is decreased to an ¡Illuminated wheat plant?
A. Its photosynthesis would decrease.
B. Its respiration would increase.
C. Its photosynthesis would increase
D. All the physiological process would stop.


A student says that he had applied a force \( F=-k \sqrt{x} \) on a particle and the
particle moves in simple harmonic
motion. He refuses to tell whether \( k \) is a
constant or not. Assume that he has
worked only with positive \( x \) and no other
force acted on the particle.
A . As \( x \) increases \( k \) increases
B. As \( x \) increases \( k \) decreases
C. As \( x \) increases \( k \) remains constant
D. The motion cannot be simple harmonic


Huygen's principle of secondary
wavelets may be used to

This question has multiple correct options
A. find the velocity of light in vacuum
B. explain the practical behaviour of light
C. find the new position of a wave front
D. explain Snell's law


Set of concentric circle in a plane