Relate all the four columns of the table
with and A in What is and \( \begin{array}{llll}\text { Metal } & \text { Ore } & \begin{array}{l}\text { Chemical } \\ \text { formula }\end{array} & \begin{array}{l}\text { Reducti } \\ \text { process }\end{array} \\ \text { Al } & \text { haemetite } & P b S & \text { blast fur } \\ \text { Cu } & \text { bauxite } & F e_{2} O_{3} & \text { besseme } \\ \text { Fe } & \begin{array}{l}\text { copper } \\ \text { pyrite }\end{array} & A l_{2} O_{3} .2 H_{2} O & \text { froth flo } \\ \text { Pb } & \text { galena } & C u F e S_{2} & \text { Hall's pro }\end{array} \)


There are three sources of the sound of
equal intensities and frequencies 400,401 and 402 vibrations per second. The maximum number of beats/sec is:
A . 0
B. 1
\( c .3 \)
D.


The material used for making the
armature of electric bell is
A . aluminum
B. soft iron
c. steel
D. bronze


Gas \( C \) that has an offensive smell as of
rotten eggs. Identify the gas.


mole of a substance (X) was treated
with an excess of water. 2 moles of
readily combustible gas were produced along with solution which when reacted
with \( C O_{2} \) gas produced a white turbidity. The substance (X) could be:
A. \( C a \)
в. \( C a H_{2} \)
\( \mathbf{c} \cdot \operatorname{Ca}(O H)_{2} \)
\( \mathrm{D} \cdot \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} \)


Integrate the rational function
\( \frac{3 x-1}{(x-1)(x-2)(x-3)} \)


The outer electronic configuration of two members of lanthanoids series are
as follows \( 4 f^{1} 5 d^{1} 6 s^{2} \) and \( 4 f^{7} 5 d^{0} 6 s^{2} \)
what are their atomic numbers? Predict
heir oxidation states.


An electron of a velocity \( x \) is found to have a certain wavelength. The velocity to be possessed by the neutron to have half the de Broglie wavelength possessed by electron is:
A \( \cdot \frac{x}{1840} \)
в. \( \frac{x}{920} \)
c. \( 3680 x \)
D. \( \frac{x}{3680} \)


\( \Delta_{f} H \) of graphite is \( 0.23 \mathrm{kJ} / \mathrm{mol} \) and
\( \Delta_{f} H \) of diamond is \( 1.896 \mathrm{kJ} / \mathrm{mol} \)
\( \boldsymbol{\Delta} \boldsymbol{H}_{t r a n s i t i o n} \) from graphite to diamond
is :
A . \( 1.66 \mathrm{kJ} / \mathrm{mol} \)
B. 2.1 kJ/mol
c. 2.33 kJ/mol
D. 1.5 kJ/mol


Find the second order derivative of the
following function:
\( x^{3}+\tan x \)


If the rate of change of area of a square plate is equal to that of the rate of change of its perimeter, then length of
the side is?
A . 1 unit
B. 2 unit
c. 3 unit
D. 4 unit


What is the reaction called when
oxidation and reduction take place simultaneously? Explain with one example.


The minimum value of \( \boldsymbol{f}(\boldsymbol{x})= \) \( \max \{x, 1+x, 2-x\} \) is
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{2} \)
c.
D. 0
E . 2


The following reaction is an example of
\( a: \)
\( \mathbf{4} \boldsymbol{N} \boldsymbol{H}_{3}(\boldsymbol{g})+\mathbf{5} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{4} \boldsymbol{N} \boldsymbol{O}(\boldsymbol{g})+ \)
\( \mathbf{6} \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
(i) displacement reaction
(ii) combination reaction
(iii) redox reaction
(iv) neutralisation reaction
\( A \). (i) and (iv)
B. (ii) and (iii)
c. (i) and (iii)
D. (iii) and (iv)


Which of the following does not have potential energy?
A. An inflated balloon
B. Water in a flowing river
c. A fruit on the tree
D. A spinning top


Three elements \( A, B, C \) belong to
\( \boldsymbol{I I} \boldsymbol{A}, \boldsymbol{I} \boldsymbol{V} \boldsymbol{A}, \boldsymbol{V} \boldsymbol{I} \boldsymbol{A} \) group respectively of
the periodic table. Identify the elements that form covalent bonds and that form electrovalent bond respectively?
\( \mathbf{A} \cdot A \) and \( B \)
B. \( B \) and \( C \)
c. \( C \) and \( B \)
D. None of the above


Find the area of quadrilateral whose vertices taken in order are
\( \boldsymbol{A}(-\mathbf{3}, \mathbf{2}), \boldsymbol{B}(\mathbf{5}, \mathbf{4}), \boldsymbol{C}(\mathbf{7},-\mathbf{6}) \) and
\( D(-5,-4)(\text { in sq. ut }) \)


What is a monohybrid cross? What is the ratio of tall and dwarf plants
obtained in \( F_{2} \) generation? Represent
the same with the help of a checker board.


Evaluate: \( ^{71} C_{71} \)


Prove the following are irrational
numbers
\( \mathbf{3}+\sqrt{\mathbf{5}} \)


Solve the equation:
\( \left(x^{2}+3 x y+y^{2}\right) d x-x^{2} d y=0, \) given
that \( y=0 \) and \( x=1 \)


The incorrect statement about the
above reaction is:

Product
A. the name of reaction is Reimer Tiemann's reaction
B. the intermediate in the reaction is dichloro carbene
c. the final product is o-hydroxy benzaldehyde
D. the final product is benzyl chloride


If \( v \) is rate corresponding to
\( P_{C H_{3} C H O}=P_{1}, \) what is the order of
reaction when \( \boldsymbol{P}_{C H_{3} C H O}=4 P_{1} ? \)
A .
в.
\( c \cdot 1.5 \)
\( D \ldots \)


G' represents
I. Mutual conductance
II. Gibbs function
III. Gravitational constant
Which combination is correct?
A. Il and III only
B. I and III only
c. ॥ only
D. I, I land III


The coil is wound on an iron core and
looped back on itself so that core has two sets of closely wound coils carrying current in opposite directions. The self inductance is
\( A \cdot 0 \)
B. \( 2 L \)
\( \mathrm{c} \cdot 2 \mathrm{L}+\mathrm{M} \)
D. \( L+2 M \)


The manifestation of band structure in
solids is due to
A. Heisenberg's uncertainty principle
B. Pauli's exclusion principle
c. Bohr's correspondence principle
D. Boltzmann's law


toppr
Q Type your question
\( A_{1}= \) last digit of the product is not the
number 1,3,7 or 9
\( A_{2}= \) last digit of the product is among
the number 1,3,5,7 or 9
\( A_{3}= \) last digit of the product is among the number 1,3,7 or 9
\( A_{4}= \) last digit of Ihe product 'is among
the number 2,4,6 or 8
\( A_{5}= \) last digit of the product is the
number 5.
\( A_{6}= \) last digit of the product is the
number 0
\( A_{7}= \) last digit of the product is
1,2,3,4,6,7,8 or \( 9.0 n \) the basis of above information answer the following
questions. The chance that last digit of the product
is \( \boldsymbol{A}_{3} \)
\( ^{\mathrm{A}} \cdot\left(\frac{3}{5}\right)^{\prime} \)
B. \( \left(\frac{2}{5}\right)^{n} \)
\( ^{c} \cdot\left(\frac{2}{3}\right)^{n} \)
D. \( \left(\frac{4}{5}\right)^{\prime} \)


Equation of the plane passing through the point of intersection of \( x+2 y+=0 \) and \( 2 x+y=0 \) and which is perpendicular to
\( 5 x+6 z=0 \)
This question has multiple correct options
A. \( x=0 \)
B. \( y=0 \)
\( c \cdot z=0 \)
D. x+y=0
E. \( x+z=0 \)


State to which quadrant does the following points belong:
\( U(-6.2,4.3) \)


Work done in stretching a wire through \( 1 \mathrm{mm} \) is \( 2 J . \) What amount of work will
be done for elongating another wire of same material, with half the length and
double the radius of cross section, by 1 \( \mathrm{mm} ? \)
A .2
в. 4
c. 8 J
D. 16


The important event of meiosis is the
crossing over. It occurs during
A. Leptotene
B. Pachytene
c. Diplotene
D. zygotene


Silver iodide is used for producing artificial rains because \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I}: \)
A. is easy to spray at high altitude
B. is insoluble in water
c. is easy to synthesize
D. has crystals similar to ice


Prove: \( \sin ^{-} 1 \frac{3}{5}+\sin ^{-1} \frac{8}{17}=\sin ^{-1} \frac{77}{85} \)


An element forms two oxides
containing, respectively, \( 50 \% \) and \( 40 \% \) by weight of the element. These oxides
illustrate the:
A. Law of constant composition
B. Law of multiple proportion
c. Law of reciprocal proportion
D. None of these


Evaluate the cube root of: \( \sqrt[3]{343} \)


If \( \boldsymbol{\alpha}=\mathbf{3} \sin ^{-1} \frac{\mathbf{6}}{\mathbf{1 1}} \) and \( \boldsymbol{\beta}=\mathbf{3} \cos ^{-1} \frac{\mathbf{4}}{\mathbf{9}} \)
where the inverse trigonometric functions take only the principal values then the correct option(s) is(are) This question has multiple correct options
\( \mathbf{A} \cdot \cos \beta>0 \)
B. \( \sin \beta<0 \)
\( \mathbf{c} \cdot \cos (\alpha+\beta)>0 \)
D. \( \cos \alpha<0 \)


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


A ring rolls without slipping on the
ground. Its centre \( C \) moves with a
constant speed \( u . P \) is any point on the
ring. The speed of \( P \) with respect to the
ground is \( \boldsymbol{v} \) This question has multiple correct options
A \( .0 \leq v \leq 2 u \)
B. \( v=u \), if \( C P \) is horizontal
c. \( v=u \), if \( C P \) makes and angle of \( 30^{\circ} \) with horizontal and \( P \) is below the horizontal level of \( C \)
D. \( v=\sqrt{2} u \), if \( C P \) is horizontal


A
numbers where each term in the
sequence is found by multiplying the previous term with a unchanging number called the common ratio.
A. geometric progression
B. arithmetic series
C. arithmetic progression
D. harmonic progression


The line \( (x-2) \cos \theta+(y-2) \sin \theta= \)
1 touches a circle for all value of \( \theta \), then
the equation of circle is
A \( \cdot x^{2}+y^{2}-4 x-4 y+7=0 \)
B . \( x^{2}+y^{2}+4 x+4 y+7=0 \)
c. \( x^{2}+y^{2}-4 x-4 y-7=0 \)
D. None of the above


A dip needle shows angle of dip \( \theta \) when
the dip circle is placed in magnetic meridian. Now, the dip circle is rotated
by an angle \( \alpha \) and the apparent angle of
dip at this place is \( \theta^{\prime} \), then
\( \left(\tan \theta^{\prime} / \tan \theta\right) \) is :
A . \( 1 / \cos \alpha \)
B. \( 1 / \sin \alpha \)
\( c \cdot \cos \alpha \)
D. sina


Prove that the straight line \( x+y= \) touches the parabola \( y=x-x^{2} \)


Down's method is used for the
extraction of :
A . \( A l \)
в. \( N a \)
\( \mathrm{c} \cdot M g \)
D. \( C u \)


\( 100 \mathrm{mL} \) of \( H_{2} O_{2} \) is oxidised by \( 100 \mathrm{mL} \)
of \( 0.01 M K M n O_{4} \) in acidic medium
\( M n O_{4}^{\ominus} \) reduced to \( M n^{2+} \) ). \( 100 \mathrm{mL} \) of
the same \( H_{2} O_{2} \) is oxidised by \( V \) mL of
\( 0.01 M K M n O_{4} \) in basic medium
\( M n O_{4}^{\ominus} \) reduced to \( M n O_{2} \) ). Hence, \( V \) is :
A. 500
в. 100
c. \( \frac{100}{3} \)
D. \( \frac{500}{3} \)


The trigonometric equation \( \sin ^{-1} x= \) \( 2 \sin ^{-1} 2 a \) has a real solution if
A \( \cdot|a|>\frac{1}{\sqrt{2}} \)
в. \( \frac{1}{2 \sqrt{2}}<|a|<\frac{1}{\sqrt{2}} \)
c. \( |a|>\frac{1}{2 \sqrt{2}} \)
D \( \cdot|a| \leq \frac{1}{2 \sqrt{2}} \)


During adsorption, enthalpy and entropy of the system are
but \( \Delta G \) must be
A. negative, positive
B. negative, negative
c. positive, negative
D. positive, positive


Diagonal relationship of elements in
due to same:
A . size
B. mass number
c. atomic number
D. electron affinity


The entropy of a gas increases on its expansion. Why?


If the energy of the second Bohr's orbit
in H-atom is \( -328 k J \) mol\( ^{-1} \), then what
is the energy of the fourth Bohr orbit?
В. \( -41 k J \) mol\( ^{-1} \)
c. \( -1312 k J \) mol \( ^{-1} \)
D. \( -164 k J \) mol \( ^{-1} \)


If \( \boldsymbol{x}+\mathbf{4}=\mathbf{8}, \) then \( \boldsymbol{x}=\mathbf{4}, \) Inverse of the
statement is-
A. If \( x+4=8 \), then \( x \neq 4 \)
B. If \( x+4 \neq 8 \), then \( x \neq 4 \)
c. If \( x+4 \neq 8 \), then \( x=4 \)
D. none of the above


An electric dipole moment \( \vec{p}=(2.0 \hat{i}+ \) \( \mathbf{3} .0 \hat{\boldsymbol{j}}) \mu C . \mathrm{m} \) is placed in a uniform
electric field \( \overrightarrow{\boldsymbol{E}}=(\boldsymbol{3} \cdot \boldsymbol{0} \hat{\boldsymbol{i}}+\boldsymbol{2} \cdot \boldsymbol{0} \widehat{\boldsymbol{k}}) \times \)
\( \mathbf{1 0}^{\mathbf{5}} \mathbf{N} \boldsymbol{C}^{-\mathbf{1}} \)
This question has multiple correct options
A. The torque that \( \vec{E} \) exerts on \( \vec{p} \) is \( (0.6 \vec{i}-0.4 \vec{j}- \) \( 0.9 \vec{k}) N m \)
B. The potential energy of the dipole is \( -0.6 J \)
C. The potential energy of the dipole is \( 0.6 J \).
D. If the dipole is rotated in the electric field, the maximum potential energy of the dipole is \( 1.3 J \)


The change in focal length of an eye lens in human eye is caused by the action of the:
A. Pupil
B. Retina
c. Ciliary muscles
D. Iriss


A body takes 't' seconds to reach the maximum height 'H' \( m \), when projected vertically upward from the ground. Find the position of the body after \( \frac{t}{2} \) seconds from the ground in terms of H.
\( A \cdot H / 3 \)
B. 3/4 H
c. \( 1 / 2 \mathrm{H} \)
D.


A source emits electromagnetic waves of wavelength \( 3 m . \) One beam reaches
the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to \( \frac{1}{4} \) as compared to
intensity due to the direct beam alone.
The resultant intensity will be.
A \( \cdot\left(\frac{1}{4}\right) \) fold
B \( \cdot\left(\frac{3}{4}\right) \) fold
c. \( \left(\frac{5}{4}\right) \) fold
D. \( \left(\frac{9}{4}\right) \) fold


Common enzyme in glycolysis and pentose phosphate pathway is
A. Hexokinase
B. Aconitase
c. Fumarase
D. Dehydrogenase


The odometer of a car reads \( 2000 \mathrm{km} \) at
the start of a trip and \( 2400 \mathrm{km} \) at the
end of the trip. If the trip took \( 8 \mathrm{h} \)
calculate the average speed of the car in \( k m h^{-1} \) and \( m s^{-1} \)
\( A \cdot 50 \mathrm{km} / \mathrm{h} \) or \( 13.9 \mathrm{m} / \mathrm{s} \)
B. 40 km/h or 12.5 m/s
c. \( 50 \mathrm{km} / \mathrm{h} \) or \( 12.5 \mathrm{m} / \mathrm{s} \)
D. \( 40 \mathrm{km} / \mathrm{h} \) or \( 13.9 \mathrm{m} / \mathrm{s} \)


Among the following which is having maximum specific heat.
A . Ice
B. water
c. Steam
D. Alcohol


The compound in which \( \underline{C} \) uses its \( s \boldsymbol{p}^{3} \) hybrid orbitals in bonding is:
A. \( H \subseteq O O H \)
B. \( \left(H_{2} N\right)_{2} \underline{C O} \)
c. \( \left(C H_{3}\right)_{3} \subseteq O H \)
D. \( C H_{3} \underline{C H O} \)


The value of \( \lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin x \cos x} \) is?
A \( \cdot \frac{2}{5} \)
B. \( \frac{3}{5} \)
\( c \cdot \frac{3}{2} \)
D.


\( S_{r} \) denotes the sum of the first \( r \) terms
of an AP. Then \( S_{3 n}:\left(S_{2 n}-S_{n}\right) \) is
This question has multiple correct options
A . \( n \)
B. \( 3 n \)
\( c .3 \)
D. independent of \( n \)


An equipotential line and a line of force
are:
A. perpendicular to each other
B. parallel to each other
c. in any direction
D. at an angle of \( 45^{\circ} \)


Two resistance \( R_{1} \) and \( R_{2} \) are made of
different materials. The temperature
coefficient of the material of \( \boldsymbol{R}_{1} \) is \( \boldsymbol{\alpha} \)
and of the material of \( \boldsymbol{R}_{2} \) is \( -\boldsymbol{\beta} \). The
resistance of the series combination of
\( R_{1} \) and \( R_{2} \) will not change with temp.
then ratio of resistance of two wire will
be :-
A \( \cdot \frac{\alpha}{\beta} \)
B. \( \frac{\alpha+\beta}{\alpha-\beta} \)
\( ^{\mathbf{C}} \cdot \frac{\alpha^{2}+\beta^{2}}{\alpha \beta} \)
D. \( \frac{\beta}{\alpha} \)


There is no ring strain in cyclohexane, but cyclobutane has an angle strin of
\( 9^{\circ} 44^{\prime} . \) If \( \Delta H_{c}^{\circ} \) of cyclohexane per
\( \left(C H_{2}\right) \) group is 660 kJ \( m o l^{-1} \) and \( \Delta H_{c}^{\circ} \)
of cyclobutane is \( 2744 \mathrm{kJ} \) mol\( ^{-1} \),what
is the ring strain in \( \mathrm{kJ} \) mol\( ^{-1} \) of
cyclobutane?
A \( .-104 \)
B. 104
\( c \cdot-2084 \)
D. 2084


Which of the following is most electronegative element?
\( A \cdot A \)
B. F
\( c \cdot c a \)
D. Li
E.


The atoms of elements belonging to the same group of periodic table have the
same :
A. number of protons
B. number of electrons
c. number of neutrons
D. number of electrons in the outermost shell


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}\frac{x-2}{x^{2}-3 x+2} & x \in R-\{1,2\} \\ 2 & x=1 \\ 1 & x=2\end{array}\right. \)
then \( \lim _{x \rightarrow 2} \frac{f(x)-f(2)}{x-2} \) is
\( A \)
B.
c. 1
\( D \cdot-\frac{1}{2} \)


Which of the following constitutes the largest ecosystem of the world?
A. Ocean
B. River
c. Forest
D. Grassland


Epiphyseal plates at the extremities of long bones help in
A. Bone moulding
B. Elongation of bone
c. Bone formation
D. Formation of Haversian canal


If the mass of the earth increases by \( 80 \% \) and radius of the earth increases
by \( 40 \% \) then the percentage charge in acceleration due to gravity on the surface of radius of earth is (where \( g_{s}=\frac{G M}{R^{2}}, M= \) mass of earth and \( R= \) radius of earth \( \} \) )
A. zero
B . \( +8.16 \% \)
c. \( -8.16 \% \)
D. \( 160 \% \)


A solid of mass 250 g at \( 90^{0} C \) is dropped in a calorimeter containing 100
\( g \) of water at \( 15^{0} C . \) The resulting
temperature of mixture becomes \( 40^{0} C \) The mass of calorimeter is 100 g and its specific heat capacity is \( 0.1 \mathrm{cal} / \mathrm{g}^{0} \mathrm{C} \) Find the specific heat capacity of the
solid.


Which one of the following is unstable
A. \( \alpha \) ray
в. \( y- \) ray
c. proton
D. neutron


Prove that the height of the cylinder of
maximum volume that can be inscribed
in a sphere of radius \( R \) is \( \frac{2 R}{\sqrt{3}} . \) Also find the maximum volume


Further growth of cancerous cells in the
body is arrested by:
A. electrotherapy
B. physiotherapy
c. chemotherapy
D. psychotherapy


What are the types of hybridization in
\( \boldsymbol{C}_{3} \boldsymbol{H}_{4} ? \)


In the diagram, \( A, B, C, D, E \) are points
on the circle. \( A B \| D C, \angle A D E=39^{\circ} \)
and \( \angle A B C=62^{\circ} . \) Then the values of
and \( y \) respectively are:
A \( \cdot 23^{\circ}, 51^{\circ} \)
B \( \cdot 79^{\circ}, 62 \)
\( c \cdot 62^{\circ}, 79^{\circ} \)
\( 0.51^{\circ}, 23 \)


The number of electric field lines
\( \operatorname{crossing} \) an area \( \Delta S \) is \( n_{1} \) when \( \Delta \vec{S} \| \vec{E}_{1} \)
while the number of field lines
crossing the same area is \( n_{2} \) when \( \Delta \overrightarrow{\boldsymbol{S}} \) makes an angle of \( 30^{\circ} \) with \( \vec{E} \). Then
A \( \cdot n_{1}=n_{2} \)
в. \( n_{1}>n_{2} \)
c. \( n_{1}<n_{2} \)
D. cannot say anything


The noble gases are unreactive because
they:
A. have same number of electrons
B. have an atomicity of one
c. are gases with low density
D. have stable electronic configuration


The law of triads is not applicable to:
This question has multiple correct options
A. \( O s, I r, P t \)
в. \( C a, S r, B a \)
c. \( F e, C o, N i \)
D. \( R u, R h, P t \)


Which can do glass etching?
\( \mathbf{A} \cdot H I O_{4} \)
B. \( \operatorname{SiF}_{4} \)
c. \( H F \)
D. \( H N O_{3} \)


Explain how sex is determined in human babies.


Greenhouse effect refers to
A. Cooling of Earth
B. Trapping of UV rays
C. Production of cereals
D. Warming of Earth


From the standard potential in acidic medium as shown in the following la-
timer diagram, the value of \( \left(\boldsymbol{E}_{1}^{\mathbf{0}}+\boldsymbol{E}_{2}^{0}\right) \)
in volts is:


Describe Haber process for the
manufacture of ammonia?


Atomic nuclear reactors use heavy water. This is different from ordinary water only to the extent that in place of hydrogen it contains:
A. deuterium, a heavier isotope of hydrogen
B. nitrogen, which is also a light element
c. tritium, an heavier isotope of hydrogen
D. a radioactive element


Find the following set is singleton set or
not.
\( A=\{x: 7 x-3=11\} \)


Cobalt as a rare element is essential in
the synthesis of this vitamin
A. \( C \)
в. \( D \)
c. \( B_{1} \)
D. \( B_{12} \)


When two dice are thrown, list the number outcomes of an even of getting
equal to 8
A .2
B. 3
\( c \cdot 4 \)
D. 5


In a meter bridge, the gaps are closed by resistances 2 and 3 ohms. The value
of shunt to be added to 3 ohm resistor
to shift the balancing point by \( 22.5 \mathrm{cm} \)
is.
A . \( 1 \Omega \)
B. 2\Omega
c. \( 2.5 \Omega \)
D. \( 5 \Omega \)


In the following letter sequence, some of the letters are missing. These are given in order as one of the alternatives below
Choose the correct alternative.
\( \boldsymbol{\alpha} \boldsymbol{\beta}_{-} \boldsymbol{\alpha} \boldsymbol{\alpha}_{-} \boldsymbol{\beta} \boldsymbol{\beta} \boldsymbol{\beta}_{-} \boldsymbol{\alpha} \boldsymbol{\alpha} \boldsymbol{\alpha} \boldsymbol{a}_{-} \boldsymbol{\beta} \boldsymbol{\beta} \boldsymbol{\beta} \ldots \)
\( \mathbf{A} \cdot \alpha \beta \beta \alpha \)
B. \( \beta \alpha \beta \alpha \)
\( \mathrm{c} \cdot \alpha \alpha \alpha \beta \)
\( \mathbf{D} \cdot \alpha \beta \alpha \beta \)


A capacitor of capacitance \( C \) has initial
charge \( Q_{0} \) is connected to a inductor of
inductance L as shown. Att = 0 switch S
is closed. Then the current though the
inductor when energy in the capacitor is
three times energy of inductor is
A \( \cdot \frac{Q_{0}}{2 \sqrt{L C}} \)
B. \( \frac{Q_{0}}{\sqrt{L C}} \)
c. \( \frac{2 Q_{0}}{\sqrt{L C}} \)
D. \( \frac{Q_{0}}{4 \sqrt{L C}} \)


How will you convert the following? Chlorobenzene to D.D.T.


The shape of the string is drawn at \( t=0 \)
and the area of the pulse enclosed by the string and the \( x \) -axis is measured. It
will be equal to
\( \mathbf{A} \cdot 2 c m^{2} \)
B. \( 2.5 \mathrm{cm}^{2} \)
c. \( 4 \mathrm{cm}^{2} \)
D. \( 5 \mathrm{cm}^{2} \)


During decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2}, \) it
undergoes:
A. oxidation
B. reduction
c. redox reaction
D. disproportionation


The zone of no combustion is
A. The middle zone
B. outermost zone
c. The base of the flame
D. Innermost zone


Which line is parallel to \( B C ? \)
A \( . P Q \)
3.57
\( c, O R \)
D \( S \) h


When a person stands on a weighing balance, working on the principle of Hooke's law, it shows a reading of \( 60 \mathrm{kg} \)
after a long time and the spring gets compressed by \( 2.5 \mathrm{cm} . \) If the person jumps on the balance from a height of \( \mathbf{1 0} c \boldsymbol{m}, \) the maximum reading of the balance will be
A. \( 60 \mathrm{kg} \)
в. \( 120 \mathrm{kg} \)
c. \( 180 \mathrm{kg} \)
D. 240 kg


Which term of \( G . P .: 3,9,27, \ldots . . \) is
\( \mathbf{2 1 8 7} ? \)


In Haber process of Ammonia
production the element used as
catalytic promoter to increase the activity of Iron catalyst is
A. NI (Nickel)
B. W (Tungston)
c. \( v \) (vanadium)
D. Mo (Molybednum)


A magnet has coercivity of \( 3 \times 10^{3} \)
\( A m^{-1} . \) It is kept in a \( 10 \mathrm{cm} \) long solenoid
with a total of 50 turns. How much
current has to be passed through the solenoid to demagnetize it?


STRUCTURED/APPLICATION/SKILL TYPE
Given below are chemical reactions 11 to
5) involving glucose and five other chemical products (A-E)

Write the reaction number of the
following:
Anaerobic respiration in plants


Which of the following mechanism involves the vasodilation?
A. ADH
B. Renin-angiotensin
c. ANF
D. None of the above


The coordination number of the
complex formed by this ligand with \( 3 d \) transition metal and the inner
transition metal is
respectively
A. 6 and 6
B. 8 and 6
\( c .6 \) and 8
D. 8 and 8


If an electron and a proton have the same de-Broglie wavelength, then the kinetic energy of the electron is :
A. zero
B. Less than that of a proton
c. More than that of a proton
D. Equal to that of a proton


Which of the following Venn diagrams correctly represents Jaipur, Rajasthan, and India?
\( A \)
B.
\( c \)
D.


\( ^{238} U \) decays with a half-life of \( 4.5 \times 10^{9} \)
years, the decay series eventually ending at \( ^{206} P b, \) which is stable. A rock sample analysis shows that the ratio of the number of atoms of \( ^{206} P b \) to \( ^{238} U \) is
\( 0.0058 . \) Assuming that all the \( ^{206} P b \) is
produced by the decay of \( ^{238} U \) and that all other half-lives on the chain are
negligible, the age of the rock sample is \( \left(\ln 1.0058=5.78 \times 10^{-3}\right) \)
A . \( 38 \times 10^{8} \) years
B. \( 38 \times 10^{6} \) years
C \( .19 \times 10^{8} \)years
D. \( 19 \times 10^{6} \) years


Incomplete burning of petrol or diesel in
vehicles creates ........... gas which is very poisonous.
A. Carbon dioxide
B. Carbon monoxide
c. Methane
D. Ozone


Isotopic number of \( _{26}^{58} \mathrm{Fe} \) is :


Given a circle of radius \( R \), the
experiment is to randomly select a chord in that circle. Identify the type of the sample space.
A. Finite sample space
B. Continuous sample space
c. Infinite discrete sample space
D. None of these


A charged conducting sphere has diameter \( 2.4 m \) and surface charge
density \( 10 \mu C / m^{2} . \) Electric flux passing through its surface will be:-
A \( \cdot 8.17 \times 10^{7} \mathrm{Nm}^{2} / \mathrm{C} \)
В . \( 16 \times 10^{7} \mathrm{Nm}^{2} / \mathrm{C} \)
c. \( 1 \times 10^{6} \mathrm{Nm}^{2} / \mathrm{C} \)
D . \( 2.2 \times 10^{8} \mathrm{Nm}^{2} / \mathrm{C} \)


Each of Kirchoff's two laws presumes
that some quantity is conserved.

Which row states Kirchhoff's first law
and names the quantity that is
conserved?

This question has multiple correct options
A. Statement: the algebraic sum of currents into a junction is zero ; quantity : charge
B. statement: the algebraic sum of currents into a junction is zero ; quantity : energy
c. statement : the e.m.f in a loop is equal to the algebraic sum of the product of current and resistance round the loop ; quantity : charge
D. statement: the e.m.f in a loop is equal to the algebraic sum of the product of current and resistance round the loop ; quantity : energy


The energy of the orbitals decreases in the order:
A \( . s>p>s p^{3}>s p>s p^{2} \)
В . \( p>s p^{3}>s p^{2}>s p>s \)
\( \mathbf{c} \cdot s p^{3}>s p^{2}>s p>s>p \)
D \( . s>s p>s p^{2}>s p^{3}>p \)
E. None of these


In nuclear reactor, graphite is used
as
A . Fuel
B. Coolant
c. Moderator
D. Electrode


Where will it be profitable to purchase one kilogram sugar?
A. At poles
B. At equator
C . At \( 45^{\circ} \) latitude
D. At \( 40^{\circ} \) latitude


\( C l_{2} \) behaves as a bleaching agent like
\( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{3}\left(\mathbf{a q} \cdot \boldsymbol{S} \boldsymbol{O}_{2}\right) \)
If true enter 1 , else enter 0 .


The correct order of variation in the
sizes of atoms is:
A. \( B e>C>F>N e \)
в. \( N e>F>C>B e \)
c. \( N e>B e>C>F \)
D. \( F>N e>B e>C \)


Find the total pressure exerted by \( 1.6 g \)
methane and \( 2.2 g C O_{2} \) contained in a
four litre flask at \( 27^{\circ} \mathrm{C} \)


Give chemical equations to manufacture of Sulphuric Acid by
Contact process.


The current through the ammeter
shown in the figure is \( 1 A \). If each of the
4 resistor is replaced by 2 resistor, the
current in the circuit will become
\( A \cdot(a) \frac{10}{9} A \)
\( \mathbf{B} \cdot(\mathbf{b}) \frac{5}{4} A \)
\( \mathbf{c} \cdot(\mathrm{c}) \frac{9}{8} A \)
\( \mathbf{D} \cdot(\mathrm{d}) \frac{5}{8} A \)


In the arrangement shown, the solid cylinder of mass \( \mathrm{m} \) is slightly rolled to the left and released. It starts
oscillating on the horizontal surface without slipping. Then time period of oscillation is
\( ^{\mathrm{A}} \cdot \pi \sqrt{\frac{3 K}{m}} \)
в. \( 2 \pi \sqrt{\frac{3 M}{2 K}} \)
c. \( _{2 \pi} \sqrt{\frac{2 K}{3 M}} \)
D. \( 2 \pi \sqrt{\frac{3 K}{2 m}} \)


Which of the following relations is
correct?
A. \( \quad \) Distance \( =\frac{\text { Speed }}{\text { Time }} \)
B. Distance\( =\frac{\text {Time}}{\text {Speed}} \)
c. Distance\( = \)Speed\( \times \)Time
Distance \( =\frac{1}{\text {Speed } \times \text { Time}} \)


A person bangs on a copper pipe that is part of a large warehouse. The sound
can be heard in the pipe 100.0 meters away in 0.02174 seconds.
If the frequency of the sound is
\( \mathbf{5 0 0 . 0} \boldsymbol{H z}, \) what is the wavelength of the
second wave in the copper pipe?
A. \( 1087 \mathrm{m} \)
в. 0.187 т
c. \( 9.200 m \)
D. \( 0.004348 \mathrm{m} \)
ह. \( 2,300,000 m \)


Which of the following are all radio active elements?
A. Transition elements
B. P block elements
c. Lathanides
D. Actinides


In a YDSE apparatus, if we use while light then :
A. the fringe next to the central will be red
B. the central fringe will be white
c. the fringe next to the central will be violet
D. there will not be a completely dark fringe


Assertion
Presence of green plant is essential for
greenhouse effect.
Reason
Chlorophyll of green plants cause greenhouse effect.
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


Read the following statement (A-E) and
answer the question which follows them.
(A) In liverworts, mosses, and ferns,
gametophytes are free-living
(B) Gymnosperms and some ferns are heterosporous.
(C) Sexual reproduction in Fucus, Volvox, and Albugo is oogamous.
(D) The sporophyte in liverworts is more elaborate than that in mosses.
(E) Both, Pinus and Marchantia are
dioecious.
How many of the above statements are
correct?
A. Two
B. Three
c. Four
D. one


If the acceleration due to gravity g at the earth's surface is \( 9.8 m s^{-2} \) and
mass of the earth is 80 times that of
moon, radius of earth 4 times that of
the moon, the value of \( g \) at the moon's surface will be approximately equal to?
\( \mathbf{A} \cdot 4 m s^{-2} \)
В. \( 1.96 m s^{-2} \)
\( \mathrm{c} \cdot 27 \mathrm{ms}^{-2} \)
D. \( 16 m s^{-2} \)


Aqueous solution of acetic acid
contains:
\( \mathbf{A} \cdot C H_{3} C O O^{-} \) and \( H^{+} \)
B. \( C H_{3} C O O^{-}, H_{3} O^{+} \) and \( C H_{3} C O O H \)
\( \mathbf{c} \cdot C H_{3} C O O^{-}, H_{2} O^{+} \) and \( H^{+} \)
D. \( C H_{3} C O O H, C H_{3} C O O^{-} \) and \( H^{+} \)


On heating coal with conc. Sulphuric acid, we get :
A. \( S O_{3} \)
в. \( C O_{2} \) and \( S O_{2} \)
\( c \cdot N_{2} \)
D. \( C O_{2} \)


A light metal \( \mathrm{M} \) is a good conductor of electricity. It forms a layer when exposed to air, which is an amphoteric
oxide of the formula \( M_{2} O_{3} \). Identify \( M \)
A . ca
в. А।
c. мg
D. Ba


Fill in the blanks
Dynamic Fluid friction is the
sliding friction of solids.
A. heigher than
B. lower than
c. same as
D. higher than or equal to


What are the main characteristic of SI
unit.


An \( n \) sided regular polygon is inscribed
in a circular region of radius \( \boldsymbol{R} \) using a
wire of cross sectional radius \( r \) and
resistivity \( \rho . \) If the magnetic field in the
circular region has a time rate of
change given by \( B \) then the current in
the wire loop at any time is given by
\( ^{\mathbf{A}} \cdot \frac{\pi R B r^{2} \cos (\pi / n)}{2 \rho} \)
\( ^{\mathbf{B}} \cdot \frac{\pi R B r^{2} \cos (\pi / n)}{\sqrt{2} \rho} \)
\( \frac{\pi R B r^{2} \sin (\pi / n)}{2 \rho} \)
D. \( \frac{\pi R B r^{2} \cos (\pi / n)}{3 \rho} \)


The coefficient of \( x^{2} \) in the expansion of
the determinant
\( \left|\begin{array}{ccc}x^{2} & x^{3}+1 & x^{5}+2 \\ x^{3}+3 & x^{2}+x & x^{3}+x^{4} \\ x+4 & x^{3}+x^{4} & 2^{3}\end{array}\right| \) is
A . -10
B. -8
\( c .-2 \)
D. - 6
E.


\( \boldsymbol{H} \boldsymbol{C l}(\boldsymbol{a q})+\boldsymbol{Z n}(\boldsymbol{s}) \rightarrow \boldsymbol{Z n l}_{2}(\boldsymbol{a q})+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \)
In the above reaction \( \boldsymbol{H} \boldsymbol{C l} \) (aq) play a
role as:
A. bronsted acid
B. oxidizing agent
c. reducing agemt
D. precipitate
E. cathode


Solve the following:
\( \frac{2 x-3}{2 x-1}=\frac{3 x-1}{3 x+5} \)
A \( \cdot 1 \frac{2}{3} \)
в. \( 5 \frac{2}{3} \)
\( c \cdot_{7} \frac{2}{3} \)
D. \( 2 \frac{2}{3} \)


Which of the following options is the only CORRECT combination?
A. \( (I I)(i i i)(S) \)
В. \( (I)(i i)(R) \)
c. \( (I I I)(i v)(P) \)
D. \( (I V)(i)(S) \)


Which of the following has extreme resistance to abrasion?
A. Nylon
B. Perlon - L
c. Dacron
D. Both A and B


To clean their spectacles, people often
breathe out on glasses to make then wet. Explain why the glasses become
wet


Explain briefly the cause of Lanthanoid
contraction


A pendulum with a bob hanging is suspended such that the electric field is in upward direction. At equilibrium of the bob, the change in tension in the string will be (assuming rest condition)
A . \( m g \)
в. \( q E \)
\( c \cdot 2 q E \)
D. \( q E / 2 \)


Sara borrowed of \( R s .5,000 \) from the
bank at the rate of \( 10 \% \) for 3 years. She given the amount to Sheela for 3 years
at the rate of \( 12 \% \) per annum. Find out
the profit Sara made from the
transaction.


Equation of a straight line passing through the point (2,3) and inclined at an angle of \( \tan ^{-1}\left(\frac{1}{2}\right) \) with the line \( y+ \) \( 2 x=5 \) is
This question has multiple correct options
\( \mathbf{A} \cdot y=3 \)
B. \( x=2 \)
c. \( 3 x+4 y-18-0 \)
D. \( 4 x+3 y-17=0 \)


In a triangle \( A B C, \) right angled at the
vertex \( A, \) if the position vectors of \( A, B \) and \( C \) are respectively \( 3 \hat{i}+\hat{j}-\hat{k},-\hat{i}+ \) \( \mathbf{3} \hat{\boldsymbol{j}}+\boldsymbol{p} \hat{\boldsymbol{k}} \) and \( \mathbf{5} \hat{\boldsymbol{i}}+\boldsymbol{q} \hat{\boldsymbol{j}}-\boldsymbol{4} \hat{\boldsymbol{k}}, \) then the
point \( (p, q) \) lies on a line:
A. Making an obtuse angle with the positive direction of x-axis
B. Making an acute angle with the positive direction of x axis
c. Parallel to x-axis
D. Parallel to y-axis


\( \alpha \) and \( \beta \) form of sulphur both are stable
at :
\( \mathbf{A} \cdot 369^{0} C \)
B . \( 369 K \)
c. \( 36^{\circ} \mathrm{C} \)
D. \( 69^{\circ} C \)


Mass of a body remains constant anywhere in the universe. State whether
the statement is true or false.
A. True
B. False
c. Either
D. Neither


In the figure shown, the spherical body
and block, each have a mass \( m \). The
moment of inertia of the spherical body
about centre of mass is \( 2 m R^{2} . \) The
spherical body rolls without slipping on the horizontal surface. The ratio of
kinetic energy of the spherical body to that of block is:
\( A \cdot \frac{1}{3} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{2}{3} \)
\( D \)


Pesticides and fertilizers should be
applied on croplands only in limited amounts because it helps in control of
A. soil pollution
B. water pollution
c. thermal pollution
D. all of above


Ratio of solubilities of gases \( N_{2} \& O_{2} \) in water from air at \( 25^{\circ} \) and 1 atm will
be if air is \( 20 \% \) by volume of \( O_{2} \) and \( 80 \% \)
by volume of \( N_{2} \) is:
\[
\begin{array}{c}
\text { Given }: \boldsymbol{K}_{\boldsymbol{H}}\left(\boldsymbol{N}_{\mathbf{2}}\right)=\mathbf{2} \times \mathbf{1 0}^{\mathbf{4}} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m} \\
\boldsymbol{K}_{\boldsymbol{H}}\left(\boldsymbol{O}_{2}\right)=\mathbf{1 0}^{4} \boldsymbol{a} \boldsymbol{t} \boldsymbol{m}
\end{array}
\]
\( A \cdot 8: 1 \)
B. 1: 8
c. 2: 1
D. 1: 2


Calculate the wavelength of \( k_{\alpha} \) line for \( Z=31 \) when \( \alpha=5 \times 10^{7} H z^{1 / 2} \) for a
characteristic X-ray spectrum.
A \( \cdot 1.33 \) a
B. 1.33 nm
c. \( 133 \times 10^{-10} \mathrm{m} \)
D. 133 пт


State Coulomb's law.


If \( \int e^{x}(1+x) \sec ^{2}\left(x e^{x}\right) d x=f(x)+c \)
then \( \boldsymbol{f}(\boldsymbol{x})= \)
A \( \cdot \cos \left(x e^{x}\right) \)
B. \( \sin \left(x e^{x}\right) \)
c. \( 2 \tan ^{-1}(x) \)
D. \( \tan \left(x e^{x}\right) \)


Which statement about enzymes is not
correct?
A. Enzymes are in colloidal state
B. Enzymes are catalysts
c. Enzymes can catalyse any reaction.
D. Urease is an enzyme


Construct a \( \Delta X Y Z \) such that:
\( (\mathrm{i}) \mathrm{XY}=4.5, \angle X=60^{\circ} \) and \( \angle Y=45^{\circ} \)


Evaluate \( \int \frac{x^{3}+1}{x^{2}+1} d x= \)


If a rubber ball is taken down to a \( 100 \mathrm{m} \) deep lake, its volume decreases by \( 0.1 \% \)
If \( \boldsymbol{g}=\mathbf{1 0} \quad \boldsymbol{m} / \boldsymbol{s}^{2} \) then the bulk modulus
of elasticity for rubber, in \( \mathrm{N} / \mathrm{m}^{2} \), is
A \( \cdot 10^{8} \)
B . \( 10^{\text {9 }} \)
c. \( 10^{11} \)
D. \( 10^{10} \)


Write notes on consecutive reactions
with an example.


Which of the following does not play a role in blood coagulation?
\( \mathbf{A} \cdot \) Vitamin \( \mathbf{K} \)
B. Vitamin D
c. calcium ions
D. Fibrinogen


The rsultant power of combination


toppr
Q Type your question_
What minimum force must be applied
on the \( 10 g \) block to keep it on the table?
What will be the tension in the cord
under this condition? What will be the
acceleration of the system and the
tension in the cord when the force is
withdrawn?
\( \left(g=9.8 m s^{-2}\right) \)


A thin metal sheet is being bent by or pounded in to a new shape. The process of being elastic to plastic behaviour is known as
A. Yield
B. Creep
c. welding
D. Tinkering


Assertion
The maximum height of a mountain on earth can be estimated from the elastic
behaviour of rocks.
Reason
At the base of mountain, the pressure is less than elastic limit of earth's
supporting material
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The space above the mercury in a simple barometer is called
A. Torcelian vacuum
B. Newton's vacuum
c. Archimede's vacuum
D. None of these


Deduce an expression for the force on a current carrying conductor placed in a magnetic field.


Find the intersection of \( \boldsymbol{A} \) and \( \boldsymbol{B}, \) and
represent it by Venn diagram:
\( \boldsymbol{A}=\{1,2,4,5\}, B=\{2,5,7,9\} \)


\( X, Y \) are mid-points of opposite sides
\( A B \) and \( D C \) of a parallelogram
\( A B C D . A Y \) and \( D X \) are joined
ntersecting in \( \mathrm{P} ; C X \) and \( B Y \) are
joined intersecting in Q. What is \( \boldsymbol{P X Q Y} \) ?
A. Rectangle
B. Rhombus
C. Parallelogram
Dauare


The primary target organ of aldosterone is :
A. the kidney
B. the pancreas
C. the liver
D. all of the above


\( A, B, C \) are three mutually independent
with probabilities 0.3,0.2 and 0.4 respectively. What is \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B} \cap \boldsymbol{C}) ? \)
A. 0.400
B. 0.240
c. 0.024
D. 0.500


Three blocks are initially placed as shown in the figure. block \( A \) has mass
\( m \) and initial velocity \( v \) to the right.
Block \( B \) with mass \( m \) and block \( C \) with
mass \( 4 m \) are both initially at rest.
Neglect friction. All collisions are
elastic. The final velocity of block \( \boldsymbol{A} \) is :
A. \( 0.6 v \) to the left
B. \( 1.4 v \) to the left
\( c . v \) to the left
D. \( 0.4 v \) to the right


\( \mathbf{2} \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O C H}_{3} \stackrel{d r y H C l}{\rightarrow} \) 'X'. \( \mathbf{X} \) is
A. Mesityl oxide
B. Diacetone alcohol
c. Acetic acid
D. Mesitylene


For metal carbonyls which of the
following is correct?
A. Filled d-orbital of metal axially overlaps with vacant anti-bonding orbitals of \( C O \)
B. Filled d-orbital of metal laterally overlaps with vacant bonding orbitals of \( C O \)
C. Filled d-orbital of metal laterally overlaps with antibonding orbitals of \( C O \)
D. Filled d-orbital of metal laterally overlaps with filled molecular orbitals of \( C O \)


Three equal resistors connected across
a source of e.m.f. together dissipate 10 watt of power. What will be the power dissipated in watts if the same resistors are connected in parallel
across the same source of e.m.f?
A . 10
в. \( \frac{10}{3} \)
\( c . \) 30
D. 90


Deacon's process is used in manufacture of:
A. bleaching powder
B. sulphonic acid
c. nitric acid
D. chlorine


Sulphur is used for vulcanization of rubber to make it:
A. hard
B. elastic
c. malleable
D. soft


Express the following as improper fractions:
\( 10 \frac{3}{5} \)


Iron rusts in presence of air and moisture.
A . True
B. False


\( f(x)=\frac{\sin [x] \pi}{x^{2}+x+1} \) where [.] denotes the
greatest integer function then \( f(x) \) is
A. one - one function
B. one - one and in to function
c. constant fuction
D. onto function


\( a m u=\frac{1}{12} \) the mass of one:
A. \( C-12 \) atom
B. \( N \) atom
\( c . O \) atom
D. \( H \) atom


The direction of velocity of a pendulum bob at the right extreme position is:
A. towards right
B. towards north
c. towards the centre
D. towards left


If in an arithmetic progression pth
terms is \( \frac{1}{q} \) and \( q \) th term is \( \frac{1}{p}, \) then prove
that
\( (p q)^{t h} \) term of arithmetic progression is
1


How will you obtain:
(i) Benzene from phenol
(ii) Ethylamine from Methyl Alcohol
(iii) Ethylene from ethyl alcohol


A's income is \( 20 \% \) less than that of \( \mathrm{B} \) 's.
How much percent is B's income is
more than A's?


An electric current of 2.0 A passes
through a wire of resistance 25 \Omega. How much heat (in joule) will be developed in 1 minute?
\( A \cdot 6 \)
B. 6000
\( c .50 \)
D. 10


Free radical polymerisation requires a
free radical initiator. The most
commonly used free radical initiator is:
\( \mathbf{A} \cdot P h-C O-O-O-C O P h(\text { benzoylperoxide }) \)
B. \( \left(C H_{3}\right)_{3} C-O-O-C\left(C H_{3}\right)_{3} \) (tert-butyl peroxide)
\( \mathbf{c} \cdot P h-N-(N O)-P h(\text { azoxybenzene }) \)
D. \( C H_{2} N_{2} \) (diazomethane)


Short / Long answer type questions. Are plasma membranes the outer
boundaries of all cells? Explain


The area of the tangent cut off from the parabola \( x 2=8 y x 2=8 y \) is:
A . 32
B. 34
c. 36
D. 38


A man travels along a straight line. He covers the first half distance with
constant velocity \( v_{1} \) and the next half
distance with constant velocity \( v_{2} . \) The average velocity of man will be :
A \( \cdot \frac{v_{1}+v_{2}}{2} \)
B. \( v=\frac{2 v_{1} v_{2}}{v_{1}+v_{2}} \)
\( \mathbf{c} \cdot\left(v_{1} v_{2}\right)^{1 / 2} \)
D \( \cdot\left(\frac{v_{2}}{v_{1}}\right)^{1 / 2} \)


The domain of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( (\sqrt{1-\sqrt{1-\sqrt{1-x^{2}}}}) \) is
A . [0,1]
в. [-1,1]
\( c \cdot(-\infty, \infty) \)
D. (-1,1)


The ratio of resistances between \( A \) and
B before and after the switch \( S \) is
closed:
\( \mathbf{A} \cdot 9: 8 \)
B .7: 8
\( c \cdot 2: 3 \)
D. 1: 2


A force of 64 dynes is inclined to the horizontal at an angle of \( 60^{\circ} . \) Find the acceleration in a mass of 8 g, which moves in a horizontal direction.
\( A \cdot 4 \mathrm{cm} \mathrm{s}^{-2} \)
B. \( 2 \mathrm{cm} \mathrm{s}^{-2} \)
\( c \cdot 8 \mathrm{cm} \mathrm{s}^{-2} \)
\( D \cdot 6 \mathrm{cm} \mathrm{s}^{-2} \)


Bands in solids are formed due to a
group of closely spaced
A. conductor bands
B. valance bands
c. energy levels
D. solid bands


9 cartilages among them 3 are paired and 3 are unpaired occurs in
A. Pharynx
B. Larynx
c. Glottis
D. Bronchial tube


\( \operatorname{In} \Delta \mathrm{ABC}, \angle \mathrm{A}=30^{\circ}, \angle \mathrm{B}=40^{\circ} \) and \( \angle \mathrm{C}= \)
\( \mathbf{1 1 0}^{\circ} \)
\( \ln \Delta \mathrm{PQR}, \angle \mathrm{P}=30^{\circ}, \angle \mathrm{Q}=40^{\circ} \) and \( \angle \mathrm{R}= \)
\( \mathbf{1 1 0}^{\circ} \)
A student says that \( \Delta A B C \cong \Delta P Q R \) by
AAA congruence criterion. Is he justified. Is he justified? Why or why
not?


The leakage flux of a toroid is less
because
A. It is asymmetrical
B. It has an open-loop core
c. It is symmetrical.
D. It has a straight core


An aeroplane is moving in a circular path with a speed \( 250 \mathrm{km} / \mathrm{hr} \) in a horizontal plane. The change in magnitude of velocity in half the revolution is:
A. \( 500 \mathrm{km} / \mathrm{hr} \)
B. \( 250 \mathrm{km} / \mathrm{hr} \)
c. \( 125 \mathrm{km} / \mathrm{hr} \)
D.


Determine the probability of 3 successes in a binomial distribution
whose mean and variance are
respectively 2 and 1.5


The ratio of mass of nitrogen and oxygen in nitric oxide is in:
\( A \cdot 7: 16 \)
B. 1: 8
c. 7: 8
D. 7: 15


The maximum frequency of operation of photodiodes is of the order of:
\( \mathbf{A} \cdot 1 k H z \)
в. \( 1 M H z \)
c. \( 1 G H z \)
D. \( 1 T H z \)


Solve the following differential equation
\( \left(\cot ^{-1} y+x\right) d y=\left(1+y^{2}\right) d x \)


f \( x, y, z \) are complex numbers, then \( \Delta= \) \( \left|\begin{array}{ccc}\mathbf{0} & -\boldsymbol{y} & -\boldsymbol{z} \\ \overline{\boldsymbol{y}} & \mathbf{0} & -\boldsymbol{x} \\ \overline{\boldsymbol{z}} & \overline{\boldsymbol{x}} & \boldsymbol{0}\end{array}\right| \) is equal
A. Purely real
B. Purely imaginary
c. complex
D.


Which of the following is true regarding
the working process of weapon?
This question has multiple correct options
A. Energy is released when those neutrons split off from the nucleus
B. splitting the nuclei in the same way, releasing more energy and more neutrons.
C. The splitting of atomic nuclei releases enormous energy
D. None of the above


According to Lewis the ligands are:
A. acidic in nature
B. basic in nature
C. neither acidic nor basic
D. some are acidic and others are basic


'The resistance of any conductor is directly proportional to length and inversely proportional to area of crosssection of the substance" from this is
concluded that
P: Value of resistance increases with
increase in the length of conductor.
Q: Value of resistance decreases with
increases in the length of conductor.
R: Value of resistance decreases with
increase in the area of cross-section.
S: Value of resistance decreases with
decrease in area of cross-section.
A. Statements \( Q \) and \( S \) are true
B. Statements P and S are true
c. Statements P and R are true
D. Statements Q and R are true


Draw a Venn diagram, showing sub-set relations of the following sets. \( \boldsymbol{A}=\{\mathbf{2}, \boldsymbol{4}\} \quad \boldsymbol{B}=\left\{\boldsymbol{x} \mid \boldsymbol{x}=\boldsymbol{2}^{n}, \boldsymbol{n} \leq\right. \)
\( \mathbf{5}, \boldsymbol{n} \in \boldsymbol{N}\} \)
\( C=\{x \mid x \text { is an even natural number } \leq \)
\( \mathbf{1 6}\} \)


The rate of change motion is called
A. speed
B. distance
c. time
D. velocity


Find the median height for the following
data:
Height(cm) \( \quad \begin{array}{ccc}50- & 100- & 150- \\ 100 & 150 & 200\end{array} \)
Number of 2 tuder
A. \( 123.33 \mathrm{cm} \)
в. \( 133.33 \mathrm{cm} \)
c. \( 143.33 \mathrm{cm} \)
D. \( 153.33 \mathrm{cm} \)


If \( z_{1}, z_{2}, z_{3} \) are the solutions of \( z^{2}+ \)
\( \bar{z}=z, \) then \( z_{1}+z_{2}+z_{3} \) is equal to
(where \( z \) is a complex number on the
argand plane and \( i=\sqrt{-1}) \)
\( \mathbf{A} \cdot 2+2 i \)
B . \( 2-2 i \)
c. 0
D. 2


Brine is electrolysed by using inert
electrodes. The reaction at anode is
\( \mathbf{A} \cdot C l_{(a q)}^{-} \rightarrow \frac{1}{2} C l_{2(g)}+e^{-} ; E_{c e l l}^{0}=1.36 V \)
B \( \cdot 2 H_{2} O_{(l)} \rightarrow O_{2(g)}+4 H^{+}+4 e^{-} ; E_{c e l l}^{0}=1.23 V \)
\( \mathbf{C} \cdot N a_{(a q)}^{+}+e^{-} \rightarrow N a_{(s)} ; E_{c e l l}^{0}=2.71 V \)
\( \mathbf{D} \cdot H_{(a q)}^{+}+e^{-} \rightarrow \frac{1}{2} H_{2(g)} ; E_{c e l l}^{0}=0.00 V \)


Write the additive inverse of the
complex number \( 4-3 i \)


Due to its semiconductor properties, the element used in computers, \( T V \), etc. is :
A. carbon
B. silicon
c. bromine
D. fluorine


In the Lewis structure for the \( O F_{2} \)
molecule, the number of lone pairs of electrons around the central oxygen atom is:
A . 1
B. 2
\( c .3 \)
\( D \cdot 4 \)


The mean of five observations is 4 and
their variance is \( 5.2 . \) If three of them are
\( 1,2,6, \) then other two are
A .2,9
B. 4,7
\( c \cdot 5,6 \)
D. 2, 10


When a wave travels in a medium, is transferred from one
place to other with the wave.
A . mass
B. velocity
c. density
D. energy


In YDSE, if \( D \) equals distance of screen
and \( d \) is separation between the slit. The
distance of nearest point to the central maximum where intensity is same as that due to a single slit is equal to
A \( \cdot \frac{D \lambda}{d} \)
в. \( \frac{D \lambda}{2 d} \)
c. \( \frac{D \lambda}{3 d} \)
D. \( \frac{3 D \lambda}{d} \)


In the given figure, \( 2 A P=5 P B \) and
\( 2 C P=5 P D \)
Then, \( \Delta A C P \) and \( \Delta B D P \) are similar.
If the above statement is true then
mention answer as 1 , else mention 0 if
false.


Solve:
\( \frac{20 x}{3}=40 \)


If \( f(x)=x^{3 / 2}(3 x-10), x \geq-0 \) ), then
\( f(x) \) is decreasing in
B. \( (2, \infty) \)
c. \( (-\infty,-1] \cup[1, \infty) \)


Depth from the surface of the earth at which is acceleration due to gravity is \( 25 \% \) of acceleration due to gravity at the
surface
A. \( 1200 \mathrm{km} \)
B. 4000 km
c. \( 3600 \mathrm{km} \)
D. \( 4800 \mathrm{km} \)


Find the angle between \( y-\sqrt{3} x=5 \& \)
\( \sqrt{\mathbf{3}} \boldsymbol{y}-\boldsymbol{x}+\boldsymbol{6}=\mathbf{0} \)


A straight conductor carries a current.
Assume that all free electrons in the
conductor move with the same drift
velocity \( v . A \) and \( B \) are two observers on
a straight line \( X Y \) parallel to the conductor. A is stationary. B moves along XY with a velocity \( v \) in the
direction of the free electrons:
A. A and B observe the same magnetic field
B. A observes a magnetic field, B does not
C. A and B observe magnetic fields of the same magnitude but opposite directions
D. A and B do not observe any electric field


Which among the following is associated with iron sulphide?
A. Element
B. Mixture
c. compound
D. None of these


The liquid non-metal belongs to which
group number?
A . 15
B. 16
c. 17
D. 18


Choose the correct statement about the
industrial preparation of hydrogen from
water gas \( \left(C O+H_{2}\right) \)
\( \mathbf{A} \cdot H_{2} \) is removed through occlussion with \( P d \)
B. \( C O \) and \( H_{2} \) are fractionally separated using differences in their densities
C. \( C O \) is removed by absorption in \( a q . C u_{2} C l_{2} \) solution
D. \( C O \) is oxidised to \( C O_{2} \) with steam in the presence of a
catalyst followed by absorption of \( C O_{2} \) in alkali


Find the Lactus Rectum of \( 9 y^{2}- \)
\( 4 x^{2}=36 \)
\( \mathbf{A} \cdot \mathbf{9} \)
B. 6
c. 11
D. 15


If the area of a triangle is 81 square \( \mathrm{cm} \) and its perimeters is \( 27 \mathrm{cm} \), them its in
radius is
A. \( 6 \mathrm{cm} \)
B. 3 \( \mathrm{cm} \)
c. \( 1.5 \mathrm{cm} \)
D. none of these


Mayonnaise represents?
A . a sol
B. an aerosol
\( c . \) a foam
D. an emulsion


Which one of the following statements is true for the velocity v and the acceleration a of a particle executing simple harmonic motion?
A. When v is maximum, a is zero
B. When v vis zero, a is zero
c. When v is maximum, a is maximum
D. Value of a is zero, whatever may be the value of \( v \)


Which of the following contributes most to transport of water from the ground to the leaves of a tall tree?
A. Breakdown of ATP
B. Cohesion of water and transpiration pull
c. Root pressure
D. Capillary rise of water in xylem


\( S I \) units of momentum is
A \( \cdot k g m / s^{2} \)
в. \( k g m / s \)
\( \mathbf{c} \cdot g k m / h r \)
D. \( k g k m / h r \)


\( I \) is the moment of inertia of a thin
circular plate about an axis of rotation perpendicular to the plane of plate and
passing through its centre. The moment of inertia of same plate about an axis passing through its diameter is :
\( \mathbf{A} \cdot 2 I \)
B. \( \sqrt{2} I \)
c. \( \frac{I}{\sqrt{2}} \)
D. \( \frac{1}{2} \)


Which of the following frequency of sound can be heard by a dog but not by a man?
A. 50,000 hertz
B. 15,000 hertz
c. 4200 ohertz
D. none


If \( \operatorname{lines} x-2 y+3=0,3 x+k y+7= \)
0 cut the coordinate axes in concyclic
points, then \( k=? \)
\( \mathbf{A} \cdot 3 / 2 \)
B. \( 1 / 2 \)
c. \( -3 / 2 \)
D. -4


A bullet fired into a fixed target loses half of its velocity after penetrating \( 3 \mathrm{cm} \) How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
\( \mathbf{A} .3 .0 \mathrm{cm} \)
B. \( 2.0 \mathrm{cm} \)
c. \( 1.5 \mathrm{cm} \)
D. \( 1.0 \mathrm{cm} \)


Which of the following is the most
accurate measurement?
\( A \cdot 9 m \)
B. 9.0 \( m \)
c. \( 9.00 \mathrm{m} \)
D. \( 9.000 \mathrm{m} \)


If \( R \) is the relation 'less than' from \( A= \)
\{1,2,3,4,5\} to \( B=\{1,4\}, \) the set of
ordered pairs corresponding to \( R \), then the inverse of \( \boldsymbol{R} \) is
A \( \cdot\{(3,1),(3,2),(3,3)\} \)
в. \{(4,1),(4,2),(4,3)\}
c. \{(4,3),(4,4),(4,5)\}
D. \{(1,3),(2,4),(3,5)\}


What is the heat of reaction for the
above reaction given the heat of
formation, \( \Delta \boldsymbol{H}_{f} \) of \( \boldsymbol{N} \boldsymbol{O}_{2}(\boldsymbol{g}) \) is
\( 34 k J / \) mole and \( N_{2} O_{4}(g) \) is
\( 10 k J / \) mole?
A. \( -58 k J \)
\( J \)
в. \( -48 k J \)
c. \( 10 k J \)
D. \( 48 k J \)
E . \( 78 k J \)


Four different circuit components are
given in each situation of List 1 and al the components are connected across
an ac source of same angular frequency \( \omega=200 \mathrm{rad} s^{-1} . \) The information of
phase difference between the current
source voltage in each situation of List 1 is given in List \( 2 . \) Match the circuit components in List 1 with the corresponding List 2


The passengers in a boat are not allowed to stand because:
A. This will raise the centre of gravity and the boat will be rocked
B. This will lower centre of gravity and the boat will rocked
c. The effective weight of system increases
D. of surface tension effects


A vessel is filled with an ideal gas at a
pressure of 10 atmospheres and temp \( 27^{\circ} \)
C. Half of the mass of the gas is removed from the vessel \& the temp. of the remaining gas is increased to \( 87^{0} \mathrm{C} \). Then
the pressure of the gas in the vessel will be
\( A \cdot 5 \) atm
B. 6 atm
c. 7 atm
\( D \cdot 8 \operatorname{atm} \)


If there were only one type of charge in
the universe, then
\( \mathbf{A} \cdot \oint_{s} \vec{E} \cdot d \vec{s} \neq 0 \) on any surface
B \( \cdot \oint_{s} \vec{E} \cdot d \vec{s}=0 \) if the charge is outside the surface
C \( \cdot \oint_{s} \vec{E} \cdot d \vec{s}=\frac{q}{\varepsilon_{0}} \) if charges of magnitude \( q \) were inside the surface
D. both (b) and (c) are correct


Find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}: \)
\( \sin \boldsymbol{x}-\boldsymbol{3} \boldsymbol{x}=\mathbf{5} \boldsymbol{y} \)


Two radio stations broadcast their
programmes at the same amplitude \( \boldsymbol{A} \)
and at slightly different frequencies \( \omega_{1} \)
and \( \omega_{2} \) respectively where \( \omega_{1}-\omega_{2}= \)
1 \( k H z . \) A detector receives the signals
from the two stations simultaneously. It can only detect signals of intensity \( > \) \( 2 A^{2} . \) Find the interval between
successive maxima of the intensity of the signal received by the detector.
A \( \cdot 2 \times 10^{-3} s \)
B. \( 4 \times 10^{-3} s \)
c. \( 1.5 \times 10^{-3} s \)
D. \( 10^{-3} s \)


The process during which a liquid on heating changes to vapour state is called boiling.
A. True
B. False


Write the electronic configuration of
Sr \( ^{2+} \) in absence of Aufbau Principle.
\( \mathbf{A} \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{5} 4 d^{1} \)
B. \( 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{3} 4 d^{3} \)
C \( \cdot 1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6} 3 d^{10}, 4 s^{2} 4 p^{6} \)
D. None of these


Give the functions of Iymph?
Differentiate between blood and lymph.


Explain the sex determination in human beings.


The electric potential inside a conductor:
A . is zero
B. increases with distance from center
c. is constant
D. decreases with distance from center


Keplers second law regarding constancy of aerial velocity of a planet is a consequence of the law of conservation
of:
A. Linear momentum
B. Angular momentum
c. energy
D. none of the above


A change of \( 200 m V \) in base-emitter
voltage causes a change of \( 100 \mu A \) in
the base current. The input resistance of the transistor is
\( \mathbf{A} \cdot 2 K \Omega \)
в. \( 2 \Omega \)
c. \( 2 m \Omega \)
D. 10 K\Omega


If piano tuner wants to correct the sound of a string which plays at a lower pitch, What should he do?
A. Tighten the string to make the fundamental frequency higher
B. Tighten the string to make the fundamental frequency lower
C. Loosen the string to make the fundamental frequency higher
D. Loosen the string to make the fundamental frequency lower
E. Find a harmonic closer to the desired pitch


A polar bear can survive in polar regions because thick fur and padded feet.
A. True
B. False


If by radiation all nitrogenase enzyme are inactivated, then there will be no
A. Conversion from ammonium to nitrate in soil
B. Fixation of nitrogen by legumes
c. conversion from nitrate to nitrite in legumes.
D. None of the above


Write a short note on digestion of fats in human body.


Rainbow is an example for continuous
spectrum. Explain.


For what value of \( x \) the matrix \( A \) is
singular? \( \boldsymbol{A}=\left[\begin{array}{ll}1+x & 7 \\ 3-x & 8\end{array}\right] \)


Assertion
The mass number of hydrogen is equal
to its atomic number.
Reason
H-atom has no neutrons.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.
C. Assertion is correct, but Reason is incorrect.
D. Assertion is incorrect, but Reason is correct.


The means of five observations is 4 and
their variance is \( 5.2 . \) If three of these
observation are \( 1,2, \) and \( 6, \) then the
other two are
A .2 and 9
B. 3 and 8
c. 4 and 7
D. 5 and 6


What is a cell?


Let a star be much brighter than our
sun but its mass is same as that of sun
If our earth has average life span of a man as 70 years, then on earth like
planet of this star system at double the distance between our earth and sun will
have an average life span of a man as
A. 25 planet years
B. 20 planet years
c. 70 planet years
D. 15 planet years


\( \ln \Psi_{321} \) the sum of angular momentum, spherical nodes and angular mode is:
A \( \cdot \frac{\sqrt{6 h}+4 \pi}{2 \pi} \)
в. \( \frac{\sqrt{6 h}}{2 \pi}+3 \)
c. \( \frac{\sqrt{6 h}+2 \pi}{2 \pi} \)
D. \( \frac{\sqrt{6 h}+8 \pi}{2 \pi} \)


A neutron travelling with a velocity \( v \) and kinetic energy E collides perfectly elastically head on with the nucleus of an atom of mass number \( A \) at rest. The
fraction of total energy retained by the neutron is:
\( ^{A} \cdot\left(\frac{A-1}{A+1}\right)^{2} \)
\( ^{\text {B. }}\left(\frac{A+1}{A-1}\right)^{2} \)
\( ^{c}\left(\frac{A-1}{A}\right)^{2} \)
\( ^{\mathrm{D}}\left(\frac{A+1}{A}\right)^{2} \)


\( \triangle L T R \sim \triangle H Y D, \triangle H Y D \) is such
that \( \boldsymbol{H} \boldsymbol{Y}=\mathbf{7 . 2} \boldsymbol{c m}, \boldsymbol{Y} \boldsymbol{D}=\boldsymbol{6} \boldsymbol{c m}, \angle \boldsymbol{Y}= \)
\( 40^{\circ} \) and \( \frac{L R}{H D}=\frac{5}{6} \) and construct
\( \triangle \boldsymbol{L} \boldsymbol{T} \boldsymbol{R} \)


Which of the following is the tallest tree of the world?
A. Eucalyptus regnans
B. Sequoia sempervirens
c. Pinus logifolia
D. Pinus roxburgii


Nitrogen can exhibit +1 oxidation state
A. True
B. False


Across the depletion region, there is a
barrier potential which
A. prevents the movement of electron from the n region into the p region
B. prevents the movement of electron from the p region into the n region
C. prevents the movement of holes from the n region into the p region
D. prevents the movement of holes from the p region into the n region


The energy of an electron in the first Bohr orbit of H atom is -13.6 eV. The
possible energy value of the excited state for the electron in Bohr orbits of
hydrogen is:
A. -3.4 eV
B. 4.2 eV
\( \mathbf{c} .-6.8 \mathrm{eV} \)
D. \( +6.8 \mathrm{eV} \)


Find the domain and range of the
relation
\( \boldsymbol{R}=\{(-\mathbf{1}, \mathbf{1}),(\mathbf{1}, \mathbf{1}),(-\mathbf{2}, \mathbf{4}),(\mathbf{2}, \mathbf{4})\} \)


The recoil speed of a hydrogen atom after it emits a photon in going from \( \boldsymbol{n}=\mathbf{5} \) state to \( \boldsymbol{n}=\mathbf{1} \) state is
\( \mathbf{A} \cdot 4.718 \mathrm{m} \mathrm{s}^{-1} \)
B. \( 7.418 \mathrm{m} \mathrm{s}^{-1} \)
c. \( 4.178 \mathrm{m} \mathrm{s}^{-1} \)
D. \( 7.148 \mathrm{m} \mathrm{s}^{-1} \)


Newton used the phrase 'quantity of motion' for
A. Momentum
B. Force
c. Acceleration due to gravity
D. None of these


The population of city was 200000 in year \( 1997 . \) It increased at the rate of \( 5 \% \)
p.a.Find the population at the end of the year 2000


The length of side of a square coil is 50 \( \mathrm{cm} \) and number of turns in it is \( 100 . \) If it
is placed at right angles to a magnetic field which is changing at the rate of 4 Tesla/s, then induced emf in the coil will
be:
A . \( 0.1 \mathrm{v} \)
B. 1.0
\( c \cdot 10 v \)
D. 100


Write the general electronic configuration of \( f \) -block elements.


A straight wire of length 0.5 metre and carrying a current of 1.2 ampere is placed in a uniform magnetic field of induction 2 tesla. If the magnetic field is perpendicular to the length of the
wire, the force acting on the wire is:
A. 2.4
B. 1.2 N
c. 3.0 N
D. 2.0 N


Find
\( \int_{0}^{1 / 4 \pi} \ln (1+\tan x) d x \)


If \( \forall \boldsymbol{m} \in \boldsymbol{N}, \) then \( \mathbf{1 1}^{m+2}+\mathbf{1 2}^{2 m-1} \) is
divisible by
A . 121
B. 132
c. 133
D. None of these


Match the columns and choose the
correct option.


An arboretum is a place for growing flowers, fruits or vegetables.
A. True
B. False


If the agar block in \( \mathrm{B} \) was placed in the center of coleoptile (not sideways) what
would have been the result?
A. Grow straight up or symmetrical growth
B. Grow downwards
\( c . \) Both (A) and (B)
Done of the above


A gas is compressed from a volume of
\( 2 m^{3} \) to a volume of \( 1 m^{3} \) at a constant
pressure of \( 100 N / m^{2} . \) Then it is heated at constant volume by supplying \( 150 J \)
of energy. As a result, the internal
energy of the gas:
A. Increases by \( 250 \mathrm{J} \)
B. Decreases by 250 J
c. Increases by \( 50 \mathrm{J} \)
D. Decreases by \( 50 \mathrm{J} \)


How many bonds are there in
\( \mathbf{A} \cdot 14 \sigma, 8 \pi \)
B. \( 18 \sigma, 8 \pi \)
\( \mathbf{c} \cdot 19 \sigma, 4 \pi \)
D. \( 14 \sigma, 2 \pi \)


Which of the following statement is
incorrect?
A. The most electronegative element is fluorine
B. Alkali metals generally have negative value of electron gain enthalpy
C. The oxidation number of \( \sin N a_{2} S_{4} O_{6} \) is greater than
in the case of \( N a_{2} S_{2} O_{3} \)
D. The electronegativity values for \( 2 p \) series elements is less than that for \( 3 p \) series elements on account of small size and high inter electronic repulsion


State whether given statement is True or False.

You fall in the forward direction when a
moving bus applies brakes to stop, and fall backward when it accelerates from
rest.
A. True
B. False


Identify the correct order of reactivity
in electrophillic substitution reactions
of the following compounds:
A. \( 1>2>3>4 \)
\( \mathbf{B} \cdot 4>3>2>1 \)
\( \mathbf{c} \cdot 2>1>3>4 \)
D. \( 2>3>1>4 \)


Construct an equilateral triangle. \( \Delta A B C . \) Construct an angle bisector of
\( \angle A \)
Let it meet side \( B C \) at \( D \). Find measures
of \( A B, A C, B D, D C \)
Find the relation between \( \frac{A B}{A C} \) and \( \frac{B D}{D C} \)
\( \mathbf{A} \cdot \frac{A B}{A C}<\frac{B D}{D C} \)
В. \( \frac{A B}{A C}>\frac{B D}{D C} \)
C \( \cdot \frac{A B}{A C}=\frac{B D}{D C} \)
D. None


Which of the following is correct?
A. Legumes fix nitrogen through bacteria in their leaves.
B. Legumes fix nitrogen through bacteria in their roots.
C. Legumes fix nitrogen independent of bacteria.
D. Legumes do not fix nitrogen.


In the given figure, \( A M \perp B C \) and \( A N \)
is the bisector of \( \angle A \). Then \( \angle M A N \) is
A \( \cdot 32 \frac{1}{2} \)
B . \( 16 \frac{1}{2} \)
\( c \cdot 16^{0} \)
\( D \cdot 32^{0} \)


The most reactive towards \( S_{N} 1 \) is:
A \( \cdot P h C H_{2} C l \)
в. \( P h C l \)
\( \mathbf{c} \cdot \operatorname{Ph} C H C l\left(C H_{3}\right) \)
D. \( p-N O_{2} C_{6} H_{4} C H_{2} C l \)


Assertion
Work done during free expansion of an ideal gas whether reversible or irreversible is positive.
Reason
During free expansion, external pressure is always less than the pressure of the system.
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


Dual behaviour of the matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other types of material. If the velocity of the electrons in this
microscope is \( 1.6 \times 10^{6} m s^{-1} \)
calculate de Broglie wavelength associated with this electron.
A. 325 pm
B. 455 pm
C. \( 474 \mathrm{pm} \)
D. 526 pm


The concentration of a solution can be
expressed in molarity, normality, formality and molality. Among them, which mode of expression is the most accurate for the all conditions?
A. Molarity
B. Formality
c. Normality
D. Molality


n the figure, \( l \| \boldsymbol{m} \) and \( \boldsymbol{n} \| \boldsymbol{p} \). If \( \angle \mathbf{1}=\mathbf{6 0}^{\circ} \)
then \( \angle 2=3 \times \angle 1 \)
4 . True
3. False


A water film is formed on a glass-block. A light ray is incident on water film from air at an angle of \( 60^{\circ} \) with the normal. The angle of incidence on glass slab is \( \left(\mu_{g}=1.5, \mu_{w}=\frac{4}{3}\right) \)
A \( \cdot \sin ^{-1}\left(\frac{3 \sqrt{3}}{8}\right) \)
в. \( \sin ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
c. \( \sin ^{-1}\left(\frac{4 \sqrt{3}}{9}\right) \)
D. \( \sin ^{-1}\left(\frac{9 \sqrt{3}}{16}\right) \)


The sides of two squares are \( x \) and \( y \)
respectively, such that \( y=x+x^{2} \). The
rate of change of area of second square with respect to area of first square is
A. \( x^{2}+3 x-1 \)
B . \( 2 x^{2}-3 x+1 \)
c. \( 2 x^{2}+3 x+1 \)
D. \( 1+2 x \)


Calculate the coefficient of variation
(C.V.) of the following data:
40,36,64,48,52


\( \mathrm{C} 6 \mathrm{H} 1206+602 \rightarrow 6 \mathrm{CO} 2+6 \mathrm{H} 2 \mathrm{O}+\mathrm{ATP} \)
The given equation indicates which of the following activities in plants?
A. Digestion
B. Respiration
c. Transpiration
D. None of the above


Bryophytes are of
A. Great economic value
B. No value at all
C . Great ecological importance
D. A lot of aesthetic value


A cart begins from rest at the top of a long incline and rolls with a constant
acceleration of \( 2 m / s^{2} . \) How far has the
cart moved along the incline after
rolling for 3 seconds?
A. 3 meters
B. 6 meters
c. 9 meters
D. 18 meters


Which of the following is used in paint removing?
A. \( C H C l_{3} \)
в. \( C H_{2} C l_{2} \)
c. \( C C l_{4} \)
D. \( C H_{3} C l \)


f \( \boldsymbol{f}: \boldsymbol{x} \rightarrow \boldsymbol{p}+\boldsymbol{q} \boldsymbol{x}, \boldsymbol{f}^{-1}(\boldsymbol{9})=(-1) \) and
\( \boldsymbol{f}(\mathbf{3})=(-11) . \) find the value of \( \boldsymbol{p} \) and \( \boldsymbol{q} \)


If \( \boldsymbol{A}=\{1,2,3\} \) and \( \boldsymbol{B}=\{3,8\}, \) then
\( (\boldsymbol{A} \cup \boldsymbol{B}) \times(\boldsymbol{A} \cap \boldsymbol{B}) \) is
A \( \cdot\{(3,1),(3,2),(3,3),(3,8)\} \)
в. \{(1,3),(2,3),(3,3),(8,3)\}
\( c \cdot\{(1,2),(2,2),(3,3),(8,8)\} \)
D. \{(8,3),(8,2),(8,1),(8,8)\}


Noble gases does show inert behaviour because?
A. They are mono atomic
B. They are found in abundance
C. The size of their atom is very small
D. They are completely paired up and have stable electrons shells


In Youngs double slit experiment, the fringes are displaced by a distance \( x \)
when a glass plate of one refractive index 1.5 is introduced in the path of one of the beams. When this plate in replaced by another plate of the same thickness, the shift of fringes is \( (3 / 2) x \) The refractive index of the second plate
is
A . 1.75
в. 1.50
c. 1.25
D. 1.00


The resistance of a wire at room
temperature \( 30^{\circ} \mathrm{C} \) is found to be \( 10 \Omega \)
Now to increase the resistance by \( 10 \% \) the temperature of the wire must be [The temperature coefficient of resistance of the material of the wire is
\( \left.\mathbf{0 . 0 0 2} \text { per }^{\circ} \boldsymbol{C}\right] \)
A \( \cdot 36^{\circ} \mathrm{C} \)
в. \( 83^{\circ} \) С
\( \mathbf{c} \cdot 63^{\circ} C \)
D. \( 33^{\circ} \mathrm{C} \)


Factorise \( \boldsymbol{x} \boldsymbol{y}\left(\boldsymbol{z}^{2}+\mathbf{1}\right)+\boldsymbol{z}\left(\boldsymbol{x}^{2}+\boldsymbol{y}^{2}\right) \)
A \( .(x y+z)(y z+x) \)
B. \( (z x+y)(x y+z) \)
c. \( (y z+x)(z x+y) \)
D. \( \left(x^{2}+y^{2}\right)(z+x) \)


Some substances completely disappear
or dissolve in water. We say that these substances are in water.
A . immiscible
B. soluble
c. insoluble
D. none of the above


Write the measure of supplementary angle of the given angles:
\( \mathbf{1 0 0}^{\circ} \)


A invests with B some rupees and B
invested Rs \( 25,000 . \) After 4 months \( A \) increase his investment with Rs 6000 . If
at the end of the year \( A \) and \( B \) have \( a \) profit of Rs 2400 and Rs 2500
respectively, find the sum invested by A


If \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{2} \\ \mathbf{3} & \mathbf{4}\end{array}\right], \) then find \( \boldsymbol{A}+\boldsymbol{A}^{\boldsymbol{T}} \)


The figure shows the elliptical orbit of a
planet \( P \) about the sun S. The shaded
area SCD is a twice shaded area SAB. if
\( t_{1} \) is the the time for the planet to move
from \( C \) to \( D \) and \( t_{2} \) is the time to move
from \( A \) to \( B \), then
A \( \cdot t_{1}=t_{2} \)
\( \mathbf{B} \cdot t_{1}=2 t_{2} \)
\( \mathbf{c} \cdot t_{1}=4 t_{2} \)
\( \mathbf{D} \cdot t_{1}>t_{2} \)


Skin is said to play an important role in
excretion, due to the presence of
A. Sweat glands
B. Sebaceous glands
c. Hair follicles
D. Hair cells
E. Both A and B


Balance the following reaction:
\( M n O_{4}^{-}+C N^{-}+H_{2} O \rightarrow M n O_{2}+ \)
\( \boldsymbol{C N O}^{-}+\boldsymbol{O H}^{-} \)


For the reaction: \( \boldsymbol{H}_{2}+\boldsymbol{C l}_{2} \stackrel{\text {sunlight}}{\longrightarrow} \mathbf{2} \boldsymbol{H} \boldsymbol{C l} \)
the order of reaction is :
\( \mathbf{A} \cdot \mathbf{0} \)
B. 2
c. 1
D. 3


Integrate \( \int_{0}^{\pi} \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x \)
\( A \cdot \frac{\pi}{12} \)
\( B \cdot \frac{\pi}{3} \)
\( \mathbf{C} \cdot \frac{\pi}{4} \)
D. \( \frac{\pi}{2} \)


Find the mean deviation about the
mean for the data in
\( \mathbf{1 5} \quad \mathbf{2 0} \) \( \boldsymbol{x}_{i} \quad \boldsymbol{5} \quad \mathbf{1 0} \)
3 \( \begin{array}{llll}f_{i} & 7 & 4 & 6\end{array} \)


How can you make a flame thrower with
orange?


If \( n \) is any positive integer, then the value of \( \frac{i^{4 n+1}-i^{4 n-1}}{2} \) equals:
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot i \)
D. \( -i \)


What are blended fibres?
A. Mixture of two natural fibres
B. Mixture of two synthetic fibre
C. Mixture of natural and synthetic fibres
D. All of above


A particle executes simple harmonic
motion with a frequency \( f \). The frequency with which the potential energy oscillates is:
\( A \cdot f \)
B. \( \frac{f}{2} \)
c. \( 2 f \)
D. zero


The proteins associated with nucleic acids are
A. Scleroproteins
B. Albumins
c. Histones
D. Globulins
E. Lipoproteins


A radioactive sample contains \( 2.3 \mathrm{mg} \) of pure \( _{6}^{11} C \) which has half-life period of
1224 second. Calculate
i) the number of atoms present initially
ii) the activity when \( 5 \mu g \) of the sample
will be left.


Complete and rewrite the balanced
chemical equation. Chlorobenzene \( _{43.4, \text { pressure }}^{N a C N+C u C N} ? \)


The stage during which the body becomes capable of reproduction is called
A. menstruation
B. puberty
c. menopause
D. adulthood


Enhancement mode is used in
A. MOSFET
в. JFET
\( \mathrm{c} . \) FET
D. None of the above


Why can dust be removed from a carpet by shaking it, or by beating it with a stick?
A. Because of inertia of rest
B. Because of inertia of motion
c. Because of inertia of direction
D. Because of momentum


Define reaction quotient (Q)


Which theory of light proposed the presence of ether medium for propogation of light?


A body falls freely for 10 sec. Its average
velocity during this journey (take \( \boldsymbol{g}= \)
\( \left.10 m s^{-2}\right) \)
A \( .100 m s^{-1} \)
B. \( 10 m s^{-1} \)
\( \mathrm{c} \cdot 50 \mathrm{ms}^{-1} \)
D. \( 5 m s^{-1} \)


Find the polynomial which represents the perimeter of the rectangle whose length is 2 more than its breadth.


Which of the following is not a neutral oxide?
A. \( C O \)
в. \( N_{2} \),
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2} \)


Complete the following acid-base
reactions and name the products:
(i) \( C H_{3} C H_{2} C H_{2} N H_{2}+H C l \rightarrow \)
\( (\mathrm{ii})\left(C_{2} H_{5}\right) N+H C l \rightarrow \)


The catcher prepares to receive a pitch from the pitcher. As the ball reaches and makes contact with his glove, the catcher pulls his hand backward. This action reduces the impact of the ball on the catcher's hand because:
A. The energy absorbed by his hand is reduced
B. The momentum of the pitch is reduced
c. The time of impact is increased
D. The time of impact is reduced
E. The force exerted on his hand remains the same


Bredig's arc method involves:
A. dispersion
B. condensation
c. peptization
D. dispersion and condensation both


Balance the following ionic equations
(i) \( \boldsymbol{C} \boldsymbol{r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-}+\boldsymbol{H}^{+}+\boldsymbol{I}^{-} \rightarrow \boldsymbol{C} \boldsymbol{r}^{\boldsymbol{3}+}+ \)
\( \boldsymbol{I}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)
(ii) \( \boldsymbol{C r}_{2} \boldsymbol{O}_{\mathbf{7}}^{2-}+\boldsymbol{F} \boldsymbol{e}_{2}^{+}+\boldsymbol{H}^{+} \rightarrow \boldsymbol{C r}^{3+}+ \)
\( \boldsymbol{F} \boldsymbol{e}^{\boldsymbol{3}+}+\boldsymbol{H}_{2} \boldsymbol{O} \)
(iii) \( M n O^{4-}+S O_{3}^{2-}+H^{+} \rightarrow \)
\( M n^{2+}+S O_{4}^{2-}+H_{2} O \)
(iv) \( M n O^{4-}+H^{+}+B r^{-} \rightarrow M n^{2+}+ \)
\( \boldsymbol{B} \boldsymbol{r}_{2}+\boldsymbol{H}_{2} \boldsymbol{O} \)


\( \{(x, y): x \text { is a person,y is the mother of } x\} \) It is both injective and surjective. If true enter 1 else 0


Carbon-12 atom has:
A. 6 electrons, 6 protons, 6 neutrons
B. 6 electrons, 12 protons, 6 neutrons
C .12 electrons, 6 protons, 6 neutrons
D. 18 electrons, 6 protons, 6 neutrons


A particle is thrown vertically upwards with a velocity of \( 4 m s^{-1} . \) The ratio of
its accelerations after \( 1 s \) and \( 2 s \) of its
motion is
A . 2
B. 9.8
c.
D. 4.9


A object starts from rest at \( t=0 \) and
accelerates at a rate given by \( a=6 t \)
What is its displacement at any time \( t ? \)
A \( \cdot t^{2} \)
в. \( t^{3} \)
\( c \cdot 3 t^{2} \)
D. \( 3 t^{3} \)


How many valence electrons are present in Eka - aluminium?
A.
B. 2
\( c \cdot 3 \)
\( D \)


A plane progressive wave of frequency \( 25 H z, \) amplitude \( 2.5 \times 10^{-5} m \) and
initial phase zero moves along the negative x-direction with a velocity of
\( 300 m s^{-1} . A \) and \( B \) are two points \( 6 m \)
a part on the line of propagation of the wave. At any instant the phase difference between \( A \) and \( B \) is \( \Theta \). The
maximum difference the displacement of the particles at \( A \) and \( B \) is \( \Delta, \) then This question has multiple correct options
\( \mathbf{A} \cdot \Theta=\pi \)
B \( \cdot \Theta=0 \)
c. \( \Delta=0 \)
D. \( \Delta=5 \times 10^{-5} m \)


Plots of p versus \( 1 / V \) at different
temperatures.
Fige
11. Plots of \( p \) versus \( 1 / V \) at different temperatures.


Find the value of
\( \lim _{x \rightarrow 3} \frac{\sqrt{16 x^{2}+112}-16}{3 x^{2}-15 x+18} \)


If \( x \) and \( y \) are positive and \( x y>1 \), then
what is \( \tan ^{-1} x+\tan ^{-1} y \) equal to?
A \( \cdot \tan ^{-1}\left(\frac{x+y}{1-x y}\right) \)
в. \( \pi+\tan ^{-1}\left(\frac{x+y}{1-x y}\right) \)
c. \( \pi-\tan ^{-1}\left(\frac{x+y}{1-x y}\right) \)
D. \( \tan ^{-1}\left(\frac{x-y}{1+x y}\right) \)


Find the roots of equation \( x^{2}-3 x- \)
\( \mathbf{1 0}=\mathbf{0} \)


The rate of change of displacement with time is
A. Speedd
B. Acceleration
c. Retardation
D. Velocity


In the adjoining figure, D is a point on
the side BC of \( \Delta A B C \) such that
\( \angle A D C=\angle B A C \) Then \( \frac{C A}{C D}=\frac{C B}{C A} \)
A. True
B. False


Beetroot is pinkish-red in color which is
due to
A. Chlorophyll
B. Betanin
c. cartenoids
D. Heamocyanine


The 35 kilogram girl is standing on a 20 kilogram wagon and jumps off, giving the wagon a kick that sends it off at 3.8
meters per second. How fast is the girl moving?
\( A \cdot 1.2 \mathrm{m} / \mathrm{s} \)
B. 3 \( \mathrm{m} / \mathrm{s} \)
\( c \cdot 4 m / s \)
D. 2.2 m/s


A bag contains 5 white, 7 red and 3
black balls. If a ball is chosen at
random, then find the probability that it
is not red.


Plot the points (0,0)(0,3)(3,4)(4,0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle.


The angle of incidence is equal to angle
of reflection.
A . True
B. False


Find the square root of 13.31 using long
division method.


The absolute zero is the temperature at which:
A. all substances exist is solid state
B. molecular motion ceases
c. water freezes
D. none of these


The speed of boat is \( 5 \mathrm{Km} / \mathrm{h} \) in still water. It crosses a river of width \( 1 \mathrm{Km} \) along shortest possible path in 15 min. The velocity of river water is
\( A \cdot 1 K m / h \)
в. 3 Кт/А
\( c .4 \mathrm{km} / \mathrm{h} \)
D. \( 5 \mathrm{Km} / \mathrm{h} \)


Mangal is the Indian name of the
A. Earth
B. Mars
c. Uranus
D. Pluto


Thermal capacity=


Find the perimeter of a rectangular hall, if its length exceeds its breadth by \( 7 \mathrm{m} \)
and the area of the hall is \( 228 m^{2} \)
A. 72 m
в. \( 70 \mathrm{m} \)
\( c .64 \mathrm{m} \)
D. \( 62 \mathrm{m} \)


Pick out the correct statement for
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{6}: \)
A . \( X e F_{6} \) is hydrolysed partially to form \( X e O F_{4} \)
B. It react with \( S i O_{2} \) to form \( X e O F_{4} \)
C. on complete hydrolysis, it forms \( X e O_{3} \)
D. All of the ablove


Atomic number of Radium is:
\( A \cdot 84 \)
B. 88
\( c \cdot 86 \)
D. 76


\( \ln C_{3} \) plants, the first stable product of photosynthesis during the dark reaction is
A. Malic acid
B. Oxaloacetic acid
c. 3- Phosphoglyceric acid
D. Phosphoglyceraldehyde


Which component present in blue-green
algae?
This question has multiple correct options
A. Cyanocobalamin
B. Phycocyanin
c. chlorophyll
D. Cartenoids


Which is not a correct order of energy
for 1 st, 2 nd and 3 rd orbit?
\( \mathbf{A} \cdot E_{1}>E_{2}>E_{3} \)
\( \mathbf{B} \cdot(P E)_{1}<(P E)_{2}<(P E)_{3} \)
\( \mathbf{C} \cdot(K E)_{1}>(K E)_{2}>(K E)_{3} \)
D. A and C both


\( \int(x+5)^{3} d x . \) Integrate this using fundamental properties of indefinite integral.


Differentiate \( \boldsymbol{y}=\sin ^{-1}\left(\frac{\mathbf{2}^{x+1} \mathbf{3}^{x}}{1+\mathbf{3 6}^{x}}\right) \)


Evaluate \( \int \frac{\boldsymbol{x}+\mathbf{9}}{(\boldsymbol{x}+\mathbf{1 0})^{2}} \boldsymbol{e}^{x} \boldsymbol{d} \boldsymbol{x}= \)
A \( \cdot \quad e^{x} \frac{1}{x+9}+c \)
B \( \cdot e^{x} \frac{1}{x+10}+c \)
c. \( \quad e^{x} \frac{1}{(x+9)^{2}}+c \)
D. \( e^{x}+c \frac{1}{(x+10)^{2}} \)


A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases
when the radius is \( 15 \mathrm{cm} \)


If the points \( (a, b),(3,-5) \) and (-5,-2) are collinear. Then find the value of \( 3 a+8 b \)
A . 20
B. -31
c. 10
D. None


If \( \vec{x} \) is a vector whose initial point divides the line joining \( 5 \hat{i} \), and \( 5 \hat{j} \) in the ratio \( \lambda: 1 \) and the terminal point is the
origin. Also given \( |\vec{x}| \leq \sqrt{37}, \) then \( \lambda \) belongs to
\( \mathbf{A} \cdot\left[-\frac{1}{6}, \frac{1}{6}\right] \)
B \( \cdot(-\infty,-6) \cup\left(-\frac{1}{6}, \infty\right) \)
c. \( (-\infty,-8) \)
D. \( (1, \infty) \)


According to Freundlich isotherm, the
above graph will be true when:
A \( . P=0 \)
B . \( P=1 \)
c. \( \frac{1}{n}=0 \)
D. \( \frac{1}{n}=\infty \)


Dissolving sugar in water is an example
of:
A. physical change
B. chemical change
c. neutralisation
D. none of these


Guttation is dependent on
A. Root pressure
B. Active absorption
C. Flaccidity of root cortical cells
D. High rate of transpiration


When enthalpy is positive and entropy is positive :
A. \( \Delta G \) is positive, at high temperature
B. \( \Delta G \) is negative, at high temperature
c. \( \Delta G \) is negative, at low temperature
D. none of these


Which of the following can be described as convection current
A. Sea Breeze and land Breeze
B. Heat transfer from one end to another in a metal rod
c. sun's radiations
D. None of these


Why is the screen of the cathode ray
tube coated ? Name the material used
for coating.
A. florocent material.
B. normal material
c. highy resistive material
D. none of these


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


Name the kind of lens required to correct myopia.


What is the \( K_{c} \) for the reaction:
\( \boldsymbol{M} \boldsymbol{g}(\boldsymbol{O} \boldsymbol{H})_{2(s)}+\boldsymbol{2} \boldsymbol{N} \boldsymbol{H}_{4(a q)}^{+} \rightleftharpoons \)
\( \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{3(\boldsymbol{g})}+\mathbf{2 H}_{\mathbf{2}} \boldsymbol{O}_{(\boldsymbol{a q})}+\boldsymbol{M} \boldsymbol{g}_{(\boldsymbol{a q})}^{\mathbf{2 +}} \)
(Given that the solubility product for \( M g(O H)_{2}, K_{s p} \) is \( 6 \times 10^{-12} \) mol \( ^{3} L^{-3} \)
and
the base dissociation constant for
\( N H_{4} O H, K_{b} \) is \( 1.8 \times 10^{-5} m o l L^{-1} \)
A \( \cdot 2.05 \times 10^{-2} \)
В. \( 1.65 \times 10^{-2} \)
c. \( 1.85 \times 10^{-2} \)
D. None of these


Match List I and List II
List-I List-II
a) Barometer
e) Charles law
b) specific gas constant
\( f \) ) \( J m o l e^{-1} K \)
-1
c) gas thermometer
g) Boyels law
d) universal gas constant
h) \( \operatorname{JKg}^{-1} \mathrm{K}^{-1} \)
A. a-h,b-e,c-f, d-g.
B. a-g, b-h, c-e,d-f.
c. a-f, b-g,c-h,d-e.
D. \( a-f, b-e, c-h, d-g . \)


What is the equation of parabolic trajectory of a projectile? \( (\boldsymbol{\theta}= \) angle between the projectile motion and the horizontal)
A \( \cdot y=x^{2} \tan \theta-\frac{g x}{2 u^{2} \cos ^{2} \theta} \)
B. \( y=x \tan \theta-\frac{g x^{2}}{2 u^{2} \cos ^{2} \theta} \)
c. \( y=x \tan \theta-\frac{g x^{2}}{u^{2} \cos 2 \theta} \)
D. \( y=x \tan \theta-\frac{g x^{2}}{u^{2} \sin ^{2} \theta} \)


External ears are characteristics of
A. Birds
B. Mammals
C. Birds and mammals
D. Mammals and reptiles


Which of the following is fully fluorinated polymer?
A. Neoprene
B. Teflon
c. Thiokol
D. PVC


In Mond's process, nickel is made to
react with :
A. \( C \)
в. \( C O \)
\( \mathrm{c} \cdot H_{2} \)
D. \( O_{2} \)


Which mode is used by snakes for taking food?
A. Swallowing
B. Chewing
c. sucking
D. Biting


The distance between the points
\( P(x,-1) \) and \( Q(3,2) \) is 5 units. Find
the value of \( x \)
A .2,8
В. -2,9
c. 1,8
D. -1,7


\( \ln \operatorname{an} A C \) Generator, if the number of
turns for the armature coil is doubled
keeping all other specifications to be the same, which of the following applies to the voltage generated
A. Peak Voltage will remain the same but the rms value of Voltage generated double
B. Peak Voltage will double but the rms value of Voltage generated will remain the same
c. Both the peak Voltage and the rms value of Voltage generated will double.
D. Both the peak Voltage and the rms value of Voltage generated will reduce to half the original value


Far point of a person is \( 5 m . \) In order that he has normal vision what kind of
spectacles should be use
A. Concave lens with focal length \( 5 m \)
B. Concave lens with focal length \( 10 \mathrm{m} \)
c. convex lens with focal length \( 5 m \)
D. Convex lens with focal length \( -2.5 \mathrm{m} \)


Amphoteric species is:
A. \( N a_{3} P O_{4} \)
B. \( H S O_{4}^{-} \)
c. КОН
D. \( H N O_{3} \)
E \( \cdot C_{2} O_{4}^{2-} \)


The average energy in one time period in simple harmonic motion is
A \( \cdot \frac{1}{2} m \omega^{2} a^{2} \)
B . \( m \omega^{2} a^{2} \)
\( \mathbf{c} \cdot 1.5 m \omega^{2} a^{2} \)
D. None of these


Write the general electronic
configuration of lanthanoids. What are
transuranic elements?


What happens when copper matte is charged into silica lined converter and
hot air blast is blown?


Which of the following is not a periodic property for the elements?
A. Electronegativity
B. Atomic size
c. occurrence in nature
D. lonization energy


A person weighs \( 60 k g . \) The area under
the foot of the person is \( 180 \mathrm{cm}^{2} \). Find the pressure exerted on the ground by
the person. (Take \( \left.g=9.8 m s^{-2}\right) \)

Round off your answer to nearest value


Three charges \( +\boldsymbol{q},+\boldsymbol{q} \) and \( -\boldsymbol{q} \) are situated in \( x \) -y plane at the point \( (0, a),(0,0),(0,-a) . \) Then, the electric potential at a point in first quadrant
whose position vector makes an angle \( \theta \) with the \( y \) -axis and at a distance \( r(r> \) \( >a) \) from the origin is :
A \( \cdot \frac{q a \cos \theta}{2 \pi \varepsilon_{0} r^{2}} \)
в. \( \frac{q}{4 \pi \varepsilon_{0} r}\left(1+\frac{2 a \cos \theta}{r}\right) \)
c. \( \frac{q}{4 \pi \varepsilon_{0} r} \)
D. \( \frac{q}{4 \pi \varepsilon_{0} r}\left(1-\frac{2 a \cos \theta}{r}\right) \)


Can we take one slab of p-type semiconductor and physicallyjoin it to another n-type semiconductor to get \( p-n \)
junction?


Write name and symbol of one transuranic element.


A ball moving with velocity \( \hat{i} \) collides
with a stationary wall and returns with a velocity \( \hat{j} / 2 . \) The coefficient of restitution for this collision is :
A. \( 1 / 2 \)
B. \( 1 / 3 \)
c. \( 1 / 4 \)
D. \( 1 / 5 \)


If two curves \( \boldsymbol{y}=\boldsymbol{a}^{x} \) and \( \boldsymbol{y}=\boldsymbol{b}^{x} \)
intersect at an angle \( \alpha \) then find the
value of tana
A \( \cdot\left|\frac{\ln a-\ln b}{1+\ln a \ln b}\right| \)
в. \( \left|\frac{\ln a-\ln b}{1-\ln a \ln b}\right| \)
c. \( \mid \frac{\ln a+\ln b}{1+\ln a \ln b} \)
D. \( \mid \frac{\ln a+\ln b}{1-\ln a \ln b} \)


\( P(3,1), Q(6,5) \) and \( R(x, y) \) are three
points such that the angle \( R P Q \) is a
right angle and the area of \( \triangle \boldsymbol{R} \boldsymbol{P} \boldsymbol{Q}=\mathbf{7} \)
then the number of such points \( \boldsymbol{R} \) is
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 4


Application based questions. A pea plant with purple flowers was crossed with white flowers, producing
50 plants with only purple flowers. On selfing, these plants produced 482 plants with purple flowers and 162 with white flowers. What genetic mechanism accounts for these results? Explain.


Differentiate w.r.t \( \boldsymbol{x} \) \( \sin ^{-1}\left(\frac{a \cos x+b \sin x}{\sqrt{a^{2}+b^{2}}}\right) \)


Choose the correct answers from the
alternatives given The maintenance of internal conditions
of an organism within a certain boundary range is called
A. evolution
B. metabolism
c. adaptation
D. homeostasis


Formula of microcosmic salt is:
A. \( N a_{2} H P O_{4} \)
в. \( \operatorname{Na}\left(N H_{4}\right) H P O_{4} \)
\( \mathbf{c} \cdot K_{2} H P O_{4} \)
D. \( N a_{2} P O_{4} . K_{2} P O_{4} \)


The type of isomerism shown by
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2}(\boldsymbol{N} \boldsymbol{C S})_{2}\right] \boldsymbol{C l} \) and
\( \left[\boldsymbol{C o}(\boldsymbol{e n})_{2}(\boldsymbol{N} \boldsymbol{C S})\right] \boldsymbol{C l} \) is :
A. ionization
B. cordination
c. linkage
D. all of these


Which of the following is not endocrine gland?
A. Thyroid
B. Adrenal
c. Testis
D. Salivary gland


Which of the following statements
is/are correct?
This question has multiple correct options
A. \( 4- \) Chlorophenol \( (I) \) will dissolve in \( N a O H \) but \( 4- \)
chloro \( -1- \) methyl benzene (II) will not.
B. \( 4- \) Methylbenzoic \( (I I I) \) acid will dissolve in
aq.NaHCO\( _{3} \) ) but \( 4- \) methylphenol(\( I V \) ) will not.
C \( .2,4,6- \) Trinitrophenol \( (V) \) will dissolve in
aq.NaHCO\( _{3} \) ) but \( 4- \) methylphenol \( (V I) \) will not
D. \( 4- \) Ethylphenol \( (V I I) \) will dissolve in aq. \( N a O H \) but
ethyl phenyl ether \( (V I I) \) will not.


Explain the Acidic nature of phenols and compare with that of alcohols.


Which of the following statement is true
for fungi?
A. Ectoparasites are non-pathogenic.
B. They are chlorophyllous.
C. Never form spores.
D. Reproduce sexually as well as asexually.


Which amongst the following reactions cannot be used for the preparation of the halogen acid?
A \( \cdot 2 K B r+H_{2} S O_{4}(\text { conc }) \rightarrow K_{2} S O_{4}+2 H B r \)
в. \( 2 \mathrm{NaCl}+\mathrm{H}_{2} \mathrm{SO}_{4}(\text { conc. }) \rightarrow \) NaH \( \mathrm{SO}_{4}+\mathrm{HCl} \)
c. \( N a H S O_{4}+N a C l(\text {conc.}) \rightarrow N a_{2} S O_{4}+H C l \)
D. \( C a F_{2}+H_{2} S O_{4}(\text {conc.}) \rightarrow C a S O_{4}+2 H F \)


Which of the following should be increased to prevent soil erosion?
A. Flow of water
B. Green areas
c. Deforestation
D. None of these


Statement 1: When a hydrocarbon is
combusted in air, carbon monoxide is
the major product. Statement 2: Air contains much more
nitrogen than oxygen.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1.
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. Statement 1 is correct but Statement 2 is not correct.
D. Statement 1 is not correct but Statement 2 is correct.
E. Both the Statement 1 and Statement 2 are not correct.


IUDs prevent pregnancy by
A. Inhibiting physiological and morphological uterine changes required for implantation
B. Increasing phagocytosis of spermatozoa within Uterus
C. Suppressing motility of sperms as well as their fertilising capacity
D. All of the above


For the detection of phosphorus, the
organic compound after fusion with
\( N a_{2} O_{2} \) is extracted with water, boiled
with \( H N O_{3} \) and then ammonium
molybdate added to it. A yellow ppt. is obtained which is due to formation of :
A. ammonium sulphate
B. ammonium phosphomolybdate
c. ferric phosphate
D. disodium ammonium phosphate


An electroscope has a charged rod brought near it, but not touching, and
the leaves open, Fig.I. Then a ground wire is attached to the electroscope and the leaves close, Fig. II. Finally, the ground wire and then the rod are
removed. It is determined that the
electroscope leaves have a net positive charge. Determine the charge of the rod and leaves in Fig. 1:
A. The rod has a net positive charge while the leaves have net negative charge
B. The rod has a net negative charge while the leaves have a net positive charge
c. Both have a negative charge
D. It is impossible to determine with the given information


A candidate got 5650 votes in an election and won by this opponent by a
margin of 3000 votes. if there only two
candidates, find the percentage of votes obtained by the defeated candidate.


The atomic number of Uut is:
\( A \cdot 113 \)
B. 114
\( c \cdot 108 \)
D. 115


Halogen elements are those which are:
A. diatomic and form \( X^{--} \) ions
B. monatomic and form \( \mathrm{X}^{-} \) ions
c. diatomic and form \( X^{-} \) ions
D. monoatomic and form \( X^{--} \) ions


The change in emitter current by \( 2.1 \mathrm{mA} \) results in change of \( 2 \mathrm{mA} \) in the collector current and a change of \( 0.05 V \) in the emitter base voltage. The input resistance is
A . \( 5 K \Omega \)
в. зкл
c. 1 К \( \Omega \)
D. 0.5к.


The molecular formula of acetic acid is
A. \( H C O O H \)
в. \( C H_{3}-C H_{3} \)
\( \mathbf{c} \cdot C_{6} H_{6} \)
D. \( C_{2} H_{4} O 2 \)


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{B r} \frac{M \boldsymbol{g}}{\text {dryether}} \boldsymbol{A} \stackrel{\boldsymbol{H}_{2} \boldsymbol{O}}{\boldsymbol{\beta}} \boldsymbol{B} \)
Identify \( A \& B \) compounds.


Which atom/group is in the axia
position?
A. Bromine
B. Methy
c. Ethyl
All of the above


\( \left[\boldsymbol{F} e^{I I}\left(\boldsymbol{O}_{2}\right)(\boldsymbol{C} \boldsymbol{N})_{4} \boldsymbol{C l}\right]^{4-} \) is named as:
A. chlorotetracyanodioxoferrate (II) ion
B. chlorotetracyanoperoxoferrrate (II) ion
c. chlorotetracyanosuperoxoferrate (II) ion
D. none of the above


van't Hoff's equation gives the quantitative relation between change in value of \( K \) with change in temperature.
A. True
B. False


Find the \( 11 t h \) term from the last term
(towards the first term) of the \( \boldsymbol{A P} \) :
\( \mathbf{1 0}, \mathbf{7}, \mathbf{4}, \dots,-\mathbf{6 2} \)


Force constants of two wires \( A \) and \( B \) of
the same material are \( K \) and \( 2 K \)
respectively. If two wires are stretched equally, then the ratio of work done in stretching \( \left(\frac{W_{A}}{W_{B}}\right) \) is:
A \( \cdot \frac{1}{2} \)
B. \( \frac{3}{2} \)
\( c \cdot \frac{1}{4} \)
D.


Which of the following is least volatile?
A \( . H C N \)
в. \( H-F \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( C S_{2} \)


What is the value of \( \sin ^{-1}\left(\sin 160^{\circ}\right) ? \)
\( \mathbf{A} \cdot 160^{\circ} \)
В. \( 70^{\circ} \)
\( \mathbf{c} \cdot-20^{0} \)
D. \( 20^{\circ} \)


Inverse of \( \boldsymbol{A}=\left[\begin{array}{cc}\mathbf{1} & \mathbf{3} \\ \mathbf{2} & -\mathbf{2}\end{array}\right] \) is equal to? \( \mathbf{A} \)
\( \mathbf{A} \cdot-\frac{1}{8}\left[\begin{array}{cc}3 & 1 \\ -2 & 2\end{array}\right] \)
В. \( -\frac{1}{8}\left[\begin{array}{rr}-2 & -3 \\ -2 & 1\end{array}\right] \)
\( ^{\mathbf{c}} \cdot \frac{1}{8}\left[\begin{array}{cc}-1 & -3 \\ -2 & 2\end{array}\right] \)
D. None of these


In the free radical chlorination, the two factors which determine the product
ratio of various monochlorination
products are the type of H being substituted and the number of a
specific type of H being substituted. If activation energy for H-abstraction by
chlorine radical is considered to be zero,
what would be the percentage of 1 chlorobutane amongthe monochlorobutanes obtained on free
radical chlorination of butane?
A . 6\%
B. 10\%
c. \( 40 \% \)
D. 60\%


A rod of mass \( \mathrm{m} \) and length lis bent into
shape of L. Its moment of inertia about
the axis shown in figure:
A \( \cdot \frac{m^{2}}{6} \)
B. \( \frac{m^{2}}{3} \)
\( c \cdot \frac{m l^{2}}{12} \)
D. None


Which of the following trees will die
first?
A. Girdled
B. Pruned
c. Hollowed trunk
D. Deciduous


Bryophytes are dependent on water
because
A. Archegonium has to remain filled with water for fertilization
B. Water is essential for fertilization for their homosporous nature
C. Water is essential for their vegetative propagation
D. The sperms can easily reach upto egg in the archegonium in presence of water


For an A.P., \( t_{3}=8 \) and \( t_{4}=12, \) find the
common difference \( d \)


Water is used as a coolant because:
A. it has lower density.
B. it has low specific heat.
C. it has high specific heat
D. it is easily available.


In a constant-volume calorimeter, \( 3.5 g \)
of gas with molecular weight 28 was
burnt in excess oxygen at \( 298.0 K . \) The
temperature of the calorimeter was
found to increase from \( 298.0 K \) to
\( 298.45 K \) due to the combustion
process. Given that the heat capacity of
the calorimeter is \( 2.5 k J K^{-1}, \) the
numerical value for the enthalpy of
combustion of the gas in \( k J m o l^{-1} \) is
\( \mathbf{A} \cdot 9 k J / \) mole
B. \( 75 k J / \) mole
\( \mathbf{c} .-8 k J / \)mole
D. \( -14 k J / \) mole


The average velocity during the first 20
seconds is
A. \( -10 m / s \)
B. \( 10 \mathrm{m} / \mathrm{s} \)
c. zero
D. \( 20 \mathrm{m} / \mathrm{s} \)


In a G.P. the first term is \( 7, \) the last term
\( 448, \) and the sum \( 889 ; \) find the common
ratio.
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


Two capacitors of plate area \( A \) are joined as shown in the figure. Their central rigid part is movable. The capacity of the combination will be:
A \( \cdot \frac{\epsilon_{0} A}{a-b} \)
в. \( \frac{\epsilon_{0} A}{a+b} \)
c. \( \frac{2 \in_{0} A}{a+b} \)
D. \( \frac{a-b}{\epsilon_{0} a} \)


In a series LCR circuit, the plot of \( \boldsymbol{I}_{\boldsymbol{m}} \) vs
\( \omega \) is shown in the figure. The bandwidth
of this plot will be then
A. Zero
B. \( 0.1 \mathrm{rads}^{-1} \)
c. \( 0.2 r a d s^{-1} \)
D. \( 0.4 \mathrm{rads}^{-1} \)


Using three wires of resistances 1 ohm, 2ohm and 3 ohm, number of different possible values of resistances are:
A. 6
в. 4
\( c \cdot 10 \)
D. 8


A ray incident at a point at an angle of
incidence of \( 60^{\circ} \) enters a glass sphere of \( R . l . n=\sqrt{3} \) and is reflected and
refracted at the further surface of the
sphere. The angel between the reflected
and refracted rays at this surface is
\( \begin{array}{l}\text { A } .50^{\circ} \\ ^{\circ}\end{array}^{\circ}^{5^{\circ}} \)
В. \( 60^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 40^{\circ} \)


Dissolution of common salt or sugar in water is an example of:
A. physical change
B. chemical change
c. both A and B
D. none of the above


An urn contains 10 black and 5 white
balls. Two balls are drawn from the urn
one after the other without replacement What is the probability that both drawn balls are black?


The value of \( \frac{d^{2} y}{d x^{2}} \) at the point where \( t= \) 0 is
A . 1
B. 2
\( c \cdot-2 \)
D. 3


Degree and order of the differential equation \( \frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2} \) are
respectively
A. 1,2
в. 2,
\( c .2,2 \)
D. \( 1, \)


Structure of eubacterial cell.


The velocity time graph of a particle
moving along a straight line has the form of a parabola \( \boldsymbol{v}=\boldsymbol{t}^{2}-\boldsymbol{6} \boldsymbol{t}+\boldsymbol{8} \mathrm{m} / \mathrm{s} . \) Find acceleration \( (\mathrm{in} \)
\( m / s^{2} \) ) when velocity is equal to zero:
This question has multiple correct options
A . 2
B. - -
c. 1
D. -