What is a rhytidome?
A. It is a bark
B. Dead tissue separated by periderm on outerside
C. Dead tissue separated by periderm on inner side
D. Secondary cortex


Succus entericus is secreted by
A. Peyer's patch
B. Crypts of Lieberkuhn
C. Auerbach's plexus
D. Brunner's glands


What is the direction of Monsoon winds
in Summer?
A. From ocean towards the land
B. From land towards the ocean
c. From equator towards the poles
D. From poles towards the equator


Which of the following activities is characterised by minimum breathing
rate?
A. Sleeping
B. Washing of clothes
c. Cleaning of floor
D. Dancing


Check if the relation \( R \) in the set \( R \) of
real numbers defined as
\( \boldsymbol{R}=\{(\boldsymbol{a}, \boldsymbol{b}): \boldsymbol{a}<\boldsymbol{b}\} \) is
(i) symmetric;
(ii) transitive


If \( \tan \theta=\frac{4}{7}, \) then \( \frac{7 \sin \theta-3 \cos \theta}{7 \sin \theta+3 \cos \theta}= \)
A \( \cdot \frac{1}{7} \)
в.
\( c \cdot \frac{3}{7} \)
D. \( \frac{5}{14} \)


Write the IUPAC names of the following ketone. If possible, give the common name(s) also.
PhCOPh


Derive an expression for the bandwidth
of interference fringes in Young's double slit experiment.


In a trapezium pqrs with \( \boldsymbol{P Q} \| \boldsymbol{S} \boldsymbol{R} \) the
diagonals \( P R \) and \( Q S \) intersect at \( x \) if \( P Q=\frac{2}{3} R S . \) Find the ratio of areas of
triangles \( P R Q \) and \( R X S \)


An electric dipole of dipole moment \( \mathrm{p} \) and rotational inertia I is allowed to
oscillate about its equilibrium position in a uniform electric field E. Then, for
small amplitudes the frequency of oscillation will be
A \( \cdot \sqrt{p E / I} \)
в. \( \sqrt{I / p E} \)
c. \( \frac{1}{2 \pi} \sqrt{p E / I} \)
D. \( 2 \pi \sqrt{p E / I} \)


REACTANT(S) \( \quad \) PRODUCT(S)
Magnesium + Oxygen 一
\[
\begin{array}{l}
\text { Magnesium Oxide }+\text { Oxygen } \\
\begin{array}{ll}
48.6 g & +50.0 g \longrightarrow 80.6 g \\
+ & ?
\end{array}
\end{array}
\]
Predict the mass of oxygen that will be left over after the reaction of 48.6 grams of magnesium with 50.0 grams of oxygen.
A . 20.6
в. 19.6
\( c \cdot 18 \)
D. 17.6


toppr
Q Type your question
B
\( c \)
\( D \)


Suppose \( \boldsymbol{f}:[\mathbf{0}, \boldsymbol{\pi}] \rightarrow \mathbb{R} \) satisfied \( \boldsymbol{f}(\boldsymbol{x})+ \)
\( \boldsymbol{f}(\boldsymbol{\pi}-\boldsymbol{x})=1 \) for all \( \boldsymbol{x} . \) Then
\( \int_{0}^{\pi} f(x) \sin x d x \) is
A \( \cdot \frac{1}{4} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{3}{4} \)
D.


Assertion
Benzyl bromide when kept in acetone
water produces benzyl alcohol.
Reason
The reaction follows \( S_{N} 2 \) mechanism.
Read the above assertion and reason
and choose the correct option regarding
¡t.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which surgical operation is undertaken in a women for planned family?
A. Vasectomy
B. Prostatectomy
c. Tubectomy
D. None of the above


What is the number of arbitrary constants in the particular solution of
differential equation of third order?
A .
в.
\( c \cdot 2 \)
D.


Match the entries of List - \( A \) and List \( -B \)


Write the chemical equation of following reaction?
(a) Wurtz reaction
(b) Finkelstein reaction.


Which of the following is/are true
regarding hydrogen economy? This question has multiple correct options
A. Hydrogen economy refers to technique of using dihydrogen in an efficient way.
B. Dihydrogen is transproted and stored in the form of liquid or gas.
C. Dihydrogen is ecofriendly and releases more energy than petrol.
D. Hydrogen economy refers to the transmission of this energy in the form of dihydrogen.


It is required to fix a pipe such that water flowing through it at a speed of \( 7 m \) per minutes fills a tank of capacity
440 cubic metres in 10 minutes. The
inner radius of the pipe should be:
A. \( \sqrt{2} m \)
в. \( 2 m \)
c. \( \frac{1}{2} m \)
D. \( \frac{1}{\sqrt{2}} m \)


The half life of a neutron is 800 sec. \( 10^{8} \)
neutrons at a certain instant are
projected from one space station towards another space station, situated \( 3200 \mathrm{km} \) away, with a velocity \( 2000 \mathrm{m} / \mathrm{s} \)
their velocity remains constant during the journey. How many neutrons reach the oyher station?
A \( .50 \times 10^{6} \)
B . \( 25 \times 10^{6} \)
c. \( 80 \times 10^{5} \)
D. \( 25 \times 10^{5} \)


Equation of normal drawn to the graph of the function defined as \( f(x)=\frac{\sin x^{2}}{x} \)
\( \boldsymbol{x} \neq \mathbf{0} \) and \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) at the origin is?
A. \( x+y=0 \)
в. \( x-y=0 \)
c. \( y=0 \)
D. \( x=0 \)


the horizontal and vertical components
of the force exerted on the beam at the
wall
A. Horizontal component is \( 500 N \) towards left and vertical component \( 75 N \) downwards
B. Horizontal component is \( 500 N \) towards right and vertical component \( 75 N \) upwards
C. Horizontal component is \( 625 N \) towards left and vertical component \( 150 N \) upwards
D. Horizontal component is \( 625 N \) towards right and vertical component \( 150 N \) downwards


The integrating factor of the differential equation \( \boldsymbol{x} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}+\boldsymbol{y}=\boldsymbol{x}^{3} \boldsymbol{y}^{\boldsymbol{6}} \) is
A \( \cdot-\frac{5}{x^{5}} \)
в. \( \frac{5}{y^{5}} \)
\( c \cdot-\frac{1}{x^{5}} \)
D. \( \frac{1}{x^{5}} \)


Write the important features of genetic
code.


A water drop of radius \( 10^{-6} \mathrm{m} \) is charged with one electron. The electric
field required to keep it stationary is (given density of water \( \boldsymbol{\rho}= \)
\( \mathbf{1 0 0 0 k g} / \boldsymbol{m}^{3} ; \boldsymbol{g}=\mathbf{9 . 8 m} / \boldsymbol{s}^{2} \)
A \( .2 .566 \times 10^{5} V / m \)
B . \( 1.283 \times 10^{5} \mathrm{V} / \mathrm{m} \)
c. \( 3.849 \times 10^{5} \mathrm{V} / \mathrm{m} \)
D. \( 5.132 \times 10^{5} \mathrm{V} / \mathrm{m} \)


Prove the following by using the principle of mathematical induction for
all \( n \in: \)
\( 1+\frac{1}{(1+2)}+\frac{1}{(1+2+3)}+\dots \dots \dots+ \)
\( \frac{1}{1+2+3+\ldots . n)}=\frac{2 n}{(n+1)} \)


The correct statement is :
\( \mathbf{A} \cdot B F_{3} \) is the strongest Lewis acid among the other boron halides
B. \( B I_{3} \) is the weakest Lewis acid among the boron halides
C. there is a maximum \( p \pi-p \pi \) back bonding in \( B F_{3} \)
D. there is a minimum \( p \pi-p \pi \) back bonding in \( B F_{3} \)


Equal volume of the following \( C a^{2+} \) and
\( F^{-} \) solutions are mixed. In which
solutions will the precipitation occur? \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C a} \boldsymbol{F}_{2}=\mathbf{1 . 7} \times \mathbf{1 0}^{-10} \)
(1) \( 10^{-2} M C a^{2+}+10^{-5} M F^{-} \)
(2) \( 10^{-3} M C a^{2+}+10^{-3} M F^{-} \)
(3) \( 10^{-4} M C a^{2+}+10^{-2} M F^{-} \)
\( (4) 10^{-2} M C a^{2+}+10^{-3} M F^{-} \)
Select the correct answer using the codes given below:
A \( \cdot \ln (4) \) only
B. In (1) and (2)
\( c \cdot \ln (3) \) and (4)
\( D \cdot \ln (2),(3) \) and (4)
E. In all these


Which class of chordate has maximum
living animals?
A. Pisces
B. Reptilia
c. Aves
D. Mammalia


Point \( (\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}) \) lies on the plane \( \boldsymbol{x}+\boldsymbol{y}+ \)
\( z=2 . \) Let \( \vec{a}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k} \) and \( \hat{k} \times \)
\( (\hat{k} \times \vec{a})=0 \) then \( \gamma= \)
A .
B. 1
c. 2
D.


A solid sphere of mass \( 2 \mathrm{kg} \) is rolling on a frictionless horizontal surface with
velocity \( 6 m / s . \) It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring \( =\mathbf{3 6} N / \boldsymbol{m} \)
A \( \cdot \sqrt{14 m} \)
в. \( \sqrt{2.8} m \)
c. \( \sqrt{1.4 m} \)
D. \( \sqrt{0.7} m \)


In Carius method, of estimation of
halogens, 250 mg of an organic
compound gave 141 mg of \( A g B r . \) The percentage of bromine in the compound is:(Atomic mass \( A g=108 ; B r=80) \)
A .24
B. 36
c. 48
D. 60


The ore chromite is:
A \( \cdot F e C r_{2} O_{4} \)
в. \( \operatorname{CoCr}_{2} \mathrm{O}_{3} \)
\( \mathbf{c} \cdot \operatorname{Cr} F e_{2} O_{4} \)
D. \( F e C r_{2} O_{3} \)


Match the following list 1 with list 2 (main product of the reaction)


Total amino acids in insulin (bovine)
are 51 in polypeptide chains \( A \) and \( B \) How many amino acids are there in
chain A?
A .21
B. 20
\( c . \) 30
D. 31


\( \mathbf{a}_{r}=\left|\begin{array}{ccc}\mathbf{2}^{r}-\mathbf{1} & \mathbf{2} \mathbf{.} \mathbf{3}^{r}-\mathbf{1} & \mathbf{4} . \mathbf{5}^{r}-\mathbf{1} \\ \boldsymbol{\alpha} & \boldsymbol{\beta} & \boldsymbol{\gamma} \\ \mathbf{2}^{n}-\mathbf{1} & \mathbf{3}^{n}-\mathbf{1} & \mathbf{5}^{n}-\mathbf{1}\end{array}\right| \)
then find the value of \( \sum_{r=1}^{n} \Delta_{r} \)
\( A \)
в. \( \alpha \beta \gamma \)
\( \mathbf{c} \cdot-\alpha \beta \gamma \)
\( D \)


Which of the following remains constant in uniform circular motion:
Speed or Velocity or both?


Match List-I with List-II.


With an increase in atomic number in a
period :
A. metallic character decreases
B. metallic character increases
c. chemical reactivity decreases
D. chemical reactivity increases


The collector plate in an experiment on photoelectric effect is kept vertically above the emitter plate. Light source is made on and a saturation photocurrent is recorded. An electric field is switched
on which has a vertically downward
direction.
A. The photocurrent will increase
B. The kinetic energy of the electrons will increase
c. The stopping potential will decrease
D. The threshold wavelength will increase


Select the group of taxons representing same category of taxonomic hierarchy.
A. sativum, tuberosum, indica
B. Solanum, nilotica, Brassica
c. Potato, tomato, Legumes
D. Petunia, Datura, Solanaceae


Where are Malpighian corpuscles seen?
A. Medulla
B. Cortex
c. Pelvis
D. Pyramid


f \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y})|\boldsymbol{y}=\boldsymbol{2} \boldsymbol{x}+\boldsymbol{7}| \text { , where } \boldsymbol{x} \in \boldsymbol{R} \)
and \( -5 \leq x \leq 5\} \) is relation, find the
domain of \( \boldsymbol{R} \)


In given figure, DEFG is a square and \( \angle B A C=90^{0} . \) Prove that
(i) \( \triangle A G F \sim \triangle D B G \)
(ii) \( \triangle A G F \sim \triangle E F C \)
(iii) \( \triangle D B G \sim \triangle E F C \)
\( (\text { iv }) \boldsymbol{D} \boldsymbol{E}^{2}=\boldsymbol{B} \boldsymbol{D} \times \boldsymbol{E} \boldsymbol{C} \)


What are hormones? Write the
structure of simple triglycerides.


Which reactions represents
heterogeneous catalysis?
This question has multiple correct options
A. Decomposition of \( \mathrm{KClO}_{3} \) in presence of \( \mathrm{MnO}_{2} \)
B. Ostwald process for HNO
C . Contact process for \( \mathrm{H}_{2} \mathrm{SO}_{4} \)
D. Acidic hydrolysis of ester


\( \sum_{p=1}^{32}(3 p+2)\left[\sum_{q=1}^{10}\left(\sin \frac{2 q \pi}{11}-i \cos \frac{2 q \pi}{11}\right)\right. \)
A \( \cdot 8(1-i) \)
B \( \cdot 16(1-i) \)
\( \mathbf{c} \cdot 48(1-i) \)
D. None of these


If \( f(x)=\int \frac{1}{x-\sqrt{x^{2}+1}} \) and \( f(0)= \)
\( \frac{1+\sqrt{2}}{2}, \) then \( f(1) \) is equal to
\( ^{A} \cdot \log (\sqrt{\sqrt{2}-1}) \)
B. \( \frac{-1}{\sqrt{2}} \)
c. \( 1+\sqrt{2} \)
D. \( \frac{1}{2} \log (1+\sqrt{2}) \)


Divide: \( -4 x^{3}-6 x^{2}+8 x \) by \( 2 x \)
A \( \cdot\left(-2 x^{2}-3 x+4\right) \)
B. \( 2 x\left(2 x^{2}-3 x+4\right) \)
C \( \cdot\left(-2 x^{2}-3 x+4\right) \)
D. \( x\left(-2 x^{2}-3 x-4\right) \)


If \( \boldsymbol{P}=\left[\begin{array}{cc}\frac{\sqrt{\mathbf{3}}}{\mathbf{2}} & \frac{\mathbf{1}}{2} \\ -\frac{\mathbf{1}}{\mathbf{2}} & \frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\end{array}\right], \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{1} \\ \mathbf{0} & \mathbf{1}\end{array}\right] \) and
\( Q=P A P^{T} \) then \( P\left(Q^{2005}\right) P^{T} \) equal to
\begin{tabular}{l}
A. \( \left[\begin{array}{cc}1 & 2005 \\
0 & 1\end{array}\right] \) \\
\hline
\end{tabular}
B. \( \left[\begin{array}{cc}\sqrt{3} / 2 & 2005 \\ 1 & 0\end{array}\right] \)
\( \mathbf{c} \cdot\left[\begin{array}{cc}1 & 2005 \\ \sqrt{3} / 2 & 1\end{array}\right] \)
D. \( \left[\begin{array}{ll}1 & \sqrt{3} / 2 \\ 0 & 2005\end{array}\right] \)


Bacteria cannot be seen with the naked
eyes, but these can be seen with the
help of a microscope. If you have to carry a sample from your home to your biology laboratory to demonstrate the presence of microbes under a
microscope, which sample would you carry and why?


A cylinder of mass \( 5 k g \) is held in
vertical position. If the height of the
cylinder is \( 6 \mathrm{cm} \) and radius of cross
section is \( 4 \mathrm{cm} \) then find the pressure acting on its bottom surface.


Read the bar graph shown in given fig. and answer the following questions
How many tickets of Assam State
Lottery were sold by the agent?
Bar graph of the tickets of different state lotteries sold by an agent on a day.


When a metallic wire is stretched with a
tension \( T_{1} \) its length is \( l_{1} \) and with a
tension \( T_{2} \) its length is \( l_{2} \). The original length of the wire is:
A. \( \frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}} \)
в. \( \frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}} \)
c. \( \sqrt{l_{1} l_{2}} \)
D. \( \frac{l_{1} l_{2}}{2} \)


Assertion
Kirchhoff's junction rule can be applied to a junction of several lines or a point in a line.
Reason
When steady current is flowing, there is no accumulation of charges at any junction or at any point in a line.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following metals is used to prevent rusting of iron, as per electrochemical method?
\( A \cdot Z n \)
B. Sn
c. \( \mathrm{Ni} \)
D. cu


Which of the following salts does not contain water of crystallisation?
A . Blue vitriol
B. Baking soda
c. washing soda
D. Gypsum


Figure shows four containers of olive oil
The pressure at depth h is
A. Greatest in A
B. Greatest in
c. Least in \( \mathrm{B} \) and \( \mathrm{c} \) both
D. Equal in all the containers


Radioactive isotope used by Calvin to elucidate Calvin cycle was
\( \mathbf{A} \cdot P^{12} \)
B \( \cdot C^{14} \)
\( c \cdot S^{3} \)
D. \( O^{13} \)


Identify the joints, which are freely movable.
A. Fibrous joints
B. Symphyses
c. synovial joints
D. Cartilaginous joints


The normal to the curve \( x^{2}=4 y \)
passing through (1,2) is
A. \( x+y=3 \)
в. \( x-y=3 \)
c. \( x+y=1 \)
D. \( x-y=1 \)


A gas is expanded from volume \( V_{0} \) to
\( 2 V_{0} \) under three different processes.
Process 1 is isobaric process, process 2
is isothermal and process 3 is
adiabasic. Let \( \triangle \boldsymbol{U}_{1}, \triangle \boldsymbol{U}_{2} \) and \( \triangle \boldsymbol{U}_{3} \) be
the change in internal energy of the gas
in these three processes. Then
A. \( \triangle U_{1}>\triangle U_{2}>\triangle U_{3} \)
В. \( \triangle U_{1}<\Delta U_{2}<\triangle U_{3} \)
c. \( \triangle U_{2}<\triangle U_{1}<\Delta U_{3} \)
D. \( \triangle U_{2}<\Delta U_{3}<\triangle U_{1} \)


A small body of mass \( m \) tied to a non-
stretchable thread moves over a smooth
horizontal plane. The other end of the
thread is being drawn into a hole \( \boldsymbol{O} \)
(figure shown above) with a constant velocity. Find the thread tension as a
function of the distance \( r \) between
the body and the hole if at \( r=r_{0} \) the
angular velocity of the thread is equal to
\( \omega_{0} \)


\( \left[\begin{array}{lll}\boldsymbol{x} & \mathbf{1} & -\mathbf{1}\end{array}\right]\left[\begin{array}{lll}\mathbf{0} & \mathbf{1} & -\mathbf{1} \\ \mathbf{2} & \mathbf{1} & \mathbf{3} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}\end{array}\right]\left[\begin{array}{l}\boldsymbol{x} \\ -\mathbf{1} \\ \mathbf{1}\end{array}\right]=\mathbf{0} \)
then find \( x \)


Change in the shape of a body caused by the application of a force (stress) is called as:
A. ductility
B. deformation
c. hardness
D. rigidity


Which one is not correct with given
marks?
A. B-carboxylation- fixation of \( C O_{2} \) the aldose sugar
B. C- reduction - reverse of glycolysis
C. A- regeneration - reformation of pentose sugar
D. C- reduction - carbohydrate formation


Which one of the following equations does not correctly represent the first law of thermodynamics for the given
process?
A. Isothermal process: \( q=-w \)
B. Cyclic process: \( q=-w \)
C. Isochoric process: \( \Delta U=q \)
D. Adiabatic process: \( \Delta U=-w \)
E. Expansion of gas into vacuum: \( \Delta U=q \)


Which of the following gas is heavier than air?
This question has multiple correct options
A. \( N_{2} \)
в. \( O_{2} \)
\( c \cdot C O_{2} \)
D. \( H_{2} \)


A block of mass m rests on a rough inclined plane. The coefficient of friction between the surface and the block if \( \mu \)
At what angle of inclination \( \theta \) of the plane to the horizontal will the block just start to slide down the plane?
A \( \cdot \theta=\tan ^{-1} \mu \)
в. \( \theta=\cos ^{-1} \mu \)
c. \( \theta=\sin ^{-1} \mu \)
D. \( \theta=s e c^{-1} \mu \)


Which of the following statement
regarding transformer is incorrect?
A. A transformer makes use of Faradays Law.
B. The ferromagnetic properties of an iron core is used by it to efficiently raise or lower AC voltage
C. It cannot increase power so that if the voltage is raised, the current is proportionally lowered and vice versa.
D. The current induced in primary circuit is of same nature as in secondary circuit with differences in amplitude only.


An inductor of inductance \( 2.0 \mathrm{mH} \) is
connect across a charge capacitor of capacittance 5.0 uF , and the resulting LC circuit is set oscillating at natural frequency. Let \( Q \) denote the instantaneous charge on the capacitor, and I the current in the circuit. It is
found the maximum value of \( Q \) is 200
uC .When \( Q=100 u C \) the value of \( \frac{d I}{d t} \) is
found to be \( 10^{x} \) A/s. Find the value of \( x \)
is then
A. \( x=-4 \)
B. x=-
\( c \cdot x=4 \)
D. x=5


Show that \( s \propto t^{2} \) for a freely falling
body


The pH of a \( 10 \mathrm{ml} \) aqueous solution of
HCl is \( 4 . \) The amount of water to be
added to this solution in order to
change its pH from 4 to 5 is
A . 30 \( m 1 \)
B. 60 \( m \)
c. \( 90 \mathrm{ml} \)
D. 120 m


An example of disaccharide is
A. Glucose
B. Ribose
c. cellulose
D. Lactose


Which of the following describes the
effects of water scarcity on plants?
A. The green character of the planet shall be lost.
B. This may mean the end of all life.
c. A world without plants shall mean no food, no oxygen not enough rain, and innumerable other problems
D. All of the above


A capacitor has some dielectric between its plates, and the capacitor is connected to a dc source. The battery is
now disconnected and then the
dielectric is removed, then
A. capacitance will increase
B. energy stored will decrease.
c. electric field will increase
D. Voltage will decrease


Find each of the following products.
\( 6 a \times 4 b^{2} \)


The vapours of \( H g \) absorb some electrons accelerated by a potential diff of 4.5 volt as a result of which light is emitted. If the full energy of single
incident \( e^{-} \) is supposed to be converted
into light emitted by single \( \boldsymbol{H} \boldsymbol{g} \) atom
find the wave no. \( \left(\operatorname{in} m^{-1}\right) \) of the light.


If block \( A \) is moving with an
acceleration of \( 5 m s^{-2}, \) the acceleration
of B w.r.t ground is
\( A \cdot 5 m s^{-2} \)
B. \( 5 \sqrt{2} \mathrm{ms}^{-2} \)
\( c \cdot 5 \sqrt{5} m s^{-2} \)
D. \( 10 m s^{-2} \)


The percent composition by mass of the phosphorus in calcium phosphate
\( C a_{3}\left(P O_{4}\right)_{2} \) is \( x . \) Then, the value of \( x \) is :


A battery of e.m.f. \( 6.0 ~ V \) and negligible
internal resistance is connected to a
network of resistors and a voltmeter, as
shown in Fig.

Resistor \( Y \) has a resistance of \( 24 \Omega \) and
resistor \( Z \) has a resistance of \( 32 \Omega \)
The resistance \( R_{X} \) of the variable
resistor \( X \) is adjusted until the
voltmeter reads \( 4.8 \mathrm{V} \)
Calculate:
The current in resistor \( Z \)
current \( = \) \( \boldsymbol{A} \)


If the temperature scale is changed
from \( ^{\circ} \boldsymbol{C} \) to \( ^{\circ} \boldsymbol{F} \), the numerical value of
specific heat will
\( A \). increase
B. decrease
c. remain unchanged
D. nothing can be said


The maximum value of \( f(x)=2 x^{3}- \)
\( 21 x^{2}+36 x+20 \) in \( 0 \leq x \leq 2 \) is
A . 37
B. 44
\( c .32 \)
D. 30


\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{O H} \frac{\text {SOCI}_{2} \boldsymbol{P}_{\boldsymbol{y} \boldsymbol{r i d i n e}}}{\boldsymbol{\}} \)
Ethanol
What will be the major organic product of the reaction?


Why do our ears pop when we go to
mountains?


Which of the following are used as
fertilizers?
This question has multiple correct options
в. \( C a\left(H_{2} P O_{4}\right)_{2} \)
c. \( C a N C N \)
D. \( C a C_{2} \)


Find the value of \( k \) so that the function \( f \)
is continuous at the indicated point. \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{cc}\boldsymbol{k} \boldsymbol{x}^{2} & , \boldsymbol{x} \leq \mathbf{2} \\ \boldsymbol{3} & , \boldsymbol{x}>\mathbf{2}\end{array}\right\} \) at \( \boldsymbol{x}=\mathbf{2} \)


Which of following can not travel through vacuum?
A. Electromagnetic wave
B. Sound wave
c. Light wave
D. X-ray


The reaction, \( C_{2} H_{6}(g) \rightleftharpoons C_{2} H_{4}(g)+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \) is at equilibrium in a closed
vessel at \( 1000 K . \) The enthalpy change
\( (\Delta H) \) for the reaction is 137.0 \( k J . m o l^{-1} . \) Which one of the following
actions would shift the equilibrium to the right?
A. Decreasing the volume of the closed reaction vessel
B. Decreasing the temperature at which the reaction is performed
c. Adding an inert gas to the closed reaction vessel
D. Increasing the volume of the closed reaction vessel


Biosystematics aims at
A. Identification and arrangement of organisms on the basic of their cytological characteristics.
B. The classification of organisms based on broad morphological characteristics.
C. Delimiting various taxa of organisms and establishing their relationships.
D. The classification of organisms based on their evolutionary history and establishing their phylogeny on the totality of various parameters from all fields of study


Select the correct option regarding genetic code of Glycine.
A. GUU, GUC, GUA
B. GAU, GAC, GAA
c. GGU, GGА, яGС
D. GGU, GGA, GCU


Select the correct statements for thiazy|
trifluoride \( \left(N S F_{3}\right) \)
This question has multiple correct options
\( \mathbf{A} \cdot S-N \) bond length is \( 141.5 \mathrm{pm}, \) probably the shortest
one between \( S \) and \( N \)
B. The three highly electronegative fluorine substituents contract the 3d-orbitals of sulphur sufficiently to effect the strong \( \pi \) -bonding with the half-filled \( p \) orbitals of nitrogen.
C. The bond angle \( F-\hat{S}-F=94^{\circ} \) indicates the
involvement of almost pure p-orbitals of \( S \) in binding the fluorine atoms.
D. The very strong bonding (due to multiple bond formation) between \( N \) and \( S \) demands the
participation of s-character enriched orbitals of sulphur.


Assertion
\( \Delta_{o} \) increases in the order of
\( \left[\boldsymbol{C r} \boldsymbol{C l}_{\boldsymbol{6}}\right]^{\boldsymbol{3}-}<\left[\boldsymbol{C r}(\boldsymbol{C N})_{\boldsymbol{6}}\right]^{\boldsymbol{3}-}< \)
\( \left[\boldsymbol{C r}\left(\boldsymbol{C}_{2} \boldsymbol{O}_{4}\right)_{3}\right]^{3-} \)
Reason
The stronger the ligand field, the higher
will be \( \Delta_{o} \) value.
A. Both Assertion and Reason are correct and the Reason is the correct explanation of the Assertion
B. Both Assertion and Reason are correct but the Reason is not the correct explanation of the Assertion
C. The Assertion is correct but the Reason is incorrect
D. The Assertion is incorrect but the Reason is correct


\( \forall n \in N, 3^{3 n}-26^{n} \) is divisible by
A .24
B. 64
c. 17
D. none of these


How did Mendel explain that it is
possible that a trait is inherited but not expressed in an organism?


The plant tissues become woody by a
process of
A. Suberisation
B. Pectification
c. Calcification
D. Lignification


A stone fails from a balloon that is
descending at a uniform rate of
\( 12 m s^{-1} . \) The displacement of the stone from the point of release after 10 sec is :
A. \( 490 \mathrm{m} \)
B. 610 \( m \)
\( c .510 \mathrm{m} \)
D. 725 \( m \)


Name the chronic respiratory disorder caused mainly by cigarette smoking:-
A. Emphysema
B. Asthma
c. Respiratory acidosis
D. Respiratory alkalosis.


Statement A: Shock absorbers reduce
the magnitude of change in momentum Statement B: Shock absorbers increase
the time of action of impulsive force
A. A \& B are correct
B. A \& B are wrong
c. A is correct and B is wrong
D. A is wrong and B is correct


The work done to transport \( 20 C \) charge
from points \( A \) to another point \( B \) over distance of \( 0.2 m \) is 2 joule The
potential difference across \( A B \) is
A \( \cdot 2 \times 10^{-2} V \)
В. \( 4 \times 10^{-1} \mathrm{V} \)
c. \( 1 \times 10^{-1} \mathrm{V} \)
D. 10V


Prove that \( (\boldsymbol{a}+\boldsymbol{b})^{5}-\boldsymbol{a}^{5}-\boldsymbol{b}^{5}= \)
\( \boldsymbol{5} \boldsymbol{a b}(\boldsymbol{a}+\boldsymbol{b})\left(\boldsymbol{a}^{2}+\boldsymbol{a} \boldsymbol{b}+\boldsymbol{b}^{2}\right) \)


\( X e F_{4} \) disproportionate in water to give:
A \( . \quad X e+H C l \)
в. \( X e \) and \( X e O_{3} \)
c. \( X e O F_{4} \) and \( H F \)
D. \( X e O_{2} F E \) and \( H F \)


Identify the product(s) which will be formed by using the information provided about the reactants:
\( M g(s)+2 H C l \rightarrow \)
A \( . M g C l_{2}+F e \)
B. \( M g F e+C l_{2} \)
c. \( M g C l_{3}+F e \)
D. \( M g C l_{2}+H_{2} \)
E \( . M g+F e+C l_{2} \)


Solve \( \int \frac{\cos x}{1+\cos x} d x \)


The IUPAC name of the following
compound is:


\( A \) is older than B. Taking present ages of \( A \) and \( B \) as \( x \) years and \( y \) years
respectively, find in terms of \( x \) and \( y \)
(i) the difference between the ages of \( A \)
and B.
(ii) the age of B when A was of \( y \) years. If the age of \( B \), obtained, in step (ii), is
half the present age of \( A \) and \( B \) is 42 years; find the present ages of A and B.


Function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{2}-\mathbf{2}}{\sqrt{\mathbf{1}+\boldsymbol{x}^{2}}} \)
A. is always increasing
B. is always decreasing
C. has exactly one point of minima
D. has exactly one point of maxima


If \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \boldsymbol{f}(\boldsymbol{x})=\mathbf{4} \boldsymbol{x}^{3}-\frac{\boldsymbol{3}}{\boldsymbol{x}^{4}} \) such that
\( \boldsymbol{f}(2)=0 . \) Then \( \boldsymbol{f}(\boldsymbol{x}) \) is
A \( \cdot x^{4}+\frac{1}{x^{3}}-\frac{129}{8} \)
B. \( x^{3}+\frac{1}{x^{4}}+\frac{129}{8} \)
c. \( x^{4}+\frac{1}{x^{3}}+\frac{129}{8} \)
D. \( x^{3}+\frac{1}{x^{4}}-\frac{129}{8} \)


If \( a, b, c \) are real, then \( f(x)= \) \( \left|\begin{array}{ccc}\boldsymbol{x}+\boldsymbol{a}^{2} & \boldsymbol{a} \boldsymbol{b} & \boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b} & \boldsymbol{x}+\boldsymbol{b}^{2} & \boldsymbol{b} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{c} & \boldsymbol{b} \boldsymbol{c} & \boldsymbol{x}+\boldsymbol{c}^{2}\end{array}\right| \) is decreasing
in
A \( \cdot\left(-\frac{2}{3}\left(a^{2}+b^{2}+c^{2}\right), 0\right) \)
B. \( \left(0, \frac{2}{3}\left(a^{2}+b^{2}+c^{2}\right)\right) \)
\( \left(\frac{a^{2}+b^{2}+c^{2}}{3}, 0\right) \)
D. None of these


The balancing length for a cell is \( 560 \mathrm{cm} \) in a potentiometer experiment. When an external resistance of \( 10 \Omega \) is connected
in parallel to the cell, the balancing length changes by \( 60 \mathrm{cm} \). If the internal resistance of the cell is \( \frac{N}{10} \Omega, \) where \( N \) is an integer then value of \( \mathrm{N} \) is


If heat is supplied to a solid, its
temperature This question has multiple correct options
A. must increase
B. may increase
c. may remain constant
D. may decrease


Which one of the following processes requires an input of energy?
A. Active transporttt
B. Diffusion
c. Facilitated diffusion
D. Osmosis


Construct a \( \triangle X Y Z \) in which \( X Y=4.5 \)
\( \mathbf{c m}, \boldsymbol{Y} \boldsymbol{Z}=\mathbf{5} \mathbf{c m} \) and \( \boldsymbol{Z} \boldsymbol{X}=\mathbf{6} \mathbf{c m} \)


If \( x \) be real then the minimum value of
\( 40-12 x+x^{2} \) is?
A . 28
B. 4
\( c \cdot-4 \)
D.


Find the dimensions of pressure.


A conducting sphere of radius \( \boldsymbol{R} \) having
charge \( q \) is joined to another
conducting sphere of radius \( 2 R \) having
charge \( -2 q . \) The charge flowing between them will be
\( \mathbf{A} \cdot \mathbf{q} \)
в. \( \frac{2 q}{3} \)
c. \( \frac{q}{3} \)
D. \( \frac{4 q}{3} \)


A particle is moving along a circular
path of radius \( 5 m \) with a uniform
speed \( 5 m s^{-1} . \) What is the magnitude of average acceleration during the interval in which particle completes half revolution?


The structure shown has:
\( \mathbf{A} \cdot 1^{o}, 2^{o} \) and \( 3^{o} \) carbon atoms
B. \( 1^{\circ} \) and \( 2^{\circ} \) carbon atoms only
C \( \cdot 1^{\circ} \) and \( 3^{\circ} \) carbon atoms only
D. \( 2^{\circ} \) and \( 3^{\circ} \) carbon atoms only


A cylinder has two faces which are
A. Square
B. Circle
c. sphere
D. Triangle


How many words can be formed with the
letters of the word 'OMEGA' when
vowels being never together?
A . 12
B. 36
\( c \cdot 24 \)
D. 84


An adult has - .............. teeth.
A . 20
B. 24
\( c \cdot 28 \)
D. 32


In how many of the permutations of \( n \) things taken \( r \) at a time will 5 things (i)
always occur,
(ii) never occur?


An alpha particle collides elastically with a stationary nucleus and
continues moving at an angle of \( 60^{\circ} \) with respect to the original direction of motion. The nucleus recoils at an angle
of \( 30^{0} \) with respect to this direction Mass number of the nucleus is :
A. 3
B. 4
\( c \cdot 6 \)
D. 8


Find the centre of mass of three
particles at the vertices of an
equilateral triangle. The masses of the
particles are \( 100 g, 150 g, \) and \( 200 g \)
respectively. Each side of the
equilateral triangle is 0.5 m long.


How that the points \( \boldsymbol{P}(-\boldsymbol{2}, \boldsymbol{3}, \boldsymbol{5}), \boldsymbol{Q}(\boldsymbol{1}, \boldsymbol{2}, \boldsymbol{3}) \) and \( \boldsymbol{R}(\boldsymbol{7}, \boldsymbol{0},-\boldsymbol{1}) \)
are collinear.


Match the extraction process with the
metals.


\( \boldsymbol{O} \)
\( \boldsymbol{P h}-\boldsymbol{C H}_{2}-\stackrel{\|}{\boldsymbol{C}}-\boldsymbol{O H} \)
\( (A) \) is :
A. \( P h-C O_{2} H \)
в. \( P h-C H_{2}-O H \)
c. \( P h-C H_{3} \)
D.


\( A B C \) is a triangle in which \( A B= \)
\( A C=4 \mathrm{cm} \) and \( \angle A=90^{\circ} . \) Calculate
the length of perpendicular from \( \boldsymbol{A} \) to \( \boldsymbol{B C} \)
A. \( 2.83 \mathrm{cm} \)
B. \( 1.414 \mathrm{cm} \)
\( c .2 .6 \mathrm{cm} \)
D. 2.20 cm


A reaction is \( 50 \% \) complete in 2 hours and \( 75 \% \) complete in 4 hours. The order
of reaction is:
A.
B.
\( c \cdot 2 \)
D.


Solve the following pair of simultaneous equations:
\( 4 x+\frac{3}{y}=1 ; 3 x-\frac{2}{y}=5 \)
A. \( x=-6, y=7 \)
в. \( x=-3, y=1 \)
c. \( x=1, y=-1 \)
D. \( x=2, y=0 \)


Which one of the following statements about Cycas is incorrect?
A. It has circinate vernation
B. Its xylem is mainly composed of xylem vessel
c. Its roots contain BGA
D. It does not have a well organized female flower


Which of the following type of forces are present in vulcanized rubber?
A. Weakest intermolecular forces
B. Hydrogen bonding
c. Three dimensional network of bonds
D. Metallic bonding


How \( \boldsymbol{O}_{3} \) is less thermodynamically
stable than \( O_{2} ? \)


Prove that the straight lines \( x+2 y+ \)
\( \mathbf{1}=\mathbf{0} \) and \( \mathbf{2} \boldsymbol{x}-\boldsymbol{y}+\mathbf{5}=\mathbf{0} \) are
perpendicular to each other.


In the pictured circuit, If the reading of
voltmeter 1 is \( 3.0 V \) the reading of
ammeter 2 is \( 20 A \) and the reading of
voltmeter 3 is \( 5.0 ~ V, \) what is the
terminal voltage of the battery?
\( \mathbf{A} \cdot 8.0 V \)
B. \( 3.0 V \)
c. \( 5.0 V \)
D. \( 10.0 V \)
E. Not enough is given to answer this
questio


What are the different oxidation states
exhibited by the lanthanoids?


Which of the following statement is not a postulate of kinetic molecular theory of gases?
A. K.E. is dependent on temperature
B. K.E. is dependent on pressure
c. The molecular collisions are perfectly elastic collisions
D. The pressure of the gas is due to collisions of gas molecules on the walls of the vesse


An athlete is given \( 100 g \) of glucose
\( C_{6} H_{12} O_{6} \) of energy equivalent to
\( 1560 k J . \) He utilizes \( 50 \% \) of this gained energy in an event. In order to avoid
storage of energy in the body what is the weight of water, he would need to perspire? The enthalpy of evaporation of water is \( 44 k J / \) mol.
A. \( 319 g \)
в. \( 638 g \)
c. \( 14040 g \)
D. 35.45 g


In which season, is Cassiopeia visible?
A. winter
B. Summer
c. Rainy
D. All seasons


Choose the correct option
This question has multiple correct options
A. \( \mathrm{MCB} \) is much more sensitive to over current than fuse
B. Fuse is much more sensitive to over current than MCB
C. Handling MCB is more electrically safe than fuse
D. Handling fuse is more electrically safe than MCB


What is the type of a lens of Power \( = \)
\( -4 D ? \)
A. Convex lens
B. Concavo convex lens
c. concave lens
D. None


Which polymer is generally used to prepare carry bags?
A. Polyester
B. Bakelite
c. Polyethylene
D. Alkyl resin


Two cards are drawn simultaneously
(without replacement) from a well-
shuffled pack of 52 cards. Find the
mean and variance of the number of red
cards.
\( \mathbf{A} \cdot \) Mean \( =0.1 \) and Variance \( =0.7 \)
B. Mean \( =0.6 \) and Variance \( =0.3 \)
C . Mean \( =0.49 \) and Variance \( =0.37 \)
D. Mean \( =0 \) and Variance \( =0.45 \)


Inertia of a body has direct dependence
on:
A. velocity
B. mass
c. area
D. volume


The electromagnetic waves
A. travel with the the speed of sound.
B. travel with the the same speed in all media.
C . travel in free space with the speed of light.
D. do not travel through a medium.


Sometimes the tubes in the well-
inflated tyres of a cycle left in the sun
burst open
A. Because the pressure of air inside the tube increases
B. Because the volume of air inside the tube increases due to rise in its temperature
C. Because the tube containing air melts
D. Because the volume and the pressure both increase
E. None of the above


Phase different between the
instantaneous velocity and acceleration of particle executing SHM is
A . zero
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D. \( 2 \pi \)


The population of a town increases evry
year at rate of \( 10 \% \). The present
population of the town is \( 12,500 . \) Find the population of the town after 2 years.
A . 15125
B. 25125
c. 35125
D. 45125


Among the following, the state
function(s) is(are):

This question has multiple correct options
A. Internal energy
B. Irreversible expansion work
C . Reversible expansion work
D. Molar enthalpy


The element eka-silicon predicted by Mendeleev is :
A . Ge
в. Ga
\( c \cdot A \)
\( D \cdot s \)


A convex lens is used to form an image of an object on a screen. If the upper half of the lens is covered so that it becomes
opaque. Then :
A. only half of the image will be visible
B. the image position shifts towards the lens
c. the image position shifts away from the lens
D. the brightness of the image reduces


On the average a human heart is found to beat 75 times in a minute. Calculate
its beat frequency of heart and period.


The property seen in \( f \) -block elements is :
A. Lanthanoid contraction
B. Actinide contraction
\( c \cdot \operatorname{both}(A) \) and \( (B) \)
D. Lanthanoid expansion


A rectangular frame of wire abcd has
dimensions \( 32 \mathrm{cm} \times 8.0 \mathrm{cm} \) and a total
resistance of \( 2.0 \Omega . \) It is pulled out of a
magnetic field \( B=0.020 T \) by applying
a force of \( 3.2 \times 10^{-5} N \) (figure). It is
found that the frame moves with
constant speed. Find the emf induced in
the loop.


The correct statement is
A. the nucleus \( _{3}^{6} L i \) can emit an alpha particle
B. the nucleus 210 84 Po can emit a proton
C . deuteron and alpha particle can undergo complete fusion


\( \operatorname{Given} \boldsymbol{A}=\left[\begin{array}{ccc}1 & \mathbf{2} & -\mathbf{3} \\ \mathbf{5} & \mathbf{0} & \mathbf{2} \\ \mathbf{1} & \mathbf{- 1} & \mathbf{1}\end{array}\right] \) and \( \boldsymbol{B}= \)
\( \left[\begin{array}{ccc}3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3\end{array}\right] \)
Find the matrix \( C \) such that \( A+2 C= \)
\( \boldsymbol{B} \)
If \( C=\left[\begin{array}{ccc}1 & \frac{-3}{2} & a \\ \frac{-1}{2} & 1 & b \\ \frac{1}{2} & \frac{1}{2} & 1\end{array}\right] \)
Find the value of \( a+b ? \)


In mammals, the adipose tissue is mainly found in
A. In epidermis
B. In muscles
c. In dermis
D. Below dermis


When conc. \( H_{2} S O_{4} \) is heated with
\( P_{2} O_{5}, \) the acid is converted into:
A . sulphur trioxide
B. sulphur dioxide
c. sulphur
D. a mixture of sulphur dioxide and sulphur trioxide


Match the List I with List II and choose
the correct option from the codes given
below:
List - I List - II
\( (P) \)
Sky in blue
(Q) Peptisation
Delta
Formation Gold
number
\( \begin{array}{llll}\text { (R) } & \text { Tyndall effect } & \text { (3) } & \text { Coagulation }\end{array} \)
(s) Adsorption
of common
ion 1
A. \( P-3, Q-4, R-1, S-2 \)
B. P-2, Q-3, R-1, S-4
c. \( \mathrm{P}-3, \mathrm{Q}-1, \mathrm{R}-4, \mathrm{S}-2 \)
D. P-4, Q-3, R-1, S-2


What is polymorphic from of Sulphur?


The radius of a sphere is \( 2.1 \mathrm{cm} \). Find its
surface area.


Let \( \mathbf{P}\left(\mathbf{x}_{1}, \mathbf{y}_{1}\right) \) be any point on the
cartesian plane then match the
following lists:

LIST - I
A) The distance from \( P \) to \( X- \)
1)
axis
B) The distance from P to Y-
2) | \( y_{1} \mid \) axis
C) The distance from \( P \) to
3) \( \sqrt{x_{1}^{2}+y_{1}^{2}} \)
origin is
4) \( \left|x_{1}\right| \)
\( \mathbf{A} \cdot A-4, B-2, C-1 \)
\( \mathbf{B} \cdot A-2, B-4, C-3 \)
\( \mathbf{c} \cdot A-4, B-2, C-3 \)
D. \( A-2, B-4, C-1 \)


When we say'sound travels in a
medium' we mean:
A. the particles of the medium travel
B. the source travels
c. the disturbance travels
D. the medium travels


\( \int \frac{x}{x^{4}-1} d x \)


A man of 30 kg jumps up to a height of \( 2 \mathrm{m} . \) What is his potential energy at the highest point?
A. 60 J
B. 50 J
c. 15 J
D. 600 J


The probability'p' of happening of an
event
A. Can be negative
В. \( 0 \leq p \leq 1 \)
c. can be greater the 1
D. None of these


A system \( X \) is neither in thermal
equilibrium with \( Y \) nor with Z. The
systems Y and Z:
A. must be in thermal equilibrium.
B. cannot be in thermal equilibrium.
c. may be in thermal equilibrium.
D. cant be in thermal equilibrium.


\( A B C \) is a triangle and \( P \) is any point on
BC. If \( P Q \) is the resultant of the vectors \( \overrightarrow{A P}, \overrightarrow{P B} \) and \( \overrightarrow{P C} \) then \( A C Q B \) is
A. Rectangle
B. Square
c. Rhombus
D. Parallelogram


Which of the following best describe the
current?
A. the rate of flow of charged particles through a conducting medium
B. only present when there is no voltage
C. the flow of a conductor through charged particles
D. faster than the speed of light
E. the random movement of electrons from atom to
atom


8
8
8
6


The geometric mean of the observations 2,4,8,16,32,64 is
A \( \cdot 2^{5 / 2} / 2 \)
2) 1
B \( \cdot 2^{7 / 2} \)
\( c \cdot 33 \)
D. None of these


Agranal chloroplasts occur in
A. Succulent plants.
B. \( C_{3} \) plants.
c. \( C_{4} \) plants.
D. Hydrophytes


What is the value of \( k \) if \( (k, 5) \) is the solution of the simultaneous equations
\( 4 x+3 y=19 \) and \( 4 x-3 y=-11 ? \)
\( A \cdot 4 \)
B. \( -1 / 3 \)
c. 5
\( D \)


Write the chemical method by which
Fe \( (O H)_{3} \) sol is prepared from \( F e C l_{3} \)


To a man walking at the rate of \( 3 \mathrm{km} / \mathrm{h} \) the rain appears to fall vertically downwards. When he increases his
speed to \( 6 \mathrm{km} / \mathrm{h} \) it appears to meet him
at an angle of \( 45^{0} \) with vertical. Find the
speed of rain.


Calculate the scalar product of the following vectors. The vector \( x \) satisfies the following conditions: \( (a) x \) is collinear with the
vector \( \boldsymbol{a}=\mathbf{6} \boldsymbol{i}-\boldsymbol{8} \boldsymbol{j}-\mathbf{7 . 5 k} ;(\boldsymbol{b}) \boldsymbol{x} \)
makes an acute angle with the Oz axis; \( (c)|x|=50 . \) Find the
coordinates of the vector \( x \)


Which of the following lanthanides have no partially filled \( 4 f \) sub-shell but have
electrons in \( 5 d \) sub-shell ?
A \( . C e \)
в. \( L u \)
c. \( P m \)
D. \( N d \)


Acidic para magnetic oxide of nitrogen:
A . NO
B. \( \mathrm{N}_{2} \mathrm{O}_{3} \)
\( c \cdot \mathrm{NO}_{2} \)
D. \( \mathrm{N}_{2} \mathrm{O}_{5} \)


Which group of elements does not show diagonal relationship?
A. \( L i, M g \)
в. \( B e, A l \)
\( \mathbf{c} \cdot B, S i \)
D. \( C, P \)


For \( Z n^{2+} / Z n, E^{\circ}=-0.76 V, \) for
\( \boldsymbol{A} \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}, \boldsymbol{E}^{\circ}=\mathbf{0 . 7 9 9} \boldsymbol{V} . \) The correct
statement is:
A. the reaction Zn getting reduced Ag getting oxidized is spontaneous
B. Zn undergoes reduction and Ag is oxidized
C. zn undergoes oxidation Ag gets reduced
D. No suitable answer


\( X \) in the above reaction is
\( \mathbf{A} \cdot H N O_{3} \)
B. \( O_{2} \)
\( c \cdot O_{3} \)
\( \mathbf{D} \cdot K M n O_{4} \)


If the concentration of \( \mathrm{H}^{+}(\mathrm{aq}) \) ions increases in a solution, the acidity:
A . increases
B. decreases
C. remains same
D. None of the above


A divergent lens produces an image of magnification 0.5 when the object distance of \( 10 \mathrm{cm} . \) Find the focal power
of the lens (in diopters)


Identify the products.
\[
\mathbf{X}^{\mathrm{NaBH}_{4}} \text { ме }-\text { СОМН }-\text { Ме } \frac{\mathrm{Li} \mathrm{AlH}_{4}}{\mathbf{\}}
\]


Which of the following hormones helps in the conversion of glucose into glycogen in the body?
A. Insulin
B. Cortisone
c. Thyroxin
D. Oxytocin


If \( a^{2}+b^{2}+c^{2}=250 \) and \( a b+b c+ \)
\( c a=3 \), then find \( a+b+c \)


If the difference between pressure
inside and outside of a soap bubble is 6 \( \mathrm{mm} \) of water above atmospheric pressure and its radius is \( 8 \mathrm{mm} \). What is the surface tension in dynes per \( \mathrm{cm} \) :
A . 116
B. 256
c. 378
D. 450


The total number of orbitals in 3rd orbit
is:
A . 3
B. 5
\( c \cdot 4 \)
\( D \)


Plankton, Nekton and Benthos are not
the components of one of ecosystems which is
A. Oceans
B. Fresh water rivers
c. Grassland
D. Pond or lake


The equation \( 2 \cos ^{-1} x+\sin ^{-1} x=\frac{11 \pi}{6} \)
has
A. No solution
B. One solution
c. Two solutions
D. Three solutions


Which of the following is the largest family?
A. Leguminosae
B. Cucurbitaceae
c. Solanaceae
D. compositae


Find drivative of \( \boldsymbol{y}=(2-\sin x)\left(e^{x}+\right. \)
\( \left.x^{3}+2\right) \) with respect to \( x \)


Find the Simple interest on Rs. 10,000
for 2 years, at \( 10 \% \) per annum.
A. 100
B. 2000
\( c .300 \)
D. 400


Assertion
12 parts by mass of carbon in \( C O \) and
\( C O_{2} \) molecules combine with 16 and 32
parts by mass of oxygen.
Reason
A given compound always contains exactly the same proportion of elements by weight.
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


Given that \( A \) is positive acute angle and \( \sin A=\frac{\sqrt{3}-1}{2}, \) then \( A \) take the value
\( (s)- \)
A .15
B. 30
c. 45
D. 75


Structural formula of ethyne is :
\( \mathbf{A} \cdot H C \equiv C H \)
в. \( H_{3} C C H \)
\( c \)
D.


\( \angle B C A \)


In a survey, one in six people said they preferred a particular brand of cola. What this fraction is? And convert this
fraction into percentage.
A . \( 25 \% \)
B. \( 17 \% \)
\( c \cdot 10 \% \)
D. \( 5 \% \)


4 bad apples accidentally got mixed up with 20 good apples. In a draw of 2 apples at random, expected number of bad apples is
A . 1
в. \( 2 / 3 \)
c. \( 1 / 3 \)
D. \( 1 / 6 \)


At \( 20^{\circ} \mathrm{C} \) and a pressure of 1 atm each gas, 1 litre of water dissolves 0.043 g of pure \( O_{2} \) or 0.019 g of pure \( N_{2} . \) Assuming that dry air is composed of \( 20 \% \mathrm{O}_{2} \) and
\( 80 \% N_{2} \) (by volume) determine the
masses of \( \boldsymbol{O}_{2} \) and \( \boldsymbol{N}_{2} \) dissolved by 1 litre
of water at \( 20^{\circ} \mathrm{C} \) exposed to air at a
total pressure of 1 atm. Assume \( V . P . \) of
\( H_{2} \) at \( 20^{\circ} C \) be 'b' atm
A \( \cdot O_{2}=4.3 \times 10^{-3} g / L, N H 2=0.75 \times 10^{-2} g / L \)
B. \( O_{2}=5.25 \times 10^{-4} g / L, N H 2=1.7 \times 10^{-3} g / L \)
C \( \cdot O_{2}=8.6 \times 10^{-3} g / L, N H 2=1.5 \times 10^{-2} g / L \)
D. \( O_{2}=10.5 \times 10^{-4} g / L, N H 2=3.4 \times 10^{-3} g / L \)


Assertion
XX-XY type of sex determination mechanism is an example of female heterogamety and is found in
Drosophila.
Reason
Male heterogamety is seen in moths
where males produce two different
types of gamete.
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


Iron can liberate \( \boldsymbol{H}_{2} \) from dil. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \)
but copper cannot liberate \( \boldsymbol{H}_{2} \) from dil.
\( H_{2} S O_{4} \) because :
A. iron is above than hydrogen in the activity series.
B. copper is below in activity series than hydrogen
c. both A and B
D. none of these


The chief function of lymph nodes in mammalian body is to
A. Produce RBCs.
B. Collect and destroy pathogens.
c. Produce a hormone.
D. Destroy the old and worn out red blood cells.


Digested food after absorption comes
into
A. Heart
B. Lungs
c. Blood
D. water


The potential of the cell at \( 25^{\circ} \mathrm{C} \) is Given
\( p K_{a} \) of \( C H_{3} C O O H \) and \( p K_{b} \) of
\( N H_{4} O H=4.74 \)
A . \( -0.04 V \)
В. \( 0.04 V \)
\( c .-0.189 V \)
\( V \)
D. \( 0.189 V \)


A bullet of mass 20 g moving with a velocity of \( 500 \mathrm{m} / \mathrm{s} \), strikes a tree and goes out from the other side with a velocity of \( 400 \mathrm{m} / \mathrm{s} \). Calculate the work done by the bullet (injoules) in passing through the tree.
\( \mathbf{A} \cdot 900 J \)
B. \( 800 J \)
c. \( 950 J \)
D. \( 500 J \)


1 amu is equal to \( 1.66 \times 10^{-24} \) g.
A. True
B. False


The mixture of concentrated \( H C l \) and
\( H N O_{3} \) made in 3: 1 ratio contains :
A. \( C l O_{2} \)
в. \( N O C l \)
c. \( N C l_{3} \)
D. \( N_{2} O_{4} \)


The cube root of a number is a number
when \( _{\text {一一一一一一 }} \) three times gives that
number.
A. divided
B. addedd
c. subtracted
D. multiplied


Slope \( =-4 \) and \( y \) -intercept \( =2, \) then
the equation of line is \( m x+y=c . \) Find
\( \boldsymbol{m}+\boldsymbol{c} \)


K. \( \boldsymbol{E} \) of a body can be calculated by the amount of work done in stopping the moving body or by the amount of the work done in imparting the present
velocity to the body from the state of
rest


Osmotic pressure of the solution obtained by dissolving \( 100 g m \) of an organic compound in 1 litre solution is \( 2.414 \times 10^{5} \frac{N}{m^{2}} \) at \( 298 K . \) The organic compound can be:
A. glucose
B. urea
c. maltose
D. Nacl


An \( \alpha \) - particle \( \& \) a proton are projected towards the same nucleus. Calculate
the ratio of the distance of their closest
approach if they are projected with the same kinetic energy


From the following, find the pair of physical quantities which are analogous to one another in translatory motion and rotatory motion:
A. Mass, Moment of inertia
B. Force, Torque
c. Linear momentum, Angular momentum
D. All of these


Which of the following can adsorb larger volume of hydrogen gas?
A. Finely divided platinum
B. Colloidal solution of palladium
c. Small pieces of palladium
D. A single metal surface of platinum


Find the slope of line having inclination
\( \mathbf{6 0}^{\circ} \)


The distance between earth and moon
is about \( 3.8 \times 10^{5} \mathrm{km} . \) At what points
will the net gravitational force of earthmoon system be zero? [Given the mass
of the earth is 81 times the moon's
mass]. (Hint: Assume a body of unit
mass at the null point)


\( f y^{\prime}=-3 x\left(2-x^{2}\right)^{\frac{1}{2}} \) then find \( y^{\prime \prime} \)


All bacteria have
A. Mesosomes
B. Mitochondria
C . Chloroplast
D. Golgi complex


\( A B C D E \) is a regular pentagon. Show
that \( \triangle A B C \cong \triangle A E D \)


Assertion
DNA is more stable while RNA is more
reactive.
Reason
DNA was first discovered by Watson and
Crick (1953)
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


Two lenses of focal length \( f_{1}=10 \mathrm{cm} \)
and \( f_{2}=20 c m \) are kept as shown. The
resultant power of combination will be:
A. \( -10 D \)
B. \( 5 D \)
\( c .-5 D \)
D. \( 10 D \)


Assertion
Ca \( F_{2} \) has been given the name
fluorspar.
Reason
Solid \( C a F_{2} \) emits light when heated.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Draw a pair of tangents to a circle of
radius 5 cm which are inclined to each
other at an angle of 60


The radius of the circle is \( 25 \mathrm{cm} \) and the length of one of its chord is \( 40 \mathrm{cm} \). find
the distance of the chord from the
centre


The molecular formula of gypsum is :
A. \( \operatorname{CaSO}_{4} . \mathrm{H}_{2} \mathrm{O} \)
в. \( \operatorname{CaSO}_{4} .2 \mathrm{H}_{2} \mathrm{O} \)
\( \mathrm{c} \cdot 2 \operatorname{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( \operatorname{CaSO}_{4} .3 \mathrm{H}_{2} \)


Which of the stoma wall is thick?
A. Inner
B. Outer
c. Lateral
D. upper


Find the co-ordinate of a points on \( x \)
axis which is equidistant from the
points (-2,5) and (2,-3)


A car is moving on a straight road. The
velocity of the car varies with time as shown in figure. Initially \( (a t t=0), \) the
car was at \( x=0, \) where, \( x \) is the
position of the car at any time \( t \)
Average speed from \( t=0 \) to \( t=70 s \) wil
be:
A \( \cdot \frac{16}{7} m / \)
в. \( \frac{24}{7} m / \)
c. \( \frac{20}{7} m / \)
\( D \)


A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag.
Find the probability that one ball is red and one is green?
A . \( 19 / 20 \)
B. 17/20
\( c \cdot 8 / 10 \)
D. 21/40
\( E \cdot 15 / 40 \)


\( \ln \) an \( A C \) circuit \( V \) and \( I \) are given by
\( \boldsymbol{V}=\mathbf{1 0 0} \sin (\mathbf{1 0 0} \boldsymbol{t}) \) volt, \( \boldsymbol{I}= \)
\( 100 \sin \left(100 t+\frac{\pi}{3}\right) \) amp the power
dissipated in the circuit is
A . \( 5.0 k W \)
в. \( 2.5 k W \)
c. \( 1.25 k W \)
D. zero


A body is initially at rest on a smooth
surface. A force \( F \), whose time variation
is shown in the adjacent figure acts on
it for a duration of \( 4 s \). The momentum of
the ball at the end of the \( 4 s \) is in \( N-s \)
A .10
B. 20
\( c .30 \)
0.40


Solve:
\( \int \frac{1}{x \log x \log (\log x)} d x \)


What the covalency of phosphorous atom in excited state?
\( A \cdot 3 \)
B. 4
\( c \cdot 5 \)
\( D \)


The average ordinate of \( y=\sin x \) over the interval \( [\mathbf{0}, \boldsymbol{\pi}] \) is -
A. \( 1 / \pi \)
B. \( 2 / \pi \)
c. \( 4 / \pi^{2} \)
D. \( 2 / \pi^{2} \)


Colloids can be purified by :
A. condensation
B. peptization
c. coagulation
D. dialysis


In case, nitrogen and sulphur both are
present in an organic compound, sodium thiocyanate is formed. If sodium fusion is carried out with
excess of sodium, sodium thiocyanate decomposes. Which of the following compounds is/are present in the extract after decomposition?
A . \( N a C N \)
в. \( N a_{2} S \)
c. Both
D. None of these


The diagram below shows a cathode ray
tube in which the arrow indicates a
beam of charged particles approaching an electric field between the plates \( A \) and B. Name the charged particles.
A. Electron
B. Proton
c. Neutron
D. Alpha


Assertion
\( \boldsymbol{I}_{2}+\boldsymbol{I}^{-} \longrightarrow \boldsymbol{I}_{\boldsymbol{3}} \)
In above reaction, \( \boldsymbol{I}_{2} \) is Lewis base.
Reason

Electron pair acceptor is Lewis base.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following elements position's was not justified in Mendeleev's periodic table?
A. Hydrogen
B. Lithium
c. Sodium
D. Potassium


Huygen's originally thought that for the propagation of light waves wavefront is required.
A. True
B. False


The marks of some students were listed
out of \( 75 . \) The standard deviation of
marks was found to be \( 9 . \) Subsequently the marks were raised to a maximum of
100 and variance of new marks was
calculated. The new variance is :
A \( \cdot 144 \)
B. 122
\( c \cdot 81 \)
D. 3


Fossil fuels are found in the earth's
crust.
A . True
B. False


A billiard ball of mass \( M \) moving with
velocity \( v_{1} \) collides with another ball of
the same mass but at rest. If the
collision is elastic the angle of divergence after the collision is
A \( \cdot 0^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 90^{\circ} \)
D. \( 45^{\circ} \)


The ratio of enzyme to substrate
molecules can be as high as
A . 1: 100,000
в. 1: 50,000
c. 1: 10,000
D. 1: 1,000


Leaves of the plant have tiny pores for exchange of oxygen and carbon dioxide. These small pores are known as
A. Nodule
B. Stomata
c. Radicle
D. None of the above


An example of a solution which is not in equilibrium is :
A. chemical pH indicator
B. acid/base buffer
c. anhydrous solution
D. hypotonic solution
E. supersaturated solution


The solution of a salt of a metal of
atomic mass 112 was electrolysed for 15 minutes with a current of
1.5 ampere. The mass of the metal
deposited was \( 0.788 g \). Find the valency of the metal.
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
\( D \)


A gas cylinder can hold \( 1 \mathrm{Kg} \) of hydrogen at mom temperature and pressure:
i) Find the number of moles of hydrogen present
ii) What weight of \( C O_{2} \) can the cylinder hold under similar conditions of
temperature and pressure? \( (\boldsymbol{H}= \) \( \mathbf{1}, \boldsymbol{C}=\mathbf{1 2}, \boldsymbol{O}=\mathbf{1 6}) \)
iii) If the number of molecules of
hydrogen in the cylinder is \( X \), calculate
the number of \( C O_{2} \) molecules in the
cylinder under the same conditions of
temperature and pressure
iv) State the law that helped you to arrive at the above result.


The average acceleration in one time period in a simple harmonic motion is
A \( \cdot A \omega^{2} \)
B. \( A \omega^{2} / 2 \)
C. \( A \omega^{2} / \sqrt{2} \)
D. zero


The \( I P_{1} \) value of potassium is less than
the \( I P_{1} \) value of sodium. This is due to:
A. large size of potassium atom
B. small size of potassium atom
c. low density of potassium
D. univalent nature of potassium


An electromagnet is a
magnet.


Chloromycetin and streptomycin are
used to cure:
A. Typhoid
B. Tuberculosis
c. Both A and B
D. Dengue


In a climax community
A. Size of individual is small
B. Food chain and food web is complex
C . Efficiency of energy use is low
D. Ecological niches are few generalised compared to adjoining communities


A pair of perpendicular tangents are
drawn to a circle from an external point. Prove that length of each tangent is equal to the radius of the circle.


The phosphorus rich fertilizer obtained
from sea birds along the coast of Chile and Peru, is
A. Guano
B. Bone meal
c. Dung
D. urea


If the mass of the earth is doubled and
the distance of the moon revolving around the earth is also doubled, then, find the new time period of revolution of moon. (Take the present time of
revolution as 28 days)
\( A \cdot 6 \)
B. 36
\( c .56 \)
D. 112


On hybridisation of one \( s \) and one \( \boldsymbol{p} \)
orbitals we get:
A. two mutually perpendicular orbitals
B. two orbitals at \( 180^{\circ} \)
c. four orbitals directed tetrahedrally
D. three orbitals in a plane


Which of the following oxides are used
in the formation of elemental sulfur
from hydrogen sulfide?
A. Sulfur trioxide
B. Sulfur dioxide
c. Sulfur oxide
D. Selenium dioxide


The excess energy which a molecule must posses to become active is known
as:
A. kinetic energy
B. threshold energy
c. potential energy
D. activation energy


The cells without nuclei are present in
A. vascular cambium
B. Root hair
c. companion cell
D. Members of sieve tube


\( \mathbf{3} \boldsymbol{C u}+\mathbf{8} \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \rightarrow \boldsymbol{3} \boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{O}_{3}\right)_{2}+ \)
\( 4 H_{2} O+2 N O \)
The volume of nitric oxide collected at
the same time is :
\( [\mathrm{Cu}=64, \mathrm{H}=1,0=16, \mathrm{N}=14] \)
A . 5.6
B. \( 11.2 \mathrm{L} \)
c. 22.4
D. 44.8


A large conducting plane has surface charge density \( 10^{-2} C / m^{2} . \) Find the
electrostatic energy stored in a cubical volume of side \( 1 \mathrm{cm} \) in the front plane.
A. 1.4
B. \( 2.8 J \)
c. \( 5.6 J \)
D. none of these


The man who is known as the Father of
Experimental Physics is
A. Newton
B. Albert Einstien
c. Galileo
D. Rutherford


A metallic wire of resistance \( 20 \Omega \) is
stretched such that its length becomes three times. The new resistance of the
wire will be
A \( .6 .67 \Omega \)
B. \( 60.0 \Omega \)
c. \( 120 \Omega \)
D. \( 180 \Omega \)


Unsıder the IOIIOwIng melaııurgıcal
processes:
\( (I) \) Heating impure metal with \( C O \) and distilling the resulting volatile carbonyl
(b.p. \( \left.43^{0} \mathrm{C}\right) \) and finally decomposition at
\( 150^{0}-200^{0} C \) to get the pure metal.
\( (I I) \) Heating the sulphide ore in air
until a part is converted to oxide and then further heating in the absence of
air to let the oxide react with
unchanged metal sulphide. \( (I I I) \) Electrolysisof the molten electrolyte containing approximately equal amounts of the metal chloride
and \( N a C l \) to obtain the metal.
The processes used for obtaining magnesium, nickel and copper are
respectively:
\( \mathbf{A} \cdot(I),(I I) \) and \( (I I I) \)
B. \( (I I),(I I I) \) and \( (I) \)
C \( .(I I I),(I) \) and \( (I I) \)
D. \( (I I),(I) \) and \( (I I I) \)


A mass \( m_{1} \) of a substance of specific
heat capacity \( c_{1} \) at temperature \( t_{1} \) is
mixed with a mass \( m_{2} \) of other
substance of specific heat capacity \( c_{2} \)
at a lower temperature \( t_{2} . \) Deduce the
expression for the temperature of the mixture. State the assumption made, if
any.
A \( \cdot \frac{m_{1} t_{1}+m_{2} t_{2}}{m_{1}+m_{2}} \)
В. \( \frac{m_{1} t_{1}+m_{2} t_{2}}{m_{1} c_{1}+m_{2} c_{2}} \)
\( \mathbf{c} \cdot \frac{m_{1} c_{1}+m_{2} c_{2}}{m_{1}+m_{2}} \)
D. \( \frac{m_{1} c_{1} t_{1}+m_{2} c_{2} t_{2}}{m_{1} c_{1}+m_{2} c_{2}} \)


If velocity (V), force (F) and time (T) are chosen as fundamental quantities,
express
(i) mass and
(ii) energy in terms of \( \mathrm{V}, \mathrm{F} \) and \( \mathrm{T} \)


The circles \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}-\boldsymbol{4} \boldsymbol{x}+\boldsymbol{4} \boldsymbol{y}+\boldsymbol{4}=\mathbf{0} \)
and \( x^{2}+y^{2}-4 x-4 y=0 \)
A. Do not intersect
B. Are not orthogonal
c. Intersect orthogonally
D. concentric


Cells are composed of highly independent and randomly interacting components.
A. True
B. False


fthe boy is standing \( 1 \mathrm{m} \) from the
mirror, where will his image seem to be
located ?
A. 2 m behind the mirror
B. \( 1 \mathrm{m} \) behind the mirror
\( c .2 \mathrm{m} \) in front of the mirro
D. \( 1 \mathrm{m} \) in front of the mirror


Cleansing action of soap based on
which principle?


In balancing the following half-reaction:
\( \boldsymbol{C N}^{-} \longrightarrow \boldsymbol{C N O}^{-}(\boldsymbol{s k e l e t a l}), \) the
number of electrons that must be added
on the right is :


Hydroperoxide ion is a stronger nucleophile but weaker base than hydroxide ion.If true enter 1 else 0
\( A \)


If a lens of focal length, \( f, \) made of glass of refractive index \( \frac{5}{3} \) is placed in a liquid of refractive index, \( 4 \frac{5}{3}, \) then the focal length of the lens becomes
\( A \cdot f \)
в. \( 2 f \)
c. \( 4 f \)
D. \( -4 f \)


Simplify \( \cot ^{-1} \frac{1}{\sqrt{x^{2}-1}} \) for \( x<-1 \)
\( A \cdot \cos ^{-1} x \)
\( \mathbf{B} \cdot \sec ^{-1} x \)
\( \mathbf{c} \cdot \operatorname{cosec}^{-1} x \)
D. \( \tan ^{-1} x \)


Fluorine, chlorine, bromine, and iodine
form a family of related elements, known as:
A . light gases
B. halogens
c. purines
D. the aromatic ring


State True or False.
Sucrose do not undergo hydrolysis.
A. True
B. False


A circuit of logic gates given below, some input signal \( A, B, C \) are given with their output signal \( x, y \) and \( z \) is given in respective option, choose correct
options:

This question has multiple correct options
A. If \( A=1, B=1, C=1 \) then \( x=0, y=1, z=1 \)
B. If \( A=0, B=0 \) and \( C=1 \) then \( x=1, y=0, z=1 \)
c. If \( A=0, B=0 \) and \( C=1 \) then \( x=1, y=0, z=0 \)
D. If OR gate is replaced by NOR gate then net output signal of the circuit becomes \( z=0 \) for the input \( A= \) \( 0, B=0 \) and \( C=1 \)


Consider the following statements:
(i) Genus comprises a group of related species.
(ii) A taxon represents a taxonomic group of individual organism.
(iii) The family comprises a group of related genera.
(iv) Taxonomic category class includes related order.
A. (i), (ii) and (iv) are correct
B. (ii) and (iv) are correct
c. (i), (iii) and (iv) are correct
D. (ii), (iii) and (iv) are correct


Phosphoric acid is prepared on large scale from
A. phosphorus
B. dolomite
c. phosphorite
D. malachite


\( 200 g \) water is heated from \( 40^{\circ} \mathrm{C} \) to
\( 60^{\circ} \mathrm{C} . \) Ignoring the slight expansion of
water, the change in its internal energy is close to:
(Given specific heat of water \( = \) \( 4184 J / k g / K) \)
A. \( 167.4 k J \)
в. \( 16.7 k J \)
c. \( 8.4 k J \)
D. \( 4.2 k J \)


Which of the following uses chromium plating?
A. Car parts
B. Bath taps
C. Kitchen gas burners
D. All of the above


The arithmetic mean of \( 1,2,3, \dots, n, \) is
A \( \cdot \frac{n-1}{2} \)
в. \( \frac{n+1}{2} \)
c. \( \frac{n}{2} \)
D. \( \frac{n}{2}+1 \)


The number of primary, secondary and tertiary amines possible with molecular
formula \( C_{3} H_{9} N \) is :
\( A \cdot 1,2,2 \)
B. 1, 2,
c. \( 2,1, \)
D. 3, 0,


Write the degree of the following polynomials.
(i) \( \boldsymbol{p}+\boldsymbol{p}^{\mathbf{3}}+\boldsymbol{p}^{\boldsymbol{7}} \)
(ii) \( a+a^{3}-a^{0} \)
(iii) \( \boldsymbol{m}+\boldsymbol{a}^{4} \boldsymbol{m}+\boldsymbol{a}^{5} \boldsymbol{m}^{3}-\boldsymbol{m}^{2}-\boldsymbol{a}^{4} \boldsymbol{m}^{\boldsymbol{7}} \)


Which of the following statements is true for fuel cells?
A. They are more efficient
B. They are free from pollution
c. They run till reactants are active
D. All of the above


Number of unpaired electrons in \( \boldsymbol{F e}^{+3} \)
ion is :
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
D. 5


\( \mu m \) is
\( A \cdot 10^{-6} m \)
B. \( 10^{-9} \mathrm{m} \)
\( \mathbf{C} \cdot 10^{-10} \mathrm{m} \)
D. \( 10^{-3} \mathrm{m} \)


For all real numbers \( a, b \) and positive
integer \( n \) prove that:
\( (a+b)^{n}=^{n} C_{0} a^{n}+^{n} C_{1} a^{n-1} b+^{n} \)
\( C_{1} a^{n-2} b^{2}+\ldots \ldots \ldots .+^{n} C_{n} b^{n} \)


Which of the following is not a plant harmone?
A . Auxin
B. Gibberellins
c. cytokinin
D. Adrenaline


Vapour pressure of \( C C l_{4} \) at \( 25^{\circ} C \) is 143 mm \( H g \). If \( 0.5 g m \) of non-volatile solute (mol. mass 65 ) is dissolved in
\( 100 m l C C l_{4}, \) then the vapour pressure
of the solution at \( 25^{\circ} \mathrm{C} \) is:
[Given: density of \( \left.C C l_{4}=1.58 g / c m^{3}\right] \)
\( \mathbf{A} \cdot 141.93 m m \)
B . \( 94.39 \mathrm{mm} \)
c. \( 199.34 \mathrm{mm} \)
D. \( 143.99 \mathrm{mm} \)


Assertion
The resultant of the three vector
\( \overrightarrow{O A}, \overrightarrow{O B} \) and \( \overrightarrow{O C} \) as shown in the figure is \( \boldsymbol{R}(1+\sqrt{2}) . \) Here \( \boldsymbol{R} \) is the radius of the
circle.(Here \( \left.\angle A O B=\angle B O C=45^{\circ}\right) \)
Reason
\( \overrightarrow{O A}+\overrightarrow{O C} \) is along \( \overrightarrow{O B} \) and \( (\overrightarrow{O A}+ \) \( \overrightarrow{O C})+\overrightarrow{O B} \) is along \( \overrightarrow{O B} \)
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 figure shows a portions of the graph
\( y=2 x-4 x^{3} . \) The line \( y=c \) is such that
the areas of the regions marked I and II are equal. If a,b are the \( x \) -coordinates of A,B respectively, then a + b equals
\( A \cdot \frac{2}{\sqrt{7}} \)
B. \( \frac{3}{\sqrt{7}} \)
\( c \cdot \frac{4}{\sqrt{7}} \)
\( D \cdot \frac{5}{\sqrt{7}} \)


A dancer demonstrating dance steps
along a straight line. The position time
\( \operatorname{graph}(x-t) \) is as shown in the given
figure. Find the average speed for the
dance step depicted by CD.
A. \( 1 \mathrm{ms}^{-1} \)
B. \( 2.66 \mathrm{ms}^{-1} \)
\( \mathbf{c} \cdot 3 m s^{-1} \)
D. \( 0.89 \mathrm{ms}^{-1} \)


If \( \boldsymbol{x} \boldsymbol{\epsilon}[-1,0), \) then find the value of
\( \cos ^{-1}\left(2 x^{2}-1\right)-2 \sin ^{-1} x \)
\( \mathbf{A} \cdot-\pi / 2 \)
в. \( +\pi / 2 \)
c. \( -\pi \)
D. \( +\pi \)


Which of the following is a rootless aquatic plant,in which, a portion of the leaf forms a tiny sac for trapping insects?
A. Nepenthes
B. Drosera
c. Utricularia
D. Dionaea


If \( \sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2} \) and \( \sin 2 x= \)
\( \cos 2 y, \) then
This question has multiple correct options
A \( \cdot x=\frac{\pi}{8}+\sqrt{\frac{1}{2}-\frac{\pi^{2}}{64}} \)
B. \( y=\sqrt{\frac{1}{2}-\frac{\pi^{2}}{64}}-\frac{\pi}{12} \)
c. \( _{x}=\frac{\pi}{12}+\sqrt{\frac{1}{2}-\frac{\pi^{2}}{64}} \)
D. \( y=\sqrt{\frac{1}{2}-\frac{\pi^{2}}{64}}-\frac{\pi}{8} \)


In one polynucleotide strand of a DNA molecule, the ratio of \( \boldsymbol{A}+\boldsymbol{T} / \boldsymbol{G}+\boldsymbol{C} \) is
0.3. What is the \( \boldsymbol{A}+\boldsymbol{G} / \boldsymbol{T}+\boldsymbol{C} \) ratio of
the entire DNA molecule?
A . 0.3
B. 0.6
c. 1.2
D.


If \( \boldsymbol{P}(\boldsymbol{n})=\mathbf{1}^{2}+\mathbf{3}^{2}+\mathbf{5}^{2}+\ldots+ \)
\( (2 n-1)^{2}=\frac{n\left(4 n^{2}-1\right)}{3}, \) then which of
the following does NOT hold good?
\( \mathbf{A} \cdot P(1) \)
B \( \cdot P(2) \)
\( \mathbf{c} \cdot P(3) \)
D. None of these.


How should the mass of a rotating body
of radius r be distributed so as to
maximize its angular velocity?
A. The mass should be concentrated at the outer edge of the body
B. The mass should be evenly distributed throughout the body
C. The mass should be concentrated at the axis of
rotation
D. The mass should be concentrated at a point midway between the axis of rotation and the outer edge of the body
E. Mass distribution has no impact on angular velocity


Suppose the gravitational force varies
inversely as the \( n^{t h} \) power of distance. Then the time period of a planet in
circular orbit of radius \( R \) around the
sun will be proportional to:
B. \( R^{(n-1) / 2} \)
\( c \cdot R^{n} \)
D. \( R^{(n-2) / 2} \)


A company has 6,435 bars of soap. If the company has sold 20 per cent of its stock, then how many bars of soap did it
sell ?
A . 1237
B. 1257
\( c \cdot 1287 \)
D. 1300


The sum of the number of elements of
fifth and sixth period is :
\( \mathbf{A} \cdot 48 \)
B. 50
c. 52
D. 54


Solve \( : \int_{0}^{1} x^{2}\left(1-x^{2}\right)^{3 / 2} d x= \)


What are elastomers?


\( \boldsymbol{P t}\left|\left(\boldsymbol{H}_{2}\right)\right| \boldsymbol{p} \boldsymbol{H}=\boldsymbol{2} \| \boldsymbol{p} \boldsymbol{H}=\boldsymbol{3} \mid\left(\boldsymbol{H}_{2}\right) \boldsymbol{P} \boldsymbol{t} . \) The
cell reaction for the given cell is :
A. spontaneous
B. non-spontaneous
c. equilibrium
D. None of the above


Give the equations of the following reaction(s):
Oxidation of Propan-1-ol with alkaline
\( K M n O_{4} \) solution


Assertion
Bacteria and Protista do not have
circulatory system.
Reason
These organisms live in moist and
watery environment.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect.


A gas takes part in two processes in
which it is heated from the same initial
state 1 to the same final temperature.
The process are shown on the P-V diagram by the straight line 1 -2 and \( 1-3 \)
2 and 3 are the points on the same
isothermal curve. \( Q_{1} \) and \( Q_{2} \) are the
heat transfer along the two processes.
Then in which case will the heat
transfer be more?


Each of the height and radius of the base of a right circular cone is
increased by \( 100 \% \). The volume of the cone will be increased by
A . \( 700 \% \)
в. \( 500 \% \)
c. \( 300 \% \)
D. \( 100 \% \)


Box I contains two white and three black
balls. Box II contains four white and one
black balls and box III contains three
white and four black balls. A dice having
three red, two yellow and one green face,
is thrown to select the box. If red face
turns up, we pick up box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the
ball drawn is white, what is the
probability that the dice had turned up with a red face?


3, 4-benzopyrene causes
A. Leukaemia
B. Cytosilicosis
C. Lung cancer
D. Tuberculosis


Construct the triangle with the following measurements and locate the
centroid:
\( \triangle \boldsymbol{X} \boldsymbol{Y} \boldsymbol{Z} \) with \( \boldsymbol{X} \boldsymbol{Y}=\mathbf{6 . 5 c m}, \boldsymbol{Y} \boldsymbol{Z}= \)
\( 5.6 c m \) and \( X Z=7.2 c m \)


If \( \boldsymbol{x}=\mathbf{9}+\mathbf{4} \sqrt{\mathbf{5}} \) then \( \sqrt{\boldsymbol{x}}-\frac{\mathbf{1}}{\sqrt{\boldsymbol{x}}} \) is equal
to?


Wrap a thin paper strip tightly around an iron rod. Try to burn the paper with candle while rotating the iron rod continuously. Does it burn?


Methyl acetylene is also known as:
A. butyne
B. propyne
c. ethyne
D. pentyne


The difference in \( \Delta H \) and \( \Delta E \) for the
combustion of methane at \( 27^{\circ} \mathrm{C} \) in
calories would be:
A . -1800
B. -162
c. -1200
D. -100


Which of the following elements has least number of electrons in its M shell?
\( A \cdot K \)
B. Ni
\( c . T i \)
\( D \)


How many products obtained on the ozonolysis of propene?


Find the perimeter of a square which
has an area of \( 121 \mathrm{cm}^{2} \)


Express 42 seconds as a percent of 6 minutes.


If the angle of banking of a road is \( 32^{\circ} \)
and if a turn has radius \( 72 m, \) what is
the maximum speed at which a car can turn, given the coefficient of friction between the car tyres and the road is \( \mathbf{0 . 3 4} ?(\operatorname{in} \mathbf{m} / \mathbf{s}) \)
A . 29.4
B. 26.3
c. 21.3
D. 62.3


Electrophile used in the nitration of
benzene is:
A. hydronium ion
B. sulphonic acid
c. nitronium ion
D. bromide ion


Pick up the correct option
(a) Primary succession begins in areas where natural communities have been
destroyed
(b) Hydrarch succession takes place in
water
(c) Climax community is the community that is near equilibrium with immediate environment
(d) In newly cooled lava secondary succession occurs
\( A \cdot \) a and \( b \)
B. b and c
c. a and \( d \)
D. b only
E. a only


mole of an ideal gas at initial temperature T was cooled is ochorically
till the gas pressure decreased n times. Then by an isobaric process, the gas was restored to the initial temperature
T. Find the net heat absorbed by the gas
in the whole process.


Let \( \boldsymbol{A}=\left\{\boldsymbol{a}_{1}, \boldsymbol{a}_{2}, \boldsymbol{a}_{3}, \boldsymbol{a}_{4} \boldsymbol{a}_{5}, \boldsymbol{a}_{6}\right\} \) and \( \boldsymbol{B}= \)
\( \left\{b_{1}, b_{2}, b_{3}\right\} . \) The number of functions of
\( \boldsymbol{f}: \boldsymbol{A} \rightarrow \boldsymbol{B} \) such that it is onto and there
are exactly three elements in \( A \) such that \( \boldsymbol{f}(\boldsymbol{A})=\boldsymbol{b}, \) is
A . 75
B. 90
c. 100
D. 120


Four charges are arranged at the corners
of a square \( \mathrm{ABCD} \) as shown in the figure. If a test charge is placed at the centre calculate the direction of net force on that
charge.
A. zero
B. along the diagonal AC
c. along the diagonal BD
D. perpendicular to side AB


The following substances are the excretory products in animals. Choose the least toxic from among them.
A. Urea
B. Uric acid
c. Ammonia
D. Carbon dioxide


A copper disc of radius \( 0.1 \mathrm{m} \) is rotated about its center with 20 revolution per
second in a uniform magnetic field of
\( 0.1 T \) with its plane perpendicular to the field. The emf induced across the radius
of the disc is?


\( \lim _{x \rightarrow \infty} \frac{x^{3}+x^{2}+1}{2 x^{2}+3 x+4}= \)
A.
B.
\( c \cdot \alpha \)
D.


The symbol for units should be written with a small letter
A . True
B. False


If the surface area of a sphere is
\( 9856 c m^{2} . \) Find its diameter.
A . 28
B. 55
\( c .56 \)
D. 30


The fractional abundance of \( C l^{35} \) in a
sample of chlorine containing only \( C l^{35} \) (atomic weight \( =\mathbf{3 4 . 9} \) ) and \( \boldsymbol{C l}^{\mathbf{3 7}} \)
(atomic weight \( =\mathbf{3 6 . 9} \) ) isotopes, is \( \mathbf{0 . 6} \)
The average mass number of chlorine
is
A . 35.7
B. 35.8
c. 18.8
D. 35.77


Which of the following function is one-
one?
A \( . f: R \rightarrow R \) given by \( f(x)=|x-1| \) for all \( x \in R \)
B. \( g:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow R \) given by \( g(x)=|\sin x| \) for all \( x \in \)
\( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
\( \mathbf{c} \cdot_{h}:\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \in R \operatorname{given} \operatorname{by} h(x)=\sin x \) for all \( x \in \)
\( \left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \)
\( \mathbf{D} \cdot \phi: R \rightarrow R \) given by \( f(x)=x^{2}-4 \) for all \( x \in R \)


Two satellites of earth, \( S_{1} \) and \( S_{2} \), are
moving in
the same orbit. The mass of \( S_{1} \) is four
times the
mass of \( S_{2} \). Which one of the following
statements is true?
A. The kinetic energies of the two satellites are
equal
B. The time period of \( S_{1} \) is four times that of \( S_{2} \)
c. The potential energies of earth and satellite in
the two cases are equal
D. \( S_{1} \) and \( S_{2} \) are moving with the same speed


If \( A, B, C \) are the angles of a triangle,
then the value of determinant
\( \left|\begin{array}{ccc}-1+\cos B & \cos C+\cos B & \cos B \\ \cos C+\cos A & -1+\cos A & \cos A \\ -1+\cos B & -1+\cos A & -1\end{array}\right| \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c .-1 \)
\( D \)


Name the scale on which the
destructive energy of an earthquake is measured.
A. Temperature scale
B. Vector scale
c. Richter scale
D. Energy scale


Consider the diagram of the trajectory
of a thrown tomato. At what point is the
kinetic energy least?


Which of the following is the biggest planet?
A. Jupiter
B. Venus
C. Mercury
D. Pluto


\( \int_{-1 / 2}^{1 / 2}(\cos x)\left[\log \left(\frac{1-x}{1+x}\right)\right] d x \) is equal
to :
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot e^{1 / 2} \)
D. \( 2 e^{1 / 2} \)


Determine the ratio of charge to mass (specific charge) for electron and alpha particle.
A .2:
B. 1: 1
c. 1: 2
D. None of these


For the circuit show below, the current
through the zener diode is :
\( A \cdot 5 \) m
B. Zero
c. \( 14 \mathrm{mA} \)
\( 0.9 \mathrm{m} \)


\( O \) is the center of the circle. \( O P=12 \)
\( \mathrm{cm}, \) and \( \boldsymbol{O B}=\mathbf{1 3} \mathrm{cm} . \) Find \( \boldsymbol{A B} \)
A. \( 8 \mathrm{cm} \)
B. \( 10 \mathrm{cm} \)
\( \mathrm{c} \cdot 12 \mathrm{cm} \)
D. \( 13 \mathrm{cm} \)


Find the energy needed to remove a neutron from the nucleus of the
calcium isotope \( 20^{46} \) Ca


A covalent bond is possible between:
A. Similar atoms
B. Dissimilar atoms
c. similar and Dissimilar atoms
D. similar molecules


The equation of the plane through the points (2,3,1) and (4,-5,3) and parallel to \( x \) -axis is
A. \( x-z-1=0 \)
в. \( 4 x+y-11=0 \)
c. \( y+4 z-7=0 \)
D. None of these


State true or false:
The probabilities of three mutually
exclusive events \( A, B, C \) are \( P(A)= \)
\( \frac{2}{3}, P(B)=\frac{1}{4}, P(C)=\frac{1}{6} \)
A. True
B. False


Find the centroid of a triangle, midpoints of whose sides are
(1,2,-3),(3,0,1) and (-1,1,-4)


If \( a=\frac{1+i}{\sqrt{2}} \) then show that \( a^{6}+a^{4}+ \)
\( \boldsymbol{a}^{2}+\mathbf{1}=\mathbf{0} \)


ype vour
In column II and write down the
matching pairs (some may not match)


If \( f(x) \) is differentiable everywhere, then
\( |\boldsymbol{f}(\boldsymbol{x})|^{2} \) is differentiable everywhere.
Enter \( 1 \text { if true or } 0 \text { otherwise }) \)


The value of \( \lim _{x \rightarrow 2} \frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2} \) is
\( A \cdot \frac{1}{8 \sqrt{3}} \)
в. \( \frac{1}{4 \sqrt{3}} \)
c. 0
D. None of these


Nitrifying bacteria convert
A. Nitrate to nitrogen
B. Ammonia to nitrogen
C. Nitrogen into soluble form
D. Ammonia to nitrate


The density of the atmosphere at sea
level is \( 1.29 \mathrm{kg} / \mathrm{m}^{2} \). assume that it does not change with altitude. then how high would the atmosphere extend?
\( A \cdot 3 \mathrm{km} \)
в. 7 кт
\( c \cdot 8 k m \)
\( D \cdot 9 \mathrm{km} \)


What are Galvanic cells? Explain the working of Galvanic cells with one example.


In the above figure both RISK and CLUE are parallelograms. Find the value of \( x \)


The differential equation representing the family of curves given by \( \boldsymbol{y}= \)
\( \boldsymbol{a} e^{-\boldsymbol{3} x}+\boldsymbol{b}, \) where \( \boldsymbol{a} \) and \( \boldsymbol{b} \) are arbitrary
constants, is :
\( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}+\boldsymbol{3} \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}-\boldsymbol{2} \boldsymbol{y}=\mathbf{0} \)
A \( \cdot \frac{d^{2} y}{d x^{2}}+3 \frac{d y}{d x}-2 y=0 \)
B. \( \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}=0 \)
c. \( \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}-2 y=0 \)
D \( \cdot \frac{d^{2} y}{d x^{2}}+3 \frac{d y}{d x}+2 y=0 \)
E \( \cdot \frac{d^{2} y}{d x^{2}}+3 \frac{d y}{d x}=0 \)


Two balls are dropped from height \( h_{1} \)
and \( h_{2} \) respectively. What is the ratio of
their velocities on reaching the ground is?
A. \( \sqrt{\frac{h_{2}}{h_{1}}} \)
B. \( \sqrt{\frac{h_{1}}{h_{2}}} \)
\( c \cdot \frac{h_{2}}{h_{1}} \)
D. \( \frac{h_{1}}{h_{2}} \)


Find the last term of the following sequence \( 2,3,4 \frac{1}{2} \ldots \ldots \) to 6 terms


Say true or false:
The following is a terminating decimal. \( 5 \div 8 \)
A. True
B. False


\( \int \frac{1}{\left(x^{6}-1\right)} d x \)
A \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \arctan \frac{2 x+1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\right. \)
\( \left.\quad \frac{1}{\sqrt{3}} \arctan \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)
B \( \cdot \)
\[
\begin{array}{l}\text { C } \mid / 2\left(\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\frac{1}{\sqrt{3}} \arctan \frac{2 x-1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\right. \\ \left.\frac{1}{\sqrt{3}} \arctan \frac{2 x+1}{\sqrt{3}}\right)+\mathrm{k}\end{array}
\]
C \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x+1}{\sqrt{3}}+\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}+\right. \)
\( \left.\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)
D \( \cdot 1 / 2\left(\frac{1}{6} \ln \frac{(x-1)^{2}}{x^{2}+x+1}-\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x+1}{\sqrt{3}}-\frac{1}{6} \ln \frac{(x+1)^{2}}{x^{2}-x+1}-\right. \)
\( \left.\frac{1}{\sqrt{3}} \operatorname{arccot} \frac{2 x-1}{\sqrt{3}}\right)+\mathrm{k} \)


Fastest rate of reaction will be when \( \boldsymbol{R} \)
is:
\( \mathbf{A} \cdot C H_{3}- \)
в. \( C H_{3}-C H_{2} \)
c. \( C H_{3}-\begin{array}{r}C H- \\ \\ C H_{3}\end{array} \)
\( \begin{array}{l}\text { D. } \\ \qquad C H_{3}-\begin{aligned} & C H_{3} \\ & C H \end{aligned} \\ & _{C H_{3}}\end{array} \)


\( \int e^{x} \sec x(1+\tan x) d x \)
A \( \cdot e^{x} \cos x+C \)
B . \( e^{x} \sec x+C \)
\( \mathbf{c} \cdot e^{x} \sin x+C \)
D. \( e^{x} \tan x+C \)


Match entries of List I and List II


Two complex numbers are represented
by ordered pairs \( z_{1}: a+i b \& z_{2}: c+i d \)
which of the following is correct
representation for \( z_{1}-z_{2}=? \)
A \( \cdot(a-c)-i(b+d) \)
B . \( (a-c)+i(b-d) \)
c. \( (a+c)-i(b+d) \)
D. None of these


Water exists both as solid and liquid at:
A \( \cdot 100^{\circ} \mathrm{C} \)
В. \( 50^{\circ} \) С
c. \( 2.5^{\circ} \mathrm{C} \)
D. \( 0^{\circ} \mathrm{C} \)
E \( .-10^{\circ} \mathrm{C} \)


State whether the following statement
is True or False.

A shaving mirror is a concave mirror
A. True
B. False


Which of the following statement about hydrogen spectrum are correct? This question has multiple correct options
A. All the lines of Lyman series lie in ultraviolet region
B. All the lines of Balmer series lie in visible region
C. All the lines of Paschen series lie in infrared region
D. None of the above


In the reaction \( \rightarrow \)
\( M N O_{2}+4 H C L \rightarrow M n C l_{2}+ \)
\( \mathbf{2} \boldsymbol{H}_{2} \boldsymbol{O}+\boldsymbol{C} \boldsymbol{l}_{2} \)
(a) name the compound (i) oxidised
(ii) reduced
(b) define oxidation of reduction on its
basis.


\( \int e^{x}\left(\tan x+\sec ^{2} x\right) d x \)


\( \frac{x^{2}+9 x+14}{x+7}= \)
\( \mathbf{A} \cdot x+2 \)
B. \( x+7 \)
\( c \cdot 2 \)
D.


According to Euclid's division algorithm, HCF of any two positive integers a and b with \( a>b \) is obtained by applying Euclid's division lemma to a and b to find \( q \) and \( r \) such that \( a=b q+ \)
\( r, \) where \( r \) must satisfy
A. \( 1<r<b \)
В. \( 0<r<b \)
c. \( 0 \leq r<b \)
D. \( 0<r \leq b \)


How does ozone react with the following
(i) \( P b S \)
(ii) \( \boldsymbol{K} \boldsymbol{I} \)
(iii) \( C_{2} H_{4} \)
(iv) \( N O \)


What is the type of chemical reaction carried out after roasting in order to obtain zinc?
A. reduction
B. oxidation
c. both \( A \) and \( B \)
D. none of the above


A concave shaving mirror has a radius of curvature of \( 35.0 \mathrm{cm} . \) It is positioned so that the (upright) image of a mans face is 2.50 times the size of the face.
How far is the mirror from the face?
A. \( 5.25 \mathrm{cm} \)
B. 21.0 \( \mathrm{cm} \)
\( c \cdot 10.5 \mathrm{cm} \)
D. \( 42 \mathrm{cm} \)


Construct \( \triangle \boldsymbol{A B C} \) with \( \boldsymbol{B C}=\mathbf{6 . 5} \mathrm{cm} \)
\( \boldsymbol{A C}=\mathbf{5} \mathrm{cm} \) and \( \angle \boldsymbol{C}=\mathbf{6 0}^{\circ} . \)


At \( p H=3 \) and rest all reductant and oxidant in change (I) being in standard
state, \( M n O_{4}^{-} \) can oxidise:
A \( \cdot I^{-} \) and \( B r^{-} \) both
B. \( I^{-} \) and \( C l^{-} \) both
c. \( I^{-}, B r^{-} \) and \( C l^{-} \) all
D. \( B r^{-} \) and \( C l^{-} \) both


If \( \sin (\theta+\alpha)=a \) and \( \sin (\theta+\beta)= \)
\( \boldsymbol{b},((\mathbf{0}<\boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\theta}<\boldsymbol{\pi} / 2)) \) then
\( 2 \cos ^{2}(\alpha-\beta)-1-4 a b \cos (\alpha-\beta) \) is
A \( \cdot 1-a^{2}-b^{2} \)
B . \( 1-2 a^{2}-2 b^{2} \)
c. \( 2+a^{2}+b^{2} \)
D . \( 2=a^{2}-b^{2} \)


Find the total number of binary
operations on \( \{a, b\} \)


Figure shows a series LCR circuit
connected to a variable frequency 230 V
source. \( L=5.0 \mathrm{H}, \mathrm{C}=80 \mu \mathrm{F}, \mathrm{R}=40 \Omega \)
(a) Determine the source frequency
which drives the circuit in resonance.
(b) Obtain the impedance of the circuit
and the amplitude of current at the
resonating frequency.
(c) Determine the rms potential drops
across the three elements of the circuit.
Show that the potential drop across the
LC combination is zero at the resonating
frequency.


The average translational energy and the rms speed of molecules in a sample
of oxygen gas at \( 300 \mathrm{K} \) are \( 6.21 \times 10^{-21} \mathrm{J} \)
and \( 484 \mathrm{m} / \mathrm{s} \) respectively. The corresponding values at \( 600 \mathrm{K} \) are nearly (assume ideal gas behaviours)
A \( .12 .42 \times 10^{-21} \mathrm{J}, 968 \mathrm{m} / \mathrm{s} \)
B. \( 8.78 \times 10^{-21} \) J, \( 684 \mathrm{m} / \mathrm{s} \)
c. \( 6.21 \times 10^{-21} \) J, \( 968 \mathrm{m} / \mathrm{s} \)
D. \( 12.42 \times 10^{-21} \) 」, \( 684 \mathrm{m} / \mathrm{s} \)


18 men can reap a filed in 35 days. For
reaping the same filed in 15 days, how many men are required?


Two isolated metallic solid sphere of radius \( R \) and \( 2 R \) are charged such that both of these have same charge density
a. the spheres are locted far away from each other and are connected by a thin
conducting wire . the new charge density on the bigger sphere is
A \( \cdot \frac{5 \sigma}{6} \)
в. \( \frac{56 \sigma}{5} \)
c. \( \frac{3 \sigma}{5} \)
D. \( \frac{52 \sigma}{6} \)


Tracheary elements of protoxylem are
A. Larger and broader
B. Formed towards the end
C. With advanced type of thickenings
D. Short narrow with primitive type of thickenings


The diagonals of rhombus are \( 8 \mathrm{cm} \) and
\( 10 \mathrm{cm} \) Then the area of the rhombus is
\( \mathbf{A} \cdot 64 \mathrm{cm}^{2} \)
В. \( 100 \mathrm{cm}^{2} \)
\( c \cdot 80 c m^{2} \)
D. \( 40 \mathrm{cm}^{2} \)


Which of the following species has less number of protons than the number of
neutrons?
This question has multiple correct options
A \( \cdot \frac{12}{6} C \)
В . \( _{9}^{9} F \)
\( \mathbf{c} \cdot_{11}^{23} N a \)
D \( \cdot \frac{24}{12} M g \)


A current \( I=1.00 A \) circulates in a
round thin-wire loop of radius \( \boldsymbol{R}= \)
100 \( m m \). Find the magnetic
induction at the centre of the loop.
A. \( 7.3 \mu T \)
B. \( 3.7 \mu T \)
c. \( 3.6 \mu T \)
D. \( 6.3 \mu T \)


What is the hybridisation of carbon that is attached to chlorine atom in \( n- \)
primary alkyl halide?
\( A \cdot s p^{3} \)
B. \( s p^{2} \)
\( c \cdot s p \)
D. \( s p^{3} d \)


The number of peroxide bonds in
perxenate ion \( \left[\boldsymbol{X} \boldsymbol{e} \boldsymbol{O}_{\boldsymbol{6}}\right]^{-4} \) is :
\( A \cdot O \)
B. 2
\( c \cdot 3 \)
D.


Two concentric coils each of radius
equal to \( 2 \pi \mathrm{cm} \) are placed at right
angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic
induction in \( w e b e r / m^{2} \) at the centre of
the coils will be
\( \left(\mu_{0}=4 \pi \times 10^{-7} w b / A . m\right) \)
A \( \cdot 10^{-5} \)
B . \( 12 \times 10^{-5} \)
C \( .7 \times 10^{-5} \)
D. \( 5 \times 10^{-5} \)


Two infinitely large sheets having
charge densities \( \sigma_{1} \) and \( \sigma_{2} \) respectively
\( \left(\sigma_{1}>\sigma_{2}\right) \) are placed near each other
separated by distance \( d . A \) charge \( q \) is placed in between two plates such that there is no effect on charge distribution on plates. Now this charge is moved at
an angle of \( 45^{\circ} \) with the horizontal
towards plate having charge density \( \sigma_{2} \) by distance \( a(a<d) . \) Find work done
by electric field in the process.


State whether the given statement is true or false:

Use of \( c i s \) -platin in cancer treatment
also causes severe kidney damage.
A. True
B. False


The human blood is a complex mixture of biochemicals. It contains many proteins. These can be separated by moving them in a solution under the influence of:
A. intense radiaton
B. an electric field
c. a magnetic force
D. an organic solvent


A particle of mass \( m \) moving in \( x \) direction with speed \( 2 v \) is hit by another
particle of mass \( 2 m \) moving in the \( y \) direction with speed \( v \). If the collisioni is
perfectly inelastic, the percentage of the energy retained by the colliding particles after the collision is close to
A . \( 56 \% \)
B. 80\%
c. \( 35 \% \)
D. 44\%


Malpighian corpuscles occur in
A. Medulla
B. Cortex
c. Pelvis
D. Pyramid


Which of the following pair of monomers are used in preparation of PHBV ?
A. \( \beta \) - hydroxy valeric acid, amino caproic acid
B. \( \beta \) - hydroxy butyric acid, \( \beta \) - hydroxy valeric acid
c. \( \beta \) - hydroxy butyric acid, adipic acid
D. Lactic acid, adipic acid


Solve :
\( \frac{4}{x}+\frac{5}{y}=7 ; \frac{3}{x}+\frac{4}{y}=5 \)


Which is the first energy level containing f-orbitals?


Let the function \( g(x)=\sqrt[3]{x}-2+c \)
and \( g(27)=-1, \) then find the value of
\( c \)
A . -10
B. -
c. 0
\( D \)


A resistance of \( 20 \Omega \) is connected to a
source of an alternating potential \( \boldsymbol{V}= \) \( 220 \sin (100 \pi t) . \) The time taken by the
current to change from the peak value
to rms value, is
A . \( 0.2 s \)
B. \( 0.25 s \)
c. \( 2.5 \times 10^{-2} s \)
D. \( 2.5 \times 10^{-3} s \)


The largest brackish water lake in India
is
A. Wullar lake
B. Sambhar lake
c. Kabar lake
D. Chilka lake


The acid in which \( 0-O \) bonding is
present in:
A. \( H_{2} S_{2} O_{3} \)
в. \( H_{2} S_{2} O_{6} \)
c. \( H_{2} S_{2} O_{8} \)
D. \( H_{2} S_{4} O_{6} \)


Of the given alkali metals, the one with the smallest size is:
\( A \cdot R b \)
B. cs
\( c \cdot k \)
D. Na


\( A L \) of \( X_{L} \) is connected in series with a
bulb \( B \) to an A.C. source as shown in the
figure. Briefly explain how does the brightness of the bulb change, when
(i) Number of turns of the inductor is
reduced.
(ii) A capacitor of reactance \( \boldsymbol{X}_{\boldsymbol{C}}=\boldsymbol{X}_{\boldsymbol{L}} \)
is included in the same circuit
(iii) If increase driving frequency \( \boldsymbol{f} \) in the circuit, does the current amplitude
\( I \) increase or stay the same?


Find the value of \( \boldsymbol{X} \)
\( \mathbf{A} \cdot 60^{\circ} \)
B. \( 70^{\circ} \)
\( \mathbf{c} \cdot 80^{\circ} \)
\( \mathbf{D} \cdot 90^{\circ} \)


Name the radiations:
(i) That are used for photography at night.
(ii) Used for detection of fraction in bones.
(iii) Whose wavelength range is from
\( 100 A \) to \( 4000 \dot{A} \) (or \( 10 n m \) to \( 400 n m \) ).


In the AC circuit shown, \( X_{L}=7 \Omega, R= \)
\( 4 \Omega \) and \( X_{c}=4 \Omega . \) The reading of the
ideal voltmeter \( V_{2} \) is \( 8 \sqrt{2} \). The reading
of the ideal ammeter will be:
A . \( 1 A \)
в. \( 2 A \)
c. \( \sqrt{2} A \)
D. \( \frac{1}{\sqrt{2}} \)


Evaluate \( \int_{0}^{2} \frac{1}{\sqrt{3+2 x-x^{2}}} d x \)


Iron loses magnetic property at:
A. melting point
В. \( 1000 K \)
C . curie point
D. boiling point


A ray of light is incident on a hollow
glass prism as shown. Then the ray will
undergo:
A. deviation and dispersion both
B. deviation but no dispersion
C. dispersion but no deviation
D. neither deviation nor dispersion


A block of mass \( 3 \mathrm{kg} \) is placed on the floor of coefficient of static friction is
0.4. The force of 3.5 N applied on the block. Calculate the force of friction and
discuss the motion of the body.
A. \( 3.5 \mathrm{N}, \) moves
B. 3.5 N, remains at rest
c. \( 11.76, \) moves
D. 11.76 N, it remains at rest


What is the side included between the
angles \( \mathrm{M} \) and \( \mathrm{N} \) of \( \triangle M N P ? \)


A \( 1 \mathrm{kg} \) block situated on a rough incline is connected to a spring of spring constant 100Nm-1100Nm-1 as shown
The block is released from rest with the
spring in the unstretched position. The
block moves \( 10 \mathrm{cm} \) down the incline
before coming to rest. Find the
coefficient of friction between the block
and the incline. Assume that the spring
has a negligible mass and the pulley is frictionless.


Eddy currents are produced in a
metallic conductor when
A. The magnetic flux linked with it changes
B. It is placed in a changing magnetic field
C. It is placed in a magnetic field.
D. Both A and B


Area under the velocity-time graph
gives
A. Displacement
B. Speedd
c. Acceleration
D. none of the above


If \( f(x) \) is differentiable function in the interval \( (0, \infty) \) such that \( f(1)=1 \) and \( \lim _{t \rightarrow x} \frac{t^{2} f(x)-x^{2} f(t)}{t-x}=1 \) for
\( \operatorname{each} x>0 \) then


Consider two statements:
A) The force with which two charges
interact is not changed by the presence of the other charges.
B) Electric force experienced by the
charge particle due to number of fixed point charges is vector resultant of the
forces experience due to individual
charge.
\( A \). Both \( A \) and \( B \) are correct
B. Only A is correct
C. Only B is correct
D. Both A and B are wrong


Explain:
(i) Zone refining
(ii) Column
chromatography.


\( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) changes black lead sulphide to
white:
A \( . P b \)
в. \( P b O_{2} \)
\( c . P b O \)
\( \mathrm{D} \cdot \mathrm{PbSO}_{4} \)


\( M_{1} \) and \( M_{2} \) are plane mirrors and kept
parallel to each other. At point 0 , there
will be a maxima for wavelength \( \lambda \). Light
from a monochromatic source \( \boldsymbol{S} \) of
wavelength \( \lambda \) is not reaching directly on
the screen. Then, \( \lambda \) is:
\( ^{A} \cdot \frac{3 d^{2}}{D} \)
B. \( \frac{3 d^{2}}{\text { on }} \) \( 2 D \)
\( c \cdot \underline{d^{2}} \)
\( \bar{D} \)
D. \( 2 d^{d} \)


Which of the following material is used in making the core of a moving coil galvanometer?
A. copper
B. Nickel
c. Iron
D. Both (a) and (b)


Find the value of \( \csc \left(-1410^{\circ}\right) \)


If the price of gas is increased by \( 20 \% \) by how much \% must a housewife reduce her consumption of gas, so as to have no extra expenditure?
A \( \cdot 16 \frac{2}{3} \% \)
в. 25 \%
c. 20 \%
D. 50 \%


Assertion
Atomic number of the element
ununtrium is 113
Reason
According to IUPAC systematic nomenclature, the numerical roots for
1,1 and 3 are un, un and tri respectively
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


Are the polysaccharides sweet like sugars?


Which one of the following fractions is more than one-third?
A \( \cdot \frac{23}{70} \)
в. \( \frac{205}{819} \)
c. \( \frac{26}{75} \)
D. \( \frac{118}{355} \)


Find the diameter of the circle if its.
Circumference is \( 62.8 \mathrm{cm}(\pi=3.14) \)


In displacement-time graph of a
particle as shown in figure, velocity of particle changes its direction at point \( \mathbf{A} \)
Reason
Sign of slope of \( s \) -t graph decides the
direction of velocity.
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


Two general types of vacuum assisted
power brakes are
A. Vacuum suspended and power suspended
B. Integral and pressure suspended
C. Atmospheric and vacuum suspended
D. Power and pressure suspended


The presence of \( \mathrm{CO}_{2} \) in blood will lower
pH because \( \mathrm{CO}_{2} \) combines with
with the rate of reaction increased by
\( A \cdot H_{2} O \) to form \( H^{+} \) and \( H C O_{3}^{-}, \) carbonic anhydrase
B. \( \mathrm{H}_{2} \mathrm{O} \) to form only \( \mathrm{HCO}_{3} \) - carbonic anhydrase
\( \mathrm{C} \cdot \mathrm{H}_{2} \mathrm{O} \) to form only \( \mathrm{H}^{+}, \) carbonic ions
D. \( H^{+} \) to form \( \mathrm{HCO}_{3}^{-} \), oxyhaemoglobin


IUPAC name of the compound \( \boldsymbol{C H}_{3}- \) \( \boldsymbol{C H}_{2}-\stackrel{0}{\boldsymbol{C}}-\boldsymbol{C H}_{2}-\stackrel{0}{\boldsymbol{C}}-\boldsymbol{C O O H} \)
A. hexanedione - 2, 4-ic-1-oic acid
B. 2, 4- dioxohexanoic acid
c. propionyl-dioxo-oic acid
D. none of these


Fill in the blanks.
Nitrogen is towards
litmus.


When water freezes, its molecules take
on a more structured order. Why doesn't
this contradict the Second Law of
Thermodynamics?
A. Because the density of the water is decreasing
B. Because the water is gaining entropy as it goes from liquid to solid state
C. Because the waters internal energy is decreasing
D. Because the surroundings are losing entropy
E. Because the surroundings are gaining entropy


The walls of an enclosure are
maintained at a steady temperature \( T \) When two similarly calibrated thermometers are placed inside the
enclosure, they give the same reading \( \boldsymbol{T} \) after thermal equilibrium has been established. Which statement correctly describes the required conditions?
A. under all circumstances
B. only if they absorb radiation at equal rates
c. only if they have equal thermal capacities
D. only if both are perfect absorbers


Which of the following is not a use of graphite?
A. Dry lubricant
B. Electrodes
c. Black paints
D. High precision thermometers