In an experiment with 15 observations
on \( x, \) then following results were
available:
\( \sum x^{2}=2830, \sum x=170 \)
One observation that was 20 was found
to be wrong and was replaced by the
correct value \( 30 . \) Then the corrected
variance is:
A . 78
B . 188.6666
c. 177.3333
D. 8.3333


When we jump on a heap of sand, we
didn't get hurted but on the floor of concrete, we get hurted. Explain.


Find the equilibrium constant for the reaction, \( \boldsymbol{F e}^{2+}+\boldsymbol{C e}^{4+} \rightleftharpoons \boldsymbol{F e}^{3+}+\boldsymbol{C e}^{3+} \)
\( \left[\text { Given: } \boldsymbol{E}_{C e^{4+} / C e^{3+}}^{o}=\right. \)
\( \left.\mathbf{1} . \mathbf{4 4} \boldsymbol{V} ; \boldsymbol{E}_{\boldsymbol{F e}^{3+} / \mathbf{F e}^{\mathbf{2 +}}}^{\boldsymbol{o}}=\mathbf{0 . 6 8} \boldsymbol{V}\right] \)
A . \( 7.6 \times 10^{12} \)
B . \( 5.4 \times 10^{12} \)
c. \( 3.3 \times 10^{12} \)
D. None of the above


Let \( A B C D \) be a parallelogram and let \( L \) and \( \mathrm{M} \) be the midpoints of the sides \( B C \) and \( C D \) respectively. Then \( \overrightarrow{A L}+ \) \( \boldsymbol{A} \overrightarrow{\boldsymbol{M}}= \)
\( A \cdot \overrightarrow{A C} \)
В \( \cdot \frac{2}{3} \overrightarrow{A C} \)
c. \( \frac{3}{2} \overrightarrow{A C} \)
D. \( 2 A C \)


Tin reacts with concentrated \( H N O_{3} \) to
give:
A. stannic nitrate
B. stannous nitrate
c. metastanic acid
D. none of these


The figure shows a solid of uniform cross-section. Find the volume of the
solid. All measurements are in
centimetre. Assume that all angles in
figure are right angles.
\( A \cdot 180 \mathrm{cm}^{3} \)
3. \( 108 \mathrm{cm}^{3} \)
\( c \cdot 188 c m^{3} \)
) \( .118 \mathrm{cm}^{3} \)


In which part of the excretory system of mammals, can you first use the term urine for contained fluid?
A. Bowman's capsulel
B. Loop of Henle
c. collecting tubule
D. Urinary bladder


Find the smallest number by which
4232 must be multiplied to make it a perfect cube.
A .2
B. 17
c. 19
D. 23


If i is the current flowing through a conductor of resistance \( R \) for time \( t \)
then the heat produced (Q) is given by
A \( \cdot \frac{i^{2} R}{t} \)
в. \( \frac{i R^{2}}{t} \)
\( \mathbf{c} \cdot i^{2} R t \)
D \( \cdot i R t^{2} \)


NAD is
A. Nicotinamide adenosine diphosphate
B. Nicotine adenosine phosphate
C. Nicotinamide adenine dinucleotide
D. None of the above


Light travels in a \( _{-}-_{-}-_{-}-_{-}- \) path
A . rectilinear
B. zig zagg
c. circular
D. helical


correct?
(i) When an animal hide, which has
negatively charged particles, is soaked in tannin, which contains positively
charged colloidal particles, mutual
coagulation does not take place.
(ii) Photographic films are prepared by coating an emulsion of the light sensitive silver bromide in gelatin over glass plates or celluloid films.
(iii) Latex is a colloidal solution of
rubber particles which are negatively
charged.
(iv) In Cottrell precipitator, the smoke, before it comes out from the chimney, is
led through a chamber containing
plates having a charge opposite to that carried by smoke particles. The
particles on coming in contact with
these plates acquire some charge and do not get precipitated.
A. (i) and (iv) only
B. (ii) and (iii) only
C. (ii), (iii) and (iv) only
D. All of these


f \( x^{2}+y^{2}=2 \) and \( y^{11}+A . y^{-3}=0 \) then
\( A \) is


A chain \( A B \) of length \( l \) is lying in a
smooth horizontal tube so that a
fraction \( h \) of its length \( l \), hangs freely
and touches the surface of the table
with its end B. At a certain moment,
the end \( A \) of the chain is set free. The
velocity of end \( A \) of the chain, when it
slips out of tube, is:
A \( \cdot h \sqrt{\frac{2 g}{l h}} \)
в. \( \sqrt{2 g h \times \log _{e}\left(\frac{l}{h}\right)} \)
c. \( \sqrt{2 g l \times \log _{e}\left(\frac{l}{h}\right)} \)
D \( \cdot \frac{1}{h l} \sqrt{2 g} \)


The magnetic field is varying as \( \boldsymbol{B}(\boldsymbol{t})= \)
\( B_{o} t \) in the circuit as shown in the figure
Then the emf induced in the circuit will
be
\( \mathbf{A} \cdot 2 \pi a^{2} B_{0} \)
В . \( \pi a^{2} B_{0} \)
c. \( \frac{a^{2} B_{0}}{2} \)
D. \( \frac{\pi a^{2} B_{0}}{2} \)


A square wire loop of \( 10.0 \mathrm{cm} \) side lies
at right angles to a uniform magnetic field of 7 T. A 10 V light bulb is in series with the loop as shown in figure. The magnetic field is decreasing steadily to zero over a time interval \( \Delta t . \) For what
value if \( \Delta t(\text { in } m s), \) the bulb will shine
with full brightness?


Which one of the following is a part of a renal pyramid?
A. Peritubular capillaries
B. convoluted tubules
c. collecting ducts
D. All of the above


Why is soap referred as a salt?
A. They are long chain of fatty acids
B. Made up of various salts
C. Gives salt on acting with water
D. None of above


According to the electromagnetic spectrum. Which of the following is NOT a pure spectral colour?
A. white
B. violet
\( c \cdot \) red
D. blue
E. yellow


Identify the decimal and whole number from the following
\( \mathbf{2 2 5 3 . 1 0 6} \)


Heating ammonium chloride with sodium hydroxide produces:
A. ammonia
B. nitrogen
c. chlorine
D. none of these


Find the number of solutions of the
equations \( (\sin x-1)^{3}+(\cos x-1)^{3}+(\sin x)^{3}= \)
\( (2 \sin x+\cos x-2)^{3} \) in \( [0,2 \pi] \)


For the given data
\( \boldsymbol{A}+\boldsymbol{B} \rightleftharpoons \boldsymbol{C}+\boldsymbol{D} ; \boldsymbol{E}^{o}=\boldsymbol{a} \boldsymbol{v} \boldsymbol{o l} \boldsymbol{t} ; \boldsymbol{K}_{c}=\boldsymbol{K}_{1} \)
\( \mathbf{2} \boldsymbol{A}+\mathbf{2} \boldsymbol{B} \rightleftharpoons \mathbf{2} \boldsymbol{C}+\mathbf{2} \boldsymbol{D} ; \boldsymbol{E}^{\boldsymbol{o}}= \)
\( \boldsymbol{b} \boldsymbol{v} \boldsymbol{o l} \boldsymbol{t} ; \boldsymbol{K}_{c}=\boldsymbol{K}_{2} \)
Select the correct choices:
This question has multiple correct options
\( \mathbf{A} \cdot a=b \)
В. \( K_{2}=K_{1}^{2} \)
\( \mathbf{c} \cdot a \neq b \)
\( \mathbf{D} \cdot b=a^{2} \)


The following acids have been arranged in the order of decreasing acid strength. Identify the correct order: CIOH (I), BrOH
(II), IOH (III).
A \( I>I I>I I I \)
\( I \)
В. \( I I>I>I I I \)
c. \( I I I>I I>I \)
I I \( I>I I I>I I \)
\( I \)


Add an express the sum as a mixed
fraction:
\( \frac{-12}{5} \) and \( \frac{43}{10} \)


Simplify \( 3 x^{2}+5 x y-4 y^{2}+x^{2}- \)
\( 8 x y-5 y^{2} \)


Which equation is correctly labeled
oxidation or reduction?
\( \mathbf{A} \cdot H_{2} S=S+2 e^{-}+2 H^{+} \)
oxidation
B \( \cdot S O_{2}+4 e^{-}+2 H_{2} O=S+4 O H^{-} \)
oxidation
\( \mathbf{C} \cdot N H_{3}+H C l=N H_{4}++C l_{2}^{-} \)
oxidation
D. \( N a C l+A g N O_{3}=A g C l+N a N O_{3} \)
reduction
\( \mathrm{E} \cdot M n^{2+}=M n O_{4} \)
reduction


Ultraviolet light of \( 6.2 \mathrm{eV} \) falls on aluminium surface (work function =
4.2eV). The kinetic energy in joules of the fastest electron emitted is
approximately:
A \( \cdot 3 \times 10^{-21} \)
B . \( 3 \times 10^{-19} \)
c. \( 3 \times 10^{-17} \)
D. \( 3 \times 10^{-15} \)


Coniferales and Cycadales have respectively.
A. Motile sperms
B. Motile and non motile sperms
c. Non motile and motile sperms
D. Non motile sperms


Let \( \vec{a}, \vec{b}, \vec{c} \) be vectors of length 3,4 and 5 respectively. Let \( \vec{a} \) be perpendicular to \( (\vec{b}+\vec{c}), \vec{b} \) to \( (\vec{c}+\vec{a}) \) and \( \vec{c} \) to \( (\vec{a}+\vec{b}) \)
Find the length of the vector \( \vec{a}+\vec{b}+\vec{c} \).


The number of solutions for
\( \sin \left(\frac{\pi x}{2}\right)=\frac{99 x}{500} \) is:
\( A \cdot 3 \)
B. 5
\( c \cdot 7 \)
\( D \)


The ability of eye to focus on both near and far objects is called:
A. Presbyopia
B. Myopia
c. Hypermetropia
D. Power of accommodation


Which of the following is not true, if \( \mathbf{A} \)
and \( B \) are two matrices each of order
\( \boldsymbol{n} \times \boldsymbol{n}, \) then
\( \mathbf{A} \cdot(A+B)^{T}=B^{T}+A^{T} \)
\( \mathbf{B} \cdot(A-B)^{T}=A^{T}-B^{T} \)
\( \mathbf{C} \cdot(A B)^{T}=A^{T} B^{T} \)
\( \mathbf{D} \cdot(A B C)^{T}=C^{T} B^{T} A^{T} \)


Solve: \( \frac{1}{3(x-1)}-\frac{1}{4(x-2)}=1 \)


Fusion reaction take place at high
temperature because
A. atoms are ionized at high temperature
B. molecules break up at high temperatures
C . nuclei break up at high temperature
D. kinetic energy is high enough to overcome repulsion between nuclei


Heavy water is:
\( \mathbf{A} \cdot H_{2} O \)
B. water obtained by repeated distillation
\( c \cdot D_{2} O \)
D. water at \( 4^{\circ} \mathrm{C} \)


Gelatin has the minimum protective
powers.
A. True
B. False
c. Ambiguous
D. Data insufficient


The velocity-time graph of a body is
given below.
The maximum acceleration in \( m s^{-2} \) is


The value of the determinant
\[
\left|\begin{array}{ccc}
\mathbf{1} & \cos (\boldsymbol{\alpha}-\boldsymbol{\beta}) & \mathbf{c o s} \boldsymbol{\alpha} \\
\cos (\boldsymbol{\alpha}-\boldsymbol{\beta}) & \mathbf{1} & \cos \beta \\
\cos \boldsymbol{\alpha} & \cos \beta & \mathbf{1}
\end{array}\right|
\]
A \( \cdot \alpha^{2}+\beta^{2} \)
B \( \cdot \alpha^{2}-\beta^{2} \)
\( c .1 \)
\( D \)


Two thin similar convex glass pieces are joined together front to front, with its rear portion silvered such that a sharp image is formed 0.2 \( \mathrm{m} \) for an object at infinity. When the air between the glass pieces is replaced by water \( \left(\mu=\frac{4}{3}\right), \) find the position of image.


In the azeotropic mixture of \( H C l \) and
water, the percentage of \( H C l \) is:
A . 20.2\%
B . 11.1\%
c. 44.4\%
D. 10\%


Write cell reactions in lead storage battery during discharge.


Consider the circuit below. The bulb will
light up if:
\( A \cdot S_{1} S_{2} \) and \( S_{3} \) are all closed
\( 3 \cdot S_{1} \) is closed but \( S_{2} \) and \( S_{3} \) are open
\( c \cdot s_{1} \) and \( S_{3} \) are closed but \( S_{2} \) is open
D. None of thes


Which of the following is not a true fossil?
A. Placoderm
B. limulus
c. Archeopteryx
D. Therapsid


The diagram represents an atom 'X!
Answer the following.

Atom 'X' will lose electrons to become
\( \boldsymbol{X}^{1+} \)
A. True
B. False


A solenoid of inductance \( 2 \mathrm{H} \) carries a
current of \( 1 A . \) What is the magnetic
energy stored in a solenoid?
A . 2
B . 1 J
c. 4 J
D. 5 J


A teak wood log is cut first in the form of a cuboid of length \( 2.3 \mathrm{m}, \) width \( 0.75 \mathrm{m} \)
and of a certain thickness. Its volume is
\( 1.104 \mathrm{m}^{3} . \) How many rectangular planks of size \( 2.3 \mathrm{m} \times 0.75 \mathrm{m} \times 0.04 \mathrm{m} \) can be
cut from the cuboid?


Radiation of wavelength 242 nm is
sufficient to ionize the sodium atom.
Calculate the ionization energy in
\( \boldsymbol{k J} \boldsymbol{m o l}^{-1} \cdot\left(\boldsymbol{n}=\mathbf{6 . 6 2 5} \times \mathbf{1 0}^{-\mathbf{3 4}} \boldsymbol{J}-\boldsymbol{s}\right) \)
A. \( 493.6 k J \)
\( J \)
B . \( 6.625 \times 10^{3} J \)
c. \( 242 k J \)
D. \( 1324 k J \)


If a parent cell has eight chromosomes, then the daughter cells following meiosis will have:
A. four chromosomes
B. sixteen chromosomes
c. eight chromosomes
D. any one of these


The weight of one molecule of \( C_{60} H_{122} \)
is:
A. \( 1.2 \times 10^{-20} g \)
B . \( 5.025 \times 10^{23} g \)
c. \( 1.4 \times 10^{-21} g \)
D. \( 6.023 \times 10^{23} g \)


The chemical method used in the
concentration of ore is also known as:
A. Bleaching
B. Leaching
c. Roasting
D. Calcination


The reaction is:
\( \mathbf{A} \cdot S_{N} \)
B. \( S_{N} \) ?
\( \mathbf{c} \cdot E_{1} \)
\( D \cdot E_{2} \)


Find out longitudinal stress and
tangential stress on the given fixed
block


A gaseous mixture contains \( 70 \% N_{2} \)
and a \( 30 \% \) unknown gas, by volume. If the average molecular weight of gaseous mixture is \( 37.60, \) the molecular weight of unknown gas is:
A . 42.2
B. 60
c. 40
D. 50


Use hund's rule to derive the electronic
configuration of \( C e^{+3} \) ion, and calculate
its magnetic moment on the basis of 'spin only' formula. ( For \( \mathrm{Ce}, \mathrm{Z}=58 \) )


What are
¡) Magnetic declination
ii) Magnetic dip
iii) Horizontal component of earth's
magnetic field at a place?


\( \ln a \Delta A B C, I f A C>A B \) and the
bisector of \( \angle A \) meets \( B C \) at \( E \), then
A. \( C E>B E \)
в. \( C E<B E \)
c. \( C D>B E \)
D. \( C D<B E \)


The intermediate image formed by the objective of a compound microscope is:
A. real, inverted and magnified
B. real, erect and magnifiedd
c. virtual, erect and magnified
D. virtual, inverted and magnified


In a
multiplying the previous term by a constant.
A. geometric sequence
B. arithmetic sequence
c. geometric series
D. harmonic sequence


A body of mass \( 2 \mathrm{kg} \) is kept by pressing to a vertical wall by a force of \( 100 \mathrm{N} \). the coefficient of friction between wall and
body is 0.3 . then the frictional force is equal to:
\( A \cdot 6 N \)
B. 20 N
c. \( 600 \mathrm{N} \)
D. 700 N


A sample of water has a hardness
expressed as 77.5 ppm \( C a^{2+} . \) This sample is passed through an ion
exchange column and \( C a^{2+} \) is replaced
by \( \boldsymbol{H}^{+} . \) Select correct statement(s).
This question has multiple correct options
A. pH of the water after it has been so treated is 2.4
B. Every \( C a^{2+} \) ion is replaced by one \( H^{+} \) ion.
C . Every \( C a^{2+} \) ion is replaced by two \( H^{+} \) ions.
D. pH of the solution remains unchanged.


The purpose of exhaust system in lime kilns where the decomposition of limestone takes place is to:
A. drive away, \( C O_{2} \) gas and make the reaction proceed for completion.
B. reduce the temperature of the reaction
c. to make the reaction attain equilibrium in less time
D. all the above


Fibres would have
A. Thick walled
B. Thin walled
C. Thickening of wall at corners
D. Dense cytoplasm


Rusting of iron is an example of reaction.
A . fast
B. slow
c. endothermic
D. can't say


The efficiency of a surfactant towards
detergency depends upon its:
\( \mathbf{A} \cdot \) СМС
B. Kraft temperature
C. nature of hydrophilic and hydrophobic core
D. all of these


Identify the mode for the following data:
12 \( \mathbf{5 6} \) 67 \begin{tabular}{r}
34 \\
\hline
\end{tabular} Height(cm)
Swimmers 1 1 2
A . 34
B. 56
c. 67
D. 10


Concentrated sulphuric acid cannot be
used to prepare \( \boldsymbol{H} \boldsymbol{B} \boldsymbol{r} \) from \( \boldsymbol{N} \boldsymbol{a} \boldsymbol{B} \boldsymbol{r} \)
because it :
A. reacts slowly with \( N a B r \)
B. oxidises \( H B r \)
c. reduces \( H B r \)
D. none of the above


How many terms are there in the
sequence \( 3,6,9,12, \ldots, 111 ? \)


The blue zone in a LPG flame indicates
A. unburnt vapours
B. partial decomposition
c. moderately hot
D. hottest and complete combustion


Find the sum of the first (i) 75 positive
integers
(ii) 125 natural numbers


Bleaching powder gives smell of chlorine because it:
A . is unstable
B. gives chlorine on exposure to atmosphere
c. is a mixture of chlorine and slaked lime
D. contains excess of chlorine


The fissionable material used in a
breeder reactor is
A \( \cdot 92 \mathrm{U}^{235} \)
55
В \( \cdot \) g \( _{9} \mathrm{Pu}^{239} \)
\( \mathrm{c} \cdot_{90} \mathrm{Th}^{234} \)
D. \( c^{12} \)


Sodium cyanide is used in the:
A. cleaning of silver
B. creation of fires
C . purification of acids
D. extraction of gold


Thermoplastics are:
A. linear polymers.
B. soften or melt on heating
C. molten polymer can be moulded in desired shape.
D. All of these


\( f(x)=\cos ^{-1}\left(\frac{\sqrt{2 x^{2}+1}}{x^{2}+1}\right), \) then
range of \( \boldsymbol{f}(\boldsymbol{x}) \) is
\( \mathbf{A} \cdot[0, \pi] \)
B \cdot \( \left(0, \frac{\pi}{4}\right. \)
\( c \cdot\left(0, \frac{\pi}{3}\right. \)
D \( \cdot\left[0, \frac{\pi}{2}\right) \)


Describe the steps involved in
glycolysis (flow chart or explanation).


A gas has an average speed of \( 10 m / s \)
and a collision frequency of \( 10 s^{-1} \)
What is its mean free path?
A. \( 1 m \)
в. \( 2 m \)
\( c .3 m \)
D. \( 0.1 m \)


Two particles A and B perform SHM along the same straight line with the same amplitude 'a', same frequency 'f and same equilibrium position '0'. The greatest distance between them is found to be \( 3 a / 2 \). at some instant of
time they have the same displacement from mean position. What is this displacement?
A \( \cdot \frac{a}{\sqrt{2}} \)
B. \( a \sqrt{7} / 4 \)
c. \( \sqrt{7} a / 4 \)
D. 3a/4


In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of
the cell are connected across \( 52 \mathrm{cm} \) of
the potentiometer wire. If the cell is shunted by a resistance of \( 5 \Omega, \) a balance is found when the cell is
connected across \( 40 \mathrm{cm} \) of the wire. Find
the internal resistance of the cell.
A . \( 1.5 \Omega \)
B . 2\Omega
\( c .2 .5 \Omega \)
D. 12


Why bacteria and fungi are called decomposers?


In a step-down transformer the
secondary coil has number of
turns
A. strength
B. less
c. alternating
D. primary


How long does it stay in the air (in s)?
A . 37
в. 37.1
\( c .36 \)
D. 35 5


D is any point on AC in \( A B C . \) Now,
\( \boldsymbol{P}, \boldsymbol{Q}, \boldsymbol{X}, \boldsymbol{Y} \) are the mid points of \( \mathbf{A B}, \mathbf{B C} \)
AD and DC respectively. Show that \( P X= \)
\( \mathrm{QY} \)


The displacement x of a particle moving in one dimension under the action of a
constant force is related to time t by the
equation \( t=\sqrt{x}+3, \) where \( x \) is in meter and \( t \) is in second. Find the
displacement of the particle when its velocity is zero.
A. zero
в. \( 12 m \)
\( c .6 m \)
D. 18 т


In soils, PAHs are most likely to stick tightly to particles; certain PAHs move through soil to contaminate
underground water
A. True
B. False


Find \( f \circ g \) and \( g \circ f, \) if \( f(x)=\sin ^{-1} x \)
\( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{2} \)


For \( \boldsymbol{X} \rightarrow \boldsymbol{B}(\boldsymbol{n}, \boldsymbol{p}), \) if \( \boldsymbol{n}=\mathbf{2 5}, \boldsymbol{E}(\boldsymbol{x})=\mathbf{1 0} \)
then \( S . D .(x)= \)
A \( .2 \sqrt{6} \)
B. 2.4
c. \( 2 \sqrt{10} \)
D. \( \sqrt{2.4} \)


Let \( \boldsymbol{f}=\boldsymbol{R} \rightarrow \boldsymbol{R} \) be a continuous
function defined by \( \boldsymbol{f}(\boldsymbol{x})=\frac{\mathbf{1}}{\boldsymbol{e}^{\boldsymbol{x}}+\mathbf{2} \boldsymbol{e}^{-\boldsymbol{x}}} \)
Statement \( 1: f(c)=\frac{1}{3}, \) for some \( c \epsilon R \) Statement \( 2: 0<f(x) \leq \frac{1}{2 \sqrt{2}}, \) for al
\( \boldsymbol{x} \epsilon \boldsymbol{R} \)


Evaluate \( \int(\ln x+1) d x \)
\( \mathbf{A} \cdot x \ln x+c \)
B. \( x^{2} \ln x+c \)
c. \( x^{-2} \ln x+c \)
D. \( -x \ln x+c \)


Assertion: The Nernst equation gives concentration dependence of EMF of the
cell.
Reason: In a Daniell cell current flows
from cathode to anode.
A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true
E. Both Assertion and Reason are false


Distinguish between step-up and step
down transformer.


Clothes of \( _{--}-_{-}-_{-}-_{-}(\text {dark, white }) \)
colors absorb heat better than clothes
of light colors.


The engulfment of food in amoeba is
known as
A. Excretion
B. Phagocytosis
c. Respiration
D. All of the above


Lanthanoids are:
A. 14 elements in the seventh period left ( atomic no. \( =90 \) to \( 103 \text { right }) \) that are filling \( 5 f \) sublevel
B. 14 elements in the sixth period left ( atomic no. 58 to 71 right ) that are filling \( 4 f \) sublevel
C. 14 elements in the seventh period left ( atomic no. \( =58 \) to \( 71 \text { right }) \) that are filling \( 4 f \) sublevel
D. 14 elements in the sixth period left ( atomic no. 90 to \( 103 \text { right }) \) that are filling \( 4 f \) sublevel


What is the product of electrolysis of 45 grams of water?
A. 40 grams of \( H_{2} \) and 45 grams of \( O_{2} \)
B. 40 grams of \( O_{2} \) and 5 grams of \( H_{2} \)
c. 30 grams of \( H_{2} \) and 15 grams \( O_{2} \)
D. 30 grams of \( O_{2} \) and 15 grams of \( H_{2} \)


micrometer is \( 10^{-a} \) hectometer. What
is value of a?


Which of the following is not a characteristic of good respiratory
surface?
A. Thin and moist
B. Large surface area
c. close to oxygen and gas transporttt
D. Thick and dry surface


Find the point on the curve \( y=x^{3}- \)
\( 2 x^{2}-x, \) where the tangents are parallel
to \( 3 x-y+1=0 \)


Solve: \( \boldsymbol{x}^{2}-(\boldsymbol{3} \sqrt{\mathbf{2}}-\mathbf{2} \boldsymbol{i}) \boldsymbol{x}-\sqrt{\mathbf{2}} \boldsymbol{i}=\mathbf{0} \)


A broader bundle of light rays is called a
A. Beam of light
B. Ray of light
c. Bundle of light
D. None of these


An artificially created surface water body to recharge ground water is called
as
A. Dam
B. well
c. Percolation tank
D. None of the above


In triangle \( A B C, D \) and \( E \) are mid-points of sides \( A B \) and \( B C \) respectively. Also, \( F \)
is a point in side \( A C \) so that DF is parallel to BC. Prove that DBEF is a parallelogram. Answer: DBEF is a parallelogram, If true then enter 1 else if False enter 0


What is amalgam?


Describe Rutherford's atomic model
and also explain its drawbacks.


\( \operatorname{Let} n(A)=n . \) Then the number of all
relations on \( \boldsymbol{A} \) is
\( \mathbf{A} \cdot 2^{n} \)
B \( \cdot 2^{(n)} \)
c. \( 2^{n^{2}} \)
D. none


Identify the action involved when a magnet attracts a piece of iron towards
¡t.
A. Pushing
B. Pulling
c. Flying
D. Picking


An aromatic primary amine A with
molecular formula \( C_{6} H_{7} N \) undergoes diazotisation to give B. B when the aqueous solution of \( \mathrm{B} \) is boiled it gives
C. Identify \( A, B \) and \( C \)


Chlorine forms stable compounds in the
presence of
A. sunlight
B. water
\( c . \) air
D. catalyst


The formula of standard deviation of
a grouped frequency distribution is
A \( \cdot \sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2}}{N}} \)
в. \( \frac{\sum\left(x_{i}-\bar{x}\right)^{2} f i}{N} \)
c. \( \sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2} f i}{N}} \)
D. \( \frac{\left.\sum\left(x_{i}-\bar{x}\right)^{2}\right\} i}{f i} \)


Give reasons:
Xenon does not form fluorides such as
\( X e F_{3} \) and \( X e F_{5} \)


Find the potentials of points \( A \) and \( B: \)
A \( \cdot V_{A}=+10 V ; V_{B}=0 V \)
B . \( V_{A}=+7.5 V ; V_{B}=-2.5 V \)
c. \( V_{A}=+2.5 V ; V_{B}=-7.5 V \)
D. \( V_{A}=+0 V ; V_{B}=-10 V \)


Which one of the following disease is caused by Nosema bombycis in mulberry silkworm?
A. Muscardine
B. Pebrine
c. Grasserie
D. Flacherie


When you use a hair straightener, while straightening your hairs, it breaks down your hairs due to:
A. Electrostatic bonds
B. Hydrogen bonds
c. lonic bonds
D. Covalent bonds


Which of the following compounds is not coloured?
A \( \cdot N a_{2}\left[C u C l_{4}\right] \)
B . \( N a_{2}\left[C d C l_{2}\right] \)
\( \mathbf{c} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{6}\right] C l_{3} \)
D. all of the above


The element with \( Z=120 \) (not yet discovered) will be an/ a:
A. transition metal
B. inner-transition metal
c. alkaline earth metal
D. alkali metal


Match list (I) with List (II)
List I List II
a) Recoil of gun e) Newtons
first law
f) Newtons
second law b) Acceleration in one dimension
and motion in two dimensions g)
Projectile
motion c) Definition of force
d) Measurement of force
\( \mathbf{A} \cdot a \rightarrow e, b \rightarrow g, c \rightarrow h, d \rightarrow f \)
В . \( a \rightarrow h, b \rightarrow g, c \rightarrow e, d \rightarrow f \)
c. \( a \rightarrow e, b \rightarrow h, c \rightarrow g, d \rightarrow f \)
D \( . a \rightarrow h, b \rightarrow e, c \rightarrow g, d \rightarrow f \)


If the color code of the carbon
resistance is Red, Orange yellow, Gold. Find the value of resistance.


Water insoluble component of starch is:
A. amylopectin
B. amylose
c. cellulose
D. none of these


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


Show that Newton's third law of motion
is contained in his second law.
State and explain the principle of conservation of angular momentum


Time taken by a 836 Wheater to heat
one litre of water from \( 10^{\circ} \mathrm{C} \) to \( 40^{\circ} \mathrm{C} \) is:
A. 50 s
B. 100 s
\( c \cdot 150 s \)
D. 200


Given that mass of earth is \( M \) and its
radius \( R \) body is dropped from a height equal to the radius of the earth above
the surface of the earth. When it
reaches the ground velocity of body will be
\( ^{A} \cdot \frac{G M}{R} \)
\( ^{\text {В. }}\left(\frac{G M}{R}\right)^{1 / 2} \)
c. \( \frac{2 G M}{R} \)
\( ^{\mathrm{D} \cdot}\left(\frac{2 G M}{R}\right)^{1 / 2} \)


When electricity is passed through a
solution of \( A l C l_{3} \) and \( 13.5 g \) of \( A l \)
is deposited, the number of Faraday required must be:
A . 0.5
в. 1.0
c. 1.5
D. 2.0


On decreasing temperature, a liquid turns into solid. This is:
A. condensation
B. melting
c. freezing
D. sublimation


Bacteria which are found in marshy
areas and among the flora of cattle rumen are called
A. Acidophiles
B. Thermophiles
c. Methanogens
D. Thermoacidophiles


Whenever, current is changed in a coil, an induced e.m.f. is produced in the same coil. This property of the coil is due to
A. mutual induction
B. eddy currents
c. self induction
D. hysteresis


Element with atomic number 113 has
been reported in August \( 2003 . \) Its
electronic configuration is similar to
that of:
\( \mathbf{A} \cdot S i \)
в. \( G a \)
\( c . B i \)
D. \( A t \)


Evaluate \( \cos ^{-1}\left(\cos \left(\frac{\pi}{4}\right)\right) \)
A.
B. \( -\frac{\pi}{4} \)
c. \( \frac{3 \pi}{4} \)
D. \( -\frac{3 \pi}{4} \)


The sum of \( n \) terms of the series whose
\( \boldsymbol{n}^{t h} \) term is \( \boldsymbol{n}(\boldsymbol{n}+1) \) is equal to
A \( \frac{n(n+1)(n+2)}{3} \)
B. \( \frac{(n+1)(n+2)(n+3)}{12} \)
c. \( n^{2}(n+2) \)
D. \( n(n+1)(n+2) \)


For the reaction \( \boldsymbol{O}_{3(g)}+\boldsymbol{O}_{(g)} \rightarrow \mathbf{2} \boldsymbol{O}_{2(g)} \)
if the rate law expression is, rate \( = \)
\( \boldsymbol{K}\left[\boldsymbol{O}_{3}\right][\boldsymbol{O}] \) the molecularity and order of
the reaction are:
A . 2 and 2
B. 2 and 1.33
c. 2 and 1
D. 1 and 2


The number of spectral line obtained in
Bohr spectrum of hydrogen atom when an electron is excited from ground level to 5 th orbit is :
A . 10
B. 5
\( c \cdot 8 \)
D. 15


If the radius of a circle is tripled, the
ares becomes.
A. 9 times
B. 3 times
c. 6 times
D. 30 times


Find the number of integral solution of
\( (1-i)^{x}=2^{x} \)


A small bee produces sound, while it moves. The sound is created due to
A. Grinding its teeth as it moves
B. Friction due to air
c. Flapping of wings
D. Sound due to its vocal chord


on by a spring with spring constant \( k \)
and a weak frictional force of constant
magnitude \( f \). The block is pulled a
distance \( x_{0} \) from equilibrium position and then released. It oscillates many
times and ultimately comes to rest. Find the number of cycles the mass oscillates before coming to rest:
\( ^{\text {A }} \cdot \frac{1}{4}\left[\frac{k x_{0}}{f}-1\right] \)
в. \( \frac{1}{2}\left[\frac{k x_{0}}{f}-1\right] \)
c. \( \frac{1}{3}\left[\frac{k x_{0}}{f}-1\right] \)
D. none of the above


Which part of the eye is a dark muscular diaphragm?
A. Iriss
B. Cornea
c. Pupil
D. Retina


Use the elements of \( \operatorname{set} A=\{x, y, z\} \) to
form all possible ordered pairs Find the number of elements in the
ordered pair.


\( f\left(\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}\right)^{2}= \)
\( \lambda\left(\frac{1-\cos \theta}{1+\cos \theta}\right), \) then \( \lambda \) equals
\( A \)
B. 1
\( c \cdot 2 \)
D.


White phosphorus \( P_{4} \) has:
This question has multiple correct options
A. \( \operatorname{six} P-P \) single bonds
B. four \( P-P \) single bonds
C. four lone pairs of electrons
D. \( P-P-P \) angle of 60 degerees


Draw a ray diagram to show how a converging lens is able to form the image of the sun.


Phenol \( \frac{1 . C H C l_{3} / N a O H}{2 . H^{+}} \)
Salicyl aldehyde
The above reaction is known as:
A. Gattermann reaction
B. Sandmeyer reaction
c. Perkin reaction
D. Reimer-Tiemann reaction


(i) What are the postulates of Werner's
theory?
(ii) Write the IUPAC names fo
\( \boldsymbol{K}_{3}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right],\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)


Potential energy of a simple harmonic oscillator at its mean position is 0.4 J. If its kinetic energy at a displacement half of its amplitude from mean position is \( 0.6 \mathrm{J}, \) its total energy
is
A . \( 1.0 J \)
в. \( 1.2 J \)
c. \( 1.4 J \)
D. 1.6 .5


Discuss the behavior of wire under
increasing load


The point charges \( -5 n C, 10 n C \) and \( 12 n C \) are located at (0,0,0),(0,0,1) and (0,0,2) respectively. Find the total energy of the system.


If the \( 3^{r d} \) and the \( 9^{t h} \) terms of an \( A P \) are
4 and -8 respectively, then which term of this \( A P \) is zero


The solution of \( \frac{x-5}{2}-\frac{x-3}{5}=\frac{1}{2} \)
is
\( \mathbf{A} \cdot x=7 \)
B. \( x=9 \)
c. \( x=8 \)
D. \( x=5 \)


Show that square matrix \( A \) and its
transpose \( A^{T} \) have the same eigen
values.


Let the function \( f(x) \) be defined as
\( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\tan ^{-1} \boldsymbol{\alpha}-\mathbf{3} \boldsymbol{x}^{2}, & \boldsymbol{0}<\boldsymbol{x}<1 \\ -\boldsymbol{6} \boldsymbol{x}, & \boldsymbol{x} \geq \mathbf{1}\end{array}\right. \)
\( f(x) \) can have a maximum at \( x=1 \) if
the value of \( \alpha \) is
A.
B. 2
\( c \)
D. None of these


For the identification of the name of
species found in an area, one would use:
A. Manuals
B. Catalogues
c. Monographs
D. Museum


Fill in the blanks:
In the Lassaigne's test, the sulphur
present in the organic compound is converted into


Find the values of \( x \) and \( y \) which satisfy the given equations \( (x, y \in R) \) \( \frac{x-1}{1+i}+\frac{y-1}{1-i}=i \)


Find the direction cosines of the sides
of the triangle whose vertices are (3,5,-4),(-1,1,2) and (-5,-5,-2)


The number of quadratic equation which are unchanged by squaring their roots is


In Blackmann's Law of limiting Factors the rate of photosynthesis continues to increase with the successive increase
in the amounts of
A. Carbon dioxide, light, temperature
B. Temperature, light, carbon dioxide
c. Light, temperature, carbon dioxide
D. Light, carbon dioxide, temperature


The type of isomerism shown by the
\( \operatorname{complex}\left[\boldsymbol{C o C I}_{2}(\boldsymbol{e n})_{2}\right] \) is:
A. linkage isomerism
B. ionization isomerism
c. coordination isomerism
D. geometrical isomerism


The structure A represents Fischer Projection of a compound. The
structures I to IV represents WedgeDash Notations for the same compound. Which Wedge-Dash Notation is the correct representation of structure \( A ? \)
\( A \)
B. II
\( c \)
\( D \cdot \mid V \)


Using IUPAC norms, write the systematic names of the following.
(i) \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \)
(ii) \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right] \boldsymbol{S} \boldsymbol{O}_{4} \)


What is the force between the layer of
carbon atoms in graphite?


A 4.0 -cm-high object is placed at a distance of \( 60 \mathrm{cm} \) from a concave lens
of focal length \( 20 \mathrm{cm} . \) Find the size of
the image.
\( \mathbf{A} \cdot 2.5 \mathrm{cm} \)
B. \( 1.0 \mathrm{cm} \)
c. \( 3.0 \mathrm{cm} \)
D. \( 4.0 \mathrm{cm} \)


When white ppt. of \( A g_{2} C O_{3} \) is dissolved
in \( N H_{3} \) solution, then compound \( X \) is
formed

Find the value of magnetic moment of
\( \mathbf{X} \)
A. 0
B. 2
\( c \cdot 1 \)
D.


Iron or steel is used in reinforcement in
concrete because:
A. Concrete has high coefficient of expansion than iron or steel
B. Concrete has low coefficient of expansion than iron or steel
c. Both have nearly equal coefficient of expansions
D. Iron or steel is a good conductor of heatt


If a train travelling at \( 72 \mathrm{km} / \mathrm{h} \) is to be
brought to rest at a distance of \( 200 \mathrm{m} \) then its retardation should be:
A \( \cdot 20 m / s^{2} \)
B. \( 2 s^{2} \)
C \( .10 \mathrm{m} / \mathrm{s}^{2} \)
D. \( 1 \mathrm{m} / \mathrm{s}^{2} \)


The difference between the heat of
reaction at constant pressure and constant volume for the reaction
\( \mathbf{2} C_{6} \boldsymbol{H}_{6}(l)+\mathbf{1 5} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \mathbf{1 2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \)
\( 6 H_{2} O(l) \) at \( 25^{\circ} C \) in \( k J \) is:
A . -7.43
в. 3.72
c. -3.72
D. 7.43


Assertion
Atom is electrically neutral
Reason
A neutral particle, neutron is present in
the nucleus of the atom
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 magnetic force acting on a charged particle of charge \( -2 \mu C \) in a magnetic
field of \( 2 T \) acting in y-direction, when the particle velocity is \( (2 \check{i}+3 j) \)
\( \times 10^{6} m s^{-1} \) is :
A. \( 8 \mathrm{N} \) in \( \mathrm{z} \) -direction
B. 4 N in Z-direction
c. 8 N in y-direction
D. 4 N in Y-direction


A ball falls on the ground from a height of \( 2.0 m \) and rebounds up to a height of 1.5 \( m . \) Find the coefficient of restitution


The vapour pressure of two pure liquids \( A \) and \( B \) are 50 and 40 torr respectively. If 8 moles of \( A \) is mixed with \( x \) moles of
B, then vapour pressure of solution obtained is 48 torr. What is the value of
x?


Which are true for a standard hydrogen
electrode?
This question has multiple correct options
A. The hydrogen ion concentration is 1 m
B. Temperature is \( 25^{\circ} \mathrm{C} \)
c. Pressure of hydrogen is 1 bar
D. It contains a metallic conductor which does not absorb hydrogen


In deriving a formula for the combined
resistance of three different resistors in
series, Kirchhoffs laws are used.
Which physics principle is involved in this derivation?
A. The conservation of charge
B. The direction of the flow of charge is from negative to positive
c. The potential difference across each resistor is the \( \operatorname{same} \)
D. The current varies in each resistor, in proportion to the resistor value


The Henry's law constant for helium gas
in water at \( 30^{\circ} \mathrm{C} \) is \( 3.70 \times 10^{-4} \mathrm{M} / \mathrm{atm} \)
When the partial pressure of helium above a sample of water is 0.650 at \( \mathrm{m} \) the concentration of helium in the water
is
M.
A. \( 5.69 \times 10^{-4} \)
В. \( 1.76 \times 10^{3} \)
c. 1.30
D. \( 2.41 \times 10^{-4} \)
E . \( 3.70 \times 10^{-4} \)


Three bulbs \( A, B \) and \( C \) are connected
as shown in figure. The bulbs \( B \) and \( C \)
are identical. If the bulb \( C \) is fused,
then:
A. Brightness of both bulbs \( A \) and \( B \) will increase
B. Brightness of both bulbs \( A \) and \( B \) will decrease
c. Brightness of the bulb \( A \) decrease and that of bulb \( B \) ncreases
D. None of the bulbs will glow


If the earth is one-fourth of its present distance from the sun, the duration of
the year will be changed to :
A. half of the present year
B. \( \frac{1}{4} t h \) of the present year
c. \( \frac{1}{8} t h \) of the present year
D. \( \frac{7}{8} t h \) of the present year
E \( \cdot \frac{1}{16} t h \) of the present yea


A sample of acetaldehyde contained some ethyl alcohol as impurity. The
reagent useful for the purification of
\( \boldsymbol{C H}_{3} \boldsymbol{C H O} \) is :
A. \( N a H C O_{3} \)
B. \( N a_{2} C O_{3} \)
\( \mathbf{c} \cdot \operatorname{NaH} S O_{3} \)
D. \( P C l_{5} \)


A substance which increases the rate of
reaction but itself remain chemically unchanged is called a/an:
A. substrate
B. enzyme
c. reactant
D. product


Fin an acute angle \( \Theta \), when
\( \frac{\cos \Theta-\sin \Theta}{\cos \Theta+\sin \Theta}=\frac{1-\sqrt{3}}{1+\sqrt{3}} \)


For \( z=x+i y \) find the real and
imaginary part of \( e^{z} \)


Form the differential equation representing the family of curves \( y= \)
\( a e^{2 x}+b e^{-2 x} \) where a and \( b \) are arbitrary
constants.


What is the colour code of a corbon
resistor having a resistance of \( 470 \Omega \)
and a tolerance of 5\%?


The angles is to be bisected to obtain an
angle of \( 90^{0} \) is
A \( \cdot 60^{0} \) and \( 45^{0} \)
B. \( 60^{0} \) and \( 120^{\circ} \)
\( \mathrm{c} \cdot 120^{0} \) and \( 180^{\circ} \)
D. \( 30^{\circ} \) and \( 60^{\circ} \)


The annual income of Ruby in 2010 was
around Rs. \( 21000 . \) If she invested one-
third of it at \( 4 \% \) interest compounded quarterly, then what would be her savings at the end of a year?
A .7184
B. 7284
\( c .7384 \)
D. 7484


A glass sphere of radius \( 15 \mathrm{cm} \) contains
a small air bubble at a distance \( 6 \mathrm{km} \)
from its centre when viewed along its diameter from the nearest side,


Find volume of Cuboid of \( l=3 m, b= \)
\( \mathbf{2} \boldsymbol{m}, \boldsymbol{h}=\mathbf{4} \boldsymbol{m} \)


Covalent compounds are usually liquids or gases due to the weak force of attraction between their molecules.
A. True
B. False


Two men and 7 children complete a
certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days. The number of days required by 1 man to complete the work is
A. 60 days
B. 15 days
c. 6 days
D. 51 days


Calculate the maximum value of the
function \( f(x)=1-\cos x \) between 0
and \( 2 \pi \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
c. 1.5
D. 2
E . 2.5


If pressure \( P, \) Velocity \( V, \) and time \( T \) are taken as fundamental physical quantities, then the
dimensional formula for force is:
A \( \cdot P V^{2} T^{2} \)
B . \( P^{-1} V^{2} T^{-1} \)
c. \( P V T^{2} \)
D. \( P^{-1} V T^{2} \)


Glycerol contains:
A \( \cdot 1^{\circ} \) Carbon
B. \( 2^{\circ} \) Carbon
\( c \cdot 3^{o} \) Carbon
D. Both \( 1^{\circ} \) and \( 2^{\circ} \) carbon


A glass is filled with water up to its
brim and a thick hand card placed on
top of it. Now keeping the card tightly closed and pressed with palm, the glass full of water is inverted and placed
upside down. The palm is gently
removed from the card. It is observed
that the piece of card dose not fall off
the glass though the glass is full of water and its whole weight is exerting pressure on the card. Why does it happen?


When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of column of water height \( \mathrm{H} \), then the depth of lake is :-
\( A \cdot H \)
B. 2H
c. 7H
D. 8H


The formula of the final product formed when acetylene reacts with ammonical silver nitrate is :
A. \( A g C \equiv C H \)
B. \( A g C \equiv C A g \)
\( \mathbf{c} \cdot(A g)_{2} C=C H_{2} \)
D. \( C H_{2}=C H_{2} \)


State the following statement is True or
False
If two distinct lines are intersecting each other in a plane then they cannot
have more than one point in common.
A. True
B. False


1
11
\( \left\{\begin{array}{l}= \\ \frac{1}{4}\end{array}\right. \)
\( \mid \begin{array}{c}- \\ + \\ ++\end{array}+ \)
\( -\quad- \)
\( \quad+\frac{j}{+} \)
\( \left\{\begin{array}{l}-- \\ ++++++\end{array}\right. \)


Integrate:
\( 2 x^{2} e^{x^{2}} \)


\( H_{2} S O_{4} \) cannot be used to dry up \( H_{2} S \)
because it oxidises \( H_{2} S \) to \( S O_{2} \) and \( S \)
If true enter 1 , else enter 0 .
A.


Which of the following statements is
not true about electric field lines?
A. Electric field lines start from positive charge and end at negative charge
B. Two electric field lines can never cross each other
C. Electrostatic field lines do not form any closed loops
D. Electric field lines cannot be taken as continuous
curve


Find the common area enclosed by the parabolas \( \boldsymbol{y}^{2}=\boldsymbol{x} \) and \( \boldsymbol{x}^{2}=\boldsymbol{y} \)


In the aqueous solution of soap, above CMC (Critical Micelle Concentration):
This question has multiple correct options
A. the cations associate to form aggregates
B. the anions associates to form the clusters of colloidal
dimension
C. the polar ends forming the clusters are directed towards water
D. the non polar (hydrocarbon) ends are directed towards water


Presence of nitrogen in which among the following compounds cannot be detected by Lassaigne method?
A. Hydrazine
B. Aniline
c. p-toluidine
D. Picric acid


Draw \( \triangle A B C, \) where \( m \angle A B C= \)
\( 90^{\circ} ; B C=4 c m \) and \( A C=5 c m \) and
then construct \( \triangle B X Y \) with \( 4 / 3 \) scale
factor. Write points of construction


How long does it take the car to pass it? (in min)
A . 4.5
B. 5.5
\( c .3 .5 \)
D. 6.5


the isotop of hydrogen Which is radioactive is
A. Tritium
B. Deuterium
c. Nacent hydrogen
D. Parahydrogen


If \( y=x \sqrt{a^{2}+x^{2}}+ \)
\( a^{2} \log (x+\sqrt{a^{2}+x^{2}}) \) then \( \frac{d y}{d x}= \)
\( 2 \sqrt{a^{2}+x^{2}} \)


Wave pulse on a string shown in the
figure is moving to the right without
changing shape. Consider two particles
at positions \( x_{1}=1.5 m \) and \( x_{2}= \)
2.5 \( m . \) Their transverse velocities at the
moment shown in the figure are along
the
A. positive y axis and positive y axis respectively
B. negative y axis and positive y axis respectively
C. positive y axis and negative y axis respectively
D. negative y axis and negative y axis respectively


In the conversion of \( \boldsymbol{O}_{2} \longrightarrow \boldsymbol{O}_{2}^{-} \) the
incoming electron goes to the orbital:
A \( \cdot \pi^{*} 2 p x \)
B . \( \pi_{2 p x} \)
\( \mathbf{c} \cdot \sigma_{2 p z}^{*} \)
\( D \cdot \sigma_{2 p^{2}} \)


Find the binomial distribution for which
the mean is 4 and variance 3


Give the structural formulae for the
following:
Diethyl ether


DNA strands
A. Have quaternary structure like protein
B. Are bonded by disulphide bonds
C. Have same polarity
D. Are antiparallel


\( x \)
\( c \)
\( = \)


The opening of right auricle into the right ventricle is guarded by
A . Mitral valve
B. Pulmonary semilunar valve
c. Bicuspid valve
D. Tricuspid valve


There are 30 tickets in a box numbered
from 1 to \( 30 . \) A ticket is drawn out at
random. Let \( A \) be the event that the
number on the ticket is a multiple of 6
Write the sample set \( S \) and outcomes of
event \( A \) in set form.


How Many words, with or without
meaning, each of 2 vowels and 3
consonants can be formed from the
letters of the word \( D A U G H T E R ? \)


Micelles are:
A. adsorbed catalyst
B. ideal solution
\( \mathbf{C} \cdot \operatorname{gel} \)
D. associated colloids


In a coil of area \( 10 \mathrm{cm}^{2} \) and 10 turns with
magnetic field directed perpendicular to the plane and is changing at the rate
of \( 10^{8} \) Gauss/second. The resistance of
the coil is \( 20 \Omega \). The current in the coil
will be
A. \( 0.5 \mathrm{A} \)
B. 5A
\( c . \) 50 A
D . \( 5 \times 10^{8} A \)


\( A, B, C \) are the three angles of a
triangle \( . \) if \( \boldsymbol{A}-\boldsymbol{B}=\mathbf{1 5}^{\circ}, \boldsymbol{B}-\boldsymbol{C}=\mathbf{3 0}^{\circ} \)
find \( \angle \boldsymbol{A}, \angle \boldsymbol{B}, \angle \boldsymbol{C} \)


Redox indicators are substances that
undergo a colour change at specific
A \( . p H \)
B. electrode potential
c. both \( A \) and \( B \)
D. none of them


A metal 'X' is prepared by the electrolysis of fused chloride. It reacts with hydrogen to form a colourless solid, from which hydrogen gas is
released on treatment with water.
The metal'X' is :
\( A \cdot A \)
в. са
\( c \cdot c u \)
D. zn


Aqueous solutions of
\( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}, \) and
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} \) of identical
concentrations are provided. The pair(s) of solutions which form a buffer upon
mixing is/ are:
This question has multiple correct options
A. \( H N O_{3} \) and \( C H_{3} \) COOH
в. \( K O H \) and \( C H_{3} C O O N a \)
c. \( H N O_{3} \) and \( C H_{3} C O O N a \)
D. \( C H_{3} C O O H \) and \( C H_{3} C O O N a \)


Grills of doors and windows are always
painted before they are used? Give
reason


A circle of radius \( 3 \mathrm{cm} \) can be drawn
through two points \( A, B \) such that
\( A B=6 \mathrm{cm} \)
State True or False
\( A \). False
B. True
c. Cannot be determined
D. None of the above


Which of the following is a complex salt?
A. Fischer salt
B. Mohrs salt
c. Glaubers salt
D. Microcosmic salt


Ancestor of man, who first time showed
bipedal movement is
A. Cro-Magnon
B. Australopithecus
c. Java ape man
D. Peking man


Find the area of the shaded region
\( (\boldsymbol{\pi}=\mathbf{3 . 1 4}, \sqrt{\mathbf{3}}=\mathbf{1 . 7 3}) \)


toppr
Q Type your question_
given data?
Times \( 0 \quad 10 \)
20
30
\( (s) \)
stanc \( \begin{array}{llll}\text { 0 } & \text { 40 } & \text { 80 } & \text { 120 }\end{array} \) \( (m) \) ne 0
\( A \)
B.
\( c \)
\( D \)


Find the amount of water displaced by a solid spherical ball of diameter
\( 0.21 \mathrm{cm} \)


The time taken (in hours) by a car to
travel \( 900 k m \) if it travels \( 600 k m \) in
\( 12 h r s \)
\( A \cdot 18 \)
B. 16
\( c \cdot 15 \)
D. None of these


If \( X \) is a point on the line \( A B . Y \) and \( Z \)
are points outside such that \( \angle A X Y= \)
\( 45^{\circ} \) and \( \angle Y X Z=150^{\circ}, \) then \( \angle A X Z \) is
equal to:
A \( \cdot 120^{\circ} \)
B. \( 135^{\circ} \)
\( c \cdot 150^{\circ} \)
D. \( 165^{\circ} \)


ldentify the correct order of various stages in the manufacture of usable form of iron:
\( \mathbf{A} \)
B.
\( \mathbf{c} \)
D. Iron ore \( \rightarrow \) Cast iron \( \rightarrow \) Pig iron


a Q Type your question 3
\( A \)
C- \( 4, B-1, A-2 \) \( \mathrm{H}-7, \mathrm{G}-8, \mathrm{F}-6, \mathrm{E}-5, \mathrm{D}-3 \)
B. \( \mathrm{H}-6, \mathrm{G}-8, \mathrm{F}-7, \mathrm{E}-5, \mathrm{D}-3, \mathrm{C}-4, \mathrm{B}-1, \mathrm{A}-2 \)
\( c \)
\( \mathrm{H}-6 \) , \( \mathrm{G}-8, \mathrm{F}-7, \mathrm{E}-4, \mathrm{D}-3, \mathrm{C}-2, \mathrm{B}-1, \mathrm{A}-5 \)
D. \( \mathrm{G}-8, \mathrm{F}-7, \mathrm{E}-4, \mathrm{D}-2, \mathrm{C}-2, \mathrm{B}-1, \mathrm{A}-5 \) \( \mathrm{H}-6 \)


A uniform metallic wire has a
resistance of \( 18 \Omega \) and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is
\( A \cdot 8 \Omega \)
B. \( 12 \Omega \)
c. \( 4 \Omega \)
D. 2\Omega


The wavefront is a surface in which
A. all points are in the same phase
B. there is a pair of points in opposite phase
C \cdot there is a pair of points with phase difference \( \left(\frac{\pi}{2}\right) \)
D. there is no relation between the phases


List three main differences between
DNA and RNA?


A function \( f \) is defined as follows:
\( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{ll}1 & \text { for }-\infty< \\ 1+\sin x & \text { for } 0 \leq x<\frac{\pi}{2} \\ 2+\left(x-\frac{\pi}{2}\right)^{2} & \text { for } \frac{\pi}{2} \leq x<+\infty\end{array}\right. \)
Discuss the continunity and
differentiability at \( \boldsymbol{x}=\mathbf{0} \& \boldsymbol{x}=\boldsymbol{\pi} / \mathbf{2} \)
This question has multiple correct options
A. continuous but not differentiable at \( x=0 \)
B. differentiable and continuous at \( x=\pi / 2 \)
c. neither continuous but nor differentiable at \( x=0 \)
D. continuous but not differentiable at \( x=\pi / 2 \)


A thin circular ring first slip down a
smooth incline then rolls down a rough
incline of identical geometry from the same height. The ratio of time taken in the two motion is :
A \( \cdot \frac{1}{2} \)
B.
c. \( \frac{1}{\sqrt{2}} \)
D.


form oxocations.
A. Lanthanides
B. Actinides
c. Noble gas
D. Alkali metalss


The given diagram represents a dividing cell stained with giemsa. From the options given below, identify the correct stage of cell division.
A. Leptotene
B. Zygotene
c. Pachytene
D. Diakinesis


When a transverse wave on a string is reflected from the free end, the phase change produced is
A. Zero rad
в. \( \frac{\pi}{2} \) rad
c. \( \frac{3 \pi}{4} \) rao
D. \( \pi \) rad


\( A B \| C D \) and \( A C M \) is a straight line
\( \angle B A C \) is equal to:
A \( \cdot 106^{\circ} \)
B. \( 108^{\circ} \)
\( \mathrm{c} \cdot 110^{\circ} \)
D. \( 109^{\circ} \)


Motion of wheel of a bicycle is (projectile, circular)
motion.


Tranquilizers are used to:
A. reduce tension
B. reduce blood pressure
C . reduce body pain
D. reduce cholesterol


What is the nature of carbon atom
marked with asterisk \( (*) \) sign in the
given compounds?
\[
\mathrm{CH}_{3}-\mathrm{CH}_{2}-\dot{\mathrm{C}} \mathrm{H}_{2}-\mathrm{CH}_{3}
\]


Which one of the following is correctly matched?
A. Emulsion-curd
B. Foam-mist
c. Aerosol-smoke
D. Solid sol-cake


What is preservative? Give the name
and formula of any two preservatives.


Given are the isomers \( C_{8} H_{8} O_{2} \)
Which isomer reacts with \( N a H C O_{3} ? \)
\( A \)
B.
\( c \)
\( D \)


Write the complete nuclear reactions:
(a) \( _{4}^{9} B e+_{2}^{4} H e \longrightarrow_{6}^{12} C+ \)
\( (b)_{1}^{3} H \longrightarrow_{2}^{3} H e+_{-} \)
\( (c) \frac{14}{7} N+_{2}^{4} H e \longrightarrow_{8}^{17} O+ \)
(d) \( _{92}^{235} U+_{0}^{1} n \longrightarrow_{38}^{92} S r+X e+3_{0}^{1} n \)
\( (\mathrm{e})_{3}^{7} L i+_{0}^{1} n \longrightarrow 2_{2}^{4} H e+ \)
\( (f)_{92}^{238} U+_{-\perp-}----\longrightarrow_{92}^{239} U \longrightarrow_{93}^{239} \)
\( N p+ \)
\( (g)_{7}^{14} N+_{0}^{1} n \longrightarrow_{-}-\ldots---+_{1}^{3} H \)
(h) \( _{3}^{7} L i+_{-} \) \( \longrightarrow_{4}^{8} B e+\gamma \)
radiations
(i) \( _{1}^{2} \boldsymbol{H}+_{\text {一一一一一一一 }}_{2}^{4} \boldsymbol{H} e+_{0}^{1} \boldsymbol{n} \)
\( (j)_{13}^{27} A l+_{0}^{1} n \longrightarrow_{11}^{24} N a+ \)
\( (\mathrm{k})_{13}^{27} A l+_{2}^{4} H e \longrightarrow_{-}------+_{1}^{1} H \)
(I) \( \frac{235}{92} \boldsymbol{U}+_{0}^{1} \boldsymbol{n} \longrightarrow \)
\( +_{52}^{137} \boldsymbol{T} \boldsymbol{e}+_{40}^{97} \boldsymbol{Z} \boldsymbol{r} \)
\( (\mathrm{m})_{34}^{86} \mathrm{Se} \longrightarrow_{-1}-\mathrm{-}_{-1} \mathrm{e} \)


Depending on the magnetic property
the materials are classified in to
diamagnetic, paramagnetic and ferro magnetic. The behaviour of magnetic field lines near a magnetic substance is shown in the figure. Which material corresponds to the figure.


Intercellular communication in
multicellular organisms occur through
A. Digestive system only
B. Nervous system only
c. Both nervous and endocrine system
D. Respiratory system only


An iron ball at \( 50^{\circ} C \) is dropped in a
beaker of water at \( 50^{\circ} C . \) The heat will
A. Not flow from iron ball to water
B. Not not flow from iron ball to water or from water to iron ball
c. Not flow from water to iron ball
D. Increase the temperature of both


What are chelates? Giving one example and write the importance of chelate?


Select the correct order of density.
This question has multiple correct options
\( A \cdot N a>K \)
B. Na<K
c. \( \mathrm{Mg}>\mathrm{ca} \)
D. Mg<ca


The single electrode potential of metal \( E \)
of \( 0.1 \mathrm{M} \) solution of \( \mathrm{M}^{+} / \)Mions\( \left[E^{0}=\right. \)
\( -2.36 V] \) is nearly:
A . \( +2.41 V \)
в. \( -2.41 V \)
c. \( 4.82 V \)
D. \( +4.82 V \)


From the following equations, pick out the possible nuclear reactions.
This question has multiple correct options
\( \begin{array}{lllllll}\mathbf{C} \cdot_{7} N^{14} & + & _{1} H^{1} & \rightarrow & 8 & O^{15} & + & 7.3 & M e V\end{array} \)
D・ \( _{92} U^{235}+_{0} n^{1} \rightarrow_{54} X^{140}+_{38} S i^{94}+ \)
\( 20 n^{1}+\gamma+200 \mathrm{MeV} \)


In the experiment of verification of Ohms law the error in the current measurement
is \( 1 \% \), while that in the voltage
measurement is \( 2 \% \). The error in the
resistance has a maximum value of
A . 1\%
B. 2\%
c. 3\%
D. none of these


Use Kirchhoff's rule to obtain conditions
for the balance condition in a
Wheatstone bridge.


Synthetic testosterone promotes
A. menstrual cycle
B. muscle growth
c. respiration
D. birth control agents


A train of mass \( M \) is moving on a
circular track of radius \( R \) with a
constant speed \( v \). The length of the train is half of the perimeter of the track. The linear momentum of the train will be
A . zero
в. \( \frac{2 M v}{\pi} \)
c. \( M v R \)
D. \( M v \)


The frequency of a particle executing SHM is 10 Hz. The particle is suspended from a vertical spring. At the highest point of its oscillation, the spring is unstretched. Maximum speed of the
particle is \( (\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s} \mathbf{2}) \)
\( ^{\text {A }} \cdot \frac{1}{2 \pi} m s \)
в. \( \frac{7}{2 \pi} m s \)
c. \( \frac{5}{2 \pi} m s \)
D. \( \frac{1}{3 \pi} m s \)


A car can finish a certain journey in 10 hours at the speed of \( 48 \mathrm{km} / \mathrm{hr} \). By how much should its speed be increased so that it may take only 8 hours to cover
the same distance ? (in km/hr)


Assertion
Competitive inhibitors compete with the natural substrate for their
attachment on the active sites of
enzymes.
Reason
In competitive inhibition, inhibitor binds to allosteric site of the enzyme.
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 particle \( X \) in the following nuclear
reaction is \( \frac{13}{7} \mathrm{N} \longrightarrow_{6}^{13} \mathrm{C}+_{1}^{0} \mathrm{e}+X \)
A. \( P \)
B.
\( \mathbf{c} \cdot e^{-} \)
\( D \)


The general solution of differentia
equation is \( (y+c)^{2}=c x \) where \( c \) is an
arbitrary constant. The order and degree of the differential equation are respectively:
A .1,2
в. 2,2
c. 1,1
D. 2,1


In the air brake, air pressure is supplied
by
A. Engine manifold
B. A compressor
c. The diaphragm valve
D. pump


One kilogramme force is the force due to gravity on a mass of
A . \( 1 g \)
B. \( 10 g \)
\( c .100 g \)
D. \( 1000 g \)


Correct form of gravitational law is:
A \( \cdot \vec{F}=-\frac{G m_{1} m_{2}}{r^{2}} \)
В \( \cdot \vec{F}=-\frac{G m_{2} m_{1}}{r^{2}} \)
c. \( \vec{F}=-\frac{G m_{1} m_{2}}{r^{2}} \hat{r} \)
D・ \( \vec{F}=-\frac{G m_{1} m_{2}}{r^{3}} \vec{r} \)


Anaerobic respiration is
A. Complete oxidation
B. Incomplete oxidation
c. Anabolic reaction
D. Fermentation


Which molecule is a meso compound?
\( \mathbf{A} \cdot V I \) and \( I I \)
B. \( I V \) and \( V \)
c. \( I, I I \) and \( I I I \)
D. none of these


A weightless ladder 20 ft long assets
against a frictionless wall at an angle
\( 60^{\circ} \) from the horizontal. A 150 pound
man is 4 ft from the top of the ladder. A horizontal force is needed to keep it from slipping. Choose the correct magnitude from the following.
A . \( 175 ~ l b \)
B. \( 100 l b \)
c. \( 120 l b \)
D. 17.3 lb


For \( \boldsymbol{C u}(\boldsymbol{s})+\boldsymbol{N O}_{3}^{-}(\boldsymbol{a} \boldsymbol{q})+\boldsymbol{H}^{+}(\boldsymbol{a} \boldsymbol{q}) \rightarrow \)
\( \boldsymbol{C u}^{2+}(\boldsymbol{a q})+\boldsymbol{N O}_{2}(\boldsymbol{g})+\boldsymbol{H}_{2} \boldsymbol{O}(l), \) which
of the following takes place?
A. \( C u(s) \) is oxidized
B . \( H^{+}(a q) \) is oxidized
c. \( C u(s) \) is reduced
D. \( H^{+}(a q) \) is reduced
E . \( N O_{3}^{-} \) is oxidized


A bird is flying due east with a velocity of \( 4 m s^{-1} . \) The wind starts to blow with a
velocity of \( 3 m s^{-1} \) due north. What is the
magnitude of relative velocity of bird
w.r.t. wind? Find out.its direction also.


A circular garden has an area of \( 314 m^{2} \)
A sprinkle at the centre of garden can
cover an area that has a radius of \( 12 \mathrm{m} \)
Will the sprinkle water the entire
garden?


\( \frac{-}{\infty} \)
of
\( \frac{\delta}{2} \)


The IUPAC name for the coordination
compound \( \mathbf{B a}\left[\mathbf{B r} \mathbf{F}_{4}\right] \) is
A. Barium tetrafluorobromate (v)
B. Barium tetrafluorobromate (III)
c. Barium bis (tetrafluorobromate) (III)
D. Nne of these


Activation energy \( \left(\boldsymbol{E}_{\boldsymbol{a}}\right) \) and rate
constants \( \left(k_{1} \text { and } k_{2}\right) \) of a chemical reaction at two different temperature
\( T_{1} \) and \( T_{2} \) ) are related by:
\( ^{\mathbf{A}} \cdot \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)
в. \( \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{2}}-\frac{1}{T_{1}}\right] \)
\( ^{\mathrm{c}} \cdot \ln \frac{k_{2}}{k_{1}}=-\frac{E_{a}}{R}\left[\frac{1}{T_{2}}+\frac{1}{T_{1}}\right] \)
D \( \cdot \ln \frac{k_{2}}{k_{1}}=\frac{E_{a}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \)


If \( A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right], B\left[\begin{array}{ll}3 & 8 \\ 7 & 2\end{array}\right] \) and \( 2 x+ \)
\( A=B \) then find \( x \)


A body of mass \( M \) is attached to one
end of a rod of mass \( M \) and length \( L \)
The entire system is rotated about an axis passing through the other end of
the rod. The \( M . I . \) of the system about die given axis of rotation is:
\( ^{\mathrm{A}} \cdot \frac{M L^{2}}{3} \)
B. \( \frac{4}{3} M L^{2} \)
\( \mathbf{c} \cdot 2 M L^{2} \)
D. \( 3 M L^{2} \)


Select the correct option:
Vascular cambium and cork cambium
are the examples of
A. Apical meristem
B. Lateral meristem
c. Intercalary meristem
D. Promeristem


What is the probability that a two digit number selected at random will be a
multiple of 3 and not a multiple of \( 5 ? \)
A \( \cdot \frac{1}{15} \)
в. \( \frac{3}{15} \)
c. \( \frac{4}{15} \)
D. \( \frac{5}{15} \)


A solenoid has a core of a substance
with relative permeability \( 600 . \) What is the magnetic permeability of the given substance?
A \( \cdot 20 \pi \times 10^{-5} N A^{-2} \)
B. \( 21 \pi \times 10^{-5} N A^{-2} \)
c. \( 22 \pi \times 10^{-5} N A^{-2} \)
D. \( 24 \pi \times 10^{-5} N A^{-2} \)


Alary muscles in cockroach are associated or connected with
A. Trachea
B. Heart
c. Legs
D. Alimentary canal


A large positive value of \( \Delta G \) corresponds to which of these?
A. Small positive \( K \)
B. Small negative \( K \)
c. Large positive \( K \)
D. Large negative \( K \)


Which of the following is not a characteristic feature during mitosis in somatic cells?
A. Spindle fibres
B. Disappearance of nucleolus
c. chromosome movement
D. Synapsis


What is biasing a diode? Write two differences between the two kinds of
biasing.


A car travelling at \( 60 k m / h \) overtakes another car travelling at \( 42 k m / h \) Assuming each car to be \( 5.0 m \) long, the time taken for the over taking is
\( \mathbf{A} \cdot 6 s \)
B . \( 4 s \)
c. \( 3 s \)
D. \( 2 s \)


Let [.] denote the greatest integer
function and \( f(x)=\left[\tan ^{2} x\right] . \) Then
\( \mathbf{A} \cdot \lim _{x \rightarrow 0} f(x) \) does not exis
B. \( f(x) \) is continuous at \( x=0 \)
c. \( f(x) \) is not differentiable at \( x=0 \)


Write the formula to find the magnitude of the gravitational force between the
earth and an object on the surface of the earth.


Using the property of determinants and with out expanding prove that \( \left|\begin{array}{lll}\boldsymbol{a}-\boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} \\ \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}-\boldsymbol{b} \\ \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}\end{array}\right|=\mathbf{0} \)


A uniformly wound solenoidal coil of
self-inductance \( 1.8 \times 10^{-4} \mathrm{H} \) and
resistance \( 6 \Omega \) is cut into two identical
coils. They are now connected in parallel across a 12 volt battery of negligible resistance. Find the current drawn by the circuit in amp.


Evaluate the following limits. \( \lim _{x \rightarrow 0} \frac{(a+x)^{2}-a^{2}}{x} \)


Which are two rational number between \( \frac{6}{5} \) and \( \frac{7}{5} \)


Angiosperms have dominated the land flora primarily because of their
A. Domestication by man
B. Power of adaptability in diverse habitat
c. Property of producing large number of seeds
D. Nature of self pollination


Assertion
Standard hydrogen electrode is a half cell having \( 1 M H^{+} \) concentration
bubbled with hydrogen at any pressure
Reason

A hydrogen electrode will always show \( \boldsymbol{E}_{c e l l}=\mathbf{0 . 0 0} \boldsymbol{V} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Find the remainder for given division \( \left(p^{2}+7 p-8\right) \div(p-1) \)


Q Type your question
molecules unite with \( \boldsymbol{H}_{2} \boldsymbol{O} \) to form
\( N H_{4} O H \) molecules. \( N H_{4} O H \) again
dissociates into \( N H_{4}^{+} \) and \( O H^{-} \) ions.
In solution therefore, we have \( \boldsymbol{N} \boldsymbol{H}_{3} \)
molecules, \( N H_{4} O H \) molecules and \( N H_{4}^{+} \) ions and the following equilibrium exist:
\( N H_{3}(g) \) (pressure \( P \) and concentration
\( c \) ) Initially \( \rightleftharpoons N H_{3}(l)+H_{2} O \rightleftharpoons \)
\( N H_{4} O H \rightleftharpoons N H_{4}^{+}+O H^{-} \)
Let \( c_{1} \) mol \( / L \) of \( N H_{3} \) pass in liquid state which on dissolution in water
froms \( c_{2} \) mol \( / L \) of \( N H_{4} O H . \) The
solution contains \( c_{3} \) mol \( / L \) of \( N H_{4}^{+} \) ions. The dissociation constant of
\( N H_{4} O H \) can be given as:
\( ^{\mathrm{A}} \cdot_{K_{b}}=\frac{\left(c_{3}\right)^{2}}{\left(c_{2}-c_{3}\right)} \)
B. \( _{K_{b}}=\frac{\left(c_{3}\right)^{2}}{c_{2}} \)
\( ^{\mathbf{c}} \cdot_{K_{b}}=\frac{c_{3}}{\left(c_{2}-c_{3}\right)} \)
D. \( _{K_{b}}=\frac{c_{3}}{\left(c_{1}-c_{2}\right)} \)


An oxyacid of phosphorus has the following properties: The complex
neutralisation of the acid with sodium
hydroxide solution given an aqueous solution of sodium ions and oxy-acid
anions in the ratio 2:1. When a solution
of the acid is warmed with silver nitrate
solution, metallic silver is deposited.
\( p H 0.01 \mathrm{M} \) solution of the sodium salt of
this acid formed (assume \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}_{1}}=\boldsymbol{2} \boldsymbol{x} \)
is
\( A \cdot 6+2 x \)
B. \( 6-2 x \)
\( c \cdot 6-x \)
D. \( 6+x \)


Evaluate:
\( \lim _{x \rightarrow 2} \frac{\sqrt{3-x}-1}{2-x} \)


Integrate the following functions with espect to \( x: \int \frac{d x}{4 x+5} \)
This question has multiple correct options
A \( \cdot \frac{1}{4} \ln (4 x+5)+c \)
B. \( \frac{1}{4} \ln (4 x+5)-c \)
\( ^{\mathbf{c}} \cdot \frac{-1}{4} \ln (4 x+5)-c \)
D. \( 4 \ln (4 x-5)-c \)


Laughing gas is prepared by heating:
A \( . N H_{4} C l \)
B. \( \left(N H_{4}\right)_{2} S O_{4} \)
c. \( N H_{4} C l+N a N O_{3} \)
D. \( N H_{4} N O_{3} \)


Calculate equilibrium constant for the equilibrium
\( 2 m n O_{4}^{-}+6 H^{+}+5 H_{2} C_{2} O_{4} \rightleftharpoons \)
\( \mathbf{2} M N^{2+}+\mathbf{8} H_{2} O+\mathbf{1 0} C O_{2} \)
Given that, \( \boldsymbol{E}_{M n O_{4} M n^{2+}}^{0}=\mathbf{1 . 5 1} \quad \boldsymbol{V} \) and
\( \boldsymbol{E}_{\mathrm{CO}_{3} \mathrm{C}_{2} \boldsymbol{O}_{4}^{2-}}^{0}=-\mathbf{0 . 4 9} \boldsymbol{V} \)


If \( \vec{b} \) is the vector whose initial point divides the joining \( 5 \hat{i} \) and \( 5 \hat{j} \) in the ratio \( \lambda: 1 \) and terminal point is at origin. If \( |\vec{b}| \leq \sqrt{37}, \) then \( \lambda \in \)
\( ^{\mathbf{A}} \cdot(-\infty,-6] \cup\left[-\frac{1}{6}, \infty\right) \)
B \( \cdot(-\infty,-3) \cup\left[-\frac{1}{4}, \infty\right) \)
\( ^{\mathbf{c}} \cdot(-\infty, 0) \cup\left(\frac{1}{2}, \infty\right) \)
D. \( \left[-6,-\frac{1}{6}\right] \)


The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
\( \mathbf{A} \cdot \mathbf{0} \)
B. \( \frac{1}{3} \)
c. \( \frac{1}{12} \)
D. \( \frac{1}{36} \)


Which statement about molecularity of reaction is not correct?
A. It can be obtained from reaction mechanism
B. It may be either whole number or fractional
C. It depends on elementary step of reaction
D. It is the number of molecules of reactants taking part in a single step reaction


Find the magnetic field at P due to the
arrangement shown
A \( \cdot \frac{\mu_{0} i}{\sqrt{2} \pi d}\left(1-\frac{1}{\sqrt{2}}\right) \& \)
B. \( \frac{2 \mu_{0} i}{\sqrt{2} \pi d} \)
c. \( \frac{\mu_{0} i}{\sqrt{2} \pi d} \)
D. \( \frac{\mu_{0} i}{\sqrt{2} \pi d}\left(1+\frac{1}{\sqrt{2}}\right) \)


Solve \( \int_{0}^{\pi / 2} \frac{x \sin x \cos x}{\cos ^{4} x+\sin ^{4} x} d x \)


In an oscillating system, a restoring force is a must. In an \( L-C \) circuit,
restoring force is provide by
A. Capacitor
B. Inductance
c. Resistance
D. Both (A) and (B)


Smoke and fog both are aerosols. In
what way are they different?


If the anti-neutrino had a mass of
\( 3 e V / c^{2}(\text { where } c \) is the speed of light) instead of zero mass, what should be
the range of the kinetic energy, K of the electron?
A \( \cdot 0 \leq K \leq 0.8 \times 10^{6} e V \)
B. \( 3.0 e V \leq K \leq 0.8 \times 10^{6} e V \)
c. \( 3.0 e V \leq K<0.8 \times 10^{6} e V \)
D. \( 0 \leq K<0.8 \times 10^{6} e V \)


Two free parallel wires carrying currents
in the opposite directions
A. attract each other
B. repel each other
C. do not affect each other
D. get rotated to be perpendicular to each other


Write down the negations for the
following:
(a) If the diagonals of a parallelogram are perpendicular then it is a rhombus.
(b) Kanchanganga is in India and Everest is in Nepal.
(c) The Sun is a star or the Jupiter is a
planet.


Write structure of pyrophosphoric acid.


Match the following:
Column II gives the order of resistivity for materials in column I


resting on a smooth horizontal ground
attached to one end of a spring of force
constant \( k \) in natural length. If another
block of same mass and moving with a
velocity u toward right is placed on the
block which stick to it due to friction.
The time it will take to reach its
extreme position. Also find the
amplitude of oscillations of the combined mass \( 2 \mathrm{m} \)
\( ^{\mathbf{A}} \cdot A=\sqrt{\frac{m}{2 k}}, t=\sqrt{\frac{k}{2 m}} \)
В. \( A=u \sqrt{\frac{m}{2 k}}, t=\frac{\pi}{2} \sqrt{\frac{2 m}{k}} \)
c. \( A=\sqrt{\frac{u m}{2 k}}, t=\pi \sqrt{\frac{2 m}{k}} \)
D. none of these


Let \( \mathbf{f}:(-\mathbf{1}, \mathbf{1}) \rightarrow \mathbf{R} \) be a differentiable
function with \( \mathbf{f}(\mathbf{0})=-\mathbf{1} \) and \( \mathbf{f}^{\prime}(\mathbf{0})=\mathbf{1} \)
Let \( \mathbf{g}(\mathbf{x})=[\mathbf{f}(\mathbf{2 f}(\mathbf{x})+\mathbf{2})]^{2} . \) Then \( \mathbf{g}^{\prime}(\mathbf{0})= \)
A . -4
B.
\( c \cdot-2 \)
D. 4


\( p \)
\( \dot{g} \)
\( \dot{q} \)
\( \dot{q} \)


State whether given statement is True or False.
Force never exists in pairs.
A. True
B. False


Two straight lines drawn on the same
displacement time graph make angles
\( 45^{\circ} \) and \( 60^{\circ} \) as shown. The ratio of the
two velocities is
4. \( \sqrt{3}: 1 \)
3.1:
\( c \cdot 1: 2 \)
\( \sqrt{3}: 2 \)


In the arrangement shown, a car of
certain mass 'm' is in equilibrium by
applying a force of 25 N. If the density of liquid taken is \( 0.9 \mathrm{cm}^{-3} \), then find the
mass of the car


The following real numbers have decimal expansions as given below. In each case, decide whether they are
rational or not. If they are rational and of
the form \( p \), you say about the prime
factors of \( q ? \)
(i) 43.123456789 (ii)
\( 0.120120012000120000 \ldots \)
\( 43 . \overline{123456789} \)


Given the following six statements:
(1) All women are good drivers
(2) Some women are good drivers
(3) No men are good drivers
(4) All men are bad drivers
(5) At least one man is a bad driver
(6) All men are good drivers. The statement that negates statement
(6) is:
A . (1)
B. (2)
\( c \cdot(3) \)
\( D \cdot(4) \)
E. (5)


On dividing the polynomial \( 9 x^{4}- \) \( 4 x^{2}+5 \) by another polynomial \( 3 x^{2}+ \)
\( x-1, \) the remainder comes out to be
\( a x-b, \) Find \( ^{\prime} a^{\prime} \) and \( ^{\prime} b^{\prime} \)


In the figure shown, a block A moving with velocity \( 10 \mathrm{m} / \mathrm{s} \) on a horizontal
surface collides with another block \( \mathrm{B} \) at
rest initially. The coefficient of restitution is \( \frac{1}{2} . \) Neglect fricition every
where. The distance between the blocks
5s after the collision takes place is \( 5 \times \)
\( (i n \quad m), \) then \( c \) is :


\( \ln L-C \) oscillations
This question has multiple correct options
A \( \cdot \) time period of oscillations is \( \frac{2 \pi}{\sqrt{L C}} \)
B. maximum current is \( \frac{q_{0}}{\sqrt{L C}} \)
C. maximum rate of change of current in circuit is \( \frac{q_{0}}{L C} \)
D. maximum potential difference across the inductor is
\( \frac{q_{0}}{2 C} . \) Here \( q_{0} \) is maximum charge on capacitor.


The value of gravitational acceleration 'g' at a height 'h' above the earth's surface is \( \frac{g}{4} \) then \( (R= \) radius of earth)
\( \mathbf{A} \cdot h=R \)
в. \( h=\frac{R}{2} \)
\( c \cdot h=\frac{R}{3} \)
D. \( h=\frac{R}{4} \)


Figure shows three cases: in all cases
the circular part has radius \( r \) and
straight ones are infinitely long. For the
same current the ratio of field \( B \) at
center \( P \) in the three cases \( B_{1}: B_{2}: B_{3} \)
is :
\( ^{\mathrm{A}} \cdot\left(-\frac{\pi}{2}\right):\left(\frac{\pi}{2}\right):\left(\frac{3 \pi}{4}-\frac{1}{2}\right) \)
\( ^{\mathrm{B}} \cdot\left(-\frac{\pi}{2}+1\right):\left(\frac{\pi}{2}+1\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)
\( ^{c} \cdot\left(-\frac{\pi}{2}\right):\left(\frac{\pi}{2}\right):\left(\frac{3 \pi}{4}\right) \)
\( \left(-\frac{\pi}{2}-1\right):\left(\frac{\pi}{2}-\frac{1}{4}\right):\left(\frac{3 \pi}{4}+\frac{1}{2}\right) \)


against the inner surface of a
larger sphere of radius 6 R. The masses of large and small spheres are \( 4 \mathrm{M} \) and
M respectively. This arrangement is placed on a horizontal table as shown.
There is no friction between any
surfaces of contact. The small sphere is
now released. The coordinates of the
centre of the large sphere when the
smaller sphere reaches the other
extreme position is
A \( \cdot(L-2 R, 0) \)
B. \( (L+2 R, O) \)
c. \( (2 R, 0) \)
D. \( (2 R-L \)


Which of the following soluble in water?
A. \( C H_{3} O H \)
в. \( C H C l_{3} \)
c. \( C C l_{4} \)
D. \( C S_{2} \)


Use identities to evaluate : \( (502)^{2} \)
A .1,62,004
в. 1,22,004
c. 2,12,004
D. 2,52,004


An ideal fluid is flowing in a tube of varying cross-section. At some point the radius of the tube is \( r \) and the velocity
of flow is \( v \). The velocity of flow at
another point, where the radius is \( r / 2 \)
is
A.
в. \( \frac{v}{2} \)
\( c \cdot 2 v \)
D. \( 4 v \)


When phenolphthalein is added to
NaOH, the colour of the solution will
become
A. colourless
B. red
c. pink
D. yellow


The electric potential due to a dipole at a point on the perpendicular bisector of its length is :
A. maximum
B. minimum
c. 0
D. None of these


Find the values of \( a \) and \( b \) such that the
function defined by \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{ccc}5, & \text { if } & x \leq 2 \\ a x+b, & \text { if } & 2<x<10 \text { is } \\ 21, & \text { if } & x \geq 10\end{array}\right. \)
continuous function.


Which of the following foods are rich in Vitamin A?
A. Carrot
B. Cauliflower
c. Green Chillies
D. Beans


Electric current is due to flow of charge
carriers in the conductors. Which of the
following is/are correct?
This question has multiple correct options
A. The drift speed of charge carriers is a very small fraction of the mean thermal agitation speed of the same charge carriers
B. The number of charge carriers per unit volume is always the same as the number of atoms of the conductor per unit volume
C. The drift velocity is proportional to the electric field applied ordinarily
D. In an intrinsic semiconductor, the charge carriers are either electrons only or holes only; both of them may not participate in conduction


Assertion
The gases \( H e \) and \( H_{2} \) are very different
in their behaviour at any temperature and pressure but their compressibility
factors are nearly the same at the
critical point.
Reason
They have nearly the same critical
constant.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In sodium extract nitrogen is present
as:
A. sodamide
B. sodium cyanide
c. sodium nitrite
D. sodium nitrate


Ramesh mixed some iron filings with
sulphur powder in a China dish. In
another dish, he mixed iron filings and
sulphur powder and heated the mixture.
Which of his observations is not
correct?
A. Dish \( X \) shows a physical change while dish \( Y \) shows chemical change.
B. In dish \( X \) sulphur powder and iron filings can be seen separately.
C. In dish \( Y \) a new substance is formed on heating the mixture.
D. The change which has taken place in dish \( Y \) is reversible


The two ends of a train moving with uniform acceleration pass a certain point with velocities 6 kmph and 8 kmph respectively. What is the velocity with which the middle point of the train
passes the same point?
\( A .7 \mathrm{kmph} \)
B. \( 2 \sqrt{5} \) kmph
c. \( 2 \sqrt{10} \mathrm{kmph} \)
D. 7.5 kmph


If speed of infrasonics, audible and
ultrasonics waves are \( v_{i}, v_{a} \) and \( v_{u} \) then
A \( \cdot v_{i}>v_{a}>v_{u} \)
В . \( v_{i}=v_{a}=v_{u} \)
c. \( v_{i}<v_{a}<v_{u} \)
D. \( v_{i}>v_{a}, v_{u}>v_{a} \)


Oxidation of cyclohexene in presence of acidic potassium permanganate leads
to.
A . Glutaric acid
B. Adipic acid
c. Pimelic acid
D. succinic acid


What is a flower? Describe the parts of a
typical angiosperm flower


Evaluate: \( \lim _{x \rightarrow \frac{\pi}{2}}\left(2 x \tan x-\frac{\pi}{\cos x}\right) \)


correct major product formed?
This question has multiple correct options
\( A \)
B
\( c \)
\( D \)


The globular head of myosin contains
A. Calcium ions in large quantities
B. Troponin
c. ATPase enzyme
D. ATP


TEL, tetra ethyl lead, acts as an antiknocking agent. It acts as
A. negative catalyst
B. catalyst
c. electophile
D. nucleophile


Which of the following statements is the converse of "If the moon is full, then
the vampires are prowling."?
A. If the vampires are prowling, then the moon is full.
B. If the moon is not full, then the vampires are prowling
C. If the vampires are not prowling, then the moon is not full
D. None of these


A feather of mass \( m \) and a hammer of
mass \( 100 m \) are both released from rest
from the same height on the surface of the moon. Mass of moon is \( M \) and
radius of moon is \( R \). Both feather and
hammer are released simultaneously. What is the acceleration of the
hammer?
A \( \cdot \frac{m v^{2}}{r} \)
в. \( \frac{G M}{R^{2}} \)
c. \( \frac{G M m}{R^{2}} \)
D. \( _{100} \frac{G M}{R^{2}} \)
E \( \cdot_{100} \frac{G M m}{R^{2}} \)


The two rails of a railway track,
insulated from each other and the
ground, are connected to millivoltmeter. What is the reading of the
millivoltmeter when a train passes at a
speed of \( 180 \mathrm{km} / \mathrm{hr} \) along the track,
given that the vertical component of
earth's magnetic field is \( 0.2 \times \)
\( 10^{-4} w b / m^{2} \) and rails are separated by 1
metre
A \( \cdot 10^{-1} \) volt
B. \( 10 \mathrm{mV} \)
c. 1 volt
\( \mathbf{D} \cdot 1 m V \)


Let \( C \) be the circle with centre at (1,1)
and radius \( =1 . \) If \( T \) is the circle
centered at \( (0, y), \) passing through origin and touching the circle \( C \)
externally, then the radius of \( T \) is equal
to :
A \( \cdot \frac{\sqrt{3}}{\sqrt{2}} \)
B. \( \frac{\sqrt{3}}{2} \)
\( c \cdot \frac{1}{2} \)
D.


\( \cos ^{-1}\left(2 x^{2}-1\right), 0 \leq x \leq 1, \) is equal to


What is the time (in sec) requried for depositing all the silver present in
\( 125 m L \) of \( 1 M A g N O_{3} \) solution by
passing a current of \( 241.24 A ? \) \( (1 F=96500 \text { coulombs }) \)
A . 10
B. 50
c. 100
D. 90


Which hormone stimulates the gastric glands to release the gastric secretion?
A. Enterogastrone
B. Gastrin
c. Pancreozymin
D. cholecystokinin


Select the correct group(s) of reagent(s)
used in the following conversions:
A \( \cdot I \Rightarrow d i l . H N O_{3}, I I \Rightarrow N a_{2} C r_{2} O_{7} / H_{2} S O_{4}, I I I \Rightarrow \)
\( K M n O_{4} / N a O H, I V \Rightarrow P b O_{4} / O^{\ominus} H, H_{3} O \oplus \)
B . \( I \Rightarrow \operatorname{dilH} N O_{3}, I I \Rightarrow K M n O_{4} / H^{\oplus}, I I I \Rightarrow \)
\( K M n O_{4} / N a O H, I V \Rightarrow T s C l+ \)acidicKMnO\( _{4}+H_{2} O \)
C \( \cdot I \Rightarrow K M n O_{4} / N a O H, I I \Rightarrow N a_{2} C r_{2} O_{7} / H^{\oplus}, I I I \Rightarrow \)
\( K M n O_{4} / O^{\ominus} H, I V \Rightarrow d i l . H N O_{3} \)
D. \( I \Rightarrow C r O_{3} / M e C O O H, I I \Rightarrow K M n O_{4} / O^{\ominus} H, I I I \Rightarrow \)
\( K M n O_{4} / H^{\oplus}, I V \Rightarrow d i l . H N O_{3} \)


The bunch of capillaries present in the Bowmans capsule is called
A. Paccinian corpuscle
B. Bowmans capsule
c. Glomerulus
D. Malpighian capsule


In acidic solution, \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) oxidises \( \boldsymbol{H} \boldsymbol{g} \) to:
A. \( H g_{2} O \)
в. \( \mathrm{HgSO}_{4} \)
c. Нg S
D. \( H g O \)


An egg cell has 5 picogram of genetic material in its nucleus. What amount of
material will be present in the organism
at the end of \( G_{2} \) -phase of mitosis?
A. \( 5 \mathrm{gm} \)
B. 5 picogram
c. 10 picogram
D. 20 picogram


Find the value of a if \( 2 x^{3}-6 x^{2}+ \)
\( 5 a x-9 \) leaves the remainder 13 when it
is divided by \( x-2 \)


State true or false.
A rhombus is a parallelogram.
A. True
B. False


When \( S O_{2} \) is passed through acidified
\( K_{2} C r_{2} O_{7} \) solution:
A. the solution turns blue.
B. the solution is decolourised
c. \( S O_{2} \) is reduced.
D. green \( C r_{2}\left(S O_{4}\right)_{3} \) is formed


Secondary succession takes place on/in
A. Newly created pond.
B. Newly cooled lava.
c. Bare rock.
D. Degraded forest.


All congruent figures are similar but the similar figures are not congruent.Is this statement true or false?
\( A \). False
B. Both A and C
c. True
D. Not applicable


Metal carbonates decompose on
heating to give metal oxide and carbon dioxide. Which of the metal carbonates
is most stable thermally?
A. \( M g C O_{3} \)
в. \( C a C O_{3} \)
\( \mathrm{c} \cdot \operatorname{Sr} \mathrm{CO}_{3} \)
D. \( B a C O_{3} \)


Three moles of oxygen are mixed with two moles of helium. What will be the
ratio of specific heats at constant pressure and constant volume for the
mixture?
A . 2.5
в. 3.
c. 1.5
D.


Upon oxidation of one molecule of
pyruvate by mitochondria, the number of ATP generated are
A . 38
B. 30
\( c \cdot 8 \)
D. 15


Assertion
The first IE of \( B e \) is greater than that of
\( \boldsymbol{B} \)
Reason
\( 2 p \) -orbital is lower in energy than \( 2 s \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


The ratio in which \( x y- \) plane divides the line joining the points (1,0,-3) and (1,-5,7) is given by
A . 7: 3
в. 3: 7
\( c .3: 4 \)
D. 4: 7


f \( a r e a=900 s q . c m \) and breadth \( = \)
\( 25 \mathrm{cm}, \) then find length of rectangle.


If \( \angle A \) and \( \angle B \) are acute angles such
that \( \cos A=\cos B \) then prove that
\( \angle A=\angle B \)


I: If \( a, b, c \) are real, the roots of \( (b- \)
\( c) x^{2}+(c-a) x+(a-b)=0 \) are real
and equal, then \( a, b, c \) are in A.P.
Il: If \( a, b, c \) are real and the roots of \( \left(a^{2}+\right. \)
\( \left.\boldsymbol{b}^{2}\right) \boldsymbol{x}^{2}-\boldsymbol{2} \boldsymbol{b}(\boldsymbol{a}+\boldsymbol{c}) \boldsymbol{x}+\boldsymbol{b}^{2}+\boldsymbol{c}^{2}=\boldsymbol{0} \) are
real and equal, then \( a, b, c \) are in H.P.
Which of the above statement(s) is(are)
true?
A. only।
B. only II
c. both I and II


The product obtained as a result of a
reaction of nitrogen with \( C a C_{2} \) is:
A \( \cdot C a(C N)_{2} \)
в. \( C a C N \)
c. \( C a C N_{3} \)
D. \( C a_{2} C N \)
E. No option


If \( y=\tan ^{-1} \frac{\cos x+\sin x}{\cos x-\sin x}, \) then find \( \frac{d y}{d x} \)


\( \frac{(1+i)^{3}}{2+i} \) is equal to
A \( \cdot \frac{2}{5}-\frac{6}{5} \)
B.
c. \( -\frac{1}{5}+\frac{6}{5} i \)
D. \( -\frac{2}{5}+\frac{6}{5} \)


Find the degree of the following polynomial
\( \boldsymbol{x}^{2}-\mathbf{9} \boldsymbol{x}+\mathbf{2 0} \)


Which of the following salts when dissolved in water will produce an
acidic solution?
\( \mathbf{1} \cdot \boldsymbol{N} \boldsymbol{H}_{\mathbf{4}} \boldsymbol{C l} \)
2. \( \boldsymbol{K} \boldsymbol{H} \boldsymbol{S} \boldsymbol{O}_{4} \)
3. \( \boldsymbol{N a C N} \)
A .2 and 3
B. 1 and 2
c. only 3
D. 2 and 4


Two convex lenses of focal length \( 0.3 \mathrm{m} \)
and \( 0.05 \mathrm{m} \) are used to make a
telescope. The distance kept between
them is equal to
A . \( 0.35 \mathrm{m} \)
B. 0.25 \( m \)
\( c .0 .175 \mathrm{m} \)
D. 0.15 \( m \)


Silicon and hydrogen form a series of compounds with general formula
\( \boldsymbol{S} \boldsymbol{i}_{\boldsymbol{x}} \boldsymbol{H}_{\boldsymbol{y}} \cdot \mathbf{A} \boldsymbol{6} .2 \boldsymbol{2} \) g sample of the
compound is burnt in oxygen. All the \( S i \)
is converted to \( 11.64 g \) of \( S i O_{2} \) and all
of the \( H \) is converted to 6.980 gof \( H_{2} O \) What is the value of \( \frac{y}{x} ?(S i=28) \)


The letters of word \( O U G H T \) are written
in all possible orders and these words
are written out as in a dictionary. Find the rank of the word \( T O U G H \) in this dictionary.
\( A \cdot 89 \)
B. 90
c. 91
D. 92


lonisation constant of \( N H_{4}^{+} \) in water is \( 5.6 \times 10^{-10} \) at \( 25^{\circ} C . \) The rate constant
for reaction of \( N H_{4}^{+} \) and \( O H^{-} \) to form
\( N H_{3} \) and \( H_{2} O \) at \( 25^{\circ} C \) is \( 3.4 \times \) \( 10^{10} \) litre.mol\( ^{-1} . \)sec\( ^{-1} \). Calculate rate
constant for proton transfer from water to \( \boldsymbol{N} \boldsymbol{H}_{3} \)


A chord of a circle of radius \( 10 \mathrm{cm} \)
subtends a right angle at the centre. Find the area of the corresponding
\( (i) \)
Minor segment,
(ii) Major segment. (use \( \boldsymbol{\pi}=\mathbf{3 . 1 4}) \)


The principle value of \( \tan ^{-1}(-\sqrt{3}) \) is
A \( \cdot \frac{2 \pi}{3} \)
в. \( \frac{4 \pi}{3} \)
c. \( \frac{-\pi}{3} \)
D. none of these


The amount of heat energy required to raise the temperature of \( 1 g \) of helium
in a container of volume \( 10 L, \) from \( T_{1} K \)
to \( T_{2} K \) is \( \left(N_{a}= \) Avogadros number, \right.
\( k_{B}= \) Boltzmann constant
A \( \cdot \frac{3}{2} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
в. \( \frac{3}{7} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
c. \( \frac{3}{4} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)
D \( \cdot \frac{3}{8} N_{a} k_{B}\left(T_{2}-T_{1}\right) \)


toppr
Q Type your question
uniform speed \( 20 \mathrm{m} / \mathrm{sec} . \) Size of
magnet is \( 2 \times 1 \times 2 \mathrm{cm} \) and size of coil
\( 4 \times 6 \mathrm{cm} \) as shown in figure. The correct
variation of induced emf with time is :
(Assume at \( t=0, \) the coil enters in the
magnetic field)
4
3
\( c \)
\( D \)


In Wheatstone's bridge the values of
resistors \( \mathrm{P} \) and \( \mathrm{Q} \) are respectively 3 and
x. If \( 4 \Omega \) and \( 2 \Omega \) are the values of
resistors \( \mathrm{R} \) and \( \mathrm{S} \) respectively, then \( \times \) is
\( A \)
B. 1.5
\( c \cdot 2.5 \)
\( D \cdot 2 \)


If a \( 3 \times 3 \) matrix \( A \) has its inverse equal
to \( A, \) then \( A^{2} \) is equal to
\( \mathbf{A} \cdot\left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 1 & 1 \\ 0 & 1 & 0\end{array}\right] \)
\( \mathbf{B} \cdot\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1\end{array}\right] \)
\( \mathbf{C} \cdot\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] \)
\( \mathbf{D} \cdot\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right] \)


A boy weighing \( 500 \mathrm{N} \) is standing on the ground wearing a pair of flat shoes. The area of contact of one shoe with the
ground is \( 100 \mathrm{cm}^{2} \). What will be the
pressure exerted by the boy on the ground if he stands on both feet?
A \( \cdot 25000 N / m^{2} \)
в. \( 50000 N / m^{2} \)
c. \( 2500 N / m^{2} \)
D. \( 5000 N / m^{2} \)


Multiply:
\( -5 c d^{2} \) by \( -5 c d^{2} \)
\( \mathbf{A} \cdot 25 c^{2} d^{5} \)
\( \mathbf{B} \cdot 25 c^{3} d^{4} \)
\( \mathbf{C} \cdot 25 c^{2} d^{3} \)
D. \( 25 c^{2} d^{4} \)


What type of fibre is cotton?
A . Acid
B. Base
c. cellulose
D. Bast


If true enter 1 , if false enter 0 .
\( H_{3} P O_{3} \) is dibasic acid.
\( \mathbf{A} \cdot \mathbf{1} \)


Equation of the parabola whose vertex is (0,0) and focus is the point of intersection of the lines \( \boldsymbol{x}+\boldsymbol{y}= \)
\( 2,2 x-y=4 \) is
A \( \cdot y^{2}=2 x \)
в. \( y^{2}=4 x \)
c. \( y^{2}=8 x \)
D . \( x^{2}=8 y \)


The largest collection of herbarium in
India is
A. Central National Herbarium, Kolkata
B. Southern Circle Herbarium, Coimbatore
c. Central Circle Herbarium, Allahabadd
D. Blatter Herbarium, Mumbai


Three circles with centre \( A, B \) and \( C \)
respectively, touch one another as
shown in the figure. If \( A, B \) and \( C \) are
collinear and PQ is a common tangent
to the two smaller circles, where \( \mathrm{PQ}=4 \)
the area of shaded region is


A sound wave is travelling from East to West. In which direction do the
molecules in the air move?
A. East to west
B. West to East
c. North to South
D. South to North


Find the difference of air pressure between the inside and outside of a
soap bubble \( 5 m m \) in diameter, if the
surface tension is \( 1.6 N / m \)
A \( \cdot 2560 N / m^{2} \)
В. \( 3720 N / m^{2} \)
\( \mathrm{c} \cdot 1208 \mathrm{N} / \mathrm{m}^{2} \)
D. \( 950 N / m^{2} \)


Identify the error in the given statement Circle the incorrect word and write the
correct word in the blank.
Atoms have more than one kind of
particles combined together in a fixed ratio by mass.


How does resistivity of a conductor very with temperature coefficient of resistivity. Draw the graph of variation
of resistivity of a conductor with temperature.


\( \mathrm{X}^{\prime} \) speaks truth in \( 60 \% \& \) 'y' is \( 50 \% \) of the cases. The probability that they contradict each other while narrating
the same incident, is
A \( \cdot \frac{1}{2} \)
в. \( \frac{1}{8} \)
\( c \cdot \frac{1}{4} \)
D.


Lack of pulmonary surfactant produces
A. Asthma
B. Emphysema
c. cystic fibrosis
D. Respiratory distress syndrome


A photography dealer ordered 60 Mode
\( X \) cameras to be sold for \( \$ 250 \) each,
which represents a 20 percent mark up over the dealer's initial cost for each
camera. Of the cameras ordered, 6 were
never sold and were returned to the
manufacturer for a refund of 50 percent of the dealer's initial cost. What was
the dealer's approximate profit or loss
as a percent of the dealer's initial cost
for the 60 cameras?
A. \( 7 \% \) loss
B. \( 13 \% \) loss
c. \( 7 \% \) profit
D. \( 13 \% \) profit
E . \( 15 \% \) profit


Copper forms two oxides. For the same
amount of copper, twice as much oxygen was used to form the first oxide
than to form the second one. What is the
ratio of the valencies of copper in the
first and second oxides?


When 60 calories of heat are supplied to \( 15 \mathrm{g} \) of water, the rise in temperature is
A \( \cdot 75^{\circ} \mathrm{C} \)
В. \( 90^{\circ} \mathrm{C} \)
\( \mathbf{c} \cdot 4^{\circ} C \)
D. \( 0.25^{\circ} \mathrm{C} \)


Cell is called as the structural and
functional units of life
because
A. All organisms are formed of cells.
B. All cells are biochemical reaction house
C. ATP is synthesized within cells.
D. All of the above


When \( M n O_{2} \) is fused with \( \mathrm{KOH} \) and
\( K C l O_{3}, \) a coloured compound is formed, the product and its colour is:
A \( \cdot K_{2} M n O_{4}, \) green
B . \( K M n O_{4} \), purple
c. \( M n_{2} O_{3} \), brown
D. \( M n_{3} O_{4} \), black


Assertion
A cyclist always bends inwards while
negotiating a curve.
Reason
By bending he lowers his centre of
gravity.
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


Oxidation number of nitrogen in which among the oxides of nitrogen is the lowest?
A. Nitric oxide
B. Nitrous oxide
c. Nitrogen dioxide
D. Dinitrogen trioxide


At the time of puberty, the hormone that
triggers changes is This question has multiple correct options
A. Testosterone
B. Estrogen
c. Adrenaline
D. Thyroxine


Find the surface area of a sphere (in
\( c m^{2} \) ) of radius: \( 14 \mathrm{cm} \)


Which one of the following is correct?
\( \mathbf{A} \cdot \sin 45^{0} \cos 45^{0}=1 \)
B \( \cdot \sin ^{2} 45^{0}-\cos ^{2} 45^{0}=1 \)
\( \mathbf{C} \cdot \sin 30^{0}+\cos 60^{0}=1 \)
D \( \cdot \cos ^{2} 30^{0}-\cos ^{2} 60^{0}=1 \)


In the given figure, \( B<A \) and \( D>C \)
then:
A \( . A D>B C \)
B . \( A D=B C \)
C \( . A D<B C \)
D. \( A D=2 B C \)


The value of rate of a pseudo first order
reaction depends upon:
A. the concentration of both the reactants present in the reaction
B. the concentration of the reactant present in small amount
c. the concentration of the reactant present in excess
D. the value of \( \Delta H \) of the reaction


Given figure shows a shovel used to lift earth (sand). A and B are hinges connecting the shovel to the two rods shown. The weight of the shovel and
sand is \( 12 k N \) acting at G. The
magnitude of the force \( F \) is \( 5 k N \). The
reactive force at B is :
(All dimension in \( c m \) )
A \( .0 k N \)
B. \( 9.8 k N \)
\( \begin{array}{ll}.17 .66 k N & N\end{array} \)
D. \( 20 k N \)


A hemisphere and a solid cone of same
density have a common base. The
centre of mass of the common structure
coincides with the centre of the
common base. If \( \boldsymbol{R} \) is the radius of
hemisphere and \( h \) is height of the cone, then :
\( \mathbf{A} \cdot \frac{h}{R}=\sqrt{3} \)
B. \( \frac{h}{R}=\frac{1}{\sqrt{3}} \)
\( ^{\mathbf{C}} \cdot \frac{h}{R}=3 \)
D \( \cdot \frac{h}{R}=\frac{1}{3} \)


Mention the specific type of isomerism exhibited by each of the following pairs


A type of electromagnetic wave has
wavelength \( 50 A \)
(i) Name the wave.
(ii) What is the speed of the wave in
vacuum ?
(iii) State one use of this type of wave.


Which of the following statements is
correct concerning the passage of white light into a glass prism?
A. All the colours of white light travel with the same speed
B. The violet colour travels slower than the red colour
C. The violet colour travels faster than the red colour
D. Greater the wavelength, slower the speed of colour


Corals belongs to the phylum
A. Porifera
B. Coelenterata
c. Mollusca
D. Echinodermata


The multiplicative inverse of \( \frac{1}{5} \) is


A person opens an account with 50 and
starts depositing every day double the amount he has deposited on the
previous day. Then find the amount he has deposited on the 10 th day from
the beginning.
A . 25000
B. 25600
c. 28500
D. 26500


State whether the given statement is true or false:
-150 is a term of A.P. \( 17,12,7,2, \dots \dots \dots \)
A. True
B. False


A bar magnet of magnetic moment \( 2 A m^{2} \) is free to rotate about a vertical axis passing through its center. The magnet is released from rest from east
west position. Then the KE of the magnet as it takes N-S position is
\( \left(B_{H}=25 \mu T\right) \)
A. \( 25 \mu J \)
в. \( 50 \mu J \)
c. \( 100 \mu J \)
D. \( 12.5 \mu J \)


If \( \boldsymbol{\alpha}, \boldsymbol{\beta}, \gamma \) are modulus of the complex
number \( 3+4 i,-5+12 i, 1-i, \) then
the increasing order for \( \alpha, \beta \) and \( \gamma \) is
A \( \cdot \alpha, \gamma, \beta \)
в. \( \alpha, \beta, \gamma \)
\( \mathrm{c} . \gamma, \alpha, \beta \)
D. can't be determined


If we cut the string slightly above the body, we see that the string
A. Moves upwards with a jerk
B. Moves downwards with a jerk
c. Both
D. None


Ine varıatıon or anoae current ın a
triode valve corresponding to a change
in grid potential at three different
values of the plate potential is shown in
the given figure. The mutual
conductance of triode is
\( \mathbf{A} \cdot 5 \times 10^{-3} m h o \)
B . \( 2.5 \times 10^{-3} \) mho
C. \( 7.5 \times 10^{-3} \) mho
D. \( 9.5 \times 10^{-3} \) mho


The structure of orthophosphoric acid
is:
\( A \)
B.
\( c \)
D.


\( D \)
\( E \)
\( D \Delta \Delta \)
\( \square \)


In a pure capacitive A.C circuit current and voltage differ in phase by
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( \mathrm{c} \cdot 90^{\circ} \)
D. \( 180^{\circ} \)


The sum of first 45 natural numbers is:
A. 1035
в. 1280
c. 2070
D. 2140


Cynohydrin of which of the following compound can give lactic acid
A. \( H C H O \)
в. \( C H_{3} C O C H_{3} \)
c. \( C H_{3} C H O \)
D. \( C H_{3} C H_{2} C H O \)


\( p K_{a} \) of weak acid is \( 3.0 . \) Effective range
of a buffer of \( \boldsymbol{H} \boldsymbol{A} \) and \( \boldsymbol{A}^{-} \) is about \( \boldsymbol{p} \boldsymbol{H}: \)
\( A \cdot 3 \) to 4
B. 3 to 6
c. 2 to 3
D. 2 to 4


Which of the following system of classification is based on gross
morphology of plants?
A. Natural system
B. Artificial system
C. Practical system
D. All system


If \( A \) is \( 4 \times 5 \) matrix, if \( A^{T} B \) and \( B A^{T} \)
are defined then \( B= \)
\( \mathbf{A} \cdot 5 \times 4 \)
B. \( 4 \times 4 \)
\( \mathbf{c} .5 \times 5 \)
D. \( 4 \times 5 \)


The total number of basic groups in the following form of lysine is:
\( A \)
B.
\( c \cdot 2 \)
\( D \)
\( E \cdot 4 \)
\( F .5 \)
\( G \cdot 6 \)
H.
8


For a firt order reaction \( \boldsymbol{A} \rightarrow \boldsymbol{P}, \) the
temperature (T) dependent rate constant (k) was found to follow the equation \( \log k=-(2000) \frac{1}{T}+6.0 . \) The
pre-exponential factor A and the
activation energy \( E_{a}, \) respectively, are?
A . \( 1.0 \times 10^{6} s^{-1} \) and \( 9.2 k J \) mol \( ^{-1} \)
B. \( 6.0^{-1} \) and \( 16.6 k J \) mol \( ^{-1} \)
C . \( 1.0 \times 10^{6} s^{-1} \) and \( 16.6 k J \) mol \( ^{-1} \)
D. \( 1.0 \times 10^{6} s^{-1} \) and \( 38.3 k J \) mol\( ^{-1} \)


Assertion
Statement-1: All inter halogens are
diamagnetic
Reason
Statement-2: AB type of interhalogen undergoes hydroglysis giving a halide
ion derived from the smaller halogen
and a hypohalite ion derived from the
larger halogen.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-
c. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True


A figure has a rotational symmetry of order more than 1 , the angle of rotation
can be
A \( \cdot 21^{\circ} \)
B . \( 22^{\circ} \)
\( c \cdot 23^{\circ} \)
D. \( 24^{\circ} \)


The mechanism of ATP formation both
in chloroplast and mitochondria is explained by
A. Relay pump theory of Godlewski
B. Cholodny-Went's model
c. chemiosmotic theory
D. Munch's pressure/ mass flow model


Which of the following are true for
Cassiopeia?
This question has multiple correct options
A. It appears in the northern sky.
B. It has 5 prominent stars
C. It is visible during winter at late night
D. It looks like a distorted letter \( \mathrm{W} \) or \( \mathrm{M} \)


Consider an iron rod of length 1 metre
and cross-section \( 1 \mathrm{cm}^{2} \) with a Young's
modulus of \( 10^{12} \) dyne \( c m^{-2} . \) We wish to
calculate the force with which the two
ends must be pulled to produce an elongation of \( 1 \mathrm{mm} \). It is equal to:


Urine is stored in
A. Kidney
B. Urinary bladder
c. Ureter
D. Urethra


Assertion
Specific gravity is dimensionless
quantity.
Reason
Specific gravity is relative density of a substance, measured with respect to
density of water at \( 4^{\circ} \mathrm{C} \)
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


Interpret the following equations geometrically on the Argand plane. \( \mathbf{1}<|\boldsymbol{z}-\mathbf{2}-\mathbf{3} \boldsymbol{i}|<\mathbf{4} \)
A. Annular
B. Straight line
c. A point
D. Ringg


Solve :
\( \int \frac{3 x+5}{\sqrt{7 x+9}} d x \)


The difference in \( P E \) of an object of mass \( 10 k g \) when it is taken from a
height of \( 6400 k m \) to \( 12800 k m \) from the surface of the earth is
B . \( 1.565 \times 10^{8} \mathrm{J} \)
C . \( 2.65 \times 10^{8} \) 」
D. \( 4.5 \times 10^{8} \) 」


Find the slope of the line passing through the points (-1,1) and (2,2)


Solute when dissolved in water:
A. increases the vapour pressure of water
B. decreases the boiling point of water
C . decreases the freezing point of water
D. all of the above


In the given fig \( A D \) divides \( \angle B A C \) in
the ratio 1: 3 and \( A D=D B \)
Determine the value of \( x \)


The points (2,5) and (5,1) are the two opposite vertices of a rectangle. If the other two vertices are points on the straight line \( y=2 x+k, \) then the value
of k is
\( A \cdot 4 \)
B. 3
\( c \cdot-4 \)
\( D \cdot-3 \)
\( E \)


The oxidation number of 'N' in NOCIO:
\( A \cdot+3 \)
B. +1
\( c \cdot+2 \)
\( D \cdot+7 \)


The standard entropies of \( N_{2}(g), H_{2}(g) \)
and \( N H_{3}(g) \) are \( 191.5,130.5,192.6 J K^{-1} \)
mol \( ^{-1} \).The value of \( \Delta S^{\circ} \) of formation of
ammonia is?


What is the correct name for an organic compound with the molecular formula
\( \boldsymbol{C}_{3} \boldsymbol{H}_{8} ? \)
A. Methane
B. Ethane
c. Isobutane
D. Propane


A plot of \( f \) vs \( (1 / T) \) gives
A. a straight line passing through the origin
B. a straight line parallel to frequency axis
C. a straight line perpendicular to frequency axis
D. a straight line having an intercept along frequency axis