In the following circuit, each resistor has a resistance of \( 15 \Omega \) and the battery
has an e.m.f. of \( 12 V \) with negligible
internal resistance.

When a resistor of resistance \( \boldsymbol{R} \) is
connected between \( D \& F, \) no current
flows through the galvanometer (not
shown in the figure) connected
between \( C \& F \). Calculate the value of \( R \)
A \( .10 \Omega \)
B. \( 15 \Omega \)
\( c .5 \Omega \)
D. 30\Omega


Find the principal value of \( \cot ^{-1}(\sqrt{3}) \)


Phosphine is prepared by the action of?
A . Pand \( H_{2} S O_{4} \)
B. P and NaOH
c. P and \( H_{2} S \)
D. P and \( H N O_{3} \)


A hydrogen atom in a state having a
binding energy of \( 0.85 e V \) makes
transition to a state with excitation
energy \( 10.2 e V \)

Find the wavelength of the emitted
radiation.


(a) In Young's double slit experiment, derive the condition for
(i) constructive interference and
(ii) destructive interference at a point
on the screen.
(b) \( A \) bream of light consisting of two
wavelengths, \( 800 n m \) and \( 600 n m \) is
used to obtain the interference fringes in a Young's double slit experiment on a screen placed \( 1.4 m \) away. If the two
slits are separated by \( 0.28 n m \) calculate the least distance from the
central bright maximum where the bright fringes of the two wavelengths coincide.


When a moving body is suddenly
stopped, then:
A. Frictional force increases.
B. Friction force remains same as it was while the car
was moving.
C. Friction force reduces but has a non zero value.
D. Frictional force reduces to zero as it is a self adjusting force.


Potential difference is also called
A. voltage
B. Biot
c. coulomb
D. Ampere


Solve \( \int_{0}^{\pi / 2} \frac{\cos ^{2} x}{\sin ^{2} x+\cos ^{2} x} d x \)
A. \( -\frac{\pi}{4} \)
в.
c. \( \frac{3 \pi}{4} \)
D. None of these


Sl unit of temperature is
\( \mathbf{A} \cdot K \)
B. \( ^{\circ} C \)
\( c \cdot^{o} F \)
D.


10 grams of steam at \( 100^{\circ} \mathrm{C} \) is mixed
with \( 50 g m \) of ice at \( 0^{\circ} C \) then final temperature is
A \( \cdot 20^{\circ} \mathrm{C} \)
В. \( 50^{\circ} \mathrm{C} \)
c. \( 40^{\circ} \mathrm{C} \)
D. \( 100^{\circ} \mathrm{C} \)


Variance remains unchanged by change
of
A. scale
B. origin
c. both
D. none of these


Give the number of stereoisomers of the
product formed in the given reaction.
A .2
B. 4
\( c .3 \)
\( D \)


The solution of differential equation
\( \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}+\left(\boldsymbol{x}-\boldsymbol{y}^{2}\right) \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)
\( \mathbf{A} \cdot e^{\frac{y}{x}}=\sin x+c \)
B. \( y=c x \log x \)
c. \( x=\frac{y^{2}}{3}+\frac{c}{y} \)
D. \( \cos \left(\frac{y-2}{x}\right)=a \)


DNA is mainly found in
A. Nucleus only
B. Nucleus and cytoplasm
c. Cytoplasm only
D. None of the above


The two isomers \( X \) and \( Y \) with the
formula \( \boldsymbol{C r}\left(\boldsymbol{H}_{2} \boldsymbol{O}\right)_{5} \boldsymbol{C l B r}_{2} \) were taken
for experiment on depression in
freezing point. It was found that one
mole of \( X \) gave depression
corresponding to 2 moles of particles
and one mole of Y gave depression due
to 3 moles of particles. The structural
formulae of \( X \) and \( Y \) respectively are:
\( \mathbf{A} \cdot\left[C r\left(H_{2} O\right)_{5} C l\right] B r_{2} ;\left[C r\left(H_{2} O\right)_{4} B r_{2}\right] C l \cdot H_{2} O \)
B \( \left.\cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{5} C l\right)\right] B r_{2} ;\left[\operatorname{Cr}\left(H_{2} O\right)_{3} C l B r\right] \cdot 2 H_{2} O \)
\( \mathbf{c} \cdot\left[C r\left(H_{2} O\right)_{5} B r\right] B r C l ;\left[C r\left(H_{2} O\right)_{4} C l B r\right] B r \cdot H_{2} O \)
\( \mathbf{D} \cdot\left[\operatorname{Cr}\left(H_{2} O\right)_{4} B r_{2}\right] C l \cdot H_{2} O ;\left[C r\left(H_{2} O\right)_{5} C l\right] B r_{2} \)


When a rubber cord is stretched, the change in volume with respect to change in its linear dimensions is negligible. The Poisson's ratio for rubber
is
\( A \)
B. 0.25
\( c \cdot 0.5 \)
D. 0.75


Define antioxidants and mention two
examples


\( D_{2} O \) is:
A \( . \) product of \( O_{2} \) and \( H_{2} \)
B. simple water in which present heavy metal salts
C. marine water
D. water which form redistillation and condensation


When 9.65 coulomb of electricity is passed through a solution of silver nitrate, the amount of silver deposited is:
A. \( 16.2 \mathrm{mg} \)
B. \( 21.2 \mathrm{mg} \)
c. \( 10.8 \mathrm{mg} \)
D. \( 6.4 \mathrm{mg} \)


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


The equation of the straight line which passes through (1,1) and making angle \( 60^{\circ} \) with the line \( x+\sqrt{3} y+2 \sqrt{3}=0 \)
is/are.
A. \( y=1 \)
B. \( x=1 \)
c. \( x+y=2 \)
D. \( x+\sqrt{3} y-\sqrt{3}-1=0 \)


Solve: \( \frac{5 a^{3}-4 a^{2}+3 a+18}{a^{2}-2 a+3} \)


The probability of selecting a rotten apple randomly from a heap of 900 apples is \( 0.18 . \) What is the number of rotten apples in the heap?


For \( \boldsymbol{x} \in \boldsymbol{R},[\boldsymbol{x}] \) denotes the greatest
integer less than or equal to \( x \). The
largest natural number \( n \) for which \( \boldsymbol{E}=\left[\frac{\boldsymbol{\pi}}{2}\right]+\left[\frac{\mathbf{1}}{\mathbf{1 0 0}}+\frac{\boldsymbol{\pi}}{\mathbf{2}}\right]+ \)
\( \left[\frac{2}{100}+\frac{\pi}{2}\right] \ldots+\left[\frac{n}{100}+\frac{\pi}{2}\right]<43 \)
is
A . 41
B . 42
\( c .43 \)
D. 97


toppr
Q Type your question
\[
0-20
\]
\( 20-30 \)
\( 30-40 \)
40
\[
20
\]
50
\[
20
\]
\( 60-70 \)
\( 70- \) Above
Total
A teacher wanted to analyze the performance of two sections of students
in a mathematics test of 100 marks.
Looking at their performance, she found
that a few students got, under 20 marks
and a few got 70 marks or above. So she
decided to group them into intervals of
varying sizes as follows: \( 0-20,20- \)
\[
30 \ldots .60-70,70-100 \text { Then she }
\]
formed the following table.
(i) Find the probability that a student obtained less than \( 20 \% \) in the
mathematics test.
(ii) Find the probability that a student
obtained marks 60 or above.


Addition of \( F e C l_{3} \) to \( K_{4} F e(C N)_{6} \) in
dilute and cold solution gives:
A. prussian blue sol
B. \( F e_{4}\left[F e(C N)_{6}\right]_{3} \) so
c. positive sol
D. All of the above


A graph is plotted taking \( ^{\circ} \boldsymbol{C} \) along the
Y-axis and \( ^{\circ} \boldsymbol{F} \) along the \( \mathbf{X} \) -axis. It is
a/an
A. parabola
B. straight line
c. ellipse
D. circle


Visible light of wavelength \( 6000 \times \)
\( 10^{-8} \mathrm{cm} \) falls normally on a single slit
and produces a diffraction pattern. It is found that the second diffraction
minimum is at \( 60^{0} \) from the central
maximum. if the first minimum is
produced at \( \theta_{1} \) then \( \theta_{1} \) is close to :
A \( \cdot 25^{\circ} \)
B. \( 30^{\circ} \)
\( c \cdot 20^{0} \)
D. \( 45^{\circ} \)


Write the following decimals in the place value table.
\( \mathbf{1 9 . 6 0} \)


Which of the following is a community of plants and animals which occupies a large geographical area within a particular climate zone?
A. Biodiversity
B. Biome
c. Habituate
D. Bogg


Find two rational numbers between \( \frac{-3}{4} \) and \( \frac{1}{2} \)


The secondary structure of protein
which exists in hair is


Out of sodium, chlorine and silicon
which one is metalloid?


Estimate the average thermal energy of a helium atom at
(i) room temperature \( \left(27^{\circ} C\right) \)
(ii) the temperature on the surface of the Sun (6000 K),
(iii) the temperature of 10 million kelvin
(the typical core temperature in the case of a star)


The number of values of \( x \) where the
function \( \boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{x}+\cos (\sqrt{\mathbf{2}} \boldsymbol{x}) \)
attains its maximum is
A .
в.
\( c \cdot 2 \)
D. infinite


\( N a \rightarrow N a^{+}+e^{-} \)
\( \boldsymbol{C l}+\boldsymbol{e}^{-} \rightarrow \boldsymbol{C l}^{-} \)
a) Is sodium a metal or a non-metal?
b) Write the name of \( C l^{-} \) ion.


Find the position of centre of mass of
the uniform lamina shown in Fig.


There are three particles shown in the figure as I, II and III. The velocity and acceleration vectors associated with
the motion of three particles are shown. Which of the above could represent the
velocity and acceleration vectors for a projectile following a parabolic path?
I.
II.
III.
A. I only
B. II only
c. III only
D. I and II only
E. II and III only


The optical path of a monochromatic light is same if it goes through \( 4.0 \mathrm{cm} \) of glass of \( 4.5 \mathrm{cm} \) of water. If the
refractive index of glass is 1.53 , the refractive index of the water is:
A . 1.30
B. 1.36
c. 1.42
D. 1.46


Delegates from 9 countries include
countries \( A, B, C, D \) are to be seated in a
row. The number of possible seating arrangements, when the delegates of the countries \( A \) and \( B \) are to be seated
next to each other and the delegates of the countries \( C \) and \( D \) are not to be
seated next to each other is :
A . 10080
B. 5040
c. 3360
D. 60480


Chloroform can be obtained from:
A. methanal
B. 2-propanal
c. methanol
D. 1-propanol


\( \int x \sec x^{2} d x \) is equal to
A \( \cdot \frac{1}{2} \log \left(\sec x^{2}+\tan x^{2}\right)+k \)
в. \( \frac{x^{2}}{2} \log \left(\sec x^{2}+\tan x^{2}\right)+k \)
c. \( 2 \log \left(\sec x^{2}=\tan x^{2}\right)+k \)
D. None of these


Two distinct
be parallel to the same line.
A. Intersecting
B. Non-intersecting
c. Parallel
D. None of these


How many geometrical isomer of \( (\boldsymbol{X}) \) is
possible?


The slope of a curve at each of its points is equal to the square of the abscissae of the point. Find the particular curve
through the point (-1,1) \( \mathbf{1}+\boldsymbol{y}=\boldsymbol{2} \boldsymbol{e}^{\boldsymbol{x}^{2} / \mathbf{2}} \)


Factorise the expression and divide them as directed.
\( 12 x y\left(9 x^{2}-16 y^{2}\right) \div 4 x y(3 x+4 y) \)


Which substance is not used as a fuel?
A. Ethanol
B. Hydrogen
C. Methane
D. oxygen


Clay is used for making bricks and flower pots. If the clay article is not dried before 'firing' in a kiln, there will be evaporation of water from the surface and the :
A. kiln fire will be put out by steam
B. article will becomes soft
c. article will become hard
D. article will develop cracks


Which of the following is not present in genetic material?
A. Cytosine
B. Thymine
c. Arginine
D. Guanine
E. Uracil


Define valency by taking examples of
silicon and oxygen.


If \( \boldsymbol{x}^{n}-\mathbf{1} \) is divisible by \( \boldsymbol{x}-\boldsymbol{k}, \) then the
least positive integral value of \( k \) is
A . 1
B . 2
\( c .3 \)
D. 4


The displacement y of a particle executing periodic motion is given by \( y=4 \cos ^{2}\left(\frac{1}{2}\right) t \sin (1000 t) . \) This
expression may be considered as a result of the superposition of
A. Two waves
B. Three waves
c. Four waves
D. Five waves


If \( 10 l \) of oxygen contains \( x \) molecules,
then \( 10 l \) of ozone contains
molecules at the same temperature
and pressure.


Construct a triangle \( A B C \), given the
following \( A B=6 c m, B C=5 c m \) and \( C A= \)
\( \mathbf{5} c \boldsymbol{m} \)


Which rays contain \( (+\mathrm{Ve}) \) charged
particle:
A. \( \alpha \) -rays
B. \( \beta \) -rays
c. \( \gamma \) -rays
D. X-rays


Prove that \( ^{n} C_{0}-^{n} C_{1}+^{n} C_{2}- \)
\( ^{n} C_{3}+\ldots+(-1)^{r} n_{r}+\ldots= \)
\( (-1)^{r-1} n-1 C_{r-1} \)


A circuit operating at \( \frac{360}{2 \pi} \mathrm{Hz} \Omega \) contains a \( 1 \mathrm{F} \mu \) capacitor and a 20 resistor. The inductor must be added in
series to make the phase angle for the circuit zero is
A . 7.7
B. 10
c. \( 3.5 \mathrm{H} \)
D. 15 H


When a wire loop is rotated in a magnetic field, the direction of induced emf changes in every
A. one revolution
B. \( \frac{1}{2} \) revolution
c. \( \frac{1}{4} \) revolution
D. 2 revolution


Which of the following is/are example(s) of isotopes?
A. Oxygen and Ozone
B. Ice and Steam
c. Nitric oxide and Nitrogen dioxide
D. Hydrogen and Deuterium


Corrosion is the natural process which
converts a refined metal to its:
A . oxide
B. hydroxide
c. sulphide
D. all of these


Which of the following is wrong?
A. order of the reaction is negative, positive or fractional
B. molecularity of the reaction is always equal to the sum of stoichiometric co-efficients.
C. the order of a reaction may be zero
D. half life is independent of the concentration of reactants in first order reaction


Chlorine gas removes hydrogen from \( \boldsymbol{H}_{2} \boldsymbol{S} \) solution forming \( \mathrm{HCl} \) and leaving behind sulphur.
A. True
B. False


Quartz, \( S i O_{2}, \) which is insoluble in
most of the solvent with a high melting point. Which type of force best describe the physical properties of quartz? This question has multiple correct options
A. Hydrogen bonding
B. Covalent bonding
c. lonic bonding
D. \( P \) bonding
E. Dispersion forces


An instantenous displacement of a simple harmonic oscillator is \( \boldsymbol{x}= \)
\( \boldsymbol{A} \cos \left(\boldsymbol{\omega} \boldsymbol{t}+\frac{\pi}{4}\right) . \) Its speed will be
maximum at time:
A \( \cdot \frac{\pi}{4 \omega} \)
в. \( \frac{\pi}{2 \omega} \)
c. \( \frac{\pi}{\omega} \)
D. \( \frac{2 \pi}{\omega} \)


Which of the curves in figure represents
the relation between Celsius and
Fahrenheit temperature?
\( A \)
B.
\( c \)
\( D \)


Waste management is
A. to develop products and processes that are kind to the environment. This can involve reducing the waste a process creates, using renewable materials, lessening the energy required to form a product, etc
B. the collection, transportation, disposal or recycling and monitoring of waste
C. the process of creating a clean and green environment
D. None of above


\( \operatorname{Let} f(x)=\frac{x^{2}-4}{x^{2}+4} \) for \( |x|>2, \) then the
function \( \boldsymbol{f}:(-\infty,-2] \cup[2, \infty) \rightarrow \)
(-1,1) is
A. One-one into
B. One-one onto
c. Many one into
D. Many one onto


State true or false:
The bisector of any two adjacent angles of a rhombus form a right-angled triangle.
A. True
B. False


Light waves travel in vaccum along the
y-axis. Then the wave front is:
A. \( y= \) constant
B. \( x= \) constant
c. \( z= \) constant
D. \( x+y+z= \) constant


\( \int \frac{x e^{x}}{(1+x)^{2}} d x \) is equal to
A \( \cdot \frac{-e^{x}}{x+1}+C \)
в. \( \frac{e^{x}}{x+1}+C \)
c. \( \frac{x e^{x}}{x+1}+C \)
D. \( \frac{-x e^{x}}{x+1}+C \)
E \( \frac{e^{x}}{(x+1)^{2}}+C \)


In a step-up transformer, if ratio of truns of primary to secondary is 1: 10 and primary voltage is \( 230 V \). If the load
current is \( 2 A \), then the current in
primary is
A . \( 20 A \)
в. \( 10 A \)
\( c . \$ 2 A \)
D. \( 1 A \)


Chief merit of Bentham and Hooker's
classification is that
A. The system mostly based on evolutionary concepts.
B. It is a natural systems of classification of all groups of plants.
C. It also considered the phylogenetic aspects.
D. The description of taxa are based on actual examination of specimen.


5 boys are to be arranged in a row. It two particular boys desire to sit in end places, the number of possible arrangements is
A . 60
в. 120
c. 240
D. 12


Which processes would you consider essential for maintaining life?


A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a
student will get 4 or more correct answers just by guessing is
A \( \cdot \frac{13}{3^{5}} \)
в. \( \frac{11}{3^{5}} \)
c. \( \frac{10}{3^{5}} \)
D. \( \frac{17}{3^{5}} \)


If \( K M n O_{4} \) is reduced by oxalic acid in an acidic medium, then the oxidation
number of \( M n \) changes from:
A. +4 to +2
B. +6 to +4
\( c \cdot+7 t o+2 \)
D. +7 to +4


Calculate work done.
A .12 atm \( \times 1 \)
B. \( 24 \operatorname{atm} \times 1 \)
c. 48 atm \( x \) ।t
D. 36 atm/l


A bag contains 15 white and some black
balls. If the probability of drawing a black ball from the bag is thrice that of
drawing a white ball, find the number of black balls in the bag.


In atmosphere, Ozone hole refers to
A. A hole in ozone layer
B. Decrease in ozone layer thickness in troposphere
C. Decrease in thickness of ozone layer in stratosphere
D. Increase in the thickness of ozone layer in troposphere


Find the value of \( k \) for which the area of
the triangle with vertices \( (2,-2),(-3,3 k) \) and (-2,3) is 20
sq.units.


Which is the only vector quantity out of the following?
A. Charge of a gold leaf electroscope
B. Electrostatic potential
c. current flowing in a metal
D. Angular momentum of a spinning body


Fertilisers are used to provide three elements needed to increase the yield of
crops

Which two compounds would provide all three of these elements?
A. ammonium nitrate and calcium phosphate
B. ammonium nitrate and potassium sulfate
c. potassium nitrate and calcium phosphate
D. potassium nitrate and potassium sulfate


What are the functions of the following in breathing? Abdominal muscles.


Write the value of the derivative of
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}-1|+|\boldsymbol{x}-\mathbf{3}| \) at \( \boldsymbol{x}=\mathbf{2} \)


According to Freundlich adsorption isotherm, which of the following is
correct?
A \( \cdot \frac{x}{m} \propto P^{o} \)
B. \( \frac{x}{m} \propto P^{1} \)
c. \( \frac{x}{m} \propto P^{1 / n} \)
D. All of the above are correct for different ranges of pressure


In two similar triangles \( A B C \) and \( P Q R \), if their corresponding altitudes \( A D \) and \( P s \) are in the ratio \( 4: 9, \) find the ratio of the
areas of \( \triangle A B C \) and \( \triangle P Q R \)
A . 16: 81
B. 9: 16
c. 81: 16
D. 16: 9


Find \( |\overrightarrow{\boldsymbol{b}}|, \) if \( (\overrightarrow{\boldsymbol{a}}+\overrightarrow{\boldsymbol{b}}) \cdot(\overrightarrow{\boldsymbol{a}}-\overrightarrow{\boldsymbol{b}})=8 \) and
\( |\overrightarrow{\boldsymbol{a}}|=\mathbf{8}|\overrightarrow{\boldsymbol{b}}| \)


Apoplast movement of water occurs
A. Through cell wall
B. Through plasma membrane
C. Through cytoplasm
D. Through middle lamella only


Name the following.
A lustrous non-metal


What is the electric flux through a cube
of side \( 1 \mathrm{cm} \) whose encloses an electric
dipole?


The group number of element with atomic number 7 in the periodic table
is:
\( A \cdot 2 \)
B. 18
c. 15
D. 14


A hemispherical bowl made of brass
has inner diameter \( 10.5 \mathrm{cm} . \) Find the
\( \operatorname{cost} \) of tin-plating it on the inside at the
rate of Rs. 4 per \( 100 c m^{2} \) in Rs.


Match the oxide of column I with their
corresponding property (ies) in column
II.


Ribosomes are sites of which reaction?
A. Respiration
B. Photosynthesis
c. Protein synthesis
D. Fat synthesis


Name the largest bacterium species.


If 2 g of an isotope has a half-life period of 7 days, the half -life period of 1 g sample is:
A. 3.5 days
B. 7 days
c. 14 days
D. 28 days


A body of mass \( 1 k g \) is thrown upwards with a velocity \( 20 m / s . \) It momentarily comes to rest after attending a height of \( 18 m . \) How much energy is lot due to air friction (in J)
A . 10
B. 20
\( c .30 \)
D. 40


Two equilateral prisms are arranged as shown in figure such that a ray of white
light is incident at point \( X \) The ray of light which emerges out of the prism
A. Will show all the colours of spectrum
B. Will be white light
c. will be orange in colour
D. will be dull white in colour


Let \( f: R \rightarrow R \) be defined by \( f(x)=\cos (5 x+2) \)
Is f invertible?
if yes enter 1 else enter 0


The eye of lobster is replaced by an
antenna like structure. It is an example of
A. Reparative regeneration
B. Heteromorphic regeneration
c. Physiological regeneration
D. All of the above


A cylinder is sandwiched between two
planks. Two constant horizontal forces
\( F \) and \( 2 F \) are applied on the planks as
shown. If there is no slipping at the top
and bottom of cylinder, then
This question has multiple correct options
A . acceleration of the centre of mass of cylinder is \( \frac{21 F}{26 M} \)
B. acceleration of the centre of mass of cylinder is \( \frac{13 F}{26 M} \)
C. acceleration of the top plank is \( \frac{F}{2 G M} \)
D. acceleration of the top plank is \( \frac{F}{13 M} \)


dentify the shape of histogram.
Height
A. Skewed left
B. Skewed right
c. Symmetric
D. Rotational


Name the method used for refining of
nickel metal?


Renal rickets is related to old age
A. Vitamin D deficiency
B. Osteoporosis
C. Chronic kidney disease
D. Both B and C


There are - m. rational numbers between
two given rational numbers.
A . 2
B. 5
c. none
D. infinite


The angle of quadrilateral are \( \boldsymbol{x}, \boldsymbol{x}+ \)
\( 60,4 x, 2 x+30 \) find \( x \)


If \( \boldsymbol{y}=\mathbf{1}+\frac{\boldsymbol{x}}{\mathbf{1} !}+\frac{\boldsymbol{x}^{2}}{\mathbf{2 !}}+\frac{\boldsymbol{x}^{\mathbf{3}}}{\mathbf{3 !}}+\cdots, \) then
\( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}}=------ \)


Two cars \( A \) and \( B \) start from the same
starting point. A is starting from rest and moving with constant acceleration
\( 2 m / s^{2} \) and car \( B \) is starting with a constant velocity \( 40 \mathrm{m} / \mathrm{s} \). After what time both cars will meet each other?


The value of \( \tan \left[\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{2}{3}\right] \) is
A \( \cdot \frac{6}{17} \)
в. \( \frac{7}{16} \)
c. \( \frac{17}{6} \)
D. none of these


If a member, whose tensile strength is more than 1.5 times the shear strength and is subjected to an axial load upto failure, the failure of the member will
occur by
A. maximum normal stress
B. maximum shear stress
c. normal stress or shear stress
D. none of the above


Absorption of mineral elements from
the soil occurs through
A. Diffusion
B. Active transportt
c. osmosis
D. All of the above


Which of the following halides would undergo nucleophilic substitution more readily?
A . 1-chloro-1-butene
B. 2-Chloro-1-butene
c. 3-Chloro-1-butene
D. 4-chloro-1-butene


Only the earth can exert gravitational force
A . True
B. False


If the normal at the end of latus rectum of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) passes
through \( (0,-b), \) then \( e^{4}+e^{2} \) (where \( E \) is eccentricity) equals
A \cdot eccentricity of the ellipse is \( \sqrt{\frac{\sqrt{5}-1}{2}} \)
B. ratio of the minor and major axes is \( \frac{\sqrt{5}+1}{2} \)
c. square of the eccentricity is equal to the ratio of the minor and major axes
D. none of these


Which of the following chemical is used in removing ink stain from clothes?
A. Ethyl alcohol
B. Glycol
c. Banzoic acid
D. Oxalic acid


How many molecules of \( C O_{2} \) are formed
when one molecule of \( C_{6} H_{12} O_{6} \) is
oxidised in our body?
A . 4
B. 2
\( c \cdot 6 \)
D.


Electric current cannot flow through
A. Silver
B. Woodd
c. copper
D. None of these


What is the torque of a force \( \boldsymbol{F}=(2 \hat{\boldsymbol{i}}- \) \( 3 \widehat{j}+4 k) N \) acting at a point \( r=(3 \hat{i}+ \) \( 2 \widehat{j}+3 \widehat{k}) \mathrm{m} \) about the origin in \( \mathrm{N}-\mathrm{m} \)
? (Given \( \boldsymbol{\tau}=\boldsymbol{r} \times \boldsymbol{F}) \)
A \( .6 \hat{i}-6 \hat{j}+12 \widehat{k} \)
B . \( 17 \hat{i}-6 \widehat{j}-13 \widehat{k} \)
\( \mathbf{c} .-6 \hat{i}+6 \widehat{j}-2 \widehat{k} \)
D. \( -17 \hat{i}+6 \hat{j}+13 \widehat{k} \)


The electric field associated with an
electromagnetic wave in vacuum is \( \operatorname{givenby}|\overrightarrow{\boldsymbol{k}}|=40 \cos \left(k z-6 \times 10^{8} t\right) \)
where \( E, z \) and \( t \) are in volt per meter,
meter and second respectively. The value of wave vector \( k \) is:
\( \mathbf{A} \cdot 2 m^{-1} \)
B . \( 0.5 m^{-1} \)
\( \mathbf{c} \cdot 3 m^{-1} \)
D. \( 6 m^{-1} \)


What are fossils?What do they tell us
about the process of evolution?


Distinguish between esterification and
saponification reactions of organic compounds:


Friction is not required in which of the following cases?
A. Man running on the ground.
B. Friction between parts of a machine
c. Writing with a pen
D. Monkey climbing a tree.


The conduction of water from root hair
to root xylem is
A. Symplastic
B. Apoplastic
c. osmotically
D. Symplastic and apoplastic


If for a G.P. \( S_{6}=126 \) and \( S_{3}=14 \) then
find \( \mathbf{r} \)
A
B. 2
\( c \cdot 3 \)
D. 4


Which of the following is an elastic
wave?
A. Sound waves
B. Light waves
c. x-rays
D. Radio waves


If \( y \) is directly proportional to \( x \& \) when
\( x=2 \& y=4, \) what is constant of
proportionality?
\( \mathbf{A} \cdot \mathbf{1} \)
B. 3
\( c .5 \)
D. 2


Which electronic level would allow the
hydrogen atom to absorb a photon but not to emit a photon:
A . \( 3 s \)
в. \( 2 p \)
\( c \cdot 2 s \)
D. \( 1 s \)


Phylloclade and cladodes commonly
occur in
A . Liliaceae
B. Solanaceae
c. Malvaceae
D. Papilionaceae


Assume 100 pm \( X \) -ray beam is passed through YDSE. Interference pattern is observed on a photographic plate placed \( 40 \mathrm{cm} \) away from the slits. What should be the separation between the slits so that the separation between two successive maxima is \( 0.1 \mathrm{mm} \)
A \( .4 \mu m \)
в. \( 0.4 \mu m \)
\( c .4 n m \)
D. \( 40 \mu m \)


\( \ln N, e, \tau \) and \( m \) are representing electron density, charge, relaxation time and mass of an electron
respectively, then the resistance of wire of length \( l \) and cross-sectional area \( \boldsymbol{A} \) is given by
A \( \cdot \frac{2 m l}{N e^{2} A \tau} \)
в. \( \frac{2 m \tau A}{N e^{2} l} \)
c. \( \frac{N e^{2} \tau A}{2 m l} \)
D. \( \frac{N e^{2} A}{2 m \tau l} \)


The ratio between the length and
breadth of a rectangular garden is 5: 3
If the perimeter of the garden is 160
meters, what will be the area of \( 5 m \)
wide road around its outside?
A. \( 600 m^{2} \)
B. \( 1200 m^{2} \)
\( \mathrm{c} \cdot 900 m^{2} \)
D. \( 1000 m^{2} \)


Match the compounds in column I with
their
characteristic(s)/test(s)/reaction(s)/re agent(s)/stereochemistry/isomer(s) given in column II. Matching can be one or more than one.


Which of the following alcohols is used as a beverage?
A. Propanol
B. 2-butanol
c. Methanol
D. Ethanol


A book is lying on a table, what is the angle between the book on the table and
the weight of the book?
A \( \cdot 0^{\circ} \)
B . \( 45^{\circ} \)
\( c .90^{\circ} \)
D. \( 180^{\circ} \)


Which of the following is a chronic inflammatory disease?
A. Asthma
B. Acapnia
c. oligopnea
D. Hypoxia


Statement 1: Oxidation and reduction
occur together Statement 2: In redox reactions,
electrons must be gained and lost.
A. Both Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement 1
B. Both Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation of Statement 1.
c. statement 1 is correct but statement 2 is not correct
D. Statement 1 is not correct but Statement 2 is correct
E. Both the Statement 1 and Statement 2 are not correct


Two blocks of mass \( 3 \mathrm{kg} \) and \( 4 \mathrm{kg} \) hang
from the ends of a massless rod marked
in seven equal parts.
Find out at which of the points
indicated should a string of mass
suspended so that whole system
remain in equilibrium?
\( \mathbf{A} \cdot \mathbf{A} \)
B.
\( c \cdot c \)
\( D \cdot D \)
\( E . \)


An aeroplane flying horizontally with speed \( 90 \mathrm{km} / \mathrm{hr} \) releases a bomb at a
height of \( 78.4 \mathrm{m} \) from the ground, when will the bomb strike the ground?
A. 8 sec
B. 6 sec
c. 4 sec
D. 10 sec


The relation between half life \( (T) \) and
decay constant \( (\lambda) \) is
A \( . \lambda T=1 \)
в. \( \lambda T=\frac{1}{2} \)
c. \( \lambda T=\log _{e} 2 \)
D. \( \lambda=\log 2 T \)


Find the equation of the circle with
center at (-3,5) and passes through
the point (5,-1)
A \( \cdot(x+3)^{2}+(y-5)^{2}=100 \)
B. \( (x-3)^{2}+(y-5)^{2} \)
C. \( (x+3)^{2}+(y-5)^{2} \)
D. None of the above


A uniform rod of length \( L \) has a mass
per unit length \( \lambda \) and area of cross
section \( A \). If the Young's modulus of the
rod is \( Y . \) The elongation in the rod due to its own weight is
A \( \cdot \frac{2 \lambda g L^{2}}{A Y} \)
B. \( \frac{\lambda g L^{2}}{2 A Y} \)
c. \( \frac{\lambda g L^{2}}{4 A Y} \)
D. \( \frac{\lambda g L^{2}}{6 A Y} \)


In Fig. 9.20 .0 is the centre of a circle of
radius \( 5 \mathrm{cm}, \) T is a point such that \( \mathrm{OT}= \)
\( 13 \mathrm{cm} \) and \( \mathrm{OT} \) intersects the circle at \( \mathrm{E} \). If
AB is the tangent to the circle at \( \mathrm{E} \) and
it intersects the tangents PT and QT at \( A \) and \( B, \) find the length of \( A B \)
A \( \cdot \frac{10}{3} \mathrm{cm} \)
B. \( \frac{20}{3} \mathrm{cm} \)
\( c .10 \mathrm{cm} \)
D. \( 15 \mathrm{cm} \)


Factorize the following
\( x^{2}+9 x-22 \)
A. \( (x-2)(x+11) \)
В. \( (x+2)(x+11) \)
c. \( (x-2)(x-11) \)
D. None of these


The lattice energy of \( C a O(s) \) is \( -3460 \mathrm{kJ} \)
\( \mathrm{mol}^{-1} ; \) the lattice energy of \( \boldsymbol{K}_{2} \boldsymbol{O} \) is
\( -2240 \mathrm{kJ} \mathrm{mol}^{-1} . \) This difference is
because \( K^{+}>C a^{2+}(\text { size }), K^{+}< \)
\( C a^{2+}(\text { charge }) \)
If true enter 1 , else enter 0 .


What do you mean by Aestivation? Explain types of aestivation.


Two balls \( A \) and \( B \) having masses \( m \) kg and \( 2 m \mathrm{kg}, \) moving with speeds \( 21 \mathrm{m} / \mathrm{s} \) and \( 4 \mathrm{m} / \mathrm{s} \) respectively in opposite direction, collide head on. After collision \( A \) moves with a speed of \( 1 \mathrm{m} / \mathrm{s} \) in the same direction, then incorrect
statement is :
A. The velocity of B after collision is 6 \( \mathrm{m} / \mathrm{s} \) opposite to the direction before collision
B. The coefficient of resitution is 0.2
c. The loss of kinetic energy due to collision is \( (200 \mathrm{m}) \) )
D. The impulse of the force between the two ball is \( (40 \mathrm{m}) \) Ns


Consider the following acids and bases. The fastest rate of reaction of an acid
and a base takes place between:
(5)
A. 1 and 4
B. 3 and 6
c. 2 and 5
D. 1 and 6


The \( x \) and \( y \) coordinates of a particle at
any time \( t \) are given by \( x=2 t+4 t^{2} \) and
\( \boldsymbol{y}=\mathbf{5} \boldsymbol{t}, \) where \( \mathbf{x} \) and \( \mathbf{y} \) are in meter and \( \boldsymbol{t} \)
in second. The acceleration of the
particle at \( t=5 s \) is:
A. \( 40 \mathrm{ms}^{-2} \)
B . \( 20 \mathrm{ms}^{-2} \)
\( c \cdot 8 m s^{-2} \)
D. zero


A reflecting surface is curved inwards. Now, the mirror formed is :
A. Concave
B. convex
c. Plane
D. None of these


Atoms having the same but different \( _{-1-} \) are called
isotopes.


Nucleated part of nerve cell is called as
A. Axon
B. Dendrites
c. Cyton
D. None of the above


Assertion
\( H_{2} O_{2} \) under goes dispropontionation on heating.
Reason
It gives \( H_{2} O \) and \( O_{2} \) on heating.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Figure shows a some of the
equipotential surface of the magnetic
scalar potential. The magnetic field at a
point in the region is :
A \( \cdot 2 \times 10^{-5} T \)
B \( \cdot 10^{-5} T \)
\( \mathbf{c} \cdot 10^{-4} T \)
D. \( 2 \times 10^{-4} T \)


Which one of the following statement is false for heartwood?
A. It is made up of living cells.
B. It forms central cylinder of wood.
c. It is solid and hard.
D. It contains gums and resins


\( C H_{3} \)
\( C H_{3}-C_{I}^{\prime}-C H_{2}-C H_{3} \)
The correct IUPAC name of the above
compound is:
A. tert-amyl alcohol
B. 2-methylbutan-2-ol
c. 2-methylpentan-2-ol
D. 1,1 dimethyl propan-1-o


If the latus rectum of an ellipse \( \boldsymbol{x}^{2} \tan ^{2} \varphi+\boldsymbol{y}^{2} \sec ^{2} \varphi=1 \) is \( 1 / 2 \) then \( \varphi \)
is
\( \mathbf{A} \cdot \pi / 2 \)
в. \( \pi / 6 \)
c. \( \pi / 3 \)
D. \( 5 \pi / 12 \)


Solve \( \int_{2}^{4} 2^{x} d x \)


Assertion
Only one out of every 20000 alpha particles rebound in Rutherford's experiment.
Reason
Most of the space in the atom is empty.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


Which of the following is wrong
statement?
A. Larger the \( T_{c} / P_{C} \) for a gas, larger would be excluded volume
B. Critical temperature, \( T_{C}> \) Boyle's temperature, \( T_{B} \) for any gas.
\( \mathbf{C} \cdot\left[\frac{\partial T}{\partial P}\right]_{T_{i}}=0 \) for a van der Waal's gas.
D \( \cdot\left[\frac{\partial P}{\partial V}\right]_{T_{C}}=0 \) for a van der Waal's gas.


Explain in detail the principle, construction and working of a single phase AC generator.


Zinc is used for the recovery of Ag from
the complex \( \left[A g(C N)_{2}\right]- \) while copper is not used because Zn is powerful reducing agent than \( \mathrm{Cu} \) If true enter 1,else enter 0.


The vapour pressure of a certain liquid is given by the equation:
\( \log _{10} P=3.54595-\frac{313.7}{T}+ \)
\( \mathbf{1} . \mathbf{4 0 6 5 5} \log _{\mathbf{1 0}} \boldsymbol{T} \)
where \( P \) is the vapour pressure in \( \mathrm{mm} \) and \( T=K \) elvin temperature. Determine
the molar latent heat of vaporisation at
\( \boldsymbol{T}=\mathbf{8 0} \boldsymbol{K} \)


Two system of rectangular axes have the same origin. If a plane cuts them at
distances, \( a, b, c \) and \( a_{1}, b_{1}, c_{1} \) from the
origin, then
A \( \cdot \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}=\frac{1}{a_{1}^{2}}+\frac{1}{b_{1}^{2}}+\frac{1}{c_{1}^{2}} \)
B. \( \frac{1}{a^{2}}-\frac{1}{b^{2}}+\frac{1}{c^{2}}=\frac{1}{a_{1}^{2}}-\frac{1}{b_{1}^{2}}+\frac{1}{c_{1}^{2}} \)
C \( \cdot a^{2}+b^{2}+c^{2}=a_{1}^{2}+b_{1}^{2}+c_{1}^{2} \)
D \cdot \( a^{2}-b^{2}+c^{2}=a_{1}^{2}-b_{1}^{2}+c_{1}^{2} \)


The upward force acting on an object immersed in a liquid is called \( \ldots \)..... force. It is alos called


The law of triad is applicable to a group
of :
This question has multiple correct options
A. \( C l, B r, I \)
в. \( C, N, O \)
c. \( N a, K, R b \)
D. \( H, O, N \)


A charged comb picks up bits of paper
because of :
A. magnetic force
B. gravitational force
c. contact force
D. electrostatic force


The pair of equations \( \boldsymbol{y}=\mathbf{0} \) and \( \boldsymbol{y}=-\mathbf{7} \)
have :
A. one solution
B. two solutions
c. infinitely many solutions
D. no solution


Assertion
On a vibrating bell, the bell will ring
continuously until the power is cut off.
Reason
These have to be mechanically
controlled
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


In this given reaction, glycerol + oxalic acid \( \stackrel{210^{\circ} \mathrm{C}}{\rightarrow}[\mathrm{X}] \)
Product \( [X] \) is :
A. нсоон
B. allyl alcohol
\( c \)
\( \mathrm{CHOH} \)
D.


Prove: \( 1^{2}+2^{2}+3^{2}+\ldots \ldots \ldots n^{2}>\frac{n^{3}}{3} \)


The equation of a transverse wave travelling along positive \( X \) axis with amplitude \( 0.2 m, \) velocity \( 360 m / s \) and wavelength 60 m can be written as:
A \( \cdot y=0.2 \sin \pi\left[6 t+\frac{x}{60}\right] \)
B. \( y=0.2 \sin \pi\left[6 t-\frac{x}{60}\right] \)
c. \( y=0.2 \sin 2 \pi\left[6 t-\frac{x}{60}\right] \)
D. \( y=0.2 \sin 2 \pi\left[6 t+\frac{x}{60}\right. \)


The area between the curves \( y=x^{2} \) and
\( \boldsymbol{y}=\frac{2}{1+x^{2}} \) is
A \( \cdot \pi-\frac{1}{3} \)
B . \( \pi-2 \)
c. \( \pi-\frac{2}{3} \)
D. \( \pi+\frac{2}{3} \)


In cold countries, ethylene glycol is used
in car radiators for both winter as well
as summer seasons.Which of the
following principle is involved here?
A. Depression of freezing point
B. Elevation of boiling point
c. Decrease in rate of evaporation
D. All the above


State whether given statement is True or False

The probability of electrons to be found in the conduction band of an intrinsic
semiconductor at a
finite temperature decreases
exponentially with increasing bandgap.
A. True
B. False


The prefix used to represent \( 10^{-2} \) is called
A . Mill
B. Centi
c. кilo
D. Deci


Kinetic energy depends on:
A. Position
B. Velocity
c. shape
D. colour


Find the geometric mean of \( \sqrt{82}-1 \) and \( \sqrt{82}+1 \)
\( A \cdot S \)
B.
\( c \cdot 81 \)
D. 27


A block of mass \( 30 \mathrm{kg} \) is being brought down by a chain. If the block acquires a speed of \( 40 \mathrm{cm} / \mathrm{s} \) in dropping down \( 2 \mathrm{m} \) Find the work done by the chain during
the process. \( \left(g=10 m / s^{2}\right) \)
A . - 297.6
B . -375 J
c. - -597.6
D. -674.6


With respect to oxygen maximum valency is shown by:
A. Halogen family
B. Oxygen family
c. Nitrogen family
D. Boron family


Light of two different frequencies whose
protons have energies \( 1 e V \) and \( 2.5 e V \)
respectively, successively illuminate a metallic surface whose work function is
\( 0.5 e V . \) Ratio of maximum speeds of
emitted electrons will be
A .1: 5
B. 1: 4
c. 1: 2
D. 1: 1


If error in measurement of radius of a
sphere is \( 1 \%, \) what will be the error in
measurement volume?
A . \( 1 \% \)
B. \( \frac{1}{3} \% \)
\( c .3 \% \)
D. None of these


Five coplanar forces (each of magnitude
\( 20 N) \) are acting on a body. The angle between two neighboring forces have
the same value. The resultant of these
forces is necessarily equal to
A . \( 20 N \)
B. \( 20 \sqrt{2} N \)
c. zero
D. none of these


f \( x \) \& y are in direct proportion then find the value of a
\( \boldsymbol{x} \mathbf{2} \mathbf{3} \mathbf{5} \)
\( \boldsymbol{y} \boldsymbol{4} \boldsymbol{6} \boldsymbol{a} \mathbf{1 4} \)
A . 8
B. 10
c. 15
D. 20


Calculate the ratio of pH of a solution
containing 1 mol. of \( C H_{3} C O O N a+ \)
1 mol of HCl per litre and of
other solution containing 1 mol of
\( \boldsymbol{C H}_{3} \boldsymbol{C O O N a +} \mathbf{1 m o l} \) of \( \boldsymbol{C H}_{3} \boldsymbol{C O O H} \)
per litre.


Differentiate the following functions
with respect to \( x \) :
\( \cos ^{-1}\left\{\frac{x}{\sqrt{x^{2}+a^{2}}}\right\} \)


If \( f(x) \) and \( g(x) \) be continuous
functions over the closed interval \( [\mathbf{0}, \boldsymbol{a}] \)
such that \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{a}-\boldsymbol{x}) \) and
\( \boldsymbol{g}(\boldsymbol{x})+\boldsymbol{g}(\boldsymbol{a}-\boldsymbol{x})=\mathbf{2} . \) Then
\( \int_{0}^{a} f(x) \dot{g}(x) d x \) is equal to
A \( \cdot \int_{0}^{a} f(x) d x \)
в. \( \int_{0}^{a} g(x) d x \)
\( c \cdot 2 a \)
D. none of these


If \( \frac{5 x-7 y+10}{1}=\frac{3 x+2 y+1}{8}= \)
\( \frac{11 x+4 y-10}{9}, \) then what is the \( x+y \)
equal to?
A . 1
B. 2
\( c \cdot 3 \)
D. -


The formation of multivalent at meiosis
in a diploid organism is due to.
A. Inversion
B. Deletion
c. Monosomy
D. Reciprocal translocation


Pressure depends on distance as, \( \boldsymbol{P}= \) \( \frac{\boldsymbol{\alpha}}{\boldsymbol{\beta}} \exp \left(-\frac{\boldsymbol{\alpha} \boldsymbol{z}}{\boldsymbol{k} \boldsymbol{\theta}}\right), \) where \( \boldsymbol{\alpha}, \boldsymbol{\beta} \) are
constants, z is distance, k is
Boltzmann's constant and \( \theta \) is
temperature. The dimension of \( \beta \) are.
A \( \cdot M^{0} L^{0} T^{0} \)
B. \( M^{-1} L^{-1} T^{-1} \)
\( \mathbf{c} \cdot M^{0} L^{2} T^{0} \)
D. \( M^{-1} L^{1} T^{2} \)


Assertion
If \( f(x)=0 \) has two distinct positive
real roots then number of non-
differentiable points of \( \boldsymbol{y}=|\boldsymbol{f}(-|\boldsymbol{x}|)| \) is
\( \mathbf{1} \)
Reason
Graph of \( \boldsymbol{y}=\boldsymbol{f}(|\boldsymbol{x}|) \) is symmetrical
about y-axis
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


Which of the following statement best
describe Nuclear fusion reaction?
A. two smaller nuclei are combined into a more massive
nuclei
B. the electrons are exchanged from one or more substances to produce a different substance, and the elements are the same in the products and reactants.
C. the nucleus of a large atom is split into two or more fragments.
D. the particles in the nucleus are changed, and one element is transformed into another element when
particles in the nucleus are gained or lost.
E. radiation is made


The two images of 1,2 -dichloroethane
are given. Can we call them isomers?
A. Yes
B. No
c. May be
D. Can't say


Consider the word
'PERMUTATION'
Out of all the permutations how many words start with the letter \( M ? \)
A. 10
в. \( \frac{10 !}{2 !} \)
c. 11
D. \( 10 ! \times 2 ! \)


If \( 2 i+j-k \) and \( i-4 j+\lambda k \) are
perpendicular to each other, then \( \lambda \) is
equal to:
A . -3
B. - -
\( c \cdot-1 \)
D.


The dissociation constant of \( N H_{4} O H \)
\( \operatorname{at} 25^{\circ} C \) is \( K_{b}=X \times 10^{-6}, \) if \( \Delta H^{o} \) and
\( \Delta S^{o} \) for the given changes are as follows: \( \boldsymbol{N} \boldsymbol{H}_{4}+\boldsymbol{H}^{+} \rightleftharpoons \)
\( \boldsymbol{N} \boldsymbol{H}_{4}^{+} ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( -\mathbf{5 2 . 2} \quad k J m o l^{-1} ; \quad \Delta S^{o}= \)
\( +1.67 J K^{-1} m o l^{-1} H_{2} O \rightleftharpoons H^{+}+ \)
\( \boldsymbol{O} \boldsymbol{H}^{-} ; \quad \boldsymbol{\Delta} \boldsymbol{H}^{o}= \)
\( \mathbf{5 6 . 6} \quad \boldsymbol{k J m o l}^{-1} ; \quad \boldsymbol{\Delta} \boldsymbol{S}^{o}= \)
\( -78.2 J K^{-1} \) mol \( ^{-1} . \) Value of \( X \) is \( =5 Y+2 \)
What is the value of Y?


Assertion: The value of \( \boldsymbol{K}_{\boldsymbol{w}} \) increases
with increase in temperature.

Reason: Water dissociates more as
temperature increases.
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


According to Ellingham diagram, the oxidation reaction of carbon to carbon
monoxide may be used to reduce which one of the following oxides at the lowest temperature?
A. \( A l_{2} O_{3} \)
в. \( C u_{2} O \)
с. \( M g O \)
D. \( Z n O \)


The \( p . d . V \) across and current \( I \) flowing
through an instrument in an \( a . c . \) circuit
are given by \( V=2 \cos \omega t V \) and \( I= \)
\( 2 \sin \omega t A . \) The power dissipated in the
instrument is:
\( \mathbf{A} \cdot 0 W \)
B . \( 2.5 W \)
c. \( 1.5 W \)
D. \( 9 ~ W \)


A meteor burns up on entering earth's atmosphere due to:
A. atmospheric pressure
B. heat of the earth
c. solar radiation
D. excessive friction


If true enter 1 , else enter 0 . The formula
for heavy water is \( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)


What happens when ortho phosphoric
acid is heated to \( 600^{\circ} \mathrm{C} \) ?
A. Phosphorus is formed
B. Phosphorus acid is formed
c. Hydrogen gas is released
D. Phosphorus pentaoxide is formed


Let \( p, q \) and \( r \) be any three logical
statements. Which one of the following is true?
\( \mathbf{A} \cdot \sim[p \wedge(\sim q)] \simeq(\sim p) \wedge q \)
В . \( (p \vee q) \wedge(\sim r) \equiv(\sim p) \vee(\sim q) \vee(\sim r) \)
c. \( \sim[p \vee(\sim q)] \equiv(\sim p) \wedge q \)
D . \( [p \wedge(\sim q)] \equiv(\sim p) \wedge \sim q \)
E . \( [p \wedge(\sim q)] \equiv p \wedge q \)


Which of the following reacts slower than benzene in electrophilic substitution?
A \( \cdot C_{6} H_{5} C H_{3} \)
в. \( C_{6} H_{5} N O_{2} \)
\( \mathbf{c} \cdot C_{6} H_{5} O H \)
D. \( C_{6} H_{5} N H_{2} \)


Find the value of \( a \) when the distance
between the points \( (3, a) \) and (4,1) is \( \sqrt{10} . \) The points (2,1) and (1,-2) are
equidistant from the point \( (x, y), \) Find
locus of point


Who proposed that equal volumes of
gases at the same temperature and pressure have same number of
molecules.
A. Heisenbergg
B. Avogadro
c. Dalton
D. Boyle


A convex lens of focal length \( 40 \mathrm{cm} \) is in
contact with a concave lens of focal
length \( 25 \mathrm{cm} . \) The power of he
combination, is :
A . \( +6.67 D \)
в. \( -6.5 D \)
c. \( -1.5 D \)
D. \( +6.5 D \)


Find the value of \( \sqrt{\frac{1-\sin ^{2} 30^{0}}{1-\cos ^{2} 30^{0}}} \)


Amount of saliva secreted daily in
humans is
A. 250 \( \mathrm{ml} \)
B. 500 m1
c. \( 100 \mathrm{ml} \)
D. 1000 \( \mathrm{m} \)


While studying the dependence of potential difference (V) across a
resistor on the current
(I) Passing through it, in order to determine the resistance of the resistor, a student
took 5 readings for different values of current and plotted a graph between
and I. He got a straight line graph passing through the origin. What does the straight line signify? Write the method of determining resistance of the resistor using this graph.


Which of the following electrolytic solutions has the least specific
conductance?
A. \( 0.002 \mathrm{N} \)
N \( \mathrm{N} \) N \( . .0000 \)
B. \( 0.1 N \)
c. \( 0.2 N \)
D. \( 2 N \)


Express as kilometre (km) using decimals:
\( 5 m \)


When the temperature of water rises
the rate of evaporation decreases. State whether true or false.
A. True
B. False


Give \( I U P A C \) name of following
compound.
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}=\boldsymbol{C H}-\boldsymbol{C H}=\boldsymbol{C H}- \)
\( \boldsymbol{C} \equiv \boldsymbol{C}-\boldsymbol{C} \boldsymbol{H}_{3} \)


n given figure, \( \angle C A B=90^{\circ} \) and
\( A D \perp B C . \) If \( A C=75 \mathrm{cm} . A B=1 \mathrm{m} \) and
\( B D=1.25 \mathrm{m}, \) find \( A D \)


A point charge is brought in an electric field. The electric field at a nearby point This question has multiple correct options
A. will increase if the charge is positive
B. will decrease if the charge is negative
c. may increase if the charge is positive
D. may decrease if the charge is negative


What are the objectives of measure of
dispersion?
A. Helpful in use of further statistical analysis as in regression, correlation etc.
B. Reliability of measure of central tendency
C. Control of variability
D. All of the above


When an equiconvex lens \( \left(\mu_{\text {lens}}=\mathbf{1 . 5}\right) \)
is placed over a plane mirror as shown,
then object needle and its image coincide at \( 15 \mathrm{cm} . \) When a liquid of
refractive index \( \mu \) is filled in the gap
between mirror and lens, the object
needle and its image coincide at \( 40 \mathrm{cm} \)
Find the refractive index \( \mu \) of the liquid.
\( A \cdot 8 \)
5
B. 5 8
\( c \cdot \frac{13}{8} \)
D. \( \frac{5}{13} \)
E \( \cdot \frac{13}{5} \)


High energy neutrons are used in a nuclear reactor to initiate the fission
reaction.
A. True
B. False


Find intervals in which the function
\( \operatorname{given} \operatorname{by} f(x)=\sin 3 x, x \in\left[0, \frac{\pi}{2}\right] \)
is increasing function


In general, capacity
A. conductors
B. Insulators
c. cant say
D. None of these


A cylinder has a diameter of \( 20 \mathrm{cm} \). The
area of curved surface is \( 1000 \mathrm{cm}^{2} \)
FindAthe height of the cylinder correct to one decimal place.The volume of the cylinder correct to one decimal place. (Take \( \boldsymbol{\pi}=\mathbf{3 . 1 4}) \)


What sensation do we feel due to heat
energy?
A. Sensation of hotness and coldness
B. Sensation of touch
c. Sensation of darkness
D. sensation of light


When \( L i N O_{3} \) is heated, it gives oxide,
\( \boldsymbol{L} \boldsymbol{i}_{2} \boldsymbol{O}, \) whereas other alkali metal
nitrates decompose to give corresponding:
A . nitrite
B. peroxide
c. both nitrite and oxide
D. none of these


A mass is at the center of a square, with
four masses at the corners as
shown. Rank the choices according to
the magnitude of the gravitational force
on the center mass.
\( \mathbf{A} \cdot F_{A}=F_{B}<F_{C}=F_{D} \)
B . \( F_{A}>F_{B}<F_{D}<F_{C} \)
\( \mathbf{c} \cdot F_{A}=F_{B}>F_{C}=F_{D} \)
D. None


\( \triangle R H P \sim \triangle N E D \) in \( \triangle N E D, N E= \)
\( 7 \mathrm{cm}, \angle E=30^{\circ}, \angle N=20^{\circ} \) and \( \frac{H P}{E D}=\frac{4}{5} \)
Construct \( \triangle R H P \)


Choose the correct answer from the
alternatives given A tree is broken by the wind. If the top of the tree struck the ground at an angle of
\( 30^{\circ} \) and at a distance of \( 30 \mathrm{m} \) from the
root, then the height of the tree is
B. \( 20 \sqrt{3} m \)
\( \mathbf{c} \cdot 25 \sqrt{3} m \)
D. \( 30 \sqrt{3} m \)


\( \frac{4}{5} \div \frac{7}{15} \) of \( \frac{8}{9} \)


The ray of light bending away from normal is called \( _{\text {一一一一一. }} \) Fill in the
blanks.
A. Refracted ray
B. Incident ray
c. Emergent ray
D. None of the above


If \( (1,1, a) \) is the centroid of the triangle formed by the points \( (1,2,-3),(\mathrm{b}, 0,1) \) and (-1,1,-4) then \( a-b= \)
A . -5
B. -7
\( c .5 \)
\( D \)


A ball of mass \( 400 g m \) is dropped from a height of 5 m. A boy on the ground hits the ball vertically upwards with a bat with an average force of \( 100 N \) so that it
attains a vertical height of 20 m. Find
the time for which the ball remains in
contact with the bat.
A. 0.12
B. 0.24
\( c \cdot 0.36 \)
D. 0.48


Range of \( \boldsymbol{f}(\boldsymbol{x}) \) is \( ? \)
A. \( R \)
B . \( R-\{0\} \)
\( c \cdot R^{+} \)
D. \( (0, e) \)


If \( f(x)=x^{2}-6 x+8 \) and there exists
a point \( c \) in the interval [2,4] such that
\( \boldsymbol{f}^{\prime}(\boldsymbol{c})=\mathbf{0}, \) then what is the value of \( \boldsymbol{c} ? \)
A . 2.5
B. 2.8
\( c \cdot 3 \)
D. 3.5


The atmospheric pressure at sea level is:
\( A \cdot 1 \) atm
B. 10 atm
c. \( 100 \mathrm{atm} \)
D. 1 pascal


Explain Halogenation reaction with
conversion of \( \boldsymbol{C H}_{4} \) to \( \boldsymbol{C C l}_{4} \) in alkanes.


is measured in moles per
litre.
A. Molality
B. Molar concentration
c. Number of moles
D. None of these


Two balls of equal masses are projected upward simultaneously, one from the ground with speed of \( 50 \mathrm{m} / \mathrm{s} \) and other from a \( 40 \mathrm{m} \) high tower with initial speed of \( 30 \mathrm{m} / \mathrm{s} \). Find the maximum height attained by their center of mass.


On every Friday, a veggie store owner offers a discount of \( 30 \% \) on potatoes,
which he sell for \( \$ 0.90 \) per pound on other days. The store also sells carrots for \( \$ 3.50 \) per pound. If a customer buys
2 pound of carrots and \( p \) pounds of
potatoes then the total cost, \( c \), customer
has to pay is
A \( c=0.63 p+7 \)
7
B. \( c=0.9 p+7 \)
c. \( c=0.3 p+3.5 \)
D. \( c=0.9 p+3.5 \)


For what value of \( x \) is \( \frac{3 x+7}{5}=11 \) true?
A . -19
B. -16
c. 16
D. 19


\( D- \) Glucose and \( D- \) fructose both form
the same osazone. Which statements
are correct about the above reaction?
This question has multiple correct options
A. Glucose and fructose are epimers
B. Glucose and fructose are anomers
c. The configurations of the \( O H \) group at \( C-3 \) and \( C \) -
4 in glucose and fructose are same
D. The configurations of the \( O H \) group at \( C-4 \) and \( C \) 5 in glucose and fructose are same


Fill in the blanks:
Full form of IUPAC system is


If \( 2 a=b, \) the pair of equations \( a x+ \)
\( b y=2 a^{2}-3 b^{2}, x+2 y=2 a-6 b \)
possess
A. no solution
B. only one solutions
c. only two solutions
D. an infinite number of solutions


\( \ln \) an \( A C \) generator, the ends of the coil are connected to
A. two slip rings
B. the split ring commutator
c. the external circuit directly
D. None of these


A wire stretches by a certain amount under a load. If the load and radius both
are increased to four times. The stretch
caused in the wire is then
\( \mathbf{A} \cdot l \)
в. \( \frac{l}{2} \)
\( c \cdot \frac{l}{3} \)
D.


Energy associated with an electric field
is analogous to whereas the
energy associated with the magnetic field is analogous to
A. kinetic energy, potential energy
B. potential energy, potential energy
c. potential energy, kinetic energy
D. kinetic energy, kinetic energy


The electrolysis of pure alumina is not feasible because:
A. it is bad conductor of electricity and its fusion temperature is highh
B. it is volatile in nature
c. it is decomposed when fused
D. it is amphoteric


Write four differences between rate of
reaction and constant.


Analyse the diagram of solar spectrum and write answer.
a. Which radiation has a wavelength greater than visible light in this
spectrum?
b. Which color has the highest
frequency in the visible part of the solar spectrum?
c. Write one merit and demerit of
infrared and ultraviolet radiations.


Select the wrong statement.
A. Proteins are heteropolymers made of amino acids.
B. Ribozymes are nucleic acids with catalytic power.
C. Nucleic acids serve as genetic material.
D. Proteins, nucleic acids are macromolecules found in the living system.
E. Collagen is the most abundant protein in the whole of the biosphere and RuBisCo is the most abundant proteins in animal world.


Briefly describe the valence bond theory
of covalent bond formation by taking an example of hydrogen. How can you interpret energy changes taking place in the formation of dihydrogen


Find the smallest number by which 2808 must be multiplied so that the product is a perfect cube.


Express the angles \( \frac{5 \pi^{c}}{12}, \frac{-7 \pi^{c}}{12} \) in degrees.


What will be the uncertainty in velocity
of an electron when the uncertainty in its position is 1000 , i?
A. \( 5.79 \times 10^{2} \mathrm{ms}^{-1} \)
В. \( 5.79 \times 10^{8} \mathrm{ms}^{-1} \)
c. \( 5.79 \times 10^{4} m s^{-1} \)
D. \( 5.79 \times 10^{-10} \mathrm{ms}^{-1} \)


Assertion
Reduction of \( Z n O \) with carbon is done
at \( 1100^{0} C \)
Reason
\( \triangle G^{0} \) is negative at this temperature
thus, process is spontaneous.
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 and Reason is correct


\( \boldsymbol{p} \boldsymbol{K}_{a} \) values of two acids \( \boldsymbol{A} \) and \( \boldsymbol{B} \) are \( \boldsymbol{4} \)
and \( 5 . \) The strengths of these two acids are related as:
A. acid A is 10 times stronger than acid B
B. strength of acid A : strength of acid \( B=4: 5 \)
c. strength of two acids cannot be compared
D. acid B is 10 times stronger than acid A


Which of the following are found as
sulphide ores?
A. \( A l, H g, P b, F \)
в. \( F e, Z n, P b \)
c. \( H g, P b, N a \)
D. \( F, C a, C u, M g \)


If the matrices has 13 elements , then
the possible dimension (order) it can have are
A . \( 1 \times 13 \) or \( 13 \times 1 \)
B. \( 1 \times 26 \) or \( 26 \times 1 \)
c. \( 2 \times 13 \) or \( 13 \times 2 \)
D. None of these


Dependent Population creates burden
on
A. resources of each family
B. public utility services
c. both (a) and (b)
D. neither (a) nor (b)


What are monocarpic and polycarpic plants?


In Fresnel's biprism expt., a mica sheet of refractive index 1.5 and thickness \( 6 x \)
\( 10^{-6} \mathrm{m} \) is placed in the path of one of interfering beams as a result of which the central fringe gets shifted through 5 fringe widths. The wavelength of light used is
A \( \cdot 6000 \stackrel{\circ}{A} \)
в. \( 8000 \stackrel{\circ}{A} \)
c. 4000 ,
D. \( 2000 \stackrel{\circ}{A} \)


A sphere is rolling up on a rough incline plane. If suddenly the friction becomes zero, the retardation of the COM of the
sphere will
A. Decrease
B. Increase
c. Remain as it is
D. None of the above


If the \( S D \) of a set of observation is 8 and
each observation is divided by \( -2, \) then the SD of the new set of observations will be.
A . -4
B. -8
\( c \cdot 8 \)
\( D \)


If the point \( P(2,1) \) lies on the segment joining Points \( A(4,2) \) and \( B(8,4) \) then
\( ^{\mathbf{A}} \cdot A P=\frac{1}{3} A B \)
B. AB = PB
\( c \cdot p B=\frac{1}{3} A B \)
D. \( A P=\frac{1}{2} A B \)


When a liquid and its vapours are at equilibrium and the pressure is suddenly decreased, cooling occurs. If true enter 1 , if false enter 0 .


The drug plant Aconitum napellus belongs to the family
A. Ranunculaceae
B. Apocynaceae
c. Papaveraceae
D. Solanaceae


The ratio of mass of proton to electron is
about:
A \( .1 .8 \times 10^{-3} \)
B . \( 1.8 \times 10^{3} \)
\( c \cdot 1 \)
D.


1 ampere current is equivalent to
\( \mathbf{A} \cdot 6.25 \times 10^{18} \) electrons \( s^{-1} \)
B. \( 2.25 \times 10^{18} \) electrons \( s^{-1} \)
C \( .6 .25 \times 10^{14} \) electrons \( s^{-1} \)
D. \( 2.25 \times 10^{14} \) electrons \( s^{-1} \)


14 apples cost Rs. 140 The cost of 1 apple
is
A. Rs. 10
B. Rs. 8
c. Rs. 4
D. Rs. 14


The electronegativity of Caesium is 0.7 and that of Fluorine is \( 4.0 . \) The bond
formed between the two is
A. covalent bond.
B. electrovalent bond
c. coordinate bond.
D. metallic bond.


Find the value of \( k \) for which the
equation \( x^{2}-6 x+k=0 \) has distinct
roots.
\( \mathbf{A} \cdot k>9 \)
B. \( k=6,7 \) only
c. \( k<9 \)
\( \mathbf{D} \cdot k=9 \)


One litre solution contains \( 1 M \) HOCl
\( \left[\boldsymbol{K}_{a}=\mathbf{1 0}^{-8}\right] \) and \( 1 M \) NaOH.What is
the \( p H \) of the solution?
A. 8
B. 1
\( c \cdot 5 \)
D. 2


The solution of \( \frac{d y}{d x}+2 x=e^{3 x} \) is:
A \( \cdot y=3 e^{3 x}-x^{2}+c \)
B. \( y=\frac{e^{3 x}}{3}-x^{2}+c \)
C . \( y=e^{3 x}-x^{2 x}+c \)
D. \( y=e^{3 x}-x^{2}+c \)


Sugarcane crop needs
A. Hot climate
B. Cool climate
c. Humid climate
D. Moderate climate


How is oxygen and carbon dioxide
transported in human body?


The number of common tangents to the
\( \operatorname{circles} x^{2}+y^{2}=4 \) and \( x^{2}+y^{2}-4 x+ \)
\( 2 y-4=0 \) is
A . 1
B . 2
\( c .3 \)
D. 4


A die is thrown. Write the sample space.
If \( P \) is the event of getting an odd number, then write the event \( P \) using
set notation.


How toroid is different from solenoid.


Assertion
Nitrous oxide is also known as laughing
gas.
Reason
It is a colourless gas having a faint
sweet odour.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A bullet of mass \( 20 \mathrm{g} \) is fired from a rifle with a velocity of \( 800 m s^{-1} . \) After passing through a mud wall \( 100 \mathrm{cm} \)
thick, velocity drops to \( 100 \mathrm{ms}^{-1} \). What
is the average resistance of the wall? (Neglect friction due to air and work of
gravity)


Using elementary transformations, find the inverse of matrix, \( \boldsymbol{A}=\left[\begin{array}{ll}\mathbf{1} & \mathbf{3} \\ \mathbf{2} & \mathbf{7}\end{array}\right] \)


Rate of respiration is directly affected
by
A \( \cdot C O_{2} \) concentration
B. \( O_{2} \) in trachea
c. concentration of \( O_{2} \)
D. Diaphragm expansion


The reduced product formed when
chlorine reacts with \( \boldsymbol{H}_{2} \boldsymbol{S} \) :
A . \( N a C l \)
в. \( C u \)
c. \( \operatorname{Fe}\left(O H_{3}\right) \)
D. \( H C l \)


Watt is equal to
\( \mathbf{A} \cdot A \Omega \)
B \( \cdot A^{2} \Omega \)
\( \mathbf{C} \cdot A \Omega^{2} \)
D. \( A \Omega^{2} s^{-1} \)


The units of conductivity of the solution
are:
\( \mathbf{A} \cdot o h m^{-1} \)
B. ohms
\( \mathbf{c} \cdot \operatorname{ohm}^{-1} c m^{-1} \)
D. \( o h m^{-1} e q^{-1} \)


In laboratory burners, we use
A. Producer gas
B. oil gas
c. Gobar Gas
D. None of the above


J.J. Thomson's atomic model could not
justify the shielding of electrons from positive charges.
A. True
B. False


State True or False.
A mixture of ideal gases is cooled up to
liquid helium temperature \( (4.2 K) \) to
form an ideal solution.
A. True
B. False


Give term that describes compounds
(a) and (b).
A. Enantiomers
B. Chiral molecule
c. Diastereomers
D. Same compounds


Water is largely absorbed in
A. Stomach
B. Oesophagus
c. Small intestine
D. Colon (large intestine)


The enthalpy change for a reaction does
not depend upon:
A. use of different reactants for the same product
B. the nature of intermediate reaction steps
C. the differences in initial or final temperatures of involved substances
D. the physical states of reactants and products


\( f\left(x^{2}+y^{2}\right)^{2}=x y, \) find \( \frac{d y}{d x} \)


A homogeneous rod \( X Y \) of length \( L \) and
mass \( M \) is pivoted at the centre \( C \)
such that it can rotate freely in the vertical plane. Initially, the rod is in the horizontal position. A blob of wax of
same mass \( M \) as that of the rod falls
vertically with the speed \( V \) and sticks
to the rod midway between points \( C \)
and \( Y . \) If the rod rotates with angular
speed \( \omega \) what will be angular speed in
terms of \( \boldsymbol{V} \) and \( \boldsymbol{L} \) ?


What kind pyramid is represented by
the given figure?
A. pyramid of numbers in a forest ecosystem
B. pyramid of numbers in a parasitic food chain
c. pyramid of biomass in a forest ecosystem
D. It is a wrong pyramid


state-wise teacher student ratio in
higher secondary schools of India. Find
the mode and mean of this data.
nterpret the two measures.
\( A \)
Mode\( =31.7, \) Mean\( =28.2 \)
B. Mode\( =33.6, \) Mean\( =25.3 \)
c. Mode\( =35.7, \) Mean\( =26.3 \)
Mean\( =29 \)
D. Mode\( =30.6, \)


The stoichiometry coefficient in rate of reaction is same for average rate as well as instantaneous rate of reaction
A. True
B. False


Assertion
Oxides and carbonates of carbon
considered to be inorganic compounds.
Reason
Inorganic carbon is carbon extracted
from ores and minerals, as opposed to organic carbon found in nature through plants and living things.
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


How much faster than its normal rate
should the earth rotate about its axis so
that the weight of the body at the equator becomes zero? (Radius of the
earth \( =6.4 \times 10^{6} m \) and \( g=9.8 m / s^{2} \)
A. Nearly 17 times
B. Nearly 12 times
c. Nearly 10 times
D. Nearly 14 times


A \( 10 \mathrm{N} \) force applied on a body produces in it an acceleration of \( 2 m s^{-2}, \) then the mass of the body is
\( A \cdot 10 \mathrm{kg} \)
B. 2 kg
\( c .5 \mathrm{kg} \)
\( D \cdot 6 \mathrm{kg} \)


Anhydrous borax is:
\( \mathbf{A} \cdot N a_{2} B_{4} O_{7} \)
B. \( N a_{2} B_{4} O_{7} .5 H_{2} O \)
\( \mathbf{c} \cdot N a_{2} B_{4} O_{7} \cdot 10 H_{2} O \)
D. \( N a_{2} B_{4} O_{7} .8 H_{2} O \)


Cuticle is made up of
A. Glycerol and hydrocarbon polymers impregnated with wax
B. Lipid and hydrocarbon polymers impregnated with wax
C. Fatty acid and hydrocarbon polymers impregnated with wax
D. None of the above


The value of the following polynomial at the indicate value of variables:
\( \boldsymbol{q}(\boldsymbol{y})=\boldsymbol{3} \boldsymbol{y}^{2}-\boldsymbol{4} \boldsymbol{y}+\sqrt{11} \) at \( \boldsymbol{y}=\boldsymbol{2} \) is
equal to \( 4+\sqrt{11} \)
A. True
B. False


A copper ball of density \( p_{c} \) and diameter
d is immersed in oil of density \( p_{o} . \) What
charge should be present on the ball, so that it could be suspended in the oil, if a homogeneous electric field E is applied vertically upward?
\( ^{\mathrm{A}} \cdot_{\mathrm{Q}}=\frac{\pi d^{2}\left(p_{c}-p_{0}\right) g}{6 E} \)
в. \( \quad Q=\frac{\pi d^{3}\left(p_{c}-p_{0}\right) g}{6 E} \)
c. \( _{Q}=\frac{\pi d^{3}\left(p_{c}-p_{0}\right) g}{E} \)
D. \( _{Q}=\frac{\pi d^{2}\left(p_{c}-p_{0}\right) g}{2 E} \)


An aeroplane is moving towards north horizontally with a speed of \( 200 \mathrm{m} / \mathrm{s} \) at a
place where the vertical component of earths magnetic field is \( 0.5 \times 10^{-4} \) tesla.
Then the induced e.m.f. set up between the tips of the wings of the plane if they are \( 10 m \) apart is:
A. 0.1 volt
B. 0.01 volt
c. 10 volt
D. 1 volt


The mean free path of the molecule of a
certain gas at \( 300 \mathrm{K} \) is \( 2.6 \times 10^{-5} \mathrm{m} \)
The collision diameter of the molecule
is \( 0.26 \mathrm{nm} . \) Calculate
(a) pressure of the gas, and
(b) number of molecules per unit
volume of the gas.
B. (a) \( 1.281 \times 10^{22} \mathrm{m}^{-3} \) (b) \( 5.306 \times 10^{3} \mathrm{Pa} \)
D. (a) 2.56 \( \times 10^{23} \mathrm{m}^{-3} \) (b) \( 10.612 \times 10^{2} \mathrm{Pa} \)


Force between two identical bar magnets
whose centres are rmeters apart is \( 4.8 N \)
when their axis are in the same line. If the
separation is increased to \( 2 r \) meters, the force between them is reduced to:
A. 2.4
B. 1.2 N
c. \( 0.6 \mathrm{N} \)
D. 0.3 N


The contrapositive of "If \( \boldsymbol{x} \in \boldsymbol{A} \cup \boldsymbol{B} \)
then \( \boldsymbol{x} \in \boldsymbol{A} \) or \( \boldsymbol{x} \in \boldsymbol{B}^{\prime \prime}, \) is
A. If \( x \in A \) or \( x \in B \), then \( x \in A \cup B \).
B. If \( x \notin A \cup B \), then \( x \notin A \) and \( x \notin B \).
c. If \( x \notin A \) and \( x \notin B, \) then \( x \notin A \cup B \)
D. If \( x \notin A \) and \( x \notin B, \) then \( x \in A \cup B \).


Figure shows a square loop of side \( 1 m \)
and resistance 1\Omega. The magnetic field on left side of line PQ has a magnitude
\( B=1.0 T . \) The work done in pulling the
loop out of the field uniformly in \( 1 s \) is
4. 1
В. \( 10 J \)
\begin{tabular}{l}
\( .0 .1 .] \) \\
\hline
\end{tabular}
0.100


Why the angle of incidence must not be
less then \( 30^{\circ} \) while calculating angle of minimum deviation?


A sector cut from a uniform disk of
radius \( 12 \mathrm{cm} \) and a uniform rod of the
same mass bent into shape of an arc
arranged facing each other as shown in
the figure. If center of mass of the
combination is at the origin, what is the
radius of the arc?
\( \mathbf{A} \cdot 8 \mathrm{cm} \)
\( \mathbf{B} \cdot 9 \mathrm{cm} \)
\( c .12 \mathrm{cm} \)
D. \( 18 \mathrm{cm} \)


The value of \( z \) is
A. 5
B. 4
\( c .3 \)
D. 2


Write Kirchhoff's first rule (law of
junction). Drawing a circuit diagram of Wheatstone bridge, derive condition for zero deflection in the bridge.


For \( \boldsymbol{a}<\mathbf{0}, \) arg \( (\boldsymbol{i} \boldsymbol{a})= \)
A \( \cdot \frac{\pi}{2} \)
B. \( -\frac{\pi}{2} \)
\( c . \pi \)
D. - \( \pi \)


toppr
Q Type your question.
lower half. The electric field lines around
the cylinder will look like figure given in
(figures are schematic and not drawn to scale)
\( A \)
B.
\( c \)
\( D \)


DCT lies close to:
A. PCT of the same nephron
B. PCT of a different nephron
C. Glomerulus of the same nephron
D. Glomerulus of a different nephron


Determine the compound amount and
compound interest on Rs. 1,000 at \( 6 \% \)
compounded semi-annually for 6 years.
Given that \( (1+i)^{n}=1.42576 \) for \( i= \)
\( 3 \% \) and \( n=12 \)
A . 16,000
B. 630.50
c. 425.76
D. 1,640


The following compound can exhibit:
A. geometrical isomerism
B. geometrical and optical isomerism
c. optical isomerism
D. tautomerism


Solve \( 0.2 x+0.3 y=1.3 \)
\( \mathbf{0 . 4 x}+\mathbf{0 . 5 y}=\mathbf{2 . 3} \)
A. \( x=-2 \) and \( y=3 \)
B. \( x=3 \) and \( y=3 \)
c. \( x=2 \) and \( y=3 \)
D. None of these


Two changes are stated below:
(i.) A piece of magnesium gives of bright flames when burned.
(ii). A piece of iron glows red when heated strongly. Which of these is a physical change?
A. Only i
c. Both i and ii
D. Neither i nor ii


The focal length of convex mirror is 20 \( \mathrm{cm}, \) its radius of curvature will be:
A . \( 10 \mathrm{cm} \)
B. \( 20 \mathrm{cm} \)
\( c .30 \mathrm{cm} \)
D. \( 40 \mathrm{cm} \)


X0 type of sex determination and XY type of sex determination are the
examples of
A. Male heterogamete
B. Female heterogamete
c. Male homogametic
D. Both B and C


When the two tuning forks of nearly same frequency are vibrated to produce beats, then the velocity of propagation of beats will be
A. less than that of sound
B. depend upon the relative frequency
c. more than that of sound
D. equal to that of sound


Assertion
The amount of BOD in the waters is a
measure of the amount of organic material in the water.
Reason
Clear water has BOD less than 5 ppm
whereas highly polluted water have BOD value of 17 ppm or more.
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


Solve the inequality and represent the
solution graphically on number line. \( \mathbf{2}(\boldsymbol{x}-\mathbf{1})<\boldsymbol{x}+\mathbf{5}, \boldsymbol{3}(\boldsymbol{x}+\mathbf{2})>\mathbf{2}-\boldsymbol{x} \)


Which of the following is false.
A. Uniform acceleration means that the acceleration doesn't change over time.
B. Variable acceleration may change over time.
c. Both \( A \& B \)
D. None of the above


An electron, practically at rest, is initially accelerated through a potential difference of 100 volts. It then has a de
Broglie wavelength \( =\lambda_{1} A . \) It then get
retarded through 19 volts and then has
a wavelength \( \lambda_{2} \). A further retardation
through 32 volts changes the wavelength to \( \lambda_{3} A, \) what is \( \frac{\lambda_{3}-\lambda_{1}}{\lambda_{1}} ? \)


For how long (approximate value) does the image remain on the retina?
A . \( 1 s \)
B. \( 0.5 s \)
c. \( 0.12 s \)
D. \( 0.06 s \)


You normally note the speed limits mentioned on highways (on straight roads without turns). Why?
A. The road law forces to write the speed limitt
B. Its is just a fashion
c. on horizontal roads, speed limit has no meaning
D. While overtaking one encounters sharp turns


Adding all the terms in a sequence is
called
A. sequence
B. series
c. term
D. constant


The volume of the reaction vessel
containing an equilibrium mixture in the reaction is increased, when
equilibrium is re-established:
\( \boldsymbol{S} \boldsymbol{O}_{2} \boldsymbol{C l}_{2}(\boldsymbol{g}) \leftrightharpoons \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}) \)
A. the amount of \( S O_{2} \) will have decreased
B. the amount of \( S O_{2} C l_{2} \) will have increased
c. the amount of \( C l_{2} \) will have increased
D. the amount of \( C l_{2} \) will have remained unchanged


Taking the wavelength of first Balmer line in hydrogen spectrum \( (n=3 \) to \( \boldsymbol{n}=2) \) as \( 660 n m, \) the wavelength of the
2nd Balmer line \( (n=4 \text { to } n=2) \) will be:
\( \mathbf{A} \cdot 889.2 n m \)
B. \( 642.7 n m \)
\( \mathbf{c} .488 .9 n m \)
D. \( 388.9 n m \)


Solve the following inequalities graphically in two-dimensional plane:
\( 2 x-3 y>6 \)


\( 14 \mathrm{g} \) of nitrogen contains \( 3.01 \times 10^{23} \) nitrogen molecules. If true then enter 1 , if false enter 0 .


A parallel plate capacitors is formed by stacking n equally spaced plates connected alternately. If capacitance between two adjacent plates is \( C \) then the resultant capacitance is :
A. \( (n-1) C \)
в. \( (n+1) C \)
\( c . c \)
D. \( n C \)


What material you use for making wicks for oil lamps?


The molecular shapes of \( S F_{4}, C F_{4} \) and
\( \boldsymbol{X} \boldsymbol{e} \boldsymbol{F}_{4} \)
A. differ with 1,0 and 2 lone pairs of electrons on the central atom, respectively.
B. differ with 0,1 and 2 lone pairs of electrons on the central atom, respectively.
c. are same with 1,1 and 1 lone pair of electrons on the central atom, respectively.
D. are same with 2,0 and 1 lone pair of electrons on the central atom, respectively.


The bond dissociation energies of the following \( \boldsymbol{C H}_{3}-\boldsymbol{H} \boldsymbol{C H}_{3} \boldsymbol{C H}_{2}-\boldsymbol{H} ; \boldsymbol{C H}_{2}=\boldsymbol{C H} \)
vary in the order of:
\( A \cdot|>||>|||>\mid V \)
B. IV>|||> || > |
c. \( |V>|>||>|| \mid \)


The order of differential equation \( \left(\frac{d y}{d x}\right)^{3}+\left(\frac{d y}{d x}\right)^{2}+y^{4}=0 \) are
\( \mathbf{A} \cdot \mathbf{4} \)
B. 3
\( c \cdot 1 \)
\( D \)


State True or False.
Mass of reactants is always equal to the mass of the products. (Don't consider nuclear reaction)
A. True
B. False


Which of the following are the properties of solid?
A. They have a definite shape
B. They have distinct boundaries
c. They have fixed volume
D. All of the above


In a step up transformer, primary and secondary currents are \( 500 A \) and
\( \mathbf{1 0 0} A \). The ratio of the number of turns
in the respective coil is
A . 1: 5
B. 5: 1
c. 25: 1
D. 1: 25


Your immune system helps to protect you against viruses and bacteria that
can cause sickness. Which cells are
part of the immune system?
A. White blood cells
B. Red blood cells
c. Nerve cells
D. None of the above


Which of the following reagents convert the acid chloride into aldehyde? \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C O}-\boldsymbol{C l} \rightarrow \)
\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H O} \)
A. \( H_{2}, P d, B a S O_{4} \)
B . \( \left(C H_{3}-C H_{2}-C H_{2}-C H_{2}\right)_{3} \) SnH
c. LiAlH\( _{4} \)
D. Nah


Jahnvi is walking at \( 1.63 m / s \). If she
weighs \( 583 N, \) what is the magnitude of
her momentum?
A. \( 951 \mathrm{kg} \mathrm{m} / \mathrm{s} 951 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
в. \( 68.8 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. 137 kg \( m / s \)
D. 672 kg \( m / s \)


What is the IUPAC name of
\( \left[N i(C N)_{4}\right]^{2-} ? \)
A. Tetracyanonickelate (II)
B. Tetracyanonickel (II)
C. Tetracyanonickelate (I)
D. None of these


Diastema is associated with
A. Presence of certain teeth
B. Absence of certain teeth
c. Absence of tongue
D. Presence of tongue


Which of the following carbohydrates is
the sweetest sugar?
A. Glucose
B. Fructose
c. Cellulose
D. Maltose


The extra stability of lyophilic colloids is due to?
A. charge on the particles
B. a protective film of the dispersion medium on the particles
c. the smallest size of the particle
D. the largest size of the particles


How is the unit bar related to the S.I.
unit pascal?
A . \( 1 b a r=10^{5} \) pascal
B. 1pascal = 10 \( ^{5} \) bar
c. \( 1 b a r=10 \) pascal
D. \( 1 b a r=1 \) pascal


Can a triangle have two obtuse angles?
If True enter 1 , else enter 0


Which of the following metal's oxide can
be reduced by Fe as reducing agent at
temperature \( \boldsymbol{T}_{\mathbf{1}} \) ?
\( A \cdot P b \)
B. \( \mathrm{ca} \)
c. \( \mathrm{Mg} \)
D. None of these


A charge of magnitude \( Q \) is placed at the origin. A second charge of magnitude \( 4 Q \) is placed at the position \( x=d \) along the \( x \) -axis.

Other than infinitely far away, at what position on the \( x \) -axis will a positive test charge experience a zero net force?
A \( . x=-d \)
B. \( x=-\frac{d}{2} \)
c. \( x=\frac{d}{3} \)
D. \( x=\frac{3 d}{2} \)
E. At no position other than infinitely far away will the positive test charge experience zero net force


The number \( s p^{2}-s p^{2} \) sigma bonds in
the compound given below is:
\( A \)
B. 3
\( c \cdot 4 \)
\( D \)


Which of the following is the correct
electron dot structure of \( N_{2} O \)
molecule?
\( A \)
\( \therefore \mathbf{N}=\mathbf{N}=\mathbf{0}^{*} \)
в. \( \therefore \ddot{N}-N=\ddot{O}: \)
\( c \)
\( \mathbf{x}=\mathbf{N}=\ddot{\mathbf{O}} \)
D. \( \therefore \mathbf{N} \equiv \mathbf{N}=\ddot{\mathbf{O}} \)


Find the vector equation of the line through \( \boldsymbol{A}(\boldsymbol{3}, \boldsymbol{4},-\boldsymbol{7}) \) and \( \boldsymbol{B}(\boldsymbol{6},-1,1) \)
Also find the cartesian form.


The sum of the focal distances of a
point on the ellipse \( \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 \) is:
A . 4 units
B. 6 units
c. 8 units
D. 10 units


Radial symmetry occurs in
A. Fishes
B. Molluscs
C. Starfishes
D. Few species of sponges
\( E . \) Both \( C \) and \( D \)


Decarboxylation occurs during
A. Glycolysis.
B. ETS
c. Krebs cycle.
D. All the above.


Given: \( \vec{a} \) and \( \vec{b} \) are unit vector, and \( \theta \) be
the angle between them. Then \( \frac{1-\vec{a} \cdot \vec{b}}{1+\vec{a} \cdot \vec{b}}= \)
\( A \cdot \sin ^{2} \frac{\theta}{2} \)
B. \( \cos ^{2} \frac{\theta}{2} \)
\( c \cdot \tan ^{2} \frac{\theta}{2} \)
\( D \cdot \cot ^{2} \frac{\theta}{2} \)


An oil drop falls through air with a
terminal velocity of \( 5 \times 10^{-4} m / s . \) The
radius of the drop will be? Neglect density of air as compared to that of oil.
(Viscosity of air \( =\frac{18 \times 10^{-5}}{5} N-s / m^{2} \)
\( g=10 m / s^{2}, \) density of oil \( =900 \mathrm{kg} / m^{3} \)
A \( .2 .5 \times 10^{-6} m \)
В . \( 2 \times 10^{-6} m \)
c. \( 3 \times 10^{-6} m \)
D. \( 4 \times 10^{-6} \mathrm{m} \)


Ordered pairs \( (x, y) \) and (3,6) are equal
if \( \boldsymbol{x}=\mathbf{3} \) and \( \boldsymbol{y}=? \)
\( A \cdot 3 \)
B. 6
c. -6
D. - 3


Estuaries are
A. Freshwater wetlands
B. Salt water wetlands
C . Least productive ecosystem
D. None of the above


The point equidistant from the point \( \boldsymbol{O}(\mathbf{0}, \mathbf{0}, \mathbf{0}), \boldsymbol{A}(\boldsymbol{a}, \mathbf{0}, \mathbf{0}), \boldsymbol{B}(\mathbf{0}, \boldsymbol{b}, \mathbf{0}) \) and
\( C(0,0, c) \) has the coordinates
\( \mathbf{A} \cdot(a, b, c) \)
B. \( (a / 2, b / 2, c / 2) \)
c. \( (a / 3, b / 3, c / 3) \)
D. \( (a / 4, b / 4, c / 4) \)


An aqueous solution of methanol in
water has vapour pressure:
A. less than that of water
B. equal to that of water
c. more than that of water
D. equal to that of methano


The electronic configuration of Gd (atomic number \( =\mathbf{6 4} \) amu) is:
\( \mathbf{A} \cdot[X e] 4 f^{8} 5 d^{9} 6 s^{2} \)
в. \( [X e] 4 f^{7} 5 d^{1} 6 s^{2} \)
\( \mathbf{c} \cdot[X e] 4 f^{5} 5 d^{2} 6 s^{2} \)
\( \mathbf{D} \cdot[X e] 4 f^{3} 5 d^{3} 6 s^{2} \)


The part of human eye which is sensitive to red, blue and green light is:
A. retina
B. lens
c. cornea
D. iris


The fringe width for red colours as compared to that for violet colour is approximately
A. 3 times
B. 2 times
c. 4 times
D. 8 times


At what stage of the cell cycle, are histone proteins synthesized in a eukaryotic cell?
A. During telophase
B. During S phase
C. During G stage of prophase
D. During entire prophase


By rounding off,
(a) 20.96 and \( (b) \)
0.0003125 to three significant figures, we get
A \( \cdot 21.0 ; 312 \times 10^{-4} \)
B . \( 21.0 ; 3.125 \times 10^{-4} \)
c. \( 2.10 ; 3.12 \times 10^{-4} \)
D. \( 210 ; 3.12 \times 10^{-4} \)


Name four categories of people who
depend on the forest resources
mentioning major needs of each
category.


(i) Verify the Rolle's theorem for the function
\( \boldsymbol{f}(\boldsymbol{x})=\sin ^{2} \boldsymbol{x}, \mathbf{0} \leq \boldsymbol{x} \leq \boldsymbol{\pi} \)
(ii) Find the critical numbers of
\( \boldsymbol{x}^{3 / 5}(\boldsymbol{4}-\boldsymbol{x}) \)


The alkane which has only \( 1^{\circ} H \) atoms
is
A. Neopentane
B. Isopentane
c. Pentane
D. 2,2 - dimethylbutane


Which of the following statements
is/are not correct?
This question has multiple correct options
A. \( \pi \) - bond always exists with sigma -bond according to Valence Bond Theory
B. \( \pi \) - bond can exist independently according to Valence Bond Theory
C \( . \sigma \) - bond is weaker than pi-bond
D. \( \pi \) - bond is less reactive than sigma-bond


When cellulose from wood or cotton is cooked in large tanks containing caustic soda and then through a narrow slit into another tank containing acid,
we get:
A. cellophane, a paper-like plastic
B. rayon, a textile fibre
c. bakelite, an insulator
D. unvulcanized rubber


If \( A, B \) are two events with \( P(A \cup B)= \)
\( \mathbf{0 . 6 5}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0 . 1 5}, \) then find the
value of \( \boldsymbol{P}\left(\boldsymbol{A}^{C}\right)+\boldsymbol{P}\left(\boldsymbol{B}^{C}\right) \)


The atomic number of carbon is :
A. 5
B. 6
\( c \cdot 12 \)
D. 14


Can we store copper sulphate in iron container and why?
A. No, because Cu is more reactive than iron
B. No, because iron is more reactive than copper therefore reaction will take place.
C. Yes, because copper is less reactive than iron.
D. Yes, because copper is more reactive than iron.


Evaluate \( \int\left(\frac{1}{7}-\frac{1}{y^{5 / 4}}\right) d y \)
A \( \cdot_{I}=\frac{y}{7}+\frac{4}{y^{1 / 4}}+c \)
B. \( I=-\frac{y}{7}+\frac{4}{y^{1 / 4}}+c \)
\( ^{\mathrm{C}} \cdot_{I}=\frac{y}{7}-\frac{4}{y^{1 / 4}}+c \)
D. None of these


Two nearby objects are just resolved, if the principle maximum in the diffraction pattern of one coincides with
A. principal maxima of other
B. first minimum of the other
c. half-way between principal maximum and first \( \operatorname{minimum} \)
D. second maximum of the other


How many benzylic hydrogens are
present in the hydrocarbon shown
given?
\( A \cdot 3 \)
B. 4
\( c .5 \)
D. 6
\( E \)


Choose the correct answers from the
alternatives given :
A particular cell has half as much DNA as some of the other cells in a
mitotically active tissue. The cell in question could be in
A. metaphase
B. prophase
c. \( G_{1} \)
D. \( G_{2} \)


Acetic acid is less acidic in sodium
acetate solution than in \( N a C l \)
solution. If true write 1 , else write 0


The force of repulsion between two
parallel wires is \( f \) when each one of
them carries a certain current I. If the
current in each is doubled, the force
between them would be
A. \( 4 / f \)
B. \( 4 f \)
\( c \cdot 2 f \)
D. \( f \)


\( \int_{\infty}^{a} \frac{\boldsymbol{d} \boldsymbol{x}}{\boldsymbol{x}^{4} \sqrt{\left(\boldsymbol{a}^{2}+\boldsymbol{x}^{2}\right)}}=\frac{\boldsymbol{k}-\sqrt{\boldsymbol{k}}}{\mathbf{3} \boldsymbol{a}^{4}} \) What is
\( k ? \)


The self inductance of a motor of an
electric fan is \( 10 H . \) In order to impart
maximum power at \( 50 H z \), it should be
connected to a capacitance of :
A \( .4 \mu F \)
в. \( 8 \mu F \)
\( \mathrm{c} \cdot 1 \mu F \)
D. \( 2 \mu F \)


Which of the following hormones is a derivative of amino acid?
A. Oestrogen
B. Epinephrine
c. Progesterone
D. Prostaglandin


Which of the following is true when soap
or detergent is added to water?
A. The anions of emulsion repel each other hence do not precipitate.
B. The anions of emulsion attract each other hence do
not precipitate.
C. The anions of emulsion repel each other hence precipitate.
D. The anions of emulsion attract each other hence precipitate.


If \( x+\frac{1}{x}=4, \) then \( x^{4}+\frac{1}{x^{4}} \) is equal to
A . 196
B. 194
\( c .192 \)
D. 19


Each of the following particles is projected with the same speed into a uniform magnetic field \( B \) such that the particle's initial velocity is perpendicular to \( B \). Which one would
move in a circular path with the largest radius?

A particle is projected at a given speed into a uniform magnetic field \( B \) and perpendicular to it. Choose the particle that will have the largest radius.
A. Proton
B. Beta particle
c. Alpha particle
D. Electron
E . Positron


A 5 kg mass moving at a speed of \( 13 m s^{-1} \) collides head on with a body of
mass \( 1 \mathrm{kg} \) at rest, if they move with a common velocity after collision in the same direction, find the velocity?
A \( \cdot 103 \mathrm{ms}^{-1} \)
B . \( 10.83 \mathrm{ms}^{-1} \)
c. \( 1.03 \mathrm{ms}^{-1} \)
D. \( 20 \mathrm{ms}^{-1} \)


The \( K_{p} \) value for \( 2 S O_{2}(g)+O_{2}(g) \rightleftharpoons \)
\( 2 S O_{3}(g) \) is \( 5.0 a t m^{-1} \)
If the equilibrium pressures of \( S O_{2} \) and
\( \boldsymbol{S} \boldsymbol{O}_{3} \) are equal. What is the equilibrium
pressure of \( \boldsymbol{O}_{2} ? \)
A. 0.2 atm
B. 0.3 atm
\( c .0 .4 \) atm
D. \( 0.1 \mathrm{atm} \)


The non-metal which is a liquid at room
temperature is:
A. chlorine
B. nitrogen
c. bromine
D. hydrogen


Find the given number is a perfect cube
or not.
\( \mathbf{5 4 0} \)


Give a one-word scientific term for the
following:
Construction of an animal such as
earthworm by repeated segments.


\( \left[\left(1-\frac{1}{n+1}\right)+\left(1-\frac{2}{n+1}\right)+\right. \)
\( \left.+\left(1-\frac{n}{n+1}\right)\right] \)


A ball is thrown from a point on ground at some angle of projection. At the time a bird starts from a point directly above
this point of projection at a height \( h \) horizontally with speed \( u \). Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes:
\( \sqrt[4]{2 u} \sqrt{\frac{h}{g}} \)
в. \( u \sqrt{\frac{2 h}{g}} \)
c. \( 2 u \sqrt{\frac{2 h}{g}} \)
\( u \sqrt{\frac{h}{g}} \)


What is the big bang?
A. The collision of galaxies.
B. The formation of galaxies.
C. The beginning of the universe's expansion.
D. The time when stars began to form.


Heroin is obtained from the plant of the
family
A. Leguminosae
B. Papaveraceae
c. Liliaceae
D. Solanaceae


If the series limit of the Balmer series
for hydrogen is 2700 Angstrom. Calculate the atomic no. of the element
which gives X-ray wavelength of \( \boldsymbol{K}_{\boldsymbol{\alpha}} \) line
as 1.0 Angstrom.
\( A \cdot z=21 \)
B. \( z=31 \)
\( c \cdot z=61 \)
\( D \cdot z=5 \)


Calculate the moment about the points \( \mathrm{C}(1,1,1) \) of a force \( 5 \mathrm{N} \). acting along the line \( \underset{A B}{\text { where } A, B \text { are the points }(2,3,4)} \) (3,5,6) respectively the distance being measured in \( \mathrm{m} \)
\( \mathbf{A} \cdot 5(-2 i+j) \)
B . \( 7(-2 i+j) \)
c. \( \frac{5}{3}(-2 i+j) \)
D. \( \frac{5}{3}(j) \)


Which of the following physical quantities has neither units nor
dimensions?
A. Relative velocity
B. Relative density
c. Angle
D. Energy


Which of the following non-metal
appears as a liquid under standard
condition?
A. \( F \)
в. \( C l \)
\( c . B r \)
D. \( I \)
E . \( A t \)


Determine whether the operation \( ^{\prime} O^{\prime} \) on
\( Z \) defined by \( a O b=a^{b} \) for all \( a, b \in Z \)
is a binary operation or not:


In the metre bridge experiment of resistances, the known and unknown resistances are inter-changed. The error so removed is:
A. end correction
B. index error
c. due to temperature effect
D. random error


Fill in the blanks.
Sulphur \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3} \) to
produce nitrogen dioxide.


A wire of initial length \( L \) and radius \( r \) is stretched by a length \( l \). Another wire of same material but with initial length \( 2 L \) and radius \( 2 r \) is stretched by a
length \( 2 l \). The ratio of the stored elastic energy per unit volume in the first and second wire is,
\( A \cdot 1: 4 \)
B. 1: 2
c. 2: 1
D. 1:


Form the greatest and the smallest \( 4- \) digit numbers using any four different digits with the condition that digit 5 is always at the ten's place.


Who was the first direct ancestor of
modern humans?


\( \ln \) an \( A C \) circuit, the instantanceous
emf and current are given by
\( e=100 \sin 30 t, i=\sin \left(30 t \frac{\pi}{4}\right) \)
In one cycle of \( A C, \) the average power consumed by the circuit and the wattles current are, respectively
A. 50,0
B. 50,10
c. \( \frac{1000}{\sqrt{2}}, 10 \)
D. \( \frac{50}{\sqrt{2}}, 0 \)


A square loop of side a lying a perpendicular magnetic field to its plane is changed to a circle. If change occusrs in \( t \) seconds in magnetic field \( B \) tesla, the induced emf is
A \( \cdot \frac{4}{\pi} \frac{B a^{2}}{t} \)
B. \( \frac{B a^{2}}{t} \)
c. \( \frac{B a^{2}}{t}\left[\frac{4}{\pi}-1\right] \)
D. zero


Identify among the following solution, which is used to distinguish between
\( N O_{3}^{-} \) and \( N O_{2}^{-} \)
A. Complexation with Zn
B. Flame test
c. copper sulphate solution
D. KI solution


When \( H C O_{3}^{-} \) acts as a Bronsted base,
which of the following is formed?
A \( \cdot C O_{2} \)
в. \( C O_{3} \)
\( \mathrm{c} \cdot \mathrm{CO}_{3}^{2-} \)
D. \( H_{2} C O_{3} \)


Assertion
\( O_{3} \) and \( N O_{2}^{-} \) are isoelectronic.
Reason
Bond angles of \( \boldsymbol{O}_{3} \) and \( \boldsymbol{N} \boldsymbol{O}_{2}^{-} \) are \( \mathbf{1 1 6 . 8}^{\circ} \)
and \( 115^{\circ} \) respectively.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


When an excess of a very dilute
aqueous solution of \( \mathrm{Kl} \) is added to a very dilute aqueous solution of silver nitrate, the colloidal particles of silver iodide
are associated with which of the
following Helmholtz double layer?
\( A \)
\[
\mathbf{A} \mathbf{g} \mathbf{I} / \mathbf{A} \mathbf{g}^{+} \vdots \mathbf{I}^{-}
\]
в.
\[
\mathbf{A} \mathbf{g} \mathbf{I} / \mathbf{K}^{+}: \mathbf{N} \mathbf{O}_{\mathbf{3}}^{-}
\]
c.
\[
\mathbf{A} \mathbf{g} \mathbf{I} / \mathbf{N} \mathbf{O}_{\mathbf{3}}^{-} \vdots \mathbf{A} \mathbf{g}^{+}
\]
D. \( \mathbf{A} \mathbf{g} \mathbf{I} / \mathbf{I}^{-} \vdots \mathbf{K}^{+} \)


Consider a differential equation of order
\( m \) and degree \( n . \) Which one of the following pairs is not feasible?
A \( \cdot(3,2) \)
В \( \cdot\left(2, \frac{3}{2}\right) \)
c. (2,4)
(年. \( (2,4)) \)
D. (2,2)


Boiling point of alkyl iodide, bromide, chloride and methane are in which of
the following order?
A . Iodide \( > \) Bromide \( > \) Chloride \( >C H_{4} \)
B. \( C H_{4}> \) Chloride \( > \) Bromide\( > \) Iodide
c. \( C H_{4}> \) Iodide \( > \) Bromide \( > \) Chloride
D. Chloride \( > \) Bromide \( > \) Iodide \( >C H_{4} \)


The mole of \( \operatorname{gases} N H_{3}, C O_{2} \) and \( H_{2} \) adsorbed by \( 1 g \) charcoal at \( 300 K \) and
1 atm pressure shows the order:
A. \( C O_{2}>H_{2}>N H_{3} \)
в. \( N H_{3}>C O_{2}>H_{2} \)
c. \( H_{2}>C O_{2}>N H_{3} \)
D. \( C O_{2}>N H_{3}>H_{2} \)


State whether the given statement is
true or false :

A horse continues to apply a force in
order to move a cart with a constant
speed.
A. True
B. False


Which of the following properties can only be a whole number?
A. Atomic mass
B. Atomic volume
c. Atomic radius
D. Mass number


A rectangular loop of wire of size \( 4 c m \times 10 c m \) carries steady current of
2 A. A straight long wire carrying 5 A current is kept near the loop as shown. If the loop and the wire are coplanar, find the magnetic flux through the
rectangular loop.


Why does \( N O_{2} \) dimerise?


A sphere of mass \( m \) and radius \( r \) is
projected in a gravity free space with speed \( v \). If coefficient of viscosity is \( \frac{1}{6 \pi} \) then the distance travelled by the body before it stops is
A \( \cdot \frac{m V}{2 r} \)
B. \( \frac{2 m V}{r} \)
\( c \cdot \frac{m V}{r} \)
D. none of these


If \( y=\sin ^{-1} \frac{1}{2}(\sqrt{1+x}+\sqrt{1-x}) \) then
\( y^{\prime}= \)
A. \( \frac{1}{2 \sqrt{1-x^{2}}} \)
B. \( \frac{-1}{2 \sqrt{1-x^{2}}} \)
c. \( \frac{1}{2 \sqrt{1+x^{2}}} \)
D. \( \frac{-1}{2 \sqrt{1+x^{2}}} \)


A girl weighing 50 kgf wears sandals of pencil heel of area of cross section 1 \( c m^{2}, \) stands on a floor. An elephant weighing 2000 kgf stands on foot each of area of cross section \( 25 \mathrm{cm}^{2}, \) on the
floor. Compare the pressure exerted by them.


A proton and an alpha particle are accelerated through the same potential difference. The ratio of wavelengths associated with proton and
alpha particle respectively is :
A. \( 1: 2 \sqrt{2} \)
B . 2: 1
\( c \cdot 2 \sqrt{2}: 1 \)
D. 4: 1


If the equation \( 2 x^{2}-6 x+p=0 \) has
real and different roots, then the values
of \( p \) are given by
\( ^{A} \cdot_{p}<\frac{9}{2} \)
в. \( \quad p \leq \frac{9}{2} \)
c. \( _{p>\frac{9}{2}} \)
\( \mathrm{D} \cdot_{p} \geq \frac{9}{2} \)


A person sells two articles together for
Rs. \( 46, \) making a profit of \( 10 \% \) on one and of \( 20 \% \) on the other. If he had sold
each article at \( 15 \% \) profit, the result would have been the same. At what
price does he sell each article?


Maximum P.E. of magnet of moment M situated in a magnetic field of induction
\( \mathrm{B}, \) is
\( ^{\mathbf{A}} \cdot \frac{1}{2} M B \)
в. \( \frac{M}{B} \)
\( \mathbf{c} .2 M B \)
D. \( M B \)


Graphite is better lubricant on the moon
than on earth.
for \( \operatorname{True}=1 \) or \( f a l s e=0 \)


Write the rational numbers which are
smaller than 2


Stage of life between childhood and
adulthood is known as


The number of \( n \) digit numbers such
that no two consecutive digits are same is
A. \( 9 ! \)
B . \( n^{9} \)
\( c \cdot 9^{n} \)
D. \( 9 n \)


A bar magnet of magnetic moment 3.0
\( A-m^{2} \) is free to rotate about a vertical
axis passing through its centre. The magnet is released from rest from east west position. Then the kinetic energy of the magnet as it takes North- South position is :
(horizontal component of earths magnetic field is \( 25 \mu \mathrm{T}) \)
B. 75 \( \mu \) J
c. \( 100 \mu \) J
D. 12.5 \( \mu \) )


Calculate the range and coefficient of range with following data
Marks \( \quad \begin{array}{cccc}0- & 10- & 20- & 30- \\ 10 & 20 & 30 & 40\end{array} \)
No. of
student
O5 , and o7 08


If \( x y \) -plane and \( y z \) -plane divides the line segment joining \( A(2,4,5) \) and \( B(3,5,-4) \) in the ratio a:b and p:q respectively then value of \( \left(\frac{a}{b}, \frac{p}{q}\right) \) may be
A \( \cdot \frac{23}{12} \)
B. \( \frac{7}{5} \)
\( c \cdot \frac{7}{12} \)
D. \( \frac{21}{10} \)


Why the current produced by the generator is called as alternating
current
A. continuous decrease and increase of current occurs
B. after every half cycle direction of flow of current is reversed.
\( c . \) both
D. none


Briefly describe the following:
(a) Transcription
(b) Polymorphism
(c) Translation
(d) Bioinformatics


Will \( C C l_{4} \) give white precipitate of
AgCl on heating it with silver nitrate?
Give reason for your answer.


At the point \( x=1, \) the function \( f(x)= \)
\( \left\{\begin{array}{ll}x^{3}-1, & 1<x<\infty \\ x-1, & -\infty<x \leq 1\end{array}\right. \)
A. continuous and differentiable
B. Continuous and not differentiable
c. Discontinuous and differentiable
D. Discontinuous and not differentiable


The component of rainwater harvesting
system is
A. Conduits
B. Damm
c. Lake
D. None of the above


Let \( \boldsymbol{f}:[\mathbf{1}, \infty] \rightarrow[\mathbf{2}, \infty] \) if \( \boldsymbol{f}(\mathbf{1})=\mathbf{2} . \) be
differentiable function such that
\( 6 \int_{1}^{x} f(t) d t=3 x f(x)-x^{3} \) then the
value of \( \boldsymbol{f}(\mathbf{2}) \) is....


Consider a circle of radius \( R \). A point charge lies at a distance \( a \) from its
center and on its axis such that \( \boldsymbol{R}= \)
\( a \sqrt{3} . \) If electric flux passing through the
circle is \( \phi, \) find the magnitude of the
point charge.


Heat is a from of
A. Energy
B. Work
c. Power
D. None of these


A number is subtracted from \( 72 . \) The
new number is divided by 6 to give 10
Find the number.


Benzene and naphthalene form an ideal
solution at room temperature. For this process, the true statements are:
(i) \( \Delta G \) is positive
(ii) \( \Delta S_{s y s t e m} \) is positive
(iii) \( \Delta S_{\text {surroundings}}=0 \)
(iv) \( \Delta \boldsymbol{H}=\mathbf{0} \)
A. (ii) and (iv) only
B. (i) and (iii) only
C. (ii), (iii) and (iv) only
D. all of these


11
the highest charge?
\( \mathbf{A} \)
\( B \)
\( \mathbf{C} \)
D. Cannot be ascertained


If the mean of the numbers \( a, b, 8,5,10 \)
is 6 and their variance is \( 68, \) then \( a b \) is
equal to
A . 6
B. 7
c. 12
D. 14
E . 25


From the elements of the following atomic numbers 9,12,16,20,38,47
and \( 56, \) identify the elements that belong to same group in periodic table:
A .9,16,39
В. 12,20,47
c. 20,38,47
D. 12,20,56


As the number of \( - \) OH groups
increases in hypophosphorous acid, phosphorous acid, and phosphoric acid, the acidic strength:
A. increases
B. decreases
c. remains nearly same
D. remains appropriately same


In which of the following transformations, the \( \beta \) -particles are
emitted?
A. Proton to neutron
B. Neutron to proton
c. Proton to proton
D. Neutron to neutron


Offspring formed due to sexual
reproduction have better chances of survival. Why?


Solve the equation \( \frac{\boldsymbol{x}+\mathbf{7}}{\mathbf{3} \boldsymbol{x}+\mathbf{1 6}}=\frac{\mathbf{4}}{\mathbf{7}} \)


Explain cleaning action?


For the reaction, \( \boldsymbol{A}_{2}+\boldsymbol{B}+\boldsymbol{C} \rightarrow \boldsymbol{A} \boldsymbol{C}+ \)
\( A B, \) it is found that tripling the
concentration of \( A_{2} \) triples the rate,
doubling the concentration of C doubles the rate and doubling the concentration of B has no effect.
(a) What is the rate law?
(b) Why the change in concentration of
B has no effect?


The diffusion of water vapours through aerial parts of the plants is called as
A. Osmosis
B. DPD
c. Transpiration
D. All of the above


The largest sphere is carved out of a cube of edge \( 14 \mathrm{cm} . \) Then the volume of the sphere is
A \( . \) 1370 \( c m^{3} \)
B . \( 1800 \mathrm{cm}^{3} \)
c. \( 1437 \mathrm{cm}^{3} \)
D. \( 1734 \mathrm{cm}^{3} \)


An electron in the hydrogen atom jumps from excited state \( n \) to the ground state. The wavelength so emitted illuminates
a photosensitive material having work function 2.75 eV. If the stopping
potential of the photoelectron is \( 10 \mathrm{V} \) then the value of \( n \) is
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
D. 5


In Mendeleev's periodic table, the elements were arranged in the increasing order of their atomic
masses. However, cobalt with atomic
mass of 58.93 amu was placed before nickel having an atomic mass of 58.69 amu. Reason for the same is that:
A. the elements with similar size can be grouped togethe
B. the elements with different properties can be grouped together
c. the elements with similar properties can not be grouped together
D. the elements with similar properties can be grouped together


The outermost electronic configuration of the most electronegative element is:
\( \mathbf{A} \cdot n s^{2} n p^{3} \)
В \( \cdot n s^{2} n p^{4} \)
c. \( n s^{2} n p^{5} \)
D. \( n s^{2} n p^{6} \)


The limit upto which the stress is directly proportional to strain is called
A. elastic limit
B. elastic fatigue
c. elastic relaxation
D. breaking limit


The outer shell electronic configuration of \( G d(Z=64) \) is
A \( \cdot 4 f^{7} 5 d^{1} 6 s^{2} \)
B \( \cdot 4 f^{8} 6 s^{2} \)
c. \( 4 f^{9} 9 s^{\text {। }} \)
D. \( 4 f^{7} 5 d^{2} 6 s^{1} \)


How do metallic character and valency of elements change in a period moving left to right in modern periodic table?