An ideal cell having a steady emf of
2 volts is connected across the
potentiometer wire of length \( 10 m \). The
potentiometer wire is of magnesium and having resistance of \( 11.5 \Omega / m . \) An another cell gives a null point at \( 6.9 m \). If
a resistance of \( 5 \Omega \) is put in series with potentiometer wire, the new position of the null point is given as \( \frac{x}{10} m . \) Find \( x \)


toppr
Q Type your question
\( N O, N_{2} O_{3}, N_{2} O_{4} \) to \( N_{2} O_{5} \) (O.S of
nitrogen +5 ).
The following points are important regarding the oxides of nitrogen.
(a) All oxides of nitrogen except \( N_{2} O_{5} \) are endothermic because large amount of energy is required to dissociate the stable molecule of oxygen and nitrogen.
(b) The small electronegativity difference between oxygen and nitrogen makes N-O bond easily breakable to give oxygen and hence oxides of nitrogen are said to be better oxidizing
agents
(c) Except \( N_{2} O_{5}, \) all are gases at
ordinary temperature. \( N_{2} O_{3} \) is stable only at a lower temperature \( (253 \mathrm{K}) \)
(d) Except \( N_{2} O \) and \( N O \) which are
neutral oxides, all are acidic oxides that
dissolve in water forming
corresponding oxyacids.
(e) They are also a good example of illustrating the concept of resonance.
The gas which is acidic in nature is
A. \( N O \)
B. \( N_{2} O \)
\( \mathbf{c} \cdot N O_{2} \)
D. Both (A) and (C)


Find the speed of the connector as a
function of time if the force \( \boldsymbol{F} \) is applied
\( \operatorname{at} t=0 \)


Pressure applied on a rubber ball reduces the ball's radius by \( 1 \% \), what is the percentage volume strain of the ball
A . 1\%
B. 3\%
c. \( 5 \% \)
D. 0.5\%


Assertion
\( N O_{2} \) is reddish brown and its dimer
\( N_{2} O_{4} \) is colourless
Reason
There is a dative bond formation
between two \( N O_{2} \) molecules
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The refractive index \( (\mu) \) of glass is found to have the values
1.49,1.50,1.52,1.54 and 1.48
Calculate percentage error.
A. \( 0.61 \% \)
B. \( 1.32 \% \)
c. \( 2.64 \% \)
D. \( 5.28 \% \)


The coagulating power of electrolytes
having ions \( N a^{+}, A l^{3+} \) and \( B a^{2+} \) for
arsenic sulphide sol increases in the order:
A \( \cdot N a^{+}<B a^{2+}<A l^{3+} \)
B. \( B a^{2+}<N a^{+}<A l^{3+} \)
c. \( A l^{3+}<N a^{+}<B a^{2+} \)
D. \( A l^{3+}<B a^{2+}<N a^{+} \)


If a variate takes values
\( a, a r, a r^{2}, \ldots \ldots a r^{n-1} \) which of the
relation between means hold?
A \( . A H=G^{2} \)
в. \( \frac{A+H}{2}=G \)
c. \( A>G>H \)
D. \( A=G=H \)


Lactose is a disaccharide of :
A. \( \alpha-D \) -Glucose and \( \alpha-D \) -Fructose
B . \( \beta-D \) -Glucose and \( \beta-D \) -Galactose
C \( . \alpha-D \) -Glucose and \( \beta-D \) -Ribose
D. \( \alpha-D \) -Glucose and \( \alpha-D \) -Galactose


A solid sphere of radius \( 20 \mathrm{cm} \) is
subjected to a uniform pressure of \( 10^{6} \)
\( N m^{-2} . \) If the bulk modulus is \( 1.7 \times \)
\( 10^{11} N m^{-2}, \) the decrease in the volume
of the solid is approximately equal to:
A \( \cdot 0.2 \mathrm{cm}^{3} \)
В. \( 0.3 \mathrm{cm}^{3} \)
\( \mathrm{c} \cdot 0.4 \mathrm{cm}^{3} \)
D. \( 0.5 \mathrm{cm}^{3} \)


Mr. Dixit resigned from the company after 4 years of service.
A. If only G can be given
B. If only PF can be given
c. If both G and Pf can be given
D. If neither G nor PF can be given


Construct a quadrilateral \( A B C D, \) when
\( A B=3.2 \mathrm{cm}, B C=5.2 \mathrm{cm}, C D=6.2 \)
\( \mathbf{c m}, \boldsymbol{D} \boldsymbol{A}=\mathbf{4 . 2} \mathbf{c m} \) and \( \boldsymbol{B} \boldsymbol{D}=\mathbf{5} . \boldsymbol{2} \mathrm{cm} \)


In given figure, \( D E \| A C \) and \( D C \| A P \) Prove that \( \frac{\boldsymbol{B} \boldsymbol{E}}{\boldsymbol{E C}}=\frac{\boldsymbol{B C}}{\boldsymbol{C P}} \)


Which one is a metal?
\( A \cdot B \)
B.
\( c \cdot D \)
D. All of the above


The strongest acid among the following is -
\( \mathbf{A} \cdot \mathrm{ClO}_{3}(\mathrm{OH}) \)
B. \( \mathrm{ClO}_{2}(\mathrm{OH}) \)
\( \mathbf{c} \cdot \operatorname{SO}(\mathrm{OH})_{2} \)
\( \mathrm{D} \cdot \mathrm{SO}_{2}(\mathrm{OH})_{2} \)


Term Species, Division and Phylum were
coined by
A. Species by John Ray, Division by Eichler and Phylum by Cuvier
B. Species by Cuvier, Division by Eichler and Phylum by Ray
C. Species by Ray and Phylum and Division by Haeckel
D. Species and Division by Ray and Phylum by Linnaeus


In a moving coil galvanometer, the
deflection \( (\Phi) \) on the scale by a pointer attached to the spring is
\( ^{\mathrm{A}} \cdot\left(\frac{N A}{k B}\right) I \)
в. \( \left(\frac{N}{k A B}\right) I \)
\( ^{\mathbf{c}} \cdot\left(\frac{N A B}{k}\right) I \)
D. \( \left(\frac{N A B}{k I}\right) \)


A question paper has 5 questions. Each question has an alternative. The number of ways in which a student can attempt at least one question is?
\( \mathbf{A} \cdot 2^{5}-1 \)
B. \( 3^{5}-1 \)
\( c \cdot 3^{4}-1 \)
D. None of these


A taxon is observed. Himgiri variety which is resistant to hill bunt disease
belongs to this taxon. In this taxon, pollen grains lose viability within 30 minutes of their release from anthers.
The taxon belongs to the order
A. Sapindales.
B. Polemoniales.
c. Rosales.
D. Poales


A car is going with a linear momentum
p. When brakes are applied, it comes to
a stop in a distance \( s \). If the same car
were going with a linear momentum \( 2 p \) and the brakes are applied, it comes to a stop in a distance of (assume that the
brake force is same in the two cases)
\( \mathbf{A} \cdot 2 s \)
B.
c. \( 4 s \)
D.


Intra-molecular hydrogen bonding is found in:
A. salicyldehyde
B. water
c. acetaldehyde
D. phenol


\( 0.73 g \) of organic compound gave \( 0.6 g \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
The \( \% \) of \( \mathrm{H} \) in the organic compound is:
A \( \cdot 10.24 \)
B. 12.42
c. 9.13
D. 8.25


An extremely long wire is uniformly charged. An electron is revolving around the wire and making \( 10^{8} \) revolutions per
second in an orbit of radius \( 2 \mathrm{cm} \). Linear
charge density of the wire is nearly?
A. \( 50 n C / m \)
B. \( 25 n C / m \)
c. \( 40 n C / m \)
D. \( 12.5 n C / m \)


Which of the following pairs of ions have the same electronic configuration?
A \( \cdot C u^{2+}, C r^{2+} \)
B . \( F e^{3+}, M n^{2+} \)
c. \( C o^{3+}, N i^{3+} \)
D. \( S c^{3+}, C r^{3+} \)


What is saturated solution explain with one example?


(a) What is lymph?
(b) Draw a labelled diagram of human
excretory system.
(c) How plants excrete waste products? Explain.


Motion which repeats itself after regular
intervals.
A. oscillatory motion
B. vibratory motion
c. periodic motion
D. none


Fluidity of cell membranes in cold
weather is maintained by
A. Increasing number of phospholipids with unsaturated hydrocarbon tails
B. Increasing the proportion of integral proteins
C. Increasing concentration of cholesterol in membrane
D. Increasing the number of phospholipids with saturated hydrocarbon tails


Factorize the following expression
\( 8 x^{3}-27 y^{3} \)
\( \mathbf{A} \cdot(2 x-3 y)\left(4 x^{2}+6 x y+9 y^{2}\right) \)
B \( \cdot(2 x+3 y)\left(4 x^{2}+6 x y+9 y^{2}\right) \)
\( \mathbf{c} \cdot(2 x-3 y)\left(4 x^{2}-6 x y+9 y^{2}\right) \)
D. None of these


Pertaining to endocrine system, what will you interpret if :
¡) You observe swollen neck in people living in the hills
ii) Over secretion of growth Hormone takes place during childhood
iii) Facial hair develops in body aged 13


A cyclic process is shown in the
figure.Work done during isobaric
expansion is:
A . 1600
B. 100
c. 400
D. 600


Which of the following halide does not contain a lone pair of electrons on the
central atom:
A \( \cdot \mathrm{PCl}_{3} \)
в. \( \mathrm{NCl}_{3} \)
c. \( \mathrm{AsCl}_{3} \)
D. PCI


A straight horizontal conducting rod of length \( 0.45 \mathrm{m} \) and mass \( 60 \mathrm{g} \) is suspended by two vertical wires at its ends. A current of \( 5.0 \mathrm{A} \) is set up in the rod through the wires.
(a) What magnetic field should be set up normal to the conductor in order that
the tension in the wires is zero?
(b) What will be the total tension in the wires if the direction of current is
reversed keeping the magnetic field same as before?(Ignore the mass of the wires.) \( g=9.8 m s^{-2} \)


Name the hormone secreted by the
thymus gland.


The purine \( \& \) pyrimidine pairs of complementry strands of DNA are held together by
A. H bonds
B. O bonds
c. c bonds
D. N bonds


Torque is the cause of:
A. Translatory motion
B. Rotatory motion
c. oscillatory motion
D. Combine translatory and rotatory motion


Which of these do not form Grignard
reagent?
A \( . C H_{3} C l \)
в. \( C H_{3} F \)
\( \mathrm{c} \cdot C H_{3} B r \)
D. \( C H_{3} I \)


The length of wire increases by \( 9 \mathrm{mm} \) when weight of \( 2.5 \mathrm{kg} \) is hung from the free end of wire. If all conditions are kept
the same and the radius of wire is made
thrice the original radius, find the increase in length.


Which is the hottest part in the flame of the candle?
A. Blue
B. Yellow
c. Black
D. Wax part


What are the Cathode Rays?


Let \( \boldsymbol{f}:[\mathbf{1}, \mathbf{3}] \rightarrow \mathbf{R} \) be a continuous
function that is differentiable in \( (\mathbf{1}, \mathbf{3}) \)
and \( f^{\prime}(x)=|f(x)|^{2}+4 \) for all \( x \in(1,3) \)
Then?
This question has multiple correct options
A \( . f(3)-f(1)=5 \) is true
B. \( f(3)-f(1)=5 \) is false
c. \( f(3)-f(1)=7 \) is false
D. \( f(3)-f(1)<0 \) only at one point of (1,3)


The non terminating non-recurring decimal cannot be represented as
A. irrational numbers
B. rational numbers
c. real numbers
D. none of these


The separation between two coherent
point sources is \( 3 \lambda . \) On a line
perpendicular to \( S_{1} S_{2} \) and passing
through \( S_{2} \). Find the smallest distance
where minimum of intensity occurs:
A \( \cdot \frac{11 \lambda}{20} \)
B. \( \frac{\lambda}{2} \)
c. \( \frac{9 \lambda}{20} \)
D. \( \frac{35 \lambda}{4} \)


The magnetic force per unit length on a wire carrying a current of \( 10 \mathrm{A} \) and
making an angle of \( 45^{0} \) with the direction of a uniform magnetic field of \( 0.20 \mathrm{T} \) is
A \( \cdot 2 \sqrt{2} N m^{-1} \)
B. \( \frac{2}{\sqrt{2}} N m^{-1} \)
\( ^{c} \cdot \frac{\sqrt{2}}{2} N m^{-1} \)
D. \( 4 \sqrt{2} N m^{-1} \)


The mole fraction of methanol in 4.5
molal aqueous solution is:
A. 0.250
B. 0.125
c. 0.100
D. 0.075
E. 0.055


Assertion
Taxon and category are same things.
Reason
Systematic shows hierarchical
classification.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect


The slope of the velocity time graph for retarded motion is
A. positive
B. negative
c. zero
D. can be +ve,- -ve or zero


A convex lens forms an image of an object on a screen. The height of the image is \( 9 \mathrm{cm} . \) The lens is now displaced until an image is again obtained on the screen. The height of this image is \( 4 \mathrm{cm} . \) The distance
between the object and the screen is 90
\( \mathrm{cm} \)
A. The distance between the two positions of the lens is 30 \( \mathrm{cm} \)
B. The distance of the object from the lens in its first position is 36 \( \mathrm{cm} \)
c. The height of the object is \( 6 \mathrm{cm} \)
D. The focal length of the lens is 21.6 \( \mathrm{cm} \)


The least count of a stop watch is 0.2 second.The time of 20 oscillations of a
pendulum is measured to be 25 seconds.The percentage error in time period is
A . 16\%
в. 0.8\%
c. \( 1.8 \% \)
D. 8\%


On the parabola \( y=x^{2}, \) the point least
distant from the straight line \( y=2 x- \)
4 is
\( \mathbf{A} \cdot(1,1) \)
B \( \cdot(1,0) \)
c. (1,-1)
D \( \cdot(0,0) \)


\( \boldsymbol{C H}_{3}-\boldsymbol{C O O H}+\boldsymbol{X} \rightarrow \) Fruity
smell compound. Then, X is :
A. aldehyde
B. chloroform
c. alcohol
D. base


A torque of \( 0.5 N m \) is required to drive a screw into a wooden frame with the help of a screw driver. If one of the two forces
of couple produced by screw driver is
\( \mathbf{5 0} N, \) the width of the screw driver is:
\( \mathbf{A} \cdot 0.5 \mathrm{cm} \)
B. \( 0.75 \mathrm{cm} \)
\( c \cdot 1 c m \)
D. \( 1.5 \mathrm{cm} \)


Represent the Relative motion of body in the graphs:
Two objects moving with unequal velocities in same direction


Assertion
During covalent bonding the electro negativity difference between two
atoms is greater than 1.7
Reason
Covalent bond is formed by sharing of
electrons between atoms that have
same size
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A mixture of ethane \( \left(C_{2} H_{6}\right) \) and ethene
\( \left(C_{2} H_{4}\right) \) occupies 40 litre at 1.00 atm
and at \( 400 \mathrm{K} \). The mixture reacts
completely with 130 g of \( O_{2} \) to produce \( C O_{2} \) and \( H_{2} O . \) Assuming ideal gas behaviour, calculate the mole fractions
of \( C_{2} H_{6} \) in the mixture and write
numerical value (upto 2 digit only) after decimal point only (as for 0.19, write 19).


Cubes of Negative integers are negative
A. True
B. False
c. Ambiguous
D. Data insufficient


A monochromatic ray of light falls on a regular prism. What is the relation between angle of incidence and angle of emergence in the case of minimum deviation?


In a certain Bohr orbit, the total energy
is \( -4.9 e V . \) For this orbit, the kinetic
energy, and potential energy are
respectively:
A. \( 9.8 e V,-4.9 e V \)
в. \( 4.9 e V,-9.8 e V \)
c. \( 4.9 e V,-4.9 e V \)
D. \( 9.8 e V,-9.8 e V \)


The \( E_{\text {cell}} \) for a given cell is 1.2346 and
\( 1.2340 V \) at \( 300 \mathrm{K} \) and \( 310 \mathrm{K} \)
respectively. Calculate the change in
entropy during the cell reaction if the redox change involves three electrons.
A. \( -17.37 \mathrm{JK}^{-1} \)
B. \( +17.37 J K^{-1} \)
c. \( 173.7 J K^{-1} \)
D. \( 5.79 J K^{-1} \)


Which of the following on hydrolysis gives sulfuric acid?
A. sulfur trioxide
B. sulfur dioxide
c. sulfur oxide
D. none of above


Which element has twice as many
electrons in its second shell as
compared to its first shell?
A. Calcium
B. Nitrogen
c. oxygen
D. carbon


Powder is a lubricant
A. True
B. False
c. None
D. Can't say


Find the circumference of the
semicircle whose diameter is 4 cm.
A. \( 3.46 \mathrm{cm} \)
B . \( 5.89 \mathrm{cm} \)
\( \mathbf{c} \cdot 6.28 \mathrm{cm} \)
D. \( 10.28 \mathrm{cm} \)


In above shown figure, a point charge \( +\mathrm{Q} \) is fixed in position and five points are near the charge. An electric field is created by a point charge, then find out the point where the magnitude of the electric field would be least :
\( A \)
B. B
\( c \cdot c \)
\( D \)
E.


ff \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) and \( \boldsymbol{g}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) are given by
\( \boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}| \) and \( \boldsymbol{g}(\boldsymbol{x})=[\boldsymbol{x}] \) for each \( \boldsymbol{x} \in \)
\( R, \) then
\( \{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{g}(\boldsymbol{f}(\boldsymbol{x})) \leq \boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x}))\}= \)
A \( \cdot Z \cup(-\infty, 0) \)
В \( \cdot(-\infty, 0) \)
\( c . z \)
D. \( R \)


The vapour pressure of ethanol and methanol are 44.5 mm \( H g \) and 88.7 mm \( H g \) respectively. An ideal
solution is formed at the same
temperature by mixing \( 60 g \) of ethanol with \( 40 g \) of methanol. The total vapour pressure of the solution and the mole
fraction of methanol in the vapour are respectively:
A. \( 43.46 \mathrm{mm} \) and 0.51
в. \( 66.13 \mathrm{mm} \) and 0.657
c. \( 66.15 \mathrm{mm} \) and 0.791
D. 70.59 \( m m \) and 0.657


The gravitational potential energy of an isolated system of three particles, each of mass \( m \), at the three corners of an
equilateral triangle of side \( l \) is
\( ^{\text {A }}-\frac{G m^{2}}{l} \)
в. \( -\frac{G m^{2}}{2 l} \)
c. \( -\frac{2 G m^{2}}{l} \)
D. \( -\frac{3 G m^{2}}{l} \)


The thylakoids occur inside
A. Mitochondria
B. Chloroplast
C . Golgi apparatus
D. Endoplasmic reticulum


Find the point of intersection of the
lines represented by \( 3 x-2 y=6 \) and
the y-axis.


Dissolution of a non-volatile solute into
a liquid leads to the-
A. Decrease of entropy.
B. Increase in tendency of the liquid to freeze
c. Increase in tendency to pass into the vapour phase.
D. Decrease in tendency of the liquid to freeze


During calcination:
A. carbonate ores are changed into oixdes
B. oxide ores are changed into carbonates
C. carbonate ores are changed into sulhides
D. oxide ores are changed into sulphides


Which metal(s) can be used to produce electrons by the photoelectric effect from given source of light?
A. Barium only
B. Barium or lithium
c. Lithium, tantalum or tungsten
D. Tungsten or tantalum


The current in an AC circuit is
represented by \( i=5 \sin \left(300 t-\frac{\pi}{4}\right) \)
where, t is in seconds and current is in amperes. Then, the frequency of AC is
\( A \cdot 50 \mathrm{Hz} \)
B. 47.75 Hz
\( c \cdot 30 \) Нz
D. 25 Hz


Number of hydroxy groups present in phosphoric acid :
A.
B. 2
\( c \cdot 3 \)
\( D \)


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


A submarine that is not moving sends out a sonar sound wave travelling at \( 200 \mathrm{m} / \mathrm{s}, \) which reflects off a boat back
to the submarine. The sonar crew
detects the reflected wave 8 s after it
was send out. how far away is the boat from the submarine?
A. \( 8000 m \)
в. \( 80 m \)
c. \( 800 m \)
D. \( 9000 m \)


The gas which burns with blue flame is:
A. \( C O \)
в. \( O_{2} \)
c. \( N_{2} \)
D. \( C O_{2} \)


The largest possible variance of a binomial variate is
A \( . n \)
в. \( \frac{n}{2} \)
c. \( \frac{n}{4} \)
D. \( \frac{n}{6} \)


Determine whether or not the definition
of \( * \) On \( Z^{+} \) define \( * \) by \( a * b=|a-b| \)
gives a binary operation. If the event that \( * \) is not a binary operation give justification of this.


Find \( \frac{d y}{d x} \) if \( y=\frac{x^{2}+x}{2} \)


a. By which process do green plants synthesize their food?
b. Name the factors which take part in
this process.
c. Write the chemical equation of the above process.


Which of the following xenon compounds may not be obtained by hydrolysis of xenon fluorides?
A. \( X e O_{2} F_{2} \)
в. \( X e O F_{4} \)
\( \mathbf{c} \cdot X e O_{3} \)
D. \( X e O_{4} \)


Given the linear equation \( 2 x+3 y- \)
\( 8=0, \) write another linear equation in
two variables such that geometrical representation of the pair so formed is
(i) intersecting lines
(ii) Parallel lines
(iii) coincident lines


Reaction by which Benzaldehyde cannot
be prepared is:
\( \mathbf{A} \)
in \( \mathrm{CS}_{2} \) followed by \( \mathrm{H}_{3} \mathrm{O}^{-} \)
\( B \)
in presence of Pd-BaSO
\( \mathbf{C} \)
presence of anhydrous AlCl
D.
and conc. HCl


If \( a^{2}+b^{2}=34 \) and \( a b=12 ; \) find
\( 7(a-b)^{2}-2(a+b)^{2} \)
A . 48
B. -46
c. -45
D. 46


The elements \( (z=117 \text { and } 120) \) have
not yet been discovered in which family or group would you place these elements and also give electronic
configuration in each case?


After spending \( 69 \% \) of his monthly earnings a man saves \( R s .2108 . \) Find his
monthly income.


A mixture of hydrogen and helium is prepared such that the number of wall collisions per unit time by molecules of each gas is the same. Which gas has the higher concentration?
A. Helium
B. Hydrogen
c. Both have same concentration
D. None of these


State whether the following statements are true or false.

A person can expel all the air from lungs by a forceful expiration
A. True
B. False


High molecular weight polymers consisting of monosaccharide-
repeating units (monomers).


Human being are different in their colour size etc but yet they belong to same species. Explain.


In a normal pregnant woman, the
amount of total gonadotropin activity
was assessed. The result expected was.
A. High level of circulating FSH and LH in the uterus to stimulates implantation of the embryo
B. High level of circulating HCG to stimulate endometrial thickening
C. High level of FSH and LH in uterus to Stimulate endometrical thickening
D. High level of circulating HCG to stimulate estrogen and progesterone synthesis


Which has the highest boiling point?
A. \( 0.1 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4} \)
В. \( 0.1 M C_{6} H_{12} O_{6} \)
c. \( 0.1 \mathrm{M} \) М \( g \) Са\( _{2} \)
D. \( 0.1 \mathrm{M} \) Аl \( \left(\mathrm{NO}_{3}\right)_{3} \)


Which of the following inequations
represents the shaded region?
A. \( 2 x+y \leq 4 \)
B. \( 2 x+y \geq 4 \)
c. \( x+2 y \leq 4 \)
D. \( x+2 y \geq 4 \)


The normal capacity of percolation tank
is
A. \( 7.0 \mathrm{mm} / \mathrm{day} \)
B. 7.87 mm/day
c. \( 5.87 \mathrm{mm} / \mathrm{day} \)
D. 0.87 mm/day


At a moment in a progressive wave, the phase of a particle executing \( \mathrm{SHM} \) is \( \frac{\pi}{3} \) Then the place of the particle \( 15 \mathrm{cm} \) ahead and at time \( \frac{T}{2} \) will be, if the wavelength is \( 60 \mathrm{cm} \)
A. zero
в. \( \frac{\pi}{2} \)
c. \( \frac{5 \pi}{6} \)
D. \( \frac{2 \pi}{3} \)


Choose best option about cavity for a charged metallic sphere:
A. Net field inside the cavity is zero
B. Net field inside the metal is non-zero constant
c. Potential inside the metal is constant
D. Potential outside metal is constant


Give the number of periods and groups in Modern Periodic Table.


If \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{l}\frac{20^{x}+3^{x}-6^{x}-10^{x}}{1-\cos 8 x} ; \text { for } x \neq 0 \\ \left(\frac{k}{16}\right) \log \left(\frac{10}{3}\right) \cdot \log 2 ; \text { for } x=0\end{array}\right. \)
continous at \( x=0, \) then the value of \( k \)
is
\( A \cdot \sin ^{2} 30^{\circ} \)
B. \( \log _{3}\left(\frac{1}{2}\right) \)
\[
3
\]
\( c \cdot \sqrt[3]{1} \)
D. \( \frac{\log 2^{2}}{3} \)


Temporary hardness of water is due to
the presence of the sulphates of Ca and Mg. If this is true enter 1 , if false enter 0 .


Let there be two integers such that one integer is 3 more than the other and
their product is \( 70 . \) Find the two integers.
A. 7 and 10
B. 6 and 9
c. 10 and 13
D. 12 and 14


\( \boldsymbol{x}=(-1)^{a^{1}}+(-1)^{a^{2}}+\ldots . .(-1)^{a^{1006}} \)
\( \boldsymbol{y}=(-1)^{a^{1007}}+(-1)^{a^{1008}}+\ldots+ \)
\( (-1)^{a^{2013}} \)
Then which of the following is true?
\( \mathbf{A} \cdot(-1)^{x}=1 ;(-1)^{y}=1 \)
B . \( (-1)^{x}=1 ;(-1)^{y}=-1 \)
C \( \cdot(-1)^{x}=-1 ;(-1)^{y}=1 \)
D \cdot \( (-1)^{x}=-1 ;(-1)^{y}=-1 \)


f \( \boldsymbol{P}(\boldsymbol{A} \cup \boldsymbol{B})=\mathbf{0 . 8}, \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})=\mathbf{0}, \mathbf{3} \)
\( \operatorname{then} P(\bar{A})+P(\bar{B})= \)
A . 0.3
в. 0.5
\( c .0 . \)
D. 0.9


\( \begin{array}{ll}\text { List }-1 & \text { List }-2 \\ \text { Fraction } & \text { Temperature } \\ \text { A) Heavy oil } & \text { 1) } u p t o 170^{0} C \\ \text { B) Anthracene oil } & \text { 2) } 170^{0}-230^{0} C \\ \text { C) Light oil } & \text { 3) } 230^{0}-270^{0} C \\ \text { D) Middle oil } & \text { 4) } 270^{0}-400^{0} C\end{array} \)
\( \mathbf{A} \)
\( A-2, B-4, C-3, D-1 \)
B \( . A-1, B-2, C-3, D-4 \)
\( \mathbf{c} \cdot A-3, B-1, C-4, D-2 \)
D \( . A-3, B-4, C-1, D-2 \)


Displacement time equation of a particle executing SHM is \( x=4 \) sin\omegat +3 \( \sin \left(\omega t+\frac{\pi}{3}\right) \) here \( x \) is in centimeter and
\( t \) is in seconds. The amplitude of oscillation of the particle is approximately:
A. \( 5 \mathrm{cm} \)
B. 6 \( \mathrm{cm} \) m
\( c \cdot 7 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \)


Glycolysis is the breakdown of glucose to pyruvic acid. How many molecules of pyruvic acid are formed from one
molecule of glucose?
\( A \cdot 1 \)
B . 2
\( c .3 \)
\( D .4 \)


According to laws of reflection, angle of incidence is equal to the angle of reflection. This statement:
A. holds good i rrespective of shape of the reflecting surface
B. holds good only for plane reflecting surface
c. holds good only for curved reflecting surface
D. never holds good


The decomposition of \( N H_{3} \) on finely
divided platinum follows the rate expression, Rate \( =\frac{\boldsymbol{k}_{\mathbf{1}}\left[\boldsymbol{N} \boldsymbol{H}_{3}\right]}{\mathbf{1}+\boldsymbol{k}_{2}\left[\boldsymbol{N} \boldsymbol{H}_{3}\right]} \)
It is a first order reaction when
concentration of \( \boldsymbol{N} \boldsymbol{H}_{3} \) is:
A. very low
B. very high
c. moderate
D. never


A mixture of He, Ne, Kr and Xe is cooled,
Which one of them condenses first?
A . \( x_{e} \)
B. Ne
c. \( \mathrm{kr} \)
D. не


A depletion in the water table of a place is caused by which of the following?
A. Constructing factories and houses
B. Making concrete roads and floors
c. Deforestation
D. All of these


In a double slit experiment, the separation between the slits is \( d=0.25 \) \( \mathrm{cm} \) and the distance of the screen \( \mathrm{D}= \)
\( 100 \mathrm{cm} \) from the slits, If the wavelength of light used is \( \lambda=6000 \mathrm{A} \) and \( \mathrm{I}_{0} \) is the
intensity of the central bright fringe, the intensity at a distance \( y=4 \times 10^{-5} \mathrm{m} \)
from the central maximum is
A . \( I_{0} \)
в. \( I_{0} / 2 \)
c. \( 3 I_{0} / 4 \)
D. \( I_{0} / 3 \)


Solve the differential equation:
\( \left(x^{2}-1\right) \frac{d y}{d x}+2(x+2) y=2(x+1) \)
\( \frac{y(x+1)^{3}}{x+1}=\left\{\frac{(x+1)^{2}}{2}-4(x+1)+4 \log (x+1)\right\}+c \)
\( \frac{y(x-1)^{3}}{x+1}=\left\{\frac{(x+1)^{2}}{2}-4(x+1)+4 \log (x+1)\right\}+c \)
\( \frac{y(x-1)^{3}}{x-1}=\left\{\frac{(x+1)^{2}}{2}-4(x+1)+4 \log (x+1)\right\}+c \)
D. None of these


If \( i^{2}=-1, \) then \( i^{162} \) is equal to
A. \( -i \)
B. -
\( c \cdot 0 \)
D.
\( E \)


The number of photons falling per second on a completely darkened plate
to produce a force of \( 6.62 \times 10^{-5} \mathrm{N} \) is 'n'
If the wavelength of the light falling is \( 5 \times 10^{-7} m, \) then \( n=_{-1-}---\times 10^{22} \)
\( \left(h=6.62 \times 10^{-34} J-s\right) \)
A . 1
B. 5
\( c .0 .2 \)
D. 3.3


Assertion
A beam of white light gives a spectrum on passing through a hollow prism.
Reason

Speed of light outside the prism is different from the speed of light inside
the prism.
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


Properties of substances like pressure, temperature and density, in thermodynamic coordinates are
A. path function
B. point function
c. cyclic function
D. real function


Fitness according to Darwin refers
to
A. Number of species in a community
B. Useful variation in population
C. Strength of an individual
D. Reproductive fitness of an organism


If the distance between nuclei is \( 2 x \)
\( 10^{-13}, \) the density of nuclear material
is:
(mass of neuclei \( \left.=10^{-27}\right) \)
\( \begin{array}{ll}\text { A } \cdot 3.21 \times 10^{-12} & k g / m^{3}\end{array} \)
В . \( 1.6 \times 10^{-3} \mathrm{kg} / \mathrm{m}^{3} \)
D. \( 1 \times 10^{17} \mathrm{kg} / \mathrm{m}^{3} \)


Express the following as a rational number i.e. in the form \( \frac{a}{b} ; \) where \( a, b \in I \) and \( \boldsymbol{b} \neq \mathbf{0} \)
\( \mathbf{0 . 5 6 2 5} \)
A \( \cdot \frac{9}{16} \)
в. \( \frac{9}{14} \)
c. \( \frac{9}{19} \)
D. \( \frac{9}{13} \)


\( A B C D \) a parallelogram, \( A_{1} \) and \( B_{1} \) are the midpoints of sides \( B C \) and \( C D \) respectively. If \( \boldsymbol{A} \boldsymbol{A}_{1}+\boldsymbol{A} \boldsymbol{B}_{1}=\boldsymbol{\lambda} \boldsymbol{A} \boldsymbol{C} \)
then \( \lambda \) is equal to
A \( \cdot \frac{1}{2} \)
B. 1
\( c \cdot \frac{3}{2} \)
D. 2


If
(2,4) and (10,10) are the ends of a latus - rectum of an ellipse with eccentricity \( \frac{1}{2}, \) then the length of semi major axis is
A \( \cdot \frac{20}{3} \)
в. \( \frac{15}{3} \)
c. \( \frac{40}{3} \)
D. None of these


Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: \( 2 x+ \)
\( \mathbf{3} \boldsymbol{y}=\mathbf{8}, \mathbf{2} \boldsymbol{x}=\mathbf{2}+\mathbf{3} \boldsymbol{y} \)
A \( \cdot x=2, y=\frac{3}{2} \)
в. \( x=3, y=5 \)
c. \( _{x}=\frac{5}{2}, y=1 \)
D. \( x=\frac{3}{2}, y=4 \)


The value of \( \int \frac{d x}{x\left(x^{n}+1\right)} \) is
A \( \cdot \frac{1}{n} \log \left(\frac{x^{n}}{x^{n}+1}\right)+C \)
в. \( \log \left(\frac{x^{n}+1}{x^{n}}\right)+C \)
c. \( \frac{1}{n} \log \left(\frac{x^{n}+1}{x^{n}}\right)+C \)
D. \( \log \left(\frac{x^{n}}{x^{n}+1}\right)+C \)


A cars initially at rest, 330m away from a stationary observer. It begins to move towards the observer with an
acceleration of \( 1.1 m s^{-2}, \) sounding its horn continuously. 20 s later, the driver stops sounding the horn. The velocity of sound in air is \( 330 m s^{-1} \). The observer
will hear the sound of the horn for a
duration of
A . \( 20 s \)
в. \( 21 s \)
\( \mathrm{c} \cdot 20 \frac{2}{3} s \)
D・ \( 19 \frac{1}{3} s \)


Potassium ferrocyanide is an example of
A. Complex salts
B. Normal salts
c. Double salts
D. Basic salts


Silver is monovalent and has an atomic
mass of \( 108 . \) Copper is divalent and has an atomic mass of \( 63.6 . \) The same
electric current is passed, for the same length of time through a silver
coulometer and a copper coulometer. If \( 27.0 \mathrm{g} \) of silver is deposited, then the corresponding amount if copper deposited is:
A. \( 31.80 g \)
B. 15.90 g
c. \( 7.95 \mathrm{g} \)
D. none of these


\( s=u+\frac{1}{2} a(2 t-1) ; \) make 't' the
subject of formula.
A \( t=\frac{(s-u)+a}{2 a} \)
B. \( t=\frac{2(s-u)+a}{2 a} \)
c. \( t=\frac{2(s-u)-a}{2 a} \)
D. \( t=\frac{2(s+u)+a}{2 a} \)


A triangular transverse wave is
propagating in the positive \( X \) -direction
Velocity of \( \boldsymbol{P} \) at this instant will be
B. Vertically downward
c. At rest
D. Cannot be determined


If the speed of electron in the Bohr's first
orbit of hydrogen is \( x, \) the speed in the third orbit is:
A. \( x / 9 \)
B. \( x / 3 \)
\( c .3 x \)
D. \( 9 x \)


Let \( f(x) \) is a quadratic function such that \( \boldsymbol{f}(\mathbf{0})=\mathbf{1}, \boldsymbol{f}(\mathbf{1})=\mathbf{7}, \boldsymbol{f}(-\mathbf{1})=\mathbf{1} \) and
\( \int \frac{f(x) d x}{x^{2}(x+1)^{3}} \) is a rational function
Find the value of \( \boldsymbol{f}^{\prime}(\mathbf{0}) \)
A . 3
B.
c. 2
D. 6


Two plane mirrors are inclined at an
angle by \( 120^{\circ}, \) as the figure shows. If a
ray strikes mirror \( M_{1} \$, \) at a \( 65^{\circ} \) angle
of incidence, at what angle \( \theta \) does it
leave mirror \( \boldsymbol{M}_{2} \)
\( A \cdot 35^{\circ} \)
B. \( 45^{\circ} \)
\( c \cdot 55^{\circ} \)
\( D \cdot 65^{\circ} \)


Which of the following metal occurs in native state?
A . ca
B. Au
\( c \cdot z n \)
\( D \cdot A \)


Assertion
Origin of seed habit begins in Pteridophyta.
Reason
It is suggested by heterosporous Selaginella.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct.


If \( \boldsymbol{A}=\left[\begin{array}{c}-2 \\ 4 \\ 5\end{array}\right] \) and \( B=\left[\begin{array}{lll}1 & 3 & -6\end{array}\right], \) then
verify that \( (A B)^{T}=B^{T} A^{T} \)


"KO \( _{2} \) is \( O_{2} \) absorber and \( C O_{2} \)
producer." It is also used in
submarines."
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


What is/are true statement?
This question has multiple correct options
A. lons of \( d \) -block elements are colored due to \( d-d \)
transition
B. Ions of \( f \) -block elements are colored due to \( f-f \)
transtition
\( ^{\mathbf{C}} \cdot\left[\operatorname{Sc}\left(H_{2} O\right)_{6}\right]^{3+},\left[T i\left(H_{2} O\right)_{6}\right]^{4+} \) are colored complexes.
D. \( C u^{+} \) is colorless ion.


A body starts from rest, what is the ratio of the distance travelled by the body during the 4 th and 3 rd second?
\( A \cdot \frac{7}{5} \)
B. \( \frac{5}{7} \)
\( c \cdot \frac{7}{3} \)
D. \( \frac{3}{7} \)


Nitrogen does not form pentahalides.
Give reason


How many molecules are planar among the following molecules?
\( \boldsymbol{I}_{3}^{-}, \boldsymbol{H}_{2} \boldsymbol{O}, \boldsymbol{I} \boldsymbol{C l}_{2}^{-}, \boldsymbol{C}_{2} \boldsymbol{H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{2}, \boldsymbol{H}_{3} \boldsymbol{O}^{+} \)


Aromatic amines are generally:
A. pleasant in smell.
B. toxic in nature.
C . low melting solids.
D. none of these


The arithmetic mean between two
distinct positive numbers is twice the
geometric mean between them. Find the ratio of greater to smaller.


The science that deals with the study of
life processes is known as
A. Psychology
B. Physiology
c. Biochemistry
D. Morphology


Consider the following reaction:
\( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}^{-}+\boldsymbol{y} \boldsymbol{C}_{2} \boldsymbol{O}_{4}^{2-}+\boldsymbol{z} \boldsymbol{H}^{+} \rightarrow \)
\( \boldsymbol{x} \boldsymbol{M} \boldsymbol{n}^{2+}+\mathbf{2} \boldsymbol{y} \boldsymbol{C} \boldsymbol{O}_{2}+\frac{\boldsymbol{z}}{2} \boldsymbol{H}_{2} \boldsymbol{O} . \) The values
of \( x, y \) and \( z \) in the reaction are, respectively:
A .2,5 and 16
B. 5,2 and 8
c. 5,2 and 16
D. 2,5 and 8


Solve \( \int 2 x^{3} e^{x^{2}} \)
A \( \cdot\left(x^{2} e^{x^{2}}-e^{x^{2}}\right)+C \)
B. \( \frac{1}{2}\left(x^{2} e^{x^{2}}-e^{x^{2}}\right)+C \)
C \( \cdot \frac{1}{2}\left(x^{2} e^{x^{2}}+e^{x^{2}}\right)+C \)
D \( \cdot \frac{1}{4}\left(x^{2} e^{x^{2}}+e^{x^{2}}\right)+C \)


A zener diode is rated as \( 1 W, \) if given
breakdown voltage is \( 6.2 V \) then max
current it can hold is
A \( .224 m A \)
в. \( 161 m A \)
\( \mathrm{c} .239 \mathrm{mA} \)
D. none of the above


In the circuit shown in fig., all wires
have equal resistance \( \mathrm{R}(=5 \Omega) \). The
equivalent resistance between \( A \) and \( B \) :
A \( \cdot 10 / 7 \Omega \)
B. 15/4 \( \Omega \)
\( c .7 \Omega \)
D. 3 \( \Omega \)


Find \( \cos ^{4}(\pi / 8)+\cos ^{4}(3 \pi / 8)+ \)
\( \cos ^{4}(5 \pi / 8)+\cos ^{4}(7 \pi / 8)-3 / 2 \)


State whether given statement is True or False

An alternating current cannot be used for electroplating.
A. True
B. False


Using valance bond theory, explain the type of hybridisation of the following given below:
\( \left[M n(C N)_{6}\right]^{3-},\left[C o\left(N H_{3}\right)_{6}\right]^{3+},\left[C r\left(H_{2} C\right.\right. \)


The \( p-V \) diagram of \( 2 g \) of helium gas
for a certain process \( A \rightarrow B \) is shown in
the figure. What is the heat given to the
gas during the process \( \boldsymbol{A} \rightarrow \boldsymbol{B} \) ?
\( A \cdot 4 p_{0} V_{0} \)
B. \( 6 p_{0} V_{0} \)
\( c \cdot 4.5 p_{0} V_{0} \)
\( \mathbf{D} \cdot 2 p_{0} V_{0} \)


The points (-5,12),(-2,-3),(9,-10),(6,5)
taken in order, form
A. Parallelogram
B. rectangle
c. rhombus
D. square


In a child of 15 years age, plasma calcium level is diagnosed below optimum level, which organ is malfunctioning?
A. Thyroid gland
B. Liver
c. Parathyroid
D. Posterior lobe of pituitary


The measurements (in \( \mathrm{mm} \) ) of the
diameters of the heads of the screws are given below. Calculate the mean
diameter of the head of the screws.
\( \begin{array}{ll}36- & 39- \\ 38 & 41\end{array} \) \( \begin{array}{ll}33- & 3 \\ 35 & 3\end{array} \) \( \begin{array}{ll}\text { Diameter } & \text { 3. } \\ \text { (in mm) } & \text { 3) }\end{array} \)
Number of 3
screws \( \left(f_{1}\right) \)


Find the area of four walls of a room
having length, breadth and height as 8 \( \mathrm{m}, 5 \mathrm{m} \) and \( 3 \mathrm{m} \) respectively. Find the cost of white-washing the walls at the rate of Rs. \( 15 / m^{2} \)


Assertion: A combination of two simple
harmonic motions with arbitrary amplitudes and phases is not necessarily periodic. Reason: A periodic motion can always be expressed as a sum of infinite number of harmonic motions with
appropriate amplitudes.
A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are true and reason is not the correct explanation of assertion
c. If assertion is true but reason is false.
D. If both assertion and reason are false


Transition metals are often para
magnetic owing to
A. high melting point and boiling point
B. the presence of vacant orbitals
C. the presence of unpaired electrons
D. malleability and ductility


\( \frac{x}{5} \)


In which one of the following processes
\( C O_{2} \) is not released?
A. Aerobic respiration in plants
B. Aerobic respiration in animals
C. Alcoholic fermentation
D. Lactate fermentation


The total molar concentration of ions in
\( 0.47 \mathrm{M} \) solution of \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) assuming
its complete ionisation is:
A . 1.88 M
В. 0.94 М
c. 1.43 М
D. 0.47 М


If two coins are tossed, then find the
probability of the event that at the most one tail turns up.


One of the commonly used plant growth hormone in tea plantation is
A. Ethylene
B. Abscisic acid
c. zeatin
D. Indole-3-acetic acid and indole butyric acid


Let there be four articles having colours blue, red, black and white. When they are heated together and allowed to cool,
the article that cool earlier is :
A. Blue
B. Red
c. Black
D. white


The pH indicators are:
A. salts of strong acids and strong bases
B. salts of weak acids and weak bases
C. either weak acids or weak bases
D. either strong acids or strong bases


To keep a body moving with constant velocity on a frictionless surface, an external force:
A. should act continuously
B. should be a variable force
c. is not required
D. should act opposite to the direction of motion


The inner transition elements are the
elements in which last electrons enters
into:
\( A \cdot(n-1) \) d-orbitals
B. (n-2) f-orbitals
C. \( (n-1) \) d-orbitals and \( (n-1) \) f-orbitals
D. \( (n-1) \) d-orbitals and ns orbitals


Q Type your question
shown in figure are connected at one
end to a charged capacitor through a
switch \( S, \) which initially open. At the
other end, they are connected by a loose
wire. The capacitor has charge \( Q \) and
mass per unit length of the rod is \( \lambda \). The
effective resistance of the circuit after
closing the switch is \( R \). If the velocity of
each rod when the capacitor is discharged after closing the switch is \( \boldsymbol{v}=\frac{\boldsymbol{\mu}_{0} \boldsymbol{Q}^{2}}{\boldsymbol{x} \pi \boldsymbol{d} \boldsymbol{R} \boldsymbol{\lambda} \boldsymbol{l}} . \) Find \( \boldsymbol{x} \)
(Assume that the displacement of rods during the discharging time is
negligible)


Beads on string of A are seen in B which
condense to form chromosomes in \( C \)
stage of cell division.
A. A- Chromonema B- Chromatin C- Metaphase
B. A-Chromatin B- Metaphase C- Metaphase
c. A- chromonema
B-Chromosome C- Anaphase
D. A- chromonema B- Chromatid C- Anaphase


Assertion
\( (A): P(n)=n^{2}+n+41 \) is a prime
\( \forall \boldsymbol{n} \in \boldsymbol{N} \)
Reason
(R): If a number is prime then it
contains only two factors; 1 and number itself.
A. Both (A) \& (R) are individually true \& (R) is correct explanation of (A).
B. Both (A) \& (R) are individually true but (R) is not the correct (proper) explanation of (A)
c. (A)is true but (R) is false.
D. (A)is false but (R) is true


If \( \boldsymbol{A}=\int_{0}^{\pi} \frac{\cos \boldsymbol{x}}{(\boldsymbol{x}+\mathbf{2})^{2}} \boldsymbol{d} \boldsymbol{x}, \) then
\( \int_{0}^{\frac{\pi}{2}} \frac{\sin 2 x}{(x+1)} d x \) is equal to
A \( \cdot \frac{1}{2}+\frac{1}{\pi+2}-A \)
B. \( \frac{1}{\pi+2}-A \)
\( c \cdot 1+\frac{1}{\pi+2}-A \)
D. \( _{A-} \frac{1}{2}-\frac{1}{\pi+2} \)


A bag contains 10 red balls and 8 green balls. 2 balls are drawn at random one
by one with replacement. Find the probability that both the balls are green that a second year student is chosen.


Draw the graph of equation \( 3 x+2 y=6 \) Find the sum of the co-ordinates of the
point where the graph intersects the \( Y \) axis.


In which classes, the polymers are
classified on the basis of molecular
forces?


Stomatal index I is equal to
A \( \cdot \frac{s}{E-S} \)
B. \( \frac{s}{E+s} \)
\( \mathbf{c} \cdot \frac{E}{E+S} \)
D. \( \frac{E+S}{E} \)


Which is true statement about \( \boldsymbol{H}_{2} \boldsymbol{O} \) ?
A. Hardness can be removed by passing through ion exchange resin
B . Its pressure can be detected by anhydrous \( C u S O_{4} \)
c. It is amphoprotic
D. All of the above


At \( 25^{\circ} C, \) the standard oxidation
potential of \( Z n \) and \( A g \) in water are:
\( Z n(s) \rightarrow Z n^{+2}(a q)+2 e^{-}, E^{0}= \)
\( 0.76 V \)
and \( A g(s) \rightarrow A g^{+}(a q)+e^{-}, E^{0}= \)
\( -0.80 V \)
Which of the following reaction actually takes place?
A \( \cdot Z n^{2+}(a q)+2 A g(s) \rightarrow 2 A g^{+}(a q)+Z n(s) \)
B. \( Z n(s)+2 A g^{+}(a q) \rightarrow Z n^{2+}(a q)+2 A g(s) \)
C. \( Z n^{2+}(a q)+2 A g^{+}(a q) \rightarrow Z n(s)+2 A g(s) \)
D. \( Z n(s)+A g(s) \rightarrow Z n^{2+}(a q)+A g^{+}(a q) \)


The displacement-time graph for an object is given below. What results can you find out for its velocity?


In \( S \) and \( P \) -block elements the oxidation
state changes by 2 units. But in transition elements, it changes by 1 unit
of
1. Explain.


\( \ln s p^{3} d^{3} \) hybridisation, which orbitals are involved?
A \( \cdot d_{x^{2}-y^{2}}, d_{z^{2}}, d_{x y} \)
B . \( d_{x y}, d_{y z}, d_{z x} \)
c. \( d_{x^{2}-y^{2}}, d_{x y}, d_{x z} \)
D. \( d_{z^{2}}, d_{y z}, d_{z x} \)


The elements \( A, B, C, D \) and \( E \) have atomic number 9,11,17,12 and 13 respectively. Which pair of elements belongs to the same group?
A. A and B
B. B and D
c. A and \( c \)
D. D and E


If force \( F, \) acceleration \( a, \) and time \( T \)
are taken as the fundamental physical quantities, the dimensions of length on
this system of units are
\( \mathbf{A} \cdot F A T^{2} \)
в. \( F A T \)
c. \( F T \)
D. \( A T^{2} \)


Find matrix \( \boldsymbol{A} \) such that
\( \left[\begin{array}{cc}2 & -1 \\ 1 & 0 \\ -3 & 4\end{array}\right] A=\left[\begin{array}{cc}-1 & -8 \\ 1 & -2 \\ 9 & 22\end{array}\right] \)


\( \ln \) a \( \Delta A B C, \) if \( \angle B=60^{\circ}, \) prove that
\( (a+b+c)(a-b+c)=3 c a \)


\( (i)^{457} \)
\( A \cdot-1 \)
B . \( -i \)
\( \mathbf{c} \cdot i \)
D. 1


Assertion (A): All the radioactive
elements are ultimately converted into lead

Reason (R): All the elements above lead
are unstable
A. Both A and R are true and R is correct explanation of A
B. Both A and R are true and R is not correct explanation of
c. A is true but R is false
D. A is false but R is true


If the temperature is increased above
\( 35^{\circ} \mathrm{C} \)
A. Rate of decline of respiration will be earlier than of photosynthesis.
B. Rate of decline of photosynthesis will be earlier than decline of respiration.
C. Both decline simultaneously.
D. Both do not show any fixed pattern.


If \( (3, \lambda, \mu) \) is a point on the line then
\( 2 x+y+z=0=x-2 y+z-1 \) then
A \( \cdot \lambda=\frac{-8}{3}, \mu=-\frac{1}{3} \)
B. \( \lambda=\frac{-1}{3}, \mu=-\frac{8}{3} \)
c. \( \lambda=\frac{-4}{3} \mu=\frac{-14}{3} \)
D. \( \lambda=-5, \mu=-1 \)


Which among the following are
intramolecular redox reactions?
This question has multiple correct options
A. \( P C l_{5} \rightarrow P C l_{3}+C l_{2} \)
в. \( C H O-C H O+O H^{-} \rightarrow C O O^{-}-C H_{2} O H \)
c. \( 2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} \)
D. \( N H_{4} N O_{2} \longrightarrow N_{2}+2 H_{2} O \)


In a single throw of a die, the probability of getting a multiple of 3 is
A \( \cdot \frac{1}{2} \)
B. \( \frac{1}{3} \)
\( c \cdot \frac{1}{6} \)
D. \( \frac{3}{4} \)


A large sheet of uniform charge passes
through a hypothetical spherical
surface. The figure shows principle
section of situation. The electric flux
through the spherical surface is given
by
\( ^{\mathbf{A}} \cdot \frac{\pi R^{2} \sigma}{\epsilon_{0}} \)
B. \( \frac{2 \pi\left(R^{2}-x^{2}\right) \sigma}{\epsilon_{0}} \)
\( c \)
\( D \)


Calculate the pH of an aqueous solution of \( 1.0 M \) ammonium formate assuming
complete dissociation. \( \boldsymbol{p} \boldsymbol{K}_{\boldsymbol{a}} \) for formic
acid \( =3.8 \) and \( p K_{b} \) of ammonia \( =4.8 \)


In electro-chemical corrosion of metals,
the metal undergoing corrosion:
A. Becomes anode
B. Becomes cathode
c. Becomes inert
D. None is correct


Using suitable identity, evaluate \( (-32)^{3}+(18)^{3}+(14)^{3} \)


What is the common difference, if \( a_{1}= \)
100 and \( a_{2}=250 \)
A. 100
в. 150
c. 200
D. 210


If \( x_{1}, x_{2}, x_{3}, x_{4} \) are in G.P then its
common ratio is,
\( ^{\mathbf{A}} \cdot\left(\frac{a r}{c p}\right)^{\frac{1}{4}} \)
\( ^{\mathrm{B}}\left(\frac{c r}{a p}\right)^{\frac{1}{3}} \)
\( ^{c} \cdot\left(\frac{c r}{a p}\right)^{\frac{1}{2}} \)
\( ^{\mathrm{D}}\left(\frac{a p}{b q}\right)^{\frac{1}{2}} \)


If \( \int \frac{d x}{\sqrt{x}(x+9)}=f(x)+ \) constant, then
\( \boldsymbol{f}(\boldsymbol{x})= \)
A \( \cdot \frac{2}{3} \tan ^{-1} \sqrt{x} \)
B \( \cdot \frac{2}{3} \tan ^{-1}\left(\frac{\sqrt{x}}{3}\right) \)
C. \( \tan ^{-1} \sqrt{x} \)
D. \( \tan ^{-1}\left(\frac{\sqrt{x}}{3}\right) \)


Magnetic flux passing through a coil is initially \( 4 \times 10^{-4} \) Wh. It reduces to \( 10 \% \)
of its original value in 't' second. If the
e.m.f. induced is \( 0.72 \mathrm{mV} \) then 't' in
second is:
A . 0.3
B. 0.4
c. 0.5
D. 0.6


What is the reduction electrode potential (in volts) of copper electrode when \( \left[C u^{2+}\right. \)
\( =0.01 \mathrm{M} \) in a solution at \( 25^{0} \mathrm{C} \) ?
(EO of \( \left.C u^{2+} / C u \text { electrode is }+0.34\right) \)
A . 0.399
B. 0.2809
c. 0.3105
D. 0.3695


Assertion
A light ray is incident on a glass slab.
Some portion of its is reflected and portion of it is reflected and some is refracted. Refracted and reflected rays
are always perpendicular to each other.
Reason

Angle of incidence is equal to angle of
reflection.
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


Assertion
Hussain died turning blue in the body
colour.
Reason
This is due to deficiency of oxygen.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is
not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The two adjacent sides of a rectangle
\( \operatorname{are} 5 p^{2}-2 p+3 \) and \( 7 p^{2}-14 p+2 \)
find the perimeter.


Which of the following units denotes the dimensions \( M L^{2} / Q^{2}, \) where \( Q \) denotes the electric charge?
A. Weber (Wb)
в. \( W b / \mathrm{m}^{2} \)
c. Henry \( (H) \)
D. H / m \( ^{2} \)


Formation of \( N i(C O)_{4} \) and its subsequent decomposition into Ni and CO (recycled) makes basis of Mond's
process. \( N i+4 C O \stackrel{T_{1}}{\longrightarrow} N i(C O)_{4} \stackrel{T_{2}}{\longrightarrow} N i+ \)
\( 4 C O \)
\( T_{1} \) and \( T_{2} \) are:
A \( \cdot 100^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)
в. \( 50^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C} \)
c. \( 50^{\circ} \mathrm{C}, 230^{\circ} \mathrm{C} \)
D. \( 230^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C} \)


Using elementary tranormtion, find the
\[
\text { inverse of }\left[\begin{array}{ccc}
\mathbf{1} & \mathbf{3} & -\mathbf{2} \\
-\mathbf{3} & \mathbf{0} & -\mathbf{5} \\
\mathbf{2} & \mathbf{5} & \mathbf{0}
\end{array}\right]
\]


A ray of light is incident on a plane
mirror at an angle of \( 30^{0} \). what is the
angle of reflection?


A single unit membrane surrounds the
organelle
A. Nucleus
B. Mitochondrion
c. Lysosome
D. chloroplast


A rocket is moving in a gravity free space with a constant acceleration of
\( 2 m s^{-2}, \) along \( +x \) direction (see figure) The length of a chamber inside the
rocket is \( 4 \mathrm{m} \). A ball is thrown from the
left end of the chamber in \( +x \) direction with a speed of \( 0.3 m s^{-1} \) relative to the rocket. At the same time, another ball
is thrown in - \( x \) direction with a speed of
\( 0.2 m s^{-1} \) from its right end relative to the rocket. The time in seconds when
the two balls hit each other is
\( A \)
\( B .3 \)
\( c \)
\( D \)


If \( \tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2} \)
then \( x=? \)
A .
B. -
c.
D.


A charge \( q \) is to be distributed on two conducting spheres. What should be the value of the charges on the spheres so that the repulsive force between them is maximum when they are placed at a fixed distance from each other in air?
A \( \cdot \frac{q}{2} \) and \( \frac{q}{2} \)
в. \( \frac{q}{4} \) and \( \frac{3 q}{4} \)
c. \( \frac{q}{3} \) and \( \frac{2 q}{3} \)
D. \( \frac{q}{5} \) and \( \frac{4 q}{5} \)


Urea is transported through
\( A \cdot \) RBCs
B. WBCs
c. Plasma
D. Lymph


Based on equations reducible to linear
equations Solve for \( x \) and \( y: \frac{2}{x-1}+\frac{y-2}{4}= \) \( 2 ; \frac{3}{2(x-1)}+\frac{2(y-2)}{5}=\frac{47}{20} \)
A \( . x=3, y=6 \)
в. \( x=1, y=5 \)
c. \( x=2, y=-7 \)
D. \( x=5, y=-9 \)


The common name of 2-chloro-2-
methylpropane is:
A. tert-butyl chloride
B. sec-butyl bromide
c. both A and B
D. none of these


\( \underset{(w h i t e)}{P_{4}}+S O C I_{2}-P C I_{3}+S O_{2}+^{\prime} x^{\prime} \)
identify the 'x'


If a full wave rectifier circuit is
operating from \( 50 H z \) mains, the
fundamental frequency in the ripple will
be
\( \mathbf{A} \cdot 25 H z \)
B. \( 50 \mathrm{Hz} \)
c. \( 70.7 \mathrm{Hz} \)
D. \( 100 H z \)


The number of vertices in a cube is
\( A \cdot 6 \)
B. 10
\( c \cdot 8 \)
D. 12


The antioxidant which is used to
prevent rancidity in foods is:
A. butylated hydroxyl anisole
B. sodium hydroxide
c. sodium carbonate
D. methylated hydroxyl anisole


Assertion
A rise in \( \mathrm{PCO}_{2}, \mathrm{H}+ \) ions and temperature
shifts the \( \mathrm{Hb} \mathrm{O}_{2} \) dissociation curve to
right.
Reason
A rise in \( \mathrm{PCO}_{2} \) or fall in pH decreases oxygen affinity for haemoglobin.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The formation of an optically active compound from a chiral molecule is called:
A. asymmetric synthesis
B. resolution
c. walden inversion
D. epimerisation


A hollow cylinder of mass \( M \) and radius
\( \boldsymbol{R} \) is pulled by a horizontal force \( \boldsymbol{F} \) acting at its centre of mass on a horizontal surface where the coefficient
of friction is \( \mu \)
If hollow cylinder is performing pure rolling then frictional force \( f \) will be :
A. \( F \)
в. \( \frac{F}{2} \)
c. \( \frac{F}{3} \)
D. \( 2 F \)


\( \ln \) a triad of \( A, B, C \) elements if the
atomic masses of \( A \) and \( C \) respectively
are 100 and \( 200, \) then the atomic mass
of \( B \) is:
A . 300
в. 175
c. 125
D. 150


If \( \boldsymbol{x}^{2}+\boldsymbol{y}^{2}=\boldsymbol{2} \) and \( \boldsymbol{y}_{2}=\boldsymbol{A} \boldsymbol{y}^{-3} \) then \( \mathbf{A}= \)
A . -2
B. -
\( c \cdot 0 \)
\( D \)


The number of \( d \) -orbitals involved in
the formation of \( \boldsymbol{P} \boldsymbol{C l}_{5} \)


Somewater at \( 0^{0} C \) is placed in a large
insulated vessel. The water vapour formed is pumped out continuously.The fraction of water that will ultimately
freeze is \( \frac{7}{8} . \) If the latent heat of vaporization is \( x \) times the latent heat
of fusion. Find out value of \( x \)
A. 5
B. 6
\( c \cdot 7 \)
D.


Two cars \( P \) and \( Q \) start from a point at the same time in a straight line and their positions are represented by \( \boldsymbol{x}_{\boldsymbol{p}}(\boldsymbol{t})=\boldsymbol{a t}+\boldsymbol{b t}^{2} \) and \( \mathbf{x}_{\mathbf{Q}}(\mathbf{t})=\mathbf{f} \mathbf{t}-\mathbf{t}^{2} \mathbf{A} \mathbf{t} \)
what time do the cars have the same
velocity?
A \( \cdot \frac{a+f}{2(1+b)} \)
B. \( \frac{f-a}{2(1+b)} \)
\( \mathbf{c} \cdot \frac{a-f}{1+b-b} \)
D. \( \frac{a+f}{2(b+1)} \)


Total number of covalent bonds in a
white phosphorous molecule is:
A.
B. 4
\( c \cdot 3 \)
D.


If \( A \) be any \( m \times n \) matrix and both \( A B \)
and BA are defined prove that B should
be \( \boldsymbol{m} \times \boldsymbol{n} \) matrix


A steel girder can bear a load of 20 tons. If the thickness of girder is double, then for the same depression it can bear a load of :
A. 40 ton
B. 80 ton
\( c . \) 160 ton
\( D \cdot 5 \) ton


Zeolite used to soften hardness of water
is, hydrated:
A. Potassium aluminium borate
B. Sodium aluminium silicate
c. Calcium aluminium borate
D. zinc aluminium borate


Find the values of \( x \), if \( \left|\begin{array}{cc}\boldsymbol{x}+\mathbf{1} & \boldsymbol{x}-\mathbf{1} \\ \boldsymbol{x}-\mathbf{3} & \boldsymbol{x}+\mathbf{2}\end{array}\right|=\left|\begin{array}{cc}\mathbf{4} & \mathbf{- 1} \\ \mathbf{1} & \mathbf{3}\end{array}\right| \)


attometer is \( -\ldots- \) nanometer.
A \( \cdot 10^{-9} \)
B. \( 10^{-8} \)
\( \mathrm{c} \cdot 10^{-7} \)
D. \( 10^{9} \)


The non-zero vectors \( \bar{a}, \bar{b} \) and \( \bar{c} \) are related \( \bar{a}=8 \bar{b} \) and \( \bar{c}=-7 \bar{b} . \) Then the
angle between \( \bar{a} \) and \( \bar{c} \) is -
A . 0
в.
c. \( \frac{\pi}{2} \)
D. \( \pi \)


Function of ear bones is to
A. stabilize the ear
B. maintain the pressure
C. magnify the force of vibration
D. do none of these


A relation \( R \) is defined on the set \( Z \) of
integers as follows: \( \mathrm{R}=(x, y) \in \boldsymbol{R}: x^{2}+ \)
\( y^{2}=25 . \) Express \( R \) and \( R^{-1} \) as the sets
of ordered pairs and hence find their
respective domains
\( \mathbf{A} \cdot \mathbf{0} \)
B. Domain of \( R=\{0,\pm 3\}= \) domain of \( R^{-1} \).
C. Domain of \( R=\{0,\pm 3,\pm 4\}= \) domain of \( R^{-1} \)
D. Domain of \( R=\{0,\pm 3,\pm 4,\pm 5\}= \) domain of \( R^{-1} \)


Determine the domain and range of the relation R defined by \( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{x}+\mathbf{5}) \)
\( \boldsymbol{x} \in\{\mathbf{0}, \mathbf{1}, \mathbf{2}, \mathbf{3}, \mathbf{4}, \mathbf{5}\}\} \)


The correct order of acidity of the alcohols is ?
\( \mathbf{A} \cdot 1^{0}>11^{0}>111^{\mathbf{0}} \)
В. \( 111^{0}>11^{0}>1^{0} \)
C. \( 1^{0}>111^{0}>11^{0} \)
D. \( 11>111>1 \)


The compound, which is soluble in
water but does not impede the oxygen
transportation, is
A . NO
в. \( S O_{2} \)
\( c \cdot c o \)
D. \( S O_{3} \)


Explain the following reaction:
(a) Sandmeyer reaction
(b) Wurtz's Fitting reaction


The foot of an elephant has an area of
\( 275 c m^{2} . \) If the mass of elephant is 2200
kg, find the pressure exerted by the elephant on the ground. \( \left(g=10 m s^{-2}\right) \) If your answers \( x \) find the value of \( \frac{x}{10^{5}} \)


Centre of autonomic nervous system is located in
A. Hypothalamus
c. Cerebellum
D. Both A and B


The area of the region bounded by the
\( \operatorname{lines} y=2 x+1, y=3 x+1 \) and \( x=4 \)
is
A. 16 sq.unit
в. \( \frac{121}{3} \) sq.unit
c. \( \frac{121}{6} \) sq.unit
D. 8 sq.unit


\( \sin 85^{\circ}-\sin 35^{\circ}-\cos 65^{\circ}= \)
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. 3


Two plano-concave lenses of glass of refractive index 1.5 have radii of
curvatures \( 20 \mathrm{cm}, 30 \mathrm{cm} . \) They are placed in contact with curved surface towards each other and the space between them is filled with a liquid of
refractive index \( 4 / 3 . \) The focal length of
the system is :
\( \mathbf{A} \cdot 48 \mathrm{cm} \)
в. \( 72 \mathrm{cm} \)
\( \mathbf{c} \cdot 12 c m \)
D. \( 24 c m \)


Show that no triangle has two sides each shorter than its corresponding altitude (from the opposite vertex).


Name the type of lens used to correct
this defect.


Transition state structure of the
substate formed during an enzymatic reaction is
A. Transient but stable
B. Permanent but unstable
c. Transient and unstable
D. Permanent and stable


The graph represents the motion of a solider during a training exercise. What is the solider's average velocity during
time interval from 10 to 20 seconds.
A. \( 2.0 \mathrm{m} / \mathrm{s} \)
B. \( 2.0 \mathrm{cm} / \mathrm{s} \)
\( c \cdot 0 m / s \)
D. \( 10 \mathrm{cm} / \mathrm{s} \)
E. \( 10 \mathrm{m} / \mathrm{s} \)


n' moles of an ideal gas undergoes a
process \( A \rightarrow B \) as shown in figure. The
maximum temperature of the gas
during the process will be :
A \( \cdot \frac{9 P_{0} V_{0}}{n R} \)
в. \( \frac{9 P_{0} V_{0}}{4 n R} \)
c. \( \frac{3 P_{0} V_{0}}{2 n R} \)
D. \( \frac{9 P_{0} V_{0}}{2 n R} \)


A segment of DNA contains 1200
nucleotides, of which 200 have adenine
base. How many cytosine bases are present in this segment of DNA?
A . 100
B. 200
\( c \cdot 400 \)
D. 800


In vehicles, catalytic converters are
used
A. To increase mileage of vehicles
B. To convert \( C O_{2} \) into carbonates
C. To increase the efficiency of lead mixed petrol
D. To convert \( C O \) to \( C O_{2} \)


\( \mathrm{n} \triangle \boldsymbol{A B C}, \sum\left(\frac{\sin ^{2} \boldsymbol{A}+\sin \boldsymbol{A}+\mathbf{1}}{\sin \boldsymbol{A}}\right) \) is
always greater than
\( A \cdot 9 \)
B. 3
c. 27
D. None of these


Statement 1: \( M g O \) has a high melting
point. Statement 2: Highly charged ions result in strong ionic forces and high lattice energies.
A. Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation of Statement1
B. Both the Statement 1 and Statement 2 are correct, but 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


The incidence of occupational disease in an industry is such that the workers have a \( 20 \% \) chance of suffering from it. The probability that out of 6 workers chosen at random, not even one will
suffer from that disease is
\( \mathbf{A} \cdot\left(\frac{1}{5}\right)^{6} \)
B. \( \left(\frac{4}{5}\right)^{6} \)
\( ^{\mathbf{c}} \cdot_{1}^{6} C\left(\frac{1}{5}\right)^{5}\left(\frac{4}{5}\right)^{1} \)
\( ^{\mathrm{D} \cdot}_{1}^{6} C\left(\frac{1}{5}\right)^{1}\left(\frac{4}{5}\right)^{5} \)


Factorize the following expression \( a^{3}+125 \)
A \( \cdot(a+5)\left(a^{2}-5 a+25\right) \)
B . \( (a+5)\left(a^{2}+5 a+25\right) \)
c. \( (a+5)\left(a^{2}-5 a-25\right) \)
D. None of these


The angle between incident ray and
normal is \( 30^{\circ}, \) then the angle of
incidence will be
A \( .60^{\circ} \)
B. \( 30^{\circ} \)
\( c .90^{\circ} \)
D. 150


A thin metal disc of radius \( 25 \mathrm{cm} \) and
mass \( 2 \mathrm{kg} \) starts from rest and rolls
down on an inclined plane. If its
rotational kinetic energy is \( 8 J \) at the foot of the inclined plane, then the linear velocity of centre of mass of disc is :
A. \( 2 \mathrm{m} / \mathrm{s} \)
в. \( 4 \mathrm{m} / \mathrm{s} \)
c. \( 6 m / s \)
D. \( 8 m / s \)


A particle covers \( 10 m \) in first \( 5 s \) and
10 \( m \) in next \( 3 s \). Assuming constant acceleration. Find initial speed,
acceleration and distance covered in
next \( 2 s \)


How many significant figures are in the measurement 8.9900 grams?
A. 3
B. 4
\( c \cdot 5 \)
D.


The first successfully cloned mammal that gained world-wide publicity was
A. Molly, a sheep
B. Polly, a sheep
c. chance, a bull
D. Dolly, a sheep


\( \frac{1}{10} \) of a rod is coloured red, \( \frac{1}{20} \) orange \( \frac{1}{30} \) yellow, \( \frac{1}{40} \) green, \( \frac{1}{50} \) blue, \( \frac{1}{60} \) black
and the rest are violet. If the lenght of the violet portion is \( 12.08 \mathrm{m} \), then what
is the lenght of the rod?
A. 16 m
B. 18 m
c. \( 20 \mathrm{m} \)
D. 30


If the two lines \( x+(a-1) y=1 \) and
\( \mathbf{2} \boldsymbol{x}+\boldsymbol{a}^{2} \boldsymbol{y}=\mathbf{1}(\boldsymbol{a} \in \boldsymbol{R}-\{\mathbf{0}, \mathbf{1}\}) \) are
perpendicular, then the distance of their point of intersection from the origin is:
A \( \cdot \frac{2}{5} \)
B. \( \frac{2}{\sqrt{5}} \)
c. \( \frac{\sqrt{2}}{5} \)
D. \( \sqrt{\frac{2}{5}} \)


The plants absorbs air for respiration from
A. Air spaces in the soil
B. Stomata in leaves
c. ovary
D. None of the above


Thermal decomposition of a compound is of first order. If \( 50 \% \) sample of the compound is decomposed in 120
minute, how long will it take for \( 90 \% \) of the compound to decompose?


A jar contains 30 mL of glycerine (whose mass is37.8 \( g \) ) and 60 mL of corn syrup (whose mass is \( 82.8 \mathrm{g} \) ). Which liquid is on top? Show your work, and explain your
answer.
A. glycerine
B. syrup
\( c . \) a and \( b \)
D. none of these


The r.m.s current in an ac circuit is \( 1 A \)
If the watt less current be \( \sqrt{3} A \), Then
what is the power factor


Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is \( 2 \mathrm{cm}, \) then how much is the elongation in steel and
copper wire respectively? Given \( Y_{\text {steel}} \) \( =20 \times 10^{11} \mathrm{dyne} / \mathrm{cm}^{2}, Y_{\text {copper}}=12 \times 10^{11} \)
dyne /cm \( ^{2} \)
A . \( 1.25 \mathrm{cm} ; 0.75 \mathrm{cm} \)
B. 0.75 \( \mathrm{cm} ; 1.25 \mathrm{cm} \)
c. \( 1.15 \mathrm{cm} ; 0.85 \mathrm{cm} \)
D. \( 0.85 \mathrm{cm} ; 1.15 \mathrm{cm} \)


Position of a particle moving along \( \boldsymbol{x}- \) axis is given by \( \boldsymbol{x}=\mathbf{3}(\mathbf{2} \boldsymbol{t}-\mathbf{3})+\mathbf{4}(\mathbf{2} \boldsymbol{t}- \)
3)\( ^{2} \)
Which of the following is correct about
the particle?
A. Initial speed is \( 21 \mathrm{m} / \mathrm{s} \)
B. Initial speed is \( 18 \mathrm{m} / \mathrm{s} \)
c. Initial speed is \( 42 \mathrm{m} / \mathrm{s} \)
D. Acceleration is \( 8 \mathrm{m} / \mathrm{s} \)


Why is tartaric acid added into baking soda to get baking powder?


If velocity of light \( c, \) Planck's constant \( h \) and gravitational constant G are taken as fundamental quantities then the dimensions of length will be:
A \( \cdot \sqrt{\frac{c h}{G}} \)
в. \( \sqrt{\frac{h G}{c^{5}}} \)
c. \( \sqrt{\frac{h G}{c^{3}}} \)
D. \( \sqrt{\frac{h c^{3}}{G}} \)


Give reason :
Why the organic compound is fused
with sodium metal during detection of
nitrogen, sulphur halogens, etc?


According to Newton's third law, for
every action there is:
A. an equal and opposite reaction
B. an equal force pointing in the same direction
c. an unbalanced force
D. a reaction that is twice the magnitude
E . an unequal and unbalanced force


Explain Faradays law of induction with the help of activity.


Which of the following is not a unit of time?
A. hour
B. nano second
c. \( \mu \) second
D. light year


We are familiar with the
semiconductors Silicon and
Germanium.
a) Draw the energy bands of a \( n \) -type semiconductor.
b) The following figure represents a


\( m \) is said to be related to \( n \), if \( m \) and \( n \)
are integers and \( m-n \) is divisible by
13. Does this define an equivalence
relation?


An increase in pressure required to decreases the 100 liters volume of a
liquid by \( 0.004 \% \) in container is:
(Bulk modulus of the liquid \( = \)
\( 2100 M P a) \)
A. \( 188 k P a \)
в. \( 8.4 k P a \)
c. \( 18.8 k P a \)
D. \( 84 k P a \)


Which of the following is a primary alcohol?
A. Butan- 2 - - ०
B. 2 - Methylpropan-1- ol
c. 2 - Methylpropan - 2- ol
D. None of the above


How many terms of the series
\( -9,-6,-3, \dots \) must be taken that the
sum may be \( 66 ? \)


Which of the following is a redox
reaction?
\( \mathbf{A} \cdot C a C O_{3} \rightarrow C a O+C O_{2} \)
\( \mathbf{B} \cdot H_{2}+C l_{2} \rightarrow 2 H C l \)
\( \mathbf{c} \cdot C a O+H C l \rightarrow C a C l_{2}+H_{2} O \)
\( \mathbf{D} \cdot N a O H+H C l \rightarrow N a C l+H_{2} O \)


The potential energy of an electron in the fifth orbit of hydrogen atom is
A. 0.54 eV
B. -0.54 eV
c. 1.08 eV
D. \( -1.08 \mathrm{eV} \)


The monocotyledonous leaf shows which of the following venation?
A. Pinnate reticulate
B. Parallel
c. Palmate reticulate
D. Pinnate parallel


A child running a temperature of \( 101^{0} F \) is given an antipyrin (i.e. a medicine
that lowers fever ) which causes an
increases in the rate of evaporation of sweat from his body. If the fever is
brought down to \( 98^{\circ} F \) in 20 min, what is the average rate of extra evaporation caused, by the drug. Assume the evaporation mechanism to be the only way by which heat is lost. The mass of
the child is 30 kg. The specific heat of human body is approximately the same as that of water and latent heat of
evaporation of water at that
temperature is about 580 cal \( g^{-1} \)


Assertion
Statement \( -1: H_{2} S O_{4} \) is more viscous
than water.
Reason
Statement \( -2: \ln H_{2} S O_{4}, \) sulphur has
highest oxidation state.
A. Statement - 1 is true, Statement - 2 is true and Statement - 2 is correct explanation for Statement -
1
B. Statement - 1 is true, Statement - 2 is true and Statement - 2 is NOT the correct explanation for Statement - 1.
c. statement -1 is true, statement - 2 is false
D. statement -1 is false, Statement - 2 is true


Consider a spring that exerts the following restoring force: \( \boldsymbol{F}=-\boldsymbol{k} \boldsymbol{x} \) for
\( \boldsymbol{x}>0 \) and \( \boldsymbol{F}=-4 \boldsymbol{k} \boldsymbol{x} \) for \( \boldsymbol{x}<\mathbf{0} \)
A mass m on a frictionless surface is
attached to the spring, displaced to \( x=A \) by stretching the spring and then
releasing:
This question has multiple correct options
A \cdot The period of motion will be \( T=\frac{3}{2} \pi \sqrt{\frac{m}{k}} \)
B. The most negative value, the mass \( m \) can reach will be \( x=-\frac{A}{2} \)
c. The time taken to move from \( x=A \) to \( x=-\frac{A}{\sqrt{2}} \) straight away will be equal to \( \frac{5 \pi}{8} \sqrt{\frac{m}{k}} \)
D. The total energy of oscillations will be \( \frac{5}{2} k A^{2} \)


In a series combination of \( \mathrm{R}, \mathrm{L} \) and \( \mathrm{C} \) to an
AC source at resonance, if \( \mathrm{R}=20 \Omega \), then impedance \( Z \) of the combination is
A . \( 20 \Omega \)
B. zero \( \Omega \)
\( c \cdot 1 \Omega \)
D. 400 \( \Omega \)


If \( z_{1} \) and \( z_{2} \) two non-zero complex
number such that \( \left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right| \)
then \( \arg z_{1}-\arg z_{2} \) is equal to
\( A \cdot-p \)
В. \( p / 2 \)
c. \( -p / 2 \)
\( D \)


A focus of an ellipse is at the origin. The directrix is the line \( \mathbf{x}=\mathbf{4} \) and the eccentricity is \( \frac{1}{2} . \) Then the length of the semi major axis is
A \( \cdot \frac{5}{3} \)
B. \( \frac{8}{3} \)
\( c \cdot \frac{2}{3} \)
D. \( \frac{4}{3} \)


Let \( F \) be the set of all human beings in town in a particular time. Then check whether the relation is as equivalence
relation
\( \boldsymbol{R}=\{(\boldsymbol{x}, \boldsymbol{y}): \boldsymbol{x} \text { is mother of } \boldsymbol{y}\} \)


A body projected vertically upwards
with a velocity u return to the starting point in 4 second \( . \) If \( g=10 m^{-2} \) the
value of \( u \) is \( \$ \$(m \mid s) \$ \$:- \)
A. 5
B. 20
\( c \cdot 40 \)
D. 10


A couple produces:
A. no motion
B. linear and rotational motion
C . purely rotational motion
D. purely linear motion


The value of \( 144^{\circ} \) in circular measure is
A \( \cdot \frac{3 \pi^{c}}{4} \)
B. \( \frac{2 \pi^{c}}{3} \)
c. \( \frac{4 \pi^{c}}{5} \)
D. \( \frac{5 \pi^{c}}{6} \)


The \( _{-}-_{-}-_{-}-_{-}- \) process is used in
the extraction of copper and lead.


Which of the following statement is
incorrect?
A. Inductive effect is distance dependent and decreases drastically on increase in distance.
B. In resonating structures, the position of nuclei remains same.
C. Except major contributor, no single resonating structure can describe all the properties of a real hybrid.
D. shows inductive effect, mesomeric effect, resonance and hyperconjugation.


Find the area of the shaded region in fig, where is circular arc of radius \( 6 \mathrm{cm} \) has
been drawn with vertex \( O \) of an
equilateral triangle \( \boldsymbol{O} \boldsymbol{A} \boldsymbol{B} \) of side \( \mathbf{1 2} \boldsymbol{c m} \)
as centre


Which material is used for making:
(i) Saucepan handles
(ii) Electric plugs/switches/plugboards
A. Bakelite
B. PVC
c. Polythene
D. Polyester


A sum of an infinite sequence it is
called a
A. term
B. constant
c. series
D. sequence


Stars twinkle but planets do not twinkle
because
A. Stars emit their own light but planets receive light from the stars
B. Stars do not from a part of solar system
C. Stars from a point source of light while planets are considered as a collection of a large number of point sources of light
D. During refraction of star light from the atmosphere, star light bends more towards the normal as compared to the planets


The area of the figure bounded by the \( \operatorname{lines} x=0, x=\frac{\pi}{2}, f(x)=\sin x \) and
\( g(x)=\cos x \) is
A \( \cdot 2(\sqrt{2}-1) \)
B. \( \sqrt{3}-1 \)
c. \( 2(\sqrt{3}-1) \)
D \( \cdot 2(\sqrt{2}+1) \)


Which of the following elements are metals?
This question has multiple correct options
A. Calcium
B. Chlorine
c. Potassium
D. Sulphur


Freshly precipitated \( A l \) and \( M g \) hydroxides are stirred vigorously in a buffer solution containing \( 0.25 M \) of \( N H_{4} C l \) and \( 0.05 M \) of \( N H_{4} O H .\left[A l^{3+}\right] \)
and \( \left[M g^{2+}\right] \) in solution are:
Given:
\( \boldsymbol{K}_{b} \) for \( \boldsymbol{N} \boldsymbol{H}_{4} \boldsymbol{O} \boldsymbol{H}=\mathbf{1} . \boldsymbol{8} \times \mathbf{1 0}^{-\mathbf{5}} \)
\( \boldsymbol{K}_{s p_{A(O H)_{3}}}=\boldsymbol{6} \times \mathbf{1 0}^{-\mathbf{3 2}} \)
\( \boldsymbol{K}_{s p_{M g(O H)_{2}}}=\mathbf{8 . 9} \times \mathbf{1 0}^{-12} \)
A. \( 0.656 M \)
A
в. 0.686 М
\( c .0 .698 M \)
D. none of these


Calculate the values of the
determinants:
\( \left|\begin{array}{cccc}\mathbf{0} & \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z} \\ -\boldsymbol{x} & \boldsymbol{0} & \boldsymbol{c} & \boldsymbol{b} \\ -\boldsymbol{y} & -\boldsymbol{c} & \boldsymbol{0} & \boldsymbol{a} \\ -\boldsymbol{z} & -\boldsymbol{b} & -\boldsymbol{a} & \boldsymbol{0}\end{array}\right| \)


Find the coordinates of the focus,
equation of the directrix and the latus
rectum of
\( 2 x^{2}+3 y=0 \)


What is photoelectric effect? Explain the effect of increase
(i) frequency (ii) intensity of incident radiation on photoelectric current with suitable graphs.


Part of the gynoecium which receives the pollen is called as
A. Ovary
B. Ovule
c. style
D. stigma


Assertion
Snow is better insulator than ice.
Reason
Snow contain air packet and air is good
insulator of heat.
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


Discharge of industrial waste into the
soil causes
A. soil pollution
B. air pollution
c. water pollution
D. all of above


The total pressure when this drop formed in torr is


For a real gas (mol. mass \( =30 \) ) if
density at critical point is \( 0.40 \mathrm{g} . \mathrm{cm}^{3} \) and its \( T_{c}=\frac{2 \times 10^{5}}{821} K, \) then calcium
Vander Waal's constant \( a \) (in atm
\( \left.\boldsymbol{L}^{2} \boldsymbol{m} \boldsymbol{o l}^{-2}\right) \)


What is Photosynthesis process? Write any two affective factors and explain
their effects.


The acceleration (a) of SHM at mean
position is :
A. zero
B. \( \propto x \)
\( c \cdot \propto x^{2} \)
D. None of these


Draw the square ABCD of area 9 square
centimetres.


The number of bonds between sulphur and oxygen atoms in \( \mathrm{S}_{2} \mathrm{O}_{8}^{2-} \) and the
number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively are :
A. 8 and 6
B. 8 and 8
\( c \cdot 4 \) and 8
D. 4 and 6


Evaluate the following \( \lim _{n \rightarrow \infty}\left\{\left(1+\frac{1}{n^{2}}\right)\left(1+\frac{2^{2}}{n^{2}}\right) \dots(1+\right. \)
\( \left.\left.\frac{n^{2}}{n^{2}}\right)\right\}^{1 / n} \)
B \( \cdot 2 e^{(\pi-4) / 2} \)
\( ^{c} \cdot \frac{e^{(\pi-4) / 2}}{2} \)
\( \mathbf{D} \cdot e^{(\pi-4)} \)


This is an example of:
Plane
MIrror
A. refraction
B. total internal reflection
c. lateral inversion
D. all of the above


The compounds which have peroxo
linkage is/are
This question has multiple correct options
A \( \cdot H_{2} S_{2} O_{3} \)
в. \( H_{2} S O_{5} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7} \)
D. \( H_{2} S_{2} O_{8} \)


Recognition of ethylene as a natural
plant hormone was done by
A. Pratt-Goeschi
B. Richmond-Lang
c. Darwin
D. Haberlandt


A conducting bar with mass \( \mathrm{m} \) and
length L slides over horizontal rails that
are connected to a voltage source. The
voltage source maintains a constant
current I in the rails and bar, and a
constant, uniform, vertical magnetic field \( \vec{B} \) fills the region between the rails (as shown in fig). Find the magnitude and direction of the net force on the
conducting bar. Ignore friction, air resistance and electrical resistance :
A. ILB, to the right
B. ILB, to the left
c. \( 21 L \) B, to the right
D. 2ILB, to the left


Two fixed charges \( -2 Q \) and \( +Q \) are located at points \( (-3 a, 0) \) and \( (+3 a, 0) \) respectively, Then which of the following statement is correct?
A. Points where the electric potential due to the two charges is zero in \( x \) -y plane, lie on a circle of radius 42 and centre (5a, 0)
B. Potential is zero at \( x=a \) and \( x=9 a \)
c. Both (a) and
(b) are wrong
D. Both (a) and (b) are correct


What is the geometrical interpretation of infinity for gravitational field and gravitational potential?


Assertion: Receptor proteins show
selectivity for one chemical messenger
Over the other

Reason: Chemical messenger binds to the receptor site and inhibits is natural
function
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Both Assertion and Reason are incorrect
D. Assertion is correct but Reason is incorrect
E. Assertion is incorrect but Reason is correct
F. Answer required


The following diseases are related to smoking except:
A . emphysema
B. measles
C. high blood pressure
D. cancer of the lungs


Which of the following name is given to the hydrochloric acid by Lavoiser?
A. Mutaric acid
B. Glutaric acid
c. Tartaric acid
D. King of acids


A : The phase difference between any
two points on a wave front is zero
\( \mathrm{R}: \) From the source light, reaches every
point on the wave front in the same
time.
\( A . \) Both \( A \) and \( R \) are true, and \( R \) is correct explanation of \( A \)
B. Both A and R are true, and R is not correct explanation of \( A \)
C. A is true but R is false
D. A is false but R is true


The equation of line on which magnetic
field is zero due to system of two
perpendicular infinitely long current
carrying straight wires, is
A. \( x=y \)
B. \( x=2 y \)
c. \( x=3 y \)
D. \( 3 x=y \)


Identify the correct statement regarding
enzymes:
A. Enzymes are specific biological catalysts that can normally function at very high temperatures \( (T-1000 K) \)
B. Enzymes are normally heterogeneous catalysts that are very specific in their action.
C. Enzymes are specific biological catalysts that cannot be poisoned
D. Enzymes are specific biological catalysts that possess well defined active sites.


Calculate Moment of force \( F_{2} \) about \( O \)
A. \( 10 N m \) (clockwise)
B. \( 10 N \) m (anti clockwise)
c. \( 12 N m \) (clockwise).
D. \( 12 N m \) (anti clockwise)


Which was the first antibacterial
discovered by Paul Ehrlich?
A. Salvarsan
B. Syphilis
c. codeine
D. None of these


Molten iron from the blast furnace
contains impurities.
The process of turning the impure iron into steel involves blowing oxygen into
the molten iron and
adding calcium oxide. What are the reasons for blowing in oxygen and adding calcium oxide?
A. Carbon is removed by reaction with oxygen, reacts with acidic impurities making slag
B. Carbon is removed by reacting with oxygen, reacts with slag and so removes it
C. Iron reacts with the oxygen, reacts with acidic impurities making slag
D. Iron reacts with the oxygen, reacts with slag and so removes it


Triradiate vascular bundles can be
traced in
A. Monocot root
B. Dicot root
c. Monocot stem
D. Dicot stem


sliding along its length on a horizontal
table whose top is partly smooth and
rest roughly with friction coefficient \( \mu . \) If
the rod after moving through the
smooth part enters the rough with
velocity \( \boldsymbol{v}_{\mathbf{0}} \)
(i) What will be the magnitude of the
friction force when its \( x \) length \( (<L) \)
lies in the rough part during sliding.
(ii) Determine the minimum velocity \( \boldsymbol{v}_{\mathbf{0}} \)
with which it must enter so that it lies
completely in a rough region before
coming to rest.
(iii) If the velocity is double the minimum velocity as calculated in part
(a) then what distance does its front
end \( A \) would have travelled in a rough region before rod comes to rest.


Which of the following statement gives the correct explanation of the fact
that solubility of alkali metal fluorides increases down the group?
A. Hydration energy increases and lattice energy decreases down the group
B. Both energy decrease down the group but decrease in hydration energy is rapid.
c. Both energy decrease down the group but decrease in lattice energy is more
D. Both energy increase down the group but increase in hydration energy is rapid.


Assertion
Increase in pressure does not cause a shift in equilibrium for the formation of
\( \boldsymbol{H} \boldsymbol{I} \)
Reason
Formation of \( H I \) is an exothermic
reaction.
A. If both assertion and reason are correct and reason is the correct explaination of the assertion.
B. If both assertion and reason are correct, but reason is not the correct explanation of the assertion
c. If assertion is correct, but reason is incorrect
D. If assertion is incorrect, but reason is correct


State true or false:
In a trapezium \( A B C D \) in which \( A B \) is
parallel to \( D C \) and \( A D=B C \), then
\( \angle A D C=\angle B C D \)
A. True
B. False


According to Bohr's model of hydrogen atom, relation between principal quantum number n and radius of stable orbit is
\( \mathbf{A} \cdot r \propto \frac{1}{n} \)
B . \( r \propto n \)
\( c \cdot r \propto \frac{1}{n^{2}} \)
D \( \cdot r \propto n^{2} \)


A farmer divided his aquare - shaped
land into three parts, as shown.he gave
two parts to mukesh and the third part to naresh. how much land did each get?


Mass of Jupiter is ............ times that of
Earth
A . 318
B. 195
\( c \cdot 95 \)
D. 0.8


Aman sold an article to Ramesh at a
loss of \( 6 \% \). Ramesh sold it to Manish at
a gain of \( 4 \% \). If Aman's original price
was \( 252.50, \) what was Manish's CP?


Which of the following represents the electronic configuration of d-block
elements?
A \( \cdot(n-1) s^{2} n d^{1-10} \)
B . \( (n-1) d^{1-10} n s^{1-2} \)
C \( \cdot(n-1) s^{2} p^{6} n s^{1} \)
D. \( n s^{2} p^{2} d^{1} \)


\( \boldsymbol{S} \boldsymbol{c}^{\boldsymbol{3}+} \) is colorless.
If the given statement is true enter 1
else enter 0


Charge can neither be \( \ldots \) nor
A. Created, Destroyed
B. Positive, Negative
c. Negative, Positive
D. None of the above


Find the smallest number by which 135
must be divided, so that the quotient is
a perfect cube
A . 3
B. 5
\( c .9 \)
D. 15


\( \left|\begin{array}{ccc}\mathbf{1} & \boldsymbol{a} & \boldsymbol{a}^{2}-\boldsymbol{b} \boldsymbol{c} \\ \mathbf{1} & \boldsymbol{b} & \boldsymbol{b}^{2}-\boldsymbol{c} \boldsymbol{a} \\ \mathbf{1} & \boldsymbol{c} & \boldsymbol{c}^{2}-\boldsymbol{a} \boldsymbol{b}\end{array}\right|=? \)
\( \mathbf{A} \cdot \mathbf{5} \)
B. abc
\( c \cdot 1 \)
\( D \)


Solve:
\( \left(\sqrt{3}+\tan 1^{0}\right) \)


Evaluate the definite integral \( \int_{0}^{\frac{\pi}{2}} \cos 2 x d x \)


If \( \boldsymbol{f}(\boldsymbol{x})=\left[\mathbf{9}^{x}-\mathbf{3}^{x}+\mathbf{1}\right], \boldsymbol{x} \in(-\infty, \mathbf{1}) \)
then number of integers in the range of
\( f(x) \) is (where [.] denotes greatest integer function)


On reaction with chlorine in sunlight, sulphur dioxide gives:
A. addition reaction
B. displacement reaction
c. substitution reaction
D. all of these


What is diazotisation?


\( \mathbf{A} \)
is a region around a magnet where magnetic lines of force
act.


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C l} \stackrel{\text {alc.KOH}}{\longrightarrow} \)
\( \frac{B r_{2} / C C l_{4}}{Z n / a l c o h o l i c} C \)
\( C \) is:
A. acetylene
B. ethylene
c. ethane
D. methane


The area of regular hexagon if its side is
\( 4 c m \)
A \( .24 \sqrt{3} \)
B. \( 4 \sqrt{3} \)
\( c \cdot 5 \sqrt{3} \)
D. \( 2 \sqrt{3} \)


A radioactive substance \( X \) decays into
another radioactive substance \( Y \)

Initially only \( X \) was present, \( \lambda x \) and \( \lambda y \)
are the disintegration constants of \( \boldsymbol{X} \)
and \( Y . N_{x} \) and \( N_{y} \) are the number of
nuclei of \( X \) and \( Y \) at any time \( t \)

Number of nuclei \( N_{y} \) will be maximum
when
A \( \cdot \frac{N_{y}}{N_{x}-N_{y}}=\frac{\lambda_{y}}{\lambda_{x}-\lambda_{y}} \)
В. \( \frac{N_{x}}{N_{x}-N_{y}}=\frac{\lambda_{x}}{\lambda_{x}-\lambda_{y}} \)
\( c \cdot \frac{\lambda_{y}}{N_{y}}=\frac{\lambda_{x}}{N_{x}} \)
\( \mathbf{D} \cdot \lambda_{y} N_{y}=\lambda_{x} N_{x} \)


If \( \boldsymbol{D}_{\boldsymbol{r}}=\left|\begin{array}{ccc}\boldsymbol{r} & \boldsymbol{x} & \frac{\boldsymbol{n}(\boldsymbol{n}+\mathbf{1})}{\mathbf{2}} \mid \\ \boldsymbol{2 r}-\boldsymbol{1} & \boldsymbol{y} & \boldsymbol{n}^{2} \\ \boldsymbol{3 r}-\boldsymbol{2} & \boldsymbol{z} & \frac{\boldsymbol{n}(\boldsymbol{3} \boldsymbol{n}-\mathbf{1})}{\mathbf{2}}\end{array}\right|, \) then
\( \sum_{r=1}^{n} D_{r} \) is equal to
A \( \cdot \frac{1}{6} n(n+1)(2 n+1) \)
B. \( \frac{1}{4} n^{2}(n+1)^{2} \)
\( c \cdot 0 \)
D. none of these


A semicircular wire of radius \( \boldsymbol{R} \) is
rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field
of strength \( B \). The induced emf between
the ends is
\( \mathbf{A} \cdot B \omega R^{2} / 2 \)
в. \( 2 B \omega R^{2} \)
C. is variable
D. none of these


An alkyl halide reacts with alcoholic ammonia in a sealed tube, the product formed will be
A . a primary amine
B. a secondary amine
c. a tertiary amine
D. All of the above


Equal volumes of two immiscible
liquids of densities \( \rho \) and \( 2 \rho \) are filled in
a vessel as shown in figure. Two small holes are punched at depth h/2 and 3h/2 from the surface of lighter liquid. If
\( V_{1} \) and \( V_{2} \) are the velocities of a flux at
these two holes, then \( V_{1} / V_{2} \) is :
\( A \)
B. \( \frac{1}{2} \)
\( c \cdot 1 \)
\( \overline{4} \)
D. \( \frac{1}{\sqrt{2}} \)


What is the average translational kinetic energy of a molecule of an ideal
gas at temperature of \( 27^{\circ} \mathrm{C} \)


An electron and a proton have the same De Broglie wavelength. Then the kinetic energy of the electron is:
A. zero
B. Infinity
c. Equal kinetic energy of proton
D. Greater than the kinetic energy of proton


If \( \bar{a}=4 \bar{i}+6 \bar{j} \) and \( \bar{b}=3 \bar{j}+4 \bar{k}, \) then the
vector form of the component of \( \bar{a} \) along \( \bar{b} \) is
A \( \cdot \frac{18(3 \bar{j}+4 \bar{k})}{10 \sqrt{3}} \)
B. \( \frac{18(3 \bar{j}+4 \bar{k})}{25} \)
c. \( \frac{18(3 \bar{j}+4 \bar{k})}{\sqrt{13}} \)
D. \( \frac{(3 \bar{j}+4 \bar{k})}{25} \)


Consider the following statements about electroplating:
I. Electroplating is the coating of metal objects with a thin layer of a different
metal.
II. Electroplating makes objects look more attractive and protects them from corrosion and rusting.
III. Electroplating forms and envelops around the object to protect them from magnetism. Which of the above statements is true?
A. Only statement I
c. Statements land II
D. Statements II and III
E. All of the above statements


Two coils \( A \) and \( B \) have mutual
inductance \( 2 \times 10^{-2} \) henry. If the
current in the primary is \( i= \)
\( 5 \sin (10 \pi t) \) then the maximum value of
e.m.f. induced in coil \( B \) is
\( \mathbf{A} \cdot \pi \) volt
в. \( \frac{\pi}{2} \) volt
c. \( \frac{\pi}{3} \) volt
D. \( \frac{\pi}{4} \) volt


The chemical properties of the elements of matter have been found to repeat is regular patterns. This pattern can be
seen in the arrangement of atoms in the:
A. nutrition table
B. calculus table
c. periodic table
D. chemical table


\( \mathrm{Zn}(30): 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} \)
How to find valency of zinc by electronic configuration?


There are six plates of equal are \( A \) and
separation between the plates is
\( d(d<<A) \) are arranged as shown in
figure. The equivalent capacitance between points 2 and \( 5, \) is \( \alpha \frac{\varepsilon_{0} A}{d} . \) Then
find the value of \( \boldsymbol{\alpha} \)


In absence of friction
A. our shoes will remain intact
B. we will not be able to walk
C. we will be able to slide smoothly
D. all the above will happen


Soft soaps are:
A. sodium salts of fatty acids
B. potassium salts of fatty acids, containing excess of free alkali
C. potassium salts of fatty acids, containing no free alkali
D. calcium salts of fatty acids


The AP whose first term is 10 and
common difference is 3 is
B. \( 5,7,9,11, \ldots \)
c. \( 8,12,16,20, \dots \)
D. All the above


The first step in the hydrometallurgical
process is
A. Filteration
B. Electrolysis
c. Reduction
D. Leaching


Which of the following forms a white precipitate when added to a solution of
NaCl?
A \( \cdot N_{2} \)
в. \( K I \)
c. \( C C l_{4} \)
D. \( A g N O_{3} \)
ह. \( C a C O_{3} \)


\( 6.24 g \) of ethanol are vaporized by
supplying \( 5.89 k j \) of heat energy. What is enthalpy of vaporisation of ethanol?


A black and a red die are rolled together. Find the conditional probability of
obtaining the sum 8 , given that the red die resulted in a number less than 4


Assertion
Every vibrating body is a source of
Sound
Reason
All sounds are audible
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


Polymer used in bullet proof glass is:
A. Iexan
в. РММА
c. nomex
D. kevlar


Rainbow is formed due to which of the
following?
A. By dispersion of sunlight through water droplets present in the atmosphere
B. By scattering of sunlight through water droplets present in the atmosphere
C. By reflection of sunlight through water droplets present in the atmosphere
D. None of the above


Which of the given element will form a
covalent compound with \( \boldsymbol{O}: \boldsymbol{K} \boldsymbol{o} \boldsymbol{r} \boldsymbol{N} \)
A . \( N \)
в. \( K \)
c. Both
D. No one


The initial velocity of a particle is \( u(\mathrm{at} \)
\( t=0 \) ) and the acceleration a is given by
\( \alpha t^{3 / 2} . \) Which of the following relations is valid?
A \( \cdot v=u+\alpha t^{3 / 2} \)
B. \( v=u+\frac{3 \alpha t^{3}}{2} \)
c. \( v=u+\frac{2}{5} \alpha t^{5 / 2} \)
D. \( v=u+\alpha t^{5 / 2} \)


If a manjumps out from a boat, the boat moves backward. Explain.


If \( \frac{\mathbf{3} \boldsymbol{x}+\boldsymbol{a}}{\boldsymbol{x}^{2}+\mathbf{3} \boldsymbol{x}+\mathbf{2}}=\frac{\boldsymbol{A}}{\boldsymbol{x}-\mathbf{2}}-\frac{\mathbf{1 0}}{\boldsymbol{x}-\mathbf{1}}, \) then
\( \boldsymbol{a}=\ldots \) and \( \boldsymbol{A}=\ldots \)
A \( \cdot a=7, A=13 \)
3
В. \( a=11, A=13 \)
c. \( a=13, A=7 \)


The structure given below is known as:
where \( \mathbf{R}=\langle\square\rangle-\mathrm{CH}_{2}-\mathrm{I}-\mathrm{NH}- \)
A. penicillin F
B. penicillin G
c. penicillin
D. ampicillin


Which among the following genus of the bryophyte have ecological value?
A. Funaria
B. Riccia
c. sphagnum
D. Anthoceros


If \( k \) is a scalar and \( A \) is an \( n \times n \) square
matrix, then \( |\boldsymbol{k} \boldsymbol{A}|= \)
A \( \cdot k|A|^{n} \)
в. \( k|A| \)
c \( \cdot k^{n}\left|A^{n}\right| \)
D \( \cdot k^{n}|A| \)


Count total number of significant figures in 3500
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c \cdot 3 \)
\( D \)


Exactly one right?
\( A \cdot \frac{2}{5} \)
B. \( \frac{2}{3} \)
\( c \cdot \frac{3}{5} \)
D.


In case of theory of light nature of light
match the following:
List - I List - II
a) Light is a collection of
e) Newton's theory photons
b) Light is a form of
f) Huygen's theory electromagnetic wave
g) Maxwell's
c) Light is a wave
d) Light is a stream of
h) Max planck's corpuscles theory
\( \mathbf{A} \cdot \mathrm{a}-\mathrm{h} ; \mathrm{b}-\mathrm{g} ; \mathrm{c}-\mathrm{f} ; \mathrm{d}-\mathrm{e} \)
B. \( a-e ; b-f ; c-g ; d-h \)
C. \( a-g ; b-h ; c-g ; d-f \)
D. \( a-h ; b-g ; c-e ; d-f \)


Identify the action that can cause motion of a book placed on a table.
A. Pulling
B. Pushing
c. Lifting
D. All of the above


Using vector method, find the incentre
of the triangle whose vertices are \( P(0,4,0), Q(0,0,3) \) and \( R(0,4,3) \)


If the pressure in a closed vessel is
reduced by drawing out some gas, the mean-free path of molecules:
A. is decreased
B. is increased
c. remains unchanged
D. increases or decreases according to the nature of the gas


Solve:
\( 16 a^{3}-\frac{128}{b^{3}} \)


What is the molecular formula of
Magnesium Pyrophosphate formed during Carius method for estimation of
phosphorous in organic compound?
A. \( M g_{2} P_{2} O_{7} \)
в. \( M g_{2} P_{2} O_{5} \)
\( \mathrm{c} \cdot M g_{2} P O_{4} \)
D. \( M g P_{2} O_{5} \)


Find the first four terms of an \( A P \) whose
first term is \( 3 x+y \) and common
Difference is \( \boldsymbol{x}-\boldsymbol{y} \)


Describe the construction and working
of Van de graff generator making the labelled diagram.


A following mechanism has been proposed for a reaction:
\( \mathbf{2} \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{D}+\boldsymbol{E} \)
\( \boldsymbol{A}+\boldsymbol{B} \rightarrow \boldsymbol{C}+\boldsymbol{D} \quad(\text { slow }) \)
\( \boldsymbol{A}+\boldsymbol{C} \rightarrow \boldsymbol{E} \quad(\text { fast }) \)
The rate law expression for the reaction
is:
\( \mathbf{A} \cdot \mathbf{r}=k[A]^{2}[B] \)
B. \( r=k[ \) A][B]
\( \mathbf{C} \cdot r=k[A]^{2} \)
D. \( r=k[A][C] \)


What is the correct order of thermal
stability of carbonates of alkaline earth metals?
A \( \cdot B e C O_{3}>M g C O_{3}>C a C O_{3}>S r C O_{3}>B a C O_{3} \)
в. \( B e C O_{3}<M g C O_{3}<C a C O_{3}<S r C O_{3}<B a C O_{3} \)
c. \( B e C O_{3}<M g C O_{3}>C a C O_{3}>S r C O_{3}<B a C O_{3} \)
D. \( B e C O_{3}>M g C O_{3}<C a C O_{3}<S r C O_{3}<B a C O_{3} \)


Which of the following is not a balanced
equation?
A \( \cdot C a(O H)_{2}+C O_{2} \rightarrow C a C O_{3}+H_{2} O \)
в. \( F e+C u S O_{4} \rightarrow F e S O_{4}+C u \)
c. \( K C l O_{4} \stackrel{\Delta}{\longrightarrow} K C l+2 O_{2} \)
D. \( C u+2 H N O_{3} \rightarrow C u\left(N O_{3}\right)_{2}+2 N O_{2}+H_{2} O \)


What are the products obtained upon the ozonolysis of 2 -pentene? This question has multiple correct options
A. \( C H_{3} C H_{2} C H O \)
в. \( C H_{3} C H O \)
c. \( C H_{3} \) COCH\( _{3} \)
D. \( C H_{3} C O C H_{2} C H_{3} \)


A table fan, rotating at a speed of 2400
rpm is switched off and the resulting
variation of the rpm with time is shown
in the figure. The total number of revolutions of the fan before it comes to
rest is:
A. 420
B. 280
\( c \cdot 480 \)
D. 380


If \( \boldsymbol{x}=\boldsymbol{y}(\log \boldsymbol{x} \boldsymbol{y}) \) then find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


In a series \( L C R \) circuit, the voltage across the resistance, capacitance and
inductance is \( 10 V \) each. If the
capacitance is short circuited, the voltage across the inductance will be :
A. \( 10 V \)
B. \( \frac{10}{\sqrt{2}} V \)
c. \( \frac{10}{3} V \)
D. 20 \( V \)


A straight conductor of uniform cross-
section carries a current, \( I \). If \( ^{\prime} s^{\prime} \) is the
specific charge of an electron, the momentum of all the free electrons per unit length of the conductor, due to their drift velocity only, is
A . Is
в. \( \sqrt{\frac{I}{s}} \)
c. \( \frac{1}{s} \)
\( \left(\frac{I}{s}\right)^{2} \)


A metal ball \( B_{1} \) (density \( 3.2 \mathrm{g} \mathrm{cm}^{-3} \) ) is dropped in water while another metal
ball \( B_{2} \) (density \( 6.0 \mathrm{g} \mathrm{cm}^{-3} \) ) is dropped
in a liquid of density \( 1.6 \mathrm{g} \mathrm{cm}^{-3} \). If both the balls have the same diameter and
attain the same terminal velocity, the ratio of viscosity of water to that of the liquid is:
A . 2.
B. 0.5
\( c \cdot 4.0 \)
D. indeterminate due to insufficient data


Total number of products in the given reaction: (excluding steroisomers) \( \boldsymbol{C}_{6} \boldsymbol{H}_{5} \boldsymbol{C H} \boldsymbol{O}+\boldsymbol{C H}_{3}-\boldsymbol{C H O} \frac{\boldsymbol{\Delta}}{_{\boldsymbol{O} \boldsymbol{H}}} \)
product will be:
A. one
B. two
c. three
D. four


0.1 mole of \( N_{2} O_{4}(g) \) was sealed in a
tube under one atmosphere conditions
at \( 25^{\circ} \mathrm{C} \). Calculate the number of moles
of \( N O_{2}(g) \) present, if the equilibrium
\( N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g)\left(K_{p}=0.14\right) \) is
reached after some time :-
A \( .1 .8 \times 10^{2} \)
B . \( 2.8 \times 10^{2} \)
c. 0.037
D. \( 2.8 \times 10^{-2} \)


The equilibrium constant for the
reaction, \( \boldsymbol{S n}(\boldsymbol{s})+\boldsymbol{2} \boldsymbol{H}^{+} \rightarrow \boldsymbol{S} \boldsymbol{n}^{2+}+ \)
\( \boldsymbol{H}_{2}(\boldsymbol{g}) \boldsymbol{a} \boldsymbol{t} \boldsymbol{2} \boldsymbol{5}^{\circ} \boldsymbol{C} \) is:
\( \boldsymbol{E}^{\circ}\left(\boldsymbol{S} \boldsymbol{n}^{2+} \mid \boldsymbol{S} \boldsymbol{n}\right)=\mathbf{0 . 1 4} \)
A \( .5 .5 \times 10^{4} \)
B. \( 2.3 \times 10^{2} \)
c. \( 1.1 \times 10^{2} \)
D. 1.009


(1) 1,2 -dihydroxybenzene \( (\|) 1,3- \) dihydroxybenzene (III) \( 1,4^{-} \) dihydroxybenzene (IV) Hydroxybenzene The increasing order of boiling points of above-mentioned alcohols is:
A. \( I<I I<I I I<I V \)
в. \( I<I I<I V<I I I \)
c. \( I V<I<I I<I I I \)
D. \( I V<I I<I<I I I \)


Which of the following is false?
This question has multiple correct options
\( \mathbf{A} \cdot C r^{2+}(g) \) ion has greater magnetic moment compared to \( C o^{3+}(g) \)
B. The magnitude of ionization potential of iron an-ion (monoanion) would be equal to electron gain enthalpy of iron.
C. Lanthanoids contraction is cause of lower I.P of \( P b \)
than \( S n \)
D. If successive ionization energy are \( 332,738,849,4080,4958 \text { (in } k J / m o l) \). Then this element can be of 15 th group.


Let \( n_{p} \) and \( n_{e} \) be the number of holes
and conduction electrons in an
extrinsic semiconductor. Then
A \( \cdot n_{p}>n_{e} \)
в. \( n_{p}=n_{e} \)
c. \( n_{p}<n_{e} \)
D \( \cdot n_{p} \neq n_{e} \)


In a metre bridge experiment null point is obtained at \( 40 \mathrm{cm} \) form one end of the
wire when resistance \( X \) is balanced
against another resistance Y. If \( \mathrm{X}<\mathrm{Y} \) then the new position of the null point from the same end, if one decides to
balance a resistance of \( 3 \mathrm{X} \) against \( \mathrm{Y} \) will be close to
\( \mathbf{A} \cdot 80 \mathrm{cm} \)
B. \( 75 \mathrm{cm} \)
\( c \cdot 67 \mathrm{cm} \)
D. \( 50 \mathrm{cm} \)


Suffix for sub species is
A. Phytina
B. Oideae
c. Ineae
D. None of the above


If \( x^{y}=y^{x} \) and \( x=2 y, \) then find the
value of \( x+y . \) (Assume that \( y \neq 0 \) )


When light rays enter the eye, most of the refraction occurs at the:
A. crystalline lens.
B. outer surface of the cornea
c. iris
D. pupil.


Find the principal value of:
\( \operatorname{cosec}^{-1}\left(2 \cos \frac{2 \pi}{3}\right) \)


In Coulomb's law, the constant of
proportionality K has the units
\( N m^{2} / C^{2} \) then the magnitude of \( \mathrm{K} \) in air
is :
A \( 9 \times 10^{5} \)
\( ^{5} \)
B. \( 9 \times 10^{9} \)
\( \mathrm{c} \cdot 9 \times 10^{3} \)
D. none of these


Which of the following are in inverse
proportion?
(i) The number of workers on a job and
the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop
harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.


What is the electron configuration for
manganese?
A \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} \)
B . \( [A r] 4 s^{1} \)
C \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{5} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{1} \)


The heaviest subatomic particle is :
A. neutron
B. positron
C . electron
D. proton


The wavelengths for the light of red and blue colours are roughly \( 7.8 \times 10^{-7} m \)
and \( 4.8 \times 10^{-7} m \) respectively. Which
colour has the greater speed in glass?
A. Red light
B. Violet light
c. Yellow light
D. All colors have same speed


Which of the following complex is useful in the dehydrogenation of alkanes?
\( \mathbf{A} \cdot\left[\left(P h_{3} P\right) R h C l\right. \)
B. \( \left[\left(P h_{3} P\right)_{3} R h_{2} C l\right. \)
\( \mathbf{c} \cdot\left[\left(P h_{3} P\right)_{3} R h C l\right] \)
D. \( \left[\left(P h_{3} P\right)_{3} R h C l_{2}\right] \)


The type of sex determination in honey
bee is
A. Diploidy
B. Haplo-diploidy
c. zz - zw
D. Haploidy


Zwitter ion can be formed by:
A . acetanilide
B. benzanilide
c. sulphanilic acid
D. benzene sulphonamide