\( \mathbf{f} \mathbf{\Delta}=\left|\begin{array}{lll}\boldsymbol{b}^{2}-\boldsymbol{a} \boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c} & \boldsymbol{b} \boldsymbol{c}-\boldsymbol{a} \boldsymbol{c} \\ \boldsymbol{a} \boldsymbol{b}-\boldsymbol{a}^{2} & \boldsymbol{a}-\boldsymbol{b} & \boldsymbol{b}^{2}-\boldsymbol{a} \boldsymbol{b} \\ \boldsymbol{b} \boldsymbol{c}-\boldsymbol{a} \boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a} & \boldsymbol{a} \boldsymbol{b}-\boldsymbol{a}^{2}\end{array}\right| \) then
\( \Delta \) equals
A \( \cdot(b-c)(c-a)(a-b) \)
B. \( a b c(b-c)(c-a)(a-b) \)
c. \( (a+b+c)(b-c)(c-a)(a-b) \)
D.


The ratio of the total surface area and
the lateral surface area of a right cone is 4: 3 and its height is \( 8 \mathrm{m}, \) then its base area is approx
A \( \cdot 24 m^{2} \)
B. \( 33 m^{2} \)
\( \mathbf{c} \cdot 21 m^{2} \)
D. \( 27 m^{2} \)


A rational number \( \frac{-2}{3} \)
A. Lies to the left side of 0 on the number line
B. Lies to the right side of 0 on the number line
C. It is not possible to represent on the number line
D. Cannot be determined on which side the number lies


Prove that \( 5 \sqrt{3} \) is an irrational.


Man dies when nitrous oxide is inhaled
in large quantities because it:
A. is poisonous
B. causes laughing hysteria
c. decomposes heamoglobin
D. react with organic tissues


From the top of a \( 40 \mathrm{m} \) tall multi-
storeyed building, a boy projects a stone vertically upwards with an initial velocity \( 10 \mathrm{m} s^{-2} \) such that, it eventually falls to the ground. After how long will the stone strike the ground? (Take \( g=10 \)
\( \left.m s^{-2}\right)(\text {in sec }) \)


If \( 10^{20} \) electrons are removed from a
conductor. The nature and magnitude of the charge developed on it is :
\( \mathbf{A} \cdot+16 C \)
в. \( -16 C \)
\( c \cdot+10 C \)
D. \( -10 C \)


Identify the gas evolved in the following reactions when: Potassium suphite is treated with dilute hydrochloric acid.


Which of the following reactions is not a
redox reaction?
A \( \cdot A g^{+}+C l^{-} \rightarrow A g C l \)
B. \( Z n(s)+C u^{2+}(a q .) \rightarrow Z n^{2+}(a q .)+C u(s) \)
\( \mathrm{c} \cdot 2 M g(s)+O_{2}(g) \rightarrow 2 M g O \)
D. \( F e O+C \rightarrow F e+C O \)


A particle is projected at an angle of \( 45^{\circ} \)
from \( 8 m \) before the foot of a wall,just
touches the top of the wall and falls on the ground on the opposite side at a distance \( 4 m \) from it. The height of wall is:
A \( \frac{2}{3} m \)
в. \( \frac{4}{3} m \)
c. \( \frac{8}{3} m \)
D. \( \frac{3}{4} m \)


The emergency hormone is
A. Thyroxine
B. Adrenaline
c. Insulin
D. Progesterone


Match column I with column II and
mark the appropriate choice.
Column I
(A) Pentise sugar in DNA
(i) Ascorbic acid
(B) Nucleic acid
(ii) Uracil
(C) RNA
(iii) Genetic material
(D) Vitamin
(iv) Furanose structure
\( \mathbf{A} \cdot(A) \rightarrow(i v) ;(B) \rightarrow(i i i) ;(C) \rightarrow(i i) ;(D) \rightarrow(i) \)
B. (A) \( \rightarrow \) (iii); (B) \( \rightarrow \) (ii); \( (C) \rightarrow(\text { iv ); }(D) \rightarrow \) (i)
C. \( (A) \rightarrow(\text { ii) } ;(B) \rightarrow(\text { iii) } ;(C) \rightarrow(i v) ;(D) \rightarrow(i) \)
\( D \cdot(A) \rightarrow(i) ;(B) \rightarrow(i i) ;(C) \rightarrow(i i i) ;(D) \rightarrow(i v) \)


In \( \triangle A B C, D \) is the midpoint of \( A B \) and \( E \)
is mid point of AC. If area of \( \triangle \mathrm{ADE}=11 \)
square units then area of \( \triangle \mathrm{ABC} \) is
A. 33 square units
B. 22 square units
c. 44 square units
D. None of the above


Two parallel plate air capacitors have the same separation. The plates of the first are squares of side \( 10 \mathrm{cm} . \) The
plates of the second are squares of side \( 20 \mathrm{cm} . \) The ratio of their capacitance is :
\( A \cdot 2: \)
B. 1: 2
\( c \cdot 4: 1 \)
D. 1: 4


If \( P(n) \) is the statement \( " n(n+1) \) is
even", then what is \( \boldsymbol{P}(\boldsymbol{4}) \) ?


Which of the following is not a natural
resource?
A. Minerals
B. water
c. Soil
D. Plastic


The oscillations represented by curve 1
in the graph are expressed by equation
\( x= \) Asinwt. The equation for the
oscillations represented by curve 2 is expressed as:
A. \( x=2 A \sin (\omega t-\pi / 2) \)
B. \( x=2 A \sin (\omega t+\pi / 2) \)
c. \( x=-2 \operatorname{Asin}(\omega t-\pi / 2) \)
D. \( x=\operatorname{Asin}(\omega t-\pi / 2) \)


The capacity of a parallel plate condenser is \( C . \) Its capacity when the separation between the plates is halved will be :
A . \( 4 C \)
в. \( 2 C \)
c. \( \frac{c}{2} \)
D. \( \frac{C}{4} \)


In the given figure, if area of \( \triangle A D E \) is
\( 60 \mathrm{cm}^{2} ; \) state, giving reason, the area
of \( \square A B C F \)
\( A \cdot 120 \mathrm{cm}^{2} \)
В. \( 110 \mathrm{cm}^{2} \)
\( c \cdot 100 \mathrm{cm}^{2} \)
D. \( 150 \mathrm{cm}^{2} \)


If \( \boldsymbol{f}(\boldsymbol{x})=\min \left(|\boldsymbol{x}|^{2}-\mathbf{5}|\boldsymbol{x}|, \mathbf{1}\right) \) then \( \boldsymbol{f}(\boldsymbol{x}) \)
is non differentiable at \( \lambda \) points, then
\( \lambda+13 \) equals


Above compound is hydrated maximum
at which position?
\( A \)
B. 2
\( c .3 \)
D. equal


Assertion
Isotopes of a particular element have nearly identical chemical behaviour.
Reason
They have identical electron
configuration.
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


\( D \) is any point on side \( A C \) of a \( \Delta A B C \) with \( A B=A C \) Show that \( C D<B D \)


All are extrinsic factors responsible for the development of an organism except
A. Light
B. Amount of oxygen
c. Temperature
D. Hormones


Find the principal value of:
\( \sec ^{-1}(2) \)


Which of the following is not a characteristic of the image formed by Convex lens?
A . Real
B. Erect
c. Virtual
D. None of these


Which of the following statements are
correct?
i) Ordinary ethyl alcohol is known as grain alcohol.
ii) Methylated spirit contains rectified spirit
iii) Absolute alcohol is \( 100 \% \) ethanol
iv) Rectified spirit is \( 100 \% \) ethanol.
A . ii, iii, iv
B. ii, ii i
D. All are correct


The material of which the lightning conductor is made up of is
A. Plastic
B. FRP
c. copper
D. Carbon


The frequency of a sonometer wire is \( f \) The frequency becomes f/2 when the mass producing the tension is completely immersed in water and on immersing the mass in a certain liquid, frequency become f/3. The relative
density of the liquid is
A . 1.32
B . 1.67
\( c \cdot 1.4 \)
D. 1.18


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


The ionisation constants of formic acid
and ammonium hydroxide are \( 2 \times 10^{-4} \)
and \( 2 \times 10^{-5} \) respectively. The pH of
aqueous solution of ammonium formate is :
\( A \cdot 7 \)
B. 6.
c. 11.5
D. 8


A solution is prepared by dissolving
\( 11 g \) glucose in \( 250 c m^{3} \) water at \( 30^{\circ} C \)
what is mass percent glucose in
solution. The density of water at \( 30^{\circ} \) is \( \mathbf{0 . 9 9 6} \boldsymbol{g} / \boldsymbol{c m}^{\mathbf{3}} \)


Which of the following statements is
correct according to New Cartesian
Sign Convention?
A. Focal length of a concave mirror is positive and that of a convex mirror is negative.
B. Focal length of a concave mirror is negative and that of a convex mirror is positive.
C. Image distance is always positive for a concave mirror.
D. The height of all the real and inverted images is positive


The Vertex of the parabola \( \boldsymbol{y}^{2}-\mathbf{1 0} \boldsymbol{y}+ \)
\( \boldsymbol{x}+\mathbf{2 2}=\mathbf{0} \) is.
\( A \cdot(3,4) \)
B. (3,5)
\( c \cdot(5,3) \)
D. none of these


In a rectangle \( A B C D \), diagonals intersect
at \( 0 . \) If \( \angle O A B=30^{\circ} \) find: \( \angle A C B, \angle A B O, \angle \)
\( \mathrm{COD}, \angle \mathrm{BOC} \)


In which of the following pairs of ions, the lower oxidation state in aqueous solution is more stable than the other?
\( \mathbf{A} \cdot T i^{+}, T i^{3+} \)
B. \( C u^{+}, C u^{2+} \)
c. \( C r^{+}, C r^{3+} \)
D. None of these


Differentiate \( -\frac{4 x+5 \sin x}{3 x+7 \cos x} \) w.r.t \( x \)


A capacitor, as shown in figure has
square plates of length land are inclined
at an angle \( \theta \) with one another. For small
value of \( \theta, \) capacitance is given by:
\( ^{\mathbf{A}} \cdot \frac{\epsilon_{0} l^{2}}{d}\left(1-\frac{\theta l}{2 d}\right) \)
\( ^{\mathbf{B}} \cdot \frac{\epsilon_{0} l^{2}}{2 d}\left(1-\frac{\theta l}{d}\right) \)
c. \( \frac{\epsilon_{0} l^{2}}{d}\left(1+\frac{\theta l}{d}\right) \)
D \( \cdot \frac{\epsilon_{0} l^{2}}{2 d}\left(1+\frac{\theta l}{d}\right) \)


The legal limit for human exposure to \( C O \) in the work place is 35 ppm. Assuming that the density of air is \( 1.3 g / l, \) how many grams of \( C O \) are in \( 1.0 L \) of air at the maximum allowable
concentration?
A \( \cdot 4.55 \times 10^{-5} g \)
В . \( 3.5 \times 10^{-5} g \)
c. \( 2.69 \times 10^{-5} g \)
D. \( 7.2 \times 10^{-5} g \)


Find a positive value of \( x \) for which the
given equation is satisfied:
\( \frac{y^{2}+4}{3 y^{2}+7}=\frac{1}{2} \)


Fluorobenzene \( C_{6} H_{5} F \) can be
synthesized in the laboratory:
A. by heating phenol with \( H F \) and \( K F \)
B. from aniline by diazotization followed by heating the diazonium salt with \( H B F_{4} \)
C. by direct fluorination of benzene with \( F_{2} \) gas
D. by reacting bromobenzene with \( N a F \) solution


Ammonia is dried over:
A. slaked lime
B. conc. \( H_{2} S O_{4} \)
c. quick lime
D. \( B a C l_{2} \)


In crossed cannizzaro reaction between
formaldehyde and benzaldehyde the alcohol formed is only benzyl alcohol and not methanol. Give reason.


An equilateral triangle has each of its
sides of length \( 6 \mathrm{cm} . \) If \( \left(x_{1}, y_{1}\right) ;\left(x_{2}, y_{2}\right) \)
\( \&\left(x_{3}, y_{3}\right) \) are its vertices then the value
of determinant (in nearest integer value) \( ,\left|\begin{array}{lll}\boldsymbol{x}_{1} & \boldsymbol{y}_{1} & \mathbf{1} \\ \boldsymbol{x}_{2} & \boldsymbol{y}_{2} & \mathbf{1} \\ \boldsymbol{x}_{3} & \boldsymbol{y}_{3} & \mathbf{1}\end{array}\right| \) is equal to a then
find \( \frac{\boldsymbol{a}}{\mathbf{3 1}} \)


\( 40 m L \) of \( 0.050 M N a_{2} C O_{3}+50 m L \)
of \( 0.040 M H C l \) (write the value to the
nearest integer)


State the change in the form of a
reaction
A \( \cdot \frac{234}{92} A \rightarrow_{888}^{232} B+\frac{4}{2} H e \)
\( e e \)
B \( \cdot \frac{238}{92} A \rightarrow_{90}^{234} B+_{2}^{4} H e \)
C \( \cdot \frac{238}{911} \mathrm{A} \rightarrow_{839}^{234} \mathrm{B}+_{2}^{4} \mathrm{He} \)
D \( \cdot \frac{234}{92} A \rightarrow_{992}^{234} B+_{2}^{4} H e \)


\( \lim _{x \rightarrow \pi / 2} \frac{2 x-\pi}{\cos x} \)
\( A \cdot-2 \)
B. - -
\( c \)
D.


A \( 2.5 k g \) ball is dropped onto a concrete floor. It strikes the floor with a
momentum of \( 20 k g m / s \) and bounces away from the floor with a momentum
of \( 16 k g m / s . \) What is the magnitude of
change of momentum of the ball?
A. \( 4 k g . m / s \)
в. \( 8 k g m / s \)
c. \( 32 k g m / s \)
D. \( 36 k g m / s \)
E . \( 40 \mathrm{kgm} / \mathrm{s} \)


In a square \( A B C D, \) diagonals meet at 0
Pis a point on BC such that \( O B=B P \).
\( \angle B O P=3 \angle C O P \)
State whether the above statement is
true or false.
A. True
B. False


The magnetic field due to a current carrying circular loop of radius \( 3 \mathrm{cm} \) at a point on the axis at a distance of \( 4 \mathrm{cm} \)
from the centre is \( 54 \mu \) T. What will be
its value at the centre of the loop?
A. 125 и \( T \)
в. \( 150 \mu T \)
c. \( 250 \mu T \)
D. \( 75 \mu T \)


The reaction that takes place when \( C l_{2} \)
gas is passed through conc. NaOH
solution is :
A . oxidation
B. reduction
c. displacement
D. disproportionation


The term 'Phyletic evolution' was proposed by
A . Lamarck
B. Mayer
c. Darwin
D. None of the above


In the series LCR circuit (figure), the
voltmeter and ammeter readings are:
A. \( V=100 V, I=2 A \)
B. \( V=100 V, I=5 A \)
\( \mathbf{c} . V=1000 V, I=2 A \)
D. \( V=300 V, I=1 A \)


If the focal lengths of objective and eyelens of a microscope are \( 1.2 \mathrm{cm} \) and \( 3 \mathrm{cm} \) respectively and the object is put \( 1.25 \mathrm{cm} \) away from the objective lens and the final image is formed at infinity, then magnifying power of the microscope is
A . 150
B. 200
c. 250
D. 400


In the electrolytic refining of a metal \( \mathrm{M} \) what would you take as the anode is:
A. impure metal M
B. thin strip of pure metal
c. solution of salt of the metal
D. none of these


Find AM of 3 digit even numbers
between 1 to 500
A . 200
в. 400
\( c .300 \)
D. 150


Which of the following is most favourable for vander waals
adsorption?
A. high pressure and high temperature
B. low pressure and low temperature
c. low pressure and high temperature
D. high pressure and low temperature


In the vacuum suspended system, the
brakes are applied when
A. Atmospheric pressure is applied to one side of diaphram
B. Vacuum is applied to both sides of diaphram
C. Atmospheric pressure is applied to both sides of diaphram
D. Vacuum is applied to one side of diaphram


The heat of combustion of ethanal
determined in a bomb calorimeter is
\( -670.48 K \) Cals mole\( ^{-1} \) at \( 25^{\circ} \) C.What
is \( \Delta H \) at \( 25^{\circ} C \) for the reaction:
A . \( -335.24 K \) Cals
В. -671.08 КСа\( l s \)
c. \( -670.48 K \) Cals.
D. +670.48 KCals.


A card from a pack of 52 cards is lost.
From the remaining cards of the pack,
two cards are drawn and are found to be
both diamonds. If the probability of the lost card is a diamond is \( \boldsymbol{p} \) enter \( \mathbf{1 0 0} \boldsymbol{p} \)


mRNA directs the synthesis of proteins based on the sequence of
A. Exons
B. Introns
c. codons
D. Anticodons


The source emits only one type of radiation. For each type of radiation,
\( \boldsymbol{\alpha}, \boldsymbol{\beta} \) and \( \gamma, \) state whether or not is
emitted, given reason for your answer in
each case.


Which of the following are bidentate monoanion ligands?
(1)Acetylacetonato
(2) Oxalato ion
(3) Dimethylglyoximato Select the correct answer using the
codes given below:
A. 1 only
B. 1 and 3 only
c. 3 only
D. 2 and 3 only


The amount of oxygen required by bacteria to break down the organic
matter present in a certain volume of a
sample of water, is called
A. BOD
в. АВЕ
\( c \cdot \cos \)
D. standard amount of oxygen


The pair of elements having same number of valence electrons are
This question has multiple correct options
A. \( Z n, M g \)
в. \( C l, \)
c. \( N a, C a \)
D. \( C, G e \)


Assuming the sum to be spherical body of radius \( R \) at a temperature of \( \boldsymbol{T} \boldsymbol{K} \) evaluate the total radiant power,
incident on Earth, at a distance \( r \) from
the Sun.
where \( r_{0} \) is the radius of the Earth and
\( \sigma \) is Stefan's constant.
\( ^{\text {A }} \cdot \frac{R^{2} \sigma T^{4}}{r^{2}} \)
\( ^{\text {В. }} \frac{4 \pi r_{0}^{2} R^{2} \sigma T^{4}}{r^{2}} \)
\( ^{\mathrm{c} \cdot} \frac{\pi r_{0}^{2} R^{2} \sigma T^{4}}{r^{2}} \)
D. \( \frac{r_{0}^{2} R^{2} \sigma T^{4}}{r^{2}} \)


Total \( 2 c-2 e \) and \( 3 c-2 e \) bonds in
\( B e\left(B H_{4}\right)_{2} \) are respectively:
\( A \cdot 8,4 \)
B. 4,8
\( c \cdot 4,4 \)
\( D .8,8 \)


What is the normal percentage composition of gases in the inspired air and expired air respectively?


Calculate the equailibrium constant for
the reaction:
\[
\boldsymbol{C u}_{(s)}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{(a q)}^{+} \longrightarrow \boldsymbol{C u}_{(a q)}^{2+}+\boldsymbol{2} \boldsymbol{A} \boldsymbol{g}_{(s)}
\]
Given that \( : \boldsymbol{E}_{A \boldsymbol{g}^{+} / \boldsymbol{A} \boldsymbol{g}}^{0}= \)
\[
\mathbf{0 . 8 0 V}, \quad \boldsymbol{E}_{\mathbf{C u}^{2+} / \mathbf{C u}}^{\mathbf{0}}=\mathbf{0 . 3 4} \boldsymbol{V}
\]


Which of the following non-metal is lustrous?
A. Diamond
B. lodine
c. Both \( A \) and \( B \)
D. None of the above


\( \sqrt{-3} \sqrt{-75}= \)
A . 15
в. 15
c. -15
D. - -15


The catalytic decomposition of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \)
was studied by titrating it at different
intervals with \( K M n O_{4} \) and the
following data were obtained:
\( \boldsymbol{t}(\text {seconds}) \)
\( \mathbf{0} \)
\( \boldsymbol{V} \boldsymbol{o} \boldsymbol{f} \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4}(\boldsymbol{m} \boldsymbol{L}) \quad \mathbf{2 2 . 8} \quad \mathbf{1 3 . 8} \)
Calculate the velocity constant for the reaction assuming it to be a first order reaction.


A rod hinged at one end is made to rotate freely in influence of gravity with initial position being horizontal(angular velocity =0) has
A. acceleration of free end making some acute angle with rod
B. acceleration of free end making some no angle with rod
c. some finite velocity of one end
D. none of these


Which of the following is not the
property of a square?
A. Each angle of a square is a right angle
B. The diagonals of a square are not equal
C. The sides of a square are equal
D. The diagonals of a square bisect each other right angle


(1):In uniform circular motion,
tangential acceleration is zero.
(2) : In uniform circular motion, velocity is constant.
A. Both 1 and 2 are true and 2 is correct explanation of
B. Both 1 and 2 are true and 2 is not correct explanation of 1
c. 1 is true and 2 is false
D. 1 is false and 2 is true


Discuss the role of cambium in
secondary growth of dicot stems.


Where should the object be placed to get the virtual image in case of convex lens?
A. object should be placed between \( F \) and 2 F
B. object should be placed between F and 0
c. object should be placed beyond 2F
D. object should be placed at 0


If \( A=\{0,1\} \) and \( B=\{1,0\}, \) then what is \( A x \)
B equal to?
B. \{(0,0),(1,1)\}
\( D \cdot A \times A \)


The scientific name of red bread mould
is
A. Neurospora
B. Mucor
c. Rhizopus
D. Aspergillus


Which of the following oxides behaves as conductor or insulator depending upon the temperature?
A. \( T i O \)
в. \( \operatorname{si} 0_{2} \)
\( \mathrm{c} \cdot \operatorname{Ti} 0_{3} \)
D. \( M g O \)


PAR range of wavelength is
A. \( 400-700 n m \)
в. \( 400-800 n m \)
c. \( 450-950 n m \)
D. \( 500-600 n m \)


Growth is maximum in the zone of
A. Cell division
B. Cell elongation
c. Cell maturation
D. All of the above


A satellite of mass \( \mathrm{m} \) is orbiting the earth in a circular orbit of radius r. It
starts losing energy due to small air
resistance at the rate of \( C J s^{-1} \). The
time taken for the satellite to reach the earth is: \( \frac{G M m}{x C}\left[\frac{1}{R}-\frac{1}{r}\right] . \) Find the value of \( \boldsymbol{x} \)


The degree of dissociation of \( N_{2} O_{4} \) into
\( N O_{2} \) at 1 atmosphere and \( 40^{\circ} C \) is 0.25
Calculate its \( \boldsymbol{K}_{\boldsymbol{p}} \) at \( \boldsymbol{4} \boldsymbol{0}^{\circ} \boldsymbol{C} \)


How many Faradays of electricity are required to deposit 10 g of calcium from molten calcium chloride using inert
electrodes? (molar mass of calcium =
\( \left.40 \text { g } m o l^{-1}\right) \)
A . \( 0.5 \mathrm{F} \)
B. 1
c. \( 0.25 \mathrm{F} \)
D. 2


Number of electrons in \( 1.8 \mathrm{mL} \) of \( \boldsymbol{H}_{2} \boldsymbol{O} \)
are:
A \( \cdot 6.02 \times 10^{23} \)
B. \( 6.02 \times 10^{24} \)
c. \( 6.02 \times 10^{22} \)
D. \( 6.02 \times 10^{25} \)


One end Of a spring initially in natura length \( l_{0} \) lying on a horizontal frictionless table is fixed and the Other
end is fastened to a small puck of mass
\( \boldsymbol{m} . \) The puck is given velocity in a direction perpendicular to the spring of
magnitude \( V_{0} . \) In the course of motion the maximum elongation of the spring
is \( \frac{l_{0}}{10} . \) The force constant of the spring is:
\( \left(\text { Take } \frac{m v_{0}^{2}}{l_{0}^{2}}=121 \text { units }\right) \)


Which of the following statements is
incorrect?
A. Every measurement by measuring instrument has some error.
B. A measurement can have more accuracy but less precision and vice versa.
C. Every calculated quantity that is based on measured values has some error.
D. The magnitude of the difference between the true value of the quantity and the individual measurement value is called the relative error of the measurement.


Select correct alternative:
Statement -1: Photoelectric effects
supports quantum nature of light because electronic charge of
the photoelectron is quantized.
Statement - 2 : The number of \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \)
238
particles emitted when \( \mathbf{9 2} \)
\( \mathbf{2 0 6} \)
into \( \quad P b \) is 6 and 8 \( \mathbf{8 2} \)
Statement - 3: If the angular
momentum of a system is constant in
magnitude then the torque (if any) acting on the system must be perpendicular to the angular momentum.
A. FFF
B. TFT
c. TFF
D. FFT


If the mid-point of the line segment joining the points \( A(6, x-2) \) and \( B(-2,4) \) is (2,-3) find the value of \( x \)


How silver nitrate reacts with
orthophosphoric acid?


Assertion
\( \left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 7\end{array}\right] \) is a diagonal matrix.
Reason
If \( \boldsymbol{A}=\left[\boldsymbol{a}_{i j}\right] \) is a square matrix such that
\( \boldsymbol{a}_{\boldsymbol{i j}}=\mathbf{0}, \forall \boldsymbol{i} \neq \boldsymbol{j}, \) then \( \boldsymbol{A} \) is called a
diagonal matrix.
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


Aspartame, an artificial sweetener is a peptide and has the following structure.
Which of the following is correct about
the molecule?
This question has multiple correct options
A. It has four functional groups
B. It has three functional groups
C. On hydrolysis it produces only one amino acid
D. on hydrolysis it produces a mixture of amino acids


\( \operatorname{lines} \frac{x-1}{2}=\frac{y-1}{2}=\frac{z-2}{3} \) and
\( \frac{x-1}{2}=\frac{y-2}{2}=\frac{z-3}{-2} \)
Check whether the lines are parallel, mutually perpendicular or intersecting in acute angle)


The number of periods present in the long form of the periodic table are:
\( \mathbf{A} \cdot \mathbf{6} \)
B. 7
c. 8
D. 18


In the laboratory preparation of Dihydrogen,which of the following species is oxidised?
A. \( Z n \)
в. \( H_{2} \)
c. Both A and B
D. None


Draw Venn diagrams to illustrate \( \boldsymbol{A} \cup \)
\( (\boldsymbol{B} \cap \boldsymbol{C}) \)


Assertion
Small quantity of soap is used to
prepare a stable emulsion.
Reason
Soap lowers the interfacial tension
between oil and water.
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


During discharge of a lead storage cell, the density of sulphuric acid in the cell:
A. increases
B. decreases
c. remains unchanged
D. initially increases but decreases subsequently


In Wheatstone bridge, three resistors
\( P, Q, R \) are connected in three arms in
order and 4 th arm \( s \) is formed by two
resistors \( s_{1} \) and \( s_{2} \) connected in
parallel. The condition for bridge to be balanced is \( \frac{\boldsymbol{P}}{\boldsymbol{Q}}= \)
A \( \cdot \frac{R\left(s_{1}+s_{2}\right)}{s_{1} s_{2}} \)
В. \( \frac{s_{1} s_{2}}{R\left(s_{1}+s_{2}\right)} \)
c. \( \frac{R s_{1} s_{2}}{\left(s_{1}+s_{2}\right)} \)
D. \( \frac{\left(s_{1}+s_{2}\right)}{R s_{1} s_{2}} \)


Here is an equation \( 2(x+12)=4 x-6 \)
Solve the equation by first dividing both sides by 2


Chloroplasts without grana are known
to occur in
A. Bundle sheath cells of \( C_{3} \) plants
B. Mesophyll cells of \( C_{4} \) plants
C. Bundle sheath cells of \( C_{4} \) plants
D. Mesophyll cells of all plants


The greatest value of \( \boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+ \)
1) \( ^{1 / 3}-(x-1)^{1 / 3} \) on [0,1] is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 3 \)
D. \( 1 / 3 \)


Limestone is present in the blast furnace in production of iron in order to
\( (I) \) provide a source of \( C a O \)
\( (I I) \) remove some impurities
\( (\boldsymbol{I I I}) \) supply \( \boldsymbol{C O}_{2} \)
A. \( I, I I, I I I \)
в. \( I, I I \)
c. \( I I, I I I \)
D. I only


Assertion
Malonic acid \( \left(\boldsymbol{H} \boldsymbol{O} \boldsymbol{O} \boldsymbol{C}-\boldsymbol{C} \boldsymbol{H}_{2} \boldsymbol{C O O H}\right) \)
does not form cyclic anhydride on heating.
Reason
It is like \( \beta \) -keto acid, on heating it prefer to decarboxylate.
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


Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) cannot be used for drying
up \( \boldsymbol{H}_{2} \boldsymbol{S} \). Explain.


\( \Delta S H R \sim \Delta S V U . \ln \Delta S H R, S H= \)
\( 4.5 \mathrm{cm}, H R=5.2 \mathrm{cm}, S R=5.8 \mathrm{cm} \)
and \( \frac{S H}{S V}=\frac{3}{5} \) Construct \( \Delta S V U \)


The sources of energy which are being produced continuously in nature and are inexhaustible are called:
A. conventional sources
B. non-conventional sources
c. non-renewable sources
D. none of these


Identify the wrong statement about Ursa major.
A. It can be used to locate Pole star.
B. It is seen during winter.
c. It is also called the Big Dipper
D. It has 7 prominent stars


The \( K_{a} \) values for \( H P O_{4}^{2-} \) and \( H S O_{3}^{-} \)
\( \operatorname{are} 4.8 \times 10^{-13} \) and \( 6.3 \times 10^{-8} \)
respectively. Therefore, it follows that \( H P O_{4}^{2-} \) is a acid
\( \operatorname{than} H S O_{3}^{-} \) and \( P O_{4}^{3-} \) is a
base than \( \boldsymbol{S O}_{3}^{2-} \)
A. weaker, stronger respectively
B. stronger, weaker respectively
c. weaker, weaker respectively
D. stronger, stronger respectively


Which of the following statements is
not correct?
This question has multiple correct options
\( \mathbf{A} \cdot L u(O H)_{3} \) is less basic than \( L a(O H)_{3} \)
B. In lanthanide series, ionic radius of \( L a^{3+}-L n^{3+} \) ion
increases
C. La is actually an element of transition series rather lanthanide
D. Atomic radius of Zr and Hf are same because of lanthanide contraction


The conjugate of a complex number is \( \frac{1}{i-1} . \) Then, that complex number is
A \( \cdot \frac{-1}{i+1} \)
B. \( \frac{1}{i-1} \)
c. \( \frac{-1}{i-1} \)
D. \( \frac{1}{i+1} \)


All members of a homologous series
have the same:
A. chemical formula
B. empirical formula.
c. boiling point
D. melting point.


Which of the following non-metal is used for the manufacture of fertilizers?
A. Chlorine
B. Sulphur
c. Phosphorus
D. None of the above


The diagram shows the outline of a 50
cent coin from Fiji
What is its order of rotational
symmetry?
\( A \)
8.
\( c \cdot 12 \)
D. 15


The number of lone pairs of electrons
present on \( \mathrm{Xe} \) in \( \mathrm{XeF}_{2} \) is:
\( A \cdot 3 \)
B. 4
\( c \cdot 2 \)
D.


The freezing point of a solution containing 0.2 g of acetic acid in 20.0 g benzene is lowered by \( 0.45^{\circ} \mathrm{C} \). The degree of association of acetic acid in benzene is:
[Assume acetic acid dimerizes in
benzene and \( K_{f} \) for benzene \( =\mathbf{5 . 1 2} \mathbf{K} \)
\( \left.\mathrm{kg} \mathrm{mol}^{-1}\right] \)
A. \( 94.5 \% \)
B . \( 54.9 \% \)
c. \( 78.2 \% \)
D. 100\%


Concentrated sulphuric acid is :
This question has multiple correct options
A. efforescent
B. hygroscopic
C. oxidizing agent
D. sulphonating agent


Whenever an electric current is passed through a conductor,it gets heated up.this means that a part of electrical energy, given to the conductor, gets converted to
A. potential energy
B. gravitational energy
c. heat energy
D. none of these


Starting from rest, the acceleration of a
particle is \( a=2(t-1) . \) The velocity of
the particle at \( t=5 s \) is:
A. \( 15 \mathrm{m} / \mathrm{s} \)
B. \( 25 \mathrm{m} / \mathrm{s} \)
\( \mathbf{c} \cdot 5 m / s \)
D. None of these


Let \( \boldsymbol{R}=\{(1, \mathbf{3}),(2,2),(3,2)\} \) and \( \boldsymbol{S}= \)
\{(2,1),(3,2),(2,3)\} be two relations on
\( \operatorname{set} A=\{1,2,3\} . \) Then \( R_{0} S \) is equal
A \( \cdot\{(2,3),(3,2),(2,2)\} \)
B . \{(1,3),(2,2),(3,2),(2,1),(2,3)\}
c. \{(3,2),(1,3)\}
D. \{(2,3),(3,2)\}


topp
Q Type your question
stationary by applying a force P paralle to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from \( \boldsymbol{P}_{1}= \)
\( m g(\sin \theta-\mu \cos \theta) \) to \( P_{2}=m g(\sin \theta+ \)
\( \mu \cos \theta), \) the frictional force f versus \( P \)
graph will look like


Two arcs of the same circle have their
lengths in the ratio \( 4: 5 . \) Then the ratio of the areas of the corresponding sectors is 4: 5
If true then enter 1 and if false then
enter 0
\( A \)


Find the domian of \( \frac{1}{\sqrt{(2-x)^{2}+1}} \)


Explain Biotic components of the Ecosystem.


If the \( H^{+} \) concentration is decreased
from \( 1 M \) to \( 10^{-4} M \) at \( 25^{\circ} C \) for the
couple \( M n O_{4}^{-} / M n^{2+}, \) then the
oxidising power of the \( M n O_{4}^{-} / M n^{2+} \) couple decreases by :
\( \mathbf{A} \cdot-0.18 V \)
B. \( 0.18 V \)
c. \( 0.38 V \)
D. \( -0.38 V \)


Which is not found in vertebrates?
A. Gill opening
B. Bilateral symmetry
c. cnidoblasts
D. Body scales


The modern man evolved
\( A \cdot 10,000 \) years ago
B. 25,000 years ago
c. 2,50,000 years ago
D. 5,00,000 years ago


Which of the following species is/are
formed when conc. \( H N O_{3} \) is added to
conc. sulphuric acid?
This question has multiple correct options
A \( \cdot N O_{3} \)
B. \( N O_{2}^{+} \)
c. \( N O^{+} \)
D. \( H S O_{4} \)


\( A(-3,2) \) and \( B(5,4) \) are the end points of a line segment, find the sum of coordinates of the mid points of the
line segment.


Adenine pairs with thymine through:
A. two hydrogen bonds
B. one hydrogen bond
c. three hydrogen bonds
D. four hydrogen bonds


Find the following limit:
\( \lim _{x \rightarrow a} \frac{\cos x-\cos a}{x-a} \)


An LC circuit has \( L=5 \mathrm{mH} \) and \( \mathrm{C}=20 \mu \boldsymbol{F} \)
\( \boldsymbol{V}=\mathbf{5} \times \mathbf{1 0}^{-3} \) coswt is supplied. \( \boldsymbol{\omega} \) is
twice the resonant frequency. Find the maximum charge stored in the capacitor.
A. 66.6 nc
B. 11.3 nC
c. 23.2 nc
D. 33.3 nc


Find the intervals in which the function
\( f(x) \) is
(i) increasing,
(ii) decreasing
\( f(x)=2 x^{3}-9 x^{2}+12 x+15 \)


Cloning is the production of an exact copy of a cell, any other living part of a complete organism. A sheep named Dolly was the first mammal to be cloned by lan Wilmut and his colleagues at the
Roslin Institute in Edinburgh. Find out the incorrect statements about the
cloning of Dolly.
(i) Dolly was born on 5th July 1996
(ii) Dolly was given birth by the Finn Dorset sheep.
(iii) Dolly was found to be absolutely identical to the Scottish blackface ewe.
(iv) The nucleus of the mammary gland cell from the Finn Dorsett sheep was inserted into the egg of the Scottish blackface ewe whose nucleus had been
removed.
A. (i) only
B. (i) and (iii) only
c. (i), (ii) and (iii) only
D. All of the above


List -1
A) Antiferromagnetic
\( N i F e_{2} O_{4} \)
B) Covalent crystal
2) \( M n O \)
C) Ferrimagnetic
3)
Diamond
The correct match is :
A. A-2, B-3, C- -
B. A-3, B-2, C-1
c. A-1, B-2, C-3
D. A-1, B-3, C-2


\( 2+\frac{1+n}{n}=\frac{7}{2} \) find \( n \)


Which of the following forms a collodial solution in water?
A. Salt
B. Glucose
c. starch
D. Barium nitrate


In the metallurgical process for the electro-refining of the metal, the anode is made of \( _{-} \ldots- \) metal
A. impure
B. pure
c. refine
D. none of these


If there is damage to the medulla
oblongata, which of the following
functions will likely be altered?
A. The organism will not be able to breathe properly.
B. The organism will not have control over its body temperature
C. The organism will have memory loss.
D. The organism will lack muscular coordination.
E. The organism will be unable to regulate thirst.


The voices of men, women and children are different due to difference in:
A. larynx
B. lungs
c. vocal coards
D. wind pipe


In nitroprusside ion, the iron and NO exist as \( \mathrm{Fe}^{+2} \) and \( \mathrm{NO}^{+} \), instead of \( \mathrm{Fe}^{+3} \)
and NO. The given conclusion can be drawn by:
A. estimating the concentration of iron
B. measuring the concentration of \( C N^{-} \) ion
c. measuring the solid state magnetic moment
D. thermally decomposing the compound


Which of the following statements about anhydrous aluminium chloride is
correct?
A . It exists as \( A l C l_{3} \) molecule in vapour
B. It is a strong Lewis base
c. It sublimes at \( 100^{\circ} \mathrm{C} \) under vacuum.
D. It is not readily hydrolyzed.


Assertion
Liquid molecule have greater potential
energy at the melting point
Reason
Intermolecular spacing between molecules increases at melting point
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 thin horizontal uniform rod \( A B \) of
mass \( M \) and length \( l \) can rotate freely about a vertical axis passing through
its end \( A \). At a certain moment the end
\( B \) starts experiencing a constant force
\( \boldsymbol{F} \) which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle \( \varphi \) counted relative to the initial position.
A \( \cdot \omega=\sqrt{\frac{6 F \sin \varphi}{M l}} \)
B. \( \omega=\sqrt{\frac{3 F \sin \varphi}{M l}} \)
c. \( \omega=\sqrt{\frac{6 F \cos \varphi}{M l}} \)
D. None of these


Three charges \( +q,-q \) and \( -q \) are kept at
the vertices of an equilateral triangle of \( 10 \mathrm{cm} \) side. The potential at the mid point in between \( -q,-q, \) if \( q=5 \mu C \) is :
A . \( -6.4 \times 10^{5} V \)
B. \( -12.8 \times 10^{4} V \)
c. \( -6.4 \times 10^{4} V \)
D. \( -12.8 \times 10^{5} V \)


The model organism that has largely been responsible for making rapid advances in research on photosynthesis is
A. Chlamydomonas
B. Spinach leaf
c. chlorella
D. Hydrilla


Which one of the following statement is
correct.
A. There is no evidence of the existence of gills during embryogenesis of mammals
B. All plants and animals cells are totipotent
C. Ontogeny repeats phylogeny
D. Stem cells are specialize cells


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\cos \left[\boldsymbol{\pi}^{2}\right] \boldsymbol{x}+ \)
\( \cos \left[-\pi^{2}\right] x, \) where \( [.] \)
represents greatest integer function
-1 and \( f(-\pi)=? \)
\( A \cdot-1 \)
в.
\( c \cdot 0 \)
D.


Find the correct relation from the
following:
A. Work done=charge \( \times \) power
B. Work done=charge \( \times \) potential difference
C. Work done=current \( \times \) voltage
D. All


A potential difference V is applied across a copper wire of diameter d and length L. when only d is doubled, the drift velocity :-
A. increases two times
B. decreases \( \frac{1}{2} \) times
c. does not change
D. decreases \( \frac{1}{4} \) times


Which rule gives the direction of induced current due to electromagnetic induction?
A. Fleming's left hand rule
B. Maxwell's left hand rule
c. Ampere's rule
D. Fleming's right hand rule


Let \( n \) be a positive integer. Call a non-
empty subset \( S \) of \( \{1,2, \ldots, n\} \) good, if
the arithmetic mean of the elements of
\( S, \) is also an integer. Further let \( t_{n} \) denote the number of good subsets of
\( \{1,2, \ldots, n\} . \) Prove that \( t_{n} \) and \( n \) are both
odd or both even


An orbital made of four lobes can have
the following quantum numbers:
A \( \cdot n=2,1=2, m=0 \)
B. \( n=3,1=1, m=-2 \)
\( c \cdot n=3,1=2, m=0 \)
D. \( n=3,1=3, m=-3 \)


Sum of 20 terms of \( 3+6+12+\ldots \) is
A \( \cdot 3\left(2^{20}-1\right) / 2 \)
B . \( 3\left(2^{19}-1\right) / 2 \)
c. \( 3\left(2^{20}-1\right) \)
D. \( 3\left(2^{19}-1\right) \)


Each of the cubes is \( 1 \mathrm{m} \) in length. The
total surface area of the cuboid is
\( \mathbf{A} \cdot 86 m^{2} \)
B. \( 85 m^{2} \)
\( \mathbf{c} \cdot 84 m^{2} \)
D. \( 80 m^{2} \)


Which of the following elements have
the lowest value of \( I E_{1} ? \)
A \( . P b \)
в. \( S n \)
\( c . s i \)
D. \( C \)


Which will have graded property
particular to \( \boldsymbol{E} \cdot \boldsymbol{C} \cdot \boldsymbol{1} \boldsymbol{s}^{2} \boldsymbol{2} \boldsymbol{s}^{2} \boldsymbol{2} \boldsymbol{p}^{6} \boldsymbol{3} \boldsymbol{s}^{2} \boldsymbol{3} \boldsymbol{p}^{\boldsymbol{6}} \boldsymbol{4} \boldsymbol{s}^{1} \) ?
\( \mathbf{A} \cdot[A r] 3 d^{10} 4 s^{1} \)
B . \( [K r] 4 d^{10} 5 s^{1} \)
c. \( [K r] 5 s^{1} \)
D. all of these


Pigment phytochrome is involved in
A. Hydrotropism
B. Photorespiration
c. Photoperiodism
D. Geotropism


For the chemical reaction \( N_{2}(g)+ \)
\( \mathbf{3} \boldsymbol{H}_{\mathbf{2}}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{N} \boldsymbol{H}_{\mathbf{3}}(\boldsymbol{g}) \) the correct option
is:
A \( \cdot-\frac{1}{3} \frac{d\left[H_{2}\right]}{d t}=-\frac{1}{2} \frac{\left[N H_{3}\right.}{d t} \)
B. \( -\frac{d\left[N_{2}\right]}{d t}=2 \frac{d\left[N H_{3}\right]}{d t} \)
c. \( -\frac{d\left[N_{2}\right]}{d t}=\frac{1}{2} \frac{d\left[N H_{3}\right]}{d t} \)
D. \( 3 \frac{d\left[H_{2}\right]}{d t}=2 \frac{d\left[N H_{3}\right]}{d t} \)


From a village people started migrating to nearby cities due to unemployment. The population of the village two years ago was \( 6,000 . \) If present population is \( 5,415, \) find the rate at which the migration is taking place.


What are drugs?


The image of the point \( 3 \hat{i}-2 \hat{j}+\hat{k} \) in the plane \( \bar{r} .(3 \hat{i}-\hat{j}+4 \hat{k})=2 \)
\( \mathbf{A} \cdot-\hat{j}+3 \hat{k} \)
B . \( \hat{j}-3 \hat{k} \)
\( \mathbf{c} .-\hat{j}-3 \hat{k} \)
D \( .-2 \hat{j}-3 \hat{k} \)


A heat engine takes in \( 900 J \) of heat from a high-temperature reservoir and produces \( 300 J \) of work in each cycle.
What is its efficiency?
A . \( 35 \% \) \%
в. 33 \%
c. \( 43 \% \)
D. \( 50 \% \)


Arrange the following combinations in the increasing order of focal length:
a) Two plano convex lenses of focal lengths \( 20 \mathrm{cm} \) and \( 30 \mathrm{cm} \) in contact.
b) Two convex lens of focal lengths 20 \( \mathrm{cm} \) and \( 10 \mathrm{cm} \) in contact.
c) Two convex lenses of focal length 25
\( \mathrm{cm} \) separated by \( 5 \mathrm{cm} \)
\( A \cdot a, b, c \)
B. b, a, c
\( c \cdot a, c, b \)
D. \( c, a, b \)


Complete the equation for the following fission process \( _{92} U^{235}+_{0} n^{1} \rightarrow_{38} \)
\( \boldsymbol{S} \boldsymbol{r}^{\boldsymbol{9 0}}+\ldots \)
В \( \cdot_{54} X e^{14} \)
\( \mathrm{c} \cdot_{57} \mathrm{Xe}^{142} \)
\( \mathrm{D} \cdot_{54} X e^{142}+3_{0} \)


External or accessory or secondary sexual characters first appear in
A. Childhood
B. Puberty
c. Foetus
D. Adulthood


Prove \( 4 \tan ^{-1}\left(\frac{1}{5}\right)-\tan ^{-1}\left(\frac{1}{70}\right)+ \)
\( \tan ^{-1}\left(\frac{1}{99}\right)=\frac{\pi}{4} \)


The figure is a part of a closed circuit
Find the currents \( i_{1}, i_{2} \) and \( i_{3} \)


The magnitude of a magnetic field at
the centre of a circular coil of radius \( R \)
having \( N \) turns and carrying a current
can be doubled by changing
\( \mathbf{A} \cdot I \) to \( 2 I \) and \( N \) keeping \( R \) unchanged
B. \( N \) to \( \frac{N}{2} \) and keeping \( I \) and \( R \) unchanged
C . \( N \) to \( 2 N \) and \( R \) keeping \( 2 R \) keeping/unchanged
D. \( R \) to \( 2 R \) and \( l \) to \( 2 I \) keeping \( N \) unchanged
E . \( I \) to \( 2 I \) and keeping \( N \) and \( R \) unchanged


Gold metal is affected by:
A. chlorine gas
B. oxygen gas
c. sulphur dioxide gas
D. helium gas


If \( \pi<\alpha<2 \pi \) then
\( \frac{1}{\sin \alpha-\sqrt{\cot ^{2} \alpha-\cos ^{2} \alpha}}= \)
\( A \cdot \sin \alpha \)
B. - \( \sin \alpha \)
c. \( \frac{1}{\sin \alpha} \)
\( D \)


Write a chemical reaction depicting
oxidising property of ozone gas.


f \( x+a \) is one of the factors of \( p(x)= \)
\( 2 x^{2}+2 a x+5 x+10, \) then find \( a \)


A point-charge of \( 6.0 \times 10^{-8} \mathrm{C} \) is
situated at the coordinate origin. How much work will be done in taking an electron from the point \( x=3 \mathrm{m} \) to \( x=6 \)
\( \mathrm{m} ? \)
B . \( 1.44 \times 10^{-27} \) J
c. \( 1.44 \times 10^{-37} \) J
D. \( 1.44 \times 10^{-7} \).


Two masses of \( 1 \mathrm{gm} \) and \( 4 \mathrm{gm} \) are moving with equal kinetic energies.The ratio of the magnitudes of their linear
momenta is:
\( A \cdot 4: 1 \)
B. 2:1
\( c \cdot 1: 2 \)
D. 1:16


\( X \) is a Normally distributed variable
with mean \( =30 \) and standard deviation
\( =4 . \) Find \( P(x<40) \)
A .0 .9789
B. 0.9938
c. 0.9838
D. 0.9538


The perimeter of a square is \( 56 \mathrm{m} \). The
area of rectangle is 8 sq.m less than the
area of the given square. If the length of the rectangle is \( 16 \mathrm{m} \), find its breadth.


Assertion
A charged particle moves along positive y-axis with constant velocity in uniform electric and magnetic fields.If magnetic field is acting along positive \( x \) -axis,then electric field should act along positive z-axis.
Reason
To keep the charged particle undeviated the relation \( \vec{E}=\vec{B} \times \vec{v} \) must hold good.
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 Equations of a chemical reaction
are given in the figure:
(a) To which type this chemical reaction belongs?
(b) Which is the monomer in this
reaction?
\[
\mathrm{n}_{\mathrm{H}_{2} \mathrm{C}=}^{\mathrm{CH}} \frac{\operatorname{high} \mathrm{T} \cdot \mathrm{P}_{.}}{\mid} \frac{\mathrm{H}_{2}}{\mathrm{c}_{\mathrm{Cl}}}-\left[_{\mathrm{Cl}}^{\mathrm{H}}-\right]_{\mathrm{n}}
\]


ldentify metal #2.
A. Carbon
B. Copper
\( c \cdot \) zinc
D. Sodium
E . Silver


The coefficient of range of a set of data is given to be \( \frac{1}{8} . \) Then the ratio of the maximum value in the data to the
minimum value is:
A \( \cdot \frac{8}{1} \)
в. \( \frac{9}{8} \)
\( c \cdot \frac{9}{7} \)
\( D \cdot \frac{8}{7} \)


\( \mathbf{f} \boldsymbol{u}_{\boldsymbol{r}}=\boldsymbol{a}_{\boldsymbol{r}} \boldsymbol{x}+\boldsymbol{b}_{\boldsymbol{r}} \boldsymbol{y}+, \boldsymbol{c}_{\boldsymbol{r}}=\mathbf{0}(r=1,2,3 \)
be the three sides of a triangle them the equations of the circumcircle of this triangle is \( \mid \begin{array}{ccc}\frac{\mathbf{1}}{\boldsymbol{u}_{1}} & \frac{\mathbf{1}}{\boldsymbol{u}_{2}} & \frac{\mathbf{1}}{\boldsymbol{u}_{3}} \\ \boldsymbol{a}_{2} \boldsymbol{a}_{3}-\boldsymbol{b}_{2} \boldsymbol{b}_{3} & \boldsymbol{a}_{3} \boldsymbol{a}_{1}-\boldsymbol{b}_{3} \boldsymbol{b}_{1} & \boldsymbol{a}_{1} \boldsymbol{a}_{2}-\boldsymbol{b}_{4} \\ \boldsymbol{a}_{2} \boldsymbol{b}_{3}+\boldsymbol{a}_{3} \boldsymbol{b}_{2} & \boldsymbol{a}_{3} \boldsymbol{b}_{1}+\boldsymbol{a}_{1} \boldsymbol{b}_{3} & \boldsymbol{a}_{1} \boldsymbol{b}_{2}+\boldsymbol{a}_{2}\end{array} \)
\( =0 \)


Calculate the number of molecules of
ammonia present in \( 5.6 d m^{3} \) of its
volume


Find the crystal field stabilization energy (CFSE) (in kJ/mol) for complex,
\( \left[T i\left(H_{2} O\right)_{6}\right]^{3+} . \) According to CFT, the
first absorption maximum is obtained
at \( 20,3000 \mathrm{cm}^{-1} \) for the transition


If \( \bar{e}=\bar{l} \bar{i}+m \bar{j}+n \bar{k} \) is a unit vector, the
maximum value of \( l m+m n+n l \) is
A \( \cdot-\frac{1}{2} \)
B. 0
c. 1
D. \( \frac{3}{2} \)


The linear structure is assumed by:
This question has multiple correct options
\( \mathbf{A} \cdot \operatorname{Sn} C l_{2} \)
в. \( N C O^{-} \)
\( \mathrm{c} \cdot \mathrm{NO}_{2}^{+} \)
D. \( C S_{2} \)


A positroniuim consists of an electron and a positron revolving about their common centre of mass. Calculate the
kinetic energy of the electron in ground
state:
A. 1.51 eV
B. 3.4 eV
c. \( 6.8 e V \)
D. 13.6 eV


Sound signal is sent through a composite tube as shown in figure. The radius of the semicircle is r. Speed of
sound in air is \( V \). The source of sound is
capable to generate frequencies in
the range \( f_{1} \) to \( f_{2}\left(f_{2}>f\right) . \) If 'n' is an
integer then frequency for maximum intensity is given by :
\( A \cdot \frac{n V}{r} \)
B. \( \frac{n V}{r(\pi-2)} \)
\( \mathbf{c} \cdot 7 V / r \)
D. \( \frac{n V}{(r-2) \pi} \)


The function \( \boldsymbol{f}:[\mathbf{2}, \infty) \rightarrow \boldsymbol{Y} \) defined by
\( f(x)=x^{2}-4 x+5 \) is one-one if (more
than one option can be correct)
A. \( Y=R \)
B. \( Y=[1, \infty) \)
c. \( Y=[0, \infty) \)
D. \( Y=[-1, \infty) \)


Why do d-block elements exhibit
variable oxidation states?


Where does electron transport system operates in moitochondria? Explain.


State whether true or false.
Regular reflection takes place when the light beam falls on a highly polished surface.
A. True
B. False


The pully of the system shown in Fig. is massless and frictionless and thread is
inextensible. The horizontal surface
over which block \( \mathrm{C} \) is placed is smooth while coefficient for all the remaining
surfaces is \( \mu \)

Calculate minimum accleration a with
which the system should be moved to the right so that suspended blocks \( A \) (mass \( m \) ) and \( B(\text { mass } M \text { and } N>m) \)
can remain stationary relative to \( C \)


\( \mathbf{f} A=\left[\begin{array}{cc}\cos \boldsymbol{x} & -\sin \boldsymbol{x} \\ \sin \boldsymbol{x} & \cos \boldsymbol{x}\end{array}\right], \) then find \( \boldsymbol{A} \boldsymbol{A}^{\boldsymbol{T}} \)


An elevator platform is going up at a
speed \( 20 \mathrm{ms}^{-1} \) and during its upward motion a small ball of 50 g mass falling
in downward direction strikes the
platform elastically at a speed \( 5 \mathrm{ms}^{-1} \) Find the speed (in \( \mathrm{ms}^{-1} \) ) with which the
ball rebounds:


Mercury is used in thermometers because:
A. it does not wet the glass
B. it expands on heating
c. it is a liquid
D. all of these


Choose the incorrect statements.
This question has multiple correct options
A. All \( S-F \) bond lengths are identical in \( S F_{4} \)
B. All \( C l-F \) bond lengths are identical in \( C l F_{3} \)
C . All \( \angle F C l F \) angles are not identical in \( C l F_{3} \)
D. All possible angle in \( B F_{2} C l \) are \( 120^{\circ} \)


The calculation of interest on the
interest of principal amount is called
A. simple interest
B. compound interest
c. multiple interest
D. interest quarterly compounded


A light of wavelength 6000 A in air
centre a medium of refractive index 1.5
What will be the frequency and wavelength of length in the medium?


An earthquake generates both transverse \( (S) \) and longitudinal \( (P) \) sound waves in the earth. The speed of \( S \) waves is about \( 4.5 k m / s \) and that of \( P \) waves about \( 8.0 k m / s . A \) seismograph records \( P \) and \( S \) waves
from an earthquake. The first \( \boldsymbol{P} \) wave arrives 4.0 min. before the first \( S \)
wave. The epicenter of the earthquake is located at a distance of about
A \( .25 k m \)
B. 250km
c. \( 2500 k m \)
D. \( 5000 k m \)


\( (64)^{\frac{-2}{3}} \times\left(\frac{1}{4}\right)^{-3} \) equals to
\( A \cdot 4 \)
B.
\( c \)
D. 16


Let \( \vec{a} \) and \( \vec{b} \) be two unit vectors such that \( |\vec{a}+\vec{b}|=\sqrt{3} . \) If \( \vec{c}=\vec{a}+2 \vec{b}+ \)
\( \mathbf{3}(\overrightarrow{\boldsymbol{a}} \times \overrightarrow{\boldsymbol{b}}), \) then \( \mathbf{2}|\overrightarrow{\boldsymbol{c}}| \) is equal to
A . \( \sqrt{55} \)
в. \( \sqrt{37} \)
c. \( \sqrt{43} \)
D. \( \sqrt{51} \)


Do you observe any soil pollution in your neighbourhood? What efforts will you make for controlling the soil pollution?


What is approximately its increase in internal energy in \( J \)


The enthalpy changes at \( 298 \mathrm{K} \) in successive breaking of \( \boldsymbol{O}-\boldsymbol{H} \) bonds of
HOH are:
\( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{g}) \rightarrow \boldsymbol{H}(\boldsymbol{g})+\boldsymbol{O} \boldsymbol{H}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=\boldsymbol{4} \boldsymbol{9} \boldsymbol{8} \)
kJ \( m o l^{-1} \)
\( \boldsymbol{O} \boldsymbol{H}(\boldsymbol{g}) \rightarrow \boldsymbol{H}(\boldsymbol{g})+\boldsymbol{O}(\boldsymbol{g}), \boldsymbol{\Delta} \boldsymbol{H}=\mathbf{4 2 8} \mathbf{k J} \)
\( m o l^{-1} \)
The bond enthalpy of the \( O-H \) bond is:
A . 498 k \( \operatorname{mol}^{-1} \)
B. 463 kJ \( m o l^{-1} \)
c. 428 ks \( m o l^{-1} \)
D. 70 kJ \( m o l^{-1} \)


A cylinder contains a gas at temperature
of \( 27^{0} \mathrm{C} \) and a pressure 1 MPa. If the temperature of the gas
is lowered to \( -23^{0} \mathrm{C} \), the change in pressure
is
A. \( 1 \mathrm{MPa} \)
B. \( 5 / 6 \) MPa
C . \( 1 / 6 \mathrm{MPa} \)
D. \( 5 \mathrm{MPa} \)


Nucleic acids are
A. small molecules
B. polymeric in nature
C. the compounds of \( \mathrm{C} \), H and 0
D. essentially proteins


\( Z n^{2+} \) salts appear acidic due to hydrolysis. Identify acid and base in the following:
\( \left[Z n\left(H_{2} O\right)_{4}\right]^{2+}+H_{2} O \rightleftharpoons \)
\( \left[Z n\left(H_{2} O\right)_{3} O H\right]^{+}+H_{3} O^{+} \)
\( \mathbf{A} \cdot\left[Z n\left(H_{2} O\right)_{4}\right]^{2+}(\text { base }),\left[Z n\left(H_{2} O\right)_{3} O H\right]^{+} \) (base)
B . \( \left[Z n\left(H_{2} O\right)_{4}\right]^{2+} \) (acid) \( ,\left[Z n\left(H_{2} O\right)_{3} O H\right]^{+} \) (base)
C \( \cdot\left[Z n\left(H_{2} O\right)_{4}\right]^{2+} \) (acid), \( H_{3} O^{+} \) (base)
D \( \cdot\left[\operatorname{Zn}\left(H_{2} O\right)_{3} O H\right]^{+} \) (acid), \( H_{3} O^{+} \) (base)


From the observation of Ohm's law \( 1 \rightarrow \) V
graph is drawn here.

From that which points are concluded?
\( P: I \rightarrow V \) graph is a straight line.
Q: Ratio of V and I remains constant
every time.
R: The electric current in a conductor
increases in same proportion with the increase in voltage
A. Statements P, Q and R are all true
B. Statements Q and R are true
c. Statements P and R are true
D. Statements P and Q are true


At what height over the earth's pole does the freefall acceleration decreases
by \( 1 \% ? \)
\( \mathbf{A} \cdot 64 k m \)
B. \( 16 k m \)
\( c .8 k m \)
\( \mathbf{D} \cdot 32 k m \)


The parabola \( y^{2}=4 x \) and \( x^{2}=4 y \)
divide the square region bounded by the
\( \operatorname{lines} x=4, y=4 \) and the coordinate
axes. If \( S_{1}, S_{2}, S_{3} \) are the areas of these
parts numbered from top to bottom
respectively, then This question has multiple correct options
A \( . S_{1}: S_{2} \equiv 1: 1 \)
B. \( S_{2}: S_{3} \equiv 1: 2 \)
c. \( S_{1}: S_{3} \equiv 1: 1 \)
\( \mathbf{D} \cdot S_{1}:\left(S_{1}+S_{2}\right) \equiv 1: 2 \)


For the reaction \( C O(g)+2 H_{2}(g) \leftrightharpoons \)
\( \boldsymbol{C H}_{2} \boldsymbol{O H}(\boldsymbol{g}) . \) If active mass of \( \boldsymbol{C O} \) is
kept constant and active mass of \( \boldsymbol{H}_{2} \) is tripled, the rate of forward reaction will
become:
A. three times
B. six times
c. eight times
D. nine times


At \( 25^{\circ} C \) and one atmospheric pressure
the partial pressures in an equilibrium
mixture of \( N_{2} O_{4} \) and \( N O_{2} \) are 0.7 and
0.3 atmosphere, respectively. Calculate the partial pressures of these gases
when they are in equilibrium at \( 25^{\circ} \mathrm{C} \)
and at a total pressure of 10
atmospheres.


In this electrolytic cell, we get pure silver after passing electric
current at
A. cathode
B. anode
c. bottom of cell
D. none of these


The valency of nitrogen is \( N H_{3} \) is:


Deoxygenated blood is carried by
I. Pulmonary veins
I. Anterior vena cava
III. Pulmonary arteries
A. I only
B. II only
c. ॥ा only
D. I and II
E. Il and III


Given the velocity-time graph of
particle. Describe the motion of the
particle


If \( \sin a=\frac{3}{7} \) and \( \cos a<0, \) what is the
value of \( \tan a \)
A \( \cdot \frac{-(3 \sqrt{20})}{10} \)
B. \( \frac{-(\sqrt{10})}{10} \)
c. \( \frac{-(3 \sqrt{10})}{20} \)
D. \( \frac{(2 \sqrt{5})}{10} \)


What weight of calcium contains the
same number of atoms as those in \( 3 g \) of
carbon?
A \( .10 g \)
B . \( 20 g \)
c. \( 30 g \)
D. \( 40 g \)


The group number, number of valence electrons, and valency of an element with the atomic number 15
respectively, of \( \boldsymbol{P}, \) are:
\( \mathbf{A} \cdot 16,5 \) and 2
B. 16,6 and 3
c. 15,5 andb 3
D. 15,6 and 2


Find the mode for the following frequency table
\( \mathbf{1 0} \) \( \mathbf{1 5} \)
\[
x
\]
and
\( \mathbf{2 0} \)
25
\( f \) 25 14
\[
37
\]
and
16


All oscillatory motions are
A. periodic
B. linear
c. rotatory
D. curvilinear


A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, the probability of at least 5 successes is \( \frac{49}{9^{x}} . \) Find the value of \( x \)


The inside of the bottle of a gold-leaf electroscope is occasionally evacuated
A. to prevent the charge on the terminal from leaking of through ionisation of the air
B. to leak off the charge on the terminal through ionisation of the air
C. to prevent the charge on the terminal from leaking off through induction.
D. None of these


Solve the integral \( \int \sqrt{\frac{1+x}{1-x}} d x \)


\( \frac{k}{k} \)


Which among the following compounds in crystalline form is used for making Nicol's prism?
A \( \cdot \operatorname{CaSO}_{4} \)
В. \( N a_{2} A l F_{6} \)
\( \mathrm{c} \cdot \mathrm{CaCO}_{3} \)
D. \( A l_{2} O_{3} \)


Gluconeogenesis is
A. Formation of ammonia from glucose
B. Breakdown of glucose
C. Formation of glycogen
D. Formation of glucose from sources other than carbohydrate


A piece of copper and another of germanium are cooled from room temperature to \( 80 \mathrm{K} \). The resistance of
A. each of them increases
B. each of them decreases
c. copper increases and germanium decreases
D. copper decreases and germanium increases


Consider the equilibrium set up:
\( \mathbf{2} \boldsymbol{H}_{\mathbf{2}(\boldsymbol{g})}+\boldsymbol{C} \boldsymbol{O}_{(\boldsymbol{g})} \rightleftharpoons \boldsymbol{C} \boldsymbol{H}_{\boldsymbol{3}} \boldsymbol{O} \boldsymbol{H}_{(\boldsymbol{g})} \)
What will be the effect of the following on the equilibrium of the reaction?
(i) Addition of \( \boldsymbol{H}_{2} \)
(ii) Addition of \( \boldsymbol{C H}_{3} \boldsymbol{O H} \)
(iii) Removal of \( \mathrm{CO} \)
(iv) Removal of \( \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H} \)
A. (i) - Forward direction
(ii) - Backward direction (iii) Backward direction (iv) - Forward direction
B. (i) - Backward direction
(ii) - Backward direction (iii) Forward direction (iv) - Forward direction
c. (i) - Forward direction
(ii) - Forward direction (iii) Backward direction
(iv) - Backward direction
D. (i) - Backward direction
(ii) - Forward direction (iii) Forward direction (iv) - Backward direction


An infinite number of charges each equal to \( Q \) are placed along the \( X \) -axis at \( X= \) \( 4, X=8 \) and so on. The potential at the
point \( X=0 \) due to set of charges is :
\( ^{A} \cdot \frac{Q}{8 \pi \epsilon_{0}} \)
в. \( \frac{Q}{3 \pi \epsilon_{0}} \)
c. \( \frac{1}{4 \pi \epsilon_{0}} \frac{2}{3} Q \)
D. \( \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{3} \)


Assertion
2-butyne on controlled hydrogenation
with \( P d / C a C O_{3} \) in presence of \( P b O \)
gives \( c i s-2 \) -butene
Reason
Hydrogenation occur at the surface of
metal containing adsorbed hydrogen.
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 shell of mass \( 10 \mathrm{kg} \) is moving with a velocity of \( 10 m s^{-1} \) when it blasts and
forms two parts of mass \( 9 \mathrm{kg} \) and \( 1 \mathrm{kg} \) respectively. If the 1 st mass is stationary, the velocity of the 2 nd is:
\( \mathbf{A} \cdot 1 \mathrm{m} / \mathrm{s} \)
B. 10 \( \mathrm{m} / \mathrm{s} \)
c. \( 100 \mathrm{m} / \mathrm{s} \)
D. \( 1000 \mathrm{m} / \mathrm{s} \)


A beam of light, consisting of red, green and blue colours, is incident on a right-
angled prism, as shown. the refractive indices of the material of the prism for
the above red, green and blue wavelengths are 1.391 .44 and 1.47
respectively. The prism will :
A. separate part of the red colour from the green and blue colours
B. separate part of the blue colour from the red and green colours
c. separate all the three colours from one another
D. not separate even partially any colour from the other tow colours


Write IUPAC name of the given
compound:
\( \boldsymbol{C}_{6} \boldsymbol{H}_{5}-\boldsymbol{N} \boldsymbol{H}-\boldsymbol{C}_{6} \boldsymbol{H}_{5} \)


Reduction in price of vehicle and machinery with time is called


Polymer used in bullet-proof glass
is
A. Nomex
B. Lexan
c. PMMA
D. Kevlar


At absolute zero temperature a semiconductor behaves like:
A. an insulator
B. a super conductor
c. a good conductor
D. a variable resistor


The value of ratio \( M / m \) is
4. 2: 3
B . 3: 2
\( c \cdot 4: 3 \)
D. 3: 4


A solution contains \( \boldsymbol{F e}^{+2}, \boldsymbol{F e}^{+\mathbf{3}} \) and \( \boldsymbol{I}^{-} \)
ions. This solution was treated with
iodine at \( 35^{\circ} \mathrm{C} \). Then the favourable
redox reaction is:
(Given that \( \boldsymbol{E}_{\boldsymbol{F} e^{+3} / \boldsymbol{F} e^{+2}}^{\boldsymbol{o}}= \)
\( \left.+\mathbf{0 . 7 7 V} ; \quad \boldsymbol{E}_{I_{2} / I^{-}}^{o}=\mathbf{0 . 5 3 6} \boldsymbol{V}\right) \)
A \( . I_{2} \) will be reduced to \( I^{-} \)
B. there will be no redox reaction
c. \( I^{-} \) will be oxidised to \( I_{2} \)
D. \( F e^{+} \) will be oxidised to \( F e^{+3} \)


A and \( B \) are two conductors carrying a
current \( i \) in the same direction, \( x \) and \( y \)
are two electron beams moving in the
same direction. There will be:
A. Repulsion between \( A \) and \( B \), attraction between \( x \) and
\( y \)
B. Attraction between \( A \) and \( B \), repulsion between \( x \) and
\( y \)
C. Repulsion between \( A \) and \( B \), and also \( x \) and \( y \)
D. Attraction between \( A \) and \( B \), and also \( x \) and \( y \)


The plant, Ziziphus rotundifolia is an
indicator of
A. Sandy loam soil
B. Highlime soil
c. Soil formation
D. Soil erosion


Find the number of water molecules
required to get the complete hydrolysis
product of \( \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{8} \)


In an electric iron heat produced is same, whether it is connected across an
A.C. source or across 50 constant
voltage. R.M.S, value of the A.C. voltage applied is
A . \( 50 V \)
B. Zero
c. \( 50 \sqrt{2} V \)
D. \( \frac{50}{\sqrt{2}} V \)


Standard deviation for first 10 natura
numbers is
A . 5.5
B. 3.87
c. 2.97
D. 2.87


The only asexual algal spores formed during favourable conditions is
A. Akinete
B. Zoospore
c. zygospore
D. Aplanospore


The exceptional character of angiosperms is
A. Presence of bitegmic ovules
B. Double fertilization
c. companion cells in phloem
D. All of the above


Explain: Propan-1-ol has higher boiling point than n-butane.


Solve the equations using elimination method:
\( 2 x+3 y=15 \) and \( 3 x+3 y=12 \)
A \( \cdot(-3,-7) \)
в. (-3,7)
c. (-3,6)
D. (3,-7)


Assertion
Oxygen is more electronegative than
sulphur,yet \( \boldsymbol{H}_{2} \boldsymbol{S} \) is acidic, while \( \boldsymbol{H}_{2} \boldsymbol{O} \) is neutral
Reason
H- - -S bond is weaker than 0 - - -H bond
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 enzymes catalysing reactions 1,2 and 3 respectively in the above steps
are
Glucose
Triose phospate (3-phosphoglyceric acid)
2-phosphoglyceric acid 2-phosphoenol pyruvate
pyruvic acid
A. Phosphoglyceromutase, Enolase, Pyruvate kinase
B. Enolase, Phosphofructoknase, Pyruvate kinase
C. Phosphoglycerokinase, Enolase, Pyruvate kinase
D. G-3-P dehydrogenase, Enolase, Phosphoglyceromutase


Give reasons for the following:
(i) Though nitrogen exhibits +5 oxidation state, it does not form
pentahalide.
(ii) Electron gain enthalpy with negative sing of flourine is less than that of
chlorine.
(iii) The two oxygen-oxygen bond lengths in ozone molecules are
identical.


Which of the following represents the features of lysosomes?
A. A lower pH than the cytoplasm
B. Reduced hydrolase activity
c. Double membrane envelope
D. All of these


Equivalent wt.of a metal is 2.5 times higher than oxygen. The ratio of weight of metal to the oxide is:
A . 0.4
в. 1.4
c. 2.4
D. 3.


The correct formula of salt formed by
the neutralization hypophosphorous acid with \( N a O H \) is:
A. \( N a_{3} P O_{2} \)
B \( . N a_{3} P O_{3} \)
c. \( N a H_{2} P O_{2} \)
D. \( N a_{2} H P O_{4} \)


A circle is inscribed in a square. If the
area of the square is 36 sq. units, what is the area of the circle?
\( \mathbf{A} \cdot 6 \pi \)
в. \( 9 \pi \)
c. \( 12 \pi \)
D. \( 18 \pi \)
\( E .36 \pi \)


\( \triangle A B C \) is right angled in which \( \angle A= \)
\( 90^{\circ} \) and \( A B=A C . \) Find \( \angle B \) and \( \angle C \)


Percentage of Cu is minimum in :
A. brass
B. bronze
c. duralumin
D. gun mental


In a flower, the male and female reproductive parts are
respectively.
A. Stamen and pistil
B. Pistil and stamen
c. Petals and pistil
D. Stamen and petalss


Express the complex number given in the form \( a+i b \)
\( \boldsymbol{i}^{9}+\boldsymbol{i}^{19} \)


A batsman hits back a ball straight in the direction of the bowler without
changing its initial speed of \( 12 m s^{-1} . \) If the mass of the ball is \( 0.15 k g \)
determine the change in momentum of the ball. (Assume linear motion of the ball)
A. \( 3.6 k g m / s \)
в. \( 5 k g m / s \)
c. \( 3.5 k g m / s \)
D. \( 7 k g m / s \)


The difference between the first and the
fifth term of a geometric progression whose all terms are positive numbers is
15 and the sum of the first and the third
term of the progression is \( 20 . \) Calculate
the sum of the first five terms of the
progression.


State True or False.
\( \mathrm{Fe}^{3+} \) is paramagnetic.
A. True
B. False


If the points \( (a, 0),(0, b) \) and (1,1) are
collinear, which of the following is true?
A \( \cdot \frac{1}{a}+\frac{1}{b}=2 \)
B. \( \frac{1}{a}-\frac{1}{b}=1 \)
c. \( \frac{1}{a}-\frac{1}{b}=2 \)
D. \( \frac{1}{a}+\frac{1}{b}=1 \)


The rate of change of volume of sphere with respect to its surface area \( S \) is
A. \( \sqrt{\frac{S}{\pi}} \)
в. \( \frac{1}{2} \sqrt{\frac{S}{\pi}} \)
\( ^{c} \cdot \frac{1}{4} \sqrt{\frac{S}{\pi}} \)
D. \( 4 \sqrt{\frac{S}{\pi}} \)


Convert the following into a fraction:
\( 0.2 \times 0.02 \times 0.002 \)
A \( \cdot \frac{1}{125} \)
в. \( \frac{1}{1250} \)
c. \( \frac{1}{125000} \)
D. None of these


The IUPAC name of the complex
\( \left[\boldsymbol{P t}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{2} \boldsymbol{C l}\left(\boldsymbol{N} \boldsymbol{H}_{2} \boldsymbol{C} \boldsymbol{H}_{3}\right)\right] \boldsymbol{C l} \) is :
A. Diamminechlorido (methanamine) platinum(II)chloride
B. Bisammine (methanamine) chlorido platinum(II)chloride
c. Diamminechlorido (aminomethane) platinum(II)chloride
D. Diammine (methanamine) chlorido platinum(II)chloride


Find the distance between the following pairs of points (-2,-3) and (3,2)


Using properties of determinant solve :\( \left|\begin{array}{ccc}1 & a & a^{2}-b c \\ 1 & b & b^{2}-a c \\ 1 & c & c^{2}-a b\end{array}\right|= \)


Where is the lower end of a lightning conductor fixed in the building?
\( A \cdot \) at the top
B. at a window
c. at the base
D. in the ground


In a reaction of \( C_{6} H_{5} Y, \) the major product \( (>60 \%) \) is m-isomer, so the
group Y is:
A. \( -C O O H \)
в. \( -C l \)
\( \mathrm{c} .-O H \)
D. \( -N H_{2} \)


Which factory has more variation in wages?
A . \( A \)
в. \( B \)
C. Equal Variation
D. Cannot be determined.


In the forward bias characteristic curve,
a diode appears as:
A. an OFF switch
B. a high resistance
c. an on switch
D. a capacitor


Boiling water reacts with
gives their
respective hydroxides and ammonia
gas.
A. magnesium nitride
B. calcium nitride
C. aluminium nitride
D. all of the above


Let \( \mathbf{P} \) and \( \mathbf{Q} \) be \( \mathbf{3} \times \mathbf{3} \) matrices with
\( \boldsymbol{P} \neq \boldsymbol{Q} . \) If \( \boldsymbol{P}^{3}=\boldsymbol{Q}^{3} \) and \( \boldsymbol{P}^{2} \boldsymbol{Q}=\boldsymbol{Q}^{2} \boldsymbol{P} \)
then determinant of \( \left(P^{2}+Q^{2}\right) \) is equal
to:
A . -2
B.
\( c \cdot 0 \)
D. -


Two mirrors at an angle \( \theta^{\circ} \) produces 5 images of a point. The number of images produced when \( \theta \) is decreased
\( \operatorname{to} \theta-30^{\circ} \) is then going to be
\( A \cdot 9 \)
B. 10
c. 11
D. 12


Find constant of variation and write
equation of variation for given below.
\( \mathbf{A} \quad \boldsymbol{p} \boldsymbol{a} \frac{\mathbf{1}}{\boldsymbol{q}}: \boldsymbol{i} \boldsymbol{f} \boldsymbol{p}=\mathbf{1 5} t h e \boldsymbol{n} \boldsymbol{q}=\boldsymbol{4} \)
\( \mathbf{B} \quad \boldsymbol{z} \boldsymbol{a} \frac{\mathbf{1}}{\boldsymbol{w}} ; \boldsymbol{w} \boldsymbol{h} \boldsymbol{e} \boldsymbol{n} \boldsymbol{z}=\mathbf{2} \)
\( c \quad s a \frac{1}{r^{2}} ; i f s=4 t h e n t=5 \)
D \( x \) a feacl \( \sqrt{y} ; \) if \( x=15 \)


A matrix \( A=\left(A_{i j}\right)_{m \times n} \) is said to be a
square matrix if
\( \mathbf{A} \cdot m=n \)
в. \( m \leq n \)
c. \( m \geq n \)
D. \( m<n \)


An air bubble is inside water. The refractive index of water is \( \frac{4}{3} . \) At what distance from the air bubble should a
point object be placed so as to form a real image at the same distance from
the bubble?
A . 2 R
B. 3R
c. 4 R
D. The air bubble cannot form a real image


If the distance between a point \( \boldsymbol{P} \) and the point (1,1,1) on the line \( \frac{x-1}{3}= \) \( \frac{\boldsymbol{y}-\mathbf{1}}{\mathbf{4}}=\frac{\boldsymbol{z}-\mathbf{1}}{\mathbf{1 2}} \) is \( \mathbf{1 3}, \) then the
coordinates of \( \boldsymbol{P} \) are
A. (3,4,12)
в. \( \left(\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right) \)
c. (4,5,13)
D. (40,53,157)


How many electrons are present in the
M shell of the atom of an element with
atomic number \( 24 ? \)
A . 5
B. 6
c. 12
D. 13


A solid sphere of mass \( M \) and radius \( R \) is hit by a cue at a height \( h \) above the
centre \( C \). If the value of \( h \) for which the
sphere will roll without slipping is \( \frac{x}{5} R \)
Find \( x \)


What will be the number of stereo
isomers of a compound contain only two asymmetric carbon atoms?
A .2
B. 3
\( c \cdot 4 \)
D. 5


Choosing a queen from a deck of cards
is an example of
A. compound event
B. complementary event
c. simple event
D. impossible event


The shape of any organic molecule depends upon:
A. sigma bonds
B. pi bonds
c. both a and \( b \)
D. none of these


The magnetic flux through a circuit of resistance R changes by an amount \( \Delta \phi \) in time \( \Delta t . \) Then the total quantity of electric charges \( Q \) that passes any point in the circuit during the time \( \Delta t \) is represented by:
A \( \cdot Q=\frac{\Delta \phi}{R} \)
в. \( Q=\frac{\Delta \phi}{\Delta t} \)
c. \( Q=R \cdot \frac{\Delta \phi}{\Delta t} \)
D. \( Q=\frac{1}{R} \cdot \frac{\Delta \phi}{\Delta t} \)


When a rod of magnetic material size \( 10 c m \times 0.5 c m \times 0.2 c m \) is located in
magentic field of \( 0.5 \times 10^{4} \mathrm{A} / \mathrm{m} \) then \( \mathrm{a} \)
magnetic moment of \( 5 A m^{2} \) is induced in it. Find out magnetic induction in rod.


How may H-bonds are formed between
the two strands of dsDNA of \( 170 A^{\circ} \)
length if the cytosine is \( 20 \% ? \)


Focal length of convex lens \( =100 \mathrm{cm} \)
and focal length of concave lens \( = \)
\( -8 c m . \) Find the magnification.


Draw the graph for the equation given below; hence find the co-ordinates of
the points where the graph drawn meets the co-ordinate axes:
\( \frac{2 x+15}{3}=y-1 \)
\( \mathbf{A} \cdot(4,0) \) and (0,9)
B \( \cdot(-1,0) \) and (0,6)
\( \mathbf{c} \cdot(-9,0) \) and (0,6)
D. (5,0) and (0,-9)


If a straight wire carrying a current \( \boldsymbol{i}_{1} \) amp runs along the axis of a circular
current carrying loop having current \( i_{2} \) amp, then the force of interaction
between the two current carrying conductors is
A. zero
B. Infinity
c. \( \frac{2 i_{1} i_{2}}{r} N m^{-1} \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{2 i_{1} i_{2}}{r} N m^{-1} \)


Out of dia, para and ferromagnetism, the
universal property of all substances is
A. diamagnetism
B. paramagnetism
C. ferromagnetism
D. antiferromagnetism


A set of points which do not lie on the same line are called as
A. collinear
B. non-collinear
c. concurrent
D. square


Assertion
The numerical value of \( \frac{1}{n} \) in Freundlich adsorption isotherm, \( \frac{x}{m}=K(P)^{1 / n} \) at
saturation pressure is zero.
Reason
At saturation pressure, the amount adsorbed per unit volume does not change with increase in pressure.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct


The largest and the shortest distance of
the earth from sun are a and b,
respectively. The distance of the earth from sun when it is at a point where perpendicular drawn from the sun on
the major axis meets the orbit is
A \( \cdot \frac{a b}{a+b} \)
в. \( \frac{a b}{2(a+b)} \)
c. \( \frac{2 a b}{a+b} \)
D. \( \frac{a+b}{2 a b} \)


In recent years, pre-soaked laundry agent (detergent) contains an enzyme
A. Pepsin
B. Flavin
c. Amylase
D. Subtilin


\( \mathbf{5}+\mathbf{3} \sqrt{\mathbf{2}} \) is an irrational number
A. True
B. False


If \( f(x)=\sec (3 x), \) then \( f^{\prime}\left(\frac{3 \pi}{4}\right)= \)
A. \( -3 \sqrt{2} \)
B. \( -\frac{3 \sqrt{2}}{2} \)
\( c \cdot \frac{3}{2} \)
D. \( \frac{3 \sqrt{2}}{2} \)
E. \( 3 \sqrt{2} \)


A bulb of \( 22 \Omega \) is producing light when connected to \( 220 \mathrm{V} \) supply. What is the electric power of the bulb.
A. 2200 watt
B. 1000 watt
c. 22 watt
D. 2 watt


The average molecular mass of drugs is approximately:
A . \( 160-480 \) g/mol
B. 1600-4800 g/mol
c. \( 10-100 \mathrm{g} / \mathrm{mol} \)
D. 0.1-100 g/mol


The values of \( a \) and \( b \) for which the
function \( \boldsymbol{y}=\boldsymbol{a} \log _{e} \boldsymbol{x}+\boldsymbol{b} \boldsymbol{x}^{2}+\boldsymbol{x}, \) has
extremum at the points \( x_{1}=1 \) and
\( \boldsymbol{x}_{2}=2 \) are
\( ^{A} \cdot_{a}=\frac{2}{3}, b=-\frac{1}{6} \)
B. \( \quad a=-\frac{2}{3}, b=-\frac{1}{6} \)
c. \( _{a=-\frac{2}{3}, b=\frac{1}{6}} \)
D. \( _{a=-\frac{1}{3}, b=-\frac{1}{6}} \)


For which of the following reactions,
\( \Delta H=\Delta E+2 R T ? \)
A \( \cdot N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g) \)
B. \( N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) \)
C \( . N H_{4} H S(s) \rightarrow N H_{3}(g)+H_{2} S(g) \)
D. \( P C l_{5}(g) \rightarrow P C l_{3}(g)+C l_{2}(g) \)


If the distance between the earth and
the sun is half its present value, the number of days in a year would have
been
A. 730
B. 182.5
\( c \cdot 129 \)
D. 64.5


A ray of light is incident on a glass slab
of refractive index \( 1.52 . \) if the reflected
and refracted rays of light are mutually perpendicular to each other then the angle of incidence will be
A \( .90^{\circ} \)
B . \( 60^{\circ} \)
c. \( 56^{\circ} \) 40
D \cdot \( 19^{\circ} 58^{\prime} \)


Is the line through (-2,3) and (4,1) perpendicular to the line \( \mathbf{3} \boldsymbol{x}=\boldsymbol{y}+\mathbf{1} ? \)
Does the line \( 3 x=y+1 \) bisect the line
joining of (-2,3) and (4,1)\( ? \)


The amount of energy that a unitary point electric charge would have, if located at any point in space, is defined
its:
A. electric potential energy
B. electric potential
c. electric potential difference
D. electric field


A wire of length \( 1 m \) and mass \( 20 g \) is stretched with a force of \( 800 N \). The
frequencies of the first two overtones
are
A. \( 200 H z, 300 H z \)
в. \( 300 H z, 200 H z \)
c. \( 100 H z, 400 H z \)
D. \( 400 H z, 100 H z \)


Which of the following are the main categories in Spherical Mirrors?
A. Plane and Curved
B. Concave and Convex
c. Virtual and Real
D. Upright and Inverted


What is the potential of the cell containing two hydrogen electrodes as represented below?
\( \boldsymbol{p t} ; \frac{1}{2} \boldsymbol{H}_{2}(\boldsymbol{g})\left|\boldsymbol{H}_{2} \boldsymbol{O}\right|\left|\boldsymbol{H}^{\oplus}(\mathbf{0 . 0 0 1} \boldsymbol{M})\right| \mathbf{1} / \mathbf{2} \boldsymbol{H} \)
A. \( -0.236 V \)
В. \( -0.0591 V \)
c. \( 0.236 V \)
D. \( 0.0591 V \)


"While comparison of \( L i^{+} \) and \( N a^{+} \)
salts in terms of property of complex
formation we found that \( \left[\boldsymbol{L} \boldsymbol{i}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right] \)
exists and \( N a \) does not form any
complex." Answer whether the above statement is
true or false.
If true enter 1 , else 0


Two solid spheres \( A \) and \( B \) each of
radius \( ^{\prime} R^{\prime} \) are made of materials of
densities \( \rho_{A} \) and \( \rho_{B} \) respectively. Their moments of inertia about a diameter
\( \operatorname{are} I_{A} \) and \( I_{B} \) respectively. The value of \( \frac{\boldsymbol{I}_{A}}{\boldsymbol{I}_{B}} \) is:
A. \( \sqrt{\frac{\rho_{A}}{\rho_{B}}} \)
в. \( \sqrt{\frac{\rho_{B}}{\rho_{A}}} \)
c. \( \frac{\rho_{A}}{\rho_{B}} \)
D. \( \frac{\rho_{B}}{\rho_{A}} \)


The harmful and unwanted substances
which degrade the quality of water are called as
A. water pollutants
B. soil pollutants
c. air pollutants
D. none of the above


Integrated circuit is defined as:
A. a single electronic circuit on a small plate of semiconductor material.
B. a set of electronic circuits on one small plate of semiconductor material.
C . a circuit capable of generating dc currents.
D. a plate of semiconductor material used to connect external multiple circuits


\( a, b, c(a>c) \) are the three digits, from left to right of a three digit number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digit 4 in its unit's place. The other two digits
from left to right are -
A. 5 and 4
B. 5 and 9
c. 4 and 5
D. 9 and 5


What happens when a sound wave is reflected from the boundary of a denser medium? The compression of the incident wave is returned as a
A. rarefaction
B. crest
c. trough
D. compression


The number of occupied sub-shell in \( \mathrm{Cr} \)
\( + \) is :
A . 3
B. 4
\( c \cdot 7 \)
D. 6


Two boys are holding a horizontal rod of length \( L \) and weight \( W \) through its two ends. If now one of the boys suddenly leaves he rod. what is the instantaneous
reaction force experienced by the other boy?
A \( \cdot \frac{W}{4} \)
в. \( \frac{W}{2} \)
c. \( \frac{3 W}{4} \)
D. \( W \)


f \( x+y+z=x y z, \) and \( x, y, z>0 \)
then find the value of \( \tan ^{-1} x+ \)
\( \tan ^{-1} y+\tan ^{-1} z \)


The most common reagent for qualitative and quantitative analysis of amino acids is:
A. Ninhydrin reagent
B. Millon's reagent
c. sangars reagent
D. Edmanns reagent


Determine the current flowing through the circuit shown above
A . \( 25 \mathrm{mA} \)
B. \( 12.5 \mathrm{mA} \)
\( c .29 \mathrm{mA} \)
D. \( 80 \mathrm{mA} \)


Two charges of \( +25 \times 10^{-9} \) coulomb
and \( -25 \times 10^{-9} \) coulomb are placed \( 6 \mathrm{m} \) apart. Find the electric field intensity ratio at points \( 4 \mathrm{m} \) from the centre of
the electric dipole
(i) on axial line
(ii) on equatorial line
A \( \cdot \frac{1000}{49} \)
в. \( \frac{49}{1000} \)
c. \( \frac{500}{49} \)
D. \( \frac{49}{500} \)


Find the cosine of the angle \( A \) of the
triangle with vertices \( \boldsymbol{A}(\mathbf{1},-\mathbf{1}), \boldsymbol{B}(\boldsymbol{6}, \mathbf{1 1}) \) and \( \boldsymbol{C}(\mathbf{1}, \boldsymbol{2}) \)


Which of the following doesn't affected by both electrical field and magnetic field?
A. Alpha rays
B. Beta rays
c. Gamma rays
D. All of the above


(i) Which particles are responsible for current in conductors?
(ii) To which wire of a cable in a power circuit should the metal case of a
geyser be connected?
(iii) To which wire should the fuse be
connected ?


What product, or products, would you
expect from the given reaction? Name
the mechanism \( \left(S N_{1} \text { or } S N_{2}\right) \) that gives each product(s).


\( 4 g \) of hydrogen and \( 128 g \) of hydrogen iodide are present in a 2 litre flask. What are their active masses?


A light whose frequency is equal to \( 6 x \) \( 10^{14} H z \) is incident on a metal whose
work function is \( 2 e V \)
\( \left(h=6.63 \times 10^{-34} J s, 1 e V=1.6 \times 10^{-}\right. \)
The maximum energy of electrons emitted will be:
A \( .2 .49 e V \)
в. \( 4.49 e V \)
c. \( 0.49 e V \)
D. \( 5.49 e V \)


Obtain all the zeroes of \( 3 x^{4}+6 x^{3}- \) \( 2 x^{2}-10 x-5, \) if of its zeroes are \( \sqrt{\frac{5}{3}} \) \( \mathfrak{Q}-\sqrt{\frac{\mathbf{5}}{\mathbf{3}}} \)


Type of asexual reproduction found in
Hydra is
A. Gemmule formation
B. Sporulation
c. Binary fission
D. Budding


Find the average of the squares of emf induced over a long period.


What is multiple reflection of sound?
A. Process in which sound waves bounces off obstacles and reflects many times before reaching destinations
B. Process in which sound waves penetrates in obstacles and reflects many times before reaching destinations
c. Process in which sound waves bounces off obstacles and deflects one time before reaching destinations
D. None


Lifting automobiles in service stations is based on the principle of
A. Apparent pressure
B. Hydraulic pressure
c. Atmospheric pressure
D. none of the above


\( \ln \operatorname{an} A P, \operatorname{given} a=5, d=3, a_{n}=50 \)
find \( n \) and \( S_{n} \)


Define the following:
(a) Total internal reflection
(b) Diffraction of light
(c) Refraction of light


Assertion
When a body dropped from a height explodes in mid-air, its center of mass
keeps moving in vertically downward
direction
Reason
Explosion occur under internal forces
only. External force is zero.
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


\( \sum_{k=1}^{6}\left[\sin \frac{2 k \pi}{7}-i \cos \frac{2 k \pi}{7}\right]= \)
A . -1
B.
\( c \cdot-i \)
D.


In order to produce many copies of a protein fast, the cell uses
A. DNA replication
B. single-unit ribosomes for high speed translation
c. codon-anticodon reciprocal duplication
D. many RNA polymerase molecules to produce mRNA transcripts at the same time


The frequencies of four sound waves are given below. Which of these sound
waves can be used to measure the
depth of sea by the echo method?
\( A \cdot 15,000 \mathrm{Hz} \)
B. 10 kHz
c. \( 50 \mathrm{kHz} \)
D. \( 10,000 \mathrm{Hz} \)


If \( u=\tan ^{-1}\left(\frac{x^{2}+y^{2}}{x+y}\right), \) then \( x \frac{d u}{d x}+ \)
\( \boldsymbol{y} \frac{\boldsymbol{d} \boldsymbol{u}}{\boldsymbol{d} \boldsymbol{y}}= \)
\( \mathbf{A} \cdot \sin 2 u \)
B. \( \frac{1}{2} \sin 2 u \)
c. \( \frac{1}{3} \sin 2 u \)
D. \( 2 \sin 2 u \)


Which of the following correctly describes teflon?
A. It is an antiseptic.
B. It is an antifreeze
c. It is an anti-corrosive plastic.
D. All of the above


The number of structural isomer for an
alkane with a molecular weight 72 is:
A .2
B. 3
\( c \cdot 4 \)
D. 5


The pair of complementary angles from the following options are:
A . \( 30^{\circ}, 150^{\circ} \)
В. \( 76^{\circ}, 14^{\circ} \)
\( \mathbf{c} \cdot 65^{\circ}, 65^{\circ} \)
D. \( 120^{\circ}, 30^{\circ} \)


The number of independent constituent simple harmonic motions yielding a resultant displacement equation of the
periodic motion as \( \boldsymbol{y}= \)
\( 8 \sin ^{2}\left(\frac{t}{2}\right) \sin (10 t) \) is:
\( A \cdot 8 \)
B. 6
\( c \cdot 4 \)
\( D .3 \)


What is the \( K_{b} \) of a weak base
that produces an \( O H^{-} \) per molecule if a 0.05 M solution is \( 2.5 \% \) ionized?
\( \mathbf{A} \cdot 7.8 \times 10^{-8} \)
B . \( 1.6 \times 10^{-6} \)
c. \( 3.125 \times 10^{-5} \)
D. \( 1.2 \times 10^{-3} \)


Perform the division \( \frac{\left(x^{2}+1\right)\left(x^{2}+2\right)}{\left(x^{2}+3\right)\left(x^{2}+4\right)} \)


The magnetic flux in a closed circuit of resistance \( 10 \Omega \) varies with time as
\( \phi=\left(2 t-4 t^{2}+1\right) . \) The current in the
loop will change its direction after a time of
A . \( 0.25 \mathrm{sec} \)
B. 0.5 sec
c. 1 sec
D. none


Which one among the following is added to soap to impart antiseptic
property?
A. Sodium lauryl sulphate
B. Sodium dodecyl benzene sulphonates
c. Rosin
D. Bithional


Eliminating \( a, b, c \) from \( x=\frac{a}{b-c}, y= \)
\( \frac{b}{c-a}, z=\frac{c}{a-b} \) we get
\( \mathbf{A} \cdot\left|\begin{array}{lll}1 & -x & x \\ 1 & -y & y \\ 1 & -z & z\end{array}\right|=0 \)
B. \( \left|\begin{array}{ccc}1 & -x & x \\ 1 & 1 & -y \\ 1 & z & 1\end{array}\right|=0 \)
c. \( \left|\begin{array}{ccc}1 & -x & x \\ y & 1 & -y \\ -z & z & 1\end{array}\right|=0 \)
D. none of these


Haemoglobin is formed from an iron-
containing part called and a
protein called


Find the area of a quadrant of a circle
whose circumference is \( 22 \mathrm{cm} \)


The effective capacitance between \( \boldsymbol{A} \)
and \( B \) will be
A. \( 0.5 F \)
В. \( 1.5 F \)
\( c .2 F \)
D. 2.5


Which of the following enzyme is used to join DNA fragments?
A. Terminase
B. Endonuclease
c. Ligase
D. DNA polymerase


In case of refraction of light
a) Frequency changes
b) Speed changes
c) Wavelength changes
A . a is correct
B. b and c are correct
\( c . a, b, c \) are correct
D. a and b are correct


Calculate the sum of the series
\( \left(x+\frac{1}{x}\right)^{2}+\left(x^{2}+\frac{1}{x^{2}}\right)^{2}+ \)
\( \left(\boldsymbol{x}^{3}+\frac{1}{\boldsymbol{x}^{3}}\right)^{2}+\ldots . .\left(\boldsymbol{x}^{\boldsymbol{n}}+\frac{1}{\boldsymbol{x}^{\boldsymbol{n}}}\right)^{2} \)
A \( \cdot \frac{x^{n}-1}{x^{2}-1} \cdot\left[\frac{x^{2 n+2}+1}{x^{2 n}}\right]+2 n \)
B. \( \frac{x^{n}-1}{x^{2}-1} \cdot\left[\frac{x^{n+1}+1}{x^{2 n}}\right]+2 n \)
\( \frac{x^{2 n}-1}{x^{2}-1} \cdot\left[\frac{x^{2 n+2}+1}{x^{2 n}}\right]+2 n \)
D \( \frac{x^{2 n}-1}{x^{2}-1} \cdot\left[\frac{x^{n+1}+1}{x^{2 n}}\right]+2 n \)


The long and short hands of a clock are
\( 6 \mathrm{cm} \) and \( 4 \mathrm{cm} \) long respectively. Find the sum of distances travelled by their
tips in 24 hrs. \( (U s e \pi=3.14) \)


Consider the following reactions at 300 \( \mathrm{K}: \mathrm{X} \rightarrow \mathrm{Y} \) (uncatalysed reaction)
\( \& X \rightarrow \)
Y (catalysed reaction). The energy of activation is lowered by 83.14 kJmol \( ^{-1} \)
for the catalysed reaction. The rate of catalysed reaction is:
A \( \cdot 3 \times 10^{14} \) times that of uncatalysed reaction
B. \( 15 \times 10^{14} \) times that of uncatalysed reaction
c. 25 times that of uncatalysed reaction
D. 22 times that of uncatalysed reaction


The acceleration of Particle starting
from rest and moving along a straight
line is as shown. Other than at \( t=0 \)
when is the velocity of the object equal
to zero?
A. At \( t=3.5 s \)
B. During the interval from \( 1 s \) to 3 s
C. At \( t=5 s \)
D. At no other time on this graph


Express as kilometre (km) using decimals:
\( \mathbf{5 5} \boldsymbol{m} \)


A parallel-plate air capacitor of
capacitance \( 245 p F \) has a charge of
magnitude \( 0.148 \mu C \) on each plate. The
plates are \( 0.328 m m \) apart. What is the
potential difference between the plates \( (\text { in } V) ? \)


Solve the differential equation:
\( \boldsymbol{y} \log \boldsymbol{y} \boldsymbol{d} \boldsymbol{x}-\boldsymbol{x} \boldsymbol{d} \boldsymbol{y}=\mathbf{0} \)


If force \( F=(500-100) t, \) then impulse as
a function of time will be:-
\( \mathbf{A} \cdot 500 t-50 t^{2} \)
B . \( 50 t-10 \)
c. \( 50-t^{2} \)
D. \( 100 t^{2} \)


If the load resistance decreases in a
zener regulator, the zener current
A. Decreases
B. Stays the same
c. Increases
D. Equals the source voltage divided by the series resistance


\( N O_{2}^{-} \) interferes in the 'ring test' of
\( N O_{3}^{-} . \) It is removed from the mixture
using urea.
If true enter 1 , else enter 0


\( \boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{f}(\boldsymbol{x}), \boldsymbol{f}(\mathbf{0})=\mathbf{1}, \) then
\( \int \frac{d x}{f(x)+f(-x)} \)
\( \mathbf{A} \cdot \log \left(e^{2 x}+1\right)+C \)
B. \( \log \left(e^{x}+e^{-x}\right)+C \)
c. \( \tan ^{-1}\left(e^{x}\right)+C \)
D. None


A bus travels \( 30 \mathrm{km} \) at a uniform speed of \( 40 \mathrm{km} / \mathrm{h} \) and the next \( 30 \mathrm{km} \) at a
uniform speed of \( 20 \mathrm{km} / \mathrm{h} \).The average speed of the bus is
\( \mathbf{A} \cdot 26.6 \mathrm{km} / \mathrm{h} \)
B. 36.8 km/h
c. \( 25 \mathrm{km} / \mathrm{h} \)
D. 28.9 km/h


Shows which type of isomerism:
\[
\mathrm{CH}_{3} \mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{2} \mathrm{CH}_{3} \quad \mathrm{CH}_{3}^{\mathrm{O}} \mathrm{C}-\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}
\]
Diethyl ether Methyl propyl ether
A. Functional group isomerism
B. Geometrical isomerism
C . Metamerism
D. Position isomerism


What is growth curve?


Q Type your question-
having track, is \( M=1 k g \) and rests
over a smooth horizontal floor. \( A \)
cylinder of radius \( r=10 \mathrm{cm} \) and mass
\( m=0.5 k g \) is hanging by thread such
that axes of cylinder and track are in
same level and surface of cylinder is in contact with the track as shown in
figure. When the thread is burnt cylinder starts to move down the track.
Sufficient friction exists between
surface of cylinder and track, so that cylinder does not slip.Calculate velocity of axis of cylinder and velocity of the block when it reaches bottom of the
track. Also find force applied by block on
the floor at that moment \( \left(\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right) \)


If the roots of the equation \( x^{3}-11 x^{2}+ \)
\( 36 x-36=0 \) are in \( H . P . \) then the
middle root is
A. an even number
B. a perfect square of an integer
c. a prime number
D. a composite number


Potassium metabisulphite is a (an):
A. preservative
B. antioxidant
c. artificial sweetener
D. both (A) and (B)


Decomposer protists are
A. Diatoms
B. Dinoflagellates
c. slime moulds
D. Euglenoid


Which are true for the reaction: \( A_{2} \rightleftharpoons \)
\( 2 C+D ? \)
This question has multiple correct options
A . If \( \Delta H=0 ; K_{p} \) increases with temperature and dissociation temperature.
B . If \( \Delta H=+v e ; K_{p} \) increases with temperature and dissociation of \( A_{2} \) increases
C . If \( \Delta H=-v e ; K_{p} \) increases with temperature and
dissociation of \( A_{2} \) decreases
D・ \( K_{p}=4 \alpha^{3}\left[\frac{P}{1+2 \alpha}\right]^{2} \)


The straight lines \( \frac{\boldsymbol{x}-\mathbf{1}}{\mathbf{1}}=\frac{\boldsymbol{y}-\mathbf{2}}{\mathbf{2}}= \)
\( \frac{z-3}{3} \) and \( \frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3} \) are
A. Parallel lines
B. Intersecting at \( 60^{\circ} \)
c. skew lines
D. Intersecting at right angle


Define Periodic motion.


Two satellites are revolving around the earth in circular orbits of same radii.
Mass of one satellite is 100 times that
of the other. Then their periods of revolution are in the ratio:
A . 100: 1
B. 1: 100
c. 1: 1
D. 10: 1


Select the object from the following which can shine (have lusture)
A. glass bowl and wooden bowls
B. towel and toys
c. shirts and scarfs
D. ornaments and brass utensils


The image of: (-4,0,0) in the \( x z \) - plane is (4,0,0)
A. True
B. False


Write balanced chemical equation for
the reaction of calcium oxide with
water?


In recent year, there has been a growing
concern about the gradually increasing average global temperatures. If this trend continues, would you expert the distributional range of some species to be affected?


There are two possible values of \( p \& \) if the distance of \( (p, 4) \) and (5,0) is 5 then the two value difference of p is
\( \mathbf{A} \cdot \mathbf{4} \)
B. 5
\( c \cdot 6 \)
D. 2


A domain in ferromagnetic iron in the
form of cube is having \( 5 \times 10^{10} \) atoms.
If the side length of this domain is
1.5 \( \mu m \) and each atom has a dipole moment of \( 8 \times 10^{-24} \mathrm{A} m^{2}, \) then
magnetisation of domain is?
A. \( 11.8 \times 10^{5} \mathrm{A} \mathrm{m}^{-1} \)
B. \( 1.18 \times 10^{4} \mathrm{A} \mathrm{m}^{-1} \)
c. \( 11.8 \times 10^{4} \mathrm{A} \mathrm{m}^{-1} \)
D. \( 1.18 \times 10^{5} \mathrm{A} \mathrm{m}^{-1} \)


When sugar is mixed with water and
stirred then:
A. it floats for some time and then starts dissolving
B. it settles down and do not dissolves
C. it dissolves immediately on stirring
D. none of the above


For the equilibrium, \( \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{s}) \Leftrightarrow \boldsymbol{H}_{2} \boldsymbol{O}(\boldsymbol{l}) \)
which of the following is true?
A. The pressure changes do not affect the equilibrium.
B. The amount of ice that melts is more, if the pressure on the system is increased
c. The amount of liquid that freezes is more, if the pressure on the system is increased.
D. At low pressure, the nature of equilibrium changes to forward direction


\( \int_{0}^{1} \frac{x e^{x}}{(x+1)^{2}} d x= \)
A. \( \frac{e}{2} \)
B. \( \frac{e-1}{2} \)
c. \( \frac{e}{2}-1 \)
D. \( \frac{e-3}{2} \)


If
\( A \) is a non-singular matrix, then
This question has multiple correct options
\( \mathbf{A} \cdot A^{-1} \) is symmetric if \( A \) is symmeteric
B. \( A^{-1} \) is skew-symmetric if \( A \) is symmeteric
\( \mathbf{C} \cdot\left|A^{-1}\right|=|A| \)
D \( \cdot\left|A^{-1}\right|=|A|^{-1} \)


\( \cos \left(\tan ^{-1} \frac{3}{4}\right) \)


A jet plane is travelling towards west at a speed of \( 1800 \mathrm{km} / \mathrm{h} \). What is the
voltage difference developed between the ends of the wing having a span of \( 25 m, \) if the Earth's magnetic field at the location has a magnitude of \( 5 \times \)
\( 10^{-4} T \) and the dip angle is \( 30^{\circ} \)
\( \begin{array}{ll}\text { A } & \text { 0.31 }\end{array} \)
в. 3.1
\( c \cdot 5 v \)
D. 10


Cytokinesis is a division of:
A . Cytoplasm
B. Nucleus
c. chromosomes
D. Nucleolus


Find irrational number between \( \frac{9}{6} \) and
\( \frac{4}{5} \)


Elements are classified as:
\( \mathbf{A} \). metals and metalloids
B. metals and alloys
C. metals and non-metals
D. non-metals and metalloids


\( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{\sin \boldsymbol{x}}{\boldsymbol{x}}\right) \)
A. \( \frac{x \cos x-\sin x}{x^{2}} \)
B. \( \frac{x \cos x+\sin x}{x^{2}} \)
c. \( \frac{x \cos x+\sin x}{x^{3}} \)
D. \( \frac{x \cos x-\sin x}{x^{3}} \)


The maximum bowling speed (kms/hour) of 33 players at a cricket coaching centre is given below:
Find the modal bowling speed of
players.
Bowling 85
\( \begin{array}{ll}100 & 115\end{array} \)
speed \( (\mathrm{kms} / \mathrm{hr}) \)
\( \begin{array}{lll}\text { DO } & 115 & 130\end{array} \)
No. of Players
A. Rs. 101kms/hour
B. Rs.106 kms/hour
c. Rs.115 kms/hour
D. Rs.118 kms/hour


The edge of a cube is measured using a vernier callipers. \( [9 \) divisions of the main scale is equal to 10 divisions of vernier scale and 1 main scale division
is \( 1 \mathrm{mm} \) ]. The main scale division reading is 10 and 1 division of vernier scale was found to be coinciding with the main scale. The mass of the cube is
2.736 gm. Calculate the density in \( \mathrm{gm} / \mathrm{cm}^{3} \) up to correct significant figures.


Number of angular nodes for \( 4 d \) orbital
is
A . 4
B. 3
\( c \cdot 2 \)
\( D \)


The number of people living per square feet is known as the density of population
A. True
B. False


\( \boldsymbol{H}_{2}(\boldsymbol{g})+\boldsymbol{I}_{2}(\boldsymbol{g}) \longrightarrow 2 \boldsymbol{H} \boldsymbol{I}(\boldsymbol{g}) \)
For this reaction, relate \( \Delta H \) and \( \Delta U \)
\( \mathbf{A} \cdot \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
\( \mathbf{c} \cdot \Delta H<\Delta U \)
D. None of these


As regards the use of international food safety standards as reference point for the dispute settlements, which one of the following does WTO collaborate with?
A. codex Alimentarius Commission
B. International Federation of Standards Users
c. International organization for standardization
D. world Standards Cooperation


State whether the following statement
is True or False.
All even numbers are composite
numbers.
A. True
B. False


The rate for a first order reaction is
\( 0.6932 \times 10^{-2} \) mol litre \( ^{-1} \min ^{-1} \) and
the initial concentration of the reactant
is \( 1 \mathrm{M}, t_{1 / 2} \) is equal to:
B. 100 minutes
c. \( 0.693 \times 10^{-3} \) minute
D. 6.932 minutes


In a group of 1000 people, there are 750
people who can speak Hindi and 400 who can speak English. Then number of persons who can speak Hindi only is
A . 300
в. 400
c. 600
D. None of these


Let \( \left[\epsilon_{0}\right] \) denote the dimensional formula
of the permittivity of vacuum. If \( \boldsymbol{M}= \) mass, \( \boldsymbol{L}= \) length \( , \boldsymbol{T}=\boldsymbol{t} \) ime and \( \boldsymbol{A}= \)
electric current, then
\( \mathbf{A} \cdot \epsilon_{0}=\left[M^{-1} L^{-3} T^{2} A\right] \)
B . \( \epsilon_{0}=\left[M^{-2} L^{-3} T^{4} A^{2}\right. \)
C \( . \epsilon_{0}=\left[M^{1} L^{2} T^{1} A^{2}\right] \)
D. \( \epsilon_{0}=\left[M^{1} L^{2} T^{1} A\right] \)


Assertion
Aqueous solution of \( C H_{3} C O O N H_{4} \) is
exactly neutral. \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{K}_{\boldsymbol{b}}\right) \)
Reason
\( C H_{3} C O O N H_{4} \) is a salt of weak acid
and strong base.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


If \( \boldsymbol{f}(\boldsymbol{a})=\boldsymbol{a}^{2}, \boldsymbol{\phi}(\boldsymbol{a})=\boldsymbol{b}^{2} \) and \( \boldsymbol{f}^{\prime}(\boldsymbol{a})= \)
\( \mathbf{3} \phi^{\prime}(\boldsymbol{a}) \) then \( \lim _{x \rightarrow 0} \frac{\sqrt{\boldsymbol{f}(\boldsymbol{x})}-\boldsymbol{a}}{\sqrt{\boldsymbol{\phi}(\boldsymbol{x})}-\boldsymbol{b}} \) is
\( \mathbf{A} \cdot b^{2} / a^{2} \)
в. \( b / a \)
c. \( 2 b / a \)
D. None of these


In a meter bridge with a standard resistance of \( 5 \Omega \) in the left gap, the ratio of balancing lengths on the meter bridge wire is \( 2: 3 . \) The unknown
resistance is
A . \( 3.3 \Omega \)
B. \( 7.5 \Omega \)
c. \( 10 \Omega \)
D. 15\Omega


From which plant is litmus paper or litmus solution obtained?
A. Moss
B. Rose
c. Hibiscus
D. Lichen


The smell of bitter almond is given by the compound:
A. benzoic acid
B. benzaldehyde
c. vanilin
D. cinnamaldehyde


Three Carnot engines operate in series
between a heat source at a temperature
\( T_{1} \) and a heat sink at temperature \( T_{4} \)
(see figure). There are two other
reservoirs at temperature \( T_{2}, \) and \( T_{3}, \) as
shown, with \( T_{2}>T_{2}>T_{3}>T_{4} . \) The
three engines are equally efficient
if \( _{--} \) ?
A \( \cdot T_{2}=\left(T_{1}^{2} T_{4}\right)^{1 / 3}: T_{3}=\left(T_{1} T_{4}^{2}\right)^{1 / 3} \)
B . \( T_{2}=\left(T_{1} T_{4}^{2}\right)^{1 / 3}: T_{3}=\left(T_{1}^{2} T_{4}\right)^{1 / 3} \)
c. \( T_{2}=\left(T_{1}^{3} T_{4}\right)^{1 / 4}: T_{3}=\left(T_{1} T_{4}^{3}\right)^{1 / 4} \)
D. \( T_{2}=\left(T_{1} T_{4}\right)^{1 / 2}: T_{3}=\left(T_{1}^{2} T_{4}\right)^{1 / 3} \)


List and explain the factors which affect the stability of coordination complexes.


Amongst the following carboxylic acids, the strongest acid is (for first dissociation of dicarboxylic acid):
\( A \)
в.
c. \( C H_{3} C H_{2} C O O H \)
D. \( C H_{3} \) COOH


Which of the following statement is true
\( ? \)
A. Fractions with same numerator are called like fractions
B. Fractions with same denominator are called unlike
fractions
C. Difference of two like fractions = \( \frac{\text {difference of numerators}}{\text {common denominator}} \)
D. A fraction with numerator greater than or equal to the denominator is called proper fraction


Two first order reaction have half-lives
in the ration \( 8: 1 . \) Calculate the ration
of time intervals \( t_{1} \) and \( t_{2} \) are the time period for the \( \left(\frac{1}{4}\right)^{t h} \) and \( \left(\frac{3}{4}\right)^{t h} \) completion.
A. 1: 0.30
в. 0.125: 0.602
c. 1: 0.602
D. none of these


A metallic rod of length \( l^{\prime} \) is tied to a
string of length \( 2 l \) and made to rotate
with angular speed \( \omega \) on a horizontal table with one end of the string fixed. If
there is a vertical magnetic field \( B^{\prime} \) in the region, the e.m.f. induced across the
ends of the rod is:
A \( \cdot \frac{3 B \omega l^{2}}{2} \)
в. \( \frac{4 B \omega l^{2}}{2} \)
c. \( \frac{5 B \omega l^{2}}{2} \)
D. \( \frac{2 B \omega l^{2}}{2} \)


With the help of a suitable diagram show the formation of sodium chloride.
\( \left[\begin{array}{cc}23 N a, & 35 C l\end{array}\right] \)