Bag \( A \) contains 2 white and 3 red balls
and bag \( B \) contains 4 white and 5 red
balls. One ball is drawn at random from
one of the bag is found to be red. Find the probability that it was drawn from
bag \( \boldsymbol{B} \)
\( A \cdot \frac{3}{8} \)
в. \( \frac{25}{52} \)
\( c \cdot \frac{1}{8} \)
D. \( \frac{3}{14} \)


The decreasing basic order of the following compounds is:
i. \( \boldsymbol{H}_{2} \boldsymbol{O} \)
ii. \( \boldsymbol{H}_{2} \boldsymbol{S} \)
iii. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{e} \)
iv. \( \boldsymbol{H}_{2} \boldsymbol{T} \boldsymbol{e} \)
A \( \cdot(i)>(i i)>(i i i)>(i v) \)
B. \( (i v)>(i i i)>(i i)>(i) \)
C. \( (i i i)>(i)>(i i)>(i v) \)
D. \( (i v)>(i i)>(i)>(i i i) \)


Although, Zr belongs to \( 4 d \) and Hf
belongs to \( 5 d \) transition series but it is quite difficult to separate them, why?


A gas has an average speed of \( 10 m / s \)
and an average time of \( 0.1 s \) between collisions.What is its mean free path?
A. \( 1 m \)
в. \( 0.1 m \)
\( c .2 m \)
D. None of the above


What is the rate of change of the area of
a circle with respect to its radius \( r \) at
\( \boldsymbol{r}=\boldsymbol{6} \boldsymbol{c m} \)
A . \( 12 \pi \mathrm{cm} \)
в. \( 16 \pi \mathrm{cm} \)
\( \mathrm{c} .18 \pi \mathrm{cm} \)
D. \( 24 \pi \mathrm{cm} \)


Fill in the blanks by choosing the appropriate option.
Conc. \( \boldsymbol{H}_{2} \boldsymbol{S} \boldsymbol{O}_{4} \) chars paper, wood, and
sugar by removing
(i) \( - \) from
them. It is also known as \( _{-1-}\left(\text {ii) }_{-1} \). It \right.
is manufactured by \( _{--} \) (iii)
process. It is a strong (iv)
and \( ---(v)_{--} \) acid.
\( \mathbf{A} \cdot(\mathbf{i}) H_{2} O, \) (ii)oil of vitriol, (iii)Contact, (iv)oxidising,
(v)dibasic
B . (i) \( O_{2} \), (ii)oil of vitriol, (iii)Oleum, (iv)dehydrating,
(v)monobasic
C . (i) \( H_{2} O \), (ii)oil of wintergreen, (iii)Solvay,
(iv)dehydrating, (v)dibasic
D. (i)S \( O_{2} \), (ii)oil of winter green, (iii)Contact, (iv)oxidising, (v) monobasic


Atomic number of element
is 19
\( \mathbf{A} \cdot M g \)
в. \( K \)
\( c . A r \)
D. \( C a \)


A point object \( \boldsymbol{O} \) is placed in front of a
concave mirror of focal length \( 10 \mathrm{cm} . \) A glass slab of refractive index \( \mu=3 / 2 \)
and thickness \( 6 \mathrm{cm} \) is inserted between
the object and mirror. Find the position and nature of the final
image when the distance \( x \) shown in
figure, is 20 cm.
A. \( 17 c m, \) virtual
B. \( 17 \mathrm{cm} \), real
c. \( 12 c m, \) virtual
D. \( 15 \mathrm{cm} \), virtual


Discuss the continuity of the function \( f \) defined by \( f(x)=\frac{1}{1+2^{\tan x}} \) for real \( x \)


There are three boys and two girls. A committee of two is to be formed. Find
the probability of the following events:
Event \( A: \) The committee contains at
least one boy.

Event \( B \) : The committee contains one
boy and one girl


If pure "p" orbitals are involved in molecule formation, then the shape of
\( \boldsymbol{H}_{3} \boldsymbol{O}^{+} \) will be:
A. pyramidal
B. tetrahedral
c. angular
D. planar


State True or False.
For a non-ideal solution, \( \Delta_{m i x} V \) and
\( \Delta_{m i x} H \) are zero.
A . True
B. False


A monobasic acid A has neutralization
equivalent 116 and does not decolorize Bayer's regent. Also, A is enantiomeric.
A on treatment with \( B r_{2} / r e d \) phosphorus produces B which is still resolvable. B on dehydrobromination produced C which shows stereoisomerism \( C \) on decarboxylation produced. D which does not show stereoisomerism. Deduce structures of
\( A, B, C, \) and \( D \)


If measurements for a given substance are close to the known value, but the measurements are far from each other, then you have without
Fill the appropriate
answers.
A. Accuracy, Precision
B. Precision, Accuracy
c. This situation is not possible
D. None of these


Find the value of \( \sqrt{a \sqrt{a \sqrt{a \ldots . . \infty}}} \)
\( A \)
B \( \cdot a^{2} \)
\( \mathbf{c} \cdot a^{3} \)
D. \( \sqrt{a} \)


For an adiabatic process
A \( . \Delta S=0 \)
в. \( \Delta U=0 \)
c. \( Q=0 \)
D. \( W=0 \)


Simpify and express following as a
rational number:
\( \left(\frac{3}{4}\right)^{2} \times\left(\frac{-1}{2}\right)^{5} \times 2^{3} \)


Assertion
An ideal gas is not expected to show any cooling on free expansion.
Reason
Ideal gas does not exist but is useful
concept.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


In context with the industrial
preparation of hydrogen from water gas
\( \left(C O+H_{2}\right), \) which of the following is the
correct statement?
\( \mathbf{A} \cdot \mathrm{H}_{2} \) is removed through occlusion with \( \mathrm{Pd} \)
B. \( C O \) is oxidised to \( \mathrm{CO}_{2} \) with steam in the presence of a
catalyst followed by absorption of \( \mathrm{CO}_{2} \) in alkal
C \( \cdot C O \) and \( \mathrm{H}_{2} \) are fractionally separated using differences in their densities
D. \( C O \) is removed by absorption in aqueous \( \mathrm{Cu}_{2} \mathrm{C} 1_{2} \) solution


Which of the following statements is
correct:
\( \mathbf{A} \cdot S F_{6} \) does not react with water
B. \( O F_{6} \) is \( d^{2} S p^{3} \) -hybridized
\( \mathrm{C} \cdot S_{2} \mathrm{O}_{3}^{2-} \) is a linear ion
D. There is no \( \pi \) -bonding in \( S O_{4}^{2-} \)


Length, breadth and thickness of a rectangular slab are \( 4.234 \mathrm{m}, 1.005 \mathrm{m} \) and \( 2.01 \mathrm{m} \) respectively. Find volume of the slab to correct significant figures.
\( \mathbf{A} \cdot 8.55 m^{3} \)
в. \( 8.552 m^{3} \)
c. \( 8.6 m^{3} \)
D. None of the above


Which of the following figures
represents the magnetic lines of force
due to an isolated south pole?
\( A \)
B.
\( c \)
D.


A force of \( 50 k g f \) is applied to the smaller piston of a hydraulic machine. Neglecting friction, The force exerted on the large piston, if the diameters of the
piston are \( 5 c m \) and \( 25 c m \) respectively
is \( ^{\prime} X^{\prime} N . \) Find \( \frac{X}{250} \)


When a car of mass \( 1200 \mathrm{kg} \) is moving
with a velocity of \( 15 \mathrm{ms}^{-1} \) on a rough horizontal road. Its engine is switched off. How far does the car travel before it
comes to rest if the coefficient of
kinetic friction between the road and
tyres of the car is \( 0.5 ?\left(g=10 m s^{-2}\right) \)
\( \mathbf{A} \cdot 6.2 m \)
в. 20 \( m \)
c. \( 22.5 m \)
D. 30


A heat engine takes in heat at 750 degrees Celsius and expels heat at 250 degrees Celsius. What is this engine's theoretically ideal (Carnot) efficiency?
A. 33 percent
B. 67 percent
c. 49 percent
D. 300 percent
E. 23 percent


A colorless gas ' \( x \) ' forms a brown colored
gas ' \( \boldsymbol{y}^{\prime} \) when mixed with air. \( \boldsymbol{x} \) and \( \boldsymbol{y} \)
could be:
A. \( N O, N O_{2} \)
в. \( N O, O_{2} \)
c. \( N O_{2}, N_{2} O_{4} \)
D. \( N O, N_{2} O_{4} \)


In which stage of the cell cycle are histone proteins synthesised in an eukaryotic cell ?
A. G2- stage of prophase
B. S-phase
c. Entire prophase
D. Telophase


The coordinates of any point, which lies in \( \boldsymbol{y} \boldsymbol{z} \) plane, are
This question has multiple correct options
A \( .(x, y, y) \)
в. \( (0, y, y) \)
c. \( (0, y, x) \)
D. \( (x, y, z) \)


Which of the following is not the function of forest?
A. It is used to make paper
B. Resin, gum and drugs are obtained.
c. controls flood.
D. Causes soil erosion.


Metals adsorb hydrogen. Explain.


A closed bottle containing water (at \( 30^{\circ} \)
C) is carried in a spaceship and place on the surface of the moon. What will
happen to the water when the bottle is opened?
A. Nothing will happen to it
B. Water will freeze
c. Water will boil
D. It will decompose into \( H_{2} \) and \( O_{2} \)


In graphite, \( C \) atom is in state
\( A \cdot s p^{3} \)
B. \( s p \)
\( c \cdot s p^{2} \)
D. None of these


The values of \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{C a C O}_{3} \) and \( \mathrm{CaC}_{2} \mathrm{O}_{4} \) are \( 4.7 \times 10^{-9} \) and \( 1.3 \times 10^{-9} \)
respectively at \( 25^{\circ} \mathrm{C} \). If the mixture of these two is washed with water, what is the concentration of \( C a^{2+} \) ions in
water?
A \( \cdot 5.831 \times 10^{-5} M \)
В. \( 6.856 \times 10^{-5} M \)
c. \( 3.606 \times 10^{-5} M \)
D. \( 7.77 \times 10^{-5} M \)


You are provided with three similar, but slightly different, tuning forks, when \( A \) and B are both struck, a beat frequency
of \( f_{A B} \) is heard. When \( A \) and \( C \) are both
struck, beat frequency of \( \boldsymbol{f}_{A C} \) is heard. It
was noticed that \( \boldsymbol{f}_{A B}<\boldsymbol{f}_{A C} \). This
experiment is repeated after coating tuning fork A with a little wax. Now it is
observed that values of both \( f_{A B} \) and
\( \boldsymbol{f}_{A C} \) increase. Which tuning fork has the highest frequency?
\( A \cdot A \)
B. B
c.
D. The answer cannot be determined from the information given


Why are equipotential surfaces perpendicular to field lines?


With the help of suitable examples, explain why certain traits cannot
be passed on to the next generation. What are such traits called?


Integrate the rational function
\( \frac{\boldsymbol{x}}{(\boldsymbol{x}+\mathbf{1})(\boldsymbol{x}+\mathbf{2})} \)


Ultra-violet light causes
A. Formation of pyrimidines dimers
B. Sticky metaphases
C. Photodynamic action
D. Destruction of hydrogen bonds between complementary DNA strands


Which process of cellular respiration takes place in the cytosol of the cell?
A. Krebs cycle
B. Glycolysis
c. Electron transport chain
D. Oxidative phosphorylation
E. Calvin cycle


The correct match between items of
List- I and List- II is:
List I
(A) Phenelzine
(P) Pyrimidine
(B) Chloroxylenol
(Q) Furan
(C) Uracil
(R) Hydrazine
(D) Rantitidine
(S) Phenol
\( A \)
\( (A)-(S) ;(B)-(R) ;(C)-(P) ;(D)-(Q) \)
B. \( (A)-(R) ;(B)-(S) ;(C)-(P) ;(D)-(Q) \)
C. \( (A)-(R) ;(B)-(S) ;(C)-(Q) ;(D)-(P) \)
\( D \cdot(A)-(S) ;(B)-(R) ;(C)-(Q) ;(D)-(P) \)


A bi-convex lens is formed with two thin
plano-convex lenses as shown in the figure. The refractive index n of the first
lens is 1.5 and that of the second lens is
1.2 Both the curved surfaces are of the
same radius of curvature \( \boldsymbol{R}=\mathbf{1 4 c m} \)
For this bi-convex lens, for an object
distance of \( 40 \mathrm{cm}, \) the image distance
will be
\( \mathbf{A} \cdot-280.0 \mathrm{cm} \)
в. \( 40.0 \mathrm{cm} \)
c. \( 21.5 \mathrm{cm} \)
D. \( 13.3 \mathrm{cm} \)


Let \( y \) be an element of the \( \operatorname{set} A= \)
\{1,2,3,5,6,10,15,30\} and \( x_{1}, x_{2}, x_{3} \) be
integers such that \( x_{1} x_{2} x_{3}=y, \) then the
number of positive integral solutions of
\( \boldsymbol{x}_{1} \boldsymbol{x}_{2} \boldsymbol{x}_{3}=\boldsymbol{y} \) is
\( \mathbf{A} \cdot 64 \)
B . 27
c. 81
D. None of these


In a cathode ray tube, what is the effect on the beam of particles if it passes through the electric field?
A. the beam will get deflected towards the cathode
B. the beam will get deflected towards the anode
c. the beam will go undeflected
D. None of the above


Select correct alternative :
Statement -1: An electric dipole can not
produce zero electric field at a point which is situated at finite distance
from the dipole. Statement -2: Mass of a moving photon is proportional to \( \lambda^{-1} \). Statement -3: Equation of continuity for fluid is based on conservation of
volume.
A. FFF
в. тт
c. тFF
D. गा


Why is \( B_{2} \) paramagnetic whereas \( C_{2} \) diamagnetic?


What is the formal charge on chlorine in
the given lewis structure?


If observed vapour pressure is greater
than ideal vapour pressure then:
A. it is known as negative deviation from Raoult's law
B. it is known as ideal solution
C. it is known as positive deviation from Raoult's law
D. None of these


In the oxoacids of halogens, halogens are \( s p^{3} \) hybridised.
If true enter 1 , else enter 0 .


Find the value of \( x \) for which;
\( \operatorname{cosec}^{-1}(\cos x) \) is real
A. \( x=-\pi \)
B . \( x=\pi \)
c. \( x=2 \pi \)
D. All of the above


a) Write a chemical equation to prepare ammonia from ammonium chloride?
b) Write a chemical equation to identify
\( C u^{+2} \& A g^{+} \) ions with the application
of \( N H_{3} ? \)
c) Draw a labeled diagram showing flowchart for the manufacture of
ammonia?


toppr
Q Type your question_
\( \mathbf{A} \)
\( B \)
\( c \)
D.


Explain why, water is a compound and not a mixture. Given any five points.


The bond angle and hybridization in ammonia is:
A \( \cdot 109^{\circ} 5^{\prime}, s p^{3} \)
В \( \cdot 104^{\circ} 31^{\prime}, s p^{3} \)
c. \( 107^{\circ}, s p^{3} \)
D. none of these


Identify the odd one out. Lemonjuice, Carbon, Brass, Milk


In dissociation of \( \boldsymbol{I}_{2}(\boldsymbol{g}) \) at \( \mathbf{1 0 0 0} \boldsymbol{K} \) in a
container of 1 litre :
\( \boldsymbol{I}_{2}(\boldsymbol{g}) \rightleftharpoons \mathbf{2} \boldsymbol{I}^{-}(\boldsymbol{g}) ; \boldsymbol{K}_{c}=\mathbf{1 0}^{-\mathbf{6}} \)
Select the correct relation:
\( \mathbf{A} \cdot\left[I_{2}\right]>\left[I^{-}\right] \)
В \( \cdot\left[I_{2}\right]<\left[I^{-}\right] \)
\( \mathbf{c} \cdot\left[I_{2}\right]=\left[I^{-}\right] \)
D. \( \quad\left[I_{2}\right]=\frac{1}{2}\left[I^{-}\right] \)


If the points (-1,3,2),(-4,2,-2) and \( (5,5, \lambda) \) are collinear, then \( \lambda \) is equal to
A . -10
B. 5
\( c .-5 \)
D. 10


If the primitive of \( \frac{e^{x}\left(1+e^{x}\right)}{\sqrt{1-e^{2 x}}} \) is \( \boldsymbol{f} \boldsymbol{o} \boldsymbol{g}(\boldsymbol{x})-\sqrt{\boldsymbol{h}(\boldsymbol{x})}+\boldsymbol{C} \) then
This question has multiple correct options
A \( \cdot f(x)=\sin ^{-1} x \)
B \( \cdot g(x)=e^{2 x} \)
\( \mathbf{c} \cdot g(x)=e^{x} \)
D. \( h(x)=1-e^{2 x} \)


A student was given a piece of rope and
told to cut it into two equal pieces, keep one piece, and pass the other piece to the next student. Each student was to
repeat this process until every student in the class had exactly one piece of rope. Which of the following could be the fraction of the original rope that one of the students had?
A \( \cdot \frac{1}{14} \)
в. \( \frac{1}{15} \)
c. \( \frac{1}{16} \)
D. \( \frac{1}{17} \)
E \( \frac{1}{18} \)


Which of the following conclusions are
made on methane in natural
environment?
A. Methane is produced by methanogenesis in anoxic environment
B. The concentration of methane is 0.1 to \( 1.0 \mu M \) for surface waters of lake
C. Methane produce in sediment bubbles and diffuses into the water column and is lost to the atmosphere, except during winter months
D. All of the above


In a reaction with two reactants, two
trials are performed. In both trials, the concentration of reactant \( \boldsymbol{A} \) is held
constant.

If the concentration of reactant \( B \) is
doubled and the rate of the reaction
increases by a factor of eight, what can be concluded from the reaction?
A. The order of reactant \( B \) in the overall rate law is 3
B. The order of reactant \( A \) in the overall rate law is 1
c. The order of reactant \( B \) in the overall rate law is 2
D. The order of reactant \( B \) in the overall rate law is 1
E. The order of reactant \( A \) in the overall rate law is 3


\( \operatorname{Let} z=\left(a-\frac{i}{2}\right) ; \in \mathrm{R} . \) Then \( |i+z|^{2} \)
\( |i-z|^{2} \) is equal to


Is zero a rational number? Can you write it in the form \( \frac{p}{q}, \) where \( p \) and \( q \) are integers and \( \boldsymbol{q} \neq \mathbf{0} ? \)
A. True
B. False


The process of guttation takes place
A. When the root pressure is high and the rate of transpiration is low
B. When the root pressure is low and the rate of transpiration is high
C. When the root pressure equals the rate of transpiration
D. When the root pressure as well as rate of transpiration are high


Find the common difference the
following A.P \( 1,4,7,10,13,16, \dots \)


The solubility of \( N_{2} \) in water at \( 300 \mathrm{K} \) and 500 torr, partial pressure is \( 0.01 \mathrm{g} \) \( L^{-1} . \) The solubility \( \left(\operatorname{in} g L^{-1}\right) \) at 750 torr partial pressure is:
A. 0.0075
B. 0.015
c. 0.02
D. 0.005


A swimming pool is \( 20 m \) in length, \( 15 m \) in breadth, and \( 4 m \) in depth. Find
the cost of corner its floor and walls at
the rate of \( R s .12 \) per square meter


Let \( \Delta_{\mathrm{o}}=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right] \) and let \( \Delta_{1} \)
denote the determinant formed by the
cofactors of elements of \( \Delta_{0} \) and \( \Delta_{2} \)
denote the determinant formed by the
cofactor of \( \Delta_{1}, \) similarly \( \Delta_{n} \) denotes the
determinant formed by the cofactors of
\( \Delta_{n-1} \) then the determinant value of \( \Delta_{n} \)
is
\( \mathbf{A} \cdot \Delta_{0}^{2 n} \)
B . \( \Delta_{0}^{2^{2}} \)
\( \mathbf{C} \cdot \Delta_{0}^{n^{2}} \)
D. \( \Delta^{2}_{0} \)


Each of these questions is followed by three statements. You have to study the question and all the three statements
given to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.
What is the cost painting the two
adjacent walls of a hall at Rs. 5 per m2 which has no windows or doors?
I. The area of the hall is 24 sq. \( m \)
Il. The breadth, length and height of the hall are in the ratio of 4: 6: 5
respectively.
III. Area of one wall is 30 sq. \( \mathrm{m} \).
A. I only
B. II only
c. III only
D. Either lor III
E. All I, II and III are required.


For an isochoric process the temperature
at which the pressure of a gas will be
double that of its pressure at \( 270^{0} \mathrm{C} \) is
A \( .543^{\circ} \mathrm{C} \)
B. \( 813^{0} \) C
\( c \cdot 3^{0} c \)
D. 270 \( ^{0} \) С


Which one is not correctly matched?
A. Cytokinin - cell division
B. IAA - cell wall elongation
C. Abscisic acid - stomatal closure
D. Gibberellic acid - Leaf fall


Q Type your question.
moving horizontally with a speed \( u \)
perpendicular to the direction of \( v \)
enters through a hole at an upper corner
\( A \) and strikes the diagonally opposite
corner \( B \). Assume \( g=10 m / s^{2} . \) Which
of the following values of \( u \) and \( v \) is(are)
correct?
This question has multiple correct options
A. \( v=20 \mathrm{m} / \mathrm{s} \)
в. \( u=3 \mathrm{m} / \mathrm{s} \)
c. \( v=15 \mathrm{m} / \mathrm{s} \)
D. \( u=2 m / s \)


In optical fiber, refractive index of inner
part is 1.68 and refractive index of outer
part is \( 1.44 . \) The numerical aperture of the fibre is
A. 0.5653
B. 0.6653
c. 0.7653
D. 0.8653


When \( C O_{2} \) is bubbled through a
solution of barium peroxide in water:
A. carbonic acid is formed
B. \( H_{2} O_{2} \) is formed
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \) is formed
D. barium hydroxide is formed


The second's hand of a watch has \( 6 \mathrm{cm} \)
length. The speed of tis tip and magnitude of difference in velocity of its at any two perpendicular positions will be respectively:
\( \mathbf{A} \cdot 2 \pi \) and \( 0 \mathrm{mm} / \mathrm{s} \)
B. \( 2 \sqrt{2} \pi \) and \( 4.44 \mathrm{mm} / \mathrm{s} \)
\( \mathrm{c} \cdot 2 \sqrt{2} \pi \) and \( 2 \pi \mathrm{mm} / \mathrm{s} \)
D. \( 2 \pi \) and \( 2 \sqrt{3} \pi \mathrm{mm} / \mathrm{s} \)


An element \( ^{\prime} A^{\prime} \) forms a chloride \( A C l_{4} \)
The number of electrons in the valence
shell of \( ^{\prime} \boldsymbol{A}^{\prime} \) is:
\( \mathbf{A} \cdot \mathbf{1} \)
B. 2
\( c .3 \)
D.


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


If mean of following data is 215 then
find \( k \)
\( \begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 30- \\ & 10 & 20 & 30 & 40\end{array} \)
1 4


For a radioactive material, half-life is 10
minutes. If initially there are 600 number of nuclei, the time taken (in
minutes) for the disintegration of 450 nuclei is?
A . 30
B . 20
c. 15
D. 10


Brownian motion is a/an:
A. electrical property
B. mechanical property
C. optical property
D. colligative property


A galvanometer, with a scale divided into 100 equal divisions, has a current
sensitivity of 10 div per \( \mathrm{m} \mathrm{A} \) and voltage sensitivity 2 div per \( \mathbf{m V} \). To read \( 5 A \) full scale deflection
A. Shunt resistance should be \( 1 \Omega \)
B. Shunt resistance should be \( 0.1 \Omega \)
c. shunt resistance should be \( 0.01 \Omega \)
D. Shunt resistance should be \( 0.001 \Omega \)


\( \boldsymbol{y}=\boldsymbol{x}^{2}+\boldsymbol{3} \boldsymbol{x}+2 \) find \( \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}} \)


For ordinary terrestrial experiments, the observer in an inertial frame in the
following cases is
A. A child revolving in a-giant wheel
B. A driver in a sports car moving with a .constant highh speed of \( 200 k m h^{-1} \) on a straight road
c. The pilot of an aeroplane which is taking off
D. A cyclist negotiating a-sharp curve


Indole-3-acetic acid called as auxin was
first isolated from
A. Human urine
B. Corn germ oil
c. Fusarium
D. Rhizopus


Which of the following is involved in the catalysis of link reaction during aerobic respiration?
A. Vitamin A
B. Vitamin \( B_{1} \)
c. Vitamin \( B_{6} \)
D. Vitamin K


Active absorption of mineral salts makes use of
A. lonic exchange
B. Carriers
c. Phosphorylation of elements
D. None of the above


Identify the best curve which represents how pressure and volume change in an isothermal process?
\( A \)
в.
c.
D.
E.


The lamprey is included in same taxonomic class as
A. Anolis
B. Myxine
c. Ambystoma
D. Neoceratodus


'The enthalpy of hydration decreases in
\( \operatorname{going} \) from \( L i^{+} \) to \( C s^{+} \)
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


Decrease in atomic number is observed
during:
This question has multiple correct options
A . \( \alpha \) -emission
B. \( \beta \) -emission
c. Positron emission
D. K-capture


Micelles are formed only:
A. above CMC and above the Kraft temperature
B. below CMC and the Kraft temperature
\( \mathrm{C} \). above \( \mathrm{CMC} \) and below the Kraft temperature
D. below CMC and above the Kraft temperature


Below is given frequency distribution of
I.Q. (Intelligent Quotient) of 80
candidates.
\[
70
\]
80
\[
90 \quad 100
\]
I.Q. \( \begin{array}{lll}\text { 80 } & \text { 90 } & \text { 100 }\end{array} \)
No. o 16
20
Candidates
Find median I.Q. of candidates
A. 100.5
B. 98.5
c. 94.5
D. None of these


The metal that gives hydrogen gas upon
treatment with both acid as well as
base is :
A. zinç
B. iron
c. magnesium
D. mercury


Two tangents PT and PT' are drawn to a
circle, with centre \( 0, \) from an external
point P. Prove that \( \angle \mathrm{TPT}^{\prime}=2 \angle \mathrm{OTT} \) '.


The minimum distance between an
object and its real image formed by a
convex lens is :
A \( \cdot \frac{2}{3} f \)
B . \( 2 f \)
c. \( \frac{5}{2} f \)
D. \( 4 f \)


The angle \( \theta \) between the vector \( p=\hat{i}+ \) \( \hat{j}+\hat{k} \) and unit vector along \( x \) -axis is
\( ^{A} \cdot \cos ^{-1}\left(\frac{1}{\sqrt{3}}\right) \)
в. \( \cos ^{-1}\left(\frac{1}{\sqrt{2}}\right) \)
\( ^{\mathrm{c}} \cdot \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
D. \( \cos ^{-1}\left(\frac{1}{2}\right) \)


Show with balanced equations what happens when the following are mixed:
potassium permanganate interacts with manganese dioxide in the
presence of potassium hydroxide.
\( \mathbf{A} \cdot 2 K M n O_{4}+4 K O H+M n O_{2} \rightarrow 3 K_{2} M n O_{4}+2 H_{2} O \)
B. \( 3 K M n O_{4}+4 K O H+M n O_{2} \rightarrow 4 K_{2} M n O_{4}+2 H_{2} O \)
c. \( 3 K M n O_{4}+3 K O H+M n O_{2} \rightarrow 3 K_{2} M n O_{4}+2 H_{2} O \)
D. None of these


Evaluate the following:
\( \cos ^{-1}(\cos 4) \)


A 100 solution of \( N a_{2} C O_{3} \) is prepared
by dissolved 8.653 of the salt in water. The density of the solution is \( 1.0816 / \) What are the Molarity and Molality of the solution?
(Atomic mass of Na is 23 , e is 12 and of
O is 14 )


What is the work done in rotating the
dipole through \( 180^{\circ} ? \)
A \( \cdot \frac{\partial q Q x}{\pi \varepsilon_{0}\left(R^{2}+x^{2}\right)^{3 / 2}} \)
В. \( \frac{\partial q Q x}{2 \pi \varepsilon_{0}\left(R^{2}+x^{2}\right)^{3 / 2}} \)
c. \( \frac{2 \partial q Q x}{\pi \varepsilon_{0}\left(R^{2}+x^{2}\right)^{3 / 2}} \)
D. \( \frac{\partial q Q x}{3 \pi \varepsilon_{0}\left(R^{2}+x^{2}\right)^{3 / 2}} \)


The first organic compound prepared from inorganic compounds was.
A . Acetic acid
B. Methane
c. urea
D. Ethyl alcohol


Which of the following product (s)
is/are obtained when \( C I_{2} O \) reacts with
\( N H_{3} ? \)
A \( \cdot N O_{2} \)
в. \( N_{2} \)
c. \( N C I_{3} \)
D. \( N H_{4} C I \)


Define the term specific latent heat of fusion of ice. State its S.I. unit.


Study the given flowchart carefully.
\( P, Q, R \) and \( S \) are respectively:
A. Salt, sawdust, iron dust, camphor
B. Sawdust, iron dust, camphor, salt
c. Iron dust, camphor, sawdust, salt
D. Camphor, iron dust, sawdust, salt


A ray of light travels from air into a perspex block of refractive index 1.5 at
an angle of incidence of \( 45^{\circ} . \) Calculate
the angle of the refraction of the ray at
air - to perpex boundary and at perpex to - air boundary.


Prove: \( 2 \sin ^{-1} \frac{3}{5}=\tan ^{-1} \frac{24}{7} \)


Disease/disorder caused due to lead
poisoning is
A. Typhoid
B. Tetanus
c. Malaria
D. Anemia


The mass of electron is \( 9.11 \times 10^{-31} \)
kg.Planck's constant is \( 6.626 \times 10^{-34} \)
Js then the uncertainty involved in the measurement of velocity within a distance of \( 0.1 \AA \) is :
\( \mathbf{A} \cdot 5.79 \times 10^{6} \mathrm{ms}^{-1} \)
B . \( 5.79 \times 10^{7} \mathrm{ms}^{-1} \)
C. \( 5.79 \times 10^{8} \mathrm{ms}^{-1} \)
D. \( 5.79 \times 10^{5} \mathrm{ms}^{-1} \)


Early wood differs from latewood in
A. Being produced in winter
B. Presence of narrow vessels
C. Being light in colour
D. Possessing high density


Which of the following has the lowest bond angle?
A \( . N H_{3} \)
в. \( B e F_{2} \)
\( \mathrm{c} \cdot \mathrm{H}_{3} \mathrm{O}^{+} \)
D. \( C H_{4} \)


What is centripetal force?


For the circuit shown in the figure,
which of the following statements is
true?
A. With S1 closed \( V 1=15 V, V 2=20 V \)
B. With \( S_{3} \) closed, \( V_{1}=V_{2}=25 \mathrm{V} \)
C. With \( S_{1} \) and \( S_{2} \) closed, \( V_{1}=V_{2}=0 \)
D. With \( S_{1} \) and \( S_{3} \) closed, \( V_{1}=30 \vee, V_{2}=20 \mathrm{V} \)


The \( \boldsymbol{K}_{s p} \) of \( \boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}, \) AgCI, \( \boldsymbol{A g B r} \) and \( \boldsymbol{A g} \)
are respectively, \( 1.1 \times 10^{-12}, 1.8 \times \)
\( 10^{-10}, 5.0 \times 10^{-13}, 8.3 \times 10^{-17} . \) Which
one of the following salts will
precipitate last if \( A g N O_{3} \) solution is added to the solution containing equal
moles of NaCl, NaBr, Nal and \( N a_{2} C r O_{4} \)
\( ? \)
A . Agc
в. Аgвт
\( \mathbf{c} \cdot A g_{2} C r O_{4} \)
D. Agl


The colour of blood is red due to the
presence of
A. magnesium
B. cytoglobin
c. haemoglobin
D. all of these


Derive an expression for de-Brogile wavelength of matter waves.


A vertical wire carries a current in
upward direction. An electron beam sent horizontally towards the wire will be deflected (gravity free space):
A. towards right
B. towards left
c. upwards
D. downwards


In an a.c. circuit the voltage applied is \( \boldsymbol{E}=\boldsymbol{E}_{0} \sin \omega \boldsymbol{t} . \) The resulting current in
the circuit is \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin \left(\boldsymbol{\omega} \boldsymbol{t}-\frac{\boldsymbol{\pi}}{2}\right) . \) The
power consumption in the circuit is given by -
A \( \cdot \quad P=\frac{E_{0} I_{0}}{\sqrt{2}} \)
B . \( P= \) zero
c. \( _{P}=\frac{E_{0} I_{0}}{2} \)
D. \( P=\sqrt{2} E_{0} I_{0} \)


Zinc is precipitated from a solution of zinc sulphate by addition of iron.
A. True
B. False


The number of unpaired electrons in a paramagnetic atom of an element with atomic number 16 is :


Differentiate between bilateral
symmetry and radial symmetry


Find the square root of 12.25 using long division method.
A . 3.2
в. 3.4
\( c .3 .5 \)
D. \( 3 . \)


The effective capacitance of
combination of equal capacitors between points \( A \) and \( B \) shown in figure
is :
\( A \)
B. \( 2 C \)
\( c \cdot 3 c \)
0.0
9


In aprotic solvent which of the following has highest nucleophilicity?
\( A \cdot F^{-} \)
B . \( C l^{-} \)
\( c \cdot B r \)
D. \( I \)


Dialysis can be used to separate:
A. glucose \& fructose
B. protein \& starch
c. glucose \& protein
D. glucose \& NaCl


The formation of \( C u S \) which is formed
by
A \( \cdot S O_{4}^{2-}+8 H^{+}+8 e^{-} \rightarrow S^{2-}+H_{2} O \)
B. \( S O_{2}+6 H^{+}+6 e^{-} \rightarrow H_{2} S+2 H_{2} O \)
c. Both (a) and (b)
D. None of the above


Fern plants reproduce by
A. Seeds
B. Spores
c. Laying eggs
D. Giving birth to young fern plants


Different forms of energies are regarded
as non-matter.
A . True
B. False


The mean of \( 7,9, x+3,12,2 x-1 \) and 3
is
9. Find the value of \( x \)


A particle \( X \) deflects towards negative plate in the presence of electric field. Identify the particle \( X ? \)
A. Neutron
B. Electron
c. \( X \) -ray
D. Proton


A solution is made of \( 0.1 ~ M C l^{-} \) and
\( \mathbf{1 0}^{-4} \mathbf{M} \mathbf{C r} \mathbf{O}_{\mathbf{4}}^{\mathbf{2 -}} . \) If solid \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3} \) is
gradually added to this solution,
then what will be the concentration of
\( C l^{-} \) when \( A g_{2} C r O_{4} \) begins to
precipitate? \( \left[\boldsymbol{K}_{s p}(\boldsymbol{A} \boldsymbol{g} \boldsymbol{C l})=\right. \)
\( \mathbf{1 0}^{-\mathbf{1 0}} \boldsymbol{M}^{\mathbf{2}} ; \boldsymbol{K}_{\boldsymbol{s p}}\left(\boldsymbol{A} \boldsymbol{g}_{2} \boldsymbol{C r} \boldsymbol{O}_{4}\right)= \)
\( \left.\mathbf{1 0}^{-\mathbf{1 2}} \mathbf{M}^{\mathbf{3}}\right] \)
В. \( 10^{-4} \) М
\( \mathbf{c} \cdot 10^{-5} M \)
D. \( 10^{-9} M \)


A balloon filled with hydrogen gas is
carried from earth to moon. Then the
balloon will:
A. neither fall nor rise
B. fall with acceleration less than \( g \)
c. fall with acceleration g
D. rise with acceleration g


Five resistors each of 1 ohm are
connected in parallel. The resultant resistance of the combination is
A . \( 5 \Omega \)
B. 12
\( c \cdot 0.2 \Omega \)
D. 2\Omega


In which of the following cases, the extent of reaction is maximum?
A \( \cdot K_{c}=1 \)
В. \( K_{c}=10^{10} \)
C \( . K_{c}=10^{-1} \)
D. \( K_{c}=10 \)


Using Dimensional analysis convert
newton into dyne.


\( 2 H_{2}(g)+O_{2}(g) \longrightarrow 2 H_{2} O(g) \)
For this reaction relate \( \Delta H \) and \( \Delta U \)
A. \( \Delta H=\Delta U \)
в. \( \Delta H>\Delta U \)
c. \( \Delta H<\Delta U \)
D. None of these


The percentage of unshaded portion in the following figure is
A . \( 25 \% \)
B. \( 50 \% \)
c. \( 75 \% \)
D. \( 100 \% \)


Two open pipes of length \( 20 \mathrm{cm} \) and \( 20 . \) \( \mathrm{cm} \) produces 10 beats/s. The velocity of sound in the gas is
A. \( 804 \mathrm{m} / \mathrm{s} \)
B. 402 m/s
c. \( 420 \mathrm{m} / \mathrm{s} \)
D. 330 \( \mathrm{m} / \mathrm{s} \)


By virtue of Faradays second law of electrolysis, the electrochemical equivalent of the two metals liberated at the electrodes has
the same ratio as that of their:
A. Atomic masse
B. Molecular masses
c. Equivalent masses
D. All the above


A steam engine delivers \( 5.4 \times 10^{8} \) Jof
work per minute and services \( 3.6 \times 10^{9} \)
Jof heat per minute from its boiler
What is the efficiency of the engine? How much heat is wasted per minute?


Synthesis of each molecule of glucose in photosynthesis involves:
A. 10 molecules of ATP
B. 8 molecules of ATP
c. 6 molecules of ATP
D. 18 molecules of ATP


\( \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{3} x}{\sin x+\cos x} d x \) is equal to?
A \( \cdot \frac{\pi}{4}-\frac{1}{4} \)
B. \( \frac{\pi}{4}+\frac{1}{4} \)
c. \( \frac{\pi}{4}+\frac{1}{2} \)
D. \( \frac{\pi}{4}-\frac{1}{2} \)


Two coins are tossed once. Find the
probability of getting:
(i) 2 heads
(ii) at least 1 tail


The correct statement about the
compounds \( A, B \) and \( C \) is:
(A)
(B)
(C)
\( A \). A and \( B \) are identical
B. A and B are diastereomers
C. \( A \) and \( C \) are enantiomers
D. \( A \) and \( B \) are enantiomers


According to Bohr's model, if the kinetic
energy of an electron in \( 2^{n d} \) orbit of
\( H e^{+} \) is \( x, \) then what should be the
ionisaion energy of the electron revolving in \( 3^{r d} \) orbit of \( m^{5+} \) ions \( > \)
\( \mathbf{A} \cdot X \)
в. \( 4 x \)
c. \( x / 4 \)
D. \( 2 X \)


Match the List I (Equations) with the List II (Type of Processes).

List I \( \quad \) List II (Type of processes) (Equations)
(а) \( K_{p}>Q \)
(i) Non-spontaneous
(b) \( \Delta G^{o}< \)
(ii) Equilibrium \( R T \log _{e} Q \)
(iii) Spontaneous and
(c) \( K_{p}=Q \quad \) endothermic
\[
\text { (d) } T>\frac{\Delta H}{\Delta S}
\]
(iv) Spontaneous
Select the correct matching code.
\( \mathbf{A} \cdot a \rightarrow i ; b \rightarrow i i ; c \rightarrow i i i ; d \rightarrow i v \)
в. \( a \rightarrow i v ; b \rightarrow i i i ; c \rightarrow i i ; d \rightarrow i \)
\( \mathbf{c} \cdot a \rightarrow i v ; b \rightarrow i ; c \rightarrow i i ; d \rightarrow i v \)
D. \( a \rightarrow i i ; b \rightarrow i ; c \rightarrow i i i ; d \rightarrow i v \)


Coagulation of blood in vessels is prevented during normal circulation by
A. Heparin
B. Prothrombin
c. Plasminogen
D. Thromplastin


Evaluate the given integral: \( \int_{0}^{1}(1- \) \( \left.\boldsymbol{x}^{2}\right) \boldsymbol{d} \boldsymbol{x} \)


If an intrinsic semiconductor is heated,
the ratio of free electrons to holes is :
A. greater than one
B. less than one
c. equal to one
D. dercease and becomes zero


Islets of Langerhans are
A. Modified lymph glands
B. Ductless glands in pancreas
C . Specialized area in pituitary
D. Small tubules in kidney


Calculate the cell potential \( \left(E_{c e l l}\right) \) of the
following cell at \( 298 K \)
\( \boldsymbol{A} \boldsymbol{g}(\boldsymbol{s}) \mid \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\boldsymbol{0} . \boldsymbol{0} \mathbf{1} \boldsymbol{M}) \| \boldsymbol{A} \boldsymbol{g} \boldsymbol{N} \boldsymbol{O}_{3}(\mathbf{1} . \boldsymbol{0} \boldsymbol{M} \)


Respiratory Pathway is
A. Catabolic
B. Amphibolic
C. Anabolic
D. Endergonic


The speed at any point is
A \( \cdot \sqrt{\frac{3 q E y}{m}} \)
B. \( \sqrt{\frac{q E y}{m}} \)
c. \( \sqrt{\frac{q E y}{2 m}} \)
D. \( \sqrt{\frac{2 q E y}{m}} \)


Use limit properties to evaluate \( \lim _{x \rightarrow 4} \frac{3 x^{2} \tan \frac{\pi}{x}}{x} \)
A . 12
B . 14
c. 16
D. 18


Uniform electric field of intensity 5 volt/m acts parallel to x axis. A charge of \( 2 C \) is moved from to \( A(1,1), \) to \( B(2,1) \)
and finally to \( \mathrm{D}(3, \mathrm{C}) \) in this field.Work done in this process is :
A. 60 joule
B. 40 joule
c. 30 joule
D. zero


Let \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{8} \boldsymbol{x}^{\mathbf{3}} \) and \( \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}^{\mathbf{1} / 3} \). Find g o
and \( f \circ g \)


The tangents drawn at the ends of a diameter of a circle are ?
A. perpendicular
B. parallel
c. adjacent
D. none of the above


A \( d \) -subshell in an atom in the presence
and absence of magnetic field is:
A . five-fold degenerate, non-degenerate
B. feven-fold degenerate, non-degenerate
c. five-fold degenerate, five-fold degenerate
D. non-degenerate, five-fold degenerate


Using IUPAC norms, write the formula of Ammonium tetrafluoridocobaltate (II).


The first amino acid in any polypeptide chain of prokaryote is always
A. Formylated methionine
B. Formylated arginine
c. Lysine
D. Methionine


A pair of fair dice is rolled together till a sum of 7 or 11 is obtained. Let \( p \) denote
the probability that 7 comes before 11
Find the value of \( 4 p \)


The sum of an infinite geometric series whose first term is the limit of the
function \( \boldsymbol{f}(\boldsymbol{x})=\frac{\tan \boldsymbol{x}-\sin \boldsymbol{x}}{\sin ^{3} \boldsymbol{x}} \) as \( \boldsymbol{x} \rightarrow \mathbf{0} \)
and whose common ratio is the limit of
the function \( g(x)=\frac{1-\sqrt{x}}{\left(\cos ^{-1} x\right)^{2}} \) as \( x \rightarrow \)
1 is
A \( \cdot \frac{1}{3} \)
в. \( \frac{1}{4} \)
c. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)


Find the multiplicative inverse of: \( \frac{2-\sqrt{3}}{2+\sqrt{3}} \)


Give the function and source of insulin
hormone?


Increase in air speed is associated with
A. increasein air pressure
B. decrease in air pressure
c. increase in air temperature
D. decrease in air temperature


How do you say boys and girls the age of
adolescence?


A moving coil galvanometer has resistance \( 50 \Omega \) and it indicates full
deflection at \( 4 m A \) current. A voltmeter
is made using this galvanometer and a 5k. \( \Omega \) resistance. The maximum voltage
that can be measured using this voltmeter, will be close to:
A . \( 10 V \)
B. 20V
c. \( 40 V \)
D. \( 15 V \)


The IUPAC name of the given compound
is 2,5 -dimethyl heptane is:
A. True
B. False


A \( 2 m m^{2} \) cross-sectional area wire is
stretched by \( 4 \mathrm{mm} \) by a certain weight.If
the same material wire of cross-
sectional area \( 8 m m^{2} \) is stretched by
the same weight, the stretched length
is
\( A \cdot 2 m m \)
B. \( 0.5 \mathrm{mm} \)
\( \mathrm{c} \cdot 1 \mathrm{mm} \)
D. \( 1.5 \mathrm{mm} \)


yo
represents the motion of 5 different
colored objects of the identical mass,
with the color of the graph
corresponding to the color of the object.
What is the order of the objects,
according to the magnitude of the net
forces they are experiencing during the
time represented by their graph,
greatest first?
A. blue, purple, red, yellow, green
B. purple, red, yellow, blue and green
c. blue and green tie, yellow, purple, redd
D. purple, red, blue, yellow, green
E. yellow, red, purple, blue and green


\( \ln B_{2} H_{6} \) number of \( 3 c-2 e \) bonds
is/are:
A
B. 2
\( c \cdot 3 \)
D. none of these


A coordination compound X gives pale
yellow colour with \( A g N O_{3} \) solution while its isomer Y gives white
precipitate with \( B a C l_{2} . \) Two
compounds are isomers of \( \operatorname{CoBr} \boldsymbol{S O}_{4} \)
\( \mathbf{5} N \boldsymbol{H}_{3} . \) What could be the possible
formula of \( X \) and \( Y ? \)
A \( \cdot X=\left[\operatorname{Co}\left(N H_{3}\right)_{5} S O_{4}\right] B r, Y=\left[\operatorname{Co}\left(N H_{3}\right)_{5} B r\right] S O_{4} \)
B . \( X=\left[C o\left(N H_{3}\right)_{5} B r\right] S O_{4}, Y=\left[C o\left(N H_{3}\right)_{5} S O_{4}\right] B r \)
c. \( X=\left[\operatorname{Co}\left(N H_{3}\right)_{5} B r\left(S O_{4}\right)\right], Y=\left[\operatorname{CoBr}\left(S O_{4}\right)\left(N H_{3}\right)_{5}\right. \)
D. \( X=\left[\operatorname{Co}(B r)_{5} N H_{3}\right] S O_{4}, Y=\left[\operatorname{CoBr}\left(S O_{4}\right)\right] N H_{3} \)


Area bounded by the curves \( \frac{y}{x}=\log x \) and \( \frac{\boldsymbol{y}}{\mathbf{2}}=-\boldsymbol{x}^{2}+\boldsymbol{x} \) equals:
A. 7/12
B. 12/7
\( c \cdot 7 / 6 \)
D. 6/7


Extraction of aluminium from
aluminium oxide \( \left(A l_{2} O_{3}\right) \) is best done
by :
A . electrolytic reduction of \( A l_{2} O_{3} \)
B. reduction of \( A l_{2} O_{3} \) with carbon
c. reduction of \( A l_{2} O_{3} \) wilh sodium
D. reduction of \( A l_{2} O_{3} \) with \( c o \)


The area of cross-section of the wider
tube show in figure is \( 800 \mathrm{cm}^{2} . \) If a
mass of \( 12 k g \) is placed on the massless
piston, the difference in heights \( h \) in the
level of water in the two tubes is:
\( \mathbf{A} \cdot 10 \mathrm{cm} \)
B. \( 6 \mathrm{cm} \)
\( c \cdot 15 c m \)
\( \mathbf{D} \cdot 2 c m \)


The exponent of 5 in \( ^{120} C_{60}, \) is
\( \mathbf{A} \cdot \mathbf{1} \)
B.
\( c \cdot 2 \)
D. 3


If the standard deviation of the numbers
\( 2,3, a \) and 11 is \( 3.5, \) then which of the
following is true?
A \( \cdot 3 a^{2}-26 a+55=0 \)
B. \( 3 a^{2}-32 a+84=0 \)
c. \( 3 a^{2}-34 a+91=0 \)
D. \( 3 a^{2}-23 a+44=0 \)


Simplify:
\( \frac{8^{-1} \times 5^{3}}{2^{-4}} \)


Out of the rational numbers
\( \frac{-5}{11}, \frac{-5}{12}, \frac{-5}{17} \) which is smallest.


How many oxygen atoms are there in
0.5 mole of \( K H S O_{4} ? \)
A \( \cdot 1.2 \times 10^{23} \)
B . \( 2.4 \times 10^{23} \)
c. \( 3.0 \times 10^{23} \)
D. \( 1.2 \times 10^{24} \)
E \( .2 .4 \times 10^{24} \)


\( 2 K C l O_{3} \rightarrow 2 K C l+3 O_{2} . \) What will be
the instantaneous rate of the reaction
in terms of the reactant?
A \( \cdot \frac{1}{2} \frac{d\left[K C l O_{3}\right]}{d t} \)
в. \( -\frac{1}{2} \frac{d\left[K C l O_{3}\right]}{d t} \)
c. \( \frac{d\left[K C l O_{3}\right]}{d t} \)
D. \( -\frac{d\left[K C l O_{3}\right]}{d t} \)


Which of the following shows correct sequence of conduction of action
potential in the heart?
A. SA node \( \rightarrow \) Bundle of His \( \rightarrow \) AV node \( \rightarrow \) Right and left branches of bundle of His \( \rightarrow \) Purkinje fibre
B. SA node \( \rightarrow \) AV node \( \rightarrow \) Purkinje fibre Bundle of His \( \rightarrow \) Right and left branches of bundle of His
C. SA node \( \rightarrow \) AV node \( \rightarrow \) Bundle of His \( \rightarrow \) Right and left branches of bundle of His \( \rightarrow \) Purkinje fibre
D. AV node \( \rightarrow \) SA node \( \rightarrow \) Bundle of His \( \rightarrow \) Right and left branches of bundle of His \( \rightarrow \) Purkinje fibre


Each of 27 identical spherical drops of a conducting liquid is charged upto a potential of Vo. They coal ease to form a bigger drop. What is the potential on the surface of this bigger drop.
\( \mathbf{A} \cdot 9 V^{\circ} \)
B. \( 3 V^{\circ} \)
\( \mathrm{c} \cdot 27 \mathrm{V}^{\circ} \)
D. \( V^{\text {d }} \)


The transmission of genes, from one generation to next in case of eukaryotic protein sequences takes place through
A. Other proteins
B. rRNA
\( c \cdot \operatorname{tRNA} \)
D. mRNA
E. DNA


If universal set \( \boldsymbol{\xi}= \) \( \{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}, \boldsymbol{h}\}, \boldsymbol{A}= \)
\( \{b, c, d, e, f\}, B=\{a, b, c, g, h\} \) and
\( \boldsymbol{C}=\{\boldsymbol{c}, \boldsymbol{d}, \boldsymbol{e}, \boldsymbol{f}, \boldsymbol{g}\} \) find \( : \boldsymbol{C}-(\boldsymbol{B} \cap \boldsymbol{A}) \)
Thus find the number of elements in the above set.


In the given, Lewis structure of \( S_{2} O_{3}^{-2} \)
formal change present on sulphur atoms 1 and 2 respectively are:
A . zero, +
B. +1,+1
\( c \cdot+2,+2 \)
D. zero, zero


A bag contains 5 red balls and 8 blue
balls. It also contains 4 green and 7
black balls. If a ball is drawn at random,
then find the probability that it is not green
A \( \cdot \frac{5}{6} \)
B. \( \frac{1}{4} \)
\( c \cdot \frac{1}{6} \)
D. \( \frac{7}{4} \)


Given the function \( f(x)=\frac{x-2}{5} \) and
\( \operatorname{gof}(x)=x-3 . \) Find the component
function \( \boldsymbol{g} \)


Salvarsan is containing drug which was
first used for the treatment of
A. Syphilis
B. Typhoid
c. Meningitis
D. Dysentry


Water rises in a capillary upto a height
h. If now this capillary is tilted by an
angle of \( 45^{\circ}, \) then the length of the
water column in the capillary becomes
\( A \cdot 2 h \)
в. \( \frac{h}{2} \)
c. \( \frac{h}{\sqrt{2}} \)
D. \( h \sqrt{2} \)


A current carrying loop of radius \( 2 \mathrm{cm} \)
has \( 4 A \) current flowing in an anti-
clockwise direction. The plane of the loop makes an angle of \( \theta \) with the direction of the magnetic field which is in an upward direction. the value of the
magnetic field is 0.7 Tesla.if potential
energy of loop in magnetic field is \( \approx \) \( 0.01 J, \) then value of \( \theta \) is:
A \( \cdot 45^{\circ} \)
B . \( 60^{\circ} \)
\( c .30^{\circ} \)
D. None of these


Find the number of acid(s) from the
following in which \( X-H \) bond is/are
present Given \( X \) is central atom:
\( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{2}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{7}, \boldsymbol{H}_{4} \boldsymbol{P}_{2} \boldsymbol{O}_{5}, \boldsymbol{H}_{2} \boldsymbol{S}_{2} \boldsymbol{O}_{6}, \boldsymbol{H} \)


\( 250 m l \) of a sodium carbonate solution
contains 2.65 grams of \( N a_{2} C O_{3} .10 m l \)
of this solution is added to \( ^{\prime} x^{\prime} m l \) of
water to obtain \( 0.001 M N a_{2} C O_{3} \)
solution.
What is the value of \( ^{\prime} x^{\prime} \) in \( m l \) ?
[Molecular weight of \( \left.\boldsymbol{N} \boldsymbol{a}_{2} \boldsymbol{C O}_{3}=\mathbf{1 0 6}\right] \)
A. 1000
в. 990
c. 9990
D. 90


The earth radiates in the infra-red
region of the spectrum. The spectrum is
correctly given by :
A. Rayleigh Jeans law
B. Planck's law of radiation
c. stefan's law of radiation
D. Wien's law


Prove that:-
\( \sin 20 \sin 40 \sin 60 \sin 80=\frac{3}{16} \)


The magnification produced by a concave mirror:
A. is always more than one
B. is always less than one
c. is always equal to one
D. may be less than, equal to or greater than one


The progressive warming up of the earth's surface is mainly due to :
A. automobile exhaust
B. blanketing effect of carbon dioxide in atmosphere
c. reforestation
D. thickening of ozone layer


Which of the following liquid pairs shows a positive deviation from
Raoult's law?
A. Water - hydrochloric acid
B. Benzene - methanol
c. water - nitric acid
D. Acetone - chloroform


Largest erythrocytes occur in
A. Llama
B. Whale
C. Amphiuma
D. Musk Deer


Water conduction in stem of tree takes
place by
A. Duramen
B. Sap wood
c. Primary xylem
D. All of the above


The F2 generation will show maximum percentage of allele.
A. Dual
B. Recessive
c. Dominant
D. None of the above


Which one of the following is a correct statement about the atom bomb?
A. a chemical reaction producing a large amount of heat
B. a nuclear explosion caused by a controlled chain reaction
c. a nuclear explosion caused by fusion of two hydrogen nuclei
D. a nuclear explosion caused by an uncontrolled chain reaction


The work done in bringing three
particles each of mass \( 10 g m \) from large distances to the vertices of an
equilateral triangle of side \( 10 \mathrm{cm} \) is
A \( \cdot 10^{-13} J \)
\( J \)
В. \( 2 \times 10^{-13} \mathrm{J} \)
c. \( 4 \times 10^{-11} J \)
D. \( 10^{-11} J \)


In the reaction, \( N_{2}+3 H_{2} \rightarrow 2 N H_{3} \)
the ratio of volumes of nitrogen,
hydrogen and ammonia is \( 1: 3: 2 . \) These figures illustrate the law of:
A. constant proportions
B. Gay-Lussac
c. multiple proportions
D. reciprocal proportions


In the adjoining figure \( A O B \) is a
diameter \( M P Q \) is a tangent at \( P \) then
the value of \( \angle M P A \) is equal to
A \( \cdot 25 \)
B \( .26^{\circ} \)
\( c \cdot 27^{\circ} \)
\( D \cdot 30^{\circ} \)


Wher
distribution of 2 black and 2 white balls
in two containers are as shown.Which
of the following statements is true?
A. (iv) has the maximum possibility of picking a black ball
B. (i) and (iv) has equal probability of picking a white ball
C. (iii) has the maximum possibility of picking a white ball
D. (ii) has the maximum possibility of picking a white ball


Teenagers are also called as
A. Adolescence
B. Adolescents
c. Adult
D. Adulthood


Fluorine is highly reactive because:
A. F-F bond energy is high
B. F-F bond energy is low
C. it is gaseous at room temperature
D. Fhas a smaller size


A convex lens of focal length \( f_{1} \) and \( a \)
concave lens of focal length \( f_{2} \) are placed in contact. The focal length of the combination is
A \( \cdot\left(f_{1}+f_{2}\right) \)
B. \( \left(f_{1}-f_{2}\right) \)
c. \( \frac{f_{1} f_{2}}{f_{2}-f_{1}} \)
D. \( \frac{f_{1} f_{2}}{f_{2}+f_{1}} \)


Among the following, which statement is/are true about acid?
This question has multiple correct options
A. Have a low \( p H \)
B. Have a high \( p H \)
c. Have sour taste
D. Have bitter taste


Area of the region bounded by the
\( \operatorname{curves} \boldsymbol{y}|\boldsymbol{y}| \pm \boldsymbol{x}|\boldsymbol{x}|=\mathbf{1} \) and \( \boldsymbol{y}=|\boldsymbol{x}| \) is:
A \( \cdot \frac{\pi}{8} \) sq.unit
B . \( \frac{\pi}{4} \) sq.unit
c. \( \frac{\pi}{2} \) sq.unit
D. \( \pi \) sq.unit


Show that the minimum of \( Z \) occurs at
more than two points. Minimise and Maximise \( Z=x+2 y \)
subject to \( x+2 y \geq 100,2 x-y \leq \)
\( \mathbf{0}, \mathbf{2} \boldsymbol{x}+\boldsymbol{y} \leq \mathbf{2 0 0} ; \boldsymbol{x}, \boldsymbol{y} \geq \mathbf{0} \)


What will be the height of a cuboid
whose volume is \( 275 \mathrm{cm}^{3} \) and base area
is \( 25 \mathrm{cm}^{2} ? \)
\( A \cdot 10 \mathrm{cm} \)
B. \( 11 \mathrm{cm} \)
\( c \cdot 9 \mathrm{cm} \)
D. None of these


A gas thermometer measures the temperature from the variation of
pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure
measured at the triple point of water
find the melting point of lead.
\( \mathbf{A} \cdot 600 K \)
B. \( 420 K \)
\( \mathbf{c} .790 K \)
D. \( 510 K \)


The freezing point of \( 1 \% \) of lead nitrate solution in water will be:
\( \mathbf{A} \cdot 2^{\circ} C \)
B. \( 1^{\circ} \mathrm{C} \)
\( c \cdot 0^{\circ} C \)
D. below \( 0^{\circ} C \)


Divide \( p(x) \) by \( g(x) \) in the following case
and verify division algorithm
\( \boldsymbol{p}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{4} \boldsymbol{x}+\boldsymbol{4} ; \boldsymbol{g}(\boldsymbol{x})=\boldsymbol{x}+\boldsymbol{2} \)


The effect of prolactin will be marked in
A. Bones
B. Pancreas
c. Mammary gland
D. Liver


What is the percentage hydrolysis of \( N a C N \) in \( \frac{N}{80} \) solution when
the dissociation constant for \( \boldsymbol{H} \boldsymbol{C} \boldsymbol{N} \) in
the solution is \( 1.3 \times 10^{-9} \) and \( K_{w} \) is
\( 1.0 \times 10^{-14} ? \)
\( \mathbf{A} \cdot 2.48 \% \)
B. \( 5.26 \% \)
c. \( 8.20 \% \)
D. \( 9.60 \% \)


Give examples of ionic hydride, molecular hydrides, interstitial hydride,
electron precise hydride.


Determine the value of \( x \) so that equal
strains are produced in each wire.
\( A \cdot 1 \)
\( 3.2 m \)
\( c .3 m \)
D. 2.2 n


The point through which the curve \( y= \)
\( x^{2}-1 \) passes through is
A. (4,15)
В. (-4,-15)
c. (-4,15)
D. (4,-15)


Where is the centre of gravity of a uniform ring situated?
A. At the centre of ring.
B. At the centre of semicircular ring
c. At the centre of radius
D. cant say


Find the vectors of magnitude 6 which are perpendicular to both the vectors \( 4 \vec{i}-\vec{j}+3 \vec{k} \) and \( -2 \vec{i}+\vec{j}-2 \vec{k} \)


A magnet of magnetic moment 20 CGS units is freely suspended in a uniform magnetic field of intensity \( 0.3 \mathrm{CGS} \) units. The moment of work done in
deflecting it by an angle of \( 30^{\circ} \) in \( C G S \)
units is
A . 6
B. \( 3 \sqrt{3} \)
c. \( 3(2-\sqrt{3}) \)
D. 3


lodine-salt mixture can be separated
through:
A. simple distillation
B. simple filtration
c. sublimation
D. fractional distillation


Percentage of unoccupied volume in case of simple cubic arrangement and body cenred arrangement of metals is
given by respectively.
A \( .52 \% \) \& \( 60 \% \)
B. \( 52 \% \& 26 \% \)
c. \( 48 \% \) \& \( 32 \% \)
D. \( 48 \% \) \& \( 26 \% \)


In above shown figure, the two plates of
the capacitor of charge \( +\mathrm{Q} \) and \( -\mathrm{Q}, \) which points lie on the same equipotential?
\( A \cdot 1 \) and 2 only
B. 1 and 3 only
C. 2 and 4 only
D. 3 and 4 only
E. \( 1,2,3, \) and 4 all lie on the same equipotential, since the electric field is uniform


State True or False.
\( \psi^{2} \) determines the probability of finding the electron in particular region of
space.
A. True
B. False


Complete the following:
\[
\boldsymbol{C}_{\boldsymbol{x}} \boldsymbol{H}_{\boldsymbol{y}}+\left(\boldsymbol{x}+\frac{\boldsymbol{y}}{\boldsymbol{4}}\right) \boldsymbol{O}_{2} \longrightarrow
\]


Which of the properties of the elements is a whole number?
A. Atomic mass
B. Atomic number
c. Atomic radius
D. Atomic volume


Phosphorus is an element belonging to :
A. VB group
B. VA group
C. VIA group
D. VIB group


Alternate name for Krebs cycle is
A . Glyoxylate cycle
B. Glycolate cycle.
c. Citric acid cycle
D. EMP pathway.


0.2 moles of an ideal gas, is taken
round the cycle \( a b c \) as shown in the
figure. The path \( b-c \) is adiabatic
process \( a-b \) is isovolumic and \( c-a \) is
isobaric process. The temperature at \( ^{\prime} a^{\prime} \)
and \( ^{\prime} b^{\prime} \) are \( T_{a}=300 K \) and \( T_{b}=500 K \)
and pressure at \( ^{\prime} a^{\prime} \) is 1 atmospheric.
The volume at \( ^{\prime} c^{\prime} \) is :
\( \left(\text {Given }: \gamma=\frac{\boldsymbol{C}_{\boldsymbol{p}}}{\boldsymbol{C}_{\boldsymbol{v}}}=\frac{\mathbf{5}}{\mathbf{3}}, \boldsymbol{R}=\mathbf{8 . 2 0 5} \times \mathbf{1}\right. \)
\( A \cdot 6.9 L \)
B. \( 6.68 L \)
0.5 .8


The electronic structure of \( \boldsymbol{S O}_{2} \)
molecule is best represented as a resonance hybrid of how many resonating structures?
\( A \cdot 2 \)
B. 3
\( c \cdot 4 \)
\( D \cdot 5 \)


Bond angle between two hybrid orbitals
is \( 105^{\circ}, \) hybrid \( s \) -character in orbital is :
A. between \( 20-21 \% \)
B. between \( 19-20 \% \)
c. between \( 21-22 \% \)
D. between \( 22-23 \% \)


Choose the functions of sympathetic
nervous system.
A. Constricts bronchi and pupil of eye
B. Increases heart rate and relaxes bronchi
C. Decreases heart rate and increase peristalisis
D. Dilates blood vessels and stimulates salivary secretions


\( (-8) \times(-2) \times(+3) \times(-4)= \)
\( \mathbf{A} \cdot+192 \)
B. -192
\( c \cdot+28 \)
D. -


\( \operatorname{Let} f(x)=\cos \left(\tan ^{-1} 2 x\right)- \)
\( \sin \left\{\tan ^{-1}\left(\frac{1}{2 x+1}\right)\right\} \) and \( a= \)
\( \cos \left(\tan ^{-1}\left(\sin \left(\cot ^{-1} 2 x\right)\right)\right) \) and \( b= \)
cos \( \left(\frac{\pi}{2}+\cos ^{-1} 2 x\right) \cdot \) If \( f(x)=0, \) then
\( b= \)
A. \( \frac{1}{\sqrt{2}} \)
B. \( -\frac{\sqrt{3}}{2} \)
c. \( \frac{\sqrt{3}}{2} \)
D. \( -\frac{1}{\sqrt{2}} \)


Which of the following is/are correct about the direction of holes/electron?
This question has multiple correct options
A. Holes are moving along the direction of electric field.
B. Electrons are moving along the direction of electric field.
C. Electrons are moving against the direction of electric field.
D. None of the above


Solution of \( \sqrt{1+x^{2}+y^{2}+x^{2} y^{2}}+ \)
\( x y \frac{d y}{d x}=0, \) is:
A \( \cdot \log \left(\frac{x}{1+\sqrt{1+x^{2}}}\right)+\sqrt{1+x^{2}}+\sqrt{1+y^{2}}=c \)
B \( \cdot \log \left(\frac{x}{\sqrt{1+x^{2}}}\right)+\sqrt{1-x^{2}}+\sqrt{1+y^{2}}=c \)
\( c \cdot \log \left(\frac{x}{\sqrt{1+x^{2}}}\right)=c \)
D \( \cdot \log (\sqrt{1+x^{2}}-\sqrt{1+y^{2}})+\log \left(\frac{x}{\sqrt{1+x^{2}}}\right)=c \)


Find the smallest natural number such
that, \( \left(\frac{1+i}{1-i}\right)^{n}=1 \)


When the reactor shuts down why does
it require cooling?
A. To cool the reactor from chain reaction
B. To cool the reactor from fission reaction
c. Both (1) and (2)
D. None of these


A focal length of a lens is \( 10 \mathrm{cm} . \) What is power of a lens in dioptre?
A. 0.10
B. 10 D
c. 15 \( D \)
D. 20 D


If \( z=\frac{\lambda D}{2 d} \)
\( A \)
B. 1/2
\( c \cdot 3 / 2 \)
D. 2


According to the law of conservation of energy, any load impedance connected to the ideal transformer's secondary
winding results in conservation of
A. reactive power
B. real
c. apparent
D. All of the above


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{O H} \stackrel{^{\prime} \boldsymbol{X}^{\prime}}{\longrightarrow} \boldsymbol{C H}_{2}=\boldsymbol{C H}_{2} \)
'X' may be:
This question has multiple correct options
A . conc. \( H_{2} S O_{4} / 170^{0} C \)
B . \( A l_{2} O_{3} / 350^{0} C \)
c. conc. \( H_{2} S O_{4} / 140^{\circ} C \)
D. conc. \( H_{2} S O_{4} / 110^{0} C \)


An electric dipole is kept in the origin
with charges along the \( x \) axis, now choose the correct option,
A. equipotential surface is on \( x y \) plane
B. equipotential surface is on \( x z \) plane
c. equipotential surface is on \( y z \) plane
D. none of the above


Which of the following equations or principle is most suitable to solve given question.

A block of mass \( m \) remains at rest on a
table when a piece of paper is pulled out
from under it.
A. Newton's first law(law of inertia)
B. Newton's second law ( \( F_{n e t}=\mathrm{ma} \) )
c. Newton's third law (For every action there is an equal and opposite reaction)
D. Newton's law of universal gravitation
E. conservation of linear momentum


State whether the following statement is true or false. Give reason to support
your answer.

For any two sets \( A \) and \( B \) either \( A \subseteq B \)
or \( \boldsymbol{B} \subseteq \boldsymbol{A} \)
A . True
B. False


Name two components of a solar cooker that are used to increase its heating
efficiency. Also explain how they do so?


In the figure, 'O' is the centre of the
circle. \( O M=3 \mathrm{cm} \) and \( \mathrm{AB}=8 \mathrm{cm} \). Find
the radius of the circle.
A \( .5 \mathrm{cm} \)
B. 4 cm
c. \( 15 \mathrm{cm} \)
D. \( 8 c m \)


A block of weight 15 N slides on a horizontal table the co-efficient of
sliding friction is \( 0.4 . \) The area of the
block in contact with the table is
\( 0.05 m^{2} . \) The shearing stress will be
B. \( 140 N m^{-2} \)
c. \( 160 N m^{-2} \)
D. \( 180 N m^{-2} \)


\( \boldsymbol{A B}=\mathbf{0} \) where
\( \boldsymbol{A}=\left[\begin{array}{cc}\cos ^{2} \boldsymbol{\theta} & \cos \boldsymbol{\theta} \sin \boldsymbol{\theta} \\ \cos \boldsymbol{\theta} \sin \boldsymbol{\theta} & \sin ^{2} \boldsymbol{\theta}\end{array}\right] \)
\( \boldsymbol{B}=\left[\begin{array}{cc}\cos ^{2} \boldsymbol{\phi} & \cos \phi \sin \phi \\ \cos \phi \sin \phi & \sin ^{2} \phi\end{array}\right] \)
then find \( |\boldsymbol{\theta}-\boldsymbol{\phi}|=? \)


Read the given statements and select
the correct option.

Statement 1: Mammals can eat while breathing.

Statement 2 : Mammals have negative-
pressure breathing.
A. Both statements 1 and 2 are Correct
B. Statement 1 is correct but statement 2 is incorrect
c. Statement 1 is incorrect but statement 2 is correct
D. Both statements 1 and 2 are incorrect.


An accelerated electron would produce
A . \( \gamma \) -rays
B. \( \beta \) -rays
c. \( \alpha \) -rays
D. electromagnetic rays


In an atom, there is \( 1 p^{+} \) and \( 1 e^{-} . \) If \( e^{-} \)
revolves around the \( p^{+} \) then angular velocity is proportional to:
\( \mathbf{A} \cdot r \)
в. \( r^{3} \)
c. \( \frac{1}{r^{3 / 2}} \)
D. \( \frac{1}{r^{2}} \)


What is the \( \% \) dissociation of \( \boldsymbol{H}_{2} \boldsymbol{S} \) if
one mole of \( H_{2} S \) is introduced in 1 litre
vessel at \( 1000 K \) if \( K_{c} \) for the reaction,
\( 2 H_{2} S(g) \rightleftharpoons 2 H_{2}(g)+S_{2}(g) \) is \( 4 \times \)
\( 10^{-6} ? \)


The major product P formed in the
following reaction is:
\( A \)
B.
\( c \)
\( D \)
\( E \)


If \( \sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}, \) then
\( \cos ^{-1} x+\cos ^{-1} y \) is equal to
A \( \cdot \frac{2 \pi}{3} \)
в.
c.
D.


Chloramines \( -\boldsymbol{T} \) is a:
A. Disinfectant
B. Antiseptic
c. Analgesic
D. Antipyretic


If I is the intensity of earth's magnetic
field, H its horizontal component and \( V \)
the vertical component, then these are
related as:
\( \mathbf{A} \cdot I=V+H \)
\( \mathbf{B} \cdot I=\sqrt{H^{2}+V^{2}} \)
\( \mathbf{C} \cdot I=\sqrt{H^{2}-V^{2}} \)
D \( \cdot I=H^{2}-V^{2} \)


How many orbitals are present in a \( \boldsymbol{p} \) subshell?
\( \mathbf{A} \cdot \mathbf{3} \)
B.
\( c \cdot 7 \)
D.


Which of the following has the \( (S) \)
configuration?
\( A \)
B.
\( c \)
\( D \)


How much electrical energy is transferred per second by a \( 4 V ; 0.5 A \) lamp?
A. 20 J/S
B. 2 J/S
\( c \cdot 6.8 \mathrm{J} / \mathrm{s} \)
D. 4.8 J/S


In the following structural formulae one
IUPAC name is incorrect. Identify it.
\( \mathbf{A} \cdot C H_{3}-C H_{2}-\underset{\| \atop O}{C}-C H_{3}- \) Butanone
\( H \)
B. \( \quad C H_{3}-C H_{2}-C=O \) -Propanal
\( \mathrm{C} \)
D. \( C H_{3}-C H_{2}-C H_{2}-C H_{2}-O H- \) Butanol


\( \triangle A B C \) is an isosceles triangle in
which \( A B=A C . \) Show that \( \angle B=\angle C \)


Assertion
Greater is critical temperature more easily a gas can be liquified.
Reason
Critical temperature depends on the magnitude of intermolecular forces of attraction between the gas.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


A vector \( \overline{\boldsymbol{m}} \) of magnitude \( 2 \sqrt{101} \) in the
direction of internal bisector of the
angle between the vector \( \bar{b}=8 \hat{i}-6 \hat{j}- \) \( 6 \hat{k} \) and \( \bar{c}=4 \hat{i}-3 \hat{j}+4 \hat{k} \) is
\( A \)
B . \( 16 \hat{i}-12 \hat{j}+2 \hat{k} \)
\( \frac{-16 \hat{i}+12 \hat{j}+2 \hat{k}}{5} \)
D . \( 16 \hat{i}+12 \hat{j}+2 \hat{k} \)


Give the IUPAC name of \( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}- \)
\( \boldsymbol{C H}(\boldsymbol{O H})-\boldsymbol{C H}_{3} \)


In January 1990 the world's population
was 5.3 billion. Assuming a growth rate
of 2 percent per year, the world's
population, in billions, for \( t \) years after
1990 can be modeled by the equation \( P=5.3(1.02)^{t} . \) With the help of the
model, calculate the growth in
population from January 1995 to
January 1996
A .106,000,000
B . 114,700,000
c. 117,000,000
D. 445,600,000
E . 562,700,000


Assertion
The surface tension of water is more
than other liquid.
Reason
Water molecules have strong inter molecular \( \boldsymbol{H}- \) bonding as attractive
force.
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 energy of an electron of mass \( m \) moving with velocity \( \mathrm{V} \) and de-Broglie wavelength \( \lambda \) is ('h' is
Planck's constant)
A \( \cdot \frac{h}{2 m \lambda} \)
в. \( \frac{h^{2}}{2 m \lambda^{2}} \)
c. \( \frac{h \lambda}{2 m} \)
D. \( \frac{h}{m \lambda} \)


The basic monosaccharide units of
lactose are glucose and galactose.
A. True
B. False


The mean square deviation of a set of \( n \)
observation \( x_{1}, x_{2}, \ldots x_{n} \) about a point \( c \)
is defined as \( \frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-c\right)^{2} \)
The mean square deviations about -2
and 2 are 18 and 10 respectively, the standard deviation of this set of
observations is
A . 3
B. 2
\( c . \)
D. None of these


Which of the following statements
is/are incorrect?
This question has multiple correct options
A. Glucose is non reducing sugar
B. Sucrose is reducing sugar
C. Maltose is non reducing sugar
D. Lactose is non reducing sugar


Why does menstruation occur?
A. Shredding blood
B. Shredding endometrium lining and mucous
C. Shredding of ovum
D. None of these


Draw a labelled diagram of human digestive system and explain it.


The accuracy of measurement also lies
in the way the result is expressed. The number of digits to which a value is to
be expressed is one digit more than
number of sure numbers. Rules do exist
to deal with number of digits after an
operation is carried out on the given values. The error can be minimised by
many trials and using the correct methods and instruments.
If the length and breadth are measured as 4.234 and \( 1.05 \mathrm{m}, \) the area of the
rectangle is
A \( .4 .4457 m^{2} \)
B . \( 4.45 \mathrm{m}^{2} \)
c. \( 4.446 m^{2} \)
D. \( 0.4446 m^{2} \)


Mention any two structural features of
the small intestine which add to its
absorptive capacity


Two reactions proceed at \( 25^{\circ} \mathrm{C} \) at the
same rate; the temperatue coefficient
of the rate of the first reaction is 2 and
that of the second reaction is \( 2.5 . \) Find
the ratio of rate of these reactions at
\( 95^{\circ} C \)


The ordinate of the point which divides the lines joining the origin and the point (1,2) externally in the ratio of 3: 2 is
A . -2
B. \( \frac{3}{5} \)
\( c \cdot \frac{2}{5} \)
D. 6


Show that 6 is not a perfect cube


The molecule which has zero dipole
moment is:
A \( \cdot C H_{2} C l_{2} \)
в. \( B F_{3} \)
c. \( N F_{3} \)
D. \( C l O_{2} \)


If the kinetic energy of free electron is made double; the new de-Broglie wavelength will be times that of initial wavelength.
\( ^{A} \cdot \frac{1}{\sqrt{2}} \)
B. \( \sqrt{2} \)
\( c \cdot 2 \)
D. \( \frac{1}{2} \)


Very short answer type.
Give an example of hyaline and calcified
cartilage.


Determine the values of a and ib for
which the given system of equations has infinitely many solutions:
\( (2 a-1) x-3 y=5 \) and \( 3 x+(b- \)
2) \( y=3 \)


Loss of top soil is called as
A. Corrosion
B. Washing
c. Denudation
D. None of the above


One hormone hastens the maturity period in juvenile conifers, a second hormone controls xylem differentiation while the third increases the tolerance
of plants to various stresses. They are
respectively
A. Auxin, gibberellin and cytokinin
B. Gibberellin, auxin, cytokinin
c. Gibberellin, auxin, ethylene
D. Gibberellin, auxin, ABA
E. Auxin, gibberellin, ABA


White phosphorus \( P_{4} \) has the following characteristics.
This question has multiple correct options
A. 6 P-P single bonds
B. 4 P-P single bonds
c. 4 lone pair of electrons
D. P-P-P angle of \( 60^{\circ} \)


Choose the correct answer from the
alternatives given.
The enzyme which catalyzes the
photosynthesis in \( C_{4} \) cycle is
A. PEP carboxylase
B. RuBP carboxylase
c. carbonic anhydrase
D. hexokinase


Which of the following reactions is
possible?
A. \( M e_{3} C-O N a+M e_{3} C-B r \rightarrow M e_{3} C-O-C M e_{3} \)
в. \( M e_{2} C H-O N a+M e_{2}+M e_{2} C H M e_{2} C H B r \rightarrow \)
\( M e_{2} C H-O-C H M e_{2} \)
c. \( P h O N a+P h B r \rightarrow P h O P h \)
D. \( P h O N a+C H_{3} B r \rightarrow P h O C H_{3} \)


Equation of a line whose inclination is
\( 45^{0} \) and making an intercept of 3 units of X-axis is
A. \( x+y-3=0 \)
в. \( x-y-3=0 \)
c. \( x-y+3=0 \)
D. \( x+y+3=0 \)


Chief source of soil and water pollution
is:
A. mining
B. agro industry
c. thermal power plant
D. all the three


The salts of phosphorous acid are
called:
A. phosphates
B. phosphites
c. hypophosphites
D. phosphides


A planoconvex lens of focal length 20
cm has its plane side silvered
This question has multiple correct options
A. The radius of curvature of curved surface of given plano-convex lens is equal to half of radius of curvature of a surface of equiconvex lens of focal length \( 20 \mathrm{cm} \)
B. An object placed at \( 15 \mathrm{cm} \) on the axis on the convex side of silvered plano-convex lens gives rise to an image at a distance of \( 30 \mathrm{cm} \) from it
C. An object placed at a distance of \( 20 \mathrm{cm} \) on the axis on the convex side of silvered plano-convex lens gives rise to an image at \( 40 \mathrm{cm} \) from it
D. silvered plano-convex lens acts as a concave mirror of focal length \( 10 \mathrm{cm} \)


State whether true or false:
Lightning conductors are used to save the building from earthquakes.
A. True
B. False


Some charge is being given to a
conductor. Then its potential:
A. is maximum somewhere between surface and centre.
B. is maximum at surface.
C. is maximum at centre.
D. remains same throughout the conductor


The addition of energy in the form of heat causes molecules or crystals of the substance to break up into ions.
A. True
B. False


List out the various excretory organs
found in the following:-
a) Sponges
b) Roundworms
c)Annelids
d) crustaceans
e) Insects
f) Flatworms
g) Echinoderms
h) Cnidarians
¡) Molluscs
j) Vertebrates


Evaluate the following definite integral:
\( \int_{0}^{4}\left(4 x-x^{2}\right) d x \)


The hydride ion \( H^{-} \) is stronger base
than hydroxide ion \( O H^{-} . \) Which of the following reaction will occur if sodium hydride \( (N a H) \) is dissolved in water?
A \( \cdot H^{-}(a q .)+H_{2} O \rightarrow H_{3} O^{-} \)
B . \( H^{-}(a q .)+H_{2} O(l) \rightarrow O H^{-}+H_{2} \)
c. \( H^{-}+H_{2} O \rightarrow \) No reaction
D. None of the above


In humans, blood vascular system has
A. Double circulation
B. Venous heart
c. Arterial heart
D. Arteriovenous heart


Assertion
\( \boldsymbol{H}_{2}+\boldsymbol{O}_{2} \) fuel cell gives a constant
voltage throughout its life.
Reason
In this fuel cell, \( H_{2} \) reacts with \( O H^{-} \) ions, yet the overall concentration of
\( O H^{-} \) ions does not change
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


Select incorrect statement(s):
A. A closed system with all adiabatic boundaries must be an isolated system
B. Total heat exchange in a cyclic process may be zero
C. Entropy of a closed system is maximum at equilibrium
D. Molar gibb's Energy is an extensive property


Which of the following is not a product of tar distillation?
A. Phenol \& naphthalene
B. Benzol \& pitch
c. Anthracene \& creosote
D. None of these


The correct structure of the product \( \boldsymbol{A} \)
formed in the reaction is :


Refer to the following statements describing Prophase I of meiosis and
answer the question
(i) Thin thread like chromosomes with a
beaded appearance
(ii) Appearence of recombination nodules
(iii) Formation of bivalents/tetrads
(iv) Terminalisation of chiasmata
(v) Appearance of chiasmata Identify the different stages with respect to the above given features and
select the correct option
A. (i) - Leptotene, (ii) - Zygotene, (iii) - Pachytene, (iv) Diplotene, (v) - Diakinesis
B. (i) - Leptotene, (ii) - Zygotene,
(iii) - Pachytene, (iv) Diakinesis, (v) - Diplotene
C. (i) - Leptotene,
(ii) - Pachytene,
(iii) - Zygotene, (iv) Diakinesis,
(v) - Diplotene
D. (i) - Leptotene,
(ii) - Pachytene,
(iii) - Diplotene, (iv) Zygotene,(v) - Diakinesis


How many spoons can be electroplated by silver when 7 ampere current is passed through electrolyte cell of \( A g N O_{3} \) for 1.93 hours? \( 0.01 g m A g \)
layer is deposited on each spoon. \( \left(A g=108 g \cdot m o l^{-1}\right) \)


Convert \( \frac{5 \pi}{6} \) in to radians.


\( \mathbf{3} \boldsymbol{F} \boldsymbol{e}^{\mathbf{2}+}+\mathbf{4} \boldsymbol{H}^{+}+\boldsymbol{N} \boldsymbol{O}_{\mathbf{3}}^{-} \longrightarrow \mathbf{3} \boldsymbol{F} \boldsymbol{e}^{\mathbf{3}+}+ \)
\( 2 H_{2} O+N O \) is balanced reaction
If the balanced reaction is true enter 1
else enter 0


The size of clay particle is less than
A. \( 0.02 \mathrm{mm} \)
B. 0.002 mm
\( c \cdot 0.2 \mathrm{mm} \)
D. 2.0 mm


If \( a>b \) maximum value of \( a \sin ^{2} x+ \)
\( b \cos ^{2} x \)
A . a
B.
\( c \cdot a+b \)
D. \( \sqrt{a^{2}+b^{2}} \)


In \( \Delta A B C, \angle A=30^{\circ}, \angle B=40^{\circ} \) and
\( \angle C=110^{\circ} \)
\( \ln \Delta P Q R, \angle P=30^{\circ}, \angle Q=40^{\circ} \) and
\( \angle R=110^{\circ} \)
Then Is \( \Delta A B C \cong \Delta P Q R \) by \( \mathrm{AAA} ? \)
A. True
B. False


Which of the following provides nutrients to the seedling to grow in forest?
A. Grubs
B. Beetles
c. Bacteria
D. Decaying animals dung


Water waves coming into shore arrive
every 4 seconds. The waves at \( 2.0 m / s \)
How long are the waves?
A . \( 4.0 \mathrm{m} \)
в. \( 8.0 m \)
\( c .2 .0 m \)
D. \( 0.50 m \)
E . \( 16.0 m \)


Evaluate:
\( \tan ^{-1}\left(\frac{\sqrt{1+\cos x}-\sqrt{1-\cos x}}{\sqrt{1+\cos x}+\sqrt{1-\cos x}}\right) \)


The group of molecules having identical
shape is:
\( \mathbf{A} \cdot B F_{3}, P C l_{3}, X e O_{3} \)
B. \( S F_{4}, X e F_{4}, C C I_{4} \)
\( \mathbf{c} \cdot P C l_{5}, I F_{5}, X e O_{2} F_{2} \)
D. \( C I F_{3}, X e O F_{2}, X e F_{3}^{+} \)


The rate that gives Rs.6400 as interest
on a sum of Rs.32000 in 5 years is:


The function \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{e}^{-|\boldsymbol{x}|} \) is
A. continuous everywhere but not differentiable at \( x=0 \)
B. continuous and differentiable everywhere
C. not continuous at \( x=0 \)
D. None of the above


A large number of liquid drops, each of radius \( r, \) coalesce to form a single drop
of radius R. The energy released in the process is converted into the kinetic
energy of the big drop so formed. The
speed of the big drop is : \( (T= \) surface tension, \( \rho=\text { density of liquid }) \)
\( ^{\mathbf{c}} \cdot \sqrt{\frac{4 T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)} \)
\( \sqrt[n]{\frac{6 T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)} \)


(A) Half-life of a first order reaction is
independent of the initial concentration of reactant
(R) \( t_{1 / 2} \) (first order) \( =\tau / 1.44 \)
where, \( \boldsymbol{\tau} \) =average life.
A. Both (R) and (A) are true and reason is the correct explanation of assertion
B. Both (R) and (A) are true but reason is not correct explanation of assertion
c. Assertion
(A) is true but reason
(R) is false
D. Assertion
(A) and reason
(R) both are false
E. Assertion (A) is false but reason (R) is true


For superposition of two waves, which
of the following is correct
A. They must have the same frequency and wavelength
B. They must have equal frequencies but may have unequal wavelengths
C. They must have the same wave-length, but may have different frequencies
D. They may have different wavelength and different frequencies


Why are bells made up of metals and
not from wood?


State Pythagoras theorem.


Briefly describe the transport of \( C O_{2} \) in
the blood.


An electron experiences a magnetic force of magnitude \( 4.60 \times 10^{-15} N \)
when moving at an angle of \( 60.0^{\circ} \) with respect to a magnetic field of magnitude \( 3.50 \times 10^{-3} T . \) If \( v \) is the
speed of the electron, find \( x, \) such that \( \boldsymbol{x}=\boldsymbol{v} / \mathbf{1 0}^{4} \)


If the vector \( b \) is collinear with the vector
\( \boldsymbol{a}=(\mathbf{2} \sqrt{\mathbf{2}},-\mathbf{1}, \mathbf{4}) \) and \( |\boldsymbol{b}|=\mathbf{1 0}, \) then
A \( \cdot a \pm b=0 \)
В . \( a+2 b=0 \)
c. \( 2 a_{\pm} b=0 \)
D. None of these


A cube of wood supporting \( 200 g m \)
mass just in water \( (\rho=1 g / c c) . \) When
the mass is removed, the cube rises by \( 2 c m . \) The volume of cube is
A . \( 1000 c c \)
B. \( 800 c c \)
c. \( 500 c c \)
D. None of these


The radius of a sphere is given by \( r=2 t \)
The rate of change of surface area at \( t= \)
1 is equal to
\( A \cdot 8 \pi \)
B. \( 32 \pi \)
c. \( 16 \pi \)
D. \( 4 \pi \)


requires a salt bridge.
A. Voltaic cell
B. Electrolytic cell
C . Geiger counter
D. pH meter
E . Calorimeter


12 g of \( \boldsymbol{C H}_{3} \) COOH and 4 g of NaOH are mixed and diluted to 1 litre solution. If
\( P^{K a} \) of \( C H_{3} C O O H \) is \( 4.8, \) then the \( p^{H} \)
of the solution is:
A . 4.8
B. 5
c. 5.6990
D. 5.3010


For the following arithmetic progressions write the first term \( a \) and
the common difference \( \boldsymbol{d} \)
\( -5,-1,3,7, \dots \)


A body dropped from the top of a tower
cover a distance \( 9 x \) in the last second of
its journey where \( x \) is the distance covered in the first second. How much
time does it take to reach the ground?
A. 3 sec
B. 4 4 sec
\( c .5 s e c \)
D. 6 sec


Sharing of valence electrons between two atoms generally takes place between \( _{\text {toms. }} \)
A. metallic
B. non-metallic
c. large
D. small


The higher values of specific heat of water in comparison to other liquids is
due to:
A. high dielectric constant
B. polarity
c. \( H \) -bonding
D. none of the above


A convex lens is immersed in water
Compared to its power in air, its power in water will.
A. Increase
B. Remain the same
c. Diminish for red light and increase for blue light
D. Diminish


A ball is moving with a momentum of 5
N. \& strikes the wall at a angle of 45
and is reflected at the same angle. calculate impulse.


The statement that is not correct is :
A. carbohydrates are optically active
B. lactose has glycosidic linkage between \( C_{4} \) of glucose and \( C_{1} \) of galactose unit
C . aldose or ketose sugars in alkaline medium do not isomerise
D. penta acetate of glucose does not react with hydroxylamine


A tennis ball is released from height \( h \) above ground level. If the ball makes inelastic collision with the ground, to
what height will it rise after third
collision, e is the coefficient resitiution
between ball and ground?
A \( \cdot h e^{6} \)
B \( \cdot e^{2} h \)
\( \mathbf{c} \cdot e^{3} h \)
D. None of these


If \( x, v \) and a denote the displacement, the velocity and the acceleration of a
particle executing simple harmonic motion of time period \( T, \) then which of the following do not change with time?
A \( \cdot \frac{a T}{v} \)
В . \( a T+2 \pi v \)
c. \( a^{2} T^{2}+4 \pi^{2} v^{2} \)
D. \( a T \)
E . \( v T \)


The digits of two - digits number is
differ by \( 5 . \) If the digits are interchanged and the resulting number is added to the original number, we get
\( 99 . \) Find the original number


What is the oxidation number of carbon
in carbon suboxide \( \left(C_{3} O_{2}\right) ? \)


Calculate the water pressure and the thrust at the bottom of a tank whose
length, width and the depth are
\( 2 m, 1.5 m \) and 1 m respectively.
Density of water is \( 1000 \mathrm{kg} \mathrm{m}^{-3} \)


Which of the following electronic
configurations represents the violation of both Aufbau principle and Hund's rule?
\( A \)
\[
\frac{\sqrt{16}}{3 s} \frac{\sqrt{111111 k}}{3 p} \cdot \frac{\sqrt{1}|1| 1 \mid}{3 d} \frac{\sqrt{11}}{4 s}
\]
в.
\( c \)
\[
\frac{\sqrt{11}}{3 \mathrm{s}} \frac{\sqrt{111 L 11}}{3 p} \quad \frac{\sqrt{141} / 1}{3 \mathrm{d}}
\]
D.


The \( 5^{t h}, 8^{t h} \) and \( 11^{t h} \) terms of a G.P. are
\( p, q \& s \) respectively. Show that \( q^{2}=p s \)


In crystalline state \( P C l_{5} \) exists as :
A \( \cdot\left[P C l_{4}\right]^{+} C l^{-} \)
B . \( \left[P C l_{4}\right]^{+}\left[P C l_{6}\right]^{-} \)
C \( \cdot\left[P C l_{3}\right]^{2+}+2 C l^{-} \)
D \( \cdot\left[P C l_{6}\right]^{+}\left[P C l_{4}\right]^{-} \)


Nitrogen is used for filling the electric bulbs, because it is:
A. Lighter than air
B. Capable of giving more light by the bulb
c. Nothelpful in burning
D. Not poisonous


Write the names of the metals used as
sacrificial electrode for the prevention of corrosion of iron metal and how it
prevents the corrosion?


Which one acts as artificial kidney in haemodialysis?
A. Dialysing liquid
B. Bubble trap
c. Blood pump
D. Dialyser


The potential at a point due to a charge
of \( 5 \times 10^{-7} C \) located \( 10 c m \) away is:
A \( \cdot 3.5 \times 10^{5} V \)
B . \( 3.5 \times 10^{4} V \)
c. \( 4.5 \times 10^{4} V \)
D. \( 4.5 \times 10^{5} V \)


Refraction of light can take place at boundary of
A. Transparent Media
B. Opaque Media
c. Any Medium
D. Rarer Medium


10 L of hard water with temporary
hardness of \( \left[\boldsymbol{C a}\left(\boldsymbol{H} \boldsymbol{C O}_{3}\right)_{2}\right] \) requires
\( 0.56 \mathrm{g} \) of lime. The reaction follows as:
\( \boldsymbol{C a}\left(\boldsymbol{H C O}_{3}\right)_{2}+\boldsymbol{C a O} \longrightarrow \boldsymbol{2} \boldsymbol{C a} \boldsymbol{C O}_{3}+ \)
\( \boldsymbol{H}_{2} \boldsymbol{O} \)
Temporary hardness in terms of ppm of
\( \boldsymbol{C a} \boldsymbol{C O}_{3} \) is:
\( A .56 \) ppm
B. \( \frac{1}{2} \) ppm
c. 100 ppm
D. 200 ppm


Vascularisation in plants occur
through
A. Differentiation of procambium followed by primary phloem and then primary xylem
B. Differentiation of procambium followed by development of xylem and phloem.
C. Simultaneous differentiation of procambium, xylem and phloem
D. Differentiation of procambium is immediately followed by development of secondary xylem and secondary phloem.


The value of \( \int_{a}^{b} f(x) d x \)


Aromatic hydrocarbons are the derivatives:
A. Benzene
B. Methane
C. Paraffins
D. Alkanes


An electron revolving in an orbit of radius \( 0.5 \dot{A} \) in a hydrogen atom executes \( 10^{16} \) revolutions per second.
The magnetic moment of electron due to its orbital motion will be
A. \( 1.256 \times 10^{-23} \mathrm{Am}^{2} \)
B. \( 653 \times 10^{-26} \mathrm{Am}^{2} \)
c. \( 10^{-3} \) Am \( ^{2} \)
D. \( 256 \times 10^{-26} \mathrm{Am}^{2} \)


A charge particle of charge \( q \) is moving
with speed \( v \) in a circle of radius \( R \) as shown in figure. Then the magnetic field at a point on axis of circle at a distance
\( x \) from centre is :
A \( \cdot \frac{\mu_{0}}{4 \pi} \frac{q V}{R^{2}} \)
в. \( \frac{\mu_{0}}{4 \pi} \frac{q V}{\left(R^{2}+x^{2}\right)} \)
c. \( \frac{\mu_{0}}{4 \pi} \frac{q V}{x^{2}} \)
D. \( \frac{\mu_{0}}{4 \pi} \frac{q V R}{\left(R^{2}+x^{2}\right)^{3 / 2}} \)


Find the given number is a perfect cube
or not.
\( \mathbf{1 3 8 2 4} \)


During which phase of meiosis do homologous chromosomes separate?
A. Anaphase
B. Prophase
c. Anaphase I
D. Prophase II
E. Metaphase!


In Braille system how are the dots made?
A. They can be made with help of hands
B. They can be made with the help of printer
c. They can be made with the help of typewriter
D. All the above


The element that has two unpaired
electrons in its \( M^{2+} \) ion form is:
A. Mn
B. cu
\( c \cdot z n \)
D. Ti


Carbon has \( _{\text {十一一一一一一一一一 }} \) isotopes.
\( A \cdot 1(\text { one }) \)
B. 2 (two)
c. 3 (three)
D. 4 (four)


An urn contains 10 balls coloured either
black or red When selecting two balls
from the urn at random, the probability
that a ball of each color is selected is
\( 8 / 15 . \) Assuming that the urn contains more black balls then red balls, the
probability that at least one black ball is selected, when selecting two balls, is
\( \mathbf{A} \cdot \frac{18}{45} \)
B. \( \frac{30}{45} \)
c. \( \frac{39}{45} \)
D. \( \frac{41}{45} \)


If the pressure difference between the two points of a horizontal pipe is
\( 0.1 p_{a t m}, \) then the velocity water flow in the pipe is :
в. \( \sqrt{20} \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 10 \mathrm{ms}^{-1} \)
D. \( 14 \mathrm{ms}^{-1} \)


Energy of the state \( S_{1} \) in units of the hydrogen atom ground state energy is:
A. 0.75
B. 1.50
c. 2.25
D. 4.50


What makes the normal rain water
acidic?
A. Presence of dust particles in air
B. Presence of \( C O_{2} \) in atmosphere
C. Presence of ozone in atmosphere
D. All of the above


Compute the summation \( \sum_{k=0}^{27} k\left(_{k}^{27}\right)\left(\frac{1}{2}\right)^{k}\left(\frac{2}{3}\right)^{27-k} \)


Water is flowing continuously from a
\( \operatorname{tap} \) an ineternal diameter \( 8 \times 10^{-3} m \)
The water as it leaves the tap is \( 0.4 m s^{-1} . \) The diameter water stream at
a distance \( 2 \times 10^{-1} m \) be tap is close to
A \( \cdot 3.6 \times 10^{-3} \mathrm{m} \)
В. \( 5.0 \times 10^{-3} \mathrm{m} \)
c. \( 7.5 \times 10^{-3} m \)
D. \( 9.6 \times 10^{-3} m \)


Identify electron-donating groups in resonance among the following:(A)
\( -\boldsymbol{C O N H}_{2}(\mathrm{B})-\boldsymbol{N O}_{2} \)
\( (\mathrm{C})-\mathrm{O} \mathrm{COCH}_{3} \)
(D) \( -\boldsymbol{C O C H}_{3} \)
\( -\boldsymbol{C H O}(\mathrm{F})-\boldsymbol{N} \boldsymbol{H} \boldsymbol{C O C H}_{3} \)


Meiosis is a must in asexual
reproduction.
A. True
B. False


In a closed blood vascular system, blood is completely enclosed within the
A. Skeleton
B. sinuses
c. vessels
D. Heart


Find the point on the curve \( y^{2}=8 x \) for
which the abscissa and ordinate
change at the same rate.


Oxalic acid dihydrate, \( \boldsymbol{H}_{2} \boldsymbol{C}_{2} \boldsymbol{O}_{4} \)
\( 2 H_{2} O(s) \) is often used as a primary
reagent to standardise sodium
hydroxide solution. Which of these facts are reasons to choose this substance as
a primary standard?
I. It is diprotic.
II. It is a stable compound that can be weighed directly in air.
III. It is available in pure form.
A. III only
B. I and II only
c. ॥ and III only
D. I. II and III


A particle is executing simple harmonic
motion of amplitude \( A . \) At a distance \( x \) from the centre, a particle moving towards the extreme position receives a blow in the direction of motion which
instantaneously doubles the velocity. Its
new amplitude will be
A. \( A \)
B. \( \sqrt{A^{2}-x^{2}} \)
c. \( \sqrt{2 A^{2}-3 x^{2}} \)
D. \( \sqrt{4 A^{2}-3 x^{2}} \)


topp
Q Type your question
microcoulombs, +2 microcoulombs and
-2 microcoulombs. Find out the
direction of the net electric force acting on the +1 microcoulombs charge.
\( A \)
B.
\( c \)
\( D \)
E


Speed of the light is
A. the same in medium-1 and medium-2
B. larger in medium-1 than in medium-2
C. larger in medium-2 than in medium- -
D. different at b and d


Taxol drug is used to cure which disease:
A. AlDS
B. Parkinsons
c. cancer
D. Heart attack


Find the equation of the ellipse referred to its centre whose minor axis is equal to the distance between the foci and
whose latus rectum is 10 .


2-Methyl butane on reacting with bromine in presence of sunlight gives mainly :
A. 1 -Bromo-2-methyl butane
B. 2-Bromo-2-methyl butane
c. 2-Bromo-3-methyl butane
D. 1-Bromo-3-methyl butane


If \( z \) is complex number such that \( z \neq 0 \)
and \( R_{e}(z)=0, \) then
\( \mathbf{A} \cdot \operatorname{Re}\left(z^{2}\right)=0 \)
В. \( \operatorname{Im}\left(z^{2}\right)=0 \)
\( \mathbf{c} \cdot \operatorname{Re}\left(z^{2}\right)=\operatorname{Im}\left(z^{2}\right) \)
D. none of these


n Fig. \( 2, \) 'O' is the centre of the circle,
find \( \angle A O C, \operatorname{given} \angle B A O=30^{\circ} \) and
\( \angle B C O=40^{\circ} \)
\( A \cdot 35 \)
В. 140
\( c \cdot 70 \)
D. Cannot be determined


Which of the following is the most
precise measurement?
A. \( 3 \times 10^{-3} \mathrm{m} \)
B . \( 0.0030 m \)
c. \( 30 \times 10^{-4} \mathrm{m} \)
D. \( 300 \times 10^{-5} \mathrm{m} \)


In a class of 60 students, 30 opted for Mathematics, 32 opted for Biology and 24 opted for both Mathematics and Biology. If one of these students is selected at random, find the probability that:
(i) The student opted for Mathematics or Biology.
(ii) The student has opted neither Mathematics nor Biology.
(iii) The student has opted
Mathematics but not Biology.


Find the square root of 2002225


Explain bacillus.


The contrapositive of "if \( x \) has courage
then \( x \) will win", is
A. If \( x \) will in, then \( x \) has courage
B. If \( x \) has no courage, then \( x \) will not win.
c. If \( x \) will not win, then \( x \) has no courage
D. If \( x \) will not win, then \( x \) has courage


Calculate the \( p H \) (nearest integer) of
\( \mathbf{0 . 0 1 0} M \mathbf{N a H C O}_{\mathbf{3}} \) solution. \( \boldsymbol{K}_{\mathbf{1}}= \)
\( 4.5 \times 10^{-7} \) and \( K_{2}=4.7 \times 10^{-11} \) for
carbonic acid.


For the equilibrium \( S O_{2} C l_{2}(g) \rightleftharpoons \)
\( \boldsymbol{S} \boldsymbol{O}_{2}(\boldsymbol{g})+\boldsymbol{C l}_{2}(\boldsymbol{g}), \) what is the
temperature at which \( \frac{\boldsymbol{K}_{\boldsymbol{p}}(\boldsymbol{a} \boldsymbol{t m})}{\boldsymbol{K}_{c}(\boldsymbol{M})}=\mathbf{3} ? \)
в. \( 0.36 K \)
c. 36.54
D. 273 K


Which one of the following pairs of chemical substances, is correctly categorized?
A. Pepsin and prolactin - Two digestive enzymes secreted in stomach
B. Troponin and myosin - Complex proteins in striated muscles
c. secretin and rhodopsin - Polypeptide hormones
D. Calcitonin and thymosin - Thyroid hormones


The value of \( \frac{1}{4} x-5(q-x) \) \( -\frac{3}{2}\left(\frac{1}{3}\left(q-\frac{x}{3}\right)-\frac{2}{9}\left[x-\frac{3}{4}\left(q-\frac{4 x}{5}\right)\right]\right) \) is
A \( \cdot \frac{9 x}{5}+\frac{q}{2} \)
в. \( \frac{9 x}{4}-\frac{q}{2} \)
c. \( \frac{9 x}{5}-\frac{q}{2} \)
D. \( \frac{11 x}{5}+2 q \)


Find gain or loss per cent. \( \mathrm{CP}=\boldsymbol{R} \boldsymbol{s} . \mathbf{7 5 0} \) and \( \mathrm{SP}=\boldsymbol{R} \boldsymbol{s} . \boldsymbol{8 5 0} \)


Petroleum gas is used in:
A. the production of carbon black needed in tyre industry
B. the production of hydrogen needed in fertilizer industry
C . manufacturing gasoline
D. all of these


Sweet potato is homologous to
A. Potato
B. colocasia.
c. Ginger.
D. Turnip


For the reaction, \( \boldsymbol{X}_{2} \boldsymbol{O}_{4}(l) \longrightarrow \)
\( \mathbf{2} \boldsymbol{X} \boldsymbol{O}_{2}(\boldsymbol{g}) \)
\( \Delta U=2.1 k c a l, \Delta S=20 \operatorname{cal} K^{-1} \mathrm{at} \)
\( 300 \mathrm{K} \) Hence \( , \Delta G \) is
A . +2.7 kcal
B. -2.7 kcal
c. +9.3 kcal
D. - -9.3 kcal


Resistance of a cconductivity cell filled with a solution of an electrolyte of concentration \( 0.1 M \) is \( 100 \Omega \). The
conductivity of this solution is \( 1.29 S m^{-1} . \) Resistance of the same cell
when filled with \( 0.02 ~ M \) of the same
solution is \( 520 \Omega \). The molar
conductivity of \( 0.02 M \) solution of the electrolyte will be:
A \( \cdot 124 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{mol}^{-1} \)
В. \( 1240 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{mol}^{-1} \)
c. \( 1.24 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{mol}^{-1} \)
D. \( 12.4 \times 10^{-4} \mathrm{Sm}^{2} \mathrm{mol}^{-1} \)


Complete the following statements.
\( \boldsymbol{S} \boldsymbol{i} \boldsymbol{C l}_{4}+\boldsymbol{H}_{2} \boldsymbol{O} \rightarrow \ldots \)


Grease is applied to parts of a motor vehicle for smooth movement. Greases are, essentially, lubrication oils made
into a jelly by:
A. soaps of fatty acids
B. blowing air under pressure
c. adding wax
D. churning of starch


A system goes from \( A \) to \( B \) via two
processes I and II as shown in the figure
If \( \Delta U_{1} \) and \( \Delta U_{2} \) are the changes in
internal energies in the processes land II respectively, the
A \( \cdot \Delta U_{1}=\Delta U_{2} \)
B. relation between \( \Delta U_{1} \) and \( \Delta U_{2} \) cannot be determined
c. \( \Delta U_{2}>\Delta U_{1} \)
D. \( \Delta U_{2}<\Delta U_{1} \)


Solve:
\( \log _{5} \frac{(25)^{4}}{\sqrt{625}} \)
\( \mathbf{A} \cdot \mathbf{4} \)
B. 5
\( c \cdot 6 \)
D.


How many \( H C l \) molecules are lost
when Acetyl chloride is converted to Ethanal by Rosenmund reduction?


A rocket works on the which law of
motion?
A. Newton's first law
B. Newton's second law
c. Newton's third law
D. None of these


A particle of mass \( m \) is executing S.H.M.
of time period \( T, \) and amplitude \( a_{0} . \) The
force on particle at the mean position is:
A \( \cdot \frac{4 \pi^{2} m}{T^{2}} a_{0} \)
\( ^{\text {В } \cdot \frac{2 \pi^{2} m}{T^{2}} a_{0}} \)
c. zero
D. \( \frac{\pi^{2} m a_{0}}{T^{2}} \)


If \( \sec ^{-1} \frac{1}{\sqrt{1-x^{2}}}+\cot ^{-1}\left(\frac{\sqrt{1-x^{2}}}{x}\right)= \)
\( \sin ^{-1}(k) \) then \( k= \)
B. \( 2 x \sqrt{1-x^{2}} \)
c. \( \sqrt{1-x^{2}} \)
D. \( 2 x \)


Find the angle made by a ladder of length \( 4 m \) with the ground if its one end is \( 2 m \) away from the wall and the other end is on the wall


Solutions that have the same osmotic
pressure are called (isotonic/isometric) solutions


Find the arithmetic mean of the
following data.
A . 59.35
B . 57.35
c. 61.35
D . 52.35


The number of Ip-bp repulsion present
in \( C l F_{3} \) at nearly 90 degree angle are :
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


The following graph was plotted
between \( \mathrm{V} \) and \( \mathrm{I} \) values. What would be
the values of \( V / I \) ratios when the
potential difference is \( 0.5 \mathrm{V} \) and \( 1 \mathrm{V} \) ?


Read the given statements and mark
the correct option.

Statement 1: While fixing a metal rim on a wooden wheel of a cart, the size of
the metal rim is kept slightly smaller than that of the wooden wheel.
Statement 2: Metals expand on heating and contract on cooling.
A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1
c. statement 1 is true and statement 2 is false.
D. Both statements 1 and 2 are false.


Haemoglobin of the blood forms carboxyhaemoglobin with:
A \( \cdot C O_{2} \)
в. \( C O \)
\( c \cdot S O_{2} \)
D. \( N O_{2} \)


Conjugate surd of \( a+\sqrt{6} \) is
A \( .6-\sqrt{a} \)
B. \( 6+\sqrt{a} \)
c. \( \sqrt{6}-a \)
D. \( a-\sqrt{6} \)


The value of \( \tan 105^{\circ} \) is
A. \( -(2+\sqrt{3}) \)
B. \( -2+\sqrt{3} \)
c. \( \sqrt{3}+\sqrt{2} \)
D. \( -(\sqrt{3}+\sqrt{2}) \)


Each human kidney has nearly
A. 10,000 nephrons
B. \( 50,000, \) nephrons
\( c .1,00,000 \) nephrons
D. 1 million nephrons


In a History examination, the average for the entire class was 80 marks. If \( 10 \% \)
of the students scored 95 marks
and \( 20 \% \) scored 90 marks, what was the
average marks of the remaining students of the class?
A . 65.5
в. 72.5
c. 75
D. 85


Absolute zero is obtained from
A . \( P-V \) graph
B. \( P-\frac{1}{V} \) graph
c. \( P-T \) graph
D. \( V-T \) graph


Pullorum disease of poultry is caused
by
A. Hemophilus
B. clostridium
c. Salmonella
D. Mycobacterium


The minimum length of a plane mirror required to view the full image of a person 6 feet tall is :
A . 3 feet
B. 6 feet
c. 4 feet
D. 5 feet


The value of the determinant \( \Delta=\left|\begin{array}{ccc}1 ! & 2 ! & 3 ! \\ 2 ! & 3 ! & 4 ! \\ 3 ! & 4 ! & 5 !\end{array}\right| \) is
A . 2
в. 3
\( c \cdot 4 \)
D. 5


A hydrogen atom is in the \( d \) -state. The values of \( m \) for this state are
в. -3,-1,0,1,3
c. 2,1,0
D. -2,-1,0,1,2


When an electron in hydrogen spectrum jumps from \( n=7 \) to \( n=2 \), the total
number of spectral lines possible are:
A . 21
B . 15
\( c .5 \)
D.


In the following reaction, we are likely to
get:
\( \boldsymbol{C H}_{3} \boldsymbol{O} \boldsymbol{N} \boldsymbol{a}+\boldsymbol{B r}-\boldsymbol{t}-\boldsymbol{B u} \rightarrow \)
A. ether
B. alkene
c. alcohol
D. none of the above


n \( \Delta A B C \) DE \( \| B C \) Find \( A D \) if \( D B= \)
\( 7.2 \mathrm{cm}, A E=1.8 \mathrm{cm}, \) and \( E C=5.4 \)
\( \mathrm{cm} \)


Column chromatography involves separation of a mixture over a column of adsorbent (stationary phase) packed in a glass tube. Depending upon the degree of adsorption complete
separation takes place. In the given column, three coloured bands \( x, y, z \) are
formed. Identify the correct statement
A. \( x, y \) and \( z \) are adsorbed to the same extent
B. The most readily adsorbed component is retained nea the top (x)
c. The most readily absorbed component comes \( \operatorname{down}(z) \)
D. \( x, y, z \) layers are formed according to the wavelengths of the colours not on the basis of adsorption


The cross-section of a trunk of a tree
showed 50 annual rings. The age of tree is
\( A \cdot 50 \) years
B. 50 months
c. 100 years
D. 25 years


If \( \alpha \) and \( \beta \) are the roots of \( 4 x^{2}-16 x+ \)
\( c=0, c>0 \) such that \( 1<\alpha<2<\beta<3 \)
then the no.of integer values of \( c \) is
A . 17
B . 14
c. 18
D. 15


The favourable condition for the
reaction \( N_{2}+O_{2} \rightleftharpoons 2 N O+ \) heat is
A. increase in the concentration of reactants
B. increase in pressure
c. decrease in temperature
D. none of the above


Assertion
Absolute error may be negative or
positive.
Reason
Absolute error is the difference between
the real value and the measured value
of a physical quantity
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct


Which of the following complex ions can exhibit linkage isomerism?
\( \mathbf{A} \cdot\left[A g\left(N H_{3}\right)_{2}\right]^{+} \)
B . \( \left[\operatorname{Co}\left(N H_{3}\right)_{5} N O_{2}\right]^{2+} \)
\( \mathbf{c} \cdot\left[P t(e n) C l_{2}\right) \)
D \( \cdot\left[\operatorname{Co}\left(N H_{3}\right)_{5} C l\right]^{2+} \)


A) Draw a typical illuminated \( \boldsymbol{P}-\boldsymbol{n} \)
junction solar cell.
B) LED convert \( _{\text {一一一一一一 }} \) energy to light.


The isotope of Uranium
is used as a fuel in
nuclear reactors.
A. \( U-232 \)
B. \( U-233 \)
c. \( U-234 \)
D. \( U-235 \)


An organisation plans to plant saplings in 25 streets in a town in such a way
that one sapling for the first street, two for the second, four for the third, eight for the fourth street and so on. How
many saplings are needed to complete the work?


\( \boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{3}+\boldsymbol{N} \boldsymbol{a} \boldsymbol{O} \boldsymbol{H} \rightarrow \)
\( \boldsymbol{N} \boldsymbol{a}\left[\boldsymbol{B}(\boldsymbol{O} \boldsymbol{H})_{4}\right]_{(a q)} \)
Then addition of which of the following proceeds the reaction in the forward direction:
A. cis-1, 2 dio
B. trans 1, 2 diol
c. borax
D. \( N a_{2} H P O_{4} \)


What is \( \mu_{\max } \) equal to?
A \( \cdot \mu_{\max } \approx 1.0 \times 10^{4} \)
B . \( \mu_{\max } \approx 2.0 \times 10^{4} \)
C \( \cdot \mu_{\max } \approx 1.0 \times 10^{3} \)
D. \( \mu_{\max } \approx 2.0 \times 10^{3} \)


What is the distance traveled by the
body during the first 100 seconds?
\( A \cdot 200 m \)
B. 50 \( m \)
\( c \cdot 100 m \)
D. 25 \( m \)


Two inductors \( L_{1} \) and \( L_{2} \) are connected
in parallel and a time varying current i flows as shown. The ratio of currents
\( \mathbf{i}_{i} / \mathrm{l}_{2} \) at any time \( \mathrm{t} \) is
\( A \cdot L_{1} / L_{2} \)
B . \( L_{2} / L_{1} \)
\( \mathbf{C} \cdot \frac{L_{1}^{2}}{\left(L_{1}+L_{2}\right)^{2}} \)
\( D \)


A uniform horizontal rod of length \( 40 \mathrm{cm} \) and mass \( 1.2 \mathrm{kg} \) is supported by
two identical wires as shown in the
figure. Where should a mass of \( 4.8 k g \)
be placed on the rod from the left end (in
\( \mathrm{cm} \) so that the same tuning fork may
excite the wire on left into its
fundamental vibrations and that on
right into its first overtone? Take \( G= \)
\( 10 m / s^{2} \)


Suppose a population \( A \) has 100
observations \( 101,102 \ldots 200 \) and other population \( B \) has 100 observations
\( 151,152 \ldots 250 \)
Find the difference in their means
A . 49
B . 50
c. 51
D. 52


The metals extracted from their fused
salts are:
A. sodium
B. potassium
c. magnesium
D. All of the above


A coin kept in a container and not visible can be viewed by pouring water into the container. It happens because
of the
A. Reflection of light.
B. Refraction of light
c. variable refractive index of water.
D. None of the above