Question Paper (Section wise)

1) A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is


2) A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms^{2})

32 N

18 N

23 N

25 N


3) If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit its L, about the canter of the Sun, its areal velocity is:


4) A particle which is experiencing a force, given by Â undergoes a displacement of. If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

9 J

12 K

10 J

15 J


5) For equal point charges Q each are placed in the XY plane at (0, 2), (4, 2), (4,  2) and (0,2). The work required to put a fifth charge Q at the origin of the coordinate system will be:


6) For the circuit shown below, the current through the Zener diode is:

9 mA

5 mA

Zero

14 mA


7) The given graph shows variation (with distance r from centre) of:

Electric field of a uniformly charged sphere

Potential of a uniformly charged spherical shell

Potential of a uniformly charged sphere

Electric field of a uniformly charged spherical shell


8) Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin (450 t â€“ 9x) where distance and time are measured in SI united. The tension in the string is:

10N

7.5 N

12.5 N

5 N


9) In an experiment, electrons are accelerated, from rest, by applying, a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 Ã— 10^{19} C Mass of the electron = 9.1 Ã— 10^{31} kg]

7.5 Ã— 10^{3 }m

7.5 Ã—10^{2} m

7.5m

7.5 Ã— 10^{4} m


10) A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in searleâ€™s apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8.
The new value of increase in length of the steel wire is:

3.0 mm

4.0 mm

5.0 mm

Zero


11) In a radioactive decay chain, the initial nucleus is Â At the end there are 6 Î± particles and 4Î² â€“ particles with are emitted. If the end nucleus is , A and Z are given by:

A = 208; Z = 80

A = 202; Z = 80

A = 208; Z = 82

A = 200; Z = 81


12) When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photo current is â€“V_{0}/ 2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is â€“V_{0}. The threshold frequency for photoelectric emission is:



2 v



13) A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping al throughout. The two climb maximum height h_{sphÂ }and h_{cyl} on the incline. The radio is given by:

1





14) The ratio of mass densities of nuclei of ^{40}C_{a} and ^{16}O is closed to:

0.1

5

2

1


15) A nucleus A, with a finite de â€“ broglie wavelength Î»_{A}, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of F. The de â€“ Broglie wavelength Î»_{B} and Î»_{c} of B and C are respectively:

Î»_{A}, 2Î»_{A}

2Î»_{A}, Î»_{A}




16) The electric field of light wave is given as. This light falls on a metal plate of work function 2eV. The stopping potential of the photoelectrons is

0.48 V

2.48 V

0.72 V

2.0 V


17) A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a nonviscous liquid. The density of the liquid is of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:


18) A capacitor with capacitance 5 Î¼F is charged to 5 Î¼C. If the plates are pulled apart to reduce the capacitance to 2 Î¼F, how much work is done?

3.75 Ã— 10^{6} J

2.55 Ã— 10^{6} J

6.25 Ã— 10^{6} J

2.16 Ã— 10^{6} J


19) Two radioactive substance A and B have decay constant 5Î» and Î» respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become will be

1/Î»

1/4Î»

2/Î»

1/2Î»


20) Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm^{2}. If the surface has an area of 25 cm^{2}, the maximum transferred to the surface in 40 min time duration will be

6.3 Ã— 10^{4} Ns

3.5 Ã— 10^{6} Ns

5.0 Ã— 10^{3} Ns

1.4 Ã— 10^{6} Ns


21) A submarine experiences a pressure of 0.5 Ã— 10^{6} Pa at a depth of d_{1} in a sea. When it goes further to a depth of d_{2}, it experiences a pressure of 8.08 Ã— 10^{6} Pa. Then d_{2} â€“d_{1} is approximately ________ m.
(Density of water = 10^{3} kg/m^{3} and acceleration due to gravity = 10 ms^{2})

22) At 40Â° C, a brass wire of 1 mm is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40Â°^{}C to 20Â°C it regains its original length of 0.2 m. The value of M is close to ______ kg.
(Coefficient of linear expansion and Youngs modules of brass are 10^{5}/Â°C and 10^{11} N/m^{2}, respectively; g = 10 ms^{2}).

23) Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 Ω. The internal resistances of the two batteries are 1 Ω and 2 Ω respectively. The voltage across the load will be approximately _______ V.

24) A satellite orbits around a planet at a height of 20 km from surface. Assuming that only gravitational field of the plant acts on the spaceship. The approximate number of revolution made by the satellite in 12 hours around the plane is ______.
[Given: Mass of plane = 8 Ã— 10^{22 }kg, Radius of planet = 2 Ã— 10^{6} m, Gravitational constant G = 6.67 Ã— 1011 Nm^{2}/kg^{2}]

25) A parallel plate capacitor has 1Î¼F capacitance. One of its two plates is given + 2Î¼C charge and the other plate, +4Î¼C charge. The potential difference developed across the capacitor is ________ V.

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1) The major product of the following reaction is

RCOOH

RCONH_{2}

RCHO

RCH_{2}NH_{2}


2) The one that is extensively used as a piezoelectric material is

tridymite

amorphous silica

quartz

mica


3) Which amongst the following is the strongest acid?

CHBr_{3}

CHI_{3}

CH(CN)_{3}

CHCI_{3}


4) The correct match between item â€˜Iâ€™ and item â€˜IIâ€™ is:

(a)â†’(q); (b) â†’ (p); (c) Ã— (s); (d) â†’ (r)

(a) â†’ (q); (b) â†’ (p); (c) â†’ (r); (d) â†’ (s)

(a) â†’ (r); (b) â†’ (p); (c) â†’ (q); (d) â†’ (s)

(a) â†’ (q); (b) â†’ (r); (c) â†’ (s); (d) â†’ (p)


5) The pair that contains two P â€“ H bonds in each of the oxoacids is:

H_{4 }P_{2 }O_{5 }and H_{4 }P_{2 }O_{6}

H_{3 }PO_{2 }and H_{4 }P_{2 }O_{5}

H_{3 }PO_{3 }and H_{3 }PO_{2}

H_{4 }P_{2 }O_{5 }and H_{3 }PO_{3}


6) Which is the most suitable reagent for the following transformation?

Tollenâ€™s reagent

l_{2 }/NaOH

CrO_{2}Cl_{2} / Cs_{2}

alkaline KMnO_{4}


7) The highest possible oxidation states of uranium and plutonium, respectively, are

6 and 4

7and 6

4 and 6

6 and 7


8) The element the usually does NOT show variable oxidation states is:

Cu

Ti

Sc

V


9) The major product of the following reaction is:


10) The major product of the following reaction is:


11) The two monomers for the synthesis Nylon 6, 6 are:

HOOC (CH_{2})_{4}COOH, H_{2}N (CH_{2})_{6}NH_{2}

HOOC (CH_{2})_{6}COOH, H_{2}N (CH_{2})_{6}NH_{2}

HOOC (CH_{2})_{4}COOH, H_{2}N (CH_{2})_{4}NH_{2}

HOOC (CH_{2})_{6}COOH, H_{2}N (CH_{2})_{4}NH_{2}


12) The pair that does NOT require calcination is:

ZnO and MgO

ZnO and Fe_{2}O_{3}.xH_{2}O

ZnCO_{3} and CaO

Fe_{2}O_{3} and CaCO_{3.}MgCO_{3}


13) For a reaction scheme,if the rate formation of B is set to be zero then the concentration of B given by


(k_{1}  k_{2})[A]

k_{1}k_{2}[A]

(k_{1 }+ k_{2})[A]


14) Given:
Co^{3+}e^{}â†’ Co^{2+}; EÂ° = 1.81 V
Pb^{4} + 2e^{}â†’ Pb^{2+}; EÂ° = +1.67V
Ce^{4+} +Â e^{}â†’ Ce^{3+}; EÂ° + 1.61 V
Bi^{3+} + 3e^{}â†’ Bi; EÂ° = +0.20 V
Oxidising power of the species will increase in the order

Ce^{4+} < Pb^{4+} < Bi^{3+} < Co^{3+}

Co^{3+} < Pb^{4+} < Ce^{4+} < Bi^{3+}

Bi^{3+} < Ce^{4+} < Pb^{4+} < Co^{3+}

Co^{3+} < Ce^{4+} < Bi^{3+} < Pb^{4+}


15) But2ene on reaction with alkaline KMnO_{4} at elevated temperature followed by acidification will give:

One molecule of CH_{3}CHO and molecule of CH_{3}COOH

2 molecules of CH_{3}CHO

2 molecules of CH_{3}COOH



16) The major product of the following reaction is:


17) The correct order of the oxidation states of nitrogen in NO_{,} N_{2}O, NO_{2} and N_{2}O_{3} is:

N_{2}O < N_{2}O_{3 }< NO < NO_{2}

NO_{2} < NO < N_{2}O_{3} < N_{2}O

NO_{2} < N_{2}O_{3} < NO < N_{2}O

N_{2}O < NO < N_{2}O_{3 }< NO_{2}


18) Hydrogen peroxide oxidises [Fe(CN)_{6}]^{4âˆ’} to [Fe(CN)_{6}]^{3âˆ’} in acidic medium but reduces [Fe(CN)_{6}]^{3âˆ’} to [Fe(CN)_{6}]^{4âˆ’} in alkaline medium. The order product formed are, respectively

H_{2}O and (H_{2}O + OH^{âˆ’})

(H_{2}O +O_{2}) and H_{2}O

(H_{2}O +O_{2}) and (H_{2}O + OH^{âˆ’})

H_{2}O and (H_{2}O +O_{2})


19) Which of these factors does not govern the stability of a conformation in acyclic compounds?

Torsional strain

Angle strain

Steric interactions

Electrostatic forces of interaction


20) The major product 'Y' in the following reaction is:


21) A solid having density of 9 × 10^{3} kg m^{3}forms face centred cubic crystal of edge length
The molar mass of the solid is ______ kg mol^{1}
[Avogadro constant ≅ 6 × 10^{23} and mol^{1}≅ 3]

22) 5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temprature becomes 200 K. If C_{v} = 28 JK^{1} mol^{1}, calculate ΔU for this process.(R = 8.0 J K^{1} mol^{1})

23) The maximum prescribed concentration of copper in drinking water is_____ ppm.

24) The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of 0.01 M BaCl_{2} in water. Assuming complete dissociation of the given ionic compounds in water ,the concentration of XY (in mol L^{1}) in solution is

25) The standard Gibbs energy for the given cell reaction in kJ mol^{1} at 298 K is:
[Faraday’s constant F = 96000 C/mol].

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1) 5 students of a class have an average height 150 cm and variance 18 cm^{2}. A new student, whose height is 156 cm, joined them. The variance (in cm^{2}) of the height of these six students is:

16

22

20

18


2) Then the sum of the elements in A is:


Ï€




3) Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:

500

200

300

350


4) , then fâ€™ (1/2) is :


5) Consider the following three statements:
P : 5 is a prime number
Q : 7 is a factor of 192
R : L.C.M of 5 and 7 is 35
Then the truth value of which one of the following statements is true?

(~P) Ë… (Q Ë„ R)

(P Ë„ Q) Ë… (~R)

(~P) Ë„ (~Q Ë„ R)

P Ë… (~Q Ë„ R)


6) Â Then S represents:

a hyperbola whose eccentricity is , when 0 < r <1.

an ellipse whose eccentricity is , when r > 1.

a hyperbola whose eccentricity is , when 0 < r < 1.

an ellipse whose eccentricity is , when r > 1.


7) If y(x) is the solution of the differential equation where y(1) , then:

y (log_{e} 2) = log_{e} 4

y (log_{e} 2)

y (x) is decreasing in

y (x) is decreasing in (0, 1)


8) The direction ratio of normal to the plane through the points (0, 1, 0) and (0, 0, 1) and making an angle Â with the plane y â€“ z + 5 = 0 is :

2, 1, 1





9) Â and Â be coplanar vectors. Then the non â€“ zero vector Â is:


10) Let f be a differentiable function such that f(1) = 2 andÂ Â f â€™(x) = f(x) for all x âˆˆ R. If h(x) = f(f(x)), then hâ€™(1) is equal to :

2e^{2}

4e

2e

4e^{2}


11) The set of all values of Î» for which the system of linear equations
x â€“ 2y â€“ 2z =Î»x
x + 2y + z = Î»y
â€“x â€“ y = Î»z,
has a nontrivial solution :

is a singleton

contains exactly two elements

is an empty set

contains more than two elements


12) If ^{n}C_{4, }^{n}C_{5} and ^{n}C_{6Â }are in A. P., then n can be:

9

14

11

12


13) Let S(Î») = {(x, y): y^{2}_{}â‰¤ 4x, 0 â‰¤ x â‰¤ Î»} and A(Î») is the area of the region S(Î»). If for Î», 0 < Î» < 4, A(Î») : A(4) = 2:5 then Î» equals:


14) If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is:

4 : 5 : 6

5 : 6 : 7

3 : 4 : 5

5 : 9 : 13


15) Let f: R→R be a differentiable function satisfying
f’(3) + f’(2) = 0. Then is equal to:

e^{2}

1

e

e^{1}


16) If the fourth term in the Binomial expansion of is 20 × 8^{7}, then the value of x is:

8^{3}

8^{2}

8

8^{2}


17) The value of dx is:


18) Four persons can hit a target correctly with probabilities Â respectively. If all hit at the target independently, then the probability that the target would be hit, is:


19) The locus of the centres of the circles, which touch the circle, x^{2} + y^{2 }= 1 externally, also touch the yaxis and lie in the first quadrant is :


20) The number of real roots of the equation 5+2^{x}1=2^{x}(2^{x}2) is:

4

3

2

1


21) If the of the series
is p, then is equal to _________.

22) then n is equal to ______.
(Here C is a constant of integration)

23) If m is the minimum value of k for which the function is increasing in the interval [0, 3] and M is the maximum value of f in [0, 3] when k = m, then the value of (m^{2} + M^{2} – 40) is equal to ________.

24) If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90âˆ˜, such that the length (in cm) of their common chord is cm, then (a – 9b) is equal to _____________.

25) A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag. Its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. Now, if a ball is drawn at random from the bag and the probability of getting this ball as red comes out to be then p + q is equal to _________

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