jbnsts.org : Jagadis Bose National Science Talent Search Exam Model Question Paper

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Document Type : Sample Question Paper

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Jagadis Bose National Science Talent Search Model Paper

Instructions :
Section A :
Section A has 4 groups, with 8 questions in each group (total 32 questions). You have to answer any 5 questions from each group, i.e. a total of 20 questions. Each question carries 4 marks.

Related / Similar Question Paper :
JBNSTS JTST Model Question Paper

Time allotted: 100 minutes;
Total Marks: 80

Answers for section A are to be written in the answer booklet as follows:
Group I : (Q. Nos. 1-8): your answers must be written on pages 1-3, page 4 is for rough work.
Group II : (Q. Nos. 9-16): your answers must be written on pages 5-7, page 8 is for rough work.
Group III : (Q. Nos. 17-24): your answers must be written on pages 9-11, page 12 is for rough work.
Group IV : (Q. Nos. 25-32): your answers must be written on pages 13-15, page 16 is for rough work.

Section B :
Section B has 4 questions. You have to answer any one of these questions. Your answer must be written on pages 17-19 of the answer booklet; page 20 is for rough work.
Time allotted: 30 minutes; Marks: 30

Group I

A massless string passes over a fixed frictionless pulley.
1. Two masses m 1 and mg (m, > m;) are suspended from the two ends of the string. The system is allowed to move from rest undergravity. Find the acceleration of the centre of mass (CM) of the system of two masses. Show that the net external force is equal to the rate of change of momentum of the CM if the total mass is imagined to be placed there

2. The earth is getting energy from the sun whose surface temperature is 7}. Its radius is R and the radius of the earth is r. The distance between the sun and the earth is d. Assume that the earth and the sun both absorb all electromagnetic radiation incident on them and the earth is in thermal equilibrium at a constant temperature T 8.
Calculate T s from the given parameters. T e = 300 K; R = 7 x 105 km;r=6.4 x103 km; d= 1.5 x 108 km
Consider the potential V/V0=-128R6/r6 +R12/r”. Find the equilibrium position, if any. What is the motion like near such a position?

3. The radiation emitted when an electron jumps from n= 3 to n=2 orbit in a hydrogen atom, falls on a metal to produce photoelectrons.
The electrons from the metal surface with maximum kinetic energy are made to move perpendicular to a magnetic ?eld of 3 x 104 T spread in a radius of 10 mm. Find,
i) the kinetic energy of the electrons.
ii) the work ?mction of the metal.
iii) the wavelength of the emitted radiation. (Eg = 13.6 eV)

4. The force given on a bullet over the time interval t = 0 to t = 6.0 X 103 s. is given by the formula F = 800 — 1.6 x 105 t (where F is in Newton and t is in seconds).
i) Plot a rough graph of F vs. t for t = 0 to t = 6 millisecond.
ii) Estimate, using the above rough sketch, the impulse given to the bullet.
iii) If the bullet achieves a speed of 200 m/s as a result of this impulse, given to it in the barre of the gun, what must its mass be

5. Discuss what happens to the force between the plates of a condenser when a dielectric material is introduced between them, in the cases when
i) the plates are charged and insulated.
ii) the plates are kept connected to the voltage source

6. Sand drops vertically from a stationary hopper at a rate}? onto a conveyor belt movmg With velocity ‘v’ in the reference frame of the laboratory.
What force is required to keep the belt moving at a speed v?

7. Two objects of same mass are falling under gravity. One is experiencing a drag force proportional to its velocity and the other proportional to the square of the velocity.
Two objects attain the same terminal velocity. Find which drag force is greater for the same velocity

Group II

8. For the reaction A(g) —-> B(g) + C(g), rate law is — 100mm of Hg and a?er 10 minutes, the pressure is 120mm of Hg. Calculate rate constant (min’l)
A (g) —» B (g)+c (g),mm—% k[A]31&1 61?” MI W? em «a 10

10. Glucose contains six carbon atoms, Prove that they lie along a straight chain.
11. Among the ?rst row transition metals of the periodic table, why does chemical reactivity increase upto manganese and decrease thereafter?
12. A large vessel was completely ?lled with water, the speci?c conductance of which was found to be 2.50><10’5 S cm]. 585 g. of NaCl was then added to the water and then the speci?c conductance was found to be 5.25><10’4 S cm”.
The solution may be assumed to be very very dilute, since the volume of water was very large. Find the capacity of the vessel. Given AdNaa) = 150 S cm2.
13. All the hydroxyl groups in Glycerol are not equivalent- Justify

14. Hydrochloric acid reacts with solid marble chips.
i) What are the products of the reaction? Give balanced equation.
ii) What are the independent variables that affect the reaction rate?
iii) Identify a dependent variable that you could measure to follow the rate of reaction.
iv) How the rate of reaction is dependent on the concentration of hydrochloric acid?
Or
ii) W W W W 8131 (independent variables) ??mx 38—5135 21W W?
iii) will? Wm We? ma?a (dependent variable ) m at W ??F’m Til? W WI
iv) mm 3mm W W m Q1? 13561731 W?
15. A current of 19.3 amp. was passed through 1 litre of a 0.5 (N) CuSO4 solution for 1000 see. using Pt electrodes.
Find out the normality of the HZSO4 solution produced during the electrolysis. Pt stem w w new 0.5 (N) cuso4 mm W ?e: 1000 sec. «a 19.3 amp. safe: m am am Greg ?ancee Wt cam st04 em minim? W m?
16. Dissociation constant of two weak acids are 104 and 10’5 at a given temperature. Calculate the difference of pH of solution of the two acids of same concentration (0.1M)

Group III

17. Prove that the probability of choosing a positive integer, which is smaller than pk and relatively prime (that is gcd of these two numbers is 1) to pk, from the ?rst pk positive integers is 1 —- i ,
where p is a prime number and k is a positive integer ?
18. Five?points lie inside an equilateral triangle of side 2 units. Prove that at least two of the points are no more than a unit distance aparts
19. Given three quadratic polynomials fl (x) = x2 + 2a1x + bl, fz (x) = x2 + Zazx + bz, Q (x) = x2 + 2a3x + b3 such that alazag = b1b2b3 > 1. Prove that one of these polynomials has two distinct real roots.
W W W W {a f1(x) = x2 + Zalx + bl! f2(X) = x2 + 2a2x + bz, f3(x) = x2 + 2a3x + b3 mam a1a2a3 = b1b2b3 > 1. am w m, 643 WET? alarms if? am am ?rst we
20. Prove that for any complex number z, Iz + II 2 717 or |z2 + 1| 2 1
21. A 2n digit number starts with 2 and all its digits are prime. Then ?nd the probability that the sum of any two consecutive digits of the number is prime
22. Give an example of a function f: [—1,1] —> R such that f is continuous exactly at two points. Justify your answer