Q1. Calculate the wavelength of a sound wave whose frequency is 220 Hz and speed is 440 m/s in a given medium.

Q2. A person is listening to a tone of 500 Hz sitting at a distance of 450 m from the source of the sound. What is the time interval between successive compressions from the source?

Q3 An echo is heard in 3 s. What is the distance of the reflecting surface from the source, given that the speed of sound is 342 ms-1?

Q4. A submarine emits a sonar pulse, which returns from an underwater cliff in 1.02 s. If the speed of sound in salt water is 1531 m/s, how far away is the cliff?

Q5. A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as 344 m s−1.

Q6. The frequency of a source of sound is 100 Hz. How many times does it vibrate in a minute?

Q7. A stone is dropped from the top of a tower 500 m high into a pond of water at the base of the tower. When is the splash heard at the top? Given, g = 10 m s−2 and speed of sound = 340 m s−1.

Q8. A sound wave travels at a speed of 339 m s-1. If its wavelength is 1.5 cm, what is the frequency of the wave? Will it be audible?

Q9. A sonar device on a submarine sends out a signal and receives an echo 5 s later. Calculate the speed of sound in water if the distance of the object from the submarine is 3625 m.

Q10. Two children are at opposite ends of an aluminum rod. One strikes the end of the rod with a stone. Find the ratio of times taken by the sound wave in the air and in aluminum to reach the second child.Speed of sound wave at 25° C, V Al = 6420 ms-1, Speed of sound in air, V air = 346 ms-1

Question 1: Let A and B be two finite sets having m and n elements respectively. Then the total number of mapping from A to B is

(a) mn                      (b) mⁿ                          (c) 2^mn                      (d) n^m

Question 2: Two sets A and B are as under:

A = {(a, b) ϵ R × R : |a − 5| < 1 and |b − 5| < 1};

B = {a, b) ϵ R × R : 4 (a − 6)² + 9(b−5) ² ≤ 36}. Then,

(a) A is subset of B

(b) A n B = φ (null set)

(c) neither A subset of B nor B is subset of A

(d) B is subset of A

Question 3: Let A and B be two sets containing 4 and 2 elements respectively. Then the number of subsets of the set AxB, each having at least 3 elements is

(a) 256                    (b) 275                       (c) 510                        (d) 219

Question 4: If A, B and C are three sets such that A ∩ B = A ∩ C and A U B = A U C then

(a) B = C

(b) A = B

(c) A = C

(d) A n B = 0 (empty set)

Question 5: Let S = {x Є R : x ≥ 0 and 2|√x − 3|+ √x (√x − 6) + 6 = 0}. Then S :

(a) is an empty set

(b) contains exactly one element

(c) contains exactly two elements

(d) contains exactly four elements

Question 6: Let S be the set of all functions f:[0,1] -> R, which are continuous on [0, 1] and differentiable on (0, 1). Then for every f in S, there exists a C Є (0, 1), depending on f, such that:

(a) |f(1) − f(C)| = (1- C)|f′(C)|

(b) |f(C) + f(1)| < (1 + c)|f′(C)|

(c) |f(C) − f(1)| < (1 − C)|f′(C)|

(d) None of these

Question 7: If f(x) + 2 f(1/x) = 3x, x not equal to 0 and S = {x Є R : f(x) = f(- x)}; then S

(a) is an empty set

(b) contains exactly one element

(c) contains more than two elements

(d) contains exactly two elements

Question 8: The general solution of sin x − 3 sin2x + sin3x = cos x − 3 cos2x + cos3x is _________.

Question 9: If sec 4θ − sec 2θ = 2, then the general value of θ is __________.

Question 10: If tan (cot x) = cot (tan x), then sin 2x = ___________.

Q1: A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

(a) A screw gauge having 100 divisions in the circular scale and pitch as 1 mm

(b) A screw gauge having 50 divisions in the circular scale and pitch as 1 mm

(c) A meter scale

(d) A vernier calliper where the 10 divisions in vernier scale match with 9 division in the main scale and main scale have 10 divisions in 1 cm

Q2: In an experiment, the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree(= 0.5⁰), then the least count of the instrument is

(a) One degree

(b) Half degree

(c) One minute

(d) Half minute

Q3: A screw gauge gives the following reading when used to measure the diameter of a wire.

Main scale reading : 0 mm

Circular scale reading: 52 divisions

Given that 1 mm on the main scale corresponds to 100 divisions of the circular scale

The diameter of the wire from the above date is

(a) 0.026 cm

(b) 0.005 cm

(c) 0.52 cm

(d) 0.052 cm

Q4: The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is

(a) 3.5 %

(b) 4.5 %

(c) 6 %

(d) 2.5 %

Q5: Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then the error in the value of resistance of the wire is

(a) 3%

(b) 6%

(c) zero

(d) 1%

Q6: The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is

(a) 0.9%

(b) 2.4%

(c) 3.1%

(d) 4.2%

Q7: Which of the following sets have different dimensions?

(a) Pressure, Young’s modulus, stress

(b) Emf, potential difference, electric potential

(c) Heat, work done, energy

(d) Dipole moment, electric flux, electric field

Q8: The least count of the main scale of a screw gauge is 1mm. The minimum number of divisions on its circular scale required to measure 5 μm diameter of a wire is

(a) 50

(b) 200

(c) 100

(d) 500

Q9: A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is

(a) 50

(b) 200

(c) 100

(d) 500

Q10: A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 Kg is fired vertically upward, with a velocity 100 m/s, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is (g = 10 m/s)

1. 10 m
2. 30 m
3. 20 m
4. 40 m

1. Number of atoms in the following samples of substances is the largest in :

(1) 127.0g of iodine

(2) 48.0g of magnesium

(3) 71.0g of chlorine

(4) 4.0g of hydrogen

2. The ratio of mass percent of C and H of an organic compound (C_xH_yO_z) is 6 : 1. If one molecule of the above compound ( C_xH_yO_Z ) contains half as much oxygen as required to burn one molecule of compound C_XH_Y completely to CO₂ and H₂O. The empirical formula of compound C_xH_yO_z is :

(1) C₂H₄O

(2) C₃H₄O₂

(3) C₂H₄O₃

(4) C₃H₆O₃

3. The concentrated sulphuric acid that is peddled commercially is 95% H₂SO₄ by weight. If the density of this commercial acid is 1.834 g cm^-3, the molarity of this solution is :-

(1) 17.8 M

(2) 15.7 M

(3) 10.5 M

(4) 12.0 M

4. The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecule is :

(1) 1 : 8

(2) 3 : 16

(3) 1 : 4

(4) 7 : 32

5. 3g of activated charcoal was added to 50 mL of acetic acid solution (0.06N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram of charcoal) is :

(1) 42 mg

(2) 54 mg

(3) 18 mg

(4) 36 mg

6. The density of a solution prepared by dissolving 120 g of urea (mol. mass = 60 u) in 1000 g of water is 1.15 g/mL. The molarity of this solution is

(1) 2.05 M

(2) 0.50 M

(3) 1.78 M

(4) 1.02 M

7. The ratio of number of oxygen atoms (O) in 16.0g oxygen (O), 28.0 g carbon monoxide (CO) and 32.0g oxygen (O₂) is :

(Atomic mass :C =12, O =16 and Avogadro’s constant N_A = 6.0 * 10²³ mol^-1)

(1) 3 : 1 : 1

(2) 1 : 1 : 2

(3) 3 : 1 : 2

(4) 1 : 1 : 1

8. When CO₂ (g) is passed over red hot coke it partially gets reduced to CO(g). Upon passing 0.5 litre of CO₂ (g) over red hot coke, the total volume of the gases increased to 700 mL. The composition of the gaseous mixture at STP is :

(1) CO₂ = 200 mL: CO = 500mL

(2) CO₂ = 350 mL: CO = 350mL

(3) CO₂ = 0.0 mL: CO = 700mL

(4) CO₂ = 300 mL: CO = 400mL

9. An open vessel at 300 K is heated till ⅖ th of the air in it is expelled. Assuming that the volume of the vessel remains constant, the temperature to which the vessel is heated is :

(1) 750 K

(2) 400 K

(3) 500 K

(4) 1500K

10. The density of 3M solution of sodium chloride is 1.252 g mL^-1. The molality of the solution will be (molar mass, NaCl = 58.5 g mol^-1)

(1) 2.18 m

(2) 3.00 m

(3) 2.60 m

(4) 2.79 m

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