In a quiz competition, Team A scored +30,-20,0 and Team B scored -20,0,+30 in three successive rounds. Which team will win? Can we say that we can add integers in any order?

{:("Team A",50,20,10,30,30),("Team B",40,60,20,20,10):} Which team is more consistent ?

A magnetic needle having magnetic moment 10 A m^2 and length 2.0 cm is clamped at its centre in such a way that it can rotate in the vertical east-west plane. A horizontal force towards east is applied at the north pole to keep the needle fixed at an angle of 30^0 with the vertical. Find the magnitude of the applied force. The vertical component of the earth's magnetic field is 40 muT .

Consider a tank which initially holds V_(0) liter of brine that contains a lb of salt. Another brine solution, containing b lb of salt per liter is poured into the tank at the rate of eL//"min" . The problem is to find the amount of salt in the tank at any time t. Let Q denote the amount of salt in the tank at any time. The time rate of change of Q, (dQ)/(dt) , equals the rate at which salt enters the tank at the rate at which salt leaves the tank. Salt enters the tank at the rate of be lb/min. To determine the rate at which salt leaves the tank, we first calculate the volume of brine in the tank at any time t, which is the initial volume V_(0) plus the volume of brine added et minus the volume of brine removed ft. Thus, the volume of brine at any time is V_(0)+et-ft The concentration of salt in the tank at any time is Q//(V_(0)+et-ft) , from which it follows that salt leaves the tank at the rate of f(Q/(V_(0)+et-ft)) lb/min. Thus, (dQ)/(dt)=be-f(Q/(V_(0)+et-ft))Q=be A tank initially holds 100 L of a brine solution containing 20 lb of salt. At t=0, fresh water is poured into the tank at the rate of 5 L/min, while the well-stirred mixture leaves the tank at the same rate. Then the amount of salt in the tank after 20 min.

A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either a win, loss, or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to a. ^20 C_(10)xx2^(10) b. ^20 C_(10)xx3^(20) c. ^20 C_(10)xx3^(10) d. ^20 C_(10)xx2^(20)

Football teams T_(1)and T_(2) have to play two games are independent. The probabilities of T_(1) winning, drawing and lossing a game against T_(2) are 1/2,1/6and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_(1) and T_(2) respectively, after two games. P(XgtY) is

Three particles of masses 1.0 kg 2.0 kg and 3.0 kg are placed at the corners A,B and C respectively of an equilateral triangle ABC of edge 1m. Locate the centre of mass of the system.

If the vertices of the parabola be at (-2,0) and (2,0) and one of the foci be at (-3,0) then which one of the following points does not lie on the hyperbola? (a) (-6, 2sqrt(10)) (b) (2sqrt6,5) (c) (4, sqrt(15)) (d) (6, 5sqrt2)

The dielectric strength of air is 3.0 xx 10^6 V/m . A parallel-plate air-capacitor has area 20 cm^2 and plate separation 0.10 mm .Find the maximum rms voltage of an AC source which can be safely connected to this capacitor.

The earth revolves round the sun due to gravitatinal attraction. Suppose that the sun and the earth are point particle with their existing masses and that Bhor's quantization rule for angular monentum is valid in the case of gravitation (a) Calculate the minimum radius the earth can have for its orbit. (b) What is the value of the principle quantum number n for the present radius ? Mass of the earth = 6.0 xx 10^(24) kg, mass of the sun = 2.0 xx 10^(30) kg, earth-sun distance = 1.5 xx 10^(11)m .