Hammed Sanusi

A lagged copper rod of uniform cross-sectional area has a length of 60cm, the free ends of the rod are maintained at 20 degree celsius and 0 degree celsius respectively at a steady state. calculate the temperature at a point 20cm from the high temperature.

A series circuit consists of a resistance 600 ohms and an inductance of 5H, an a.c voltage of 15(r.m.s) and frequency 50HZ is applied across the series circuit. Calculate 

i) The current flowing through the circuit

ii) the voltage across the inductor

iii) the phase angle between current and the applied voltage

iv) the average power supply 

v) the potential difference across the resistance

vi) the instantaneous power

vii) power absorbed

A series circuit consists of a resistance 600 ohms and an inductance of 5H, an a.c voltage of 15(r.m.s) and frequency 50HZ is applied across the series circuit. Calculate 

i) The current flowing through the circuit

ii) the voltage across the inductor

iii) the phase angle between current and the applied voltage

iv) the average power supply 

v) the potential difference across the resistance

vi) the instantaneous power

vii) power absorbed

A pipe can fill up a tank in 12 minutes. Another pipe flows out 14 litres of water per minute. If the two pipes are opened together and the empty tank is filled up in  96 minutes, how much water does the tank contain?

A barometer tube has some air at the top above the mercury.When the length of the air column is 300mm,the reading of the mercury above the outside level is 750mm. When the length is reduced to 250mm,the reading becomes 7.36mm. Calculate the atmospheric pressure.

At 30 degree, by how much is a reaction's activation energy decrease by the addition of a catalyst if the catalyst triples the rate of the reaction?

A gas  X  has a root mean square velocity of  214.7 m/s at a pressure of  2.3 atmosphere and temperature of  34 degree celcius. What is the molecular mass of the gas?

A gas  X  has a root mean square velocity of  214.7 m/s at a pressure of  2.3 atmosphere and temperature of  34 degree celcius. What is the molecular mass of the gas?

The density of helium gas at 0 degree celcius and 760 mmHg is 0.14kgm/s³. Calculate the root mean square velocity of the gas.

3.A man answers 10 maths problems, one after the other. He answers the first problem correctly and the second problem incorrectly, for each of the remaining 8 problems the probability that he answers the problem correctly equals to the ratio of the number of problems that he has already answered correctly to the total number of problems that he has already answered. What is the probability that he answers exactly 5 out of 10 problems correctly

A man answers 10 maths problems, one after the other. He answers the first problem correctly and the second problem incorrectly, for each of the remaining 8 problems the probability that he answers the problem correctly equals to the ratio of the number of problems that he has already answered correctly to the total number of problems that he has already answered. What is the probability that he answers exactly 5 out of 10 problems correctly.

A ball is thrown straight up from the edge of a cliff with an initial speed of 15.0 m/s. As it falls back, it just missed the edge and strikes the ground 7m below the point from which it was thrown. What height does the ball reach and how long is it in the air? (g = 9.80 m/s²)

A kid kicks a ball in such a way that the successive displacements of the ball are 6.00 m to the north, 4.50 m northest, 2.10 m at 30.0 degree west of south.

Find out the resultant displacement covered by the ball from starting point till ball becomes stationary again ?

A test of the tensile strength of  6 flat metal sheets manufactured by a rolling mill showed a mean breaking strength of  7750N and a standard deviation of  145N, whereas the manufacturer claimed a mean tensile strength of 8000N, as a building contractor, can you support the manufacturer's claim at  0.01 level of significant?

The stochastic process {Xn} is defined to be:

Xn = Y₁  +  Y₂,  ... , Yn;   n  =  1, 2, ... , and  X₀ = 0.

Where the  Yi are independent, identical random variable,

Yi∈{-1, +1} with P(Yi = 1} = 0.4; P(Yi = -1) = 0.6.

Calculate:

(a)   E[X₉]

(b)   Var(X₉)

(c)  corr(X₁₂,  X₉)

(d)   P(X₂₀  =  10  |  X₁₀  =  6)

Hint:  The number of upward steps has a binomial distribution

From a point on top of a tree the angle of depression of a small plant on horizontal ground is 24°15‘. From a point on a wall 10m above the ground , 50m from the tree and due north of it, the angle of depression of the plant is 11°17‘ and its bearing is 63°. Find the height above the ground of the point on the tree.

if 4 math textbook are selected from 6 different maths textbook and 3 English book are chosen from 5 different English books.how many ways can the 7 book be arranged on a shelf if maths and English are alternatively arrange

An investor invested Le x in bank M at the rate of 6 percent simple interest per annum and Le Y in bank N at the rate of 8 percent simple interest per annum. If a total of Le 8,000,000.00 was invested in the two banks and the investor received a total of Le 2,230,000 as interest from the two banks after 4 years. Calculate the :

*(i)* value of X and Y

*(ii)* interest paid by the second bank.

A cement factory produce 340 tonnes of cement after a certain number of hours in the next 2 hours it produce only 12 tonnes and its average ( tonnes of cement per hours ) dropped by one tonnes what was the final average

A cement factory produce 340 tonnes of cement after a certain number of hours in the next 2 hours it produce only 12 tines and its average ( tonnes of cement per hours ) dropped by one tonnes what was the final average