Two straight roads intersect at an angle 60*. A car is moving away from the crossing at the rate of 25 km/hr at 10 a.m. Another car is 52 km away from the crossing on the other road and is moving towards the crossing at the rate of 47 km/hr at 10 a.m. Find the distance between the cars at 11 a.m.

An object falling from rest in air is subject not only to the gravitational force but also to air resistance. Assume that the air resistance is proportional to the velocity 

with constant of proportionality as k > 0, and acts in a direction opposite to motion (g = 9.8 m/s^2). If the velocity cannot exceed A m/s, what can be the value of 10 Ak?

.If O be the origin and the coordinates of P be (1, 2, -3), then find the equation of the plane passing through P and perpendicular to OP.

.Evaluate integral pi/2 to –pi/2 of |sinx|dx. Compare the value with integral pi/2 to –pi/2 of sin|x| dx. What do you find? Explain.

“For every integer x, x^3/2 is a rational number”. Is this statement true? Support your answer with explanation.

Find the area  of the closed planar figure formed by the intersection of x^2+y^2 = 1 and x+z=0.

 

  Find the area  of the closed planar figure formed by the intersection of x^2+y^2 = 1 and x+z=0.

Ans: pi root(2)

what will be the graph of curve (x^2 - 4)/(x-2) at point x = 2. is it defined there , a disontunity is there in the graph??

Thirty cubes are stacked in square layer to form a tower. The bottom layer

 measures 4 cubes by 4 cubes , the next layer 3 cubes by three cubes, the next layer

 2 cubes by 2 cubes and top layer is single cube.

a) Determine the total surface area of the towers of cubes (do not include the bottom ).

 

b) what would be the volume if the bottom layer of cubes was 8 cubes by 8 cubes.

1) In a jar there are 3 white marbles and 7 black marbles.You draw a marble and see

if it is black .If so , you stop.Otherwise,you keep the marble and draw again.You

repeat this process untill u draw a black marble.

a) Find the probablity that 3 draws are needed.

c) Find the probablity that 5 draws are needed.

Bilbo has a gold chain with 20 links.  He is staying in town for 20 days at an inn and wishes to pay each day with one gold link.  When he cuts the chain, the remaining links looks like the diagram below: 

The diagram shows 10 links but there are 20 on Bilbo’s chain.

If you cut at the 10^th link, you will have 10 links on one side, one link in between and 9 links on the other side.

He wants to cut the least number of links possible and pay just one link per day.  The innkeeper does not want to take the 20 links up front and does not want more than his share per day.  But, he is willing to trade Bilbo the links to make even. 

For example, if Bilbo pays with the extra link on day one, he can give a chain with two links on day two and get the extra link back.

Thus, help Bilbo out and tell him what is the least number of cuts he needs to make.  Also, make a diagram describing how the transactions go each day.

armer Gray owns productive cropland that abuts a highway. But the land that is 25 meters or more from the highway is yields twice as much per square meter as the land that is within 25 meters of the highway. Farmer Gray wants to fence-in some of the land to keep the farm animals out. Zoning regulations require that one section of any fence be right along the highway. Farmer Gray has only 600 meters of fencing material. If he fences a rectangular area, what are the dimensions of the rectangle that maximizes the total yield of the fenced-in land (assume that the highway is straight).

My sock drawer contains 6 black socks, 4 blue socks and 5 brown socks. On a dark winter morning, I randomly select two of these socks to wear. Find the chance that they are a matching pair, i.e., they have the same color.

Find the sum of the series

1^2 – 2^2 + 3^2 - …………….- 2002^2 + 2003^2