Scholarship : 19th Bhavishya Jyoti Scholarship 2009 by NIIT

India’s largest IT Scholarship Test 19th Bhavishya Jyoti Scholarship announced

India's largest IT Scholarship Test - '19th Bhavishya Jyoti Scholarship' announced NIIT to conduct the Annual Scholarship Test on September 13th across the country

New Delhi: India's largest IT Scholarship Program— '19th Bhavishya Jyoti Scholarship Test' will be conducted on Sunday, September 13, 2009 by leading Global Talent Development Corporation, NIIT, across the country.

Chapter 17

Co-ordinate Geometry

1. A(3, 2) and B(-2, 1) are two vertices of a triangle ABC, whose centroid has coordinates (5/3, -1/3). Find the coordinates of the third vertex C of the triangle.
    

2. Show that the points A(2, -2), B(14, 10), C(11, 13) and D(-1, 1) are the vertices of a rectangle.
    

3. Determine the ratio in which the points (6, a) divides the join of A(-3, -1) and B(-8, 9). Also find the value of a.
    

4. Find the point on the x-axis which is equidistant from the points (-2, 5) and (2, -3).
    

5. The co-ordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q.
    

6. Two vertices of a triangle are (1, 2) and (3, 5). If the centroid of the triangle is at the origin, find the coordinates of the third vertex.
    

7. If ‘a’ is the length of one of the sides of an equilateral triangle ABC, base BC lies on x-axis and vertex B is at the origin, find the coordinates of the vertices of the triangle ABC.

Chapter 16

Probability

Sometimes we say, “probably it may rain” or “Probably he may get more than 90% in the examination" etc. These are elements of certainty. Means we are not certain about some things. In mathematics these comes under Probability.

The theory of probability is widely used in the area of natural as well as social science.

Probability as a Measure of Uncertainty

Suppose we through a die which is a well balanced cube with its six faces marked numbers from 1 to 6, one number of one face, we see the number which come up on its uppermost face. A die can fall with any of its face upper most.

The number on each of the face is equally libely and possible outcome. There are six equally likely ealy outcomes: 1, 2, 3, 4, 5 or 6 in a single throw of a die. The chance of any number ‘say 3’ to come up is 1 out of 6. That is probability of 3 coming up is 1/6
i.e. p(3) = 1/6

Similarly in tossing a coin, we may get either head (H) or tail (T) up and P(H) = ½ .............

Chapter 15

Statistics

Statistics

Statistics is the science which studies the methods and techniques used in the collection, presentation and analysis of data and draws. conclusion on the basis of the same. The statistics is thus, used in two senses:

1. In the sense of data and
2. In the sence of science.

In this portion we shall learn the pictorial representation of data such as Pie charts, the mean of grouped data and primary idea of probability.

Pictorial Representation of data:

Some times different. Charts are drawn to interprete any data. They are:

(i) Histogram
(ii) Frequency polygon
(iii) Frequency curve
(iv) Bar diagram
(v) Line graph
(vi) Pictograph and
(vii) Pie charts..............

Chapter 14

Mensuration

1. The total surface area of a closed right circular cylinder is 65/2cm² and the circumference of its base is 88cm. Find the volume of the cylinder.
    
2. The height of a cylinder is 15cm and its curved surface area is 660 sq.cm. Find its radius.
    
3. A cylindrical tank has a capacity of 6160 cu.cm. Find its depth if the diameter of its base is 28m. Also, Find the area of the inside curved surface of the tank.
    
4. The volume of a right circular cylinder is 1100 cu.cm and the radius of its base is 5cm. Find its curved surface area.
    
5. If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.
    
6. 50 circular plates, each of radius 7cm and thickness 0.5cm are placed one above the other to form a solid right circular cylinder. Find the total surface area and volume of the cylinder so formed.
    
7. A well of diameter 3m is dug 14m deep. The earth taken out of it has been spread evenly all around it to a width of 4m to form an embankment. Find the height of the embankment formed.

Chapter 13

Height and Distance

1. Determine the height of a mountain if the elevation if the elevation of its top at an unknown distance from the base is 45⁰ and at a distance 10km further off from the mountain, along the same line, the angle of elevation is 30⁰ (USE tan30⁰ = 0.5774).
    
2. The angle of elevation of the top of a rock from the top and foot of a 100m high tower are respectively 30⁰ and 45⁰. Find the height of the rock.
    
3. The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60⁰. At a point Y, 40m vertically above X, the angle of elevation is 45⁰. Find the height of the tower PQ and the distance XQ.
    
4. An aeroplane, when 3000m high, pass vertically above another aeroplane at an instance when the angles of elevation of the two aeroplanes from the same point on the ground are 60⁰ and 45⁰ respectively. Find the vertical distance between the two aeroplans.
    
5. A pole 5m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60⁰ and the angle of depression of the point ‘A’ from the top of the tower is 45⁰. Find the height of the tower.
    
6. A tower is 50m high. Its shadow is x m shorter when the sun’s altitude is 45⁰ than when it is 30⁰. Find x. .....................

Chapter 12

Trigonometry