No. of Printed Pages: 4 IBET-on I
DIPLOMA IN CIVIL ENGINEERING (DCLE(G»I DIPLOMA IN MECHANICAL ENGINEERING I DCLEVI I DMEVII DELVI I DECVI I DCSVI I ACCLEVI I ACMEVIIACELVI I ACECVI I ACCSVI
Term-End Examination
December, 2016
0105?
BET-011 MATHEMATICS
Time hours Maximum Marks: 70
Note: Question number 1 is compulsory. Attempt any four questions out of the remaining questions. Use of calculator is permitted.

1. Answer any seven of the following: 7x2=14 Prove that 3v8 is not a surd. Find the seventh root of(0.0043). Solve the equation

3x^2 4x 4 0.

(d) Find the 12th term of the sequence

2, 18, If the third term of an AP is 18 and the seventh term is 30, find the series. What is the meaning of the following box in a flow chart <img src='./qimages/8515-1(f).jpg'> Prove that

2 sin A cos sin sin Determine the equation of a line with slope 3 and intercept 2 at y-axis. The unit vector along i j is

(i) K

(ii) i j

(iii) j)/sqrt(2)

(iv) i j/2

(j) Find the distance between the line

3x-4y 12 and the point 1).

2. Given cot e e in the IIIrd quadrant, find the value of the other trigonometric functions. Prove that
cos 2A =cos2 A -sm2 A 1-tan2 A 1 tan2 A

(c) From the top of a cliff, 150 m high, the angles of depression of two boats which are due north of the observer are 60° and 30°. Find the distance between them. 4 4 6

3. Insert six arithmetic means between 2 and 16 and prove that their sum is 6 times the arithmetic mean between 2 and 16. Find the cube root of 127 up to four places of decimal. If the first term of a GP exceeds the second term by 2 and the sum of infinite terms is 50, find the GP. 4 5 5


4. Determine the equation of a line passing through the points and Find the equation of the line parallel to the y-axis and drawn through the point of intersection of x -7y 5 0 and 3x y-7 =O. Show that the lines

3x 2y-5=0
4x 3y 7=0
2lx 13y-76

are concurrent. 4 5 5

5. Does x2 r -l2x 6y 45 represent a circle? If yes, find the radius and centre of the circle. Find the equation of the tangent and normal to the circle

x2 r -2x -10y 1 at the point 2).
Find the vertex, focus and directrix of the parabola

4y^2 l2x l2y 39 0. 4 5 5

6. If the sum of two unit vectors is a unit vector, prove that the magnitude of their difference is sqrt(3) .
Give a representation of work done by a force in terms of scalar product. " Show that the vectors A 2i -3j and B i 9j 3k are parallel. 5 4 5