DAE Math 113 Past paper All Technology Download Pdf,

DAE / IIA – 2011/4 MATH 113 APPLIED MATHEMATICS – I PAPER – B (Part – A)

## DAE Math 113 Past paper All Technology Download Pdf

Q.1 Encircle the correct answer.

- Area of an equilateral triangle if side a = 4cm is: (a) a) sq.cm .cm a) 4,5 ‘Wm d) f sq.’. 4
- A prism with polygonal base is known as: (b) a) Cubic prism b) Polygonal prism a) Circtilar prism d) None of these
- Volume of hollow cylinder if R and r are external and internal radii respectively is: (c) a) /T(R – r) b) 274R’ -71 a) 702 r(R-‘)h

4.A solid figure whose base is a plane polygon and sides are triangles that meet in a common Oertex is known as: (a) a) Pyramid b) Cubc o). Frustum of a 4) None of these Pyramid

- Volume of a cone of height 12cm and radius of base is 3cm is: (b) a) 108 cu.cm b) 3671 cu.cm a) 1211 cu.c,n d) 54 cu.cm
- If R and r are the external and internal radii of spherical shell respectively, then its volume is: (a) a) 43(R2 – r’) b) 3(R3 -1,) a) 4ff (le – r’) 4) 3(R3 – r3)
- The length of diagonal of a .0be if edge of cube is ‘a’: a) \ha b) a) 3a
- Area of circle whose radius is 2cm is: a) 47 b)
- A six sided figure is called: (a) a) Octagon b) Pentagon a) Hexagon d) Heptagon
- The magnitude b) of vector ,-1- k is: (c) a) a) I) d) -1
- The cross product of two vectors a and b is:_ a) Fillb1Cost) b) PlibiSine a) PrilSin01 d) l all ICos9r5
- Two vector a and b are parallel if (a) a) axb=0 b) a.1,0 a) a xb=1 d) a .b =1
- The order of Matrix El 2 3 4 ] is: (a) a) 1 x 4 b) 4a1 a) 1 xl d) None ofthese
- If all the elements of a row or a column are zero, then value of the determinant is: (c) a) 1 b) 2 c) Zero d) None of these
- A matrix A is singular if: (a) a) lAl= 0 b) IAI= 0 a) IAI=1 ‘ 4) lilll

DAE / IIA – 2011/4 MATH 113 APPLIED MATHEMATICS – I PAPER – B (Part – B) ).

2 Write short answers to any eighteen from the following questions:

- The length of each side of a rhombus is 120cm and two of its opposite angles are each 60°, find the area.

- Define plane figures.
- Write the formula of Trapezoidal Rule.
- Find the area of Equilateral Triangle if side a = 4cm.
- Write the formula of Area of regular polygon of n sides when the radius of the circumscribed circle ‘R’ is given.
- fhe length, width and height of a rectangular prism are 6, 4 and 3 meters respectively. Find the volume of rectangular prism.
- The diameter of a right circular cylinder is 38cm and its length is 28cm. Find its volume.
- Write the formula of total surface area of cylinder.
- Find the volume of the square pyramid of perpendicular height 9.41 cm and the length of the side of base 2.92cm.
- Find the volume of a cone of radius 6.6cm and height is I 2.5cm.

11 I . The diameter of a sphere is 13.5m. Find its surface area.

- The radius of the base of a right circular cone is 6m and slant height is 6.5m. Find the lateral surface area.
- A regular pentagon is circumscribed about circle with a radius of 20cm. Find the area of the pentagon.
- Find the area of a parallelogram whose base is 24cm and height 13cm respectively.
- Write the formula of area of a cyclic quadrilateral.
- The diagonals of a rhombus area 40m and 30m. Find its area.
- Define Equilateral Triangle.
- Given the vectors a = 3i – 2 j + 4k and b = 2i+ j+ 3k .Find the magnitude of a – b .
- If t; = 2i + 4j- 7k , b = 2i -6j+ xk are perpendicular vectors. Find
- If a = + 3j- 7k and b = 51- 2j+ 4k . Find a b
- Define a unit vector.
- Find ax 17 if a =i+ 31- 7k, b= 5i- 2j+ 4k. 1 -1
- If A = [,3 2, B = [2 I . Find AB.JJ 3 1
- Find k such that matrix [4k 36] is singular.
- Find the inverse of matrix [4 ].
- If a matrix A =[41 25 63]. Then find Transpose of A.

(Note: Attempt any three questions)

Q.3 (a) Solve the following system of equation: (4) x – 2y + =I 3x+y-2a= 4 y – = I (b) Find )a such that the following matrix: (4) 2 -3 5 4 6 is singular. 0 0 8

Q.4 (a) From a point within a triangle, it is found that the three sides subtend equal angles. From this point, three lines are drawn to meet the opposite edges. If these lines measure 5, 6 and 7cm respectively. Find the area of Triangle. (4)

(b) The base of a right prism is a trapezium whose parallel sides are 17cm and 13cm, the distance between them being 18cm. If the height of prism is 10, Find the volume. (4)

Q.5 (a) Find the weight of 360m of lead pipe with inside diameter of 1.09cm and outer diameter of 3.09cm. Assume that lead has a density of 11.85g/cu.cm. (4) (b) Find the cross sectional area of the largest hexagonal shank that can be cut from a round bar of copper 2cm in diameter. , (4)

Q.6 (a) A pyramid on a square base has very edge 100m long. Find the edge of a cube of equal volume. (4) (b) Two spheres each a 10M diameter are melted down and recast into a cone with a height equal to the radius of its base, Find the height of the cone. (4)

Q.7 (a) Find the vector whose magnitude is 5 and which is in the direction of the vector: (4) 4i-3j+k (b) Find the Cosine of the angle between the vectors: (4) a = 2i-8j+ 3k = 4 j +3k