Punjab State Board of Technical Education and Industrial Training 2011 Diploma Information Technology Applied mathematics 1st common to all trades of in engineering. - Question Paper

APPLIED MATHEMATICS

first Exam/Common/2455/Dec-2011

Duration: 3Hrs. Max. Marks 75


Section- A

Q.1. select the accurate ans [Marks 5X1=5]

(1) If (3-4i)(x+iy)=1, then value of x and y are
(a) (3/25,2/25) (b) (1/25,2/25)
(c) (3/25,4/25) (d) (4/25,1/25)

(2) If 1+k, 5/6+k, 13/18+k are in GP value of k is
(a) ½ (b) -1/2
(c) two (d) -2

(3) If 5pr=2, 6pr-1 then the value of r is
(a) three (b) 5
(c) one (d) 2

(4) In a triangle of angle A = 1200 , angle B =380 – 13' then angle C is
(a) 210 -74' (b) 210-47'
(c) 210-37' (d) 210-87'

(5) The centroid of a triangle with 2 vertices (3,4) (-1,-9) is (2,-4) then third vertex is
(a) (-4,-7) (b) (4,-7)

Q.2. State actual or false [Marks 5X1=5]

(1) Number of ways of permutation n distinct objects along a circle is n-1 factorial.
(2) Angle -18370 lies in fourth quardrant.
(3) Sin (A+B)(Sin A-B)= Cos2B-Cos2A.
(4) In a rectangle opposite sides are equal and diagonals unequal.
(5) The points (3,4)(7,7)(x,4) are collinear then x=3.

Q.3. Fill in the blanks [Marks 5X1=5]

(a) If the nth term of a GP is 32n-1 then tenth term is …………………………. .
(b) No. of ways of selecting four players out of five are …………………… .
(c) The expression (1-4x)-2 is valid for ……………………………. .
(d) The angle of a rectangular decagon in degree are ………………… .
(e) Area of trapezium = Sum of || sides + …………………………… .

SECTION- B

Q.4. Attempt any 6 questions: [Marks six X five = 30]

(1) provided log2=.301303 and Log5=.69897
Solve the formula for x+y
2x+5y=1, 5x+1.2y=2

(2) The vibration of a system and damped so that the amplitude of successive deflection are 12,8,16/3,………………. obtain the amplitude in sixth deflection before system comes to rest.

(3) obtain the number of various & letter words formed the word " TRIANGLE" if every is to have consonants never together.

(4) Show that
Cot?+cosec?-1/cot?-cosec?+1=1+cos?/sin?

(5) obtain the value of 3sin?-4sin3?/1+2cos2? if cot?= root 3.

(6) Prove that
4sinASin(600-A)Sin(600+A)=Sin3A

(7) 3 verticals of a parallelogram taken in order are (1,0) (4,3) (1,2)
obtain fourth vertex.

(8) If A(10,4), B(-4,9), C(-2,-1) are vertices of a triangle ABC? obtain formula of altitude through B.

(9) obtain formula of straigh line parallel to 2x+3y+11=0 and which is such that sum of its intercepts on axis is 15.

SECTION- C

Q.5. Attempt 3 questions: [Marks 3X10=30]

(1) obtain standred formula of ellipse which passes through points (2,-2) (-3,1) also obtain eccentricity.

(2) 2 Pillars of equal height stands on earlier side of roadway which is 30m wide. At a point in the roadway ranging from the pillar the angle of elevations of the tops of pillars are 300, 600. Determine their height and position of point.

(3) If x2 and higher powers are neglected show that
{(1+2/3x)^(-5)+v4+2x}/v(4+3x)3 = 3/8-95/192x.

(4) Resolve into partial fraction:-
(6x3+5x2+7)/(3x2-2x-1).

(5) obtain the formula of a circle which passes through the center of circle x2+y2+8x+10y-7=0 and concentric with circle 2x2+2y2-8x-12y-9=0.

Earning:   Approval pending.