2011 Punjab State Board of Technical Education and Industrial Training Diploma Information Technology Applied mathematics 1st exam dec. 2011 common to all trades of diploma in engineering. University Question paper
APPLIED MATHEMATICS
1st Exam/Common/2455/Dec2011
Duration: 3Hrs. Max. Marks 75
Section A
Q.1. Choose the correct answer [Marks 5X1=5]
(1) If (34i)(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) 2 (d) 2
(3) If 5pr=2, 6pr1 then the value of r is (a) 3 (b) 5 (c) 1 (d) 2
(4) In a triangle of angle A = 1200 , angle B =380 – 13' then angle C is (a) 210 74' (b) 21047' (c) 21037' (d) 21087'
(5) The centroid of a triangle with two vertices (3,4) (1,9) is (2,4) then 3rd vertex is (a) (4,7) (b) (4,7)
Q.2. State true or false [Marks 5X1=5]
(1) Number of ways of permutation n distinct objects along a circle is n1 factorial. (2) Angle 18370 lies in 4th quardrant. (3) Sin (A+B)(Sin AB)= Cos2BCos2A. (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 32n1 then 10th term is …………………………. . (b) No. of ways of selecting 4 players out of 5 are …………………… . (c) The expression (14x)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 six questions: [Marks 6 X 5 = 30]
(1) Given log2=.301303 and Log5=.69897 Solve the equation 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,………………. Find the amplitude in 6th deflection before system comes to rest.
(3) Find the number of different & letter words formed the word " TRIANGLE" if each is to have consonants never together.
(4) Show that Cot?+cosec?1/cot?cosec?+1=1+cos?/sin?
(5) Find the value of 3sin?4sin3?/1+2cos2? if cot?= root 3.
(6) Prove that 4sinASin(600A)Sin(600+A)=Sin3A
(7) Three verticals of a parallelogram taken in order are (1,0) (4,3) (1,2) Find 4th vertex.
(8) If A(10,4), B(4,9), C(2,1) are vertices of a triangle ABC? Find equation of altitude through B.
(9) Find equation 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 three questions: [Marks 3X10=30]
(1) Find standred equation of ellipse which passes through points (2,2) (3,1) also find eccentricity.
(2) Two Pillars of equal height stands on earlier side of roadway which is 30m wide. At a point in the roadway between 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 = 3/895/192x.
(4) Resolve into partial fraction: (6x3+5x2+7)/(3x22x1).
(5) Find the equation of a circle which passes through the center of circle x2+y2+8x+10y7=0 and concentric with circle 2x2+2y28x12y9=0.
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