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August 2015 T05/T24/TES12/TML012/EE/20150812 APPLIED MATHEMATICS-1 Instructions Marks-80 Time: 3 Hrs 1. All questions are compulsory. 2. “Long Answer type Question (LAQ)” is a supply type question of 15 marks which required a typical answer of about 60-80 lines in bout 32-40 minutes. 3. “Sort Answer type Question (SAQ)” is a supply type question of 5 marks which required a typical answer of about 15-20 lines in bout 08-10 minutes. 4. Figures to the right indicate marks allotted to the questions. 5. Assume suitable data if necessary 6. Use a nonprogrammable type of scientific calculator is allowed Marks SECTION-A Q.1 A)Find sum and product of roots of x2+px+k=0. B)Find the value of i] ׀9- ׀-׀7-׀ 10 ii] ׀13 ׀+׀25-׀ 5 OR Q.1 A) Simplify:-i) ii) √ 3 2√ +√ B)Find the antilog of 10 −√ −√ −√ i] 3.1596 ii]0.7689 Q.2 A)Show that : cos(A+B).cos (A-B)= cos2A-sin2B. B)What is de-moivre's theorem? 5 10 5 OR Q.2 A) In a triangle ABC show that: ( − ) +( + ) 10 =a 2 B) Find the modulus and argument of 2+2√3i. 5 Q.3 Find the sum of the Arithmetic progressions of -3,3,9,15……..to 20 terms. 5 Q.4 Find the area of triangle whose c=4,b=6 and angle A=600. 5 SECTION-B Q.5 A)Draw the graph of y=2sinx and write down the period and amplitude of that function. 10 B)Find the slope of the line passing through (3,0),(8,0). 5 OR Q.5 A)Find the equation of a line i) with slope 2 and passing through (5,7). 10 ii) with slope 5 and y-intercept 3. B) Find the equation of the circle with the following points as the ends of a diameter (2,3),(5,-1). Q.6 A) Find two unit vectors perpendicular to both the vectors i+j-k and 3i+j- 5 10 2k. B)Two fair dice are rolled.Find the probability that the score is 8. 5 OR 10 Q.6 A) Find the mean and standard deviation of the following data. Class-interval Frequency 5-15 8 15-25 10 25-35 15 35-45 20 45-55 12 55-65 5 B)Find the 1's compliment: i) 0101 ii)1111 5 Q.7 Find the centres and the radius of the circles x2+y2-4x-5=0. 5 Q.8 Show that the points A(-1,1,-2), B(1,2,3), C(5,4,13) are collinear. 5