Please provide a neat solution. You may use a calculator technique but explain the concepts or formula you will use. Thank you.

Items 78-88:

72. An um contains 4 black balls and six white balls. What is the probability of getting one black ball and one white ball in two consecutive draws from the um without replacement? A. 0 040 C. 0.27 B. 024 D. 0.53 73. What is the exponential form of the complex number 3 + 4i? A. e raised to 53.1"i B. 5e raised to 53. 19i C. Se raised to 128.9i D. 7e raised to 53.1'i 74. What is the product of the complex numbers 2 - 2j and v32 emu? A. 16 C. 10emmi4 B. j16 D. 16(1 -i) 75. What is the rationalized value of the complex quotient? (6 + j2.5) / (3 + 14) A. - 0.32 + j0.86 C. 1.1-j0.68 B. 0.32-10.68 D. - 1.7 + j1.1 76. Water is pouring at a varying rate into a swimming pool that is initially empty. Aftert hours, there are t + vt liters in the pool. At what rate is the water pouring into the pool when t = 9 h? A 1/6 L/h C. 1Lh B. 1/2 L/h D. 7/6 /h 77. A spherical balloon is filled with air at a rate of 1 m'/'s. Compute the time rate of change of the surface area of the balloon at the instant the balloon's volume is 113.1 m. A 0.67 mil's C. 3.1 m/s B. 1.7 mal's D. 3.7 m/'s 78. Compute the limit lim +2 I-40X-2 AO B. 1 C. 2 D. CO 70. Simplify the following expression lim x - 16 3-4 X-4 A. O B. B C. 12 D. 16 80. What is the Laplace transform of e -? A. 1/ (s+8) C. e-6. B. 1/ (5-6) 81. How many numbers between 20 and 1,058 are exactly divisible by 14? A 73 B. 74 C. 75 D. 76 82. A can do a piece of work alone in 2 days, B alone in 3 days, and C alone in 6 days. If they work together. how many days would it take them to finish the work? A 1.50 days C. 0.5 day 1.60 days D. 1 day 83. A chord measuring 1.25 m is 0.85 m from the center of a circle. Find the area of the circle. A. 5.60 sq. m C. 2.55 sq, m B. 4 34 sq. m D. 8.24 sq m 84. Find the general solution of the differential equation dyldx + yx = 1 A 2y= X+ C C. xy = 2x3 + C B. 2xy= x+ C D. xy = 2x + C 85. A card is drawn from an ordinary deck of 52 cards. Find the probability that the card is a face card or heart. A 1/18 B. 3/52 C. 11/26 D. 1/4 38. What is the probability of getting 7 or 11 when a pair of dice is thrown? A. 2/9 B. 1/6 C. 1/18 D. 3/8 87. If the surface area of the sphere is 2.123.72 sq. cm., find its volume. A. 11,404.04 cu. cm. B. 9 202.77 GUL Cm. C. 5,575.28 Gu. cm. D. 7.238.23 cu Cm.88. The third term of an arithmetic progression is - 7 and the eighth term is 23. Find the sum of the first 12 terms. A. 280 B. 221 C. 121 D. 168 80. Mrs. Smith is twice as old as her daughter Sam. Ten years ago. the sum of their ages was 46 years. How old is Sam? A 12 B. 15 C. 22 D. 19 80. The angle or inclination of ascend of a road having 8.25% grade is _ degrees. A. 4.72 B. 4.27 C. 5.12 D. 1.88 01. Find the volume generated by revolving about the y awis the area bounded by the curve y = (x squared) +4 and y = 2 ( x squared ) A 6 pi B. 18/3 pi C. 7 pi D. 8 pi 82. Find the number of ways in which 6 teachers can be assigned to 4 sections of an introductory psychology course if no teacher is assigned to more than one section. A. 60 B. 240 C. 120 D. 360 83. Justine's average in 5 subjects is 80. Disregarding the lowest grade his average is 90. What is Justine's lowest grade? A. 85 B. 86 C. 87 D. Be 04. A triangle is defined by the points (2,6). (-2,2) & (5,2). Find the area of the triangle. A. 28 B. 14 C. 12 D. 10 85. What is the number of the sides of the polygon if the sum of the angles is 1440 degrees? A 6 B. 8 C. 9 D. 10 08. The largest triangle that can be inscribed in semi-circle. A. Right Triangle C. Isosceles Triangle B. Scalene Triangle D. Equilateral Triangle 07. The plate number of a vehicle consists of 5 alphanumeric sequence is arranged such that the first 2 characters are alphabet and the remaining 3 are digits. How many arrangements are possible if the first character is a vowel and the repetitions are not allowed? A. 20 900 C. 8000 D. 20000 08. Joey gives 1/4 of his candies to Jake. Jake gives 1/5 of his candies to Jose. Jose receives 2 candies. How many candies does Joey has at first? A. 10 B. 20 C. 30 D. 40 82. In how many ways can a person choose 1 or more of 4 electrical appliances? A 12 B. 13 C. 14 D. 15 100. A square garden with a side of 20 m is to be illuminated by a bulb at the center. If the radius of the covered light is 10 m, what should be the area of un-shaded garden? A. 65 sq. meters C. 85 sq meters B. 75 sq. meters D. 95 sq meters