Title Week 1 Exam.docx ✅

1. From the equation 7x 2 + (2k – 1) x – 3k + 2 = 0, determine the value of k so that the sum and product of the roots are equal. a. 2 b. b. 4 c. c. 1 d. d. 3 2. The age of Mr. Chetan in 2002 was 1/90 of his birth year. What is his age in 2006? 30 B. 28 C. 26 D. 22 3. If 10 x = 4, then the value of 10 12x is a. 26 b. 160 c. 40 d. 900 4. If 1/x = a + b, 1/y = a – b, then x – y is equal to a. 2b/(b 2 - a 2 ) b. 1/2a c. 2a/(a 2 -b 2 ) d. 1/2b 5. 8 is 4% of a, and 4 is 8% of b. c equals b/a. What is the value of c? B. C. 1 D. 4 6. A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was 12 B. 11 C. 10 D. 9 7. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank in gallons is 100 B. 110 C. 120 D. 140
8. Which of the following is a factor of: f(x) = x 4 - 4x 3 -7x 2 + 22x + 24? a. (x-3) b. (x-2) c. (x-1) d. (x+3) 9. Simplify : / a. b. c. d. 10. Solve for x in the equation: a. 0.438 b. 0.416 c. 0.460 d. 0.482 11. A sequence of numbers such that the same quotient is obtained by dividing a term by the preceding term is called Arithmetic progression b. harmonic progression c. Infinite progression d. geometric progression 12. A nonterminating and nonperiodic decimal is a. rational b. prime c. irrational d. imaginary 13. What is the remainder when 7 187  is divided by 800? 143 B. 243 C. 343 D. 443 14. Walking at the rate of 4kmph a man cover certain distance in 2hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in. 12 min B. 25 min C. 40 min D. 60 min 15. If b = 0, then the number a + bi is a. complex
b. real c. imaginary d. irrational 16. What is the remainder when the polynomial x 4 - 5x 3 + 5x 2 + 7x + 6 is divided by x + 2? a. 16 b. 32 c. 48 d. 68 17. A harmonic progression is a sequence of numbers such that the reciprocals of the numbers will form a a. geometric progression b. arithmetic progression c. infinite progression d. finite progression 18. What is the third proportional of the square of 2 and the cube root of 8? a. 1 b. 2 c. 2 d.4 19. A boatman rows to a place 45 km distant and back in 20 hour. He finds that he can row 12 km with the stream in the same time as 4km against the stream. Find the speed of the stream. 3 km/hr B. 2.5 km/hr C. 4 km/hr D. 3.5 km/hr 20. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? 10 B. 13 C. 14 D. 15 21. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 am and travel towards B at 20 km/hr speed. Another train starts from B at 8 am and travel towards A at 25 km/hr speed. At what time will they meet? 9 am B. 10 am C. 11 am D. None of these
22. Which of the following laws states that the factors of a product may be grouped in any manner without affecting the result? a. commutative law b. associative law c. distributive law d. inverse law 23. If the discriminant of a quadratic equation is greater than zero, the roots of the equation are a. real and equal b. real and distinct c. complex and unequal d. imaginary and distinct 24. 21 pencils and 29 pens cost Rs 79. But if the number of pencils and pens were interchanged, the cost would have reduced by Rs 8. Find the cost of each pen. Rs 1 B. Rs 2 C. Rs 3 D. Rs 4 25. Which of the following best describes (-3) 1/2 ? a. irrational number b. pure imaginary number c. natural number d. complex number 26. What is the greatest common factor (GCF) of 48 and 72? a. 12 b. 24 c. 36 d. 42 27. If x, y and 5x are three consecutive terms of an arithmetic progression whose sum is 81, find x. a. 9 b. 10 c. 11 d. 12 28. From the top of tower A, the angle of elevation of the top of the tower B is 46o. From the foot of tower B the angle of elevation of the top of tower A is 28o. Both towers are on a level ground. If the height of tower B is 120 m, how high is tower A? a) 40.7 m b) 44.1 m c) 42.3 m d) 38.6 m 29. Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number you think? a. 12