26/03/2020 Algebra(Study by Topics Senior Class Test) 26/03/2020 0Comments by Gate Academy Please, fill out the information below to continue. Note: This is a sample test, and you can only take it for a limited period, after which you will be required to subscribe to a plan NAME EMAIL PHONE NUMBER 1. Find the real numbers n satisfying n(3/n) + n > 2 n < 1 All real numbers n > -1 n > 2 2. The 11th term of the A.P 15, 9, 3, -3, ... is 51 -51 75 -45 3. Find the sum to infinity of the sequence 3, 2, 4/3, 8/9 , ... 10 8 18 9 4. Solve the inequality:3x + 3 > 9 x > 4 x > 6 x > 2 x > 3 5. Solve the equation:(log_{3}a) – 6log_{3}a + 9 = 0 27 81 9 18 6. The largest root of the equation (x - 1)² = 4x - 7 is 4 7 6 2 7. The first term of an A.P. is equal to one-half the common difference, d. The 8th term of the A.P is (13/2)d 4d (15/2)d 6d 8. The common ratio in the G.P log 2, log 4, log 16, ... is log 2 2 3 4 9. A mother is now twice as old as her daughter. Ten years ago the mother was four times as old as her daughter. The present ages of the daughter and the mother are, respectively 30, 60 15, 30 25, 50 20, 40 10. What integral values of x satisfy the inequality-2 ≤ x < 2 ? -1, 0, 1 -2, 0, 1, 2 -2, -1, 1, 2 -2, -1, 0, 1 11. What is the common factor to the expressions y²-y, 2y²+y-1 and y²-1 ? none y-1 y+1 y 12. The cost(y) of feeding n people for a week is given as y = 250 + 80n, where y is expressed in dollar ($). What is the cost of feeding two persons? $160 $410 $80 $660 13. If x varies directly as the square root of n, and x = 9 when n = 9, the value of x when n = 16/9 is 16/9 4 9/4 3/2 14. Solve the inequality:18 < x² - 3x x > -3 or x > 6 -3 < x < 6 x < -3 or x < 6 x 6 15. One of the roots of the equation x² + kx - 15 = 0 is 3. The value of K is 5 -2 -5 2 16. The seventh term of the G.P 16/9, -8/3, 4, ... is -32/3 16 81/4 -9/2 17. Given that a² + b² + c² = 50 and a = 5, √b = 2, find c 2 5.7 4.2 3 18. The length of a rectangular plot of land exceeds the width by 7m. If the area of the plot is 198m² , the length is 24 m 27 m 18 m 21 m 19. Solve the equation 3x + 10 = x² 5 or -2 -5 or 2 5 or 2 -5 or -2 20. Evaluate: (xy² - yz²) (x²z - xyz) when x = 2, y = -2 and z = -½ -34 -28 -30 0 21. The sum of the digits in a 2-digit number is 13. With the digits interchanged, the new number exceeds the original number by 27. The original number is 76 67 49 58 22. A G.P has 6 and 24 as its 2nd and 4th terms respectively. The sum of the first four terms is 40 45 60 66 23. Simplify : 8a - 3(2a - 3b) 2a + 3b 2a - 9b 2a + 9b 5a - 9b 24. John was 40 years old in 1995 while his father was 65. In what year was John exactly half his father's age? 1990 1980 1978 1985 25. Solve the equation: 6z² - 7z - 5 = 0 z = -5/3 or 1/2 z = 1/2 or -5/2 z = 5/3 or -1/2 z = 1/3 or 5/2 1 out of 25 Time is Up! Time's up