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. The real numbers m which satisfy the inequality (3/5)m + 3 > (2/3 )m - 4 are (m : m < 105) (m : m < 7) (m : m > 7) (m : m > 105) 2. The 1st and 4th terms of a G.P are -3 and 24 respectively. The sum of the first four terms is -15 -45 15 45 3. What integral values of x satisfy the inequality-2 ≤ x < 2 ? -1, 0, 1 -2, -1, 0, 1 -2, -1, 1, 2 -2, 0, 1, 2 4. Find the values p and q in the arithmetic progression -12, p, q, 18, ... 1, 11 -2, 8 0, 9 -1, 8 5. Given that a² + b² + c² = 50 and a = 5, √b = 2, find c 4.2 2 5.7 3 6. The values of p and q in the G.P 10, p, q, -5/4 are respectively -5, 5/2 -5/2, 5 5, -5/2 5/2, -5 7. Given that the quadratic expression 3m² - 7m + K is a perfect square, the value of K is 49/4 49/36 49/24 49/12 8. What is the least possible value of 9 / (1 + 2y²) if 0 ≤ y ≤ 2 ? 1 2 9 0 9. What must be added to the expression y² - 18y to make it a perfect square? 36 9 2 81 10. The sum of the ages of a father and his daughter is 85 years. Five years ago, the father was exactly four times as old as his daughter. The present age of the father is 65 yr. 53 yr. 61 yr. 57 yr. 11. The sum of the first five terms of the G.P 3, -6, 12, is -33 33 93 31 12. If 4x - 2 = 3x -5, the value of 7x is -21 -49 7 -3 13. A motorist drove a distance of 90km at constant speed for the first 40km and then drove 20km/hr faster for the rest of the journey. If the whole journey took him one hour, his average speed for the first 40km was 60 km/hr 80 km/hr 40 km/hr 70 km/hr 14. The nth term of the A.P 10, 3, -4, ... is 16 - 7n 18 - 7n 17 - 7n 18 + 7n 15. If y is negative, for what range of values of y is y + 1/3 > 1/y + 3 ? -3 < y < 0 3 < y < 4 -2 < y < -1 -4 < y < -3 16. P is directly proportional to M and inversely proportional to N. If P = 9 when M = 24 and N = 8, find the value of P when M = 5 and N = 6 5/4 5/2 18/5 11 17. Find the value of x for which 3^{2x} + 6(3^{x}) = 27 1 3 -1 -3 18. What is the common factor to the binomial expressions 4x²-9y², 8x³+27y³ and (4x+6y)² ? 4x-6y 2x+3y 2x-3y 4x+6y 19. Factorize: 9 - (a²-3a-1)² -(a-2)(a+1)(a+2)(a+4) -(a-4)(a+1)(a-1)(a-2) (a-4)(a-2)(a-1)(a+1) (a-4)(a-3)(a-2)(a+1) 20. 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 67 76 49 58 21. Evaluate: (xy² - yz²) (x²z - xyz) when x = 2, y = -2 and z = -½ -30 0 -34 -28 22. Solve the inequality:3x + 3 > 9 x > 4 x > 2 x > 3 x > 6 23. Factorize: 32a³ - 8ab² 4(2a+b)(4a-b) 4(4a+b)(2a-b) 8a(2a+b)(2a-b) 8a(2a-b) 24. If 4/3, m, 1, n form a G.P, the product of m and n is 4/3 3/4 1 9/16 25. The 2nd and 5th terms of a G.P are 2/3 and 1/12 respectively. The 1st term is 5/3 4/3 7/3 1/2 1 out of 25 Time is Up! Time's up