Algebra
Practice Questions - Algebra
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Q1) If y + 1/y = 5, what is the value of y2 + 1/y2? 1) 25 2) 3 3) 23 4) None of these
y + 1/y = 5 On squaring both sides, y2 + 1/y2 + 2 = 25 y2 + 1/y2 = 23 Hence, option 3. Q2) If y2 + 1/y2 = 18, find the value of y - 1/y? 1) 4 2) 0 3) 16 4) None of these
y2 + 1/y2 = 18 y2 + 1/y2 - 2 = 16 (y - 1/y)2 = 16 ⇒ y - 1/y = ±4 Hence, option 4. Q3) An amphitheater had 28 seats in first row, 31 seats in the second row, 34 seats in the third row, and so on. If there are 40 rows in the amphitheater, what is the amphitheater's seating capacity? 1) 2900 2) 3460 3) 2680 4) None of these
S40 = (40/2)×[2×28 + (40 - 1)×3] = 3460 Hence, option 2. Q4) How many numbers between 200 and 2580 are exactly divisible by 12 and 40? 1) 21 2) 19 3) 18 4) 20
If a number is divisible by 12 and 40 then it must be divisible by their LCM which is 120. Numbers between 200 and 2580 which are divisible by 120 are 240, 360,..., 2520. i.e., the first number greater than 200 and divisible by 120 is 240. The last number which is divisible by 120 and less than 2580 is 2520. So, the required numbers form an A.P where a = 240, d = 120 and  = 2520 2520 = 240 + (n - 1)120 On solving, n = 20 Hence, option 4. Q5) Find the number of 2-digit numbers which are exactly divisible by 4. 1) 24 2) 22 3) 25 4) None of these
Two digit numbers which are exactly divisible by 4 are 12, 16, 20,...,96 This is an A.P where a = 12, d = 4 and = 9696 = 12 + (n - 1)3 On solving, n = 22 Hence, option 2. |