Math Test 1
The product of the roots of the quadratic equation 2x2−5x+6=0 is :
  • 5
  • 6
Explanation: Given equation: 2x^2−5x+6=0 Coefficients: • a=2 • b=−5 • c=6 Formula for product of roots: Product of roots = c/a Substitute values: 6/2 = 3 Final Answer: Product of the roots = 3
Grandmother was cooking at a picnic, attended by her son and daughter-in-law, with their four sons and their wives and one son and two daughters to each of the sons. How many ladies were there at the picnic ?
  • 8
  • 12
  • 14
  • 10
Explanation: Who were at the picnic ? • 1 Grandmother • 1 Daughter-in-law • 4 Sons, each with: 1 Wife - 4 Ladies 2 Daughters each - 4 × 2 = 8 Girls Total Ladies: • Grandmother = 1 • Daughter-in-law = 1 • Wives = 4 • Daughters = 8 Ans: Total Ladies = 1 + 1 + 4 + 8 = 14
squrt 225/729- squrt 25/144-squrt 16/81= ?
  • − 7 / 12
  • − 20 / 27
  • − 5 / 9
  • − 11 / 36
Explanation:

To simplify the expression sqrt 225 / 729 - sqrt 25 / 144 - sqrt 16 / 81

Each square root:

    • sqrt 225/729   225729=15/27 = 5/9
    • sqrt 25/144=5/12
    • sqrt 16/81=4/9

Substitute these values back:

5/9−5/12−4/9

Find a common denominator (36):

    • Convert 5/9=20/36
    • Convert 5/12=15/36
    • Convert 4/9=16/36

Perform the subtraction:

20/36−15/36−16/36=20−15−16/36 = −11/36

Identify the incorrect term in the series. {5, 8, 13, 20, 31, 40, 53}
  • 13
  • 31
  • 20
  • 40
Explanation: Given Sequence: 5, 8, 13, 20, 31, 40, 53 Find the differences between terms • 8 − 5 = 3 • 13 − 8 = 5 • 20 − 13 = 7 • 31 − 20 = 11 • 40 − 31 = 9 - Wrong • 53 − 40 = 13 Look at the pattern The differences are: 3, 5, 7, 11, 9, 13 This is not a smooth increasing pattern. After 7, we expect 9, but instead we got 11, and then the next is 9. Conclusion: • The number 40 breaks the expected pattern. • So, 40 is the incorrect number in the sequence. Ans: Incorrect term is 40
What would replace # in the sets ? {5, 120, 3}, {9, 630, 5}, {9, 810, #}
  • 8
  • 7
  • 6
  • 4
Explanation: Set: {5, 120, 3} • Take the middle number: 120 • Divide it by the first number: 120 ÷ 5 = 24 • Now divide that result by the last number: 24 ÷ 3 = 8 So the pattern is: Middle ÷ First ÷ Last = 8 Set: {9, 630, 5} • 630 ÷ 9 = 70 • 70 ÷ 5 = 14 Pattern again: Middle ÷ First ÷ Last = 14 Set: {9, 810, ?} find ? • 810 ÷ 9 = 90 • We want 90 ÷ ? = 15 So: ? = 90 ÷ 15 = 6 Ans: The missing number is 6
A person purchases x number of items at the rate of ` x per item. The shop-keeper gives him a total discount of ` x after which he pays ` 156. The cost per item after the discount is :
  • 13
  • 12
  • 16
  • 14
Explanation: Problem: A person buys x items at ₹x each. He gets a discount of ₹x in total. He paid ₹156 after the discount. Solution: Total Cost without Discount If each item costs ₹x and he buys x items, Total cost = x × x = x² Discount Discount = ₹x Amount Paid So, total paid = x² - x We’re told: x² - x = 156 Solve the Equation: x² - x = 156 x² - x - 156 = 0 Now factor it: (x - 13)(x + 12) = 0 So, x = 13 or -12 We ignore -12 because x must be positive. Final Calculation: • x = 13 • Original cost per item = ₹13 • Discount = ₹13 total = ₹1 per item • New price per item = 13 - 1 = ₹12 Ans: Cost per item after discount = ₹12
The population of a town increases at the rate of 10% every year. If the present population of the town is 10,000, then after 3 years the population of the town would be :
  • 13,310
  • 15,310
  • 13,510
    • Explanation:

    To find the population of a town after 3 years with a 10% annual increase:

    1. Current Population: 10,000
    2. Growth Rate: 10% (or 0.10)

    Formula:
    Future Population = Current Population × (1 + Growth Rate) ^ Number of Years

    Calculation:
    Future Population  = 10,000 × (1 + 0.10)^3
                                  = 10,000 × (1.10)^3
                                  = 10,000 × 1.331
    Future Population ≈ 13,310

    So, after 3 years, the population will be 13,310.