The sum of two numbers is 42 and their product is 437.Then, the difference between the number is:
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Solution
Let the numbers are x & y.
∴ (x – y)2 = (x + y)2 – 4xy
(x – y)2 = 42 × 42 – 4 × 437
x – y = 4
A wall of 100 meters can be built 7 men or 10 women in 10 days. How many days will 14 men and 20 women take to build a wall of 600 meters?
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Solution
7 m = 10 w
∴ 14 m + 20 w = 20w + 20 w = 40 w
∴
⇒ Days = 15
Successive discounts of 20% and 30% are equivalent to a single discount of:
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Solution
Equivalent discount = 100 – 100 ×
= 44%
If the equation (1 + m2) x2 + 2mc x + c2 – a2 = 0 has equal roots, then find the value of a2 (1 + m2) :
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Solution
According to question
(2mc)2 = 4 (1 + m2) (c2 – a2)
⇒ 4m2c2 = 4 (1 + m2) (c2 – a2)
⇒ a2 (1 + m2) = c2 + m2c2 – m2c2 = c2
A bag contains Rs. 90 in coins of denominations of 50 paise, 25 paise and 10 paise. If the coins of 50 paise, 25 paise and 10 paise are in the ratio of 2 : 3 : 5, then the number of 25 paise coins in the bag is-
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Solution
Let the number of coins are 2x, 3x and 5x respectively
∴ 90 =
x = 40
∴ Number of 25 paise coins = 3 × 40 = 120
If x2 + x + 1 = 0 then the value of x6 is:
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Solution
x2 + x + 1 = 0
⇒ (x – 1) (x2 + x + 1) = 0
⇒ x3 – 13 = 0
⇒ x3 = 1
∴ x6 = 12 = 1
If 2x– 1 + 2x+1 = 320, then the value of x is
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Solution
2x–1 + 2x+1 = 320
⇒ 2x–1 [1 + 22] = 320
⇒ 2x–1 =
A sphere and a hemisphere have the same radius. Then ratio of their respective total surface area is:
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Solution
Ratio =
Find the value of cot 9° cot 27° cot 30° cot 63° cot 81°
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Solution
cot 9° cot 27° cot 30° cot 63° cot 81° = cot 9° cot 27° cot 30° tan 27° tan 9°
cot 9° cot 27° cot 30° cot 63° cot 81° = cot 30°
cot 9° cot 27° cot 30° cot 63° cot 81° =
If = 66 then the value of :
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Solution
x2 +
⇒
⇒
⇒
Now,