Algebra
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If the line x - y = 1 a b
passes through the points (2, –3) and (4, –5) then (a, b) is
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The line x + y = 1, passes through (2, –3) a b ∴ 2 - 5 = 1 a b
Similarly, The line passes through (4, –5)∴ 4 - 5 = 1 a b
Point (–1, –1) satisfies both the equation.Correct Option: D
The line x + y = 1, passes through (2, –3) a b ∴ 2 - 5 = 1 a b
Similarly, The line passes through (4, –5)∴ 4 - 5 = 1 a b
Point (–1, –1) satisfies both the equation.
- What will be the co-ordinates of centroid of a triangle whose vertices are A(1, 2), B (2, 4) and C(6, 2).
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Co-ordinates of centroid
x = x1 + x2 + x3 3 y = y1 + y2 + y3 3 
⇒ x = 1 + 2 + 6 3
x = 3⇒ y = 2 + 4 + 2 3 ⇒ y = 8 3
Co-ordinates of Centroid= 
3, 8 
3
Correct Option: B
Co-ordinates of centroid
x = x1 + x2 + x3 3 y = y1 + y2 + y3 3 ⇒ x = 1 + 2 + 6 3
x = 3⇒ y = 2 + 4 + 2 3 ⇒ y = 8 3
Co-ordinates of Centroid= 3, 8 3
- What is the digit in the unit’s place in the number 15!/100 .
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15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Number of 5’s = 3
Number of 2’s = More than 3
∴ Number of zeroes in the product = 3∴ Unit’s digit in = 15! = 0 100 Correct Option: D
15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Number of 5’s = 3
Number of 2’s = More than 3
∴ Number of zeroes in the product = 3∴ Unit’s digit in = 15! = 0 100
- If ⊕ is an operation such that
a ⊕ b = 2a when a > b
= a + b when a < b
= a² when a = b,then, 
(5 ⊕ 7) + (4 ⊕ 4) 
is equal to : 3(5 ⊕ 5) - (15 ⊕ 11) - 3
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a ⊕ b = 2a if a > b
= a + b if a < b
= a² if a = b,∴ (5 ⊕ 7) + (4 ⊕ 4) 3(5 ⊕ 5) - (15 ⊕ 11) - 3 = (5 + 7) + 4² 3 × 5² - 2 × 15 - 3 = 12 + 16 = 28 = 2 75 - 30 - 3 42 3 Correct Option: C
a ⊕ b = 2a if a > b
= a + b if a < b
= a² if a = b,∴ (5 ⊕ 7) + (4 ⊕ 4) 3(5 ⊕ 5) - (15 ⊕ 11) - 3 = (5 + 7) + 4² 3 × 5² - 2 × 15 - 3 = 12 + 16 = 28 = 2 75 - 30 - 3 42 3
- If ✪ is an operation such that a ✪ b = a + b when a > 0, b >0 a ✪ b = √a² + b² for all other values of a and b. The value of
8 ☟ (7 - 13) - (3 ☟ 1) is (3 - 6) ☟ (9 - 5)
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Given a ✪ b = a + b when a > 0, b >0
a ✪ b = √a² + b² for other values of a and b.
Expression,8 ☟ (7 - 13) - (3 ☟ 1) is (3 - 6) ☟ (9 - 5) = 8 ☟ (-6) - (3 + 1) (- 3) ☟ (- 4) = √8² + (-6)² - 4 √(- 3)² + (- 4)² = √64 + 36 - 4 √9 + 16 = √100 - 4 = 10 - 4 = 6 √25 5 5 Correct Option: C
Given a ✪ b = a + b when a > 0, b >0
a ✪ b = √a² + b² for other values of a and b.
Expression,8 ☟ (7 - 13) - (3 ☟ 1) is (3 - 6) ☟ (9 - 5) = 8 ☟ (-6) - (3 + 1) (- 3) ☟ (- 4) = √8² + (-6)² - 4 √(- 3)² + (- 4)² = √64 + 36 - 4 √9 + 16 = √100 - 4 = 10 - 4 = 6 √25 5 5
