MATHS MCQS
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چار آپشن میں سے کسی ایک پر کلک کرنے سے جواب سرخ ہو جائے گا۔
- 540
- 450
- 350
- None of these
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Explanation
The least number of students that can be divided exactly by 15, 18, 27, 36, and 45 is the Least Common Multiple (LCM) of these numbers.
LCM of 15, 18, 27, 36, and 45 = 540, making it the correct answer.
- 8
- 6
- 14
- None of these
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Explanation
The given equations can be rewritten using identity formulas:
- a² - 2ab + b² = (a - b)² = 36 → (a - b) = ±6
- a² - 3ab + b² = 22 → (a - b)² - ab = 22
Substituting (a - b)² = 36 in 36 - ab = 22, solving for ab gives:
- 3(a + b)³
- (a + b)³
- (3a + 3b)³
- None of these
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Explanation
The given expression is:
a³ + 3ab(a + b) + b³
Factor the expression:
(a + b)(a² - ab + b²) + 3ab(a + b)
Combine like terms:
(a + b)(a² - ab + b² + 3ab)
Simplify:
(a + b)(a² + 2ab + b²)
Recognize the perfect cube:
(a + b)³
- (A.B)⁻¹
- A⁻¹.B⁻¹
- (B A)⁻¹
- None of these
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Explanation
The property of inverse matrices states that (A.B)⁻¹ = B⁻¹.A⁻¹.
This means that the inverse of the product of two matrices is the product of their inverses in reverse order.
- -1
- 1
- 0
- None of these
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Explanation
The slope of a line is given by rise/run. In a horizontal line, there is no rise (change in y), so the slope is 0/any number = 0.
A horizontal line has a constant y-value, meaning it does not incline or decline, resulting in a slope of 0.
- b - a < 0
- a < b
- a > b
- None of these
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Explanation
The condition a - b < 0 means that a is smaller than b because subtracting a larger number (b) from a smaller number (a) gives a negative result.
This directly translates to a < b as the correct inequality.
- 5
- 8
- 49
- None of these
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Explanation
The given equation a² - b² = 56 can be rewritten as (a - b)(a + b) = 56.
Since a + b = 7, substituting it gives (a - b) × 7 = 56, solving for a - b gives 8.
- 488
- 512
- 500
- None of these
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Explanation
Given:
x + (1/x) = 8
Cube both sides:
(x + (1/x))³ = 8³
Expand the left side:
x³ + 3x²(1/x) + 3x(1/x)² + (1/x)³ = 512
Simplify:
x³ + 3x + 3(1/x) + (1/x)³ = 512
Rearrange:
x³ + (1/x)³ + 3(x + (1/x)) = 512
Substitute x + (1/x) = 8:
x³ + (1/x)³ + 3(8) = 512
x³ + (1/x)³ + 24 = 512
Subtract 24 from both sides:
x³ + (1/x)³ = 488
- 32
- 5
- 16
- None of these
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Explanation
To find the number of subsets of a set A:
Number of subsets = 2^n
where n is the number of elements in the set.
In this case:
A = {a, e, i, o, u}
n = 5
Number of subsets = 2^5 = 32
- 3y²
- 9y⁴
- y²
- None of these
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Explanation
To divide the expression, follow the quotient rule:
9y⁴ ÷ 3y² = (9/3) × (y⁴/y²)
Simplify:
3 × y²
So, the correct answer is:
3y²
