Algebra
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Q141.The solution set of equation x-3 =4?
Correct Answer: A
Solving for x: x - 3 = 4 => x = 4 + 3 = 7.
Q142.The sum of four consecutive even numbers is 292 what is the smallest number?
Correct Answer: C
Let the consecutive even numbers be x, x+2, x+4, x+6. Sum = 4x + 12 = 292 => 4x = 280 => x = 70. Smallest is 70.
Q143.What is the additive inverse of matrix? Matrix = [ -7 8 ] [ 6 3 ]
Correct Answer: A
The additive inverse of a matrix A is -A, where each element is negated. This yields [ 7 -8 ] [ -6 -3 ].
Q144.(a² - b²) = ?
Correct Answer: A
The algebraic identity for the difference of two squares is: a² - b² = (a - b)(a + b).
Q145.If x + 1/x = 3, find the value of x³ + 1/x³.
Correct Answer: B
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 3³ − 3*3 = 27 − 9 = 18.
Q146.If R = xS⁴, and R = 6 when S = 5, find the value of R when S = 8.
Correct Answer: A
R = xS⁴. At S=5, R=6 => 6 = x * 625 => x = 6/625. When S=8, R = (6/625) * (8⁴) = 39.3 approx.
Q147.What is the value of 8.73 × 8.73 × 8.73 + 4.27 × 4.27 × 4.27?
Correct Answer: C
Using the algebraic expansion a³ + b³ = (a+b)((a+b)² - 3ab) where a = 8.73 and b = 4.27, we get a+b = 13 and ab = 37.2671. Sum = 13 × (169 - 111.8013) = 742.57 approx.
Q148.Does the parabola y = 2x² - 13x + 5 have a tangent whose slope is -1? If so, what is its equation?
Correct Answer: A
Slope dy/dx = 4x - 13 = -1 => x = 3. At x=3, y = 2(9) - 13(3) + 5 = -16. Tangent equation: y + 16 = -1(x - 3) => y = -x - 13.
Q149.Solve: 5x − {3x + [4x − 2x]}
Correct Answer: D
5x - [3x + 2x] = 5x - 5x = 0.
Q150.What is the value of x in the equation 3x − 2 = 24?
Correct Answer: C
3x = 26 => x = 26/3 ≈ 8.67.
Q151.Expand the expression: (x + 4)(x - 2)
Correct Answer: B
(x + 4)(x - 2) = x^2 - 2x + 4x - 8 = x^2 + 2x - 8.
Q152.What are the roots of the equation: x^2 + x - 2 = 0?
Correct Answer: B
Factorize: (x + 2)(x - 1) = 0. So, roots are x = -2 and x = 1.
Q153.What is the numerical coefficient in the algebraic term 6X^2Y?
Correct Answer: A
The numerical coefficient is the constant multiplier of the variables, which is 6.
Q154.What are the factored roots of the expression: X² - 5X + 6?
Correct Answer: A
We factor 6 into -2 and -3 (whose sum is -5): (x-2)(x-3) = x² - 5x + 6.
Q155.Which of the following represents the commutative property of addition?
Correct Answer: A
The commutative property of addition states that numbers can be added in any order and yield the same sum: A + B = B + A.
Q156.What is the expansion of A(b+c)?
Correct Answer: C
By applying the distributive property of multiplication over addition, we get: A(b+c) = ab + ac.
Q157.What is (a² - b²) equal to?
Correct Answer: C
The difference of squares formula states: a² - b² = (a+b)(a-b).
Q158.What is the value of 6² - 4²?
Correct Answer: B
Calculated as: 6² - 4² = 36 - 16 = 20.
Q159.Solve for x in the equation: 2x + 5 = 13.
Correct Answer: C
Subtract 5 from both sides: 2x = 8. Divide both sides by 2: x = 4.
Q160.Simplify the expression: (7 - √2)(7 + √2).
Correct Answer: B
Using the difference of squares identity (a - b)(a + b) = a² - b²: (7)² - (√2)² = 49 - 2 = 47.