Algebra
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Q81.A retail store has monthly fixed costs of $3,000 and monthly salary costs of $2,500 for each employee. If the store hires x employees for an entire year, which of the following equations represents the store's total cost c, in dollars, for the year
Correct Answer: A
C = 12(3000 + 2, 500x) is the correct factual response to “A retail store has monthly fixed costs of $3,000 and monthly salary costs of $2,500 for each employee. If the store hires x employees for an entire year, which of the following equations represents the store's total cost c, in dollars, for the year”.
Q82.If x = 7 - 43 then find the value of x+(1 / x)?
Correct Answer: B
14 is the result obtained by evaluating the expression in the question.
Q83.If x = 7-4√ 3 then find the value of x +( 1/x).
Correct Answer: B
14 is the result obtained by evaluating the expression in the question.
Q84.In mathematics, a solution to an equation that emerges from the process of solving the problem but is not a valid solution to the problem is called solution:
Correct Answer: C
An extraneous solution is produced during algebraic manipulation but does not satisfy the original equation. Such solutions often appear after squaring both sides or multiplying by expressions that may be zero, so they must be checked.
Q85.If X =28 and Y=51, then(X+Y)+(X-Y)=?
Correct Answer: B
56 is the correct answer because it matches the fact or concept tested by this question.
Q86.In the equation of a straight line, what does the letter 'c' represents?
Correct Answer: C
y Intercept is the correct answer because it matches the fact or concept tested by this question.
Q87.0.009/x=0.01.Find the value of x
Correct Answer: B
x = 0.009/0.01 = 0.9.
Q88.Find the value of x 3889 +12.952 -x=3854.002
Correct Answer: B
x = 3889 + 12.952 - 3854.002 = 47.95.
Q89.If x=3+ √8, Find the value of x² + 1/x²
Correct Answer: B
Since x=3+√8, 1/x=3-√8 (as (3+√8)(3-√8)=1). x+1/x=6, so x²+1/x²=(x+1/x)²-2=36-2=34.
Q90.There are 54 coins in total. Some are 20-cent coins and some are 50-cent coins. Their total value is $20.70. How many 20-cent coins are there?
Correct Answer: B
Let x be 20c coins. 0.20x + 0.50(54-x) = 20.70 => -0.30x + 27 = 20.70 => -0.30x = -6.30 => x = 23.
Q91.If x+y=16 and x-y=3, then x^2 - y^2 =?
Correct Answer: B
Using algebraic identity: x^2 - y^2 = (x+y)(x-y). Here, x^2 - y^2 = 16 * 3 = 48.
Q92.HCF of 48 and 80 = 48P - 80. Find P.
Correct Answer: B
HCF of 48 and 80: 48=2^4*3, 80=2^4*5. HCF = 16. Therefore, 48P - 80 = 16 => 48P = 96 => P = 2.
Q93.If sqrt(4x-3) = 4, find the value of x.
Correct Answer: C
Square both sides: 4x - 3 = 16 => 4x = 19 => x = 19/4 = 4.75.
Q94.What is the common factor in X^3 + X^2 + X?
Correct Answer: A
Factoring X out of the expression: X * (X^2 + X + 1). The common factor is X.
Q95.If (x - 3)(x - 4) = 1, what is the value of x?
Correct Answer: D
Expanding: x² - 7x + 12 = 1 => x² - 7x + 11 = 0. Solving via quadratic formula: x = [7 ± √(49 - 44)]/2 = (7 ± √5)/2.
Q96.Solve the equation: 2√(x + 2) = 3√2. If x > 0, what is the value of x?
Correct Answer: A
Square both sides: 4(x + 2) = 18 => 4x + 8 = 18 => 4x = 10 => x = 2.5.
Q97.If 3x = 12, what is the value of x?
Correct Answer: B
Divide both sides by 3: x = 12 / 3 = 4.
Q98.Simplify the exponential expression: a⁴ × a⁸ × a³
Correct Answer: A
When multiplying bases, add the exponents: 4 + 8 + 3 = 15. Thus, the result is a¹⁵.
Q99.Mr. Rehman spends 1/3 of his salary on personal affairs, gives half of the remaining to his wife, and invests 75% of the final remainder. If he has Rs. 1000 left, what is his total salary?
Correct Answer: C
Let salary = S. Left after personal: 2/3S. Left after wife: 1/3S. Left after investment: 25% of 1/3S = 1/12S. Given 1/12S = 1000 => S = Rs. 12,000.
Q100.If a² − b² = 9 and (a − b)² = 3, then ab is equal to?
Correct Answer: C
We know (a+b)(a-b) = 9. Since (a-b)² = 3 => a-b = √3. Thus a+b = 9/√3 = 3√3. Squaring both sides: (a+b)² = 27 => a²+b²+2ab = 27. Also (a-b)² = 3 => a²+b²-2ab = 3. Subtracting the two: 4ab = 24 => ab = 6.