Algebra
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Q1.If x^51+51 is divided by x+1 then the remainder is :
Correct Answer: B
By Remainder Theorem: f(-1) = (-1)^51 + 51 = -1 + 51 = 50.
Q2.The Solution of the expression 9X^2-6x÷3x
Correct Answer: B
(9x² - 6x) ÷ 3x = 3x(3x - 2) ÷ 3x = 3x - 2.
Q3.y=2x, and z=5y then find x+3y+z in terms of x.
Correct Answer: A
Substituting y=2x and z=5y=10x gives x+3(2x)+10x = x+6x+10x = 17x.
Q4.If 6/x = x/12, what is the value of 6(x)^2?
Correct Answer: C
Q5.Solve: Log3 + Log7x?
Correct Answer: D
Q6.X(X^3)^2 X/X^3 = ?
Correct Answer: A
Q7.If Lambda is equal to T =1/2 then?
Correct Answer: A
Q8.What is k, given that 27^k = 9?
Correct Answer: B
27^k = 9 means (3^3)^k = 3^2, so 3k = 2, giving k = 2/3.
Q9.Find an integer such that four times the number subtracted from two times the square of the number gives 15.
Correct Answer: D
2x^2 - 4x = 15 has no integer solution among the given options; solving the quadratic gives non-integer/irrational roots, so 'None of these' is correct.
Q10.Find two consecutive positive numbers such that the sum of their squares is 7 less than 120.
Correct Answer: A
Let the numbers be n and n+1: n^2 + (n+1)^2 = 113. Testing n=7: 49+64=113. So the numbers are 7, 8.
Q11.Find the value of x, where A = (2pi + y)x^2, where A = 36 and y = 2.77.
Correct Answer: C
36 = (2π+2.77)x^2 → x^2 = 36/8.9 ≈ 4.04 → x ≈ 2.
Q12.What is k, given that 27^k = 9.
Correct Answer: B
Correct answer is B: 2/3
Q13.Find the value of x, when A = (2pi + y)x^2, where A=36 and y=2.77
Correct Answer: C
Correct answer is C: 2
Q14.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.
Q15.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.
Q16.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.
Q17.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.
Q18.If 3x = 12, what is the value of x?
Correct Answer: B
Divide both sides by 3: x = 12 / 3 = 4.
Q19.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.
Q20.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.