Showing 1–20 of 69

Q1.If x^51+51 is divided by x+1 then the remainder is :

Hard
A 49
B 50
C 51
D None of these
Algebraic Expressions PPSC 2026

Correct Answer: B

By Remainder Theorem: f(-1) = (-1)^51 + 51 = -1 + 51 = 50.

Q2.The Solution of the expression 9X^2-6x÷3x

Medium
A 2x+3
B 3x-2
C x-3
D 2x-3
Algebraic Expressions PPSC 2026

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.

Medium
A 17x
B 16x
C 15x
D 14x
Algebraic Expressions PPSC 2026

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?

Easy
A 9
B 1
C 3
D 5
Algebraic Expressions PPSC 2025

Correct Answer: C

Q5.Solve: Log3 + Log7x?

Easy
A log 3*7x ^2
B log 21x
C log_3(7x)
D None of these
Algebraic Expressions PPSC 2025

Correct Answer: D

Q6.X(X^3)^2 X/X^3 = ?

Hard
A X^4
B X^3
C X^5
D X^2
Algebraic Expressions PPSC 2026

Correct Answer: A

Q7.If Lambda is equal to T =1/2 then?

Hard
A Lambda =log (2)T 1/2
B Lambda =log (2)T 1/3
C Lambda =log (2)T 1/4
D Lambda =log (2)T 1/5
Algebraic Expressions PPSC 2026

Correct Answer: A

Q8.What is k, given that 27^k = 9?

Medium
A 1/3
B 2/3
C 4/3
D None of these
Algebraic Expressions CSS 2026

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.

Hard
A 3
B -3
C -5/3
D None of these
Algebraic Expressions CSS 2026

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.

Medium
A 7, 8
B 8, 9
C 7, 9
D None of these
Algebraic Expressions CSS 2026

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.

Hard
A 3
B 4
C 2
D None of these
Algebraic Expressions CSS 2026

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.

Medium
A 1/3
B 2/3
C 4/3
D None of these
Algebraic Expressions CSS 2024

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

Medium
A 3
B 4
C 2
D None of these
Algebraic Expressions CSS 2024

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?

Medium
A 21
B 23
C 27
D 31
Algebraic Expressions PPSC

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.

Medium
A 3
B 4
C 19/4
D 5
Algebraic Expressions PPSC

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?

Medium
A 2
B 1
C 3.5
D (7 ± √5)/2
Algebraic Expressions PPSC

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?

Medium
A 2.5
B 3
C 3.5
D 4
Algebraic Expressions PPSC

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?

Medium
A 3
B 4
C 6
D 5
Algebraic Expressions PPSC

Correct Answer: B

Divide both sides by 3: x = 12 / 3 = 4.

Q19.Simplify the exponential expression: a⁴ × a⁸ × a³

Medium
A a¹⁵
B a¹²
C a²⁴
D a¹¹
Algebraic Expressions PPSC

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?

Medium
A 13,000
B 16,000
C 12,000
D 11,000
Algebraic Expressions PPSC

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.