PPSC Assistant (BS-16) Punjab Police 2026

Correct answer: 144. Area of a square = side² = 12 × 12 = 144 cm².

Background: All sides of a square are equal.

• 145: 145 is not 12 × 12.
• 156: 156 is not 12 × 12.
• 146: 146 is not 12 × 12.

Did you know? The perimeter would be 4 × 12 = 48 cm.

Memory trick: Square → side × side.

Correct answer: 6. Radius = diameter ÷ 2 = 12 ÷ 2 = 6 cm.

Background: The diameter is twice the radius.

• 9: 9 cm is not half of 12 cm.
• 12: 12 cm is the diameter.
• 18: 18 cm is more than the diameter.

Did you know? The circumference is 2πr = 12π cm.

Memory trick: Radius = half of diameter.

Correct answer: 10x² + xy + √x. Combine the like terms 3x² + 7x² = 10x². The terms xy and √x stay as they are.

Background: Only like terms (same variables and powers) can be combined.

• 10x + √(25x) + xy: The x² terms add to 10x², not 10x.
• 10x + √(25x) + xy: The x² terms add to 10x², not 10x.
• 10x² − xy + √x: The sign of xy should stay positive.

Did you know? xy and √x are not like terms of x².

Memory trick: 3x² + 7x² = 10x².

Correct answer: Two different roots. The discriminant is b² − 4ac = 25 + 48 = 73, which is positive, so there are two different real roots.

Background: D > 0 gives two different real roots, D = 0 gives equal roots, and D < 0 gives no real roots.

• Two same roots: Two equal roots need a discriminant of zero.
• Both A & B: “Both A & B” is incorrect because only one option is true.
• None of these: “None of these” is incorrect because two different roots is correct.

Did you know? 73 is not a perfect square, so the roots are irrational.

Memory trick: D = 73 > 0 → two roots.

Correct answer: x = 4, x = −3/2. Factorise: 2x² − 8x + 3x − 12 = 2x(x − 4) + 3(x − 4) = (2x + 3)(x − 4), so x = 4 or x = −3/2.

Background: Split the middle term −5x into −8x + 3x.

• x = −4, x = −3/2: x = −4 does not satisfy the equation.
• x = −3/2, x = −4: x = −4 does not satisfy the equation.
• None of these: “None of these” is incorrect because x = 4 and x = −3/2 are correct.

Did you know? Check: 2(16) − 20 − 12 = 0.

Memory trick: Product ac = −24; sum = −5.

Correct answer: x² + 4x + 3 = 0. The equation is x² − (sum)x + (product) = 0, so x² − (−4)x + 3 = x² + 4x + 3 = 0.

Background: For ax² + bx + c = 0, the sum of roots = −b/a and the product = c/a.

• x² − 4x + 3 = 0: This would have a sum of roots equal to +4.
• x² + 4x − 3 = 0: This would have a product of −3.
• x² + 4x + 3 = 1: This is not a standard-form equation for the given roots.

Did you know? The roots here are −1 and −3.

Memory trick: x² − (sum)x + product.

Correct answer: 4W + 12. Length = W + 6, so the perimeter = 2(W + 6 + W) = 4W + 12.

Background: The perimeter of a rectangle is 2 × (length + width).

• 4P + 12: P is not the width in this problem.
• 4A + 12: A is not the width in this problem.
• 4L + 12: L is the length, not the width.

Did you know? Name the smaller side W and write the other in terms of W.

Memory trick: 2(2W + 6) = 4W + 12.

Correct answer: 1. A negative one raised to an even power equals 1, and 300 is even.

Background: (−1)ⁿ = 1 if n is even and −1 if n is odd.

• −1: −1 would result from an odd power.
• 0: 0 cannot result from raising −1 to a power.
• 300: 300 is not the value of this expression.

Did you know? Pairs of −1 multiply to give +1.

Memory trick: Even power → +1.

Correct answer: m^(1/5) n^(−6/5). Multiply each exponent by 3/5: m has (1/3)(3/5) = 1/5 and n has (−2)(3/5) = −6/5.

Background: The rule is (aᵐ)ⁿ = aᵐⁿ.

• m^(1/5) n^(6/5): This option makes the exponent of n positive.
• m^(1/5) n^(−6/5)·n: This option adds an extra factor of n.
• m^(1/5) n^(1/5): This option does not multiply the exponent of n correctly.

Did you know? Multiply the outside power with each exponent inside.

Memory trick: Power outside multiplies inside.

Correct answer: 18. Each term is multiplied by 3: 2, 6, 18, 54, 162, 486. The 4th from the last is 18.

Background: A series where each term is multiplied by the same number is a geometric progression.

• 20: 20 is not in the series.
• 22: 22 is not in the series.
• 19: 19 is not in the series.

Did you know? To count from the end, write all terms first.

Memory trick: × 3 each time.

Correct answer: 7. x + y = 5 + 2 = 7.

Background: Substitute the given values and add.

• 9: 9 is not 5 + 2.
• 10: 10 is not 5 + 2.
• 8: 8 is not 5 + 2.

Did you know? 5 + 2 = 7.

Memory trick: Replace and add.