Past Paper 2025 11th Class Karachi Board Mathematics Objective (Science General Group)

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MATHEMATICS 2025

(Science General Group)

TIME: 3 Hours (100 Marks)

SECTION 'A' (Multiple Choice Questions)(40)

NOTE: i) This section consists of 20 part questions and all are to be answered. Each part question carries one mark. ii) Do not copy the part questions in your answer script. Write only the answer in full against the proper number of the question and its part. iii) All notations are used in their usual meanings. The use of Scientific Calculator is allowed.

1. Choose the correct answer for each from the given options:

i) (−i)2 = : * −i * i * −1√ * 1

ii) For the complex numbers (3, −4), (1, 0) = : * (1, 0) * (3, 4) * (3, −4) ✓ * (−3, −4)

iii) If A and B are square matrices then (AB)t: * AtBt * AtB * ABt * BtAt ✓

iv)

|

10
56
| − |
12
34
| = :
*2 *4 *6 *8✓

v) The unit vector in the direction of \vec r = 2î + ĵ − k̂ is: * 1√6 (2î + ĵ − k̂) ✓ * √6 (2î + ĵ − k̂) * 6(2î + ĵ − k̂) * 16 (2î + ĵ − k̂)

vi) If \vec a = 4î + 6k̂ and \vec b = 6î − 4ĵ then | \vec a − \vec b |: * √8 * 2√14 ✓ * 2√26 * 2√3

vii) If a−bb−c = ab then a, b and c are in: * A.P. * G.P. * H.P. ✓ * A.G.P

viii) General term of a sequence is (−1)nn2 then its 4th term is: * −4 * −16 * 16 ✓ * 4

ix) ∑n = : * n(n+1)2 ✓ * n(n+1)(2n+1)6 * n3(n+1)24 * n3

x) The probability of getting the head in a single toss of a coin is: * 13 * 23 * 12 ✓ * 14

xi) nCr = : * n!r!(n-r)! ✓ * (n-r)!r! * (n-r)!r! * (n-r)!r!

xii) The number of terms in the expansion of (a + b)2n are: * n + 1 * n + 2 * 2(n + 1) * 2n + 1 ✓

xiii) For |x| < 1, 1 − x + x2 − x3 + ⋯ = : * (1 + x)−1 ✓ * (1 − x)−1 * (1 + x)−2 * (1 − x)−2

xiv) If a function f: N → Y is one-to-one and onto then the function is called: * Bijective ✓ * Injective * Surjective * Quadratic function

xv) The graph of Linear function is: * Parabola * Hyperbola * ellipse * Straight line ✓

xvi) cos 2θ = : * 2cos2θ + 1 * cos2θ − sin2θ ✓ * 1 + 2sin2θ * sin2θ + sin2θ

xvii) In ΔABC, √(x−b)(x−c)bc = : * cos α2 ✓ * cos β2 * cos γ2 * sin α2

xviii) In ΔABC, Area of triangle is: * 12 bc sinβ ✓ * 12 ca sinα * 12 ca sinγ * 12 ab sinβ

xix) Period of cos 4x is: * π2 ✓ * 2π * π * 4π

xx) Tan−1(−1) = : * π4 * −π4 ✓ * π2 * −π2

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