Past Paper 2025 12th Class Karachi Board Mathematics Objective (Science Pre-Engineering Group)

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MATHEMATICS 2025

(Science Pre-Engineering Group)

TIME: 3 Hours (100 Marks)

SECTION 'A' (Multiple Choice Questions)(20)

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) The Maple command of the function f(x) = 5xy, differentiate with respect to x:
* diff f(5*x*y,y)
* diff f(5*x*y,x)✓
* diff f(5*x*y,x)
* diff f(5*x*y,y)

ii) The Maple command to evaluate π to 5 digits is:
* > evalf(Pi,5) ✓
* > evalf(Pi,5)
* > evalf (pi *5)
* > evalf(5 + Pi)

iii) In interval [4,5] ∩ [4,5] is:
* ∅
* (4,5)✓
* [4,5]
* [4,5]

iv) If "x" is in radian, sin a x / x :
* 0
* a✓
* 1
* 1/a

v) If y = tan-1√x , then dy/dx =:
* 12√x(1+x)✓
* 12x(1+x2)
* √x2(1+x)
* 12x(1+√x)

vi) If f(x) = x2 - 3x - 5 and f'(x) = 2 then x =:
* 0
* 5/2✓
* 2/5
* 3

vii) d/dx [a f(x)] = :
* a'
* a f'(x) ✓
* a' f(x)
* f'(x)

viii) Second order derivation of f'(x) = A sin x + B cos x is:
* f(x)
* -f(x) ✓
* +f(x)
* f'(x)

ix) If f(t) = (e2t + I) k̂ then f'(t) at t = 0 is:
* k̂
* 2k̂ ✓
* 0
* 2

x) ∫ xn dx, where n ≠ -1 is:
* xn+1n+1 + C ✓
* n xn+1 + C
* xn-1n-1 + C
* ln x + C

xi) ∫0π/2 cos x dx =:
* 0
* 1 ✓
* -1
* ∞

xii) The equation of the line parallel to y-axis which is at a distance of 3 units on its left:
* x - 3 = 0
* x + 3 = 0 ✓
* y - 3 = 0
* y + 3 = 0

xiii) The point of concurrency of the altitudes of a triangle is:
* Incentre
* Orthocentre ✓
* Circumcentre
* Centroid

xiv) If the circle x2 + y2 + 2gx + 2fy + c = 0 touches y-axis then the radius is:
* |f + g|
* |f - g|
* |f|
* |g| ✓

xv) The centre of circle (x - 3)2 + (y + 5)2 = 36 is:
* (3, -5) ✓
* (-3, 5)
* (3, 5)
* (-3, -5)

xvi) The latus rectum of the parabola (x + 3)2 = -6(y - 4) is:
* -6
* 6 ✓
* -3
* 4

xvii) The eccentricity of a rectangular hyperbola is:
* ±√2 i
* -√2
* √2 ✓
* √2 i

xviii) The order and degree of differential equation d3y / dx3 = √[1 + (dy/dx)3] are respectively:
* 2 and 2
* 2 and 3
* 3 and 2 ✓
* 3 and 3

xix) The general solution of the differential equation dy/dx = ex-y is:
* ex-y = c
* ey = ex + c ✓
* exy = c
* ex + e-y = c

xx) If f(x,y) = sin (x/y), then fy = :
* (x/y2) cos (x/y)
* (x/y2) sin (x/y)
* - (x/y2) cos (x/y) ✓
* - (x/y2) sin (x/y)

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