All Forces Interbase Math Quiz| Pro Genius Forces Academy

⚔️ ALL FORCES Inter Base – Math Quiz ⚔️

This Inter Base Mathematics quiz is specially designed for candidates preparing to join the Pakistan Army, Pakistan Air Force, Pakistan Navy, and AFNS. It builds strong math concepts, including integration, and prepares students for all forces’ entry tests as well as academic exams.

🎯 What This Quiz Will Prepare You For
• Clear concepts of Algebra, Geometry, Trigonometry, Arithmetic, and Integration
• Faster MCQ-solving skills
• Confidence for all forces’ entry tests

⏱️ Quiz Format & Duration
• Total MCQs: 50
• Time Limit: 18 minutes
• Question Type: Multiple Choice Questions
• Passing Marks: 50%

🚀 Sharpen Your Mind – Train Like a Future Cadet!
💪 Stay focused, stay sharp — your mission to wear the uniform of Pakistan’s Armed Forces starts now!

Forces Inter base Math Quiz 04

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1 / 50

What is the integral of sin³x * cosx ?

-(cos⁴x) / 4 + C

(tan²x) / 2 + C

(sin²x) / 2 + C

(sin⁴x) / 4 + C

2 / 50

∫ (x+2)/(x+1) dx = ?

x + ln(x+1) + c

x - ln(x+1) + c

ln(x+2) + c

(x^2)/2 + c

3 / 50

General solution of dy/dx = -y/x ?

x*y = c

y = cx

y = e^(-x)

y = ln(x) + c

4 / 50

∫ f'(x) / f(x) dx = ?

f(x) + c

f(x)^2 + c

ln(f(x)) + c

f(x) / f'(x) + c

5 / 50

If then f(x) is called:

Derivative

Integral

Integrand

Differential

6 / 50

∫ sec x dx = ?

ln|sec x + tan x| + c

tan x + c

cos x + c

sec^2 x + c

7 / 50

∫ a^x dx = ?

1/a^x + c

a^x / ln(a) + c

ln(a^x) + c

x * a^x + c

8 / 50

∫ dx / (x ln(x)) = ?

ln(x^2) + c

ln(x) + c

ln(ln(x)) + c

1/ln(x) + c

9 / 50

∫ e^(-λx) dx = ?

(e^(-λx)) / (-λ)

(e^(-λx)) / λ

-λ e^(-λx)

λ e^(-λx)

10 / 50

To determine the area under a curve by the use of integration, the idea was given by

Leibnitz

Archimedes

Newton

Taylor

11 / 50

What is the suitable substitution for ∫ √(2ax - x^2) dx ?

x = a tan(θ)

x = a cos(θ)

x - a = a sin(θ)

x = a sec(θ)

12 / 50

∫ e^(ax) [a f(x) + f'(x)] dx = ?

a e^(ax) f(x)

e^(ax) f'(x)

a e^(ax) f'(x)

e^(ax) f(x)

13 / 50

If y = f(x), then differential of y is:

dy=f(x)dx

None of these

dy=f′(x)dx

dy=f′(x)dy/dx

14 / 50

∫ [f(x)]^n * f′(x) dx = ?

f(x)

[f(x)]^(n+1) / (n+1)

[f(x)]^n / n

n [f(x)]^(n+1)

15 / 50

∫ cos x dx = ?

cos²x + c

–sin x + c

sin x + c

tan x + c

16 / 50

∫ dx / [ x · √(x² − 1) ] = ?

tan⁻¹ x + C

sin⁻¹ x + C

sec⁻¹ x + C

ln|x + √(x² − 1)| + C

17 / 50

∫ sin(3x) dx is equal to:

−3 cos(3x)

−(1/3) cos(3x) + C

3 cos(3x) + C

3 cos(3x) + C

18 / 50

∫ from π/6 to π/3 cos(t) dt = ?

1/2 - (√3)/2

1

(√3)/2 + 1/2

(√3)/2 - 1/2

19 / 50

The equation y = x² - 2x + c (c being a parameter) represents:

two parabolas

family of lines

family of parabolas

one parabola

20 / 50

The derivative of x is:

1

x

0

2x

21 / 50

∫ from 0 to 2 2x dx = ?

1

8

4

2

22 / 50

Solve dv/dt = 2t - 7

v = t^2 - 7t^2 + C

v = t^2 + 7t + C

v = t^2 - 7t + C

v = 2t - 7 + C

23 / 50

The solution of the differential equation dy/dx = sec^2 x is:

y = cos x + C

y = tan x + C

y = cot x + C

y = sec x + C

24 / 50

What is the solution to the differential equation dy/dx = -y ?

y = -C * e^(-x)

y = C * e^(x)

y = C * x

y = C * e^(-x)

25 / 50

∫ e^(a x) sin(b x) dx = ?

e^(a x) / (a^2 - b^2) * (a cos(b x) + b sin(b x)) + C

e^(a x) / (a + b) * (sin(b x) - cos(b x)) + C

e^(a x) * (sin(b x) + cos(b x)) / (a b) + C

e^(a x) / (a^2 + b^2) * (a sin(b x) - b cos(b x)) + C

26 / 50

∫ e^(sin x) · cos x dx = ?

e^(sin x)

e^(cos x)

cos x

sin x

27 / 50

∫ dx / √(x + a + √x) can be evaluated if:

x < 0, a < 0

x 0

x > 0, a < 0

x > 0, a > 0

28 / 50

For ∫ √(x^2 - a^2) dx, what is the correct substitution?

x = a sec(θ)

x = a cos(θ)

x = a sin(θ)

x = a tan(θ)

29 / 50

What is the integral of x * e^x ?

e^x / x + C

ln(x) * e^x + C

xe^x - e^x + C

(x^2 * e^x) / 2 + C

30 / 50

∫ from 0 to π sin(x) dx = ?

1

0

π

2

31 / 50

∫ [ cos x dx ] / [ sin x * ln(sin x) ] = ?

ln(ln(sin x)) + C

ln(cos x) + C

ln(sin x) + C

ln(tan x) + C

32 / 50

∫ a^(x^2) · x dx = ?

a^{x^2}·ln(a)

a^{x^2} / ln(a)

a^{x^2} / (2·ln(a))

(1/2)·a^{x^2}

33 / 50

If ∫ from 1 to 2 f(x) dx = 5, and ∫ from 1 to 2 g(x) dx = 4, then find the value of:

∫ from 1 to 2 [3f(x)] dx − ∫ from 1 to 2 [2g(x)] dx

7

15

5

10

34 / 50

∫ a^(λx) dx = ?

(a^(λx)) / (λ ln(a))

a^(λx) * λ * ln(a)

(a^(λx)) / λ

(a^(λx)) / ln(a)

35 / 50

What is the inverse of the integral operator?

∫ dx

1/x

ln(x)

d/dx

36 / 50

∫ [ e^(tan⁻¹x) / (1 + x²) ] dx = ?

(d) e^(tan⁻¹x) + C

e^(tan x) + C

x·e^(tan⁻¹x) + C

1·tan⁻¹x + C

37 / 50

What is the formula for integration by parts, ∫ u dv ?

uv + ∫ v du

uv / ∫ v du

u - v + ∫ du

uv - ∫ v du

38 / 50

∫ x^n dx = x^(n+1) / (n+1) is true for all values of n except

n = 1

n = -1

n=2

n = 0

39 / 50

∫ √(2x + 3) dx = ?

(1/3)(2x+3)^(3/2)

(1/3)(2x + 3)^(-1/2)

3(2x + 3)

3(2x + 3)^(3/2)

40 / 50

∫ dx / (1 + x^2) = ?

x / (1 + x^2) + c

sin^(-1)(x) + c

ln(1 + x^2) + c

tan^(-1)(x) + c

41 / 50

∫ (from 1 to 2) a^x dx = ?

(a² − a) log a

(a² − a) ln a

(a² − a) In a

(a² − a) / ln a

42 / 50

−∫ from a to b f(x) dx is equal to?

∫ from b to a f(x) dx

−∫ from a to b f(x) dx

∫ from a to b [−f(x)] dx

∫ from a to b f(x) dx

43 / 50

What is the order of the differential equation:x * d^2y/dx^2 + dy/dx - 2x = 0

1

2

More than 2

0

44 / 50

∫ sin(ax + b) dx = ?

−1/a cos(ax+b)

1 /𝑎 cos ( 𝑎 𝑥 + 𝑏 )

a cos(ax+b)

−cos(ax+b)

45 / 50

∫ x * cos(x) dx = ?

x*sin(x) + cos(x) + C

sin(x) + x*cos(x) + C

x*cos(x) - sin(x) + C

x*sin(x) - cos(x) + C

46 / 50

∫ x / √(x² + 3) dx = ?

(√(x² + 3)) / 2

-5√(x² + 3)

√(x² + 3)

-√(x² + 3)

47 / 50

∫ 1 / (ax + b) dx = ?

a * ln(|ax + b|) + C

ln(|ax + b|) + C

(1/a) * ln(|ax + b|) + C

1 / (ax + b)^2 + C

48 / 50

∫ (f′(x) / f(x)) dx = ?

ln|f(x)|

ln|f′(x)|

f′(x)

f(x)

49 / 50

∫ e^x [sin x + cos x] dx = ?

- e^x sin x

e^x cos x

- e^x cos x

e^x sin x

50 / 50

What is the formula for the integral of f(x) * g'(x) dx ?

f(x) * g(x) - ∫ f(x) * g(x) dx

f(x) * g(x) + ∫ g(x) * f'(x) dx

f(x) * g(x) - ∫ g(x) * f'(x) dx

f'(x) * g(x) - ∫ f(x) * g(x) dx

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ALL FORCES Inter Base – Math Quiz 04

⚔️ ALL FORCES Inter Base – Math Quiz ⚔️

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