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

−∫ from a to b f(x) dx is equal to?

∫ from a to b f(x) dx

∫ from b to a f(x) dx

∫ from a to b [−f(x)] dx

−∫ from a to b f(x) dx

2 / 50

∫ e^(-λx) dx = ?

λ e^(-λx)

(e^(-λx)) / (-λ)

(e^(-λx)) / λ

-λ e^(-λx)

3 / 50

∫ e^(a x) sin(b x) dx = ?

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

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

4 / 50

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

y = ln(x) + c

y = e^(-x)

x*y = c

y = cx

5 / 50

∫ e^x [sin x + cos x] dx = ?

- e^x cos x

- e^x sin x

e^x sin x

e^x cos x

6 / 50

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

uv + ∫ v du

u - v + ∫ du

uv - ∫ v du

uv / ∫ v du

7 / 50

∫ x / √(x² + 3) dx = ?

-5√(x² + 3)

(√(x² + 3)) / 2

√(x² + 3)

-√(x² + 3)

8 / 50

What is the formula for the integral of 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

f'(x) * g(x) - ∫ f(x) * g(x) dx

9 / 50

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

dy=f(x)dx

dy=f′(x)dx

dy=f′(x)dy/dx

None of these

10 / 50

∫ e^(ax) [a f(x) + f'(x)] dx = ?

e^(ax) f'(x)

a e^(ax) f'(x)

a e^(ax) f(x)

e^(ax) f(x)

11 / 50

∫ [f(x)]^n * f′(x) dx = ?

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

f(x)

[f(x)]^n / n

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

12 / 50

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

x < 0, a < 0

x > 0, a < 0

x > 0, a > 0

x 0

13 / 50

∫ from 0 to 2 2x dx = ?

8

1

2

4

14 / 50

∫ e^(sin x) · cos x dx = ?

cos x

e^(sin x)

e^(cos x)

sin x

15 / 50

∫ dx / [ x · √(x² − 1) ] = ?

ln|x + √(x² − 1)| + C

tan⁻¹ x + C

sec⁻¹ x + C

sin⁻¹ x + C

16 / 50

∫ x * cos(x) dx = ?

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

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

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

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

17 / 50

∫ [ e^(tan⁻¹x) / (1 + x²) ] dx = ?

e^(tan x) + C

x·e^(tan⁻¹x) + C

(d) e^(tan⁻¹x) + C

1·tan⁻¹x + C

18 / 50

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

2

0

More than 2

1

19 / 50

∫ from π/6 to π/3 cos(t) dt = ?

1/2 - (√3)/2

(√3)/2 + 1/2

(√3)/2 - 1/2

1

20 / 50

∫ (f′(x) / f(x)) dx = ?

f(x)

f′(x)

ln|f′(x)|

ln|f(x)|

21 / 50

∫ 1 / (ax + b) dx = ?

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

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

1 / (ax + b)^2 + C

ln(|ax + b|) + C

22 / 50

If then f(x) is called:

Differential

Integrand

Derivative

Integral

23 / 50

∫ from 0 to π sin(x) dx = ?

1

π

2

0

24 / 50

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

x = a cos(θ)

x = a sec(θ)

x = a sin(θ)

x = a tan(θ)

25 / 50

∫ cos x dx = ?

sin x + c

tan x + c

cos²x + c

–sin x + c

26 / 50

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

x - a = a sin(θ)

x = a sec(θ)

x = a cos(θ)

x = a tan(θ)

27 / 50

The derivative of x is:

2x

0

1

x

28 / 50

∫ √(2x + 3) dx = ?

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

3(2x + 3)

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

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

29 / 50

∫ dx / (x ln(x)) = ?

ln(x^2) + c

ln(ln(x)) + c

1/ln(x) + c

ln(x) + c

30 / 50

∫ a^x dx = ?

x * a^x + c

a^x / ln(a) + c

ln(a^x) + c

1/a^x + c

31 / 50

∫ dx / (1 + x^2) = ?

x / (1 + x^2) + c

ln(1 + x^2) + c

tan^(-1)(x) + c

sin^(-1)(x) + c

32 / 50

∫ (x+2)/(x+1) dx = ?

x - ln(x+1) + c

ln(x+2) + c

x + ln(x+1) + c

(x^2)/2 + c

33 / 50

∫ a^(λx) dx = ?

(a^(λx)) / λ

a^(λx) * λ * ln(a)

(a^(λx)) / (λ ln(a))

(a^(λx)) / ln(a)

34 / 50

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

Leibnitz

Newton

Taylor

Archimedes

35 / 50

∫ sin(ax + b) dx = ?

−1/a cos(ax+b)

−cos(ax+b)

1 /𝑎 cos ( 𝑎 𝑥 + 𝑏 )

a cos(ax+b)

36 / 50

Solve dv/dt = 2t - 7

v = 2t - 7 + C

v = t^2 + 7t + C

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

v = t^2 - 7t + C

37 / 50

What is the inverse of the integral operator?

d/dx

ln(x)

∫ dx

1/x

38 / 50

What is the integral of sin³x * cosx ?

-(cos⁴x) / 4 + C

(sin²x) / 2 + C

(tan²x) / 2 + C

(sin⁴x) / 4 + C

39 / 50

∫ f'(x) / f(x) dx = ?

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

ln(f(x)) + c

f(x)^2 + c

f(x) + c

40 / 50

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

y = C * e^(x)

y = C * x

y = C * e^(-x)

y = -C * e^(-x)

41 / 50

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

ln(cos x) + C

ln(tan x) + C

ln(sin x) + C

ln(ln(sin x)) + C

42 / 50

∫ sec x dx = ?

sec^2 x + c

cos x + c

tan x + c

ln|sec x + tan x| + c

43 / 50

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

one parabola

family of lines

two parabolas

family of parabolas

44 / 50

What is the integral of x * e^x ?

xe^x - e^x + C

e^x / x + C

ln(x) * e^x + C

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

45 / 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

10

15

7

5

46 / 50

∫ sin(3x) dx is equal to:

3 cos(3x) + C

−(1/3) cos(3x) + C

3 cos(3x) + C

−3 cos(3x)

47 / 50

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

n=2

n = 0

n = 1

n = -1

48 / 50

∫ a^(x^2) · x dx = ?

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

a^{x^2} / (2·ln(a))

a^{x^2}·ln(a)

(1/2)·a^{x^2}

49 / 50

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

y = cot x + C

y = tan x + C

y = cos x + C

y = sec x + C

50 / 50

∫ (from 1 to 2) a^x dx = ?

(a² − a) ln a

(a² − a) log a

(a² − a) In a

(a² − a) / ln a

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ALL FORCES Inter Base – Math Quiz 04

⚔️ ALL FORCES Inter Base – Math Quiz ⚔️

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