ALL FORCES Inter Base – Math Quiz 04

⚔️ 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

∫ x / √(x² + 3) dx = ?

√(x² + 3)
(√(x² + 3)) / 2
-5√(x² + 3)
-√(x² + 3)

2 / 50

Solve dv/dt = 2t - 7

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

3 / 50

∫ a^x dx = ?

a^x / ln(a) + c
ln(a^x) + c
1/a^x + c
x * a^x + c

4 / 50

If then f(x) is called:

Differential
Derivative
Integrand
Integral

5 / 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

15
5
10
7

6 / 50

∫ from π/6 to π/3 cos(t) dt = ?

1
(√3)/2 + 1/2
(√3)/2 - 1/2
1/2 - (√3)/2

7 / 50

∫ e^(-λx) dx = ?

(e^(-λx)) / (-λ)
λ e^(-λx)
-λ e^(-λx)
(e^(-λx)) / λ

8 / 50

∫ dx / (1 + x^2) = ?

sin^(-1)(x) + c
ln(1 + x^2) + c
x / (1 + x^2) + c
tan^(-1)(x) + c

9 / 50

∫ sec x dx = ?

tan x + c
sec^2 x + c
cos x + c
ln|sec x + tan x| + c

10 / 50

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

ln(sin x) + C
ln(tan x) + C
ln(ln(sin x)) + C
ln(cos x) + C

11 / 50

−∫ from a to b f(x) dx is equal to?

−∫ from a to b f(x) dx
∫ from a to b f(x) dx
∫ from a to b [−f(x)] dx
∫ from b to a f(x) dx

12 / 50

∫ a^(x^2) · x dx = ?

a^{x^2} / ln(a)
a^{x^2} / (2·ln(a))
(1/2)·a^{x^2}
a^{x^2}·ln(a)

13 / 50

∫ e^x [sin x + cos x] dx = ?

e^x sin x
e^x cos x
- e^x sin x
- e^x cos x

14 / 50

∫ dx / [ x · √(x² − 1) ] = ?

tan⁻¹ x + C
ln|x + √(x² − 1)| + C
sin⁻¹ x + C
sec⁻¹ x + C

15 / 50

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

y = e^(-x)
x*y = c
y = ln(x) + c
y = cx

16 / 50

∫ (f′(x) / f(x)) dx = ?

f(x)
ln|f(x)|
f′(x)
ln|f′(x)|

17 / 50

∫ e^(ax) [a f(x) + f'(x)] dx = ?

a e^(ax) f'(x)
a e^(ax) f(x)
e^(ax) f'(x)
e^(ax) f(x)

18 / 50

∫ (x+2)/(x+1) dx = ?

x + ln(x+1) + c
(x^2)/2 + c
x - ln(x+1) + c
ln(x+2) + c

19 / 50

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

x - a = a sin(θ)
x = a cos(θ)
x = a tan(θ)
x = a sec(θ)

20 / 50

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

dy=f′(x)dy/dx
None of these
dy=f′(x)dx
dy=f(x)dx

21 / 50

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

y = sec x + C
y = cot x + C
y = cos x + C
y = tan x + C

22 / 50

∫ from 0 to π sin(x) dx = ?

0
1
2
π

23 / 50

The derivative of x is:

1
2x
0
x

24 / 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) - ∫ f(x) * g(x) dx
f(x) * g(x) + ∫ g(x) * f'(x) dx
f'(x) * g(x) - ∫ f(x) * g(x) dx

25 / 50

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

x = a cos(θ)
x = a sec(θ)
x = a tan(θ)
x = a sin(θ)

26 / 50

∫ e^(a x) sin(b x) dx = ?

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

27 / 50

∫ √(2x + 3) dx = ?

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

28 / 50

∫ sin(3x) dx is equal to:

3 cos(3x) + C
3 cos(3x) + C
−(1/3) cos(3x) + C
−3 cos(3x)

29 / 50

∫ (from 1 to 2) a^x dx = ?

(a² − a) ln a
(a² − a) / ln a
(a² − a) log a
(a² − a) In a

30 / 50

∫ [f(x)]^n * f′(x) dx = ?

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

31 / 50

∫ from 0 to 2 2x dx = ?

8
1
4
2

32 / 50

What is the integral of sin³x * cosx ?

-(cos⁴x) / 4 + C
(tan²x) / 2 + C
(sin⁴x) / 4 + C
(sin²x) / 2 + C

33 / 50

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

Taylor
Leibnitz
Newton
Archimedes

34 / 50

What is the inverse of the integral operator?

ln(x)
∫ dx
1/x
d/dx

35 / 50

∫ dx / (x ln(x)) = ?

ln(x) + c
1/ln(x) + c
ln(x^2) + c
ln(ln(x)) + c

36 / 50

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

1
0
More than 2
2

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

∫ [ e^(tan⁻¹x) / (1 + x²) ] dx = ?

e^(tan x) + C
x·e^(tan⁻¹x) + C
(d) e^(tan⁻¹x) + C
1·tan⁻¹x + C

39 / 50

∫ sin(ax + b) dx = ?

−1/a cos(ax+b)
−cos(ax+b)
a cos(ax+b)
1 /𝑎 cos ( 𝑎 𝑥 + 𝑏 )

40 / 50

∫ x * cos(x) dx = ?

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

41 / 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

42 / 50

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

x 0
x > 0, a > 0
x < 0, a < 0
x > 0, a < 0

43 / 50

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

n = 1
n = 0
n = -1
n=2

44 / 50

∫ a^(λx) dx = ?

(a^(λx)) / ln(a)
(a^(λx)) / (λ ln(a))
a^(λx) * λ * ln(a)
(a^(λx)) / λ

45 / 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)

46 / 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

47 / 50

∫ e^(sin x) · cos x dx = ?

cos x
sin x
e^(sin x)
e^(cos x)

48 / 50

∫ f'(x) / f(x) dx = ?

f(x)^2 + c
f(x) / f'(x) + c
f(x) + c
ln(f(x)) + c

49 / 50

∫ cos x dx = ?

cos²x + c
tan x + c
sin x + c
–sin x + c

50 / 50

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

one parabola
two parabolas
family of parabolas
family of lines

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ALL FORCES Inter Base – Math Quiz 04

⚔️ ALL FORCES Inter Base – Math Quiz ⚔️

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