All Forces Interbase Math Quiz| Pro Genius Forces Academy

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, derivatives, and matrices, 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, Integration, Derivatives, and Matrixs
• 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 07

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1 / 50

Derivative of tan(3x) is:

tan(3x)

3sec²(3x)

6sec²(3x)

sec²(3x)

2 / 50

1 − x + x² − x³ + x⁴ − ⋯ = ?

1 / (x − 1)

1 / (1 − x)

1 / (1 + x)

(−1 + x)⁻¹

3 / 50

The notation Df(x) or Dy is used by:

Leibnitz

Newton

Lagrange

Cauchy

4 / 50

The notation dx/dy or dx/df is used by:

Cauchy

Newton

Lagrange

Leibnitz

5 / 50

f(x) = f(0) + x f′(0) + (x² / 2!) f′′(0) + ⋯ + (xⁿ / n!) f⁽ⁿ⁾(0) + ⋯ is called:

Taylor's series expansion

Convergent series

Taylor's Theorem

Maclaurin's series expansion

6 / 50

If a > 0, a ≠ 1, and x = aʸ, then the function defined by y = logₐx (x > 0) is a logarithmic function with base:

10

a

x

e

7 / 50

y = tanh⁻¹x iff x = tanhy is valid when:

x∈(−1, 1), y∈R

x>0, y>0

x∈[−1, 1], y∈R

x∈R, y∈R

8 / 50

If y = cos(ax + b), then y″ = ?

−a² sin(ax + b)

a² sin(ax + b)

a² cos(ax + b)

−a² cos(ax + b)

9 / 50

If f(x) = x³ + 2x + 9, then f''(x) = ?

3x² + 2

6x

3x

2x

10 / 50

If f(x) = sinx, then f′(cos⁻¹(3x)) = ?

3x

-4

3 / √(1 − 9x²)

−3 / √(1 − 9x²)

11 / 50

f is said to be decreasing on [a, b] if for x₁, x₂ ∈ (a, b):

f(x₂) > f(x₁) whenever x₂ < x₁

f(x₂) x₁

f(x₂) x₁

f(x₂) < f(x₁) whenever x₂ < x₁

12 / 50

(dy/dx) | (x₁, y₁) represents:

Increments of x and y at (x₁, y₁)

Slope of horizontal line at (x₁, y₁)

Slope of tangent at (x₁, y₁)

Slope of normal at (x₁, y₁)

13 / 50

If a function f is increasing within [a, b], then slope of the tangent to its graph within [a, b] remains:

Undefined

Negative

Positive

Zero

14 / 50

If y = e^(−ax), then dy/dx = ?

a² e^(−2ax)

−a e^(−ax)

−a² e^(−2ax)

−a e^(2ax)

15 / 50

d/dx (ax+b)ⁿ = n·a(ax+b)ⁿ⁻¹ is valid only when n must be:

A real number

A rational number

An imaginary number

An irrational number

16 / 50

y = sech⁻¹ x if and only if x = sech y is valid when:

x ∈ ]−1, 1[, y ∈ R

x ∈ (0, 1], y ∈ [0, ∞)

x ∈ [−1, 1], y ∈ R

x ∈ R, y ∈ R

17 / 50

The second derivative of y = e^(2x) is:

e^(2x)

2e^(2x)

4e^(2x)

8e^(2x)

18 / 50

d/dx (xⁿ) = n·xⁿ⁻¹ is called:

Constant rule

Quotient rule

Product rule

Power rule

19 / 50

If y = e^(−ax), then y″ = ?

a² e^(−ax)

a² e^(ax)

−a e^(−ax)

−a² e^(−ax)

20 / 50

logₐa = ?

Not defined

a²

1

a

21 / 50

The change in variable x is called increment of x. It is denoted by δx which is:

-ve only

none of these

+ve or -ve

+ve only

22 / 50

y = cosh⁻¹x iff x = coshy is valid when:

x∈R, y∈R

x<0, y<0

x∈[1, ∞), y∈[0, ∞)

x∈(1, ∞], y∈(0, ∞]

23 / 50

d/dx [f(x) + g(x)] = ?

f′(x) + g′(x)

f′(x) − g′(x)

f′(x) g′(x)

f(x) + g(x)

24 / 50

d/dx (log₁₀x) = ?

ln(x) / x

1 / (x log₁₀e)

1 / (x ln10)

x / ln10

25 / 50

d/dx (sin a) = ?

−a cos a

a cos a

0

cos a

26 / 50

If f(x) = 1/x, then f′′(a) = ?

1 / a²

2 / a³

−2 / a³

−1 / a²

27 / 50

f(x) = sin(x) is:

Odd function

Even function

Linear function

Identity function

28 / 50

d/dx ln[f(x)] = ?

f′(x) / f(x)

f′(x)

f(x) f′(x)

ln f′(x)

29 / 50

Derivative of 2^x is:

x·2^(x−1)

e^x

2^x ln(2)

ln(x)·2^x

30 / 50

[f(x)g(x)]′ = ?

f′(x) − g′(x)

f(x)g′(x) + f′(x)g(x)

f′(x) + g′(x)

f(x)g′(x) − f′(x)g(x)

31 / 50

d/dx [1/g(x)] = ?

1 / [g(x)]²

1 / g′(x)

−g′(x) / [g(x)]²

g′(x) / [g(x)]²

32 / 50

d/dx [g(x)]ⁿ = ?

n[g(x)]ⁿ⁻¹ g(x)

[g(x)]ⁿ⁻¹ g′(x)

n[g(x)]ⁿ⁻¹

n[g(x)]ⁿ⁻¹ g′(x)

33 / 50

y = coth⁻¹x iff x = cothy is valid when:

|x|>1, y∈[0, ∞)

|x|<1, y∈R

x∈R, y∈R

|x|>1, y∈R{0}

34 / 50

d/dx (cosx) - d²/dx² (sinx) = ?

2cosx

−2sinx

2sinx

0

35 / 50

d/dx (csc⁻¹x) = ?

−1 / (|x|√(x²−1))

1 / (|x|(1+x²))

−1 / (|x|(1+x²))

1 / (|x|√(x²−1))

36 / 50

y = sinh⁻¹x iff x = sinhy is valid when:

x>0, y>0

x∈R, y>0

x<0, y<0

x∈R, y∈R

37 / 50

The function f(x) = aˣ, where a > 0, a ≠ 0, and x is any real number, is called:

Logarithmic function

Exponential function

Composite function

Algebraic function

38 / 50

If y = cosh⁻¹(sec x), then dy/dx = ?

cos x

−sin(sec x)

−sinh⁻¹(sec x)·tan x

sec x

39 / 50

If a function f is decreasing within [a, b], then slope of the tangent to its graph within [a, b] remains:

Positive

Negative

Zero

Undefined

40 / 50

y = cosech⁻¹ x if and only if x = cosech y is valid when:

x ∈ (0, 1], y ∈ [0, ∞)

x ∈ [−1, 1], y ∈ R

x ∈ R, y ∈ R

x ∈ R − {0}, y ∈ R − {0}

41 / 50

d/dx (10^sinx) = ?

10^sinx · cosx · ln10

10cosx

10cosx · ln10

10sinx · ln10

42 / 50

Derivative of (ax+b)^n is:

n(ax+b)^n

na(ax+b)^(n−1)

(ax+b)^(n−1)

a(ax+b)^n

43 / 50

The notation f′(x) or y′ is used by:

Newton

Leibnitz

Lagrange

Cauchy

44 / 50

The notation f′(x) is used by:

Newton

Lagrange

Leibnitz

Cauchy

45 / 50

f is said to be increasing on [a, b] if for x₁, x₂ ∈ (a, b):

If x₁ f(x₂)

If x₁ < x₂, then f(x₁) = f(x₂)

If x₁ < x₂, then f(x₁) ≤ f(x₂)

If x₁ < x₂, then f(x₁) ≥ f(x₂)

46 / 50

If y = sinh⁻¹(ax + b), then dy/dx = ?

a / √(1 + (ax + b)²)

1 / √(1 + (ax + b)²)

a·cosh⁻¹(ax + b)

cosh⁻¹(ax + b)

47 / 50

The maximum value of the function f(x) = x² − x − 2 is:

− 9/4

−1

−2/9

0

48 / 50

A point where the 1st derivative of a function is zero, is called:

Common point

Point of concurrency

Corner point

Stationary point

49 / 50

(fog)′(x) = ?

Cannot be calculated

f′g

f′(g(x))

f′(g(x))·g′(x)

50 / 50

d/dx (sec⁻¹x) = ?

−1 / (|x|(1+x²))

−1 / (|x|√(x²−1))

1 / (|x|√(x²−1))

1 / (|x|(1+x²))

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ALL FORCES Inter Base – Math Quiz 07

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