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

d/dx (xⁿ) = n·xⁿ⁻¹ is called:

Constant rule

Power rule

Quotient rule

Product rule

2 / 50

f(x) = sin(x) is:

Odd function

Identity function

Even function

Linear function

3 / 50

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

+ve only

+ve or -ve

-ve only

none of these

4 / 50

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

3 / √(1 − 9x²)

−3 / √(1 − 9x²)

-4

3x

5 / 50

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

x

e

a

10

6 / 50

Derivative of (ax+b)^n is:

a(ax+b)^n

n(ax+b)^n

(ax+b)^(n−1)

na(ax+b)^(n−1)

7 / 50

d/dx (10^sinx) = ?

10^sinx · cosx · ln10

10cosx

10cosx · ln10

10sinx · ln10

8 / 50

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

Zero

Positive

Undefined

Negative

9 / 50

(dy/dx) | (x₁, y₁) represents:

Slope of tangent at (x₁, y₁)

Slope of horizontal line at (x₁, y₁)

Slope of normal at (x₁, y₁)

Increments of x and y at (x₁, y₁)

10 / 50

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

x∈R, y∈R

x∈[−1, 1], y∈R

x>0, y>0

x∈(−1, 1), y∈R

11 / 50

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

x ∈ (0, 1], y ∈ [0, ∞)

x ∈ ]−1, 1[, y ∈ R

x ∈ R, y ∈ R

x ∈ [−1, 1], y ∈ R

12 / 50

The notation f′(x) is used by:

Leibnitz

Cauchy

Lagrange

Newton

13 / 50

If y = cos(ax + b), then y″ = ?

−a² sin(ax + b)

a² sin(ax + b)

−a² cos(ax + b)

a² cos(ax + b)

14 / 50

d/dx [g(x)]ⁿ = ?

n[g(x)]ⁿ⁻¹ g(x)

n[g(x)]ⁿ⁻¹

n[g(x)]ⁿ⁻¹ g′(x)

[g(x)]ⁿ⁻¹ g′(x)

15 / 50

If y = e^(−ax), then y″ = ?

−a e^(−ax)

a² e^(ax)

a² e^(−ax)

−a² e^(−ax)

16 / 50

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

g′(x) / [g(x)]²

1 / [g(x)]²

−g′(x) / [g(x)]²

1 / g′(x)

17 / 50

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

Maclaurin's series expansion

Convergent series

Taylor's series expansion

Taylor's Theorem

18 / 50

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

2e^(2x)

e^(2x)

4e^(2x)

8e^(2x)

19 / 50

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

Leibnitz

Cauchy

Newton

Lagrange

20 / 50

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

x∈R, y>0

x>0, y>0

x∈R, y∈R

x<0, y<0

21 / 50

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

Algebraic function

Logarithmic function

Composite function

Exponential function

22 / 50

The notation f′(x) or y′ is used by:

Leibnitz

Lagrange

Newton

Cauchy

23 / 50

d/dx (sec⁻¹x) = ?

−1 / (|x|√(x²−1))

−1 / (|x|(1+x²))

1 / (|x|(1+x²))

1 / (|x|√(x²−1))

24 / 50

If y = sinh⁻¹(ax + b), then dy/dx = ?

cosh⁻¹(ax + b)

a / √(1 + (ax + b)²)

a·cosh⁻¹(ax + b)

1 / √(1 + (ax + b)²)

25 / 50

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

Undefined

Negative

Zero

Positive

26 / 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)

27 / 50

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

|x|>1, y∈R{0}

|x|>1, y∈[0, ∞)

x∈R, y∈R

|x|<1, y∈R

28 / 50

d/dx (sin a) = ?

0

−a cos a

a cos a

cos a

29 / 50

logₐa = ?

a²

1

Not defined

a

30 / 50

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

6x

3x² + 2

2x

3x

31 / 50

If f(x) = 1/x, then f′′(a) = ?

−1 / a²

1 / a²

−2 / a³

2 / a³

32 / 50

Derivative of tan(3x) is:

tan(3x)

sec²(3x)

6sec²(3x)

3sec²(3x)

33 / 50

1 − x + x² − x³ + x⁴ − ⋯ = ?

(−1 + x)⁻¹

1 / (x − 1)

1 / (1 + x)

1 / (1 − x)

34 / 50

If y = cosh⁻¹(sec x), then dy/dx = ?

cos x

−sin(sec x)

sec x

−sinh⁻¹(sec x)·tan x

35 / 50

(fog)′(x) = ?

Cannot be calculated

f′g

f′(g(x))·g′(x)

f′(g(x))

36 / 50

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

Point of concurrency

Common point

Corner point

Stationary point

37 / 50

Derivative of 2^x is:

e^x

2^x ln(2)

ln(x)·2^x

x·2^(x−1)

38 / 50

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

If x₁ < x₂, then f(x₁) = f(x₂)

If x₁ < x₂, then f(x₁) ≤ f(x₂)

If x₁ < x₂, then f(x₁) ≥ f(x₂)

If x₁ f(x₂)

39 / 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 − {0}, y ∈ R − {0}

x ∈ R, y ∈ R

40 / 50

d/dx (csc⁻¹x) = ?

1 / (|x|√(x²−1))

−1 / (|x|√(x²−1))

−1 / (|x|(1+x²))

1 / (|x|(1+x²))

41 / 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

42 / 50

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

f′(x) − g′(x)

f′(x) g′(x)

f′(x) + g′(x)

f(x) + g(x)

43 / 50

If y = e^(−ax), then dy/dx = ?

a² e^(−2ax)

−a e^(−ax)

−a e^(2ax)

−a² e^(−2ax)

44 / 50

d/dx (log₁₀x) = ?

x / ln10

1 / (x ln10)

1 / (x log₁₀e)

ln(x) / x

45 / 50

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

x∈[1, ∞), y∈[0, ∞)

x∈(1, ∞], y∈(0, ∞]

x∈R, y∈R

x<0, y<0

46 / 50

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

An imaginary number

An irrational number

A real number

A rational number

47 / 50

d/dx (cosx) - d²/dx² (sinx) = ?

2sinx

−2sinx

0

2cosx

48 / 50

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

f′(x) / f(x)

ln f′(x)

f′(x)

f(x) f′(x)

49 / 50

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

Newton

Leibnitz

Cauchy

Lagrange

50 / 50

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

−2/9

0

− 9/4

−1

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ALL FORCES Inter Base – Math Quiz 07

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