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

The notation f′(x) or y′ is used by:

Cauchy

Newton

Lagrange

Leibnitz

2 / 50

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

−g′(x) / [g(x)]²

1 / g′(x)

g′(x) / [g(x)]²

1 / [g(x)]²

3 / 50

(fog)′(x) = ?

f′g

f′(g(x))

Cannot be calculated

f′(g(x))·g′(x)

4 / 50

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

3x

3x² + 2

2x

6x

5 / 50

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

|x|>1, y∈R{0}

|x|>1, y∈[0, ∞)

|x|<1, y∈R

x∈R, y∈R

6 / 50

If f(x) = 1/x, then f′′(a) = ?

−1 / a²

1 / a²

2 / a³

−2 / a³

7 / 50

(dy/dx) | (x₁, y₁) represents:

Slope of horizontal line at (x₁, y₁)

Slope of normal at (x₁, y₁)

Slope of tangent at (x₁, y₁)

Increments of x and y at (x₁, y₁)

8 / 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

9 / 50

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

f(x) f′(x)

f′(x) / f(x)

f′(x)

ln f′(x)

10 / 50

f(x) = sin(x) is:

Odd function

Even function

Linear function

Identity function

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 ∈ [−1, 1], y ∈ R

x ∈ R, y ∈ R

12 / 50

d/dx (cosx) - d²/dx² (sinx) = ?

0

2sinx

2cosx

−2sinx

13 / 50

d/dx (10^sinx) = ?

10cosx

10^sinx · cosx · ln10

10cosx · ln10

10sinx · ln10

14 / 50

If y = cosh⁻¹(sec x), then dy/dx = ?

−sin(sec x)

−sinh⁻¹(sec x)·tan x

cos x

sec x

15 / 50

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

Lagrange

Leibnitz

Newton

Cauchy

16 / 50

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

f′(x) − g′(x)

f(x) + g(x)

f′(x) + g′(x)

f′(x) g′(x)

17 / 50

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

x<0, y<0

x>0, y>0

x∈R, y>0

x∈R, y∈R

18 / 50

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

a

x

10

e

19 / 50

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

Convergent series

Taylor's series expansion

Taylor's Theorem

Maclaurin's series expansion

20 / 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)

21 / 50

d/dx (log₁₀x) = ?

x / ln10

1 / (x log₁₀e)

ln(x) / x

1 / (x ln10)

22 / 50

d/dx [g(x)]ⁿ = ?

n[g(x)]ⁿ⁻¹

[g(x)]ⁿ⁻¹ g′(x)

n[g(x)]ⁿ⁻¹ g(x)

n[g(x)]ⁿ⁻¹ g′(x)

23 / 50

If y = e^(−ax), then dy/dx = ?

−a e^(−ax)

−a e^(2ax)

a² e^(−2ax)

−a² e^(−2ax)

24 / 50

Derivative of (ax+b)^n is:

(ax+b)^(n−1)

na(ax+b)^(n−1)

n(ax+b)^n

a(ax+b)^n

25 / 50

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

Corner point

Common point

Point of concurrency

Stationary point

26 / 50

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

+ve only

-ve only

+ve or -ve

none of these

27 / 50

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

x∈[−1, 1], y∈R

x∈R, y∈R

x>0, y>0

x∈(−1, 1), y∈R

28 / 50

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

2e^(2x)

4e^(2x)

8e^(2x)

e^(2x)

29 / 50

If y = sinh⁻¹(ax + b), then dy/dx = ?

1 / √(1 + (ax + b)²)

a·cosh⁻¹(ax + b)

cosh⁻¹(ax + b)

a / √(1 + (ax + b)²)

30 / 50

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

Undefined

Zero

Positive

Negative

31 / 50

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

x<0, y<0

x∈R, y∈R

x∈(1, ∞], y∈(0, ∞]

x∈[1, ∞), y∈[0, ∞)

32 / 50

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

Lagrange

Newton

Cauchy

Leibnitz

33 / 50

d/dx (csc⁻¹x) = ?

1 / (|x|√(x²−1))

1 / (|x|(1+x²))

−1 / (|x|(1+x²))

−1 / (|x|√(x²−1))

34 / 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)

35 / 50

d/dx (xⁿ) = n·xⁿ⁻¹ is called:

Quotient rule

Product rule

Constant rule

Power rule

36 / 50

If y = cos(ax + b), then y″ = ?

−a² sin(ax + b)

a² cos(ax + b)

−a² cos(ax + b)

a² sin(ax + b)

37 / 50

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

−1

− 9/4

0

−2/9

38 / 50

The notation f′(x) is used by:

Newton

Cauchy

Leibnitz

Lagrange

39 / 50

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

x ∈ [−1, 1], y ∈ R

x ∈ R − {0}, y ∈ R − {0}

x ∈ (0, 1], y ∈ [0, ∞)

x ∈ R, y ∈ R

40 / 50

Derivative of tan(3x) is:

sec²(3x)

3sec²(3x)

6sec²(3x)

tan(3x)

41 / 50

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

Algebraic function

Exponential function

Composite function

Logarithmic function

42 / 50

d/dx (sec⁻¹x) = ?

−1 / (|x|(1+x²))

1 / (|x|√(x²−1))

1 / (|x|(1+x²))

−1 / (|x|√(x²−1))

43 / 50

1 − x + x² − x³ + x⁴ − ⋯ = ?

1 / (x − 1)

1 / (1 − x)

1 / (1 + x)

(−1 + x)⁻¹

44 / 50

d/dx (sin a) = ?

a cos a

0

−a cos a

cos a

45 / 50

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

−3 / √(1 − 9x²)

3 / √(1 − 9x²)

-4

3x

46 / 50

If y = e^(−ax), then y″ = ?

−a² e^(−ax)

−a e^(−ax)

a² e^(ax)

a² e^(−ax)

47 / 50

Derivative of 2^x is:

e^x

ln(x)·2^x

x·2^(x−1)

2^x ln(2)

48 / 50

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

Undefined

Positive

Negative

Zero

49 / 50

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

A rational number

An irrational number

A real number

An imaginary number

50 / 50

logₐa = ?

a²

1

a

Not defined

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ALL FORCES Inter Base – Math Quiz 07

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