ALL FORCES Inter Base – Math Quiz 07

⚔️ 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, 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 [f(x) + g(x)] = ?

f′(x) + g′(x)
f(x) + g(x)
f′(x) − g′(x)
f′(x) g′(x)

2 / 50

d/dx (sin a) = ?

a cos a
0
cos a
−a cos a

3 / 50

(dy/dx) | (x₁, y₁) represents:

Slope of normal at (x₁, y₁)
Slope of horizontal line at (x₁, y₁)
Increments of x and y at (x₁, y₁)
Slope of tangent at (x₁, y₁)

4 / 50

If y = cos(ax + b), then y″ = ?

a² cos(ax + b)
−a² cos(ax + b)
−a² sin(ax + b)
a² sin(ax + b)

5 / 50

If y = e^(−ax), then y″ = ?

−a² e^(−ax)
a² e^(ax)
−a e^(−ax)
a² e^(−ax)

6 / 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)

7 / 50

The notation f′(x) is used by:

Leibnitz
Cauchy
Newton
Lagrange

8 / 50

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

x ∈ R, y ∈ R
x ∈ [−1, 1], y ∈ R
x ∈ R − {0}, y ∈ R − {0}
x ∈ (0, 1], y ∈ [0, ∞)

9 / 50

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

Common point
Corner point
Point of concurrency
Stationary point

10 / 50

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

8e^(2x)
4e^(2x)
e^(2x)
2e^(2x)

11 / 50

d/dx (csc⁻¹x) = ?

−1 / (|x|√(x²−1))
−1 / (|x|(1+x²))
1 / (|x|√(x²−1))
1 / (|x|(1+x²))

12 / 50

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

A rational number
A real number
An imaginary number
An irrational number

13 / 50

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

f(x₂) x₁
f(x₂) < f(x₁) whenever x₂ < x₁
f(x₂) x₁
f(x₂) > f(x₁) whenever x₂ < x₁

14 / 50

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

Negative
Undefined
Positive
Zero

15 / 50

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

−1
−2/9
− 9/4
0

16 / 50

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

Zero
Positive
Negative
Undefined

17 / 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

18 / 50

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

ln f′(x)
f′(x) / f(x)
f′(x)
f(x) f′(x)

19 / 50

d/dx [g(x)]ⁿ = ?

n[g(x)]ⁿ⁻¹ g(x)
n[g(x)]ⁿ⁻¹ g′(x)
n[g(x)]ⁿ⁻¹
[g(x)]ⁿ⁻¹ g′(x)

20 / 50

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

x∈[1, ∞), y∈[0, ∞)
x<0, y<0
x∈(1, ∞], y∈(0, ∞]
x∈R, y∈R

21 / 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)

22 / 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)

23 / 50

d/dx (xⁿ) = n·xⁿ⁻¹ is called:

Constant rule
Product rule
Power rule
Quotient rule

24 / 50

logₐa = ?

a
Not defined
1
a²

25 / 50

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

g′(x) / [g(x)]²
−g′(x) / [g(x)]²
1 / [g(x)]²
1 / g′(x)

26 / 50

d/dx (10^sinx) = ?

10cosx · ln10
10^sinx · cosx · ln10
10sinx · ln10
10cosx

27 / 50

Derivative of 2^x is:

2^x ln(2)
e^x
x·2^(x−1)
ln(x)·2^x

28 / 50

1 − x + x² − x³ + x⁴ − ⋯ = ?

1 / (x − 1)
1 / (1 − x)
(−1 + x)⁻¹
1 / (1 + x)

29 / 50

If f(x) = 1/x, then f′′(a) = ?

−1 / a²
2 / a³
−2 / a³
1 / a²

30 / 50

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

Cauchy
Leibnitz
Newton
Lagrange

31 / 50

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

Algebraic function
Exponential function
Logarithmic function
Composite function

32 / 50

d/dx (sec⁻¹x) = ?

1 / (|x|(1+x²))
−1 / (|x|√(x²−1))
1 / (|x|√(x²−1))
−1 / (|x|(1+x²))

33 / 50

d/dx (log₁₀x) = ?

1 / (x log₁₀e)
x / ln10
1 / (x ln10)
ln(x) / x

34 / 50

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

x∈R, y∈R
|x|>1, y∈[0, ∞)
|x|<1, y∈R
|x|>1, y∈R{0}

35 / 50

f(x) = sin(x) is:

Even function
Identity function
Linear function
Odd function

36 / 50

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

Lagrange
Leibnitz
Cauchy
Newton

37 / 50

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

+ve or -ve
+ve only
-ve only
none of these

38 / 50

If y = cosh⁻¹(sec x), then dy/dx = ?

sec x
cos x
−sin(sec x)
−sinh⁻¹(sec x)·tan x

39 / 50

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

3x
6x
2x
3x² + 2

40 / 50

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

Taylor's series expansion
Taylor's Theorem
Convergent series
Maclaurin's series expansion

41 / 50

Derivative of (ax+b)^n is:

na(ax+b)^(n−1)
n(ax+b)^n
a(ax+b)^n
(ax+b)^(n−1)

42 / 50

Derivative of tan(3x) is:

sec²(3x)
tan(3x)
6sec²(3x)
3sec²(3x)

43 / 50

The notation f′(x) or y′ is used by:

Leibnitz
Lagrange
Newton
Cauchy

44 / 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
e
x
a

45 / 50

d/dx (cosx) - d²/dx² (sinx) = ?

2sinx
0
−2sinx
2cosx

46 / 50

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

x>0, y>0
x∈R, y∈R
x∈[−1, 1], y∈R
x∈(−1, 1), y∈R

47 / 50

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

-4
3 / √(1 − 9x²)
3x
−3 / √(1 − 9x²)

48 / 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

49 / 50

If y = e^(−ax), then dy/dx = ?

a² e^(−2ax)
−a e^(−ax)
−a² e^(−2ax)
−a e^(2ax)

50 / 50

(fog)′(x) = ?

f′(g(x))
f′g
Cannot be calculated
f′(g(x))·g′(x)

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ALL FORCES Inter Base – Math Quiz 07

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