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Mathematics and Statistics

**Differentiate the following w.r.t.x: **

(x^{3} – 2x – 1)^{5}

Chapter: [0.021] Differentiation

Concept: Differentiation

Concept: Differentiation

**Without using truth table show that**

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)

Chapter: [0.011000000000000001] Mathematical Logic

Concept: Truth Value of Statement

Concept: Truth Value of Statement

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Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis

Chapter: [0.026000000000000002] Differential Equations

Concept: Formation of Differential Equations

Concept: Formation of Differential Equations

**Without using truth table show that**

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)

Chapter: [0.01] Mathematical Logic

Concept: Truth Value of Statement

Concept: Truth Value of Statement

What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?

Chapter: [0.03] Trigonometric Functions

Concept: Inverse Trigonometric Functions > Inverse Trigonometric Functions - Principal Value Branch

Concept: Inverse Trigonometric Functions > Inverse Trigonometric Functions - Principal Value Branch

Prove that `tan^-1x + tan^-1 (2x)/(1 - x^2) = tan^-1 (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`

Chapter: [0.03] Trigonometric Functions

Concept: Properties of Inverse Trigonometric Functions

Concept: Properties of Inverse Trigonometric Functions

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