# HSC Arts (Marathi Medium) 12th Board Exam [इयत्ता १२ वि] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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Differentiate the following w.r.t.x:

(x3 – 2x – 1)5

[0.021] Differentiation
Chapter: [0.021] Differentiation
Concept: Differentiation

Without using truth table show that

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

[0.011000000000000001] Mathematical Logic
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Truth Value of Statement

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

[0.026000000000000002] Differential Equations
Chapter: [0.026000000000000002] Differential Equations
Concept: Formation of Differential Equations

Without using truth table show that

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

[0.01] Mathematical Logic
Chapter: [0.01] Mathematical Logic
Concept: Truth Value of Statement

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

[0.03] Trigonometric Functions
Chapter: [0.03] Trigonometric Functions
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)

[0.03] Trigonometric Functions
Chapter: [0.03] Trigonometric Functions
Concept: Properties of Inverse Trigonometric Functions
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