HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Determine whether the following statement pattern is a tautology, contradiction, or contingency:

[(p ∨ q) ∧ ∼p] ∧ ∼q

Determine whether the following statement pattern is a tautology, contradiction, or contingency:

(p → q) ∧ (p ∧ ∼q)

Determine whether the following statement pattern is a tautology, contradiction or contingency:

[p → (q → r)] ↔ [(p ∧ q) → r]

Determine whether the following statement pattern is a tautology, contradiction or contingency:

[(p ∧ (p → q)] → q

Determine whether the following statement pattern is a tautology, contradiction or contingency:

(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)

Determine whether the following statement pattern is a tautology, contradiction or contingency:

[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r

Determine whether the following statement pattern is a tautology, contradiction or contingency:

(p → q) ∨ (q → p)

In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA

In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `(A/2)`.

In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`

In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`

In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)

In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA.

In ΔABC prove that `(b + c - a) tan  "A"/(2) = (c + a - b)tan  "B"/(2) = (a + b - c)tan  "C"/(2)`.

In ΔABC prove that `sin  "A"/(2). sin  "B"/(2). sin  "C"/(2) = ["A(ΔABC)"]^2/"abcs"`

Find the principal value of the following: `sin^-1 (1/2)`

Find the principal value of the following: cosec^{- 1}(2)

Find the principal value of the following: tan^-1(– 1)

Find the principal value of the following: tan^{- 1}( - √3)

Find the principal value of the following: sin^-1 `(1/sqrt(2))`