HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Evaluate : `∫1/(3+2sinx+cosx)dx`

With usual notations, in ΔABC, prove that a(b cos C − c cos B) = b² − c²

Find the co-ordinates of the point, which divides the line segment joining the points A(2, − 6, 8) and B(− 1, 3, − 4) externally in the ratio 1 : 3.

Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p

Evaluate: `int 1/(x(x-1)) dx`

Solve:

dy/dx = cos(x + y)

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

Evaluate `int 1/(3+ 2 sinx + cosx) dx`

Which of the following statements is correct?

The principal solutions of cot x = -`sqrt3`  are .................

`int "dx"/(9"x"^2 + 1)= ______. `

Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`

 In , ΔABC prove that 

`"sin"(("B" - "C")/2) = (("b" - "c")/"a") "cos"("A"/2)`                               

 In ,Δ ABC with usual notations prove that 
b² = c² +a² - 2 ca cos B

 In , ΔABC with usual notations prove that

(a-b)² cos² `("C"/2) +("a"+"b")^2 "sin"^2("C"/2) = "c"^2`

 Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log  |"x" +sqrt("x"^2 +"a"^2) | + "c"`

 Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`

Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 

Write the following compound statement symbolically.

The angle is right angle if and only if it is of measure 90°.

Write the following compound statement symbolically.

Angle is neither acute nor obtuse.