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

Solve:

dy/dx = cos(x + y)

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

if `y = tan^2(log x^3)`, find `(dy)/(dx)`

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.

Write the following compound statement symbolically.

If ΔABC is right-angled at B, then m∠A + m∠C = 90°.

Write the following compound statement symbolically. 

Hima Das wins gold medal if and only if she runs fast.

Write the following compound statement symbolically.

x is not irrational number but is a square of an integer.

Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p