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

Find: `int(x+3)sqrt(3-4x-x^2dx)`

Find `intsqrtx/sqrt(a^3-x^3)dx`

In Δ ABC, if a = 13, b = 14 and c = 15, then sin (A/2)= _______.

(A) `1/5`

(B) `sqrt(1/5)`

(C) `4/5`

(D) `2/5`

The angles of the ΔABC are in A.P. and b:c=`sqrt3:sqrt2` then find`angleA,angleB,angleC`

Evaluate: `int sqrt(tanx)/(sinxcosx) dx`

If in ∆ABC with usual notations a = 18, b = 24, c = 30 then sin A/2 is equal to

(A) `1/sqrt5`

(B) `1/sqrt10`

(C) `1/sqrt15`

(D) `1/(2sqrt5)`

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