HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

Solve the following system of equations by the method of inversion.

x – y + z = 4, 2x + y – 3z = 0, x + y + z = 2

Solve the following system of equations by the method of reduction:

x + y + z = 6, y + 3z = 11, x + z = 2y.

In Δ ABC with the usual notations prove that `(a-b)^2 cos^2(C/2)+(a+b)^2sin^2(C/2)=c^2`

In any ΔABC if  a² , b² , c² are in arithmetic progression, then prove that Cot A, Cot B, Cot C are in arithmetic progression.

In a Δ ABC, with usual notations prove that:` (a -bcos C) /(b -a cos C )= cos B/ cos A`

In ΔABC with usual notations, prove that 2a `{sin^2(C/2)+csin^2 (A/2)}` = (a +   c - b)

In any ΔABC, with usual notations, prove that b² = c² + a² – 2ca cos B.

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`

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)`

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

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

 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`

Find the general solution of the following equation:

sinθ = `1/2`.

Find the general solution of the following equation:

4 cos² θ  = 3

State whether the following equation has a solution or not?

2sinθ = 3

Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(sqrt(2), pi/4)`

Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(3/4, (3pi)/4)`