HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Prove the following:

`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx 

Find the value of determinant : 

`|(2, -4),(7, -15)|`

Find the value of determinant :

`|(2"i", 3),(4, -"i")|`

Find the value of determinant :

`|(3, -4, 5),(1, 1, -2),(2, 3, 1)|`

Find the value of determinant :

`|("a", "h", "g"),("h", "b", "f"),("g", "f", "c")|`

Find the value of x if

`|(x^2 - x + 1, x + 1),(x + 1, x + 1)|` = 0

Find the value of x if `|(x, -1, 2),(2x, 1, -3),(3, -4, 5)|` = 29 

Find x and y if `|(4i, i^3, 2i),(1, 3i^2, 4),(5, -3, i)|` = x + iy where i² = –1

Answer the following question:

Evaluate `|(2, -5, 7),(5, 2, 1),(9, 0, 2)|`

Answer the following question:

Evaluate `|(1, -3, 12),(0, 2, -4),(9, 7, 2)|`

Answer the following question:

Find the value of x if

`|(1, 4, 20),(1, -2, -5),(1, 2x, 5x^2)|` = 0

Answer the following question:

Find the value of x if

`|(1, 2x, 4x),(1, 4, 16),(1, 1, 1)| = 0`

If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.

A(−5, 2) and B(4, 1). Find the equation of the locus of point P, which is equidistant from A and B

If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.

If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA² = 3PB² 

A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA² − PB² = 13

A(1, 6) and B(3, 5), find the equation of the locus of point P such that segment AB subtends right angle at P. (∠APB = 90°)

If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the point A(1, 3)

If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new coordinates of the point B(2, 5)