HSC Science (Computer Science) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Prove the following:

If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`

Prove the following:

`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)

Prove the following:

tanA + tan(60° + A) + tan(120° + A) = 3 tan 3A

Prove the following:

3tan⁶10° – 27 tan⁴10° + 33tan²10° = 1

Prove the following:

tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A

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.