HSC Science (Computer Science) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Find the combined equation of lines passing through the origin and each of which making an angle of 60° with the Y-axis.

Choose correct alternatives:

If acute angle between lines ax² + 2hxy + by² = 0 is, `pi/4`, then 4h² = ______.

Find the joint equation of the pair of lines which bisect angles between the lines given by x² + 3xy + 2y² = 0 

Show that the lines x² − 4xy + y² = 0 and x + y = 10 contain the sides of an equilateral triangle. Find the area of the triangle. 

If the slope of one of the lines given by ax² + 2hxy + by² = 0 is three times the other, prove that 3h² = 4ab.

Show that the line 3x + 4y + 5 = 0 and the lines (3x + 4y)² - 3(4x - 3y)² = 0 form the sides of an equilateral triangle.

Show that the lines x² - 4xy + y² = 0 and the line x + y = `sqrt6` form an equilateral triangle. Find its area and perimeter.

If the slope of one of the lines given by ax² + 2hxy + by² = 0 is square of the slope of the other line, show that a²b + ab² + 8h³ = 6abh.

Prove that the product of length of perpendiculars drawn from P(x₁, y₁) to the lines represented by ax² + 2hxy + by² = 0 is `|("ax"_1^2 + "2hx"_1"y"_1 + "by"_1^2)/(sqrt("a - b")^2 + "4h"^2)|`

Show that the difference between the slopes of the lines given by (tan²θ + cos²θ)x² − 2xy tan θ + (sin²θ)y² = 0 is two.

In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA

In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `(A/2)`.

In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`

In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`

In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)

In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA.

In ΔABC prove that `(b + c - a) tan  "A"/(2) = (c + a - b)tan  "B"/(2) = (a + b - c)tan  "C"/(2)`.

In ΔABC prove that `sin  "A"/(2). sin  "B"/(2). sin  "C"/(2) = ["A(ΔABC)"]^2/"abcs"`

Find the principal value of the following: `sin^-1 (1/2)`

Find the principal value of the following: cosec^{- 1}(2)