HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find p and q, if the equation 2x² + 8xy + py² + qx + 2y - 15 = 0 represents a pair of parallel lines.

Equations of pairs of opposite sides of a parallelogram are x² - 7x + 6 = 0 and y² − 14y + 40 = 0. Find the joint equation of its diagonals.

Find the separate equation of the line represented by the following equation:

10(x + 1)² + (x + 1)(y - 2) - 3(y - 2)² = 0 

ΔOAB is formed by the lines x² - 4xy + y² = 0 and the line AB. The equation of line AB is 2x + 3y - 1 = 0. Find the equation of the median of the triangle drawn from O.

Find the coordinates of the points of intersection of the lines represented by x² − y² − 2x + 1 = 0

Find k, if the slopes of lines given by kx² + 5xy + y² = 0 differ by 1.

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following:

y = `sqrt(x)`

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^-1(y) in the following: y = `sqrt(2 - sqrt(x)`

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^-1(y) in the following: y = `root(3)(x - 2)`

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following:

y = log(2x – 1)

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following: y = 2x + 3

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following: y = e^x – 3

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following: y = e^2x-3 

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following: y = `log_2(x/2)`

Find the derivative of the inverse function of the following : y = x²·e^x 

Find the derivative of the inverse function of the following : y = x cos x

Find the derivative of the inverse function of the following : y = x ·7^x 

Find the derivative of the inverse function of the following : y = x² + log x

Find the derivative of the inverse function of the following : y = x log x

Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = x⁵ + 2x³ + 3x, at x = 1