HSC Science (Computer Science) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Choose the correct option from the given alternatives:

If the surrounding air is kept at 20° C and a body cools from 80° C to 70° C in 5 minutes, the temperature of the body after 15 minutes will be

Show that the general solution of differential equation `"dy"/"dx" + ("y"^2 + "y" + 1)/("x"^2 + "x" + 1) = 0` is given by (x + y + 1) = (1 - x - y - 2xy).

The normal lines to a given curve at each point (x, y) on the curve pass through (2, 0). The curve passes through (2, 3). Find the equation of the curve.

The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after t seconds.

A person’s assets start reducing in such a way that the rate of reduction of assets is proportional to the square root of the assets existing at that moment. If the assets at the beginning ax ‘ 10 lakhs and they dwindle down to ‘ 10,000 after 2 years, show that the person will be bankrupt in `2 2/9` years from the start.

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers. Find E(X).

The separate equations of the lines represented by `3x^2 - 2sqrt(3)xy - 3y^2` = 0 are ______ 

The equation 4x² + 4xy + y² = 0 represents two ______ 

Auxillary equation of 2x² + 3xy − 9y² = 0 is ______ 

If 2x + y = 0 is one of the line represented by 3x² + kxy + 2y² = 0 then k = ______ 

Find the separate equations of the lines given by x² + 2xy tan α − y² = 0 

Find the joint equation of pair of lines through the origin which is perpendicular to the lines represented by 5x² + 2xy - 3y² = 0 

If f(x) = log_x (log x) then f'(e) is ______

If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` = ______.

If y = log [cos(x⁵)] then find `("d"y)/("d"x)`

If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`

If y = `log[4^(2x)((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)]`, find `("d"y)/("d"x)`

If log₅ `((x^4 + "y"^4)/(x^4 - "y"^4))` = 2, show that `("dy")/("d"x) = (12x^3)/(13"y"^2)`

If y = 5^x. x⁵. x^x. 5⁵ , find `("d"y)/("d"x)`

If x⁷ . y⁵ = (x + y)¹², show that `("d"y)/("d"x) = y/x`