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

Find the slope of tangent to the curve x = sin θ and y = cos 2θ at θ = `pi/6`

Find the equation of normal to the curve y = 2x³ – x² + 2 at `(1/2, 2)` 

Find points on the curve given by y = x³ − 6x² + x + 3, where the tangents are parallel to the line y = x + 5.

Find the cartesian equation of the plane passing through A(1, 2, 3) and the direction ratios of whose normal are 3, 2, 5.

Find the vector equation of the line `x/1 = (y - 1)/2 = (z - 2)/3`

Verify if the point having position vector `4hat"i" - 11hat"j" + 2hat"k"` lies on the line `bar"r" = (6hat"i" - 4hat"j" + 5hat"k") + lambda (2hat"i" + 7hat"j" + 3hat"k")`

Find the Cartesian equation of the line passing through  A(1, 2, 3) and having direction ratios 2, 3, 7

Find the vector equation of the line passing through the point having position vector `4hat i - hat j + 2hat"k"` and parallel to the vector `-2hat i - hat j + hat k`.

Find the Cartesian equation of the plane passing through the points (3, 2, 1) and (1, 3, 1)

Find the direction ratios of the line perpendicular to the lines

`(x - 7)/2 = (y + 7)/(-3) = (z - 6)/1` and `(x + 5)/1 = (y + 3)/2 = (z - 6)/(-2)`

Reduce the equation `bar"r"*(3hat"i" + 4hat"j" + 12hat"k")` = 8 to normal form

Find the Cartesian equation of the line passing through A(1, 2, 3) and B(2, 3, 4)

Find Cartesian equation of the line passing through the point A(2, 1, −3) and perpendicular to vectors `hat"i" + hat"j" + hat"k"` and `hat"i" + 2hat"j" - hat"k"`

Find the vector equation of the line passing through the point having position vector `-hat"i"- hat"j" + 2hat"k"` and parallel to the line `bar"r" = (hat"i" + 2hat"j" + 3hat"k") + mu(3hat"i" + 2hat"j" + hat"k")`, µ is a parameter

Find the Cartesian equation of the line passing through (−1, −1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z – 2

Find the Cartesian equation of the plane passing through A(7, 8, 6)and parallel to XY plane

Find the Cartesian equation of the plane passing through the points A(1, 1, 2), B(0, 2, 3) C(4, 5, 6)

Find m, if the lines `(1 - x)/3 =(7y - 14)/(2"m") = (z - 3)/2` and `(7 - 7x)/(3"m") = (y - 5)/1 = (6 - z)/5` are at right angles

Find the Cartesian and vector equation of the line passing through the point having position vector `hat"i" + 2hat"j" + 3hat"k"` and perpendicular to vectors `hat"i" + hat"j" + hat"k"` and `2hat"i" - hat"j" + hat"k"`

Find vector equation of the plane passing through A(−2 ,7 ,5) and parallel to vectors `4hat"i"  - hat"j" + 3hat"k"` and `hat"i" + hat"j" + hat"k"`