HSC Arts (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

By computing the shortest distance, determine whether following lines intersect each other.

`(x - 5)/(4) = (y -7)/(-5) = (z + 3)/(-5) and (x - 8)/(7) = (y - 7)/(1) = (z - 5)/(3)`

By computing the shortest distance determine whether following lines intersect each other : `bar"r" = (hat"i" + hat"j" - hat"k") + lambda(2hat"i"  - hat"j" + hat"k") and bar"r" (2hat"i" + 2hat"j" - 3hat"k") + mu(hat"i" + hat"j" - 2hat"k")`

By computing the shortest distance determine whether the following lines intersect each other: `(x -5)/(4) = (y - 7)/(5) = (z + 3)/(5)` and x – 6 = y – 8 = z + 2.

Find the direction cosines of the lines `bar"r" = (-2hat"i" + 5/2hat"j" - hat"k") + lambda(2hat"i" + 3hat"j")`.

Choose correct alternatives :

The shortest distance between the lines `vecr = (hati + 2hatj + hatk) + lambda(hati - hatj + hatk) and vecr = (2hati - hatj - hatk) + μ(2hati + hatj + 2hatk)` is ______.

The direction ratios of the line 3x + 1 = 6y – 2 = 1 – z are ______.

Choose correct alternatives :

If the planes `bar"r".(2hat"i" - lambdahat"j" + hat"k") = 3 and bar"r".(4hat"i" - hat"j" + muhat"k") = 5` are parallel, then the values of λ and μ are respectively

Find the approximate values of : `sqrt(8.95)`

Find the approximate values of: `root(3)(28)`

Find the approximate values of : `root(5)(31.98)`

Find the approximate values of : (3.97)⁴ 

Find the approximate values of (4.01)³ 

Find the approximate values of : sin 61° , given that 1° = 0.0174^c, `sqrt(3) = 1.732`

Find the approximate values of sin (29° 30'), given that 1° = 0.0175°, `sqrt(3) = 1.732`.

Find the approximate values of : cos(60° 30°), given that 1° = 0.0175°, `sqrt(3) = 1.732`

Find the approximate values of : tan (45° 40'), given that 1° = 0.0175°.

Find the approximate values of : tan^–1(0.999)

Find the approximate values of : cot^–1 (0.999)

Find the approximate values of : tan^–1 (1.001)

Find the approximate values of : e^0.995, given that e = 2.7183.