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

Assume that `f'(3) = -1,"g"'(2) = 5, "g"(2) = 3 and y = f["g"(x)], "then" ["dy"/"dx"]_(x = 2) = ?`

If h(x) = `sqrt(4f(x) + 3"g"(x)), f(1) = 4, "g"(1) = 3, f'(1) = 3, "g"'(1) = 4, "find h"'(1)`.

Find the x co-ordinates of all the points on the curve y = sin 2x − 2 sin x, 0 ≤ x < 2π, where `"dy"/"dx"` = 0.

Select the appropriate hint from the hint basket and fill up the blank spaces in the following paragraph. [Activity]:

"Let f(x) = x² + 5 and g (x) = e^x + 3 then
f[g(x)] = .......... and g[f(x)] =...........
Now f'(x) = .......... and g'(x) = ..........
The derivative of f[g(x)] w. r. t. x in terms of f and g is ..........

Therefore `"d"/"dx"[f["g"(x)]]` = .......... and

`["d"/"dx"[f["g"(x)]]]_(x  =  0)` = ..........
The derivative of g[f(x)] w. r. t. x in terms of f and g is

Therefore `"d"/"dx"["g"[f(x)]]` = .......... and

`["d"/"dx"["g"[f(x)]]]_(x  = -1)` = .........."

Hint basket : `{f'["g"(x)]·"g"'(x), 2e^(2x) + 6e^x, 8, "g"' [ f (x)]· f'(x),2xe^(x^2+5),  − 2e^6,e^(2x) + 6e^x + 14, e^(x^2+5) + 3, 2x, e^x}`

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.

Find the approximate values of : e^2.1, given that e² = 7.389

Find the approximate values of : 3^2.01, given that log 3 = 1.0986

Find the approximate values of : log_e(101), given that log_e10 = 2.3026.