HSC Arts (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find k if following function is continuous at the point indicated against them:

f(x) `{:(= (45^x - 9^x - 5^x + 1)/(("k"^x - 1)(3^x - 1))",", "for"  x ≠ 0),(= 2/3",", "for"  x = 0):}}` at x = 0

Find a and b if following function is continuous at the point or on the interval indicated against them:

f(x) `{:(= (4tanx + 5sinx)/("a"^x - 1)",", "for"  x < 0),(= (9)/(log2)",", "for"  x = 0),(= (11x + 7x*cosx)/("b"^x - 1)",", "for"  x > 0):}`

Find a and b if following function is continuous at the point or on the interval indicated against them:

f(x) `{:(= "a"x^2 + "b"x + 1",", "for"  |2x - 3| ≥ 2),(= 3x + 2",", "for"  1/2 < x < 5/2):}`

Find f(a), if f is continuous at x = a where,

f(x) = `(1 + cos(pi x))/(pi(1 - x)^2)`, for x ≠ 1 and at a = 1

Find f(a), if f is continuous at x = a where,

f(x) = `(1 - cos[7(x - pi)])/(5(x - pi)^2`, for x ≠ π at a = π

Solve using intermediate value theorem:

Show that 5^x − 6x = 0 has a root in [1, 2]

Solve using intermediate value theorem:

Show that x³ − 5x² + 3x + 6 = 0 has at least two real root between x = 1 and x = 5

Evaluate the limit:

`lim_(x->0)[(sqrt(6+x+x^2) -sqrt6)/x]`

Answer the following:

Find the trigonometric functions of :

90°

Answer the following:

Find the trigonometric functions of :

240°

Find the value of:

sin 15°

Find the values of:

cos 75°

Find the values of:

tan 105°

Find the values of:

cot 225°

Find the value of sin 690°.

Find the value of :

sin (495°)

Find the value of :

cos 315°

Find the value of :

cos (600°)

Find the value of :

tan 225°

Find the value of :

tan (– 690°)