HSC Science (General) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

Identify discontinuity for the following function as either a jump or a removable discontinuity on their respective domain:

f(x) `{:(= x^2 + 5x + 1"," , "for"  0 ≤ x ≤ 3),(= x^3 + x + 5"," , "for"  3 < x ≤ 6):}`

Identify discontinuity for the following function as either a jump or a removable discontinuity on their respective domain:

f(x) `{:(= (x^2 + x + 1)/(x + 1)"," , "for"  x ∈ [0, 3)),(=(3x +4)/(x^2 - 5)"," , "for"  x ∈ [3, 6]):}`

Discuss the continuity of the following function at the point or on the interval indicated against them. If the function is discontinuous, identify the type of discontinuity and state whether the discontinuity is removable. If it has a removable discontinuity, redefine the function so that it becomes continuous:

f(x) = `((x + 3)(x^2 - 6x + 8))/(x^2 - x - 12)`

Discuss the continuity of the following function at the point or on the interval indicated against them. If the function is discontinuous, identify the type of discontinuity and state whether the discontinuity is removable. If it has a removable discontinuity, redefine the function so that it becomes continuous:

f(x) `{:(= x^2 + 2x + 5"," , "for"  x ≤ 3),( = x^3 - 2x^2 - 5",", "for"  x > 3):}`

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

f(x) `{:(= ((5x - 8)/(8 - 3x))^(3/(2x - 4))",", "for"  x ≠ 2),(= "k"",", "for"  x = 2):}}` at x = 2

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°.