HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions

Select the correct answer from the given alternatives:

f(x) = `(x^2 - 7x + 10)/(x^2 + 2x - 8)`, for x ∈ [– 6, – 3]

Select the correct answer from the given alternatives:

If f(x) `{:(= "a"x^2 + "b"x + 1",", "for"  |x −1| ≥ 3), (= 4x + 5",", "for"  -2 < x < 4):}` is continuous everywhere then,

Select the correct answer from the given alternatives:

f(x) `{:(= ((16^x - 1)(9^x - 1))/((27^x - 1)(32^x - 1))",", "for"  x ≠ 0),(= "k"",", "for"  x = 0):}` is continuous at x = 0, then ‘k’ =

Select the correct answer from the given alternatives:

f(x) `{:(= (32^x - 8^x - 4^x + 1)/(4^x - 2^(x + 1) + 1)",", "for"  x ≠ 0),(= "k""," , "for"  x = 0):}` is continuous at x = 0, then value of ‘k’ is

Select the correct answer from the given alternatives:

If f(x) = `(12^x - 4^x - 3^x + 1)/(1 - cos 2x)`, for x ≠ 0 is continuous at x = 0 then the value of f(0) is ______.

Select the correct answer from the given alternatives:

If f(x) = `((4 + 5x)/(4 - 7x))^(4/x)`, for x ≠ 0 and f(0) = k, is continuous at x = 0, then k is

Select the correct answer from the given alternatives:

If f(x) = [x] for x ∈ (–1, 2) then f is discontinuous at

Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

f(x) `{:(= (x^2 - 3x - 10)/(x - 5)",", "for"  3 ≤ x ≤ 6","  x ≠ 5),(= 10",", "for"  x = 5),(=(x^2 - 3x - 10)/(x - 5)",", "for"  6 < x ≤ 9):}`

Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

f(x) `{:(= 2x^2 - 2x + 5",", "for"  0 ≤ x ≤ 2),(= (1 - 3x - x^2)/(1 - x) "," , "for"  2 < x < 4),(= (x^2 - 25)/(x - 5)",", "for"  4 ≤ x ≤ 7 and x ≠ 5),(= 7",", "for"  x = 5):}`

Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

f(x) = `(cos4x - cos9x)/(1 - cosx)`, for x ≠ 0

f(0) = `68/15`, at x = 0 on `- pi/2 ≤ x ≤ pi/2`

Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

f(x) `{:( = (sin^2pix)/(3(1 - x)^2) ",", "for"  x ≠ 1),(= (pi^2sin^2((pix)/2))/(3 + 4cos^2 ((pix)/2)) ",", "for"  x = 1):}}` at x = 1

Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

f(x) `{:(= (|x + 1|)/(2x^2 + x - 1)",", "for"  x ≠ -1),(= 0",", "for"  x = -1):}}` at x = – 1

Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

f(x) = [x + 1] for x ∈ [−2, 2)

Where [*] is greatest integer function.

Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

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

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

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

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