MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 49

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MHT-CET

IMPORTANT

Earn 100

The number of discontinuities of the greatest integer function $f (x) = [x], x \in (- \frac{7}{2}, 100)$ is equal to

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Important Questions on Continuity

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 50

If the function

f (x) = \{\begin{cases} 5 x - 4, & if 0 < x \leq 1 \\ 4 x^{2} + 3 b x, & if 1 < x < 2 \end{cases}

is continuous at every point of its domain, then the value of

b

is

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 51

Let

f (x) = \{\begin{cases} \frac{x^{3} + x^{2} - 16 x + 20}{{(x - 2)}^{2}}; & if x \neq 2 \\ k; & x = 2 \end{cases}

. If

f (x)

is continuous for all

x

, then

k =

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 52

The function

f (x) = [x]

, where

[x]

the greatest function is continuous at

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 53

The function

f (x) = \sin |x|

is

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 54

Let

f (x) = \frac{1 - \tan x}{4 x - π}, x \neq \frac{π}{4}, x \in [0, \frac{π}{2}]

. If

f (x)

is continuous in

[0, \frac{π}{2}]

, then

f (\frac{π}{4})

is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 55

If the function

f (x) = \frac{2 x - \sin^{- 1} x}{2 x + \tan^{- 1} x}, (x \neq 0)

is continuous at each point of its domain, then the value of

f (0)

is

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 56

The function

f (x) = \{\begin{cases} x + 2 & , 1 \leq x < 2 \\ 4 & , x = 2 \\ 3 x - 2 & , x > 2 \end{cases}

is continuous at

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 2 - Continuity>Competitive Thinking>Q 57

The value(s) of

x

for which the function

f (x) = \{\begin{matrix} 1 - x & , & x < 1 \\ (1 - x) (2 - x) & , & 1 \leq x \leq 2 \\ 3 - x & , & x > 2 \end{matrix}

fails to be continuous is (are)