MCQ (Previous Year Questions) - Continuity And Differentiability (Competition Level 1) - JEE MCQ

    Continuous at x = 0

    Continuous in (-1, 0)

    Differentiable at x = 1

    Differentiable in (-1, 1)

3

4

5

6

discontinuous everywhere

continuous as well as differentiable for all x

continuous for all x but not differentiable at x = 0

neither differentiable nor continuous at x = 0

1

1/2

– 1/2

–1

–1

0

2

1

3

4

5

6

2

–1

0

1

f(x) ≥ 1 for al l x ∈ R

f(x) i s not differentiable at x = 1

f(x) is differentiable everywhere

f(x) i s not differentiable at x = 0

f is differentiable at x = 0 and at x = 1

f is differentiable at x = 0 but not at x = 1

f is differentiable at x = 1 but not at x = 0

f is neither differentiable at x = 0 nor at x = 1

Statement - 1 is true, Statement - 2 is true; S tatement - 2 is a correct explanation for Statement -1

Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.

Statement -1 is true, Statement -2 is false.

Statement -1 is false, Statement -2 is ture.

Statement (1) is true and statement (2) is true and st atem ent ( 2) is correct ex planation for Statement (1)

Statement (1) is true and statement (2) i s tr ue an d statem ent ( 2) i s NOT a cor rect explanation for Statement (1)

Statement (1) is true but (2) is false

Statement (1) is false but (2) is true

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for statement 1.

Statement 1 is true, Statement 2 is false.

Statement 1 is false, Statement 2 is true.

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for statement 1.

discontinuous only at non-zero integral values of x.

continuous only at x = 0.

continuous for every real x.

discontinuous only at x = 0.

all integers

all integers except 0 & 1

all integers except 0

all integers except 1

a = ln 2/3 ;b = 3/2 ; c = 1

a = ln 2/3 ;b = 2/2 ; c = 1

a = ln 3/2 ;b = 3/2 ; c = 1

{–1, 1}

{–1, 0}

{0, 1}

{–1, 0, 1}

(–1)^k(k – 1)π

(–1)^{k – 1}(k – 1)π

(–1)^k kπ

(–1)^{k – 1} k π

cos (| x |) + | x |

cos (| x |) – | x |

sin (| x |) + | x |

sin (| x |) – | x |

1

e^1/2

e²

e³

f(x) is continuous 

f(x) is not differentiable but continious

f(x) is not differentiable for two values of x

n = 1, m = 1

n = 1, m = –1

n = 2, m = 2

n > 2, m = n