﻿ IIT - JEE Main Important Questions of Continuity and Differentiability | Zigya

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# Continuity and Differentiability

#### Multiple Choice Questions

1.  is equal to
• 18/e4

• 27/e2

• 9/e2

• 9/e2

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2.

The area (in sq. units) of the region is

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3.

If a curve y=f(x) passes through the point (1, −1) and satisfies the differential equation, y(1+xy) dx=x dy, then f(-1/2) is equal to

• -2/5

• -4/5

• 2/5

• 2/5

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4.

If f and ga re differentiable  functions in (0,1) satisfying f(0) =2= g(1), g(0) = 0 and f(1) = 6, then for some c ε] 0,1[

• 2f'(c) = g'(c)

• 2f'(c) = 3g'(c)

• f'(c) = g'(c)

• f'(c) = g'(c)

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5.

The population p(t) at time t of a certain mouse species satisfies the differential equation . if p (0) = 850, then the  time at which the population becomes zero is

• 2 log 18

• log 9

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6.

Consider the function f(x) = |x – 2| + |x – 5|, x ∈ R.
Statement 1: f′(4) = 0
Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).

• 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

• 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 true; statement 2 is not a correct explanation for statement 1

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7.  equal to
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8.

The shortest distance between line y - x = 1 and curve x = y2 is

• √3/4

• 3√2 /8

• 8/3√2

• 8/3√2

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9.
• does not exist

• equal

• equal

• equal

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10.

Let f : R → R be a continuous function defined
by f(x) = 1/ex + 2e-x
Statement - 1: f(c) = 1/3, for some c ∈ R.
Statement-2: 0 < f(x)≤ , for all x ∈ R.

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

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