﻿ Engineering Entrance Exam Question and Answers | Continuity and Differentiability - Zigya

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# Continuity and Differentiability

#### Multiple Choice Questions

1.

• $y\frac{\partial z}{\partial y}$

• $2\mathrm{y}\frac{\partial \mathrm{z}}{\partial \mathrm{y}}$

• $2\mathrm{y}\frac{\partial \mathrm{z}}{\partial \mathrm{x}}$

2.  is equal to
• 18/e4

• 27/e2

• 9/e2

• 9/e2

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3.

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

299 Views

4.

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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5.

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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6.

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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7.

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

154 Views

8.  equal to
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9.

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

• √3/4

• 3√2 /8

• 8/3√2

• 8/3√2

349 Views

10.
• does not exist

• equal

• equal

• equal

153 Views