\(\int _{ 2 }^{ 4 }{ \frac { dx }{ x } } \) is _______.

(a)

log 4

(b)

0

(c)

log 2

(d)

log 8

\(\int { \frac { { e }^{ log\sqrt { x } } }{ x } } \) dx = ________________ +c

(a)

2\( \sqrt { x } \)

(b)

\(\sqrt { x } \)

(c)

\(\frac { 1 }{ \sqrt { x } } \)

(d)

\(\frac { 1 }{ x } \)

Area bounded by y = x between the lines y = 1, y = 2 with y = axis is ________.

(a)

\(\frac{1}{2}\) sq.units

(b)

\(\frac{5}{2}\) sq.units

(c)

\(\frac{3}{2}\) sq.units

(d)

1 sq.unit

The are bounded by the demand curve xy = 1, the X-axis, x = 1 and x = 2 is ________

(a)

log 2

(b)

log \(\frac{1}{2}\)

(c)

2 log 2

(d)

\(\frac{1}{2}\)log 2

The particular integral of the differential equation is \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx } \) + 16y = 2e^4x ______.

(a)

\(\frac { { x }^{ 2 }{ e }^{ 4x } }{ 2! } \)

(b)

\(\frac { { e }^{ 4x } }{ 2! } \)

(c)

x²e^4x

(d)

xe^4x

Let y = f(x) be a given function of x and y₀, _y1., yn be the values of y at x = x₀, x₁, x₂ ... respectively, then ∇y₁ is ______________

(a)

y₁ - y₂

(b)

y₀ - y₂

(c)

y₀ - y₁

(d)

y₁ - y₀

A discrete probability function p(x) is always non-negative and always lies between ________.

(a)

0 and \(\infty \)

(b)

0 and 1

(c)

–1 and +1

(d)

–∞ and +∞

Variance of the random variable. X is 4, Its mean is 2. Then E(X²) is _________

(a)

2

(b)

4

(c)

6

(d)

8

Errors in sampling are of  ______.

(a)

Two types

(b)

three types

(c)

four types

(d)

five types

How many causes of variation will affect the quality of a product?

(a)

4

(b)

3

(c)

2

(d)

1