If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

(a)

3

(b)

± 3

(c)

± 6

(d)

6

\(\int { { 3 }^{ x+2 } } \) dx = ______________ +c

(a)

\(\frac { { 3 }^{ x } }{ log3 } \)

(b)

\(\frac { 9\left( { 3 }^{ x } \right) }{ log3 } \)

(c)

\(\frac { 3.{ 3 }^{ x } }{ log3 } \)

(d)

\(\frac { { 3 }^{ x } }{ 9log3 } \)

\(\int { \frac { { x }^{ 5 }-{ x }^{ 4 } }{ { x }^{ 3 }-{ x }^{ 2 } } } \)dx = __________ +c

(a)

1

(b)

\(\frac { x }{ 2 } \)

(c)

\(\frac { { x }^{ 3 } }{ 2 } \)

(d)

\(\frac { { x }^{ 2 } }{ 2 } \)

\(\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,\) where f(x) =  \(\begin{cases} 7x+3\quad if\quad 1\le x\le 3 \\ 8x\quad if\quad 3\le x\le 4 \end{cases}\) is _____________.

(a)

58

(b)

60

(c)

62

(d)

52

The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.

(a)

\(\frac{13}{3}\)

(b)

13

(c)

\(\frac{26}{3}\)

(d)

\(\frac{3}{13}\)

The area bounded by y = x, the Y-axis and y = 1is_________.

(a)

1

(b)

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

(c)

log 2

(d)

2

The differential equation satisfied by all the straight lines in xy plane is _____________

(a)

\(\frac { dy }{ dx } \)=a constant

(b)

\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)=0

(c)

y+ \(\frac { dy }{ dx } \) = 0

(d)

\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } \)+y=0

The integrating factor of x\(\frac { dy }{ dx } \)-y = e^x is _____________

(a)

log x

(b)

e^-yx

(c)

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

(d)

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

If \(\frac { dy }{ dx } =\frac { x-y }{ x+y } \), then the solution is _______

(a)

2xy+y²+x²=c

(b)

x²+y²-x+y=c

(c)

x²+y²-2xy=c

(d)

x²-y²-2xy=c

If c is a constant, then Δc.f(x) ______________

(a)

0

(b)

c.f(Δx)

(c)

c.Δf(x)

(d)

f(Δcx)

If the values of x are not at equi-distant then we can use ______________

(a)

Newton's forward interpolation

(b)

Newton's backward interpolation

(c)

Lagrange's formula

(d)

graphical method.

The differences of the first differences are ________________

(a)

Δ²y₀, Δ²y₁,...,∆²y_n

(b)

Δy₀, Δy₁,..., Δy_n

(c)

Δ²y₀

(d)

Δy₀

If y is to be estimated for the value of x between two extreme points in a set of values, it is called ___________

(a)

Interpolation

(b)

extrapolation

(c)

Forward interpolation

(d)

backward interpolation

X is a discrete random variable. Which take values 0,1,2 and P(X = 0) = \(\frac{144}{169}\), P(X = 1) = \(\frac{1}{169}\), then the value of P(X = 2) is ________

(a)

\(\frac{145}{169}\)

(b)

\(\frac{24}{169}\)

(c)

\(\frac{2}{169}\)

(d)

\(\frac{143}{169}\)

If f(x) = cx², 0

(a)

\(\frac{1}{3}\)

(b)

\(\frac{4}{3}\)

(c)

\(\frac{8}{3}\)

(d)

\(\frac{3}{8}\)

If f(x) = kx(1-x), 0< x < 1 is a p.d.f. then the value of k is ________.

(a)

\(\frac{1}{5}\)

(b)

\(\frac{2}{5}\)

(c)

\(\frac{3}{5}\)

(d)

6

If f(x) = kx(1-x), 0< x < 1 is a p.d.f. then the value of k is ________.

(a)

\(\frac{1}{5}\)

(b)

\(\frac{2}{5}\)

(c)

\(\frac{3}{5}\)

(d)

6

If X is a discrete random variable then which of the following is correct?

(a)

0 ≤ F(x) ≤ 1

(b)

F(-∞) = 0,F(∞) ≤ 1

(c)

P(X = X_n) = F(X_n)-F(X_n-1)

(d)

F(x) is a constant function

In case of normal distribution, skewness is ___________

(a)

1

(b)

0

(c)

2

(d)

3

If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to ________

(a)

\(\frac{5}{16}\)

(b)

\(\frac{11}{16}\)

(c)

\(\frac{10}{16}\)

(d)

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

For a standard normal distribution, the mean and variance are _________

(a)

μ,σ²

(b)

μ,σ

(c)

0,1

(d)

1,1

Which of the following statements is true?

(a)

point estimate gives a range of value

(b)

sampling is done only to estimate a statistic

(c)

sampling is done to estimate the population parameter

(d)

sampling is not possible for an infinite population

The point estimate mean of the following data is __________.
21.1, 25.0, 20.0, 16.0, 12.0, 10.0, 17.0, 18.0, 13.0,11.0

(a)

16.3

(b)

13.6

(c)

21.21

(d)

212:10

The causes leading to vast variation in the specification of a product are usually due to _____

(a)

random process

(b)

assignable causes

(c)

non-traceable causes

(d)

all the above

Choose the odd one out

(a)

Secular trend

(b)

seasonal variation

(c)

Simple averages

(d)

cyclic variations

Vogel's approximation method yields an initial basic feasible solution which is very close to the solution.

(a)

maximum

(b)

minimum

(c)

optimum

(d)

unique

Operation research is an analytical method of ___________

(a)

problem solving

(b)

decision making

(c)

optimal cost of transportation

(d)

unit cost of transportation