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

If \(\int { \frac { 1 }{ \left( x+2 \right) \left( { x }^{ 2 }+1 \right) } } \) dx = a log \(\left| 1+{ x }^{ 2 } \right| \) +b tan^-1 x + \(\frac { 1 }{ 5 } log\left| x+2 \right| \) +c then ___________

(a)

\(a=-\frac { 1 }{ 10 } ,b=\frac { -2 }{ 5 } \)

(b)

\(a=\frac { 1 }{ 10 } ,b=\frac { -2 }{ 5 } \)

(c)

\(a=-\frac { 1 }{ 10 } ,b=\frac { 2 }{ 5 } \)

(d)

\(a=\frac { 1 }{ 10 } ,b=\frac { 2 }{ 5 } \)

∫ e^{3 log x} (x⁴ +1)^-1 dx = ____________ +c

(a)

\(\log { \left| { x }^{ 4 }+1 \right| } \)

(b)

\(4\log { \left| { x }^{ 4 }+1 \right| } \)

(c)

-4 log |x⁴ +1|

(d)

\(\frac { 1 }{ 4 } \log { \left| { x }^{ 4 }+1 \right| } \)

\(\int { \frac { 1 }{ 1+sinx } } \) dx = ____________ +c

(a)

tan x - sec x

(b)

sec x - tan x

(c)

- tan x - sec x

(d)

tan x +sec x

\(\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,\) 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 Consumer's surplus for the demand function P =f(x) for the quantity X_o and price P_o is_________

(a)

\(\int _{ 0 }^{ x0 }{ f(x)dx-{ p }_{ 0 }{ x }_{ 0 } } \)

(b)

\(\int _{ 0 }^{ x0 }{ f(x)dx } \)

(c)

p₀x₀-\(\int _{ 0 }^{ x0 }{ g(x)dx } \)

(d)

\(\int _{ 0 }^{ p0 }{ f(x)dx } \)

The area below the demand curve p = f(x) and above the line p = p_o is________.

(a)

Producer's Surplus

(b)

Consumer's Surplus

(c)

\(\int _{ 0 }^{ p0 }{ g(x)dx } \)

(d)

\(\int _{ 0 }^{ x0 }{ g(x)dx } \)

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

(a)

e^ye^x = c

(b)

y=log ce^x

(c)

y=log(e^x+c)

(d)

e^x+y = c

The solution of \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) - y = 0 is _____________

(a)

(A+B)e^x

(b)

(Ax+B)e^-x

(c)

Aex+\(\frac { B }{ e^{ x } } \)

(d)

(A+Bx)e^-x

The equation of ydx + xdy = e^-xy dx if it cuts the Y-axis is ______

(a)

e^xy

(b)

e^xy = c

(c)

e^xy = x + 1

(d)

e^xy = y + 1

Δ[f{x) . g(x)] = __________

(a)

Δf(x). Δg(x)

(b)

f(x) . Δg(x) + g(x) .Δf(x)

(c)

f(x) . Δg(x)

(d)

f(Δx) . g(Δx)

 The nationality of the mathematician Joseph Louis Laguange is _________

(a)

German

(b)

Spain

(c)

Italian

(d)

French

In Newtons forward and backward interpolation formula, the first two terms will give the __________ interpolation

(a)

linear

(b)

parabolic

(c)

quadratic

(d)

cubic

Given E(X + c) = 8 and E(X - c) = 12, then the value of c is ___________

(a)

-2

(b)

4

(c)

-4

(d)

2

If F(x) is the probability distribution function, then F(- ∞) is_______.

(a)

1

(b)

2

(c)

∞

(d)

0

If F(x) is the probability distribution function, then F(- ∞) is_______.

(a)

1

(b)

2

(c)

∞

(d)

0

Which of the following are correct?
(i) E(aX+b) = a E(X) + b
(ii) μ₂= μ₂¹ - (μ₁¹)²
(iii) μ²= variance
(iv) V (a X + b) = a² V(x)

(a)

all

(b)

i, ii and iii

(c)

ii and iii

(d)

i and iv

In a binomial distribution if the mean is 8 and the variance is 6, then the number of trials is ___________

(a)

32

(b)

48

(c)

16

(d)

12

In a binomial distribution, n = 4, p(X = 0) = \(\frac{16}{81}\), then p(X = 4) is ___________

(a)

\(\frac{1}{16}\)

(b)

\(\frac{1}{81}\)

(c)

\(\frac{1}{27}\)

(d)

\(\frac{1}{8}\)

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

(a)

μ,σ²

(b)

μ,σ

(c)

0,1

(d)

1,1

The standard error of the sample mean is __________

(a)

Type I error

(b)

Type II error

(c)

Standard deviation of the sampling distribution of the mean

(d)

Variance of the sampling distribution of the mean.

The point estimate variance of 21, 25, 20, 16, 12, 10, 17, 18, 13 and 11 is _______

(a)

23.5

(b)

2.35

(c)

4.85

(d)

48.5

The normal equations for estimating a and b so that the line y = ax + b may be the line of best fit are __________

(a)

aΣx² + bΣx = Σxy, aΣx + nb = Σy

(b)

aΣx + bΣx² = Σxy, aΣx² + nb = Σy

(c)

aΣx + nb = Σxy, aΣx² + bΣx = Σy

(d)

aΣx² + nb = Σxy, aΣx + bΣx = Σy

Seasonal variations are __________

(a)

Selling of umbrellas in rainy season

(b)

cool drinks in summer season

(c)

Prices of electronic gadgets

(d)

Sugarcane in Pongal

The optimum_______schedule remains, unaltered if we add or subtract a constant from all the elements of the row or which of the cost________matrix.

(a)

transportation

(b)

assignment

(c)

unique

(d)

optimal

The penalty is the difference between the ___ costs in each row and column.

(a)

smallest

(b)

biggest

(c)

minimum

(d)

least