Question 11 Mark
State whether the following statement is True or False:
A differential equation in which the dependent variable, say $y$, depends only on one independent variable, say $x$, is called as ordinary differential equation
View full question & answer→Question 21 Mark
$
\int e ^{4 x-7} d x=\frac{ e ^{4 x-7}}{-7}+ c
$
View full question & answer→Question 31 Mark
If $x =2 at , y =2 a$, where $t$ is parameter, then $\frac{ d y}{ d x}=\frac{1}{ t }$
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The idle time for a machine is the when machine is available but is not waiting for any job to be processed
Question 51 Mark
$\sum \frac{ P _1 q _1}{ p _0 q _0} \times 100$ is the Value Index Number by Simple Aggregate Method
View full question & answer→Question 61 Mark
The cumulative distribution function (c.d.f.) of a continuous random variable $X$ is denoted by $F$ and defined by
$
F ( x )=\begin{array}{ll}
0, & \text { for all } x \leq a \\
\int_{ a }^x f(x) d x, & \text { for all } x \geq a
\end{array}
$
View full question & answer→Question 71 Mark
State whether the following statement is True or False:
Number of arbitrary constant in the general solution of a differential equation is equal to order of D.E.
Question 81 Mark
$
\int 3^{2 x+3} d x=\frac{3^{2 x+3}}{2}+ c
$
View full question & answer→Question 91 Mark
If $x ^2+ y ^2= a ^2$, then $\frac{ d y}{ d x}=2 x +2 y =2 a$
View full question & answer→Question 101 Mark
The Total Elapsed is the time required to complete all the jobs i.e. entire task
Question 111 Mark
$\left[\sqrt{\frac{\sum p _1 q _1}{\sum p _0 q _1}}+\frac{\sum \sqrt{ q _0 q _1}}{\sum\left( p _0+ p _1\right)}\right] \times 100$ is Fisher's Price Index Number.
View full question & answer→Question 121 Mark
If n is very large and p is very small then X follows Poisson distribution with n = mp
Question 131 Mark
State whether the following statement is True or False:
Order and degree of differential equation $x \frac{ d ^3 y}{ d x^3}+6\left(\frac{ d ^2 y}{ d x^2}\right)^2+y=0$ is $(2,2)$
View full question & answer→Question 141 Mark
If $f ( x )= k$, where $k$ is constant, then $\int k d x=0$
View full question & answer→Question 151 Mark
If $\sqrt{x}+\sqrt{y}=\sqrt{ a }$, then $\frac{ d y}{ d x}=\frac{1}{2 \sqrt{x}}+\frac{1}{2 \sqrt{y}}=\frac{1}{2 \sqrt{ a }}$
View full question & answer→Question 161 Mark
One of the assumptions is made while sequencing n jobs on 2 machines is: two jobs must be loaded at a time on any machine
Question 171 Mark
$\frac{\sum p _0 \sqrt{ q _0+ q _1}}{\sum p _1 \sqrt{ q _0+ q _1}} \times 100$ is Marshall-Edgeworth Price Index Number
View full question & answer→Question 181 Mark
For the Binomial distribution, Mean E(X) = m and Variance = Var(X) = m
Question 191 Mark
State whether the following statement is True or False:
A homogeneous differential equation is solved by substituting $y=v x$ and integrating it
View full question & answer→Question 201 Mark
$
\int_{-5}^5 \frac{x}{x^2+7} d x=10
$
View full question & answer→Question 211 Mark
If $f^{\prime}(x)=3 x^2+2 x$, then by definition of integration, we get $f(x)=x^3+x^2+c$
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If the marginal revenue is 50 and the price is $\text{₹} 75$, then elasticity of demand is 4
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If $y =4^{ x }$, then $\frac{ d y}{ d x}=4^{ x }$
View full question & answer→Question 241 Mark
In assignment problem each worker or machine is assigned only one job
Question 251 Mark
$\frac{\sum p _1 q _1}{\sum p _0 q _1} \times 100$ is Paasche's Price Index Number
View full question & answer→Question 261 Mark
A discrete random variable $X$ is said to follow the Poisson distribution with parameter $m \geq 0$ if its p.m.f. is given by $P(X=x)=\frac{e^{-m} m^x}{x}, x=0,1,2, \ldots$.
View full question & answer→Question 271 Mark
State whether the following statement is True or False:
If only one discount is given then List price = Invoice price
Question 281 Mark
State whether the following statement is True or False:
The degree of a differential equation $e ^{-\frac{ d y}{ d x}}=\frac{ d y}{ d x}+ c$ is not defined
View full question & answer→Question 291 Mark
$
\int_0^{2 a } f (x) d x=\int_0^{ a } f (x) d x+\int_0^{ a } f ( a -x) d x
$
View full question & answer→Question 301 Mark
For $\int \frac{x-1}{(x+1)^3} e ^x d x= e ^{ x } f ( x )+ c , f ( x )=( x +1)^2$
View full question & answer→Question 311 Mark
If the function $f(x)=x^2+2 x-5$ is an increasing function, then $x<-1$
View full question & answer→Question 321 Mark
If $y = e ^{ x }$, then $\frac{ d y}{ d x}= e ^{ x }$
View full question & answer→Question 331 Mark
The Hungarian method is used to assign n jobs on 2 machines to get the optimal sequence
Question 341 Mark
$\sum \frac{ q _1}{ q _0} \times 100$ is the Quantity Index Number by Simple Aggregate Method
View full question & answer→Question 351 Mark
State whether the following statement is True or False:
Least squares method of finding trend is very simple and does not involve any calculations
Question 361 Mark
Let X ~ B(n, p), then the mean or expected value of r.v. X is denoted by E(X). It is also denoted by E(X) and is given by µ = E(X) = npq
Question 371 Mark
State whether the following statement is True or False:
The sum due is also called as Cash value
Question 381 Mark
Order of highest derivative occurring in the differential equation is called the degree of the differential equation
AnswerThis statement is
False. Explanation:
The order of highest derivative occurring in the differential equation is called degree of the differential equation.
View full question & answer→Question 391 Mark
$
\int_{ a }^{ b } f (x) d x=\int_{ a }^{ b } f ( a + b -x) d x
$
View full question & answer→Question 401 Mark
If $\int \frac{(x-1) d x}{(x+1)(x-2)}= A \log | x +1|+ B \log | x -2|$, then $A + B =1$
View full question & answer→Question 411 Mark
The function $f ( x )=x-\frac{1}{x}, x \in R , x \neq 0$ is increasing
View full question & answer→Question 421 Mark
If $y=7 x+1$, then the rate of change of demand $(x)$ of a commodity with respect to its price $(y)$ is 7
View full question & answer→Question 431 Mark
In assignment problem, if number of columns is greater than number of rows, then a dummy row is added
Question 441 Mark
Purchasing power of money $=\frac{1}{\text { Cost of Living Index Number }}$
View full question & answer→Question 451 Mark
State whether the following statement is True or False:
Moving average method of finding trend is very complicated and involves several calculations
Question 461 Mark
If r.v. X assumes the values 1, 2, 3, …….., 9 with equal probabilities, then E(X) = 5
Question 471 Mark
State whether the following statement is True or False:
A person can get both, trade discount and cash discount
Question 481 Mark
State whether the following statement is True or False:
The degree of a differential equation is the power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any
Question 491 Mark
$
\int_2^3 \frac{x}{x^2+1} d x=\frac{1}{2} \log 2
$
View full question & answer→Question 501 Mark
If $\int x f (x) d x=\frac{ f (x)}{2}$, then $f ( x )= e ^{x^2}$
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