Question 511 Mark
The function $f ( x )=x-\frac{1}{x}, x \in R , x \neq 0$ is increasing
View full question & answer→Question 521 Mark
If $y=x^2$, then the rate of change of demand ( $x$ ) of a commodity with respect to its price $(y)$ is $\frac{1}{2 x}$
View full question & answer→Question 531 Mark
Optimal assignments are made in the Hungarian method to cells in the reduced matrix that contain a zero
Question 541 Mark
For Cost of Living Index Number CLI $=\frac{\sum I W}{\sum W}$, where $I=\frac{P_0}{P_1} \times 100$ and $w=p_0 q_0$
View full question & answer→Question 551 Mark
Cyclical variation can occur several times in a year.
AnswerThis statement is
False.
Explanation:
Seasonal variation can occur several times in a year.
View full question & answer→Question 561 Mark
If $X \sim B(n, p)$ and $n=6$ and $P(X=4)=P(X=2)$, then $p=\frac{1}{2}$
View full question & answer→Question 571 Mark
State whether the following statement is True or False:
A factor is an agent who is given the possession of goods and enters a contract for sale in his/her own name
Question 581 Mark
State whether the following statement is True or False:
Order and degree of differential equation are always positive integers.
Question 591 Mark
$
\int_0^1 \frac{1}{2 x+5} d x=\log \left(\frac{7}{5}\right)
$
View full question & answer→Question 601 Mark
If $\int x e ^{2 x} dx$ is equal to $e ^{2 x} f ( x )+ c$, where $c$ is constant of integration, then $f ( x )$ is $\frac{2 x-1}{2}$.
AnswerFalse
Explanation:
$ \text { Let } I =\int x \cdot e ^{2 x } dx$
$= x \int e ^{2 x } \cdot dx -\int\left[\frac{ d }{ dx }( x ) \int e ^{2 x } \cdot dx \right] dx$
$= x \cdot \frac{ e ^{2 x }}{2}-\int 1 \cdot \frac{ e ^{2 x }}{2} \cdot dx$
$=\frac{ x }{2} e ^{2 x }-\frac{1}{2} \int e ^{2 x }+ c$
$=\frac{ x }{2} e ^{2 x }-\frac{1}{2} \cdot \frac{ e ^{2 x }}{2}+ c$
$= e ^{2 x }\left(\frac{ x }{2}-\frac{1}{4}\right)+ c$
$= e ^{2 x }\left(\frac{2 x -1}{4}\right)+ c $
$\therefore f(x)=\frac{2 x-1}{4}$
View full question & answer→Question 611 Mark
The function $f ( x )=\frac{3}{x}+10, x \neq 0$ is decreasing
View full question & answer→Question 621 Mark
If $y =10^{ x }+1$, then $\frac{ d y}{ d x}=10^{ x } \cdot \log 10$
View full question & answer→Question 631 Mark
To convert the assignment problem into maximization problem, the smallest element in the matrix is to deducted from all other elements
Question 641 Mark
The three types of Index numbers are
i. Price Index Number
ii. Quantity Index Number
iii. Value Index Number
Question 651 Mark
State whether the following statement is True or False:
Seasonal variation can be observed over several years
Question 661 Mark
If $f ( x )=\begin{array}{ll} k x(1-x), & \text { for } 0
View full question & answer→Question 671 Mark
State whether the following statement is True or False:
The trade discount is first calculated on the catalogue (list) price
Question 681 Mark
State whether the following statement is True or False:
The integrating factor of the differential equation $\frac{ d y}{ d x}-y= x$ is $e ^{- x }$
View full question & answer→Question 691 Mark
$
\int_0^{ a } 3 x^2 d x=27, \text { then } a =2.5
$
View full question & answer→Question 701 Mark
The proper substitution for $\int x\left(x^x\right)^x(2 \log x+1) d x$ is $\left(x^x\right)^x= t$
AnswerTrue
Explanation:
Let $I=\int x\left(x^x\right)^x(2 \log x+1) d x$
Put $\left( x ^{ x }\right)^{ x }= t$
Taking logarithm of both sides, we get
$ \log \left( x ^{ x }\right)^{ x }=\log t$
$\therefore x ^2 \cdot \log x =\log t $
Differentiating w.r.t. $x$, we get
$ x ^2 \cdot \frac{1}{ x }+(\log x ) \cdot 2 x =\frac{1}{ t } \cdot \frac{ dt }{ dx }$
$\therefore( x +2 x \log x ) dx =\frac{1}{ t } \cdot dt$
$\therefore x (1+2 \log x ) dx =\frac{1}{ t } \cdot dt $
$\therefore I =\int t \cdot \frac{1}{ t } \cdot dt =\int 1 \cdot dt = t + c =\left( x ^{ x }\right)^{ x }+ c$
View full question & answer→Question 711 Mark
An absolute maximum must occur at a critical point or at an end point.
Question 721 Mark
If $y =\log (\log x )$, then $\frac{ d y}{ d x}=\log x$
View full question & answer→Question 731 Mark
The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost
Question 741 Mark
Walsh's Price Index Number is given by $\frac{\sum p_1 \sqrt{q_0 q_1}}{\sum p_0 \sqrt{q_0 q_1}} \times 100$
View full question & answer→Question 751 Mark
State whether the following statement is True or False:
The secular trend component of time series represents irregular variations
Question 761 Mark
In sequencing problem each machine is of different type
Question 771 Mark
If $y = e ^{ x }$, then $\frac{ d ^2 y}{ d x^2}= e ^{ x }$
View full question & answer→Question 781 Mark
In sequencing problem each job once started on any machine must be processed still its completion
Question 791 Mark
The function $y = cx$ is the solution of differential equation $\frac{ d y}{ d x}=\frac{y}{x}$
View full question & answer→Question 801 Mark
$
\int \sqrt{1+x^2} \cdot x d x=\frac{1}{3}\left(1+x^2\right)^{\frac{3}{2}}+ c
$
View full question & answer→Question 811 Mark
If $x =5 m , y = m$, where $m$ is parameter, then $\frac{ d y}{ d x}=\frac{1}{5}$
View full question & answer→Question 821 Mark
In sequencing problem the processing times are dependent of order of processing the jobs on machine
Question 831 Mark
X is the number obtained on upper most face when a die is thrown, then E(x) = 3.5
Question 841 Mark
After applying elementary transformation $R_1-3 R_2$ on matrix $\left[\begin{array}{cc}3 & -2 \\ 1 & 4\end{array}\right]$ we get $\left[\begin{array}{cc}0 & -12 \\ 1 & 4\end{array}\right]$
View full question & answer→Question 851 Mark
State whether the following statement is True or False:
If equation of regression lines are $3 x+2 y-26=0$ and $6 x+y-31=0$, then mean of $X$ is 7
View full question & answer→Question 861 Mark
$p \vee \sim p \equiv \sim c$
View full question & answer→Question 871 Mark
If O(A) = m × n and O(B) = n × p with m ≠ p, then BA exists but AB does not exist.
Question 881 Mark
State whether the following statement is True or False:
If $u=x-a$ and $v=y-b$ then $b_{x y}=b_{u v}$
View full question & answer→Question 891 Mark
State whether the following statement is True or False:
An annuity where payments continue forever is called perpetuity
Question 901 Mark
Mathematical identities are true statements
Question 911 Mark
$\left[\begin{array}{ccc}2 & 0 & 0 \\ 3 & -1 & 0 \\ -7 & 3 & 1\end{array}\right]$ is a skew symmetric matrix
View full question & answer→Question 921 Mark
State whether the following statement is True or False:
The following data is not consistent: $b_{y x}+b_{x y}=1.3$ and $r=0.75$
View full question & answer→Question 931 Mark
State whether the following statement is True or False:
Annuity contingent begins and ends on certain fixed dates
Question 941 Mark
The dual of $(p \wedge q) \vee \sim q$ is $(p \vee q) \wedge \sim q$
View full question & answer→Question 951 Mark
Matrix $\left[\begin{array}{ccc} a & b & c \\ p & q & r \\ 2 a - p & 2 b - q & 2 c - r \end{array}\right]$ is a singular
View full question & answer→Question 961 Mark
State whether the following statement is True or False:
If $b_{x y}<0$ and $b_{y x}<0$ then ' $r$ ' is $>0$
View full question & answer→Question 971 Mark
State whether the following statement is True or False:
The future value of an annuity is the accumulated values of all instalments
Question 981 Mark
p ↔ q is false when p and q have different truth values
Question 991 Mark
If $A=\left[\begin{array}{ccc}1 & 2 & -5 \\ 2 & -3 & 4 \\ -5 & 4 & 9\end{array}\right]$, then $A^{\top}=A$
View full question & answer→Question 1001 Mark
State whether the following statement is True or False:
Correlation analysis is the theory of games