MCQ 11 Mark
Choose the correct alternative:
The solution of $\frac{d y}{d x}=1$ is ____.
- A
$x+y=c$
- B
$x y=c$
- C
$x^2+y^2=c$
- ✓
$y-x=c$
AnswerCorrect option: D. $y-x=c$
The solution of $\frac{d y}{d x}=1$ is $y - x = c$.
View full question & answer→MCQ 21 Mark
$
\int_{-9}^9 \frac{x^3}{4-x^2} d x=
$ ________
View full question & answer→MCQ 31 Mark
$\int(1-x)^{-2} d x=$
- ✓
$(1-x)^{-1}+c$
- B
$(1+x)^{-1}+c$
- C
$(1-x)^{-1}-1+c$
- D
$(1-x)^{-1}+1+c$
AnswerCorrect option: A. $(1-x)^{-1}+c$
$\int(1-x)^{-2} d x=\underline{( 1 - x )^{- 1 }+ c .}$
Explanation:
$\int(1-x)^{-2} d x=\frac{(1-x)^{-2+1}}{(-2+1)} \cdot \frac{d}{d x}(1-x)+c$
$=\frac{(1-x)^{-1}}{(-1)} \cdot(0-1)+c \$
$=(1- x )^{-1}+c$
View full question & answer→MCQ 41 Mark
If $x =2 am , y =2 am ^2$, where $m$ be the parameter, then $\frac{ d y}{ d x}=$ ?
View full question & answer→MCQ 51 Mark
If $A$ is a non singular matrix of $\operatorname{order} 3$, then $|\operatorname{adj}(A)|=$ ______
- ✓
$| A |^2$
- B
$| A |^3$
- C
$0$
- D
AnswerCorrect option: A. $| A |^2$
$| A |^2$
View full question & answer→MCQ 61 Mark
If there are 3 machines A, B and C, conditions for reducing a 3 machine problem to a 2 machine problem with respect to minimum processing time is ______
- ✓
$\operatorname{Min} A_i \geq \operatorname{Max} B_i$ OR Min $C_i \geq \operatorname{Max} B_i, i=1,2,3 \ldots n$
- B
$\operatorname{Min} A_i \leq \operatorname{Max} B_i$ OR Min $C \leq \operatorname{Max} B_i, i=1,2,3 \ldots n$
- C
$\operatorname{Max} A_i \geq \operatorname{Min} B_i$ OR Max $B \geq \operatorname{Min} A_i, i=1,2,3 \ldots n$
- D
$\operatorname{Max} A_i \leq \operatorname{Min} B_i$ OR Max $B \leq \operatorname{Min} A_i, i=1,2,3 \ldots n$
AnswerCorrect option: A. $\operatorname{Min} A_i \geq \operatorname{Max} B_i$ OR Min $C_i \geq \operatorname{Max} B_i, i=1,2,3 \ldots n$
$\operatorname{Min} A_i \geq \operatorname{Max} B_i$ OR Min $C_i \geq \operatorname{Max} B_i, i=1,2,3 \ldots n$
View full question & answer→MCQ 71 Mark
The Cost of Living Index Number by Aggregate Expenditure Method is same as
- A
Fisher’s Price Index Number
- ✓
Laspeyre’s Price Index Number
- C
Paasche’s Price Index Number
- D
Dorbish-Bowley’s Price Index Number
AnswerCorrect option: B. Laspeyre’s Price Index Number
Laspeyre’s Price Index Number
View full question & answer→MCQ 81 Mark
Choose the correct alternative:
There are _____ types of regression equations
AnswerThere are 2 types of regression equations.
View full question & answer→MCQ 91 Mark
Multiple choice questions:
If for an immediate annuity $r=10 \%$ p.a., P=₹ 12,679.46 and A=₹ 18,564, then the amount of each annuity paid is_____.
- ✓
$₹ 4,000$
- B
$₹ 4,500$
- C
$₹ 3,500$
- D
$₹ 4,200$
AnswerCorrect option: A. $₹ 4,000$
View full question & answer→MCQ 101 Mark
The dual of the statement $(p \vee q) \wedge(r \vee s)$ is
- A
$(p \wedge q) \wedge(r \wedge s)$
- ✓
$(p \wedge q) \vee(r \wedge s)$
- C
$(p \vee q) \vee(r \vee s)$
- D
$(p \vee q) \wedge(r \vee s)$
AnswerCorrect option: B. $(p \wedge q) \vee(r \wedge s)$
The dual of the statement (p ˅ q) ˄ ( r ˅ s) is
(p ˄ q) ˅ (r ˄ s).
Explanation:
The dual of a proposition that contains only the logical operators ∨, ∧ can be obtained by replacing each ∨ by ∧ and each ∧ by ∨.
View full question & answer→MCQ 111 Mark
A distance random variable $X$ is said to have the Poisson distribution with parameter $m$ if its p.m.f. is given by $P(x)=\frac{e^{-m} m^x}{x !}$ the condition for $m$ is ______
- ✓
$m >0$
- B
$m \geq 0$
- C
$m \neq 1$
- D
$m =0$
AnswerCorrect option: A. $m >0$
View full question & answer→MCQ 121 Mark
Choose the correct alternative:
The order and degree of $\left(1+\left(\frac{ d y}{ d x}\right)^3\right)^{\frac{2}{3}}=8 \frac{ d ^3 y}{ d x^3}$ are respectively
View full question & answer→MCQ 131 Mark
$\int_2^7 \frac{\sqrt{x}}{\sqrt{x}+\sqrt{9-x}} d x=$
- A
$\frac{7}{2}$
- ✓
$\frac{5}{2}$
- C
- D
AnswerCorrect option: B. $\frac{5}{2}$
$\int_2^7 \frac{\sqrt{x}}{\sqrt{x}+\sqrt{9-x}}{ }^{\prime \prime} d$ " $x =\frac{ 5 }{\underline{ 2 }}$
View full question & answer→MCQ 141 Mark
$
\int\left(\frac{ e ^{2 x}+ e ^{-2 x}}{ e ^x}\right) d x=
$
- ✓
$e ^x-\frac{1}{3 e ^{3 x}}+ c$
- B
$e ^x+\frac{1}{3 e ^{3 x}}+ c$
- C
$e ^{-x}-\frac{1}{3 e ^{3 x}}+ c$
- D
$e ^{-x}+\frac{1}{3 e ^{3 x}}+ c$
AnswerCorrect option: A. $e ^x-\frac{1}{3 e ^{3 x}}+ c$
$e ^x-\frac{1}{3 e ^{3 x}}+ c$
View full question & answer→MCQ 151 Mark
If $x ^{ y }=2^{ x - y }$, then $\frac{ d y}{ d x}=$ ________
- A
$\frac{x \log 2-y}{x \log 2 x}$
- ✓
$\frac{x \log 2+y}{x \log 2 x}$
- C
$\frac{x \log 2+x}{y \log 2 x}$
- D
$\frac{y \log 2-x}{x \log 2 x}$
AnswerCorrect option: B. $\frac{x \log 2+y}{x \log 2 x}$
If $x^y=2^{x-y}$, then $\frac{d y}{d x}=\frac{ x \log 2+ y }{ x \log 2 x }$
View full question & answer→MCQ 161 Mark
If $A=\left[\begin{array}{cc}1 & 2 \\ 2 & -1\end{array}\right]$, then $\operatorname{adj}(A)=$ ______
- A
$\left[\begin{array}{ll}1 & -2 \\ 2 & -1\end{array}\right]$
- B
$\left[\begin{array}{cc}-1 & 2 \\ 2 & 1\end{array}\right]$
- ✓
$\left[\begin{array}{cc}-1 & -2 \\ -2 & 1\end{array}\right]$
- D
$\left[\begin{array}{cc}1 & 2 \\ -2 & -1\end{array}\right]$
AnswerCorrect option: C. $\left[\begin{array}{cc}-1 & -2 \\ -2 & 1\end{array}\right]$
$\left[\begin{array}{cc}-1 & -2 \\ -2 & 1\end{array}\right]$
View full question & answer→MCQ 171 Mark
In sequencing, an optimal path that minimizes ______
- A
- B
- ✓
Both elapsed time and idle time
- D
AnswerCorrect option: C. Both elapsed time and idle time
Both elapsed time and idle time
View full question & answer→MCQ 181 Mark
The Cost of Living Index Number using Weighted Relative Method is given by
- A
$\frac{\sum IW }{\sum W } \times 100$
- ✓
$\frac{\sum IW }{\sum W }$
- C
$\frac{\sum W }{\sum IW } \times 100$
- D
$\frac{\sum W }{\sum IW }$
AnswerCorrect option: B. $\frac{\sum IW }{\sum W }$
$\frac{\sum IW }{\sum W }$
View full question & answer→MCQ 191 Mark
Choose the correct alternative:
We can estimate the value of one variable with the help of other known variable only if they are____.
AnswerWe can estimate the value of one variable with the help of other known variable only if they are correlated.
View full question & answer→MCQ 201 Mark
Multiple choice questions:
In annuity calculations, the interest is usually taken as_____.
- A
simple interest per annum
- ✓
interest compounded every year
- C
interest compounded per month
- D
simple interest per month
AnswerCorrect option: B. interest compounded every year
interest compounded every year
View full question & answer→MCQ 211 Mark
If $p \rightarrow q$ is an implication, then the implication $\sim q \rightarrow \sim p$ is called its
View full question & answer→MCQ 221 Mark
For the Poisson distribution ______
- A
- B
- ✓
Mean = E(X) = m and Var(X) = m
- D
Mean = E(X) ≠ m and Var(X) = m
AnswerCorrect option: C. Mean = E(X) = m and Var(X) = m
Mean = E(X) = m and Var(X) = m
View full question & answer→MCQ 231 Mark
The order and degree of $\left(\frac{d y}{d x}\right)^3-\frac{d^3 y}{d x^3}+y e^x=0$ are ____
AnswerThe order and degree of $\left(\frac{d y}{d x}\right)^3-\frac{d^3 y}{d x^3}+y e^x=0$ are $\underline{ 3 }, \underline{ 1 }$.
Explanation:
$
\frac{d y}{d x}+x= c
$
Highest order derivative
$
\left(\frac{d^3 y}{d x^3}\right)^1+\left(\frac{d^2 y}{d x^2}\right)^2
$
View full question & answer→MCQ 241 Mark
$\int_{ a }^{ b } f (x) d x=$ ______
- A
$\int_{ b }^{ a } f (x) d x$
- B
$-\int_{ a }^{ b } f (x) d x$
- ✓
$-\int_{ b }^{ a } f (x) d x$
- D
$\int_0^{ a } f (x) d x$
AnswerCorrect option: C. $-\int_{ b }^{ a } f (x) d x$
$-\int_{ b }^{ a } f (x) d x$
View full question & answer→MCQ 251 Mark
$\int\left(x+\frac{1}{x}\right)^3 d x=$
- A
$\frac{1}{4}\left(x+\frac{1}{x}\right)^4+c$
- ✓
$\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$
- C
$\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x+\frac{1}{x^2}+c$
- D
$\left(x-x^{-1}\right)^3+c$
AnswerCorrect option: B. $\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$
$\int\left(x+\frac{1}{x}\right)^3 d x=\frac{ x ^4}{4}+\frac{3 x ^2}{2}+3 \log x -\frac{1}{2 x ^2}+ c .$
Explanation:
$\left(x+\frac{1}{x}\right)^3=x^3+3 x+\frac{3}{x}+\frac{1}{x^3}$
$\therefore \int\left(x+\frac{1}{x}\right)^3 d x=\int\left(x^3+3 x+\frac{3}{x}+\frac{1}{x^3}\right) d x$
$=\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$
View full question & answer→MCQ 261 Mark
If 0 < η < 1, then the demand is ______.
AnswerIf 0 < η < 1, then the demand is inelastic.
View full question & answer→MCQ 271 Mark
If $x^m \cdot y^n=(x+y)^{(m+n)}$, then $\frac{d y}{d x}=$ ?
- ✓
$\frac{ y }{ x }$
- B
$\frac{- y }{ x }$
- C
$\frac{ x }{ y }$
- D
$\frac{- x }{ y }$
AnswerCorrect option: A. $\frac{ y }{ x }$
$\frac{ y }{ x }$
View full question & answer→MCQ 281 Mark
If $A$ and $B$ are two square matrices of order 3 , then $(A B)^{\top}=$______
- ✓
$B^{\top} A^{\top}$
- B
$A^{\top} B^{\top}$
- C
$(B A)^{\top}$
- D
AnswerCorrect option: A. $B^{\top} A^{\top}$
$B^{\top} A^{\top}$
View full question & answer→MCQ 291 Mark
Choose the correct alternative:| Machine | Job |
| A | B | C | D |
| I | 5 | 6 | 8 | 4 |
| II | 4 | 7 | 9 | 10 |
The optimal sequence for above data is
MCQ 301 Mark
Fisher’s Price Index Number is
- ✓
$\sqrt{ P _{01}( L ) \times P _{01}( P )}$
- B
$P_{01}(L) \times P_{01}(P)$
- C
$\sqrt{ P _{01}( L ) \times P _{01}( P )} \times 100$
- D
$\sqrt{ P _{01}( L )+ P _{01}( P )}$
AnswerCorrect option: A. $\sqrt{ P _{01}( L ) \times P _{01}( P )}$
$\sqrt{ P _{01}( L ) \times P _{01}( P )}$
View full question & answer→MCQ 311 Mark
Choose the correct alternative:
Regression analysis is the theory of____.
- A
- B
- ✓
Estimation and Prediction.
- D
AnswerCorrect option: C. Estimation and Prediction.
Regression analysis is the theory of Estimation and Prediction.
View full question & answer→MCQ 321 Mark
Multiple choice questions:
Premium is paid on value______.
MCQ 331 Mark
A biconditional statement is the conjunction of two statements
MCQ 341 Mark
A sequence of dichotomous experiments is called a sequence of Bernoulli trials if it satisfies ______
- A
The trials are independent.
- B
The probability of success remains the same in all trials.
- C
The trials are independent but not the probability of success remains the same in all trials.
- ✓
both trials are independent but not the probability of success remains the same in all trials.
AnswerCorrect option: D. both trials are independent but not the probability of success remains the same in all trials.
both trials are independent but not the probability of success remains the same in all trials.
View full question & answer→MCQ 351 Mark
Choose the correct alternative:
General solution of $y-x \frac{ d y}{ d x}=0$ is
AnswerCorrect option: C. $\log x-\log y=\log c$
View full question & answer→MCQ 361 Mark
$
\int_2^3 \frac{x}{x^2-1} d x=
$
- A
$\log \left(\frac{8}{3}\right)$
- B
$-\log \left(\frac{8}{3}\right)$
- ✓
$\frac{1}{2} \log \left(\frac{8}{3}\right)$
- D
$-\frac{1}{2} \log \left(\frac{8}{3}\right)$
AnswerCorrect option: C. $\frac{1}{2} \log \left(\frac{8}{3}\right)$
$\frac{1}{2} \log \left(\frac{8}{3}\right)$
View full question & answer→MCQ 371 Mark
$
\int \frac{ d x}{(x-8)(x+7)}=
$
- A
$\frac{1}{15} \log \left(\frac{x+2}{x-1}\right)+ c$
- B
$\frac{1}{15} \log \left(\frac{x+8}{x+7}\right)+ c$
- ✓
$\frac{1}{15} \log \left(\frac{x-8}{x+7}\right)+ c$
- D
$(x-8)(x-7)+c$
AnswerCorrect option: C. $\frac{1}{15} \log \left(\frac{x-8}{x+7}\right)+ c$
$\frac{1}{15} \log \left(\frac{x-8}{x+7}\right)+ c$
View full question & answer→MCQ 381 Mark
If the elasticity of demand η = 1, then demand is ______.
AnswerIf the elasticity of the demand η = 1, then demand is
unitary elastic.
Explanation:
0 < η < 1 – inelastic
η > 1 – elastic
η = 1 – unitary elastic
View full question & answer→MCQ 391 Mark
If $y =( x )^{ x }+(10)^{ x }$, then $\frac{ d y}{ d x}=$ ?
- A
$x ^{ x }(1-\log x )+10^{ x } \log 10$
- B
$x ^{ x }(1+\log x )-10^{ x } \log 10$
- C
$x(1+\log x)+10^x \log 10$
- ✓
$x ^{ x }(1+\log x )+10^{ x } \log 10$
AnswerCorrect option: D. $x ^{ x }(1+\log x )+10^{ x } \log 10$
$x ^{ x }(1+\log x )+10^{ x } \log 10$
View full question & answer→MCQ 401 Mark
For any square matrix $B$, matrix $B+B^{\top}$ is ______.
View full question & answer→MCQ 411 Mark
The assignment problem is said to be balanced if ______
- ✓
no. of rows = no. of columns
- B
no. of rows ≠ no. of columns
- C
no. of rows < no. of columns
- D
no. of rows > no. of columns
AnswerCorrect option: A. no. of rows = no. of columns
no. of rows = no. of columns
View full question & answer→MCQ 421 Mark
Quantity Index Number by Simple Aggregate Method is given by ______.
- A
$\sum \frac{q_1}{q_0} \times 100$
- B
$\sum \frac{q_0}{q_1} \times 100$
- ✓
$\frac{\sum q_1}{\sum q_0} \times 100$
- D
$\frac{\sum q_0}{\sum q_1} \times 100$
AnswerCorrect option: C. $\frac{\sum q_1}{\sum q_0} \times 100$
Quantity Index Number by Simple Aggregate Method is given by $\frac{\sum q _1}{\sum q _{ 0 }} \times 1 0 0$.
View full question & answer→MCQ 431 Mark
Choose the correct alternative:
The slope of the line of regression of $y$ on $x$ is called the_____.
- A
regression coefficient of x on y
- B
correlation coefficient between y and x
- C
covariance between y and x
- ✓
regression coefficient of y on x
AnswerCorrect option: D. regression coefficient of y on x
regression coefficient of Y on X
View full question & answer→MCQ 441 Mark
Multiple choice questions:
The period for the fire insurance policy is_____.
MCQ 451 Mark
If $p:$ He is intelligent.
$q$ : He is strong
Then, symbolic form of statement "It is wrong that, he is intelligent or strong" is
- A
$\sim p \vee \sim p$
- B
$\sim(p \wedge q)$
- ✓
$\sim(p \vee q)$
- D
$p \vee \sim q$
AnswerCorrect option: C. $\sim(p \vee q)$
View full question & answer→MCQ 461 Mark
If $X \sim B\left(20, \frac{1}{10}\right)$, then $E(X)=$ _______
AnswerIf $X \sim B\left(20, \frac{1}{10}\right)$, then $E(X)=\underline{ 2 }$.
Explanation:
$X \sim B\left(20, \frac{1}{10}\right) \ldots . .(\text { Given) }$
$\therefore n=20, p=\frac{1}{10} $
$E(X)=n p $
$=20 \times \frac{1}{10} $
$=2 .$
View full question & answer→MCQ 471 Mark
Choose the correct alternative:
The marked price is also called as____.
MCQ 481 Mark
Choose the correct alternative:
Differential equation of the function $c+4 y x=0$ is
- A
$x y+\frac{ d y}{ d x}=0$
- ✓
$x \frac{ d y}{ d x}+y=0$
- C
$\frac{ d y}{ d x}-4 x y=0$
- D
$x \frac{ d y}{ d x}+1=0$
AnswerCorrect option: B. $x \frac{ d y}{ d x}+y=0$
$x \frac{ d y}{ d x}+y=0$
View full question & answer→MCQ 491 Mark
$
\int_{-2}^3 \frac{1}{x+5} d x=
$
- A
$\log \left(\frac{3}{8}\right)$
- ✓
$\log \left(\frac{8}{3}\right)$
- C
$\log \left(\frac{8}{5}\right)$
- D
$0$
AnswerCorrect option: B. $\log \left(\frac{8}{3}\right)$
$\log \left(\frac{8}{3}\right)$
View full question & answer→MCQ 501 Mark
$\int \frac{ d x}{x-x^2}=$ ________
Answer$\int \frac{ d x}{x-x^2}=\log x -\log (1- x )+ c$
View full question & answer→MCQ 511 Mark
The price P for the demand D is given as P = 183 + 120D − 3D2, then the value of D for which price is increasing, is ______.
- A
$D < 60$
- B
$D < 60$
- ✓
$D < 20$
- D
$D > 20$
AnswerCorrect option: C. $D < 20$
The price $P$ for the demand $D$ is given as $P=183+120 D-3 D^2$, then the value of $D$ for which price is increasing, is $D<20$.
View full question & answer→MCQ 521 Mark
If $y =x^{\sqrt{x}}$, then $\frac{ d y}{ d x}=$ ?
- ✓
$\frac{y}{2 \sqrt{x}}(\log x+2)$
- B
$\frac{y}{\sqrt{x}}(\log x+2)$
- C
$\frac{y}{2 \sqrt{x}}(\log x-2)$
- D
$\frac{y}{\sqrt{x}}(\log x-2)$
AnswerCorrect option: A. $\frac{y}{2 \sqrt{x}}(\log x+2)$
$\frac{y}{2 \sqrt{x}}(\log x+2)$
View full question & answer→MCQ 531 Mark
If $A=\left[\begin{array}{ll}2 & 0 \\ 0 & 2\end{array}\right]$, then $A^2-3 \mid=$
View full question & answer→MCQ 541 Mark
When an assignment problem has more than one solution, then it is ______
- A
- B
infinite optimal solution
- ✓
multiple optimal solution
- D
AnswerCorrect option: C. multiple optimal solution
multiple optimal solution
View full question & answer→MCQ 551 Mark
Walsh's Price Index Number is given by
- A
$\frac{\sum p _0 \sqrt{ p _0 p _1}}{\sum q _1 \sqrt{ p _0 p _1}} \times 100$
- B
$\frac{\sum p_0 \sqrt{q_0 q_1}}{\sum p_1 \sqrt{q_0 q_1}} \times 100$
- C
$\frac{\sum q _1 \sqrt{ p _0 p _1}}{\sum q _0 \sqrt{ p _0 p _1}} \times 100$
- ✓
$\frac{\sum p_1 \sqrt{q_0 q_1}}{\sum p_0 \sqrt{q_0 q_1}} \times 100$
AnswerCorrect option: D. $\frac{\sum p_1 \sqrt{q_0 q_1}}{\sum p_0 \sqrt{q_0 q_1}} \times 100$
$\frac{\sum p _1 \sqrt{ q _0 q _1}}{\sum p _0 \sqrt{ q _0 q _1}} \times 100$
View full question & answer→MCQ 561 Mark
Choose the correct alternative:
Moving averages are useful in identifying_____.
AnswerMoving averages are useful in identifying trend component.
View full question & answer→MCQ 571 Mark
Choose the correct alternative:
Find the value of the covariance between $X$ and $Y$, if the regression coefficient of $Y$ on $X$ is 3.75 and $\sigma_x=2, \sigma_y=8$
View full question & answer→MCQ 581 Mark
Multiple choice questions:
If the claim under the policy is ₹ 4,000 and ratio of property value to policy value is $5: 4$ then loss occurred is_____.
- A
$₹ 4,400$
- B
$₹ 4,000$
- ✓
$₹ 5,000$
- D
$₹ 5,500$
AnswerCorrect option: C. $₹ 5,000$
View full question & answer→MCQ 591 Mark
Negation of $p \rightarrow(p \vee \sim q)$ is
- A
$\sim p \rightarrow(\sim p \vee q)$
- ✓
$p \wedge(\sim p \wedge q)$
- C
$\sim p \vee(\sim p \vee \sim q)$
- D
$\sim p \rightarrow(\sim p \rightarrow q)$
AnswerCorrect option: B. $p \wedge(\sim p \wedge q)$
View full question & answer→MCQ 601 Mark
The expected value of the sum of two numbers obtained when two fair dice are rolled is ______
MCQ 611 Mark
Choose the correct alternative:
The date on which the period of the bill expires is called____.
MCQ 621 Mark
Choose the correct alternative:
The integrating factor of $\frac{ d ^2 y}{ d x^2}-y= e ^{ x }$, is $e ^{- x }$, then its solution is
- ✓
$y e^{-x}=x+c$
- B
$y e^x=x+c$
- C
$y e^x=2 x+c$
- D
$y e^{-x}=2 x+c$
AnswerCorrect option: A. $y e^{-x}=x+c$
$y e^{-x}=x+c$
View full question & answer→MCQ 631 Mark
$\int_0^2 e^x d x=$
- ✓
$e ^2-1$
- B
$1- e ^2$
- C
$e -1$
- D
$1- e$
AnswerCorrect option: A. $e ^2-1$
$\int_0^2 e^x d x=\underline{ e ^2- 1 }$
Explanation:
$\int_0^2 e^x d x=\left[e^x\right]_0^2 $
$= e ^2- e ^0 $
$= e ^2-1$
View full question & answer→MCQ 641 Mark
$
\int \frac{x+2}{2 x^2+6 x+5} d x= p \int \frac{4 x+6}{2 x^2+6 x+5} d x+\frac{1}{2} \int \frac{1}{2 x^2+6 x+5} d x \text {, then } p =\text { ? }
$
- A
$\frac{1}{3}$
- B
$\frac{1}{2}$
- ✓
$\frac{1}{4}$
- D
AnswerCorrect option: C. $\frac{1}{4}$
$\frac{1}{4}$
View full question & answer→MCQ 651 Mark
If the marginal revenue is 28 and elasticity of demand is 3, then the price is ______.
AnswerIf the marginal revenue is 28 and elasticity of demand is 3, then the price is 42.
View full question & answer→MCQ 661 Mark
What is the rate of change of demand $(x)$ of a commodity with respect to its price (y) if $y=$ $\frac{3 x+7}{2 x^2+5}$
- A
$\frac{\left(2 x^2+5\right)^2}{\left(-6 x^2-38 x+15\right)}$
- ✓
$\frac{\left(2 x^2+5\right)^2}{\left(-6 x^2-28 x+15\right)}$
- C
$\frac{\left(2 x^2+5\right)^2}{\left(6 x^2-28 x+15\right)}$
- D
$\frac{\left(2 x^2+5\right)^2}{\left(6 x^2-38 x+15\right)}$
AnswerCorrect option: B. $\frac{\left(2 x^2+5\right)^2}{\left(-6 x^2-28 x+15\right)}$
$\frac{\left(2 x^2+5\right)^2}{\left(-6 x^2-28 x+15\right)}$
View full question & answer→MCQ 671 Mark
$ \begin{bmatrix}3 & 2 & 1\end{bmatrix} \begin{bmatrix}2 \\ -2 \\ -1\end{bmatrix}=$
View full question & answer→MCQ 681 Mark
The cost matrix of an unbalanced assignment problem is not a ______
MCQ 691 Mark
$\frac{\sum p _1 q _1 w }{\sum p _0 q _0 w } \times 100$ gives
- ✓
Value Index Number by Simple Aggregate method
- B
Value Index Number by Simple Aggregate method
- C
Cost of Living Index Number
- D
AnswerCorrect option: A. Value Index Number by Simple Aggregate method
Value Index Number by Weighted Aggregate method
View full question & answer→MCQ 701 Mark
Choose the correct alternative:
An overall upward or downward pattern in an annual time series would be contained in which component of the times series?
MCQ 711 Mark
Choose the correct alternative:
$
\left|b_{y x}+b_{x y}\right| \geq
$
AnswerCorrect option: B. $2|r|$
View full question & answer→MCQ 721 Mark
Multiple choice questions:A shop valued ₹ 2,00,000 is insured at $80 \%$ of it's value. If the rate of premium is $4 \%$, then the
premium is______.
View full question & answer→MCQ 731 Mark
If $p$ and $q$ are two statements then $(p \rightarrow q ) \leftrightarrow(\sim q \rightarrow \sim p )$ is
View full question & answer→MCQ 741 Mark
If p.m.f. of r.v. X is given below.
| x |
0 |
1 |
2 |
| P(x) |
$q^2$ |
2pq |
$p^2$ |
then Var(x) = ______ - A
$p ^2$
- B
$q ^2$
- C
$p q$
- ✓
$2 pq$
AnswerCorrect option: D. $2 pq$
If p.m.f. of r.v. X is given below.
| x |
0 |
1 |
2 |
| P(x) |
$q^2$ |
2pq |
$p^2$ |
then Var(x) $2 pq$ View full question & answer→MCQ 751 Mark
Choose the correct alternative:
If A bill of ₹ 6,395 drawn on 15th February 2015 for 10 months was discounted on 28th May 2015 at $8 \%$ p.a. interest, then legal due date is____.
- A
$15^{\text {th }}$ December 2015
- B
$15^{\text {th }}$ November 2015
- ✓
$18^{\text {th }}$ December 2015
- D
$18^{\text {th }}$ November 2015
AnswerCorrect option: C. $18^{\text {th }}$ December 2015
$18^{\text {th }}$ December 2015
View full question & answer→MCQ 761 Mark
Choose the correct alternative:
The integrating factor of $\frac{ d y}{ d x}+y= e ^{- x }$ is
- A
$x$
- B
$-x$
- ✓
$e^x$
- D
$y=e^{-x}$
View full question & answer→MCQ 771 Mark
$
\int_4^9 \frac{ d x}{\sqrt{x}}=
$
View full question & answer→MCQ 781 Mark
$\int x^2 3^{x^3} d x=$
AnswerCorrect option: B. $\frac{(3)^{x^3}}{3 \log 3}+c$
$\frac{(3)^{x^3}}{3 \log 3}+ c$
View full question & answer→MCQ 791 Mark
The function $f(x)=x^3-3 x^2+3 x-100, x \in R$ is
- ✓
increasing for all $x \in R, x \neq 1$
- B
- C
neither increasing nor decreasing
- D
decreasing for all $x \in R, x \neq 1$
AnswerCorrect option: A. increasing for all $x \in R, x \neq 1$
increasing for all x ∈ R, x ≠ 1
View full question & answer→MCQ 801 Mark
What is the rate of change of demand ( $x$ ) of a commodity with respect to its price (y) if $y=10+$ $x+25 x^3$.
- A
$\frac{10}{1+75 x^2}$
- ✓
$\frac{1}{1+75 x^2}$
- C
$1+75 x^2$
- D
$\frac{-1}{1+75 x^2}$
AnswerCorrect option: B. $\frac{1}{1+75 x^2}$
$\frac{1}{1+75 x^2}$
View full question & answer→MCQ 811 Mark
If $A =\left[\begin{array}{ccc}1 & \frac{3}{5} & x \\ y & -5 & -7 \\ -4 & -7 & 0\end{array}\right]$ is a symmetric matrix, then the values of $x$ and $y$ are respectively.
- A
$\frac{3}{5}$ and 4
- B
$\frac{5}{3}$ and -4
- C
$\frac{3}{5}$ and -4
- ✓
-4 and $\frac{3}{5}$
AnswerCorrect option: D. -4 and $\frac{3}{5}$
$-4$ and $\frac{3}{5}$
View full question & answer→MCQ 821 Mark
The assignment problem is solved by ______
MCQ 831 Mark
Dorbish–Bowley’s Price Index Number is
- A
$P _{01}( L )+ P _{01}( P )$
- B
$P _{01}( L )- P _{01}( P )$
- C
$\frac{ P _{01}( L )+ P _{01}( P )}{2} \times 100$
- ✓
$\frac{ P _{01}( L )+ P _{01}( P )}{2}$
AnswerCorrect option: D. $\frac{ P _{01}( L )+ P _{01}( P )}{2}$
$\frac{ P _{01}( L )+ P _{01}( P )}{2}$
View full question & answer→MCQ 841 Mark
Choose the correct alternative:
The following trend line equation was developed for annual sales from 1984 to 1990 with 1984 as base or zero year.
$Y=500+60 X$ (in 1000 ₹). The estimated sales for 1984 (in 1000 ₹) is
View full question & answer→MCQ 851 Mark
Choose the correct alternative:
If $b_{y x}<0$ and $b_{x y}<0$, then $r$ is____.
View full question & answer→MCQ 861 Mark
Multiple choice questions:
The amount which can be demanded under the policy is_____.
MCQ 871 Mark
If $p$ is any statement, then $(p \vee \sim p)$ is a
View full question & answer→MCQ 881 Mark
X : is number obtained on upper most face when a fair die is thrown then E(X) = ______
AnswerX : is number obtained on upper most face when a fair die is thrown then E(X) = 3.5
View full question & answer→MCQ 891 Mark
Choose the correct alternative:
The present worth of ₹ 11,660 due 9 months hence is ₹ 11,000. The True discount is___.
- ✓
- B
$₹ 750$
- C
$₹ 400$
- D
$₹ 5,940$
View full question & answer→MCQ 901 Mark
Choose the correct alternative:
Bacterial increases at the rate proportional to the number present. If original number $M$ doubles in 3 hours, then number of bacteria will be $4 M$ in
View full question & answer→MCQ 911 Mark
$
\int_0^{ a } 3 x^5 d x=8 \text {, then } a =
$
View full question & answer→MCQ 921 Mark
$\int \sqrt{1+x} d x=$
- A
$\frac{x}{2} \sqrt{1+x}+ c$
- ✓
$\frac{2}{3}(1+x)^{\frac{3}{2}}+ c$
- C
$\frac{2}{\sqrt{1+x}}+ c$
- D
$\frac{-3}{2}(1+x)+ c$
AnswerCorrect option: B. $\frac{2}{3}(1+x)^{\frac{3}{2}}+ c$
$\frac{2}{3}(1+x)^{\frac{3}{2}}+ c$
View full question & answer→MCQ 931 Mark
Slope of the normal to the curve $2 x^2+3 y^2=5$ at the point $(1,1)$ on it is
- A
$-\frac{2}{3}$
- B
$\frac{2}{3}$
- ✓
$\frac{3}{2}$
- D
$-\frac{3}{2}$
AnswerCorrect option: C. $\frac{3}{2}$
$\frac{3}{2}$
View full question & answer→MCQ 941 Mark
If $y =\sqrt[3]{\left(3 x^2+8 x-6\right)^5}$, then $\frac{ d y}{ d x}=$ ?
- ✓
$\frac{5}{3}(6 x+8)\left(3 x^2+8 x-6\right)^{\frac{2}{3}}$
- B
$\frac{-5}{3}(6 x+8)\left(3 x^2+8 x-6\right)^{\frac{2}{3}}$
- C
$\frac{3}{5}(3 x+4)\left(3 x^2+8 x-6\right)^{\frac{2}{3}}$
- D
$\frac{-3}{5}(3 x+4)\left(3 x^2+8 x-6\right)^{\frac{2}{3}}$
AnswerCorrect option: A. $\frac{5}{3}(6 x+8)\left(3 x^2+8 x-6\right)^{\frac{2}{3}}$
$\frac{5}{3}(6 x+8)\left(3 x^2+8 x-6\right)^{\frac{2}{3}}$
View full question & answer→MCQ 951 Mark
If $B=\left[\begin{array}{cc}6 & 3 \\ -2 & k \end{array}\right]$ is singular matrix, then the value of $k$ is
View full question & answer→MCQ 961 Mark
Assignment Problem is special case of ______
- ✓
Linear Programming Problem
- B
- C
- D
AnswerCorrect option: A. Linear Programming Problem
Linear Programming Problem
View full question & answer→MCQ 971 Mark
The formula $P_{01}=\frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$ is for
- ✓
Laspeyre’s Price Index Number
- B
Paasche’s Price Index Number
- C
Fisher’s Price Index Number
- D
Walsh’s Price Index Number
AnswerCorrect option: A. Laspeyre’s Price Index Number
Laspeyre’s Price Index Number
View full question & answer→MCQ 981 Mark
Which component of time series refers to erratic time series movements that follow no recognizable or regular pattern?
MCQ 991 Mark
Choose the correct alternative:
If the regression equation $X$ on $Y$ is $3 x+2 y=26$, then $b_{x y}$ equal to
- A
$\frac{3}{2}$
- B
$\frac{2}{3}$
- C
$-\frac{3}{2}$
- ✓
$-\frac{2}{3}$
AnswerCorrect option: D. $-\frac{2}{3}$
$-\frac{2}{3}$
View full question & answer→MCQ 1001 Mark
Multiple choice questions:
In an ordinary annuity, payments or receipts occur at____.
MCQ 1011 Mark
Which of the following is not a statement?
- A
$2+2=4$
- B
2 is the only even prime number
- ✓
- D
Mumbai is not in Maharashtra
View full question & answer→MCQ 1021 Mark
f(x) is c.d.f. of discete r.v. X whose distribution is
| $x_i$ |
– 2 |
– 1 |
0 |
1 |
2 |
| $p_i$ |
0.2 |
0.3 |
0.15 |
0.25 |
0.1 |
then F(– 3) = ______ View full question & answer→MCQ 1031 Mark
Choose the correct alternative:
A salesman receives $3 \%$ commission on the sales up to ₹ 50,000 and $4 \%$ commission on the sales over $₹ 50,000$. His total income on the sale of $₹ 2,00,000$ is______.
- A
$₹ 6,000$
- B
$₹ 7,550$
- ✓
$₹ 7,500$
- D
$₹ 1,500$
AnswerCorrect option: C. $₹ 7,500$
A salesman receives $3 \%$ commission on the sales up to $\text{₹} 50,000$ and $4 \%$ commission on the sales over $\text{₹} 50,000$. His total income on the sale of \text{₹} $2,00,000$ is $\text{₹} 7, \underline{500}$.
Explanation -
Salesman earns $3 \%$ commission on the sales upto $\text{₹} 50,000$ and $4 \%$ commission on the sales over $\text{₹} 50,000 .$
His total sales is $\text{₹} 2,00,000$.
Commission on sales upto $\text{₹} 50,000$
$=50,000 \times \frac{3}{100} $
$=\text{₹} 1,500$
Commission on sales over $\text{₹} 50,000$
$=(2,00,000-50,000) \times \frac{4}{100} $
$=1,50,000 \times \frac{4}{100} $
$=\text{₹} 6,000$
Total commission $=1,500+6,000=\text{₹} 7,500$
Total income on the sale of $\text{₹} 2,00,000$ is $\text{₹} 7,500 .$
View full question & answer→MCQ 1041 Mark
Choose the correct alternative:
Solution of the equation $x \frac{ d y}{ d x}= y \log y$ is
- A
$y=a e^x$
- B
$y=b e^{2 x}$
- C
$y=b e^{-2 x}$
- ✓
$y=e^{a x}$
AnswerCorrect option: D. $y=e^{a x}$
$y=b e^{2 x}$
View full question & answer→MCQ 1051 Mark
$
\int_2^3 x^4 d x=
$
- A
$\frac{1}{2}$
- B
$\frac{5}{2}$
- C
$\frac{5}{211}$
- ✓
$\frac{211}{5}$
AnswerCorrect option: D. $\frac{211}{5}$
$\frac{211}{5}$
View full question & answer→MCQ 1061 Mark
The value of $\int \frac{ d x}{\sqrt{1-x}}$ is
- A
$2 \sqrt{1-x}+ c$
- ✓
$-2 \sqrt{1-x}+ c$
- C
$\sqrt{x}+ c$
- D
$x+c$
AnswerCorrect option: B. $-2 \sqrt{1-x}+ c$
$-2 \sqrt{1-x}+ c$
View full question & answer→MCQ 1071 Mark
The slope of the tangent to the curve $y=x^3-x^2-1$ at the point whose abscissa is -2 , is _______
AnswerThe slope of the tangent to the curve $y=x^3-x^2-1$ at the point whose abscissa is -2 , is 16 .
View full question & answer→MCQ 1081 Mark
If $y =\frac{1}{\sqrt{3 x^2-2 x-1}}$, then $\frac{ d y}{ d x}=$ ?
- A
$\frac{-2}{3}(3 x-2)\left(3 x^2-2 x-1\right)^{\frac{-3}{2}}$
- B
$\frac{-3}{2}(3 x-2)\left(3 x^2-2 x-1\right)^{\frac{-3}{2}}$
- C
$(3 x-1)\left(3 x^2-2 x-1\right)^{\frac{-3}{2}}$
- ✓
$-(3 x-1)\left(3 x^2-2 x-1\right)^{\frac{-3}{2}}$
AnswerCorrect option: D. $-(3 x-1)\left(3 x^2-2 x-1\right)^{\frac{-3}{2}}$
$-(3 x-1)\left(3 x^2-2 x-1\right)^{\frac{-3}{2}}$
View full question & answer→MCQ 1091 Mark
If $A=\left[\begin{array}{ll}6 & 0 \\ p & q\end{array}\right]$ is a scalar matrix, then the values of $p$ and $q$ are respectively.
View full question & answer→MCQ 1101 Mark
The assignment problem is generally defined as a problem of ______
MCQ 1111 Mark
Price Index Number by using Weighted Aggregate Method is given by
- A
$\frac{\sum p_1 q}{\sum p_0 q} \times 100$
- B
$\sum p _1 w \times 100$
- ✓
$\frac{\sum p _1 w }{\sum p _0 w } \times 100$
- D
$\frac{\sum p _0 w }{\sum p _1 w } \times 100$
AnswerCorrect option: C. $\frac{\sum p _1 w }{\sum p _0 w } \times 100$
$\frac{\sum p _1 w }{\sum p _0 w } \times 100$
View full question & answer→MCQ 1121 Mark
Choose the correct alternative:
Which of the following can't be a component of a time series?
MCQ 1131 Mark
Choose the correct alternative:
If for a bivariate data, $b_{Y X}=-1.2$ and $b_{X Y}=-0.3$, then $r=$_____.
View full question & answer→MCQ 1141 Mark
Multiple choice questions:
Rental payment for an apartment is an example of_____.
MCQ 1151 Mark
Which of the following statement is true?
- A
$3+7=4$ or $3-7=4$
- B
If Pune is in Maharashtra, then Hyderabad is in Kerala
- ✓
It is false that 12 is not divisible by 3
- D
The square of any odd integer is even
AnswerCorrect option: C. It is false that 12 is not divisible by 3
It is false that 12 is not divisible by 3
View full question & answer→MCQ 1161 Mark
Choose the correct alternative:
If $r=0.5, \sigma_x=3, \sigma_y^2=16$, then $b_{x y}=$_____.
View full question & answer→MCQ 1171 Mark
Choose the correct alternative:
$y=5-2.8 x$ and $x=3-0.5 y$ be the regression lines, then the value of $b_{y x}$ is
View full question & answer→MCQ 1181 Mark
Choose the correct alternative:
$u =\frac{x-20}{5}$ and $v =\frac{y-30}{4}$, then $b _{ xy }=$
- A
$\frac{4}{5} b_{v u}$
- B
$\frac{4}{5} b_{u v}$
- ✓
$\frac{5}{4} b_{u v}$
- D
$\frac{5}{4} b_{u v}$
AnswerCorrect option: C. $\frac{5}{4} b_{u v}$
$\frac{5}{4} b _{ uv }$
View full question & answer→MCQ 1191 Mark
Choose the correct alternative:
The regression line is obtained by
- ✓
Minimizing the sum of squares of deviations of the predicted values from the observed values
- B
Minimizing the sum of deviations of the predicted values from the observed values
- C
Maximizing the sum of squares deviations of the predicted values from the observed values
- D
Maximizing the sum of deviations of the predicted values from the observed values
AnswerCorrect option: A. Minimizing the sum of squares of deviations of the predicted values from the observed values
Minimizing the sum of squares of deviations of the predicted values from the observed values
View full question & answer→MCQ 1201 Mark
Choose the correct alternative:
If $r=0.5, \sigma_x=3, \sigma_y^2=16$, then $b_{y x}=$_______.
View full question & answer→MCQ 1211 Mark
In solving 2 machine and n jobs sequencing problem, the following assumption is wrong
- A
- B
Processing times are known
- C
Handling time is negligible
- ✓
The time of passing depends on the order of machining
AnswerCorrect option: D. The time of passing depends on the order of machining
The time of passing depends on the order of machining
View full question & answer→MCQ 1221 Mark
Choose the correct alternative:
If the lines of regression of $Y$ on $X$ is $y=\frac{x}{4}$ and $X$ on $Y$ is $x=\frac{y}{9}+1$ then the value of $r$ is
- ✓
$\frac{1}{6}$
- C
$-\frac{1}{4}$
- D
$-\frac{1}{6}$
AnswerCorrect option: A. $\frac{1}{6}$
$\frac{1}{6}$
View full question & answer→MCQ 1231 Mark
If $x = at ^2, y =2 at$, then $\frac{ d ^2 y}{ d x^2}=$ ?
- A
$\frac{1}{ at ^3}$
- B
$\frac{-1}{2 at ^3}$
- C
$\frac{-1}{ at ^2}$
- ✓
$\frac{1}{ at ^2}$
AnswerCorrect option: D. $\frac{1}{ at ^2}$
$\frac{-1}{2 a t^3}$
View full question & answer→MCQ 1241 Mark
If there are n jobs and m machines, then there will be _______ sequence of doing jobs.
AnswerCorrect option: D. $(n!)^m$
If there are n jobs and m machines, then there will be $(n!)^m$ sequence of doing jobs.
View full question & answer→MCQ 1251 Mark
Choose the correct alternative:
$b_{x y}$ and $b_{y x}$ are___.
- A
Independent of change of origin and scale
- ✓
Independent of change of origin but not of scale
- C
Independent of change of scale but not of origin
- D
Affected by change of origin and scale
AnswerCorrect option: B. Independent of change of origin but not of scale
Independent of change of origin but not of scale
View full question & answer→MCQ 1261 Mark
Choose the correct alternative:
The solution of $\frac{ d y}{ d x}+\frac{x^2}{y^2}=0$ is
- A
$x^3+y^3=7$
- B
$x^2+y^2=c$
- ✓
$x^3+y^3=c$
- D
$x+y=c$
AnswerCorrect option: C. $x^3+y^3=c$
$x^3+y^3=c$
View full question & answer→MCQ 1271 Mark
$
\int \frac{\left(x^3+3 x^2+3 x+1\right)}{(x+1)^5} d x=
$
AnswerCorrect option: A. $\frac{-1}{x+1}+ c$
$\frac{-1}{x+1}+ c$
View full question & answer→MCQ 1281 Mark
If $x = a \left( t -\frac{1}{ t }\right), y = a \left( t +\frac{1}{ t }\right)$, where $t$ be the parameter, then $\frac{ d y}{ d x}=$ ?
- ✓
$\frac{x}{y}$
- B
$\frac{-x}{y}$
- C
$\frac{y}{x}$
- D
$\frac{-y}{x}$
AnswerCorrect option: A. $\frac{x}{y}$
$\frac{x}{y}$
View full question & answer→MCQ 1291 Mark
If $A^2+5 A+3|=0| A \mid, \neq 0$, then $A^{-1}=$ ______
- ✓
$\frac{-1}{3}( A +5 I )$
- B
$\frac{-1}{5}( A +3 I )$
- C
$(A+15 I)$
- D
$\frac{-1}{3}( I +5 A )$
AnswerCorrect option: A. $\frac{-1}{3}( A +5 I )$
If $A^2+5 A+3|=0| A \mid, \neq 0$, then $A^{-1}=\frac{- 1 }{ 3 }( A + 5 I )$
View full question & answer→MCQ 1301 Mark
The objective of sequencing problem is ______
- A
to find the order in which jobs are to be made
- B
to find the time required for the completing all the job on hand
- ✓
to find the sequence in which jobs on hand are to be processed to minimize the total time required for processing the jobs
- D
AnswerCorrect option: C. to find the sequence in which jobs on hand are to be processed to minimize the total time required for processing the jobs
to find the sequence in which jobs on hand are to be processed to minimize the total time required for processing the jobs
View full question & answer→MCQ 1311 Mark
Choose the correct alternative:
In the regression equation of $X$ on $Y$
- A
X is independent and Y is dependent
- ✓
Y is independent and X is dependent
- C
Both X and Y are independent
- D
Both X and Y are dependent
AnswerCorrect option: B. Y is independent and X is dependent
Y is independent and X is dependent.
View full question & answer→MCQ 1321 Mark
Multiple choice questions:
The present value of an immediate annuity of ₹ 10,000 paid each quarter for four quarters at $16 \%$ p.a. compounded quarterly is_____.
View full question & answer→MCQ 1331 Mark
The false statement in the following is ______.
- A
$p \wedge(\sim p)$ is contradiction
- ✓
$( p \rightarrow q ) \leftrightarrow(\sim q \rightarrow \sim p )$ is a contradiction
- C
$\sim(\sim p) \leftrightarrow p$ is a tautology
- D
$p \vee(\sim p) \leftrightarrow p$ is a tautology
AnswerCorrect option: B. $( p \rightarrow q ) \leftrightarrow(\sim q \rightarrow \sim p )$ is a contradiction
The false statement in the following is
(p → q) ↔ (∼ q → ∼ p) is a contradiction.
Explanation:
(p → q) ↔ (∼ q → ∼ p)
| p | q | ∼ p | ∼ q | p → q | ∼ q → ∼ p | (p → q) ↔ (∼ q → ∼ p) |
| T | T | F | F | T | T | T |
| T | F | F | T | F | F | T |
| F | T | T | F | T | T | T |
| F | F | T | T | T | T | T |
In the above table, all the entries in the last column are T. Therefore, the given statement pattern is a tautology.
∴ The false statement is (p → q) ↔ (∼ q → ∼ p) is a contradiction.
View full question & answer→MCQ 1341 Mark
The variance of a Binomial distribution is given by ______
MCQ 1351 Mark
The corner points of the feasible region are $(0,3),(3,0),(8,0),\left(\frac{12}{5}, \frac{38}{5}\right)$ and $(0,10)$, then the point of maximum $Z=6 x+4 y=48$ is at
AnswerCorrect option: B. $(8,0)$
View full question & answer→MCQ 1361 Mark
The corner points of feasible region for the inequations, $x+y \leq 5, x+2 y \leq 6, x \geq 0$, $y$ $\geq 0$ are
- A
$(0,3),(5,0),(0,5),(6,0)$
- ✓
$(0,3),(5,0),(4,1),(0,0)$
- C
$(0,0),(1,4),(5,0),(0,3)$
- D
$(3,0),(0,5),(0,0),(4,1)$
AnswerCorrect option: B. $(0,3),(5,0),(4,1),(0,0)$
(0, 3), (5, 0), (4, 1), (0, 0)
View full question & answer→MCQ 1371 Mark
Area of the region bounded by the parabola $y^2=25 x$ and the lines $x=5$ is ______
- A
$\frac{75 \sqrt{5}}{2}$ sq.units
- B
$\frac{20 \sqrt{5}}{3}$ sq.units
- ✓
$\frac{100 \sqrt{5}}{3}$ sq.units
- D
$\frac{75 \sqrt{5}}{3}$ sq.units
AnswerCorrect option: C. $\frac{100 \sqrt{5}}{3}$ sq.units
$\frac{100 \sqrt{5}}{3}$ sq.units
View full question & answer→MCQ 1381 Mark
$Z=9 x+13 y$ subjected to constraints $2 x+3 y \leq 18,2 x+y \leq 10,0 \leq x, y$ was found to be maximum at the point
View full question & answer→MCQ 1391 Mark
Area of the region bounded by $x=y^4, y=1$ and $y=5$ and the $Y$-axis lying in the first quadrant is _______
- ✓
$\frac{3124}{5}$ sq.units
- B
$\frac{3142}{5}$ sq.units
- C
$\frac{3124}{3}$ sq.units
- D
$\frac{3142}{3}$ sq.units
AnswerCorrect option: A. $\frac{3124}{5}$ sq.units
$\frac{3124}{5}$ sq.units
View full question & answer→MCQ 1401 Mark
The point at which the maximum value of $Z=4 x+6 y$ subject to the constraints $3 x+$ $2 y \leq 12, x+y \geq 4, x \geq 0, y \geq 0$ is obtained at the point
View full question & answer→MCQ 1411 Mark
Area of the region bounded by $y^2=16 x, x=1$ and $x=4$ and the $X$ axis, lying in the first quadrant is _______
- ✓
$\frac{56}{3}$ sq.units
- B
$\frac{3}{56}$ sq.units
- C
- D
AnswerCorrect option: A. $\frac{56}{3}$ sq.units
$\frac{56}{3}$ sq.units
View full question & answer→MCQ 1421 Mark
The point at which the minimum value of $Z=8 x+12 y$ subject to the constraints $2 x+$ $y \geq 8, x+2 y \geq 10, x \geq 0, y \geq 0$ is obtained at the point
View full question & answer→MCQ 1431 Mark
Area of the region bounded by the curve $x^2=8 y$, the positive $Y$-axis lying in the first quadrant and the lines $y=4$ and $y=9$ is _________
- ✓
$\frac{76 \sqrt{2}}{3}$ sq.units
- B
$\frac{76 \sqrt{2}}{2}$ sq.units
- C
$\frac{38 \sqrt{2}}{3}$ sq.units
- D
$76 \sqrt{2}$ sq.units
AnswerCorrect option: A. $\frac{76 \sqrt{2}}{3}$ sq.units
$\frac{76 \sqrt{2}}{3}$ sq.units
View full question & answer→MCQ 1441 Mark
The minimum value of $Z=4 x+5 y$ subjected to the constraints $x+y \geq 6,5 x+y \geq 10,$ $x, y \geq 0$ is
View full question & answer→MCQ 1451 Mark
Area of the region bounded by the curve $x=y^2$, the positive $Y$ axis and the lines $y=1$ and $y=3$ is _____
- A
- B
- C
$\frac{3}{26}$ sq.units
- ✓
$\frac{26}{3}$ sq.units
AnswerCorrect option: D. $\frac{26}{3}$ sq.units
Area of the region bounded by the curve $x=y^2$, the positive $Y$ axis and the lines $y=1$ and $y$ $=3$ is $\frac{ 2 6 }{ 3 }$ sq.units
View full question & answer→MCQ 1461 Mark
The maximum value of $Z=3 x+5 y$ subjected to the constraints $x+y \leq 2,4 x+3 y \leq$ $12, x \geq 0, y \geq 0$ is
View full question & answer→MCQ 1471 Mark
Using the definite integration area of the circle $x^2+y^2=16$ is ______
View full question & answer→MCQ 1481 Mark
- A
common region determined by all the constraints
- B
common region determined by the non-negativity constraints
- C
either common region determined by all the constraints or common region determined by the non-negativity constraints
- ✓
both common region determined by all the constraints and common region determined by the non-negativity constraints
AnswerCorrect option: D. both common region determined by all the constraints and common region determined by the non-negativity constraints
both common region determined by all the constraints and common region determined by the non-negativity constraints
View full question & answer→MCQ 1491 Mark
Area of the region bounded by the curve $y=x^3, x=1, x=4$ and the $X$-axis is _______
- ✓
$\frac{225}{4}$ sq.units
- B
$\frac{256}{4}$ sq.units
- C
$\frac{255}{3}$ sq.units
- D
$\frac{256}{3}$ sq.units
AnswerCorrect option: A. $\frac{225}{4}$ sq.units
$\frac{225}{4}$ sq.units
View full question & answer→MCQ 1501 Mark
If LPP has optimal solution at two point, then
- A
LPP will give unique solution
- B
LPP will give two solutions
- ✓
LPP will give infinite solutions
- D
LPP will not give any convex set
AnswerCorrect option: C. LPP will give infinite solutions
LPP will give infinite solutions
View full question & answer→MCQ 1511 Mark
How does a constraint, “A washing machine can hold up to 8 kilograms of cloths (X)” can be given?
- A
$X \geq 8$
- ✓
$X \leq 8$
- C
$X \neq 8$
- D
$X=8$
AnswerCorrect option: B. $X \leq 8$
View full question & answer→MCQ 1521 Mark
The constraint that in a college there are more scholarship holders in FYJC class (X) than in SYJC class (Y) is given by
- ✓
$X>Y$
- B
$X
- C
$X=Y$
- D
$X \neq Y$
View full question & answer→MCQ 1531 Mark
The corner points of the feasible region are (4, 2), (5, 0), (4, 1) and (6, 0), then the point of minimum Z = 3.5x + 2y = 16 is at