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Recent questions tagged isi2017-mma
6
votes
5
answers
31
ISI2017-MMA-21
There are four machines and it is known that exactly two of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. The probability that only two tests are required is $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{6}\right)$
There are four machines and it is known that exactly two of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. Th...
jjayantamahata
2.7k
views
jjayantamahata
asked
Mar 28, 2018
Probability
isi2017-mma
engineering-mathematics
probability
+
–
3
votes
2
answers
32
ISI2017-MMA-19
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 - px +q = 0$, then the value of the determinant $\begin{vmatrix}\alpha & \beta & \gamma\\\beta & \gamma & \alpha\\\gamma & \alpha & \beta\end{vmatrix}$ is $p$ $p^2$ $0$ $p^2+6q$
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 - px +q = 0$, then the value of the determinant$$\begin{vmatrix}\alpha & \beta & \gamma\\\beta & \gamma & \alpha\\\g...
jjayantamahata
825
views
jjayantamahata
asked
Mar 28, 2018
Linear Algebra
isi2017-mma
engineering-mathematics
linear-algebra
determinant
+
–
4
votes
1
answer
33
ISI2017-MMA-17
Suppose that $X$ is chosen uniformly from $\{1,2,\ldots,100\}$ and given $X =x$, $Y$ is chosen uniformly from $\{1,2,\ldots,x\}. $Then $P(Y = 30)=$ $\dfrac{1}{100}$ $\dfrac{1}{100} \times \left(\dfrac{1}{30} + \ldots+\dfrac{1}{100}\right)$ $\dfrac{1}{30}$ $\dfrac{1}{100} \times \left(\dfrac{1}{1} + \ldots +\dfrac{1}{30}\right)$
Suppose that $X$ is chosen uniformly from $\{1,2,\ldots,100\}$ and given $X =x$, $Y$ is chosen uniformly from $\{1,2,\ldots,x\}. $Then $P(Y = 30)=$$\dfrac{1}{100}$$\dfrac...
jjayantamahata
1.5k
views
jjayantamahata
asked
Mar 27, 2018
Probability
isi2017-mma
engineering-mathematics
probability
uniform-distribution
+
–
2
votes
2
answers
34
ISI2017-MMA-15
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then $M$ must be singular $M$ must be nonsingular There is not enough information to decide the singularity of $M$ $M$ must have a positive eigenvalue.
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then$M$ must be singular$M$ must be nonsingularThere is not enoug...
jjayantamahata
1.3k
views
jjayantamahata
asked
Mar 27, 2018
Linear Algebra
isi2017-mma
engineering-mathematics
linear-algebra
matrix
+
–
3
votes
2
answers
35
ISI2017-MMA-14
Let $(v_n)$ be a sequence defined by $v_1 = 1$ and $v_{n+1} = \sqrt{v_n^2 +\left(\dfrac{1}{5}\right)^n}$ for $n\geq1$. Then $\displaystyle{\lim_{n \rightarrow \infty}v_n}$ is $\sqrt{5/3}$ $\sqrt{5/4}$ $1$ $\text{non existent}$
Let $(v_n)$ be a sequence defined by $v_1 = 1$ and $v_{n+1} = \sqrt{v_n^2 +\left(\dfrac{1}{5}\right)^n}$ for $n\geq1$. Then $\displaystyle{\lim_{n \rightarrow \infty}v_n}...
jjayantamahata
1.4k
views
jjayantamahata
asked
Mar 27, 2018
Calculus
isi2017-mma
engineering-mathematics
calculus
limits
+
–
3
votes
3
answers
36
ISI2017-MMA-13
An even function $f(x)$ has left derivative $5$ at $x=0$. Then the right derivative of $f(x)$ at $x=0$ need not exist the right derivative of $f(x)$ at $x=0$ exists and is equal to $5$ the right derivative of $f(x)$ at $x=0$ exists and is equal to $-5$ none of the above is necessarily true
An even function $f(x)$ has left derivative $5$ at $x=0$. Thenthe right derivative of $f(x)$ at $x=0$ need not existthe right derivative of $f(x)$ at $x=0$ exists and is ...
jjayantamahata
2.0k
views
jjayantamahata
asked
Mar 27, 2018
Calculus
isi2017-mma
engineering-mathematics
calculus
differentiation
+
–
2
votes
3
answers
37
ISI2017-MMA-12
Which of the following statements is true? There are three consecutive integers with sum $2015$ There are four consecutive integers with sum $2015$ There are five consecutive integers with sum $2015$ There are three consecutive integers with product $2015$
Which of the following statements is true?There are three consecutive integers with sum $2015$There are four consecutive integers with sum $2015$There are five consecutiv...
jjayantamahata
1.1k
views
jjayantamahata
asked
Mar 27, 2018
Quantitative Aptitude
isi2017-mma
general-aptitude
quantitative-aptitude
+
–
8
votes
3
answers
38
ISI2017-MMA-5
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$? $1$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{2}\right)$
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$?$1$$\left(\dfrac{1}{3}\right)$$\left(\dfrac{1}{6}\right)$$\left(\dfr...
jjayantamahata
1.6k
views
jjayantamahata
asked
Mar 26, 2018
Linear Algebra
isi2017-mma
engineering-mathematics
linear-algebra
rank-of-matrix
+
–
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