1
GATE CSE 2017 Set 2
Numerical
+1
-0
Consider a quadratic equation $${x^2} - 13x + 36 = 0$$ with coefficients in a base $$b.$$ The solutions of this equation in the same base $$b$$ are $$x=5$$ and $$x=6$$. Then $$b=$$ ______.
Your input ____
2
GATE CSE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
$$P$$ and $$Q$$ are considering to apply for a job. The probability that $$P$$ applies for the job is $${1 \over 4},$$ the probability that $$P$$ applies for the job given that $$Q$$ applies for the job is $${1 \over 2},$$ and the probability that $$Q$$ applies for the job given that $$P$$ applies for the job is $${1 \over 3}.$$ Then the probability that $$P$$ does not apply for the job given that $$Q$$ does not apply for the job is
A
$${4 \over 5}$$
B
$${5 \over 6}$$
C
$${7 \over 8}$$
D
$${11 \over 12}$$
3
GATE CSE 2017 Set 2
Numerical
+2
-0
If a random variable $$X$$ has a Poisson distribution with mean $$5,$$ then the expectation $$E\left[ {{{\left( {X + 2} \right)}^2}} \right]$$ equals _________.
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4
GATE CSE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
For any discrete random variable $$X,$$ with probability mass function $$P\left( {X = j} \right) = {p_j},$$
$${p_j}\,\, \ge 0,\,j \in \left\{ {0,..........,\,\,\,N} \right\},$$ and $$\,\,\sum\limits_{j = 0}^N {{p_j} = 1,\,\,} $$ define the polynomial function $${g_x}\left( z \right) = \sum\limits_{j = 0}^N {{p_j}{z^j}} .$$ For a certain discrete random variable $$Y$$, there exists a scalar $$\beta $$ $$ \in \left[ {0,1} \right]$$ such that $${g_y}\left( z \right) = {\left\{ {1 - \beta + \left. {\beta z} \right)} \right.^N}.$$ The expectation of $$Y$$ is
A
$$N\beta \left( {1 - \beta } \right)$$
B
$$N\beta \left( {1 - \beta } \right)$$
C
$$N\left( {1 - \beta } \right)$$
D
Not expressible in terms of $$N$$ and $$\beta $$ alone
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