1
GATE CSE 2016 Set 1
Numerical
+1
-0
Two eigenvalues of a $$3 \times 3$$ real matrix $$P$$ are $$\left( {2 + \sqrt { - 1} } \right)$$ and $$3.$$ The determinant of $$P$$ is _______.
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2
GATE CSE 2016 Set 1
Numerical
+1
-0
$$\mathop {\lim }\limits_{x \to 4} {{\sin \left( {x - 4} \right)} \over {x - 4}} = \_\_\_\_\_\_\_.$$
Your input ____
3
GATE CSE 2016 Set 1
Numerical
+2
-0
Consider the following experiment.
Step1: Flip a fair coin twice.
Step2: If the outcomes are (TAILS, HEADS) then output $$Y$$ and stop.
Step3: If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $$N$$ and stop.
Step4: If the outcomes are (TAILS, TAILS), then go to Step 1.

The probability that the output of the experiment is $$Y$$ is (up to two decimal places) _____________.

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4
GATE CSE 2016 Set 1
Numerical
+1
-0
A probability density function on the interval $$\left[ {a,1} \right]$$ is given by $$1/{x^2}$$ and outside this interval the value of the function is zero. The value of $$a$$ is _________.
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