1
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the system, each consisting of m linear equations in $$n$$ variables.
$$I.$$ $$\,\,\,$$ If $$m < n,$$ then all such system have a solution
$$II.$$ $$\,\,\,$$ If $$m > n,$$ then none of these systems has a solution
$$III.$$ $$\,\,\,$$ If $$m = n,$$ then there exists a system which has a solution

Which one of the following is CORRECT?

A
$$I$$ , $$II$$ and $$III$$ are true
B
Only $$II$$ and $$III$$ are true
C
Only $$III$$ is true
D
None of them is true
2
GATE CSE 2016 Set 2
Numerical
+1
-0
Suppose that the eigen values of matrix $$A$$ are $$1, 2, 4.$$ The determinant of $${\left( {{A^{ - 1}}} \right)^T}$$ is _______.
Your input ____
3
GATE CSE 2016 Set 2
Numerical
+2
-0
Let $${A_1},\,{A_2},\,{A_3}$$ and $${A_4}$$ be four matrices of dimensions $$10 \times 5,\,5 \times 20,\,20 \times 10,$$ and $$10 \times 5,$$ respectively. The minimum number of scalar multiplications required to find the product $${A_1}{A_2}{A_3}{A_4}$$ using the basic matrix multiplication method is _________.
Your input ____
4
GATE CSE 2016 Set 2
Numerical
+2
-0
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $$100$$ hours given that it is of Type $$1$$ is $$0.7,$$ and given that it is of Type $$2$$ is $$0.4.$$ The probability that an LED bulb chosen uniformly at random lasts more than $$100$$ hours is _________.
Your input ____
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