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Having built a decision tree, we are using reduced error pruning to reduce the size of the tree. We select a node to collapse. For this particular node, on the left branch, there are 3 training data points with the following outputs: 5, 7, 9.6 and for the right branch, there are four training data points with the following outputs: 8.7, 9.8, 10.5, 11. What were the original responses for data points along the two branches (left & right respectively) and what is the new response after collapsing the node?
A
10.8, 13.33, 14.48
B
10.8, 13.33, 12.06
C
7.2, 10, 8.8
D
7.2, 10, 8.6
Correct Answer:
7.2, 10, 8.8
Consider the 5 × 5 matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&2&3&4&5 \\ 5&1&2&3&4 \\ 4&5&1&2&3 \\ 3&4&5&1&2 \\ 2&3&4&5&1 \end{array}} \right
A
\
B
<br>It is given that A has only one real eigen value.<br>Then the real eigen value of A is
C
<p><span>A.</span> -2.5
D
</span> 0
Suppose on performing reduced error pruning, we collapsed a node and observed an improvement in the prediction accuracy on the validation set. Which among the following statements are possible in light of the performance improvement observed? (a) The collapsed node helped overcome the effect of one or more noise affected data points in the training set (b) The validation set had one or more noise affected data points in the region corresponding to the collapsed node (c) The validation set did not have any data points along at least one of the collapsed branches (d) The validation set did have data points adversely affected by the collapsed node
A
a and b
B
a and d
C
b, c and d
D
all of the above
Let the function
\[{\text{f}}\left( \theta \right) = \left| {\begin{array}{*{20}{c}} {\sin \theta }&{\cos \theta }&{\tan \theta } \\ {\sin \left( {\frac{\pi }{6}} \right)}&{\cos \left( {\frac{\pi }{6}} \right)}&{\tan \left( {\frac{\pi }{6}} \right)} \\ {\sin \left( {\frac{\pi }{3}} \right)}&{\cos \left( {\frac{\pi }{3}} \right)}&{\tan \left( {\frac{\pi }{3}} \right)} \end{array}} \right|\
A
<br>where \\
B
and \ denote the derivative of f with respect to \. Which of the following statements is/are TRUE?<br>I. There exists \ such that \<br>II. There exists \ such that\
C
<p><span>A.</span> l only
D
</span> ll only
Let A be an m × n matrix and Ban n × m matrix. It is given that determinant ($$I$$
m
+ AB) = determinant ($$I$$
n
+ BA), where $$I$$
k
is the k × k identity matrix. Using the above property, the determinant of the matrix given below is
\[\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right
A
\
B
<p><span>A.</span> 2
C
</span> 5
Eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 0&1&0&0 \\ 1&0&0&0 \\ 0&0&0&{ - 2i} \\ 0&0&{2i}&0 \end{array}} \right
A
\
B
are
C
<p><span>A.</span> -2, -1, 1, 2
D
</span> -1, 1, 0, 2
If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$ + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$ + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$ + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$ is?
A
0
B
5
C
1
D
4
If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$ + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$ + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$ + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$ is?
A
0
B
1
C
4
D
1 + abcd
A university library budget committee must reduce exactly five of eight areas of expenditure—I, J, K, L, M, N, O and P—in accordance with the following conditions: If both I and O are reduced, P is also reduced.
If L is reduced, neither N nor O is reduced.
If M is reduced, J is not reduced.
Of the three areas J, K, and N exactly two are reduced. Question : If both K and N are reduced, which one of the following is a pair of areas neither of which could be reduced?
A
I, L
B
J, L
C
J, M
D
I, J
Some birds settled on the branches of a tree. First, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?
A
3
B
4
C
5
D
6
E
2
The impulse response functions of four linear systems S
1
, S
2
, S
3
, S
4
are given respectively by
$${h_1}\left( t \right) = 1,$$ $${h_2}\left( t \right) = u\left( t \right),$$ $${h_3}\left( t \right) = \frac{{u\left( t \right)}}{{t + 1}},$$ $${h_4}\left( t \right) = {e^{ - 3t}}u\left( t \right)$$
Where u(t) is the unit step function. Which of these systems is time invariant, causal, and stable?
A
S<sub>1</sub>
B
S<sub>2</sub>
C
S<sub>3</sub>
D
S<sub>4</sub>