1
GATE CSE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let $$A$$ be $$n\,\, \times \,\,n$$ real valued square symmetric matrix of rank $$2$$ with $$\sum\limits_{i = 1}^n {\sum\limits_{j = 1}^n {A_{ij}^2 = 50.} } $$
Consider the following statements.
$$(I)$$ One eigenvalue must be in $$\left[ { - 5,5} \right]$$
$$(II)$$ The eigenvalue with the largest magnitude must be strictly greater than $$5$$
Which of the above statements about engenvalues of $$A$$ is/are necessarily correct?
A
Both $$(I)$$ and $$(II)$$
B
$$(I)$$ only
C
$$(II)$$ only
D
Neither $$(I)$$ nor $$(II)$$
2
GATE CSE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Let $${c_1},.....,\,\,{c_n}$$ be scalars, not all zero, such that $$\sum\limits_{i = 1}^n {{c_i}{a_i} = 0} $$ where $${{a_i}}$$ are column vectors in $${R^{11}}.$$ Consider the set of linear equations $$AX=b$$

Where $$A = \left[ {{a_1},.....,\,\,{a_n}} \right]$$ and $$b = \sum\limits_{i = 1}^n {{a_i}.} $$
The set of equations has

A
a unique solution at $$x\,\,\, = \,\,\,{J_n}$$ where $${J_n}$$ denotes a $$n$$-dimensional vector of all $$1$$
B
no solution
C
infinitely many solutions
D
finitely many solutions
3
GATE CSE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
The value of $$\mathop {\lim }\limits_{x \to 1} {{{x^7} - 2{x^5} + 1} \over {{x^3} - 3{x^2} + 2}}.$$
A
is $$0$$
B
is $$-1$$
C
is $$1$$
D
does not exit
4
GATE CSE 2017 Set 1
Numerical
+1
-0
Let $$X$$ be a Gaussian random variable with mean $$0$$ and variance $${\sigma ^2}$$ . Let $$Y=max(X,0)$$ where $$max(a, b)$$ is the maximum of $$a$$ and $$b$$. The median of $$Y$$ is ___________.
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