GATE CSE 2017 Set 1 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-0.3

A sender S sends a message m to receiver R, which is digitally signed by S with its private key. In this scenario, one or more of the following security violations can take place.

I. S can launch a birthday attack to replace m with a fraudulent message.
II. A third party attacker can launch a birthday attack to replace m with a fraudulent message.
III. R can launch a birthday attack to replace m with a fraudulent message.

Which of the following are possible security violations?

I and II only

I only

II only

II and III only

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-0.33

Let $T$ be a binary search tree with 15 nodes. The minimum and maximum possible heights of $T$ are :

Note : The height of a tree with a single node is 0.

4 and 15 respectively

3 and 14 respectively

4 and 14 respectively

3 and 15 respectively

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-0.33

The $n$-bit fixed-point representation of an unsigned real number $X$ uses $f$ bits for the fraction part. Let $i=n-f$. The range of decimal values for $X$ in this representation is

$2^{-f}$ to $2^i$

$2^{-f}$ to $\left(2^i-2^{-f}\right)$

0 to $2^i$

0 to $\left(2^i-2^{-f}\right)$

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-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 unique solution at $$x\,\,\, = \,\,\,{J_n}$$ where $${J_n}$$ denotes a $$n$$-dimensional vector of all $$1$$

no solution

infinitely many solutions

finitely many solutions

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