1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Choose the most appropriate equation for the function drawn as a thick line, in the plot below. GATE CSE 2015 Set 3 Discrete Mathematics - Calculus Question 12 English
A
$$x = y - \left| y \right|$$
B
$$x = - \left( {y - \left| y \right|} \right)$$
C
$$x = y + \left| y \right|$$
D
$$x = - \left( {y + \left| y \right|} \right)$$
2
GATE CSE 2015 Set 3
Numerical
+2
-0
Suppose $${X_i}$$ for $$i=1,2,3$$ are independent and identically distributed random variables whose probability mass functions are $$\,\,\Pr \left[ {{X_i} = 0} \right] = \Pr \left[ {{X_i} = 1} \right] = 1/2\,\,$$ for $$i=1,2,3.$$ Define another random variable $$\,\,Y = {X_1}{X_2} \oplus {X_3},\,\,$$ where $$ \oplus $$ denotes $$XOR.$$ Then $$\Pr \left[ {Y = 0\left| {{X_3} = 0} \right.} \right]$$ =________.
Your input ____
3
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If the following system has non - trivial solution $$$px+qy+rz=0$$$ $$$qx+ry+pz=0$$$ $$$rx+py+qz=0$$$

Then which one of the following Options is TRUE?

A
$$p-q+r=0$$ or $$p=q=-r$$
B
$$p+q-r=0$$ or $$p=-q=r$$
C
$$p+q+r=0$$ or $$p=q=r$$
D
$$p-q+r=0$$ or $$p=-q=-r$$
4
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Suppose $$š‘ˆ$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T \right|$$ denote the number of elements in $$š‘‡$$ and $$T'$$ denote the complement of $$š‘‡.$$ For any $$T,R \in U,$$ let $$T\backslash R$$ be the set of all elements in $$š‘‡$$ which are not in $$š‘….$$ Which one of the following is true?
A
$$\forall X \in U\,\,$$ $$\left( {\left| X \right| = \left| {X'} \right|} \right)$$
B
$$\exists X \in U$$ $$\exists Y \in U\,\,$$ $$\left( {\left| X \right| = 5,\left| Y \right| = 5} \right.$$ and $$\left. {X \cap Y = \phi } \right)$$
C
$$\forall X \in U\,$$ $$\forall Y \in U\,\,$$ $$\,\,\left( {\left| X \right| = 2,\left| Y \right| = 3{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} and{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} X\backslash Y = \phi } \right)$$
D
$$\forall X \in U\,\,$$ $$\forall Y \in U\,\,$$ $$\,\left( {X\backslash Y = Y'\backslash X'} \right)$$
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