1
GATE CSE 2015 Set 3
+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 $$p=-q=-r$$
2
GATE CSE 2015 Set 2
Numerical
+2
-0
Perform the following operations on the matrix $$\left[ {\matrix{ 3 & 4 & {45} \cr 7 & 9 & {105} \cr {13} & 2 & {195} \cr } } \right]$$
(i) Add the third row to the second row
(ii) Subtract the third column from the first column.

The determinant of the resultant matrix is _________.

3
GATE CSE 2015 Set 1
+2
-0.6
Consider the following $$2 \times 2$$ matrix $$A$$ where two elements are unknown and are marked by $$a$$ and $$b.$$ The eigenvalues of this matrix ar $$-1$$ and $$7.$$ What are the values of $$a$$ and $$b$$?
$$A = \left( {\matrix{ 1 & 4 \cr b & a \cr } } \right)$$
A
$$a=6, b=4$$
B
$$a=4, b=6$$
C
$$a=3, b=5$$
D
$$a=5,b=3$$
4
GATE CSE 2015 Set 1
Numerical
+2
-0
$$\sum\limits_{x = 1}^{99} {{1 \over {x\left( {x + 1} \right)}}}$$ = _____________.
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
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