1
GATE CSE 2016 Set 1
Numerical
+2
-0
Consider the recurrence relation $${a_1} = 8,\,{a_n} = 6{n^2} + 2n + {a_{n - 1}}.$$ Let $${a_{99}} = K \times {10^4}.$$ The value of $$K$$ is ____________.
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2
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 $$p=-q=-r$$
3
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 _________.

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4
GATE CSE 2015 Set 1
MCQ (Single Correct Answer)
+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
$$a=5,b=3$$
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