GATE CSE 1996 | GATE CSE Year Wise Previous Years Questions

GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

The recurrence relation $$\,\,\,\,\,$$ $$T\left( 1 \right) = 2$$
$$T\left( n \right) = 3T\left( {{n \over 4}} \right) + n$$ has the solution $$T(n)$$ equal to

$$O(n)$$

$$O$$ (log n)

$$O\left( {{n^{3/4}}} \right)$$

None of the above

GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

The matrices$$\left[ {\matrix{ {\cos \,\theta } & { - \sin \,\theta } \cr {\sin \,\,\theta } & {\cos \,\,\theta } \cr } } \right]\,\,and$$
$$\left[ {\matrix{ a & 0 \cr 0 & b \cr } } \right]\,$$ commute under multiplication

if a = b or $$\theta = n\,\pi $$, n an integer

always

never

if a cos $$\theta \,\, \ne \,\,b\,\,\sin \,\theta $$

GATE CSE 1996

MCQ (Single Correct Answer)

-0.3

The formula used to compute an approximation for the second derivative of a function $$f$$ at a point $${x_0}$$ is

$${{f\left( {{x_0} + h} \right) + f\left( {{x_0} - h} \right)} \over 2}$$

$${{f\left( {{x_0} + h} \right) - f\left( {{x_0} - h} \right)} \over 2h}$$

$${{f\left( {{x_0} + h} \right) + 2f\left( {{x_0}} \right) + f\left( {{x_0} - h} \right)} \over {{h^2}}}$$

$${{f\left( {{x_0} + h} \right) - 2f\left( {{x_0}} \right) + f\left( {{x_0} - h} \right)} \over {{h^2}}}$$

GATE CSE 1996

MCQ (Single Correct Answer)

-0.6

Which one of the following is false? Read $$ \wedge $$ as AND, $$ \vee $$ as OR, $$ \sim $$ as NOT, $$ \to $$ as one way implication and $$ \leftrightarrow $$ two way implication.

$$\left( {\left( {x \to y} \right) \wedge x} \right) \to y$$

$$\left( {\left( { \sim x \to y} \right) \wedge \left( { \sim x \to \sim y} \right)} \right) \to x$$

$$\left( {x \to \left( {x \vee y} \right)} \right)$$

$$\left( {\left( {x \vee y} \right) \leftrightarrow \left( { \sim x \to \sim y} \right)} \right)$$

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