1
GATE PI 2007
MCQ (Single Correct Answer)
+1
-0.3
If $$A$$ is square symmetric real valued matrix of dimension $$2n$$, then the eigen values of $$A$$ are
A
$$2n$$ distinct real values
B
$$2n$$ real values not neccessarily distinct
C
$$n$$ distinct pairs of complex conjugate numbers
D
$$n$$ pairs of complex conjugate numbers, not necessarily distinct
2
GATE PI 2007
MCQ (Single Correct Answer)
+1
-0.3
For the function $$\,\,f\left( {x,y} \right) = {x^2} - {y^2}\,\,$$ defined on $${R^2},$$ the point $$(0,0)$$ is
A
a local minimum
B
Neither a local minimum (nor) a local maximum.
C
a local maximum
D
Both a local minimum and a local maximum
3
GATE PI 2007
MCQ (Single Correct Answer)
+1
-0.3
What is the value of $$\mathop {Lim}\limits_{x \to \pi /4} {{\cos x - \sin x} \over {x - \pi /4}}\,\,$$
A
$$\sqrt 2 $$
B
$$0$$
C
$$-\sqrt 2 $$
D
Limit does not exist
4
GATE PI 2007
MCQ (Single Correct Answer)
+2
-0.6
The angle (in degrees) between two planar vectors $$\vec a = {{\sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ and $$\vec b = {{ - \sqrt 3 } \over 2}\widehat i + {1 \over 2}\widehat j$$ is
A
$$30$$
B
$$60$$
C
$$90$$
D
$$120$$
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