1
GATE CSE 1996
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following is false?
A
The set of all bijective functions on a finite set forms a group under function composition.
B
The set {1, 2, ..., p - 1} forms a group under multiplication mod p where p is a prime number.
C
The set of all strings over a finite alphabet $$\sum $$ forms a group under concatenation.
D
A subset $$s\, \ne \,\phi $$ of G is a subgroup of the group if and only if for any pair of elements $$a,\,\,b\,\, \in \,\,s,\,\,a\,\,*\,\,{b^{ - 1}}\,\, \in \,s$$.
2
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-0.3
The formula used to compute an approximation for the second derivative of a function $$f$$ at a point $${x_0}$$ is
A
$${{f\left( {{x_0} + h} \right) + f\left( {{x_0} - h} \right)} \over 2}$$
B
$${{f\left( {{x_0} + h} \right) - f\left( {{x_0} - h} \right)} \over 2h}$$
C
$${{f\left( {{x_0} + h} \right) + 2f\left( {{x_0}} \right) + f\left( {{x_0} - h} \right)} \over {{h^2}}}$$
D
$${{f\left( {{x_0} + h} \right) - 2f\left( {{x_0}} \right) + f\left( {{x_0} - h} \right)} \over {{h^2}}}$$
3
GATE CSE 1996
MCQ (Single Correct Answer)
+2
-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
A
if a = b or $$\theta = n\,\pi $$, n an integer
B
always
C
never
D
if a cos $$\theta \,\, \ne \,\,b\,\,\sin \,\theta $$
4
GATE CSE 1996
MCQ (Single Correct Answer)
+2
-0.6
Let R denote the set of real numbers. Let f: $$R\,x\,R \to \,R\,x\,R\,$$ be a bijective function defined by f (x, y ) = (x + y, x - y). The inverse function of f is given by
A
$${f^{ - 1}}\,(x,\,y)\, = \,\left( {{1 \over {x\, + \,y}},\,{1 \over {x\, - \,y}}} \right)$$
B
$${f^{ - 1}}\,(x,\,y)\, = \,\,(x\, - \,y,\,\,x\, + y)$$
C
$${f^{ - 1}}\,(x,\,y)\, = \,\left( {{{x\, + \,y} \over 2},\,{{x\, - \,y} \over 2}} \right)$$
D
$${f^{ - 1}}\,(x,\,y)\, = \,(2\,(x\, - \,y),\,2\,(x\, + y))$$