1
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
How many 4 digit even numbers have all 4 digits distinct?
A
2240
B
2296
C
2620
D
4536
2
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
how many undirected graphs (not necessarily connected) can be constructed out of a given $$\,\,\,\,V = \left\{ {{v_1},\,\,{v_2},\,....,\,\,{v_n}} \right\}$$ of $$n$$ vertices?
A
$$n\left( {n - 1} \right)/2$$
B
$${2^n}$$
C
$$n!$$
D
$${2^{n\left( {n - 1} \right)/2}}$$
3
GATE CSE 2001
MCQ (Single Correct Answer)
+1
-0.3
The value of the integral is $${\rm I} = \int\limits_0^{{\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}} {{{\cos }^2}x\,dx} $$
A
$${\pi \over 8} + {1 \over 4}$$
B
$${\pi \over 8} - {1 \over 4}$$
C
$${{ - \pi } \over 8} - {1 \over 4}$$
D
$${{ - \pi } \over 8} + {1 \over 4}$$
4
GATE CSE 2001
MCQ (Single Correct Answer)
+1
-0.3
Consider two well-formed formulas in propositional logic
$$F1:P \Rightarrow \neg P$$
$$F2:\left( {P \Rightarrow \neg P} \right) \vee \left( {\neg P \Rightarrow } \right)$$

Which of the following statements is correct?

A
F1 is satisfiable, F2 is valid
B
F1 is unsatisfiable, F2 is satisfiable
C
F1 is unsatisfiable, F2 is valid
D
F1 and F2 are both satisfiable
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