1
GATE ECE 2009
+1
-0.3
A fair coin is tossed $$10$$ times. What is the probability that only the first two tosses will yield heads?
A
$${\left( {{1 \over 2}} \right)^2}$$
B
$$10{c_2}\,{\left( {{1 \over 2}} \right)^2}$$
C
$${\left( {{1 \over 2}} \right)^{10}}$$
D
$$\,10{c_2}\,{\left( {{1 \over 2}} \right)^{10}}$$
2
GATE ECE 2009
+2
-0.6
A discrete random variable $$X$$ takes value from $$1$$ to $$5$$ with probabilities as shown in the table. A student calculates the mean of $$X$$ as $$3.5$$ and her teacher calculates the variance to $$X$$ as $$1.5.$$ Which of the following statements is true?
A
Both the student and the teacher are right
B
Both the student and the teacher are wrong
C
The student is wrong but the teacher is right
D
The student is right but the teacher is wrong
3
GATE ECE 2009
+2
-0.6
Consider two independent random variables $$X$$ and $$Y$$ with identical distributions. The variables $$X$$ and $$Y$$ take values $$0, 1$$ and $$2$$ with probability $$1/2,$$ $$1/4$$ and $$1/4$$ respectively. What is the conditional probability $$P(X+Y=2/X-Y=0)?$$
A
$$0$$
B
$$1/16$$
C
$$1/6$$
D
$$1$$
4
GATE ECE 2009
+2
-0.6
Match each differential equation in Group $$I$$ to its family of solution curves from Group $$II.$$

Group $$I$$
$$P:$$$$\,\,\,$$ $${{dy} \over {dx}} = {y \over x}$$
$$Q:$$$$\,\,\,$$ $${{dy} \over {dx}} = {{ - y} \over x}$$
$$R:$$$$\,\,\,$$ $${{dy} \over {dx}} = {x \over y}$$
$$S:$$$$\,\,\,$$ $${{dy} \over {dx}} = {{ - x} \over y}$$

Group $$II$$
$$(1)$$$$\,\,\,$$ Circle
$$(2)$$$$\,\,\,$$ straight lines
$$(3)$$$$\,\,\,$$ Hyperbola

A
$$P - 2,\,Q - 3,\,R - 3,S - 1$$
B
$$P - 1,\,Q - 3,\,R - 2,S - 1$$
C
$$P - 2,\,Q - 1,\,R - 3,S - 3$$
D
$$P - 3,\,Q - 2,\,R - 1,S - 2$$
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