1
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
Decrease in atomic number is observed during
A
alpha emission
B
beta amission
C
positron emisson
D
electron capture
2
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss equals
A
$$1/2$$
B
$$1/32$$
C
$$31/32$$
D
$$1/5$$
3
IIT-JEE 1998
Subjective
+8
-0
For any two vectors $$u$$ and $$v,$$ prove that
(a) $${\left( {u\,.\,v} \right)^2} + {\left| {u \times v} \right|^2} = {\left| u \right|^2}{\left| v \right|^2}$$ and
(b) $$\left( {1 + {{\left| u \right|}^2}} \right)\left( {1 + {{\left| v \right|}^2}} \right) = {\left( {1 - u.v} \right)^2} + {\left| {u + v + \left( {u \times v} \right)} \right|^2}.$$
4
IIT-JEE 1998
Subjective
+8
-0
Prove, by vector methods or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line passing through the mid-points of the parallel sides. (You may assume that the trapezium is not a parallelogram.)
JEE Advanced Papers
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