1
IIT-JEE 1983
Subjective
+3
-0
Cards are drawn one by one at random from a well - shuffled full pack of $$52$$ playing cards until $$2$$ aces are obtained for the first time. If $$N$$ is the number of cards required to be drawn, then show that $${P_r}\left\{ {N = n} \right\} = {{\left( {n - 1} \right)\left( {52 - n} \right)\left( {51 - n} \right)} \over {50 \times 49 \times 17 \times 13}}$$ where $$2 \le n \le 50$$
2
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
Fifteen coupons are numbered $$1, 2 ........15,$$ respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is $$9,$$ is
A
$${\left( {{9 \over {16}}} \right)^6}$$
B
$${\left( {{18 \over {15}}} \right)^7}$$
C
$${\left( {{3 \over {5}}} \right)^7}$$
D
none of these
3
IIT-JEE 1983
True or False
+1
-0
If the letters of the word "Assassin" are written down at random in a row, the probability that no two S's occur together is $$1/35$$
A
TRUE
B
FALSE
4
IIT-JEE 1983
Subjective
+3
-0
If $$\left( {a + bx} \right){e^{y/x}} = x,$$ then prove that $${x^3}{{{d^2}y} \over {d{x^2}}} = {\left( {x{{dy} \over {dx}} - y} \right)^2}$$
JEE Advanced Papers
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