1
IIT-JEE 1985
MCQ (Single Correct Answer)
+2
-0.5
If $${\log _{0.3}}\,(x\, - \,1) < {\log _{0.09}}(x - 1)$$, then x lies in the interval-
A
$$(2,\infty )$$
B
(1, 2)
C
(- 2, - 1)
D
none of these
2
IIT-JEE 1985
True or False
+1
-0
The product of any r consecutive natural numbers is always divisible by r!
A
TRUE
B
FALSE
3
IIT-JEE 1985
Subjective
+5
-0
Use method of mathematical induction $${2.7^n} + {3.5^n} - 5$$ is divisible by $$24$$ for all $$n > 0$$
4
IIT-JEE 1985
Subjective
+5
-0
7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?
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