Mathematical Reasoning & Induction · JEE Main previous year questions

2010 2 questions

1. Q252010 · 25 Apr 2010 · Shift 1

   Let $s_1=\sum _{j=1}^{10}j(j-1){}^{10}{C}_j$, $s_2=\sum _{j=1}^{10}j\cdot {}^{10}{C}_j$ and $s_3=\sum _{j=1}^{10}{j}^2\cdot {}^{10}{C}_j$. Statement-1 : $S_3=55\times 2^9$. Statement-2 : $S_1=90\times 2^8$ and $S_2=10\times 2^8$.

   1. A.Statement - 1 is true, Statement- 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
   2. B.Statement - 1 is true, Statement-2 is false.
   3. C.Statement - 1 is false, Statement-2 is true.
   4. D.Statement - 1 is true, Statement-2 is true; Statement - 2 is a correct explanation for Statement - 1.
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   Answer: B

2. Q302010 · 25 Apr 2010 · Shift 1

   Let S be a non-empty subset of R. Consider the following statement: $P$ : There is a rational number $x\in S$ such that $x>0$. Which of the following statements is the negation of the statement P?

   1. A.There is no rational number $x\in S$ such that $x\le 0$
   2. B.Every rational number $x\in S$ satisfies $x\le 0$
   3. C.$x\in S$ and $x\le 0\Rightarrow x$ is not rational
   4. D.There is a rational number $x\in S$ such that $x\le 0$
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   Answer: B