Mathematical Reasoning & Induction · JEE Main previous year questions

2009 3 questions

1. Q12009 · 27 Apr 2009 · Shift 1

   Let A and B denote the statements A: $\cos \alpha +\cos \beta +\cos \gamma =0$ B: $\sin \alpha +\sin \beta +\sin \gamma =0$ If $\cos (\beta -\gamma )+\cos (\gamma -\alpha )+\cos (\alpha -\beta )=-\frac{3}{2}$, then:

   1. A.A is false and B is true
   2. B.both A and B are true
   3. C.both A and B are false
   4. D.A is true and B is false
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   Answer: B

2. Q182009 · 27 Apr 2009 · Shift 1

   Let $f(x)=(x+1{)}^2-1,x\ge -1$ Statement - 1 : The set $\{x:f(x)=f^{-1}(x)\}=\{0,-1\}$. Statement - 2 : $f$ is a bijection.

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

3. Q302009 · 27 Apr 2009 · Shift 1

   Statement-1 : $\sim (p\leftrightarrow \sim q)$ is equivalent to $p\leftrightarrow q$. Statement-2 : $\sim (p\leftrightarrow \sim q)$ is a tautology.

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

   Answer: C