Mathematical Reasoning & Induction · JEE Main previous year questions

2012 6 questions

1. Q272012 · 26 May 2012 · Shift 1

   Let $p$ and $q$ denote the following statements $p$: The sun is shining $q$: I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is

   1. A.$q\Rightarrow \sim p$
   2. B.$q\wedge \sim p$
   3. C.$p\wedge \sim q$
   4. D.$\sim q\Rightarrow \sim p$
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   Answer: C

2. Q252012 · 12 May 2012 · Shift 1

   The logically equivalent proposition of $p\iff q$ is

   1. A.$(p\Rightarrow q)\wedge (q\Rightarrow p)$
   2. B.$p\wedge q$
   3. C.$(p\wedge q)\vee (q\ne p)$
   4. D.$(p\wedge q)\Rightarrow (q\vee p)$
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   Answer: A

3. Q292012 · 12 May 2012 · Shift 1

   Statement 1: If the points $(1,2,2),(2,1,2)$ and $(2,2,z)$ and $(1,1,1)$ are coplanar, then $z=2$. Statement 2: If the 4 points $P,Q,R$ and $S$ are coplanar, then the volume of the tetrahedron $PQRS$ is 0.

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

   Answer: A

4. Q102012 · 7 May 2012 · Shift 1

   Let $X$ and $Y$ are two events such that $P(X\cup Y)=P(X\cap Y)$. Statement 1: $P(X\cap Y^{\prime })=P(X^{\prime }\cap Y)=0$ Statement 2: $P(X)+P(Y)=2P(X\cap Y)$

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

5. Q142012 · 7 May 2012 · Shift 1

   Let $f(x)=\sin x,g(x)=x$. Statement 1: $f(x)\le g(x)$ for $x$ in $(0,\infty )$ Statement 2: $f(x)\le 1$ for $x$ in $(0,\infty )$ but $g(x)\to \infty$ as $x\to \infty$.

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

6. Q262012 · 7 May 2012 · Shift 1

   The Statement that is TRUE among the following is

   1. A.The contrapositive of $3x+2=8\Rightarrow x=2$ is $x\ne 2\Rightarrow 3x+2\ne 8$.
   2. B.The converse of $\tan x=0\Rightarrow x=0$ is $x\ne 0\Rightarrow \tan x=0$.
   3. C.$p\Rightarrow q$ is equivalent to $p\vee \sim q$.
   4. D.$p\vee q$ and $p\wedge q$ have the same truth table.
   Show answer

   Answer: A