Mathematical Reasoning & Induction · JEE Main previous year questions

2019 14 questions

1. Q272019 · 12 Apr 2019 · Shift 1

   If the truth value of the statement $p\to (\sim q\vee r)$ is false (F), then the truth values of the statements p, q, r are respectively :

   1. A.T, F, T
   2. B.F, T, T
   3. C.T, T, F
   4. D.T, F, F
   Show answer

   Answer: C

2. Q32019 · 12 Apr 2019 · Shift 2

   Let A, B and C be sets such that $\varphi \ne \text{A}\cap \text{B}\subseteq \text{C}$. Then which of the following statements is not true ?

   1. A.If $(\text{A}-\text{B})\subseteq \text{C}$, then $\text{A}\subseteq \text{C}$
   2. B.$\text{B}\cap \text{C}\ne \varphi$
   3. C.$(\text{C}\cup \text{A})\cap (\text{C}\cup \text{B})=\text{C}$
   4. D.If $(\text{A}-\text{C})\subseteq \text{B}$, then $\text{A}\subseteq \text{B}$
   Show answer

   Answer: D

3. Q92019 · 10 Apr 2019 · Shift 1

   Let $f(x)=x^2$ , $x\in \mathrm{R}$. For any $\mathrm{A}\subseteq \mathrm{R}$, define $g(\mathrm{A})=\{x\in \mathrm{R}:f(x)\in \mathrm{A}\}$. If S = [0, 4], then which one of the following statements is not true ?

   1. A.$g(f(\mathrm{S}))\ne \mathrm{S}$
   2. B.$f(g(\mathrm{S}))=\mathrm{S}$
   3. C.$f(g(\mathrm{S}))\ne f(\mathrm{S})$
   4. D.$g(f(\mathrm{S}))=g(\mathrm{S})$
   Show answer

   Answer: D

4. Q222019 · 10 Apr 2019 · Shift 1

   Which one of the following Boolean expressions is a tautology?

   1. A.$(p\vee q)\wedge (\sim p\vee \sim q)$
   2. B.$(p\vee q)\vee (p\vee \sim q)$
   3. C.$(p\wedge q)\vee (p\wedge \sim q)$
   4. D.$(p\vee q)\wedge (p\vee \sim q)$
   Show answer

   Answer: B

5. Q292019 · 10 Apr 2019 · Shift 2

   The negation of the Boolean expression $\sim s\vee (\sim r\wedge s)$ is equivalent to :

   1. A.$\sim s\wedge \sim r$
   2. B.r
   3. C.$s\vee r$
   4. D.$s\wedge r$
   Show answer

   Answer: D

6. Q232019 · 9 Apr 2019 · Shift 1

   For any two statements p and q, the negation of the expression $p\vee (\sim p\wedge q)$ is :

   1. A.$p\leftrightarrow q$
   2. B.$\sim p\wedge \sim q$
   3. C.$p\wedge q$
   4. D.$\sim p\vee \sim q$
   Show answer

   Answer: B

7. Q292019 · 9 Apr 2019 · Shift 2

   If $p\Rightarrow (q\vee r)$ is false, then the truth values of p, q, r are respectively :-

   1. A.F, F, F
   2. B.T, F, F
   3. C.F, T, T
   4. D.T, T, F
   Show answer

   Answer: B

8. Q102019 · 8 Apr 2019 · Shift 2

   If three distinct numbers a, b, c are in G.P. and the equations $a{x}^2+2bx+c=0$ and $d{x}^2+2ex+f=0$ have a common root, then which one of the following statements is correct?

   1. A.$\frac{d}{a},\frac{e}{b},\frac{f}{c}$ are in G.P.
   2. B.d, e, f are in A.P
   3. C.d, e, f are in G.P
   4. D.$\frac{d}{a},\frac{e}{b},\frac{f}{c}$ are in A.P.
   Show answer

   Answer: D

9. Q272019 · 8 Apr 2019 · Shift 2

   Which one of the following statements is not a tautology?

   1. A.$(p\wedge q)\to (\sim p)\vee q$
   2. B.$(p\wedge q)\to p$
   3. C.$(p\vee q)\to (p\vee (\sim q))$
   4. D.$p\to (p\vee q)$
   Show answer

   Answer: C

10. Q282019 · 12 Jan 2019 · Shift 1

    The Boolean expression $((p\wedge q)\vee (p\vee \sim q))\wedge (\sim p\wedge \sim q)$ is equivalent to :

    1. A.$p\wedge q$
    2. B.$p\wedge (\sim q)$
    3. C.$p\vee (\sim q)$
    4. D.$(\sim p)\wedge (\sim q)$
    Show answer

    Answer: D

11. Q222019 · 12 Jan 2019 · Shift 2

    The expression $\sim (\sim p\to q)$ is logically equivalent to :

    1. A.$p\wedge q$
    2. B.$\sim p\wedge \sim q$
    3. C.$p\wedge \sim q$
    4. D.$\sim p\wedge q$
    Show answer

    Answer: B

12. Q262019 · 11 Jan 2019 · Shift 2

    Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is :

    1. A.If the squares of two numbers are equal, then the numbers are not equal
    2. B.If the squares of two numbers are equal, then the numbers are equal
    3. C.If the squares of two numbers are not equal, then the numbers are equal
    4. D.If the squares of two numbers are not equal, then the numbers are not equal
    Show answer

    Answer: B

13. Q242019 · 9 Jan 2019 · Shift 1

    If the Boolean expression $(p\oplus q)\wedge (\sim p\odot q)$ is equivalent to $p\wedge q$, where $\oplus ,\odot \in \{\wedge ,\vee \}$, then the ordered pair $(\oplus ,\odot )$ is :

    1. A.$(\vee ,\wedge )$
    2. B.$(\vee ,\vee )$
    3. C.$(\wedge ,\vee )$
    4. D.$(\wedge ,\wedge )$
    Show answer

    Answer: C

14. Q262019 · 9 Jan 2019 · Shift 1

    Consider the set of all lines $px+qy+r=0$ such that $3p+2q+4r=0$. Which one of the following statements is true?

    1. A.The lines are not concurrent
    2. B.The lines are concurrent at the point $\left(\frac{3}{4},\frac{1}{2}\right)$
    3. C.The lines are all parallel
    4. D.Each line passes through the origin
    Show answer

    Answer: B