Other Maths · JEE Main previous year questions

2020 24 questions

1. Q42020 · 6 Sept 2020 · Shift 1

   Let a , b, c , d and p be any non zero distinct real numbers such that $(a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2)=0$. Then :

   1. A.a, c, p are in G.P.
   2. B.a, b, c, d are in G.P.
   3. C.a, b, c, d are in A.P.
   4. D.a, c, p are in A.P.
   Show answer

   Answer: B

2. Q112020 · 6 Sept 2020 · Shift 1

   If $\{p\}$ denotes the fractional part of the number $p$, then $\left\{\frac{3^{200}}{8}\right\}$, is equal to :

   1. A.$\frac{5}{8}$
   2. B.$\frac{7}{8}$
   3. C.$\frac{1}{8}$
   4. D.$\frac{3}{8}$
   Show answer

   Answer: C

3. Q152020 · 6 Sept 2020 · Shift 1

   If $I_1={\int }_0^1(1-x^{50}{)}^{100}dx$ and $I_2={\int }_0^1(1-x^{50}{)}^{101}dx$ such that $I_2=\alpha I_1$ then $\alpha$ equals to :

   1. A.$\frac{5051}{5050}$
   2. B.$\frac{5050}{5051}$
   3. C.$\frac{5050}{5049}$
   4. D.$\frac{5049}{5050}$
   Show answer

   Answer: B

4. Q122020 · 3 Sept 2020 · Shift 1

   The value of $(2\cdot {}^1{\mathrm{P}}_0-3\cdot {}^2{\mathrm{P}}_1+4\cdot {}^3{\mathrm{P}}_2\dots \text{up to }51^{\mathrm{th}}\text{term})+(1!-2!+3!-\dots \text{up to }51^{\mathrm{th}}\text{term})$ is equal to :

   1. A.1
   2. B.$1+(51)!$
   3. C.$1-51(51)!$
   4. D.$1+(52)!$
   Show answer

   Answer: D

5. Q202020 · 3 Sept 2020 · Shift 1

   The proposition $p\to \sim (p\wedge \sim q)$ is equivalent to :

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

   Answer: A

6. Q242020 · 3 Sept 2020 · Shift 1· Numerical answer

   The value of $(0.16{)}^{{\log }_{2.5}\left(\frac{1}{3}+\frac{1}{3^2}+\dots to\infty \right)}$ is equal to _______.

   Show answer

   Answer: 4

7. Q252020 · 3 Sept 2020 · Shift 1· Numerical answer

   If ${\left(\frac{1+i}{1-i}\right)}^{\frac{m}{2}}={\left(\frac{1+i}{i-1}\right)}^{\frac{n}{3}}=1$, $(m,n\in \mathbb{N})$ then the greatest common divisor of the least values of m and n is _______.

   Show answer

   Answer: 4

8. Q232020 · 2 Sept 2020 · Shift 1· Numerical answer

   If ${\lim }_{x\to 1}\frac{x+x^2+x^3+\dots +x^n-n}{x-1}=820$, ($n\in \mathbb{N}$) then the value of n is equal to _______.

   Show answer

   Answer: 40

9. Q22020 · 2 Sept 2020 · Shift 2

   Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is :

   1. A.201
   2. B.199
   3. C.101
   4. D.200
   Show answer

   Answer: A

10. Q162020 · 2 Sept 2020 · Shift 2

    The imaginary part of ${\left(3+2\sqrt{-54}\right)}^{\frac{1}{2}}-{\left(3-2\sqrt{-54}\right)}^{\frac{1}{2}}$ can be :

    1. A.$-2\sqrt{6}$
    2. B.6
    3. C.$\sqrt{6}$
    4. D.$-\sqrt{6}$
    Show answer

    Answer: A

11. Q242020 · 2 Sept 2020 · Shift 2· Numerical answer

    Let $[t]$ denote the greatest integer less than or equal to $t$. Then the value of ${\int }_1^2|2x-[3x]|dx$ is _______.

    Show answer

    Answer: 1

12. Q162020 · 9 Jan 2020 · Shift 1

    If for all real triplets $(a,b,c)$, $f(x)=a+bx+c{x}^2$; then ${\int }_0^{1}f(x)dx$ is equal to :

    1. A.$\frac{1}{6}\left\{f(0)+f(1)+4f\left(\frac{1}{2}\right)\right\}$
    2. B.$2\left\{3f(1)+2f\left(\frac{1}{2}\right)\right\}$
    3. C.$\frac{1}{3}\left\{f(0)+f\left(\frac{1}{2}\right)\right\}$
    4. D.$\frac{1}{2}\left\{f(1)+3f\left(\frac{1}{2}\right)\right\}$
    Show answer

    Answer: A

13. Q192020 · 9 Jan 2020 · Shift 1

    The product $2^{\frac{1}{4}}\cdot 4^{\frac{1}{16}}\cdot 8^{\frac{1}{48}}\cdot 16^{\frac{1}{128}}\dots \text{ to }\infty$ is equal to :

    1. A.$2^{\frac{1}{4}}$
    2. B.$2^{\frac{1}{2}}$
    3. C.1
    4. D.2
    Show answer

    Answer: B

14. Q102020 · 9 Jan 2020 · Shift 2

    If $\mathrm{A}=\{x\in \mathbb{R}:|x|<2\}$ and $\mathrm{B}=\{x\in \mathbb{R}:|x-2|\ge 3\}$; then :

    1. A.$\mathrm{A}-\mathrm{B}=[-1,2)$
    2. B.$\mathrm{A}\cup \mathrm{B}=\mathbb{R}-(2,5)$
    3. C.$\mathrm{A}\cap \mathrm{B}=(-2,-1)$
    4. D.$\mathrm{B}-\mathrm{A}=\mathbb{R}-(-2,5)$
    Show answer

    Answer: D

15. Q112020 · 9 Jan 2020 · Shift 2

    If $\frac{dy}{dx}=\frac{xy}{x^2+y^2}$; $y(1)=1$; then a value of x satisfying $y(x)=e$ is :

    1. A.$\sqrt{2}e$
    2. B.$\frac{1}{2}\sqrt{3}e$
    3. C.$\frac{e}{\sqrt{2}}$
    4. D.$\sqrt{3}e$
    Show answer

    Answer: D

16. Q252020 · 9 Jan 2020 · Shift 2· Numerical answer

    If ${\mathrm{C}}_r\equiv {}^{25}{\mathrm{C}}_r$ and ${\mathrm{C}}_0+5.{\mathrm{C}}_1+9.{\mathrm{C}}_2+\dots +(101).{\mathrm{C}}_{25}=2^{25}.k$, then k is equal to _______.

    Show answer

    Answer: 51

17. Q12020 · 8 Jan 2020 · Shift 1

    If a, b and c are the greatest value of ${}^{19}{\mathrm{C}}_p$, ${}^{20}{\mathrm{C}}_q$ and ${}^{21}{\mathrm{C}}_r$ respectively, then :

    1. A.$\frac{a}{11}=\frac{b}{22}=\frac{c}{21}$
    2. B.$\frac{a}{10}=\frac{b}{22}=\frac{c}{21}$
    3. C.$\frac{a}{10}=\frac{b}{11}=\frac{c}{42}$
    4. D.$\frac{a}{11}=\frac{b}{22}=\frac{c}{42}$
    Show answer

    Answer: D

18. Q52020 · 8 Jan 2020 · Shift 1

    Let two points be A(1, -1) and B(0, 2). If a point P(x', y') be such that the area of $\Delta \mathrm{PAB}=5\text{ sq. units}$ and it lies on the line, $3x+y-4\lambda =0$, then a value of $\lambda$ is :

    1. A.4
    2. B.1
    3. C.-3
    4. D.3
    Show answer

    Answer: D

19. Q252020 · 8 Jan 2020 · Shift 1· Numerical answer

    The sum ${\sum }_{k=1}^{20}(1+2+3+\dots +k)$ is :

    Show answer

    Answer: 1540

20. Q102020 · 8 Jan 2020 · Shift 2

    If $A=\left(\begin{array}{cc}2& 2\\ 9& 4\end{array}\right)$ and $I=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$ then $10A^{-1}$ is equal to :

    1. A.$6I-A$
    2. B.$4I-A$
    3. C.$A-6I$
    4. D.$A-4I$
    Show answer

    Answer: C

21. Q252020 · 8 Jan 2020 · Shift 2· Numerical answer

    The sum, ${\sum }_{n=1}^7\frac{n(n+1)(2n+1)}{4}$ is equal to _______.

    Show answer

    Answer: 504

22. Q12020 · 7 Jan 2020 · Shift 1

    Let $x^k+y^k=a^k$, $(a,k>0)$ and $\frac{dy}{dx}+{\left(\frac{y}{x}\right)}^{\frac{1}{3}}=0$, then k is:

    1. A.$\frac{1}{3}$
    2. B.$\frac{2}{3}$
    3. C.$\frac{4}{3}$
    4. D.$\frac{3}{2}$
    Show answer

    Answer: B

23. Q102020 · 7 Jan 2020 · Shift 1

    The greatest positive integer k, for which $49^k+1$ is a factor of the sum $49^{125}+49^{124}+\cdots +49^2+49+1$, is:

    1. A.32
    2. B.60
    3. C.63
    4. D.65
    Show answer

    Answer: C

24. Q22020 · 7 Jan 2020 · Shift 2

    The number of ordered pairs $(r,k)$ for which $6\cdot {}^{35}{\mathrm{C}}_r=(k^2-3)\cdot {}^{36}{\mathrm{C}}_{r+1}$, where $k$ is an integer, is :

    1. A.6
    2. B.3
    3. C.2
    4. D.4
    Show answer

    Answer: D