Other Maths · JEE Main previous year questions

2026 44 questions

1. Q82026 · 8 Apr 2026 · Shift 2

   If $26\left(\frac{2^3}{3}({}^{12}{\mathrm{C}}_2)+\frac{2^5}{5}({}^{12}{\mathrm{C}}_4)+\frac{2^7}{7}({}^{12}{\mathrm{C}}_6)+\cdots +\frac{2^{13}}{13}({}^{12}{\mathrm{C}}_{12})\right)=3^{13}-\alpha$, then $\alpha$ is equal to :

   1. A.$45$
   2. B.$48$
   3. C.$51$
   4. D.$54$
   Show answer

   Answer: C

2. Q152026 · 8 Apr 2026 · Shift 2

   n-Butane on monochlorination under photochemical condition gives an optically active compound " P ". " P " on further chlorination gives dichloro compounds. The number of dichloro compounds obtained (ignore stereoisomers) is :

   1. A.3
   2. B.4
   3. C.5
   4. D.6
   Show answer

   Answer: C

3. Q52026 · 6 Apr 2026 · Shift 1

   The value of $1^3-2^3+3^3-...+15^3$ is:

   1. A.1706
   2. B.1856
   3. C.1982
   4. D.2403
   Show answer

   Answer: B

4. Q32026 · 6 Apr 2026 · Shift 2

   Let $S=\{z\in \mathbb{C}:z^2+\sqrt{6}iz-3=0\}$. Then ${\sum }_{z\in S}{z}^8$ is equal to :

   1. A.162
   2. B.184
   3. C.262
   4. D.324
   Show answer

   Answer: A

5. Q52026 · 6 Apr 2026 · Shift 2

   Let $\mathrm{A}=\left[\begin{array}{ccc}1& 0& 0\\ 3& 1& 0\\ 9& 3& 1\end{array}\right]$ and $\mathrm{B}=[b_{ij}]$, $1\le i,j\le 3$. If $\mathrm{B}={\mathrm{A}}^{99}-\mathrm{I}$, then the value of $\frac{b_{31}-b_{21}}{b_{32}}$ is :

   1. A.99
   2. B.199
   3. C.149
   4. D.159
   Show answer

   Answer: C

6. Q62026 · 6 Apr 2026 · Shift 2

   The sum $1+\frac{1}{2}(1^2+2^2)+\frac{1}{3}(1^2+2^2+3^2)+\dots$ upto 10 terms is equal to :

   1. A.130
   2. B.155
   3. C.$\frac{315}{2}$
   4. D.$\frac{325}{2}$
   Show answer

   Answer: C

7. Q52026 · 5 Apr 2026 · Shift 1

   ${\sum }_{n=1}^{10}\left(\frac{528}{n(n+1)(n+2)}\right)$ is equal to:

   1. A.65
   2. B.130
   3. C.220
   4. D.440
   Show answer

   Answer: B

8. Q32026 · 5 Apr 2026 · Shift 2

   If $f:\mathbb{N}\to \mathbb{Z}$ is defined by $$f(n)=\left|\begin{array}{ccc}n& -1& -5\\ -2n^2& 3(2k+1)& 2k+1\\ -3n^3& 3k(2k+1)& 3k(k+2)+1\end{array}\right|,k\in \mathbb{N},$$ and ${\sum }_{n=1}^{k}f(n)=98$, then $k$ is equal to :

   1. A.$3$
   2. B.$4$
   3. C.$5$
   4. D.$6$
   Show answer

   Answer: A

9. Q162026 · 5 Apr 2026 · Shift 2

   Let $\mathrm{O}$ be the origin, $\overrightarrow{\mathrm{OP}}=\vec{a}$ and $\overrightarrow{\mathrm{OQ}}=\vec{b}$. If $\mathrm{R}$ is the point on $\overrightarrow{\mathrm{OP}}$ such that $\overrightarrow{\mathrm{OP}}=5\overrightarrow{\mathrm{OR}}$, and $\mathrm{M}$ is the point such that $\overrightarrow{\mathrm{OQ}}=5\overrightarrow{\mathrm{RM}}$, then $\overrightarrow{\mathrm{PM}}$ is equal to :

   1. A.$\frac{1}{5}(\vec{a}-4\vec{b})$
   2. B.$\frac{1}{5}(\vec{b}-4\vec{a})$
   3. C.$\frac{1}{5}(-\vec{a}+4\vec{b})$
   4. D.$\frac{1}{5}(-\vec{b}+4\vec{a})$
   Show answer

   Answer: B

10. Q152026 · 4 Apr 2026 · Shift 1

    The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line $\frac{x+5}{1}=\frac{y+5}{-1}=\frac{z}{2}$ is equal to:

    1. A.3
    2. B.6
    3. C.8
    4. D.12
    Show answer

    Answer: B

11. Q72026 · 4 Apr 2026 · Shift 2

    Let $\alpha =\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\dots \infty$ and $\beta =\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\dots \infty$. Then the value of $(0.2{)}^{{\log }_{\sqrt{5}}(\alpha )}+(0.04{)}^{{\log }_5(\beta )}$ is equal to:

    1. A.4
    2. B.5
    3. C.8
    4. D.25
    Show answer

    Answer: C

12. Q142026 · 4 Apr 2026 · Shift 2

    If $\left(2\alpha +1,{\alpha }^2-3\alpha ,\frac{\alpha -1}{2}\right)$ is the image of $(\alpha ,2\alpha ,1)$ in the line $\frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}$, then the possible value(s) of $\alpha$ is (are)

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

    Answer: A

13. Q172026 · 4 Apr 2026 · Shift 2

    Let $A=\{(a,b,c):a,b,c\text{ are non-negative integers and }a+b+2c=22\}$. Then $n(A)$ is equal to:

    1. A.121
    2. B.124
    3. C.144
    4. D.169
    Show answer

    Answer: C

14. Q22026 · 2 Apr 2026 · Shift 1

    Let $x$ and $y$ be real numbers such that $50\left(\frac{2x}{1+3i}-\frac{y}{1-2i}\right)=31+17i,i=\sqrt{-1}$. Then the value of $10(x-3y)$ is :

    1. A.20
    2. B.31
    3. C.35
    4. D.75
    Show answer

    Answer: D

15. Q222026 · 2 Apr 2026 · Shift 1· Numerical answer

    If ${\sum }_{k=1}^n{a}_k=6n^3$, then ${\sum }_{k=1}^6{\left(\frac{a_{k+1}-a_k}{36}\right)}^2$ is equal to ____.

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    Answer: 91

16. Q52026 · 2 Apr 2026 · Shift 2

    The sum $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\dots$ up to 8 terms, is :

    1. A.70
    2. B.71
    3. C.72
    4. D.73
    Show answer

    Answer: B

17. Q62026 · 2 Apr 2026 · Shift 2

    If for $3⩽r⩽30$, $\left({}^{30}{\mathrm{C}}_{30-r}\right)+3\left({}^{30}{\mathrm{C}}_{31-r}\right)+3\left({}^{30}{\mathrm{C}}_{32-r}\right)+\left({}^{30}{\mathrm{C}}_{33-r}\right)={}^m{\mathrm{C}}_r$, then $m$ equals :

    1. A.31
    2. B.32
    3. C.33
    4. D.34
    Show answer

    Answer: C

18. Q132026 · 28 Jan 2026 · Shift 1

    The value of $\sum _{k=1}^{\infty }(-1{)}^{k+1}\left(\frac{k(k+1)}{k!}\right)$ is

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

    Answer: D

19. Q192026 · 28 Jan 2026 · Shift 1

    If the distances of the point $(1,2,a)$ from the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$ along the lines ${\mathrm{L}}_1:\frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}$ and ${\mathrm{L}}_2:\frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}$ are equal, then $a+b+c$ is equal to

    1. A.4
    2. B.6
    3. C.7
    4. D.5
    Show answer

    Answer: C

20. Q242026 · 28 Jan 2026 · Shift 1· Numerical answer

    The value of $\sum _{r=1}^{20}\left(\left|\sqrt{\pi \left(\underset{0}{\overset{r}{\int }}x|\sin \pi x|dx\right)}\right|\right)$ is ____

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    Answer: 210

21. Q252026 · 28 Jan 2026 · Shift 1· Numerical answer

    Let $PQR$ be a triangle such that $\overrightarrow{PQ}=-2\hat{i}-\hat{j}+2\hat{k}$ and $\overrightarrow{PR}=a\hat{i}+b\hat{j}-4\hat{k},a,b\in \mathbb{Z}$. Let S be the point on QR , which is equidistant from the lines PQ and PR . If $|\overrightarrow{PR}|=9$ and $\overrightarrow{PS}=\hat{i}-7\hat{j}+2\hat{k}$, then the value of $3a-4b$ is ____

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    Answer: 37

22. Q82026 · 28 Jan 2026 · Shift 2

    Let $f(x)=\int \frac{dx}{x^{2/3}+2x^{1/2}}$, be such that $f(0)=-26+24{\log }_e(2)$. If $f(1)=a+b{\log }_e(3)$, where $a,b\in \mathbb{Z}$, then $a+b$ is equal to :

    1. A.$-5$
    2. B.$-11$
    3. C.$-18$
    4. D.$-26$
    Show answer

    Answer: B

23. Q112026 · 28 Jan 2026 · Shift 2

    Let $A=\{z\in \mathbb{C}:|z-2|\le 4\}$ and $B=\{z\in \mathbb{C}:|z-2|+|z+2|=5\}$. Then the $\max \{|z_1-z_2|:z_1\in A\text{ and }{z}_2\in B\}$ is :

    1. A.$\frac{17}{2}$
    2. B.8
    3. C.9
    4. D.$\frac{15}{2}$
    Show answer

    Answer: A

24. Q142026 · 28 Jan 2026 · Shift 2

    $\frac{6}{3^{26}}+\frac{10\cdot 1}{3^{25}}+\frac{10\cdot 2}{3^{24}}+\frac{10\cdot 2^2}{3^{23}}+\cdots +\frac{10\cdot 2^{24}}{3}$ is equal to :

    1. A.$2^{26}$
    2. B.$3^{25}$
    3. C.$3^{26}$
    4. D.$2^{25}$
    Show answer

    Answer: A

25. Q212026 · 28 Jan 2026 · Shift 2· Numerical answer

    If ${\sum }_{r=1}^{25}\left(\frac{r}{r^4+r^2+1}\right)=\frac{p}{q}$, where p and q are positive integers such that $\gcd (p,q)=1$, then $p+q$ is equal to ________.

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    Answer: 976