Other Maths · JEE Main previous year questions

2023 63 questions

1. Q22023 · 25 Jan 2023 · Shift 2

   The foot of perpendicular of the point (2, 0, 5) on the line $\frac{x+1}{2}=\frac{y-1}{5}=\frac{z+1}{-1}$ is $(\alpha ,\beta ,\gamma )$. Then, which of the following is NOT correct?

   1. A.$\frac{\alpha }{\beta }=-8$
   2. B.$\frac{\alpha \beta }{\gamma }=\frac{4}{15}$
   3. C.$\frac{\beta }{\gamma }=-5$
   4. D.$\frac{\gamma }{\alpha }=\frac{5}{8}$
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   Answer: C

2. Q162023 · 25 Jan 2023 · Shift 2

   Let $f(x)=2x^n+\lambda ,\lambda \in R,n\in N$, and $f(4)=133,f(5)=255$. Then the sum of all the positive integer divisors of $(f(3)-f(2))$ is

   1. A.60
   2. B.58
   3. C.61
   4. D.59
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   Answer: A

3. Q202023 · 25 Jan 2023 · Shift 2

   $\sum _{k=0}^6{}^{51-k}{C}_3$ is equal to :

   1. A.${}^{51}{\mathrm{C}}_4-{}^{45}{\mathrm{C}}_4$
   2. B.${}^{51}{\mathrm{C}}_3-{}^{45}{\mathrm{C}}_3$
   3. C.${}^{52}{\mathrm{C}}_3-{}^{45}{\mathrm{C}}_3$
   4. D.${}^{52}{\mathrm{C}}_4-{}^{45}{\mathrm{C}}_4$
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   Answer: D

4. Q222023 · 25 Jan 2023 · Shift 2· Numerical answer

   A triangle is formed by X-axis, Y-axis and the line $3x+4y=60$. Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is ____.

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   Answer: 31

5. Q232023 · 25 Jan 2023 · Shift 2· Numerical answer

   The remainder when $(2023{)}^{2023}$ is divided by 35 is ____.

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   Answer: 7

6. Q122023 · 24 Jan 2023 · Shift 1

   Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that $\frac{QA}{AR}=\frac{RB}{BP}=\frac{PC}{CQ}=\frac{1}{2}$. Then $\frac{Area(\Delta PQR)}{Area(\Delta ABC)}$ is equal to :

   1. A.$\frac{5}{2}$
   2. B.4
   3. C.2
   4. D.3
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   Answer: D

7. Q152023 · 24 Jan 2023 · Shift 1

   The value of ${\sum }_{r=0}^{22}{}^{22}{C}_r{}^{23}{C}_r$ is

   1. A.${}^{44}{C}_{23}$
   2. B.${}^{45}{C}_{23}$
   3. C.${}^{44}{C}_{22}$
   4. D.${}^{45}{C}_{24}$
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   Answer: B

8. Q192023 · 24 Jan 2023 · Shift 1

   Let $\vec{u}=\hat{i}-\hat{j}-2\hat{k},\vec{v}=2\hat{i}+\hat{j}-\hat{k},\vec{v}\cdot \vec{w}=2$ and $\vec{v}\times \vec{w}=\vec{u}+\lambda \vec{v}$. Then $\vec{u}\cdot \vec{w}$ is equal to :

   1. A.$-\frac{2}{3}$
   2. B.$\frac{3}{2}$
   3. C.2
   4. D.1
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   Answer: D

9. Q262023 · 24 Jan 2023 · Shift 1· Numerical answer

   The value of $12{\int }_0^3|x^2-3x+2|dx$ is ____

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   Answer: 22

10. Q22023 · 24 Jan 2023 · Shift 2

    The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is

    1. A.3
    2. B.4
    3. C.0
    4. D.2
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    Answer: C

11. Q92023 · 24 Jan 2023 · Shift 2

    If $f(x)=\frac{2^{2x}}{2^{2x}+2},x\in \mathbb{R}$, then $f\left(\frac{1}{2023}\right)+f\left(\frac{2}{2023}\right)+\dots +f\left(\frac{2022}{2023}\right)$ is equal to

    1. A.2011
    2. B.2010
    3. C.1010
    4. D.1011
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    Answer: D

12. Q202023 · 24 Jan 2023 · Shift 2

    If $({}^{30}{\mathrm{C}}_1{)}^2+2({}^{30}{\mathrm{C}}_2{)}^2+3({}^{30}{\mathrm{C}}_3{)}^2+\dots +30({}^{30}{\mathrm{C}}_{30}{)}^2=\frac{\alpha 60!}{(30!{)}^2}$ then $\alpha$ is equal to :

    1. A.30
    2. B.10
    3. C.15
    4. D.60
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    Answer: C

13. Q302023 · 24 Jan 2023 · Shift 2· Numerical answer

    If $\frac{1^3+2^3+3^3+\dots uptonterms}{1\cdot 3+2\cdot 5+3\cdot 7+\dots uptonterms}=\frac{9}{5}$, then the value of $n$ is

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    Answer: 5