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JEE Main 2024 Question Paper & Answers

The official JEE Main 2024 question paper, with the official answer key. Attempt as a real timed exam (with negative marking) or switch to practice mode for instant per-question answers and explanations.

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Official PYQ

JEE Main 2024 - January 27 Shift 1

180 Mins 300 Marks
75Questions
300Max Marks

Sample questions from JEE Main 2024 - January 27 Shift 1

1The value(s) of kk for which n+1Cr=(k2−8) nCr+1^{n+1}C_r = (k^2-8)\,^nC_{r+1} can hold (for suitable n,rn,r) is given by the range:
  • A) −3≤k<−22-3 \le k < -2\sqrt{2} or 22<k≤32\sqrt{2} < k \le 3
  • B) −23<k<32-2\sqrt{3} < k < 3\sqrt{2}
  • C) 23<k<332\sqrt{3} < k < 3\sqrt{3}
  • D) 22<k<232\sqrt{2} < k < 2\sqrt{3}
Answer: A
2The distance of the point (7,−2,11)(7,-2,11) from the line x−61=y−40=z−83\frac{x-6}{1}=\frac{y-4}{0}=\frac{z-8}{3}, measured along a line parallel to x−52=y−13=z−56\frac{x-5}{2}=\frac{y-1}{3}=\frac{z-5}{6}, is:
  • A) 12
  • B) 14
  • C) 18
  • D) 21
Answer: B
3Let x=x(t)x=x(t) and y=y(t)y=y(t) be solutions of the differential equations dxdt+ax=0\frac{dx}{dt}+ax=0 and dydt+by=0\frac{dy}{dt}+by=0 respectively, a,b∈Ra,b\in\mathbb{R}. Given that x(0)=2x(0)=2, y(0)=1y(0)=1 and 3y(1)=2x(1)3y(1)=2x(1), the value of tt for which x(t)=y(t)x(t)=y(t) is:
  • A) log⁡e2\log_e 2
  • B) log⁡e3\log_e 3
  • C) log⁡e4\log_e 4
  • D) 12log⁡e3\frac{1}{2}\log_e 3
Answer: D
4If (a,b)(a,b) is the orthocentre of the triangle with vertices (1,2)(1,2), (2,3)(2,3) and (3,1)(3,1), and I1=∫04xsin⁡(x(4−x)) dxI_1=\int_0^4 x\sin(x(4-x))\,dx, I2=∫04sin⁡(x(4−x)) dxI_2=\int_0^4 \sin(x(4-x))\,dx, then 36I1a I2\frac{36 I_1}{a\,I_2} is equal to:
  • A) 72
  • B) 88
  • C) 80
  • D) 66
Answer: A
5If AA denotes the sum of all the coefficients in the expansion of (1−3x+10x2)n(1-3x+10x^2)^n and BB denotes the sum of all the coefficients in the expansion of (1+x2)n(1+x^2)^n, then:
  • A) A=BA=B
  • B) 3A=B3A=B
  • C) B=A5B=A^5
  • D) A=3BA=3B
Answer: A

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JEE Main 2024 Previous Year Question Paper with Answers (PYQ) | ClassScribe