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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 28 June 2022, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

The area of the region S={(x,y):y2≤8x, y≥2x, x≥1}S=\{(x, y): y^2\le8x,\ y\ge\sqrt{2}x,\ x\ge1\} is
  1. (1)1326\frac{13\sqrt{2}}{6}
  2. (2)1126\frac{11\sqrt{2}}{6}Official answer
  3. (3)526\frac{5\sqrt{2}}{6}
  4. (4)1926\frac{19\sqrt{2}}{6}

Official answer

Option 2

NTA final key.

Chapter
Application of Integrals
Topic
Area Under Curves
Idea tested
Area of Inequalities

Same idea in other shifts

Asked 15× in all
  1. 5 Apr 2026, Shift 1 · Q16The area of the region R={(x,y):xy≤27, 1≤y≤x2}R = \{(x, y) : xy \leq 27,\ 1 \leq y \leq x^2\} is equal to:MediumSingle correct
  2. 6 Apr 2026, Shift 1 · Q19The area of the region {(x,y):0≤y≤6−x, y2≥4x−3, x≥0}\{(x,y): 0\le y\le 6-x,\ y^2\ge 4x-3,\ x\ge 0\} is:MediumSingle correct
  3. 3 Apr 2025, Shift 2 · Q19The area of the region {(x,y):∣x−y∣≤y≤4x}\left\{(x, y) : |x - y| \leq y \leq 4\sqrt{x}\right\} isMediumSingle correct
  4. 8 Apr 2025, Shift 2 · Q25Let the area of the bounded region {(x,y):0≤9x≤y2,y≥3x−6}\{(x, y) : 0 \le 9x \le y^2, y \ge 3x - 6\} be AA. Then 6A6A is equal to __________MediumNumerical value
  5. 27 Jan 2024, Shift 1 · Q26Let the area of the region {(x,y):x−2y+4≥0, x+2y2≥0, x+4y2≤8, y≥0}\{(x,y): x-2y+4\geq0,\ x+2y^2\geq0,\ x+4y^2\leq8,\ y\geq0\} be mn\dfrac{m}{n}, where m and n are coprime…MediumNumerical value
  6. 31 Jan 2024, Shift 1 · Q10The area of the region {(x,y):y2≤4x, x<4, xy(x−1)(x−2)(x−3)(x−4)>0, x≠3}\left\{(x,y):y^2\leq4x,\ x<4,\ \frac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,\ x\neq3\right\} isHardSingle correct
  7. 6 Apr 2023, Shift 1 · Q26If the area of the region S={(x,y):2y−y2≤x2≤2y, x≥y}S=\{(x,y):2y-y^2\le x^2\le 2y,\ x\ge y\} is equal to n+2n+1−πn−1\frac{n+2}{n+1}-\frac{\pi}{n-1}, then the natural…HardNumerical value
  8. 11 Apr 2023, Shift 1 · Q9Area of the region {(x,y):x2+(y−2)2≤4, x2≥2y}\{(x,y) : x^2 + (y-2)^2 \le 4,\ x^2 \ge 2y\} isMediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.