JEE Main 2022 · 29 Jul · Shift 2 · Mathematics Q27

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MathematicsInteger+4 / -1Question 27 of 90

If the tangent to the curve $y=x^3-x^2+x$ at the point (a, b) is also tangent to the curve $y=5x^2+2x-25$ at the point (2, −1), then |2a + 9b| is equal to _______.

Your answer

Answer and worked solution

Official answer: 195

Common tangent. At (2, −1) on the parabola the slope is 22: $y=22x-45$ .

On the cubic $3a^2-2a+1=22$ gives $a=3$ or $-\frac73$ ; only $a=3$ , $b=21$ lies on the line.

Value $|6+189|=195$ .

Answer: 195

Topics:Tangents and normals

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JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 27