JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 January 2024, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

Let

y = f(x)

be a thrice differentiable function in

(-5, 5)

. Let the tangents to the curve

y = f(x)

(1, f(1))

and

(3, f(3))

make angles

\pi/6

and

\pi/4

, respectively with positive

x

-axis. If

27\int_1^3 \left((f'(t))^2 + 1\right) f''(t)dt = \alpha + \beta\sqrt{3}

where

\alpha, \beta

are integers, then the value of

\alpha + \beta

equals

(1) $26$ Official answer
(2) $36$
(3) $-14$
(4) $-16$

Official answer

Option 1

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Composite Function Substitution

Same idea in other shifts

Asked 5× in all

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16 Mar 2021, Shift 2 · Q81For real numbers $\alpha,\beta,\gamma$ and $\delta$ , if…HardNumerical value
18 Mar 2021, Shift 1 · Q73The integral $\int\dfrac{(2x-1)\cos\sqrt{(2x-1)^2+5}}{\sqrt{4x^2-4x+6}}\,dx$ is equal to : (where c is a constant of integration)MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.