JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 January 2024, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let

\left(5,\frac{a}{4}\right)

be the circumcenter of a triangle with vertices

A(a,-2)

B(a,6)

and

C\left(\frac{a}{4},-2\right)

. Let

\alpha

denote the circumradius,

\beta

denote the area and

\gamma

denote the perimeter of the triangle. Then

\alpha+\beta+\gamma

(1) $30$
(2) $60$
(3) $62$
(4) $53$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Straight Lines
Topic: Properties of Triangles
Idea tested: Inradius and Circumradius

Same idea in other shifts

Asked 6× in all

29 Jul 2022, Shift 1 · Q13Let the circumcentre of a triangle with vertices $A(a, 3)$ , $B(b, 5)$ and $C(a, b)$ , $ab > 0$ be $P(1, 1)$ . If the line AP intersects the…HardSingle correct
29 Jul 2022, Shift 2 · Q13Let A $(\alpha,-2)$ , B $(\alpha, 6)$ and C $\left(\frac{\alpha}{4},-2\right)$ be vertices of a $\Delta$ ABC. If…MediumSingle correct
25 Jun 2022, Shift 1 · Q3Let a, b and c be the length of sides of a triangle ABC such that $\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}$ If r and R are the radius of…MediumSingle correct
16 Mar 2021, Shift 2 · Q82In $\triangle$ ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of $\triangle$ ABC is 30 $\mathrm{cm^2}$ …MediumNumerical value
18 Mar 2021, Shift 2 · Q63A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be…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 108 of the 174 JEE Main shifts held from 2017 to 2026.