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Day 250: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Complex Numbers. Asked once: 27 Jan 2024 (same type asked 5 times) See all 5 of this type

    90
    If α\alpha satisfies the equation x2+x+1=0x^{2}+ x + 1 = 0 and (1+α)7=A+Bα+Cα2, A, B,C≥0(1 + \alpha)^{7}= A + B\alpha +C\alpha^{2},\text{ }A,\text{ }B,C \geq 0, then 5(3 A−2 B−C)5(3\text{ }A - 2\text{ }B - C) is equal to

  2. Question 2

    Conic Sections. Asked once: 14 Jun 2022 (same type asked 5 times) See all 5 of this type

    75
    Let λx−2y=μ\lambda x- 2y=\mu be a tangent to the hyperbola a2x2−y2=b2a^{2}x^{2}-y^{2}=b^{2}. Then (λa)2−(μb)2\left( \frac{\lambda}{a} \right)^{2}-\left( \frac{\mu}{b} \right)^{2} is equal to:

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  3. Question 3

    Permutations and Combinations. Asked once: 2021 Paper 6 (same type asked 5 times) See all 5 of this type

    71
    Consider a rectangle ABCDABCD having 5, 7, 6, 9 points in the interior of the line segments ABAB, CD,BC,DACD,BC,DA respectively. Let α\alpha be the number of triangles having these points from different sides as vertices and β\beta be the number of quadrilaterals having these points from different sides as vertices. Then (β−α)(\beta-\alpha) is equal to:

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  4. Question 4

    Trigonometric Identities. Asked once: 27 Jun 2022 (same type asked 5 times) See all 5 of this type

    169
    α=sin⁡36∘\alpha = \sin36^{\circ} is a root of which of the following equations?

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  5. Question 5

    Application of Integrals. Asked once: 29 Jan 2024 (same type asked 5 times) See all 5 of this type

    175
    Let the area of the region {(x,y)\{(x,y) : 0≤x≤3,0≤y≤0 \leq x\leq 3,0 \leq y\leq  min⁡{x2+2,2x+2}}\left. \ \min\left\{ x^{2}+ 2,2x + 2 \right\} \right\} be AA. Then 12 A12\text{ }A is equal to