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Day 152: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 25 Jul 2022 (same type asked 5 times) See all 5 of this type

    88
    Let the equation of two diameters of a circle x2+y2x^{2}+y^{2} −2x+2fy+1=0- 2x + 2fy + 1 = 0 be 2px−y=12px - y = 1 and 2x+py=4p2x + py = 4p. Then the slope m∈(0,∞)m \in (0,\infty) of the tangent to the hyperbola 3x2−y2=33x^{2}-y^{2}= 3 passing through the centre of the circle is equal to

  2. Question 2

    Permutations and Combinations. Asked once: 3 Apr 2025 (same type asked 5 times) See all 5 of this type

    133
    Line L1L_{1} of slope 2 and line L2L_{2} of slope 12\frac{1}{2} intersect at the origin O . In the first quadrant, P1,P2,….P12P_{1},P_{2},\ldots.P_{12} are 12 points on line L1L_{1} and Q1,Q2,…..Q9Q_{1},Q_{2},\ldots..Q_{9} are 9 points on line L2L_{2}. Then the total number of triangles, that can be formed having vertices at three of the 22 points O,P1,P2,…P12O,P_{1},P_{2},\ldots P_{12}, Q1,Q2,….Q9Q_{1},Q_{2},\ldots.Q_{9}, is:

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  3. Question 3

    Trigonometric Identities. Asked once: 8 Apr 2024 (same type asked 5 times) See all 5 of this type

    159
    If the value of 3cos⁡36∘+5sin⁡18∘5cos⁡36∘−3sin⁡18∘\frac{3\cos36^{\circ}+ 5\sin18^{\circ}}{5\cos36^{\circ}- 3\sin18^{\circ}} is a5−bc\frac{a\sqrt{5}-b}{c}, where a,b,ca,b,c are natural numbers and gcd⁡(a,c)=1\gcd(a,c) = 1, then a+b+ca + b + c is equal to:

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  4. Question 4

    Application of Integrals. Asked once: 28 Jan 2025 (same type asked 5 times) See all 5 of this type

    70
    The area (in sq. units) of the region {(x,y):0≤y≤2∣x∣+1,0≤y≤x2+1,∣x∣≤3}\left\{ (x,y):0 \leq y \leq 2|x| + 1,0 \leq y \leq x^{2}+ 1,|x| \leq 3 \right\} is

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  5. Question 5

    Complex Numbers. Asked once: 9 Apr 2024 (same type asked 5 times) See all 5 of this type

    154
    Let zz be a complex number such that the real part of z−2iz+2i\frac{z- 2i}{z+ 2i} is zero. Then, the maximum value of ∣z−(6+8i)∣|z - (6 + 8i)| is equal to:

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