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Day 199: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 21 Jan 2026 S2 (same type asked 2 times) See all 2 of this type

    55
    Let y2=12xy^{2}= 12x be the parabola with its vertex at O . Let P be a point on the parabola and A be a point on the x -axis such that ∠OPA=90∘\angle OPA =90^{\circ}. Then the locus of the centroid of such triangles OPA is :

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  2. Question 2

    Permutations and Combinations. Asked once: 1 Feb 2024 (same type asked 2 times) See all 2 of this type

    82
    The number of elements in the set S={(x,y,z):x,y,z∈Z,x+2y+3z=42,x,y,z\mathbf{S = \{(x,y,z):x,y,z \in Z,x + 2y + 3z = 42,x,y,z} ≥0}\geq 0\} equals

  3. Question 3

    Probability. Asked once: 2 Apr 2025 (same type asked 2 times) See all 2 of this type

    74
    Three distinct numbers are selected randomly from the set {1,2,3,……,40}\{ 1,2,3,\ldots\ldots,40\}. If the probability, that the selected numbers are in an increasing G.P. is mn\frac{m}{n}, gcd(m,n)=1gcd(m,n) = 1, then m+nm + n is equal to

  4. Question 4

    Conic Sections. Asked once: 31 Jan 2023 (same type asked 2 times) See all 2 of this type

    168
    The set of all values of a2a^{2} for which the line x+y=0x + y = 0 bisects two distinct chords drawn from a point P(1+a2,1−a2)P\left( \frac{1 + a}{2},\frac{1 - a}{2} \right) on the circle 2x2+2y2−(1+a)x−(1−a)y=02x^{2}+ 2y^{2}- (1 + a)x - (1 - a)y = 0, is equal to:

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  5. Question 5

    Trigonometric Identities. Asked once: 28 Jan 2025 (same type asked 2 times) See all 2 of this type

    141
    If ∑r=113{1sin⁡(π4+(r−1)π6)sin⁡(π4+rπ6)}=a3+b\sum_{r = 1}^{13} \left\{ \frac{1}{\sin\left( \frac{\pi}{4}+ (r - 1)\frac{\pi}{6} \right)\sin\left( \frac{\pi}{4}+\frac{r\pi}{6} \right)} \right\}= a\sqrt{3}+ b, a,b∈Za,b \in Z, then a2+b2a^{2}+b^{2} is equal to :

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