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Day 187: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 5 Apr 2024 (same type asked 3 times) See all 3 of this type

    70
    The coefficients a,b,ca,b,c in the quadratic equation ax2+bx+c=0ax^{2}+ bx + c = 0 are chosen from the set {1,2,3,4,5,6,7,8}\mathbf{\{ 1,2,3,4,5,6,7,8\}}. The probability of this equation having repeated roots is:

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  2. Question 2

    Relations and Functions. Asked once: 30 Jan 2023 (same type asked 3 times) See all 3 of this type

    80
    Suppose f:R→(0,∞)f:R \rightarrow (0,\infty) be a differentiable function such that 5f(x+y)=f(x)⋅f(y),∀x,y∈R5f(x + y) = f(x) \cdot f(y),\forall x,y \in R. If f(3)=320f(3) = 320, then ∑n=05f(n)\sum_{n = 0}^{5} f(n) is equal to:

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  3. Question 3

    Sequences and Series. Asked once: 27 Jul 2022 (same type asked 3 times) See all 3 of this type

    157
    Let the sum of an infinite G.P., whose first term is aa and the common ratio is rr, be 5 . Let the sum of its first five terms be 9825\frac{98}{25}. Then the sum of the first 21 terms of an AP, whose first term is 10ar,nth 10ar,n^{\text{th~}} term is ana_{n} and the common difference is 10ar210ar^{2}, is equal to:

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  4. Question 4

    Straight Lines. Asked once: 6 Apr 2024 (same type asked 3 times) See all 3 of this type

    73
    Let a variable line of slope m>0m > 0 passing through the point (4,−9)(4, - 9) intersect the coordinate axes at the points AA and BB. the minimum value of the sum of the distances of AA and BB from the origin is

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  5. Question 5

    Definite Integration. Asked once: 6 Apr 2024 (same type asked 3 times) See all 3 of this type

    83
    Let rk=∫01(1−x7)kdx∫01(1−x7)k+1dx,k∈Nr_{k} = \frac{\int_{0}^{1} \left( 1 - x^{7} \right)^{k}dx}{\int_{0}^{1} \left( 1 - x^{7} \right)^{k + 1}dx},k \in N. Then the value of ∑k=11017(rk−1)\sum_{k = 1}^{10} \frac{1}{7\left( r_{k} - 1 \right)} is equal to .