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Day 69: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. This type asked 3 times: 31 Jan 2023, 6 Apr 2023, 5 Apr 2024. This one: 5 Apr 2024 See all 3 of this type

    76
    If 11+2+12+3+…+199+100=m\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+ \ldots +\frac{1}{\sqrt{99}+\sqrt{100}}= m and 11⋅2+12⋅3+…+199⋅100=n\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+ \ldots +\frac{1}{99 \cdot 100}= n, then the point (m,n)(m,n) lies on the line

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  2. Question 2

    Differential Equations. This type asked 3 times: 27 Jan 2024, 1 Feb 2024, 4 Apr 2024. This one: 4 Apr 2024 See all 3 of this type

    180
    Let y=y(x)y=y(x) be the solution of the differential equation (x+y+2)2dx=dy,y(0)=−2(x+y+ 2)^{2}dx=dy,y(0) = - 2. Let the maximum and minimum values of the function y=y(x)y=y(x) in [0,π3]\left\lbrack 0,\frac{\pi}{3} \right\rbrack be α\alpha and β\beta, respectively. If (3α+π)2+β2=γ+δ3,γ,δ∈Z(3\alpha+\pi)^{2}+\beta^{2}=\gamma+\delta\sqrt{3},\gamma,\delta\in\mathbb{Z}, then γ+δ\gamma+\delta equals...........

  3. Question 3

    Limits and Continuity. This type asked 3 times: 2021 Paper 17, 27 Jul 2022, 4 Apr 2024. This one: 4 Apr 2024 See all 3 of this type

    81
    If lim⁡x→1(5x+1)1/3−(x+5)1/3(2x+3)1/2−(x+4)1/2=m5n(2n)2/3\lim_{x\rightarrow 1} \frac{(5x+ 1)^{1/3}- (x+ 5)^{1/3}}{(2x+ 3)^{1/2}- (x+ 4)^{1/2}}=\frac{m\sqrt{5}}{n(2n)^{2/3}}, where gcd(m,n)=1gcd(m,n) = 1, then 8 m+12n8\text{ }m + 12n is equal to

  4. Question 4

    Quadratic Equations. This type asked 3 times: 27 Jul 2022, 28 Jul 2022, 4 Apr 2024. This one: 4 Apr 2024 See all 3 of this type

    74
    If 2 and 6 are the roots of the equation ax2+bx+1=0ax^{2}+ bx + 1 = 0, then the quadratic equation, whose roots are 12a+b\frac{1}{2a + b} and 16a+b\frac{1}{6a + b}, is :

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  5. Question 5

    Relations and Functions. This type asked 3 times: 26 Jun 2022, 30 Jan 2023, 4 Apr 2024. This one: 4 Apr 2024 See all 3 of this type

    174
    Consider the function f:R→Rf:R \rightarrow R defined by f(x)=2x1+9x2f(x) =\frac{2x}{\sqrt{1 + 9x^{2}}}. If the composition of f,( f o f o f o...o f)10 times (x)=210x1+9αx2,f,\underset{10\text{~times~}}{\overset{(\text{~f o f o f o...o~}f)}{}}(x) =\frac{2^{10}x}{\sqrt{1 + 9\alpha x^{2}}}, then the value of 3α+1\sqrt{3\alpha + 1} is equal to .....