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Day 320: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 2021 Paper 25 (same type asked 4 times) See all 4 of this type

    82
    The number of integral values of ' kk ' for which the equation 3sin⁡x+4cos⁡x=k+13\sin x + 4\cos x = k + 1 has a solution, k∈Rk \in R is

  2. Question 2

    Binomial Theorem. Asked once: 2021 Paper 2 (same type asked 4 times) See all 4 of this type

    77
    If n≥2n\geq 2 is a positive integer, then the sum of the series  n+1C2+2( 2C2+ 3C2+ 4C2+….+ nC2)\ ^{n + 1}C_{2}+ 2\left( \ ^{2}C_{2}+\ ^{3}C_{2}+\ ^{4}C_{2}+ \ldots. +\ ^{n}C_{2} \right) is :

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  3. Question 3

    Differential Equations. Asked once: 29 Jun 2022 (same type asked 4 times) See all 4 of this type

    159
    If y=y(x)y = y(x) is the solution of the differential equation (1+e2x)dydx+2(1+y2)ex=0\left( 1 +e^{2x} \right)\frac{dy}{dx}+ 2\left( 1 +y^{2} \right)e^{x}= 0 and y(0)=0y(0) = 0, then 6(y′(0)+(y(log⁡e3))2)6\left( y^{'}(0) +\left( y\left( \log_{e}\sqrt{3} \right) \right)^{2} \right) is equal to:

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  4. Question 4

    Differentiation. Asked once: 2021 Paper 7 (same type asked 4 times) See all 4 of this type

    83
    If f(x)=sin⁡(cos⁡−1(1−22x1+22x))f(x) = \sin\left( \cos^{- 1}\left( \frac{1 -2^{2x}}{1 +2^{2x}} \right) \right) and its first derivative with respect to xx is −balog⁡e2-\frac{b}{a}\log_{e}2 when x=1x = 1, where aa and bb are integers, then the minimum value of ∣a2−b2∣\left| a^{2}-b^{2} \right| is

  5. Question 5

    Permutations and Combinations. Asked once: 8 Apr 2023 (same type asked 4 times) See all 4 of this type

    67
    The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is

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