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Day 316: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 29 Jan 2023 (same type asked 5 times) See all 5 of this type

    84
    Let the coefficients of three consecutive terms in the binomial expansion of (1+2x)n(1 + 2x)^{n} be in the ratio 2:5:82:5:8. Then the coefficient of the term, which is in the middle of these three terms, is

  2. Question 2

    Differential Equations. Asked once: 2021 Paper 21 (same type asked 5 times) See all 5 of this type

    65
    A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is the distance of the point (2,−3)(2, - 3) from the line 3x+4y=53x+ 4y= 5, is given by:

    Tap an option to check your answer.

  3. Question 3

    Three Dimensional Geometry. Asked once: 25 Jun 2022 (same type asked 5 times) See all 5 of this type

    88
    Let the lines
    L1:r→=λ(i^+2j^+3k^),λ∈RL_{1}:\overrightarrow{r}=\lambda(\widehat{i}+ 2\widehat{j}+ 3\widehat{k}),\lambda\in R
    L2:r→=(i^+3j^+k^)+μ(i^+j^+5k^);μ∈RL_{2}:\overrightarrow{r}= (\widehat{i}+ 3\widehat{j}+\widehat{k}) +\mu(\widehat{i}+\widehat{j}+ 5\widehat{k});\mu\in R
    intersect at the point SS. If a plane ax+by−zax+by-z +d=0+ d = 0 passes through SS and is parallel to both the lines L1L_{1} and L2L_{2}, then the value of a+b+a + b + dd is equal to

  4. Question 4

    Differential Equations. Asked once: 2021 Paper 10 (same type asked 5 times) See all 5 of this type

    61
    Let y=y(x)y = y(x) be the solution of the differential equation dydx=(y+1)((y+1)ex2/2−x),0<x<2.1\frac{dy}{dx}= (y + 1)\left( (y + 1)e^{x^{2}/2}- x \right),0 < x < 2.1, with y(2)=0y(2) = 0. Then the value of dydx\frac{dy}{dx} at x=1x = 1 is equal to:

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  5. Question 5

    Quadratic Equations. Asked once: 28 Jun 2022 (same type asked 5 times) See all 5 of this type

    82
    The number of real solutions of the equation e4x+4e3x−58e2x+4ex+1=0e^{4x}+ 4e^{3x}- 58e^{2x}+ 4e^{x}+ 1 = 0 is