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Day 254: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 8 Apr 2023 (same type asked 5 times) See all 5 of this type

    72
    If the coefficients of the three consecutive terms in the expansion of (1+x)n(1 + x)^{n} are in the ratio 1:5:201:5:20, then the coefficient of the fourth term is

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  2. Question 2

    Differential Equations. Asked once: 2021 Paper 25 (same type asked 5 times) See all 5 of this type

    88
    The difference between degree and order of differential equation that represents the family of curves given by y2=a(x+a2),a>0y^{2}=a\left( x+\frac{\sqrt{a}}{2} \right),a> 0 is

  3. Question 3

    Vector Algebra. Asked once: 25 Jun 2022 (same type asked 5 times) See all 5 of this type

    83
    Let θ\theta be the angle between the vectors a→\overrightarrow{a} and b→\overrightarrow{b}, where ∣a→∣=4,∣b→∣=3 θ∈(π4,π3)|\overrightarrow{a}| = 4,|\overrightarrow{b}| = 3\ \theta \in\left( \frac{\pi}{4},\frac{\pi}{3} \right). Then ∣(a→−b→)×(a→+b→)∣2+4(a→⋅b→)2|(\overrightarrow{a}-\overrightarrow{b}) \times (\overrightarrow{a}+\overrightarrow{b})|^{2}+ 4(\overrightarrow{a}\cdot\overrightarrow{b})^{2} is equal to

  4. Question 4

    Three Dimensional Geometry. Asked once: 28 Jul 2022 (same type asked 5 times) See all 5 of this type

    166
    A plane PP is parallel to two lines whose direction ratios are −2,1,−3- 2,1, - 3, and −1,2,−2- 1,2, - 2 and it contains the point (2,2,−2)(2,2, - 2). Let PP intersect the co-ordinate axes at the points A,B,CA,B,C making the intercepts α,β,γ\alpha,\beta,\gamma. If VV is the volume of the tetrahedron OABCOABC, where OO is the origin and p=α+β+γp = \alpha + \beta + \gamma, then the ordered pair (V,p)(V,p) is equal to

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  5. Question 5

    Differential Equations. Asked once: 2021 Paper 26 (same type asked 5 times) See all 5 of this type

    66
    Let slope of the tangent line to a curve at any point P(x,y)P(x,y) be given by xy2+yx\frac{xy^{2}+y}{x}. If the curve intersects the line x+2y=4x+ 2y= 4 at x=−2x= - 2, then the value of yy, for which the point (3,y)(3,y) lies on the curve, is:

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