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Day 268: JEE Mains Maths

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

  1. Question 1

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

    176
    Let ff and gg be twice differentiable even functions on (−2,2)( - 2,2) such that f(14)=0,f(12)=0,f(1)=1f\left( \frac{1}{4} \right)= 0,f\left( \frac{1}{2} \right)= 0,f(1) = 1 and g(34)=0,g(1)=2g\left( \frac{3}{4} \right)= 0,g(1) = 2 Then, the minimum number of solutions of f(x)g′′(x)+f′(x)g′(x)=0f(x)g^{''}(x) +f^{'}(x)g^{'}(x) = 0 in (−2,2)( - 2,2) is equal to

  2. Question 2

    Differential Equations. Asked once: 14 Jun 2022 (same type asked 4 times) See all 4 of this type

    158
    A particle is moving in the xy-plane along a curve C passing through the point (3,3)(3,3). The tangent to the curve CC at the point PP meets the XX-axis at QQ. If the yy-axis bisects the segment PQPQ, then CC is a parabola with

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  3. Question 3

    Relations and Functions. Asked once: 28 Jun 2022 (same type asked 4 times) See all 4 of this type

    62
    Let a function f:N→Nf:\mathbb{N}\rightarrow\mathbb{N} be defined by
    f(n)=[2n,n=2,4,6,8,…..n−1,n=3,7,11,15,…..n+12,n=1,5,9,13,…..f(n) =\left\lbrack \begin{matrix} 2n, & n= 2,4,6,8,\ldots.. \\ n- 1, & n= 3,7,11,15,\ldots.. \\ \frac{n+ 1}{2}, & n= 1,5,9,13,\ldots.. \end{matrix} \right.
    then, ff is

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  4. Question 4

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

    76
    If the constant term in the expansion of (3x3−2x2+5x5)10\left( 3x^{3}- 2x^{2}+\frac{5}{x^{5}} \right)^{10} is 2k.l2^{k}.l, where ll is an odd integer, then the value of kk is equal to:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 17 (same type asked 4 times) See all 4 of this type

    82
    The distance of the point P(3,4,4)P(3,4,4) from the point of intersection of the line joining the points Q(3,−4,−5)Q(3,-4,-5) and R(2,−3,1)R(2,-3,1), and the plane 2x+y+z=72x+y+z=7, is equal to