PYQ Vault

Day 216: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 30 Jan 2023 (same type asked 2 times) See all 2 of this type

    161
    If PP is a 3×33 \times 3 real matrix such that PT=aP+(a−1)IP^{T}= aP + (a - 1)I, where a>1a > 1, then

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  2. Question 2

    Sequences and Series. Asked once: 14 Jun 2022 (same type asked 2 times) See all 2 of this type

    154
    Let x,y>0x,y> 0. If x3y2=215x^{3}y^{2}=2^{15}, then the least value of 3x+2y3x + 2y is

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  3. Question 3

    Application of Derivatives. Asked once: 2021 Paper 21 (same type asked 2 times) See all 2 of this type

    72
    A box open from top is made from a rectangular sheet of dimension a×ba \times b by cutting squares each of side xx from each of the four corners and folding up the flaps. If the volume of the box is maximum, then xx is equal to:

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  4. Question 4

    Limits and Continuity. Asked once: 14 Jun 2022 (same type asked 2 times) See all 2 of this type

    155
    Let f(x)={sin⁡(x−[x])x−[x],x∈(−2,−1)max{2x,3[∣x∣]},∣x∣<11, otherwise f(x) =\left\{ \begin{matrix} \frac{\sin(x - \lbrack x\rbrack)}{x - \lbrack x\rbrack} & , & x \in ( - 2, - 1) \\ \mathbf{max\{ 2x,3\lbrack|x|\rbrack\}} & , & |x| < 1 \\ 1, & & \text{~otherwise~} \end{matrix} \right. where [t]\lbrack t\rbrack denotes greatest integer ≤t\leq t. If mm is the number of points where ff is not continuous and nn is the number of points where ff is not differentiable, then the ordered pair (m,n)(m,n) is :

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  5. Question 5

    Permutations and Combinations. Asked once: 2021 Paper 7 (same type asked 2 times) See all 2 of this type

    75
    Team 'A' consists of 7 boys and nn girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then nn is equal to:

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