PYQ Vault

Day 513: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 15 Apr 2023

    64
    Let ABCDABCD be a quadrilateral. If EE and FF are the mid points of the diagonals ACAC and BDBD respectively and (AB→−BC→)+(AD→−DC→)=kFE→(\overrightarrow{AB}-\overrightarrow{BC}) + (\overrightarrow{AD}-\overrightarrow{DC}) =k\overrightarrow{FE}, then kk is equal to

    Tap an option to check your answer.

  2. Question 2

    Application of Derivatives. Asked once: 4 Apr 2024

    162
    Let f(x)=3x−2+4−xf(x) = 3\sqrt{x - 2}+\sqrt{4 - x} be a real valued function. If α\alpha and β\beta are respectively the minimum and the maximum values of ff, then α2+2β2\alpha^{2}+ 2\beta^{2} is equal to

    Tap an option to check your answer.

  3. Question 3

    Application of Integrals. Asked once: 22 Jan 2025

    52
    Let f:R→Rf:R \rightarrow R be a twice differentiable function such that f(x+y)=f(x)f(y)f(x + y) =f(x)f(y) for all x,y∈Rx,y \in R. If f′(0)=4af^{'}(0) = 4a and ff satisfies f′′(x)−3af′(x)−f(x)=0f^{''}(x) - 3af^{'}(x) -f(x) = 0, a>0a> 0, then the area of the region R={(x,y)∣0≤y≤f(ax),0≤x≤2}R = \{(x,y) \mid 0 \leq y \leq f(ax),0 \leq x \leq 2\} is:

    Tap an option to check your answer.

  4. Question 4

    Binomial Theorem. Asked once: 12 Apr 2023

    72
    The sum, of the coefficients of the first 50 terms in the binomial expansion of (1−x)100(1 - x)^{100}, is equal to

    Tap an option to check your answer.

  5. Question 5

    Complex Numbers. Asked once: 6 Apr 2024

    159
    If z1,z2z_{1},z_{2} are two distinct complex number such that ∣z1−2z212−z1zˉ2∣=2\left| \frac{z_{1}- 2z_{2}}{\frac{1}{2}-z_{1}{\bar{z}}_{2}} \right|= 2, then

    Tap an option to check your answer.