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Day 266: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked once: 26 Jun 2022 (same type asked 4 times) See all 4 of this type

    171
    Let f:R→Rf:R \rightarrow R satisfy f(x+y)=2xf(y)+4yf(x),∀xf(x + y) =2^{x}f(y) +4^{y}f(x),\forall x, y∈Ry \in R. If f(2)=3f(2) = 3, then 14⋅f′(4)f′(2)14 \cdot\frac{f^{'}(4)}{f^{'}(2)} is equal to

  2. Question 2

    Three Dimensional Geometry. Asked once: 29 Jan 2024 (same type asked 4 times) See all 4 of this type

    176
    Let OO be the origin, and MM and NN be the points on the lines x−54=y−41=z−53\frac{x- 5}{4}=\frac{y- 4}{1}=\frac{z- 5}{3} and x+812=y+25=z+119\frac{x + 8}{12}=\frac{y + 2}{5}=\frac{z + 11}{9} respectively such that MNMN is the shortest distance between the given lines. Then OM→⋅ON→\overrightarrow{OM}\cdot\overrightarrow{ON} is equal to

  3. Question 3

    Straight Lines. Asked once: 28 Jun 2022 (same type asked 4 times) See all 4 of this type

    85
    A ray of light passing through the point P(2,3)P(2,3) reflects on the XX-axis at point AA and the reflected ray passes through the point Q(5,4)Q(5,4). Let RR be the point that divides the line segment AQAQ internally into the ratio 2:12:1. Let the co-ordinates of the foot of the perpendicular MM from RR on the bisector of the angle PAQ be (α,β)(\alpha,\beta). Then, the value of 7α+3β7\alpha+ 3\beta is equal to

  4. Question 4

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

    152
    The sum of all the real roots of the equation (e2x−4)(6e2x−5ex+1)=0\left( e^{2x}- 4 \right)\left( 6e^{2x}- 5e^{x}+ 1 \right)= 0 is

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  5. Question 5

    Definite Integration. Asked once: 28 Jun 2022 (same type asked 4 times) See all 4 of this type

    67
    Let [t]\lbrack t\rbrack denote the greatest integer less than or equal to tt. Then, the value of the integral ∫01[−8x2+6x−1]dx\int_{0}^{1} \left\lbrack - 8x^{2}+ 6x - 1 \right\rbrack dx is equal to

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