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Day 558: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 11 Apr 2023

    179
    If the line l1:3y−2x=3\mathcal{l}_{1}:3y - 2x = 3 is the angular bisector of the lines l2:x−y+1=0\mathcal{l}_{2}:x - y + 1 = 0 and l3:αx+βy+17=0\mathcal{l}_{3}:\alpha x + \beta y + 17 = 0, then α2+β2−α−β\alpha^{2}+\beta^{2}- \alpha - \beta is equal to

  2. Question 2

    Three Dimensional Geometry. Asked once: 2021 Paper 25

    67
    Consider the three planes P1:3x+15y+21z=9P_{1}:3x + 15y + 21z = 9, P2:x−3y−z=5P_{2}:x - 3y - z = 5, and
    P3:2x+10y+14z=5P_{3}:2x + 10y + 14z = 5
    Then, which one of the following is true?

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  3. Question 3

    Vector Algebra. Asked once: 29 Jul 2022

    168
    Let a→,b→,c→\overrightarrow{a},\overrightarrow{b},\overrightarrow{c} be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and (a→×b→)⋅(b→×c→)+(b→×c→)⋅(c→×a→)+(c→×a→)⋅(a→×b→)=168(\overrightarrow{a}\times\overrightarrow{b}) \cdot (\overrightarrow{b}\times\overrightarrow{c}) + (\overrightarrow{b}\times\overrightarrow{c}) \cdot (\overrightarrow{c}\times\overrightarrow{a}) + (\overrightarrow{c}\times\overrightarrow{a}) \cdot (\overrightarrow{a}\times\overrightarrow{b}) = 168 then ∣a→∣+∣b→∣+∣c→∣|\overrightarrow{a}| + |\overrightarrow{b}| + |\overrightarrow{c}| is equal to:

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  4. Question 4

    Application of Derivatives. Asked once: 25 Jan 2023

    157
    Let the function f(x)=2x3+(2p−7)x2+3(2p−9)x−6f(x) = 2x^{3}+ (2p - 7)x^{2}+ 3(2p - 9)x - 6 have a maxima for some value of x<0x < 0 and a minima for some value of x>0x > 0. Then, the set of all values of pp is

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  5. Question 5

    Application of Integrals. Asked once: 8 Apr 2023

    180
    Let the area enclosed by the lines x+y=2,y=0x + y = 2,y = 0, x=0x = 0 and the curve f(x)=min{x2+34,1+[x]}f(x) = min\left\{ x^{2}+\frac{3}{4},1 + \lbrack x\rbrack \right\} where [x]\lbrack x\rbrack denotes the greatest integer ≤x\leq x, be AA. Then the value of 12 A12\text{ }A is