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Day 204: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 25 Jul 2022 (same type asked 2 times) See all 2 of this type

    75
    Let ABCABC be a triangle such that BC→=a→,CA→=b→\overrightarrow{BC}=\overrightarrow{a},\overrightarrow{CA}=\overrightarrow{b}, AB→=c→,∣a→∣=62,∣b→∣=23\overrightarrow{AB}=\overrightarrow{c},|\overrightarrow{a}| = 6\sqrt{2},|\overrightarrow{b}| = 2\sqrt{3} and b→⋅c→=12\overrightarrow{b}\cdot\overrightarrow{c}= 12 Consider the statements : (S1): ∣(a→×b→)+(c→×b→)∣−∣c→∣=6(22−1)|(\overrightarrow{a}\times\overrightarrow{b}) + (\overrightarrow{c}\times\overrightarrow{b})| - |\overrightarrow{c}| = 6(2\sqrt{2}- 1) (S2): ∠ABC=cos⁡−1(23)\angle ABC =\cos^{- 1}\left( \sqrt{\frac{2}{3}} \right). Then

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  2. Question 2

    Conic Sections. Asked once: 30 Jan 2024 (same type asked 2 times) See all 2 of this type

    83
    Let the latus rectum of the hyperbola x29−y2b2=1\frac{x^{2}}{9}-\frac{y^{2}}{b^{2}}= 1 subtend an angle of π3\frac{\pi}{3} at the centre of the hyperbola. If b2b^{2} is equal to l m(1+n)\frac{l}{\text{ }m}(1 +\sqrt{n}), where ll and mm are co-prime numbers, then l2+m2+n2l^{2}+m^{2}+n^{2} is equal to

  3. Question 3

    Relations and Functions. Asked once: 31 Jan 2023 (same type asked 2 times) See all 2 of this type

    170
    Let f:R−{2,6}→R\mathbf{f:R - \{ 2,6\} \rightarrow R} be real valued function defined as f(x)=x2+2x+1x2−8x+12f(x) =\frac{x^{2}+ 2x + 1}{x^{2}- 8x + 12}. Then range of ff is

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  4. Question 4

    Three Dimensional Geometry. Asked once: 31 Jan 2024 (same type asked 2 times) See all 2 of this type

    84
    Let QQ and RR be the feet of perpendiculars from the point P(a,a,a)P(a,a,a) on the lines x=y,z=1x = y,z = 1 and x=−yx = - y, z=−1z = - 1 respectively. If ∠QPR\angle QPR is a right angle, then 12a212a^{2} is equal to

  5. Question 5

    Definite Integration. Asked once: 6 Apr 2023 (same type asked 2 times) See all 2 of this type

    61
    Let 5f(x)+4f(1x)=1x+3,x>05f(x) + 4f\left( \frac{1}{x} \right)=\frac{1}{x}+ 3,x > 0. Then 18∫12f(x)dx18\int_{1}^{2} f(x)dx is equal to:

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