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Day 105: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. This type asked 2 times: 25 Jul 2022, 21 Jan 2026 S2. This one: 21 Jan 2026 S2 See all 2 of this type

    65
    For a triangle ABCABC, let p→=BC→,q→=CA→\overrightarrow{p}=\overrightarrow{BC},\overrightarrow{q}=\overrightarrow{CA} and r→=BA→\overrightarrow{r}=\overrightarrow{BA}. If ∣p→∣=23,∣q→∣=2|\overrightarrow{p}| = 2\sqrt{3},|\overrightarrow{q}| = 2 and cos⁡θ=13\cos\theta =\frac{1}{\sqrt{3}}, where θ\theta is the angle between p→\overrightarrow{p} and q→\overrightarrow{q}, then ∣p→×(q→−3r→)∣2+3∣r→∣2|\overrightarrow{p}\times (\overrightarrow{q}- 3\overrightarrow{r})|^{2}+ 3|\overrightarrow{r}|^{2} is equal to:

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  2. Question 2

    Conic Sections. This type asked 2 times: 30 Jan 2024, 7 Apr 2025. This one: 7 Apr 2025 See all 2 of this type

    73
    Consider the hyperbola x2a2−y2b2=1\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 having one of its focus at P(−3,0)P( - 3,0). If the latus rectum through its other focus subtends a right angle at PP and a2b2=α2−β,α,β∈Na^{2}b^{2} = \alpha\sqrt{2} - \beta,\alpha,\beta \in \mathbb{N}, then α+β\alpha + \beta is equal to

  3. Question 3

    Relations and Functions. This type asked 2 times: 31 Jan 2023, 7 Apr 2025. This one: 7 Apr 2025 See all 2 of this type

    129
    If the range of the function f(x)=5−xx2−3x+2f\left( x \right)=\frac{5 -x}{x^{2}- 3x+ 2}, x≠1,2x\neq 1,2, is (−∞,α)∪[β,∞)\left( - \infty,\alpha \right)\cup\left\lbrack \beta,\infty \right), then α2+β2\alpha^{2}+\beta^{2} is equal to :

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  4. Question 4

    Three Dimensional Geometry. This type asked 2 times: 31 Jan 2024, 7 Apr 2025. This one: 7 Apr 2025 See all 2 of this type

    141
    Consider the lines L1:x−1=y−2=zL_{1}:x- 1 =y- 2 =z and L2:x−2=y=z−1L_{2}:x - 2 = y = z - 1. Let the feet of the perpendiculars from the point P(5,1,−3)P(5,1, - 3) on the lines L1L_{1} and L2L_{2} be QQ and RR respectively. If the area of the triangle PQRPQR is AA, then 4A24A^{2} is equal to :

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  5. Question 5

    Definite Integration. This type asked 2 times: 6 Apr 2023, 4 Apr 2025. This one: 4 Apr 2025 See all 2 of this type

    143
    Let f(x)+2f(1x)=x2+5f(x) + 2f\left( \frac{1}{x} \right)=x^{2}+ 5 and 2g(x)−3g(12)=x,x>02g(x) - 3g\left( \frac{1}{2} \right)=x,x> 0. If α=∫12f(x)dx\alpha=\int_{1}^{2} f(x)dx, and β=∫12g(x)dx\beta=\int_{1}^{2} g(x)dx, then the value of 9α+β9\alpha+\beta is :

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