PYQ Vault
EbooksTutor

Day 548: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 29 Jun 2022

    164
    Let QQ be the mirror image of the point P(1,2,1)P(1,2,1) with respect to the plane x+2y+2z=16x + 2y + 2z = 16. Let TT be a plane passing through the point QQ and containing the line r→=−k^+λ(i^+j^+2k^), λ∈R\overrightarrow{r}= -\widehat{k}+ \lambda(\widehat{i}+\widehat{j}+ 2\widehat{k}),\ \lambda \in R. Then which of the following points lies on TT?

    Tap an option to check your answer.

  2. Question 2

    Vector Algebra. Asked once: 31 Jan 2023

    179
    Let a→,b→,c→\overrightarrow{a},\overrightarrow{b},\overrightarrow{c} be three vectors such that ∣a→∣=31,4∣b→∣=∣c→∣=2|\overrightarrow{a}| =\sqrt{31},4|\overrightarrow{b}| = |\overrightarrow{c}| = 2 and 2(a→×b→)=3(c→×a→)2(\overrightarrow{a}\times\overrightarrow{b}) = 3(\overrightarrow{c}\times\overrightarrow{a}). If the angle between b→\overrightarrow{b} and c→\overrightarrow{c} is 2π3\frac{2\pi}{3}, then (a→×c→a→⋅b→)2\left( \frac{\overrightarrow{a}\times\overrightarrow{c}}{\overrightarrow{a}\cdot\overrightarrow{b}} \right)^{2} is equal to

  3. Question 3

    Application of Derivatives. Asked once: 29 Jan 2023

    176
    If the equation of the normal to the curve y=x−a(x+b)(x−2)y =\frac{x - a}{(x + b)(x - 2)} at the point (1,−3)(1, - 3) is x−4y=13x - 4y = 13, then the value of a+ba + b is equal to

  4. Question 4

    Application of Integrals. Asked once: 27 Jan 2024

    84
    Let the area of the region {(x,y):x−2y+4≥0\{(x,y):x- 2y+ 4 \geq 0,  x+2y2≥0,x+4y2≤8,y≥0}\left. \ x+ 2y^{2}\geq 0,x+ 4y^{2}\leq 8,y\geq 0 \right\} be mn\frac{m}{n}, where mm and nn are coprime numbers. Then m+nm + n is equal to

  5. Question 5

    Binomial Theorem. Asked once: 27 Jul 2022

    173
    Let for the 9th 9^{\text{th~}} term in the binomial expansion of (3+6x)n(3 + 6x)^{n}, in the increasing powers of 6x6x, to be the greatest for x=32x =\frac{3}{2}, the least value of nn is n0n_{0}. If kk is the ratio of the coefficient of x6x^{6} to the coefficient of x3x^{3}, then k+n0k +n_{0} is equal to: