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Day 445: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 6 Apr 2026 S2

    71
    Let R={(x,y)∈N×N:log⁡e(x+y)≤2}R = \left\{ (x,y) \in N \times N:\log_{e}(x + y) \leq 2 \right\}. Then the minimum number of elements, required to be added in R to make it a transitive relation, is ____\_\_\_\_ .

  2. Question 2

    Sequences and Series. Asked once: 6 Apr 2026 S2

    52
    Consider the quadratic equation (n2−2n+2)x2−3x+(n2−2n+2)2=0,n∈R\left( n^{2}- 2n + 2 \right)x^{2}- 3x +\left( n^{2}- 2n + 2 \right)^{2}= 0,n \in R. Let α\alpha be the minimum value of the product of its roots and β\beta be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is α\alpha and the common ratio is αβ\frac{\alpha}{\beta}, is :

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  3. Question 3

    Statistics. Asked once: 8 Apr 2024

    178
    Let a,b,c∈Na,b,c \in N and a<b<ca < b < c. Let the mean, the mean deviation about the mean and the variance of the 5 observations 9,25,a,b,c9,25,a,b,c be 18,4 and 1365\frac{136}{5}, respectively. Then 2a+b−c2a + b - c is equal to

  4. Question 4

    Straight Lines. Asked once: 4 Apr 2026 S2

    73
    Let A,BA,B be points on the two half-lines x−3∣y∣=α,α>0x - \sqrt{3}|y| = \alpha,\alpha > 0 at a distance of α\alpha from their point of intersection P. The line segment AB meets the angle bisector of the given half-lines at the point Q. If PQ=92PQ = \frac{9}{2} and R is the radius of the circumcircle of △PAB\bigtriangleup PAB, then α2R\frac{\alpha^{2}}{R} is equal to ____\_\_\_\_ .

  5. Question 5

    Three Dimensional Geometry. Asked once: 24 Jan 2026 S1

    53
    Let the lines L1:r→=i^+2j^+3k^+λ(2i^+3j^+4k^)L_{1}:\overrightarrow{r}=\widehat{i}+ 2\widehat{j}+ 3\widehat{k}+ \lambda(2\widehat{i}+ 3\widehat{j}+ 4\widehat{k}), λ∈R\lambda \in R and L2:r→=(4i^+j^)+μ(5i^+2j^+k^),μ∈RL_{2}:\overrightarrow{r}= (4\widehat{i}+\widehat{j}) + \mu(5\widehat{i}+ 2\widehat{j}+\widehat{k}),\mu \in R, intersect at the point R . Let P and Q be the points lying on lines L1L_{1} and L2L_{2}, respectively, such that ∣PR→∣=29|\overrightarrow{PR}| =\sqrt{29} and ∣PQ→∣=473|\overrightarrow{PQ}| =\sqrt{\frac{47}{3}}. If the point P lies in the first octant, then 27(QR)227(QR)^{2} is equal to

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