Aspire Faculty ID #17991 · Topic: JEE Main 2026 (23 January Morning Shift) · Just now
JEE Main 2026 (23 January Morning Shift)

Let $A = {-2, -1, 0, 1, 2, 3, 4}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $2x + y \le 2$. Let $\ell$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations respectively. Then $\ell + m + n$ is equal to:

Solution

$R = {(-2,a), (-1,b), (0,c), (1,d), (2,e)}$

$a = {-2,-1,0,1,2,3,4}$
$b = {-2,-1,0,1,2,3,4}$
$c = {-2,-1,0,1,2}$
$d = {-2,-1,0}$
$e = {-2}$

$\therefore$ No. of elements in $R = 7 + 7 + 5 + 3 + 1 = 23 = \ell$

Minimum number of elements to be added to make it reflexive

$m = 4 \Rightarrow (1,1), (2,2), (3,3), (4,4)$

Minimum number of elements to be added to make it symmetric

$n = 6$

$\therefore \ell + m + n = 23 + 4 + 6 = 33$
← Previous Next →

Previous 10 Questions — JEE Main 2026 (23 January Morning Shift)

Nearest first
1
Let the line $y - x = 1$ intersect the ellipse $\frac{x^2}{2} + \frac{y^2}{1} = 1$ at the points $A$ and $B$. Then the …
Topic: JEE Main 2026 (23 January Morning Shift)
 2
A rectangle is formed by the lines $x = 0, y = 0, x = 3$ and $y = 4$. Let the line $L$ be perpendicular to $3x + y + 6 …
Topic: JEE Main 2026 (23 January Morning Shift)
 3
Let $\vec{a} = -\hat{i} + \hat{j} + 2\hat{k}$, $\vec{b} = \hat{i} - \hat{j} - 3\hat{k}$, $\vec{c} = \vec{a} \times \vec…
Topic: JEE Main 2026 (23 January Morning Shift)
 4
Let $f(x) = \displaystyle \int \frac{(2 - x^2)e^x}{\sqrt{1+x}(1-x)^{3/2}},dx$. If $f(0) = 0$, then $f\left(\frac{1}{2}\…
Topic: JEE Main 2026 (23 January Morning Shift)
 5
Let the domain of the function $f(x) = \log_5\log_7(9x - x^2 - 13)$ be the interval $(m,n)$. Let the hyperbola $\dfrac{…
Topic: JEE Main 2026 (23 January Morning Shift)

Next 10 Questions — JEE Main 2026 (23 January Morning Shift)

Ascending by ID
1
Let $y = y(x)$ be the solution of the differential equation $x^4dy + (4x^3y + 2\sin x)dx = 0,; x > 0,; y\left(\frac{…
Topic: JEE Main 2026 (23 January Morning Shift)
 2
If $\alpha$ and $\beta$ $(\alpha < \beta)$ are the roots of the equation$(-2+\sqrt{3})\left(|\sqrt{x}-3|\right) + (x…
Topic: JEE Main 2026 (23 January Morning Shift)
 3
The sum of all possible values of $n \in \mathbb{N}$, so that the coefficients of $x$, $x^2$ and $x^3$ in the expansion…
Topic: JEE Main 2026 (23 January Morning Shift)
 4
The vertices $B$ and $C$ of a triangle $ABC$ lie on the line $\frac{x}{1} = \frac{1 - y}{-2} = \frac{z - 2}{3}$. The …
Topic: JEE Main 2026 (23 January Morning Shift)
 5
Number of solutions of $\sqrt{3}\cos2\theta + 8\cos\theta + 3\sqrt{3} = 0,; \theta \in [-3\pi, 2\pi]$ is:
Topic: JEE Main 2026 (23 January Morning Shift)
 6
Let $S = {z : 3 \le |2z - 3(1 + i)| \le 7}$ be a set of complex numbers. Then $\min_{z \in S} \left|z + \frac{1}{2}(5 +…
Topic: JEE Main 2026 (23 January Morning Shift)
 7
Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function$f(\theta) = 4\left(\sin^4\l…
Topic: JEE Main 2026 (23 January Morning Shift)
 8
A building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can co…
Topic: JEE Main 2026 (23 January Morning Shift)
 9
Let \( f(x) = \begin{cases} \dfrac{ax^2 + 2ax + 3}{4x^2 + 4x - 3}, & x \ne -\frac{3}{2}, \frac{1}{2} \\ b, & x = -\frac…
Topic: JEE Main 2026 (23 January Morning Shift)
 10
The value of the integral $\displaystyle \int_{\pi/24}^{5\pi/24} \frac{dx}{1 + \sqrt{3}\tan 2x}$ is:
Topic: JEE Main 2026 (23 January Morning Shift)
Ask Your Question or Put Your Review.

loading...