Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Let $R$ be a relation defined on $A\times B$ such that $R=\{\,((a_1,b_1),(a_2,b_2)) : a_1 \le b_2 \text{ and } b_1 \le a_2 \,\}$. Then the number of elements in the set $R$ is:
Previous 10 Questions — JEE Main 2023 (11 April Evening Shift)
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If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with ser…
Topic: JEE Main 2023 (11 April Evening Shift)
Let $a,b,c,d$ be positive real numbers such that $a+b+c+d=11$.
If the maximum value of $a^5 b^3 c^2 d$ is $3750\beta$,…
Topic: JEE Main 2023 (11 April Evening Shift)
For $a \in \mathbb{C}$, let
$A = \{\, z \in \mathbb{C} : \Re(a + \bar z) > \Im(\bar a + z) \,\}$
and
$B = \{\, z \in…
Topic: JEE Main 2023 (11 April Evening Shift)
If the system of linear equations
$7x + 11y + \alpha z = 13$
$5x + 4y + 7z = \beta$
$175x + 194y + 57z = 361$
has i…
Topic: JEE Main 2023 (11 April Evening Shift)
The sum of the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{\,n+2}$,
which are in the r…
Topic: JEE Main 2023 (11 April Evening Shift)
Next 10 Questions — JEE Main 2023 (11 April Evening Shift)
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If the $1011^{\text{th}}$ term from the end in the binomial expansion of
\(\left(\dfrac{4x}{5}-\dfrac{5}{2x}\right)^{2…
Topic: JEE Main 2023 (11 April Evening Shift)
If
\[
\begin{vmatrix}
x+1 & x & x \\
x & x+\lambda & x \\
x & x & x+\lambda^2
\end{vmatrix}
= \dfrac{9}{8}\,(103x+81),…
Topic: JEE Main 2023 (11 April Evening Shift)
Let the mean of 6 observations $1, 2, 4, 5, x, y$ be $5$ and their variance be $10$.
Then their mean deviation about t…
Topic: JEE Main 2023 (11 April Evening Shift)
If $f:\mathbb{R}\to\mathbb{R}$ is a continuous function satisfying
\[
\int_{0}^{\pi/2} f(\sin 2x)\,\sin x\,dx \;+\; \al…
Topic: JEE Main 2023 (11 April Evening Shift)
Let $f$ and $g$ be two functions defined by
\[
f(x)=
\begin{cases}
x+1, & x
Topic: JEE Main 2023 (11 April Evening Shift)
Let $y=y(x)$ be the solution of the differential equation
\[
\frac{dy}{dx}+\frac{5}{x(x^5+1)}\,y=\frac{(x^5+1)^2}{x^7},…
Topic: JEE Main 2023 (11 April Evening Shift)
Let the function $f:[0,2]\to\mathbb{R}$ be defined as
\[
f(x)=
\begin{cases}
e^{\min\{x^2,\; x-[x]\}}, & x\in[0,1),\\[4…
Topic: JEE Main 2023 (11 April Evening Shift)
The domain of the function
\[
f(x)=\frac{1}{\sqrt{[x]^2-3[x]-10}}
\]
(where $[x]$ denotes the greatest integer less th…
Topic: JEE Main 2023 (11 April Evening Shift)
