The sum of the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{\,n+2}$, which are in the ratio $1:3:5$, is equal to:
Next 10 Questions — JEE Main 2023 (11 April Evening Shift)
Ascending by ID
1
2
3
4
5
6
7
8
9
10
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)
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)
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)
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 $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$.
Let $R$ be a relation defined on $A\times B$ such that
$R=\{\,((a_1,b_1…
Topic: JEE Main 2023 (11 April Evening Shift)
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)
