Let $f(x)$ be a function such that $f(x+y)=f(x)\cdot f(y)$ for all $x,y\in \mathbb{N}$. If $f(1)=3$ and $\displaystyle \sum_{k=1}^{n} f(k)=3279$, then the value of $n$ is:

1

The number of real solutions of the equation $3\left(x^{2}+\dfrac{1}{x^{2}}\right)-2\left(x+\dfrac{1}{x}\right)+5=0$ i…

Topic: JEE Main 2023 (24 January Evening Shift)

2

The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :

Topic: JEE Main 2023 (24 January Evening Shift)

3

Let $\vec{\alpha}=4\hat{i}+3\hat{j}+5\hat{k}$ and $\vec{\beta}=\hat{i}+2\hat{j}-4\hat{k}$. Let $\vec{\beta}_{1}$ be p…

Topic: JEE Main 2023 (24 January Evening Shift)

4

If the system of equations $x + 2y + 3z = 3$ $4x + 3y - 4z = 4$ $8x + 4y - \lambda z = 9 + \mu$ has infinitel…

Topic: JEE Main 2023 (24 January Evening Shift)

5

The set of all values of $a$ for which $\displaystyle \lim_{x\to a}\big([x-5]-[2x+2]\big)=0$, where $[\alpha]$ denotes…

Topic: JEE Main 2023 (24 January Evening Shift)

6

The locus of the mid-points of the chords of the circle $C_{1} : (x-4)^{2}+(y-5)^{2}=4$ which subtend an angle $\theta_…

Topic: JEE Main 2023 (24 January Evening Shift)

7

Let $y=y(x)$ be the solution of the differential equation $(x^{2}-3y^{2})\,dx+3xy\,dy=0$, with $y(1)=1$. Then $6y^{2}…

Topic: JEE Main 2023 (24 January Evening Shift)

8

If $f(x)=\dfrac{2^{2x}}{2^{2x}+2},\ x\in\mathbb{R}$, then $f\!\left(\dfrac{1}{2023}\right)+f\!\left(\dfrac{2}{2023}\ri…

Topic: JEE Main 2023 (24 January Evening Shift)

9

The number of square matrices of order $5$ with entries from the set $\{0,1\}$, such that the sum of all the elements i…

Topic: JEE Main 2023 (24 January Evening Shift)

10

Let the six numbers $a_{1},a_{2},a_{3},a_{4},a_{5},a_{6}$ be in A.P. and $a_{1}+a_{3}=10$. If the mean of these six n…

Topic: JEE Main 2023 (24 January Evening Shift)