JEE MAIN 2023 Previous Year Questions (PYQs) – Page 14 of 34
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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:
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The number of triplets , where are distinct non negative integers satisfying , is :
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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:
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Solution
An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?
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The number of real solutions of the equation
$3\left(x^{2}+\dfrac{1}{x^{2}}\right)-2\left(x+\dfrac{1}{x}\right)+5=0$ is:
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The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0$ is :
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The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :
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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:
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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 parallel to $\vec{\alpha}$ and $\vec{\beta}_{2}$ be perpendicular to $\vec{\alpha}$.
If $\vec{\beta}=\vec{\beta}_{1}+\vec{\beta}_{2}$, then the value of $5\,\vec{\beta}_{2}\cdot(\hat{i}+\hat{j}+\hat{k})$ is:
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If the system of linear equations
$7x + 11y + \alpha z = 13$
$5x + 4y + 7z = \beta$
$175x + 194y + 57z = 361$
has infinitely many solutions, then $\alpha + \beta + 2$ is equal to:
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Solution
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