Two fair dice, each with faces | Maths | JEE ADVANCED 2020

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JEE Advanced 2020

Paper-2 2020

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Two fair dice, each with faces numbered 1,2,3,4,5 and 6, are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns out to be a perfect square before it turns out to be a prime number. If 𝑝 is the probability that this perfect square is an odd number, then the value of 14𝑝 is _____

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QJEE Advanced 20202020

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Let 𝑓:ℝ→ℝ be a differentiable function such that its derivative 𝑓′ is continuous and ƒ(𝜋) = −6.
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QJEE Advanced 20202020

Let the function $f:[0,1] \rightarrow \mathbb{R}$ be defined by $\mathrm{f}(\mathrm{x})=\frac{4^{\mathrm{x}}}{4^{\mathrm{x}}+2}$ Then the value of $\mathrm{f}\left(\frac{1}{40}\right)+\mathrm{f}\left(\frac{2}{40}\right)+\mathrm{f}\left(\frac{3}{40}\right)+\ldots \ldots \ldots+\mathrm{f}\left(\frac{39}{40}\right)-\mathrm{f}\left(\frac{1}{2}\right)$ is

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QJEE Advanced 20202020

Two fair dice, each with faces numbered 1,2,3,4,5 and 6, are rolled together and the sum of the numbers on...

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For non-negative integers s and r, let
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Let a and b be positive real numbers. Suppose $\overrightarrow{\mathrm{PQ}}=a \hat{\mathrm{i}}+b \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{PS}}=a \hat{\mathrm{i}}-b \hat{\mathrm{j}}$ are adjacent sides of...

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Let $\alpha, \beta, \gamma, \delta$ be real numbers such that $\alpha^2+\beta^2+\gamma^2 \neq 0$ and $\alpha+\gamma=1$. Suppose the point $(3,2,-1)$ is...

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QJEE Advanced 20202020

Let 𝒇:ℝ→ℝ and 𝒈:ℝ→ℝ be functions satisfying 𝑓(𝑥+𝑦)=𝑓(𝑥)+𝑓(𝑦)+𝑓(𝑥)𝑓(𝑦) and 𝑓(𝑥)=𝑥𝑔(𝑥) for all 𝑥,𝑦∈ℝ. If $\lim _{x \rightarrow 0} g(x)=1$, then...

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QJEE Advanced 20202020

Let b be a nonzero real number. Suppose $f: \mathbb{R} \rightarrow \mathbb{R}$ is a differentiable function such that $(0)=1$. If...

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The value of the limit
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QJEE Advanced 20202020

Let the functions : (−1,1)→ℝ and 𝑔 : (−1,1)→(−1,1) be defined by ƒ(𝑥) = |2𝑥−1|+|2𝑥+1| and 𝑔(𝑥) = 𝑥−[𝑥], where...

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QJEE Advanced 20202020

The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a...

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QJEE Advanced 20202020

The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least...

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For a complex number z, let $\operatorname{Re}(z)$ denote the real part of $z$. Let $S$ be the set of all...

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QJEE Advanced 20202020

Let e denote the base of the natural logarithm. The value of the real number a for which the right...

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