Q JEE_Advanced 2019

Let $\mathrm{x} \in \mathbb{R}$ and let $...

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Q JEE Advanced 2019

Answer the following by appropriately matching the lists based on the information given in the paragraph Let the circles $...

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Q JEE Advanced 2019

Answer the following by appropriately matching the lists based on the information given in the paragraph Let $...

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Q JEE Advanced 2019

Let $\vec{a}=2 \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+2 \hat{j}+\hat{k}$ be two vectors. Consider a vector $\vec{c}=\alpha \vec{a}+\beta \vec{b}, \alpha, \beta \in \mathbb{R}$. If...

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Q JEE_Advanced 2019

Suppose $\operatorname{det}\left[\begin{array}{cc}\sum_{k=0}^n k & \sum_{k=0}^n{ }^n C_k k^2 \\ \sum_{k=0}^n{ }^n C_k k & \sum_{k=0}^n{ }^n C_k 3^k\end{array}\right]=0$, holds for...

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Q JEE_Advanced 2019

Five person A,B,C,D and E are seated in a ciruclar arrangement. If each of them is given a hat of...

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Q JEE Advanced 2019

Let $|X|$ denote the number of elements in set $X$. Let $S=\{1,2,3,4,5,6\}$ be a sample space, where each element is...

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Q JEE_Advanced 2019

The value of $\sec ^{-1}\left(\frac{1}{4} \sum_{k=0}^{10} \sec \left(\frac{7 \pi}{12}+\frac{k \pi}{2}\right) \sec \left(\frac{7 \pi}{12}+\frac{(k+1) \pi}{2}\right)\right)$ in the interval $\left[-\frac{\pi}{4}, \frac{3 \pi}{4}\right]$...

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Q JEE Advance 2019

For non-negative integers n, let $f(n)=\frac{\sum_{k=0}^n \sin \left(\frac{k+1}{n+2} \pi\right) \sin \left(\frac{k+2}{n+2} \pi\right)}{\sum_{k=0}^n \sin ^2\left(\frac{k+1}{n+2} \pi\right)}$ Assuming $\cos ^{-1} \mathrm{x}$ takes...

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Q JEE Advance 2019

Let $\mathrm{F}: \mathbb{R} \rightarrow \mathbb{R}$ be a function. We say that f has PROPERTY 1 if $...

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Q JEE Advance 2019

Three lines: $$ \begin{aligned} & L_1: \vec{r}=\lambda \hat{i}, \lambda \in \mathbb{R} \\ & L_2: \vec{r}=\vec{k}+\mu \hat{j}, \mu \in \mathbb{R} \text...

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Q JEE Advance 2019

For $a \in \mathbb{R},|a|>1$, let $\lim _{n \rightarrow \infty}\left(\frac{1+\sqrt[3]{2}+\ldots . .+\sqrt[3]{n}}{n^{7 / 3}\left(\frac{1}{(a n+1)^2}+\frac{1}{(a n+2)^2}+\ldots \ldots+\frac{1}{(a n+n)^2}\right)}\right)=54$. Then the possible...

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Q JEE Advance 2019

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x)=(x-1)(x-2)(x-5)$. Define $F(x)=\int_0^x f(t) d t, x>0$. Then which of the following...

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