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Content Writer | Updated On - Jun 14, 2024
JEE Advanced 2024 AAT Question paper will be available for download here. JEE Advanced 2024 for AAT paper was conducted on June 12, 2024. The exam was successfully organized by Indian Institute of Technology, Madras. The question paper comprised a total of 16 questions.
JEE Advanced 2024 AAT Question Paper with Answer Key PDF
JEE Advanced 2024 AAT Question Paper | JEE Advanced 2024 AAT Answer Key |
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Similar Engineering Exam Question Papers
JEE Advanced Questions
1. Let \(S=\left\{a+b\sqrt2:a,b\in Z\right\},T_1=\left\{(-1+\sqrt2)^n:n\in \N\right\},\ \text{and}\ T_2=\left\{(1+\sqrt2)^n:n\in\N\right\}\). Then which of the following statements is (are) TRUE ?
2. Let S be the set of all \((α, β) ∈ \R\times\R\) such that
\(\lim\limits_{x\rightarrow\infin}\frac{\sin(x^2)(\log_ex)^\alpha\sin(\frac{1}{x^2})}{x^{αβ}(\log_e(1+x))^β}=0\)
Then which of the following is (are) correct ?
\(\lim\limits_{x\rightarrow\infin}\frac{\sin(x^2)(\log_ex)^\alpha\sin(\frac{1}{x^2})}{x^{αβ}(\log_e(1+x))^β}=0\)
Then which of the following is (are) correct ?
3. A disc of mass \(M\) and radius \(R\) is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass \(M\) and radius \(R/2\) is fixed to the motor’s thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed \(\omega\). If the angular speed at which the large disc rotates is \(\omega/n\), then the value of \(n\) is _____
![Alternative_Text](https://images.collegedunia.com/public/qa/images/content/2024_05_28/9i_d1d8fb141716869655370.png)
![Alternative_Text](https://images.collegedunia.com/public/qa/images/content/2024_05_28/9i_d1d8fb141716869655370.png)
4. In the following reaction sequence, the major product Q is
\(\text{L-Glucose}\xrightarrow[ii)Cr_2,775K,10-20 \text{atm}]{i)HI, \Delta}P\xrightarrow[UV]{Cl_2(excess)}Q\)
\(\text{L-Glucose}\xrightarrow[ii)Cr_2,775K,10-20 \text{atm}]{i)HI, \Delta}P\xrightarrow[UV]{Cl_2(excess)}Q\)
5. Let the function \(f:[1,\infin)→\R\) be defined by
\(f(t) = \begin{cases} (-1)^{n+1}2, & \text{if } t=2n-1,n\in\N, \\ \frac{(2n+1-t)}{2}f(2n-1)+\frac{(t-(2n-1))}{2}f(2n+1) & \text{if } 2n-1<t<2n+1,n\in\N. \end{cases}\)
Define \(g(x)=\int\limits_{1}^{x}f(t)dt,x\in(1,\infin).\) Let α denote the number of solutions of the equation g(x) = 0 in the interval (1, 8] and \(β=\lim\limits_{x→1+}\frac{g(x)}{x-1}\). Then the value of α + β is equal to _____.
\(f(t) = \begin{cases} (-1)^{n+1}2, & \text{if } t=2n-1,n\in\N, \\ \frac{(2n+1-t)}{2}f(2n-1)+\frac{(t-(2n-1))}{2}f(2n+1) & \text{if } 2n-1<t<2n+1,n\in\N. \end{cases}\)
Define \(g(x)=\int\limits_{1}^{x}f(t)dt,x\in(1,\infin).\) Let α denote the number of solutions of the equation g(x) = 0 in the interval (1, 8] and \(β=\lim\limits_{x→1+}\frac{g(x)}{x-1}\). Then the value of α + β is equal to _____.
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