JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT

For the given hypothetical reactions, the equilibrium constants are as follows :

$$\begin{aligned} & \mathrm{X} \rightleftharpoons \mathrm{Y} ; \mathrm{K}_1=1.0 \\ & \mathrm{Y} \rightleftharpoons \mathrm{Z} ; \mathrm{K}_2=2.0 \\ & \mathrm{Z} \rightleftharpoons \mathrm{W} ; \mathrm{K}_3=4.0 \end{aligned}$$

The equilibrium constant for the reaction \(\mathrm{X} \rightleftharpoons \mathrm{W}\) is

A clock has \(75 \mathrm{~cm}, 60 \mathrm{~cm}\) long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel \(x\) distance more than the tip of minute hand. The value of \(x\) in meter is nearly (Take \(\pi=3.14\)) :

Let \(A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]\). If the sum of the diagonal elements of \(A^{13}\) is \(3^n\), then \(n\) is equal to ________.

Consider the following reaction

$$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$$

The time taken for A to become \(1 / 4^{\text {th }}\) of its initial concentration is twice the time taken to become \(1 / 2\) of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis.

The overall order of the reaction is ________.

Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyne}}{\mathrm{cm}^2}\) where \(M\) is the mass and \(l\) is the extension of wire used in the experiment. Now error in Young modules \((Y)\) is estimated by taking data from \(M-l\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02 \mathrm{~cm}\) along load axis and extension axis respectively. If the value of $M$ and $l$ are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(Y\) is :

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables \(X\) and \(Y\) respectively denote the number of blue and yellow balls. If \(\bar{X}\) and \(\bar{Y}\) are the means of \(X\) and \(Y\) respectively, then \(7 \bar{X}+4 \bar{Y}\) is equal to ___________.