If \(I=\int \frac{x^4+x^2+1}{x^2-x+1} d x=a x+\beta x^2+\gamma x^3+\delta\), where \(\delta\) is the constant of integration, then \((a+2 \beta+3 \gamma)\) equals

The probability that a plant \(A\) survives is \(\frac{3}{4}\) and the probability that another plant \(B\) survives is \(\frac{1}{3}\).
The probability that only one of them survives is :

Which of the following is not correct about the Central Limit Theorem?

Determinant is unaltered if :

During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20\%\) respectively. He has option to choose any of the two options with equal probabilities. If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20 \%\) respectively. He has option to choose any of the two options with equal probabilities.
If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:

If \(A=\left[\begin{array}{ccc}2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0\end{array}\right]\), then the value of \(\operatorname{det}(\operatorname{adj}(2 A))\) is :

During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20\%\) respectively. He has option to choose any of the two options with equal probabilities.
If Amit goes through one of the two options selected at random and suffers a heart attack, then the probability that he had selected yoga is:

If a discrete random variable \(X\) has the following probability distribution: \(\begin{array}{lll}X & \frac{2}{3}^1 & \frac{4}{3} \\& & \\P(X) & & c \\& & c^2 \\& c^2\end{array}\) then \(c\) is:

If \(A^T=\left[\begin{array}{cc}-2 & 3 \\ 1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{cc}-1 & 0 \\ 1 & 2\end{array}\right]\), then the matrix \((A+2 B)^T\) is

Which disease is not the sexually transmitted infection?

A first order reaction is found to have a rate constant, k = 5.5 × 10^-14 s^-1. The half life of the reaction will be :

If 525 = (10 + K) (mod 7) where \(K \in N\), then the least value of K is:

Answer the question on basis of passage given below :
In zwitter ionic form, amino acids show amphoteric behaviour as they react both with acids and bases.
Except glycine, all other naturally occurring \(\alpha\) - amino acids are optically active, since the \(\alpha\) -carbon atom is asymmetric. These exist both in 'D' and 'L' forms. Most naturally occurring amino acids have L-configuration. L-Aminoacids are represented by writing the \(-NH_2\) group on left hand side.
Which of the following amino acid is essential?