For the problem \(\max Z=a x+b y, x \geq 0, y \geq 0\), which of the following is NOT a valid constraint to make it a linear programming problem?

The integral \(I=\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x\) is :

If A speaks truth in \(75\%\) cases and B speaks truth in \(80\%\) cases, then the probability that they contradict each other in a statement, is :

\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{1+\cos 2 x}\) is equal to

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

If \(A\) is a square matrix of order 3 and \(\operatorname{det}(A)=1\). If \(B=2 A\) is another matrix, the value of \(\operatorname{det}(B)\) is:

If the given function \(f(x)\), defined as
\(f(x)=\left\{\begin{array}{ll} 5, & x \leq 2 \\ a x+b, & 2 < x<10 \\ 21, & x \geq 10 \end{array}\right.\)
is continuous, then value of \(2 a+b\) is:

Fossils are generally found in:

Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of CX bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom \(X\) is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
Which of the following bromo isomer of butane will react at a faster rate towards SN2 reaction?

If \(A=\left[\begin{array}{cc}-2 & 3 \\ k & 4\end{array}\right]\) is a singular matrix then value of \(k\) is :

In the given reaction \(CH_3CH_2OH + HCl \xrightarrow{Anhy ZnCl_2} X \xrightarrow{KCN(alc)} Y \xrightarrow{Na/Alcohol} Z\) \(Y\) and \(Z\) are:

What sum of money is needed to invest now, so as to get ₹5000 at the beginning of every month forever, if the money is worth \(6\%\) per annum compounded monthly?

Statins are produced by: