The area bounded by the curve \(y=\log x, y=0\) and \(x=e\), is

A pipe can fill a tank in 2 hours. Because of a leak in the tank, the pipe takes 2 hours 40 minutes to fill the tank. The time the leakage takes to empty the full tank is :

If \(y=t-\frac{1}{t}\) and \(x=t+\frac{1}{t}\), then \(\frac{d y}{d x}\) is equal to

The value of the determinant \(\left|\begin{array}{ccc}66 & 18 & 36 \\ 1 & 3 & 4 \\ 11 & 3 & 6\end{array}\right|\) is:

Which of the following statements are NOT correct about Standard Normal Distribution?
(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.
(B) The Standard Normal variate ( Z ) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.
(C) The Z -score is negative if the data point lies above the mean, and positive if it lies below the mean.
(D) There is a \(95.45 \%\) probability of randomly selecting a score between \(\mu-\sigma\) and \(\mu+\sigma\), when \(\sigma\) is standard deviation and \(\mu\) is mean.
Choose the correct answer from the options given below :

A motorbike costing Rs. 1, 25, 000 has a scrap value of Rs. 25, 000.
If the annual depreciation charge is Rs. 12, 500, then the useful life of the bike is (by using linear method):

Let \(y=\sin \left(\cos x^2\right)\), then the value of \(\frac{d y}{d x}\) at \(x=\frac{\sqrt{\pi}}{2}\) is equal to:

The relationship between \(a\) and \(b\) making \(f(x)\) continuous at \(x=3\), where \(f(x)=\left\{\begin{array}{ll}a x+1, & x \leq 3 \\ b x+3, & x>3\end{array}\right.\) is:

The current changes in a coil from 10 A to 2 A in 0.2 s. The induced emf produced is 50 V. The self inductance of the coil is:

Identify the incorrect statement:

Let \(\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)\). Then \(y\) is :

If \(17^{241} \equiv R(\bmod 13)\), then value of \(R\) is \(:\)

If \(\int \frac{2 x}{x^2+3 x+2} d x=m \log |x+2|+n \log |x+1|+C\), then the values of m and n are: