In a pair of adjacent coils, if current in one coil changes from 0 A to 10 A in 0.25 s , causing a magnetic flux change of 15 Wb in the adjacent coil, the mutual inductance of the coils is :

A person started keeping aside 10,000 each year for his child's college education in a sinking fund. The amount he will receive after 6 years, if the rate of interest is \(10 \%\) p.a., is: [Use \((1.1)^{\wedge} 6=1.771\) ]

Value of \(\int\left(\frac{1}{\log x}-\frac{1}{(\log x)^2}\right) d x\) is

Probability distribution of random variable \(X\) is

X	-2	-1	0	1	2
P(X)	2/11	1/11	4/11	3/11	1/11

Then the value of \(E(X)\) is

The area bounded by \(x = 1, x = 2, xy = 1\) and x-axis is :

If \(x=2 a t, y=a t^2\), where ' a ' is a constant, then \(\frac{d^2 y}{d x^2}\) at \(x=2\) is :

The maximum value of \(\left(\frac{1}{x}\right)^x\) for \(x>0\) is

Arrange the following steps \(( A , B , C\) and D \()\) in proper sequence to determine the index correction in the given arrangement.

(A) The difference between the two gives the correction to be applied to the observed distance.
(B) The positions of the uprights are read on the scale. Their difference gives the observed distance between tip of the pin and the pole of the mirror.
(C) A thin straight index needle OP is placed so that its one end O touches the tip of the pin and the other end P touches the pole of the mirror.
(D) Length of the needle OP is measured by placing it on the scale which is the actual distance between the points in question.
Choose the correct answer from the options given below:

\(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x\) is equal to

The pattern and behavior of the data in any time series are based on which of the following components:
(A) Secular trend component
(B) Seasonal component
(C) Cyclical component
(D) Irregular component
Choose the correct answer from the options given below :

If order of matrix \(A\) is \(m \times p\) and order of matrix \(B\) is \(p \times n\), then what is the order of matrix \(A B\) ?

What is the packing efficiency of simple cubic lattice?

Consider the curves, \(x^2+y^2=1\) and \((x-1)^2+y^2=1\).
Points of intersection of two curves are :