10-question readiness test

Magnetic materials used for making permanent magnets (P) and magnets in a
transformer (T) have different properties of the following, which property best matches
for the type of magnet required ?

An LCR series circuit of capacitance 62.5 nF and resistance of 50 Ω, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is _____mH.(Take π2 = 10)

(Numerical Answer Type)

In an examination, there are 10 true-false type questions. Out of 10 , at student can guess the answer of 4 questions correctly with probability   \(\frac{3}{4} \)  and the remaining 6 questions correctly with probability \(\frac{1}{4}.\) If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is  \( \frac{27 k}{4^{10}}\) , then k is equal to

72 km/hour, respectively. A person is walking in train A in the direction opposite to its
motion with a speed of 1.8 km/hour. Speed ( \(in ms^{-1}\) ) of this person as observed from
train B will be close to : (take the distance between the tracks as negligible)

Match LIST-I with LIST-II.

Choose the correct answer from the options given below.

If the tangent to the curve y = x + siny at a point (a, b) is parallel to the line joining
\(\begin{pmatrix}0,\frac{3}{2}\end{pmatrix}\)  and \(\begin{pmatrix}\frac{1}{2}, 2\end{pmatrix}\) ,, then:

Match List I with List II

Choose the correct answer from the options given below:

The mass of gas adsorbed, x, per unit mass of adsorbate, m, was measured at various
pressures, p. A graph between log  \(\frac{X}{m}\) and log p gives a straight line with slope equal to 2
and the intercept equal to 0.4771. The value of  \(\frac{X}{m}\) at a pressure of 4 atm is :
(Given log 3 = 0.4771)

A 25 m long antenna is mounted on an antenna tower. The height of the antenna tower is 75
m. The wavelength (in meter) of the signal transmitted by this antenna would be :

The soft -iron is a suitable material for making an electromagnet. This is because soft iron has