A convex lens of focal length \(0.15 \mathrm{~m}\) is made of a material of refractive index \(\frac{3}{2}\). When it is placed in a liquid, its focal length is increased by \(0.225 \mathrm{~m}\). The refractive index of the liquid is

A wire of length $1 \mathrm{m}$ and radius $2 \mathrm{mm}$ is vertically clamped. The lower end is twisted through an angle of $45°$. The angle of shear is _____

A calorimeter contains \(0.5 \mathrm{~kg}\) of water at \(30^{\circ} \mathrm{C}\). When \(0.3 \mathrm{~kg}\) of water at \(60^{\circ} \mathrm{C}\) is added to it, the resulting temperature is found to be \(40^{\circ} \mathrm{C}\). The water equivalent of the calorimeter is

\(1 \mathrm{amu}\) is equal to

Two slits separated by \(0.5 \mathrm{~mm}\) are illuminated by light of wavelength \(500 \mathrm{~nm}\). The screen is at a distance of \(120 \mathrm{~cm}\) from the slits. The phase difference between the interfering waves at a point \(3 \mathrm{~mm}\) on the screen from the central bright fringe is ........... .

The sum of two point positive charges separated by a distance of 1.5 m in air is \(25 \mu \mathrm{C}\). If the electrostatic force between the two charges is 0.6 N, then the difference between the two charges is

A solenoid has a core of a material with relative permeability 400 . The windings of the solenoid are insulated from the core and carry a current of \(4 \mathrm{~A}\). If the number of turns is 500 per metre, then the magnetizing field is

A projectile is thrown in the upward direction making an angle of \(60^{\circ}\) with the horizontal with a velocity of \(140 \mathrm{~ms}^{-1}\). Then the time after which its velocity makes an angle \(45^{\circ}\) with the horizontal is (Acceleration due to gravity, \(g=10 \mathrm{~ms}^{-2}\) )

Which of the following reactions are not feasible?
I. \(\mathrm{CH}_3 \mathrm{CH}=\mathrm{CH}_2 \frac{\mathrm{HCl}}{\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}\right)_2 \mathrm{O}_2} \longrightarrow \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl}\)
II. \(\mathrm{C}_6 \mathrm{H}_6+\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl} \stackrel{\mathrm{AlCl}_3}{\longrightarrow} \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}\left(\mathrm{CH}_3\right)_2\)
III. \(\mathrm{CH}_3 \mathrm{CHClCH}_2 \mathrm{Cl} \underset{\Delta}{\stackrel{\mathrm{KOH}}{\longrightarrow}} \mathrm{CH}_3 \mathrm{C} \equiv \stackrel{+}{\mathrm{CH}}\)
IV. \(\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHCH}_3 \stackrel{\mathrm{KMnO}_4 / \mathrm{H}^{+}}{\longrightarrow} \mathrm{CH}_3 \mathrm{COOH}\)

Three students \(\mathrm{X}, \mathrm{Y}\) and \(\mathrm{Z}\) appear for an examination. The probability of \(X\) passing the examination is \(\frac{1}{5}\), the probability of \(\mathrm{Y}\) passing the examination is \(\frac{1}{4}\) and the probability of \(\mathrm{Z}\) failing the examination is \(\frac{2}{3}\). The probability that atleast two of them pass the exam is

The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee contains at most 5 men and at least 5 women is

The sum of the values of \(x\) so that the matrix \(\left(\begin{array}{lll}2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2\end{array}\right)-x\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right)\) is singular, is

The polymer obtained with methylene bridges by condensation polymerisation