List of practice Questions

Surface of certain metal is first illuminated with light of wavelength $\lambda_1 =350 \; nm$ and then, by light of wavelength $\lambda_2=54\, \; nm$. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of $2$. The work function of the metal (in eV) is close to : (Energjr of photon = $\frac{1240}{\lambda (in \; nm)} eV$)

Three particles of masses $50\, g, 100\, g$ and $150\, g$ are placed at the vertices of an equilateral triangle of side $1\, m$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be :

Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:

For a uniformly charged ring of radius $R$, the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then value of $h$ is :

Charge is distributed within a sphere of radius $R$ with a volume charge density $p (r) = \frac{A}{r^2} e^{-2r/a}$ where $A$ and $a$ are constants. If $Q$ is the total charge of this charge distribution, the radius $R$ is :

A copper wire is stretched to make it $0.5 \%$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:

A potentiometer wire $AB$ having length $L$ and resistance $12\, r$ is joined to a cell $D$ of emf $\varepsilon$ and internal resistance $r$. A cell $C$ having $emf \, \varepsilon /2$ and internal resistance $3r$ is connected. The length $AJ$ at which the galvanometer as shown in fig. shows no deflection is :

A resistance is shown in the figure. Its value and tolerance are given respectively by :

${5.1g \; NH_4SH }$ is introduced in $3.0\, L$ evacuated flask at ${327^{\circ}C}$. 30% of the solid ${NH4SH}$ decomposed to ${NH_3}$ and ${H2S}$ as gases. The Kp of the reaction at ${327^{\circ}C}$ is ${(R = 0.082 \; L \; atm \; mol^{-1} K^{-1}}}$, Molar mass of ${S = 32 \; g \; mol/^{01}}$, molar mass of ${N = 14g \, mol^{-1}}$)

Let f : R $/to$ R be given by f(x) = (x - 1)(x - 2)(x - 5). Define $F\left(x\right) = \int\limits^{x}_{0} f\left(t\right) dt, x > 0.$ Then which of the following options is/are correct?

A carnot engine takes 300 calories of heat at 500 K and rejects 150 calories of heat to the sink. The temperature of the sink is

If the value of a third order determinant is $16$, then the value of the determinant formed by replacing each of its elements by its cofactor is

The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

Which of the following is not permissible arrangement of electrons in an atom.

If det $\begin{bmatrix}1&1&2\\ 2&4&9\\ t&t^{2}&1+t^{3}\end{bmatrix} = 0 $ , then the values of t are

Which one of the following properties has same value for $H_2$ and $D_2$ ?

Induction furnace uses ______ to produce heat

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. Then the total number of persons in the room is:

If \( x = t \) and \( y = \frac{1}{t} \), then \(\frac{dy}{dx}\) is equal to:

\[\log(\sin 1^\circ) \times \log(\sin 2^\circ) \times \ldots \times \log(\sin 90^\circ) \text{ is}\]

The probability that a leap year will have 53 Fridays or 53 Saturday is

A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 sec, yellow for 5 sec and red for 30 sec. At a randomly chosen time, the probability that the light will not be green is

Which one of the following is a mineral of iron?

E° for the cell, \(Zn|Zn^{2+} (aq) ||Cu^{2+} (aq)|Cu(s)\) is 1.01 V at 25°C. The equilibrium constant for the cell reaction \(Zn + Cu^{2+} (aq) ⇋ Cu+ Zn^{2+} (aq)\) is of the order of