According to Einstein's photoelectric equation, the plot of the Kinetic Energy of the emitted photoelectrons from a metal versus the frequency of the incident radiation gives a straight line whose slope :

Charge on a conducting metal sphere is present :

Two long straight parallel wires are carrying charges \( \lambda_1 \) and \( \lambda_2 \) per unit length, respectively. The separation between their axes is d. The magnitude of the force exerted on unit length of one wire due to the charge on the other wire is

An electric motor operating on a 50 V dc supply draws a current of 12 A. If the efficiency of the motor is 30%, the estimated resistance of the motor would be :

A charge Q is divided into two parts, q and (Q-q). The repulsion between them is maximum when Q : q is

Arrange the following materials in increasing order of their resistivities
(A) Tungsten
(B) Aluminium
(C) Gold
(D) Copper
Choose the correct answer from the options given below:

An ammeter of resistance \( 0.54 \text{ } \Omega \) reads current unto 1 A. The value of the shunt required to increase the range to 10 A is

The solution of the differential equation \(\frac{d y}{d x}=\frac{6}{x^2} ; y(1)=3\) is :

Which of the following statements are true?
(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector \(3 \hat{i}+2 \hat{j}-8 \hat{k}\) is \(\vec{r}=(5 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-8 \hat{k})\)
(B) Vector form of the equation of line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is \(\vec{r}=(5 \hat{i}-4 \hat{j}+6 \hat{k})+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})\)
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are \(-2 / 3,-1 / 3,-2 / 3\).
Choose the correct answer from the options given below:

The solution of \(\frac{7 x+12}{x-9}<4, x \neq 9\) is:

The corner points of the bounded feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0) then

When a positive charge (+ q) is brought near one face of a metal cube, the

A boat covers 32 km upstream and 36 km downstream in 7 hours.
Also, it covers 40 km upstream and 48 km downstream in 9 hours.
The speed of the boat in still water is :