Class 12th

If the electric potential at any point (x, y, z)m in space is given by V = 3x² volt. The electric field at the point (1, 0, 3)m will be:

Given below two statements : One is labeled as Assertion (A) and other is labeled as Reason (R).

Assertion (A) : Non-polar materials do not have any permanent dipole moment.

Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negativne charge distribution .

In the light of above statements, choose the most appropriate answer from the options given below:

Two capacitors having C₁ and C₂ respectively are connected as shown in figure. Initially, capacitor C₁ is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C₁ is not connected to uncharged capacitor C₂ by closing the switch S. The amount of charge on the capacitor C₂, after equilibrium, is:

Given below are two statements:

Statement I : The electric force changes the speed of the charged particle and hence charges its kinetic energy; whereas the magnetic force does not change like kinetic energy of the charged particle.

Statement II : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerated the moving charged particle along the direction of magnetic field.

In the light of the above statements, chose the most appropriate answer from the option given below:

Let A, B, C be three points whose position vectors respectively are

$\overrightarrow{a}=\widehat{i}+4\widehat{j}+3\widehat{k}$  

$\overrightarrow{b}=2\widehat{i}+\alpha \widehat{j}+4\widehat{k},\alpha \in R$

$\overrightarrow{c}=3\widehat{i}-2\widehat{j}+5\widehat{k}$

 If a is the smallest positive integer for which $\overrightarrow{a},\overleftarrow{b},\overrightarrow{c}$ are noncollinear, then the length of the median, in $\Delta ABC,$  through A is:

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y +2z = 16. Let T be a plane passing through the point Q and contains the line $\overrightarrow{r}=-\widehat{k}+\lambda \left(\widehat{i}+\widehat{j}+2\widehat{k}\right),\lambda \in R.$  Then, which of the following points lies on T?

The TV transmission tower at a particular station has a height of 125 m. For doubling the coverage of its range, the height of the tower should be increased by

The distance of the origin from the centroid of the triangle whose two sides have the equations x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is $\left(\frac{7}{3},\frac{7}{3}\right)is:$

Two long current carrying conductors are placed parallel to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 300 $\mu T$ . the equal current flowing in the two conductors is:

Let $\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}$ lie on the plane px – qy + z = 5, for some $p,q\in R.$  The shortest distance of the plane form the origin is: