Class 12th

AB µ r² long straight wire with a circular cross-section having radius R, is carrying a steady current I: The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r(r < R) from its centre will be:

Match List – I with List – II.

(A) AC generator(I) Detects the presence of current in the circuit

(B) Galvanometer(II) Converts mechanical energy into electrical energy

(C) Transformer (III) Works on the principle of resonance in AC circuit

(D) Metal detector(IV) Changes an alternating voltage for smaller or greater value

Choose the correct answer from the options given below:

In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance $\mathcal{l}and2\mathcal{l}$ $$ from the charge distribution. If $\sigma$ $$ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are:

The area of the region bounded by y - x = 2 and x² = y is equal to :

Let f : [0,∞) → be a function defined by f(x) = { max{sint: 0≤ t ≤x}, 0≤x≤π, 2 + cos x, x > π
Then which of the following is true?

Let y = y(x) be the solution of the differential equation (x - x³) dy = (y + yx² – 3x? )dx, x > 2. If y(3) = 3 then y(4) is equal to

Let a,b and c be three vectors such that a = b*(bxc). If magnitudes of the vectors a,b and c are √2, 1 and 2 respectively and the angle between b and c is θ(0<

Let a = i - αj + βk, b = 3i + βj - αk and c = -αi - 2j + k, where α and β are integers. If a . b = -1and b . c = 10, then (a * b) . c is equal to ……… equal to ………

Let y = y(x) be the solution of the differential equation dy = e^(αx+y)dx; α ∈ N . If y(logₑ2) = -logₑ2 and y(0) = -logₑα, then the value of α is equal to………

If A = [1 1 1; 0 1 1; 0 0 1] and M = A + A² + A³ + . + A²?, then the sum of all the elements of the matrix M is equal to………