Class 12th

A uniform conducting wire of length 12a and resistance ' R ' is wound up as a current
carrying coil in the shape of,
(i) an equilateral triangle of side ' a '.
(ii) a square of side ' a '.
The magnetic dipole moments of the coil in each case respectively are:

Let A₁ = {(x,y):|x|≤y², |x|+2y≤8} and A₂ = {(x,y):|x|+|y|≤k}: If 27 (Area A₁) = 5 (Area A₂), then k is equal to:

A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

The positive value of the determinant of the matrix A, whose Adj(Adj(A)) = [ [14, 28, -14], [-14, 14, 28], [28, -14, 14] ], is .

For the given circuit, the input digital signals are applied at the terminals A, B and C. What would be the output at the terminal y?

Let f : R → R be a function defined by f(x) = 2e²ˣ / (e²ˣ + e). Then f(1/100) + f(2/100) + f(3/100) + . + f(99/100) is equal to.

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of:

sin^-1(sin(2π/3)) + cos^-1(cos(7π/6)) + tan^-1(tan(3π/4)) is equal to:

The value of cos(2π/7) + cos(4π/7) + cos(6π/7) is equal to:

Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(X = 4), then the sum of the mean and the variance of X is: