Class 12th

ABCD is a square, having side 12cm, in which ABC and ABD are two quadrant of a circle. If a circle is drawn touching both the quadrants and the square as shown in figure as show in figure given below, then find the area of circle.

An unpolarised light beam strikes a glass surface at Brewster's angle. Then

If P₁ + P₂ + P₃ = 59, where P₁, P₂ and P₃ are prime numbers and P₁ < P₂ < P₃, then how many values can P₃ take?

In a uniform magnetic field of 0.049 T, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $9.8*10^{-6} kg m^2$ . If the magnitude of magnetic moment of the needle is $x*10^{-5}A{m}^2$ , then the value of ' $x$  ' is :

How many pairs of positive integers x, y satisfy $\frac{1}{x}+\frac{6}{y}=\frac{1}{15}$ , where y is a two digit odd integer?

An alcohol solution is formed by mixing two solutions. Solution 1 had a concentration of 20 percent and a volume of 3L while solution 2 had a concentration of 40 percent with a volume of 1L. The resultant solution was named solution 3. Three litres of solution 4 which had an unknown concentration was mixed with solution 3. What must be concentration of solution 4 if that the new resultant solution has a concentration of 50 percent?

Two geometric means a, b are inserted between x and y such that a³ + b³ = n (ab) A, where A is the arithmetic mean of x and y. What is value of n?

A square with maximum possible length of the side is inscribed in an equilateral triangle and a circle of maximum possible radius is inscribed in the square. Find the ratio of the length of equilateral of the equilateral triangle to the radius of circle.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: The potential ( $V$ ) at any axial point, at 2 m distance ( $r$ ) from the centre of the dipole of dipole moment vector $\dot{P}$ of magnitude, $4*10^{-6}Cm$ , is $\pm 9*10^3 V$ .

(Take $\frac{1}{4\pi {ϵ}_0}=9*10^9$ SI units)

Reason R :  $V=\pm \frac{2P}{4\pi {?}_0{r}^2}$ , where $r$  is the distance of any axial point, situated at 2 m from the centre of the dipole.

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

A certain sum of money invested at CI becomes Rs 3380 in 2 years & Rs 3515.20 in 3 years. What is the sum invested & what is rate % per annum?