Class 12th

An electron, a doubly ionized helium ion (He?) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelength λe, λHe? and λp is:

Let a,b,c,d and p be any non-zero distinct real numbers such that (a²+b²+c²)p² - 2(ab+bc+cd)p + (b²+c²+d²)=0. Then:

The negation of the Boolean expression p∨(¬p∧q) is equivalent to:

If {p} denotes the fractional part of the number p, then {3²⁰⁰/8}, is equal to

If Σᵢ₌₁ⁿ(xᵢ-a)=n and Σᵢ₌₁ⁿ(xᵢ-a)²=na, (n,a>1) then the standard deviation of n observations x₁,x₂,.,xₙ is:

If the value of (1 + 2/3 + 6/3² + 10/3³ + .upto ∞) / (log?.?(1/3 + 1/3² + 1/3³ + .upto ∞)) is l, then l² is equal to……….

A particle of charge q and mass m is moving with a velocity -vi (v ≠ 0) towards a large screen placed in the Y-Z plane at a distance d. If there is a magnetic field B = B?k, the minimum value of v for which the particle will not hit the screen is:

The region represented by {z = x+iy∈C: |z|-Re(z)≤1} is also given by the inequality:

For the given input voltage waveform Vin(t), the output voltage waveform Vo(t), across the capacitor is correctly depicted by:

Let S = {n ∈ N | [n,i;0,1][a,b;c,d] = [a,b;c,d] ∀ a,b,c,d ∈ R}, where i = √-1. Then the number of 2-digit numbers in the set S is …….