Let SK = \(\frac{1+2+...+ K}{K}\) and \(\displaystyle\sum_{j=1}^{n}S_j^2=\frac{n}{A}(Bn^2+Cn+D)\), where A,B,C,D∈N and A has least value. Then
A body of mass \( 5 \, \text{kg} \) is moving with a momentum of \( 10 \, \text{kg} \cdot \text{ms}^{-1} \). Now a force of \( 2 \, \text{N} \) acts on the body in the direction of its motion for \( 5 \, \text{s} \). The increase in the kinetic energy of the body is _____ J.
Consider the word INDEPENDENCE. The number of words such that all the vowels are together is?
Let P = \(\left[\begin{matrix} \frac{\sqrt3}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt3}{2} \end{matrix}\right]\) A = \(\left[\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right]\) and Q = PAPT. If PTQ2007P = \(\left[\begin{matrix} a & b \\ c & d \end{matrix}\right]\), then 2a+b-3c-4d equal to
The ratio of the wavelength of spectral lines \( H_\alpha \) and \( H_\beta \) in the Balmer series is \( \frac{x}{20} \). The value of \( x \) is _______.
Let α, β, γ be the three roots of the equation x3+bx+c=0. If βγ =1=-α, then b3+2c3-3α3-6β3-8γ3 is equal to
If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation
For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ2. If combined variance is 13 then find variance of second group?
A body of mass \( (5 \pm 0.5) \, \text{kg} \) is moving with a velocity of \( (20 \pm 0.4) \, \text{m/s} \). Its kinetic energy will be:
An engine operating between the boiling and freezing points of water will have A. efficiency more than 27% B. efficiency less than the efficiency a Carnot engine operating between the same two temperatures. C. efficiency equal to 27% D. efficiency less than 27%
