Mathematics Tes...

If the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference, then which one of the following is correct?

Consider the following statements:

1. Both variance and standard deviation are measures of variability in the population.

2. Standard deviation is the square of the variance.

Which of the above statements is/are correct?

For the differential equation find the general solution:

\(\left(e^{x}+e^{-x}\right) d y-\left(e^{x}-e^{-x}\right) d x=0\)

The equation of the ellipse whose vertices are at (± 5, 0) and foci at (± 4, 0) is-

Find the distance between the straight lines 3x + 4y + 15 = 0 and 6x + 8y - 13 = 0

Which one of the following differential equations has a periodic solution? (where μ > 0)

The shortest distance between the lines \(\frac{x+1}{7}=\frac{y+1}{-6}=\frac{z+1}{1}\) and \(\frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}\) is equal to:

In a group of \(100\) higher secondary students, \(50\) students have cleared the NDA exam, \(40\) students have cleared JEE exam and 30 students have cleared both the exams. How many such students are there who have neither qualified NDA nor JEE exam.

If the arcs of equal length of two circles make angles at their center at$60°$ and$75°$ respectively, find the ratio of their radii.