Mathematics Tes...

In the given circle, \(\mathrm{O}\) is the centre, \(\mathrm{AB}=\mathrm{BC}\) and \(\mathrm{OM}=5\) units. The length of \(\mathrm{ON}\) is equal to_____________

If nth term of a series is given by T_n = 3n + 2, where n is a natural number then find the value of\(S_{n}=\sum_{k=1}^{n} T_{k}=?\)

The order and degree of the differential equation \(\left(\frac{d^4 y}{d x^4}\right)^{\frac{1}{2}}=\left[1+\left(\frac{d^2 y}{d x^2}\right)^2\right]^{\frac{1}{3}}\) respectively are:

If \(a, b, c\) are three consecutive positive integers, then \(\log (1+c a)=\)

An equilateral triangle is inscribed in the parabola \(y^2=4 a x\), where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

Evaluate \(\int_{0}^{2} \frac{1}{\sqrt{3+2 x-x^{2}}} d x\):

If \({ }^{n}C_{r}={ }^{n} C_{r-1}\) and \({ }^{n}P_{r}={ }^{n} P_{r+1}\) then the value of r is:

If \(a+b+c=0,|a|=3,|b|=5,|c|=7\), then the angle between \(a\) and \(b\) is:

What is the modulus of the complex number \(i^{2 n+1}(-i)^{2 n-1}\), where \(n \in N\) and \(i=\sqrt{-1}\)?