Mathematics Tes...

Find the sum of the series whose nth term is n (n + 2).

Probability of Ankit passing in Maths, English and Science is \(\frac{5}{8}, \frac{7}{9}\) and \(\frac{3}{5}\) respectively. Find the probability of him failing in atleast two subjects.

In a frequency distribution, if the mean and median are 10 and 9 respectively, then its mode is approximately:

If \(n=100 !\), then what is the value of the following?

\(\frac{1}{\log _{2} n}+\frac{1}{\log _{3} n}+\frac{1}{\log _{4} n}+\ldots \ldots+\frac{1}{\log _{100} n}\)

\(\text { If } a, b, c \text { are distinct + ve real numbers and } a^2+b^2+c^2=1 \text { then } a b+b c+c a \text { is }\)

The point whose abscissa is equal to its ordinate and which is equidistant from \(\mathrm{A}(-1,0)\) and \(\mathrm{B}(0,5)\) is:

If \(f(x)=\left(\frac{3}{5}\right)^x+\left(\frac{4}{5}\right)^x-1, x \in R\), then the equation \(f(x)=0\) has :

Let \(g(x)=\int_0^x f(t) d t\), where \(f\) is continuous function in \([0,3]\) such that \(\frac{1}{3} \leq \mathrm{f}(\mathrm{t}) \leq 1\) for all \(\mathrm{t} \in[0,1]\) and \(0 \leq \mathrm{f}(\mathrm{t}) \leq \frac{1}{2}\) for all \(\mathrm{t} \in(1,3]\). The largest possible interval in which \(\mathrm{g}(3)\) lies is:

Let \(P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\) and \(Q=P_{A P}{ }^T\). If \(\mathrm{P}^{\mathrm{T}} \mathrm{Q}^{2007} \mathrm{P}=\left[\begin{array}{ll}\mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{d}\end{array}\right]\), then \(2 \mathrm{a}+\mathrm{b}-3 \mathrm{c}-4 \mathrm{~d}\) equal to:

The relation \(\mathrm{R}\) on the set of integer is given by \(\mathrm{R}=\{(\mathrm{a}, \mathrm{b}):\) \(a- b\) is divisible by 7, where \(a, b \in Z\}\), then \(\mathrm{R}\) is a/an: