MCA Entrance Previous Year Question Bank

The value of the sum $\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+\cdots +\frac{1}{25\sqrt{24}+24\sqrt{25}}$ is:

If $H$ is the harmonic mean between $P$ and $Q$, then $\frac{H}{P}+\frac{H}{Q}$ is:

The sum of first $n$ terms of an arithmetic series is $216$. The value of the first term is $n$ and the value of the $n^{\text{th}}$ term is $2n$. The common difference $d$ is:

The harmonic mean of two number is 4, Their arithmetic mean A and the geometric mean G satisfythe relation $2A+G^{<}/span></strong><strong><spanstyle="font-size:14pt;">2</span></strong><strong><spanstyle="font-size:14pt;">=27$, then the two numbers are

The coefficient of $x^n$ in the expansion of (1 - 2x + 3x^2 - 4x^3 + ... to &infin; - n) is

An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms.What is the common difference?