List of top Mathematics Questions asked in MET

The value of \(\frac{C(n,2){(n+1)!}\) is}
The coefficient of \(x\) in the expansion of \((1 + x + x^2 + x^3)^{-3\) is}
The middle term of \(\left(\sqrt{x} - \frac{1}{\sqrt{x}}\right)^6\) is
In the usual notation, \(\frac{^nC_1}{2} + \frac{^nC_2}{3} + \cdots + \frac{^nC_n}{n+1}\) is equal to
The term independent of \( x \) in the expansion of \( \left( 2x^4 - \frac{1}{x^2} \right)^{12} \) is
The middle term in the expansion of \( \left(x - \frac{1}{2y}\right)^{10} \) is
If \( \frac{C(2n,3)}{C(n,2)} = \frac{44}{3} \), then \( n \) is equal to
If \(\log_3 2\), \(\log_3(2x-5)\) and \(\log_3(2x-\tfrac{7}{2})\) are in AP, then the value of \(x\) is
\( \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n+1} \) is equal to
The sum of the series \(0.2 + 0.004 + 0.00006 + 0.0000008 + \dots\) is
\[ \sum_{r=1}^{\infty} \left(3\cdot 2^{-r} - 2\cdot 3^{1-r}\right) \]
The sum of the first n terms of two AP's are in the ratio \((2n+3):(3n-1)\). The ratio of their 5th terms is
The sum of the even multiples of 9 between 300 and 500 is
\[ 1 + \frac{3}{1!} + \frac{5}{2!} + \frac{7}{3!} + \cdots \infty \]
The number of three digit numbers which have at least two identical digits is
The complex number \(z\) which satisfy the equation \(\left|\frac{1+z}{1-z}\right| = 1\) lies on
If \(\omega\) is a cube root of unity, then \((1 + \omega - \omega^2)(1 - \omega + \omega^2)\) is
If \(\alpha\) and \(\beta\) are roots of \(4x^2 + 3x + 7 = 0\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is
The equation \((\cos p - 1)x^2 + \cos p \, x + \sin p = 0\) has real roots. Then \(p\) lies in
If the roots \(x^2 + ax + 9 = 0\) are complex, then
If \(a<b\), then \(a<\frac{a+b}{2}<\ldots\)
If \(a^2 + b^2 + c^2 = 1\), then \(ab + bc + ca\) lies in the interval
\(\frac{1}{\log_2 10} + \frac{1}{\log_4 10} + \frac{1}{\log_8 10} + \frac{1}{\log_{16} 10}\) is equal to 11
\(\log x + \log x^3 + \log x^5 + \dots + \log x^{2n-1}\) is equal to
\(|\frac{x}{2} - 1|<3\) implies that \(x\) lies in the interval