List of top Questions asked in MET- 2021

The sum of the even multiples of 9 between 300 and 500 is

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

If \(\alpha\) and \(\beta\) are roots of \(4x^2 + 3x + 7 = 0\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is

The number of three digit numbers which have at least two identical digits is

\[ 1 + \frac{3}{1!} + \frac{5}{2!} + \frac{7}{3!} + \cdots \infty \]

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

The equation \((\cos p - 1)x^2 + \cos p \, x + \sin p = 0\) has real roots. Then \(p\) lies in

\(\log x + \log x^3 + \log x^5 + \dots + \log x^{2n-1}\) is equal to

If the roots \(x^2 + ax + 9 = 0\) are complex, then

If \(a^2 + b^2 + c^2 = 1\), then \(ab + bc + ca\) lies in the interval

If \(a<b\), then \(a<\frac{a+b}{2}<\ldots\)

y is the sum of three numbers, one of which is a constant, the 2nd varies as x and the 3rd varies inversely as x. The values of y at x = 1, -1 and 3 are respectively 6, -4 and 8. Then, y is equal to

\(\frac{1}{\log_2 10} + \frac{1}{\log_4 10} + \frac{1}{\log_8 10} + \frac{1}{\log_{16} 10}\) is equal to 11

\[ 9^{-z} = \frac{1}{27^x \cdot 27^y} = (81)^{-y} \]

\[ \frac{5^{\frac{3}{2}} - 2^{\frac{3}{2}}}{\sqrt{5}-\sqrt{2}} + \frac{5^{\frac{3}{2}} + 2^{\frac{3}{2}}}{\sqrt{5}+\sqrt{2}} \]

\(|\frac{x}{2} - 1|<3\) implies that \(x\) lies in the interval

The reagent \(NH_4Cl\) and aqueous \(NH_3\) will precipitate:

If \(x = \frac{2\sqrt{2}-\sqrt{7}}{2\sqrt{2}+\sqrt{7}}\), then \(x + x^{-1}\) is equal to

If \(x^{4/3} + x^{-1/3} = 1\), \(x^5 + 3x^2 - x\) is equal to

A sample of 4.12 mg of unknown alcohol is added to \(CH_3MgBr\). 1.56 mL of methane at STP was liberated. The alcohol is :

Acrilan is a hard, horny and a high melting material. Its structure is :

An ester (A) with molecular formula \(C_9H_{10}O_2\) was treated with excess \(CH_3MgBr\) and the compound so formed was treated with conc. \(H_2SO_4\) to form olefin (B). Ozonolysis of B gave ketone with formula \(C_8H_8O\) which shows positive iodoform test. The structure of A is :