If $a = i + j + k$,$b = i + j$,$c = i$ and $(a \times b) \times c = \lambda a + \mu b$,then $\lambda + \mu = $

An air column in a tube $32 ~cm$ long,closed at one end,is in resonance with a tuning fork. The air column in another tube,open at both ends,of length $66 ~cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together,they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

$A$ transition metal $M$ forms a volatile chloride with a vapor density of $94.8$. If it contains $74.75\%$ chlorine,what is the formula of the metal chloride?

An atomic power nuclear reactor can deliver $300\, MW$. The energy released due to fission of each nucleus of uranium atom $^{235}U$ is $170\, MeV$. The number of uranium atoms fissioned per hour will be

The value of $\int_{0}^{1} \tan ^{-1}\left(\frac{2 x-1}{1+x-x^{2}}\right) d x$ is

If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$ where $p \neq q$,then the equation whose roots are $3p - 2q$ and $3q - 2p$ is: