JEE MAIN 2023 ONLINE 29TH JANUARY EVENING SHIFT

Match List I and List II

Choose the correct answer from the options given below :

Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of \(\frac{1}{2}\) day. If both A and B simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days.

The set of all values of \(\mathrm{t\in \mathbb{R}}\), for which the matrix

\(\left[ {\matrix{ {{e^t}} & {{e^{ - t}}(\sin t - 2\cos t)} & {{e^{ - t}}( - 2\sin t - \cos t)} \cr {{e^t}} & {{e^{ - t}}(2\sin t + \cos t)} & {{e^{ - t}}(\sin t - 2\cos t)} \cr {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr } } \right]\) is invertible, is :

The major component of which of the following ore is sulphide based mineral?

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is

(A) directly proportional to the length of the potentiometer wire

(B) directly proportional to the potential gradient of the wire

(C) inversely proportional to the potential gradient of the wire

(D) inversely proportional to the length of the potentiometer wire

Choose the correct option for the above statements :

If the lines \({{x - 1} \over 1} = {{y - 2} \over 2} = {{z + 3} \over 1}\) and \({{x - a} \over 2} = {{y + 2} \over 3} = {{z - 3} \over 1}\) intersect at the point P, then the distance of the point P from the plane \(z = a\) is :