JEE MAIN 2022 ONLINE 27TH JULY EVENING SHIFT

In \(1^{\text {st }}\) case, Carnot engine operates between temperatures \(300 \mathrm{~K}\) and \(100 \mathrm{~K}\). In \(2^{\text {nd }}\) case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in \(2^{\text {nd }}\) case) will be :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Boron is unable to form \(\mathrm{BF}_{6}^{3-}\).

Reason (R) : Size of B is very small.

In the light of the above statements, choose the correct answer from the options given below :

If the line of intersection of the planes \(a x+b y=3\) and \(a x+b y+c z=0\), a \(>0\) makes an angle \(30^{\circ}\) with the plane \(y-z+2=0\), then the direction cosines of the line are :

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place \(\mathrm{P}\) of \(\operatorname{dip} 30^{\circ}\). The number of oscillations per minute become 10 at another place \(\mathrm{Q}\) of \(60^{\circ}\) dip. The ratio of the total magnetic field at the two places \(\left(B_{Q}: B_{P}\right)\) is :

An element A of group 1 shows similarity to an element B belonging to group 2. If A has maximum hydration enthalpy in group 1 then B is :

Let \(A=\left(\begin{array}{rr}4 & -2 \\ \alpha & \beta\end{array}\right)\).

If \(\mathrm{A}^{2}+\gamma \mathrm{A}+18 \mathrm{I}=\mathrm{O}\), then \(\operatorname{det}(\mathrm{A})\) is equal to _____________.