JEE MAIN 2022 ONLINE 27TH JULY MORNING SHIFT

A magnet hung at \(45^{\circ}\) with magnetic meridian makes an angle of \(60^{\circ}\) with the horizontal. The actual value of the angle of dip is -

Given below are two statements.

Statement I : Hydrogen peroxide can act as an oxidizing agent in both acidic and basic conditions.

Statement II : Density of hydrogen peroxide at \(298 \mathrm{~K}\) is lower than that of \(\mathrm{D}_{2} \mathrm{O}\).

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

If the plane \(P\) passes through the intersection of two mutually perpendicular planes \(2 x+k y-5 z=1\) and \(3 k x-k y+z=5, k<3\) and intercepts a unit length on positive \(x\)-axis, then the intercept made by the plane \(P\) on the \(y\)-axis is :

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

Given below are two statements.

Statement I: The chlorides of \(\mathrm{Be}\) and \(\mathrm{Al}\) have Cl-bridged structure. Both are soluble in organic solvents and act as Lewis bases.

Statement II: Hydroxides of \(\mathrm{Be}\) and \(\mathrm{Al}\) dissolve in excess alkali to give beryllate and aluminate ions.

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

\(\text { Let } \vec{a}=2 \hat{i}-\hat{j}+5 \hat{k} \text { and } \vec{b}=\alpha \hat{i}+\beta \hat{j}+2 \hat{k} \text {. If }((\vec{a} \times \vec{b}) \times \hat{i}) \cdot \hat{k}=\frac{23}{2} \text {, then }|\vec{b} \times 2 \hat{j}|\) is equal to :