JEE Main 2026 (Online) 5th April Morning Shift

From 18 m height above the ground a ball is dropped from rest . The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is $\_\_\_\_$ m.

(Take $g=10 \mathrm{~m} / \mathrm{s}^2$ and neglect the air resistance)

Consider the following species:

$$\mathrm{BrF}_5, \mathrm{XeF}_5^{-}, \mathrm{BF}_4^{-}, \mathrm{ICl}_4^{-}, \mathrm{XeF}_4, \mathrm{SF}_4, \mathrm{NH}_4^{+}, \mathrm{ClF}_3, \mathrm{XeF}_2, \mathrm{ICl}_2^{-}$$

Number of species having $\mathrm{sp}^3 \mathrm{~d}$ hybridized central atom is $\_\_\_\_$ .

If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3}-x^4\right)^n, x \neq 0$, is zero, then the value of $n$ is $\_\_\_\_$ .

A cube has side length 5 cm and modulus of rigidity $10^5 \mathrm{~N} / \mathrm{m}^2$. The displacement produced by a force of 10 N in the upper face of cube is $\_\_\_\_$ mm.

One mole of phenol is treated with dilute $\mathrm{HNO}_3$ at 298 K to give a mixture of products. The mixture is separated by steam distillation. The steam volatile compound $(\mathrm{X})$ is separated. The increase in percentage of oxygen in $(\mathrm{X})$ with respect to phenol is $\_\_\_\_$ $\times 10^{-1} \%$

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14, \mathrm{O}: 16$ )

Let $y=y(x)$ be the solution of the differential equation $x \sin \left(\frac{y}{x}\right) d y=\left(y \sin \left(\frac{y}{x}\right)-x\right) d x, y(1)=\frac{\pi}{2}$ and let $\alpha=\cos \left(\frac{y\left(e^{12}\right)}{e^{12}}\right)$. Then the number of integral value of $p$, for which the equation $x^2+y^2-2 p x+2 p y+\alpha+2=0$ represents a circle of radius $r \leq 6$, is $\_\_\_\_$ .