NTA JEE Main 25th June 2022 Shift 2

For $$z = a^2 x^3 y^{\frac{1}{2}}$$, where '$$a$$' is a constant. If percentage error in measurement of '$$x$$' and '$$y$$' are $$4\%$$ and $$12\%$$, respectively, then the percentage error for '$$z$$' will be ______ %.

A curved in a level road has a radius $$75$$ m. The maximum speed of a car turning this curved road can be $$30$$ m s$$^{-1}$$ without skidding. If radius of curved road is changed to $$48$$ m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ______ m s$$^{-1}$$.

A block of mass $$200$$ g is kept stationary on a smooth inclined plane by applying a minimum horizontal force $$F = \sqrt{x}$$ N as shown in figure. The value of $$x$$ = ______.

Moment of Inertia (M.I.) of four bodies having same mass $$M$$ and radius $$2R$$ are as follows
$$I_1$$ = M.I. of solid sphere about its diameter
$$I_2$$ = M.I. of solid cylinder about its axis
$$I_3$$ = M.I. of solid circular disc about its diameter
$$I_4$$ = M.I. of thin circular ring about its diameter
If $$2(I_2 + I_3) + I_4 = xI_1$$ then the value of $$x$$ will be ______.

Two satellites $$S_1$$ and $$S_2$$ are revolving in circular orbits around a planet with radius $$R_1 = 3200$$ km and $$R_2 = 800$$ km respectively. The ratio of speed of satellite $$S_1$$ to the speed of satellite $$S_2$$ in their respective orbits would be $$\frac{1}{x}$$ where $$x =$$ ______.

When a gas filled in a closed vessel is heated by raising the temperature by $$1°$$C, its pressure increases by $$0.4\%$$. The initial temperature of the gas is ______ K.

$$27$$ identical drops are charged at $$22$$ V each. They combine to form a bigger drop. The potential of the bigger drop will be ______ V.

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______ %.

In a series LCR circuit, the inductance, capacitance and resistance are $$L = 100$$ mH, $$C = 100$$ $$\mu$$F and $$R = 10$$ $$\Omega$$ respectively. They are connected to an AC source of voltage $$220$$ V and frequency of $$50$$ Hz. The approximate value of current in the circuit will be ______ A.

In an experiment of CE configuration of $$n-p-n$$ transistor, the transfer characteristics are observed as given in figure. If the input resistance is $$200\Omega$$ and output resistance is $$60\Omega$$, the voltage gain in this experiment will be ______.