Three logic gates are connected as shown in the figure. If the inputs are \( A = 0 \), \( B = 1 \), and \( C = 1 \), then the values of \( y_1 \), \( y_2 \), and \( y_3 \) are respectively:
If \( m \) and \( M \) are respectively the absolute minimum and absolute maximum values of a function \( f(x) = 2x^3 + 9x^2 + 12x + 1 \) defined on \([-3,0]\), then \( m + M \) is:
If the function
\[ f(x) = \begin{cases} \frac{(e^x - 1) \sin kx}{4 \tan x}, & x \neq 0 \\ P, & x = 0 \end{cases} \]
is differentiable at \( x = 0 \), then:
Evaluate the integral: \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{dx}{\sec^2 x + (\tan^{2022} x - 1)(\sec^2 x - 1)} \]
The velocities of air above and below the surfaces of a flying aeroplane wing are 50 m/s and 40 m/s respectively. If the area of the wing is 10 m² and the mass of the aeroplane is 500 kg, then as time passes by (density of air = 1.3 kg/m³), the aeroplane will:
A liquid cools from a temperature of 368 K to 358 K in 22 minutes. In the same room, the same liquid takes 12.5 minutes to cool from 358 K to 353 K. The room temperature is:
At 27°C, 100 mL of 0.5 M HCl is mixed with 100 mL of 0.4 M NaOH solution. To this resultant solution, 800 mL of distilled water is added. What is the pH of the final solution?
