Class 12th

IF the foot of the perpendicular from the point A(1, 4, 3) on the plane P : 2x + my + nz = 4, is $\left(-2,\frac{7}{2},\frac{3}{2}\right),$ then the distance of the point A form the plane P, measured parallel to a line with direction ratios 3, 1, 4, is equal to:

Given below are two statements : One is labeled as Assertion A and the other is labeled as Reason R.

Assertion A : n-p-n transistor permits more current that a p-n-p transistor.

Reason R : Electrons have greater mobility as a change carrier.

Choose the correct answer form the options given below

Let a line L pass through the point of intersection of the lines bx + 10y – 8 = 0 and $2x-3y=0,b\in R-\left\{\frac{4}{3}\right\}.$ If the line L also passes through the point (1, 1) and touches the circle 17(x2 + y2) = 16, then the eccentricity of the ellipse $\frac{x^2}{5}+\frac{y^2}{b^2}=1$ is:

For using a multimeter to identify diode from electrical compounds, choose the correct statement out of the following about the diode

Let the solution curve y = y(x) of the differential equation $\left(1+e^{2x}\right)\left(\frac{dy}{dx}+y\right)=1$ pass through the point $\left(0,\frac{\pi }{2}\right).$ Then, $\underset{x\to \infty }{lim}{e}^{x}y\left(x\right)$ is equal to:

The integral ${\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{1}{3+2sinx+cosx}dx}$ is equal to:

In the following circuit, the correct relation between output (Y) and inputs A and B will be

If $\underset{x\to 0}{lim}\frac{\alpha e^x+\beta e^{-x}+\gamma sinx}{xsi{n}^{2}x}=\frac{2}{3},$ where $\alpha ,\beta ,\gamma \in R,$ then which of the following is NOT correct?

 $\frac{1}{\left(20-a\right)\left(40-a\right)}+\frac{1}{\left(40-a\right)\left(60-a\right)}+...+\frac{1}{\left(180-a\right)\left(200-a\right)}=\frac{1}{256},$ then the maximum value of a is:

Let A and B be two 3 * 3 non-zero real matrices such that AB is a zero matrix. Then