Maths NCERT Exemplar Solutions Class 12th Chapter Twelve

Let C be the circle x² + (y - 1)² = 2, E? and E? be two ellipses whose centres lie at the origin and major axes lie on x-axis and y-axis respectively. Let the straight line x + y = 3 touch the curves C, E?, and E? at P(x?, y?), Q(x?, y?), and R(x?, y?) respectively. Given that P is the mid-point of the line segment QR and PQ = 2√2/3, the value of 9(x?y? + x?y? + x?y?) is equal to ___.

Let $c,k\in R.Iff\left(x\right)=\left(c+1\right)x^2+\left(1-c^2\right)x+2k$ and $f\left(x+y\right)=f\left(x\right)+f\left(y\right)-xy,$ for all x, y $\in$ R, then the value of $\left|2\left(f\left(1\right)+f\left(2\right)+f\left(3\right)+....+f\left(20\right)\right)\right|$ is equal to………….

Let the mean and the variance of 5 observations $x_1,x_2,x_3,x_4,x_{5}be\frac{24}{5}and\frac{194}{25}$ respectively. If the mean and variance of the first 4 observation are $\frac{7}{2}$ and a respectively, then (4a + x₅) is equal to:

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38{\sigma }^2$ is equal to………

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