Let \(x_i\) and \(y_i\) are two data such that \(y_i=a x_i+b\). If \(\bar{x}, \bar{y}\) are mean and \(\sigma_x, \sigma_y\) are standard deviation of the given data x, and y, respectively. Then, we have \(\vec{y}=a \vec{x}+b\) and \(a_y=|a| \sigma_y\)
On the basis of above information, answer th. following question.
(i) If \(y_t=4 x_i-3\) and x² is 10 , then y=

(ii) If \(y_i=\frac{a x_i+b}{c}\), then \(\sigma_y=\)

(iii) If \(y_i=x_i+10\), then

(iv) If \(x_i=3 y_i+2\), then

(v) If \(y_i=a x_i+b\), then

The marks of students of class XI in Maths test (out of 20) are given below:
\(\begin{array}{c|c|c|c|c|c|c|c} \hline \text { Marks }\left(x_i\right) & 5 & 7 & 9 & 11 & 13 & 15 & 17 \\ \hline \begin{array}{c} \text { Number of } \\ \text { students }\left(f_i\right) \end{array} & 2 & 4 & 6 & 8 & 10 & 12 & 8 \\ \hline \end{array}\)
On the basis of above information, answer the following questions.
(i) Total number of students in the class is

(ii) Cumulative frequency corresponding to mark 11 is

(iii) Median (M) of given data is

(iv) The value of \(\sum_{i=1}^n f_i\left|x_i-M\right|\) is

(v) The value of mean deviation from median of given data is

Salim made a flower-bed in his garden. Surprisingly which is in the shape of a parabola whose equation is y² =8x, the flower-bed is shown as in below figure.

Then, answer the following questions which are based on above figure.
(i) Focus of given parabola is

(ii) Axis of the parabola is

(iii) Equation of the directrix of the parabola is

(iv) Length of the latusrectum of the parabola is

(v) If the focal distance of a point on the parabola is 3, then abscissa of the point is

Mr. Sharma a sincere citizen of "Laxmi Nikunj Society" in Jaipur. He makes a green gardenin his plot which is in the shape of ellipse, i.e.shown in the below figure.

Now, answer the following questions which are based on above garden.
(i) Value of (a + b) is

(ii) Value of eccentricity(e) is

(iii) Which of the following is equation of directrices?

(iv) Length of the latusrectum is

(v) Which of the following is equation of latusrectum?

Mr. Ankt Triwedi a mathematics teacher of class XI write two things about Mohan and Sohan, which are below in figure.
\(\begin{array}{|c|c|c|} \hline & \text { Mohan } & \text { Sohan } \\ \hline \text { Age } & { }^n P & { }^n P_{r+1} \\ \hline \text { Height (in feet) } & { }^n C_r & { }^n C_{r-1} \\ \hline \end{array}\)
Now,answer the following question which are based on above data.
(i)) If the age of mohan and Sohan are equal, then find the value of (n -r).

(ii) Which of the following formula is used to find ⁿP_r ?

(iii) If the height of Mohan and Sohan are equal, then find the value of (n - 2r).

(iv) Find the age of Mohan.

(v) Find the height of Sohan

Mr. Arvind Shukla a mathematics teacher of class XI. He writes a word INDEPENDENCE on the white board. He asks some questions which are based on the arrangements of the letters of the above word.
Then, answer the following questions.
(i) The number of permutations of n objects, where p objects are of the one kind, p₂ are of second kind, ...p_k are of kth kind and the rest, if any are of dfferent kind is

(ii) Find the number of arrangements of the letters of the word starting with P.

(iii) Find the number of arrangements of the letter of word, when all the vowels always occur together.

(iv) Find the number of arrarngements of the letter of word, when all the vowels never occur together.

(v) Find the number of arrangements of the letter of word when wor begins with Iand ends in P