Question 1 :
The remainder obtained when the polynomial $x^{4}-3 x^3+9x^{2}-27x+81$ is divided by $(x-3)$ is:<br/>

Question 2 :
Find the value of 'a' in&#160;$4x^{2}\, +\, ax\, +\, 9\, =\, (2x\, -\, 3)^{2}$

Question 4 :
If n is an integer, what is the remainder when $5x^{2n + 1}- 10x^{2n} + 3x^{2n-1} + 5$ is divided by x + 1?

Question 5 :
Find the value of $k$ for which the following system of linear equation becomes infinitely many solution or represent the coincident lines.<br>$6x+3y=k-3$; $2kx+6y=k$

Question 7 :
The sum of the ages of $X$ and $Y$ $12$ years ago was $48$ years and the sum of the ages of $X$ and $Y$ $12$ years hence will be _____ years.

Question 8 :
In a class the ratio of the number of boys to that of the girls is $7: 3$. Each boy is given only a $50$ paise coin and each girl is given a $75$ paise coin (assuming $75$ paise coins are available) &#160;The difference in the amount present with the boys and the girls is Rs. $3.75$. How many coins should the boys and girls exchange so that the amount with the boys becomes twice the amount with the girls?

Question 14 :
State whether the following statement is True or False<br>The conjugate of $\sqrt {3} + \sqrt {2}$ is $\sqrt {2} - \sqrt {3}$

Question 16 :
The average marks, in a class of $30$ students, are found to be $45$. On checking two mistakes were found. After correction, if one student got $45$ &#160;marks more and another students got &#160;$15$ marks less, then the correct average marks are

Question 17 :
The value of $\sum_{n= 0}^{88}\dfrac{1}{cos\,&#160; nk.cos \, (n +1)\,&#160; k}$, where k is $1^o$ is equal to<br/>

Question 18 :
If variable takes values 0,1,2,......, n with frequencies $q^n$. $\dfrac{n}{1}$ $q^{n-1}$ p , $\dfrac{n(n-1)}{1.2}$ $q^n-2$ $p^2$..........,$p^n$ where p+q = 1, then the mean is&#160;

Question 19 :
The captain of a cricket team of 11 members is 26 years old and the wicketkeeper is 3 years older than the captain. If the ages of these two are excluded, the average age of the remaining players is one year less than the whole team. What is the average age of the team?

Question 20 :
If the ratio of mean and median of a certain data is $5:7$, then find the ratio of its mode and mean.