Question 1 :
If $kx^3 + 9x^2+4x -10 $ divided by $x+3$ leaves a remainder $5$, then the value of $k$ will be 

Question 5 :
Use the identity $(x + a) (x + b) = x^2 + (a + b) x + ab$ to find the given product.<br/>Multiply $(x + 3) (x + 7).$

Question 7 :
If&#160;$8a-64b-c=24\sqrt [ 3 ]{ abc } $, where a, b,&#160;$c\neq 0$, then which of the following can be true ?

Question 8 :
When a positive integer $y$ is divided by $47,$ the remainder is $11$. Therefore, when $\displaystyle y^{2}$ is divided by $47$, the remainder will be&#160;

Question 9 :
When a number P is divided by 4 it leaves remainder 3. If twice of the number P is divided by the same divisor 4, then what will be the remainder?

Question 11 :
If A's income be Rs. 80,000 per annum and the difference between the income of B and D be the same as A's income, B's income is

Question 12 :
The graph of the equation $y = a$ is a straight line parallel to _____

Question 13 :
After covering a distance of $30\ km$ with a uniform speed there is some defect in a train engine and therefore its speed is reduced to $\dfrac{4}{5}$ of its original speed. Consequently the train reaches its destination late by $45$ minutes. Had it happened after covering $18$ kilometers more the train would have reached $9$ minutes earlier, find the speed of the train and the distance of journey.

Question 16 :
Twice a number minus three times another is equal to $2$. The sum of these numbers is $11$. The difference of these numbers is

Question 17 :
Consider the equation:<br/>$\displaystyle y+7x=3x-2y+28$<br/>If $y = 2$, what is the value of $x$?

Question 18 :
Find the value of<br>${ \left( \sqrt { { x }^{ 2 }-{ a }^{ 2 } } +x \right) }^{ 5 }-{ \left( \sqrt { { x }^{ 2 }-{ a }^{ 2 } } -x \right) }^{ 5 }$

Question 19 :
In a fraction, if the numerator is decreased by $1$ and the denominator is increased by $1$, then the resulting fraction is $\dfrac14$. Instead if the numerator is increased by $1$ and the denominator is decreased by $1$, then the resulting fraction is $\dfrac23$. Find the absolute difference of the numerator and the denominator of the fraction.

Question 21 :
Manoj, the landscaper buyer intends to buy a new commercial grade lawn mower that costs $\$2,800$. He expects it to last about $8$ years, and then he can sell it for scrap metal with a salvage value of about $\$240$. Calculate it's approximate value after $x$ years $(x&lt;8)$ assuming that it's value depreciates at a constant rate.<br/>

Question 24 :
State true or false:If a, b, c, d are rationals, $b&gt; 0, d&gt; 0,$ and $\sqrt{b}, &#160; &#160;\sqrt{d}$ are surds and $a+\sqrt{b}=c+\sqrt{d}$, then $a=c,\ b=d.$

Question 26 :
Simplify the square root of the polynomial using factorisation method: $\dfrac{a^2}{a^2-b^2}+\dfrac{b^2}{b^2-a^2}$<br/>

Question 30 :
Find the square root of $x^{4} - 2x^{3} + 3x^{2} - 2x + 1$ using the division method

Question 31 :
A computer is programmed to add $3$ to the number $N$, multiply the result by $3$, subtract $3$, and divide&#160;this result by $3$. The computer answer will be