Question 1 :
Find out whether or not the first polynomial is a factor of the second polynomial:$4a-1, 12a^2-7a-2$

Question 2 :
When $2f^3 + 3f^2 - 1$ is divided by $f+2$, find the remainder.<br/>

Question 3 :
What is the radius of a circular field whose area is equal to the sum of the areas of three smaller circular fields of radii $12m, 9m$ and $8m$ respectively?

Question 4 :
One circle touches all sides of $\Box ABCD$. If $AB=5,BC=8,CD=6$; then $AD=$

Question 5 :
A chord of length $16$ cm is drawn in a circle at a distance of $15$ cm from its center. Find the radius of the circle.<br/>

Question 6 :
The construction of $\triangle ABC$ in which $AB = 5\ cm, \angle A = 45^\circ$, is possible when $AC+BC = $

Question 7 :
If the radius and slant height of a cone are $20 \ cm$ and $29 \ cm$ respectively. Find its volume.

Question 8 :
Find the volume of the sphere whose diameter is 30 cm

Question 9 :
Water is flowing at the rate of $3$ km/hr through a circular pipe of $20 cm$ internal diameter into a circular cistern of diameter $10 m$ and depth $2 m$. In how much time will the cistern be filled?

Question 10 :
Observe the table given.<table class="wysiwyg-table"><tbody><tr><td>Club</td><td>English</td><td>Maths</td><td>Science</td></tr><tr><td>Number of students</td><td>$99$</td><td>$121$</td><td>$154$</td></tr></tbody></table>A student is chosen randomly from the group as the co-ordinator of all the clubs. What is the probability that the student is from the science club?

Question 11 :
A box contains coupons labeled 1, 2, 3, ... , n. A coupon is picked at random and the number x is noted. The coupon is put back into box and a new coupon is picked at random. The new number is y. Then the probability that one of the numbers x, y divides the other is :&#160;(in the options below [r] denotes the largest integer less than or equal to r)

Question 12 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d172f59b460d7261f44c.jpg' /> A recent survey found that the ages of workers in a factory is distributed as shown in the figure above. If a person is selected at random, find the probability that the person is having age from 30 to 39 years.

Question 13 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d15df59b460d7261f42d.jpg' /> 80 bulbs are selected at random from a lot and their life time (in hrs) is recorded in the form of a frequency table given above. One bulb is selected at random from the lot. The probability that its life is 1150 hours, is:

Question 16 :
The volume of a right circular cone is 9856 $cm^3$ . If the diameter of the base is 28 cm, find height of the cone.

Question 17 :
State true or false: In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

Question 19 :
State true or falseIn a square $ABCD$, diagonals meet at $O$. $P$ is a point on $BC$ such that $OB= BP$, then<br/>$\angle BOP= 3\, \angle COP$<br/>