Question 1 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d23cf59b460d7261f570.jpeg' />
In the above image, a right circular cylinder just encloses a sphere of radius r. Find surface area of the sphere.
Question 2 :
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in $m^2$ .Assume $\pi$ =$\frac{22}{7}$.
Question 3 :
Find the volume of the right circular cone with radius 6 cm, height 7 cm.
Question 4 :
The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.
Question 5 :
A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the graphite .
Question 6 :
State true or false : Cuboid whose length = l, breadth = b and height = h ; Lateral surface area of cuboid = 2 h (l + b)
Question 7 :
State true or false: The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
Question 8 :
Find the curved surface area of a hemisphere of radius 21 cm.
Question 9 :
A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 $m^3$.If the present depth of water is 1.3 m, find the volume of water already used from the tank.
Question 10 :
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
Question 12 :
If $\displaystyle  a^{2}+b^{2}=13 \ and \ ab=6 $ find :<br/>$\displaystyle  a^{2}-b^{2}$<br/>
Question 13 :
The value of (a - b)(a$^2$ + ab + b$^2$) is
Question 14 :
Factorise : $(a - b)^3 + (b - c)^3 + (c - a)^3$
Question 15 :
If $\dfrac{a}{b}$ + $\dfrac{b}{a}$ = 1, then $a^3$ + $b^3$ $=$
Question 16 :
If $P=\dfrac {{x}^{2}-36}{{x}^{2}-49}$ and $Q=\dfrac {x+6}{x+7}$ then the value of $\dfrac {P}{Q}$ is:
Question 19 :
If $(y - 3)$ is a factor of $y^{3} + 2y^{2} - 9y - 18$, then find the other two factors
Question 20 :
If the quotient $=\, 3x^2\, -\, 2x\, +\, 1,$ remainder $= 2x - 5$ and the divisor $= x + 2$, then the dividend is
Question 22 :
One factor of $x^4 + x^2-20$ is $x^2+ 5$. The other factor is
Question 23 :
The value of p for which $(x-2)$ is a factor of polynomial $x^4 - x^3 + 2x^2 - px +4$ is:<br/>
Question 24 :
If $a\, -\displaystyle \frac{1}{a}\, =\, 8$ and $a\, \neq\, 0$; find $a^{2}\, -\, \displaystyle \frac{1}{a^{2}}$
Question 25 :
If $\displaystyle \dfrac{x^{2} + 1}{x} = 3\dfrac{1}{3}$ and $\displaystyle x > 1$; find the value of  $\displaystyle x - \dfrac{1}{x}$
Question 28 :
If $p(x) = x^3-3x^2+6x-4$ and $p\left (\dfrac{\sqrt{3}}{2}\right) = 0$ then by factor theorem the corresponding factor of $p(x)$ is <br/>
Question 29 :
The product of $x^2y$ and $\cfrac{x}{y}$ is equal to the quotient obtained when $x^2$ is divided by ____.<br/>
Question 30 :
If $p(x) = 2x^3-3x^2+4x-5$. Find the remainder when $p(x)$ is divided by , $x-1$
Question 31 :
$p(x)=(x^2-10x-24)$ , when divided by $x+2$ and $x\neq -2$ gives the quotient $Q$. Find $Q$.<br/>
Question 34 :
If ${ \left( x+\cfrac { 1 }{ x } \right) }^{ 2 }=9$, then the value of ${x}^{3}+\cfrac{1}{{x}^{3}}$ is-