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$\text{The volume of a sphere of radius 2r is}\left(a\right)\frac{32\pi r^3}{3}\left(b\right)\frac{16\pi r^3}{3}\left(c\right)\frac{8\pi r^3}{3}\left(a\right)\frac{64\pi r^3}{3}$

From the given figure, find out what is AC : AB.

What is the difference in perimeters of the ${17}^{\text{th}}and{16}^{\text{th}}$ triangles in the Spiral of Theodorus?

In the given figure, O is equidistant from the sides AC and AB. Then the value of x - 3 is
___.

Two lines AB and CD intersect at a point O such that $\angle BOC+\angle AOD={280}^{\circ }$, as shown in the figure. Find all the four angles.

A spherical iron ball of radius $10\text{cm}$ is coated with a layer of ice of uniform thickness that melts at a rate of $50{\text{cm}}^3\text{/min}.$ When the thickness of ice is $5\text{cm}$, then the rate at which the thickness $\left(\text{in}\text{cm/min}\right)$ of the ice decreases, is:

if all the chord of the curve $3x^2-y^2-2x+4y=0$ which subtend a right angle at origin passes through fixed point $(a,b)$. Then $|a+b|$ is equal to:

Find the capacity in litres of a conical vessel with

(i) radius 7 cm, slant height 25 cm

(ii) height 12 cm, slant height 13 cm

In the figure, if AB||HF and DE||FG, then the measure of $\angle$ FDE is

A water tank has two faces congruent isosceles trapeziums and the other faces rectangles. Its dimensions are as shown below:

What would be the cost of painting its inside and out at the rate of 75 rupees per square metre?

Line DE intersects PQ at O. If $\angle POE=3Y,\angle QOE=2X$ and X = ${30}^{\circ }$, then (6Y - 3X)=

Sides of a triangle are in the ratio of 2: 7: 6 and the length of its shortest side is 8 cm. Its perimeter is ___.

Factrorise
$4x^2+9y^2+16z^2+12xy-24xyz-16zx$

Factorise:
$(x+2{)}^3-(x-2{)}^3$

Question 4(i)

Evaluate:



$\frac{8^{-1}\times 5^3}{2^{-4}}$

Question 8
Two solid cones A and B are placed in a cylindrical tube. The ratio of their capacities are 2:1. Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder.

Verify the division algorithm for the polynomials
$p\left(x\right)=2x^4-6x^3+2x^2-x+2$ and $g\left(x\right)=x+2$.

An expression that contains only one term is called a __.

If $3x=2y-2$ is written in the standard form $ax+by+c=0$, what will be the possible values of $a,b$ and $c$?

A(2,2) , B(-2,-2),C(-2√3,2√3) . Show that the following points take in order form an equilateral triangle ?

If $x=0.\overline{18}$, which of the following statements are true?

(i) $100x=18.\overline{18}$

(ii) $100x-x=17.\overline{18}$

(iii) $99x=18$

A toy is in the form of a cylinder with hemispherical ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, find the cost of painting the toy at the rate of 70 paise per sq cm.

Which one of the following is not a logical statement?

The value of ${}^{\prime }{a}^{\prime }$ for which the system of equations $(a+1{)}^{3}x+(a+2{)}^{3}y=(a+3{)}^3,(a+1)x+(a+2)y=a+3,x+y=1$ is consistent, is

Factorise:
$x^2+y^2-z^2-2xy$

Below is a list of other expressions. Decide what each expression means, by writing D for difference or S for similarity against each. Try to add more expressions to your list and make use of them in writing your article in B.6.

If x be a non zero number and y is an irrational number prove that xy is irrational.

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