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Factorise $81-x^4$ is ____

Suppose $A_1,A_2,.....................A_{3}0$ are thirty sets each having 5 elements and $B_1,B_2,................B_n$ are n sets each with 3 elements, let $\bigcup _{i=1}^{30}$$A_i$=$\bigcup _{j=1}^n$$B_j=S$ and each element of S belongs to exactly 10 of $A_i$'S and exactly 9 of the $B_j$'S. Then $n$ is equal to

In figure, O is the centre of the circle of radius 10 cm. OQ WZ, OP XY, XY || WZ, WZ = 16 cm and XY = 12 cm. then length of PQ is:

In the adjoining figure, ABCD and PQRC are rectangles, where Q is the midpoint of AC. Then DP is equal to

The ordinate of all points on the x-axis is ___.

If cosec A = √10, then tan A is

The numbers of sides of two regular sides of two regular polygons are in the ratio 2: 1 and their interior angles are in the ratio 4: 3, find the sum of the number of sides of the polygons.

Find the values of x and y in the given pair of equations.

$\frac{2}{x}$ + $\frac{3}{y}$ = 13

$\frac{5}{x}$ - $\frac{4}{y}$ = -2

Question 2
Find the area of a quadrilateral ABCD in which AB=3cm,BC=4cm,CD=4cm, DA = 5cm and AC= 5cm.

A metal cylinder has height of 7m. The inner radius of cylinder is 1 m and outer radius is 1.5 m. Calculate

1) Inner surface area

2) Outer surface area

3) Total surface area . (Take pi=$\frac{22}{7}$) [4 MARKS]

In the given figure, ABCD is a parallelogram. E and F are midpoints of BC and AD respectively. The ratio of area $\Delta AFE$ : area of parallelogram ABCD is

The distances of points that lie above the origin, which are measured along the Y-axis, are taken as ____, and the distances of points that lie below the origin, which are measured along the Y-axis, are taken as ____.

In the given figure, E is the midpoint of side AC and D is the midpoint of side AB, then

S1: DE = $\frac{1}{2}$BC and DE || BC

S2: Midpoint Theorem: A line segment joining midpoints of 2 sides of a triangle is parallel to the third side and is half of it.

In the following figure, $△ABC\cong △ACD$ if ___.

$Rationalise:\frac{1}{\sqrt{3}-2\sqrt{11}}$

In the given figure, $AB\parallel CD$, $\Delta AOB$ and $\Delta DOC$ are isosceles triangles

$\angle ABOis{32}^{\circ }$, then $\angle BOD$ is

In $a^2{x}^2+ax$, if ${}^{\prime }{a}^{\prime }$ is a constant and ${}^{\prime }{x}^{\prime }$ is a variable, this expression is a polynomial in ___ variable(s). (Write in words)

Question 3
A soft drink is available in two packs−
(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm
(ii) a plastic cylinder with a circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

$[Assume\pi =\frac{22}{7}]$

Which of the following statement is incorrect?

1. 90

1. 1

If two angles of a quadrilateral are ${36}^{\circ }$ and ${72}^{\circ }$ and the other two angles are in the ratio 2:4, then the measure of the other two angles are _____.

The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres How many square metres of metal sheet would be needed to make it ?

$\text{A cone is 8.4 cm high and the radius of its base is 2.1 cm.It is melted and recast into a sphere. The radius of the sphere is}\left(a\right)4.2cm\left(b\right)2.1cm\left(c\right)2.4cm\left(d\right)1.6cm$

If two ratios are in proportion then how are they represented symbolically?

Factorise:
$x^2-(a+b)x+ab$

A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs 5 per metre sheet, sheet being 2 m wide.

In the figure ABCD is a trapezium. Find the values of $x$ and $y$.

Can we draw a triangle with the sides 4 cm,7 cm and 3 cm? Give reason.

The sum of all zeroes of the polynomial p(x) = $5x^5-20x^4+5x^3+50x^2-20x-40$ is ___ and the product is ___ .

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone are 10 cm and 7 cm respectively. Find the area of aluminium sheet required to make the cone.(Use $\pi =\frac{22}{7}$)

In a rhombus XYZW if angle X measures 80 degrees then the measure of angle Y is:

Factorise:
$a^8-2a^4{b}^4+b^8$

Class mark of a class is _____

If $\frac{3+\sqrt{5}}{2\sqrt{5}+3}=a+b\sqrt{5}$, then the numbers $a$ and $b$ are:

Question 1 (iv)
Classify $\frac{1}{\sqrt{2}}$ as rational or irrational.

Line segments AB and CD inersect at O such that $AC\left|\right|DB.$ If $\angle CAB={45}^{\circ }$ and $\angle CDB={55}^{\circ },$ then $\angle BOD=$

Linear Pair of angles are always

An arc is _________ .