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In the given right-angled triangle, if AB = 3 cm, BC = 4 cm, then the length of AC is

If $x=2,y=5andz=4$ Find the value of:
$\frac{xz}{yz}$

Question 59

State whether the statement is True or False.

Two supplementary angles are always obtuse angles.

How long does it take for light from the sun to reach earth approximately?

Solve -12x >30 when

(i)x is a natural number

(ii)x is an integer

24(38)-445(676)

What is the volume of the rectangular box of length = 8xy, breadth = 3xy and height = xy?

Which of the following is/are correct?

$i.1km={10}^{3}m$

$ii.1km={10}^{5}cm$

$iii.1km={10}^{7}mm$

Question 94 (g)

Taking $x=\frac{-4}{9},y=\frac{5}{12}$ and $z=\frac{7}{18}$

Find $(x÷y)\times z$.

Question 52

In questions 24 to 59, fill in the blanks to make the statements true.
Interest $=\frac{P\times R\times T}{100}$, where T is ___ , R % is ___ and P is ___ .

Find the area of a rectangle whose length is $5xy$ cm and breadth is $8x{y}^2$ cm when $x=2$ and $y=3$.

Question 19

In standard form 72 crore is written as:
(a)$72\times {10}^7$
(b)$72\times {10}^8$
(c)$7.2\times {10}^8$
(d)$7.2\times {10}^7$

In the figure below, lines XY and MN intersect at point O.
If $\angle POY={90}^{\circ }$ and A:B = 2:3,
$\text{then find}\frac{C}{2}$.

If any line of symmetry in a regular polygon connects midpoint of two of its sides, then which of the following may be the number of sides of that polygon?

Question 13

The equation having -3 as the solution is

(a) x + 3 = 1

(b) 8 + 2x = 3

(c) 10 + 3x = 1

(d) 2x + 1 = 3

Question 78

In the following question, state whether the given statements are true (T) or false (F).

$(-7{)}^{-4}\times (-7{)}^2=(-7{)}^{-2}$

The ratio of weights of zinc and copper in an alloy is 5:8. If the weight of copper in a sample of this alloy is 12 g, what is the weight of zinc?

The pie chart given below represents the number of stationery items sold in a month at a shop. If the total no. of items sold was 1080, find the number of pens, notebooks, books and other items sold.

Which one of the following is an example for rate ?

The product of $(x+7y)and(7x-y)$ is

Find the ratio between the place values of number 7 in the given number 984756722

(a) In the following figure, the base of the triangle is parallel to the line $l$ and $\angle 1=\angle 2$. Prove that line BC & $m$ are parallel to each other.

(b) Consider the following figure. Find the angle y.

[4 MARKS]

A businessman makes 1 lakh of rupees every month, he pays 12% tax and puts 30% into a savings bank account. He also pays 10% of the amount as an installment for the loan. How much money is left with him?

What should be subtracted from 0.4 to get 0.08

Which of the following could represent the sides of a triangle?

In measuring the length and breadth of a rectangle, errors of $5\%$ and $3\%$ in excess, respectively, are made. The error percent in the calculated area is

Question 1 (i)

If m = 2, find the value of:
m – 2

Question 3(f)
Fill in the blanks:
___ $÷$ 48 = - 1

Find the value of 'x' if 5/6 + x = -1

A number is multipled by 4 then diminished by 7 what is the number ???

Subtract : 4x – 3z from 9x + 8y + 9z

Simplify
2xy-[4yx-{3xy-(4xy-2xy)}]

What is the value of the expression ${13}^2\times 5^2$

Pentacontagon is the name given to a polygon which has 50 sides. What will be the measure of one side of a regular pentacontagon if its perimeter is 1250 cm?

Which among the following properties holds good for addition?

Question 9 (i)

Which is greater in each of the following:
$\frac{2}{3},\frac{5}{2}$

Find the missing term: 2, 6, 12, 20, 30, 42, 56, 72, _

Which of the following figures have both line symmetry and rotational symmetry?

(i) Square
(ii) Rectangle
(iii) Scalene triangle
(iv) Isosceles triangle

If a triangle and a parallelogram are on the same base and between the same parallels as shown in the figure below, then ___.

In $△$ ABC and $△$ XYZ, if $\angle$ ABC = $\angle XYZ={90}^{\circ }$, AC = XZ and BC = YZ, then by which postulate is $△ABC\cong △XYZ$ ?

Which of the following show the correct representation of $1\frac{1}{4}$ and $2\frac{5}{8}$ on a number line?

Step 1: $3x+2=17$
Step 2: $3x=17-2$
This process of shifting the number from one side of the equation to the other side is called as ___.

A proper fraction is:

(a) What are the three conditions you need in order to say that the given two angles are adjacent angles? [3 MARKS]

(b) In the given figure, $\angle 1$ and $\angle 2$ are supplementary angles. If $\angle 1$ is decreased, what changes should take place in $\angle 2$ so that both the angles still remain supplementary?