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How many diagonals are there in a triangle?

If $x$ = $\frac{2}{3}$ and $y$ = $\frac{50}{45}$ , then $\frac{x}{y}$ = _________

A rectangle's length is 5 cm less than twice its width. If the length is decreased by 5 cm and width is increased by 2 cm; the perimeter of the resulting will be 74 cm. Find the length and width of the original rectangle.

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm, is_________.

If the Indian cricket team won 6 matches and lost 4, then Indian cricket team has won of the total matches played.

$(5-x)(6-5x)(2-x)$

The diagonal of a cube measures 44 cm. Its volume is

(a) $8c{m}^3$

(b) $16c{m}^3$

(c) $27c{m}^3$

(d) $64c{m}^3$

The difference in simple interest and compound interest on a certain sum of money at $6\frac{2}{3}$ per annum for 3 years is Rs. 46. Determine the sum.

Question 81 (v)

Add :

$2p^4-3p^3+p^2-5p+7,-3p^4-7p^3-3p^2-p-12$

Find the capacity of a rectangular cistern in litres whose dimensions are $11.2m\times 6m\times 5.8m$ Find the area of the iron sheet required to make the cistern.

Using the formula for squaring a binomial, evaluate the following:

$\left(i\right)(102{)}^2$ $\left(ii\right)(99{)}^2$ $\left(iii\right)(1001{)}^2$ $\left(iv\right)(999{)}^2$ $\left(v\right)(703{)}^2$

2437 is divided by which number?

200% of 12 is

Find the leftmost and the rightmost number when the following numbers are represented on the number line.

$-\frac{19}{10}$, $-\frac{9}{5}$, $-\frac{8}{5}$, $-\frac{3}{2}$, $-\frac{17}{10}$

Find the product of algebraic expressions $\frac{2x}{7}$ and $\frac{3y}{5}$

A girl scored 60 out of 75 in English, 60 out of 90 in Mathematics and 80 out of 100 in Science. Find girl's aggregate score as percentage in all the three subjects.

(a) Two cubes of dimensions $2cm\times 2cm\times 2cm$ are placed side by side. What is the length of the resulting cuboid?

(b) How many faces, vertices and edges does a triangular prism have?

[3 MARKS]

Check the following rational numbers for distributive property of multiplication over addition

$\frac{1}{4},\frac{1}{3}$ and $\frac{3}{2}$

Question 101 (i)

Here is a keyboard for a harmonium.
Find the ratio of white key to black keys on the keyboard.

$(-1{)}^{-3}$ is:

Question 73

On throwing a die once, the probability of occurence of an even number is $\frac{1}{2}$.

Which of the following is an example of non polyhedron?

If there are 22 sides in a polygon. How many diagonals are there?

The count of bacteria in a culture was initially $5,25,000$. If it is increasing at the rate of $3\frac{1}{2}\%$ per hour, find the count of bacteria at the end of $2$ hours.

Use suitable identity and find the value of ${97}^2$

What is rational numbers mean

The radius of Jupiter is 11 times the radius of the earth. calculate ratio of the volumes of Jupiter and there earth. How many earth's can Jupiter accommodate?

Numbers of significant figures in the volume of a cube of side 6.103 m are:

Find a single discount equivalent to successive discounts of $10\%$ and $20\%$.

Evaluate : ${\left(6\frac{2}{3}\right)}^2-{\left(2\frac{1}{3}\right)}^2$

What is the value of m?

$2m+7=21$

${\left(1.05\right)}^2-{\left(0.95\right)}^2=$

.

Mohan deposited Rs.80 per month in a cumulative deposit account for six years. Find the amount payable to him on maturity, if the rate of interest is 6 % per annum.

The speed of light is $3\times {10}^{8}m/s$ and the speed of sound is $3.43\times {10}^{2}m/s$. Then the speed of light is almost _____ times greater than that of sound.

Cost of production of each unit of electricity is 3 less than twice the total number of units produced. The expression for total cost of production is

Which of the following is the top view of the given figure?

In a fort 150 men had provisions for 45 days. After 10 days, 25 men left the fort. How long would the food last at the same rate?

In an election, three candidates contested and secured 29200, 58800 and 72000 votes. Find the percentage of votes scored by winning candidate.

Question 87

Solve the following question:

Write the first five square numbers.