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Are 256Hz,288Hz and 320Hz in simple mathematical ratio?how to remove their ratio?

The minor arc formed by two radii subtending an angle of $50$ degree at the center of a circle is $20$ cm in length. Find the radius of the circle.

Take $\pi =3.14$

Question 5 (v)

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

6412

The cost of an article is first decreased by 25% and then further decreased by 40%. Find the percentage change in the cost of the article.

If $x=\frac{1}{2}$, then the value of $x+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}$ is equal to

The sum of the square of three consecutive natural numbers is 194. Find the integers.

Evaluate the following:

$\left(i\right)102\times 106$ $\left(ii\right)109\times 107$ $\left(iii\right)35\times 37$ $\left(iv\right)53\times 55$

$\left(v\right)103\times 96$ $\left(vi\right)34\times 36$ $\left(vii\right)994\times 1006$

The value of $\frac{35}{100}$% of 80 is :

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle.

1. 6

To construct the following rectangle inside a circle, the 2 diametres we consider must be ___.

Question 86 (ii)

Using suitable identities, evaluate the following:

$(49{)}^2$

Which of the following are like terms?
a) $5xy{z}^2,-3x{y}^{2}z$
b) $-5xy{z}^2,7xy{z}^2$
c) $5xy{z}^2,5x^{2}yz$
d) $5xy{z}^2,x^2{y}^2{z}^2$

In which quadrant are sin, cos and tan positive?

Integrate x/x^4+2x^2+3

Find the value of x.

$3x+\frac{9}{3}=5x+\frac{5}{9}$

According to a survey conducted in a city, 25% were doctors, 30% engineers, 15% businessmen and rest were illiterates. What is the number of illiterates if the total population of the city is 5000?

Question 57

State whether the following statement is true or false:

The square root of 0.9 is 0.3

Question 47



​​​​​​​Sate weather the given statement is true or false.

Length of a side of an equilateral triangle and its perimeter vary inversely with each other.

Subtract:

The distance between two stations is 340 km. Two trains start simultaneously from the stations on parallel tracks and cross each other. The speed of one of them is greater than that of the Other by 5 km per hour. If the distance between two trains after 2 hours of day start is 30 km., find the speed of each train.

Find the sum of three consecutive largest positive integers such that the sum of one-third of first, one - fourth of second and one -fifth of third is atmost 20.

The value of $(\frac{2}{5}{)}^{-3}$ is

$\left(a\right)-\frac{8}{125}$

$\left(b\right)\frac{25}{4}$

$\left(c\right)\frac{125}{8}$

$-\frac{2}{5}$

Find the ratio of the following:

(a) 30 minutes to 1.5 hours (b) 40 cm to 1.5 m

(c) 55
paise to Re1 (d) 500 mL to 2 litres

Various modes of transport used by 1260 students in a given school are given below :

$\begin{array}{ccccc}\text{School bus}& \text{Private bus}& \text{Bicycle}& \text{Rickshaw}& \text{On foot}\\ 350& 245& 210& 175& 280\end{array}$

Represent the above data by a pie char.

Nandini invests a certain amount for 3 years at 10% p.a. CI. She earns Rs 1408 interest for the second year. Calculate:

The amount due to her at the end of the third year.

$\text{The function}$ $f:R+\to (1,e)\text{defined by}f\left(x\right)=\frac{X^2+e}{X^2+1}$ is

If x + y = 7 and xy = 12, find x² + y².