Proportion

Q. Question 21
Which of the following is equal to x?

A) $x^{\frac{12}{7}}-x^{\frac{5}{7}}$
B) $\sqrt[12]{12(x^4{)}^{\frac{1}{3}}}$
C) ${\left(\sqrt{x^3}\right)}^{\frac{2}{3}}$
D) $x^{\frac{12}{7}}\times x^{\frac{7}{12}}$

Q.

Find the third proportional to $12$ and $30$.

Q.

Question 1(a)

Determine if the following are in proportion:

15, 45, 40, 120

Q.

Question 7(d)

Find the ratio of the following:

500 ml to 2 litres

Q.

The fourth proportional to 5, 8, 15 is ____________

___

Q.

If a, b, and c are in continued proportion, then $a\times c=b^2$.

1. False

2. True

Q. $6$ is the mean proportion between two numbers $x$ and $y$ and $48$ is third proportion to $x$ and $y$. Find the numbers.

Q.

Observe the following tables and find which pair of variables (here x and y) are in inverse proportion.

1. 

2. 

3. 

4. None of these

Q.

When four quantities are in proportion then the product of extreme terms is equal to the product of ___ .

Q.

If the cost of 48 bags of paddy is Rs 16, 800, then cost of 36 bags of paddy is Rs__________

1. 12, 800

2. 12, 600

3. 14, 800

4. 14, 600

Q.

If a, b, c are in continued proportion and a(b-c)=2b, prove that:

a-c = 2(a + b) / a

Q. 36. A person wanted to distribute 96 apples and 112 orange among poor children in an orphange.He packed all the fruits in boxes in such a way that each box contains fruits of the same variety, and also every box contains an equal no. of fruits. i) Find the minimum no. of boxes in which all fruits can be packed.

Q.

What should be added to each of the numbers $13,17$ and $22$ so that, the resulting numbers are in continued proportion?

1. $4$

2. $5$

3. $6$

4. $3$

Q.

Question 1(d)

Determine if the following are in proportion:

32, 48, 70, 210

Q.

If y is the mean proportional between x and z ; show that xy + yz is the mean proportional between $x^2+y^2$ and $y^2+z^2$.

Q.

Find the third proportional to :

(i) $2\frac{2}{3}$ and 4

(ii) a - b and $a^2-b^2$

Q.

Question 85

When 0.02964 is divided by 0.004, what will be the quotient?

Q.

If 8, x, 48, and 18 are in proportion then the value of x is ___

Q.

If y is the mean proportional between x and z, prove that : $\frac{x^2-y^2+z^2}{x^{-2}-y^{-2}+z^{-2}}=y^4$

Q.

If q is the mean proportional between p and r prove that :

$\frac{p^3+q^3+r^3}{p^2{q}^2{r}^2}=\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3}$

Q.

What number should be subtracted from each of the numbers 11, 15, 23 and 35 so that the remainders are in proportion?

1. x =8

2. x =5

3. x =2

4. x =3

Q.

In the given figure, $BC\perp AB,AD\perp AB,BC=4,AD=8,$ then find $\frac{A\left(\Delta ABC\right)}{A\left(\Delta ADB\right)}$.

Q.

Find the mean proportional between :

(i) $6+3\sqrt{3}$ and $8-4\sqrt{3}$

(ii) a - b and $a^3-a^{2}b.$

Q.

What number should be added to 2, 4, 7 so that resulting numbers are in continued proportion.

1. x =8

2. x =3

3. x =5

4. x =2

Q.

If $\text{a:b::c:d}$, then $\text{a and d}$ are called _____ while $\text{b and c}$ are called _____

Q.

Find the fourth proportional in $3,4,15$

Q.

The ratio of the area of a smaller circle to the bigger circle is 1 : 4 . Find the ratio of $\frac{\text{radius of smaller circle}}{\text{radius of bigger circle}}$?

1. 1

2. $\frac{1}{4}$

3. $\frac{1}{2}$

4. $\frac{1}{8}$

Q.

A sum of money is to be distributed among A, B, C, D in the proportion of 3:5:10:4. If C gets Rs. 600 more than D, what is A's share?

1. 400

2. 900

3. 300

4. 600

Q. Ratio of present age of mother and daughter is 8:3 years five yers after ratio of their ages will be 9:3 find their present age

Q.

Find the fourth proportional to :

(i) 1.5, 4.5 and 3.5

(ii) 3a. $6a^2$ and $2a{b}^2$