Duplicate Ratio

Q.

Let $A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$, $x\in \mathrm{ℝ}$ and $A^4=\left[a_{ij}\right]$. If $a_{11}=109$, then $a_{22}$ is equal to

Q. The duplicate ratio of 2 : 3 is

1. 16 : 84
2. 4 : 9
3. 8 : 19
4. 5 : 12

Q.

If three quantities are in continued proportion ; show that the ratio of the first to the third is the duplicate ratio of the first to the second.

Q.

What is the duplicate ratio of 9:17

1. 81 : 289

2. 81 : 290

3. 80 : 289

4. 91 : 289

Q. The sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300 m. Find the area of the plot.

1. $1500\sqrt{2}{m}^2$
2. $1500\sqrt{3}{m}^2$
3. $1425\sqrt{2}{m}^2$
4. $1500m^2$

Q.

Find duplicate ratio of :

(i) 3 : 4 (ii) $3\sqrt{3}:2\sqrt{5}$

Q.

The angles of a 9 sided polygon are in AP . Which degree measure is always a term of the series

Q.

ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.

Q. Duplicate ratio of $2\sqrt{2}:3\sqrt{5}$ is $8:45$

1. False
2. True

Q. _____ is the duplicate ratio of $\sqrt{2}:\sqrt{3}$

1. $4:9$
2. $\sqrt{3}:\sqrt{2}$
3. $2:3$
4. $\sqrt{6}:\sqrt{3}$

Q. What is the sub-duplicate ratio of 49 : 121? $\left[1\text{Mark}\right]$

Q. Find the angles of a cyclic quadrilateral ABCD in which $\angle A=(4x+20)°,\angle B=(3x-5)°,\angle C=\left(4y\right)°\mathrm{and}\angle D\mathit{=}(7y+5)°.$

Q. In a cyclic quadrilateral ABCD, it is being given that $\angle A=(x+y+10)°,\angle B=(y+20)°,\angle C=(x+y-30)°\mathrm{and}\angle D=(\mathrm{x}+\mathrm{y})°.\mathrm{Then},\angle B\mathit{=}\mathit{?}$
(a) 70°
(b) 80°
(c) 100°
(d) 110°

Q. Duplicate ratio of $2\sqrt{2}:3\sqrt{5}$ is $8:45$

1. True
2. False

Q.

Find the duplicate ratio of $\surd 5:7$

Q. The duplicate ratio of $\frac{1}{6}:\frac{1}{5}$ is ____

1. $36:25$
2. $\frac{1}{5}:\frac{1}{6}$
3. $25:36$
4. $30:15$

Q.

What is the duplicate ratio of 2 : 3?

1. 16 : 84

2. 4 : 9

3. 8 : 19

4. None of these

Q. If $(x-9):(3x+6)$ is the duplicate ratio of $4:9$, find the value of $x$.

Q. Write the sub-duplicate ratio of $4:9$.

Q.

Find the :

(i) duplicate ratio of $2\sqrt{2}:3\sqrt{5}$

(ii) triplicate ratio of 2a : 3b,

(iii) sub- duplicate ratio of $9x^2{a}^4:25y^6{b}^2$

(iv) sub-triplicate ratio of 216 : 343

(v) reciprocal ratio of 3 :5

(vi) ratio compounded of the duplicate ratio of 5 :6, the reciprocal ratio of 25 : 42 and the sub - duplicate ratio of 36 : 49.

Q. Duplicate ratio of 7 : 9 is 49 : 81

1. False
2. True

Q. Duplicate ratio of $a:b$ will be:

1. $\sqrt{a}:\sqrt{b}$
2. $a^2:b^2$
3. $\sqrt[3]{3a}:\sqrt[3]{3b}$
4. $a^3:b^3$

Q. If the ratio of the circumference of two circles is $3:1$, then find the ratio of their areas.

Q. _____ is the duplicate ratio of $3a:4b$

1. $3a^2:4b^2$
2. $9a:16b$
3. $\sqrt{3a}:\sqrt{4b}$
4. $9a^2:16b^2$

Q. The duplicate ratio of $2\sqrt{2}:3\sqrt{5}$ is _____

1. $16:45$
2. $16:250$
3. $4:15$
4. $8:45$

Q.

If A : B is 3 : 4 and B : C is 2 : 3, then A:B:C is ____.

1. 3 : 4: 6

2. 3 : 6: 4

3. 4 : 3 : 6

4. 6 :4: 3

Q. If $a:b=2:3$ and $b:c=9:8$ then the duplicate ratio of $a:c$ is ____

1. $9:16$
2. $81:64$
3. $4:9$
4. $4:64$

Q. Burst out the ratios which are equivalent to the ratio 3 : 4.

1. 6 : 8
2. 9 : 12
3. 12 : 16
4. 21 : 28
5. 27 : 36
6. 31 : 41
7. 33 : 43
8. 38 : 40

Q. The duplicate ratio of $\frac{2}{5}$ is _____

1. $\frac{4}{10}$
2. $\frac{7}{5}$
3. $\frac{4}{25}$
4. $\frac{8}{125}$

Q. If $x:y=4:9$ and $y:z=3:8$, then the duplicate ratio of $x:z$ is ____

1. $9:64$
2. $16:81$
3. $1:36$
4. $16:64$