Componendo

Q.

If $a,b$and $c$ are unit coplanar vectors, then $[2a-b2b-c2c-a]$is equal to $?$

1. $1$

2. $0$

3. $-\sqrt{3}$

4. $\sqrt{3}$

5. $6$

Q.

What number must be added to each of the numbers $10,18,22,38$ to make them in proportion?

1. 4

2. 8

3. 2

4. 6

Q.

If$A={\left[a_{\mathrm{ij}}\right]}_{2\times 2}$, where $a_{\mathrm{ij}}=i+j$, then $A$ is equal to

1. $\mathrm{\left[}\begin{array}{cc}\mathrm{1}& \mathrm{1}\\ \mathrm{2}& \mathrm{2}\end{array}\mathrm{\right]}$

2. $\mathrm{\left[}\begin{array}{cc}\mathrm{1}& \mathrm{2}\\ \mathrm{1}& \mathrm{2}\end{array}\mathrm{\right]}$

3. $\mathrm{\left[}\begin{array}{cc}\mathrm{1}& \mathrm{2}\\ \mathrm{3}& \mathrm{4}\end{array}\mathrm{\right]}$

4. $\mathrm{\left[}\begin{array}{cc}\mathrm{2}& \mathrm{3}\\ \mathrm{3}& \mathrm{4}\end{array}\mathrm{\right]}$

Q. 21x + 47y = 110
47x + 21y = 162

Q.

Evaluate:
$8\frac{1}{2}-3\frac{5}{8}$

Q.

Question 16

The product of $7and6\frac{3}{4}$ is

(a) $42\frac{1}{4}$
(b) $47\frac{1}{4}$
(c) $42\frac{3}{4}$
(d) $47\frac{3}{4}$

Q.

What least number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?

1. x =8

2. x =3

3. x =5

4. x =2

Q. If (ma+nb):b::(mc+nd):d, prove that a, b, c, d are are in proportion.

Q. Question 3 (vii)
Multiply the following fractions
$3\frac{4}{7}\times \frac{3}{5}$

Q.

What number must be subtracted from each of the numbers 23, 30, 57 & 78 so that the remainders are in proportion?

1. 3

2. 12

3. 6

4. 9

5. 15

Q. If the sum and the difference of two expressions P and Q is 2x^2 - 8x + 6 and 2x - 2 respectively, then find the HCF of P and Q.

Q.

If three positive real numbers $\mathrm{a},\mathrm{b}$ and $\mathrm{c}$ are in AP and $\mathrm{abc}=4$, then the minimum possible value of $\mathrm{b}$ is

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

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

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

4. $2^{\frac{5}{2}}$

Q. Given that $\frac{a^3+3a{b}^2}{b^3+3a^{2}b}=\frac{63}{62}$.
Using Componendo and Dividendo find $a:b$.

Q. If $\frac{x^3+3x{y}^2}{3x^{2}y+y^3}=\frac{m^3+3m{n}^2}{3m^{2}n+n^3}$, show that : nx = my.
$\left[2Marks\right]$

Q. If $\frac{a}{b}=\frac{5}{8}$, find the value of the following raios:
$\frac{a+b}{a-b}$

Q. If $\frac{a}{b}=\frac{2}{3}$ then find the value of the following expression:
$\frac{4a+3b}{3b}$

Q. If 4 : 5 = 8 : 10, then 9 :5 = __________.

1. 8 : 10
2. 4 : 9
3. 18 : 5
4. 18 : 10

Q.

If (a + 2b + c), (a –c)and (a - 2b + c) are in proportion, then.

1. b² = ac

2. b= ac²

3. b² = a²c

4. b² = c

Q.

If a: b = c : d, then according to componendo property

1. a + b : b = c + d : d

2. a + b : a = c + d : c

3. a - b : a = c - d : c

4. a - b : b = c - d : d

Q.

If p : q = r : s; then show that :

mp + nq : q = mr + ns : s.

Q. If 7 : 9 = 14 : 18 , then 16 : 9 = __________.

1. 9 : 16
2. 7 : 9
3. 18 : 32
4. 32 : 18

Q.

If a : b = c : d , prove that :

(6a + 7b) (3c - 4d) = (6c + 7d) (3a- 4b).

Q. $3\left(x^2+\frac{1}{x^2}\right)-4\left(x-\frac{1}{x}\right)-6=0$

Q.

If $\frac{5}{8}=\frac{20}{p}$, Then value of $p$ is :

Q. Show that:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Q. Look at the statements given below:

I. $(3x+4y=5\mathrm{and}2\mathrm{x}+3\mathrm{y}=9)\Rightarrow (x=-21\mathrm{and}\mathrm{y}=17)$
II. $(x-y+1=0\mathrm{and}3\mathrm{x}-5\mathrm{y}+1=0)\Rightarrow (x=-2\mathrm{and}y=-1)$
III. $\left(\frac{x}{a}+\frac{y}{b}=2\mathrm{and}\frac{\mathrm{x}}{\mathrm{a}}-\frac{\mathrm{y}}{\mathrm{b}}=4\right)\Rightarrow (x=2a\mathrm{and}y=2b)$
Which of the above statements are true?
(a) I only
(b) II only
(c) I and II
(d) I and III

Q. if x+y /xy=7 and 3x+4y /xy=25, then what is the value of xy?

Q.

1. 2x + 3y = 1

2. 2x + y = 3

3. x + 3y = 1

4. 2x + 3y = 5

Q.

How (x³+y³)+z³-3xyz = [(x+y)³-3xy(x+y)]+z³-3xyz

Q.

$2\mathrm{paise}=\mathrm{\_\_}\mathrm{Rs}$