2 Mark Question

Question 12 Marks

How much less is $x^2-2 x y+3 y^2$ than $2 x^2-3 y^2+x y$ ?

Answer

We have:
$\left(2 x^2-3 y^2+x y\right)-\left(x^2-2 x y+3 y^2\right)$
$=2 x^2-3 y^2+x y-x^2+2 x y-3 y^2$
$=2 x^2-x^2-3 y^2-3 y^2+x y+2 x y$
$=x^2-6 y^2+3 x y$
$x^2-2 x y+3 y^2$ is less than $2 x^2-3 y^2+x b y x^2-6 y^2+3 x y$.

View full question & answer→

Question 22 Marks

Find the product $\Big(\frac{3}{5}\text{abc}^3\Big)\times\Big(\frac{-25}{12}\text{a}^3\text{b}^2\Big)\times(-8\text{b}^3\text{c})$

Answer

We have:
$\frac{3}{5}\text{abc}^3\times\frac{(-25)}{12}\text{a}^3\text{b}^2\times(-8\text{b}^3\text{c})$
$=\frac{3}{5}\text{abc}^3\times\frac{(-25)}{12}\text{a}^3\text{b}^2\times(-8^2\text{b}^3\text{c})$
$=\text{abc}^3\times(-5\text{a}^3\text{b}^2)\times(-2\text{b}^3\text{c})$
$=10\text{a}^4\text{b}^6\text{c}^4$

View full question & answer→

Question 32 Marks

A number when multiplied by 4, exceeds itself by 45. Find the number.

Answer

Let the required number = x
Then, 4x = x + 45
⇒ 4x - x = 45
⇒ 3x = 45
⇒ x = 15
Required number = 15

View full question & answer→

Question 42 Marks

$\frac{2}{3}$ of a number is less than the original number by 20. Find the number.

Answer

Let the original number = x
Then $\frac{2}{3}$ of the number $=\frac{2}{3}\text{x}$
Then $\text{x}-\frac{2}{3}\text{x}=20$
$\Rightarrow\frac{3\text{x}-2\text{x}}{3}=20$
$\Rightarrow\frac{\text{x}}{3}=20$
$\Rightarrow\text{x}=20\times3=60$
$\therefore$ Original number = 60

View full question & answer→

Question 52 Marks

Simplify:$(3 a+4)(2 a-3)+(5 a-4)(a+2)$.

Answer

We have:
$(3 a+4)(2 a-3)+(5 a-4)(a+2)$
$=\{3 a(2 a-3)+4(2 a-3)\}+\{5 a(a+2)-4(a+2)\}$
$=\left(6 a^2-9 a+8 a-12\right)+\left(5 a^2+10 a-4 a-8\right)$
$=\left(6 a^2-a-12\right)+\left(5 a^2+6 a-8\right)$
$=\left(11 a^2+5 a-20\right)$

View full question & answer→

Question 62 Marks

Reenu’s father is thrice as old as Reenu. After 12 years he will be just twice his daughter. Find their present ages.

Answer

Let Reenu’s present age be x
Then, her father’s present age will be 3x
Reenu’s age after 12 years = (x + 12)
3x + 12 = 2x + 24
x = 12
Reenu’s present age = x = 12 years
And her father’s age = 3x = (3 × 12) = 36 years

View full question & answer→

Question 72 Marks

A number is as much greater than 21 as it is less than 71. Find the number.

Answer

Let the required number = x
Then x - 21 = 71 - x
⇒ x + x = 71 + 21
⇒ 2x = 92
⇒ x = 46

View full question & answer→

Question 82 Marks

The sum of two consecutive odd numbers is 68. Find the numbers.

Answer

Let the consecutive odd number be
x and (x + 2)
x + (x + 2) = 68
2x + 2 = 68
2x = 68 - 2 = 66
x = 33
The required numbers are 33 and (33 + 2), i.e., 35.

View full question & answer→

Question 92 Marks

Subtract $x^2-2 x y+5 y^2-4$ from $4 x y-5 x^2-y^2+6$.

Answer

We have:
$\left(4 x y-5 x^2-y^2+6\right)-\left(x^2-2 x y+5 y^2-4\right)$
$=4 x y-5 x^2-y^2+6-x^2+2 x y-5 y^2+4$
$=-6 x^2-6 y^2+6 x y+10$
$=-2\left(3 x^2+3 y^2-3 x y-5\right)$

View full question & answer→

Question 102 Marks

Twice a number when decreased by 7 gives 45. Find the number.

Answer

Let the required number = x
Then 2x - 7 = 45
2x = 45 + 7 = 52
x = 26
Required number = 26

View full question & answer→

Question 112 Marks

A number added to its two-thirds is equal to 55. Find the number.

Answer

Let the required number = x
Two third of the number $=\frac{2}{3}\text{x}$
$\therefore\frac{2\text{x}}{3}+\text{x}=55$
$\Rightarrow\frac{2\text{x}+3\text{x}}{3}=55$
$\Rightarrow\frac{5\text{x}}{3}=55$
$\Rightarrow\text{x}=\frac{55\times3}{5}=33$
$\therefore$ Required number = 33

View full question & answer→

Question 122 Marks

Thrice a number when increased by 5 gives 44. Find the number.

Answer

Let the required number = x Then
3x + 5 = 44
⇒ 3x = 44 - 5 = 39
x = 13
Required number = 13

View full question & answer→

Question 132 Marks

Evaluate $x ^3+ y ^3+ z ^3-3 xyz$ when $x =-2, y =-1$ and $z =3$.

Answer

We have:
$x^3+y^3+z^3-3 x y z$
$=(-2)^3+(-1)^3+(3)^3-3 \times(-2) \times(-1) \times 3$
$=-8-1+27-18=-27+27=0$

View full question & answer→

Maths 2 Mark Question

Take a timed test