MATHS M.C.Q. [1 Marks Each]

Let $5x$ be the smallest multiple of $5.$
Then, the three consecutive multiples shall be $5x, 5x + 5$ and $5x + 10$
According to the question,
$5x + 5x + 5 + 5x + 10 = 45$
$\therefore 5x + 5x + 5x = 45 - 15$
$\therefore 15x = 30$
$\therefore x = 2$
$\therefore$ The Smallest multiple $= 5x = 5 × 2 = 10$

A linear equation in one variable has only one solution. e.g. Solution of the linear equation $ax + b = 0$ is unique, i.e. $\text{x}=-\frac{\text{b}}{\text{a}}.$

$\frac{\text{4x}}{7}-12=0 \Rightarrow \frac{\text{4x}}{7}= 12$
$ \Rightarrow \text{4x}= 7 \times 12 = 84$
$\Rightarrow \text{x}=\frac{\text{84}}{4}= 21$

Taking, $3(x - 3) = 4(2x + 4)$
$⇒ 3x - 9 = 8x + 16$
$⇒ 3x - 8x = 16 + 9$
$⇒ -5x = 25$
$⇒ x = -5$
Therefore, the solution of the given equation is $-5.$

Let the required number be $x.$
$\text{x}+\frac{2}{5}=-\frac{3}{7}$
$\text{x}=\frac{3}{7}-\frac{3}{5}$
$\text{x} = -\frac{(15-14)}{35}$
$\text{x} = -\frac{15}{35}$

Given, $8x - 3 = 25 + 17x$
$8x - 17x = 25 + 3$
$-9x = 28$
$\text{x} = -\frac{28}{9}$
Hence, $x$ is a rational number.

Given, the two numbers are in the ratio $3 : 5.$
Then the numbers be $3x, 5x.$
According to the problem,
$3x + 5x = 96$
or, $8x = 96$
or, $x = 12.$
So the numbers are $36, 60.$

$2x - 3 = 7$
$2x = 7 + 3 = 10$
$\text{x} = \frac{10}{2} = 5$

We have two expressions such that,
$\Rightarrow 4x + 4 = 2x + 8$
$\Rightarrow 4x - 2x = 8 - 4$
$\Rightarrow 2x = 4$
$\Rightarrow x = 2$
Therefore, for $x = 2$ the given two expressions will become equal.

 Given,
Speed of the stream in still water $= 1\ km/ hr$
Let speed of the streamer $= x \ km/ hr$
Speed downstream $= (x + 1)\ km/ hr$
Speed upstream $= (x - 1)\ km/ hr$
According to the given condition,
$(x + 1) × 5 = (x - 1) × 6$
$5x + 5 = 6x - 6$
$x = 11$
Hence, Speed of streamer in still water is $11\ km/ hr$ and
Distance between two ports $= (11 + 1) × 5 = 60\ km/ hr.$

 Let the angles be $4x$ and $5x.$ Third angle $= 4x + 5x = 9x$
We have,
$4x + 5x + 9x = 180^\circ $
$x = 10^\circ $
$\therefore$ Third angle $= 9x = 9 \times 10^\circ = 90^\circ $

$2x + 3 = 2(x - 4)$
$⇒ 2x + 3 = 2x - 8$
$⇒ 3 = -8$ which is impossible.

 Current volume of alcohol $=\text{100ml}\times\frac{15}{100}=\text{60ml}.$
Required strength $=\frac{15}{100}\times400=\text{128ml}$
Required pure alcohol $=128-\text{60ml}=68$

Given, $\frac{1}{3}+\text{S}=\frac{2}{5}$
$\text{S}=\frac{2}{5}-\frac{1}{3}$
$\text{S}=\frac{6-5}{15}$
$\text{S}=\frac{1}{15}$

 Given, $\frac{5\text{x}}{3}-4=\frac{2\text{x}}{5}$
$\frac{5\text{x}}{3}-\frac{2\text{x}}{5}=4$
$\frac{25\text{x}-6\text{x}}{15}=4$
$19\text{x}=60$
$\frac{19\text{x}}{19}=\frac{60}{19}$
$\text{x}=\frac{60}{19}$
$\text{Now, }2\text{x}-7=2\times\frac{60}{19}-7$
$\frac{120-133}{19}=-\frac{13}{19}$
Hence, the numerical value of $2x - 7$ is $-\frac{13}{19}.$

$(x + 3) + x = 23$
$\Rightarrow 2x = 20$
$\Rightarrow x = 10$
$\Rightarrow x + 3 = 13$

$\frac{\text{7}}{\text{x}}= 3$
$ \Rightarrow \text{3x}= 7$
$ \Rightarrow \text{x}= \frac{7}{3}$

$x + 3 = 5$
$\Rightarrow x = 5 - 3$
$= 2.$

$X$ plus an odd number will always equal an even number if $x$ is odd.
Vice versa is true if $x$ is even.
Think about it: If $x = 1 (1$ is an odd number$),$ the next odd numbers would be $3, 5, 7, 9,$ etc.
Therefore, $x + 2$ would be the next odd number.

 Taking, $3x - 3 = 25 + 17x$
$⇒ 3x - 17x = 25 + 3$
$⇒ -14x = 28$
$\Rightarrow\text{x}=\frac{28}{(-14)}$
$⇒ x = -2$
$-2$ is an integer.

$(2\text{x} - 1) + (\text{x}-1) = \text{x} + 2$
$\Rightarrow\text{2y = 4 }\Rightarrow\text{x}= \frac{4}{2}= 2.$

Let the three consecutive integers be $x, x + 1$ and $x + 2.$
Equation $= \text{x} + \text{x} + 1 + \text{x} + 2 = 51$
$\Rightarrow3\text{x} + 3 = 51$
$\Rightarrow3\text{x} = 51 - 3$
$\Rightarrow3\text{x} = 48$
$\Rightarrow\text{x} = \frac{48}{3}= 16$
Middle integer $= \text{x}+1 = 16 + 1 = 17$

Let the age of the father is $x$
Given: $x = 3 × ($age of son$) = 3 × (15) = 45$ years.

 Let the equal side of the isosceles triangle be $x.$
Then, the perimeter of the triangle would be $(x + x + 6).$
$\therefore2\text{x} + 6 = 16 $
$\Rightarrow2\text{x} = 16 - 6$
$\Rightarrow2\text{x} = 10$
$\Rightarrow\text{x} = \frac{10}{2}= 5$
$\therefore$ Length of each equal side $= 5\ cm$

Speed of the man in still water $= 8\ km/ ph.$
Speed of the river $= 2\ km/ ph$
Downstream $= 8 + 2 = 10\ km/ ph$
Upstream $= 8 - 2 = 6\ km/ ph$
$\Rightarrow\frac{\text{x}}{10}+\frac{\text{x}}{6}=\frac{48}{60}$
$\Rightarrow\text{8x}=24$
$\Rightarrow\text{x}=\text{3km}$

Let the number be $x.$
$\therefore\frac{4}{5}\text{x}=\frac{3}{4}\text{x}+4$
$\Rightarrow\frac{4}{5}\text{x}=\frac{3\text{x}+16}{4}$
$\Rightarrow16\text{x} = 15\text{x} + 80$
$\Rightarrow16\text{x} - 15\text{x} = 80$
$\Rightarrow \text{x} = 80$

Given, Shilpa’s age three years ago $= x$
Then, Shilpa’s present age $= (x + 3)$
Arpita’s present age $3\ ×$ Shilpa’s present age $= 3 (x + 3)$

$\frac{\text{y}}{3}-7= 11$
$\Rightarrow \frac{\text{y}}{3}=7 + 11 = 18$
$\Rightarrow \text{y} = 3 \times 18 = 54$

Let the number be $x.$

 Let the number be $x.$