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

Multiple of $6$ like $6, 12, 18,24, 30$ and they can all be divided evenly by $3.$
So option $C$ is correct.

$6th$ multiple of $7 = 42$
$10th$ multiple of $7 = 70$
Now, $x = 2 × (70 − 42) = 2 × 28 = 56$

A unit fraction is a rational number written as a fraction in which numerator is $1$ and denominator is a positive integer.
Example- $\frac{1}{2},\frac{1}{3},\frac{1}{5}$​ etc.

$LCM$ of $9,10,129 = 3 \times 310 = 2 \times 512 = 2 = 2 \times 2 \times 3$
$LCM (9,10,12) = 2 \times 2 \times 3 \times 3 \times 5 = 180$
$180$ is also multiply of $18,36,45.$
If $v$ is $18,36$ and $45$ than $LCM$ of all the number would be $180$ but its $540$

$(a) 4th$ multiple of $52 = 52 \times 4 = 208$
$(b) 8th$ multiple of $37=37 \times 8 = 296$
$(c) 5th$ multiple of $25=25 \times 5 = 125$
$(d) 7th$ multiple of $50 = 50 \times 7 = 350$
So, $350$ is the greatest value amongst all.

Taking out the factors of the given numbers, $12 = 2 \times 2 \times 3$
$24 = 2 \times 2 \times 2 \times 3$
$36 = 2 \times 2 \times 3 \times 3$
$\therefore LCM$ of $12, 24$ and $36 = 2 \times 2 \times 2 \times 3 \times 3 = 72$

 We know:
$HCF \times LCM =$ Product of two numbers
$\because 16 \times LCM = 3,072$
$\therefore LCM = 3,07216=192$

The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over.
Moreover, any repeating or terminating decimal represents a rational number.
So,Decimal expansion of a rational number cannot be
Answer $(A)$ Non-terminating and non-recrring

Factors of the given numbers are, $4 = 2 \times 2$
$9 = 3 \times 3$
$\therefore LCM$ of $4$ and $9 = 2 \times 2 \times 3 \times 3 = 36$

Let the divisor be $a$ and remainder be $r$
Let $31513 = am + r$ and $34369 = an + r$
Then, $a (n - m) = 2856 = 24 \times 119 = 12 \times 238 = 8 \times 357 = 6 \times 476 = 4 \times 714$
All three digit numbers give same remainder $= 97$

Factors of $24$ are $1, 2, 3, 4, 6, 8, 12, 24$

Required smallest number $= LCM$ of $(11, 28, 36, 45) + 3 = 13,860 + 3 = 13,863$

Factor of $1955 = 5 × 17 × 23$
$1, 5, 17, 23$ are not even, so there are no even factors.

A decimal is a fractional number and is indicated by digits after a period which is called a decimal point.
Tenths have one digit after the decimal point. The decimal $0.8$ is pronounced as eight tenths.
Hundredths have two digits after the decimal point.
The decimal $0.06$ is pronounced as six hundredths.
Thousandths follow a similar pattern.
They have three digits after the decimal point.
The decimal $0.005$ is pronounced as five thousandths.
Hence, five thousandths is $0.005.$

$75\%$ can be written in regular fraction as $75\%=\frac{75}{100}$
On reducing the fraction, we get
$\frac{75}{100}=\frac{3}{4}$

Denominator is the number at the bottomOut of the given options, only $\frac{9}{4}$ has denominator as $4.$
Hence, the answer is $\frac{9}{4}.$

A prime number is a whole number greater than $1$ whose only factors are $1$ and itself.
A factor is a whole numbers that can be divided evenly into another number.
The first few prime numbers are $2, 3, 5, 7, 11, 13, 17, 19, 23$ and $29.$
The next prime number after $43$ is $47,$So option C is the correct answer.

 Consider the given expression.
$\Bigg[\bigg(-2\frac{3}{4}\bigg)-\bigg(-1\frac{3}{4}\bigg)\Bigg]+\Bigg[\bigg(-2\frac{3}{4}\bigg)-\bigg(-1\frac{3}{4}\bigg)\Bigg]+ ....$ upto $30$ times
Sum $=\Bigg[\bigg(\frac{-11}{4}\bigg)-\bigg(\frac{-7}{4}\bigg)\Bigg]+\Bigg[\bigg(\frac{-11}{4}\bigg)-\bigg(\frac{-7}{4}\bigg)\Bigg]+ ....$ upto $30$ times
$=\big[-1\big]+\big[-1\big]+....$ upto $30$ times
$=-30$
Hence, the value of the expression is $-30.$

 Factors of $1955 = 5 \times 17 \times 23$
Number of factors are $3.$

Sum of the given digits $= 1 + 5 + 4 + 8 = 18$
Since $18$ is a multiple of $3,$ the required digit is $0.$

 The place value of every one-digit number is the same as and equal to its face value.
$(i)$ Place value and face value of $1, 2, 3, 4, 5, 6, 7, 8$ and $9$ are $1, 2, 3, 4, 5, 6, 7, 8$ and $9$ respectively.
$(ii)$ The place value of zero $(0)$ is always $0.$ As, in $105, 350, 42017, 90218$ the place value of $0$ in each number is $0.$
So option $A$ is the correct answer.

Improper fraction is a fraction in which the numerator is greater than the denominator, such as $\frac{3}{2}$
Hence, $\frac{15}{14}$ is an improper fraction.

 Given, $0.8\times\frac{\frac{7}{12}}{\frac{5}{24}}=0.8\times\frac{7}{12}\times\frac{24}{5}=0.8\times\frac{14}{5}$
$=\frac{8}{10}\times\frac{14}{5}$
$=\frac{56}{25}$
$=2\frac{6}{25}$

Sum of the given digits $= 1 + 5 + 4 + 8 = 18$
Since $18$ is a multiple of $3,$ the required digit is $0.$

Numerator of a fraction is the upper number.
So, the numerator of the fraction $\frac{5}{6}$ is $5.$
Hence, the answer is $5.$

Taking out the factors of the given numbers,$12 = 2 \times 2 \times 3$
$24 = 2 \times 2 \times 2 \times 3$
$36 = 2 \times 2 \times 3 \times 3$
$\therefore LCM$ of 12, 24 and $36 = 2 \times 2 \times 2 \times 3 \times 3 = 72$

The least number divisible by $15, 20, 24, 32,$ and $36$ can be found by taking their $LCM$ as:

$\therefore LCM$ of $15, 20, 24, 32$ and $36 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 = 1,440$
Hence, $1,440$ is the least number that is divisible by $15, 20, 24, 32$ and $36.$