Sample QuestionsStatistics questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If n is a natural number, then $9^{2 n}-4^{2 n}$ is always divisible by:
- A
$5$
- B
$3$
- ✓
both $5$ and $13$
- D
Answer: C.
View full solution →The exponent of $2$ in the prime factorisation of $144$, is:
Answer: A.
View full solution →The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after:
Answer: D.
View full solution →For some integer $q$, every odd integer is of the form:
- A
$q$
- B
$q + 1$
- C
$2q$
- ✓
$2q + 1$
Answer: D.
View full solution →The smallest rational number by which $\frac{1}{3}$ should be multiplied so that its decimal expansion terminates after one place of decimal, is:
- ✓
$\frac{3}{10}$
- B
$\frac{1}{10}$
- C
$3$
- D
$\frac{3}{100}$
Answer: A.
View full solution →The product of two irrational numbers is an irrational number (True/ False).
Two numbers have $12$ as their $HCF$ and $350$ as their $LCM$ (True/ False).
View full solution →Every even integer is of the form $2m$, where m is an integer (True/ False).
View full solution →Every odd integer is of the form $2m - 1$, where m is an integer (True/ False).
View full solution →The product of any three consecutive natural number is divisible by $6$ (True/ False).
View full solution →If $a$ and $b$ are relatively prime numbers, then what is their $LCM$?
View full solution →Write the condition to be satisfied by $q$ so that a rational number $\frac{\text{p}}{\text{q}}$ has a terminating decimal expansion.
View full solution →View full solution →Given that $HCF (306. 657) = 9$, find $LCM (306, 657).$
View full solution →Determine the prime factorisation of the following positive integer:
$20570$
View full solution →Check whether $6^n$ can end with the digit $0$ for any natural number $n$.
View full solution →Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion.
$\frac{987}{10500}$
View full solution →Find the $LCM$ and $HCF$ of the following integer by applying the prime factorisation method.
$17, 23$ and $29$
View full solution →Define $HCF$ of two positive integers and find the $HCF$ of the following pairs of numbers:
$475$ and $495$
View full solution →What is a composite number?
During a sale, colour pencils were being sold in packs of $24$ each and crayons in packs of $32$ each. If you want full packs of both and the same number of pencils and crayons, how many of each would you need to buy$?$
View full solution →The length, breadth and height of a room are $8m\ 25\ cm, 6m\ 75\ cm$ and $4m\ 50\ cm,$ respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
View full solution →Prove that the square of any positive integer is of the form $5q, 5q + 1, 5q + 4$ for some integer $q.$
View full solution →Find the $HCF$ of the following pairs of integers and express it as a linear combination of them.
$963$ and $657$
View full solution →Show that the following numbers are irrational.
$3-\sqrt{5}$
View full solution →Prove that the product of three consecutive positive integer is divisible by $6.$
View full solution →Show that the cube of a positive integer is of the form $6q + r$, where q is an integer and $r = 0, 1, 2, 3, 4, 5.$
View full solution →Show that the square of any positive integer cannot be of the form $6m + 2$ or $6m + 5$ for any integer m.
View full solution →Determine the number nearest to $110000$ but greater than $100000$ which is exactly divisible by each of $8, 15$ and $21.$
View full solution →In a morning walk three persons step off together, their steps measure $80\ cm, 85\ cm$ and $90\ cm$ respectively. What is the minimum distance each should walk so that he can cover the distance in complete steps?
View full solution →