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If n is a natural number, then $9^{2\mathrm{n}}-4^{2\mathrm{n}}$ is always divisible by _________.
1.  5
2.  13
3.  Both (1) and (2)
4.  Neither (1) nor (2)

N is a natural number such that when N³ is divided by 9, it leaves remainder a. It can be concluded that
1.  a is a perfect square
2.  a  is a perfect cube.
3.  Both (1) and (2)
4.  Neither (1) nor (2)

The remainder of any perfect square divided by 3 is ______.
1.  0
2.  1
3.  Either (1) or (2)
4.  Neither (1) nor (2)

Find the HCF of 432 and 504 using prime factorization method.
1.  36
2.  72
3.  96
4.  108

If n is any natural number, then $6^{\mathrm{n}} - 5^{\mathrm{n}}$ always ends with _______.
1.  1
2.  3
3.  5
4.  7

The LCM of two number is 1200. Which of the following cannot be their HCF?
1.  600
2.  500
3.  200
4.  400

Which of the following is always true?
1.  The rationalizing factor of a number is unique.
2.  The sum of two distinct irrational numbers is rational.
3.  The product of two distinct irrational numbers is irrational.
4.  None of these.

Find the remainder when the square of any number is divided by 4.
1.  0
2.  1
3.  Either (1) or (2)
4.  Neither (1) nor (2)

Ashok has two vessels which contain 720 ml and 405 ml of milk, respectively. Milk in each vessel is poured into glasses of equal capacity to their brim. Find the minimum number of glasses which can be filled with milk.
1.  45
2.  35
3.  25
4.  30

If n is an odd natural number, $3^{2\mathrm{n}}+2^{2\mathrm{n}}$ is always divisible by
1.  13
2.  5
3.  17
4.  19

For what values of x, 2^x$\times$5^x ends in 5?
1.  0
2.  1
3.  2
4.  No value of x

Which of the following is a terminating decimal?
1.  $\frac{4}{7}$
2.  $\frac{3}{7}$
3.  $\frac{2}{3}$
4.  $\frac{1}{2}$

LCM of two co-primes (say x and y) is ___________.
1.  x+y
2.  x-y
3.  xy
4.  $\frac{\mathrm{x}}{\mathrm{y}}$

HCF of two co-prime (say x and y) is ___________.
1.  x
2.  y
3.  xy
4.  1

If we apply Euclid's division lemma for two numbers 15 and 4, then we get,
1.  $15=4\times 3+3.$
2.  $15=4\times 2+7.$
3.  $15=4\times 1+11.$
4.  $15=4\times 4+\left(-1\right).$

Given that the units digits of A³ and A are the same, where A is a single digit natural number. How many possibilities can A assume?
1.  6
2.  5
3.  4
4.  3

If the product of two irrational numbers is rational, then which of the following can be concluded?
1.  The ration of the greater and the smaller numbers is an integer.
2.  The sum of the numbers must be rational.
3.  The excess of the greater irrational number over the smaller irrational number must be rational.
4.  None of these.

The LCM and HCF of two numbers are equal, then the numbers must be _______.
1.  prime
2.  co-prime
3.  composite
4.  equal

Which of the following is/are always true?
1.  Every irrational number is a surd.
2.  Any surd of the form $\sqrt[\mathrm{n}]{\mathrm{a}}+\sqrt[\mathrm{n}]{\mathrm{b}}$ can be rationalized by a surd of the form $\sqrt[\mathrm{n}]{\mathrm{a}}-\sqrt[\mathrm{n}]{\mathrm{b}}$, where $\sqrt[\mathrm{n}]{\mathrm{a}}$ and $\sqrt[\mathrm{n}]{\mathrm{b}}$ are surds.
3.  Both (1) and (2).
4.  Neither (1) nor (2).

The sum of LCM and HCF of two numbers is 1260. If their LCM is 900 more than their HCF, find the product of two numbers.
1.  203400
2.  194400
3.  198400
4.  205400

The following sentences are the steps involved in finding the HCF of 29 and 24 by using Euclid's division algorithm. Arrange them in sequential order from first to last.
$\left(\mathrm{A}\right) 5=1\times 5+0 \left(\mathrm{B}\right) 29=24\times 1+5 \left(\mathrm{C}\right) 24=5\times 4+1$
1.  BAC
2.  ABC
3.  BCA
4.  CAB

The following are the steps involved in finding the LCM of 72 and 48 by the prime factorization method. Arrange them in sequential order from first to last
(A) $72=2^3\times 3^2 \mathrm{and} 48=2^4\times 3^1$
(B) $\mathrm{LCM}=24\times 32$
(C) All the distinct factors with the highest exponents are 24 and 32
1.  ABC
2.  ACB
3.  CAB
4.  BCA

Find the remainder when the square of any prime number greater than 3 is divided by 6.
1.  1
2.  3
3.  2
4.  4

If HCF (72, q)=12 then how many values can q take? (Assume q be a product of a power of 2 and a power of 3 only)
1.  1
2.  2
3.  3
4.  4

Find the HCF of 120 and 156 using Euclid's division algorithm.
1.  18
2.  12
3.  6
4.  24

The HCF of the polynomials $\left({\mathrm{x}}^2-4\mathrm{x}+4\right)\left(\mathrm{x}+3\right)$ and $\left({\mathrm{x}}^2+2\mathrm{x}-3\right)\left(\mathrm{x}-2\right)$ is _________.
1.  $\mathrm{x}+3$
2.  $\mathrm{x}-2$
3.  $\left(\mathrm{x}+3\right)\left(\mathrm{x}-2\right)$
4.  $\left(\mathrm{x}+3\right){\left(\mathrm{x}-2\right)}^2$

$\sqrt{3+\sqrt{5}}=\_\_\_\_\_\_\_\_.$
1.  $\sqrt{2}+1$
2.  $\sqrt{\frac{5}{2}}+\sqrt{\frac{1}{2}}$
3.  $\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}$
4.  $\sqrt{\frac{9}{2}}-\sqrt{\frac{3}{2}}$

The value of ${\left(37\right)}^{3^x}-{\left(33\right)}^{3^x}$ ends in _______ $\left(\mathrm{x}\in \mathrm{N}\right)$
1.  4
2.  6
3.  0
4.  Either (1) or (2)

P=2(4)(6)...(20) and Q=1(3)(5)....(19). What is the HCF of P and Q?
1.  $3^3·5·7$
2.  $3^4·5$
3.  $3^4·5^2·7$
4.  $3^3·5^2$

The LCM and the HCF of two numbers are 1001 and 7 respectively. How many such pairs are possible?
1.  0
2.  1
3.  2
4.  7

There are apples and 112 oranges. These fruits are packed in boxes in such a way that each box contains fruits of the same variety, and every box contains an equal number of fruits. Find the minimum number of boxes in which all the fruits can be packed.
1.  12
2.  13
3.  14
4.  15

Two runners A and B are running on a circular track. A takes 40 seconds to complete every round and B takes 30 seconds to complete every round. If they start simultaneously at 9:00 AM, then which of the following is the time at which they can meet at the starting point?
1.  9:05 AM
2.  9:10 AM
3.  9:15 AM
4.  9:13 AM

In how many ways can 1500 be resolved into two factors?
1.  18
2.  12
3.  24
4.  36

Four bells toll at intervals of 10 seconds, 15 seconds, 20 seconds and 30 seconds respectively. If they toll together at 10:00 AM at what time will they toll together for the first time after 10 AM?
1.  10:01 AM
2.  10:02 AM
3.  10:00:30 AM
4.  10:00:45 AM

If $\mathrm{a}=\sqrt[8]{6}-\sqrt[8]{5}, \mathrm{b}=\sqrt[8]{6}+\sqrt[8]{5}, \mathrm{c}=\sqrt[6]{6}+\sqrt[6]{5}, \mathrm{d}=\sqrt[4]{6}+\sqrt[4]{5}, \mathrm{and} \mathrm{e}=\sqrt{6}+\sqrt{5},$ then which of the following is a rational number?
1.  abcde
2.  abde
3.  ab
4.  cd

Find the units digit of ${\left(12\right)}^{3^x}+{\left(18\right)}^{3^x} \left(\mathrm{x}\in \mathrm{N}\right).$
1.  2
2.  8
3.  0
4.  1

If X=28+(1$\times$2$\times$3$\times$4$\times$....$\times$16$\times$28) and Y=17+(1$\times$2$\times$3$\times$....$\times$17), then which of the following is/are true?
(A) X is a composite number                   (B) Y is a prime number
(C) X$-$Y is a prime number                     (D) X+Y is a composite number
1.  Both (1) and (4)
2.  Both (2) and (3)
3.  Both (2) and (4)
4.  Both (1) and (2)

P is the LCM of 2, 4, 6, 8, 10, Q is the LCM of 1, 3, 5, 7, 9 and L is the LCM of P and Q. Then, which of the following is true?
1.  L = 21P
2.  L = 4Q
3.  L = 63P
4.  L = 16Q

The LCM and the HCF of two numbers are 144 and 12 respectively. How many such pairs of numbers are possible?
1.  0
2.  1
3.  2
4.  10

Two bells toll in every 45 seconds and 60 seconds. If they toll together at 8:00 Am, then which of the following is the probable time at which they can toll together?
1.  8:55 AM
2.  8:50 AM
3.  8:45 AM
4.  8:40 AM