Mathematics Paper 1 (Number System I) - CTET & State TET MCQ

Given:

Number is 720 × 650

Concept used:

Number of zeroes in the product = (2 × 5)ⁿ

n = Number of pairs 

Calculation:

720 = 2 × 2 × 2 × 2 × 3 × 3 × 5 

Number of 2 in 720 = 4

Number of 5 in 720 = 1

650 = 2 × 5 × 5 × 13

Number of 2 in 650 = 1

Number of 5 in 650 = 2

Total number of 2 = 5

Total number of 5 = 3

Pair that gives zero = 2 × 2 × 2 × 5 × 5 × 5 = 1000

∴ The number of zeroes is 3.

Formula used:

HCF of different fractions = HCF of numerators / LCM of denominators

Calculations:

HCF = HCF of (3,4,7)/LCM of (4,5,60) 

⇒ 1/60

Hence HCF of  and $\frac{7}{60}$  is 1/60.

Concept used:

Twin prime numbers are pairs of prime numbers that have a difference of 2. In other words, twin primes are prime numbers that are either 2 units apart or have only one even number between them.

Calculation:

Option 1: 15 is not a prime number, as 15 = 3 × 5

Option 2: 43 - 41 = 2 

Option 3: 33 is not a prime number, as 33 = 3 × 11

Option 4: 41 - 31 = 10 > 2

∴ The twin prime numbers are 41, 43.

Given:

1/2, 1/3, 1/4, 1/5, 1/6

Calculation:

If the Numerator of all fractions is equal to each other, then a larger denominator gives a smaller value and vice versa.

The descending order of fraction is:

1/2 > 1/3 > 1/4 > 1/5 > 1/6

∴  The descending order is 1/2, 1/3, 1/4, 1/5, 1/6.

Mathematics is a science that involves dealing with numbers, different kinds of calculations, measurement of shapes and structures, organization and interpretation of data and establishing relationships among variables, etc.

Key PointsPlace value and face value: The digits in the unit place have unitary value i.e. in 26, the number in the unit place is 6 and its value is also 6. The digit in the tenth place i.e. 2 in the number 26 has the place value of two tens (i.e. 20) instead of the face value of 2. Similarly, the place value of a digit in the hundredth place of a number is 100 times the face value of the digit. You are quite familiar with such place values.

• For example in 687 the place value of 8 is 80 and the face value of 6 is 6. Now according to the question, the sum of place value and face value is 80+6 = 86.

Hence, we can conclude that the sum of the place value of 8 and the face value of 6 in 687 is 86.

Calculations:

The number of rational numbers between any two rational numbers is unlimited.

This is because between any two distinct rational numbers, one can always find another rational number.

For instance, the average (or mid-point) of two rational numbers is also a rational number.

So the correct answer is Option 3.

Given:

A number when divided by 28, 42 and 56, leaves the remainder 11 in each case.

Concept used:

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of the numbers.

Calculation:

Factors(28) = 2 × 2 × 7

Factors(42) = 2 × 3 × 7

Factors(56) = 2 × 2 × 2 × 7

LCM (28, 42, 56) = 2 × 2 × 2 × 3 × 7 = 168

The smallest possible number divisible = 168 + 11 = 179

∴ The smallest possible number is 179.

Calculation:

By taking the option, 

3/2 + 1.5 = 1.5 + 1.5 = 3

∴ The option 1 is wrong.

Calculation:

The given fractions are 1/2, 1/3, 4/5, 5/6, 3/4

Now, the L.C.M. of the denominators (2, 3, 5, 6, 4) is 60.

Now, let's make each fraction an equivalent fraction of denominator 60.

1/2 = 30/60

1/3 = 20/60

4/5 = 48/60

5/6 = 50/60

3/4 = 45/60

Now, after looking at these equivalent fractions, we get that the largest fraction is 50/60 and the smallest fraction is 20/60.

Hence, the largest and smallest fractions are 5/6 and 1/3 respectively.

Calculation:
Let the two numbers be x and y.
x + y = 19 --- [1]
x - y = 7 --- [2]
By the method of elimination, we get
2x = 26
x = 26/2 = 13
Put x = 13 in eq [1], we get
13 + y = 19
y = 19 - 13
y = 6
Therefore, the two numbers are 13, 6
Sum of their squares = 13² + 6²
⇒ 169 + 36 = 205
Hence, 205 is the correct answer.