Mathematics Paper 2 (Surds & Indicies) - CTET & State TET MCQ

Given : 

Formula used : 

a² - b²  = (a + b)(a - b)

Calculation : 

Let the unknown number be x.

⇒ (8 × 3 + 5 × 3) × (7× 3 + 6 × 3) - 32 × 32 = x

⇒ (24 + 15) × (21 + 18) - 32 × 32 = x 

⇒ 39 × 39 - 32 × 32  = x 

⇒ 39² - 32² = x 

⇒ (39 + 32 )( 39 - 32) = x

⇒ 71 × 7 = x

⇒ x = 497 

∴ Option (1) is the correct answer.

Calculation:

⇒ 2y-4  × 6y-4 = 12-4

⇒  2y-4  × 6y-4 = 1/12⁴

⇒ 2y-4  × 6y-4 = 1/ 2⁴ × 6⁴

⇒ 2^y × 6^y = 1

⇒ 2y × 6y = 2⁰ × 6⁰

We can see the value of y = 0

Now putting the value of y in (2y - 8) :

⇒ (2 × 0 - 8) = - 8

∴ The correct answer is -8.

Calculation:

51 ÷ {25 + (25 of 12 ÷ 30) - (5⁴ ÷ 5 of 125)}

⇒ 51 ÷ {25 + (25 ×  12 / 30) - (5⁴ ÷ 5× 5³)}

⇒ 51 ÷{25 + (25 ×  12 / 30) - 1}

⇒ 51 ÷ {25 + 10 - 1}

⇒ 51 ÷ 34 = 3/2

∴ The correct option is 2

Calculations:

⇒  (1/4 + 1/8)/(3/2) = (1/2)^{2x - 1}

⇒  (3/8) × (2/3) = (1/2)^2x-1

⇒ 1/4 = (1/2)^2x-1

⇒  (1/2)² = (1/2)^{2x - 1}

⇒  2 = 2x - 1

⇒ x = 3/2

so

x² + x - 2 = (3/2)² + 3/2 - 2 

⇒ 9/4 - 1/2

⇒ 7/4

Given:

(256)0.16 × (256)0.09 = ?

Calculation:

(256)0.16 × (256)0.09 = ?

Let the unknown number be x.

⇒ (256)0.16 × (256)0.09 = x

⇒ (256)(0.16 + 0.09) = x 

⇒ (256)0.25 = x

⇒ x = (44)1/4 = 4

∴ (256)0.16 × (256)0.09 = 4

Given:

(92 + 43 ÷ 8) × 5

Concept used:

Calculation

(92 + 43 ÷ 8) × 5

⇒ (81 + 64 ÷ 8) × 5

⇒ (81 + 8) × 5

⇒ 89 × 5

⇒ 445

Formula Used:

• a^m × aⁿ = a^m+n
• am  ÷ an = am-n 
• (ab)^m = a^m.aⁿ​^​

Calculation:

We have  

⇒ 

⇒   [Using Formula]

⇒ 2^3-3 × 3^4-3 × 5^3+2-5 = 3 

∴ The right answer is 3.

Given:

The expression 

Concept used:

a^n×(1/m) = a^n/m 

Calculation:

We know that, 8 = 2³ and 125 = 5³

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 7

Hence, the value of the expression is 7.

Calculation : 

⇒ (3/2)³/ (1/2)² × (2/3)²

⇒ 27/8 × 4 × 4/9

⇒ 3 × 2 = 6

Reciprocal of x = 1/6

∴ The correct answer is 1/6.

Given:

7-1 × 3-3

Concept used:

The value, which on adding with the original number results in zero value.

Calculation:

Let's assume the additive inverse of 7-1 × 3-3 be k, then,

⇒ 7-1 × 3-3 + k = 0

⇒ k = - [7-1 × 3-3]

⇒ k = - [ 1/7 × 1/27] = - 1/189

∴ The correct answer is −1/189