Number Operations and Properties

when bases are same powers are added (in multiplication) and subtracted (in the division) 3⁴ * 3⁶ ÷ 3⁹ = 3^x3¹⁰ ÷ 3⁹ = 3^x3^10-9 = 3^x3¹ = 3^xx = 1This option is correct

1:(d) 28[Soln: an = a + (n - 1)× d⇒ 4 = a + (7 - 1) × -4⇒ 4 = a - 24⇒ a = 4 + 24 = 28]

See the pattern 1-3+4-6= -2-2-2....to 25 terms. =-50

90 + 32 = 122 is an even number.

31 + 41 = 72 is an even number.

This is the right answer.

Place value of “2” in units place = 2 x 1 = 2 Place value of “2” in thousand's place = 2 x 1000 = 2000 Therefore, difference = 2000 - 2 = 1998

H.C.F x L.C.M = Product of two numbers H.C.F = 1320/40 = 33

The prime factorisation of 36 = 2^{2 _$\times$} 3² The prime factorisation of 24 = 2^{3 _$\times$} 3 The prime factorisation of 72 = 2^{3 _$\times$} 3² 2 _^$\times$ 3 = 4 _^$\times$ 3 = 12

    It is clear from options.It is just expressed in mathematical form.

Let the number be $x$.

Since,

$ \dfrac{x}{2}=12 $

$ x=24 $

Since,

$ \Rightarrow \dfrac{3}{4}\times 24 $

$ \Rightarrow 18 $

Hence, this is the answer.

'Ekadhikena Purvena'   means  “by one more than the previous”
So, Ekadhikena Purvena of the number 99 is 100.

'Ekanyunena Purvena'   means  “by one less than the previous”
So, Ekadhikena Purvena of the number 99 is 99 - 1 = 98.

As we know, $1$ hour $=60$ minutes
So, $5$ hours $=5\times 60=300$ minutes.
Hence, $5$ hours $=300$ minutes.

$1\div 28=\dfrac { 1 }{ 28 } $