43865.$\left(\dfrac{a}{b}\right)^{x-1}=\left(\dfrac{b}{a}\right)^{x-3}$, then the value of x is:
1/2
1
2
7/2
Explanation:
Given $\left(\dfrac{a}{b}\right)^{x-1}=\left(\dfrac{b}{a}\right)^{x-3}$
$\Rightarrow \left(\dfrac{a}{b}\right)^{x-1}=\left(\dfrac{a}{b}\right)^{-(x-3)} = \left(\dfrac{a}{b}\right)^{3-x}$
$\Rightarrow$ x - 1 = 3 - x
$\Rightarrow$2x = 4
$\Rightarrow$x = 2.
Given $\left(\dfrac{a}{b}\right)^{x-1}=\left(\dfrac{b}{a}\right)^{x-3}$
$\Rightarrow \left(\dfrac{a}{b}\right)^{x-1}=\left(\dfrac{a}{b}\right)^{-(x-3)} = \left(\dfrac{a}{b}\right)^{3-x}$
$\Rightarrow$ x - 1 = 3 - x
$\Rightarrow$2x = 4
$\Rightarrow$x = 2.
43866.If 3(x - y)= 27 and 3(x + y) = 243, then x is equal to:
0
2
4
6
Explanation:
3(x - y)= 27=33 $\Leftrightarrow $x - y = 3 ....(i)
3(x + y) = 243=35 $\Leftrightarrow$ x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.
3(x - y)= 27=33 $\Leftrightarrow $x - y = 3 ....(i)
3(x + y) = 243=35 $\Leftrightarrow$ x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.
43867.If 5a = 3125, then the value of 5(a - 3) is:
25
125
625
1625
Explanation:
5a = 3125 $\Leftrightarrow$ 5a = 55
$\Rightarrow$ a = 5.
therefore, 5(a - 3) = 5(5 - 3) = 52 = 25.
5a = 3125 $\Leftrightarrow$ 5a = 55
$\Rightarrow$ a = 5.
therefore, 5(a - 3) = 5(5 - 3) = 52 = 25.
43871.Given that 100.48 = x, 100.70 = y and xz = y2 , then the value of z is close to:
1.45
1.88
2.9
3.7
Explanation:
xz = y2 $\Leftrightarrow$ 10(0.48z) = 10(2 x 0.70) = 101.40
$\Rightarrow$ 0.48z = 1.40
$\Rightarrow$ z =$\dfrac{140}{48}=\dfrac{35}{12}$= 2.9 (approx.)
xz = y2 $\Leftrightarrow$ 10(0.48z) = 10(2 x 0.70) = 101.40
$\Rightarrow$ 0.48z = 1.40
$\Rightarrow$ z =$\dfrac{140}{48}=\dfrac{35}{12}$= 2.9 (approx.)
43873.The value of [(10)150 ÷ (10)146]
1000
10000
100000
106
Explanation:
[(10)150 ÷ (10)146] = $\dfrac{10^{150}}{10^{146}}$
=10150-146
=104
=10000
[(10)150 ÷ (10)146] = $\dfrac{10^{150}}{10^{146}}$
=10150-146
=104
=10000
43874.(256)0.16 x (256)0.09 = ?
4
16
64
256.25
Explanation:
(256)0.16 x (256)0.09 =(256)0.16+0.09
= (256)0.25
= (256)(25/100)
= (256)(1/4)
= (44)(1/4)
= 44(1/4)
= 41
= 4
(256)0.16 x (256)0.09 =(256)0.16+0.09
= (256)0.25
= (256)(25/100)
= (256)(1/4)
= (44)(1/4)
= 44(1/4)
= 41
= 4
43875.If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:
1
10
121
1000
Explanation:
We know that 112= 121.
Putting m = 11 and n = 2, we get:
(m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000.
We know that 112= 121.
Putting m = 11 and n = 2, we get:
(m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000.
43876.$\dfrac{1}{1+a^{n-m}}+\dfrac{1}{1+a^{m-n}}=?$
0
1/2
1
am + n
Explanation:
$\dfrac{1}{1+a^{n-m}}+\dfrac{1}{1+a^{m-n}}=\dfrac{1}{\left(1+\dfrac{a^{n}}{a^{m}}\right)}+\dfrac{1}{\left(1+\dfrac{a^{m}}{a^{n}}\right)}$
=$\dfrac{a^{m}}{\left(a^{m}+a^{n}\right)}+\dfrac{a^{n}}{\left(a^{m}+a^{n}\right)}$
=$\dfrac{\left(a^{m}+a^{n}\right)}{\left(a^{m}+a^{n}\right)}$
=1
$\dfrac{1}{1+a^{n-m}}+\dfrac{1}{1+a^{m-n}}=\dfrac{1}{\left(1+\dfrac{a^{n}}{a^{m}}\right)}+\dfrac{1}{\left(1+\dfrac{a^{m}}{a^{n}}\right)}$
=$\dfrac{a^{m}}{\left(a^{m}+a^{n}\right)}+\dfrac{a^{n}}{\left(a^{m}+a^{n}\right)}$
=$\dfrac{\left(a^{m}+a^{n}\right)}{\left(a^{m}+a^{n}\right)}$
=1
43877.(17)3.5 x (17)? = 178
2.29
2.75
4.25
4.5
Explanation:
Let (17)3.5 x (17)? = 178.
Then, (17)3.5+x= 178.
therefore, 3.5 + x = 8
x = (8 - 3.5)
x = 4.5
Let (17)3.5 x (17)? = 178.
Then, (17)3.5+x= 178.
therefore, 3.5 + x = 8
x = (8 - 3.5)
x = 4.5
43878.(0.04)-1.5 = ?
25
125
250
625
Explanation:
(0.04)-1.5 =$\left(\dfrac{4}{100}\right)^{-1.5}$
=$\left(\dfrac{1}{25}\right)^{-(3/2)}$
= (25)(3/2)
= (5(2))(3/2)
= (52 x (3/2))
= 53
= 125
(0.04)-1.5 =$\left(\dfrac{4}{100}\right)^{-1.5}$
=$\left(\dfrac{1}{25}\right)^{-(3/2)}$
= (25)(3/2)
= (5(2))(3/2)
= (52 x (3/2))
= 53
= 125