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1.

A ceiling fan is marked Rs.1940 cash or for Rs. 420 cash down payment followed by three equal monthly instalments. If the rate of interest charged under the instalment plan is 16% per annum, find the monthly instalment.

Answer» Market price=1940Rs
Down payment=420Rs
Let monthly installment=xRs
Total price=(3x_420)Rs
Intersect=(3x+420)-1940
(3x-1520)Rs
Buyer owes to seller in 1 month=1520Rs
Buyer owes to sellers in 2 months=1520-x
buyer owes to sellers in 3 months=1520-2x
total amount=4560-3x
Rate =16%
Interest=(P*R*T)/100
(3x-1520)=(4560-3x)*16/100
(3-1520)*75=(4560-3x)
228x=1520(3+75)
x=520Rs.
Discussion
2.

Find the value of x : `log_x 0.001 = -3`

Answer» `log_x(0.001) = -3`
`=>log(0.001)/logx = -3`
`=> log(0.001) = -3logx`
`=> log(0.001) = logx^-3`
`=>x^-3 = 0.001`
`=>x^-3 = 10^-3`
`=>x =10`
Discussion
3.

Show that `0. 2353535. . .=0. 2 bar 35`can be expressed in the form `p/q`, where p and q are integers and `q!=0`.

Answer» `x= 0.2 bar35`
multiply by 10
`10x= 2.bar 35` eqn(1)
multiply b 100
`1000x= 235.bar35` eqn(2)
subtracting eqn (2)- (1)
`990x = 233`
`x= 233/990`
answer
Discussion
4.

Express the following in the form `P/q` where p and q are integers and `q ne 0.` (i) 0.2 , (ii) 0.888…. , (iii) `5.bar2` (iv) `0. bar(001)` , ( v) 0.2555…. ,(vi) `0.1bar(34)` (vii) 0.00323232….. ,(vii) 0.404040…

Answer» Let `x=0.2 =2/10 -1/5`
(ii) Let x=0.888…….
On multiplying both sides of Eq.(i) by 10 we, get
10 x. 8.888…….
On subtracting Eq. (i) from Eq. (ii),we get
10x-x=(8.88) - (0.888)
9x=8
`x=8/9`
(iii) Let `x=5.bar2=5.222.... `
On multiplying both sides of Eq. (i) by 10, we get
10x=52.222......
On subtracting Eq. (i) from Eq. (ii) , we get
10x-x=(52.222.....)-(5.222......)
9x =47
`x=47/9`
(v) Let `x=0.bar(001)`
`x=0.bar(001) = 0.001001`
On multiply both sides of Eq. (i) by 1000, we get
1000x=001.001.....
On subtrating Eq. (i) from Eq. (ii) we, get
`1000x-x=001.001 .... -(0.001001....)`
999x = 001
`x=1/999`
Let x= 0.2555......
On multplying both sides of Eq. (i) by 10, we get
10x=2.555....
On multiplying both sides of Eq. (ii) by 10, we get
100x=25.55......
On subtracting Eq. (ii) from Eq. (iii) , we get
100x-10x=25.55...-(2.555...)
90x=23
`x=23/90`
(vi) Let `x= bar(134)`
`x=0 bar(134)= 0.13434......`
On multiplying both sides of Eq. (i) by 10, we get
10x=13434.........
On multplying both sides of Eq. (ii) by 100 , we get
1000x= 134.3434.........
On subtracting Eq. (ii) from Eq. (iii) we, get
100x-10x= 134.34..... -(1.3434....)
990x=133
`x=133/990`
(vii) Let x= 0.00323232
On Multiplying both sides of Eq. (i) by 100 we get
100x = 0.3232......
On multiplying both sides of Eq. (ii) by 100 , we get
1000x=32.3232.........
On subtracting Eq. (ii) [from Eq. (iii) we get
1000x-100x=32.32 ......-0.3232.......
9900x=32
x=`32/9900 = 8/2475` [dividing numerator and denominator by 4]
(viii) Let x=0.404040.
On multiplying both sides of eq. (i) by 100, we get
100x = 40.4040
On subtracting Eq. (i) from (ii),we get
100x -x =40.4040 ...... - 0.404040.......
99x =40
`x= 40/99`
Discussion
5.

The value of `1.999`….. In the form of `p/q`, where p and q are integers and `q ne 0`, isA. `(19)/(10)`B. `(1999)/(1000)`C. `2`D. `1/9`

Answer» Correct Answer - C
Let `x = 1.999"…."`
Now, `10x = 19.999"…."`
On subtracting Eq. (i) from Eq. (ii), we get
`10x - x = (19.999…) - (1.9999……)`
`rArr 9x = 18`
`:. x = (18)/(9) = 2`
Discussion
6.

Express `0.6+0.bar7+0.4bar7` in the form `p/q` where p and q are integers and `q ne 0`.

Answer» Let `x=0.bar7= 0.777`
on multiplying both sides of Eq. (i) by 10, we get
10x=7.77…..
on subtrracting Eq. (i) from Eq. (ii) we get
10x-x= (7.77…)-(0.77….)
9x=7
`x=7/9`
now let `y=0.4bar7 =0.4777…..`
on multiplying both sides of Eq. (ii) by 10, we get
10y= 4.777....
on multiplying both sides . Eq . (iv) by 10, we get
100y= 47.777.....
on subtracting Eq. (iv) from (v), we get
(100y-10y)= (47.777....) - (4.777....)
90y = 43 `43/90`
`0.6 + 0.bar7+ 0.4bar7=6/10 + 7/9+43/90`
`(54+70+43)/90=167/90`
Discussion
7.

If `2^(-m)xx(1)/(2^(m))=(1)/(4)` then `(1)/(14)[(4^(m))^(1//2)+((1)/(5^(m)))^(-1)]`=_______A. `(1)/(2)`B. 2C. 4D. `(-1)/(4)`

Answer» Correct Answer - A
Find the value of m.
Discussion
8.

If `m` and `n` are positive integers, then for a positive number `a, {root(m)((root(n)(a)))}^(mn)`=_______A. `a^(mn)`B. aC. `a^(m//n)`D. 1

Answer» Correct Answer - B
Recall the laws of radicals
Discussion
9.

MNOP is a parallelogram. Q and R are point on sides MN and ON respectively. `(trianglePRM)=12cm^2`, find `ar(trianglePOQ)`

Answer» `Delta PRM` and parallelogram `MNOP` have same base and `R` is a point on side `ON` of the parallelogram.
`:. ar(MNOP) = 2**ar(PRM) = 2**12 = 24cm^2`
Now, `Delta POQ` and parallelogram `MNOP` have same base `PO` and `Q` is a point on side `MN` of the parallelogram.
`:. ar(MNOP) = 2**ar(DeltaPOQ)`
`=> ar (Delta POQ) = 24/2 = 12cm^2`
Discussion
10.

If `a=(3+sqrt5)/2` then find the vaule of `a^(2)+1/(a^(2))`

Answer» `given , a=(3+sqrt5)/2`
`1/a=2/(3+sqrt5)=2/(3+sqrt5)xx(3-sqrt5)/(3-sqrt5)`
[multiplying numerator and denominator by `3-sqrt5`)
`(6-2sqrt5)/(3^(2)-(sqrt5)^(2)) " " ["using identity" , (a-b)(a+b)=a^(2)-b^(2)]`
`(6-2sqrt5)/(9-5)=(6-2sqrt5)/4`
`1/a=(2(3-sqrt5))/4=(3-sqrt5)/2`
`a^(2)+1/(a^(2))a^(2)+1/a^(2)+2-2=(a+1/a)^(2)-2" " ["adding and subtarcting2"]`
`((3+sqrt5)/2+(3-sqrt5)/2)^(2)-2 " " ["from Eqs. (i)and (ii)"]`
`(6/2)^(2)-2=(3)^(2)-2=9-2=7`
Discussion
11.

The following number of goals were scored by a team in a series of 10 matches 2, 3, 4, 5, 0 1, 3, 3, 4, 3 Find the mean, median and mode of these scores.

Answer» First we arrange scores in ascending order.
Scores in ascending order are `0,1,2,3,3,3,3,4,4,5.`
`:.` Mean of the scores ` = (0+1+2+3+3+3+3+4+4+5)/10 = 28/10 = 2.8`
Median will be the mean of `(10/2)^(th) and (10/2+1)^(th)` terms.
`:.` Median `= (T_5+T_6)/2 = (3+3)/2 = 3`
Mode is `3` as it has maximum frequency and appeared `4` times in the given data.
Discussion
12.

If `x=(sqrt3+sqrt2)/(sqrt3-sqrt2)andy=(sqrt3-sqrt2)/(sqrt3+sqrt2)` then find the value of `x^(2)+y^(2)` ?

Answer» `given , a=(3+sqrt5)/2`
`1/a=2/(3+sqrt5)=2/(3+sqrt5)xx(3-sqrt5)/(3-sqrt5)`
[multiplying numerator and denominator by `3-sqrt5`)
`(6-2sqrt5)/(3^(2)-(sqrt5)^(2)) " " ["using identity" , (a-b)(a+b)=a^(2)-b^(2)]`
`(6-2sqrt5)/(9-5)=(6-2sqrt5)/4`
`1/a=(2(3-sqrt5))/4=(3-sqrt5)/2`
`a^(2)+1/(a^(2))a^(2)+1/a^(2)+2-2=(a+1/a)^(2)-2" " ["adding and subtarcting2"]`
`((3+sqrt5)/2+(3-sqrt5)/2)^(2)-2 " " ["from Eqs. (i)and (ii)"]`
`(6/2)^(2)-2=(3)^(2)-2=9-2=7`
Discussion
13.

Find the value of `(sqrt(32)+sqrt(48))/(sqrt(8)+sqrt(12))`

Answer» `(sqrt32+sqrt48)/(sqrt8+sqrt12) = (sqrt(8**4)+sqrt(12**4))/(sqrt8+sqrt12) `
`=(2(sqrt8+sqrt12))/(sqrt8+sqrt12) = 2`
`:. (sqrt32+sqrt48)/(sqrt8+sqrt12) = = 2`
Discussion
14.

Simplify:`4/((216)^(-2/3))+1/((256)^(-3/4))+2/((243)^(-1/5))`

Answer» `4/((216)^(-3/4))+1/((257)^(-3/4))+2/((243)^(-1/5.))`
`4/((6^(3))^(-2/3))+1/((16^(2))^(-3/4))+2/((3^(5))^(-1/5))`
`4/(6^(3xx(-2/3)))+1/(16^(2xx(-3/4)))+2/((3^(5))^(-1/5))`
`4/(6^(2))+1/(16^(-3/2))+2/(3^(-1))`
`4xx6^(2)+16^(3/4)+2xx3^(1)`
`4xx36+((4)^(2))^(3//2)+2xx3^(1)`
`4xx36+4^(3)+6`
`144+64+6=214`
Discussion
15.

Simplify:`(256)^-(4^(((-3)/2)))`

Answer» `(256)^-(4^(-3/2))=(256)^((-4)^(-3/2)=(256)^((2^(2)))^(-(3)/(2))`
`=(256)^(-(2^(2xx-3/2)))=(256)^(-(2^(-3)))`
`(2^(8))^((1/2^(3)))=(2^(8))^(-1/8)`
`2^(8xx-1/8)=2^(-1=1/2)`
Discussion
16.

Find the value of `(sqrt(32)+sqrt(48))/(sqrt(8)+sqrt(12))`A. `sqrt2`B. 2C. 4D. 8

Answer» Correct Answer - B
`(sqrt(32)+sqrt(48))/(sqrt8+sqrt(12))=(sqrt(16xx2)+sqrt(16xx3))/(sqrt(4xx2)+sqrt(4xx3)`
`(4sqrt2+4sqrt3)/(2sqrt2+2sqrt3)=(4(sqrt2+sqrt3))/(2(sqrt2+sqrt(3)))=2`
Discussion
17.

L.C.M of two numbers is 48. If two numbers are in ratio 2:3, sum of the two numbers is ?

Answer» Let two number are `2x` and `3x`. Then, their `LCM` will be `6x`.
`:. 6x = 48 => x = 8`
So, the numbers are `16` and `24`.
`:.` Sum of these two numbers ` = 16+24 = 40`
Discussion
18.

Factorise `a^2x^2+(ax^2+1)x+a`

Answer» `a2x^2+(ax^2+1)x+a`
`=a^2x^2+ax^3+x+a`
`=ax^3+a^2x^2+x+a`
`=ax^2(x+a)+1(x+a)`
`=(ax^2+1)(x+a)`, which are the required factors.
Discussion
19.

`sqrt(7+sqrt(48))`=______

Answer» Correct Answer - `2+sqrt(3)`
Discussion
20.

factorize(i) 4(a+b) - 6`(a+b)^2`(ii)`8(3a-2b)^2 -10(3a-2b) `

Answer» 1) `4(a+b)-6(a+b)^2`
=(a+b)(4-6(a+b))
=(a+b)(4-6a-6b)
2)`8(3a-2b)^2-10(3a-2b)`
2(3a-2b)(4(3a-2b)-5)
2(3a-2b)(12a-8b-5).
Discussion
21.

`(256)^(0. 16)xx(256)^(0. 09)=?``4`b. `16`c. `64`d. `256. 25`A. 4B. 16C. 64D. 256.25

Answer» Correct Answer - A
`(256)^(0.18)xx(256)^(0.09)=(256)^(16/100)xx(256)^(9/100)`
`(256)^((16/100+9/100))`
`(256)^(25/100)=(256)^(1/4)`
`(4^(4))^(1/4)=4`
Discussion
22.

Factorize: `x^2+xy-2xz-2yz`

Answer» `x^2 + xy - 2xz -2yz`
`= x(x+y) - 2z(x +y)`
`= (x+y)(x--2z) `
answer
Discussion
23.

Factorise `y^2+2y-48`

Answer» `y^2 +2y-48`
`y^2 +8x-6y-48`
`y(y+8)-6(y+8)`
`(y-6)(y+8)`
`y= -8,6`
answer
Discussion
24.

Factorize: `12(2x-3y)^2-16 (3y-2x)`

Answer» `12(2x-3y)^2 - 16(3y-2x)`
`= 12(2x-3y) + 16(2x-3y)`
`= 4(2x-3y)(3(2x-3y)+4)`
`= 4(2x-3y)(6x-9y+4)`
`= 4(2x-3y)(6x-9y+ 4)`
`= (8x-12y)(6x-9y+4)`
answer
Discussion
25.

Which of the following surd is the smallest ? `sqrt(10)-sqrt(5),sqrt(19)-sqrt(14),sqrt(22)-sqrt(17) and sqrt(8)-sqrt(3)`A. `sqrt(10)-sqrt(5)`B. `sqrt(19)-sqrt(14)`C. `sqrt(22)-sqrt(17)`D. `sqrt(8)-sqrt(3)`

Answer» Correct Answer - C
Rationalize each binomial.
Discussion
26.

If `x=(1)/(sqrt(3)+2)`, then `(x+(1)/(x))^(2)`=______A. 16B. 3C. 12D. 6

Answer» Correct Answer - A
Given that `x=(1)/(sqrt(3)+2)`
`implies x=(2-sqrt(3))/((2+sqrt(3))(2-sqrt(3)))`
`implies x=(2-sqrt(3))/(4-3)`
`implies x=2-sqrt(3)`
And `(1)/(x)=sqrt(3)+2`
Now `(x+(1)/(x))^(2)=(2-sqrt(3)+sqrt(3)+2)^(2)`
`=(4)^(2)=16`
Discussion
27.

`(root(3)(3))^(4)` =________ .

Answer» Correct Answer - `3xxroot(3)(3)`
Discussion
28.

The perimeter of a triangular field is 540 m and its sides are in the ratio `25: 17:12`. Find the area of the triangle. Also, find the cost ploughing the field at `Rs. 18.80` per `10 m^2`

Answer» perimeter =540m
25x+17x+12x=540m
54x=540m
x=10m
sides of triangle are
25x=250m
17x=170m
12x=120m
S=250+170+120/2=270
area of triangle=`sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(270(270-250)(270-170)(270-120))`
=9000`m^2`
cost
10`m^2`=18.80Rs
1`m^2`=1.880Rs
9000`m^2`=9000*1.880=16920Rs.
Discussion
29.

If `root(x)(3)xxroot(y)(5)=10125`, then `12xy` =________.A. 1B. `1/3`C. 2D. `1/2`

Answer» Correct Answer - A
`root(x)(3)xxroot(y)(5)=10125`
`3^(1//x).51^(1//y)=3^(4)xx5^(3)`
`implies (1)/(x)=4, (1)/(y)=3`
`implies 4x=1, 3y=1`
`implies 12xy=1`
Discussion
30.

`sqrt(sqrt(63)+sqrt(56))=`A. `root(4)(7)(sqrt(3)+sqrt(5))`B. `root(4)(7)(sqrt(3)+1)`C. `root(4)(7)(sqrt(3)+sqrt(5))`D. `root(4)(7)(sqrt(2)+1)`

Answer» Correct Answer - D
(i) Bring a possible term out of the root.
(ii) `sqrt(sqrt(63)+sqrt(56))=root(4)(7)sqrt(sqrt(7)+sqrt(8))`
(iii) Let `sqrt(3+2sqrt(2))=sqrt(x)+sqrt(y)`
Discussion
31.

If `a=sqrt(17)-sqrt(16) and b=sqrt(16)-sqrt(15)` thenA. `a lt b`B. `a gt b`C. `a=b`D. None of these

Answer» Correct Answer - A
(i) If `a gt b ` , then `(1)/(a) lt (1)/(b)`
(ii) Rationalize the numerators of given surds and then compare.
Discussion
32.

If `x=(1)/(5+2sqrt(6))` , then `x^(2)-10x+1=`_______.A. 1B. `-1`C. 1D. 10

Answer» Correct Answer - C
`x=(1)/(5+2sqrt(6))`
`x=(5-2sqrt(6))/(25-24) =x =5-2sqrt(6)`
`(1)/(x)=5+2sqrt(6) implies x+(1)/(x)=10`
`x^(2)+1=10x implies x^(2) -10x+1=0`
Discussion
33.

`(root(6)(15-2sqrt(56)))*(root(3)(sqrt(7)+2sqrt(2)))`=_______.

Answer» Correct Answer - C
`(root(6)(15-2sqrt(56)))(root(3)(sqrt(7)+2sqrt(2)))`
`root(3)(sqrt(15-2sqrt(56)))root(3)(sqrt(7)+2sqrt(2))`
`=root(3)(sqrt(8)-sqrt(7))root(3)(sqrt(7)+sqrt(8))=root(3)(8-7)=1`
Discussion
34.

`sqrt(x^(2)sqrt(9^(2)sqrt((81)^(2)sqrt(16)^(16))))`=______.A. `6xx2^(4)`B. `3^(3)xx2`C. `6^(3)xx2^(3)`D. `6^(3)xx2`

Answer» Correct Answer - D
`sqrt(3^(2)sqrt(9^(2)sqrt((81)^(2)sqrt(16^(16)))))`
`=(3^(2))^(1//2)xx(9^(2))^(1//4)xx[(81)^(2)]^(1//8)xx[(16)^(16)]^(1//16)`
`=3xx3xx3xx16=6^(3)xx2`
Discussion
35.

Express the following surds with rational denominators `(a) 2/sqrt14 (b) (2.3^(1/3))/25^(1/3)`

Answer» (a) `(2)/(sqrt(14))xx(sqrt(14))/(sqrt(14))=(2sqrt(14))/(14)=(sqrt(14))/(7)`
(b) `(2root(3)(3))/(root(3)(25))=(2root(3)(3))/(root(3)(25))xx(root(3)(5))/(root(3)(5))=(2root(3)(3xx5))/(root(3)(5^(3)))=(2root(3)(15))/(5)`
Discussion
36.

If `(3^(5x)xx(81)^(2)xx6561)/(3^(2x))=3^(7)` , then x =_______A. 3B. `-3`C. `(1)/(3)`D. `(-1)/(3)`

Answer» Correct Answer - B
Apply laws of indices.
Discussion
37.

Two mixed quadratic surds, `a + sqrt(b) and a-sqrt(b)`, whose sum and product are rational , are called _____ surds.

Answer» Correct Answer - conjugate
Discussion
38.

Arrange the following in ascending or descending order of magnitude: `root(6)(6)root(3)(7),sqrt(5)`

Answer» `root(4)(6)=6^(1//4),root(3)(7)=7^(1//3),sqrt(5)=r^(1//2)`
LCM of the denominators of the exponents of these three terms, 4,3 and 2 is 12.
Now express the exponent of each term, as a fraction in which the denominator is 12.
`6^((1)/(4))=6^((3)/(12))=(6^(3))^((1)/(12))=root(12)(216)`
`7^((1)/(3))=7^((4)/(12))=(7^(4))^((1)/(12))=root(12)(2401)`
`5^((1)/(2))=5^((6)/(12))=(5^(6))^((1)/(12))=root(12)(15625)`
Now `root(4)(6)=root(12)(216),root(3)(7)=root(12)(2401),sqrt(5)=root(12)(15625)`
Hence , their ascending order is
`root(12)(216),root(12)(2401), root(12)(15623),` i.e., `root(4)(6), root(3)(7), sqrt(5)`
`therefore` The descending order of magnitude of the given radicals is `sqrt(5),root(3)(7), root(4)(6)`.
Discussion
39.

If the product of two surds is a rational number,then each of the two is a _____ of the other

Answer» Correct Answer - rationalizing factor
Discussion
40.

Find the remainder when `f (x) = 12x^3 -13x^2 -5x +7` is divided by `(3x+2)`.

Answer» `f(x) = 12x^3 -13x^2 - 5x + 7`
`3x+ 2 = 0`
`x = -2/3`
now as `f(x) = p(g(x)) + R`
`f(-2/3) = p(g(-2/3)) + R`
`f(-2/3) = R`
`R= 12(-2/3)^3 - 13(-2/3)^2 - 5(-2/3) + 7`
`= 12*(-8/27) - 13*4/9 + 10/3 + 7`
`= -32/9-52/9 + 10/3 + 7`
`= (-32-52+30+63)/9`
`= (-84+93)/9`
`= 9/9 = 1` remainder
answer
Discussion
41.

If `x=2^(1//3)-2`, then `x^(3)+6x^(2)+12x`=_______A. 6B. `-6`C. 8D. `-8`

Answer» Correct Answer - B
Given `x=2^(1//3)-2`
`implies x+2=2^(1//3)`
Taking the cubes of the terms on both the sides ,
`implies (x+2)^(3)=(2^(1//3))^(3)`
`implies x^(3)+6x^(2)+12x=-6`
Discussion
42.

Arrange the following surds in an ascending order of magnitude : `root(3)(4),root(4)(5),sqrt(8)`

Answer» Correct Answer - `root(4)(5),root(3)(4),sqrt(8)`
Discussion
43.

(a) `sqrt15xxsqrt35.` (b) `2sqrt3 div3sqrt27.` (c ) Muliple `root(3)(3)" by " root(4)(2).`(d) Divide `""root(6)(5)" by "root(3)(10).`

Answer» `(a) (sqrt15)(sqrt35)=sqrt((15)(35))=sqrt((5)(3)(5)(7))=5sqrt(21).`
(b) `2sqrt3div3sqrt27=(2sqrt3)/(3sqrt27`
`=(2sqrt3)/((3)sqrt(3^(2)(3)))=(2sqrt3)/((3)(3)sqrt3)9/3.`
(c ) `""^(3)sqrt3=3^(1//3)and""^(4)sqrt2=2^(1//4)`
The LCM of 3 and 4 is 12
`therefore3^(1//3)=3^(4//12)=""^(12)sqrt(3^(4))`
`2^(1//4)=2^(3//12)=""^(12)sqrt(2^(3))`
`(""^(3)sqrt3)(""^(4)sqrt2)=(""^(12)sqrt(3^(4)))(""^(12)sqrt(2^(3)))`
`=""^(12)sqrt((3^(4))(""^(12)sqrt(2^(3))))`
`=""^(12)sqrt((81)(8))=""^(12)sqrt(648).`
(d) `""^(6)sqrt5=5^(1//6)`
LCM of 3 and 6 is 6
`""^(3)sqrt10=10^(1//3)=10^(2//6)=""^(6)sqrt(10^(2))=""^(6)sqrt100`
`therefore(""^(6)sqrt5)/(""^(3)sqrt10)=(""^(6)sqrt10)/(""^(6)sqrt100)`
`=""^(6)sqrt((5)/(100))=""^(6)sqrt((1)/(20)).`
Discussion
44.

Arrange the following surds in an ascending order of magnitude: `root(3)(9),root(9)(5),root(3)(7)`

Answer» Correct Answer - `root(9)(5),root(6)(9),root(3)(7)`
Discussion
45.

Express the following in the simplest form : `root(4)(root(5)(1048576))`

Answer» Correct Answer - 2
Discussion
46.

If `x=1+5^(1/3)+5^(2/3)` then find the value of `x^3-3x^2-12x+6.`A. 22B. 20C. 16D. 14

Answer» Correct Answer - A
Discussion
47.

Divide :` root(6)(144)` by `root(6)(4)`.

Answer» Correct Answer - `root(6)(36)`
Discussion
48.

`(3)/(7)` lies between the fractions _______.A. `(4)/(9),(5)/(9)`B. `(43)/(99),(4)/(9)`C. `(42)/(99),(4)/(9)`D. `(41)/(99),(42)/(99)`

Answer» Correct Answer - C
`(3)/(7)=0.bar(428571)`
(a) `(4)/(9)=0.444…. (5)/(9)=0.555…`
(b) `(43)/(99)=0.434343… (4)/(9)=0.4444 ….`
(c) `(4)/(9)=0.4444… (42)/(99)=0.424242…`
(d) `(41)/(99)=0.0414141… (42)/(99)=0.424242 …`
Discussion
49.

If `x=(1)/(2-sqrt(3))`, the value of `x^(3)-2x^(2)-7x+10` is equal toA. `2+sqrt(3)`B. 10C. `7+2sqrt(3)`D. 8

Answer» Correct Answer - D
Discussion
50.

Classify the following numbers as rational or irrational:(i) `2-sqrt(5)` (ii) `(3+sqrt(23))-sqrt(23)` (iii) `(2sqrt(7))/(7sqrt(7))` (iv) `1/(sqrt(2))` (v) `2pi`

Answer» (i) `2-sqrt(5) = 2-2.23606797... = -0.23606797...`Since, decimal representation of this number is non-terminating, it is an irrational number.

(ii)`(3+sqrt(23))-sqrt23 = 3 = 3/1`Since, the above number can be represented as `p/q`, where both `p` and `q` are integers, this number is rational number.

(iii)`(2sqrt7)/(7sqrt7) = 2/7`Since, the above number can be represented as `p/q`, where both `p` and `q` are integers, this number is rational number.

(iv)`1/sqrt2 = 0.70710678...`
Since, decimal representation of this number is non-terminating, it is an irrational number.

(v)`2pi = 2(3.14159265...) = 6.28318530...`
Since, decimal representation of this number is non-terminating, it is an irrational number.
Discussion