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1.

`8^(2//3)` के बराबर है ?A. `5 1/2`B. `21 1/3`C. `4`D. `3 1/2`

Answer» Correct Answer - C
`8^(2/3)=(2^(3))^(2/3)`
`implies2^(3xx2/3)`
`implies2^(2)=4`
Discussion
2.

`(sqrt(8)-sqrt(4)-sqrt(2))` के बराबर है?A. `2-sqrt(2)`B. `sqrt(2)-2`C. `2`D. `-2`

Answer» Correct Answer - B
`(sqrt(8)-sqrt(4)-sqrt(2))`
`implies2sqrt(2)-2-sqrt(2)`
`implies 2sqrt(2)-sqrt(2)-2`
`impliessqrt(2)-2`
Discussion
3.

`root(3)(0.00125)` का मान क्‍या है?A. `0.005`B. `0.05`C. `0.5`D. `0.005`

Answer» Correct Answer - B
`root(3)(0.000125)`
`implies root(3)(0.05xx0.05xx0.05)implies0.05`
Discussion
4.

यदि `(3x-2y): (2x+3y)=5:6` तो `((root(3)(x)+root(3)(y))/(root(3)(x)-root(3)(y)))` का मान क्या है?A. `1/25`B. `5`C. `1/5`D. `25`

Answer» Correct Answer - D
`(3x-2y)/(2x+36)=5/6`
`18x-12y=10x+15y`
`8x=27y`
`x/y=27/8`
`=[(root(3)(x)+root(3)(y))/(root(3)(x)-root(3)(y))]^(2)`
`=((root(3)(27)+root(3)(8))/(root(3)(27)-root(3)(8)))^(2)`
`implies ((3+2)/(3-2)^(2))=(5)^(2)=25` Ans.
Discussion
5.

`sqrt(5)=2.236` and `sqrt(3)=1.732` दिया गया है तो `1/(sqrt(5)+sqrt(3))` का मान क्या है?A. `0.564`B. `0.504`C. `0.252`D. `0.202`

Answer» Correct Answer - C
`1/(sqrt(5)+sqrt(3))xx(sqrt(5)-sqrt(3))/(sqrt(5)-sqrt(3))=(sqrt(5)-sqrt(3))/(5-3)implies(2.236-1.732)/2`
`implies 0.504/2=0.252`
Discussion
6.

दिया गया है `sqrt(2)=1.414` तो `1/(sqrt(2)+1)` का मान क्या है?A. `0.414`B. `2.414`C. `3.414`D. `5.414`

Answer» Correct Answer - A
`1/(sqrt(2)+1)`
`implies1/(sqrt(2)+1)xx(sqrt(2)-1)/(sqrt(2)-1)`
`implies1/(sqrt(2)+1)xx(sqrt(2)-1)/(sqrt(2)-1)`
`implies(sqrt(2)-1)/(2-1)=(sqrt(2)-1)`
`implies 1.414-1`
`implies 0.414`
Discussion
7.

यदि `3^(x+8)=27^(2x+1)`, है तो `x` का मान क्या है ?A. 7B. 3C. `-2`D. 1

Answer» Correct Answer - D
`3^(x+8)=27^(2x+1)`
`3^(x+6)=(3^(3))^(2x+1)`
`3^(x+8)=3^(6x+3)`
`x+8=6x+3`
`5x=5, x=1`
Discussion
8.

यदि `sqrt(3)=1.732` दिया गया है तो `(2+sqrt(3))/(2-sqrt(3))` का मान क्या है?A. 11.732B. 13.928C. 12.928D. 13.925

Answer» Correct Answer - B
`sqrt(3)=1.732`
`implies(2+sqrt(3))/(2-sqrt(3))xx(2+sqrt(3))/(2+sqrt(3))`
`implies((2+sqrt(3))^(2))/(4-3)`
`implies4+3+4sqrt(3)`
`implies7+4xx1.732`
`implies 7+6.928implies13.928`
Discussion
9.

यदि `27^(2n-1)=(243)^(3)` है तो `n` का मान ज्ञात करें।A. 3B. 6C. 7D. 9

Answer» Correct Answer - A
`23^(2n-1)=243^(3)`
`3^(3(2n-1)=3^(5xx3)`
`3^(6n-3)=3^(15)`
`6n-3=15`
`6n=18`
`n=18/6,n=3`
Discussion
10.

यदि `x=1+sqrt(2)+sqrt(3)` है तो `(x+1/(x-1))` का मान क्या है?A. `1+2sqrt(3)`B. `2+sqrt(3)`C. `3+sqrt(2)`D. `2sqrt(3)-1`

Answer» Correct Answer - A
`x=1+sqrt(2)+sqrt(3)`
`implies x+1/(x-1)`
`implies 1+sqrt(2)+sqrt(3)+1/(1+sqrt(2)+sqrt(3)-1)`
`implies1+sqrt(2)+sqrt(3)+(sqrt(3)-sqrt(2))/(3-2)`
`implies 1+2sqrt(3)`
Discussion
11.

यदि `x+1/x=-2` है तो `x^(2n+1)+1/(x^(2n+1))` का मान क्या है, जहां `n` एक धनात्मक पूर्णांक है।

Answer» Correct Answer - C
Shortcut method
`x+1/x=-2`
Let `x=-1`
`implies-1+1/(-1)=-2` (matched so `x=-1`)
Put `n=1`
`x^(2n+1)+1/(x^(2n+1))`
`impliesx^(3)+1/(x^(3))implies(-1)^(3)+1/((-1)^(3))=-2`
Discussion
12.

`((5.624)^(3)+(4.376)^(3))/(5.624xx5.624-(5.624xx4.376)+4.376xx4.376)` के बराबर है।A. 10B. 1.248C. 20.44D. 1

Answer» Correct Answer - A
`a=5.624,b=4.376`
`implies(a^(3)+b^(3))/(a^(2)-ab+b^(2))=((a+b)(a^(2)+b^(2)-ab))/(a^(2)-ab+b^(2))`
`implies(a+b)`
`implies5.624+4.376implies10`
Discussion
13.

`1/(sqrt((12-sqrt(140))))-1/(sqrt((8-sqrt(60))))-2/(sqrt(10+sqrt(84)))` का मान ज्ञात करें।

Answer» Correct Answer - A
`1/(sqrt((12-sqrt(140))))-1/(sqrt((8-sqrt(60))))`
`2/(sqrt((10+sqrt(84))))`
`implies1/(sqrt(12-sqrt(4xx35)))-1/(sqrt(8-sqrt(4xx15)))`
`-2/(sqrt(10+sqrt(4xx21)))`
`implies1/(sqrt(12-2sqrt(35)))-1/(sqrt(8-2sqrt(15)))-2/(sqrt(10+2sqrt(21)))`
`implies 1/(sqrt((sqrt(7))^(2)+(sqrt(5))^(2)-2sqrt(7)sqrt(5)))-1/(sqrt((sqrt(5)^(2)+(sqrt(3)^(2)-sqrt(5)sqrt(3)))-`
`2/(sqrt((sqrt(7))^(2)+(sqrt(3))^(2)-2sqrt(7)sqrt(3)))`
`implies1/(sqrt((sqrt(7)-sqrt(5))^(2)))1/(sqrt((sqrt(5)-sqrt(3))^(2)))-2/(sqrt((sqrt(7)+sqrt(3))^(2)))`
`implies1/(sqrt(7)-sqrt(5))-1/(sqrt(5)-sqrt(3))-2/(sqrt(7)-sqrt(3))`
Relationlizing in above equation.
`implies1/(sqrt(7)-sqrt(5))xx(sqrt(7)+sqrt(5))/(sqrt(7)+sqrt(5))-1/(sqrt(5)-sqrt(3))xx`
`(sqrt(5)+sqrt(3))/(sqrt(5)+sqrt(3))-2/(sqrt(7)+sqrt(3))xx(sqrt(7)-sqrt(3))/(sqrt(7)-sqrt(3))`
`implies (sqrt(7)+sqrt(5))/2-((sqrt(5)+sqrt(3)))/2-((sqrt(7)-sqrt(3)))/2`
`implies sqrt(7)+sqrt(5)-sqrt(5)-sqrt(3)-sqrt(7)+sqrt(3)/2`
`implies0`
Discussion
14.

यदि `3^(x+y)=81` और `81^(x-y)=3` है तो `x` का मान ज्ञात करें।A. `42`B. `15/8`C. `17/8`D. `39`

Answer» Correct Answer - C
`3^(x+y)=81`
`3^(x+y)=3^(4)`
`impliesx+y=4`
`81^(x-y)=3` ………..i
`3^(4x-46)=3^(1)`
`implies4x-4y=1`……………ii
from equation i and ii
`4x-4y=1`
`4x+4y=16`
`=8x=17`
`x=17/8`
Discussion
15.

`[(root(5)sqrt(x^(-3//5)))^(-5//3)]^(5)` का सरलीकृत रूप क्या है?A. `x^(5)`B. `x^(5)`C. `x`D. `1/x`

Answer» Correct Answer - D
`[(root(5)(x^(-3//5))^(-5//3)]^(-5)`
`=[(x^(-3/25))^(-5//3)]^(-5)=[(x^(1/5))]^(5)`
`=x^(-1/5xx5)=x^(-1)=1/x`
Discussion
16.

`sqrt(11+2sqrt(30))-1/(sqrt(11+2sqrt(30))` का मान ज्ञात करें।A. `2sqrt(5)`B. `2sqrt(6)`C. `1+sqrt(6)`D. `1+sqrt(5)`

Answer» Correct Answer - A
`sqrt(11+2sqrt(30))-1/(sqrt(11+2sqrt(30)))`
`impliessqrt((sqrt(6))^(2)+(sqrt(5))^(2)+2sqrt(6).sqrt(5))`
`-1/(sqrt((sqrt(6))^(2)+(sqrt(5))^(2)+2sqrt(6).sqrt(5)))`
`impliessqrt((sqrt(6)+sqrt(5))^(2))-1/(sqrt((sqrt(6)+sqrt(5))^(2)))`
`impliessqrt(6)+sqrt(5)-1/(sqrt(6)+sqrt(5))`
Relationalising above question
`impliessqrt(6)+sqrt(5)-1/(sqrt(6)+sqrt(5))xx(sqrt(6)-sqrt(5))/(sqrt(6)-sqrt(5))`
`impliessqrt(6)+sqrt(5)-(sqrt(6)-sqrt(5))`
`impliessqrt(6)+sqrt(5)-sqrt(6)+sqrt(5)`
`implies2sqrt(5)`
Discussion
17.

`(1.49xx14.9-0.51xx5.1)/(14.9-5.1)` के बराबर है।A. `0.20`B. `20.00`C. `2.00`D. `22.00`

Answer» Correct Answer - C
`(1.49xx14.9-0.51xx5.1)/(14.9-5.1)`
`implies(149/100xx149/10-051/100xx51/10)/(149/10-51/.10)`
`implies(((149^(2))/1000-(51^(2))/1000)/(((149-51)/10)))`
`implies(1/1000(149^(2)-51^(2)))/(1/10(149-51))`
`implies(1(149-51)(149+51))/(100(149-51))`
`implies200/100=2`
Discussion
18.

`(3sqrt(2)+2sqrt(3))/(3sqrt(2)-2sqrt(3))` के बराबर है।A. `5+2sqrt(6)`B. `(3+2sqrt(6))/2`C. `5-2sqrt(3)`D. `5+2sqrt(3)`

Answer» Correct Answer - A
`(3sqrt(2)+2sqrt(3))/(3sqrt(2)-2sqrt(3))`
`implies(3sqrt(2)+2sqrt(3))/(3sqrt(2)-2sqrt(3))xx(3sqrt(2)+2sqrt(3))/(3sqrt(2)+2sqrt(3))`
`implies((3sqrt(2)+2sqrt(3))^(2))/(18-12)`
`implies(18+12+2xx3xx2sqrt(3).sqrt(2))/6`
`implies(30+12sqrt(6))/6implies5+2sqrt(6)`
Discussion
19.

`(3+2sqrt(2))^(-3)+(3-2sqrt(2))^(-3)` का मान ज्ञात करें।A. 189B. 180C. 108D. 198

Answer» Correct Answer - D
`(3+2sqrt(2))^(-3)+(3-2sqrt(2))^(-3)`
`implies(1/(3+2sqrt(2)))^(3)+(1/(3-2sqrt(2)))^(3)`
`implies (1/((3-2sqrt(2)))xx(3+2sqrt(2))/(3+2sqrt(2)))^(3)+(1/((3+2sqrt(2)))xx(3-2sqrt(2))/(3-2sqrt(2)))^(3)`
`implies ((3-2sqrt(2))/(9-8))^(3)+((3+2sqrt(2))/(9-8))^(3)`
`implies(3-2sqrt(2))^(3)+(3+2sqrt(2))^(3)`
`a=3-2sqrt(2)`
`b=3+2sqrt(2)`
`a^(3)+b^(3)implies(a+b)(a^(2)+b^(2)-ab)`
`implies(3-2sqrt(2)+3+2sqrt(2))(17+17-1)`
`implies (6)(33)`
`implies 198`
Discussion
20.

`(10.3xx10.3xx10.3+1)/(10.3xx10.3-10.3+1)` के बराबर है।A. `9.3`B. `10.3`C. `11.3`D. `12.3`

Answer» Correct Answer - C
`(10.3xx10.3xx10.3+1)/(10.3xx10.3-10.3+1)`
`implies((10.3)^(3)+1^(3))/((10.3)^(2)-10.3+(1)^(2))`
`implies((10.3+1)((10.3)^(2)+(1)^(2)-10.3xx1))/((10.3)^(2)-10.3+1^(2))`
`implies10.3+1implies11.3`
Discussion
21.

`(sqrt(5))/(sqrt(3)+sqrt(2))-(3sqrt(3))/(sqrt(5)+sqrt(2))+(2sqrt(2))/(sqrt(5)+sqrt(2))+(2sqrt(2))/(sqrt(5)+sqrt(3))` के बराबर है।A. `0`B. `2sqrt(15)`C. `2sqrt(10)`D. `2sqrt(6)`

Answer» Correct Answer - A
`(sqrt(5))/(sqrt(3))+sqrt(2)-(3sqrt(3))/(sqrt(5)+sqrt(2))+(2sqrt(2))/(sqrt(5)+sqrt(3))`
`implies (sqrt(5))/(sqrt(3)+sqrt(2))xx((sqrt(3)-sqrt(2)))/(sqrt(3)-sqrt(2))-`
`((3sqrt(3))/(sqrt(5)+sqrt(2))xx(sqrt(5)-sqrt(2))/((sqrt(5)-sqrt(2)))+(2sqrt(2))/(sqrt(5)+sqrt(3))((sqrt(5)-sqrt(3)))/((sqrt(5)-sqrt(3))))`
`implies (sqrt(15)-sqrt(10))/(3-2)-(3sqrt(3)(sqrt(5)-sqrt(2)))/(5-2)`
`+(2sqrt(2)(sqrt(5)-sqrt(3)))/(5-3)`
`impliessqrt(15)-sqrt(10)-(sqrt(15)-sqrt(6))+sqrt(10)-sqrt(6)`
`implies sqrt(15)-sqrt(10)-sqrt(15)+sqrt(6)+sqrt(10)-sqrt(6)`
`0`
Discussion
22.

`(3^(0)+3^(-1))/(3^(-1)-3^(0))` का सरलीकरण क्या है?A. `-2`B. `-1`C. `1`D. `2`

Answer» Correct Answer - A
`(3^(0)+3^(-1))/(3^(-1)-3^(0))`
`implies (1+1/3)/(1/3-1)=(4/3)/(-2/3)=-2`
Discussion
23.

यदि `2^(n-1)+2^(n+1)=320` है तो `n` का मान ज्ञात करें।A. 6B. 8C. 5D. 7

Answer» Correct Answer - D
`2^(n-1)=2^(n+1)=320`
`implies2^(n-1)(1+2^(2))=320`
`implies2^(n-1)(1+2^(2))=320`
`implies2^(n-1)xx5=320`
`implies2^(n-1)xx5=320`
`implies2^(n-1)=320/5=64`
`implies(2)^(n-1)=(2)^(6)`
`impliesn=7`
Discussion
24.

`4^(61)+4^(62)+4^(63)+4^(64)` ‌ किससे विभाजित है?A. 17B. 3C. 11D. 13

Answer» Correct Answer - A
`4^(61)+4^(62)+4^(53)+4^(64)`
`4^(61)(4^(0)+4^(1)+4^(2)+4^(3))`
`4^(61)xx85`
Now check with option 85 is divisible by 17
Discussion
25.

यदि `(125)^(2//3)xx(625)^(-1//4)=(5)^(x)` है तो `x` का मान ज्ञात करें।A. 3B. 2C. 0D. `1`

Answer» Correct Answer - D
`125^(2//3)xx625^(-1//4)=5^(x)`
`5^(3x2//3)xx5^(4x-1//4)=5^(x)`
`5^(2)xx5^(-1)=5^(x)`
`5^(2-1)=5^(x)`
`x=2-1=x=1`
Discussion
26.

यदि `3^(10)xx27^(2)=9^(2)xx3^(n)` हो तो `n` का बताइए?A. `10`B. `12`C. `15`D. `30`

Answer» Correct Answer - B
`3^(10)xx27^(2)=9^(2)xx3^(n)`
`3^(10)xx(3^(3))^(2)=(3^(2))^(2)xx3^(n)`
`3^(10+6)=3^(4+n)`
So,
`10+6=4+n`
`n=12`
Discussion
27.

`(d^(s+t-:d^(s))-:d^(t)` का मान ज्ञात करें।A. `d^(2(s+1))`B. `1`C. `0`D. `d^(s-t)`

Answer» Correct Answer - B
`(d^(s+t)-:d^(s))-:d^(t)`
`=(d^(s+t))/(d^(s))-:d^(t)`
`implies(d^(s+t-s))-:d^(t)=(d^(t))-:d^(t)`
`=(d^(t))/(d^(t))=d^(s-t)=d^(o)=1`
Discussion
28.

यदि `x=(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))` और `(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))` है तो `(x+y)` का मान क्या है?A. 8B. 16C. `2sqrt(15)`D. `2(sqrt(5)+sqrt(3))`

Answer» Correct Answer - A
`x=(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))xx(sqrt(5)+sqrt(3))/(sqrt(5)+sqrt(3))implies((sqrt(5)+sqrt(3))^(2))/2`
`implies` Similarly
`y=(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))implies((sqrt(5)-sqrt(3))^(2))/2`
`implies x+y`
`implies(5+3+2sqrt(15)+5+3-2sqrt(15))/2`
`implies16/2=8`
Discussion
29.

`sqrt(2^(4))+root(3)(64)+root(4)(2^(8))` का मान क्या है?A. 12B. 16C. 18D. 24

Answer» Correct Answer - A
`sqrt(2^(4))+root(3)(64)+root(4)(2^(8))`
`implies 2^(4xx1/2)+4^(3xx1/3)+2^(8xx1/4)`
`implies2^(2)+4^(1)+2^(2)`
`implies4+4+4=12`
Discussion
30.

वह कौन सी संख्या है जिसे `(sqrt(3)+sqrt(2))` से गुणा करने पर परिणाम `(sqrt(12)+sqrt(18))` प्राप्त होता है?A. `3sqrt(2)-2sqrt(3)`B. `3sqrt(2)+2sqrt(3)`C. `sqrt(6)`D. `2sqrt(3)-3sqrt(2)`

Answer» Correct Answer - C
Shortcut method
Take outoption and try
Let number is `sqrt(6)`
`impliessqrt(6)(sqrt(3)+sqrt(2))=sqrt(12)+sqrt(18)`
`impliessqrt(18)+sqrt(12)=sqrt(12)+sqrt(18)`
Matched
So this is answer
Discussion
31.

`sqrt(5+2sqrt(6))-1/(sqrt(5+2sqrt(6))` का मान क्या है?A. `2sqrt(2)`B. `2sqrt(3)`C. `1+sqrt(5)`D. `sqrt(5)-1`

Answer» Correct Answer - A
`(sqrt(5+2sqrt(6))-1/(sqrt(5+2sqrt(6)))`
`implies (sqrt(3)+sqrt(2))-1/((sqrt(3)+sqrt(2)))`
`[(sqrt(5+2sqrt(6))=sqrt((sqrt(3)+sqrt(2))^(2))impliessqrt(3)+sqrt(2)),(a^(2)+b^(2)+2ab=(a+b)^(2))]`
`impliessqrt(3)+sqrt(2)-(1/(sqrt(3)+sqrt(2))xx(sqrt(3)-sqrt(2))/(sqrt(3)-sqrt(2)))`
`impliessqrt(3)+sqrt(2)-((sqrt(3)-sqrt(2))/(3-2))`
`impliessqrt(3)+sqrt(2)-sqrt(3)+sqrt(2)`
`implies 2sqrt(2)`
Discussion
32.

`sqrt(3)+sqrt(2)` से `sqrt(12)+sqrt(18)` कितना अधिक है?A. `2(sqrt(3)-sqrt(2))`B. `2(sqrt(3)+sqrt(2))`C. `sqrt(3)+2sqrt(2)`D. `sqrt(3)-2sqrt(2)`

Answer» Correct Answer - C
`(sqrt(12)+sqrt(18))-(sqrt(3)+sqrt(2))`
`implies 2sqrt(3)+3sqrt(2)-sqrt(3)-sqrt(2)`
`impliessqrt(3)+2sqrt(2)`
Discussion
33.

यदि `(2^(3))^(2)=4^(x)` हो तो `3^(x)` किसके बराबर है?A. 3B. 6C. 9D. 27

Answer» Correct Answer - D
`(2^(3))^(2)=4^(x)`
`(8)^(2)=4^(x)`
`64=4^(x)`
`(4)^(3)=4^(x)`
On comparing both sides `x=3`
So, vlaue of `3^(x)=(3)^(3)=27`
Discussion
34.

`(6.5xx6.5-45.5+3.5xx3.5)` के बराबर है?A. 10B. 9C. 7D. 9

Answer» Correct Answer - B
`a=6.5`
`b=3.5`
`implies(axxa-2xxaxxb+bxxb)`
`implies(a^(2)-2ab+b^(2)`
`implies(a-b)^(2)`
`(6.5-3.5)^(2)implies3^(2)=9`
Discussion
35.

`((sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3)))^(2)+((sqrt(5)-sqrt(3))/(sqrt(5)-sqrt(3)))^(2)` के बराबर है?A. 64B. 62C. 66D. 68

Answer» Correct Answer - B
`((sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3)))^(2)implies((sqrt(5)+sqrt(3))^(2))/((sqrt(5)-sqrt(3))^(2))`
`implies (5+3+2sqrt(15))/(5+3-2sqrt(15))implies(8+2sqrt(15))/(8-2sqrt(15))`
`implies(4+sqrt(15))/(4-sqrt(15))`
Similarly: `((sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3)))^(2)=(4-sqrt(15))/(4+sqrt(15))`
Thus, the expression
`implies(4+sqrt(15))/(4-sqrt(15))+(4-sqrt(15))/(4+sqrt(15))`
`implies (16+15+8sqrt(15)+16+15-8sqrt(15))/((16-15))`
`implies62`
Discussion
36.

`((2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)-1)/(sqrt(3)+1))` का सरलीकरण हैA. `2-sqrt(3)`B. `2+sqrt(3)`C. `16-sqrt(3)`D. `40-sqrt(3)`

Answer» Correct Answer - C
`((2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)-1)/(sqrt(3)+1))`
`(((2+sqrt(3))^(2)+(2-sqrt(3))^(2))/((2-sqrt(3))(2+sqrt(3)))+(sqrt(3)-1)/(sqrt(3)+1)xx(sqrt(3)-1)/(sqrt(3)-1))`
`implies((4+3+4sqrt(3)+4+3-4sqrt(3))/(4-3)+((sqrt(3)-1)^(2))/(3-1))`
`implies (14+(3+1-2sqrt(3))/2)`
`implies14+(2(2-sqrt(3)))/2`
`implies14+2-sqrt(3)=16-sqrt(3)`
Discussion
37.

`((1+sqrt(2))/(sqrt(5)+sqrt(3))+(1-sqrt(2))/(sqrt(5)-sqrt(3)))` का सरलीकरण हैA. `sqrt(5)+sqrt(6)`B. `2sqrt(5)+sqrt(6)`C. `sqrt(5)-sqrt(6)`D. `2sqrt(5)-3sqrt(6)`

Answer» Correct Answer - C
`((1+sqrt(2))/(sqrt(5)+sqrt(3))+(1-sqrt(2))/(sqrt(5)-sqrt(3)))`
`implies ((1+sqrt(2))(sqrt(5)-sqrt(3))+(1-sqrt(2))(sqrt(5)+sqrt(3)))/((sqrt(5)+sqrt(3))(sqrt(5)-sqrt(3)))`
`implies (sqrt(5)-sqrt(3)+sqrt(10)-sqrt(6)+sqrt(5)+sqrt(3)-sqrt(10)-sqrt(6))/((sqrt(5))^(2)-(sqrt(3))^(2))`
`implies (2sqrt(5)-2sqrt(6))/2implies(2(sqrt(5)-sqrt(6)))/2`
`implies (sqrt(5)-sqrt(6))`
Discussion
38.

`(1/2)^(1/2)` के बराबर है।A. `1/(sqrt(2))`B. `2sqrt(2)`C. `sqrt(2)`D. `sqrt(2)`

Answer» Correct Answer - A
`(1/2)^(1//2)impliessqrt(1/2)implies1/(sqrt(2))`
Discussion
39.

`2/(sqrt(7)+sqrt(5))+7/(sqrt(12)-sqrt(5))-5/(sqrt(12)-sqrt(7))` का सरलीकरण क्या है?A. 5B. 2C. 1D. 0

Answer» Correct Answer - D
`2/(sqrt(7)+sqrt(5)+7/(sqrt(12)-sqrt(5))-5/(sqrt(12)-sqrt(7))`
`implies 2/(sqrt(7)+sqrt(5))xx(sqrt(7)-sqrt(5))/(sqrt(7)-sqrt(5))+`
`7/(sqrt(12)-sqrt(5))xx((sqrt(12)+sqrt(5)))/((sqrt(12)+sqrt(5)))-`
`(5/(sqrt(12)-sqrt(7))xx(sqrt(12)+sqrt(7))/(sqrt(12)+sqrt(7)))`
`implies (2(sqrt(7)-sqrt(5)))/2+(7(sqrt(12)+sqrt(5)))/7`
`-(5(sqrt(12)+sqrt(7))/5)`
`impliessqrt(7)-sqrt(5)+sqrt(12)+sqrt(5)-sqrt(12)-sqrt(7)`
`implies0`
Discussion
40.

जब `(4+sqrt(7))` को पूर्ण वर्ग रूप में लिखा जाता है तो वह निम्न में से किसके बराबर होगा?A. `(2+sqrt(7))^(2)`B. `((sqrt(7))/2+1/2)^(2)`C. `[1/(sqrt(2))(sqrt(7)+)^(2)`D. `(sqrt(3)+sqrt(4))^(2)`

Answer» Correct Answer - C
`4+sqrt(7)`
`implies(8+2sqrt(4))/2`
`implies((sqrt(7))^(2)+1+2.sqrt(7).1)/2`
`implies((sqrt(7)+1)^(2))/((sqrt(2))^(2))implies{1/(sqrt(2))(sqrt(7)+1)}^(2)`
Discussion
41.

इनमें से सबसे बड़ी संख्या कौन सी है? `2^(60),3^(48)` and `5^(24)`A. `5^(60)`B. `3^(48)`C. `4^(36)`D. `5^(24)`

Answer» Correct Answer - B
`2^(60)to(2^(5))^(12)to(32)^(12)`
`implies3^(48)to(3^(4))^(12)to(81)^(12)`
`implies4^(36)to(4^(3))^(12)to(64)^(12)`
`implies5^(24)to(5^(2))^(12)to(25)^(12)`
`=3^(48)` Greatest
Discussion
42.

`(0.2)^(3)xx200-:2000` if `(0.2)^(2)` का सरलीकृत मान क्‍या है?A. `1/100`B. `1/50`C. `1/10`D. `1`

Answer» Correct Answer - B
`(0.2)^(3)xx200-:2000` of `(0.2)^(2)`
`implies(0.2xx0.2xx0.2xx200)/(2000xx0.2xx0.2)`
`implies(0.2xx200)/2000`
`implies(40.0)/2000implies1/50`
Discussion
43.

`(3sqrt(7))/(sqrt(5)+sqrt(2))-(5sqrt(5))/(sqrt(2)+sqrt(7))+(2sqrt(2))/(sqrt(7)+sqrt(5))` का मान क्‍या है?A. 1B. 0C. `2sqrt(3)`D. `sqrt(7)`

Answer» Correct Answer - B
`(3sqrt(7))/(sqrt(5)+sqrt(2))-(5sqrt(5))/(sqrt(2)+sqrt(7))+(sqrt(2))/(sqrt(7)+sqrt(5))`
`implies(3sqrt(7))/(sqrt(5)+sqrt(2))xx(sqrt(5)-sqrt(2))/(sqrt(5)-sqrt(2))-(5sqrt(5))/(sqrt(7)+sqrt(2))xx`
`(sqrt(7)-sqrt(2))/(sqrt(7)-sqrt(2))+(2sqrt(2))/(sqrt(7)+sqrt(5))xx(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))`
`implies(3sqrt(7)(sqrt(5)-sqrt(2)))/((sqrt(5))^(2)-(sqrt(2))^(2))-(5sqrt(5)(sqrt(7)-sqrt(2)))/((sqrt(7))^(2)-(sqrt(2))^(2))`
`+(2sqrt(2)(sqrt(7)-sqrt(5)))/((sqrt(7))^(2)-(sqrt(5)^(2))`
`impliessqrt(35)-sqrt(12)-sqrt(35)+sqrt(10)+sqrt(14)-sqrt(10)`
`=0`
Discussion
44.

`(3.25xx3.25+1.75xx1.75-2xx3.25xx1.75)/(3.25xx3.25-1.75xx1.75)` का सरलीकृत मान क्या है?A. `0.5`B. `0.4`C. `0.3`D. `0.2`

Answer» Correct Answer - C
`(a=3.25, b=1.75)`
`implies(axxa+bxxb-2xxaxxb)/(axxa-bxxb)`
`implies(a^(2)+b^(2)-2ab)/(a^(2)-b^(2))`
`((a-b)^(2))/((a-b)(a+b))=(a-b)/(a+b)`
`implies(3.25-1.75)/(3.25+1.75)`
`implies1.50/5.00implies3/10implies0.3`
Discussion
45.

`(0.08xx0.08xx0.08+0.02xx0.02xx0.02)/(0.08xx0.08-0.0016+0.002xx0.02)` का सरलीकृत मान क्या है?A. `0.001`B. `0.1`C. `0.0016`D. `0.016`

Answer» Correct Answer - B
`a=0.08,b=0.02`
`implies(axxaxxa+bxxbxxb)/(axxa-ab+bxxb)`
`implies(a^(3)+b^(3))/(a^(2)-ab+b^(2))`
`((a+b)(a^(2)-ab+b^(2)))/(a^(2)-ab+b^(2))`
`implies a+b`
`implies0.08+0.02implies0.10`
Discussion
46.

`(sqrt(6)+2)/(sqrt(2)+sqrt(2+sqrt(3)))-(sqrt(6)-2)/(sqrt(2)-sqrt(2-sqrt(3)))-(2sqrt(2))/(2+sqrt(2))` का सरलीकृत मान क्‍या है?A. `2sqrt(6)`B. `2`C. `sqrt(3)`D. `0`

Answer» Correct Answer - D
`(sqrt(6)+2)/(sqrt(2)+sqrt(2+sqrt(3)))-(sqrt(6)-2)/(sqrt(2)-sqrt(2-sqrt(3)))-(2sqrt(2))/(2+sqrt(2))`
`implies(sqrt(6)+2)/(sqrt(2)+(sqrt(3)+1)/(sqrt(2)))-(sqrt(6)-2)/(sqrt(2)-(sqrt(3)-1)/(sqrt(2)))-2/(sqrt(2)+1)`
`implies ((sqrt(6)+2)sqrt(2))/(2+sqrt(3)+1)-((sqrt(6)-2)sqrt(2))/(2-sqrt(3)+1)-2/(sqrt(2+1)`
`(sqrt(2))/(sqrt(3))[(sqrt(6)+2)/((sqrt(3)+1))-(sqrt(6)_2)/((sqrt(3)-1))]-2/(sqrt(2)+1)xx(sqrt(2)-1)/(sqrt(2)-1)`
`(sqrt(2))/(sqrt(3))[(sqrt918)+2sqrt(3)-sqrt(6)-2-sqrt(18)+2sqrt(3)-sqrt(6)+2)/(3-1)`
`-((sqrt(2)-1))/(2-1)`
`implies(sqrt(2))/(sqrt(3))[2((-sqrt(6)+2sqrt(3)))/2]-2(sqrt(2)-1)`
`implies-sqrt(3)xxsqrt(2)xx(sqrt(2))/(sqrt(3))+2sqrt(3)xx(sqrt(2))/(sqrt(3)-2(sqrt(2)-1)`
`implies-2+2sqrt(2)-2sqrt(2)+2=0`
Discussion
47.

इनमें से कौन-सी संख्या `sqrt(3)` के निकटतम है?A. `9/5`B. `1.75`C. `173/100`D. `1.69`

Answer» Correct Answer - C
`sqrt(3)=1.732implies173/100`
Discussion
48.

`sqrt(2), root(3)(3),root(4)(4),root(6)(6)` इनमें से सबसे बड़ी संख्या कौन सी है?A. `sqrt(2)`B. `root(3)(3)`C. `root(4)(4)`D. `root(6)(6)`

Answer» Correct Answer - B
`sqrt(2)=2^(1/2)to2^(6/12)to2^(6/12)toroot(12)(2^(6))toroot(12)(64)`
`impliesroot(3)(3)=3^(1/3)to3^(4/12)toroot(12)(3^(4))toroot(12)(81)`
`impliesroot(4)(4)=4^(1/4)to4^(3/12)toroot(12)(4^(3))toroot(12)(64)`
`implies root(6)(6)=6^(1/6)to6^(2/12)toroot(12)(6^(2))toroot(12)(36)`
Discussion
49.

इनमें से सबसे छोटी संख्या कौन सी है? `sqrt(8)+sqrt(5),sqrt(7)+sqrt(6),sqrt(10)+sqrt(3)` and `sqrt(11)+sqrt(2)`A. `sqrt(8)+sqrt(5)`B. `sqrt(7)+sqrt(6)`C. `sqrt(10)+sqrt(3)`D. `sqrt(11)+sqrt(2)`

Answer» Correct Answer - D
`sqrt(8)+sqrt(5)=(sqrt(8)+sqrt(5))^(2)`
`=8+5+2sqrt(40)=13+2sqrt(40)`
`(sqrt(7)+sqrt(6))implies(sqrt(7)+sqrt(6))^(2)implies7+6+2sqrt(42)`
`implies 13+2sqrt(42)`
`implies(sqrt(10)+sqrt(3))implies(sqrt(10)+sqrt(3))^(2)`
`implies10+3+2sqrt(30)implies13+2sqrt(30)`
`impliessqrt(11)+sqrt(2)implies(sqrt(11)+sqrt(2))^(2)`
`implies 11+2+2sqrt(22)implies13+2sqrt(22)`
`sqrt(11)+sqrt(12)`
Discussion
50.

`(sqrt(19)-sqrt(17)), (sqrt(13)-sqrt(11)),(sqrt(7)-sqrt(5))` and `(sqrt(5)-sqrt(3))` इनमें से सबसे बड़ी संख्या कौन सी है?A. `sqrt(19)-sqrt(17)`B. `sqrt(13)-sqrt(11)`C. `sqrt(7)-sqrt(5)`D. `sqrt(5)-sqrt(3)`

Answer» Correct Answer - D
`(sqrt(19)-sqrt(17))implies(sqrt(19)-sqrt(17))xx`
`(sqrt(19)+sqrt(17))/(sqrt(19)+sqrt(17))implies(19-17)/(sqrt(19)+sqrt(17))=2/(sqrt(19+sqrt(17))`
Similarly: `(sqrt(13)-sqrt(11))implies2/(sqrt(13)+sqrt(11))`
`(sqrt(5)-sqrt(3))implies2/(sqrt(5)+sqrt(3))`
Largest (Because Same Numerator is divided by Smallest denominator
Discussion