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51.

इनमें से सबसे बड़ा कौन सा है ? `root(3)(4), root(4)(6),root(6)(15)` and `root(12)(245)`A. `root(3)(4)`B. `root(4)(6)`C. `root(6)(15)`D. `root(12)(245)`

Answer» Correct Answer - A
`root(3)(4),root(4)(6),root(6)(15),root(12)(245)`
`implies4^(1/3),6^(1/4),15^(1/6),245^(1/12)`
Take LCM of 3,4,12 & 6
`implies4^(4/12),6^(3/12),15^(2/12),245^(1/12)`
`implies root(12)(4^(4)),root(12)(6^(3)),root(12)(15^(2)),root(12)(245)`
`impliesroot(12)(256), root(12)(216), root(12)(225), root(12)(245)`
`implies` Bggest `=root(3)(4)`
Discussion
52.

`((2.75xx2.75xx2.75-2.25xx2.25xx2.25)/(2.75xx2.75+2.75xx2.25+2.25xx2.25))` के बराबर है।A. `-5`B. `0.5`C. `-0.5`D. `5`

Answer» Correct Answer - B
`a=2.75, b= 2.25`
`implies(a^(3)-b^(3))/(a^(2)+ab+b^(2))`
`implies((a-b)(a^(2)+ab+b))/(a^(2)+ab+b^(2))`
`implies (a-b)implies2.75-2.25`
`=0.50`
Discussion
53.

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

Answer» Correct Answer - B
`sqrt(3), root(3)(2),sqrt(2),root(3)(4)`
`implies3^(1/2),2^(1/3),2^(1/2),4^(1/3)`
Take LCM of 3 & 2
`implies3^(3/6),2^(2/6),2^(3/6),4^(2/6)`
`impliesroot(6)(3^(3)),root(6)(2^(2)),root(6)(2^(3)),root(6)(4^(2))`
`impliesroot(6)(27), root(6)(4),root(6)(8),root(6)(18)impliesroot(3)(2)`
Discussion
54.

सरल करें: `((6.25)^(1//2)(0.0144)^(1/2)+1)/((0.024)^(1/3)xx(81)^(1/4))`A. `0.14`B. `1.4`C. `1`D. `1.bar4`

Answer» Correct Answer - D
`((6.25)^(1/2)xx(0.0144)^(1/2)+1)/((0.027)^(1/3)xx(81)^(1/4))`
`implies((2.5xx0.12)+1)/(0.3xx3)implies(0.3+1)/0.9implies1.3/0.9`
`implies 1.44………implies1.bar4`.
Discussion
55.

माना कि `a=1/(2-sqrt(3))+1/(2-sqrt(3))+1/(3-sqrt(8))+1/(4-sqrt(15))` है तोA. `alt18` but `a!=9`B. `alt 18`C. `a=18`D. `a=9`

Answer» Correct Answer - A
`1/(2-sqrt(3))+1/(3-sqrt(8))+1/(4-sqrt(15))`
`implies1/(2-sqrt(3))xx(2+sqrt(3))/(2+sqrt(3))+1/(3-sqrt(8))xx(3+sqrt(8))/(3+sqrt(8))`
`+1/(4-sqrt(15))xx(4+sqrt(15))/(4+sqrt(15))`
`implies (2+sqrt(3))/(4-3)+(3+sqrt(3))/(9-8)+(4+sqrt(15))/(16-15)`
`implies9+sqrt(3)+2sqrt(3)+sqrt(15)`
`a=9lt9+sqrt(3)+2sqrt(2)+sqrt(15)lt18`
`sqrt(3)=1.73, sqrt(2)=1.41, sqrt(15)=3.9`
`implies 9lt9+1.73+(2xx1.41)+3.9`
`17.4lt18`
Discussion
56.

इनमें से कौन सा परिमेय सबसे बड़ा है: `sqrt(7)-sqrt(5),sqrt(5)-sqrt(3),sqrt(9)-sqrt(7),sqrt(11),sqrt(9)`A. `sqrt(7)-sqrt(5)`B. `sqrt(5)-sqrt(3)`C. `sqrt(9)-sqrt(7)`D. `sqrt(11)-sqrt(9)`

Answer» Correct Answer - B
`sqrt(7)-sqrt(5)implies(sqrt(7)-sqrt(5))((sqrt(7)+sqrt(5)))/((sqrt(7)+sqrt(5)))implies2/((sqrt(7)+sqrt(5)))`
`implies sqrt(5)-sqrt(3)implies2/(sqrt(5)+sqrt(3))` Largest
`impliessqrt(9)-sqrt(7)implies2/(sqrt(9)+sqrt(7))`
`implies sqrt(11)-sqrt(9)implies2/(sqrt(11)+sqrt(9))`
`=sqrt(5)-sqrt(9)`
Discussion
57.

सरल करें: `((0.96)^(3)-(0.1)^(3))/((0.96)^(2)+0.096(0.1)^(2))`A. `1.06`B. `0.95`C. `0.86`D. `0.97`

Answer» Correct Answer - C
`(0.96^(3)-0.1^(3))/(0.96^(3)+0.096+0.1^(2))`
`implies a=0.96`
`implies b=0.1`
`implies(a^(3)-b^(3))/(a^(2)+ab+b^(2))`
`implies ((a-b)(a^(2)+b^(2)+ab))/((a^(2)+ab+b^(2))`
`implies a-b`
`implies0.96-0.1=0.86`
Discussion
58.

यदि `sqrt(15)=3.88` है तो `sqrt(5/3)` का मान क्या है?A. `1.293bar3`B. `1.2934`C. `1.29`D. `1.295`

Answer» Correct Answer - A
`sqrt(5/3)impliessqrt((5xx3)/(3xx3))=sqrt(15/9)=sqrt(15)/3`
`implies 3.88/3=1.29bar3`
Discussion
59.

`sqrt(root(3)(0.004096))` के बराबर है?A. `4`B. `0.4`C. `0.04`D. `0.004`

Answer» Correct Answer - B
`sqrt(root(3)(0.0004096))`
`impliessqrt(0.16)(16^(3)=4096)`
`implies(0.4xx0.4)`
`implies0.4`
Discussion
60.

यदि `a,b` परिमेय है और `asqrt(2)+bsqrt(3)=sqrt(98)+sqrt(108)-sqrt(48)-sqrt(72)` है तो `a,b` का मान क्रमश्: क्या होगा?A. `1,2`B. `1,3`C. `2,1`D. `2,3`

Answer» Correct Answer - A
`asqrt(2)+bsqrt(3)=sqrt(98)+sqrt(108)`
`-sqrt(48)-sqrt(72)`
`impliessqrt(7xx7xx2)+sqrt(3xx3xx3xx2xx2)`
`implies7sqrt(2)+6sqrt(3)-4sqrt(3)-6sqrt(2)`
`asqrt(2)+bsqrt(3)=1sqrt(2)+2sqrt(3)`
`a=1`
`b=1`
Discussion
61.

सरल करें `(5.32xx56+5.32xx44)/((7.66)^(2)-(2.34)^(2))`A. `7.2`B. `8.5`C. `10`D. `12

Answer» Correct Answer - C
`(5.32xx56+5.32xx4)/((7.66)^(2)-(2.34)^(2))`
`implies(5.32(56+44))/((7.66-2.34)(7.66+2.34))`
`implies(5.32(100))/((5.32)(10))`
`implies100/10=10`
Discussion
62.

`14+6sqrt(5)` का वर्गमूल ज्ञात करें।A. `2+sqrt(5)`B. `3+sqrt(5)`C. `5+sqrt(3)`D. `3+2sqrt(5)`

Answer» Correct Answer - B
`sqrt(14+6sqrt(5))`
`impliessqrt(((3)^(2)+(sqrt(5))^(2)+2xx3xxsqrt(5))`
`impliessqrt((3+sqrt(5))^(2))implies3+sqrt(5)`
Discussion
63.

`sqrt(-sqrt(3)+sqrt(3+8sqrt(7+4sqrt(3))))` का मान ज्ञात करें।A. 1B. 2C. 3D. 8

Answer» Correct Answer - B
`sqrt(-sqrt(3)+sqrt(3+8sqrt(7+4sqrt(3))))`
`impliessqrt(-sqrt(3)+sqrt(3+8sqrt((2+sqrt(3))^(2))))`
`impliessqrt(-sqrt(3)+sqrt(3+8(2+sqrt(3))))`
`impliessqrt(-sqrt(3)-sqrt(((sqrt3)^(2)+(4)^(2)+2xx4xxsqrt(3)))`
`impliessqrt(-sqrt(3)+sqrt((4+sqrt(3))^(2))`
`impliessqrt(-sqrt(3)+4+sqrt(3))impliessqrt(4)=2`
Discussion
64.

`3sqrt(3)` का मान परिमेय गुणनखण्ड ज्ञात करें।A. `1/3`B. `3`C. `-3`D. `sqrt(3)`

Answer» Correct Answer - D
`3sqrt(3)xxsqrt(3)=3x3=9`
`:.` Required rationaising factor is `sqrt(3)`
Discussion
65.

`(0.05xx0.05xx0.05-0.04xx0.04xx0.04)/(0.05xx0.05+0.002+0.004xx0.04)` सरल करेंA. 1B. 0.1C. 0.01D. 0.001

Answer» Correct Answer - C
`(0.05xx0.05xx0.05-0.04xx0.04xx0.04)/(0.05xx0.05+0.002+0.04xx0.04)`
`implies((0.05)^(3)-(0.04)^(3))/(0.05^(2)+0.02+0.04^(2))`
`a=0.05` (Description : same as above question)
`b=0.04`
`impliesa=bimplies0.05-0.04`
`=0.01`
Discussion
66.

`((0.05)^(2)+(0.41)^(2)+(0.073)^(2))/((0.005)^(2)+(0.041)^(2)+(0.0073)^(2))=?`A. `10`B. `100`C. `1000`D. none of these

Answer» Correct Answer - B
Let `P=0.05`
then`P/10=0.005`
Let `0.41=q`
`:.0.041=q/10`
and `0.073=r`
`:. 0.0073=r/10`
According to question
`(p^(2)+q^(2)+r^(2))/((P/10)^(2)+(q/10)^(2)+(r/10)^(2))`
`implies((p^(2)+q^(2)+r^(2)))/(1/100(P^(2)+q^(2)+r^(2)))implies100`
Discussion
67.

`(3sqrt(2))/(sqrt(3)+sqrt(6))-(4sqrt(3))/(sqrt(6)+sqrt(2))+(sqrt(6))/(sqrt(3)+sqrt(2))` का मान ज्ञात करें।A. `4`B. `0`C. `sqrt(2)`D. `3sqrt(6)`

Answer» Correct Answer - B
`(3sqrt(2))/(sqrt(3)+sqrt(6))-(4sqrt(3))/(sqrt(6)+sqrt(2))+(sqrt(6))/(sqrt(3)+sqrt(2))`
(rationalisation)
`=(3sqrt(2))/(sqrt(3)+sqrt(6))xx(sqrt(6)-sqrt(3))/(sqrt(6)-sqrt(3))-(4sqrt(3))/(sqrt(6)+sqrt(2))xx(sqrt(6)-sqrt(2))/(sqrt(6)-sqrt(2))`
`+(sqrt(6))/(sqrt(3)+sqrt(2))xx(sqrt(3)-sqrt(2))/(sqrt(3)-sqrt(2))`
`implies (3sqrt(2)(sqrt(6)-sqrt(3)))/(6-3)-((4sqrt(3)(sqrt(6)-sqrt(2))/(6-2))+`
`=(sqrt(6)(sqrt(3)-sqrt(2))/(3-2)`
`impliessqrt(12)-sqrt(6)-(sqrt(18)-sqrt(6))+sqrt(18)-sqrt(12)`
`impliessqrt(12)-sqrt(6)-sqrt(18)+sqrt(6)+sqrt(18)-sqrt(12)=0`
Discussion
68.

`1/(sqrt(2)+1+1/(sqrt(3)+sqrt(2))+1/(sqrt(4)+sqrt(3))+…..+ 1/(sqrt(100)+sqrt(99))` का मान ज्ञात करें।A. `1`B. `9`C. `sqrt(199)`D. `sqrt(99)-1`

Answer» Correct Answer - B
`1/(sqrt(2)+1)=1/(sqrt(2)+1)xx(sqrt(2)-1)/(sqrt(2)-1)`
`implies((sqrt(2)-1)/(2-1))=sqrt(2)-1`
Similarly
`implies1/(sqrt(3)+sqrt(2)=sqrt(3)-sqrt(2)` and so on.
Now put value
`impliessqrt(2)-1+sqrt(3)-sqrt(2)+sqrt(4)-sqrt(3)…………`
`+ sqrt(100)-sqrt(99)`
`implies sqrt(100)-1implies10-1=9`
Discussion
69.

`1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+1/(sqrt(5)-sqrt(2))-1/(sqrt(8)-sqrt(7))+1/(3-sqrt(8))` का मान ज्ञात करें।

Answer» Correct Answer - C
`1/(sqrt(7)-sqrt(6))-1/(sqrt(6)-sqrt(5))+`
`1/(sqrt(5)-2)-1/(sqrt(8)-sqrt(7))+1/(3-sqrt(8))`
`implies` Rationalising
`implies(sqrt(7)+sqrt(6))/((sqrt(7)+sqrt(6))(sqrt(7)-sqrt(6)))-1/((sqrt(6)-sqrt(5)))`
`xx((sqrt(6)+sqrt(5))/((sqrt(6)+sqrt(5))))+(sqrt(5)+sqrt(4))/((sqrt(5)-sqrt(4))(sqrt(5)+sqrt(4)))`
`-((sqrt(8)+sqrt(7)))/((sqrt(8)+sqrt(7))(sqrt(8)-sqrt(7)))+((sqrt(9)+sqrt(8)))/((sqrt(9)+sqrt(8))(sqrt(9)-sqrt(8)))`
`implies (sqrt(7)+sqrt(6))/1-((sqrt(6)+sqrt(5)))/1+`
`((sqrt(5)+sqrt(4)))/1-((sqrt(8)+sqrt(7)))/1+(sqrt(9)+sqrt(8))/1`
`implies sqrt(7)+sqrt(6)-sqrt(6)-sqrt(5)+sqrt(5)+sqrt(4)-sqrt(8)-`........
`sqrt(7)+sqrt(9)+sqrt(8)`
`implies sqrt(4)+sqrt(9)=2+3=5`
Discussion
70.

`16^(3/4)` के बराबर है?A. `4sqrt(2)`B. `8`C. `sqrt(2)`D. `16`

Answer» Correct Answer - B
`16^(3/4)`
`implies(2^(4))^(3/4)`
`implies 2^(4xx3/4)implies2^(3)=8`
Discussion
71.

`((1.5)^(3)+(4.7)^(3)+(3.8)^(3)-3xx1.5xx4.7xx3.8)/((1.5)^(2)+(4.7)^(2)+(3.8)^(2)-1.5xx4.7xx3.8-3.8xx1.5)` का मान ज्ञात करें।

Answer» Correct Answer - C
`((1.5)^(3)+(4.7)^(3)+(3.8)^(3))/((1.5)^(2)+(4.7)^(2)+(3.8)^(2)-1.5xx4.7)`………………
`(-3xx1.5xx4.7xx3.8)/(-4.7xx3.8-3.8xx1.5)`
`impliesa=1.5 impliesb=4.7`
`impliesc=3.8`
`implies(a^(3)+b^(3)+c^(3)-3abc)/(a^(2)+b^(2)+c^(2)-ab-bc-ca)`
`implies ((a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca))/((a^(2)+b^(2)+c^(2)-ab-bc-ca))`
`implies a+b+c`
`implies1.5+4.7+3.8=10.0implies10`
Discussion
72.

`[3-4(3-4)^(-1)]^(-1)` के बराबर है।A. 7B. `-7`C. `1/7`D. `-1/7`

Answer» Correct Answer - C
`[3-4(3-4)^(-1)]^(-1)`
`implies[3-4(-1)^(-1)]^(-1)`
`implies(3-4)/((-1)^(1)]^(-1)`
`implies[3+4]^(-1)implies7^(-1)=1/7`
Discussion
73.

`(1/1.4+1/4.7+1/7.10+1/10.13+1/13.16)` के बराबर है।A. `1/3`B. `5/16`C. `6/8`D. `41/7280`

Answer» Correct Answer - B
`[1/1.4+1/4.7+1/7.10+1/10.13+1/13.16]`
Formula:
`1/("Difference of denominator value")[1/("first value")-1/("Last value")]`
`implies1/3[1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16]`
`implies1/3[1-1/16]implies1/3xx15/16=5/16`
Discussion
74.

`(16)^(0.16)xx(16)^(0.04)xx(2)^(0.2)` के बराबर है।A. 1B. 2C. 4D. 16

Answer» Correct Answer - B
`(16)^(0.16)xx(16)^(0.04)xx(2)^(0.2)`
`implies16^(0.16+0.04)xx2^(0.2)`
`implies(2^(4))^(0.20)xx2^(0.2)`
`implies2^(0.8)xx2^(0.2)`
`implies2^(0.8+0.02)`
`implies2^(1)=2`
Discussion
75.

`(5.71xx5.71xx5.71-2.79xx2.79xx2.79)/(5.71xx5.71+5.71xx2.79+2.79xx2.79)` का सरलीकरण मान क्या है?A. 8.5B. 8.6C. 2.82D. 2.92

Answer» Correct Answer - D
`a=5.71,b=2.79`
`implies(axxaxxa-bxxbxxb)/(axxa+axxb+bxxb)`
`implies(a^(3)-b^(3))/(a^(2)+ab+b^(2))`
`implies((a-b)(a^(2)+b^(2)+ab))/((a^(2)+ab+b^(2)))`
`implies(a-b)`
`implies5.71-2.79`
`implies2.92`
Discussion
76.

`[((0.73)^(3)+(0.27^(3)))/((0.73)^(2)+(0.27)^(2)-(0.73)xx(0.27))]` का सरलीकरण क्या है?A. `1`B. `0.4087`C. `0.73`D. `0.27`

Answer» Correct Answer - A
`a=0.73, b=0.27`
`implies(a^(3)+b^(3))/(a^(2)+b^(2)-ab)`
`implies ((a+b)(a^(2)+b^(2)-ab))/((a^(2)+b^(2)-ab))`
`implies a+b=.0.73+0.27=1`
Discussion
77.

`(16^(0.16)xx2^(0.36))` के बराबर है ?A. `2`B. `16`C. `32`D. `64`

Answer» Correct Answer - A
`(16^(0.16)xx2^(0.36))`
`implies(2^(4))^(0.16)xx(2)^(0.36)`
`implies2^(0.64)xx2^(0.36)`
`implies2^(0.64+0.36)`
`implies 2^(1)implies2`
Discussion
78.

`(36)^(1/6)` के बराबर है?A. 1B. 6C. `sqrt(6)`D. `root(3)(6)`

Answer» Correct Answer - D
`36^(1/6)implies(6^(2))^(1/6)implies6^(2xx1/6)`
`implies6^(1/3)impliesroot(3)(6)`
Discussion
79.

`256^(-[2^(-3//2)])` का सरलीकरण मान क्या है?A. `8`B. `1/8`C. `2`D. `1/2`

Answer» Correct Answer - D
`256^(-[4^(-3//2)])implies256^(-[1/4^(3//2)])`
`implies256^(-[1/8])`
`=1/(256^(1//8))`
`implies2^(1/(8xx1/8))`
`implies1/2`
Discussion
80.

`(256)^(0.16)xx(4)^(0.36)` के बराबर है।A. 64B. 16C. 256.25D. 4

Answer» Correct Answer - D
`256^(0.16)xx4^(0.36)`
`implies4^(4xx0.16)xx4^(0.36)`
`implies4^(0.64+0.36)implies4^(1)implies4`
Discussion
81.

`(256)^(0.16)xx(256)^(0.09)` का मान क्या है?A. `256.25`B. `64`C. `16`D. `4`

Answer» Correct Answer - D
`(256)^(0.16)xx(256)^(0.09)`
`implies(256)^(0.16+0.09)`
`implies256^(0.25)implies256^(1/4)`
`impliesroot(4)(256)=4`
Discussion
82.

`2+sqrt(0.09)-root(3)(0.008)-75%` of `2.80` का मान ज्ञात करें।A. `0`B. `0.01`C. `-1`D. `0.001`

Answer» Correct Answer - A
`2+sqrt(0.09)-root(3)(0.008)-75%` of `2.80`
`implies2+0.3-0.2-(3/4xx2.80)`
`implies2+0.3-0.2-2.10`
`implies2.3-2.3=0`
Discussion
83.

व्यंजक : `root(4)(3x+1)=2` में `x` का मान ज्ञात करें।A. 3B. 6C. 4D. 5

Answer» Correct Answer - D
`root(4)((3x+1))=2`
`(root(4)((3x+1)))^(4)=2^(4)`
`(3x+1)^(4xx1/4)=16`
`=3x=15, x=5`
Discussion
84.

`2+6/(sqrt(3))+1/(2+sqrt(3))+1/(sqrt(3)-2)` के बराबर है।A. `+(2sqrt(3))`B. `-(2+sqrt(3))`C. `1`D. `2`

Answer» Correct Answer - D
`2+6/(sqrt(3))+1/(2+sqrt(3))+1/(sqrt(3)-2)`
`=2+(2xx3sqrt(3))/(sqrt(3)xxsqrt(3))+1/(2+sqrt(3))-(2-sqrt(3))`
`implies 2+2sqrt(3)+(((2-sqrt(3))-(2+sqrt(3)))/((2+sqrt(3))(2-sqrt(3))))`
`implies2+2sqrt(3)+((3-sqrt(3)-2-sqrt(3))/(4-3))`
`implies2+2sqrt(3)-2sqrt(3)`
`implies2`
Discussion
85.

`root(3)(1372)xxroot(3)(1458)-:root(3)(343)` का मान ज्ञात करें।A. 18B. 15C. 13D. 12

Answer» Correct Answer - A
`root(3)(1372)xxroot(3)(1458)-:root(3)(343)`
`impliesroot(3)((1372xx1458)/343)impliesroot(3)(5832)`
`impliesroot(3)(18xx18xx18)implies18`
Discussion
86.

`55^(3)+17^(3)-72^(3)+201960` के बराबर है।A. `-1`B. `0`C. `1`D. `17`

Answer» Correct Answer - B
`a=55, b=17`
`c=-72`
`a+b+c=55+17-72=0`
`:. a^(3)+b^(3)+c^(3)-3abc=0`
`(a+b+c)=0`
Answer `=0`
Discussion
87.

`(sqrt(72)xxsqrt(363)xxsqrt(175))/(sqrt(32)xxsqrt(147)xxsqrt(252))` का मान क्‍या है?A. `55/42`B. `45/56`C. `45/25`D. `55/28`

Answer» Correct Answer - D
`(sqrt(72)xxsqrt(363)xxsqrt(175))/(sqrt(32)xxsqrt(147)xxsqrt(252))`
`implies(sqrt(2xx2xx2xx3x3)xxsqrt(11xx11xx3xxsqrt(5xx5xx7)))/(sqrt(2xx2xx2x2xx)xxsqrt(3xx7xx7)xxsqrt(2xx2xx3xx3xx7)`
`implies(6sqrt(2)xx11sqrt(3)xx5sqrt(7))/(4sqrt(2)xx7sqrt(3)xx6sqrt(7))`
`implies (6xx11xx5)/(4xx7xx6)=55/28`
Discussion
88.

`[root(3)(2)xxsqrt(2)xxroot(3)(3)xxsqrt(3)]` के बराबर है।A. `6^(5)`B. `6^(5//6)`C. `6`D. none of these

Answer» Correct Answer - B
`root(3)(2)xxsqrt(2)xxroot(3)(3)xxsqrt(3)`
`implies2^(1//3)xx2^(1//2)xx3^(1//3)xx3^(1//2)`
`implies2^(5//6)xx3^(5//6)implies6^(5//6)`
Discussion
89.

`sqrt(2root(3)(4sqrt(2root(3)(4.....).................)))` का मान क्‍या है?A. 2B. `2^(2)`C. `2^(3)`D. `2^(5)`

Answer» Correct Answer - A
`x=sqrt(2root(3)(4sqrt(2root(3)(4))))………..`
`implies` Squaring both sides
`impliesx^(2)=2root(3)(4sqrt(2root(3)(4)))…….`
Now cubing both sides
`x^(6)=8xx4x`
`impliesx^(5)=32`
`impliesx^(5)=2^(5)`
`impliesx^(5)=2^(5)`
`impliesx=2`
Discussion
90.

`sqrt(sqrt(2)xxsqrt(3))` का घातांक रूप क्‍या है?A. `6^(-1//2)`B. `6^(1//2)`C. `6^(1//4)`D. `6`

Answer» Correct Answer - C
The exponential form of
`impliessqrt(2sqrt(2)xxsqrt(3))impliessqrt(6^(1//2))`
`implies(6^(1//2))^(1//2)implies6^(1//4)`
Discussion
91.

`1/(1+sqrt(2)+sqrt(3))+1/(1-sqrt(2)+sqrt(3))` का मान क्‍या है?A. `sqrt(2)`B. `sqrt(3)`C. `1`D. `4(sqrt(3)+sqrt(2))`

Answer» Correct Answer - C
`1/(1+sqrt(2)+sqrt(3))+1/(1-sqrt(2)+sqrt(3))`
`implies1/(1+sqrt(3)+sqrt(2))+1/(1+sqrt(3)-sqrt(2))`
`implies (1+sqrt(3)-sqrt(2)+1+sqrt(3)+sqrt(2))/((1+sqrt(3))^(2)-(sqrt(2))^(2))`
`implies(2+2sqrt(3))/(4+2sqrt(3)-2)`
`implies(2+2sqrt(3))/(2+2sqrt(3))`
`implies 1`
Discussion
92.

`1/(sqrt(3.25)+sqrt(2.25))+1/(sqrt(2.45)+sqrt(3.25))+1/(sqrt(5.25)+sqrt(4.25))+1/(sqrt(6.25)+sqrt(5.25))` का मान ज्ञात करें।A. `1.00`B. `1.25`C. `1.50`D. `2.25`

Answer» Correct Answer - A
`1/(sqrt(3.25)+sqrt(2.25))xx(sqrt(3.55)-sqrt(2.25))/(sqrt(3.25)-sqrt(2.25))`
`implies (sqrt(3.25)-sqrt(2.25))/(3.25-2.25)`
`impliessqrt(3.25)-sqrt(2.25)`……………i
Similarly : `1/(sqrt(4.25)+sqrt(3.25))`
`impliessqrt(4.25)-sqrt(3.25)`………….ii
`implies1/(sqrt(5.25)-sqrt(4.25))`
`impliessqrt(5.25)-sqrt(4.25)`..........iii
`implies1/(sqrt(6.25)+sqrt(5.25))`
`implies sqrt(6.25)-sqrt(5.25)`...........iv
`implies` Now add all them
`impliessqrt(3.25)-sqrt(2.25)+sqrt(4.25)-sqrt(3.25)`
`+sqrt(5.25)-sqrt(4.25)+sqrt(6.25)-sqrt(5.25)`
`implies sqrt(6.25)-sqrt(2.25)implies2.5-1.5=1`
Discussion
93.

`((998)^(2)-(997)^(2)-45)/((98)^(2)-(97)^(2))=?`A. 1995B. 195C. 95D. 0

Answer» Correct Answer - D
`((998)^(2)-(997)^(2)-45)/((98)^(2)-(97)^(2))`
`implies([(998)^(2)-(997)^(2)]-45)/((98)^(2)-(97)^(2))`
`implies ((1995)-45)/195implies1950/195=10`
Discussion
94.

`sqrt(40sqrt(9sqrt(81)))` का मान क्‍या है?A. `sqrt(111)`B. 9C. 7D. 11

Answer» Correct Answer - C
`sqrt(40+sqrt(9sqrt(81)))`
`impliessqrt(40+sqrt(9+9))`
`impliessqrt(40+9)impliessqrt(49)=7`
Discussion