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201.

यदि `a-1/(a-3)=5` तो `(a-3)^(3)-1/((a-3)^(3))` का मान क्या होगा?A. 7B. 14C. 2D. 5

Answer» Correct Answer - B
`a-1/((a-3))=5`
`a-3-1/(a-3)=5-3`
`(a-3)-1/((a-3))=2`
Cubing both sides
`[(a-3)-1/((a-3))]^(3)=2^(3)`
`(a-3)^(3)-1/((a-3)^(3)-3(a-3))xx1/((a-3))`
`[(a-3)-1/((a-3))]=8`
`(a-3)^(3)-1/((a-3)^(3))-3[2]=8`
`(a-3)^(3)-1/((a-3)^(3))=8+6=14`
Discussion
202.

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

Answer» Correct Answer - D
`(3x-2y)/(2x+3y)=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`
Discussion
203.

यदि `(x-1/x)^(2)=3` तो `x^(6)+1/(x^(6))` का मान निकालेंA. 90B. 10C. 100D. 120

Answer» Correct Answer - B
`(x-1/x)^(2)=3`
`x-1/x=sqrt(3)`
`x-1/x=sqrt(3)`
Now `x^(2)+1/(x^(2))=(sqrt(3))^(2)+2`
`x^(2)+1/x=5`
again `(x^(2))^(3)+(1/(x^(2)))^(3)=(5)^(3)-3xx5`
`x^(6)+1/(x^(6)=125-15)=110`
Discussion
204.

यदि `x-sqrt(3)-sqrt(2)=0` और `y-sqrt(3)+sqrt(2)=0` है तो `(x^(3)-20sqrt(2))-(y^(3)+2sqrt(2))` का मान क्या होगा?A. 2B. 3C. 1D. 0

Answer» Correct Answer - D
According to the question
`x=sqrt(3)+sqrt(2)`
`y=sqrt(3)-sqrt(2)`
`(x^(3)-20sqrt(2))-(y^(2)+2sqrt(2))`
`=[(sqrt(3)+sqrt(2))^(2)-20sqrt(2)-(sqrt(3)-`
`sqrt(2))^(3)-2sqrt(2)`
`=3sqrt(3)+2sqrt(2)+9sqrt(2)+6sqrt(3)-`
`20sqrt(2)-3sqrt(3)+2sqrt(2)+9sqrt(2)-`
`6sqrt(3)-2sqrt(2)`
`=9sqrt(3)-9sqrt(2)-9sqrt(3)+9sqrt(2)=0`
Discussion
205.

यदि `x=a^(1/2)+a^(-1/2),t=a^(1/2)-a^(-1/2)` है तो `(x^(4)-x^(2)y^(2)-1)+(y^(4)-x^(2)y^(2)+1)` का मान हैA. 13B. 12C. 14D. 16

Answer» Correct Answer - D
According to the question
`x=sqrt(a)+1/(sqrt(a))` & `y=sqrt(a)-1/(sqrt(a))`
`:. x^(4)-x^(2)y^(2)-1+y^(4)-x^(2)y^(2)+1`
`=x^(4)-2x^(2)y^(2)+y^(4)`
`=[x^(2)-y^(2)]^(2)`
`[(sqrt(a)+1/(sqrt(a)))^(2)-(sqrt(a)-1/(sqrt(a)))^(2)]^(2)`
`=[a+1/a+2-a-1/a+2]^(2)`
`=[4]^(2)=16`
Discussion
206.

यदि `(a+1/a)^(2)=3` तो `a^(30)+a^(24)+a^(18)+a^(12)+a^(6)+1` का मान ज्ञात कीजिए।

Answer» Correct Answer - A
`(a+1/a)^(2)=3`
`a+1/a=sqrt(3)`
cube both sides
`a^(3)+1/(a^(3))+3xxaxx1/a(a+1/a)=(sqrt(3))^(3)`
`a^(3)+1/(a^(3))+3sqrt(3)=3sqrt(3)`
`a^(3)+1/(a^(3))=0`
`a^(6)+1=0`
`implies a^(30)+a^(24)+a^(18)+a^(12)+a^(6)+1`
`implies a^(24)(a^(6)+1)+a^(12)(a^(6)+1)+a^(6)+1`
`=a^(24)(0)+a^(12)(0)+0=0`
Discussion
207.

यदि `1/(a+b)=1/b+1/b`, तो `a^(3)-b^(3)` का मान क्या होगा?A. 3B. 2C. 1D. 0

Answer» Correct Answer - D
`1/(a+b) =1/a+1/b`
`1/(a+b)=(b+a)/(ab)`
`ab=a^(2)+b^(2)+2ab`
`a^(2)+b^(2)+ab=0`
`a^(3)-b^(3)=(a-b)(a^(2)+b^(2)+ab)`
`=(a-b)(0)=0`
Discussion
208.

यदि `x:y=3:5` और `x-y=-2` तो `x+y` का मान क्या होगा?A. 8B. 2C. 3D. 5

Answer» Correct Answer - A
`x:y=3:5`
`x=y=-2`
`x/y=3/5`
`x-y=3-5=-2to-2`
`x=3,y=5`
`x+y=3+5=8`
Discussion
209.

यदि `x,y` और `z` ऐसी वास्तविक संख्याएं है कि `(x-3)^(2)+(y-4)^(2)+(z-5)^(2)=0` है तो `(x+y+z)` किसके बराबर है?A. 10B. 14C. 11D. 12

Answer» Correct Answer - D
This is possible only when
`(x-3)^(2)=0`
`x=3`,
`(y-4)^(2)=0`
`y=4`
`(z-5)^(2)=0`
`z=5`
then `=x+y+z=3+4+5=12`
Discussion
210.

यदि `a+b=1` है तो `a^(4)+b^(4)-a^(3)-b^(3)-2a^(2)b^(2)+ab` किसके बराबर होगा?A. 1B. 2C. 4D. 0

Answer» Correct Answer - D
If `a+b=1`
`a^(4)+b^(4)-a^(3)-b^(3)-2a^(2)b^(2)+ab`
`(a+b)=1`
`(a+b)^(3)=1`
`a^(3)+b^(3)+3ab(a+b)=1`
`a^(3)+b^(3)+3ab=1`
`a^(4)+b4-2a^(2)b^(2)-a^(3)-b^(3)+ab`
`(a^(2)-b^(2))^(2)-1+3ab+ab`
`((a+b)(a-b)^(3))-1+4ab`
`(a-b)^(2)-1+4ab`
`a^(2)+b^(2)-2ab+4ab`
`a^(2)+b^(2)+4ab-1`
`(a^(2)+b^(2)+2ab)-1=(a+b)^(2)-1`
`=1-1=0`
Discussion
211.

यदि `x+1=sqrt(y)+3,ygt0`, तो `1/2 xx((x^(3)-6x^(2)+12x-8)/(sqrt(y))-y)` का मान क्या होगा?A. `1/2`B. `-1`C. `1`D. `0`

Answer» Correct Answer - D
According to the question
`x+1=sqrt(y)+3,ygt0`
`implies 1/2((x^(3)-6x^(2)+12x-8)/(sqrt(y))-y)=?`
Put `x=4` & `y=4`
Now
`implies 1/2((x^(3)-6x^(2)+12x-8)/(sqrt(y))-y)`
`=1/2((x-2)(3))/(sqrt(y))-y)`
`=1/2(((4-2)^(3))/(sqrt(4))-4)`
`=1/2(8/2-4)=1/2(4-4)=0`
Discussion
212.

यदि `2x+1/(3x)=5` हो तो `(5x)/(6x^(2)+20x+1)` एक का मान क्या होगा?A. `1//4`B. `1//6`C. `1//5`D. `1//7`

Answer» Correct Answer - D
`2x+1/(3x)=5`
`6x^(2)+1=15x`…………..i
Now
`=(5x)/(6x^(2)+20x+1)=(5x)/(6x^(2)+1+20x)`
`=(5x)/(15x+20x)` From equation i
`=(5x)/(35x)=1/7`
Discussion
213.

यदि `a+b+c+d=4` हो तो `1/((1-a)(1-b)(1-c))+1/((a-d)(1-a)(1-b))` का मान बताइए?

Answer» Correct Answer - A
`1/((1-a)(1-b)(1-c))+1/((1-b)(1-c)(1-d))`
`1/((1-a)(1-a)(1-b))`
`=(1-a+1-a+1-b+1-c)/((1-a)(1-b)(1-c)(1-d))`
`(4-(a+b+c+d))/((1-a)(1-b)(1-c)(1-d))`
`(4-4)/((1-a)(1-b)(1-c)(1-d))=0`
Discussion
214.

यदि `(x-5)^(2)+(y-2)^(2)+(z-9)^(2)=0` हो तो `1(x+y-z)` का मान क्या है?A. 16B. -1C. -2D. 12

Answer» Correct Answer - C
`(x-5)^(2)+(y-2)^(2)+(z-9)^(2)=0`
It is possible only when `x-5`
`=0`
`x=5`
`y-2=0`
`y=2`
`z-9=0`
`z=9`
`:. x+y-z=5+2-9`
`=7-9=-2`
Discussion
215.

यदि `a^(3)+1/(a^(3))=2` हो तो `(a^(2)+1)/a` का मान कितना है ? जहां `a` एक धनात्मक संख्या है।A. 1B. 2C. 3D. 4

Answer» Correct Answer - B
but `a=1`
`a^(2)+1/(a^(3))=2, 1^(3)+1/(1^(3))=2`
(satisfy)
So, `(a^(2)+1)/a=(1^(2)+1)/1=2`
Discussion
216.

यदि `a+1/a=2` तो `a^(1000)+a^(-1000)` का मान निकालें।A. 2B. 1C. 0D. `1//2`

Answer» Correct Answer - A
`a+1/a=-2`
but `a=-1`
Now,
`a^(1000)+a^(-1000)=a^(1000+1/(a^(1000)`
`=1^(100)+1/(1^(1000))=1+1=2`
Discussion
217.

यदि `x(x+y+z)=20,y(x+y+z)=30,` और `z(x+y+z)=50`, तो `2(x+y+z)` का मान क्या होगा?A. 20B. 10C. 15D. 18

Answer» Correct Answer - A
Put `(x+y+z)=10`
`x=2`
`y=3`
`z=5`
`x(x+y+z)=20`
`2(10)=20`
Similarly other will satisfied so value of `2(x+y+z)`
`implies 2(10)=20`
Discussion
218.

If x3 + y3 = 243 and x + y = 9, then find the value of xy.1. 92. 183. 274. 36

Answer» Correct Answer - Option 2 : 18

Given:

x3 + y3 = 243

x + y = 9

Formula used:

(x + y)3 = x3 + y3 + 3xy(x + y)

Calculations:

x + y = 9

Cubing on both the sides,

(x + y)3 = 729

⇒ x3 + y3 + 3xy(x + y) = 729

⇒ 243 + 3xy × 9 = 729

⇒ 27xy = 486

⇒ xy = 18

∴ The value of xy is 18
Discussion
219.

यदि `a/b+b/a=2` है तो `a-b` का मान है:A. 2B. -1C. 0D. 1

Answer» Correct Answer - C
`a/b+b/a=2`
`a^(2)+b^(2)=2ab`
`(a-b)^(2)=0`
`a-b=0`
Discussion
220.

यदि `x=y=z` है तो `((x+y+z)^(2))/(x^(2)+y^(2)+z^(2))` हैA. 2B. 3C. 1D. 4

Answer» Correct Answer - B
`((x+y+z)^(2))/(x^(2)+y^(2)+z^(2))`
Assume `x=y=z=1`
`((1+1+1)^(3))/(1+1+1)=(3)`
Discussion
221.

If \(a^2 + b^2 + c^2+ 216 = 12(a+b-2c)\), then \(\sqrt{ab-bc+ca}\) is:1. 62. 43. 84. 3

Answer» Correct Answer - Option 1 : 6

Given:

a2 + b2 + c2 + 216 = 12(a + b – 2c)

Identity used:

(a + b)2 = a2 + b2 + 2ab

(a – b)2 = a2 + b2 – 2ab

Calculation:

a2 + b2 + c2 + 216 = 12(a + b – 2c)

⇒ a2 – 12a + b2 – 12b + c2 + 24c + 216 = 0

⇒ a2 – 12a + 36 + b2 – 12b + 36 + c2 + 24c + 144 = 0

⇒ (a – 6)2 + (b – 6)2 + (c + 12)2 = 0

⇒ a = 6, b = 6, c = –12

\(\sqrt{ab-bc+ca}\)

⇒ \(\sqrt{6\times 6-(6 \times (-12)+(-12 \times 6)}\)

⇒ √36

⇒ 6

∴ \(\sqrt{ab-bc+ca}\) is 6
Discussion
222.

यदि `a+1/b=1` और `b+1/c=1` हो तो `c+1/a` का मान क्या होगा?

Answer» Correct Answer - C
`a+1/b=1` and `b+1/c=1`
Let `a=2` and `b=-1`
`2+1/(-1)=1`
`1=1` True
Now find value of C
`b+1/c=1` (Put value of b)
`-1+1/c=1`
`1/c=2implies c=1/2`
So `c+1/a=1/2+1/2=1`
Discussion
223.

यदि `x/y=(a+2)/(a-2)` है तो `(x^(2)-y^(2))/(x^(2)+y^(2))` का मान है:A. `(2a)/(a^(2)+2)`B. `(4a)/(a^(2)+4)`C. `(2a)/(a^(2)+4)`D. `(4a)/(a^(2)+2)`

Answer» Correct Answer - B
`x/y=(a+2)/(a-2)`
`(x^(2))/(y^(2))=((a+2)^(2))/((a-2)^(2))`
Applying componendo & Dividendo
`(x^(2)-y^(2))/(x^(2)+y^(2))=((a+2)^(2)-(a-2)^(2))/((a+2)^(2)+(a-2)^(2))=(8a)/(2a^(2)+8)=(4a)/(a^(2)+4)`
Discussion
224.

यदि `a-b=2, a^(3)-b^(3)=26` हो तो `(a+b)^(2)` का मान क्या होगा?A. 9B. 4C. 16D. 12

Answer» Correct Answer - C
`a-b=2`
`a^(3)-b^(3)=(a-b)(a^(2)+ab+b^(2))`
`26=2(a^(2)+ab+b^(2))`
`13=a^(2)+ab+b^(2)`…………..i
`4=13+ab`
`(a-b)^(2)=a^(2)+b^(2)-2ab`
`(2)^(2)=a^(2)+b^(2)+ab-3ab`
`3ab=9`
`ab=3`
`(a+b)^(2)=(a-b)^(2)+4ab`
`=4+4xx3=16`
Discussion
225.

यदि `a+b+c=m` और `1/a+1/b+1/c=0` तो `a^(2), b^(2),c^(2)` का औसत कितना है ?A. `m^(2)`B. `m^(2)//3`C. `m^(2)//9`D. `m^(2)//27`

Answer» Correct Answer - B
`a+b+c=m`
`implies 1/a+1/b+1/cimplies (ab+bc=ca)/(abc)=0`
`implies ab+bc+ca=0`
`(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2(ab+bc+ca)`
`m^(2)=a^(2)+b^(2)+c^(2)`
`implies (a^(2)+b^(2)+c^(2))/3=(m^(2))/3`
Discussion
226.

यदि `x^(2)-3x+1=0` है तो `(x^(6)+x^(4)+x^(2)+1)/(x^(3))` का मान क्या होगा?A. 18B. 15C. 21D. 30

Answer» Correct Answer - C
`x^(2)-3x+1=0`
`implies x^(2)+1=3x`
`x+1/x=3`
`implies x^(3)+1/(x^(3))+3xx3=27`
`x^(3)+1/(x^(3))=18`
`implies (x^(6)+x^(4)+x^(2)+1)/(x^(3))`
`implies (x^(6))/(x^(3))+(x^(4))/(x^(3))+(x^(2))/(x^(3))+1/(x^(3))`
`implies x^(3)+1/(x^(3))+1/x+x`
`implies 18+3=21`
Discussion
227.

यदि `x=(0.25)^(1//2),y=(0.4)^(2),z=(0.216)^(1//2)` हो तोA. `XgtXgtZ`B. `XgtYgtZ`C. `ZgtXgtY`D. `XgtZgtY`

Answer» Correct Answer - D
`x=root(2)(0.05)=0.5`
`y=(0.4)^(2)=0.16`
`z=(0.216)^(1//2)=0.464`
`:. Xgtzgty`
Discussion
228.

यदि `p^(3)-q^(3)=(p-q){(p+q)^(2)-xpq}` हो तो `x` का मान क्या है?A. 1B. -1C. 2D. -2

Answer» Correct Answer - A
`p^(3)-q^(3)=(p-q)(p^(2)+q^(2)+pq)`
`(p-q){(p+q)^(2)-xpq}=(p-q)(p^(2)`
`+q^(2)+pq)`
`p^(2)+q^(2)_2pq-xpq=p^(2)+q^(2)+pq`
`2pq-pq=xpq`
`pq=xpq`
`:. x=1`
Discussion
229.

यदि `sqrt(y)=4x,` है `(x^(2))/y` हैA. `1/16`B. `1/4`C. 4D. 2

Answer» Correct Answer - A
`sqrt(y)=4x`
`x/(sqrt(y))=1/4`
Sq. both sides
`(x^(2))/y=1/16`
Discussion
230.

य‌द‌ि `(a^(2)+b^(2))/(c^(2))=(b^(2)+c^(2))/(a^(2))=(c^(2)+a^(2))/(b^(2))=1/k (k!=0)` है तो `k=`A. 2B. 1C. 0D. `1//2`

Answer» Correct Answer - D
`(a^(2)+b^(2))/(c^(2))=(b^(2)+c^(2))/(a^(2))=(c^(2)+a^(2))/(b^(2))=1/k`
Put `a=b=c=1`
`(1+1)/1+(1+1)/1+(1+1)/1=1/k`
`2=2=2=1/k`
`k=1/2`
Discussion
231.

यदि `p^(3)-q^(3)=(p-q)[(p-q)^(2)+xpq]` हो तो `x` का मान बताइये?A. 1B. -1C. 3D. 2

Answer» Correct Answer - C
`p^(3)-q^(3)=(p-1)[(p-q)^(2)+xpq]`
`(p-q)(p^(2)+q^(2)+pq)=(p-q)`
`[p^(2)+q^(2)-2bq+xpq]`
`implies p^(2)+q^(2)+pq=p^(2)+q^(2)-2p+xpq`
`3pq=xpq`
`x=3`
Discussion
232.

यद‌ि `p^(3)-q^(3)=(p-q){(p-q)^(2)-xpq}` है `x` का मान हैA. -1B. 3C. 1D. -3

Answer» Correct Answer - D
`p^(3)-q^(3)=(p-1){(p-q)^(2)-xpq}`
`impliesp^(3)-q^(3)=(p-q)[p^(2)+q^(2)-2pq`
`-xpq]`
`implies p^(3)-q^(3)-(p-q)[p^(2)+q^(2)-2pq`
`-(-3)pq]`
`implies p^(3)-q^(3)=(p-q)(p^(2)+q^(2)+pq)`
`implies` So `x=-3`
`implies` because `a^(3)-b^(2)-(a-b)`
`(a^(2)+b^(2)+ab)`
Discussion
233.

`4x+1/x=5` हो तो `(5x)/(4x^(2)+10x+1)` का मान बताओ?A. `1//2`B. `1//3`C. `2//3`D. `3`

Answer» Correct Answer - B
`implies (5x)/(4x^(2)+10x+1)`
`=(5x)/(x(4x+10x+1/x))`
`=5/(4x+1/x+10)=5/(5+10)=5/15=1/3`
Discussion
234.

यदि `x+1/x=5` है तो `x^(6)+1/(x^(6))=?`A. 12098B. 12048C. 14062D. 12092

Answer» Correct Answer - A
`x+1/x=5`
`:.` Take cube on both sides
`implies (x+1/x)^(3)=(5)^(3)`
`impliesx^(3)+1/(x^(3))+3xx5=125`
`implies x^(3)+1/(x^(3))=110`
`:.` Squaring both sides
`(x^(3)+1/(x^(3)))^(2)=(110)^(2)`
`impliesx^(6)+1/(x^(6))+2=12100`
`x^(6)+1/(x^(6))=12100-2=12098`
Discussion
235.

यदि `x=a(b-c),y=b(c-a),z=c(a-b)` है तो `(x/a)^(3)+(y/b)^(3)+(z/c)^(3)` का मान है :A. `(xyz)/(abc)`B. 0C. `(3xyz)/(abc)`D. `(2xyz)/(abc)`

Answer» Correct Answer - C
`x=a(b-c)`
`y=b(c-a)`
`z=c(a-b)`
Let `x/a=b-c , x/a=A`
`y/b=c-a, y/b=B`
`z/c=a-b, z/c=C`
`:. A+B+C=a-c+c-a-b=0`
`:. A^(3)+B^(3)+C^(3)=3ABC`
`:. (x/a)^(3)+(y/b)^(3)+(z/c)^(3)`
`=3xx x/axx y/bxxz/c=(3xyz)/(abc)`
Discussion
236.

यदि `x+1/x!=0` और `x^(3)+1/(x^(3))=0` हो तो `(x+1/x)^(4)` का मान बताइए?A. 9B. 12C. 15D. 16

Answer» Correct Answer - A
`x^(3)+1/(x^(3))=0`
It is possible only when `x+1/x=sqrt(3)`
So `(x+1/x)^(4)=(sqrt(3))^(4)=9`
Discussion
237.

`sqrt((x^(2)+y^(2)+z)(x+y-3z))+root(3)(xy^(3)z^(2))` का मान ज्ञात करें जब `x=+1,y=-3,z=-1` हैA. 1B. 0C. -1D. `1/2`

Answer» Correct Answer - B
`sqrt((x^(2)+y^(2)+z)(x+y-3z))+root(3)(xy^(3)z^(2))`
`x=1y=-3z=-1` (given)
`implies sqrt((1+9-1)(1-3+3))+root(3)(1xx(-3)^(3)xx1)`
`=3+(-3)=0`
Discussion
238.

यदि `(x-4)(x^(2)+4x+16)=x^(3)-P`, हो तब `P` किसके बराबर है?A. 27B. 8C. 64D. 0

Answer» Correct Answer - C
We know that
`a^(3)-b^(3)=(a-b)(a^(2)+ab+b^(2))`
`x^(3)-P=(x-4)(x^(2)+4x+16)`
`x^(3)-P=x^(3)-4^(3)`
`P=4^(3)` (By comparison)
So `P=64`
Discussion
239.

यदि `x=a+1/a` और `y=a-1/a` हो तो `x^(4)+y^(4)-2x^(2)y^(2)` का मान ज्ञात करें?A. 4B. 8C. 16D. 64

Answer» Correct Answer - C
`x=a+1/a`
`x^(2)=a^(2)+1/(a^(2))+2`
Now
`x^(4)+y^(4)-2x^(2)y^(2)=(x^(2)-y^(2))^(2)`
`=(a^(2)+1/(a^(2))+2-a^(2)-1/(a^(2))+2)^(2)`
`=(4)^(2)=16`
Discussion
240.

यदि `x:y=7:3` है तो `(xy+y^(2))/(x^(2)-y^(2))` का मान क्या होगा?A. `3/4`B. `4/3`C. `3/7`D. `7/3`

Answer» Correct Answer - A
`x:y`
`7:3`
`:.(xy+y^(2))/(x^(2)-y^(2))=(21+9)/(49-9)=30/40=3/4`
Discussion
241.

यदि `a+b=10` और `ab=21` हो तब `(a-b)^(2)` का मान ज्ञात करें?A. 15B. 16C. 17D. 18

Answer» Correct Answer - B
`a+b=10` and `ab=21`
`(a+b)=10`
`a^(2)+b^(2)+2ab=100`
`a^(2)+b^(2)=100-2ab`
`a^(2)+b^(2)=100-2xx21`
`=100-42`
`a^(2)+b^(2)=58`…………….i
`(a-b)^(2)=a^(2)+b^(2)-2ab`
`=58-2xx21`
from equation i
`=58-42`
`(a-b)^(2)=16`
Discussion
242.

यदि `x-1/x=2` तो निम्नलिखित का मान क्या होगा-`x^(3)-1/(x^(3))=?`A. 2B. 11C. 15D. 14

Answer» Correct Answer - D
`x-1/x=2` to find `x^(3)-1/(x^(3))=?`
`implies x-1/x=2implies(x-1/x)^(3)`
`=2^(3)` cubing both side
`implies x^(3)-1/(x^(3))-3xx x xx 1/x(x-1/x)=8`
`implies x^(3)-1/(x^(3))-3xx 1xx(2)=8`
`implies x^(3)-1/(x^(3))=14`
Discussion
243.

यदि `a^(2)+a+1=0`, तो `a^(5)+a^(4)+1` का मान क्या होगा?A. 1B. 0C. `a+1`D. `a^(2)`

Answer» Correct Answer - B
Given
`implies a^(2)+a+1=0`……………..i
`implies` to find `a^(5)+a^(4)+1=?`
by formula
`a^(3)-b^(3)=(a-b)(a^(2)+b^(2)+ab)`
`implies a^(3)-1=(a-1)(a^(2)+a+1)`
`implies a^(3)-1=(a-1)(a^(2)+a+1)`
`(b=1)`
`implies a^(3)-1=(a-1)xx0`
`implies a^(3)-1=0`
`implies a^(3)=1`
`implies a^(5)+a^(4)+1`
`implies a^(3)xxa^(3)+a^(3)+a+1`
`implies a^(2)xx1+ax1+1`
`implies a^(2)+a+1=0` from equation ............i
`implies` Answer will be 0
Discussion
244.

यदि `a^(2)+b^(2)+c^(2)-ab-bc-ca=0` तो `a:b:c` क्या होगा?A. `1:2:1`B. `2:1:1`C. `1:1:2`D. `1:1:1`

Answer» Correct Answer - D
Given
`a^(2)+b^(2)+c^(2)-ab-bc-ca=0`
to find `a:b:c=?`
`implies` According to the question
`a^(2)+b^(2)+c^(2)-ab-bc=ca=0`
`implies a^(2)+b^(2)+c^(2)=ab+bc+ca`
`implies` Let `a=b=c=1`
`implies 1^(2)+1^(2)+1^(2)=1xx+(1xx1)+(1xx1)`
`implies 3=3`
`implies` So ratio of `a:b:c=1:1:1`
Discussion
245.

यदि `x=1//(sqrt(2)+1)` हो तो `x^(2)+2x-1` का मान क्या होगा?A. `2sqrt(2)`B. `4`C. `0`D. `2`

Answer» Correct Answer - C
Giventhat `x=1/(sqrt(2)+1)`
and `x^(2)+2x-1`
`=x^(2)+2x-1+1-1`
`=x^(2)+2x+1-2`
`=(x+1)^(2)-2`
Now put the value of `x`
`=(1/(sqrt(2)+1)+1)^(2)-2`
`=((1+sqrt(2)+1)/(sqrt(2)+1))^(2)-2`
`=((sqrt(2)+2)/(sqrt(2)+1))^(2)-2`
`=(((sqrt(2)+1)xxsqrt(2))/(sqrt(2)+1))^(2)-2`
`[sqrt(2)]^(2)-2=2-2=0`
Discussion
246.

यदि `2x-1/(2x)=5,x!=0` हों तो `x^(2)+1/(16x^(2))-2` का मान ज्ञात कीजिये?A. `19/4`B. `23/4`C. `27/4`D. `31/4`

Answer» Correct Answer - A
`2x-1/(2x)=5`
divide by 2 both side
`x-1/(4x)=5/2`
Squaring both side
`x^(2)+1/(16x^(2))-2xx x xx 1/(4x)=25/4`
`x^(2)+1/(16x^(2))-1/2=25/4` ltbgt `x^(2)+1/(16x^(2))=25/4+1/2=27/4`
So,
`x^(2)+1/(16x^(2))-2=27/4-2`
`x^(2)+1/(16x^(2))-2=19/4`
Discussion
247.

यदि `x^(2)-3x+1=0, (x!=0)` है तो `x+1/x` का मान क्या है?A. 1B. 0C. 3D. 2

Answer» Correct Answer - C
`x^(2)-3x+1=0`
Divide by `x`
`x-3+1/x=0`
`x+1/x=3`
Discussion
248.

यदि `(x+1)/(x-1)=a/b` और `(1-y)/(1+y)=b/a`, तो `(x-y)/(1+xy)` का मान क्या होगा?A. `(a^(2)-b^(2))/(ab)`B. `(a^(2)+b^(2))/(2ab)`C. `(a^(2)-b^(2))/(2ab)`D. `(2ab)/(a^(2)-b^(2))`

Answer» Correct Answer - D
Given:
`implies(x+1)/(x-1)=a/b`
`implies x/1=(a+b)/(a-b)`
(using componento & dividendo)
`implies x=(a+b)/(a-b)`…………i
Again,
`implies (1-y)/(1+y)=b/a`
`implies (1+y)/(1-y)=a/b`
`implies 1/y=(a+b)/(a-b)`
`implies y=(a-b)/(a+b)`…………i
`implies` Fro question `(x-y)/(1+xy)`
`implies (((a+b)/(a-b)-((a-b))/(a+b)))/(1+((a+b)/(a-b))((a-b)/(a+b)))`
`implies ((a+b)^(2)-(a-b)^(2))/((a^(2)-b^(2))(1+1))`
`implies (4ab)/(2(a^(2)-b^(2)))implies(2ab)/(a^(2)-b^(2))`
Discussion
249.

`x+y+z=1, 1/x+1/y+1/z=1` और `xyz=-1` तो `x^(3)+y^(3)+z^(3)` का मान क्या है?A. -1B. 1C. -2D. 2

Answer» Correct Answer - B
`1/x+1/y+1/z=1`
`(xy+yz+zx)/(xyz)=1`
`=xy+yz+zx=xyz=-1`
`(x+y+z)^(2)=x^(2)+y^(2)+z^(2)+2(xy+yz+zx)`
`(x+y+z)^(2)=x^(2)+y^(2)+z^(2)+2(xy+yz+zx)`
`(1)^(2)=x^(2)+y^(2)+z^(2)+2(-1)`
`x^(2)+y^(2)+z^(2)=3`
`x^(3)+y^(3)+z^(3)-3xyz`
`=(x+y+z)[x^(2)+y^(2)+z^(2)-(xy+yx`
`+zx]`
`x^(3)+y^(3)+z^(3)-3(-1)=1[3-(-1)]`
`x^(3)+y^(3)+z^(3)=4-3=1`
Discussion
250.

यदि `a+b+c=0` तो `((a+b)/c+(b+c)/a+(c+a)/b)(a/(b+c)+b/(c+a)+c/(a+b))` का मान ज्ञात करें।A. 8B. -3C. 9D. 0

Answer» Correct Answer - C
`a+b+c=0`
Have values
`a=1`
`b=2`
`c=-3`
`implies((a+b)/c+(b+c)/a+(c+a)/a) (a/(b+c)+b/(c+a)+c/(a+b))`
`implies ((1+2)/(-3)+(2-3)/1+(-3+1)/2)(1/(2-3)+2/(-3+1)+(-3)/(1+2))`
`implies (-1-1-1)(-1-1-1)`
`implies -3xx -3=9`
Discussion