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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 601. |
If p+q=12 and pq=22, then find p2 +q2 . |
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Answer» Given, p+q=12 and pq=22 We know that, (p+q)2 =p2 +q2 +2pq ... (i) By putting the given values in equation (i), (12)2 =p2 +q2 +2(22) 144=p2 +q2 +44 144—44=p2 +q2 100=p2 +q2 So. the value of p2 +q22 is 100. |
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| 602. |
If the sum of two numbers is 10 and the sum of their reciprocals is 5/12 then what will be the numbers?1. 7, 32. 9, 13. 8, 24. 6, 4 |
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Answer» Correct Answer - Option 4 : 6, 4 Given: Sum of two numbers = 10 Sum of their reciprocals = 5/12 Calculation: Let the numbers be x and y So, x + y = 10 ----(i) And, (1/x) + (1/y) = 5/12 ----(ii) ⇒ (x + y)/xy = 5/12 Now, ⇒ 10/xy = 5/12 ⇒ xy = 12 × 2 = 24 ----(iii) Now, (10 – y) × y = 24 ⇒ 10y – y2 = 24 ⇒ y2 – 10y + 24 = 0 ⇒ y2 – 6y – 4y + 24 = 0 ⇒ y(y – 6) – 4(y – 6) = 0 ⇒ (y – 6) (y – 4) = 0 ⇒ y = 6, 4 ∴ The required numbers are 6 and 4 |
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| 603. |
If 3x - 2(x + 3) = 2(2x - 5), then the value of \(\frac{5x - 2}{3x - 5}\) is:1. -14/32. \(2 \frac{4}{7}\)3. \(2 \frac{3}{7}\)4. -11/3 |
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Answer» Correct Answer - Option 1 : -14/3 Given: 3x - 2(x + 3) = 2(2x - 5) Claculations: 3x - 2x - 6 = 4x - 10 ⇒ x - 6 = 4x -10 ⇒ x - 4x = -10 + 6 ⇒ -3x = - 4 ⇒ x = 4/3 \(\frac{5x - 2}{3x - 5} = \frac{5\times \frac{4}{3} - 2}{3\times\frac{4}{3} - 5}\) ⇒ (20/3) - 2)/(4 - 5) ⇒ (14/3)/(-1) ⇒ (-14/3) ∴ The required value is (- 14/3) |
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| 604. |
If \(x + \frac{4}{x}-4=0,\) then the value of x2 – 4 is equal to:1. 42. 13. 24. 0 |
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Answer» Correct Answer - Option 4 : 0 Given: \(x + \frac{4}{x}-4=0\) Calculation: To find, x2 – 4 \(x + \frac{4}{x} - 4 = 0\) Multiply by x on both side ⇒ x2 + 4 – 4x = 0 ⇒ x2 – 2x – 2x + 4 = 0 ⇒ x(x – 2) – 2(x – 2) = 0 ⇒ (x – 2)(x – 2) = 0 ⇒ x = 2 Now, ⇒ x2 – 4 ⇒ 22 – 4 ⇒ 0 ∴ The value of x2 – 4 is 0
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| 605. |
Find the unit place of 3674 × 8596 + 5699 × 15891. 32. 43. 54. 6 |
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Answer» Correct Answer - Option 3 : 5 Given: 3674 × 8596 + 5699 × 1589 Calculation: Unit place of 3674 x 8596 ⇒ 4 × 6 = 24 Unit place of 24 ⇒ 4 Again, Unit place of 5699 x 1589 ⇒ 9 × 9 = 81 Unit place of 81 ⇒ 1 Required unit place = (1 + 4) = 5 ∴ Required unit place is 5. |
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| 606. |
In the given questions, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answerI. x2 + x – 56 = 0II. y2 – 23y + 132 = 01. x > y2. x ≥ y3. x < y4. x ≤ y5. x = y or the relationship cannot be established |
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Answer» Correct Answer - Option 3 : x < y Given: I. x2 + x – 56 = 0 II. y2 – 23y + 132 = 0 Calculation: I. x2 + x – 56 = 0 ⇒ x2 + 8x – 7x – 56 = 0 ⇒ x(x + 8) – 7(x – 8) = 0 ⇒ (x + 8)(x – 7) = 0 Then, x = – 8 or x = 7 Now, II. y2 – 23y + 132 = 0 ⇒ y2 – 12y – 11y + 132 = 0 ⇒ y(y – 12) – 11(y – 12) = 0 ⇒ (y – 12)(y – 11) = 0 Then, y = 12 or y = 11 Now, Comparison between x and y (via Tabulation):
∴ We can clearly see that x < y |
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| 607. |
यदि `(m-a^(2))/(b^(2)+c^(2))+(m-b^(2))/(c^(2)+a^(2))+(m-c^(2))/(a^(2)+b^(2))=3` है तो `m` का मान ज्ञात करें?A. `a^(2)+b^(2)`B. `a^(2)+b^(2)+c^(2)`C. `a^(2)-b^(2)-c^(2)`D. `a^(2)+b^(2)-c^(2)` |
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Answer» Correct Answer - B Given `(m-a^(2))/(b^(2)+c^(2))+(m-b^(2))/(c^(2)+a^(2))+(m-c^(2))/(a^(2)+b^(2))=3` `implies m=?` `implies (m-a^(2))/(b^(2)+c^(2))+(m-b^(2))/(c^(2)+a^(2))+(m-c^(2))/(a^(2)+b^(2))=1+1+1` Put `m=a^(2)+b^(2)+c^(2)` from option (b) LHS`=(a^(2)+b^(2)+c^(2)-a^(2))/(b^(2)+c^(2))+` `(a^(2)+b^(2)+c^(2)-b^(2))/(c^(2)+a^(2))+(a^(2)+b^(2)+c^(2)-c^(2))/(a^(2)+b^(2))` `(b^(2)+c^(2))/(b^(2)+c^(2))+(c^(2)+a^(2))/(c^(2)+a^(2))+(a^(2)+b^(2))/(a^(2)+b^(2))=1+1+1` `=` RHS `implies m=a^(2)+b^(2)+c^(2)` |
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| 608. |
`2+xsqrt(3)=1/(2+sqrt(3))` है तो `x` का मान क्या होगा?A. 1B. -2C. 2D. -1 |
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Answer» Correct Answer - D If `2+xsqrt(3)=1/(2+sqrt(3))` Find `x=?` `implies 2+sqrt(3)x=1/(2+sqrt(3))` `implies 2+sqrt(3)xx x=(2-sqrt(3))/1` `implies 2+xsqrt(3)=2-sqrt(3)` `implies x=-1` |
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| 609. |
`(1/3 . 1/3 . 1/3 +1/4 . 1/4 . 1/4 - 3 1/3 . 1/4 . 1/5 + 1/5 . 1/5 . 1/5)/(1/3 . 1/3 + 1/4 . 1/4 + 1/5 . 1/5 - (1/3 . 1/4 + 1/4 . 1/5 + 1/5 . 1/3))` किसके बराबर है?A. `2/3`B. `3/4`C. `47/60`D. `49/60` |
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Answer» Correct Answer - C `(1/3xx1/3xx1/3+1/4xx1/1xx1/4-3xx1/3xx1/4xx1/5+1/5xx1/5xx1/5)/(1/3xx1/3+1/4xx1/4+1/5xx1/5-(1/3xx1/4+1/4xx1/5+1/5xx1/3))` `A^(3)+B^(3)+C^(3)-3ABC=(A+B+C)(A^(2)+B^(2)+C^(2)-AB-BC-CA)` `:. ((1/3)^(3)+(1/4)^(3)-3xx1/3xx1/4xx1/5+(1/5)^(3))/((1/3)^(3)+(1/4)^(2)+(1/5)^(2)-1/3xx1/4-1/4xx1/5-1/5xx1/3)` `=((1/3+1/4+1/5)|__(1/3)^(2)+(1/4)^(2)+(1/5)^(2)-1/3xx1/4-1/4xx1/5-1/5xx1/3__|)/([(1/3)^(2)+(1/4)^(2)+(1/5)^(2)-1/3xx1/4-1/4xx1/5-1/5xx1/3])` `=(20+15+12)/60=47/60` |
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| 610. |
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2 + 16x + 64 = 0II. y2 – 4y – 96 = 0 1. x > y2. x < y3. x ≥ y4. x ≤ y5.x = y or the relationship between x and y cannot be esta |
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Answer» Correct Answer - Option 4 : x ≤ y I. x2 + 16x + 64 = 0 ⇒ x2 + 8x + 8x + 64 = 0 ⇒ (x + 8)(x + 8) = 0 ⇒ x = -8, -8 II. y2 – 4y – 96 = 0 ⇒ y2 - 12y + 8y - 96 = 0 ⇒ (y - 12)(y + 8) = 0 ⇒ y = 12, -8
Hence, x ≤ y |
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| 611. |
यदि `sqrt(x)=sqrt(3)-sqrt(5)` है तो `x^(2)-16x+6` का मान क्या होगा? |
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Answer» Correct Answer - C `sqrt(x)=sqrt(3)-sqrt(5)` Squaring both sides `x=3+5-2sqrt(3)sqrt(5)` `x=8-2sqrt(5)xxsqrt(3)` `x-8=-2sqrt(15)` (Squaring both sides) `x^(2)+64-16x=60` `x^(2)+4-16x=0` `x^(2)+6-16x=2` |
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| 612. |
यदि `x=332, y=333` तथा `z=335,` तब `x^(3)+y^(3)+z^(3)-3xyz` का मान ज्ञात करें?A. 7000B. 8000C. 9000D. 10000 |
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Answer» Correct Answer - A Here `x=332, y=333,z=335` Find `x^(3)+y^(3)+z^(3)-3xyz=` `1/2(x+y+z)` `[(x-y)^(2)+(y-z)^(2)+(z-x)]` `=((332+333+335)/2)[(333-332)^(2)+(335-333)^(2)` `+(335-332)^(2)]` `=1000/2(1^(2)+2^(2)+3^(2))=1000/2(14)=7000` |
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| 613. |
यदि `7^(x)=1/343` है तो `x` का मान क्या होगा?A. `-`B. `-3`C. `1/3`D. `1/7` |
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Answer» Correct Answer - B `7^(x)=1/343=1/(7^(3))` `7^(x)=1/(7^(3))` `7^(x)=7^(-3)` `x=-3` (if bases are equal then their power are also equal) |
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| 614. |
यदि `x^(xsqrt(x))=(xsqrt(x))^(x)` है तो `x` किसके बराबर है?A. `4/9`B. `2/3`C. `9/4`D. `3/2` |
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Answer» Correct Answer - C `x^(xsqrt(x))=(xsqrt(x))^(x)` `x^(xsqrt(x))=(x^(3/2))^(x)` `x^(xsqrt(x))=x^(3/2 x)` (if bases are same then their power is also same) `:. xsqrt(x)=3/2x` or `sqrt(x)=3/2` `x=(3/2)^(2)=9/4` |
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| 615. |
यदि `(2+a)/a+(2+b)/b+(2+c)/c=4`, तो `(ab+bc+ca)/(abc)` का मान क्या है?A. 2B. 1C. 0D. `1/2` |
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Answer» Correct Answer - D `(2+a)a+(2+b)/b+(2+c)/c=4` `(2bc+abc+2ac+abc+2ab+abc)/(abc)=4` `(2(bc+ab+ca))/(abc)+(3abc)/(abc)=4` `(2(bc+ab+ca))/(abc)+3=4` `(ab+bc+ca)/(abc)=1/2` |
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| 616. |
यदि `x+1/x=sqrt(3)` हो तो `x^(3)+1/(x^(3))` का मान ज्ञात करें?A. -2B. 0C. 2D. 4 |
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Answer» Correct Answer - B `x+1/x=sqrt(3)` cubing both side `x^(3)+1/(x^(3))+3x xx1/x(x+1/x)=3sqrt(3)` `x^(3)+1/(x^(3))+3(sqrt(3))=3sqrt(3)` `x^(3)+1/(x^(3))=3sqrt(3)-3sqrt(3)=0` |
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| 617. |
यदि `P+1/(p+2)=1` का `(p+2)^(3)+1/((p+2)^(3))-3` मान बताइएA. 12B. 16C. 18D. 15 |
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Answer» Correct Answer - D `P+(P+2)=1`, find the value of `(P+2)^(3)+1/((P+2)^(3))-3` Adding 2 on both sides `(P+2)+1/((P+2))=3` Taking cube on both sides `(P+2)^(3)+1/((P+2)^(3))+3(P+2)xx1/((P+2))` `[(P+2)+1/(P+2)]=((P+2)+1/((P+2)))^(3)` `=3^(3)=27` `(P+2)^(3)+1/((P+2)^(3)+9)=27` `(P+2)^(3)+1/((P+2)^(3))=18` According to the questions `18-3implies15` |
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| 618. |
यदि `m=-4,n=-2` है तो `m^(3)-3m^(2)+3m+3n+3n^(2)+n^(3)` का मान क्या होगा?A. 124B. -124C. 126D. -126 |
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Answer» Correct Answer - D Given `m=-4,n=-2` Find `m^(3)-3m^(2)S+3m+3n+3n^(2)+n^(3)` Putting value of `m` and `n` `implies (-4)^(3)-3(-4)^(2)+3(-4)+3xx` `(-2)+3(-2)^(2)+(-2)^(3)` `implies -64-48-12-6-12-8` `implies-64-60-2` `implies-126` |
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| 619. |
यदि `a+1/a=2` हो तो `a^(109)+1/(a^(109))` का मान ज्ञात करें?A. 1B. 2C. 0D. 109 |
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Answer» Correct Answer - B `a+1/a=2` put `a=1` (satisfy) `a^(109)+1/(a^(109))=1^(109)+1/(1^(109))=1+1=2` |
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| 620. |
यदि `x^(2)+1//x^(2)=2` हो तो `x-1//x` का मान बताइए?A. `-2`B. `0`C. `1`D. `-1` |
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Answer» Correct Answer - B `x^(2)+1/(x^(2))=2` `(x-1/x)^(2)+2=2` `x-1/x=0` |
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| 621. |
यदि `xy(x+y)=m` हो तो `x^(3)+y^(3)+3m` का मान बताइए?A. `m^(3)//xy`B. `m^(3)(x+y)^(2)`C. `m^(3)//x^(3)y^(3)`D. `mx^(3)y^(3)` |
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Answer» Correct Answer - C `xy(x+y)-m` find `x^(3)+y^(3)+3m` `xy(x+y)=m`…………….i `(x+y)=m/(xy)` Cubing both side `x^(3)+y^(3)+.xy(x=y)=(m^(3))/(x^(3)y^(3))` from equation i `x^(3)+y^(3)+3xxm=(m^(3))/(x^(3)y^(3))` `x^(3)+y^(3)+3x=(m^(3))/(x^(3)y^(3))` |
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| 622. |
यदि `p^(2)+q^(2)=7pq,` तो `p/q+q/p` का मान क्या होगा?A. 9B. 5C. 7D. 3 |
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Answer» Correct Answer - C `p^(2)+q^(2)=7pq` `p/q+q/p=7` (divide whole eqn by `pq`) |
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| 623. |
यदि `a+b+c=26` और `ab+bc+ca=109` तो `a^(2)+b^(2)+c^(2)` का मान ज्ञात करें?A. 458B. 472C. 452D. 476 |
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Answer» Correct Answer - A `(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2` `(ab+bc+ca)` `676=a^(2)+b^(2)+c^(2)+2(109)` `a^(2)+b^(2)+c^(2)=458` |
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| 624. |
यदि `a=7, b=5` और `c=3` है तो `a^(2)+b^(2)+c^(2)-ab-bc-ca` का मान क्या होगा?A. 12B. `-12`C. 0D. 8 |
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Answer» Correct Answer - A `a^(2)+b^(2)+c^(2)-ab-bc-ca` `=1/2[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]` `=1/2[(7-5)^(2)+(5-3)^(2)+(3-7)^(2)]` `=1/294+4+16)=24/2=12` |
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| 625. |
यदि `pq(p+q)=1` हो तो `1/(p^(3)q^(3))-p^(3)-q^(3)` का मान क्या होगा?A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - C `pq(p+q)=1` `p+q=1/(pq)` `p3+q3+3pq(p+q)=1/(p^(3)q^(3))` `1/(p^(3)q^(3))-p^(3)-q^(3)=(13/(p+q))(p+q)` `=3` |
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| 626. |
यदि `x=3^(1/3)-3^(1/3)` का `3x^(3)+9x` मान क्या होगा?A. 8B. 9C. 7D. 16 |
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Answer» Correct Answer - A `x+3^(-1/3)=3^(1/3)` `x^(3)+1/3+3xx x3^(-1/3)(x+3^(-1/3))=3` `x^(3)+1/3+3xx x3^(-1/3)xx 3^(1/3)=3` `3x^(3)+9x=9-1=8` |
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| 627. |
`2x+2/(9x)=4` तो `27x^(3)+1/(27x^(3))` का मान क्या है?A. 180B. 198C. 234D. 252 |
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Answer» Correct Answer - B `2x+2/(9x)=4` Multiply by `3/2` on both sides `3x+1/(3x)=6` Taking cube on both sides `(3x+1/(3x))^(2)=(6)^(3)` `27x^(3)+1/(27x^(3))+3xx3x xx 1/(3x)` `(3x+1/(3x))=216` `27x^(3)+1/(27x^(3))+3xx6=216` `27x^(3)+1/(27x^(3))` `=216-18=198` |
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| 628. |
यदि `a=2,B=-3` हो तो `27a^(3)-54a^(2)b+36ab^(2)-8b^(3)` का मान क्या होगा?A. 1562B. 1616C. 1676D. 1728 |
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Answer» Correct Answer - D `a=2,b=-3` So `=27a^(3)+36ab^(2)-8b^(3)-54a^(2)b` `=27xx(2)^(3)+36xx2xx(-3)^(2)-8xx` `(-3)^(3)-54xx(2)^(2)xx(-3)` `=27xx8+36xx2xx9+8xx27+` `54xx4xx3` `=216+648+216+6481728` |
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| 629. |
यदि `x^(2)=1/(x^(2))=1` तो `x^(18)+x^(12)+x^(6)+1` का मान कितना होगा?A. 1B. 2C. 0D. -1 |
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Answer» Correct Answer - C `x^(2)+1/(x^(2))=1` `implies (x+1/x)^(2)=3` `implies x+1/x=sqrt(3)` `implies x^(3)+1/(x^(3))=0=x^(6)+1=0` Now `x^(18)+x^(12)+x^(6)+1` `x^(12)+(x^(5)+1)+(x^(6)+1)=x^(12)xx0+0=0` |
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| 630. |
यदि `a+b+c=0` तो `(a^(2)+b^(2)+c^(2))/(ab+bc+ca)` का मान कितना होगा?A. 2B. -2C. 0D. 4 |
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Answer» Correct Answer - B If `a+b+c=0` put `a=1 b=1` and `c=-2` `(a^(2)+b^(2)+c^(2))/(ab+bc+ca)=(1+1+4)/(1-2-2)=6/(-3)=-2` |
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| 631. |
यदि `x+1/(9x)=4` हो तो `9x^(2)+1/(9x^(2))` का मान क्या होगा?A. 140B. 142C. 144D. 146 |
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Answer» Correct Answer - B `x+1/(9x)=4` Multiply by 3 both side `3x+1/(3x)=12` squaring both side `9x^(2)+1/(9x^(2))+2xx3xx x1/(3x)=144` `9x^(2)+1/(9x^(2))+2=144` `9x^(2)+1/(9x^(2))=142` |
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| 632. |
यदि `x=sqrt(2)+1` है तो `x^(4)-1//x^(4)` का मान कितना होगा?A. `8sqrt(2)`B. `18sqrt(2)`C. `6sqrt(2)`D. `24sqrt(2)` |
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Answer» Correct Answer - D `x=sqrt(2)+1,1/x=sqrt(2)-1` `x=1/x=2` `x+1/x=2sqrt(2)` `x^(2)+1/(x^(2))=6` `x^(4)1/(x^(4))=(x^(2)-1/(x^(2)))(x^(2)+1/(x^(2)))` `=(x-1/x)(x+1/x)(x^(2)+1/(x^(2)))` `=2xx2sqrt(2)xx6=24sqrt(2)` |
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| 633. |
`a+b+c=0` है `1/((a+b)(b+c))+1/((a+c)(b+a))+1/((c+a)(c+b))` का मान ज्ञात करें? |
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Answer» Correct Answer - A given `a+b+c=0` `=1/((a+b)(b+c))+1/((b+c)(c+a))` `+1/((c+a)(a+b))` `=((a+b)+(a+b)+(b+c))/((a+b)(b+c)(c+a))` `=(2(a+b+c))/((a+b)(b+c)(c+a))` `=(2xx0)/((a+b)(b+c)(c+a))=0` |
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| 634. |
`(2a+b)^(2)-(2a-b)^(2)` का मान कितना है?A. `8ab`B. `-8ab`C. `8a^(2)+2b^(2)`D. `8a^(2)-2b^(2)` |
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Answer» Correct Answer - A `(2a+b)^(2)-(2a-b)^(2)` `implies 4a^(2)+b^(2)+4ab-4a^(2)-b^(2)+4ab` `=8ab` |
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| 635. |
यदि `x^(2)+y^(2)+2x+1=0` हो तो `x^(31)+y^(35)` का मान निकालें।A. -1B. 1C. 0D. 2 |
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Answer» Correct Answer - A `x^(2)+y^(2)+2x+1=0` `(x+1)^(2)+y^(2)=0` Let `(x+1)^(2)=0, y^(2)=0` `x=-1,y=0` Now `x^(31)+y^(35)=(-1)^(31)+(0)^(35)` `=-1` |
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| 636. |
यदि `x+y+z=9` हो तो `(x-4)^(3)+(y-2)^(3)+(z-3)^(3)-3(x-4)(y-2)(z-3)` का मान कितना है?A. 6B. 9C. 0D. 1 |
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Answer» Correct Answer - C `(x-4)^(3)+(y-2)^(3)+(z-3)^(3)` `((darr, darr, darr),(a^(3),b^(3),c^(3)-abc))` `-3(x-1)(y-2)(z-3)` `a+b+c=x-4+y-2+z-3` `=x+y+z-9` `=9-9=0` `a+b+c=0` So `(x-4)^(3)+(y-2)^(3)+(z-3)^(3)-3` `(x-4)(y-2)(z-3)=0` |
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| 637. |
यदि `x=y+2` हो तो `x^(3)-y^(3)-z^(3)` का मान बताइए? |
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Answer» Correct Answer - B Given `x=y+z` `:. x-y-z=0` then `x^(3)-y^(3)-z^(3)=3xyz` |
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| 638. |
यदि `x^(2)+1/(x^(2))=98(xgt0)`, हो तो `x^(3)+1/(x^(3))` का मान बताइए?A. 970B. 1030C. -970D. -1030 |
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Answer» Correct Answer - A `x^(2)+1/(x^(2))=98` `x^(2)+1/(x^(2))+2=100` `(x+1/x)^(2)=100` `x+1/x=10` `x^(3)+1/(x^(3))=10^(3)-3xx10` `x^(3)+1/(x^(3))=970` |
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| 639. |
यदि `x+1/x=3` हो तो `x^(8)+1/(x^(8))` कितना है?A. 2201B. 2203C. 2207D. 2213 |
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Answer» Correct Answer - C `x+1/x=3` On squaring both side we get `x^(2)+1/(x^(2))=7` Again on squaring both side `x^(4)+1/(x^(4))=47` And again squaring both side `x^(8)+1/(x^(8))=2207` |
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| 640. |
यदि `x+1/x=sqrt(3)` हो तो `x^(15)+x^(12)+x^(6)+1` का मान बताइए? |
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Answer» Correct Answer - A `x+1/x=sqrt(3)` `x^(3)+1/(x^(3))=(x+1/x)^(3)-3(x+1/x)` `=3sqrt(3)-3sqrt(3)=0` `x^(3)+1/(x^(3))=0` `x^(6)+1=0` `x^(18)+x^(12)+x^(6)+1` `x(x^(6)+1)+(x^(6)+1)` `x^(12)xx0+0=0` |
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| 641. |
यदि `x^(2)+y^(2)+6x+5=4(x-y)` हो तो `x-y` क्या होगा?A. 1B. -1C. 0D. 4 |
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Answer» Correct Answer - A `x^(2)+y^(2) +6x+5=4(x-y)` `x^(2)+y^(2)+6x+5-4x+4y=0` `x^(2)+2x+1+y^(2)+4y+4=0` `x^(2)+2x+1+y^(2)+4y+4=0` `(x+1)^(2)+(y+2)^(2)=0` `0 , 0` `x+1=0` `x=-1` `y+2=0` `y=-2` `(x-y=-1-(-2)=-1+2=1` |
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| 642. |
संख्याऐं `x,y,z` क्रमशः `2,3,5` के अनुपात में है और `x,y,z` का योगफल 80 है। यदि संख्या `z` का समीकरण `z=ax-8` हो तो `a` का मान ज्ञात कीजिए?A. 6B. `3//2`C. `3`D. `5//2` |
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Answer» Correct Answer - C Let numbers are `x=24, y=3r, z=5r` Sum `x+y+z=2r+3r+5r` `=10r=80` `r=8, x=16, y=24, z=40` Then `z=ax-8` `40=axx16-8` `a=13` |
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| 643. |
यदि `a^(3)=117+b^(3)` और `a=3+b` हो तो `a+b` का मान निकालें?A. 7B. 13C. 49D. 0 |
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Answer» Correct Answer - A `a^(3)=117+b^(3),a=3+b` `a^(3)-b^(3)117`……………i `a-b=3`……..ii put `a=6,b=2` both eq satisfy Now `a+b=5+2-7` |
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| 644. |
यदि `a=299, b=298, c=297` हो तो `2a^(3)+2b^(3)+2c^(3)-6abc` का मान बताइए?A. 5154B. 5267C. 5364D. 5456 |
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Answer» Correct Answer - C `a=299` `b=298` `c=297` `2a^(3)+2b^(3)+2c^(3)-6abc` `=2(a^(3)+b^(3)+c^(3)-3abc)` `=2(a+b+c)[(a^(2)+ b^(2)+c^(2)-a b-bc-ca)]` `2xx1/2(a+b+c)` `[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]` `=(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]` `=(299+298+297)[(299-298)^(2)` `+(298-297)^(2)+(297-299)^(2)` `=894xx[1^(2)+1^(2)+2^(2)]` `894xx[1+1+4]` `894xx6=5364` |
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| 645. |
यदि `a/(1-2a)+b/(1-2b)+c/(1-2c)=1/2`, हो तो `1/(1-2a)+1/(1-2b)+1/(1-2c)` का मान क्या है?A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - D `a/(1-2a)+b/(1-2b)+c/(1-2c)=1/2` Multiply by 2 both side `implies (2a)/(1-2a)+(2a)/(1-2b)+(2c)/(1-2c)=1` Adding 3 both side `implies 1+(2a)/(1-2a)+1+(2b)/(1-2b)+1` `(2c)/(1-2c)=1+3` `implies 1/(1-2a)+1/(1-2b)+1/(1-2b)=4` |
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| 646. |
यदि `(3-5x)/(2x)+(3-5y)/(2y)+(3-5z)/(2z)=0`, तो `2/x+2/y+2/z` क मान क्या है?A. 20B. 10C. 5D. 15 |
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Answer» Correct Answer - B `(3-5x)/(2x)+(3-5y)/(2y)+(3-5z)/(2z)=0` or `3/(2x)-5/2+3/(2y)-5/2+3/(2z)-5/2=0` or `3/(2x)+3/(2y)+3/(2z)=(3xx5)/2` or `1/x+1/y+1/z=(3xx5xx2)/(2xx3)` or `2/x+2/y+2/z=(3xx5xx2xx2)/(2xx3)` `=10` |
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| 647. |
`x` का मान बताइए जो भिन्न `(x+a^(2)+2c^(2))/(b+c)+(x+b^(2)+2a^(2))/(c+a)+(x+c+2b^(2))/(a+b)=0` को संतुष्ट करता है।A. `(a^(2)+b^(2)+c^(2))`B. `(a^(2)+2b^(2)+c^(2))`C. `-(a^(2)+b^(2)+c^(2))`D. `-(a^(2)+b^(2)+2c^(2))` |
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Answer» Correct Answer - C `(x+a^(2)+2c^(2))/(b+c)+(x+b^(2)+2a^(2))/(c+a)+` `(x+c+2b^(2))/(a+b)=0` Let `(x+a^(2)+2c^(2))/(b+c)=0` `(x+b^(2)+2a^(2))/(c+a)=0` `x=-2c^(2)-a^(2)`……………..i `x=-2a^(2)-b^(2)`……………ii `(x+c+2b^(2))/(a+b)=0, x=-2b^(2)-c`…………….iii From eq i, ii and iii `3x=-2c^(2)-a^(2)-2a^(2)-b^(2)-2b^(2)-c^(2)` `3x=-3(a^(2)+b^(2)+c^(2))` `x=-(a^(2)+b^(2)+c^(2))` Alternate: `(x+a^(2)+2c^(2))/(b+c)+(x+b^(3)+2a^(2))/(c+a)` `(x+c^(2)+2b^(2))/(a+b)=0` put `a=b=c=1` `(x+1+2)/2+(x+1+2)/2+(x+1+2)/2=0` `(x+3+x+3+x+3)/2=0` `3x+9=0` `3x=-9` `x=-3` Now option C `-[a^(2)+b^(2)+c^(2)]` `=-[1+1+1]=-3` (satisfy) |
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| 648. |
यदि `m=sqrt(5+sqrt(5+sqrt(5+………….)))` और `n=sqrt(5-sqrt(5-sqrt(5-……..)))` हो तो `m` और `n` होल्ड के बीच निम्नलिखित में से क्या संबंध है?A. `m-n+1=0`B. `m+n+1=0`C. `m+n-1=0`D. `m-n-1=0` |
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Answer» Correct Answer - D Let `m=sqrt(5+sqrt(5+sqrt(5)))` Factor `=(a)xx(a+1)` Here `m=a+1` or `m-1=a` …………….i Let `n=sqrt(5-sqrt(5-sqrt(5)))` Factor `=(a)xx(a+1)` Here `n=1`…………ii From i & iii `m-1=n` or `m-n-1=0` |
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| 649. |
यदि `3(a^(2)+b^(2)+c^(2))=(a+b+c)^(2)` है तो `a,b` और `c` के बीच क्या संबंध है?A. `a=b!=c`B. `a!=c!=c`C. `a!=b=c`D. `a=b=c` |
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Answer» Correct Answer - D Shortcut Method Always do these types of question with the help of Put `a=b=c=1` `3(1^(2)+1^(2)+1^(2))=(a+b+c)^(2)` `3=3` satisfied So this is answer `to a=b=c` |
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| 650. |
यदि `x^(4)+2x^(3)+ax^(2)+bx+9` एक सम्पूर्ण वर्ग है जहां `a` और `b` का मान क्या होगा?A. `a=5,b=6`B. `a=6,b=7`C. `a=7,b=7`D. `a=7,b=8` |
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Answer» Correct Answer - B `x^(4)+2x^(3)+ax^(2)+bx+9` put `x=1` `=1+2xx1+a+b+9` `=1+2+a+b+9` `12+a+b` To make perfect square no. value of `a+b` must be either 4 or 13. Now option (b) `a=6, b=7, a+b=13`. makes perfect square `(25=5^(2))` |
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