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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.
| 12001. |
Prove that root 2 is a irrational |
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Answer» 2 is a rational not irrational because it can write in the form of p/q(2/1) Take a any value of this like a and b Then solve itBy following method |
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| 12002. |
Sinø*cosø |
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| 12003. |
Ap=2.3.4.5......... find sn |
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| 12004. |
Find the 17th term from the end of the AP.1,6,11,16,......211,216 |
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Answer» a = 216 d=-5n=17a17= a + 16d = 216 +16 (-5) =216-80 136 216 , 211, ............... 16,11,6,1a=216d= - 5 (211 - 216)n = 17a17=a+16(-5) = 216 - 80 = 136 |
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| 12005. |
show that square of any positive integer cannot be of the form 5q+2 or 5q+3 for any integer q |
| Answer» Let n be any positive integer. Applying Euclids division lemma with divisor = 5, we get{tex}\\style{font-family:Arial}{\\begin{array}{l}n=5q+1,5q+2,5q+3\\;and\\;5q+4\\;\\\\\\end{array}}{/tex}Now (5q)2 = 25q2 = 5m, where m = 5q2, which is an integer;{tex}\\style{font-family:Arial}{\\begin{array}{l}(5q\\;+\\;1)^{\\;2}\\;=\\;25q^2\\;+\\;10q\\;+\\;1\\;=\\;5(5q^2\\;+\\;2q)\\;+\\;1\\;=\\;5m\\;+\\;1\\\\where\\;m\\;=\\;5q^2\\;+\\;2q,\\;which\\;is\\;an\\;integer;\\\\\\;(5q\\;+\\;2)^2\\;=\\;25q^2\\;+\\;20q\\;+\\;4\\;=\\;5(5q^2\\;+\\;4q)\\;+\\;4\\;=\\;5m\\;+\\;4,\\\\\\;where\\;m\\;=\\;5q^2\\;+\\;4q,\\;which\\;is\\;an\\;integer;\\\\\\;(5q\\;+\\;3)^{\\;2}\\;=\\;25q^2\\;+\\;30q\\;+\\;9\\;=\\;5(5q^2\\;+\\;6q+\\;1)\\;+\\;4\\;=\\;5m\\;+\\;4,\\\\\\;where\\;m\\;=\\;5q^2\\;+\\;6q\\;+\\;1,\\;which\\;is\\;an\\;integer;\\\\\\;(5q\\;+\\;4)^2\\;=\\;25q^2\\;+\\;40q\\;+\\;16\\;=\\;5(5q^2\\;+\\;8q\\;+\\;3)\\;+\\;1\\;=\\;5m\\;+\\;1,\\;\\\\where\\;m\\;=\\;5q^2\\;+\\;8q\\;+\\;3,\\;which\\;is\\;an\\;integer\\\\\\end{array}}{/tex}Thus, the square of any positive integer is of the form 5m, 5m + 1 or 5m + 4 for some integer m.It follows that the square of any positive integer cannot be of the form 5m + 2 or 5m + 3 for some integer m. | |
| 12006. |
If 14th term of an AP is twice its 8th term is -8, then find the sum of its first 20 terms. |
| Answer» Let first term be a and common difference be d.Here, a14 = 2a8a + 13d = 2(a + 7d)a + 13d = 2a + 14da = - d...(i)a\u200b\u200b\u200b\u200b\u200b\u200b6\xa0= - 8a + 5d = -8 ... (ii)Putting the value of a from (i) in (ii), we get-d + 5d = -84d = -8d = -2Put d = -2 in (i)a = -(-2)a = 2So ,a = 2, d = - 2{tex}S _ { 20 } = \\frac { 20 } { 2 } [ 2 \\times 2 + ( 20 - 1 ) ( - 2 ) ]{/tex}{tex}= 10 [ 4 + 19 \\times ( - 2 ) ]{/tex}= 10(4 - 38)= 10\xa0{tex}\\times{/tex}(-34)= - 340. Which is the required sum of first 20 terms. | |
| 12007. |
Formula of crossmultiplication in linear equation in two variables |
| Answer» X/b1c2 -b2c1 +y/c1a2-c2a1 -1/a1b2-b2a1 | |
| 12008. |
Proof od pythagorus theroum |
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| 12009. |
Find the value of 10 square 10 - cot square 80 |
| Answer» Given, tan210°-cot280°=\xa0tan2(90° - 80°) - cot280°{tex}[\\because tan(90^o-\\theta)=cot\\theta]{/tex}= cot280° - cot280°= 0 | |
| 12010. |
Find the value of a when the distance between the points (3,a) and (4,1)is 10 |
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Answer» 10=√(4-3)whole sq+(1-a)whole sq distance =√x1-x2+y1+y2 |
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| 12011. |
Proof BPT Therom ? |
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| 12012. |
find the trigonometric ratios of 30 and 60 |
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| 12013. |
Show that 3+1 is a composite number |
| Answer» 3+1=4.4 is a composite number. As its factor are more than 2.i.e.(1,2,4) | |
| 12014. |
How to solve quadratic equation by complet sqare |
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| 12015. |
If m=cosec A-SinA and n=secA-tan A ,prove that (m^2.n)^2/3 + (n^2.m)^2/3=1 |
| Answer» Given,(cot{tex}\\theta{/tex}\xa0+ tan{tex}\\theta{/tex}) = m and (sec{tex}\\theta{/tex}\xa0- cos{tex}\\theta{/tex}) = n{tex}\\Rightarrow \\left( \\frac { 1 } { \\tan \\theta } + \\tan \\theta \\right) = m{/tex}\xa0and\xa0{tex}\\left( \\frac { 1 } { \\cos \\theta } - \\cos \\theta \\right){/tex}\xa0= n{tex}\\Rightarrow \\left( \\frac { 1 + \\tan ^ { 2 } \\theta } { \\tan \\theta } \\right) = m{/tex}\xa0and\xa0{tex}\\frac { \\left( 1 - \\cos ^ { 2 } \\theta \\right) } { \\cos \\theta }{/tex}\xa0= n{tex}\\Rightarrow \\left( \\frac { \\sec ^ { 2 } \\theta } { \\tan \\theta } \\right){/tex}\xa0= m and\xa0{tex}\\frac { \\left( 1 - \\cos ^ { 2 } \\theta \\right) } { \\cos \\theta }{/tex}\xa0= n{tex}\\Rightarrow m = \\frac { 1 } { \\cos ^ { 2 } \\theta \\times \\frac { \\sin \\theta } { \\cos \\theta } }{/tex} and\xa0{tex}\\frac { \\sin ^ { 2 } \\theta } { \\cos \\theta } = n{/tex}\xa0{tex}\\Rightarrow m = \\frac { 1 } { \\cos \\theta \\sin \\theta } {/tex}\xa0and\xa0{tex}n = \\frac { \\sin ^ { 2 } \\theta } { \\cos \\theta } {/tex}.......(1)Now, L.H.S.{tex}= \\left( m ^ { 2 } n \\right) ^ { \\frac { 2 } { 3 } } - \\left( m n ^ { 2 } \\right) ^ { \\frac { 2 } { 3 } } {/tex}{tex}= \\left[ \\frac { 1 } { \\cos ^ { 2 } \\theta \\sin ^ { 2 } \\theta } \\times \\frac { \\sin ^ { 2 } \\theta } { \\cos \\theta } \\right] ^ { \\frac { 2 } { 3 } } - \\left[ \\frac { 1 } { \\cos \\theta \\sin \\theta } \\times \\frac { \\sin ^ { 4 } \\theta } { \\cos ^ { 2 } \\theta } \\right] ^ { \\frac { 2 } { 3 } }{/tex}. [from (1)]{tex}= \\left( \\frac { 1 } { \\cos ^ { 3 } \\theta } \\right) ^ { \\frac { 2 } { 3 } } - \\left( \\frac { \\sin ^ { 3 } \\theta } { \\cos ^ { 3 } \\theta } \\right) ^ { \\frac { 2 } { 3 } } = \\frac { 1 } { \\cos ^ { 2 } \\theta } - \\frac { \\sin ^ { 2 } \\theta } { \\cos ^ { 2 } \\theta }{/tex}= sec2{tex}\\theta{/tex}\xa0- tan2{tex}\\theta{/tex}\xa0= 1 [{tex}\\because{/tex} sec2{tex}\\theta{/tex}\xa0- tan2{tex}\\theta{/tex}\xa0= 1]= R.H.S. Hence, Proved. | |
| 12016. |
Divide 15 into 2 equal parts such that the sum of their reciprocals would be 3/10(3 by 10) |
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Answer» Let the nos be x and yThen x+y= 15 》y=15-xAnd You should take the two part of fifteen = x and (15-x) hence the equation of this condition was 1/x+1/15-x=3/10 Let one be xOther be y X+Y=151/x+1/Y=160X+y/xy=160 |
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| 12017. |
What is a formula of triangle |
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Answer» 1/2 *b*h Area of triangle= Half of base×height |
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| 12018. |
Matrics |
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| 12019. |
how to prove triangle by thales theorem? |
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| 12020. |
Find the sum of all 3 digit natural numbers which are multiples of 11 and 7 |
| Answer» 777 | |
| 12021. |
What a2 + b2 |
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| 12022. |
Find the value of x if the distance between the points (x,-1) and (3,-2) is x+5 |
| Answer» We have to find the value of x, if the distance between the points (x, -1) and (3, 2) is 5.Let P(x, -1) and Q(3, 2) be the given points. Then,PQ = 5{tex}\\Rightarrow \\quad \\sqrt { ( x - 3 ) ^ { 2 } + ( - 1 - 2 ) ^ { 2 } } = 5{/tex}Squaring both sides,we get,{tex}\\Rightarrow{/tex}(x - 3)2 + 9 = 52\xa0{tex} \\Rightarrow{/tex}x2 - 6x + 18 = 25{tex}\\Rightarrow{/tex}\xa0x2 - 6 x - 7 = 0{tex}\\Rightarrow{/tex}(x - 7) (x + 1) = 0{tex}\\Rightarrow{/tex}\xa0x = 7 or, x = -1 | |
| 12023. |
What is biggest prime number |
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Answer» Infinite Impossible to tell |
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| 12024. |
If tan A= cot B prove that A+B=90° |
| Answer» tanA =tan(90-B)A=90\'-B90\'=A *B | |
| 12025. |
Hcf of 4052 and 12576 by euclid algorithm |
| Answer» {tex}12576 = 4052 \\times 3 + 420{/tex}{tex}4052 = 420 \\times 9 + 272{/tex}{tex}420 = 272 \\times 1 + 148{/tex}{tex}272 = 148 \\times 1 + 124{/tex}{tex}148 = 124 \\times 1 + 24{/tex}{tex}124 = 24 \\times 5 + 4{/tex}{tex}24 = 4 \\times 6 + 0{/tex}HCF of 12576 and 4052 is \'4\'. | |
| 12026. |
Show that the square of any positive odd integer is of the form 8m+1 |
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| 12027. |
Find the 5th term of ap 5,9,13........ |
| Answer» 21 | |
| 12028. |
Subscribe khopda king on YouTube |
| Answer» Subscribe khopda king on YouTube | |
| 12029. |
Find the HCF of 135 and 225 by Euclid division algorithm |
| Answer» By using EDL we find the HCF of 135 and 225p=aq+r225=135×1+90135=90×1+4590=45×2+0 ^ HCF | |
| 12030. |
Who is the father of geometry. |
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Answer» Euclid Eculid Euclid is the father of geometry. |
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| 12031. |
Prove 1/√2 |
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| 12032. |
Sin60 + sin90 + cto67 |
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| 12033. |
7x - 2y = 13x + 4y= 15Solve by elimination method |
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| 12034. |
Express each of the following as a fraction in simplest form(1)0.365 recring on 65 |
| Answer» We have to express the given decimal in fractional form. So for that, let {tex}x = 0.3 \\overline { 65 }{/tex}, thenx = 0.3656565.... ...(i)10x = 3.656565.... ...(ii)1000x = 365.656565.... ....(iii)Subtracting (ii) from (iii), we obtain\xa0{tex}990x = 362 \\\\ \\Rightarrow x = \\frac { 362 } { 990 } = \\frac { 181 } { 495 }{/tex} | |
| 12035. |
+2-(-2) |
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Answer» 4 +4 +4 4 4 4 |
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| 12036. |
2.1 |
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| 12037. |
If a+b=10 .and ab=9 then (a, b)=.......? |
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Answer» Ab=9 ,A=9/b9/b+b=109+b²=10bb²-10b+9=0b²-9b-b+9=0b(b-9)-1(b-9)=0(b-1)(b-9)=0b=1,9If b=1A=9And if b=9A=1 Vansh 1 Hello |
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| 12038. |
Sbdudjdjdjdbx |
| Answer» Wrong question | |
| 12039. |
In a lottery there are 10prizes and 25 blanks what is the probability of getting a prize |
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Answer» And is 10/35=2/7 2/7 is a right answer 10 by 25 10 by 25 2/7 |
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| 12040. |
Express the trignometric ratios sinA,secA,tanA in term ofcotA |
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| 12041. |
Is it Same syllabus of 2018 or 2019 |
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| 12042. |
Can u pls give me this year question paper 2018 |
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Answer» But how please give your whatsapp number Yes |
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| 12043. |
Prove that line segment joining points of contact of two parallel tangent pass through center |
| Answer» Given: l and m are the tangent to a circle such that l || m, intersecting at A and B respectively.To prove: AB is a diameter of the circle.Proof:A tangent at any point of a circle is perpendicular to the radius through the point of contact.{tex}\\therefore{/tex}\xa0{tex}\\angle X A O = 90 ^ { \\circ }{/tex}and\xa0{tex}\\angle Y B O = 90 ^ { \\circ }{/tex}Since\xa0{tex}\\angle X A O + \\angle Y B O = 180 ^ { \\circ }{/tex}\xa0An angle on the same side of the transversal is 180°.Hence the line AB passes through the centre and is the diameter of the circle. | |
| 12044. |
X-3y-3, |
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| 12045. |
Quadra |
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| 12046. |
Ab 2 |
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| 12047. |
(alpha +beta) square - (beta -alpha)square=4 (alpha×beta) why?? |
| Answer» Yes it\'s possible | |
| 12048. |
What is the definition of integer |
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Answer» Combination of whole number as well as negative numbers .. It is a whole number that can be positive,negative or zero. |
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| 12049. |
Rs aggarwal solutions new edition chapter 1 |
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| 12050. |
Tenth maths question paper 2018 solutions |
| Answer» Check question papers here :\xa0https://mycbseguide.com/cbse-question-papers.html | |