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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.
| 10001. |
What is division algorithm for polynomials |
| Answer» In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones. | |
| 10002. |
Find a quadratic polynomial whose sum of zeros and product of zeros are -3 and 4 |
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Answer» X²-3x+4 x^2+3x+4 |
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| 10003. |
Prove that root 8 is irrational number |
| Answer» suppose √8 = a/b with integers a, band gcd(a,b) = 1 (meaning the ratio is simplified)then 8 = a²/b²and 8b² = a²this implies 8 divides a² which also means 8 divides a.so there exists a p within the integers such that:a = 8pand thus,√8 = 8p/bwhich implies8 = 64p²/b²which is:1/8 = p²/b²or:b²/p² = 8which impliesb² = 8p²which implies 8 divides b² which means 8 divides b.8 divides a, and 8 divides b, which is a contradiction because gcd (a, b) = 1therefore, the square root of 8 is irrational. | |
| 10004. |
The HCF and LCM of two numbers 9 and 459 respectively. If one number is 27 .then find the other |
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Answer» second\xa0number\xa0=\xa0153Explanation:Let\xa0first\xa0number\xa0=\xa0a,second\xa0number\xa0=\xa0ba\xa0=\xa027\xa0( given )HCF(a,b)\xa0=\xa09andLCM\xa0(a,b)\xa0=\xa0459To\xa0find:Value of bsolution:We know that,$\\implies b = \\frac{9\\times 459}{27}$After cancellation, we get$\\implies b = 153$Therefore,second\xa0number\xa0=\xa0b\xa0=\xa0153 The other number is 153. Lesson 15 exercise 15.1 |
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| 10005. |
What is the meaning of Ap |
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Answer» a sequence of numbers in which each differs from the preceding one by a constant quantity (e.g. 1, 2, 3, 4, etc.; 9, 7, 5, 3, etc.). An Arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... The sum of a finite arithmetic progression is called an arithmetic series. |
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| 10006. |
What is different between sum of zero and product of zero |
| Answer» In\xa0any quadratic polynomial: The\xa0sum\xa0of the zeroes is equal to the negative of the coefficient of x by the coefficient of x2. The\xa0product\xa0of the zeroes is equal to the constant term by the coefficient of x2 | |
| 10007. |
If A,B,C are interior angles of ΔABC, show that : tan² ( B+C/2\u200b ) = Cosec² (A/2-1) |
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| 10008. |
Roor p - Root q= 20 find the maximum value of (p=5q)/20 |
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| 10009. |
Root 3 minus root cube is equals to hundred find the maximum value of P - 5q/.20 |
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| 10010. |
Find the zero of the polynomial of 7/3x + 4 |
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| 10011. |
Root 2,root 8,root 18,root 32,.... |
| Answer» root 50, root 72 | |
| 10012. |
Is x^2 -9/16x+1/16 same as 16x^2-9x+1 ?? |
| Answer» S | |
| 10013. |
Express the trigonometric ratios sinA , secA ,and tan A in terms of cot A |
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Answer» SinA= cotA/cosA.SecA= cot A×SineATan A =1/cotA To convert the given trigonometric ratios in terms of cot functions, use trigonometric formulasWe know that,cosec2A – cot2A = 1cosec2A = 1 + cot2ASince cosec function is the inverse of sin function, it is written as1/sin2A = 1 + cot2ANow, rearrange the terms, it becomessin2A = 1/(1+cot2A)Now, take square roots on both sides, we getsin A = ±1/(√(1+cot2A)The above equation defines the sin function in terms of cot functionNow, to express sec function in terms of cot function, use this formulasin2A = 1/ (1+cot2A)Now, represent the sin function as cos function1 – cos2A = 1/ (1+cot2A)Rearrange the terms,cos2A = 1 – 1/(1+cot2A)⇒cos2A = (1-1+cot2A)/(1+cot2A)Since sec function is the inverse of cos function,⇒ 1/sec2A = cot2A/(1+cot2A)Take the reciprocal and square roots on both sides, we get⇒ sec A = ±√ (1+cot2A)/cotANow, to express tan function in terms of cot functiontan A = sin A/cos A and cot A = cos A/sin ASince cot function is the inverse of tan function, it is rewritten astan A = 1/cot A |
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| 10014. |
2x+3y+5=03x+2y-12=0 |
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Answer» 2x+3y=-5 (1)3x-2y=12 (2)Add eq 1 and 2 we get5x+1y=7 (3)NowSubtract 1 from 2,we getX-5y =17 (4)Multiply 3 by 5 we get,25x+5y=35 (5)Now ,Add 4 and 5 we get,26x=52X=2now ,Substitute x=2 in eq35x+1y=75×2+1y=710+y=7y=7-10y=-3(x,y)=(2,-3) Thanks https://doubtnut.app.link/krNEmWdGxhb |
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| 10015. |
Please send rd Sharma Pdf of class 10 chapter 2 and 3. |
| Answer» https://drive.google.com/file/d/12Dazkzy3UKpbv6BUjrAg42ZMmH67msVL/view | |
| 10016. |
136 and 225 by Euclids division algorithm |
| Answer» 225=136×1+89136=89×1+4789=47×1+4247=42×1+542=5×8+25=2×2 +12=1×2+0 So the HCF is 1 | |
| 10017. |
The graph of the equation x minus y + 1 is equal to zero and x |
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| 10018. |
Does Euclid\'s Division Lemma will be deleted for the exam 2022? |
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Answer» No Nooo..CBSE has not informed about any deducted syllabus for this session |
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| 10019. |
Please send me maths rd sharma pdf |
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Answer» 1 chapter 1 chapter Of which chapter |
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| 10020. |
Probability of an event E + probability of the event `not E ` = |
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Answer» 1 1 1 |
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| 10021. |
m-7=3 |
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Answer» M-7=3 M=3+7=10 M=3+7=10 |
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| 10022. |
√x-5 -√x-8 =√2x-17 factorise this equation |
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| 10023. |
If A=2n+13,B=n+7 where n is a natural number , HCF of A and B |
| Answer» Given A = 2n + 13 and B = n + 7 and since n is a natural number A > B.A = 2(n + 7) - 1A = 2B - 1On dividing throughout with B,A/B = 2 - (1/B)B is always an integer => 1/B can never be an integer => A/B also can\'t be an integerSince A/B is not an integer we can conclude that\xa0A and B cannot have any integer in common. Therefore HCF of A and B is 1. | |
| 10024. |
Find the number of terms in the finite AP 3,6,9....111. |
| Answer» So, first term = a = 3Common difference = d = 3Last term = Tn = 111Let number of terms be n.Now, Tn = a + (n-1)dSo, 111 = 3 + (n-1)×3So, 108 = 3×(n-1)So, 108/3 = n-1So, n-1 = 36So, n = 37Thus, number if terms is 37. | |
| 10025. |
In a trapezium ABCD ,diagonals intersect at o .If OA =3x-19, OB=x-3,OC=x-5,OD=3, find x |
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| 10026. |
In given AP a = 7 ,a13=35 find d and S13 |
| Answer» d = 7/3S13 = 273 | |
| 10027. |
0.2x+0.3y=1.3;0.4x+0.5y=2.3 Find it by substitution method |
| Answer» Y=3 and X=2 | |
| 10028. |
x²-4x-1=0 |
| Answer» x2−4x+1=0(x−2)2−4+1=0(x−2)2=3(x−2)=+3\u200bor−3\u200bx=2+3\u200borx=2−3\u200b | |
| 10029. |
6 √x/x+4-2√x+4/x=11 |
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| 10030. |
Wht is composite number? |
| Answer» A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. | |
| 10031. |
Use Euclids division algorithm,find HCF of 1266 and 7344 |
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| 10032. |
Find the zeros of the polynomial f(x)=x²-√2x-3/2 |
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| 10033. |
Find the zeros of the polynomial f(x) x²+4x/3-32/9 |
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| 10034. |
Find HCF and division 652 and 375 |
| Answer» Using Euclid\'s division lemma 652= 375 multiply by 1+227375= 277 multiply by 1+98277= 98 multiply by 2+8198= 81 multiply by 1+1781= 17 multiply by 5+617= 6 multiply by 2+56= 5 multiply by 1+15= 1 multiply by 5+0So HCF=1HOPE THE ANSWER IS CORRECT | |
| 10035. |
Euclid s theoram |
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Answer» a=bq+r (0 |
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| 10036. |
If zeros of x^2-kx+6 are in the ratio 3:2 find k |
| Answer» 2ײ+k×+3=0 | |
| 10037. |
Formula of Euclid\'s algorithm |
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Answer» a = bq+r ,where 0_ a=bq+r where 0 | |
| 10038. |
If ?, ? and ? are the zeroes of the polynomial ?(?) = ?3 − ??2 + ?? − ?, then find 1?? +1?? +1??. |
| Answer» q | |
| 10039. |
4x²+x-5=0 solve this quadratic equation by completing the square method |
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| 10040. |
6{x^2+(1/x^2)} -25{x-(1/x)} +12 = 0Find the value of x. |
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| 10041. |
Find the roots of the equation x+3/x+2=3x-7/2x-3 |
| Answer» (x+1)(x-5) | |
| 10042. |
Find the sum of m terms of an A.P, a-3d, a-2d, a-d ,a, a+d ,a+2d +...... |
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| 10043. |
3x-4y=7 by substitution |
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Answer» 3x-4y=7_eq1x=7+4y/3_eq2Put value of x in eq 1You get y=0Put value of y in eq 1x=7/3 The second equation please Plz type the whole question |
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| 10044. |
3x=7+4y |
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| 10045. |
(sin 30° + cos 30°)-(sin 60°+ cos 60°) |
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Answer» 0 Answer will be 0. Sorry it\'s 1 2 |
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| 10046. |
4-5✓3 |
| Answer» 4-5√3= a/b-5√3= a/b-4√3=4/5-a/bRHS is not equal to LHSHENCE IT IS AN IRRATIONAL NUMBER. | |
| 10047. |
Sin 30 degree + cos 30 degree minus sin 60 degree + cos 60 degree |
| Answer» 1 | |
| 10048. |
Real number exercise 1.1 |
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| 10049. |
If 2sinΦ/(1+cosΦ+sinΦ) = X then find the value of 1-cosΦ+sinΦ/(1+sinΦ) |
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| 10050. |
What is the relation between zeros and coefficient of biquadratic polynomial |
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Answer» Like in 3x^2 + 5In this 3 is a coefficient Zeroes are number like a and b. Coefficient are numbers side the x and y. ? |
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