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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.
| 301. |
QuADRATIC BOUATIONS23consecutive positive integers is 306. We need to find the() The product of twointegers. |
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Answer» Let the numbers be n and n+1 According to question n ( n + 1) = 306 Rather then solving equation observen ( n + 1) = 17 × 18 So, n must be 17 So, consecutive number are 17 and 18 |
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| 302. |
2Two Marks Question3. In the given figure, O is the centre ofcircle and A, B, C, D and E are points on thecircle such that AB BC CD DE EA. Findthe value of ZAOB |
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| 303. |
SECTION-DQuestion numbers 23 to 30 carry 4 marks each.23. Let p and q are the remainders when the polynomials xxax -12xvalue of a.2x2 - 5ax 7 and6 are divided by (x +1) and (x-2) respectively. If 2p+q 6, find the |
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Answer» Thanks |
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| 304. |
Question numbers 23 to 30 carry 4 marks each.23. If the equation(++2mcx+ (e- 0 has equal roots, prove that d21+of an A p. prove that. S20 = 3(San-S10) |
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| 305. |
Question numbers 23 to 30 carry 4 marks each.23. Anil takes 6 days less than the time taken by Varun to finish a piece of work. Iftaken by Varun to finish the work independently. |
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| 306. |
6.215750什130°эт⑨f 6.28 |
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Answer» Thanks |
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| 307. |
Question numbers 23 to 30 carry 4 marks each.23. Anil takes 6 days less than the time taken by Varun to finish a piece of work. Ifboth Anil and Varun together can finish that work in 4 days, find the timetaken by Varun to finish the work independently. |
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Answer» LET ANIL BE xAND VARUN BE yAccording To Question x=y-6 y=x+6..........(1) ANIL TAKES 1/xVARUN TAKES 1/y NOW, 1/x+1/y=1/4 x+y/xy=1/4............(2)put the value of x in eq. 2 x+x+6/x(x+6)=1/4 2x+6/x²+6x=1/4NOW CROSS MULTIPLY 8x+24=x²+6x x²+6x-8x-24 x²-2x-24 x²-6x+4x-24 x(x-6)+4(x-6) (x+4)(x-6) x=-4(neg) x=6ANIL TAKE 6DAYS FINISH WORK SEPARATELY NOWVARUN TAKE (X+6) FINISH WORK SEPARATELY∴ 6+6=12 ( |
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| 308. |
n numbers 23 to 30 carry 4 marks each.E4 is a root of the equation 12 + 2x + 4p0,find the values of k for which the equation+pr(1 + 3k) + 7(3 + 2k) = 0 has equal roots. |
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Answer» Like if you find it useful |
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| 309. |
हू. .िनर [् ट) | 6—— = —x— |+ ,éके. 157 8) \is )) |
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Answer» -6/15 * (7/8 + - 5/12) = (-6/15 * 7/8) + (-6/15 * - 5/12) LHS: - 6/15 * (7/8 - 5/12)= -2/5 * (21 - 10)/24= - 2/5 * 11/24= - 11/60 RHS: (-6/15 * 7/8) + (-6/15 * - 5/12) = (-14/40) + (10/60)= (-14*3 + 20)/120= (-52 + 30)/120= (-22)/120 = - 11/60 LHS = RHSHence proved |
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| 310. |
I157-6r+7 में से 8-4x+3x-x' को घटाइए। |
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Answer» 2.5×(10) |
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| 311. |
The sum of a nalulAlthe number.The sum of two natural numbers isnumbers.28 and their product is 192. Find thenf twe consecutive positive integers is 365. Fin |
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Answer» let the two number be X and yhence X+y=28and xy=192hencex]=192/yso192/y+y=28192+y^2=28yy^2-28y+192=0 y=-b+-√b^2-4ac/2a y=16 and 12hence y=16then X=192/16=12and when y=12X=16 |
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| 312. |
What is the cost of 9 bananas, ifthe cosI dozen= 12 units3:t of a dozen bananas is ?R20 |
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Answer» cost of 12 bananas=20cost of 1 banana=20/12=5/3cost of 9 banana=5/3×9=15 |
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| 313. |
Question numbers 13 to 22 carry 3 marks each.Ifxsin3 θ + ycos3 θsin θ cos θ and x sin θ-ycos θ, prove that |
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Answer» Like if you find it useful |
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| 314. |
42. A question paper has descriptive questions carrying 3 marks each and multiple choicequestions carrying 1 mark each. There are 24 questions in all and the total marks of thepaper is 50. Find the number of questions that carry 3 marks. |
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Answer» 13,11 is the correct answer of the given question |
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| 315. |
uestion numbers 13 to 22 carry 3 marks each.13. Prove that v3+ V5 is an irrational number |
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| 316. |
tion numbers 13 to 22 carry 3 marks each.in figure, S and T trisect the side QR of a right triangle PQR, pro |
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Answer» Let,QS=xQS=ST=TR=xQT=2xQR=3xInΔPQT,∠Q=90°PT²=PQ²+QT² =PQ²+4x² -------------- 1InΔPQR,∠Q=90°PR²=PQ²+QR² =PQ²+9x²InΔPQS,∠Q=90°PS²=PQ²+QS² =PQ²+x²From eq.18PT²=8PQ²+32x²--------------------- eq.2[by multiplying eq.1 by 8]3PR²+5PS²=3(PQ²+9x²)+5(PQ²+x²) =3PQ²+27x²+5PQ²+5x² =8PQ²+32x² =8(PQ²+4x²) =8PT² [from eq.2] |
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| 317. |
SECTIOestion number 19 to 28 carry 3 marks eaProve that sqrt 7 is an irrational number.OR |
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| 318. |
Question Numbers 13 to 22 carry 3 marks each.gosative13. Show that any positive odd integer is of the form Aq - 1 or Aq+3 wibem swa |
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Answer» Show that any positive odd integer is of the form 4q+1 or 4q+3 where q is some integer. Show that the square of an odd positive integer can be of the form 6q+1 or 6q+3 for some integer q. Prove that the square of any positive integer is of the form 3m or 3m+1. For any positive integers n, prove that n3-n is divisible by 6. Show that one and only out of n,n+4,n+8,n+12 and n+16 is divisible by 5, Where n is any positive integer. Write the prime factors of 546. |
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| 319. |
Q.8 15 जुलाई 2019 को 12:46 p.m. से 16 जुलाई 2020 12:38 p.m. तक की अवधि के बीच का कुल समय कितना| 3है?Ans* X1. 367 दिन 8 मिनटX2. 366 दिन 8 मिनटX3. 365 दिन 23 घंटे 52 मिनटVisit wwww.examsguruji.com for tons free study materilas &Downloaded from www.examsguruji.com4. 366 दिन 23 घंटे 52 मिनट |
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Answer» 366 days 23 hour 52 minutes and 42 seconds |
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| 320. |
5.The year 2023 will have:i. 364 daysii. 365 daysiii. 366 daysiv. none of these |
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Answer» There are 365 days in 2023 thanks |
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| 321. |
o friends were born in the year 2000. What is the probability that they have the samethday?72(C) 365(D) 183366365 |
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| 322. |
365 दिन का 20% कितना है ?| Find 20% of 365 days: |
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Answer» To find:20% of 365 days =(20/100)×365=73 days |
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| 323. |
६, ५16. 20, 24, 28, 32 का ल.स. ज्ञात कीजिए।(1) 300 20 3306 3) 33% (4) 366 |
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Answer» 3 3366 is the correct answer of your question 3366 is the right answer..... 3366 I the rightv answer 3366 is the right answer..... 3366 is the right answer |
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| 324. |
lcm of 366 and 54 |
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Answer» 366 = 2 × 3 × 61 54 = 2 × 3³ So, LCM (366, 54) = 2 x 3 x 3 x 3 x 61 = 3294 |
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| 325. |
a distanceof 366C1าวConney fro, would have taken 21mus find thu ousin al sRaxd oF the tha |
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| 326. |
12.Avesselhas4litersand500mi of curd In how many glasses each of 25 ml capacity, can it befilled? |
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Answer» If you find this solution helpful, Please give it a 👍 |
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| 327. |
13.Are the following pair of statements negation of each ather?The number π is not a rational number.The number π is 1101 an irrational number.The number π is a rational number.The number t is an irrational number.ii) |
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| 328. |
TuT3 tu LUBlete 10,000 runsple 8 : A vessel has 4 / 500 m/ of curd. In how many glasses, each of 25 ml of capacity,lution:can it be filled?Total quantity of curd 4 5 m |
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Answer» plz take a New photo |
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| 329. |
2. Give one example each to the following statements.i A number which is rational but not an integerii. A whole number which is not a natural numberiii. An integer which is not a whole numberiv. A number which is natural number, whole number, integer and rational number.v. Anumber which is an integer but not a natural number. |
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Answer» (1.) 2.5(2.) 0(3.) -5(4.) 100(5.) -7 |
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| 330. |
A motor boat whose speed is 20km/hr in still water takes 1 hr more to 21 km up stream than to downstream to the same .Find the speed of the stream. |
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| 331. |
x 2400 : speed cannot be negativeloriginal speed2400 kmph., original duration of the flightdistancespeed60002400 hrs 2hrsA motorboat whose speed in still water is 5 km/hr, takes 1 hourmore to go 12 km upstream than to return downstream to the samespot. Find the speed of the stream.CBSE 2009CSpeed of the motorboat in still water-5 km/hr.Let the speed of the stream be x km/hr.Then, speed upstream (5- x) km/hr.Speed downstream- (5+x) km/hr.Time taken to go 12 km upstreamhrs.(5-x) |
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| 332. |
a24.alA motor boat whose speed water isdownstream to the same spot. Find theSd in still water is 5 km/hr, takes 1 hour more to go 12 km upstream than to return[41speed of the stream |
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| 333. |
motorboat whose speed in still water is 5takes 1 hour more to go 12 kmstream than to return downstream to then/hr,me spot. Find the speed of the stream. |
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| 334. |
by 100 km/hr. istream that to return down stream to the same spot. Find the speed of the stream.nd the ongitalpee) ioul UltIit4. A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km upICBSE 2014] |
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| 335. |
r whose speed is 18 km/hr in still water takes 1hr more to go 24 kmupstream than to return downstream to the same spot. Fidthe speod of the stream |
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Answer» Given : The speed of the motor bike instill water is 18 kmph, It takes 1 hour to travel upstream & return to same spot,. From this information we can say that, ⇒ The speed of motor boat (boat's engine) = 18 kmph , ⇒ It traveled 24 km upstream & 24km downstream in 1 hour,. To Find :The speed of stream Distance upstream = Distance downstream = 24 km Speed of the boat going upstream, vup=18−x Speed of the boat going downstream, vdown=18+x Time taken going upstream, tup=Distance upstreamSpeed upstream =2418−x tup=2418−x -------- (1) Time taken going downstream, tdown=Distance downstreamSpeed downstream =2418+xor tdown=2418+x --------- (2) Using equation (1), (2) and (A):2418−x=2418+x+1 24(18+x)=24(18−x)+(18+x)(18−x) 24∗18+24x=24∗18−24x+182−x2x^2+48x−182=0x^2+54x−6x−324=0(x+54)(x−6)=0x =6 (Rejecting negative value of x) |
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| 336. |
Question numbers 13 to 22 carry 3 marks eache13. Find HCF and LCM of 404 and 96 and verify that HCF x LCMProduct of the two |
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Answer» HCF of 404 and 96 404 = 2*2*101 96 = 2*2*2*2*2*3 Common Factors = 2*2 HCF of 404 and 96 = 4 LCM of 404 and 96 404 = 2*2*101 96 = 2*2*2*2*2*3 LCM = 2*2*2*2*2*3*101 = 9696 LCM of 404 and 96 is 9696 HCF× LCM = Product of the two numbers ⇒ 4*9696 = 404*96 ⇒ 38784 = 38784 LHS = RHS Hence, it is verified |
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| 337. |
the perimeter of a rectangle is 56 CM. the ratio of length and it's breath is 4:3 . find the length and breath of the rectangle. |
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Answer» wrong wrong answer is length=16 and breath =12 thanks The Perimeter of a rectangle is 56cm. THE Ratio of the length to width is 4:3. Find the length and width of the rectangle/-----------------------4:3 is the same as 4x:3x where 4x is length and 3x is width.------------Perimeter = 2(length + width)------56 = 2(4x+3x)7x = 28x = 4-----length = 4x = 16 cmwidth = 3x = 12 cm-----Area = 12*16 = 192 cm^2 |
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| 338. |
Question mumbers 13 to 22 carry 3 marks each.13. Find HCF and LCM of 404 and 96 and verify thatHCF x LCM Product of the two given numbers. |
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Answer» 404 = 2×2×101 96 = 2×2×2×2×2×3 HCF = 2×2 = 4 LCM = 2×2×2×2×2×3×101 = 9696 HCF × LCM = 9696×4 = 38784 Product of two numbers = 404×96 = 38784 HCF×LCM = Product of two numbers |
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| 339. |
alune o f cuboid rhase length 20mÄ°breath is 15 cm and h is-10cm |
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Answer» 2(lb)(bh)(hl) formula of Volume of cuboid Volume of the cuboid =length×breadth×height=(20×15×10)cm³=3000 cm³ |
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| 340. |
What value is depicted By mof students of Class-V and VI who participated in "SAVE ENVIRONMENTcampaign is given by the expression (2pq + 3p. 29") and (4p" + + 3pq) respectively.a p-2, q 5, find how many more students of Class-V participated in the campaignrod hy narticipating students? |
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Answer» Number of class v students= (2pq + 3p^2 + 2q^2) Number of class VI students= (4p^2 + q^2 + 3pq) If p = 2, q = 5Then,Number of class V students = 2*2*5 + 3*2*2 + 2*5*5= 20 + 12 + 50 = 82 Number of class VI students = 4*2*2 + 5*5 + 3*2*5= 16 + 25 + 30 = 71 Therefore, Number of more students of class V participated = 82 - 71 = 11 Thanks the beginning of the year is a very good Night for solving the qua of the problem of the |
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| 341. |
examples of two irrational numbers whose is rational |
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Answer» √3,√5 is the required answer root3,root5 is required ans |
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| 342. |
6. Give an example of two irrational numbers whose(i) difference is an irrational number. |
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Answer» 10 +√ 3 , 5 - √3Difference=10+√3-5+√3=5+2√3=irrational |
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| 343. |
[206. Give an example of two irrational numbers whose(i) difference is an irrational number. |
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Answer» The difference can be either irrational or rational. The difference between two pi and pi is pi, which is irrational. The difference between pi and pi +1 is one, which is rational 10 +√ 3 , 5 - √3Difference=10+√3-5+√3=5+2√3=irrational |
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| 344. |
SECTION-Aive an example of two irrational numbers whose product is a rational n |
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| 345. |
I. Give an example of two irrational numbers whose product is a rational n |
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| 346. |
A motor boat whose speed is 18km/h in still water takes 1hour more to go 24 km upstream than to return downstreamto the same point. Find the speed of the stream |
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| 347. |
(ii) One million two hundred eighty(iii) Forty-nine million six hundredIn the Hindu-Arabic system, these n(i) Fifty-three thousand six hundr(i) Twelve lakh eighty-six thousan(iii) Four crore ninety-six lakh thirEXERC1. Write the numeral for each of the followin(i) Nine thousand eighteen(ii) Fifty-four thousand seventy-three |
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| 348. |
A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 kmupstream than to returndaurstream to the same spot. Find the speed of the stream |
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| 349. |
If the ratio of the 11h term of an AP to its 18th term is 2:3, find theratio of the sum of the first five terms to the sum of its first 10 terms |
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Answer» Solution:-(a + 10d)/(a + 17d) = 2/33a + 30d = 2a + 34d3a - 2a = 34 - 30a = 4da₅ = a + 4d= 4d + 4da₅ = 8da₂₁ = a + 20d= 4d + 20da₂₁ = 24dSo, a₅ : a₂₁ = 8 : 24 = 1 : 3The ratio of the sum of the first 5 terms to the sum of the first 21 terms.S₅ = 5/2(8d + 4d)= 60d/2S₅ = 30dS₂₁ = 21/2(8d + 20d)= 588d/2S₂₁ = 294dSo,S₅ : S₂₁ = 30d : 294d= 5 : 49 hit like if you find it useful |
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| 350. |
87xample 15- A motor boat whose speed is 1S km/h in still water takes I hour monego2km upstream than to return downstream to the same spot. Find the speed ofhe stream |
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