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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
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9. Find the prime factors of the following nu(ii) 765al 99 |
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Answer» Is 765 a prime number? For765, the answer is: No,765is not aprime number. The list of all positive divisors (i.e., the list of all integers that divide765) is as follows: 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255,765 Is 765 a prime number? For765, the answer is: No,765is not aprime number. The list of all positive divisors (i.e., the list of all integers that divide765) is as follows: 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255,765 765 is not a prime number and the list of all positive division are as follows: 1,3,5,9,15,17,45,51,85,153,255 and 765 765 is not a prime number and the list of all positive division are follows:1,3,5,9,15,17,45,51,85,153,255 and 765. |
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| 2. |
of the prayerxample 6 Fiad the dimensionssation : In Section 4.1., we found that ieo- o Applying thethe equation 2r' +1-300%0.2r-24r + 25r- 300-25-12)-o12X21 +25)oSo, the roots of the given equation areThas the breadth of the hall is 12 m. Its lenprescnt age sof the hall. it cannot begth 2tpositive mumhEXERCISE 42onsider he-9 Takin1. Find the roots of the follow ing quadratics of the eVr-0(iv) 2i-rithe ro(v) 100 20r+1=02 Solve the problens given in Evampie .3 Fiad two nambers whose4 Fiad two coasecutive positive integers, sum of whoseS. The alarude of a right ariangle is 7cm less than its busesum is 27 and product is 1825. The alinude of a right triangle is 7emthe other two sides,Acoage industry prodices a certain number of poceyon a purticular day that the cost of production of each uricietwice the number of articles praduced on that day. Etheday was 90 find the number of articles proiuced und be44 Solution of a Quadratic Equation by CompletingIn the prev ious section, you have learnt one methou of obuiningquation. In this section, we shall study another imethodConsider the following situation:The product of Sunita's age (in yearsi wo yeurs |
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| 3. |
Find the time taken by a train 180m long,running with the speed of 72 km/hr tocross an electrical pole- |
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Answer» Let the Time Taken by the Train be = TLength of the train(d) = 180mSpeed of the train(s)= 72km/h We know that,s = d/T∴ T = d/s T = 180/72 = 2.5s Time taken by the train to cross a man standing on a platform = 2.5s Like my answer if you find it useful! |
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| 4. |
magnification0.1f x=5 +2/6, find the values of x-+-2 and x3+21a. |
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Answer» hit like if you find it useful |
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| 5. |
1.If x3-x2-5x + 6 is divided by (x-2), then the remainder is |
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| 6. |
express the following as the product of exponent through prime factorizationI- 288 |
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| 7. |
U) -2)(5)Express ás a power of rational number with positive exponent:(c) 59x50 (359) *27 |
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Answer» 7) i) (1/5)^-3=(5)^3=125; ii) (-1/3)^-7=(-3)^7=-2187,; iii) (5)^-4×(5)^4=(5)^4/(5)^4=1; iv) (-2/3)^-5 × (-2//3)^-10= (-2/3)^5 ×(3/-2)^10=(3/2)^2; (v)[(-5/7)^3]-4=[(-125/343)]^-4=(343/-125)^4; vi)(3^-4)÷(9)^2×27; 81/81×27=1×27=27 a) (1/5)^-3=125; b) (-1/3)^-7=(-3)^7=-2187; c)5^4 × 5^-5= 1/5 (1/5)^-3=(5)^3=125, (-1/3)^-7=(-3)^7=-2187 5^4 × 5^-5=5^4-5=5^-1=1/5 |
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| 8. |
DSimplify and express the answer with positive exponent: |
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| 9. |
(512) 3 x (16)4 x (9)3. Simplify and express the answer with positive exponent: yx1 |
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Answer» (x^(4/3)×y^(1/3))/(x^(1/3)×y^(2/3))=x^(4/3-1/3)×y^(1/3-2/3)=x×y^(-1/3)=x/(y^3) |
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| 10. |
Simplify and express the answer with positive exponent:\sqrt{x^{4} y \times \frac{1}{\sqrt{x y^{2}}}} |
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| 11. |
Calculate the change in momentum of a van weighing 1200 kg when its speed decreases from 72 km/hr to 54 km/hr uniformly. |
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Answer» change in momentum is m(v1-v2)=1200((72-54)/3.6))=1200(5)=6000kgm/s..divided by 3.6 to convert km/hr to m/s |
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| 12. |
2. Simplify and express the result in power notation with positive exponent.2o (-4)4)8 (143-5(v) 2-3 х (-7) 3)3/(İİİ)(iii)(-3)4X(-3)4x(iv)_ (3-13-19) |
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| 13. |
5. Simplify and express the result with positive exponent.2 x 2" x3312 x 26. Solve for x. 27, 355-2. |
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Answer» 12^15/6^15 is answer |
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| 14. |
(1) ſ(sin x + cos x) dx |
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| 15. |
what is the base and exponent of 103 |
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Answer» 10 is the base and 3 is the exponent An expression that represents repeated multiplication of the same factor is called an exponent and factor is called as base Therefore,For 10^3 Base = 10, exponent = 3 the base is10 and exponent is 3 10 is the base 3 is exponent. 10 is base 3 is exponent |
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| 16. |
Write the base and the exponent in each case.Also, write the term in the expandedWnte the base and the exponent in each case. Also, write the term in the expanded1 34(iii) (5aby(iv) (4y)1V |
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| 17. |
Find:-10 2012cos xdxJ (1 - sin x) (1 +sin x) |
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| 18. |
Prove that : (sec 0+ cosec 6) (sin θ + cise-tan.D+cut α +2+2+ser 6cnsrch |
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| 19. |
List the elements of the following se(i) {X : x2 - 2x - 3 = 0}(ii) {X : X = 2y + 5; y e N and 2 syiii) {x : x is a factor of 24}iv) {x: Xe Z and x2 < 4}(v) {X: 3x - 2 s 10 and Xe N}vi) {x :4 - 2x >– 6, XE Z} |
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| 20. |
CISE 2.5ations.2.n 31 Sn=21A 6 |
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Answer» n=36 is the correct answer of the given question Yes 36 is the correct answer |
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| 21. |
OMS | Pago No.DatoExerAnswcr the followinaHou many nits arcise.6units are there n |
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Answer» 7 units are there in 27.27 = 20 + 7 |
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| 22. |
(6% o .16८ की xe 10801 + है)अल 2 |
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| 23. |
ve the following:I . 3sin-i x = sin-i (3-4x), xe |2 . 3cos-1x = cos-1 (4x3-30, xe-, l, tan--+ tan-IA-tan-1242 tan-ı+ tan-i-= tan-1-17ite the following functions in the simplest form:tan Vt -6. tan12-111-cos x1+cosxtan-cosx+sinx |
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| 24. |
26, in ΔRST (See Fig. 9.51), what is the value ofx?(a) 40(b) 90°(c) 80(d) 100bobo140a°Fig. 9.51 |
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| 25. |
7. If'a man travels 65 km in 3 days by walking 72 hours a day, in how many days will he travel 156 km by walking8 hours a day? |
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Answer» Every day he walks 7.5 hrsSo in three days he walks 7.5×3 =22.5hrsAnd he travelled 65km in these 22.5hrsSo the speed = distance/time = 65/22.5 = 2.88km/hr Speed of the man will remain same,So time = distance/speed = 156/2.88 = 54 hrs Everyday he walks 8hrs, so for 54 hrs, he has to walk 54/8 = 6.75 days |
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| 26. |
mnutes t6 2 hours.(ii) Is the statement true?54 km 72 km 20 hours : 25 hours. |
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Answer» No, the statement is not true, they are two different units, which cannot be compared. |
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| 27. |
A) 16nita passed around a basket of strawberries to the girls at her party Before the party she atstrawberries and gave a friend 3. Eight girls arrived at the party. The first girl took a strawberryecond girl took 3 strawberries, the third girl took 5 strawberries and so on. After the last gird tookrawberries, the basket was empty. How many strawberries were there in the basket at the beginn1 72(B) 6065(D) 45 |
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Answer» Let the number of strawberries in the basket at the beginning ben. Number of strawberries eaten by Anita and her friends before the arrival of 8 girls = (5 + 3) = 8 Total number of remaining strawberries in the basket = (n– 8) Number of strawberries taken by 1stgirl = 1 Number of strawberries taken by 2ndgirl = 3 Number of strawberries taken by 3rtgirl = 5 Number of strawberries taken by 4thgirl =7 Number of strawberries taken by 5thgirl = 9 Number of strawberries taken by 6thgirl =11 Number of strawberries taken by 7thgirl =13 Number of strawberries taken by 8thgirl =15 Total number of strawberries taken by 8 girls = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 ∴n– 8 = 64 ⇒n= 64 + 8 = 72 Thus, number of strawberries in the basket at the beginning = 72. Like my answer if you find it useful! |
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| 28. |
6.A man walks 10 km, then travels a certain distance by train and then by bus as far as twiceby the train. If the whole journey is of 70km, how far did he travel by train? |
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| 29. |
work to empty the tank in 1 day ?6. Ifa man travels 65 km in 3 days by walking 72 hours a day, in how many days will he travel 156kmby walking 8 hours a day? |
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Answer» Every day he walks 7.5 hrsSo in three days he walks 7.5×3 =22.5hrsAnd he travelled 65km in these 22.5hrsSo the speed = distance/time = 65/22.5 = 2.88km/hr Speed of the man will remain same,So time = distance/speed = 156/2.88 = 54 hrs Everyday he walks 8hrs, so for 54 hrs, he has to walk 54/8 = 6.75 days |
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| 30. |
can i write sinx•2cosx as 2sinx•cosx ??? is this possible? |
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Answer» yes you can write because when we put value like example: when x= 30° then sin30°.2cos30°=root 3/2 and 2sin30°.cos30°=root 3/2 hence both value are same .So you can write it as . hope this will help you like my answer and MARK IT AS BEST ANSWER. your answer is 2sim 30° |
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| 31. |
integrate1/(Sinx-2cosx)(2sinx +cosx)I am posting this 18th time |
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Answer» replace “t” with tanx and there you go! but answer given is this one put t= tanx u will get it but answer given is different |
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| 32. |
4) The teacher said, "I have thought of anumber. If you add 7 to 3 times the number,you get 31. What number have I thoughtof?" Can you answer the teacher'squestion? |
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Answer» 7+3x=31 3x=24 X=8 so the number the teacher thought of is 8 right answer is 8because 7+3x=313x=31-73x= 24x=24÷3x=8 7+3×=31 3×=24 x=8 So the number the teachers thought of is 8 is the correct answer right number is 8because 7+3x=313x=31-73x=24x=24÷3x=8 |
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| 33. |
4) The teacher said, "I have thought of anumber. If you add 7 to 3 times the number,you get 31. What number have I thoughtof?" Can you answer the teacher'sCortion2 |
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Answer» I tell the teacher the answer is 21 the answer is 10 because 7×3=21+10=31 Let the number be x 7+3x = 313x = 31-73x = 24X= 8 Ans. let the number be x7+3x=313x=31-73x=8 ans. let the no. be x; 7 + 3x = 31 3x = 31 - 7 3x = 24 x= = 24/3 = 8 3x+7 =313x = 31-73x =24x =24÷3x =8 3x +7 =313x=31-73x=24x=24÷3x=8 Let the number be x7 + 3x = 31Therefore, 3x = 31 - 7Therefore, 3x = 24Therefore, x = 24 ÷ 3Therefore, x = 8 |
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| 34. |
Q.2od subtracted 25 fromonju thought of a number. He multiplied the number by itself and suhteshe result. He got 2000. What was the number he thought of?2352 25133 454 80 |
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Answer» I think the answer is 25 itself I thing the answer is 25 and 80 itself 45 is the correct answer |
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| 35. |
Sides of a triangle are in the ratio 3:5:7 and its perimeter is 300m. Find itsarea. |
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| 36. |
which ONLY ONE is correctThe sides of a triangular plot are in the ratio 3:5:7 and its perimeter is 300m. Its area is |
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Answer» PLEASE LIKE IT, IF YOU FIND THIS SOLUTION HELPFUL. writeeeeee |
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| 37. |
a man travels 370 km bu train de gas if the250 km hain &rest cas it dekes this he that120km by draink sest by cas its takes 18 hintenfind the speed of hain for |
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Answer» Let the speed of the car be C kmphLet the speed of the train be T kmph 4 hours = 250 km/T kmph + (370 - 250) km/C kmph 4 = 250/T + 120/C --------eq(1) 4 hrs 18 minutes = 130 km / T kmph + (370 - 130)km / C kmph 258/60 = 4.3 = 130 / T + 240 / C ----------eq(2) Multiply eq(1) by 2 and subtract eq(2) from it 8 - 4.3 = 500/T - 130/T + 240/C - 240/C 3.7 = 370 / T T = 370/3.7 = 100 kmph Substitute the value of T in eq(1) to get, 4 = 250/T + 120/C4 = 250/100 + 120/C4 - 2.5 = 120/C C = 120/1.5 = 80 kmph The train runs at 100 kmph and the car runs at 80 kmph |
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| 38. |
da cas (xiby |
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Answer» d/dx (acos(x+b) = a*(-sin(x+b)*(1)= -asin(x+b) |
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| 39. |
I+ SIAACas A |
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| 40. |
2 (i) casINCERT |
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Answer» cos theta = 1/2 so theta is pi/ 3 = 60° |
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| 41. |
roots of x-px+-0, then the value ofα-α |
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| 42. |
11then evaluate12CosxLet f(x)=1** 102Cosx112Cosxnmetrico |
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| 43. |
px=2x×x+11x+5 |
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Answer» please like my answer if you find it useful |
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| 44. |
ind the vahel abcos² 16tcas 274. |
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Answer» hi please like my answer |
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| 45. |
8.Write the family of quadratic polynomials havingand 1 as its zeros |
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Answer» I don't know the answer of this question let α and β be the zeroesα=-1/4β=1the required quadratic polynomial isx²-(α+β)x+αβ=0x²-(-1/4+1)x+(-1/4x1)=0x²-[(-1+4)/4]x-1/4=0x²-3/4x-1/4=04x²-3x-1=0(multiply both sides by 4)so 4x²-3x-1 is the correct answer sum of zeroes= 1+(-1/4)= 4-1/4= 3/4product of zeroes= 1×(-1/4) = -1/4polynomial= x^2-x(sum of zero)+product of zerox^2-x(3/4)+(-1/4)1/4(4x^2-3x-1) |
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| 46. |
( 2 x - 1 ) ( x - 3 ) = ( x + 5 ) ( x - 1 ) |
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| 47. |
9. Write the family of quadratic polynomials havingand 1 as its zeros.4 |
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| 48. |
5. Prove that:- tnxsinx- 3xsincas 5x-Con |
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| 49. |
1.Ravish ordered a pizza and paid Rs 285 inclusive of taxes of Rs 35. Find the tax%. |
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| 50. |
ationAn ice piece floats in the water with 2 th of is volume below the water, What is the density of ie ?Ans. 900 kg/m3What 1s10usaldd nart remains below the water. What is the relative de |
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Answer» Answer: 1018 kg/m^3 (assuming density of ice= 916.8 kg/m^3 Explaination:Since the cube is displacing 9/10 of its volume of water, and that water must have the same weight as the entire ice cube, the density of water must be 10/9 times the density of ice.” If the density of ice at 0C is 916.8kg/m^3 so the density ofthiswater is 10/9 x 916.8 = 1018.7kg/m^3. |
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