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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.
| 1. |
Without performing the actual division, find the quotient when the sum of 17 and 71 is divided by0) 11Without performing any actual division, find the quotient when the difference of 25 and the num |
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Answer» 17 + 71 = 88 which is 8 x 11.So when divided by 11 quotient = 8.And when divided by 8 quotient = 11. |
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| 2. |
Without actual division 13/3125 |
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Answer» 3125 = 5*5*5*5*5 = 5⁵13/3125= 13/5⁵= (13*2⁵)/(5⁵*2⁵) {Multiplying the numerator as well as the denominator with 2⁵}= (13*32)/(10⁵)= 416/10⁵= 0.00416 |
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| 3. |
state thenatureofWithoutdecimalactual divisionexpansion.100 |
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Answer» 1) terminating decimals2) non terminating decimal is the correct answer of the given question 7/100=0.07; 9/2^3 5^7 3^2=9/8×78125x9= 9/72×78125=625000 |
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| 4. |
(ii) Without actual division, prove that 2xin With2) Is a factor of the polynomial -division, prove that 2x1-572 + 2x2 - x + 2 is divisible by x - 3x + 2. |
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Answer» x²-3x+2Sum=-3; product=2 x²-2x-1x+2x(x-2)-1(x-2)(x-2)(x-1)Therefore,(x-2)(x-1)are the factors. a)(x-2)x-2=0x=2So,p(x)=2 p(x)=2x⁴-5x³+2x²-x+2p(2)=2(2)⁴-5(2)³+2(2)²-2+2=32-40+8= -40+40=0Hence,it proves that (x-2) is a factor . b) (x-1)x-1=0x=1So,p(x)=1 p(x)=2x⁴-5x³+2x²-x+2p(1)=2(1)⁴-5(1)³+2(1)²-1+2=2-5+2-1+2=6-6=0 Hence,it proves that (x-1) is a factor. Thus 2x⁴-5x³+2x²-x+2 is divisible by x²-3x+2 |
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| 5. |
10. Write the decimal expansionof the Rational Numberwithout actual division. |
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Answer» 35/50 =35/2*5^2 =35*2^2*5^2/2*2*5^2 =35*4*25/2^2*5^2 =3500/10^4 =0.35 |
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| 6. |
6. Without actual division find whether the rational number132363x352 |
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Answer» The given number is rational number because it is p/q form where p and q are integers and q is not zero |
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| 7. |
I. Write down the decimal expansion of10 without actual division.3125 |
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Answer» 16/3125=16/5*5*5*5*5=16*2*2*2*2*2/10*10*10*10*10=512/100000=0.00512 Like my answer if you find it useful! |
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| 8. |
6. Without actual division find whether the rational number -132363 x352 |
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Answer» 1323÷6×6×6×35×351323÷ 2×3×2×3×2×3× 5×7× 5×7 it has a non terminating decimal expansion because the factors of denominator is not in the form of (2^m × 5^n). it has 3 &7 also in the factor of denominator |
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| 9. |
statethenatureofwithoutdecimalactual divisionexpansion.(i) The(ii) 73573 |
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Answer» I) 7/100=0.07; ii)!9\2^3×5^7×3^2=9/8×9×78125=1/8×78125=1/625000=250 |
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| 10. |
JACXASC-MAT (Opt. ASCArts/Science/CommerceHow many 3-digit numbers can be formed by using the digits 1 to 9 if nodigit is repeated ?24. |
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| 11. |
Number of students in Arts and Science in an institute are in the ratio of 1:8 respectively. If150 more students join Arts faculty while 80 more students join Science facuity, the respectivea nscomes 3.4. Originally what was the total number of students in both faculties together?(2) 1400 (3) 1150 (4) Cann't be determined (5) 1170 |
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Answer» The correct answer for this question is option (2) 1400 option 2.1400 is the right answer |
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| 12. |
XASC-MAT-IOpt.)-AscArts/Science/CommerceJACThe equation theand cut off equal intercept on axes,(1) x+y=7n of the straight line which passes through the point ( 2, 3 )44.will be |
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| 13. |
Given below is the data of students who participated in differentactivities26.ActivityYoga WalkingSports4035100120Number of GirlsDraw the bar graph. For the given data. |
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Answer» sorry ,Diagram nahi dya satya ok friend aap ka phone number mil sakta hai thank you,😊☺️ |
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| 14. |
d ZAOBFig. 2, ОАРВ is a sector of a circle of radius 3.5 cm with the centre at Oane length of OAPBO.n120°Fig. 2 |
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| 15. |
Ulal Ineome is 280, how much has he invested in each?36/Divide20304 into two parts such that if one part is invested in 9%,750 shares at 8%discount, thenthepremium and the other part is invested in 8% 725 shares at 8%annual incomes from both the investments are equal. |
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| 16. |
A big bowl contains 4 litre and 500 ml curd. How many glasses having capacity of 25 ml can be filledwith this curd? |
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| 17. |
12. In a UG and PG College with a total strength of1000, 26% of the students are girls. There are520 PGs and 38 more male UGs than female UGs.What percent of the males are UGs?(A) 45%(B) 65%(C) 26%(D) 35% |
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| 18. |
A a2 + b2 e 1, सिद्ध कीजिए कि : :1011न 215 |
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| 19. |
Fig. 1Fig. 2In Fig. 2, the shaded area between two concentric circles is 346.5 cm2. If the radius of theinner circle is 88 cm, find the radius of the outer circle.7. |
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| 20. |
AMPLE 17 Two tangents TP and TQare drawn to a circle with centre O from an external point TNCERT, CBSE 20091Prove that LPTQ = 2OPQ |
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Answer» We know that, the lengths of tangents drawn from an external point to a circle are equal.∴ TP = TQIn ΔTPQ,TP = TQ⇒ ∠TQP = ∠TPQ ...(1) (In a triangle, equal sides have equal angles opposite to them)∠TQP + ∠TPQ + ∠PTQ = 180º (Angle sum property)∴ 2 ∠TPQ + ∠PTQ = 180º (Using(1))⇒ ∠PTQ = 180º – 2 ∠TPQ ...(1)We know that, a tangent to a circle is perpendicular to the radius through the point of contact.OP ⊥ PT,∴ ∠OPT = 90º⇒ ∠OPQ + ∠TPQ = 90º⇒ ∠OPQ = 90º – ∠TPQ⇒ 2∠OPQ = 2(90º – ∠TPQ) = 180º – 2 ∠TPQ ...(2)From (1) and (2), we get∠PTQ = 2∠OPQ |
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| 21. |
3.Two tangents are drawn from an external pointP (as shown in figure) such thatThen 4 BPA is:OBA 10109(a) 10°b) 20°(d) 40°() 30° |
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Answer» I cannot understand anything written in these handwriting |
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| 22. |
√9261 + √12544 |
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Answer» √9261 + √12544=96.234+112=208.234 √9261= 96.234√12544= 112.96.234+112.=208.234 |
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| 23. |
onafa 3In Pig. 3, from an external point P, two tangents PT and PS are drawcircle with centre O and radius r. ItOP - 2r, show that zOrs-osn to aFigure 3 |
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Answer» 1 2 |
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| 24. |
(c) What sum of money will amount to Rs.9261 in 3 years at 5% pa. compound interest? |
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Answer» 9261=P(1+5/100)^3=P(1.05)^3=1.157625Pso P=8000 |
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| 25. |
In Fig. 3, from an external point P, two tangents PT and PS are drawn to acircle with centre O and radius r. If OP= 2r. show that LOTS-LOST-30° |
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| 26. |
Find the area of the segment AYBshown in Fig. 12.9, if radius of the circle is 21 cm and <AOB = 120°. (Use π=22/7) |
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Answer» 1 2 3 Thank you so much 4 |
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| 27. |
y ale seated in a lineample 4 : Find a relation between r and v such that the point (x , y) is equidistantfrom the points (7, 1) and (3, 5).Solution : Let P(.he couid |
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Answer» ✔Let the Points be => => A ( x , y ) => B ( 7 , 1 ) => C ( 3, 5 ) ♦According to the given question -> => AB = AC ◾Applying Distance Formula , => √ ( x2 - x1 )² + ( y2 - y1 )² ♦Distance AB => => √ ( 7 - x )² + ( 1 - y )² => √ 49 + x² - 14x + 1 + y² - 2y => √ x² + y² + 50 - 14x - 2y .....................(1) ♦Distance AC => => √ ( x - 3)² + ( y - 5 )² => √ x² + 9 - 6x + y² + 25 - 10y => √ x² + y² + 36 - 6x - 10 y.....................(2) ◾Putting (1 ) and (2 ) Equal & Squaring both Sides , => x² + y² + 36 - 6x - 10y = x² + y² + 50 - 14x -2y => -8x + 8y + 16 = 0 => -8 ( x - y -2 ) = 0 => x - y = 2 => x = y + 2 Like my answer if you find it useful! |
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| 28. |
85. Find the area of thesegment AYB shown inthe given figure. If radius Aof the circle is 21 cm and 7ZAOB 120°120 |
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Answer» In ∆AOB, draw a perpendicular line from O which intersect AB at M. In ∆AOM, angle AMO = 90angle OAM = 30cos 30 = AM/AO√3/2 = AM/21AM = 21×√3/2AB = 2(AM)=2(21×√3/2)=21√3 OM^2 = AO^2-AM^2=21^2-(21√3/2)^2=441-330.51=110.48OM =√110.48OM =10.51 OM = 10.51cm Area of ∆AOM = 1/2 AB × OM=1/2 ×21√3 ×10.51=191.14cm^2 Area of sector AOBY = 120πr^2/360=120×21×21×22/2520=462cm^2 Area of segment AYB = Area of sector OAYB -Area of∆OAB=462-191.14=270.86 Area of segment AYB is 270.86cm^2. |
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| 29. |
12021 cmFind the area of the segment AYB shown in Fig. if radius of the circle is 21 cm and AOB1200. (Use π227) |
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| 30. |
ample 3 : Find the area of the segment AYBshown in Fig. 12.9, if radius of the circle is 21 cm and A120°AOB = 120°. (Use π =-)21 em21 cm0Fig. 12.9 |
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Answer» In ∆AOB, draw a perpendicular line from O which intersect AB at M. In ∆AOM, angle AMO = 90angle OAM = 30cos 30 = AM/AO√3/2 = AM/21AM = 21×√3/2AB = 2(AM)=2(21×√3/2)=21√3 OM^2 = AO^2-AM^2=21^2-(21√3/2)^2=441-330.51=110.48OM =√110.48OM =10.51 OM = 10.51cm Area of ∆AOM = 1/2 AB × OM=1/2 ×21√3 ×10.51=191.14cm^2 Area of sector AOBY = 120πr^2/360=120×21×21×22/2520=462cm^2 Area of segment AYB = Area of sector OAYB -Area of∆OAB=462-191.14=270.86 Area of segment AYB is 270.86cm^2 |
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| 31. |
14.Thelengthof a side of a square garden ABCDA.is 70 m. A minor segment of Î (O, OA) is drawneach of two opposite sides for developinglawn, as shown in the figure. Find the area ofonthe lawn. |
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| 32. |
13area of he segment shown in Fig 2,if radins of the circle is2120PFig 2 |
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| 33. |
. The length of a side of a square garden ABCDis 70 m. A minor segment of o (O, OA) is drawnA on each of two opposite sides for developinglawn, as shown in the fngure. Find the area ofthe lawn. |
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| 34. |
Without actual division find whether the rational number 1323/6^3 x35^2 |
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Answer» 1323÷6×6×6×35×351323÷ 2×3×2×3×2×3× 5×7× 5×7 it has a non terminating decimal expansion because the factors of denominator is not in the form of (2^m × 5^n). it has 3 &7 also in the factor of denominator |
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| 35. |
-6-II4. Expressas a rational number with the following:-63(1minator 215(numer |
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| 36. |
Find the smallest number by which 1323 should be multiplied so that the product is a perfect cube |
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Answer» 7 is multiplying and getting a perfect cube |
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| 37. |
V9261Find the smallest number by which 1323 must be multiplied so that the product is aperfect cube. |
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Answer» thanks |
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| 38. |
cast Out of them 0.5% votes were declared invalid. The winning candidate0, In an election 55,000 votes arescored 56% of the total valid votes. How many votes did the winning candidate get? |
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Answer» Number of votes cast = 55000Number of votes invalid = 0.5% of 55000=0.5/100 of 55000=5/1000 of 55000=275So, number of valid votes = 55000 - 275= 54725 Now, number of votes the winning candidate got = 56% of 54725=56/100 of 54725=30646 So,number of votes the winning candidate got =30646 |
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| 39. |
19. In a recent election, the losing candidate received 9347 votes,849 votes lessthan the winning candidate. How many votes did the winner get? |
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Answer» winning candidate got9347+849 votes=10,196 votes |
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| 40. |
8. The temperature table shows the variationof temperature of two cites over 7 consecutive daysDraw a double bar graph to represent the data.City ACity BDayMondaytuesdayWednesdayThursdayFridaySaturdaySundayTemperature (°C) | Temperature (C)404124232321204548399. Use a different scale to draw a double bargraph again for the data in Q8 |
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| 41. |
In an election, the winning candidate got48,000 votes which represented 60% ofthe electorate. The only other candidatereceived 25% of the electorate. Calculate thefollowing:a. The number of the electorateb. The number of people who did not casttheir votes |
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| 42. |
16. In an election, the winning candidate got48,000 votes which represented 60% ofthe electorate. The only other candidatereceived 25% of the electorate. Calculate thefollowing:a. The number of the electorateb. The number of people who did not casttheir votes |
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Answer» sorry by mistake I wrote 4800 instead of 48000 so multiply the answer by 10 |
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| 43. |
2. Varun invests75,000 for 3 years in a fixed depositthat offers 10% per annum. How much compoundinterest does he earn at the end of the term? |
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| 44. |
Example 6: A juice sellerwas serving hiscustomers using glasses as shown in Fig. 13.13The inner diameter of the cylindrical glass was5 cm, but the bottom of the glass had ahemispherical raised portion which reduced thecapacity of the glass. If the height of a glassvas 10 cm, find the apparent capacity of thelass and its actual capacity. (Use π = 3.14.) |
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| 45. |
10. A juice seller was serving his customers using glasses as shown in Fig. 13.16. Theinnerdiameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemisphericalraised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, findthe apparent capacity of the glass and its actual capacity. (Use π = 3.14). |
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| 46. |
Q28. The result of pass percentage of class X and XI in C.B.S.E. examination for yoare given in the following table .Plot the double bar graph for the data given belowWrite scale used.year| 19941995199696Class X9095Class XII19585 |
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Answer» 289eywho white 92e73hbez9eg |
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| 47. |
Define Bar graph. |
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Answer» A bar graph is a chart that uses bars to show comparisons between categories of data. The bars can be either horizontal or vertical. Bar graphs with vertical bars are sometimes called vertical bar graphs. |
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| 48. |
(a) 5 (b).25 (c) 52, (d) 50 |
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| 49. |
Example 6 : A juice seller was serving hiscustomers using glasses as shown in Fig. 13.13.The inner diameter of the cylindrical glass was5 cm, but the bottom of the glass had ahemispherical raised portion which reduced thecapacity of the glass. If the height of a glasswas 10 cm, fit the apparent capacity of theglass and its actual capacity. (Use it = 3.14.) |
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| 50. |
=\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{1 \times 10^{-10}} |
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Answer» by basic multiplication division(6.63×3)×10^(-34+8+10)=19.89×10^(-16) |
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