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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. |
What are the possible unit digits of the square root of the followingnumbers?(a) 9,604(b) 99,225 |
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Answer» a)9604possible unit digits of square root of 9604 are 2,8b) possible unit digit of square root of 99225 is 5 The Square root 9604=98The Square root of 99225=315 |
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| 2. |
Just observe the unit digits and state which of the following are not perfectsquares1.(i) 3136 (i) 3722 iii) 9348 (iv) 2304 (v) 8343 |
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Answer» Any number is perfect square if its unit digit is sqaure of some natural number. i) √(3136) = 56, perfect square , as unit digit is 6 so 6² is possible. ii) 3722, not perfect square as square of any any natural number is not 2. iii) 9348, not perfect square as square of any any natural number is not 8. iv) 2304, possible as last digit is 4 and 2 and 8 have square whose unit digit is 4.√(2304) = 48 v) 8343, not perfect square as square of any any natural number is not 3. |
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| 3. |
(√(1+x) + √(1-x)) ÷ (√(1+x) - √(1-x)) = a÷b |
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| 4. |
A number of two digit do suchthat its unit digits nameenth is 12 - 1 when I the digis3 uzition the number incins byEind the orignial no |
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| 5. |
7. A certain number of articles are bought at 3 for 150 and all of them are sold at 4 forัะต180. Find the loss or gain as percent |
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Answer» 3 article cp=150 therefore 1 article cost=150/3=50 sp of 4 article=180 therefore sp of 1 article=180/4=45 therefore loss=50-45=5 loss percent=(5/50)*100%=10% Like my answer if you find it useful! |
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| 6. |
A certain number of articles are bought at 3 for180. Find the loss or gain as percent.150 and all of them are sold at 4 for |
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Answer» 3 article cp=150 therefore 1 article cost=150/3=50 sp of 4 article=180 therefore sp of 1 article=180/4=45 therefore loss=50-45=5 loss percent=(5/50)*100%=10% Like my answer if you find it useful! |
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| 7. |
\left| \begin{array} { l l l } { x } & { 1 } & { 1 } \\ { 1 } & { x } & { 1 } \\ { 1 } & { 1 } & { x } \end{array} \right| = ( x + 2 ) ( x - 1 ) ^ { 2 } |
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| 8. |
IfA=3x2-7x + 8B=x²+8x-3C=5x2-3x + 2Find the value of B - C-A & A+ B+ C |
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Answer» A + B + C = 3x*x - 7x + 8 + x*x + 8x - 3 + 5x*x - 3x + 2 = 9x*x - 2x + 7 B - C - A = x*x + 8x - 3 - 5x*x + 3x - 2 - 3x*x + 7x - 8 = -7x*x + 18x - 13 |
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| 9. |
Using integration find the area of the triangular region whose sides have theequations y 2x + 1, y-3x + 1 and x 4. |
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| 10. |
the base of a triangular region is three times its altitude if its area is 27 square metre find its base and altitude |
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Answer» Area= 0.5*base* altitude=> 27 = 0.5*3*altitude*altitude=> altitude^2 = 18=> altitude= 3*(2^0.5)Therefore, base = 9*(2^0.5) |
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| 11. |
le in a colony were trying toarden in the region ABC and a pond tor fishes26. On environment day, peopdevelop a gin the triangular region FED. What value is being exhibitedby them by doing so?Such that BA DE and BF EC and L AB LDEFshow that AABC ADEFClass-IX/Math/3 |
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Answer» BA = DE (given)angle ABC = angle DEF (given)BF = EC (given)so, BF + FC = FC + EC => BC = FCso, triangle ABC is congruent to triangle DEF by SAS congruency |
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| 12. |
A toy company manufactures two types of dolls, A and B. Market tests and available resources haveindicated that the combined production level should not exceed 1200 dolls per week and the demand for dollsof type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceedthree times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order timaximize the profit?Q.11 |
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| 13. |
is the imaximuin prTA toy company manufactures two types of dolls, A and B. Market tests and availableresources have indicated that the combined production level should not exceed 1200dolls per week and the demand for dolls of type B is at most half of that for dolls oftype A. Further, the production level of dolls of type A can exceed three times theproduction of dolls of other type by at most 600 units. If the company makes profit ofRs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should beproduced weekly in order to maximise the profit? 1 266く.y. |
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| 14. |
Find the su(a) 105°Find the angle which is equal to its complement.Which angle is equal to its supplement?(b) 999 |
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| 15. |
Uf α and β are the zeros of the quadratic polynomial f(x)x2 +1-2, find the value of |
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| 16. |
7. Draw the graphs of the equations x -y+10 and 3x + 2y 122U.Delellulecoordinates of the vertices of the triangle formed by these lines and the x-axis,shade the triangular region. |
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| 17. |
find x if 2x-7×5x-4=1250 |
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Answer» 2x - 7×5x-4 = 12502x -35x = 1254-33x = 1254x = 1254/(-33)x = -38 |
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| 18. |
18. If 2n-7 ×5n-4-1250, find the value of n. |
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Answer» Thanks |
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| 19. |
2) How many 2-digit numbers are there in all? |
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Answer» 👇ans. |
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| 20. |
The product of 2-digit numbers is 2117. The product of their unit digits is 27 and that of tensdigits is 14. Find the numbers. |
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Answer» 73×29.3×9=277×2=14So, the numbers are73 and 29. |
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| 21. |
2^(n - 7)*5^(n - 4)=1250 |
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| 22. |
| (९५ 905 1० 14 “95 8 की...हि ५ 9/ के 979 jo anjea sy} puld |
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| 23. |
(1)3x2+11x-4-0 |
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| 24. |
p(x)=3x2-1 x =-1 |
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Answer» P(x)= 3x^2-1now x= -1so3(-1)^2-1= 3-1= 2thanks |
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| 25. |
(c) SP=1250 , Loss =* 150 |
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Answer» selling price = ₹1250loss = ₹150actual rate = 1250+150₹1400. Let cp be the x. SP=CP-Loss. 1250=x-150. x=1250+150. x=1400 Selling price =1250Loss=1501250-150=1100 Ans. let CP be xSP = CP - Loss 1250 = x - 150X = 150 + 1250x = Rs.1400 1400 is answers of this question sp=cp-loss1250=x-150x=1200+150=1400 Let , the CP be x SP= CP-Lossx=1250+150 x= 1400 CP=SP+Loss =1250+150 = 1400The another method is:Let the CP be xSP=CP-Loss 1250 =x-150x=1250+150x=1400 let cp be xsp=cp-loss1250=x-150x=1250+150x=1400 Profit=SP-CPSo,₹1250-₹150=₹1100 Ans. let Cost Price be 'x'Selling Price = Cost Price - loss1250= x -150X=1250+150X=1400 x=1400 C P = SP-loss1250-150=1100 CP=SP+ LOSS1250+150=1400 1400is the correct answer sP= CP - loss1250 = CP - 150CP = 1250-1501100 selling price =1250 loss = 150 actual rate=1250+1501400 S.P =Rs.1250loss=Rs.150C.p findS.p=C.p- loss1250=x-1501250+150=xx =Rs.1400 ans. 1250-150 1100 sp-cp=150 selling price-1250Loss-150Actual rate -1250+1501400 Let cp be xsp=cp-loss1250=x+150x=1250+150x=1400The cup is Rs 1400 CP=SP-lossso,1250-150=1100rupees Let CP=x SP=CP-loss1250=x-150x=1250+150x=1400 what we have to find??? SP=1250,Loss =150 CP when loss = SP+Loss CP = 1250+150 = 1400 rs selling price =1250loss=150actual rate=150+150₹1400 let Cp be x SP = CP _LOSS1250=X _150X = 1250 + 150X =1400 sp=cp_loss1250=×_150×=1200+150=1400 |
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| 26. |
(i) 3x2 7x 1 |
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| 27. |
i5:â 3(b-4)-2(4-b) |
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Answer» 3(b-4)=2(4-b) 3b-12=8-2b 5b=20b=4. |
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| 28. |
1) / ंUiy Smdundity + रण 2 products:\left(\frac{a}{2}+\frac{3 b}{4}\right) \quad\left(\frac{a}{2}+\frac{3 b}{4}\right) |
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| 29. |
\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=\frac{2 a-3 b+4 c}{p} |
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Answer» Mostly thanks |
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| 30. |
1llgl 22 terms of the AP is - 979.ple 12 : If the suExamfind the 20th term.m of the first 14 terms of an AP is 1050 and its first term is 10, |
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| 31. |
the maximum amount of lmOUA toy company manufactures two types of dolls A and B. Market tests anresources have indicated that the combined production level should not exced 2dolls per week and the demand for dolls of type B is at most half of that for d dtype A. Further, the production level of dolis of ype A can exceed three tims teproduction of dolls of other type by at most 600 uuts lr the company makes poitdRs 12 and Rs 16 per doll respectively on dolis A and B, how many of each shouldteproduced weekly in order to maximise the profitests and available10. |
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| 32. |
. Define stopping distance. |
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Answer» The stopping distanceis thedistance traveled between the time when the body decides tostopa moving vehicle and the time when the vehicle stops completely. Thestopping distance depends on factors including road surface, and reflexes of the car's driver and it is denoted by d. |
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| 33. |
x ^ { 3 } + 9 x ^ { 2 } y + 27 x y ^ { 2 } + 27 y ^ { 3 } \text { when } x = 9 , y = - 3 |
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| 34. |
fox and ßare the roots ofx2 + 5x-1-othen find(ii) α2+ β2There are 37 terms in an A.P. the sum of three terms plaexactly at the middle is 225 and the sum of last three term429. Write the A.P |
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Answer» Let the first term and the common difference of the A.P areaanddrespectively. Since the A.P contains 37 terms. So, the middle most term is (37+1)/2 th term = 19thterm. Thus, three middle most terms of this A.P.are 18th, 19thand 20thterms. Givena18+a19+a20= 225 ⇒ (a+ 17d) + (a+ 18d) + (a+ 19d) = 225 ⇒ 3(a+ 18d) = 225 ⇒a+ 18d= 75 ⇒a= 75 – 18d… (1) According to given information a35+a36+a37= 429 ⇒ (a+ 34d) + (a+ 35d) + (a+ 36d) = 429 ⇒ 3(a+ 35d) = 429 ⇒ (75 – 18d) + 35d= 143 ⇒ 17d= 143 – 75 = 68 ⇒d= 4 Substituting the value ofdin equation (1), it is obtained a= 75 – 18 × 4 = 3 Thus, the A.P. is 3, 7, 11, 15 … |
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| 35. |
\left. \begin{array} { l } { x + y = 14 } \\ { x - y = 4 } \\ { 3 x - y = 3 } \\ { 9 x - 3 y = 9 } \end{array} \right. |
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Answer» qedhbibrajgxicxu0vjfuzdo |
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| 36. |
Find the least number that should be added to 1000 so that 35 divides the sumexactly |
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Answer» A number divides a sum exactly means, remainder is zero. Divide 1000 by 35 |
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| 37. |
ind the least number which should be added to 10,000, so that the sum is exactly divisible by 37 |
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| 38. |
4ŃĐ°Priyanka deposited 6500 in a bend of the first year. What amount will she get after three years?7.ank which pays 9% per annum interest. She withdrew1250 after the |
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| 39. |
2 ^ n - 7 \times 5 ^ n - 4 = 1250 , \text find the value of r |
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| 40. |
The incomes of X and Y are in the ratio of 8:7 and their expenditures are in the ratio19:16. If each saves 1250, find their incomes. |
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| 41. |
20) The incomes of X and Y are in the ratio of 8:7 and their expenditures are in the ratio 19: 16. If each saves 1250,find their incomes.by ue naii alnuins olglal rate or waikingthe whddone the9, A train o |
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Answer» Let the income of X be Rs. 'a' and his expenditure be Rs. 'b'. And, income of Y be Rs. 'c' and his expenditure be rs. 'd'. Therefore, a/c = 8/7 ⇒ a = 8c/7 Similarly, b/d = 19/16 ⇒ b = 19d/16 Savings of X = a - b ⇒ 1250 = 8c/7 - 19d/16 Taking L.C.M. of the denominators and then solving it, we get. ⇒ 1250 = (128c - 133d)/112 ⇒ 128c - 133d = (1250*112) ⇒ 128c - 133d = 140000 .............(1) Savings of Y = c - d ⇒ c = 1250 + d ............(2) Substituting (2) in (1), we get. ⇒ 128*(1250 + d) - 133d = 140000 ⇒ 160000 + 128d - 133d = 140000 ⇒ 128d - 133d = 140000 - 160000 ⇒ - 5d = - 20000 ⇒ 5d = 20000 ⇒ d = 20000/5 ⇒ d = 4000 Putting d = 4000 in (2), we get. Now, c = 1250 + 4000⇒ c = 5250 Now, putting c = 5250 in a = 8c/7 ⇒ a = (8*5250)/7 ⇒ a = 42000/7 ⇒ a = 6000 And, b = 6000 - 1250 b = 4750 Hence, the income of X is Rs. 6000 and income of Y is Rs. 5250 |
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| 42. |
LetAs {1, 2, 3), B-{ 4, 5, 6, 7 } and letf : {(1, 4), (2, 5), (3, 6)) be a fufrom A to B. Show that f is one-one. |
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| 43. |
Find a rational number betweenand 13.How many two digits numbers are divisible by 3? |
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Answer» (1) We knowRoot 2 = 1.414Root 3 = 1.732 Now, we can write n number of rational number between these. That is just greater than 1.414 and less than 1.732 and it should be terminating or not terminating but repeating.For example1.415659756, 1.416893, 1.715644, ... (2) Two digits numbers divisible by 3 form an AP The A.P. will be12,15,.......99We need to find number of terms of an AP Last term of this series is 99 So, an = 99 & a =12d =15–12= 3 Now, an = a + (n – 1) d Putting values,99 =12+ (n – 1)(3) 99 =12+ 3n – 3 99 = 9 + 3n 3n = 99 – 9 3n =90n =90/3 = 30 Therefore, there are30 twodigit numbers divisible by 3. |
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| 44. |
6In the given figureIf 4B 40° then find) BAC(i) ZACDAACB is a right angled triangle at C and CD L AB(ii) ZBCDProof |
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Answer» BAC = 180 - B - C = 180 - 40 - 90 = 50ACD = C - (180-B-CDB)=90-(180-40-90)=40BCD = 180-B-CDB=180-40-90=50 |
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| 45. |
What is chemical fertilization? Give two examples |
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Answer» fertilisation oof crops by chemical methods is called chemical fertilisation |
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| 46. |
whosemeFindwequadraticquadraticpolynomialsale accial_and 300 |
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| 47. |
6. ABC is a triangle in which 2 B 2C. D is a point on BC such that AD bisectsBAand AB = CD. Prove that < BAC = 720. |
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| 48. |
6. ABC is a triangle in which B 2C. D is a point on BC such that AD bisects 4BAOand AB = CD. Prove that < BAC = 720.3 x 39 |
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| 49. |
20. 3x2-14x +8 |
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Answer» To solve: 3x^2 - 14 x + 8SolutionSum= -14; product = 24numbers are -12, -23x^2-12x-2x+8=0(3x-2) (x-4)therefore x= 4 or x= 2/3 |
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| 50. |
which least number should be added to 1000 so that 53 divides the sum exactly |
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Answer» when we divide 1000 by 53 we get quotient 18 and remainder is 46. it means number is 7 less than the number so that number is completely divisible . so after adding 7 in 1000 the number becomes 1007 and it is completely divisible by 53. when we divide 1007 by 53, we get quotient 19. so the least no. which added in 1000 such that number is divisible by 53 is 7. |
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