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. |
Area : 35y + 13y-12 |
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| 2. |
65xy - 13y from 50xy |
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| 3. |
>e = = v =1%e that xi cos 0, prosin =y=+ i s 6 and x9 = sin 9 ८०“xsin® + y cosIf x sinf the 30.veng |
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| 4. |
IU DUC Siue.e Construct a parallelogram ABCD in which AB = 6.5 cm, AC = 3.4 cm and the altitude ALfrom A is 2.5 cm. Draw the altitude from C and measure it.Construot naralleledram Ann |
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| 5. |
डा 1-8)e ‘. F‘/ffe (o 2ट) टु0* |
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| 6. |
vvilalproperSubsetsl.ISuietotalHtriberörofaset consisting of n e.12. If A is any set, prove that. A-фе? As ф.12 Pro |
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| 7. |
ff nth term of an AP is 9 - 5n, find the sum of first three terms. |
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Answer» nth term = 9 - 5n 1st term = 9 - 5*1 = 9 - 5 = 4 2nd term = 9 - 5*2 = 9 - 10 = -1 3rd term = 9 - 5*3 = 9 - 15 = -6 Sum of first three terms = 4 - 1 - 6 = 3 - 6 = -3 If you find this answer helpful then like it. |
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| 8. |
\frac{77}{210} has a terminating decimal express |
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| 9. |
12] 395 x= 156025 |
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Answer» Let in place of blank value = nThen,395*n = 156025n = 156025/395n = 396 Therefore ans is 395 |
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| 10. |
How many lines of symmetry does a rhombus have ? |
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| 11. |
How many lines of symmetry does a parallelogram have |
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Answer» A parallelogram does have zero lines of symmetry. |
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| 12. |
How many lines can draw with six non collinear point |
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| 13. |
res (7) to (), a pair of Pallettered angle135°21 |
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| 14. |
8. In the given figure, PAL AB, 9B丄AB and PA = 9B.Prove that △OAPIs OA = OB?LOB9 |
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| 15. |
\operatorname { sin } ^ { - 1 } \frac { 3 } { 5 } + \operatorname { sin } ^ { - 1 } \frac { 8 } { 17 } = \operatorname { cos } ^ { - 1 } \frac { 36 } { 85 } |
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Answer» sin^(-1)(3/5)=tan^(-1)(3/4)sin^(-1)(8/17)=tan^(-1)(8/15)tan^(-1)(3/4)+tan^(-1)(8/15)=tan^(-1)((3/4+8/15)/(1-3/4*8/15))=tan^(-1)((77/60)/(9/15))=tan^(-1)(77/36)=cos^(-1)(36/85) |
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| 16. |
\operatorname { sin } ^ { - 1 } \frac { 3 } { 5 } + \operatorname { sin } ^ { - 1 } \frac { 8 } { 17 } = \operatorname { sin } ^ { - 1 } \frac { 77 } { 85 } |
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| 17. |
Pr. I x* 8, find the value of Bx tx-5 |
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Answer» 8√x+x-5 x=88√8+8-516√2+3 |
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| 18. |
2Tx+yEXAMPLE 6. If5+2find the values of x,y and 2.xy58 |
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Answer» After comparison,x + y = 6, ( i )5 + z = 5, ( ii )x * y = 8, ( III )From equation ( ii ),z = 0,From equation ( i ) and ( iii ),( x - y )^2 = ( x + y )^2 - 4 * x * y, = 36 - 32, = 4,( x - y ) = 2, ( iv )From equation ( i ) and ( iv ),x = 4,y = 2. |
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| 19. |
\operatorname sin ^ - 1 \frac 3 5 %2B \operatorname sin ^ - 1 \frac 6 17 = \operatorname sin ^ - 1 \frac 77 85 |
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Answer» sin^-1(3/5) + sin^-1(8/17) = sin^-1{3/5√[1 - (8/17)^2] + 8/17√[1 - (3/5)^2} =sin^-1[ 3/5 *15/17 + 8/17 * 4/5 ] =sin^-1[ 45/85 + 32/85 ] = sin^-1[ 77/85 ] |
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| 20. |
10. p(x - 2y) - p(x - 2y)11. ar + br + at + bt12. 4x2 - 3xy - 16x + 12y13. 3ax + 4bx - 6ay - 8by14. 6ab- 12 + 12ac - 2bc15. p + p-3p² - 316. 2ax + bx + 2ay + by17. px - 2py - qx + 2qy18. 12x - 8 + 3x - 2y19. d + ac + bc + ab20. x + xy + 9x + 9y. |
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Answer» 1- p, -p is the answer 2- 2(a,r,b,t) is the your answer 20.x²+xy+9x+9y=x(x+y)+9(x+y)=(x+y)(x+9) b is the best answer |
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| 21. |
(a)P=1650, T=2 yearsand SI = 82.50 |
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Answer» SI = (P×R×T)/10082.50 = (1650×R×2)/10082.50×100 = 1650×R×28250/1650×2 =RR =2.5A = 1650+82.50 = 1732.50 answer 1732.50 hoga right P= 1650T= 2 years SI = 82.50R=?1) R=SI×100/P×T= 82.50×100/1650×2=2.5% p.c.p.a.2) Amount = P+SI= 1,650 + 82.50=1,732.50 rs. |
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| 22. |
5x-4y+8=07x+6y-9=0 |
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| 23. |
A and B start a business with Rs. 15,000 andRs. 45,000 respectively. After 6 months B receivedRs. 3,030 as profit. What is A's profit? |
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Answer» thanks |
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| 24. |
Mark a point on your notebook. Draw a line passing through this point. Howmany lines can you draw to pass through this point? |
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Answer» We make infinity lines to only one point the possibility of no of line in a point is : infinite |
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| 25. |
10. A bought an article for Rs.1900 and sold it to B at a profit of 5%, B sold itto Cataprofit of 10%. Find the money paid by C to B. |
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Answer» 100 percentage price= 1900now it was sold to B on profit of 5 means 105 percentageso 19*105= 1995nowhe sent it to 10 percentage of 1995now 115 percentage of 1995= 2294.25 |
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| 26. |
nthepointP(02equidiss, ) ls31. Find the perimeter of the triangle formed by32. The midngint of the linthe points (o, 0), (1, 0), (0, 1).nts Alx, y+ 1) and B (x1,y2 |
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Answer» Consider A (0,0),B (1,0),C (0,1) =>AB=root(X2-X1)^2+(Y2-Y1)^2 =>AB=root (1-0)^2+(1-0)^2 =>AB=1 similarly, BC=root2 and AC=1 Perimeter=AB+BC+AC =1+root1+1=2+root2 |
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| 27. |
SR FO ORISR तर उप कि 4 |दुन्ठ्त 2 T PO by |05 TPIS TH I T T o )| |
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Answer» Side=aPerimeter=4aP=48mm4a=48mma=48/4a=12mm |
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| 28. |
() 5x-4y+8=07x+6y-9=0 |
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| 29. |
anif α, β are the roots of the quadratic equation2r+1 0, then which one of the following iscorrect?(a) (014-β4) is real(d) (018 + β8)(opf(c) Given that, α and β are the roots of the equation |
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| 30. |
(0 2x2-7x +3 0 |
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| 31. |
(0 2x2 -7x +3 0 |
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| 32. |
.(B) Selv(1) The v(1) The solution of the quadratic equation 2r-3x is given below(2) Drawpointconcl2x.rx.r = 3 xx(3) If thGivAccording to you, is this solution correct or not? Explain your answer with the reasons? |
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Answer» Given solution is not correct as given equation is quadratic equation so it should have 2 roots We solve this equation as follows:2x^2 = 3x2x^2 - 3x = 0x(2x - 3) = 0x = 0, x = 3/2 So given equation have 2 roots 0 and 3/2 |
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| 33. |
13)(b) Find the values of k so that the equation (k + 4)+ (k+1)x1 -0 has real and equal roots |
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| 34. |
If one root of equation (e -m)x+x1 0 be double of the other and if e be real, show that m |
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Answer» Sum of roots is -L/(L-m)=3r, product of roots is 1/(L-m)=2r^2 where r is one of the roots. So 1 / 2(L-m) = L^2 / 9(L-m)^2 9(L-m)=2L^2 2L^2 - 9L + 9m=0 For L to be real, the discriminant is non-negative. 81>=8X9m m<=9/8 The greatest value of m is therefore 9/8. |
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| 35. |
15. Solve for x : V3 x2-2V2 x- 2-13 =0OR,Solve the equation by method of completing the square. |
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| 36. |
Vo)LTED "Till) .11 81 %LTE7:12 aQ.7: On a horizontal plane there is a verticaltower with a flagpole on the top of the tower.At a point, 9 meters away from the foot of thetower, the angle of elevation of the top andbottom of the flagpole are 60° and 30°respectively. Find the height of the tower andthe flagpole mounted on it. [TakeV3 1.73] |
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Answer» AB= FLAG POLE BC = TOWER CD = BASE = 9M TAN 60 = AC/CD ROOT3 = AC/9 AC = 9 ROOT3 TAN 30 = BC/CD 1/ROOT3 = BC /9 BC = 9/ROOT3 (ROOT3/ROOT3) BC = 3 ROOT3 AC = AB +BC 9 ROOT 3 = AB + 3 ROOT3 AB = 9 ROOT 3 - 3 TOOT 3 AB = 6 ROOT 3 |
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| 37. |
A farmer has four sheepdaqs and thtoodomly choases ado fo accomonee beatles-4 hehim on a Walk whot |
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Answer» Total possibilities = 4 + 3 = 7 Favourable possiblity = 4 So, Probablity = 4/7 |
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| 38. |
What does the balance in share allotment indicates elfer the entry cash for amountdue & received has been passed ? |
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Answer» Sorry we are currently not taking questions from accounts. |
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| 39. |
9. In which of the following expressions, prime factorisation hasbe(a) 24-2x3x4(c) 70 =2x5x1(b) 56 = 7 ×2×2×2(d) 54 2x 3x9i t |
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| 40. |
he mean of the median, the mode and the range of the following data:84,56,39,45,54,39,56,54,84,21,77,56 isa) 559. Tb) 56c) 58d) 63 |
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Answer» Median = 55.Mode = 56.Range = 63.Mean = (55+56+63)/3= 58 |
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| 41. |
eTh |
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Answer» 45 = (9)(5)= (3)(3)(5) is the prime factorization of 45 since 3 and 5 are both prime numbers, and therefore, each cannot be "broken down" or factored any further.Three (3) and 5 are prime numbers because each is a positive integer that is exactly divisible (a zero remainder) by exactly two positive integers: itself and 1, i.e., 3/3 = 1 and 3/1 = 3; Also, 5/5 = 1 and 5/1 = 5.45 = 9 x 5= 3×3×5 done. 3 and 5 are prime |
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| 42. |
280 Cast off 3Shiats ano twcank ado find the Prtes 300Shit and ane Pan |
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Answer» 7s+4p=28003s+2p=300 7s+4p-6s-4p=2800-600so s=22008800+4p=2800so p=-1500 |
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| 43. |
1120 and "or term of thegop0.2, 0.040.008. |
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| 44. |
6 Hind the talu eth7 Find the ratio between 5 dozen and 2 scores. [1 score-20] |
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Answer» 5 dozens =5*12=60 and 2 scores=2*20=40ratio =60/40=3/2=3:2 |
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| 45. |
ind the prime factors of the following56b. 72C. |
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Answer» Sahi h |
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| 46. |
n is a pesitive odd intcger, her.Show,"that n., is divisible byĺou 8 |
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Answer» Any odd positive integerncan be written in form of 4q+ 1 or 4q+ 3. Ifn= 4q+ 1, Thenn^2- 1 = (4q+ 1)^2- 1 = 16q^2+ 8q+ 1 - 1 = 8q(2q+ 1)which is divisible by 8. Ifn= 4q+ 3, Thenn^2- 1 = (4q+ 3)^2- 1 = 16q^2+ 24q+ 9 - 1 = 8(2q^2+ 3q+ 1) which is divisible by 8. So, it is clear thatn^2- 1 is divisible by 8, if n is an odd positive integer. |
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| 47. |
ind tha) 12, 20 and 36 b) 14, 70 and 126 c) 15, 25 and 145 ) 84, 108 and 14รก.by prime factorization and division method. |
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| 48. |
52)V2)" +(B-2)f |
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Answer» {(√3+√2)³}²+{(√3-√2)³}2=2× {(√3)^6+(√2)^6}=2×{27+8}= 70 |
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| 49. |
2 )( 1B. V2 |
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Answer» a²-b² = (a+b)(a-b) = (√3)² - (√2)² = 3-2 = 1 Like my answer if you find it useful! |
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| 50. |
ise Bachd's dreision lemma to show that the cube of any pesitive inneget is ofThe Fundamental Theorem of Arithmeticher can he written as a |
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Answer» Let a be any positive integer and b = 3 a = 3q + r, where q ≥ 0 and 0 ≤ r < 3 ∴ r = 0,1,2 . Therefore, every number can be represented as these three forms. There are three cases. Case 1: When a = 3q, Where m is an integer such that m = Case 2: When a = 3q + 1, a = (3q +1) ³ a = 27q ³+ 27q ² + 9q + 1 a = 9(3q ³ + 3q ² + q) + 1 a = 9m + 1 [ Where m = 3q³ + 3q² + q ) . Case 3: When a = 3q + 2, a = (3q +2) ³ a = 27q³ + 54q² + 36q + 8 a = 9(3q³ + 6q² + 4q) + 8 a = 9m + 8 Where m is an integer such that m = (3q³ + 6q² + 4q) Therefore, the cube of any positive integer is of the form 9m, 9m + 1, or 9m + 8. Hence, it is proved . |
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