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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. |
(a) Mean(b) Range2. The mean of n observations is X. If k is added to each observation, then the new mean is(c) X-k(a)b) X+k(d) kX |
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| 2. |
The mean of 10 observatons ts 28. IF 2 Isadded to cach observation and then eachresult is divided by 3, find the mean of newobservations so obtained. |
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| 3. |
lina a auualienapsaraointwrite mรถre sharpen less22 |
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Answer» PLEASE LIKE IT, IF YOU FIND THE ANSWER HELPFUL. |
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| 4. |
oint on the x-axis which is equidistant from (2,-5) and (-2.9). |
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| 5. |
(c) If the third sixth and the last terms of G.P. are 6, 48, and 3072 respectively, find the first term andthe number of terms in the G.P. (3) |
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| 6. |
4. The first, second and third terms of a proportion are60. 35 and 48. Find the fourth term. |
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Answer» let the fourth term be xfirst term =60second term =35third term =48product of extreme = product of means=60*x=35*48=x=35*48/60x=28thus, the fourth term is 28 28 is the correct answer of given question 28 is the correct answer |
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| 7. |
Il.Is (2h+1), what is the sum of its first three terms?In figure if AD-6cm, DB-9cm, AE = 8cm and EC-12cm and ADE=48. Find2ABC1480 |
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| 8. |
tan β-tan α68. From an aeroplane vertically above a straight horizontal road, the angles ofdepression of two consecutive mile stones on opposite sides of the aeroplane areobserved to be oz and ß. Show that the height in miles of aeroplane above the roadisgiven bytan α tan βtan α + tanß[CBSE 2004]litno Tf and R are the |
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| 9. |
ii) The mean of a set of 20 observations is19.3. The mean is reduced by 0.5 whena new observation is added to the set.Find the new mean. |
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Answer» Given - Mean of 20 observations = 19.3 Mean = Sum of observations/Total number of observations ⇒ 19.3 = Sum of 20 observations/20 ⇒ Sum of 20 observations = 20*19.3 Sum of 20 observations = 386 When a new observation is added then the new mean decreases by 0.5 Then, Mean of 21 observations = Sum of 21 observations/21 ⇒ 19.3 - 0.5 = Sum of 20 observations + 21st observation/21 ⇒ 18.8 = 386 + 21st observation/21 ⇒ 386 + 21st observation = 18.8*21⇒ 386 + 21st observation = 394.8 ⇒ 21st observation = 394.8 - 386 ⇒ 21st observation = 8.8 So, 21st observation is 8.8 New mean = 394.8/21 New Mean = 18.8 |
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| 10. |
An aeroplane, when flying at a height of 4000 m from the groundces vertically above another aeroplane at an instant when the angles ofevation of the two planes from the same point on the ground are 60° andg respectively. Find the vertical distance between the aeroplanes at thatrstant. (Take v3 1.73)[CBSE (F) 2016] |
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Answer» Thank you |
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| 11. |
.An aeroplane when flying at a height of 4000 m from the ground passes vertically above anotheraeroplane at an instant when the angles of the elevation of the two planes from the same poinon the ground are 60° and 45°, respectively. Find the vertical distance between the aeroplanes athat instant.L49 |
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| 12. |
9. An aeroplane when flying at height of 3125m from the ground verticallybelow another plane at an instant when the angle of elevation of the two passesvertically below another plane at an instant when the angle of elevation of the twoplanes from the same point on the ground are 30° and 60° respectively. Find thedistance between the two planes at that instant. |
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| 13. |
Q9. An aeroplane when flying at height of 3125m from the ground verticallybelow another plane at an instant when the angle of elevation of the two passesvertically below another plane at an instant when the angle of elevation of the twoplanes from the same point on the ground are 30° and 60° respectively. Find thedistance between the two planes at that instant. |
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| 14. |
7th term of an arithmetic sequence is 17 and its 17th term is 7.a) What is its common difference?b) Find 24th term.c) What is the sum of first 47 terms?d) What is the sum of first 48 terms? |
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Answer» a+6d=17a+16d=7a+16d-a-6d=7-17d=-1=common differencea-6=17 so a=2324th term=a+23d=23-23=0S47=47/2(2a+46d)=47/2(46-46)=0S48=48/2(2a+47d)=24(46-47)=-24 |
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| 15. |
The n" term of a sequence is given by a, -2n+7. Show that it isits 7th term. |
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| 16. |
5. In the given figure, BE and CF are twoequal altitudes of AABC.Show that (i) ΔΑΒΕ ΔACF,(ii) AB AC. |
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Answer» thank you uncle |
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| 17. |
6 from – 29Sóct 16212+(-20) 2 E 14) + 38 x- 36°C and the temperature of In the two cities? 490.2t above the ground level. There i |
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Answer» Q. Subtract 6 from -29= -29 - (6)= -29 - 6= - 35 .Ans -29-(6)-29-6-35 is the correct ans -29-6-35is the correct ans - 35 is the right answee -35 is the answer of the following |
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| 18. |
2, 3Find the distance between the points (0, 0) and (36, 15). Can vouhetween the two towns A and B discussed in Section 7.2,2, |
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| 19. |
scale of a map is given as 1:30000. Two cities are 4 cm apart on the map.Find the actual distance between them.le |
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| 20. |
5. In the given figure, BE and CF are twoequal altitudes of AABCShow that (i) ΔΑΒΕ ΔACF.(ii) AB AC. |
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| 21. |
=l JIM:%/LMI बलि o obye, ,a',coéakLtl,,_,,, w8 |
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Answer» 1057 = 7 × 151 So, there are only one term not in pair,So it is not perfect sqaure |
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| 22. |
22)(1- tan A)-= tan 2 A.hove thatom vertically sitrated aeroplane to the straight horizontal |
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Answer» L.H.S1+tan^2A/1+cot^2A=(1+sin^2A/cos2A)/(1+cos^2A/sin^2A)=((cos^2A+sin^2A)/cos^2A)/(sin^2A+cos^2A)/sin^2A=(1/cos^2A)/(1/sin^2A)=1/cos^2A*sin^2A/1=sin^2A/cos^2A=tan^2A M.H.S(1-tanA/1-cotA)^2=(1+tan^2A-2tanA)/(1+cot^2-2cotA)=(sec^2A-2tanA)/(cosec^2A-2cosA/sinA)=(sec^2A-2*sinA/cos A)/(cosec^2A-2cosA/sinA)=(1/cos^2A-2sinA/cosA)/(1/sin^2A-2cosA/sinA)=[(1-2sinAcosA)/cos^2A]/[(1-2cosAsinA)sin^2A]=(1-2sinAcosA)/cos^2A*sin^2A/(1-2sinAcosA)=sin^2A/cos^2A=tan^2A R.H.S=tan^2A Hence L.H.S=M.H.S=R.H.S |
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| 23. |
2. Find the distance between the points (0,0) and (36,15). Can you now find the distancebetween the two towns A and B discussed in Section 7.2.. |
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| 24. |
2. Find the fourth term from the end in an A.P.-11,-8,-5, . . . , 49.3. In an A.P. the 10th term is 46, sum of the 5th and 7th term is 52. Find the A.P.4. The A.P. in which 4th term is -15 and 9th term is -30. Find the sum of the first 10numbers5. Two A.P.'s are given 9, 7, s,... and 24, 21, 18,... .If nth term of both theprogressions are equal then find the value of n and nh term.6. If sum of 3rd and 8th terms of an A.P. is 7 and sum of 7th and 14th terms is -3 then7. In an A.P. the first term is -5 and last term is 45. If sum of all numbers in the A.P.8. Sum of 1 to n natural numbers is 36, then find the value of n.find the 10th term.is 120, then how many terms are there? What is the common difference? |
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Answer» number name in international sum 3148175 |
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| 25. |
) Consider an arithmetic sequence whose 7th term is 34 and 15th term is 66a) Find the common differenceb) Find the 20th term. |
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Answer» the correct value of common differences in this question is 4 and 20th term is 86 7th term =34, 15th tern =66; a+6d=34; a+14d=66/8d=32; d=32/4=8, a+6d=34 :; a+14d=66/8d=32; d=32/8=4; a+6d=34=a+6(4)=35; a=35-24=10; 25th term; a+( n-1)d=10+( 25-1)4=10+24(4)=10+96=106 20 th term ; a=10, d=4; 10+(19)(4)=10+76=86 c d is 4 and 20th terms is 86 10,14,18,22,26,30,34,38,42,46,50,54,58,62,66 is the arithmetic sequence common difference---4 82 is the 20th term |
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| 26. |
\frac { ( 39 ) ^ { 2 } - ( 1.7 ) ^ { 2 } } { 39 - 1.7 } |
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Answer» 3.9² - 1.7²----------- 3.9 - 1.7 = (3.9 +1.7)(3.9-1.7)----------------------- 3.9 - 1.7= 3.9+1.7= 5.6 5.6 |
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| 27. |
8. Find 21st term of the A.P. whose first twotermsare3and4ct the system of equations-2ys 3, 3r + kv1 has a unique solution? |
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Answer» First terms are a,a+dhencea=-3and a+d=4d=7hence ap with first term 3 and common difference is 7 |
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| 28. |
8. Find 21st term of the A.P. whose first two terms are - 3 and 4. |
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| 29. |
Prove that sine (1 + tane) + cose (1 + cotets. The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is aullturde and BD isatangent to the smaller circle touching it at D and intersecting the larger circle at P on producing, Findthe length of APthen prove that&PTS ~ ÎÎĄRQ. |
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Answer» from right triangle BOD BD = √(OB²-OD²) = √(13²- 8²) = √105 from right triangle POD PD = √(OP²-OD²) = √(13²-8²) = √105 PB = BD + PD = 2√105 PB²= 420 from right triangle APB AP = √(AB²- PB²) =√26²- 420 = √676-420 = √256 = 16 cm |
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| 30. |
/dii)What is the probability orA coin is flipped to decide which team starts the game. What is the prooyour team will start?Wr DISCUSSED |
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| 31. |
IE md Care two equal altitudes of a triangle AC.UsingHS congruenrule, prove that the triangle AllC is isosceles |
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| 32. |
1.Construct a quadrilateral ABCD, given thatBC-4.5cm, AD-5.5cm, CD-5cm the diagonalAC-5,5cm and diagonal BD-7cm. |
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Answer» thank you for the answer |
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| 33. |
hoveits Jacestin |
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Answer» (i) Apolyhedroncannothave3 triangles forits faces. (ii) Apolyhedron can havefour triangles which is known as pyramid on triangular base. |
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| 34. |
n theHove that0 |
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| 35. |
taxablevalueofelectricfans, if the rate of GST is 12%2) The Sth term and the 21st term of an A.P. are 75 and 183 respectively. Find 81th term of the A.P |
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Answer» an=a+(n-1)d.so,for the 9th term,75=a+8d(1)st equationso,for the 21st trm,183=a+20d(2)nd equationequate both equationsso,12d=108d=9put,d=9 in eq. (1)75=a+72a=3now,we have to find the 81st terman=3+80×981st=3+72081st term =723 |
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| 36. |
1. Rajan purchased a geometry box forăŚ136.75, a colour bot for 48.80 and a register for64.50. What amount did he pay to the shopkeeper? |
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Answer» The total Amount he had to pay= 136.75+48.80+64.50=Rs 250.05 |
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| 37. |
4. Which termof the AP: 3,15, 27, 39,... will be 120 more than its 21st term? |
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Answer» thanks |
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| 38. |
find the 21st term to the A.P. whose first two terms are -3 and 4 |
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Answer» first term =-3so.a=3difference=second term- first termso,d=4-(-3)=7n=21=a+(n-1)d=3+(21-1)7=3+(20)7=3+140=143so the answer of this question is 143 this question answer is 143 a= -3 answersdifference= 4-(-3)=721th term = a+(n-1)d = -3+(21-1)×7 = -3+20×7 = -3+140 = 137 is the |
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| 39. |
if the 21st term of a.p is 25,find the sum of its first 41terms |
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| 40. |
R »olid hos Lo Fows ond o sdqu.How o et एक 4 hove D |
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Answer» Euler's Formula: V-E+F = 2 Given,F = 40, E = 60 Then,V - 60 + 40 = 2V - 20 = 2V = 22 Therefore, Number of vertices are 22 |
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| 41. |
Con. a poly he olsion hove yot its Jaces z tonianglo9 |
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Answer» (i) Apolyhedroncannothave3 triangles forits faces. (ii) Apolyhedron can havefour triangles which is known as pyramid on triangular base. |
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| 42. |
4.ABCD is a trapezium in which ABIDC, BD is a diagonal and E is the mid-pA line is drawn through E parallel to AB intersecting BC at F(see Fig. 8.30Fis the mid-point of BC. |
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| 43. |
4. ABCD is atrapezum in which AB | DC, BD isa diagonal and E is the mid-point of AthatA line is drawn through E paralle to AB intersecting BC at F (sce Fig. 8.30). Showc(F is the mid-point of BC.Fig. 8.30 |
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| 44. |
ABCD is a trapezium in which AB| DC, BD is a diagonal and E is the mid-point of A4.A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). ShowoF is the mid-point of BC.Fig. 8.30 |
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| 45. |
xsec45° cosec?45° + 2(sin60° + cos30°) tan60° RCT X~PR e डक, है L TN TG N FO T |
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Answer» x (2)(1/2) + 2(√3/2 + √3/2) = √3/2 x + 2√3 = √3/2 x = √3/2 - 2√3 = -1/2√3 |
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| 46. |
ABCD is a trapezium in which AB II DC, BD is a diagonal and E is the mid-point of ADA line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show thatF is the mid-point of BC. |
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| 47. |
35. Find the ratio in which the line segment joining the points A (3, -6) andB (5, 3) isdivided by x-axis. |
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| 48. |
Find the 21st term of the A.P. -43,22 |
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| 49. |
Estimate the sum or the difference by rounding u(a) 386+ 205(d) 3287 2469Estimate the sum or the difference by rounding off the numb(b) 1386-408(e) 5968- 2530(c)1472-12() 947-2 |
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| 50. |
hat hoppens to the careere creveleand hreauty bottale |
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Answer» Since, we know area of a rectangle=length×breadth1)If its length is doubled and breadth is halved, the area remains same.2) If its length is doubled and breadth remains the same, then the area becomes twice that of the original one.3) If its length and breadth both are doubled, then its area becomes 4 times of the original one. may this question help u |
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