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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. |
In figure, S and T are the points on the sides PQ and PR respectively of APOR, suchPT-: 4 cm, TR-4 cm and ST is parallel to QR. Find the ratio of the areas 01 ΔΙ4cm4 cm |
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| 2. |
I 1. Explain why x /I comp12. If tan(A B) and tan(A + B) 3, find A and B |
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| 3. |
The perimeter of a square carpet is 48 m. Find the side of the carpet. |
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Answer» Perimeter of a square carpet is 4a. 4a= 48 a=12 m thanks thanks |
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| 4. |
EXAMPLE 11Prove that the tangent drawn at the midpoint of an arc of a circle isparallel to the chord joining the end points of the arc.ICBSE 2015]SOLUTIONGVEN Point Pis the midpoint of arc QR of a circle with centreO. ST is the tangent to the circle at point P.TO PROVE Chord QRI|ST.PROOF P is the midpoint of QR0.chord QP chord PR |
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Answer» A circle with Centre O, P is the midpoint of Arc APB. PT is a tangent to the circle at P. To Prove: AB || PT Construction: join OA ,OB, & OP Proof: OP ⟂PT [Radius is ⟂ to tangent through point of contact] ∠OPT= 90° Since P is the midpoint of Arc APB Arc AAP =arc BP ∠AOP = ∠BOP ∠AOM= ∠BOM In ∆ AOM & ∆BOM OA= OB= r OM = OM (Common) ∠AOM= ∠BOM (proved above) ∠AOM≅∠BOM (by SAS congruency axiom) ∠AMO = ∠BMO (c.p.c.t) ∠AMO + ∠BMO= 180° ∠AMO = ∠BMO= 90° ∠BMO = ∠OPT= 90° But, they are corresponding angles. Hence, AD||PT |
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| 5. |
4. In Fig. 6.31, if PQ Il ST, PQR 110 and130°ST 130°, find ZQRS.[Hint: Draw a line parallel to ST throughpoint R.]110° |
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| 6. |
19. Inthe given figure PQ 1l ST, <Pthe given fQR-<110°, and RST=130°find <QRS |
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Answer» Interior angles on the same side of thetransversal: The pair of interior angles on the same side ofthe transversal are called consecutive interior angles or allied angles or cointerior angles. If a transversal intersects two Parallel Linesthen each pair of interior angles on the same side of the transversal is supplementary. If a transversal intersects two lines such thata pair of alternate interior angles is equal then the two lines are parallel. _________________________________________________________________ Given, PQ || ST, ∠PQR = 110° and ∠RST = 130° Construction, A line XY parallel to PQ and ST is drawn. ∠PQR+∠QRX= 180° (Angles on the same side of transversal.)⇒110° + ∠QRX= 180°⇒∠QRX= 70° Also,∠RST+ ∠SRY= 180° (Angles on the same side of transversal.)⇒130° + ∠SRY= 180°⇒∠SRY= 50° Now,∠QRX+∠SRY+∠QRS = 180°⇒70°+ 50°+ ∠QRS= 180°⇒∠QRS= 60°Please like the solution 👍 ✔️👍 |
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| 7. |
(10) A floor is 5 m long and 4 m wide. Asquare carpet of side 3.5 m is laid onthe floor. Find the area of the floor notcarpeted. |
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| 8. |
15e A room is 26 m long and 15 m wide. A 14 msquare carpet is laid on the floor. What area isnot carpeted? |
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| 9. |
4in Fig. 631, ST. TOR 110 andARST-130°. ind. ORS(ht: Draw a line parallel to ST throughpoint)6.31 |
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Answer» Question 4. In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS.[Hint : Draw a line parallel to ST through point R.] Solution:Let us draw a parallel line XY to PQ || ST and passing through point R.Sum of interior angle on the same side of the transversal is always = 180° So that∠ PQR + ∠ QRX = 180°Given that ∠ PQR= 110°110° + ∠QRX = 180°∠QRX = 180° -110°∠QRX = 70°Sum of interior angle on the same side of the transversal is always = 180° ∠RST + ∠SRY = 180° (Co-interior angles on the same side of transversal SR)Also130° + ∠SRY = 180°∠SRY = 50°XY is a straight line. Use property of linear pair we get∠QRX + ∠QRS + ∠SRY = 180°70° + ∠QRS + 50° = 180°∠QRS = 180° − 120°= 60° plz like my answer ali |
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| 10. |
In the figure,seg PS is the median of APQR and PTORProve : PRP = PS2 + QR X ST+ ()т |
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Answer» Given : PS divides QR equally QS = RS = 1/2 QR Ang QTR = 90° To prove : PR² = PS² + QR x ST + (QR/2)² Proof :By Pythagoras Theorem,In ΔPTS, PT² + TS² = PS² _________(1)In ΔPTR, PT² + TR² = PR² _________(2) QS = RS = QR/2 ( Given) _________(3)So, QR = 2QS = 2RS ________(4) From (2),PR² = PT² + TR²PR² = PT² + (TS+RS)² [ (a+b)² = a² + 2ab + b² ]PR² = PT² + TS² + RS² + 2*TS*RSPR² = PS² + TS*2RS + RS² ( Using (1) )PR² = Continue... PR² = PS² + TS x QR + (QR/2)²(From (3) and (4) ) Hence proved |
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| 11. |
Solve by the method of elimination(i) 2x-y 3; 3x + y 7 |
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Answer» 2x - y = 3.....(1)3x + y = 7.....(2) Add eq(1) and eq(2) 5x = 10x = 2 Put value of x = 2 in eq(1)2*2 - y = 3y = 4-3y = 1 Therefore x = 2, y = 1 |
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| 12. |
parallelógraill.PORS is a parallelogram, T is the midpoint of PQ (Fig. 11.23) ST bisectsS. Prove that(a) QR=QT (b) RT bisects<R (c)STR-90。袞 |
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| 13. |
Solve4x + y = 7, 2x-3y = 7 using method of elimination by substitutioní3¡u" |
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Answer» 4x + y = 7 .....(1)2x - 3y = 7 ......(2) eq(1) - eq(2) × 2 4x + y = 74x - 6y = 14 7y = - 7y = -1So,4x - 1 = 74x = 8x = 8/4x = 2 So, x = 2 and y = -1 thank u by substitution method |
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| 14. |
4, in Fig. 6.31, if PQ 11 ST. < PQR = 110° andZRST 130, find 2ORS.130IHint : Draw a line parallel to ST throughpoint R.] |
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Answer» Given, PQ || ST, ∠PQR = 110° and ∠RST = 130° Construction, A line XY parallel to PQ and ST is drawn. ∠PQR+∠QRX= 180° (Angles on the same side of transversal.)⇒110° + ∠QRX= 180°⇒∠QRX= 70° Also,∠RST+ ∠SRY= 180° (Angles on the same side of transversal.)⇒130° + ∠SRY= 180°⇒∠SRY= 50° Now,∠QRX+∠SRY+∠QRS = 180°⇒70°+ 50°+ ∠QRS= 180°⇒∠QRS= 60° HIT THE LIKE BUTTON IF YOU ARE SATISFIED t |
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| 15. |
an you calculateof İ in heasd, lika this?I A string of length one metre is cout no five oual parta. Whatis the length of half of one sach piece? How manycentimetres? |
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Answer» Thanku |
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| 16. |
1. Find the product:(i) 4.74Ă10() 0.45 x 10 () 0 0215x10(0 0D0354, Ruiel(ii) 0.0215 x 10 (iv) 0.0054, BuleII w |
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Answer» 1) 0.45*10= 4.52)0.0215*100.2153)4.74*1047.4 |
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| 17. |
ix2-3x-10 0(ii),2x2 + x-6=0(iv) 2x2-x+8=0(v)100 x2-20x + 1 = 0 |
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| 18. |
0) x2-3x- 10 0 |
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Answer» x²-3x-10=0x²-5x+2x-10=0x(x-5)+2(x-5)=0(x+2)(x-5)=0x=-2,5 |
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| 19. |
m is 12.5 m long and 8 m wide. A square carpet of side 8 m is laid on itsof the floor which is not carpeted. |
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| 20. |
solve the elimination method substitusion method x+y=5 and 2x-3y=4 |
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Answer» X+y=5X=5-yput in equation 22(5-y)-3y=410-2y-3y=410-5y=4-5y=-6y=6/5hence X=5-6/5X=25-6/5X=19/5 x+5=5x=5-5x=0 2x-3y=4 thank you for helpmy x+y=5so, y=5-xputting y value in eq. 22x-3(5-x)=42x-15-3x=4-1x=4+15-1x=19so, x =19 |
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| 21. |
solvedelimination methodant sy= 20sy - 4x = 10 |
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| 22. |
Use the elimination method6x -y 8-2x + y -20 |
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Answer» 6x - y = 8.....(1)-2x + y = - 20......(2) Add equations (1) and (2)4x = - 12x = - 12/4 = - 3 Put value of x = - 3 in eq(1)6*(-3) - y = 8-18 - y = 8y = - 26 Value of x = - 3, y = -26 |
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| 23. |
Solve elimination method 3x+4y=10 and 2x-2y =2 |
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Answer» Like if you find it useful |
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| 24. |
2 तुलना करने के लिए >,< व = च|_0 है |
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Answer» As we know3/7= 0.422/5= 0.42/5> 3/7 |
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| 25. |
पूचिमघाथठ डिपी ठाछ I8 बठें।उ+ व न 10 शव 2-2क2e25 - |
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| 26. |
solve (x-y)=26x=3y by using elimination method |
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Answer» x-y=26x=3y3y-1y=262y=26y=26/2y=13x=3×13x=39 |
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| 27. |
o s St T s s है८ = कि धका व उ 2 ८८. है शी है 2 5-५४ 2. एनककबाशकंए इन, नर: हु भव न 7 2-27 |
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| 28. |
' नफिएफीबेलवाए प- पे व मसिशिया 1 (6कूसकान व 2१0 वर्णthe Digdonce, किया o‘h_im%neh,m‘__‘ dB T Ghal g d Mdomee दी हल शाS ) i |
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Answer» Area of parallelogram = Base*HeightFor base = 8m, height = 4m.For base = 5m, height = x m (Let)=> 8*4 = 5*x=> x = 32/5=> x = 6.4mThis is the distance between the shorter sides. PLEASE HIT THE LIKE BUTTON |
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| 29. |
Total of sum 1 to 100? |
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Answer» 1.2,3,4........99,100 is a series Sum of series = n/2(first number + last number) Where n = no. of integers= 100/2(1 + 100)= 50(101)= 5050 Sum of 1 to 100 = 5050 |
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| 30. |
11.き45000 amounts to? 65250 in 3 years. In how many years will 625 amount to812.5at the same rate of interest? |
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| 31. |
arr10,800 for 3 years at 12 2 % per annum compounded annually. |
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| 32. |
Qu/calculate the Amount and Cl forPrincipal= Rs 625Rate of Interest = 4 % p.a.Time = 2 years |
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| 33. |
Mr. Mohanty bought a carpet measuring8.5 m by 7 m. what is the area of the carpet? |
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Answer» area=length× breadth=(8.5)×(7)m^2=59.5m^2 |
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| 34. |
arma bought 5346 chairs for the auditorium. If each chair costs 398, how muchMr Shmoney did Mr Sharma pay to the shopkeeper?ra nrinted last year If each book had 329 pages, how many |
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Answer» total money paid = 5346×398=rs.2,127,7 08 |
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| 35. |
Mr Sharma bought a square-shaped photo frame of side 1.8 m. Find the area ofthe photo frame.d) |
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Answer» Area of frame=side²=1.8²=3.24 cm² |
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| 36. |
UJJ Vvllat will be the cost of 12 apples?ozen eggs cost? 90. Find the cost of 22 eggs. 9204.3d- |
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Answer» 1 dozen=12 3 dozen of egg = 36 eggs36 egg = Rs 901 egg = Rs 5/2Cost of 22 egg = Rs 5/2 × 22 = Rs 55 cost of 3 dozen eggs =₹90 Number of 1 dozen eggs =12Number or 3 dozen eggs =3×12=36cost of 1 dozen eggs =90÷36=5÷2cost of 22 eggs =5÷2×22 =₹55 |
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| 37. |
The cost of 7 meters of cloth is 3 12. Find the cost per metre.Thecmete |
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Answer» 7(2/3)=23/3=7.66_________(1); cloth==51/4=12.75_______(2); 12.75/7.66=1.66 |
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| 38. |
The cost of 7 books is 483. Find the cost of 12 such books. |
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Answer» the cost of seven books = 483 rs,, ,, ,, one ,, = 483 divide by 7 = 69 rs. ,, ,, ,, 12 ,, = 69 into 12 |
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| 39. |
If cost of 12 caps is420. find the cost of 7 such caps. |
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Answer» cost of 12 caps=420₹let the cost of 1 cap be x cost of 12 caps =12x 12x=420x=420/12x=35 cost of 7 such caps=7x7x=7×357x=245 is correct answer |
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| 40. |
3.If 5 books cost Rs. 75, find the cost of 12 books of the same kind. |
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Answer» the cost of 12 book is 180 Given:5 books cost =Rs 7512 books=?=75×12 --------- 5=180Rs |
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| 41. |
ll De le 8ost of 12 a3cost of 2 egsdozen eggs cost90. Find the |
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Answer» Like if you find it useful |
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| 42. |
15. Komal has20 more than Seeta and Malahas 40 less than Komal. If the total sum,they have, is 150, how much does eachone have? |
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| 43. |
2. ਕਿਹੜਾ ਵਿਅੰਜਕ ਦਿੱਤੀ ਸੰਖਿਆ ਰੇਖਾ ਦੁਆਰਾ ਹੱਲवीउ मा प्रवरा चै? Which expression canbe solved by given number line? दी गईसंख्या रेखा द्वारा किस व्यंजक को हल किया जासकता है?-2007189180718+20400718+2040718+2400718+402 |
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Answer» c. is correct answer 718 +240 c is correct answer718+240 |
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| 44. |
16. The ratio of income to expendiure of a laăŚ14000.17. The ratilo of zinc and copper infind the weight of zinc in it.is 7:9.n alloy is 7:9. If the weight of copper in the alloy is1hours. Findtheus covers 128 km in 2 hours and a train covers 240 km in 3their speeds.8. A b |
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Answer» 7)Zinc : copper = 7 : 9 : : x : 11.7= 7/9 x/11.7cross multiplication= 7*11.7=9*x= 81.9 = 9x= 81.9/9 = x= 9.1 = x hit like if you find it useful |
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| 45. |
6. Magic Square: By using every number between 1 and 16complete the given number square so that every line, upand down, left to right and diagonal adds up to 3413151116 |
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| 46. |
the ratio of ages of abha and her mother is 2:5. At time of abha's birth her mother age was 27year . find the present ages of abha and her mother |
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Answer» abha/mother=2/55*abha=2*mother when abha=0 mother=27after 18 yearsabha=18 and mother=4518*5=45*2so present ages are 18 and 45 thanks |
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| 47. |
If a train covers 240 Km in 6 hours, then find the distance it will cover in 140.1hours. |
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Answer» 560 km is the answer of the following 240/6=40In 1 hour it cover =40 KMSO in 14 hours train will cover =14*40=560km 240/6=40one hour = 40 km14 house =40×14=560 240/6=40one hour=40km14 hour=40×14=560 560km is your right answer 560 km is the correct answer of the given question 560km is the correct answer |
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| 48. |
ages of Abha and her mother is 2 15. At the time of Abha's birth her motnersAbha and her mother.27 625Ld Sr arr 14 years and 10 years respectively. After how manywas 27 year Find the present ages of |
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Answer» Let the present age of Abha be x years and the age of her mother is x + 27 years. Given: x/(x + 27) = 2/5 5x = 2 (x + 27) 5x = 2x + 54 3x = 54 x = 18 years Answer - The present age of Abha is 18 years and her mother's age is (18 + 27 = 45 years) |
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| 49. |
determine the horizontal force P to be applied to A block weight 450N,to hold it in position on a smooth inclined plane which makes an angle of 30 degree with the horizontal |
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Answer» F =Mgcos thetaas Mg= N 450cos30450*√3/2389.7 |
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| 50. |
Sumita is half the age of her mother Seeta. Find their ages(i)(ii)2.After 4 years?After 3 years? |
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