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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 4501. |
Let f be the subset of Z x Z defined by f [(ab, a + b): a, b e Z]. Is f afunction from Z to Z? Justify your answer.11. |
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| 4502. |
company manufactures two types of novelty souvenirs made ofplywood. Souvenirs of type A require 5 minutes each for cutting and10 minutes each for assembling. Souvenirs of type B require 8 minuteseach for cutting and 8 minutes each for assembling. There are 3 hoursand 20 minutes available for cutting and 4 hours available forassembling. The profitǐs?h each for type A and 60 each for type Bsouvenirs. How many souvenirs of each type should the companymanufacture in order to maximize profit ? Formulate the above LPP andsolve it graphically and also find the maximum profit. |
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| 4503. |
In a right-angled triangle prove that 4 times the sum of the squares on the medians drawn fromthe acute angles is equal to 5 times the square on the hypotenuse.15. |
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Answer» Like if you find it useful |
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| 4504. |
15. In a right-angled triangle prove that 4 times the sum of the squares on the medians drawn fromthe acute angles is equal to 5 times the square on the hypotenuse. |
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| 4505. |
times the5. Divide 16 into two parts such that 2square of larger part is 164 more than thesquare of smaller part. |
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| 4506. |
Which has greater perimeter a square ground of side 85 m or a rectangular groundwith sides 10 m and 75 m and by how much.14. |
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| 4507. |
Convert the following into minutes.(a) 3 hours 20.minutes |
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Answer» 1 hour = 60 minutes.3 hours 20 minutes = (3*60)+ 20 = 200 minutes. PLEASE HIT THE LIKE BUTTON |
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| 4508. |
Change 3 hours 20 minutes into seconds |
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Answer» 60 minutes= 1 hour1minute= 1/60 hour20 minute= 1/3 hourtotal seconds in 3.33 hours will be 3600*3*3312000 thank you |
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| 4509. |
fast train covers 360 km in 3 hours 20 minutes.Howr much time will it take to cover a distance of 90 km ? |
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Answer» what the ck xxxxxxxxxxxxxxxx |
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| 4510. |
If figure, ABII CD. Determine Za.X De+38°YR |
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Answer» Angle A is the sum of angle 1 and angle 2 so, angle 1 = 55° .... ( alternate interior angle) and angle 2 = 58° ....( alternate interior angle) => angle a = 55°+38° = 93° |
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| 4511. |
2. Convert the following into minutes.a. 11 hoursb. 4 hours 15 minutes3. Convert the following into hour.a. 75 minutesb. 830 minutes172Functional Mathematics Book 3 |
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Answer» 11 hours is 11x60 min which is 660 4 hours is 240 min therefore 255 min a.660 b.255c.1 hour. 15 minutesd.13 hours 38 minutes 75 min is 1 hour 15 min 830 min is 13 hours 50 min 11 hours 11*60 min 660 1.25= 1 hour and 15 minutes a.660b.255c. 1 hour. 15 minutes d.13 hours 38 minutes a) 11*60= 660 minutes a,660b,255c,1hour1minutesd,,13hour 38 minutes |
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| 4512. |
A train covers a distance of 3549 km to reach a station in 42 hours 15 minutes. What is the speed? |
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Answer» .....when 42 hrs nd 15 min is given then we have to convert it into hours then will get the answer .....when 42 hrs nd 15 min is given then we have to convert it into hours then will get the answer 42hrs15min = 42.25hrs speed = 3549/42.25 = 84 km/h |
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| 4513. |
1. In the given figure (12.51), AD CB, AB CD and EF bisects BD at G. Prove Rthat G is the mid point of EF. |
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| 4514. |
. In the adjoiningfigure, ABCD is am in which Eand F are theGPmid-points ofAB and CDrespectively. If GH is a line segmentthat cuts AD, EF and BC at G, P andH respectively, prove that GP PH. |
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| 4515. |
3. In the adjoining figure, ABCD is a llgm inwhich E and F are the midpoints of AB andCD respectively. If GH is a line segmentthat cuts AD, EF and BC at G, P and H orespectively, prove that GP PH |
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| 4516. |
3. In the adjoining figure, ABCD is a llgm inwhich E and F are the midpoints of AB andCD respectively. If GH is a line segmentthat cuts AD, EF and BC at G, P and H Grespectively, prove that GP = PH |
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| 4517. |
In the given figure, ABCD is quadrilateral, inwhich AB AD and BC DC. Diagonals ACand BD intersect each other at O. Show that(b) ΔΑΟΒ ΔΑ0D(c) AO L BD(d) AC bisects BD |
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| 4518. |
11. Two lines AB and CD are parallel to each other. The transversal BD bisects the other transversalAC. Prove that AC also bisects BD |
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Answer» Let the intersection of BD and AC be point E. Angles BAC and DCA are congruent [alternate interior angles]Angles BAC and BAE are congruent [same angle]Angles BAE and DCA are congruent [transitivity of congruence]Angles DCA and DCE are congruent [same angle]Angles BAE and DCE are congruent [transitivity of congruence]Angles AEB and CED are congruent [vertical angles]AE = CE [definition of bisection]triangles AEB and CED are congruent [angle, side, angle]BE = DE [corresponding sides of congruent triangles]AC bisects BD [definition of bisection] |
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| 4519. |
9. In a triangle ABC,D, E and Fare the mid-pointsof sides BC, CA and AB respectively, then provethat EF bisects AlD |
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| 4520. |
5. In the adjoining figure, BMLAC andACDN丄AC. Ifbisects BDBM=DN,provethat |
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| 4521. |
In Fig. 6.130, ABCD is a trapezium, EF || AD and EF || BC. Find the measure of Zxº, Zyº and Zzº.120 de50°Fig. 6.130 |
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Answer» since AD is parallel to BC and AC is transversalthere fore m(dac)=m (ACB)X=50 degree (Alternate Angle)since AD parallel to EF and FD is transversaltherefore y=180-m. (DYE)=180-120=60 degree(interior angles)since AD parallel to EF and AZ is transversal therefore z=xsince x=50therefore z=50 too 💖 y+120°= 180° (internet ang.)y=180-120= 60° z°=50° (alternate ang.) x°=z° (corresponding ang.)x°=50° 50° is the right answer. plz like my answer |
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| 4522. |
In the figure 11.34, ABCD is a quadrilateral in which AB3.and BC = DC. Diagonals AC and BD intersect each other at o.Show that-(i) AABC AADC(iii)ACLBD(iv) AC bisects BDFia. 11.34 |
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| 4523. |
12. In what two ways can you say that aline segment bisecting another linesegment is a perpendicular bisector? |
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Answer» Thanq sir |
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| 4524. |
A line segment AB is bisected at point P andthrough point P another line segment PQ,which is perpendicular to AB, is drawn. Showthat : QA QB. |
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Answer» Consider the figure for reference, In Triangles APQ & BPQ, P bisects AB thus PA =PB...(1) PQ is perpendicular to AB, thus∠ QPA =∠ QPB = 90° PQ is a common segment to both the trianglesAPQ & BPQ Thus by the definition of congruence that 2 triangles are congruent if 2 sides and an angle formed by them are equal in each triangle. ALso knon as Side-ANgle-SIde(SAS) Thus trianglesAPQ & BPQ are congruent Thus side QA = QB |
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| 4525. |
at right angles dCalculate the unknown(s) in each of the following:117°300r"40° |
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Answer» we make eq 117= k+30+40, vertically opposite angle, we get k= 47 then for r we use sum of Angle in straight line so r+30+40+47=180 so r is 180-117 =63 so r= k = 63 as they are vertically opposite angle. |
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| 4526. |
ABCD is a parallelogram whose diagonals intersect each other at a point o. a line segment EF is drawn through O and is terminated by AB and CD. prove that OE=OF |
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Answer» 1st AB//EF//AD and we have to proof OE =OF in //gm oppo. sides of //gm are equal OBC lie on the same base and between the //BC AND EF (1)THEN SEE AOD LIE ON THE SAME BASE AD and between the same//EFandAD so it is prove that OE=OF |
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| 4527. |
Ia the figure calculate Za. What type of angleis270 |
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Answer» angle a = 360 - 270 angle a = 90° thnks |
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| 4528. |
15. ABCD is a parallelogram whose diagonalsDintersect each other at a point O. A linesegment EF is drawn through O and isterminated by AB and CD. Prove thatOE OF. |
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Answer» In∆ODFand∆OBE, we have:OD = OB (Diagonals bisects each other)∠DOF= ∠BOE (Vertically opposite angles)∠FDO= ∠OBE (Alternate interior angles)i.e., ∆ODF≅∆OBE∴OF = OE (CPCT)Hence, proved. |
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| 4529. |
1. In the adjoining figure, ABCD is a trapeziumDin which AB|| DC and E is the midpoint ofAD. A line segment EF I| AB meets BC at F. EShow that F is the midpoint of BC. |
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| 4530. |
83 5356 esAB/ CD, CD//EFdRy : z-3 : 7君atx万天ftenfyr536 |
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| 4531. |
1. In the figure, ABCD is a trapezium inwhich AB l DC and E is the mid-pointof AD.BC at F. Show that F is the mid-pointof BC.A line segment EF Il AB meets |
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| 4532. |
3. Attempt the following:3 marks each/In the figure, ABCD is a trapezium in which AB | Dc.E is the midpoint of AD. A line segment EF I AB meetsBC at F. Show that F is the midpoint of BCHint: Draw diagonal DB]Proof: |
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| 4533. |
az-al2d X 2) = 8I AB .CD, mL API=20and mL PRD = 129ยบ.finds andy2)A).Choose thealternative |
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Answer» x=50°(alternate angles)y=127°-50°=77° x=50° as it is alternate angles 127°=50°+y y=127°-50°y= 77° hope it helped you X= 50° ,y = 77° is the correct answer of the given question |
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| 4534. |
34. A train travels 360km at a uniform speed. If the speed had been 5km/hrthe train. |
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Answer» Let the original speed of the train be x km/h.Time taken to cover a distance of 360 km = 360/x hours.New speed of the train = (x+5) km/h.Time taken to cover a distance of 360 km at new speed = 360/x+5 hours.Since, the train takes 1 hour less time,∴ 360/x - 360/ x+5 = 1⇒360 (x+5-x)/x(x+5) = 1⇒360 (5) = x² + 5x⇒1800 = x² + 5x⇒x² + 5x - 1800 = 0⇒x² + 45x - 40x - 1800 = 0⇒x (x+45) - 40( x +45) = 0⇒(x+45) (x-40) = 0⇒x = (-45), 40But since speed cannot be in negative.∴ x = 40 km/hr.Hence, the original speed of the train is 40 km/h. |
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| 4535. |
1.In ADEF and ΔPQR, If <Dz < 0, L< E, then find the true statement fromthe following.(A)-=(C)-=EF DFPR-PO (B) P =DE DFDE EFEF DIEF RA |
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Answer» So the answer is option D Like my answer if you find it useful! |
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| 4536. |
In Fig. 6.29, ifAB Il CD, CD 11 EF and y: z = 3 : 7,find x.2.Fig. 6.29 |
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| 4537. |
If.v3x-yz 3y3each ratio is equal to 1andy# 0 then show that the value ofZ-x-y |
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Answer» If you like the solution, Please give it a 👍 |
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| 4538. |
Measure EF aodWhar do you observe? You will find that:Esamplesee FigSolutionsa EFBCRepear this activity with some more triangles.Se, you arive at the following theorem:Fiheorem 89: The line segment joining the mid-points of two sidesparallel to the third side.d BCYo cae prove this theorgem using the followingObserve Fig &.25 in which E and Fare mid-points8 and AC respectively and CD II BAowÎ AEFr Î CDFDF and BE=AE = DC(ASA Rule)(Why?)EF:BL |
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Answer» The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it. Take a triangle ABC,E and F are the mid-points of side AB and AC resp. Construction:-Through C,draw a line II BA to meet EF produced at D. Proof:-In Triangle AEF and CDF1.AF=CF(F is midpoint of AC)2.<AFE=<CFD (Vertically opp. angles)3.<EAF=<DCF [Alt. angles,BA II CD(by construction) and AC is a transversal]4.So,Triangle AEF = CDF(ASA)5.EF=FD AND AE = CD (c.p.c.t)6.AE=BE(E is midpoint of AB)7.BE=CD(from 5 and 6)8.EBCD is a IIgm [BA II CD (by construction) and BE = CD(from 7)]9.EF II BC AND ED=BC (Since EBCD is a IIgm)10.EF = 1/2 ED (Since EF = FD,from 5)11.EF = 1/2 BC (Since ED = BC,from 9)Hence,EF II BC AND EF = 1/2 BC which proves the mid-point theorem. |
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| 4539. |
2, E is the midpoint of DF. DE, 9. Find EF and DF. |
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Answer» I can't see |
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| 4540. |
ĐŚĐ.gype-3snortAnswerlypeQuestions-11A letter of English alphabet is chosen at random, find the probability that the chosen letter isconsonant. |
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Answer» Total alphabet = 26consonants= 21probability = 21/26 |
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| 4541. |
3Inthegiven figure, if AB | CD, ZAPQ 40° and PRD118°, find x and y.40°118° |
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Answer» x = angle APQ Alternate anglesx = 40 Angle PRQ + 118 = 180 linear pairAngle PRQ = 68 40 + y + 68 = 180y = 180-108y = 72 thankyou |
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| 4542. |
ype IV.3. निम्नलिखित का गुणनफर(a) 101 x99(c) 115x854. निम्नलिखित का मान ज्ञा |
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Answer» (a) 101 × 99 = 9999(c) 115 × 85 = 9775 is the best answer. ( A) 101×99=9999(c) 115×85=9775 99999775 is the correct answer a) 101×99=9999c) 115×85=9775 answer. 101×99=99×100+99×1 =9900+99 =9999115×85=9775 101 ×99=9999115×85=9775 101×99=9999115×85=9775 a Answer=9999 and b Answer 9775 |
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| 4543. |
rype .Short Answer euestions. Observe the following tables and find in whichcase a and b are in direct proportion:7 812b 18 30 42 48 72l) a |
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Answer» b=18=6×3=6a b=30=6×5=6a b=42=6×7=6a b=48=6×8=6a b=72=6×12=6a b = 6a |
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| 4544. |
3. Find the area of A ABC in which AB BC 4cm and B 904. Find the area of an equilateral triangle with side 2/3 cm.5. The perimeter of a triangle is 36 cm and its sides are in the ratio a:b:c 3:4:5 thevolume of a, b and c (in cm)ype-26. The sides of a triangle are x, x +1,2x - 1 and its area is 10. Find the value of x.7. Find the area of a triangle whose sides are 11,60 and 61 m.8. The semi-perimeter of a triangular ground is 450 units and its side are in the ratioShort Answer Type Questions |
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| 4545. |
ype I+na_n(n+1)(2 ilmifstatement i2 +22+3Show that P (1), P (2) and P (3) aOW |
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Answer» P(1) L.H.S.=1*1=1 R.H.S.=1(2)(3)/6=1 P(2) L.H.S.=1*1+2*2=1+4=5 R.H.S.=2(3)(5)/6=5 P(3) L.H.S.=1*1+2*2+3*3=1+4+9=14 R.H.S.=3(4)(7)/6=14 |
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| 4546. |
15) A car with a uniform speed travels a distance of 165 km in 3 hours. At the sameTaj how long will it take to cover a distance of 330 km? thi how far will it travel in |
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| 4547. |
In Fig. 6.30, if AB || CD, EF CD andGED=126”, find AGE, GEF and FGE. |
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| 4548. |
the area of AABC4. In a Δ/l BC. A»-15 cm, BC-13 cm and AC-14 cm, hindhence its altitude on AC |
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| 4549. |
L)e poyhomil ype) are threewill be 132 more than its 54th term?2. Which term of the AP 3, 15, 27, 39, |
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| 4550. |
3. In the adjacent figure AB CD, EF L CDZAGE,GEFand <GED=126", findand ZFGE.Ce |
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Answer» age = 64gef = 36fge = 54 |
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