81279 + Interview Questions in Mathematics QA in Mathematics Page 1393 InterviewSolution

69601.	much?8. Michael finished colouring a picture in 12 hour Vaibhav finished colouringthe3picture in hour. Who worked longer? By what fraction was it longer?4IONS
Answer»

Discussion

69602.	UCI PICE14. A film show lasted for 3 2 hours. Out of this time 1hours was spent on advertisementsWhat was the actual duration of the film?
Answer» thanks

Discussion

69603.	Find the duration of time:6:15 a.m. to 12:00 noor
Answer» 6:15 am to 12:00 noon 5 hours 45 minutes

69603.

Find the duration of time:6:15 a.m. to 12:00 noor

Answer»

6:15 am to 12:00 noon

5 hours 45 minutes

Discussion

69604.	- On a TV channel, a popular film lasted for 3 hours. Out of this time theyadvertisements wereour. What was the actual duration of the film!hours. Out of this time the commercial
Answer» Two whole one by two

Discussion

69605.	Add hour andhour1212
Answer» 5/12 + 3/12= 8/12hour =2/3 hour

Discussion

69606.	13. A girl walks 12 km at the speed of 3 km/h. What change should she make in her speed totake (i) an hour less and (ii) an hour more to cover the distance?lf nn hour at the end of every 75 km. How
Answer»

Discussion

69607.	UrolNS.44.What percent is 12 minutes of 1 hour?
Answer»

Discussion

69608.	The power of engine of a car of mass 1200 kg is25 kW. The minimum time required to reach a velocityof 90 km/h by the car after starting from rest is(1) 15 s(3) 60 s(2) 25 s(4) 12 s
Answer» Velocity = 90 km/hr = 25 m/s. Power = 25 kW = 25,000 W. Work = Kinetic energy ∴ W =1/2 mv² ⇒ W = 375000 Since, Power = Work/time. ⇒ Time = Work/Power ⇒ Time = 375000/25000 ∴ t = 15 s.

69608.

The power of engine of a car of mass 1200 kg is25 kW. The minimum time required to reach a velocityof 90 km/h by the car after starting from rest is(1) 15 s(3) 60 s(2) 25 s(4) 12 s

Answer»

Velocity = 90 km/hr = 25 m/s.

Power = 25 kW = 25,000 W.

Work = Kinetic energy

∴ W =1/2 mv²

⇒ W = 375000

Since, Power = Work/time.

⇒ Time = Work/Power

⇒ Time = 375000/25000

∴ t = 15 s.

Discussion

69609.	1.Find three different solutions of the each of the following equations.i) 3x +4y 7ii) y 6xii) 2x - y-7
Answer» i) 3x +4y = 7 put x = 0 , y = 7/4 put y = 0, x = 7/3 ii) solutions are (0,0) , (1,6) , (2,12) iii) 2x = 7+y => put x = 0 , y = -7=> put x = 1 , y = -5 thnks

69609.

1.Find three different solutions of the each of the following equations.i) 3x +4y 7ii) y 6xii) 2x - y-7

Answer»

i) 3x +4y = 7

put x = 0 , y = 7/4 put y = 0, x = 7/3

ii) solutions are (0,0) , (1,6) , (2,12)

iii) 2x = 7+y => put x = 0 , y = -7=> put x = 1 , y = -5

thnks

Discussion

69610.	if the duration of each period of a class is 11/12 hour, what is the duration of 6 period.
Answer» Duration of each period = 11/12 hrDuration of 6 period = 6*11/12= 11/2 = 5.5 hrs

Discussion

69611.	14. A field is in the form of a circle. The cost ofploughing the field at R 15 per m2 is 57,750Find the cost of fencing the field atmetre.34 per
Answer» Area ploughed for Rs. 15= 1 m2 Area ploughed for Rs. 57750= (1/15) × 57750 = 3850m2 area of circular field = 3850 m2 let r be the radius of the field. so, π r2= 3850 ⇒ r2= 3850 / π = (3850×7) / 22 = 1225 so, r = 35 m perimeter of field = 2 π r = 2 × 22/7 × 35 = 220 m so, total cost of fencing = 34 × 220 = Rs. 7480

69611.

14. A field is in the form of a circle. The cost ofploughing the field at R 15 per m2 is 57,750Find the cost of fencing the field atmetre.34 per

Answer»

Area ploughed for Rs. 15= 1 m2

Area ploughed for Rs. 57750= (1/15) × 57750 = 3850m2

area of circular field = 3850 m2

let r be the radius of the field.

so, π r2= 3850 ⇒ r2= 3850 / π = (3850×7) / 22 = 1225

so, r = 35 m

perimeter of field = 2 π r = 2 × 22/7 × 35 = 220 m

so, total cost of fencing = 34 × 220 = Rs. 7480

Discussion

69612.	3. What is the expenditure of levelling a square ground with side 80 m at15 per m2?
Answer» Area of the square ground=80²=6400 m² ∴Cost of levelling the ground at Rs.15 per m²=Rs.(6400×15)=Rs.96,000

69612.

3. What is the expenditure of levelling a square ground with side 80 m at15 per m2?

Answer»

Area of the square ground=80²=6400 m²

∴Cost of levelling the ground at Rs.15 per m²=Rs.(6400×15)=Rs.96,000

Discussion

69613.	A cy lindrical pillar is i m in diameter and 4.2 m in height. Find the cost of white washing thesurface of the pillar at the rate of 15 per m2
Answer» Thanks !!!Really thanks

Discussion

69614.	Ramya and Ramana collected Rs. 600 and contributed for Keralaflood relief fund, through C.M. relief fund. Write the linear equationand find four different solutions.
Answer»

Discussion

69615.	find the four different solutions of of the equation x+2y=6
Answer» x+2y=6 let x=1 then 1+2y=62y=6-1=5now put values of x as 2 now 2+2y=62y=6-22y=4y=4÷2y=2 now let x=3 3+2y=62y=6-3=3y=3/2 now let x= 4 now4+2y=62y=6-42y=2y=2÷2=1 so from different values of x and y we got infinite many solutions

Discussion

69616.	Write any four different solutions for 7x-2y-25.
Answer»

Discussion

69617.	Find three different solutions of the equation x + 2y 6.
Answer»

Discussion

69618.	19. As observed from the top of a lighthouse, 100 m above sea level, theangle of depression of a ship, sailing directly towards it, changes from30° to 600. Determine the distance travelled by the ship during the[CBSE 2004, '08C]period of observation. [Use
Answer»

Discussion

69619.	27. As observed from the top of a lighthouse, 100 m above sea level, theangle of depression of a ship, sailing directly towards it, changes from30° to 60°. Determine the distance travelled by the ship during the[CBSE 2004, '08C]period of observation. [Use /3-1.732.]
Answer»

Discussion

69620.	12 The hypotenuse of a right-angled triangle is 1 m less thantwice the shortest side: If the third side is 1 m more than the
Answer»

Discussion

69621.	)Places A and B are 100 km apart on a highway. One car starts fromAandanotherfrom B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour. Whatare the speeds of the two cars?
Answer» Thanks a lot🔥✌️

Discussion

69622.	Places A and B are 100 km apart on a highway. One car starts from A and anotherfrom B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour.Whatare the speeds of the two cars?
Answer» Let the speed of car at A be x kmph and the speed of car at B be y kmph As per the question, 5x - 5y = 100 x - y = 20... (1) andx + y = 100... (2) Solving (1) and (2), we get, x = 60 and y = 40 Speed of the car at A = 60 kmph Speed of the car at B = 40 kmph Let the speeds of the cars be x km/hr and y km/hr Case 1: When the cars are going in the same direction Relative speed = x - yDistance = 100 km Time = 100 / (x - y) = 5 hrs x - y = 100 / 5x – y = 20 ------------- (1) Case 2: When the cars are going in the opposite direction Relative speed = x + y Time =100 / (x + y) = 1 hrs x + y = 100 ------------- (2) Solving the equations (1) and (2), we getx = 60 and y = 40 Hence the speeds of the cars are 60 km/hr and 40 km/hr.

69622.

Places A and B are 100 km apart on a highway. One car starts from A and anotherfrom B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour.Whatare the speeds of the two cars?

Answer»

Let the speed of car at A be x kmph

and the speed of car at B be y kmph

As per the question,

5x - 5y = 100

x - y = 20... (1)

andx + y = 100... (2)

Solving (1) and (2), we get,

x = 60 and y = 40

Speed of the car at A = 60 kmph

Speed of the car at B = 40 kmph

Let the speeds of the cars be x km/hr and y km/hr

Case 1: When the cars are going in the same direction Relative speed = x - yDistance = 100 km Time = 100 / (x - y) = 5 hrs x - y = 100 / 5x – y = 20 ------------- (1)

Case 2: When the cars are going in the opposite direction Relative speed = x + y Time =100 / (x + y) = 1 hrs x + y = 100 ------------- (2)

Solving the equations (1) and (2), we getx = 60 and y = 40

Hence the speeds of the cars are 60 km/hr and 40 km/hr.

Discussion

69623.	Places A and B are 100 km apart on a highway.One car starts from A and another from B at thesame time. If the cars travel in the same direction atdifferent speeds, they meet in 5 hours. If theytravel towards each other, they meet in 1 hour.What are the speeds of the two cars?
Answer» A =60kmph and B = 40 kmph is the answer of this problem the speed of car at A be X kmph; The speed of car at B be y kmph. 5x-5km=100, x-y=20 __(1), x+y=100____(2), solving (1) and (2) x=60 and Y=40, car at A =60 kmph,.B= 40 Kmph.,

69623.

Places A and B are 100 km apart on a highway.One car starts from A and another from B at thesame time. If the cars travel in the same direction atdifferent speeds, they meet in 5 hours. If theytravel towards each other, they meet in 1 hour.What are the speeds of the two cars?

Answer»

A =60kmph and B = 40 kmph is the answer of this problem

the speed of car at A be X kmph; The speed of car at B be y kmph. 5x-5km=100, x-y=20 __(1), x+y=100____(2), solving (1) and (2) x=60 and Y=40, car at A =60 kmph,.B= 40 Kmph.,

Discussion

69624.	14. A field is in the form of a circle. The cost ofploughing the field at R 15 per m^2 is Rs 57,750.Find the cost of fencing the field at 34 permetre
Answer» Area ploughed for Rs. 15 = 1 m2 Area ploughed for Rs. 57750 = (1/15) × 57750= 3850 m2 area of circular field = 3850 m2 let r be the radius of the field. so, π r2= 3850 ⇒ r2= 3850 / π = (3850×7) / 22 = 1225 so, r = 35 m perimeter of field = 2 π r = 2 × 22/7 × 35 = 220 m so, total cost of fencing = 34 × 220 = Rs. 7480

69624.

14. A field is in the form of a circle. The cost ofploughing the field at R 15 per m^2 is Rs 57,750.Find the cost of fencing the field at 34 permetre

Answer»

Area ploughed for Rs. 15 = 1 m2

Area ploughed for Rs. 57750 = (1/15) × 57750= 3850 m2

area of circular field = 3850 m2

let r be the radius of the field.

so, π r2= 3850 ⇒ r2= 3850 / π = (3850×7) / 22 = 1225

so, r = 35 m

perimeter of field = 2 π r = 2 × 22/7 × 35 = 220 m

so, total cost of fencing = 34 × 220 = Rs. 7480

Discussion

69625.	16. Places A and B are 100 km apart on a highway. One car starts from A and another from B atthe same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If theytravel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Answer»

Discussion

69626.	71Write any four different solutions for 7x-2y -25.(or)Ramya and Ramana collected Rs. 600 and contributed for Keralaflood relief fund, through C.M. relief fund. Write the linear equationand find four different solutions.
Answer» suppose Ramya's contribution=x and Ramana's contribution = yx + y = 600different solutions are400,200500,100100,500200,400

Discussion

69627.	12. Find four different solutions of 2x+3y6.
Answer» ThnQ

Discussion

69628.	del Find four different solutions of the equation 2x=5410.
Answer»

Discussion

69629.	Question numbers 1 to 6 carry 1 mark each1. z and b are two positive integers such that the least prime factor of a is SăŤ(5Then calculate the least prime factor of (a + b).v3 1. What is thee ratio of the height of a tower and the length of its shadow on the ground isangle of elevation of the sun ?e.oe ORs45 ml aA = 6am and AP = 4 cm, then find Q8.
Answer»

Discussion

69630.	Find four different solutions of the equation x + 2y = 6.
Answer» plz..... answer me my test tomorrow

Discussion

69631.	17. The hypotenuse of a right-angled triangle is 1 m less thantwice the shortest side. If the third side is 1 m more than theshortest side, find the sides of the triangle.
Answer»

Discussion

69632.	he hypotenuse of a right-angled triangle is 1 metre less than twice theshortest side. If the third side is 1 metre more than the shortest side,find the sides of the triangle.71. T
Answer»

Discussion

69633.	by 1 cm. Find the lerngul U71. The hypotenuse of a right-angled triangle is 1 metre less than twice shoshortest side. If the third side is 1 metre more than the shortestfind the sides of the triangle.
Answer» thank you thanks

69633.

by 1 cm. Find the lerngul U71. The hypotenuse of a right-angled triangle is 1 metre less than twice shoshortest side. If the third side is 1 metre more than the shortestfind the sides of the triangle.

Answer»

thank you

thanks

Discussion

69634.	2these citiese distance between city A and B is 510 km. Two cars begin their journey fromnd move directly towards each other, with speeds of 100 km/hour nd 70 km/hourhave started at the same time, where is the meeting point of the carsIf the2carsthat of th
Answer»

Discussion

69635.	l) A person is running along a circular track of area625 π mn 2 (π .22/7) with a constant speed. Find thedisplacement in 15 seconds if he has to complete therace in 30 seconds.100 m
Answer»

Discussion

69636.	iv) Places A and B are 100 km apart on a highway. One cafrom B at the same time. If the cars travel in the same dthey meet in 5 hours. If they travel towards each otherare the speeds of the two cars?
Answer»

Discussion

69637.	The inner circumference of a circular race track is 264 m and the width of the track is 7m. Calculatethe cost of putting up a fence along the outer circle of the track at the rate of 15 per metre.L.
Answer»

Discussion

69638.	ii) Leta and b be two unit vectors and θ is the angle betweenthem. Then at b is a unit vector if:(A) θ = π4(B) θ = π2π(Choose the correct one)
Answer»

Discussion

69639.	A race track is in the form of a ring whose Inner circumference is 352 m, find the circumference is 396 m. Find the width of the track.
Answer»

Discussion

69640.	A race track is in the form of a ring whose inner and outer circumferences are 440 m and 528 mrespectively. Find the width of the track and also its area
Answer» Let radius of inner ring is r1radius of outer ring r2 Now,Circumference of inner ring= 2pir12pir1 = 440222/7r1 = 440r1 = 107 = 70 Circumference of outer ring= 2pir22pir2 = 528222/7r2 = 528r^2 = 127 = 84 Width of track = 84-70 = 14 m Area of track = pir2r2 - pir1r1= 22/7(8484 - 7070)= 22(1284 - 1070)= 22(1008 - 700)= 22(308)= 6776 m^2

69640.

A race track is in the form of a ring whose inner and outer circumferences are 440 m and 528 mrespectively. Find the width of the track and also its area

Answer»

Let radius of inner ring is r1radius of outer ring r2

Now,Circumference of inner ring= 2pi*r12pi*r1 = 4402*22/7*r1 = 440r1 = 10*7 = 70

Circumference of outer ring= 2pi*r22pi*r2 = 5282*22/7*r2 = 528r^2 = 12*7 = 84

Width of track = 84-70 = 14 m

Area of track = pi*r2*r2 - pi*r1*r1= 22/7(84*84 - 70*70)= 22(12*84 - 10*70)= 22(1008 - 700)= 22(308)= 6776 m^2

Discussion

69641.	19. The points (-3, 7); (0, -3.5): (1, -3): (4, 4): (2, -3) and (4. 0) are onwhich axis or in which quadrant ?OR19,Find four different solution of the equation 2x-y=12. Draw the graph.
Answer»

Discussion

69642.	et 2i. Which of the following expressions are polynomials?(4)x2+4(b) 3xx +1
Answer»

Discussion

69643.	27- 2xy +eroes ofNow, leate to start with. We need to tind at least one factor tirst as you will see allbe appropriatethe following example.r 15 Factoriser -23+ 142x - 120.ibilities fo
Answer» like pver here....help me plz

Discussion

69644.	14. If cosB_ sin Î¸ # V2 sin 0,prove that cos9+ sin 0-2 cose./15. Determine the value ofxech that 2 cosecao
Answer»

Discussion

69645.	A B15. 1fcos 0 + sin 6 = V2 cos 8, show that cos 8- sin 0 = ¥2 sin®.
Answer» Let theta be A cosA+sinA=√2cosAsquaring both the sides =>(cosA+sinA)²=2cos²A=>cos²A+sin²A+2sinAcosA=2cos²A=>cos²A-2cos²A+2sinAcosA= -sin²A=> -cos²A+2sinAcosA= -sin²A=> cos²A-2sinAcosA=sin²Aadding sin²A on both the sides => cos²A+sin²A-2sinAcosA=2sin²A=> (cosA-sinA)²=2sin²A=> cosA-sinA=√2sinA

69645.

A B15. 1fcos 0 + sin 6 = V2 cos 8, show that cos 8- sin 0 = ¥2 sin®.

Answer»

Let theta be A

cosA+sinA=√2cosAsquaring both the sides =>(cosA+sinA)²=2cos²A=>cos²A+sin²A+2sinAcosA=2cos²A=>cos²A-2cos²A+2sinAcosA= -sin²A=> -cos²A+2sinAcosA= -sin²A=> cos²A-2sinAcosA=sin²Aadding sin²A on both the sides => cos²A+sin²A-2sinAcosA=2sin²A=> (cosA-sinA)²=2sin²A=> cosA-sinA=√2sinA

Discussion

69646.	About goes 30km upstream and 44km downstream in 20 hours. In 13hour, it can go 40km upstream and 55km upstream.find speed of stream and boat in still water.
Answer»

Discussion

69647.	15. I 13+ 4 3 219. If x = 3 + 2 v2 find a) x+21 -1 find the value ofly+1)b) x 1
Answer»

Discussion

69648.	The harmonic mean of the roots of the equation (5+V2)x2-(4+15)x+8+2.5-0is(A) 2(C) 4(B) 6(D) none of these
Answer»

Discussion

69649.	1. A boat goes 30km upstream and 44km downstream in 10 hourskm down stream.In 13 hours, it can go 40km upstream and 55Determine the speed of the stream and that of the boat in stilwater.
Answer»

Discussion

69650.	croes die v215. Show that the points (12, 8), (-2, 6) and (6, 0) are the vertices of right-angled triangle and alsoshow that the mid-point of the hypotenuse is equidistant from the angular points.
Answer» Taking A(12, 8), B(-2, 6) and C(6, 0) AB² = (12--2)² + (8-6)²= 196+4=200 AC² = (12-6)² + (8-0)²= 36+64=100 BC² = (-2-6)² + (6-0)²=64+36=100 By Pythogoras theorem Since AB² = AC² + BC², the points (12, 8), (-2, 6) and (6, 0) are vertices of a right angledtriangle. AB is the hypotenuse. Mid-point of AB = [(12+-2)/2 , (8+6)/2] = (5, 7)Let the mid-point be M (5, 7) AM =√(12-5)² + (8-7)²=√49+1=√50= 5√2 MB =√(5- -2)² + (7-6)²=√49+1= 5√2 AM = MB = 5√2 This proves thatthe midpoint of the hypotenuse is equidistant from the angular points.

69650.

croes die v215. Show that the points (12, 8), (-2, 6) and (6, 0) are the vertices of right-angled triangle and alsoshow that the mid-point of the hypotenuse is equidistant from the angular points.

Answer»

Taking A(12, 8), B(-2, 6) and C(6, 0)

AB² = (12--2)² + (8-6)²= 196+4=200

AC² = (12-6)² + (8-0)²= 36+64=100

BC² = (-2-6)² + (6-0)²=64+36=100

By Pythogoras theorem

Since AB² = AC² + BC², the points (12, 8), (-2, 6) and (6, 0) are vertices of a right angledtriangle.

AB is the hypotenuse.

Mid-point of AB = [(12+-2)/2 , (8+6)/2] = (5, 7)Let the mid-point be M (5, 7)

AM =√(12-5)² + (8-7)²=√49+1=√50= 5√2

MB =√(5- -2)² + (7-6)²=√49+1= 5√2

AM = MB = 5√2

This proves thatthe midpoint of the hypotenuse is equidistant from the angular points.

Discussion

Explore topic-wise InterviewSolutions in .

much?8. Michael finished colouring a picture in 12 hour Vaibhav finished colouringthe3picture in hour. Who worked longer? By what fraction was it longer?4IONS

UCI PICE14. A film show lasted for 3 2 hours. Out of this time 1hours was spent on advertisementsWhat was the actual duration of the film?

Find the duration of time:6:15 a.m. to 12:00 noor

- On a TV channel, a popular film lasted for 3 hours. Out of this time theyadvertisements wereour. What was the actual duration of the film!hours. Out of this time the commercial

Add hour andhour1212

13. A girl walks 12 km at the speed of 3 km/h. What change should she make in her speed totake (i) an hour less and (ii) an hour more to cover the distance?lf nn hour at the end of every 75 km. How

UrolNS.44.What percent is 12 minutes of 1 hour?

The power of engine of a car of mass 1200 kg is25 kW. The minimum time required to reach a velocityof 90 km/h by the car after starting from rest is(1) 15 s(3) 60 s(2) 25 s(4) 12 s

1.Find three different solutions of the each of the following equations.i) 3x +4y 7ii) y 6xii) 2x - y-7

if the duration of each period of a class is 11/12 hour, what is the duration of 6 period.

14. A field is in the form of a circle. The cost ofploughing the field at R 15 per m2 is 57,750Find the cost of fencing the field atmetre.34 per

3. What is the expenditure of levelling a square ground with side 80 m at15 per m2?

A cy lindrical pillar is i m in diameter and 4.2 m in height. Find the cost of white washing thesurface of the pillar at the rate of 15 per m2

Ramya and Ramana collected Rs. 600 and contributed for Keralaflood relief fund, through C.M. relief fund. Write the linear equationand find four different solutions.

find the four different solutions of of the equation x+2y=6

Write any four different solutions for 7x-2y-25.

Find three different solutions of the equation x + 2y 6.

19. As observed from the top of a lighthouse, 100 m above sea level, theangle of depression of a ship, sailing directly towards it, changes from30° to 600. Determine the distance travelled by the ship during the[CBSE 2004, '08C]period of observation. [Use

27. As observed from the top of a lighthouse, 100 m above sea level, theangle of depression of a ship, sailing directly towards it, changes from30° to 60°. Determine the distance travelled by the ship during the[CBSE 2004, '08C]period of observation. [Use /3-1.732.]

12 The hypotenuse of a right-angled triangle is 1 m less thantwice the shortest side: If the third side is 1 m more than the

)Places A and B are 100 km apart on a highway. One car starts fromAandanotherfrom B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour. Whatare the speeds of the two cars?

Places A and B are 100 km apart on a highway. One car starts from A and anotherfrom B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour.Whatare the speeds of the two cars?

Places A and B are 100 km apart on a highway.One car starts from A and another from B at thesame time. If the cars travel in the same direction atdifferent speeds, they meet in 5 hours. If theytravel towards each other, they meet in 1 hour.What are the speeds of the two cars?

14. A field is in the form of a circle. The cost ofploughing the field at R 15 per m^2 is Rs 57,750.Find the cost of fencing the field at 34 permetre

16. Places A and B are 100 km apart on a highway. One car starts from A and another from B atthe same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If theytravel towards each other, they meet in 1 hour. What are the speeds of the two cars?

71Write any four different solutions for 7x-2y -25.(or)Ramya and Ramana collected Rs. 600 and contributed for Keralaflood relief fund, through C.M. relief fund. Write the linear equationand find four different solutions.

12. Find four different solutions of 2x+3y6.

del Find four different solutions of the equation 2x=5410.

Find four different solutions of the equation x + 2y = 6.

17. The hypotenuse of a right-angled triangle is 1 m less thantwice the shortest side. If the third side is 1 m more than theshortest side, find the sides of the triangle.

he hypotenuse of a right-angled triangle is 1 metre less than twice theshortest side. If the third side is 1 metre more than the shortest side,find the sides of the triangle.71. T

by 1 cm. Find the lerngul U71. The hypotenuse of a right-angled triangle is 1 metre less than twice shoshortest side. If the third side is 1 metre more than the shortestfind the sides of the triangle.

2these citiese distance between city A and B is 510 km. Two cars begin their journey fromnd move directly towards each other, with speeds of 100 km/hour nd 70 km/hourhave started at the same time, where is the meeting point of the carsIf the2carsthat of th

l) A person is running along a circular track of area625 π mn 2 (π .22/7) with a constant speed. Find thedisplacement in 15 seconds if he has to complete therace in 30 seconds.100 m

iv) Places A and B are 100 km apart on a highway. One cafrom B at the same time. If the cars travel in the same dthey meet in 5 hours. If they travel towards each otherare the speeds of the two cars?

The inner circumference of a circular race track is 264 m and the width of the track is 7m. Calculatethe cost of putting up a fence along the outer circle of the track at the rate of 15 per metre.L.

ii) Leta and b be two unit vectors and θ is the angle betweenthem. Then at b is a unit vector if:(A) θ = π4(B) θ = π2π(Choose the correct one)

A race track is in the form of a ring whose Inner circumference is 352 m, find the circumference is 396 m. Find the width of the track.

A race track is in the form of a ring whose inner and outer circumferences are 440 m and 528 mrespectively. Find the width of the track and also its area

19. The points (-3, 7); (0, -3.5): (1, -3): (4, 4): (2, -3) and (4. 0) are onwhich axis or in which quadrant ?OR19,Find four different solution of the equation 2x-y=12. Draw the graph.

et 2i. Which of the following expressions are polynomials?(4)x2+4(b) 3xx +1

27- 2xy +eroes ofNow, leate to start with. We need to tind at least one factor tirst as you will see allbe appropriatethe following example.r 15 Factoriser -23+ 142x - 120.ibilities fo

14. If cosB_ sin Î¸ # V2 sin 0,prove that cos9+ sin 0-2 cose./15. Determine the value ofxech that 2 cosecao

A B15. 1fcos 0 + sin 6 = V2 cos 8, show that cos 8- sin 0 = ¥2 sin®.

About goes 30km upstream and 44km downstream in 20 hours. In 13hour, it can go 40km upstream and 55km upstream.find speed of stream and boat in still water.

15. I 13+ 4 3 219. If x = 3 + 2 v2 find a) x+21 -1 find the value ofly+1)b) x 1

The harmonic mean of the roots of the equation (5+V2)x2-(4+15)x+8+2.5-0is(A) 2(C) 4(B) 6(D) none of these

1. A boat goes 30km upstream and 44km downstream in 10 hourskm down stream.In 13 hours, it can go 40km upstream and 55Determine the speed of the stream and that of the boat in stilwater.

croes die v215. Show that the points (12, 8), (-2, 6) and (6, 0) are the vertices of right-angled triangle and alsoshow that the mid-point of the hypotenuse is equidistant from the angular points.