UNIT-4. File downloaded from For the things of this world cannot be made known without a knowledge of mathematics.
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1 File downloded from UNIT- For the things of this world cnnot e mde known without knowledge of mthemtics.. Solve y fctoriztion. - + ( ) = 0 Ans: + ( - ) = 0. [( + ) + ( - )] + ( - ) ( + ) = 0. [-( + )] - ( - ) [ - ( + ) = 0. Ans: + =. + ( + = + ) + = = = ( ) + 0. Ans: c. ( ( ) ) (+){(++)+}=0 (++)+=0 +++=0 (+)(+)=0 =- =- + 0 File downloded from Pge
2 File downloded from d. ( ) ( ) = Ans : (-) (-) = -7+= or 0 Ans: e. = File downloded from Pge
3 File downloded from ( ) ( ) - =- -6+=0 (-) =0 =,.. By the method of completion of squres show tht the eqution + +5 = 0 hs no rel roots. Ans: ++5= not rel no. Hence QE hs no rel roots.. The sum of res of two squres is 6m If the difference of their perimeters is cm, find the sides of the two squres. Ans: Let the side of the lrger squre e. Let the side of the smller squre e y. APQ +y = 6 Cond. II -y = y = 6 File downloded from Pge 5
4 File downloded from = 6 + y + y = 6 (6+y) +y = 6 on solving we get y = = (+6) = m sides re m & m.. A deler sells toy for Rs. nd gins s much percent s the cost price of the toy. Find the cost price of the toy. Ans: Let the C.P e Gin = % Gin = SP =. 00 S.P = C.P +Gin = 00 On solving =0 or -0 (rej) C.P of toy = Rs.0 5. A fo nd n egle lived t the top of cliff of height 6m, whose se ws t distnce of 0m from point A on the ground. The fo descends the cliff nd went stright to the point A. The egle flew verticlly up to height metres nd then flew in stright line to point A, the distnce trveled y ech eing the sme. Find the vlue of. Q Ans: Distnce trveled y the fo = distnce trveled y the egle (6+) + (0) = (6 ) on solving we get =.7m. Top 6m A 0m P File downloded from Pge 6
5 File downloded from 6. A lotus is m ove the wter in pond. Due to wind the lotus slides on the side nd only the stem completely sumerges in the wter t distnce of 0m from the originl position. Find the depth of wter in the pond. Ans: (+) = = = 00 = Depth of the pond = m 7 Solve = Ans: = = 6 = = 0 ( -) ( + ) = 0 =. The hypotenuse of right tringle is 0m. If the difference etween the length of the other sides is m. Find the sides. Ans: APQ + y = 0 + y = 00 lso - y = = 0 + y ( + y) + y = 00 y + y = 0 (y + 6) (y ) = 0 y = y = 6 (N.P) sides re cm & 6cm 9. The positive vlue of k for which +K +6 = 0 & - + k = 0 will hve rel roots. Ans: + K + 6 = 0 -c > 0 K - 56 > 0 K > 6 or K < K = 0 6 K > 0 () File downloded from Pge 7
6 File downloded from K < 6 K < 6 From () & () K = 6 () 0. A techer on ttempting to rrnge the students for mss drill in the form of solid squre found tht students were left over. When he incresed the size of the squre y one student he found he ws short of 5 students. Find the numer of students. Ans: Let the side of the squre e. No. of students = + New side = + No. of students = ( + ) 5 APQ + = ( + ) 5 + = = = side of squre = No. of students = = 600. A pole hs to e erected t point on the oundry of circulr prk of dimeter m in such wy tht the differences of its distnces from two dimetriclly opposite fied gtes A & B on the oundry in 7m. Is it possile to do so? If nswer is yes t wht distnces from the two gtes should the pole e erected. Ans: AB = m P BP = AP BP = 7 AP = + 7 APQ A () = ( + 7) + B = 0 O ( + ) ( 5) = 0 = - N.P = 5 Pole hs to e erected t distnce of 5m from gte B & m from gte A.. If the roots of the eqution (-) + (-c) + (c - )= 0 re equl. Prove tht =+c. Ans: (-) + (-c) + (c - ) = 0 T.P = + c B AC = 0 (-c) [(-) (c - )] = 0 -c + c [(c- c + )] = 0 -c + c c + + c - = 0 File downloded from Pge
7 File downloded from + c + c + c = 0 ( + c - ) = 0 + c =. X nd Y re centers of circles of rdius 9cm nd cm nd XY = 7cm. Z is the centre of circle of rdius cm, which touches the ove circles eternlly. Given tht XZY=90 o, write n eqution in r nd solve it for r. Ans: Let r e the rdius of the third circle XY = 7cm XZ = 9 + r YZ = APQ (r + 9) + (r + ) = ( + r) r + r + + r + r + = 9S r + r - 0r = 0 (r + 7) (r 6) = 0 r = - 7 (N.P) r = 6 cm X rdius = 6cm. Z Y File downloded from Pge 9
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